LMFDB - Embedded newform 81.9.f.a.71.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	81.71
Dual form			81.9.f.a.8.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.46646 - 0.434904i) q^{2} +(-234.667 + 85.4118i) q^{4} +(411.949 - 490.942i) q^{5} +(243.334 + 88.5664i) q^{7} +(-1096.91 + 633.301i) q^{8} +(802.546 - 1390.05i) q^{10} +(-4355.96 - 5191.23i) q^{11} +(-733.507 + 4159.93i) q^{13} +(638.693 + 112.619i) q^{14} +(46543.3 - 39054.5i) q^{16} +(27580.9 + 15923.8i) q^{17} +(-31761.5 - 55012.5i) q^{19} +(-54738.7 + 150393. i) q^{20} +(-13001.5 - 10909.6i) q^{22} +(67576.8 + 185666. i) q^{23} +(-3490.62 - 19796.3i) q^{25} +10579.3i q^{26} -64667.1 q^{28} +(-1.01674e6 + 179279. i) q^{29} +(-1.67239e6 + 608702. i) q^{31} +(306236. - 364958. i) q^{32} +(74952.5 + 27280.5i) q^{34} +(143722. - 82978.2i) q^{35} +(-711454. + 1.23227e6i) q^{37} +(-102264. - 121873. i) q^{38} +(-140957. + 799407. i) q^{40} +(-47826.5 - 8433.11i) q^{41} +(670492. - 562610. i) q^{43} +(1.46559e6 + 846160. i) q^{44} +(247423. + 428549. i) q^{46} +(-2.11724e6 + 5.81707e6i) q^{47} +(-4.36473e6 - 3.66244e6i) q^{49} +(-17219.0 - 47308.8i) q^{50} +(-183177. - 1.03885e6i) q^{52} +9.95902e6i q^{53} -4.34303e6 q^{55} +(-323005. + 56954.4i) q^{56} +(-2.42979e6 + 884370. i) q^{58} +(-9.92151e6 + 1.18240e7i) q^{59} +(-2.00776e7 - 7.30764e6i) q^{61} +(-3.86018e6 + 2.22867e6i) q^{62} +(-7.18042e6 + 1.24369e7i) q^{64} +(1.74012e6 + 2.07379e6i) q^{65} +(2.15182e6 - 1.22036e7i) q^{67} +(-7.83240e6 - 1.38106e6i) q^{68} +(318399. - 267168. i) q^{70} +(2.36946e6 + 1.36801e6i) q^{71} +(874977. + 1.51550e6i) q^{73} +(-1.21886e6 + 3.34878e6i) q^{74} +(1.21521e7 + 1.01968e7i) q^{76} +(-600185. - 1.64900e6i) q^{77} +(7.53737e6 + 4.27466e7i) q^{79} -3.89386e7i q^{80} -121630. q^{82} +(5.86063e7 - 1.03339e7i) q^{83} +(1.91796e7 - 6.98080e6i) q^{85} +(1.40906e6 - 1.67926e6i) q^{86} +(8.06570e6 + 2.93568e6i) q^{88} +(3.32007e7 - 1.91684e7i) q^{89} +(-546917. + 947288. i) q^{91} +(-3.17161e7 - 3.77978e7i) q^{92} +(-2.69223e6 + 1.52684e7i) q^{94} +(-4.00921e7 - 7.06932e6i) q^{95} +(1.06250e8 - 8.91546e7i) q^{97} +(-1.23583e7 - 7.13504e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	2.46646	−	0.434904i	0.154154	−	0.0271815i	−0.0960385	−	0.995378i	$-0.530617\pi$
$2$	2.46646	−	0.434904i	0.154154	−	0.0271815i	0.250193	+	0.968196i	$0.419506\pi$
$3$		0			0
$3$		0			0
$4$	−234.667	+	85.4118i	−0.916668	+	0.333640i
$5$	411.949	−	490.942i	0.659119	−	0.785508i	−0.328140	−	0.944629i	$-0.606422\pi$
$5$	411.949	−	490.942i	0.659119	−	0.785508i	0.987259	+	0.159122i	$0.0508662\pi$
$6$		0			0
$7$	243.334	+	88.5664i	0.101347	+	0.0368873i	0.392196	−	0.919882i	$-0.371715\pi$
$7$	243.334	+	88.5664i	0.101347	+	0.0368873i	−0.290849	+	0.956769i	$0.593938\pi$
$8$	−1096.91	+	633.301i	−0.267800	+	0.154614i
$9$		0			0
$10$	802.546	−	1390.05i	0.0802546	−	0.139005i
$11$	−4355.96	−	5191.23i	−0.297518	−	0.354568i	0.596489	−	0.802621i	$-0.296562\pi$
$11$	−4355.96	−	5191.23i	−0.297518	−	0.354568i	−0.894007	+	0.448053i	$0.852118\pi$
$12$		0			0
$13$	−733.507	+	4159.93i	−0.0256821	+	0.145651i	−0.994952	−	0.100347i	$-0.968005\pi$
$13$	−733.507	+	4159.93i	−0.0256821	+	0.145651i	0.969270	+	0.245998i	$0.0791157\pi$
$14$	638.693	+	112.619i	0.0166257	+	0.00293156i
$15$		0			0
$16$	46543.3	−	39054.5i	0.710195	−	0.595924i
$17$	27580.9	+	15923.8i	0.330227	+	0.190656i	0.655942	−	0.754812i	$-0.272272\pi$
$17$	27580.9	+	15923.8i	0.330227	+	0.190656i	−0.325715	+	0.945468i	$0.605605\pi$
$18$		0			0
$19$	−31761.5	−	55012.5i	−0.243717	−	0.422131i	0.718053	−	0.695989i	$-0.245034\pi$
$19$	−31761.5	−	55012.5i	−0.243717	−	0.422131i	−0.961770	+	0.273858i	$0.911700\pi$
$20$	−54738.7	+	150393.i	−0.342117	+	0.939958i
$21$		0			0
$22$	−13001.5	−	10909.6i	−0.0555013	−	0.0465711i
$23$	67576.8	+	185666.i	0.241483	+	0.663469i	0.999931	+	0.0117355i	$0.00373562\pi$
$23$	67576.8	+	185666.i	0.241483	+	0.663469i	−0.758448	+	0.651733i	$0.774042\pi$
$24$		0			0
$25$	−3490.62	−	19796.3i	−0.00893599	−	0.0506785i
$26$			10579.3i			0.0231507i
$27$		0			0
$28$	−64667.1			−0.105209
$29$	−1.01674e6	+	179279.i	−1.43753	+	0.253476i	−0.837474	−	0.546478i	$-0.815968\pi$
$29$	−1.01674e6	+	179279.i	−1.43753	+	0.253476i	−0.600061	+	0.799954i	$0.704857\pi$
$30$		0			0
$31$	−1.67239e6	+	608702.i	−1.81089	+	0.659110i	−0.813950	+	0.580935i	$0.802687\pi$
$31$	−1.67239e6	+	608702.i	−1.81089	+	0.659110i	−0.996940	+	0.0781752i	$0.975091\pi$
$32$	306236.	−	364958.i	0.292050	−	0.348051i
$33$		0			0
$34$	74952.5	+	27280.5i	0.0560881	+	0.0204144i
$35$	143722.	−	82978.2i	0.0957750	−	0.0552957i
$36$		0			0
$37$	−711454.	+	1.23227e6i	−0.379612	+	0.657507i	−0.991006	−	0.133819i	$-0.957276\pi$
$37$	−711454.	+	1.23227e6i	−0.379612	+	0.657507i	0.611394	+	0.791327i	$0.290609\pi$
$38$	−102264.	−	121873.i	−0.0490442	−	0.0584486i
$39$		0			0
$40$	−140957.	+	799407.i	−0.0550613	+	0.312268i
$41$	−47826.5	−	8433.11i	−0.0169252	−	0.00298437i	0.165179	−	0.986264i	$-0.447180\pi$
$41$	−47826.5	−	8433.11i	−0.0169252	−	0.00298437i	−0.182104	+	0.983279i	$0.558291\pi$
$42$		0			0
$43$	670492.	−	562610.i	0.196119	−	0.164564i	−0.539440	−	0.842024i	$-0.681364\pi$
$43$	670492.	−	562610.i	0.196119	−	0.164564i	0.735559	+	0.677461i	$0.236920\pi$
$44$	1.46559e6	+	846160.i	0.391023	+	0.225757i
$45$		0			0
$46$	247423.	+	428549.i	0.0552597	+	0.0957125i
$47$	−2.11724e6	+	5.81707e6i	−0.433889	+	1.19210i	0.509517	+	0.860460i	$0.329824\pi$
$47$	−2.11724e6	+	5.81707e6i	−0.433889	+	1.19210i	−0.943406	+	0.331639i	$0.892398\pi$
$48$		0			0
$49$	−4.36473e6	−	3.66244e6i	−0.757134	−	0.635311i
$50$	−17219.0	−	47308.8i	−0.00275504	−	0.00756941i
$51$		0			0
$52$	−183177.	−	1.03885e6i	−0.0250529	−	0.142082i
$53$			9.95902e6i			1.26216i	0.775719	+	0.631078i	$0.217387\pi$
$53$			9.95902e6i			1.26216i	−0.775719	+	0.631078i	$0.782613\pi$
$54$		0			0
$55$	−4.34303e6			−0.474616
$56$	−323005.	+	56954.4i	−0.0328440	+	0.00579129i
$57$		0			0
$58$	−2.42979e6	+	884370.i	−0.214712	+	0.0781487i
$59$	−9.92151e6	+	1.18240e7i	−0.818785	+	0.975790i	−0.999971	−	0.00765928i	$-0.997562\pi$
$59$	−9.92151e6	+	1.18240e7i	−0.818785	+	0.975790i	0.181186	+	0.983449i	$0.442006\pi$
$60$		0			0
$61$	−2.00776e7	−	7.30764e6i	−1.45008	−	0.527786i	−0.507466	−	0.861672i	$-0.669418\pi$
$61$	−2.00776e7	−	7.30764e6i	−1.45008	−	0.527786i	−0.942613	+	0.333886i	$0.891640\pi$
$62$	−3.86018e6	+	2.22867e6i	−0.261240	+	0.150827i
$63$		0			0
$64$	−7.18042e6	+	1.24369e7i	−0.427987	+	0.741295i
$65$	1.74012e6	+	2.07379e6i	0.0974821	+	0.116175i
$66$		0			0
$67$	2.15182e6	−	1.22036e7i	0.106784	−	0.605602i	−0.883709	−	0.468037i	$-0.844961\pi$
$67$	2.15182e6	−	1.22036e7i	0.106784	−	0.605602i	0.990493	−	0.137565i	$-0.0439276\pi$
$68$	−7.83240e6	−	1.38106e6i	−0.366319	−	0.0645919i
$69$		0			0
$70$	318399.	−	267168.i	0.0132611	−	0.0111274i
$71$	2.36946e6	+	1.36801e6i	0.0932429	+	0.0538338i	0.545896	−	0.837853i	$-0.316189\pi$
$71$	2.36946e6	+	1.36801e6i	0.0932429	+	0.0538338i	−0.452654	+	0.891686i	$0.649523\pi$
$72$		0			0
$73$	874977.	+	1.51550e6i	0.0308109	+	0.0533661i	0.881020	−	0.473080i	$-0.156858\pi$
$73$	874977.	+	1.51550e6i	0.0308109	+	0.0533661i	−0.850209	+	0.526446i	$0.823524\pi$
$74$	−1.21886e6	+	3.34878e6i	−0.0406467	+	0.111676i
$75$		0			0
$76$	1.21521e7	+	1.01968e7i	0.364248	+	0.305640i
$77$	−600185.	−	1.64900e6i	−0.0170735	−	0.0469091i
$78$		0			0
$79$	7.53737e6	+	4.27466e7i	0.193514	+	1.09747i	0.914520	+	0.404542i	$0.132569\pi$
$79$	7.53737e6	+	4.27466e7i	0.193514	+	1.09747i	−0.721006	+	0.692929i	$0.756320\pi$
$80$		−	3.89386e7i		−	0.950648i
$81$		0			0
$82$	−121630.			−0.00269020
$83$	5.86063e7	−	1.03339e7i	1.23490	−	0.217746i	0.482172	−	0.876077i	$-0.339848\pi$
$83$	5.86063e7	−	1.03339e7i	1.23490	−	0.217746i	0.752729	+	0.658330i	$0.228737\pi$
$84$		0			0
$85$	1.91796e7	−	6.98080e6i	0.367421	−	0.133730i
$86$	1.40906e6	−	1.67926e6i	0.0257595	−	0.0306990i
$87$		0			0
