LMFDB - Embedded newform 51.2.i.a.29.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(5,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	51.29
Dual form			51.2.i.a.44.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34436 + 0.556851i) q^{2} +(-1.69899 + 0.336782i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-0.595296 + 2.99276i) q^{5} +(2.09652 - 1.39884i) q^{6} +(-2.11533 + 0.420765i) q^{7} +(1.04834 - 2.53091i) q^{8} +(2.77316 - 1.14438i) q^{9} +(-0.866229 - 4.35483i) q^{10} +(1.37013 + 0.915491i) q^{11} +(-0.113066 + 0.168973i) q^{12} +(3.12551 + 3.12551i) q^{13} +(2.60946 - 1.74358i) q^{14} +(0.00349923 - 5.28516i) q^{15} +4.22099i q^{16} +(-3.95657 + 1.15998i) q^{17} +(-3.09087 + 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(0.198994 + 0.297816i) q^{20} +(3.45222 - 1.42728i) q^{21} +(-2.35174 - 0.467790i) q^{22} +(-0.425893 + 0.637394i) q^{23} +(-0.928755 + 4.65306i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(-5.94226 - 2.46136i) q^{26} +(-4.32617 + 2.87824i) q^{27} +(-0.140652 + 0.210501i) q^{28} +(7.83789 + 1.55905i) q^{29} +(2.93834 + 7.10709i) q^{30} +(1.60475 + 2.40167i) q^{31} +(-0.253786 - 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} +(4.67311 - 3.76265i) q^{34} -6.58114i q^{35} +(0.135192 - 0.325163i) q^{36} +(-1.98027 + 1.32318i) q^{37} +(0.888394 + 0.888394i) q^{38} +(-6.36284 - 4.25761i) q^{39} +(6.95033 + 4.64406i) q^{40} +(-0.600791 - 3.02038i) q^{41} +(-3.84624 + 3.84115i) q^{42} +(4.38037 - 10.5751i) q^{43} +(0.189711 - 0.0377359i) q^{44} +(1.77400 + 8.98063i) q^{45} +(0.217619 - 1.09405i) q^{46} +(2.21238 - 2.21238i) q^{47} +(-1.42155 - 7.17143i) q^{48} +(-2.16958 + 0.898671i) q^{49} +6.27299 q^{50} +(6.33153 - 3.30330i) q^{51} +0.518848 q^{52} +(5.88369 - 2.43710i) q^{53} +(4.21317 - 6.27842i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-1.15266 + 5.79482i) q^{56} +(0.830022 + 1.24400i) q^{57} +(-11.4051 + 2.26861i) q^{58} +(-2.33146 + 5.62864i) q^{59} +(-0.438389 - 0.438969i) q^{60} +(-1.14061 - 5.73423i) q^{61} +(-3.49473 - 2.33510i) q^{62} +(-5.38462 + 3.58759i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-11.2145 + 7.49329i) q^{65} +(4.15313 + 0.00274973i) q^{66} +7.19481i q^{67} +(-0.232123 + 0.424684i) q^{68} +(0.508927 - 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(-1.20808 - 1.80802i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(12.3377 + 2.45412i) q^{73} +(1.92538 - 2.88154i) q^{74} +(7.32238 + 1.46155i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(-3.28348 - 1.36006i) q^{77} +(10.9248 + 2.18060i) q^{78} +(-3.31013 + 4.95397i) q^{79} +(-12.6324 - 2.51274i) q^{80} +(6.38079 - 6.34708i) q^{81} +(2.48958 + 3.72592i) q^{82} +(4.96993 + 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +(-1.11620 - 12.5316i) q^{85} +16.6560i q^{86} +(-13.8416 - 0.00916431i) q^{87} +(3.75339 - 2.50793i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(-7.38576 - 11.0853i) q^{90} +(-7.92660 - 5.29638i) q^{91} +(0.0175550 + 0.0882551i) q^{92} +(-3.53529 - 3.53997i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(2.58400 - 0.513989i) q^{95} +(0.637525 + 0.955492i) q^{96} +(-0.692072 + 3.47928i) q^{97} +(2.41627 - 2.41627i) q^{98} +(4.84725 + 0.970853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−1.34436	+	0.556851i	−0.950605	+	0.393753i	−0.803458	−	0.595361i	$-0.797009\pi$
$2$	−1.34436	+	0.556851i	−0.950605	+	0.393753i	−0.147147	+	0.989115i	$0.547009\pi$
$3$	−1.69899	+	0.336782i	−0.980914	+	0.194441i
$3$	−1.69899	+	0.336782i	−0.980914	+	0.194441i
$4$	0.0830021	−	0.0830021i	0.0415010	−	0.0415010i
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	0.583902	+	0.811824i	$0.301525\pi$
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	−0.850127	+	0.526578i	$0.823475\pi$
$6$	2.09652	−	1.39884i	0.855900	−	0.571075i
$7$	−2.11533	+	0.420765i	−0.799519	+	0.159034i	−0.577909	−	0.816101i	$-0.696131\pi$
$7$	−2.11533	+	0.420765i	−0.799519	+	0.159034i	−0.221610	+	0.975135i	$0.571131\pi$
$8$	1.04834	−	2.53091i	0.370644	−	0.894813i
$9$	2.77316	−	1.14438i	0.924385	−	0.381460i
$10$	−0.866229	−	4.35483i	−0.273926	−	1.37712i
$11$	1.37013	+	0.915491i	0.413110	+	0.276031i	0.744709	−	0.667389i	$-0.232588\pi$
$11$	1.37013	+	0.915491i	0.413110	+	0.276031i	−0.331599	+	0.943420i	$0.607588\pi$
$12$	−0.113066	+	0.168973i	−0.0326395	+	0.0487784i
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	0.992124	−	0.125262i	$-0.0399772\pi$
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	−0.125262	+	0.992124i	$0.539977\pi$
$14$	2.60946	−	1.74358i	0.697407	−	0.465992i
$15$	0.00349923	−	5.28516i	0.000903497	−	1.36462i
$16$			4.22099i			1.05525i
$17$	−3.95657	+	1.15998i	−0.959609	+	0.281336i
$17$	−3.95657	+	1.15998i	−0.959609	+	0.281336i
$18$	−3.09087	+	3.08269i	−0.728524	+	0.726597i
$19$	−0.330416	−	0.797694i	−0.0758025	−	0.183004i	0.881436	−	0.472304i	$-0.156577\pi$
$19$	−0.330416	−	0.797694i	−0.0758025	−	0.183004i	−0.957238	+	0.289300i	$0.906577\pi$
$20$	0.198994	+	0.297816i	0.0444964	+	0.0665936i
$21$	3.45222	−	1.42728i	0.753337	−	0.311458i
$22$	−2.35174	−	0.467790i	−0.501392	−	0.0997331i
$23$	−0.425893	+	0.637394i	−0.0888049	+	0.132906i	−0.873212	−	0.487340i	$-0.837967\pi$
$23$	−0.425893	+	0.637394i	−0.0888049	+	0.132906i	0.784407	+	0.620246i	$0.212967\pi$
$24$	−0.928755	+	4.65306i	−0.189581	+	0.949803i
$25$	−3.98282	−	1.64974i	−0.796563	−	0.329947i
$26$	−5.94226	−	2.46136i	−1.16537	−	0.482713i
$27$	−4.32617	+	2.87824i	−0.832571	+	0.553918i
$28$	−0.140652	+	0.210501i	−0.0265808	+	0.0397810i
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.858521	−	0.512778i	$-0.171384\pi$
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.596938	+	0.802287i	$0.296384\pi$
$30$	2.93834	+	7.10709i	0.536466	+	1.29757i
$31$	1.60475	+	2.40167i	0.288221	+	0.431353i	0.947121	−	0.320878i	$-0.103978\pi$
$31$	1.60475	+	2.40167i	0.288221	+	0.431353i	−0.658900	+	0.752231i	$0.728978\pi$
$32$	−0.253786	−	0.612694i	−0.0448635	−	0.108310i
$33$	−2.63616	−	1.09398i	−0.458897	−	0.190437i
$34$	4.67311	−	3.76265i	0.801432	−	0.645289i
$35$		−	6.58114i		−	1.11242i
$36$	0.135192	−	0.325163i	0.0225320	−	0.0541939i
$37$	−1.98027	+	1.32318i	−0.325555	+	0.217529i	−0.707597	−	0.706616i	$-0.750221\pi$
$37$	−1.98027	+	1.32318i	−0.325555	+	0.217529i	0.382042	+	0.924145i	$0.375221\pi$
$38$	0.888394	+	0.888394i	0.144117	+	0.144117i
$39$	−6.36284	−	4.25761i	−1.01887	−	0.681763i
$40$	6.95033	+	4.64406i	1.09894	+	0.734291i
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	−0.998919	−	0.0464865i	$-0.985198\pi$
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	0.905091	−	0.425218i	$-0.139802\pi$
$42$	−3.84624	+	3.84115i	−0.593488	+	0.592703i
$43$	4.38037	−	10.5751i	0.668000	−	1.61269i	−0.116952	−	0.993138i	$-0.537312\pi$
$43$	4.38037	−	10.5751i	0.668000	−	1.61269i	0.784952	−	0.619557i	$-0.212688\pi$
$44$	0.189711	−	0.0377359i	0.0286000	−	0.00568890i
$45$	1.77400	+	8.98063i	0.264452	+	1.33875i
$46$	0.217619	−	1.09405i	0.0320862	−	0.161308i
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	−0.527097	−	0.849805i	$-0.676719\pi$
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	0.849805	+	0.527097i	$0.176719\pi$
$48$	−1.42155	−	7.17143i	−0.205183	−	1.03511i
$49$	−2.16958	+	0.898671i	−0.309940	+	0.128382i
$50$	6.27299			0.887135
$51$	6.33153	−	3.30330i	0.886591	−	0.462554i
$52$	0.518848			0.0719513
$53$	5.88369	−	2.43710i	0.808187	−	0.334762i	0.0599567	−	0.998201i	$-0.480904\pi$
$53$	5.88369	−	2.43710i	0.808187	−	0.334762i	0.748230	+	0.663439i	$0.230904\pi$
$54$	4.21317	−	6.27842i	0.573340	−	0.854385i
$55$	−3.55548	+	3.55548i	−0.479420	+	0.479420i
$56$	−1.15266	+	5.79482i	−0.154031	+	0.774365i
$57$	0.830022	+	1.24400i	0.109939	+	0.164772i
$58$	−11.4051	+	2.26861i	−1.49756	+	0.297884i
$59$	−2.33146	+	5.62864i	−0.303530	+	0.732786i	0.696356	+	0.717696i	$0.254803\pi$
$59$	−2.33146	+	5.62864i	−0.303530	+	0.732786i	−0.999886	+	0.0150898i	$0.995197\pi$
$60$	−0.438389	−	0.438969i	−0.0565957	−	0.0566707i
$61$	−1.14061	−	5.73423i	−0.146040	−	0.734193i	−0.982514	−	0.186187i	$-0.940387\pi$
$61$	−1.14061	−	5.73423i	−0.146040	−	0.734193i	0.836474	−	0.548006i	$-0.184613\pi$
$62$	−3.49473	−	2.33510i	−0.443831	−	0.296558i
$63$	−5.38462	+	3.58759i	−0.678399	+	0.451993i
$64$	−5.28702	−	5.28702i	−0.660877	−	0.660877i
$65$	−11.2145	+	7.49329i	−1.39099	+	0.929429i
$66$	4.15313	+	0.00274973i	0.511215	+	0.000338468i
$67$			7.19481i			0.878985i	0.898246	+	0.439493i	$0.144842\pi$
$67$			7.19481i			0.878985i	−0.898246	+	0.439493i	$0.855158\pi$
$68$	−0.232123	+	0.424684i	−0.0281490	+	0.0515005i
$69$	0.508927	−	1.22636i	0.0612676	−	0.147637i
$70$	3.66472	+	8.84742i	0.438018	+	1.05747i
$71$	−1.20808	−	1.80802i	−0.143373	−	0.214573i	0.752832	−	0.658212i	$-0.228687\pi$
$71$	−1.20808	−	1.80802i	−0.143373	−	0.214573i	−0.896205	+	0.443639i	$0.853687\pi$
$72$	0.0108825	−	8.21831i	0.00128251	−	0.968537i
$73$	12.3377	+	2.45412i	1.44402	+	0.287233i	0.854049	−	0.520193i	$-0.174140\pi$
$73$	12.3377	+	2.45412i	1.44402	+	0.287233i	0.589969	+	0.807426i	$0.299140\pi$
$74$	1.92538	−	2.88154i	0.223821	−	0.334972i
$75$	7.32238	+	1.46155i	0.845516	+	0.168766i
$76$	−0.0936354	−	0.0387851i	−0.0107407	−	0.00444895i
$77$	−3.28348	−	1.36006i	−0.374187	−	0.154994i
$78$	10.9248	+	2.18060i	1.23699	+	0.246904i
$79$	−3.31013	+	4.95397i	−0.372419	+	0.557365i	−0.969586	−	0.244753i	$-0.921293\pi$
$79$	−3.31013	+	4.95397i	−0.372419	+	0.557365i	0.597166	+	0.802117i	$0.296293\pi$
