LMFDB - Embedded newform 966.2.s.a.97.5

Newspace parameters

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.5

$q$-expansion

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0416256 - 0.289512i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-0.445694 + 2.60794i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0416256 - 0.289512i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-0.445694 + 2.60794i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.121504 + 0.266058i) q^{10} +(-0.513628 - 1.74926i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(-2.34999 - 1.07320i) q^{13} +(1.16238 - 2.37673i) q^{14} +(-0.221049 + 0.191540i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.948993 - 0.609881i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-2.71507 - 1.74487i) q^{19} +(0.191540 - 0.221049i) q^{20} +(2.04467 - 1.67908i) q^{21} +1.82310i q^{22} +(4.54715 - 1.52428i) q^{23} +1.00000i q^{24} +(4.71538 + 1.38456i) q^{25} +(1.95244 + 1.69180i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-1.78490 + 1.95298i) q^{28} +(3.78361 - 2.43158i) q^{29} +(0.266058 - 0.121504i) q^{30} +(-2.26832 + 1.96551i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.757345 + 1.65835i) q^{33} +(-1.08238 + 0.317814i) q^{34} +(0.736478 + 0.237591i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(4.55467 - 0.654863i) q^{37} +(2.11351 + 2.43912i) q^{38} +(1.07320 + 2.34999i) q^{39} +(-0.246058 + 0.158132i) q^{40} +(2.18956 + 0.314812i) q^{41} +(-2.43490 + 1.03502i) q^{42} +(3.03177 + 2.62705i) q^{43} +(0.513628 - 1.74926i) q^{44} +0.292489 q^{45} +(-4.79240 + 0.181459i) q^{46} -9.34327i q^{47} +(0.281733 - 0.959493i) q^{48} +(-6.60271 - 2.32469i) q^{49} +(-4.13430 - 2.65695i) q^{50} +(-1.11659 - 0.160541i) q^{51} +(-1.39672 - 2.17334i) q^{52} +(10.4199 - 4.75862i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-0.527811 + 0.0758877i) q^{55} +(2.26282 - 1.37100i) q^{56} +(0.909268 + 3.09668i) q^{57} +(-4.31540 + 1.26712i) q^{58} +(11.1766 + 5.10418i) q^{59} +(-0.289512 + 0.0416256i) q^{60} +(-6.30483 - 7.27616i) q^{61} +(2.73018 - 1.24683i) q^{62} +(-2.64482 - 0.0700092i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.408525 + 0.635678i) q^{65} +(1.19388 - 1.37781i) q^{66} +(2.51321 - 8.55921i) q^{67} +1.12807 q^{68} +(-4.43470 - 1.82577i) q^{69} +(-0.639708 - 0.435457i) q^{70} +(-12.9475 - 3.80174i) q^{71} +(0.654861 - 0.755750i) q^{72} +(3.01076 - 4.68483i) q^{73} +(-4.55467 - 0.654863i) q^{74} +(-2.65695 - 4.13430i) q^{75} +(-1.34072 - 2.93576i) q^{76} +(4.79088 - 0.559877i) q^{77} +(-0.367663 - 2.55716i) q^{78} +(6.36288 + 2.90583i) q^{79} +(0.280641 - 0.0824037i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-2.01218 - 0.918931i) q^{82} +(-1.09286 - 7.60102i) q^{83} +(2.62787 - 0.307101i) q^{84} +(-0.137065 - 0.300132i) q^{85} +(-2.16884 - 3.37478i) q^{86} +(-4.45181 - 0.640073i) q^{87} +(-0.985644 + 1.53369i) q^{88} +(-6.28806 + 7.25681i) q^{89} +(-0.280641 - 0.0824037i) q^{90} +(3.84623 - 5.65031i) q^{91} +(4.64939 + 1.17607i) q^{92} +3.00142 q^{93} +(-2.63230 + 8.96480i) q^{94} +(-0.618178 + 0.713415i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(1.34152 - 9.33048i) q^{97} +(5.68032 + 4.09072i) q^{98} +(1.65835 - 0.757345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} + O(q^{10}) $	$ 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} - 22q^{14} - 16q^{16} + 16q^{18} - 36q^{23} + 96q^{25} + 22q^{28} - 20q^{29} - 16q^{32} - 50q^{35} + 16q^{36} + 22q^{37} + 4q^{39} - 110q^{43} + 8q^{46} - 36q^{50} + 22q^{51} - 88q^{53} + 22q^{57} + 24q^{58} - 16q^{64} - 72q^{70} + 48q^{71} + 16q^{72} - 22q^{74} + 24q^{77} + 4q^{78} + 88q^{79} - 16q^{81} + 22q^{84} + 76q^{85} + 44q^{86} - 44q^{88} + 8q^{92} - 14q^{95} + 22q^{98} - 22q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$3$	−0.755750	−	0.654861i	−0.436332	−	0.378084i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	0.0416256	−	0.289512i	0.0186155	−	0.129474i	−0.978394	−	0.206747i	$-0.933712\pi$
$5$	0.0416256	−	0.289512i	0.0186155	−	0.129474i	0.997010	+	0.0772733i	$0.0246214\pi$
$6$	0.540641	+	0.841254i	0.220716	+	0.343440i
$7$	−0.445694	+	2.60794i	−0.168457	+	0.985709i
$7$	−0.445694	+	2.60794i	−0.168457	+	0.985709i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	0.142315	+	0.989821i	0.0474383	+	0.329940i
$10$	−0.121504	+	0.266058i	−0.0384231	+	0.0841348i
$11$	−0.513628	−	1.74926i	−0.154865	−	0.527420i	0.845110	−	0.534593i	$-0.179535\pi$
$11$	−0.513628	−	1.74926i	−0.154865	−	0.527420i	−0.999974	+	0.00717260i	$0.997717\pi$
$12$	−0.281733	−	0.959493i	−0.0813292	−	0.276982i
$13$	−2.34999	−	1.07320i	−0.651770	−	0.297653i	0.0619555	−	0.998079i	$-0.480266\pi$
$13$	−2.34999	−	1.07320i	−0.651770	−	0.297653i	−0.713725	+	0.700426i	$0.752994\pi$
$14$	1.16238	−	2.37673i	0.310660	−	0.635209i
$15$	−0.221049	+	0.191540i	−0.0570745	+	0.0494553i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	0.948993	−	0.609881i	0.230165	−	0.147918i	−0.420476	−	0.907304i	$-0.638137\pi$
$17$	0.948993	−	0.609881i	0.230165	−	0.147918i	0.650640	+	0.759386i	$0.274501\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	−2.71507	−	1.74487i	−0.622881	−	0.400301i	0.190787	−	0.981631i	$-0.438896\pi$
$19$	−2.71507	−	1.74487i	−0.622881	−	0.400301i	−0.813668	+	0.581330i	$0.802532\pi$
$20$	0.191540	−	0.221049i	0.0428296	−	0.0494280i
$21$	2.04467	−	1.67908i	0.446184	−	0.366406i
$22$			1.82310i			0.388687i
$23$	4.54715	−	1.52428i	0.948146	−	0.317835i
$23$	4.54715	−	1.52428i	0.948146	−	0.317835i
$24$			1.00000i			0.204124i
$25$	4.71538	+	1.38456i	0.943076	+	0.276912i
$26$	1.95244	+	1.69180i	0.382905	+	0.331789i
$27$	0.540641	−	0.841254i	0.104046	−	0.161899i
$28$	−1.78490	+	1.95298i	−0.337315	+	0.369078i
$29$	3.78361	−	2.43158i	0.702599	−	0.451533i	−0.139946	−	0.990159i	$-0.544693\pi$
$29$	3.78361	−	2.43158i	0.702599	−	0.451533i	0.842545	+	0.538626i	$0.181057\pi$
$30$	0.266058	−	0.121504i	0.0485752	−	0.0221836i
$31$	−2.26832	+	1.96551i	−0.407402	+	0.353016i	−0.834326	−	0.551272i	$-0.814143\pi$
$31$	−2.26832	+	1.96551i	−0.407402	+	0.353016i	0.426924	+	0.904288i	$0.359597\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	−0.757345	+	1.65835i	−0.131837	+	0.288682i
$34$	−1.08238	+	0.317814i	−0.185626	+	0.0545047i
$35$	0.736478	+	0.237591i	0.124488	+	0.0401602i
$36$	−0.415415	+	0.909632i	−0.0692358	+	0.151605i
$37$	4.55467	−	0.654863i	0.748784	−	0.107659i	0.242650	−	0.970114i	$-0.421983\pi$
$37$	4.55467	−	0.654863i	0.748784	−	0.107659i	0.506134	+	0.862455i	$0.331074\pi$
$38$	2.11351	+	2.43912i	0.342856	+	0.395677i
$39$	1.07320	+	2.34999i	0.171850	+	0.376300i
$40$	−0.246058	+	0.158132i	−0.0389051	+	0.0250028i
$41$	2.18956	+	0.314812i	0.341952	+	0.0491653i	0.311152	−	0.950360i	$-0.399285\pi$
$41$	2.18956	+	0.314812i	0.341952	+	0.0491653i	0.0308006	+	0.999526i	$0.490194\pi$
$42$	−2.43490	+	1.03502i	−0.375713	+	0.159707i
$43$	3.03177	+	2.62705i	0.462341	+	0.400621i	0.854643	−	0.519215i	$-0.173776\pi$
$43$	3.03177	+	2.62705i	0.462341	+	0.400621i	−0.392302	+	0.919836i	$0.628321\pi$
$44$	0.513628	−	1.74926i	0.0774323	−	0.263710i
$45$	0.292489			0.0436017
$46$	−4.79240	+	0.181459i	−0.706600	+	0.0267547i
$47$		−	9.34327i		−	1.36286i	−0.731885	−	0.681428i	$-0.761359\pi$
$47$		−	9.34327i		−	1.36286i	0.731885	−	0.681428i	$-0.238641\pi$
$48$	0.281733	−	0.959493i	0.0406646	−	0.138491i
$49$	−6.60271	−	2.32469i	−0.943245	−	0.332099i
$50$	−4.13430	−	2.65695i	−0.584678	−	0.375750i
$51$	−1.11659	−	0.160541i	−0.156354	−	0.0224803i
