LMFDB - Embedded newform 177.3.g.a.10.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(10,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("177.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.82290067918$
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			10.15
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89981 + 0.756953i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(0.132311 + 0.125332i) q^{4} +(3.62948 - 4.27295i) q^{5} +(-3.12952 - 1.65917i) q^{6} +(-2.21876 - 1.33498i) q^{7} +(-3.27829 - 7.08590i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(1.89981 + 0.756953i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(0.132311 + 0.125332i) q^{4} +(3.62948 - 4.27295i) q^{5} +(-3.12952 - 1.65917i) q^{6} +(-2.21876 - 1.33498i) q^{7} +(-3.27829 - 7.08590i) q^{8} +(2.92986 + 0.644911i) q^{9} +(10.1297 - 5.37045i) q^{10} +(14.9816 + 0.812281i) q^{11} +(-0.204356 - 0.240587i) q^{12} +(-3.95392 - 17.9628i) q^{13} +(-3.20470 - 4.21571i) q^{14} +(-7.04977 + 6.67790i) q^{15} +(-0.903891 - 16.6713i) q^{16} +(11.3882 - 6.85207i) q^{17} +(5.07801 + 3.44297i) q^{18} +(-7.70702 + 27.7582i) q^{19} +(1.01576 - 0.110471i) q^{20} +(3.57048 + 2.71421i) q^{21} +(27.8474 + 12.8836i) q^{22} +(-12.2459 + 8.30293i) q^{23} +(4.31792 + 12.8151i) q^{24} +(-1.04046 - 6.34651i) q^{25} +(6.08532 - 37.1188i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(-0.126251 - 0.454716i) q^{28} +(-4.15885 - 10.4379i) q^{29} +(-18.4481 + 7.35038i) q^{30} +(47.1041 - 13.0784i) q^{31} +(0.930361 - 2.76121i) q^{32} +(-25.6447 - 4.20424i) q^{33} +(26.8222 - 4.39727i) q^{34} +(-13.7573 + 4.63536i) q^{35} +(0.306826 + 0.452535i) q^{36} +(-14.9472 + 32.3079i) q^{37} +(-35.6535 + 46.9014i) q^{38} +(3.44438 + 31.6706i) q^{39} +(-42.1762 - 11.7102i) q^{40} +(-20.4051 + 30.0953i) q^{41} +(4.72870 + 7.85916i) q^{42} +(13.2243 - 0.717002i) q^{43} +(1.88044 + 1.98515i) q^{44} +(13.3895 - 10.1785i) q^{45} +(-29.5498 + 6.50440i) q^{46} +(-34.0965 + 28.9618i) q^{47} +(-1.56559 + 28.8755i) q^{48} +(-19.8113 - 37.3681i) q^{49} +(2.82734 - 12.8447i) q^{50} +(-20.8925 + 9.66592i) q^{51} +(1.72817 - 2.87224i) q^{52} +(-20.9578 + 39.5306i) q^{53} +(-8.09905 - 6.87940i) q^{54} +(57.8464 - 61.0677i) q^{55} +(-2.18583 + 20.0984i) q^{56} +(18.4689 - 46.3535i) q^{57} -22.9781i q^{58} +(35.4693 - 47.1480i) q^{59} -1.76972 q^{60} +(68.9967 + 27.4908i) q^{61} +(99.3885 + 10.8092i) q^{62} +(-5.63972 - 5.34222i) q^{63} +(-39.3769 + 46.3580i) q^{64} +(-91.1049 - 48.3008i) q^{65} +(-45.5376 - 27.3991i) q^{66} +(-16.4442 - 35.5437i) q^{67} +(2.36558 + 0.520703i) q^{68} +(22.6411 - 12.0035i) q^{69} +(-29.6449 - 1.60730i) q^{70} +(77.8248 + 91.6224i) q^{71} +(-5.03515 - 22.8749i) q^{72} +(17.4449 + 22.9484i) q^{73} +(-52.8525 + 50.0645i) q^{74} +(0.603065 + 11.1229i) q^{75} +(-4.49872 + 2.70679i) q^{76} +(-32.1563 - 21.8025i) q^{77} +(-17.4295 + 62.7752i) q^{78} +(143.847 - 15.6443i) q^{79} +(-74.5163 - 56.6458i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-61.5466 + 41.7296i) q^{82} +(2.37138 + 7.03801i) q^{83} +(0.132238 + 0.806616i) q^{84} +(12.0548 - 73.5308i) q^{85} +(25.6664 + 8.64802i) q^{86} +(5.20642 + 18.7518i) q^{87} +(-43.3584 - 108.821i) q^{88} +(-37.0843 + 14.7757i) q^{89} +(33.1422 - 9.20188i) q^{90} +(-15.2073 + 45.1336i) q^{91} +(-2.66090 - 0.436232i) q^{92} +(-83.5576 + 13.6986i) q^{93} +(-86.6996 + 29.2125i) q^{94} +(90.6369 + 133.679i) q^{95} +(-2.11907 + 4.58030i) q^{96} +(84.0542 - 110.571i) q^{97} +(-9.35180 - 85.9884i) q^{98} +(43.3703 + 12.0417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9}+O(q^{10}) $ 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9	$ 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9} + 24 q^{12} - 24 q^{15} + 8 q^{16} - 16 q^{17} + 60 q^{19} + 164 q^{20} - 40 q^{22} - 100 q^{25} + 156 q^{26} - 200 q^{28} + 60 q^{29} + 32 q^{35} + 120 q^{36} - 28 q^{41} - 1572 q^{46} - 638 q^{47} + 96 q^{48} - 1328 q^{49} - 1856 q^{50} + 24 q^{51} - 1392 q^{52} - 572 q^{53} - 522 q^{55} - 928 q^{56} - 24 q^{57} + 268 q^{59} + 72 q^{60} + 348 q^{61} + 472 q^{62} + 24 q^{63} + 2580 q^{64} + 1218 q^{65} + 120 q^{66} + 1044 q^{67} + 1936 q^{68} + 2784 q^{70} + 1416 q^{71} + 870 q^{73} + 1752 q^{74} - 240 q^{75} - 120 q^{76} + 468 q^{78} + 420 q^{79} - 376 q^{80} - 180 q^{81} - 168 q^{84} + 348 q^{85} - 232 q^{86} - 144 q^{87} + 212 q^{88} - 152 q^{94} - 788 q^{95} - 3306 q^{98}+O(q^{100}) $ 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9 + 24 * q^12 - 24 * q^15 + 8 * q^16 - 16 * q^17 + 60 * q^19 + 164 * q^20 - 40 * q^22 - 100 * q^25 + 156 * q^26 - 200 * q^28 + 60 * q^29 + 32 * q^35 + 120 * q^36 - 28 * q^41 - 1572 * q^46 - 638 * q^47 + 96 * q^48 - 1328 * q^49 - 1856 * q^50 + 24 * q^51 - 1392 * q^52 - 572 * q^53 - 522 * q^55 - 928 * q^56 - 24 * q^57 + 268 * q^59 + 72 * q^60 + 348 * q^61 + 472 * q^62 + 24 * q^63 + 2580 * q^64 + 1218 * q^65 + 120 * q^66 + 1044 * q^67 + 1936 * q^68 + 2784 * q^70 + 1416 * q^71 + 870 * q^73 + 1752 * q^74 - 240 * q^75 - 120 * q^76 + 468 * q^78 + 420 * q^79 - 376 * q^80 - 180 * q^81 - 168 * q^84 + 348 * q^85 - 232 * q^86 - 144 * q^87 + 212 * q^88 - 152 * q^94 - 788 * q^95 - 3306 * q^98

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 $

$2$	1.89981	+	0.756953i	0.949904	+	0.378476i	0.793058	−	0.609147i	$-0.208488\pi$
$2$	1.89981	+	0.756953i	0.949904	+	0.378476i	0.156846	+	0.987623i	$0.449867\pi$
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$3$	−1.72190	−	0.187268i	−0.573966	−	0.0624225i
$4$	0.132311	+	0.125332i	0.0330779	+	0.0313330i
$5$	3.62948	−	4.27295i	0.725896	−	0.854590i	−0.268170	−	0.963372i	$-0.586419\pi$
$5$	3.62948	−	4.27295i	0.725896	−	0.854590i	0.994066	+	0.108781i	$0.0346948\pi$
$6$	−3.12952	−	1.65917i	−0.521587	−	0.276528i
$7$	−2.21876	−	1.33498i	−0.316966	−	0.190712i	0.348176	−	0.937429i	$-0.386801\pi$
$7$	−2.21876	−	1.33498i	−0.316966	−	0.190712i	−0.665142	+	0.746717i	$0.731629\pi$
$8$	−3.27829	−	7.08590i	−0.409786	−	0.885738i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	10.1297	−	5.37045i	1.01297	−	0.537045i
$11$	14.9816	+	0.812281i	1.36197	+	0.0738437i	0.720579	−	0.693373i	$-0.243876\pi$
$11$	14.9816	+	0.812281i	1.36197	+	0.0738437i	0.641388	+	0.767217i	$0.278359\pi$
$12$	−0.204356	−	0.240587i	−0.0170297	−	0.0200489i
$13$	−3.95392	−	17.9628i	−0.304147	−	1.38176i	−0.842346	−	0.538937i	$-0.818826\pi$
$13$	−3.95392	−	17.9628i	−0.304147	−	1.38176i	0.538199	−	0.842818i	$-0.319105\pi$
$14$	−3.20470	−	4.21571i	−0.228907	−	0.301122i
$15$	−7.04977	+	6.67790i	−0.469985	+	0.445193i
$16$	−0.903891	−	16.6713i	−0.0564932	−	1.04196i
$17$	11.3882	−	6.85207i	0.669896	−	0.403063i	−0.139584	−	0.990210i	$-0.544577\pi$
$17$	11.3882	−	6.85207i	0.669896	−	0.403063i	0.809480	+	0.587147i	$0.199749\pi$
$18$	5.07801	+	3.44297i	0.282112	+	0.191276i
$19$	−7.70702	+	27.7582i	−0.405633	+	1.46096i	0.425539	+	0.904940i	$0.360085\pi$
$19$	−7.70702	+	27.7582i	−0.405633	+	1.46096i	−0.831171	+	0.556016i	$0.812329\pi$
$20$	1.01576	−	0.110471i	0.0507880	−	0.00552353i
$21$	3.57048	+	2.71421i	0.170023	+	0.129248i
$22$	27.8474	+	12.8836i	1.26579	+	0.585617i
$23$	−12.2459	+	8.30293i	−0.532431	+	0.360997i	−0.797583	−	0.603210i	$-0.793888\pi$
$23$	−12.2459	+	8.30293i	−0.532431	+	0.360997i	0.265152	+	0.964207i	$0.414578\pi$
$24$	4.31792	+	12.8151i	0.179913	+	0.533963i
$25$	−1.04046	−	6.34651i	−0.0416183	−	0.253860i
$26$	6.08532	−	37.1188i	0.234051	−	1.42765i
$27$	−4.92415	−	1.65914i	−0.182376	−	0.0614496i
$28$	−0.126251	−	0.454716i	−0.00450897	−	0.0162398i
$29$	−4.15885	−	10.4379i	−0.143409	−	0.359928i	0.839674	−	0.543091i	$-0.182746\pi$
$29$	−4.15885	−	10.4379i	−0.143409	−	0.359928i	−0.983083	+	0.183162i	$0.941367\pi$
$30$	−18.4481	+	7.35038i	−0.614936	+	0.245013i
$31$	47.1041	−	13.0784i	1.51949	−	0.421884i	0.595199	−	0.803578i	$-0.297073\pi$
$31$	47.1041	−	13.0784i	1.51949	−	0.421884i	0.924289	+	0.381694i	$0.124659\pi$
$32$	0.930361	−	2.76121i	0.0290738	−	0.0862879i
$33$	−25.6447	−	4.20424i	−0.777113	−	0.127401i
$34$	26.8222	−	4.39727i	0.788887	−	0.129331i
$35$	−13.7573	+	4.63536i	−0.393065	+	0.132439i
$36$	0.306826	+	0.452535i	0.00852295	+	0.0125704i
$37$	−14.9472	+	32.3079i	−0.403979	+	0.873187i	0.593673	+	0.804706i	$0.297677\pi$
$37$	−14.9472	+	32.3079i	−0.403979	+	0.873187i	−0.997652	+	0.0684809i	$0.978185\pi$
$38$	−35.6535	+	46.9014i	−0.938250	+	1.23425i
$39$	3.44438	+	31.6706i	0.0883175	+	0.812066i
$40$	−42.1762	−	11.7102i	−1.05441	−	0.292754i
$41$	−20.4051	+	30.0953i	−0.497686	+	0.734032i	−0.990711	−	0.135983i	$-0.956581\pi$
$41$	−20.4051	+	30.0953i	−0.497686	+	0.734032i	0.493025	+	0.870015i	$0.335891\pi$
$42$	4.72870	+	7.85916i	0.112588	+	0.187123i
$43$	13.2243	−	0.717002i	0.307542	−	0.0166745i	0.100278	−	0.994959i	$-0.468027\pi$
$43$	13.2243	−	0.717002i	0.307542	−	0.0166745i	0.207264	+	0.978285i	$0.433544\pi$
$44$	1.88044	+	1.98515i	0.0427372	+	0.0451171i
$45$	13.3895	−	10.1785i	0.297545	−	0.226188i
$46$	−29.5498	+	6.50440i	−0.642387	+	0.141400i
$47$	−34.0965	+	28.9618i	−0.725458	+	0.616210i	−0.932097	−	0.362208i	$-0.882023\pi$
$47$	−34.0965	+	28.9618i	−0.725458	+	0.616210i	0.206640	+	0.978417i	$0.433747\pi$
$48$	−1.56559	+	28.8755i	−0.0326164	+	0.601573i
$49$	−19.8113	−	37.3681i	−0.404312	−	0.762614i
$50$	2.82734	−	12.8447i	0.0565468	−	0.256895i
$51$	−20.8925	+	9.66592i	−0.409658	+	0.189528i
$52$	1.72817	−	2.87224i	0.0332340	−	0.0552354i
$53$	−20.9578	+	39.5306i	−0.395430	+	0.745861i	−0.998662	−	0.0517050i	$-0.983534\pi$
$53$	−20.9578	+	39.5306i	−0.395430	+	0.745861i	0.603232	+	0.797566i	$0.293879\pi$
$54$	−8.09905	−	6.87940i	−0.149982	−	0.127396i
$55$	57.8464	−	61.0677i	1.05175	−	1.11032i
$56$	−2.18583	+	20.0984i	−0.0390327	+	0.358900i
$57$	18.4689	−	46.3535i	0.324016	−	0.813218i
