LMFDB - Embedded newform 27.11.f.a.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,11,Mod(2,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.2"); S:= CuspForms(chi, 11); N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.f (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$174$
Relative dimension:	$29$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	27.11
Dual form			27.11.f.a.5.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-38.9263 + 46.3906i) q^{2} +(-46.9192 - 238.427i) q^{3} +(-459.012 - 2603.19i) q^{4} +(-1837.35 + 5048.08i) q^{5} +(12887.2 + 7104.49i) q^{6} +(-3579.43 + 20300.0i) q^{7} +(84927.2 + 49032.7i) q^{8} +(-54646.2 + 22373.6i) q^{9} +(-162662. - 281739. i) q^{10} +(48830.0 + 134159. i) q^{11} +(-599135. + 231581. i) q^{12} +(-144420. + 121183. i) q^{13} +(-802394. - 956256. i) q^{14} +(1.28981e6 + 201223. i) q^{15} +(-3.03701e6 + 1.10538e6i) q^{16} +(112839. - 65147.7i) q^{17} +(1.08925e6 - 3.40599e6i) q^{18} +(-388272. + 672507. i) q^{19} +(1.39845e7 + 2.46584e6i) q^{20} +(5.00801e6 - 99024.0i) q^{21} +(-8.12450e6 - 2.95708e6i) q^{22} +(-1.21316e6 + 213913. i) q^{23} +(7.70603e6 - 2.25495e7i) q^{24} +(-1.46263e7 - 1.22729e7i) q^{25} -1.14169e7i q^{26} +(7.89844e6 + 1.19794e7i) q^{27} +5.44877e7 q^{28} +(-3.86179e6 + 4.60230e6i) q^{29} +(-5.95423e7 + 5.20020e7i) q^{30} +(1.47173e6 + 8.34659e6i) q^{31} +(3.25951e7 - 8.95543e7i) q^{32} +(2.96962e7 - 1.79370e7i) q^{33} +(-1.37017e6 + 7.77063e6i) q^{34} +(-9.58991e7 - 5.53674e7i) q^{35} +(8.33261e7 + 1.31985e8i) q^{36} +(-6.91634e7 - 1.19794e8i) q^{37} +(-1.60840e7 - 4.41904e7i) q^{38} +(3.56694e7 + 2.87479e7i) q^{39} +(-4.03562e8 + 3.38629e8i) q^{40} +(-1.20268e7 - 1.43329e7i) q^{41} +(-1.90350e8 + 2.36179e8i) q^{42} +(1.89878e8 - 6.91101e7i) q^{43} +(3.26828e8 - 1.88694e8i) q^{44} +(-1.25397e7 - 3.16966e8i) q^{45} +(3.73003e7 - 6.46060e7i) q^{46} +(-4.77847e7 - 8.42574e6i) q^{47} +(4.06048e8 + 6.72243e8i) q^{48} +(-1.33837e8 - 4.87126e7i) q^{49} +(1.13870e9 - 2.00783e8i) q^{50} +(-2.08273e7 - 2.38472e7i) q^{51} +(3.81753e8 + 3.20329e8i) q^{52} +7.90746e7i q^{53} +(-8.63188e8 - 9.99002e7i) q^{54} -7.66964e8 q^{55} +(-1.29935e9 + 1.54851e9i) q^{56} +(1.78562e8 + 6.10212e7i) q^{57} +(-6.31782e7 - 3.58301e8i) q^{58} +(2.33178e8 - 6.40650e8i) q^{59} +(-6.82167e7 - 3.44997e9i) q^{60} +(-2.81178e8 + 1.59464e9i) q^{61} +(-4.44492e8 - 2.56628e8i) q^{62} +(-2.58582e8 - 1.18940e9i) q^{63} +(1.23093e9 + 2.13203e9i) q^{64} +(-3.46390e8 - 9.51699e8i) q^{65} +(-3.23853e8 + 2.07585e9i) q^{66} +(-6.50744e8 + 5.46039e8i) q^{67} +(-2.21386e8 - 2.63838e8i) q^{68} +(1.07923e8 + 2.79214e8i) q^{69} +(6.30153e9 - 2.29357e9i) q^{70} +(-1.99969e9 + 1.15452e9i) q^{71} +(-5.73799e9 - 7.79321e8i) q^{72} +(1.63438e9 - 2.83084e9i) q^{73} +(8.24962e9 + 1.45463e9i) q^{74} +(-2.23995e9 + 4.06315e9i) q^{75} +(1.92889e9 + 7.02057e8i) q^{76} +(-2.89821e9 + 5.11033e8i) q^{77} +(-2.72211e9 + 5.35674e8i) q^{78} +(-3.03995e8 - 2.55082e8i) q^{79} -1.73620e10i q^{80} +(2.48562e9 - 2.44527e9i) q^{81} +1.13307e9 q^{82} +(-5.56977e7 + 6.63779e7i) q^{83} +(-2.55652e9 - 1.29914e10i) q^{84} +(1.21546e8 + 6.89319e8i) q^{85} +(-4.18521e9 + 1.14988e10i) q^{86} +(1.27851e9 + 7.04819e8i) q^{87} +(-2.43120e9 + 1.37880e10i) q^{88} +(5.40536e9 + 3.12078e9i) q^{89} +(1.51924e10 + 1.17566e10i) q^{90} +(-1.94307e9 - 3.36549e9i) q^{91} +(1.11371e9 + 3.05989e9i) q^{92} +(1.92100e9 - 7.42515e8i) q^{93} +(2.25096e9 - 1.88878e9i) q^{94} +(-2.68148e9 - 3.19566e9i) q^{95} +(-2.28815e10 - 3.56975e9i) q^{96} +(1.05618e10 - 3.84417e9i) q^{97} +(7.46958e9 - 4.31256e9i) q^{98} +(-5.67000e9 - 6.23878e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) $ 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−38.9263	+	46.3906i	−1.21645	+	1.44971i	−0.360410	+	0.932794i	$0.617363\pi$
$2$	−38.9263	+	46.3906i	−1.21645	+	1.44971i	−0.856038	+	0.516912i	$0.827081\pi$
$3$	−46.9192	−	238.427i	−0.193083	−	0.981182i
$3$	−46.9192	−	238.427i	−0.193083	−	0.981182i
$4$	−459.012	−	2603.19i	−0.448254	−	2.54218i
$5$	−1837.35	+	5048.08i	−0.587952	+	1.61538i	0.186290	+	0.982495i	$0.440354\pi$
$5$	−1837.35	+	5048.08i	−0.587952	+	1.61538i	−0.774242	+	0.632890i	$0.781869\pi$
$6$	12887.2	+	7104.49i	1.65730	+	0.913644i
$7$	−3579.43	+	20300.0i	−0.212973	+	1.20783i	0.671417	+	0.741080i	$0.265686\pi$
$7$	−3579.43	+	20300.0i	−0.212973	+	1.20783i	−0.884390	+	0.466749i	$0.845425\pi$
$8$	84927.2	+	49032.7i	2.59177	+	1.49636i
$9$	−54646.2	+	22373.6i	−0.925438	+	0.378900i
$10$	−162662.	−	281739.i	−1.62662	−	2.81739i
$11$	48830.0	+	134159.i	0.303196	+	0.833023i	0.993940	+	0.109924i	$0.0350608\pi$
$11$	48830.0	+	134159.i	0.303196	+	0.833023i	−0.690744	+	0.723099i	$0.742717\pi$
$12$	−599135.	+	231581.i	−2.40779	+	0.930671i
$13$	−144420.	+	121183.i	−0.388965	+	0.326381i	−0.816210	−	0.577755i	$-0.803929\pi$
$13$	−144420.	+	121183.i	−0.388965	+	0.326381i	0.427245	+	0.904136i	$0.359484\pi$
$14$	−802394.	−	956256.i	−1.49193	−	1.77801i
$15$	1.28981e6	+	201223.i	1.69851	+	0.264984i
$16$	−3.03701e6	+	1.10538e6i	−2.89632	+	1.05417i
$17$	112839.	−	65147.7i	0.0794721	−	0.0458832i	−0.459737	−	0.888055i	$-0.652056\pi$
$17$	112839.	−	65147.7i	0.0794721	−	0.0458832i	0.539209	+	0.842172i	$0.318723\pi$
$18$	1.08925e6	−	3.40599e6i	0.576454	−	1.80252i
$19$	−388272.	+	672507.i	−0.156808	+	0.271600i	−0.933716	−	0.358015i	$-0.883454\pi$
$19$	−388272.	+	672507.i	−0.156808	+	0.271600i	0.776908	+	0.629614i	$0.216787\pi$
$20$	1.39845e7	+	2.46584e6i	4.37014	+	0.770574i
$21$	5.00801e6	−	99024.0i	1.22622	−	0.0242462i
$22$	−8.12450e6	−	2.95708e6i	−1.57646	−	0.573785i
$23$	−1.21316e6	+	213913.i	−0.188486	+	0.0332351i	−0.267094	−	0.963670i	$-0.586063\pi$
$23$	−1.21316e6	+	213913.i	−0.188486	+	0.0332351i	0.0786083	+	0.996906i	$0.474952\pi$
$24$	7.70603e6	−	2.25495e7i	0.967775	−	2.83192i
$25$	−1.46263e7	−	1.22729e7i	−1.49773	−	1.25675i
$26$		−	1.14169e7i		−	0.960911i
$27$	7.89844e6	+	1.19794e7i	0.550456	+	0.834864i
$28$	5.44877e7			3.16598
$29$	−3.86179e6	+	4.60230e6i	−0.188277	+	0.224380i	−0.851923	−	0.523667i	$-0.824564\pi$
$29$	−3.86179e6	+	4.60230e6i	−0.188277	+	0.224380i	0.663646	+	0.748047i	$0.269008\pi$
$30$	−5.95423e7	+	5.20020e7i	−2.45030	+	2.14000i
$31$	1.47173e6	+	8.34659e6i	0.0514066	+	0.291542i	0.999663	−	0.0259646i	$-0.00826571\pi$
$31$	1.47173e6	+	8.34659e6i	0.0514066	+	0.291542i	−0.948256	+	0.317506i	$0.897155\pi$
$32$	3.25951e7	−	8.95543e7i	0.971410	−	2.66893i
$33$	2.96962e7	−	1.79370e7i	0.758806	−	0.458333i
$34$	−1.37017e6	+	7.77063e6i	−0.0301565	+	0.171026i
$35$	−9.58991e7	−	5.53674e7i	−1.82589	−	1.05418i
$36$	8.33261e7	+	1.31985e8i	1.37806	+	2.18278i
$37$	−6.91634e7	−	1.19794e8i	−0.997396	−	1.72754i	−0.561156	−	0.827710i	$-0.689643\pi$
$37$	−6.91634e7	−	1.19794e8i	−0.997396	−	1.72754i	−0.436240	−	0.899830i	$-0.643690\pi$
$38$	−1.60840e7	−	4.41904e7i	−0.202991	−	0.557712i
$39$	3.56694e7	+	2.87479e7i	0.395342	+	0.318627i
$40$	−4.03562e8	+	3.38629e8i	−3.94103	+	3.30692i
$41$	−1.20268e7	−	1.43329e7i	−0.103808	−	0.123713i	0.711639	−	0.702545i	$-0.247953\pi$
$41$	−1.20268e7	−	1.43329e7i	−0.103808	−	0.123713i	−0.815447	+	0.578832i	$0.803509\pi$
$42$	−1.90350e8	+	2.36179e8i	−1.45648	+	1.80716i
$43$	1.89878e8	−	6.91101e7i	1.29162	−	0.470109i	0.397358	−	0.917664i	$-0.369927\pi$
$43$	1.89878e8	−	6.91101e7i	1.29162	−	0.470109i	0.894257	+	0.447554i	$0.147705\pi$
$44$	3.26828e8	−	1.88694e8i	1.98178	−	1.14418i
$45$	−1.25397e7	−	3.16966e8i	−0.0679556	−	1.71771i
$46$	3.73003e7	−	6.46060e7i	0.181102	−	0.313678i
$47$	−4.77847e7	−	8.42574e6i	−0.208353	−	0.0367383i	0.0684973	−	0.997651i	$-0.478180\pi$
$47$	−4.77847e7	−	8.42574e6i	−0.208353	−	0.0367383i	−0.276850	+	0.960913i	$0.589291\pi$
$48$	4.06048e8	+	6.72243e8i	1.59357	+	2.63828i
$49$	−1.33837e8	−	4.87126e7i	−0.473800	−	0.172449i
$50$	1.13870e9	−	2.00783e8i	3.64383	−	0.642506i
$51$	−2.08273e7	−	2.38472e7i	−0.0603646	−	0.0691174i
$52$	3.81753e8	+	3.20329e8i	1.00407	+	0.842517i
$53$			7.90746e7i			0.189085i	0.995521	+	0.0945426i	$0.0301389\pi$
$53$			7.90746e7i			0.189085i	−0.995521	+	0.0945426i	$0.969861\pi$
$54$	−8.63188e8	−	9.99002e7i	−1.87991	−	0.217569i
$55$	−7.66964e8			−1.52392
$56$	−1.29935e9	+	1.54851e9i	−2.35932	+	2.81173i
$57$	1.78562e8	+	6.10212e7i	0.296766	+	0.101416i
$58$	−6.31782e7	−	3.58301e8i	−0.0962558	−	0.545894i
$59$	2.33178e8	−	6.40650e8i	0.326157	−	0.896109i	−0.662918	−	0.748692i	$-0.730682\pi$
$59$	2.33178e8	−	6.40650e8i	0.326157	−	0.896109i	0.989075	−	0.147416i	$-0.0470957\pi$
$60$	−6.82167e7	−	3.44997e9i	−0.0877273	−	4.43669i
$61$	−2.81178e8	+	1.59464e9i	−0.332914	+	1.88805i	0.114013	+	0.993479i	$0.463629\pi$
$61$	−2.81178e8	+	1.59464e9i	−0.332914	+	1.88805i	−0.446927	+	0.894570i	$0.647482\pi$
$62$	−4.44492e8	−	2.56628e8i	−0.485183	−	0.280121i
$63$	−2.58582e8	−	1.18940e9i	−0.260553	−	1.19847i
$64$	1.23093e9	+	2.13203e9i	1.14639	+	1.98561i
$65$	−3.46390e8	−	9.51699e8i	−0.298537	−	0.820225i
$66$	−3.23853e8	+	2.07585e9i	−0.258600	+	1.65758i
$67$	−6.50744e8	+	5.46039e8i	−0.481988	+	0.404436i	−0.851145	−	0.524931i	$-0.824091\pi$
$67$	−6.50744e8	+	5.46039e8i	−0.481988	+	0.404436i	0.369156	+	0.929367i	$0.379647\pi$
$68$	−2.21386e8	−	2.63838e8i	−0.152267	−	0.181465i
$69$	1.07923e8	+	2.79214e8i	0.0690032	+	0.178522i
$70$	6.30153e9	−	2.29357e9i	3.74935	−	1.36465i
$71$	−1.99969e9	+	1.15452e9i	−1.10834	+	0.639898i	−0.938398	−	0.345556i	$-0.887690\pi$
$71$	−1.99969e9	+	1.15452e9i	−1.10834	+	0.639898i	−0.169938	+	0.985455i	$0.554357\pi$
$72$	−5.73799e9	−	7.79321e8i	−2.96549	−	0.402767i
$73$	1.63438e9	−	2.83084e9i	0.788388	−	1.36553i	−0.138567	−	0.990353i	$-0.544250\pi$
$73$	1.63438e9	−	2.83084e9i	0.788388	−	1.36553i	0.926954	−	0.375174i	$-0.122417\pi$
$74$	8.24962e9	+	1.45463e9i	3.71771	+	0.655532i
$75$	−2.23995e9	+	4.06315e9i	−0.943912	+	1.71221i
$76$	1.92889e9	+	7.02057e8i	0.760744	+	0.276888i
$77$	−2.89821e9	+	5.11033e8i	−1.07072	+	0.188797i
$78$	−2.72211e9	+	5.35674e8i	−0.942829	+	0.185536i
