LMFDB - Embedded newform 912.2.cn.a.91.73

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(67,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 0, 34]))

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

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

chi := DirichletCharacter("912.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.cn (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$80$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			91.73
Character	$\chi$	$=$	912.91
Dual form			912.2.cn.a.451.73

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36897 + 0.354847i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.74817 + 0.971551i) q^{4} +(3.14735 + 0.275358i) q^{5} +(-0.917864 - 1.07588i) q^{6} +(-0.694115 + 1.20224i) q^{7} +(2.04844 + 1.95036i) q^{8} +(0.342020 + 0.939693i) q^{9} +O(q^{10})$	\(q+(1.36897 + 0.354847i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.74817 + 0.971551i) q^{4} +(3.14735 + 0.275358i) q^{5} +(-0.917864 - 1.07588i) q^{6} +(-0.694115 + 1.20224i) q^{7} +(2.04844 + 1.95036i) q^{8} +(0.342020 + 0.939693i) q^{9} +(4.21093 + 1.49379i) q^{10} +(1.29491 + 0.346971i) q^{11} +(-0.874756 - 1.79856i) q^{12} +(4.16655 - 2.91745i) q^{13} +(-1.37684 + 1.39953i) q^{14} +(-2.42022 - 2.03081i) q^{15} +(2.11218 + 3.39687i) q^{16} +(-6.46157 - 2.35182i) q^{17} +(0.134769 + 1.40778i) q^{18} +(-4.35861 + 0.0502942i) q^{19} +(5.23457 + 3.53919i) q^{20} +(1.25816 - 0.586692i) q^{21} +(1.64958 + 0.934490i) q^{22} +(5.23295 + 4.39097i) q^{23} +(-0.559303 - 2.77258i) q^{24} +(4.90597 + 0.865054i) q^{25} +(6.73914 - 2.51542i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-2.38147 + 1.42735i) q^{28} +(-1.24034 - 0.578380i) q^{29} +(-2.59259 - 3.63893i) q^{30} +(-4.91591 + 8.51461i) q^{31} +(1.68614 + 5.39972i) q^{32} +(-0.861717 - 1.02695i) q^{33} +(-8.01117 - 5.51244i) q^{34} +(-2.51567 + 3.59275i) q^{35} +(-0.315051 + 1.97503i) q^{36} +(3.20263 - 3.20263i) q^{37} +(-5.98466 - 1.47779i) q^{38} -5.08642 q^{39} +(5.91011 + 6.70252i) q^{40} +(-1.95339 - 11.0782i) q^{41} +(1.93058 - 0.356708i) q^{42} +(0.289997 - 3.31468i) q^{43} +(1.92663 + 1.86464i) q^{44} +(0.817706 + 3.05172i) q^{45} +(5.60564 + 7.86801i) q^{46} +(-1.99696 - 5.48660i) q^{47} +(0.218170 - 3.99405i) q^{48} +(2.53641 + 4.39319i) q^{49} +(6.40917 + 2.92510i) q^{50} +(3.94406 + 5.63270i) q^{51} +(10.1183 - 1.05217i) q^{52} +(6.68032 - 0.584452i) q^{53} +(0.697072 - 1.23048i) q^{54} +(3.98001 + 1.44860i) q^{55} +(-3.76666 + 1.10895i) q^{56} +(3.59921 + 2.45880i) q^{57} +(-1.49275 - 1.23192i) q^{58} +(-1.06746 - 2.28918i) q^{59} +(-2.25792 - 5.90156i) q^{60} +(8.94979 - 0.783005i) q^{61} +(-9.75113 + 9.91186i) q^{62} +(-1.36714 - 0.241064i) q^{63} +(0.392205 + 7.99038i) q^{64} +(13.9170 - 8.03496i) q^{65} +(-0.815254 - 1.71165i) q^{66} +(1.81643 - 3.89534i) q^{67} +(-9.01099 - 10.3891i) q^{68} +(-1.76803 - 6.59837i) q^{69} +(-4.71876 + 4.02570i) q^{70} +(7.45429 + 8.88367i) q^{71} +(-1.13213 + 2.59196i) q^{72} +(-13.5361 + 2.38679i) q^{73} +(5.52076 - 3.24787i) q^{74} +(-3.52256 - 3.52256i) q^{75} +(-7.66844 - 4.14669i) q^{76} +(-1.31596 + 1.31596i) q^{77} +(-6.96317 - 1.80490i) q^{78} +(-2.61293 - 14.8187i) q^{79} +(5.71241 + 11.2727i) q^{80} +(-0.766044 + 0.642788i) q^{81} +(1.25694 - 15.8589i) q^{82} +(-9.27759 + 2.48592i) q^{83} +(2.76948 + 0.196736i) q^{84} +(-19.6892 - 9.18124i) q^{85} +(1.57320 - 4.43479i) q^{86} +(0.684282 + 1.18521i) q^{87} +(1.97583 + 3.23630i) q^{88} +(-1.62798 + 9.23276i) q^{89} +(0.0365222 + 4.46788i) q^{90} +(0.615418 + 7.03426i) q^{91} +(4.88203 + 12.7602i) q^{92} +(8.91066 - 4.15511i) q^{93} +(-0.786876 - 8.21961i) q^{94} +(-13.7319 - 1.04188i) q^{95} +(1.71594 - 5.39032i) q^{96} +(3.23866 - 8.89815i) q^{97} +(1.91336 + 6.91419i) q^{98} +(0.116840 + 1.33549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q+O(q^{10}) $ 960 * q	$ 960 q + 48 q^{10} + 12 q^{16} - 60 q^{32} - 120 q^{34} + 12 q^{36} + 108 q^{38} + 60 q^{40} + 180 q^{46} - 480 q^{49} - 108 q^{50} - 24 q^{51} + 48 q^{52} + 12 q^{54} + 72 q^{68} - 144 q^{69} - 72 q^{70} - 48 q^{76} + 72 q^{78} - 120 q^{80} + 120 q^{82} + 96 q^{85} + 84 q^{98}+O(q^{100}) $ 960 * q + 48 * q^10 + 12 * q^16 - 60 * q^32 - 120 * q^34 + 12 * q^36 + 108 * q^38 + 60 * q^40 + 180 * q^46 - 480 * q^49 - 108 * q^50 - 24 * q^51 + 48 * q^52 + 12 * q^54 + 72 * q^68 - 144 * q^69 - 72 * q^70 - 48 * q^76 + 72 * q^78 - 120 * q^80 + 120 * q^82 + 96 * q^85 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.36897	+	0.354847i	0.968009	+	0.250915i
$2$	1.36897	+	0.354847i	0.968009	+	0.250915i
$3$	−0.819152	−	0.573576i	−0.472938	−	0.331155i
$3$	−0.819152	−	0.573576i	−0.472938	−	0.331155i
$4$	1.74817	+	0.971551i	0.874084	+	0.485776i
$5$	3.14735	+	0.275358i	1.40754	+	0.123144i	0.765454	−	0.643490i	$-0.222514\pi$
$5$	3.14735	+	0.275358i	1.40754	+	0.123144i	0.642084	+	0.766634i	$0.278070\pi$
$6$	−0.917864	−	1.07588i	−0.374716	−	0.439228i
$7$	−0.694115	+	1.20224i	−0.262351	+	0.454405i	−0.966866	−	0.255284i	$-0.917831\pi$
$7$	−0.694115	+	1.20224i	−0.262351	+	0.454405i	0.704515	+	0.709689i	$0.251164\pi$
$8$	2.04844	+	1.95036i	0.724233	+	0.689556i
$9$	0.342020	+	0.939693i	0.114007	+	0.313231i
$10$	4.21093	+	1.49379i	1.33161	+	0.472377i
$11$	1.29491	+	0.346971i	0.390431	+	0.104616i	0.448694	−	0.893686i	$-0.351889\pi$
$11$	1.29491	+	0.346971i	0.390431	+	0.104616i	−0.0582626	+	0.998301i	$0.518556\pi$
$12$	−0.874756	−	1.79856i	−0.252520	−	0.519198i
$13$	4.16655	−	2.91745i	1.15559	−	0.809155i	0.171217	−	0.985233i	$-0.445230\pi$
$13$	4.16655	−	2.91745i	1.15559	−	0.809155i	0.984376	+	0.176078i	$0.0563411\pi$
$14$	−1.37684	+	1.39953i	−0.367975	+	0.374041i
$15$	−2.42022	−	2.03081i	−0.624899	−	0.524352i
$16$	2.11218	+	3.39687i	0.528044	+	0.849217i
$17$	−6.46157	−	2.35182i	−1.56716	−	0.570400i	−0.594798	−	0.803875i	$-0.702768\pi$
$17$	−6.46157	−	2.35182i	−1.56716	−	0.570400i	−0.972363	+	0.233476i	$0.924990\pi$
$18$	0.134769	+	1.40778i	0.0317653	+	0.331816i
$19$	−4.35861	+	0.0502942i	−0.999933	+	0.0115383i
$19$	−4.35861	+	0.0502942i	−0.999933	+	0.0115383i
$20$	5.23457	+	3.53919i	1.17049	+	0.791386i
$21$	1.25816	−	0.586692i	0.274554	−	0.128027i
$22$	1.64958	+	0.934490i	0.351691	+	0.199234i
$23$	5.23295	+	4.39097i	1.09115	+	0.915581i	0.996798	−	0.0799587i	$-0.0254789\pi$
$23$	5.23295	+	4.39097i	1.09115	+	0.915581i	0.0943482	+	0.995539i	$0.469923\pi$
$24$	−0.559303	−	2.77258i	−0.114167	−	0.565950i
$25$	4.90597	+	0.865054i	0.981193	+	0.173011i
$26$	6.73914	−	2.51542i	1.32165	−	0.493314i
$27$	0.258819	−	0.965926i	0.0498097	−	0.185893i
$28$	−2.38147	+	1.42735i	−0.450056	+	0.269744i
$29$	−1.24034	−	0.578380i	−0.230326	−	0.107403i	0.304030	−	0.952663i	$-0.401668\pi$
$29$	−1.24034	−	0.578380i	−0.230326	−	0.107403i	−0.534355	+	0.845260i	$0.679446\pi$
$30$	−2.59259	−	3.63893i	−0.473340	−	0.664374i
$31$	−4.91591	+	8.51461i	−0.882924	+	1.52927i	−0.0348483	+	0.999393i	$0.511095\pi$
$31$	−4.91591	+	8.51461i	−0.882924	+	1.52927i	−0.848075	+	0.529876i	$0.822239\pi$
$32$	1.68614	+	5.39972i	0.298070	+	0.954544i
$33$	−0.861717	−	1.02695i	−0.150006	−	0.178770i
$34$	−8.01117	−	5.51244i	−1.37390	−	0.945376i
$35$	−2.51567	+	3.59275i	−0.425226	+	0.607286i
$36$	−0.315051	+	1.97503i	−0.0525085	+	0.329172i
$37$	3.20263	−	3.20263i	0.526510	−	0.526510i	−0.393020	−	0.919530i	$-0.628570\pi$
$37$	3.20263	−	3.20263i	0.526510	−	0.526510i	0.919530	+	0.393020i	$0.128570\pi$
$38$	−5.98466	−	1.47779i	−0.970840	−	0.239729i
$39$	−5.08642			−0.814479
$40$	5.91011	+	6.70252i	0.934471	+	1.05976i
$41$	−1.95339	−	11.0782i	−0.305069	−	1.73013i	−0.623182	−	0.782077i	$-0.714160\pi$
$41$	−1.95339	−	11.0782i	−0.305069	−	1.73013i	0.318113	−	0.948053i	$-0.396951\pi$
$42$	1.93058	−	0.356708i	0.297894	−	0.0550413i
$43$	0.289997	−	3.31468i	0.0442241	−	0.505484i	−0.941488	−	0.337046i	$-0.890572\pi$
$43$	0.289997	−	3.31468i	0.0442241	−	0.505484i	0.985712	−	0.168438i	$-0.0538722\pi$
$44$	1.92663	+	1.86464i	0.290450	+	0.281105i
$45$	0.817706	+	3.05172i	0.121896	+	0.454924i
$46$	5.60564	+	7.86801i	0.826507	+	1.16008i
$47$	−1.99696	−	5.48660i	−0.291286	−	0.800302i	−0.995879	−	0.0906906i	$-0.971093\pi$
$47$	−1.99696	−	5.48660i	−0.291286	−	0.800302i	0.704593	−	0.709612i	$-0.251130\pi$
$48$	0.218170	−	3.99405i	0.0314902	−	0.576491i
$49$	2.53641	+	4.39319i	0.362344	+	0.627598i
$50$	6.40917	+	2.92510i	0.906393	+	0.413672i
$51$	3.94406	+	5.63270i	0.552279	+	0.788736i
$52$	10.1183	−	1.05217i	1.40315	−	0.145910i
$53$	6.68032	−	0.584452i	0.917612	−	0.0802806i	0.381444	−	0.924392i	$-0.375427\pi$
$53$	6.68032	−	0.584452i	0.917612	−	0.0802806i	0.536168	+	0.844111i	$0.319871\pi$
$54$	0.697072	−	1.23048i	0.0948595	−	0.167448i
$55$	3.98001	+	1.44860i	0.536664	+	0.195330i
$56$	−3.76666	+	1.10895i	−0.503341	+	0.148189i
$57$	3.59921	+	2.45880i	0.476727	+	0.325676i
$58$	−1.49275	−	1.23192i	−0.196008	−	0.161759i
$59$	−1.06746	−	2.28918i	−0.138972	−	0.298026i	0.824488	−	0.565880i	$-0.191463\pi$
$59$	−1.06746	−	2.28918i	−0.138972	−	0.298026i	−0.963460	+	0.267854i	$0.913686\pi$
$60$	−2.25792	−	5.90156i	−0.291496	−	0.761888i
$61$	8.94979	−	0.783005i	1.14590	−	0.100254i	0.501653	−	0.865069i	$-0.332725\pi$
$61$	8.94979	−	0.783005i	1.14590	−	0.100254i	0.644250	+	0.764815i	$0.277170\pi$
$62$	−9.75113	+	9.91186i	−1.23839	+	1.25881i
$63$	−1.36714	−	0.241064i	−0.172243	−	0.0303712i
$64$	0.392205	+	7.99038i	0.0490256	+	0.998798i
$65$	13.9170	−	8.03496i	1.72619	−	0.996614i
$66$	−0.815254	−	1.71165i	−0.100351	−	0.210689i
$67$	1.81643	−	3.89534i	0.221912	−	0.475892i	−0.763558	−	0.645739i	$-0.776549\pi$