$80$	−12.6324	−	2.51274i	−1.41234	−	0.280933i
$81$	6.38079	−	6.34708i	0.708977	−	0.705232i
$82$	2.48958	+	3.72592i	0.274928	+	0.411459i
$83$	4.96993	+	11.9985i	0.545521	+	1.31700i	0.920779	+	0.390084i	$0.127554\pi$
$83$	4.96993	+	11.9985i	0.545521	+	1.31700i	−0.375258	+	0.926920i	$0.622446\pi$
$84$	0.168074	−	0.405009i	0.0183384	−	0.0441901i
$85$	−1.11620	−	12.5316i	−0.121069	−	1.35924i
$86$			16.6560i			1.79606i
$87$	−13.8416	−	0.00916431i	−1.48397	−	0.000982518i
$88$	3.75339	−	2.50793i	0.400112	−	0.267347i
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	0.502205	−	0.864749i	$-0.332522\pi$
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	−0.864749	+	0.502205i	$0.832522\pi$
$90$	−7.38576	−	11.0853i	−0.778528	−	1.16850i
$91$	−7.92660	−	5.29638i	−0.830933	−	0.555212i
$92$	0.0175550	+	0.0882551i	0.00183024	+	0.00920123i
$93$	−3.53529	−	3.53997i	−0.366592	−	0.367078i
$94$	−1.74226	+	4.20619i	−0.179701	+	0.433836i
$95$	2.58400	−	0.513989i	0.265113	−	0.0527342i
$96$	0.637525	+	0.955492i	0.0650671	+	0.0975195i
$97$	−0.692072	+	3.47928i	−0.0702692	+	0.353267i	−0.999883	−	0.0152668i	$-0.995140\pi$
$97$	−0.692072	+	3.47928i	−0.0702692	+	0.353267i	0.929614	+	0.368534i	$0.120140\pi$
$98$	2.41627	−	2.41627i	0.244080	−	0.244080i
$99$	4.84725	+	0.970853i	0.487167	+	0.0975744i
$100$	−0.467514	+	0.193650i	−0.0467514	+	0.0193650i
$101$	3.73948			0.372092			0.186046	−	0.982541i	$-0.440433\pi$
$101$	3.73948			0.372092			0.186046	+	0.982541i	$0.440433\pi$
$102$	−6.67240	+	7.96653i	−0.660666	+	0.788804i
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	11.1870	−	4.63380i	1.09698	−	0.454382i
$105$	2.21641	+	11.1813i	0.216299	+	1.09119i
$106$	−6.55268	+	6.55268i	−0.636453	+	0.636453i
$107$	0.368714	−	1.85365i	0.0356449	−	0.179199i	−0.958862	−	0.283874i	$-0.908380\pi$
$107$	0.368714	−	1.85365i	0.0356449	−	0.179199i	0.994506	+	0.104675i	$0.0333802\pi$
$108$	−0.120181	+	0.597981i	−0.0115644	+	0.0575407i
$109$	4.12226	−	0.819969i	0.394841	−	0.0785388i	0.00632347	−	0.999980i	$-0.497987\pi$
$109$	4.12226	−	0.819969i	0.394841	−	0.0785388i	0.388518	+	0.921441i	$0.372987\pi$
$110$	2.79996	−	6.75970i	0.266966	−	0.644513i
$111$	2.91885	−	2.91499i	0.277045	−	0.276678i
$112$	−1.77604	−	8.92878i	−0.167820	−	0.843690i
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.293917	−	0.955831i	$-0.594959\pi$
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.995550	+	0.0942363i	$0.969959\pi$
$114$	−1.80857	−	1.21018i	−0.169388	−	0.113344i
$115$	−1.65403	−	1.65403i	−0.154239	−	0.154239i
$116$	0.779965	−	0.521156i	0.0724180	−	0.0483881i
$117$	12.2443	+	5.09076i	1.13199	+	0.470641i
$118$		−	8.86518i		−	0.816106i
$119$	7.88137	−	4.11852i	0.722484	−	0.377544i
$120$	−13.3726	−	5.54949i	−1.22075	−	0.506597i
$121$	−3.17039	−	7.65399i	−0.288217	−	0.695817i
$122$	4.72650	+	7.07371i	0.427917	+	0.640424i
$123$	2.03795	+	4.92927i	0.183756	+	0.444457i
$124$	0.332541	+	0.0661465i	0.0298630	+	0.00594013i
$125$	−1.16808	+	1.74816i	−0.104477	+	0.156360i
$126$	5.24111	−	7.82144i	0.466915	−	0.696789i
$127$	11.3753	+	4.71179i	1.00939	+	0.418104i	0.825233	−	0.564792i	$-0.191044\pi$
$127$	11.3753	+	4.71179i	1.00939	+	0.418104i	0.184159	+	0.982896i	$0.441044\pi$
$128$	11.2771	+	4.67113i	0.996766	+	0.412874i
$129$	−3.88070	+	19.4423i	−0.341677	+	1.71180i
$130$	10.9037	−	16.3185i	0.956315	−	1.43123i
$131$	3.45873	+	0.687984i	0.302191	+	0.0601094i	0.343857	−	0.939022i	$-0.388267\pi$
$131$	3.45873	+	0.687984i	0.302191	+	0.0601094i	−0.0416661	+	0.999132i	$0.513267\pi$
$132$	−0.309609	+	0.128004i	−0.0269480	+	0.0111413i
$133$	1.03458	+	1.54836i	0.0897094	+	0.134260i
$134$	−4.00644	−	9.67240i	−0.346103	−	0.835568i
$135$	−6.03852	−	14.6606i	−0.519713	−	1.26178i
$136$	−1.21202	+	11.2298i	−0.103930	+	0.962946i
$137$		−	14.6484i		−	1.25150i	−0.780025	−	0.625748i	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$	−0.00127919	+	1.93207i	−0.000108892	+	0.164468i
$139$	−4.19445	+	2.80264i	−0.355768	+	0.237717i	−0.720591	−	0.693360i	$-0.756130\pi$
$139$	−4.19445	+	2.80264i	−0.355768	+	0.237717i	0.364823	+	0.931077i	$0.381130\pi$
$140$	−0.546249	−	0.546249i	−0.0461664	−	0.0461664i
$141$	−3.01373	+	4.50390i	−0.253802	+	0.379297i
$142$	2.63090	+	1.75791i	0.220780	+	0.147520i
$143$	1.42098	+	7.14374i	0.118828	+	0.597389i
$144$	4.83041	+	11.7055i	0.402534	+	0.975455i
$145$	−9.33173	+	22.5288i	−0.774958	+	1.87091i
$146$	−17.9529	+	3.57105i	−1.48579	+	0.295542i
$147$	3.38345	−	2.25751i	0.279062	−	0.186196i
$148$	−0.0545404	+	0.274193i	−0.00448319	+	0.0225385i
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	−0.865423	−	0.501041i	$-0.832950\pi$
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	0.501041	+	0.865423i	$0.332950\pi$
$150$	−10.6578	+	2.11263i	−0.870203	+	0.172495i
$151$	−14.0551	+	5.82179i	−1.14378	+	0.473771i	−0.872445	−	0.488713i	$-0.837467\pi$
$151$	−14.0551	+	5.82179i	−1.14378	+	0.473771i	−0.271339	+	0.962484i	$0.587467\pi$
$152$	−2.36528			−0.191850
$153$	−9.64473	+	7.74462i	−0.779730	+	0.626115i
$154$	5.17153			0.416734
$155$	−8.14291	+	3.37291i	−0.654055	+	0.270918i
$156$	−0.881519	+	0.174738i	−0.0705780	+	0.0139903i
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	−0.634025	−	0.773312i	$-0.718598\pi$
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	0.773312	+	0.634025i	$0.218598\pi$
$158$	1.69138	−	8.50316i	0.134559	−	0.676475i
$159$	−9.17558	+	6.12214i	−0.727671	+	0.485518i
$160$	1.98472	−	0.394786i	0.156906	−	0.0312105i
$161$	0.632711	−	1.52750i	0.0498646	−	0.120384i
$162$	−5.04369	+	12.0859i	−0.396270	+	0.949559i
$163$	−0.216722	−	1.08953i	−0.0169749	−	0.0853388i	0.971369	−	0.237575i	$-0.0763526\pi$
$163$	−0.216722	−	1.08953i	−0.0169749	−	0.0853388i	−0.988344	+	0.152236i	$0.951353\pi$
$164$	−0.300565	−	0.200831i	−0.0234702	−	0.0156823i
$165$	4.84331	−	7.23815i	0.377051	−	0.563489i
$166$	−13.3627	−	13.3627i	−1.03715	−	1.03715i
$167$	16.5131	−	11.0337i	1.27782	−	0.853815i	0.283373	−	0.959010i	$-0.408547\pi$
$167$	16.5131	−	11.0337i	1.27782	−	0.853815i	0.994452	+	0.105195i	$0.0335466\pi$
$168$	0.00677549	−	10.2335i	0.000522740	−	0.789535i
$169$			6.53766i			0.502897i
$170$	8.47880	+	16.2254i	0.650295	+	1.24443i
$171$	−1.82916	−	1.83401i	−0.139879	−	0.140250i
$172$	−0.514179	−	1.24134i	−0.0392058	−	0.0946511i
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	0.499946	−	0.866056i	$-0.333353\pi$
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	−0.991453	+	0.130465i	$0.958353\pi$
$174$	18.6131	−	7.69538i	1.41106	−	0.583385i
$175$	9.11912	+	1.81391i	0.689341	+	0.137118i
$176$	−3.86428	+	5.78330i	−0.291281	+	0.435933i
$177$	2.06551	−	10.3482i	0.155253	−	0.777819i
$178$	6.50257	+	2.69345i	0.487389	+	0.201883i
$179$	0.782216	+	0.324004i	0.0584656	+	0.0242172i	0.411725	−	0.911308i	$-0.364927\pi$
$179$	0.782216	+	0.324004i	0.0584656	+	0.0242172i	−0.353259	+	0.935526i	$0.614927\pi$
$180$	0.892656	+	0.598165i	0.0665347	+	0.0445846i
$181$	−0.796600	+	1.19220i	−0.0592108	+	0.0886152i	−0.859894	−	0.510473i	$-0.829470\pi$
$181$	−0.796600	+	1.19220i	−0.0592108	+	0.0886152i	0.800683	+	0.599088i	$0.204470\pi$
$182$	13.6055	+	2.70630i	1.00851	+	0.200604i
$183$	3.86907	+	9.35828i	0.286010	+	0.691784i
$184$	1.16671	+	1.74610i	0.0860109	+	0.128724i
$185$	−2.78110	−	6.71416i	−0.204470	−	0.493635i
$186$	6.72393	+	2.79036i	0.493023	+	0.204599i
$187$	−6.48296	−	2.03288i	−0.474081	−	0.148659i
$188$		−	0.367264i		−	0.0267855i
$189$	7.94021	−	7.90873i	0.577565	−	0.575275i
$190$	−3.18760	+	2.12989i	−0.231253	+	0.154518i
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	0.688420	−	0.725312i	$-0.258304\pi$
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	−0.725312	+	0.688420i	$0.758304\pi$
$192$	10.7632	+	7.20204i	0.776765	+	0.519762i
$193$	−9.66292	−	6.45656i	−0.695552	−	0.464753i	0.156862	−	0.987621i	$-0.449862\pi$
$193$	−9.66292	−	6.45656i	−0.695552	−	0.464753i	−0.852414	+	0.522867i	$0.824862\pi$
$194$	−1.00705	−	5.06278i	−0.0723019	−	0.363486i
$195$	16.5298	−	16.5079i	1.18372	−	1.18215i
$196$	−0.105488	+	0.254671i	−0.00753488	+	0.0181908i
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.703643	−	0.710553i	$-0.251555\pi$
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.921999	+	0.387193i	$0.126555\pi$
$198$	−7.05706	+	1.39403i	−0.501524	+	0.0990691i
$199$	4.70456	−	23.6514i	0.333497	−	1.67661i	−0.342357	−	0.939570i	$-0.611225\pi$
$199$	4.70456	−	23.6514i	0.333497	−	1.67661i	0.675854	−	0.737035i	$-0.263775\pi$
$200$	−8.35068	+	8.35068i	−0.590482	+	0.590482i
$201$	−2.42308	−	12.2239i	−0.170911	−	0.862209i
$202$	−5.02720	+	2.08233i	−0.353712	+	0.146512i
$203$	−17.2357			−1.20971
$204$	0.251349	−	0.799710i	0.0175980	−	0.0559909i
$205$	9.39691			0.656309
$206$	−12.5483	+	5.19767i	−0.874281	+	0.362139i
$207$	−0.451648	+	2.25498i	−0.0313917	+	0.156732i
$208$	−13.1927	+	13.1927i	−0.914753	+	0.914753i
$209$	0.277570	−	1.39544i	0.0191999	−	0.0965244i
$210$	−9.20598	−	13.7975i	−0.635273	−	0.952117i
$211$	15.3100	−	3.04535i	1.05398	−	0.209651i	0.362457	−	0.932000i	$-0.381938\pi$
$211$	15.3100	−	3.04535i	1.05398	−	0.209651i	0.691528	+	0.722350i	$0.256938\pi$
$212$	0.286074	−	0.690643i	0.0196476	−	0.0474336i
$213$	2.66143	+	2.66496i	0.182358	+	0.182600i
$214$	0.536524	+	2.69729i	0.0366760	+	0.184383i
$215$	29.0412	+	19.4047i	1.98059	+	1.32339i
$216$	2.74929	+	13.9665i	0.187065	+	0.950301i
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$	−5.08520	+	3.39782i	−0.344413	+	0.230130i
$219$	−21.7882	−	0.0144256i	−1.47231	−	0.000974794i