$88$	8.06570e6	+	2.93568e6i	0.134497	+	0.0489528i
$89$	3.32007e7	−	1.91684e7i	0.529161	−	0.305511i	−0.211514	−	0.977375i	$-0.567839\pi$
$89$	3.32007e7	−	1.91684e7i	0.529161	−	0.305511i	0.740675	+	0.671864i	$0.234506\pi$
$90$		0			0
$91$	−546917.	+	947288.i	−0.00797547	+	0.0138139i
$92$	−3.17161e7	−	3.77978e7i	−0.442719	−	0.527612i
$93$		0			0
$94$	−2.69223e6	+	1.52684e7i	−0.0344826	+	0.195561i
$95$	−4.00921e7	−	7.06932e6i	−0.492226	−	0.0867927i
$96$		0			0
$97$	1.06250e8	−	8.91546e7i	1.20017	−	1.00706i	0.200546	−	0.979684i	$-0.435728\pi$
$97$	1.06250e8	−	8.91546e7i	1.20017	−	1.00706i	0.999625	−	0.0273787i	$-0.00871601\pi$
$98$	−1.23583e7	−	7.13504e6i	−0.133984	−	0.0773557i
$99$		0			0
$100$	2.50997e6	+	4.34740e6i	0.0250997	+	0.0434740i
$101$	−4.55685e7	+	1.25198e8i	−0.437904	+	1.20313i	0.502949	+	0.864316i	$0.332249\pi$
$101$	−4.55685e7	+	1.25198e8i	−0.437904	+	1.20313i	−0.940853	+	0.338816i	$0.889974\pi$
$102$		0			0
$103$	−9.13908e7	−	7.66860e7i	−0.811995	−	0.681345i	0.139088	−	0.990280i	$-0.455583\pi$
$103$	−9.13908e7	−	7.66860e7i	−0.811995	−	0.681345i	−0.951083	+	0.308935i	$0.900027\pi$
$104$	−1.82989e6	−	5.02759e6i	−0.0156420	−	0.0429761i
$105$		0			0
$106$	4.33122e6	+	2.45636e7i	0.0343073	+	0.194567i
$107$		−	1.15116e8i		−	0.878216i	−0.898434	−	0.439108i	$-0.855295\pi$
$107$		−	1.15116e8i		−	0.878216i	0.898434	−	0.439108i	$-0.144705\pi$
$108$		0			0
$109$	3.18734e7			0.225799			0.112900	−	0.993606i	$-0.463986\pi$
$109$	3.18734e7			0.225799			0.112900	+	0.993606i	$0.463986\pi$
$110$	−1.07119e7	+	1.88880e6i	−0.0731639	+	0.0129008i
$111$		0			0
$112$	1.47845e7	−	5.38112e6i	0.0939582	−	0.0341980i
$113$	4.45785e7	−	5.31266e7i	0.273408	−	0.325835i	−0.611816	−	0.791000i	$-0.709561\pi$
$113$	4.45785e7	−	5.31266e7i	0.273408	−	0.325835i	0.885224	+	0.465165i	$0.154005\pi$
$114$		0			0
$115$	1.18989e8	+	4.33086e7i	0.680326	+	0.247618i
$116$	2.23283e8	−	1.28913e8i	1.23317	−	0.711972i
$117$		0			0
$118$	−1.93287e7	+	3.34784e7i	−0.0996955	+	0.172678i
$119$	5.30105e6	+	6.31755e6i	0.0264347	+	0.0315036i
$120$		0			0
$121$	2.92485e7	−	1.65877e8i	0.136447	−	0.773827i
$122$	−5.26987e7	−	9.29221e6i	−0.237882	−	0.0419449i
$123$		0			0
$124$	3.40466e8	−	2.85685e8i	1.44008	−	1.20837i
$125$	2.05647e8	+	1.18730e8i	0.842331	+	0.486320i
$126$		0			0
$127$	2.33645e8	+	4.04684e8i	0.898133	+	1.55561i	0.829878	+	0.557944i	$0.188410\pi$
$127$	2.33645e8	+	4.04684e8i	0.898133	+	1.55561i	0.0682548	+	0.997668i	$0.478257\pi$
$128$	−5.40153e7	+	1.48406e8i	−0.201223	+	0.552855i
$129$		0			0
$130$	5.19383e6	+	4.35814e6i	0.0181851	+	0.0152591i
$131$	−1.80234e8	−	4.95187e8i	−0.611998	−	1.68145i	−0.725763	−	0.687944i	$-0.758513\pi$
$131$	−1.80234e8	−	4.95187e8i	−0.611998	−	1.68145i	0.113765	−	0.993508i	$-0.463709\pi$
$132$		0			0
$133$	−2.85640e6	−	1.61994e7i	−0.00912876	−	0.0517718i
$134$		−	3.10355e7i		−	0.0962586i
$135$		0			0
$136$	−4.03382e7			−0.117913
$137$	3.13130e8	−	5.52133e7i	0.888879	−	0.156733i	0.289480	−	0.957184i	$-0.406518\pi$
$137$	3.13130e8	−	5.52133e7i	0.888879	−	0.156733i	0.599399	+	0.800451i	$0.295406\pi$
$138$		0			0
$139$	−5.17739e8	+	1.88442e8i	−1.38692	+	0.504798i	−0.924269	−	0.381742i	$-0.875324\pi$
$139$	−5.17739e8	+	1.88442e8i	−1.38692	+	0.504798i	−0.462652	+	0.886540i	$0.653102\pi$
$140$	−2.66396e7	+	3.17478e7i	−0.0693450	+	0.0826422i
$141$		0			0
$142$	6.43914e6	+	2.34365e6i	0.0158370	+	0.00576421i
$143$	2.47903e7	−	1.43127e7i	0.0592839	−	0.0342276i
$144$		0			0
$145$	−3.30830e8	+	5.73015e8i	−0.748399	+	1.29627i
$146$	2.81720e6	+	3.35741e6i	0.00620020	+	0.00738912i
$147$		0			0
$148$	6.17040e7	−	3.49941e8i	0.128608	−	0.729370i
$149$	−6.98309e8	−	1.23131e8i	−1.41678	−	0.249817i	−0.587761	−	0.809035i	$-0.699990\pi$
$149$	−6.98309e8	−	1.23131e8i	−1.41678	−	0.249817i	−0.829021	+	0.559218i	$0.811101\pi$
$150$		0			0
$151$	−2.61562e8	+	2.19476e8i	−0.503114	+	0.422163i	−0.858698	−	0.512481i	$-0.828726\pi$
$151$	−2.61562e8	+	2.19476e8i	−0.503114	+	0.422163i	0.355584	+	0.934644i	$0.384282\pi$
$152$	6.96789e7	+	4.02291e7i	0.130535	+	0.0753644i
$153$		0			0
$154$	−2.19749e6	−	3.80617e6i	−0.00390701	−	0.00676714i
$155$	−3.90105e8	+	1.07180e9i	−0.675856	+	1.85690i
$156$		0			0
$157$	−6.89517e8	−	5.78573e8i	−1.13487	−	0.952269i	−0.135612	−	0.990762i	$-0.543300\pi$
$157$	−6.89517e8	−	5.78573e8i	−1.13487	−	0.952269i	−0.999259	+	0.0384927i	$0.987744\pi$
$158$	3.71813e7	+	1.02155e8i	0.0596618	+	0.163920i
$159$		0			0
$160$	−5.30195e7	−	3.00689e8i	−0.0809014	−	0.458815i
$161$			5.11639e7i			0.0761483i
$162$		0			0
$163$	−5.07912e8			−0.719512			−0.359756	−	0.933046i	$-0.617140\pi$
$163$	−5.07912e8			−0.719512			−0.359756	+	0.933046i	$0.617140\pi$
$164$	1.19436e7	−	2.10598e6i	0.0165105	−	0.00291124i
$165$		0			0
$166$	1.40056e8	−	5.09763e7i	0.184446	−	0.0671330i
$167$	−5.64103e8	+	6.72272e8i	−0.725258	+	0.864329i	−0.995130	−	0.0985671i	$-0.968574\pi$
$167$	−5.64103e8	+	6.72272e8i	−0.725258	+	0.864329i	0.269872	+	0.962896i	$0.413019\pi$
$168$		0			0
$169$	7.49769e8	+	2.72894e8i	0.919138	+	0.334539i
$170$	4.42698e7	−	2.55592e7i	0.0530044	−	0.0306021i
$171$		0			0
$172$	−1.09289e8	+	1.89294e8i	−0.124871	+	0.216283i
$173$	9.08559e8	+	1.08278e9i	1.01430	+	1.20880i	0.977816	+	0.209467i	$0.0671730\pi$
$173$	9.08559e8	+	1.08278e9i	1.01430	+	1.20880i	0.0364893	+	0.999334i	$0.488383\pi$
$174$		0			0
$175$	903900.	−	5.12627e6i	0.000963758	−	0.00546574i
$176$	−4.05482e8	−	7.14974e7i	−0.422591	−	0.0745143i
$177$		0			0
$178$	7.35520e7	−	6.17174e7i	0.0732680	−	0.0614792i
$179$	1.09594e8	+	6.32741e7i	0.106752	+	0.0616330i	0.552425	−	0.833562i	$-0.313702\pi$
$179$	1.09594e8	+	6.32741e7i	0.106752	+	0.0616330i	−0.445674	+	0.895196i	$0.647036\pi$
$180$		0			0
$181$	−2.30450e8	−	3.99152e8i	−0.214715	−	0.371898i	0.738469	−	0.674287i	$-0.235549\pi$
$181$	−2.30450e8	−	3.99152e8i	−0.214715	−	0.371898i	−0.953185	+	0.302389i	$0.902216\pi$
$182$	−936972.	+	2.57431e6i	−0.000853967	+	0.00234626i
$183$		0			0
$184$	−1.91708e8	−	1.60862e8i	−0.167251	−	0.140340i
$185$	3.11893e8	+	8.56918e8i	0.266268	+	0.731564i
$186$		0			0
$187$	−3.74769e7	−	2.12542e8i	−0.0306477	−	0.173811i
$188$		−	1.54591e9i		−	1.23752i
$189$		0			0
$190$	−1.01960e8			−0.0782378
$191$	−7.37923e8	+	1.30116e8i	−0.554469	+	0.0977679i	−0.443860	−	0.896096i	$-0.646391\pi$
$191$	−7.37923e8	+	1.30116e8i	−0.554469	+	0.0977679i	−0.110609	+	0.993864i	$0.535280\pi$
$192$		0			0
$193$	−1.25557e9	+	4.56992e8i	−0.904927	+	0.329366i	−0.752225	−	0.658906i	$-0.771019\pi$
$193$	−1.25557e9	+	4.56992e8i	−0.904927	+	0.329366i	−0.152701	+	0.988272i	$0.548797\pi$
$194$	2.23289e8	−	2.66105e8i	0.157638	−	0.187865i
$195$		0			0
$196$	1.33707e9	+	4.86655e8i	0.906005	+	0.329759i
$197$	8.27317e8	−	4.77652e8i	0.549297	−	0.317137i	−0.199541	−	0.979889i	$-0.563945\pi$
$197$	8.27317e8	−	4.77652e8i	0.549297	−	0.317137i	0.748838	+	0.662753i	$0.230612\pi$
$198$		0			0
$199$	−4.23487e8	+	7.33501e8i	−0.270040	+	0.467723i	−0.968872	−	0.247563i	$-0.920370\pi$
$199$	−4.23487e8	+	7.33501e8i	−0.270040	+	0.467723i	0.698832	+	0.715286i	$0.253704\pi$
$200$	1.63659e7	+	1.95041e7i	0.0102287	+	0.0121901i
$201$		0			0
$202$	−5.79438e7	+	3.28615e8i	−0.0348018	+	0.197371i
$203$	−2.63286e8	−	4.64244e7i	−0.155040	−	0.0273377i
$204$		0			0
$205$	−2.38423e7	+	2.00060e7i	−0.0135000	+	0.0113278i
$206$	−2.58763e8	−	1.49397e8i	−0.143692	−	0.0829608i
$207$		0			0
$208$	1.28324e8	+	2.22264e8i	0.0685574	+	0.118745i
$209$	−1.47231e8	+	4.04514e8i	−0.0771638	+	0.212006i
$210$		0			0
$211$	−1.74069e8	−	1.46061e8i	−0.0878195	−	0.0736893i	0.597821	−	0.801630i	$-0.296033\pi$
$211$	−1.74069e8	−	1.46061e8i	−0.0878195	−	0.0736893i	−0.685641	+	0.727940i	$0.740478\pi$
$212$	−8.50618e8	−	2.33705e9i	−0.421106	−	1.15698i
$213$		0			0
$214$	−5.00645e7	−	2.83930e8i	−0.0238712	−	0.135381i
$215$		−	5.60940e8i		−	0.262520i
$216$		0			0
$217$	−4.60861e8			−0.207841
$218$	7.86146e7	−	1.38619e7i	0.0348079	−	0.00613757i
$219$		0			0
$220$	1.01917e9	−	3.70946e8i	0.435065	−	0.158351i
