LMFDB - Embedded newform 177.3.g.a.10.8

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			10.8
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.8

$q$-expansion

$f(q)$	$=$	$q+(-1.45950 - 0.581520i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-1.11199 - 1.05334i) q^{4} +(-2.61612 + 3.07994i) q^{5} +(-2.40422 - 1.27464i) q^{6} +(-1.72503 - 1.03791i) q^{7} +(3.64916 + 7.88752i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(-1.45950 - 0.581520i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-1.11199 - 1.05334i) q^{4} +(-2.61612 + 3.07994i) q^{5} +(-2.40422 - 1.27464i) q^{6} +(-1.72503 - 1.03791i) q^{7} +(3.64916 + 7.88752i) q^{8} +(2.92986 + 0.644911i) q^{9} +(5.60928 - 2.97385i) q^{10} +(20.6277 + 1.11840i) q^{11} +(-1.71748 - 2.02198i) q^{12} +(1.53510 + 6.97403i) q^{13} +(1.91412 + 2.51798i) q^{14} +(-5.08146 + 4.81342i) q^{15} +(-0.407516 - 7.51619i) q^{16} +(6.88982 - 4.14547i) q^{17} +(-3.90112 - 2.64502i) q^{18} +(-2.17048 + 7.81737i) q^{19} +(6.15332 - 0.669214i) q^{20} +(-2.77595 - 2.11022i) q^{21} +(-29.4558 - 13.6277i) q^{22} +(23.1399 - 15.6893i) q^{23} +(4.80639 + 14.2649i) q^{24} +(1.40263 + 8.55569i) q^{25} +(1.81505 - 11.0713i) q^{26} +(4.92415 + 1.65914i) q^{27} +(0.824947 + 2.97119i) q^{28} +(15.4520 + 38.7815i) q^{29} +(10.2155 - 4.07023i) q^{30} +(2.83849 - 0.788103i) q^{31} +(7.32385 - 21.7364i) q^{32} +(35.3093 + 5.78867i) q^{33} +(-12.4664 + 2.04376i) q^{34} +(7.70959 - 2.59766i) q^{35} +(-2.57868 - 3.80327i) q^{36} +(3.58245 - 7.74334i) q^{37} +(7.71378 - 10.1473i) q^{38} +(1.33727 + 12.2960i) q^{39} +(-33.8397 - 9.39554i) q^{40} +(-13.3440 + 19.6810i) q^{41} +(2.82438 + 4.69415i) q^{42} +(19.6128 - 1.06338i) q^{43} +(-21.7598 - 22.9716i) q^{44} +(-9.65116 + 7.33662i) q^{45} +(-42.8964 + 9.44222i) q^{46} +(-1.59298 + 1.35309i) q^{47} +(0.705838 - 13.0184i) q^{48} +(-21.0536 - 39.7112i) q^{49} +(2.92815 - 13.3027i) q^{50} +(12.6399 - 5.84783i) q^{51} +(5.63898 - 9.37206i) q^{52} +(-33.9932 + 64.1180i) q^{53} +(-6.22200 - 5.28501i) q^{54} +(-57.4091 + 60.6061i) q^{55} +(1.89168 - 17.3937i) q^{56} +(-5.20129 + 13.0542i) q^{57} -65.5874i q^{58} +(24.8967 + 53.4898i) q^{59} +10.7207 q^{60} +(-76.4249 - 30.4505i) q^{61} +(-4.60109 - 0.500398i) q^{62} +(-4.38473 - 4.15344i) q^{63} +(-42.8214 + 50.4133i) q^{64} +(-25.4956 - 13.5169i) q^{65} +(-48.1679 - 28.9817i) q^{66} +(-17.7291 - 38.3208i) q^{67} +(-12.0280 - 2.64756i) q^{68} +(42.7827 - 22.6819i) q^{69} +(-12.7628 - 0.691977i) q^{70} +(-63.6327 - 74.9142i) q^{71} +(5.60477 + 25.4627i) q^{72} +(-27.6076 - 36.3171i) q^{73} +(-9.73151 + 9.21818i) q^{74} +(0.812988 + 14.9947i) q^{75} +(10.6479 - 6.40662i) q^{76} +(-34.4225 - 23.3390i) q^{77} +(5.19863 - 18.7238i) q^{78} +(36.6316 - 3.98393i) q^{79} +(24.2155 + 18.4081i) q^{80} +(8.16818 + 3.77900i) q^{81} +(30.9206 - 20.9647i) q^{82} +(16.4242 + 48.7452i) q^{83} +(0.864066 + 5.27057i) q^{84} +(-5.25683 + 32.0652i) q^{85} +(-29.2434 - 9.85325i) q^{86} +(19.3442 + 69.6714i) q^{87} +(66.4522 + 166.783i) q^{88} +(35.0851 - 13.9792i) q^{89} +(18.3523 - 5.09549i) q^{90} +(4.59036 - 13.6237i) q^{91} +(-42.2575 - 6.92777i) q^{92} +(5.03517 - 0.825475i) q^{93} +(3.11181 - 1.04849i) q^{94} +(-18.3987 - 27.1361i) q^{95} +(16.6815 - 36.0564i) q^{96} +(74.8346 - 98.4432i) q^{97} +(7.63490 + 70.2018i) q^{98} +(59.7150 + 16.5798i) 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 $

$2$	−1.45950	−	0.581520i	−0.729752	−	0.290760i	−0.0244838	−	0.999700i	$-0.507794\pi$
$2$	−1.45950	−	0.581520i	−0.729752	−	0.290760i	−0.705268	+	0.708940i	$0.749174\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	−1.11199	−	1.05334i	−0.277998	−	0.263334i
$5$	−2.61612	+	3.07994i	−0.523224	+	0.615987i	−0.958771	−	0.284179i	$-0.908279\pi$
$5$	−2.61612	+	3.07994i	−0.523224	+	0.615987i	0.435547	+	0.900166i	$0.356555\pi$
$6$	−2.40422	−	1.27464i	−0.400703	−	0.212439i
$7$	−1.72503	−	1.03791i	−0.246432	−	0.148273i	0.386979	−	0.922088i	$-0.373518\pi$
$7$	−1.72503	−	1.03791i	−0.246432	−	0.148273i	−0.633412	+	0.773815i	$0.718346\pi$
$8$	3.64916	+	7.88752i	0.456144	+	0.985940i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	5.60928	−	2.97385i	0.560928	−	0.297385i
$11$	20.6277	+	1.11840i	1.87524	+	0.101673i	0.956242	−	0.292578i	$-0.0945132\pi$
$11$	20.6277	+	1.11840i	1.87524	+	0.101673i	0.919003	+	0.394251i	$0.128996\pi$
$12$	−1.71748	−	2.02198i	−0.143124	−	0.168498i
$13$	1.53510	+	6.97403i	0.118085	+	0.536464i	0.998105	+	0.0615285i	$0.0195975\pi$
$13$	1.53510	+	6.97403i	0.118085	+	0.536464i	−0.880021	+	0.474935i	$0.842471\pi$
$14$	1.91412	+	2.51798i	0.136723	+	0.179856i
$15$	−5.08146	+	4.81342i	−0.338764	+	0.320895i
$16$	−0.407516	−	7.51619i	−0.0254697	−	0.469762i
$17$	6.88982	−	4.14547i	0.405283	−	0.243851i	−0.298287	−	0.954476i	$-0.596415\pi$
$17$	6.88982	−	4.14547i	0.405283	−	0.243851i	0.703571	+	0.710625i	$0.251588\pi$
$18$	−3.90112	−	2.64502i	−0.216729	−	0.146946i
$19$	−2.17048	+	7.81737i	−0.114236	+	0.411440i	−0.998451	−	0.0556396i	$-0.982280\pi$
$19$	−2.17048	+	7.81737i	−0.114236	+	0.411440i	0.884215	+	0.467080i	$0.154694\pi$
$20$	6.15332	−	0.669214i	0.307666	−	0.0334607i
$21$	−2.77595	−	2.11022i	−0.132188	−	0.100487i
$22$	−29.4558	−	13.6277i	−1.33890	−	0.619442i
$23$	23.1399	−	15.6893i	1.00608	−	0.682142i	0.0573946	−	0.998352i	$-0.481721\pi$
$23$	23.1399	−	15.6893i	1.00608	−	0.682142i	0.948689	+	0.316210i	$0.102410\pi$
$24$	4.80639	+	14.2649i	0.200266	+	0.594370i
$25$	1.40263	+	8.55569i	0.0561054	+	0.342228i
$26$	1.81505	−	11.0713i	0.0698096	−	0.425820i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	0.824947	+	2.97119i	0.0294624	+	0.106114i
$29$	15.4520	+	38.7815i	0.532826	+	1.33729i	0.911324	+	0.411690i	$0.135061\pi$
$29$	15.4520	+	38.7815i	0.532826	+	1.33729i	−0.378498	+	0.925602i	$0.623559\pi$
$30$	10.2155	−	4.07023i	0.340517	−	0.135674i
$31$	2.83849	−	0.788103i	0.0915642	−	0.0254227i	−0.221444	−	0.975173i	$-0.571077\pi$
$31$	2.83849	−	0.788103i	0.0915642	−	0.0254227i	0.313008	+	0.949750i	$0.398663\pi$
$32$	7.32385	−	21.7364i	0.228870	−	0.679263i
$33$	35.3093	+	5.78867i	1.06998	+	0.175414i
$34$	−12.4664	+	2.04376i	−0.366658	+	0.0601106i
$35$	7.70959	−	2.59766i	0.220274	−	0.0742190i
$36$	−2.57868	−	3.80327i	−0.0716300	−	0.105646i
$37$	3.58245	−	7.74334i	0.0968230	−	0.209280i	−0.853111	−	0.521729i	$-0.825287\pi$
$37$	3.58245	−	7.74334i	0.0968230	−	0.209280i	0.949934	+	0.312449i	$0.101149\pi$
$38$	7.71378	−	10.1473i	0.202994	−	0.267034i
$39$	1.33727	+	12.2960i	0.0342891	+	0.315283i
$40$	−33.8397	−	9.39554i	−0.845992	−	0.234889i
$41$	−13.3440	+	19.6810i	−0.325465	+	0.480024i	−0.954858	−	0.297062i	$-0.903993\pi$
$41$	−13.3440	+	19.6810i	−0.325465	+	0.480024i	0.629394	+	0.777087i	$0.283303\pi$
$42$	2.82438	+	4.69415i	0.0672471	+	0.111766i
$43$	19.6128	−	1.06338i	0.456113	−	0.0247297i	0.175348	−	0.984506i	$-0.443895\pi$
$43$	19.6128	−	1.06338i	0.456113	−	0.0247297i	0.280764	+	0.959777i	$0.409412\pi$
$44$	−21.7598	−	22.9716i	−0.494541	−	0.522081i
$45$	−9.65116	+	7.33662i	−0.214470	+	0.163036i
$46$	−42.8964	+	9.44222i	−0.932531	+	0.205266i
$47$	−1.59298	+	1.35309i	−0.0338932	+	0.0287891i	−0.664173	−	0.747579i	$-0.731216\pi$
$47$	−1.59298	+	1.35309i	−0.0338932	+	0.0287891i	0.630280	+	0.776368i	$0.282940\pi$
$48$	0.705838	−	13.0184i	0.0147050	−	0.271217i
$49$	−21.0536	−	39.7112i	−0.429665	−	0.810433i
$50$	2.92815	−	13.3027i	0.0585630	−	0.266055i
$51$	12.6399	−	5.84783i	0.247841	−	0.114663i
