LMFDB - Embedded newform 966.2.be.a.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	966.19
Dual form			966.2.be.a.661.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(1.83046 - 0.943666i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.58469 - 0.565134i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(1.83046 - 0.943666i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.58469 - 0.565134i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(1.91187 - 0.765397i) q^{10} +(-0.336895 - 3.52813i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-2.03520 - 0.292618i) q^{13} +(-2.51927 - 0.808265i) q^{14} +(0.580197 - 1.97597i) q^{15} +(0.928368 + 0.371662i) q^{16} +(1.97637 - 5.71035i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(0.991489 + 2.86472i) q^{19} +(1.97597 - 0.580197i) q^{20} +(-2.19265 + 1.48064i) q^{21} -3.54418i q^{22} +(3.99757 - 2.64942i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.440218 + 0.618200i) q^{25} +(-1.99817 - 0.484751i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-2.43103 - 1.04408i) q^{28} +(0.0135770 + 0.0156687i) q^{29} +(0.765397 - 1.91187i) q^{30} +(7.10133 - 1.72276i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.78591 - 2.19086i) q^{33} +(2.51023 - 5.49663i) q^{34} +(-5.26446 + 1.40463i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.158895 + 0.00756912i) q^{37} +(0.714690 + 2.94599i) q^{38} +(-1.61623 + 1.27101i) q^{39} +(2.02217 - 0.389742i) q^{40} +(-6.38905 + 9.94155i) q^{41} +(-2.32346 + 1.26551i) q^{42} +(0.590557 + 2.01125i) q^{43} +(0.336895 - 3.52813i) q^{44} +(-1.02969 - 1.78348i) q^{45} +(4.23132 - 2.25742i) q^{46} +(6.67305 + 3.85269i) q^{47} +(0.909632 - 0.415415i) q^{48} +(6.36125 + 2.92139i) q^{49} +(-0.496989 + 0.573555i) q^{50} +(-2.76892 - 5.37096i) q^{51} +(-1.94304 - 0.672494i) q^{52} +(2.81037 + 3.57368i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-3.94605 - 6.14017i) q^{55} +(-2.32078 - 1.27043i) q^{56} +(2.75750 + 1.25931i) q^{57} +(0.0120262 + 0.0168884i) q^{58} +(-1.60779 - 4.01608i) q^{59} +(0.943666 - 1.83046i) q^{60} +(-9.65600 + 9.20698i) q^{61} +(7.23293 - 1.03994i) q^{62} +(-0.441509 + 2.60865i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-4.00148 + 1.38493i) q^{65} +(-2.56504 - 2.44576i) q^{66} +(-0.752631 - 0.535946i) q^{67} +(3.02135 - 5.23313i) q^{68} +(0.841170 - 4.72149i) q^{69} +(-5.37414 + 0.897852i) q^{70} +(-2.49706 - 5.46779i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-1.10393 + 5.72772i) q^{73} +(-0.158895 - 0.00756912i) q^{74} +(0.143627 + 0.745208i) q^{75} +(0.431420 + 3.00059i) q^{76} +(-1.12309 + 9.30951i) q^{77} +(-1.72973 + 1.11163i) q^{78} +(4.70761 - 5.98621i) q^{79} +(2.05006 - 0.195757i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-7.30512 + 9.28922i) q^{82} +(4.70541 - 3.02398i) q^{83} +(-2.43324 + 1.03892i) q^{84} +(-1.77100 - 12.3176i) q^{85} +(0.396701 + 2.05828i) q^{86} +(0.0207092 + 0.000986502i) q^{87} +(0.670740 - 3.48013i) q^{88} +(-1.84929 + 7.62286i) q^{89} +(-0.855501 - 1.87328i) q^{90} +(5.09500 + 1.90649i) q^{91} +(4.42674 - 1.84499i) q^{92} +(3.65366 - 6.32832i) q^{93} +(6.27661 + 4.46956i) q^{94} +(4.51821 + 4.30811i) q^{95} +(0.945001 - 0.327068i) q^{96} +(4.96671 + 3.19191i) q^{97} +(6.05475 + 3.51284i) q^{98} +(-3.50810 + 0.504389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$2$	0.995472	+	0.0950560i	0.703905	+	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	1.83046	−	0.943666i	0.818605	−	0.422020i	0.00255171	−	0.999997i	$-0.499188\pi$
$5$	1.83046	−	0.943666i	0.818605	−	0.422020i	0.816053	+	0.577976i	$0.196157\pi$
$6$	0.755750	−	0.654861i	0.308533	−	0.267346i
$7$	−2.58469	−	0.565134i	−0.976921	−	0.213601i
$7$	−2.58469	−	0.565134i	−0.976921	−	0.213601i
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	1.91187	−	0.765397i	0.604586	−	0.242040i
$11$	−0.336895	−	3.52813i	−0.101578	−	1.06377i	−0.892253	−	0.451535i	$-0.850877\pi$
$11$	−0.336895	−	3.52813i	−0.101578	−	1.06377i	0.790675	−	0.612235i	$-0.209730\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	−2.03520	−	0.292618i	−0.564463	−	0.0811576i	−0.145825	−	0.989310i	$-0.546584\pi$
$13$	−2.03520	−	0.292618i	−0.564463	−	0.0811576i	−0.418639	+	0.908153i	$0.637493\pi$
$14$	−2.51927	−	0.808265i	−0.673302	−	0.216018i
$15$	0.580197	−	1.97597i	0.149806	−	0.510193i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	1.97637	−	5.71035i	0.479341	−	1.38496i	−0.403366	−	0.915039i	$-0.632160\pi$
$17$	1.97637	−	5.71035i	0.479341	−	1.38496i	0.882706	−	0.469925i	$-0.155719\pi$
$18$	0.0475819	−	0.998867i	0.0112152	−	0.235435i
$19$	0.991489	+	2.86472i	0.227463	+	0.657211i	0.999759	+	0.0219486i	$0.00698702\pi$
$19$	0.991489	+	2.86472i	0.227463	+	0.657211i	−0.772296	+	0.635263i	$0.780892\pi$
$20$	1.97597	−	0.580197i	0.441840	−	0.129736i
$21$	−2.19265	+	1.48064i	−0.478475	+	0.323102i
$22$		−	3.54418i		−	0.755621i
$23$	3.99757	−	2.64942i	0.833552	−	0.552441i
$23$	3.99757	−	2.64942i	0.833552	−	0.552441i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−0.440218	+	0.618200i	−0.0880436	+	0.123640i
$26$	−1.99817	−	0.484751i	−0.391873	−	0.0950675i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−2.43103	−	1.04408i	−0.459421	−	0.197312i
$29$	0.0135770	+	0.0156687i	0.00252119	+	0.00290961i	0.757009	−	0.653405i	$-0.226660\pi$
$29$	0.0135770	+	0.0156687i	0.00252119	+	0.00290961i	−0.754488	+	0.656314i	$0.772115\pi$
$30$	0.765397	−	1.91187i	0.139742	−	0.349058i
$31$	7.10133	−	1.72276i	1.27544	−	0.309417i	0.459821	−	0.888012i	$-0.347914\pi$
$31$	7.10133	−	1.72276i	1.27544	−	0.309417i	0.815616	+	0.578594i	$0.196399\pi$
$32$	0.888835	+	0.458227i	0.157125	+	0.0810038i
$33$	−2.78591	−	2.19086i	−0.484965	−	0.381381i
$34$	2.51023	−	5.49663i	0.430500	−	0.942664i
$35$	−5.26446	+	1.40463i	−0.889856	+	0.237426i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	−0.158895	+	0.00756912i	−0.0261222	+	0.00124436i	−0.0606390	−	0.998160i	$-0.519314\pi$
$37$	−0.158895	+	0.00756912i	−0.0261222	+	0.00124436i	0.0345167	+	0.999404i	$0.489011\pi$
$38$	0.714690	+	2.94599i	0.115938	+	0.477903i
$39$	−1.61623	+	1.27101i	−0.258803	+	0.203525i
$40$	2.02217	−	0.389742i	0.319733	−	0.0616236i
$41$	−6.38905	+	9.94155i	−0.997801	+	1.55261i	−0.174773	+	0.984609i	$0.555919\pi$
$41$	−6.38905	+	9.94155i	−0.997801	+	1.55261i	−0.823028	+	0.568001i	$0.807717\pi$
$42$	−2.32346	+	1.26551i	−0.358518	+	0.195273i
$43$	0.590557	+	2.01125i	0.0900590	+	0.306713i	0.992188	−	0.124754i	$-0.0398142\pi$
$43$	0.590557	+	2.01125i	0.0900590	+	0.306713i	−0.902129	+	0.431467i	$0.857996\pi$
$44$	0.336895	−	3.52813i	0.0507889	−	0.531885i
$45$	−1.02969	−	1.78348i	−0.153498	−	0.265866i
$46$	4.23132	−	2.25742i	0.623873	−	0.332839i
$47$	6.67305	+	3.85269i	0.973365	+	0.561972i	0.900260	−	0.435352i	$-0.143376\pi$
$47$	6.67305	+	3.85269i	0.973365	+	0.561972i	0.0731043	+	0.997324i	$0.476709\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	6.36125	+	2.92139i	0.908750	+	0.417342i
$50$	−0.496989	+	0.573555i	−0.0702848	+	0.0811130i
$51$	−2.76892	−	5.37096i	−0.387727	−	0.752085i
$52$	−1.94304	−	0.672494i	−0.269452	−	0.0932582i
$53$	2.81037	+	3.57368i	0.386035	+	0.490883i	0.939769	−	0.341810i	$-0.111040\pi$
$53$	2.81037	+	3.57368i	0.386035	+	0.490883i	−0.553734	+	0.832693i	$0.686798\pi$
$54$	−0.690079	−	0.723734i	−0.0939079	−	0.0984877i
$55$	−3.94605	−	6.14017i	−0.532085	−	0.827940i
$56$	−2.32078	−	1.27043i	−0.310127	−	0.169769i
$57$	2.75750	+	1.25931i	0.365240	+	0.166799i
$58$	0.0120262	+	0.0168884i	0.00157911	+	0.00221755i
$59$	−1.60779	−	4.01608i	−0.209317	−	0.522849i	0.786141	−	0.618047i	$-0.212076\pi$
$59$	−1.60779	−	4.01608i	−0.209317	−	0.522849i	−0.995458	+	0.0951982i	$0.969652\pi$
$60$	0.943666	−	1.83046i	0.121827	−	0.236311i
$61$	−9.65600	+	9.20698i	−1.23632	+	1.17883i	−0.259278	+	0.965803i	$0.583485\pi$
$61$	−9.65600	+	9.20698i	−1.23632	+	1.17883i	−0.977046	+	0.213030i	$0.931667\pi$
$62$	7.23293	−	1.03994i	0.918583	−	0.132072i
$63$	−0.441509	+	2.60865i	−0.0556249	+	0.328659i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−4.00148	+	1.38493i	−0.496323	+	0.171779i
$66$	−2.56504	−	2.44576i	−0.315735	−	0.301052i
$67$	−0.752631	−	0.535946i	−0.0919485	−	0.0654763i	0.533158	−	0.846016i	$-0.321005\pi$
$67$	−0.752631	−	0.535946i	−0.0919485	−	0.0654763i	−0.625107	+	0.780539i	$0.714945\pi$
$68$	3.02135	−	5.23313i	0.366392	−	0.634610i
$69$	0.841170	−	4.72149i	0.101265	−	0.568400i
$70$	−5.37414	+	0.897852i	−0.642333	+	0.107314i
$71$	−2.49706	−	5.46779i	−0.296346	−	0.648908i	0.701627	−	0.712545i	$-0.252457\pi$
$71$	−2.49706	−	5.46779i	−0.296346	−	0.648908i	−0.997973	+	0.0636368i	$0.979730\pi$
$72$	0.235759	−	0.971812i	0.0277845	−	0.114529i
$73$	−1.10393	+	5.72772i	−0.129205	+	0.670379i	0.858345	+	0.513073i	$0.171493\pi$
$73$	−1.10393	+	5.72772i	−0.129205	+	0.670379i	−0.987550	+	0.157306i	$0.949719\pi$
$74$	−0.158895	−	0.00756912i	−0.0184712	−	0.000879892i
$75$	0.143627	+	0.745208i	0.0165846	+	0.0860492i
$76$	0.431420	+	3.00059i	0.0494872	+	0.344191i
$77$	−1.12309	+	9.30951i	−0.127988	+	1.06092i
$78$	−1.72973	+	1.11163i	−0.195853	+	0.125867i
$79$	4.70761	−	5.98621i	0.529647	−	0.673501i	−0.445443	−	0.895310i	$-0.646954\pi$
$79$	4.70761	−	5.98621i	0.529647	−	0.673501i	0.975090	+	0.221809i	$0.0711962\pi$
$80$	2.05006	−	0.195757i	0.229204	−	0.0218863i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−7.30512	+	9.28922i	−0.806716	+	1.02582i