$221$	−8.64727e7	+	1.03054e8i	−0.0362501	+	0.0432012i
$222$		0			0
$223$	6.09381e8	+	2.21796e8i	0.246416	+	0.0896882i	0.462276	−	0.886736i	$-0.347033\pi$
$223$	6.09381e8	+	2.21796e8i	0.246416	+	0.0896882i	−0.215859	+	0.976424i	$0.569255\pi$
$224$	1.06841e8	−	6.16846e7i	0.0424371	−	0.0245010i
$225$		0			0
$226$	8.68463e7	−	1.50422e8i	0.0332903	−	0.0576605i
$227$	6.84046e8	+	8.15215e8i	0.257622	+	0.307021i	0.879316	−	0.476238i	$-0.158000\pi$
$227$	6.84046e8	+	8.15215e8i	0.257622	+	0.307021i	−0.621695	+	0.783260i	$0.713556\pi$
$228$		0			0
$229$	3.42445e8	−	1.94210e9i	0.124523	−	0.706205i	−0.857067	−	0.515205i	$-0.827716\pi$
$229$	3.42445e8	−	1.94210e9i	0.124523	−	0.706205i	0.981590	−	0.191000i	$-0.0611731\pi$
$230$	3.12318e8	+	5.50701e7i	0.111606	+	0.0196791i
$231$		0			0
$232$	1.00173e9	−	8.40555e8i	0.345781	−	0.290145i
$233$	3.99283e9	+	2.30526e9i	1.35474	+	0.782161i	0.988910	−	0.148519i	$-0.0474507\pi$
$233$	3.99283e9	+	2.30526e9i	1.35474	+	0.782161i	0.365833	+	0.930680i	$0.380784\pi$
$234$		0			0
$235$	1.98365e9	+	3.43578e9i	0.650419	+	1.12656i
$236$	1.31834e9	−	3.62212e9i	0.424991	−	1.16765i
$237$		0			0
$238$	1.58224e7	+	1.32766e7i	0.00493133	+	0.00413788i
$239$	−4.79266e8	−	1.31677e9i	−0.146888	−	0.403570i	0.844328	−	0.535827i	$-0.180000\pi$
$239$	−4.79266e8	−	1.31677e9i	−0.146888	−	0.403570i	−0.991216	+	0.132256i	$0.957778\pi$
$240$		0			0
$241$	−5.55644e8	−	3.15122e9i	−0.164713	−	0.934136i	−0.949359	−	0.314192i	$-0.898266\pi$
$241$	−5.55644e8	−	3.15122e9i	−0.164713	−	0.934136i	0.784646	−	0.619944i	$-0.212845\pi$
$242$		−	4.21849e8i		−	0.122997i
$243$		0			0
$244$	5.33570e9			1.50533
$245$	−3.59609e9	+	6.34088e8i	−0.998083	+	0.175989i
$246$		0			0
$247$	2.52145e8	−	9.17734e7i	0.0677428	−	0.0246564i
$248$	1.44897e9	−	1.72682e9i	0.383048	−	0.456499i
$249$		0			0
$250$	5.58858e8	+	2.03408e8i	0.143068	+	0.0520723i
$251$	−2.82883e9	+	1.63323e9i	−0.712709	+	0.411483i	−0.812063	−	0.583569i	$-0.801656\pi$
$251$	−2.82883e9	+	1.63323e9i	−0.712709	+	0.411483i	0.0993540	+	0.995052i	$0.468322\pi$
$252$		0			0
$253$	6.69472e8	−	1.15956e9i	0.163399	−	0.283016i
$254$	7.52275e8	+	8.96526e8i	0.180735	+	0.215391i
$255$		0			0
$256$	5.69712e8	−	3.23100e9i	0.132646	−	0.752275i
$257$	1.01335e9	+	1.78680e8i	0.232287	+	0.0409585i	0.288580	−	0.957456i	$-0.406817\pi$
$257$	1.01335e9	+	1.78680e8i	0.232287	+	0.0409585i	−0.0562927	+	0.998414i	$0.517928\pi$
$258$		0			0
$259$	−2.82259e8	+	2.36844e8i	−0.0627262	+	0.0526336i
$260$	−5.85474e8	−	3.38023e8i	−0.128119	−	0.0739696i
$261$		0			0
$262$	−6.59899e8	−	1.14298e9i	−0.140046	−	0.242568i
$263$	1.69620e9	−	4.66027e9i	0.354531	−	0.974066i	−0.626364	−	0.779530i	$-0.715458\pi$
$263$	1.69620e9	−	4.66027e9i	0.354531	−	0.974066i	0.980895	−	0.194536i	$-0.0623200\pi$
$264$		0			0
$265$	4.88931e9	+	4.10261e9i	0.991434	+	0.831912i
$266$	−1.40904e7	−	3.87131e7i	−0.00281447	−	0.00773270i
$267$		0			0
$268$	5.37368e8	+	3.04756e9i	0.104168	+	0.590764i
$269$		−	1.08134e9i		−	0.206516i	−0.994655	−	0.103258i	$-0.967073\pi$
$269$		−	1.08134e9i		−	0.206516i	0.994655	−	0.103258i	$-0.0329267\pi$
$270$		0			0
$271$	−4.66467e9			−0.864855			−0.432428	−	0.901669i	$-0.642343\pi$
$271$	−4.66467e9			−0.864855			−0.432428	+	0.901669i	$0.642343\pi$
$272$	1.90560e9	−	3.36009e8i	0.348142	−	0.0613868i
$273$		0			0
$274$	7.48312e8	−	2.72363e8i	0.132764	−	0.0483221i
$275$	−8.75622e7	+	1.04353e8i	−0.0153104	+	0.0182462i
$276$		0			0
$277$	−8.24991e9	−	3.00272e9i	−1.40130	−	0.510030i	−0.472734	−	0.881205i	$-0.656733\pi$
$277$	−8.24991e9	−	3.00272e9i	−1.40130	−	0.510030i	−0.928563	+	0.371175i	$0.878955\pi$
$278$	−1.19503e9	+	6.89951e8i	−0.200078	+	0.115515i
$279$		0			0
$280$	−1.05100e8	+	1.82039e8i	−0.0170990	+	0.0296164i
$281$	−3.27244e9	−	3.89994e9i	−0.524864	−	0.625508i	0.436860	−	0.899530i	$-0.356091\pi$
$281$	−3.27244e9	−	3.89994e9i	−0.524864	−	0.625508i	−0.961724	+	0.274021i	$0.911646\pi$
$282$		0			0
$283$	−1.36212e9	+	7.72497e9i	−0.212359	+	1.20435i	0.673073	+	0.739576i	$0.264974\pi$
$283$	−1.36212e9	+	7.72497e9i	−0.212359	+	1.20435i	−0.885432	+	0.464770i	$0.846137\pi$
$284$	−6.72878e8	−	1.18646e8i	−0.103434	−	0.0182382i
$285$		0			0
$286$	5.49197e7	−	4.60831e7i	0.00820850	−	0.00688775i
$287$	−1.08909e7	−	6.28789e6i	−0.00160523	−	0.000926781i
$288$		0			0
$289$	−2.98074e9	−	5.16280e9i	−0.427300	−	0.740106i
$290$	−5.66775e8	+	1.55720e9i	−0.0801343	+	0.220167i
$291$		0			0
$292$	−3.34770e8	−	2.80905e8i	−0.0460485	−	0.0386393i
$293$	4.13715e9	+	1.13667e10i	0.561347	+	1.54229i	0.817665	+	0.575695i	$0.195268\pi$
$293$	4.13715e9	+	1.13667e10i	0.561347	+	1.54229i	−0.256318	+	0.966592i	$0.582510\pi$
$294$		0			0
$295$	1.71774e9	+	9.74178e9i	0.226813	+	1.28632i
$296$		−	1.80226e9i		−	0.234774i
$297$		0			0
$298$	−1.77591e9			−0.225193
$299$	−8.21924e8	+	1.44927e8i	−0.102836	+	0.0181328i
$300$		0			0
$301$	2.12982e8	−	7.75192e7i	0.0259464	−	0.00944372i
$302$	−5.49682e8	+	6.55085e8i	−0.0660820	+	0.0787535i
$303$		0			0
$304$	−3.62677e9	−	1.32004e9i	−0.424645	−	0.154558i
$305$	−1.18586e10	+	6.84655e9i	−1.37035	+	0.791175i
$306$		0			0
$307$	6.47222e9	−	1.12102e10i	0.728618	−	1.26200i	−0.228849	−	0.973462i	$-0.573496\pi$
$307$	6.47222e9	−	1.12102e10i	0.728618	−	1.26200i	0.957467	−	0.288542i	$-0.0931705\pi$
$308$	2.81687e8	+	3.35702e8i	0.0313015	+	0.0373036i
$309$		0			0
$310$	−4.96047e8	+	2.81322e9i	−0.0537126	+	0.304619i
$311$	1.24197e10	+	2.18993e9i	1.32761	+	0.234093i	0.792076	−	0.610423i	$-0.209000\pi$
$311$	1.24197e10	+	2.18993e9i	1.32761	+	0.234093i	0.535531	+	0.844516i	$0.320112\pi$
$312$		0			0
$313$	−6.91530e9	+	5.80262e9i	−0.720499	+	0.604571i	−0.927523	−	0.373765i	$-0.878067\pi$
$313$	−6.91530e9	+	5.80262e9i	−0.720499	+	0.604571i	0.207024	+	0.978336i	$0.433622\pi$
$314$	−1.95229e9	−	1.12716e9i	−0.200829	−	0.115949i
$315$		0			0
$316$	−5.41983e9	−	9.38743e9i	−0.543548	−	0.941452i
$317$	8.52565e8	−	2.34240e9i	0.0844287	−	0.231966i	−0.890293	−	0.455388i	$-0.849501\pi$
$317$	8.52565e8	−	2.34240e9i	0.0844287	−	0.231966i	0.974722	+	0.223422i	$0.0717228\pi$
$318$		0			0
$319$	5.35956e9	+	4.49721e9i	0.517567	+	0.434290i
$320$	3.14781e9	+	8.64853e9i	0.300198	+	0.824788i
$321$		0			0
$322$	2.22514e7	+	1.26194e8i	0.00206983	+	0.0117386i
$323$		−	2.02306e9i		−	0.185865i
$324$		0			0
$325$	8.49116e7			0.00761085
$326$	−1.25275e9	+	2.20893e8i	−0.110916	+	0.0195574i
$327$		0			0
$328$	5.78020e7	−	2.10382e7i	0.00499399	−	0.00181766i
$329$	−1.03039e9	+	1.22798e9i	−0.0879467	+	0.104811i
$330$		0			0
$331$	−1.23169e10	−	4.48300e9i	−1.02610	−	0.373471i	−0.226507	−	0.974010i	$-0.572731\pi$
$331$	−1.23169e10	−	4.48300e9i	−1.02610	−	0.373471i	−0.799596	+	0.600539i	$0.794953\pi$
$332$	−1.28703e10	+	7.43069e9i	−1.05935	+	0.611614i
$333$		0			0
$334$	−1.09897e9	+	1.90347e9i	−0.0883077	+	0.152953i
$335$	−5.10481e9	−	6.08367e9i	−0.405322	−	0.483044i
$336$		0			0
$337$	−2.91787e8	+	1.65481e9i	−0.0226228	+	0.128300i	−0.994028	−	0.109129i	$-0.965194\pi$
$337$	−2.91787e8	+	1.65481e9i	−0.0226228	+	0.128300i	0.971405	+	0.237430i	$0.0763049\pi$
$338$	1.96796e9	+	3.47005e8i	0.150782	+	0.0265870i
$339$		0			0
$340$	−3.90457e9	+	3.27633e9i	−0.292185	+	0.245172i
$341$	1.04448e10	+	6.03031e9i	0.772472	+	0.445987i
$342$		0			0
$343$	−1.48412e9	−	2.57057e9i	−0.107224	−	0.185717i
$344$	−3.79168e8	+	1.04176e9i	−0.0270768	+	0.0743930i
$345$		0			0
$346$	2.71183e9	+	2.27550e9i	0.189216	+	0.158771i
$347$	−2.77675e9	−	7.62907e9i	−0.191522	−	0.526203i	0.806347	−	0.591442i	$-0.201441\pi$
$347$	−2.77675e9	−	7.62907e9i	−0.191522	−	0.526203i	−0.997870	+	0.0652390i	$0.979219\pi$
$348$		0			0
$349$	1.80498e7	+	1.02366e8i	0.00121667	+	0.00690006i	0.985410	−	0.170197i	$-0.0544404\pi$
$349$	1.80498e7	+	1.02366e8i	0.00121667	+	0.00690006i	−0.984193	+	0.177097i	$0.943329\pi$
$350$		−	1.30369e7i		−	0.000868763i
$351$		0			0
$352$	−3.22854e9			−0.210298
$353$	9.42955e9	−	1.66268e9i	0.607285	−	0.107081i	0.138454	−	0.990369i	$-0.455787\pi$