$58$		−	22.9781i		−	0.396174i
$59$	35.4693	−	47.1480i	0.601174	−	0.799118i
$59$	35.4693	−	47.1480i	0.601174	−	0.799118i
$60$	−1.76972			−0.0294954
$61$	68.9967	+	27.4908i	1.13109	+	0.450669i	0.859190	−	0.511656i	$-0.170968\pi$
$61$	68.9967	+	27.4908i	1.13109	+	0.450669i	0.271903	+	0.962325i	$0.412347\pi$
$62$	99.3885	+	10.8092i	1.60304	+	0.174341i
$63$	−5.63972	−	5.34222i	−0.0895193	−	0.0847972i
$64$	−39.3769	+	46.3580i	−0.615263	+	0.724344i
$65$	−91.1049	−	48.3008i	−1.40161	−	0.743089i
$66$	−45.5376	−	27.3991i	−0.689964	−	0.415138i
$67$	−16.4442	−	35.5437i	−0.245436	−	0.530502i	0.745230	−	0.666807i	$-0.232339\pi$
$67$	−16.4442	−	35.5437i	−0.245436	−	0.530502i	−0.990667	+	0.136305i	$0.956477\pi$
$68$	2.36558	+	0.520703i	0.0347879	+	0.00765740i
$69$	22.6411	−	12.0035i	0.328131	−	0.173964i
$70$	−29.6449	−	1.60730i	−0.423499	−	0.0229614i
$71$	77.8248	+	91.6224i	1.09612	+	1.29046i	0.953736	+	0.300645i	$0.0972020\pi$
$71$	77.8248	+	91.6224i	1.09612	+	1.29046i	0.142387	+	0.989811i	$0.454522\pi$
$72$	−5.03515	−	22.8749i	−0.0699327	−	0.317707i
$73$	17.4449	+	22.9484i	0.238971	+	0.314361i	0.899908	−	0.436081i	$-0.143634\pi$
$73$	17.4449	+	22.9484i	0.238971	+	0.314361i	−0.660936	+	0.750442i	$0.729841\pi$
$74$	−52.8525	+	50.0645i	−0.714222	+	0.676547i
$75$	0.603065	+	11.1229i	0.00804087	+	0.148305i
$76$	−4.49872	+	2.70679i	−0.0591936	+	0.0356156i
$77$	−32.1563	−	21.8025i	−0.417614	−	0.283149i
$78$	−17.4295	+	62.7752i	−0.223455	+	0.804811i
$79$	143.847	−	15.6443i	1.82085	−	0.198030i	0.867000	−	0.498308i	$-0.166045\pi$
$79$	143.847	−	15.6443i	1.82085	−	0.198030i	0.953851	+	0.300279i	$0.0970797\pi$
$80$	−74.5163	−	56.6458i	−0.931454	−	0.708073i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	−61.5466	+	41.7296i	−0.750568	+	0.508898i
$83$	2.37138	+	7.03801i	0.0285709	+	0.0847953i	0.960990	−	0.276584i	$-0.0892025\pi$
$83$	2.37138	+	7.03801i	0.0285709	+	0.0847953i	−0.932419	+	0.361379i	$0.882306\pi$
$84$	0.132238	+	0.806616i	0.00157426	+	0.00960258i
$85$	12.0548	−	73.5308i	0.141821	−	0.865069i
$86$	25.6664	+	8.64802i	0.298447	+	0.100558i
$87$	5.20642	+	18.7518i	0.0598440	+	0.215538i
$88$	−43.3584	−	108.821i	−0.492709	−	1.23661i
$89$	−37.0843	+	14.7757i	−0.416678	+	0.166020i	−0.569049	−	0.822304i	$-0.692688\pi$
$89$	−37.0843	+	14.7757i	−0.416678	+	0.166020i	0.152371	+	0.988323i	$0.451309\pi$
$90$	33.1422	−	9.20188i	0.368246	−	0.102243i
$91$	−15.2073	+	45.1336i	−0.167113	+	0.495974i
$92$	−2.66090	−	0.436232i	−0.0289228	−	0.00474165i
$93$	−83.5576	+	13.6986i	−0.898469	+	0.147297i
$94$	−86.6996	+	29.2125i	−0.922336	+	0.310771i
$95$	90.6369	+	133.679i	0.954072	+	1.40715i
$96$	−2.11907	+	4.58030i	−0.0220737	+	0.0477114i
$97$	84.0542	−	110.571i	0.866539	−	1.13991i	−0.122531	−	0.992465i	$-0.539101\pi$
$97$	84.0542	−	110.571i	0.866539	−	1.13991i	0.989070	−	0.147447i	$-0.0471057\pi$
$98$	−9.35180	−	85.9884i	−0.0954265	−	0.877432i
$99$	43.3703	+	12.0417i	0.438084	+	0.121633i
$100$	0.657757	−	0.970119i	0.00657757	−	0.00970119i
$101$	4.75676	+	7.90580i	0.0470966	+	0.0782752i	0.879511	−	0.475878i	$-0.157870\pi$
$101$	4.75676	+	7.90580i	0.0470966	+	0.0782752i	−0.832415	+	0.554153i	$0.813042\pi$
$102$	−47.0085	+	2.54872i	−0.460867	+	0.0249875i
$103$	31.3026	+	33.0457i	0.303908	+	0.320832i	0.860005	−	0.510285i	$-0.170460\pi$
$103$	31.3026	+	33.0457i	0.303908	+	0.320832i	−0.556097	+	0.831118i	$0.687702\pi$
$104$	−114.321	+	86.9044i	−1.09924	+	0.835619i
$105$	24.5567	−	5.40533i	0.233873	−	0.0514793i
$106$	−69.7386	+	59.2365i	−0.657911	+	0.558835i
$107$	−7.00595	+	129.217i	−0.0654762	+	1.20764i	0.762543	+	0.646937i	$0.223950\pi$
$107$	−7.00595	+	129.217i	−0.0654762	+	1.20764i	−0.828019	+	0.560700i	$0.810532\pi$
$108$	−0.443578	−	0.836677i	−0.00410721	−	0.00774701i
$109$	−7.10920	+	32.2974i	−0.0652220	+	0.296307i	−0.997929	−	0.0643291i	$-0.979509\pi$
$109$	−7.10920	+	32.2974i	−0.0652220	+	0.296307i	0.932707	+	0.360636i	$0.117440\pi$
$110$	156.122	−	72.2299i	1.41929	−	0.656635i
$111$	31.7878	−	52.8318i	0.286377	−	0.475962i
$112$	−20.2504	+	38.1963i	−0.180807	+	0.341038i
$113$	−106.564	−	90.5167i	−0.943049	−	0.801033i	0.0370970	−	0.999312i	$-0.488189\pi$
$113$	−106.564	−	90.5167i	−0.943049	−	0.801033i	−0.980146	+	0.198279i	$0.936465\pi$
$114$	70.1747	−	74.0826i	0.615568	−	0.649847i
$115$	−8.96823	+	82.4615i	−0.0779846	+	0.717056i
$116$	0.757943	−	1.90229i	0.00653399	−	0.0163991i
$117$		−	55.1785i		−	0.471611i
$118$	103.074	−	62.7235i	0.873505	−	0.531555i
$119$	−34.4152			−0.289203
$120$	70.4302	+	28.0619i	0.586918	+	0.233850i
$121$	103.499	+	11.2562i	0.855363	+	0.0930263i
$122$	110.271	+	104.454i	0.903863	+	0.856184i
$123$	40.7714	−	47.9998i	0.331475	−	0.390242i
$124$	7.87156	+	4.17324i	0.0634803	+	0.0336551i
$125$	89.2015	+	53.6708i	0.713612	+	0.429366i
$126$	−6.67057	−	14.4182i	−0.0529410	−	0.114430i
$127$	143.120	+	31.5030i	1.12693	+	0.248055i	0.739046	−	0.673655i	$-0.235277\pi$
$127$	143.120	+	31.5030i	1.12693	+	0.248055i	0.387880	+	0.921710i	$0.373208\pi$
$128$	−120.197	+	63.7242i	−0.939036	+	0.497845i
$129$	−22.9052	−	1.24188i	−0.177560	−	0.00962700i
$130$	−136.520	−	160.724i	−1.05016	−	1.23634i
$131$	−26.9654	−	122.505i	−0.205842	−	0.935152i	−0.960336	−	0.278845i	$-0.910049\pi$
$131$	−26.9654	−	122.505i	−0.205842	−	0.935152i	0.754494	−	0.656307i	$-0.227882\pi$
$132$	−2.86617	−	3.77038i	−0.0217134	−	0.0285635i
$133$	54.1567	−	51.3000i	0.407194	−	0.385714i
$134$	−4.33604	−	79.9736i	−0.0323585	−	0.596818i
$135$	−24.9615	+	15.0188i	−0.184900	+	0.111251i
$136$	−85.8871	−	58.2329i	−0.631522	−	0.428183i
$137$	54.9802	−	198.021i	0.401315	−	1.44541i	−0.436624	−	0.899644i	$-0.643826\pi$
$137$	54.9802	−	198.021i	0.401315	−	1.44541i	0.837939	−	0.545763i	$-0.183760\pi$
$138$	52.0998	−	5.66619i	0.377535	−	0.0410594i
$139$	7.82788	+	5.95060i	0.0563157	+	0.0428101i	0.632953	−	0.774190i	$-0.281842\pi$
$139$	7.82788	+	5.95060i	0.0563157	+	0.0428101i	−0.576638	+	0.817000i	$0.695636\pi$
$140$	−2.40120	−	1.11092i	−0.0171515	−	0.00793511i
$141$	64.1343	−	43.4842i	0.454853	−	0.308398i
$142$	78.4983	+	232.975i	0.552805	+	1.64067i
$143$	−44.6453	−	272.324i	−0.312205	−	1.90436i
$144$	8.10323	−	49.4275i	0.0562724	−	0.343247i
$145$	−59.6952	−	20.1136i	−0.411691	−	0.138715i
$146$	15.7711	+	56.8024i	0.108021	+	0.389058i
$147$	27.1152	+	68.0540i	0.184457	+	0.462952i
$148$	−6.02691	+	2.40134i	−0.0407224	+	0.0162253i
$149$	−162.744	+	45.1857i	−1.09224	+	0.303259i	−0.766529	−	0.642209i	$-0.778018\pi$
$149$	−162.744	+	45.1857i	−1.09224	+	0.303259i	−0.325713	+	0.945469i	$0.605604\pi$
$150$	−7.27379	+	21.5878i	−0.0484919	+	0.143919i
$151$	−196.988	−	32.2945i	−1.30455	−	0.213871i	−0.530876	−	0.847450i	$-0.678137\pi$
$151$	−196.988	−	32.2945i	−1.30455	−	0.213871i	−0.773678	+	0.633579i	$0.781585\pi$
$152$	221.958	−	36.3881i	1.46025	−	0.239395i
$153$	37.7849	−	12.7312i	0.246960	−	0.0832106i
$154$	−44.5873	−	65.7614i	−0.289528	−	0.427022i
$155$	115.080	−	248.741i	0.742452	−	1.60478i
$156$	−3.51361	+	4.62207i	−0.0225231	+	0.0296287i
$157$	8.77357	+	80.6717i	0.0558826	+	0.513832i	0.988308	+	0.152470i	$0.0487227\pi$
$157$	8.77357	+	80.6717i	0.0558826	+	0.513832i	−0.932425	+	0.361362i	$0.882312\pi$
$158$	285.124	+	79.1643i	1.80458	+	0.501040i
$159$	43.4900	−	64.1429i	0.273522	−	0.403415i
$160$	−8.42180	−	13.9971i	−0.0526363	−	0.0874822i
$161$	38.2550	−	2.07413i	0.237609	−	0.0128828i
$162$	12.6574	+	13.3623i	0.0781324	+	0.0824834i
$163$	−237.919	+	180.861i	−1.45963	+	1.10958i	−0.488060	+	0.872810i	$0.662295\pi$
$163$	−237.919	+	180.861i	−1.45963	+	1.10958i	−0.971566	+	0.236768i	$0.923912\pi$
$164$	−6.47174	+	1.42454i	−0.0394618	+	0.00868621i
$165$	−111.041	+	94.3195i	−0.672979	+	0.571633i
$166$	−0.822271	+	15.1659i	−0.00495344	+	0.0913608i
$167$	−29.5765	−	55.7872i	−0.177105	−	0.334055i	0.779028	−	0.626990i	$-0.215713\pi$
$167$	−29.5765	−	55.7872i	−0.177105	−	0.334055i	−0.956133	+	0.292934i	$0.905368\pi$
$168$	7.52756	−	34.1980i	0.0448069	−	0.203560i
$169$	−153.649	+	71.0857i	−0.909167	+	0.420625i
$170$	78.5611	−	130.570i	0.462124	−	0.768056i
$171$	−40.4821	+	76.3573i	−0.236737	+	0.446534i
$172$	1.83959	+	1.56256i	0.0106953	+	0.00908467i
$173$	2.99989	−	3.16694i	0.0173404	−	0.0183060i	−0.717268	−	0.696798i	$-0.754607\pi$
$173$	2.99989	−	3.16694i	0.0173404	−	0.0183060i	0.734608	+	0.678492i	$0.237366\pi$
$174$	−4.30305	+	39.5659i	−0.0247302	+	0.227390i
$175$	−6.16396	+	15.4704i	−0.0352226	+	0.0884022i
$176$		−	250.497i		−	1.42328i
$177$	−69.9037	+	74.5417i	−0.394936	+	0.421140i
$178$	−81.6377			−0.458639
$179$	−230.638	−	91.8944i	−1.28848	−	0.513377i	−0.377568	−	0.925982i	$-0.623240\pi$
$179$	−230.638	−	91.8944i	−1.28848	−	0.513377i	−0.910910	+	0.412605i	$0.864619\pi$
$180$	3.04728	+	0.331412i	0.0169293	+	0.00184118i
$181$	13.2384	+	12.5400i	0.0731401	+	0.0692820i	0.723396	−	0.690433i	$-0.242580\pi$
$181$	13.2384	+	12.5400i	0.0731401	+	0.0692820i	−0.650256	+	0.759715i	$0.725339\pi$
$182$	−63.0549	+	74.2340i	−0.346456	+	0.407879i
$183$	−113.657	−	60.2572i	−0.621077	−	0.329274i
$184$	98.9794	+	59.5539i	0.537931	+	0.323663i
$185$	83.7996	+	181.130i	0.452971	+	0.979080i
$186$	−169.113	−	37.2245i	−0.909208	−	0.200132i
$187$	176.180	−	93.4048i	0.942140	−	0.499491i
$188$	−8.14121	−	0.441404i	−0.0433043	−	0.00234789i
$189$	8.71059	+	10.2549i	0.0460878	+	0.0542587i
$190$	71.0037	+	322.573i	0.373704	+	1.69775i
$191$	170.575	+	224.388i	0.893065	+	1.17481i	0.983860	+	0.178937i	$0.0572660\pi$
$191$	170.575	+	224.388i	0.893065	+	1.17481i	−0.0907954	+	0.995870i	$0.528941\pi$
$192$	76.4843	−	72.4497i	0.398356	−	0.377342i
$193$	−8.89977	−	164.147i	−0.0461128	−	0.850501i	−0.926511	−	0.376267i	$-0.877208\pi$
$193$	−8.89977	−	164.147i	−0.0461128	−	0.850501i	0.880399	−	0.474234i	$-0.157275\pi$
$194$	243.384	−	146.439i	1.25456	−	0.754843i