$83$	4.70541	−	3.02398i	0.516486	−	0.331925i	−0.256295	−	0.966599i	$-0.582502\pi$
$83$	4.70541	−	3.02398i	0.516486	−	0.331925i	0.772780	+	0.634674i	$0.218865\pi$
$84$	−2.43324	+	1.03892i	−0.265488	+	0.113356i
$85$	−1.77100	−	12.3176i	−0.192092	−	1.33603i
$86$	0.396701	+	2.05828i	0.0427774	+	0.221950i
$87$	0.0207092		0.000986502i	0.00222026		0.000105764i
$88$	0.670740	−	3.48013i	0.0715011	−	0.370983i
$89$	−1.84929	+	7.62286i	−0.196024	+	0.808021i	0.785839	+	0.618431i	$0.212231\pi$
$89$	−1.84929	+	7.62286i	−0.196024	+	0.808021i	−0.981863	+	0.189591i	$0.939284\pi$
$90$	−0.855501	−	1.87328i	−0.0901777	−	0.197462i
$91$	5.09500	+	1.90649i	0.534101	+	0.199854i
$92$	4.42674	−	1.84499i	0.461519	−	0.192354i
$93$	3.65366	−	6.32832i	0.378866	−	0.656216i
$94$	6.27661	+	4.46956i	0.647383	+	0.461000i
$95$	4.51821	+	4.30811i	0.463559	+	0.442003i
$96$	0.945001	−	0.327068i	0.0964487	−	0.0333812i
$97$	4.96671	+	3.19191i	0.504293	+	0.324089i	0.767931	−	0.640532i	$-0.221286\pi$
$97$	4.96671	+	3.19191i	0.504293	+	0.324089i	−0.263638	+	0.964622i	$0.584923\pi$
$98$	6.05475	+	3.51284i	0.611622	+	0.354850i
$99$	−3.50810	+	0.504389i	−0.352578	+	0.0506930i
$100$	−0.549258	+	0.523716i	−0.0549258	+	0.0523716i
$101$	−6.04833	+	11.7321i	−0.601831	+	1.16739i	0.369405	+	0.929269i	$0.379562\pi$
$101$	−6.04833	+	11.7321i	−0.601831	+	1.16739i	−0.971236	+	0.238121i	$0.923469\pi$
$102$	−2.24584	−	5.60984i	−0.222372	−	0.555457i
$103$	−10.5327	−	14.7911i	−1.03782	−	1.45741i	−0.882945	−	0.469477i	$-0.844443\pi$
$103$	−10.5327	−	14.7911i	−1.03782	−	1.45741i	−0.154873	−	0.987934i	$-0.549497\pi$
$104$	−1.87032	−	0.854147i	−0.183400	−	0.0837560i
$105$	−2.61631	+	4.77938i	−0.255326	+	0.466419i
$106$	2.45795	+	3.82464i	0.238737	+	0.371482i
$107$	9.35247	+	9.80859i	0.904138	+	0.948232i	0.998882	−	0.0472691i	$-0.0150518\pi$
$107$	9.35247	+	9.80859i	0.904138	+	0.948232i	−0.0947443	+	0.995502i	$0.530203\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	−13.2078	−	4.57126i	−1.26508	−	0.437847i	−0.389544	−	0.921008i	$-0.627367\pi$
$109$	−13.2078	−	4.57126i	−1.26508	−	0.437847i	−0.875532	+	0.483161i	$0.839489\pi$
$110$	−3.34452	−	6.48746i	−0.318887	−	0.618555i
$111$	−0.104172	+	0.120221i	−0.00988760	+	0.0114109i
$112$	−2.18950	−	1.48528i	−0.206889	−	0.140346i
$113$	11.1363	−	5.08577i	1.04761	−	0.478429i	0.184181	−	0.982892i	$-0.441037\pi$
$113$	11.1363	−	5.08577i	1.04761	−	0.478429i	0.863433	+	0.504463i	$0.168309\pi$
$114$	2.62531	+	1.51572i	0.245883	+	0.141960i
$115$	4.81722	−	8.62201i	0.449208	−	0.804007i
$116$	0.0103664	+	0.0179551i	0.000962492	+	0.00166708i
$117$	−0.195448	+	2.04682i	−0.0180691	+	0.189229i
$118$	−1.21876	−	4.15072i	−0.112196	−	0.382105i
$119$	−8.33542	+	13.6426i	−0.764107	+	1.25061i
$120$	1.11339	−	1.73247i	0.101638	−	0.158152i
$121$	−1.53298	+	0.295457i	−0.139361	+	0.0268597i
$122$	−10.4875	+	8.24743i	−0.949490	+	0.746687i
$123$	2.78609	+	11.4844i	0.251213	+	1.03552i
$124$	7.29903	−	0.347696i	0.655473	−	0.0312240i
$125$	−1.68783	+	11.7391i	−0.150964	+	1.04998i
$126$	−0.687478	+	2.55487i	−0.0612454	+	0.227606i
$127$	−3.64194	+	7.97474i	−0.323170	+	0.707644i	−0.999583	−	0.0288791i	$-0.990806\pi$
$127$	−3.64194	+	7.97474i	−0.323170	+	0.707644i	0.676413	+	0.736523i	$0.263534\pi$
$128$	0.786053	+	0.618159i	0.0694779	+	0.0546381i
$129$	1.86314	+	0.960516i	0.164040	+	0.0845687i
$130$	−4.11501	+	0.998290i	−0.360910	+	0.0875558i
$131$	4.51209	−	11.2706i	0.394223	−	0.984721i	−0.589939	−	0.807448i	$-0.700848\pi$
$131$	4.51209	−	11.2706i	0.394223	−	0.984721i	0.984162	−	0.177273i	$-0.0567276\pi$
$132$	−2.32094	−	2.67851i	−0.202012	−	0.233134i
$133$	−0.943742	−	7.96473i	−0.0818328	−	0.690630i
$134$	−0.698278	−	0.605062i	−0.0603221	−	0.0522694i
$135$	−2.00134	−	0.485519i	−0.172248	−	0.0417868i
$136$	3.50511	−	4.92223i	0.300560	−	0.422078i
$137$	9.68726	−	5.59294i	0.827638	−	0.477837i	−0.0254050	−	0.999677i	$-0.508088\pi$
$137$	9.68726	−	5.59294i	0.827638	−	0.477837i	0.853043	+	0.521840i	$0.174754\pi$
$138$	1.28617	−	4.62015i	0.109486	−	0.393293i
$139$		−	2.68360i		−	0.227620i	−0.993503	−	0.113810i	$-0.963694\pi$
$139$		−	2.68360i		−	0.227620i	0.993503	−	0.113810i	$-0.0363056\pi$
$140$	−5.43515	+	0.382942i	−0.459354	+	0.0323645i
$141$	7.39325	−	2.17086i	0.622624	−	0.182819i
$142$	−1.96600	−	5.68040i	−0.164983	−	0.476688i
$143$	−0.346743	+	7.27903i	−0.0289961	+	0.608703i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	0.0396382	+	0.0158688i	0.00329178	+	0.00131783i
$146$	−1.64338	+	5.59685i	−0.136007	+	0.463199i
$147$	6.50407	−	2.58786i	0.536447	−	0.213443i
$148$	−0.157456	−	0.0226388i	−0.0129428	−	0.00186090i
$149$	10.1771	−	7.24708i	0.833741	−	0.593704i	−0.0814717	−	0.996676i	$-0.525962\pi$
$149$	10.1771	−	7.24708i	0.833741	−	0.593704i	0.915213	+	0.402971i	$0.132023\pi$
$150$	0.0721402	+	0.755486i	0.00589022	+	0.0616852i
$151$	3.10620	−	1.24354i	0.252779	−	0.101197i	−0.241812	−	0.970323i	$-0.577742\pi$
$151$	3.10620	−	1.24354i	0.252779	−	0.101197i	0.494592	+	0.869126i	$0.335318\pi$
$152$	0.144242	+	3.02801i	0.0116996	+	0.245604i
$153$	−5.79792	−	1.70242i	−0.468734	−	0.137633i
$154$	−2.00293	+	9.16060i	−0.161401	+	0.738182i
$155$	11.3730	−	9.85473i	0.913498	−	0.791551i
$156$	−1.82756	+	0.942173i	−0.146322	+	0.0754342i
$157$	18.4477	+	3.55549i	1.47228	+	0.283759i	0.861386	−	0.507951i	$-0.169597\pi$
$157$	18.4477	+	3.55549i	1.47228	+	0.283759i	0.610897	+	0.791710i	$0.290809\pi$
$158$	5.25532	−	5.51162i	0.418091	−	0.438481i
$159$	4.52578	+	0.432159i	0.358917	+	0.0342725i
$160$	2.05939			0.162809
$161$	−11.8298	+	4.58875i	−0.932316	+	0.361644i
$162$	−1.00000			−0.0785674
$163$	−4.07522	−	0.389137i	−0.319196	−	0.0304795i	−0.0657717	−	0.997835i	$-0.520951\pi$
$163$	−4.07522	−	0.389137i	−0.319196	−	0.0304795i	−0.253425	+	0.967355i	$0.581557\pi$
$164$	−8.15504	+	8.55276i	−0.636802	+	0.667858i
$165$	−7.16693	−	1.38131i	−0.557945	−	0.107535i
$166$	4.97155	−	2.56301i	0.385867	−	0.198928i
$167$	−18.1760	+	15.7496i	−1.40650	+	1.21874i	−0.463433	+	0.886132i	$0.653383\pi$
$167$	−18.1760	+	15.7496i	−1.40650	+	1.21874i	−0.943066	+	0.332607i	$0.892072\pi$
$168$	−2.52097	+	0.802925i	−0.194497	+	0.0619470i
$169$	−8.41699	−	2.47145i	−0.647461	−	0.190112i
$170$	−0.592121	−	12.4302i	−0.0454136	−	0.953349i
$171$	2.81430	−	1.12667i	0.215215	−	0.0861589i
$172$	0.199253	+	2.08667i	0.0151929	+	0.159107i
$173$	−15.3251	+	10.9130i	−1.16515	+	0.829699i	−0.987995	−	0.154484i	$-0.950628\pi$
$173$	−15.3251	+	10.9130i	−1.16515	+	0.829699i	−0.177154	+	0.984183i	$0.556689\pi$
$174$	0.0205217	+	0.00295057i	0.00155574	+	0.000223682i
$175$	1.48719	−	1.34907i	0.112421	−	0.101980i
$176$	0.998510	−	3.40061i	0.0752655	−	0.256331i
$177$	−4.01608	−	1.60779i	−0.301867	−	0.120849i
$178$	−2.56551	+	7.41256i	−0.192293	+	0.555595i
$179$	−0.243142	+	5.10419i	−0.0181733	+	0.381505i	0.971398	+	0.237459i	$0.0763144\pi$
$179$	−0.243142	+	5.10419i	−0.0181733	+	0.381505i	−0.989571	+	0.144046i	$0.953989\pi$
$180$	−0.673560	−	1.94612i	−0.0502042	−	0.145055i
$181$	−17.3584	+	5.09687i	−1.29024	+	0.378848i	−0.853665	−	0.520822i	$-0.825626\pi$
$181$	−17.3584	+	5.09687i	−1.29024	+	0.378848i	−0.436571	+	0.899670i	$0.643807\pi$
$182$	4.89070	+	2.38216i	0.362523	+	0.176578i
$183$			13.3419i			0.986263i
$184$	4.58207	−	1.41585i	0.337795	−	0.104378i
$185$	−0.283708	+	0.163799i	−0.0208586	+	0.0120427i
$186$	4.23866	−	5.95236i	0.310793	−	0.436448i
$187$	−20.8127	−	5.04910i	−1.52197	−	0.369227i
$188$	5.82334	+	5.04595i	0.424710	+	0.368014i
$189$	1.58329	+	2.11971i	0.115168	+	0.154186i
$190$	4.08824	+	4.71809i	0.296592	+	0.342286i
$191$	−2.87787	+	7.18856i	−0.208235	+	0.520146i	−0.995313	−	0.0967077i	$-0.969169\pi$
$191$	−2.87787	+	7.18856i	−0.208235	+	0.520146i	0.787078	+	0.616854i	$0.211593\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	24.3853	+	12.5715i	1.75530	+	0.904918i	0.950122	+	0.311879i	$0.100958\pi$
$193$	24.3853	+	12.5715i	1.75530	+	0.904918i	0.805174	+	0.593039i	$0.202072\pi$
$194$	4.64081	+	3.64957i	0.333191	+	0.262024i
$195$	−1.75902	+	3.85172i	−0.125966	+	0.275827i
$196$	5.69341	+	4.07247i	0.406672	+	0.290891i
$197$	−1.24153	+	8.63502i	−0.0884553	+	0.615220i	0.896582	+	0.442878i	$0.146043\pi$
$197$	−1.24153	+	8.63502i	−0.0884553	+	0.615220i	−0.985037	+	0.172342i	$0.944867\pi$
$198$	−3.54016	+	0.168639i	−0.251588	+	0.0119846i
$199$	−0.182062	−	0.750468i	−0.0129060	−	0.0531993i	0.964994	−	0.262270i	$-0.0844712\pi$
$199$	−0.182062	−	0.750468i	−0.0129060	−	0.0531993i	−0.977900	+	0.209071i	$0.932956\pi$
$200$	−0.596553	+	0.469135i	−0.0421827	+	0.0331728i
$201$	−0.907258	+	0.174860i	−0.0639930	+	0.0123336i
$202$	−7.13615	+	11.1041i	−0.502098	+	0.781279i
$203$	−0.0262375	−	0.0481717i	−0.00184151	−	0.00338099i
$204$	−1.70242	−	5.79792i	−0.119194	−	0.405936i
$205$	−2.31337	+	24.2267i	−0.161573	+	1.69207i
$206$	−9.07902	−	15.7253i	−0.632565	−	1.09564i
$207$	−2.83663	−	3.86698i	−0.197159	−	0.268774i
$208$	−1.78066	−	1.02806i	−0.123467	−	0.0712835i
$209$	9.77307	−	4.46321i	0.676017	−	0.308727i
$210$	−3.05878	+	4.50904i	−0.211076	+	0.311153i
$211$	9.66277	−	11.1514i	0.665213	−	0.767696i	−0.318407	−	0.947954i	$-0.603148\pi$
$211$	9.66277	−	11.1514i	0.665213	−	0.767696i	0.983619	+	0.180258i	$0.0576932\pi$
$212$	2.08326	+	4.04097i	0.143079	+	0.277535i
$213$	−5.68040	−	1.96600i	−0.389214	−	0.134708i
$214$	8.37776	+	10.6532i	0.572692	+	0.728237i