$52$	5.63898	−	9.37206i	0.108442	−	0.180232i
$53$	−33.9932	+	64.1180i	−0.641381	+	1.20977i	0.323286	+	0.946301i	$0.395212\pi$
$53$	−33.9932	+	64.1180i	−0.641381	+	1.20977i	−0.964667	+	0.263471i	$0.915133\pi$
$54$	−6.22200	−	5.28501i	−0.115222	−	0.0978706i
$55$	−57.4091	+	60.6061i	−1.04380	+	1.10193i
$56$	1.89168	−	17.3937i	0.0337800	−	0.310602i
$57$	−5.20129	+	13.0542i	−0.0912506	+	0.229022i
$58$		−	65.5874i		−	1.13082i
$59$	24.8967	+	53.4898i	0.421977	+	0.906606i
$59$	24.8967	+	53.4898i	0.421977	+	0.906606i
$60$	10.7207			0.178678
$61$	−76.4249	−	30.4505i	−1.25287	−	0.499188i	−0.353111	−	0.935581i	$-0.614876\pi$
$61$	−76.4249	−	30.4505i	−1.25287	−	0.499188i	−0.899756	+	0.436393i	$0.856256\pi$
$62$	−4.60109	−	0.500398i	−0.0742111	−	0.00807094i
$63$	−4.38473	−	4.15344i	−0.0695989	−	0.0659275i
$64$	−42.8214	+	50.4133i	−0.669085	+	0.787708i
$65$	−25.4956	−	13.5169i	−0.392240	−	0.207952i
$66$	−48.1679	−	28.9817i	−0.729816	−	0.439116i
$67$	−17.7291	−	38.3208i	−0.264613	−	0.571952i	0.729036	−	0.684475i	$-0.239969\pi$
$67$	−17.7291	−	38.3208i	−0.264613	−	0.571952i	−0.993649	+	0.112524i	$0.964107\pi$
$68$	−12.0280	−	2.64756i	−0.176882	−	0.0389348i
$69$	42.7827	−	22.6819i	0.620039	−	0.328724i
$70$	−12.7628	−	0.691977i	−0.182325	−	0.00988539i
$71$	−63.6327	−	74.9142i	−0.896235	−	1.05513i	−0.998178	−	0.0603392i	$-0.980782\pi$
$71$	−63.6327	−	74.9142i	−0.896235	−	1.05513i	0.101943	−	0.994790i	$-0.467494\pi$
$72$	5.60477	+	25.4627i	0.0778440	+	0.353649i
$73$	−27.6076	−	36.3171i	−0.378186	−	0.497495i	0.567141	−	0.823621i	$-0.308050\pi$
$73$	−27.6076	−	36.3171i	−0.378186	−	0.497495i	−0.945326	+	0.326126i	$0.894257\pi$
$74$	−9.73151	+	9.21818i	−0.131507	+	0.124570i
$75$	0.812988	+	14.9947i	0.0108398	+	0.199929i
$76$	10.6479	−	6.40662i	0.140104	−	0.0842976i
$77$	−34.4225	−	23.3390i	−0.447046	−	0.303105i
$78$	5.19863	−	18.7238i	0.0666491	−	0.240048i
$79$	36.6316	−	3.98393i	0.463691	−	0.0504295i	0.126708	−	0.991940i	$-0.459559\pi$
$79$	36.6316	−	3.98393i	0.463691	−	0.0504295i	0.336983	+	0.941511i	$0.390593\pi$
$80$	24.2155	+	18.4081i	0.302694	+	0.230102i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	30.9206	−	20.9647i	0.377080	−	0.255667i
$83$	16.4242	+	48.7452i	0.197881	+	0.587291i	0.999951	−	0.00993995i	$-0.00316404\pi$
$83$	16.4242	+	48.7452i	0.197881	+	0.587291i	−0.802069	+	0.597231i	$0.796267\pi$
$84$	0.864066	+	5.27057i	0.0102865	+	0.0627449i
$85$	−5.25683	+	32.0652i	−0.0618450	+	0.377238i
$86$	−29.2434	−	9.85325i	−0.340040	−	0.114573i
$87$	19.3442	+	69.6714i	0.222347	+	0.800820i
$88$	66.4522	+	166.783i	0.755139	+	1.89526i
$89$	35.0851	−	13.9792i	0.394215	−	0.157069i	−0.164603	−	0.986360i	$-0.552634\pi$
$89$	35.0851	−	13.9792i	0.394215	−	0.157069i	0.558818	+	0.829290i	$0.311255\pi$
$90$	18.3523	−	5.09549i	0.203914	−	0.0566166i
$91$	4.59036	−	13.6237i	0.0504435	−	0.149711i
$92$	−42.2575	−	6.92777i	−0.459321	−	0.0753019i
$93$	5.03517	−	0.825475i	0.0541417	−	0.00887608i
$94$	3.11181	−	1.04849i	0.0331043	−	0.0111541i
$95$	−18.3987	−	27.1361i	−0.193671	−	0.285643i
$96$	16.6815	−	36.0564i	0.173765	−	0.375587i
$97$	74.8346	−	98.4432i	0.771491	−	1.01488i	−0.227663	−	0.973740i	$-0.573108\pi$
$97$	74.8346	−	98.4432i	0.771491	−	1.01488i	0.999153	−	0.0411387i	$-0.0130985\pi$
$98$	7.63490	+	70.2018i	0.0779072	+	0.716345i
$99$	59.7150	+	16.5798i	0.603182	+	0.167473i
$100$	7.45230	−	10.9913i	0.0745230	−	0.109913i
$101$	93.7819	+	155.867i	0.928534	+	1.54323i	0.836840	+	0.547448i	$0.184400\pi$
$101$	93.7819	+	155.867i	0.928534	+	1.54323i	0.0916937	+	0.995787i	$0.470772\pi$
$102$	−21.8486	+	1.18460i	−0.214202	+	0.0116137i
$103$	32.9985	+	34.8361i	0.320373	+	0.338214i	0.866212	−	0.499676i	$-0.166548\pi$
$103$	32.9985	+	34.8361i	0.320373	+	0.338214i	−0.545839	+	0.837890i	$0.683789\pi$
$104$	−49.4060	+	37.5575i	−0.475058	+	0.361129i
$105$	13.7616	−	3.02915i	0.131063	−	0.0288491i
$106$	86.8991	−	73.8127i	0.819802	−	0.696346i
$107$	7.96589	−	146.922i	0.0744476	−	1.37310i	−0.687838	−	0.725864i	$-0.741440\pi$
$107$	7.96589	−	146.922i	0.0744476	−	1.37310i	0.762286	−	0.647240i	$-0.224077\pi$
$108$	−3.72799	−	7.03174i	−0.0345185	−	0.0651087i
$109$	10.4589	−	47.5153i	0.0959533	−	0.435920i	−0.904011	−	0.427509i	$-0.859391\pi$
$109$	10.4589	−	47.5153i	0.0959533	−	0.435920i	0.999965	−	0.00841181i	$-0.00267759\pi$
$110$	119.033	−	55.0703i	1.08211	−	0.500639i
$111$	7.61869	−	12.6624i	0.0686369	−	0.114075i
$112$	−7.09818	+	13.3886i	−0.0633766	+	0.119541i
$113$	14.8444	+	12.6090i	0.131367	+	0.111584i	0.710661	−	0.703535i	$-0.248396\pi$
$113$	14.8444	+	12.6090i	0.131367	+	0.111584i	−0.579294	+	0.815118i	$0.696672\pi$
$114$	15.1826	−	16.0281i	0.133181	−	0.140597i
$115$	−12.2149	+	112.315i	−0.106217	+	0.976648i
$116$	23.6675	−	59.4009i	0.204030	−	0.512077i
$117$			21.4229i			0.183102i
$118$	−5.23144	−	92.5465i	−0.0443342	−	0.784292i
$119$	−16.1878			−0.136032
$120$	−56.5090	−	22.5152i	−0.470908	−	0.187627i
$121$	303.960	+	33.0576i	2.51207	+	0.273204i
$122$	93.8349	+	88.8852i	0.769139	+	0.728567i
$123$	−26.6627	+	31.3897i	−0.216770	+	0.255201i
$124$	−3.98652	−	2.11352i	−0.0321494	−	0.0170445i
$125$	−116.586	−	70.1472i	−0.932684	−	0.561178i
$126$	3.98423	+	8.61176i	0.0316208	+	0.0683473i
$127$	−30.7718	−	6.77339i	−0.242298	−	0.0533338i	0.0921611	−	0.995744i	$-0.470623\pi$
$127$	−30.7718	−	6.77339i	−0.242298	−	0.0533338i	−0.334459	+	0.942410i	$0.608554\pi$
$128$	10.7536	−	5.70118i	0.0840123	−	0.0445405i
$129$	33.9705	+	1.84182i	0.263337	+	0.0142777i
$130$	29.3506	+	34.5542i	0.225774	+	0.265801i
$131$	−4.16884	−	18.9392i	−0.0318232	−	0.144574i	0.958030	−	0.286668i	$-0.0925476\pi$
$131$	−4.16884	−	18.9392i	−0.0318232	−	0.144574i	−0.989853	+	0.142094i	$0.954617\pi$
$132$	−33.1663	−	43.6296i	−0.251260	−	0.330527i
$133$	11.8579	−	11.2324i	0.0891571	−	0.0844541i
$134$	3.59138	+	66.2391i	0.0268014	+	0.494322i
$135$	−17.9922	+	10.8256i	−0.133276	+	0.0801893i
$136$	57.8395	+	39.2161i	0.425290	+	0.288354i
$137$	66.8643	−	240.823i	0.488060	−	1.75783i	−0.150853	−	0.988556i	$-0.548202\pi$
$137$	66.8643	−	240.823i	0.488060	−	1.75783i	0.638913	−	0.769279i	$-0.279384\pi$
$138$	−75.6315	+	8.22542i	−0.548054	+	0.0596045i
$139$	129.095	+	98.1352i	0.928738	+	0.706008i	0.955922	−	0.293622i	$-0.0948608\pi$
$139$	129.095	+	98.1352i	0.928738	+	0.706008i	−0.0271835	+	0.999630i	$0.508654\pi$
$140$	−11.3092	−	5.23221i	−0.0807802	−	0.0373729i
$141$	−2.99634	+	2.03157i	−0.0212506	+	0.0144083i
$142$	49.3081	+	146.341i	0.347240	+	1.03057i
$143$	23.8658	+	145.575i	0.166894	+	1.01801i
$144$	3.65331	−	22.2842i	0.0253702	−	0.154751i
$145$	−159.869	−	53.8660i	−1.10254	−	0.371490i
$146$	19.1742	+	69.0593i	0.131330	+	0.473009i
$147$	−28.8154	−	72.3213i	−0.196023	−	0.491982i
$148$	−12.1400	+	4.83702i	−0.0820271	+	0.0326826i
$149$	−231.551	+	64.2897i	−1.55403	+	0.431474i	−0.935220	−	0.354066i	$-0.884799\pi$
$149$	−231.551	+	64.2897i	−1.55403	+	0.431474i	−0.618810	+	0.785541i	$0.712385\pi$
$150$	7.53315	−	22.3576i	0.0502210	−	0.149051i
$151$	−263.522	−	43.2022i	−1.74518	−	0.286107i	−0.797030	−	0.603940i	$-0.793597\pi$
$151$	−263.522	−	43.2022i	−1.74518	−	0.286107i	−0.948147	+	0.317833i	$0.897045\pi$
$152$	−69.5801	+	11.4071i	−0.457764	+	0.0750465i
$153$	22.8597	−	7.70232i	0.149410	−	0.0503420i
$154$	36.6677	+	54.0808i	0.238102	+	0.351174i
$155$	−4.99853	+	10.8041i	−0.0322486	+	0.0697041i
$156$	11.4648	−	15.0817i	0.0734925	−	0.0966777i
$157$	11.2860	+	103.773i	0.0718853	+	0.660974i	0.973540	+	0.228517i	$0.0733877\pi$
