LMFDB - Embedded newform 177.3.g.a.10.11

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.g (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$20$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.11

$q$-expansion

$f(q)$	$=$	$q+(0.140866 + 0.0561262i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.88729 - 2.73499i) q^{4} +(1.82294 - 2.14613i) q^{5} +(0.232047 + 0.123023i) q^{6} +(-8.41764 - 5.06473i) q^{7} +(-0.507898 - 1.09780i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(0.140866 + 0.0561262i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.88729 - 2.73499i) q^{4} +(1.82294 - 2.14613i) q^{5} +(0.232047 + 0.123023i) q^{6} +(-8.41764 - 5.06473i) q^{7} +(-0.507898 - 1.09780i) q^{8} +(2.92986 + 0.644911i) q^{9} +(0.377244 - 0.200002i) q^{10} +(-7.27840 - 0.394624i) q^{11} +(-4.45944 - 5.25006i) q^{12} +(-2.70845 - 12.3046i) q^{13} +(-0.901497 - 1.18590i) q^{14} +(3.54081 - 3.35403i) q^{15} +(0.851313 + 15.7015i) q^{16} +(-2.95697 + 1.77915i) q^{17} +(0.376522 + 0.255288i) q^{18} +(2.43835 - 8.78214i) q^{19} +(-11.1330 + 1.21078i) q^{20} +(-13.5459 - 10.2973i) q^{21} +(-1.00313 - 0.464098i) q^{22} +(32.9657 - 22.3513i) q^{23} +(-0.668965 - 1.98542i) q^{24} +(2.76179 + 16.8462i) q^{25} +(0.309082 - 1.88532i) q^{26} +(4.92415 + 1.65914i) q^{27} +(10.4522 + 37.6454i) q^{28} +(-18.1509 - 45.5554i) q^{29} +(0.687030 - 0.273738i) q^{30} +(33.0183 - 9.16750i) q^{31} +(-2.30626 + 6.84473i) q^{32} +(-12.4588 - 2.04251i) q^{33} +(-0.516395 + 0.0846586i) q^{34} +(-26.2144 + 8.83265i) q^{35} +(-6.69553 - 9.87517i) q^{36} +(-22.3197 + 48.2433i) q^{37} +(0.836389 - 1.10025i) q^{38} +(-2.35941 - 21.6945i) q^{39} +(-3.28189 - 0.911213i) q^{40} +(-5.08728 + 7.50318i) q^{41} +(-1.33021 - 2.21082i) q^{42} +(39.5683 - 2.14533i) q^{43} +(19.9356 + 21.0457i) q^{44} +(6.72501 - 5.11222i) q^{45} +(5.89825 - 1.29830i) q^{46} +(37.9147 - 32.2050i) q^{47} +(-1.47452 + 27.1959i) q^{48} +(22.2532 + 41.9740i) q^{49} +(-0.556469 + 2.52806i) q^{50} +(-5.42478 + 2.50977i) q^{51} +(-25.8328 + 42.9345i) q^{52} +(-13.1088 + 24.7259i) q^{53} +(0.600525 + 0.510091i) q^{54} +(-14.1150 + 14.9010i) q^{55} +(-1.28477 + 11.8133i) q^{56} +(5.84320 - 14.6653i) q^{57} -7.43595i q^{58} +(-57.4886 - 13.2688i) q^{59} -19.3966 q^{60} +(-12.1354 - 4.83519i) q^{61} +(5.16570 + 0.561804i) q^{62} +(-21.3962 - 20.2676i) q^{63} +(40.0105 - 47.1040i) q^{64} +(-31.3445 - 16.6178i) q^{65} +(-1.64038 - 0.986984i) q^{66} +(46.6801 + 100.897i) q^{67} +(13.4036 + 2.95035i) q^{68} +(60.9492 - 32.3132i) q^{69} +(-4.18846 - 0.227092i) q^{70} +(52.6376 + 61.9698i) q^{71} +(-0.780085 - 3.54396i) q^{72} +(-13.3077 - 17.5060i) q^{73} +(-5.85181 + 5.54313i) q^{74} +(1.60077 + 29.5246i) q^{75} +(-31.0592 + 18.6877i) q^{76} +(59.2683 + 40.1849i) q^{77} +(0.885266 - 3.18844i) q^{78} +(65.5741 - 7.13161i) q^{79} +(35.2494 + 26.7959i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-1.13775 + 0.771415i) q^{82} +(-5.55224 - 16.4785i) q^{83} +(10.9479 + 66.7790i) q^{84} +(-1.57209 + 9.58931i) q^{85} +(5.69425 + 1.91862i) q^{86} +(-22.7230 - 81.8407i) q^{87} +(3.26347 + 8.19069i) q^{88} +(86.8699 - 34.6121i) q^{89} +(1.23426 - 0.342690i) q^{90} +(-39.5207 + 117.293i) q^{91} +(-156.312 - 25.6261i) q^{92} +(58.5710 - 9.60222i) q^{93} +(7.14844 - 2.40859i) q^{94} +(-14.4026 - 21.2423i) q^{95} +(-5.25293 + 11.3540i) q^{96} +(-55.0723 + 72.4464i) q^{97} +(0.778882 + 7.16170i) q^{98} +(-21.0702 - 5.85012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) $	$ 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{7}{58}\right)$	$1$

Coefficient data

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

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

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

$2$	0.140866	+	0.0561262i	0.0704331	+	0.0280631i	0.405089	−	0.914277i	$-0.367241\pi$
$2$	0.140866	+	0.0561262i	0.0704331	+	0.0280631i	−0.334656	+	0.942341i	$0.608620\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	−2.88729	−	2.73499i	−0.721822	−	0.683746i
$5$	1.82294	−	2.14613i	0.364587	−	0.429225i	−0.549029	−	0.835803i	$-0.685002\pi$
$5$	1.82294	−	2.14613i	0.364587	−	0.429225i	0.913616	+	0.406578i	$0.133278\pi$
$6$	0.232047	+	0.123023i	0.0386744	+	0.0205039i
$7$	−8.41764	−	5.06473i	−1.20252	−	0.723532i	−0.233944	−	0.972250i	$-0.575163\pi$
$7$	−8.41764	−	5.06473i	−1.20252	−	0.723532i	−0.968576	+	0.248718i	$0.919991\pi$
$8$	−0.507898	−	1.09780i	−0.0634873	−	0.137225i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	0.377244	−	0.200002i	0.0377244	−	0.0200002i
$11$	−7.27840	−	0.394624i	−0.661673	−	0.0358749i	−0.279755	−	0.960071i	$-0.590253\pi$
$11$	−7.27840	−	0.394624i	−0.661673	−	0.0358749i	−0.381918	+	0.924196i	$0.624736\pi$
$12$	−4.45944	−	5.25006i	−0.371620	−	0.437505i
$13$	−2.70845	−	12.3046i	−0.208342	−	0.946507i	−0.958465	−	0.285209i	$-0.907937\pi$
$13$	−2.70845	−	12.3046i	−0.208342	−	0.946507i	0.750123	−	0.661298i	$-0.229994\pi$
$14$	−0.901497	−	1.18590i	−0.0643926	−	0.0847071i
$15$	3.54081	−	3.35403i	0.236054	−	0.223602i
$16$	0.851313	+	15.7015i	0.0532071	+	0.981347i
$17$	−2.95697	+	1.77915i	−0.173940	+	0.104656i	−0.599861	−	0.800104i	$-0.704778\pi$
$17$	−2.95697	+	1.77915i	−0.173940	+	0.104656i	0.425922	+	0.904760i	$0.359950\pi$
$18$	0.376522	+	0.255288i	0.0209179	+	0.0141827i
$19$	2.43835	−	8.78214i	0.128334	−	0.462218i	−0.871256	−	0.490828i	$-0.836694\pi$
$19$	2.43835	−	8.78214i	0.128334	−	0.462218i	0.999591	+	0.0286102i	$0.00910814\pi$
$20$	−11.1330	+	1.21078i	−0.556648	+	0.0605392i
$21$	−13.5459	−	10.2973i	−0.645041	−	0.490347i
$22$	−1.00313	−	0.464098i	−0.0455969	−	0.0210954i
$23$	32.9657	−	22.3513i	1.43329	−	0.971796i	0.435872	−	0.900009i	$-0.356440\pi$
$23$	32.9657	−	22.3513i	1.43329	−	0.971796i	0.997420	−	0.0717869i	$-0.0228702\pi$
$24$	−0.668965	−	1.98542i	−0.0278736	−	0.0827258i
$25$	2.76179	+	16.8462i	0.110472	+	0.673846i
$26$	0.309082	−	1.88532i	0.0118878	−	0.0725122i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	10.4522	+	37.6454i	0.373293	+	1.34448i
$29$	−18.1509	−	45.5554i	−0.625893	−	1.57087i	−0.809018	−	0.587784i	$-0.800000\pi$
$29$	−18.1509	−	45.5554i	−0.625893	−	1.57087i	0.183124	−	0.983090i	$-0.441379\pi$
$30$	0.687030	−	0.273738i	0.0229010	−	0.00912459i
$31$	33.0183	−	9.16750i	1.06511	−	0.295726i	0.309601	−	0.950867i	$-0.399805\pi$
$31$	33.0183	−	9.16750i	1.06511	−	0.295726i	0.755507	+	0.655141i	$0.227391\pi$
$32$	−2.30626	+	6.84473i	−0.0720705	+	0.213898i
$33$	−12.4588	−	2.04251i	−0.377538	−	0.0618943i
$34$	−0.516395	+	0.0846586i	−0.0151881	+	0.00248996i
$35$	−26.2144	+	8.83265i	−0.748982	+	0.252361i
$36$	−6.69553	−	9.87517i	−0.185987	−	0.274310i
$37$	−22.3197	+	48.2433i	−0.603236	+	1.30387i	0.329787	+	0.944055i	$0.393023\pi$
$37$	−22.3197	+	48.2433i	−0.603236	+	1.30387i	−0.933023	+	0.359817i	$0.882839\pi$
$38$	0.836389	−	1.10025i	0.0220102	−	0.0289540i
$39$	−2.35941	−	21.6945i	−0.0604978	−	0.556268i
$40$	−3.28189	−	0.911213i	−0.0820473	−	0.0227803i
$41$	−5.08728	+	7.50318i	−0.124080	+	0.183004i	−0.884656	−	0.466245i	$-0.845607\pi$
$41$	−5.08728	+	7.50318i	−0.124080	+	0.183004i	0.760576	+	0.649249i	$0.224917\pi$
$42$	−1.33021	−	2.21082i	−0.0316715	−	0.0526385i
$43$	39.5683	−	2.14533i	0.920194	−	0.0498915i	0.412048	−	0.911162i	$-0.364814\pi$
$43$	39.5683	−	2.14533i	0.920194	−	0.0498915i	0.508146	+	0.861271i	$0.330331\pi$
$44$	19.9356	+	21.0457i	0.453081	+	0.478312i
$45$	6.72501	−	5.11222i	0.149445	−	0.113605i
$46$	5.89825	−	1.29830i	0.128223	−	0.0282240i
$47$	37.9147	−	32.2050i	0.806695	−	0.685213i	−0.145952	−	0.989292i	$-0.546624\pi$
$47$	37.9147	−	32.2050i	0.806695	−	0.685213i	0.952647	+	0.304079i	$0.0983486\pi$