$195$	147.828	+	100.230i	0.758093	+	0.514000i
$196$	2.06216	−	7.42722i	0.0105212	−	0.0378940i
$197$	−161.044	+	17.5145i	−0.817480	+	0.0889063i	−0.507298	−	0.861771i	$-0.669356\pi$
$197$	−161.044	+	17.5145i	−0.817480	+	0.0889063i	−0.310182	+	0.950677i	$0.600390\pi$
$198$	73.2802	+	55.7062i	0.370102	+	0.281344i
$199$	104.151	+	48.1854i	0.523372	+	0.242138i	0.663742	−	0.747961i	$-0.268967\pi$
$199$	104.151	+	48.1854i	0.523372	+	0.242138i	−0.140370	+	0.990099i	$0.544829\pi$
$200$	−41.5598	+	28.1783i	−0.207799	+	0.140891i
$201$	21.6591	+	64.2820i	0.107757	+	0.319811i
$202$	3.05262	+	18.6201i	0.0151120	+	0.0921789i
$203$	−4.70697	+	28.7112i	−0.0231870	+	0.141435i
$204$	−3.97577	−	1.33959i	−0.0194891	−	0.00656664i
$205$	54.5359	+	196.420i	0.266029	+	0.958148i
$206$	34.4548	+	86.4751i	0.167256	+	0.419782i
$207$	−41.2335	+	16.4289i	−0.199195	+	0.0793667i
$208$	−295.890	+	82.1533i	−1.42255	+	0.394968i
$209$	−138.011	+	409.603i	−0.660341	+	1.95982i
$210$	50.7445	+	8.31914i	0.241641	+	0.0396150i
$211$	−328.508	+	53.8562i	−1.55691	+	0.255243i	−0.877885	−	0.478872i	$-0.841046\pi$
$211$	−328.508	+	53.8562i	−1.55691	+	0.255243i	−0.679026	+	0.734114i	$0.737598\pi$
$212$	−7.72741	+	2.60367i	−0.0364501	+	0.0122815i
$213$	−116.848	−	172.338i	−0.548584	−	0.809101i
$214$	−111.121	+	240.185i	−0.519258	+	1.12236i
$215$	44.9337	−	59.1092i	0.208994	−	0.274927i
$216$	4.38628	+	40.3312i	0.0203069	+	0.186719i
$217$	−121.972	−	33.8654i	−0.562084	−	0.156062i
$218$	−37.9538	+	55.9776i	−0.174100	+	0.256778i
$219$	−25.7408	−	42.7816i	−0.117538	−	0.195350i
$220$	15.3075	−	0.829947i	0.0695794	−	0.00377249i
$221$	−168.111	−	177.472i	−0.760682	−	0.803042i
$222$	100.382	−	76.3084i	0.452171	−	0.343732i
$223$	−356.234	+	78.4130i	−1.59746	+	0.351628i	−0.922431	−	0.386162i	$-0.873800\pi$
$223$	−356.234	+	78.4130i	−1.59746	+	0.351628i	−0.675030	+	0.737790i	$0.735869\pi$
$224$	−5.75042	+	4.88445i	−0.0256715	+	0.0218056i
$225$	1.04454	−	19.2654i	0.00464240	−	0.0856240i
$226$	−133.935	−	252.629i	−0.592634	−	1.11783i
$227$	−24.2742	+	110.279i	−0.106935	+	0.485810i	0.892463	+	0.451120i	$0.148975\pi$
$227$	−24.2742	+	110.279i	−0.106935	+	0.485810i	−0.999398	+	0.0346900i	$0.988956\pi$
$228$	8.25322	−	3.81835i	0.0361983	−	0.0167471i
$229$	109.774	−	182.445i	0.479361	−	0.796704i	−0.518950	−	0.854805i	$-0.673677\pi$
$229$	109.774	−	182.445i	0.479361	−	0.796704i	0.998311	+	0.0581006i	$0.0185044\pi$
$230$	−79.4573	+	149.872i	−0.345467	+	0.651619i
$231$	51.2869	+	43.5635i	0.222021	+	0.188587i
$232$	−60.3282	+	63.6877i	−0.260035	+	0.274516i
$233$	−5.09345	+	46.8335i	−0.0218603	+	0.201002i	−0.999975	−	0.00706396i	$-0.997751\pi$
$233$	−5.09345	+	46.8335i	−0.0218603	+	0.201002i	0.978115	+	0.208066i	$0.0667170\pi$
$234$	41.7675	−	104.829i	0.178494	−	0.447985i
$235$			250.809i			1.06727i
$236$	10.6021	−	1.79278i	0.0449243	−	0.00759653i
$237$	−250.620			−1.05747
$238$	−65.3822	−	26.0507i	−0.274715	−	0.109457i
$239$	278.069	+	30.2418i	1.16347	+	0.126535i	0.669409	−	0.742894i	$-0.266547\pi$
$239$	278.069	+	30.2418i	1.16347	+	0.126535i	0.494059	+	0.869429i	$0.335513\pi$
$240$	117.701	+	111.493i	0.490423	+	0.464553i
$241$	−88.5531	+	104.253i	−0.367440	+	0.432584i	−0.914548	−	0.404478i	$-0.867453\pi$
$241$	−88.5531	+	104.253i	−0.367440	+	0.432584i	0.547107	+	0.837063i	$0.315729\pi$
$242$	188.108	+	99.7284i	0.777304	+	0.412101i
$243$	−13.3571	−	8.03669i	−0.0549674	−	0.0330728i
$244$	5.68358	+	12.2848i	0.0232933	+	0.0503477i
$245$	−231.577	−	50.9739i	−0.945211	−	0.208057i
$246$	113.791	−	60.3284i	0.462567	−	0.245237i
$247$	529.088	+	28.6863i	2.14206	+	0.116139i
$248$	−247.093	−	290.901i	−0.996344	−	1.17299i
$249$	−2.76528	−	12.5628i	−0.0111056	−	0.0504531i
$250$	128.840	+	169.486i	0.515358	+	0.677942i
$251$	54.2296	−	51.3690i	0.216054	−	0.204657i	−0.572017	−	0.820242i	$-0.693839\pi$
$251$	54.2296	−	51.3690i	0.216054	−	0.204657i	0.788071	+	0.615585i	$0.211080\pi$
$252$	−0.0766472	−	1.41367i	−0.000304156	−	0.00560982i
$253$	−190.208	+	114.444i	−0.751810	+	0.452349i
$254$	248.053	+	168.184i	0.976588	+	0.662143i
$255$	−34.5270	+	124.355i	−0.135400	+	0.487667i
$256$	−34.7154	+	3.77553i	−0.135607	+	0.0147482i
$257$	−17.9431	−	13.6400i	−0.0698175	−	0.0530739i	0.569683	−	0.821864i	$-0.307066\pi$
$257$	−17.9431	−	13.6400i	−0.0698175	−	0.0530739i	−0.639501	+	0.768790i	$0.720859\pi$
$258$	−42.5754	−	19.6975i	−0.165021	−	0.0763468i
$259$	76.2949	−	51.7292i	0.294575	−	0.199727i
$260$	−6.00059	−	17.8091i	−0.0230792	−	0.0684966i
$261$	−5.45332	−	33.2638i	−0.0208939	−	0.127447i
$262$	41.5014	−	253.147i	0.158402	−	0.966211i
$263$	−419.527	−	141.355i	−1.59516	−	0.537472i	−0.625144	−	0.780509i	$-0.714960\pi$
$263$	−419.527	−	141.355i	−1.59516	−	0.537472i	−0.970017	+	0.243037i	$0.921856\pi$
$264$	54.2800	+	195.499i	0.205606	+	0.740526i
$265$	92.8465	+	233.027i	0.350364	+	0.879348i
$266$	141.719	−	56.4661i	0.532779	−	0.212278i
$267$	66.6224	−	18.4976i	0.249522	−	0.0692795i
$268$	2.27900	−	6.76383i	0.00850372	−	0.0252382i
$269$	63.8330	+	10.4649i	0.237297	+	0.0389029i	0.279257	−	0.960216i	$-0.409912\pi$
$269$	63.8330	+	10.4649i	0.237297	+	0.0389029i	−0.0419597	+	0.999119i	$0.513360\pi$
$270$	−58.7907	+	9.63824i	−0.217743	+	0.0356972i
$271$	87.6230	−	29.5236i	0.323332	−	0.108943i	−0.152955	−	0.988233i	$-0.548879\pi$
$271$	87.6230	−	29.5236i	0.323332	−	0.108943i	0.476287	+	0.879290i	$0.341982\pi$
$272$	−124.527	−	183.663i	−0.457819	−	0.675232i
$273$	34.6374	−	74.8676i	0.126877	−	0.274240i
$274$	254.344	−	334.584i	0.928264	−	1.22111i
$275$	−10.4326	−	95.9262i	−0.0379367	−	0.348823i
$276$	4.50010	+	1.24945i	0.0163047	+	0.00452698i
$277$	237.823	−	350.762i	0.858565	−	1.26629i	−0.103819	−	0.994596i	$-0.533106\pi$
$277$	237.823	−	350.762i	0.858565	−	1.26629i	0.962384	−	0.271693i	$-0.0875835\pi$
$278$	10.3671	+	17.2303i	0.0372919	+	0.0619796i
$279$	146.443	−	7.93991i	0.524885	−	0.0284585i
$280$	77.9460	+	82.2866i	0.278379	+	0.293881i
$281$	−358.894	+	272.825i	−1.27720	+	0.970906i	−0.277256	+	0.960796i	$0.589425\pi$
$281$	−358.894	+	272.825i	−1.27720	+	0.970906i	−0.999949	+	0.0101095i	$0.996782\pi$
$282$	154.758	−	34.0649i	0.548789	−	0.120797i
$283$	214.637	−	182.314i	0.758435	−	0.644220i	−0.182346	−	0.983234i	$-0.558369\pi$
$283$	214.637	−	182.314i	0.758435	−	0.644220i	0.940781	+	0.339014i	$0.110093\pi$
$284$	−1.18612	+	21.8766i	−0.00417647	+	0.0770304i
$285$	−131.034	−	247.156i	−0.459767	−	0.867213i
$286$	121.319	−	551.158i	0.424192	−	1.92713i
$287$	85.4509	−	39.5338i	0.297738	−	0.137748i
$288$	4.50657	−	7.48997i	0.0156478	−	0.0260068i
$289$	−52.6291	+	99.2690i	−0.182108	+	0.343491i
$290$	−98.1843	−	83.3985i	−0.338567	−	0.287581i
$291$	−165.439	+	174.652i	−0.568520	+	0.600179i
$292$	−0.568007	+	5.22274i	−0.00194523	+	0.0178861i
$293$	148.594	−	372.943i	0.507147	−	1.27284i	−0.423158	−	0.906056i	$-0.639078\pi$
$293$	148.594	−	372.943i	0.507147	−	1.27284i	0.930305	−	0.366787i	$-0.119542\pi$
$294$			149.814i			0.509573i
$295$	−72.7261	−	322.681i	−0.246529	−	1.09383i
$296$	277.932			0.938960
$297$	−72.4241	−	28.8564i	−0.243852	−	0.0971596i
$298$	−343.386	−	37.3455i	−1.15230	−	0.125320i
$299$	197.563	+	187.142i	0.660747	+	0.625893i
$300$	−1.31426	+	1.54727i	−0.00438087	+	0.00515756i
$301$	−30.2988	−	16.0634i	−0.100660	−	0.0533668i
$302$	−349.793	−	210.464i	−1.15826	−	0.696900i
$303$	−6.71015	−	14.5038i	−0.0221457	−	0.0478672i
$304$	469.731	+	103.396i	1.54517	+	0.340117i
$305$	367.889	−	195.042i	1.20619	−	0.639483i
$306$	81.4210	+	4.41452i	0.266082	+	0.0144265i
$307$	118.957	+	140.047i	0.387482	+	0.456179i	0.920973	−	0.389627i	$-0.127396\pi$
$307$	118.957	+	140.047i	0.387482	+	0.456179i	−0.533491	+	0.845806i	$0.679120\pi$
$308$	−1.52209	−	6.91494i	−0.00494186	−	0.0224511i
$309$	−47.7114	−	62.7633i	−0.154406	−	0.203117i
$310$	406.916	−	385.451i	1.31263	−	1.24339i
$311$	22.2975	+	411.253i	0.0716961	+	1.32236i	0.784121	+	0.620608i	$0.213114\pi$
$311$	22.2975	+	411.253i	0.0716961	+	1.32236i	−0.712425	+	0.701749i	$0.752403\pi$
$312$	213.123	−	128.232i	0.683086	−	0.410999i
$313$	48.4137	+	32.8253i	0.154676	+	0.104873i	0.636070	−	0.771631i	$-0.280559\pi$
$313$	48.4137	+	32.8253i	0.154676	+	0.104873i	−0.481394	+	0.876504i	$0.659869\pi$
$314$	−44.3965	+	159.902i	−0.141390	+	0.509242i
$315$	−43.2963	+	4.70875i	−0.137449	+	0.0149484i
$316$	20.9934	+	15.9588i	0.0664347	+	0.0505024i
$317$	−287.571	−	133.044i	−0.907163	−	0.419698i	−0.0898919	−	0.995952i	$-0.528652\pi$
$317$	−287.571	−	133.044i	−0.907163	−	0.419698i	−0.817271	+	0.576253i	$0.804514\pi$
$318$	131.176	−	88.9394i	0.412503	−	0.279684i
$319$	−53.8278	−	159.755i	−0.168739	−	0.500800i
$320$	55.1682	+	336.511i	0.172400	+	1.05160i
$321$	36.2617	−	221.187i	0.112965	−	0.689055i
$322$	74.2472	+	25.0168i	0.230581	+	0.0776919i
$323$	102.432	+	368.926i	0.317126	+	1.14218i
$324$	0.607114	+	1.52374i	0.00187381	+	0.00470290i
$325$	−109.887	+	43.7831i	−0.338115	+	0.134717i
$326$	−588.904	+	163.508i	−1.80645	+	0.501559i
$327$	18.2896	−	54.2815i	0.0559314	−	0.165999i
$328$	280.146	+	45.9277i	0.854105	+	0.140023i
$329$	114.316	−	18.7411i	0.347464	−	0.0569638i
$330$	−282.353	+	95.1358i	−0.855615	+	0.288290i
$331$	−205.535	−	303.141i	−0.620952	−	0.915835i	0.379003	−	0.925396i	$-0.376267\pi$
$331$	−205.535	−	303.141i	−0.620952	−	0.915835i	−0.999954	+	0.00956038i	$0.996957\pi$
$332$	−0.568328	+	1.22842i	−0.00171183	+	0.00370006i
$333$	−64.6291	+	85.0181i	−0.194081	+	0.255310i
$334$	−13.9614	−	128.373i	−0.0418006	−	0.384351i
$335$	−211.560	−	58.7394i	−0.631523	−	0.175342i
$336$	42.0220	−	61.9779i	0.125066	−	0.184458i
$337$	18.1314	+	30.1346i	0.0538023	+	0.0894201i	0.882591	−	0.470141i	$-0.155797\pi$
$337$	18.1314	+	30.1346i	0.0538023	+	0.0894201i	−0.828789	+	0.559562i	$0.810970\pi$
$338$	−345.712	+	18.7440i	−1.02282	+	0.0554556i
