LMFDB - Embedded newform 690.3.k.a.277.9

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.9
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.9

$q$-expansion

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(4.32717 + 5.59246i) q^{10} -11.9521 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.79511 + 6.79511i) q^{13} +6.22373i q^{14} +(-6.84933 + 5.29968i) q^{15} -4.00000 q^{16} +(-3.44295 - 3.44295i) q^{17} +(3.00000 - 3.00000i) q^{18} +27.8436i q^{19} +(-1.26529 + 9.91963i) q^{20} -7.62248 q^{21} +(-11.9521 - 11.9521i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(24.1995 + 6.27559i) q^{25} -13.5902 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.22373 + 6.22373i) q^{28} +26.4720i q^{29} +(-12.1490 - 1.54965i) q^{30} -16.0271 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.6383 - 14.6383i) q^{33} -6.88590i q^{34} +(13.4656 + 17.4030i) q^{35} +6.00000 q^{36} +(13.6416 + 13.6416i) q^{37} +(-27.8436 + 27.8436i) q^{38} -16.6446i q^{39} +(-11.1849 + 8.65434i) q^{40} +32.3332 q^{41} +(-7.62248 - 7.62248i) q^{42} +(-22.4332 + 22.4332i) q^{43} -23.9043i q^{44} +(1.89793 - 14.8794i) q^{45} +6.78233 q^{46} +(-35.7929 - 35.7929i) q^{47} +(4.89898 - 4.89898i) q^{48} -29.6326i q^{49} +(17.9239 + 30.4751i) q^{50} +8.43348 q^{51} +(-13.5902 - 13.5902i) q^{52} +(-41.6197 + 41.6197i) q^{53} +7.34847i q^{54} +(-59.2803 - 7.56143i) q^{55} -12.4475 q^{56} +(-34.1013 - 34.1013i) q^{57} +(-26.4720 + 26.4720i) q^{58} +59.3699i q^{59} +(-10.5994 - 13.6987i) q^{60} +9.79153 q^{61} +(-16.0271 - 16.0271i) q^{62} +(9.33560 - 9.33560i) q^{63} -8.00000i q^{64} +(-38.0014 + 29.4036i) q^{65} +29.2766 q^{66} +(-35.1732 - 35.1732i) q^{67} +(6.88590 - 6.88590i) q^{68} +8.30662i q^{69} +(-3.93740 + 30.8686i) q^{70} +28.4741 q^{71} +(6.00000 + 6.00000i) q^{72} +(-2.27141 + 2.27141i) q^{73} +27.2833i q^{74} +(-37.3242 + 21.9523i) q^{75} -55.6872 q^{76} +(-37.1934 - 37.1934i) q^{77} +(16.6446 - 16.6446i) q^{78} +21.6053i q^{79} +(-19.8393 - 2.53057i) q^{80} -9.00000 q^{81} +(32.3332 + 32.3332i) q^{82} +(-48.0807 + 48.0807i) q^{83} -15.2450i q^{84} +(-14.8982 - 19.2546i) q^{85} -44.8664 q^{86} +(-32.4215 - 32.4215i) q^{87} +(23.9043 - 23.9043i) q^{88} -113.080i q^{89} +(16.7774 - 12.9815i) q^{90} -42.2909 q^{91} +(6.78233 + 6.78233i) q^{92} +(19.6291 - 19.6291i) q^{93} -71.5858i q^{94} +(-17.6151 + 138.099i) q^{95} +9.79796 q^{96} +(43.1625 + 43.1625i) q^{97} +(29.6326 - 29.6326i) q^{98} +35.8564i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) $	$ 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	4.95981	+	0.632643i	0.991963	+	0.126529i
$5$	4.95981	+	0.632643i	0.991963	+	0.126529i
$6$	−2.44949			−0.408248
$7$	3.11187	+	3.11187i	0.444552	+	0.444552i	0.893539	−	0.448986i	$-0.148215\pi$
$7$	3.11187	+	3.11187i	0.444552	+	0.444552i	−0.448986	+	0.893539i	$0.648215\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	4.32717	+	5.59246i	0.432717	+	0.559246i
$11$	−11.9521			−1.08656			−0.543278	−	0.839553i	$-0.682817\pi$
$11$	−11.9521			−1.08656			−0.543278	+	0.839553i	$0.682817\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	−6.79511	+	6.79511i	−0.522701	+	0.522701i	−0.918386	−	0.395685i	$-0.870507\pi$
$13$	−6.79511	+	6.79511i	−0.522701	+	0.522701i	0.395685	+	0.918386i	$0.370507\pi$
$14$			6.22373i			0.444552i
$15$	−6.84933	+	5.29968i	−0.456622	+	0.353312i
$16$	−4.00000			−0.250000
$17$	−3.44295	−	3.44295i	−0.202527	−	0.202527i	0.598555	−	0.801082i	$-0.295742\pi$
$17$	−3.44295	−	3.44295i	−0.202527	−	0.202527i	−0.801082	+	0.598555i	$0.795742\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			27.8436i			1.46545i	0.680524	+	0.732726i	$0.261752\pi$
$19$			27.8436i			1.46545i	−0.680524	+	0.732726i	$0.738248\pi$
$20$	−1.26529	+	9.91963i	−0.0632643	+	0.495981i
$21$	−7.62248			−0.362975
$22$	−11.9521	−	11.9521i	−0.543278	−	0.543278i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	24.1995	+	6.27559i	0.967981	+	0.251023i
$26$	−13.5902			−0.522701
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	−6.22373	+	6.22373i	−0.222276	+	0.222276i
$29$			26.4720i			0.912829i	0.889767	+	0.456415i	$0.150867\pi$
$29$			26.4720i			0.912829i	−0.889767	+	0.456415i	$0.849133\pi$
$30$	−12.1490	−	1.54965i	−0.404967	−	0.0516551i
$31$	−16.0271			−0.517003			−0.258501	−	0.966011i	$-0.583229\pi$
$31$	−16.0271			−0.517003			−0.258501	+	0.966011i	$0.583229\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	14.6383	−	14.6383i	0.443585	−	0.443585i
$34$		−	6.88590i		−	0.202527i
$35$	13.4656	+	17.4030i	0.384731	+	0.497228i
$36$	6.00000			0.166667
$37$	13.6416	+	13.6416i	0.368693	+	0.368693i	0.867000	−	0.498307i	$-0.166045\pi$
$37$	13.6416	+	13.6416i	0.368693	+	0.368693i	−0.498307	+	0.867000i	$0.666045\pi$
$38$	−27.8436	+	27.8436i	−0.732726	+	0.732726i
$39$		−	16.6446i		−	0.426783i
$40$	−11.1849	+	8.65434i	−0.279623	+	0.216359i
$41$	32.3332			0.788615			0.394307	−	0.918979i	$-0.370985\pi$
$41$	32.3332			0.788615			0.394307	+	0.918979i	$0.370985\pi$
$42$	−7.62248	−	7.62248i	−0.181488	−	0.181488i
$43$	−22.4332	+	22.4332i	−0.521702	+	0.521702i	−0.918085	−	0.396383i	$-0.870265\pi$
$43$	−22.4332	+	22.4332i	−0.521702	+	0.521702i	0.396383	+	0.918085i	$0.370265\pi$
$44$		−	23.9043i		−	0.543278i
$45$	1.89793	−	14.8794i	0.0421762	−	0.330654i
$46$	6.78233			0.147442
$47$	−35.7929	−	35.7929i	−0.761551	−	0.761551i	0.215052	−	0.976603i	$-0.431008\pi$
$47$	−35.7929	−	35.7929i	−0.761551	−	0.761551i	−0.976603	+	0.215052i	$0.931008\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	29.6326i		−	0.604746i
$50$	17.9239	+	30.4751i	0.358479	+	0.609502i
$51$	8.43348			0.165362
$52$	−13.5902	−	13.5902i	−0.261350	−	0.261350i
$53$	−41.6197	+	41.6197i	−0.785277	+	0.785277i	−0.980716	−	0.195439i	$-0.937387\pi$