$220$			0.590224i			0.0397929i
$221$	−15.9918	−	8.74079i	−1.07573	−	0.587969i
$222$	−2.30077	+	5.54415i	−0.154417	+	0.372099i
$223$	0.930718	+	2.24695i	0.0623255	+	0.150467i	0.951974	−	0.306179i	$-0.0990506\pi$
$223$	0.930718	+	2.24695i	0.0623255	+	0.150467i	−0.889648	+	0.456646i	$0.849051\pi$
$224$	0.794641	+	1.18926i	0.0530942	+	0.0794611i
$225$	−12.9329	−	0.0171254i	−0.862193	−	0.00114169i
$226$	23.5276	+	4.67992i	1.56503	+	0.311304i
$227$	0.780250	−	1.16773i	0.0517870	−	0.0775048i	−0.804673	−	0.593719i	$-0.797659\pi$
$227$	0.780250	−	1.16773i	0.0517870	−	0.0775048i	0.856460	+	0.516214i	$0.172659\pi$
$228$	0.172148	+	0.0343609i	0.0114008	+	0.00227560i
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	0.0250960	−	0.999685i	$-0.492011\pi$
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	−0.689139	+	0.724630i	$0.742011\pi$
$230$	3.14466	+	1.30256i	0.207353	+	0.0858884i
$231$	6.03666	+	1.20492i	0.397183	+	0.0792780i
$232$	12.1626	−	18.2026i	0.798513	−	1.19506i
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.288334	−	0.957530i	$-0.593101\pi$
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.632817	+	0.774302i	$0.718101\pi$
$234$	−19.2955	−	0.0255506i	−1.26139	−	0.00167030i
$235$	5.30409	+	7.93813i	0.346000	+	0.517826i
$236$	0.273673	+	0.660704i	0.0178146	+	0.0430082i
$237$	3.95549	−	9.53155i	0.256937	−	0.619140i
$238$	−8.30198	+	9.92552i	−0.538137	+	0.643376i
$239$			23.7093i			1.53362i	0.641872	+	0.766812i	$0.278158\pi$
$239$			23.7093i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$240$	22.3086	+	0.0147702i	1.44001	+	0.000953412i
$241$	2.34007	−	1.56359i	0.150737	−	0.100719i	−0.477914	−	0.878406i	$-0.658607\pi$
$241$	2.34007	−	1.56359i	0.150737	−	0.100719i	0.628652	+	0.777687i	$0.283607\pi$
$242$	8.52427	+	8.52427i	0.547961	+	0.547961i
$243$	−8.70334	+	12.9326i	−0.558320	+	0.829626i
$244$	−0.570626	−	0.381280i	−0.0365306	−	0.0244090i
$245$	−1.39796	−	7.02801i	−0.0893123	−	0.449003i
$246$	−5.48460	−	5.49187i	−0.349686	−	0.350149i
$247$	1.46048	−	3.52592i	0.0929284	−	0.224349i
$248$	7.76073	−	1.54371i	0.492807	−	0.0980254i
$249$	−12.4847	−	18.7116i	−0.791189	−	1.18580i
$250$	0.596858	−	3.00061i	0.0377486	−	0.189775i
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	−0.959034	−	0.283289i	$-0.908574\pi$
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	0.283289	+	0.959034i	$0.408574\pi$
$252$	−0.149158	+	0.744712i	−0.00939606	+	0.0469124i
$253$	−1.16706	+	0.483411i	−0.0733723	+	0.0303918i
$254$	−17.9162			−1.12416
$255$	6.11683	+	20.9152i	0.383050	+	1.30976i
$256$	−2.80767			−0.175479
$257$	−18.3799	+	7.61319i	−1.14650	+	0.474898i	−0.873360	−	0.487075i	$-0.838064\pi$
$257$	−18.3799	+	7.61319i	−1.14650	+	0.474898i	−0.273145	+	0.961973i	$0.588064\pi$
$258$	−5.60943	−	28.2984i	−0.349228	−	1.76178i
$259$	3.63218	−	3.63218i	0.225693	−	0.225693i
$260$	−0.308868	+	1.55279i	−0.0191552	+	0.0962997i
$261$	23.5198	−	4.64602i	1.45584	−	0.287581i
$262$	−5.03288	+	1.00110i	−0.310932	+	0.0618482i
$263$	0.0501727	−	0.121128i	0.00309378	−	0.00746905i	−0.922325	−	0.386415i	$-0.873713\pi$
$263$	0.0501727	−	0.121128i	0.00309378	−	0.00746905i	0.925419	+	0.378946i	$0.123713\pi$
$264$	−5.53235	+	5.52503i	−0.340493	+	0.340042i
$265$	3.79112	+	19.0593i	0.232887	+	1.17080i
$266$	−2.25305	−	1.50544i	−0.138143	−	0.0923045i
$267$	6.96282	+	4.65908i	0.426118	+	0.285131i
$268$	0.597184	+	0.597184i	0.0364788	+	0.0364788i
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	−0.697075	−	0.716999i	$-0.745515\pi$
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	0.395661	+	0.918396i	$0.370515\pi$
$270$	16.2817	+	16.3465i	0.990873	+	0.994817i
$271$		−	6.87483i		−	0.417616i	−0.977957	−	0.208808i	$-0.933042\pi$
$271$		−	6.87483i		−	0.417616i	0.977957	−	0.208808i	$-0.0669584\pi$
$272$	−4.89625	−	16.7006i	−0.296879	−	1.01262i
$273$	15.2510	+	6.32899i	0.923030	+	0.383048i
$274$	8.15697	+	19.6927i	0.492781	+	1.18968i
$275$	−3.94666	−	5.90659i	−0.237992	−	0.356181i
$276$	−0.0595485	−	0.144033i	−0.00358440	−	0.00866974i
$277$	−8.13797	−	1.61874i	−0.488963	−	0.0972608i	−0.0555495	−	0.998456i	$-0.517691\pi$
$277$	−8.13797	−	1.61874i	−0.488963	−	0.0972608i	−0.433414	+	0.901195i	$0.642691\pi$
$278$	4.07818	−	6.10344i	0.244593	−	0.366060i
$279$	7.19863	+	4.82377i	0.430971	+	0.288792i
$280$	−16.6563	−	6.89927i	−0.995404	−	0.412310i
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.716651	−	0.697432i	$-0.245674\pi$
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.0135893	+	0.999908i	$0.495674\pi$
$282$	1.54352	−	7.73306i	0.0919155	−	0.460497i
$283$	−7.79633	+	11.6680i	−0.463444	+	0.693593i	−0.987416	−	0.158142i	$-0.949450\pi$
$283$	−7.79633	+	11.6680i	−0.463444	+	0.693593i	0.523972	+	0.851735i	$0.324450\pi$
$284$	−0.250343	−	0.0497963i	−0.0148551	−	0.00295487i
$285$	−4.21709	+	1.74351i	−0.249799	+	0.103276i
$286$	−5.88830	−	8.81247i	−0.348183	−	0.521092i
$287$	2.54174	+	6.13631i	0.150034	+	0.362215i
$288$	−1.40494	−	1.40867i	−0.0827870	−	0.0830066i
$289$	14.3089	−	9.17907i	0.841700	−	0.539945i
$290$		−	35.4832i		−	2.08364i
$291$	0.00406809	−	6.14435i	0.000238475	−	0.360188i
$292$	1.22775	−	0.820357i	0.0718487	−	0.0480078i
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.995440	+	0.0953949i	$0.0304114\pi$
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.0953949	+	0.995440i	$0.469589\pi$
$294$	−3.29147	+	4.91898i	−0.191963	+	0.286881i
$295$	−15.4572	−	10.3282i	−0.899955	−	0.601331i
$296$	1.27285	+	6.39904i	0.0739827	+	0.371936i
$297$	−8.56241	−	0.0170072i	−0.496842	−	0.000986857i
$298$	3.50271	−	8.45629i	0.202907	−	0.489860i
$299$	−3.32332	+	0.661049i	−0.192193	+	0.0382295i
$300$	0.729085	−	0.486461i	0.0420937	−	0.0280858i
$301$	−4.81627	+	24.2130i	−0.277605	+	1.39561i
$302$	15.6531	−	15.6531i	0.900738	−	0.900738i
$303$	−6.35335	+	1.25939i	−0.364990	+	0.0723499i
$304$	3.36705	−	1.39468i	0.193114	−	0.0799904i
$305$	17.8402			1.02152
$306$	8.65338	−	15.7822i	0.494681	−	0.902210i
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	−0.385424	+	0.159648i	−0.0219616	+	0.00909677i
$309$	−15.8585	+	3.14353i	−0.902157	+	0.178829i
$310$	9.06879	−	9.06879i	0.515073	−	0.515073i
$311$	4.55265	−	22.8877i	0.258157	−	1.29784i	−0.606340	−	0.795206i	$-0.707363\pi$
$311$	4.55265	−	22.8877i	0.258157	−	1.29784i	0.864497	−	0.502638i	$-0.167637\pi$
$312$	−17.4460	+	11.6404i	−0.987688	+	0.659007i
$313$	1.58360	−	0.314998i	0.0895106	−	0.0178048i	−0.150132	−	0.988666i	$-0.547970\pi$
$313$	1.58360	−	0.314998i	0.0895106	−	0.0178048i	0.239642	+	0.970861i	$0.422970\pi$
$314$	−1.37441	+	3.31812i	−0.0775624	+	0.187252i
$315$	−7.53133	−	18.2505i	−0.424342	−	1.02830i
$316$	0.136441	+	0.685937i	0.00767543	+	0.0385870i
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.974251	−	0.225464i	$-0.0723900\pi$
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.164528	+	0.986372i	$0.447390\pi$
$318$	8.92614	−	13.3398i	0.500553	−	0.748058i
$319$	9.31162	+	9.31162i	0.521351	+	0.521351i
$320$	18.9701	−	12.6754i	1.06046	−	0.708577i
$321$	−0.00216735	+	3.27351i	−0.000120970	+	0.182710i
$322$			2.40583i			0.134072i
$323$	2.23262	+	2.77286i	0.124226	+	0.154286i
$324$	0.00279782	−	1.05644i	0.000155435	−	0.0586911i
$325$	−7.29207	−	17.6046i	−0.404491	−	0.976529i
$326$	0.898060	+	1.34404i	0.0497389	+	0.0744396i
$327$	−6.72755	+	2.78143i	−0.372034	+	0.153813i
$328$	−8.27415	−	1.64583i	−0.456863	−	0.0908758i
$329$	−3.74901	+	5.61080i	−0.206690	+	0.309333i
$330$	−2.48057	+	12.4277i	−0.136551	+	0.684121i
$331$	28.1459	+	11.6584i	1.54704	+	0.640804i	0.982777	−	0.184793i	$-0.0591614\pi$
$331$	28.1459	+	11.6584i	1.54704	+	0.640804i	0.564260	+	0.825597i	$0.309161\pi$
$332$	1.40841	+	0.583384i	0.0772967	+	0.0320173i
$333$	−3.97739	+	5.93556i	−0.217960	+	0.325267i
$334$	−16.0554	+	24.0286i	−0.878514	+	1.31479i
$335$	−21.5323	−	4.28304i	−1.17644	−	0.234008i
$336$	6.02453	+	14.5718i	0.328665	+	0.794956i
$337$	−9.57025	−	14.3229i	−0.521325	−	0.780218i	0.473611	−	0.880734i	$-0.342950\pi$
$337$	−9.57025	−	14.3229i	−0.521325	−	0.780218i	−0.994935	+	0.100517i	$0.967950\pi$
$338$	−3.64051	−	8.78896i	−0.198018	−	0.478057i
$339$	26.3730	+	10.9445i	1.43239	+	0.594425i
$340$	−1.13279	−	0.947500i	−0.0614344	−	0.0513854i
$341$			4.75973i			0.257754i
$342$	3.48031	+	1.44700i	0.188194	+	0.0782446i
$343$	16.7643	−	11.2015i	0.905186	−	0.604826i
$344$	−22.1727	−	22.1727i	−1.19547	−	1.19547i
$345$	3.36724	+	2.25314i	0.181286	+	0.121305i
$346$	14.0786	+	9.40702i	0.756870	+	0.505724i
$347$	−3.94759	−	19.8459i	−0.211918	−	1.06538i	−0.929476	−	0.368884i	$-0.879740\pi$
$347$	−3.94759	−	19.8459i	−0.211918	−	1.06538i	0.717558	−	0.696499i	$-0.245260\pi$
$348$	−1.14964	+	1.14812i	−0.0616272	+	0.0615456i
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	−0.982421	−	0.186681i	$-0.940227\pi$
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	0.826680	+	0.562673i	$0.190227\pi$
$350$	−13.2694	+	2.63946i	−0.709281	+	0.141085i
$351$	−22.5175	−	4.52552i	−1.20189	−	0.241554i
$352$	0.213196	−	1.07181i	0.0113634	−	0.0571276i
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$354$	2.98563	+	15.0619i	0.158684	+	0.800530i
$355$	6.13014	−	2.53919i	0.325354	−	0.134766i
$356$	−0.567772			−0.0300919
$357$	−12.0034	+	9.65164i	−0.635285	+	0.510819i
$358$	−1.23200			−0.0651133
$359$	21.2469	−	8.80076i	1.12137	−	0.464487i	0.256531	−	0.966536i	$-0.417420\pi$
$359$	21.2469	−	8.80076i	1.12137	−	0.464487i	0.864839	+	0.502049i	$0.167420\pi$