$79$	−3.03995e8	−	2.55082e8i	−0.0987941	−	0.0828981i	0.592053	−	0.805899i	$-0.298318\pi$
$79$	−3.03995e8	−	2.55082e8i	−0.0987941	−	0.0828981i	−0.690847	+	0.723001i	$0.742762\pi$
$80$		−	1.73620e10i		−	5.29848i
$81$	2.48562e9	−	2.44527e9i	0.712870	−	0.701296i
$82$	1.13307e9			0.305624
$83$	−5.56977e7	+	6.63779e7i	−0.0141399	+	0.0168513i	−0.773068	−	0.634323i	$-0.781279\pi$
$83$	−5.56977e7	+	6.63779e7i	−0.0141399	+	0.0168513i	0.758928	+	0.651174i	$0.225723\pi$
$84$	−2.55652e9	−	1.29914e10i	−0.611297	−	3.10640i
$85$	1.21546e8	+	6.89319e8i	0.0273933	+	0.155355i
$86$	−4.18521e9	+	1.14988e10i	−0.889662	+	2.44433i
$87$	1.27851e9	+	7.04819e8i	0.256511	+	0.141410i
$88$	−2.43120e9	+	1.37880e10i	−0.460689	+	2.61270i
$89$	5.40536e9	+	3.12078e9i	0.967998	+	0.558874i	0.898625	−	0.438717i	$-0.144567\pi$
$89$	5.40536e9	+	3.12078e9i	0.967998	+	0.558874i	0.0693725	+	0.997591i	$0.477900\pi$
$90$	1.51924e10	+	1.17566e10i	2.57284	+	1.99099i
$91$	−1.94307e9	−	3.36549e9i	−0.311373	−	0.539314i
$92$	1.11371e9	+	3.05989e9i	0.168979	+	0.464267i
$93$	1.92100e9	−	7.42515e8i	0.276130	−	0.106731i
$94$	2.25096e9	−	1.88878e9i	0.306710	−	0.257361i
$95$	−2.68148e9	−	3.19566e9i	−0.346542	−	0.412993i
$96$	−2.28815e10	−	3.56975e9i	−2.80627	−	0.437806i
$97$	1.05618e10	−	3.84417e9i	1.22992	−	0.447655i	0.356351	−	0.934352i	$-0.384021\pi$
$97$	1.05618e10	−	3.84417e9i	1.22992	−	0.447655i	0.873571	+	0.486697i	$0.161798\pi$
$98$	7.46958e9	−	4.31256e9i	0.826353	−	0.477095i
$99$	−5.67000e9	−	6.23878e9i	−0.596221	−	0.656030i
$100$	−2.52351e10	+	4.37085e10i	−2.52351	+	4.37085i
$101$	1.15089e10	+	2.02934e9i	1.09504	+	0.193085i	0.691856	−	0.722036i	$-0.256793\pi$
$101$	1.15089e10	+	2.02934e9i	1.09504	+	0.193085i	0.403181	+	0.915120i	$0.367904\pi$
$102$	1.91702e9	−	3.79054e7i	0.173630	−	0.00343321i
$103$	−1.70549e10	−	6.20748e9i	−1.47117	−	0.535463i	−0.522753	−	0.852484i	$-0.675095\pi$
$103$	−1.70549e10	−	6.20748e9i	−1.47117	−	0.535463i	−0.948418	+	0.317021i	$0.897317\pi$
$104$	−1.82071e10	+	3.21041e9i	−1.49649	+	0.263872i
$105$	−8.70159e9	+	2.54628e10i	−0.681792	+	1.99507i
$106$	−3.66832e9	−	3.07808e9i	−0.274118	−	0.230012i
$107$			1.43066e10i			1.02004i	0.860162	+	0.510021i	$0.170362\pi$
$107$			1.43066e10i			1.02004i	−0.860162	+	0.510021i	$0.829638\pi$
$108$	2.75591e10	−	2.60598e10i	1.87563	−	1.77359i
$109$	−1.27174e10			−0.826543			−0.413272	−	0.910608i	$-0.635614\pi$
$109$	−1.27174e10			−0.826543			−0.413272	+	0.910608i	$0.635614\pi$
$110$	2.98551e10	−	3.55799e10i	1.85377	−	2.20923i
$111$	−2.53172e10	+	2.21111e10i	−1.50245	+	1.31219i
$112$	−1.15685e10	−	6.56079e10i	−0.656425	−	3.72277i
$113$	−1.69462e9	+	4.65592e9i	−0.0919769	+	0.252705i	−0.977148	−	0.212562i	$-0.931819\pi$
$113$	−1.69462e9	+	4.65592e9i	−0.0919769	+	0.252705i	0.885171	+	0.465266i	$0.154042\pi$
$114$	−9.78156e9	+	5.90825e9i	−0.508024	+	0.306856i
$115$	1.14915e9	−	6.51715e9i	0.0571331	−	0.324018i
$116$	1.37533e10	+	7.94045e9i	0.654810	+	0.378055i
$117$	5.18071e9	−	9.85339e9i	0.236298	−	0.449424i
$118$	2.06434e10	+	3.57554e10i	0.902342	+	1.56290i
$119$	9.18596e8	+	2.52382e9i	0.0384937	+	0.105761i
$120$	9.96731e10	+	8.03320e10i	4.00564	+	3.22836i
$121$	4.25489e9	−	3.57027e9i	0.164044	−	0.137650i
$122$	−6.30311e10	−	7.51175e10i	−2.33214	−	2.77934i
$123$	−2.85308e9	+	3.54000e9i	−0.101342	+	0.125741i
$124$	2.10522e10	−	7.66237e9i	0.718107	−	0.261370i
$125$	4.33954e10	−	2.50544e10i	1.42198	−	0.820981i
$126$	6.52427e10	+	3.43032e10i	2.05437	+	1.08015i
$127$	4.29602e9	−	7.44092e9i	0.130031	−	0.225221i	−0.793657	−	0.608365i	$-0.791826\pi$
$127$	4.29602e9	−	7.44092e9i	0.130031	−	0.225221i	0.923688	+	0.383145i	$0.125159\pi$
$128$	−5.07152e10	−	8.94246e9i	−1.47601	−	0.260260i
$129$	−2.53867e10	−	4.20296e10i	−0.710652	−	1.17654i
$130$	5.76336e10	+	2.09769e10i	1.55224	+	0.564969i
$131$	2.90199e10	−	5.11699e9i	0.752211	−	0.132635i	0.215620	−	0.976477i	$-0.430823\pi$
$131$	2.90199e10	−	5.11699e9i	0.752211	−	0.132635i	0.536591	+	0.843842i	$0.319712\pi$
$132$	−6.03244e10	−	6.90714e10i	−1.50530	−	1.72357i
$133$	−1.22621e10	−	1.02891e10i	−0.294650	−	0.247241i
$134$		−	5.14437e10i		−	1.19072i
$135$	−7.49851e10	+	1.78616e10i	−1.67227	+	0.398338i
$136$	1.27775e10			0.274631
$137$	−2.58640e10	+	3.08236e10i	−0.535912	+	0.638675i	−0.964266	−	0.264936i	$-0.914649\pi$
$137$	−2.58640e10	+	3.08236e10i	−0.535912	+	0.638675i	0.428354	+	0.903611i	$0.359094\pi$
$138$	−1.71539e10	−	5.86215e9i	−0.342743	−	0.117128i
$139$	−1.61516e10	−	9.16002e10i	−0.311273	−	1.76532i	−0.592399	−	0.805645i	$-0.701819\pi$
$139$	−1.61516e10	−	9.16002e10i	−0.311273	−	1.76532i	0.281126	−	0.959671i	$-0.409292\pi$
$140$	−1.00113e11	+	2.75058e11i	−1.86144	+	5.11427i
$141$	2.33096e8	+	1.17885e10i	0.00418253	+	0.211526i
$142$	2.42817e10	−	1.37708e11i	0.420569	−	2.38516i
$143$	−2.33098e10	−	1.34579e10i	−0.389815	−	0.225060i
$144$	1.41230e11	−	1.28354e11i	2.28094	−	2.07299i
$145$	−1.61373e10	−	2.79506e10i	−0.251762	−	0.436065i
$146$	6.77036e10	+	1.86014e11i	1.02058	+	2.80402i
$147$	−5.33490e9	+	3.41959e10i	−0.0777212	+	0.498181i
$148$	−2.80101e11	+	2.35033e11i	−3.94463	+	3.30993i
$149$	4.63315e10	+	5.52157e10i	0.630877	+	0.751850i	0.982900	−	0.184142i	$-0.0589505\pi$
$149$	4.63315e10	+	5.52157e10i	0.630877	+	0.751850i	−0.352023	+	0.935991i	$0.614506\pi$
$150$	−1.01299e11	−	2.62076e11i	−1.33398	−	3.45121i
$151$	5.89282e10	−	2.14481e10i	0.750652	−	0.273215i	0.0617717	−	0.998090i	$-0.480325\pi$
$151$	5.89282e10	−	2.14481e10i	0.750652	−	0.273215i	0.688880	+	0.724875i	$0.258103\pi$
$152$	−6.59498e10	+	3.80761e10i	−0.812822	+	0.469283i
$153$	−4.70863e9	+	6.08469e9i	−0.0561614	+	0.0725740i
$154$	8.91097e10	−	1.54342e11i	1.02878	−	1.78189i
$155$	−4.48383e10	−	7.90620e9i	−0.501176	−	0.0883709i
$156$	5.84635e10	−	1.06050e11i	0.632794	−	1.14785i
$157$	−8.64885e10	−	3.14792e10i	−0.906692	−	0.330009i	−0.153761	−	0.988108i	$-0.549139\pi$
$157$	−8.64885e10	−	3.14792e10i	−0.906692	−	0.330009i	−0.752931	+	0.658099i	$0.771361\pi$
$158$	2.36668e10	−	4.17310e9i	0.240356	−	0.0423812i
$159$	1.88535e10	−	3.71012e9i	0.185527	−	0.0365092i
$160$	3.92189e11	+	3.29085e11i	3.74020	+	3.13840i
$161$		−	2.53928e10i		−	0.234737i
$162$	1.66812e10	+	2.10495e11i	0.149504	+	1.88654i
$163$	4.00494e10			0.348063			0.174032	−	0.984740i	$-0.444321\pi$
$163$	4.00494e10			0.348063			0.174032	+	0.984740i	$0.444321\pi$
$164$	−3.17909e10	+	3.78869e10i	−0.267968	+	0.319352i
$165$	3.59853e10	+	1.82865e11i	0.294243	+	1.49524i
$166$	−9.11204e8	−	5.16770e9i	−0.00722895	−	0.0409974i
$167$	1.80192e10	−	4.95072e10i	0.138724	−	0.381141i	−0.850804	−	0.525484i	$-0.823884\pi$
$167$	1.80192e10	−	4.95072e10i	0.138724	−	0.381141i	0.989528	+	0.144342i	$0.0461066\pi$
$168$	4.30172e11	+	2.37147e11i	3.21437	+	1.77203i
$169$	−1.77670e10	+	1.00762e11i	−0.128878	+	0.730906i
$170$	−3.67092e10	−	2.11941e10i	−0.258542	−	0.149269i
$171$	6.17116e9	−	4.54370e10i	0.0422072	−	0.310763i
$172$	−2.67063e11	−	4.62567e11i	−1.77407	−	3.07279i
$173$	−4.01751e10	−	1.10380e11i	−0.259255	−	0.712297i	−0.999214	−	0.0396449i	$-0.987377\pi$
$173$	−4.01751e10	−	1.10380e11i	−0.259255	−	0.712297i	0.739959	−	0.672652i	$-0.234845\pi$
$174$	−8.24645e10	+	3.18746e10i	−0.517036	+	0.199847i
$175$	3.01494e11	−	2.52984e11i	1.83691	−	1.54135i
$176$	−2.96595e11	−	3.53468e11i	−1.75630	−	2.09308i
$177$	−1.63689e11	−	2.55371e10i	−0.942222	−	0.146996i
$178$	−3.55186e11	+	1.29277e11i	−1.98772	+	0.723472i
$179$	−2.80217e10	+	1.61783e10i	−0.152486	+	0.0880378i	−0.574302	−	0.818644i	$-0.694726\pi$
$179$	−2.80217e10	+	1.61783e10i	−0.152486	+	0.0880378i	0.421816	+	0.906682i	$0.361393\pi$
$180$	−8.19367e11	+	1.78135e11i	−4.33627	+	0.942727i
$181$	−1.09113e11	+	1.88989e11i	−0.561673	+	0.972847i	0.435677	+	0.900103i	$0.356509\pi$
$181$	−1.09113e11	+	1.88989e11i	−0.561673	+	0.972847i	−0.997351	+	0.0727440i	$0.976824\pi$
$182$	2.31764e11	+	4.08662e10i	1.16062	+	0.204648i
$183$	3.93398e11	−	7.77871e9i	1.91680	−	0.0379011i
$184$	−1.13519e11	−	4.13175e10i	−0.538244	−	0.195905i
$185$	7.31809e11	−	1.29038e11i	3.37706	−	0.595467i
$186$	−4.03318e10	+	1.18020e11i	−0.181169	+	0.530140i
$187$	1.42501e10	+	1.19572e10i	0.0623174	+	0.0522905i
$188$			1.28260e11i			0.546138i
$189$	−2.71453e11	+	1.17459e11i	−1.12560	+	0.487053i
$190$	2.52629e11			1.02027
$191$	−1.16074e11	+	1.38332e11i	−0.456634	+	0.544195i	−0.944408	−	0.328774i	$-0.893364\pi$
$191$	−1.16074e11	+	1.38332e11i	−0.456634	+	0.544195i	0.487774	+	0.872970i	$0.337809\pi$
$192$	4.50580e11	−	3.93520e11i	1.72689	−	1.50821i
$193$	−9.32604e9	−	5.28906e10i	−0.0348266	−	0.197511i	0.962430	−	0.271529i	$-0.0875291\pi$
$193$	−9.32604e9	−	5.28906e10i	−0.0348266	−	0.197511i	−0.997257	+	0.0740173i	$0.976418\pi$
$194$	−2.32797e11	+	6.39606e11i	−0.847168	+	2.32758i
$195$	−2.10659e11	+	1.27242e11i	−0.747148	+	0.451291i
$196$	−6.53754e10	+	3.70762e11i	−0.226013	+	1.28178i
$197$	−1.04587e10	−	6.03831e9i	−0.0352489	−	0.0203509i	0.482272	−	0.876022i	$-0.339812\pi$
$197$	−1.04587e10	−	6.03831e9i	−0.0352489	−	0.0203509i	−0.517521	+	0.855671i	$0.673145\pi$
$198$	5.10133e11	−	2.01817e10i	1.67632	−	0.0663182i
$199$	5.03117e10	+	8.71425e10i	0.161214	+	0.279232i	0.935304	−	0.353844i	$-0.115126\pi$
$199$	5.03117e10	+	8.71425e10i	0.161214	+	0.279232i	−0.774090	+	0.633076i	$0.781792\pi$
$200$	−6.40396e11	−	1.75947e12i	−2.00124	−	5.49836i
$201$	1.60723e11	+	1.29536e11i	0.489889	+	0.394829i
$202$	−5.42143e11	+	4.54912e11i	−1.61197	+	1.35260i
$203$	−7.96035e10	−	9.48678e10i	−0.230915	−	0.275194i
$204$	−5.25189e10	+	6.51636e10i	−0.148650	+	0.184440i
$205$	9.44510e10	−	3.43774e10i	0.260878	−	0.0949518i
$206$	9.51854e11	−	5.49553e11i	2.56587	−	1.48140i
$207$	6.15085e10	−	3.88323e10i	0.161839	−	0.102174i
$208$	3.04653e11	−	5.27674e11i	0.782507	−	1.35534i
$209$	−1.09182e11	−	1.92518e10i	−0.273792	−	0.0482770i
$210$	−8.42512e11	−	1.39484e12i	−2.06291	−	3.41530i
$211$	3.07519e11	+	1.11928e11i	0.735291	+	0.267624i	0.682403	−	0.730977i	$-0.260935\pi$
$211$	3.07519e11	+	1.11928e11i	0.735291	+	0.267624i	0.0528880	+	0.998600i	$0.483157\pi$