$53$	−41.6197	+	41.6197i	−0.785277	+	0.785277i	0.195439	+	0.980716i	$0.437387\pi$
$54$			7.34847i			0.136083i
$55$	−59.2803	−	7.56143i	−1.07782	−	0.137481i
$56$	−12.4475			−0.222276
$57$	−34.1013	−	34.1013i	−0.598268	−	0.598268i
$58$	−26.4720	+	26.4720i	−0.456415	+	0.456415i
$59$			59.3699i			1.00627i	0.864208	+	0.503135i	$0.167820\pi$
$59$			59.3699i			1.00627i	−0.864208	+	0.503135i	$0.832180\pi$
$60$	−10.5994	−	13.6987i	−0.176656	−	0.228311i
$61$	9.79153			0.160517			0.0802584	−	0.996774i	$-0.474425\pi$
$61$	9.79153			0.160517			0.0802584	+	0.996774i	$0.474425\pi$
$62$	−16.0271	−	16.0271i	−0.258501	−	0.258501i
$63$	9.33560	−	9.33560i	0.148184	−	0.148184i
$64$		−	8.00000i		−	0.125000i
$65$	−38.0014	+	29.4036i	−0.584636	+	0.452363i
$66$	29.2766			0.443585
$67$	−35.1732	−	35.1732i	−0.524972	−	0.524972i	0.394097	−	0.919069i	$-0.371058\pi$
$67$	−35.1732	−	35.1732i	−0.524972	−	0.524972i	−0.919069	+	0.394097i	$0.871058\pi$
$68$	6.88590	−	6.88590i	0.101263	−	0.101263i
$69$			8.30662i			0.120386i
$70$	−3.93740	+	30.8686i	−0.0562486	+	0.440979i
$71$	28.4741			0.401044			0.200522	−	0.979689i	$-0.435736\pi$
$71$	28.4741			0.401044			0.200522	+	0.979689i	$0.435736\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−2.27141	+	2.27141i	−0.0311152	+	0.0311152i	−0.722493	−	0.691378i	$-0.757004\pi$
$73$	−2.27141	+	2.27141i	−0.0311152	+	0.0311152i	0.691378	+	0.722493i	$0.257004\pi$
$74$			27.2833i			0.368693i
$75$	−37.3242	+	21.9523i	−0.497656	+	0.292697i
$76$	−55.6872			−0.732726
$77$	−37.1934	−	37.1934i	−0.483031	−	0.483031i
$78$	16.6446	−	16.6446i	0.213392	−	0.213392i
$79$			21.6053i			0.273485i	0.990607	+	0.136742i	$0.0436632\pi$
$79$			21.6053i			0.273485i	−0.990607	+	0.136742i	$0.956337\pi$
$80$	−19.8393	−	2.53057i	−0.247991	−	0.0316322i
$81$	−9.00000			−0.111111
$82$	32.3332	+	32.3332i	0.394307	+	0.394307i
$83$	−48.0807	+	48.0807i	−0.579286	+	0.579286i	−0.934706	−	0.355421i	$-0.884338\pi$
$83$	−48.0807	+	48.0807i	−0.579286	+	0.579286i	0.355421	+	0.934706i	$0.384338\pi$
$84$		−	15.2450i		−	0.181488i
$85$	−14.8982	−	19.2546i	−0.175273	−	0.226524i
$86$	−44.8664			−0.521702
$87$	−32.4215	−	32.4215i	−0.372661	−	0.372661i
$88$	23.9043	−	23.9043i	0.271639	−	0.271639i
$89$		−	113.080i		−	1.27057i	−0.772279	−	0.635283i	$-0.780883\pi$
$89$		−	113.080i		−	1.27057i	0.772279	−	0.635283i	$-0.219117\pi$
$90$	16.7774	−	12.9815i	0.186415	−	0.144239i
$91$	−42.2909			−0.464736
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	19.6291	−	19.6291i	0.211065	−	0.211065i
$94$		−	71.5858i		−	0.761551i
$95$	−17.6151	+	138.099i	−0.185422	+	1.45367i
$96$	9.79796			0.102062
$97$	43.1625	+	43.1625i	0.444974	+	0.444974i	0.893680	−	0.448705i	$-0.148115\pi$
$97$	43.1625	+	43.1625i	0.444974	+	0.444974i	−0.448705	+	0.893680i	$0.648115\pi$
$98$	29.6326	−	29.6326i	0.302373	−	0.302373i
$99$			35.8564i			0.362186i
$100$	−12.5512	+	48.3991i	−0.125512	+	0.483991i
$101$	53.6055			0.530747			0.265374	−	0.964146i	$-0.414505\pi$
$101$	53.6055			0.530747			0.265374	+	0.964146i	$0.414505\pi$
$102$	8.43348	+	8.43348i	0.0826811	+	0.0826811i
$103$	−8.64457	+	8.64457i	−0.0839279	+	0.0839279i	−0.747824	−	0.663897i	$-0.768902\pi$
$103$	−8.64457	+	8.64457i	−0.0839279	+	0.0839279i	0.663897	+	0.747824i	$0.268902\pi$
$104$		−	27.1804i		−	0.261350i
$105$	−37.8061	−	4.82231i	−0.360058	−	0.0459268i
$106$	−83.2394			−0.785277
$107$	39.5516	+	39.5516i	0.369641	+	0.369641i	0.867346	−	0.497705i	$-0.165824\pi$
$107$	39.5516	+	39.5516i	0.369641	+	0.369641i	−0.497705	+	0.867346i	$0.665824\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	6.74005i		−	0.0618353i	−0.999522	−	0.0309176i	$-0.990157\pi$
$109$		−	6.74005i		−	0.0618353i	0.999522	−	0.0309176i	$-0.00984296\pi$
$110$	−51.7189	−	66.8418i	−0.470172	−	0.607652i
$111$	−33.4151			−0.301037
$112$	−12.4475	−	12.4475i	−0.111138	−	0.111138i
$113$	116.074	−	116.074i	1.02720	−	1.02720i	0.0275812	−	0.999620i	$-0.491220\pi$
$113$	116.074	−	116.074i	1.02720	−	1.02720i	0.999620	−	0.0275812i	$-0.00878050\pi$
$114$		−	68.2026i		−	0.598268i
$115$	18.9649	−	14.6742i	0.164913	−	0.127601i
$116$	−52.9441			−0.456415
$117$	20.3853	+	20.3853i	0.174234	+	0.174234i
$118$	−59.3699	+	59.3699i	−0.503135	+	0.503135i
$119$		−	21.4280i		−	0.180067i
$120$	3.09931	−	24.2980i	0.0258275	−	0.202484i
$121$	21.8533			0.180606
$122$	9.79153	+	9.79153i	0.0802584	+	0.0802584i
$123$	−39.5999	+	39.5999i	−0.321951	+	0.321951i
$124$		−	32.0542i		−	0.258501i
$125$	116.055	+	46.4354i	0.928440	+	0.371483i
$126$	18.6712			0.148184
$127$	2.15703	+	2.15703i	0.0169845	+	0.0169845i	0.715548	−	0.698564i	$-0.246177\pi$
$127$	2.15703	+	2.15703i	0.0169845	+	0.0169845i	−0.698564	+	0.715548i	$0.746177\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	54.9499i		−	0.425968i
$130$	−67.4050	−	8.59776i	−0.518500	−	0.0661366i
$131$	260.534			1.98881			0.994404	−	0.105640i	$-0.0336892\pi$
$131$	260.534			1.98881			0.994404	+	0.105640i	$0.0336892\pi$
$132$	29.2766	+	29.2766i	0.221792	+	0.221792i
$133$	−86.6455	+	86.6455i	−0.651470	+	0.651470i
$134$		−	70.3463i		−	0.524972i
$135$	15.8990	+	20.5480i	0.117771	+	0.152207i
$136$	13.7718			0.101263
$137$	−0.350640	−	0.350640i	−0.00255941	−	0.00255941i	0.705826	−	0.708385i	$-0.250576\pi$
$137$	−0.350640	−	0.350640i	−0.00255941	−	0.00255941i	−0.708385	+	0.705826i	$0.750576\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$			115.396i			0.830185i	0.909779	+	0.415092i	$0.136251\pi$
$139$			115.396i			0.830185i	−0.909779	+	0.415092i	$0.863749\pi$
$140$	−34.8060	+	26.9312i	−0.248614	+	0.192365i
$141$	87.6743			0.621803
$142$	28.4741	+	28.4741i	0.200522	+	0.200522i
$143$	81.2160	−	81.2160i	0.567944	−	0.567944i
$144$			12.0000i			0.0833333i
$145$	−16.7474	+	131.296i	−0.115499	+	0.905493i
$146$	−4.54282			−0.0311152
$147$	36.2923	+	36.2923i	0.246887	+	0.246887i
