LMFDB - Embedded newform 177.4.f.a.2.8

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.f (of order $58$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$1624$
Relative dimension:	$58$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	177.2
Dual form			177.4.f.a.89.8

$q$-expansion

$f(q)$	$=$	$q+(-0.238865 + 4.40561i) q^{2} +(-4.39778 - 2.76759i) q^{3} +(-11.3992 - 1.23974i) q^{4} +(-6.88505 + 20.4341i) q^{5} +(13.2434 - 18.7138i) q^{6} +(12.3388 + 18.1984i) q^{7} +(2.47433 - 15.0928i) q^{8} +(11.6809 + 24.3425i) q^{9} +O(q^{10})$	\(q+(-0.238865 + 4.40561i) q^{2} +(-4.39778 - 2.76759i) q^{3} +(-11.3992 - 1.23974i) q^{4} +(-6.88505 + 20.4341i) q^{5} +(13.2434 - 18.7138i) q^{6} +(12.3388 + 18.1984i) q^{7} +(2.47433 - 15.0928i) q^{8} +(11.6809 + 24.3425i) q^{9} +(-88.3800 - 35.2138i) q^{10} +(-46.5935 + 10.2560i) q^{11} +(46.7002 + 37.0005i) q^{12} +(15.2475 - 12.9514i) q^{13} +(-83.1225 + 50.0131i) q^{14} +(86.8321 - 70.8095i) q^{15} +(-23.6852 - 5.21350i) q^{16} +(68.4735 + 46.4262i) q^{17} +(-110.034 + 45.6467i) q^{18} +(27.3237 - 51.5379i) q^{19} +(103.817 - 224.397i) q^{20} +(-3.89761 - 114.182i) q^{21} +(-34.0544 - 207.723i) q^{22} +(4.92299 - 4.66330i) q^{23} +(-52.6522 + 59.5266i) q^{24} +(-270.636 - 205.732i) q^{25} +(53.4166 + 70.2683i) q^{26} +(16.0003 - 139.381i) q^{27} +(-118.092 - 222.745i) q^{28} +(201.980 - 10.9511i) q^{29} +(291.218 + 399.462i) q^{30} +(-73.5277 + 38.9819i) q^{31} +(61.3593 - 220.996i) q^{32} +(233.292 + 83.8483i) q^{33} +(-220.892 + 290.578i) q^{34} +(-456.822 + 126.836i) q^{35} +(-102.974 - 291.967i) q^{36} +(327.232 - 53.6470i) q^{37} +(220.529 + 132.688i) q^{38} +(-102.899 + 14.7583i) q^{39} +(291.371 + 154.475i) q^{40} +(-282.573 + 298.308i) q^{41} +(503.970 + 10.1026i) q^{42} +(-74.2998 + 337.547i) q^{43} +(543.845 - 59.1468i) q^{44} +(-577.840 + 71.0884i) q^{45} +(19.3688 + 22.8027i) q^{46} +(-138.274 + 46.5899i) q^{47} +(89.7332 + 88.4787i) q^{48} +(-51.9785 + 130.456i) q^{49} +(971.022 - 1143.18i) q^{50} +(-172.642 - 393.679i) q^{51} +(-189.867 + 128.733i) q^{52} +(226.216 - 90.1328i) q^{53} +(610.235 + 103.784i) q^{54} +(111.226 - 1022.71i) q^{55} +(305.195 - 141.198i) q^{56} +(-262.799 + 151.031i) q^{57} +892.462i q^{58} +(-453.134 - 6.98137i) q^{59} +(-1077.60 + 699.525i) q^{60} +(444.493 + 24.0997i) q^{61} +(-154.176 - 333.246i) q^{62} +(-298.867 + 512.932i) q^{63} +(775.106 + 261.164i) q^{64} +(159.670 + 400.740i) q^{65} +(-425.128 + 1007.77i) q^{66} +(-453.541 - 74.3542i) q^{67} +(-722.989 - 614.112i) q^{68} +(-34.5563 + 6.88333i) q^{69} +(-449.671 - 2042.87i) q^{70} +(-118.589 - 351.959i) q^{71} +(396.298 - 116.065i) q^{72} +(248.173 + 412.466i) q^{73} +(158.183 + 1454.47i) q^{74} +(620.814 + 1653.78i) q^{75} +(-375.363 + 553.619i) q^{76} +(-761.554 - 721.382i) q^{77} +(-40.4401 - 456.860i) q^{78} +(437.328 + 202.329i) q^{79} +(269.607 - 448.090i) q^{80} +(-456.115 + 568.683i) q^{81} +(-1246.73 - 1316.16i) q^{82} +(-151.738 - 546.510i) q^{83} +(-97.1257 + 1306.41i) q^{84} +(-1420.12 + 1079.55i) q^{85} +(-1469.35 - 407.964i) q^{86} +(-918.572 - 510.839i) q^{87} +(39.5037 + 728.602i) q^{88} +(71.6390 + 1321.30i) q^{89} +(-175.162 - 2562.72i) q^{90} +(423.832 + 117.676i) q^{91} +(-61.8996 + 47.0548i) q^{92} +(431.244 + 32.0610i) q^{93} +(-172.228 - 620.310i) q^{94} +(865.006 + 913.176i) q^{95} +(-881.473 + 802.075i) q^{96} +(263.303 - 437.613i) q^{97} +(-562.323 - 260.158i) q^{98} +(-793.910 - 1014.40i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) $	$ 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.238865	+	4.40561i	−0.0844516	+	1.55762i	0.582695	+	0.812691i	$0.301998\pi$
$2$	−0.238865	+	4.40561i	−0.0844516	+	1.55762i	−0.667146	+	0.744927i	$0.732484\pi$
$3$	−4.39778	−	2.76759i	−0.846352	−	0.532624i
$3$	−4.39778	−	2.76759i	−0.846352	−	0.532624i
$4$	−11.3992	−	1.23974i	−1.42490	−	0.154968i
$5$	−6.88505	+	20.4341i	−0.615817	+	1.82768i	−0.0570245	+	0.998373i	$0.518161\pi$
$5$	−6.88505	+	20.4341i	−0.615817	+	1.82768i	−0.558793	+	0.829307i	$0.688735\pi$
$6$	13.2434	−	18.7138i	0.901100	−	1.27331i
$7$	12.3388	+	18.1984i	0.666235	+	0.982623i	0.999212	+	0.0396880i	$0.0126364\pi$
$7$	12.3388	+	18.1984i	0.666235	+	0.982623i	−0.332977	+	0.942935i	$0.608053\pi$
$8$	2.47433	−	15.0928i	0.109351	−	0.667012i
$9$	11.6809	+	24.3425i	0.432624	+	0.901574i
$10$	−88.3800	−	35.2138i	−2.79482	−	1.11356i
$11$	−46.5935	+	10.2560i	−1.27713	+	0.281119i	−0.801218	−	0.598372i	$-0.795815\pi$
$11$	−46.5935	+	10.2560i	−1.27713	+	0.281119i	−0.475916	+	0.879491i	$0.657884\pi$
$12$	46.7002	+	37.0005i	1.12343	+	0.890094i
$13$	15.2475	−	12.9514i	0.325300	−	0.276313i	−0.469823	−	0.882761i	$-0.655682\pi$
$13$	15.2475	−	12.9514i	0.325300	−	0.276313i	0.795123	+	0.606448i	$0.207406\pi$
$14$	−83.1225	+	50.0131i	−1.58682	+	0.954755i
$15$	86.8321	−	70.8095i	1.49466	−	1.21886i
$16$	−23.6852	−	5.21350i	−0.370081	−	0.0814609i
$17$	68.4735	+	46.4262i	0.976898	+	0.662353i	0.941498	−	0.337020i	$-0.109419\pi$
$17$	68.4735	+	46.4262i	0.976898	+	0.662353i	0.0354006	+	0.999373i	$0.488729\pi$
$18$	−110.034	+	45.6467i	−1.44084	+	0.597724i
$19$	27.3237	−	51.5379i	0.329920	−	0.622295i	−0.661950	−	0.749548i	$-0.730271\pi$
$19$	27.3237	−	51.5379i	0.329920	−	0.622295i	0.991870	+	0.127252i	$0.0406158\pi$
$20$	103.817	−	224.397i	1.16071	−	2.50884i
$21$	−3.89761	−	114.182i	−0.0405014	−	1.18650i
$22$	−34.0544	−	207.723i	−0.330019	−	2.01303i
$23$	4.92299	−	4.66330i	0.0446311	−	0.0422768i	−0.665059	−	0.746791i	$-0.731594\pi$
$23$	4.92299	−	4.66330i	0.0446311	−	0.0422768i	0.709690	+	0.704514i	$0.248835\pi$
$24$	−52.6522	+	59.5266i	−0.447816	+	0.506284i
$25$	−270.636	−	205.732i	−2.16509	−	1.64586i
$26$	53.4166	+	70.2683i	0.402917	+	0.530029i
$27$	16.0003	−	139.381i	0.114047	−	0.993475i
$28$	−118.092	−	222.745i	−0.797046	−	1.50339i
$29$	201.980	−	10.9511i	1.29334	−	0.0701227i	0.605417	−	0.795908i	$-0.293006\pi$
$29$	201.980	−	10.9511i	1.29334	−	0.0701227i	0.687921	+	0.725786i	$0.258524\pi$
$30$	291.218	+	399.462i	1.77230	+	2.43105i
$31$	−73.5277	+	38.9819i	−0.425999	+	0.225850i	−0.667592	−	0.744527i	$-0.732675\pi$
$31$	−73.5277	+	38.9819i	−0.425999	+	0.225850i	0.241593	+	0.970378i	$0.422330\pi$
$32$	61.3593	−	220.996i	0.338966	−	1.22084i
$33$	233.292	+	83.8483i	1.23064	+	0.442307i
$34$	−220.892	+	290.578i	−1.11419	+	1.46570i
$35$	−456.822	+	126.836i	−2.20620	+	0.612548i
$36$	−102.974	−	291.967i	−0.476733	−	1.35170i
$37$	327.232	−	53.6470i	1.45396	−	0.238365i	0.617579	−	0.786509i	$-0.288114\pi$
$37$	327.232	−	53.6470i	1.45396	−	0.238365i	0.836384	+	0.548144i	$0.184665\pi$
$38$	220.529	+	132.688i	0.941436	+	0.566443i
$39$	−102.899	+	14.7583i	−0.422489	+	0.0605952i
$40$	291.371	+	154.475i	1.15174	+	0.610616i
$41$	−282.573	+	298.308i	−1.07635	+	1.13629i	−0.0862024	+	0.996278i	$0.527473\pi$
$41$	−282.573	+	298.308i	−1.07635	+	1.13629i	−0.990150	+	0.140013i	$0.955285\pi$
$42$	503.970	+	10.1026i	1.85153	+	0.0371160i
$43$	−74.2998	+	337.547i	−0.263503	+	1.19710i	0.639950	+	0.768417i	$0.278955\pi$
$43$	−74.2998	+	337.547i	−0.263503	+	1.19710i	−0.903453	+	0.428688i	$0.858976\pi$
$44$	543.845	−	59.1468i	1.86336	−	0.202652i
$45$	−577.840	+	71.0884i	−1.91421	+	0.235494i
$46$	19.3688	+	22.8027i	0.0620819	+	0.0730885i
$47$	−138.274	+	46.5899i	−0.429135	+	0.144592i	−0.525577	−	0.850746i	$-0.676150\pi$
$47$	−138.274	+	46.5899i	−0.429135	+	0.144592i	0.0964418	+	0.995339i	$0.469254\pi$
$48$	89.7332	+	88.4787i	0.269831	+	0.266058i
$49$	−51.9785	+	130.456i	−0.151541	+	0.380339i
$50$	971.022	−	1143.18i	2.74647	−	3.23339i
