LMFDB - Embedded newform 64.2.i.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	64.37
Dual form			64.2.i.a.45.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797087 + 1.16818i) q^{2} +(-0.894167 + 1.33822i) q^{3} +(-0.729306 + 1.86229i) q^{4} +(0.631428 - 3.17440i) q^{5} +(-2.27601 + 0.0221224i) q^{6} +(-0.127129 + 0.306917i) q^{7} +(-2.75681 + 0.632441i) q^{8} +(0.156763 + 0.378460i) q^{9} +O(q^{10})$	\(q+(0.797087 + 1.16818i) q^{2} +(-0.894167 + 1.33822i) q^{3} +(-0.729306 + 1.86229i) q^{4} +(0.631428 - 3.17440i) q^{5} +(-2.27601 + 0.0221224i) q^{6} +(-0.127129 + 0.306917i) q^{7} +(-2.75681 + 0.632441i) q^{8} +(0.156763 + 0.378460i) q^{9} +(4.21159 - 1.79265i) q^{10} +(3.52624 - 2.35616i) q^{11} +(-1.84002 - 2.64117i) q^{12} +(-0.690738 - 3.47257i) q^{13} +(-0.459869 + 0.0961292i) q^{14} +(3.68343 + 3.68343i) q^{15} +(-2.93623 - 2.71635i) q^{16} +(-2.19074 + 2.19074i) q^{17} +(-0.317157 + 0.484794i) q^{18} +(-6.74130 + 1.34093i) q^{19} +(5.45115 + 3.49101i) q^{20} +(-0.297047 - 0.444562i) q^{21} +(5.56314 + 2.24123i) q^{22} +(-0.672631 + 0.278613i) q^{23} +(1.61871 - 4.25472i) q^{24} +(-5.05873 - 2.09540i) q^{25} +(3.50602 - 3.57485i) q^{26} +(-5.38223 - 1.07059i) q^{27} +(-0.478852 - 0.460588i) q^{28} +(7.95458 + 5.31508i) q^{29} +(-1.36691 + 7.23894i) q^{30} +0.880409i q^{31} +(0.832774 - 5.59522i) q^{32} +6.82567i q^{33} +(-4.30540 - 0.812978i) q^{34} +(0.894006 + 0.597355i) q^{35} +(-0.819129 + 0.0159251i) q^{36} +(-5.44280 - 1.08264i) q^{37} +(-6.93985 - 6.80624i) q^{38} +(5.26469 + 2.18070i) q^{39} +(0.266893 + 9.15058i) q^{40} +(3.05507 - 1.26545i) q^{41} +(0.282558 - 0.701359i) q^{42} +(1.59134 + 2.38161i) q^{43} +(1.81614 + 8.28523i) q^{44} +(1.30037 - 0.258659i) q^{45} +(-0.861616 - 0.563678i) q^{46} +(3.23201 - 3.23201i) q^{47} +(6.26055 - 1.50043i) q^{48} +(4.87171 + 4.87171i) q^{49} +(-1.58444 - 7.57974i) q^{50} +(-0.972796 - 4.89058i) q^{51} +(6.97069 + 1.24622i) q^{52} +(-7.45949 + 4.98427i) q^{53} +(-3.03946 - 7.14079i) q^{54} +(-5.25283 - 12.6815i) q^{55} +(0.156365 - 0.926515i) q^{56} +(4.23340 - 10.2203i) q^{57} +(0.131499 + 13.5290i) q^{58} +(0.795535 - 3.99942i) q^{59} +(-9.54596 + 4.17326i) q^{60} +(2.62163 - 3.92355i) q^{61} +(-1.02848 + 0.701762i) q^{62} -0.136085 q^{63} +(7.20004 - 3.48704i) q^{64} -11.4595 q^{65} +(-7.97364 + 5.44065i) q^{66} +(-3.03636 + 4.54423i) q^{67} +(-2.48207 - 5.67751i) q^{68} +(0.228601 - 1.14925i) q^{69} +(0.0147790 + 1.52051i) q^{70} +(2.69641 - 6.50971i) q^{71} +(-0.671521 - 0.944200i) q^{72} +(4.10841 + 9.91857i) q^{73} +(-3.07366 - 7.22115i) q^{74} +(7.32745 - 4.89605i) q^{75} +(2.41928 - 13.5322i) q^{76} +(0.274857 + 1.38180i) q^{77} +(1.64895 + 7.88833i) q^{78} +(-1.54370 - 1.54370i) q^{79} +(-10.4768 + 7.60558i) q^{80} +(5.37632 - 5.37632i) q^{81} +(3.91344 + 2.56021i) q^{82} +(14.5352 - 2.89122i) q^{83} +(1.04454 - 0.228965i) q^{84} +(5.57100 + 8.33759i) q^{85} +(-1.51372 + 3.75733i) q^{86} +(-14.2254 + 5.89237i) q^{87} +(-8.23105 + 8.72563i) q^{88} +(-1.64085 - 0.679662i) q^{89} +(1.33867 + 1.31290i) q^{90} +(1.15360 + 0.229466i) q^{91} +(-0.0283034 - 1.45583i) q^{92} +(-1.17818 - 0.787233i) q^{93} +(6.35178 + 1.19939i) q^{94} +22.2463i q^{95} +(6.74297 + 6.11750i) q^{96} -2.43552i q^{97} +(-1.80788 + 9.57423i) q^{98} +(1.44450 + 0.965182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	0.797087	+	1.16818i	0.563625	+	0.826031i
$2$	0.797087	+	1.16818i	0.563625	+	0.826031i
$3$	−0.894167	+	1.33822i	−0.516248	+	0.772619i	−0.994403	−	0.105656i	$-0.966306\pi$
$3$	−0.894167	+	1.33822i	−0.516248	+	0.772619i	0.478155	+	0.878276i	$0.341306\pi$
$4$	−0.729306	+	1.86229i	−0.364653	+	0.931143i
$5$	0.631428	−	3.17440i	0.282383	−	1.41964i	−0.535638	−	0.844448i	$-0.679929\pi$
$5$	0.631428	−	3.17440i	0.282383	−	1.41964i	0.818021	−	0.575188i	$-0.195071\pi$
$6$	−2.27601	+	0.0221224i	−0.929178	+	0.00903143i
$7$	−0.127129	+	0.306917i	−0.0480503	+	0.116004i	−0.946082	−	0.323927i	$-0.894997\pi$
$7$	−0.127129	+	0.306917i	−0.0480503	+	0.116004i	0.898032	+	0.439930i	$0.144997\pi$
$8$	−2.75681	+	0.632441i	−0.974681	+	0.223602i
$9$	0.156763	+	0.378460i	0.0522544	+	0.126153i
$10$	4.21159	−	1.79265i	1.33182	−	0.566886i
$11$	3.52624	−	2.35616i	1.06320	−	0.710409i	0.104414	−	0.994534i	$-0.466703\pi$
$11$	3.52624	−	2.35616i	1.06320	−	0.710409i	0.958787	+	0.284125i	$0.0917032\pi$
$12$	−1.84002	−	2.64117i	−0.531168	−	0.762439i
$13$	−0.690738	−	3.47257i	−0.191576	−	0.963118i	−0.950212	−	0.311604i	$-0.899134\pi$
$13$	−0.690738	−	3.47257i	−0.191576	−	0.963118i	0.758636	−	0.651515i	$-0.225866\pi$
$14$	−0.459869	+	0.0961292i	−0.122905	+	0.0256916i
$15$	3.68343	+	3.68343i	0.951059	+	0.951059i
$16$	−2.93623	−	2.71635i	−0.734056	−	0.679088i
$17$	−2.19074	+	2.19074i	−0.531333	+	0.531333i	−0.920969	−	0.389636i	$-0.872601\pi$
$17$	−2.19074	+	2.19074i	−0.531333	+	0.531333i	0.389636	+	0.920969i	$0.372601\pi$
$18$	−0.317157	+	0.484794i	−0.0747546	+	0.114267i
$19$	−6.74130	+	1.34093i	−1.54656	+	0.307630i	−0.893285	−	0.449491i	$-0.851605\pi$
$19$	−6.74130	+	1.34093i	−1.54656	+	0.307630i	−0.653275	+	0.757121i	$0.726605\pi$
$20$	5.45115	+	3.49101i	1.21891	+	0.780614i
$21$	−0.297047	−	0.444562i	−0.0648209	−	0.0970113i
$22$	5.56314	+	2.24123i	1.18607	+	0.477833i
$23$	−0.672631	+	0.278613i	−0.140253	+	0.0580948i	−0.451706	−	0.892167i	$-0.649184\pi$
$23$	−0.672631	+	0.278613i	−0.140253	+	0.0580948i	0.311453	+	0.950262i	$0.399184\pi$
$24$	1.61871	−	4.25472i	0.330418	−	0.868491i
$25$	−5.05873	−	2.09540i	−1.01175	−	0.419079i
$26$	3.50602	−	3.57485i	0.687588	−	0.701086i
$27$	−5.38223	−	1.07059i	−1.03581	−	0.206036i
$28$	−0.478852	−	0.460588i	−0.0904945	−	0.0870429i
$29$	7.95458	+	5.31508i	1.47713	+	0.986985i	0.993757	+	0.111570i	$0.0355879\pi$
$29$	7.95458	+	5.31508i	1.47713	+	0.986985i	0.483371	+	0.875415i	$0.339412\pi$
$30$	−1.36691	+	7.23894i	−0.249563	+	1.32164i
$31$			0.880409i			0.158126i	0.996870	+	0.0790630i	$0.0251928\pi$
$31$			0.880409i			0.158126i	−0.996870	+	0.0790630i	$0.974807\pi$
$32$	0.832774	−	5.59522i	0.147215	−	0.989105i
$33$			6.82567i			1.18820i
$34$	−4.30540	−	0.812978i	−0.738370	−	0.139425i
$35$	0.894006	+	0.597355i	0.151115	+	0.100972i
$36$	−0.819129	+	0.0159251i	−0.136522	+	0.00265418i
$37$	−5.44280	−	1.08264i	−0.894791	−	0.177985i	−0.273785	−	0.961791i	$-0.588276\pi$
$37$	−5.44280	−	1.08264i	−0.894791	−	0.177985i	−0.621006	+	0.783806i	$0.713276\pi$
$38$	−6.93985	−	6.80624i	−1.12579	−	1.10412i
$39$	5.26469	+	2.18070i	0.843025	+	0.349192i
$40$	0.266893	+	9.15058i	0.0421995	+	1.44683i
$41$	3.05507	−	1.26545i	0.477122	−	0.197631i	−0.131144	−	0.991363i	$-0.541865\pi$
$41$	3.05507	−	1.26545i	0.477122	−	0.197631i	0.608267	+	0.793733i	$0.291865\pi$
$42$	0.282558	−	0.701359i	0.0435996	−	0.108222i
$43$	1.59134	+	2.38161i	0.242677	+	0.363192i	0.932735	−	0.360562i	$-0.117415\pi$
$43$	1.59134	+	2.38161i	0.242677	+	0.363192i	−0.690058	+	0.723754i	$0.742415\pi$
$44$	1.81614	+	8.28523i	0.273793	+	1.24905i
$45$	1.30037	−	0.258659i	0.193848	−	0.0385587i
$46$	−0.861616	−	0.563678i	−0.127038	−	0.0831098i
$47$	3.23201	−	3.23201i	0.471438	−	0.471438i	−0.430942	−	0.902380i	$-0.641819\pi$
$47$	3.23201	−	3.23201i	0.471438	−	0.471438i	0.902380	+	0.430942i	$0.141819\pi$
$48$	6.26055	−	1.50043i	0.903632	−	0.216568i
$49$	4.87171	+	4.87171i	0.695959	+	0.695959i
$50$	−1.58444	−	7.57974i	−0.224074	−	1.07194i
$51$	−0.972796	−	4.89058i	−0.136219	−	0.684818i
$52$	6.97069	+	1.24622i	0.966660	+	0.172819i
$53$	−7.45949	+	4.98427i	−1.02464	+	0.684643i	−0.949898	−	0.312560i	$-0.898813\pi$
$53$	−7.45949	+	4.98427i	−1.02464	+	0.684643i	−0.0747420	+	0.997203i	$0.523813\pi$
$54$	−3.03946	−	7.14079i	−0.413618	−	0.971739i
$55$	−5.25283	−	12.6815i	−0.708291	−	1.70997i
$56$	0.156365	−	0.926515i	0.0208951	−	0.123811i
$57$	4.23340	−	10.2203i	0.560727	−	1.35372i
$58$	0.131499	+	13.5290i	0.0172667	+	1.77644i
$59$	0.795535	−	3.99942i	0.103570	−	0.520681i	−0.893817	−	0.448432i	$-0.851983\pi$
$59$	0.795535	−	3.99942i	0.103570	−	0.520681i	0.997387	−	0.0722484i	$-0.0230174\pi$
$60$	−9.54596	+	4.17326i	−1.23238	+	0.538766i
$61$	2.62163	−	3.92355i	0.335666	−	0.502359i	−0.624790	−	0.780793i	$-0.714815\pi$
$61$	2.62163	−	3.92355i	0.335666	−	0.502359i	0.960455	+	0.278434i	$0.0898153\pi$
$62$	−1.02848	+	0.701762i	−0.130617	+	0.0891238i
$63$	−0.136085			−0.0171451
$64$	7.20004	−	3.48704i	0.900005	−	0.435880i
$65$	−11.4595			−1.42138
$66$	−7.97364	+	5.44065i	−0.981487	+	0.669698i
$67$	−3.03636	+	4.54423i	−0.370950	+	0.555166i	−0.969241	−	0.246113i	$-0.920847\pi$
$67$	−3.03636	+	4.54423i	−0.370950	+	0.555166i	0.598291	+	0.801279i	$0.295847\pi$
$68$	−2.48207	−	5.67751i	−0.300995	−	0.688499i
$69$	0.228601	−	1.14925i	0.0275203	−	0.138354i
$70$	0.0147790	+	1.52051i	0.00176643	+	0.181735i
$71$	2.69641	−	6.50971i	0.320005	−	0.772561i	−0.679248	−	0.733909i	$-0.737694\pi$
$71$	2.69641	−	6.50971i	0.320005	−	0.772561i	0.999253	−	0.0386517i	$-0.0123063\pi$
$72$	−0.671521	−	0.944200i	−0.0791394	−	0.111275i
$73$	4.10841	+	9.91857i	0.480853	+	1.16088i	0.959205	+	0.282713i	$0.0912344\pi$
$73$	4.10841	+	9.91857i	0.480853	+	1.16088i	−0.478352	+	0.878168i	$0.658766\pi$
$74$	−3.07366	−	7.22115i	−0.357306	−	0.839441i
$75$	7.32745	−	4.89605i	0.846101	−	0.565347i
$76$	2.41928	−	13.5322i	0.277510	−	1.55225i