$215$	2.97894	+	3.12422i	0.203162	+	0.213070i
$216$	−0.540641	−	0.841254i	−0.0367859	−	0.0572401i
$217$	−19.3283	+	0.439609i	−1.31209	+	0.0298426i
$218$	−12.7134	−	5.80604i	−0.861063	−	0.393234i
$219$	3.38355	+	4.75153i	0.228639	+	0.321079i
$220$	−2.71270	−	6.77600i	−0.182890	−	0.456838i
$221$	−5.69326	+	11.0434i	−0.382970	+	0.742859i
$222$	−0.115128	+	0.109775i	−0.00772691	+	0.00736759i
$223$	−21.4267	+	3.08069i	−1.43483	+	0.206298i	−0.815467	−	0.578803i	$-0.803520\pi$
$223$	−21.4267	+	3.08069i	−1.43483	+	0.206298i	−0.619368	+	0.785101i	$0.712611\pi$
$224$	−2.03841	−	1.68668i	−0.136197	−	0.112696i
$225$	0.638446	+	0.410304i	0.0425631	+	0.0273536i
$226$	11.5693	−	4.00417i	0.769578	−	0.266354i
$227$	2.27474	+	2.16896i	0.150979	+	0.143959i	0.761805	−	0.647807i	$-0.224314\pi$
$227$	2.27474	+	2.16896i	0.150979	+	0.143959i	−0.610825	+	0.791766i	$0.709162\pi$
$228$	2.46934	+	1.75841i	0.163536	+	0.116454i
$229$	10.4239	−	18.0547i	0.688831	−	1.19309i	−0.283386	−	0.959006i	$-0.591458\pi$
$229$	10.4239	−	18.0547i	0.688831	−	1.19309i	0.972216	−	0.234084i	$-0.0752089\pi$
$230$	5.61499	−	8.12507i	0.370241	−	0.535751i
$231$	5.96259	+	7.23712i	0.392309	+	0.476167i
$232$	0.00861268	+	0.0188591i	0.000565450	+	0.00123816i
$233$	−0.636936	+	2.62549i	−0.0417271	+	0.172001i	−0.988862	−	0.148833i	$-0.952448\pi$
$233$	−0.636936	+	2.62549i	−0.0417271	+	0.172001i	0.947135	+	0.320835i	$0.103963\pi$
$234$	−0.389125	+	2.01897i	−0.0254379	+	0.131984i
$235$	15.8504	+	0.755047i	1.03397	+	0.0492538i
$236$	−0.818692	−	4.24778i	−0.0532923	−	0.276507i
$237$	−1.08380	−	7.53802i	−0.0704006	−	0.489647i
$238$	−9.59449	+	12.7885i	−0.621918	+	0.828953i
$239$	−3.93305	+	2.52762i	−0.254408	+	0.163498i	−0.661628	−	0.749832i	$-0.730134\pi$
$239$	−3.93305	+	2.52762i	−0.254408	+	0.163498i	0.407221	+	0.913330i	$0.366498\pi$
$240$	1.27303	−	1.61879i	0.0821737	−	0.104492i
$241$	−2.04668	+	0.195434i	−0.131838	+	0.0125890i	−0.160766	−	0.986992i	$-0.551397\pi$
$241$	−2.04668	+	0.195434i	−0.131838	+	0.0125890i	0.0289284	+	0.999581i	$0.490791\pi$
$242$	−1.55412	+	0.148400i	−0.0999026	+	0.00953954i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	−11.2239	+	7.21318i	−0.718539	+	0.461777i
$245$	14.4008	−	0.655412i	0.920034	−	0.0418727i
$246$	1.68181	+	11.6973i	0.107228	+	0.745790i
$247$	−1.17961	−	6.12041i	−0.0750569	−	0.389432i
$248$	7.29903	+	0.347696i	0.463489	+	0.0220787i
$249$	1.05854	−	5.49225i	0.0670825	−	0.348057i
$250$	−2.79607	+	11.5255i	−0.176839	+	0.728939i
$251$	9.70166	+	21.2437i	0.612364	+	1.34089i	0.920946	+	0.389691i	$0.127418\pi$
$251$	9.70166	+	21.2437i	0.612364	+	1.34089i	−0.308582	+	0.951198i	$0.599854\pi$
$252$	−0.927221	+	2.47795i	−0.0584095	+	0.156096i
$253$	−10.6942	−	13.2114i	−0.672341	−	0.830592i
$254$	−4.38350	+	7.59244i	−0.275045	+	0.476392i
$255$	−10.1368	−	7.21837i	−0.634790	−	0.452032i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	−22.0231	+	7.62228i	−1.37376	+	0.475465i	−0.911508	−	0.411282i	$-0.865081\pi$
$257$	−22.0231	+	7.62228i	−1.37376	+	0.475465i	−0.462256	+	0.886746i	$0.652960\pi$
$258$	1.76340	+	1.13327i	0.109785	+	0.0705543i
$259$	0.414973	+	0.0702333i	0.0257852	+	0.00436409i
$260$	−4.19127	+	0.602613i	−0.259931	+	0.0373725i
$261$	0.0150050	−	0.0143072i	0.000928784	−	0.000885594i
$262$	5.56300	−	10.7907i	0.343683	−	0.666653i
$263$	−3.53701	−	8.83502i	−0.218101	−	0.544790i	0.778456	−	0.627699i	$-0.216003\pi$
$263$	−3.53701	−	8.83502i	−0.218101	−	0.544790i	−0.996557	+	0.0829088i	$0.973579\pi$
$264$	−2.05582	−	2.88700i	−0.126527	−	0.177683i
$265$	8.51663	+	3.88942i	0.523173	+	0.238925i
$266$	−0.182372	−	8.01838i	−0.0111820	−	0.491638i
$267$	4.24077	+	6.59877i	0.259531	+	0.403838i
$268$	−0.637602	−	0.668697i	−0.0389477	−	0.0408472i
$269$	−2.08379	−	2.64976i	−0.127051	−	0.161559i	0.718366	−	0.695665i	$-0.244890\pi$
$269$	−2.08379	−	2.64976i	−0.127051	−	0.161559i	−0.845417	+	0.534107i	$0.820648\pi$
$270$	−1.94612	−	0.673560i	−0.118437	−	0.0409915i
$271$	−7.93681	−	15.3953i	−0.482127	−	0.935196i	−0.996961	−	0.0779056i	$-0.975177\pi$
$271$	−7.93681	−	15.3953i	−0.482127	−	0.935196i	0.514834	−	0.857290i	$-0.327854\pi$
$272$	3.95712	−	4.56676i	0.239936	−	0.276901i
$273$	4.89574	−	2.37180i	0.296304	−	0.143548i
$274$	10.1750	−	4.64678i	0.614696	−	0.280722i
$275$	2.32940	+	1.34488i	0.140468	+	0.0810992i
$276$	1.71952	−	4.47697i	0.103503	−	0.269482i
$277$	12.7293	+	22.0478i	0.764829	+	1.32472i	0.940337	+	0.340244i	$0.110510\pi$
$277$	12.7293	+	22.0478i	0.764829	+	1.32472i	−0.175508	+	0.984478i	$0.556157\pi$
$278$	0.255093	−	2.67145i	0.0152994	−	0.160223i
$279$	−2.05871	−	7.01131i	−0.123252	−	0.419756i
$280$	−5.44694	−	0.135436i	−0.325517	−	0.00809386i
$281$	12.9848	−	20.2047i	0.774605	−	1.20531i	−0.199651	−	0.979867i	$-0.563981\pi$
$281$	12.9848	−	20.2047i	0.774605	−	1.20531i	0.974256	−	0.225443i	$-0.0723828\pi$
$282$	7.56613	−	1.45825i	0.450557	−	0.0868376i
$283$	11.5143	−	9.05498i	0.684457	−	0.538263i	−0.214269	−	0.976775i	$-0.568737\pi$
$283$	11.5143	−	9.05498i	0.684457	−	0.538263i	0.898725	+	0.438512i	$0.144494\pi$
$284$	−1.41715	−	5.84156i	−0.0840921	−	0.346633i
$285$	6.23585	−	0.297050i	0.369380	−	0.0175957i
$286$	−1.03709	+	7.21311i	−0.0613244	+	0.426520i
$287$	22.1320	−	22.0852i	1.30641	−	1.30365i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−15.3392	−	12.0629i	−0.902304	−	0.709580i
$290$	0.0379503	+	0.0195648i	0.00222852	+	0.00114888i
$291$	5.73752	−	1.39191i	0.336339	−	0.0815950i
$292$	−2.16796	+	5.41530i	−0.126870	+	0.316906i
$293$	6.65607	+	7.68151i	0.388851	+	0.448759i	0.916098	−	0.400954i	$-0.131321\pi$
$293$	6.65607	+	7.68151i	0.388851	+	0.448759i	−0.527247	+	0.849712i	$0.676776\pi$
$294$	6.72061	−	1.95789i	0.391954	−	0.114186i
$295$	−6.73283	−	5.83403i	−0.392001	−	0.339671i
$296$	−0.154591	−	0.0375035i	−0.00898544	−	0.00217984i
$297$	−2.05582	+	2.88700i	−0.119291	+	0.167521i
$298$	10.8199	−	6.24687i	0.626780	−	0.361872i
$299$	−8.91113	+	4.22233i	−0.515344	+	0.244184i
$300$			0.758923i			0.0438164i
$301$	−0.389780	−	5.53220i	−0.0224665	−	0.318871i
$302$	3.21034	−	0.942641i	0.184734	−	0.0542429i
$303$	4.31711	+	12.4735i	0.248011	+	0.716582i
$304$	−0.144242	+	3.02801i	−0.00827285	+	0.173668i
$305$	−8.98658	+	25.9650i	−0.514570	+	1.48675i
$306$	−5.60984	−	2.24584i	−0.320693	−	0.128386i
$307$	−1.89639	+	6.45850i	−0.108232	+	0.368606i	−0.995742	−	0.0921834i	$-0.970615\pi$
$307$	−1.89639	+	6.45850i	−0.108232	+	0.368606i	0.887510	+	0.460789i	$0.152434\pi$
$308$	−2.86464	+	8.92873i	−0.163228	+	0.508761i
$309$	−17.9732	−	2.58416i	−1.02246	−	0.147008i
$310$	12.2582	−	8.72904i	0.696220	−	0.495776i
$311$	0.295880	+	3.09860i	0.0167778	+	0.175705i	0.999977	−	0.00683250i	$-0.00217487\pi$
$311$	0.295880	+	3.09860i	0.0167778	+	0.175705i	−0.983199	+	0.182538i	$0.941569\pi$
$312$	−1.90884	+	0.764186i	−0.108067	+	0.0432635i
$313$	−1.01926	−	21.3970i	−0.0576122	−	1.20943i	−0.823826	−	0.566843i	$-0.808164\pi$
$313$	−1.01926	−	21.3970i	−0.0576122	−	1.20943i	0.766213	−	0.642586i	$-0.222139\pi$
$314$	18.0261	+	5.29295i	1.01727	+	0.298699i
$315$	1.65353	+	5.19166i	0.0931661	+	0.292517i
$316$	5.75543	−	4.98711i	0.323768	−	0.280547i
$317$	27.5864	−	14.2218i	1.54940	−	0.798774i	0.550065	−	0.835122i	$-0.314603\pi$
$317$	27.5864	−	14.2218i	1.54940	−	0.798774i	0.999339	+	0.0363479i	$0.0115724\pi$
$318$	4.46420	+	0.860405i	0.250340	+	0.0482491i
$319$	0.0507073	−	0.0531803i	0.00283906	−	0.00297752i
$320$	2.05006	+	0.195757i	0.114602	+	0.0109432i
$321$	13.5528			0.756441
$322$	−12.2124	+	3.44348i	−0.680570	+	0.191898i
$323$	18.3181			1.01925
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	1.07683	−	1.12935i	0.0597317	−	0.0626448i
$326$	−4.01978	−	0.774749i	−0.222635	−	0.0429094i
$327$	−12.4228	+	6.40439i	−0.686982	+	0.354164i
$328$	−8.93110	+	7.73885i	−0.493138	+	0.427306i
$329$	−15.0705	−	13.7292i	−0.830863	−	0.756914i
$330$	−7.00318	−	2.05632i	−0.385512	−	0.113197i
$331$	−1.02738	−	21.5674i	−0.0564701	−	1.18545i	−0.832232	−	0.554427i	$-0.812937\pi$
$331$	−1.02738	−	21.5674i	−0.0564701	−	1.18545i	0.775762	−	0.631026i	$-0.217366\pi$
$332$	5.19267	−	2.07883i	0.284985	−	0.114091i
$333$	0.0151211	+	0.158355i	0.000828630	+	0.00867781i
$334$	−19.5908	+	13.9505i	−1.07196	+	0.763338i
$335$	−1.88341	−	0.270794i	−0.102902	−	0.0147951i
$336$	−2.58588	+	0.559655i	−0.141071	+	0.0305317i
$337$	−5.36534	+	18.2727i	−0.292269	+	0.995376i	0.674191	+	0.738557i	$0.264493\pi$
$337$	−5.36534	+	18.2727i	−0.292269	+	0.995376i	−0.966460	+	0.256819i	$0.917326\pi$
$338$	−8.14395	−	3.26035i	−0.442973	−	0.177339i
$339$	4.00417	−	11.5693i	0.217477	−	0.628358i
$340$	0.592121	−	12.4302i	0.0321123	−	0.674120i
$341$	−8.47054	−	24.4740i	−0.458705	−	1.32534i
$342$	2.90865	−	0.854057i	0.157282	−	0.0461821i
$343$	−14.7909	−	11.1458i	−0.798632	−	0.601819i
$344$			2.09616i			0.113017i
$345$	−2.91578	−	9.43626i	−0.156980	−	0.508031i
$346$	−16.2931	+	9.40682i	−0.875922	+	0.505714i
$347$	−4.52172	+	6.34987i	−0.242739	+	0.340879i	−0.917915	−	0.396778i	$-0.870128\pi$
$347$	−4.52172	+	6.34987i	−0.242739	+	0.340879i	0.675176	+	0.737657i	$0.264068\pi$
$348$	0.0201483	+	0.00488792i	0.00108006	+	0.000262020i
$349$	1.90905	+	1.65420i	0.102189	+	0.0885475i	0.704457	−	0.709747i	$-0.251191\pi$
$349$	1.90905	+	1.65420i	0.102189	+	0.0885475i	−0.602268	+	0.798294i	$0.705736\pi$
$350$	1.60870	−	1.20160i	0.0859885	−	0.0642281i