$52$	−1.39672	−	2.17334i	−0.193690	−	0.301388i
$53$	10.4199	−	4.75862i	1.43129	−	0.653647i	0.459213	−	0.888326i	$-0.348131\pi$
$53$	10.4199	−	4.75862i	1.43129	−	0.653647i	0.972073	+	0.234679i	$0.0754040\pi$
$54$	−0.755750	+	0.654861i	−0.102844	+	0.0891153i
$55$	−0.527811	+	0.0758877i	−0.0711700	+	0.0102327i
$56$	2.26282	−	1.37100i	0.302382	−	0.183208i
$57$	0.909268	+	3.09668i	0.120435	+	0.410165i
$58$	−4.31540	+	1.26712i	−0.566640	+	0.166381i
$59$	11.1766	+	5.10418i	1.45507	+	0.664507i	0.976887	−	0.213754i	$-0.0685692\pi$
$59$	11.1766	+	5.10418i	1.45507	+	0.664507i	0.478180	+	0.878262i	$0.341296\pi$
$60$	−0.289512	+	0.0416256i	−0.0373758	+	0.00537384i
$61$	−6.30483	−	7.27616i	−0.807250	−	0.931616i	0.191505	−	0.981492i	$-0.438663\pi$
$61$	−6.30483	−	7.27616i	−0.807250	−	0.931616i	−0.998755	+	0.0498752i	$0.984118\pi$
$62$	2.73018	−	1.24683i	0.346734	−	0.158348i
$63$	−2.64482	−	0.0700092i	−0.333217	−	0.00882033i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.408525	+	0.635678i	−0.0506713	+	0.0788461i
$66$	1.19388	−	1.37781i	0.146956	−	0.169597i
$67$	2.51321	−	8.55921i	0.307038	−	1.04567i	−0.651011	−	0.759068i	$-0.725655\pi$
$67$	2.51321	−	8.55921i	0.307038	−	1.04567i	0.958049	−	0.286606i	$-0.0925269\pi$
$68$	1.12807			0.136799
$69$	−4.43470	−	1.82577i	−0.533875	−	0.219797i
$70$	−0.639708	−	0.435457i	−0.0764598	−	0.0520470i
$71$	−12.9475	−	3.80174i	−1.53659	−	0.451183i	−0.599530	−	0.800353i	$-0.704646\pi$
$71$	−12.9475	−	3.80174i	−1.53659	−	0.451183i	−0.937060	+	0.349169i	$0.886464\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	3.01076	−	4.68483i	0.352382	−	0.548318i	−0.619135	−	0.785284i	$-0.712517\pi$
$73$	3.01076	−	4.68483i	0.352382	−	0.548318i	0.971518	+	0.236966i	$0.0761532\pi$
$74$	−4.55467	−	0.654863i	−0.529470	−	0.0761263i
$75$	−2.65695	−	4.13430i	−0.306798	−	0.477388i
$76$	−1.34072	−	2.93576i	−0.153791	−	0.336755i
$77$	4.79088	−	0.559877i	0.545971	−	0.0638039i
$78$	−0.367663	−	2.55716i	−0.0416297	−	0.289541i
$79$	6.36288	+	2.90583i	0.715880	+	0.326931i	0.739841	−	0.672782i	$-0.234901\pi$
$79$	6.36288	+	2.90583i	0.715880	+	0.326931i	−0.0239615	+	0.999713i	$0.507628\pi$
$80$	0.280641	−	0.0824037i	0.0313767	−	0.00921302i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−2.01218	−	0.918931i	−0.222208	−	0.101479i
$83$	−1.09286	−	7.60102i	−0.119957	−	0.834320i	−0.957600	−	0.288102i	$-0.906976\pi$
$83$	−1.09286	−	7.60102i	−0.119957	−	0.834320i	0.837643	−	0.546219i	$-0.183933\pi$
$84$	2.62787	−	0.307101i	0.286724	−	0.0335075i
$85$	−0.137065	−	0.300132i	−0.0148668	−	0.0325538i
$86$	−2.16884	−	3.37478i	−0.233872	−	0.363912i
$87$	−4.45181	−	0.640073i	−0.477284	−	0.0686230i
$88$	−0.985644	+	1.53369i	−0.105070	+	0.163492i
$89$	−6.28806	+	7.25681i	−0.666533	+	0.769220i	−0.983830	−	0.179106i	$-0.942679\pi$
$89$	−6.28806	+	7.25681i	−0.666533	+	0.769220i	0.317297	+	0.948326i	$0.397225\pi$
$90$	−0.280641	−	0.0824037i	−0.0295822	−	0.00868612i
$91$	3.84623	−	5.65031i	0.403195	−	0.592314i
$92$	4.64939	+	1.17607i	0.484733	+	0.122613i
$93$	3.00142			0.311232
$94$	−2.63230	+	8.96480i	−0.271501	+	0.924649i
$95$	−0.618178	+	0.713415i	−0.0634237	+	0.0731949i
$96$	−0.540641	+	0.841254i	−0.0551789	+	0.0858601i
$97$	1.34152	−	9.33048i	0.136211	−	0.947367i	−0.801015	−	0.598644i	$-0.795706\pi$
$97$	1.34152	−	9.33048i	0.136211	−	0.947367i	0.937226	−	0.348723i	$-0.113384\pi$
$98$	5.68032	+	4.09072i	0.573799	+	0.413225i
$99$	1.65835	−	0.757345i	0.166671	−	0.0761160i
$100$	3.21828	+	3.71409i	0.321828	+	0.371409i
$101$	15.8015	−	2.27192i	1.57231	−	0.226064i	0.699685	−	0.714452i	$-0.253324\pi$
$101$	15.8015	−	2.27192i	1.57231	−	0.226064i	0.872627	+	0.488387i	$0.162415\pi$
$102$	1.02613	+	0.468617i	0.101602	+	0.0464000i
$103$	−14.5845	+	4.28239i	−1.43705	+	0.421956i	−0.905237	−	0.424906i	$-0.860307\pi$
$103$	−14.5845	+	4.28239i	−1.43705	+	0.421956i	−0.531813	+	0.846862i	$0.678489\pi$
$104$	0.727842	+	2.47880i	0.0713708	+	0.243067i
$105$	−0.401004	−	0.661850i	−0.0391340	−	0.0645899i
$106$	−11.3385	+	1.63023i	−1.10129	+	0.158342i
$107$	6.78277	−	5.87730i	0.655715	−	0.568180i	−0.262173	−	0.965021i	$-0.584439\pi$
$107$	6.78277	−	5.87730i	0.655715	−	0.568180i	0.917887	+	0.396841i	$0.129894\pi$
$108$	0.909632	−	0.415415i	0.0875294	−	0.0399733i
$109$	5.27743	+	8.21185i	0.505486	+	0.786552i	0.996411	−	0.0846501i	$-0.0269772\pi$
$109$	5.27743	+	8.21185i	0.505486	+	0.786552i	−0.490924	+	0.871202i	$0.663341\pi$
$110$	0.527811	+	0.0758877i	0.0503248	+	0.00723561i
$111$	−3.87104	−	2.48776i	−0.367423	−	0.236128i
$112$	−2.55741	+	0.677960i	−0.241653	+	0.0640612i
$113$	4.58115	−	15.6019i	0.430958	−	1.46771i	−0.402651	−	0.915353i	$-0.631911\pi$
$113$	4.58115	−	15.6019i	0.430958	−	1.46771i	0.833609	−	0.552355i	$-0.186271\pi$
$114$		−	3.22741i		−	0.302275i
$115$	−0.252021	−	1.37990i	−0.0235011	−	0.128677i
$116$	4.49759			0.417590
$117$	0.727842	−	2.47880i	0.0672890	−	0.229165i
$118$	−9.28585	−	8.04623i	−0.854831	−	0.740716i
$119$	1.16757	+	2.74674i	0.107031	+	0.251793i
$120$	0.289512	+	0.0416256i	0.0264287	+	0.00379988i
$121$	6.45771	−	4.15012i	0.587064	−	0.377283i
$122$	3.99951	+	8.75770i	0.362098	+	0.792885i
$123$	−1.44860	−	1.67178i	−0.130616	−	0.150739i
$124$	−2.97087	+	0.427146i	−0.266792	+	0.0383589i
$125$	1.20465	−	2.63781i	0.107747	−	0.235933i
$126$	2.51797	+	0.812307i	0.224318	+	0.0723660i
$127$	4.38883	−	1.28868i	0.389446	−	0.114352i	−0.0811468	−	0.996702i	$-0.525858\pi$
$127$	4.38883	−	1.28868i	0.389446	−	0.114352i	0.470593	+	0.882350i	$0.344040\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	−0.570912	−	3.97078i	−0.0502660	−	0.349608i
$130$	0.571068	−	0.494833i	0.0500860	−	0.0433998i
$131$	−3.35174	+	1.53069i	−0.292843	+	0.133737i	−0.556419	−	0.830902i	$-0.687825\pi$
$131$	−3.35174	+	1.53069i	−0.292843	+	0.133737i	0.263576	+	0.964639i	$0.415098\pi$
$132$	−1.53369	+	0.985644i	−0.133491	+	0.0857893i
$133$	5.76062	−	6.30307i	0.499509	−	0.546546i
$134$	−4.82282	+	7.50445i	−0.416628	+	0.648286i
$135$	−0.221049	−	0.191540i	−0.0190248	−	0.0164851i
$136$	−1.08238	−	0.317814i	−0.0928129	−	0.0272523i
$137$		−	3.37551i		−	0.288389i	−0.989549	−	0.144195i	$-0.953941\pi$
$137$		−	3.37551i		−	0.288389i	0.989549	−	0.144195i	$-0.0460591\pi$
$138$	3.74068	+	3.00122i	0.318428	+	0.255480i
$139$			10.6290i			0.901540i	0.892640	+	0.450770i	$0.148851\pi$
$139$			10.6290i			0.901540i	−0.892640	+	0.450770i	$0.851149\pi$
$140$	0.491113	+	0.598044i	0.0415067	+	0.0505440i
$141$	−6.11854	+	7.06117i	−0.515274	+	0.594658i
$142$	11.3520	+	7.29548i	0.952638	+	0.612223i
$143$	−0.670289	+	4.66196i	−0.0560524	+	0.389853i
$144$	−0.841254	+	0.540641i	−0.0701045	+	0.0450534i
$145$	−0.546476	−	1.19662i	−0.0453824	−	0.0993736i
$146$	−4.20867	+	3.64683i	−0.348312	+	0.301814i
$147$	3.46765	+	6.08074i	0.286007	+	0.501531i
$148$	4.18568	+	1.91154i	0.344061	+	0.157127i
$149$	2.17600	+	7.41079i	0.178265	+	0.607115i	0.999341	+	0.0362963i	$0.0115560\pi$
$149$	2.17600	+	7.41079i	0.178265	+	0.607115i	−0.821076	+	0.570819i	$0.806626\pi$
$150$	1.38456	+	4.71538i	0.113049	+	0.385009i
$151$	−5.15066	+	11.2784i	−0.419155	+	0.917821i	0.575809	+	0.817584i	$0.304687\pi$
$151$	−5.15066	+	11.2784i	−0.419155	+	0.917821i	−0.994964	+	0.100237i	$0.968040\pi$
$152$	0.459309	+	3.19456i	0.0372549	+	0.259113i
$153$	0.738729	+	0.852538i	0.0597227	+	0.0689237i
$154$	−4.75455	−	0.812547i	−0.383132	−	0.0654769i
$155$	0.474619	+	0.738521i	0.0381223	+	0.0593195i
$156$	−0.367663	+	2.55716i	−0.0294366	+	0.204736i