$148$	−27.2833	+	27.2833i	−0.184346	+	0.184346i
$149$		−	276.290i		−	1.85429i	−0.374699	−	0.927146i	$-0.622254\pi$
$149$		−	276.290i		−	1.85429i	0.374699	−	0.927146i	$-0.377746\pi$
$150$	−59.2765	−	15.3720i	−0.395177	−	0.102480i
$151$	37.7638			0.250091			0.125046	−	0.992151i	$-0.460092\pi$
$151$	37.7638			0.250091			0.125046	+	0.992151i	$0.460092\pi$
$152$	−55.6872	−	55.6872i	−0.366363	−	0.366363i
$153$	−10.3289	+	10.3289i	−0.0675089	+	0.0675089i
$154$		−	74.3868i		−	0.483031i
$155$	−79.4913	−	10.1394i	−0.512847	−	0.0654156i
$156$	33.2891			0.213392
$157$	122.971	+	122.971i	0.783253	+	0.783253i	0.980378	−	0.197126i	$-0.0631607\pi$
$157$	122.971	+	122.971i	0.783253	+	0.783253i	−0.197126	+	0.980378i	$0.563161\pi$
$158$	−21.6053	+	21.6053i	−0.136742	+	0.136742i
$159$		−	101.947i		−	0.641176i
$160$	−17.3087	−	22.3698i	−0.108179	−	0.139811i
$161$	21.1057			0.131091
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−21.6235	+	21.6235i	−0.132659	+	0.132659i	−0.770319	−	0.637659i	$-0.779903\pi$
$163$	−21.6235	+	21.6235i	−0.132659	+	0.132659i	0.637659	+	0.770319i	$0.279903\pi$
$164$			64.6664i			0.394307i
$165$	81.8641	−	63.3425i	0.496146	−	0.383894i
$166$	−96.1615			−0.579286
$167$	79.3633	+	79.3633i	0.475229	+	0.475229i	0.903602	−	0.428373i	$-0.140913\pi$
$167$	79.3633	+	79.3633i	0.475229	+	0.475229i	−0.428373	+	0.903602i	$0.640913\pi$
$168$	15.2450	−	15.2450i	0.0907439	−	0.0907439i
$169$			76.6530i			0.453568i
$170$	4.35632	−	34.1528i	0.0256254	−	0.200899i
$171$	83.5308			0.488484
$172$	−44.8664	−	44.8664i	−0.260851	−	0.260851i
$173$	167.187	−	167.187i	0.966399	−	0.966399i	−0.0330549	−	0.999454i	$-0.510524\pi$
$173$	167.187	−	167.187i	0.966399	−	0.966399i	0.999454	+	0.0330549i	$0.0105236\pi$
$174$		−	64.8430i		−	0.372661i
$175$	55.7769	+	94.8345i	0.318725	+	0.541911i
$176$	47.8085			0.271639
$177$	−72.7130	−	72.7130i	−0.410808	−	0.410808i
$178$	113.080	−	113.080i	0.635283	−	0.635283i
$179$		−	88.2952i		−	0.493269i	−0.969109	−	0.246635i	$-0.920675\pi$
$179$		−	88.2952i		−	0.493269i	0.969109	−	0.246635i	$-0.0793247\pi$
$180$	29.7589	+	3.79586i	0.165327	+	0.0210881i
$181$	275.272			1.52084			0.760420	−	0.649432i	$-0.224993\pi$
$181$	275.272			1.52084			0.760420	+	0.649432i	$0.224993\pi$
$182$	−42.2909	−	42.2909i	−0.232368	−	0.232368i
$183$	−11.9921	+	11.9921i	−0.0655307	+	0.0655307i
$184$			13.5647i			0.0737210i
$185$	59.0297	+	76.2903i	0.319080	+	0.412380i
$186$	39.2582			0.211065
$187$	41.1506	+	41.1506i	0.220057	+	0.220057i
$188$	71.5858	−	71.5858i	0.380775	−	0.380775i
$189$			22.8675i			0.120992i
$190$	−155.714	+	120.484i	−0.819548	+	0.634126i
$191$	284.801			1.49111			0.745553	−	0.666447i	$-0.232186\pi$
$191$	284.801			1.49111			0.745553	+	0.666447i	$0.232186\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	−71.5610	+	71.5610i	−0.370782	+	0.370782i	−0.867762	−	0.496980i	$-0.834442\pi$
$193$	−71.5610	+	71.5610i	−0.370782	+	0.370782i	0.496980	+	0.867762i	$0.334442\pi$
$194$			86.3250i			0.444974i
$195$	10.5301	−	82.5539i	0.0540003	−	0.423353i
$196$	59.2652			0.302373
$197$	214.648	+	214.648i	1.08958	+	1.08958i	0.995571	+	0.0940112i	$0.0299690\pi$
$197$	214.648	+	214.648i	1.08958	+	1.08958i	0.0940112	+	0.995571i	$0.470031\pi$
$198$	−35.8564	+	35.8564i	−0.181093	+	0.181093i
$199$			89.3086i			0.448787i	0.974499	+	0.224394i	$0.0720401\pi$
$199$			89.3086i			0.448787i	−0.974499	+	0.224394i	$0.927960\pi$
$200$	−60.9502	+	35.8479i	−0.304751	+	0.179239i
$201$	86.1563			0.428638
$202$	53.6055	+	53.6055i	0.265374	+	0.265374i
$203$	−82.3775	+	82.3775i	−0.405800	+	0.405800i
$204$			16.8670i			0.0826811i
$205$	160.367	+	20.4554i	0.782277	+	0.0997823i
$206$	−17.2891			−0.0839279
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	27.1804	−	27.1804i	0.130675	−	0.130675i
$209$		−	332.790i		−	1.59230i
$210$	−32.9838	−	42.6284i	−0.157066	−	0.202992i
$211$	−320.246			−1.51775			−0.758876	−	0.651235i	$-0.774251\pi$
$211$	−320.246			−1.51775			−0.758876	+	0.651235i	$0.774251\pi$
$212$	−83.2394	−	83.2394i	−0.392639	−	0.392639i
$213$	−34.8735	+	34.8735i	−0.163725	+	0.163725i
$214$			79.1032i			0.369641i
$215$	−125.457	+	97.0723i	−0.583520	+	0.451499i
$216$	−14.6969			−0.0680414
$217$	−49.8741	−	49.8741i	−0.229835	−	0.229835i
$218$	6.74005	−	6.74005i	0.0309176	−	0.0309176i
$219$		−	5.56379i		−	0.0254055i
$220$	15.1229	−	118.561i	0.0687403	−	0.538912i
$221$	46.7905			0.211722
$222$	−33.4151	−	33.4151i	−0.150518	−	0.150518i
$223$	−58.8321	+	58.8321i	−0.263821	+	0.263821i	−0.826604	−	0.562783i	$-0.809731\pi$
$223$	−58.8321	+	58.8321i	−0.263821	+	0.263821i	0.562783	+	0.826604i	$0.309731\pi$
$224$		−	24.8949i		−	0.111138i
$225$	18.8268	−	72.5986i	0.0836745	−	0.322660i
$226$	232.147			1.02720
$227$	−80.2967	−	80.2967i	−0.353730	−	0.353730i	0.507766	−	0.861495i	$-0.330472\pi$
$227$	−80.2967	−	80.2967i	−0.353730	−	0.353730i	−0.861495	+	0.507766i	$0.830472\pi$
$228$	68.2026	−	68.2026i	0.299134	−	0.299134i
$229$		−	93.0094i		−	0.406154i	−0.979163	−	0.203077i	$-0.934906\pi$
$229$		−	93.0094i		−	0.406154i	0.979163	−	0.203077i	$-0.0650942\pi$
$230$	33.6391	+	4.29079i	0.146257	+	0.0186556i
$231$	91.1049			0.394393
$232$	−52.9441	−	52.9441i	−0.228207	−	0.228207i
$233$	−182.811	+	182.811i	−0.784598	+	0.784598i	−0.980603	−	0.196005i	$-0.937203\pi$
$233$	−182.811	+	182.811i	−0.784598	+	0.784598i	0.196005	+	0.980603i	$0.437203\pi$
$234$			40.7707i			0.174234i
$235$	−154.882	−	200.170i	−0.659072	−	0.851788i
$236$	−118.740			−0.503135
$237$	−26.4610	−	26.4610i	−0.111650	−	0.111650i
$238$	21.4280	−	21.4280i	0.0900337	−	0.0900337i
$239$			180.221i			0.754061i	0.926201	+	0.377030i	$0.123055\pi$
$239$			180.221i			0.754061i	−0.926201	+	0.377030i	$0.876945\pi$
$240$	27.3973	−	21.1987i	0.114156	−	0.0883280i