$77$	0.274857	+	1.38180i	0.0313229	+	0.157471i
$78$	1.64895	+	7.88833i	0.186707	+	0.893178i
$79$	−1.54370	−	1.54370i	−0.173680	−	0.173680i	0.614914	−	0.788594i	$-0.289191\pi$
$79$	−1.54370	−	1.54370i	−0.173680	−	0.173680i	−0.788594	+	0.614914i	$0.789191\pi$
$80$	−10.4768	+	7.60558i	−1.17134	+	0.850330i
$81$	5.37632	−	5.37632i	0.597369	−	0.597369i
$82$	3.91344	+	2.56021i	0.432167	+	0.282728i
$83$	14.5352	−	2.89122i	1.59544	−	0.317353i	0.684221	−	0.729275i	$-0.260142\pi$
$83$	14.5352	−	2.89122i	1.59544	−	0.317353i	0.911219	+	0.411922i	$0.135142\pi$
$84$	1.04454	−	0.228965i	0.113969	−	0.0249821i
$85$	5.57100	+	8.33759i	0.604260	+	0.904339i
$86$	−1.51372	+	3.75733i	−0.163229	+	0.405163i
$87$	−14.2254	+	5.89237i	−1.52513	+	0.631729i
$88$	−8.23105	+	8.72563i	−0.877433	+	0.930155i
$89$	−1.64085	−	0.679662i	−0.173930	−	0.0720441i	0.294019	−	0.955799i	$-0.405007\pi$
$89$	−1.64085	−	0.679662i	−0.173930	−	0.0720441i	−0.467949	+	0.883755i	$0.655007\pi$
$90$	1.33867	+	1.31290i	0.141108	+	0.138391i
$91$	1.15360	+	0.229466i	0.120931	+	0.0240546i
$92$	−0.0283034	−	1.45583i	−0.00295083	−	0.151780i
$93$	−1.17818	−	0.787233i	−0.122171	−	0.0816322i
$94$	6.35178	+	1.19939i	0.655136	+	0.123708i
$95$			22.2463i			2.28242i
$96$	6.74297	+	6.11750i	0.688202	+	0.624364i
$97$		−	2.43552i		−	0.247289i	−0.992327	−	0.123645i	$-0.960542\pi$
$97$		−	2.43552i		−	0.247289i	0.992327	−	0.123645i	$-0.0394583\pi$
$98$	−1.80788	+	9.57423i	−0.182623	+	0.967143i
$99$	1.44450	+	0.965182i	0.145177	+	0.0970044i
$100$	7.59159	−	7.89263i	0.759159	−	0.789263i
$101$	−0.776702	−	0.154496i	−0.0772847	−	0.0153729i	0.156296	−	0.987710i	$-0.450044\pi$
$101$	−0.776702	−	0.154496i	−0.0772847	−	0.0153729i	−0.233581	+	0.972337i	$0.575044\pi$
$102$	4.93769	−	5.03462i	0.488904	−	0.498501i
$103$	−5.94004	−	2.46045i	−0.585290	−	0.242435i	0.0703329	−	0.997524i	$-0.477594\pi$
$103$	−5.94004	−	2.46045i	−0.585290	−	0.242435i	−0.655623	+	0.755089i	$0.727594\pi$
$104$	4.10043	+	9.13638i	0.402080	+	0.895896i
$105$	−1.59878	+	0.662237i	−0.156025	+	0.0646277i
$106$	−11.7684	−	4.74116i	−1.14305	−	0.460502i
$107$	3.42296	+	5.12283i	0.330910	+	0.495242i	0.959197	−	0.282740i	$-0.0912433\pi$
$107$	3.42296	+	5.12283i	0.330910	+	0.495242i	−0.628286	+	0.777982i	$0.716243\pi$
$108$	5.91905	−	9.24248i	0.569561	−	0.889358i
$109$	−9.42451	+	1.87465i	−0.902704	+	0.179559i	−0.624557	−	0.780979i	$-0.714720\pi$
$109$	−9.42451	+	1.87465i	−0.902704	+	0.179559i	−0.278148	+	0.960538i	$0.589720\pi$
$110$	10.6273	−	16.2445i	1.01327	−	1.54885i
$111$	6.31558	−	6.31558i	0.599448	−	0.599448i
$112$	1.20698	−	0.555850i	0.114048	−	0.0525229i
$113$	−4.53709	−	4.53709i	−0.426814	−	0.426814i	0.460728	−	0.887541i	$-0.347588\pi$
$113$	−4.53709	−	4.53709i	−0.426814	−	0.426814i	−0.887541	+	0.460728i	$0.847588\pi$
$114$	15.3136	−	3.20110i	1.43425	−	0.299810i
$115$	0.459712	+	2.31113i	0.0428683	+	0.215514i
$116$	−15.6995	+	10.9374i	−1.45766	+	1.01551i
$117$	1.20595	−	0.805788i	0.111490	−	0.0744951i
$118$	5.30617	−	2.25856i	0.488473	−	0.207917i
$119$	−0.393869	−	0.950883i	−0.0361059	−	0.0871673i
$120$	−12.4841	−	7.82499i	−1.13964	−	0.714320i
$121$	2.67337	−	6.45409i	0.243034	−	0.586735i
$122$	6.67310	−	0.0648613i	0.604154	−	0.00587226i
$123$	−1.03830	+	5.21988i	−0.0936202	+	0.470660i
$124$	−1.63957	−	0.642087i	−0.147238	−	0.0576611i
$125$	−0.855086	+	1.27973i	−0.0764812	+	0.114462i
$126$	−0.108472	−	0.158972i	−0.00966341	−	0.0141624i
$127$	−13.1460			−1.16652			−0.583260	−	0.812285i	$-0.698223\pi$
$127$	−13.1460			−1.16652			−0.583260	+	0.812285i	$0.698223\pi$
$128$	9.81256	+	5.63149i	0.867316	+	0.497758i
$129$	−4.61004			−0.405891
$130$	−9.13421	−	13.3868i	−0.801123	−	1.17410i
$131$	−8.01070	+	11.9889i	−0.699898	+	1.04747i	0.295839	+	0.955238i	$0.404401\pi$
$131$	−8.01070	+	11.9889i	−0.699898	+	1.04747i	−0.995737	+	0.0922342i	$0.970599\pi$
$132$	−12.7114	−	4.97800i	−1.10638	−	0.433280i
$133$	0.445462	−	2.23949i	0.0386265	−	0.194188i
$134$	−7.72874	+	0.0751219i	−0.667661	+	0.00648954i
$135$	−6.79699	+	16.4094i	−0.584992	+	1.41229i
$136$	4.65395	−	7.42498i	0.399073	−	0.636687i
$137$	−2.01913	−	4.87460i	−0.172506	−	0.416465i	0.813854	−	0.581069i	$-0.197365\pi$
$137$	−2.01913	−	4.87460i	−0.172506	−	0.416465i	−0.986360	+	0.164604i	$0.947365\pi$
$138$	1.52475	−	0.649006i	0.129796	−	0.0552471i
$139$	−4.06094	+	2.71344i	−0.344445	+	0.230151i	−0.715744	−	0.698363i	$-0.753912\pi$
$139$	−4.06094	+	2.71344i	−0.344445	+	0.230151i	0.371299	+	0.928513i	$0.378912\pi$
$140$	−1.76445	+	1.22924i	−0.149123	+	0.103890i
$141$	1.43517	+	7.21509i	0.120863	+	0.607620i
$142$	9.75382	−	2.03890i	0.818522	−	0.171101i
$143$	−10.6176	−	10.6176i	−0.887891	−	0.887891i
$144$	0.567739	−	1.53707i	0.0473116	−	0.128089i
$145$	21.8949	−	21.8949i	1.81828	−	1.81828i
$146$	−8.31196	+	12.7053i	−0.687903	+	1.05150i
$147$	−10.8755	+	2.16328i	−0.896998	+	0.178424i
$148$	5.98565	−	9.34648i	0.492018	−	0.768276i
$149$	−5.32373	−	7.96752i	−0.436137	−	0.652725i	0.546673	−	0.837346i	$-0.315894\pi$
$149$	−5.32373	−	7.96752i	−0.436137	−	0.652725i	−0.982810	+	0.184622i	$0.940894\pi$
$150$	11.5601	+	4.65723i	0.943878	+	0.380262i
$151$	15.2438	−	6.31419i	1.24052	−	0.513841i	0.336645	−	0.941632i	$-0.390708\pi$
$151$	15.2438	−	6.31419i	1.24052	−	0.513841i	0.903878	+	0.427791i	$0.140708\pi$
$152$	17.7364	−	7.96016i	1.43861	−	0.645654i
$153$	−1.17254	−	0.485680i	−0.0947939	−	0.0392649i
$154$	−1.39511	+	1.42250i	−0.112421	+	0.114628i
$155$	2.79477	+	0.555915i	0.224481	+	0.0446521i
$156$	−7.90067	+	8.21396i	−0.632560	+	0.657643i
$157$	0.183668	+	0.122723i	0.0146583	+	0.00979438i	0.562878	−	0.826540i	$-0.309694\pi$
$157$	0.183668	+	0.122723i	0.0146583	+	0.00979438i	−0.548219	+	0.836335i	$0.684694\pi$
$158$	0.572863	−	3.03379i	0.0455746	−	0.241356i
$159$		−	14.4392i		−	1.14510i
$160$	−17.2356	−	6.17654i	−1.36260	−	0.488298i
$161$		−	0.241862i		−	0.0190614i
$162$	10.5659	+	1.99514i	0.830137	+	0.156753i
$163$	14.8711	+	9.93653i	1.16479	+	0.778289i	0.978912	−	0.204283i	$-0.0654864\pi$
$163$	14.8711	+	9.93653i	1.16479	+	0.778289i	0.185880	+	0.982572i	$0.440486\pi$
$164$	0.128553	+	6.61233i	0.0100383	+	0.516336i
$165$	21.6674	+	4.30992i	1.68681	+	0.335527i
$166$	14.9633	+	14.6752i	1.16137	+	1.13901i
$167$	16.9720	+	7.03005i	1.31334	+	0.544001i	0.925856	−	0.377877i	$-0.123346\pi$
$167$	16.9720	+	7.03005i	1.31334	+	0.544001i	0.387480	+	0.921878i	$0.373346\pi$
$168$	1.10006	+	1.03771i	0.0848715	+	0.0800610i
$169$	0.428795	−	0.177613i	0.0329842	−	0.0136625i
$170$	−5.29927	+	13.1537i	−0.406435	+	1.00885i
$171$	−1.56427	−	2.34110i	−0.119623	−	0.179029i
$172$	−5.59582	+	1.22661i	−0.426677	+	0.0935283i
$173$	−12.9081	+	2.56758i	−0.981384	+	0.195210i	−0.659611	−	0.751607i	$-0.729279\pi$
$173$	−12.9081	+	2.56758i	−0.981384	+	0.195210i	−0.321773	+	0.946817i	$0.604279\pi$
$174$	−18.2223	−	11.9212i	−1.38143	−	0.903744i
$175$	1.28623	−	1.28623i	0.0972296	−	0.0972296i
$176$	−16.7540	−	2.66030i	−1.26288	−	0.200528i
$177$	4.64075	+	4.64075i	0.348820	+	0.348820i
$178$	−0.513929	−	2.45856i	−0.0385206	−	0.184277i
$179$	−4.41588	−	22.2001i	−0.330058	−	1.65932i	−0.688105	−	0.725612i	$-0.741557\pi$
$179$	−4.41588	−	22.2001i	−0.330058	−	1.65932i	0.358046	−	0.933704i	$-0.383443\pi$
$180$	−0.466669	+	2.61030i	−0.0347834	+	0.194560i
$181$	−12.2894	+	8.21153i	−0.913466	+	0.610358i	−0.920978	−	0.389613i	$-0.872609\pi$
$181$	−12.2894	+	8.21153i	−0.913466	+	0.610358i	0.00751269	+	0.999972i	$0.497609\pi$
$182$	0.651464	+	1.53053i	0.0482897	+	0.113450i
$183$	2.90638	+	7.01663i	0.214846	+	0.518684i
$184$	1.67811	−	1.19348i	0.123712	−	0.0879848i
$185$	−6.87347	+	16.5940i	−0.505348	+	1.22002i
$186$	−0.0194767	−	2.00382i	−0.00142810	−	0.146927i
$187$	−2.56335	+	12.8868i	−0.187450	+	0.942377i
$188$	3.66181	+	8.37606i	0.267065	+	0.610887i
$189$	1.01282	−	1.51580i	0.0736720	−	0.110258i
$190$	−25.9877	+	17.7322i	−1.88535	+	1.28643i
$191$	6.69554			0.484472			0.242236	−	0.970217i	$-0.422119\pi$
$191$	6.69554			0.484472			0.242236	+	0.970217i	$0.422119\pi$
$192$	−1.77162	+	12.7532i	−0.127856	+	0.920383i
$193$	3.13547			0.225696			0.112848	−	0.993612i	$-0.464003\pi$
$193$	3.13547			0.225696			0.112848	+	0.993612i	$0.464003\pi$
$194$	2.84513	−	1.94132i	0.204268	−	0.139378i
$195$	10.2467	−	15.3353i	0.733782	−	1.09818i
$196$	−12.6255	+	5.51956i	−0.901821	+	0.394254i
$197$	3.05543	−	15.3607i	0.217690	−	1.09440i	−0.705102	−	0.709106i	$-0.749099\pi$
$197$	3.05543	−	15.3607i	0.217690	−	1.09440i	0.922793	−	0.385297i	$-0.125901\pi$
$198$	0.0238793	+	2.45677i	0.00169703	+	0.174595i
$199$	−1.63780	+	3.95399i	−0.116100	+	0.280291i	−0.971238	−	0.238109i	$-0.923472\pi$
$199$	−1.63780	+	3.95399i	−0.116100	+	0.280291i	0.855138	+	0.518400i	$0.173472\pi$
$200$	15.2712	+	2.57727i	1.07984	+	0.182240i
$201$	−3.36615	−	8.12661i	−0.237430	−	0.573207i
$202$	−0.438619	−	1.03048i	−0.0308612	−	0.0725041i
$203$	−2.64255	+	1.76569i	−0.185471	+	0.123927i
$204$	9.81712	+	1.75510i	0.687336	+	0.122882i
$205$	−2.08800	−	10.4971i	−0.145832	−	0.733148i
$206$	−1.86048	−	8.90025i	−0.129625	−	0.620110i
$207$	−0.210888	−	0.210888i	−0.0146577	−	0.0146577i
$208$	−7.40457	+	12.0725i	−0.513415	+	0.837080i
$209$	−20.6120	+	20.6120i	−1.42576	+	1.42576i
$210$	−2.04798	−	1.33981i	−0.141324	−	0.0924557i
$211$	20.2759	−	4.03313i	1.39585	−	0.277652i	0.560857	−	0.827912i	$-0.310472\pi$