$67$	1.81643	−	3.89534i	0.221912	−	0.475892i	0.985470	+	0.169847i	$0.0543273\pi$
$68$	−9.01099	−	10.3891i	−1.09274	−	1.25987i
$69$	−1.76803	−	6.59837i	−0.212846	−	0.794351i
$70$	−4.71876	+	4.02570i	−0.564000	+	0.481163i
$71$	7.45429	+	8.88367i	0.884661	+	1.05430i	0.998152	+	0.0607590i	$0.0193521\pi$
$71$	7.45429	+	8.88367i	0.884661	+	1.05430i	−0.113491	+	0.993539i	$0.536203\pi$
$72$	−1.13213	+	2.59196i	−0.133423	+	0.305466i
$73$	−13.5361	+	2.38679i	−1.58428	+	0.279352i	−0.895313	−	0.445437i	$-0.853048\pi$
$73$	−13.5361	+	2.38679i	−1.58428	+	0.279352i	−0.688971	+	0.724789i	$0.741937\pi$
$74$	5.52076	−	3.24787i	0.641775	−	0.377557i
$75$	−3.52256	−	3.52256i	−0.406750	−	0.406750i
$76$	−7.66844	−	4.14669i	−0.879630	−	0.475658i
$77$	−1.31596	+	1.31596i	−0.149968	+	0.149968i
$78$	−6.96317	−	1.80490i	−0.788423	−	0.204365i
$79$	−2.61293	−	14.8187i	−0.293978	−	1.66723i	−0.671329	−	0.741160i	$-0.734276\pi$
$79$	−2.61293	−	14.8187i	−0.293978	−	1.66723i	0.377351	−	0.926070i	$-0.376835\pi$
$80$	5.71241	+	11.2727i	0.638667	+	1.26033i
$81$	−0.766044	+	0.642788i	−0.0851160	+	0.0714208i
$82$	1.25694	−	15.8589i	0.138806	−	1.75133i
$83$	−9.27759	+	2.48592i	−1.01835	+	0.272865i	−0.729113	−	0.684393i	$-0.760067\pi$
$83$	−9.27759	+	2.48592i	−1.01835	+	0.272865i	−0.289234	+	0.957258i	$0.593401\pi$
$84$	2.76948	+	0.196736i	0.302175	+	0.0214657i
$85$	−19.6892	−	9.18124i	−2.13560	−	0.995846i
$86$	1.57320	−	4.43479i	0.169643	−	0.478216i
$87$	0.684282	+	1.18521i	0.0733628	+	0.127068i
$88$	1.97583	+	3.23630i	0.210625	+	0.344990i
$89$	−1.62798	+	9.23276i	−0.172566	+	0.978671i	0.768350	+	0.640030i	$0.221078\pi$
$89$	−1.62798	+	9.23276i	−0.172566	+	0.978671i	−0.940916	+	0.338641i	$0.890033\pi$
$90$	0.0365222	+	4.46788i	0.00384978	+	0.470956i
$91$	0.615418	+	7.03426i	0.0645133	+	0.737390i
$92$	4.88203	+	12.7602i	0.508986	+	1.33035i
$93$	8.91066	−	4.15511i	0.923992	−	0.430865i
$94$	−0.786876	−	8.21961i	−0.0811600	−	0.847788i
$95$	−13.7319	−	1.04188i	−1.40887	−	0.106895i
$96$	1.71594	−	5.39032i	0.175133	−	0.550147i
$97$	3.23866	−	8.89815i	0.328836	−	0.903470i	−0.659571	−	0.751643i	$-0.729262\pi$
$97$	3.23866	−	8.89815i	0.328836	−	0.903470i	0.988407	−	0.151828i	$-0.0485159\pi$
$98$	1.91336	+	6.91419i	0.193279	+	0.698438i
$99$	0.116840	+	1.33549i	0.0117429	+	0.134222i
$100$	7.73601	+	6.27866i	0.773601	+	0.627866i
$101$	−10.1247	+	7.08938i	−1.00744	+	0.705420i	−0.956033	−	0.293258i	$-0.905260\pi$
$101$	−10.1247	+	7.08938i	−1.00744	+	0.705420i	−0.0514102	+	0.998678i	$0.516372\pi$
$102$	3.40056	+	9.11054i	0.336705	+	0.902078i
$103$	−9.09887	+	5.25323i	−0.896538	+	0.517616i	−0.876075	−	0.482174i	$-0.839847\pi$
$103$	−9.09887	+	5.25323i	−0.896538	+	0.517616i	−0.0204626	+	0.999791i	$0.506514\pi$
$104$	14.2250	+	2.15005i	1.39488	+	0.210830i
$105$	4.12144	−	1.50008i	0.402211	−	0.146393i
$106$	9.35255	+	1.57039i	0.908400	+	0.152530i
$107$	−9.34466	+	2.50389i	−0.903382	+	0.242061i	−0.680468	−	0.732778i	$-0.738224\pi$
$107$	−9.34466	+	2.50389i	−0.903382	+	0.242061i	−0.222914	+	0.974838i	$0.571557\pi$
$108$	1.39091	−	1.43714i	0.133840	−	0.138289i
$109$	−8.88612	−	0.777435i	−0.851136	−	0.0744648i	−0.346765	−	0.937952i	$-0.612720\pi$
$109$	−8.88612	−	0.777435i	−0.851136	−	0.0744648i	−0.504371	+	0.863487i	$0.668276\pi$
$110$	4.93449	+	3.39539i	0.470485	+	0.323738i
$111$	−4.46040	+	0.786488i	−0.423362	+	0.0746502i
$112$	−5.54995	+	0.181531i	−0.524421	+	0.0171530i
$113$			5.83692i			0.549092i	0.961574	+	0.274546i	$0.0885275\pi$
$113$			5.83692i			0.549092i	−0.961574	+	0.274546i	$0.911472\pi$
$114$	4.05472	+	4.64319i	0.379759	+	0.434875i
$115$	15.2609	+	15.2609i	1.42308	+	1.42308i
$116$	−1.60640	−	2.21616i	−0.149150	−	0.205765i
$117$	4.16655	+	2.91745i	0.385198	+	0.269718i
$118$	−0.649017	−	3.51261i	−0.0597469	−	0.323362i
$119$	7.31253	−	6.13594i	0.670339	−	0.562481i
$120$	−0.996875	−	8.88028i	−0.0910018	−	0.810655i
$121$	−7.96987	−	4.60140i	−0.724533	−	0.418309i
$122$	12.5299	+	2.10390i	1.13440	+	0.190478i
$123$	−4.75409	+	10.1952i	−0.428662	+	0.919268i
$124$	−16.8662	+	10.1089i	−1.51463	+	0.907806i
$125$	−0.0560006	−	0.0150053i	−0.00500885	−	0.00134212i
$126$	−1.78604	−	0.815135i	−0.159113	−	0.0726180i
$127$	3.10576	−	17.6136i	0.275592	−	1.56296i	−0.461485	−	0.887148i	$-0.652683\pi$
$127$	3.10576	−	17.6136i	0.275592	−	1.56296i	0.737076	−	0.675810i	$-0.236206\pi$
$128$	−2.29845	+	11.0778i	−0.203156	+	0.979146i
$129$	−2.13877	+	2.54889i	−0.188308	+	0.224417i
$130$	21.9031	−	6.06124i	1.92103	−	0.531606i
$131$	2.76298	+	5.92524i	0.241403	+	0.517691i	0.989260	−	0.146170i	$-0.0466946\pi$
$131$	2.76298	+	5.92524i	0.241403	+	0.517691i	−0.747856	+	0.663861i	$0.768917\pi$
$132$	−0.508686	−	2.63249i	−0.0442755	−	0.229129i
$133$	2.96491	−	5.27502i	0.257090	−	0.457402i
$134$	3.86889	−	4.68806i	0.334221	−	0.404987i
$135$	1.08057	−	2.96884i	0.0930006	−	0.255517i
$136$	−8.64924	−	17.4199i	−0.741666	−	1.49375i
$137$	8.78507	−	10.4696i	0.750559	−	0.894481i	−0.246653	−	0.969104i	$-0.579331\pi$
$137$	8.78507	−	10.4696i	0.750559	−	0.894481i	0.997212	+	0.0746227i	$0.0237752\pi$
$138$	−0.0789676	−	9.66036i	−0.00672217	−	0.822345i
$139$	−9.29934	−	13.2808i	−0.788760	−	1.12647i	−0.989173	−	0.146754i	$-0.953117\pi$
$139$	−9.29934	−	13.2808i	−0.788760	−	1.12647i	0.200413	−	0.979711i	$-0.435771\pi$
$140$	−7.88836	+	3.83663i	−0.666688	+	0.324254i
$141$	−1.51117	+	5.63976i	−0.127264	+	0.474954i
$142$	7.05236	+	14.8066i	0.591821	+	1.24254i
$143$	6.40760	−	2.33217i	0.535830	−	0.195026i
$144$	−2.46961	+	3.14659i	−0.205800	+	0.262216i
$145$	−3.74453	−	2.16190i	−0.310966	−	0.179536i
$146$	−19.3775	−	1.53582i	−1.60370	−	0.127105i
$147$	0.442125	−	5.05351i	0.0364659	−	0.416807i
$148$	8.71026	−	2.48721i	0.715979	−	0.204448i
$149$	1.26273	−	1.80337i	0.103447	−	0.147738i	−0.764091	−	0.645108i	$-0.776812\pi$
$149$	1.26273	−	1.80337i	0.103447	−	0.147738i	0.867538	+	0.497371i	$0.165701\pi$
$150$	−3.57231	−	6.07225i	−0.291678	−	0.495797i
$151$		−	20.6566i		−	1.68101i	−0.541805	−	0.840504i	$-0.682259\pi$
$151$		−	20.6566i		−	1.68101i	0.541805	−	0.840504i	$-0.317741\pi$
$152$	−9.02644	−	8.39782i	−0.732141	−	0.681153i
$153$		−	6.87626i		−	0.555912i
$154$	−2.26848	+	1.33455i	−0.182799	+	0.107541i
$155$	−17.8167	+	25.4448i	−1.43107	+	2.04378i
$156$	−8.89191	−	4.94172i	−0.711923	−	0.395654i
$157$	−1.64952	+	18.8542i	−0.131646	+	1.50473i	0.587135	+	0.809489i	$0.300256\pi$
$157$	−1.64952	+	18.8542i	−0.131646	+	1.50473i	−0.718781	+	0.695236i	$0.755300\pi$
$158$	1.68133	−	21.2135i	0.133760	−	1.68766i
$159$	−5.80742	−	3.35292i	−0.460559	−	0.265904i
$160$	3.82002	+	17.4591i	0.301999	+	1.38026i
$161$	−8.91129	+	3.24344i	−0.702308	+	0.255619i
$162$	−1.27678	+	0.608129i	−0.100314	+	0.0477792i
$163$	0.179062	−	0.668269i	0.0140252	−	0.0523429i	−0.958559	−	0.284895i	$-0.908041\pi$
$163$	0.179062	−	0.668269i	0.0140252	−	0.0523429i	0.972584	+	0.232553i	$0.0747078\pi$
$164$	7.34822	−	21.2644i	0.573800	−	1.66047i
$165$	−2.42935	−	3.46947i	−0.189124	−	0.270098i
$166$	−13.5829	+	0.111032i	−1.05424	+	0.00861774i
$167$	−3.21215	+	3.82809i	−0.248563	+	0.296226i	−0.875871	−	0.482545i	$-0.839712\pi$
$167$	−3.21215	+	3.82809i	−0.248563	+	0.296226i	0.627308	+	0.778772i	$0.284157\pi$
$168$	3.72153	+	1.25207i	0.287122	+	0.0965992i
$169$	4.40237	−	12.0954i	0.338644	−	0.930417i
$170$	−23.6961	−	19.5555i	−1.81741	−	1.49984i
$171$	−1.53799	−	4.07855i	−0.117613	−	0.311895i
$172$	3.72734	−	5.51286i	0.284207	−	0.420352i
$173$	6.65917	+	14.2806i	0.506287	+	1.08574i	0.978876	+	0.204453i	$0.0655417\pi$
$173$	6.65917	+	14.2806i	0.506287	+	1.08574i	−0.472589	+	0.881283i	$0.656681\pi$
$174$	0.516194	+	1.86534i	0.0391326	+	0.141411i
$175$	−4.44531	+	5.29772i	−0.336034	+	0.400470i
$176$	1.55647	+	5.13152i	0.117323	+	0.386803i
$177$	−0.438606	+	2.48746i	−0.0329677	+	0.186969i
$178$	−5.50488	+	12.0617i	−0.412609	+	0.904063i
$179$	1.95971	+	0.525102i	0.146475	+	0.0392480i	0.331312	−	0.943521i	$-0.392509\pi$
$179$	1.95971	+	0.525102i	0.146475	+	0.0392480i	−0.184836	+	0.982769i	$0.559175\pi$
$180$	−1.53542	+	6.12936i	−0.114443	+	0.456856i
$181$	−0.331579	+	0.711074i	−0.0246461	+	0.0528537i	−0.918245	−	0.396012i	$-0.870394\pi$
$181$	−0.331579	+	0.711074i	−0.0246461	+	0.0528537i	0.893599	+	0.448865i	$0.148172\pi$
$182$	−1.65360	+	9.84808i	−0.122573	+	0.729988i
$183$	−7.78035	−	4.49199i	−0.575140	−	0.332057i
$184$	2.15542	+	19.2008i	0.158900	+	1.41550i
$185$	10.9617	−	9.19794i	0.805919	−	0.676246i
$186$	13.6729	−	2.52630i	1.00254	−	0.185238i
$187$	−7.55116	−	5.28738i	−0.552196	−	0.386652i
$188$	1.83949	−	11.5316i	0.134159	−	0.841031i
$189$	0.981627	+	0.981627i	0.0714029	+	0.0714029i
$190$	−18.4289	−	6.29904i	−1.33697	−	0.456981i
$191$		−	5.61208i		−	0.406076i	−0.979171	−	0.203038i	$-0.934919\pi$
$191$		−	5.61208i		−	0.406076i	0.979171	−	0.203038i	$-0.0650814\pi$
$192$	4.26182	−	6.77030i	0.307570	−	0.488604i
$193$	5.19548	−	0.916103i	0.373979	−	0.0659425i	0.0165001	−	0.999864i	$-0.494748\pi$
$193$	5.19548	−	0.916103i	0.373979	−	0.0659425i	0.357479	+	0.933921i	$0.383637\pi$
$194$	7.59112	−	11.0321i	0.545011	−	0.792058i
$195$	−16.0088	−	1.40058i	−1.14641	−	0.100298i
$196$	0.165858	+	10.1443i	0.0118470	+	0.724591i
$197$	−9.08387	+	2.43401i	−0.647199	+	0.173416i	−0.567462	−	0.823400i	$-0.692075\pi$
$197$	−9.08387	+	2.43401i	−0.647199	+	0.173416i	−0.0797367	+	0.996816i	$0.525408\pi$
$198$	−0.313944	+	1.86971i	−0.0223111	+	0.132875i
$199$	3.08188	−	1.12171i	0.218469	−	0.0795161i	−0.230467	−	0.973080i	$-0.574025\pi$