$241$	−79.4799			−0.329792			−0.164896	−	0.986311i	$-0.552729\pi$
$241$	−79.4799			−0.329792			−0.164896	+	0.986311i	$0.552729\pi$
$242$	21.8533	+	21.8533i	0.0903029	+	0.0903029i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			19.5831i			0.0802584i
$245$	18.7468	−	146.972i	0.0765177	−	0.599886i
$246$	−79.1998			−0.321951
$247$	−189.200	−	189.200i	−0.765993	−	0.765993i
$248$	32.0542	−	32.0542i	0.129251	−	0.129251i
$249$		−	117.773i		−	0.472985i
$250$	69.6196	+	162.490i	0.278478	+	0.649961i
$251$	348.706			1.38927			0.694633	−	0.719364i	$-0.255567\pi$
$251$	348.706			1.38927			0.694633	+	0.719364i	$0.255567\pi$
$252$	18.6712	+	18.6712i	0.0740921	+	0.0740921i
$253$	−40.5316	+	40.5316i	−0.160204	+	0.160204i
$254$			4.31405i			0.0169845i
$255$	41.8285	+	5.33538i	0.164033	+	0.0209231i
$256$	16.0000			0.0625000
$257$	−170.411	−	170.411i	−0.663077	−	0.663077i	0.293027	−	0.956104i	$-0.405337\pi$
$257$	−170.411	−	170.411i	−0.663077	−	0.663077i	−0.956104	+	0.293027i	$0.905337\pi$
$258$	54.9499	−	54.9499i	0.212984	−	0.212984i
$259$			84.9019i			0.327807i
$260$	−58.8072	−	76.0027i	−0.226182	−	0.292318i
$261$	79.4161			0.304276
$262$	260.534	+	260.534i	0.994404	+	0.994404i
$263$	−92.8602	+	92.8602i	−0.353081	+	0.353081i	−0.861254	−	0.508174i	$-0.830321\pi$
$263$	−92.8602	+	92.8602i	−0.353081	+	0.353081i	0.508174	+	0.861254i	$0.330321\pi$
$264$			58.5532i			0.221792i
$265$	−232.756	+	180.096i	−0.878326	+	0.679606i
$266$	−173.291			−0.651470
$267$	138.495	+	138.495i	0.518707	+	0.518707i
$268$	70.3463	−	70.3463i	0.262486	−	0.262486i
$269$		−	71.4621i		−	0.265658i	−0.991139	−	0.132829i	$-0.957594\pi$
$269$		−	71.4621i		−	0.265658i	0.991139	−	0.132829i	$-0.0424062\pi$
$270$	−4.64896	+	36.4470i	−0.0172184	+	0.134989i
$271$	115.820			0.427380			0.213690	−	0.976902i	$-0.431452\pi$
$271$	115.820			0.427380			0.213690	+	0.976902i	$0.431452\pi$
$272$	13.7718	+	13.7718i	0.0506316	+	0.0506316i
$273$	51.7956	−	51.7956i	0.189728	−	0.189728i
$274$		−	0.701280i		−	0.00255941i
$275$	−289.236	−	75.0066i	−1.05177	−	0.272751i
$276$	−16.6132			−0.0601929
$277$	252.887	+	252.887i	0.912949	+	0.912949i	0.996503	−	0.0835544i	$-0.0266273\pi$
$277$	252.887	+	252.887i	0.912949	+	0.912949i	−0.0835544	+	0.996503i	$0.526627\pi$
$278$	−115.396	+	115.396i	−0.415092	+	0.415092i
$279$			48.0812i			0.172334i
$280$	−61.7371	−	7.87480i	−0.220490	−	0.0281243i
$281$	505.455			1.79877			0.899386	−	0.437156i	$-0.144014\pi$
$281$	505.455			1.79877			0.899386	+	0.437156i	$0.144014\pi$
$282$	87.6743	+	87.6743i	0.310902	+	0.310902i
$283$	−291.311	+	291.311i	−1.02937	+	1.02937i	−0.0298108	+	0.999556i	$0.509490\pi$
$283$	−291.311	+	291.311i	−1.02937	+	1.02937i	−0.999556	+	0.0298108i	$0.990510\pi$
$284$			56.9482i			0.200522i
$285$	−147.562	−	190.710i	−0.517762	−	0.669158i
$286$	162.432			0.567944
$287$	100.617	+	100.617i	0.350580	+	0.350580i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	265.292i		−	0.917966i
$290$	−148.044	+	114.549i	−0.510496	+	0.394997i
$291$	−105.726			−0.363320
$292$	−4.54282	−	4.54282i	−0.0155576	−	0.0155576i
$293$	−155.811	+	155.811i	−0.531778	+	0.531778i	−0.921101	−	0.389323i	$-0.872709\pi$
$293$	−155.811	+	155.811i	−0.531778	+	0.531778i	0.389323	+	0.921101i	$0.372709\pi$
$294$			72.5847i			0.246887i
$295$	−37.5600	+	294.464i	−0.127322	+	0.998182i
$296$	−54.5666			−0.184346
$297$	−43.9149	−	43.9149i	−0.147862	−	0.147862i
$298$	276.290	−	276.290i	0.927146	−	0.927146i
$299$			46.0867i			0.154136i
$300$	−43.9045	−	74.6485i	−0.146348	−	0.248828i
$301$	−139.618			−0.463848
$302$	37.7638	+	37.7638i	0.125046	+	0.125046i
$303$	−65.6530	+	65.6530i	−0.216677	+	0.216677i
$304$		−	111.374i		−	0.366363i
$305$	48.5642	+	6.19454i	0.159227	+	0.0203100i
$306$	−20.6577			−0.0675089
$307$	−1.45006	−	1.45006i	−0.00472331	−	0.00472331i	0.704741	−	0.709464i	$-0.251063\pi$
$307$	−1.45006	−	1.45006i	−0.00472331	−	0.00472331i	−0.709464	+	0.704741i	$0.751063\pi$
$308$	74.3868	−	74.3868i	0.241516	−	0.241516i
$309$		−	21.1748i		−	0.0685268i
$310$	−69.3519	−	89.6308i	−0.223716	−	0.289131i
$311$	421.289			1.35463			0.677314	−	0.735694i	$-0.263144\pi$
$311$	421.289			1.35463			0.677314	+	0.735694i	$0.263144\pi$
$312$	33.2891	+	33.2891i	0.106696	+	0.106696i
$313$	−97.7145	+	97.7145i	−0.312187	+	0.312187i	−0.845756	−	0.533569i	$-0.820850\pi$
$313$	−97.7145	+	97.7145i	−0.312187	+	0.312187i	0.533569	+	0.845756i	$0.320850\pi$
$314$			245.941i			0.783253i
$315$	52.2089	−	40.3967i	0.165743	−	0.128244i
$316$	−43.2106			−0.136742
$317$	−314.471	−	314.471i	−0.992023	−	0.992023i	0.00794582	−	0.999968i	$-0.497471\pi$
$317$	−314.471	−	314.471i	−0.992023	−	0.992023i	−0.999968	+	0.00794582i	$0.997471\pi$
$318$	101.947	−	101.947i	0.320588	−	0.320588i
$319$		−	316.397i		−	0.991841i
$320$	5.06115	−	39.6785i	0.0158161	−	0.123995i
$321$	−96.8812			−0.301811
$322$	21.1057	+	21.1057i	0.0655457	+	0.0655457i
$323$	95.8641	−	95.8641i	0.296793	−	0.296793i
$324$		−	18.0000i		−	0.0555556i
$325$	−207.082	+	121.795i	−0.637175	+	0.374754i
$326$	−43.2470			−0.132659
$327$	8.25484	+	8.25484i	0.0252442	+	0.0252442i
$328$	−64.6664	+	64.6664i	−0.197154	+	0.197154i
$329$		−	222.765i		−	0.677098i
$330$	145.207	+	18.5216i	0.440020	+	0.0561262i
$331$	−49.4958			−0.149534			−0.0747670	−	0.997201i	$-0.523821\pi$
$331$	−49.4958			−0.149534			−0.0747670	+	0.997201i	$0.523821\pi$
$332$	−96.1615	−	96.1615i	−0.289643	−	0.289643i
$333$	40.9249	−	40.9249i	0.122898	−	0.122898i
$334$			158.727i			0.475229i
$335$	−152.200	−	196.704i	−0.454329	−	0.587177i
$336$	30.4899			0.0907439
$337$	278.322	+	278.322i	0.825883	+	0.825883i	0.986944	−	0.161062i	$-0.0514918\pi$
$337$	278.322	+	278.322i	0.825883	+	0.825883i	−0.161062	+	0.986944i	$0.551492\pi$
$338$	−76.6530	+	76.6530i	−0.226784	+	0.226784i
$339$			284.321i			0.838706i