$339$	166.542	+	175.817i	0.491275	+	0.518633i
$340$	10.8108	−	8.21812i	0.0317963	−	0.0241710i
$341$	716.320	−	157.674i	2.10065	−	0.462387i
$342$	−134.707	+	114.421i	−0.393880	+	0.334565i
$343$	−12.7985	+	236.054i	−0.0373133	+	0.688204i
$344$	−48.4337	−	91.3557i	−0.140796	−	0.265569i
$345$	30.8847	−	140.311i	0.0895210	−	0.406698i
$346$	8.09644	−	3.74581i	0.0234001	−	0.0108260i
$347$	−66.5395	+	110.590i	−0.191756	+	0.318702i	−0.937788	−	0.347209i	$-0.887129\pi$
$347$	−66.5395	+	110.590i	−0.191756	+	0.318702i	0.746031	+	0.665911i	$0.231957\pi$
$348$	−1.66134	+	3.13362i	−0.00477396	+	0.00900465i
$349$	−237.034	−	201.339i	−0.679182	−	0.576902i	0.239982	−	0.970777i	$-0.422858\pi$
$349$	−237.034	−	201.339i	−0.679182	−	0.576902i	−0.919164	+	0.393875i	$0.871134\pi$
$350$	−23.4207	+	24.7249i	−0.0669163	+	0.0706426i
$351$	−10.3331	+	95.0117i	−0.0294392	+	0.270689i
$352$	16.1812	−	40.6118i	0.0459693	−	0.115374i
$353$			141.345i			0.400410i	0.979754	+	0.200205i	$0.0641609\pi$
$353$			141.345i			0.400410i	−0.979754	+	0.200205i	$0.935839\pi$
$354$	−189.228	+	88.7012i	−0.534543	+	0.250568i
$355$	673.961			1.89848
$356$	−6.75856	−	2.69286i	−0.0189847	−	0.00756420i
$357$	59.2594	+	6.44485i	0.165993	+	0.0180528i
$358$	−368.607	−	349.163i	−1.02963	−	0.975317i
$359$	−118.924	+	140.008i	−0.331263	+	0.389993i	−0.902427	−	0.430843i	$-0.858216\pi$
$359$	−118.924	+	140.008i	−0.331263	+	0.389993i	0.571164	+	0.820836i	$0.306492\pi$
$360$	−116.018	−	61.5091i	−0.322273	−	0.170859i
$361$	−401.793	−	241.751i	−1.11300	−	0.669669i
$362$	15.6581	+	33.8445i	0.0432545	+	0.0934930i
$363$	−176.107	−	38.7640i	−0.485142	−	0.106788i
$364$	−7.66879	+	4.06573i	−0.0210681	+	0.0111696i
$365$	161.373	+	8.74939i	0.442118	+	0.0239709i
$366$	−170.315	−	200.510i	−0.465341	−	0.547842i
$367$	19.2508	+	87.4572i	0.0524545	+	0.238303i	0.995552	−	0.0942130i	$-0.0300335\pi$
$367$	19.2508	+	87.4572i	0.0524545	+	0.238303i	−0.943098	+	0.332516i	$0.892102\pi$
$368$	149.490	+	196.650i	0.406222	+	0.534375i
$369$	−79.1930	+	75.0156i	−0.214615	+	0.203294i
$370$	22.0964	+	407.544i	0.0597200	+	1.10147i
$371$	99.2731	−	59.7306i	0.267582	−	0.160999i
$372$	−12.7725	−	8.65997i	−0.0343347	−	0.0232795i
$373$	143.397	−	516.470i	0.384443	−	1.38464i	−0.477945	−	0.878390i	$-0.658618\pi$
$373$	143.397	−	516.470i	0.384443	−	1.38464i	0.862388	−	0.506248i	$-0.168968\pi$
$374$	405.412	−	44.0912i	1.08399	−	0.117891i
$375$	−143.545	−	109.120i	−0.382787	−	0.290987i
$376$	316.999	+	146.659i	0.843083	+	0.390052i
$377$	−171.051	+	115.975i	−0.453716	+	0.307627i
$378$	8.78597	+	26.0758i	0.0232433	+	0.0689837i
$379$	−11.7270	−	71.5316i	−0.0309420	−	0.188738i	0.966833	−	0.255409i	$-0.0822103\pi$
$379$	−11.7270	−	71.5316i	−0.0309420	−	0.188738i	−0.997775	+	0.0666717i	$0.978762\pi$
$380$	−4.76202	+	29.0470i	−0.0125316	+	0.0764396i
$381$	−240.538	−	81.0466i	−0.631333	−	0.212721i
$382$	154.209	+	555.412i	0.403689	+	1.45396i
$383$	48.3460	+	121.339i	0.126230	+	0.316813i	0.978487	−	0.206311i	$-0.0661458\pi$
$383$	48.3460	+	121.339i	0.126230	+	0.316813i	−0.852257	+	0.523124i	$0.824766\pi$
$384$	218.900	−	87.2176i	0.570051	−	0.227129i
$385$	−209.872	+	58.2705i	−0.545121	+	0.151352i
$386$	107.343	−	318.584i	0.278092	−	0.825347i
$387$	39.2078	+	6.42780i	0.101312	+	0.0166093i
$388$	24.9795	−	4.09518i	0.0643801	−	0.0105546i
$389$	−316.889	+	106.773i	−0.814626	+	0.274479i	−0.695616	−	0.718414i	$-0.744869\pi$
$389$	−316.889	+	106.773i	−0.814626	+	0.274479i	−0.119010	+	0.992893i	$0.537972\pi$
$390$	204.976	+	302.317i	0.525579	+	0.775171i
$391$	−82.5670	+	178.466i	−0.211169	+	0.456434i
$392$	−199.839	+	262.884i	−0.509794	+	0.670623i
$393$	23.4904	+	215.991i	0.0597720	+	0.549594i
$394$	−319.210	−	88.6281i	−0.810176	−	0.224944i
$395$	455.243	−	671.433i	1.15251	−	1.69983i
$396$	4.22917	+	7.02894i	0.0106797	+	0.0177499i
$397$	701.604	−	38.0399i	1.76727	−	0.0958184i	0.858419	−	0.512949i	$-0.171447\pi$
$397$	701.604	−	38.0399i	1.76727	−	0.0958184i	0.908847	+	0.417131i	$0.136964\pi$
$398$	161.393	+	170.380i	0.405510	+	0.428092i
$399$	−102.859	+	78.1915i	−0.257792	+	0.195969i
$400$	−104.864	+	23.0823i	−0.262160	+	0.0577058i
$401$	249.392	−	211.835i	0.621924	−	0.528267i	−0.280090	−	0.959974i	$-0.590364\pi$
$401$	249.392	−	211.835i	0.621924	−	0.528267i	0.902014	+	0.431706i	$0.142088\pi$
$402$	−7.51025	+	138.518i	−0.0186822	+	0.344573i
$403$	−421.171	−	794.412i	−1.04509	−	1.97125i
$404$	−0.361476	+	1.64220i	−0.000894743	+	0.00406486i
$405$	45.7937	−	21.1864i	0.113071	−	0.0523122i
$406$	−30.6754	+	50.9829i	−0.0755552	+	0.125574i
$407$	−250.177	+	471.884i	−0.614686	+	1.15942i
$408$	136.984	+	116.355i	0.335744	+	0.285184i
$409$	44.8765	−	47.3756i	0.109723	−	0.115833i	−0.668820	−	0.743424i	$-0.733200\pi$
$409$	44.8765	−	47.3756i	0.109723	−	0.115833i	0.778543	+	0.627591i	$0.215959\pi$
$410$	−45.0733	+	414.442i	−0.109935	+	1.01083i
$411$	−131.753	+	330.675i	−0.320567	+	0.804563i
$412$			8.29554i			0.0201348i
$413$	−141.640	+	57.2592i	−0.342953	+	0.138642i
$414$	−90.7716			−0.219255
$415$	38.6800	+	15.4115i	0.0932047	+	0.0371362i
$416$	−53.2777	−	5.79430i	−0.128071	−	0.0139286i
$417$	−12.3645	−	11.7122i	−0.0296510	−	0.0280869i
$418$	−572.245	+	673.698i	−1.36901	+	1.61172i
$419$	383.893	+	203.527i	0.916212	+	0.485745i	0.858630	−	0.512596i	$-0.171316\pi$
$419$	383.893	+	203.527i	0.916212	+	0.485745i	0.0575821	+	0.998341i	$0.481661\pi$
$420$	3.92659	+	2.36255i	0.00934902	+	0.00562512i
$421$	299.777	+	647.957i	0.712059	+	1.53909i	0.837167	+	0.546948i	$0.184210\pi$
$421$	299.777	+	647.957i	0.712059	+	1.53909i	−0.125107	+	0.992143i	$0.539927\pi$
$422$	−664.869	−	146.349i	−1.57552	−	0.346798i
$423$	−118.576	+	62.8650i	−0.280321	+	0.148617i
$424$	348.816	+	18.9122i	0.822679	+	0.0446044i
$425$	−55.3357	−	65.1462i	−0.130202	−	0.153285i
$426$	−91.5374	−	415.859i	−0.214877	−	0.976194i
$427$	−116.387	−	153.105i	−0.272570	−	0.358560i
$428$	−17.1220	+	16.2188i	−0.0400047	+	0.0378945i
$429$	25.8771	+	477.275i	0.0603195	+	1.11253i
$430$	130.108	−	78.2835i	0.302577	−	0.182055i
$431$	522.182	+	354.048i	1.21156	+	0.821457i	0.988183	−	0.153276i	$-0.0489822\pi$
$431$	522.182	+	354.048i	1.21156	+	0.821457i	0.223375	+	0.974733i	$0.428293\pi$
$432$	−23.2091	+	83.5916i	−0.0537248	+	0.193499i
$433$	331.260	−	36.0266i	0.765034	−	0.0832024i	0.282722	−	0.959202i	$-0.408763\pi$
$433$	331.260	−	36.0266i	0.765034	−	0.0832024i	0.482312	+	0.876000i	$0.339797\pi$
$434$	−206.089	−	156.665i	−0.474860	−	0.360979i
$435$	99.0224	+	45.8126i	0.227638	+	0.105316i
$436$	−4.98853	+	3.38231i	−0.0114416	+	0.00775759i
$437$	−136.095	−	403.915i	−0.311430	−	0.924290i
$438$	−16.5190	−	100.761i	−0.0377146	−	0.230049i
$439$	0.187606	−	1.14435i	0.000427349	−	0.00260671i	−0.986612	−	0.163085i	$-0.947855\pi$
$439$	0.187606	−	1.14435i	0.000427349	−	0.00260671i	0.987039	+	0.160478i	$0.0513037\pi$
$440$	−622.357	−	209.696i	−1.41445	−	0.476583i
$441$	−33.9453	−	122.260i	−0.0769734	−	0.277233i
$442$	−185.040	−	464.415i	−0.418642	−	1.05071i
$443$	−375.115	+	149.460i	−0.846761	+	0.337380i	−0.752844	−	0.658200i	$-0.771318\pi$
$443$	−375.115	+	149.460i	−0.846761	+	0.337380i	−0.0939175	+	0.995580i	$0.529939\pi$
$444$	10.8274	−	3.00622i	0.0243861	−	0.00677076i
$445$	−71.4607	+	212.088i	−0.160586	+	0.476602i
$446$	−736.131	−	120.683i	−1.65052	−	0.270589i
$447$	288.690	−	47.3284i	0.645840	−	0.105880i
$448$	149.255	−	50.2899i	0.333159	−	0.112254i
$449$	−101.228	−	149.300i	−0.225452	−	0.332517i	0.698093	−	0.716007i	$-0.254032\pi$
$449$	−101.228	−	149.300i	−0.225452	−	0.332517i	−0.923545	+	0.383490i	$0.874722\pi$
$450$	16.5674	−	35.8099i	0.0368165	−	0.0795775i
$451$	−330.148	+	434.302i	−0.732036	+	0.962976i
$452$	−2.75506	−	25.3323i	−0.00609526	−	0.0560450i
$453$	333.145	+	92.4972i	0.735419	+	0.204188i
$454$	−129.592	+	191.134i	−0.285446	+	0.421001i
$455$	137.659	+	228.791i	0.302548	+	0.502838i
$456$	−389.003	+	21.0911i	−0.853076	+	0.0462524i
$457$	286.525	+	302.480i	0.626969	+	0.661883i	0.959663	−	0.281152i	$-0.0907164\pi$
$457$	286.525	+	302.480i	0.626969	+	0.661883i	−0.332695	+	0.943035i	$0.607958\pi$
$458$	346.651	−	263.517i	0.756881	−	0.575366i
$459$	−67.4459	+	14.8460i	−0.146941	+	0.0323442i
$460$	−11.5217	+	9.78659i	−0.0250471	+	0.0212752i
$461$	18.0873	−	333.601i	0.0392349	−	0.723646i	−0.911056	−	0.412282i	$-0.864732\pi$
$461$	18.0873	−	333.601i	0.0392349	−	0.723646i	0.950291	−	0.311363i	$-0.100786\pi$
$462$	64.4598	+	121.584i	0.139523	+	0.263169i
$463$	69.1319	−	314.069i	0.149313	−	0.678335i	−0.841178	−	0.540758i	$-0.818137\pi$
$463$	69.1319	−	314.069i	0.149313	−	0.678335i	0.990491	−	0.137577i	$-0.0439315\pi$
$464$	−170.255	+	78.7681i	−0.366928	+	0.169759i
$465$	−244.737	+	406.756i	−0.526317	+	0.874745i
$466$	−45.1274	+	85.1192i	−0.0968398	+	0.182659i
$467$	−626.155	−	531.861i	−1.34080	−	1.13889i	−0.978366	−	0.206879i	$-0.933669\pi$
$467$	−626.155	−	531.861i	−1.34080	−	1.13889i	−0.362436	−	0.932009i	$-0.618055\pi$
$468$	6.91564	−	7.30075i	0.0147770	−	0.0155999i
$469$	−10.9644	+	100.816i	−0.0233782	+	0.214959i
$470$	−189.851	+	476.489i	−0.403938	+	1.01381i
$471$		−	140.551i		−	0.298411i
$472$	−450.365	−	96.7671i	−0.954162	−	0.205015i
$473$	198.704			0.420094
$474$	−476.130	−	189.707i	−1.00449	−	0.400227i
$475$	184.186	+	20.0315i	0.387761	+	0.0421715i
$476$	−4.55352	−	4.31333i	−0.00956622	−	0.00906161i
$477$	−86.8972	+	102.303i	−0.182174	+	0.214472i
$478$	505.386	+	267.939i	1.05729	+	0.560541i
$479$	438.909	+	264.083i	0.916303	+	0.551321i	0.893820	−	0.448426i	$-0.148015\pi$
$479$	438.909	+	264.083i	0.916303	+	0.551321i	0.0224833	+	0.999747i	$0.492843\pi$
$480$	11.8803	+	25.6788i	0.0247506	+	0.0534975i
$481$	639.442	+	140.752i	1.32940	+	0.292623i
$482$	−247.148	+	131.030i	−0.512756	+	0.271846i
$483$	−66.2596	−	3.59249i	−0.137183	−	0.00743787i