$48$	−1.47452	+	27.1959i	−0.0307191	+	0.566581i
$49$	22.2532	+	41.9740i	0.454147	+	0.856612i
$50$	−0.556469	+	2.52806i	−0.0111294	+	0.0505613i
$51$	−5.42478	+	2.50977i	−0.106368	+	0.0492112i
$52$	−25.8328	+	42.9345i	−0.496785	+	0.825663i
$53$	−13.1088	+	24.7259i	−0.247336	+	0.466526i	−0.975831	−	0.218526i	$-0.929875\pi$
$53$	−13.1088	+	24.7259i	−0.247336	+	0.466526i	0.728495	+	0.685051i	$0.240220\pi$
$54$	0.600525	+	0.510091i	0.0111208	+	0.00944612i
$55$	−14.1150	+	14.9010i	−0.256636	+	0.270927i
$56$	−1.28477	+	11.8133i	−0.0229424	+	0.210951i
$57$	5.84320	−	14.6653i	0.102512	−	0.257286i
$58$		−	7.43595i		−	0.128206i
$59$	−57.4886	−	13.2688i	−0.974383	−	0.224895i
$59$	−57.4886	−	13.2688i	−0.974383	−	0.224895i
$60$	−19.3966			−0.323276
$61$	−12.1354	−	4.83519i	−0.198941	−	0.0792654i	0.268540	−	0.963269i	$-0.413459\pi$
$61$	−12.1354	−	4.83519i	−0.198941	−	0.0792654i	−0.467481	+	0.884003i	$0.654838\pi$
$62$	5.16570	+	0.561804i	0.0833178	+	0.00906136i
$63$	−21.3962	−	20.2676i	−0.339623	−	0.321708i
$64$	40.0105	−	47.1040i	0.625165	−	0.736001i
$65$	−31.3445	−	16.6178i	−0.482224	−	0.255659i
$66$	−1.64038	−	0.986984i	−0.0248542	−	0.0149543i
$67$	46.6801	+	100.897i	0.696717	+	1.50593i	0.855051	+	0.518544i	$0.173526\pi$
$67$	46.6801	+	100.897i	0.696717	+	1.50593i	−0.158333	+	0.987386i	$0.550612\pi$
$68$	13.4036	+	2.95035i	0.197112	+	0.0433875i
$69$	60.9492	−	32.3132i	0.883322	−	0.468308i
$70$	−4.18846	−	0.227092i	−0.0598352	−	0.00324417i
$71$	52.6376	+	61.9698i	0.741375	+	0.872814i	0.995539	−	0.0943468i	$-0.0300762\pi$
$71$	52.6376	+	61.9698i	0.741375	+	0.872814i	−0.254164	+	0.967161i	$0.581800\pi$
$72$	−0.780085	−	3.54396i	−0.0108345	−	0.0492217i
$73$	−13.3077	−	17.5060i	−0.182297	−	0.239808i	0.695863	−	0.718175i	$-0.255022\pi$
$73$	−13.3077	−	17.5060i	−0.182297	−	0.239808i	−0.878160	+	0.478367i	$0.841229\pi$
$74$	−5.85181	+	5.54313i	−0.0790785	+	0.0749071i
$75$	1.60077	+	29.5246i	0.0213437	+	0.393661i
$76$	−31.0592	+	18.6877i	−0.408674	+	0.245891i
$77$	59.2683	+	40.1849i	0.769718	+	0.521882i
$78$	0.885266	−	3.18844i	0.0113496	−	0.0408774i
$79$	65.5741	−	7.13161i	0.830051	−	0.0902735i	0.316779	−	0.948499i	$-0.397399\pi$
$79$	65.5741	−	7.13161i	0.830051	−	0.0902735i	0.513272	+	0.858226i	$0.328433\pi$
$80$	35.2494	+	26.7959i	0.440617	+	0.334949i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	−1.13775	+	0.771415i	−0.0138750	+	0.00940750i
$83$	−5.55224	−	16.4785i	−0.0668945	−	0.198536i	0.908992	−	0.416813i	$-0.136853\pi$
$83$	−5.55224	−	16.4785i	−0.0668945	−	0.198536i	−0.975887	+	0.218277i	$0.929956\pi$
$84$	10.9479	+	66.7790i	0.130332	+	0.794988i
$85$	−1.57209	+	9.58931i	−0.0184952	+	0.112815i
$86$	5.69425	+	1.91862i	0.0662122	+	0.0223095i
$87$	−22.7230	−	81.8407i	−0.261183	−	0.940698i
$88$	3.26347	+	8.19069i	0.0370849	+	0.0930760i
$89$	86.8699	−	34.6121i	0.976066	−	0.388900i	0.173086	−	0.984907i	$-0.444626\pi$
$89$	86.8699	−	34.6121i	0.976066	−	0.388900i	0.802980	+	0.596006i	$0.203247\pi$
$90$	1.23426	−	0.342690i	0.0137140	−	0.00380766i
$91$	−39.5207	+	117.293i	−0.434293	+	1.28894i
$92$	−156.312	−	25.6261i	−1.69904	−	0.278544i
$93$	58.5710	−	9.60222i	0.629795	−	0.103250i
$94$	7.14844	−	2.40859i	0.0760473	−	0.0256233i
$95$	−14.4026	−	21.2423i	−0.151607	−	0.223603i
$96$	−5.25293	+	11.3540i	−0.0547181	+	0.118271i
$97$	−55.0723	+	72.4464i	−0.567756	+	0.746870i	−0.986950	−	0.161027i	$-0.948519\pi$
$97$	−55.0723	+	72.4464i	−0.567756	+	0.746870i	0.419194	+	0.907896i	$0.362313\pi$
$98$	0.778882	+	7.16170i	0.00794778	+	0.0730786i
$99$	−21.0702	−	5.85012i	−0.212830	−	0.0590921i
$100$	38.0999	−	56.1932i	0.380999	−	0.561932i
$101$	−42.7381	−	71.0313i	−0.423149	−	0.703280i	0.569805	−	0.821780i	$-0.307019\pi$
$101$	−42.7381	−	71.0313i	−0.423149	−	0.703280i	−0.992954	+	0.118500i	$0.962191\pi$
$102$	−0.905032	+	0.0490694i	−0.00887286	+	0.000481073i
$103$	−119.322	−	125.966i	−1.15846	−	1.22297i	−0.970579	−	0.240781i	$-0.922596\pi$
$103$	−119.322	−	125.966i	−1.15846	−	1.22297i	−0.187882	−	0.982192i	$-0.560162\pi$
$104$	−12.1324	+	9.22282i	−0.116658	+	0.0886810i
$105$	−46.7925	+	10.2998i	−0.445643	+	0.0980934i
$106$	−3.23436	+	2.74729i	−0.0305128	+	0.0259178i
$107$	10.9872	−	202.647i	0.102684	−	1.89390i	−0.265450	−	0.964125i	$-0.585520\pi$
$107$	10.9872	−	202.647i	0.102684	−	1.89390i	0.368134	−	0.929773i	$-0.379997\pi$
$108$	−9.67972	−	18.2579i	−0.0896271	−	0.169055i
$109$	28.8590	−	131.108i	0.264761	−	1.20282i	−0.637095	−	0.770786i	$-0.719864\pi$
$109$	28.8590	−	131.108i	0.264761	−	1.20282i	0.901856	−	0.432037i	$-0.142205\pi$
$110$	−2.82466	+	1.30683i	−0.0256787	+	0.0118802i
$111$	−47.4667	+	78.8902i	−0.427628	+	0.710723i
$112$	72.3580	−	136.482i	0.646053	−	1.21859i
$113$	−96.4039	−	81.8862i	−0.853132	−	0.724657i	0.109929	−	0.993939i	$-0.464938\pi$
$113$	−96.4039	−	81.8862i	−0.853132	−	0.724657i	−0.963061	+	0.269283i	$0.913213\pi$
$114$	1.64622	−	1.73789i	0.0144405	−	0.0152447i
$115$	12.1257	−	111.494i	0.105440	−	0.969509i
$116$	−72.1863	+	181.174i	−0.622296	+	1.56184i
$117$		−	37.7975i		−	0.323055i
$118$	−7.35347	−	5.09575i	−0.0623176	−	0.0431843i
$119$	33.9016			0.284888
$120$	−5.48044	−	2.18361i	−0.0456703	−	0.0181967i
$121$	−67.4713	−	7.33794i	−0.557614	−	0.0606442i
$122$	−1.43809	−	1.36223i	−0.0117876	−	0.0111658i
$123$	−10.1649	+	11.9670i	−0.0826413	+	0.0972929i
$124$	−120.406	−	63.8355i	−0.971020	−	0.514802i
$125$	101.508	+	61.0753i	0.812063	+	0.488602i
$126$	−1.87646	−	4.05591i	−0.0148926	−	0.0321897i
$127$	−25.4719	−	5.60679i	−0.200566	−	0.0441479i	0.113551	−	0.993532i	$-0.463777\pi$
$127$	−25.4719	−	5.60679i	−0.200566	−	0.0441479i	−0.314117	+	0.949384i	$0.601708\pi$
$128$	33.8057	−	17.9226i	0.264107	−	0.140021i
$129$	68.5344	+	3.71583i	0.531274	+	0.0288049i
$130$	−3.48269	−	4.10014i	−0.0267899	−	0.0315395i
$131$	19.0164	+	86.3922i	0.145163	+	0.659483i	0.991852	+	0.127395i	$0.0406615\pi$
$131$	19.0164	+	86.3922i	0.145163	+	0.659483i	−0.846689	+	0.532088i	$0.821407\pi$
$132$	30.3858	+	39.9719i	0.230196	+	0.302817i
$133$	−65.0043	+	61.5753i	−0.488754	+	0.462972i
$134$	0.912659	+	16.8330i	0.00681089	+	0.125619i
$135$	12.5371	−	7.54334i	0.0928677	−	0.0558766i
$136$	3.45500	+	2.34255i	0.0254044	+	0.0172246i
$137$	51.7869	−	186.519i	0.378006	−	1.36146i	−0.492934	−	0.870067i	$-0.664075\pi$
$137$	51.7869	−	186.519i	0.378006	−	1.36146i	0.870940	−	0.491389i	$-0.163511\pi$
$138$	10.3993	−	1.13099i	0.0753573	−	0.00819560i
$139$	−13.4698	−	10.2395i	−0.0969054	−	0.0736656i	0.555600	−	0.831450i	$-0.312489\pi$
$139$	−13.4698	−	10.2395i	−0.0969054	−	0.0736656i	−0.652505	+	0.757784i	$0.726282\pi$
$140$	99.8456	+	46.1935i	0.713183	+	0.329953i
$141$	71.3161	−	48.3535i	0.505788	−	0.342933i
$142$	3.93673	+	11.6838i	0.0277235	+	0.0822803i
$143$	14.8575	+	90.6266i	0.103898	+	0.633752i
$144$	−7.63188	+	46.5524i	−0.0529991	+	0.323280i
$145$	−130.855	−	44.0903i	−0.902452	−	0.304071i
$146$	−0.892060	−	3.21291i	−0.00611000	−	0.0220062i
$147$	30.4574	+	76.4422i	0.207193	+	0.520015i
$148$	196.388	−	78.2482i	1.32695	−	0.528704i
$149$	29.7790	−	8.26811i	0.199859	−	0.0554907i	−0.166156	−	0.986099i	$-0.553136\pi$
$149$	29.7790	−	8.26811i	0.199859	−	0.0554907i	0.366015	+	0.930609i	$0.380722\pi$
$150$	−1.43161	+	4.24886i	−0.00954405	+	0.0283257i
$151$	44.2090	+	7.24770i	0.292775	+	0.0479980i	0.306379	−	0.951909i	$-0.400882\pi$
$151$	44.2090	+	7.24770i	0.292775	+	0.0479980i	−0.0136047	+	0.999907i	$0.504331\pi$
$152$	−10.8795	+	1.78360i	−0.0715756	+	0.0117342i
$153$	−9.81091	+	3.30568i	−0.0641236	+	0.0216058i
$154$	6.09348	+	8.98720i	0.0395680	+	0.0583585i
$155$	40.5157	−	87.5733i	0.261392	−	0.564989i