$353$	9.42955e9	−	1.66268e9i	0.607285	−	0.107081i	0.468830	+	0.883288i	$0.344676\pi$
$354$		0			0
$355$	1.64771e9	−	5.99717e8i	0.103745	−	0.0377601i
$356$	−6.15390e9	+	7.33394e9i	−0.383134	+	0.456601i
$357$		0			0
$358$	2.97828e8	+	1.08400e8i	0.0181315	+	0.00659931i
$359$	−2.20697e10	+	1.27419e10i	−1.32867	+	0.767109i	−0.985094	−	0.172015i	$-0.944972\pi$
$359$	−2.20697e10	+	1.27419e10i	−1.32867	+	0.767109i	−0.343578	+	0.939124i	$0.611639\pi$
$360$		0			0
$361$	6.47420e9	−	1.12136e10i	0.381204	−	0.660264i
$362$	−7.41991e8	−	8.84270e8i	−0.0432080	−	0.0514933i
$363$		0			0
$364$	4.74338e7	−	2.69011e8i	0.00270198	−	0.0153237i
$365$	1.10447e9	+	1.94748e8i	0.0622276	+	0.0109724i
$366$		0			0
$367$	−4.98172e8	+	4.18016e8i	−0.0274609	+	0.0230424i	−0.656415	−	0.754400i	$-0.727928\pi$
$367$	−4.98172e8	+	4.18016e8i	−0.0274609	+	0.0230424i	0.628954	+	0.777443i	$0.283483\pi$
$368$	1.03963e10	+	6.00232e9i	0.566877	+	0.327287i
$369$		0			0
$370$	1.14195e9	+	1.97791e9i	0.0609312	+	0.105536i
$371$	−8.82035e8	+	2.42337e9i	−0.0465576	+	0.127916i
$372$		0			0
$373$	9.77422e8	+	8.20154e8i	0.0504948	+	0.0423702i	0.667686	−	0.744443i	$-0.267285\pi$
$373$	9.77422e8	+	8.20154e8i	0.0504948	+	0.0423702i	−0.617191	+	0.786813i	$0.711729\pi$
$374$	−1.84871e8	−	5.07929e8i	−0.00944892	−	0.0259607i
$375$		0			0
$376$	−1.36153e9	−	7.72164e9i	−0.0681204	−	0.386330i
$377$		−	4.36107e9i		−	0.215888i
$378$		0			0
$379$	2.22343e10			1.07762			0.538811	−	0.842427i	$-0.318874\pi$
$379$	2.22343e10			1.07762			0.538811	+	0.842427i	$0.318874\pi$
$380$	1.00121e10	−	1.76540e9i	0.480165	−	0.0846661i
$381$		0			0
$382$	−1.76347e9	+	6.41851e8i	−0.0828162	+	0.0301426i
$383$	2.13080e10	−	2.53939e10i	0.990258	−	1.18014i	0.00662182	−	0.999978i	$-0.497892\pi$
$383$	2.13080e10	−	2.53939e10i	0.990258	−	1.18014i	0.983636	−	0.180166i	$-0.0576634\pi$
$384$		0			0
$385$	−1.05681e9	−	3.84647e8i	−0.0481009	−	0.0175073i
$386$	−2.89808e9	+	1.67321e9i	−0.130545	+	0.0753704i
$387$		0			0
$388$	−1.73186e10	+	2.99967e10i	−0.764162	+	1.32357i
$389$	−2.54213e10	−	3.02959e10i	−1.11019	−	1.32308i	−0.941349	−	0.337435i	$-0.890441\pi$
$389$	−2.54213e10	−	3.02959e10i	−1.11019	−	1.32308i	−0.168845	−	0.985643i	$-0.554004\pi$
$390$		0			0
$391$	−1.09268e9	+	6.19690e9i	−0.0467505	+	0.265135i
$392$	7.10713e9	+	1.25318e9i	0.300989	+	0.0530724i
$393$		0			0
$394$	1.83282e9	−	1.53792e9i	0.0760561	−	0.0638186i
$395$	2.40911e10	+	1.39090e10i	0.989620	+	0.571357i
$396$		0			0
$397$	1.01278e10	+	1.75419e10i	0.407712	+	0.706179i	0.994633	−	0.103466i	$-0.0329932\pi$
$397$	1.01278e10	+	1.75419e10i	0.407712	+	0.706179i	−0.586921	+	0.809645i	$0.699660\pi$
$398$	−7.25513e8	+	1.99333e9i	−0.0289143	+	0.0794414i
$399$		0			0
$400$	−9.35600e8	−	7.85061e8i	−0.0365469	−	0.0306665i
$401$	−9.60582e9	−	2.63918e10i	−0.371498	−	1.02068i	−0.974783	−	0.223157i	$-0.928364\pi$
$401$	−9.60582e9	−	2.63918e10i	−0.371498	−	1.02068i	0.603284	−	0.797526i	$-0.293858\pi$
$402$		0			0
$403$	−1.30544e9	−	7.40353e9i	−0.0494923	−	0.280685i
$404$		−	3.32720e10i		−	1.24897i
$405$		0			0
$406$	−6.69576e8			−0.0246431
$407$	9.49609e9	−	1.67442e9i	0.346073	−	0.0610219i
$408$		0			0
$409$	2.22849e10	−	8.11103e9i	0.796374	−	0.289856i	0.0883910	−	0.996086i	$-0.471828\pi$
$409$	2.22849e10	−	8.11103e9i	0.796374	−	0.289856i	0.707983	+	0.706229i	$0.249605\pi$
$410$	−5.01054e7	+	5.97133e7i	−0.00177317	+	0.00211318i
$411$		0			0
$412$	2.79963e10	+	1.01898e10i	0.971654	+	0.353653i
$413$	−3.46145e9	+	1.99847e9i	−0.118976	+	0.0686906i
$414$		0			0
$415$	1.90695e10	−	3.30294e10i	0.642906	−	1.11355i
$416$	1.29357e9	+	1.54162e9i	0.0431934	+	0.0514759i
$417$		0			0
$418$	−1.87215e8	+	1.06175e9i	−0.00613248	+	0.0347790i
$419$	−1.55067e10	−	2.73425e9i	−0.503111	−	0.0887120i	−0.0836677	−	0.996494i	$-0.526663\pi$
$419$	−1.55067e10	−	2.73425e9i	−0.503111	−	0.0887120i	−0.419443	+	0.907782i	$0.637775\pi$
$420$		0			0
$421$	3.24333e9	−	2.72148e9i	0.103244	−	0.0866316i	−0.589705	−	0.807619i	$-0.700756\pi$
$421$	3.24333e9	−	2.72148e9i	0.103244	−	0.0866316i	0.692948	+	0.720987i	$0.256311\pi$
$422$	−4.92857e8	−	2.84551e8i	−0.0155407	−	0.00897244i
$423$		0			0
$424$	−6.30706e9	−	1.09241e10i	−0.195148	−	0.338006i
$425$	2.18958e8	−	6.01583e8i	0.00671128	−	0.0184391i
$426$		0			0
$427$	−4.23835e9	−	3.55640e9i	−0.127493	−	0.106979i
$428$	9.83228e9	+	2.70140e10i	0.293008	+	0.805033i
$429$		0			0
$430$	−2.43955e8	−	1.38354e9i	−0.00713569	−	0.0404685i
$431$		−	5.43801e10i		−	1.57591i	−0.615734	−	0.787954i	$-0.711140\pi$
$431$		−	5.43801e10i		−	1.57591i	0.615734	−	0.787954i	$-0.288860\pi$
$432$		0			0
$433$	1.01330e10			0.288261			0.144130	−	0.989559i	$-0.453962\pi$
$433$	1.01330e10			0.288261			0.144130	+	0.989559i	$0.453962\pi$
$434$	−1.13670e9	+	2.00431e8i	−0.0320395	+	0.00564944i
$435$		0			0
$436$	−7.47964e9	+	2.72237e9i	−0.206983	+	0.0753356i
$437$	8.06760e9	−	9.61459e9i	0.221217	−	0.263636i
$438$		0			0
$439$	4.09720e10	+	1.49126e10i	1.10314	+	0.401509i	0.828471	−	0.560031i	$-0.189211\pi$
$439$	4.09720e10	+	1.49126e10i	1.10314	+	0.401509i	0.274665	+	0.961540i	$0.411433\pi$
$440$	4.76391e9	−	2.75044e9i	0.127102	−	0.0733824i
$441$		0			0
$442$	−1.68463e8	+	2.91787e8i	−0.00441383	+	0.00764498i
$443$	2.87742e10	+	3.42918e10i	0.747117	+	0.890379i	0.996961	−	0.0779071i	$-0.0248238\pi$
$443$	2.87742e10	+	3.42918e10i	0.747117	+	0.890379i	−0.249844	+	0.968286i	$0.580379\pi$
$444$		0			0
$445$	4.26642e9	−	2.41961e10i	0.108799	−	0.617028i
$446$	1.59948e9	+	2.82031e8i	0.0404239	+	0.00712783i
$447$		0			0
$448$	−2.84873e9	+	2.39037e9i	−0.0707195	+	0.0593407i
$449$	3.94571e10	+	2.27806e10i	0.970823	+	0.560505i	0.899487	−	0.436947i	$-0.143940\pi$
$449$	3.94571e10	+	2.27806e10i	0.970823	+	0.560505i	0.0713360	+	0.997452i	$0.477274\pi$
$450$		0			0
$451$	1.64552e8	+	2.85013e8i	0.00397738	+	0.00688903i
$452$	−5.92346e9	+	1.62746e10i	−0.141913	+	0.389903i
$453$		0			0
$454$	2.04172e9	+	1.71320e9i	0.0480587	+	0.0403260i
$455$	2.39762e8	+	6.58740e8i	0.00559415	+	0.0153698i
$456$		0			0
$457$	−7.31714e9	−	4.14976e10i	−0.167755	−	0.951388i	−0.946178	−	0.323647i	$-0.895091\pi$
$457$	−7.31714e9	−	4.14976e10i	−0.167755	−	0.951388i	0.778422	−	0.627741i	$-0.216020\pi$
$458$		−	4.93906e9i		−	0.112249i
$459$		0			0
$460$	−3.16220e10			−0.706248
$461$	−1.81731e10	+	3.20440e9i	−0.402369	+	0.0709484i	−0.371170	−	0.928565i	$-0.621043\pi$
$461$	−1.81731e10	+	3.20440e9i	−0.402369	+	0.0709484i	−0.0311982	+	0.999513i	$0.509932\pi$
$462$		0			0
$463$	−2.73595e10	+	9.95805e9i	−0.595367	+	0.216696i	−0.622088	−	0.782947i	$-0.713715\pi$
$463$	−2.73595e10	+	9.95805e9i	−0.595367	+	0.216696i	0.0267215	+	0.999643i	$0.491493\pi$
$464$	−4.03209e10	+	4.80525e10i	−0.869877	+	1.03668i
$465$		0			0
$466$	1.08507e10	+	3.94934e9i	0.230099	+	0.0837493i
$467$	−4.63413e10	+	2.67552e10i	−0.974319	+	0.562523i	−0.900550	−	0.434752i	$-0.856836\pi$
$467$	−4.63413e10	+	2.67552e10i	−0.974319	+	0.562523i	−0.0737688	+	0.997275i	$0.523503\pi$
$468$		0			0
$469$	1.60444e9	−	2.77897e9i	0.0331613	−	0.0574370i
$470$	6.38683e9	+	7.61153e9i	0.130886	+	0.155984i
$471$		0			0
$472$	3.39485e9	−	1.92531e10i	0.0683994	−	0.387912i
$473$	−5.84128e9	−	1.02997e9i	−0.116698	−	0.0205770i
$474$		0			0
$475$	−9.78177e8	+	8.20788e8i	−0.0192151	+	0.0161234i
$476$	−1.78357e9	−	1.02975e9i	−0.0347427	−	0.0200587i
$477$		0			0
$478$	−1.75476e9	−	3.03934e9i	−0.0336130	−	0.0582194i
$479$	−9.54151e9	+	2.62151e10i	−0.181249	+	0.497977i	−0.996730	−	0.0808069i	$-0.974250\pi$
$479$	−9.54151e9	+	2.62151e10i	−0.181249	+	0.497977i	0.815481	+	0.578784i	$0.196473\pi$
$480$		0			0
$481$	−4.60432e9	−	3.86348e9i	−0.0860171	−	0.0721769i
$482$	−2.74095e9	−	7.53071e9i	−0.0507825	−	0.139524i
$483$		0			0
$484$	7.30416e9	+	4.14240e10i	0.133103	+	0.754867i
$485$		−	8.88899e10i		−	1.60652i
$486$		0			0
$487$	−5.43062e10			−0.965458			−0.482729	−	0.875770i	$-0.660354\pi$
$487$	−5.43062e10			−0.965458			−0.482729	+	0.875770i	$0.660354\pi$
