LMFDB - Embedded newform 51.2.i.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,2,Mod(5,51)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
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			29.4
Character	$\chi$	$=$	51.29
Dual form			51.2.i.a.44.4

$q$-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} +(-0.961322 + 1.44078i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(0.595296 - 2.99276i) q^{5} +(-0.490059 + 2.47224i) q^{6} +(-2.11533 + 0.420765i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-1.15172 - 2.77012i) q^{9} +(-0.866229 - 4.35483i) q^{10} +(-1.37013 - 0.915491i) q^{11} +(0.0397964 + 0.199380i) q^{12} +(3.12551 + 3.12551i) q^{13} +(-2.60946 + 1.74358i) q^{14} +(3.73965 + 3.73470i) 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} +(1.42728 - 3.45222i) q^{21} +(-2.35174 - 0.467790i) q^{22} +(0.425893 - 0.637394i) q^{23} +(-2.63871 - 3.94345i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(5.09831 + 1.00359i) q^{27} +(-0.140652 + 0.210501i) q^{28} +(-7.83789 - 1.55905i) q^{29} +(7.10709 + 2.93834i) 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} +(-0.325520 - 0.134330i) q^{36} +(-1.98027 + 1.32318i) q^{37} +(-0.888394 - 0.888394i) q^{38} +(-7.50782 + 1.49857i) q^{39} +(6.95033 + 4.64406i) q^{40} +(0.600791 + 3.02038i) q^{41} +(-0.00359897 - 5.43581i) q^{42} +(4.38037 - 10.5751i) q^{43} +(-0.189711 + 0.0377359i) q^{44} +(-8.97590 + 1.79778i) q^{45} +(0.217619 - 1.09405i) q^{46} +(-2.21238 + 2.21238i) q^{47} +(-6.08153 - 4.05773i) q^{48} +(-2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +(-2.13226 + 6.81568i) q^{51} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(7.41281 - 1.48981i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(1.15266 - 5.79482i) q^{56} +(1.46694 + 0.290783i) q^{57} +(-11.4051 + 2.26861i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.620386 - 0.000410749i) q^{60} +(-1.14061 - 5.73423i) q^{61} +(3.49473 + 2.33510i) q^{62} +(3.60183 + 5.37510i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(11.2145 - 7.49329i) q^{65} +(2.93476 - 2.93865i) 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} +(8.21831 - 0.0108825i) q^{72} +(12.3377 + 2.45412i) q^{73} +(-1.92538 + 2.88154i) q^{74} +(6.20569 - 4.15245i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(-9.25872 + 6.19535i) q^{78} +(-3.31013 + 4.95397i) q^{79} +(12.6324 + 2.51274i) q^{80} +(-6.34708 + 6.38079i) 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} +(9.78099 - 9.79395i) q^{87} +(3.75339 - 2.50793i) q^{88} +(3.42023 + 3.42023i) q^{89} +(-11.0657 + 7.41510i) q^{90} +(-7.92660 - 5.29638i) q^{91} +(-0.0175550 - 0.0882551i) q^{92} +(-5.00297 + 0.00331239i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(-2.58400 + 0.513989i) q^{95} +(-1.12673 - 0.223345i) q^{96} +(-0.692072 + 3.47928i) q^{97} +(-2.41627 + 2.41627i) q^{98} +(-0.958012 + 4.84981i) 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	0.147147	−	0.989115i	$-0.452991\pi$
$2$	1.34436	−	0.556851i	0.950605	−	0.393753i	0.803458	+	0.595361i	$0.202991\pi$
$3$	−0.961322	+	1.44078i	−0.555020	+	0.831837i
$3$	−0.961322	+	1.44078i	−0.555020	+	0.831837i
$4$	0.0830021	−	0.0830021i	0.0415010	−	0.0415010i
$5$	0.595296	−	2.99276i	0.266225	−	1.33840i	−0.583902	−	0.811824i	$-0.698475\pi$
$5$	0.595296	−	2.99276i	0.266225	−	1.33840i	0.850127	−	0.526578i	$-0.176525\pi$
$6$	−0.490059	+	2.47224i	−0.200066	+	1.00929i
$7$	−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
$9$	−1.15172	−	2.77012i	−0.383906	−	0.923372i
$10$	−0.866229	−	4.35483i	−0.273926	−	1.37712i
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	0.331599	−	0.943420i	$-0.392412\pi$
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	−0.744709	+	0.667389i	$0.767412\pi$
$12$	0.0397964	+	0.199380i	0.0114882	+	0.0575560i
$13$	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
$15$	3.73965	+	3.73470i	0.965572	+	0.964295i
$16$			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
$21$	1.42728	−	3.45222i	0.311458	−	0.753337i
$22$	−2.35174	−	0.467790i	−0.501392	−	0.0997331i
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	−0.784407	−	0.620246i	$-0.787033\pi$
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	0.873212	+	0.487340i	$0.162033\pi$
$24$	−2.63871	−	3.94345i	−0.538624	−	0.804954i
$25$	−3.98282	−	1.64974i	−0.796563	−	0.329947i
$26$	5.94226	+	2.46136i	1.16537	+	0.482713i
$27$	5.09831	+	1.00359i	0.981171	+	0.193142i
$28$	−0.140652	+	0.210501i	−0.0265808	+	0.0397810i
$29$	−7.83789	−	1.55905i	−1.45546	−	0.289509i	−0.596938	−	0.802287i	$-0.703616\pi$
$29$	−7.83789	−	1.55905i	−1.45546	−	0.289509i	−0.858521	+	0.512778i	$0.828616\pi$
$30$	7.10709	+	2.93834i	1.29757	+	0.536466i
$31$	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
$36$	−0.325520	−	0.134330i	−0.0542534	−	0.0223884i
$37$	−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
$39$	−7.50782	+	1.49857i	−1.20221	+	0.239963i
$40$	6.95033	+	4.64406i	1.09894	+	0.734291i
$41$	0.600791	+	3.02038i	0.0938278	+	0.471704i	0.998919	+	0.0464865i	$0.0148024\pi$
$41$	0.600791	+	3.02038i	0.0938278	+	0.471704i	−0.905091	+	0.425218i	$0.860198\pi$
$42$	−0.00359897	−	5.43581i	−0.000555333	−	0.838764i
$43$	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
$45$	−8.97590	+	1.79778i	−1.33805	+	0.267997i
$46$	0.217619	−	1.09405i	0.0320862	−	0.161308i
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	−0.849805	−	0.527097i	$-0.823281\pi$
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	0.527097	+	0.849805i	$0.323281\pi$
$48$	−6.08153	−	4.05773i	−0.877793	−	0.585683i
$49$	−2.16958	+	0.898671i	−0.309940	+	0.128382i
$50$	−6.27299			−0.887135
$51$	−2.13226	+	6.81568i	−0.298576	+	0.954386i
$52$	0.518848			0.0719513
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.748230	−	0.663439i	$-0.769096\pi$
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.0599567	+	0.998201i	$0.519096\pi$
$54$	7.41281	−	1.48981i	1.00876	−	0.202738i
$55$	−3.55548	+	3.55548i	−0.479420	+	0.479420i
$56$	1.15266	−	5.79482i	0.154031	−	0.774365i
$57$	1.46694	+	0.290783i	0.194301	+	0.0385152i
$58$	−11.4051	+	2.26861i	−1.49756	+	0.297884i
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	−0.696356	−	0.717696i	$-0.745197\pi$
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	0.999886	−	0.0150898i	$-0.00480343\pi$
$60$	0.620386		0.000410749i	0.0800915		5.30274e-5i
$61$	−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
$63$	3.60183	+	5.37510i	0.453788	+	0.677199i
$64$	−5.28702	−	5.28702i	−0.660877	−	0.660877i
$65$	11.2145	−	7.49329i	1.39099	−	0.929429i
$66$	2.93476	−	2.93865i	0.361244	−	0.361723i
$67$			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	0.896205	−	0.443639i	$-0.146313\pi$
$71$	1.20808	+	1.80802i	0.143373	+	0.214573i	−0.752832	+	0.658212i	$0.771313\pi$
$72$	8.21831	−	0.0108825i	0.968537	−	0.00128251i
$73$	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
$75$	6.20569	−	4.15245i	0.716571	−	0.479484i
$76$	−0.0936354	−	0.0387851i	−0.0107407	−	0.00444895i
$77$	3.28348	+	1.36006i	0.374187	+	0.154994i
$78$	−9.25872	+	6.19535i	−1.04834	+	0.701485i