$360$	24.5889	+	4.92490i	1.29595	+	0.259565i
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$	0.407040	−	2.04633i	0.0213935	−	0.107553i
$363$	7.96419	+	11.9364i	0.418012	+	0.626496i
$364$	−1.09753	+	0.218313i	−0.0575264	+	0.0114427i
$365$	−14.6892	+	35.4628i	−0.768866	+	1.85621i
$366$	−10.4126	−	10.4264i	−0.544275	−	0.544996i
$367$	−3.20154	−	16.0952i	−0.167119	−	0.840163i	−0.969828	−	0.243792i	$-0.921609\pi$
$367$	−3.20154	−	16.0952i	−0.167119	−	0.840163i	0.802709	−	0.596371i	$-0.203391\pi$
$368$	−2.69043	−	1.79769i	−0.140249	−	0.0937111i
$369$	−5.12255	−	7.68845i	−0.266669	−	0.400245i
$370$	7.47758	+	7.47758i	0.388741	+	0.388741i
$371$	−11.4205	+	7.63093i	−0.592923	+	0.396178i
$372$	−0.587261		0.000388817i	−0.0304481		2.01592e-5i
$373$			1.61824i			0.0837894i	0.999122	+	0.0418947i	$0.0133394\pi$
$373$			1.61824i			0.0837894i	−0.999122	+	0.0418947i	$0.986661\pi$
$374$	9.84744	−	0.877122i	0.509199	−	0.0453549i
$375$	1.39582	−	3.36351i	0.0720798	−	0.173691i
$376$	−3.28001	−	7.91865i	−0.169154	−	0.408373i
$377$	19.6246	+	29.3703i	1.01072	+	1.51265i
$378$	−6.27050	+	15.0537i	−0.322520	+	0.774278i
$379$	−15.2311	−	3.02965i	−0.782368	−	0.155623i	−0.212283	−	0.977208i	$-0.568090\pi$
$379$	−15.2311	−	3.02965i	−0.782368	−	0.155623i	−0.570085	+	0.821586i	$0.693090\pi$
$380$	0.171815	−	0.257139i	0.00881393	−	0.0131910i
$381$	−20.9134	−	4.17432i	−1.07142	−	0.213857i
$382$	0.969330	+	0.401510i	0.0495952	+	0.0205430i
$383$	−20.4588	−	8.47433i	−1.04540	−	0.433018i	−0.207151	−	0.978309i	$-0.566419\pi$
$383$	−20.4588	−	8.47433i	−1.04540	−	0.433018i	−0.838247	+	0.545291i	$0.816419\pi$
$384$	−20.7329	−	4.13830i	−1.05802	−	0.211182i
$385$	6.02498	−	9.01702i	0.307061	−	0.459550i
$386$	16.5858	+	3.29912i	0.844194	+	0.167921i
$387$	0.0454712	−	34.3393i	0.00231143	−	1.74557i
$388$	0.231344	+	0.346231i	0.0117447	+	0.0175772i
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	−0.999998	−	0.00207747i	$-0.999339\pi$
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	0.705636	−	0.708574i	$-0.250661\pi$
$390$	−13.0295	+	31.3972i	−0.659774	+	1.58986i
$391$	0.945713	−	3.01592i	0.0478268	−	0.152522i
$392$			6.43314i			0.324922i
$393$	−6.10806	−	0.00404406i	−0.308111	−	0.000203996i
$394$	−28.1469	+	18.8071i	−1.41802	+	0.947490i
$395$	−12.8555	−	12.8555i	−0.646831	−	0.646831i
$396$	0.482915	−	0.321749i	0.0242674	−	0.0161685i
$397$	31.2942	+	20.9101i	1.57061	+	1.04945i	0.967850	+	0.251526i	$0.0809325\pi$
$397$	31.2942	+	20.9101i	1.57061	+	1.04945i	0.602760	+	0.797922i	$0.294068\pi$
$398$	6.84571	+	34.4157i	0.343145	+	1.72510i
$399$	−2.27920	−	2.28222i	−0.114103	−	0.114254i
$400$	6.96352	−	16.8114i	0.348176	−	0.840571i
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	−0.280870	−	0.959746i	$-0.590623\pi$
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	0.107789	+	0.994174i	$0.465623\pi$
$402$	10.0644	+	15.0840i	0.501966	+	0.752324i
$403$	−2.49080	+	12.5221i	−0.124076	+	0.623770i
$404$	0.310384	−	0.310384i	0.0154422	−	0.0154422i
$405$	15.1968	+	22.8746i	0.755136	+	1.13665i
$406$	23.1710	−	9.59773i	1.14996	−	0.476327i
$407$	−3.92459			−0.194535
$408$	−1.72277	−	19.4875i	−0.0852898	−	0.964776i
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	−12.6328	+	5.23268i	−0.623890	+	0.258424i
$411$	4.93331	+	24.8875i	0.243342	+	1.22761i
$412$	0.774744	−	0.774744i	0.0381689	−	0.0381689i
$413$	2.56347	−	12.8874i	0.126140	−	0.634148i
$414$	−0.648511	−	3.28300i	−0.0318726	−	0.161351i
$415$	−38.8671	+	7.73115i	−1.90791	+	0.379507i
$416$	1.12177	−	2.70819i	0.0549993	−	0.132780i
$417$	6.18246	−	6.17428i	0.302756	−	0.302356i
$418$	0.403898	+	2.03053i	0.0197553	+	0.0993165i
$419$	−26.1021	−	17.4409i	−1.27517	−	0.852042i	−0.280985	−	0.959712i	$-0.590661\pi$
$419$	−26.1021	−	17.4409i	−1.27517	−	0.852042i	−0.994187	+	0.107670i	$0.965661\pi$
$420$	1.11204	+	0.744106i	0.0542619	+	0.0363087i
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	0.918380	−	0.395699i	$-0.129498\pi$
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	−0.395699	+	0.918380i	$0.629498\pi$
$422$	−18.8863	+	12.6194i	−0.919373	+	0.614305i
$423$	3.60347	−	8.66707i	0.175207	−	0.421407i
$424$		−	17.4460i		−	0.847253i
$425$	17.6720	+	1.90732i	0.857216	+	0.0925185i
$426$	−5.06191	−	2.10064i	−0.245250	−	0.101776i
$427$	4.82553	+	11.6499i	0.233524	+	0.563776i
$428$	−0.123253	−	0.184461i	−0.00595764	−	0.00891625i
$429$	−4.82011	−	11.6586i	−0.232717	−	0.562883i
$430$	−49.8473	−	9.91525i	−2.40385	−	0.478156i
$431$	6.36331	−	9.52337i	0.306510	−	0.458724i	−0.645954	−	0.763376i	$-0.723540\pi$
$431$	6.36331	−	9.52337i	0.306510	−	0.458724i	0.952464	+	0.304652i	$0.0985402\pi$
$432$	−12.1490	−	18.2607i	−0.584520	−	0.878568i
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.301930	−	0.953330i	$-0.597631\pi$
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.887603	+	0.460610i	$0.847631\pi$
$434$	8.37502	+	3.46905i	0.402014	+	0.166520i
$435$	8.26727	−	41.4190i	0.396385	−	1.98589i
$436$	0.274097	−	0.410216i	0.0131269	−	0.0196458i
$437$	0.649167	+	0.129127i	0.0310539	+	0.00617700i
$438$	29.2991	−	12.1134i	1.39997	−	0.578799i
$439$	4.73699	+	7.08940i	0.226084	+	0.338359i	0.927118	−	0.374769i	$-0.122278\pi$
$439$	4.73699	+	7.08940i	0.226084	+	0.338359i	−0.701034	+	0.713128i	$0.747278\pi$
$440$	5.27126	+	12.7259i	0.251297	+	0.606685i
$441$	−4.98817	+	4.97498i	−0.237532	+	0.236904i
$442$	26.3661	+	2.84567i	1.25411	+	0.135355i
$443$			18.8773i			0.896886i	0.893811	+	0.448443i	$0.148021\pi$
$443$			18.8773i			0.896886i	−0.893811	+	0.448443i	$0.851979\pi$
$444$	0.000320596	−	0.484221i	1.52148e−5	−	0.0229801i
$445$	12.2720	−	8.19987i	0.581747	−	0.388711i
$446$	−2.50244	−	2.50244i	−0.118494	−	0.118494i
$447$	6.05891	−	9.05482i	0.286577	−	0.428278i
$448$	13.4084	+	8.95919i	0.633486	+	0.423282i
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	0.876373	+	0.481633i	$0.159956\pi$
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	−0.625350	+	0.780345i	$0.715044\pi$
$450$	17.3960	−	7.17868i	0.820055	−	0.338406i
$451$	1.94197	−	4.68833i	0.0914438	−	0.220765i
$452$	−1.89793	+	0.377522i	−0.0892713	+	0.0177572i
$453$	21.9188	−	14.6247i	1.02983	−	0.687127i
$454$	−0.398685	+	2.00433i	−0.0187112	+	0.0940677i
$455$	20.5695	−	20.5695i	0.964311	−	0.964311i
$456$	4.01860	−	0.796583i	0.188188	−	0.0373034i
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	−0.143082	−	0.989711i	$-0.545701\pi$
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	0.598657	+	0.801006i	$0.295701\pi$
$458$	15.8270			0.739546
$459$	13.7781	−	16.4062i	0.643106	−	0.765777i
$460$	−0.274576			−0.0128022
$461$	9.13414	−	3.78349i	0.425419	−	0.176215i	−0.159693	−	0.987167i	$-0.551050\pi$
$461$	9.13414	−	3.78349i	0.425419	−	0.176215i	0.585112	+	0.810952i	$0.301050\pi$
$462$	−8.78639	+	1.74168i	−0.408780	+	0.0810301i
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	−0.975121	−	0.221673i	$-0.928848\pi$
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	0.221673	+	0.975121i	$0.428848\pi$
$464$	−6.58074	+	33.0836i	−0.305503	+	1.53587i
$465$	12.6988	−	8.47293i	0.588894	−	0.392923i
$466$	20.4601	−	4.06977i	0.947797	−	0.188529i
$467$	9.89105	−	23.8791i	0.457703	−	1.10499i	−0.511621	−	0.859211i	$-0.670955\pi$
$467$	9.89105	−	23.8791i	0.457703	−	1.10499i	0.969325	−	0.245783i	$-0.0790450\pi$
$468$	1.43885	−	0.593759i	0.0665107	−	0.0274465i
$469$	−3.02732	−	15.2194i	−0.139789	−	0.702766i
$470$	−11.5509	−	7.71810i	−0.532806	−	0.356009i
$471$	−2.37742	+	3.55297i	−0.109546	+	0.163712i
$472$	11.8014	+	11.8014i	0.543205	+	0.543205i
$473$	15.6831	−	10.4791i	0.721111	−	0.481831i
$474$	−0.00994217	+	15.0164i	−0.000456659	+	0.689728i
$475$			3.72217i			0.170785i
$476$	0.312324	−	0.996016i	0.0143153	−	0.0456523i
$477$	13.5274	−	13.4916i	0.619378	−	0.617740i
$478$	−13.2025	−	31.8737i	−0.603870	−	1.45787i
$479$	−4.81385	−	7.20443i	−0.219950	−	0.329179i	0.705041	−	0.709166i	$-0.250928\pi$
$479$	−4.81385	−	7.20443i	−0.219950	−	0.329179i	−0.924992	+	0.379987i	$0.875928\pi$
$480$	−3.23907	+	1.33916i	−0.147843	+	0.0611238i
$481$	−10.3250	−	2.05377i	−0.470778	−	0.0936437i
$482$	−2.27521	+	3.40509i	−0.103633	+	0.155098i
$483$	−0.560538	+	2.80830i	−0.0255054	+	0.127782i
$484$	−0.898446	−	0.372148i	−0.0408384	−	0.0169158i
$485$	−10.0006	−	4.14240i	−0.454106	−	0.188097i
$486$	4.49888	−	22.2325i	0.204073	−	1.00849i
$487$	−21.5656	+	32.2752i	−0.977229	+	1.46253i	−0.0928931	+	0.995676i	$0.529611\pi$
$487$	−21.5656	+	32.2752i	−0.977229	+	1.46253i	−0.884336	+	0.466851i	$0.845389\pi$
$488$	−15.7086	−	3.12463i	−0.711094	−	0.141445i
$489$	0.735143	+	1.77812i	0.0332443	+	0.0804094i
$490$	5.79291	+	8.66971i	0.261697	+	0.391658i
$491$	4.84934	+	11.7073i	0.218848	+	0.528345i	0.994730	−	0.102533i	$-0.0326948\pi$
$491$	4.84934	+	11.7073i	0.218848	+	0.528345i	−0.775882	+	0.630878i	$0.782695\pi$
$492$	0.578293	+	0.239986i	0.0260715	+	0.0108194i
$493$	−32.8196	+	2.92328i	−1.47812	+	0.131658i
$494$			5.55337i			0.249858i
$495$	−5.79108	+	13.9287i	−0.260290	+	0.626049i
$496$	−10.1374	+	6.77361i	−0.455184	+	0.304144i
$497$	3.31625	+	3.31625i	0.148754	+	0.148754i
$498$	27.2035	+	18.2029i	1.21902	+	0.815691i
$499$	−30.8610	−	20.6206i	−1.38153	−	0.923106i	−0.381527	−	0.924358i	$-0.624602\pi$
$499$	−30.8610	−	20.6206i	−1.38153	−	0.923106i	−0.999999	+	0.00125143i	$0.999602\pi$
$500$	0.0481476	+	0.242054i	0.00215323	+	0.0108250i
$501$	−24.3397	+	24.3075i	−1.08742	+	1.08598i
$502$	8.43090	−	20.3540i	0.376290	−	0.908444i