$340$	38.5091	−	29.7965i	0.113262	−	0.0876367i
$341$	191.558			0.561753
$342$	83.5308	+	83.5308i	0.244242	+	0.244242i
$343$	244.694	−	244.694i	0.713394	−	0.713394i
$344$		−	89.7328i		−	0.260851i
$345$	−5.25513	+	41.1993i	−0.0152323	+	0.119418i
$346$	334.374			0.966399
$347$	−169.044	−	169.044i	−0.487158	−	0.487158i	0.420250	−	0.907408i	$-0.361942\pi$
$347$	−169.044	−	169.044i	−0.487158	−	0.487158i	−0.907408	+	0.420250i	$0.861942\pi$
$348$	64.8430	−	64.8430i	0.186330	−	0.186330i
$349$		−	407.984i		−	1.16901i	−0.811390	−	0.584505i	$-0.801289\pi$
$349$		−	407.984i		−	1.16901i	0.811390	−	0.584505i	$-0.198711\pi$
$350$	−39.0576	+	150.611i	−0.111593	+	0.430318i
$351$	−49.9337			−0.142261
$352$	47.8085	+	47.8085i	0.135820	+	0.135820i
$353$	356.837	−	356.837i	1.01087	−	1.01087i	0.0109302	−	0.999940i	$-0.496521\pi$
$353$	356.837	−	356.837i	1.01087	−	1.01087i	0.999940	−	0.0109302i	$-0.00347925\pi$
$354$		−	145.426i		−	0.410808i
$355$	141.226	+	18.0139i	0.397821	+	0.0507435i
$356$	226.161			0.635283
$357$	26.2438	+	26.2438i	0.0735122	+	0.0735122i
$358$	88.2952	−	88.2952i	0.246635	−	0.246635i
$359$		−	321.635i		−	0.895919i	−0.894054	−	0.447960i	$-0.852151\pi$
$359$		−	321.635i		−	0.895919i	0.894054	−	0.447960i	$-0.147849\pi$
$360$	25.9630	+	33.5547i	0.0721195	+	0.0932076i
$361$	−414.265			−1.14755
$362$	275.272	+	275.272i	0.760420	+	0.760420i
$363$	−26.7647	+	26.7647i	−0.0737320	+	0.0737320i
$364$		−	84.5819i		−	0.232368i
$365$	−12.7028	+	9.82878i	−0.0348021	+	0.0269282i
$366$	−23.9842			−0.0655307
$367$	201.984	+	201.984i	0.550364	+	0.550364i	0.926546	−	0.376182i	$-0.122763\pi$
$367$	201.984	+	201.984i	0.550364	+	0.550364i	−0.376182	+	0.926546i	$0.622763\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	96.9996i		−	0.262872i
$370$	−17.2606	+	135.320i	−0.0466502	+	0.365730i
$371$	−259.030			−0.698194
$372$	39.2582	+	39.2582i	0.105533	+	0.105533i
$373$	304.698	−	304.698i	0.816884	−	0.816884i	−0.168771	−	0.985655i	$-0.553980\pi$
$373$	304.698	−	304.698i	0.816884	−	0.816884i	0.985655	+	0.168771i	$0.0539800\pi$
$374$			82.3012i			0.220057i
$375$	−199.009	+	85.2662i	−0.530691	+	0.227377i
$376$	143.172			0.380775
$377$	−179.880	−	179.880i	−0.477136	−	0.477136i
$378$	−22.8675	+	22.8675i	−0.0604959	+	0.0604959i
$379$			665.410i			1.75570i	0.478937	+	0.877849i	$0.341022\pi$
$379$			665.410i			1.75570i	−0.478937	+	0.877849i	$0.658978\pi$
$380$	−276.198	−	35.2301i	−0.726837	−	0.0927108i
$381$	−5.28361			−0.0138678
$382$	284.801	+	284.801i	0.745553	+	0.745553i
$383$	−160.655	+	160.655i	−0.419466	+	0.419466i	−0.885020	−	0.465554i	$-0.845855\pi$
$383$	−160.655	+	160.655i	−0.419466	+	0.419466i	0.465554	+	0.885020i	$0.345855\pi$
$384$			19.5959i			0.0510310i
$385$	−160.942	−	208.003i	−0.418032	−	0.540267i
$386$	−143.122			−0.370782
$387$	67.2996	+	67.2996i	0.173901	+	0.173901i
$388$	−86.3250	+	86.3250i	−0.222487	+	0.222487i
$389$		−	303.465i		−	0.780117i	−0.920790	−	0.390058i	$-0.872455\pi$
$389$		−	303.465i		−	0.780117i	0.920790	−	0.390058i	$-0.127545\pi$
$390$	93.0840	−	72.0238i	0.238677	−	0.184677i
$391$	−23.3512			−0.0597218
$392$	59.2652	+	59.2652i	0.151187	+	0.151187i
$393$	−319.088	+	319.088i	−0.811928	+	0.811928i
$394$			429.295i			1.08958i
$395$	−13.6684	+	107.158i	−0.0346036	+	0.271287i
$396$	−71.7128			−0.181093
$397$	69.7386	+	69.7386i	0.175664	+	0.175664i	0.789463	−	0.613799i	$-0.210359\pi$
$397$	69.7386	+	69.7386i	0.175664	+	0.175664i	−0.613799	+	0.789463i	$0.710359\pi$
$398$	−89.3086	+	89.3086i	−0.224394	+	0.224394i
$399$		−	212.237i		−	0.531923i
$400$	−96.7981	−	25.1023i	−0.241995	−	0.0627559i
$401$	92.9627			0.231827			0.115914	−	0.993259i	$-0.463020\pi$
$401$	92.9627			0.231827			0.115914	+	0.993259i	$0.463020\pi$
$402$	86.1563	+	86.1563i	0.214319	+	0.214319i
$403$	108.906	−	108.906i	0.270238	−	0.270238i
$404$			107.211i			0.265374i
$405$	−44.6383	−	5.69379i	−0.110218	−	0.0140587i
$406$	−164.755			−0.405800
$407$	−163.047	−	163.047i	−0.400606	−	0.400606i
$408$	−16.8670	+	16.8670i	−0.0413406	+	0.0413406i
$409$		−	302.309i		−	0.739141i	−0.929203	−	0.369571i	$-0.879505\pi$
$409$		−	302.309i		−	0.739141i	0.929203	−	0.369571i	$-0.120495\pi$
$410$	139.911	+	180.822i	0.341247	+	0.441029i
$411$	0.858889			0.00208975
$412$	−17.2891	−	17.2891i	−0.0419639	−	0.0419639i
$413$	−184.751	+	184.751i	−0.447340	+	0.447340i
$414$		−	20.3470i		−	0.0491473i
$415$	−268.889	+	208.054i	−0.647926	+	0.501334i
$416$	54.3609			0.130675
$417$	−141.330	−	141.330i	−0.338921	−	0.338921i
$418$	332.790	−	332.790i	0.796148	−	0.796148i
$419$		−	654.635i		−	1.56237i	−0.624297	−	0.781187i	$-0.714615\pi$
$419$		−	654.635i		−	1.56237i	0.624297	−	0.781187i	$-0.285385\pi$
$420$	9.64462	−	75.6122i	0.0229634	−	0.180029i
$421$	77.9606			0.185180			0.0925898	−	0.995704i	$-0.470485\pi$
$421$	77.9606			0.185180			0.0925898	+	0.995704i	$0.470485\pi$
$422$	−320.246	−	320.246i	−0.758876	−	0.758876i
$423$	−107.379	+	107.379i	−0.253850	+	0.253850i
$424$		−	166.479i		−	0.392639i
$425$	−61.7113	−	104.924i	−0.145203	−	0.246881i
$426$	−69.7470			−0.163725
$427$	30.4699	+	30.4699i	0.0713581	+	0.0713581i
$428$	−79.1032	+	79.1032i	−0.184821	+	0.184821i
$429$			198.938i			0.463724i
$430$	−222.529	−	28.3844i	−0.517510	−	0.0660103i
$431$	486.621			1.12905			0.564526	−	0.825415i	$-0.309059\pi$
$431$	486.621			1.12905			0.564526	+	0.825415i	$0.309059\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	−305.280	+	305.280i	−0.705034	+	0.705034i	−0.965487	−	0.260453i	$-0.916128\pi$
$433$	−305.280	+	305.280i	−0.705034	+	0.705034i	0.260453	+	0.965487i	$0.416128\pi$
$434$		−	99.7482i		−	0.229835i
$435$	−140.293	−	181.316i	−0.322514	−	0.416818i
$436$	13.4801			0.0309176
$437$	94.4222	+	94.4222i	0.216069	+	0.216069i
$438$	5.56379	−	5.56379i	0.0127027	−	0.0127027i
