LMFDB - Embedded newform 64.10.i.a.5.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [64,10,Mod(5,64)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("64.5"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(64, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, 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:	$32.9622935145$
Analytic rank:	$0$
Dimension:	$568$
Relative dimension:	$71$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	64.5
Dual form			64.10.i.a.13.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-17.9892 - 13.7255i) q^{2} +(-12.8383 - 8.57826i) q^{3} +(135.223 + 493.820i) q^{4} +(-684.820 - 136.219i) q^{5} +(113.210 + 330.528i) q^{6} +(-1821.12 + 4396.58i) q^{7} +(4345.35 - 10739.4i) q^{8} +(-7441.12 - 17964.5i) q^{9} +(10449.7 + 11849.9i) q^{10} +(-21661.9 - 32419.3i) q^{11} +(2500.09 - 7499.79i) q^{12} +(-48344.7 + 9616.36i) q^{13} +(93105.7 - 54095.3i) q^{14} +(7623.39 + 7623.39i) q^{15} +(-225573. + 133552. i) q^{16} +(112513. - 112513. i) q^{17} +(-112711. + 425299. i) q^{18} +(37491.5 + 188483. i) q^{19} +(-25335.9 - 356598. i) q^{20} +(61095.2 - 40822.5i) q^{21} +(-55289.7 + 880517. i) q^{22} +(-840637. + 348203. i) q^{23} +(-147913. + 100600. i) q^{24} +(-1.35403e6 - 560857. i) q^{25} +(1.00167e6 + 490563. i) q^{26} +(-117863. + 592540. i) q^{27} +(-2.41738e6 - 304788. i) q^{28} +(-373089. + 558367. i) q^{29} +(-32504.2 - 241773. i) q^{30} +8.05240e6i q^{31} +(5.89095e6 + 693599. i) q^{32} +602029. i q^{33} +(-3.56831e6 + 479726. i) q^{34} +(1.84604e6 - 2.76280e6i) q^{35} +(7.86500e6 - 6.10379e6i) q^{36} +(569878. - 2.86497e6i) q^{37} +(1.91257e6 - 3.90524e6i) q^{38} +(703155. + 291256. i) q^{39} +(-4.43870e6 + 6.76267e6i) q^{40} +(3.13384e7 - 1.29808e7i) q^{41} +(-1.65936e6 - 104195. i) q^{42} +(2.13395e7 - 1.42586e7i) q^{43} +(1.30801e7 - 1.50809e7i) q^{44} +(2.64873e6 + 1.33160e7i) q^{45} +(1.99016e7 + 5.27423e6i) q^{46} +(1.15786e7 - 1.15786e7i) q^{47} +(4.04162e6 + 220447. i) q^{48} +(1.25209e7 + 1.25209e7i) q^{49} +(1.66599e7 + 2.86741e7i) q^{50} +(-2.40964e6 + 479306. i) q^{51} +(-1.12861e7 - 2.25733e7i) q^{52} +(4.16779e7 + 6.23754e7i) q^{53} +(1.02532e7 - 9.04159e6i) q^{54} +(1.04184e7 + 2.51521e7i) q^{55} +(3.93034e7 + 3.86626e7i) q^{56} +(1.13553e6 - 2.74140e6i) q^{57} +(1.43754e7 - 4.92377e6i) q^{58} +(1.73238e7 + 3.44592e6i) q^{59} +(-2.73372e6 + 4.79544e6i) q^{60} +(-2.44493e7 - 1.63365e7i) q^{61} +(1.10523e8 - 1.44856e8i) q^{62} +9.25335e7 q^{63} +(-9.64536e7 - 9.33333e7i) q^{64} +3.44174e7 q^{65} +(8.26313e6 - 1.08300e7i) q^{66} +(5.80769e6 + 3.88057e6i) q^{67} +(7.07755e7 + 4.03468e7i) q^{68} +(1.37793e7 + 2.74087e6i) q^{69} +(-7.11295e7 + 2.43628e7i) q^{70} +(-2.47478e7 + 5.97465e7i) q^{71} +(-2.25263e8 + 1.85164e6i) q^{72} +(3.20074e6 + 7.72727e6i) q^{73} +(-4.95747e7 + 4.37167e7i) q^{74} +(1.25722e7 + 1.88157e7i) q^{75} +(-8.80068e7 + 4.40013e7i) q^{76} +(1.81983e8 - 3.61987e7i) q^{77} +(-8.65157e6 - 1.48906e7i) q^{78} +(3.38448e8 + 3.38448e8i) q^{79} +(1.72669e8 - 6.07318e7i) q^{80} +(-2.64033e8 + 2.64033e8i) q^{81} +(-7.41919e8 - 1.96620e8i) q^{82} +(1.60426e7 + 8.06517e7i) q^{83} +(2.84205e7 + 2.46499e7i) q^{84} +(-9.23774e7 + 6.17246e7i) q^{85} +(-5.79586e8 - 3.63935e7i) q^{86} +(9.57964e6 - 3.96802e6i) q^{87} +(-4.42294e8 + 9.17633e7i) q^{88} +(-1.87923e8 - 7.78403e7i) q^{89} +(1.35120e8 - 2.75900e8i) q^{90} +(4.57626e7 - 2.30064e8i) q^{91} +(-2.85624e8 - 3.68038e8i) q^{92} +(6.90756e7 - 1.03379e8i) q^{93} +(-3.67210e8 + 4.93681e7i) q^{94} -1.34184e8i q^{95} +(-6.96798e7 - 5.94387e7i) q^{96} +1.12316e9i q^{97} +(-5.33858e7 - 3.97095e8i) q^{98} +(-4.21206e8 + 6.30380e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 568 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 157456 q^{99}+O(q^{100}) $ 568 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 + 3576336 * q^22 - 8 * q^23 + 12096992 * q^24 - 8 * q^25 - 2105968 * q^26 - 8 * q^27 - 21791488 * q^28 - 8 * q^29 + 44263272 * q^30 + 29441312 * q^32 - 38537008 * q^34 - 8 * q^35 - 110500728 * q^36 - 8 * q^37 + 66947312 * q^38 - 8 * q^39 + 97089632 * q^40 - 8 * q^41 - 224559088 * q^42 - 8 * q^43 + 146176992 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 182758288 * q^50 - 360057320 * q^51 - 25227512 * q^52 - 8 * q^53 - 646232264 * q^54 + 280217656 * q^55 + 203163008 * q^56 - 8 * q^57 + 855153280 * q^58 - 576150472 * q^59 + 230939416 * q^60 - 8 * q^61 - 597609496 * q^62 + 1260236864 * q^63 - 1364809832 * q^64 - 16 * q^65 + 186013784 * q^66 - 1007094968 * q^67 + 1004327944 * q^68 - 8 * q^69 + 1869092056 * q^70 - 476202952 * q^71 - 714729104 * q^72 - 8 * q^73 - 2182183312 * q^74 + 2309166136 * q^75 - 888710984 * q^76 - 8 * q^77 + 5243787376 * q^78 - 2269128680 * q^79 - 5193915232 * q^80 - 8 * q^81 + 3136405672 * q^82 - 8 * q^83 + 6148771880 * q^84 - 8 * q^85 - 988828368 * q^86 - 8 * q^87 - 4940685368 * q^88 - 8 * q^89 - 7222410008 * q^90 - 8 * q^91 + 1729489584 * q^92 + 157456 * q^93 + 6710490136 * q^94 + 10366581632 * q^96 + 2543861360 * q^98 + 157456 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$1$

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 $

$2$	−17.9892	−	13.7255i	−0.795018	−	0.606585i
$2$	−17.9892	−	13.7255i	−0.795018	−	0.606585i
$3$	−12.8383	−	8.57826i	−0.0915084	−	0.0611440i	0.508974	−	0.860782i	$-0.330025\pi$
$3$	−12.8383	−	8.57826i	−0.0915084	−	0.0611440i	−0.600483	+	0.799638i	$0.705025\pi$
$4$	135.223	+	493.820i	0.264108	+	0.964493i
$5$	−684.820	−	136.219i	−0.490017	−	0.0974705i	−0.0561036	−	0.998425i	$-0.517868\pi$
$5$	−684.820	−	136.219i	−0.490017	−	0.0974705i	−0.433914	+	0.900954i	$0.642868\pi$
$6$	113.210	+	330.528i	0.0356618	+	0.104118i
$7$	−1821.12	+	4396.58i	−0.286681	+	0.692109i	−0.999962	−	0.00876984i	$-0.997208\pi$
$7$	−1821.12	+	4396.58i	−0.286681	+	0.692109i	0.713281	+	0.700878i	$0.247208\pi$
$8$	4345.35	−	10739.4i	0.375077	−	0.926994i
$9$	−7441.12	−	17964.5i	−0.378048	−	0.912689i
$10$	10449.7	+	11849.9i	0.330449	+	0.374728i
$11$	−21661.9	−	32419.3i	−0.446097	−	0.667631i	0.538469	−	0.842645i	$-0.319003\pi$
$11$	−21661.9	−	32419.3i	−0.446097	−	0.667631i	−0.984566	+	0.175014i	$0.944003\pi$
$12$	2500.09	−	7499.79i	0.0348048	−	0.104408i
$13$	−48344.7	+	9616.36i	−0.469466	+	0.0933826i	−0.424154	−	0.905590i	$-0.639428\pi$
$13$	−48344.7	+	9616.36i	−0.469466	+	0.0933826i	−0.0453123	+	0.998973i	$0.514428\pi$
$14$	93105.7	−	54095.3i	0.647739	−	0.376343i
$15$	7623.39	+	7623.39i	0.0388810	+	0.0388810i
$16$	−225573.	+	133552.i	−0.860494	+	0.509461i
$17$	112513.	−	112513.i	0.326725	−	0.326725i	−0.524615	−	0.851340i	$-0.675791\pi$
$17$	112513.	−	112513.i	0.326725	−	0.326725i	0.851340	+	0.524615i	$0.175791\pi$
$18$	−112711.	+	425299.i	−0.253069	+	0.954923i
$19$	37491.5	+	188483.i	0.0659997	+	0.331803i	0.999652	−	0.0263777i	$-0.00839726\pi$
$19$	37491.5	+	188483.i	0.0659997	+	0.331803i	−0.933652	+	0.358180i	$0.883397\pi$
$20$	−25335.9	−	356598.i	−0.0354080	−	0.498361i
$21$	61095.2	−	40822.5i	0.0685520	−	0.0458050i
$22$	−55289.7	+	880517.i	−0.0503201	+	0.801375i
$23$	−840637.	+	348203.i	−0.626373	+	0.259452i	−0.673211	−	0.739450i	$-0.735086\pi$
$23$	−840637.	+	348203.i	−0.626373	+	0.259452i	0.0468381	+	0.998902i	$0.485086\pi$
$24$	−147913.	+	100600.i	−0.0910028	+	0.0618941i
$25$	−1.35403e6	−	560857.i	−0.693263	−	0.287159i
$26$	1.00167e6	+	490563.i	0.429878	+	0.210530i
$27$	−117863.	+	592540.i	−0.0426818	+	0.214576i
$28$	−2.41738e6	−	304788.i	−0.743249	−	0.0937100i
$29$	−373089.	+	558367.i	−0.0979539	+	0.146598i	−0.877209	−	0.480108i	$-0.840597\pi$
$29$	−373089.	+	558367.i	−0.0979539	+	0.146598i	0.779255	+	0.626706i	$0.215597\pi$
$30$	−32504.2	−	241773.i	−0.00732646	−	0.0544957i
$31$			8.05240e6i			1.56602i	0.622009	+	0.783010i	$0.286317\pi$
$31$			8.05240e6i			1.56602i	−0.622009	+	0.783010i	$0.713683\pi$
$32$	5.89095e6	+	693599.i	0.993140	+	0.116932i
$33$			602029.i			0.0883700i
$34$	−3.56831e6	+	479726.i	−0.457938	+	0.0615657i
$35$	1.84604e6	−	2.76280e6i	0.207939	−	0.311202i
$36$	7.86500e6	−	6.10379e6i	0.780437	−	0.605674i
$37$	569878.	−	2.86497e6i	0.0499890	−	0.251312i	−0.947708	−	0.319138i	$-0.896607\pi$
$37$	569878.	−	2.86497e6i	0.0499890	−	0.251312i	0.997697	+	0.0678268i	$0.0216065\pi$
$38$	1.91257e6	−	3.90524e6i	0.148796	−	0.303824i
$39$	703155.	+	291256.i	0.0486699	+	0.0201597i
$40$	−4.43870e6	+	6.76267e6i	−0.274149	+	0.417684i
$41$	3.13384e7	−	1.29808e7i	1.73200	−	0.717419i	0.732683	−	0.680570i	$-0.238268\pi$
$41$	3.13384e7	−	1.29808e7i	1.73200	−	0.717419i	0.999321	−	0.0368494i	$-0.0117322\pi$
$42$	−1.65936e6	−	104195.i	−0.0822847	−	0.00516684i
$43$	2.13395e7	−	1.42586e7i	0.951866	−	0.636016i	0.0203793	−	0.999792i	$-0.493513\pi$
$43$	2.13395e7	−	1.42586e7i	0.951866	−	0.636016i	0.931486	+	0.363776i	$0.118513\pi$
$44$	1.30801e7	−	1.50809e7i	0.526108	−	0.606584i
$45$	2.64873e6	+	1.33160e7i	0.0962899	+	0.484082i
$46$	1.99016e7	+	5.27423e6i	0.655358	+	0.173680i
$47$	1.15786e7	−	1.15786e7i	0.346110	−	0.346110i	−0.512548	−	0.858658i	$-0.671298\pi$
$47$	1.15786e7	−	1.15786e7i	0.346110	−	0.346110i	0.858658	+	0.512548i	$0.171298\pi$
$48$	4.04162e6	+	220447.i	0.109893	+	0.00599402i
$49$	1.25209e7	+	1.25209e7i	0.310278	+	0.310278i
$50$	1.66599e7	+	2.86741e7i	0.376970	+	0.648820i
$51$	−2.40964e6	+	479306.i	−0.0498753	+	0.00992082i
$52$	−1.12861e7	−	2.25733e7i	−0.214057	−	0.428133i
$53$	4.16779e7	+	6.23754e7i	0.725545	+	1.08586i	0.992512	+	0.122149i	$0.0389787\pi$
$53$	4.16779e7	+	6.23754e7i	0.725545	+	1.08586i	−0.266966	+	0.963706i	$0.586021\pi$
$54$	1.02532e7	−	9.04159e6i	0.164091	−	0.144701i
$55$	1.04184e7	+	2.51521e7i	0.153521	+	0.370632i
$56$	3.93034e7	+	3.86626e7i	0.534053	+	0.525345i
$57$	1.13553e6	−	2.74140e6i	0.0142482	−	0.0343982i
$58$	1.43754e7	−	4.92377e6i	0.166800	−	0.0571310i
$59$	1.73238e7	+	3.44592e6i	0.186127	+	0.0370229i	0.287273	−	0.957849i	$-0.407251\pi$
$59$	1.73238e7	+	3.44592e6i	0.186127	+	0.0370229i	−0.101147	+	0.994872i	$0.532251\pi$
$60$	−2.73372e6	+	4.79544e6i	−0.0272317	+	0.0477692i
$61$	−2.44493e7	−	1.63365e7i	−0.226091	−	0.151069i	0.437366	−	0.899283i	$-0.355911\pi$
$61$	−2.44493e7	−	1.63365e7i	−0.226091	−	0.151069i	−0.663457	+	0.748215i	$0.730911\pi$
$62$	1.10523e8	−	1.44856e8i	0.949925	−	1.24502i
$63$	9.25335e7			0.740059
$64$	−9.64536e7	−	9.33333e7i	−0.718635	−	0.695387i
$65$	3.44174e7			0.239148
$66$	8.26313e6	−	1.08300e7i	0.0536040	−	0.0702558i