$199$	3.08188	−	1.12171i	0.218469	−	0.0795161i	0.448936	+	0.893564i	$0.351803\pi$
$200$	8.36241	+	11.3404i	0.591312	+	0.801888i
$201$	−3.72221	+	2.14902i	−0.262544	+	0.151580i
$202$	−16.3760	+	6.11244i	−1.15221	+	0.430070i
$203$	1.55629	−	1.08973i	0.109230	−	0.0764839i
$204$	1.42242	+	13.6788i	0.0995891	+	0.957705i
$205$	−3.09754	−	35.4050i	−0.216341	−	2.47279i
$206$	−14.3202	+	3.96282i	−0.997735	+	0.276103i
$207$	−2.33639	+	6.41917i	−0.162390	+	0.446163i
$208$	18.7107	+	7.99106i	1.29735	+	0.554080i
$209$	−5.66147	−	1.44718i	−0.391612	−	0.100104i
$210$	6.17443	−	0.591087i	0.426076	−	0.0407889i
$211$	−6.51602	+	3.03847i	−0.448581	+	0.209177i	−0.633763	−	0.773527i	$-0.718490\pi$
$211$	−6.51602	+	3.03847i	−0.448581	+	0.209177i	0.185181	+	0.982704i	$0.440713\pi$
$212$	12.2461	+	5.46855i	0.841068	+	0.375582i
$213$	−1.01073	−	11.5527i	−0.0692540	−	0.791577i
$214$	−13.6811	+	0.111834i	−0.935219	+	0.00764485i
$215$	1.82544	−	10.3526i	0.124494	−	0.706042i
$216$	2.41408	−	1.47385i	0.164257	−	0.100283i
$217$	−6.82442	−	11.8202i	−0.463272	−	0.802410i
$218$	−11.8890	−	4.21750i	−0.805223	−	0.285645i
$219$	12.4572	+	5.80887i	0.841776	+	0.392527i
$220$	5.55033	+	6.39919i	0.374203	+	0.431433i
$221$	−33.7838	+	9.05234i	−2.27254	+	0.608926i
$222$	−6.38524	−	0.506079i	−0.428549	−	0.0339658i
$223$	8.50631	−	7.13764i	0.569624	−	0.477972i	−0.311897	−	0.950116i	$-0.600964\pi$
$223$	8.50631	−	7.13764i	0.569624	−	0.477972i	0.881521	+	0.472144i	$0.156520\pi$
$224$	−7.66215	−	1.72087i	−0.511949	−	0.114981i
$225$	0.865054	+	4.90597i	0.0576703	+	0.327064i
$226$	−2.07122	+	7.99058i	−0.137775	+	0.531526i
$227$	11.8804	−	11.8804i	0.788533	−	0.788533i	−0.192721	−	0.981254i	$-0.561731\pi$
$227$	11.8804	−	11.8804i	0.788533	−	0.788533i	0.981254	+	0.192721i	$0.0617311\pi$
$228$	3.90317	+	7.79521i	0.258494	+	0.516250i
$229$	−9.52920	−	9.52920i	−0.629707	−	0.629707i	0.318287	−	0.947994i	$-0.396892\pi$
$229$	−9.52920	−	9.52920i	−0.629707	−	0.629707i	−0.947994	+	0.318287i	$0.896892\pi$
$230$	15.4764	+	26.3070i	1.02048	+	1.73463i
$231$	1.83278	−	0.323168i	0.120588	−	0.0212629i
$232$	−1.41271	−	3.60389i	−0.0927492	−	0.236607i
$233$	5.20707	+	6.20555i	0.341127	+	0.406539i	0.909147	−	0.416476i	$-0.136735\pi$
$233$	5.20707	+	6.20555i	0.341127	+	0.406539i	−0.568020	+	0.823015i	$0.692290\pi$
$234$	4.66864	+	5.47240i	0.305199	+	0.357742i
$235$	−4.77435	−	17.8181i	−0.311445	−	1.16233i
$236$	0.357954	−	5.03897i	0.0233008	−	0.328009i
$237$	−6.35925	+	13.6375i	−0.413078	+	0.885848i
$238$	12.1880	−	5.80510i	0.790029	−	0.376289i
$239$	6.83043	−	3.94355i	0.441824	−	0.255087i	−0.262547	−	0.964919i	$-0.584562\pi$
$239$	6.83043	−	3.94355i	0.441824	−	0.255087i	0.704371	+	0.709832i	$0.251229\pi$
$240$	1.78645	−	12.5106i	0.115315	−	0.807555i
$241$	−1.29540	−	0.228414i	−0.0834442	−	0.0147135i	0.131770	−	0.991280i	$-0.457934\pi$
$241$	−1.29540	−	0.228414i	−0.0834442	−	0.0147135i	−0.215214	+	0.976567i	$0.569045\pi$
$242$	−9.27773	−	9.12728i	−0.596395	−	0.586724i
$243$	0.996195	−	0.0871557i	0.0639059	−	0.00559104i
$244$	16.4065	+	7.32636i	1.05032	+	0.469022i
$245$	6.77327	+	14.5253i	0.432728	+	0.927989i
$246$	−10.1259	+	12.2699i	−0.645607	+	0.782303i
$247$	−18.0136	+	12.9256i	−1.14618	+	0.822435i
$248$	−26.6765	+	7.85387i	−1.69396	+	0.498721i
$249$	9.02562	+	3.28506i	0.571976	+	0.208182i
$250$	−0.0713387	−	0.0404135i	−0.00451185	−	0.00255597i
$251$	−9.18071	+	0.803208i	−0.579481	+	0.0506980i	−0.373129	−	0.927780i	$-0.621715\pi$
$251$	−9.18071	+	0.803208i	−0.579481	+	0.0506980i	−0.206353	+	0.978478i	$0.566159\pi$
$252$	−2.15578	−	1.74967i	−0.135802	−	0.110219i
$253$	5.25269	+	7.50161i	0.330234	+	0.471622i
$254$	10.5018	−	23.0105i	0.658945	−	1.44381i
$255$	10.8623	+	18.8141i	0.680226	+	1.17819i
$256$	−7.07743	+	14.3496i	−0.442339	+	0.896848i
$257$	−2.97595	−	8.17635i	−0.185635	−	0.510027i	0.811611	−	0.584198i	$-0.198591\pi$
$257$	−2.97595	−	8.17635i	−0.185635	−	0.510027i	−0.997245	+	0.0741716i	$0.976369\pi$
$258$	−3.83238	+	2.73042i	−0.238594	+	0.169989i
$259$	1.62735	+	6.07334i	0.101118	+	0.377379i
$260$	32.1355	−	0.525412i	1.99296	−	0.0325847i
$261$	0.119278	−	1.36336i	0.00738314	−	0.0843897i
$262$	1.67989	+	9.09192i	0.103784	+	0.561701i
$263$	4.34429	+	24.6377i	0.267880	+	1.51923i	0.760706	+	0.649097i	$0.224853\pi$
$263$	4.34429	+	24.6377i	0.267880	+	1.51923i	−0.492825	+	0.870128i	$0.664036\pi$
$264$	0.237754	−	3.78431i	0.0146328	−	0.232908i
$265$	21.1862			1.30146
$266$	5.93070	−	6.16926i	0.363635	−	0.378261i
$267$	6.62926	−	6.62926i	0.405704	−	0.405704i
$268$	6.95995	−	5.04496i	0.425146	−	0.308170i
$269$	−8.14264	+	11.6289i	−0.496466	+	0.709027i	−0.986698	−	0.162565i	$-0.948023\pi$
$269$	−8.14264	+	11.6289i	−0.496466	+	0.709027i	0.490232	+	0.871592i	$0.336912\pi$
$270$	2.53275	−	3.68082i	0.154139	−	0.224008i
$271$	−12.5082	−	14.9067i	−0.759818	−	0.905516i	0.238019	−	0.971261i	$-0.423502\pi$
$271$	−12.5082	−	14.9067i	−0.759818	−	0.905516i	−0.997836	+	0.0657449i	$0.979058\pi$
$272$	−5.65915	−	26.9165i	−0.343136	−	1.63206i
$273$	3.53056	−	6.11511i	0.213679	−	0.370103i
$274$	15.7416	−	11.2153i	0.950986	−	0.677540i
$275$	6.05266	+	2.82240i	0.364989	+	0.170197i
$276$	3.31985	−	13.2528i	0.199831	−	0.797724i
$277$	3.53583	−	13.1959i	0.212447	−	0.792864i	−0.774602	−	0.632449i	$-0.782050\pi$
$277$	3.53583	−	13.1959i	0.212447	−	0.792864i	0.987050	−	0.160416i	$-0.0512834\pi$
$278$	−8.01787	−	21.4809i	−0.480880	−	1.28834i
$279$	−9.68245	−	1.70728i	−0.579673	−	0.102212i
$280$	−12.1604	+	2.45307i	−0.726720	+	0.146599i
$281$	6.07483	+	5.09739i	0.362394	+	0.304085i	0.805744	−	0.592264i	$-0.201766\pi$
$281$	6.07483	+	5.09739i	0.362394	+	0.304085i	−0.443350	+	0.896349i	$0.646210\pi$
$282$	−4.07000	+	7.18444i	−0.242365	+	0.427827i
$283$	−13.7505	+	6.41198i	−0.817384	+	0.381153i	−0.785901	−	0.618352i	$-0.787801\pi$
$283$	−13.7505	+	6.41198i	−0.817384	+	0.381153i	−0.0314828	+	0.999504i	$0.510023\pi$
$284$	4.40039	+	22.7724i	0.261115	+	1.35129i
$285$	10.6509	+	8.72977i	0.630907	+	0.517107i
$286$	9.59939	−	0.918964i	0.567624	−	0.0543395i
$287$	14.6746	+	5.34112i	0.866215	+	0.315276i
$288$	−4.49738	+	3.43127i	−0.265011	+	0.202189i
$289$	23.1981	+	19.4655i	1.36459	+	1.14503i
$290$	−4.35901	−	4.28832i	−0.255970	−	0.251819i
$291$	−7.75673	+	5.43132i	−0.454707	+	0.318390i
$292$	−25.9823	−	8.97855i	−1.52050	−	0.525430i
$293$	23.0153	+	6.16693i	1.34457	+	0.360276i	0.858127	−	0.513437i	$-0.171628\pi$
$293$	23.0153	+	6.16693i	1.34457	+	0.360276i	0.486441	+	0.873713i	$0.338295\pi$
$294$	2.39848	−	6.76123i	0.139882	−	0.394323i
$295$	−2.72934	−	7.49880i	−0.158908	−	0.436597i
$296$	12.8067	−	0.314116i	0.744373	−	0.0182576i
$297$	0.670297	−	1.16099i	0.0388946	−	0.0673674i
$298$	2.36857	−	2.02068i	0.137207	−	0.117055i
$299$	34.6138	+	3.02832i	2.00177	+	0.175132i
$300$	−2.73567	−	9.58037i	−0.157944	−	0.553123i
$301$	3.78376	+	2.64941i	0.218092	+	0.152710i
$302$	7.32993	−	28.2783i	0.421790	−	1.62723i
$303$	12.3600			0.710061
$304$	−9.37699	−	14.6994i	−0.537807	−	0.843068i
$305$	28.3837			1.62525
$306$	2.44002	−	9.41340i	0.139487	−	0.538128i
$307$	18.3297	+	12.8346i	1.04613	+	0.732508i	0.964481	−	0.264153i	$-0.0850924\pi$
$307$	18.3297	+	12.8346i	1.04613	+	0.732508i	0.0816492	+	0.996661i	$0.473981\pi$
$308$	−3.57905	+	1.02200i	−0.203935	+	0.0582337i
$309$	10.4665	+	0.915699i	0.595418	+	0.0520923i
$310$	−33.4195	+	28.5111i	−1.89810	+	1.61932i
$311$	−2.20679	+	3.82228i	−0.125136	+	0.216741i	−0.921786	−	0.387699i	$-0.873270\pi$
$311$	−2.20679	+	3.82228i	−0.125136	+	0.216741i	0.796650	+	0.604440i	$0.206603\pi$
$312$	−10.4192	−	9.92034i	−0.589872	−	0.561629i
$313$	10.0825	+	27.7014i	0.569896	+	1.56578i	0.804668	+	0.593726i	$0.202344\pi$
$313$	10.0825	+	27.7014i	0.569896	+	1.56578i	−0.234772	+	0.972051i	$0.575434\pi$
$314$	−8.94849	+	25.2255i	−0.504993	+	1.42356i
$315$	−4.23649	−	1.13516i	−0.238699	−	0.0639593i
$316$	9.82926	−	28.4441i	0.552939	−	1.60011i
$317$	−2.98437	+	2.08968i	−0.167619	+	0.117368i	−0.654376	−	0.756169i	$-0.727069\pi$
$317$	−2.98437	+	2.08968i	−0.167619	+	0.117368i	0.486757	+	0.873537i	$0.338180\pi$
$318$	−6.76042	−	6.65080i	−0.379106	−	0.372958i
$319$	−1.40545	−	1.17932i	−0.0786903	−	0.0660290i
$320$	−0.965806	+	25.2565i	−0.0539902	+	1.41188i
$321$	9.09087	+	3.30881i	0.507403	+	0.184680i
$322$	−13.3502	+	1.27804i	−0.743979	+	0.0712222i
$323$	28.2817	+	9.92568i	1.57364	+	0.552279i
$324$	−1.96367	+	0.379449i	−0.109093	+	0.0210805i
$325$	22.9647	−	10.7086i	1.27385	−	0.594008i
$326$	0.482265	−	0.851302i	0.0267102	−	0.0471493i
$327$	6.83317	+	5.73371i	0.377875	+	0.317075i
$328$	17.6051	−	26.5029i	0.972081	−	1.46338i
$329$	7.98234	+	1.40750i	0.440081	+	0.0775981i
$330$	−2.09458	−	5.61165i	−0.115303	−	0.308911i
$331$	2.64760	−	9.88097i	0.145525	−	0.543107i	−0.854206	−	0.519934i	$-0.825956\pi$
$331$	2.64760	−	9.88097i	0.145525	−	0.543107i	0.999731	−	0.0231730i	$-0.00737685\pi$
$332$	−18.6340	−	4.66785i	−1.02267	−	0.256181i
$333$	4.10485	+	1.91413i	0.224945	+	0.104893i
$334$	−5.75573	+	4.10072i	−0.314939	+	0.224382i
$335$	6.78955	−	11.7599i	0.370953	−	0.642509i
$336$	4.65038	+	3.03462i	0.253699	+	0.165552i
$337$	3.32887	+	3.96719i	0.181335	+	0.216107i	0.849053	−	0.528308i	$-0.177173\pi$
$337$	3.32887	+	3.96719i	0.181335	+	0.216107i	−0.667718	+	0.744414i	$0.732729\pi$
$338$	10.3187	−	14.9961i	0.561266	−	0.815681i
$339$	3.34792	−	4.78133i	0.181834	−	0.259686i
$340$	−25.5000	−	35.1795i	−1.38293	−	1.90787i
$341$	−9.32000	+	9.32000i	−0.504706	+	0.504706i
$342$	−0.658207	−	6.12917i	−0.0355918	−	0.331428i
$343$	−16.7599			−0.904947