$79$	−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
$81$	−6.34708	+	6.38079i	−0.705232	+	0.708977i
$82$	2.48958	+	3.72592i	0.274928	+	0.411459i
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	−0.920779	−	0.390084i	$-0.872446\pi$
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	0.375258	−	0.926920i	$-0.377554\pi$
$84$	−0.168074	−	0.405009i	−0.0183384	−	0.0441901i
$85$	−1.11620	−	12.5316i	−0.121069	−	1.35924i
$86$		−	16.6560i		−	1.79606i
$87$	9.78099	−	9.79395i	1.04863	−	1.05002i
$88$	3.75339	−	2.50793i	0.400112	−	0.267347i
$89$	3.42023	+	3.42023i	0.362544	+	0.362544i	0.864749	−	0.502205i	$-0.167478\pi$
$89$	3.42023	+	3.42023i	0.362544	+	0.362544i	−0.502205	+	0.864749i	$0.667478\pi$
$90$	−11.0657	+	7.41510i	−1.16643	+	0.781620i
$91$	−7.92660	−	5.29638i	−0.830933	−	0.555212i
$92$	−0.0175550	−	0.0882551i	−0.00183024	−	0.00920123i
$93$	−5.00297	+	0.00331239i	−0.518783	+	0.000343479i
$94$	−1.74226	+	4.20619i	−0.179701	+	0.433836i
$95$	−2.58400	+	0.513989i	−0.265113	+	0.0527342i
$96$	−1.12673	−	0.223345i	−0.114996	−	0.0227951i
$97$	−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
$99$	−0.958012	+	4.84981i	−0.0962839	+	0.487424i
$100$	−0.467514	+	0.193650i	−0.0467514	+	0.0193650i
$101$	−3.73948			−0.372092			−0.186046	−	0.982541i	$-0.559567\pi$
$101$	−3.73948			−0.372092			−0.186046	+	0.982541i	$0.559567\pi$
$102$	0.928799	+	10.3501i	0.0919648	+	1.02481i
$103$	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
$105$	−9.48201	−	6.32660i	−0.925350	−	0.617413i
$106$	−6.55268	+	6.55268i	−0.636453	+	0.636453i
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	−0.994506	−	0.104675i	$-0.966620\pi$
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	0.958862	+	0.283874i	$0.0916198\pi$
$108$	0.506471	−	0.339870i	0.0487352	−	0.0327040i
$109$	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
$111$	−0.00273120	−	4.12515i	−0.000259234	−	0.391542i
$112$	−1.77604	−	8.92878i	−0.167820	−	0.843690i
$113$	13.7072	+	9.15888i	1.28947	+	0.861595i	0.995550	−	0.0942363i	$-0.0300409\pi$
$113$	13.7072	+	9.15888i	1.28947	+	0.861595i	0.293917	+	0.955831i	$0.405041\pi$
$114$	2.13402	−	0.425951i	0.199869	−	0.0398940i
$115$	−1.65403	−	1.65403i	−0.154239	−	0.154239i
$116$	−0.779965	+	0.521156i	−0.0724180	+	0.0483881i
$117$	5.05832	−	12.2577i	0.467642	−	1.13323i
$118$		−	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
$123$	−4.92927	−	2.03795i	−0.444457	−	0.183756i
$124$	0.332541	+	0.0661465i	0.0298630	+	0.00594013i
$125$	1.16808	−	1.74816i	0.104477	−	0.156360i
$126$	7.83529	+	5.22038i	0.698023	+	0.465068i
$127$	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
$129$	11.0256	+	16.4773i	0.970746	+	1.45074i
$130$	10.9037	−	16.3185i	0.956315	−	1.43123i
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	0.0416661	−	0.999132i	$-0.486733\pi$
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	−0.343857	+	0.939022i	$0.611733\pi$
$132$	0.128004	−	0.309609i	0.0111413	−	0.0269480i
$133$	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	$0.215206\pi$
$137$			14.6484i			1.25150i	−0.780025	+	0.625748i	$0.784794\pi$
$138$	1.36708	+	1.36527i	0.116374	+	0.116220i
$139$	−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
$141$	−1.06075	−	5.31437i	−0.0893314	−	0.447550i
$142$	2.63090	+	1.75791i	0.220780	+	0.147520i
$143$	−1.42098	−	7.14374i	−0.118828	−	0.597389i
$144$	11.6926	−	4.86139i	0.974385	−	0.405116i
$145$	−9.33173	+	22.5288i	−0.774958	+	1.87091i
$146$	17.9529	−	3.57105i	1.48579	−	0.295542i
$147$	0.790878	−	3.98981i	0.0652305	−	0.329074i
$148$	−0.0545404	+	0.274193i	−0.00448319	+	0.0225385i
$149$	4.44785	−	4.44785i	0.364382	−	0.364382i	−0.501041	−	0.865423i	$-0.667050\pi$
$149$	4.44785	−	4.44785i	0.364382	−	0.364382i	0.865423	+	0.501041i	$0.167050\pi$
$150$	6.03037	−	9.03803i	0.492377	−	0.737952i
$151$	−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
$153$	−7.77013	−	9.62419i	−0.628178	−	0.778070i
$154$	5.17153			0.416734
$155$	8.14291	−	3.37291i	0.654055	−	0.270918i
$156$	−0.498780	+	0.747548i	−0.0399344	+	0.0598518i
$157$	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
$159$	2.14478	−	10.8200i	0.170092	−	0.858080i
$160$	1.98472	−	0.394786i	0.156906	−	0.0312105i
$161$	−0.632711	+	1.52750i	−0.0498646	+	0.120384i
$162$	−4.97960	+	12.1125i	−0.391235	+	0.951644i
$163$	−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
$165$	−1.70472	−	8.54063i	−0.132712	−	0.664887i
$166$	−13.3627	−	13.3627i	−1.03715	−	1.03715i
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.994452	−	0.105195i	$-0.966453\pi$
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.283373	+	0.959010i	$0.591453\pi$
$168$	7.24100	+	7.23142i	0.558655	+	0.557916i
$169$			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	0.991453	−	0.130465i	$-0.0416470\pi$
$173$	6.46476	+	9.67520i	0.491507	+	0.735591i	−0.499946	+	0.866056i	$0.666647\pi$
$174$	7.69538	−	18.6131i	0.583385	−	1.41106i
$175$	9.11912	+	1.81391i	0.689341	+	0.137118i
$176$	3.86428	−	5.78330i	0.291281	−	0.435933i
$177$	5.86837	+	8.77006i	0.441094	+	0.659198i
$178$	6.50257	+	2.69345i	0.487389	+	0.201883i
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	0.353259	−	0.935526i	$-0.385073\pi$
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	−0.411725	+	0.911308i	$0.635073\pi$
$180$	−0.595799	+	0.894237i	−0.0444082	+	0.0666525i
$181$	−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
$183$	9.35828	+	3.86907i	0.691784	+	0.286010i
$184$	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
$189$	−11.2069	+	0.0222598i	−0.815181	+	0.00161916i
$190$	−3.18760	+	2.12989i	−0.231253	+	0.154518i
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	0.725312	−	0.688420i	$-0.241696\pi$
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	−0.688420	+	0.725312i	$0.741696\pi$
$192$	12.7000	−	2.53493i	0.916542	−	0.182942i
$193$	−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
$195$	0.0154671	+	23.3612i	0.00110762	+	1.67293i
$196$	−0.105488	+	0.254671i	−0.00753488	+	0.0181908i
$197$	−22.8170	+	4.53858i	−1.62564	+	0.323360i	−0.921999	−	0.387193i	$-0.873445\pi$
$197$	−22.8170	+	4.53858i	−1.62564	+	0.323360i	−0.703643	+	0.710553i	$0.748445\pi$
$198$	1.41271	+	7.05335i	0.100397	+	0.501260i
$199$	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
$201$	−10.3662	−	6.91653i	−0.731173	−	0.487854i
$202$	−5.02720	+	2.08233i	−0.353712	+	0.146512i
$203$	17.2357			1.20971
$204$	0.388733	+	0.742697i	0.0272168	+	0.0519992i
$205$	9.39691			0.656309
$206$	12.5483	−	5.19767i	0.874281	−	0.362139i
$207$	−2.25617	−	0.445674i	−0.156814	−	0.0309765i
$208$	−13.1927	+	13.1927i	−0.914753	+	0.914753i
$209$	−0.277570	+	1.39544i	−0.0191999	+	0.0965244i
$210$	−16.2702	−	3.22515i	−1.12275	−	0.222556i
$211$	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
$213$	−3.76633	+	0.00249363i	−0.258065	+	0.000170861i
$214$	0.536524	+	2.69729i	0.0366760	+	0.184383i
$215$	−29.0412	−	19.4047i	−1.98059	−	1.32339i
$216$	−7.88477	+	11.8513i	−0.536490	+	0.806377i
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$	5.08520	−	3.39782i	0.344413	−	0.230130i
$219$	−15.3964	+	15.4168i	−1.04039	+	1.04177i