$67$	5.80769e6	+	3.88057e6i	0.0352100	+	0.0235266i	0.573051	−	0.819520i	$-0.305760\pi$
$67$	5.80769e6	+	3.88057e6i	0.0352100	+	0.0235266i	−0.537841	+	0.843047i	$0.680760\pi$
$68$	7.07755e7	+	4.03468e7i	0.401414	+	0.228833i
$69$	1.37793e7	+	2.74087e6i	0.0731824	+	0.0145569i
$70$	−7.11295e7	+	2.43628e7i	−0.354086	+	0.121279i
$71$	−2.47478e7	+	5.97465e7i	−0.115578	+	0.279029i	−0.971074	−	0.238780i	$-0.923252\pi$
$71$	−2.47478e7	+	5.97465e7i	−0.115578	+	0.279029i	0.855496	+	0.517810i	$0.173252\pi$
$72$	−2.25263e8	+	1.85164e6i	−0.987854	+	0.00812006i
$73$	3.20074e6	+	7.72727e6i	0.0131916	+	0.0318473i	0.930338	−	0.366703i	$-0.119513\pi$
$73$	3.20074e6	+	7.72727e6i	0.0131916	+	0.0318473i	−0.917146	+	0.398550i	$0.869513\pi$
$74$	−4.95747e7	+	4.37167e7i	−0.192184	+	0.169475i
$75$	1.25722e7	+	1.88157e7i	0.0458814	+	0.0686663i
$76$	−8.80068e7	+	4.40013e7i	−0.302590	+	0.151288i
$77$	1.81983e8	−	3.61987e7i	0.589961	−	0.117350i
$78$	−8.65157e6	−	1.48906e7i	−0.0264648	−	0.0455498i
$79$	3.38448e8	+	3.38448e8i	0.977619	+	0.977619i	0.999755	−	0.0221359i	$-0.00704665\pi$
$79$	3.38448e8	+	3.38448e8i	0.977619	+	0.977619i	−0.0221359	+	0.999755i	$0.507047\pi$
$80$	1.72669e8	−	6.07318e7i	0.471314	−	0.165772i
$81$	−2.64033e8	+	2.64033e8i	−0.681516	+	0.681516i
$82$	−7.41919e8	−	1.96620e8i	−1.81215	−	0.480247i
$83$	1.60426e7	+	8.06517e7i	0.0371043	+	0.186536i	0.994893	−	0.100938i	$-0.0321845\pi$
$83$	1.60426e7	+	8.06517e7i	0.0371043	+	0.186536i	−0.957788	+	0.287474i	$0.907184\pi$
$84$	2.84205e7	+	2.46499e7i	0.0622837	+	0.0540204i
$85$	−9.23774e7	+	6.17246e7i	−0.191947	+	0.128255i
$86$	−5.79586e8	−	3.63935e7i	−1.14255	−	0.0717433i
$87$	9.57964e6	−	3.96802e6i	0.0179272	−	0.00742569i
$88$	−4.42294e8	+	9.17633e7i	−0.786210	+	0.163116i
$89$	−1.87923e8	−	7.78403e7i	−0.317486	−	0.131507i	0.218249	−	0.975893i	$-0.429966\pi$
$89$	−1.87923e8	−	7.78403e7i	−0.317486	−	0.131507i	−0.535735	+	0.844386i	$0.679966\pi$
$90$	1.35120e8	−	2.75900e8i	0.217085	−	0.443262i
$91$	4.57626e7	−	2.30064e8i	0.0699559	−	0.351692i
$92$	−2.85624e8	−	3.68038e8i	−0.415670	−	0.535609i
$93$	6.90756e7	−	1.03379e8i	0.0957528	−	0.143304i
$94$	−3.67210e8	+	4.93681e7i	−0.485109	+	0.0652185i
$95$		−	1.34184e8i		−	0.169022i
$96$	−6.96798e7	−	5.94387e7i	−0.0837310	−	0.0714248i
$97$			1.12316e9i			1.28816i	0.764959	+	0.644079i	$0.222759\pi$
$97$			1.12316e9i			1.28816i	−0.764959	+	0.644079i	$0.777241\pi$
$98$	−5.33858e7	−	3.97095e8i	−0.0584667	−	0.434887i
$99$	−4.21206e8	+	6.30380e8i	−0.440694	+	0.659544i
$100$	9.38664e7	−	7.44488e8i	0.0938664	−	0.744488i
$101$	−1.60260e8	+	8.05682e8i	−0.153243	+	0.770402i	0.825354	+	0.564615i	$0.190975\pi$
$101$	−1.60260e8	+	8.05682e8i	−0.153243	+	0.770402i	−0.978597	+	0.205787i	$0.934025\pi$
$102$	4.99261e7	+	2.44510e7i	0.0456696	+	0.0223664i
$103$	8.22817e8	+	3.40822e8i	0.720337	+	0.298374i	0.712575	−	0.701596i	$-0.247529\pi$
$103$	8.22817e8	+	3.40822e8i	0.720337	+	0.298374i	0.00776279	+	0.999970i	$0.497529\pi$
$104$	−1.06800e8	+	5.60982e8i	−0.0895206	+	0.470218i
$105$	−4.74000e7	+	1.96337e7i	−0.0380563	+	0.0157634i
$106$	1.06378e8	−	1.69413e9i	0.0818422	−	1.30338i
$107$	1.16659e9	−	7.79493e8i	0.860385	−	0.574891i	−0.0452374	−	0.998976i	$-0.514404\pi$
$107$	1.16659e9	−	7.79493e8i	0.860385	−	0.574891i	0.905622	+	0.424086i	$0.139404\pi$
$108$	−3.08546e8	+	2.19218e7i	−0.218229	+	0.0155049i
$109$	−3.62108e8	−	1.82044e9i	−0.245708	−	1.23526i	−0.884743	−	0.466079i	$-0.845666\pi$
$109$	−3.62108e8	−	1.82044e9i	−0.245708	−	1.23526i	0.639036	−	0.769177i	$-0.279334\pi$
$110$	1.57807e8	−	5.95464e8i	0.102768	−	0.387783i
$111$	−3.18927e7	+	3.18927e7i	−0.0199406	+	0.0199406i
$112$	−1.76376e8	−	1.23497e9i	−0.105915	−	0.741608i
$113$	2.87692e8	+	2.87692e8i	0.165988	+	0.165988i	0.785213	−	0.619226i	$-0.212553\pi$
$113$	2.87692e8	+	2.87692e8i	0.165988	+	0.165988i	−0.619226	+	0.785213i	$0.712553\pi$
$114$	−5.80543e7	+	3.37301e7i	−0.0321931	+	0.0187045i
$115$	6.23117e8	−	1.23946e8i	0.332223	−	0.0660832i
$116$	−3.26184e8	−	1.08735e8i	−0.167263	−	0.0557580i
$117$	5.32492e8	+	7.96930e8i	0.262710	+	0.393173i
$118$	−2.64345e8	−	2.99766e8i	−0.125517	−	0.142336i
$119$	2.89772e8	+	6.99572e8i	0.132463	+	0.319795i
$120$	1.14997e8	−	4.87446e7i	0.0506258	−	0.0214591i
$121$	3.20574e8	−	7.73933e8i	0.135955	−	0.328223i
$122$	2.15598e8	+	6.29459e8i	0.0881100	+	0.257246i
$123$	−5.13683e8	−	1.02178e8i	−0.202359	−	0.0402517i
$124$	−3.97644e9	+	1.08887e9i	−1.51042	+	0.413599i
$125$	1.98478e9	+	1.32619e9i	0.727138	+	0.485858i
$126$	−1.66460e9	−	1.27006e9i	−0.588361	−	0.448909i
$127$	−3.07269e9			−1.04810			−0.524048	−	0.851689i	$-0.675579\pi$
$127$	−3.07269e9			−1.04810			−0.524048	+	0.851689i	$0.675579\pi$
$128$	4.54081e8	+	3.00286e9i	0.149516	+	0.988759i
$129$	−3.96276e8			−0.125992
$130$	−6.19141e8	−	4.72394e8i	−0.190127	−	0.145064i
$131$	2.13612e9	+	1.42731e9i	0.633730	+	0.423445i	0.830511	−	0.557003i	$-0.188049\pi$
$131$	2.13612e9	+	1.42731e9i	0.633730	+	0.423445i	−0.196781	+	0.980447i	$0.563049\pi$
$132$	−2.97294e8	+	8.14085e7i	−0.0852323	+	0.0233392i
$133$	−8.96956e8	−	1.78416e8i	−0.248564	−	0.0494425i
$134$	−5.12131e7	−	1.49522e8i	−0.0137217	−	0.0400620i
$135$	1.61431e8	−	3.89728e8i	0.0418296	−	0.100986i
$136$	−7.19417e8	−	1.69723e9i	−0.180325	−	0.425418i
$137$	5.98510e8	+	1.44493e9i	0.145154	+	0.350433i	0.979689	−	0.200522i	$-0.0642637\pi$
$137$	5.98510e8	+	1.44493e9i	0.145154	+	0.350433i	−0.834535	+	0.550955i	$0.814264\pi$
$138$	−2.10259e8	−	2.38434e8i	−0.0493513	−	0.0559643i
$139$	3.94328e9	+	5.90154e9i	0.895966	+	1.34091i	0.939748	+	0.341867i	$0.111059\pi$
$139$	3.94328e9	+	5.90154e9i	0.895966	+	1.34091i	−0.0437826	+	0.999041i	$0.513941\pi$
$140$	1.61395e9	+	5.38018e8i	0.355071	+	0.118364i
$141$	−2.47973e8	+	4.93249e7i	−0.0528346	+	0.0105094i
$142$	1.26524e9	−	7.35118e8i	0.261142	−	0.151726i
$143$	1.35899e9	+	1.35899e9i	0.271772	+	0.271772i
$144$	4.07771e9	+	3.05852e9i	0.790288	+	0.592762i
$145$	3.31559e8	−	3.31559e8i	0.0622881	−	0.0622881i
$146$	4.84815e7	−	1.82939e8i	0.00883057	−	0.0333210i
$147$	−5.33390e7	−	2.68153e8i	−0.00942144	−	0.0473648i
$148$	1.49184e9	−	1.05994e8i	0.255591	−	0.0181594i
$149$	−3.38423e9	+	2.26127e9i	−0.562500	+	0.375850i	−0.804071	−	0.594533i	$-0.797337\pi$
$149$	−3.38423e9	+	2.26127e9i	−0.562500	+	0.375850i	0.241572	+	0.970383i	$0.422337\pi$
$150$	3.20893e7	−	5.11039e8i	0.00517546	−	0.0824220i
$151$	7.72659e9	−	3.20046e9i	1.20946	−	0.500975i	0.315416	−	0.948954i	$-0.397856\pi$
$151$	7.72659e9	−	3.20046e9i	1.20946	−	0.500975i	0.894044	+	0.447979i	$0.147856\pi$
$152$	2.18711e9	+	4.16385e8i	0.332334	+	0.0632701i
$153$	−2.85845e9	−	1.18401e9i	−0.421716	−	0.174680i
$154$	−3.77058e9	−	1.84662e9i	−0.540212	−	0.264566i
$155$	1.09689e9	−	5.51444e9i	0.152641	−	0.767377i
$156$	−4.87453e7	+	3.86617e8i	−0.00658980	+	0.0522661i
$157$	−5.41635e9	+	8.10614e9i	−0.711473	+	1.06479i	0.282930	+	0.959140i	$0.408693\pi$
$157$	−5.41635e9	+	8.10614e9i	−0.711473	+	1.06479i	−0.994403	+	0.105654i	$0.966307\pi$
$158$	−1.44306e9	−	1.07338e10i	−0.184216	−	1.37023i
$159$		−	1.15832e9i		−	0.143728i
$160$	−3.93976e9	−	1.27745e9i	−0.475258	−	0.154101i
$161$		−	4.33005e9i		−	0.507898i
$162$	8.37373e9	−	1.12577e9i	0.955216	−	0.128420i
$163$	5.27763e9	−	7.89853e9i	0.585592	−	0.876400i	−0.413832	−	0.910353i	$-0.635810\pi$
$163$	5.27763e9	−	7.89853e9i	0.585592	−	0.876400i	0.999423	+	0.0339535i	$0.0108098\pi$
$164$	1.06478e10	+	1.37202e10i	1.14938	+	1.48103i
$165$	8.20079e7	−	4.12282e8i	0.00861347	−	0.0433028i
$166$	8.18388e8	−	1.67105e9i	0.0836513	−	0.170806i
$167$	9.55375e9	+	3.95729e9i	0.950494	+	0.393708i	0.803417	−	0.595417i	$-0.203013\pi$
$167$	9.55375e9	+	3.95729e9i	0.950494	+	0.393708i	0.147078	+	0.989125i	$0.453013\pi$
$168$	−1.72931e8	−	8.33516e8i	−0.0167487	−	0.0807276i
$169$	−7.55254e9	+	3.12837e9i	−0.712202	+	0.295004i
$170$	2.50900e9	+	1.57546e8i	0.230399	+	0.0144673i
$171$	3.10701e9	−	2.07604e9i	0.277882	−	0.185675i
$172$	9.92678e9	+	8.60978e9i	0.864829	+	0.750091i
$173$	−2.88875e9	−	1.45227e10i	−0.245190	−	1.23265i	−0.885538	−	0.464568i	$-0.846210\pi$
$173$	−2.88875e9	−	1.45227e10i	−0.245190	−	1.23265i	0.640348	−	0.768085i	$-0.278790\pi$
$174$	−2.26793e8	−	6.01035e7i	−0.0187568	−	0.00497082i
$175$	4.93171e9	−	4.93171e9i	0.397490	−	0.397490i
$176$	9.21601e9	+	4.41994e9i	0.723996	+	0.347223i
$177$	−1.92848e8	−	1.92848e8i	−0.0147684	−	0.0147684i
$178$	2.31219e9	+	3.97962e9i	0.172637	+	0.297133i
$179$	−1.53352e9	+	3.05037e8i	−0.111648	+	0.0222082i	−0.250598	−	0.968091i	$-0.580627\pi$
$179$	−1.53352e9	+	3.05037e8i	−0.111648	+	0.0222082i	0.138950	+	0.990299i	$0.455627\pi$
$180$	−6.21757e9	+	3.10864e9i	−0.441463	+	0.220721i
$181$	−3.58879e9	−	5.37100e9i	−0.248539	−	0.371965i	0.686133	−	0.727476i	$-0.259307\pi$
$181$	−3.58879e9	−	5.37100e9i	−0.248539	−	0.371965i	−0.934672	+	0.355511i	$0.884307\pi$
$182$	−3.98097e9	+	3.51056e9i	−0.268948	+	0.237168i
$183$	1.73748e8	+	4.19465e8i	0.0114522	+	0.0276482i
$184$	8.66462e7	+	1.05410e10i	0.00557275	+	0.677958i
$185$	−7.80528e8	+	1.88436e9i	−0.0489909	+	0.118275i
$186$	−2.66154e9	+	9.11611e8i	−0.163051	+	0.0558472i
$187$	−6.08483e9	−	1.21035e9i	−0.363882	−	0.0723807i
$188$	7.28342e9	+	4.15204e9i	0.425231	+	0.242410i
$189$	−2.39051e9	−	1.59729e9i	−0.136274	−	0.0910551i
$190$	−1.84173e9	+	2.41386e9i	−0.102526	+	0.134376i
$191$	−8.57218e9			−0.466059			−0.233030	−	0.972470i	$-0.574864\pi$
$191$	−8.57218e9			−0.466059			−0.233030	+	0.972470i	$0.574864\pi$
$192$	4.37660e8	+	2.02564e9i	0.0232424	+	0.107574i
$193$	−2.85393e10			−1.48059			−0.740297	−	0.672280i	$-0.765315\pi$
$193$	−2.85393e10			−1.48059			−0.740297	+	0.672280i	$0.765315\pi$
$194$	1.54159e10	−	2.02048e10i	0.781378	−	1.02411i
$195$	−4.41860e8	−	2.95241e8i	−0.0218841	−	0.0146225i
$196$	−4.48994e9	+	7.87617e9i	−0.217314	+	0.381208i
$197$	−1.53379e10	−	3.05090e9i	−0.725551	−	0.144321i	−0.181521	−	0.983387i	$-0.558102\pi$
$197$	−1.53379e10	−	3.05090e9i	−0.725551	−	0.144321i	−0.544030	+	0.839066i	$0.683102\pi$
$198$	1.62294e10	−	5.55879e9i	0.750429	−	0.257032i
$199$	3.78861e9	−	9.14650e9i	0.171254	−	0.413444i	−0.814828	−	0.579703i	$-0.803169\pi$
$199$	3.78861e9	−	9.14650e9i	0.171254	−	0.413444i	0.986082	+	0.166259i	$0.0531688\pi$
$200$	−1.19070e10	+	1.21044e10i	−0.526221	+	0.534944i
$201$	−4.12721e7	−	9.96398e7i	−0.00178351	−	0.00430577i
$202$	1.39413e10	−	1.22939e10i	0.589146	−	0.519529i