$503$	−31.3353	+	6.23297i	−1.39717	+	0.277914i	−0.835520	−	0.549460i	$-0.814833\pi$
$503$	−31.3353	+	6.23297i	−1.39717	+	0.277914i	−0.561650	+	0.827375i	$0.689833\pi$
$504$	3.43496	+	17.3890i	0.153005	+	0.774568i
$505$	−2.22610	+	11.1913i	−0.0990600	+	0.498008i
$506$	1.29976	−	1.29976i	0.0577812	−	0.0577812i
$507$	−2.20176	−	11.1074i	−0.0977838	−	0.493299i
$508$	1.33526	−	0.553083i	0.0592426	−	0.0245391i
$509$	−2.30289			−0.102074			−0.0510369	−	0.998697i	$-0.516253\pi$
$509$	−2.30289			−0.102074			−0.0510369	+	0.998697i	$0.516253\pi$
$510$	−19.8698	−	24.7113i	−0.879851	−	1.09424i
$511$	−27.1309			−1.20020
$512$	−18.7797	+	7.77882i	−0.829954	+	0.343778i
$513$	3.72539	+	2.49994i	0.164480	+	0.110375i
$514$	20.4697	−	20.4697i	0.902880	−	0.902880i
$515$	−5.55652	+	27.9345i	−0.244849	+	1.23094i
$516$	1.29165	+	1.93586i	0.0568616	+	0.0852214i
$517$	5.05666	−	1.00583i	0.222391	−	0.0442364i
$518$	−2.86037	+	6.90554i	−0.125677	+	0.303412i
$519$	14.2420	+	14.2609i	0.625155	+	0.625983i
$520$	7.20827	+	36.2384i	0.316104	+	1.58916i
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	0.504423	−	0.863456i	$-0.331705\pi$
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	−0.604695	+	0.796457i	$0.706705\pi$
$522$	−29.0319	+	19.3430i	−1.27069	+	0.846619i
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.926313	+	0.376755i	$0.122960\pi$
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.376755	+	0.926313i	$0.377040\pi$
$524$	0.344186	−	0.229978i	0.0150358	−	0.0100466i
$525$	−16.1042	−	0.0106624i	−0.702846	−	0.000465344i
$526$			0.190778i			0.00831830i
$527$	−9.13517	−	7.64091i	−0.397934	−	0.332843i
$528$	4.61767	−	11.1272i	0.200958	−	0.484249i
$529$	8.57683	+	20.7063i	0.372906	+	0.900274i
$530$	−15.7098	−	23.5114i	−0.682390	−	1.02127i
$531$	−0.0242021	+	18.2772i	−0.00105028	+	0.793161i
$532$	0.214389	+	0.0426446i	0.00929494	+	0.00184888i
$533$	7.56246	−	11.3180i	0.327566	−	0.490238i
$534$	−11.9549	−	2.38621i	−0.517341	−	0.103262i
$535$	5.32803	+	2.20694i	0.230351	+	0.0954144i
$536$	18.2094	+	7.54259i	0.786527	+	0.325790i
$537$	−1.43810	−	0.287045i	−0.0620585	−	0.0123869i
$538$	4.80652	−	7.19347i	0.207224	−	0.310132i
$539$	−3.79534	−	0.754939i	−0.163477	−	0.0325175i
$540$	−1.71807	−	0.715648i	−0.0739339	−	0.0307966i
$541$	−8.13164	−	12.1699i	−0.349606	−	0.523223i	0.614438	−	0.788965i	$-0.289383\pi$
$541$	−8.13164	−	12.1699i	−0.349606	−	0.523223i	−0.964044	+	0.265742i	$0.914383\pi$
$542$	3.82826	+	9.24223i	0.164438	+	0.396988i
$543$	0.951908	−	2.29381i	0.0408503	−	0.0984369i
$544$	1.71483	+	2.12978i	0.0735229	+	0.0913135i
$545$			12.8251i			0.549365i
$546$	−24.0271	−	0.0159080i	−1.02826	−	0.000680798i
$547$	22.8049	−	15.2378i	0.975068	−	0.651520i	0.0374912	−	0.999297i	$-0.488063\pi$
$547$	22.8049	−	15.2378i	0.975068	−	0.651520i	0.937577	+	0.347777i	$0.113063\pi$
$548$	−1.21585	−	1.21585i	−0.0519384	−	0.0519384i
$549$	−9.72522	−	14.5966i	−0.415062	−	0.622969i
$550$	8.59481	+	5.74287i	0.366484	+	0.244877i
$551$	−1.34611	−	6.76737i	−0.0573464	−	0.288300i
$552$	−2.57029	−	2.57369i	−0.109399	−	0.109544i
$553$	4.91757	−	11.8721i	0.209116	−	0.504851i
$554$	11.8417	−	2.35547i	0.503107	−	0.100074i
$555$	6.98627	+	10.4707i	0.296551	+	0.444456i
$556$	−0.115523	+	0.580773i	−0.00489926	+	0.0246302i
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.399984	+	0.916522i	$0.630984\pi$
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.916522	+	0.399984i	$0.869016\pi$
$558$	−12.3637	−	2.47631i	−0.523396	−	0.104831i
$559$	46.7436	−	19.3619i	1.97705	−	0.818919i
$560$	27.7789			1.17387
$561$	11.6992	+	1.27052i	0.493939	+	0.0536412i
$562$	−19.2798			−0.813270
$563$	33.9044	−	14.0437i	1.42890	−	0.591870i	0.471821	−	0.881695i	$-0.343597\pi$
$563$	33.9044	−	14.0437i	1.42890	−	0.591870i	0.957080	+	0.289825i	$0.0935970\pi$
$564$	0.123688	+	0.623979i	0.00520819	+	0.0262742i
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$	3.98370	−	20.0274i	0.167448	−	0.841815i
$567$	−10.8268	+	16.1110i	−0.454685	+	0.676598i
$568$	−5.84243	+	1.16213i	−0.245143	+	0.0487620i
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	−0.591472	−	0.806326i	$-0.701453\pi$
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	0.988392	−	0.151925i	$-0.0485472\pi$
$570$	4.69841	−	4.69219i	0.196795	−	0.196534i
$571$	0.384503	+	1.93303i	0.0160910	+	0.0808947i	0.987996	−	0.154477i	$-0.0493693\pi$
$571$	0.384503	+	1.93303i	0.0160910	+	0.0808947i	−0.971905	+	0.235372i	$0.924369\pi$
$572$	0.710889	+	0.475001i	0.0297238	+	0.0198608i
$573$	1.03794	+	0.694522i	0.0433605	+	0.0290141i
$574$	−6.83402	−	6.83402i	−0.285247	−	0.285247i
$575$	2.74779	−	1.83601i	0.114591	−	0.0765671i
$576$	−20.7121	−	8.61137i	−0.863003	−	0.358807i
$577$			26.8179i			1.11645i	0.829691	+	0.558223i	$0.188517\pi$
$577$			26.8179i			1.11645i	−0.829691	+	0.558223i	$0.811483\pi$
$578$	−14.1249	+	20.3079i	−0.587519	+	0.844697i
$579$	18.5917	+	7.71536i	0.772644	+	0.320639i
$580$	1.09538	+	2.64449i	0.0454833	+	0.109806i
$581$	−15.5616	−	23.2896i	−0.645603	−	0.966214i
$582$	3.41602	+	8.26247i	0.141599	+	0.342490i
$583$	10.2926	+	2.04732i	0.426275	+	0.0847913i
$584$	19.1452	−	28.6529i	0.792235	−	1.18566i
$585$	−22.5244	+	33.6137i	−0.931270	+	1.38976i
$586$	−35.4995	−	14.7044i	−1.46647	−	0.607433i
$587$	−41.3023	−	17.1080i	−1.70473	−	0.706122i	−0.704735	−	0.709471i	$-0.748934\pi$
$587$	−41.3023	−	17.1080i	−1.70473	−	0.706122i	−0.999994	+	0.00334911i	$0.998934\pi$
$588$	0.0934554	−	0.468212i	0.00385403	−	0.0193087i
$589$	1.38557	−	2.07364i	0.0570912	−	0.0854430i
$590$	26.5313	+	5.27741i	1.09228	+	0.217268i
$591$	−37.2374	+	15.3953i	−1.53174	+	0.633280i
$592$	−5.58511	−	8.35871i	−0.229547	−	0.343541i
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	−0.996993	−	0.0774935i	$-0.975308\pi$
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	0.650184	−	0.759777i	$-0.274692\pi$
$594$	11.5204	−	4.74513i	0.472689	−	0.194695i
$595$	7.63399	+	26.0388i	0.312963	+	1.06749i
$596$			0.738361i			0.0302444i
$597$	−0.0276540	+	41.7680i	−0.00113180	+	1.70945i
$598$	4.09963	−	2.73928i	0.167646	−	0.112018i
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	0.962655	−	0.270729i	$-0.0872649\pi$
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	−0.270729	+	0.962655i	$0.587265\pi$
$600$	11.3754	−	17.0001i	0.464398	−	0.694026i
$601$	2.19329	+	1.46551i	0.0894662	+	0.0597794i	0.599499	−	0.800376i	$-0.295367\pi$
$601$	2.19329	+	1.46551i	0.0894662	+	0.0597794i	−0.510033	+	0.860155i	$0.670367\pi$
$602$	−7.00826	−	35.2329i	−0.285635	−	1.43599i
$603$	8.23359	+	19.9523i	0.335298	+	0.812521i
$604$	−0.683377	+	1.64982i	−0.0278062	+	0.0671302i
$605$	24.7939	−	4.93180i	1.00801	−	0.200506i
$606$	7.83988	−	5.23094i	0.318473	−	0.212492i
$607$	7.07635	−	35.5752i	0.287220	−	1.44395i	−0.520234	−	0.854024i	$-0.674155\pi$
$607$	7.07635	−	35.5752i	0.287220	−	1.44395i	0.807454	−	0.589930i	$-0.200845\pi$
$608$	−0.404887	+	0.404887i	−0.0164203	+	0.0164203i
$609$	29.2833	−	5.80467i	1.18662	−	0.235217i
$610$	−23.9836	+	9.93432i	−0.971066	+	0.402229i
$611$	13.8296			0.559487
$612$	−0.157713	+	1.44335i	−0.00637519	+	0.0583440i
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	32.8447	−	13.6047i	1.32550	−	0.549041i
$615$	−15.9653	+	3.16471i	−0.643783	+	0.127613i
$616$	−6.88440	+	6.88440i	−0.277380	+	0.277380i
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	0.922475	+	0.386057i	$0.126163\pi$
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	−0.999993	+	0.00365472i	$0.998837\pi$
$618$	19.5690	−	13.0568i	0.787180	−	0.525223i
$619$	31.6886	−	6.30326i	1.27367	−	0.253349i	0.488466	−	0.872583i	$-0.337557\pi$
$619$	31.6886	−	6.30326i	1.27367	−	0.253349i	0.785207	+	0.619233i	$0.212557\pi$
$620$	−0.395921	+	0.955837i	−0.0159006	+	0.0383873i
$621$	0.00791187	−	3.98330i	0.000317492	−	0.159844i
$622$	6.62467	+	33.3044i	0.265625	+	1.33539i
$623$	8.67402	+	5.79580i	0.347517	+	0.232204i
$624$	17.9713	−	26.8575i	0.719428	−	1.07516i
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$	−1.95352	+	1.30530i	−0.0780785	+	0.0521704i
$627$	−0.00163159	+	2.46432i	−6.51594e−5	+	0.0984154i
$628$		−	0.289721i		−	0.0115611i
$629$	6.30024	−	7.53232i	0.251207	−	0.300333i
$630$	20.2876	+	20.3414i	0.808279	+	0.810422i
$631$	−1.47845	−	3.56930i	−0.0588563	−	0.142092i	0.891716	−	0.452596i	$-0.149502\pi$
$631$	−1.47845	−	3.56930i	−0.0588563	−	0.142092i	−0.950572	+	0.310504i	$0.899502\pi$
$632$	9.06791	+	13.5711i	0.360702	+	0.539829i
$633$	−24.9860	+	10.3302i	−0.993104	+	0.410587i
$634$	−34.8014	−	6.92242i	−1.38214	−	0.274925i
$635$	−20.8729	+	31.2385i	−0.828316	+	1.23966i
$636$	−0.253442	+	1.26974i	−0.0100496	+	0.0503486i
$637$	−9.58987	−	3.97225i	−0.379964	−	0.157386i
$638$	−17.7033	−	7.33297i	−0.700882	−	0.290315i
$639$	−5.41927	−	3.63143i	−0.214383	−	0.143657i
$640$	−20.6928	+	30.9690i	−0.817955	+	1.22416i
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.856242	−	0.516575i	$-0.172793\pi$
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.593380	+	0.804922i	$0.297793\pi$
$642$	−1.81995	−	4.40198i	−0.0718276	−	0.173732i
$643$	−23.5997	−	35.3195i	−0.930682	−	1.39286i	−0.919570	−	0.392925i	$-0.871463\pi$
$643$	−23.5997	−	35.3195i	−0.930682	−	1.39286i	−0.0111111	−	0.999938i	$-0.503537\pi$
$644$	−0.0742693	−	0.179302i	−0.00292662	−	0.00706549i
$645$	−55.8760	−	23.1879i	−2.20011	−	0.913024i
$646$	−4.54551	−	2.48448i	−0.178841	−	0.0977504i
$647$		−	48.3331i		−	1.90017i	−0.311989	−	0.950086i	$-0.600995\pi$
$647$		−	48.3331i		−	1.90017i	0.311989	−	0.950086i	$-0.399005\pi$