$344$	7.05885	−	6.22432i	0.380588	−	0.335593i
$345$	−3.74770	−	21.2542i	−0.201769	−	1.14429i
$346$	4.04877	+	21.9128i	0.217663	+	1.17804i
$347$	−2.26703	+	25.9123i	−0.121701	+	1.39105i	0.652348	+	0.757920i	$0.273784\pi$
$347$	−2.26703	+	25.9123i	−0.121701	+	1.39105i	−0.774049	+	0.633126i	$0.781771\pi$
$348$	0.0447457	+	2.73676i	0.00239862	+	0.146706i
$349$	−8.30836	−	31.0072i	−0.444736	−	1.65978i	−0.716631	−	0.697452i	$-0.754317\pi$
$349$	−8.30836	−	31.0072i	−0.444736	−	1.65978i	0.271895	−	0.962327i	$-0.412350\pi$
$350$	−7.96539	+	5.67502i	−0.425768	+	0.303342i
$351$	−1.73966	−	4.77967i	−0.0928561	−	0.255120i
$352$	0.309861	+	7.57721i	0.0165156	+	0.403867i
$353$	1.41749	+	2.45517i	0.0754455	+	0.130675i	0.901280	−	0.433237i	$-0.142629\pi$
$353$	1.41749	+	2.45517i	0.0754455	+	0.130675i	−0.825834	+	0.563913i	$0.809295\pi$
$354$	−1.48311	+	3.24962i	−0.0788263	+	0.172716i
$355$	21.0151	+	30.0126i	1.11536	+	1.59291i
$356$	−11.8161	+	14.5587i	−0.626252	+	0.771612i
$357$	−9.50951	+	0.831974i	−0.503296	+	0.0440327i
$358$	2.49645	+	1.41425i	0.131942	+	0.0747452i
$359$	−9.84934	−	3.58487i	−0.519828	−	0.189202i	0.0687626	−	0.997633i	$-0.478095\pi$
$359$	−9.84934	−	3.58487i	−0.519828	−	0.189202i	−0.588591	+	0.808431i	$0.700317\pi$
$360$	−4.27693	+	7.84609i	−0.225414	+	0.413525i
$361$	18.9949	−	0.438426i	0.999734	−	0.0230750i
$362$	−0.706245	+	0.855780i	−0.0371194	+	0.0449788i
$363$	3.88928	+	8.34058i	0.204134	+	0.437767i
$364$	−5.75829	+	12.8950i	−0.301816	+	0.675880i
$365$	−43.2602	+	3.78478i	−2.26434	+	0.198104i
$366$	−9.05711	−	8.91024i	−0.473423	−	0.465746i
$367$	−21.9793	−	3.87554i	−1.14731	−	0.202301i	−0.432508	−	0.901630i	$-0.642371\pi$
$367$	−21.9793	−	3.87554i	−1.14731	−	0.202301i	−0.714800	+	0.699329i	$0.753482\pi$
$368$	−3.86263	+	27.0502i	−0.201353	+	1.41009i
$369$	9.74204	−	5.62457i	0.507150	−	0.292803i
$370$	18.2701	−	8.70200i	0.949817	−	0.452396i
$371$	−3.93426	+	8.43704i	−0.204256	+	0.438029i
$372$	19.6142	+	1.39334i	1.01695	+	0.0722412i
$373$	6.45597	+	24.0940i	0.334278	+	1.24754i	0.904650	+	0.426155i	$0.140132\pi$
$373$	6.45597	+	24.0940i	0.334278	+	1.24754i	−0.570373	+	0.821386i	$0.693201\pi$
$374$	−8.46111	−	9.91778i	−0.437514	−	0.512836i
$375$	0.0372663	+	0.0444123i	0.00192442	+	0.00229344i
$376$	6.61018	−	15.1337i	0.340894	−	0.780463i
$377$	−6.85534	+	1.20878i	−0.353068	+	0.0622554i
$378$	0.995492	+	1.69215i	0.0512026	+	0.0870347i
$379$	11.1061	+	11.1061i	0.570483	+	0.570483i	0.932263	−	0.361781i	$-0.117831\pi$
$379$	11.1061	+	11.1061i	0.570483	+	0.570483i	−0.361781	+	0.932263i	$0.617831\pi$
$380$	−22.9935	−	15.1627i	−1.17954	−	0.777828i
$381$	−12.6469	+	12.6469i	−0.647918	+	0.647918i
$382$	1.99143	−	7.68277i	0.101890	−	0.393085i
$383$	2.17551	+	12.3379i	0.111164	+	0.630440i	0.988578	+	0.150707i	$0.0481551\pi$
$383$	2.17551	+	12.3379i	0.111164	+	0.630440i	−0.877415	+	0.479732i	$0.840734\pi$
$384$	8.23673	−	7.75605i	0.420329	−	0.395799i
$385$	−4.50416	+	3.77944i	−0.229553	+	0.192618i
$386$	7.43754	+	0.589481i	0.378561	+	0.0300038i
$387$	3.21396	−	0.861179i	0.163375	−	0.0437762i
$388$	14.3067	−	12.4089i	0.726314	−	0.629968i
$389$	23.1343	+	10.7877i	1.17295	+	0.546957i	0.908681	−	0.417491i	$-0.137090\pi$
$389$	23.1343	+	10.7877i	1.17295	+	0.546957i	0.264273	+	0.964448i	$0.414868\pi$
$390$	−21.4185	−	7.59802i	−1.08457	−	0.384741i
$391$	−23.4863	−	40.6795i	−1.18775	−	2.05725i
$392$	−3.37261	+	13.9461i	−0.170343	+	0.704383i
$393$	1.13527	−	6.43846i	0.0572670	−	0.324777i
$394$	−13.2993	+	0.108713i	−0.670007	+	0.00547690i
$395$	−4.14338	−	47.3591i	−0.208476	−	2.38289i
$396$	−1.09324	+	2.44818i	−0.0549375	+	0.123026i
$397$	13.3976	−	6.24741i	0.672407	−	0.313549i	−0.0562605	−	0.998416i	$-0.517918\pi$
$397$	13.3976	−	6.24741i	0.672407	−	0.313549i	0.728668	+	0.684868i	$0.240140\pi$
$398$	4.61704	−	0.441996i	0.231431	−	0.0221553i
$399$	−5.45434	+	2.62044i	−0.273058	+	0.131186i
$400$	7.42379	+	18.4921i	0.371190	+	0.924603i
$401$	8.68390	−	23.8588i	0.433653	−	1.19145i	−0.509901	−	0.860233i	$-0.670318\pi$
$401$	8.68390	−	23.8588i	0.433653	−	1.19145i	0.943554	−	0.331219i	$-0.107460\pi$
$402$	−5.85817	+	1.62113i	−0.292179	+	0.0808546i
$403$	4.35855	+	49.8185i	0.217115	+	2.48164i
$404$	−24.5873	+	2.55677i	−1.22327	+	0.127204i
$405$	−2.58801	+	1.81214i	−0.128599	+	0.0900461i
$406$	2.51721	−	0.939561i	0.124927	−	0.0466296i
$407$	5.25835	−	3.03591i	0.260647	−	0.150485i
$408$	−2.90662	+	19.2306i	−0.143899	+	0.952055i
$409$	14.4506	−	5.25959i	0.714537	−	0.260070i	0.0409322	−	0.999162i	$-0.486967\pi$
$409$	14.4506	−	5.25959i	0.714537	−	0.260070i	0.673605	+	0.739092i	$0.264745\pi$
$410$	8.32292	−	49.5676i	0.411040	−	2.44797i
$411$	−13.2014	+	3.53732i	−0.651179	+	0.174483i
$412$	−21.0101	+	0.343513i	−1.03509	+	0.0169237i
$413$	3.49310	+	0.305606i	0.171884	+	0.0150379i
$414$	−5.47627	+	7.95860i	−0.269144	+	0.391144i
$415$	−29.8844	+	5.26942i	−1.46697	+	0.258666i
$416$	22.7788	+	17.5790i	1.11682	+	0.861880i
$417$			16.2129i			0.793949i
$418$	−7.23687	−	3.99011i	−0.353967	−	0.195163i
$419$	−2.93219	−	2.93219i	−0.143247	−	0.143247i	0.631846	−	0.775094i	$-0.282297\pi$
$419$	−2.93219	−	2.93219i	−0.143247	−	0.143247i	−0.775094	+	0.631846i	$0.782297\pi$
$420$	8.66236	+	1.38180i	0.422680	+	0.0674248i
$421$	−21.2486	−	14.8784i	−1.03559	−	0.725130i	−0.0733460	−	0.997307i	$-0.523368\pi$
$421$	−21.2486	−	14.8784i	−1.03559	−	0.725130i	−0.962247	+	0.272176i	$0.912257\pi$
$422$	−9.99844	+	1.84739i	−0.486717	+	0.0899295i
$423$	4.47271	−	3.75305i	0.217471	−	0.182480i
$424$	14.8241	+	11.8318i	0.719922	+	0.574603i
$425$	−29.6658	−	17.1276i	−1.43900	−	0.830808i
$426$	2.71578	−	16.1739i	0.131580	−	0.783630i
$427$	−5.27082	+	11.3033i	−0.255073	+	0.547006i
$428$	−18.7687	−	4.70159i	−0.907219	−	0.227260i
$429$	−6.58648	−	1.76484i	−0.317998	−	0.0852073i
$430$	6.17257	−	13.5247i	0.297668	−	0.652217i
$431$	1.73689	−	9.85039i	0.0836630	−	0.474477i	−0.913974	−	0.405773i	$-0.867002\pi$
$431$	1.73689	−	9.85039i	0.0836630	−	0.474477i	0.997637	−	0.0687040i	$-0.0218864\pi$
$432$	3.82779	−	1.16103i	0.184165	−	0.0558601i
$433$	16.7472	−	19.9585i	0.804819	−	0.959146i	−0.194947	−	0.980814i	$-0.562453\pi$
$433$	16.7472	−	19.9585i	0.804819	−	0.959146i	0.999765	+	0.0216683i	$0.00689778\pi$
$434$	−5.14806	−	18.6032i	−0.247115	−	0.892982i
$435$	1.82732	+	3.91870i	0.0876133	+	0.187887i
$436$	−14.7791	−	9.99241i	−0.707791	−	0.478550i
$437$	−23.0292	−	18.8753i	−1.10164	−	0.902930i
$438$	14.9922	+	12.3726i	0.716357	+	0.591184i
$439$	−1.78517	+	4.90472i	−0.0852016	+	0.234090i	−0.974976	−	0.222312i	$-0.928640\pi$
$439$	−1.78517	+	4.90472i	−0.0852016	+	0.234090i	0.889774	+	0.456401i	$0.150862\pi$
$440$	5.32751	+	10.7298i	0.253979	+	0.511524i
$441$	−3.26074	+	3.88600i	−0.155273	+	0.185048i
$442$	−49.4612	+	0.404315i	−2.35263	+	0.0192313i
$443$	13.1608	+	18.7956i	0.625290	+	0.893006i	0.999409	−	0.0343744i	$-0.0109439\pi$
$443$	13.1608	+	18.7956i	0.625290	+	0.893006i	−0.374119	+	0.927381i	$0.622055\pi$
$444$	−8.56163	−	2.95859i	−0.406317	−	0.140409i
$445$	−7.66615	+	28.6105i	−0.363411	+	1.35627i
$446$	14.1777	−	6.75279i	0.671332	−	0.319754i
$447$	−2.06874	+	0.752960i	−0.0978481	+	0.0356138i
$448$	−9.87861	−	5.07472i	−0.466721	−	0.239758i
$449$	30.0867	+	17.3706i	1.41988	+	0.819767i	0.996288	−	0.0860860i	$-0.0274360\pi$
$449$	30.0867	+	17.3706i	1.41988	+	0.819767i	0.423591	+	0.905853i	$0.360769\pi$
$450$	−0.556633	+	7.02309i	−0.0262399	+	0.331072i
$451$	1.31435	−	15.0231i	0.0618905	−	0.707412i
$452$	−5.67087	+	10.2039i	−0.266735	+	0.479952i
$453$	−11.8481	+	16.9209i	−0.556673	+	0.795012i
$454$	20.4797	−	12.0483i	0.961162	−	0.565453i
$455$			22.3087i			1.04585i
$456$	2.57723	+	12.0564i	0.120690	+	0.564595i
$457$			9.10855i			0.426080i	0.977043	+	0.213040i	$0.0683364\pi$
$457$			9.10855i			0.426080i	−0.977043	+	0.213040i	$0.931664\pi$
$458$	−9.66379	−	16.4266i	−0.451559	−	0.767565i
$459$	−3.94406	+	5.63270i	−0.184093	+	0.262912i
$460$	11.8518	+	41.5053i	0.552594	+	1.93519i
$461$	−1.95252	+	22.3174i	−0.0909379	+	1.03943i	0.804415	+	0.594068i	$0.202479\pi$
$461$	−1.95252	+	22.3174i	−0.0909379	+	1.03943i	−0.895353	+	0.445357i	$0.853077\pi$
$462$	2.62370	+	0.207948i	0.122065	+	0.00967462i
$463$	−4.20992	−	2.43060i	−0.195652	−	0.112960i	0.398974	−	0.916962i	$-0.369366\pi$
$463$	−4.20992	−	2.43060i	−0.195652	−	0.112960i	−0.594626	+	0.804003i	$0.702700\pi$
$464$	−0.655136	−	5.43492i	−0.0304139	−	0.252310i
$465$	29.1891	−	10.6240i	1.35361	−	0.492675i
$466$	4.92632	+	10.3429i	0.228207	+	0.479127i
$467$	2.51548	−	9.38789i	0.116402	−	0.434420i	−0.882986	−	0.469400i	$-0.844470\pi$
$467$	2.51548	−	9.38789i	0.116402	−	0.434420i	0.999388	+	0.0349803i	$0.0111368\pi$
$468$	4.44938	+	9.14821i	0.205672	+	0.422876i
$469$	3.42234	+	4.88761i	0.158029	+	0.225689i
$470$	−0.213243	−	26.0867i	−0.00983616	−	1.20329i
$471$	12.1655	−	14.4983i	0.560557	−	0.668046i
$472$	2.27809	−	6.77119i	0.104858	−	0.311669i
$473$	1.52562	−	4.19160i	0.0701480	−	0.192730i
$474$	−13.5448	+	16.4127i	−0.622135	+	0.753862i
$475$	−21.4267	−	3.52369i	−0.983124	−	0.161678i
$476$	18.7449	−	3.62215i	0.859171	−	0.166021i
$477$	2.83401	+	6.07755i	0.129760	+	0.278272i
$478$	10.7500	−	2.97485i	0.491695	−	0.136067i
$479$	−0.705415	+	0.840681i	−0.0322312	+	0.0384117i	−0.781919	−	0.623380i	$-0.785759\pi$
$479$	−0.705415	+	0.840681i	−0.0322312	+	0.0384117i	0.749688	+	0.661791i	$0.230204\pi$
$480$	6.88495	−	16.4927i	0.314253	−	0.752787i
$481$	4.00041	−	22.6875i	0.182403	−	1.03446i
$482$	−1.69232	−	0.772363i	−0.0770830	−	0.0351802i
$483$	9.16006	+	2.45443i	0.416797	+	0.111680i