$488$	2.66512e10	−	4.69932e9i	0.469934	−	0.0828621i
$489$		0			0
$490$	−8.59387e9	+	3.12791e9i	−0.149075	+	0.0542588i
$491$	−2.12598e10	+	2.53364e10i	−0.365791	+	0.435933i	−0.917276	−	0.398252i	$-0.869617\pi$
$491$	−2.12598e10	+	2.53364e10i	−0.365791	+	0.435933i	0.551485	+	0.834185i	$0.314061\pi$
$492$		0			0
$493$	−3.08974e10	−	1.12457e10i	−0.523039	−	0.190371i
$494$	5.81995e8	−	3.36015e8i	0.00977263	−	0.00564223i
$495$		0			0
$496$	−5.40663e10	+	9.36455e10i	−0.893305	+	1.54725i
$497$	4.55411e8	+	5.42737e8i	0.00746410	+	0.00889537i
$498$		0			0
$499$	−7.01014e9	+	3.97565e10i	−0.113064	+	0.641218i	0.874626	+	0.484798i	$0.161107\pi$
$499$	−7.01014e9	+	3.97565e10i	−0.113064	+	0.641218i	−0.987691	+	0.156421i	$0.950004\pi$
$500$	−5.83996e10	−	1.02974e10i	−0.934393	−	0.164759i
$501$		0			0
$502$	−6.26692e9	+	5.25857e9i	−0.0986823	+	0.0828043i
$503$	1.03883e11	+	5.99768e10i	1.62283	+	0.936940i	0.986159	+	0.165801i	$0.0530211\pi$
$503$	1.03883e11	+	5.99768e10i	1.62283	+	0.936940i	0.636668	+	0.771138i	$0.280312\pi$
$504$		0			0
$505$	4.26933e10	+	7.39469e10i	0.656438	+	1.13698i
$506$	1.14693e9	−	3.15117e9i	0.0174959	−	0.0480695i
$507$		0			0
$508$	−8.93935e10	−	7.50100e10i	−1.34230	−	1.12633i
$509$	−1.99802e10	−	5.48952e10i	−0.297666	−	0.817830i	−0.994889	−	0.100976i	$-0.967803\pi$
$509$	−1.99802e10	−	5.48952e10i	−0.297666	−	0.817830i	0.697223	−	0.716854i	$-0.254419\pi$
$510$		0			0
$511$	7.86890e7	+	4.46268e8i	0.00115407	+	0.00654503i
$512$		−	4.86471e10i		−	0.707908i
$513$		0			0
$514$	2.57709e9			0.0369213
$515$	−7.52968e10	+	1.32768e10i	−1.07040	+	0.188741i
$516$		0			0
$517$	3.94203e10	−	1.43478e10i	0.551770	−	0.200828i
$518$	−5.93178e8	+	7.06922e8i	−0.00823884	+	0.00981867i
$519$		0			0
$520$	−3.22208e9	−	1.17274e9i	−0.0440680	−	0.0160394i
$521$	−6.93877e9	+	4.00610e9i	−0.0941741	+	0.0543715i	−0.546347	−	0.837559i	$-0.683982\pi$
$521$	−6.93877e9	+	4.00610e9i	−0.0941741	+	0.0543715i	0.452173	+	0.891930i	$0.350649\pi$
$522$		0			0
$523$	−2.54192e10	+	4.40273e10i	−0.339746	+	0.588457i	−0.984385	−	0.176030i	$-0.943674\pi$
$523$	−2.54192e10	+	4.40273e10i	−0.339746	+	0.588457i	0.644639	+	0.764487i	$0.277008\pi$
$524$	8.45897e10	+	1.00810e11i	1.12200	+	1.33715i
$525$		0			0
$526$	2.15685e9	−	1.22321e10i	0.0281758	−	0.159793i
$527$	−5.58189e10	−	9.84238e9i	−0.723667	−	0.127602i
$528$		0			0
$529$	3.00845e10	−	2.52439e10i	0.384168	−	0.322355i
$530$	1.38435e10	+	7.99257e9i	0.175446	+	0.101294i
$531$		0			0
$532$	2.05392e9	+	3.55750e9i	0.0256412	+	0.0444118i
$533$	7.01622e7	−	1.92769e8i	0.000869349	−	0.00238852i
$534$		0			0
$535$	−5.65154e10	−	4.74221e10i	−0.689845	−	0.578849i
$536$	5.36818e9	+	1.47489e10i	0.0650381	+	0.178691i
$537$		0			0
$538$	−4.70280e8	−	2.66709e9i	−0.00561342	−	0.0318353i
$539$			3.86117e10i			0.457472i
$540$		0			0
$541$	4.99438e10			0.583032			0.291516	−	0.956566i	$-0.405840\pi$
$541$	4.99438e10			0.583032			0.291516	+	0.956566i	$0.405840\pi$
$542$	−1.15052e10	+	2.02868e9i	−0.133321	+	0.0235081i
$543$		0			0
$544$	1.42578e10	−	5.18941e9i	0.162801	−	0.0592546i
$545$	1.31302e10	−	1.56480e10i	0.148829	−	0.177367i
$546$		0			0
$547$	−2.21042e10	−	8.04528e9i	−0.246903	−	0.0898653i	0.215604	−	0.976481i	$-0.430828\pi$
$547$	−2.21042e10	−	8.04528e9i	−0.246903	−	0.0898653i	−0.462507	+	0.886616i	$0.653050\pi$
$548$	−6.87654e10	+	3.97017e10i	−0.762514	+	0.440238i
$549$		0			0
$550$	−1.70586e8	+	2.95463e8i	−0.00186420	+	0.00322888i
$551$	4.21558e10	+	5.02393e10i	0.457352	+	0.545051i
$552$		0			0
$553$	−1.95181e9	+	1.10693e10i	−0.0208707	+	0.118364i
$554$	−2.16540e10	−	3.81819e9i	−0.229879	−	0.0405339i
$555$		0			0
$556$	1.05401e11	−	8.84420e10i	1.10293	−	0.925464i
$557$	1.24286e11	+	7.17563e10i	1.29122	+	0.745486i	0.978870	−	0.204482i	$-0.0655509\pi$
$557$	1.24286e11	+	7.17563e10i	1.29122	+	0.745486i	0.312349	+	0.949968i	$0.398884\pi$
$558$		0			0
$559$	1.84861e9	+	3.20188e9i	0.0189320	+	0.0327912i
$560$	3.44865e9	−	9.47509e9i	0.0350669	−	0.0963454i
$561$		0			0
$562$	−9.76746e9	−	8.19588e9i	−0.0979121	−	0.0821580i
$563$	−1.27931e10	−	3.51488e10i	−0.127334	−	0.349846i	0.859601	−	0.510965i	$-0.170712\pi$
$563$	−1.27931e10	−	3.51488e10i	−0.127334	−	0.349846i	−0.986935	+	0.161119i	$0.948490\pi$
$564$		0			0
$565$	−7.71799e9	−	4.37709e10i	−0.0757375	−	0.429528i
$566$			1.96458e10i			0.191427i
$567$		0			0
$568$	−3.46544e9			−0.0332939
$569$	−1.61367e11	+	2.84534e10i	−1.53945	+	0.271447i	−0.878043	−	0.478581i	$-0.841151\pi$
$569$	−1.61367e11	+	2.84534e10i	−1.53945	+	0.271447i	−0.661407	+	0.750028i	$0.730040\pi$
$570$		0			0
$571$	−1.72062e11	+	6.26253e10i	−1.61860	+	0.589122i	−0.983115	−	0.182990i	$-0.941422\pi$
$571$	−1.72062e11	+	6.26253e10i	−1.61860	+	0.589122i	−0.635486	+	0.772112i	$0.719200\pi$
$572$	−4.59499e9	+	5.47609e9i	−0.0429240	+	0.0511548i
$573$		0			0
$574$	−2.95967e7	−	1.07723e7i	−0.000272644	−	9.92344e-5i
$575$	3.43961e9	−	1.98586e9i	0.0314657	−	0.0181668i
$576$		0			0
$577$	−1.38743e10	+	2.40309e10i	−0.125172	+	0.216804i	−0.921800	−	0.387665i	$-0.873282\pi$
$577$	−1.38743e10	+	2.40309e10i	−0.125172	+	0.216804i	0.796628	+	0.604470i	$0.206615\pi$
$578$	−9.59722e9	−	1.14375e10i	−0.0859873	−	0.102476i
$579$		0			0
$580$	2.86927e10	−	1.62725e11i	0.253548	−	1.43794i
$581$	1.51762e10	+	2.67597e9i	0.133186	+	0.0234842i
$582$		0			0
$583$	5.16996e10	−	4.33811e10i	0.447520	−	0.375514i
$584$	−1.91954e9	−	1.10825e9i	−0.0165023	−	0.00952763i
$585$		0			0
$586$	1.51476e10	+	2.62364e10i	0.128456	+	0.222492i
$587$	−1.84410e10	+	5.06662e10i	−0.155322	+	0.426743i	−0.992808	−	0.119715i	$-0.961802\pi$
$587$	−1.84410e10	+	5.06662e10i	−0.155322	+	0.426743i	0.837487	+	0.546458i	$0.184024\pi$
$588$		0			0
$589$	8.66040e10	+	7.26694e10i	0.719576	+	0.603796i
$590$	8.47348e9	+	2.32807e10i	0.0699284	+	0.192127i
$591$		0			0
$592$	1.50124e10	+	8.51396e10i	0.122226	+	0.693178i
$593$		−	1.98579e11i		−	1.60589i	−0.596054	−	0.802945i	$-0.703265\pi$
$593$		−	1.98579e11i		−	1.60589i	0.596054	−	0.802945i	$-0.296735\pi$
$594$		0			0
$595$	5.28532e9			0.0421700
$596$	1.74387e11	−	3.07491e10i	1.38207	−	0.243696i
$597$		0			0
$598$	−1.96422e9	+	7.14917e8i	−0.0153598	+	0.00559050i
$599$	1.00906e11	−	1.20255e11i	0.783808	−	0.934105i	−0.215291	−	0.976550i	$-0.569070\pi$
$599$	1.00906e11	−	1.20255e11i	0.783808	−	0.934105i	0.999099	+	0.0424444i	$0.0135145\pi$
$600$		0			0
$601$	1.23406e10	+	4.49162e9i	0.0945887	+	0.0344275i	0.388881	−	0.921288i	$-0.372862\pi$
$601$	1.23406e10	+	4.49162e9i	0.0945887	+	0.0344275i	−0.294292	+	0.955715i	$0.595084\pi$
$602$	4.91599e8	−	2.83825e8i	0.00374305	−	0.00216105i
$603$		0			0
$604$	4.26340e10	−	7.38443e10i	0.320338	−	0.554842i
$605$	−6.93870e10	−	8.26922e10i	−0.517912	−	0.617224i
$606$		0			0
$607$	−2.69000e10	+	1.52558e11i	−0.198152	+	1.12377i	0.709706	+	0.704497i	$0.248828\pi$
$607$	−2.69000e10	+	1.52558e11i	−0.198152	+	1.12377i	−0.907858	+	0.419277i	$0.862284\pi$
$608$	−2.98038e10	−	5.25521e9i	−0.218101	−	0.0384571i
$609$		0			0
$610$	−2.62711e10	+	2.20441e10i	−0.189740	+	0.159211i
$611$	−2.26456e10	−	1.30744e10i	−0.162487	−	0.0938118i
$612$		0			0
$613$	−6.82522e10	−	1.18216e11i	−0.483364	−	0.837212i	0.516453	−	0.856315i	$-0.327252\pi$
$613$	−6.82522e10	−	1.18216e11i	−0.483364	−	0.837212i	−0.999818	+	0.0191038i	$0.993919\pi$
$614$	1.10881e10	−	3.04644e10i	0.0780163	−	0.214348i
$615$		0			0
$616$	1.70266e9	+	1.42870e9i	0.0118251	+	0.00992244i
$617$	−1.05167e10	−	2.88945e10i	−0.0725672	−	0.199377i	0.898106	−	0.439778i	$-0.144943\pi$
$617$	−1.05167e10	−	2.88945e10i	−0.0725672	−	0.199377i	−0.970673	+	0.240402i	$0.922721\pi$
$618$		0			0
$619$	2.29396e10	+	1.30097e11i	0.156251	+	0.886143i	0.957633	+	0.287991i	$0.0929872\pi$
$619$	2.29396e10	+	1.30097e11i	0.156251	+	0.886143i	−0.801382	+	0.598152i	$0.795902\pi$
$620$		−	2.84837e11i		−	1.92765i
$621$		0			0
$622$	3.15852e10			0.211019
$623$	9.77655e9	−	1.72387e9i	0.0648983	−	0.0114433i