$351$	1.34648	+	1.55392i	0.0718697	+	0.0829421i
$352$	1.31724	−	3.29030i	0.0702090	−	0.175374i
$353$	−19.8838	+	4.82377i	−1.05831	+	0.256743i	−0.726900	−	0.686743i	$-0.759040\pi$
$353$	−19.8838	+	4.82377i	−1.05831	+	0.256743i	−0.331410	+	0.943487i	$0.607524\pi$
$354$	−3.84506	−	1.98227i	−0.204363	−	0.105356i
$355$	−9.73053	−	7.65217i	−0.516443	−	0.406135i
$356$	−3.25850	+	7.13512i	−0.172700	+	0.378161i
$357$	4.12150	+	15.4471i	0.218133	+	0.817546i
$358$	−0.727225	+	5.05796i	−0.0384350	+	0.267322i
$359$	−28.9794	+	1.38046i	−1.52948	+	0.0728579i	−0.795348	−	0.606154i	$-0.792712\pi$
$359$	−28.9794	+	1.38046i	−1.52948	+	0.0728579i	−0.734128	+	0.679011i	$0.762409\pi$
$360$	−0.485519	−	2.00134i	−0.0255891	−	0.105480i
$361$	7.71145	−	6.06435i	0.405866	−	0.319176i
$362$	−17.7642	+	3.42378i	−0.933668	+	0.179950i
$363$	−0.844042	+	1.31336i	−0.0443007	+	0.0689333i
$364$	4.64212	+	2.83627i	0.243313	+	0.148661i
$365$	3.38436	+	11.5261i	0.177146	+	0.603303i
$366$	−1.26823	+	13.2815i	−0.0662914	+	0.694235i
$367$	3.35232	+	5.80638i	0.174989	+	0.303091i	0.940158	−	0.340740i	$-0.110678\pi$
$367$	3.35232	+	5.80638i	0.174989	+	0.303091i	−0.765168	+	0.643830i	$0.777344\pi$
$368$	4.69591	−	0.973884i	0.244791	−	0.0507672i
$369$	10.2343	+	5.90877i	0.532776	+	0.307598i
$370$	−0.297994	+	0.136089i	−0.0154920	+	0.00707494i
$371$	−5.24434	−	10.8251i	−0.272273	−	0.562011i
$372$	4.78527	−	5.52250i	0.248105	−	0.286328i
$373$	−5.29268	−	10.2664i	−0.274045	−	0.531573i	0.711144	−	0.703046i	$-0.248177\pi$
$373$	−5.29268	−	10.2664i	−0.274045	−	0.531573i	−0.985189	+	0.171474i	$0.945147\pi$
$374$	−20.2385	−	7.00461i	−1.04651	−	0.362200i
$375$	7.33128	+	9.32247i	0.378585	+	0.481411i
$376$	5.31732	+	5.57664i	0.274220	+	0.287593i
$377$	−0.0230470	−	0.0358619i	−0.00118698	−	0.00184698i
$378$	1.37463	+	2.26062i	0.0707035	+	0.116274i
$379$	7.48990	+	3.42052i	0.384730	+	0.175700i	0.598385	−	0.801209i	$-0.295809\pi$
$379$	7.48990	+	3.42052i	0.384730	+	0.175700i	−0.213655	+	0.976909i	$0.568537\pi$
$380$	3.62125	+	5.08533i	0.185766	+	0.260872i
$381$	3.25836	+	8.13900i	0.166931	+	0.416973i
$382$	−3.54815	+	6.88245i	−0.181539	+	0.352137i
$383$	7.78472	−	7.42272i	0.397781	−	0.379283i	−0.464619	−	0.885511i	$-0.653809\pi$
$383$	7.78472	−	7.42272i	0.397781	−	0.379283i	0.862400	+	0.506227i	$0.168960\pi$
$384$	0.989821	−	0.142315i	0.0505116	−	0.00726247i
$385$	6.72929	+	18.1005i	0.342957	+	0.922486i
$386$	23.0799	+	14.8326i	1.17474	+	0.754958i
$387$	1.98087	−	0.685587i	0.100693	−	0.0348503i
$388$	4.27288	+	4.07418i	0.216923	+	0.206835i
$389$	11.9609	+	8.51729i	0.606440	+	0.431844i	0.841591	−	0.540115i	$-0.181619\pi$
$389$	11.9609	+	8.51729i	0.606440	+	0.431844i	−0.235151	+	0.971959i	$0.575559\pi$
$390$	−2.11718	+	3.66707i	−0.107208	+	0.185689i
$391$	−7.22840	−	28.0638i	−0.365556	−	1.41925i
$392$	5.28052	+	4.59523i	0.266707	+	0.232094i
$393$	−5.04326	−	11.0432i	−0.254399	−	0.557055i
$394$	−2.05672	+	8.47791i	−0.103616	+	0.427111i
$395$	2.96809	−	15.3999i	0.149341	−	0.774854i
$396$	−3.54016	−	0.168639i	−0.177900	−	0.00847441i
$397$	1.95701	+	10.1539i	0.0982195	+	0.509611i	0.997402	+	0.0720371i	$0.0229500\pi$
$397$	1.95701	+	10.1539i	0.0982195	+	0.509611i	−0.899183	+	0.437574i	$0.855838\pi$
$398$	−0.109901	−	0.764376i	−0.00550882	−	0.0383147i
$399$	−6.41561	−	4.81328i	−0.321182	−	0.240965i
$400$	−0.638446	+	0.410304i	−0.0319223	+	0.0205152i
$401$	−1.49462	+	1.90056i	−0.0746377	+	0.0949095i	−0.821938	−	0.569577i	$-0.807107\pi$
$401$	−1.49462	+	1.90056i	−0.0746377	+	0.0949095i	0.747301	+	0.664486i	$0.231350\pi$
$402$	−0.919771	+	0.0878275i	−0.0458740	+	0.00438044i
$403$	−14.9567	+	1.42820i	−0.745048	+	0.0711435i
$404$	−8.15934	+	10.3754i	−0.405943	+	0.516198i
$405$	−1.73247	+	1.11339i	−0.0860870	+	0.0553247i
$406$	−0.0215397	−	0.0504476i	−0.00106900	−	0.00250367i
$407$	0.0802359	+	0.558053i	0.00397715	+	0.0276617i
$408$	−1.14359	−	5.93350i	−0.0566160	−	0.293752i
$409$	−9.51068	−	0.453049i	−0.470273	−	0.0224018i	−0.188892	−	0.981998i	$-0.560489\pi$
$409$	−9.51068	−	0.453049i	−0.470273	−	0.0224018i	−0.281381	+	0.959596i	$0.590793\pi$
$410$	−4.60579	+	23.8971i	−0.227464	+	1.18019i
$411$	2.63717	−	10.8706i	0.130082	−	0.536206i
$412$	−7.54312	−	16.5171i	−0.371623	−	0.813741i
$413$	1.88603	+	11.2889i	0.0928055	+	0.555492i
$414$	−2.45620	−	4.11911i	−0.120716	−	0.202443i
$415$	5.75942	−	9.97560i	0.282719	−	0.489683i
$416$	−1.67487	−	1.19267i	−0.0821174	−	0.0584756i
$417$	−1.94222	−	1.85190i	−0.0951107	−	0.0906879i
$418$	10.1531	−	3.51401i	0.496603	−	0.171876i
$419$	−1.02868	−	0.661095i	−0.0502545	−	0.0322966i	0.515272	−	0.857026i	$-0.327691\pi$
$419$	−1.02868	−	0.661095i	−0.0502545	−	0.0322966i	−0.565527	+	0.824730i	$0.691327\pi$
$420$	−3.47354	+	4.19787i	−0.169491	+	0.204835i
$421$	−3.23241	+	0.464751i	−0.157538	+	0.0226506i	−0.220633	−	0.975357i	$-0.570812\pi$
$421$	−3.23241	+	0.464751i	−0.157538	+	0.0226506i	0.0630944	+	0.998008i	$0.479903\pi$
$422$	10.6790	−	10.1824i	0.519847	−	0.495673i
$423$	3.53081	−	6.84881i	0.171674	−	0.333001i
$424$	1.68971	+	4.22070i	0.0820597	+	0.204975i
$425$	2.66010	+	3.73559i	0.129034	+	0.181203i
$426$	−5.46779	−	2.49706i	−0.264915	−	0.120983i
$427$	30.1609	−	18.3403i	1.45959	−	0.887547i
$428$	7.32717	+	11.4013i	0.354172	+	0.551103i
$429$	5.02880	+	5.27406i	0.242793	+	0.254634i
$430$	2.66847	+	3.39324i	0.128685	+	0.163637i
$431$	20.5772	+	7.12182i	0.991167	+	0.343046i	0.774067	−	0.633103i	$-0.218219\pi$
$431$	20.5772	+	7.12182i	0.991167	+	0.343046i	0.217099	+	0.976150i	$0.430340\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	10.1097	−	11.6672i	0.485841	−	0.560690i	−0.458909	−	0.888483i	$-0.651759\pi$
$433$	10.1097	−	11.6672i	0.485841	−	0.560690i	0.944750	+	0.327793i	$0.106305\pi$
$434$	−19.2826	−	1.39966i	−0.925594	−	0.0671856i
$435$	0.0388383	−	0.0177368i	0.00186215	−	0.000850417i
$436$	−12.1040	−	6.98824i	−0.579676	−	0.334676i
$437$	11.5534	+	8.82506i	0.552673	+	0.422160i
$438$	2.91657	+	5.05164i	0.139359	+	0.241377i
$439$	0.442045	−	4.62931i	0.0210977	−	0.220945i	−0.978774	−	0.204941i	$-0.934300\pi$
$439$	0.442045	−	4.62931i	0.0210977	−	0.220945i	0.999872	−	0.0160035i	$-0.00509429\pi$
$440$	−2.05632	−	7.00318i	−0.0980312	−	0.333863i
$441$	2.61540	−	6.49305i	0.124543	−	0.309193i
$442$	−6.71723	+	10.4522i	−0.319506	+	0.497161i
$443$	14.2733	−	2.75096i	0.678147	−	0.130702i	0.161464	−	0.986879i	$-0.448379\pi$
$443$	14.2733	−	2.75096i	0.678147	−	0.130702i	0.516683	+	0.856177i	$0.327166\pi$
$444$	−0.125042	+	0.0983339i	−0.00593422	+	0.00466672i
$445$	3.80840	+	15.6984i	0.180535	+	0.744177i
$446$	−21.6225	+	1.03001i	−1.02385	+	0.0487722i
$447$	1.77805	−	12.3666i	0.0840987	−	0.584919i
$448$	−1.86885	−	1.87281i	−0.0882946	−	0.0884820i
$449$	15.6466	−	34.2614i	0.738411	−	1.61689i	−0.0477405	−	0.998860i	$-0.515202\pi$
$449$	15.6466	−	34.2614i	0.738411	−	1.61689i	0.786151	−	0.618034i	$-0.212071\pi$
$450$	0.596553	+	0.469135i	0.0281218	+	0.0221152i
$451$	37.2275	+	19.1921i	1.75297	+	0.903721i
$452$	11.8975	−	2.88631i	0.559613	−	0.135761i
$453$	1.24354	−	3.10620i	0.0584264	−	0.145942i
$454$	2.05826	+	2.37536i	0.0965991	+	0.111481i
$455$	11.1253	−	1.31823i	0.521560	−	0.0617997i
$456$	2.29101	+	1.98517i	0.107287	+	0.0929643i
$457$	−16.0168	−	3.88562i	−0.749232	−	0.181762i	−0.157078	−	0.987586i	$-0.550207\pi$
$457$	−16.0168	−	3.88562i	−0.749232	−	0.181762i	−0.592155	+	0.805824i	$0.701723\pi$
$458$	12.0929	−	16.9821i	0.565064	−	0.793522i
$459$	−5.23313	+	3.02135i	−0.244261	+	0.141024i
$460$	6.36190	−	7.55454i	0.296625	−	0.352232i
$461$			2.79228i			0.130049i	0.997884	+	0.0650247i	$0.0207126\pi$
$461$			2.79228i			0.130049i	−0.997884	+	0.0650247i	$0.979287\pi$
$462$	5.24765	+	7.77113i	0.244143	+	0.361546i
$463$	−13.8528	+	4.06755i	−0.643795	+	0.189035i	−0.587302	−	0.809368i	$-0.699810\pi$
$463$	−13.8528	+	4.06755i	−0.643795	+	0.189035i	−0.0564929	+	0.998403i	$0.517992\pi$
$464$	0.00678100	+	0.0195924i	0.000314800	+	0.000909556i
$465$	0.716040	−	15.0315i	0.0332056	−	0.697071i
$466$	−0.883621	+	2.55305i	−0.0409329	+	0.118268i
$467$	−8.92934	−	3.57477i	−0.413201	−	0.165421i	0.155742	−	0.987798i	$-0.450223\pi$
$467$	−8.92934	−	3.57477i	−0.413201	−	0.165421i	−0.568943	+	0.822377i	$0.692647\pi$
$468$	−0.579279	+	1.97284i	−0.0267772	+	0.0911946i
$469$	1.64244	+	1.81059i	0.0758407	+	0.0836054i
$470$	15.7068	+	2.25830i	0.724503	+	0.104168i
$471$	15.3036	−	10.8976i	0.705151	−	0.502136i
$472$	−0.411208	−	4.30636i	−0.0189274	−	0.198217i
$473$	6.89700	−	2.76114i	0.317124	−	0.126957i
$474$	−0.362362	−	7.60690i	−0.0166438	−	0.349397i
$475$	−2.20744	−	0.648163i	−0.101284	−	0.0297398i
$476$	−10.7667	+	11.8185i	−0.493489	+	0.541702i
$477$	3.43591	−	2.97723i	0.157320	−	0.136318i
$478$	−4.15550	+	2.14231i	−0.190068	+	0.0979871i
$479$	8.76504	+	1.68932i	0.400485	+	0.0771871i	0.385517	−	0.922701i	$-0.374023\pi$
$479$	8.76504	+	1.68932i	0.400485	+	0.0771871i	0.0149682	+	0.999888i	$0.495235\pi$
$480$	1.42114	−	1.49045i	0.0648659	−	0.0680294i
$481$	0.325599	+	0.0310909i	0.0148460	+	0.00141762i
$482$	−2.05599			−0.0936476
$483$	−4.84244	+	11.7282i	−0.220338	+	0.533652i
$484$	−1.56119			−0.0709631
$485$	12.1034	+	1.15574i	0.549589	+	0.0524794i
$486$	−0.690079	+	0.723734i	−0.0313026	+	0.0328292i
$487$	12.3357	+	2.37751i	0.558984	+	0.107735i	0.460915	−	0.887444i	$-0.347521\pi$
$487$	12.3357	+	2.37751i	0.558984	+	0.107735i	0.0980690	+	0.995180i	$0.468733\pi$