$439$			12.3810i			0.0282028i	0.999901	+	0.0141014i	$0.00448877\pi$
$439$			12.3810i			0.0282028i	−0.999901	+	0.0141014i	$0.995511\pi$
$440$	133.684	−	103.438i	0.303826	−	0.235086i
$441$	−88.8977			−0.201582
$442$	46.7905	+	46.7905i	0.105861	+	0.105861i
$443$	−35.7800	+	35.7800i	−0.0807676	+	0.0807676i	−0.746336	−	0.665569i	$-0.768189\pi$
$443$	−35.7800	+	35.7800i	−0.0807676	+	0.0807676i	0.665569	+	0.746336i	$0.268189\pi$
$444$		−	66.8301i		−	0.150518i
$445$	71.5396	−	560.858i	0.160763	−	1.26036i
$446$	−117.664			−0.263821
$447$	338.384	+	338.384i	0.757012	+	0.757012i
$448$	24.8949	−	24.8949i	0.0555690	−	0.0555690i
$449$			586.729i			1.30675i	0.757036	+	0.653373i	$0.226647\pi$
$449$			586.729i			1.30675i	−0.757036	+	0.653373i	$0.773353\pi$
$450$	91.4253	−	53.7718i	0.203167	−	0.119493i
$451$	−386.450			−0.856875
$452$	232.147	+	232.147i	0.513600	+	0.513600i
$453$	−46.2510	+	46.2510i	−0.102099	+	0.102099i
$454$		−	160.593i		−	0.353730i
$455$	−209.755	−	26.7551i	−0.461001	−	0.0588024i
$456$	136.405			0.299134
$457$	−202.555	−	202.555i	−0.443227	−	0.443227i	0.449868	−	0.893095i	$-0.351471\pi$
$457$	−202.555	−	202.555i	−0.443227	−	0.443227i	−0.893095	+	0.449868i	$0.851471\pi$
$458$	93.0094	−	93.0094i	0.203077	−	0.203077i
$459$		−	25.3004i		−	0.0551208i
$460$	29.3483	+	37.9299i	0.0638007	+	0.0824563i
$461$	−527.587			−1.14444			−0.572220	−	0.820100i	$-0.693918\pi$
$461$	−527.587			−1.14444			−0.572220	+	0.820100i	$0.693918\pi$
$462$	91.1049	+	91.1049i	0.197197	+	0.197197i
$463$	−358.778	+	358.778i	−0.774898	+	0.774898i	−0.978958	−	0.204060i	$-0.934586\pi$
$463$	−358.778	+	358.778i	−0.774898	+	0.774898i	0.204060	+	0.978958i	$0.434586\pi$
$464$		−	105.888i		−	0.228207i
$465$	109.775	−	84.9384i	0.236075	−	0.182663i
$466$	−365.623			−0.784598
$467$	−485.338	−	485.338i	−1.03927	−	1.03927i	−0.999197	−	0.0400718i	$-0.987241\pi$
$467$	−485.338	−	485.338i	−1.03927	−	1.03927i	−0.0400718	−	0.999197i	$-0.512759\pi$
$468$	−40.7707	+	40.7707i	−0.0871168	+	0.0871168i
$469$		−	218.908i		−	0.466755i
$470$	45.2882	−	355.052i	0.0963579	−	0.755430i
$471$	−301.215			−0.639523
$472$	−118.740	−	118.740i	−0.251567	−	0.251567i
$473$	268.124	−	268.124i	0.566859	−	0.566859i
$474$		−	52.9219i		−	0.111650i
$475$	−174.735	+	673.802i	−0.367863	+	1.41853i
$476$	42.8560			0.0900337
$477$	124.859	+	124.859i	0.261759	+	0.261759i
$478$	−180.221	+	180.221i	−0.377030	+	0.377030i
$479$		−	319.112i		−	0.666204i	−0.942891	−	0.333102i	$-0.891905\pi$
$479$		−	319.112i		−	0.666204i	0.942891	−	0.333102i	$-0.108095\pi$
$480$	48.5961	+	6.19861i	0.101242	+	0.0129138i
$481$	−185.393			−0.385432
$482$	−79.4799	−	79.4799i	−0.164896	−	0.164896i
$483$	−25.8491	+	25.8491i	−0.0535178	+	0.0535178i
$484$			43.7066i			0.0903029i
$485$	186.772	+	241.385i	0.385096	+	0.497700i
$486$	22.0454			0.0453609
$487$	−394.168	−	394.168i	−0.809380	−	0.809380i	0.175160	−	0.984540i	$-0.443956\pi$
$487$	−394.168	−	394.168i	−0.809380	−	0.809380i	−0.984540	+	0.175160i	$0.943956\pi$
$488$	−19.5831	+	19.5831i	−0.0401292	+	0.0401292i
$489$		−	52.9665i		−	0.108316i
$490$	165.719	−	128.225i	0.338202	−	0.261684i
$491$	403.304			0.821393			0.410696	−	0.911772i	$-0.365286\pi$
$491$	403.304			0.821393			0.410696	+	0.911772i	$0.365286\pi$
$492$	−79.1998	−	79.1998i	−0.160975	−	0.160975i
$493$	91.1420	−	91.1420i	0.184872	−	0.184872i
$494$		−	378.400i		−	0.765993i
$495$	−22.6843	+	177.841i	−0.0458268	+	0.359275i
$496$	64.1083			0.129251
$497$	88.6076	+	88.6076i	0.178285	+	0.178285i
$498$	117.773	−	117.773i	0.236492	−	0.236492i
$499$		−	970.563i		−	1.94502i	−0.232868	−	0.972508i	$-0.574811\pi$
$499$		−	970.563i		−	1.94502i	0.232868	−	0.972508i	$-0.425189\pi$
$500$	−92.8708	+	232.110i	−0.185742	+	0.464220i
$501$	−194.400			−0.388023
$502$	348.706	+	348.706i	0.694633	+	0.694633i
$503$	−526.039	+	526.039i	−1.04580	+	1.04580i	−0.0469034	+	0.998899i	$0.514935\pi$
$503$	−526.039	+	526.039i	−1.04580	+	1.04580i	−0.998899	+	0.0469034i	$0.985065\pi$
$504$			37.3424i			0.0740921i
$505$	265.873	+	33.9131i	0.526481	+	0.0671547i
$506$	−81.0633			−0.160204
$507$	−93.8803	−	93.8803i	−0.185168	−	0.185168i
$508$	−4.31405	+	4.31405i	−0.00849223	+	0.00849223i
$509$			928.920i			1.82499i	0.409088	+	0.912495i	$0.365847\pi$
$509$			928.920i			1.82499i	−0.409088	+	0.912495i	$0.634153\pi$
$510$	36.4931	+	47.1639i	0.0715551	+	0.0924782i
$511$	−14.1366			−0.0276647
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−102.304	+	102.304i	−0.199423	+	0.199423i
$514$		−	340.822i		−	0.663077i
$515$	−48.3444	+	37.4065i	−0.0938726	+	0.0726341i
$516$	109.900			0.212984
$517$	427.801	+	427.801i	0.827468	+	0.827468i
$518$	−84.9019	+	84.9019i	−0.163903	+	0.163903i
$519$			409.523i			0.789061i
$520$	17.1955	−	134.810i	0.0330683	−	0.259250i
$521$	−299.847			−0.575522			−0.287761	−	0.957702i	$-0.592911\pi$
$521$	−299.847			−0.575522			−0.287761	+	0.957702i	$0.592911\pi$
$522$	79.4161	+	79.4161i	0.152138	+	0.152138i
$523$	−421.509	+	421.509i	−0.805944	+	0.805944i	−0.984017	−	0.178073i	$-0.943014\pi$
$523$	−421.509	+	421.509i	−0.805944	+	0.805944i	0.178073	+	0.984017i	$0.443014\pi$
$524$			521.068i			0.994404i
$525$	−184.460	−	47.8356i	−0.351353	−	0.0911153i
$526$	−185.720			−0.353081
$527$	55.1805	+	55.1805i	0.104707	+	0.104707i
$528$	−58.5532	+	58.5532i	−0.110896	+	0.110896i
$529$		−	23.0000i		−	0.0434783i
$530$	−412.852	−	52.6608i	−0.778966	−	0.0993601i
$531$	178.110			0.335423
$532$	−173.291	−	173.291i	−0.325735	−	0.325735i
$533$	−219.708	+	219.708i	−0.412210	+	0.412210i
$534$			276.989i			0.518707i
$535$	171.147	+	221.191i	0.319900	+	0.413440i
$536$	140.693			0.262486
$537$	108.139	+	108.139i	0.201376	+	0.201376i
$538$	71.4621	−	71.4621i	0.132829	−	0.132829i
$539$			354.172i			0.657091i