$484$	12.2833	+	14.4611i	0.0253788	+	0.0298782i
$485$	−167.394	−	760.476i	−0.345141	−	1.56799i
$486$	−19.2925	−	25.3788i	−0.0396965	−	0.0522198i
$487$	−649.044	+	614.807i	−1.33274	+	1.26244i	−0.393436	+	0.919352i	$0.628714\pi$
$487$	−649.044	+	614.807i	−1.33274	+	1.26244i	−0.939304	+	0.343086i	$0.888528\pi$
$488$	−31.3939	−	579.027i	−0.0643318	−	1.18653i
$489$	443.542	−	266.870i	0.907038	−	0.545747i
$490$	−401.366	−	272.133i	−0.819115	−	0.555374i
$491$	11.3302	−	40.8077i	0.0230758	−	0.0831114i	−0.951116	−	0.308835i	$-0.900061\pi$
$491$	11.3302	−	40.8077i	0.0230758	−	0.0831114i	0.974191	+	0.225724i	$0.0724747\pi$
$492$	11.4104	−	1.24096i	0.0231920	−	0.00252228i
$493$	−118.883	−	90.3728i	−0.241143	−	0.183312i
$494$	983.451	+	454.993i	1.99079	+	0.921039i
$495$	208.865	−	141.614i	0.421950	−	0.286089i
$496$	−260.611	−	773.465i	−0.525425	−	1.55941i
$497$	−50.3601	−	307.183i	−0.101328	−	0.618074i
$498$	4.25595	−	25.9601i	0.00854608	−	0.0521288i
$499$	−105.095	−	35.4107i	−0.210612	−	0.0709634i	0.212018	−	0.977266i	$-0.431996\pi$
$499$	−105.095	−	35.4107i	−0.210612	−	0.0709634i	−0.422630	+	0.906302i	$0.638893\pi$
$500$	5.07571	+	18.2811i	0.0101514	+	0.0365621i
$501$	40.4806	+	101.599i	0.0807996	+	0.202792i
$502$	141.910	−	56.5420i	0.282689	−	0.112633i
$503$	4.63556	−	1.28706i	0.00921582	−	0.00255876i	−0.262917	−	0.964818i	$-0.584685\pi$
$503$	4.63556	−	1.28706i	0.00921582	−	0.00255876i	0.272133	+	0.962260i	$0.412271\pi$
$504$	−19.3659	+	57.4758i	−0.0384243	+	0.114039i
$505$	51.0456	+	8.36851i	0.101080	+	0.0165713i
$506$	−447.988	+	73.4439i	−0.885351	+	0.145146i
$507$	277.880	−	93.6287i	0.548087	−	0.184672i
$508$	14.9880	+	22.1057i	0.0295040	+	0.0435151i
$509$	103.991	−	224.773i	0.204305	−	0.441598i	−0.778155	−	0.628072i	$-0.783844\pi$
$509$	103.991	−	224.773i	0.204305	−	0.441598i	0.982460	+	0.186475i	$0.0597063\pi$
$510$	−159.726	+	210.115i	−0.313187	+	0.411991i
$511$	−8.07034	−	74.2056i	−0.0157932	−	0.145216i
$512$	455.531	+	126.477i	0.889708	+	0.247026i
$513$	84.0052	−	123.898i	0.163753	−	0.241517i
$514$	−23.7636	−	39.4955i	−0.0462327	−	0.0768394i
$515$	254.815	−	13.8157i	0.494786	−	0.0268265i
$516$	−2.87497	−	3.03507i	−0.00557165	−	0.00588192i
$517$	−534.347	+	406.200i	−1.03355	+	0.785686i
$518$	184.102	−	40.5240i	0.355410	−	0.0782316i
$519$	−5.75857	+	4.89137i	−0.0110955	+	0.00942460i
$520$	−43.5864	+	803.905i	−0.0838201	+	1.54597i
$521$	22.5048	+	42.4486i	0.0431955	+	0.0814753i	0.904170	−	0.427173i	$-0.140490\pi$
$521$	22.5048	+	42.4486i	0.0431955	+	0.0814753i	−0.860975	+	0.508648i	$0.830146\pi$
$522$	14.8188	−	67.3227i	0.0283886	−	0.128971i
$523$	634.925	−	293.748i	1.21401	−	0.561659i	0.294846	−	0.955545i	$-0.404732\pi$
$523$	634.925	−	293.748i	1.21401	−	0.561659i	0.919159	+	0.393886i	$0.128869\pi$
$524$	11.7860	−	19.5884i	0.0224923	−	0.0373825i
$525$	13.5108	−	25.4841i	0.0257349	−	0.0485411i
$526$	−690.022	−	586.110i	−1.31183	−	1.11428i
$527$	446.819	−	471.701i	0.847853	−	0.895068i
$528$	−46.9101	+	431.331i	−0.0888448	+	0.816915i
$529$	−114.780	+	288.075i	−0.216975	+	0.544565i
$530$			512.987i			0.967901i
$531$	134.326	−	115.263i	0.252969	−	0.217067i
$532$	13.5951			0.0255547
$533$	621.277	+	247.539i	1.16562	+	0.464427i
$534$	140.572	+	15.2881i	0.263243	+	0.0286294i
$535$	526.711	+	498.927i	0.984506	+	0.932574i
$536$	−197.950	+	233.045i	−0.369310	+	0.434785i
$537$	379.925	+	201.424i	0.707496	+	0.375091i
$538$	113.349	+	68.1999i	0.210686	+	0.126766i
$539$	−266.452	−	575.927i	−0.494346	−	1.06851i
$540$	−5.18504	−	1.14131i	−0.00960192	−	0.00211354i
$541$	−36.9333	+	19.5808i	−0.0682686	+	0.0361937i	−0.502193	−	0.864756i	$-0.667473\pi$
$541$	−36.9333	+	19.5808i	−0.0682686	+	0.0361937i	0.433924	+	0.900949i	$0.357128\pi$
$542$	188.815	+	10.2372i	0.348367	+	0.0188879i
$543$	−20.4468	−	24.0718i	−0.0376552	−	0.0443311i
$544$	−8.32486	−	37.8202i	−0.0153031	−	0.0695225i
$545$	112.203	+	147.600i	0.205877	+	0.270826i
$546$	122.476	−	116.015i	0.224315	−	0.212482i
$547$	−43.1806	−	796.420i	−0.0789408	−	1.45598i	−0.722919	−	0.690933i	$-0.757200\pi$
$547$	−43.1806	−	796.420i	−0.0789408	−	1.45598i	0.643978	−	0.765044i	$-0.277283\pi$
$548$	32.0929	−	19.3096i	0.0585636	−	0.0352366i
$549$	184.422	+	125.041i	0.335923	+	0.227761i
$550$	52.7917	−	190.138i	0.0959848	−	0.345706i
$551$	321.790	−	34.9968i	0.584011	−	0.0635150i
$552$	−159.280	−	121.081i	−0.288550	−	0.219350i
$553$	−340.048	−	157.323i	−0.614914	−	0.284490i
$554$	717.328	−	486.360i	1.29482	−	0.877907i
$555$	−110.374	−	327.580i	−0.198873	−	0.590234i
$556$	0.289917	+	1.76842i	0.000521434	+	0.00318061i
$557$	149.582	−	912.412i	0.268550	−	1.63808i	−0.416178	−	0.909283i	$-0.636631\pi$
$557$	149.582	−	912.412i	0.268550	−	1.63808i	0.684728	−	0.728799i	$-0.259921\pi$
$558$	284.224	+	95.7661i	0.509361	+	0.171624i
$559$	−65.1672	−	234.711i	−0.116578	−	0.419877i
$560$	89.7126	+	225.162i	0.160201	+	0.402074i
$561$	−320.856	+	127.841i	−0.571936	+	0.227880i
$562$	−888.346	+	246.648i	−1.58069	+	0.438876i
$563$	−301.530	+	894.909i	−0.535577	+	1.58954i	0.248341	+	0.968673i	$0.420115\pi$
$563$	−301.530	+	894.909i	−0.535577	+	1.58954i	−0.783918	+	0.620864i	$0.786782\pi$
$564$	13.9357	+	2.28464i	0.0247086	+	0.00405077i
$565$	−773.547	+	126.817i	−1.36911	+	0.224454i
$566$	545.773	−	183.892i	0.964263	−	0.324898i
$567$	−13.0783	−	19.2891i	−0.0230658	−	0.0340196i
$568$	394.096	−	851.823i	0.693830	−	1.49969i
$569$	−502.180	+	660.606i	−0.882565	+	1.16099i	0.103499	+	0.994630i	$0.466996\pi$
$569$	−502.180	+	660.606i	−0.882565	+	1.16099i	−0.986064	+	0.166365i	$0.946797\pi$
$570$	−61.8536	−	568.734i	−0.108515	−	0.997780i
$571$	−543.315	−	150.851i	−0.951516	−	0.264187i	−0.243115	−	0.969997i	$-0.578169\pi$
$571$	−543.315	−	150.851i	−0.951516	−	0.264187i	−0.708401	+	0.705810i	$0.750583\pi$
$572$	28.2239	−	41.6271i	0.0493424	−	0.0727746i
$573$	−251.693	−	418.317i	−0.439254	−	0.730046i
$574$	192.265	−	10.4243i	0.334957	−	0.0181609i
$575$	65.4360	+	69.0799i	0.113802	+	0.120139i
$576$	−145.266	+	110.428i	−0.252197	+	0.191715i
$577$	805.209	−	177.240i	1.39551	−	0.307175i	0.547345	−	0.836907i	$-0.315639\pi$
$577$	805.209	−	177.240i	1.39551	−	0.307175i	0.848165	+	0.529733i	$0.177708\pi$
$578$	−175.127	+	148.754i	−0.302988	+	0.257360i
$579$	−15.4149	+	284.310i	−0.0266232	+	0.491037i
$580$	−5.37747	−	10.1430i	−0.00927150	−	0.0174879i
$581$	4.13410	−	18.7814i	0.00711549	−	0.0323260i
$582$	−446.506	+	206.576i	−0.767193	+	0.354941i
$583$	−346.092	+	575.210i	−0.593640	+	0.986637i
$584$	105.421	−	198.844i	0.180515	−	0.340487i
$585$	−235.775	−	200.269i	−0.403034	−	0.342340i
$586$	564.601	−	596.042i	0.963482	−	1.01714i
$587$	−22.0431	+	202.683i	−0.0375522	+	0.345287i	0.960256	+	0.279120i	$0.0900426\pi$
$587$	−22.0431	+	202.683i	−0.0375522	+	0.345287i	−0.997809	+	0.0661672i	$0.978923\pi$
$588$	−4.94170	+	12.4027i	−0.00840425	+	0.0210931i
$589$			1408.32i			2.39104i
$590$	106.089	−	668.082i	0.179811	−	1.13234i
$591$	280.580			0.474755
$592$	552.126	+	219.987i	0.932645	+	0.371600i
$593$	−513.528	−	55.8495i	−0.865983	−	0.0941813i	−0.335666	−	0.941981i	$-0.608961\pi$
$593$	−513.528	−	55.8495i	−0.865983	−	0.0941813i	−0.530316	+	0.847800i	$0.677927\pi$
$594$	−115.749	−	109.643i	−0.194864	−	0.184585i
$595$	−124.909	+	147.054i	−0.209931	+	0.247150i
$596$	−27.1961	−	14.4185i	−0.0456311	−	0.0241921i
$597$	−170.314	−	102.474i	−0.285283	−	0.171649i
$598$	233.675	+	505.080i	0.390761	+	0.844615i
$599$	−221.702	−	48.8003i	−0.370120	−	0.0814696i	0.0260158	−	0.999662i	$-0.491718\pi$
$599$	−221.702	−	48.8003i	−0.370120	−	0.0814696i	−0.396136	+	0.918192i	$0.629649\pi$
$600$	76.8387	−	40.7373i	0.128064	−	0.0678955i
$601$	−433.675	−	23.5132i	−0.721589	−	0.0391234i	−0.310313	−	0.950634i	$-0.600434\pi$
$601$	−433.675	−	23.5132i	−0.721589	−	0.0391234i	−0.411276	+	0.911511i	$0.634917\pi$
$602$	−45.4026	−	53.4521i	−0.0754197	−	0.0887909i
$603$	−25.2569	−	114.743i	−0.0418853	−	0.190287i
$604$	−22.0162	−	28.9618i	−0.0364506	−	0.0479500i
$605$	423.744	−	401.392i	0.700403	−	0.663457i
$606$	−1.76934	−	32.6336i	−0.00291971	−	0.0538509i
$607$	−126.432	+	76.0716i	−0.208290	+	0.125324i	−0.615877	−	0.787843i	$-0.711198\pi$
$607$	−126.432	+	76.0716i	−0.208290	+	0.125324i	0.407587	+	0.913167i	$0.366370\pi$
$608$	69.4759	+	47.1058i	0.114270	+	0.0774767i
$609$	13.4816	−	48.5564i	0.0221373	−	0.0797313i
$610$	846.556	−	92.0685i	1.38780	−	0.150932i
$611$	655.051	+	497.957i	1.07210	+	0.814987i
$612$	6.59501	+	3.05118i	0.0107762	+	0.00498558i
$613$	−275.455	+	186.763i	−0.449356	+	0.304671i	−0.764794	−	0.644275i	$-0.777159\pi$
$613$	−275.455	+	186.763i	−0.449356	+	0.304671i	0.315438	+	0.948946i	$0.397849\pi$
$614$	119.986	+	356.107i	0.195418	+	0.579979i
$615$	−57.1220	−	348.429i	−0.0928813	−	0.566551i
$616$	−49.0729	+	299.331i	−0.0796637	+	0.485927i
$617$	−603.406	−	203.311i	−0.977968	−	0.329516i	−0.215473	−	0.976510i	$-0.569129\pi$
$617$	−603.406	−	203.311i	−0.977968	−	0.329516i	−0.762495	+	0.646994i	$0.776026\pi$
$618$	−43.1337	−	155.353i	−0.0697956	−	0.251381i
$619$	−57.8051	−	145.080i	−0.0933847	−	0.234378i	0.874863	−	0.484370i	$-0.160951\pi$
$619$	−57.8051	−	145.080i	−0.0933847	−	0.234378i	−0.968248	+	0.249992i	$0.919572\pi$
$620$	46.4017	−	18.4881i	0.0748414	−	0.0298196i
$621$	74.0764	−	20.5672i	0.119286	−	0.0331195i
$622$	−268.938	+	798.180i	−0.432376	+	1.28325i
$623$	102.007	+	16.7231i	0.163735	+	0.0268429i
$624$	524.876	−	86.0491i	0.841148	−	0.137899i
$625$	705.452	−	237.694i	1.12872	−	0.380311i
$626$	67.1296	+	99.0087i	0.107236	+	0.158161i
$627$	314.346	−	679.449i	0.501350	−	1.08365i
$628$	−8.94991	+	11.7734i	−0.0142514	+	0.0187475i
$629$	51.1536	+	470.350i	0.0813253	+	0.747774i
$630$	−85.8189	−	23.8275i	−0.136221	−	0.0378214i
$631$	−101.293	+	149.396i	−0.160527	+	0.236760i	−0.899443	−	0.437038i	$-0.856028\pi$