$157$	12.8772	+	8.27569i	1.02771	+	0.660472i	0.941919	−	0.335841i	$-0.109020\pi$
$157$	12.8772	+	8.27569i	1.02771	+	0.660472i	0.0857956	+	0.996313i	$0.472657\pi$
$158$	−5.28647	−	4.58075i	−0.420569	−	0.364425i
$159$	−10.9911	−	3.22727i	−0.871650	−	0.255939i
$160$	−0.292489			−0.0231233
$161$	1.94860	+	12.5381i	0.153571	+	0.988138i
$162$	1.00000			0.0785674
$163$	−19.6351	−	5.76539i	−1.53794	−	0.451580i	−0.600471	−	0.799647i	$-0.705020\pi$
$163$	−19.6351	−	5.76539i	−1.53794	−	0.451580i	−0.937470	+	0.348067i	$0.886838\pi$
$164$	1.67178	+	1.44860i	0.130544	+	0.113117i
$165$	0.448589	+	0.288290i	0.0349226	+	0.0224434i
$166$	−1.09286	+	7.60102i	−0.0848225	+	0.589954i
$167$	0.381032	+	0.592897i	0.0294851	+	0.0458797i	0.855683	−	0.517500i	$-0.173137\pi$
$167$	0.381032	+	0.592897i	0.0294851	+	0.0458797i	−0.826198	+	0.563380i	$0.809501\pi$
$168$	−2.60794	−	0.445694i	−0.201207	−	0.0343861i
$169$	−4.14250	−	4.78071i	−0.318654	−	0.367747i
$170$	0.0469565	+	0.326590i	0.00360140	+	0.0250483i
$171$	1.34072	−	2.93576i	0.102527	−	0.224503i
$172$	1.13020	+	3.84911i	0.0861771	+	0.293492i
$173$	−5.26871	−	17.9436i	−0.400572	−	1.36422i	−0.875082	−	0.483974i	$-0.839193\pi$
$173$	−5.26871	−	17.9436i	−0.400572	−	1.36422i	0.474510	−	0.880250i	$-0.342625\pi$
$174$	4.09115	+	1.86836i	0.310149	+	0.141640i
$175$	−5.71247	+	11.6803i	−0.431822	+	0.882951i
$176$	1.37781	−	1.19388i	0.103856	−	0.0899920i
$177$	−5.10418	−	11.1766i	−0.383653	−	0.840084i
$178$	8.07783	−	5.19131i	0.605459	−	0.389105i
$179$	2.41746	−	16.8138i	0.180690	−	1.25672i	−0.674448	−	0.738322i	$-0.735618\pi$
$179$	2.41746	−	16.8138i	0.180690	−	1.25672i	0.855138	−	0.518401i	$-0.173473\pi$
$180$	0.246058	+	0.158132i	0.0183400	+	0.0117864i
$181$	−3.60708	+	4.16279i	−0.268112	+	0.309418i	−0.873801	−	0.486284i	$-0.838352\pi$
$181$	−3.60708	+	4.16279i	−0.268112	+	0.309418i	0.605689	+	0.795702i	$0.292898\pi$
$182$	−5.28231	+	4.33783i	−0.391551	+	0.321541i
$183$			9.62774i			0.711703i
$184$	−4.12973	−	2.43831i	−0.304447	−	0.179755i
$185$		−	1.34589i		−	0.0989520i
$186$	−2.87984	−	0.845597i	−0.211160	−	0.0620022i
$187$	−1.55427	−	1.34678i	−0.113659	−	0.0984863i
$188$	5.05135	−	7.86006i	0.368408	−	0.573254i
$189$	1.95298	+	1.78490i	0.142058	+	0.129832i
$190$	0.794130	−	0.510356i	0.0576122	−	0.0370251i
$191$	−12.6791	+	5.79033i	−0.917425	+	0.418974i	−0.817439	−	0.576015i	$-0.804607\pi$
$191$	−12.6791	+	5.79033i	−0.917425	+	0.418974i	−0.0999856	+	0.994989i	$0.531880\pi$
$192$	0.755750	−	0.654861i	0.0545415	−	0.0472605i
$193$	2.81334	+	19.5672i	0.202508	+	1.40848i	0.796807	+	0.604233i	$0.206520\pi$
$193$	2.81334	+	19.5672i	0.202508	+	1.40848i	−0.594299	+	0.804244i	$0.702570\pi$
$194$	−3.91588	+	8.57458i	−0.281144	+	0.615619i
$195$	0.725023	−	0.212886i	0.0519200	−	0.0152451i
$196$	−4.29773	−	5.52535i	−0.306981	−	0.394668i
$197$	−3.72179	+	8.14958i	−0.265166	+	0.580633i	−0.994643	−	0.103373i	$-0.967037\pi$
$197$	−3.72179	+	8.14958i	−0.265166	+	0.580633i	0.729476	+	0.684006i	$0.239764\pi$
$198$	−1.80455	+	0.259455i	−0.128244	+	0.0184386i
$199$	11.9825	+	13.8285i	0.849414	+	0.980276i	0.999965	−	0.00832588i	$-0.00265024\pi$
$199$	11.9825	+	13.8285i	0.849414	+	0.980276i	−0.150551	+	0.988602i	$0.548105\pi$
$200$	−2.04154	−	4.47034i	−0.144358	−	0.316101i
$201$	−7.50445	+	4.82282i	−0.529323	+	0.340175i
$202$	−15.8015	−	2.27192i	−1.11179	−	0.159852i
$203$	4.65508	+	10.9512i	0.326722	+	0.768622i
$204$	−0.852538	−	0.738729i	−0.0596896	−	0.0517214i
$205$	0.182284	−	0.620801i	0.0127312	−	0.0433586i
$206$	15.2002			1.05905
$207$	2.15589	+	4.28394i	0.149845	+	0.297754i
$208$		−	2.58345i		−	0.179130i
$209$	−1.65769	+	5.64557i	−0.114665	+	0.390512i
$210$	0.198296	+	0.748016i	0.0136837	+	0.0516180i
$211$	−3.07083	−	1.97350i	−0.211404	−	0.135861i	0.430654	−	0.902517i	$-0.358283\pi$
$211$	−3.07083	−	1.97350i	−0.211404	−	0.135861i	−0.642058	+	0.766656i	$0.721919\pi$
$212$	11.3385	+	1.63023i	0.778731	+	0.111965i
$213$	7.29548	+	11.3520i	0.499878	+	0.777826i
$214$	−8.16384	+	3.72830i	−0.558069	+	0.254862i
$215$	0.886761	−	0.768383i	0.0604766	−	0.0524033i
$216$	−0.989821	+	0.142315i	−0.0673488	+	0.00968330i
$217$	−4.11496	−	6.79166i	−0.279341	−	0.461048i
$218$	−2.75012	−	9.36603i	−0.186261	−	0.634348i
$219$	−5.34329	+	1.56893i	−0.361066	+	0.106019i
$220$	−0.485051	−	0.221515i	−0.0327021	−	0.0149345i
$221$	−2.88465	+	0.414750i	−0.194043	+	0.0278991i
$222$	3.01335	+	3.47759i	0.202243	+	0.233401i
$223$	−10.6619	+	4.86912i	−0.713973	+	0.326061i	−0.739074	−	0.673624i	$-0.764737\pi$
$223$	−10.6619	+	4.86912i	−0.713973	+	0.326061i	0.0251009	+	0.999685i	$0.492009\pi$
$224$	2.64482	+	0.0700092i	0.176715	+	0.00467769i
$225$	−0.699399	+	4.86443i	−0.0466266	+	0.324295i
$226$	−8.79115	+	13.6793i	−0.584779	+	0.909934i
$227$	−8.76605	+	10.1166i	−0.581823	+	0.671460i	−0.967996	−	0.250967i	$-0.919251\pi$
$227$	−8.76605	+	10.1166i	−0.581823	+	0.671460i	0.386173	+	0.922427i	$0.373797\pi$
$228$	−0.909268	+	3.09668i	−0.0602177	+	0.205083i
$229$	22.5201			1.48817			0.744085	−	0.668085i	$-0.232886\pi$
$229$	22.5201			1.48817			0.744085	+	0.668085i	$0.232886\pi$
$230$	−0.146952	+	1.39501i	−0.00968970	+	0.0919843i
$231$	−3.98734	−	2.71423i	−0.262348	−	0.178583i
$232$	−4.31540	−	1.26712i	−0.283320	−	0.0831903i
$233$	−5.82388	+	6.72112i	−0.381535	+	0.440315i	−0.913739	−	0.406301i	$-0.866818\pi$
$233$	−5.82388	+	6.72112i	−0.381535	+	0.440315i	0.532204	+	0.846616i	$0.321364\pi$
$234$	−1.39672	+	2.17334i	−0.0913064	+	0.142076i
$235$	−2.70499	−	0.388919i	−0.176454	−	0.0253703i
$236$	6.64282	+	10.3364i	0.432411	+	0.672844i
$237$	−2.90583	−	6.36288i	−0.188754	−	0.413313i
$238$	−0.346432	−	2.96442i	−0.0224558	−	0.192155i
$239$	3.45818	+	24.0521i	0.223691	+	1.55580i	0.723904	+	0.689901i	$0.242346\pi$
$239$	3.45818	+	24.0521i	0.223691	+	1.55580i	−0.500213	+	0.865902i	$0.666745\pi$
$240$	−0.266058	−	0.121504i	−0.0171739	−	0.00784308i
$241$	15.8570	−	4.65602i	1.02144	−	0.299921i	0.272212	−	0.962237i	$-0.412245\pi$
$241$	15.8570	−	4.65602i	1.02144	−	0.299921i	0.749224	+	0.662317i	$0.230427\pi$
$242$	−7.36535	+	2.16266i	−0.473463	+	0.139021i
$243$	0.909632	+	0.415415i	0.0583529	+	0.0266489i
$244$	−1.37017	−	9.52974i	−0.0877161	−	0.610079i
$245$	−0.947867	+	1.81480i	−0.0605570	+	0.115943i
$246$	0.918931	+	2.01218i	0.0585889	+	0.128292i
$247$	4.50779	+	7.01426i	0.286824	+	0.446307i
$248$	2.97087	+	0.427146i	0.188650	+	0.0271238i
$249$	−4.15168	+	6.46014i	−0.263102	+	0.409395i
$250$	−1.89901	+	2.19158i	−0.120104	+	0.138607i
$251$	−10.0717	−	2.95731i	−0.635718	−	0.186664i	−0.0520349	−	0.998645i	$-0.516571\pi$
$251$	−10.0717	−	2.95731i	−0.635718	−	0.186664i	−0.583683	+	0.811982i	$0.698389\pi$
$252$	−2.18712	−	1.48880i	−0.137776	−	0.0937853i
$253$	−5.00190	−	7.17121i	−0.314467	−	0.450850i
$254$	−4.57412			−0.287006
$255$	−0.0929572	+	0.316583i	−0.00582120	+	0.0198252i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−0.294668	+	0.458512i	−0.0183809	+	0.0286012i	−0.850322	−	0.526262i	$-0.823593\pi$
$257$	−0.294668	+	0.458512i	−0.0183809	+	0.0286012i	0.831942	+	0.554863i	$0.187229\pi$
$258$	−0.570912	+	3.97078i	−0.0355434	+	0.247210i
$259$	−0.322148	+	12.1702i	−0.0200173	+	0.756219i
$260$	−0.687347	+	0.313901i	−0.0426274	+	0.0194673i
$261$	2.94529	+	3.39905i	0.182309	+	0.210396i
$262$	3.64721	−	0.524390i	0.225326	−	0.0323969i
$263$	−2.57654	−	1.17666i	−0.158876	−	0.0725563i	0.334390	−	0.942435i	$-0.391470\pi$
$263$	−2.57654	−	1.17666i	−0.158876	−	0.0725563i	−0.493266	+	0.869879i	$0.664197\pi$
$264$	1.74926	−	0.513628i	0.107659	−	0.0316116i