$220$			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
$225$	0.0171254	+	12.9329i	0.00114169	+	0.862193i
$226$	23.5276	+	4.67992i	1.56503	+	0.311304i
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	−0.856460	−	0.516214i	$-0.827341\pi$
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	0.804673	+	0.593719i	$0.202341\pi$
$228$	0.145895	−	0.0976235i	0.00966211	−	0.00646527i
$229$	−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
$231$	−5.11604	+	3.42333i	−0.336611	+	0.225239i
$232$	12.1626	−	18.2026i	0.798513	−	1.19506i
$233$	14.0608	+	2.79686i	0.921151	+	0.183228i	0.632817	−	0.774302i	$-0.281899\pi$
$233$	14.0608	+	2.79686i	0.921151	+	0.183228i	0.288334	+	0.957530i	$0.406899\pi$
$234$	−0.0255506	−	19.2955i	−0.00167030	−	1.26139i
$235$	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	$-0.721842\pi$
$239$		−	23.7093i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$240$	−15.7641	+	15.7850i	−1.01757	+	1.01892i
$241$	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
$243$	−3.09175	−	15.2788i	−0.198336	−	0.980134i
$244$	−0.570626	−	0.381280i	−0.0365306	−	0.0244090i
$245$	1.39796	+	7.02801i	0.0893123	+	0.449003i
$246$	−7.76154	+	0.00513881i	−0.494858	+	0.000327638i
$247$	1.46048	−	3.52592i	0.0929284	−	0.224349i
$248$	−7.76073	+	1.54371i	−0.492807	+	0.0980254i
$249$	22.0649	+	4.37380i	1.39831	+	0.277178i
$250$	0.596858	−	3.00061i	0.0377486	−	0.189775i
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	−0.283289	−	0.959034i	$-0.591426\pi$
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	0.959034	+	0.283289i	$0.0914257\pi$
$252$	0.745104	+	0.147185i	0.0469372	+	0.00927179i
$253$	−1.16706	+	0.483411i	−0.0733723	+	0.0303918i
$254$	17.9162			1.12416
$255$	19.1283	+	10.4387i	1.19786	+	0.653696i
$256$	−2.80767			−0.175479
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.273145	−	0.961973i	$-0.411936\pi$
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.873360	+	0.487075i	$0.161936\pi$
$258$	23.9977	+	16.0118i	1.49403	+	0.996850i
$259$	3.63218	−	3.63218i	0.225693	−	0.225693i
$260$	0.308868	−	1.55279i	0.0191552	−	0.0962997i
$261$	4.70829	+	23.5074i	0.291436	+	1.45507i
$262$	−5.03288	+	1.00110i	−0.310932	+	0.0618482i
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	−0.925419	−	0.378946i	$-0.876287\pi$
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	0.922325	+	0.386415i	$0.126287\pi$
$264$	0.00517669	+	7.81875i	0.000318603	+	0.481211i
$265$	3.79112	+	19.0593i	0.232887	+	1.17080i
$266$	2.25305	+	1.50544i	0.138143	+	0.0923045i
$267$	−8.21576	+	1.63987i	−0.502796	+	0.100358i
$268$	0.597184	+	0.597184i	0.0364788	+	0.0364788i
$269$	4.94355	−	3.30317i	0.301413	−	0.201398i	−0.395661	−	0.918396i	$-0.629485\pi$
$269$	4.94355	−	3.30317i	0.301413	−	0.201398i	0.697075	+	0.716999i	$0.254485\pi$
$270$	−0.0458262	−	23.0716i	−0.00278890	−	1.40409i
$271$		−	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
$276$	0.144033	+	0.0595485i	0.00866974	+	0.00358440i
$277$	−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
$279$	4.80469	−	7.21138i	0.287649	−	0.431734i
$280$	−16.6563	−	6.89927i	−0.995404	−	0.412310i
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.0135893	−	0.999908i	$-0.504326\pi$
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.716651	+	0.697432i	$0.754326\pi$
$282$	−4.38534	−	6.55373i	−0.261143	−	0.390269i
$283$	−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
$285$	1.74351	−	4.21709i	0.103276	−	0.249799i
$286$	−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
$291$	−4.34759	−	4.34183i	−0.254860	−	0.254523i
$292$	1.22775	−	0.820357i	0.0718487	−	0.0480078i
$293$	−18.6721	−	18.6721i	−1.09083	−	1.09083i	−0.995440	−	0.0953949i	$-0.969589\pi$
$293$	−18.6721	−	18.6721i	−1.09083	−	1.09083i	−0.0953949	−	0.995440i	$-0.530411\pi$
$294$	−1.15851	−	5.80414i	−0.0675657	−	0.338504i
$295$	−15.4572	−	10.3282i	−0.899955	−	0.601331i
$296$	−1.27285	−	6.39904i	−0.0739827	−	0.371936i
$297$	−6.06657	−	6.04252i	−0.352018	−	0.350622i
$298$	3.50271	−	8.45629i	0.202907	−	0.489860i
$299$	3.32332	−	0.661049i	0.192193	−	0.0382295i
$300$	0.170423	−	0.859747i	0.00983935	−	0.0496375i
$301$	−4.81627	+	24.2130i	−0.277605	+	1.39561i
$302$	−15.6531	+	15.6531i	−0.900738	+	0.900738i
$303$	3.59484	−	5.38778i	0.206518	−	0.309520i
$304$	3.36705	−	1.39468i	0.193114	−	0.0799904i
$305$	−17.8402			−1.02152
$306$	−15.8051	−	8.61155i	−0.903517	−	0.492289i
$307$	−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
$309$	−8.97302	+	13.4483i	−0.510457	+	0.765049i
$310$	9.06879	−	9.06879i	0.515073	−	0.515073i
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	0.606340	+	0.795206i	$0.292637\pi$
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	−0.864497	+	0.502638i	$0.832363\pi$
$312$	4.07799	−	20.5726i	0.230871	−	1.16470i
$313$	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
$315$	18.2305	−	7.57963i	1.02717	−	0.427064i
$316$	0.136441	+	0.685937i	0.00767543	+	0.0385870i
$317$	−20.2754	−	13.5476i	−1.13878	−	0.760908i	−0.164528	−	0.986372i	$-0.552610\pi$
$317$	−20.2754	−	13.5476i	−1.13878	−	0.760908i	−0.974251	+	0.225464i	$0.927610\pi$
$318$	−3.14176	−	15.7402i	−0.176181	−	0.882669i
$319$	9.31162	+	9.31162i	0.521351	+	0.521351i
$320$	−18.9701	+	12.6754i	−1.06046	+	0.708577i
$321$	−2.31626	−	2.31319i	−0.129281	−	0.129110i
$322$			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
$327$	−2.78143	+	6.72755i	−0.153813	+	0.372034i
$328$	−8.27415	−	1.64583i	−0.456863	−	0.0908758i
$329$	3.74901	−	5.61080i	0.206690	−	0.309333i
$330$	−7.04761	−	10.5324i	−0.387958	−	0.579789i
$331$	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
$333$	5.94607	+	3.96166i	0.325843	+	0.217098i
$334$	−16.0554	+	24.0286i	−0.878514	+	1.31479i
$335$	21.5323	+	4.28304i	1.17644	+	0.234008i
$336$	14.5718	+	6.02453i	0.794956	+	0.328665i
$337$	−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
$342$	−1.43777	+	3.48413i	−0.0777459	+	0.188400i
$343$	16.7643	−	11.2015i	0.905186	−	0.604826i
$344$	22.1727	+	22.1727i	1.19547	+	1.19547i
$345$	3.97317	−	0.793047i	0.213908	−	0.0426962i
$346$	14.0786	+	9.40702i	0.756870	+	0.505724i
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	0.929476	+	0.368884i	$0.120260\pi$
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	−0.717558	+	0.696499i	$0.754740\pi$
$348$	−0.00107573	−	1.62476i	−5.76652e−5	−	0.0870963i
$349$	−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
$351$	12.7981	+	19.0716i	0.683112	+	1.01797i
$352$	0.213196	−	1.07181i	0.0113634	−	0.0571276i
$353$	−8.44344	+	8.44344i	−0.449399	+	0.449399i	−0.895155	−	0.445756i	$-0.852935\pi$
$353$	−8.44344	+	8.44344i	−0.449399	+	0.449399i	0.445756	+	0.895155i	$0.352935\pi$
$354$	12.7728	+	8.52230i	0.678867	+	0.452955i
$355$	6.13014	−	2.53919i	0.325354	−	0.134766i
$356$	0.567772			0.0300919
$357$	1.64263	−	15.3146i	0.0869373	−	0.810534i
$358$	−1.23200			−0.0651133
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.864839	−	0.502049i	$-0.832580\pi$
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.256531	+	0.966536i	$0.582580\pi$
$360$	4.85976	−	24.6019i	0.256132	−	1.29663i