$156$	−52.5217	+	69.0911i	−0.336678	+	0.442892i
$157$	10.7388	+	98.7413i	0.0683998	+	0.628926i	0.977292	+	0.211895i	$0.0679636\pi$
$157$	10.7388	+	98.7413i	0.0683998	+	0.628926i	−0.908893	+	0.417030i	$0.863071\pi$
$158$	9.63744	+	2.67582i	0.0609965	+	0.0169356i
$159$	−27.2024	+	40.1205i	−0.171084	+	0.252330i
$160$	10.4855	+	17.4270i	0.0655343	+	0.108919i
$161$	−390.697	+	21.1830i	−2.42669	+	0.131571i
$162$	0.938519	+	0.990783i	0.00579333	+	0.00611594i
$163$	68.7748	−	52.2812i	0.421931	−	0.320744i	−0.372573	−	0.928003i	$-0.621524\pi$
$163$	68.7748	−	52.2812i	0.421931	−	0.320744i	0.794504	+	0.607259i	$0.207731\pi$
$164$	35.2096	−	7.75021i	0.214692	−	0.0472574i
$165$	−27.0950	+	23.0147i	−0.164212	+	0.139483i
$166$	0.142751	−	2.63289i	0.000859945	−	0.0158608i
$167$	133.226	+	251.292i	0.797763	+	1.50474i	0.862058	+	0.506810i	$0.169175\pi$
$167$	133.226	+	251.292i	0.797763	+	1.50474i	−0.0642949	+	0.997931i	$0.520480\pi$
$168$	−4.42449	+	20.1007i	−0.0263363	+	0.119647i
$169$	9.31292	−	4.30862i	0.0551060	−	0.0254948i
$170$	−0.759666	+	1.26258i	−0.00446862	+	0.00742691i
$171$	12.8077	−	24.1579i	0.0748990	−	0.141274i
$172$	−120.113	−	102.025i	−0.698330	−	0.593167i
$173$	−24.4378	+	25.7987i	−0.141259	+	0.149125i	−0.792786	−	0.609500i	$-0.791370\pi$
$173$	−24.4378	+	25.7987i	−0.141259	+	0.149125i	0.651527	+	0.758626i	$0.274129\pi$
$174$	1.39251	−	12.8039i	0.00800295	−	0.0735859i
$175$	62.0734	−	155.793i	0.354705	−	0.890243i
$176$		−	114.618i		−	0.651239i
$177$	−96.5046	−	33.6133i	−0.545224	−	0.189906i
$178$	14.1797			0.0796611
$179$	70.9562	+	28.2715i	0.396403	+	0.157941i	0.559817	−	0.828616i	$-0.310871\pi$
$179$	70.9562	+	28.2715i	0.396403	+	0.157941i	−0.163414	+	0.986558i	$0.552251\pi$
$180$	−33.3989	−	3.63235i	−0.185549	−	0.0201797i
$181$	121.406	+	115.002i	0.670751	+	0.635370i	0.945299	−	0.326204i	$-0.105770\pi$
$181$	121.406	+	115.002i	0.670751	+	0.635370i	−0.274548	+	0.961573i	$0.588528\pi$
$182$	−12.1503	+	14.3045i	−0.0667602	+	0.0785961i
$183$	−19.9905	−	10.5983i	−0.109237	−	0.0579140i
$184$	−41.2806	−	24.8377i	−0.224351	−	0.134987i
$185$	62.8487	+	135.845i	0.339723	+	0.734299i
$186$	8.78961	+	1.93474i	0.0472559	+	0.0104018i
$187$	22.2241	−	11.7825i	0.118846	−	0.0630080i
$188$	−197.551	−	10.7109i	−1.05080	−	0.0569729i
$189$	−33.0466	−	38.9055i	−0.174850	−	0.205849i
$190$	−0.836594	−	3.80069i	−0.00440313	−	0.0200036i
$191$	−19.9498	−	26.2435i	−0.104449	−	0.137400i	0.740899	−	0.671617i	$-0.234400\pi$
$191$	−19.9498	−	26.2435i	−0.104449	−	0.137400i	−0.845348	+	0.534216i	$0.820607\pi$
$192$	77.7151	−	73.6157i	0.404766	−	0.383415i
$193$	10.1440	+	187.094i	0.0525594	+	0.969401i	0.899283	+	0.437368i	$0.144089\pi$
$193$	10.1440	+	187.094i	0.0525594	+	0.969401i	−0.846723	+	0.532033i	$0.821428\pi$
$194$	−11.8240	+	7.11424i	−0.0609483	+	0.0366714i
$195$	−50.8601	−	34.4840i	−0.260821	−	0.176841i
$196$	50.5468	−	182.053i	0.257892	−	0.928843i
$197$	63.9954	−	6.95992i	0.324850	−	0.0353296i	0.0557588	−	0.998444i	$-0.482242\pi$
$197$	63.9954	−	6.95992i	0.324850	−	0.0353296i	0.269091	+	0.963115i	$0.413277\pi$
$198$	−2.63974	−	2.00668i	−0.0133320	−	0.0101347i
$199$	37.1697	+	17.1965i	0.186782	+	0.0864148i	0.511051	−	0.859550i	$-0.329256\pi$
$199$	37.1697	+	17.1965i	0.186782	+	0.0864148i	−0.324269	+	0.945965i	$0.605118\pi$
$200$	17.0911	−	11.5880i	0.0854554	−	0.0579402i
$201$	61.4835	+	182.476i	0.305888	+	0.907843i
$202$	−2.03364	−	12.4046i	−0.0100675	−	0.0614091i
$203$	−77.9375	+	475.398i	−0.383929	+	2.34186i
$204$	22.5271	+	7.59026i	0.110427	+	0.0372072i
$205$	6.82898	+	24.5958i	0.0333121	+	0.119979i
$206$	−9.73836	−	24.4414i	−0.0472736	−	0.118648i
$207$	111.000	−	44.2263i	0.536230	−	0.213653i
$208$	190.895	−	53.0018i	0.917766	−	0.254817i
$209$	−21.2129	+	62.9577i	−0.101497	+	0.301233i
$210$	−7.16957	−	1.17539i	−0.0341408	−	0.00559710i
$211$	−47.5852	+	7.80120i	−0.225522	+	0.0369725i	−0.273484	−	0.961877i	$-0.588176\pi$
$211$	−47.5852	+	7.80120i	−0.225522	+	0.0369725i	0.0479611	+	0.998849i	$0.484728\pi$
$212$	105.474	−	35.5383i	0.497518	−	0.167633i
$213$	79.0317	+	116.563i	0.371041	+	0.547244i
$214$	12.9215	−	27.9295i	0.0603810	−	0.130511i
$215$	67.5264	−	88.8295i	0.314076	−	0.413160i
$216$	−0.679557	−	6.24842i	−0.00314610	−	0.0289279i
$217$	−324.367	−	90.0601i	−1.49478	−	0.415024i
$218$	11.4238	−	16.8489i	0.0524029	−	0.0772885i
$219$	−19.6362	−	32.6356i	−0.0896629	−	0.149021i
$220$	81.5080	−	4.41924i	0.370491	−	0.0200874i
$221$	29.9005	+	31.5656i	0.135297	+	0.142831i
$222$	−11.1143	+	8.44884i	−0.0500642	+	0.0380578i
$223$	−184.463	+	40.6033i	−0.827188	+	0.182078i	−0.608335	−	0.793680i	$-0.708162\pi$
$223$	−184.463	+	40.6033i	−0.827188	+	0.182078i	−0.218852	+	0.975758i	$0.570231\pi$
$224$	54.0799	−	45.9359i	0.241428	−	0.205071i
$225$	−2.77262	+	51.1380i	−0.0123228	+	0.227280i
$226$	−8.98409	−	16.9458i	−0.0397526	−	0.0749814i
$227$	53.2372	−	241.859i	0.234525	−	1.06546i	−0.701265	−	0.712901i	$-0.747381\pi$
$227$	53.2372	−	241.859i	0.234525	−	1.06546i	0.935790	−	0.352558i	$-0.114688\pi$
$228$	−56.9804	+	26.3620i	−0.249914	+	0.115623i
$229$	−118.370	+	196.732i	−0.516898	+	0.859091i	−0.999863	−	0.0165483i	$-0.994732\pi$
$229$	−118.370	+	196.732i	−0.516898	+	0.859091i	0.482965	+	0.875640i	$0.339560\pi$
$230$	7.96581	−	15.0251i	0.0346340	−	0.0653266i
$231$	94.5286	+	80.2933i	0.409215	+	0.347590i
$232$	−40.7920	+	43.0636i	−0.175828	+	0.185619i
$233$	−31.7464	+	291.903i	−0.136251	+	1.25280i	0.703840	+	0.710358i	$0.251467\pi$
$233$	−31.7464	+	291.903i	−0.136251	+	1.25280i	−0.840091	+	0.542445i	$0.817499\pi$
$234$	2.12143	−	5.32439i	0.00906594	−	0.0227538i
$235$		−	140.077i		−	0.596074i
$236$	129.696	+	195.541i	0.549560	+	0.828565i
$237$	114.247			0.482056
$238$	4.77560	+	1.90277i	0.0200655	+	0.00799484i
$239$	360.499	+	39.2066i	1.50836	+	0.164044i	0.824624	−	0.565681i	$-0.191387\pi$
$239$	360.499	+	39.2066i	1.50836	+	0.164044i	0.683740	+	0.729726i	$0.260352\pi$
$240$	55.6778	+	52.7408i	0.231991	+	0.219754i
$241$	−86.5482	+	101.892i	−0.359121	+	0.422790i	−0.911819	−	0.410591i	$-0.865322\pi$
$241$	−86.5482	+	101.892i	−0.359121	+	0.422790i	0.552698	+	0.833381i	$0.313598\pi$
$242$	−9.09257	−	4.82058i	−0.0375726	−	0.0199197i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	21.8143	+	47.1508i	0.0894027	+	0.193241i
$245$	130.648	+	28.7577i	0.533256	+	0.117378i
$246$	−2.10355	+	1.11523i	−0.00855103	+	0.00453347i
$247$	−114.665	−	6.21694i	−0.464230	−	0.0251698i
$248$	−26.8341	−	31.5915i	−0.108202	−	0.127385i
$249$	−6.47451	−	29.4140i	−0.0260020	−	0.118128i
$250$	10.8711	+	14.3007i	0.0434844	+	0.0572028i
$251$	−56.0547	+	53.0978i	−0.223325	+	0.211545i	−0.791179	−	0.611584i	$-0.790533\pi$
$251$	−56.0547	+	53.0978i	−0.223325	+	0.211545i	0.567854	+	0.823129i	$0.307774\pi$
$252$	6.34555	+	117.037i	0.0251807	+	0.464431i
$253$	−248.758	+	149.673i	−0.983233	+	0.591592i
$254$	−3.27344	−	2.21945i	−0.0128876	−	0.00873799i
$255$	−4.50274	+	16.2174i	−0.0176578	+	0.0635977i
$256$	−239.996	+	26.1011i	−0.937483	+	0.101957i
$257$	36.3099	+	27.6020i	0.141284	+	0.107401i	0.673429	−	0.739252i	$-0.264821\pi$
$257$	36.3099	+	27.6020i	0.141284	+	0.107401i	−0.532145	+	0.846653i	$0.678614\pi$
$258$	9.44563	+	4.37001i	0.0366110	+	0.0169380i
$259$	432.218	−	293.051i	1.66880	−	1.13147i
$260$	45.0512	+	133.707i	0.173274	+	0.514259i
$261$	−23.8005	−	145.177i	−0.0911896	−	0.556232i
$262$	−2.17011	+	13.2371i	−0.00828285	+	0.0505232i
$263$	−446.502	−	150.444i	−1.69773	−	0.572031i	−0.706918	−	0.707295i	$-0.749915\pi$
$263$	−446.502	−	150.444i	−1.69773	−	0.572031i	−0.990810	+	0.135264i	$0.956812\pi$
$264$	4.08551	+	14.7147i	0.0154754	+	0.0557374i
$265$	29.1683	+	73.2068i	0.110069	+	0.276252i