$157$	11.2860	+	103.773i	0.0718853	+	0.660974i	−0.901655	+	0.432457i	$0.857647\pi$
$158$	−55.7807	−	15.4874i	−0.353043	−	0.0980218i
$159$	−70.5400	+	104.039i	−0.443648	+	0.654332i
$160$	47.7867	+	79.4221i	0.298667	+	0.496388i
$161$	−56.2011	+	3.04714i	−0.349075	+	0.0189263i
$162$	−9.72393	−	10.2654i	−0.0600243	−	0.0633668i
$163$	−102.030	+	77.5608i	−0.625948	+	0.475833i	−0.869419	−	0.494075i	$-0.835507\pi$
$163$	−102.030	+	77.5608i	−0.625948	+	0.475833i	0.243471	+	0.969908i	$0.421714\pi$
$164$	35.5692	−	7.82938i	0.216885	−	0.0477401i
$165$	−110.202	+	93.6066i	−0.667892	+	0.567313i
$166$	4.37514	−	80.6948i	0.0263563	−	0.486113i
$167$	−39.3970	−	74.3106i	−0.235910	−	0.444974i	0.737085	−	0.675800i	$-0.236202\pi$
$167$	−39.3970	−	74.3106i	−0.235910	−	0.444974i	−0.972995	+	0.230827i	$0.925857\pi$
$168$	6.51455	−	29.5959i	0.0387771	−	0.176166i
$169$	107.100	−	49.5496i	0.633726	−	0.293193i
$170$	26.3189	−	43.7424i	0.154817	−	0.257308i
$171$	−11.4007	+	21.5040i	−0.0666709	+	0.125755i
$172$	−22.9295	−	19.4765i	−0.133311	−	0.113235i
$173$	156.663	−	165.387i	0.905564	−	0.955993i	−0.0936508	−	0.995605i	$-0.529854\pi$
$173$	156.663	−	165.387i	0.905564	−	0.955993i	0.999215	+	0.0396125i	$0.0126123\pi$
$174$	12.2824	−	112.935i	0.0705884	−	0.649050i
$175$	6.46049	−	16.2146i	0.0369171	−	0.0926549i
$176$		−	155.497i		−	0.883507i
$177$	32.8526	+	96.7662i	0.185608	+	0.546702i
$178$	−59.3360			−0.333349
$179$	55.8243	+	22.2424i	0.311867	+	0.124259i	0.520820	−	0.853666i	$-0.325626\pi$
$179$	55.8243	+	22.2424i	0.311867	+	0.124259i	−0.208953	+	0.977926i	$0.567005\pi$
$180$	18.4600	+	2.00764i	0.102555	+	0.0111536i
$181$	−210.726	−	199.610i	−1.16423	−	1.10282i	−0.993064	−	0.117576i	$-0.962488\pi$
$181$	−210.726	−	199.610i	−1.16423	−	1.10282i	−0.171167	−	0.985242i	$-0.554754\pi$
$182$	−14.6221	+	17.2145i	−0.0803412	+	0.0945849i
$183$	−125.893	−	66.7445i	−0.687942	−	0.364724i
$184$	208.191	+	125.264i	1.13147	+	0.680783i
$185$	14.4769	+	31.2912i	0.0782534	+	0.169142i
$186$	−7.82889	−	1.72327i	−0.0420908	−	0.00926489i
$187$	146.757	−	77.8058i	0.784798	−	0.416074i
$188$	3.19664	+	0.173317i	0.0170034	+	0.000921898i
$189$	−6.77225	−	7.97291i	−0.0358320	−	0.0421847i
$190$	11.0729	+	50.3045i	0.0582782	+	0.264761i
$191$	116.344	+	153.048i	0.609131	+	0.801298i	0.992493	−	0.122300i	$-0.0390271\pi$
$191$	116.344	+	153.048i	0.609131	+	0.801298i	−0.383362	+	0.923598i	$0.625234\pi$
$192$	−83.1749	+	78.7875i	−0.433203	+	0.410351i
$193$	−2.37844	−	43.8677i	−0.0123235	−	0.227294i	−0.998207	−	0.0598598i	$-0.980935\pi$
$193$	−2.37844	−	43.8677i	−0.0123235	−	0.227294i	0.985883	−	0.167434i	$-0.0535481\pi$
$194$	−166.468	+	100.161i	−0.858083	+	0.516291i
$195$	−41.3695	−	28.0492i	−0.212151	−	0.143842i
$196$	−18.4179	+	66.3351i	−0.0939687	+	0.338445i
$197$	71.2864	−	7.75287i	0.361860	−	0.0393547i	0.0746167	−	0.997212i	$-0.476227\pi$
$197$	71.2864	−	7.75287i	0.361860	−	0.0393547i	0.287243	+	0.957858i	$0.407261\pi$
$198$	−77.5128	−	58.9237i	−0.391479	−	0.297595i
$199$	−15.0353	−	6.95609i	−0.0755545	−	0.0349552i	0.381748	−	0.924266i	$-0.375322\pi$
$199$	−15.0353	−	6.95609i	−0.0755545	−	0.0349552i	−0.457302	+	0.889311i	$0.651184\pi$
$200$	−62.3648	+	42.2844i	−0.311824	+	0.211422i
$201$	−23.3514	−	69.3045i	−0.116176	−	0.344799i
$202$	−46.2355	−	282.024i	−0.228889	−	1.39616i
$203$	13.5968	−	82.9369i	0.0669794	−	0.408556i
$204$	−20.2152	−	6.81129i	−0.0990941	−	0.0333887i
$205$	−25.7066	−	92.5867i	−0.125398	−	0.451642i
$206$	−27.9036	−	70.0326i	−0.135454	−	0.339964i
$207$	77.9150	−	31.0442i	0.376401	−	0.149972i
$208$	51.7925	−	14.3801i	0.249003	−	0.0691352i
$209$	−53.5150	+	158.827i	−0.256052	+	0.759937i
$210$	−21.8466	−	3.58157i	−0.104031	−	0.0170551i
$211$	102.214	−	16.7571i	0.484426	−	0.0794176i	0.0853800	−	0.996348i	$-0.472790\pi$
$211$	102.214	−	16.7571i	0.484426	−	0.0794176i	0.399046	+	0.916931i	$0.369341\pi$
$212$	105.338	−	35.4925i	0.496877	−	0.167417i
$213$	−95.5400	−	140.911i	−0.448544	−	0.661553i
$214$	−97.0644	+	209.801i	−0.453572	+	0.980380i
$215$	−48.0345	+	63.1882i	−0.223416	+	0.293899i
$216$	4.88249	+	44.8938i	0.0226041	+	0.207842i
$217$	−5.71446	−	1.58661i	−0.0263339	−	0.00731157i
$218$	−42.8959	+	63.2668i	−0.196770	+	0.290215i
$219$	−40.7364	−	67.7043i	−0.186011	−	0.309152i
$220$	127.677	−	6.92246i	0.580351	−	0.0314657i
$221$	39.4872	+	41.6861i	0.178675	+	0.188625i
$222$	−18.4829	+	14.0504i	−0.0832564	+	0.0632899i
$223$	−88.9950	+	19.5893i	−0.399081	+	0.0878443i	−0.409976	−	0.912096i	$-0.634463\pi$
$223$	−88.9950	+	19.5893i	−0.399081	+	0.0878443i	0.0108953	+	0.999941i	$0.496532\pi$
$224$	−35.1944	+	29.8944i	−0.157118	+	0.133457i
$225$	−1.40814	+	25.9716i	−0.00625839	+	0.115429i
$226$	−14.3331	−	27.0352i	−0.0634210	−	0.119625i
$227$	−39.9474	+	181.483i	−0.175980	+	0.799483i	0.803074	+	0.595879i	$0.203196\pi$
$227$	−39.9474	+	181.483i	−0.175980	+	0.799483i	−0.979053	+	0.203604i	$0.934735\pi$
$228$	19.5343	−	9.03753i	0.0856768	−	0.0396383i
$229$	−102.453	+	170.278i	−0.447392	+	0.743571i	−0.995693	−	0.0927097i	$-0.970447\pi$
$229$	−102.453	+	170.278i	−0.447392	+	0.743571i	0.548301	+	0.836281i	$0.315275\pi$
$230$	83.1409	−	156.820i	0.361482	−	0.681827i
$231$	−54.9014	−	46.6337i	−0.237668	−	0.201877i
$232$	−249.503	+	263.397i	−1.07544	+	1.13533i
$233$	21.4096	−	196.858i	0.0918866	−	0.844884i	−0.853975	−	0.520314i	$-0.825815\pi$
$233$	21.4096	−	196.858i	0.0918866	−	0.844884i	0.945862	−	0.324570i	$-0.105220\pi$
$234$	12.4579	−	31.2669i	0.0532387	−	0.133619i
$235$		−	8.44611i		−	0.0359409i
$236$	28.6578	−	85.7049i	0.121431	−	0.363156i
$237$	63.8220			0.269291
$238$	23.6261	+	9.41350i	0.0992694	+	0.0395525i
$239$	255.608	+	27.7990i	1.06949	+	0.116314i	0.625890	−	0.779912i	$-0.284736\pi$
$239$	255.608	+	27.7990i	1.06949	+	0.116314i	0.443599	+	0.896225i	$0.353702\pi$
$240$	38.2493	+	36.2317i	0.159372	+	0.150965i
$241$	197.155	−	232.109i	0.818073	−	0.963109i	−0.181723	−	0.983350i	$-0.558167\pi$
$241$	197.155	−	232.109i	0.818073	−	0.963109i	0.999795	+	0.0202404i	$0.00644315\pi$
$242$	−424.407	−	225.007i	−1.75375	−	0.929779i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	52.9094	+	114.362i	0.216842	+	0.468696i
$245$	177.387	+	39.0458i	0.724027	+	0.159370i
$246$	57.1681	−	30.3086i	0.232391	−	0.123206i
$247$	−57.8505	−	3.13656i	−0.234212	−	0.0126986i
$248$	16.5743	+	19.5127i	0.0668317	+	0.0786804i
$249$	19.1523	+	87.0099i	0.0769170	+	0.349437i
$250$	129.365	+	170.177i	0.517461	+	0.680708i
$251$	−206.197	+	195.320i	−0.821502	+	0.778168i	−0.977800	−	0.209542i	$-0.932803\pi$
$251$	−206.197	+	195.320i	−0.821502	+	0.778168i	0.156298	+	0.987710i	$0.450044\pi$
$252$	0.500826	+	9.23719i	0.00198740	+	0.0366555i
$253$	494.870	−	297.753i	1.95601	−	1.17689i
$254$	40.9728	+	27.7802i	0.161310	+	0.109371i
$255$	−15.0565	+	54.2286i	−0.0590451	+	0.212661i
$256$	244.019	−	26.5387i	0.953200	−	0.103667i
$257$	−306.897	−	233.297i	−1.19415	−	0.907772i	−0.196798	−	0.980444i	$-0.563054\pi$
$257$	−306.897	−	233.297i	−1.19415	−	0.907772i	−0.997356	+	0.0726722i	$0.976847\pi$
$258$	−48.5090	−	22.4426i	−0.188019	−	0.0869870i
$259$	−14.2168	+	9.63920i	−0.0548909	+	0.0372170i
$260$	14.1131	+	41.8861i	0.0542811	+	0.161101i
$261$	20.2615	+	123.590i	0.0776302	+	0.473523i
$262$	−4.92910	+	30.0662i	−0.0188133	+	0.114756i
$263$	−220.226	−	74.2027i	−0.837361	−	0.282140i	−0.132232	−	0.991219i	$-0.542214\pi$
$263$	−220.226	−	74.2027i	−0.837361	−	0.282140i	−0.705129	+	0.709079i	$0.749111\pi$