$51$	−172.642	−	393.679i	−0.474015	−	1.08090i
$52$	−189.867	+	128.733i	−0.506341	+	0.343308i
$53$	226.216	−	90.1328i	0.586287	−	0.233598i	−0.0580834	−	0.998312i	$-0.518499\pi$
$53$	226.216	−	90.1328i	0.586287	−	0.233598i	0.644370	+	0.764714i	$0.277120\pi$
$54$	610.235	+	103.784i	1.53782	+	0.261542i
$55$	111.226	−	1022.71i	0.272687	−	2.50731i
$56$	305.195	−	141.198i	0.728275	−	0.336936i
$57$	−262.799	+	151.031i	−0.610678	+	0.350958i
$58$			892.462i			2.02045i
$59$	−453.134	−	6.98137i	−0.999881	−	0.0154050i
$59$	−453.134	−	6.98137i	−0.999881	−	0.0154050i
$60$	−1077.60	+	699.525i	−2.31864	+	1.50514i
$61$	444.493	+	24.0997i	0.932974	+	0.0505844i	0.514355	−	0.857577i	$-0.328031\pi$
$61$	444.493	+	24.0997i	0.932974	+	0.0505844i	0.418619	+	0.908162i	$0.362514\pi$
$62$	−154.176	−	333.246i	−0.315812	−	0.682617i
$63$	−298.867	+	512.932i	−0.597678	+	1.02577i
$64$	775.106	+	261.164i	1.51388	+	0.510085i
$65$	159.670	+	400.740i	0.304686	+	0.764703i
$66$	−425.128	+	1007.77i	−0.792874	+	1.87951i
$67$	−453.541	−	74.3542i	−0.826997	−	0.135579i	−0.266604	−	0.963806i	$-0.585902\pi$
$67$	−453.541	−	74.3542i	−0.826997	−	0.135579i	−0.560393	+	0.828227i	$0.689350\pi$
$68$	−722.989	−	614.112i	−1.28934	−	1.09518i
$69$	−34.5563	+	6.88333i	−0.0602912	+	0.0120095i
$70$	−449.671	−	2042.87i	−0.767799	−	3.48815i
$71$	−118.589	−	351.959i	−0.198224	−	0.588307i	0.801732	−	0.597683i	$-0.203912\pi$
$71$	−118.589	−	351.959i	−0.198224	−	0.588307i	−0.999956	+	0.00937623i	$0.997015\pi$
$72$	396.298	−	116.065i	0.648669	−	0.189978i
$73$	248.173	+	412.466i	0.397896	+	0.661309i	0.989437	−	0.144967i	$-0.0463075\pi$
$73$	248.173	+	412.466i	0.397896	+	0.661309i	−0.591540	+	0.806276i	$0.701480\pi$
$74$	158.183	+	1454.47i	0.248492	+	2.28485i
$75$	620.814	+	1653.78i	0.955806	+	2.54616i
$76$	−375.363	+	553.619i	−0.566540	+	0.835584i
$77$	−761.554	−	721.382i	−1.12711	−	1.06765i
$78$	−40.4401	−	456.860i	−0.0587043	−	0.663194i
$79$	437.328	+	202.329i	0.622826	+	0.288150i	0.705810	−	0.708401i	$-0.250583\pi$
$79$	437.328	+	202.329i	0.622826	+	0.288150i	−0.0829844	+	0.996551i	$0.526445\pi$
$80$	269.607	−	448.090i	0.376787	−	0.626224i
$81$	−456.115	+	568.683i	−0.625672	+	0.780086i
$82$	−1246.73	−	1316.16i	−1.67901	−	1.77251i
$83$	−151.738	−	546.510i	−0.200667	−	0.722738i	−0.993553	−	0.113368i	$-0.963836\pi$
$83$	−151.738	−	546.510i	−0.200667	−	0.722738i	0.792886	−	0.609370i	$-0.208578\pi$
$84$	−97.1257	+	1306.41i	−0.126158	+	1.69692i
$85$	−1420.12	+	1079.55i	−1.81216	+	1.37757i
$86$	−1469.35	−	407.964i	−1.84238	−	0.511534i
$87$	−918.572	−	510.839i	−1.13197	−	0.629514i
$88$	39.5037	+	728.602i	0.0478535	+	0.882605i
$89$	71.6390	+	1321.30i	0.0853227	+	1.57369i	0.657436	+	0.753510i	$0.271641\pi$
$89$	71.6390	+	1321.30i	0.0853227	+	1.57369i	−0.572113	+	0.820175i	$0.693876\pi$
$90$	−175.162	−	2562.72i	−0.205152	−	3.00149i
$91$	423.832	+	117.676i	0.488238	+	0.135559i
$92$	−61.8996	+	47.0548i	−0.0701465	+	0.0533240i
$93$	431.244	+	32.0610i	0.480838	+	0.0357481i
$94$	−172.228	−	620.310i	−0.188979	−	0.680639i
$95$	865.006	+	913.176i	0.934187	+	0.986209i
$96$	−881.473	+	802.075i	−0.937135	+	0.852723i
$97$	263.303	−	437.613i	0.275612	−	0.458070i	−0.687874	−	0.725830i	$-0.741456\pi$
$97$	263.303	−	437.613i	0.275612	−	0.458070i	0.963486	+	0.267760i	$0.0862834\pi$
$98$	−562.323	−	260.158i	−0.579624	−	0.268163i
$99$	−793.910	−	1014.40i	−0.805969	−	1.02981i
$100$	2829.99	+	2680.71i	2.82999	+	2.68071i
$101$	554.103	−	817.240i	0.545894	−	0.805133i	−0.450247	−	0.892904i	$-0.648664\pi$
$101$	554.103	−	817.240i	0.545894	−	0.805133i	0.996141	+	0.0877709i	$0.0279743\pi$
$102$	1775.63	−	666.559i	1.72367	−	0.647050i
$103$	76.3595	+	702.114i	0.0730478	+	0.671664i	0.972220	+	0.234069i	$0.0752041\pi$
$103$	76.3595	+	702.114i	0.0730478	+	0.671664i	−0.899172	+	0.437595i	$0.855830\pi$
$104$	−157.745	−	262.173i	−0.148732	−	0.247194i
$105$	2360.03	+	706.501i	2.19348	+	0.656642i
$106$	343.055	+	1018.15i	0.314344	+	0.932938i
$107$	104.655	+	475.452i	0.0945549	+	0.429567i	0.999987	+	0.00507646i	$0.00161590\pi$
$107$	104.655	+	475.452i	0.0945549	+	0.429567i	−0.905432	+	0.424491i	$0.860453\pi$
$108$	−355.188	+	1569.00i	−0.316462	+	1.39793i
$109$	139.919	+	118.848i	0.122952	+	0.104436i	0.706753	−	0.707460i	$-0.250159\pi$
$109$	139.919	+	118.848i	0.122952	+	0.104436i	−0.583801	+	0.811897i	$0.698435\pi$
$110$	4479.09	+	734.310i	3.88241	+	0.636488i
$111$	−1587.57	−	669.718i	−1.35752	−	0.572674i
$112$	−197.370	−	495.361i	−0.166515	−	0.417922i
$113$	−1062.34	−	357.943i	−0.884392	−	0.297987i	−0.159788	−	0.987151i	$-0.551081\pi$
$113$	−1062.34	−	357.943i	−0.884392	−	0.297987i	−0.724605	+	0.689165i	$0.757978\pi$
$114$	−602.612	−	1193.87i	−0.495086	−	0.980842i
$115$	61.3953	+	132.704i	0.0497839	+	0.107606i
$116$	−2316.00	−	125.570i	−1.85375	−	0.100507i
$117$	493.373	+	219.880i	0.389849	+	0.173743i
$118$	138.995	−	1994.66i	0.108437	−	1.55613i
$119$			1818.96i			1.40121i
$120$	−853.860	−	1485.74i	−0.649553	−	1.13024i
$121$	857.790	−	396.856i	0.644470	−	0.298164i
$122$	−212.348	+	1952.50i	−0.157582	+	1.44895i
$123$	2068.29	−	529.847i	1.51619	−	0.388412i
$124$	886.487	−	353.209i	0.642007	−	0.255799i
$125$	3836.38	−	2601.13i	2.74509	−	1.86122i
$126$	−2188.39	−	1439.21i	−1.54728	−	1.01758i
$127$	−783.850	+	922.819i	−0.547680	+	0.644779i	−0.964460	−	0.264228i	$-0.914883\pi$
$127$	−783.850	+	922.819i	−0.547680	+	0.644779i	0.416780	+	0.909007i	$0.363159\pi$
$128$	−656.582	+	1647.90i	−0.453392	+	1.13793i
$129$	1260.95	−	1278.83i	0.860622	−	0.872824i
$130$	−1803.64	+	607.719i	−1.21685	+	0.410003i
$131$	−1160.09	−	1365.76i	−0.773722	−	0.910896i	0.224251	−	0.974531i	$-0.428006\pi$
$131$	−1160.09	−	1365.76i	−0.773722	−	0.910896i	−0.997973	+	0.0636354i	$0.979731\pi$
$132$	−2555.40	−	1245.03i	−1.68500	−	0.820953i
$133$	1275.05	−	138.670i	0.831286	−	0.0904078i
$134$	435.911	−	1980.36i	0.281022	−	1.27670i
$135$	2737.95	+	1286.60i	1.74552	+	0.820241i
$136$	870.126	−	918.581i	0.548623	−	0.579174i
$137$	−2053.15	−	1088.51i	−1.28038	−	0.678816i	−0.317378	−	0.948299i	$-0.602802\pi$
$137$	−2053.15	−	1088.51i	−1.28038	−	0.678816i	−0.963005	+	0.269483i	$0.913147\pi$
$138$	−22.0710	−	153.886i	−0.0136145	−	0.0949249i
$139$	−502.177	−	302.150i	−0.306432	−	0.184374i	0.354029	−	0.935235i	$-0.384812\pi$
$139$	−502.177	−	302.150i	−0.306432	−	0.184374i	−0.660461	+	0.750860i	$0.729639\pi$
$140$	5364.66	−	879.491i	3.23855	−	0.530933i
$141$	737.040	+	177.794i	0.440213	+	0.106191i
$142$	1578.92	−	438.385i	0.933098	−	0.259073i
$143$	−577.607	+	759.829i	−0.337776	+	0.444337i
$144$	−149.753	−	637.454i	−0.0866629	−	0.368897i
$145$	−1166.87	+	4202.68i	−0.668298	+	2.40699i
$146$	−1876.45	+	994.829i	−1.06367	+	0.563922i
$147$	589.639	−	429.861i	0.330834	−	0.241186i
$148$	−3796.70	+	205.851i	−2.10870	+	0.114330i
$149$	327.531	+	617.789i	0.180083	+	0.339673i	0.957076	−	0.289836i	$-0.0936008\pi$
$149$	327.531	+	617.789i	0.180083	+	0.339673i	−0.776993	+	0.629509i	$0.783256\pi$
$150$	−7434.18	+	2340.04i	−4.04666	+	1.27375i
$151$	549.358	+	722.668i	0.296067	+	0.389470i	0.919942	−	0.392055i	$-0.128236\pi$
$151$	549.358	+	722.668i	0.296067	+	0.389470i	−0.623875	+	0.781524i	$0.714442\pi$
$152$	−710.242	−	539.912i	−0.379001	−	0.288109i
$153$	−330.300	+	2209.11i	−0.174531	+	1.16730i
$154$	3360.04	−	3182.80i	1.75818	−	1.66543i
$155$	−290.318	−	1770.86i	−0.150445	−	0.917672i
$156$	1191.27	−	40.6643i	0.611397	−	0.0208702i
$157$	61.5975	−	133.141i	0.0313122	−	0.0676802i	−0.891288	−	0.453437i	$-0.850198\pi$