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$	−0.407040	+	2.04633i	−0.0213935	+	0.107553i
$363$	14.0755	+	2.79011i	0.738773	+	0.146443i
$364$	−1.09753	+	0.218313i	−0.0575264	+	0.0114427i
$365$	14.6892	−	35.4628i	0.768866	−	1.85621i
$366$	14.7354	−	0.00975609i	0.770231	−	0.000509959i
$367$	−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
$369$	7.67486	−	5.14289i	0.399537	−	0.267728i
$370$	7.47758	+	7.47758i	0.388741	+	0.388741i
$371$	11.4205	−	7.63093i	0.592923	−	0.396178i
$372$	−0.414982	+	0.415531i	−0.0215158	+	0.0215443i
$373$			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
$378$	−15.0537	+	6.27050i	−0.774278	+	0.322520i
$379$	−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
$381$	−17.7240	+	11.8598i	−0.908027	+	0.607594i
$382$	0.969330	+	0.401510i	0.0495952	+	0.0205430i
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.838247	−	0.545291i	$-0.183581\pi$
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.207151	+	0.978309i	$0.433581\pi$
$384$	17.5710	−	11.7574i	0.896668	−	0.599994i
$385$	6.02498	−	9.01702i	0.307061	−	0.459550i
$386$	−16.5858	−	3.29912i	−0.844194	−	0.167921i
$387$	−34.3393	+	0.0454712i	−1.74557	+	0.00231143i
$388$	0.231344	+	0.346231i	0.0117447	+	0.0175772i
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	0.999998	+	0.00207747i	$0.000661280\pi$
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	−0.705636	+	0.708574i	$0.749339\pi$
$390$	13.0295	+	31.3972i	0.659774	+	1.58986i
$391$	0.945713	−	3.01592i	0.0478268	−	0.152522i
$392$		−	6.43314i		−	0.324922i
$393$	4.31619	−	4.32191i	0.217723	−	0.218011i
$394$	−28.1469	+	18.8071i	−1.41802	+	0.947490i
$395$	12.8555	+	12.8555i	0.646831	+	0.646831i
$396$	0.323027	+	0.482061i	0.0162327	+	0.0242245i
$397$	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
$399$	−3.22541	+	0.00213550i	−0.161473	+	0.000106909i
$400$	6.96352	−	16.8114i	0.348176	−	0.840571i
$401$	3.46595	−	0.689420i	0.173081	−	0.0344280i	−0.107789	−	0.994174i	$-0.534377\pi$
$401$	3.46595	−	0.689420i	0.173081	−	0.0344280i	0.280870	+	0.959746i	$0.409377\pi$
$402$	−17.7873	−	3.52588i	−0.887151	−	0.175855i
$403$	−2.49080	+	12.5221i	−0.124076	+	0.623770i
$404$	−0.310384	+	0.310384i	−0.0154422	+	0.0154422i
$405$	15.3178	+	22.7937i	0.761146	+	1.13263i
$406$	23.1710	−	9.59773i	1.14996	−	0.476327i
$407$	3.92459			0.194535
$408$	−15.0146	−	12.5417i	−0.743331	−	0.620907i
$409$	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
$411$	−21.1052	−	14.0818i	−1.04104	−	0.694605i
$412$	0.774744	−	0.774744i	0.0381689	−	0.0381689i
$413$	−2.56347	+	12.8874i	−0.126140	+	0.634148i
$414$	−3.28127	+	0.657203i	−0.161266	+	0.0322998i
$415$	−38.8671	+	7.73115i	−1.90791	+	0.379507i
$416$	−1.12177	+	2.70819i	−0.0549993	+	0.132780i
$417$	−0.00578500	−	8.73753i	−0.000283293	−	0.427879i
$418$	0.403898	+	2.03053i	0.0197553	+	0.0993165i
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.994187	−	0.107670i	$-0.0343389\pi$
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.280985	+	0.959712i	$0.409339\pi$
$420$	−1.31215	+	0.261906i	−0.0640262	+	0.0127797i
$421$	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
$423$	8.67658	+	3.58050i	0.421870	+	0.174090i
$424$		−	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
$429$	11.6586	+	4.82011i	0.562883	+	0.232717i
$430$	−49.8473	−	9.91525i	−2.40385	−	0.478156i
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	−0.952464	−	0.304652i	$-0.901460\pi$
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	0.645954	+	0.763376i	$0.276460\pi$
$432$	−4.23616	+	21.5199i	−0.203812	+	1.03538i
$433$	−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
$435$	−23.4883	−	35.1024i	−1.12618	−	1.68303i
$436$	0.274097	−	0.410216i	0.0131269	−	0.0196458i
$437$	−0.649167	−	0.129127i	−0.0310539	−	0.00617700i
$438$	−12.1134	+	29.2991i	−0.578799	+	1.39997i
$439$	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	$-0.851979\pi$
$443$		−	18.8773i		−	0.896886i	0.893811	−	0.448443i	$-0.148021\pi$
$444$	−0.342622	−	0.342169i	−0.0162601	−	0.0162386i
$445$	12.2720	−	8.19987i	0.581747	−	0.388711i
$446$	2.50244	+	2.50244i	0.118494	+	0.118494i
$447$	2.13257	+	10.6842i	0.100867	+	0.505345i
$448$	13.4084	+	8.95919i	0.633486	+	0.423282i
$449$	−5.31908	−	26.7408i	−0.251023	−	1.26198i	−0.876373	−	0.481633i	$-0.840044\pi$
$449$	−5.31908	−	26.7408i	−0.251023	−	1.26198i	0.625350	−	0.780345i	$-0.284956\pi$
$450$	7.22473	+	17.3769i	0.340577	+	0.819156i
$451$	1.94197	−	4.68833i	0.0914438	−	0.220765i
$452$	1.89793	−	0.377522i	0.0892713	−	0.0177572i
$453$	5.12348	−	25.8469i	0.240722	−	1.21439i
$454$	−0.398685	+	2.00433i	−0.0187112	+	0.0940677i
$455$	−20.5695	+	20.5695i	−0.964311	+	0.964311i
$456$	−2.27380	+	3.40786i	−0.106480	+	0.159588i
$457$	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
$459$	21.3360	−	1.94314i	0.995878	−	0.0906981i
$460$	−0.274576			−0.0128022
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	−0.585112	−	0.810952i	$-0.698950\pi$
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	0.159693	+	0.987167i	$0.448950\pi$
$462$	−4.97150	+	7.45106i	−0.231295	+	0.346655i
$463$	−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
$465$	−2.96833	+	14.9746i	−0.137653	+	0.694432i
$466$	20.4601	−	4.06977i	0.947797	−	0.188529i
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	0.511621	+	0.859211i	$0.329045\pi$
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	−0.969325	+	0.245783i	$0.920955\pi$
$468$	−0.597567	−	1.43727i	−0.0276226	−	0.0664378i
$469$	−3.02732	−	15.2194i	−0.139789	−	0.702766i
$470$	11.5509	+	7.71810i	0.532806	+	0.356009i
$471$	0.836789	+	4.19231i	0.0385572	+	0.193172i
$472$	11.8014	+	11.8014i	0.543205	+	0.543205i
$473$	−15.6831	+	10.4791i	−0.721111	+	0.481831i
$474$	−10.6253	−	10.6112i	−0.488034	−	0.487388i
$475$			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	0.924992	−	0.379987i	$-0.124072\pi$
$479$	4.81385	+	7.20443i	0.219950	+	0.329179i	−0.705041	+	0.709166i	$0.749072\pi$
$480$	−1.33916	+	3.23907i	−0.0611238	+	0.147843i
$481$	−10.3250	−	2.05377i	−0.470778	−	0.0936437i
$482$	2.27521	−	3.40509i	0.103633	−	0.155098i
$483$	−1.59256	−	2.38002i	−0.0724639	−	0.108295i
$484$	−0.898446	−	0.372148i	−0.0408384	−	0.0169158i
$485$	10.0006	+	4.14240i	0.454106	+	0.188097i
$486$	−12.6644	−	18.8185i	−0.574470	−	0.853625i
$487$	−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
$489$	1.77812	+	0.735143i	0.0804094	+	0.0332443i
$490$	5.79291	+	8.66971i	0.261697	+	0.391658i
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	0.775882	−	0.630878i	$-0.217305\pi$
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	−0.994730	+	0.102533i	$0.967305\pi$
$492$	−0.578293	+	0.239986i	−0.0260715	+	0.0108194i
$493$	−32.8196	+	2.92328i	−1.47812	+	0.131658i
$494$		−	5.55337i		−	0.249858i
$495$	13.9440	+	5.75417i	0.626736	+	0.258631i
$496$	−10.1374	+	6.77361i	−0.455184	+	0.304144i
$497$	−3.31625	−	3.31625i	−0.148754	−	0.148754i
$498$	32.0987	−	6.40693i	1.43838	−	0.287101i
$499$	−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
$501$	−0.0227750	−	34.3988i	−0.00101751	−	1.53683i
$502$	8.43090	−	20.3540i	0.376290	−	0.908444i