$264$	83.1910	+	299.627i	0.315117	+	1.13495i
$265$	−108.549	−	272.437i	−0.409618	−	1.02806i
$266$	−23.8385	+	9.49813i	−0.0896185	+	0.0357073i
$267$	63.0308	−	17.5004i	0.236070	−	0.0655446i
$268$	−20.6500	+	61.2872i	−0.0770524	+	0.228683i
$269$	−338.489	−	55.4924i	−1.25832	−	0.206291i	−0.504524	−	0.863398i	$-0.668332\pi$
$269$	−338.489	−	55.4924i	−1.25832	−	0.206291i	−0.753798	+	0.657106i	$0.771780\pi$
$270$	32.5550	−	5.33712i	0.120574	−	0.0197671i
$271$	−473.982	+	159.703i	−1.74901	+	0.589310i	−0.997517	−	0.0704301i	$-0.977563\pi$
$271$	−473.982	+	159.703i	−1.74901	+	0.589310i	−0.751494	+	0.659740i	$0.770666\pi$
$272$	−33.9658	−	50.0958i	−0.124874	−	0.184176i
$273$	10.4554	−	22.5990i	0.0382982	−	0.0827801i
$274$	−237.632	+	312.600i	−0.867271	+	1.14088i
$275$	19.3644	+	178.053i	0.0704160	+	0.647465i
$276$	−71.4658	−	19.8424i	−0.258934	−	0.0718927i
$277$	271.319	−	400.165i	0.979490	−	1.44464i	0.0856122	−	0.996329i	$-0.472715\pi$
$277$	271.319	−	400.165i	0.979490	−	1.44464i	0.893878	−	0.448311i	$-0.147974\pi$
$278$	−131.347	−	218.300i	−0.472470	−	0.785251i
$279$	8.82464	−	0.478458i	0.0316295	−	0.00171490i
$280$	48.6226	+	51.3303i	0.173652	+	0.183322i
$281$	−47.6965	+	36.2579i	−0.169738	+	0.129032i	−0.686595	−	0.727040i	$-0.740895\pi$
$281$	−47.6965	+	36.2579i	−0.169738	+	0.129032i	0.516856	+	0.856072i	$0.327102\pi$
$282$	5.55456	−	1.22265i	0.0196970	−	0.00433564i
$283$	−30.8898	+	26.2380i	−0.109151	+	0.0927139i	−0.700300	−	0.713849i	$-0.746950\pi$
$283$	−30.8898	+	26.2380i	−0.109151	+	0.0927139i	0.591149	+	0.806563i	$0.298675\pi$
$284$	−8.15070	+	150.331i	−0.0286996	+	0.529334i
$285$	−26.5990	−	50.1711i	−0.0933300	−	0.176039i
$286$	49.8225	−	226.346i	0.174204	−	0.791419i
$287$	43.4460	−	20.1003i	0.151380	−	0.0700358i
$288$	35.4759	−	58.9615i	0.123180	−	0.204727i
$289$	−105.085	+	198.212i	−0.363617	+	0.685855i
$290$	202.005	+	171.584i	0.696568	+	0.591671i
$291$	147.293	−	155.495i	0.506161	−	0.534347i
$292$	−7.55472	+	69.4645i	−0.0258723	+	0.237892i
$293$	182.272	−	457.469i	0.622090	−	1.56133i	−0.192504	−	0.981296i	$-0.561661\pi$
$293$	182.272	−	457.469i	0.622090	−	1.56133i	0.814594	−	0.580032i	$-0.196960\pi$
$294$			122.310i			0.416021i
$295$	−229.878	−	63.2556i	−0.779247	−	0.214426i
$296$	74.1487			0.250502
$297$	99.7183	+	39.7314i	0.335752	+	0.133776i
$298$	375.335	+	40.8201i	1.25951	+	0.136980i
$299$	144.939	+	137.294i	0.484747	+	0.459177i
$300$	14.8904	−	17.5304i	0.0496347	−	0.0584345i
$301$	−34.9364	−	18.5221i	−0.116068	−	0.0615352i
$302$	359.488	+	216.297i	1.19036	+	0.716215i
$303$	132.294	+	285.949i	0.436614	+	0.943726i
$304$	59.6413	+	13.1280i	0.196188	+	0.0431843i
$305$	293.722	−	155.722i	0.963024	−	0.510563i
$306$	−37.8428	−	2.05178i	−0.123669	−	0.00670516i
$307$	−173.538	−	204.305i	−0.565271	−	0.665488i	0.403056	−	0.915175i	$-0.367948\pi$
$307$	−173.538	−	204.305i	−0.565271	−	0.665488i	−0.968327	+	0.249687i	$0.919672\pi$
$308$	13.6938	+	62.2114i	0.0444603	+	0.201985i
$309$	50.2963	+	66.1637i	0.162771	+	0.214122i
$310$	13.5782	−	12.8619i	0.0438006	−	0.0414902i
$311$	20.7825	+	383.310i	0.0668247	+	1.23251i	0.819097	+	0.573656i	$0.194475\pi$
$311$	20.7825	+	383.310i	0.0668247	+	1.23251i	−0.752272	+	0.658853i	$0.771042\pi$
$312$	−92.1053	+	55.4179i	−0.295209	+	0.177622i
$313$	−397.371	−	269.424i	−1.26956	−	0.860781i	−0.274646	−	0.961545i	$-0.588561\pi$
$313$	−397.371	−	269.424i	−1.26956	−	0.860781i	−0.994910	+	0.100765i	$0.967871\pi$
$314$	43.8741	−	158.020i	0.139726	−	0.503249i
$315$	24.2633	−	2.63879i	0.0770263	−	0.00837712i
$316$	−44.9306	−	34.1553i	−0.142185	−	0.108086i
$317$	144.559	+	66.8799i	0.456021	+	0.210978i	0.634432	−	0.772978i	$-0.281234\pi$
$317$	144.559	+	66.8799i	0.456021	+	0.210978i	−0.178412	+	0.983956i	$0.557096\pi$
$318$	163.454	−	110.825i	0.514006	−	0.348505i
$319$	275.365	+	817.254i	0.863213	+	2.56192i
$320$	−43.2437	−	263.775i	−0.135136	−	0.824296i
$321$	41.2302	−	251.493i	0.128443	−	0.783468i
$322$	83.7978	+	28.2347i	0.260241	+	0.0876856i
$323$	17.4524	+	62.8579i	0.0540322	+	0.194606i
$324$	−5.10240	−	12.8061i	−0.0157482	−	0.0395249i
$325$	−57.5145	+	22.9159i	−0.176968	+	0.0705103i
$326$	194.016	−	53.8682i	0.595140	−	0.165240i
$327$	26.9073	−	79.8579i	0.0822852	−	0.244214i
$328$	−203.929	−	33.4324i	−0.621734	−	0.101928i
$329$	4.15232	−	0.680738i	0.0126210	−	0.00206911i
$330$	215.275	−	72.5345i	0.652348	−	0.219801i
$331$	2.66683	+	3.93328i	0.00805688	+	0.0118830i	0.831696	−	0.555231i	$-0.187370\pi$
$331$	2.66683	+	3.93328i	0.00805688	+	0.0118830i	−0.823639	+	0.567114i	$0.808060\pi$
$332$	33.0815	−	71.5045i	0.0996431	−	0.215375i
$333$	15.4899	−	20.3766i	0.0465161	−	0.0611909i
$334$	14.2870	+	131.367i	0.0427754	+	0.393314i
$335$	164.407	+	45.6474i	0.490767	+	0.136261i
$336$	−14.7296	+	21.7245i	−0.0438381	+	0.0646563i
$337$	−311.405	−	517.559i	−0.924050	−	1.53578i	−0.842218	−	0.539138i	$-0.818750\pi$
$337$	−311.405	−	517.559i	−0.924050	−	1.53578i	−0.0818329	−	0.996646i	$-0.526077\pi$
$338$	−185.127	+	10.0373i	−0.547712	+	0.0296961i
$339$	23.1993	+	24.4912i	0.0684346	+	0.0722455i
$340$	39.6211	−	30.1191i	0.116533	−	0.0885857i
$341$	59.4329	−	13.0822i	0.174290	−	0.0383641i
$342$	29.1444	−	24.7555i	0.0852176	−	0.0723845i
$343$	−10.2395	+	188.857i	−0.0298529	+	0.550604i
$344$	79.9577	+	150.816i	0.232435	+	0.438420i
$345$	−42.0657	+	191.107i	−0.121930	+	0.553932i
$346$	−324.825	+	150.280i	−0.938802	+	0.434336i
$347$	−211.379	+	351.314i	−0.609160	+	1.01243i	0.386759	+	0.922181i	$0.373595\pi$
$347$	−211.379	+	351.314i	−0.609160	+	1.01243i	−0.995919	+	0.0902512i	$0.971233\pi$
$348$	51.8768	−	97.8501i	0.149071	−	0.281178i
$349$	79.9581	+	67.9171i	0.229106	+	0.194605i	0.754585	−	0.656202i	$-0.227838\pi$
$349$	79.9581	+	67.9171i	0.229106	+	0.194605i	−0.525479	+	0.850807i	$0.676114\pi$
$350$	−18.8582	+	19.9084i	−0.0538807	+	0.0568811i
$351$	−4.01182	+	36.8881i	−0.0114297	+	0.105094i
$352$	175.384	−	440.181i	0.498251	−	1.25051i
$353$			449.951i			1.27465i	0.770596	+	0.637324i	$0.219959\pi$
$353$			449.951i			1.27465i	−0.770596	+	0.637324i	$0.780041\pi$
$354$	8.32295	−	160.335i	0.0235112	−	0.452924i
$355$	397.202			1.11888
$356$	−53.7392	−	21.4117i	−0.150953	−	0.0601451i
$357$	−27.8737	−	3.03144i	−0.0780775	−	0.00849144i
$358$	−68.5414	−	64.9258i	−0.191456	−	0.181357i
$359$	−26.2435	+	30.8962i	−0.0731017	+	0.0860619i	−0.797497	−	0.603323i	$-0.793843\pi$
$359$	−26.2435	+	30.8962i	−0.0731017	+	0.0860619i	0.724396	+	0.689385i	$0.242119\pi$
$360$	−93.0863	−	49.3512i	−0.258573	−	0.137087i
$361$	252.925	+	152.180i	0.700624	+	0.421551i
$362$	191.478	+	413.873i	0.528945	+	1.14330i
$363$	517.197	+	113.844i	1.42479	+	0.313619i
$364$	−19.4548	+	10.3143i	−0.0534472	+	0.0283359i
$365$	184.079	+	9.98048i	0.504326	+	0.0273438i
$366$	144.929	+	170.623i	0.395980	+	0.466184i
$367$	−53.9392	−	245.048i	−0.146973	−	0.667706i	−0.991272	−	0.131833i	$-0.957914\pi$
$367$	−53.9392	−	245.048i	−0.146973	−	0.667706i	0.844299	−	0.535873i	$-0.180017\pi$
$368$	−127.353	−	167.530i	−0.346069	−	0.455246i
$369$	−51.7887	+	49.0569i	−0.140349	+	0.132945i
$370$	−2.93258	−	54.0883i	−0.00792590	−	0.146185i
$371$	125.188	−	75.3232i	0.337434	−	0.203027i
$372$	−6.46859	−	4.38581i	−0.0173887	−	0.0117898i
$373$	−55.1450	+	198.614i	−0.147842	+	0.532478i	0.852116	+	0.523352i	$0.175319\pi$
$373$	−55.1450	+	198.614i	−0.147842	+	0.532478i	−0.999958	+	0.00912613i	$0.997095\pi$
$374$	−259.439	+	28.2156i	−0.693686	+	0.0754429i
$375$	−187.612	−	142.619i	−0.500299	−	0.380317i