$488$	−11.8588	+	6.11362i	−0.536821	+	0.276751i
$489$	−3.09386	+	2.68084i	−0.139909	+	0.121232i
$490$	14.3979	+	0.716440i	0.650431	+	0.0323655i
$491$	−10.0350	−	2.94653i	−0.452871	−	0.132975i	0.0473393	−	0.998879i	$-0.484926\pi$
$491$	−10.0350	−	2.94653i	−0.452871	−	0.132975i	−0.500210	+	0.865904i	$0.666744\pi$
$492$	0.562301	+	11.8042i	0.0253505	+	0.532173i
$493$	0.116307	−	0.0465624i	0.00523822	−	0.00209707i
$494$	−0.592489	−	6.20482i	−0.0266573	−	0.279168i
$495$	−5.94545	+	4.23374i	−0.267228	+	0.190292i
$496$	7.23293	+	1.03994i	0.324768	+	0.0466946i
$497$	3.36409	+	15.5437i	0.150900	+	0.697231i
$498$	1.57582	−	5.36676i	0.0706143	−	0.240490i
$499$	−27.0318	−	10.8219i	−1.21011	−	0.484454i	−0.323169	−	0.946341i	$-0.604748\pi$
$499$	−27.0318	−	10.8219i	−1.21011	−	0.484454i	−0.886939	+	0.461887i	$0.847172\pi$
$500$	−3.87898	+	11.2076i	−0.173473	+	0.501218i
$501$	−1.14436	+	24.0230i	−0.0511261	+	1.07327i
$502$	7.63839	+	22.0697i	0.340918	+	0.985018i
$503$	27.4994	−	8.07456i	1.22614	−	0.360027i	0.396348	−	0.918101i	$-0.370278\pi$
$503$	27.4994	−	8.07456i	1.22614	−	0.360027i	0.829791	+	0.558074i	$0.188459\pi$
$504$	−1.15857	+	2.37860i	−0.0516067	+	0.105951i
$505$			27.1827i			1.20962i
$506$	−9.39000	−	14.1681i	−0.417436	−	0.629849i
$507$	−7.59706	+	4.38617i	−0.337397	+	0.194796i
$508$	−5.08535	+	7.14138i	−0.225626	+	0.316848i
$509$	−39.5893	−	9.60425i	−1.75476	−	0.425701i	−0.776006	−	0.630725i	$-0.782758\pi$
$509$	−39.5893	−	9.60425i	−1.75476	−	0.425701i	−0.978757	+	0.205024i	$0.934273\pi$
$510$	−9.40474	−	8.14925i	−0.416449	−	0.360855i
$511$	6.09024	−	14.1805i	0.269416	−	0.627309i
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	1.12667	−	2.81430i	0.0497439	−	0.124254i
$514$	−22.6479	+	5.49433i	−0.998958	+	0.242345i
$515$	−33.2375	−	17.1351i	−1.46462	−	0.755064i
$516$	1.64769	+	1.29576i	0.0725357	+	0.0570427i
$517$	11.3447	−	24.8413i	0.498938	−	1.09252i
$518$	0.406418	+	0.109361i	0.0178570	+	0.00480504i
$519$	−2.67746	+	18.6221i	−0.117527	+	0.817422i
$520$	−4.22957	+	0.201479i	−0.185479	+	0.00883545i
$521$	2.07599	+	8.55734i	0.0909507	+	0.374904i	0.999037	−	0.0438796i	$-0.0139718\pi$
$521$	2.07599	+	8.55734i	0.0909507	+	0.374904i	−0.908086	+	0.418783i	$0.862457\pi$
$522$	0.0162970	−	0.0128161i	0.000713301	−	0.000560946i
$523$	0.341415	−	0.0658024i	0.0149291	−	0.00287734i	−0.181781	−	0.983339i	$-0.558186\pi$
$523$	0.341415	−	0.0658024i	0.0149291	−	0.00287734i	0.196710	+	0.980462i	$0.436974\pi$
$524$	6.56353	−	10.2131i	0.286729	−	0.446159i
$525$	0.0499108	−	2.00730i	0.00217828	−	0.0876057i
$526$	−2.68117	−	9.13122i	−0.116905	−	0.398140i
$527$	4.19728	−	43.9559i	0.182836	−	1.91475i
$528$	−1.77209	−	3.06935i	−0.0771202	−	0.133576i
$529$	8.96120	−	21.1825i	0.389617	−	0.920977i
$530$	8.10836	+	4.68136i	0.352204	+	0.203345i
$531$	−3.93503	+	1.79707i	−0.170766	+	0.0779860i
$532$	0.580649	−	7.99940i	0.0251743	−	0.346818i
$533$	15.9121	−	18.3635i	0.689228	−	0.795412i
$534$	3.59431	+	6.97200i	0.155541	+	0.301708i
$535$	26.3753	+	9.12859i	1.14031	+	0.394663i
$536$	−0.571151	−	0.726277i	−0.0246700	−	0.0313704i
$537$	3.52629	+	3.69826i	0.152170	+	0.159592i
$538$	−1.82248	−	2.83584i	−0.0785728	−	0.122262i
$539$	8.16397	−	23.4275i	0.351647	−	1.00909i
$540$	−1.87328	−	0.855501i	−0.0806133	−	0.0368149i
$541$	−6.61357	−	9.28746i	−0.284340	−	0.399299i	0.647561	−	0.762014i	$-0.275789\pi$
$541$	−6.61357	−	9.28746i	−0.284340	−	0.399299i	−0.931900	+	0.362715i	$0.881850\pi$
$542$	−6.43746	−	16.0800i	−0.276512	−	0.690695i
$543$	−8.28986	+	16.0801i	−0.355752	+	0.690062i
$544$	4.37330	−	4.16994i	0.187504	−	0.178785i
$545$	−28.4900	+	4.09624i	−1.22038	+	0.175464i
$546$	5.09902	−	1.89569i	0.218218	−	0.0811279i
$547$	5.35749	+	3.44305i	0.229070	+	0.147214i	0.650141	−	0.759813i	$-0.274710\pi$
$547$	5.35749	+	3.44305i	0.229070	+	0.147214i	−0.421072	+	0.907027i	$0.638346\pi$
$548$	10.5707	−	3.65854i	0.451557	−	0.156285i
$549$	9.65600	+	9.20698i	0.412108	+	0.392944i
$550$	2.19101	+	1.56021i	0.0934250	+	0.0665276i
$551$	−0.0314250	+	0.0544298i	−0.00133875	+	0.00231879i
$552$	2.13729	−	4.29325i	0.0909692	−	0.182733i
$553$	−15.5507	+	12.8121i	−0.661284	+	0.544825i
$554$	10.5759	+	23.1579i	0.449326	+	0.983886i
$555$	−0.0772342	+	0.318364i	−0.00327841	+	0.0135138i
$556$	0.507875	−	2.63511i	0.0215387	−	0.111753i
$557$	−27.2524	−	1.29819i	−1.15472	−	0.0550061i	−0.538532	−	0.842605i	$-0.681021\pi$
$557$	−27.2524	−	1.29819i	−1.15472	−	0.0550061i	−0.616188	+	0.787599i	$0.711324\pi$
$558$	−1.38292	−	7.17526i	−0.0585436	−	0.303753i
$559$	−0.613374	−	4.26611i	−0.0259429	−	0.180437i
$560$	−5.40941	−	0.652588i	−0.228589	−	0.0275769i
$561$	−18.0166	+	11.5786i	−0.760662	+	0.488848i
$562$	14.8465	−	18.8789i	0.626263	−	0.796358i
$563$	42.2825	−	4.03749i	1.78199	−	0.170160i	0.848606	−	0.529026i	$-0.177442\pi$
$563$	42.2825	−	4.03749i	1.78199	−	0.170160i	0.933389	+	0.358866i	$0.116836\pi$
$564$	7.67049	−	0.732443i	0.322986	−	0.0308414i
$565$	15.5852	−	19.8182i	0.655676	−	0.833759i
$566$	12.3229	−	7.91947i	0.517972	−	0.332880i
$567$	2.62671	+	0.316884i	0.110311	+	0.0133079i
$568$	−0.855454	−	5.94981i	−0.0358940	−	0.249649i
$569$	−7.07518	−	36.7095i	−0.296607	−	1.53894i	−0.758301	−	0.651904i	$-0.773970\pi$
$569$	−7.07518	−	36.7095i	−0.296607	−	1.53894i	0.461694	−	0.887039i	$-0.347242\pi$
$570$	6.23585	+	0.297050i	0.261191	+	0.0124421i
$571$	6.20103	−	32.1740i	0.259505	−	1.34644i	−0.585061	−	0.810989i	$-0.698930\pi$
$571$	6.20103	−	32.1740i	0.259505	−	1.34644i	0.844566	−	0.535451i	$-0.179858\pi$
$572$	−1.71804	+	7.08187i	−0.0718350	+	0.296108i
$573$	3.21665	+	7.04349i	0.134378	+	0.294246i
$574$	24.1311	−	19.8814i	1.00721	−	0.829833i
$575$	−0.121937	+	3.63762i	−0.00508511	+	0.151699i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	5.98858	+	4.26445i	0.249308	+	0.177531i	0.697879	−	0.716216i	$-0.254127\pi$
$577$	5.98858	+	4.26445i	0.249308	+	0.177531i	−0.448571	+	0.893747i	$0.648067\pi$
$578$	−14.1231	−	13.4663i	−0.587442	−	0.560125i
$579$	25.9263	−	8.97316i	1.07746	−	0.372912i
$580$	0.0359187	+	0.0230836i	0.00149144	+	0.000958493i
$581$	−13.8710	+	5.15687i	−0.575465	+	0.213943i
$582$	5.84385	−	0.840218i	0.242235	−	0.0348282i
$583$	11.6616	−	11.1193i	0.482974	−	0.460515i
$584$	−2.67290	+	5.18470i	−0.110605	+	0.214544i
$585$	1.57376	+	3.93105i	0.0650668	+	0.162529i
$586$	5.89575	+	8.27943i	0.243551	+	0.342020i
$587$	−15.4203	−	7.04220i	−0.636463	−	0.290663i	0.0709324	−	0.997481i	$-0.477403\pi$
$587$	−15.4203	−	7.04220i	−0.636463	−	0.290663i	−0.707395	+	0.706818i	$0.750130\pi$
$588$	6.87629	−	1.31019i	0.283574	−	0.0540313i
$589$	11.9761	+	18.6352i	0.493467	+	0.767850i
$590$	−6.14779	−	6.44761i	−0.253100	−	0.265444i
$591$	5.39271	+	6.85739i	0.221826	+	0.282075i
$592$	−0.150326	−	0.0520285i	−0.00617838	−	0.00213836i
$593$	−21.0611	−	40.8528i	−0.864875	−	1.67762i	−0.726416	−	0.687255i	$-0.758816\pi$
$593$	−21.0611	−	40.8528i	−0.864875	−	1.67762i	−0.138458	−	0.990368i	$-0.544215\pi$
$594$	−2.32094	+	2.67851i	−0.0952294	+	0.109901i
$595$	−2.38359	+	32.8380i	−0.0977179	+	1.34623i
$596$	11.3647	−	5.19009i	0.465517	−	0.212594i
$597$	−0.668776	−	0.386118i	−0.0273712	−	0.0158028i
$598$	−9.27214	+	3.35616i	−0.379166	+	0.137243i
$599$	1.86846	+	3.23627i	0.0763432	+	0.132230i	0.901670	−	0.432426i	$-0.142342\pi$
$599$	1.86846	+	3.23627i	0.0763432	+	0.132230i	−0.825326	+	0.564656i	$0.809009\pi$
$600$	−0.0721402	+	0.755486i	−0.00294511	+	0.0308426i
$601$	7.36144	+	25.0708i	0.300280	+	1.02266i	0.962032	+	0.272936i	$0.0879947\pi$
$601$	7.36144	+	25.0708i	0.300280	+	1.02266i	−0.661753	+	0.749722i	$0.730187\pi$
$602$	0.137855	−	5.54421i	0.00561853	−	0.225965i
$603$	−0.499528	+	0.777280i	−0.0203423	+	0.0316533i
$604$	3.28541	−	0.633211i	0.133681	−	0.0257650i
$605$	−2.52723	+	1.98744i	−0.102747	+	0.0808009i
$606$	3.11188	+	12.8274i	0.126412	+	0.521076i
$607$	22.0563	−	1.05067i	0.895239	−	0.0426455i	0.405083	−	0.914280i	$-0.367243\pi$
$607$	22.0563	−	1.05067i	0.895239	−	0.0426455i	0.490156	+	0.871635i	$0.336940\pi$
$608$	−0.431420	+	3.00059i	−0.0174964	+	0.121690i
$609$	−0.0529694	−	0.0142533i	−0.00214643	−	0.000577572i
$610$	−11.4140	+	24.9932i	−0.462140	+	1.01195i
$611$	−12.4536	−	9.79365i	−0.503820	−	0.396209i
$612$	−5.37096	−	2.76892i	−0.217108	−	0.111927i
$613$	2.26436	−	0.549328i	0.0914567	−	0.0221872i	−0.189769	−	0.981829i	$-0.560774\pi$
$613$	2.26436	−	0.549328i	0.0914567	−	0.0221872i	0.281226	+	0.959642i	$0.409259\pi$
$614$	−2.50172	+	6.24899i	−0.100961	+	0.252189i
$615$	15.9373	+	18.3926i	0.642653	+	0.741661i
$616$	−3.70039	+	8.61600i	−0.149093	+	0.347148i
$617$	−18.9835	−	16.4493i	−0.764246	−	0.662223i	0.182862	−	0.983139i	$-0.441464\pi$
$617$	−18.9835	−	16.4493i	−0.764246	−	0.662223i	−0.947108	+	0.320916i	$0.896009\pi$
$618$	−17.6462	−	4.28092i	−0.709834	−	0.172204i
$619$	−12.7272	+	17.8728i	−0.511548	+	0.718369i	−0.986883	−	0.161436i	$-0.948388\pi$
$619$	−12.7272	+	17.8728i	−0.511548	+	0.718369i	0.475335	+	0.879805i	$0.342327\pi$
$620$	13.0325	−	7.52429i	0.523396	−	0.302183i
$621$	−4.75616	−	0.615560i	−0.190858	−	0.0247016i
$622$			3.11269i			0.124808i
$623$	9.08777	−	18.6576i	0.364094	−	0.747502i
$624$	−1.97284	+	0.579279i	−0.0789769	+	0.0231897i
$625$	6.74722	+	19.4948i	0.269889	+	0.779793i
$626$	1.01926	−	21.3970i	0.0407380	−	0.855196i
$627$	3.51401	−	10.1531i	0.140336	−	0.405474i
$628$	17.4414	+	6.98248i	0.695988	+	0.278631i