$212$	2.05846e11	−	3.62962e10i	0.480688	−	0.0847583i
$213$	3.69094e11	+	4.22612e11i	0.841858	+	0.963926i
$214$	−6.63692e11	−	5.56904e11i	−1.47876	−	1.24083i
$215$			1.08550e12i			2.36286i
$216$	8.34104e10	+	1.40466e12i	0.177399	+	2.98746i
$217$	−1.74703e11			−0.363080
$218$	4.95041e11	−	5.89967e11i	1.00545	−	1.19824i
$219$	−7.51633e11	−	2.56861e11i	−1.49206	−	0.509892i
$220$	3.52046e11	+	1.99655e12i	0.683103	+	3.87407i
$221$	−8.40145e9	+	2.30828e10i	−0.0159365	+	0.0437852i
$222$	−4.02419e10	−	2.03518e12i	−0.0746301	−	3.77432i
$223$	4.75841e10	−	2.69863e11i	0.0862855	−	0.489349i	−0.910786	−	0.412878i	$-0.864524\pi$
$223$	4.75841e10	−	2.69863e11i	0.0862855	−	0.489349i	0.997072	−	0.0764711i	$-0.0243653\pi$
$224$	1.70128e12	+	9.82234e11i	3.01672	+	1.74171i
$225$	1.07386e12	+	3.43425e11i	1.86224	+	0.595552i
$226$	−1.50026e11	−	2.59852e11i	−0.254462	−	0.440742i
$227$	8.70728e9	+	2.39231e10i	0.0144462	+	0.0396906i	0.946706	−	0.322099i	$-0.104388\pi$
$227$	8.70728e9	+	2.39231e10i	0.0144462	+	0.0396906i	−0.932260	+	0.361789i	$0.882166\pi$
$228$	7.68878e10	−	4.92839e11i	0.124791	−	0.799891i
$229$	2.49143e11	−	2.09056e11i	0.395614	−	0.331960i	−0.423181	−	0.906045i	$-0.639087\pi$
$229$	2.49143e11	−	2.09056e11i	0.395614	−	0.331960i	0.818796	+	0.574085i	$0.194642\pi$
$230$	2.57602e11	+	3.06999e11i	0.400231	+	0.476977i
$231$	2.57826e11	+	6.67036e11i	0.391983	+	1.01412i
$232$	−5.53634e11	+	2.01506e11i	−0.823726	+	0.299812i
$233$	1.47144e11	−	8.49537e10i	0.214271	−	0.123709i	−0.389024	−	0.921228i	$-0.627188\pi$
$233$	1.47144e11	−	8.49537e10i	0.214271	−	0.123709i	0.603295	+	0.797518i	$0.293854\pi$
$234$	2.55439e11	+	6.23892e11i	0.364089	+	0.889263i
$235$	1.30331e11	−	2.25740e11i	0.181848	−	0.314970i
$236$	−1.77476e12	−	3.12939e11i	−2.42427	−	0.427464i
$237$	−4.65554e10	+	8.44490e10i	−0.0622627	+	0.112941i
$238$	−1.52839e11	−	5.56289e10i	−0.200147	−	0.0728477i
$239$	−1.23725e12	+	2.18160e11i	−1.58660	+	0.279760i	−0.896194	−	0.443662i	$-0.853679\pi$
$239$	−1.23725e12	+	2.18160e11i	−1.58660	+	0.279760i	−0.690406	+	0.723423i	$0.742568\pi$
$240$	−4.13959e12	+	8.14614e11i	−5.19877	+	1.02305i
$241$	−8.15863e11	−	6.84590e11i	−1.00353	−	0.842065i	−0.0160635	−	0.999871i	$-0.505113\pi$
$241$	−8.15863e11	−	6.84590e11i	−1.00353	−	0.842065i	−0.987470	+	0.157806i	$0.949558\pi$
$242$			3.36364e11i			0.405260i
$243$	−6.99642e11	−	4.77911e11i	−0.825743	−	0.564047i
$244$	4.28021e12			4.94899
$245$	4.91810e11	−	5.86116e11i	0.557143	−	0.663977i
$246$	−5.31628e10	−	2.70155e11i	−0.0590109	−	0.299873i
$247$	−2.54220e10	−	1.44176e11i	−0.0276520	−	0.156822i
$248$	−2.84266e11	+	7.81015e11i	−0.303017	+	0.832532i
$249$	1.84396e10	+	1.01654e10i	0.0192644	+	0.0106201i
$250$	−5.26938e11	+	2.98841e12i	−0.539585	+	3.06014i
$251$	−1.12212e12	−	6.47855e11i	−1.12634	−	0.650294i	−0.183329	−	0.983052i	$-0.558687\pi$
$251$	−1.12212e12	−	6.47855e11i	−1.12634	−	0.650294i	−0.943012	+	0.332758i	$0.892021\pi$
$252$	−2.97754e12	+	1.21909e12i	−2.92992	+	1.19959i
$253$	−8.79369e10	−	1.52311e11i	−0.0848337	−	0.146936i
$254$	1.77961e11	+	4.88943e11i	0.168328	+	0.462476i
$255$	1.58650e11	−	6.13221e10i	0.147143	−	0.0568743i
$256$	4.57851e11	−	3.84183e11i	0.416413	−	0.349412i
$257$	−1.17211e12	−	1.39687e12i	−1.04545	−	1.24592i	−0.968534	−	0.248881i	$-0.919937\pi$
$257$	−1.17211e12	−	1.39687e12i	−1.04545	−	1.24592i	−0.0769155	−	0.997038i	$-0.524507\pi$
$258$	2.93799e12	+	4.58355e11i	2.57011	+	0.400962i
$259$	2.67939e12	−	9.75219e11i	2.29899	−	0.836764i
$260$	−2.31846e12	+	1.33856e12i	−1.95134	+	1.12660i
$261$	1.08062e11	−	3.37900e11i	0.0892214	−	0.278988i
$262$	−8.92258e11	+	1.54544e12i	−0.722743	+	1.25183i
$263$	−1.04298e12	−	1.83905e11i	−0.828890	−	0.146156i	−0.256922	−	0.966432i	$-0.582708\pi$
$263$	−1.04298e12	−	1.83905e11i	−0.828890	−	0.146156i	−0.571967	+	0.820276i	$0.693820\pi$
$264$	3.40151e12	−	6.72585e10i	2.65248	−	0.0524478i
$265$	−3.99174e11	−	1.45288e11i	−0.305445	−	0.111173i
$266$	9.54636e11	−	1.68328e11i	0.716852	−	0.126400i
$267$	4.90465e11	−	1.43521e12i	0.361453	−	1.05769i
$268$	1.72014e12	+	1.44337e12i	1.24420	+	1.04401i
$269$			1.87777e12i			1.33316i	0.745435	+	0.666578i	$0.232242\pi$
$269$			1.87777e12i			1.33316i	−0.745435	+	0.666578i	$0.767758\pi$
$270$	2.09028e12	−	4.17389e12i	1.45675	−	2.90886i
$271$	7.62803e11			0.521874			0.260937	−	0.965356i	$-0.415968\pi$
$271$	7.62803e11			0.521874			0.260937	+	0.965356i	$0.415968\pi$
$272$	−2.70681e11	+	3.22585e11i	−0.181808	+	0.216670i
$273$	−7.11258e11	+	6.21187e11i	−0.469044	+	0.409646i
$274$	−4.23131e11	−	2.39970e12i	−0.273982	−	1.55383i
$275$	9.32325e11	−	2.56154e12i	0.592794	−	1.62869i
$276$	6.77308e11	−	4.09107e11i	0.422903	−	0.255441i
$277$	−2.07379e10	+	1.17611e11i	−0.0127165	+	0.0721187i	−0.990506	−	0.137472i	$-0.956102\pi$
$277$	−2.07379e10	+	1.17611e11i	−0.0127165	+	0.0721187i	0.977789	+	0.209591i	$0.0672133\pi$
$278$	4.87811e12	+	2.81638e12i	2.93784	+	1.69616i
$279$	−2.67168e11	−	4.23181e11i	−0.158039	−	0.250326i
$280$	−5.42963e12	−	9.40439e12i	−3.15486	−	5.46438i
$281$	−3.89260e11	−	1.06948e12i	−0.222182	−	0.610440i	0.777652	−	0.628696i	$-0.216411\pi$
$281$	−3.89260e11	−	1.06948e12i	−0.222182	−	0.610440i	−0.999833	+	0.0182560i	$0.994189\pi$
$282$	−5.55950e11	−	4.48070e11i	−0.311738	−	0.251247i
$283$	−1.99969e12	+	1.67794e12i	−1.10162	+	0.924368i	−0.997533	−	0.0702007i	$-0.977636\pi$
$283$	−1.99969e12	+	1.67794e12i	−1.10162	+	0.924368i	−0.104086	+	0.994568i	$0.533192\pi$
$284$	3.92333e12	+	4.67564e12i	2.12355	+	2.53075i
$285$	−6.36120e11	+	7.89275e11i	−0.338310	+	0.419763i
$286$	1.53169e12	−	5.57489e11i	0.800461	−	0.291344i
$287$	3.34007e11	−	1.92839e11i	0.171532	−	0.0990343i
$288$	2.22458e11	+	5.62307e12i	0.112276	+	2.83799i
$289$	−9.99509e11	+	1.73120e12i	−0.495789	+	0.858733i
$290$	1.92481e12	+	3.39396e11i	0.938422	+	0.165469i
$291$	−1.41210e12	−	2.33785e12i	−0.676709	−	1.12034i
$292$	−8.11940e12	−	2.95522e12i	−3.82481	−	1.39212i
$293$	−1.93664e12	+	3.41483e11i	−0.896833	+	0.158136i	−0.603019	−	0.797727i	$-0.706036\pi$
$293$	−1.93664e12	+	3.41483e11i	−0.896833	+	0.158136i	−0.293814	+	0.955863i	$0.594925\pi$
$294$	−1.37870e12	−	1.57861e12i	−0.627673	−	0.718684i
$295$	2.80562e12	+	2.35420e12i	1.25580	+	1.05374i
$296$		−	1.35651e13i		−	5.96985i
$297$	−1.22146e12	+	1.64460e12i	−0.528565	+	0.711670i
$298$	−4.36500e12			−1.85739
$299$	1.49282e11	−	1.77908e11i	0.0624672	−	0.0744455i
$300$	1.16053e13	+	3.96597e12i	4.77585	+	1.63209i
$301$	7.23276e11	+	4.10190e12i	0.292733	+	1.66017i
$302$	−1.29887e12	+	3.56861e12i	−0.517047	+	1.42058i
$303$	−5.61411e10	−	2.83926e12i	−0.0219820	−	1.11171i
$304$	4.35810e11	−	2.47160e12i	0.167853	−	0.951943i
$305$	−7.53324e12	−	4.34932e12i	−2.85419	−	1.64787i
$306$	−9.89826e10	−	4.55291e11i	−0.0368937	−	0.169700i
$307$	9.32081e11	+	1.61441e12i	0.341792	+	0.592001i	0.984766	−	0.173888i	$-0.0556329\pi$
$307$	9.32081e11	+	1.61441e12i	0.341792	+	0.592001i	−0.642974	+	0.765888i	$0.722300\pi$
$308$	2.66063e12	+	7.31003e12i	0.959911	+	2.63733i
$309$	−6.79830e11	+	4.35761e12i	−0.241328	+	1.54688i
$310$	2.11216e12	−	1.77232e12i	0.737767	−	0.619060i
$311$	2.23515e12	+	2.66374e12i	0.768253	+	0.915568i	0.998340	−	0.0576022i	$-0.0183455\pi$
$311$	2.23515e12	+	2.66374e12i	0.768253	+	0.915568i	−0.230087	+	0.973170i	$0.573901\pi$
$312$	1.61971e12	+	4.19045e12i	0.547854	+	1.41738i
$313$	−3.41648e12	+	1.24350e12i	−1.13725	+	0.413926i	−0.840920	−	0.541159i	$-0.817986\pi$
$313$	−3.41648e12	+	1.24350e12i	−1.13725	+	0.413926i	−0.296332	+	0.955085i	$0.595763\pi$
$314$	4.82702e12	−	2.78688e12i	1.58136	−	0.912999i
$315$	6.47929e12	+	8.80004e11i	2.08917	+	0.283747i
$316$	−5.24490e11	+	9.08443e11i	−0.166457	+	0.288312i
$317$	−1.75851e12	−	3.10072e11i	−0.549349	−	0.0968650i	−0.107917	−	0.994160i	$-0.534418\pi$
$317$	−1.75851e12	−	3.10072e11i	−0.549349	−	0.0968650i	−0.441432	+	0.897295i	$0.645529\pi$
$318$	−5.61785e11	+	1.01905e12i	−0.172756	+	0.313371i
$319$	−8.06011e11	−	2.93364e11i	−0.243999	−	0.0888083i
$320$	−1.30243e13	+	2.29653e12i	−3.88154	+	0.684420i
$321$	3.41109e12	−	6.71255e11i	1.00085	−	0.196953i
$322$	1.17799e12	+	9.88448e11i	0.340299	+	0.285545i
$323$			1.01180e11i			0.0287795i
$324$	−7.50643e12	−	5.34814e12i	−2.10237	−	1.49788i
$325$	3.59960e12			0.992746
$326$	−1.55898e12	+	1.85792e12i	−0.423401	+	0.504589i
$327$	5.96690e11	+	3.03217e12i	0.159592	+	0.810990i
$328$	−3.18616e11	−	1.80696e12i	−0.0839263	−	0.475970i
$329$	3.42085e11	−	9.39869e11i	0.0887470	−	0.243831i
$330$	−9.88400e12	−	5.44889e12i	−2.52559	−	1.39232i
$331$	1.10234e12	−	6.25166e12i	0.277443	−	1.57346i	−0.453649	−	0.891180i	$-0.649878\pi$
$331$	1.10234e12	−	6.25166e12i	0.277443	−	1.57346i	0.731092	−	0.682279i	$-0.239011\pi$
$332$	1.98360e11	+	1.14523e11i	0.0491772	+	0.0283925i
$333$	6.45975e12	+	4.99887e12i	1.57759	+	1.22082i
$334$	1.59525e12	+	2.76305e12i	0.383792	+	0.664748i
$335$	−1.56080e12	−	4.28827e12i	−0.369934	−	1.01639i
$336$	−1.50999e13	+	5.83651e12i	−3.52597	+	1.36288i
$337$	3.86218e12	−	3.24075e12i	0.888553	−	0.745584i	−0.0793667	−	0.996845i	$-0.525290\pi$
$337$	3.86218e12	−	3.24075e12i	0.888553	−	0.745584i	0.967919	+	0.251261i	$0.0808454\pi$
$338$	−3.98279e12	−	4.74650e12i	−0.902825	−	1.07595i
$339$	1.18961e12	+	1.85591e11i	0.265708	+	0.0414532i
$340$	1.73864e12	−	6.32812e11i	0.382661	−	0.139277i
$341$	−1.04791e12	+	6.05009e11i	−0.227275	+	0.131217i
$342$	1.86763e12	+	2.05498e12i	0.399172	+	0.439215i
$343$	−1.44343e12	+	2.50009e12i	−0.304035	+	0.526605i
$344$	1.95145e13	+	3.44093e12i	4.05102	+	0.714305i
$345$	−1.60778e12	+	3.17909e10i	−0.328952	+	0.00650440i
$346$	6.68448e12	+	2.43295e12i	1.34799	+	0.490629i
$347$	−6.23934e12	+	1.10016e12i	−1.24020	+	0.218680i	−0.755001	−	0.655724i	$-0.772364\pi$
$347$	−6.23934e12	+	1.10016e12i	−1.24020	+	0.218680i	−0.485198	+	0.874404i	$0.661252\pi$
$348$	1.24793e12	−	3.65171e12i	0.244508	−	0.715485i
$349$	3.67912e12	+	3.08715e12i	0.710587	+	0.596253i	0.924764	−	0.380541i	$-0.124262\pi$
$349$	3.67912e12	+	3.08715e12i	0.710587	+	0.596253i	−0.214177	+	0.976795i	$0.568707\pi$