$484$	−9.46216	−	15.7872i	−0.430098	−	0.717598i
$485$	12.6434	−	27.1138i	0.574107	−	1.23118i
$486$	1.39469	+	0.234183i	0.0632644	+	0.0106228i
$487$	18.7789	+	10.8420i	0.850952	+	0.491297i	0.860972	−	0.508653i	$-0.169856\pi$
$487$	18.7789	+	10.8420i	0.850952	+	0.491297i	−0.0100202	+	0.999950i	$0.503190\pi$
$488$	19.8602	+	15.8514i	0.899031	+	0.717557i
$489$	−0.529983	+	0.444708i	−0.0239667	+	0.0201104i
$490$	4.11815	+	22.2882i	0.186039	+	1.00688i
$491$	28.3263	+	19.8343i	1.27835	+	0.895110i	0.997901	−	0.0647590i	$-0.0206279\pi$
$491$	28.3263	+	19.8343i	1.27835	+	0.895110i	0.280449	+	0.959869i	$0.409517\pi$
$492$	−18.2161	+	13.2040i	−0.821245	+	0.595284i
$493$	6.65430	+	6.65430i	0.299695	+	0.299695i
$494$	−29.2468	+	11.3027i	−1.31587	+	0.508531i
$495$			4.23544i			0.190369i
$496$	−39.3063	+	1.28565i	−1.76490	+	0.0577273i
$497$	−15.8545	+	2.79557i	−0.711170	+	0.125398i
$498$	11.1901	+	7.69987i	0.501442	+	0.345039i
$499$	−23.5240	−	2.05808i	−1.05308	−	0.0921325i	−0.452553	−	0.891738i	$-0.649487\pi$
$499$	−23.5240	−	2.05808i	−1.05308	−	0.0921325i	−0.600526	+	0.799605i	$0.705042\pi$
$500$	−0.0833200	−	0.0806393i	−0.00372618	−	0.00360630i
$501$	4.82694	−	1.29337i	0.215652	−	0.0577837i
$502$	−12.8531	−	2.15818i	−0.573664	−	0.0963243i
$503$	1.73515	−	0.631545i	0.0773667	−	0.0281592i	−0.303047	−	0.952976i	$-0.598004\pi$
$503$	1.73515	−	0.631545i	0.0773667	−	0.0281592i	0.380414	+	0.924816i	$0.375782\pi$
$504$	−2.33034	−	3.16022i	−0.103802	−	0.140767i
$505$	−33.8181	+	19.5249i	−1.50488	+	0.868845i
$506$	4.52885	+	12.1334i	0.201332	+	0.539395i
$507$	−10.5439	+	7.38289i	−0.468269	+	0.327886i
$508$	22.5419	−	27.7742i	1.00014	−	1.23228i
$509$	−0.0405594	−	0.463596i	−0.00179777	−	0.0205486i	0.995243	−	0.0974254i	$-0.0310607\pi$
$509$	−0.0405594	−	0.463596i	−0.00179777	−	0.0205486i	−0.997041	+	0.0768768i	$0.975505\pi$
$510$	8.19410	+	29.6105i	0.362841	+	1.31117i
$511$	6.52614	−	17.9304i	0.288699	−	0.793195i
$512$	−14.7807	+	17.1327i	−0.653221	+	0.757168i
$513$	−1.07951	+	4.22311i	−0.0476616	+	0.186455i
$514$	−1.17263	−	12.2492i	−0.0517227	−	0.540289i
$515$	−30.0839	+	14.0283i	−1.32565	+	0.618162i
$516$	−6.21531	+	2.37796i	−0.273614	+	0.104684i
$517$	−0.682198	−	7.79756i	−0.0300030	−	0.342936i
$518$	0.0726841	+	8.89169i	0.00319356	+	0.390678i
$519$	2.73616	−	15.5175i	0.120104	−	0.681145i
$520$	44.1791	+	10.6839i	1.93738	+	0.468521i
$521$	10.5286	+	18.2361i	0.461268	+	0.798939i	0.999024	−	0.0441607i	$-0.0140614\pi$
$521$	10.5286	+	18.2361i	0.461268	+	0.798939i	−0.537757	+	0.843100i	$0.680728\pi$
$522$	0.647072	−	1.82407i	0.0283216	−	0.0798374i
$523$	22.4879	+	10.4863i	0.983329	+	0.458534i	0.846690	−	0.532087i	$-0.178592\pi$
$523$	22.4879	+	10.4863i	0.983329	+	0.458534i	0.136639	+	0.990621i	$0.456370\pi$
$524$	−0.926516	+	13.0427i	−0.0404750	+	0.569773i
$525$	6.68003	−	1.78991i	0.291540	−	0.0781180i
$526$	−2.79540	+	35.2699i	−0.121885	+	1.53784i
$527$	51.7893	−	43.4564i	2.25598	−	1.89299i
$528$	1.66833	−	5.09625i	0.0726048	−	0.221786i
$529$	4.10928	+	23.3049i	0.178665	+	1.01326i
$530$	29.0034	+	7.51788i	1.25983	+	0.326556i
$531$	1.78603	−	1.78603i	0.0775073	−	0.0775073i
$532$	10.3081	−	6.34105i	0.446913	−	0.274919i
$533$	−40.4591	−	40.4591i	−1.75248	−	1.75248i
$534$	11.4276	−	6.72290i	0.494523	−	0.290928i
$535$	−30.1004	+	5.30751i	−1.30135	+	0.229464i
$536$	11.3182	−	4.43669i	0.488870	−	0.191636i
$537$	−1.30411	−	1.55418i	−0.0562766	−	0.0670678i
$538$	−15.2735	+	13.0302i	−0.658489	+	0.561774i
$539$	1.76012	+	6.56886i	0.0758138	+	0.282941i
$540$	4.77340	−	4.14020i	0.205414	−	0.178166i
$541$	−8.07437	+	17.3155i	−0.347144	+	0.744454i	−0.999914	−	0.0131028i	$-0.995829\pi$
$541$	−8.07437	+	17.3155i	−0.347144	+	0.744454i	0.652770	+	0.757556i	$0.273607\pi$
$542$	−11.8338	−	24.8453i	−0.508303	−	1.06720i
$543$	0.679469	−	0.392292i	0.0291588	−	0.0168348i
$544$	1.80404	−	38.8561i	0.0773476	−	1.66594i
$545$	−27.7537	−	4.89372i	−1.18884	−	0.209624i
$546$	7.00317	−	7.11861i	0.299708	−	0.304648i
$547$	20.1646	−	1.76418i	0.862178	−	0.0754308i	0.352516	−	0.935806i	$-0.385326\pi$
$547$	20.1646	−	1.76418i	0.862178	−	0.0754308i	0.509662	+	0.860375i	$0.329771\pi$
$548$	25.5295	−	9.76753i	1.09057	−	0.417248i
$549$	3.79679	+	8.14225i	0.162043	+	0.347503i
$550$	7.28439	+	6.01155i	0.310608	+	0.256333i
$551$	5.43525	+	2.45855i	0.231549	+	0.104738i
$552$	9.24749	−	16.9646i	0.393599	−	0.722063i
$553$	19.6293	+	7.14449i	0.834723	+	0.303814i
$554$	9.52297	−	16.8101i	0.404592	−	0.714194i
$555$	−14.2550	+	1.24715i	−0.605091	+	0.0529386i
$556$	−3.35379	−	32.2519i	−0.142232	−	1.36779i
$557$	11.5111	+	16.4395i	0.487739	+	0.696564i	0.985294	−	0.170869i	$-0.0546574\pi$
$557$	11.5111	+	16.4395i	0.487739	+	0.696564i	−0.497554	+	0.867433i	$0.665769\pi$
$558$	−12.6492	−	5.77301i	−0.535483	−	0.244391i
$559$	−8.46212	−	14.6568i	−0.357910	−	0.619918i
$560$	−17.5176	−	0.956881i	−0.740256	−	0.0404356i
$561$	3.15283	+	8.66234i	0.133113	+	0.365724i
$562$	6.50748	+	9.13382i	0.274501	+	0.385287i
$563$	−2.44148	−	9.11171i	−0.102896	−	0.384013i	0.895202	−	0.445661i	$-0.147031\pi$
$563$	−2.44148	−	9.11171i	−0.102896	−	0.384013i	−0.998098	+	0.0616476i	$0.980365\pi$
$564$	−8.12110	+	8.39107i	−0.341960	+	0.353328i
$565$	−1.60724	+	18.3709i	−0.0676172	+	0.772868i
$566$	−21.0994	+	3.89848i	−0.886872	+	0.163865i
$567$	−0.241064	−	1.36714i	−0.0101237	−	0.0574145i
$568$	−2.05669	+	32.7362i	−0.0862970	+	1.37358i
$569$	−43.6040			−1.82797			−0.913986	−	0.405745i	$-0.867012\pi$
$569$	−43.6040			−1.82797			−0.913986	+	0.405745i	$0.867012\pi$
$570$	11.4831	+	15.7303i	0.480974	+	0.658868i
$571$	4.65200	−	4.65200i	0.194680	−	0.194680i	−0.603035	−	0.797715i	$-0.706042\pi$
$571$	4.65200	−	4.65200i	0.194680	−	0.194680i	0.797715	+	0.603035i	$0.206042\pi$
$572$	13.4674	+	2.14828i	0.563099	+	0.0898241i
$573$	−3.21895	+	4.59714i	−0.134474	+	0.192048i
$574$	18.1938	+	12.5191i	0.759396	+	0.522537i
$575$	21.8743	+	26.0687i	0.912220	+	1.08714i
$576$	−7.37436	+	3.10142i	−0.307265	+	0.129226i
$577$	−6.50045	+	11.2591i	−0.270617	+	0.468723i	−0.969020	−	0.246982i	$-0.920561\pi$
$577$	−6.50045	+	11.2591i	−0.270617	+	0.468723i	0.698403	+	0.715705i	$0.253894\pi$
$578$	24.8502	+	34.8795i	1.03363	+	1.45079i
$579$	−4.78134	−	2.22958i	−0.198706	−	0.0926580i
$580$	−4.44566	−	7.41737i	−0.184596	−	0.307990i
$581$	3.45103	−	12.8794i	0.143173	−	0.534329i
$582$	−12.5460	+	4.68287i	−0.520050	+	0.194111i
$583$	8.85322	+	1.56106i	0.366663	+	0.0646526i
$584$	−32.3830	−	21.5111i	−1.34002	−	0.890137i
$585$	12.3103	+	10.3295i	0.508967	+	0.427074i
$586$	29.3190	+	16.6093i	1.21116	+	0.686123i
$587$	−2.79755	+	1.30452i	−0.115467	+	0.0538432i	−0.479493	−	0.877545i	$-0.659180\pi$
$587$	−2.79755	+	1.30452i	−0.115467	+	0.0538432i	0.364026	+	0.931389i	$0.381402\pi$
$588$	5.68266	−	8.40484i	0.234349	−	0.346610i
$589$	20.9983	−	37.3591i	0.865220	−	1.53935i
$590$	−1.07546	−	11.2341i	−0.0442760	−	0.462502i
$591$	8.83716	+	3.21646i	0.363512	+	0.132308i
$592$	17.6434	+	4.11440i	0.725141	+	0.169101i
$593$	11.8745	+	9.96389i	0.487627	+	0.409168i	0.853175	−	0.521625i	$-0.174674\pi$
$593$	11.8745	+	9.96389i	0.487627	+	0.409168i	−0.365548	+	0.930793i	$0.619118\pi$
$594$	1.32959	−	1.35151i	0.0545538	−	0.0554530i
$595$	24.7047	−	17.2984i	1.01279	−	0.709166i
$596$	3.95953	−	1.92578i	0.162189	−	0.0788831i
$597$	−3.16791	−	0.848840i	−0.129654	−	0.0347407i
$598$	46.3107	+	16.4283i	1.89379	+	0.671803i
$599$	4.84205	+	13.3034i	0.197841	+	0.543563i	0.998452	−	0.0556211i	$-0.0177139\pi$
$599$	4.84205	+	13.3034i	0.197841	+	0.543563i	−0.800611	+	0.599184i	$0.795492\pi$
$600$	−0.345495	−	14.0860i	−0.0141048	−	0.575058i
$601$	−5.68466	+	9.84612i	−0.231882	+	0.401632i	−0.958362	−	0.285556i	$-0.907822\pi$
$601$	−5.68466	+	9.84612i	−0.231882	+	0.401632i	0.726480	+	0.687188i	$0.241155\pi$
$602$	4.23972	+	4.96963i	0.172798	+	0.202547i
$603$	4.28168	+	0.374599i	0.174364	+	0.0152548i
$604$	20.0689	−	36.1111i	0.816593	−	1.46934i
$605$	−23.8169	−	16.6768i	−0.968297	−	0.678009i
$606$	16.9204	+	4.38589i	0.687345	+	0.178165i
$607$	28.9493			1.17502			0.587509	−	0.809218i	$-0.300109\pi$
$607$	28.9493			1.17502			0.587509	+	0.809218i	$0.300109\pi$
$608$	−7.62080	−	23.4504i	−0.309064	−	0.951041i
$609$	−1.89988			−0.0769872
$610$	38.8565	+	10.0719i	1.57326	+	0.407799i
$611$	−24.3273	−	17.0342i	−0.984178	−	0.689129i
$612$	6.68064	−	12.0208i	0.270049	−	0.485914i
$613$	2.97950	+	0.260673i	0.120341	+	0.0105285i	0.147167	−	0.989112i	$-0.452984\pi$
$613$	2.97950	+	0.260673i	0.120341	+	0.0105285i	−0.0268261	+	0.999640i	$0.508540\pi$
$614$	20.5385	+	24.0744i	0.828866	+	0.971564i
$615$	−17.7701	+	30.7788i	−0.716560	+	1.24112i
$616$	−5.26227	+	0.129071i	−0.212023	+	0.00520040i
$617$	−14.7852	−	40.6221i	−0.595231	−	1.63538i	−0.760651	−	0.649161i	$-0.775120\pi$
$617$	−14.7852	−	40.6221i	−0.595231	−	1.63538i	0.165420	−	0.986223i	$-0.447102\pi$
$618$	14.0034	+	4.96757i	0.563299	+	0.199825i
$619$	21.4027	+	5.73483i	0.860246	+	0.230502i	0.661865	−	0.749623i	$-0.269765\pi$
$619$	21.4027	+	5.73483i	0.860246	+	0.230502i	0.198381	+	0.980125i	$0.436432\pi$
$620$	−55.8675	+	27.1720i	−2.24369	+	1.09125i
$621$	5.59574	−	3.91818i	0.224549	−	0.157231i
$622$	−4.37736	+	4.44951i	−0.175516	+	0.178409i
$623$	−9.97001	−	8.36583i	−0.399440	−	0.335170i
$624$	−10.7434	−	17.2779i	−0.430081	−	0.691670i
$625$	−23.5782	−	8.58177i	−0.943129	−	0.343271i
$626$	3.97288	+	41.5002i	0.158788	+	1.65868i
$627$	3.80754	+	4.43275i	0.152058	+	0.177027i
$628$	−21.2014	+	31.3576i	−0.846029	+	1.25130i