$157$	61.5975	−	133.141i	0.0313122	−	0.0676802i	0.922600	+	0.385757i	$0.126060\pi$
$158$	−995.847	+	1878.37i	−0.501426	+	0.945790i
$159$	−1244.30	−	229.691i	−0.620625	−	0.114564i
$160$	4093.40	+	2775.39i	2.02257	+	1.37134i
$161$	145.609	+	32.0509i	0.0712769	+	0.0156892i
$162$	−2396.44	−	2145.30i	−1.16224	−	1.04044i
$163$	310.460	−	186.798i	0.149185	−	0.0897615i	−0.439004	−	0.898485i	$-0.644669\pi$
$163$	310.460	−	186.798i	0.149185	−	0.0897615i	0.588189	+	0.808723i	$0.299841\pi$
$164$	3590.94	−	3050.17i	1.70979	−	1.45231i
$165$	−3319.59	+	4189.82i	−1.56624	+	1.97683i
$166$	2443.95	−	537.955i	1.14270	−	0.251526i
$167$	63.5459	+	25.3190i	0.0294451	+	0.0117320i	0.384814	−	0.922994i	$-0.374266\pi$
$167$	63.5459	+	25.3190i	0.0294451	+	0.0117320i	−0.355369	+	0.934726i	$0.615645\pi$
$168$	−1732.96	−	223.697i	−0.795837	−	0.102730i
$169$	−290.686	+	1773.10i	−0.132310	+	0.807057i
$170$	−4416.85	−	6514.36i	−1.99269	−	2.93899i
$171$	1573.73	+	63.1195i	0.703777	+	0.0282273i
$172$	1265.43	−	3755.67i	0.560978	−	1.66492i
$173$	407.229	+	44.2888i	0.178965	+	0.0194637i	0.197163	−	0.980371i	$-0.436827\pi$
$173$	407.229	+	44.2888i	0.178965	+	0.0194637i	−0.0181974	+	0.999834i	$0.505793\pi$
$174$	2469.97	−	3924.85i	1.07614	−	1.71001i
$175$	404.668	−	7463.66i	0.174800	−	3.22400i
$176$	1157.05			0.495543
$177$	1973.46	+	1284.79i	0.838047	+	0.545598i
$178$	−5838.26			−2.45841
$179$	117.806	−	2172.81i	0.0491913	−	0.907280i	−0.864943	−	0.501869i	$-0.832646\pi$
$179$	117.806	−	2172.81i	0.0491913	−	0.907280i	0.914135	−	0.405411i	$-0.132871\pi$
$180$	6675.06	−	93.9814i	2.76405	−	0.0389164i
$181$	−326.924	−	35.5552i	−0.134255	−	0.0146011i	0.0407449	−	0.999170i	$-0.487027\pi$
$181$	−326.924	−	35.5552i	−0.134255	−	0.0146011i	−0.175000	+	0.984569i	$0.555992\pi$
$182$	−619.674	+	1839.13i	−0.252381	+	0.749040i
$183$	−1888.08	−	1336.16i	−0.762683	−	0.539736i
$184$	−58.2010	−	85.8401i	−0.0233187	−	0.0343925i
$185$	−1156.78	+	7056.05i	−0.459720	+	2.80417i
$186$	−244.258	+	1892.24i	−0.0962894	+	0.745943i
$187$	−3666.57	−	1460.90i	−1.43383	−	0.571290i
$188$	1633.98	−	359.665i	0.633883	−	0.139528i
$189$	2733.94	−	1428.62i	1.05219	−	0.549823i
$190$	−4229.71	+	3592.75i	−1.61503	+	1.37182i
$191$	−669.059	+	402.560i	−0.253463	+	0.152504i	−0.636615	−	0.771182i	$-0.719666\pi$
$191$	−669.059	+	402.560i	−0.253463	+	0.152504i	0.383152	+	0.923685i	$0.374838\pi$
$192$	−2685.95	−	3293.72i	−1.00959	−	1.23804i
$193$	−1821.35	−	400.910i	−0.679294	−	0.149524i	−0.138096	−	0.990419i	$-0.544098\pi$
$193$	−1821.35	−	400.910i	−0.679294	−	0.149524i	−0.541198	+	0.840895i	$0.682029\pi$
$194$	1865.06	+	1264.54i	0.690223	+	0.467983i
$195$	406.895	−	2204.27i	0.149428	−	0.809491i
$196$	754.246	−	1422.66i	0.274871	−	0.518462i
$197$	−1289.98	+	2788.24i	−0.466533	+	1.00840i	0.521371	+	0.853330i	$0.325421\pi$
$197$	−1289.98	+	2788.24i	−0.466533	+	1.00840i	−0.987904	+	0.155065i	$0.950441\pi$
$198$	4658.71	−	3255.35i	1.67212	−	1.16842i
$199$	−34.5386	−	210.676i	−0.0123034	−	0.0750474i	0.979961	−	0.199189i	$-0.0638307\pi$
$199$	−34.5386	−	210.676i	−0.0123034	−	0.0750474i	−0.992265	+	0.124141i	$0.960382\pi$
$200$	−3774.71	+	3575.60i	−1.33456	+	1.26417i
$201$	1788.79	+	1582.21i	0.627718	+	0.555226i
$202$	3468.09	+	2636.37i	1.20799	+	0.918289i
$203$	2691.50	+	3540.60i	0.930571	+	1.22415i
$204$	1479.93	+	4701.67i	0.507921	+	1.61364i
$205$	−4150.13	−	7827.98i	−1.41394	−	2.66697i
$206$	−3111.48	+	168.700i	−1.05236	+	0.0570575i
$207$	171.021	+	65.3665i	0.0574241	+	0.0219482i
$208$	−428.662	+	227.262i	−0.142896	+	0.0757587i
$209$	−744.534	+	2681.57i	−0.246414	+	0.887502i
$210$	−3676.29	+	10228.6i	−1.20804	+	3.36115i
$211$	−79.1515	+	104.122i	−0.0258247	+	0.0339718i	−0.808824	−	0.588051i	$-0.799896\pi$
$211$	−79.1515	+	104.122i	−0.0258247	+	0.0339718i	0.782999	+	0.622022i	$0.213689\pi$
$212$	−2690.43	+	746.995i	−0.871602	+	0.241999i
$213$	−452.552	+	1876.04i	−0.145579	+	0.603494i
$214$	−2119.66	+	347.500i	−0.677087	+	0.111003i
$215$	−6385.92	−	3842.28i	−2.02565	−	1.21880i
$216$	−2064.05	−	586.364i	−0.650189	−	0.184708i
$217$	−1616.66	−	857.097i	−0.505741	−	0.268127i
$218$	−557.019	+	588.038i	−0.173056	+	0.182693i
$219$	50.1308	−	2500.78i	0.0154682	−	0.771629i
$220$	−2535.79	+	11520.2i	−0.777104	+	3.53042i
$221$	1645.34	−	178.941i	0.500802	−	0.0544655i
$222$	3329.73	−	6834.22i	1.00665	−	2.06614i
$223$	1986.99	+	2339.26i	0.596675	+	0.702461i	0.974746	−	0.223316i	$-0.0716882\pi$
$223$	1986.99	+	2339.26i	0.596675	+	0.702461i	−0.378071	+	0.925777i	$0.623412\pi$
$224$	4778.89	−	1610.20i	1.42546	−	0.480293i
$225$	1846.78	−	8991.10i	0.547193	−	2.66403i
$226$	1830.71	−	4594.75i	0.538838	−	1.35238i
$227$	2665.89	−	3138.53i	0.779479	−	0.917673i	−0.218833	−	0.975762i	$-0.570225\pi$
$227$	2665.89	−	3138.53i	0.779479	−	0.917673i	0.998311	+	0.0580891i	$0.0185008\pi$
$228$	3182.95	−	1395.84i	0.924544	−	0.405446i
$229$	1361.89	−	923.387i	0.392998	−	0.266459i	−0.348644	−	0.937255i	$-0.613358\pi$
$229$	1361.89	−	923.387i	0.392998	−	0.266459i	0.741642	+	0.670796i	$0.234047\pi$
$230$	−599.307	+	238.786i	−0.171813	+	0.0684567i
$231$	1352.65	+	5280.15i	0.385272	+	1.50393i
$232$	334.485	−	3075.54i	0.0946552	−	0.870340i
$233$	−4155.41	+	1922.50i	−1.16837	+	0.540545i	−0.905525	−	0.424293i	$-0.860523\pi$
$233$	−4155.41	+	1922.50i	−1.16837	+	0.540545i	−0.262845	+	0.964838i	$0.584661\pi$
$234$	−1086.56	+	2121.09i	−0.303548	+	0.592563i
$235$		−	3146.28i		−	0.873364i
$236$	5156.72	+	641.351i	1.42235	+	0.176900i
$237$	−1363.30	−	2100.15i	−0.373655	−	0.575608i
$238$	−8013.61	−	434.485i	−2.18254	−	0.118334i
$239$	2445.25	+	5285.33i	0.661800	+	1.43046i	0.889596	+	0.456749i	$0.150986\pi$
$239$	2445.25	+	5285.33i	0.661800	+	1.43046i	−0.227795	+	0.973709i	$0.573152\pi$
$240$	−2425.80	+	1224.44i	−0.652436	+	0.329321i
$241$	−3810.80	−	1284.01i	−1.01857	−	0.343196i	−0.240012	−	0.970770i	$-0.577152\pi$
$241$	−3810.80	−	1284.01i	−1.01857	−	0.343196i	−0.778557	+	0.627574i	$0.784048\pi$
$242$	1543.50	+	3873.88i	0.409999	+	1.02902i
$243$	3579.77	−	1238.60i	0.945031	−	0.326980i
$244$	−5037.00	−	825.774i	−1.32156	−	0.216659i
$245$	−2307.88	−	1960.33i	−0.601816	−	0.511187i
$246$	1840.26	+	9238.63i	0.476953	+	2.39444i
$247$	−250.868	−	1139.71i	−0.0646250	−	0.293594i
$248$	406.413	+	1206.19i	0.104061	+	0.308843i
$249$	−845.208	+	2823.38i	−0.215112	+	0.718571i
$250$	10543.2	+	17522.9i	2.66724	+	4.43299i
$251$	−605.218	−	5564.89i	−0.152195	−	1.39941i	−0.782299	−	0.622903i	$-0.785953\pi$
$251$	−605.218	−	5564.89i	−0.152195	−	1.39941i	0.630104	−	0.776511i	$-0.283012\pi$
$252$	4042.76	−	5476.51i	1.01059	−	1.36900i
$253$	−181.553	+	267.770i	−0.0451151	+	0.0665398i
$254$	−3878.35	−	3673.76i	−0.958067	−	0.907529i
$255$	9233.12	−	817.292i	2.26745	−	0.200709i
$256$	−1164.55	−	538.777i	−0.284314	−	0.131537i
$257$	1761.02	−	2926.84i	0.427430	−	0.710395i	−0.566053	−	0.824369i	$-0.691530\pi$
$257$	1761.02	−	2926.84i	0.427430	−	0.710395i	0.993484	+	0.113974i	$0.0363580\pi$
$258$	5332.81	+	5860.71i	1.28685	+	1.41423i
$259$	5013.96	+	5293.17i	1.20290	+	1.26989i
$260$	−1323.30	−	4766.08i	−0.315643	−	1.13685i
$261$	2625.88	+	4788.79i	0.622750	+	1.13570i
$262$	6294.13	−	4784.67i	1.48417	−	1.12824i
$263$	−1524.71	−	423.334i	−0.357482	−	0.0992543i	0.0841442	−	0.996454i	$-0.473184\pi$
$263$	−1524.71	−	423.334i	−0.357482	−	0.0992543i	−0.441626	+	0.897199i	$0.645598\pi$
$264$	1842.75	−	3313.56i	0.429595	−	0.772483i
$265$	284.272	+	5243.09i	0.0658970	+	1.21540i
$266$	306.361	+	5650.50i	0.0706174	+	1.30246i
$267$	3341.78	−	6009.07i	0.765969	−	1.37734i