$203$	−1.77547e9	−	2.65717e9i	−0.0733805	−	0.109822i
$204$	−5.62530e8	−	1.12511e9i	−0.0227410	−	0.0454842i
$205$	−2.32294e10	+	4.62061e9i	−0.918639	+	0.182729i
$206$	−1.01239e10	−	1.74247e10i	−0.391692	−	0.674159i
$207$	1.25106e10	+	1.25106e10i	0.473598	+	0.473598i
$208$	9.62099e9	−	8.62574e9i	0.356398	−	0.319530i
$209$	5.29834e9	−	5.29834e9i	0.192080	−	0.192080i
$210$	1.12217e9	+	2.97392e8i	0.0398173	+	0.0105522i
$211$	−7.70160e9	−	3.87186e10i	−0.267492	−	1.34477i	−0.847775	−	0.530356i	$-0.822058\pi$
$211$	−7.70160e9	−	3.87186e10i	−0.267492	−	1.34477i	0.580283	−	0.814415i	$-0.302942\pi$
$212$	−2.51664e10	+	2.90160e10i	−0.855677	+	0.986567i
$213$	8.30241e8	−	5.54749e8i	0.0276373	−	0.0184667i
$214$	−3.16850e10	−	1.98957e9i	−1.03274	−	0.0648482i
$215$	−1.65560e10	+	6.85772e9i	−0.528424	+	0.218880i
$216$	5.85139e9	+	3.84058e9i	0.182901	+	0.120048i
$217$	−3.54030e10	−	1.46644e10i	−1.08386	−	0.448948i
$218$	−1.84723e10	+	3.77184e10i	−0.553946	+	1.13109i
$219$	2.51946e7	−	1.26662e8i	0.000740130	−	0.00372089i
$220$	−1.10118e10	+	8.54596e9i	−0.316926	+	0.245957i
$221$	−4.35744e9	+	6.52137e9i	−0.122876	+	0.183896i
$222$	1.01147e9	−	1.35983e8i	0.0279488	−	0.00375747i
$223$			1.21803e10i			0.329828i	0.986308	+	0.164914i	$0.0527346\pi$
$223$			1.21803e10i			0.329828i	−0.986308	+	0.164914i	$0.947265\pi$
$224$	−1.37776e10	+	2.46369e10i	−0.365644	+	0.653838i
$225$			2.84978e10i			0.741294i
$226$	−1.22665e9	−	9.12407e9i	−0.0312775	−	0.232649i
$227$	9.47563e9	−	1.41813e10i	0.236860	−	0.354486i	−0.693929	−	0.720044i	$-0.744122\pi$
$227$	9.47563e9	−	1.41813e10i	0.236860	−	0.354486i	0.930789	+	0.365558i	$0.119122\pi$
$228$	1.50731e9	+	1.90044e8i	0.0369399	+	0.00465745i
$229$	1.40152e9	−	7.04594e9i	0.0336776	−	0.169309i	−0.960286	−	0.279017i	$-0.909992\pi$
$229$	1.40152e9	−	7.04594e9i	0.0336776	−	0.169309i	0.993964	+	0.109708i	$0.0349915\pi$
$230$	−1.29106e10	−	6.32288e9i	−0.304208	−	0.148984i
$231$	−2.64687e9	−	1.09637e9i	−0.0611616	−	0.0253340i
$232$	4.37535e9	+	6.43307e9i	0.0991555	+	0.145788i
$233$	−6.41200e10	+	2.65594e10i	−1.42525	+	0.590359i	−0.956175	−	0.292797i	$-0.905414\pi$
$233$	−6.41200e10	+	2.65594e10i	−1.42525	+	0.590359i	−0.469079	+	0.883156i	$0.655414\pi$
$234$	1.35913e9	−	2.16448e10i	0.0296339	−	0.471936i
$235$	−9.50645e9	+	6.35201e9i	−0.203335	+	0.135864i
$236$	6.40918e8	+	9.02081e9i	0.0134493	+	0.189296i
$237$	−1.44179e9	−	7.24838e9i	−0.0296849	−	0.149236i
$238$	4.38918e9	−	1.65620e10i	0.0886720	−	0.334593i
$239$	4.22018e10	−	4.22018e10i	0.836643	−	0.836643i	−0.151773	−	0.988415i	$-0.548498\pi$
$239$	4.22018e10	−	4.22018e10i	0.836643	−	0.836643i	0.988415	+	0.151773i	$0.0484982\pi$
$240$	−2.73775e9	−	7.01512e8i	−0.0532652	−	0.0136485i
$241$	−1.53920e10	−	1.53920e10i	−0.293913	−	0.293913i	0.544711	−	0.838624i	$-0.316639\pi$
$241$	−1.53920e10	−	1.53920e10i	−0.293913	−	0.293913i	−0.838624	+	0.544711i	$0.816639\pi$
$242$	−1.63895e10	+	9.52243e9i	−0.307182	+	0.178476i
$243$	1.73176e10	−	3.44469e9i	0.318611	−	0.0633756i
$244$	4.76118e9	−	1.42827e10i	0.0859925	−	0.257961i
$245$	−6.86895e9	−	1.02801e10i	−0.121799	−	0.182285i
$246$	7.83831e9	+	8.88864e9i	0.136463	+	0.154749i
$247$	−3.62503e9	−	8.75160e9i	−0.0619692	−	0.149607i
$248$	8.64783e10	+	3.49905e10i	1.45169	+	0.587378i
$249$	4.85892e8	−	1.17305e9i	0.00801019	−	0.0193383i
$250$	−1.75021e10	−	5.10990e10i	−0.283374	−	0.827337i
$251$	6.58852e10	+	1.31054e10i	1.04775	+	0.208410i	0.688802	−	0.724949i	$-0.258137\pi$
$251$	6.58852e10	+	1.31054e10i	1.04775	+	0.208410i	0.358945	+	0.933359i	$0.383137\pi$
$252$	1.25127e10	+	4.56949e10i	0.195456	+	0.713782i
$253$	2.94983e10	+	1.97101e10i	0.452641	+	0.302445i
$254$	5.52752e10	+	4.21740e10i	0.833256	+	0.635760i
$255$	1.71546e9			0.0254067
$256$	3.30471e10	−	6.02516e10i	0.480899	−	0.876776i
$257$	−5.62717e10			−0.804620			−0.402310	−	0.915503i	$-0.631793\pi$
$257$	−5.62717e10			−0.804620			−0.402310	+	0.915503i	$0.631793\pi$
$258$	7.12869e9	+	5.43907e9i	0.100166	+	0.0764251i
$259$	1.15583e10	+	7.72299e9i	0.159604	+	0.106644i
$260$	4.65403e9	+	1.69960e10i	0.0631611	+	0.230657i
$261$	1.28070e10	+	2.54746e9i	0.170830	+	0.0339802i
$262$	−1.88366e10	−	5.49953e10i	−0.246971	−	0.721057i
$263$	−2.56705e10	+	6.19742e10i	−0.330852	+	0.798748i	0.667673	+	0.744455i	$0.267291\pi$
$263$	−2.56705e10	+	6.19742e10i	−0.330852	+	0.798748i	−0.998525	+	0.0542931i	$0.982709\pi$
$264$	6.46546e9	+	2.61603e9i	0.0819185	+	0.0331455i
$265$	−2.00451e10	−	4.83932e10i	−0.249691	−	0.602807i
$266$	1.36867e10	+	1.55207e10i	0.167622	+	0.190083i
$267$	1.74488e9	+	2.61139e9i	0.0210118	+	0.0314464i
$268$	−1.13097e9	+	3.39270e9i	−0.0133920	+	0.0401734i
$269$	1.53321e11	−	3.04975e10i	1.78533	−	0.355123i	0.811842	−	0.583878i	$-0.198465\pi$
$269$	1.53321e11	−	3.04975e10i	1.78533	−	0.355123i	0.973484	+	0.228754i	$0.0734653\pi$
$270$	−8.25320e9	+	4.79519e9i	−0.0945117	+	0.0549122i
$271$	6.24280e10	+	6.24280e10i	0.703101	+	0.703101i	0.965075	−	0.261974i	$-0.0843734\pi$
$271$	6.24280e10	+	6.24280e10i	0.703101	+	0.703101i	−0.261974	+	0.965075i	$0.584373\pi$
$272$	−1.03536e10	+	4.04062e10i	−0.114691	+	0.447598i
$273$	−2.56107e9	+	2.56107e9i	−0.0279054	+	0.0279054i
$274$	9.06563e9	−	3.42080e10i	0.0971674	−	0.366649i
$275$	1.11482e10	+	5.60459e10i	0.117546	+	0.590945i
$276$	5.09785e8	+	7.17513e9i	0.00528806	+	0.0744285i
$277$	3.00445e10	−	2.00751e10i	0.306624	−	0.204880i	−0.392732	−	0.919653i	$-0.628470\pi$
$277$	3.00445e10	−	2.00751e10i	0.306624	−	0.204880i	0.699356	+	0.714773i	$0.253470\pi$
$278$	1.00648e10	−	1.60287e11i	0.101066	−	1.60953i
$279$	1.44657e11	−	5.99189e10i	1.42929	−	0.592031i
$280$	−2.16492e10	−	3.18308e10i	−0.210490	−	0.309483i
$281$	5.08575e10	+	2.10659e10i	0.486605	+	0.201559i	0.612478	−	0.790488i	$-0.290173\pi$
$281$	5.08575e10	+	2.10659e10i	0.486605	+	0.201559i	−0.125872	+	0.992046i	$0.540173\pi$
$282$	5.13784e9	+	2.51623e9i	0.0483793	+	0.0236935i
$283$	2.95272e10	−	1.48443e11i	0.273642	−	1.37569i	−0.562326	−	0.826916i	$-0.690093\pi$
$283$	2.95272e10	−	1.48443e11i	0.273642	−	1.37569i	0.835968	−	0.548778i	$-0.184907\pi$
$284$	−3.28505e10	−	4.14185e9i	−0.299647	−	0.0377800i
$285$	−1.15106e9	+	1.72269e9i	−0.0103347	+	0.0154669i
$286$	−5.79441e9	−	4.31000e10i	−0.0512108	−	0.380917i
$287$			1.61421e11i			1.40440i
$288$	−3.13752e10	−	1.10989e11i	−0.268732	−	0.950634i
$289$			9.32696e10i			0.786502i
$290$	−1.05153e10	+	1.41369e9i	−0.0873032	+	0.0117371i
$291$	9.63477e9	−	1.44195e10i	0.0787631	−	0.117877i
$292$	−3.38307e9	+	2.62550e9i	−0.0272325	+	0.0211343i
$293$	−6.94274e9	+	3.49035e10i	−0.0550334	+	0.276672i	−0.998497	−	0.0548042i	$-0.982547\pi$
$293$	−6.94274e9	+	3.49035e10i	−0.0550334	+	0.276672i	0.943464	+	0.331476i	$0.107547\pi$
$294$	−2.72100e9	+	5.55597e9i	−0.0212406	+	0.0433708i
$295$	−1.13943e10	−	4.71966e9i	−0.0875967	−	0.0362837i
$296$	−2.82919e10	−	1.85695e10i	−0.214215	−	0.140601i
$297$	2.17629e10	−	9.01448e9i	0.162298	−	0.0672259i
$298$	9.19167e10	+	5.77166e9i	0.675183	+	0.0423963i
$299$	3.72919e10	−	2.49177e10i	0.269832	−	0.180296i
$300$	−7.59150e9	+	8.75274e9i	−0.0541106	+	0.0623876i
$301$	2.38272e10	+	1.19787e11i	0.167311	+	0.841128i
$302$	−1.82923e11	−	4.84773e10i	−1.26543	−	0.335357i
$303$	8.96882e9	−	8.96882e9i	0.0611285	−	0.0611285i
$304$	−3.36293e10	−	3.75096e10i	−0.225833	−	0.251890i
$305$	1.45180e10	+	1.45180e10i	0.0960635	+	0.0960635i
$306$	3.51702e10	+	6.05330e10i	0.229313	+	0.394681i
$307$	−1.18151e11	+	2.35017e10i	−0.759128	+	0.151000i	−0.559453	−	0.828862i	$-0.688989\pi$
$307$	−1.18151e11	+	2.35017e10i	−0.759128	+	0.151000i	−0.199675	+	0.979862i	$0.563989\pi$
$308$	4.24840e10	+	8.49721e10i	0.268997	+	0.538020i
$309$	−7.63990e9	−	1.14339e10i	−0.0476732	−	0.0713480i
$310$	−9.54205e10	+	8.41451e10i	−0.586832	+	0.517489i
$311$	7.90955e10	+	1.90953e11i	0.479435	+	1.15746i	0.959874	+	0.280431i	$0.0904773\pi$
$311$	7.90955e10	+	1.90953e11i	0.479435	+	1.15746i	−0.480439	+	0.877028i	$0.659523\pi$
$312$	6.18338e9	−	6.28588e9i	0.0369429	−	0.0375552i
$313$	−6.45839e10	+	1.55919e11i	−0.380342	+	0.918227i	0.611557	+	0.791200i	$0.290543\pi$
$313$	−6.45839e10	+	1.55919e11i	−0.380342	+	0.918227i	−0.991899	+	0.127027i	$0.959457\pi$
$314$	2.08696e11	−	7.14812e10i	1.21152	−	0.414962i
$315$	−6.33688e10	−	1.26048e10i	−0.362642	−	0.0721339i
$316$	−1.21366e11	+	2.12898e11i	−0.684710	+	1.20110i
$317$	8.40993e9	+	5.61933e9i	0.0467763	+	0.0312549i	0.578739	−	0.815513i	$-0.303545\pi$
$317$	8.40993e9	+	5.61933e9i	0.0467763	+	0.0312549i	−0.531962	+	0.846768i	$0.678545\pi$
$318$	−1.58984e10	+	2.08372e10i	−0.0871831	+	0.114266i
$319$	2.61837e10			0.141570
$320$	5.33395e10	+	7.70553e10i	0.284364	+	0.410798i
$321$	−2.16638e10			−0.113884
$322$	−5.94320e10	+	7.78942e10i	−0.308084	+	0.403788i
$323$	2.54250e10	+	1.69884e10i	0.129972	+	0.0868444i
$324$	−1.66089e11	−	9.46816e10i	−0.837312	−	0.477324i
$325$	7.08536e10	+	1.40937e10i	0.352279	+	0.0700726i
$326$	−2.03351e11	+	6.96505e10i	−0.997167	+	0.341543i
$327$	−1.09674e10	+	2.64776e10i	−0.0530441	+	0.128060i
$328$	−3.23011e9	−	3.92963e11i	−0.0154094	−	1.87464i
$329$	2.98201e10	+	7.19921e10i	0.140323	+	0.338769i
$330$	−7.13401e9	+	6.29103e9i	−0.0331147	+	0.0292017i
$331$	−2.19330e11	−	3.28250e11i	−1.00432	−	1.50307i	−0.857880	−	0.513850i	$-0.828219\pi$
$331$	−2.19330e11	−	3.28250e11i	−1.00432	−	1.50307i	−0.146440	−	0.989220i	$-0.546781\pi$
$332$	−3.76581e10	+	1.88282e10i	−0.170113	+	0.0850524i
$333$	−5.57082e10	+	1.10810e10i	−0.248268	+	0.0493835i
$334$	−1.17549e11	−	2.02318e11i	−0.516843	−	0.889561i
$335$	−3.44861e9	−	3.44861e9i	−0.0149604	−	0.0149604i
$336$	−8.32950e9	+	1.73679e10i	−0.0356527	+	0.0743395i
$337$	6.28422e10	−	6.28422e10i	0.265410	−	0.265410i	−0.561838	−	0.827247i	$-0.689905\pi$
$337$	6.28422e10	−	6.28422e10i	0.265410	−	0.265410i	0.827247	+	0.561838i	$0.189905\pi$
$338$	1.78803e11	+	4.73853e10i	0.745158	+	0.197478i
$339$	−1.22557e9	−	6.16138e9i	−0.00504012	−	0.0253384i
$340$	−4.29725e10	−	3.72712e10i	−0.174395	−	0.151258i
$341$	2.61053e11	−	1.74430e11i	1.04552	−	0.698597i
$342$	−8.43872e10	−	5.29886e9i	−0.333549	−	0.0209443i
$343$	−2.55269e11	+	1.05736e11i	−0.995806	+	0.412476i
$344$	−6.04017e10	−	2.91133e11i	−0.232561	−	1.12093i
$345$	−9.06298e9	−	3.75401e9i	−0.0344418	−	0.0142662i
$346$	−1.47365e11	+	3.00902e11i	−0.552779	+	1.12871i
$347$	−3.03805e10	+	1.52733e11i	−0.112490	+	0.565523i	0.882896	+	0.469568i	$0.155590\pi$