$376$	−16.4855	−	7.62702i	−0.0438445	−	0.0202846i
$377$	−246.743	+	167.296i	−0.654490	+	0.443756i
$378$	5.24772	+	15.5747i	0.0138829	+	0.0412029i
$379$	−4.19954	−	25.6160i	−0.0110806	−	0.0675885i	0.980707	−	0.195481i	$-0.0626269\pi$
$379$	−4.19954	−	25.6160i	−0.0110806	−	0.0675885i	−0.991788	+	0.127893i	$0.959179\pi$
$380$	−8.12418	+	49.5553i	−0.0213794	+	0.130409i
$381$	−51.7175	−	17.4257i	−0.135741	−	0.0457366i
$382$	−80.8042	−	291.030i	−0.211529	−	0.761860i
$383$	−226.019	−	567.265i	−0.590128	−	1.48111i	−0.855935	−	0.517084i	$-0.827018\pi$
$383$	−226.019	−	567.265i	−0.590128	−	1.48111i	0.265807	−	0.964026i	$-0.414362\pi$
$384$	19.5842	−	7.80305i	0.0510005	−	0.0203205i
$385$	161.936	−	44.9614i	0.420614	−	0.116783i
$386$	−22.0386	+	65.4082i	−0.0570948	+	0.169451i
$387$	58.1487	+	9.53300i	0.150255	+	0.0246331i
$388$	−186.910	+	30.6423i	−0.481726	+	0.0789749i
$389$	332.703	−	112.101i	0.855277	−	0.288176i	0.142696	−	0.989767i	$-0.454423\pi$
$389$	332.703	−	112.101i	0.855277	−	0.288176i	0.712581	+	0.701590i	$0.247526\pi$
$390$	44.0678	+	64.9951i	0.112994	+	0.166654i
$391$	94.3906	−	204.022i	0.241408	−	0.521795i
$392$	236.395	−	310.973i	0.603050	−	0.793298i
$393$	−3.63161	−	33.3921i	−0.00924074	−	0.0849672i
$394$	−108.551	−	30.1391i	−0.275511	−	0.0764952i
$395$	−83.5625	+	123.245i	−0.211551	+	0.312014i
$396$	−48.9386	−	81.3366i	−0.123582	−	0.205396i
$397$	−541.375	+	29.3525i	−1.36366	+	0.0739357i	−0.721384	−	0.692535i	$-0.756494\pi$
$397$	−541.375	+	29.3525i	−1.36366	+	0.0739357i	−0.642279	+	0.766471i	$0.722011\pi$
$398$	17.8990	+	18.8958i	0.0449725	+	0.0474768i
$399$	22.5215	−	17.1204i	0.0564450	−	0.0429084i
$400$	63.7346	−	14.0290i	0.159336	−	0.0350726i
$401$	−197.339	+	167.621i	−0.492118	+	0.418009i	−0.858779	−	0.512346i	$-0.828777\pi$
$401$	−197.339	+	167.621i	−0.492118	+	0.418009i	0.366661	+	0.930354i	$0.380501\pi$
$402$	−6.22046	+	114.730i	−0.0154738	+	0.285397i
$403$	9.85362	+	18.5859i	0.0244507	+	0.0461189i
$404$	59.8952	−	272.107i	0.148256	−	0.673532i
$405$	−33.0080	+	15.2711i	−0.0815013	+	0.0377065i
$406$	−68.0741	+	113.140i	−0.167670	+	0.278670i
$407$	82.5579	−	155.721i	0.202845	−	0.382606i
$408$	92.2497	+	78.3576i	0.226102	+	0.192053i
$409$	−100.378	+	105.967i	−0.245422	+	0.259089i	−0.837055	−	0.547118i	$-0.815725\pi$
$409$	−100.378	+	105.967i	−0.245422	+	0.259089i	0.591633	+	0.806207i	$0.298483\pi$
$410$	−16.3221	+	150.080i	−0.0398101	+	0.366048i
$411$	160.232	−	402.152i	0.389859	−	0.978471i
$412$		−	73.4960i		−	0.178388i
$413$	12.5704	−	118.112i	0.0304367	−	0.285985i
$414$	−131.770			−0.318285
$415$	−193.100	−	76.9379i	−0.465300	−	0.185393i
$416$	162.833	+	17.7092i	0.391426	+	0.0425702i
$417$	203.910	+	193.154i	0.488993	+	0.463199i
$418$	170.466	−	200.688i	0.407814	−	0.480116i
$419$	−12.3607	−	6.55321i	−0.0295004	−	0.0156401i	0.453593	−	0.891209i	$-0.350142\pi$
$419$	−12.3607	−	6.55321i	−0.0295004	−	0.0156401i	−0.483093	+	0.875569i	$0.660487\pi$
$420$	−18.4935	−	11.1272i	−0.0440322	−	0.0264933i
$421$	−271.836	−	587.565i	−0.645692	−	1.39564i	−0.903139	−	0.429348i	$-0.858743\pi$
$421$	−271.836	−	587.565i	−0.645692	−	1.39564i	0.257447	−	0.966292i	$-0.417119\pi$
$422$	−158.926	−	34.9823i	−0.376603	−	0.0828965i
$423$	−5.53983	+	2.93703i	−0.0130965	+	0.00694334i
$424$	−629.778	−	34.1456i	−1.48533	−	0.0805320i
$425$	45.1312	+	53.1326i	0.106191	+	0.125018i
$426$	57.4985	+	261.218i	0.134973	+	0.613189i
$427$	100.230	+	131.850i	0.234731	+	0.308783i
$428$	−163.617	+	154.986i	−0.382282	+	0.362116i
$429$	13.8330	+	255.134i	0.0322447	+	0.594719i
$430$	106.852	−	64.2905i	0.248492	−	0.149513i
$431$	56.0608	+	38.0101i	0.130071	+	0.0881906i	0.624488	−	0.781035i	$-0.285308\pi$
$431$	56.0608	+	38.0101i	0.130071	+	0.0881906i	−0.494416	+	0.869225i	$0.664618\pi$
$432$	10.4637	−	37.6870i	0.0242216	−	0.0872383i
$433$	−287.172	+	31.2318i	−0.663215	+	0.0721290i	−0.433534	−	0.901137i	$-0.642734\pi$
$433$	−287.172	+	31.2318i	−0.663215	+	0.0721290i	−0.229681	+	0.973266i	$0.573768\pi$
$434$	7.41763	+	5.63873i	0.0170913	+	0.0129925i
$435$	−265.190	−	122.690i	−0.609632	−	0.282046i
$436$	−61.6799	+	41.8200i	−0.141468	+	0.0959174i
$437$	72.4239	+	214.947i	0.165730	+	0.491869i
$438$	20.0835	+	122.504i	0.0458527	+	0.279689i
$439$	−40.5659	+	247.441i	−0.0924053	+	0.563648i	0.899526	+	0.436868i	$0.143912\pi$
$439$	−40.5659	+	247.441i	−0.0924053	+	0.563648i	−0.991931	+	0.126779i	$0.959536\pi$
$440$	−687.527	−	231.655i	−1.56256	−	0.526488i
$441$	−36.0738	−	129.926i	−0.0818000	−	0.294617i
$442$	−33.3904	−	83.8036i	−0.0755439	−	0.189601i
$443$	648.335	−	258.320i	1.46351	−	0.583116i	0.503729	−	0.863862i	$-0.331961\pi$
$443$	648.335	−	258.320i	1.46351	−	0.583116i	0.959782	+	0.280746i	$0.0905818\pi$
$444$	−21.8097	+	6.05543i	−0.0491209	+	0.0136383i
$445$	−48.7319	+	144.631i	−0.109510	+	0.325014i
$446$	141.280	+	23.1617i	0.316771	+	0.0519320i
$447$	−410.746	+	67.3383i	−0.918894	+	0.150645i
$448$	126.193	−	42.5193i	0.281680	−	0.0949092i
$449$	−218.637	−	322.466i	−0.486943	−	0.718187i	0.502264	−	0.864714i	$-0.332501\pi$
$449$	−218.637	−	322.466i	−0.486943	−	0.718187i	−0.989207	+	0.146528i	$0.953190\pi$
$450$	17.1582	−	37.0868i	0.0381292	−	0.0824150i
$451$	−297.268	+	391.049i	−0.659131	+	0.867072i
$452$	−3.22542	−	29.6573i	−0.00713589	−	0.0656134i
$453$	−445.667	−	123.739i	−0.983812	−	0.273154i
$454$	163.839	−	241.645i	0.360879	−	0.532257i
$455$	29.9512	+	49.7792i	0.0658268	+	0.109405i
$456$	−121.946	+	6.61171i	−0.267425	+	0.0144994i
$457$	399.884	+	422.153i	0.875020	+	0.923748i	0.997637	−	0.0687062i	$-0.0218871\pi$
$457$	399.884	+	422.153i	0.875020	+	0.923748i	−0.122616	+	0.992454i	$0.539128\pi$
$458$	248.550	−	188.943i	0.542686	−	0.412539i
$459$	40.8044	−	8.98173i	0.0888985	−	0.0195680i
$460$	131.888	−	112.027i	0.286713	−	0.243536i
$461$	−18.1851	+	335.404i	−0.0394470	+	0.727557i	0.910187	+	0.414197i	$0.135937\pi$
$461$	−18.1851	+	335.404i	−0.0394470	+	0.727557i	−0.949634	+	0.313360i	$0.898545\pi$
$462$	53.0104	+	99.9883i	0.114741	+	0.216425i
$463$	10.6114	−	48.2081i	0.0229188	−	0.104121i	−0.963773	−	0.266725i	$-0.914058\pi$
$463$	10.6114	−	48.2081i	0.0229188	−	0.104121i	0.986691	+	0.162604i	$0.0519894\pi$
$464$	285.192	−	131.944i	0.614638	−	0.284362i
$465$	−10.6302	+	17.6676i	−0.0228607	+	0.0379948i
$466$	−145.724	+	274.865i	−0.312713	+	0.589839i
$467$	−245.519	−	208.546i	−0.525737	−	0.446565i	0.344794	−	0.938678i	$-0.387949\pi$
$467$	−245.519	−	208.546i	−0.525737	−	0.446565i	−0.870531	+	0.492113i	$0.836225\pi$
$468$	22.5656	−	23.8222i	0.0482170	−	0.0509021i
$469$	−9.19054	+	84.5056i	−0.0195960	+	0.180183i
$470$	−4.91158	+	12.3271i	−0.0104502	+	0.0262280i
$471$			180.800i			0.383864i
$472$	−331.050	+	391.565i	−0.701377	+	0.829588i
$473$	405.757			0.857837
$474$	−93.1484	−	37.1137i	−0.196516	−	0.0782990i
$475$	−69.9274	−	7.60506i	−0.147215	−	0.0160107i
$476$	18.0007	+	17.0512i	0.0378166	+	0.0358218i
$477$	−140.946	+	165.934i	−0.295484	+	0.347870i
$478$	−356.895	−	189.214i	−0.746642	−	0.395845i
$479$	408.495	+	245.783i	0.852808	+	0.513118i	0.873588	−	0.486666i	$-0.161787\pi$
$479$	408.495	+	245.783i	0.852808	+	0.513118i	−0.0207796	+	0.999784i	$0.506615\pi$
$480$	67.4106	+	145.706i	0.140439	+	0.303553i
$481$	59.5017	+	13.0973i	0.123704	+	0.0272294i
$482$	−422.725	+	224.115i	−0.877024	+	0.464969i
$483$	−97.3432	−	5.27779i	−0.201539	−	0.0109271i
$484$	−303.181	−	356.932i	−0.626407	−	0.737463i
$485$	107.422	+	488.025i	0.221490	+	1.00624i