$268$	5077.83	+	1409.85i	1.15738	+	0.321345i
$269$	532.229	−	404.590i	0.120634	−	0.0917036i	−0.543118	−	0.839657i	$-0.682756\pi$
$269$	532.229	−	404.590i	0.120634	−	0.0917036i	0.663752	+	0.747953i	$0.268963\pi$
$270$	−6322.24	+	11755.0i	−1.42503	+	2.64959i
$271$	174.427	+	628.229i	0.0390985	+	0.140820i	0.980523	−	0.196403i	$-0.0629261\pi$
$271$	174.427	+	628.229i	0.0390985	+	0.140820i	−0.941425	+	0.337223i	$0.890512\pi$
$272$	−1379.76	−	1456.60i	−0.307575	−	0.324703i
$273$	−1538.24	−	1690.51i	−0.341019	−	0.374777i
$274$	5285.98	−	8785.37i	1.16547	−	1.93702i
$275$	14719.9	+	6810.15i	3.22780	+	1.49334i
$276$	402.449	−	35.6238i	0.0877703	−	0.00776920i
$277$	203.989	+	193.228i	0.0442472	+	0.0419132i	0.709504	−	0.704702i	$-0.248919\pi$
$277$	203.989	+	193.228i	0.0442472	+	0.0419132i	−0.665256	+	0.746615i	$0.731678\pi$
$278$	1451.11	−	2140.22i	0.313063	−	0.461734i
$279$	−1807.78	−	1334.51i	−0.387918	−	0.286361i
$280$	783.976	+	7208.54i	0.167327	+	1.53854i
$281$	3970.11	+	6598.38i	0.842836	+	1.40081i	0.915018	+	0.403414i	$0.132176\pi$
$281$	3970.11	+	6598.38i	0.842836	+	1.40081i	−0.0721813	+	0.997392i	$0.522996\pi$
$282$	−959.344	+	3204.64i	−0.202582	+	0.676715i
$283$	441.859	+	1311.39i	0.0928121	+	0.275456i	0.983997	−	0.178183i	$-0.0570219\pi$
$283$	441.859	+	1311.39i	0.0928121	+	0.275456i	−0.891185	+	0.453639i	$0.850125\pi$
$284$	915.482	+	4159.08i	0.191281	+	0.868999i
$285$	−1276.80	−	6409.92i	−0.265373	−	1.33225i
$286$	−3209.54	−	2726.21i	−0.663581	−	0.563651i
$287$	−8915.36	−	1461.60i	−1.83365	−	0.300611i
$288$	6096.34	−	1087.79i	1.24733	−	0.222564i
$289$	714.742	+	1793.87i	0.145480	+	0.365127i
$290$	−18236.6	−	6144.64i	−3.69273	−	1.24423i
$291$	−2369.08	+	1195.81i	−0.477244	+	0.240892i
$292$	−2317.63	−	5009.47i	−0.464483	−	1.00396i
$293$	−8260.01	−	447.845i	−1.64695	−	0.0892948i	−0.792852	−	0.609414i	$-0.791405\pi$
$293$	−8260.01	−	447.845i	−1.64695	−	0.0892948i	−0.854094	+	0.520119i	$0.825888\pi$
$294$	1752.96	+	2700.40i	0.347737	+	0.535682i
$295$	3262.50	−	9211.31i	0.643900	−	1.81798i
$296$		−	5071.58i		−	0.995876i
$297$	683.978	+	6658.34i	0.133631	+	1.30086i
$298$	−2799.97	+	1295.41i	−0.544289	+	0.251815i
$299$	14.6673	−	134.863i	0.00283689	−	0.0260848i
$300$	−5026.55	−	19621.4i	−0.967360	−	3.77615i
$301$	−7059.61	+	2812.80i	−1.35186	+	0.538629i
$302$	−3315.02	+	2247.64i	−0.631648	+	0.428268i
$303$	−4698.61	+	2060.51i	−0.890851	+	0.390670i
$304$	−915.859	+	1078.23i	−0.172790	+	0.203424i
$305$	−3552.81	+	8916.87i	−0.666994	+	1.67403i
$306$	−9653.60	−	1982.86i	−1.80346	−	0.370432i
$307$	−5078.27	+	1711.07i	−0.944078	+	0.318097i	−0.748909	−	0.662673i	$-0.769422\pi$
$307$	−5078.27	+	1711.07i	−0.944078	+	0.318097i	−0.195169	+	0.980770i	$0.562526\pi$
$308$	7786.80	+	9167.33i	1.44057	+	1.69596i
$309$	1607.35	−	3299.07i	0.295920	−	0.607371i
$310$	7871.08	−	856.031i	1.44209	−	0.156837i
$311$	1377.38	−	6257.50i	0.251138	−	1.14093i	−0.667119	−	0.744951i	$-0.732473\pi$
$311$	1377.38	−	6257.50i	0.251138	−	1.14093i	0.918258	−	0.395983i	$-0.129596\pi$
$312$	−31.8643	+	1589.55i	−0.00578193	+	0.288432i
$313$	5288.66	−	5583.17i	0.955056	−	1.00824i	−0.0449007	−	0.998991i	$-0.514297\pi$
$313$	5288.66	−	5583.17i	0.955056	−	1.00824i	0.999957	−	0.00924941i	$-0.00294422\pi$
$314$	571.853	+	303.177i	0.102776	+	0.0544881i
$315$	−8423.58	−	9638.63i	−1.50671	−	1.72405i
$316$	−4734.37	−	2848.57i	−0.842813	−	0.507104i
$317$	−8813.24	+	1444.86i	−1.56152	+	0.255998i	−0.879701	−	0.475526i	$-0.842258\pi$
$317$	−8813.24	+	1444.86i	−1.56152	+	0.255998i	−0.681816	+	0.731524i	$0.738809\pi$
$318$	1309.15	−	5427.03i	0.230860	−	0.957021i
$319$	−9298.67	+	2581.76i	−1.63205	+	0.453138i
$320$	−10673.3	+	14040.5i	−1.86454	+	2.45277i
$321$	855.609	−	2380.58i	0.148771	−	0.413928i
$322$	−175.985	+	633.840i	−0.0304573	+	0.109697i
$323$	4263.66	−	2260.45i	0.734478	−	0.389396i
$324$	5904.38	−	5917.08i	1.01241	−	1.01459i
$325$	−6791.06	+	368.200i	−1.15908	+	0.0628433i
$326$	748.800	+	1412.39i	0.127215	+	0.239953i
$327$	−286.408	−	909.905i	−0.0484355	−	0.153877i
$328$	3803.12	+	5002.92i	0.640220	+	0.842194i
$329$	−2554.00	−	1941.50i	−0.427984	−	0.325345i
$330$	−17665.8	−	15625.6i	−2.94687	−	2.60655i
$331$	−45.5243	+	43.1229i	−0.00755964	+	0.00716087i	−0.691470	−	0.722405i	$-0.743037\pi$
$331$	−45.5243	+	43.1229i	−0.00755964	+	0.00716087i	0.683910	+	0.729566i	$0.260278\pi$
$332$	1052.16	+	6417.91i	0.173930	+	1.06093i
$333$	5128.25	+	7339.01i	0.843924	+	1.20773i
$334$	−126.725	+	273.911i	−0.0207607	+	0.0448734i
$335$	4642.01	−	8755.76i	0.757075	−	1.42799i
$336$	−502.970	+	2724.73i	−0.0816644	+	0.442399i
$337$	−6100.89	−	4136.50i	−0.986162	−	0.668634i	−0.0423447	−	0.999103i	$-0.513483\pi$
$337$	−6100.89	−	4136.50i	−0.986162	−	0.668634i	−0.943817	+	0.330469i	$0.892793\pi$
$338$	−7742.17	−	1704.18i	−1.24591	−	0.274246i
$339$	3681.28	+	4514.27i	0.589793	+	0.723250i
$340$	17526.6	−	10545.4i	2.79563	−	1.68208i
$341$	3026.12	−	2570.41i	0.480567	−	0.408197i
$342$	−653.988	+	6918.15i	−0.103402	+	1.09383i
$343$	4349.79	−	957.460i	0.684742	−	0.150723i
$344$	4910.68	+	1956.59i	0.769669	+	0.306664i
$345$	97.2673	−	753.519i	0.0151788	−	0.117589i
$346$	−292.392	+	1783.51i	−0.0454309	+	0.277116i
$347$	619.364	+	913.493i	0.0958190	+	0.141322i	0.872577	−	0.488477i	$-0.162447\pi$
$347$	619.364	+	913.493i	0.0958190	+	0.141322i	−0.776758	+	0.629799i	$0.783137\pi$
$348$	9837.71	+	6961.96i	1.51539	+	1.07241i
$349$	744.888	−	2210.75i	0.114249	−	0.339079i	−0.875240	−	0.483690i	$-0.839296\pi$
$349$	744.888	−	2210.75i	0.114249	−	0.339079i	0.989489	+	0.144610i	$0.0461929\pi$
$350$	32785.3	+	3565.62i	5.00699	+	0.544543i
$351$	−1561.21	−	2332.44i	−0.237410	−	0.354691i
$352$	−592.407	+	10926.3i	−0.0897029	+	1.65447i
$353$	5684.20			0.857052			0.428526	−	0.903529i	$-0.359033\pi$
$353$	5684.20			0.857052			0.428526	+	0.903529i	$0.359033\pi$
$354$	−6131.68	+	8387.40i	−0.920608	+	1.25928i
$355$	8008.44			1.19731
$356$	821.445	−	15150.7i	0.122294	−	2.25557i
$357$	5034.13	−	7999.36i	0.746315	−	1.18591i
$358$	9544.39	+	1038.02i	1.40904	+	0.153242i
$359$	−1646.44	+	4886.46i	−0.242049	+	0.718377i	0.755919	+	0.654665i	$0.227190\pi$
$359$	−1646.44	+	4886.46i	−0.242049	+	0.718377i	−0.997968	+	0.0637120i	$0.979706\pi$
$360$	−356.848	+	8897.10i	−0.0522431	+	1.30255i
$361$	1939.61	+	2860.71i	0.282783	+	0.417073i
$362$	234.733	−	1431.81i	0.0340809	−	0.207884i
$363$	−4870.70	−	628.730i	−0.704258	−	0.0909085i
$364$	−4685.47	−	1866.86i	−0.674685	−	0.268819i
$365$	−10137.1	+	2231.33i	−1.45369	+	0.319982i
$366$	6337.59	−	7998.98i	0.905113	−	1.14239i
$367$	9520.86	−	8087.09i	1.35418	−	1.15025i	0.379873	−	0.925039i	$-0.375968\pi$
$367$	9520.86	−	8087.09i	1.35418	−	1.15025i	0.974309	−	0.225214i	$-0.0723081\pi$
$368$	−140.914	+	84.7851i	−0.0199610	+	0.0120101i
$369$	−10562.3	−	3394.03i	−1.49011	−	0.478824i
$370$	−30809.9	−	6781.77i	−4.32900	−	0.952885i
$371$	4431.52	+	3004.65i	0.620143	+	0.420468i
$372$	−4876.11	−	900.102i	−0.679608	−	0.125452i
$373$	−3866.11	+	7292.26i	−0.536675	+	1.01228i	0.455830	+	0.890067i	$0.349343\pi$
$373$	−3866.11	+	7292.26i	−0.536675	+	1.01228i	−0.992504	+	0.122209i	$0.961002\pi$
$374$	7311.95	−	15804.5i	1.01094	−	2.18511i
$375$	−24070.4	+	821.649i	−3.31464	+	0.113146i
$376$	361.035	+	2202.22i	0.0495185	+	0.302049i
$377$	2937.87	−	2782.90i	0.401348	−	0.380177i
$378$	5640.88	+	12385.9i	0.767554	+	1.68535i
$379$	7065.88	+	5371.34i	0.957651	+	0.727987i	0.962297	−	0.272002i	$-0.0876857\pi$
$379$	7065.88	+	5371.34i	0.957651	+	0.727987i	−0.00464567	+	0.999989i	$0.501479\pi$