$624$		0			0
$625$	1.50385e11	−	5.47355e10i	0.985561	−	0.358715i
$626$	−1.45327e10	+	1.73195e10i	−0.0946347	+	0.112781i
$627$		0			0
$628$	2.11224e11	+	7.68792e10i	1.35801	+	0.494277i
$629$	−3.92450e10	+	2.26581e10i	−0.250716	+	0.144751i
$630$		0			0
$631$	6.47545e10	−	1.12158e11i	0.408463	−	0.707478i	−0.586255	−	0.810127i	$-0.699398\pi$
$631$	6.47545e10	−	1.12158e11i	0.408463	−	0.707478i	0.994718	+	0.102648i	$0.0327316\pi$
$632$	−3.53392e10	−	4.21157e10i	−0.221508	−	0.263983i
$633$		0			0
$634$	1.08410e9	−	6.14824e9i	0.00670984	−	0.0380534i
$635$	2.94926e11	+	5.20035e10i	1.81392	+	0.319843i
$636$		0			0
$637$	1.84370e10	−	1.54705e10i	0.111978	−	0.0939609i
$638$	1.51750e10	+	8.76130e9i	0.0915897	+	0.0528793i
$639$		0			0
$640$	5.06071e10	+	8.76541e10i	0.301642	+	0.522459i
$641$	5.46839e10	−	1.50243e11i	0.323912	−	0.889941i	−0.665706	−	0.746215i	$-0.731869\pi$
$641$	5.46839e10	−	1.50243e11i	0.323912	−	0.889941i	0.989617	−	0.143726i	$-0.0459085\pi$
$642$		0			0
$643$	1.61080e11	+	1.35162e11i	0.942318	+	0.790699i	0.977987	−	0.208665i	$-0.0669118\pi$
$643$	1.61080e11	+	1.35162e11i	0.942318	+	0.790699i	−0.0356691	+	0.999364i	$0.511356\pi$
$644$	−4.37000e9	−	1.20065e10i	−0.0254061	−	0.0698027i
$645$		0			0
$646$	−8.79836e8	−	4.98980e9i	−0.00505210	−	0.0286519i
$647$			1.78264e11i			1.01730i	0.860974	+	0.508648i	$0.169855\pi$
$647$			1.78264e11i			1.01730i	−0.860974	+	0.508648i	$0.830145\pi$
$648$		0			0
$649$	1.04599e11			0.589587
$650$	2.09431e8	−	3.69284e7i	0.00117324	−	0.000206875i
$651$		0			0
$652$	1.19190e11	−	4.33817e10i	0.659554	−	0.240058i
$653$	−6.49968e10	+	7.74602e10i	−0.357470	+	0.426016i	−0.914569	−	0.404430i	$-0.867470\pi$
$653$	−6.49968e10	+	7.74602e10i	−0.357470	+	0.426016i	0.557099	+	0.830446i	$0.311914\pi$
$654$		0			0
$655$	−3.17356e11	−	1.15508e11i	−1.72417	−	0.627548i
$656$	−2.55536e9	+	1.47534e9i	−0.0137986	+	0.00796664i
$657$		0			0
$658$	−2.00738e9	+	3.47688e9i	−0.0107084	+	0.0185475i
$659$	1.04978e9	+	1.25108e9i	0.00556616	+	0.00663349i	0.768820	−	0.639465i	$-0.220844\pi$
$659$	1.04978e9	+	1.25108e9i	0.00556616	+	0.00663349i	−0.763254	+	0.646098i	$0.776400\pi$
$660$		0			0
$661$	−1.54225e10	+	8.74653e10i	−0.0807884	+	0.458174i	0.917398	+	0.397971i	$0.130286\pi$
$661$	−1.54225e10	+	8.74653e10i	−0.0807884	+	0.458174i	−0.998186	+	0.0602023i	$0.980825\pi$
$662$	−3.23290e10	−	5.70047e9i	−0.168329	−	0.0296810i
$663$		0			0
$664$	−5.77414e10	+	4.84508e10i	−0.297040	+	0.249246i
$665$	−9.12968e9	−	5.27102e9i	−0.0466841	−	0.0269531i
$666$		0			0
$667$	−1.01994e11	−	1.76659e11i	−0.515314	−	0.892549i
$668$	7.49564e10	−	2.05941e11i	0.376446	−	1.03428i
$669$		0			0
$670$	−1.52366e10	−	1.27851e10i	−0.0756119	−	0.0634459i
$671$	4.95214e10	+	1.36059e11i	0.244289	+	0.671177i
$672$		0			0
$673$	−1.34793e10	−	7.64450e10i	−0.0657064	−	0.372640i	−0.999875	−	0.0158078i	$-0.994968\pi$
$673$	−1.34793e10	−	7.64450e10i	−0.0657064	−	0.372640i	0.934169	−	0.356832i	$-0.116143\pi$
$674$			4.20842e9i			0.0203929i
$675$		0			0
$676$	−1.99254e11			−0.954160
$677$	1.68693e11	−	2.97451e10i	0.803050	−	0.141599i	0.242965	−	0.970035i	$-0.421880\pi$
$677$	1.68693e11	−	2.97451e10i	0.803050	−	0.141599i	0.560084	+	0.828436i	$0.310769\pi$
$678$		0			0
$679$	3.37504e10	−	1.22842e10i	0.158782	−	0.0577918i
$680$	−1.66173e10	+	1.98037e10i	−0.0777187	+	0.0926215i
$681$		0			0
$682$	2.83843e10	+	1.03311e10i	0.131202	+	0.0477537i
$683$	−3.58504e11	+	2.06982e11i	−1.64744	+	0.951153i	−0.669362	+	0.742937i	$0.733432\pi$
$683$	−3.58504e11	+	2.06982e11i	−1.64744	+	0.951153i	−0.978083	+	0.208216i	$0.933234\pi$
$684$		0			0
$685$	1.01887e11	−	1.76474e11i	0.462762	−	0.801527i
$686$	−4.77848e9	−	5.69477e9i	−0.0215771	−	0.0257146i
$687$		0			0
$688$	9.23450e9	−	5.23715e10i	0.0412154	−	0.233744i
$689$	−4.14288e10	−	7.30502e9i	−0.183834	−	0.0324149i
$690$		0			0
$691$	−3.19102e11	+	2.67758e11i	−1.39964	+	1.17444i	−0.438383	+	0.898788i	$0.644449\pi$
$691$	−3.19102e11	+	2.67758e11i	−1.39964	+	1.17444i	−0.961258	+	0.275650i	$0.911107\pi$
$692$	−3.05691e11	−	1.76491e11i	−1.33309	−	0.769657i
$693$		0			0
$694$	−1.01667e10	−	1.76092e10i	−0.0438269	−	0.0759105i
$695$	−1.20768e11	+	3.31808e11i	−0.517623	+	1.42216i
$696$		0			0
$697$	−1.18481e9	−	9.94173e8i	−0.00502016	−	0.00421241i
$698$	8.90386e7	+	2.44632e8i	0.000375108	+	0.00103060i
$699$		0			0
$700$	2.25729e8	+	1.28017e9i	0.000940144	+	0.00533182i
$701$			4.23591e11i			1.75418i	0.480326	+	0.877090i	$0.340518\pi$
$701$			4.23591e11i			1.75418i	−0.480326	+	0.877090i	$0.659482\pi$
$702$		0			0
$703$	9.03874e10			0.370072
$704$	9.58403e10	−	1.68992e10i	0.390173	−	0.0687980i
$705$		0			0
$706$	2.25345e10	−	8.20191e9i	0.0907048	−	0.0330138i
$707$	−2.21767e10	+	2.64292e10i	−0.0887606	+	0.105781i
$708$		0			0
$709$	−1.98886e11	−	7.23886e10i	−0.787081	−	0.286474i	−0.0829588	−	0.996553i	$-0.526437\pi$
$709$	−1.98886e11	−	7.23886e10i	−0.787081	−	0.286474i	−0.704122	+	0.710079i	$0.748659\pi$
$710$	3.80320e9	−	2.19578e9i	0.0149663	−	0.00864082i
$711$		0			0
$712$	−2.42788e10	+	4.20521e10i	−0.0944728	+	0.163632i
$713$	−2.26030e11	−	2.69372e11i	−0.874598	−	1.04231i
$714$		0			0
$715$	3.18564e9	−	1.80667e10i	0.0121891	−	0.0691281i
$716$	−3.11224e10	−	5.48772e9i	−0.118419	−	0.0208805i
$717$		0			0
$718$	−4.88925e10	+	4.10257e10i	−0.183969	+	0.154368i
$719$	3.55351e11	+	2.05162e11i	1.32966	+	0.767681i	0.985247	−	0.171137i	$-0.0547439\pi$
$719$	3.55351e11	+	2.05162e11i	1.32966	+	0.767681i	0.344415	+	0.938817i	$0.388077\pi$
$720$		0			0
$721$	−1.54467e10	−	2.67545e10i	−0.0571603	−	0.0990046i
$722$	1.10915e10	−	3.04737e10i	0.0408171	−	0.112144i
$723$		0			0
$724$	8.81714e10	+	7.39846e10i	0.320903	+	0.269269i
$725$	7.09812e9	+	1.95019e10i	0.0256916	+	0.0705871i
$726$		0			0
$727$	−5.40742e10	−	3.06670e11i	−0.193576	−	1.09783i	−0.914432	−	0.404741i	$-0.867362\pi$
$727$	−5.40742e10	−	3.06670e11i	−0.193576	−	1.09783i	0.720855	−	0.693086i	$-0.243749\pi$
$728$		−	1.38545e9i		−	0.00493249i
$729$		0			0
$730$	2.80884e9			0.00989088
$731$	2.74517e10	−	4.84047e9i	0.0961389	−	0.0169519i
$732$		0			0
$733$	−1.43090e11	+	5.20803e10i	−0.495669	+	0.180409i	−0.577745	−	0.816217i	$-0.696067\pi$
$733$	−1.43090e11	+	5.20803e10i	−0.495669	+	0.180409i	0.0820759	+	0.996626i	$0.473845\pi$
$734$	−1.04693e9	+	1.24768e9i	−0.00360688	+	0.00429851i
$735$		0			0
$736$	8.84547e10	+	3.21949e10i	0.301446	+	0.109717i
$737$	−7.27248e10	+	4.19877e10i	−0.246497	+	0.142315i
$738$		0			0
$739$	−3.62658e10	+	6.28143e10i	−0.121596	+	0.210611i	−0.920397	−	0.390984i	$-0.872135\pi$
$739$	−3.62658e10	+	6.28143e10i	−0.121596	+	0.210611i	0.798801	+	0.601595i	$0.205468\pi$
$740$	−1.46382e11	−	1.74451e11i	−0.488158	−	0.581764i
$741$		0			0
$742$	−1.12157e9	+	6.36076e9i	−0.00370009	+	0.0209842i
$743$	2.97391e11	+	5.24380e10i	0.975826	+	0.172064i	0.638751	−	0.769413i	$-0.279451\pi$
$743$	2.97391e11	+	5.24380e10i	0.975826	+	0.172064i	0.337075	+	0.941478i	$0.390562\pi$
$744$		0			0
$745$	−3.48118e11	+	2.92106e11i	−1.13006	+	0.948234i
$746$	2.76746e9	+	1.59780e9i	0.00893566	+	0.00515901i
$747$		0			0
$748$	2.69482e10	+	4.66756e10i	0.0860842	+	0.149102i
$749$	1.01954e10	−	2.80117e10i	0.0323950	−	0.0890046i
$750$		0			0
$751$	1.35125e11	+	1.13384e11i	0.424793	+	0.356443i	0.829983	−	0.557789i	$-0.188350\pi$
$751$	1.35125e11	+	1.13384e11i	0.424793	+	0.356443i	−0.405190	+	0.914232i	$0.632795\pi$
$752$	1.28639e11	+	3.53433e11i	0.402255	+	1.10519i
$753$		0			0
$754$	−1.89665e9	−	1.07564e10i	−0.00586815	−	0.0332799i
$755$			2.18825e11i			0.673455i
$756$		0			0
$757$	1.08704e11			0.331025			0.165513	−	0.986208i	$-0.447072\pi$
$757$	1.08704e11			0.331025			0.165513	+	0.986208i	$0.447072\pi$
$758$	5.48401e10	−	9.66979e9i	0.166120	−	0.0292914i
$759$		0			0
$760$	4.84544e10	−	1.76360e10i	0.145237	−	0.0528621i
$761$	3.21895e11	−	3.83619e11i	0.959788	−	1.14383i	−0.0297499	−	0.999557i	$-0.509471\pi$
$761$	3.21895e11	−	3.83619e11i	0.959788	−	1.14383i	0.989538	−	0.144273i	$-0.0460845\pi$