$540$	−41.0960	+	31.7981i	−0.0761037	+	0.0588853i
$541$	−437.815			−0.809270			−0.404635	−	0.914478i	$-0.632601\pi$
$541$	−437.815			−0.809270			−0.404635	+	0.914478i	$0.632601\pi$
$542$	115.820	+	115.820i	0.213690	+	0.213690i
$543$	−337.138	+	337.138i	−0.620880	+	0.620880i
$544$			27.5436i			0.0506316i
$545$	4.26404	−	33.4294i	0.00782394	−	0.0613383i
$546$	103.591			0.189728
$547$	194.907	+	194.907i	0.356321	+	0.356321i	0.862455	−	0.506134i	$-0.168926\pi$
$547$	194.907	+	194.907i	0.356321	+	0.356321i	−0.506134	+	0.862455i	$0.668926\pi$
$548$	0.701280	−	0.701280i	0.00127971	−	0.00127971i
$549$		−	29.3746i		−	0.0535056i
$550$	−214.229	−	364.242i	−0.389508	−	0.662259i
$551$	−737.077			−1.33771
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	−67.2328	+	67.2328i	−0.121578	+	0.121578i
$554$			505.774i			0.912949i
$555$	−165.733	−	21.1398i	−0.298617	−	0.0380897i
$556$	−230.791			−0.415092
$557$	496.792	+	496.792i	0.891907	+	0.891907i	0.994703	−	0.102795i	$-0.0327786\pi$
$557$	496.792	+	496.792i	0.891907	+	0.891907i	−0.102795	+	0.994703i	$0.532779\pi$
$558$	−48.0812	+	48.0812i	−0.0861671	+	0.0861671i
$559$		−	304.872i		−	0.545389i
$560$	−53.8623	−	69.6119i	−0.0961827	−	0.124307i
$561$	−100.798			−0.179676
$562$	505.455	+	505.455i	0.899386	+	0.899386i
$563$	−165.676	+	165.676i	−0.294273	+	0.294273i	−0.838766	−	0.544493i	$-0.816722\pi$
$563$	−165.676	+	165.676i	−0.294273	+	0.294273i	0.544493	+	0.838766i	$0.316722\pi$
$564$			175.349i			0.310902i
$565$	649.137	−	502.271i	1.14892	−	0.888975i
$566$	−582.621			−1.02937
$567$	−28.0068	−	28.0068i	−0.0493947	−	0.0493947i
$568$	−56.9482	+	56.9482i	−0.100261	+	0.100261i
$569$			1045.26i			1.83702i	0.395397	+	0.918510i	$0.370607\pi$
$569$			1045.26i			1.83702i	−0.395397	+	0.918510i	$0.629393\pi$
$570$	43.1479	−	338.272i	0.0756981	−	0.593460i
$571$	76.1504			0.133363			0.0666816	−	0.997774i	$-0.478759\pi$
$571$	76.1504			0.133363			0.0666816	+	0.997774i	$0.478759\pi$
$572$	162.432	+	162.432i	0.283972	+	0.283972i
$573$	−348.809	+	348.809i	−0.608741	+	0.608741i
$574$			201.233i			0.350580i
$575$	103.346	−	60.7830i	0.179732	−	0.105710i
$576$	−24.0000			−0.0416667
$577$	−356.490	−	356.490i	−0.617833	−	0.617833i	0.327142	−	0.944975i	$-0.393914\pi$
$577$	−356.490	−	356.490i	−0.617833	−	0.617833i	−0.944975	+	0.327142i	$0.893914\pi$
$578$	265.292	−	265.292i	0.458983	−	0.458983i
$579$		−	175.288i		−	0.302743i
$580$	−262.593	−	33.4947i	−0.452746	−	0.0577495i
$581$	−299.242			−0.515046
$582$	−105.726	−	105.726i	−0.181660	−	0.181660i
$583$	497.444	−	497.444i	0.853248	−	0.853248i
$584$		−	9.08564i		−	0.0155576i
$585$	88.2108	+	114.004i	0.150788	+	0.194879i
$586$	−311.622			−0.531778
$587$	−82.5345	−	82.5345i	−0.140604	−	0.140604i	0.633301	−	0.773905i	$-0.281699\pi$
$587$	−82.5345	−	82.5345i	−0.140604	−	0.140604i	−0.773905	+	0.633301i	$0.781699\pi$
$588$	−72.5847	+	72.5847i	−0.123443	+	0.123443i
$589$		−	446.251i		−	0.757642i
$590$	−332.024	+	256.904i	−0.562752	+	0.435430i
$591$	−525.777			−0.889640
$592$	−54.5666	−	54.5666i	−0.0921732	−	0.0921732i
$593$	542.153	−	542.153i	0.914255	−	0.914255i	−0.0823485	−	0.996604i	$-0.526242\pi$
$593$	542.153	−	542.153i	0.914255	−	0.914255i	0.996604	+	0.0823485i	$0.0262420\pi$
$594$		−	87.8298i		−	0.147862i
$595$	13.5563	−	106.279i	0.0227837	−	0.178620i
$596$	552.579			0.927146
$597$	−109.380	−	109.380i	−0.183217	−	0.183217i
$598$	−46.0867	+	46.0867i	−0.0770680	+	0.0770680i
$599$		−	846.862i		−	1.41379i	−0.707317	−	0.706896i	$-0.750095\pi$
$599$		−	846.862i		−	1.41379i	0.707317	−	0.706896i	$-0.249905\pi$
$600$	30.7440	−	118.553i	0.0512399	−	0.197588i
$601$	−768.954			−1.27946			−0.639729	−	0.768600i	$-0.720953\pi$
$601$	−768.954			−1.27946			−0.639729	+	0.768600i	$0.720953\pi$
$602$	−139.618	−	139.618i	−0.231924	−	0.231924i
$603$	−105.519	+	105.519i	−0.174991	+	0.174991i
$604$			75.5275i			0.125046i
$605$	108.388	+	13.8253i	0.179154	+	0.0228518i
$606$	−131.306			−0.216677
$607$	203.884	+	203.884i	0.335889	+	0.335889i	0.854818	−	0.518929i	$-0.173669\pi$
$607$	203.884	+	203.884i	0.335889	+	0.335889i	−0.518929	+	0.854818i	$0.673669\pi$
$608$	111.374	−	111.374i	0.183181	−	0.183181i
$609$		−	201.783i		−	0.331335i
$610$	42.3696	+	54.7587i	0.0694584	+	0.0897684i
$611$	486.433			0.796126
$612$	−20.6577	−	20.6577i	−0.0337544	−	0.0337544i
$613$	−68.5345	+	68.5345i	−0.111802	+	0.111802i	−0.760795	−	0.648993i	$-0.775191\pi$
$613$	−68.5345	+	68.5345i	−0.111802	+	0.111802i	0.648993	+	0.760795i	$0.275191\pi$
$614$		−	2.90011i		−	0.00472331i
$615$	−221.461	+	171.356i	−0.360099	+	0.278627i
$616$	148.774			0.241516
$617$	−150.157	−	150.157i	−0.243366	−	0.243366i	0.574875	−	0.818241i	$-0.305051\pi$
$617$	−150.157	−	150.157i	−0.243366	−	0.243366i	−0.818241	+	0.574875i	$0.805051\pi$
$618$	21.1748	−	21.1748i	0.0342634	−	0.0342634i
$619$		−	457.106i		−	0.738459i	−0.929338	−	0.369230i	$-0.879622\pi$
$619$		−	457.106i		−	0.738459i	0.929338	−	0.369230i	$-0.120378\pi$
$620$	20.2788	−	158.983i	0.0327078	−	0.256424i
$621$	24.9199			0.0401286
$622$	421.289	+	421.289i	0.677314	+	0.677314i
$623$	351.891	−	351.891i	0.564833	−	0.564833i
$624$			66.5782i			0.106696i
$625$	546.234	+	303.732i	0.873974	+	0.485972i
$626$	−195.429			−0.312187
$627$	407.583	+	407.583i	0.650052	+	0.650052i
$628$	−245.941	+	245.941i	−0.391626	+	0.391626i
$629$		−	93.9350i		−	0.149340i
$630$	92.6057	+	11.8122i	0.146993	+	0.0187495i
$631$	−305.258			−0.483768			−0.241884	−	0.970305i	$-0.577765\pi$
$631$	−305.258			−0.483768			−0.241884	+	0.970305i	$0.577765\pi$
$632$	−43.2106	−	43.2106i	−0.0683712	−	0.0683712i
$633$	392.219	−	392.219i	0.619620	−	0.619620i
$634$		−	628.942i		−	0.992023i
$635$	9.33382	+	12.0631i	0.0146989	+	0.0189970i
$636$	203.894			0.320588
$637$	201.357	+	201.357i	0.316101	+	0.316101i