$629$	−28.2260	+	13.1620i	−1.12545	+	0.524804i
$630$	−5.39683	−	3.05732i	−0.215015	−	0.121806i
$631$	4.53558	+	3.80581i	0.180559	+	0.151507i	0.728588	−	0.684953i	$-0.240177\pi$
$631$	4.53558	+	3.80581i	0.180559	+	0.151507i	−0.548029	+	0.836459i	$0.684622\pi$
$632$	23.5493	−	35.4513i	0.936740	−	1.41018i
$633$	7.08041	+	1.24847i	0.281421	+	0.0496221i
$634$	−4.82704	+	1.80172i	−0.191706	+	0.0715554i
$635$	14.6250	−	54.5811i	0.580374	−	2.16599i
$636$	−6.89481	−	11.5037i	−0.273397	−	0.456150i
$637$	23.3850	+	10.9046i	0.926547	+	0.432056i
$638$	−1.50555	−	2.11317i	−0.0596053	−	0.0836612i
$639$	−5.79841	+	10.0431i	−0.229381	+	0.397300i
$640$	−10.2844	+	34.2328i	−0.406525	+	1.35317i
$641$	−5.72767	−	6.82597i	−0.226229	−	0.269610i	0.640975	−	0.767561i	$-0.278530\pi$
$641$	−5.72767	−	6.82597i	−0.226229	−	0.269610i	−0.867205	+	0.497952i	$0.834086\pi$
$642$	11.2710	+	7.75553i	0.444832	+	0.306086i
$643$	25.8847	−	36.9671i	1.02079	−	1.45784i	0.136652	−	0.990619i	$-0.456366\pi$
$643$	25.8847	−	36.9671i	1.02079	−	1.45784i	0.884140	−	0.467222i	$-0.154745\pi$
$644$	−18.7296	−	2.98769i	−0.738049	−	0.117732i
$645$	−7.43333	+	7.43333i	−0.292687	+	0.292687i
$646$	35.1948	+	23.6237i	1.38472	+	0.929461i
$647$	19.6210			0.771381			0.385690	−	0.922628i	$-0.373963\pi$
$647$	19.6210			0.771381			0.385690	+	0.922628i	$0.373963\pi$
$648$	−2.82286	−	0.177350i	−0.110892	−	0.00696696i
$649$	−0.587993	−	3.33467i	−0.0230807	−	0.130897i
$650$	35.2380	−	6.51084i	1.38215	−	0.255376i
$651$	−1.18957	+	13.5969i	−0.0466231	+	0.532904i
$652$	0.962289	−	0.994278i	0.0376861	−	0.0389389i
$653$	−5.61320	−	20.9488i	−0.219662	−	0.819788i	−0.984473	−	0.175534i	$-0.943835\pi$
$653$	−5.61320	−	20.9488i	−0.219662	−	0.819788i	0.764812	−	0.644254i	$-0.222832\pi$
$654$	7.31982	+	10.2740i	0.286228	+	0.401746i
$655$	7.06453	+	19.4096i	0.276034	+	0.758397i
$656$	33.5054	−	30.0346i	1.30817	−	1.17265i
$657$	−6.87247	−	11.9035i	−0.268121	−	0.464399i
$658$	10.4282	+	4.75934i	0.406532	+	0.185538i
$659$	−8.36199	−	11.9422i	−0.325737	−	0.465201i	0.622566	−	0.782567i	$-0.286090\pi$
$659$	−8.36199	−	11.9422i	−0.325737	−	0.465201i	−0.948303	+	0.317367i	$0.897201\pi$
$660$	−0.876139	−	8.42544i	−0.0341037	−	0.327960i
$661$	6.82627	−	0.597221i	0.265511	−	0.0232292i	0.0463771	−	0.998924i	$-0.485232\pi$
$661$	6.82627	−	0.597221i	0.265511	−	0.0232292i	0.219134	+	0.975695i	$0.429677\pi$
$662$	7.13072	−	12.5873i	0.277143	−	0.489218i
$663$	32.8663	+	11.9623i	1.27642	+	0.464579i
$664$	−23.8530	−	13.0024i	−0.925677	−	0.504590i
$665$	10.7841	−	15.7859i	0.418191	−	0.612152i
$666$	4.94021	+	4.07698i	0.191429	+	0.157980i
$667$	−3.95100	−	8.47294i	−0.152983	−	0.328073i
$668$	−9.33455	+	3.57137i	−0.361165	+	0.138181i
$669$	−11.0619	+	0.967794i	−0.427679	+	0.0374171i
$670$	13.4677	−	13.6897i	0.520301	−	0.528877i
$671$	11.8609	+	2.09139i	0.457884	+	0.0807374i
$672$	5.28941	+	5.80448i	0.204043	+	0.223913i
$673$	0.605551	−	0.349615i	0.0233423	−	0.0134767i	−0.488283	−	0.872685i	$-0.662377\pi$
$673$	0.605551	−	0.349615i	0.0233423	−	0.0134767i	0.511626	+	0.859208i	$0.329043\pi$
$674$	3.14938	+	6.61221i	0.121310	+	0.254693i
$675$	2.10534	−	4.51491i	0.0810344	−	0.173779i
$676$	19.4474	−	16.8677i	0.747977	−	0.648757i
$677$	6.58658	+	24.5815i	0.253143	+	0.944742i	0.969114	+	0.246612i	$0.0793174\pi$
$677$	6.58658	+	24.5815i	0.253143	+	0.944742i	−0.715971	+	0.698130i	$0.754016\pi$
$678$	6.27985	−	5.35750i	0.241176	−	0.205754i
$679$	8.44974	+	10.0700i	0.324271	+	0.386451i
$680$	−22.4255	−	57.2083i	−0.859978	−	2.19384i
$681$	−16.5462	+	2.91755i	−0.634053	+	0.111801i
$682$	−16.0660	+	9.45164i	−0.615199	+	0.361922i
$683$	−2.93068	−	2.93068i	−0.112139	−	0.112139i	0.648811	−	0.760950i	$-0.275267\pi$
$683$	−2.93068	−	2.93068i	−0.112139	−	0.112139i	−0.760950	+	0.648811i	$0.775267\pi$
$684$	1.27385	−	8.62423i	0.0487070	−	0.329756i
$685$	30.5326	−	30.5326i	1.16659	−	1.16659i
$686$	−22.9438	−	5.94719i	−0.875997	−	0.227065i
$687$	2.34014	+	13.2716i	0.0892819	+	0.506343i
$688$	11.8720	−	6.01610i	0.452617	−	0.229362i
$689$	26.1288	−	21.9246i	0.995427	−	0.835262i
$690$	2.41152	−	30.4263i	0.0918049	−	1.15831i
$691$	7.64867	−	2.04945i	0.290969	−	0.0779649i	−0.110382	−	0.993889i	$-0.535207\pi$
$691$	7.64867	−	2.04945i	0.290969	−	0.0779649i	0.401351	+	0.915924i	$0.368541\pi$
$692$	−2.23303	+	31.4347i	−0.0848870	+	1.19497i
$693$	−1.68669	−	0.786515i	−0.0640719	−	0.0298772i
$694$	−12.2984	+	34.6688i	−0.466841	+	1.31601i
$695$	−25.6113	−	44.3601i	−0.971493	−	1.68267i
$696$	−0.909877	+	3.76243i	−0.0344888	+	0.142615i
$697$	−13.4320	+	76.1768i	−0.508774	+	2.88540i
$698$	−0.371087	−	45.3962i	−0.0140458	−	1.71827i
$699$	−0.706028	−	8.06994i	−0.0267044	−	0.305233i
$700$	−12.9182	+	4.94244i	−0.488260	+	0.186807i
$701$	−30.8133	+	14.3685i	−1.16380	+	0.542689i	−0.905904	−	0.423483i	$-0.860807\pi$
$701$	−30.8133	+	14.3685i	−1.16380	+	0.542689i	−0.257897	+	0.966172i	$0.583030\pi$
$702$	−0.685490	−	7.16055i	−0.0258722	−	0.270257i
$703$	−13.7979	+	14.1201i	−0.520399	+	0.532549i
$704$	−2.26456	+	10.4829i	−0.0853488	+	0.395091i
$705$	−6.30914	+	17.3342i	−0.237616	+	0.652844i
$706$	1.06930	+	3.86405i	0.0402435	+	0.145425i
$707$	−1.49546	−	17.0932i	−0.0562425	−	0.642855i
$708$	−3.18345	+	3.92237i	−0.119641	+	0.147412i
$709$	−21.9873	+	15.3957i	−0.825752	+	0.578198i	−0.908267	−	0.418392i	$-0.862594\pi$
$709$	−21.9873	+	15.3957i	−0.825752	+	0.578198i	0.0825144	+	0.996590i	$0.473705\pi$
$710$	18.1191	+	48.5436i	0.680000	+	1.82181i
$711$	13.0313	−	7.52363i	0.488713	−	0.282158i
$712$	−21.3420	+	15.7376i	−0.799826	+	0.589791i
$713$	−63.1121	+	22.9709i	−2.36357	+	0.860268i
$714$	−13.3135	−	2.23547i	−0.498244	−	0.0836604i
$715$	20.8092	−	5.57580i	0.778218	−	0.208523i
$716$	2.91573	+	2.82192i	0.108966	+	0.105460i
$717$	−7.85709	−	0.687407i	−0.293429	−	0.0256717i
$718$	−12.2114	−	8.40259i	−0.455725	−	0.313582i
$719$	−8.37677	+	1.47705i	−0.312401	+	0.0550847i	−0.327650	−	0.944799i	$-0.606257\pi$
$719$	−8.37677	+	1.47705i	−0.312401	+	0.0550847i	0.0152496	+	0.999884i	$0.495146\pi$
$720$	−8.63916	+	9.22341i	−0.321962	+	0.343736i
$721$		−	14.5854i		−	0.543189i
$722$	26.1591	+	6.14011i	0.973541	+	0.228511i
$723$	0.930119	+	0.930119i	0.0345915	+	0.0345915i
$724$	−1.27050	+	0.920930i	−0.0472178	+	0.0342261i
$725$	−5.58474	−	3.91048i	−0.207412	−	0.145232i
$726$	2.36468	+	12.7981i	0.0877614	+	0.474983i
$727$	−8.53736	+	7.16370i	−0.316633	+	0.265687i	−0.787227	−	0.616663i	$-0.788484\pi$
$727$	−8.53736	+	7.16370i	−0.316633	+	0.265687i	0.470594	+	0.882350i	$0.344040\pi$
$728$	−12.4587	+	15.6095i	−0.461749	+	0.578528i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	−60.5650	−	10.1695i	−2.24161	−	0.376390i
$731$	−9.66935	+	20.7360i	−0.357634	+	0.766948i
$732$	−9.23716	−	15.4118i	−0.341415	−	0.569635i
$733$	8.12471	+	2.17701i	0.300093	+	0.0804097i	0.405724	−	0.913996i	$-0.367019\pi$
$733$	8.12471	+	2.17701i	0.300093	+	0.0804097i	−0.105631	+	0.994405i	$0.533686\pi$
$734$	−28.7138	−	13.1048i	−1.05984	−	0.483706i
$735$	2.78305	−	15.7834i	0.102654	−	0.582181i
$736$	−14.8865	+	35.6603i	−0.548723	+	1.31445i
$737$	3.70369	−	4.41389i	0.136427	−	0.162588i
$738$	15.3324	−	4.24294i	0.564395	−	0.156185i
$739$	7.53891	+	16.1672i	0.277323	+	0.594721i	0.994798	−	0.101862i	$-0.0324802\pi$
$739$	7.53891	+	16.1672i	0.277323	+	0.594721i	−0.717475	+	0.696584i	$0.754702\pi$
$740$	28.0991	−	5.42970i	1.03294	−	0.199600i
$741$	22.1697	−	0.255818i	0.814425	−	0.00939770i
$742$	−8.37974	+	10.1540i	−0.307630	+	0.372765i
$743$	12.4351	−	34.1651i	0.456199	−	1.25340i	−0.472094	−	0.881548i	$-0.656502\pi$
$743$	12.4351	−	34.1651i	0.456199	−	1.25340i	0.928293	−	0.371849i	$-0.121276\pi$
$744$	26.3569	+	8.86749i	0.966290	+	0.325098i
$745$	4.47084	−	5.32814i	0.163799	−	0.195208i
$746$	0.288351	+	35.2749i	0.0105573	+	1.29151i
$747$	−5.50913	−	7.86785i	−0.201568	−	0.287869i
$748$	−8.06373	−	16.5796i	−0.294839	−	0.606209i
$749$	3.47598	−	12.9725i	0.127010	−	0.474006i
$750$	0.0352570	+	0.0740230i	0.00128740	+	0.00270294i
$751$	−11.7429	+	4.27408i	−0.428506	+	0.155963i	−0.547264	−	0.836960i	$-0.684331\pi$
$751$	−11.7429	+	4.27408i	−0.428506	+	0.155963i	0.118758	+	0.992923i	$0.462109\pi$
$752$	14.4193	−	18.3721i	0.525818	−	0.669960i
$753$	7.98110	+	4.60789i	0.290847	+	0.167921i
$754$	−9.81370	−	0.777810i	−0.357394	−	0.0283262i
$755$	5.68795	−	65.0135i	0.207006	−	2.36608i
$756$	0.762347	+	2.66975i	0.0277263	+	0.0970979i
$757$	23.5621	−	33.6501i	0.856377	−	1.22303i	−0.116841	−	0.993151i	$-0.537277\pi$
$757$	23.5621	−	33.6501i	0.856377	−	1.22303i	0.973218	−	0.229883i	$-0.0738343\pi$
$758$	11.2630	+	19.1449i	0.409090	+	0.695375i
$759$		−	9.15778i		−	0.332406i
$760$	−26.0970	−	28.9164i	−0.946637	−	1.04891i
$761$			23.0462i			0.835426i	0.908579	+	0.417713i	$0.137168\pi$
$761$			23.0462i			0.835426i	−0.908579	+	0.417713i	$0.862832\pi$
$762$	−21.8009	+	12.8255i	−0.789763	+	0.464619i
$763$	7.10266	−	10.1436i	0.257134	−	0.367225i
$764$	5.45242	−	9.81085i	0.197262	−	0.354944i
$765$	1.89343	−	21.6420i	0.0684571	−	0.782468i
$766$	−1.39987	+	17.6623i	−0.0505793	+	0.638164i
$767$	−11.1262	−	6.42373i	−0.401744	−	0.231947i
$768$	14.0281	−	7.69503i	0.506194	−	0.277671i
$769$	−20.5358	+	7.47441i	−0.740539	+	0.269534i	−0.684619	−	0.728901i	$-0.740031\pi$
$769$	−20.5358	+	7.47441i	−0.740539	+	0.269534i	−0.0559200	+	0.998435i	$0.517809\pi$
$770$	−7.50719	+	3.57566i	−0.270540	+	0.128858i
$771$	−2.25201	+	8.40461i	−0.0811041	+	0.302685i
$772$	9.97261	+	3.44617i	0.358922	+	0.124030i
$773$	1.16822	+	1.66839i	0.0420178	+	0.0600077i	0.839611	−	0.543188i	$-0.182783\pi$