$265$	−0.943943	−	3.21477i	−0.0579859	−	0.197482i
$266$	−7.30305	+	4.42480i	−0.447779	+	0.271302i
$267$	9.50440	−	1.36653i	0.581660	−	0.0836301i
$268$	6.74170	−	5.84172i	0.411815	−	0.356840i
$269$	10.7231	−	4.89710i	0.653802	−	0.298581i	−0.0607612	−	0.998152i	$-0.519353\pi$
$269$	10.7231	−	4.89710i	0.653802	−	0.298581i	0.714563	+	0.699571i	$0.246626\pi$
$270$	0.158132	+	0.246058i	0.00962358	+	0.0149746i
$271$	15.4690	+	2.22411i	0.939677	+	0.135105i	0.595099	−	0.803652i	$-0.297113\pi$
$271$	15.4690	+	2.22411i	0.939677	+	0.135105i	0.344578	+	0.938758i	$0.388022\pi$
$272$	0.948993	+	0.609881i	0.0575411	+	0.0369795i
$273$	−6.60696	+	1.75148i	−0.399871	+	0.106004i
$274$	−0.950990	+	3.23878i	−0.0574514	+	0.195662i
$275$		−	8.95955i		−	0.540281i
$276$	−2.74362	−	3.93352i	−0.165146	−	0.236770i
$277$	−2.74582			−0.164980			−0.0824901	−	0.996592i	$-0.526287\pi$
$277$	−2.74582			−0.164980			−0.0824901	+	0.996592i	$0.526287\pi$
$278$	2.99454	−	10.1985i	0.179600	−	0.611663i
$279$	−2.26832	−	1.96551i	−0.135801	−	0.117672i
$280$	−0.302731	−	0.712182i	−0.0180917	−	0.0425610i
$281$	−5.94412	−	0.854635i	−0.354596	−	0.0509833i	−0.0372850	−	0.999305i	$-0.511871\pi$
$281$	−5.94412	−	0.854635i	−0.354596	−	0.0509833i	−0.317311	+	0.948321i	$0.602780\pi$
$282$	7.86006	−	5.05135i	0.468060	−	0.300804i
$283$	10.1166	+	22.1523i	0.601371	+	1.31682i	0.928322	+	0.371777i	$0.121251\pi$
$283$	10.1166	+	22.1523i	0.601371	+	1.31682i	−0.326951	+	0.945041i	$0.606021\pi$
$284$	−8.83678	−	10.1982i	−0.524367	−	0.605151i
$285$	0.934375	−	0.134343i	0.0553476	−	0.00795779i
$286$	1.95656	−	4.28428i	0.115694	−	0.253335i
$287$	−1.79689	+	5.56994i	−0.106067	+	0.328783i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−6.53342	+	14.3062i	−0.384319	+	0.841541i
$290$	0.187214	+	1.30211i	0.0109936	+	0.0764623i
$291$	−7.12402	+	6.17300i	−0.417617	+	0.361867i
$292$	5.06562	−	2.31339i	0.296443	−	0.135381i
$293$	−5.26488	+	3.38353i	−0.307577	+	0.197668i	−0.685319	−	0.728243i	$-0.740337\pi$
$293$	−5.26488	+	3.38353i	−0.307577	+	0.197668i	0.377742	+	0.925911i	$0.376701\pi$
$294$	−1.61404	−	6.81138i	−0.0941329	−	0.397248i
$295$	1.94295	−	3.02329i	0.113123	−	0.176023i
$296$	−3.47759	−	3.01335i	−0.202131	−	0.175147i
$297$	−1.74926	−	0.513628i	−0.101502	−	0.0298037i
$298$		−	7.72365i		−	0.447419i
$299$	−12.3216	−	1.29797i	−0.712578	−	0.0750636i
$300$		−	4.91445i		−	0.283736i
$301$	−8.20243	+	6.73583i	−0.472780	+	0.388247i
$302$	8.11951	−	9.37041i	0.467225	−	0.539206i
$303$	−13.4298	−	8.63080i	−0.771522	−	0.495827i
$304$	0.459309	−	3.19456i	0.0263432	−	0.183221i
$305$	−2.36898	+	1.52245i	−0.135647	+	0.0871752i
$306$	−0.468617	−	1.02613i	−0.0267891	−	0.0586599i
$307$	7.15298	−	6.19809i	0.408242	−	0.353744i	−0.426402	−	0.904534i	$-0.640219\pi$
$307$	7.15298	−	6.19809i	0.408242	−	0.353744i	0.834644	+	0.550790i	$0.185674\pi$
$308$	4.33303	+	2.11914i	0.246898	+	0.120749i
$309$	13.8266	+	6.31438i	0.786566	+	0.359213i
$310$	−0.247328	−	0.842321i	−0.0140473	−	0.0478406i
$311$	3.29406	+	11.2185i	0.186789	+	0.636145i	0.998633	+	0.0522704i	$0.0166458\pi$
$311$	3.29406	+	11.2185i	0.186789	+	0.636145i	−0.811844	+	0.583874i	$0.801536\pi$
$312$	1.07320	−	2.34999i	0.0607582	−	0.133042i
$313$	−2.11146	−	14.6855i	−0.119347	−	0.830074i	−0.958278	−	0.285837i	$-0.907728\pi$
$313$	−2.11146	−	14.6855i	−0.119347	−	0.830074i	0.838932	−	0.544237i	$-0.183181\pi$
$314$	−10.0241	−	11.5684i	−0.565691	−	0.652842i
$315$	−0.130361	+	0.762795i	−0.00734500	+	0.0429786i
$316$	3.78178	+	5.88457i	0.212742	+	0.331033i
$317$	0.584546	−	4.06561i	0.0328314	−	0.228347i	−0.966799	−	0.255539i	$-0.917747\pi$
$317$	0.584546	−	4.06561i	0.0328314	−	0.228347i	0.999630	+	0.0271913i	$0.00865631\pi$
$318$	9.63664	+	6.19309i	0.540396	+	0.347291i
$319$	−6.19682	−	5.36957i	−0.346955	−	0.300638i
$320$	0.280641	+	0.0824037i	0.0156883	+	0.00460651i
$321$	−8.97489			−0.500929
$322$	1.66271	−	12.5792i	0.0926592	−	0.701009i
$323$	−3.64075			−0.202577
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−9.59518	−	8.31427i	−0.532245	−	0.461193i
$326$	17.2155	+	11.0637i	0.953476	+	0.612762i
$327$	1.38920	−	9.66208i	0.0768228	−	0.534314i
$328$	−1.19594	−	1.86092i	−0.0660348	−	0.102752i
$329$	24.3667	+	4.16424i	1.34338	+	0.229582i
$330$	−0.349197	−	0.402995i	−0.0192226	−	0.0221841i
$331$	−0.263251	−	1.83095i	−0.0144696	−	0.100638i	0.981307	−	0.192450i	$-0.0616433\pi$
$331$	−0.263251	−	1.83095i	−0.0144696	−	0.100638i	−0.995776	+	0.0918117i	$0.970734\pi$
$332$	3.19005	−	6.98523i	0.175077	−	0.383364i
$333$	1.29640	+	4.41512i	0.0710420	+	0.241947i
$334$	−0.198559	−	0.676229i	−0.0108647	−	0.0370016i
$335$	−2.37338	−	1.08389i	−0.129672	−	0.0592190i
$336$	2.37673	+	1.16238i	0.129661	+	0.0634132i
$337$	17.1364	−	14.8487i	0.933477	−	0.808863i	−0.0483128	−	0.998832i	$-0.515384\pi$
$337$	17.1364	−	14.8487i	0.933477	−	0.808863i	0.981790	+	0.189970i	$0.0608390\pi$
$338$	2.62782	+	5.75413i	0.142935	+	0.312984i
$339$	−13.6793	+	8.79115i	−0.742958	+	0.477470i
$340$	0.0469565	−	0.326590i	0.00254658	−	0.0177118i
$341$	4.60325	+	2.95833i	0.249280	+	0.160203i
$342$	−2.11351	+	2.43912i	−0.114285	+	0.131892i
$343$	9.00545	−	16.1834i	0.486248	−	0.873821i
$344$		−	4.01161i		−	0.216292i
$345$	−0.713180	+	1.20790i	−0.0383963	+	0.0650312i
$346$			18.7011i			1.00538i
$347$	−16.5798	−	4.86828i	−0.890053	−	0.261343i	−0.195430	−	0.980718i	$-0.562610\pi$
$347$	−16.5798	−	4.86828i	−0.890053	−	0.261343i	−0.694622	+	0.719375i	$0.744428\pi$
$348$	−3.39905	−	2.94529i	−0.182208	−	0.157884i
$349$	−2.49074	+	3.87566i	−0.133326	+	0.207459i	−0.901497	−	0.432786i	$-0.857531\pi$
$349$	−2.49074	+	3.87566i	−0.133326	+	0.207459i	0.768171	+	0.640245i	$0.221167\pi$
$350$	8.77181	−	9.59782i	0.468873	−	0.513025i
$351$	−2.17334	+	1.39672i	−0.116004	+	0.0745514i
$352$	−1.65835	+	0.757345i	−0.0883905	+	0.0403666i
$353$	0.868685	−	0.752720i	0.0462354	−	0.0400632i	−0.631437	−	0.775428i	$-0.717534\pi$
$353$	0.868685	−	0.752720i	0.0462354	−	0.0400632i	0.677672	+	0.735364i	$0.262989\pi$
$354$	1.74861	+	12.1619i	0.0929377	+	0.646396i
$355$	−1.63960	+	3.59022i	−0.0870208	+	0.190549i
$356$	−9.21318	+	2.70523i	−0.488298	+	0.143377i
$357$	0.916339	−	2.84044i	0.0484978	−	0.150332i
$358$	−7.05654	+	15.4517i	−0.372950	+	0.816646i
$359$	−11.7732	+	1.69274i	−0.621367	+	0.0893392i	−0.445806	−	0.895129i	$-0.647083\pi$
$359$	−11.7732	+	1.69274i	−0.621367	+	0.0893392i	−0.175561	+	0.984469i	$0.556174\pi$
$360$	−0.191540	−	0.221049i	−0.0100950	−	0.0116503i
$361$	−3.56584	−	7.80810i	−0.187676	−	0.410952i
$362$	4.63376	−	2.97794i	0.243545	−	0.156517i
$363$	−7.59816	−	1.09245i	−0.398800	−	0.0573388i
$364$	6.29045	−	2.67392i	0.329709	−	0.140151i
$365$	−1.23099	−	1.06666i	−0.0644330	−	0.0558315i
$366$	2.71245	−	9.23774i	0.141782	−	0.482865i
$367$	19.9227			1.03995			0.519977	−	0.854180i	$-0.325940\pi$
$367$	19.9227			1.03995			0.519977	+	0.854180i	$0.325940\pi$
$368$	3.27549	+	3.50302i	0.170747	+	0.182608i
$369$			2.21208i			0.115156i
$370$	−0.379182	+	1.29137i	−0.0197127	+	0.0671353i
$371$	7.76610	+	29.2954i	0.403196	+	1.52094i
$372$	2.52495	+	1.62269i	0.130913	+	0.0841325i
$373$	24.7994	+	3.56561i	1.28406	+	0.184620i	0.750348	−	0.661043i	$-0.229886\pi$
$373$	24.7994	+	3.56561i	1.28406	+	0.184620i	0.533716	+	0.845664i	$0.320795\pi$
$374$	1.11188	+	1.73011i	0.0574937	+	0.0894620i
$375$	−2.63781	+	1.20465i	−0.136216	+	0.0622078i
$376$	−7.06117	+	6.11854i	−0.364152	+	0.315540i
$377$	−11.5010	+	1.65360i	−0.592333	+	0.0851646i