$347$	−3.03805e10	+	1.52733e11i	−0.112490	+	0.565523i	−0.995386	+	0.0959549i	$0.969410\pi$
$348$	3.25488e9	+	4.19405e9i	0.0118968	+	0.0153295i
$349$	9.94384e10	−	1.48820e11i	0.358789	−	0.536966i	−0.607535	−	0.794293i	$-0.707842\pi$
$349$	9.94384e10	−	1.48820e11i	0.358789	−	0.536966i	0.966325	+	0.257327i	$0.0828416\pi$
$350$	−1.56408e11	+	2.10276e10i	−0.557124	+	0.0749003i
$351$		−	2.97796e10i		−	0.104722i
$352$	−1.05123e11	−	2.06005e11i	−0.364969	−	0.715214i
$353$			1.26024e11i			0.431982i	0.976395	+	0.215991i	$0.0692982\pi$
$353$			1.26024e11i			0.431982i	−0.976395	+	0.215991i	$0.930702\pi$
$354$	8.22254e8	+	6.11610e9i	0.00278286	+	0.0206995i
$355$	2.50864e10	−	3.75445e10i	0.0838323	−	0.125464i
$356$	1.30275e10	−	1.03326e11i	0.0429870	−	0.340946i
$357$	2.28094e9	−	1.14670e10i	0.00743201	−	0.0373632i
$358$	3.17736e10	+	1.55609e10i	0.102234	+	0.0500682i
$359$	1.37818e11	+	5.70859e10i	0.437905	+	0.181386i	0.590734	−	0.806867i	$-0.298838\pi$
$359$	1.37818e11	+	5.70859e10i	0.437905	+	0.181386i	−0.152829	+	0.988253i	$0.548838\pi$
$360$	1.54517e11	+	2.94170e10i	0.484857	+	0.0923077i
$361$	2.64005e11	−	1.09354e11i	0.818142	−	0.338886i
$362$	−9.16001e9	+	1.45878e11i	−0.0280354	+	0.446479i
$363$	−1.07546e10	+	7.18601e9i	−0.0325099	+	0.0217224i
$364$	1.19799e11	−	8.51155e9i	0.357681	−	0.0254128i
$365$	−1.13933e9	−	5.72779e9i	−0.00335993	−	0.0168915i
$366$	2.63176e9	−	9.93063e9i	0.00766623	−	0.0289276i
$367$	−3.59364e11	+	3.59364e11i	−1.03404	+	1.03404i	−0.0346392	+	0.999400i	$0.511028\pi$
$367$	−3.59364e11	+	3.59364e11i	−1.03404	+	1.03404i	−0.999400	+	0.0346392i	$0.988972\pi$
$368$	1.43122e11	−	1.90814e11i	0.406809	−	0.542370i
$369$	−4.66385e11	−	4.66385e11i	−1.30956	−	1.30956i
$370$	3.99048e10	−	2.31851e10i	0.110692	−	0.0643133i
$371$	−3.50139e11	+	6.96471e10i	−0.959530	+	0.190862i
$372$	6.03913e10	+	2.01317e10i	0.163505	+	0.0545051i
$373$	−5.15199e9	−	7.71050e9i	−0.0137811	−	0.0206249i	0.824515	−	0.565840i	$-0.191448\pi$
$373$	−5.15199e9	−	7.71050e9i	−0.0137811	−	0.0206249i	−0.838296	+	0.545215i	$0.816448\pi$
$374$	9.28487e10	+	1.05290e11i	0.245388	+	0.278270i
$375$	−1.41048e10	−	3.40519e10i	−0.0368320	−	0.0889202i
$376$	−7.40344e10	−	1.74660e11i	−0.191024	−	0.450660i
$377$	1.26674e10	−	3.05819e10i	0.0322963	−	0.0779701i
$378$	2.10798e10	+	6.15447e10i	0.0531073	+	0.155052i
$379$	2.61528e11	+	5.20212e10i	0.651092	+	0.129510i	0.509576	−	0.860426i	$-0.329802\pi$
$379$	2.61528e11	+	5.20212e10i	0.651092	+	0.129510i	0.141516	+	0.989936i	$0.454802\pi$
$380$	6.62626e10	−	1.81448e10i	0.163021	−	0.0446401i
$381$	3.94480e10	+	2.63583e10i	0.0959097	+	0.0640848i
$382$	1.54207e11	+	1.17657e11i	0.370526	+	0.282705i
$383$	−1.28621e11			−0.305434			−0.152717	−	0.988270i	$-0.548802\pi$
$383$	−1.28621e11			−0.305434			−0.152717	+	0.988270i	$0.548802\pi$
$384$	1.99297e10	−	4.24468e10i	0.0467747	−	0.0996218i
$385$	−1.29557e11			−0.300529
$386$	5.13400e11	+	3.91716e11i	1.17710	+	0.898107i
$387$	−4.14937e11	−	2.77252e11i	−0.940336	−	0.628313i
$388$	−5.54640e11	+	1.51878e11i	−1.24242	+	0.340213i
$389$	6.09690e11	+	1.21275e11i	1.35001	+	0.268533i	0.816540	−	0.577288i	$-0.195889\pi$
$389$	6.09690e11	+	1.21275e11i	1.35001	+	0.268533i	0.533466	+	0.845821i	$0.320889\pi$
$390$	3.89639e9	+	1.13759e10i	0.00852847	+	0.0248997i
$391$	−5.54051e10	+	1.33760e11i	−0.119882	+	0.289421i
$392$	1.88874e11	−	8.00595e10i	0.404004	−	0.171248i
$393$	−1.51802e10	−	3.66483e10i	−0.0321005	−	0.0774975i
$394$	2.34042e11	+	2.65403e11i	0.489283	+	0.554847i
$395$	−1.85673e11	−	2.77879e11i	−0.383761	−	0.574339i
$396$	−3.68252e11	−	1.22758e11i	−0.752517	−	0.250855i
$397$	8.16485e11	−	1.62409e11i	1.64965	−	0.328135i	0.719268	−	0.694733i	$-0.244477\pi$
$397$	8.16485e11	−	1.62409e11i	1.64965	−	0.328135i	0.930380	+	0.366598i	$0.119477\pi$
$398$	−1.93694e11	+	1.12538e11i	−0.386939	+	0.224815i
$399$	9.98488e9	+	9.98488e9i	0.0197226	+	0.0197226i
$400$	3.80337e11	−	5.43191e10i	0.742845	−	0.106092i
$401$	−5.86216e11	+	5.86216e11i	−1.13216	+	1.13216i	−0.142343	+	0.989817i	$0.545464\pi$
$401$	−5.86216e11	+	5.86216e11i	−1.13216	+	1.13216i	−0.989817	+	0.142343i	$0.954536\pi$
$402$	−6.25148e8	+	2.35892e9i	−0.00119389	+	0.00450501i
$403$	−7.74348e10	−	3.89291e11i	−0.146239	−	0.735193i
$404$	−4.19533e11	+	2.98074e10i	−0.783520	+	0.0556682i
$405$	2.16782e11	−	1.44849e11i	0.400382	−	0.267527i
$406$	−4.53169e9	+	7.21696e10i	−0.00827738	+	0.131822i
$407$	−1.05225e11	+	4.35856e10i	−0.190083	+	0.0787351i
$408$	−5.32323e9	+	2.79609e10i	−0.00951052	+	0.0499552i
$409$	−3.90562e11	−	1.61776e11i	−0.690136	−	0.285864i	0.00992096	−	0.999951i	$-0.496842\pi$
$409$	−3.90562e11	−	1.61776e11i	−0.690136	−	0.285864i	−0.700057	+	0.714087i	$0.746842\pi$
$410$	4.81298e11	+	2.35713e11i	0.841175	+	0.411960i
$411$	4.71116e9	−	2.36846e10i	0.00814404	−	0.0409429i
$412$	−5.70408e10	+	4.52411e11i	−0.0975322	+	0.773563i
$413$	−4.66990e10	+	6.98901e10i	−0.0789828	+	0.118206i
$414$	−5.33419e10	−	3.96768e11i	−0.0892415	−	0.663797i
$415$		−	5.74172e10i		−	0.0950223i
$416$	−2.91466e11	+	2.31177e10i	−0.477165	+	0.0378463i
$417$		−	1.09592e11i		−	0.177487i
$418$	−1.68035e11	+	2.25908e10i	−0.269219	+	0.0361941i
$419$	3.39184e11	−	5.07625e11i	0.537616	−	0.804600i	−0.458857	−	0.888510i	$-0.651741\pi$
$419$	3.39184e11	−	5.07625e11i	0.537616	−	0.804600i	0.996473	+	0.0839104i	$0.0267410\pi$
$420$	−1.61051e10	−	2.07521e10i	−0.0252547	−	0.0325418i
$421$	9.77391e10	−	4.91368e11i	0.151635	−	0.762320i	−0.827873	−	0.560915i	$-0.810449\pi$
$421$	9.77391e10	−	4.91368e11i	0.151635	−	0.762320i	0.979508	−	0.201405i	$-0.0645506\pi$
$422$	−3.92884e11	+	8.02224e11i	−0.603058	+	1.23137i
$423$	−2.94160e11	−	1.21845e11i	−0.446737	−	0.185045i
$424$	8.50982e11	−	1.76555e11i	1.27872	−	0.265297i
$425$	−2.15449e11	+	8.92420e10i	−0.320328	+	0.132684i
$426$	−2.25496e10	−	1.41594e9i	−0.0331738	−	0.00208306i
$427$	1.16350e11	−	7.77426e10i	0.169372	−	0.113171i
$428$	5.42680e11	+	4.70682e11i	0.781713	+	0.678002i
$429$	−5.78933e9	−	2.91049e10i	−0.00825222	−	0.0414867i
$430$	3.91955e11	+	1.03874e11i	0.552876	+	0.146520i
$431$	−4.39862e11	+	4.39862e11i	−0.614000	+	0.614000i	−0.943986	−	0.329986i	$-0.892956\pi$
$431$	−4.39862e11	+	4.39862e11i	−0.614000	+	0.614000i	0.329986	+	0.943986i	$0.392956\pi$
$432$	−5.25481e10	−	1.49402e11i	−0.0725906	−	0.206386i
$433$	6.40184e11	+	6.40184e11i	0.875205	+	0.875205i	0.993034	−	0.117829i	$-0.0375936\pi$
$433$	6.40184e11	+	6.40184e11i	0.875205	+	0.875205i	−0.117829	+	0.993034i	$0.537594\pi$
$434$	4.35597e11	+	7.49724e11i	0.589360	+	1.01437i
$435$	−7.10085e9	+	1.41245e9i	−0.00950843	+	0.00189134i
$436$	8.50005e11	−	4.24982e11i	1.12650	−	0.563225i
$437$	−9.71470e10	−	1.45391e11i	−0.127427	−	0.190709i
$438$	−2.19172e9	+	1.93273e9i	−0.00284545	+	0.00250922i
$439$	4.04207e9	+	9.75841e9i	0.00519413	+	0.0125398i	0.926455	−	0.376405i	$-0.122840\pi$
$439$	4.04207e9	+	9.75841e9i	0.00519413	+	0.0125398i	−0.921261	+	0.388944i	$0.872840\pi$
$440$	3.15391e11	−	2.59249e9i	0.401156	−	0.00329746i
$441$	1.31761e11	−	3.18100e11i	0.165888	−	0.400488i
$442$	1.67896e11	−	5.75064e10i	0.209237	−	0.0716664i
$443$	−9.66287e11	−	1.92207e11i	−1.19204	−	0.237111i	−0.441083	−	0.897466i	$-0.645406\pi$
$443$	−9.66287e11	−	1.92207e11i	−1.19204	−	0.237111i	−0.750953	+	0.660355i	$0.770406\pi$
$444$	−2.00619e10	−	1.14366e10i	−0.0244991	−	0.0139661i
$445$	1.18090e11	+	7.89053e10i	0.142756	+	0.0953864i
$446$	1.67181e11	−	2.19114e11i	0.200069	−	0.262219i
$447$	6.28455e10			0.0744544
$448$	5.86002e11	−	2.54095e11i	0.687302	−	0.298019i
$449$	−1.48389e11			−0.172303			−0.0861517	−	0.996282i	$-0.527457\pi$
$449$	−1.48389e11			−0.172303			−0.0861517	+	0.996282i	$0.527457\pi$
$450$	3.91146e11	−	5.12653e11i	0.449658	−	0.589342i
$451$	−1.09968e12	−	7.34780e11i	−1.25161	−	0.836301i
$452$	−1.03166e11	+	1.80971e11i	−0.116255	+	0.203932i
$453$	−1.26650e11	−	2.51923e10i	−0.141307	−	0.0281078i
$454$	−3.65104e11	+	1.25053e11i	−0.403334	+	0.138147i
$455$	−6.26783e10	+	1.51319e11i	−0.0685592	+	0.165517i
$456$	−2.45069e10	−	2.41073e10i	−0.0265428	−	0.0261100i
$457$	1.50468e11	+	3.63261e11i	0.161369	+	0.389579i	0.983796	−	0.179291i	$-0.0573805\pi$
$457$	1.50468e11	+	3.63261e11i	0.161369	+	0.389579i	−0.822427	+	0.568871i	$0.807380\pi$
$458$	−1.21921e11	+	1.07514e11i	−0.129475	+	0.114175i
$459$	5.34072e10	+	7.99295e10i	0.0561620	+	0.0840524i
$460$	1.45467e11	+	2.90947e11i	0.151479	+	0.302973i
$461$	8.11228e11	−	1.61363e11i	0.836544	−	0.166399i	0.241812	−	0.970323i	$-0.422258\pi$
$461$	8.11228e11	−	1.61363e11i	0.836544	−	0.166399i	0.594732	+	0.803924i	$0.297258\pi$
$462$	3.25670e10	+	5.60524e10i	0.0332574	+	0.0572407i
$463$	8.40803e11	+	8.40803e11i	0.850315	+	0.850315i	0.990172	−	0.139857i	$-0.0446642\pi$
$463$	8.40803e11	+	8.40803e11i	0.850315	+	0.850315i	−0.139857	+	0.990172i	$0.544664\pi$
$464$	9.58776e9	−	1.75780e11i	0.00960254	−	0.176051i
$465$	−6.13865e10	+	6.13865e10i	−0.0608884	+	0.0608884i
$466$	1.51801e12	+	4.02295e11i	1.49121	+	0.395191i
$467$	−3.58259e10	−	1.80109e11i	−0.0348555	−	0.175230i	0.959436	−	0.281926i	$-0.0909731\pi$
$467$	−3.58259e10	−	1.80109e11i	−0.0348555	−	0.175230i	−0.994292	+	0.106695i	$0.965973\pi$
$468$	−3.21535e11	+	3.70719e11i	−0.309829	+	0.357222i
$469$	−2.76378e10	+	1.84670e10i	−0.0263770	+	0.0176246i
$470$	2.58198e11	+	1.62128e10i	0.244069	+	0.0153256i
$471$	1.39073e11	−	5.76060e10i	0.130212	−	0.0539354i
$472$	1.12285e11	−	1.71074e11i	0.104132	−	0.158652i
$473$	−9.24507e11	−	3.82943e11i	−0.849249	−	0.351770i
$474$	−7.35507e10	+	1.50182e11i	−0.0669243	+	0.136652i
$475$	5.49472e10	−	2.76238e11i	0.0495250	−	0.248979i
$476$	−3.06279e11	+	2.37694e11i	−0.273455	+	0.212220i
$477$	8.10410e11	−	1.21286e12i	0.716757	−	1.07270i
$478$	−1.33842e12	+	1.79938e11i	−1.17264	+	0.157651i
$479$			1.73780e12i			1.50831i	0.656697	+	0.754154i	$0.271953\pi$
$479$			1.73780e12i			1.50831i	−0.656697	+	0.754154i	$0.728047\pi$
$480$	3.96214e10	+	5.01966e10i	0.0340678	+	0.0431607i
$481$			1.43986e11i			0.122650i
$482$	6.56276e10	+	4.88152e11i	0.0553828	+	0.411949i
$483$	−3.71443e10	+	5.55904e10i	−0.0310549	+	0.0464770i
$484$	4.25533e11	+	5.36519e10i	0.352476	+	0.0444407i
$485$	1.52996e11	−	7.69163e11i	0.125557	−	0.631220i
$486$	−3.58811e11	−	1.75725e11i	−0.291744	−	0.142880i
$487$	8.88919e11	+	3.68202e11i	0.716114	+	0.296624i	0.710832	−	0.703362i	$-0.248319\pi$