$350$			2.38342e13i			4.53796i
$351$	−2.59239e12	−	7.72909e11i	−0.486592	−	0.145075i
$352$	1.36062e13			2.51781
$353$	−3.74249e12	+	4.46012e12i	−0.682789	+	0.813716i	−0.990464	−	0.137775i	$-0.956005\pi$
$353$	−3.74249e12	+	4.46012e12i	−0.682789	+	0.813716i	0.307674	+	0.951492i	$0.400449\pi$
$354$	7.55649e12	−	6.59956e12i	1.35926	−	1.18713i
$355$	−2.15399e12	−	1.22159e13i	−0.382033	−	2.16662i
$356$	5.64287e12	−	1.55036e13i	0.986847	−	2.71134i
$357$	5.58648e11	−	3.37434e11i	0.0963379	−	0.0581899i
$358$	3.40260e11	−	1.92971e12i	0.0578622	−	0.328153i
$359$	1.68234e11	+	9.71297e10i	0.0282124	+	0.0162885i	0.514040	−	0.857766i	$-0.328148\pi$
$359$	1.68234e11	+	9.71297e10i	0.0282124	+	0.0162885i	−0.485827	+	0.874055i	$0.661482\pi$
$360$	1.44768e13	−	2.75339e13i	2.39419	−	4.55360i
$361$	2.76402e12	+	4.78743e12i	0.450822	+	0.780847i
$362$	−4.51996e12	−	1.24185e13i	−0.727096	−	1.99768i
$363$	−1.05089e12	−	8.46967e11i	−0.166733	−	0.134380i
$364$	−7.86912e12	+	6.60298e12i	−1.23146	+	1.03332i
$365$	1.12873e13	+	1.34517e13i	1.74232	+	2.07641i
$366$	−1.49527e13	+	1.85528e13i	−2.27674	+	2.82490i
$367$	−6.70297e12	+	2.43968e12i	−1.00679	+	0.366440i	−0.792197	−	0.610265i	$-0.791063\pi$
$367$	−6.70297e12	+	2.43968e12i	−1.00679	+	0.366440i	−0.214588	+	0.976705i	$0.568841\pi$
$368$	3.44793e12	−	1.99066e12i	0.510880	−	0.294957i
$369$	9.77896e11	+	5.14157e11i	0.142942	+	0.0751561i
$370$	−2.25005e13	+	3.89720e13i	−3.24477	+	5.62010i
$371$	−1.60521e12	−	2.83042e11i	−0.228382	−	0.0402700i
$372$	−2.81467e12	−	4.65991e12i	−0.395106	−	0.654128i
$373$	−2.88847e12	−	1.05132e12i	−0.400058	−	0.145609i	0.134152	−	0.990961i	$-0.457169\pi$
$373$	−2.88847e12	−	1.05132e12i	−0.400058	−	0.145609i	−0.534211	+	0.845351i	$0.679391\pi$
$374$	−1.10941e12	+	1.95618e11i	−0.151612	+	0.0267333i
$375$	−8.00972e12	−	9.17113e12i	−1.08009	−	1.23671i
$376$	−3.64509e12	−	3.05859e12i	−0.485030	−	0.406988i
$377$		−	1.13265e12i		−	0.148726i
$378$	5.11770e12	−	1.71651e13i	0.663156	−	2.22427i
$379$	1.13314e13			1.44907			0.724533	−	0.689240i	$-0.242055\pi$
$379$	1.13314e13			1.44907			0.724533	+	0.689240i	$0.242055\pi$
$380$	−7.08807e12	+	8.44724e12i	−0.894562	+	1.06610i
$381$	−1.97569e12	−	6.75166e11i	−0.246089	−	0.0840980i
$382$	−1.89895e12	−	1.07695e13i	−0.233452	−	1.32397i
$383$	1.02812e12	−	2.82473e12i	0.124752	−	0.342754i	−0.861557	−	0.507661i	$-0.830510\pi$
$383$	1.02812e12	−	2.82473e12i	0.124752	−	0.342754i	0.986309	+	0.164907i	$0.0527324\pi$
$384$	2.47391e11	+	1.25115e13i	0.0296297	+	1.49848i
$385$	2.74530e12	−	1.55693e13i	0.324553	−	1.84063i
$386$	2.81665e12	+	1.62620e12i	0.328698	+	0.189774i
$387$	−8.82988e12	+	8.02487e12i	−1.01719	+	0.924449i
$388$	−1.48551e13	−	2.57297e13i	−1.68934	−	2.92602i
$389$	−1.17981e12	−	3.24149e12i	−0.132453	−	0.363912i	0.855681	−	0.517503i	$-0.173138\pi$
$389$	−1.17981e12	−	3.24149e12i	−0.132453	−	0.363912i	−0.988135	+	0.153591i	$0.950916\pi$
$390$	2.29735e12	−	1.47256e13i	0.254626	−	1.63212i
$391$	−1.22956e11	+	1.03172e11i	−0.0134544	+	0.0112896i
$392$	−8.97787e12	−	1.06994e13i	−0.969935	−	1.15592i
$393$	−2.58162e12	−	6.67905e12i	−0.275378	−	0.712446i
$394$	6.87239e11	−	2.50134e11i	0.0723813	−	0.0263446i
$395$	1.84622e12	−	1.06592e12i	0.191999	−	0.110850i
$396$	−1.36381e13	+	1.76238e13i	−1.40049	+	1.80977i
$397$	4.73751e12	−	8.20561e12i	0.480394	−	0.832067i	−0.519353	−	0.854560i	$-0.673827\pi$
$397$	4.73751e12	−	8.20561e12i	0.480394	−	0.832067i	0.999747	+	0.0224930i	$0.00716034\pi$
$398$	−6.00104e12	−	1.05815e12i	−0.600913	−	0.105957i
$399$	−1.87788e12	+	3.40637e12i	−0.185696	+	0.336843i
$400$	5.79866e13	+	2.11054e13i	5.66275	+	2.06107i
$401$	1.57904e13	−	2.78427e12i	1.52290	−	0.268528i	0.651328	−	0.758796i	$-0.274212\pi$
$401$	1.57904e13	−	2.78427e12i	1.52290	−	0.268528i	0.871572	+	0.490268i	$0.163101\pi$
$402$	−1.22656e13	+	2.41370e12i	−1.16831	+	0.229907i
$403$	−1.22401e12	−	1.02707e12i	−0.115149	−	0.0966215i
$404$		−	3.08915e13i		−	2.87033i
$405$	7.77694e12	+	1.70404e13i	0.713729	+	1.56389i
$406$	7.49965e12			0.679846
$407$	1.26943e13	−	1.51285e13i	1.13668	−	1.35464i
$408$	−5.99509e11	−	3.04650e12i	−0.0530267	−	0.269464i
$409$	1.77829e12	+	1.00852e13i	0.155377	+	0.881188i	0.958440	+	0.285294i	$0.0920911\pi$
$409$	1.77829e12	+	1.00852e13i	0.155377	+	0.881188i	−0.803063	+	0.595894i	$0.796798\pi$
$410$	−2.08185e12	+	5.71983e12i	−0.179692	+	0.493700i
$411$	8.56270e12	+	4.72048e12i	0.730132	+	0.402510i
$412$	−8.33083e12	+	4.72465e13i	−0.701782	+	3.98000i
$413$	1.21705e13	+	7.02666e12i	1.01288	+	0.584788i
$414$	−5.92847e11	+	4.36502e12i	−0.0487462	+	0.358909i
$415$	−2.32745e11	−	4.03126e11i	−0.0189077	−	0.0327491i
$416$	6.14506e12	+	1.68834e13i	0.493242	+	1.35517i
$417$	−2.10822e13	+	8.14879e12i	−1.67199	+	0.646268i
$418$	5.14317e12	−	4.31563e12i	0.403041	−	0.338192i
$419$	−1.28419e13	−	1.53043e13i	−0.994393	−	1.18507i	−0.982712	−	0.185139i	$-0.940726\pi$
$419$	−1.28419e13	−	1.53043e13i	−0.994393	−	1.18507i	−0.0116802	−	0.999932i	$-0.503718\pi$
$420$	7.02785e13	+	1.09642e13i	5.37745	+	0.838936i
$421$	1.90023e13	−	6.91627e12i	1.43680	−	0.522951i	0.497925	−	0.867220i	$-0.334095\pi$
$421$	1.90023e13	−	6.91627e12i	1.43680	−	0.522951i	0.938871	+	0.344269i	$0.111873\pi$
$422$	−1.71630e13	+	9.90904e12i	−1.28242	+	0.740405i
$423$	2.79977e12	−	6.08684e11i	0.206738	−	0.0449459i
$424$	−3.87724e12	+	6.71558e12i	−0.282940	+	0.490066i
$425$	−2.44997e12	−	4.31996e11i	−0.176692	−	0.0311555i
$426$	−3.39727e13	+	6.71746e11i	−2.42149	+	0.0478803i
$427$	−3.13647e13	−	1.14158e13i	−2.20954	−	0.804206i
$428$	3.72428e13	−	6.56691e12i	2.59313	−	0.457238i
$429$	−2.11506e12	+	6.18914e12i	−0.145558	+	0.425935i
$430$	−5.03570e13	−	4.22545e13i	−3.42545	−	2.87429i
$431$			2.59707e12i			0.174621i	0.996181	+	0.0873107i	$0.0278273\pi$
$431$			2.59707e12i			0.174621i	−0.996181	+	0.0873107i	$0.972173\pi$
$432$	−3.72295e13	−	2.76508e13i	−2.47439	−	1.83776i
$433$	4.35926e12			0.286400			0.143200	−	0.989694i	$-0.454261\pi$
$433$	4.35926e12			0.286400			0.143200	+	0.989694i	$0.454261\pi$
$434$	6.80057e12	−	8.10460e12i	0.441668	−	0.526360i
$435$	−5.90704e12	+	5.15899e12i	−0.379248	+	0.331222i
$436$	5.83744e12	+	3.31058e13i	0.370502	+	2.10122i
$437$	3.27178e11	−	8.98915e11i	0.0205295	−	0.0564042i
$438$	4.11743e13	−	2.48700e13i	2.55420	−	1.54279i
$439$	2.30424e12	−	1.30680e13i	0.141320	−	0.801467i	−0.828928	−	0.559355i	$-0.811049\pi$
$439$	2.30424e12	−	1.30680e13i	0.141320	−	0.801467i	0.970248	−	0.242112i	$-0.0778401\pi$
$440$	−6.51361e13	−	3.76063e13i	−3.94965	−	2.28033i
$441$	8.40354e12	−	3.32458e11i	0.503813	−	0.0199317i
$442$	−7.43787e11	−	1.28828e12i	−0.0440897	−	0.0763656i
$443$	4.25674e12	+	1.16953e13i	0.249493	+	0.685476i	0.999705	+	0.0242790i	$0.00772899\pi$
$443$	4.25674e12	+	1.16953e13i	0.249493	+	0.685476i	−0.750212	+	0.661197i	$0.770049\pi$
$444$	6.91803e13	+	5.57562e13i	4.00929	+	3.23131i
$445$	−2.56855e13	+	2.15527e13i	−1.47193	+	1.23510i
$446$	1.06668e13	+	1.27122e13i	0.604451	+	0.720356i
$447$	1.09911e13	−	1.36374e13i	0.615890	−	0.764175i
$448$	−4.76862e13	+	1.73563e13i	−2.64242	+	0.961763i
$449$	−2.08018e13	+	1.20099e13i	−1.13991	+	0.658126i	−0.946408	−	0.322974i	$-0.895317\pi$
$449$	−2.08018e13	+	1.20099e13i	−1.13991	+	0.658126i	−0.193500	+	0.981100i	$0.561984\pi$
$450$	−5.77332e13	+	3.64488e13i	−3.12870	+	1.97525i
$451$	1.33563e12	−	2.31338e12i	0.0715818	−	0.123983i
$452$	1.28981e13	+	2.27428e12i	0.683649	+	0.120546i
$453$	−7.87868e12	−	1.30438e13i	−0.413012	−	0.683773i
$454$	−1.44875e12	−	5.27301e11i	−0.0751127	−	0.0273388i
$455$	2.05594e13	−	3.62517e12i	1.05427	−	0.185897i
$456$	1.21727e13	+	1.39377e13i	0.617394	+	0.706916i
$457$	1.24342e13	+	1.04335e13i	0.623786	+	0.523419i	0.898991	−	0.437967i	$-0.144301\pi$
$457$	1.24342e13	+	1.04335e13i	0.623786	+	0.523419i	−0.275205	+	0.961386i	$0.588746\pi$
$458$			1.96957e13i			0.977336i
$459$	1.67168e12	+	8.37178e11i	0.0820522	+	0.0410917i
$460$	−1.74929e13			−0.849320
$461$	−6.75102e12	+	8.04556e12i	−0.324239	+	0.386413i	−0.903399	−	0.428801i	$-0.858936\pi$
$461$	−6.75102e12	+	8.04556e12i	−0.324239	+	0.386413i	0.579160	+	0.815214i	$0.303381\pi$
$462$	−4.09804e13	−	1.40046e13i	−1.94700	−	0.665364i
$463$	−4.32525e12	−	2.45297e13i	−0.203286	−	1.15289i	−0.900115	−	0.435653i	$-0.856517\pi$
$463$	−4.32525e12	−	2.45297e13i	−0.203286	−	1.15289i	0.696829	−	0.717237i	$-0.254594\pi$
$464$	6.64100e12	−	1.82460e13i	0.308776	−	0.848355i
$465$	2.18723e11	+	1.10616e13i	0.0100607	+	0.508808i
$466$	−1.78673e12	+	1.01330e13i	−0.0813071	+	0.461116i
$467$	2.15403e13	+	1.24363e13i	0.969769	+	0.559896i	0.899166	−	0.437608i	$-0.144174\pi$
$467$	2.15403e13	+	1.24363e13i	0.969769	+	0.559896i	0.0706032	+	0.997504i	$0.477508\pi$
$468$	−2.80282e13	−	8.96353e12i	−1.24844	−	0.399255i
$469$	−8.75529e12	−	1.51646e13i	−0.385839	−	0.668293i
$470$	5.39890e12	+	1.48334e13i	0.235405	+	0.646771i
$471$	−3.44754e12	+	2.20982e13i	−0.148732	+	0.953350i
$472$	5.12159e13	−	4.29753e13i	2.18623	−	1.83446i
$473$	1.85435e13	+	2.20993e13i	0.783224	+	0.933410i
$474$	−2.10541e12	−	5.44702e12i	−0.0879924	−	0.227650i
$475$	1.39326e13	−	5.07106e12i	0.576189	−	0.209716i
$476$	6.14834e12	−	3.54974e12i	0.251607	−	0.145265i
$477$	−1.76919e12	−	4.32112e12i	−0.0716443	−	0.174987i
$478$	3.80410e13	−	6.58889e13i	1.52445	−	2.64042i
$479$	−2.95007e13	−	5.20177e12i	−1.16992	−	0.206288i	−0.445262	−	0.895400i	$-0.646889\pi$
$479$	−2.95007e13	−	5.20177e12i	−1.16992	−	0.206288i	−0.724654	+	0.689113i	$0.758001\pi$
$480$	6.00617e13	−	1.08949e14i	2.35717	−	4.27579i
$481$	2.45056e13	+	8.91932e12i	0.951789	+	0.346423i
$482$	6.35171e13	−	1.11998e13i	2.44149	−	0.430501i
$483$	−6.05434e12	+	1.19141e12i	−0.230320	+	0.0453237i
$484$	−1.12471e13	−	9.43747e12i	−0.423463	−	0.355328i
$485$			6.03797e13i			2.25000i
$486$	4.94051e13	−	1.38535e13i	1.82218	−	0.510950i
$487$	−2.24079e13			−0.818005			−0.409003	−	0.912533i	$-0.634123\pi$
$487$	−2.24079e13			−0.818005			−0.409003	+	0.912533i	$0.634123\pi$