$648$	−9.37469	−	22.8031i	−0.368272	−	0.895791i
$649$	−8.34737	+	5.57753i	−0.327663	+	0.218937i
$650$	19.6063	+	19.6063i	0.769023	+	0.769023i
$651$	8.96780	+	6.00068i	0.351476	+	0.235185i
$652$	−0.108422	−	0.0724451i	−0.00424613	−	0.00283717i
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	0.997592	−	0.0693542i	$-0.0220939\pi$
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	−0.948196	+	0.317687i	$0.897094\pi$
$654$	7.49540	−	7.48548i	0.293093	−	0.292705i
$655$	−4.11794	+	9.94158i	−0.160901	+	0.388450i
$656$	12.7490	−	2.53593i	0.497764	−	0.0990114i
$657$	37.0228	−	7.31334i	1.44440	−	0.285321i
$658$	1.91564	−	9.63056i	0.0746794	−	0.375439i
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	−0.962125	−	0.272610i	$-0.912113\pi$
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	0.272610	+	0.962125i	$0.412113\pi$
$660$	−0.198776	−	1.00279i	−0.00773736	−	0.0390334i
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.782474	−	0.622683i	$-0.786043\pi$
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.112990	+	0.993596i	$0.536043\pi$
$662$	−44.3302			−1.72294
$663$	30.1138	+	9.46478i	1.16952	+	0.367582i
$664$	35.5773			1.38067
$665$	−5.24974	+	2.17451i	−0.203576	+	0.0843240i
$666$	2.04182	−	10.1943i	0.0791188	−	0.395022i
$667$	−4.33184	+	4.33184i	−0.167729	+	0.167729i
$668$	0.454802	−	2.28645i	0.0175968	−	0.0884652i
$669$	−2.33802	−	3.50411i	−0.0903929	−	0.135477i
$670$	31.3321	−	6.23235i	1.21047	−	0.240777i
$671$	3.68686	−	8.90086i	0.142329	−	0.343614i
$672$	−1.75061	−	1.75293i	−0.0675313	−	0.0676208i
$673$	3.66436	+	18.4220i	0.141251	+	0.710115i	0.984887	+	0.173200i	$0.0554106\pi$
$673$	3.66436	+	18.4220i	0.141251	+	0.710115i	−0.843636	+	0.536915i	$0.819589\pi$
$674$	20.8416	+	13.9259i	0.802787	+	0.536405i
$675$	21.9787	−	4.32647i	0.845960	−	0.166526i
$676$	0.542640	+	0.542640i	0.0208708	+	0.0208708i
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	−0.703754	−	0.710444i	$-0.748494\pi$
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	0.387049	+	0.922059i	$0.373494\pi$
$678$	−41.5493	−	0.0275092i	−1.59569	−	0.00105648i
$679$		−	7.65102i		−	0.293619i
$680$	−32.8865	−	10.3123i	−1.26114	−	0.395460i
$681$	−0.932371	+	2.24673i	−0.0357285	+	0.0860950i
$682$	−2.65046	−	6.39878i	−0.101491	−	0.245022i
$683$	−1.32660	−	1.98540i	−0.0507610	−	0.0759692i	0.805221	−	0.592975i	$-0.202047\pi$
$683$	−1.32660	−	1.98540i	−0.0507610	−	0.0759692i	−0.855982	+	0.517006i	$0.827047\pi$
$684$	−0.304050		0.000402615i	−0.0116257		1.53944e-5i
$685$	43.8391	+	8.72013i	1.67500	+	0.333179i
$686$	−16.2996	+	24.3941i	−0.622322	+	0.931370i
$687$	18.4746	+	3.68755i	0.704851	+	0.140689i
$688$	44.6375	+	18.4895i	1.70179	+	0.704905i
$689$	26.0068	+	10.7724i	0.990779	+	0.410394i
$690$	−5.78144	−	1.15398i	−0.220096	−	0.0439313i
$691$	18.1140	−	27.1095i	0.689088	−	1.03129i	−0.307722	−	0.951476i	$-0.599567\pi$
$691$	18.1140	−	27.1095i	0.689088	−	1.03129i	0.996810	−	0.0798165i	$-0.0254334\pi$
$692$	−1.33965	−	0.266473i	−0.0509258	−	0.0101298i
$693$	−10.6620	−	0.0141184i	−0.405017	−	0.000536313i
$694$	16.3582	+	24.4818i	0.620948	+	0.929315i
$695$	−5.89068	−	14.2214i	−0.223446	−	0.539447i
$696$	−14.5338	+	35.0222i	−0.550904	+	1.32751i
$697$	5.88065	+	11.2534i	0.222745	+	0.426254i
$698$		−	11.0631i		−	0.418743i
$699$	24.8311	+	0.0164403i	0.939197	+	0.000621829i
$700$	0.907464	−	0.606348i	0.0342989	−	0.0229178i
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.974807	−	0.223051i	$-0.928398\pi$
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.223051	−	0.974807i	$-0.571602\pi$
$702$	32.7916	−	6.45497i	1.23764	−	0.243627i
$703$	1.70980	+	1.14245i	0.0644864	+	0.0430885i
$704$	−2.40368	−	12.0841i	−0.0905921	−	0.455437i
$705$	−11.6850	−	11.7005i	−0.440083	−	0.440667i
$706$	−6.64926	+	16.0527i	−0.250248	+	0.604153i
$707$	−7.91022	+	1.57344i	−0.297495	+	0.0591753i
$708$	−0.687481	−	1.03036i	−0.0258371	−	0.0387235i
$709$	−7.70314	+	38.7263i	−0.289297	+	1.45440i	0.513472	+	0.858106i	$0.328359\pi$
$709$	−7.70314	+	38.7263i	−0.289297	+	1.45440i	−0.802769	+	0.596290i	$0.796641\pi$
$710$	−6.82716	+	6.82716i	−0.256219	+	0.256219i
$711$	−3.51030	+	17.5262i	−0.131647	+	0.657283i
$712$	−12.2419	+	5.07074i	−0.458783	+	0.190034i
$713$	−2.21426			−0.0829248
$714$	10.7623	−	19.6593i	0.402768	−	0.735733i
$715$	−22.2254			−0.831182
$716$	0.0918186	−	0.0380325i	0.00343142	−	0.00142134i
$717$	−7.98484	−	40.2819i	−0.298199	−	1.50435i
$718$	−23.6628	+	23.6628i	−0.883086	+	0.883086i
$719$	−8.57373	+	43.1030i	−0.319746	+	1.60747i	0.402220	+	0.915543i	$0.368239\pi$
$719$	−8.57373	+	43.1030i	−0.319746	+	1.60747i	−0.721966	+	0.691929i	$0.756761\pi$
$720$	−37.9071	+	7.48802i	−1.41271	+	0.279062i
$721$	−19.7446	+	3.92744i	−0.735326	+	0.146265i
$722$	−10.1650	+	24.5406i	−0.378304	+	0.913307i
$723$	−3.44918	+	3.44461i	−0.128276	+	0.128107i
$724$	0.0328353	+	0.165074i	0.00122031	+	0.00613493i
$725$	−28.6448	−	19.1399i	−1.06384	−	0.710837i
$726$	−17.3535	−	11.6119i	−0.644049	−	0.430957i
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	0.705617	−	0.708594i	$-0.250670\pi$
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	−0.708594	+	0.705617i	$0.750670\pi$
$728$	−21.7144	+	14.5091i	−0.804790	+	0.537744i
$729$	10.4315	−	24.9035i	0.386351	−	0.922352i
$730$		−	55.8544i		−	2.06726i
$731$	−5.06429	+	46.9224i	−0.187310	+	1.73549i
$732$	1.09790	+	0.455616i	0.0405795	+	0.0168400i
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	0.855579	−	0.517673i	$-0.173201\pi$
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	−0.971035	+	0.238936i	$0.923201\pi$
$734$	13.2667	+	19.8549i	0.489681	+	0.732860i
$735$	4.74203	+	11.4697i	0.174912	+	0.423068i
$736$	0.498613	+	0.0991804i	0.0183791	+	0.00365584i
$737$	−6.58678	+	9.85781i	−0.242627	+	0.363117i
$738$	11.1679	+	7.48354i	0.411095	+	0.275473i
$739$	−10.8531	−	4.49550i	−0.399237	−	0.165370i	0.174025	−	0.984741i	$-0.444323\pi$
$739$	−10.8531	−	4.49550i	−0.399237	−	0.165370i	−0.573263	+	0.819372i	$0.694323\pi$
$740$	−0.788126	−	0.326452i	−0.0289721	−	0.0120006i
$741$	−1.29389	+	6.48238i	−0.0475322	+	0.238136i
$742$	11.1039	−	16.6182i	0.407639	−	0.610074i
$743$	40.2557	+	8.00737i	1.47684	+	0.293762i	0.866819	−	0.498623i	$-0.166161\pi$
$743$	40.2557	+	8.00737i	1.47684	+	0.293762i	0.610021	+	0.792385i	$0.291161\pi$
$744$	−12.6655	+	5.23642i	−0.464341	+	0.191976i
$745$	−10.6635	−	15.9591i	−0.390682	−	0.584697i
$746$	−0.901121	−	2.17550i	−0.0329924	−	0.0796507i
$747$	27.5132	+	27.5862i	1.00666	+	1.00933i
$748$	−0.706833	+	0.369366i	−0.0258444	+	0.0135053i
$749$			4.07622i			0.148942i
$750$	−0.00350841	+	5.29902i	−0.000128109	+	0.193493i
$751$	−1.40436	+	0.938366i	−0.0512460	+	0.0342414i	−0.580929	−	0.813954i	$-0.697311\pi$
$751$	−1.40436	+	0.938366i	−0.0512460	+	0.0342414i	0.529683	+	0.848195i	$0.322311\pi$
$752$	9.33841	+	9.33841i	0.340537	+	0.340537i
$753$	14.5836	−	21.7946i	0.531456	−	0.794241i
$754$	−42.7373	−	28.5562i	−1.55640	−	1.03995i
$755$	−9.05629	−	45.5290i	−0.329592	−	1.65697i
$756$	0.00261291	−	1.31549i	9.50307e−5	−	0.0478441i
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.242954	+	0.970038i	$0.578116\pi$
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.514126	+	0.857715i	$0.671884\pi$
$758$	22.1631	−	4.40851i	0.805000	−	0.160124i
$759$	1.82002	−	1.21436i	0.0660625	−	0.0440783i
$760$	1.40804	−	7.07871i	0.0510751	−	0.256772i
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	−0.117963	−	0.993018i	$-0.537636\pi$
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	0.993018	+	0.117963i	$0.0376365\pi$
$762$	30.4395	−	6.03385i	1.10271	−	0.218583i
$763$	−8.37493	+	3.46901i	−0.303193	+	0.125587i
$764$	−0.0846370			−0.00306206
$765$	−17.4363	−	33.4747i	−0.630410	−	1.21028i
$766$	32.2229			1.16426
$767$	−24.8794	+	10.3054i	−0.898343	+	0.372106i
$768$	4.77021	−	0.945571i	0.172130	−	0.0341204i
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.139204	−	0.990264i	$-0.455546\pi$
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.990264	−	0.139204i	$-0.0444544\pi$
$770$	−3.07859	+	15.4771i	−0.110945	+	0.557757i
$771$	28.6633	−	19.1248i	1.03228	−	0.688761i
$772$	−1.33795	+	0.266135i	−0.0481539	+	0.00957840i
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	−0.799126	−	0.601164i	$-0.794704\pi$
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	0.990154	+	0.139980i	$0.0447039\pi$
$774$	19.0608	+	46.1897i	0.685125	+	1.66025i
$775$	−2.42928	−	12.2128i	−0.0872624	−	0.438698i
$776$	8.08023	+	5.39903i	0.290063	+	0.193814i
$777$	−4.94780	+	7.39431i	−0.177501	+	0.265269i
$778$	15.6099	+	15.6099i	0.559643	+	0.559643i
$779$	−2.21083	+	1.47723i	−0.0792111	+	0.0529272i
$780$	0.00181557	−	2.74219i	6.50078e−5	−	0.0981863i
$781$		−	3.58322i		−	0.128218i
$782$	0.408044	+	4.58110i	0.0145916	+	0.163820i
$783$	−38.3954	+	15.8146i	−1.37214	+	0.565168i
$784$	−3.79328	−	9.15778i	−0.135474	−	0.327064i
$785$	4.18421	+	6.26211i	0.149341	+	0.223504i
$786$	8.21367	−	3.39584i	0.292972	−	0.121126i
$787$	−23.4782	−	4.67010i	−0.836907	−	0.166471i	−0.242011	−	0.970274i	$-0.577807\pi$
$787$	−23.4782	−	4.67010i	−0.836907	−	0.166471i	−0.594896	+	0.803802i	$0.702807\pi$
$788$	1.51714	−	2.27057i	0.0540460	−	0.0808856i
$789$	−0.0444496	+	0.222692i	−0.00158245	+	0.00792806i
$790$	24.4410	+	10.1238i	0.869572	+	0.360189i
$791$	32.8490	+	13.6065i	1.16798	+	0.483792i
$792$	7.53870	−	11.2502i	0.267876	−	0.399758i
$793$	14.3574	−	21.4874i	0.509847	−	0.763040i