$629$	−0.270814	+	0.922308i	−0.0107981	+	0.0367748i
$630$	1.15255	+	5.32533i	0.0459186	+	0.212166i
$631$	−3.08472	−	0.443516i	−0.122801	−	0.0176561i	0.0806404	−	0.996743i	$-0.474303\pi$
$631$	−3.08472	−	0.443516i	−0.122801	−	0.0176561i	−0.203441	+	0.979087i	$0.565213\pi$
$632$	6.20343	−	4.41744i	0.246759	−	0.175716i
$633$	−1.40260	−	14.6886i	−0.0557482	−	0.583821i
$634$	28.8133	−	11.5351i	1.14432	−	0.458118i
$635$	0.859074	+	18.0342i	0.0340913	+	0.715665i
$636$	4.36220	+	1.28086i	0.172973	+	0.0507893i
$637$	−12.0916	−	7.80703i	−0.479085	−	0.309326i
$638$	0.0555328	−	0.0481194i	0.00219856	−	0.00190507i
$639$	−5.34279	+	2.75440i	−0.211357	+	0.108962i
$640$	2.02217	+	0.389742i	0.0799334	+	0.0154059i
$641$	−27.2835	+	28.6141i	−1.07763	+	1.13019i	−0.0866454	+	0.996239i	$0.527615\pi$
$641$	−27.2835	+	28.6141i	−1.07763	+	1.13019i	−0.990988	+	0.133950i	$0.957234\pi$
$642$	13.4914	+	1.28827i	0.532463	+	0.0508440i
$643$	15.2822			0.602673			0.301336	−	0.953518i	$-0.402567\pi$
$643$	15.2822			0.602673			0.301336	+	0.953518i	$0.402567\pi$
$644$	−12.4844	+	2.26703i	−0.491955	+	0.0893335i
$645$	4.31681			0.169974
$646$	18.2352	+	1.74125i	0.717453	+	0.0685084i
$647$	−12.3344	+	12.9360i	−0.484916	+	0.508566i	−0.920050	−	0.391800i	$-0.871852\pi$
$647$	−12.3344	+	12.9360i	−0.484916	+	0.508566i	0.435134	+	0.900366i	$0.356701\pi$
$648$	−0.981929	−	0.189251i	−0.0385738	−	0.00743449i
$649$	−13.6276	+	7.02550i	−0.534929	+	0.275775i
$650$	1.17930	−	1.02187i	0.0462561	−	0.0400812i
$651$	−13.0199	+	14.2919i	−0.510291	+	0.560145i
$652$	−3.92793	−	1.15335i	−0.153830	−	0.0451685i
$653$	−0.502893	−	10.5570i	−0.0196797	−	0.413128i	−0.987115	−	0.160011i	$-0.948847\pi$
$653$	−0.502893	−	10.5570i	−0.0196797	−	0.413128i	0.967436	−	0.253117i	$-0.0814559\pi$
$654$	−12.9753	+	5.19453i	−0.507375	+	0.203122i
$655$	−2.37655	−	24.8883i	−0.0928594	−	0.972468i
$656$	−9.62629	+	6.85485i	−0.375843	+	0.267637i
$657$	5.77376	+	0.830142i	0.225256	+	0.0323869i
$658$	−13.6972	−	15.0995i	−0.533973	−	0.588642i
$659$	8.29991	−	28.2669i	0.323319	−	1.10112i	−0.624158	−	0.781298i	$-0.714558\pi$
$659$	8.29991	−	28.2669i	0.323319	−	1.10112i	0.947477	−	0.319824i	$-0.103624\pi$
$660$	−6.77600	−	2.71270i	−0.263756	−	0.105592i
$661$	−11.0153	+	31.8267i	−0.428446	+	1.23791i	0.499863	+	0.866105i	$0.333384\pi$
$661$	−11.0153	+	31.8267i	−0.428446	+	1.23791i	−0.928309	+	0.371810i	$0.878737\pi$
$662$	1.02738	−	21.5674i	0.0399304	−	0.838242i
$663$	4.06368	+	11.7412i	0.157820	+	0.455991i
$664$	5.36676	−	1.57582i	0.208271	−	0.0611538i
$665$	−9.24353	−	13.6885i	−0.358449	−	0.530818i
$666$			0.159076i			0.00616405i
$667$	0.0957882	+	0.0266657i	0.00370893	+	0.00103250i
$668$	−20.8281	+	12.0251i	−0.805865	+	0.465266i
$669$	−12.5565	+	17.6331i	−0.485462	+	0.681736i
$670$	−1.84914	−	0.448598i	−0.0714387	−	0.0173308i
$671$	35.7365	+	30.9658i	1.37959	+	1.19542i
$672$	−2.62737	+	0.311317i	−0.101353	+	0.0120093i
$673$	−19.2982	−	22.2713i	−0.743892	−	0.858497i	0.250069	−	0.968228i	$-0.419547\pi$
$673$	−19.2982	−	22.2713i	−0.743892	−	0.858497i	−0.993961	+	0.109731i	$0.965001\pi$
$674$	−7.07798	+	17.6799i	−0.272633	+	0.681005i
$675$	0.737530	−	0.178923i	0.0283875	−	0.00688674i
$676$	−7.79716	−	4.01971i	−0.299891	−	0.154604i
$677$	−27.0405	−	21.2649i	−1.03925	−	0.817275i	−0.0557970	−	0.998442i	$-0.517770\pi$
$677$	−27.0405	−	21.2649i	−1.03925	−	0.817275i	−0.983452	+	0.181168i	$0.942012\pi$
$678$	5.08577	−	11.1363i	0.195318	−	0.427687i
$679$	−11.0336	−	11.0570i	−0.423429	−	0.424327i
$680$	1.77100	−	12.3176i	0.0679148	−	0.472358i
$681$	3.13949	−	0.149553i	0.120306	−	0.00573087i
$682$	−6.10578	−	25.1684i	−0.233802	−	0.963746i
$683$	−0.00435078	+	0.00342149i	−0.000166478	+	0.000130920i	−0.618242	−	0.785988i	$-0.712155\pi$
$683$	−0.00435078	+	0.00342149i	−0.000166478	+	0.000130920i	0.618076	+	0.786119i	$0.287912\pi$
$684$	2.97666	−	0.573705i	0.113816	−	0.0219362i
$685$	12.4542	−	19.3792i	0.475852	−	0.740440i
$686$	−13.6644	−	12.5013i	−0.521710	−	0.477303i
$687$	−5.87350	−	20.0033i	−0.224088	−	0.763174i
$688$	−0.199253	+	2.08667i	−0.00759644	+	0.0795535i
$689$	−4.67396	−	8.09553i	−0.178064	−	0.308415i
$690$	−2.00560	−	9.67069i	−0.0763521	−	0.368157i
$691$	36.4253	+	21.0302i	1.38568	+	0.800025i	0.992825	−	0.119573i	$-0.0381527\pi$
$691$	36.4253	+	21.0302i	1.38568	+	0.800025i	0.392859	+	0.919599i	$0.371486\pi$
$692$	−17.1135	+	7.81547i	−0.650557	+	0.297100i
$693$	9.35240	+	0.678858i	0.355268	+	0.0257877i
$694$	−5.10484	+	5.89130i	−0.193777	+	0.223631i
$695$	−2.53243	−	4.91222i	−0.0960604	−	0.186331i
$696$	0.0195924	+	0.00678100i	0.000742649	+	0.000257033i
$697$	44.1426	+	56.1319i	1.67202	+	2.12615i
$698$	1.74317	+	1.82818i	0.0659798	+	0.0691977i
$699$	1.46062	+	2.27277i	0.0552457	+	0.0859639i
$700$	1.71563	−	1.04324i	0.0648448	−	0.0394308i
$701$	−25.4538	−	11.6243i	−0.961375	−	0.439045i	−0.128013	−	0.991772i	$-0.540860\pi$
$701$	−25.4538	−	11.6243i	−0.961375	−	0.439045i	−0.833362	+	0.552727i	$0.813587\pi$
$702$	1.19267	+	1.67487i	0.0450145	+	0.0632140i
$703$	−0.179226	−	0.447686i	−0.00675965	−	0.0168848i
$704$	1.62404	−	3.15019i	0.0612082	−	0.118727i
$705$	11.4845	−	10.9504i	0.432530	−	0.412417i
$706$	−20.2523	+	2.91185i	−0.762207	+	0.109589i
$707$	22.2633	−	26.9058i	0.837296	−	1.01190i
$708$	−3.63922	−	2.33879i	−0.136770	−	0.0878970i
$709$	−43.8584	+	15.1795i	−1.64713	+	0.570079i	−0.983961	−	0.178386i	$-0.942912\pi$
$709$	−43.8584	+	15.1795i	−1.64713	+	0.570079i	−0.663174	+	0.748465i	$0.730791\pi$
$710$	−8.95908	−	8.54247i	−0.336228	−	0.320593i
$711$	−6.20343	−	4.41744i	−0.232647	−	0.165667i
$712$	−3.92198	+	6.79308i	−0.146983	+	0.254581i
$713$	23.8238	−	25.7012i	0.892207	−	0.962519i
$714$	2.63450	+	15.7689i	0.0985935	+	0.590137i
$715$	6.23428	+	13.6512i	0.233149	+	0.510525i
$716$	−1.20472	+	4.96593i	−0.0450226	+	0.185586i
$717$	−0.884792	+	4.59074i	−0.0330432	+	0.171444i
$718$	−28.9794	−	1.38046i	−1.08150	−	0.0515183i
$719$	2.05962	+	10.6863i	0.0768107	+	0.398532i	0.999903	+	0.0139525i	$0.00444136\pi$
$719$	2.05962	+	10.6863i	0.0768107	+	0.398532i	−0.923092	+	0.384579i	$0.874347\pi$
$720$	−0.293081	−	2.03843i	−0.0109225	−	0.0759677i
$721$	18.8648	+	44.1828i	0.702562	+	1.64545i
$722$	8.25298	−	5.30387i	0.307144	−	0.197390i
$723$	−1.27093	+	1.61611i	−0.0472662	+	0.0601039i
$724$	−18.0093	+	1.71968i	−0.669309	+	0.0639113i
$725$	−0.0156633	+	0.00149566i	−0.000581719	+	5.55475e-5i
$726$	−0.965063	+	1.22718i	−0.0358168	+	0.0455448i
$727$	18.4107	−	11.8319i	0.682816	−	0.438819i	−0.152709	−	0.988271i	$-0.548800\pi$
$727$	18.4107	−	11.8319i	0.682816	−	0.438819i	0.835525	+	0.549452i	$0.185163\pi$
$728$	4.35149	+	3.26469i	0.161277	+	0.120997i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	2.27342	+	11.7956i	0.0841429	+	0.436575i
$731$	12.6521	+	0.602694i	0.467955	+	0.0222915i
$732$	−2.52497	+	13.1008i	−0.0933257	+	0.484220i
$733$	−8.76940	+	36.1480i	−0.323905	+	1.33516i	0.544275	+	0.838907i	$0.316805\pi$
$733$	−8.76940	+	36.1480i	−0.323905	+	1.33516i	−0.868180	+	0.496249i	$0.834710\pi$
$734$	2.78520	+	6.09875i	0.102804	+	0.225109i
$735$	9.46335	−	10.8746i	0.349061	−	0.401117i
$736$	4.76722	−	0.523100i	0.175722	−	0.0192817i
$737$	−1.63733	+	2.83594i	−0.0603118	+	0.104463i
$738$	9.62629	+	6.85485i	0.354349	+	0.252330i
$739$	−26.6272	−	25.3890i	−0.979496	−	0.933948i	0.0183309	−	0.999832i	$-0.494165\pi$
$739$	−26.6272	−	25.3890i	−0.979496	−	0.933948i	−0.997827	+	0.0658840i	$0.979013\pi$
$740$	−0.309580	+	0.107147i	−0.0113804	+	0.00393880i
$741$	−5.24357	−	3.36984i	−0.192627	−	0.123794i
$742$	−4.19160	−	11.2746i	−0.153879	−	0.413903i
$743$	−24.1038	+	3.46560i	−0.884282	+	0.127141i	−0.569468	−	0.822013i	$-0.692851\pi$
$743$	−24.1038	+	3.46560i	−0.884282	+	0.127141i	−0.314813	+	0.949154i	$0.601942\pi$
$744$	5.28855	−	5.04262i	0.193888	−	0.184871i
$745$	11.7899	−	22.8693i	0.431949	−	0.837865i
$746$	−4.29284	−	10.7230i	−0.157172	−	0.392597i
$747$	−3.24445	−	4.55619i	−0.118708	−	0.166702i
$748$	−19.4810	−	8.89668i	−0.712297	−	0.325295i
$749$	−18.6301	−	30.6376i	−0.680728	−	1.11947i
$750$	6.41192	+	9.97714i	0.234130	+	0.364314i
$751$	21.5590	+	22.6104i	0.786698	+	0.825065i	0.987998	−	0.154465i	$-0.0493652\pi$
$751$	21.5590	+	22.6104i	0.786698	+	0.825065i	−0.201300	+	0.979530i	$0.564517\pi$
$752$	4.76315	+	6.05684i	0.173694	+	0.220870i
$753$	22.0697	+	7.63839i	0.804264	+	0.278359i
$754$	−0.0195338	−	0.0378903i	−0.000711379	−	0.00137988i
$755$	4.51229	−	5.20745i	0.164219	−	0.189519i
$756$	1.15352	+	2.38105i	0.0419533	+	0.0865978i
$757$	−49.0369	+	22.3944i	−1.78228	+	0.813939i	−0.807799	+	0.589459i	$0.799341\pi$
$757$	−49.0369	+	22.3944i	−1.78228	+	0.813939i	−0.974479	+	0.224480i	$0.927932\pi$
$758$	7.13084	+	4.11699i	0.259004	+	0.149536i
$759$	−16.9414	−	1.37711i	−0.614934	−	0.0499859i
$760$	3.12146	+	5.40653i	0.113227	+	0.196115i
$761$	−3.12718	+	32.7493i	−0.113360	+	1.18716i	0.742461	+	0.669889i	$0.233659\pi$
$761$	−3.12718	+	32.7493i	−0.113360	+	1.18716i	−0.855821	+	0.517272i	$0.826948\pi$
$762$	2.46995	+	8.41187i	0.0894768	+	0.304730i
$763$	31.5546	+	19.2794i	1.14235	+	0.697963i
$764$	−4.18630	+	6.51402i	−0.151455	+	0.235669i
$765$	−12.2194	+	2.35509i	−0.441792	+	0.0851485i
$766$	8.45505	−	6.64912i	0.305493	−	0.240243i
$767$	2.09701	+	8.64399i	0.0757186	+	0.312116i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	2.24983	−	15.6479i	0.0811309	−	0.564278i	−0.908194	−	0.418550i	$-0.862539\pi$