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.561650	−	0.827375i	$-0.310167\pi$
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.835520	+	0.549460i	$0.185167\pi$
$504$	−17.3799	+	3.48100i	−0.774160	+	0.155056i
$505$	−2.22610	+	11.1913i	−0.0990600	+	0.498008i
$506$	−1.29976	+	1.29976i	−0.0577812	+	0.0577812i
$507$	−9.41937	−	6.28480i	−0.418329	−	0.279118i
$508$	1.33526	−	0.553083i	0.0592426	−	0.0245391i
$509$	2.30289			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$509$	2.30289			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$510$	31.5281	+	3.38169i	1.39609	+	0.149744i
$511$	−27.1309			−1.20020
$512$	18.7797	−	7.77882i	0.829954	−	0.343778i
$513$	−0.884001	−	4.39850i	−0.0390296	−	0.194198i
$514$	20.4697	−	20.4697i	0.902880	−	0.902880i
$515$	5.55652	−	27.9345i	0.244849	−	1.23094i
$516$	2.28279	+	0.452505i	0.100494	+	0.0199204i
$517$	5.05666	−	1.00583i	0.222391	−	0.0442364i
$518$	2.86037	−	6.90554i	0.125677	−	0.303412i
$519$	−20.1546	+	0.0133441i	−0.884688	+	0.000585740i
$520$	7.20827	+	36.2384i	0.316104	+	1.58916i
$521$	2.28875	+	1.52929i	0.100272	+	0.0669995i	0.604695	−	0.796457i	$-0.293295\pi$
$521$	2.28875	+	1.52929i	0.100272	+	0.0669995i	−0.504423	+	0.863456i	$0.668295\pi$
$522$	19.4198	+	28.9806i	0.849981	+	1.26845i
$523$	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
$525$	−11.3799	+	11.3949i	−0.496658	+	0.497316i
$526$			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
$531$	−18.2772	+	0.0242021i	−0.793161	+	0.00105028i
$532$	0.214389	+	0.0426446i	0.00929494	+	0.00184888i
$533$	−7.56246	+	11.3180i	−0.327566	+	0.490238i
$534$	−10.1318	+	6.77953i	−0.438444	+	0.293379i
$535$	5.32803	+	2.20694i	0.230351	+	0.0954144i
$536$	−18.2094	−	7.54259i	−0.786527	−	0.325790i
$537$	1.21878	−	0.815532i	0.0525943	−	0.0351928i
$538$	4.80652	−	7.19347i	0.207224	−	0.310132i
$539$	3.79534	+	0.754939i	0.163477	+	0.0325175i
$540$	−0.715648	−	1.71807i	−0.0307966	−	0.0739339i
$541$	−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
$546$	16.9784	−	17.0009i	0.726610	−	0.727573i
$547$	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
$549$	−14.5708	+	9.76385i	−0.621868	+	0.416711i
$550$	8.59481	+	5.74287i	0.366484	+	0.244877i
$551$	1.34611	+	6.76737i	0.0573464	+	0.288300i
$552$	−3.63734	+	0.00240823i	−0.154816	+	0.000102501i
$553$	4.91757	−	11.8721i	0.209116	−	0.504851i
$554$	−11.8417	+	2.35547i	−0.503107	+	0.100074i
$555$	−12.3472	−	2.44751i	−0.524109	−	0.103891i
$556$	−0.115523	+	0.580773i	−0.00489926	+	0.0246302i
$557$	31.0707	−	31.0707i	1.31651	−	1.31651i	0.399984	−	0.916522i	$-0.369016\pi$
$557$	31.0707	−	31.0707i	1.31651	−	1.31651i	0.916522	−	0.399984i	$-0.130984\pi$
$558$	2.44356	−	12.3702i	0.103444	−	0.523671i
$559$	46.7436	−	19.3619i	1.97705	−	0.818919i
$560$	−27.7789			−1.17387
$561$	9.16117	−	7.38630i	0.386785	−	0.311850i
$562$	−19.2798			−0.813270
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.957080	−	0.289825i	$-0.906403\pi$
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.471821	+	0.881695i	$0.656403\pi$
$564$	−0.529148	−	0.353059i	−0.0222811	−	0.0148665i
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$	−3.98370	+	20.0274i	−0.167448	+	0.841815i
$567$	10.7414	−	16.1681i	0.451095	−	0.678997i
$568$	−5.84243	+	1.16213i	−0.245143	+	0.0487620i
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	0.591472	+	0.806326i	$0.298547\pi$
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	−0.988392	+	0.151925i	$0.951453\pi$
$570$	−0.00439636	−	6.64016i	−0.000184143	−	0.278126i
$571$	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
$573$	−1.22471	+	0.244453i	−0.0511631	+	0.0102122i
$574$	−6.83402	−	6.83402i	−0.285247	−	0.285247i
$575$	−2.74779	+	1.83601i	−0.114591	+	0.0765671i
$576$	−8.55649	+	20.7348i	−0.356520	+	0.863951i
$577$			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
$582$	−8.26247	−	3.41602i	−0.342490	−	0.141599i
$583$	10.2926	+	2.04732i	0.426275	+	0.0847913i
$584$	−19.1452	+	28.6529i	−0.792235	+	1.18566i
$585$	−33.6733	−	22.4353i	−1.39222	−	0.927586i
$586$	−35.4995	−	14.7044i	−1.46647	−	0.607433i
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.999994	−	0.00334911i	$-0.00106606\pi$
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.704735	+	0.709471i	$0.251066\pi$
$588$	−0.265518	−	0.396807i	−0.0109498	−	0.0163641i
$589$	1.38557	−	2.07364i	0.0570912	−	0.0854430i
$590$	−26.5313	−	5.27741i	−1.09228	−	0.217268i
$591$	15.3953	−	37.2374i	0.633280	−	1.53174i
$592$	−5.58511	−	8.35871i	−0.229547	−	0.343541i
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	0.996993	+	0.0774935i	$0.0246917\pi$
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	−0.650184	+	0.759777i	$0.725308\pi$
$594$	−11.5204	−	4.74513i	−0.472689	−	0.194695i
$595$	7.63399	+	26.0388i	0.312963	+	1.06749i
$596$		−	0.738361i		−	0.0302444i
$597$	29.5540	+	29.5149i	1.20956	+	1.20796i
$598$	4.09963	−	2.73928i	0.167646	−	0.112018i
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	0.270729	−	0.962655i	$-0.412735\pi$
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	−0.962655	+	0.270729i	$0.912735\pi$
$600$	4.00384	+	20.0592i	0.163456	+	0.818914i
$601$	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
$603$	19.9304	−	8.28640i	0.811630	−	0.337448i
$604$	−0.683377	+	1.64982i	−0.0278062	+	0.0671302i
$605$	−24.7939	+	4.93180i	−1.00801	+	0.200506i
$606$	1.83256	−	9.24490i	0.0744428	−	0.375548i
$607$	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
$609$	−16.5691	+	24.8329i	−0.671412	+	1.00628i
$610$	−23.9836	+	9.93432i	−0.971066	+	0.402229i
$611$	−13.8296			−0.559487
$612$	−1.44376	−	0.153890i	−0.0583607	−	0.00622065i
$613$	−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
$615$	−9.03346	+	13.5389i	−0.364264	+	0.545942i
$616$	−6.88440	+	6.88440i	−0.277380	+	0.277380i
$617$	1.92552	−	9.68025i	0.0775186	−	0.389712i	−0.922475	−	0.386057i	$-0.873837\pi$
$617$	1.92552	−	9.68025i	0.0775186	−	0.389712i	0.999993	−	0.00365472i	$-0.00116334\pi$
$618$	−4.57422	+	23.0760i	−0.184002	+	0.928253i
$619$	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
$621$	2.81102	−	2.82221i	0.112802	−	0.113251i
$622$	6.62467	+	33.3044i	0.265625	+	1.33539i
$623$	−8.67402	−	5.79580i	−0.347517	−	0.232204i
$624$	−6.32543	−	31.6904i	−0.253220	−	1.26863i
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$	1.95352	−	1.30530i	0.0780785	−	0.0521704i
$627$	−1.74369	−	1.74138i	−0.0696362	−	0.0695441i
$628$		−	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
$633$	−10.3302	+	24.9860i	−0.410587	+	0.993104i
$634$	−34.8014	−	6.92242i	−1.38214	−	0.274925i
$635$	20.8729	−	31.2385i	0.828316	−	1.23966i
$636$	−0.720059	−	1.07610i	−0.0285522	−	0.0426702i
$637$	−9.58987	−	3.97225i	−0.379964	−	0.157386i
$638$	17.7033	+	7.33297i	0.700882	+	0.290315i
$639$	3.61706	−	5.42887i	0.143089	−	0.214763i
$640$	−20.6928	+	30.9690i	−0.817955	+	1.22416i
$641$	−36.7015	−	7.30038i	−1.44962	−	0.288348i	−0.593380	−	0.804922i	$-0.702207\pi$
$641$	−36.7015	−	7.30038i	−1.44962	−	0.288348i	−0.856242	+	0.516575i	$0.827207\pi$
$642$	−4.40198	−	1.81995i	−0.173732	−	0.0718276i