$762$		0			0
$763$	7.75589e9	+	2.82291e9i	0.0228841	+	0.00832913i
$764$	1.62053e11	−	9.35612e10i	0.475645	−	0.274614i
$765$		0			0
$766$	4.15116e10	−	7.19002e10i	0.120574	−	0.208841i
$767$	−4.19094e10	−	4.99457e10i	−0.121096	−	0.144317i
$768$		0			0
$769$	−7.36249e10	+	4.17547e11i	−0.210533	+	1.19399i	0.677960	+	0.735099i	$0.262864\pi$
$769$	−7.36249e10	+	4.17547e11i	−0.210533	+	1.19399i	−0.888493	+	0.458891i	$0.848247\pi$
$770$	−2.77386e9	−	4.89107e8i	−0.00789082	−	0.00139136i
$771$		0			0
$772$	2.55609e11	−	2.14482e11i	0.719627	−	0.603839i
$773$	−2.87823e11	−	1.66175e11i	−0.806134	−	0.465422i	0.0394773	−	0.999220i	$-0.487431\pi$
$773$	−2.87823e11	−	1.66175e11i	−0.806134	−	0.465422i	−0.845612	+	0.533799i	$0.820764\pi$
$774$		0			0
$775$	1.78877e10	+	3.09825e10i	0.0495848	+	0.0858834i
$776$	−6.00852e10	+	1.65083e11i	−0.165699	+	0.455255i
$777$		0			0
$778$	−7.58765e10	−	6.36679e10i	−0.207104	−	0.173781i
$779$	1.05512e9	+	2.89891e9i	0.00286517	+	0.00787198i
$780$		0			0
$781$	−3.21962e9	−	1.82594e10i	−0.00865368	−	0.0490775i
$782$			1.57596e10i			0.0421424i
$783$		0			0
$784$	−3.46184e11			−0.916310
$785$	−5.68092e11	+	1.00170e11i	−1.49603	+	0.263790i
$786$		0			0
$787$	−4.41598e11	+	1.60728e11i	−1.15114	+	0.418980i	−0.845924	−	0.533303i	$-0.820951\pi$
$787$	−4.41598e11	+	1.60728e11i	−1.15114	+	0.418980i	−0.305215	+	0.952283i	$0.598728\pi$
$788$	−1.53347e11	+	1.82752e11i	−0.397714	+	0.473977i
$789$		0			0
$790$	6.54690e10	+	2.38288e10i	0.168084	+	0.0611777i
$791$	1.55527e10	−	8.97936e9i	0.0397283	−	0.0229371i
$792$		0			0
$793$	4.51263e10	−	7.81610e10i	0.114113	−	0.197650i
$794$	3.26090e10	+	3.88618e10i	0.0820455	+	0.0977781i
$795$		0			0
$796$	3.67288e10	−	2.08299e11i	0.0914859	−	0.518842i
$797$	4.55285e10	+	8.02790e9i	0.112837	+	0.0198961i	0.229781	−	0.973242i	$-0.426199\pi$
$797$	4.55285e10	+	8.02790e9i	0.112837	+	0.0198961i	−0.116945	+	0.993138i	$0.537310\pi$
$798$		0			0
$799$	−1.51025e11	+	1.26725e11i	−0.370563	+	0.310939i
$800$	−8.29378e9	−	4.78842e9i	−0.0202485	−	0.0116905i
$801$		0			0
$802$	−3.51703e10	−	6.09168e10i	−0.0850117	−	0.147245i
$803$	4.05597e9	−	1.11437e10i	0.00975512	−	0.0268020i
$804$		0			0
$805$	2.51185e10	+	2.10769e10i	0.0598150	+	0.0501908i
$806$	−6.43965e9	−	1.76928e10i	−0.0152589	−	0.0419234i
$807$		0			0
$808$	−2.93037e10	−	1.66190e11i	−0.0687508	−	0.389905i
$809$			1.18357e11i			0.276312i	0.990410	+	0.138156i	$0.0441175\pi$
$809$			1.18357e11i			0.276312i	−0.990410	+	0.138156i	$0.955882\pi$
$810$		0			0
$811$	9.39449e10			0.217165			0.108582	−	0.994087i	$-0.465369\pi$
$811$	9.39449e10			0.217165			0.108582	+	0.994087i	$0.465369\pi$
$812$	6.57497e10	−	1.15935e10i	0.151241	−	0.0266679i
$813$		0			0
$814$	2.26936e10	−	8.25978e9i	0.0516898	−	0.0188136i
$815$	−2.09234e11	+	2.49355e11i	−0.474244	+	0.565182i
$816$		0			0
$817$	−5.22464e10	−	1.90161e10i	−0.117265	−	0.0426810i
$818$	5.14373e10	−	2.96974e10i	0.114886	−	0.0663292i
$819$		0			0
$820$	3.88624e9	−	6.73117e9i	0.00859557	−	0.0148880i
$821$	−1.46122e11	−	1.74141e11i	−0.321619	−	0.383291i	0.580875	−	0.813993i	$-0.302710\pi$
$821$	−1.46122e11	−	1.74141e11i	−0.321619	−	0.383291i	−0.902494	+	0.430702i	$0.858266\pi$
$822$		0			0
$823$	6.39160e9	−	3.62485e10i	0.0139319	−	0.0790117i	−0.977049	−	0.213014i	$-0.931672\pi$
$823$	6.39160e9	−	3.62485e10i	0.0139319	−	0.0790117i	0.990981	+	0.134003i	$0.0427830\pi$
$824$	1.48813e11	+	2.62397e10i	0.322798	+	0.0569180i
$825$		0			0
$826$	−7.66841e9	+	6.43456e9i	−0.0164735	+	0.0138229i
$827$	−3.00935e11	−	1.73745e11i	−0.643354	−	0.371441i	0.142551	−	0.989787i	$-0.454469\pi$
$827$	−3.00935e11	−	1.73745e11i	−0.643354	−	0.371441i	−0.785906	+	0.618347i	$0.787803\pi$
$828$		0			0
$829$	−2.97922e11	−	5.16016e11i	−0.630790	−	1.09256i	−0.987391	−	0.158303i	$-0.949398\pi$
$829$	−2.97922e11	−	5.16016e11i	−0.630790	−	1.09256i	0.356601	−	0.934257i	$-0.383936\pi$
$830$	3.26697e10	−	8.97592e10i	0.0688387	−	0.189133i
$831$		0			0
$832$	−4.64695e10	−	3.89926e10i	−0.0969784	−	0.0813745i
$833$	−6.20629e10	−	1.70516e11i	−0.128900	−	0.354149i
$834$		0			0
$835$	9.76647e10	+	5.53884e11i	0.200905	+	1.13939i
$836$		−	1.07501e11i		−	0.220084i
$837$		0			0
$838$	−3.94359e10			−0.0799678
$839$	3.77521e11	−	6.65672e10i	0.761892	−	0.134342i	0.220816	−	0.975316i	$-0.429128\pi$
$839$	3.77521e11	−	6.65672e10i	0.761892	−	0.134342i	0.541077	+	0.840973i	$0.318017\pi$
$840$		0			0
$841$	5.31543e11	−	1.93466e11i	1.06256	−	0.386741i
$842$	6.81598e9	−	8.12297e9i	0.0135606	−	0.0161609i
$843$		0			0
$844$	5.33235e10	+	1.94082e10i	0.105087	+	0.0382486i
$845$	4.42842e11	−	2.55675e11i	0.868604	−	0.501489i
$846$		0			0
$847$	2.18083e10	−	3.77730e10i	0.0423729	−	0.0733919i
$848$	3.88945e11	+	4.63526e11i	0.752150	+	0.896377i
$849$		0			0
$850$	2.78422e8	−	1.57901e9i	0.000533369	−	0.00302489i
$851$	−2.76869e11	−	4.88195e10i	−0.527906	−	0.0930840i
$852$		0			0
$853$	6.58027e11	−	5.52150e11i	1.24293	−	1.04294i	0.245644	−	0.969360i	$-0.421001\pi$
$853$	6.58027e11	−	5.52150e11i	1.24293	−	1.04294i	0.997289	−	0.0735846i	$-0.0234439\pi$
$854$	−1.20004e10	−	6.92845e9i	−0.0225614	−	0.0130258i
$855$		0			0
$856$	7.29032e10	+	1.26272e11i	0.135785	+	0.235186i
$857$	1.21489e11	−	3.33788e11i	0.225223	−	0.618795i	−0.774685	−	0.632347i	$-0.782092\pi$
$857$	1.21489e11	−	3.33788e11i	0.225223	−	0.618795i	0.999908	+	0.0135519i	$0.00431385\pi$
$858$		0			0
$859$	3.20921e11	+	2.69285e11i	0.589421	+	0.494583i	0.888026	−	0.459794i	$-0.152077\pi$
$859$	3.20921e11	+	2.69285e11i	0.589421	+	0.494583i	−0.298605	+	0.954377i	$0.596521\pi$
$860$	4.79109e10	+	1.31634e11i	0.0875872	+	0.240644i
$861$		0			0
$862$	−2.36501e10	−	1.34127e11i	−0.0428356	−	0.242933i
$863$			3.69630e11i			0.666383i	0.942859	+	0.333191i	$0.108125\pi$
$863$			3.69630e11i			0.666383i	−0.942859	+	0.333191i	$0.891875\pi$
$864$		0			0
$865$	9.05862e11			1.61807
$866$	2.49926e10	−	4.40687e9i	0.0444365	−	0.00783536i
$867$		0			0
$868$	1.08149e11	−	3.93630e10i	0.190521	−	0.0693441i
$869$	1.89075e11	−	2.25331e11i	0.331554	−	0.395131i
$870$		0			0
$871$	4.91876e10	+	1.79028e10i	0.0854639	+	0.0311063i
$872$	−3.49622e10	+	2.01855e10i	−0.0604691	+	0.0349118i
$873$		0			0
$874$	1.57170e10	−	2.72227e10i	0.0269355	−	0.0466536i
$875$	3.95255e10	+	4.71046e10i	0.0674287	+	0.0803584i
$876$		0			0
$877$	1.45845e11	−	8.27127e11i	0.246543	−	1.39821i	−0.570339	−	0.821409i	$-0.693188\pi$
$877$	1.45845e11	−	8.27127e11i	0.246543	−	1.39821i	0.816882	−	0.576805i	$-0.195701\pi$
$878$	1.07542e11	+	1.89625e10i	0.180967	+	0.0319093i
$879$		0			0
$880$	−2.02139e11	+	1.69615e11i	−0.337070	+	0.282835i
$881$	−6.57619e11	−	3.79677e11i	−1.09162	−	0.630246i	−0.157612	−	0.987501i	$-0.550379\pi$
$881$	−6.57619e11	−	3.79677e11i	−1.09162	−	0.630246i	−0.934007	+	0.357255i	$0.883713\pi$
$882$		0			0
$883$	5.00897e11	+	8.67579e11i	0.823959	+	1.42714i	0.902712	+	0.430245i	$0.141573\pi$
$883$	5.00897e11	+	8.67579e11i	0.823959	+	1.42714i	−0.0787530	+	0.996894i	$0.525094\pi$
$884$	1.14902e10	−	3.15692e10i	0.0188157	−	0.0516957i
$885$		0			0
$886$	8.58842e10	+	7.20654e10i	0.139373	+	0.116948i
$887$	−2.56509e11	−	7.04753e11i	−0.414389	−	1.13853i	−0.954832	−	0.297145i	$-0.903966\pi$
$887$	−2.56509e11	−	7.04753e11i	−0.414389	−	1.13853i	0.540443	−	0.841380i	$-0.318257\pi$
$888$		0			0
$889$	2.10123e10	+	1.19167e11i	0.0336408	+	0.190786i
$890$		−	6.15342e10i		−	0.0980747i
$891$		0			0
$892$	−1.61946e11			−0.255805
$893$	3.87258e11	−	6.82841e10i	0.608968	−	0.107378i
$894$		0			0
$895$	7.62111e10	−	2.77386e10i	0.118775	−	0.0432306i
$896$	−2.62876e10	+	3.13283e10i	−0.0407867	+	0.0486077i
$897$		0			0
$898$	1.07227e11	+	3.90274e10i	0.164892	+	0.0600157i
$899$	1.59126e12	−	9.18717e11i	2.43615	−	1.40651i
$900$		0			0
$901$	−1.58586e11	+	2.74678e11i	−0.240638	+	0.416798i
$902$	5.29815e8	+	6.31409e8i	0.000800384	+	0.000953861i
$903$		0			0
$904$	−1.52534e10	+	8.65066e10i	−0.0228399	+	0.129532i