$486$	−14.8212	−	19.4970i	−0.0304964	−	0.0401173i
$487$	−36.0074	+	34.1080i	−0.0739371	+	0.0700370i	−0.723776	−	0.690035i	$-0.757595\pi$
$487$	−36.0074	+	34.1080i	−0.0739371	+	0.0700370i	0.649839	+	0.760072i	$0.274836\pi$
$488$	−38.7077	−	713.921i	−0.0793191	−	1.46295i
$489$	−190.209	+	114.445i	−0.388976	+	0.234039i
$490$	−236.191	−	160.141i	−0.482022	−	0.326819i
$491$	154.447	−	556.269i	0.314557	−	1.13293i	−0.622174	−	0.782879i	$-0.713750\pi$
$491$	154.447	−	556.269i	0.314557	−	1.13293i	0.936730	−	0.350051i	$-0.113836\pi$
$492$	62.7127	−	6.82042i	0.127465	−	0.0138626i
$493$	267.228	+	203.142i	0.542045	+	0.412052i
$494$	82.6090	+	38.2190i	0.167225	+	0.0773664i
$495$	−207.286	+	140.544i	−0.418760	+	0.283927i
$496$	−7.08026	−	21.0135i	−0.0142747	−	0.0423658i
$497$	32.0136	+	195.274i	0.0644137	+	0.392906i
$498$	22.6451	−	138.129i	0.0454720	−	0.277367i
$499$	−578.886	−	195.050i	−1.16009	−	0.390881i	−0.327546	−	0.944835i	$-0.606222\pi$
$499$	−578.886	−	195.050i	−1.16009	−	0.390881i	−0.832547	+	0.553954i	$0.813118\pi$
$500$	55.7538	+	200.807i	0.111508	+	0.401614i
$501$	−53.9216	−	135.333i	−0.107628	−	0.270126i
$502$	414.528	−	165.163i	0.825753	−	0.329010i
$503$	−301.859	+	83.8108i	−0.600118	+	0.166622i	−0.554285	−	0.832327i	$-0.687008\pi$
$503$	−301.859	+	83.8108i	−0.600118	+	0.166622i	−0.0458332	+	0.998949i	$0.514594\pi$
$504$	16.7597	−	49.7412i	0.0332535	−	0.0986928i
$505$	−725.404	−	118.924i	−1.43644	−	0.235493i
$506$	−895.415	+	146.796i	−1.76959	+	0.290110i
$507$	193.694	−	65.2630i	0.382039	−	0.128724i
$508$	27.0834	+	39.9451i	0.0533138	+	0.0786320i
$509$	133.754	−	289.104i	0.262777	−	0.567984i	−0.730610	−	0.682795i	$-0.760764\pi$
$509$	133.754	−	289.104i	0.262777	−	0.567984i	0.993387	+	0.114811i	$0.0366263\pi$
$510$	53.5100	−	70.3913i	0.104922	−	0.138022i
$511$	9.92972	+	91.3023i	0.0194319	+	0.178674i
$512$	−418.491	−	116.193i	−0.817365	−	0.226940i
$513$	−23.6579	+	34.8928i	−0.0461167	+	0.0680171i
$514$	312.251	+	518.965i	0.607493	+	1.00966i
$515$	−193.621	+	10.4978i	−0.375963	+	0.0203841i
$516$	−35.8349	−	37.8304i	−0.0694474	−	0.0733148i
$517$	−34.3728	+	26.1295i	−0.0664850	+	0.0505406i
$518$	26.3548	−	5.80113i	0.0508780	−	0.0111991i
$519$	300.729	−	255.441i	0.579438	−	0.492179i
$520$	13.5775	−	250.422i	0.0261106	−	0.481581i
$521$	129.023	+	243.364i	0.247646	+	0.467110i	0.975906	−	0.218191i	$-0.0700156\pi$
$521$	129.023	+	243.364i	0.247646	+	0.467110i	−0.728260	+	0.685301i	$0.759671\pi$
$522$	42.2980	−	192.162i	0.0810307	−	0.368126i
$523$	585.607	−	270.931i	1.11971	−	0.518032i	0.229373	−	0.973338i	$-0.426332\pi$
$523$	585.607	−	270.931i	1.11971	−	0.518032i	0.890335	+	0.455306i	$0.150470\pi$
$524$	−15.3137	+	25.4515i	−0.0292246	+	0.0485716i
$525$	14.1608	−	26.7101i	0.0269729	−	0.0508763i
$526$	278.270	+	236.365i	0.529031	+	0.449363i
$527$	16.2896	−	17.1967i	0.0309101	−	0.0326314i
$528$	29.1196	−	267.750i	0.0551508	−	0.507103i
$529$	93.5003	−	234.668i	0.176749	−	0.443607i
$530$			460.747i			0.869333i
$531$	38.4476	+	172.774i	0.0724061	+	0.325374i
$532$	−25.0174			−0.0470252
$533$	−157.740	−	62.8495i	−0.295948	−	0.117916i
$534$	−102.171	−	11.1117i	−0.191331	−	0.0208085i
$535$	431.671	+	408.901i	0.806862	+	0.764300i
$536$	237.560	−	279.677i	0.443208	−	0.521785i
$537$	91.9584	+	48.7533i	0.171245	+	0.0907882i
$538$	461.756	+	277.829i	0.858282	+	0.516411i
$539$	−389.873	−	842.697i	−0.723327	−	1.56345i
$540$	31.4102	+	6.91391i	0.0581670	+	0.0128035i
$541$	683.800	−	362.528i	1.26396	−	0.670107i	0.304647	−	0.952465i	$-0.401461\pi$
$541$	683.800	−	362.528i	1.26396	−	0.670107i	0.959309	+	0.282358i	$0.0911166\pi$
$542$	784.649	+	42.5424i	1.44769	+	0.0784916i
$543$	−325.468	−	383.170i	−0.599388	−	0.705654i
$544$	−39.6476	−	180.121i	−0.0728816	−	0.331104i
$545$	118.982	+	156.519i	0.218316	+	0.287190i
$546$	−28.4015	+	26.9033i	−0.0520173	+	0.0492734i
$547$	31.6129	+	583.065i	0.0577932	+	1.06593i	0.873299	+	0.487184i	$0.161976\pi$
$547$	31.6129	+	583.065i	0.0577932	+	1.06593i	−0.815506	+	0.578748i	$0.803541\pi$
$548$	−328.021	+	197.364i	−0.598578	+	0.360152i
$549$	−204.277	−	138.503i	−0.372088	−	0.252282i
$550$	75.2788	−	271.130i	0.136871	−	0.492963i
$551$	−336.707	+	36.6191i	−0.611084	+	0.0664594i
$552$	335.025	+	254.679i	0.606929	+	0.461376i
$553$	−67.3255	−	31.1481i	−0.121746	−	0.0563257i
$554$	−628.695	+	426.266i	−1.13483	+	0.769433i
$555$	19.0679	+	56.5914i	0.0343565	+	0.101966i
$556$	−40.1830	−	245.106i	−0.0722717	−	0.440838i
$557$	−93.5475	+	570.614i	−0.167949	+	1.02444i	0.759504	+	0.650503i	$0.225442\pi$
$557$	−93.5475	+	570.614i	−0.167949	+	1.02444i	−0.927453	+	0.373940i	$0.878007\pi$
$558$	−13.1578	−	4.43339i	−0.0235803	−	0.00794514i
$559$	37.5237	+	135.148i	0.0671265	+	0.241768i
$560$	−22.6663	−	56.8881i	−0.0404755	−	0.101586i
$561$	267.272	−	106.491i	0.476420	−	0.189823i
$562$	90.6979	−	25.1821i	0.161384	−	0.0448081i
$563$	52.7202	−	156.468i	0.0936415	−	0.277918i	−0.890589	−	0.454809i	$-0.849707\pi$
$563$	52.7202	−	156.468i	0.0936415	−	0.277918i	0.984230	+	0.176891i	$0.0566040\pi$
$564$	5.47183	+	0.897061i	0.00970183	+	0.00159053i
$565$	−77.6696	+	12.7333i	−0.137468	+	0.0225368i
$566$	60.3418	−	20.3315i	0.106611	−	0.0359214i
$567$	−10.1681	−	14.9968i	−0.0179331	−	0.0264493i
$568$	358.682	−	775.278i	0.631482	−	1.36493i
$569$	184.524	−	242.737i	0.324295	−	0.426603i	−0.604838	−	0.796348i	$-0.706762\pi$
$569$	184.524	−	242.737i	0.324295	−	0.426603i	0.929133	+	0.369746i	$0.120555\pi$
$570$	9.64593	+	88.6928i	0.0169227	+	0.155601i
$571$	398.229	+	110.568i	0.697424	+	0.193639i	0.598106	−	0.801417i	$-0.295920\pi$
$571$	398.229	+	110.568i	0.697424	+	0.193639i	0.0993181	+	0.995056i	$0.468334\pi$
$572$	126.801	−	187.017i	0.221680	−	0.326953i
$573$	171.671	+	285.320i	0.299601	+	0.497941i
$574$	−75.0984	+	4.07172i	−0.130833	+	0.00709358i
$575$	166.689	+	175.972i	0.289894	+	0.306038i
$576$	−157.973	+	120.088i	−0.274259	+	0.208486i
$577$	897.838	−	197.629i	1.55605	−	0.342512i	0.648085	−	0.761568i	$-0.275570\pi$
$577$	897.838	−	197.629i	1.55605	−	0.342512i	0.907960	+	0.419056i	$0.137639\pi$
$578$	268.637	−	228.182i	0.464769	−	0.394779i
$579$	4.11958	−	75.9811i	0.00711498	−	0.131228i
$580$	121.034	+	228.294i	0.208679	+	0.393611i
$581$	22.2612	−	101.134i	0.0383153	−	0.174068i
$582$	−305.398	+	141.292i	−0.524739	+	0.242770i
$583$	−772.910	+	1284.59i	−1.32575	+	2.20341i
$584$	185.708	−	350.282i	0.317993	−	0.599798i
$585$	−65.9813	−	56.0450i	−0.112789	−	0.0958035i
$586$	−532.054	+	561.683i	−0.907943	+	0.958504i
$587$	−7.24664	+	66.6317i	−0.0123452	+	0.113512i	−0.998689	−	0.0511865i	$-0.983700\pi$
$587$	−7.24664	+	66.6317i	−0.0123452	+	0.113512i	0.986344	+	0.164699i	$0.0526652\pi$
$588$	−44.1361	+	110.773i	−0.0750614	+	0.188390i
$589$			23.9001i			0.0405774i
$590$	298.723	+	226.000i	0.506311	+	0.383051i
$591$	124.200			0.210152
$592$	−59.6603	−	23.7708i	−0.100778	−	0.0401534i
$593$	358.569	+	38.9967i	0.604670	+	0.0657618i	0.405333	−	0.914169i	$-0.367156\pi$
$593$	358.569	+	38.9967i	0.604670	+	0.0657618i	0.199337	+	0.979931i	$0.436121\pi$
$594$	−122.435	−	115.976i	−0.206119	−	0.195246i
$595$	42.3491	−	49.8573i	0.0711750	−	0.0837937i
$596$	325.201	+	172.411i	0.545640	+	0.289280i
$597$	−24.5867	−	14.7933i	−0.0411837	−	0.0247794i
$598$	−131.701	−	284.666i	−0.220235	−	0.476031i
$599$	777.556	+	171.153i	1.29809	+	0.285731i	0.809674	−	0.586880i	$-0.199644\pi$
$599$	777.556	+	171.153i	1.29809	+	0.285731i	0.488416	+	0.872611i	$0.337575\pi$
$600$	−115.304	+	61.1304i	−0.192174	+	0.101884i