$266$	−12.6129	+	5.02544i	−0.0474169	+	0.0188926i
$267$	156.063	−	43.3306i	0.584505	−	0.162287i
$268$	141.174	−	418.989i	0.526768	−	1.56339i
$269$	16.8625	+	2.76446i	0.0626858	+	0.0102768i	0.193043	−	0.981190i	$-0.438164\pi$
$269$	16.8625	+	2.76446i	0.0626858	+	0.0102768i	−0.130357	+	0.991467i	$0.541613\pi$
$270$	2.18944	−	0.358940i	0.00810903	−	0.00132941i
$271$	471.752	−	158.952i	1.74078	−	0.586538i	0.744111	−	0.668055i	$-0.232873\pi$
$271$	471.752	−	158.952i	1.74078	−	0.586538i	0.996672	+	0.0815173i	$0.0259766\pi$
$272$	−30.4527	−	44.9144i	−0.111959	−	0.165127i
$273$	−90.0157	+	194.566i	−0.329728	+	0.712695i
$274$	17.7637	−	23.3677i	0.0648309	−	0.0852836i
$275$	−13.4535	−	123.703i	−0.0489219	−	0.449829i
$276$	−264.354	−	73.3976i	−0.957805	−	0.265933i
$277$	−164.185	+	242.155i	−0.592725	+	0.874204i	−0.999222	−	0.0394480i	$-0.987440\pi$
$277$	−164.185	+	242.155i	−0.592725	+	0.874204i	0.406496	+	0.913652i	$0.366750\pi$
$278$	−1.32274	−	2.19841i	−0.00475806	−	0.00790796i
$279$	102.651	−	5.56560i	0.367926	−	0.0199484i
$280$	23.0107	+	24.2921i	0.0821812	+	0.0867576i
$281$	74.4264	−	56.5775i	0.264863	−	0.201343i	−0.464311	−	0.885672i	$-0.653698\pi$
$281$	74.4264	−	56.5775i	0.264863	−	0.201343i	0.729173	+	0.684329i	$0.239905\pi$
$282$	12.7599	−	2.80867i	0.0452480	−	0.00995984i
$283$	55.8205	−	47.4143i	0.197245	−	0.167542i	−0.543321	−	0.839525i	$-0.682833\pi$
$283$	55.8205	−	47.4143i	0.197245	−	0.167542i	0.740566	+	0.671983i	$0.234557\pi$
$284$	17.5065	−	322.888i	0.0616425	−	1.13693i
$285$	−20.8219	−	39.2742i	−0.0730591	−	0.137804i
$286$	−2.99361	+	13.6001i	−0.0104672	+	0.0475529i
$287$	80.8245	−	37.3934i	0.281618	−	0.130291i
$288$	−11.1713	+	18.5668i	−0.0387891	+	0.0644679i
$289$	−129.792	+	244.813i	−0.449106	+	0.847104i
$290$	−15.9585	−	13.5553i	−0.0550293	−	0.0467423i
$291$	−108.396	+	114.432i	−0.372494	+	0.393237i
$292$	−9.45542	+	86.9411i	−0.0323816	+	0.297744i
$293$	5.05095	−	12.6769i	0.0172387	−	0.0432659i	−0.920105	−	0.391671i	$-0.871897\pi$
$293$	5.05095	−	12.6769i	0.0172387	−	0.0432659i	0.937344	+	0.348405i	$0.113277\pi$
$294$			12.4776i			0.0424407i
$295$	−133.275	+	99.1896i	−0.451778	+	0.336236i
$296$	64.2978			0.217222
$297$	−35.1852	−	14.0191i	−0.118469	−	0.0472023i
$298$	4.65892	+	0.506688i	0.0156340	+	0.00170030i
$299$	−364.310	−	345.092i	−1.21843	−	1.15415i
$300$	76.1273	−	89.6240i	0.253758	−	0.298747i
$301$	−343.938	−	182.344i	−1.14265	−	0.605795i
$302$	5.82077	+	3.50224i	0.0192741	+	0.0115968i
$303$	−60.2888	−	130.312i	−0.198973	−	0.430073i
$304$	139.969	+	30.8095i	0.460424	+	0.101347i
$305$	−32.4990	+	17.2299i	−0.106554	+	0.0564914i
$306$	−1.56756	−	0.0849907i	−0.00512275	−	0.000277747i
$307$	182.544	+	214.907i	0.594606	+	0.700024i	0.974342	−	0.225071i	$-0.0722613\pi$
$307$	182.544	+	214.907i	0.594606	+	0.700024i	−0.379737	+	0.925095i	$0.623985\pi$
$308$	−61.2196	−	278.123i	−0.198765	−	0.902998i
$309$	−181.870	−	239.246i	−0.588576	−	0.774259i
$310$	10.6225	−	10.0621i	0.0342660	−	0.0324585i
$311$	−20.7882	−	383.415i	−0.0668430	−	1.23285i	−0.818973	−	0.573832i	$-0.805456\pi$
$311$	−20.7882	−	383.415i	−0.0668430	−	1.23285i	0.752130	−	0.659014i	$-0.229026\pi$
$312$	−22.6179	+	13.6087i	−0.0724933	+	0.0436178i
$313$	−216.734	−	146.950i	−0.692442	−	0.469488i	0.163510	−	0.986542i	$-0.447718\pi$
$313$	−216.734	−	146.950i	−0.692442	−	0.469488i	−0.855953	+	0.517054i	$0.827029\pi$
$314$	−4.02925	+	14.5120i	−0.0128320	+	0.0462167i
$315$	−82.5007	+	8.97249i	−0.261907	+	0.0284841i
$316$	−208.836	−	158.753i	−0.660874	−	0.502383i
$317$	−68.6211	−	31.7475i	−0.216470	−	0.100150i	0.308657	−	0.951173i	$-0.400120\pi$
$317$	−68.6211	−	31.7475i	−0.216470	−	0.100150i	−0.525128	+	0.851023i	$0.675982\pi$
$318$	−6.08371	+	4.12486i	−0.0191312	+	0.0129713i
$319$	114.132	+	338.733i	0.357782	+	1.06186i
$320$	−28.1546	−	171.735i	−0.0879831	−	0.536673i
$321$	56.8681	−	346.880i	0.177159	−	1.08062i
$322$	−56.2249	−	18.9444i	−0.174611	−	0.0588334i
$323$	8.41462	+	30.3067i	0.0260515	+	0.0938289i
$324$	−13.2484	−	33.2509i	−0.0408901	−	0.102626i
$325$	199.805	−	79.6096i	0.614785	−	0.244953i
$326$	12.6224	−	3.50459i	0.0387190	−	0.0107503i
$327$	74.2444	−	220.350i	0.227047	−	0.673852i
$328$	10.8208	+	1.77399i	0.0329904	+	0.00540850i
$329$	−482.262	+	79.0628i	−1.46584	+	0.240312i
$330$	−5.10850	+	1.72125i	−0.0154803	+	0.00521592i
$331$	98.1585	+	144.773i	0.296551	+	0.437380i	0.946551	−	0.322554i	$-0.104541\pi$
$331$	98.1585	+	144.773i	0.296551	+	0.437380i	−0.650000	+	0.759934i	$0.725231\pi$
$332$	−29.0374	+	62.7634i	−0.0874622	+	0.189046i
$333$	−96.5063	+	126.952i	−0.289809	+	0.381237i
$334$	4.66305	+	42.8760i	0.0139612	+	0.128371i
$335$	301.633	+	83.7480i	0.900397	+	0.249994i
$336$	150.152	−	221.457i	0.446880	−	0.659098i
$337$	−37.5317	−	62.3782i	−0.111370	−	0.185098i	0.796159	−	0.605087i	$-0.206862\pi$
$337$	−37.5317	−	62.3782i	−0.111370	−	0.185098i	−0.907529	+	0.419989i	$0.862034\pi$
$338$	1.55370	−	0.0842393i	0.00459675	−	0.000249229i
$339$	−150.663	−	159.053i	−0.444434	−	0.469183i
$340$	30.7657	−	23.3875i	0.0904874	−	0.0687867i
$341$	−243.938	+	53.6949i	−0.715362	+	0.157463i
$342$	3.16007	−	2.68419i	0.00923997	−	0.00784850i
$343$	−0.793471	+	14.6347i	−0.00231333	+	0.0426668i
$344$	−22.4518	−	42.3487i	−0.0652670	−	0.123107i
$345$	41.7583	−	189.710i	0.121038	−	0.549883i
$346$	−4.89044	+	2.26256i	−0.0141342	+	0.00653919i
$347$	−283.238	+	470.744i	−0.816246	+	1.35661i	0.115427	+	0.993316i	$0.463176\pi$
$347$	−283.238	+	470.744i	−0.816246	+	1.35661i	−0.931674	+	0.363296i	$0.881651\pi$
$348$	−158.225	+	298.445i	−0.454671	+	0.857600i
$349$	400.999	+	340.612i	1.14899	+	0.975964i	0.999917	−	0.0128611i	$-0.00409394\pi$
$349$	400.999	+	340.612i	1.14899	+	0.975964i	0.149077	+	0.988826i	$0.452370\pi$
$350$	17.4881	−	18.4620i	0.0499660	−	0.0527485i
$351$	7.07824	−	65.0834i	0.0201659	−	0.185423i
$352$	19.4870	−	48.9086i	0.0553607	−	0.138945i
$353$		−	523.402i		−	1.48272i	−0.671105	−	0.741362i	$-0.734180\pi$
$353$		−	523.402i		−	1.48272i	0.671105	−	0.741362i	$-0.265820\pi$
$354$	−11.7077	−	10.1514i	−0.0330725	−	0.0286763i
$355$	228.950			0.644930
$356$	−345.482	−	137.653i	−0.970455	−	0.386665i
$357$	58.3751	+	6.34868i	0.163516	+	0.0177834i
$358$	8.40855	+	7.96500i	0.0234876	+	0.0222486i
$359$	303.328	−	357.106i	0.844925	−	0.994723i	−0.155051	−	0.987906i	$-0.549554\pi$
$359$	303.328	−	357.106i	0.844925	−	0.994723i	0.999977	−	0.00681666i	$-0.00216983\pi$
$360$	−9.02784	−	4.78626i	−0.0250773	−	0.0132952i
$361$	238.145	+	143.287i	0.659681	+	0.396917i
$362$	10.6474	+	23.0139i	0.0294127	+	0.0635744i
$363$	−114.804	−	25.2704i	−0.316266	−	0.0696153i
$364$	434.903	−	230.571i	1.19479	−	0.633436i
$365$	−61.8291	−	3.35228i	−0.169395	−	0.00918432i
$366$	−2.22114	−	2.61493i	−0.00606869	−	0.00714461i
$367$	55.3604	+	251.505i	0.150846	+	0.685299i	0.989960	+	0.141345i	$0.0451426\pi$
$367$	55.3604	+	251.505i	0.150846	+	0.685299i	−0.839115	+	0.543954i	$0.816926\pi$
$368$	379.014	+	498.585i	1.02993	+	1.35485i
$369$	−19.7439	+	18.7024i	−0.0535066	+	0.0506841i
$370$	1.22878	+	22.6635i	0.00332102	+	0.0612527i
$371$	235.575	−	141.741i	0.634973	−	0.382051i
$372$	−195.373	−	132.466i	−0.525197	−	0.356092i
$373$	−74.9471	+	269.935i	−0.200931	+	0.723686i	0.792562	+	0.609791i	$0.208747\pi$
$373$	−74.9471	+	269.935i	−0.200931	+	0.723686i	−0.993493	+	0.113895i	$0.963667\pi$
$374$	3.79194	−	0.412398i	0.0101389	−	0.00110267i
$375$	163.349	+	124.174i	0.435597	+	0.331132i
$376$	−54.6116	−	25.2660i	−0.145244	−	0.0671968i
$377$	−511.379	+	346.724i	−1.35644	+	0.919692i
$378$	−2.47154	−	7.33525i	−0.00653845	−	0.0194054i