$631$	−101.293	+	149.396i	−0.160527	+	0.236760i	0.738916	+	0.673798i	$0.235338\pi$
$632$	−582.427	−	968.001i	−0.921562	−	1.53165i
$633$	575.743	−	31.2159i	0.909547	−	0.0493142i
$634$	−445.621	−	470.436i	−0.702872	−	0.742013i
$635$	654.060	−	497.204i	1.03002	−	0.782998i
$636$	13.7934	−	3.03616i	0.0216877	−	0.00477383i
$637$	−592.904	+	503.617i	−0.930775	+	0.790607i
$638$	18.6647	−	344.249i	0.0292550	−	0.539576i
$639$	168.927	+	318.631i	0.264362	+	0.498640i
$640$	−163.960	+	744.880i	−0.256188	+	1.16387i
$641$	−982.549	+	454.576i	−1.53284	+	0.709166i	−0.991314	−	0.131519i	$-0.958015\pi$
$641$	−982.549	+	454.576i	−1.53284	+	0.709166i	−0.541524	+	0.840685i	$0.682153\pi$
$642$	236.318	−	392.764i	0.368097	−	0.611782i
$643$	468.176	−	883.073i	0.728111	−	1.37336i	−0.191877	−	0.981419i	$-0.561458\pi$
$643$	468.176	−	883.073i	0.728111	−	1.37336i	0.919989	−	0.391945i	$-0.128198\pi$
$644$	5.32153	+	4.52015i	0.00826325	+	0.00701887i
$645$	−88.4404	+	93.3654i	−0.137117	+	0.144753i
$646$	−84.6587	+	778.424i	−0.131051	+	1.20499i
$647$	−414.896	+	1041.31i	−0.641262	+	1.60945i	0.143502	+	0.989650i	$0.454164\pi$
$647$	−414.896	+	1041.31i	−0.641262	+	1.60945i	−0.784764	+	0.619795i	$0.787216\pi$
$648$		−	70.2676i		−	0.108438i
$649$	569.685	−	677.543i	0.877789	−	1.04398i
$650$	−241.907			−0.372164
$651$	203.682	+	81.1542i	0.312875	+	0.124661i
$652$	−54.1471	−	5.88886i	−0.0830478	−	0.00903199i
$653$	−303.909	−	287.878i	−0.465405	−	0.440855i	0.418713	−	0.908119i	$-0.362481\pi$
$653$	−303.909	−	287.878i	−0.465405	−	0.440855i	−0.884118	+	0.467264i	$0.845240\pi$
$654$	75.8353	−	89.2802i	0.115956	−	0.136514i
$655$	−621.328	−	329.407i	−0.948592	−	0.502912i
$656$	520.172	+	312.977i	0.792945	+	0.477099i
$657$	36.3115	+	78.4859i	0.0552686	+	0.119461i
$658$	231.364	+	50.9270i	0.351617	+	0.0773967i
$659$	768.928	−	407.660i	1.16681	−	0.618603i	0.231640	−	0.972802i	$-0.425591\pi$
$659$	768.928	−	407.660i	1.16681	−	0.618603i	0.935170	+	0.354198i	$0.115246\pi$
$660$	−26.5133	−	1.43751i	−0.0401717	−	0.00217805i
$661$	−358.896	−	422.525i	−0.542960	−	0.639221i	0.420431	−	0.907325i	$-0.361879\pi$
$661$	−358.896	−	422.525i	−0.542960	−	0.639221i	−0.963390	+	0.268103i	$0.913603\pi$
$662$	−161.013	−	731.491i	−0.243223	−	1.10497i
$663$	256.234	+	337.071i	0.386477	+	0.508402i
$664$	42.0966	−	39.8760i	0.0633985	−	0.0600542i
$665$	−22.6417	−	417.601i	−0.0340477	−	0.627972i
$666$	−187.138	+	112.597i	−0.280987	+	0.169064i
$667$	137.594	+	93.2912i	0.206288	+	0.139867i
$668$	3.07862	−	11.0882i	0.00460871	−	0.0165991i
$669$	628.082	−	68.3081i	0.938838	−	0.102105i
$670$	−357.461	−	271.735i	−0.533524	−	0.405574i
$671$	1011.35	+	467.902i	1.50723	+	0.697320i
$672$	10.8163	−	7.33366i	0.0160957	−	0.0109132i
$673$	80.8437	+	239.936i	0.120124	+	0.356517i	0.990799	−	0.135343i	$-0.0432138\pi$
$673$	80.8437	+	239.936i	0.120124	+	0.356517i	−0.870674	+	0.491860i	$0.836317\pi$
$674$	11.6357	+	70.9745i	0.0172636	+	0.105303i
$675$	−5.40637	+	32.9774i	−0.00800944	+	0.0488554i
$676$	−29.2389	−	9.85172i	−0.0432528	−	0.0145736i
$677$	144.133	+	519.120i	0.212899	+	0.766794i	0.990438	+	0.137959i	$0.0440542\pi$
$677$	144.133	+	519.120i	0.212899	+	0.766794i	−0.777539	+	0.628835i	$0.783532\pi$
$678$	183.314	+	460.082i	0.270374	+	0.678588i
$679$	−334.107	+	133.121i	−0.492058	+	0.196054i
$680$	−560.551	+	155.636i	−0.824340	+	0.228877i
$681$	62.4494	−	185.343i	0.0917025	−	0.272163i
$682$	1480.22	+	242.670i	2.17041	+	0.355821i
$683$	−1032.25	+	169.229i	−1.51135	+	0.247773i	−0.859721	−	0.510763i	$-0.829363\pi$
$683$	−1032.25	+	169.229i	−1.51135	+	0.247773i	−0.651630	+	0.758537i	$0.725915\pi$
$684$	−14.9263	+	5.02924i	−0.0218220	+	0.00735269i
$685$	−646.584	−	953.640i	−0.943918	−	1.39217i
$686$	−202.996	+	438.769i	−0.295913	+	0.639605i
$687$	−223.185	+	293.595i	−0.324869	+	0.427358i
$688$	−23.9067	−	219.818i	−0.0347481	−	0.319503i
$689$	792.947	+	220.161i	1.15087	+	0.319536i
$690$	164.884	−	243.185i	0.238962	−	0.352442i
$691$	−594.532	−	988.119i	−0.860393	−	1.42998i	−0.902415	−	0.430868i	$-0.858208\pi$
$691$	−594.532	−	988.119i	−0.860393	−	1.42998i	0.0420220	−	0.999117i	$-0.486620\pi$
$692$	0.793839	−	0.0430407i	0.00114717	−	6.21976e-5i
$693$	−80.1528	−	84.6163i	−0.115661	−	0.122101i
$694$	−210.123	+	159.732i	−0.302771	+	0.230161i
$695$	53.8377	−	11.8506i	0.0774644	−	0.0170512i
$696$	115.806	−	98.3662i	0.166387	−	0.141331i
$697$	−26.1631	+	482.550i	−0.0375367	+	0.692324i
$698$	−297.916	−	561.929i	−0.426814	−	0.805056i
$699$	17.5408	−	79.6887i	0.0250942	−	0.114004i
$700$	−2.75450	+	1.27437i	−0.00393500	+	0.00182052i
$701$	101.014	−	167.887i	0.144100	−	0.239496i	−0.776398	−	0.630242i	$-0.782955\pi$
$701$	101.014	−	167.887i	0.144100	−	0.239496i	0.920498	+	0.390746i	$0.127783\pi$
$702$	−91.5504	+	172.682i	−0.130414	+	0.245986i
$703$	−781.610	−	663.906i	−1.11182	−	0.944390i
$704$	−627.585	+	662.534i	−0.891457	+	0.941099i
$705$	46.9684	−	431.868i	0.0666219	−	0.612578i
$706$	−106.991	+	268.528i	−0.151546	+	0.380351i
$707$		−	23.8913i		−	0.0337925i
$708$	−18.5915	+	1.10155i	−0.0262592	+	0.00155586i
$709$	1340.77			1.89107			0.945536	−	0.325517i	$-0.105538\pi$
$709$	1340.77			1.89107			0.945536	+	0.325517i	$0.105538\pi$
$710$	1280.40	+	510.157i	1.80338	+	0.718531i
$711$	431.542	+	46.9330i	0.606950	+	0.0660098i
$712$	226.273	+	214.337i	0.317799	+	0.301035i
$713$	−468.244	+	551.259i	−0.656723	+	0.773154i
$714$	107.703	+	57.1005i	0.150845	+	0.0799727i
$715$	−1325.67	−	797.627i	−1.85408	−	1.11556i
$716$	−18.9987	−	41.0650i	−0.0265345	−	0.0573533i
$717$	−473.143	−	104.147i	−0.659892	−	0.145253i
$718$	−331.911	+	175.968i	−0.462272	+	0.245081i
$719$	49.9595	+	2.70872i	0.0694846	+	0.00376735i	0.0888485	−	0.996045i	$-0.471681\pi$
$719$	49.9595	+	2.70872i	0.0694846	+	0.00376735i	−0.0193638	+	0.999813i	$0.506164\pi$
$720$	−181.791	−	214.021i	−0.252487	−	0.297251i
$721$	−25.3374	−	115.109i	−0.0351420	−	0.159652i
$722$	−580.335	−	763.418i	−0.803788	−	1.05737i
$723$	172.003	−	162.930i	0.237901	−	0.225352i
$724$	0.179917	+	3.31838i	0.000248505	+	0.00458340i
$725$	−61.9173	+	37.2544i	−0.0854031	+	0.0513853i
$726$	−305.226	−	206.948i	−0.420422	−	0.285053i
$727$	0.923583	−	3.32645i	0.00127040	−	0.00457558i	−0.962912	−	0.269815i	$-0.913037\pi$
$727$	0.923583	−	3.32645i	0.00127040	−	0.00457558i	0.964182	+	0.265240i	$0.0854511\pi$
$728$	369.666	−	40.2036i	0.507783	−	0.0552248i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	299.955	+	138.774i	0.410897	+	0.190101i
$731$	145.689	−	98.7794i	0.199300	−	0.135129i
$732$	−7.48598	−	22.2176i	−0.0102267	−	0.0303519i
$733$	217.294	+	1325.44i	0.296445	+	1.80824i	0.543694	+	0.839284i	$0.317025\pi$
$733$	217.294	+	1325.44i	0.296445	+	1.80824i	−0.247249	+	0.968952i	$0.579526\pi$
$734$	−29.6282	+	180.724i	−0.0403654	+	0.246218i
$735$	389.205	+	131.139i	0.529531	+	0.178420i
$736$	11.5330	+	41.5383i	0.0156699	+	0.0564379i
$737$	−217.490	−	545.859i	−0.295102	−	0.740650i
$738$	−207.235	+	82.5699i	−0.280806	+	0.111883i
$739$	259.477	−	72.0435i	0.351119	−	0.0974878i	−0.0874905	−	0.996165i	$-0.527885\pi$
$739$	259.477	−	72.0435i	0.351119	−	0.0974878i	0.438610	+	0.898678i	$0.355471\pi$
$740$	−11.6137	+	34.4683i	−0.0156942	+	0.0465788i
$741$	−905.663	−	148.476i	−1.22222	−	0.200372i
$742$	233.813	−	38.3317i	0.315112	−	0.0516600i
$743$	−370.580	+	124.863i	−0.498761	+	0.168052i	−0.557428	−	0.830225i	$-0.688212\pi$
$743$	−370.580	+	124.863i	−0.498761	+	0.168052i	0.0586666	+	0.998278i	$0.481315\pi$
$744$	370.993	+	547.174i	0.498646	+	0.735448i
$745$	−397.600	+	859.398i	−0.533691	+	1.15355i
$746$	663.371	−	872.649i	0.889237	−	1.16977i
$747$	2.40893	+	22.1497i	0.00322480	+	0.0296516i
$748$	35.0173	+	9.72250i	0.0468145	+	0.0129980i
$749$	188.047	−	277.349i	0.251065	−	0.370293i
$750$	−190.109	−	315.964i	−0.253479	−	0.421286i
$751$	−163.370	+	8.85768i	−0.217537	+	0.0117945i	−0.162585	−	0.986695i	$-0.551983\pi$
$751$	−163.370	+	8.85768i	−0.217537	+	0.0117945i	−0.0549517	+	0.998489i	$0.517500\pi$
$752$	513.651	+	542.255i	0.683047	+	0.721083i
$753$	−102.998	+	78.2967i	−0.136783	+	0.103980i
$754$	−412.751	+	90.8535i	−0.547416	+	0.120495i
$755$	−852.955	+	724.507i	−1.12974	+	0.959611i
$756$	−0.132757	+	2.44856i	−0.000175604	+	0.00323883i
$757$	109.527	+	206.590i	0.144686	+	0.272906i	0.945254	−	0.326335i	$-0.105814\pi$
$757$	109.527	+	206.590i	0.144686	+	0.272906i	−0.800569	+	0.599241i	$0.795469\pi$
$758$	31.8670	−	144.773i	0.0420408	−	0.190993i
$759$	348.950	−	161.442i	0.459750	−	0.212703i
$760$	650.106	−	1080.48i	0.855402	−	1.42169i
$761$	−452.605	+	853.704i	−0.594751	+	1.12182i	0.385248	+	0.922813i	$0.374116\pi$
$761$	−452.605	+	853.704i	−0.594751	+	1.12182i	−0.979998	+	0.199006i	$0.936229\pi$
$762$	−395.627	−	336.049i	−0.519196	−	0.441009i
$763$	58.8902	−	62.1696i	0.0771824	−	0.0814805i
$764$	−5.55395	+	51.0677i	−0.00726956	+	0.0668425i
$765$	82.7397	−	207.661i	0.108156	−	0.271452i
$766$			267.117i			0.348717i
$767$	−987.153	−	450.709i	−1.28703	−	0.587626i
$768$	60.4835			0.0787545
$769$	595.839	+	237.404i	0.774823	+	0.308718i	0.723827	−	0.689981i	$-0.242381\pi$
$769$	595.839	+	237.404i	0.774823	+	0.308718i	0.0509958	+	0.998699i	$0.483760\pi$
$770$	−442.824	−	48.1600i	−0.575096	−	0.0625454i
$771$	28.3419	+	26.8468i	0.0367599	+	0.0348208i
$772$	19.3953	−	22.8339i	0.0251234	−	0.0295776i
$773$	266.727	+	141.410i	0.345055	+	0.182936i	0.631918	−	0.775035i	$-0.282268\pi$
$773$	266.727	+	141.410i	0.345055	+	0.182936i	−0.286864	+	0.957971i	$0.592613\pi$
$774$	69.6218	+	41.8900i	0.0899506	+	0.0541215i
$775$	−132.012	−	285.339i	−0.170338	−	0.368180i
$776$	−1059.05	−	233.115i	−1.36476	−	0.300406i
$777$	−141.059	+	74.7849i	−0.181543	+	0.0962482i
$778$	−682.851	−	37.0231i	−0.877700	−	0.0475875i