$378$	−1.37100	−	2.26282i	−0.0705169	−	0.116387i
$379$	−5.08926	−	17.3324i	−0.261418	−	0.890307i	−0.980688	−	0.195577i	$-0.937342\pi$
$379$	−5.08926	−	17.3324i	−0.261418	−	0.890307i	0.719270	−	0.694730i	$-0.244476\pi$
$380$	−0.905746	+	0.265951i	−0.0464638	+	0.0136430i
$381$	−4.16076	−	1.90016i	−0.213162	−	0.0973480i
$382$	13.7968	−	1.98368i	0.705905	−	0.101494i
$383$	−11.7755	−	13.5896i	−0.601698	−	0.694396i	0.370427	−	0.928862i	$-0.379211\pi$
$383$	−11.7755	−	13.5896i	−0.601698	−	0.694396i	−0.972124	+	0.234466i	$0.924666\pi$
$384$	−0.909632	+	0.415415i	−0.0464195	+	0.0211991i
$385$	0.0373316	−	1.41032i	0.00190259	−	0.0718766i
$386$	2.81334	−	19.5672i	0.143195	−	0.995944i
$387$	−2.16884	+	3.37478i	−0.110248	+	0.171550i
$388$	6.17300	−	7.12402i	0.313386	−	0.361667i
$389$	0.0713974	−	0.243157i	0.00361999	−	0.0123286i	−0.957663	−	0.287891i	$-0.907046\pi$
$389$	0.0713974	−	0.243157i	0.00361999	−	0.0123286i	0.961283	+	0.275562i	$0.0888641\pi$
$390$	−0.755632			−0.0382629
$391$	3.38558	−	4.21975i	0.171216	−	0.213402i
$392$	2.56697	+	6.51235i	0.129652	+	0.328923i
$393$	3.53546	+	1.03811i	0.178341	+	0.0523655i
$394$	5.86703	−	6.77091i	0.295577	−	0.341114i
$395$	1.10613	−	1.72117i	0.0556555	−	0.0866016i
$396$	1.80455	+	0.259455i	0.0906819	+	0.0130381i
$397$	−18.8121	−	29.2722i	−0.944152	−	1.46913i	−0.882103	−	0.471056i	$-0.843873\pi$
$397$	−18.8121	−	29.2722i	−0.944152	−	1.46913i	−0.0620489	−	0.998073i	$-0.519763\pi$
$398$	−7.60115	−	16.6442i	−0.381011	−	0.834298i
$399$	−8.48122	+	0.991143i	−0.424592	+	0.0496192i
$400$	0.699399	+	4.86443i	0.0349700	+	0.243221i
$401$	16.7200	+	7.63578i	0.834959	+	0.381313i	0.786559	−	0.617515i	$-0.211861\pi$
$401$	16.7200	+	7.63578i	0.834959	+	0.381313i	0.0483998	+	0.998828i	$0.484588\pi$
$402$	8.55921	−	2.51321i	0.426895	−	0.125348i
$403$	7.43992	−	2.18456i	0.370609	−	0.108821i
$404$	14.5214	+	6.63170i	0.722466	+	0.329939i
$405$	0.0416256	+	0.289512i	0.00206839	+	0.0143860i
$406$	−1.38121	−	11.8191i	−0.0685485	−	0.586570i
$407$	−3.48493	−	7.63093i	−0.172742	−	0.378251i
$408$	0.609881	+	0.948993i	0.0301936	+	0.0469822i
$409$	−24.1200	−	3.46794i	−1.19266	−	0.171479i	−0.482741	−	0.875763i	$-0.660359\pi$
$409$	−24.1200	−	3.46794i	−1.19266	−	0.171479i	−0.709918	+	0.704284i	$0.751268\pi$
$410$	−0.349800	+	0.544299i	−0.0172754	+	0.0268810i
$411$	−2.21049	+	2.55104i	−0.109035	+	0.125833i
$412$	−14.5845	−	4.28239i	−0.718525	−	0.210978i
$413$	−18.2927	+	26.8730i	−0.900127	+	1.32233i
$414$	−0.861641	−	4.71779i	−0.0423474	−	0.231867i
$415$	−2.24608			−0.110256
$416$	−0.727842	+	2.47880i	−0.0356854	+	0.121533i
$417$	6.96052	−	8.03286i	0.340858	−	0.393371i
$418$	3.18108	−	4.94986i	0.155592	−	0.242106i
$419$	2.41978	−	16.8299i	0.118214	−	0.822196i	−0.841307	−	0.540558i	$-0.818213\pi$
$419$	2.41978	−	16.8299i	0.118214	−	0.822196i	0.959521	−	0.281638i	$-0.0908777\pi$
$420$	0.0204769	−	0.773583i	0.000999172	−	0.0377470i
$421$	−9.49986	+	4.33844i	−0.462995	+	0.211443i	−0.633234	−	0.773960i	$-0.718273\pi$
$421$	−9.49986	+	4.33844i	−0.462995	+	0.211443i	0.170240	+	0.985403i	$0.445546\pi$
$422$	2.39044	+	2.75871i	0.116365	+	0.134292i
$423$	9.24817	−	1.32969i	0.449661	−	0.0646516i
$424$	−10.4199	−	4.75862i	−0.506036	−	0.231099i
$425$	5.31928	−	1.56188i	0.258023	−	0.0757624i
$426$	−3.80174	−	12.9475i	−0.184195	−	0.627310i
$427$	21.7858	−	13.1997i	1.05429	−	0.638777i
$428$	8.88354	−	1.27726i	0.429402	−	0.0617387i
$429$	3.55950	−	3.08433i	0.171855	−	0.148913i
$430$	−1.06732	+	0.487429i	−0.0514707	+	0.0235059i
$431$	−8.44605	−	13.1423i	−0.406832	−	0.633043i	0.576021	−	0.817435i	$-0.304605\pi$
$431$	−8.44605	−	13.1423i	−0.406832	−	0.633043i	−0.982853	+	0.184392i	$0.940968\pi$
$432$	0.989821	+	0.142315i	0.0476228	+	0.00684713i
$433$	8.37556	+	5.38264i	0.402504	+	0.258673i	0.726194	−	0.687490i	$-0.241287\pi$
$433$	8.37556	+	5.38264i	0.402504	+	0.258673i	−0.323691	+	0.946163i	$0.604924\pi$
$434$	2.03484	+	7.67587i	0.0976754	+	0.368453i
$435$	−0.370618	+	1.26221i	−0.0177698	+	0.0605183i
$436$			9.76144i			0.467488i
$437$	−15.0055	−	3.79565i	−0.717811	−	0.181571i
$438$	5.56887			0.266091
$439$	−7.57542	+	25.7995i	−0.361555	+	1.23134i	0.555141	+	0.831756i	$0.312664\pi$
$439$	−7.57542	+	25.7995i	−0.361555	+	1.23134i	−0.916696	+	0.399586i	$0.869154\pi$
$440$	0.402995	+	0.349197i	0.0192120	+	0.0166473i
$441$	1.36136	−	6.86634i	0.0648268	−	0.326969i
$442$	2.88465	+	0.414750i	0.137209	+	0.0197277i
$443$	−13.8971	+	8.93111i	−0.660270	+	0.424330i	−0.827406	−	0.561604i	$-0.810184\pi$
$443$	−13.8971	+	8.93111i	−0.660270	+	0.424330i	0.167136	+	0.985934i	$0.446548\pi$
$444$	−1.91154	−	4.18568i	−0.0907175	−	0.198644i
$445$	1.83919	+	2.12254i	0.0871860	+	0.100618i
$446$	11.6018	−	1.66809i	0.549361	−	0.0789862i
$447$	3.20852	−	7.02568i	0.151758	−	0.332303i
$448$	−2.51797	−	0.812307i	−0.118963	−	0.0383779i
$449$	10.2992	−	3.02412i	0.486050	−	0.142717i	−0.0295209	−	0.999564i	$-0.509398\pi$
$449$	10.2992	−	3.02412i	0.486050	−	0.142717i	0.515571	+	0.856847i	$0.327580\pi$
$450$	2.04154	−	4.47034i	0.0962389	−	0.210734i
$451$	−0.573934	−	3.99180i	−0.0270255	−	0.187967i
$452$	12.2890	−	10.6484i	0.578024	−	0.500861i
$453$	11.2784	−	5.15066i	0.529904	−	0.241999i
$454$	11.2611	−	7.23709i	0.528511	−	0.339653i
$455$	−1.47573	−	1.34873i	−0.0691834	−	0.0632293i
$456$	1.74487	−	2.71507i	0.0817111	−	0.127145i
$457$	−14.9037	−	12.9141i	−0.697164	−	0.604096i	0.232460	−	0.972606i	$-0.425323\pi$
$457$	−14.9037	−	12.9141i	−0.697164	−	0.604096i	−0.929624	+	0.368510i	$0.879868\pi$
$458$	−21.6079	−	6.34465i	−1.00967	−	0.296466i
$459$		−	1.12807i		−	0.0526538i
$460$	0.534019	−	1.29710i	0.0248988	−	0.0604777i
$461$		−	18.4747i		−	0.860455i	−0.902721	−	0.430227i	$-0.858433\pi$
$461$		−	18.4747i		−	0.860455i	0.902721	−	0.430227i	$-0.141567\pi$
$462$	3.06114	+	3.72765i	0.142417	+	0.173426i
$463$	−0.760666	+	0.877855i	−0.0353511	+	0.0407974i	−0.773150	−	0.634223i	$-0.781320\pi$
$463$	−0.760666	+	0.877855i	−0.0353511	+	0.0407974i	0.737799	+	0.675021i	$0.235865\pi$
$464$	3.78361	+	2.43158i	0.175650	+	0.112883i
$465$	0.124936	−	0.868946i	0.00579375	−	0.0402964i
$466$	7.48153	−	4.80809i	0.346575	−	0.222730i
$467$	0.289863	+	0.634712i	0.0134133	+	0.0293710i	0.916220	−	0.400675i	$-0.131224\pi$
$467$	0.289863	+	0.634712i	0.0134133	+	0.0293710i	−0.902807	+	0.430046i	$0.858497\pi$
$468$	1.95244	−	1.69180i	0.0902517	−	0.0782035i
$469$	21.2018	+	10.3691i	0.979008	+	0.478800i
$470$	2.48585	+	1.13525i	0.114664	+	0.0523651i
$471$	−4.31253	−	14.6871i	−0.198711	−	0.676748i
$472$	−3.46163	−	11.7892i	−0.159334	−	0.542643i
$473$	3.03817	−	6.65267i	0.139695	−	0.305890i
$474$	0.995493	+	6.92380i	0.0457245	+	0.318021i
$475$	−10.3867	−	11.9869i	−0.476576	−	0.549998i
$476$	−0.502775	+	2.94194i	−0.0230446	+	0.134844i
$477$	6.19309	+	9.63664i	0.283562	+	0.441231i
$478$	3.45818	−	24.0521i	0.158173	−	1.10012i
$479$	−19.7422	−	12.6875i	−0.902043	−	0.579708i	0.00535213	−	0.999986i	$-0.498296\pi$
$479$	−19.7422	−	12.6875i	−0.902043	−	0.579708i	−0.907396	+	0.420278i	$0.861933\pi$
$480$	0.221049	+	0.191540i	0.0100894	+	0.00874255i
$481$	−11.4062	−	3.34917i	−0.520080	−	0.152709i
$482$	−16.5264			−0.752756
$483$	6.73803	−	10.7517i	0.306591	−	0.489219i
$484$	7.67629			0.348922
$485$	−2.64545	−	0.776773i	−0.120123	−	0.0352714i
$486$	−0.755750	−	0.654861i	−0.0342815	−	0.0297051i
$487$	33.0892	+	21.2651i	1.49942	+	0.963616i	0.994970	+	0.100172i	$0.0319394\pi$
$487$	33.0892	+	21.2651i	1.49942	+	0.963616i	0.504445	+	0.863444i	$0.331697\pi$
$488$	−1.37017	+	9.52974i	−0.0620247	+	0.431391i