$379$	101.178	+	617.155i	0.266959	+	1.62838i	0.691084	+	0.722775i	$0.257134\pi$
$379$	101.178	+	617.155i	0.266959	+	1.62838i	−0.424125	+	0.905604i	$0.639418\pi$
$380$	−16.5128	+	100.724i	−0.0434547	+	0.265062i
$381$	−42.8100	−	14.4244i	−0.112362	−	0.0378593i
$382$	−1.33730	−	4.81652i	−0.00350079	−	0.0126087i
$383$	−58.3474	−	146.441i	−0.152343	−	0.382352i	0.832921	−	0.553392i	$-0.186667\pi$
$383$	−58.3474	−	146.441i	−0.152343	−	0.382352i	−0.985264	+	0.171039i	$0.945287\pi$
$384$	61.5663	−	24.5302i	0.160329	−	0.0638808i
$385$	194.284	−	53.9428i	0.504634	−	0.140111i
$386$	−9.07196	+	26.9246i	−0.0235025	+	0.0697529i
$387$	117.313	+	19.2325i	0.303135	+	0.0496965i
$388$	357.149	−	58.5517i	0.920488	−	0.150906i
$389$	420.442	−	141.664i	1.08083	−	0.364174i	0.278121	−	0.960546i	$-0.410288\pi$
$389$	420.442	−	141.664i	1.08083	−	0.364174i	0.802708	+	0.596372i	$0.203392\pi$
$390$	−5.22901	−	7.71222i	−0.0134077	−	0.0197749i
$391$	−57.7123	+	124.743i	−0.147602	+	0.319036i
$392$	34.7768	−	45.7481i	0.0887164	−	0.116704i
$393$	16.5658	+	152.320i	0.0421521	+	0.387582i
$394$	9.40543	+	2.61140i	0.0238716	+	0.00662793i
$395$	104.232	−	153.731i	0.263878	−	0.389192i
$396$	44.8358	+	74.5177i	0.113222	+	0.188176i
$397$	−700.614	+	37.9862i	−1.76477	+	0.0956831i	−0.907727	−	0.419561i	$-0.862184\pi$
$397$	−700.614	+	37.9862i	−1.76477	+	0.0956831i	−0.857043	+	0.515244i	$0.827701\pi$
$398$	4.27078	+	4.50861i	0.0107306	+	0.0113282i
$399$	−123.462	+	93.8532i	−0.309428	+	0.235221i
$400$	−262.160	+	57.7057i	−0.655399	+	0.144264i
$401$	152.712	−	129.714i	0.380827	−	0.323477i	−0.436443	−	0.899732i	$-0.643762\pi$
$401$	152.712	−	129.714i	0.380827	−	0.323477i	0.817270	+	0.576254i	$0.195486\pi$
$402$	−1.58077	+	29.1556i	−0.00393227	+	0.0725264i
$403$	−202.231	−	381.447i	−0.501813	−	0.946520i
$404$	−70.8722	+	321.976i	−0.175426	+	0.796970i
$405$	23.0003	−	10.6411i	0.0567908	−	0.0262742i
$406$	−37.6611	+	62.5932i	−0.0927612	+	0.154170i
$407$	181.490	−	342.326i	0.445921	−	0.841096i
$408$	5.51047	+	4.68064i	0.0135061	+	0.0114721i
$409$	405.034	−	427.589i	0.990303	−	1.04545i	−0.00866202	−	0.999962i	$-0.502757\pi$
$409$	405.034	−	427.589i	0.990303	−	1.04545i	0.998965	−	0.0454876i	$-0.0144841\pi$
$410$	−0.418495	+	3.84800i	−0.00102072	+	0.00938536i
$411$	124.101	−	311.469i	0.301948	−	0.757833i
$412$			690.043i			1.67486i
$413$	416.715	+	402.856i	1.00900	+	0.975439i
$414$	18.1183			0.0437641
$415$	−45.4863	−	18.1234i	−0.109605	−	0.0436708i
$416$	90.4679	+	9.83898i	0.217471	+	0.0236514i
$417$	−21.2762	−	20.1539i	−0.0510220	−	0.0483306i
$418$	−6.52176	+	7.67801i	−0.0156023	+	0.0183685i
$419$	−574.686	−	304.679i	−1.37157	−	0.727158i	−0.390459	−	0.920620i	$-0.627684\pi$
$419$	−574.686	−	304.679i	−1.37157	−	0.727158i	−0.981108	+	0.193462i	$0.938028\pi$
$420$	163.273	+	98.2383i	0.388746	+	0.233901i
$421$	−70.8790	−	153.202i	−0.168359	−	0.363901i	0.804970	−	0.593315i	$-0.202181\pi$
$421$	−70.8790	−	153.202i	−0.168359	−	0.363901i	−0.973329	+	0.229414i	$0.926319\pi$
$422$	−7.14101	−	1.57185i	−0.0169218	−	0.00372477i
$423$	131.854	−	69.9046i	0.311712	−	0.165259i
$424$	33.8021	+	1.83270i	0.0797219	+	0.00432239i
$425$	−38.1384	−	44.9000i	−0.0897374	−	0.105647i
$426$	4.59065	+	20.8555i	0.0107762	+	0.0489567i
$427$	77.6626	+	102.163i	0.181880	+	0.239259i
$428$	−585.960	+	555.051i	−1.36907	+	1.29685i
$429$	8.61162	+	158.832i	0.0200737	+	0.370238i
$430$	14.4979	−	8.72307i	0.0337159	−	0.0202862i
$431$	409.991	+	277.980i	0.951254	+	0.644966i	0.934904	−	0.354900i	$-0.115485\pi$
$431$	409.991	+	277.980i	0.951254	+	0.644966i	0.0163499	+	0.999866i	$0.494795\pi$
$432$	−21.8591	+	78.7292i	−0.0505997	+	0.182244i
$433$	−642.492	+	69.8752i	−1.48381	+	0.161375i	−0.813875	−	0.581041i	$-0.802646\pi$
$433$	−642.492	+	69.8752i	−1.48381	+	0.161375i	−0.669940	+	0.742415i	$0.733680\pi$
$434$	−40.6377	−	30.8919i	−0.0936352	−	0.0711796i
$435$	−217.063	−	100.424i	−0.498995	−	0.230860i
$436$	−441.902	+	299.617i	−1.01354	+	0.687195i
$437$	−115.910	−	344.010i	−0.265241	−	0.787208i
$438$	−0.934362	−	5.69935i	−0.00213325	−	0.0130122i
$439$	54.1222	−	330.131i	0.123285	−	0.752007i	−0.850743	−	0.525582i	$-0.823848\pi$
$439$	54.1222	−	330.131i	0.123285	−	0.752007i	0.974029	−	0.226425i	$-0.0727039\pi$
$440$	23.5273	+	7.92728i	0.0534712	+	0.0180166i
$441$	38.1293	+	137.329i	0.0864610	+	0.311404i
$442$	2.44032	+	6.12473i	0.00552108	+	0.0138569i
$443$	−108.556	+	43.2527i	−0.245047	+	0.0976358i	−0.489428	−	0.872043i	$-0.662795\pi$
$443$	−108.556	+	43.2527i	−0.245047	+	0.0976358i	0.244381	+	0.969679i	$0.421415\pi$
$444$	352.814	−	97.9582i	0.794625	−	0.220627i
$445$	84.0762	−	249.529i	0.188935	−	0.560740i
$446$	−28.2635	−	4.63356i	−0.0633711	−	0.0103892i
$447$	52.8248	−	8.66019i	0.118176	−	0.0193740i
$448$	−575.363	+	193.862i	−1.28429	+	0.432729i
$449$	168.490	+	248.504i	0.375256	+	0.553461i	0.967685	−	0.252161i	$-0.0811414\pi$
$449$	168.490	+	248.504i	0.375256	+	0.553461i	−0.592429	+	0.805623i	$0.701831\pi$
$450$	−3.26075	+	7.04800i	−0.00724612	+	0.0156622i
$451$	39.9882	−	52.6036i	0.0886657	−	0.116638i
$452$	54.3883	+	500.092i	0.120328	+	1.10640i
$453$	74.7661	+	20.7587i	0.165047	+	0.0458250i
$454$	21.0740	−	31.0818i	0.0464184	−	0.0684620i
$455$	179.682	+	298.634i	0.394906	+	0.656339i
$456$	−19.0674	+	1.03380i	−0.0418145	+	0.00226711i
$457$	204.728	+	216.128i	0.447982	+	0.472929i	0.910398	−	0.413735i	$-0.135776\pi$
$457$	204.728	+	216.128i	0.447982	+	0.472929i	−0.462416	+	0.886663i	$0.653017\pi$
$458$	−27.7161	+	21.0692i	−0.0605155	+	0.0460027i
$459$	−17.5124	+	3.85478i	−0.0381535	+	0.00839821i
$460$	−339.944	+	288.751i	−0.739008	+	0.627719i
$461$	19.0024	−	350.479i	0.0412200	−	0.760258i	−0.902738	−	0.430191i	$-0.858446\pi$
$461$	19.0024	−	350.479i	0.0412200	−	0.760258i	0.943958	−	0.330066i	$-0.107071\pi$
$462$	8.80933	+	16.6162i	0.0190678	+	0.0359657i
$463$	−121.246	+	550.827i	−0.261871	+	1.18969i	0.643626	+	0.765340i	$0.277429\pi$
$463$	−121.246	+	550.827i	−0.261871	+	1.18969i	−0.905497	+	0.424352i	$0.860502\pi$
$464$	699.837	−	323.779i	1.50827	−	0.697800i
$465$	86.1635	−	143.205i	0.185298	−	0.307968i
$466$	−20.8554	+	39.3375i	−0.0447541	+	0.0844152i
$467$	584.237	+	496.256i	1.25104	+	1.06265i	0.995393	+	0.0958768i	$0.0305655\pi$
$467$	584.237	+	496.256i	1.25104	+	1.06265i	0.255650	+	0.966769i	$0.417710\pi$
$468$	−103.376	+	109.132i	−0.220888	+	0.233188i
$469$	118.081	−	1085.74i	0.251772	−	2.31501i
$470$	7.86201	−	19.7322i	0.0167277	−	0.0419833i
$471$			172.033i			0.365252i
$472$	14.6318	+	69.8504i	0.0309995	+	0.147988i
$473$	−288.841			−0.610657
$474$	16.0936	+	6.41227i	0.0339527	+	0.0135280i
$475$	154.680	+	16.8224i	0.325641	+	0.0354156i
$476$	−97.8838	−	92.7205i	−0.205638	−	0.194791i
$477$	−54.3530	+	63.9893i	−0.113948	+	0.134149i
$478$	48.5816	+	25.7563i	0.101635	+	0.0538835i
$479$	681.961	+	410.322i	1.42372	+	0.856622i	0.998817	−	0.0486178i	$-0.0154816\pi$
$479$	681.961	+	410.322i	1.42372	+	0.856622i	0.424900	+	0.905240i	$0.360309\pi$
$480$	14.7914	+	31.9711i	0.0308155	+	0.0666065i
$481$	654.066	+	143.971i	1.35980	+	0.299315i
$482$	−17.9106	+	9.49557i	−0.0371588	+	0.0197004i
$483$	−676.706	−	36.6900i	−1.40105	−	0.0759626i
$484$	174.740	+	205.720i	0.361033	+	0.425041i
$485$	55.0858	+	250.257i	0.113579	+	0.515994i
$486$	1.43049	+	1.88178i	0.00294340	+	0.00387198i
$487$	178.225	−	168.824i	0.365965	−	0.346660i	−0.482515	−	0.875888i	$-0.660277\pi$
$487$	178.225	−	168.824i	0.365965	−	0.346660i	0.848480	+	0.529227i	$0.177518\pi$
$488$	0.855463	+	15.7781i	0.00175300	+	0.0323321i
$489$	128.214	−	77.1436i	0.262196	−	0.157758i
$490$	16.7898	+	11.3837i	0.0342648	+	0.0232321i
$491$	160.266	−	577.226i	0.326407	−	1.17561i	−0.600283	−	0.799787i	$-0.704945\pi$