$488$	−1.02069e14	+	1.21641e14i	−3.68804	+	4.39523i
$489$	−1.87909e12	−	9.54887e12i	−0.0672051	−	0.341514i
$490$	8.04592e12	+	4.56307e13i	0.284836	+	1.61539i
$491$	6.77084e12	−	1.86027e13i	0.237266	−	0.651883i	−0.762721	−	0.646728i	$-0.776137\pi$
$491$	6.77084e12	−	1.86027e13i	0.237266	−	0.651883i	0.999987	−	0.00515482i	$-0.00164084\pi$
$492$	1.05249e13	+	5.80219e12i	0.365083	+	0.201264i
$493$	−1.35931e11	+	7.70905e11i	−0.00466751	+	0.0264708i
$494$	7.67798e12	+	4.43288e12i	0.260983	+	0.150679i
$495$	4.19116e13	−	1.71598e13i	1.41029	−	0.577412i
$496$	−1.36958e13	−	2.37219e13i	−0.456226	−	0.790207i
$497$	−1.62790e13	−	4.47263e13i	−0.536842	−	1.47496i
$498$	−1.18937e12	+	4.59720e11i	−0.0388302	+	0.0150088i
$499$	−6.95420e12	+	5.83527e12i	−0.224773	+	0.188607i	−0.748219	−	0.663452i	$-0.769091\pi$
$499$	−6.95420e12	+	5.83527e12i	−0.224773	+	0.188607i	0.523446	+	0.852059i	$0.324646\pi$
$500$	−8.51403e13	−	1.01466e14i	−2.72449	−	3.24692i
$501$	−1.26493e13	−	1.97342e12i	−0.400755	−	0.0625217i
$502$	7.37344e13	−	2.68371e13i	2.31287	−	0.841816i
$503$	−4.50488e13	+	2.60089e13i	−1.39908	+	0.807760i	−0.994296	−	0.106652i	$-0.965987\pi$
$503$	−4.50488e13	+	2.60089e13i	−1.39908	+	0.807760i	−0.404785	+	0.914412i	$0.632654\pi$
$504$	3.63589e13	−	1.13691e14i	1.11804	−	3.49603i
$505$	−3.13902e13	+	5.43694e13i	−0.955735	+	1.65538i
$506$	1.04889e13	+	1.84947e12i	0.316210	+	0.0557564i
$507$	2.48579e13	−	4.91519e11i	0.742036	−	0.0146724i
$508$	−2.13421e13	−	7.76787e12i	−0.630838	−	0.229606i
$509$	1.44783e13	−	2.55291e12i	0.423768	−	0.0747217i	0.0423024	−	0.999105i	$-0.486531\pi$
$509$	1.44783e13	−	2.55291e12i	0.423768	−	0.0747217i	0.381465	+	0.924383i	$0.375420\pi$
$510$	−3.33088e12	+	9.74690e12i	−0.0965403	+	0.282498i
$511$	5.16157e13	+	4.33107e13i	1.48142	+	1.24306i
$512$		−	1.65387e13i		−	0.470058i
$513$	−1.11230e13	+	6.60496e11i	−0.313065	+	0.0185902i
$514$	1.10428e14			3.07795
$515$	6.26717e13	−	7.46892e13i	1.72996	−	2.06168i
$516$	−9.77582e13	+	8.53784e13i	−2.67242	+	2.33399i
$517$	−1.20294e12	−	6.82219e12i	−0.0325679	−	0.184702i
$518$	−5.90579e13	+	1.62260e14i	−1.58354	+	4.35074i
$519$	−2.44327e13	+	1.47578e13i	−0.648835	+	0.391909i
$520$	1.72465e13	−	9.78096e13i	0.453611	−	2.57256i
$521$	1.85680e13	+	1.07203e13i	0.483701	+	0.279265i	0.721958	−	0.691937i	$-0.243243\pi$
$521$	1.85680e13	+	1.07203e13i	0.483701	+	0.279265i	−0.238256	+	0.971202i	$0.576576\pi$
$522$	1.14689e13	+	1.81663e13i	0.295918	+	0.468719i
$523$	1.46608e13	+	2.53933e13i	0.374671	+	0.648949i	0.990278	−	0.139104i	$-0.0444224\pi$
$523$	1.46608e13	+	2.53933e13i	0.374671	+	0.648949i	−0.615607	+	0.788053i	$0.711089\pi$
$524$	−2.66410e13	−	7.31955e13i	−0.674363	−	1.85280i
$525$	−7.44641e13	−	6.00147e13i	−1.86703	−	1.50474i
$526$	4.91308e13	−	4.12257e13i	1.22018	−	1.02386i
$527$	7.09829e11	+	8.45941e11i	0.0174623	+	0.0208107i
$528$	−7.03604e13	+	8.73007e13i	−1.71458	+	2.12739i
$529$	−3.75022e13	+	1.36497e13i	−0.905270	+	0.329491i
$530$	2.22784e13	−	1.28624e13i	0.532726	−	0.307570i
$531$	1.59141e12	+	4.02261e13i	0.0376973	+	0.952874i
$532$	−2.11561e13	+	3.66434e13i	−0.496451	+	0.859879i
$533$	3.47381e12	+	6.12527e11i	0.0807551	+	0.0142393i
$534$	4.74882e13	+	7.86204e13i	1.09365	+	1.81063i
$535$	−7.22209e13	−	2.62862e13i	−1.64776	−	0.599735i
$536$	−8.20397e13	+	1.44658e13i	−1.85439	+	0.326978i
$537$	5.17212e12	+	5.92207e12i	0.115824	+	0.132618i
$538$	−8.71109e13	−	7.30947e13i	−1.93268	−	1.62171i
$539$		−	2.03341e13i		−	0.446972i
$540$	8.09162e13	+	1.87002e14i	1.76225	+	4.07264i
$541$	−2.97276e13			−0.641467			−0.320733	−	0.947170i	$-0.603929\pi$
$541$	−2.97276e13			−0.641467			−0.320733	+	0.947170i	$0.603929\pi$
$542$	−2.96931e13	+	3.53869e13i	−0.634833	+	0.756565i
$543$	5.01797e13	+	1.71483e13i	1.06299	+	0.363264i
$544$	−2.15625e12	−	1.22287e13i	−0.0452590	−	0.256677i
$545$	2.33663e13	−	6.41983e13i	0.485967	−	1.33518i
$546$	−1.13055e12	−	5.71762e13i	−0.0232985	−	1.17829i
$547$	7.00051e12	−	3.97019e13i	0.142953	−	0.810727i	−0.826035	−	0.563619i	$-0.809409\pi$
$547$	7.00051e12	−	3.97019e13i	0.142953	−	0.810727i	0.968988	−	0.247108i	$-0.0794802\pi$
$548$	9.21115e13	+	5.31806e13i	1.86385	+	1.07609i
$549$	−2.03126e13	−	9.34319e13i	−0.407290	−	1.87341i
$550$	8.25395e13	+	1.42963e14i	1.64002	+	2.84059i
$551$	−1.59565e12	−	4.38402e12i	−0.0314182	−	0.0863207i
$552$	−4.52501e12	+	2.90046e13i	−0.0882925	+	0.565941i
$553$	6.26629e12	−	5.25804e12i	0.121167	−	0.101671i
$554$	−4.64878e12	−	5.54020e12i	−0.0890820	−	0.106164i
$555$	−6.51020e13	−	1.68429e14i	−1.23632	−	3.19854i
$556$	−2.31039e14	+	8.40912e13i	−4.34821	+	1.58262i
$557$	−8.03769e13	+	4.64056e13i	−1.49918	+	0.865555i	−1.00000		0.000940570i	$-0.999701\pi$
$557$	−8.03769e13	+	4.64056e13i	−1.49918	+	0.865555i	−0.499185	+	0.866495i	$0.666367\pi$
$558$	3.00315e13	+	4.07881e12i	0.555144	+	0.0753985i
$559$	−1.90473e13	+	3.29909e13i	−0.348959	+	0.604415i
$560$	3.52449e14	+	6.21463e13i	6.39965	+	1.12843i
$561$	2.18233e12	−	3.95863e12i	0.0392741	−	0.0712412i
$562$	6.47665e13	+	2.35731e13i	1.15523	+	0.420470i
$563$	3.68704e12	−	6.50125e11i	0.0651833	−	0.0114936i	−0.140961	−	0.990015i	$-0.545019\pi$
$563$	3.68704e12	−	6.50125e11i	0.0651833	−	0.0114936i	0.206145	+	0.978522i	$0.433908\pi$
$564$	3.05807e13	−	6.01787e12i	0.535861	−	0.105450i
$565$	−2.03898e13	−	1.71091e13i	−0.354137	−	0.297156i
$566$		−	1.58083e14i		−	2.72147i
$567$	4.07417e13	+	5.92108e13i	0.695223	+	1.01038i
$568$	−2.26438e14			−3.83007
$569$	−6.07616e13	+	7.24129e13i	−1.01875	+	1.21410i	−0.0421348	+	0.999112i	$0.513416\pi$
$569$	−6.07616e13	+	7.24129e13i	−1.01875	+	1.21410i	−0.976617	+	0.214989i	$0.931029\pi$
$570$	−1.18531e13	−	6.02336e13i	−0.196997	−	1.00107i
$571$	−1.27527e13	−	7.23240e13i	−0.210098	−	1.19152i	−0.889214	−	0.457492i	$-0.848748\pi$
$571$	−1.27527e13	−	7.23240e13i	−0.210098	−	1.19152i	0.679116	−	0.734031i	$-0.262363\pi$
$572$	−2.43341e13	+	6.68573e13i	−0.397406	+	1.09186i
$573$	3.84282e13	+	2.11848e13i	0.622123	+	0.342966i
$574$	−4.05575e12	+	2.30013e13i	−0.0650896	+	0.369142i
$575$	2.03694e13	+	1.17603e13i	0.324070	+	0.187102i
$576$	−1.14967e14	−	8.89669e13i	−1.81326	−	1.40319i
$577$	4.95592e13	+	8.58391e13i	0.774900	+	1.34217i	0.934851	+	0.355041i	$0.115533\pi$
$577$	4.95592e13	+	8.58391e13i	0.774900	+	1.34217i	−0.159951	+	0.987125i	$0.551134\pi$
$578$	−4.14042e13	−	1.13757e14i	−0.641808	−	1.76335i
$579$	−1.21730e13	+	4.70517e12i	−0.187070	+	0.0723073i
$580$	−6.53535e13	+	5.48381e13i	−0.995701	+	0.835492i
$581$	−1.14810e12	−	1.36826e12i	−0.0173421	−	0.0206675i
$582$	1.63422e14	+	2.54955e13i	2.44735	+	0.381811i
$583$	−1.06086e13	+	3.86121e12i	−0.157512	+	0.0573298i
$584$	2.77607e14	−	1.60277e14i	4.08664	−	2.35942i
$585$	4.02219e13	+	4.42567e13i	0.587061	+	0.645951i
$586$	5.95449e13	−	1.03135e14i	0.861701	−	1.49251i
$587$	2.07208e12	+	3.65363e11i	0.0297314	+	0.00524245i	0.188494	−	0.982074i	$-0.439639\pi$
$587$	2.07208e12	+	3.65363e11i	0.0297314	+	0.00524245i	−0.158763	+	0.987317i	$0.550750\pi$
$588$	9.14672e13	−	1.80859e12i	1.30130	−	0.0257308i
$589$	−6.18457e12	−	2.25100e12i	−0.0872435	−	0.0317540i
$590$	−2.18425e14	+	3.85142e13i	−3.05522	+	0.538718i
$591$	−9.48987e11	+	2.77694e12i	−0.0131620	+	0.0385150i
$592$	3.42469e14	+	2.87366e14i	4.70991	+	3.95208i
$593$		−	5.89844e13i		−	0.804384i	−0.915555	−	0.402192i	$-0.868248\pi$
$593$		−	5.89844e13i		−	0.804384i	0.915555	−	0.402192i	$-0.131752\pi$
$594$	−2.87469e13	−	1.20683e14i	−0.388740	−	1.63197i
$595$	−1.44282e13			−0.193476
$596$	1.22470e14	−	1.45954e14i	1.62854	−	1.94082i
$597$	1.84166e13	−	1.60843e13i	0.242849	−	0.212096i
$598$	2.44223e12	+	1.38506e13i	0.0319360	+	0.181118i
$599$	−3.22623e13	+	8.86399e13i	−0.418371	+	1.14946i	0.534256	+	0.845322i	$0.320592\pi$
$599$	−3.22623e13	+	8.86399e13i	−0.418371	+	1.14946i	−0.952627	+	0.304141i	$0.901631\pi$
$600$	−3.89460e14	+	2.35241e14i	−5.00849	+	3.02522i
$601$	−1.19969e11	+	6.80378e11i	−0.00153002	+	0.00867716i	−0.985563	−	0.169308i	$-0.945847\pi$
$601$	−1.19969e11	+	6.80378e11i	−0.00153002	+	0.00867716i	0.984033	+	0.177985i	$0.0569579\pi$
$602$	−2.18444e14	−	1.26119e14i	−2.76285	−	1.59513i
$603$	2.33438e13	−	4.43985e13i	0.292809	−	0.556906i
$604$	−8.28823e13	−	1.43556e14i	−1.03104	−	1.78582i
$605$	1.02053e13	+	2.80388e13i	0.125907	+	0.345926i
$606$	1.33900e14	+	1.07918e14i	1.63840	+	1.32047i
$607$	9.59389e12	−	8.05023e12i	0.116426	−	0.0976934i	−0.582716	−	0.812676i	$-0.698010\pi$
$607$	9.59389e12	−	8.05023e12i	0.116426	−	0.0976934i	0.699142	+	0.714983i	$0.253565\pi$
$608$	4.75702e13	+	5.66919e13i	0.572555	+	0.682344i
$609$	−1.88841e13	+	2.34308e13i	−0.225429	+	0.279705i
$610$	4.95009e14	−	1.80169e14i	5.86089	−	2.13319i
$611$	7.92213e12	−	4.57385e12i	0.0930328	−	0.0537125i
$612$	1.80009e13	+	9.46451e12i	0.209671	+	0.110240i
$613$	2.46953e13	−	4.27734e13i	0.285306	−	0.494165i	−0.687377	−	0.726301i	$-0.741238\pi$
$613$	2.46953e13	−	4.27734e13i	0.285306	−	0.494165i	0.972683	+	0.232136i	$0.0745714\pi$
$614$	−1.11176e14	−	1.96033e13i	−1.27400	−	0.224640i
$615$	−1.26281e13	−	2.09067e13i	−0.143536	−	0.237635i
$616$	−2.71194e14	−	9.87067e13i	−3.05758	−	1.11287i
$617$	1.46064e14	−	2.57551e13i	1.63350	−	0.288030i	0.719726	−	0.694259i	$-0.244268\pi$
$617$	1.46064e14	−	2.57551e13i	1.63350	−	0.288030i	0.913771	+	0.406229i	$0.133156\pi$
$618$	−1.75689e14	−	2.01163e14i	−1.94895	−	2.23155i
$619$	1.65221e13	+	1.38637e13i	0.181808	+	0.152555i	0.729150	−	0.684354i	$-0.239916\pi$
$619$	1.65221e13	+	1.38637e13i	0.181808	+	0.152555i	−0.547342	+	0.836909i	$0.684360\pi$
$620$			1.20352e14i			1.31369i
$621$	−1.21446e13	−	1.28433e13i	−0.131500	−	0.139066i
$622$	−2.10579e14			−2.26184
$623$	−8.27000e13	+	9.85580e13i	−0.881181	+	1.05015i
$624$	−1.40106e14	−	4.78795e13i	−1.48093	−	0.506088i
$625$	1.43657e13	+	8.14718e13i	0.150635	+	0.854294i
$626$	7.53044e13	−	2.06897e14i	0.783337	−	2.15220i
$627$	5.32596e11	+	2.69353e13i	0.00549617	+	0.277962i
$628$	−4.22471e13	+	2.39595e14i	−0.432513	+	2.45290i