$643$	−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	$0.399005\pi$
$647$			48.3331i			1.90017i	−0.311989	+	0.950086i	$0.600995\pi$
$648$	−9.49533	−	22.7531i	−0.373012	−	0.893828i
$649$	−8.34737	+	5.57753i	−0.327663	+	0.218937i
$650$	−19.6063	−	19.6063i	−0.769023	−	0.769023i
$651$	10.5815	−	2.11208i	0.414723	−	0.0827790i
$652$	−0.108422	−	0.0724451i	−0.00424613	−	0.00283717i
$653$	−1.26227	−	6.34586i	−0.0493965	−	0.248333i	0.948196	−	0.317687i	$-0.102906\pi$
$653$	−1.26227	−	6.34586i	−0.0493965	−	0.248333i	−0.997592	+	0.0693542i	$0.977906\pi$
$654$	0.00701353	+	10.5931i	0.000274251	+	0.414222i
$655$	−4.11794	+	9.94158i	−0.160901	+	0.388450i
$656$	−12.7490	+	2.53593i	−0.497764	+	0.0990114i
$657$	−7.41136	−	37.0033i	−0.289145	−	1.44364i
$658$	1.91564	−	9.63056i	0.0746794	−	0.375439i
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	−0.272610	−	0.962125i	$-0.587887\pi$
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	0.962125	+	0.272610i	$0.0878869\pi$
$660$	−0.850385	−	0.567395i	−0.0331012	−	0.0220858i
$661$	−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
$663$	−27.9669	+	14.6381i	−1.08614	+	0.568496i
$664$	35.5773			1.38067
$665$	5.24974	−	2.17451i	0.203576	−	0.0843240i
$666$	10.1997	+	2.01481i	0.395231	+	0.0780723i
$667$	−4.33184	+	4.33184i	−0.167729	+	0.167729i
$668$	−0.454802	+	2.28645i	−0.0175968	+	0.0884652i
$669$	−4.13210	−	0.819081i	−0.159756	−	0.0316675i
$670$	31.3321	−	6.23235i	1.21047	−	0.240777i
$671$	−3.68686	+	8.90086i	−0.142329	+	0.343614i
$672$	2.47738	−	0.00164024i	0.0955670	−	6.32736e-5i
$673$	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
$675$	−18.6500	−	12.4080i	−0.717838	−	0.477584i
$676$	0.542640	+	0.542640i	0.0208708	+	0.0208708i
$677$	8.24041	−	5.50607i	0.316705	−	0.211615i	−0.387049	−	0.922059i	$-0.626506\pi$
$677$	8.24041	−	5.50607i	0.316705	−	0.211615i	0.703754	+	0.710444i	$0.251506\pi$
$678$	−29.3603	+	29.3992i	−1.12758	+	1.12907i
$679$		−	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	0.855982	−	0.517006i	$-0.172953\pi$
$683$	1.32660	+	1.98540i	0.0507610	+	0.0759692i	−0.805221	+	0.592975i	$0.797953\pi$
$684$	0.000402615		0.304050i	1.53944e−5		0.0116257i
$685$	43.8391	+	8.72013i	1.67500	+	0.333179i
$686$	16.2996	−	24.3941i	0.622322	−	0.931370i
$687$	15.6572	−	10.4768i	0.597358	−	0.399714i
$688$	44.6375	+	18.4895i	1.70179	+	0.704905i
$689$	−26.0068	−	10.7724i	−0.990779	−	0.410394i
$690$	4.89975	−	3.27860i	0.186530	−	0.124814i
$691$	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
$693$	−0.0141184	−	10.6620i	−0.000536313	−	0.405017i
$694$	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
$699$	−17.5466	+	17.5698i	−0.663673	+	0.664552i
$700$	0.907464	−	0.606348i	0.0342989	−	0.0229178i
$701$	31.7150	+	31.7150i	1.19786	+	1.19786i	0.974807	+	0.223051i	$0.0716016\pi$
$701$	31.7150	+	31.7150i	1.19786	+	1.19786i	0.223051	+	0.974807i	$0.428398\pi$
$702$	27.8253	+	18.5124i	1.05020	+	0.698706i
$703$	1.70980	+	1.14245i	0.0644864	+	0.0430885i
$704$	2.40368	+	12.0841i	0.0905921	+	0.455437i
$705$	−16.5361	+	0.0109483i	−0.622784	+	0.000412337i
$706$	−6.64926	+	16.0527i	−0.250248	+	0.604153i
$707$	7.91022	−	1.57344i	0.297495	−	0.0591753i
$708$	1.21502	+	0.240846i	0.0456633	+	0.00905156i
$709$	−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
$711$	17.5354	+	3.46388i	0.657629	+	0.129906i
$712$	−12.2419	+	5.07074i	−0.458783	+	0.190034i
$713$	2.21426			0.0829248
$714$	−6.31966	−	21.5030i	−0.236507	−	0.804729i
$715$	−22.2254			−0.831182
$716$	−0.0918186	+	0.0380325i	−0.00343142	+	0.00142134i
$717$	34.1599	+	22.7922i	1.27573	+	0.851191i
$718$	−23.6628	+	23.6628i	−0.883086	+	0.883086i
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	−0.402220	−	0.915543i	$-0.631761\pi$
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	0.721966	−	0.691929i	$-0.243239\pi$
$720$	−7.58839	−	37.8871i	−0.282803	−	1.41197i
$721$	−19.7446	+	3.92744i	−0.735326	+	0.146265i
$722$	10.1650	−	24.5406i	0.378304	−	0.913307i
$723$	0.00322743	+	4.87465i	0.000120030	+	0.181290i
$724$	0.0328353	+	0.165074i	0.00122031	+	0.00613493i
$725$	28.6448	+	19.1399i	1.06384	+	0.710837i
$726$	20.4762	−	4.08707i	0.759943	−	0.151685i
$727$	−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
$729$	24.9856	+	10.2333i	0.925392	+	0.379010i
$730$		−	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
$735$	−11.4697	−	4.74203i	−0.423068	−	0.174912i
$736$	0.498613	+	0.0991804i	0.0183791	+	0.00365584i
$737$	6.58678	−	9.85781i	0.242627	−	0.363117i
$738$	7.45394	−	11.1876i	0.274383	−	0.411823i
$739$	−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
$741$	3.67610	+	5.49379i	0.135045	+	0.201819i
$742$	11.1039	−	16.6182i	0.407639	−	0.610074i
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.610021	−	0.792385i	$-0.708839\pi$
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.866819	+	0.498623i	$0.833839\pi$
$744$	5.23642	−	12.6655i	0.191976	−	0.464341i
$745$	−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
$750$	3.74945	+	3.74449i	0.136911	+	0.136730i
$751$	−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
$753$	5.13303	+	25.7165i	0.187058	+	0.937162i
$754$	−42.7373	−	28.5562i	−1.55640	−	1.03995i
$755$	9.05629	+	45.5290i	0.329592	+	1.65697i
$756$	−0.928347	+	0.932042i	−0.0337637	+	0.0338980i
$757$	−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
$759$	0.425427	−	2.14619i	0.0154420	−	0.0779019i
$760$	1.40804	−	7.07871i	0.0510751	−	0.256772i
$761$	−24.1395	+	24.1395i	−0.875055	+	0.875055i	−0.993018	−	0.117963i	$-0.962364\pi$
$761$	−24.1395	+	24.1395i	−0.875055	+	0.875055i	0.117963	+	0.993018i	$0.462364\pi$
$762$	−17.2233	+	25.8134i	−0.623933	+	0.935121i
$763$	−8.37493	+	3.46901i	−0.303193	+	0.125587i
$764$	0.0846370			0.00306206
$765$	−33.4284	+	17.5249i	−1.20861	+	0.633613i
$766$	32.2229			1.16426
$767$	24.8794	−	10.3054i	0.898343	−	0.372106i
$768$	2.69907	−	4.04525i	0.0973944	−	0.145970i
$769$	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
$771$	−6.70001	+	33.8002i	−0.241295	+	1.21728i
$772$	−1.33795	+	0.266135i	−0.0481539	+	0.00957840i
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	−0.990154	−	0.139980i	$-0.955296\pi$
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	0.799126	+	0.601164i	$0.205296\pi$
$774$	−46.1390	+	19.1830i	−1.65843	+	0.689520i
$775$	−2.42928	−	12.2128i	−0.0872624	−	0.438698i
$776$	−8.08023	−	5.39903i	−0.290063	−	0.193814i
$777$	1.74150	+	8.72489i	0.0624758	+	0.313004i
$778$	15.6099	+	15.6099i	0.559643	+	0.559643i
$779$	2.21083	−	1.47723i	0.0792111	−	0.0529272i
$780$	1.94031	+	1.93774i	0.0694742	+	0.0693822i
$781$		−	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
$786$	3.39584	−	8.21367i	0.121126	−	0.292972i
$787$	−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
$789$	−0.126287	−	0.188731i	−0.00449593	−	0.00671899i
$790$	24.4410	+	10.1238i	0.869572	+	0.360189i
$791$	−32.8490	−	13.6065i	−1.16798	−	0.483792i
$792$	−11.2701	−	7.50888i	−0.400466	−	0.266817i
$793$	14.3574	−	21.4874i	0.509847	−	0.763040i
$794$	53.7144	+	10.6845i	1.90625	+	0.379178i
$795$	−31.1048	−	12.8599i	−1.10317	−	0.456094i
$796$	−1.57263	−	2.35361i	−0.0557403	−	0.0834213i