$773$	1.16822	+	1.66839i	0.0420178	+	0.0600077i	−0.797593	+	0.603195i	$0.793894\pi$
$774$	4.70541	−	0.0384639i	0.169132	−	0.00138256i
$775$	−31.4829	+	37.5198i	−1.13090	+	1.34775i
$776$	23.9888	−	11.9108i	0.861147	−	0.427572i
$777$	2.15048	−	5.90839i	0.0771480	−	0.211962i
$778$	27.8422	+	22.9772i	0.998190	+	0.823771i
$779$	9.07124	+	48.1875i	0.325011	+	1.72649i
$780$	−26.6252	−	18.0018i	−0.953337	−	0.644567i
$781$	6.57028	+	14.0900i	0.235103	+	0.504180i
$782$	−17.7171	−	64.0232i	−0.633562	−	2.28946i
$783$	−0.879696	+	1.04838i	−0.0314378	+	0.0374661i
$784$	−9.56574	+	17.8950i	−0.341634	+	0.639108i
$785$	−10.3833	+	58.8865i	−0.370595	+	2.10175i
$786$	3.83882	−	8.41122i	0.136926	−	0.300018i
$787$	−3.97520	−	1.06515i	−0.141700	−	0.0379685i	0.187272	−	0.982308i	$-0.440036\pi$
$787$	−3.97520	−	1.06515i	−0.141700	−	0.0379685i	−0.328972	+	0.944340i	$0.606702\pi$
$788$	−18.2449	−	4.57038i	−0.649947	−	0.162813i
$789$	10.5730	−	22.6738i	0.376408	−	0.807209i
$790$	11.1331	−	66.3035i	0.396096	−	2.35897i
$791$	−7.01740	−	4.05150i	−0.249510	−	0.144055i
$792$	−2.36535	+	2.96356i	−0.0840490	+	0.105305i
$793$	35.0054	−	29.3730i	1.24308	−	1.04307i
$794$	20.5578	−	3.79842i	0.729570	−	0.134801i
$795$	−17.3548	−	12.1519i	−0.615510	−	0.430985i
$796$	6.47744	+	1.03326i	0.229587	+	0.0366230i
$797$	−3.19301	−	3.19301i	−0.113102	−	0.113102i	0.648291	−	0.761393i	$-0.275484\pi$
$797$	−3.19301	−	3.19301i	−0.113102	−	0.113102i	−0.761393	+	0.648291i	$0.775484\pi$
$798$	−8.39669	+	1.65185i	−0.297240	+	0.0584748i
$799$			40.1485i			1.42035i
$800$	3.60110	+	27.9494i	0.127318	+	0.988162i
$801$	−9.23276	+	1.62798i	−0.326224	+	0.0575220i
$802$	20.3542	−	29.5806i	0.718733	−	1.04453i
$803$	−18.3563	−	1.60597i	−0.647779	−	0.0566733i
$804$	−8.59492	+	0.140526i	−0.303120	+	0.00495597i
$805$	−28.9401	+	7.75447i	−1.02000	+	0.273309i
$806$	−11.7112	+	69.7467i	−0.412510	+	2.45672i
$807$	13.3401	−	4.85541i	0.469595	−	0.170919i
$808$	−34.5666	−	5.22460i	−1.21605	−	0.183801i
$809$	−9.25402	+	5.34281i	−0.325354	+	0.187843i	−0.653777	−	0.756688i	$-0.726816\pi$
$809$	−9.25402	+	5.34281i	−0.325354	+	0.187843i	0.328422	+	0.944531i	$0.393483\pi$
$810$	−4.18594	+	1.56243i	−0.147079	+	0.0548980i
$811$	20.4631	−	14.3284i	0.718558	−	0.503139i	−0.156185	−	0.987728i	$-0.549920\pi$
$811$	20.4631	−	14.3284i	0.718558	−	0.503139i	0.874742	+	0.484588i	$0.161031\pi$
$812$	3.77939	−	0.393008i	0.132631	−	0.0137919i
$813$	1.69599	+	19.3852i	0.0594809	+	0.679870i
$814$	8.27582	−	2.29017i	0.290067	−	0.0802703i
$815$	0.747585	−	2.05397i	0.0261868	−	0.0719475i
$816$	−10.8030	+	25.2947i	−0.378180	+	0.885492i
$817$	−1.09727	+	14.4620i	−0.0383887	+	0.505960i
$818$	21.6488	−	2.07248i	0.756934	−	0.0724624i
$819$	−6.39955	+	2.98416i	−0.223618	+	0.104275i
$820$	28.9828	−	64.9033i	1.01212	−	2.26652i
$821$	1.37173	+	15.6789i	0.0478736	+	0.547198i	0.981824	+	0.189795i	$0.0607822\pi$
$821$	1.37173	+	15.6789i	0.0478736	+	0.547198i	−0.933950	+	0.357403i	$0.883662\pi$
$822$	−19.3276	+	0.157991i	−0.674128	+	0.00551058i
$823$	−8.24426	+	46.7555i	−0.287377	+	1.62979i	0.409293	+	0.912403i	$0.365775\pi$
$823$	−8.24426	+	46.7555i	−0.287377	+	1.62979i	−0.696670	+	0.717392i	$0.745336\pi$
$824$	−28.8842	−	6.98512i	−1.00623	−	0.243338i
$825$	−3.33918	−	5.78364i	−0.116255	−	0.201360i
$826$	4.67351	+	1.65788i	0.162612	+	0.0576851i
$827$	−5.39141	−	2.51405i	−0.187478	−	0.0874222i	0.326613	−	0.945158i	$-0.394093\pi$
$827$	−5.39141	−	2.51405i	−0.187478	−	0.0874222i	−0.514090	+	0.857736i	$0.671870\pi$
$828$	−10.3209	+	8.95186i	−0.358678	+	0.311099i
$829$	−26.1190	+	6.99856i	−0.907150	+	0.243070i	−0.682084	−	0.731274i	$-0.738926\pi$
$829$	−26.1190	+	6.99856i	−0.907150	+	0.243070i	−0.225065	+	0.974344i	$0.572260\pi$
$830$	−42.7807	−	3.39069i	−1.48494	−	0.117693i
$831$	−10.4652	+	8.78137i	−0.363035	+	0.304623i
$832$	24.9457	+	32.1481i	0.864836	+	1.11453i
$833$	−6.05719	−	34.3521i	−0.209869	−	1.19023i
$834$	−5.75310	+	22.1950i	−0.199214	+	0.768550i
$835$	−11.1639	+	11.1639i	−0.386341	+	0.386341i
$836$	−8.49119	−	8.03033i	−0.293674	−	0.277735i
$837$	6.95215	+	6.95215i	0.240301	+	0.240301i
$838$	−2.97361	−	5.05457i	−0.102722	−	0.174607i
$839$	28.6046	−	5.04376i	0.987541	−	0.174130i	0.343526	−	0.939143i	$-0.388379\pi$
$839$	28.6046	−	5.04376i	0.987541	−	0.174130i	0.644015	+	0.765013i	$0.277268\pi$
$840$	11.3682	+	4.96545i	0.392240	+	0.171324i
$841$	−17.4369	−	20.7805i	−0.601273	−	0.716569i
$842$	−23.8092	−	27.9082i	−0.820518	−	0.961778i
$843$	−2.05247	−	7.65992i	−0.0706908	−	0.263822i
$844$	−14.3431	−	1.01890i	−0.493711	−	0.0350718i
$845$	17.1864	−	36.8563i	0.591230	−	1.26790i
$846$	7.45478	−	3.55069i	0.256301	−	0.122075i
$847$	11.0640	−	6.38781i	0.380164	−	0.219488i
$848$	16.0953	+	21.4577i	0.552715	+	0.736860i
$849$	14.9415	+	2.63460i	0.512792	+	0.0904191i
$850$	−34.5340	−	33.9740i	−1.18451	−	1.16530i
$851$	30.8219	−	2.69657i	1.05656	−	0.0924371i
$852$	9.45710	−	21.1780i	0.323995	−	0.725546i
$853$	12.7877	+	27.4234i	0.437844	+	0.938960i	0.994153	+	0.107984i	$0.0344395\pi$
$853$	12.7877	+	27.4234i	0.437844	+	0.938960i	−0.556308	+	0.830976i	$0.687783\pi$
$854$	−11.2266	+	13.6036i	−0.384165	+	0.465505i
$855$	−3.71755	−	13.2601i	−0.127137	−	0.453487i
$856$	−24.0255	−	13.0964i	−0.821173	−	0.447624i
$857$	−22.8438	−	8.31447i	−0.780330	−	0.284017i	−0.0790199	−	0.996873i	$-0.525179\pi$
$857$	−22.8438	−	8.31447i	−0.780330	−	0.284017i	−0.701310	+	0.712856i	$0.747401\pi$
$858$	−8.39045	−	4.75321i	−0.286445	−	0.162272i
$859$	−46.6467	+	4.08105i	−1.59156	+	0.139244i	−0.848212	−	0.529657i	$-0.822321\pi$
$859$	−46.6467	+	4.08105i	−1.59156	+	0.139244i	−0.743352	+	0.668901i	$0.766765\pi$
$860$	13.2493	−	16.3246i	0.451796	−	0.556663i
$861$	−8.95720	−	12.7922i	−0.305260	−	0.435957i
$862$	5.87314	−	12.8686i	0.200040	−	0.438305i
$863$	3.39340	+	5.87754i	0.115513	+	0.200074i	0.917985	−	0.396616i	$-0.129816\pi$
$863$	3.39340	+	5.87754i	0.115513	+	0.200074i	−0.802472	+	0.596690i	$0.796482\pi$
$864$	5.65213	−	0.231137i	0.192289	−	0.00786345i
$865$	17.0265	+	46.7798i	0.578917	+	1.59056i
$866$	30.0087	−	21.3800i	1.01974	−	0.726521i
$867$	−7.83779	−	29.2510i	−0.266185	−	0.993418i
$868$	−0.446254	−	27.2940i	−0.0151468	−	0.926419i
$869$	1.75813	−	20.0955i	0.0596405	−	0.681693i
$870$	1.11101	+	6.01301i	0.0376668	+	0.203860i
$871$	−3.79623	−	21.5295i	−0.128630	−	0.729499i
$872$	−16.6864	−	18.9237i	−0.565073	−	0.640836i
$873$	9.46922			0.320484
$874$	−24.8285	−	34.0117i	−0.839837	−	1.15046i
$875$	0.0569109	−	0.0569109i	0.00192394	−	0.00192394i
$876$	16.1336	+	22.2576i	0.545103	+	0.752016i
$877$	−15.2972	+	21.8467i	−0.516550	+	0.737709i	−0.989682	−	0.143282i	$-0.954234\pi$
$877$	−15.2972	+	21.8467i	−0.516550	+	0.737709i	0.473132	+	0.880991i	$0.343123\pi$
$878$	−4.18428	+	6.08096i	−0.141212	+	0.205222i
$879$	−15.3158	−	18.2527i	−0.516590	−	0.615648i
$880$	3.48576	+	16.5793i	0.117505	+	0.558887i
$881$	11.4639	−	19.8560i	0.386228	−	0.668967i	−0.605711	−	0.795685i	$-0.707111\pi$
$881$	11.4639	−	19.8560i	0.386228	−	0.668967i	0.991939	+	0.126718i	$0.0404444\pi$
$882$	−5.84280	+	4.16276i	−0.196737	+	0.140167i
$883$	8.56590	+	3.99435i	0.288266	+	0.134420i	0.561373	−	0.827563i	$-0.310273\pi$
$883$	8.56590	+	3.99435i	0.288266	+	0.134420i	−0.273107	+	0.961984i	$0.588051\pi$
$884$	−67.8545	−	16.9977i	−2.28219	−	0.571694i
$885$	−2.06539	+	7.70814i	−0.0694273	+	0.259106i
$886$	11.3472	+	30.4007i	0.381218	+	1.02133i
$887$	−26.3205	−	4.64102i	−0.883757	−	0.155830i	−0.286692	−	0.958023i	$-0.592556\pi$
$887$	−26.3205	−	4.64102i	−0.883757	−	0.155830i	−0.597065	+	0.802193i	$0.703667\pi$
$888$	−10.6708	−	7.08830i	−0.358088	−	0.237868i
$889$	19.0201	+	15.9598i	0.637914	+	0.535274i
$890$	−20.6471	+	36.4466i	−0.692092	+	1.22169i
$891$	−1.21499	+	0.566559i	−0.0407037	+	0.0189805i
$892$	21.8050	−	4.21347i	0.730086	−	0.141077i
$893$	8.97990	+	23.8135i	0.300501	+	0.796888i
$894$	−3.09923	+	0.296694i	−0.103654	+	0.00992294i
$895$	6.02330	+	2.19230i	0.201337	+	0.0732806i
$896$	−11.7228	−	10.4525i	−0.391631	−	0.349195i
$897$	−26.6170	−	22.3343i	−0.888716	−	0.745721i
$898$	35.0239	+	34.4560i	1.16876	+	1.14981i
$899$	11.0221	−	7.71775i	0.367607	−	0.257401i
$900$	−3.25414	+	9.41689i	−0.108471	+	0.313896i
$901$	−44.5398	−	11.9344i	−1.48384	−	0.397593i
$902$	7.13023	−	20.0999i	0.237411	−	0.669252i
$903$	−1.57983	−	4.34055i	−0.0525734	−	0.144444i
$904$	−11.3841	+	11.9566i	−0.378629	+	0.397670i
$905$	−1.23940	+	2.14670i	−0.0411989	+	0.0713586i
$906$	−22.2241	+	18.9599i	−0.738345	+	0.629901i
$907$	−32.2969	−	2.82561i	−1.07240	−	0.0938229i	−0.462746	−	0.886491i	$-0.653136\pi$
$907$	−32.2969	−	2.82561i	−1.07240	−	0.0938229i	−0.609654	+	0.792668i	$0.708692\pi$
$908$	32.3115	−	9.22654i	1.07229	−	0.306194i
$909$	−10.1247	−	7.08938i	−0.335815	−	0.235140i
$910$	−7.91619	+	30.5400i	−0.262419	+	1.01239i
$911$	−21.3208			−0.706389			−0.353194	−	0.935550i	$-0.614905\pi$
$911$	−21.3208			−0.706389			−0.353194	+	0.935550i	$0.614905\pi$
$912$	−0.750041	+	17.4195i	−0.0248363	+	0.576816i
$913$	−12.8762			−0.426141
$914$	−3.23214	+	12.4693i	−0.106910	+	0.412449i
$915$	−23.2506	−	16.2802i	−0.768641	−	0.538208i
$916$	−7.40052	−	25.9167i	−0.244520	−	0.856313i
$917$	−9.04141	−	0.791021i	−0.298574	−	0.0261218i
$918$	−7.39805	+	6.31147i	−0.244172	+	0.208310i
$919$	19.4277	−	33.6498i	0.640861	−	1.11000i	−0.344380	−	0.938830i	$-0.611911\pi$
$919$	19.4277	−	33.6498i	0.640861	−	1.11000i	0.985241	−	0.171173i	$-0.0547558\pi$
$920$	1.49680	+	61.0251i	0.0493479	+	2.01194i
$921$	−7.65318	−	21.0269i	−0.252181	−	0.692861i