$380$	−8728.30	−	11481.9i	−1.17830	−	1.55002i
$381$	6001.18	−	1888.97i	0.806955	−	0.254003i
$382$	−1613.71	−	3043.77i	−0.216137	−	0.407678i
$383$	−2329.84	+	126.320i	−0.310834	+	0.0168529i	−0.208896	−	0.977938i	$-0.566987\pi$
$383$	−2329.84	+	126.320i	−0.310834	+	0.0168529i	−0.101938	+	0.994791i	$0.532504\pi$
$384$	7448.21	−	5429.93i	0.989817	−	0.721601i
$385$	19984.1	−	10594.9i	2.64542	−	1.40251i
$386$	2201.31	−	7928.40i	0.290269	−	1.04545i
$387$	−9084.63	+	2134.20i	−1.19328	+	0.280329i
$388$	−3543.98	+	4662.02i	−0.463706	+	0.609995i
$389$	211.410	−	58.6976i	0.0275550	−	0.00765061i	−0.253723	−	0.967277i	$-0.581655\pi$
$389$	211.410	−	58.6976i	0.0275550	−	0.00765061i	0.281278	+	0.959626i	$0.409242\pi$
$390$	9613.94	+	2319.14i	1.24826	+	0.301114i
$391$	553.594	−	90.7571i	0.0716022	−	0.0117386i
$392$	1840.33	+	1107.29i	0.237119	+	0.142670i
$393$	1321.94	+	9216.98i	0.169677	+	1.18304i
$394$	−11975.8	−	6349.15i	−1.53130	−	0.811842i
$395$	−7145.44	+	7543.35i	−0.910193	+	0.960879i
$396$	7792.36	+	12547.7i	0.988841	+	1.59228i
$397$	−566.907	+	2575.49i	−0.0716681	+	0.325592i	−0.998791	−	0.0491669i	$-0.984343\pi$
$397$	−566.907	+	2575.49i	−0.0716681	+	0.325592i	0.927122	+	0.374759i	$0.122274\pi$
$398$	936.407	−	101.840i	0.117934	−	0.0128261i
$399$	−5991.18	−	2918.98i	−0.751714	−	0.366246i
$400$	5337.48	+	6283.77i	0.667185	+	0.785471i
$401$	11917.4	−	4015.45i	1.48411	−	0.500055i	0.543461	−	0.839434i	$-0.317114\pi$
$401$	11917.4	−	4015.45i	1.48411	−	0.500055i	0.940650	+	0.339379i	$0.110217\pi$
$402$	−7397.87	+	7502.76i	−0.917842	+	0.930855i
$403$	−616.247	+	1546.66i	−0.0761723	+	0.191178i
$404$	−7329.51	+	8628.97i	−0.902616	+	1.06264i
$405$	−8480.14	−	13235.7i	−1.04045	−	1.62392i
$406$	−16241.4	+	11011.9i	−1.98534	+	1.34609i
$407$	−14696.7	+	5855.70i	−1.78990	+	0.713160i
$408$	−6368.88	+	1631.56i	−0.772810	+	0.197976i
$409$	−1196.28	+	10999.6i	−0.144627	+	1.32982i	0.666744	+	0.745287i	$0.267688\pi$
$409$	−1196.28	+	10999.6i	−0.144627	+	1.32982i	−0.811370	+	0.584532i	$0.801278\pi$
$410$	35478.3	−	16414.0i	4.27354	−	1.97715i
$411$	6016.74	+	10469.3i	0.722102	+	1.25648i
$412$		−	8098.22i		−	0.968376i
$413$	−5464.10	−	8332.47i	−0.651018	−	0.992770i
$414$	−328.830	+	737.839i	−0.0390365	+	0.0875913i
$415$	12212.1	+	662.123i	1.44451	+	0.0783189i
$416$	−1926.63	−	4164.34i	−0.227069	−	0.490802i
$417$	1372.23	+	2718.61i	0.161148	+	0.319259i
$418$	−11636.1	−	3920.66i	−1.36158	−	0.458769i
$419$	5948.04	+	14928.5i	0.693510	+	1.74058i	0.671706	+	0.740818i	$0.265562\pi$
$419$	5948.04	+	14928.5i	0.693510	+	1.74058i	0.0218045	+	0.999762i	$0.493059\pi$
$420$	−26026.6	−	10979.4i	−3.02374	−	1.27557i
$421$	8971.08	+	1470.73i	1.03854	+	0.170259i	0.656841	−	0.754029i	$-0.271892\pi$
$421$	8971.08	+	1470.73i	1.03854	+	0.170259i	0.381695	+	0.924288i	$0.375341\pi$
$422$	−439.814	−	373.582i	−0.0507342	−	0.0430940i
$423$	−2749.28	−	2821.73i	−0.316015	−	0.324343i
$424$	−800.619	−	3637.25i	−0.0917016	−	0.416605i
$425$	−8980.05	−	26651.8i	−1.02493	−	3.04189i
$426$	−8157.00	−	2441.89i	−0.927718	−	0.277723i
$427$	5045.95	+	8386.43i	0.571875	+	0.950463i
$428$	−603.548	−	5549.54i	−0.0681626	−	0.626745i
$429$	4643.09	−	1742.98i	0.522542	−	0.196158i
$430$	18452.9	−	27216.1i	2.06949	−	3.05227i
$431$	7157.44	+	6779.88i	0.799911	+	0.757716i	0.973887	−	0.227034i	$-0.0729029\pi$
$431$	7157.44	+	6779.88i	0.799911	+	0.757716i	−0.173976	+	0.984750i	$0.555662\pi$
$432$	−1105.63	+	3217.84i	−0.123136	+	0.358376i
$433$	9539.89	+	4413.62i	1.05879	+	0.489850i	0.870452	−	0.492253i	$-0.163827\pi$
$433$	9539.89	+	4413.62i	1.05879	+	0.489850i	0.188342	+	0.982104i	$0.439689\pi$
$434$	4162.20	−	6917.62i	0.460350	−	0.765107i
$435$	16762.9	−	15253.0i	1.84764	−	1.68121i
$436$	−1447.62	−	1528.24i	−0.159011	−	0.167865i
$437$	−105.823	−	381.139i	−0.0115840	−	0.0417217i
$438$	11005.5	+	818.205i	1.20060	+	0.0892588i
$439$	−11294.5	+	8585.85i	−1.22792	+	0.933440i	−0.999198	−	0.0400515i	$-0.987248\pi$
$439$	−11294.5	+	8585.85i	−1.22792	+	0.933440i	−0.228722	+	0.973492i	$0.573455\pi$
$440$	−15160.3	−	4209.24i	−1.64259	−	0.456063i
$441$	−3782.78	+	258.553i	−0.408464	+	0.0279185i
$442$	395.331	+	7291.45i	0.0425429	+	0.784658i
$443$	28.7694	+	530.620i	0.00308549	+	0.0569086i	0.999671	−	0.0256626i	$-0.00816957\pi$
$443$	28.7694	+	530.620i	0.00308549	+	0.0569086i	−0.996585	+	0.0825712i	$0.973687\pi$
$444$	17266.8	+	9602.44i	1.84559	+	1.02638i
$445$	−27492.9	−	7633.36i	−2.92874	−	0.813160i
$446$	−10780.5	+	8195.13i	−1.14456	+	0.870068i
$447$	269.381	−	3623.37i	0.0285040	−	0.383400i
$448$	4811.14	+	17328.2i	0.507377	+	1.82741i
$449$	9717.14	+	10258.3i	1.02134	+	1.07821i	0.996913	+	0.0785106i	$0.0250164\pi$
$449$	9717.14	+	10258.3i	1.02134	+	1.07821i	0.0244236	+	0.999702i	$0.492225\pi$
$450$	39170.1	+	10283.8i	4.10333	+	1.07730i
$451$	10106.6	−	16797.3i	1.05521	−	1.75378i
$452$	11666.1	+	5397.30i	1.21400	+	0.561654i
$453$	−415.902	−	4698.53i	−0.0431364	−	0.487321i
$454$	13190.4	+	12494.6i	1.36356	+	1.29163i
$455$	−5322.71	+	7850.41i	−0.548423	+	0.808863i
$456$	1629.23	+	4340.07i	0.167315	+	0.445707i
$457$	953.259	+	8765.07i	0.0975746	+	0.897183i	0.935960	+	0.352106i	$0.114534\pi$
$457$	953.259	+	8765.07i	0.0975746	+	0.897183i	−0.838386	+	0.545077i	$0.816500\pi$
$458$	3742.77	+	6220.53i	0.381852	+	0.634643i
$459$	7566.52	−	8801.05i	0.769444	−	0.894985i
$460$	−535.341	−	1588.84i	−0.0542618	−	0.161043i
$461$	3080.31	+	13994.0i	0.311203	+	1.41381i	0.829451	+	0.558579i	$0.188653\pi$
$461$	3080.31	+	13994.0i	0.311203	+	1.41381i	−0.518248	+	0.855230i	$0.673416\pi$
$462$	−23585.4	+	4698.01i	−2.37509	+	0.473098i
$463$	−6350.58	−	5394.23i	−0.637444	−	0.541450i	0.269340	−	0.963045i	$-0.413194\pi$
$463$	−6350.58	−	5394.23i	−0.637444	−	0.541450i	−0.906784	+	0.421595i	$0.861470\pi$
$464$	−4841.03	−	793.647i	−0.484352	−	0.0794054i
$465$	−3624.27	+	8591.34i	−0.361444	+	0.856804i
$466$	−7477.19	−	18766.3i	−0.743293	−	1.86552i
$467$	−987.449	−	332.710i	−0.0978452	−	0.0329679i	0.269953	−	0.962873i	$-0.412992\pi$
$467$	−987.449	−	332.710i	−0.0978452	−	0.0329679i	−0.367798	+	0.929906i	$0.619888\pi$
$468$	−5351.48	−	3118.12i	−0.528573	−	0.307981i
$469$	−4243.04	−	9171.17i	−0.417751	−	0.902954i
$470$	13861.3	+	751.536i	1.36037	+	0.0737570i
$471$	−639.371	+	415.047i	−0.0625492	+	0.0406037i
$472$	−1226.57	+	6821.77i	−0.119613	+	0.665248i
$473$		−	16489.6i		−	1.60294i
$474$	9578.06	−	5504.54i	0.928133	−	0.533400i
$475$	−17997.8	+	8326.67i	−1.73852	+	0.804324i
$476$	2255.03	−	20734.7i	0.217141	−	1.99658i
$477$	4836.46	+	4453.84i	0.464248	+	0.427521i
$478$	−23869.2	+	9510.35i	−2.28400	+	0.910028i
$479$	8161.58	−	5533.69i	0.778522	−	0.527851i	−0.105991	−	0.994367i	$-0.533801\pi$
$479$	8161.58	−	5533.69i	0.778522	−	0.527851i	0.884513	+	0.466516i	$0.154491\pi$
$480$	−10320.7	−	23534.4i	−0.981402	−	2.23790i
$481$	4294.68	−	5056.09i	0.407111	−	0.479289i
$482$	6567.11	−	16482.2i	0.620588	−	1.55756i
$483$	−551.651	−	543.939i	−0.0519689	−	0.0512424i
$484$	−10270.1	+	3460.41i	−0.964514	+	0.324983i
$485$	7129.36	+	8393.33i	0.667480	+	0.785818i
$486$	4601.70	+	16066.9i	0.429500	+	1.49961i
$487$	2405.45	−	261.609i	0.223822	−	0.0243422i	0.00447943	−	0.999990i	$-0.498574\pi$
$487$	2405.45	−	261.609i	0.223822	−	0.0243422i	0.219343	+	0.975648i	$0.429609\pi$
$488$	1463.55	−	6648.99i	0.135762	−	0.616774i
$489$	−1882.31	−	37.7331i	−0.174072	−	0.00348947i
$490$	9187.71	−	9699.35i	0.847058	−	0.894229i
$491$	12500.4	+	6627.29i	1.14895	+	0.609135i	0.930348	−	0.366679i	$-0.119505\pi$