$491$	160.266	−	577.226i	0.326407	−	1.17561i	0.926691	−	0.375825i	$-0.122641\pi$
$492$	62.0786	−	6.75145i	0.126176	−	0.0137225i
$493$	134.722	+	102.413i	0.273269	+	0.207734i
$494$	−15.8035	−	7.31146i	−0.0319908	−	0.0148005i
$495$	−50.9648	+	34.5550i	−0.102959	+	0.0698080i
$496$	172.053	+	510.634i	0.346881	+	1.02951i
$497$	−129.225	−	788.235i	−0.260009	−	1.58599i
$498$	0.738857	−	4.50683i	0.00148365	−	0.00904985i
$499$	−107.616	−	36.2600i	−0.215663	−	0.0726654i	0.209396	−	0.977831i	$-0.432850\pi$
$499$	−107.616	−	36.2600i	−0.215663	−	0.0726654i	−0.425059	+	0.905166i	$0.639747\pi$
$500$	−126.043	−	453.964i	−0.252085	−	0.907929i
$501$	182.343	+	457.648i	0.363959	+	0.913468i
$502$	−10.8764	+	4.33355i	−0.0216661	+	0.00863257i
$503$	−610.779	+	169.582i	−1.21427	+	0.337141i	−0.814875	−	0.579636i	$-0.803195\pi$
$503$	−610.779	+	169.582i	−1.21427	+	0.337141i	−0.399398	+	0.916778i	$0.630781\pi$
$504$	−11.3827	+	33.7827i	−0.0225848	+	0.0670292i
$505$	−230.351	−	37.7641i	−0.456140	−	0.0747804i
$506$	−43.4422	+	7.12198i	−0.0858541	+	0.0140751i
$507$	16.8428	−	5.67499i	0.0332204	−	0.0111933i
$508$	58.2102	+	85.8537i	0.114587	+	0.169003i
$509$	−143.587	+	310.357i	−0.282095	+	0.609739i	−0.995885	−	0.0906206i	$-0.971115\pi$
$509$	−143.587	+	310.357i	−0.282095	+	0.609739i	0.713790	+	0.700360i	$0.246977\pi$
$510$	−1.54451	+	2.03176i	−0.00302844	+	0.00398385i
$511$	23.3564	+	214.759i	0.0457073	+	0.420271i
$512$	−182.745	−	50.7389i	−0.356924	−	0.0990994i
$513$	26.5776	−	39.1990i	0.0518082	−	0.0764113i
$514$	3.56564	+	5.92613i	0.00693703	+	0.0115294i
$515$	−487.855	+	26.4507i	−0.947291	+	0.0513606i
$516$	−187.716	−	198.169i	−0.363790	−	0.384049i
$517$	−288.667	+	219.439i	−0.558350	+	0.424447i
$518$	77.3328	−	17.0222i	0.149291	−	0.0328615i
$519$	−46.9106	+	39.8463i	−0.0903866	+	0.0767751i
$520$	−2.32328	+	42.8503i	−0.00446784	+	0.0824044i
$521$	330.897	+	624.139i	0.635120	+	1.19796i	0.967033	+	0.254653i	$0.0819611\pi$
$521$	330.897	+	624.139i	0.635120	+	1.19796i	−0.331913	+	0.943310i	$0.607694\pi$
$522$	4.79553	−	21.7863i	0.00918684	−	0.0417362i
$523$	849.655	−	393.092i	1.62458	−	0.751610i	0.625000	−	0.780625i	$-0.285099\pi$
$523$	849.655	−	393.092i	1.62458	−	0.751610i	0.999579	+	0.0290142i	$0.00923682\pi$
$524$	181.376	−	301.449i	0.346137	−	0.575284i
$525$	136.059	−	256.635i	0.259160	−	0.488828i
$526$	−54.4533	−	46.2530i	−0.103523	−	0.0879335i
$527$	−81.3239	+	85.8526i	−0.154315	+	0.162908i
$528$	21.4643	−	197.361i	0.0406520	−	0.373789i
$529$	391.354	−	982.224i	0.739800	−	1.85676i
$530$			11.9495i			0.0225462i
$531$	−159.876	−	75.9509i	−0.301086	−	0.143034i
$532$	356.094			0.669349
$533$	106.102	+	42.2750i	0.199066	+	0.0793152i
$534$	24.4159	+	2.65539i	0.0457228	+	0.00497265i
$535$	−414.877	−	392.993i	−0.775471	−	0.734565i
$536$	87.0567	−	102.491i	0.162419	−	0.191215i
$537$	116.885	+	61.9684i	0.217663	+	0.115397i
$538$	2.22019	+	1.33585i	0.00412675	+	0.00248298i
$539$	−145.404	−	314.285i	−0.269766	−	0.583089i
$540$	−56.8293	−	12.5091i	−0.105239	−	0.0231649i
$541$	−134.230	+	71.1640i	−0.248114	+	0.131542i	−0.587825	−	0.808988i	$-0.700016\pi$
$541$	−134.230	+	71.1640i	−0.248114	+	0.131542i	0.339711	+	0.940530i	$0.389671\pi$
$542$	75.3753	+	4.08673i	0.139069	+	0.00754010i
$543$	187.513	+	220.757i	0.345327	+	0.406550i
$544$	−5.35826	−	24.3428i	−0.00984975	−	0.0447479i
$545$	−228.766	−	300.936i	−0.419753	−	0.552176i
$546$	−23.6004	+	22.3555i	−0.0432242	+	0.0409442i
$547$	−2.68370	−	49.4979i	−0.00490621	−	0.0904898i	0.995055	−	0.0993282i	$-0.0316694\pi$
$547$	−2.68370	−	49.4979i	−0.00490621	−	0.0904898i	−0.999961	+	0.00883841i	$0.997187\pi$
$548$	−659.652	+	396.899i	−1.20374	+	0.724269i
$549$	−32.4368	−	21.9927i	−0.0590834	−	0.0400596i
$550$	5.04784	−	18.1807i	0.00917789	−	0.0330558i
$551$	−444.332	+	48.3240i	−0.806410	+	0.0877023i
$552$	−66.4296	−	50.4985i	−0.120343	−	0.0914827i
$553$	−588.098	−	272.083i	−1.06347	−	0.492013i
$554$	−36.7193	+	24.8963i	−0.0662804	+	0.0449392i
$555$	82.7797	+	245.681i	0.149153	+	0.442669i
$556$	10.8864	+	66.4043i	0.0195799	+	0.119432i
$557$	−65.8877	+	401.897i	−0.118290	+	0.721539i	0.859371	+	0.511352i	$0.170855\pi$
$557$	−65.8877	+	401.897i	−0.118290	+	0.721539i	−0.977661	+	0.210186i	$0.932593\pi$
$558$	14.7725	+	4.97743i	0.0264740	+	0.00892013i
$559$	−133.566	−	481.062i	−0.238938	−	0.860576i
$560$	−161.003	−	404.087i	−0.287505	−	0.721583i
$561$	40.4741	−	16.1264i	0.0721464	−	0.0287458i
$562$	13.6597	−	3.79258i	0.0243054	−	0.00674837i
$563$	−139.419	+	413.780i	−0.247636	+	0.734956i	0.749685	+	0.661795i	$0.230205\pi$
$563$	−139.419	+	413.780i	−0.247636	+	0.734956i	−0.997320	+	0.0731608i	$0.976691\pi$
$564$	−338.157	−	55.4379i	−0.599568	−	0.0982942i
$565$	−351.476	+	57.6216i	−0.622082	+	0.101985i
$566$	10.5244	−	3.54609i	0.0185944	−	0.00626517i
$567$	−49.6172	−	73.1799i	−0.0875082	−	0.129065i
$568$	41.2961	−	89.2601i	0.0727045	−	0.157148i
$569$	392.017	−	515.690i	0.688958	−	0.906309i	−0.310055	−	0.950719i	$-0.600347\pi$
$569$	392.017	−	515.690i	0.688958	−	0.906309i	0.999013	+	0.0444093i	$0.0141406\pi$
$570$	−0.728784	−	6.70106i	−0.00127857	−	0.0117562i
$571$	−144.181	−	40.0317i	−0.252506	−	0.0701081i	0.138969	−	0.990297i	$-0.455621\pi$
$571$	−144.181	−	40.0317i	−0.252506	−	0.0701081i	−0.391475	+	0.920189i	$0.628035\pi$
$572$	204.965	−	302.300i	0.358330	−	0.528497i
$573$	−29.4369	−	48.9245i	−0.0513733	−	0.0853830i
$574$	13.4842	−	0.731092i	0.0234916	−	0.00127368i
$575$	467.578	+	493.616i	0.813179	+	0.858463i
$576$	147.603	−	112.205i	0.256256	−	0.194801i
$577$	181.958	−	40.0520i	0.315352	−	0.0694142i	−0.0544742	−	0.998515i	$-0.517348\pi$
$577$	181.958	−	40.0520i	0.315352	−	0.0694142i	0.369826	+	0.929101i	$0.379417\pi$
$578$	−32.0237	+	27.2012i	−0.0554043	+	0.0470609i
$579$	−17.5699	+	324.057i	−0.0303452	+	0.559684i
$580$	257.231	+	485.189i	0.443502	+	0.836533i
$581$	−36.7221	+	166.830i	−0.0632051	+	0.287144i
$582$	−21.6919	+	10.0358i	−0.0372714	+	0.0172436i
$583$	105.169	−	174.792i	0.180392	−	0.299814i
$584$	−12.4592	+	23.5005i	−0.0213342	+	0.0402405i
$585$	−81.1181	−	68.9024i	−0.138663	−	0.117782i
$586$	1.42302	−	1.50226i	0.00242835	−	0.00256358i
$587$	−7.76261	+	71.3760i	−0.0132242	+	0.121595i	−0.998889	−	0.0471193i	$-0.984996\pi$
$587$	−7.76261	+	71.3760i	−0.0132242	+	0.121595i	0.985665	+	0.168714i	$0.0539614\pi$
$588$	121.129	−	304.011i	0.206002	−	0.517026i
$589$		−	312.325i		−	0.530263i
$590$	−24.3410	+	6.49226i	−0.0412560	+	0.0110038i
$591$	111.497			0.188658
$592$	−776.495	−	309.384i	−1.31165	−	0.522608i
$593$	1033.78	+	112.431i	1.74331	+	0.189597i	0.923647	−	0.383244i	$-0.125193\pi$
$593$	1033.78	+	112.431i	1.74331	+	0.189597i	0.819666	+	0.572841i	$0.194159\pi$
$594$	−4.16957	−	3.94963i	−0.00701948	−	0.00664920i
$595$	61.8005	−	72.7572i	0.103866	−	0.122281i
$596$	−108.594	−	57.5728i	−0.182204	−	0.0965987i
$597$	60.7821	+	36.5714i	0.101813	+	0.0612586i
$598$	−31.9502	−	69.0592i	−0.0534284	−	0.115484i
$599$	−488.503	−	107.528i	−0.815531	−	0.179512i	−0.212430	−	0.977176i	$-0.568138\pi$
$599$	−488.503	−	107.528i	−0.815531	−	0.179512i	−0.603102	+	0.797664i	$0.706069\pi$
$600$	31.5991	−	16.7528i	0.0526652	−	0.0279213i
$601$	−768.259	−	41.6538i	−1.27830	−	0.0693075i	−0.597556	−	0.801827i	$-0.703861\pi$
$601$	−768.259	−	41.6538i	−1.27830	−	0.0693075i	−0.680746	+	0.732520i	$0.738344\pi$
$602$	−38.2149	−	44.9901i	−0.0634799	−	0.0747343i
$603$	71.6963	+	325.720i	0.118899	+	0.540165i
$604$	−107.822	−	141.837i	−0.178513	−	0.234830i
$605$	−138.744	+	131.425i	−0.229329	+	0.217232i
$606$	−1.17873	−	21.7403i	−0.00194509	−	0.0358752i