$629$	−1.56087e13	−	9.01166e12i	−0.158530	−	0.0915275i
$630$	−2.93039e14	+	2.66323e14i	−2.95272	+	2.68353i
$631$	6.15655e13	+	1.06635e14i	0.615447	+	1.06599i	0.990306	+	0.138904i	$0.0443579\pi$
$631$	6.15655e13	+	1.06635e14i	0.615447	+	1.06599i	−0.374859	+	0.927082i	$0.622309\pi$
$632$	−1.33101e13	−	3.65691e13i	−0.132006	−	0.362685i
$633$	1.22581e13	−	7.85724e13i	0.120616	−	0.773128i
$634$	8.28367e13	−	6.95083e13i	0.808680	−	0.678563i
$635$	2.96691e13	+	3.53582e13i	0.287366	+	0.342469i
$636$	−1.83121e13	−	4.73763e13i	−0.175976	−	0.455277i
$637$	2.52319e13	−	9.18365e12i	0.240576	−	0.0875625i
$638$	4.49844e13	−	2.59718e13i	0.425558	−	0.245696i
$639$	8.34447e13	−	1.07831e14i	0.783239	−	1.01213i
$640$	1.38324e14	−	2.39584e14i	1.28824	−	2.23130i
$641$	−1.04940e14	−	1.85038e13i	−0.969732	−	0.170990i	−0.333723	−	0.942671i	$-0.608305\pi$
$641$	−1.04940e14	−	1.85038e13i	−0.969732	−	0.170990i	−0.636010	+	0.771681i	$0.719416\pi$
$642$	−1.01641e14	+	1.84372e14i	−0.931954	+	1.69052i
$643$	−1.04590e14	−	3.80676e13i	−0.951558	−	0.346339i	−0.180838	−	0.983513i	$-0.557881\pi$
$643$	−1.04590e14	−	3.80676e13i	−0.951558	−	0.346339i	−0.770720	+	0.637174i	$0.780103\pi$
$644$	−6.61022e13	+	1.16556e13i	−0.596742	+	0.105222i
$645$	2.58813e14	−	5.09308e13i	2.31839	−	0.456228i
$646$	−4.69381e12	−	3.93857e12i	−0.0417218	−	0.0350087i
$647$		−	3.16961e13i		−	0.279566i	−0.990182	−	0.139783i	$-0.955360\pi$
$647$		−	3.16961e13i		−	0.279566i	0.990182	−	0.139783i	$-0.0446405\pi$
$648$	3.30995e14	−	8.57927e13i	2.89699	−	0.750889i
$649$	9.73352e13			0.845369
$650$	−1.40119e14	+	1.66988e14i	−1.20762	+	1.43919i
$651$	8.19695e12	+	4.16541e13i	0.0701047	+	0.356248i
$652$	−1.83832e13	−	1.04256e14i	−0.156021	−	0.884838i
$653$	7.16485e13	−	1.96853e14i	0.603450	−	1.65797i	−0.140779	−	0.990041i	$-0.544961\pi$
$653$	7.16485e13	−	1.96853e14i	0.603450	−	1.65797i	0.744229	−	0.667924i	$-0.232817\pi$
$654$	−1.63891e14	−	9.03506e13i	−1.36983	−	0.755166i
$655$	−2.74887e13	+	1.55896e14i	−0.228007	+	1.29309i
$656$	5.23688e13	+	3.02351e13i	0.431075	+	0.248881i
$657$	−2.59767e13	+	1.91261e14i	−0.212206	+	1.56243i
$658$	3.02850e13	+	5.24552e13i	0.245526	+	0.425264i
$659$	6.28562e13	+	1.72696e14i	0.505732	+	1.38949i	0.885601	+	0.464448i	$0.153747\pi$
$659$	6.28562e13	+	1.72696e14i	0.505732	+	1.38949i	−0.379868	+	0.925041i	$0.624031\pi$
$660$	4.59515e14	−	1.77614e14i	3.66927	−	1.41827i
$661$	−1.33476e14	+	1.12000e14i	−1.05778	+	0.887584i	−0.993890	−	0.110373i	$-0.964795\pi$
$661$	−1.33476e14	+	1.12000e14i	−1.05778	+	0.887584i	−0.0638911	+	0.997957i	$0.520351\pi$
$662$	2.47108e14	+	2.94492e14i	1.94356	+	2.31624i
$663$	5.89776e12	+	9.20109e11i	0.0460383	+	0.00718243i
$664$	−7.98494e12	+	2.90628e12i	−0.0618630	+	0.0225163i
$665$	7.44700e13	−	4.29953e13i	0.572628	−	0.330607i
$666$	−4.83355e14	+	1.05084e14i	−3.68889	+	0.801983i
$667$	3.70047e12	−	6.40940e12i	0.0280303	−	0.0485499i
$668$	−1.37148e14	−	2.41828e13i	−1.03111	−	0.181813i
$669$	−6.65753e13	+	1.31640e12i	−0.496801	+	0.00982330i
$670$	2.59692e14	+	9.45201e13i	1.92347	+	0.700084i
$671$	−2.27666e14	+	4.01436e13i	−1.67373	+	0.295123i
$672$	1.54369e14	−	4.51717e14i	1.12645	−	3.29625i
$673$	5.27415e13	+	4.42554e13i	0.382012	+	0.320546i	0.813492	−	0.581577i	$-0.197564\pi$
$673$	5.27415e13	+	4.42554e13i	0.382012	+	0.320546i	−0.431480	+	0.902123i	$0.642008\pi$
$674$			3.05320e14i			2.19510i
$675$	3.14971e13	−	2.72151e14i	0.224777	−	1.94219i
$676$	2.70457e14			1.91586
$677$	1.66653e14	−	1.98609e14i	1.17184	−	1.39655i	0.270904	−	0.962606i	$-0.412677\pi$
$677$	1.66653e14	−	1.98609e14i	1.17184	−	1.39655i	0.900940	−	0.433944i	$-0.142878\pi$
$678$	−5.49167e13	+	4.79623e13i	−0.383315	+	0.334774i
$679$	4.02314e13	+	2.28163e14i	0.278751	+	1.58087i
$680$	−2.34767e13	+	6.45016e13i	−0.161470	+	0.443635i
$681$	5.29537e12	−	3.19850e12i	0.0361544	−	0.0218379i
$682$	1.27244e13	−	7.21638e13i	0.0862416	−	0.489100i
$683$	−1.24431e14	−	7.18401e13i	−0.837189	−	0.483352i	0.0191184	−	0.999817i	$-0.493914\pi$
$683$	−1.24431e14	−	7.18401e13i	−0.837189	−	0.483352i	−0.856308	+	0.516466i	$0.827247\pi$
$684$	−1.21114e14	+	4.79147e12i	−0.808934	+	0.0320028i
$685$	−1.08078e14	−	1.87197e14i	−0.716615	−	1.24121i
$686$	−5.97933e13	−	1.64281e14i	−0.393579	−	1.08135i
$687$	−6.15343e13	−	4.95938e13i	−0.402099	−	0.324074i
$688$	−5.00270e14	+	4.19776e14i	−3.24536	+	2.72318i
$689$	−9.58249e12	−	1.14200e13i	−0.0617138	−	0.0735476i
$690$	6.11104e13	−	7.58236e13i	0.390723	−	0.484796i
$691$	−1.11442e14	+	4.05616e13i	−0.707390	+	0.257469i	−0.670563	−	0.741853i	$-0.733947\pi$
$691$	−1.11442e14	+	4.05616e13i	−0.707390	+	0.257469i	−0.0368272	+	0.999322i	$0.511725\pi$
$692$	−2.68900e14	+	1.55249e14i	−1.69457	+	0.978362i
$693$	1.46943e14	−	9.27696e13i	0.919351	−	0.580416i
$694$	1.91837e14	−	3.32272e14i	1.19161	−	2.06394i
$695$	4.92081e14	+	8.67671e13i	3.03468	+	0.535095i
$696$	7.40206e13	+	1.22547e14i	0.453217	+	0.750337i
$697$	−2.29084e12	−	8.33799e11i	−0.0139262	−	0.00506871i
$698$	−2.86430e14	+	5.05053e13i	−1.72878	+	0.304831i
$699$	−2.71592e13	−	3.10972e13i	−0.162754	−	0.186353i
$700$	−7.96954e14	−	6.68724e14i	−4.74180	−	3.97884i
$701$			1.28842e14i			0.761146i	0.924751	+	0.380573i	$0.124273\pi$
$701$			1.28842e14i			0.761146i	−0.924751	+	0.380573i	$0.875727\pi$
$702$	1.36768e14	−	9.01761e13i	0.802230	−	0.528939i
$703$	1.07417e14			0.625599
$704$	−2.25925e14	+	2.69247e14i	−1.30648	+	1.55700i
$705$	−5.99376e13	−	2.04829e13i	−0.344155	−	0.117611i
$706$	−6.12264e13	−	3.47232e14i	−0.349072	−	1.97969i
$707$	−8.23910e13	+	2.26367e14i	−0.466426	+	1.28150i
$708$	8.65736e12	+	4.37835e14i	0.0486653	+	2.46119i
$709$	1.81312e13	−	1.02827e14i	0.101204	−	0.573954i	−0.891465	−	0.453089i	$-0.850322\pi$
$709$	1.81312e13	−	1.02827e14i	0.101204	−	0.573954i	0.992669	−	0.120865i	$-0.0385668\pi$
$710$	6.50548e14	+	3.75594e14i	3.60568	+	2.08174i
$711$	2.23193e13	+	7.13779e12i	0.122838	+	0.0392840i
$712$	3.06041e14	+	5.30079e14i	1.67255	+	2.89695i
$713$	−3.57088e12	−	9.81092e12i	−0.0193788	−	0.0532429i
$714$	−6.09236e12	+	3.90511e13i	−0.0328318	+	0.210447i
$715$	1.10765e14	−	9.29429e13i	0.592751	−	0.497377i
$716$	5.49776e13	+	6.55198e13i	0.292160	+	0.348183i
$717$	1.10066e14	+	2.84758e14i	0.580842	+	1.50273i
$718$	−1.10546e13	+	4.02356e12i	−0.0579324	+	0.0210857i
$719$	−7.47444e13	+	4.31537e13i	−0.388986	+	0.224581i	−0.681721	−	0.731612i	$-0.738768\pi$
$719$	−7.47444e13	+	4.31537e13i	−0.388986	+	0.224581i	0.292735	+	0.956194i	$0.405435\pi$
$720$	3.88452e14	+	9.48770e14i	2.00759	+	4.90341i
$721$	1.87059e14	−	3.23995e14i	0.960067	−	1.66288i
$722$	−3.29685e14	−	5.81323e13i	−1.68040	−	0.296300i
$723$	−1.24945e14	+	2.26644e14i	−0.632454	+	1.14724i
$724$	5.42059e14	+	1.97293e14i	2.72492	+	0.991790i
$725$	1.12967e14	−	1.99192e13i	0.563979	−	0.0994447i
$726$	8.01985e13	−	1.57820e13i	0.397634	−	0.0782488i
$727$	2.50119e14	+	2.09875e14i	1.23161	+	1.03345i	0.998132	+	0.0610866i	$0.0194566\pi$
$727$	2.50119e14	+	2.09875e14i	1.23161	+	1.03345i	0.233482	+	0.972361i	$0.424988\pi$
$728$		−	3.81096e14i		−	1.86370i
$729$	−8.11203e13	+	1.89237e14i	−0.393996	+	0.919112i
$730$	−1.06341e15			−5.12963
$731$	1.69233e13	−	2.01684e13i	0.0810772	−	0.0966241i
$732$	−2.00824e14	−	1.02052e15i	−0.955566	−	4.85586i
$733$	2.92836e13	+	1.66075e14i	0.138390	+	0.784848i	0.972439	+	0.233158i	$0.0749058\pi$
$733$	2.92836e13	+	1.66075e14i	0.138390	+	0.784848i	−0.834049	+	0.551690i	$0.813983\pi$
$734$	1.47744e14	−	4.05922e14i	0.693472	−	1.90530i
$735$	−1.62821e14	−	8.97608e13i	−0.759058	−	0.418456i
$736$	−2.03863e13	+	1.15616e14i	−0.0943949	+	0.535340i
$737$	−1.05032e14	−	6.06403e13i	−0.483042	−	0.278884i
$738$	−6.19180e13	+	2.53509e13i	−0.282836	+	0.115801i
$739$	−1.17342e14	−	2.03243e14i	−0.532393	−	0.922132i	−0.999285	−	0.0378173i	$-0.987960\pi$
$739$	−1.17342e14	−	2.03243e14i	−0.532393	−	0.922132i	0.466892	−	0.884315i	$-0.345374\pi$
$740$	−6.71819e14	−	1.84581e15i	−3.02757	−	8.31817i
$741$	−3.31826e13	+	1.28259e13i	−0.148532	+	0.0574113i
$742$	7.56155e13	−	6.34489e13i	0.336195	−	0.282101i
$743$	−2.65609e14	−	3.16541e14i	−1.17300	−	1.39793i	−0.899984	−	0.435922i	$-0.856422\pi$
$743$	−2.65609e14	−	3.16541e14i	−1.17300	−	1.39793i	−0.273019	−	0.962009i	$-0.588022\pi$
$744$	1.99553e14	+	3.11322e13i	0.875373	+	0.136567i
$745$	−3.63860e14	+	1.32434e14i	−1.58545	+	0.577057i
$746$	1.61209e14	−	9.30739e13i	0.697741	−	0.402841i
$747$	1.55855e12	−	4.87346e12i	0.00670066	−	0.0209524i
$748$	2.45860e13	−	4.25842e13i	0.104998	−	0.181861i
$749$	−2.90424e14	−	5.12096e13i	−1.23204	−	0.217241i
$750$	7.37243e14	−	1.45776e13i	3.10674	−	0.0614299i
$751$	−1.94022e14	−	7.06181e13i	−0.812177	−	0.295608i	−0.0976542	−	0.995220i	$-0.531134\pi$
$751$	−1.94022e14	−	7.06181e13i	−0.812177	−	0.295608i	−0.714523	+	0.699612i	$0.753356\pi$
$752$	1.54437e14	−	2.72313e13i	0.642186	−	0.113235i
$753$	−1.01818e14	+	2.97941e14i	−0.420579	+	1.23071i
$754$	5.25442e13	+	4.40898e13i	0.215609	+	0.180918i
$755$			3.36882e14i			1.37323i
$756$	4.30368e14	+	6.52729e14i	1.74273	+	2.64316i
$757$	−9.64237e13			−0.387886			−0.193943	−	0.981013i	$-0.562128\pi$
$757$	−9.64237e13			−0.387886			−0.193943	+	0.981013i	$0.562128\pi$
$758$	−4.41091e14	+	5.25671e14i	−1.76271	+	2.10072i
$759$	−3.21892e13	+	2.81129e13i	−0.127791	+	0.111608i
$760$	−7.10383e13	−	4.02878e14i	−0.280172	−	1.58893i
$761$	3.77829e13	−	1.03808e14i	0.148038	−	0.406730i	−0.843404	−	0.537280i	$-0.819452\pi$
$761$	3.77829e13	−	1.03808e14i	0.148038	−	0.406730i	0.991442	+	0.130550i	$0.0416742\pi$
$762$	1.08228e14	−	6.53715e13i	0.421272	−	0.254456i
$763$	4.55210e13	−	2.58163e14i	0.176031	−	0.998322i
$764$	4.13383e14	+	2.38667e14i	1.58813	+	0.916907i
$765$	−2.20646e13	−	3.49492e13i	−0.0842148	−	0.133392i
$766$	9.10200e13	+	1.57651e14i	0.345138	+	0.597797i
$767$	4.39603e13	+	1.20780e14i	0.165609	+	0.455007i
$768$	−1.13082e14	−	9.11387e13i	−0.423239	−	0.341112i
$769$	2.23240e14	−	1.87320e14i	0.830118	−	0.696551i	−0.125200	−	0.992131i	$-0.539957\pi$