$922$	−10.5922	+	29.8591i	−0.348836	+	0.983356i
$923$	56.9764	+	15.2668i	1.87540	+	0.502512i
$924$	3.51798	+	1.21569i	0.115733	+	0.0399932i
$925$	18.4825	−	12.9416i	0.607700	−	0.425516i
$926$	−4.90077	−	4.82130i	−0.161049	−	0.158438i
$927$	−8.04842	−	6.75343i	−0.264345	−	0.221812i
$928$	1.03170	−	7.67272i	0.0338673	−	0.251869i
$929$	−8.54705	−	3.11087i	−0.280420	−	0.102064i	0.197982	−	0.980206i	$-0.436561\pi$
$929$	−8.54705	−	3.11087i	−0.280420	−	0.102064i	−0.478401	+	0.878141i	$0.658784\pi$
$930$	43.7290	−	4.18624i	1.43393	−	0.137272i
$931$	−11.2762	−	19.0206i	−0.369561	−	0.623376i
$932$	3.07383	+	15.9073i	0.100686	+	0.521060i
$933$	4.00006	−	1.86526i	0.130956	−	0.0610659i
$934$	6.77489	−	11.9591i	0.221681	−	0.391315i
$935$	−22.3102	−	18.7205i	−0.729623	−	0.612226i
$936$	2.84485	+	14.1025i	0.0929869	+	0.460954i
$937$	8.51345	+	1.50115i	0.278122	+	0.0490405i	0.310969	−	0.950420i	$-0.399346\pi$
$937$	8.51345	+	1.50115i	0.278122	+	0.0490405i	−0.0328471	+	0.999460i	$0.510457\pi$
$938$	2.95073	+	7.90540i	0.0963448	+	0.258121i
$939$	7.62978	−	28.4747i	0.248989	−	0.929238i
$940$	8.96486	−	35.7876i	0.292402	−	1.16726i
$941$	48.8499	+	22.7791i	1.59246	+	0.742576i	0.998100	−	0.0616223i	$-0.0196274\pi$
$941$	48.8499	+	22.7791i	1.59246	+	0.742576i	0.594361	+	0.804199i	$0.297405\pi$
$942$	21.7989	−	15.5309i	0.710247	−	0.506022i
$943$	38.4222	−	66.5492i	1.25120	−	2.16714i
$944$	5.52138	−	8.46119i	0.179706	−	0.275388i
$945$	2.81923	+	3.35983i	0.0917095	+	0.109295i
$946$	3.57591	−	5.19682i	0.116263	−	0.168963i
$947$	−23.8424	+	34.0504i	−0.774773	+	1.10649i	0.216708	+	0.976236i	$0.430468\pi$
$947$	−23.8424	+	34.0504i	−0.774773	+	1.10649i	−0.991481	+	0.130254i	$0.958421\pi$
$948$	−24.3665	+	17.6622i	−0.791388	+	0.573642i
$949$	−49.4357	+	49.4357i	−1.60475	+	1.60475i
$950$	−28.0822	−	12.4270i	−0.911106	−	0.403186i
$951$	3.64325			0.118140
$952$	26.9466	+	1.69295i	0.873343	+	0.0548689i
$953$	7.86650	+	44.6131i	0.254821	+	1.44516i	0.796532	+	0.604596i	$0.206666\pi$
$953$	7.86650	+	44.6131i	0.254821	+	1.44516i	−0.541711	+	0.840565i	$0.682223\pi$
$954$	1.72308	+	9.32563i	0.0557866	+	0.301928i
$955$	1.54533	−	17.6632i	0.0500056	−	0.571567i
$956$	15.7721	−	0.257872i	0.510106	−	0.00834017i
$957$	0.474852	+	1.77217i	0.0153498	+	0.0572862i
$958$	−1.26401	+	0.900553i	−0.0408382	+	0.0290956i
$959$	6.48919	+	17.8289i	0.209547	+	0.575726i
$960$	15.2777	−	20.1350i	0.493086	−	0.649854i
$961$	−32.8323	−	56.8673i	−1.05911	−	1.83443i
$962$	13.5270	−	29.6390i	0.436129	−	0.955598i
$963$	−5.54895	−	7.92473i	−0.178812	−	0.255371i
$964$	−2.04266	−	1.65786i	−0.0657898	−	0.0533960i
$965$	16.6043	−	1.45268i	0.534510	−	0.0467636i
$966$	11.6689	+	6.61047i	0.375441	+	0.212688i
$967$	23.2726	+	8.47052i	0.748395	+	0.272394i	0.687930	−	0.725777i	$-0.258519\pi$
$967$	23.2726	+	8.47052i	0.748395	+	0.272394i	0.0604649	+	0.998170i	$0.480742\pi$
$968$	−7.35140	−	24.9698i	−0.236283	−	0.802559i
$969$	−17.4739	−	24.3524i	−0.561343	−	0.782311i
$970$	26.9297	−	32.6316i	0.864661	−	1.04774i
$971$	−13.1823	−	28.2696i	−0.423041	−	0.907215i	−0.996144	−	0.0877314i	$-0.972038\pi$
$971$	−13.1823	−	28.2696i	−0.423041	−	0.907215i	0.573103	−	0.819483i	$-0.305739\pi$
$972$	1.82619	+	0.815491i	0.0585751	+	0.0261569i
$973$	22.4216	−	1.96164i	0.718803	−	0.0628872i
$974$	21.8605	+	21.5060i	0.700455	+	0.689096i
$975$	−24.9538	−	4.40003i	−0.799162	−	0.140914i
$976$	21.5633	+	28.7474i	0.690224	+	0.920182i
$977$	−19.7277	+	11.3898i	−0.631145	+	0.364392i	−0.781195	−	0.624287i	$-0.785390\pi$
$977$	−19.7277	+	11.3898i	−0.631145	+	0.364392i	0.150050	+	0.988678i	$0.452056\pi$
$978$	−0.883335	+	0.420730i	−0.0282459	+	0.0134535i
$979$	−5.31160	+	11.3908i	−0.169760	+	0.364051i
$980$	−2.27129	+	31.9733i	−0.0725538	+	1.02135i
$981$	−2.30868	−	8.61612i	−0.0737106	−	0.275092i
$982$	31.7398	+	37.2041i	1.01286	+	1.18723i
$983$	24.8114	+	29.5690i	0.791359	+	0.943105i	0.999387	−	0.0350177i	$-0.0111487\pi$
$983$	24.8114	+	29.5690i	0.791359	+	0.943105i	−0.208027	+	0.978123i	$0.566704\pi$
$984$	−29.6227	+	11.6120i	−0.944338	+	0.370178i
$985$	−29.2604	+	5.15939i	−0.932312	+	0.164392i
$986$	6.74829	+	11.4708i	0.214909	+	0.365305i
$987$	−5.73144	−	5.73144i	−0.182434	−	0.182434i
$988$	−44.0487	+	5.09490i	−1.40138	+	0.162090i
$989$	16.0722	−	16.0722i	0.511066	−	0.511066i
$990$	−1.50293	+	5.79819i	−0.0477663	+	0.184279i
$991$	7.30375	+	41.4217i	0.232011	+	1.31580i	0.848817	+	0.528687i	$0.177315\pi$
$991$	7.30375	+	41.4217i	0.232011	+	1.31580i	−0.616806	+	0.787115i	$0.711574\pi$
$992$	−54.2654	−	12.1877i	−1.72293	−	0.386960i
$993$	−7.83627	+	6.57542i	−0.248677	+	0.208665i
$994$	−22.6963	−	1.79886i	−0.719883	−	0.0570562i
$995$	10.0086	−	2.68180i	0.317295	−	0.0850189i
$996$	12.5867	+	14.5117i	0.398825	+	0.459820i
$997$	38.4357	+	17.9229i	1.21727	+	0.567623i	0.921776	−	0.387722i	$-0.126738\pi$
$997$	38.4357	+	17.9229i	1.21727	+	0.567623i	0.295494	+	0.955345i	$0.404516\pi$
$998$	−31.4734	−	11.1649i	−0.996273	−	0.353418i
$999$	−2.26460	−	3.92241i	−0.0716489	−	0.124099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.cn.a.91.73	✓	960
16.3	odd	4	inner	912.2.cn.a.547.11	yes	960
19.14	odd	18	inner	912.2.cn.a.907.11	yes	960
304.147	even	36	inner	912.2.cn.a.451.73	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.cn.a.91.73	✓	960	1.1	even	1	trivial
912.2.cn.a.451.73	yes	960	304.147	even	36	inner
912.2.cn.a.547.11	yes	960	16.3	odd	4	inner
912.2.cn.a.907.11	yes	960	19.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cn (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36897 + 0.354847i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.74817 + 0.971551i) q^{4} +(3.14735 + 0.275358i) q^{5} +(-0.917864 - 1.07588i) q^{6} +(-0.694115 + 1.20224i) q^{7} +(2.04844 + 1.95036i) q^{8} +(0.342020 + 0.939693i) q^{9} +O(q^{10})\)	\(q+(1.36897 + 0.354847i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.74817 + 0.971551i) q^{4} +(3.14735 + 0.275358i) q^{5} +(-0.917864 - 1.07588i) q^{6} +(-0.694115 + 1.20224i) q^{7} +(2.04844 + 1.95036i) q^{8} +(0.342020 + 0.939693i) q^{9} +(4.21093 + 1.49379i) q^{10} +(1.29491 + 0.346971i) q^{11} +(-0.874756 - 1.79856i) q^{12} +(4.16655 - 2.91745i) q^{13} +(-1.37684 + 1.39953i) q^{14} +(-2.42022 - 2.03081i) q^{15} +(2.11218 + 3.39687i) q^{16} +(-6.46157 - 2.35182i) q^{17} +(0.134769 + 1.40778i) q^{18} +(-4.35861 + 0.0502942i) q^{19} +(5.23457 + 3.53919i) q^{20} +(1.25816 - 0.586692i) q^{21} +(1.64958 + 0.934490i) q^{22} +(5.23295 + 4.39097i) q^{23} +(-0.559303 - 2.77258i) q^{24} +(4.90597 + 0.865054i) q^{25} +(6.73914 - 2.51542i) q^{26} +(0.258819 - 0.965926i) q^{27} +(-2.38147 + 1.42735i) q^{28} +(-1.24034 - 0.578380i) q^{29} +(-2.59259 - 3.63893i) q^{30} +(-4.91591 + 8.51461i) q^{31} +(1.68614 + 5.39972i) q^{32} +(-0.861717 - 1.02695i) q^{33} +(-8.01117 - 5.51244i) q^{34} +(-2.51567 + 3.59275i) q^{35} +(-0.315051 + 1.97503i) q^{36} +(3.20263 - 3.20263i) q^{37} +(-5.98466 - 1.47779i) q^{38} -5.08642 q^{39} +(5.91011 + 6.70252i) q^{40} +(-1.95339 - 11.0782i) q^{41} +(1.93058 - 0.356708i) q^{42} +(0.289997 - 3.31468i) q^{43} +(1.92663 + 1.86464i) q^{44} +(0.817706 + 3.05172i) q^{45} +(5.60564 + 7.86801i) q^{46} +(-1.99696 - 5.48660i) q^{47} +(0.218170 - 3.99405i) q^{48} +(2.53641 + 4.39319i) q^{49} +(6.40917 + 2.92510i) q^{50} +(3.94406 + 5.63270i) q^{51} +(10.1183 - 1.05217i) q^{52} +(6.68032 - 0.584452i) q^{53} +(0.697072 - 1.23048i) q^{54} +(3.98001 + 1.44860i) q^{55} +(-3.76666 + 1.10895i) q^{56} +(3.59921 + 2.45880i) q^{57} +(-1.49275 - 1.23192i) q^{58} +(-1.06746 - 2.28918i) q^{59} +(-2.25792 - 5.90156i) q^{60} +(8.94979 - 0.783005i) q^{61} +(-9.75113 + 9.91186i) q^{62} +(-1.36714 - 0.241064i) q^{63} +(0.392205 + 7.99038i) q^{64} +(13.9170 - 8.03496i) q^{65} +(-0.815254 - 1.71165i) q^{66} +(1.81643 - 3.89534i) q^{67} +(-9.01099 - 10.3891i) q^{68} +(-1.76803 - 6.59837i) q^{69} +(-4.71876 + 4.02570i) q^{70} +(7.45429 + 8.88367i) q^{71} +(-1.13213 + 2.59196i) q^{72} +(-13.5361 + 2.38679i) q^{73} +(5.52076 - 3.24787i) q^{74} +(-3.52256 - 3.52256i) q^{75} +(-7.66844 - 4.14669i) q^{76} +(-1.31596 + 1.31596i) q^{77} +(-6.96317 - 1.80490i) q^{78} +(-2.61293 - 14.8187i) q^{79} +(5.71241 + 11.2727i) q^{80} +(-0.766044 + 0.642788i) q^{81} +(1.25694 - 15.8589i) q^{82} +(-9.27759 + 2.48592i) q^{83} +(2.76948 + 0.196736i) q^{84} +(-19.6892 - 9.18124i) q^{85} +(1.57320 - 4.43479i) q^{86} +(0.684282 + 1.18521i) q^{87} +(1.97583 + 3.23630i) q^{88} +(-1.62798 + 9.23276i) q^{89} +(0.0365222 + 4.46788i) q^{90} +(0.615418 + 7.03426i) q^{91} +(4.88203 + 12.7602i) q^{92} +(8.91066 - 4.15511i) q^{93} +(-0.786876 - 8.21961i) q^{94} +(-13.7319 - 1.04188i) q^{95} +(1.71594 - 5.39032i) q^{96} +(3.23866 - 8.89815i) q^{97} +(1.91336 + 6.91419i) q^{98} +(0.116840 + 1.33549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q+O(q^{10}) \) 960 * q	\( 960 q + 48 q^{10} + 12 q^{16} - 60 q^{32} - 120 q^{34} + 12 q^{36} + 108 q^{38} + 60 q^{40} + 180 q^{46} - 480 q^{49} - 108 q^{50} - 24 q^{51} + 48 q^{52} + 12 q^{54} + 72 q^{68} - 144 q^{69} - 72 q^{70} - 48 q^{76} + 72 q^{78} - 120 q^{80} + 120 q^{82} + 96 q^{85} + 84 q^{98}+O(q^{100}) \) 960 * q + 48 * q^10 + 12 * q^16 - 60 * q^32 - 120 * q^34 + 12 * q^36 + 108 * q^38 + 60 * q^40 + 180 * q^46 - 480 * q^49 - 108 * q^50 - 24 * q^51 + 48 * q^52 + 12 * q^54 + 72 * q^68 - 144 * q^69 - 72 * q^70 - 48 * q^76 + 72 * q^78 - 120 * q^80 + 120 * q^82 + 96 * q^85 + 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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