$607$	639.318	−	384.665i	1.05324	−	0.633715i	0.119931	−	0.992782i	$-0.461733\pi$
$607$	639.318	−	384.665i	1.05324	−	0.633715i	0.933312	+	0.359067i	$0.116905\pi$
$608$	54.4879	+	36.9437i	0.0896182	+	0.0607627i
$609$	−223.227	+	803.991i	−0.366547	+	1.32018i
$610$	−5.54506	+	0.603062i	−0.00909026	+	0.000988626i
$611$	−498.959	−	379.299i	−0.816628	−	0.620784i
$612$	37.3679	+	17.2882i	0.0610587	+	0.0282488i
$613$	−256.029	+	173.592i	−0.417665	+	0.283184i	−0.751864	−	0.659319i	$-0.770845\pi$
$613$	−256.029	+	173.592i	−0.417665	+	0.283184i	0.334198	+	0.942503i	$0.391534\pi$
$614$	13.6523	+	40.5187i	0.0222351	+	0.0659913i
$615$	7.15282	+	43.6303i	0.0116306	+	0.0709435i
$616$	14.0129	−	85.4748i	0.0227482	−	0.138758i
$617$	555.750	+	187.254i	0.900730	+	0.303491i	0.731304	−	0.682052i	$-0.238912\pi$
$617$	555.750	+	187.254i	0.900730	+	0.303491i	0.169426	+	0.985543i	$0.445809\pi$
$618$	−12.1914	−	43.9093i	−0.0197271	−	0.0710507i
$619$	−316.291	−	793.829i	−0.510970	−	1.28244i	−0.927672	−	0.373395i	$-0.878193\pi$
$619$	−316.291	−	793.829i	−0.510970	−	1.28244i	0.416702	−	0.909043i	$-0.363186\pi$
$620$	−356.492	+	142.039i	−0.574987	+	0.229096i
$621$	199.412	−	55.3665i	0.321114	−	0.0891570i
$622$	18.5913	−	55.1770i	0.0298895	−	0.0887090i
$623$	−906.540	−	148.620i	−1.45512	−	0.238555i
$624$	338.628	−	55.5152i	0.542673	−	0.0889667i
$625$	−88.3182	+	29.7579i	−0.141309	+	0.0476126i
$626$	−22.2828	−	32.8647i	−0.0355956	−	0.0524996i
$627$	−48.3164	+	104.434i	−0.0770597	+	0.166562i
$628$	239.050	−	314.465i	0.380653	−	0.500741i
$629$	−19.8333	−	182.364i	−0.0315315	−	0.289927i
$630$	−12.1252	−	3.36653i	−0.0192463	−	0.00534370i
$631$	−135.388	+	199.682i	−0.214560	+	0.316453i	−0.919705	−	0.392611i	$-0.871572\pi$
$631$	−135.388	+	199.682i	−0.214560	+	0.316453i	0.705144	+	0.709064i	$0.250882\pi$
$632$	−41.1340	−	68.3653i	−0.0650855	−	0.108173i
$633$	−83.3978	+	4.52170i	−0.131750	+	0.00714328i
$634$	−7.88453	−	8.32359i	−0.0124362	−	0.0131287i
$635$	−58.4665	+	44.4451i	−0.0920732	+	0.0699923i
$636$	188.270	−	41.4414i	0.296022	−	0.0651594i
$637$	456.201	−	387.501i	0.716171	−	0.608321i
$638$	−2.93440	+	54.1219i	−0.00459938	+	0.0848305i
$639$	114.256	+	215.510i	0.178804	+	0.337261i
$640$	23.1614	−	105.223i	0.0361896	−	0.164411i
$641$	80.9284	−	37.4415i	0.126253	−	0.0584110i	−0.355745	−	0.934583i	$-0.615773\pi$
$641$	80.9284	−	37.4415i	0.126253	−	0.0584110i	0.481999	+	0.876172i	$0.339911\pi$
$642$	27.4798	−	45.6719i	0.0428035	−	0.0711400i
$643$	442.972	−	835.533i	0.688914	−	1.29943i	−0.254262	−	0.967135i	$-0.581833\pi$
$643$	442.972	−	835.533i	0.688914	−	1.29943i	0.943176	−	0.332294i	$-0.107823\pi$
$644$	1185.99	+	1007.39i	1.84160	+	1.56427i
$645$	132.908	−	140.310i	0.206060	−	0.217534i
$646$	−0.515667	+	4.74148i	−0.000798245	+	0.00733975i
$647$	390.115	−	979.115i	0.602960	−	1.51332i	−0.237469	−	0.971395i	$-0.576318\pi$
$647$	390.115	−	979.115i	0.602960	−	1.51332i	0.840429	−	0.541921i	$-0.182303\pi$
$648$		−	10.8864i		−	0.0168000i
$649$	413.189	+	119.262i	0.636655	+	0.183763i
$650$	32.6140			0.0501753
$651$	−541.662	−	215.818i	−0.832046	−	0.331517i
$652$	−341.561	−	37.1470i	−0.523867	−	0.0569739i
$653$	830.960	+	787.127i	1.27253	+	1.20540i	0.967447	+	0.253075i	$0.0814421\pi$
$653$	830.960	+	787.127i	1.27253	+	1.20540i	0.305081	+	0.952326i	$0.401317\pi$
$654$	22.8259	−	26.8728i	0.0349020	−	0.0410898i
$655$	220.074	+	116.676i	0.335991	+	0.178131i
$656$	−122.142	−	73.4907i	−0.186193	−	0.112028i
$657$	−27.6999	−	59.8723i	−0.0421612	−	0.0911299i
$658$	−72.3719	−	15.9303i	−0.109988	−	0.0242101i
$659$	−1006.30	+	533.507i	−1.52701	+	0.809571i	−0.999208	−	0.0397951i	$-0.987329\pi$
$659$	−1006.30	+	533.507i	−1.52701	+	0.809571i	−0.527805	+	0.849366i	$0.676985\pi$
$660$	141.176	+	7.65434i	0.213903	+	0.0115975i
$661$	−537.454	−	632.740i	−0.813092	−	0.957246i	0.186590	−	0.982438i	$-0.440256\pi$
$661$	−537.454	−	632.740i	−0.813092	−	0.957246i	−0.999683	+	0.0251914i	$0.991980\pi$
$662$	5.70166	+	25.9029i	0.00861277	+	0.0391282i
$663$	45.5744	+	59.9521i	0.0687397	+	0.0904255i
$664$	−15.2702	+	14.4647i	−0.0229972	+	0.0217841i
$665$	13.6498	+	251.755i	0.0205260	+	0.378579i
$666$	−20.7198	+	12.4667i	−0.0311108	+	0.0187188i
$667$	−1616.58	−	1096.07i	−2.42366	−	1.64328i
$668$	302.616	−	1089.92i	0.453018	−	1.63162i
$669$	−325.230	+	35.3709i	−0.486143	+	0.0528712i
$670$	37.7895	+	28.7268i	0.0564022	+	0.0428758i
$671$	86.4183	+	39.9814i	0.128790	+	0.0595848i
$672$	101.722	−	68.9695i	0.151373	−	0.102633i
$673$	262.997	+	780.547i	0.390783	+	1.15980i	0.944899	+	0.327363i	$0.106160\pi$
$673$	262.997	+	780.547i	0.390783	+	1.15980i	−0.554115	+	0.832440i	$0.686943\pi$
$674$	−1.78590	−	10.8935i	−0.00264970	−	0.0161624i
$675$	−14.3507	+	87.5352i	−0.0212603	+	0.129682i
$676$	−38.6731	−	13.0305i	−0.0572087	−	0.0192759i
$677$	−167.728	−	604.101i	−0.247752	−	0.892321i	−0.977907	−	0.209040i	$-0.932966\pi$
$677$	−167.728	−	604.101i	−0.247752	−	0.892321i	0.730155	−	0.683281i	$-0.239448\pi$
$678$	−12.2963	−	30.8613i	−0.0181361	−	0.0455182i
$679$	830.500	−	330.901i	1.22312	−	0.487336i
$680$	11.3256	−	3.14455i	0.0166554	−	0.00462434i
$681$	136.961	−	406.487i	0.201118	−	0.596897i
$682$	−37.3764	−	6.12755i	−0.0548041	−	0.00898467i
$683$	−1087.21	+	178.238i	−1.59181	+	0.260964i	−0.891549	−	0.452924i	$-0.850381\pi$
$683$	−1087.21	+	178.238i	−1.59181	+	0.260964i	−0.700260	+	0.713888i	$0.746933\pi$
$684$	−103.051	+	34.7220i	−0.150660	+	0.0507631i
$685$	−305.890	−	451.154i	−0.446555	−	0.658619i
$686$	−0.933164	+	2.01700i	−0.00136030	+	0.00294024i
$687$	−240.662	+	316.585i	−0.350309	+	0.460823i
$688$	67.3701	+	619.458i	0.0979217	+	0.900375i
$689$	339.746	+	94.3300i	0.493100	+	0.136909i
$690$	16.5300	−	24.3800i	0.0239566	−	0.0353333i
$691$	102.567	+	170.468i	0.148433	+	0.246698i	0.922149	−	0.386835i	$-0.126432\pi$
$691$	102.567	+	170.468i	0.148433	+	0.246698i	−0.773716	+	0.633533i	$0.781604\pi$
$692$	141.118	−	7.65119i	0.203928	−	0.0110566i
$693$	147.732	+	155.959i	0.213178	+	0.225049i
$694$	−66.3197	+	50.4149i	−0.0955615	+	0.0726440i
$695$	−46.5300	+	10.2420i	−0.0669496	+	0.0147367i
$696$	−78.3041	+	66.5121i	−0.112506	+	0.0955634i
$697$	1.69366	−	31.2377i	0.00242993	−	0.0448174i
$698$	37.3700	+	70.4872i	0.0535386	+	0.100985i
$699$	−109.328	+	496.682i	−0.156406	+	0.710561i
$700$	−605.314	+	280.048i	−0.864735	+	0.400069i
$701$	−45.5353	+	75.6803i	−0.0649576	+	0.107960i	−0.887634	−	0.460550i	$-0.847652\pi$
$701$	−45.5353	+	75.6803i	−0.0649576	+	0.107960i	0.822676	+	0.568510i	$0.192480\pi$
$702$	4.64997	−	8.77077i	0.00662389	−	0.0124940i
$703$	369.256	+	313.649i	0.525257	+	0.446158i
$704$	−309.801	+	327.053i	−0.440059	+	0.464564i
$705$	26.2320	−	241.199i	0.0372084	−	0.342126i
$706$	29.3766	−	73.7296i	0.0416099	−	0.104433i
$707$			814.372i			1.15187i
$708$	186.705	+	360.990i	0.263707	+	0.509873i
$709$	−184.163			−0.259751			−0.129875	−	0.991530i	$-0.541458\pi$
$709$	−184.163			−0.259751			−0.129875	+	0.991530i	$0.541458\pi$
$710$	32.2513	+	12.8501i	0.0454244	+	0.0180987i
$711$	196.722	+	21.3948i	0.276684	+	0.0300912i
$712$	−82.1183	−	77.7866i	−0.115335	−	0.109251i
$713$	883.567	−	1040.22i	1.23922	−	1.45893i
$714$	7.86676	+	4.17069i	0.0110179	+	0.00584130i
$715$	221.580	+	133.320i	0.309903	+	0.186462i
$716$	−127.549	−	275.692i	−0.178141	−	0.385045i
$717$	613.400	+	135.020i	0.855509	+	0.188312i
$718$	62.7717	−	33.2794i	0.0874258	−	0.0463502i
$719$	809.889	+	43.9109i	1.12641	+	0.0610722i	0.607910	−	0.794006i	$-0.292008\pi$
$719$	809.889	+	43.9109i	1.12641	+	0.0610722i	0.518500	+	0.855078i	$0.326491\pi$
$720$	85.9949	+	101.241i	0.119437	+	0.140612i
$721$	366.421	+	1664.67i	0.508213	+	2.30883i