$211$	20.2759	−	4.03313i	1.39585	−	0.277652i	0.834993	+	0.550261i	$0.185472\pi$
$212$	−3.84190	−	17.5268i	−0.263862	−	1.20374i
$213$	6.30036	+	9.42916i	0.431694	+	0.646075i
$214$	−3.25600	+	8.08199i	−0.222576	+	0.552473i
$215$	8.56501	−	3.54775i	0.584129	−	0.241954i
$216$	15.5149	−	0.452520i	1.05566	−	0.0307901i
$217$	−0.270212	−	0.111926i	−0.0183432	−	0.00759801i
$218$	−9.70209	−	9.51530i	−0.657108	−	0.644457i
$219$	−16.9468	−	3.37093i	−1.14516	−	0.227786i
$220$	27.4474	−	0.533618i	1.85050	−	0.0359765i
$221$	9.12074	+	6.09428i	0.613527	+	0.409946i
$222$	12.4118	+	2.34369i	0.833027	+	0.157298i
$223$		−	18.1462i		−	1.21516i	−0.794258	−	0.607581i	$-0.792140\pi$
$223$		−	18.1462i		−	1.21516i	0.794258	−	0.607581i	$-0.207860\pi$
$224$	1.61140	+	0.966909i	0.107666	+	0.0646043i
$225$		−	2.24301i		−	0.149534i
$226$	1.68370	−	8.91661i	0.111998	−	0.593124i
$227$	−13.4874	−	9.01200i	−0.895191	−	0.598148i	0.0206063	−	0.999788i	$-0.493440\pi$
$227$	−13.4874	−	9.01200i	−0.895191	−	0.598148i	−0.915798	+	0.401640i	$0.868440\pi$
$228$	15.9457	+	15.3375i	1.05603	+	1.01575i
$229$	1.15657	+	0.230055i	0.0764281	+	0.0152025i	0.233156	−	0.972439i	$-0.425095\pi$
$229$	1.15657	+	0.230055i	0.0764281	+	0.0152025i	−0.156728	+	0.987642i	$0.550095\pi$
$230$	−2.33339	+	2.37920i	−0.153859	+	0.156879i
$231$	−2.09492	−	0.867742i	−0.137835	−	0.0570933i
$232$	−25.2908	−	9.62188i	−1.66042	−	0.631707i
$233$	−3.25867	+	1.34979i	−0.213483	+	0.0884274i	−0.486862	−	0.873479i	$-0.661859\pi$
$233$	−3.25867	+	1.34979i	−0.213483	+	0.0884274i	0.273379	+	0.961906i	$0.411859\pi$
$234$	1.90255	+	0.766485i	0.124374	+	0.0501067i
$235$	−8.21893	−	12.3005i	−0.536144	−	0.802396i
$236$	6.86789	+	4.39832i	0.447061	+	0.286306i
$237$	3.44614	−	0.685479i	0.223851	−	0.0445266i
$238$	0.796859	−	1.21805i	0.0516527	−	0.0789543i
$239$	−5.54582	+	5.54582i	−0.358729	+	0.358729i	−0.863344	−	0.504615i	$-0.831634\pi$
$239$	−5.54582	+	5.54582i	−0.358729	+	0.358729i	0.504615	+	0.863344i	$0.331634\pi$
$240$	−0.809884	−	20.8209i	−0.0522778	−	1.34398i
$241$	−5.98668	−	5.98668i	−0.385636	−	0.385636i	0.487492	−	0.873128i	$-0.337912\pi$
$241$	−5.98668	−	5.98668i	−0.385636	−	0.385636i	−0.873128	+	0.487492i	$0.837912\pi$
$242$	9.67047	−	2.02148i	0.621641	−	0.129946i
$243$	−0.824430	−	4.14469i	−0.0528872	−	0.265882i
$244$	5.39481	+	7.74371i	0.345367	+	0.495740i
$245$	18.5409	−	12.3886i	1.18454	−	0.791481i
$246$	−6.92539	+	2.94777i	−0.441547	+	0.187943i
$247$	9.31293	+	22.4834i	0.592568	+	1.43058i
$248$	−0.556806	−	2.42712i	−0.0353572	−	0.154122i
$249$	−9.12778	+	22.0364i	−0.578450	+	1.39650i
$250$	−2.17653	+	0.0211555i	−0.137656	+	0.00133799i
$251$	0.437354	−	2.19873i	0.0276055	−	0.138782i	−0.964525	−	0.263993i	$-0.914961\pi$
$251$	0.437354	−	2.19873i	0.0276055	−	0.138782i	0.992130	+	0.125210i	$0.0399605\pi$
$252$	0.0992476	−	0.253429i	0.00625201	−	0.0159646i
$253$	−1.71540	+	2.56728i	−0.107846	+	0.161404i
$254$	−10.4785	−	15.3570i	−0.657480	−	0.963581i
$255$	−16.1389			−1.01066
$256$	1.24284	+	15.9517i	0.0776777	+	0.996979i
$257$	19.0558			1.18867			0.594334	−	0.804218i	$-0.297416\pi$
$257$	19.0558			1.18867			0.594334	+	0.804218i	$0.297416\pi$
$258$	−3.67460	−	5.38537i	−0.228771	−	0.335279i
$259$	1.02422	−	1.53285i	0.0636419	−	0.0952469i
$260$	8.35748	−	21.3409i	0.518309	−	1.32350i
$261$	−0.764559	+	3.84370i	−0.0473250	+	0.237919i
$262$	−20.3904	+	0.198191i	−1.25972	+	0.0122443i
$263$	2.42000	−	5.84240i	0.149224	−	0.360258i	−0.831538	−	0.555468i	$-0.812539\pi$
$263$	2.42000	−	5.84240i	0.149224	−	0.360258i	0.980761	+	0.195211i	$0.0625390\pi$
$264$	−4.31683	−	18.8171i	−0.265683	−	1.15811i
$265$	11.1120	+	26.8266i	0.682602	+	1.64795i
$266$	2.97121	−	1.26469i	0.182176	−	0.0775429i
$267$	2.37673	−	1.58808i	0.145453	−	0.0971889i
$268$	−6.24823	−	8.96871i	−0.381671	−	0.547851i
$269$	−2.01219	−	10.1159i	−0.122685	−	0.616780i	−0.992383	−	0.123195i	$-0.960686\pi$
$269$	−2.01219	−	10.1159i	−0.122685	−	0.616780i	0.869697	−	0.493585i	$-0.164314\pi$
$270$	−24.5870	+	5.13957i	−1.49631	+	0.312784i
$271$	4.18042	+	4.18042i	0.253942	+	0.253942i	0.822585	−	0.568642i	$-0.192531\pi$
$271$	4.18042	+	4.18042i	0.253942	+	0.253942i	−0.568642	+	0.822585i	$0.692531\pi$
$272$	12.3833	−	0.481682i	0.750850	−	0.0292063i
$273$	−1.33859	+	1.33859i	−0.0810152	+	0.0810152i
$274$	4.08501	−	6.24419i	0.246785	−	0.377225i
$275$	−22.7754	+	4.53031i	−1.37341	+	0.273188i
$276$	1.97352	+	1.26388i	0.118792	+	0.0760764i
$277$	−1.05525	−	1.57930i	−0.0634040	−	0.0948909i	0.798413	−	0.602110i	$-0.205673\pi$
$277$	−1.05525	−	1.57930i	−0.0634040	−	0.0948909i	−0.861817	+	0.507220i	$0.830673\pi$
$278$	−6.40672	−	2.58108i	−0.384249	−	0.154803i
$279$	−0.333199	+	0.138016i	−0.0199481	+	0.00826278i
$280$	−2.84240	−	1.08139i	−0.169866	−	0.0646255i
$281$	20.6297	+	8.54511i	1.23067	+	0.509759i	0.900786	−	0.434264i	$-0.142991\pi$
$281$	20.6297	+	8.54511i	1.23067	+	0.509759i	0.329881	+	0.944023i	$0.392991\pi$
$282$	−7.28460	+	7.42760i	−0.433792	+	0.442307i
$283$	0.153600	+	0.0305529i	0.00913055	+	0.00181618i	0.199653	−	0.979867i	$-0.436018\pi$
$283$	0.153600	+	0.0305529i	0.00913055	+	0.00181618i	−0.190523	+	0.981683i	$0.561018\pi$
$284$	10.1564	+	9.76907i	0.602674	+	0.579687i
$285$	−29.7703	−	19.8919i	−1.76344	−	1.17829i
$286$	3.94017	−	20.8665i	0.232987	−	1.23386i
$287$			1.09853i			0.0648442i
$288$	2.24812	−	0.561953i	0.132471	−	0.0331134i
$289$			7.40130i			0.435371i
$290$	43.0295	+	8.12515i	2.52678	+	0.477125i
$291$	3.25925	+	2.17776i	0.191060	+	0.127662i
$292$	−21.4675	+	0.417360i	−1.25629	+	0.0244241i
$293$	−8.18241	−	1.62758i	−0.478022	−	0.0950844i	−0.0498021	−	0.998759i	$-0.515859\pi$
$293$	−8.18241	−	1.62758i	−0.478022	−	0.0950844i	−0.428220	+	0.903675i	$0.640859\pi$
$294$	−11.1958	−	10.9803i	−0.652955	−	0.640384i
$295$	−12.1935	−	5.05070i	−0.709931	−	0.294063i
$296$	15.6895	−	0.457612i	0.911933	−	0.0265981i
$297$	−21.5015	+	8.90623i	−1.24765	+	0.516792i
$298$	5.06405	−	12.5699i	0.293353	−	0.728154i
$299$	1.43212	+	2.14331i	0.0828214	+	0.123951i
$300$	3.77389	+	17.2165i	0.217886	+	0.993997i
$301$	−0.933264	+	0.185638i	−0.0537924	+	0.0107000i
$302$	19.5268	+	12.7746i	1.12364	+	0.735095i
$303$	0.901250	−	0.901250i	0.0517755	−	0.0517755i
$304$	23.4364	+	14.3745i	1.34417	+	0.824433i
$305$	−10.7996	−	10.7996i	−0.618381	−	0.618381i
$306$	−0.367249	−	1.75687i	−0.0209942	−	0.100433i
$307$	6.67898	+	33.5775i	0.381190	+	1.91637i	0.399931	+	0.916545i	$0.369034\pi$
$307$	6.67898	+	33.5775i	0.381190	+	1.91637i	−0.0187412	+	0.999824i	$0.505966\pi$
$308$	−2.77376	−	0.495892i	−0.158050	−	0.0282561i
$309$	8.60400	−	5.74901i	0.489465	−	0.327050i
$310$	1.57826	+	3.70792i	0.0896394	+	0.210596i
$311$	−5.03970	−	12.1669i	−0.285775	−	0.689923i	0.714174	−	0.699968i	$-0.246802\pi$
$311$	−5.03970	−	12.1669i	−0.285775	−	0.689923i	−0.999950	+	0.0100453i	$0.996802\pi$
$312$	−15.8929	−	2.68219i	−0.899760	−	0.151849i
$313$	−0.161015	+	0.388724i	−0.00910110	+	0.0219720i	−0.928365	−	0.371670i	$-0.878785\pi$
$313$	−0.161015	+	0.388724i	−0.00910110	+	0.0219720i	0.919264	+	0.393642i	$0.128785\pi$
$314$	0.00303627	+	0.312379i	0.000171347	+	0.0176286i
$315$	−0.0859279	+	0.431989i	−0.00484149	+	0.0243398i
$316$	4.00065	−	1.74899i	0.225054	−	0.0983881i
$317$	−9.33099	+	13.9648i	−0.524081	+	0.784342i	−0.995214	−	0.0977198i	$-0.968845\pi$
$317$	−9.33099	+	13.9648i	−0.524081	+	0.784342i	0.471133	+	0.882062i	$0.343845\pi$
$318$	16.8676	−	11.5093i	0.945889	−	0.645408i
$319$	40.5729			2.27165
$320$	−6.52297	−	25.0576i	−0.364645	−	1.40076i
$321$	−9.91615			−0.553466
$322$	0.282539	−	0.192785i	0.0157453	−	0.0107435i
$323$	11.8308	−	17.7061i	0.658284	−	0.985192i
$324$	6.09127	+	13.9332i	0.338404	+	0.774069i
$325$	−3.78216	+	19.0142i	−0.209796	+	1.05472i
$326$	0.245837	+	25.2924i	0.0136157	+	1.40082i
$327$	5.91840	−	14.2883i	0.327288	−	0.790144i
$328$	−7.62195	+	5.42077i	−0.420852	+	0.299312i
$329$	0.581077	+	1.40284i	0.0320358	+	0.0773413i
$330$	12.2360	+	28.7469i	0.673572	+	1.58247i
$331$	−27.3548	+	18.2779i	−1.50355	+	1.00464i	−0.514433	+	0.857530i	$0.671998\pi$
$331$	−27.3548	+	18.2779i	−1.50355	+	1.00464i	−0.989120	+	0.147112i	$0.953002\pi$
$332$	−5.21629	+	29.1772i	−0.286281	+	1.60131i
$333$	−0.443495	−	2.22960i	−0.0243034	−	0.122181i
$334$	5.31580	+	25.4300i	0.290867	+	1.39147i
$335$	12.5080	+	12.5080i	0.683384	+	0.683384i
$336$	−0.335391	+	2.11222i	−0.0182971	+	0.115231i
$337$	−1.93221	+	1.93221i	−0.105254	+	0.105254i	−0.757773	−	0.652519i	$-0.773712\pi$
$337$	−1.93221	+	1.93221i	−0.105254	+	0.105254i	0.652519	+	0.757773i	$0.273712\pi$
$338$	0.549271	+	0.359338i	0.0298764	+	0.0195454i
$339$	10.1285	−	2.01469i	0.550106	−	0.109423i
$340$	−19.5900	+	4.29415i	−1.06241	+	0.232883i
$341$	2.07438	+	3.10453i	0.112334	+	0.168120i
$342$	1.48798	−	3.69342i	0.0804605	−	0.199717i
$343$	−4.26297	+	1.76578i	−0.230179	+	0.0953431i
$344$	−5.89326	−	5.55923i	−0.317743	−	0.299734i
$345$	−3.50385	−	1.45134i	−0.188641	−	0.0781375i
$346$	−13.2883	−	13.0324i	−0.714382	−	0.700629i
$347$	5.95710	+	1.18494i	0.319794	+	0.0636110i	0.352377	−	0.935858i	$-0.385373\pi$
$347$	5.95710	+	1.18494i	0.319794	+	0.0636110i	−0.0325833	+	0.999469i	$0.510373\pi$
$348$	−0.598587	−	30.7892i	−0.0320876	−	1.65047i