$779$	−678.128	−	798.354i	−0.870511	−	1.02485i
$780$	6.99733	+	31.7892i	0.00897093	+	0.0407554i
$781$	1091.52	+	1435.87i	1.39759	+	1.83850i
$782$	−291.951	+	276.551i	−0.373339	+	0.353646i
$783$	3.16083	+	58.2980i	0.00403681	+	0.0744547i
$784$	−605.067	+	364.057i	−0.771769	+	0.464358i
$785$	376.550	+	255.307i	0.479681	+	0.325232i
$786$	−118.867	+	428.122i	−0.151231	+	0.544684i
$787$	−720.944	+	78.4074i	−0.916066	+	0.0996282i	−0.553993	−	0.832521i	$-0.686897\pi$
$787$	−720.944	+	78.4074i	−0.916066	+	0.0996282i	−0.362073	+	0.932150i	$0.617931\pi$
$788$	−23.5030	−	17.8665i	−0.0298262	−	0.0226733i
$789$	695.912	+	321.963i	0.882018	+	0.408065i
$790$	1373.12	−	930.997i	1.73812	−	1.17848i
$791$	115.603	+	343.097i	0.146148	+	0.433751i
$792$	−56.8539	−	346.794i	−0.0717853	−	0.437871i
$793$	221.005	−	1348.07i	0.278695	−	1.69996i
$794$	1361.71	+	458.813i	1.71500	+	0.577850i
$795$	−116.234	−	418.636i	−0.146206	−	0.526586i
$796$	7.74120	+	19.4289i	0.00972513	+	0.0244082i
$797$	−807.203	+	321.619i	−1.01280	+	0.403537i	−0.816710	−	0.577049i	$-0.804204\pi$
$797$	−807.203	+	321.619i	−1.01280	+	0.403537i	−0.196092	+	0.980586i	$0.562825\pi$
$798$	−254.600	+	70.6893i	−0.319048	+	0.0885831i
$799$	−189.850	+	563.456i	−0.237610	+	0.705202i
$800$	−18.4921	−	3.03162i	−0.0231151	−	0.00378952i
$801$	−118.181	+	19.3748i	−0.147542	+	0.0241883i
$802$	634.146	−	213.669i	0.790705	−	0.266420i
$803$	242.712	+	357.974i	0.302257	+	0.445796i
$804$	−5.19085	+	11.2198i	−0.00645628	+	0.0139550i
$805$	129.983	−	170.990i	0.161470	−	0.212410i
$806$	−198.811	−	1828.04i	−0.246664	−	2.26804i
$807$	−107.954	−	29.9733i	−0.133772	−	0.0371417i
$808$	40.4257	−	59.6234i	0.0500318	−	0.0737914i
$809$	13.7833	+	22.9080i	0.0170374	+	0.0283164i	0.865259	−	0.501325i	$-0.167154\pi$
$809$	13.7833	+	22.9080i	0.0170374	+	0.0283164i	−0.848221	+	0.529642i	$0.822326\pi$
$810$	103.036	−	5.58647i	0.127205	−	0.00689688i
$811$	−727.530	−	768.044i	−0.897078	−	0.947033i	0.101781	−	0.994807i	$-0.467546\pi$
$811$	−727.530	−	768.044i	−0.897078	−	0.947033i	−0.998858	+	0.0477736i	$0.984787\pi$
$812$	−4.22123	+	3.20889i	−0.00519855	+	0.00395184i
$813$	−156.407	+	34.4277i	−0.192382	+	0.0423465i
$814$	−832.483	+	707.117i	−1.02271	+	0.868694i
$815$	−90.7101	+	1673.05i	−0.111301	+	2.05282i
$816$	180.028	+	339.569i	0.220622	+	0.416138i
$817$	−82.0174	+	372.609i	−0.100388	+	0.456070i
$818$	121.118	−	56.0351i	0.148066	−	0.0685026i
$819$	−73.6624	+	122.428i	−0.0899419	+	0.149485i
$820$	−17.4021	+	32.8238i	−0.0212220	+	0.0400290i
$821$	731.205	+	621.091i	0.890628	+	0.756506i	0.970703	−	0.240283i	$-0.0772402\pi$
$821$	731.205	+	621.091i	0.890628	+	0.756506i	−0.0800752	+	0.996789i	$0.525516\pi$
$822$	−500.611	+	528.489i	−0.609016	+	0.642931i
$823$	−73.3831	+	674.746i	−0.0891654	+	0.819862i	0.861103	+	0.508430i	$0.169774\pi$
$823$	−73.3831	+	674.746i	−0.0891654	+	0.819862i	−0.950269	+	0.311432i	$0.899191\pi$
$824$	131.540	−	330.140i	0.159636	−	0.400656i
$825$			167.129i			0.202580i
$826$	−312.431	+	1.56696i	−0.378245	+	0.00189705i
$827$	−525.995			−0.636028			−0.318014	−	0.948086i	$-0.603016\pi$
$827$	−525.995			−0.636028			−0.318014	+	0.948086i	$0.603016\pi$
$828$	−7.51473	−	2.99414i	−0.00907576	−	0.00361611i
$829$	−1460.47	−	158.836i	−1.76173	−	0.191600i	−0.830744	−	0.556654i	$-0.812085\pi$
$829$	−1460.47	−	158.836i	−1.76173	−	0.191600i	−0.930986	+	0.365054i	$0.881050\pi$
$830$	61.8187	+	58.5578i	0.0744804	+	0.0705516i
$831$	−475.193	+	559.440i	−0.571832	+	0.673213i
$832$	988.414	+	524.024i	1.18800	+	0.629836i
$833$	−481.664	−	289.808i	−0.578229	−	0.347909i
$834$	−14.6245	−	31.6103i	−0.0175353	−	0.0379020i
$835$	−345.724	−	76.0995i	−0.414040	−	0.0911371i
$836$	−69.5968	+	36.8979i	−0.0832498	+	0.0441362i
$837$	−253.647	−	13.7523i	−0.303043	−	0.0164305i
$838$	575.262	+	677.251i	0.686471	+	0.808176i
$839$	−108.864	−	494.574i	−0.129754	−	0.589480i	−0.995960	−	0.0897933i	$-0.971379\pi$
$839$	−108.864	−	494.574i	−0.129754	−	0.589480i	0.866206	−	0.499687i	$-0.166552\pi$
$840$	−118.805	−	156.286i	−0.141435	−	0.186055i
$841$	518.908	−	491.536i	0.617013	−	0.584466i
$842$	79.0457	+	1457.91i	0.0938785	+	1.73149i
$843$	669.071	−	402.566i	0.793678	−	0.477540i
$844$	−50.2153	−	34.0468i	−0.0594968	−	0.0403398i
$845$	−253.921	+	914.539i	−0.300498	+	1.08230i
$846$	−272.857	+	29.6750i	−0.322526	+	0.0350769i
$847$	−214.612	−	163.144i	−0.253380	−	0.192614i
$848$	677.970	+	313.662i	0.799493	+	0.369885i
$849$	−403.725	+	273.732i	−0.475530	+	0.322417i
$850$	−55.8146	−	165.652i	−0.0656642	−	0.194885i
$851$	−85.2080	−	519.746i	−0.100127	−	0.610747i
$852$	6.13916	−	37.4472i	0.00720558	−	0.0439521i
$853$	178.133	+	60.0201i	0.208832	+	0.0703636i	0.421773	−	0.906701i	$-0.361408\pi$
$853$	178.133	+	60.0201i	0.208832	+	0.0703636i	−0.212942	+	0.977065i	$0.568304\pi$
$854$	−105.220	−	378.970i	−0.123209	−	0.443759i
$855$	179.342	+	450.115i	0.209757	+	0.526450i
$856$	938.588	−	373.968i	1.09648	−	0.436878i
$857$	485.305	−	134.744i	0.566284	−	0.157228i	0.0274247	−	0.999624i	$-0.491269\pi$
$857$	485.305	−	134.744i	0.566284	−	0.157228i	0.538859	+	0.842396i	$0.318856\pi$
$858$	−312.113	+	926.318i	−0.363768	+	1.07962i
$859$	999.610	+	163.878i	1.16369	+	0.190777i	0.712514	−	0.701658i	$-0.247556\pi$
$859$	999.610	+	163.878i	1.16369	+	0.190777i	0.451176	+	0.892435i	$0.351005\pi$
$860$	13.3535	−	2.18920i	0.0155273	−	0.00254558i
$861$	−154.541	+	52.0709i	−0.179490	+	0.0604773i
$862$	724.047	+	1067.89i	0.839962	+	1.23885i
$863$	182.618	−	394.721i	0.211608	−	0.457383i	−0.772486	−	0.635032i	$-0.780987\pi$
$863$	182.618	−	394.721i	0.211608	−	0.457383i	0.984094	+	0.177649i	$0.0568491\pi$
$864$	−9.16247	+	12.0530i	−0.0106047	+	0.0139503i
$865$	−2.64417	−	24.3127i	−0.00305684	−	0.0281072i
$866$	656.600	+	182.304i	0.758199	+	0.210513i
$867$	109.212	−	161.075i	0.125965	−	0.185785i
$868$	−11.8939	−	19.7678i	−0.0137027	−	0.0227740i
$869$	2167.77	−	117.533i	2.49456	−	0.135251i
$870$	153.445	+	161.990i	0.176374	+	0.186196i
$871$	−573.445	+	435.922i	−0.658376	+	0.500484i
$872$	252.163	−	55.5052i	0.289177	−	0.0636527i
$873$	317.576	−	269.752i	0.363776	−	0.308994i
$874$	47.1905	−	870.378i	0.0539937	−	0.995856i
$875$	−126.267	−	238.165i	−0.144305	−	0.272189i
$876$	1.95610	−	8.88665i	0.00223299	−	0.0101446i
$877$	−443.153	+	205.024i	−0.505305	+	0.233779i	−0.655944	−	0.754810i	$-0.727729\pi$
$877$	−443.153	+	205.024i	−0.505305	+	0.233779i	0.150639	+	0.988589i	$0.451867\pi$
$878$	1.22263	−	2.03203i	0.00139252	−	0.00231439i
$879$	−325.704	+	614.343i	−0.370539	+	0.698911i
$880$	−1070.36	−	909.175i	−1.21632	−	1.03315i
$881$	29.4533	−	31.0934i	0.0334316	−	0.0352933i	−0.709065	−	0.705143i	$-0.750883\pi$
$881$	29.4533	−	31.0934i	0.0334316	−	0.0352933i	0.742497	+	0.669850i	$0.233641\pi$
$882$	28.0554	−	257.965i	0.0318088	−	0.292477i
$883$	−380.329	+	954.553i	−0.430723	+	1.08103i	0.540178	+	0.841551i	$0.318357\pi$
$883$	−380.329	+	954.553i	−0.430723	+	1.08103i	−0.970901	+	0.239482i	$0.923022\pi$
$884$		−	44.5513i		−	0.0503974i
$885$	64.7992	+	569.243i	0.0732194	+	0.643212i
$886$	−825.781			−0.932032
$887$	−942.320	−	375.455i	−1.06237	−	0.423286i	−0.227524	−	0.973773i	$-0.573063\pi$
$887$	−942.320	−	375.455i	−1.06237	−	0.423286i	−0.834844	+	0.550486i	$0.814442\pi$
$888$	−478.571	−	52.0477i	−0.538931	−	0.0586123i
$889$	−275.492	−	260.960i	−0.309890	−	0.293543i
$890$	−296.302	+	348.834i	−0.332924	+	0.391948i
$891$	119.303	+	63.2505i	0.133898	+	0.0709882i
$892$	−56.9615	−	34.2726i	−0.0638582	−	0.0384222i
$893$	−541.145	−	1169.67i	−0.605986	−	1.30982i
$894$	584.282	+	128.610i	0.653559	+	0.143859i
$895$	−1229.75	+	651.975i	−1.37403	+	0.728463i
$896$	351.758	+	19.0718i	0.392587	+	0.0212855i
$897$	−305.138	−	359.236i	−0.340176	−	0.400487i
$898$	−79.3006	−	360.266i	−0.0883080	−	0.401187i
$899$	−332.410	−	437.278i	−0.369755	−	0.486405i
$900$	2.55278	−	2.41812i	0.00283642	−	0.00268680i
$901$	32.1943	+	593.788i	0.0357317	+	0.659033i
$902$	−955.964	+	575.185i	−1.05983	+	0.637677i
$903$	49.1632	+	33.3335i	0.0544443	+	0.0369142i
$904$	−292.044	+	1051.85i	−0.323057	+	1.16355i
$905$	101.631	−	11.0531i	0.112300	−	0.0122133i
$906$	562.895	+	427.902i	0.621297	+	0.472298i
$907$	−828.267	−	383.197i	−0.913194	−	0.422489i	−0.0937161	−	0.995599i	$-0.529875\pi$
$907$	−828.267	−	383.197i	−0.913194	−	0.422489i	−0.819478	+	0.573110i	$0.805737\pi$
$908$	−17.0332	+	11.5488i	−0.0187591	+	0.0127190i
$909$	8.83811	+	26.2306i	0.00972289	+	0.0288565i
$910$	88.3418	+	538.861i	0.0970789	+	0.592155i
$911$	131.301	−	800.904i	0.144129	−	0.879148i	−0.811452	−	0.584419i	$-0.801322\pi$
$911$	131.301	−	800.904i	0.144129	−	0.879148i	0.955581	−	0.294729i	$-0.0952293\pi$
$912$	−789.466	−	266.002i	−0.865642	−	0.291669i
$913$	29.8103	+	107.367i	0.0326510	+	0.117598i
$914$	315.379	+	791.541i	0.345053	+	0.866018i
$915$	−669.992	+	266.949i	−0.732232	+	0.291748i
$916$	37.3906	−	10.3814i	0.0408194	−	0.0113334i
$917$	−103.712	+	307.807i	−0.113100	+	0.335668i
$918$	−139.372	−	22.8489i	−0.151821	−	0.0248898i
$919$	1489.04	−	244.115i	1.62028	−	0.265631i	0.717764	−	0.696287i	$-0.245166\pi$
$919$	1489.04	−	244.115i	1.62028	−	0.265631i	0.902516	+	0.430655i	$0.141718\pi$
$920$	613.715	−	206.785i	0.667081	−	0.224766i
$921$	−178.605	−	263.423i	−0.193925	−	0.286019i
$922$	286.882	−	620.086i	0.311152	−	0.672544i
$923$	1338.08	−	1760.22i	1.44971	−	1.90706i
$924$	1.32594	+	12.1918i	0.00143500	+	0.0131946i
$925$	220.595	+	61.2478i	0.238481	+	0.0662138i
$926$	369.073	−	544.342i	0.398567	−	0.587842i
$927$	70.4006	+	117.007i	0.0759446	+	0.126221i
$928$	−32.6905	+	1.77243i	−0.0352269	+	0.00190995i
$929$	−851.563	−	898.984i	−0.916645	−	0.967691i	0.0829382	−	0.996555i	$-0.473570\pi$
$929$	−851.563	−	898.984i	−0.916645	−	0.967691i	−0.999583	+	0.0288642i	$0.990811\pi$