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	−0.833529	−	0.552476i	$-0.813683\pi$
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	0.198734	−	0.980053i	$-0.436317\pi$
$798$	−4.33492	+	1.79895i	−0.153455	+	0.0636820i
$799$	−6.18712	+	11.3197i	−0.218884	+	0.400463i
$800$		−	2.85893i		−	0.101078i
$801$	5.53529	−	13.4136i	0.195580	−	0.473945i
$802$	4.27557	−	2.85685i	0.150976	−	0.100879i
$803$	−14.6575	−	14.6575i	−0.517252	−	0.517252i
$804$	−1.43450	+	0.286327i	−0.0505909	+	0.0100980i
$805$	4.19478	+	2.80287i	0.147847	+	0.0987880i
$806$	3.62442	+	18.2212i	0.127665	+	0.641814i
$807$	0.00681816	+	10.2980i	0.000240011	+	0.362507i
$808$	3.92024	−	9.46429i	0.137913	−	0.332952i
$809$	11.4907	−	2.28565i	0.403993	−	0.0803592i	0.0110886	−	0.999939i	$-0.496470\pi$
$809$	11.4907	−	2.28565i	0.403993	−	0.0803592i	0.392904	+	0.919579i	$0.371470\pi$
$810$	33.2853	+	22.1132i	1.16953	+	0.776980i
$811$	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
$813$	9.90514	+	6.60892i	0.347389	+	0.231785i
$814$	5.27605	−	2.18541i	0.184926	−	0.0765987i
$815$	−3.38972			−0.118737
$816$	−28.7689	−	9.00024i	−1.00711	−	0.315071i
$817$	−9.88307			−0.345765
$818$	16.4118	−	6.79797i	0.573824	−	0.237686i
$819$	−5.54238	+	28.0575i	−0.193666	+	0.980410i
$820$	0.779963	−	0.779963i	0.0272375	−	0.0272375i
$821$	−5.91006	+	29.7119i	−0.206263	+	1.03695i	0.729408	+	0.684079i	$0.239795\pi$
$821$	−5.91006	+	29.7119i	−0.206263	+	1.03695i	−0.935671	+	0.352874i	$0.885205\pi$
$822$	−36.2144	−	7.17857i	−1.26312	−	0.250381i
$823$	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
$825$	−12.3041	+	0.00814639i	−0.428375	+	0.000283621i
$826$	3.73016	+	18.7528i	0.129789	+	0.652493i
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	0.782324	−	0.622871i	$-0.214034\pi$
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	−0.276076	+	0.961136i	$0.589034\pi$
$828$	−0.224258	+	0.150275i	−0.00779351	+	0.00522240i
$829$	−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
$831$	10.1555	−	10.1689i	0.352289	−	0.352756i
$832$		−	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
$837$	5.77119	+	13.8550i	0.199481	+	0.478898i
$838$	44.8026	+	8.91178i	1.54768	+	0.307852i
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	−0.971186	−	0.238325i	$-0.923402\pi$
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	0.591840	+	0.806056i	$0.298402\pi$
$840$	25.9524	−	17.3657i	0.895444	−	0.599174i
$841$	32.2093	+	13.3415i	1.11067	+	0.460053i
$842$	20.3896	+	8.44564i	0.702671	+	0.291056i
$843$	19.0730	−	12.7624i	0.656908	−	0.439561i
$844$	1.01799	−	1.52353i	0.0350407	−	0.0524422i
$845$	19.5656	+	3.89185i	0.673078	+	0.133884i
$846$	13.6582	−	0.0180859i	0.469580	−	0.000621805i
$847$	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
$852$	−0.312406	+	0.312820i	−0.0107029	+	0.0107170i
$853$	−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
$855$	4.39985	+	6.56600i	0.150472	+	0.224553i
$856$	−4.30489	−	2.87643i	−0.147138	−	0.0983145i
$857$	−5.07296	−	25.5035i	−0.173289	−	0.871184i	−0.965393	−	0.260798i	$-0.916014\pi$
$857$	−5.07296	−	25.5035i	−0.173289	−	0.871184i	0.792104	−	0.610386i	$-0.208986\pi$
$858$	18.3574	−	0.0121542i	0.626712	−	0.000414937i
$859$	−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
$861$	11.2845	+	2.23687i	0.384576	+	0.0762322i
$862$	−3.25147	+	16.3462i	−0.110745	+	0.556755i
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	−0.861504	−	0.507750i	$-0.830477\pi$
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	0.507750	+	0.861504i	$0.330477\pi$
$864$	0.678985	+	3.37840i	0.0230995	+	0.114936i
$865$	32.8040	−	13.5878i	1.11537	−	0.462000i
$866$	−38.9856			−1.32479
$867$	−0.530397	+	29.4401i	−0.0180132	+	0.999838i
$868$	−0.731265			−0.0248208
$869$	9.07062	−	3.75718i	0.307700	−	0.127453i
$870$	−51.1236	−	34.1107i	−1.73325	−	1.15646i
$871$	−22.4875	+	22.4875i	−0.761958	+	0.761958i
$872$	−2.24626	+	11.2927i	−0.0760679	+	0.382419i
$873$	10.4351	−	2.09003i	0.353174	−	0.0707370i
$874$	−0.944618	+	0.187896i	−0.0319522	+	0.00635569i
$875$	−1.73532	+	4.18943i	−0.0586644	+	0.141629i
$876$	0.00169332	+	2.55755i	5.72119e−5	+	0.0864117i
$877$	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
$879$	44.8523	−	8.95256i	1.51283	−	0.301962i
$880$	−15.0076	−	15.0076i	−0.505907	−	0.505907i
$881$	16.3958	−	10.9553i	0.552389	−	0.369094i	−0.247829	−	0.968804i	$-0.579717\pi$
$881$	16.3958	−	10.9553i	0.552389	−	0.369094i	0.800218	+	0.599709i	$0.204717\pi$
$882$	9.47622	+	3.91048i	0.319081	+	0.131673i
$883$		−	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	0.642137	−	0.766590i	$-0.278048\pi$
$887$	−9.28722	−	13.8993i	−0.311834	−	0.466693i	−0.953972	+	0.299896i	$0.903048\pi$
$888$	10.4432	+	4.31764i	0.350452	+	0.144890i
$889$	−26.0450	−	5.18067i	−0.873522	−	0.173754i
$890$	11.9318	−	17.8572i	0.399955	−	0.598575i
$891$	14.5379	−	2.93181i	0.487038	−	0.0982194i
$892$	0.263753	+	0.109250i	0.00883111	+	0.00365797i
$893$	2.49580	+	1.03380i	0.0835189	+	0.0345947i
$894$	8.81646	+	13.1759i	0.294866	+	0.440667i
$895$	−1.43532	+	2.14810i	−0.0479773	+	0.0718032i
$896$	25.8203	+	5.13597i	0.862594	+	0.171581i
$897$	−2.24235	+	5.42367i	−0.0748699	+	0.181091i
$898$	−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
$903$	−30.2557	−	30.2157i	−1.00685	−	1.00552i
$904$	−37.5501	+	25.0902i	−1.24890	+	0.834487i
$905$	3.09374	+	3.09374i	0.102839	+	0.102839i
$906$	−7.50509	−	37.6005i	−0.249340	−	1.24919i
$907$	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
$909$	4.30683	+	10.3588i	0.142848	+	0.343579i
$910$	−16.1986	+	39.1068i	−0.536978	+	1.29638i
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	−0.227564	−	0.973763i	$-0.573076\pi$
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	0.162402	+	0.986725i	$0.448076\pi$
$912$	−1.22739	+	6.19194i	−0.0406430	+	0.205036i
$913$	−4.17505	+	20.9894i	−0.138174	+	0.694648i
$914$	10.8464	−	10.8464i	0.358768	−	0.358768i
$915$	17.1501	−	25.7038i	0.566966	−	0.849742i
$916$	−1.17955	+	0.488587i	−0.0389735	+	0.0161434i
$917$	7.60583			0.251167
$918$	27.6012	−	14.4933i	0.910974	−	0.478349i
$919$	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
$921$	23.4865	−	35.2005i	0.773907	−	1.15990i
$922$	−10.1727	+	10.1727i	−0.335021	+	0.335021i
$923$	−1.87512	+	9.42688i	−0.0617204	+	0.310290i
$924$	−0.140498	+	0.708785i	−0.00462206	+	0.0233173i
$925$	10.0700	−	2.00304i	0.331098	−	0.0658595i
$926$	−12.7673	+	30.8229i	−0.419558	+	1.01290i
$927$	−10.7502	−	25.8564i	−0.353083	−	0.849234i
$928$	−1.03392	−	5.19789i	−0.0339402	−	0.170629i
$929$	20.3321	+	13.5854i	0.667073	+	0.445724i	0.842448	−	0.538778i	$-0.181114\pi$
$929$	20.3321	+	13.5854i	0.667073	+	0.445724i	−0.175375	+	0.984502i	$0.556114\pi$
$930$	4.34814	+	21.7842i	0.142581	+	0.714332i
$931$	1.43373	+	1.43373i	0.0469885	+	0.0469885i
$932$	1.39922	−	0.934927i	0.0458329	−	0.0306245i
$933$	−28.5997	−	28.5619i	−0.936312	−	0.935073i
$934$			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
$939$	−1.06851	+	2.58445i	−0.0348695	+	0.0843403i
$940$	1.09913	+	0.218631i	0.0358497	+	0.00713095i
$941$	2.00221	−	2.99651i	0.0652701	−	0.0976836i	−0.797399	−	0.603453i	$-0.793791\pi$