$487$	8.88919e11	+	3.68202e11i	0.716114	+	0.296624i	0.00528185	+	0.999986i	$0.498319\pi$
$488$	−2.81686e11	+	1.91584e11i	−0.224841	+	0.152922i
$489$	−1.35511e11	+	5.61307e10i	−0.107173	+	0.0443926i
$490$	−1.75323e10	+	2.79211e11i	−0.0137390	+	0.218801i
$491$	9.24082e11	−	6.17452e11i	0.717536	−	0.479442i	−0.142422	−	0.989806i	$-0.545489\pi$
$491$	9.24082e11	−	6.17452e11i	0.717536	−	0.479442i	0.859959	+	0.510364i	$0.170489\pi$
$492$	−1.90044e10	−	2.67484e11i	−0.0146222	−	0.205805i
$493$	2.08462e10	+	1.04801e11i	0.0158933	+	0.0799012i
$494$	−5.49083e10	+	2.07190e11i	−0.0414827	+	0.156530i
$495$	3.74320e11	−	3.74320e11i	0.280234	−	0.280234i
$496$	−1.07542e12	−	1.81641e12i	−0.797827	−	1.34755i
$497$	−2.17612e11	−	2.17612e11i	−0.159985	−	0.159985i
$498$	−2.48414e10	+	1.44331e10i	−0.0180986	+	0.0105154i
$499$	−6.00205e11	+	1.19388e11i	−0.433358	+	0.0862003i	−0.406949	−	0.913451i	$-0.633407\pi$
$499$	−6.00205e11	+	1.19388e11i	−0.433358	+	0.0862003i	−0.0264093	+	0.999651i	$0.508407\pi$
$500$	−3.86509e11	+	1.15946e12i	−0.276564	+	0.829639i
$501$	−8.87070e10	−	1.32759e11i	−0.0629054	−	0.0941446i
$502$	−1.00535e12	−	1.14006e12i	−0.706560	−	0.801238i
$503$	−2.15719e11	−	5.20791e11i	−0.150256	−	0.362750i	0.830773	−	0.556611i	$-0.187899\pi$
$503$	−2.15719e11	−	5.20791e11i	−0.150256	−	0.362750i	−0.981029	+	0.193862i	$0.937899\pi$
$504$	4.02090e11	−	9.93758e11i	0.277579	−	0.686030i
$505$	2.19499e11	−	5.29917e11i	0.150183	−	0.362574i
$506$	−2.60120e11	−	7.59447e11i	−0.176399	−	0.515015i
$507$	1.23798e11	+	2.46249e10i	0.0832102	+	0.0165515i
$508$	−4.15499e11	−	1.51735e12i	−0.276811	−	1.01088i
$509$	1.91067e12	+	1.27667e12i	1.26170	+	0.843042i	0.992760	−	0.120115i	$-0.0383263\pi$
$509$	1.91067e12	+	1.27667e12i	1.26170	+	0.843042i	0.268941	+	0.963157i	$0.413326\pi$
$510$	−3.08597e10	−	2.35454e10i	−0.0201988	−	0.0154114i
$511$	−3.98025e10			−0.0258236
$512$	−1.42147e12	+	6.30292e11i	−0.914163	+	0.405347i
$513$	−1.16102e11			−0.0740138
$514$	1.01228e12	+	7.72355e11i	0.639688	+	0.488071i
$515$	−5.17055e11	−	3.45485e11i	−0.323895	−	0.216420i
$516$	−5.35858e10	−	1.95689e11i	−0.0332756	−	0.121519i
$517$	−6.26182e11	−	1.24555e11i	−0.385473	−	0.0766752i
$518$	−1.01923e11	−	2.97573e11i	−0.0621994	−	0.181597i
$519$	−8.74932e10	+	2.11227e11i	−0.0529324	+	0.127790i
$520$	1.49556e11	−	3.69623e11i	0.0896990	−	0.221689i
$521$	−1.13019e11	−	2.72851e11i	−0.0672016	−	0.162239i	0.886711	−	0.462325i	$-0.152985\pi$
$521$	−1.13019e11	−	2.72851e11i	−0.0672016	−	0.162239i	−0.953912	+	0.300086i	$0.902985\pi$
$522$	−1.95422e11	−	2.21608e11i	−0.115201	−	0.130638i
$523$	−5.92216e10	−	8.86314e10i	−0.0346117	−	0.0518000i	0.813760	−	0.581201i	$-0.197417\pi$
$523$	−5.92216e10	−	8.86314e10i	−0.0346117	−	0.0518000i	−0.848372	+	0.529401i	$0.822417\pi$
$524$	−4.15980e11	+	1.24786e12i	−0.241036	+	0.723063i
$525$	−1.05620e11	+	2.10092e10i	−0.0606779	+	0.0120696i
$526$	1.31242e12	−	7.62526e11i	0.747542	−	0.434329i
$527$	9.05998e11	+	9.05998e11i	0.511658	+	0.511658i
$528$	−8.04023e10	−	1.35802e11i	−0.0450211	−	0.0760418i
$529$	−6.88183e11	+	6.88183e11i	−0.382079	+	0.382079i
$530$	−3.03623e11	+	1.14569e12i	−0.167145	+	0.630702i
$531$	−6.70044e10	−	3.36854e11i	−0.0365745	−	0.183872i
$532$	−3.31842e10	−	4.67061e11i	−0.0179609	−	0.252797i
$533$	−1.39022e12	+	9.28913e11i	−0.746122	+	0.498543i
$534$	4.45361e9	−	7.09261e10i	0.00237015	−	0.0377459i
$535$	−9.05089e11	+	3.74900e11i	−0.477638	+	0.197844i
$536$	6.69116e10	−	4.55089e10i	0.0350155	−	0.0238152i
$537$	2.23045e10	+	9.23882e9i	0.0115746	+	0.00479438i
$538$	−3.17672e12	−	1.55578e12i	−1.63478	−	0.800623i
$539$	1.34692e11	−	6.77143e11i	0.0687373	−	0.345566i
$540$	2.14285e11	+	2.70174e10i	0.108447	+	0.0136732i
$541$	−6.08480e11	+	9.10655e11i	−0.305393	+	0.457053i	−0.952145	−	0.305648i	$-0.901127\pi$
$541$	−6.08480e11	+	9.10655e11i	−0.305393	+	0.457053i	0.646752	+	0.762701i	$0.276127\pi$
$542$	−2.66177e11	−	1.97988e12i	−0.132487	−	0.985469i
$543$			9.97400e10i			0.0492346i
$544$	7.40846e11	−	5.84769e11i	0.362688	−	0.286279i
$545$			1.29600e12i			0.629246i
$546$	8.12233e10	−	1.09197e10i	0.0391124	−	0.00525830i
$547$	−1.06037e12	+	1.58696e12i	−0.506426	+	0.757919i	−0.993301	−	0.115552i	$-0.963136\pi$
$547$	−1.06037e12	+	1.58696e12i	−0.506426	+	0.757919i	0.486876	+	0.873471i	$0.338136\pi$
$548$	−6.32604e11	+	4.90945e11i	−0.299654	+	0.232552i
$549$	−1.11546e11	+	5.60781e11i	−0.0524058	+	0.263462i
$550$	5.68708e11	−	1.16124e12i	0.265007	−	0.541114i
$551$	−1.19230e11	−	4.93867e10i	−0.0551066	−	0.0228259i
$552$	8.93114e10	−	1.36072e11i	0.0409431	−	0.0623797i
$553$	−2.10437e12	+	8.71658e11i	−0.956883	+	0.396354i
$554$	−8.16018e11	−	5.12396e10i	−0.368049	−	0.0231106i
$555$	2.61852e10	−	1.74964e10i	0.0117149	−	0.00782762i
$556$	−2.38108e12	+	2.74530e12i	−1.05666	+	1.21830i
$557$	4.28400e11	+	2.15371e12i	0.188582	+	0.948067i	0.952913	+	0.303243i	$0.0980693\pi$
$557$	4.28400e11	+	2.15371e12i	0.188582	+	0.948067i	−0.764331	+	0.644824i	$0.776931\pi$
$558$	−3.42468e12	−	9.07590e11i	−1.49543	−	0.396311i
$559$	−8.94535e11	+	8.94535e11i	−0.387476	+	0.387476i
$560$	−4.74402e10	+	8.69756e11i	−0.0203845	+	0.373724i
$561$	6.77360e10	+	6.77360e10i	0.0288727	+	0.0288727i
$562$	−6.25748e11	−	1.07700e12i	−0.264598	−	0.455411i
$563$	2.28247e12	−	4.54012e11i	0.957453	−	0.190449i	0.308455	−	0.951239i	$-0.400188\pi$
$563$	2.28247e12	−	4.54012e11i	0.957453	−	0.190449i	0.648998	+	0.760790i	$0.275188\pi$
$564$	−5.78893e10	−	1.15784e11i	−0.0240903	−	0.0481829i
$565$	−1.57828e11	−	2.36207e11i	−0.0651579	−	0.0975156i
$566$	−2.56862e12	+	2.26510e12i	−1.05203	+	0.927714i
$567$	−6.80007e11	−	1.64168e12i	−0.276306	−	0.667061i
$568$	5.34107e11	+	5.25398e11i	0.215308	+	0.211797i
$569$	6.22890e11	−	1.50379e12i	0.249119	−	0.601426i	−0.749011	−	0.662557i	$-0.769471\pi$
$569$	6.22890e11	−	1.50379e12i	0.249119	−	0.601426i	0.998130	+	0.0611319i	$0.0194710\pi$
$570$	4.43514e10	−	1.51909e10i	0.0175983	−	0.00602764i
$571$	3.34197e12	+	6.64759e11i	1.31565	+	0.261699i	0.802526	−	0.596617i	$-0.203489\pi$
$571$	3.34197e12	+	6.64759e11i	1.31565	+	0.261699i	0.513122	+	0.858316i	$0.328489\pi$
$572$	−4.87331e11	+	8.54867e11i	−0.190345	+	0.333900i
$573$	1.10052e11	+	7.35344e10i	0.0426483	+	0.0284967i
$574$	2.21558e12	−	2.90384e12i	0.851892	−	1.11653i
$575$	1.33354e12			0.508745
$576$	−9.58960e11	+	2.42724e12i	−0.362994	+	0.918780i
$577$	−2.97569e12			−1.11763			−0.558813	−	0.829294i	$-0.688743\pi$
$577$	−2.97569e12			−1.11763			−0.558813	+	0.829294i	$0.688743\pi$
$578$	1.28017e12	−	1.67785e12i	0.477081	−	0.625284i
$579$	3.66396e11	+	2.44818e11i	0.135487	+	0.0905294i
$580$	2.08565e11	+	1.18896e11i	0.0765272	+	0.0436256i
$581$	−3.83808e11	−	7.63441e10i	−0.139740	−	0.0277960i
$582$	−3.71236e11	+	1.27153e11i	−0.134121	+	0.0459381i
$583$	1.11934e12	−	2.70234e12i	0.401287	−	0.968793i
$584$	9.68949e10	−	7.96466e8i	0.0344701	−	0.000283341i
$585$	−2.56104e11	−	6.18289e11i	−0.0904096	−	0.218268i
$586$	6.03961e11	−	5.32594e11i	0.211578	−	0.186577i
$587$	2.16291e12	+	3.23702e12i	0.751912	+	1.12532i	0.988131	+	0.153615i	$0.0490917\pi$
$587$	2.16291e12	+	3.23702e12i	0.751912	+	1.12532i	−0.236219	+	0.971700i	$0.575908\pi$
$588$	1.25207e11	−	6.26005e10i	0.0431947	−	0.0215963i
$589$	−1.51774e12	+	3.01897e11i	−0.519610	+	0.103357i
$590$	1.40194e11	+	2.41295e11i	0.0476318	+	0.0819811i
$591$	1.70741e11	+	1.70741e11i	0.0575697	+	0.0575697i
$592$	2.54074e11	+	7.22369e11i	0.0850183	+	0.241719i
$593$	−1.49788e12	+	1.49788e12i	−0.497430	+	0.497430i	−0.910637	−	0.413207i	$-0.864409\pi$
$593$	−1.49788e12	+	1.49788e12i	−0.497430	+	0.497430i	0.413207	+	0.910637i	$0.364409\pi$
$594$	−5.15225e11	−	1.36542e11i	−0.169808	−	0.0450016i
$595$	−1.03147e11	−	5.18553e11i	−0.0337387	−	0.169616i
$596$	−1.57429e12	−	1.36543e12i	−0.511066	−	0.443262i
$597$	−1.27100e11	+	8.49257e10i	−0.0409508	+	0.0273624i
$598$	−1.01286e12	−	6.35997e10i	−0.323887	−	0.0203376i
$599$	4.74338e12	−	1.96477e12i	1.50545	−	0.623579i	0.530839	−	0.847473i	$-0.321877\pi$
$599$	4.74338e12	−	1.96477e12i	1.50545	−	0.623579i	0.974614	+	0.223894i	$0.0718769\pi$
$600$	2.56701e11	−	5.32580e10i	0.0808623	−	0.0167766i
$601$	3.60417e12	+	1.49290e12i	1.12686	+	0.466761i	0.866712	−	0.498808i	$-0.166229\pi$
$601$	3.60417e12	+	1.49290e12i	1.12686	+	0.466761i	0.260148	+	0.965569i	$0.416229\pi$
$602$	1.21551e12	−	2.48192e12i	0.377201	−	0.770201i
$603$	2.64967e10	−	1.33208e11i	0.00816138	−	0.0410300i
$604$	2.62527e12	+	3.38277e12i	0.802615	+	1.03420i
$605$	−3.24960e11	+	4.86337e11i	−0.0986122	+	0.147584i
$606$	−2.84443e11	+	3.82408e10i	−0.0856779	+	0.0115186i
$607$			1.57044e12i			0.469540i	0.972051	+	0.234770i	$0.0754336\pi$
$607$			1.57044e12i			0.469540i	−0.972051	+	0.234770i	$0.924566\pi$
$608$	9.01293e10	+	1.13635e12i	0.0267485	+	0.337244i
$609$			4.93440e10i			0.0145364i
$610$	−6.19013e10	−	4.60435e11i	−0.0181015	−	0.134643i
$611$	−4.48419e11	+	6.71106e11i	−0.130166	+	0.194808i
$612$	1.98159e11	−	1.57167e12i	0.0570994	−	0.452876i
$613$	6.19636e11	−	3.11512e12i	0.177241	−	0.891051i	−0.785134	−	0.619326i	$-0.787406\pi$
$613$	6.19636e11	−	3.11512e12i	0.177241	−	0.891051i	0.962375	−	0.271725i	$-0.0875942\pi$
$614$	2.44802e12	+	1.19890e12i	0.695115	+	0.340428i
$615$	3.37862e11	+	1.39947e11i	0.0952360	+	0.0394480i
$616$	4.02027e11	−	2.11169e12i	0.112497	−	0.590905i
$617$	4.55324e12	−	1.88601e12i	1.26484	−	0.523916i	0.353451	−	0.935453i	$-0.385008\pi$
$617$	4.55324e12	−	1.88601e12i	1.26484	−	0.523916i	0.911393	+	0.411537i	$0.135008\pi$
$618$	−1.95000e10	+	3.10548e11i	−0.00537758	+	0.0856408i
$619$	3.29393e12	−	2.20093e12i	0.901791	−	0.602558i	−0.0158904	−	0.999874i	$-0.505058\pi$
$619$	3.29393e12	−	2.20093e12i	0.901791	−	0.602558i	0.917682	+	0.397316i	$0.130058\pi$
$620$	2.87147e12	−	2.04015e11i	0.780444	−	0.0554496i
$621$	−1.07244e11	−	5.39151e11i	−0.0289374	−	0.145478i
$622$	1.19806e12	−	4.52072e12i	0.320938	−	1.21102i
$623$	6.84463e11	−	6.84463e11i	0.182035	−	0.182035i
$624$	−1.97511e11	+	2.82082e10i	−0.0521507	+	0.00744809i
$625$	8.45517e11	+	8.45517e11i	0.221647	+	0.221647i
$626$	3.30188e12	−	1.91842e12i	0.859362	−	0.499298i
$627$	−1.13472e11	+	2.25710e10i	−0.0293214	+	0.00583239i
$628$	−4.73539e12	−	1.57856e12i	−1.21489	−	0.404990i
$629$	−2.58227e11	−	3.86465e11i	−0.0657771	−	0.0984423i
$630$	9.66947e11	+	1.09652e12i	0.244551	+	0.277321i
$631$	1.73487e12	+	4.18834e12i	0.435647	+	1.05174i	0.977436	+	0.211230i	$0.0677469\pi$