$769$	2.24983	−	15.6479i	0.0811309	−	0.564278i	0.989325	−	0.145728i	$-0.0465524\pi$
$770$	4.97826	+	18.6582i	0.179404	+	0.672394i
$771$	−9.68119	+	21.1989i	−0.348660	+	0.763458i
$772$	21.5655	+	16.9593i	0.776159	+	0.610378i
$773$	−35.3771	−	18.2382i	−1.27243	−	0.655982i	−0.316224	−	0.948685i	$-0.602415\pi$
$773$	−35.3771	−	18.2382i	−1.27243	−	0.655982i	−0.956203	+	0.292703i	$0.905445\pi$
$774$	2.03707	−	0.494189i	0.0732211	−	0.0177632i
$775$	−2.06112	+	5.14843i	−0.0740377	+	0.184937i
$776$	3.86626	+	4.46190i	0.138791	+	0.160173i
$777$	0.337194	−	0.251863i	0.0120968	−	0.00903555i
$778$	11.0971	+	9.61568i	0.397850	+	0.344739i
$779$	−34.8144	−	8.44588i	−1.24736	−	0.302605i
$780$	−2.45617	+	3.44921i	−0.0879451	+	0.123502i
$781$	−18.4498	+	10.6520i	−0.660187	+	0.381159i
$782$	−4.52804	−	28.6238i	−0.161922	−	1.02359i
$783$		−	0.0207327i		−	0.000740927i
$784$	4.81981	+	5.07636i	0.172136	+	0.181299i
$785$	37.1228	−	10.9002i	1.32497	−	0.389046i
$786$	−3.97070	−	11.4726i	−0.141630	−	0.409213i
$787$	1.23229	−	25.8689i	0.0439263	−	0.922127i	−0.864127	−	0.503273i	$-0.832129\pi$
$787$	1.23229	−	25.8689i	0.0439263	−	0.922127i	0.908054	−	0.418854i	$-0.137568\pi$
$788$	−2.85328	+	8.24402i	−0.101644	+	0.293681i
$789$	−8.83502	−	3.53701i	−0.314535	−	0.125921i
$790$	4.41850	−	15.0480i	0.157203	−	0.535385i
$791$	−31.6580	+	6.85166i	−1.12563	+	0.243617i
$792$	−3.50810	−	0.504389i	−0.124655	−	0.0179227i
$793$	22.3460	−	15.9125i	0.793531	−	0.565071i
$794$	0.982955	+	10.2940i	0.0348838	+	0.365319i
$795$	8.69205	−	3.47977i	0.308275	−	0.123415i
$796$	−0.0367445	−	0.771362i	−0.00130237	−	0.0273402i
$797$	28.9803	+	8.50937i	1.02653	+	0.301417i	0.751301	−	0.659960i	$-0.229427\pi$
$797$	28.9803	+	8.50937i	1.02653	+	0.301417i	0.275233	+	0.961378i	$0.411245\pi$
$798$	−5.92902	−	5.40132i	−0.209885	−	0.191205i
$799$	35.1886	−	30.4911i	1.24488	−	1.07870i
$800$	−0.674557	+	0.347758i	−0.0238492	+	0.0122951i
$801$	7.70222	+	1.48448i	0.272144	+	0.0524515i
$802$	−1.66851	+	1.74988i	−0.0589172	+	0.0617905i
$803$	20.5801	+	1.96516i	0.726254	+	0.0693489i
$804$	−0.923955			−0.0325854
$805$	−17.3236	+	19.5629i	−0.610577	+	0.689500i
$806$	−15.0248			−0.529225
$807$	−3.35570	−	0.320431i	−0.118126	−	0.0112797i
$808$	−9.10865	+	9.55287i	−0.320441	+	0.336069i
$809$	26.9696	+	5.19797i	0.948202	+	0.182751i	0.639831	−	0.768515i	$-0.279004\pi$
$809$	26.9696	+	5.19797i	0.948202	+	0.182751i	0.308370	+	0.951266i	$0.400216\pi$
$810$	−1.83046	+	0.943666i	−0.0643157	+	0.0331570i
$811$	−37.6162	+	32.5946i	−1.32088	+	1.14455i	−0.342096	+	0.939665i	$0.611137\pi$
$811$	−37.6162	+	32.5946i	−1.32088	+	1.14455i	−0.978786	+	0.204886i	$0.934318\pi$
$812$	−0.0166468	−	0.0522666i	−0.000584188	−	0.00183420i
$813$	−16.6191	−	4.87981i	−0.582857	−	0.171142i
$814$	0.0268263	+	0.563153i	0.000940261	+	0.0197385i
$815$	−7.82674	+	3.13335i	−0.274159	+	0.109757i
$816$	−0.574395	−	6.01533i	−0.0201078	−	0.210579i
$817$	−5.17614	+	3.68591i	−0.181090	+	0.128954i
$818$	−9.42455	−	1.35505i	−0.329522	−	0.0473780i
$819$	1.66190	−	5.17994i	0.0580714	−	0.181002i
$820$	−6.85650	+	23.3511i	−0.239439	+	0.815455i
$821$	37.3567	+	14.9554i	1.30376	+	0.521946i	0.916504	−	0.400026i	$-0.130999\pi$
$821$	37.3567	+	14.9554i	1.30376	+	0.521946i	0.387255	+	0.921972i	$0.373423\pi$
$822$	3.65854	−	10.5707i	0.127606	−	0.368694i
$823$	0.339807	−	7.13342i	0.0118449	−	0.248655i	−0.985177	−	0.171540i	$-0.945126\pi$
$823$	0.339807	−	7.13342i	0.0118449	−	0.248655i	0.997022	−	0.0771158i	$-0.0245711\pi$
$824$	−5.93891	−	17.1594i	−0.206892	−	0.597775i
$825$	2.58080	−	0.757792i	0.0898520	−	0.0263829i
$826$	0.804409	+	11.4171i	0.0279890	+	0.397251i
$827$			0.774372i			0.0269275i	0.999909	+	0.0134638i	$0.00428578\pi$
$827$			0.774372i			0.0269275i	−0.999909	+	0.0134638i	$0.995714\pi$
$828$	−2.05353	−	4.33394i	−0.0713652	−	0.150615i
$829$	−31.9920	+	18.4706i	−1.11113	+	0.641511i	−0.939122	−	0.343585i	$-0.888359\pi$
$829$	−31.9920	+	18.4706i	−1.11113	+	0.641511i	−0.172008	+	0.985096i	$0.555025\pi$
$830$	6.68158	−	9.38296i	0.231921	−	0.325687i
$831$	24.7409	+	6.00209i	0.858254	+	0.208210i
$832$	−1.55392	−	1.34648i	−0.0538724	−	0.0466807i
$833$	29.2544	−	30.5512i	1.01360	−	1.05854i
$834$	−1.75739	−	2.02813i	−0.0608533	−	0.0702285i
$835$	−18.4080	+	45.9810i	−0.637035	+	1.59124i
$836$	10.4411	−	2.53299i	0.361114	−	0.0876053i
$837$	−6.49500	−	3.34840i	−0.224500	−	0.115738i
$838$	−0.961185	−	0.755884i	−0.0332036	−	0.0261116i
$839$	−5.42771	+	11.8850i	−0.187385	+	0.410316i	−0.979887	−	0.199553i	$-0.936051\pi$
$839$	−5.42771	+	11.8850i	−0.187385	+	0.410316i	0.792502	+	0.609870i	$0.208778\pi$
$840$	−3.85684	+	3.84868i	−0.133074	+	0.132792i
$841$	4.12707	−	28.7044i	0.142313	−	0.989807i
$842$	−3.26195	+	0.155386i	−0.112414	+	0.00535496i
$843$	−5.66230	−	23.3403i	−0.195020	−	0.803884i
$844$	11.5986	−	9.12122i	0.399239	−	0.313965i
$845$	−17.7392	+	3.41894i	−0.610246	+	0.117615i
$846$	4.16584	−	6.48218i	0.143225	−	0.222862i
$847$	4.12924	+	0.102672i	0.141882	+	0.00352785i
$848$	1.28086	+	4.36220i	0.0439849	+	0.149799i
$849$	1.39241	−	14.5820i	0.0477874	−	0.500452i
$850$	2.29297	+	3.97154i	0.0786482	+	0.136223i
$851$	−0.615142	+	0.451238i	−0.0210868	+	0.0154682i
$852$	−5.20567	−	3.00550i	−0.178343	−	0.102967i
$853$	−21.5542	+	9.84349i	−0.738003	+	0.337035i	−0.748701	−	0.662908i	$-0.769322\pi$
$853$	−21.5542	+	9.84349i	−0.738003	+	0.337035i	0.0106977	+	0.999943i	$0.496595\pi$
$854$	31.7677	−	15.3902i	1.08707	−	0.526643i
$855$	4.08824	−	4.71809i	0.139815	−	0.161355i
$856$	6.21023	+	12.0462i	0.212261	+	0.411730i
$857$	41.8489	+	14.4840i	1.42953	+	0.494765i	0.928717	−	0.370790i	$-0.120913\pi$
$857$	41.8489	+	14.4840i	1.42953	+	0.494765i	0.500813	+	0.865555i	$0.333034\pi$
$858$	4.50470	+	5.72819i	0.153788	+	0.195557i
$859$	−25.3223	−	26.5572i	−0.863984	−	0.906121i	0.132390	−	0.991198i	$-0.457735\pi$
$859$	−25.3223	−	26.5572i	−0.863984	−	0.906121i	−0.996374	+	0.0850770i	$0.972886\pi$
$860$	2.33384	+	3.63153i	0.0795834	+	0.123834i
$861$	−0.710946	−	31.2582i	−0.0242290	−	1.06528i
$862$	19.8070	+	9.04556i	0.674629	+	0.308093i
$863$	10.0152	+	14.0644i	0.340921	+	0.478756i	0.949069	−	0.315067i	$-0.102027\pi$
$863$	10.0152	+	14.0644i	0.340921	+	0.478756i	−0.608149	+	0.793823i	$0.708088\pi$
$864$	−0.371662	−	0.928368i	−0.0126442	−	0.0315837i
$865$	−17.7538	+	34.4376i	−0.603647	+	1.17091i
$866$	11.1730	−	10.6534i	0.379672	−	0.362017i
$867$	−19.3155	+	2.77715i	−0.655990	+	0.0943171i
$868$	−19.0622	−	3.22624i	−0.647014	−	0.109506i
$869$	−22.7061	−	14.5923i	−0.770251	−	0.495011i
$870$	0.0403484	−	0.0139647i	0.00136794	−	0.000473448i
$871$	1.37493	+	1.31099i	0.0465877	+	0.0444213i
$872$	−11.3849	−	8.10715i	−0.385541	−	0.274543i
$873$	2.95197	−	5.11296i	0.0999090	−	0.173048i
$874$	10.6622	+	9.88332i	0.360654	+	0.334308i
$875$	10.9967	−	29.3882i	0.371757	−	0.993502i
$876$	2.42317	+	5.30601i	0.0818714	+	0.179273i
$877$	−5.91924	+	24.3994i	−0.199879	+	0.823910i	0.780237	+	0.625484i	$0.215098\pi$
$877$	−5.91924	+	24.3994i	−0.199879	+	0.823910i	−0.980116	+	0.198427i	$0.936417\pi$
$878$	0.880087	−	4.56633i	0.0297015	−	0.154106i
$879$	10.1526	+	0.483627i	0.342438	+	0.0163123i
$880$	−1.38131	−	7.16693i	−0.0465641	−	0.241597i
$881$	−4.32567	−	30.0857i	−0.145736	−	1.01361i	−0.923099	−	0.384562i	$-0.874353\pi$
$881$	−4.32567	−	30.0857i	−0.145736	−	1.01361i	0.777364	−	0.629051i	$-0.216556\pi$
$882$	3.22076	−	6.21504i	0.108449	−	0.209271i
$883$	−36.3848	+	23.3831i	−1.22445	+	0.786904i	−0.983017	−	0.183515i	$-0.941253\pi$
$883$	−36.3848	+	23.3831i	−1.22445	+	0.786904i	−0.241429	+	0.970418i	$0.577616\pi$
$884$	−7.68036	+	9.76637i	−0.258318	+	0.328478i
$885$	−8.86847	+	0.846837i	−0.298111	+	0.0284661i
$886$	14.4702	−	1.38174i	0.486136	−	0.0464204i
$887$	−28.3610	+	36.0640i	−0.952271	+	1.21091i	0.0251660	+	0.999683i	$0.491989\pi$
$887$	−28.3610	+	36.0640i	−0.952271	+	1.21091i	−0.977437	+	0.211228i	$0.932254\pi$
$888$	−0.133823	+	0.0860027i	−0.00449080	+	0.00288606i
$889$	13.9201	−	18.5540i	0.466865	−	0.622283i
$890$	2.29892	+	15.9893i	0.0770600	+	0.535964i
$891$	0.670740	+	3.48013i	0.0224706	+	0.116589i
$892$	−21.6225	−	1.03001i	−0.723974	−	0.0344871i
$893$	−4.42061	+	22.9363i	−0.147930	+	0.767534i
$894$	2.94551	−	12.1416i	0.0985127	−	0.406075i
$895$	4.37159	+	9.57244i	0.146126	+	0.319971i
$896$	−1.68236	−	2.04197i	−0.0562037	−	0.0682176i
$897$	−3.09354	+	9.36303i	−0.103290	+	0.312623i
$898$	18.8325	−	32.6189i	0.628450	−	1.08851i
$899$	0.123409	+	0.0878788i	0.00411590	+	0.00293092i
$900$	0.549258	+	0.523716i	0.0183086	+	0.0174572i
$901$	25.9613	−	8.98530i	0.864897	−	0.299344i
$902$	35.2346	+	22.6439i	1.17318	+	0.753960i
$903$	−4.27282	−	3.53556i	−0.142191	−	0.117656i
$904$	12.1180	−	1.74231i	0.403039	−	0.0579483i
$905$	−26.9640	+	25.7101i	−0.896313	+	0.854633i
$906$	1.53317	−	2.97393i	0.0509361	−	0.0988022i
$907$	−9.82592	−	24.5440i	−0.326264	−	0.814969i	−0.997292	−	0.0735372i	$-0.976571\pi$
$907$	−9.82592	−	24.5440i	−0.326264	−	0.814969i	0.671028	−	0.741432i	$-0.265853\pi$
$908$	1.82315	+	2.56026i	0.0605034	+	0.0849651i
$909$	12.0066	+	5.48324i	0.398234	+	0.181868i
$910$	11.2002	−	0.254740i	0.371283	−	0.00844456i
$911$	−5.91820	−	9.20890i	−0.196079	−	0.305104i	0.729267	−	0.684230i	$-0.239861\pi$
$911$	−5.91820	−	9.20890i	−0.196079	−	0.305104i	−0.925345	+	0.379125i	$0.876225\pi$