$491$	12500.4	+	6627.29i	1.14895	+	0.609135i	0.218603	+	0.975814i	$0.429850\pi$
$492$	−24233.8	+	3475.71i	−2.22061	+	0.318490i
$493$	14338.7	+	8627.32i	1.30991	+	0.788144i
$494$	5081.02	−	832.991i	0.462765	−	0.0758665i
$495$	26194.5	−	9238.60i	2.37850	−	0.838877i
$496$	1944.75	−	539.957i	0.176052	−	0.0488806i
$497$	4941.85	−	6500.89i	0.446020	−	0.586730i
$498$	−12236.8	−	4398.06i	−1.10109	−	0.395747i
$499$	2671.49	−	9621.85i	0.239664	−	0.863193i	−0.741651	−	0.670786i	$-0.765957\pi$
$499$	2671.49	−	9621.85i	0.239664	−	0.863193i	0.981315	−	0.192407i	$-0.0616293\pi$
$500$	−46956.5	+	24894.8i	−4.19992	+	2.22666i
$501$	−209.388	−	287.216i	−0.0186722	−	0.0256125i
$502$	24661.3	−	1337.10i	2.19260	−	0.118880i
$503$	−1013.39	−	1911.47i	−0.0898311	−	0.169439i	0.834525	−	0.550970i	$-0.185742\pi$
$503$	−1013.39	−	1911.47i	−0.0898311	−	0.169439i	−0.924356	+	0.381530i	$0.875397\pi$
$504$	7002.06	+	5779.89i	0.618842	+	0.510827i
$505$	12884.5	+	16949.3i	1.13536	+	1.49353i
$506$	−1136.32	−	863.811i	−0.0998335	−	0.0758915i
$507$	6185.60	−	6993.22i	0.541839	−	0.612583i
$508$	10079.3	−	9547.66i	0.880312	−	0.833876i
$509$	−1262.79	−	7702.66i	−0.109965	−	0.670755i	−0.983071	−	0.183225i	$-0.941346\pi$
$509$	−1262.79	−	7702.66i	−0.109965	−	0.670755i	0.873106	−	0.487530i	$-0.162102\pi$
$510$	1395.20	+	40872.7i	0.121138	+	3.54877i
$511$	−4444.08	+	9605.72i	−0.384725	+	0.831569i
$512$	−3995.40	+	7536.13i	−0.344870	+	0.650494i
$513$	−6746.21	−	4633.02i	−0.580609	−	0.398738i
$514$	12473.9	+	8457.50i	1.07043	+	0.725767i
$515$	−14872.8	−	3273.75i	−1.27257	−	0.280114i
$516$	−15959.2	+	13014.4i	−1.36156	+	1.11032i
$517$	5964.85	−	3588.93i	0.507415	−	0.305302i
$518$	−24517.3	+	20825.2i	−2.07959	+	1.76642i
$519$	−1668.33	−	1321.81i	−0.141101	−	0.111794i
$520$	6443.35	−	1418.29i	0.543384	−	0.119608i
$521$	−6038.54	−	2405.97i	−0.507780	−	0.202318i	0.102157	−	0.994768i	$-0.467426\pi$
$521$	−6038.54	−	2405.97i	−0.507780	−	0.202318i	−0.609936	+	0.792450i	$0.708805\pi$
$522$	−21724.8	+	10424.7i	−1.82158	+	0.874095i
$523$	1235.23	−	7534.60i	0.103275	−	0.629952i	−0.883572	−	0.468296i	$-0.844868\pi$
$523$	1235.23	−	7534.60i	0.103275	−	0.629952i	0.986847	−	0.161656i	$-0.0516836\pi$
$524$	11530.9	+	17006.9i	0.961320	+	1.41784i
$525$	−22436.0	+	31703.5i	−1.86512	+	2.63553i
$526$	2229.24	−	6616.16i	0.184790	−	0.548438i
$527$	−6844.48	−	744.382i	−0.565750	−	0.0615290i
$528$	−5088.43	−	3202.23i	−0.419404	−	0.263938i
$529$	−656.219	+	12103.2i	−0.0539343	+	0.994760i
$530$	−23166.9			−1.89869
$531$	−5123.05	−	11112.0i	−0.418684	−	0.908132i
$532$	−14706.5			−1.19851
$533$	−445.034	+	8208.17i	−0.0361662	+	0.667046i
$534$	25675.4	+	16157.9i	2.08068	+	1.30940i
$535$	−10436.0	−	1134.98i	−0.843340	−	0.0917188i
$536$	−2244.42	+	6661.20i	−0.180866	+	0.536791i
$537$	−6531.53	+	9229.47i	−0.524872	+	0.741678i
$538$	1655.33	+	2441.43i	0.132651	+	0.195646i
$539$	1083.90	−	6611.51i	0.0866177	−	0.528345i
$540$	−29615.5	−	18060.5i	−2.36009	−	1.43926i
$541$	1244.93	+	496.024i	0.0989345	+	0.0394191i	0.419080	−	0.907949i	$-0.362353\pi$
$541$	1244.93	+	496.024i	0.0989345	+	0.0394191i	−0.320146	+	0.947368i	$0.603732\pi$
$542$	−2809.40	+	618.395i	−0.222646	+	0.0490080i
$543$	1339.34	+	1061.16i	0.105850	+	0.0838648i
$544$	14461.5	−	12283.7i	1.13977	−	0.968125i
$545$	−3391.90	+	2040.84i	−0.266592	+	0.160403i
$546$	7815.15	−	6373.06i	0.612559	−	0.499527i
$547$	9120.09	+	2007.48i	0.712882	+	0.156917i	0.556582	−	0.830792i	$-0.312112\pi$
$547$	9120.09	+	2007.48i	0.712882	+	0.156917i	0.156300	+	0.987710i	$0.450043\pi$
$548$	22054.9	+	14953.6i	1.71923	+	1.16567i
$549$	4605.41	+	11101.6i	0.358022	+	0.863030i
$550$	−33518.9	+	63223.4i	−2.59864	+	4.90156i
$551$	4954.45	−	10708.9i	0.383061	−	0.827973i
$552$	18.3846	+	538.582i	0.00141757	+	0.0415282i
$553$	1714.04	+	10455.2i	0.131806	+	0.803978i
$554$	−900.014	+	852.538i	−0.0690215	+	0.0653807i
$555$	24615.5	−	27829.4i	1.88265	−	2.12846i
$556$	5349.84	+	4066.85i	0.408065	+	0.310203i
$557$	−6026.16	−	7927.28i	−0.458414	−	0.603033i	0.507578	−	0.861606i	$-0.330541\pi$
$557$	−6026.16	−	7927.28i	−0.458414	−	0.603033i	−0.965992	+	0.258573i	$0.916748\pi$
$558$	6311.13	−	7645.62i	0.478802	−	0.580045i
$559$	3238.81	+	6109.05i	0.245058	+	0.462228i
$560$	11481.2	−	622.490i	0.866371	−	0.0469733i
$561$	12081.6	+	16572.3i	0.909243	+	1.24720i
$562$	−30018.2	+	15914.6i	−2.25310	+	1.19452i
$563$	−6018.64	+	21677.2i	−0.450542	+	1.62271i	0.294473	+	0.955660i	$0.404856\pi$
$563$	−6018.64	+	21677.2i	−0.450542	+	1.62271i	−0.745015	+	0.667047i	$0.767558\pi$
$564$	−8181.27	−	2940.45i	−0.610804	−	0.219531i
$565$	14628.5	−	19243.4i	1.08925	−	1.43288i
$566$	−5883.02	+	1633.41i	−0.436894	+	0.121303i
$567$	−15977.1	−	1283.69i	−1.18338	−	0.0950793i
$568$	−5605.45	+	918.968i	−0.414084	+	0.0678856i
$569$	−21000.8	−	12635.8i	−1.54727	−	0.930964i	−0.995273	−	0.0971217i	$-0.969036\pi$
$569$	−21000.8	−	12635.8i	−1.54727	−	0.930964i	−0.552002	−	0.833843i	$-0.686136\pi$
$570$	28544.6	−	4093.99i	2.09755	−	0.300839i
$571$	−17090.4	−	9060.73i	−1.25255	−	0.664063i	−0.295881	−	0.955225i	$-0.595613\pi$
$571$	−17090.4	−	9060.73i	−1.25255	−	0.664063i	−0.956674	+	0.291162i	$0.905958\pi$
$572$	7526.27	−	7945.39i	0.550156	−	0.580793i
$573$	4056.49	+	81.3169i	0.295746	+	0.00592855i
$574$	8568.81	−	38928.5i	0.623092	−	2.83074i
$575$	−2291.73	+	249.241i	−0.166212	+	0.0180766i
$576$	2696.53	+	21918.6i	0.195061	+	1.58555i
$577$	−7280.32	−	8571.05i	−0.525275	−	0.618401i	0.433987	−	0.900919i	$-0.357106\pi$
$577$	−7280.32	−	8571.05i	−0.525275	−	0.618401i	−0.959262	+	0.282518i	$0.908830\pi$
$578$	−8073.81	+	2720.38i	−0.581014	+	0.195766i
$579$	6900.34	+	6803.87i	0.495282	+	0.488358i
$580$	18511.6	−	46460.7i	1.32527	−	3.32617i
$581$	8073.35	−	9504.69i	0.576487	−	0.678693i
$582$	−4702.37	−	10722.9i	−0.334913	−	0.763707i
$583$	−9615.82	+	6519.68i	−0.683098	+	0.463152i
$584$	6839.32	−	2725.03i	0.484611	−	0.193087i
$585$	−7889.94	+	8567.75i	−0.557622	+	0.605526i
$586$	3946.06	−	36283.4i	0.278174	−	2.55777i
$587$	22252.6	−	10295.1i	1.56467	−	0.723893i	0.569494	−	0.821996i	$-0.307139\pi$
$587$	22252.6	−	10295.1i	1.56467	−	0.723893i	0.995176	+	0.0981024i	$0.0312773\pi$
$588$	−7254.35	+	4169.09i	−0.508783	+	0.292399i
$589$			4854.59i			0.339610i
$590$	39802.1	+	16573.6i	2.77733	+	1.15648i
$591$	13389.7	−	8691.92i	0.931947	−	0.604971i
$592$	−8030.24	−	435.387i	−0.557501	−	0.0302268i
$593$	−6021.46	−	13015.2i	−0.416985	−	0.901297i	−0.996280	−	0.0861795i	$-0.972534\pi$
$593$	−6021.46	−	13015.2i	−0.416985	−	0.901297i	0.579295	−	0.815118i	$-0.303328\pi$
$594$	−29497.4	+	1422.89i	−2.03753	+	0.0982863i
$595$	−37168.7	−	12523.6i	−2.56096	−	0.862886i
$596$	−2967.70	−	7448.38i	−0.203963	−	0.511908i
$597$	−431.173	+	1022.10i	−0.0295590	+	0.0700696i
$598$	590.652	+	96.8325i	0.0403906	+	0.00662169i
$599$	11702.8	+	9940.45i	0.798270	+	0.678057i	0.950650	−	0.310265i	$-0.100418\pi$
$599$	11702.8	+	9940.45i	0.798270	+	0.678057i	−0.152380	+	0.988322i	$0.548694\pi$
$600$	26496.2	−	5277.81i	1.80283	−	0.359110i
$601$	−2075.29	−	9428.12i	−0.140853	−	0.639902i	−0.993150	−	0.116844i	$-0.962722\pi$
$601$	−2075.29	−	9428.12i	−0.140853	−	0.639902i	0.852297	−	0.523058i	$-0.175209\pi$
$602$	−10705.8	−	31773.7i	−0.724812	−	2.15116i
$603$	−3487.78	−	11908.8i	−0.235544	−	0.804254i
$604$	−5366.34	−	8918.93i	−0.361512	−	0.600838i
$605$	2203.47	+	20260.5i	0.148072	+	1.36150i
$606$	−7955.46	−	21192.4i	−0.533282	−	1.42060i
$607$	−13596.5	+	20053.3i	−0.909168	+	1.34092i	0.0307512	+	0.999527i	$0.490210\pi$
$607$	−13596.5	+	20053.3i	−0.909168	+	1.34092i	−0.939920	+	0.341396i	$0.889100\pi$