$794$	−53.7144	−	10.6845i	−1.90625	−	0.379178i
$795$	−12.8599	−	31.1048i	−0.456094	−	1.10317i
$796$	−1.57263	−	2.35361i	−0.0557403	−	0.0834213i
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	0.833529	+	0.552476i	$0.186317\pi$
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	−0.198734	+	0.980053i	$0.563683\pi$
$798$	4.33492	+	1.79895i	0.153455	+	0.0636820i
$799$	−6.18712	+	11.3197i	−0.218884	+	0.400463i
$800$			2.85893i			0.101078i
$801$	−13.3989	−	5.57079i	−0.473426	−	0.196834i
$802$	4.27557	−	2.85685i	0.150976	−	0.100879i
$803$	14.6575	+	14.6575i	0.517252	+	0.517252i
$804$	−1.21573	−	0.813491i	−0.0428755	−	0.0286896i
$805$	4.19478	+	2.80287i	0.147847	+	0.0987880i
$806$	−3.62442	−	18.2212i	−0.127665	−	0.641814i
$807$	7.28661	−	7.27696i	0.256501	−	0.256161i
$808$	3.92024	−	9.46429i	0.137913	−	0.332952i
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.392904	−	0.919579i	$-0.628530\pi$
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.0110886	+	0.999939i	$0.503530\pi$
$810$	−33.1677	−	22.2892i	−1.16539	−	0.783164i
$811$	3.67314	−	18.4661i	0.128982	−	0.648434i	−0.861157	−	0.508340i	$-0.830259\pi$
$811$	3.67314	−	18.4661i	0.128982	−	0.648434i	0.990138	−	0.140094i	$-0.0447406\pi$
$812$	−1.43060	+	1.43060i	−0.0502042	+	0.0502042i
$813$	2.31531	+	11.6803i	0.0812016	+	0.409645i
$814$	5.27605	−	2.18541i	0.184926	−	0.0765987i
$815$	3.38972			0.118737
$816$	13.9432	+	26.7253i	0.488108	+	0.935572i
$817$	−9.88307			−0.345765
$818$	−16.4118	+	6.79797i	−0.573824	+	0.237686i
$819$	−28.0428	−	5.61666i	−0.979893	−	0.196262i
$820$	0.779963	−	0.779963i	0.0272375	−	0.0272375i
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	−0.729408	−	0.684079i	$-0.760205\pi$
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	0.935671	−	0.352874i	$-0.114795\pi$
$822$	−20.4908	−	30.7106i	−0.714698	−	1.07116i
$823$	22.5083	−	4.47717i	0.784589	−	0.156064i	0.213489	−	0.976945i	$-0.431517\pi$
$823$	22.5083	−	4.47717i	0.784589	−	0.156064i	0.571099	+	0.820881i	$0.306517\pi$
$824$	9.78523	−	23.6236i	0.340884	−	0.822968i
$825$	8.69457	+	8.70609i	0.302706	+	0.303107i
$826$	3.73016	+	18.7528i	0.129789	+	0.652493i
$827$	−14.5585	−	9.72768i	−0.506249	−	0.338265i	0.276076	−	0.961136i	$-0.410966\pi$
$827$	−14.5585	−	9.72768i	−0.506249	−	0.338265i	−0.782324	+	0.622871i	$0.785966\pi$
$828$	0.149680	+	0.224655i	0.00520174	+	0.00780732i
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.996380	−	0.0850121i	$-0.972907\pi$
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.0850121	−	0.996380i	$-0.527093\pi$
$830$	47.9462	−	32.0366i	1.66424	−	1.11201i
$831$	14.3715	+	0.00951518i	0.498542	+	0.000330078i
$832$		−	33.0493i		−	1.14578i
$833$	7.54167	−	6.07232i	0.261303	−	0.210394i
$834$	−4.87328	+	11.7432i	−0.168748	+	0.406632i
$835$	23.1910	+	55.9881i	0.802559	+	1.93755i
$836$	−0.0927852	−	0.138863i	−0.00320904	−	0.00480267i
$837$	−13.8550	−	5.77119i	−0.478898	−	0.199481i
$838$	44.8026	+	8.91178i	1.54768	+	0.307852i
$839$	10.9879	−	16.4446i	0.379346	−	0.567731i	−0.591840	−	0.806056i	$-0.701598\pi$
$839$	10.9879	−	16.4446i	0.379346	−	0.567731i	0.971186	+	0.238325i	$0.0765982\pi$
$840$	30.6225	+	6.11227i	1.05658	+	0.210893i
$841$	32.2093	+	13.3415i	1.11067	+	0.460053i
$842$	−20.3896	−	8.44564i	−0.702671	−	0.291056i
$843$	−22.5051	−	4.49203i	−0.775116	−	0.154714i
$844$	1.01799	−	1.52353i	0.0350407	−	0.0524422i
$845$	−19.5656	−	3.89185i	−0.673078	−	0.133884i
$846$	−0.0180859	+	13.6582i	−0.000621805	+	0.469580i
$847$	9.92694	+	14.8567i	0.341094	+	0.510483i
$848$	10.2870	+	24.8350i	0.353257	+	0.852837i
$849$	9.31634	−	22.4496i	0.319736	−	0.770468i
$850$	−24.8195	+	7.27654i	−0.851303	+	0.249583i
$851$		−	1.82575i		−	0.0625858i
$852$	0.442102		0.000292709i	0.0151462		1.00281e-5i
$853$	−5.13456	+	3.43080i	−0.175804	+	0.117469i	−0.640359	−	0.768076i	$-0.721214\pi$
$853$	−5.13456	+	3.43080i	−0.175804	+	0.117469i	0.464555	+	0.885544i	$0.346214\pi$
$854$	−12.9745	−	12.9745i	−0.443977	−	0.443977i
$855$	6.57763	−	4.38245i	0.224950	−	0.149877i
$856$	−4.30489	−	2.87643i	−0.147138	−	0.0983145i
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	0.965393	+	0.260798i	$0.0839856\pi$
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	−0.792104	+	0.610386i	$0.791014\pi$
$858$	12.9721	+	12.9893i	0.442859	+	0.443446i
$859$	−1.25664	+	3.03380i	−0.0428761	+	0.103512i	−0.943867	−	0.330326i	$-0.892841\pi$
$859$	−1.25664	+	3.03380i	−0.0428761	+	0.103512i	0.900991	+	0.433838i	$0.142841\pi$
$860$	4.02111	−	0.799849i	0.137119	−	0.0272746i
$861$	−6.38500	−	9.56953i	−0.217600	−	0.326129i
$862$	−3.25147	+	16.3462i	−0.110745	+	0.556755i
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	−0.507750	−	0.861504i	$-0.669523\pi$
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	0.861504	+	0.507750i	$0.169523\pi$
$864$	2.86140	+	1.92016i	0.0973468	+	0.0653251i
$865$	32.8040	−	13.5878i	1.11537	−	0.462000i
$866$	38.9856			1.32479
$867$	−21.2194	+	20.4142i	−0.720648	+	0.693301i
$868$	−0.731265			−0.0248208
$869$	−9.07062	+	3.75718i	−0.307700	+	0.127453i
$870$	11.9501	+	60.2856i	0.405145	+	2.04387i
$871$	−22.4875	+	22.4875i	−0.761958	+	0.761958i
$872$	2.24626	−	11.2927i	0.0760679	−	0.382419i
$873$	2.06239	+	10.4406i	0.0698014	+	0.353360i
$874$	−0.944618	+	0.187896i	−0.0319522	+	0.00635569i
$875$	1.73532	−	4.18943i	0.0586644	−	0.141629i
$876$	−1.80966	+	1.80726i	−0.0611427	+	0.0610618i
$877$	2.60180	+	13.0801i	0.0878565	+	0.441684i	0.999527	+	0.0307618i	$0.00979334\pi$
$877$	2.60180	+	13.0801i	0.0878565	+	0.441684i	−0.911670	+	0.410923i	$0.865207\pi$
$878$	−10.3160	−	6.89290i	−0.348146	−	0.232624i
$879$	−38.0121	−	25.4353i	−1.28212	−	0.857912i
$880$	−15.0076	−	15.0076i	−0.505907	−	0.505907i
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	−0.800218	−	0.599709i	$-0.795283\pi$
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	0.247829	+	0.968804i	$0.420283\pi$
$882$	3.93557	−	9.46583i	0.132517	−	0.318731i
$883$		−	44.5932i		−	1.50068i	−0.661051	−	0.750341i	$-0.729889\pi$
$883$		−	44.5932i		−	1.50068i	0.661051	−	0.750341i	$-0.270111\pi$
$884$	−2.05286	+	0.601853i	−0.0690451	+	0.0202425i
$885$	29.7401	+	12.3418i	0.999702	+	0.414866i
$886$	−10.5118	−	25.3778i	−0.353152	−	0.852584i
$887$	9.28722	+	13.8993i	0.311834	+	0.466693i	0.953972	−	0.299896i	$-0.0969521\pi$
$887$	9.28722	+	13.8993i	0.311834	+	0.466693i	−0.642137	+	0.766590i	$0.721952\pi$
$888$	−4.31764	−	10.4432i	−0.144890	−	0.350452i
$889$	−26.0450	−	5.18067i	−0.873522	−	0.173754i
$890$	−11.9318	+	17.8572i	−0.399955	+	0.598575i
$891$	14.5532	−	2.85477i	0.487551	−	0.0956383i
$892$	0.263753	+	0.109250i	0.00883111	+	0.00365797i
$893$	−2.49580	−	1.03380i	−0.0835189	−	0.0345947i
$894$	−3.10316	+	15.5468i	−0.103785	+	0.519964i
$895$	−1.43532	+	2.14810i	−0.0479773	+	0.0718032i
$896$	−25.8203	−	5.13597i	−0.862594	−	0.171581i
$897$	5.42367	−	2.24235i	0.181091	−	0.0748699i
$898$	−22.0414	−	32.9873i	−0.735532	−	1.10080i
$899$	8.83348	+	21.3259i	0.294613	+	0.711259i
$900$	−1.07488	+	1.07204i	−0.0358293	+	0.0357345i
$901$	−20.4523	+	16.4675i	−0.681363	+	0.548613i
$902$			7.38418i			0.245866i
$903$	0.0283106	−	42.7598i	0.000942119	−	1.42296i
$904$	−37.5501	+	25.0902i	−1.24890	+	0.834487i
$905$	−3.09374	−	3.09374i	−0.102839	−	0.102839i
$906$	−21.3229	+	31.8663i	−0.708406	+	1.05869i
$907$	7.66078	+	5.11877i	0.254372	+	0.169966i	0.676218	−	0.736702i	$-0.263618\pi$
$907$	7.66078	+	5.11877i	0.254372	+	0.169966i	−0.421846	+	0.906668i	$0.638618\pi$
$908$	−0.0321614	−	0.161686i	−0.00106731	−	0.00536574i
$909$	10.3702	−	4.27938i	0.343956	−	0.141938i
$910$	−16.1986	+	39.1068i	−0.536978	+	1.29638i
$911$	1.96677	−	0.391215i	0.0651621	−	0.0129615i	−0.162402	−	0.986725i	$-0.551924\pi$
$911$	1.96677	−	0.391215i	0.0651621	−	0.0129615i	0.227564	+	0.973763i	$0.426924\pi$
$912$	−5.25090	+	3.50351i	−0.173875	+	0.116013i
$913$	−4.17505	+	20.9894i	−0.138174	+	0.694648i
$914$	−10.8464	+	10.8464i	−0.358768	+	0.358768i
$915$	−30.3103	+	6.00824i	−1.00203	+	0.198626i
$916$	−1.17955	+	0.488587i	−0.0389735	+	0.0161434i
$917$	−7.60583			−0.251167
$918$	−9.38686	+	29.7282i	−0.309813	+	0.981177i
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	−5.92020	+	2.45223i	−0.195183	+	0.0808475i
$921$	41.5089	−	8.22807i	1.36777	−	0.271124i
$922$	−10.1727	+	10.1727i	−0.335021	+	0.335021i
$923$	1.87512	−	9.42688i	0.0617204	−	0.310290i
$924$	0.601066	−	0.401044i	0.0197736	−	0.0131934i
$925$	10.0700	−	2.00304i	0.331098	−	0.0658595i
$926$	12.7673	−	30.8229i	0.419558	−	1.01290i
$927$	25.8847	−	10.6817i	0.850166	−	0.350832i
$928$	−1.03392	−	5.19789i	−0.0339402	−	0.170629i
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	0.175375	−	0.984502i	$-0.443886\pi$
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	−0.842448	+	0.538778i	$0.818886\pi$
$930$	−12.3536	+	18.4620i	−0.405091	+	0.605393i
$931$	1.43373	+	1.43373i	0.0469885	+	0.0469885i
$932$	−1.39922	+	0.934927i	−0.0458329	+	0.0306245i
$933$	−0.0267611	+	40.4193i	−0.000876118	+	1.32327i
$934$			37.6099i			1.23063i
$935$	9.94321	−	18.1918i	0.325178	−	0.594934i
$936$	25.7205	−	25.6524i	0.840699	−	0.838476i
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	−0.836252	−	0.548345i	$-0.815258\pi$
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	0.203582	−	0.979058i	$-0.434742\pi$
$938$	12.5447	+	18.7745i	0.409600	+	0.613010i
$939$	−2.58445	+	1.06851i	−0.0843403	+	0.0348695i
$940$	1.09913	+	0.218631i	0.0358497	+	0.00713095i
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	−0.862669	−	0.505769i	$-0.831209\pi$