$769$	2.23240e14	−	1.87320e14i	0.830118	−	0.696551i	0.955318	+	0.295580i	$0.0955129\pi$
$770$	6.15407e14	+	7.33413e14i	2.27357	+	2.70954i
$771$	−2.78057e14	+	3.45003e14i	−1.02061	+	1.26634i
$772$	−1.33403e14	+	4.85549e13i	−0.486497	+	0.177071i
$773$	2.68730e14	−	1.55151e14i	0.973685	−	0.562157i	0.0733271	−	0.997308i	$-0.476638\pi$
$773$	2.68730e14	−	1.55151e14i	0.973685	−	0.562157i	0.900358	+	0.435151i	$0.143305\pi$
$774$	−2.85636e13	−	7.22002e14i	−0.102827	−	2.59916i
$775$	8.09112e13	−	1.40142e14i	0.289401	−	0.501257i
$776$	1.08547e15	+	1.91398e14i	3.85753	+	0.680187i
$777$	−3.58234e14	−	5.93084e14i	−1.26491	−	2.09416i
$778$	1.96300e14	+	7.14474e13i	0.688688	+	0.250662i
$779$	1.43087e13	−	2.52300e12i	0.0498783	−	0.00879489i
$780$	4.27930e14	+	4.89979e14i	1.48217	+	1.69709i
$781$	−2.52535e14	−	2.11902e14i	−0.869093	−	0.729256i
$782$		−	9.72011e12i		−	0.0332382i
$783$	−8.56348e13	−	9.91085e12i	−0.290965	−	0.0336746i
$784$	4.60310e14			1.55407
$785$	3.17819e14	−	3.78762e14i	1.06618	−	1.27063i
$786$	4.10338e14	+	1.40228e14i	1.36782	+	0.467436i
$787$	−7.21283e13	−	4.09060e14i	−0.238909	−	1.35492i	−0.834223	−	0.551427i	$-0.814084\pi$
$787$	−7.21283e13	−	4.09060e14i	−0.238909	−	1.35492i	0.595314	−	0.803493i	$-0.297027\pi$
$788$	−1.09182e13	+	2.99976e13i	−0.0359352	+	0.0987313i
$789$	5.08769e12	+	2.57303e14i	0.0166393	+	0.841512i
$790$	−2.24181e13	+	1.27139e14i	−0.0728557	+	0.413185i
$791$	−8.84493e13	−	5.10662e13i	−0.285635	−	0.164912i
$792$	−1.75633e14	−	8.07858e14i	−0.563611	−	2.59244i
$793$	−1.52635e14	−	2.64372e14i	−0.486731	−	0.843043i
$794$	1.96249e14	+	5.39190e14i	0.621878	+	1.70860i
$795$	−1.59116e13	+	1.01991e14i	−0.0501046	+	0.321163i
$796$	2.03755e14	−	1.70970e14i	0.637591	−	0.535002i
$797$	−1.80523e14	−	2.15138e14i	−0.561358	−	0.669001i	0.408475	−	0.912769i	$-0.366061\pi$
$797$	−1.80523e14	−	2.15138e14i	−0.561358	−	0.669001i	−0.969833	+	0.243769i	$0.921616\pi$
$798$	−8.49248e13	−	2.19714e14i	−0.262434	−	0.678957i
$799$	−5.94090e12	+	2.16231e12i	−0.0182439	+	0.00664025i
$800$	−1.57584e15	+	9.09812e14i	−4.80909	+	2.77653i
$801$	−3.65205e14	−	4.96014e13i	−1.10758	−	0.150429i
$802$	−4.85498e14	+	8.40908e14i	−1.46324	+	2.53441i
$803$	4.59590e14	+	8.10381e13i	1.37655	+	0.242723i
$804$	2.63432e14	−	4.77851e14i	0.784129	−	1.42237i
$805$	1.28185e14	+	4.66554e13i	0.379190	+	0.138014i
$806$	9.52925e13	−	1.68026e13i	0.280145	−	0.0493972i
$807$	4.47712e14	−	8.81035e13i	1.30807	−	0.257410i
$808$	8.77919e14	+	7.36661e14i	2.54916	+	2.13900i
$809$		−	2.18270e13i		−	0.0629871i	−0.999504	−	0.0314935i	$-0.989974\pi$
$809$		−	2.18270e13i		−	0.0629871i	0.999504	−	0.0314935i	$-0.0100264\pi$
$810$	−1.09324e15	−	3.02545e14i	−3.13539	−	0.867690i
$811$	−6.19697e13			−0.176634			−0.0883171	−	0.996092i	$-0.528149\pi$
$811$	−6.19697e13			−0.176634			−0.0883171	+	0.996092i	$0.528149\pi$
$812$	−2.10420e14	+	2.50768e14i	−0.596082	+	0.710383i
$813$	−3.57901e13	−	1.81873e14i	−0.100765	−	0.512054i
$814$	2.07676e14	+	1.17779e15i	0.581119	+	3.29569i
$815$	−7.35848e13	+	2.02172e14i	−0.204644	+	0.562256i
$816$	8.96131e13	+	4.94022e13i	0.247697	+	0.136551i
$817$	−2.72475e13	+	1.54528e14i	−0.0748542	+	0.424519i
$818$	−5.37082e14	−	3.10084e14i	−1.46647	−	0.846668i
$819$	1.81480e14	+	1.40438e14i	0.492502	+	0.381122i
$820$	−1.32845e14	−	2.30094e14i	−0.358324	−	0.620635i
$821$	2.17806e14	+	5.98417e14i	0.583921	+	1.60431i	0.781419	+	0.624007i	$0.214496\pi$
$821$	2.17806e14	+	5.98417e14i	0.583921	+	1.60431i	−0.197497	+	0.980303i	$0.563281\pi$
$822$	−5.52300e14	+	2.13478e14i	−1.47169	+	0.568845i
$823$	−5.73956e13	+	4.81606e13i	−0.152012	+	0.127554i	−0.715622	−	0.698488i	$-0.753857\pi$
$823$	−5.73956e13	+	4.81606e13i	−0.152012	+	0.127554i	0.563610	+	0.826041i	$0.309412\pi$
$824$	−1.14406e15	−	1.36343e15i	−3.01170	−	3.58920i
$825$	−6.54486e14	−	1.02106e14i	−1.71250	−	0.267167i
$826$	−7.99725e14	+	2.91076e14i	−2.07989	+	0.757019i
$827$	2.23474e14	−	1.29023e14i	0.577695	−	0.333532i	−0.182522	−	0.983202i	$-0.558426\pi$
$827$	2.23474e14	−	1.29023e14i	0.577695	−	0.333532i	0.760217	+	0.649669i	$0.225093\pi$
$828$	−1.29321e14	−	1.42294e14i	−0.332290	−	0.365624i
$829$	2.50976e14	−	4.34704e14i	0.641003	−	1.11025i	−0.344206	−	0.938894i	$-0.611852\pi$
$829$	2.50976e14	−	4.34704e14i	0.641003	−	1.11025i	0.985209	−	0.171356i	$-0.0548147\pi$
$830$	2.77611e13	+	4.89504e12i	0.0704769	+	0.0124270i
$831$	2.90146e13	−	5.73709e11i	0.0732169	−	0.00144773i
$832$	−4.36136e14	−	1.58741e14i	−1.09397	−	0.398173i
$833$	−1.82755e13	+	3.22247e12i	−0.0455664	+	0.00803459i
$834$	4.42624e14	−	1.29522e15i	1.09700	−	3.21005i
$835$	2.16809e14	+	1.81924e14i	0.534127	+	0.448186i
$836$			2.93059e14i			0.717669i
$837$	−8.83626e13	+	8.35554e13i	−0.215100	+	0.203398i
$838$	1.20986e15			2.92763
$839$	−4.48579e14	+	5.34596e14i	−1.07902	+	1.28593i	−0.123070	+	0.992398i	$0.539274\pi$
$839$	−4.48579e14	+	5.34596e14i	−1.07902	+	1.28593i	−0.955950	+	0.293528i	$0.905170\pi$
$840$	−1.98751e15	+	1.73582e15i	−4.75240	+	4.15057i
$841$	6.67873e13	+	3.78770e14i	0.158750	+	0.900316i
$842$	−4.18840e14	+	1.15075e15i	−0.989663	+	2.71908i
$843$	−2.36730e14	+	1.42990e14i	−0.556053	+	0.335866i
$844$	1.50214e14	−	8.51905e14i	0.350750	−	1.98920i
$845$	−4.76008e14	−	2.74823e14i	−1.10492	−	0.637926i
$846$	−8.07475e13	+	1.53577e14i	−0.186328	+	0.354384i
$847$	5.72464e13	+	9.91537e13i	0.131320	+	0.227453i
$848$	−8.74076e13	−	2.40151e14i	−0.199329	−	0.547651i
$849$	4.93891e14	+	3.98054e14i	1.11968	+	0.902409i
$850$	1.15409e14	−	9.68397e13i	0.260103	−	0.218252i
$851$	1.09532e14	+	1.30535e14i	0.245410	+	0.292468i
$852$	9.30721e14	−	1.15481e15i	2.07311	−	2.57224i
$853$	−1.01352e14	+	3.68890e13i	−0.224433	+	0.0816869i	−0.451789	−	0.892125i	$-0.649214\pi$
$853$	−1.01352e14	+	3.68890e13i	−0.224433	+	0.0816869i	0.227356	+	0.973812i	$0.426992\pi$
$854$	1.75050e15	−	1.01065e15i	3.85365	−	2.22491i
$855$	2.18031e14	+	1.14636e14i	0.477186	+	0.250894i
$856$	−7.01492e14	+	1.21502e15i	−1.52635	+	2.64372i
$857$	1.51235e13	+	2.66668e12i	0.0327151	+	0.00576855i	0.189982	−	0.981788i	$-0.439157\pi$
$857$	1.51235e13	+	2.66668e12i	0.0327151	+	0.00576855i	−0.157267	+	0.987556i	$0.550268\pi$
$858$	−2.04786e14	−	3.39039e14i	−0.440417	−	0.729145i
$859$	−2.78505e14	−	1.01367e14i	−0.595479	−	0.216737i	0.0266585	−	0.999645i	$-0.491513\pi$
$859$	−2.78505e14	−	1.01367e14i	−0.595479	−	0.216737i	−0.622138	+	0.782908i	$0.713736\pi$
$860$	2.82576e15	−	4.98258e14i	6.00680	−	1.05916i
$861$	−6.16494e13	−	7.05885e13i	−0.130291	−	0.149183i
$862$	−1.20480e14	−	1.01094e14i	−0.253150	−	0.212418i
$863$		−	7.29933e14i		−	1.52486i	−0.647073	−	0.762428i	$-0.724007\pi$
$863$		−	7.29933e14i		−	1.52486i	0.647073	−	0.762428i	$-0.275993\pi$
$864$	1.33026e15	−	3.16870e14i	2.76291	−	0.658132i
$865$	6.31024e14			1.30306
$866$	−1.69690e14	+	2.02229e14i	−0.348391	+	0.415197i
$867$	4.59661e14	+	1.57084e14i	0.938302	+	0.320653i
$868$	8.01911e13	+	4.54786e14i	0.162752	+	0.923015i
$869$	1.93776e13	−	5.32394e13i	0.0391021	−	0.107432i
$870$	−9.38930e12	−	4.74852e14i	−0.0188381	−	0.952713i
$871$	2.78100e13	−	1.57718e14i	0.0554766	−	0.314623i
$872$	−1.08005e15	−	6.23568e14i	−2.14221	−	1.23681i
$873$	−4.91152e14	+	4.46374e14i	−0.968600	+	0.880294i
$874$	2.89654e13	+	5.01695e13i	0.0567965	+	0.0983745i
$875$	3.53272e14	+	9.70607e14i	0.688762	+	1.89236i
$876$	−3.23650e14	+	2.07454e15i	−0.627414	+	4.02163i
$877$	5.14661e14	−	4.31852e14i	0.992026	−	0.832408i	0.00616603	−	0.999981i	$-0.498037\pi$
$877$	5.14661e14	−	4.31852e14i	0.992026	−	0.832408i	0.985860	+	0.167573i	$0.0535928\pi$
$878$	5.16536e14	+	6.15583e14i	0.989983	+	1.17982i
$879$	1.72285e14	+	4.45727e14i	0.328324	+	0.849424i
$880$	2.32928e15	−	8.47788e14i	4.41375	−	1.60648i
$881$	−2.55001e14	+	1.47225e14i	−0.480466	+	0.277397i	−0.720611	−	0.693340i	$-0.756139\pi$
$881$	−2.55001e14	+	1.47225e14i	−0.480466	+	0.277397i	0.240145	+	0.970737i	$0.422805\pi$
$882$	−3.11696e14	+	4.02787e14i	−0.583967	+	0.754627i
$883$	5.78185e12	−	1.00145e13i	0.0107712	−	0.0186562i	−0.860590	−	0.509299i	$-0.829905\pi$
$883$	5.78185e12	−	1.00145e13i	0.0107712	−	0.0186562i	0.871361	+	0.490643i	$0.163238\pi$
$884$	6.39453e13	+	1.12753e13i	0.118453	+	0.0208865i
$885$	4.29667e14	−	7.79394e14i	0.791436	−	1.43562i
$886$	−7.08250e14	−	2.57782e14i	−1.29723	−	0.472154i
$887$	−8.31494e14	+	1.46615e14i	−1.51440	+	0.267030i	−0.868230	−	0.496162i	$-0.834742\pi$
$887$	−8.31494e14	+	1.46615e14i	−1.51440	+	0.267030i	−0.646172	+	0.763192i	$0.723631\pi$
$888$	−3.23429e15	+	6.36463e14i	−5.85752	+	1.15268i
$889$	1.35673e14	+	1.13843e14i	0.244335	+	0.205021i
$890$		−	2.03053e15i		−	3.63630i
$891$	4.49428e14	+	2.14067e14i	0.800335	+	0.381208i
$892$	−7.24346e14			−1.28269
$893$	2.42199e13	−	2.88641e13i	0.0426495	−	0.0508277i
$894$	2.04802e14	+	1.04074e15i	0.358631	+	1.82244i
$895$	−3.01838e13	−	1.71181e14i	−0.0525605	−	0.298085i
$896$	3.63063e14	−	9.97508e14i	0.628698	−	1.72733i
$897$	−4.94222e13	−	2.72457e13i	−0.0851060	−	0.0469175i
$898$	2.52591e14	−	1.43251e15i	0.432549	−	2.45311i
$899$	−4.40970e13	−	2.54594e13i	−0.0750949	−	0.0433560i
$900$	4.01084e14	−	2.95310e15i	0.679240	−	5.00111i
$901$	5.15152e12	+	8.92270e12i	0.00867584	+	0.0150270i
$902$	5.53278e13	+	1.52012e14i	0.0926639	+	0.254592i
$903$	9.44070e14	−	3.64907e14i	1.57241	−	0.607775i
$904$	−3.72211e14	+	3.12322e14i	−0.616520	+	0.517322i
$905$	−7.53554e14	−	8.98051e14i	−1.24128	−	1.47931i
$906$	9.11796e14	+	1.42249e14i	1.49368	+	0.233029i
$907$	4.13815e14	−	1.50616e14i	0.674170	−	0.245378i	0.0178279	−	0.999841i	$-0.494325\pi$
$907$	4.13815e14	−	1.50616e14i	0.674170	−	0.245378i	0.656342	+	0.754463i	$0.272103\pi$
$908$	5.82795e13	−	3.36477e13i	0.0944249	−	0.0545162i
$909$	−6.74324e14	+	1.46602e14i	−1.08655	+	0.236221i
$910$	−6.32127e14	+	1.09488e15i	−1.01297	+	1.75452i
$911$	−6.46486e14	−	1.13993e14i	−1.03031	−	0.181671i	−0.367159	−	0.930158i	$-0.619669\pi$
$911$	−6.46486e14	−	1.13993e14i	−1.03031	−	0.181671i	−0.663149	+	0.748487i	$0.730781\pi$
$912$	−6.09746e14	+	1.20566e13i	−0.966439	+	0.0191095i