$631$	1.73487e12	+	4.18834e12i	0.435647	+	1.05174i	−0.541790	+	0.840514i	$0.682253\pi$
$632$	5.10541e12	−	2.16407e12i	1.27293	−	0.539565i
$633$	−2.33263e11	+	5.63146e11i	−0.0577469	+	0.139413i
$634$	−7.41600e10	−	2.16517e11i	−0.0182292	−	0.0532220i
$635$	2.10424e12	+	4.18559e11i	0.513585	+	0.102159i
$636$	5.72001e11	−	1.56632e11i	0.138624	−	0.0379597i
$637$	−7.25722e11	−	4.84912e11i	−0.174640	−	0.116691i
$638$	−4.71024e11	−	3.59383e11i	−0.112551	−	0.0858746i
$639$	1.25747e12			0.298361
$640$	9.80837e10	−	2.11827e12i	0.0231093	−	0.499083i
$641$	−5.52916e12			−1.29359			−0.646797	−	0.762662i	$-0.723892\pi$
$641$	−5.52916e12			−1.29359			−0.646797	+	0.762662i	$0.723892\pi$
$642$	3.89714e11	+	2.97345e11i	0.0905395	+	0.0690801i
$643$	7.88265e11	+	5.26702e11i	0.181854	+	0.121511i	0.643165	−	0.765727i	$-0.277621\pi$
$643$	7.88265e11	+	5.26702e11i	0.181854	+	0.121511i	−0.461311	+	0.887238i	$0.652621\pi$
$644$	2.13827e12	−	5.85524e11i	0.489864	−	0.134140i
$645$	2.71378e11	+	5.39804e10i	0.0617384	+	0.0122805i
$646$	−2.24201e11	−	6.54578e11i	−0.0506514	−	0.147882i
$647$	7.95763e11	−	1.92114e12i	0.178531	−	0.431013i	−0.809128	−	0.587633i	$-0.800060\pi$
$647$	7.95763e11	−	1.92114e12i	0.178531	−	0.431013i	0.987659	+	0.156620i	$0.0500599\pi$
$648$	1.68825e12	+	3.98289e12i	0.376141	+	0.887382i
$649$	−2.63552e11	−	6.36270e11i	−0.0583129	−	0.140780i
$650$	−1.08116e12	−	1.22603e12i	−0.237563	−	0.269396i
$651$	3.28719e11	+	4.91963e11i	0.0717315	+	0.107354i
$652$	4.61412e12	+	1.53814e12i	0.999941	+	0.333335i
$653$	−1.80544e12	+	3.59125e11i	−0.388575	+	0.0772923i	−0.385512	−	0.922703i	$-0.625975\pi$
$653$	−1.80544e12	+	3.59125e11i	−0.388575	+	0.0772923i	−0.00306319	+	0.999995i	$0.500975\pi$
$654$	5.60711e11	−	3.25778e11i	0.119850	−	0.0696341i
$655$	−1.26843e12	−	1.26843e12i	−0.269265	−	0.269265i
$656$	−5.33548e12	+	7.11342e12i	−1.12488	+	1.49972i
$657$	1.14999e11	−	1.14999e11i	0.0240797	−	0.0240797i
$658$	4.51685e11	−	1.70438e12i	0.0939332	−	0.354445i
$659$	−1.08008e10	−	5.42994e10i	−0.00223086	−	0.0112153i	0.979654	−	0.200695i	$-0.0643199\pi$
$659$	−1.08008e10	−	5.42994e10i	−0.00223086	−	0.0112153i	−0.981885	+	0.189479i	$0.939320\pi$
$660$	2.14683e11	−	1.52529e10i	0.0440402	−	0.00312900i
$661$	−3.73372e12	+	2.49479e12i	−0.760739	+	0.508309i	−0.874397	−	0.485210i	$-0.838743\pi$
$661$	−3.73372e12	+	2.49479e12i	−0.760739	+	0.508309i	0.113659	+	0.993520i	$0.463743\pi$
$662$	−5.59816e11	+	8.91537e12i	−0.113288	+	1.80417i
$663$	1.11884e11	−	4.63439e10i	0.0224883	−	0.00931497i
$664$	9.35865e11	+	1.78171e11i	0.186834	+	0.0355698i
$665$	5.89950e11	+	2.44365e11i	0.116982	+	0.0484554i
$666$	1.15424e12	+	5.65281e11i	0.227333	+	0.111335i
$667$	1.19207e11	−	5.99295e11i	0.0233204	−	0.117240i
$668$	−6.62301e11	+	5.25295e12i	−0.128695	+	1.02073i
$669$	1.04486e11	−	1.56374e11i	0.0201670	−	0.0301820i
$670$	1.47040e10	+	1.09372e11i	0.00281903	+	0.0209685i
$671$			1.14651e12i			0.218336i
$672$	3.88223e11	−	1.98108e11i	0.0734378	−	0.0374748i
$673$			4.02147e12i			0.755645i	0.925878	+	0.377822i	$0.123327\pi$
$673$			4.02147e12i			0.755645i	−0.925878	+	0.377822i	$0.876673\pi$
$674$	−1.99302e12	+	2.67943e11i	−0.371999	+	0.0500119i
$675$	4.91921e11	−	7.36212e11i	0.0912070	−	0.136501i
$676$	−2.56613e12	−	3.30657e12i	−0.472627	−	0.609001i
$677$	4.56677e11	−	2.29587e12i	0.0835526	−	0.420047i	−0.916258	−	0.400588i	$-0.868806\pi$
$677$	4.56677e11	−	2.29587e12i	0.0835526	−	0.420047i	0.999811	−	0.0194587i	$-0.00619428\pi$
$678$	−6.25206e10	+	1.27660e11i	−0.0113629	+	0.0232018i
$679$	−4.93807e12	−	2.04542e12i	−0.891546	−	0.369290i
$680$	2.61476e11	+	1.26030e12i	0.0468966	+	0.226039i
$681$	−2.43301e11	+	1.00779e11i	−0.0433494	+	0.0179559i
$682$	−7.09027e12	−	4.45214e11i	−1.25497	−	0.0788024i
$683$	−1.52510e12	+	1.01904e12i	−0.268167	+	0.179184i	−0.682382	−	0.730995i	$-0.739056\pi$
$683$	−1.52510e12	+	1.01904e12i	−0.268167	+	0.179184i	0.414215	+	0.910179i	$0.364056\pi$
$684$	1.44533e12	+	1.25358e12i	0.252473	+	0.218977i
$685$	−2.13044e11	−	1.07105e12i	−0.0369711	−	0.185866i
$686$	6.04336e12	+	1.60158e12i	1.04189	+	0.276115i
$687$	−7.84351e10	+	7.84351e10i	−0.0134340	+	0.0134340i
$688$	−2.90935e12	+	6.06629e12i	−0.495049	+	1.03223i
$689$	−2.61473e12	−	2.61473e12i	−0.442019	−	0.442019i
$690$	1.11510e11	+	1.91925e11i	0.0187281	+	0.0322338i
$691$	−9.73715e12	+	1.93684e12i	−1.62473	+	0.323179i	−0.921676	−	0.387960i	$-0.873180\pi$
$691$	−9.73715e12	+	1.93684e12i	−1.62473	+	0.323179i	−0.703052	+	0.711138i	$0.748180\pi$
$692$	6.78099e12	−	3.39034e12i	1.12413	−	0.562038i
$693$	−2.00445e12	−	2.99987e12i	−0.330138	−	0.494086i
$694$	2.64285e12	−	2.33056e12i	0.432470	−	0.381367i
$695$	−1.89654e12	−	4.57864e12i	−0.308340	−	0.744398i
$696$	−9.87394e8	−	1.20122e11i	−0.000159496	−	0.0194036i
$697$	2.06546e12	−	4.98647e12i	0.331490	−	0.800287i
$698$	−3.83144e12	+	1.31232e12i	−0.610960	+	0.209262i
$699$	1.05102e12	+	2.09062e11i	0.166520	+	0.0331228i
$700$	3.10226e12	+	1.76850e12i	0.488357	+	0.278396i
$701$	4.40073e12	+	2.94048e12i	0.688326	+	0.459925i	0.849906	−	0.526935i	$-0.176659\pi$
$701$	4.40073e12	+	2.94048e12i	0.688326	+	0.459925i	−0.161580	+	0.986860i	$0.551659\pi$
$702$	−4.08739e11	+	5.35711e11i	−0.0635227	+	0.0832557i
$703$	5.61363e11			0.0866851
$704$	−9.36434e11	+	5.14873e12i	−0.143681	+	0.789993i
$705$	1.76536e11			0.0269142
$706$	1.72973e12	−	2.26706e12i	0.262034	−	0.343434i
$707$	−3.25040e12	−	2.17185e12i	−0.489270	−	0.326920i
$708$	6.91546e10	−	1.21310e11i	0.0103436	−	0.0181445i
$709$	−1.03714e13	−	2.06299e12i	−1.54145	−	0.306613i	−0.650069	−	0.759876i	$-0.725260\pi$
$709$	−1.03714e13	−	2.06299e12i	−1.54145	−	0.306613i	−0.891377	+	0.453263i	$0.850260\pi$
$710$	−9.66600e11	+	3.31073e11i	−0.142753	+	0.0488946i
$711$	3.56160e12	−	8.59846e12i	0.522675	−	1.26185i
$712$	−1.65255e12	+	1.67995e12i	−0.240988	+	0.244983i
$713$	−2.80387e12	−	6.76914e12i	−0.406308	−	0.980913i
$714$	−1.98423e11	+	1.74976e11i	−0.0285726	+	0.0251963i
$715$	−7.45545e11	−	1.11579e12i	−0.106683	−	0.159663i
$716$	−3.58002e11	−	7.16037e11i	−0.0509069	−	0.101819i
$717$	−9.03816e11	+	1.79780e11i	−0.127716	+	0.0254042i
$718$	−1.69570e12	−	2.91854e12i	−0.238116	−	0.409832i
$719$	1.06506e12	+	1.06506e12i	0.148626	+	0.148626i	0.777504	−	0.628878i	$-0.216486\pi$
$719$	1.06506e12	+	1.06506e12i	0.148626	+	0.148626i	−0.628878	+	0.777504i	$0.716486\pi$
$720$	−2.37587e12	−	2.65000e12i	−0.329478	−	0.367494i
$721$	−2.99691e12	+	2.99691e12i	−0.413014	+	0.413014i
$722$	−6.25017e12	−	1.65639e12i	−0.856001	−	0.226853i
$723$	6.55701e10	+	3.29643e11i	0.00892450	+	0.0448665i
$724$	2.16702e12	−	2.49850e12i	0.293116	−	0.337953i
$725$	8.18338e11	−	5.46796e11i	0.110005	−	0.0735029i
$726$	2.92098e11	+	1.83415e10i	0.0390224	+	0.00245031i
$727$	−1.86307e12	+	7.71708e11i	−0.247357	+	0.102459i	−0.502917	−	0.864335i	$-0.667740\pi$
$727$	−1.86307e12	+	7.71708e11i	−0.247357	+	0.102459i	0.255561	+	0.966793i	$0.417740\pi$
$728$	−2.27191e12	−	1.49118e12i	−0.299778	−	0.196760i
$729$	6.53829e12	+	2.70825e12i	0.857413	+	0.355152i
$730$	−5.81209e10	+	1.18676e11i	−0.00757495	+	0.0154672i
$731$	7.96691e11	−	4.00524e12i	0.103196	−	0.518800i
$732$	−1.83646e11	+	1.42522e11i	−0.0236418	+	0.0183477i
$733$	−5.94881e12	+	8.90302e12i	−0.761135	+	1.13912i	0.225191	+	0.974315i	$0.427699\pi$
$733$	−5.94881e12	+	8.90302e12i	−0.761135	+	1.13912i	−0.986326	+	0.164805i	$0.947301\pi$
$734$	1.13971e13	−	1.53224e12i	1.44931	−	0.194847i
$735$			1.90903e11i			0.0241279i
$736$	−5.19366e12	+	1.46818e12i	−0.652414	+	0.184429i
$737$		−	2.72342e11i		−	0.0340025i
$738$	1.98855e12	+	1.47913e13i	0.246765	+	1.83549i
$739$	−3.56108e12	+	5.32953e12i	−0.439219	+	0.657338i	−0.983362	−	0.181654i	$-0.941855\pi$
$739$	−3.56108e12	+	5.32953e12i	−0.439219	+	0.657338i	0.544143	+	0.838992i	$0.316855\pi$
$740$	−1.03608e12	−	1.30631e11i	−0.127014	−	0.0160141i
$741$	−2.85344e10	+	1.43452e11i	−0.00347686	+	0.0174793i
$742$	7.25467e12	+	3.55293e12i	0.878618	+	0.430298i
$743$	−1.37871e13	−	5.71082e12i	−1.65968	−	0.687462i	−0.661627	−	0.749833i	$-0.730134\pi$
$743$	−1.37871e13	−	5.71082e12i	−1.65968	−	0.687462i	−0.998053	+	0.0623717i	$0.980134\pi$
$744$	−8.10074e11	−	1.19105e12i	−0.0969274	−	0.142512i
$745$	2.62562e12	−	1.08757e12i	0.312269	−	0.129346i
$746$	−1.31499e10	+	2.09419e11i	−0.00155453	+	0.0247566i
$747$	1.32949e12	−	8.88336e11i	0.156222	−	0.104384i
$748$	−2.25117e11	−	3.16848e12i	−0.0262936	−	0.370078i
$749$	1.30259e12	+	6.54858e12i	0.151231	+	0.760290i
$750$	−2.13645e11	+	8.06161e11i	−0.0246556	+	0.0930349i
$751$	−6.87784e12	+	6.87784e12i	−0.788992	+	0.788992i	−0.981329	−	0.192337i	$-0.938393\pi$
$751$	−6.87784e12	+	6.87784e12i	−0.788992	+	0.788992i	0.192337	+	0.981329i	$0.438393\pi$
$752$	−1.06547e12	+	4.15816e12i	−0.121496	+	0.474155i
$753$	−7.33432e11	−	7.33432e11i	−0.0831347	−	0.0831347i
$754$	−6.47627e11	+	3.76277e11i	−0.0729716	+	0.0423972i
$755$	−5.72728e12	+	1.13923e12i	−0.641486	+	0.127600i
$756$	4.65520e11	−	1.39647e12i	0.0518311	−	0.155483i
$757$	−4.74053e12	−	7.09471e12i	−0.524681	−	0.785241i	0.470592	−	0.882351i	$-0.344040\pi$
$757$	−4.74053e12	−	7.09471e12i	−0.524681	−	0.785241i	−0.995274	+	0.0971095i	$0.969040\pi$
$758$	−3.99067e12	−	4.52542e12i	−0.439071	−	0.497906i
$759$	−2.09629e11	−	5.06088e11i	−0.0229278	−	0.0553526i
$760$	−1.44106e12	−	5.83075e11i	−0.156682	−	0.0633962i
$761$	3.75686e12	−	9.06985e12i	0.406063	−	0.980323i	−0.580100	−	0.814545i	$-0.696987\pi$
$761$	3.75686e12	−	9.06985e12i	0.406063	−	0.980323i	0.986163	−	0.165778i	$-0.0530135\pi$
$762$	−3.47858e11	−	1.01561e12i	−0.0373771	−	0.109126i
$763$	8.66316e12	+	1.72321e12i	0.925371	+	0.184068i
$764$	−1.15916e12	−	4.23312e12i	−0.123090	−	0.449511i
$765$	1.79624e12	+	1.20021e12i	0.189622	+	0.126701i
$766$	2.31379e12	+	1.76538e12i	0.242825	+	0.185272i
$767$	−8.70651e11			−0.0908375
$768$	−9.41122e11	+	4.90040e11i	−0.0976159	+	0.0508283i
$769$	1.04461e13			1.07717			0.538585	−	0.842571i	$-0.318959\pi$
$769$	1.04461e13			1.07717			0.538585	+	0.842571i	$0.318959\pi$
$770$	2.33062e12	+	1.77822e12i	0.238926	+	0.182297i
$771$	7.22432e11	+	4.82714e11i	0.0736296	+	0.0491977i
$772$	−3.85919e12	−	1.40933e13i	−0.391037	−	1.42802i
$773$	−1.54872e13	−	3.08060e12i	−1.56015	−	0.310333i	−0.661821	−	0.749662i	$-0.730216\pi$
$773$	−1.54872e13	−	3.08060e12i	−1.56015	−	0.310333i	−0.898326	+	0.439329i	$0.855216\pi$