$608$	−9713.13	−	9200.77i	−0.647894	−	0.613718i
$609$	−2037.65	−	23019.7i	−0.135582	−	1.53170i
$610$	−38435.6	−	17782.2i	−2.55117	−	1.18030i
$611$	−1504.93	+	2501.22i	−0.0996451	+	0.165611i
$612$	6503.90	−	24772.7i	0.429583	−	1.63624i
$613$	18177.7	+	19190.0i	1.19770	+	1.26440i	0.955774	+	0.294102i	$0.0950207\pi$
$613$	18177.7	+	19190.0i	1.19770	+	1.26440i	0.241927	+	0.970295i	$0.422221\pi$
$614$	−6325.27	−	22781.6i	−0.415745	−	1.49738i
$615$	−3413.31	+	45911.6i	−0.223802	+	3.01030i
$616$	−12772.0	+	9709.01i	−0.835386	+	0.635044i
$617$	8859.46	+	2459.82i	0.578069	+	0.160500i	0.544243	−	0.838928i	$-0.316817\pi$
$617$	8859.46	+	2459.82i	0.578069	+	0.160500i	0.0338259	+	0.999428i	$0.489231\pi$
$618$	14150.5	+	7869.41i	0.921061	+	0.512223i
$619$	813.071	+	14996.2i	0.0527950	+	0.973746i	0.898191	+	0.439606i	$0.144882\pi$
$619$	813.071	+	14996.2i	0.0527950	+	0.973746i	−0.845396	+	0.534140i	$0.820635\pi$
$620$	1113.99	+	20546.4i	0.0721598	+	1.33091i
$621$	−571.205	−	760.784i	−0.0369109	−	0.0491614i
$622$	27239.1	+	7562.90i	1.75593	+	0.487532i
$623$	−23161.7	+	17607.1i	−1.48949	+	1.13228i
$624$	2514.13	+	186.914i	0.161291	+	0.0119913i
$625$	15369.6	+	55356.4i	0.983655	+	3.54281i
$626$	23334.0	+	24633.4i	1.48980	+	1.57276i
$627$	10695.8	−	9732.37i	0.681257	−	0.619894i
$628$	−867.224	+	1441.34i	−0.0551051	+	0.0915854i
$629$	24897.4	+	11518.7i	1.57826	+	0.730179i
$630$	44476.1	−	34808.6i	2.81265	−	2.20129i
$631$	−17427.2	−	16507.9i	−1.09947	−	1.04148i	−0.998916	−	0.0465438i	$-0.985179\pi$
$631$	−17427.2	−	16507.9i	−1.09947	−	1.04148i	−0.100556	−	0.994931i	$-0.532062\pi$
$632$	4135.80	−	6099.86i	0.260306	−	0.383923i
$633$	636.258	−	238.846i	0.0399510	−	0.0149973i
$634$	−4260.30	−	39172.8i	−0.266874	−	2.45387i
$635$	−13460.1	−	22370.9i	−0.841179	−	1.39805i
$636$	13899.3	+	4160.91i	0.866577	+	0.259419i
$637$	897.042	+	2662.33i	0.0557961	+	0.165597i
$638$	−9153.11	−	41583.0i	−0.567986	−	2.58039i
$639$	7182.34	−	6997.92i	0.444646	−	0.433229i
$640$	−29152.7	−	24762.5i	−1.80056	−	1.52941i
$641$	13552.4	+	2221.80i	0.835079	+	0.136904i	0.564127	−	0.825688i	$-0.309213\pi$
$641$	13552.4	+	2221.80i	0.835079	+	0.136904i	0.270953	+	0.962593i	$0.412661\pi$
$642$	10283.5	+	4338.12i	0.632177	+	0.266685i
$643$	−2692.87	−	6758.61i	−0.165158	−	0.414515i	0.822983	−	0.568066i	$-0.192308\pi$
$643$	−2692.87	−	6758.61i	−0.165158	−	0.414515i	−0.988141	+	0.153551i	$0.950929\pi$
$644$	−1620.09	−	545.873i	−0.0991314	−	0.0334013i
$645$	17450.0	+	34571.1i	1.06526	+	2.11044i
$646$	8940.22	+	19324.0i	0.544502	+	1.17692i
$647$	4510.96	+	244.577i	0.274102	+	0.0148614i	0.190678	−	0.981653i	$-0.438931\pi$
$647$	4510.96	+	244.577i	0.274102	+	0.0148614i	0.0834246	+	0.996514i	$0.473414\pi$
$648$	7454.41	+	8291.15i	0.451909	+	0.502634i
$649$	21184.7	−	4322.06i	1.28131	−	0.261411i
$650$		−	30006.7i		−	1.81071i
$651$	4737.60	+	8243.57i	0.285224	+	0.496299i
$652$	−3770.59	+	1744.46i	−0.226484	+	0.104783i
$653$	−1419.28	+	13050.0i	−0.0850545	+	0.782063i	0.871477	+	0.490435i	$0.163162\pi$
$653$	−1419.28	+	13050.0i	−0.0850545	+	0.782063i	−0.956532	+	0.291627i	$0.905803\pi$
$654$	4077.10	−	1044.46i	0.243772	−	0.0624488i
$655$	35895.4	−	14302.0i	2.14130	−	0.853171i
$656$	8248.01	−	5592.29i	0.490901	−	0.332839i
$657$	−7141.60	+	10859.1i	−0.424079	+	0.644831i
$658$	9163.57	−	10788.2i	0.542908	−	0.639160i
$659$	3833.69	−	9621.82i	0.226615	−	0.568760i	−0.771071	−	0.636749i	$-0.780279\pi$
$659$	3833.69	−	9621.82i	0.226615	−	0.568760i	0.997686	+	0.0679885i	$0.0216581\pi$
$660$	43035.1	−	43645.3i	2.53809	−	2.57408i
$661$	−19581.5	+	6597.76i	−1.15224	+	0.388235i	−0.829639	−	0.558300i	$-0.811454\pi$
$661$	−19581.5	+	6597.76i	−1.15224	+	0.388235i	−0.322601	+	0.946535i	$0.604557\pi$
$662$	−179.108	−	210.863i	−0.0105155	−	0.0123798i
$663$	−7731.05	−	3766.68i	−0.452865	−	0.220642i
$664$	−8623.79	+	937.894i	−0.504018	+	0.0548153i
$665$	−5945.19	+	27009.3i	−0.346684	+	1.57500i
$666$	−33557.8	+	20840.0i	−1.95246	+	1.21252i
$667$	943.279	−	995.807i	0.0547585	−	0.0578078i
$668$	−692.985	−	367.398i	−0.0401383	−	0.0212800i
$669$	−2264.20	−	15786.7i	−0.130851	−	0.912332i
$670$	37465.6	+	22542.3i	2.16033	+	1.29983i
$671$	−20957.7	+	3435.83i	−1.20575	+	0.197673i
$672$	−25472.9	−	6144.74i	−1.46226	−	0.352736i
$673$	−9068.55	+	2517.87i	−0.519416	+	0.144215i	−0.517335	−	0.855783i	$-0.673076\pi$
$673$	−9068.55	+	2517.87i	−0.519416	+	0.144215i	−0.00208037	+	0.999998i	$0.500662\pi$
$674$	19681.1	−	25890.1i	1.12476	−	1.47960i
$675$	−33005.4	+	34429.7i	−1.88204	+	1.96326i
$676$	5511.78	−	19851.7i	0.313597	−	1.12948i
$677$	18342.1	−	9724.34i	1.04127	−	0.552048i	0.142197	−	0.989838i	$-0.454583\pi$
$677$	18342.1	−	9724.34i	1.04127	−	0.552048i	0.899077	+	0.437790i	$0.144239\pi$
$678$	−20767.5	+	15140.0i	−1.17636	+	0.857593i
$679$	11212.7	−	607.936i	0.633733	−	0.0343600i
$680$	12779.5	+	24104.7i	0.720693	+	1.35937i
$681$	−20410.2	+	6424.46i	−1.14849	+	0.361506i
$682$	10601.4	+	13945.9i	0.595231	+	0.783013i
$683$	−21153.2	−	16080.2i	−1.18507	−	0.900868i	−0.188377	−	0.982097i	$-0.560323\pi$
$683$	−21153.2	−	16080.2i	−1.18507	−	0.900868i	−0.996696	+	0.0812284i	$0.974116\pi$
$684$	−17861.0	−	2670.53i	−0.998440	−	0.149284i
$685$	36378.8	−	34459.8i	2.02914	−	1.92210i
$686$	3179.18	+	19392.2i	0.176941	+	1.07929i
$687$	−8544.86	+	291.681i	−0.474537	+	0.0161984i
$688$	3519.61	−	7607.51i	0.195035	−	0.421560i
$689$	2281.90	−	4304.11i	0.126173	−	0.237988i
$690$	3296.48	+	608.511i	0.181876	+	0.0335734i
$691$	−11637.9	−	7890.67i	−0.640702	−	0.434407i	0.197098	−	0.980384i	$-0.436848\pi$
$691$	−11637.9	−	7890.67i	−0.640702	−	0.434407i	−0.837800	+	0.545977i	$0.816159\pi$
$692$	−4587.19	−	1009.72i	−0.251992	−	0.0554677i
$693$	8664.64	−	26964.5i	0.474953	−	1.47806i
$694$	−4172.44	+	2510.47i	−0.228218	+	0.137314i
$695$	9631.67	−	8181.21i	0.525683	−	0.446520i
$696$	−9982.82	+	12599.8i	−0.543675	+	0.686199i
$697$	−33198.1	+	7307.45i	−1.80411	+	0.397115i
$698$	9561.77	+	3809.76i	0.518508	+	0.206592i
$699$	23595.3	+	3045.77i	1.27676	+	0.164809i
$700$	−13865.9	+	84578.3i	−0.748688	+	4.56680i
$701$	1672.05	+	2466.09i	0.0900891	+	0.132872i	0.870063	−	0.492941i	$-0.164078\pi$
$701$	1672.05	+	2466.09i	0.0900891	+	0.132872i	−0.779974	+	0.625812i	$0.784768\pi$
$702$	10648.7	−	6320.93i	0.572522	−	0.339840i
$703$	6176.33	−	18330.7i	0.331358	−	0.983436i
$704$	−38793.4	−	4219.04i	−2.07682	−	0.225868i
$705$	−8707.61	+	13836.6i	−0.465174	+	0.739173i
$706$	−1357.76	+	25042.4i	−0.0723794	+	1.33496i
$707$	21709.5			1.15484
$708$	−20903.1	−	17092.2i	−1.10959	−	0.907295i
$709$	−23426.0			−1.24088			−0.620439	−	0.784255i	$-0.713046\pi$
$709$	−23426.0			−1.24088			−0.620439	+	0.784255i	$0.713046\pi$
$710$	−1912.94	+	35282.1i	−0.101114	+	1.86495i
$711$	183.160	+	13009.0i	0.00966112	+	0.686184i
$712$	20119.4	+	2188.12i	1.05900	+	0.115173i
$713$	−180.192	+	534.790i	−0.00946455	+	0.0280898i
$714$	34039.6	+	24089.2i	1.78417	+	1.26263i
$715$	−11549.6	−	17034.3i	−0.604097	−	0.890976i
$716$	−4036.61	+	24622.3i	−0.210692	+	1.28516i
$717$	3873.96	−	30011.2i	0.201779	−	1.56316i
$718$	−21134.6	−	8420.77i	−1.09852	−	0.437689i
$719$	24595.9	−	5413.97i	1.27576	−	0.280817i	0.475100	−	0.879932i	$-0.342412\pi$
$719$	24595.9	−	5413.97i	1.27576	−	0.280817i	0.800663	+	0.599115i	$0.204481\pi$
$720$	14056.9	+	1328.83i	0.727595	+	0.0687812i
$721$	−11835.2	+	10052.9i	−0.611325	+	0.519264i
$722$	−13066.5	+	7861.83i	−0.673522	+	0.405245i
$723$	13205.4	+	16193.5i	0.679274	+	0.832979i
$724$	3682.61	+	810.603i	0.189037	+	0.0416102i