$912$	2.09194	+	2.19396i	0.0692710	+	0.0726493i
$913$	−12.2542	−	15.5825i	−0.405556	−	0.515706i
$914$	−15.5749	−	5.39052i	−0.515171	−	0.178303i
$915$	12.5903	+	24.4218i	0.416223	+	0.807360i
$916$	13.6524	−	15.7557i	0.451088	−	0.520583i
$917$	−18.0318	+	26.5812i	−0.595462	+	0.877789i
$918$	−5.49663	+	2.51023i	−0.181416	+	0.0828498i
$919$	−15.7630	−	9.10076i	−0.519973	−	0.300206i	0.216951	−	0.976183i	$-0.430389\pi$
$919$	−15.7630	−	9.10076i	−0.519973	−	0.300206i	−0.736924	+	0.675976i	$0.763722\pi$
$920$	7.05119	−	6.91559i	0.232471	−	0.228000i
$921$	3.36558	+	5.82935i	0.110900	+	0.192084i
$922$	−0.265423	+	2.77964i	−0.00874124	+	0.0915424i
$923$	3.48204	+	11.8587i	0.114613	+	0.390335i
$924$	4.48520	+	8.23476i	0.147552	+	0.270904i
$925$	0.0652694	−	0.101561i	0.00214604	−	0.00333931i
$926$	−14.1767	+	2.73234i	−0.465877	+	0.0897903i
$927$	−14.2732	+	11.2246i	−0.468793	+	0.368663i
$928$	0.00488792	+	0.0201483i	0.000160454	+	0.000661400i
$929$	31.2680	−	1.48948i	1.02587	−	0.0488682i	0.472106	−	0.881542i	$-0.343494\pi$
$929$	31.2680	−	1.48948i	1.02587	−	0.0488682i	0.553764	+	0.832674i	$0.313191\pi$
$930$	2.14164	−	14.8954i	0.0702270	−	0.488440i
$931$	−2.06186	+	21.1197i	−0.0675747	+	0.692171i
$932$	−1.12230	+	2.45750i	−0.0367623	+	0.0804981i
$933$	2.44674	+	1.92414i	0.0801027	+	0.0629935i
$934$	−8.54911	−	4.40737i	−0.279735	−	0.144214i
$935$	−42.8614	+	10.3981i	−1.40172	+	0.340053i
$936$	−0.764186	+	1.90884i	−0.0249782	+	0.0623925i
$937$	0.770964	+	0.889739i	0.0251863	+	0.0290665i	0.768203	−	0.640206i	$-0.221151\pi$
$937$	0.770964	+	0.889739i	0.0251863	+	0.0290665i	−0.743017	+	0.669273i	$0.766606\pi$
$938$	1.46289	+	1.95852i	0.0477651	+	0.0639479i
$939$	−16.1891	−	14.0279i	−0.528312	−	0.457785i
$940$	15.4211	+	3.74111i	0.502979	+	0.122021i
$941$	−18.2382	+	25.6119i	−0.594548	+	0.834925i	−0.996744	−	0.0806279i	$-0.974307\pi$
$941$	−18.2382	+	25.6119i	−0.594548	+	0.834925i	0.402197	+	0.915553i	$0.368247\pi$
$942$	16.2702	−	9.39358i	0.530110	−	0.306059i
$943$	0.798607	+	56.6693i	0.0260062	+	1.84541i
$944$		−	4.32595i		−	0.140798i
$945$	4.89845	+	2.38594i	0.159347	+	0.0776146i
$946$	7.12823	−	2.09304i	0.231759	−	0.0680505i
$947$	18.1474	+	52.4336i	0.589713	+	1.70386i	0.703805	+	0.710393i	$0.251483\pi$
$947$	18.1474	+	52.4336i	0.589713	+	1.70386i	−0.114092	+	0.993470i	$0.536396\pi$
$948$	0.362362	−	7.60690i	0.0117690	−	0.247061i
$949$	3.92275	−	11.3340i	0.127338	−	0.367918i
$950$	−2.13583	−	0.855059i	−0.0692956	−	0.0277418i
$951$	8.74400	−	29.7793i	0.283544	−	0.965661i
$952$	−11.8413	+	10.7416i	−0.383780	+	0.348137i
$953$	−9.33642	−	1.34237i	−0.302436	−	0.0434838i	−0.0105739	−	0.999944i	$-0.503366\pi$
$953$	−9.33642	−	1.34237i	−0.302436	−	0.0434838i	−0.291862	+	0.956460i	$0.594275\pi$
$954$	3.70336	−	2.63715i	0.119901	−	0.0853809i
$955$	1.51579	+	15.8741i	0.0490499	+	0.513674i
$956$	−4.34033	+	1.73761i	−0.140376	+	0.0561982i
$957$	−0.00349634	−	0.0733972i	−0.000113021	−	0.00237259i
$958$	8.56477	+	2.51484i	0.276715	+	0.0812509i
$959$	−28.1993	+	8.98142i	−0.910604	+	0.290025i
$960$	1.55638	−	1.34861i	0.0502320	−	0.0435263i
$961$	19.9071	−	10.2628i	0.642163	−	0.331058i
$962$	0.321169	+	0.0619003i	0.0103549	+	0.00199574i
$963$	9.35247	−	9.80859i	0.301379	−	0.316077i
$964$	−2.04668	−	0.195434i	−0.0659190	−	0.00629450i
$965$	56.4996			1.81879
$966$	−5.93535	+	11.2148i	−0.190967	+	0.360830i
$967$	20.7509			0.667304			0.333652	−	0.942696i	$-0.391719\pi$
$967$	20.7509			0.667304			0.333652	+	0.942696i	$0.391719\pi$
$968$	−1.55412	−	0.148400i	−0.0499513	−	0.00476977i
$969$	12.6409	−	13.2574i	0.406085	−	0.425890i
$970$	11.9388	+	2.30101i	0.383331	+	0.0738810i
$971$	23.7771	−	12.2580i	0.763044	−	0.393377i	−0.0323441	−	0.999477i	$-0.510297\pi$
$971$	23.7771	−	12.2580i	0.763044	−	0.393377i	0.795388	+	0.606100i	$0.207267\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	−1.51660	+	6.93628i	−0.0486198	+	0.222367i
$974$	12.0538	+	3.53933i	0.386230	+	0.113407i
$975$	−0.0742489	−	1.55868i	−0.00237787	−	0.0499176i
$976$	−12.3862	+	4.95869i	−0.396473	+	0.158724i
$977$	2.06902	+	21.6678i	0.0661939	+	0.693214i	0.966279	+	0.257499i	$0.0828983\pi$
$977$	2.06902	+	21.6678i	0.0661939	+	0.693214i	−0.900085	+	0.435715i	$0.856496\pi$
$978$	−3.33468	+	2.37461i	−0.106631	+	0.0759318i
$979$	27.5174	+	3.95641i	0.879461	+	0.126447i
$980$	14.2646	+	2.08180i	0.455666	+	0.0665008i
$981$	−3.93763	+	13.4103i	−0.125719	+	0.428159i
$982$	−9.70943	−	3.88707i	−0.309840	−	0.124041i
$983$	−15.7225	+	45.4272i	−0.501470	+	1.44890i	0.356058	+	0.934464i	$0.384120\pi$
$983$	−15.7225	+	45.4272i	−0.501470	+	1.44890i	−0.857528	+	0.514437i	$0.828001\pi$
$984$	−0.562301	+	11.8042i	−0.0179255	+	0.376303i
$985$	5.87601	+	16.9776i	0.187225	+	0.540952i
$986$	0.120207	−	0.0352959i	0.00382816	−	0.00112405i
$987$	−20.3361	+	1.43281i	−0.647305	+	0.0456069i
$988$		−	6.23304i		−	0.198300i
$989$	7.68943	+	6.47550i	0.244510	+	0.205909i
$990$	−6.32098	+	3.64942i	−0.200894	+	0.115986i
$991$	−12.1129	+	17.0101i	−0.384778	+	0.540345i	−0.960856	−	0.277050i	$-0.910643\pi$
$991$	−12.1129	+	17.0101i	−0.384778	+	0.540345i	0.576078	+	0.817395i	$0.304583\pi$
$992$	7.10133	+	1.72276i	0.225467	+	0.0546978i
$993$	−16.3181	−	14.1397i	−0.517838	−	0.448709i
$994$	1.87133	+	15.7931i	0.0593549	+	0.500927i
$995$	−1.04145	−	1.20189i	−0.0330161	−	0.0381026i
$996$	2.07883	−	5.19267i	0.0658703	−	0.164536i
$997$	46.0885	−	11.1810i	1.45964	−	0.354105i	0.574144	−	0.818754i	$-0.305335\pi$
$997$	46.0885	−	11.1810i	1.45964	−	0.354105i	0.885495	+	0.464650i	$0.153820\pi$
$998$	−25.8807	−	13.3424i	−0.819238	−	0.422347i
$999$	0.125042	+	0.0983339i	0.00395615	+	0.00311115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.19.14	✓	320
7.3	odd	6	inner	966.2.be.a.157.14	yes	320
23.17	odd	22	inner	966.2.be.a.523.14	yes	320
161.17	even	66	inner	966.2.be.a.661.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.19.14	✓	320	1.1	even	1	trivial
966.2.be.a.157.14	yes	320	7.3	odd	6	inner
966.2.be.a.523.14	yes	320	23.17	odd	22	inner
966.2.be.a.661.14	yes	320	161.17	even	66	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(1.83046 - 0.943666i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.58469 - 0.565134i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.995472 + 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(1.83046 - 0.943666i) q^{5} +(0.755750 - 0.654861i) q^{6} +(-2.58469 - 0.565134i) q^{7} +(0.959493 + 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(1.91187 - 0.765397i) q^{10} +(-0.336895 - 3.52813i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-2.03520 - 0.292618i) q^{13} +(-2.51927 - 0.808265i) q^{14} +(0.580197 - 1.97597i) q^{15} +(0.928368 + 0.371662i) q^{16} +(1.97637 - 5.71035i) q^{17} +(0.0475819 - 0.998867i) q^{18} +(0.991489 + 2.86472i) q^{19} +(1.97597 - 0.580197i) q^{20} +(-2.19265 + 1.48064i) q^{21} -3.54418i q^{22} +(3.99757 - 2.64942i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.440218 + 0.618200i) q^{25} +(-1.99817 - 0.484751i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-2.43103 - 1.04408i) q^{28} +(0.0135770 + 0.0156687i) q^{29} +(0.765397 - 1.91187i) q^{30} +(7.10133 - 1.72276i) q^{31} +(0.888835 + 0.458227i) q^{32} +(-2.78591 - 2.19086i) q^{33} +(2.51023 - 5.49663i) q^{34} +(-5.26446 + 1.40463i) q^{35} +(0.142315 - 0.989821i) q^{36} +(-0.158895 + 0.00756912i) q^{37} +(0.714690 + 2.94599i) q^{38} +(-1.61623 + 1.27101i) q^{39} +(2.02217 - 0.389742i) q^{40} +(-6.38905 + 9.94155i) q^{41} +(-2.32346 + 1.26551i) q^{42} +(0.590557 + 2.01125i) q^{43} +(0.336895 - 3.52813i) q^{44} +(-1.02969 - 1.78348i) q^{45} +(4.23132 - 2.25742i) q^{46} +(6.67305 + 3.85269i) q^{47} +(0.909632 - 0.415415i) q^{48} +(6.36125 + 2.92139i) q^{49} +(-0.496989 + 0.573555i) q^{50} +(-2.76892 - 5.37096i) q^{51} +(-1.94304 - 0.672494i) q^{52} +(2.81037 + 3.57368i) q^{53} +(-0.690079 - 0.723734i) q^{54} +(-3.94605 - 6.14017i) q^{55} +(-2.32078 - 1.27043i) q^{56} +(2.75750 + 1.25931i) q^{57} +(0.0120262 + 0.0168884i) q^{58} +(-1.60779 - 4.01608i) q^{59} +(0.943666 - 1.83046i) q^{60} +(-9.65600 + 9.20698i) q^{61} +(7.23293 - 1.03994i) q^{62} +(-0.441509 + 2.60865i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-4.00148 + 1.38493i) q^{65} +(-2.56504 - 2.44576i) q^{66} +(-0.752631 - 0.535946i) q^{67} +(3.02135 - 5.23313i) q^{68} +(0.841170 - 4.72149i) q^{69} +(-5.37414 + 0.897852i) q^{70} +(-2.49706 - 5.46779i) q^{71} +(0.235759 - 0.971812i) q^{72} +(-1.10393 + 5.72772i) q^{73} +(-0.158895 - 0.00756912i) q^{74} +(0.143627 + 0.745208i) q^{75} +(0.431420 + 3.00059i) q^{76} +(-1.12309 + 9.30951i) q^{77} +(-1.72973 + 1.11163i) q^{78} +(4.70761 - 5.98621i) q^{79} +(2.05006 - 0.195757i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-7.30512 + 9.28922i) q^{82} +(4.70541 - 3.02398i) q^{83} +(-2.43324 + 1.03892i) q^{84} +(-1.77100 - 12.3176i) q^{85} +(0.396701 + 2.05828i) q^{86} +(0.0207092 + 0.000986502i) q^{87} +(0.670740 - 3.48013i) q^{88} +(-1.84929 + 7.62286i) q^{89} +(-0.855501 - 1.87328i) q^{90} +(5.09500 + 1.90649i) q^{91} +(4.42674 - 1.84499i) q^{92} +(3.65366 - 6.32832i) q^{93} +(6.27661 + 4.46956i) q^{94} +(4.51821 + 4.30811i) q^{95} +(0.945001 - 0.327068i) q^{96} +(4.96671 + 3.19191i) q^{97} +(6.05475 + 3.51284i) q^{98} +(-3.50810 + 0.504389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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