$349$	−2.40994	−	1.61027i	−0.129001	−	0.0861956i	0.489396	−	0.872062i	$-0.337217\pi$
$349$	−2.40994	−	1.61027i	−0.129001	−	0.0861956i	−0.618397	+	0.785866i	$0.712217\pi$
$350$	2.52778	+	0.477315i	0.135116	+	0.0255135i
$351$			19.4297i			1.03708i
$352$	−10.2467	−	21.6922i	−0.546149	−	1.15620i
$353$		−	34.9802i		−	1.86181i	−0.365261	−	0.930905i	$-0.619020\pi$
$353$		−	34.9802i		−	1.86181i	0.365261	−	0.930905i	$-0.380980\pi$
$354$	−1.72217	+	9.12033i	−0.0915323	+	0.484740i
$355$	−18.9619	−	12.6699i	−1.00639	−	0.672449i
$356$	2.46241	−	2.56005i	0.130507	−	0.135682i
$357$	1.62467	+	0.323167i	0.0859868	+	0.0171038i
$358$	22.4140	−	22.8540i	1.18462	−	1.20787i
$359$	11.4132	+	4.72748i	0.602363	+	0.249507i	0.662959	−	0.748655i	$-0.269300\pi$
$359$	11.4132	+	4.72748i	0.602363	+	0.249507i	−0.0605961	+	0.998162i	$0.519300\pi$
$360$	−3.42129	+	1.53548i	−0.180318	+	0.0809270i
$361$	26.0933	−	10.8082i	1.37333	−	0.568852i
$362$	−19.3883	−	7.81100i	−1.01903	−	0.410537i
$363$	6.24652	+	9.34858i	0.327857	+	0.490673i
$364$	−1.26866	+	1.98099i	−0.0664960	+	0.103832i
$365$	34.0797	−	6.77888i	1.78381	−	0.354823i
$366$	−5.88007	+	8.98805i	−0.307356	+	0.469813i
$367$	−7.30233	+	7.30233i	−0.381178	+	0.381178i	−0.871527	−	0.490348i	$-0.836870\pi$
$367$	−7.30233	+	7.30233i	−0.381178	+	0.381178i	0.490348	+	0.871527i	$0.336870\pi$
$368$	2.73181	+	1.00903i	0.142405	+	0.0525995i
$369$	0.957847	+	0.957847i	0.0498635	+	0.0498635i
$370$	−24.8636	+	5.19740i	−1.29260	+	0.270200i
$371$	−0.581439	−	2.92309i	−0.0301868	−	0.151759i
$372$	2.32530	−	1.61997i	0.120561	−	0.0839915i
$373$	18.9156	−	12.6390i	0.979413	−	0.654423i	0.0407173	−	0.999171i	$-0.487036\pi$
$373$	18.9156	−	12.6390i	0.979413	−	0.654423i	0.938695	+	0.344748i	$0.112036\pi$
$374$	−17.0974	+	7.27745i	−0.884084	+	0.376308i
$375$	−0.947960	−	2.28858i	−0.0489525	−	0.118182i
$376$	−6.86600	+	10.9541i	−0.354087	+	0.564915i
$377$	12.9625	−	31.2942i	0.667601	−	1.61173i
$378$	2.57804	−	0.0250580i	0.132600	−	0.00128885i
$379$	4.20965	−	21.1633i	0.216235	−	1.08709i	−0.708277	−	0.705934i	$-0.750527\pi$
$379$	4.20965	−	21.1633i	0.216235	−	1.08709i	0.924512	−	0.381152i	$-0.124473\pi$
$380$	−41.4290	−	16.2243i	−2.12526	−	0.832292i
$381$	11.7547	−	17.5922i	0.602213	−	0.901276i
$382$	5.33692	+	7.82162i	0.273061	+	0.400189i
$383$	−18.3977			−0.940079			−0.470039	−	0.882646i	$-0.655760\pi$
$383$	−18.3977			−0.940079			−0.470039	+	0.882646i	$0.655760\pi$
$384$	−16.3102	+	8.09583i	−0.832328	+	0.413139i
$385$	4.55994			0.232396
$386$	2.49924	+	3.66280i	0.127208	+	0.186432i
$387$	−0.651881	+	0.975609i	−0.0331370	+	0.0495930i
$388$	4.53563	+	1.77624i	0.230262	+	0.0901747i
$389$	−3.48084	+	17.4994i	−0.176486	+	0.887253i	0.786477	+	0.617619i	$0.211903\pi$
$389$	−3.48084	+	17.4994i	−0.176486	+	0.887253i	−0.962963	+	0.269634i	$0.913097\pi$
$390$	26.0819	−	0.253511i	1.32071	−	0.0128371i
$391$	0.863192	−	2.08393i	0.0436535	−	0.105389i
$392$	−16.5115	−	10.3493i	−0.833955	−	0.522720i
$393$	−8.88078	−	21.4401i	−0.447976	−	1.08151i
$394$	20.3795	−	8.67449i	1.02671	−	0.437014i
$395$	−5.87507	+	3.92560i	−0.295607	+	0.197518i
$396$	−2.85093	+	1.98615i	−0.143264	+	0.0998080i
$397$	2.30374	+	11.5817i	0.115621	+	0.581268i	0.994545	+	0.104306i	$0.0332621\pi$
$397$	2.30374	+	11.5817i	0.115621	+	0.581268i	−0.878924	+	0.476962i	$0.841738\pi$
$398$	−5.92445	+	1.23843i	−0.296966	+	0.0620767i
$399$	2.59860	+	2.59860i	0.130093	+	0.130093i
$400$	9.16175	+	19.8939i	0.458087	+	0.994694i
$401$	−14.2513	+	14.2513i	−0.711677	+	0.711677i	−0.966886	−	0.255209i	$-0.917856\pi$
$401$	−14.2513	+	14.2513i	−0.711677	+	0.711677i	0.255209	+	0.966886i	$0.417856\pi$
$402$	6.81026	−	10.4099i	0.339665	−	0.519198i
$403$	3.05728	−	0.608131i	0.152294	−	0.0302932i
$404$	0.854169	−	1.33377i	0.0424965	−	0.0663574i
$405$	−13.6719	−	20.4614i	−0.679360	−	1.01673i
$406$	−4.16899	−	1.67957i	−0.206904	−	0.0833557i
$407$	−21.7435	+	9.00645i	−1.07778	+	0.446433i
$408$	5.77482	+	12.8672i	0.285896	+	0.637020i
$409$	−21.7113	−	8.99313i	−1.07356	−	0.444682i	−0.225312	−	0.974287i	$-0.572340\pi$
$409$	−21.7113	−	8.99313i	−1.07356	−	0.444682i	−0.848244	+	0.529605i	$0.822340\pi$
$410$	10.5982	−	10.8062i	0.523408	−	0.533683i
$411$	8.32871	+	1.65668i	0.410825	+	0.0817182i
$412$	8.91417	−	9.26765i	0.439169	−	0.456584i
$413$	1.12636	+	0.752607i	0.0554243	+	0.0370334i
$414$	0.0782598	−	0.414451i	0.00384626	−	0.0203692i
$415$		−	47.9660i		−	2.35456i
$416$	−20.0050	+	0.972961i	−0.980827	+	0.0477033i
$417$		−	7.86069i		−	0.384940i
$418$	−40.5081	−	7.64905i	−1.98132	−	0.374127i
$419$	−2.46480	−	1.64693i	−0.120413	−	0.0804577i	0.493905	−	0.869516i	$-0.335569\pi$
$419$	−2.46480	−	1.64693i	−0.120413	−	0.0804577i	−0.614319	+	0.789058i	$0.710569\pi$
$420$	−0.0672745	−	3.46036i	−0.00328266	−	0.168848i
$421$	−33.4984	−	6.66325i	−1.63261	−	0.324747i	−0.708162	−	0.706050i	$-0.750475\pi$
$421$	−33.4984	−	6.66325i	−1.63261	−	0.324747i	−0.924450	+	0.381303i	$0.875475\pi$
$422$	20.8731	+	20.4712i	1.01609	+	0.996523i
$423$	1.72985	+	0.716527i	0.0841081	+	0.0348387i
$424$	17.4122	−	18.4584i	0.845610	−	0.896419i
$425$	15.6729	−	6.49191i	0.760245	−	0.314904i
$426$	−5.99305	+	14.8758i	−0.290364	+	0.720736i
$427$	0.870919	+	1.30342i	0.0421467	+	0.0630770i
$428$	−12.0366	+	2.63843i	−0.581809	+	0.127533i
$429$	23.7026	−	4.71475i	1.14437	−	0.227630i
$430$	10.9715	+	7.17765i	0.529092	+	0.346137i
$431$	−27.7891	+	27.7891i	−1.33855	+	1.33855i	−0.441094	+	0.897461i	$0.645409\pi$
$431$	−27.7891	+	27.7891i	−1.33855	+	1.33855i	−0.897461	+	0.441094i	$0.854591\pi$
$432$	12.8953	+	17.7636i	0.620428	+	0.854650i
$433$	19.5120	+	19.5120i	0.937689	+	0.937689i	0.998169	−	0.0604807i	$-0.0192634\pi$
$433$	19.5120	+	19.5120i	0.937689	+	0.937689i	−0.0604807	+	0.998169i	$0.519263\pi$
$434$	−0.0846330	−	0.404872i	−0.00406251	−	0.0194345i
$435$	9.72242	+	48.8779i	0.466154	+	2.34352i
$436$	3.38221	−	18.9183i	0.161979	−	0.906024i
$437$	4.16081	−	2.78016i	0.199038	−	0.132993i
$438$	−9.57020	−	22.4839i	−0.457282	−	1.07432i
$439$	10.7454	+	25.9416i	0.512849	+	1.23813i	0.942219	+	0.334998i	$0.108736\pi$
$439$	10.7454	+	25.9416i	0.512849	+	1.23813i	−0.429370	+	0.903129i	$0.641264\pi$
$440$	22.5013	+	31.6383i	1.07271	+	1.50830i
$441$	−1.08004	+	2.60745i	−0.0514306	+	0.124164i
$442$	0.150777	+	15.5124i	0.00717174	+	0.737848i
$443$	1.40022	−	7.03938i	0.0665264	−	0.334451i	−0.933161	−	0.359459i	$-0.882961\pi$
$443$	1.40022	−	7.03938i	0.0665264	−	0.334451i	0.999687	+	0.0250082i	$0.00796118\pi$
$444$	7.15543	+	16.3674i	0.339582	+	0.776763i
$445$	−3.19360	+	4.77956i	−0.151391	+	0.226573i
$446$	21.1981	−	14.4641i	1.00376	−	0.684896i
$447$	15.4226			0.729462
$448$	0.154898	+	2.65312i	0.00731823	+	0.125348i
$449$	9.76361			0.460773			0.230387	−	0.973099i	$-0.426001\pi$
$449$	9.76361			0.460773			0.230387	+	0.973099i	$0.426001\pi$
$450$	2.62025	−	1.78787i	0.123520	−	0.0842811i
$451$	7.79132	−	11.6605i	0.366879	−	0.549073i
$452$	11.7583	−	5.14044i	0.553063	−	0.241786i
$453$	−5.18076	+	26.0454i	−0.243413	+	1.22372i
$454$	−0.222964	−	22.9391i	−0.0104642	−	1.07659i
$455$	1.45684	−	3.51712i	0.0682976	−	0.164885i
$456$	−5.20693	+	30.8529i	−0.243837	+	1.44482i
$457$	−12.2635	−	29.6067i	−0.573662	−	1.38494i	−0.898417	−	0.439144i	$-0.855282\pi$
$457$	−12.2635	−	29.6067i	−0.573662	−	1.38494i	0.324755	−	0.945798i	$-0.394718\pi$
$458$	0.653137	+	1.53446i	0.0305191	+	0.0717004i
$459$	14.1365	−	9.44569i	0.659834	−	0.440887i
$460$	−4.63925	−	0.829403i	−0.216306	−	0.0386711i
$461$	6.86998	+	34.5377i	0.319967	+	1.60858i	0.721281	+	0.692642i	$0.243553\pi$
$461$	6.86998	+	34.5377i	0.319967	+	1.60858i	−0.401314	+	0.915940i	$0.631447\pi$
$462$	−0.656147	−	3.13891i	−0.0305267	−	0.146035i
$463$	−20.0285	−	20.0285i	−0.930804	−	0.930804i	0.0669525	−	0.997756i	$-0.478672\pi$
$463$	−20.0285	−	20.0285i	−0.930804	−	0.930804i	−0.997756	+	0.0669525i	$0.978672\pi$
$464$	−8.91880	−	37.2137i	−0.414045	−	1.72760i
$465$	−3.24293	+	3.24293i	−0.150387	+	0.150387i
$466$	−4.17424	−	2.73083i	−0.193368	−	0.126503i
$467$	−15.7542	+	3.13370i	−0.729015	+	0.145010i	−0.545624	−	0.838030i	$-0.683707\pi$
$467$	−15.7542	+	3.13370i	−0.729015	+	0.145010i	−0.183391	+	0.983040i	$0.558707\pi$
$468$	0.621104	+	2.83349i	0.0287106	+	0.130978i
$469$	−1.00869	−	1.50962i	−0.0465771	−	0.0697076i
$470$	7.81804	−	19.4058i	0.360619	−	0.895122i
$471$	−0.328461	+	0.136053i	−0.0151347	+	0.00626898i
$472$	0.336258	+	11.5288i	0.0154775	+	0.530656i
$473$	11.2229	+	4.64868i	0.516030	+	0.213747i
$474$	3.54763	+	3.47933i	0.162948	+	0.159811i
$475$	36.9122	+	7.34229i	1.69365	+	0.336888i
$476$	2.05807	−	0.0400118i	0.0943314	−	0.00183394i
$477$	−3.05572	−	2.04177i	−0.139912	−	0.0934861i
$478$	−10.8990	−	2.05804i	−0.498511	−	0.0941325i
$479$			30.8222i			1.40830i	0.710050	+	0.704151i	$0.248672\pi$
$479$			30.8222i			1.40830i	−0.710050	+	0.704151i	$0.751328\pi$
$480$	23.6771	−	17.5422i	1.08071	−	0.800686i
$481$			19.6483i			0.895887i
$482$	2.22164	−	11.7654i	0.101193	−	0.535901i
$483$	0.323663	+	0.216265i	0.0147272	+	0.00984040i
$484$	10.0697	+	9.68559i	0.457712	+	0.440254i
$485$	−7.73131	−	1.53785i	−0.351061	−	0.0698303i
$486$	4.18462	−	4.26676i	0.189818	−	0.193544i
$487$	−33.8967	−	14.0405i	−1.53601	−	0.636235i	−0.555288	−	0.831658i	$-0.687392\pi$
$487$	−33.8967	−	14.0405i	−1.53601	−	0.636235i	−0.980719	+	0.195423i	$0.937392\pi$