$722$	25.5044	+	33.5505i	0.0353247	+	0.0464688i
$723$	−168.108	+	159.241i	−0.232515	+	0.220250i
$724$	−36.0058	−	664.087i	−0.0497317	−	0.917248i
$725$	717.304	−	431.587i	0.989385	−	0.595293i
$726$	−14.7537	−	10.0033i	−0.0203220	−	0.0137786i
$727$	−261.228	+	940.857i	−0.359323	+	1.29416i	0.534281	+	0.845307i	$0.320582\pi$
$727$	−261.228	+	940.857i	−0.359323	+	1.29416i	−0.893604	+	0.448857i	$0.851831\pi$
$728$	148.837	−	16.1870i	0.204447	−	0.0222349i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	−8.52148	−	3.94246i	−0.0116733	−	0.00540062i
$731$	−113.186	+	76.7418i	−0.154837	+	0.104982i
$732$	28.7321	+	85.2739i	0.0392515	+	0.116494i
$733$	−88.2933	−	538.565i	−0.120455	−	0.734741i	−0.976123	−	0.217217i	$-0.930302\pi$
$733$	−88.2933	−	538.565i	−0.120455	−	0.734741i	0.855669	−	0.517524i	$-0.173146\pi$
$734$	−6.31761	+	38.5357i	−0.00860709	+	0.0525009i
$735$	219.576	+	73.9839i	0.298743	+	0.100658i
$736$	76.9612	+	277.189i	0.104567	+	0.376616i
$737$	−299.940	−	752.792i	−0.406974	−	1.02143i
$738$	−3.83095	+	1.52639i	−0.00519099	+	0.00206828i
$739$	198.667	−	55.1597i	0.268833	−	0.0746410i	−0.130496	−	0.991449i	$-0.541657\pi$
$739$	198.667	−	55.1597i	0.268833	−	0.0746410i	0.399329	+	0.916808i	$0.369243\pi$
$740$	190.073	−	564.115i	0.256855	−	0.762318i
$741$	−196.277	−	32.1779i	−0.264881	−	0.0434250i
$742$	41.1399	−	6.74455i	0.0554446	−	0.00908969i
$743$	−825.429	+	278.119i	−1.11094	+	0.374319i	−0.814168	−	0.580629i	$-0.802807\pi$
$743$	−825.429	+	278.119i	−1.11094	+	0.374319i	−0.296772	+	0.954948i	$0.595910\pi$
$744$	−40.2894	−	59.4225i	−0.0541525	−	0.0798689i
$745$	36.5409	−	78.9818i	0.0490482	−	0.106016i
$746$	−25.7080	+	33.8182i	−0.0344611	+	0.0453328i
$747$	−5.64015	−	51.8603i	−0.00755040	−	0.0694248i
$748$	−96.3924	−	26.7632i	−0.128867	−	0.0357797i
$749$	−1118.84	+	1650.16i	−1.49378	+	2.20315i
$750$	16.0409	+	26.6601i	0.0213878	+	0.0355468i
$751$	959.801	−	52.0389i	1.27803	−	0.0692928i	0.597414	−	0.801933i	$-0.296195\pi$
$751$	959.801	−	52.0389i	1.27803	−	0.0692928i	0.680616	+	0.732640i	$0.261712\pi$
$752$	537.946	+	567.902i	0.715353	+	0.755189i
$753$	−106.464	+	80.9318i	−0.141386	+	0.107479i
$754$	−91.4964	+	20.1399i	−0.121348	+	0.0267107i
$755$	96.1446	−	81.6660i	0.127344	−	0.108167i
$756$	−10.9908	+	202.714i	−0.0145381	+	0.268140i
$757$	106.722	+	201.298i	0.140980	+	0.265916i	0.943940	−	0.330116i	$-0.107088\pi$
$757$	106.722	+	201.298i	0.140980	+	0.265916i	−0.802961	+	0.596032i	$0.796743\pi$
$758$	−20.3861	+	92.6151i	−0.0268946	+	0.122183i
$759$	−456.365	+	211.137i	−0.601271	+	0.278178i
$760$	−16.0048	+	26.6002i	−0.0210589	+	0.0350002i
$761$	−54.6605	+	103.101i	−0.0718272	+	0.135481i	−0.916825	−	0.399289i	$-0.869257\pi$
$761$	−54.6605	+	103.101i	−0.0718272	+	0.135481i	0.844998	+	0.534770i	$0.179602\pi$
$762$	−5.22090	−	4.43467i	−0.00685157	−	0.00581978i
$763$	−906.949	+	957.454i	−1.18866	+	1.25485i
$764$	−14.1748	+	130.335i	−0.0185533	+	0.170595i
$765$	−10.7903	+	27.0815i	−0.0141049	+	0.0354007i
$766$		−	23.9034i		−	0.0312055i
$767$	−7.56275	+	743.312i	−0.00986017	+	0.969116i
$768$	−418.136			−0.544447
$769$	427.950	+	170.511i	0.556502	+	0.221731i	0.631396	−	0.775461i	$-0.282482\pi$
$769$	427.950	+	170.511i	0.556502	+	0.221731i	−0.0748935	+	0.997192i	$0.523862\pi$
$770$	30.3957	+	3.30573i	0.0394749	+	0.00429316i
$771$	57.3529	+	54.3276i	0.0743877	+	0.0704638i
$772$	482.412	−	567.939i	0.624886	−	0.735673i
$773$	−539.323	−	285.931i	−0.697701	−	0.369898i	0.0814985	−

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.g (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140866 + 0.0561262i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.88729 - 2.73499i) q^{4} +(1.82294 - 2.14613i) q^{5} +(0.232047 + 0.123023i) q^{6} +(-8.41764 - 5.06473i) q^{7} +(-0.507898 - 1.09780i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(0.140866 + 0.0561262i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-2.88729 - 2.73499i) q^{4} +(1.82294 - 2.14613i) q^{5} +(0.232047 + 0.123023i) q^{6} +(-8.41764 - 5.06473i) q^{7} +(-0.507898 - 1.09780i) q^{8} +(2.92986 + 0.644911i) q^{9} +(0.377244 - 0.200002i) q^{10} +(-7.27840 - 0.394624i) q^{11} +(-4.45944 - 5.25006i) q^{12} +(-2.70845 - 12.3046i) q^{13} +(-0.901497 - 1.18590i) q^{14} +(3.54081 - 3.35403i) q^{15} +(0.851313 + 15.7015i) q^{16} +(-2.95697 + 1.77915i) q^{17} +(0.376522 + 0.255288i) q^{18} +(2.43835 - 8.78214i) q^{19} +(-11.1330 + 1.21078i) q^{20} +(-13.5459 - 10.2973i) q^{21} +(-1.00313 - 0.464098i) q^{22} +(32.9657 - 22.3513i) q^{23} +(-0.668965 - 1.98542i) q^{24} +(2.76179 + 16.8462i) q^{25} +(0.309082 - 1.88532i) q^{26} +(4.92415 + 1.65914i) q^{27} +(10.4522 + 37.6454i) q^{28} +(-18.1509 - 45.5554i) q^{29} +(0.687030 - 0.273738i) q^{30} +(33.0183 - 9.16750i) q^{31} +(-2.30626 + 6.84473i) q^{32} +(-12.4588 - 2.04251i) q^{33} +(-0.516395 + 0.0846586i) q^{34} +(-26.2144 + 8.83265i) q^{35} +(-6.69553 - 9.87517i) q^{36} +(-22.3197 + 48.2433i) q^{37} +(0.836389 - 1.10025i) q^{38} +(-2.35941 - 21.6945i) q^{39} +(-3.28189 - 0.911213i) q^{40} +(-5.08728 + 7.50318i) q^{41} +(-1.33021 - 2.21082i) q^{42} +(39.5683 - 2.14533i) q^{43} +(19.9356 + 21.0457i) q^{44} +(6.72501 - 5.11222i) q^{45} +(5.89825 - 1.29830i) q^{46} +(37.9147 - 32.2050i) q^{47} +(-1.47452 + 27.1959i) q^{48} +(22.2532 + 41.9740i) q^{49} +(-0.556469 + 2.52806i) q^{50} +(-5.42478 + 2.50977i) q^{51} +(-25.8328 + 42.9345i) q^{52} +(-13.1088 + 24.7259i) q^{53} +(0.600525 + 0.510091i) q^{54} +(-14.1150 + 14.9010i) q^{55} +(-1.28477 + 11.8133i) q^{56} +(5.84320 - 14.6653i) q^{57} -7.43595i q^{58} +(-57.4886 - 13.2688i) q^{59} -19.3966 q^{60} +(-12.1354 - 4.83519i) q^{61} +(5.16570 + 0.561804i) q^{62} +(-21.3962 - 20.2676i) q^{63} +(40.0105 - 47.1040i) q^{64} +(-31.3445 - 16.6178i) q^{65} +(-1.64038 - 0.986984i) q^{66} +(46.6801 + 100.897i) q^{67} +(13.4036 + 2.95035i) q^{68} +(60.9492 - 32.3132i) q^{69} +(-4.18846 - 0.227092i) q^{70} +(52.6376 + 61.9698i) q^{71} +(-0.780085 - 3.54396i) q^{72} +(-13.3077 - 17.5060i) q^{73} +(-5.85181 + 5.54313i) q^{74} +(1.60077 + 29.5246i) q^{75} +(-31.0592 + 18.6877i) q^{76} +(59.2683 + 40.1849i) q^{77} +(0.885266 - 3.18844i) q^{78} +(65.5741 - 7.13161i) q^{79} +(35.2494 + 26.7959i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-1.13775 + 0.771415i) q^{82} +(-5.55224 - 16.4785i) q^{83} +(10.9479 + 66.7790i) q^{84} +(-1.57209 + 9.58931i) q^{85} +(5.69425 + 1.91862i) q^{86} +(-22.7230 - 81.8407i) q^{87} +(3.26347 + 8.19069i) q^{88} +(86.8699 - 34.6121i) q^{89} +(1.23426 - 0.342690i) q^{90} +(-39.5207 + 117.293i) q^{91} +(-156.312 - 25.6261i) q^{92} +(58.5710 - 9.60222i) q^{93} +(7.14844 - 2.40859i) q^{94} +(-14.4026 - 21.2423i) q^{95} +(-5.25293 + 11.3540i) q^{96} +(-55.0723 + 72.4464i) q^{97} +(0.778882 + 7.16170i) q^{98} +(-21.0702 - 5.85012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + O(q^{10}) \)	\( 560q + 40q^{4} + 8q^{7} - 60q^{9} + 24q^{12} - 24q^{15} + 8q^{16} - 16q^{17} + 60q^{19} + 164q^{20} - 40q^{22} - 100q^{25} + 156q^{26} - 200q^{28} + 60q^{29} + 32q^{35} + 120q^{36} - 28q^{41} - 1572q^{46} - 638q^{47} + 96q^{48} - 1328q^{49} - 1856q^{50} + 24q^{51} - 1392q^{52} - 572q^{53} - 522q^{55} - 928q^{56} - 24q^{57} + 268q^{59} + 72q^{60} + 348q^{61} + 472q^{62} + 24q^{63} + 2580q^{64} + 1218q^{65} + 120q^{66} + 1044q^{67} + 1936q^{68} + 2784q^{70} + 1416q^{71} + 870q^{73} + 1752q^{74} - 240q^{75} - 120q^{76} + 468q^{78} + 420q^{79} - 376q^{80} - 180q^{81} - 168q^{84} + 348q^{85} - 232q^{86} - 144q^{87} + 212q^{88} - 152q^{94} - 788q^{95} - 3306q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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