$489$	11.0637	+	17.2155i	0.500318	+	0.778510i
$490$	1.42076	−	1.47424i	0.0641834	−	0.0665994i
$491$	−2.13883	−	2.46834i	−0.0965239	−	0.111395i	0.705432	−	0.708777i	$-0.250753\pi$
$491$	−2.13883	−	2.46834i	−0.0965239	−	0.111395i	−0.801956	+	0.597383i	$0.796207\pi$
$492$	−0.314812	−	2.18956i	−0.0141928	−	0.0987131i
$493$	2.10765	−	4.61510i	0.0949236	−	0.207854i
$494$	−2.34905	−	8.00012i	−0.105689	−	0.359943i
$495$	−0.150231	−	0.511638i	−0.00675236	−	0.0229964i
$496$	−2.73018	−	1.24683i	−0.122589	−	0.0559845i
$497$	15.6854	−	32.0720i	0.703584	−	1.43863i
$498$	5.80354	−	5.02880i	0.260063	−	0.225346i
$499$	−2.25578	−	4.93947i	−0.100983	−	0.221121i	0.852397	−	0.522896i	$-0.175148\pi$
$499$	−2.25578	−	4.93947i	−0.100983	−	0.221121i	−0.953379	+	0.301775i	$0.902421\pi$
$500$	2.43953	−	1.56779i	0.109099	−	0.0701136i
$501$	0.100300	−	0.697604i	0.00448109	−	0.0311667i
$502$	8.83052	+	5.67503i	0.394125	+	0.253289i
$503$	−23.9568	+	27.6476i	−1.06818	+	1.23275i	−0.0967782	+	0.995306i	$0.530854\pi$
$503$	−23.9568	+	27.6476i	−1.06818	+	1.23275i	−0.971402	+	0.237440i	$0.923692\pi$
$504$	1.67908	+	2.04467i	0.0747923	+	0.0910769i
$505$		−	4.66931i		−	0.207781i
$506$	2.77893	+	8.28992i	0.123538	+	0.368532i
$507$			6.32578i			0.280938i
$508$	4.38883	+	1.28868i	0.194723	+	0.0571758i
$509$	5.19708	+	4.50329i	0.230356	+	0.199605i	0.762389	−	0.647119i	$-0.224026\pi$
$509$	5.19708	+	4.50329i	0.230356	+	0.199605i	−0.532033	+	0.846724i	$0.678572\pi$
$510$	0.178384	−	0.277570i	0.00789896	−	0.0122910i
$511$	10.8759	+	9.93988i	0.481121	+	0.439714i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−2.93576	+	1.34072i	−0.129617	+	0.0591941i
$514$	0.411909	−	0.356921i	0.0181685	−	0.0157431i
$515$	0.632716	+	4.40064i	0.0278808	+	0.193915i
$516$	1.66648	−	3.64909i	0.0733629	−	0.160642i
$517$	−16.3438	+	4.79896i	−0.718798	+	0.211058i
$518$	3.73784	−	11.5865i	0.164231	−	0.509080i
$519$	−7.76871	+	17.0111i	−0.341009	+	0.746705i
$520$	0.747940	−	0.107538i	0.0327994	−	0.00471583i
$521$	13.1239	+	15.1458i	0.574968	+	0.663549i	0.966515	−	0.256610i	$-0.0826054\pi$
$521$	13.1239	+	15.1458i	0.574968	+	0.663549i	−0.391547	+	0.920158i	$0.628060\pi$
$522$	−1.86836	−	4.09115i	−0.0817761	−	0.179065i
$523$	15.6106	−	10.0323i	0.682604	−	0.438683i	−0.152845	−	0.988250i	$-0.548844\pi$
$523$	15.6106	−	10.0323i	0.682604	−	0.438683i	0.835450	+	0.549567i	$0.185207\pi$
$524$	−3.64721	−	0.524390i	−0.159329	−	0.0229081i
$525$	11.9662	−	5.08654i	0.522248	−	0.221995i
$526$	2.14066	+	1.85490i	0.0933374	+	0.0808773i
$527$	−0.953892	+	3.24866i	−0.0415522	+	0.141514i
$528$	−1.82310			−0.0793404
$529$	18.3531	−	13.8623i	0.797962	−	0.602708i
$530$			3.35049i			0.145536i
$531$	−3.46163	+	11.7892i	−0.150222	+	0.511609i
$532$	8.25384	−	2.18806i	0.357849	−	0.0948643i
$533$	−4.80759	−	3.08965i	−0.208240	−	0.133828i
$534$	−9.50440	−	1.36653i	−0.411296	−	0.0591354i
$535$	−1.41921	−	2.20834i	−0.0613579	−	0.0954748i
$536$	−8.11442	+	3.70573i	−0.350490	+	0.160063i
$537$	−12.8377	+	11.1239i	−0.553988	+	0.480033i
$538$	−11.6685	+	1.67767i	−0.503063	+	0.0723295i
$539$	−0.675140	+	12.7439i	−0.0290803	+	0.548917i
$540$	−0.0824037	−	0.280641i	−0.00354609	−	0.0120769i
$541$	3.39365	−	0.996466i	0.145904	−	0.0428414i	−0.207965	−	0.978136i	$-0.566684\pi$
$541$	3.39365	−	0.996466i	0.145904	−	0.0428414i	0.353869	+	0.935295i	$0.384866\pi$
$542$	−14.2158	−	6.49215i	−0.610622	−	0.278862i
$543$	5.45210	−	0.783893i	0.233972	−	0.0336401i
$544$	−0.738729	−	0.852538i	−0.0316727	−	0.0365523i
$545$	2.59710	−	1.18606i	0.111248	−	0.0508051i
$546$	6.83278	+	0.180865i	0.292416	+	0.00774033i
$547$	3.96179	−	27.5548i	0.169394	−	1.17816i	−0.710747	−	0.703448i	$-0.751643\pi$
$547$	3.96179	−	27.5548i	0.169394	−	1.17816i	0.880141	−	0.474713i	$-0.157448\pi$
$548$	1.82494	−	2.83966i	0.0779575	−	0.121304i
$549$	6.30483	−	7.27616i	0.269083	−	0.310539i
$550$	−2.52420	+	8.59663i	−0.107632	+	0.366561i
$551$	−14.5156			−0.618384
$552$	1.52428	+	4.54715i	0.0648778	+	0.193540i
$553$	−10.4141	+	15.2989i	−0.442854	+	0.650575i
$554$	2.63459	+	0.773586i	0.111933	+	0.0328665i
$555$	−0.881372	+	1.01716i	−0.0374122	+	0.0431759i
$556$	−5.74647	+	8.94169i	−0.243705	+	0.379212i
$557$	42.2197	+	6.07028i	1.78891	+	0.257206i	0.955402	−	0.295308i	$-0.0954222\pi$
$557$	42.2197	+	6.07028i	1.78891	+	0.257206i	0.833504	+	0.552514i	$0.186331\pi$
$558$	1.62269	+	2.52495i	0.0686939	+	0.106890i
$559$	−4.30528	−	9.42725i	−0.182094	−	0.398730i
$560$	0.0898238	+	0.768623i	0.00379575	+	0.0324802i
$561$	0.292683	+	2.03566i	0.0123571	+	0.0859455i
$562$	5.46256	+	2.49467i	0.230424	+	0.105231i
$563$	13.8977	−	4.08072i	0.585717	−	0.171982i	0.0245697	−	0.999698i	$-0.492178\pi$
$563$	13.8977	−	4.08072i	0.585717	−	0.171982i	0.561147	+	0.827716i	$0.310360\pi$
$564$	−8.96480	+	2.63230i	−0.377486	+	0.110840i
$565$	−4.32626	−	1.97574i	−0.182007	−	0.0831199i
$566$	−3.46580	−	24.1052i	−0.145678	−	1.01322i
$567$	−0.307101	−	2.62787i	−0.0128970	−	0.110360i
$568$	5.60567	+	12.2747i	0.235209	+	0.515035i
$569$	3.74887	+	5.83336i	0.157161	+	0.244547i	0.910900	−	0.412626i	$-0.135388\pi$
$569$	3.74887	+	5.83336i	0.157161	+	0.244547i	−0.753740	+	0.657173i	$0.771752\pi$
$570$	−0.934375	−	0.134343i	−0.0391367	−	0.00562700i
$571$	−1.40076	+	2.17963i	−0.0586200	+	0.0912145i	−0.869326	−	0.494238i	$-0.835447\pi$
$571$	−1.40076	+	2.17963i	−0.0586200	+	0.0912145i	0.810706	+	0.585453i	$0.199083\pi$
$572$	−3.08433	+	3.55950i	−0.128962	+	0.148830i
$573$	13.3741	+	3.92698i	0.558709	+	0.164052i
$574$	3.29333	−	4.83808i	0.137461	−	0.201938i
$575$	23.5520	−	0.891771i	0.982186	−	0.0371894i
$576$	−1.00000			−0.0416667
$577$	−5.75426	+	19.5972i	−0.239553	+	0.815842i	0.748686	+	0.662925i	$0.230685\pi$
$577$	−5.75426	+	19.5972i	−0.239553	+	0.815842i	−0.988239	+	0.152918i	$0.951133\pi$
$578$	10.2993	−	11.8860i	0.428394	−	0.494393i
$579$	10.6876	−	16.6302i	0.444162	−	0.691129i
$580$	0.187214	−	1.30211i	0.00777366	−	0.0540670i
$581$	20.3101	+	0.537614i	0.842605	+	0.0223040i
$582$	8.57458	−	3.91588i	0.355428	−	0.162318i
$583$	−13.6760	−	15.7829i	−0.566402	−	0.653663i
$584$	−5.51218	+	0.792532i	−0.228096	+	0.0327952i
$585$	−0.687347	−	0.313901i	−0.0284183	−	0.0129782i
$586$	6.00486	−	1.76319i	0.248059	−	0.0728366i
$587$	−6.75148	−	22.9934i	−0.278663	−	0.949040i	−0.973273	−	0.229653i	$-0.926241\pi$
$587$	−6.75148	−	22.9934i	−0.278663	−	0.949040i	0.694609	−	0.719387i	$-0.255577\pi$
$588$	−0.370324	+	6.99020i	−0.0152719	+	0.288271i
$589$	9.58822	−	1.37858i	0.395076	−	0.0568033i
$590$	−2.71601	+	2.35344i	−0.111816	+	0.0968894i
$591$	8.14958	−	3.72179i	0.335229	−	0.153094i
$592$	2.48776	+	3.87104i	0.102246	+	0.159099i
$593$	−26.1653	−	3.76201i	−1.07448	−	0.154487i	−0.417713	−	0.908579i	$-0.637168\pi$
$593$	−26.1653	−	3.76201i	−1.07448	−	0.154487i	−0.656769	+	0.754092i	$0.728077\pi$
$594$	1.53369	+	0.985644i	0.0629282	+	0.0404415i
$595$	0.843815	−	0.223692i	0.0345930	−	0.00917047i
$596$	−2.17600	+	7.41079i	−0.0891326	+	0.303558i
$597$		−	18.2977i		−	0.748876i
$598$	11.4568	+	4.71680i	0.468505	+	0.192884i
$599$	−12.4704			−0.509525			−0.254763	−	0.967004i	$-0.581997\pi$
$599$	−12.4704			−0.509525			−0.254763	+	0.967004i	$0.581997\pi$
$600$	−1.38456	+	4.71538i	−0.0565244	+	0.192505i
$601$	7.74456	+	6.71070i	0.315907	+	0.273735i	0.798352	−	0.602191i	$-0.205706\pi$
$601$	7.74456	+	6.71070i	0.315907	+	0.273735i	−0.482445	+	0.875926i	$0.660251\pi$
$602$	9.76788	−	4.15209i	0.398109	−	0.169226i
$603$	8.82976	+	1.26953i	0.359575	+	0.0516991i