$774$	3.65898e12	+	1.06828e13i	0.366459	+	1.06991i
$775$	4.51625e12	−	1.09032e13i	0.449697	−	1.08566i
$776$	1.20621e13	+	4.88053e12i	1.19411	+	0.483158i
$777$	−8.21384e10	−	1.98300e11i	−0.00808448	−	0.0195177i
$778$	−9.30329e12	−	1.05499e13i	−0.910392	−	1.03238i
$779$	3.62157e12	+	5.42006e12i	0.352353	+	0.527334i
$780$	8.60464e10	−	2.58123e11i	0.00832352	−	0.0249690i
$781$	2.47303e12	−	4.91915e11i	0.237848	−	0.0473108i
$782$	2.83261e12	−	1.64577e12i	0.270867	−	0.157376i
$783$	−2.86881e11	−	2.86881e11i	−0.0272756	−	0.0272756i
$784$	−4.49656e12	−	1.15218e12i	−0.425067	−	0.108918i
$785$	4.81344e12	−	4.81344e12i	0.452420	−	0.452420i
$786$	−2.29935e11	+	8.67630e11i	−0.0214884	+	0.0810836i
$787$	3.37767e12	+	1.69807e13i	0.313856	+	1.57786i	0.739618	+	0.673027i	$0.235006\pi$
$787$	3.37767e12	+	1.69807e13i	0.313856	+	1.57786i	−0.425762	+	0.904835i	$0.639994\pi$
$788$	−5.67448e11	−	7.98673e12i	−0.0524273	−	0.737906i
$789$	8.61196e11	−	5.75433e11i	0.0791144	−	0.0528626i
$790$	−4.73910e11	+	7.54726e12i	−0.0432886	+	0.689394i
$791$	−1.78879e12	+	7.40940e11i	−0.162467	+	0.0672959i
$792$	4.93964e12	+	7.26275e12i	0.446100	+	0.655900i
$793$	1.33909e12	+	5.54671e11i	0.120249	+	0.0498088i
$794$	−1.69171e13	−	8.28503e12i	−1.51054	−	0.739779i
$795$	−1.57785e11	+	7.93239e11i	−0.0140092	+	0.0704290i
$796$	5.02904e12	+	6.34070e11i	0.443993	+	0.0559794i
$797$	2.66182e12	−	3.98369e12i	0.233677	−	0.349722i	−0.696036	−	0.718007i	$-0.745055\pi$
$797$	2.66182e12	−	3.98369e12i	0.233677	−	0.349722i	0.929713	+	0.368284i	$0.120055\pi$
$798$	−4.25730e10	−	3.16667e11i	−0.00371639	−	0.0276433i
$799$		−	2.60547e12i		−	0.226165i
$800$	−7.58751e12	−	4.24314e12i	−0.654929	−	0.366254i
$801$			3.95516e12i			0.339483i
$802$	1.85916e13	−	2.49948e12i	1.58684	−	0.213336i
$803$	1.81179e11	−	2.71153e11i	0.0153775	−	0.0230141i
$804$	4.36232e10	−	3.38547e10i	0.00368184	−	0.00285737i
$805$	−5.89836e11	+	2.96531e12i	−0.0495051	+	0.248879i
$806$	−3.95021e12	+	8.06586e12i	−0.329695	+	0.673199i
$807$	−2.23000e12	−	9.23696e11i	−0.185086	−	0.0766651i
$808$	7.95619e12	+	5.22208e12i	0.656681	+	0.431015i
$809$	1.74954e13	−	7.24684e12i	1.43600	−	0.594813i	0.477179	−	0.878806i	$-0.341659\pi$
$809$	1.74954e13	−	7.24684e12i	1.43600	−	0.594813i	0.958826	+	0.283994i	$0.0916595\pi$
$810$	−5.88785e12	−	3.69712e11i	−0.480589	−	0.0301773i
$811$	4.32838e12	−	2.89213e12i	0.351343	−	0.234760i	−0.367357	−	0.930080i	$-0.619737\pi$
$811$	4.32838e12	−	2.89213e12i	0.351343	−	0.234760i	0.718700	+	0.695320i	$0.244737\pi$
$812$	1.07208e12	−	1.23607e12i	0.0865418	−	0.0997797i
$813$	−2.65944e11	−	1.33699e12i	−0.0213493	−	0.107330i
$814$	2.49115e12	+	6.60191e11i	0.198879	+	0.0527059i
$815$	−4.69016e12	+	4.69016e12i	−0.372373	+	0.372373i
$816$	4.79537e11	−	4.29931e11i	0.0378631	−	0.0339463i
$817$	3.48754e12	+	3.48754e12i	0.273855	+	0.273855i
$818$	4.80545e12	+	8.27086e12i	0.375270	+	0.645893i
$819$	−4.47351e12	+	8.89836e11i	−0.347432	+	0.0691086i
$820$	−5.42290e12	−	1.08463e13i	−0.418861	−	0.837761i
$821$	−9.31104e11	−	1.39350e12i	−0.0715244	−	0.107044i	0.793983	−	0.607940i	$-0.208004\pi$
$821$	−9.31104e11	−	1.39350e12i	−0.0715244	−	0.107044i	−0.865507	+	0.500896i	$0.833004\pi$
$822$	−4.09833e11	+	3.61405e11i	−0.0313100	+	0.0276103i
$823$	−4.17222e12	−	1.00726e13i	−0.317007	−	0.765322i	−0.999410	−	0.0343459i	$-0.989065\pi$
$823$	−4.17222e12	−	1.00726e13i	−0.317007	−	0.765322i	0.682403	−	0.730976i	$-0.260935\pi$
$824$	7.23567e12	−	7.35561e12i	0.546772	−	0.555835i
$825$	3.37653e11	−	8.15166e11i	0.0253762	−	0.0612637i
$826$	1.79935e12	−	6.16301e11i	0.134495	−	0.0460662i
$827$	1.04774e13	+	2.08407e12i	0.778891	+	0.154931i	0.568497	−	0.822686i	$-0.307525\pi$
$827$	1.04774e13	+	2.08407e12i	0.778891	+	0.154931i	0.210394	+	0.977617i	$0.432525\pi$
$828$	−4.48625e12	+	7.86969e12i	−0.331701	+	0.581864i
$829$	1.61020e13	+	1.07590e13i	1.18409	+	0.791181i	0.982128	−	0.188214i	$-0.0602697\pi$
$829$	1.61020e13	+	1.07590e13i	1.18409	+	0.791181i	0.201958	+	0.979394i	$0.435270\pi$
$830$	−7.88078e11	+	1.03289e12i	−0.0576392	+	0.0755445i
$831$	−5.57930e11			−0.0405859
$832$	5.56055e12	+	3.58464e12i	0.402312	+	0.259353i
$833$	2.81751e12			0.202751
$834$	−1.50420e12	+	1.97148e12i	−0.107661	+	0.141106i
$835$	−6.00354e12	−	4.01144e12i	−0.427384	−	0.285569i
$836$	3.33289e12	+	1.89997e12i	0.235989	+	0.134530i
$837$	−4.77137e12	−	9.49084e11i	−0.336030	−	0.0668405i
$838$	−1.30690e13	+	4.47631e12i	−0.915473	+	0.313561i
$839$	3.92514e12	−	9.47613e12i	0.273481	−	0.660241i	−0.726147	−	0.687540i	$-0.758691\pi$
$839$	3.92514e12	−	9.47613e12i	0.273481	−	0.660241i	0.999627	+	0.0272990i	$0.00869064\pi$
$840$	4.88562e9	+	5.94365e11i	0.000338581	+	0.0411904i
$841$	5.37907e12	+	1.29862e13i	0.370787	+	0.895160i
$842$	−8.50250e12	+	7.49780e12i	−0.582965	+	0.514079i
$843$	−4.72215e11	−	7.06719e11i	−0.0322044	−	0.0481973i
$844$	1.80786e13	−	9.03886e12i	1.22638	−	0.613159i
$845$	5.59827e12	−	1.11357e12i	0.377745	−	0.0751382i
$846$	3.61933e12	+	6.22938e12i	0.242919	+	0.418098i
$847$	2.81886e12	+	2.81886e12i	0.188191	+	0.188191i
$848$	−1.77318e13	−	8.50405e12i	−1.17753	−	0.564735i
$849$	−1.65246e12	+	1.65246e12i	−0.109156	+	0.109156i
$850$	5.10065e12	+	1.35175e12i	0.335151	+	0.0888199i
$851$	5.18531e11	+	2.60683e12i	0.0338916	+	0.170385i
$852$	3.86215e11	+	3.34975e11i	0.0251102	+	0.0217788i
$853$	−5.14838e12	+	3.44004e12i	−0.332966	+	0.222481i	−0.710803	−	0.703391i	$-0.751668\pi$
$853$	−5.14838e12	+	3.44004e12i	−0.332966	+	0.222481i	0.377837	+	0.925872i	$0.376668\pi$
$854$	−3.16010e12	−	1.98430e11i	−0.203301	−	0.0127658i
$855$	−2.41054e12	+	9.98477e11i	−0.154265	+	0.0638985i
$856$	−3.30206e12	−	1.59157e13i	−0.210210	−	1.01320i
$857$	−3.06076e12	−	1.26781e12i	−0.193828	−	0.0802860i	0.283658	−	0.958925i	$-0.408452\pi$
$857$	−3.06076e12	−	1.26781e12i	−0.193828	−	0.0802860i	−0.477486	+	0.878639i	$0.658452\pi$
$858$	−2.95333e11	+	6.03036e11i	−0.0186046	+	0.0379884i
$859$	−4.82851e12	+	2.42745e13i	−0.302582	+	1.52118i	0.467933	+	0.883764i	$0.344999\pi$
$859$	−4.82851e12	+	2.42745e13i	−0.302582	+	1.52118i	−0.770516	+	0.637421i	$0.780001\pi$
$860$	−5.62524e12	−	7.24836e12i	−0.350669	−	0.451853i
$861$	1.38471e12	−	2.07237e12i	0.0858709	−	0.128515i
$862$	1.39501e13	−	1.87546e12i	0.860585	−	0.115698i
$863$			1.45626e13i			0.893697i	0.894610	+	0.446848i	$0.147454\pi$
$863$			1.45626e13i			0.893697i	−0.894610	+	0.446848i	$0.852546\pi$
$864$	−1.10531e12	+	3.40887e12i	−0.0674797	+	0.208113i
$865$			1.03390e13i			0.627920i
$866$	−2.72959e12	−	2.03032e13i	−0.164917	−	1.22669i
$867$	8.00091e11	−	1.19742e12i	0.0480899	−	0.0719716i
$868$	2.45427e12	−	1.94657e13i	0.146752	−	1.16394i
$869$	3.64082e12	−	1.83037e13i	0.216576	−	1.08880i
$870$	1.47125e11	+	7.20536e10i	0.00870664	+	0.00426402i
$871$	−3.18088e11	−	1.31756e11i	−0.0187269	−	0.00775693i
$872$	−2.11240e13	−	4.02161e12i	−1.23723	−	0.235546i
$873$	2.01770e13	−	8.35758e12i	1.17569	−	0.486986i
$874$	−2.47957e11	+	3.94885e12i	−0.0143739	+	0.228912i
$875$	−9.44522e12	+	6.31109e12i	−0.544723	+	0.363972i
$876$	6.59550e10	−	4.68602e9i	0.00378424	−	0.000268866i
$877$	6.55463e12	+	3.29523e13i	0.374153	+	1.88100i	0.465290	+	0.885158i	$0.345950\pi$
$877$	6.55463e12	+	3.29523e13i	0.374153	+	1.88100i	−0.0911366	+	0.995838i	$0.529050\pi$
$878$	6.12251e10	−	2.31025e11i	0.00347700	−	0.0131200i
$879$	3.88544e11	−	3.88544e11i	0.0219528	−	0.0219528i
$880$	−5.70923e12	−	4.28226e12i	−0.320926	−	0.240714i
$881$	2.37115e13	+	2.37115e13i	1.32607	+	1.32607i	0.908764	+	0.417311i	$0.137027\pi$
$881$	2.37115e13	+	2.37115e13i	1.32607	+	1.32607i	0.417311	+	0.908764i	$0.362973\pi$
$882$	−6.73634e12	+	3.91388e12i	−0.374814	+	0.217770i
$883$	−2.56190e13	+	5.09594e12i	−1.41821	+	0.282099i	−0.843882	−	0.536528i	$-0.819735\pi$
$883$	−2.56190e13	+	5.09594e12i	−1.41821	+	0.282099i	−0.574325	+	0.818627i	$0.694735\pi$
$884$	−3.80961e12	−	1.26995e12i	−0.209819	−	0.0699442i
$885$	1.05796e11	+	1.58335e11i	0.00579730	+	0.00867628i
$886$	1.47446e13	+	1.67204e13i	0.803863	+	0.911579i
$887$	−9.15958e12	−	2.21132e13i	−0.496843	−	1.19949i	−0.951175	−	0.308653i	$-0.900122\pi$
$887$	−9.15958e12	−	2.21132e13i	−0.496843	−	1.19949i	0.454332	−	0.890833i	$-0.349878\pi$
$888$	2.03925e11	+	4.81095e11i	0.0110056	+	0.0259641i
$889$	5.59574e12	−	1.35093e13i	0.300469	−	0.725397i
$890$	−1.04134e12	−	3.04029e12i	−0.0556335	−	0.162427i
$891$	1.42792e13	+	2.84032e12i	0.759024	+	0.150979i
$892$	−6.01490e12	+	1.64707e12i	−0.318117	+	0.0871102i
$893$	2.61645e12	+	1.74826e12i	0.137683	+	0.0919971i
$894$	−1.13054e12	−	8.62584e11i	−0.0591926	−	0.0451630i
$895$	1.09174e12			0.0568742
$896$	−1.40293e13	−	3.47218e12i	−0.727192	−	0.179977i
$897$	−6.92514e11			−0.0357160
$898$	2.66941e12	+	2.03671e12i	0.136984	+	0.104517i
$899$	−4.49619e12	−	3.00426e12i	−0.229576	−	0.153398i
$900$	−1.40728e13	+	3.85357e12i	−0.714973	+	0.195782i
$901$	1.17073e13	+	2.32873e12i	0.591829	+	0.117722i
$902$	9.69710e12	+	2.83117e13i	0.487767	+	1.42408i
$903$	7.21668e11	−	1.74226e12i	0.0361196	−	0.0872004i
$904$	4.33978e12	−	1.83953e12i	0.216127	−	0.0916114i
$905$	1.72604e12	+	4.16703e12i	0.0855328	+	0.206494i
$906$	1.93257e12	+	2.19153e12i	0.0952922	+	0.108061i
$907$	2.23603e13	+	3.34645e13i	1.09710	+	1.64192i	0.680331	+	0.732905i	$0.261836\pi$
$907$	2.23603e13	+	3.34645e13i	1.09710	+	1.64192i	0.416764	+	0.909015i	$0.363164\pi$
$908$	8.28433e12	+	2.76162e12i	0.404456	+	0.134827i
$909$	1.56662e13	−	3.11619e12i	0.761071	−	0.151386i
$910$	3.20445e12	−	1.86182e12i	0.154906	−	0.0900017i
$911$	−6.14093e11	−	6.14093e11i	−0.0295394	−	0.0295394i	0.692183	−	0.721722i	$-0.256649\pi$
$911$	−6.14093e11	−	6.14093e11i	−0.0295394	−	0.0295394i	−0.721722	+	0.692183i	$0.756649\pi$
$912$	1.09976e11	+	7.70039e11i	0.00526406	+	0.0368584i
$913$	2.26716e12	−	2.26716e12i	0.107985	−	0.107985i
$914$	2.27913e12	−	8.60002e12i	0.108022	−	0.407607i
$915$	−6.18470e10	−	3.10926e11i	−0.00291692	−	0.0146643i
$916$	3.66895e12	−	2.60675e11i	0.172192	−	0.0122340i
$917$	−1.01654e13	+	6.79231e12i	−0.474748	+	0.317216i
$918$	1.36316e11	−	2.17091e12i	0.00633513	−	0.100890i
$919$	1.19007e13	−	4.92943e12i	0.550367	−	0.227970i	−0.0901300	−	0.995930i	$-0.528728\pi$
$919$	1.19007e13	−	4.92943e12i	0.550367	−	0.227970i	0.640497	+	0.767960i	$0.278728\pi$
$920$	1.37655e12	−	7.23051e12i	0.0633502	−	0.332755i
$921$	1.71846e12	+	7.11810e11i	0.0786994	+	0.0325983i