$913$	−1.16249e13	−	4.23113e12i	−0.0183247	−	0.00666964i
$914$	−9.68033e14	+	1.70690e14i	−1.51761	+	0.267595i
$915$	−6.83543e14	+	2.00020e15i	−1.06576	+	3.11865i
$916$	−6.58572e14	−	5.52608e14i	−1.02124	−	0.856919i
$917$			6.07419e14i			0.936789i
$918$	−1.03910e14	+	4.49621e13i	−0.159383	+	0.0689656i
$919$	−1.11946e15			−1.70778			−0.853892	−	0.520451i	$-0.825764\pi$
$919$	−1.11946e15			−1.70778			−0.853892	+	0.520451i	$0.825764\pi$
$920$	4.17148e14	−	4.97138e14i	0.632923	−	0.754288i
$921$	3.41187e14	−	2.97980e14i	0.514866	−	0.449665i
$922$	−1.10446e14	−	6.26368e14i	−0.165765	−	0.940102i
$923$	1.48887e14	−	4.09065e14i	0.222254	−	0.610638i
$924$	1.61808e15	−	9.77348e14i	2.40236	−	1.45107i
$925$	−4.58625e14	+	2.60099e15i	−0.677250	+	3.84087i
$926$	1.30632e15	+	7.54202e14i	1.91864	+	1.10773i
$927$	1.07087e15	−	4.23654e13i	1.56436	−	0.0618889i
$928$	2.86280e14	+	4.95852e14i	0.415960	+	0.720464i
$929$	−3.31054e14	−	9.09564e14i	−0.478432	−	1.31448i	−0.910824	−	0.412796i	$-0.864552\pi$
$929$	−3.31054e14	−	9.09564e14i	−0.478432	−	1.31448i	0.432391	−	0.901686i	$-0.357670\pi$
$930$	−5.21669e14	−	4.20442e14i	−0.749861	−	0.604354i
$931$	8.47247e13	−	7.10925e13i	0.121133	−	0.101642i
$932$	−2.88691e14	−	3.44049e14i	−0.410539	−	0.489261i
$933$	5.30238e14	−	6.57901e14i	0.750002	−	0.930577i
$934$	−1.41542e15	+	5.15169e14i	−1.99136	+	0.724795i
$935$	−8.65434e13	+	4.99659e13i	−0.121109	+	0.0699223i
$936$	9.23121e14	−	5.82796e14i	1.28493	−	0.811218i
$937$	2.00782e14	−	3.47764e14i	0.277988	−	0.481489i	−0.692897	−	0.721037i	$-0.743666\pi$
$937$	2.00782e14	−	3.47764e14i	0.277988	−	0.481489i	0.970885	+	0.239548i	$0.0769991\pi$
$938$	1.04431e15	+	1.84139e14i	1.43818	+	0.253590i
$939$	4.56782e14	+	7.56237e14i	0.625721	+	1.03593i
$940$	−6.47467e14	−	2.35659e14i	−0.882223	−	0.321103i
$941$	6.00203e14	−	1.05832e14i	0.813486	−	0.143440i	0.248598	−	0.968607i	$-0.420030\pi$
$941$	6.00203e14	−	1.05832e14i	0.813486	−	0.143440i	0.564888	+	0.825167i	$0.308919\pi$
$942$	−8.90949e14	−	1.02014e15i	−1.20115	−	1.37532i
$943$	1.76564e13	+	1.48154e13i	0.0236779	+	0.0198681i
$944$			2.20341e15i			2.93925i
$945$	−9.41864e13	−	1.58613e15i	−0.124977	−	2.10465i
$946$	−1.74703e15			−2.30592
$947$	2.19498e12	−	2.61587e12i	0.00288191	−	0.00343452i	−0.764602	−	0.644503i	$-0.777064\pi$
$947$	2.19498e12	−	2.61587e12i	0.00288191	−	0.00343452i	0.767483	+	0.641069i	$0.221509\pi$
$948$	2.41206e14	+	8.24292e13i	0.315026	+	0.107656i
$949$	1.07011e14	+	6.06889e14i	0.139026	+	0.788458i
$950$	−3.07097e14	+	8.43741e14i	−0.396878	+	1.09041i
$951$	8.57806e12	+	4.33825e14i	0.0110277	+	0.557714i
$952$	−4.57361e13	+	2.59382e14i	−0.0584890	+	0.331708i
$953$	4.14535e14	+	2.39332e14i	0.527347	+	0.304464i	0.739935	−	0.672678i	$-0.234856\pi$
$953$	4.14535e14	+	2.39332e14i	0.527347	+	0.304464i	−0.212589	+	0.977142i	$0.568189\pi$
$954$	2.69327e14	+	8.61319e13i	0.340831	+	0.108999i
$955$	−4.85040e14	−	8.40114e14i	−0.610606	−	1.05760i
$956$	1.13582e15	+	3.12065e15i	1.42240	+	3.90801i
$957$	−3.21286e13	+	2.05940e14i	−0.0400251	+	0.256555i
$958$	1.38967e15	−	1.16607e15i	1.72220	−	1.44510i
$959$	−5.33139e14	−	6.35370e14i	−0.657275	−	0.783310i
$960$	1.15865e15	+	2.99759e15i	1.42100	+	3.67635i
$961$	7.02699e14	−	2.55762e14i	0.857339	−	0.312046i
$962$	−1.36769e15	+	7.89635e14i	−1.66001	+	0.958409i
$963$	−3.20091e14	−	7.81802e14i	−0.386493	−	0.943985i
$964$	−1.40763e15	+	2.43808e15i	−1.69084	+	2.92862i
$965$	2.84131e14	+	5.00999e13i	0.339533	+	0.0598688i
$966$	1.80403e14	−	3.27241e14i	0.214466	−	0.389030i
$967$	5.92446e14	+	2.15633e14i	0.700674	+	0.255025i	0.667699	−	0.744432i	$-0.267279\pi$
$967$	5.92446e14	+	2.15633e14i	0.700674	+	0.255025i	0.0329756	+	0.999456i	$0.489502\pi$
$968$	5.36416e14	−	9.45846e13i	0.631139	−	0.111287i
$969$	2.41241e13	−	4.74729e12i	0.0282379	−	0.00555683i
$970$	−2.80105e15	−	2.35036e15i	−3.26183	−	2.73700i
$971$		−	6.94424e14i		−	0.804505i	−0.915529	−	0.402253i	$-0.868227\pi$
$971$		−	6.94424e14i		−	0.804505i	0.915529	−	0.402253i	$-0.131773\pi$
$972$	−9.22948e14	+	2.04067e15i	−1.06377	+	2.35202i
$973$	1.91729e15			2.19849
$974$	8.72257e14	−	1.03952e15i	0.995061	−	1.18587i
$975$	−1.68891e14	−	8.58244e14i	−0.191682	−	0.974065i
$976$	−9.08745e14	−	5.15375e15i	−1.02611	−	5.81935i
$977$	1.32510e13	−	3.64069e13i	0.0148860	−	0.0408989i	−0.932027	−	0.362389i	$-0.881961\pi$
$977$	1.32510e13	−	3.64069e13i	0.0148860	−	0.0408989i	0.946913	+	0.321490i	$0.104184\pi$
$978$	5.16124e14	+	2.84531e14i	0.576846	+	0.318006i
$979$	−1.54739e14	+	8.77566e14i	−0.172062	+	0.975813i
$980$	−1.75152e15	−	1.01124e15i	−1.93769	−	1.11873i
$981$	6.94957e14	−	2.84534e14i	0.764914	−	0.313177i
$982$	5.99428e14	+	1.03824e15i	0.656417	+	1.13695i
$983$	−2.79756e14	−	7.68622e14i	−0.304797	−	0.837424i	−0.993649	−	0.112522i	$-0.964107\pi$
$983$	−2.79756e14	−	7.68622e14i	−0.304797	−	0.837424i	0.688852	−	0.724902i	$-0.258115\pi$
$984$	−4.15879e14	+	1.60748e14i	−0.450808	+	0.174249i
$985$	4.96981e13	−	4.17017e13i	0.0535992	−	0.0449751i
$986$	−3.04714e13	−	3.63144e13i	−0.0326970	−	0.0389668i
$987$	−2.40141e14	−	3.74644e13i	−0.256378	−	0.0399975i
$988$	−3.63647e14	+	1.32357e14i	−0.386274	+	0.140592i
$989$	−2.15569e14	+	1.24459e14i	−0.227827	+	0.131536i
$990$	−8.35414e14	+	2.61227e15i	−0.878468	+	2.74690i
$991$	−2.50247e14	+	4.33441e14i	−0.261819	+	0.453483i	−0.966725	−	0.255817i	$-0.917656\pi$
$991$	−2.50247e14	+	4.33441e14i	−0.261819	+	0.453483i	0.704907	+	0.709300i	$0.250989\pi$
$992$	7.95444e14	+	1.40258e14i	0.828040	+	0.146006i
$993$	−1.54229e15	+	3.04958e13i	−1.59742	+	0.0315860i
$994$	2.70856e15	+	9.85835e14i	2.79130	+	1.01595i
$995$	−5.32342e14	+	9.38663e13i	−0.545853	+	0.0962486i
$996$	1.79986e13	−	5.26678e13i	0.0183629	−	0.0537339i
$997$	4.00925e14	+	3.36416e14i	0.406994	+	0.341508i	0.823190	−	0.567767i	$-0.192192\pi$
$997$	4.00925e14	+	3.36416e14i	0.406994	+	0.341508i	−0.416196	+	0.909275i	$0.636637\pi$
$998$		−	5.49755e14i		−	0.555286i
$999$	8.88782e14	−	1.77472e15i	0.893239	−	1.78363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.f.a.11.2	yes	174
3.2	odd	2		81.11.f.a.35.28		174
27.5	odd	18	inner	27.11.f.a.5.2	✓	174
27.22	even	9		81.11.f.a.44.28		174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.11.f.a.5.2	✓	174	27.5	odd	18	inner
27.11.f.a.11.2	yes	174	1.1	even	1	trivial
81.11.f.a.35.28		174	3.2	odd	2
81.11.f.a.44.28		174	27.22	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-38.9263 + 46.3906i) q^{2} +(-46.9192 - 238.427i) q^{3} +(-459.012 - 2603.19i) q^{4} +(-1837.35 + 5048.08i) q^{5} +(12887.2 + 7104.49i) q^{6} +(-3579.43 + 20300.0i) q^{7} +(84927.2 + 49032.7i) q^{8} +(-54646.2 + 22373.6i) q^{9} +(-162662. - 281739. i) q^{10} +(48830.0 + 134159. i) q^{11} +(-599135. + 231581. i) q^{12} +(-144420. + 121183. i) q^{13} +(-802394. - 956256. i) q^{14} +(1.28981e6 + 201223. i) q^{15} +(-3.03701e6 + 1.10538e6i) q^{16} +(112839. - 65147.7i) q^{17} +(1.08925e6 - 3.40599e6i) q^{18} +(-388272. + 672507. i) q^{19} +(1.39845e7 + 2.46584e6i) q^{20} +(5.00801e6 - 99024.0i) q^{21} +(-8.12450e6 - 2.95708e6i) q^{22} +(-1.21316e6 + 213913. i) q^{23} +(7.70603e6 - 2.25495e7i) q^{24} +(-1.46263e7 - 1.22729e7i) q^{25} -1.14169e7i q^{26} +(7.89844e6 + 1.19794e7i) q^{27} +5.44877e7 q^{28} +(-3.86179e6 + 4.60230e6i) q^{29} +(-5.95423e7 + 5.20020e7i) q^{30} +(1.47173e6 + 8.34659e6i) q^{31} +(3.25951e7 - 8.95543e7i) q^{32} +(2.96962e7 - 1.79370e7i) q^{33} +(-1.37017e6 + 7.77063e6i) q^{34} +(-9.58991e7 - 5.53674e7i) q^{35} +(8.33261e7 + 1.31985e8i) q^{36} +(-6.91634e7 - 1.19794e8i) q^{37} +(-1.60840e7 - 4.41904e7i) q^{38} +(3.56694e7 + 2.87479e7i) q^{39} +(-4.03562e8 + 3.38629e8i) q^{40} +(-1.20268e7 - 1.43329e7i) q^{41} +(-1.90350e8 + 2.36179e8i) q^{42} +(1.89878e8 - 6.91101e7i) q^{43} +(3.26828e8 - 1.88694e8i) q^{44} +(-1.25397e7 - 3.16966e8i) q^{45} +(3.73003e7 - 6.46060e7i) q^{46} +(-4.77847e7 - 8.42574e6i) q^{47} +(4.06048e8 + 6.72243e8i) q^{48} +(-1.33837e8 - 4.87126e7i) q^{49} +(1.13870e9 - 2.00783e8i) q^{50} +(-2.08273e7 - 2.38472e7i) q^{51} +(3.81753e8 + 3.20329e8i) q^{52} +7.90746e7i q^{53} +(-8.63188e8 - 9.99002e7i) q^{54} -7.66964e8 q^{55} +(-1.29935e9 + 1.54851e9i) q^{56} +(1.78562e8 + 6.10212e7i) q^{57} +(-6.31782e7 - 3.58301e8i) q^{58} +(2.33178e8 - 6.40650e8i) q^{59} +(-6.82167e7 - 3.44997e9i) q^{60} +(-2.81178e8 + 1.59464e9i) q^{61} +(-4.44492e8 - 2.56628e8i) q^{62} +(-2.58582e8 - 1.18940e9i) q^{63} +(1.23093e9 + 2.13203e9i) q^{64} +(-3.46390e8 - 9.51699e8i) q^{65} +(-3.23853e8 + 2.07585e9i) q^{66} +(-6.50744e8 + 5.46039e8i) q^{67} +(-2.21386e8 - 2.63838e8i) q^{68} +(1.07923e8 + 2.79214e8i) q^{69} +(6.30153e9 - 2.29357e9i) q^{70} +(-1.99969e9 + 1.15452e9i) q^{71} +(-5.73799e9 - 7.79321e8i) q^{72} +(1.63438e9 - 2.83084e9i) q^{73} +(8.24962e9 + 1.45463e9i) q^{74} +(-2.23995e9 + 4.06315e9i) q^{75} +(1.92889e9 + 7.02057e8i) q^{76} +(-2.89821e9 + 5.11033e8i) q^{77} +(-2.72211e9 + 5.35674e8i) q^{78} +(-3.03995e8 - 2.55082e8i) q^{79} -1.73620e10i q^{80} +(2.48562e9 - 2.44527e9i) q^{81} +1.13307e9 q^{82} +(-5.56977e7 + 6.63779e7i) q^{83} +(-2.55652e9 - 1.29914e10i) q^{84} +(1.21546e8 + 6.89319e8i) q^{85} +(-4.18521e9 + 1.14988e10i) q^{86} +(1.27851e9 + 7.04819e8i) q^{87} +(-2.43120e9 + 1.37880e10i) q^{88} +(5.40536e9 + 3.12078e9i) q^{89} +(1.51924e10 + 1.17566e10i) q^{90} +(-1.94307e9 - 3.36549e9i) q^{91} +(1.11371e9 + 3.05989e9i) q^{92} +(1.92100e9 - 7.42515e8i) q^{93} +(2.25096e9 - 1.88878e9i) q^{94} +(-2.68148e9 - 3.19566e9i) q^{95} +(-2.28815e10 - 3.56975e9i) q^{96} +(1.05618e10 - 3.84417e9i) q^{97} +(7.46958e9 - 4.31256e9i) q^{98} +(-5.67000e9 - 6.23878e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 4965 q^{5} + 18234 q^{6} - 6 q^{7} - 9 q^{8} + 119124 q^{9} - 3 q^{10} - 978 q^{11} - 1015107 q^{12} - 6 q^{13} + 2134569 q^{14} - 2548539 q^{15} - 3078 q^{16} - 9 q^{17}+ \cdots - 72892391589 q^{99}+O(q^{100}) \) 174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Introduction

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