$488$	−4.74594	+	12.4745i	−0.214839	+	0.564695i
$489$	−26.5945	+	11.0158i	−1.20264	+	0.498151i
$490$	29.2509	+	11.7844i	1.32142	+	0.532363i
$491$	6.13196	+	9.17712i	0.276731	+	0.414158i	0.943636	−	0.330985i	$-0.107381\pi$
$491$	6.13196	+	9.17712i	0.276731	+	0.414158i	−0.666904	+	0.745143i	$0.732381\pi$
$492$	−8.96367	−	5.74050i	−0.404114	−	0.258802i
$493$	−29.0704	+	5.78246i	−1.30926	+	0.260429i
$494$	−18.8415	+	28.8004i	−0.847721	+	1.29579i
$495$	3.97597	−	3.97597i	0.178707	−	0.178707i
$496$	2.39150	−	2.58508i	0.107382	−	0.116073i
$497$	1.65515	+	1.65515i	0.0742436	+	0.0742436i
$498$	−33.0182	+	6.90200i	−1.47958	+	0.309286i
$499$	−2.51984	−	12.6681i	−0.112804	−	0.567102i	−0.995305	−	0.0967914i	$-0.969142\pi$
$499$	−2.51984	−	12.6681i	−0.112804	−	0.567102i	0.882501	−	0.470310i	$-0.155858\pi$
$500$	−1.75960	−	2.52573i	−0.0786916	−	0.112954i
$501$	−24.5836	+	16.4262i	−1.09831	+	0.733869i
$502$	2.91713	−	1.24167i	0.130198	−	0.0554183i
$503$	−5.73399	−	13.8431i	−0.255666	−	0.617232i	0.742977	−	0.669317i	$-0.233413\pi$
$503$	−5.73399	−	13.8431i	−0.255666	−	0.617232i	−0.998643	+	0.0520853i	$0.983413\pi$
$504$	0.375161	−	0.0860657i	0.0167110	−	0.00383367i
$505$	−0.980863	+	2.36801i	−0.0436478	+	0.105375i
$506$	−4.36638	+	0.0424404i	−0.194109	+	0.00188671i
$507$	−0.145730	+	0.732635i	−0.00647211	+	0.0325375i
$508$	9.58747	−	24.4817i	0.425375	−	1.08620i
$509$	−13.9117	+	20.8204i	−0.616627	+	0.922848i	−1.00000		0.000745744i	$-0.999763\pi$
$509$	−13.9117	+	20.8204i	−0.616627	+	0.922848i	0.383372	+	0.923594i	$0.374763\pi$
$510$	−12.8641	−	18.8532i	−0.569632	−	0.834834i
$511$	−3.56648			−0.157772
$512$	−17.6438	+	14.1667i	−0.779754	+	0.626087i
$513$	37.7188			1.66533
$514$	15.1891	+	22.2607i	0.669964	+	0.981876i
$515$	−11.5612	+	17.3025i	−0.509446	+	0.762439i
$516$	3.36213	−	8.58521i	0.148009	−	0.377943i
$517$	3.78172	−	19.0120i	0.166320	−	0.836146i
$518$	2.60705	−	0.0253400i	0.114547	−	0.00111338i
$519$	8.10602	−	19.5697i	0.355815	−	0.859013i
$520$	31.5917	−	7.24745i	1.38539	−	0.317822i
$521$	−7.37291	−	17.7998i	−0.323013	−	0.779822i	−0.999076	−	0.0429783i	$-0.986315\pi$
$521$	−7.37291	−	17.7998i	−0.323013	−	0.779822i	0.676063	−	0.736844i	$-0.263685\pi$
$522$	−5.09956	+	2.17061i	−0.223202	+	0.0950052i
$523$	−2.21124	+	1.47750i	−0.0966907	+	0.0646067i	−0.602976	−	0.797760i	$-0.706018\pi$
$523$	−2.21124	+	1.47750i	−0.0966907	+	0.0646067i	0.506285	+	0.862366i	$0.331018\pi$
$524$	−16.4845	−	23.6618i	−0.720127	−	1.03367i
$525$	0.571147	+	2.87135i	0.0249269	+	0.125316i
$526$	8.75394	−	1.82989i	0.381690	−	0.0797871i
$527$	−1.92875	−	1.92875i	−0.0840176	−	0.0840176i
$528$	18.5409	−	20.0417i	0.806891	−	0.872204i
$529$	−15.8886	+	15.8886i	−0.690811	+	0.690811i
$530$	−22.4812	+	34.3640i	−0.976523	+	1.49268i
$531$	1.63833	−	0.325885i	0.0710976	−	0.0141422i
$532$	3.84570	+	2.46285i	0.166732	+	0.106778i
$533$	−6.50463	−	9.73487i	−0.281747	−	0.421664i
$534$	3.74963	+	1.51062i	0.162262	+	0.0653709i
$535$	18.4233	−	7.63117i	0.796507	−	0.329924i
$536$	5.49672	−	14.4479i	0.237422	−	0.624055i
$537$	33.6571	+	13.9412i	1.45241	+	0.601608i
$538$	10.2134	−	10.4139i	0.440331	−	0.448974i
$539$	28.6573	+	5.70030i	1.23436	+	0.245529i
$540$	−25.6019	−	24.6254i	−1.10173	−	1.05971i
$541$	17.3178	+	11.5714i	0.744550	+	0.497492i	0.869048	−	0.494728i	$-0.164732\pi$
$541$	17.3178	+	11.5714i	0.744550	+	0.497492i	−0.124498	+	0.992220i	$0.539732\pi$
$542$	−1.55134	+	8.21566i	−0.0666358	+	0.352893i
$543$		−	23.7884i		−	1.02086i
$544$	10.4333	+	14.0821i	0.447324	+	0.603764i
$545$			31.1009i			1.33222i
$546$	−2.63069	−	0.496747i	−0.112583	−	0.0212588i
$547$	3.42930	+	2.29138i	0.146626	+	0.0979725i	0.626719	−	0.779245i	$-0.284397\pi$
$547$	3.42930	+	2.29138i	0.146626	+	0.0979725i	−0.480093	+	0.877217i	$0.659397\pi$
$548$	10.5505	−	0.205117i	0.450694	−	0.00876214i
$549$	1.89588	+	0.377115i	0.0809143	+	0.0160949i
$550$	−23.4462	−	22.9948i	−0.999749	−	0.980502i
$551$	−60.7513	−	25.1640i	−2.58809	−	1.07202i
$552$	0.0966252	+	3.31285i	0.00411264	+	0.141004i
$553$	0.670038	−	0.277539i	0.0284929	−	0.0118022i
$554$	1.00378	−	2.49157i	0.0426466	−	0.105857i
$555$	−16.0604	−	24.0360i	−0.681724	−	1.02027i
$556$	−2.09153	−	9.54157i	−0.0887005	−	0.404653i
$557$	29.9106	−	5.94959i	1.26735	−	0.252092i	0.484772	−	0.874640i	$-0.338902\pi$
$557$	29.9106	−	5.94959i	1.26735	−	0.252092i	0.782582	+	0.622548i	$0.213902\pi$
$558$	−0.426816	−	0.279228i	−0.0180686	−	0.0118206i
$559$	7.17112	−	7.17112i	0.303306	−	0.303306i
$560$	−1.00237	−	4.18241i	−0.0423580	−	0.176739i
$561$	−14.9533	−	14.9533i	−0.631328	−	0.631328i
$562$	6.46142	+	30.9105i	0.272559	+	1.30388i
$563$	2.46552	+	12.3950i	0.103909	+	0.522387i	0.997321	+	0.0731484i	$0.0233047\pi$
$563$	2.46552	+	12.3950i	0.103909	+	0.522387i	−0.893412	+	0.449239i	$0.851695\pi$
$564$	−14.4833	−	2.58931i	−0.609855	−	0.109030i
$565$	−17.2674	+	11.5377i	−0.726445	+	0.485395i
$566$	0.0867409	+	0.203786i	0.00364599	+	0.00856576i
$567$	0.966598	+	2.33357i	0.0405933	+	0.0980008i
$568$	−3.31650	+	19.6514i	−0.139157	+	0.824554i
$569$	1.98587	−	4.79431i	0.0832520	−	0.200988i	−0.876772	−	0.480907i	$-0.840308\pi$
$569$	1.98587	−	4.79431i	0.0832520	−	0.200988i	0.960024	+	0.279919i	$0.0903075\pi$
$570$	−0.492141	−	50.6328i	−0.0206135	−	2.12077i
$571$	5.46069	−	27.4528i	0.228523	−	1.14886i	−0.680703	−	0.732559i	$-0.738326\pi$
$571$	5.46069	−	27.4528i	0.228523	−	1.14886i	0.909226	−	0.416303i	$-0.136674\pi$
$572$	27.5166	−	12.0296i	1.15053	−	0.502982i
$573$	−5.98693	+	8.96008i	−0.250108	+	0.374313i
$574$	−1.28329	+	0.875624i	−0.0535633	+	0.0365478i
$575$	3.98647			0.166247
$576$	2.44841	+	2.17829i	0.102017	+	0.0907619i
$577$	−5.80892			−0.241829			−0.120914	−	0.992663i	$-0.538583\pi$
$577$	−5.80892			−0.241829			−0.120914	+	0.992663i	$0.538583\pi$
$578$	−8.64608	+	5.89948i	−0.359630	+	0.245386i
$579$	−2.80363	+	4.19593i	−0.116515	+	0.174377i
$580$	24.8066	+	56.7428i	1.03004	+	2.35612i
$581$	−0.960477	+	4.82865i	−0.0398473	+	0.200326i
$582$	0.0538794	+	5.54326i	0.00223337	+	0.229776i
$583$	−14.5602	+	35.1515i	−0.603023	+	1.45583i
$584$	−17.5990	−	24.7453i	−0.728253	−	1.02397i
$585$	−1.79643	−	4.33696i	−0.0742731	−	0.179311i
$586$	−4.62078	−	10.8559i	−0.190883	−	0.448453i
$587$	38.7045	−	25.8615i	1.59751	−	1.06742i	0.644441	−	0.764654i	$-0.277090\pi$
$587$	38.7045	−	25.8615i	1.59751	−	1.06742i	0.953065	−	0.302766i	$-0.0979100\pi$
$588$	3.90294	−	21.8310i	0.160955	−	0.900297i
$589$	−1.18056	−	5.93509i	−0.0486443	−	0.244551i
$590$	−3.81910	−	18.2700i	−0.157230	−	0.752166i
$591$	17.8238	+	17.8238i	0.733175	+	0.733175i
$592$	13.0405	+	17.9634i	0.535959	+	0.738293i
$593$	10.6123	−	10.6123i	0.435796	−	0.435796i	−0.454799	−	0.890594i	$-0.650289\pi$
$593$	10.6123	−	10.6123i	0.435796	−	0.435796i	0.890594	+	0.454799i	$0.150289\pi$
$594$	−27.5427	−	18.0187i	−1.13009	−	0.739317i
$595$	−3.26719	+	0.649884i	−0.133942	+	0.0266426i
$596$	18.7204	−	4.10355i	0.766819	−	0.168088i
$597$	−3.82683	−	5.72726i	−0.156622	−	0.234401i
$598$	−1.36226	+	3.38138i	−0.0557070	+	0.138275i
$599$	37.1396	−	15.3837i	1.51748	−	0.628561i	0.540396	−	0.841411i	$-0.318274\pi$
$599$	37.1396	−	15.3837i	1.51748	−	0.628561i	0.977085	+	0.212850i	$0.0682744\pi$
$600$	−17.1040	+	18.1317i	−0.698266	+	0.740222i
$601$	−10.9322	−	4.52827i	−0.445934	−	0.184712i	0.148405	−	0.988927i	$-0.452586\pi$
$601$	−10.9322	−	4.52827i	−0.445934	−	0.184712i	−0.594339	+	0.804215i	$0.702586\pi$
$602$	−0.960751	−	0.942254i	−0.0391573	−	0.0384034i
$603$	−2.19580	−	0.436772i	−0.0894199	−	0.0177867i
$604$	0.641438	+	32.9933i	0.0260997	+	1.34248i
$605$	−18.7998	−	12.5616i	−0.764322	−	0.510704i
$606$	1.77120	+	0.334451i	0.0719501	+	0.0135862i
$607$			20.3426i			0.825679i	0.910804	+	0.412840i	$0.135463\pi$
$607$			20.3426i			0.825679i	−0.910804	+	0.412840i	$0.864537\pi$
$608$	1.88881	+	38.8357i	0.0766012	+	1.57500i
$609$		−	5.11513i		−	0.207275i
$610$	4.00769	−	21.2241i	0.162266	−	0.859337i
$611$	−13.4559	−	8.99093i	−0.544366	−	0.363734i
$612$	1.75961	−	1.82939i	0.0711281	−	0.0739486i
$613$	26.9544	+	5.36156i	1.08868	+	0.216552i	0.706625	−	0.707589i	$-0.250217\pi$
$613$	26.9544	+	5.36156i	1.08868	+	0.216552i	0.382053	+	0.924140i	$0.375217\pi$
$614$	−33.9010	+	34.5665i	−1.36813	+	1.39499i
$615$	15.9144	+	6.59195i	0.641730	+	0.265813i
$616$	−1.63164	−	3.63553i	−0.0657405	−	0.146480i
$617$	12.8642	−	5.32854i	0.517895	−	0.214519i	−0.108397	−	0.994108i	$-0.534572\pi$
$617$	12.8642	−	5.32854i	0.517895	−	0.214519i	0.626292	+	0.779589i	$0.284572\pi$
$618$	13.5740	+	5.46860i	0.546028	+	0.219979i
$619$	−19.3117	−	28.9020i	−0.776204	−	1.16167i	−0.983057	−	0.183299i	$-0.941322\pi$
$619$	−19.3117	−	28.9020i	−0.776204	−	1.16167i	0.206854	−	0.978372i	$-0.433678\pi$
$620$	−3.07352	+	4.79923i	−0.123435	+	0.192742i
$621$	3.91854	−	0.779446i	0.157246	−	0.0312781i
$622$	10.1961	−	15.5854i	0.408827	−	0.624917i
$623$	0.417200	−	0.417200i	0.0167148	−	0.0167148i
$624$	−9.53474	−	20.7038i	−0.381695	−	0.828815i
$625$	−15.8365	−	15.8365i	−0.633460	−	0.633460i
$626$	−0.582444	+	0.121752i	−0.0232792	+	0.00486619i
$627$	−9.15273	−	46.0139i	−0.365525	−	1.83762i
$628$	−0.362496	+	0.252540i	−0.0144652	+	0.0100775i
$629$	14.2956	−	9.55198i	0.570001	−	0.380862i
$630$	−0.573134	+	0.243953i	−0.0228342	+	0.00971931i