$725$	−56916.2	−	38590.1i	−2.91561	−	1.97683i
$726$	3933.38	−	21308.2i	0.201076	−	1.08929i
$727$	3972.69	−	7493.28i	0.202667	−	0.382270i	−0.761256	−	0.648451i	$-0.775417\pi$
$727$	3972.69	−	7493.28i	0.202667	−	0.382270i	0.963923	+	0.266181i	$0.0857619\pi$
$728$	2824.76	−	6105.62i	0.143808	−	0.310837i
$729$	−19171.0	−	4460.28i	−0.973987	−	0.226606i
$730$	−7409.00	−	45192.9i	−0.375643	−	2.29132i
$731$	−20758.6	+	19663.6i	−1.05032	+	0.994917i
$732$	19866.2	+	17571.9i	1.00311	+	0.887263i
$733$	−1009.42	−	767.343i	−0.0508648	−	0.0386664i	0.579433	−	0.815020i	$-0.303274\pi$
$733$	−1009.42	−	767.343i	−0.0508648	−	0.0386664i	−0.630298	+	0.776354i	$0.717067\pi$
$734$	33354.4	+	43876.9i	1.67729	+	2.20644i
$735$	4724.13	+	15008.4i	0.237078	+	0.753186i
$736$	−728.502	−	1374.10i	−0.0364850	−	0.0688179i
$737$	21894.6	−	1187.09i	1.09430	−	0.0593313i
$738$	17475.7	−	45722.5i	0.871667	−	2.28058i
$739$	4915.15	−	2605.85i	0.244664	−	0.129713i	−0.341565	−	0.939858i	$-0.610957\pi$
$739$	4915.15	−	2605.85i	0.244664	−	0.129713i	0.586229	+	0.810146i	$0.300612\pi$
$740$	21934.1	−	78999.4i	1.08961	−	3.92443i
$741$	−2050.98	+	5706.47i	−0.101680	+	0.282905i
$742$	−14295.8	+	18805.8i	−0.707300	+	0.930437i
$743$	−17548.8	+	4872.40i	−0.866491	+	0.240580i	−0.672205	−	0.740365i	$-0.734653\pi$
$743$	−17548.8	+	4872.40i	−0.866491	+	0.240580i	−0.194286	+	0.980945i	$0.562239\pi$
$744$	1550.93	−	6429.34i	0.0764246	−	0.316816i
$745$	−14879.0	+	2439.29i	−0.731712	+	0.119958i
$746$	−31203.4	−	18774.4i	−1.53142	−	0.921423i
$747$	11531.0	−	10077.4i	0.564788	−	0.493590i
$748$	39985.0	+	21198.7i	1.95454	+	1.03623i
$749$	−7361.17	+	7771.09i	−0.359107	+	0.379105i
$750$	2129.72	−	106241.i	0.103689	−	5.17250i
$751$	−5633.81	+	25594.7i	−0.273743	+	1.24362i	0.616214	+	0.787579i	$0.288666\pi$
$751$	−5633.81	+	25594.7i	−0.273743	+	1.24362i	−0.889956	+	0.456046i	$0.849265\pi$
$752$	3517.94	−	382.599i	0.170593	−	0.0185531i
$753$	−12739.7	+	26148.1i	−0.616550	+	1.26546i
$754$	11558.6	+	13607.8i	0.558276	+	0.657253i
$755$	−18549.4	+	6250.03i	−0.894149	+	0.301274i
$756$	−32935.9	+	12895.7i	−1.58448	+	0.620389i
$757$	13969.6	−	35061.0i	0.670718	−	1.68337i	−0.0577829	−	0.998329i	$-0.518403\pi$
$757$	13969.6	−	35061.0i	0.670718	−	1.68337i	0.728501	−	0.685045i	$-0.240218\pi$
$758$	−25351.8	+	29846.5i	−1.21480	+	1.43017i
$759$	1539.51	−	675.129i	0.0736239	−	0.0322867i
$760$	15922.7	−	10795.8i	0.759968	−	0.515271i
$761$	12349.4	−	4920.45i	0.588260	−	0.234384i	−0.0569660	−	0.998376i	$-0.518143\pi$
$761$	12349.4	−	4920.45i	0.588260	−	0.234384i	0.645226	+	0.763992i	$0.276763\pi$
$762$	6888.61	+	26890.1i	0.327491	+	1.27838i
$763$	−436.412	+	4012.75i	−0.0207067	+	0.190395i
$764$	8125.83	−	3759.41i	0.384793	−	0.178024i
$765$	−42867.1	−	21959.2i	−2.02597	−	1.03783i
$766$		−	10294.5i		−	0.485584i
$767$	−6999.59	+	5762.26i	−0.329518	+	0.271269i
$768$	3630.31	+	5592.42i	0.170570	+	0.262759i
$769$	4745.51	+	257.294i	0.222532	+	0.0120654i	0.165068	−	0.986282i	$-0.447216\pi$
$769$	4745.51	+	257.294i	0.222532	+	0.0120654i	0.0574644	+	0.998348i	$0.481698\pi$
$770$	41903.5	+	90573.0i	1.96117	+	4.23899i
$771$	−15844.9	+	7997.80i	−0.740129	+	0.373585i
$772$	20265.0	+	6828.07i	0.944757	+	0.318326i
$773$	−3811.07	−	9565.07i	−0.177328	−	0.445061i	0.813266	−	0.581892i	$-0.197687\pi$

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.f (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.238865 + 4.40561i) q^{2} +(-4.39778 - 2.76759i) q^{3} +(-11.3992 - 1.23974i) q^{4} +(-6.88505 + 20.4341i) q^{5} +(13.2434 - 18.7138i) q^{6} +(12.3388 + 18.1984i) q^{7} +(2.47433 - 15.0928i) q^{8} +(11.6809 + 24.3425i) q^{9} +O(q^{10})\)	\(q+(-0.238865 + 4.40561i) q^{2} +(-4.39778 - 2.76759i) q^{3} +(-11.3992 - 1.23974i) q^{4} +(-6.88505 + 20.4341i) q^{5} +(13.2434 - 18.7138i) q^{6} +(12.3388 + 18.1984i) q^{7} +(2.47433 - 15.0928i) q^{8} +(11.6809 + 24.3425i) q^{9} +(-88.3800 - 35.2138i) q^{10} +(-46.5935 + 10.2560i) q^{11} +(46.7002 + 37.0005i) q^{12} +(15.2475 - 12.9514i) q^{13} +(-83.1225 + 50.0131i) q^{14} +(86.8321 - 70.8095i) q^{15} +(-23.6852 - 5.21350i) q^{16} +(68.4735 + 46.4262i) q^{17} +(-110.034 + 45.6467i) q^{18} +(27.3237 - 51.5379i) q^{19} +(103.817 - 224.397i) q^{20} +(-3.89761 - 114.182i) q^{21} +(-34.0544 - 207.723i) q^{22} +(4.92299 - 4.66330i) q^{23} +(-52.6522 + 59.5266i) q^{24} +(-270.636 - 205.732i) q^{25} +(53.4166 + 70.2683i) q^{26} +(16.0003 - 139.381i) q^{27} +(-118.092 - 222.745i) q^{28} +(201.980 - 10.9511i) q^{29} +(291.218 + 399.462i) q^{30} +(-73.5277 + 38.9819i) q^{31} +(61.3593 - 220.996i) q^{32} +(233.292 + 83.8483i) q^{33} +(-220.892 + 290.578i) q^{34} +(-456.822 + 126.836i) q^{35} +(-102.974 - 291.967i) q^{36} +(327.232 - 53.6470i) q^{37} +(220.529 + 132.688i) q^{38} +(-102.899 + 14.7583i) q^{39} +(291.371 + 154.475i) q^{40} +(-282.573 + 298.308i) q^{41} +(503.970 + 10.1026i) q^{42} +(-74.2998 + 337.547i) q^{43} +(543.845 - 59.1468i) q^{44} +(-577.840 + 71.0884i) q^{45} +(19.3688 + 22.8027i) q^{46} +(-138.274 + 46.5899i) q^{47} +(89.7332 + 88.4787i) q^{48} +(-51.9785 + 130.456i) q^{49} +(971.022 - 1143.18i) q^{50} +(-172.642 - 393.679i) q^{51} +(-189.867 + 128.733i) q^{52} +(226.216 - 90.1328i) q^{53} +(610.235 + 103.784i) q^{54} +(111.226 - 1022.71i) q^{55} +(305.195 - 141.198i) q^{56} +(-262.799 + 151.031i) q^{57} +892.462i q^{58} +(-453.134 - 6.98137i) q^{59} +(-1077.60 + 699.525i) q^{60} +(444.493 + 24.0997i) q^{61} +(-154.176 - 333.246i) q^{62} +(-298.867 + 512.932i) q^{63} +(775.106 + 261.164i) q^{64} +(159.670 + 400.740i) q^{65} +(-425.128 + 1007.77i) q^{66} +(-453.541 - 74.3542i) q^{67} +(-722.989 - 614.112i) q^{68} +(-34.5563 + 6.88333i) q^{69} +(-449.671 - 2042.87i) q^{70} +(-118.589 - 351.959i) q^{71} +(396.298 - 116.065i) q^{72} +(248.173 + 412.466i) q^{73} +(158.183 + 1454.47i) q^{74} +(620.814 + 1653.78i) q^{75} +(-375.363 + 553.619i) q^{76} +(-761.554 - 721.382i) q^{77} +(-40.4401 - 456.860i) q^{78} +(437.328 + 202.329i) q^{79} +(269.607 - 448.090i) q^{80} +(-456.115 + 568.683i) q^{81} +(-1246.73 - 1316.16i) q^{82} +(-151.738 - 546.510i) q^{83} +(-97.1257 + 1306.41i) q^{84} +(-1420.12 + 1079.55i) q^{85} +(-1469.35 - 407.964i) q^{86} +(-918.572 - 510.839i) q^{87} +(39.5037 + 728.602i) q^{88} +(71.6390 + 1321.30i) q^{89} +(-175.162 - 2562.72i) q^{90} +(423.832 + 117.676i) q^{91} +(-61.8996 + 47.0548i) q^{92} +(431.244 + 32.0610i) q^{93} +(-172.228 - 620.310i) q^{94} +(865.006 + 913.176i) q^{95} +(-881.473 + 802.075i) q^{96} +(263.303 - 437.613i) q^{97} +(-562.323 - 260.158i) q^{98} +(-793.910 - 1014.40i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} + O(q^{10}) \)	\( 1624q - 21q^{3} - 278q^{4} - 29q^{6} - 42q^{7} - 25q^{9} - 58q^{10} - 57q^{12} - 58q^{13} - 11q^{15} - 926q^{16} - 29q^{18} + 126q^{19} + 159q^{21} + 2q^{22} - 29q^{24} + 656q^{25} - 99q^{27} - 54q^{28} - 29q^{30} - 58q^{31} - 29q^{33} - 58q^{34} + 859q^{36} - 58q^{37} - 29q^{39} - 58q^{40} - 29q^{42} - 58q^{43} + 1703q^{45} + 602q^{46} + 9507q^{48} - 1192q^{49} + 1511q^{51} - 58q^{52} - 7743q^{54} - 58q^{55} - 7441q^{57} - 18722q^{60} - 58q^{61} - 3251q^{63} - 4634q^{64} - 1751q^{66} - 58q^{67} + 6003q^{69} - 58q^{70} + 21547q^{72} - 58q^{73} + 3869q^{75} + 5622q^{76} - 3253q^{78} + 1446q^{79} + 247q^{81} - 58q^{82} + 3303q^{84} + 790q^{85} - 2199q^{87} - 5818q^{88} - 29q^{90} - 58q^{91} - 29q^{93} - 946q^{94} - 29q^{96} - 58q^{97} - 29q^{99} + O(q^{100}) \)

Introduction

L-functions

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