$604$	−10.4306	+	6.70331i	−0.424413	+	0.272754i
$605$	−0.932703	−	2.04234i	−0.0379198	−	0.0830327i
$606$	10.4542	+	12.0648i	0.424673	+	0.490099i
$607$	22.8627	−	3.28717i	0.927970	−	0.133422i	0.338274	−	0.941048i	$-0.390157\pi$
$607$	22.8627	−	3.28717i	0.927970	−	0.133422i	0.589696	+	0.807626i	$0.299248\pi$
$608$	−1.34072	+	2.93576i	−0.0543732	+	0.119061i
$609$	3.65342	−	11.3248i	0.148044	−	0.458903i
$610$	2.70194	−	0.793361i	0.109398	−	0.0321223i
$611$	−10.0272	+	21.9566i	−0.405659	+	0.888269i
$612$	0.160541	+	1.11659i	0.00648949	+	0.0451354i
$613$	−28.2915	+	24.5147i	−1.14268	+	0.990140i	−0.142682	+	0.989769i	$0.545573\pi$
$613$	−28.2915	+	24.5147i	−1.14268	+	0.990140i	−1.00000		0.000371333i	$0.999882\pi$
$614$	−8.60944	+	3.93180i	−0.347449	+	0.158674i
$615$	−0.544299	+	0.349800i	−0.0219482	+	0.0141053i
$616$	−3.56048	−	3.25406i	−0.143456	−	0.131110i
$617$	−10.3746	+	16.1431i	−0.417664	+	0.649898i	−0.984793	−	0.173731i	$-0.944418\pi$
$617$	−10.3746	+	16.1431i	−0.417664	+	0.649898i	0.567129	+	0.823629i	$0.308054\pi$
$618$	−11.4875	−	9.95400i	−0.462096	−	0.400409i
$619$	−5.64355	−	1.65710i	−0.226834	−	0.0666044i	0.166341	−	0.986068i	$-0.446805\pi$
$619$	−5.64355	−	1.65710i	−0.226834	−	0.0666044i	−0.393174	+	0.919464i	$0.628623\pi$
$620$			0.877882i			0.0352566i
$621$	1.17607	−	4.64939i	0.0471939	−	0.186574i
$622$		−	11.6922i		−	0.468813i
$623$	−16.1228	−	19.6332i	−0.645945	−	0.786588i
$624$	−1.69180	+	1.95244i	−0.0677262	+	0.0781602i
$625$	19.9580	+	12.8262i	0.798318	+	0.513048i
$626$	−2.11146	+	14.6855i	−0.0843908	+	0.586951i
$627$	4.94986	−	3.18108i	0.197678	−	0.127040i
$628$	6.35883	+	13.9239i	0.253745	+	0.555624i
$629$	3.92297	−	3.39927i	0.156419	−	0.135538i
$630$	0.339984	−	0.695169i	0.0135453	−	0.0276962i
$631$	−21.8518	−	9.97938i	−0.869906	−	0.397273i	−0.0701062	−	0.997540i	$-0.522334\pi$
$631$	−21.8518	−	9.97938i	−0.869906	−	0.397273i	−0.799800	+	0.600267i	$0.795061\pi$
$632$	−1.97072	−	6.71166i	−0.0783910	−	0.266975i
$633$	1.02841	+	3.50243i	0.0408755	+	0.139209i
$634$	−1.70628	+	3.73624i	−0.0677651	+	0.148385i
$635$	−0.190400	−	1.32426i	−0.00755580	−	0.0525518i
$636$	−7.50149	−	8.65718i	−0.297454	−	0.343280i
$637$	13.0214	+	12.5491i	0.515928	+	0.497212i
$638$	4.43302	+	6.89791i	0.175505	+	0.273091i
$639$	1.92042	−	13.3568i	0.0759705	−	0.528386i
$640$	−0.246058	−	0.158132i	−0.00972628	−	0.00625070i
$641$	−37.3819	−	32.3916i	−1.47650	−	1.27939i	−0.878364	−	0.477993i	$-0.841364\pi$
$641$	−37.3819	−	32.3916i	−1.47650	−	1.27939i	−0.598132	−	0.801398i	$-0.704090\pi$
$642$	8.61134	+	2.52852i	0.339863	+	0.0997926i
$643$	37.1825			1.46634			0.733168	−	0.680048i	$-0.238041\pi$
$643$	37.1825			1.46634			0.733168	+	0.680048i	$0.238041\pi$
$644$	−5.13932	+	11.6012i	−0.202518	+	0.457151i
$645$	−1.17335			−0.0462007
$646$	3.49327	+	1.02572i	0.137441	+	0.0403563i
$647$	−22.9163	−	19.8571i	−0.900933	−	0.780663i	0.0753509	−	0.997157i	$-0.475992\pi$
$647$	−22.9163	−	19.8571i	−0.900933	−	0.780663i	−0.976284	+	0.216494i	$0.930538\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	3.18790	−	22.1724i	0.125136	−	0.870341i
$650$	6.86411	+	10.6808i	0.269232	+	0.418934i
$651$	−1.33771	+	7.82752i	−0.0524292	+	0.306785i
$652$	−13.4011	−	15.4657i	−0.524828	−	0.605683i
$653$	4.76595	+	33.1479i	0.186506	+	1.29718i	0.840969	+	0.541084i	$0.181986\pi$
$653$	4.76595	+	33.1479i	0.186506	+	1.29718i	−0.654463	+	0.756094i	$0.727105\pi$
$654$	−4.05505	+	8.87932i	−0.158565	+	0.347209i
$655$	0.303635	+	1.03408i	0.0118640	+	0.0404050i
$656$	0.623215	+	2.12247i	0.0243324	+	0.0828687i
$657$	5.06562	+	2.31339i	0.197629	+	0.0902540i
$658$	−22.2065	−	10.8605i	−0.865699	−	0.423385i
$659$	−15.9223	+	13.7968i	−0.620246	+	0.537446i	−0.907309	−	0.420465i	$-0.861867\pi$
$659$	−15.9223	+	13.7968i	−0.620246	+	0.537446i	0.287062	+	0.957912i	$0.407321\pi$
$660$	0.221515	+	0.485051i	0.00862247	+	0.0188806i
$661$	7.41650	−	4.76630i	0.288468	−	0.185387i	−0.388401	−	0.921490i	$-0.626972\pi$
$661$	7.41650	−	4.76630i	0.288468	−	0.185387i	0.676870	+	0.736103i	$0.263336\pi$
$662$	−0.263251	+	1.83095i	−0.0102315	+	0.0711619i
$663$	2.45168	+	1.57560i	0.0952152	+	0.0611911i
$664$	−5.02880	+	5.80354i	−0.195155	+	0.225221i
$665$	−1.58503	−	1.93014i	−0.0614647	−	0.0748475i
$666$		−	4.60151i		−	0.178305i
$667$	13.4982	−	16.8240i	0.522653	−	0.651429i
$668$			0.704778i			0.0272687i
$669$	11.2463	+	3.30222i	0.434808	+	0.127671i
$670$	1.97188	+	1.70864i	0.0761802	+	0.0660105i
$671$	−9.48952	+	14.7660i	−0.366339	+	0.570035i
$672$	−1.95298	−	1.78490i	−0.0753378	−	0.0688541i
$673$	−29.7376	+	19.1112i	−1.14630	+	0.736683i	−0.968899	−	0.247456i	$-0.920405\pi$
$673$	−29.7376	+	19.1112i	−1.14630	+	0.736683i	−0.177401	+	0.984139i	$0.556769\pi$
$674$	−20.6256	+	9.41939i	−0.794468	+	0.362821i
$675$	3.71409	−	3.21828i	0.142956	−	0.123872i
$676$	−0.900252	−	6.26139i	−0.0346251	−	0.240823i
$677$	7.91470	−	17.3308i	0.304187	−	0.666076i	−0.694379	−	0.719609i	$-0.744321\pi$
$677$	7.91470	−	17.3308i	0.304187	−	0.666076i	0.998566	+	0.0535332i	$0.0170483\pi$
$678$	15.6019	−	4.58115i	0.599189	−	0.175938i
$679$	23.7354	+	7.65715i	0.910882	+	0.293854i
$680$	−0.137065	+	0.300132i	−0.00525622	+	0.0115095i
$681$	13.2499	−	1.90504i	0.507736	−	0.0730014i
$682$	−3.58333	−	4.13538i	−0.137213	−	0.158352i
$683$	−17.9825	−	39.3762i	−0.688081	−	1.50669i	−0.853848	−	0.520522i	$-0.825737\pi$
$683$	−17.9825	−	39.3762i	−0.688081	−	1.50669i	0.165767	−	0.986165i	$-0.446990\pi$
$684$	2.71507	−	1.74487i	0.103813	−	0.0667168i
$685$	−0.977250	−	0.140507i	−0.0373388	−	0.00536851i
$686$	−13.2000	+	12.9907i	−0.503980	+	0.495988i
$687$	−17.0196	−	14.7475i	−0.649337	−	0.562653i
$688$	−1.13020	+	3.84911i	−0.0430885	+	0.146746i
$689$	−29.5937			−1.12743
$690$	1.02460	−	0.958046i	0.0390057	−	0.0364722i
$691$			19.2228i			0.731272i	0.930758	+	0.365636i	$0.119148\pi$
$691$			19.2228i			0.731272i	−0.930758	+	0.365636i	$0.880852\pi$
$692$	5.26871	−	17.9436i	0.200286	−	0.682112i
$693$	1.23599	+	4.66243i	0.0469514	+	0.177111i
$694$	14.5367	+	9.34216i	0.551805	+	0.354624i
$695$	3.07722	+	0.442438i	0.116726	+	0.0167826i
$696$	2.43158	+	3.78361i	0.0921687	+	0.143417i
$697$	2.26988	−	1.03662i	0.0859778	−	0.0392647i
$698$	3.48174	−	3.01695i	0.131786	−	0.114193i
$699$	8.80279	−	1.26565i	0.332952	−	0.0478713i
$700$	−11.1205	+	6.73773i	−0.420316	+	0.254662i
$701$	9.14124	+	31.1322i	0.345260	+	1.17585i	0.930900	+	0.365275i	$0.119025\pi$
$701$	9.14124	+	31.1322i	0.345260	+	1.17585i	−0.585640	+	0.810571i	$0.699157\pi$
$702$	2.47880	−	0.727842i	0.0935564	−	0.0274706i
$703$	−13.5089	−	6.16932i	−0.509499	−	0.232680i
$704$	1.80455	−	0.259455i	0.0680114	−	0.00977857i
$705$	1.78961	+	2.06532i	0.0674005	+	0.0777843i
$706$	−1.04556	+	0.477493i	−0.0393503	+	0.0179707i
$707$	−1.11763	+	42.2221i	−0.0420328	+	1.58792i
$708$	1.74861	−	12.1619i	0.0657169	−	0.457071i
$709$	−5.92865	+	9.22515i	−0.222655	+	0.346458i	−0.934552	−	0.355826i	$-0.884200\pi$
$709$	−5.92865	+	9.22515i	−0.222655	+	0.346458i	0.711897	+	0.702283i	$0.247836\pi$
$710$	2.58466	−	2.98286i	0.0970007	−	0.111945i
$711$	−1.97072	+	6.71166i	−0.0739078	+	0.251707i
$712$	9.60214			0.359855
$713$	−7.31839	+	12.3950i	−0.274076	+	0.464197i
$714$	−1.67947	+	2.46722i	−0.0628524	+	0.0923335i
$715$	1.32179	+	0.388113i	0.0494322	+	0.0145146i
$716$	11.1239	−	12.8377i	0.415721	−	0.479767i
$717$	13.1373	−	20.4420i	0.490621	−	0.763421i
$718$	11.7732	+	1.69274i	0.439373	+	0.0631723i
$719$	−18.6670	−	29.0464i	−0.696162	−	1.08325i	−0.991781	−	0.127943i	$-0.959162\pi$