$631$	−10.3488	−	24.9842i	−0.411980	−	0.994607i	−0.984606	−	0.174790i	$-0.944075\pi$
$631$	−10.3488	−	24.9842i	−0.411980	−	0.994607i	0.572626	−	0.819817i	$-0.305925\pi$
$632$	5.23200	+	3.27940i	0.208118	+	0.130447i
$633$	−12.7329	+	30.7398i	−0.506085	+	1.22180i
$634$	−23.7511	+	0.230856i	−0.943276	+	0.00916846i
$635$	−8.30076	+	41.7307i	−0.329406	+	1.65603i
$636$	26.8899	+	10.5306i	1.06625	+	0.417565i
$637$	13.5523	−	20.2824i	0.536961	−	0.803620i
$638$	32.3401	+	47.3966i	1.28036	+	1.87645i
$639$	2.88636			0.114183
$640$	24.0725	−	27.5931i	0.951551	−	1.09071i
$641$	−26.5599			−1.04905			−0.524527	−	0.851394i	$-0.675758\pi$
$641$	−26.5599			−1.04905			−0.524527	+	0.851394i	$0.675758\pi$
$642$	−7.90403	−	11.5839i	−0.311947	−	0.457180i
$643$	−7.23987	+	10.8352i	−0.285513	+	0.427300i	−0.946308	−	0.323266i	$-0.895219\pi$
$643$	−7.23987	+	10.8352i	−0.285513	+	0.427300i	0.660795	+	0.750566i	$0.270219\pi$
$644$	0.450416	+	0.176391i	0.0177489	+	0.00695079i
$645$	−2.91091	+	14.6341i	−0.114617	+	0.576218i
$646$	30.1141	−	0.292703i	1.18482	−	0.0115163i
$647$	4.72206	−	11.4001i	0.185643	−	0.448183i	−0.803469	−	0.595347i	$-0.797015\pi$
$647$	4.72206	−	11.4001i	0.185643	−	0.448183i	0.989112	+	0.147164i	$0.0470146\pi$
$648$	−11.4213	+	18.2217i	−0.448671	+	0.715817i
$649$	−6.61803	−	15.9773i	−0.259780	−	0.627165i
$650$	−25.2268	+	10.7377i	−0.989475	+	0.421167i
$651$	0.391396	−	0.261522i	0.0153400	−	0.0102499i
$652$	−29.3502	+	20.4474i	−1.14944	+	0.800783i
$653$	1.67322	+	8.41182i	0.0654780	+	0.329180i	0.999615	−	0.0277336i	$-0.00882902\pi$
$653$	1.67322	+	8.41182i	0.0654780	+	0.329180i	−0.934137	+	0.356914i	$0.883829\pi$
$654$	21.4088	−	4.47522i	0.837151	−	0.174995i
$655$	32.9993	+	32.9993i	1.28939	+	1.28939i
$656$	−12.4078	−	4.58301i	−0.484443	−	0.178936i
$657$	−3.10974	+	3.10974i	−0.121322	+	0.121322i
$658$	−1.17561	+	1.79699i	−0.0458301	+	0.0700541i
$659$	−30.9667	+	6.15965i	−1.20629	+	0.239946i	−0.756985	−	0.653432i	$-0.773328\pi$
$659$	−30.9667	+	6.15965i	−1.20629	+	0.239946i	−0.449305	+	0.893378i	$0.648328\pi$
$660$	−23.8285	+	37.2077i	−0.927523	+	1.44831i
$661$	12.7193	+	19.0357i	0.494722	+	0.740403i	0.991869	−	0.127263i	$-0.0406192\pi$
$661$	12.7193	+	19.0357i	0.494722	+	0.740403i	−0.497147	+	0.867666i	$0.665619\pi$
$662$	−43.1560	−	17.3863i	−1.67731	−	0.675739i
$663$	−16.3109	+	6.75621i	−0.633464	+	0.262389i
$664$	−38.2422	+	17.1632i	−1.48408	+	0.666061i
$665$	−6.82777	−	2.82815i	−0.264769	−	0.109671i
$666$	2.25108	−	2.29527i	0.0872275	−	0.0889398i
$667$	−6.83135	−	1.35884i	−0.264511	−	0.0526145i
$668$	−25.4698	+	26.4797i	−0.985455	+	1.02453i
$669$	24.2836	+	16.2258i	0.938857	+	0.627324i
$670$	−4.64167	+	24.5816i	−0.179324	+	0.949669i
$671$		−	20.0124i		−	0.772569i
$672$	−2.73479	+	1.29182i	−0.105497	+	0.0498331i
$673$		−	24.9965i		−	0.963543i	−0.876297	−	0.481772i	$-0.839993\pi$
$673$		−	24.9965i		−	0.963543i	0.876297	−	0.481772i	$-0.160007\pi$
$674$	−3.79731	−	0.717037i	−0.146267	−	0.0276192i
$675$	24.9840	+	16.6938i	0.961634	+	0.642543i
$676$	0.0180431	+	0.928073i	0.000693965	+	0.0356951i
$677$	33.5580	+	6.67509i	1.28974	+	0.256545i	0.791860	−	0.610703i	$-0.209113\pi$
$677$	33.5580	+	6.67509i	1.28974	+	0.256545i	0.497877	+	0.867247i	$0.334113\pi$
$678$	10.4268	+	10.2261i	0.400440	+	0.392731i
$679$	0.747501	+	0.309625i	0.0286865	+	0.0118823i
$680$	−20.6312	−	19.4619i	−0.791172	−	0.746328i
$681$	24.1200	−	9.99084i	0.924281	−	0.382850i
$682$	−1.97320	+	4.89784i	−0.0755578	+	0.187548i
$683$	0.339438	+	0.508005i	0.0129882	+	0.0194383i	0.837907	−	0.545813i	$-0.183779\pi$
$683$	0.339438	+	0.508005i	0.0129882	+	0.0194383i	−0.824919	+	0.565251i	$0.808779\pi$
$684$	5.50064	−	1.20575i	0.210322	−	0.0461029i
$685$	−16.7489	+	3.33156i	−0.639942	+	0.127292i
$686$	−5.46071	−	3.57245i	−0.208491	−	0.136397i
$687$	−1.34203	+	1.34203i	−0.0512016	+	0.0512016i
$688$	1.79676	−	11.3156i	0.0685009	−	0.431403i
$689$	22.4608	+	22.4608i	0.855688	+	0.855688i
$690$	−1.09744	−	5.24998i	−0.0417787	−	0.199863i
$691$	8.80950	+	44.2884i	0.335129	+	1.68481i	0.669854	+	0.742492i	$0.266357\pi$
$691$	8.80950	+	44.2884i	0.335129	+	1.68481i	−0.334725	+	0.942316i	$0.608643\pi$
$692$	4.63238	−	25.9111i	0.176097	−	0.984994i
$693$	−0.479869	+	0.320638i	−0.0182287	+	0.0121800i
$694$	3.36410	+	7.90349i	0.127699	+	0.300012i
$695$	6.04935	+	14.6044i	0.229465	+	0.553977i
$696$	35.4903	−	25.2409i	1.34526	−	0.956755i
$697$	−3.92060	+	9.46516i	−0.148503	+	0.358518i
$698$	−0.0398393	−	4.09877i	−0.00150794	−	0.155141i
$699$	1.10749	−	5.56774i	0.0418892	−	0.210591i
$700$	1.45727	+	3.33337i	0.0550796	+	0.125990i
$701$	18.1076	−	27.1000i	0.683915	−	1.02355i	−0.313349	−	0.949638i	$-0.601451\pi$
$701$	18.1076	−	27.1000i	0.683915	−	1.02355i	0.997265	−	0.0739139i	$-0.0235490\pi$
$702$	−22.6975	+	15.4872i	−0.856660	+	0.584525i
$703$	38.1433			1.43860
$704$	17.1730	−	29.2606i	0.647233	−	1.10280i
$705$	23.8098			0.896730
$706$	40.8633	−	27.8823i	1.53791	−	1.04936i
$707$	0.146159	−	0.218742i	0.00549687	−	0.00822665i
$708$	−12.0269	+	5.25788i	−0.452000	+	0.197603i
$709$	8.67202	−	43.5972i	0.325684	−	1.63733i	−0.377279	−	0.926100i	$-0.623140\pi$
$709$	8.67202	−	43.5972i	0.325684	−	1.63733i	0.702963	−	0.711226i	$-0.251860\pi$
$710$	−0.313463	−	32.2500i	−0.0117641	−	1.21032i
$711$	0.342234	−	0.826225i	0.0128348	−	0.0309859i
$712$	4.95336	+	0.835961i	0.185635	+	0.0313290i
$713$	−0.245293	−	0.592190i	−0.00918630	−	0.0221777i
$714$	0.917486	+	2.15551i	0.0343360	+	0.0806679i
$715$	−40.4089	+	27.0004i	−1.51121	+	1.00976i
$716$	44.5635	+	7.96705i	1.66542	+	0.297743i
$717$	−2.46262	−	12.3804i	−0.0919681	−	0.462355i
$718$	3.57470	+	17.1009i	0.133407	+	0.638199i
$719$	−10.7756	−	10.7756i	−0.401864	−	0.401864i	0.477026	−	0.878889i	$-0.341715\pi$
$719$	−10.7756	−	10.7756i	−0.401864	−	0.401864i	−0.878889	+	0.477026i	$0.841715\pi$
$720$	−4.52079	−	2.77278i	−0.168480	−	0.103335i
$721$	1.51031	−	1.51031i	0.0562467	−	0.0562467i
$722$	33.4245	+	21.8667i	1.24393	+	0.813793i
$723$	13.3646	−	2.65838i	0.497033	−	0.0988661i
$724$	−6.32948	−	28.8752i	−0.235233	−	1.07314i
$725$	−29.1029	−	43.5556i	−1.08085	−	1.61761i
$726$	−5.94184	+	14.7487i	−0.220522	+	0.547376i
$727$	8.49854	−	3.52021i	0.315193	−	0.130557i	−0.219478	−	0.975617i	$-0.570435\pi$
$727$	8.49854	−	3.52021i	0.315193	−	0.130557i	0.534671	+	0.845060i	$0.320435\pi$
$728$	−3.32540	+	0.0969911i	−0.123247	+	0.00359473i
$729$	27.3572	+	11.3317i	1.01323	+	0.419693i
$730$	35.0835	+	34.4080i	1.29850	+	1.27350i
$731$	−8.70372	−	1.73128i	−0.321919	−	0.0640336i
$732$	−15.1866	+	0.295250i	−0.561313	+	0.0109127i
$733$	−5.58778	−	3.73364i	−0.206389	−	0.137905i	0.448080	−	0.893993i	$-0.352108\pi$
$733$	−5.58778	−	3.73364i	−0.206389	−	0.137905i	−0.654469	+	0.756088i	$0.727108\pi$
$734$	−14.3510	−	2.70987i	−0.529707	−	0.100023i
$735$			35.8893i			1.32380i
$736$	0.998751	+	3.99554i	0.0368145	+	0.147278i
$737$			23.1782i			0.853780i
$738$	−0.355454	+	1.88243i	−0.0130844	+	0.0692931i
$739$	−28.0412	−	18.7365i	−1.03151	−	0.689235i	−0.0799848	−	0.996796i	$-0.525487\pi$
$739$	−28.0412	−	18.7365i	−1.03151	−	0.689235i	−0.951528	+	0.307561i	$0.900487\pi$
$740$	−25.8900	−	24.9025i	−0.951735	−	0.915434i
$741$	−38.4150	−	7.64121i	−1.41121	−	0.280707i
$742$	2.95125	−	3.00919i	0.108344	−	0.110471i
$743$	31.3039	+	12.9665i	1.14843	+	0.475694i	0.874006	−	0.485915i	$-0.161514\pi$
$743$	31.3039	+	12.9665i	1.14843	+	0.475694i	0.274421	+	0.961610i	$0.411514\pi$
$744$	3.74589	+	1.42513i	0.137331	+	0.0522477i
$745$	−28.6537	+	11.8687i	−1.04979	+	0.434837i
$746$	29.8420	+	12.0225i	1.09259	+	0.440176i
$747$	3.37279	+	5.04774i	0.123404	+	0.184687i
$748$	−22.1295	−	14.1721i	−0.809134	−	0.518184i
$749$	−2.00744	+	0.399305i	−0.0733503	+	0.0145903i
$750$	1.91787	−	2.93159i	0.0700308	−	0.107046i
$751$	−22.7813	+	22.7813i	−0.831303	+	0.831303i	−0.987695	−	0.156392i	$-0.950014\pi$
$751$	−22.7813	+	22.7813i	−0.831303	+	0.831303i	0.156392	+	0.987695i	$0.450014\pi$
$752$	−18.2692	+	0.710629i	−0.666210	+	0.0259140i
$753$	2.55130	+	2.55130i	0.0929747	+	0.0929747i
$754$	46.8895	−	9.80162i	1.70762	−	0.356954i
$755$	−10.4184	−	52.3769i	−0.379165	−	1.90619i
$756$	2.08419	+	2.99165i	0.0758013	+	0.108805i
$757$	−35.0984	+	23.4520i	−1.27567	+	0.852378i	−0.994237	−	0.107202i	$-0.965811\pi$
$757$	−35.0984	+	23.4520i	−1.27567	+	0.852378i	−0.281437	+	0.959580i	$0.590811\pi$
$758$	28.0781	−	11.9514i	1.01984	−	0.434093i
$759$	−1.90172	−	4.59116i	−0.0690281	−	0.166649i
$760$	−14.0695	−	61.3289i	−0.510353	−	2.22463i
$761$	−0.451808	+	1.09076i	−0.0163780	+	0.0395401i	−0.931857	−	0.362826i	$-0.881812\pi$
$761$	−0.451808	+	1.09076i	−0.0163780	+	0.0395401i	0.915479	+	0.402366i	$0.131812\pi$
$762$	29.9205	−	0.290821i	1.08390	−	0.0105353i
$763$	0.622768	−	3.13087i	0.0225457	−	0.113345i
$764$	−4.88310	+	12.4690i	−0.176664	+	0.451113i
$765$	−2.28212	+	3.41543i	−0.0825101	+	0.123485i
$766$	−14.6646	−	21.4919i	−0.529852	−	0.776534i
$767$	−14.4378			−0.521318
$768$	−22.4581	−	12.6003i	−0.810386	−	0.454673i
$769$	−46.3441			−1.67121			−0.835605	−	0.549331i	$-0.814883\pi$
$769$	−46.3441			−1.67121			−0.835605	+	0.549331i	$0.814883\pi$
$770$	3.63467	+	5.32685i	0.130984	+	0.191966i
$771$	−17.0391	+	25.5008i	−0.613647	+	0.918388i
$772$	−2.28671	+	5.83914i	−0.0823007	+	0.210155i