$930$	−772.849	+	587.505i	−0.831021	+	0.631726i
$931$	1189.96	−	261.929i	1.27815	−	0.281342i
$932$	−6.54367	+	5.55824i	−0.00702110	+	0.00596378i
$933$	38.6204	−	712.311i	0.0413938	−	0.763463i
$934$	−786.981	−	1484.40i	−0.842592	−	1.58930i
$935$	240.328	−	1091.82i	0.257035	−	1.16772i
$936$	−390.990	+	180.891i	−0.417724	+	0.193260i
$937$	845.309	−	1404.92i	0.902144	−	1.49938i	0.0361358	−	0.999347i	$-0.488495\pi$
$937$	845.309	−	1404.92i	0.902144	−	1.49938i	0.866009	−	0.500029i	$-0.166677\pi$
$938$	−97.1429	+	183.231i	−0.103564	+	0.195342i
$939$	−77.2163	−	65.5882i	−0.0822325	−	0.0698489i
$940$	−31.4344	+	33.1849i	−0.0334409	+	0.0353031i
$941$	−115.028	+	1057.67i	−0.122240	+	1.12398i	0.758927	+	0.651176i	$0.225724\pi$
$941$	−115.028	+	1057.67i	−0.122240	+	1.12398i	−0.881167	+	0.472805i	$0.843242\pi$
$942$	106.391	−	267.021i	0.112941	−	0.283461i
$943$		−	537.967i		−	0.570484i
$944$	−818.078	−	548.702i	−0.866608	−	0.581252i
$945$	75.4336			0.0798239
$946$	377.500	+	150.410i	0.399049	+	0.158996i
$947$	−59.2760	−	6.44666i	−0.0625935	−	0.00680745i	0.0767687	−	0.997049i	$-0.475540\pi$
$947$	−59.2760	−	6.44666i	−0.0625935	−	0.00680745i	−0.139362	+	0.990241i	$0.544505\pi$
$948$	−33.1599	−	31.4107i	−0.0349788	−	0.0331337i
$949$	343.242	−	404.095i	0.361688	−	0.425812i
$950$	334.756	+	177.476i	0.352374	+	0.186817i
$951$	470.252	+	282.941i	0.494482	+	0.297520i
$952$	112.823	+	243.863i	0.118511	+	0.256158i
$953$	1523.85	+	335.425i	1.59901	+	0.351968i	0.922961	−	0.384893i	$-0.125762\pi$
$953$	1523.85	+	335.425i	1.59901	+	0.351968i	0.676045	+	0.736861i	$0.263693\pi$
$954$	−242.527	+	128.580i	−0.254221	+	0.134779i
$955$	1577.90	+	85.5512i	1.65225	+	0.0895824i
$956$	33.0014	+	38.8523i	0.0345203	+	0.0406405i
$957$	62.7690	+	285.162i	0.0655893	+	0.297975i
$958$	633.945	+	833.941i	0.661738	+	0.870502i
$959$	−386.342	+	365.963i	−0.402860	+	0.381609i
$960$	−31.9763	−	589.768i	−0.0333087	−	0.614342i
$961$	1224.31	−	736.646i	1.27400	−	0.766541i
$962$	1108.27	+	751.428i	1.15205	+	0.781111i
$963$	−103.860	+	374.070i	−0.107851	+	0.388443i
$964$	−24.7828	+	2.69529i	−0.0257083	+	0.00279595i
$965$	−733.692	−	557.738i	−0.760303	−	0.577967i
$966$	−123.161	−	56.9805i	−0.127496	−	0.0589860i
$967$	854.705	−	579.505i	0.883873	−	0.599281i	−0.0325596	−	0.999470i	$-0.510366\pi$
$967$	854.705	−	579.505i	0.883873	−	0.599281i	0.916433	+	0.400189i	$0.131056\pi$
$968$	−259.539	−	770.284i	−0.268119	−	0.795748i
$969$	−107.289	−	654.434i	−0.110721	−	0.675371i
$970$	257.629	−	1571.47i	0.265597	−	1.62007i
$971$	−102.860	−	34.6577i	−0.105932	−	0.0356928i	0.265836	−	0.964018i	$-0.414352\pi$
$971$	−102.860	−	34.6577i	−0.105932	−	0.0356928i	−0.371769	+	0.928325i	$0.621249\pi$
$972$	−0.760040	−	2.73742i	−0.000781934	−	0.00281627i
$973$	−9.42424	−	23.6530i	−0.00968575	−	0.0243094i
$974$	−1698.44	+	676.720i	−1.74378	+	0.694785i
$975$	197.414	−	54.8117i	0.202476	−	0.0562171i
$976$	395.942	−	1175.11i	0.405678	−	1.20401i
$977$	1180.35	+	193.509i	1.20814	+	0.198064i	0.732000	−	0.681305i	$-0.238587\pi$
$977$	1180.35	+	193.509i	1.20814	+	0.198064i	0.476140	+	0.879370i	$0.342036\pi$
$978$	1044.65	−	171.262i	1.06815	−	0.175115i
$979$	−567.586	+	191.242i	−0.579761	+	0.195344i
$980$	−24.2516	−	35.7684i	−0.0247465	−	0.0364984i
$981$	−41.6580	+	90.0422i	−0.0424648	+	0.0917861i
$982$	52.4147	−	68.9503i	0.0533754	−	0.0702142i
$983$	−81.8255	−	752.373i	−0.0832406	−	0.765384i	−0.959148	−	0.282905i	$-0.908702\pi$
$983$	−81.8255	−	752.373i	−0.0832406	−	0.765384i	0.875907	−	0.482479i	$-0.160264\pi$
$984$	−473.783	−	131.545i	−0.481486	−	0.133684i
$985$	−509.665	+	751.700i	−0.517427	+	0.763147i
$986$	−157.448	−	261.680i	−0.159683	−	0.265395i
$987$	−200.349	+	10.8626i	−0.202988	+	0.0110057i
$988$	66.4091	+	70.1072i	0.0672157	+	0.0709587i
$989$	−155.991	+	118.581i	−0.157726	+	0.119900i
$990$	503.999	−	110.938i	0.509089	−	0.112059i
$991$	−298.197	+	253.291i	−0.300905	+	0.255591i	−0.785100	−	0.619369i	$-0.787389\pi$
$991$	−298.197	+	253.291i	−0.300905	+	0.255591i	0.484195	+	0.874960i	$0.339113\pi$
$992$	7.71160	−	142.232i	0.00777379	−	0.143379i
$993$	297.142	+	560.469i	0.299236	+	0.564420i
$994$	136.848	−	621.709i	0.137675	−	0.625462i
$995$	583.908	−	270.145i	0.586842	−	0.271502i
$996$	1.20864	−	2.00878i	0.00121350	−	0.00201685i
$997$	591.642	−	1115.95i	0.593422	−	1.11931i	−0.386940	−	0.922105i	$-0.626468\pi$
$997$	591.642	−	1115.95i	0.593422	−	1.11931i	0.980362	−	0.197207i	$-0.0631873\pi$
$998$	−172.857	−	146.826i	−0.173203	−	0.147120i
$999$	127.206	−	134.290i	0.127333	−	0.134424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.g.a.10.15	✓	560
59.6	odd	58	inner	177.3.g.a.124.15	yes	560

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.g.a.10.15	✓	560	1.1	even	1	trivial
177.3.g.a.124.15	yes	560	59.6	odd	58	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.89981 + 0.756953i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(0.132311 + 0.125332i) q^{4} +(3.62948 - 4.27295i) q^{5} +(-3.12952 - 1.65917i) q^{6} +(-2.21876 - 1.33498i) q^{7} +(-3.27829 - 7.08590i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(1.89981 + 0.756953i) q^{2} +(-1.72190 - 0.187268i) q^{3} +(0.132311 + 0.125332i) q^{4} +(3.62948 - 4.27295i) q^{5} +(-3.12952 - 1.65917i) q^{6} +(-2.21876 - 1.33498i) q^{7} +(-3.27829 - 7.08590i) q^{8} +(2.92986 + 0.644911i) q^{9} +(10.1297 - 5.37045i) q^{10} +(14.9816 + 0.812281i) q^{11} +(-0.204356 - 0.240587i) q^{12} +(-3.95392 - 17.9628i) q^{13} +(-3.20470 - 4.21571i) q^{14} +(-7.04977 + 6.67790i) q^{15} +(-0.903891 - 16.6713i) q^{16} +(11.3882 - 6.85207i) q^{17} +(5.07801 + 3.44297i) q^{18} +(-7.70702 + 27.7582i) q^{19} +(1.01576 - 0.110471i) q^{20} +(3.57048 + 2.71421i) q^{21} +(27.8474 + 12.8836i) q^{22} +(-12.2459 + 8.30293i) q^{23} +(4.31792 + 12.8151i) q^{24} +(-1.04046 - 6.34651i) q^{25} +(6.08532 - 37.1188i) q^{26} +(-4.92415 - 1.65914i) q^{27} +(-0.126251 - 0.454716i) q^{28} +(-4.15885 - 10.4379i) q^{29} +(-18.4481 + 7.35038i) q^{30} +(47.1041 - 13.0784i) q^{31} +(0.930361 - 2.76121i) q^{32} +(-25.6447 - 4.20424i) q^{33} +(26.8222 - 4.39727i) q^{34} +(-13.7573 + 4.63536i) q^{35} +(0.306826 + 0.452535i) q^{36} +(-14.9472 + 32.3079i) q^{37} +(-35.6535 + 46.9014i) q^{38} +(3.44438 + 31.6706i) q^{39} +(-42.1762 - 11.7102i) q^{40} +(-20.4051 + 30.0953i) q^{41} +(4.72870 + 7.85916i) q^{42} +(13.2243 - 0.717002i) q^{43} +(1.88044 + 1.98515i) q^{44} +(13.3895 - 10.1785i) q^{45} +(-29.5498 + 6.50440i) q^{46} +(-34.0965 + 28.9618i) q^{47} +(-1.56559 + 28.8755i) q^{48} +(-19.8113 - 37.3681i) q^{49} +(2.82734 - 12.8447i) q^{50} +(-20.8925 + 9.66592i) q^{51} +(1.72817 - 2.87224i) q^{52} +(-20.9578 + 39.5306i) q^{53} +(-8.09905 - 6.87940i) q^{54} +(57.8464 - 61.0677i) q^{55} +(-2.18583 + 20.0984i) q^{56} +(18.4689 - 46.3535i) q^{57} -22.9781i q^{58} +(35.4693 - 47.1480i) q^{59} -1.76972 q^{60} +(68.9967 + 27.4908i) q^{61} +(99.3885 + 10.8092i) q^{62} +(-5.63972 - 5.34222i) q^{63} +(-39.3769 + 46.3580i) q^{64} +(-91.1049 - 48.3008i) q^{65} +(-45.5376 - 27.3991i) q^{66} +(-16.4442 - 35.5437i) q^{67} +(2.36558 + 0.520703i) q^{68} +(22.6411 - 12.0035i) q^{69} +(-29.6449 - 1.60730i) q^{70} +(77.8248 + 91.6224i) q^{71} +(-5.03515 - 22.8749i) q^{72} +(17.4449 + 22.9484i) q^{73} +(-52.8525 + 50.0645i) q^{74} +(0.603065 + 11.1229i) q^{75} +(-4.49872 + 2.70679i) q^{76} +(-32.1563 - 21.8025i) q^{77} +(-17.4295 + 62.7752i) q^{78} +(143.847 - 15.6443i) q^{79} +(-74.5163 - 56.6458i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-61.5466 + 41.7296i) q^{82} +(2.37138 + 7.03801i) q^{83} +(0.132238 + 0.806616i) q^{84} +(12.0548 - 73.5308i) q^{85} +(25.6664 + 8.64802i) q^{86} +(5.20642 + 18.7518i) q^{87} +(-43.3584 - 108.821i) q^{88} +(-37.0843 + 14.7757i) q^{89} +(33.1422 - 9.20188i) q^{90} +(-15.2073 + 45.1336i) q^{91} +(-2.66090 - 0.436232i) q^{92} +(-83.5576 + 13.6986i) q^{93} +(-86.6996 + 29.2125i) q^{94} +(90.6369 + 133.679i) q^{95} +(-2.11907 + 4.58030i) q^{96} +(84.0542 - 110.571i) q^{97} +(-9.35180 - 85.9884i) q^{98} +(43.3703 + 12.0417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9}+O(q^{10}) \) 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9	\( 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9} + 24 q^{12} - 24 q^{15} + 8 q^{16} - 16 q^{17} + 60 q^{19} + 164 q^{20} - 40 q^{22} - 100 q^{25} + 156 q^{26} - 200 q^{28} + 60 q^{29} + 32 q^{35} + 120 q^{36} - 28 q^{41} - 1572 q^{46} - 638 q^{47} + 96 q^{48} - 1328 q^{49} - 1856 q^{50} + 24 q^{51} - 1392 q^{52} - 572 q^{53} - 522 q^{55} - 928 q^{56} - 24 q^{57} + 268 q^{59} + 72 q^{60} + 348 q^{61} + 472 q^{62} + 24 q^{63} + 2580 q^{64} + 1218 q^{65} + 120 q^{66} + 1044 q^{67} + 1936 q^{68} + 2784 q^{70} + 1416 q^{71} + 870 q^{73} + 1752 q^{74} - 240 q^{75} - 120 q^{76} + 468 q^{78} + 420 q^{79} - 376 q^{80} - 180 q^{81} - 168 q^{84} + 348 q^{85} - 232 q^{86} - 144 q^{87} + 212 q^{88} - 152 q^{94} - 788 q^{95} - 3306 q^{98}+O(q^{100}) \) 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9 + 24 * q^12 - 24 * q^15 + 8 * q^16 - 16 * q^17 + 60 * q^19 + 164 * q^20 - 40 * q^22 - 100 * q^25 + 156 * q^26 - 200 * q^28 + 60 * q^29 + 32 * q^35 + 120 * q^36 - 28 * q^41 - 1572 * q^46 - 638 * q^47 + 96 * q^48 - 1328 * q^49 - 1856 * q^50 + 24 * q^51 - 1392 * q^52 - 572 * q^53 - 522 * q^55 - 928 * q^56 - 24 * q^57 + 268 * q^59 + 72 * q^60 + 348 * q^61 + 472 * q^62 + 24 * q^63 + 2580 * q^64 + 1218 * q^65 + 120 * q^66 + 1044 * q^67 + 1936 * q^68 + 2784 * q^70 + 1416 * q^71 + 870 * q^73 + 1752 * q^74 - 240 * q^75 - 120 * q^76 + 468 * q^78 + 420 * q^79 - 376 * q^80 - 180 * q^81 - 168 * q^84 + 348 * q^85 - 232 * q^86 - 144 * q^87 + 212 * q^88 - 152 * q^94 - 788 * q^95 - 3306 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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