$601$	913.753	+	49.5422i	1.52039	+	0.0824330i	0.795297	−	0.606220i	$-0.207315\pi$
$601$	913.753	+	49.5422i	1.52039	+	0.0824330i	0.725091	+	0.688653i	$0.241798\pi$
$602$	40.2189	+	47.3493i	0.0668087	+	0.0786533i
$603$	−27.2302	−	123.708i	−0.0451579	−	0.205155i
$604$	247.528	+	325.618i	0.409815	+	0.539102i
$605$	−897.012	+	849.695i	−1.48266	+	1.40445i
$606$	−26.7988	−	494.275i	−0.0442225	−	0.815636i
$607$	543.746	−	327.161i	0.895792	−	0.538980i	0.00838367	−	0.999965i	$-0.497331\pi$
$607$	543.746	−	327.161i	0.895792	−	0.538980i	0.887408	+	0.460985i	$0.152504\pi$
$608$	154.025	+	104.432i	0.253331	+	0.171763i
$609$	38.9437	−	140.263i	0.0639470	−	0.230316i
$610$	−519.244	+	56.4712i	−0.851220	+	0.0925758i
$611$	−11.8819	−	9.03235i	−0.0194466	−	0.0147829i
$612$	−33.5329	−	15.5140i	−0.0547924	−	0.0253497i
$613$	249.855	−	169.406i	0.407593	−	0.276355i	−0.340113	−	0.940385i	$-0.610465\pi$
$613$	249.855	−	169.406i	0.407593	−	0.276355i	0.747707	+	0.664029i	$0.231155\pi$
$614$	134.472	+	399.100i	0.219010	+	0.649999i
$615$	−26.9256	−	164.239i	−0.0437814	−	0.267055i
$616$	58.4741	−	356.676i	0.0949255	−	0.579020i
$617$	−459.363	−	154.777i	−0.744510	−	0.250855i	−0.0786199	−	0.996905i	$-0.525051\pi$
$617$	−459.363	−	154.777i	−0.744510	−	0.250855i	−0.665890	+	0.746050i	$0.731948\pi$
$618$	−34.9322	−	125.814i	−0.0565246	−	0.203583i
$619$	402.488	+	1010.17i	0.650224	+	1.63194i	0.769175	+	0.639038i	$0.220667\pi$
$619$	402.488	+	1010.17i	0.650224	+	1.63194i	−0.118952	+	0.992900i	$0.537953\pi$
$620$	16.9387	−	6.74901i	0.0273205	−	0.0108855i
$621$	139.975	−	38.8639i	0.225403	−	0.0625828i
$622$	192.570	−	571.528i	0.309599	−	0.918856i
$623$	−75.0320	−	12.3009i	−0.120437	−	0.0197446i
$624$	91.8743	−	15.0620i	0.147235	−	0.0241379i
$625$	315.649	−	106.355i	0.505039	−	0.170167i
$626$	423.289	+	624.305i	0.676181	+	0.997292i
$627$	−121.890	+	263.462i	−0.194403	+	0.420194i
$628$	96.7579	−	127.283i	0.154073	−	0.202680i
$629$	−7.41732	−	68.2011i	−0.0117922	−	0.108428i
$630$	−36.9469	−	10.2583i	−0.0586459	−	0.0162829i
$631$	214.643	−	316.574i	0.340163	−	0.501702i	−0.618679	−	0.785644i	$-0.712332\pi$
$631$	214.643	−	316.574i	0.340163	−	0.501702i	0.958842	+	0.283942i	$0.0916422\pi$
$632$	165.098	+	274.395i	0.261231	+	0.434169i
$633$	179.140	−	9.71269i	0.283002	−	0.0153439i
$634$	−172.092	−	181.675i	−0.271438	−	0.286554i
$635$	101.364	−	77.0553i	0.159629	−	0.121347i
$636$	188.028	−	41.3881i	0.295641	−	0.0650756i
$637$	244.628	−	207.789i	0.384031	−	0.326199i
$638$	73.3529	−	1352.92i	0.114973	−	2.12056i
$639$	−138.122	−	260.526i	−0.216153	−	0.407708i
$640$	−10.5734	+	48.0353i	−0.0165209	+	0.0750551i
$641$	762.815	−	352.916i	1.19004	−	0.550571i	0.277963	−	0.960592i	$-0.410341\pi$
$641$	762.815	−	352.916i	1.19004	−	0.550571i	0.912076	+	0.410021i	$0.134479\pi$
$642$	−206.424	+	343.079i	−0.321533	+	0.534391i
$643$	151.276	−	285.336i	0.235265	−	0.443757i	−0.737565	−	0.675276i	$-0.764025\pi$
$643$	151.276	−	285.336i	0.235265	−	0.443757i	0.972830	+	0.231519i	$0.0743694\pi$
$644$	65.7050	+	55.8103i	0.102026	+	0.0866620i
$645$	−94.5435	+	99.8084i	−0.146579	+	0.154742i
$646$	11.0812	−	101.890i	0.0171536	−	0.157725i
$647$	173.238	−	434.795i	0.267756	−	0.672018i	−0.732203	−	0.681087i	$-0.761508\pi$
$647$	173.238	−	434.795i	0.267756	−	0.672018i	0.999959	+	0.00906924i	$0.00288687\pi$
$648$			78.2168i			0.120705i
$649$	453.738	+	1131.21i	0.699134	+	1.74301i
$650$	97.2686			0.149644
$651$	−9.54259	−	3.80211i	−0.0146584	−	0.00584042i
$652$	195.154	+	21.2243i	0.299316	+	0.0325526i
$653$	−743.419	−	704.204i	−1.13847	−	1.07841i	−0.996067	−	0.0886046i	$-0.971759\pi$
$653$	−743.419	−	704.204i	−1.13847	−	1.07841i	−0.142401	−	0.989809i	$-0.545482\pi$
$654$	−85.7102	+	100.906i	−0.131055	+	0.154290i
$655$	69.2378	+	36.7076i	0.105707	+	0.0560421i
$656$	153.364	+	92.2760i	0.233786	+	0.140665i
$657$	−57.4650	−	124.209i	−0.0874657	−	0.189054i
$658$	−6.45619	−	1.42112i	−0.00981184	−	0.00215975i
$659$	810.780	−	429.848i	1.23032	−	0.652274i	0.278943	−	0.960308i	$-0.410016\pi$
$659$	810.780	−	429.848i	1.23032	−	0.652274i	0.951375	+	0.308034i	$0.0996710\pi$
$660$	221.143	+	11.9900i	0.335066	+	0.0181667i
$661$	−118.506	−	139.516i	−0.179283	−	0.211069i	0.665179	−	0.746684i	$-0.268355\pi$
$661$	−118.506	−	139.516i	−0.179283	−	0.211069i	−0.844462	+	0.535616i	$0.820080\pi$
$662$	−1.60497	−	7.29145i	−0.00242442	−	0.0110143i
$663$	60.1864	+	79.1738i	0.0907789	+	0.119418i
$664$	−324.544	+	307.425i	−0.488771	+	0.462989i
$665$	3.57337	+	65.9069i	0.00537348	+	0.0991081i
$666$	−34.4569	+	20.7320i	−0.0517371	+	0.0311292i
$667$	966.010	+	654.971i	1.44829	+	0.981965i
$668$	−34.4649	+	124.131i	−0.0515941	+	0.185825i
$669$	−156.909	+	17.0648i	−0.234542	+	0.0255080i
$670$	−213.408	−	162.228i	−0.318519	−	0.242132i
$671$	−1542.41	−	713.596i	−2.29868	−	1.06348i
$672$	−66.1994	+	44.8843i	−0.0985110	+	0.0667921i
$673$	17.4230	+	51.7096i	0.0258886	+	0.0768345i	0.959818	−	0.280622i	$-0.0905407\pi$
$673$	17.4230	+	51.7096i	0.0258886	+	0.0768345i	−0.933930	+	0.357456i	$0.883644\pi$
$674$	153.526	+	936.468i	0.227784	+	1.38942i
$675$	−7.28830	+	44.4567i	−0.0107975	+	0.0658617i
$676$	−171.287	−	57.7132i	−0.253383	−	0.0853745i
$677$	−41.2744	−	148.657i	−0.0609667	−	0.219582i	0.926791	−	0.375577i	$-0.122555\pi$
$677$	−41.2744	−	148.657i	−0.0609667	−	0.219582i	−0.987758	+	0.155995i	$0.950142\pi$
$678$	−19.6174	−	49.2359i	−0.0289342	−	0.0726194i
$679$	−231.267	+	92.1453i	−0.340600	+	0.135707i
$680$	−272.098	+	75.5477i	−0.400144	+	0.111100i
$681$	−102.771	+	305.014i	−0.150912	+	0.447891i
$682$	−94.3501	−	15.4679i	−0.138343	−	0.0226802i
$683$	−1233.50	+	202.222i	−1.80600	+	0.296079i	−0.968252	−	0.249977i	$-0.919577\pi$
$683$	−1233.50	+	202.222i	−1.80600	+	0.296079i	−0.837749	+	0.546055i	$0.816129\pi$
$684$	35.3285	−	11.9036i	0.0516499	−	0.0174029i
$685$	566.796	+	835.961i	0.827439	+	1.22038i
$686$	124.769	−	269.683i	0.181879	−	0.393124i
$687$	−208.301	+	274.015i	−0.303203	+	0.398857i
$688$	−15.9851	−	146.980i	−0.0232341	−	0.213634i
$689$	−499.343	−	138.642i	−0.724737	−	0.201222i
$690$	172.527	−	254.459i	0.250040	−	0.368781i
$691$	−131.577	−	218.683i	−0.190416	−	0.316473i	0.746912	−	0.664923i	$-0.231536\pi$
$691$	−131.577	−	218.683i	−0.190416	−	0.316473i	−0.937327	+	0.348450i	$0.886708\pi$
$692$	−348.416	+	18.8906i	−0.503491	+	0.0272985i
$693$	−85.8016	−	90.5797i	−0.123812	−	0.130707i
$694$	512.804	−	389.823i	0.738911	−	0.561705i
$695$	−639.977	+	140.870i	−0.920830	+	0.202690i
$696$	−478.945	+	406.819i	−0.688139	+	0.584510i
$697$	−10.3512	+	190.916i	−0.0148510	+	0.273911i
$698$	−77.2041	−	145.622i	−0.110608	−	0.208628i
$699$	73.7302	−	334.960i	0.105480	−	0.479199i
$700$	−24.2635	+	11.2255i	−0.0346621	+	0.0160364i
$701$	−293.870	+	488.416i	−0.419215	+	0.696742i	−0.992450	−	0.122650i	$-0.960861\pi$
$701$	−293.870	+	488.416i	−0.419215	+	0.696742i	0.573235	+	0.819391i	$0.305688\pi$
$702$	27.3064	−	51.5054i	0.0388981	−	0.0733695i
$703$	52.7569	+	44.8121i	0.0750454	+	0.0637441i
$704$	−939.690	+	992.018i	−1.33479	+	1.40912i
$705$	1.58168	−	14.5433i	0.00224352	−	0.0206289i
$706$	261.655	−	656.705i	0.370616	−	0.930177i
$707$		−	366.212i		−	0.517980i
$708$	65.3955	−	142.208i	0.0923666	−	0.200859i
$709$	−781.596			−1.10239			−0.551196	−	0.834376i	$-0.685828\pi$
$709$	−781.596			−1.10239			−0.551196	+	0.834376i	$0.685828\pi$
$710$	−579.718	−	230.981i	−0.816504	−	0.325325i
$711$	109.895	+	11.9518i	0.154564	+	0.0168098i