$773$	−3.29586	+	16.5694i	−0.118544	+	0.595960i	0.875152	+	0.483848i	$0.160761\pi$
$773$	−3.29586	+	16.5694i	−0.118544	+	0.595960i	−0.993696	+	0.112111i	$0.964239\pi$
$774$	−1.65930	+	0.0161280i	−0.0596421	+	0.000579710i
$775$	1.84481	−	4.45375i	0.0662674	−	0.159984i
$776$	1.54032	+	6.71426i	0.0552942	+	0.241028i
$777$	1.13546	+	2.74125i	0.0407346	+	0.0983420i
$778$	−23.2170	+	9.88224i	−0.832369	+	0.354296i
$779$	−18.8983	+	12.6274i	−0.677101	+	0.452425i
$780$	21.0857	+	30.2664i	0.754989	+	1.08371i
$781$	−5.82972	−	29.3080i	−0.208604	−	1.04872i
$782$	3.12245	−	0.652706i	0.111659	−	0.0233407i
$783$	−37.1231	−	37.1231i	−1.32667	−	1.32667i
$784$	−1.07115	−	27.5377i	−0.0382554	−	0.983491i
$785$	0.505546	−	0.505546i	0.0180437	−	0.0180437i
$786$	17.9672	−	27.4640i	0.640870	−	0.979609i
$787$	29.7168	−	5.91104i	1.05929	−	0.210706i	0.365447	−	0.930832i	$-0.380916\pi$
$787$	29.7168	−	5.91104i	1.05929	−	0.210706i	0.693843	+	0.720126i	$0.255916\pi$
$788$	26.3776	+	16.8927i	0.939665	+	0.601778i
$789$	5.65450	+	8.46256i	0.201306	+	0.301275i
$790$	−9.26876	−	3.73412i	−0.329768	−	0.132854i
$791$	1.96931	−	0.815714i	0.0700205	−	0.0290034i
$792$	−4.59263	−	1.74727i	−0.163192	−	0.0620864i
$793$	−15.4357	−	6.39367i	−0.548137	−	0.227046i
$794$	−11.6933	+	11.9228i	−0.414978	+	0.423124i
$795$	−45.8358	−	9.11731i	−1.62563	−	0.323358i
$796$	−6.16901	−	5.93372i	−0.218655	−	0.210315i
$797$	−25.2213	−	16.8523i	−0.893385	−	0.596940i	0.0218948	−	0.999760i	$-0.493030\pi$
$797$	−25.2213	−	16.8523i	−0.893385	−	0.596940i	−0.915279	+	0.402820i	$0.868030\pi$
$798$	−0.964334	+	5.10696i	−0.0341371	+	0.180784i
$799$			14.1610i			0.500981i
$800$	−15.9370	+	26.5597i	−0.563458	+	0.939029i
$801$		−	0.727542i		−	0.0257064i
$802$	−28.0077	−	5.28862i	−0.988986	−	0.186748i
$803$	37.8570	+	25.2952i	1.33594	+	0.892649i
$804$	17.5890	−	0.341956i	0.620317	−	0.0120599i
$805$	−0.767767	−	0.152718i	−0.0270602	−	0.00538261i
$806$	3.14733	+	3.08673i	0.110860	+	0.108726i
$807$	15.3365	+	6.35261i	0.539872	+	0.223622i
$808$	2.23893	−	0.0653024i	0.0787653	−	0.00229733i
$809$	−2.77252	+	1.14841i	−0.0974765	+	0.0403761i	−0.430889	−	0.902405i	$-0.641800\pi$
$809$	−2.77252	+	1.14841i	−0.0974765	+	0.0403761i	0.333412	+	0.942781i	$0.391800\pi$
$810$	13.0050	−	32.2807i	0.456949	−	1.13423i
$811$	23.3343	+	34.9223i	0.819378	+	1.22629i	0.971291	+	0.237893i	$0.0764566\pi$
$811$	23.3343	+	34.9223i	0.819378	+	1.22629i	−0.151913	+	0.988394i	$0.548543\pi$
$812$	−1.36100	−	6.20891i	−0.0477619	−	0.217890i
$813$	−9.33230	+	1.85631i	−0.327298	+	0.0651036i
$814$	−27.8526	−	18.2215i	−0.976234	−	0.638662i
$815$	40.9326	−	40.9326i	1.43381	−	1.43381i
$816$	−10.4282	+	17.0023i	−0.365059	+	0.595199i
$817$	−13.9213	−	13.9213i	−0.487044	−	0.487044i
$818$	−6.80019	−	32.5311i	−0.237763	−	1.13742i
$819$	0.0939990	+	0.472565i	0.00328459	+	0.0165128i
$820$	21.0714	+	3.76713i	0.735844	+	0.131554i
$821$	32.4829	−	21.7044i	1.13366	−	0.757487i	0.160368	−	0.987057i	$-0.448732\pi$
$821$	32.4829	−	21.7044i	1.13366	−	0.757487i	0.973292	+	0.229570i	$0.0737320\pi$
$822$	4.70339	+	11.0500i	0.164050	+	0.385412i
$823$	13.3449	+	32.2174i	0.465173	+	1.12303i	0.966246	+	0.257622i	$0.0829388\pi$
$823$	13.3449	+	32.2174i	0.465173	+	1.12303i	−0.501073	+	0.865405i	$0.667061\pi$
$824$	17.9317	+	3.02627i	0.624680	+	0.105425i
$825$	14.3025	−	34.5293i	0.497949	−	1.20215i
$826$	0.0186201	+	1.91568i	0.000647875	+	0.0666551i
$827$	−7.94105	+	39.9224i	−0.276137	+	1.38824i	0.554852	+	0.831949i	$0.312775\pi$
$827$	−7.94105	+	39.9224i	−0.276137	+	1.38824i	−0.830990	+	0.556288i	$0.812225\pi$
$828$	0.546535	−	0.238932i	0.0189934	−	0.00830345i
$829$	31.8213	−	47.6240i	1.10520	−	1.65405i	0.466740	−	0.884395i	$-0.345428\pi$
$829$	31.8213	−	47.6240i	1.10520	−	1.65405i	0.638460	−	0.769655i	$-0.279572\pi$
$830$	56.0331	−	38.2331i	1.94494	−	1.32709i
$831$	3.05702			0.106047
$832$	−17.0823	−	22.5940i	−0.592224	−	0.783307i
$833$	−21.3453			−0.739571
$834$	9.18273	−	6.26565i	0.317972	−	0.216962i
$835$	33.0328	−	49.4371i	1.14315	−	1.71084i
$836$	−23.3530	−	53.4179i	−0.807680	−	1.84750i
$837$	0.942559	−	4.73857i	0.0325796	−	0.163789i
$838$	−0.0407462	−	4.19208i	−0.00140756	−	0.144813i
$839$	−14.5831	+	35.2068i	−0.503465	+	1.21547i	0.444119	+	0.895968i	$0.353517\pi$
$839$	−14.5831	+	35.2068i	−0.503465	+	1.21547i	−0.947585	+	0.319505i	$0.896483\pi$
$840$	3.98872	−	2.83680i	0.137624	−	0.0978788i
$841$	23.9274	+	57.7659i	0.825083	+	1.99193i
$842$	−18.9172	−	44.4435i	−0.651931	−	1.53162i
$843$	−29.8816	+	19.9663i	−1.02918	+	0.687675i
$844$	−7.27649	+	40.7009i	−0.250467	+	1.40098i
$845$	−0.293061	−	1.47332i	−0.0100816	−	0.0506836i
$846$	0.541804	+	2.59191i	0.0186276	+	0.0891119i
$847$	1.64101	+	1.64101i	0.0563856	+	0.0563856i
$848$	35.4418	+	5.62767i	1.21708	+	0.193255i
$849$	−0.178230	+	0.178230i	−0.00611684	+	0.00611684i
$850$	20.0764	+	13.1342i	0.688613	+	0.450498i
$851$	3.96263	−	0.788217i	0.135837	−	0.0270197i
$852$	−22.1547	+	4.85634i	−0.759007	+	0.166375i
$853$	30.9971	+	46.3904i	1.06132	+	1.58838i	0.776845	+	0.629692i	$0.216819\pi$
$853$	30.9971	+	46.3904i	1.06132	+	1.58838i	0.284474	+	0.958684i	$0.408181\pi$
$854$	−0.828439	+	2.05633i	−0.0283486	+	0.0703663i
$855$	−8.41933	+	3.48740i	−0.287935	+	0.119267i
$856$	−12.6764	−	11.9579i	−0.433269	−	0.408711i
$857$	15.6625	+	6.48761i	0.535020	+	0.221612i	0.633800	−	0.773497i	$-0.281494\pi$
$857$	15.6625	+	6.48761i	0.535020	+	0.221612i	−0.0987804	+	0.995109i	$0.531494\pi$
$858$	24.4007	+	23.9310i	0.833028	+	0.816990i
$859$	−5.32236	−	1.05868i	−0.181597	−	0.0361218i	0.103454	−	0.994634i	$-0.467010\pi$
$859$	−5.32236	−	1.05868i	−0.181597	−	0.0361218i	−0.285051	+	0.958512i	$0.592010\pi$
$860$	0.360404	+	18.5379i	0.0122897	+	0.632137i
$861$	−1.47007	−	0.982270i	−0.0500999	−	0.0334757i
$862$	−54.6131	−	10.3125i	−1.86013	−	0.351244i
$863$			12.0786i			0.411160i	0.978640	+	0.205580i	$0.0659081\pi$
$863$			12.0786i			0.411160i	−0.978640	+	0.205580i	$0.934092\pi$
$864$	−10.4724	+	29.2232i	−0.356278	+	0.994194i
$865$			42.5967i			1.44833i
$866$	−7.24086	+	38.3464i	−0.246054	+	1.30306i
$867$	−9.90454	−	6.61800i	−0.336376	−	0.224759i
$868$	0.405505	−	0.421585i	0.0137637	−	0.0143095i
$869$	−9.08067	−	1.80626i	−0.308041	−	0.0612731i
$870$	−49.3488	+	50.3175i	−1.67308	+	1.70592i
$871$	17.8775	+	7.40510i	0.605756	+	0.250912i
$872$	24.7960	−	11.1285i	0.839699	−	0.376859i
$873$	0.921745	−	0.381799i	0.0311963	−	0.0129219i
$874$	6.56426	+	2.64456i	0.222039	+	0.0894534i
$875$	−0.284063	−	0.425131i	−0.00960310	−	0.0143721i
$876$	18.6370	−	29.1014i	0.629687	−	0.983244i
$877$	19.9561	−	3.96951i	0.673868	−	0.134041i	0.153717	−	0.988115i	$-0.450876\pi$
$877$	19.9561	−	3.96951i	0.673868	−	0.134041i	0.520151	+	0.854074i	$0.325876\pi$
$878$	−21.7396	+	33.2303i	−0.733676	+	1.12147i
$879$	9.49451	−	9.49451i	0.320242	−	0.320242i
$880$	−19.0238	+	51.5041i	−0.641293	+	1.73620i
$881$	20.2066	+	20.2066i	0.680777	+	0.680777i	0.960175	−	0.279398i	$-0.0901350\pi$
$881$	20.2066	+	20.2066i	0.680777	+	0.680777i	−0.279398	+	0.960175i	$0.590135\pi$
$882$	−3.90687	+	0.816678i	−0.131551	+	0.0274990i
$883$	−2.71690	−	13.6588i	−0.0914310	−	0.459655i	−0.999193	−	0.0401690i	$-0.987210\pi$
$883$	−2.71690	−	13.6588i	−0.0914310	−	0.459655i	0.907762	−	0.419486i	$-0.137790\pi$
$884$	−18.0011	+	12.5408i	−0.605443	+	0.421794i
$885$	17.6619	−	11.8013i	0.593699	−	0.396697i
$886$	9.33938	−	3.97528i	0.313763	−	0.133552i
$887$	−2.29326	−	5.53641i	−0.0770000	−	0.185894i	0.880692	−	0.473689i	$-0.157078\pi$
$887$	−2.29326	−	5.53641i	−0.0770000	−	0.185894i	−0.957692	+	0.287795i	$0.907078\pi$
$888$	−13.4166	+	21.4051i	−0.450233	+	0.718308i
$889$	1.67124	−	4.03474i	0.0560517	−	0.135321i
$890$	−8.12898	+	0.0790121i	−0.272484	+	0.00264849i
$891$	6.29074	−	31.6257i	0.210748	−	1.05950i
$892$	33.7935	+	13.2341i	1.13149	+	0.443112i
$893$	−17.4541	+	26.1219i	−0.584078	+	0.874134i
$894$	12.2931	+	18.0164i	0.411143	+	0.602558i
$895$	−73.2605			−2.44883
$896$	−2.97586	+	2.29572i	−0.0994166	+	0.0766945i
$897$	−4.14877			−0.138523
$898$	7.78244	+	11.4057i	0.259703	+	0.380613i
$899$	−4.67944	+	7.00328i	−0.156068	+	0.233572i
$900$	4.17713	+	1.63584i	0.139238	+	0.0545280i
$901$	5.42256	−	27.2611i	0.180652	−	0.908198i
$902$	19.8320	−	0.192763i	0.660333	−	0.00641831i
$903$	0.586071	−	1.41490i	0.0195032	−	0.0470849i
$904$	15.3773	+	9.63847i	0.511443	+	0.320571i
$905$	18.3068	+	44.1966i	0.608539	+	1.46914i
$906$	−34.5554	+	14.7084i	−1.14802	+	0.488653i
$907$	41.9267	−	28.0145i	1.39215	−	0.930207i	0.392207	−	0.919877i	$-0.371712\pi$
$907$	41.9267	−	28.0145i	1.39215	−	0.930207i	0.999947	−	0.0103304i	$-0.00328832\pi$
$908$	26.6194	−	18.5449i	0.883396	−	0.615435i
$909$	−0.0632879	−	0.318170i	−0.00209913	−	0.0105530i
$910$	5.26986	−	1.10159i	0.174694	−	0.0365174i
$911$	10.6573	+	10.6573i	0.353092	+	0.353092i	0.861259	−	0.508167i	$-0.169677\pi$
$911$	10.6573	+	10.6573i	0.353092	+	0.353092i	−0.508167	+	0.861259i	$0.669677\pi$
$912$	−40.1922	+	18.5098i	−1.33090	+	0.612920i
$913$	44.4423	−	44.4423i	1.47082	−	1.47082i
$914$	24.8110	−	37.9251i	0.820674	−	1.25445i
$915$	24.1088	−	4.79553i	0.797011	−	0.158535i
$916$	−1.27192	+	1.98608i	−0.0420254	+	0.0656219i
$917$	−2.66119	−	3.98276i	−0.0878804	−	0.131522i
$918$	22.3023	+	8.98497i	0.736086	+	0.296548i