$922$	−1.68081e13	−	8.23168e12i	−0.766003	−	0.375145i
$923$	6.21882e11	−	3.12641e12i	0.0282033	−	0.141788i
$924$	1.83491e11	−	1.45533e12i	0.00828116	−	0.0656809i
$925$	−2.37847e12	+	3.55964e12i	−0.106822	+	0.159870i
$926$	−3.58497e12	−	2.66658e13i	−0.160227	−	1.19180i
$927$		−	1.73176e13i		−	0.770244i
$928$	−2.58513e12	+	3.03054e12i	−0.114424	+	0.134139i
$929$		−	9.69754e12i		−	0.427160i	−0.976926	−	0.213580i	$-0.931488\pi$
$929$		−	9.69754e12i		−	0.427160i	0.976926	−	0.213580i	$-0.0685125\pi$
$930$	1.94685e12	−	2.61737e11i	0.0853415	−	0.0114734i
$931$	−1.89054e12	+	2.82939e12i	−0.0824729	+	0.123429i
$932$	−2.17861e13	−	2.80723e13i	−0.945819	−	1.21873i
$933$	6.22598e11	−	3.13001e12i	0.0268993	−	0.135232i
$934$	−1.82760e12	+	3.73175e12i	−0.0785815	+	0.160454i
$935$	4.00214e12	+	1.65774e12i	0.171254	+	0.0709356i
$936$	1.08725e13	−	2.25572e12i	0.463006	−	0.0960605i
$937$	3.54787e11	−	1.46957e11i	0.0150362	−	0.00622821i	−0.375153	−	0.926963i	$-0.622410\pi$
$937$	3.54787e11	−	1.46957e11i	0.0150362	−	0.00622821i	0.390189	+	0.920735i	$0.372410\pi$
$938$	7.50650e11	+	4.71350e10i	0.0316610	+	0.00198807i
$939$	2.16666e12	−	1.44772e12i	0.0909486	−	0.0607699i
$940$	−4.42225e12	−	3.83554e12i	−0.184743	−	0.160233i
$941$	−7.41007e12	−	3.72529e13i	−0.308084	−	1.54884i	−0.755882	−	0.654708i	$-0.772792\pi$
$941$	−7.41007e12	−	3.72529e13i	−0.308084	−	1.54884i	0.447798	−	0.894135i	$-0.352208\pi$
$942$	−3.29249e12	−	8.72557e11i	−0.136237	−	0.0361048i
$943$	−2.18242e13	+	2.18242e13i	−0.898744	+	0.898744i
$944$	−4.36799e12	+	1.53632e12i	−0.179023	+	0.0629664i
$945$	1.41949e12	+	1.41949e12i	0.0579012	+	0.0579012i
$946$	1.13751e13	+	1.95781e13i	0.461789	+	0.794806i
$947$	1.27442e13	−	2.53498e12i	0.514918	−	0.102424i	0.0692102	−	0.997602i	$-0.477952\pi$
$947$	1.27442e13	−	2.53498e12i	0.514918	−	0.102424i	0.445708	+	0.895179i	$0.352952\pi$
$948$	3.38443e12	−	1.69214e12i	0.136097	−	0.0680453i
$949$	−2.29047e11	−	3.42793e11i	−0.00916699	−	0.0137194i
$950$	−4.77996e12	+	4.21513e12i	−0.190400	+	0.167902i
$951$	−5.97649e10	−	1.44285e11i	−0.00236937	−	0.00572017i
$952$	8.77218e12	−	7.21064e10i	0.346131	−	0.00284516i
$953$	1.85979e13	−	4.48993e13i	0.730375	−	1.76328i	0.0890317	−	0.996029i	$-0.471623\pi$
$953$	1.85979e13	−	4.48993e13i	0.730375	−	1.76328i	0.641344	−	0.767254i	$-0.278377\pi$
$954$	−3.12258e13	+	1.06952e13i	−1.22052	+	0.418044i
$955$	5.87040e12	+	1.16769e12i	0.228377	+	0.0454270i
$956$	2.65468e13	+	1.51334e13i	1.02790	+	0.585972i
$957$	−3.36153e11	−	2.24611e11i	−0.0129549	−	0.00865618i
$958$	2.38521e13	−	3.12617e13i	0.914918	−	1.19913i
$959$	−7.44273e12			−0.284150
$960$	−2.37870e10	−	1.44682e12i	−0.000903898	−	0.0549786i
$961$	−3.84015e13			−1.45242
$962$	1.97628e12	−	2.59020e12i	0.0743979	−	0.0975092i
$963$	−2.26839e13	−	1.51569e13i	−0.849963	−	0.567927i
$964$	5.51952e12	−	9.68224e12i	0.205852	−	0.361101i
$965$	1.95443e13	+	3.88761e12i	0.725517	+	0.144314i
$966$	1.43120e12	−	4.90205e11i	0.0528815	−	0.0181126i
$967$	−9.46909e12	+	2.28604e13i	−0.348248	+	0.840746i	0.648579	+	0.761148i	$0.275364\pi$
$967$	−9.46909e12	+	2.28604e13i	−0.348248	+	0.840746i	−0.996827	+	0.0795981i	$0.974636\pi$
$968$	−6.91861e12	−	6.80580e12i	−0.253268	−	0.249138i
$969$	−1.80682e11	−	4.36204e11i	−0.00658351	−	0.0158940i
$970$	−1.33094e13	+	1.17367e13i	−0.482709	+	0.425670i
$971$	−2.97550e13	−	4.45316e13i	−1.07417	−	1.60761i	−0.749776	−	0.661691i	$-0.769839\pi$
$971$	−2.97550e13	−	4.45316e13i	−1.07417	−	1.60761i	−0.324396	−	0.945921i	$-0.605161\pi$
$972$	4.04281e12	+	8.08600e12i	0.145273	+	0.290560i
$973$	−3.31278e13	+	6.58954e12i	−1.18491	+	0.235693i
$974$	−1.09372e13	−	1.88245e13i	−0.389396	−	0.670206i
$975$	−7.88739e11	−	7.88739e11i	−0.0279520	−	0.0279520i
$976$	7.69689e12	+	4.19821e11i	0.271513	+	0.0148095i
$977$	−4.87353e12	+	4.87353e12i	−0.171127	+	0.171127i	−0.787474	−	0.616348i	$-0.788612\pi$
$977$	−4.87353e12	+	4.87353e12i	−0.171127	+	0.171127i	0.616348	+	0.787474i	$0.288612\pi$
$978$	3.20816e12	+	8.50210e11i	0.112133	+	0.0297168i
$979$	1.54724e12	+	7.77850e12i	0.0538314	+	0.270629i
$980$	4.14769e12	−	4.78214e12i	0.143644	−	0.165617i
$981$	−3.00087e13	+	2.00512e13i	−1.03452	+	0.691241i
$982$	−2.50983e13	−	1.57598e12i	−0.861277	−	0.0540816i
$983$	2.27508e13	−	9.42369e12i	0.777152	−	0.321907i	0.0413862	−	0.999143i	$-0.486823\pi$
$983$	2.27508e13	−	9.42369e12i	0.777152	−	0.321907i	0.735765	+	0.677236i	$0.236823\pi$
$984$	−3.32947e12	+	5.07267e12i	−0.113213	+	0.172488i
$985$	1.00881e13	+	4.17863e12i	0.341466	+	0.141440i
$986$	1.06343e12	−	2.17141e12i	0.0358314	−	0.0731636i
$987$	2.34729e11	−	1.18006e12i	0.00787297	−	0.0395801i
$988$	3.83153e12	−	2.97354e12i	0.127928	−	0.0992812i
$989$	−1.29739e13	+	1.94168e13i	−0.431207	+	0.645347i
$990$	−1.18715e13	+	1.59601e12i	−0.392776	+	0.0528052i
$991$			9.97622e12i			0.328575i	0.986413	+	0.164287i	$0.0525325\pi$
$991$			9.97622e12i			0.328575i	−0.986413	+	0.164287i	$0.947468\pi$
$992$	−5.58513e12	+	4.74363e13i	−0.183118	+	1.55528i
$993$			6.09564e12i			0.198952i
$994$	9.27842e11	+	6.90149e12i	0.0301464	+	0.224235i
$995$	−3.84044e12	+	5.74763e12i	−0.124216	+	0.185902i
$996$	6.44978e11	+	8.13200e10i	0.0207672	+	0.00261836i
$997$	−3.63941e12	+	1.82965e13i	−0.116655	+	0.586463i	0.877597	+	0.479399i	$0.159145\pi$
$997$	−3.63941e12	+	1.82965e13i	−0.116655	+	0.586463i	−0.994252	+	0.107065i	$0.965855\pi$
$998$	1.24359e13	+	6.09039e12i	0.396816	+	0.194338i
$999$	1.63044e12	+	6.75351e11i	0.0517917	+	0.0214528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.10.i.a.5.16	✓	568
64.13	even	16	inner	64.10.i.a.13.16	yes	568

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.10.i.a.5.16	✓	568	1.1	even	1	trivial
64.10.i.a.13.16	yes	568	64.13	even	16	inner

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.9892 - 13.7255i) q^{2} +(-12.8383 - 8.57826i) q^{3} +(135.223 + 493.820i) q^{4} +(-684.820 - 136.219i) q^{5} +(113.210 + 330.528i) q^{6} +(-1821.12 + 4396.58i) q^{7} +(4345.35 - 10739.4i) q^{8} +(-7441.12 - 17964.5i) q^{9} +(10449.7 + 11849.9i) q^{10} +(-21661.9 - 32419.3i) q^{11} +(2500.09 - 7499.79i) q^{12} +(-48344.7 + 9616.36i) q^{13} +(93105.7 - 54095.3i) q^{14} +(7623.39 + 7623.39i) q^{15} +(-225573. + 133552. i) q^{16} +(112513. - 112513. i) q^{17} +(-112711. + 425299. i) q^{18} +(37491.5 + 188483. i) q^{19} +(-25335.9 - 356598. i) q^{20} +(61095.2 - 40822.5i) q^{21} +(-55289.7 + 880517. i) q^{22} +(-840637. + 348203. i) q^{23} +(-147913. + 100600. i) q^{24} +(-1.35403e6 - 560857. i) q^{25} +(1.00167e6 + 490563. i) q^{26} +(-117863. + 592540. i) q^{27} +(-2.41738e6 - 304788. i) q^{28} +(-373089. + 558367. i) q^{29} +(-32504.2 - 241773. i) q^{30} +8.05240e6i q^{31} +(5.89095e6 + 693599. i) q^{32} +602029. i q^{33} +(-3.56831e6 + 479726. i) q^{34} +(1.84604e6 - 2.76280e6i) q^{35} +(7.86500e6 - 6.10379e6i) q^{36} +(569878. - 2.86497e6i) q^{37} +(1.91257e6 - 3.90524e6i) q^{38} +(703155. + 291256. i) q^{39} +(-4.43870e6 + 6.76267e6i) q^{40} +(3.13384e7 - 1.29808e7i) q^{41} +(-1.65936e6 - 104195. i) q^{42} +(2.13395e7 - 1.42586e7i) q^{43} +(1.30801e7 - 1.50809e7i) q^{44} +(2.64873e6 + 1.33160e7i) q^{45} +(1.99016e7 + 5.27423e6i) q^{46} +(1.15786e7 - 1.15786e7i) q^{47} +(4.04162e6 + 220447. i) q^{48} +(1.25209e7 + 1.25209e7i) q^{49} +(1.66599e7 + 2.86741e7i) q^{50} +(-2.40964e6 + 479306. i) q^{51} +(-1.12861e7 - 2.25733e7i) q^{52} +(4.16779e7 + 6.23754e7i) q^{53} +(1.02532e7 - 9.04159e6i) q^{54} +(1.04184e7 + 2.51521e7i) q^{55} +(3.93034e7 + 3.86626e7i) q^{56} +(1.13553e6 - 2.74140e6i) q^{57} +(1.43754e7 - 4.92377e6i) q^{58} +(1.73238e7 + 3.44592e6i) q^{59} +(-2.73372e6 + 4.79544e6i) q^{60} +(-2.44493e7 - 1.63365e7i) q^{61} +(1.10523e8 - 1.44856e8i) q^{62} +9.25335e7 q^{63} +(-9.64536e7 - 9.33333e7i) q^{64} +3.44174e7 q^{65} +(8.26313e6 - 1.08300e7i) q^{66} +(5.80769e6 + 3.88057e6i) q^{67} +(7.07755e7 + 4.03468e7i) q^{68} +(1.37793e7 + 2.74087e6i) q^{69} +(-7.11295e7 + 2.43628e7i) q^{70} +(-2.47478e7 + 5.97465e7i) q^{71} +(-2.25263e8 + 1.85164e6i) q^{72} +(3.20074e6 + 7.72727e6i) q^{73} +(-4.95747e7 + 4.37167e7i) q^{74} +(1.25722e7 + 1.88157e7i) q^{75} +(-8.80068e7 + 4.40013e7i) q^{76} +(1.81983e8 - 3.61987e7i) q^{77} +(-8.65157e6 - 1.48906e7i) q^{78} +(3.38448e8 + 3.38448e8i) q^{79} +(1.72669e8 - 6.07318e7i) q^{80} +(-2.64033e8 + 2.64033e8i) q^{81} +(-7.41919e8 - 1.96620e8i) q^{82} +(1.60426e7 + 8.06517e7i) q^{83} +(2.84205e7 + 2.46499e7i) q^{84} +(-9.23774e7 + 6.17246e7i) q^{85} +(-5.79586e8 - 3.63935e7i) q^{86} +(9.57964e6 - 3.96802e6i) q^{87} +(-4.42294e8 + 9.17633e7i) q^{88} +(-1.87923e8 - 7.78403e7i) q^{89} +(1.35120e8 - 2.75900e8i) q^{90} +(4.57626e7 - 2.30064e8i) q^{91} +(-2.85624e8 - 3.68038e8i) q^{92} +(6.90756e7 - 1.03379e8i) q^{93} +(-3.67210e8 + 4.93681e7i) q^{94} -1.34184e8i q^{95} +(-6.96798e7 - 5.94387e7i) q^{96} +1.12316e9i q^{97} +(-5.33858e7 - 3.97095e8i) q^{98} +(-4.21206e8 + 6.30380e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 568 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20}+ \cdots + 157456 q^{99}+O(q^{100}) \) 568 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 + 3576336 * q^22 - 8 * q^23 + 12096992 * q^24 - 8 * q^25 - 2105968 * q^26 - 8 * q^27 - 21791488 * q^28 - 8 * q^29 + 44263272 * q^30 + 29441312 * q^32 - 38537008 * q^34 - 8 * q^35 - 110500728 * q^36 - 8 * q^37 + 66947312 * q^38 - 8 * q^39 + 97089632 * q^40 - 8 * q^41 - 224559088 * q^42 - 8 * q^43 + 146176992 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 + 182758288 * q^50 - 360057320 * q^51 - 25227512 * q^52 - 8 * q^53 - 646232264 * q^54 + 280217656 * q^55 + 203163008 * q^56 - 8 * q^57 + 855153280 * q^58 - 576150472 * q^59 + 230939416 * q^60 - 8 * q^61 - 597609496 * q^62 + 1260236864 * q^63 - 1364809832 * q^64 - 16 * q^65 + 186013784 * q^66 - 1007094968 * q^67 + 1004327944 * q^68 - 8 * q^69 + 1869092056 * q^70 - 476202952 * q^71 - 714729104 * q^72 - 8 * q^73 - 2182183312 * q^74 + 2309166136 * q^75 - 888710984 * q^76 - 8 * q^77 + 5243787376 * q^78 - 2269128680 * q^79 - 5193915232 * q^80 - 8 * q^81 + 3136405672 * q^82 - 8 * q^83 + 6148771880 * q^84 - 8 * q^85 - 988828368 * q^86 - 8 * q^87 - 4940685368 * q^88 - 8 * q^89 - 7222410008 * q^90 - 8 * q^91 + 1729489584 * q^92 + 157456 * q^93 + 6710490136 * q^94 + 10366581632 * q^96 + 2543861360 * q^98 + 157456 * q^99

Introduction

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