$941$	2.00221	−	2.99651i	0.0652701	−	0.0976836i	0.862669	+	0.505769i	$0.168791\pi$
$942$	3.45944	+	5.17001i	0.112715	+	0.168448i
$943$	2.18105	+	0.903419i	0.0710246	+	0.0294194i
$944$	23.7584	+	9.84105i	0.773270	+	0.320299i
$945$	−6.60480	+	33.5527i	−0.214854	+	1.09147i
$946$	−15.2484	+	22.8209i	−0.495769	+	0.741970i
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.602783	−	0.797905i	$-0.294059\pi$
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.251554	+	0.967843i	$0.419059\pi$
$948$	−1.11945	−	0.462824i	−0.0363581	−	0.0150318i
$949$	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	$0.128535\pi$
$953$			24.2594i			0.785838i	−0.919573	+	0.392919i	$0.871465\pi$
$954$	25.6985	+	10.6048i	0.832021	+	0.343344i
$955$	1.82937	−	1.22234i	0.0591969	−	0.0395541i
$956$	−1.96792	−	1.96792i	−0.0636470	−	0.0636470i
$957$	−22.3675	+	4.46457i	−0.723039	+	0.144319i
$958$	10.4833	+	7.00474i	0.338701	+	0.226313i
$959$	−6.16353	−	30.9862i	−0.199031	−	1.00060i
$960$	−0.0261636	−	39.5170i	−0.000844428	−	1.27541i
$961$	8.67037	−	20.9321i	0.279689	−	0.675230i
$962$	−15.0241	+	2.98848i	−0.484397	+	0.0963525i
$963$	5.55948	−	1.11350i	0.179152	−	0.0358822i
$964$	0.0644499	−	0.324012i	0.00207579	−	0.0104357i
$965$	−25.0752	+	25.0752i	−0.807200	+	0.807200i
$966$	−3.46629	−	2.31278i	−0.111526	−	0.0744125i
$967$	−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
$969$	6.14136	−	0.551116i	0.197289	−	0.0177044i
$970$	15.7512			0.505739
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	−0.600012	−	0.799991i	$-0.704837\pi$
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	0.141407	+	0.989952i	$0.454837\pi$
$972$	−1.52479	−	1.01155i	−0.0489077	−	0.0324454i
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$	−11.0194	+	55.3982i	−0.353084	+	1.77507i
$975$	32.3745	+	6.41741i	1.03681	+	0.205522i
$976$	24.2041	−	4.81450i	0.774755	−	0.154108i
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	−0.750670	−	0.660677i	$-0.770269\pi$
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	0.997973	+	0.0636347i	$0.0202693\pi$
$978$	2.79980	−	0.00185371i	0.0895277	−	5.92750e-5i
$979$	−1.55497	−	7.81735i	−0.0496970	−	0.249844i
$980$	0.699373	+	0.467306i	0.0223406	+	0.0149275i
$981$	−7.01910	−	10.4748i	−0.224103	−	0.334434i
$982$	−13.0385	−	13.0385i	−0.416075	−	0.416075i
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	−0.159315	−	0.987228i	$-0.550929\pi$
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	0.851112	+	0.524984i	$0.175929\pi$
$984$	10.3254	−	10.3391i	0.329162	−	0.329598i
$985$			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
$990$	21.9499	−	0.0290655i	0.697615	−	0.000923762i
$991$	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
$993$	−43.8545	+	29.3447i	−1.39168	+	0.931225i
$994$	−6.30488	−	2.61157i	−0.199979	−	0.0828339i
$995$	−67.9824	−	28.1592i	−2.15519	−	0.892707i
$996$	2.19447	−	1.46840i	0.0695344	−	0.0465280i
$997$	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
$999$	−11.4240	+	4.75858i	−0.361439	+	0.150555i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	3.2	odd	2	inner
51.2.i.a.29.4	yes	32	1.1	even	1	trivial
51.2.i.a.44.1	yes	32	17.10	odd	16	inner
51.2.i.a.44.4	yes	32	51.44	even	16	inner
816.2.cj.c.401.3		32	204.95	odd	16
816.2.cj.c.401.4		32	68.27	even	16
816.2.cj.c.641.3		32	4.3	odd	2
816.2.cj.c.641.4		32	12.11	even	2
867.2.i.b.65.1		32	51.32	odd	8
867.2.i.b.65.4		32	17.15	even	8
867.2.i.b.827.1		32	17.12	odd	16
867.2.i.b.827.4		32	51.29	even	16
867.2.i.c.158.1		32	17.13	even	4
867.2.i.c.158.4		32	51.47	odd	4
867.2.i.c.653.1		32	51.23	even	16
867.2.i.c.653.4		32	17.6	odd	16
867.2.i.d.158.1		32	17.4	even	4
867.2.i.d.158.4		32	51.38	odd	4
867.2.i.d.653.1		32	51.11	even	16
867.2.i.d.653.4		32	17.11	odd	16
867.2.i.f.224.1		32	17.8	even	8
867.2.i.f.224.4		32	51.8	odd	8
867.2.i.f.329.1		32	51.14	even	16
867.2.i.f.329.4		32	17.14	odd	16
867.2.i.g.224.1		32	17.9	even	8
867.2.i.g.224.4		32	51.26	odd	8
867.2.i.g.329.1		32	51.20	even	16
867.2.i.g.329.4		32	17.3	odd	16
867.2.i.h.131.1		32	51.50	odd	2
867.2.i.h.131.4		32	17.16	even	2
867.2.i.h.503.1		32	17.7	odd	16
867.2.i.h.503.4		32	51.41	even	16
867.2.i.i.65.1		32	51.2	odd	8
867.2.i.i.65.4		32	17.2	even	8
867.2.i.i.827.1		32	17.5	odd	16
867.2.i.i.827.4		32	51.5	even	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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34436 - 0.556851i) q^{2} +(-0.961322 + 1.44078i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(0.595296 - 2.99276i) q^{5} +(-0.490059 + 2.47224i) q^{6} +(-2.11533 + 0.420765i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-1.15172 - 2.77012i) q^{9} +(-0.866229 - 4.35483i) q^{10} +(-1.37013 - 0.915491i) q^{11} +(0.0397964 + 0.199380i) q^{12} +(3.12551 + 3.12551i) q^{13} +(-2.60946 + 1.74358i) q^{14} +(3.73965 + 3.73470i) 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} +(1.42728 - 3.45222i) q^{21} +(-2.35174 - 0.467790i) q^{22} +(0.425893 - 0.637394i) q^{23} +(-2.63871 - 3.94345i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(5.09831 + 1.00359i) q^{27} +(-0.140652 + 0.210501i) q^{28} +(-7.83789 - 1.55905i) q^{29} +(7.10709 + 2.93834i) 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} +(-0.325520 - 0.134330i) q^{36} +(-1.98027 + 1.32318i) q^{37} +(-0.888394 - 0.888394i) q^{38} +(-7.50782 + 1.49857i) q^{39} +(6.95033 + 4.64406i) q^{40} +(0.600791 + 3.02038i) q^{41} +(-0.00359897 - 5.43581i) q^{42} +(4.38037 - 10.5751i) q^{43} +(-0.189711 + 0.0377359i) q^{44} +(-8.97590 + 1.79778i) q^{45} +(0.217619 - 1.09405i) q^{46} +(-2.21238 + 2.21238i) q^{47} +(-6.08153 - 4.05773i) q^{48} +(-2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +(-2.13226 + 6.81568i) q^{51} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(7.41281 - 1.48981i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(1.15266 - 5.79482i) q^{56} +(1.46694 + 0.290783i) q^{57} +(-11.4051 + 2.26861i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.620386 - 0.000410749i) q^{60} +(-1.14061 - 5.73423i) q^{61} +(3.49473 + 2.33510i) q^{62} +(3.60183 + 5.37510i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(11.2145 - 7.49329i) q^{65} +(2.93476 - 2.93865i) 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} +(8.21831 - 0.0108825i) q^{72} +(12.3377 + 2.45412i) q^{73} +(-1.92538 + 2.88154i) q^{74} +(6.20569 - 4.15245i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(-9.25872 + 6.19535i) q^{78} +(-3.31013 + 4.95397i) q^{79} +(12.6324 + 2.51274i) q^{80} +(-6.34708 + 6.38079i) 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} +(9.78099 - 9.79395i) q^{87} +(3.75339 - 2.50793i) q^{88} +(3.42023 + 3.42023i) q^{89} +(-11.0657 + 7.41510i) q^{90} +(-7.92660 - 5.29638i) q^{91} +(-0.0175550 - 0.0882551i) q^{92} +(-5.00297 + 0.00331239i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(-2.58400 + 0.513989i) q^{95} +(-1.12673 - 0.223345i) q^{96} +(-0.692072 + 3.47928i) q^{97} +(-2.41627 + 2.41627i) q^{98} +(-0.958012 + 4.84981i) 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

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