$712$	238.292	+	225.722i	0.334680	+	0.317026i
$713$	53.3177	−	62.7705i	0.0747794	−	0.0880371i
$714$	38.9189	+	20.6335i	0.0545082	+	0.0288984i
$715$	−510.797	−	307.337i	−0.714402	−	0.429841i
$716$	−38.6475	−	83.5352i	−0.0539770	−	0.116669i
$717$	434.925	+	95.7341i	0.606589	+	0.133520i
$718$	56.2693	−	29.8321i	0.0783694	−	0.0415488i
$719$	−605.524	−	32.8306i	−0.842176	−	0.0456614i	−0.371998	−	0.928233i	$-0.621327\pi$
$719$	−605.524	−	32.8306i	−0.842176	−	0.0456614i	−0.470177	+	0.882572i	$0.655810\pi$
$720$	59.0764	+	69.5501i	0.0820506	+	0.0965974i
$721$	−20.7664	−	94.3427i	−0.0288022	−	0.130850i
$722$	−280.650	−	369.188i	−0.388712	−	0.511341i
$723$	382.948	−	362.748i	0.529665	−	0.501726i
$724$	24.0692	+	443.930i	0.0332448	+	0.613163i
$725$	−310.129	+	186.598i	−0.427764	+	0.257377i
$726$	−688.649	−	466.916i	−0.948553	−	0.643135i
$727$	−245.483	+	884.149i	−0.337665	+	1.21616i	0.578608	+	0.815606i	$0.303596\pi$
$727$	−245.483	+	884.149i	−0.337665	+	1.21616i	−0.916273	+	0.400554i	$0.868818\pi$
$728$	124.208	−	13.5084i	0.170616	−	0.0185556i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	−262.860	−	121.612i	−0.360083	−	0.166592i
$731$	130.721	−	88.6309i	0.178825	−	0.121246i
$732$	69.6884	+	206.828i	0.0952027	+	0.282551i
$733$	85.5043	+	521.553i	0.116650	+	0.711532i	0.978791	+	0.204863i	$0.0656750\pi$
$733$	85.5043	+	521.553i	0.116650	+	0.711532i	−0.862141	+	0.506669i	$0.830877\pi$
$734$	−63.7759	+	389.016i	−0.0868881	+	0.529994i
$735$	298.130	+	100.452i	0.405619	+	0.136669i
$736$	−171.555	−	617.885i	−0.233091	−	0.839518i
$737$	−322.852	−	810.297i	−0.438062	−	1.09945i
$738$	104.113	−	41.4826i	0.141075	−	0.0562094i
$739$	858.993	−	238.498i	1.16237	−	0.322731i	0.367803	−	0.929904i	$-0.380110\pi$
$739$	858.993	−	238.498i	1.16237	−	0.322731i	0.794570	+	0.607173i	$0.207696\pi$
$740$	16.8620	−	50.0447i	0.0227865	−	0.0676280i
$741$	−99.0252	−	16.2344i	−0.133637	−	0.0219087i
$742$	−226.515	+	37.1352i	−0.305276	+	0.0500474i
$743$	−119.416	+	40.2360i	−0.160722	+	0.0541534i	−0.398512	−	0.917163i	$-0.630473\pi$
$743$	−119.416	+	40.2360i	−0.160722	+	0.0541534i	0.237791	+	0.971316i	$0.423577\pi$
$744$	24.8851	+	36.7028i	0.0334477	+	0.0493317i
$745$	407.756	−	881.350i	0.547324	−	1.18302i
$746$	195.983	−	257.811i	0.262711	−	0.345591i
$747$	16.6842	+	153.409i	0.0223349	+	0.205366i
$748$	−245.149	−	68.0653i	−0.327739	−	0.0909963i
$749$	−166.234	+	245.177i	−0.221941	+	0.327339i
$750$	190.885	+	317.253i	0.254513	+	0.423004i
$751$	−229.017	+	12.4170i	−0.304950	+	0.0165339i	−0.205979	−	0.978556i	$-0.566038\pi$
$751$	−229.017	+	12.4170i	−0.304950	+	0.0165339i	−0.0989709	+	0.995090i	$0.531555\pi$
$752$	10.8192	+	11.4217i	0.0143873	+	0.0151885i
$753$	−391.627	+	297.707i	−0.520089	+	0.395362i
$754$	457.408	−	100.683i	0.606642	−	0.133532i
$755$	822.465	−	698.608i	1.08936	−	0.925308i
$756$	−0.867456	+	15.9993i	−0.00114743	+	0.0211631i
$757$	229.900	+	433.637i	0.303699	+	0.572836i	0.987647	−	0.156694i	$-0.0500836\pi$
$757$	229.900	+	433.637i	0.303699	+	0.572836i	−0.683949	+	0.729530i	$0.739739\pi$
$758$	−8.76699	+	39.8288i	−0.0115659	+	0.0525446i
$759$	907.875	−	420.028i	1.19615	−	0.553396i
$760$	146.897	−	244.144i	0.193285	−	0.321243i
$761$	−556.630	+	1049.92i	−0.731445	+	1.37965i	0.186304	+	0.982492i	$0.440349\pi$
$761$	−556.630	+	1049.92i	−0.731445	+	1.37965i	−0.917749	+	0.397160i	$0.869996\pi$
$762$	65.3486	+	55.5076i	0.0857593	+	0.0728446i
$763$	−67.3588	+	71.1098i	−0.0882815	+	0.0931976i
$764$	31.8371	−	292.738i	0.0416717	−	0.383165i
$765$	−36.0810	+	90.5565i	−0.0471647	+	0.118375i
$766$			959.361i			1.25243i
$767$	−334.820	+	255.742i	−0.436532	+	0.333432i
$768$	425.146			0.553575
$769$	−955.333	−	380.639i	−1.24231	−	0.494980i	−0.345924	−	0.938263i	$-0.612434\pi$
$769$	−955.333	−	380.639i	−1.24231	−	0.494980i	−0.896382	+	0.443283i	$0.853814\pi$
$770$	−262.493	−	28.5478i	−0.340899	−	0.0370751i
$771$	−484.757	−	459.186i	−0.628738	−	0.595572i
$772$	−43.5627	+	51.2859i	−0.0564283	+	0.0664326i
$773$	197.453	+	104.683i	0.255437	+	0.135424i	0.591207	−	0.806520i	$-0.298652\pi$
$773$	197.453	+	104.683i	0.255437	+	0.135424i

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)

\(f(q)\)	\(=\)	\(q+(-1.45950 - 0.581520i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-1.11199 - 1.05334i) q^{4} +(-2.61612 + 3.07994i) q^{5} +(-2.40422 - 1.27464i) q^{6} +(-1.72503 - 1.03791i) q^{7} +(3.64916 + 7.88752i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(-1.45950 - 0.581520i) q^{2} +(1.72190 + 0.187268i) q^{3} +(-1.11199 - 1.05334i) q^{4} +(-2.61612 + 3.07994i) q^{5} +(-2.40422 - 1.27464i) q^{6} +(-1.72503 - 1.03791i) q^{7} +(3.64916 + 7.88752i) q^{8} +(2.92986 + 0.644911i) q^{9} +(5.60928 - 2.97385i) q^{10} +(20.6277 + 1.11840i) q^{11} +(-1.71748 - 2.02198i) q^{12} +(1.53510 + 6.97403i) q^{13} +(1.91412 + 2.51798i) q^{14} +(-5.08146 + 4.81342i) q^{15} +(-0.407516 - 7.51619i) q^{16} +(6.88982 - 4.14547i) q^{17} +(-3.90112 - 2.64502i) q^{18} +(-2.17048 + 7.81737i) q^{19} +(6.15332 - 0.669214i) q^{20} +(-2.77595 - 2.11022i) q^{21} +(-29.4558 - 13.6277i) q^{22} +(23.1399 - 15.6893i) q^{23} +(4.80639 + 14.2649i) q^{24} +(1.40263 + 8.55569i) q^{25} +(1.81505 - 11.0713i) q^{26} +(4.92415 + 1.65914i) q^{27} +(0.824947 + 2.97119i) q^{28} +(15.4520 + 38.7815i) q^{29} +(10.2155 - 4.07023i) q^{30} +(2.83849 - 0.788103i) q^{31} +(7.32385 - 21.7364i) q^{32} +(35.3093 + 5.78867i) q^{33} +(-12.4664 + 2.04376i) q^{34} +(7.70959 - 2.59766i) q^{35} +(-2.57868 - 3.80327i) q^{36} +(3.58245 - 7.74334i) q^{37} +(7.71378 - 10.1473i) q^{38} +(1.33727 + 12.2960i) q^{39} +(-33.8397 - 9.39554i) q^{40} +(-13.3440 + 19.6810i) q^{41} +(2.82438 + 4.69415i) q^{42} +(19.6128 - 1.06338i) q^{43} +(-21.7598 - 22.9716i) q^{44} +(-9.65116 + 7.33662i) q^{45} +(-42.8964 + 9.44222i) q^{46} +(-1.59298 + 1.35309i) q^{47} +(0.705838 - 13.0184i) q^{48} +(-21.0536 - 39.7112i) q^{49} +(2.92815 - 13.3027i) q^{50} +(12.6399 - 5.84783i) q^{51} +(5.63898 - 9.37206i) q^{52} +(-33.9932 + 64.1180i) q^{53} +(-6.22200 - 5.28501i) q^{54} +(-57.4091 + 60.6061i) q^{55} +(1.89168 - 17.3937i) q^{56} +(-5.20129 + 13.0542i) q^{57} -65.5874i q^{58} +(24.8967 + 53.4898i) q^{59} +10.7207 q^{60} +(-76.4249 - 30.4505i) q^{61} +(-4.60109 - 0.500398i) q^{62} +(-4.38473 - 4.15344i) q^{63} +(-42.8214 + 50.4133i) q^{64} +(-25.4956 - 13.5169i) q^{65} +(-48.1679 - 28.9817i) q^{66} +(-17.7291 - 38.3208i) q^{67} +(-12.0280 - 2.64756i) q^{68} +(42.7827 - 22.6819i) q^{69} +(-12.7628 - 0.691977i) q^{70} +(-63.6327 - 74.9142i) q^{71} +(5.60477 + 25.4627i) q^{72} +(-27.6076 - 36.3171i) q^{73} +(-9.73151 + 9.21818i) q^{74} +(0.812988 + 14.9947i) q^{75} +(10.6479 - 6.40662i) q^{76} +(-34.4225 - 23.3390i) q^{77} +(5.19863 - 18.7238i) q^{78} +(36.6316 - 3.98393i) q^{79} +(24.2155 + 18.4081i) q^{80} +(8.16818 + 3.77900i) q^{81} +(30.9206 - 20.9647i) q^{82} +(16.4242 + 48.7452i) q^{83} +(0.864066 + 5.27057i) q^{84} +(-5.25683 + 32.0652i) q^{85} +(-29.2434 - 9.85325i) q^{86} +(19.3442 + 69.6714i) q^{87} +(66.4522 + 166.783i) q^{88} +(35.0851 - 13.9792i) q^{89} +(18.3523 - 5.09549i) q^{90} +(4.59036 - 13.6237i) q^{91} +(-42.2575 - 6.92777i) q^{92} +(5.03517 - 0.825475i) q^{93} +(3.11181 - 1.04849i) q^{94} +(-18.3987 - 27.1361i) q^{95} +(16.6815 - 36.0564i) q^{96} +(74.8346 - 98.4432i) q^{97} +(7.63490 + 70.2018i) q^{98} +(59.7150 + 16.5798i) 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

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