$719$	−18.6670	−	29.0464i	−0.696162	−	1.08325i	0.295620	−	0.955306i	$-0.404474\pi$
$720$	0.121504	+	0.266058i	0.00452820	+	0.00991538i
$721$	−4.66799	−	39.9441i	−0.173845	−	1.48759i
$722$	1.22160	+	8.49643i	0.0454633	+	0.316204i
$723$	−15.0329	−	6.86531i	−0.559081	−	0.255324i
$724$	−5.28504	+	1.55183i	−0.196417	+	0.0576733i
$725$	21.2078	−	6.22718i	0.787639	−	0.231272i
$726$	6.98260	+	3.18885i	0.259149	+	0.118349i
$727$	−0.982118	−	6.83078i	−0.0364247	−	0.253340i	0.963470	−	0.267814i	$-0.0863014\pi$
$727$	−0.982118	−	6.83078i	−0.0364247	−	0.253340i	−0.999895	+	0.0144749i	$0.995392\pi$
$728$	−6.78897	+	0.793381i	−0.251616	+	0.0294047i
$729$	−0.415415	−	0.909632i	−0.0153857	−	0.0336901i
$730$	0.880614	+	1.37026i	0.0325930	+	0.0507157i
$731$	4.47932	+	0.644029i	0.165674	+	0.0238203i
$732$	−5.20515	+	8.09937i	−0.192388	+	0.299361i
$733$	−16.7151	+	19.2902i	−0.617386	+	0.712501i	−0.975208	−	0.221288i	$-0.928974\pi$
$733$	−16.7151	+	19.2902i	−0.617386	+	0.712501i	0.357823	+	0.933790i	$0.383519\pi$
$734$	−19.1156	−	5.61286i	−0.705571	−	0.207174i
$735$	1.90479	−	0.750812i	0.0702593	−	0.0276941i
$736$	−2.15589	−	4.28394i	−0.0794673	−	0.157908i
$737$	−16.2631			−0.599059
$738$	0.623215	−	2.12247i	0.0229409	−	0.0781294i
$739$	−30.6602	+	35.3837i	−1.12785	+	1.30161i	−0.179726	+	0.983717i	$0.557521\pi$
$739$	−30.6602	+	35.3837i	−1.12785	+	1.30161i	−0.948126	+	0.317894i	$0.897024\pi$
$740$	0.727644	−	1.13224i	0.0267487	−	0.0416218i
$741$	1.18660	−	8.25300i	0.0435909	−	0.303182i
$742$	0.801962	−	30.2967i	0.0294410	−	1.11223i
$743$	12.8539	−	5.87018i	0.471564	−	0.215356i	−0.165435	−	0.986221i	$-0.552903\pi$
$743$	12.8539	−	5.87018i	0.471564	−	0.215356i	0.636999	+	0.770865i	$0.280176\pi$
$744$	−1.96551	−	2.26832i	−0.0720591	−	0.0831606i
$745$	2.23609	−	0.321501i	0.0819240	−	0.0117789i
$746$	−22.7903	−	10.4080i	−0.834412	−	0.381063i
$747$	7.36812	−	2.16348i	0.269585	−	0.0791574i
$748$	−0.579408	−	1.97328i	−0.0211853	−	0.0721504i
$749$	12.3046	+	20.3085i	0.449601	+	0.742058i
$750$	2.87035	−	0.412694i	0.104810	−	0.0150695i
$751$	7.47462	−	6.47679i	0.272753	−	0.236342i	−0.507734	−	0.861514i	$-0.669517\pi$
$751$	7.47462	−	6.47679i	0.272753	−	0.236342i	0.780487	+	0.625172i	$0.214971\pi$
$752$	8.49894	−	3.88134i	0.309924	−	0.141538i
$753$	5.67503	+	8.83052i	0.206810	+	0.321802i
$754$	11.5010	+	1.65360i	0.418843	+	0.0602205i
$755$	3.05083	+	1.96065i	0.111031	+	0.0713552i
$756$	0.677960	+	2.55741i	0.0246572	+	0.0930123i
$757$	8.79498	−	29.9530i	0.319659	−	1.08866i	−0.630318	−	0.776337i	$-0.717075\pi$
$757$	8.79498	−	29.9530i	0.319659	−	1.08866i	0.949977	−	0.312321i	$-0.101107\pi$
$758$			18.0642i			0.656120i
$759$	−0.915959	+	8.69519i	−0.0332472	+	0.315615i
$760$	0.943984			0.0342419
$761$	−6.96007	+	23.7038i	−0.252302	+	0.859263i	0.731779	+	0.681542i	$0.238690\pi$
$761$	−6.96007	+	23.7038i	−0.252302	+	0.859263i	−0.984081	+	0.177720i	$0.943128\pi$
$762$	3.45689	+	2.99541i	0.125230	+	0.108512i
$763$	−23.7681	+	10.1033i	−0.860464	+	0.365763i
$764$	−13.7968	−	1.98368i	−0.499151	−	0.0717670i
$765$	0.277570	−	0.178384i	0.0100356	−	0.00644947i
$766$	7.46983	+	16.3567i	0.269896	+	0.590990i
$767$	−20.7870	−	23.9895i	−0.750577	−	0.866212i
$768$	0.989821	−	0.142315i	0.0357171	−	0.00513534i
$769$	−5.53142	+	12.1121i	−0.199468	+	0.436774i	−0.982761	−	0.184878i	$-0.940811\pi$
$769$	−5.53142	+	12.1121i	−0.199468	+	0.436774i	0.783293	+	0.621652i	$0.213538\pi$
$770$	−0.433153	+	1.34268i	−0.0156097	+	0.0483867i
$771$	0.522956	−	0.153554i	0.0188338	−	0.00553011i
$772$	−8.21209	+	17.9820i	−0.295560	+	0.647185i
$773$	2.03005	+	14.1193i	0.0730158	+	0.507836i	0.993206	+	0.116365i	$0.0371244\pi$
$773$	2.03005	+	14.1193i	0.0730158	+	0.507836i	−0.920191	+	0.391470i	$0.871967\pi$
$774$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0416256 - 0.289512i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-0.445694 + 2.60794i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(0.841254 + 0.540641i) q^{4} +(0.0416256 - 0.289512i) q^{5} +(0.540641 + 0.841254i) q^{6} +(-0.445694 + 2.60794i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(0.142315 + 0.989821i) q^{9} +(-0.121504 + 0.266058i) q^{10} +(-0.513628 - 1.74926i) q^{11} +(-0.281733 - 0.959493i) q^{12} +(-2.34999 - 1.07320i) q^{13} +(1.16238 - 2.37673i) q^{14} +(-0.221049 + 0.191540i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.948993 - 0.609881i) q^{17} +(0.142315 - 0.989821i) q^{18} +(-2.71507 - 1.74487i) q^{19} +(0.191540 - 0.221049i) q^{20} +(2.04467 - 1.67908i) q^{21} +1.82310i q^{22} +(4.54715 - 1.52428i) q^{23} +1.00000i q^{24} +(4.71538 + 1.38456i) q^{25} +(1.95244 + 1.69180i) q^{26} +(0.540641 - 0.841254i) q^{27} +(-1.78490 + 1.95298i) q^{28} +(3.78361 - 2.43158i) q^{29} +(0.266058 - 0.121504i) q^{30} +(-2.26832 + 1.96551i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(-0.757345 + 1.65835i) q^{33} +(-1.08238 + 0.317814i) q^{34} +(0.736478 + 0.237591i) q^{35} +(-0.415415 + 0.909632i) q^{36} +(4.55467 - 0.654863i) q^{37} +(2.11351 + 2.43912i) q^{38} +(1.07320 + 2.34999i) q^{39} +(-0.246058 + 0.158132i) q^{40} +(2.18956 + 0.314812i) q^{41} +(-2.43490 + 1.03502i) q^{42} +(3.03177 + 2.62705i) q^{43} +(0.513628 - 1.74926i) q^{44} +0.292489 q^{45} +(-4.79240 + 0.181459i) q^{46} -9.34327i q^{47} +(0.281733 - 0.959493i) q^{48} +(-6.60271 - 2.32469i) q^{49} +(-4.13430 - 2.65695i) q^{50} +(-1.11659 - 0.160541i) q^{51} +(-1.39672 - 2.17334i) q^{52} +(10.4199 - 4.75862i) q^{53} +(-0.755750 + 0.654861i) q^{54} +(-0.527811 + 0.0758877i) q^{55} +(2.26282 - 1.37100i) q^{56} +(0.909268 + 3.09668i) q^{57} +(-4.31540 + 1.26712i) q^{58} +(11.1766 + 5.10418i) q^{59} +(-0.289512 + 0.0416256i) q^{60} +(-6.30483 - 7.27616i) q^{61} +(2.73018 - 1.24683i) q^{62} +(-2.64482 - 0.0700092i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.408525 + 0.635678i) q^{65} +(1.19388 - 1.37781i) q^{66} +(2.51321 - 8.55921i) q^{67} +1.12807 q^{68} +(-4.43470 - 1.82577i) q^{69} +(-0.639708 - 0.435457i) q^{70} +(-12.9475 - 3.80174i) q^{71} +(0.654861 - 0.755750i) q^{72} +(3.01076 - 4.68483i) q^{73} +(-4.55467 - 0.654863i) q^{74} +(-2.65695 - 4.13430i) q^{75} +(-1.34072 - 2.93576i) q^{76} +(4.79088 - 0.559877i) q^{77} +(-0.367663 - 2.55716i) q^{78} +(6.36288 + 2.90583i) q^{79} +(0.280641 - 0.0824037i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-2.01218 - 0.918931i) q^{82} +(-1.09286 - 7.60102i) q^{83} +(2.62787 - 0.307101i) q^{84} +(-0.137065 - 0.300132i) q^{85} +(-2.16884 - 3.37478i) q^{86} +(-4.45181 - 0.640073i) q^{87} +(-0.985644 + 1.53369i) q^{88} +(-6.28806 + 7.25681i) q^{89} +(-0.280641 - 0.0824037i) q^{90} +(3.84623 - 5.65031i) q^{91} +(4.64939 + 1.17607i) q^{92} +3.00142 q^{93} +(-2.63230 + 8.96480i) q^{94} +(-0.618178 + 0.713415i) q^{95} +(-0.540641 + 0.841254i) q^{96} +(1.34152 - 9.33048i) q^{97} +(5.68032 + 4.09072i) q^{98} +(1.65835 - 0.757345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} + O(q^{10}) \)	\( 160q - 16q^{2} - 16q^{4} - 16q^{8} + 16q^{9} - 22q^{14} - 16q^{16} + 16q^{18} - 36q^{23} + 96q^{25} + 22q^{28} - 20q^{29} - 16q^{32} - 50q^{35} + 16q^{36} + 22q^{37} + 4q^{39} - 110q^{43} + 8q^{46} - 36q^{50} + 22q^{51} - 88q^{53} + 22q^{57} + 24q^{58} - 16q^{64} - 72q^{70} + 48q^{71} + 16q^{72} - 22q^{74} + 24q^{77} + 4q^{78} + 88q^{79} - 16q^{81} + 22q^{84} + 76q^{85} + 44q^{86} - 44q^{88} + 8q^{92} - 14q^{95} + 22q^{98} - 22q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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