$905$	−2.90895e11	−	5.12925e10i	−0.433652	−	0.0764645i
$906$		0			0
$907$	1.50108e11	−	1.25956e11i	0.221807	−	0.186118i	−0.525112	−	0.851033i	$-0.675977\pi$
$907$	1.50108e11	−	1.25956e11i	0.221807	−	0.186118i	0.746919	+	0.664915i	$0.231532\pi$
$908$	−2.30152e11	−	1.32878e11i	−0.338588	−	0.195484i
$909$		0			0
$910$	8.77852e8	+	1.52049e9i	0.00128014	+	0.00221726i
$911$	2.20777e11	−	6.06578e11i	0.320538	−	0.880671i	−0.669868	−	0.742480i	$-0.733649\pi$
$911$	2.20777e11	−	6.06578e11i	0.320538	−	0.880671i	0.990406	−	0.138190i	$-0.0441285\pi$
$912$		0			0
$913$	−3.08932e11	−	2.59225e11i	−0.444611	−	0.373073i
$914$	−3.60949e10	−	9.91700e10i	−0.0517204	−	0.142101i
$915$		0			0
$916$	8.55180e10	+	4.84997e11i	0.121472	+	0.688901i
$917$		−	1.36459e11i		−	0.192985i
$918$		0			0
$919$	−6.41781e11			−0.899756			−0.449878	−	0.893090i	$-0.648532\pi$
$919$	−6.41781e11			−0.899756			−0.449878	+	0.893090i	$0.648532\pi$
$920$	−1.57948e11	+	2.78505e10i	−0.220477	+	0.0388760i
$921$		0			0
$922$	−4.34296e10	+	1.58071e10i	−0.0600983	+	0.0218740i
$923$	−7.42882e9	+	8.85333e9i	−0.0102356	+	0.0121983i
$924$		0			0
$925$	2.68779e10	+	9.78276e9i	0.0367137	+	0.0133627i
$926$	−6.31505e10	+	3.64600e10i	−0.0858881	+	0.0495875i
$927$		0			0
$928$	−2.45934e11	+	4.25970e11i	−0.331609	+	0.574363i
$929$	8.58049e11	+	1.02258e12i	1.15199	+	1.37289i	0.916021	+	0.401129i	$0.131382\pi$
$929$	8.58049e11	+	1.02258e12i	1.15199	+	1.37289i	0.235970	+	0.971760i	$0.424173\pi$
$930$		0			0
$931$	−6.28498e10	+	3.56439e11i	−0.0836576	+	0.474446i
$932$	−1.13388e12	−	1.99934e11i	−1.50281	−	0.264986i
$933$		0			0
$934$	−1.02663e11	+	8.61448e10i	−0.134905	+	0.113199i
$935$	−1.19784e11	−	6.91576e10i	−0.156731	−	0.0904885i
$936$		0			0
$937$	−2.84345e11	−	4.92500e11i	−0.368882	−	0.638922i	0.620509	−	0.784199i	$-0.286926\pi$
$937$	−2.84345e11	−	4.92500e11i	−0.368882	−	0.638922i	−0.989391	+	0.145277i	$0.953593\pi$
$938$	2.74870e9	−	7.55200e9i	0.00355072	−	0.00975552i
$939$		0			0
$940$	−7.58953e11	−	6.36837e11i	−0.972083	−	0.815675i
$941$	−1.33808e11	−	3.67635e11i	−0.170657	−	0.468876i	0.824650	−	0.565643i	$-0.191372\pi$
$941$	−1.33808e11	−	3.67635e11i	−0.170657	−	0.468876i	−0.995307	+	0.0967671i	$0.969150\pi$
$942$		0			0
$943$	−1.66622e9	−	9.44963e9i	−0.00210711	−	0.0119500i
$944$			9.37807e11i			1.18093i
$945$		0			0
$946$	−1.48552e10			−0.0185488
$947$	−1.36936e12	+	2.41455e11i	−1.70262	+	0.300218i	−0.938608	−	0.344986i	$-0.887884\pi$
$947$	−1.36936e12	+	2.41455e11i	−1.70262	+	0.300218i	−0.764011	+	0.645203i	$0.776773\pi$
$948$		0			0
$949$	−6.94619e9	+	2.52821e9i	−0.00856410	+	0.00311708i
$950$	−2.05568e9	+	2.44986e9i	−0.00252383	+	0.00300778i
$951$		0			0
$952$	−9.81568e9	−	3.57261e9i	−0.0119501	−	0.00434949i
$953$	2.09625e11	−	1.21027e11i	0.254139	−	0.146727i	−0.367519	−	0.930016i	$-0.619793\pi$
$953$	2.09625e11	−	1.21027e11i	0.254139	−	0.146727i	0.621658	+	0.783289i	$0.286459\pi$
$954$		0			0
$955$	−2.40108e11	+	4.15879e11i	−0.288664	+	0.499980i
$956$	2.24936e11	+	2.68068e11i	0.269294	+	0.320932i
$957$		0			0
$958$	−1.21327e10	+	6.88082e10i	−0.0144045	+	0.0816918i
$959$	8.10853e10	+	1.42975e10i	0.0958667	+	0.0169039i
$960$		0			0
$961$	1.77303e12	−	1.48775e12i	2.07885	−	1.74436i
$962$	−1.30366e10	−	7.52670e9i	−0.0152218	−	0.00878829i
$963$		0			0
$964$	3.99542e11	+	6.92028e11i	0.462652	+	0.801337i
$965$	−2.92877e11	+	8.04672e11i	−0.337735	+	0.927918i
$966$		0			0
$967$	−2.96716e11	−	2.48974e11i	−0.339340	−	0.284740i	0.457153	−	0.889388i	$-0.348869\pi$
$967$	−2.96716e11	−	2.48974e11i	−0.339340	−	0.284740i	−0.796492	+	0.604648i	$0.793314\pi$
$968$	7.29668e10	+	2.00475e11i	0.0831044	+	0.228328i
$969$		0			0
$970$	−3.86586e10	−	2.19244e11i	−0.0436676	−	0.247651i
$971$			4.12689e11i			0.464243i	0.972687	+	0.232122i	$0.0745668\pi$
$971$			4.12689e11i			0.464243i	−0.972687	+	0.232122i	$0.925433\pi$
$972$		0			0
$973$	−1.42673e11			−0.159181
$974$	−1.33944e11	+	2.36180e10i	−0.148829	+	0.0262426i
$975$		0			0
$976$	−1.21987e12	+	4.43997e11i	−1.34436	+	0.489307i
$977$	−2.63596e11	+	3.14142e11i	−0.289308	+	0.344784i	−0.891049	−	0.453907i	$-0.850030\pi$
$977$	−2.63596e11	+	3.14142e11i	−0.289308	+	0.344784i	0.601741	+	0.798692i	$0.294474\pi$
$978$		0			0
$979$	−2.44129e11	−	8.88556e10i	−0.265759	−	0.0967285i
$980$	7.89726e11	−	4.55948e11i	0.856194	−	0.494324i
$981$		0			0
$982$	−4.14176e10	+	7.17374e10i	−0.0445389	+	0.0771436i
$983$	1.47538e11	+	1.75829e11i	0.158012	+	0.188311i	0.839242	−	0.543758i	$-0.182999\pi$
$983$	1.47538e11	+	1.75829e11i	0.158012	+	0.188311i	−0.681230	+	0.732069i	$0.738555\pi$
$984$		0			0
$985$	1.06313e11	−	6.02934e11i	0.112939	−	0.640508i
$986$	−8.10981e10	−	1.42998e10i	−0.0858031	−	0.0151294i
$987$		0			0
$988$	−5.13317e10	+	4.30724e10i	−0.0538713	+	0.0452034i
$989$	1.49767e11	+	8.64681e10i	0.156542	+	0.0903797i
$990$		0			0
$991$	2.92488e11	+	5.06604e11i	0.303259	+	0.525260i	0.976872	−	0.213824i	$-0.0685920\pi$
$991$	2.92488e11	+	5.06604e11i	0.303259	+	0.525260i	−0.673613	+	0.739084i	$0.735259\pi$
$992$	−2.89997e11	+	7.96761e11i	−0.299466	+	0.822775i
$993$		0			0
$994$	1.35929e9	+	1.14058e9i	0.00139241	+	0.00116837i
$995$	1.85651e11	+	5.10073e11i	0.189411	+	0.520403i
$996$		0			0
$997$	−5.61372e10	−	3.18370e11i	−0.0568160	−	0.322219i	0.943132	−	0.332418i	$-0.107865\pi$
$997$	−5.61372e10	−	3.18370e11i	−0.0568160	−	0.322219i	−0.999948	+	0.0101990i	$0.996753\pi$
$998$			1.01107e11i			0.101920i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.71.12		138
3.2	odd	2		27.9.f.a.14.12	yes	138
27.2	odd	18	inner	81.9.f.a.8.12		138
27.25	even	9		27.9.f.a.2.12	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.12	✓	138	27.25	even	9
27.9.f.a.14.12	yes	138	3.2	odd	2
81.9.f.a.8.12		138	27.2	odd	18	inner
81.9.f.a.71.12		138	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.46646 - 0.434904i) q^{2} +(-234.667 + 85.4118i) q^{4} +(411.949 - 490.942i) q^{5} +(243.334 + 88.5664i) q^{7} +(-1096.91 + 633.301i) q^{8} +(802.546 - 1390.05i) q^{10} +(-4355.96 - 5191.23i) q^{11} +(-733.507 + 4159.93i) q^{13} +(638.693 + 112.619i) q^{14} +(46543.3 - 39054.5i) q^{16} +(27580.9 + 15923.8i) q^{17} +(-31761.5 - 55012.5i) q^{19} +(-54738.7 + 150393. i) q^{20} +(-13001.5 - 10909.6i) q^{22} +(67576.8 + 185666. i) q^{23} +(-3490.62 - 19796.3i) q^{25} +10579.3i q^{26} -64667.1 q^{28} +(-1.01674e6 + 179279. i) q^{29} +(-1.67239e6 + 608702. i) q^{31} +(306236. - 364958. i) q^{32} +(74952.5 + 27280.5i) q^{34} +(143722. - 82978.2i) q^{35} +(-711454. + 1.23227e6i) q^{37} +(-102264. - 121873. i) q^{38} +(-140957. + 799407. i) q^{40} +(-47826.5 - 8433.11i) q^{41} +(670492. - 562610. i) q^{43} +(1.46559e6 + 846160. i) q^{44} +(247423. + 428549. i) q^{46} +(-2.11724e6 + 5.81707e6i) q^{47} +(-4.36473e6 - 3.66244e6i) q^{49} +(-17219.0 - 47308.8i) q^{50} +(-183177. - 1.03885e6i) q^{52} +9.95902e6i q^{53} -4.34303e6 q^{55} +(-323005. + 56954.4i) q^{56} +(-2.42979e6 + 884370. i) q^{58} +(-9.92151e6 + 1.18240e7i) q^{59} +(-2.00776e7 - 7.30764e6i) q^{61} +(-3.86018e6 + 2.22867e6i) q^{62} +(-7.18042e6 + 1.24369e7i) q^{64} +(1.74012e6 + 2.07379e6i) q^{65} +(2.15182e6 - 1.22036e7i) q^{67} +(-7.83240e6 - 1.38106e6i) q^{68} +(318399. - 267168. i) q^{70} +(2.36946e6 + 1.36801e6i) q^{71} +(874977. + 1.51550e6i) q^{73} +(-1.21886e6 + 3.34878e6i) q^{74} +(1.21521e7 + 1.01968e7i) q^{76} +(-600185. - 1.64900e6i) q^{77} +(7.53737e6 + 4.27466e7i) q^{79} -3.89386e7i q^{80} -121630. q^{82} +(5.86063e7 - 1.03339e7i) q^{83} +(1.91796e7 - 6.98080e6i) q^{85} +(1.40906e6 - 1.67926e6i) q^{86} +(8.06570e6 + 2.93568e6i) q^{88} +(3.32007e7 - 1.91684e7i) q^{89} +(-546917. + 947288. i) q^{91} +(-3.17161e7 - 3.77978e7i) q^{92} +(-2.69223e6 + 1.52684e7i) q^{94} +(-4.00921e7 - 7.06932e6i) q^{95} +(1.06250e8 - 8.91546e7i) q^{97} +(-1.23583e7 - 7.13504e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

L-functions

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