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	0.797399	+	0.603453i	$0.206209\pi$
$942$	1.21763	−	6.10033i	0.0396726	−	0.198760i
$943$	2.18105	+	0.903419i	0.0710246	+	0.0294194i
$944$	−23.7584	−	9.84105i	−0.773270	−	0.320299i
$945$	18.9421	+	28.4711i	0.616187	+	0.926166i
$946$	−15.2484	+	22.8209i	−0.495769	+	0.741970i
$947$	−26.2908	−	5.22957i	−0.854336	−	0.169938i	−0.251554	−	0.967843i	$-0.580941\pi$
$947$	−26.2908	−	5.22957i	−0.854336	−	0.169938i	−0.602783	+	0.797905i	$0.705941\pi$
$948$	−0.462824	−	1.11945i	−0.0150318	−	0.0363581i
$949$	30.8912	+	46.2320i	1.00277	+	1.50075i
$950$	−2.07269	−	5.00393i	−0.0672471	−	0.162349i
$951$	−39.0103	−	16.1889i	−1.26500	−	0.524960i
$952$	−2.16128	−	24.2647i	−0.0700475	−	0.786422i
$953$		−	24.2594i		−	0.785838i	−0.919573	−	0.392919i	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$	−10.6729	+	25.6704i	−0.345547	+	0.831109i
$955$	1.82937	−	1.22234i	0.0591969	−	0.0395541i
$956$	1.96792	+	1.96792i	0.0636470	+	0.0636470i
$957$	−18.9564	−	12.6844i	−0.612772	−	0.410028i
$958$	10.4833	+	7.00474i	0.338701	+	0.226313i
$959$	6.16353	+	30.9862i	0.199031	+	1.00060i
$960$	−27.9612	+	27.9242i	−0.902445	+	0.901250i
$961$	8.67037	−	20.9321i	0.279689	−	0.675230i
$962$	15.0241	−	2.98848i	0.484397	−	0.0963525i
$963$	−1.09878	−	5.56241i	−0.0354076	−	0.179246i
$964$	0.0644499	−	0.324012i	0.00207579	−	0.0104357i
$965$	25.0752	−	25.0752i	0.807200	−	0.807200i
$966$	−0.810240	−	4.08749i	−0.0260691	−	0.131513i
$967$	−12.2636	+	5.07976i	−0.394372	+	0.163354i	−0.571051	−	0.820914i	$-0.693464\pi$
$967$	−12.2636	+	5.07976i	−0.394372	+	0.163354i	0.176680	+	0.984268i	$0.443464\pi$
$968$	−22.6952			−0.729452
$969$	−4.72705	−	3.95916i	−0.151855	−	0.127187i
$970$	15.7512			0.505739
$971$	14.2905	−	5.91933i	0.458605	−	0.189960i	−0.141407	−	0.989952i	$-0.545163\pi$
$971$	14.2905	−	5.91933i	0.458605	−	0.189960i	0.600012	+	0.799991i	$0.295163\pi$
$972$	0.351036	+	1.79583i	0.0112595	+	0.0576012i
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$	11.0194	−	55.3982i	0.353084	−	1.77507i
$975$	18.3181	+	27.4543i	0.586649	+	0.879241i
$976$	24.2041	−	4.81450i	0.774755	−	0.154108i
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	−0.997973	−	0.0636347i	$-0.979731\pi$
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	0.750670	+	0.660677i	$0.229731\pi$
$978$	−1.97845	−	1.98107i	−0.0632637	−	0.0633475i
$979$	−1.55497	−	7.81735i	−0.0496970	−	0.249844i
$980$	−0.699373	−	0.467306i	−0.0223406	−	0.0149275i
$981$	10.4933	−	6.99134i	0.335026	−	0.223216i
$982$	−13.0385	−	13.0385i	−0.416075	−	0.416075i
$983$	−21.6898	+	14.4927i	−0.691797	+	0.462244i	−0.851112	−	0.524984i	$-0.824071\pi$
$983$	−21.6898	+	14.4927i	−0.691797	+	0.462244i	0.159315	+	0.987228i	$0.449071\pi$
$984$	14.6120	+	0.00967440i	0.465814	+	0.000308409i
$985$			70.9874i			2.26185i
$986$	42.4935	−	22.2056i	1.35327	−	0.707170i
$987$	4.47994	−	10.7953i	0.142598	−	0.343618i
$988$	−0.171435	−	0.413882i	−0.00545409	−	0.0131673i
$989$	4.87497	+	7.29590i	0.155015	+	0.231996i
$990$	0.0290655	−	21.9499i	0.000923762	−	0.697615i
$991$	35.4161	+	7.04470i	1.12503	+	0.223782i	0.722329	−	0.691549i	$-0.243072\pi$
$991$	35.4161	+	7.04470i	1.12503	+	0.223782i	0.402701	+	0.915332i	$0.368072\pi$
$992$	1.06423	−	1.59273i	0.0337892	−	0.0505692i
$993$	−51.7460	−	10.3285i	−1.64211	−	0.327766i
$994$	−6.30488	−	2.61157i	−0.199979	−	0.0828339i
$995$	67.9824	+	28.1592i	2.15519	+	0.892707i
$996$	−2.58936	−	0.516838i	−0.0820469	−	0.0163766i
$997$	8.20777	−	12.2838i	0.259943	−	0.389032i	−0.678425	−	0.734669i	$-0.737337\pi$
$997$	8.20777	−	12.2838i	0.259943	−	0.389032i	0.938368	+	0.345638i	$0.112337\pi$
$998$	52.9708	+	10.5365i	1.67676	+	0.333529i
$999$	4.75858	−	11.4240i	0.150555	−	0.361439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.i.a.29.1	✓	32
3.2	odd	2	inner	51.2.i.a.29.4	yes	32
4.3	odd	2		816.2.cj.c.641.4		32
12.11	even	2		816.2.cj.c.641.3		32
17.2	even	8		867.2.i.i.65.1		32
17.3	odd	16		867.2.i.g.329.1		32
17.4	even	4		867.2.i.d.158.4		32
17.5	odd	16		867.2.i.i.827.4		32
17.6	odd	16		867.2.i.c.653.1		32
17.7	odd	16		867.2.i.h.503.4		32
17.8	even	8		867.2.i.f.224.4		32
17.9	even	8		867.2.i.g.224.4		32
17.10	odd	16	inner	51.2.i.a.44.4	yes	32
17.11	odd	16		867.2.i.d.653.1		32
17.12	odd	16		867.2.i.b.827.4		32
17.13	even	4		867.2.i.c.158.4		32
17.14	odd	16		867.2.i.f.329.1		32
17.15	even	8		867.2.i.b.65.1		32
17.16	even	2		867.2.i.h.131.1		32
51.2	odd	8		867.2.i.i.65.4		32
51.5	even	16		867.2.i.i.827.1		32
51.8	odd	8		867.2.i.f.224.1		32
51.11	even	16		867.2.i.d.653.4		32
51.14	even	16		867.2.i.f.329.4		32
51.20	even	16		867.2.i.g.329.4		32
51.23	even	16		867.2.i.c.653.4		32
51.26	odd	8		867.2.i.g.224.1		32
51.29	even	16		867.2.i.b.827.1		32
51.32	odd	8		867.2.i.b.65.4		32
51.38	odd	4		867.2.i.d.158.1		32
51.41	even	16		867.2.i.h.503.1		32
51.44	even	16	inner	51.2.i.a.44.1	yes	32
51.47	odd	4		867.2.i.c.158.1		32
51.50	odd	2		867.2.i.h.131.4		32
68.27	even	16		816.2.cj.c.401.3		32
204.95	odd	16		816.2.cj.c.401.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	1.1	even	1	trivial
51.2.i.a.29.4	yes	32	3.2	odd	2	inner
51.2.i.a.44.1	yes	32	51.44	even	16	inner
51.2.i.a.44.4	yes	32	17.10	odd	16	inner
816.2.cj.c.401.3		32	68.27	even	16
816.2.cj.c.401.4		32	204.95	odd	16
816.2.cj.c.641.3		32	12.11	even	2
816.2.cj.c.641.4		32	4.3	odd	2
867.2.i.b.65.1		32	17.15	even	8
867.2.i.b.65.4		32	51.32	odd	8
867.2.i.b.827.1		32	51.29	even	16
867.2.i.b.827.4		32	17.12	odd	16
867.2.i.c.158.1		32	51.47	odd	4
867.2.i.c.158.4		32	17.13	even	4
867.2.i.c.653.1		32	17.6	odd	16
867.2.i.c.653.4		32	51.23	even	16
867.2.i.d.158.1		32	51.38	odd	4
867.2.i.d.158.4		32	17.4	even	4
867.2.i.d.653.1		32	17.11	odd	16
867.2.i.d.653.4		32	51.11	even	16
867.2.i.f.224.1		32	51.8	odd	8
867.2.i.f.224.4		32	17.8	even	8
867.2.i.f.329.1		32	17.14	odd	16
867.2.i.f.329.4		32	51.14	even	16
867.2.i.g.224.1		32	51.26	odd	8
867.2.i.g.224.4		32	17.9	even	8
867.2.i.g.329.1		32	17.3	odd	16
867.2.i.g.329.4		32	51.20	even	16
867.2.i.h.131.1		32	17.16	even	2
867.2.i.h.131.4		32	51.50	odd	2
867.2.i.h.503.1		32	51.41	even	16
867.2.i.h.503.4		32	17.7	odd	16
867.2.i.i.65.1		32	17.2	even	8
867.2.i.i.65.4		32	51.2	odd	8
867.2.i.i.827.1		32	51.5	even	16
867.2.i.i.827.4		32	17.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34436 + 0.556851i) q^{2} +(-1.69899 + 0.336782i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-0.595296 + 2.99276i) q^{5} +(2.09652 - 1.39884i) q^{6} +(-2.11533 + 0.420765i) q^{7} +(1.04834 - 2.53091i) q^{8} +(2.77316 - 1.14438i) q^{9} +(-0.866229 - 4.35483i) q^{10} +(1.37013 + 0.915491i) q^{11} +(-0.113066 + 0.168973i) q^{12} +(3.12551 + 3.12551i) q^{13} +(2.60946 - 1.74358i) q^{14} +(0.00349923 - 5.28516i) q^{15} +4.22099i q^{16} +(-3.95657 + 1.15998i) q^{17} +(-3.09087 + 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(0.198994 + 0.297816i) q^{20} +(3.45222 - 1.42728i) q^{21} +(-2.35174 - 0.467790i) q^{22} +(-0.425893 + 0.637394i) q^{23} +(-0.928755 + 4.65306i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(-5.94226 - 2.46136i) q^{26} +(-4.32617 + 2.87824i) q^{27} +(-0.140652 + 0.210501i) q^{28} +(7.83789 + 1.55905i) q^{29} +(2.93834 + 7.10709i) q^{30} +(1.60475 + 2.40167i) q^{31} +(-0.253786 - 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} +(4.67311 - 3.76265i) q^{34} -6.58114i q^{35} +(0.135192 - 0.325163i) q^{36} +(-1.98027 + 1.32318i) q^{37} +(0.888394 + 0.888394i) q^{38} +(-6.36284 - 4.25761i) q^{39} +(6.95033 + 4.64406i) q^{40} +(-0.600791 - 3.02038i) q^{41} +(-3.84624 + 3.84115i) q^{42} +(4.38037 - 10.5751i) q^{43} +(0.189711 - 0.0377359i) q^{44} +(1.77400 + 8.98063i) q^{45} +(0.217619 - 1.09405i) q^{46} +(2.21238 - 2.21238i) q^{47} +(-1.42155 - 7.17143i) q^{48} +(-2.16958 + 0.898671i) q^{49} +6.27299 q^{50} +(6.33153 - 3.30330i) q^{51} +0.518848 q^{52} +(5.88369 - 2.43710i) q^{53} +(4.21317 - 6.27842i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-1.15266 + 5.79482i) q^{56} +(0.830022 + 1.24400i) q^{57} +(-11.4051 + 2.26861i) q^{58} +(-2.33146 + 5.62864i) q^{59} +(-0.438389 - 0.438969i) q^{60} +(-1.14061 - 5.73423i) q^{61} +(-3.49473 - 2.33510i) q^{62} +(-5.38462 + 3.58759i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-11.2145 + 7.49329i) q^{65} +(4.15313 + 0.00274973i) q^{66} +7.19481i q^{67} +(-0.232123 + 0.424684i) q^{68} +(0.508927 - 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(-1.20808 - 1.80802i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(12.3377 + 2.45412i) q^{73} +(1.92538 - 2.88154i) q^{74} +(7.32238 + 1.46155i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(-3.28348 - 1.36006i) q^{77} +(10.9248 + 2.18060i) q^{78} +(-3.31013 + 4.95397i) q^{79} +(-12.6324 - 2.51274i) q^{80} +(6.38079 - 6.34708i) q^{81} +(2.48958 + 3.72592i) q^{82} +(4.96993 + 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +(-1.11620 - 12.5316i) q^{85} +16.6560i q^{86} +(-13.8416 - 0.00916431i) q^{87} +(3.75339 - 2.50793i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(-7.38576 - 11.0853i) q^{90} +(-7.92660 - 5.29638i) q^{91} +(0.0175550 + 0.0882551i) q^{92} +(-3.53529 - 3.53997i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(2.58400 - 0.513989i) q^{95} +(0.637525 + 0.955492i) q^{96} +(-0.692072 + 3.47928i) q^{97} +(2.41627 - 2.41627i) q^{98} +(4.84725 + 0.970853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

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