$919$	−48.0863	+	19.9180i	−1.58622	+	0.657034i	−0.989383	−	0.145328i	$-0.953576\pi$
$919$	−48.0863	+	19.9180i	−1.58622	+	0.657034i	−0.596837	+	0.802362i	$0.703576\pi$
$920$	−2.72899	−	6.08060i	−0.0899721	−	0.200472i
$921$	−50.9061	−	21.0860i	−1.67741	−	0.694807i
$922$	−34.8704	+	35.5550i	−1.14840	+	1.17094i
$923$	−24.4680	−	4.86698i	−0.805373	−	0.160199i
$924$	3.14382	−	3.26848i	0.103424	−	0.107525i
$925$	25.2651	+	16.8816i	0.830712	+	0.555064i
$926$	7.43252	−	39.3614i	0.244248	−	1.29350i
$927$		−	2.63378i		−	0.0865046i
$928$	36.3634	−	40.0814i	1.19369	−	1.31573i
$929$		−	47.7676i		−	1.56721i	−0.621262	−	0.783603i	$-0.713380\pi$
$929$		−	47.7676i		−	1.56721i	0.621262	−	0.783603i	$-0.286620\pi$
$930$	−6.37323	−	1.20344i	−0.208986	−	0.0394624i
$931$	−39.3743	−	26.3090i	−1.29044	−	0.862244i
$932$	−0.137120	−	7.05299i	−0.00449153	−	0.231028i
$933$	20.7883	+	4.13505i	0.680579	+	0.135375i
$934$	−16.2182	−	15.9059i	−0.530674	−	0.520458i
$935$	39.2894	+	16.2742i	1.28490	+	0.532223i
$936$	−2.81496	+	2.98410i	−0.0920098	+	0.0975383i
$937$	−40.2328	+	16.6650i	−1.31435	+	0.544421i	−0.926150	−	0.377155i	$-0.876902\pi$
$937$	−40.2328	+	16.6650i	−1.31435	+	0.544421i	−0.388198	+	0.921576i	$0.626902\pi$
$938$	0.959492	−	2.38163i	0.0313285	−	0.0777631i
$939$	−0.376223	−	0.563057i	−0.0122776	−	0.0183747i
$940$	28.9012	−	6.33518i	0.942652	−	0.206631i
$941$	−38.6865	+	7.69522i	−1.26114	+	0.250857i	−0.779997	−	0.625783i	$-0.784780\pi$
$941$	−38.6865	+	7.69522i	−1.26114	+	0.250857i	−0.481147	+	0.876640i	$0.659780\pi$
$942$	−0.420746	−	0.275256i	−0.0137086	−	0.00896834i
$943$	−1.70237	+	1.70237i	−0.0554367	+	0.0554367i
$944$	−13.1997	+	9.58226i	−0.429614	+	0.311876i
$945$	−4.17222	−	4.17222i	−0.135722	−	0.135722i
$946$	3.51512	+	16.8158i	0.114286	+	0.546730i
$947$	3.32492	+	16.7155i	0.108045	+	0.543180i	0.996455	+	0.0841288i	$0.0268107\pi$
$947$	3.32492	+	16.7155i	0.108045	+	0.543180i	−0.888410	+	0.459052i	$0.848189\pi$
$948$	−1.23673	+	6.91762i	−0.0401671	+	0.224674i
$949$	31.6051	−	21.1179i	1.02595	−	0.685515i
$950$	20.8451	+	48.9727i	0.676304	+	1.58888i
$951$	−10.3445	−	24.9738i	−0.335443	−	0.809830i
$952$	1.68720	+	2.37231i	0.0546825	+	0.0768870i
$953$	−0.606561	+	1.46437i	−0.0196484	+	0.0474355i	−0.933399	−	0.358840i	$-0.883173\pi$
$953$	−0.606561	+	1.46437i	−0.0196484	+	0.0474355i	0.913751	+	0.406275i	$0.133173\pi$
$954$	−0.0505149	−	5.19711i	−0.00163548	−	0.168263i
$955$	4.22775	−	21.2543i	0.136807	−	0.687774i
$956$	−6.28331	−	14.3725i	−0.203217	−	0.464840i
$957$	−36.2790	+	54.2953i	−1.17273	+	1.75512i
$958$	−36.0060	+	24.5680i	−1.16330	+	0.793755i
$959$	1.75279			0.0566005
$960$	39.3652	+	13.6766i	1.27051	+	0.441410i
$961$	30.2249			0.974996
$962$	−22.9529	+	15.6614i	−0.740030	+	0.504945i
$963$	−1.40219	+	2.09853i	−0.0451849	+	0.0676240i
$964$	15.5150	−	6.78279i	0.499705	−	0.218459i
$965$	1.97982	−	9.95324i	0.0637327	−	0.320406i
$966$	0.00535056	+	0.550480i	0.000172152	+	0.0177114i
$967$	20.5832	−	49.6922i	0.661910	−	1.59799i	−0.132896	−	0.991130i	$-0.542428\pi$
$967$	20.5832	−	49.6922i	0.661910	−	1.59799i	0.794806	−	0.606863i	$-0.207572\pi$
$968$	−3.28815	+	19.4835i	−0.105685	+	0.626222i
$969$	13.1158	+	31.6644i	0.421341	+	1.01721i
$970$	−4.36603	−	10.2574i	−0.140185	−	0.329345i
$971$	44.7859	−	29.9250i	1.43725	−	0.960338i	0.439167	−	0.898405i	$-0.355274\pi$
$971$	44.7859	−	29.9250i	1.43725	−	0.960338i	0.998080	−	0.0619328i	$-0.0197265\pi$
$972$	8.31987	+	1.48742i	0.266860	+	0.0477091i
$973$	−0.316535	−	1.59133i	−0.0101477	−	0.0510157i
$974$	−10.6168	−	50.7891i	−0.340183	−	1.62739i
$975$	−22.0632	−	22.0632i	−0.706588	−	0.706588i
$976$	−18.3555	+	4.39915i	−0.587544	+	0.140813i
$977$	10.3049	−	10.3049i	0.329682	−	0.329682i	−0.522783	−	0.852466i	$-0.675106\pi$
$977$	10.3049	−	10.3049i	0.329682	−	0.329682i	0.852466	+	0.522783i	$0.175106\pi$
$978$	−34.0665	−	22.2867i	−1.08933	−	0.712649i
$979$	−7.38742	+	1.46945i	−0.236103	+	0.0469638i
$980$	9.54921	+	43.5636i	0.305038	+	1.39159i
$981$	−2.18690	−	3.27292i	−0.0698223	−	0.104496i
$982$	−5.83286	+	14.4782i	−0.186134	+	0.462018i
$983$	−3.68355	+	1.52578i	−0.117487	+	0.0486647i	−0.440653	−	0.897678i	$-0.645253\pi$
$983$	−3.68355	+	1.52578i	−0.117487	+	0.0486647i	0.323166	+	0.946342i	$0.395253\pi$
$984$	−0.438869	−	15.0469i	−0.0139906	−	0.479677i
$985$	−46.8317	−	19.3983i	−1.49218	−	0.618082i
$986$	−29.9266	−	29.3504i	−0.953057	−	0.934708i
$987$	−2.39689	−	0.476771i	−0.0762938	−	0.0151758i
$988$	−48.6625	+	0.946070i	−1.54816	+	0.0300985i
$989$	−1.73393	−	1.15858i	−0.0551359	−	0.0368406i
$990$	7.81386	+	1.47547i	0.248341	+	0.0468935i
$991$		−	22.4878i		−	0.714348i	−0.934038	−	0.357174i	$-0.883740\pi$
$991$		−	22.4878i		−	0.714348i	0.934038	−	0.357174i	$-0.116260\pi$
$992$	4.92608	+	0.733181i	0.156403	+	0.0232785i
$993$		−	52.9500i		−	1.68032i
$994$	−0.614221	+	3.25282i	−0.0194819	+	0.103173i
$995$	11.5174	+	7.69569i	0.365127	+	0.243970i
$996$	−34.3812	−	33.0698i	−1.08941	−	1.04786i
$997$	36.8027	+	7.32050i	1.16555	+	0.231843i	0.739691	−	0.672946i	$-0.234972\pi$
$997$	36.8027	+	7.32050i	1.16555	+	0.231843i	0.425860	+	0.904789i	$0.359972\pi$
$998$	12.7901	−	13.0412i	0.404864	−	0.412812i
$999$	28.1354	+	11.6540i	0.890163	+	0.368718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.37.6	✓	56
3.2	odd	2		576.2.bd.a.37.2		56
4.3	odd	2		256.2.i.a.241.6		56
8.3	odd	2		512.2.i.a.225.2		56
8.5	even	2		512.2.i.b.225.6		56
64.13	even	16		512.2.i.b.289.6		56
64.19	odd	16		256.2.i.a.17.6		56
64.45	even	16	inner	64.2.i.a.45.6	yes	56
64.51	odd	16		512.2.i.a.289.2		56
192.173	odd	16		576.2.bd.a.109.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.6	✓	56	1.1	even	1	trivial
64.2.i.a.45.6	yes	56	64.45	even	16	inner
256.2.i.a.17.6		56	64.19	odd	16
256.2.i.a.241.6		56	4.3	odd	2
512.2.i.a.225.2		56	8.3	odd	2
512.2.i.a.289.2		56	64.51	odd	16
512.2.i.b.225.6		56	8.5	even	2
512.2.i.b.289.6		56	64.13	even	16
576.2.bd.a.37.2		56	3.2	odd	2
576.2.bd.a.109.2		56	192.173	odd	16

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

\(f(q)\)	\(=\)	\(q+(0.797087 + 1.16818i) q^{2} +(-0.894167 + 1.33822i) q^{3} +(-0.729306 + 1.86229i) q^{4} +(0.631428 - 3.17440i) q^{5} +(-2.27601 + 0.0221224i) q^{6} +(-0.127129 + 0.306917i) q^{7} +(-2.75681 + 0.632441i) q^{8} +(0.156763 + 0.378460i) q^{9} +O(q^{10})\)	\(q+(0.797087 + 1.16818i) q^{2} +(-0.894167 + 1.33822i) q^{3} +(-0.729306 + 1.86229i) q^{4} +(0.631428 - 3.17440i) q^{5} +(-2.27601 + 0.0221224i) q^{6} +(-0.127129 + 0.306917i) q^{7} +(-2.75681 + 0.632441i) q^{8} +(0.156763 + 0.378460i) q^{9} +(4.21159 - 1.79265i) q^{10} +(3.52624 - 2.35616i) q^{11} +(-1.84002 - 2.64117i) q^{12} +(-0.690738 - 3.47257i) q^{13} +(-0.459869 + 0.0961292i) q^{14} +(3.68343 + 3.68343i) q^{15} +(-2.93623 - 2.71635i) q^{16} +(-2.19074 + 2.19074i) q^{17} +(-0.317157 + 0.484794i) q^{18} +(-6.74130 + 1.34093i) q^{19} +(5.45115 + 3.49101i) q^{20} +(-0.297047 - 0.444562i) q^{21} +(5.56314 + 2.24123i) q^{22} +(-0.672631 + 0.278613i) q^{23} +(1.61871 - 4.25472i) q^{24} +(-5.05873 - 2.09540i) q^{25} +(3.50602 - 3.57485i) q^{26} +(-5.38223 - 1.07059i) q^{27} +(-0.478852 - 0.460588i) q^{28} +(7.95458 + 5.31508i) q^{29} +(-1.36691 + 7.23894i) q^{30} +0.880409i q^{31} +(0.832774 - 5.59522i) q^{32} +6.82567i q^{33} +(-4.30540 - 0.812978i) q^{34} +(0.894006 + 0.597355i) q^{35} +(-0.819129 + 0.0159251i) q^{36} +(-5.44280 - 1.08264i) q^{37} +(-6.93985 - 6.80624i) q^{38} +(5.26469 + 2.18070i) q^{39} +(0.266893 + 9.15058i) q^{40} +(3.05507 - 1.26545i) q^{41} +(0.282558 - 0.701359i) q^{42} +(1.59134 + 2.38161i) q^{43} +(1.81614 + 8.28523i) q^{44} +(1.30037 - 0.258659i) q^{45} +(-0.861616 - 0.563678i) q^{46} +(3.23201 - 3.23201i) q^{47} +(6.26055 - 1.50043i) q^{48} +(4.87171 + 4.87171i) q^{49} +(-1.58444 - 7.57974i) q^{50} +(-0.972796 - 4.89058i) q^{51} +(6.97069 + 1.24622i) q^{52} +(-7.45949 + 4.98427i) q^{53} +(-3.03946 - 7.14079i) q^{54} +(-5.25283 - 12.6815i) q^{55} +(0.156365 - 0.926515i) q^{56} +(4.23340 - 10.2203i) q^{57} +(0.131499 + 13.5290i) q^{58} +(0.795535 - 3.99942i) q^{59} +(-9.54596 + 4.17326i) q^{60} +(2.62163 - 3.92355i) q^{61} +(-1.02848 + 0.701762i) q^{62} -0.136085 q^{63} +(7.20004 - 3.48704i) q^{64} -11.4595 q^{65} +(-7.97364 + 5.44065i) q^{66} +(-3.03636 + 4.54423i) q^{67} +(-2.48207 - 5.67751i) q^{68} +(0.228601 - 1.14925i) q^{69} +(0.0147790 + 1.52051i) q^{70} +(2.69641 - 6.50971i) q^{71} +(-0.671521 - 0.944200i) q^{72} +(4.10841 + 9.91857i) q^{73} +(-3.07366 - 7.22115i) q^{74} +(7.32745 - 4.89605i) q^{75} +(2.41928 - 13.5322i) q^{76} +(0.274857 + 1.38180i) q^{77} +(1.64895 + 7.88833i) q^{78} +(-1.54370 - 1.54370i) q^{79} +(-10.4768 + 7.60558i) q^{80} +(5.37632 - 5.37632i) q^{81} +(3.91344 + 2.56021i) q^{82} +(14.5352 - 2.89122i) q^{83} +(1.04454 - 0.228965i) q^{84} +(5.57100 + 8.33759i) q^{85} +(-1.51372 + 3.75733i) q^{86} +(-14.2254 + 5.89237i) q^{87} +(-8.23105 + 8.72563i) q^{88} +(-1.64085 - 0.679662i) q^{89} +(1.33867 + 1.31290i) q^{90} +(1.15360 + 0.229466i) q^{91} +(-0.0283034 - 1.45583i) q^{92} +(-1.17818 - 0.787233i) q^{93} +(6.35178 + 1.19939i) q^{94} +22.2463i q^{95} +(6.74297 + 6.11750i) q^{96} -2.43552i q^{97} +(-1.80788 + 9.57423i) q^{98} +(1.44450 + 0.965182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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