$638$	316.397	−	316.397i	0.495920	−	0.495920i
$639$		−	85.4223i		−	0.133681i
$640$	44.7397	−	34.6174i	0.0699057	−	0.0540896i
$641$	280.793			0.438055			0.219028	−	0.975719i	$-0.429711\pi$
$641$	280.793			0.438055			0.219028	+	0.975719i	$0.429711\pi$
$642$	−96.8812	−	96.8812i	−0.150905	−	0.150905i
$643$	−713.836	+	713.836i	−1.11017	+	1.11017i	−0.117038	+	0.993127i	$0.537340\pi$
$643$	−713.836	+	713.836i	−1.11017	+	1.11017i	−0.993127	+	0.117038i	$0.962660\pi$
$644$			42.2114i			0.0655457i
$645$	34.7637	−	272.541i	0.0538972	−	0.422545i
$646$	191.728			0.296793
$647$	397.749	+	397.749i	0.614759	+	0.614759i	0.944182	−	0.329424i	$-0.106854\pi$
$647$	397.749	+	397.749i	0.614759	+	0.614759i	−0.329424	+	0.944182i	$0.606854\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	709.597i		−	1.09337i
$650$	−328.877	−	85.2866i	−0.505964	−	0.131210i
$651$	122.166			0.187659
$652$	−43.2470	−	43.2470i	−0.0663297	−	0.0663297i
$653$	−217.770	+	217.770i	−0.333491	+	0.333491i	−0.853911	−	0.520419i	$-0.825776\pi$
$653$	−217.770	+	217.770i	−0.333491	+	0.333491i	0.520419	+	0.853911i	$0.325776\pi$
$654$			16.5097i			0.0252442i
$655$	1292.20	+	164.825i	1.97282	+	0.251641i
$656$	−129.333			−0.197154
$657$	6.81423	+	6.81423i	0.0103717	+	0.0103717i
$658$	222.765	−	222.765i	0.338549	−	0.338549i
$659$			1073.09i			1.62836i	0.580610	+	0.814182i	$0.302814\pi$
$659$			1073.09i			1.62836i	−0.580610	+	0.814182i	$0.697186\pi$
$660$	126.685	+	163.728i	0.191947	+	0.248073i
$661$	−326.114			−0.493365			−0.246683	−	0.969096i	$-0.579340\pi$
$661$	−326.114			−0.493365			−0.246683	+	0.969096i	$0.579340\pi$
$662$	−49.4958	−	49.4958i	−0.0747670	−	0.0747670i
$663$	−57.3064	+	57.3064i	−0.0864350	+	0.0864350i
$664$		−	192.323i		−	0.289643i
$665$	−484.561	+	374.930i	−0.728664	+	0.563804i
$666$	81.8498			0.122898
$667$	89.7711	+	89.7711i	0.134589	+	0.134589i
$668$	−158.727	+	158.727i	−0.237615	+	0.237615i
$669$		−	144.109i		−	0.215409i
$670$	44.5041	−	348.905i	0.0664240	−	0.520753i
$671$	−117.030			−0.174411
$672$	30.4899	+	30.4899i	0.0453719	+	0.0453719i
$673$	557.149	−	557.149i	0.827859	−	0.827859i	−0.159361	−	0.987220i	$-0.550943\pi$
$673$	557.149	−	557.149i	0.827859	−	0.827859i	0.987220	+	0.159361i	$0.0509435\pi$
$674$			556.645i			0.825883i
$675$	65.8568	+	111.973i	0.0975656	+	0.165885i
$676$	−153.306			−0.226784
$677$	−819.127	−	819.127i	−1.20994	−	1.20994i	−0.971047	−	0.238890i	$-0.923216\pi$
$677$	−819.127	−	819.127i	−1.20994	−	1.20994i	−0.238890	−	0.971047i	$-0.576784\pi$
$678$	−284.321	+	284.321i	−0.419353	+	0.419353i
$679$			268.632i			0.395629i
$680$	68.3056	+	8.71264i	0.100449	+	0.0128127i
$681$	196.686			0.288819
$682$	191.558	+	191.558i	0.280876	+	0.280876i
$683$	220.351	−	220.351i	0.322622	−	0.322622i	−0.527150	−	0.849772i	$-0.676739\pi$
$683$	220.351	−	220.351i	0.322622	−	0.322622i	0.849772	+	0.527150i	$0.176739\pi$
$684$			167.062i			0.244242i
$685$	−1.51728	−	1.96094i	−0.00221501	−	0.00286268i
$686$	489.388			0.713394
$687$	113.913	+	113.913i	0.165812	+	0.165812i
$688$	89.7328	−	89.7328i	0.130426	−	0.130426i
$689$		−	565.621i		−	0.820930i
$690$	−46.4544	+	35.9442i	−0.0673253	+	0.0520930i
$691$	−256.102			−0.370626			−0.185313	−	0.982680i	$-0.559330\pi$
$691$	−256.102			−0.370626			−0.185313	+	0.982680i	$0.559330\pi$
$692$	334.374	+	334.374i	0.483199	+	0.483199i
$693$	−111.580	+	111.580i	−0.161010	+	0.161010i
$694$		−	338.088i		−	0.487158i
$695$	−73.0043	+	572.341i	−0.105042	+	0.823512i
$696$	129.686			0.186330
$697$	−111.322	−	111.322i	−0.159715	−	0.159715i
$698$	407.984	−	407.984i	0.584505	−	0.584505i
$699$		−	447.794i		−	0.640622i
$700$	−189.669	+	111.554i	−0.270956	+	0.159363i
$701$	−58.5051			−0.0834595			−0.0417297	−	0.999129i	$-0.513287\pi$
$701$	−58.5051			−0.0834595			−0.0417297	+	0.999129i	$0.513287\pi$
$702$	−49.9337	−	49.9337i	−0.0711306	−	0.0711306i
$703$	−379.832	+	379.832i	−0.540302	+	0.540302i
$704$			95.6170i			0.135820i
$705$	434.848	+	55.4665i	0.616806	+	0.0786759i
$706$	713.675			1.01087
$707$	166.813	+	166.813i	0.235945	+	0.235945i
$708$	145.426	−	145.426i	0.205404	−	0.205404i
$709$		−	775.572i		−	1.09390i	−0.837167	−	0.546948i	$-0.815789\pi$
$709$		−	775.572i		−	1.09390i	0.837167	−	0.546948i	$-0.184211\pi$
$710$	123.212	+	159.240i	0.173539	+	0.224282i
$711$	64.8159			0.0911615
$712$	226.161	+	226.161i	0.317642	+	0.317642i
$713$	−54.3505	+	54.3505i	−0.0762279	+	0.0762279i
$714$			52.4877i			0.0735122i
$715$	454.197	−	351.436i	0.635241	−	0.491518i
$716$	176.590			0.246635
$717$	−220.724	−	220.724i	−0.307844	−	0.307844i
$718$	321.635	−	321.635i	0.447960	−	0.447960i
$719$			434.665i			0.604541i	0.953222	+	0.302271i	$0.0977446\pi$
$719$			434.665i			0.604541i	−0.953222	+	0.302271i	$0.902255\pi$
$720$	−7.59172	+	59.5178i	−0.0105441	+	0.0826636i
$721$	−53.8015			−0.0746207
$722$	−414.265	−	414.265i	−0.573775	−	0.573775i
$723$	97.3426	−	97.3426i	0.134637	−	0.134637i
$724$			550.544i			0.760420i
$725$	−166.128	+	640.611i	−0.229141	+	0.883601i
$726$	−53.5294			−0.0737320
$727$	−495.930	−	495.930i	−0.682159	−	0.682159i	0.278327	−	0.960486i	$-0.410220\pi$
$727$	−495.930	−	495.930i	−0.682159	−	0.682159i	−0.960486	+	0.278327i	$0.910220\pi$
$728$	84.5819	−	84.5819i	0.116184	−	0.116184i
$729$			27.0000i			0.0370370i
$730$	−22.5315	−	2.87398i	−0.0308651	−	0.00393696i
$731$	154.473			0.211317
$732$	−23.9842	−	23.9842i	−0.0327654	−	0.0327654i
$733$	2.73615	−	2.73615i	0.00373282	−	0.00373282i	−0.705238	−	0.708971i	$-0.749160\pi$
$733$	2.73615	−	2.73615i	0.00373282	−	0.00373282i	0.708971	+	0.705238i	$0.249160\pi$
$734$			403.967i			0.550364i
$735$	157.043	+	202.963i	0.213664	+	0.276141i
$736$	−27.1293			−0.0368605
$737$	420.394	+	420.394i	0.570412	+	0.570412i
$738$	96.9996	−	96.9996i	0.131436	−	0.131436i
$739$		−	850.579i		−	1.15099i	−0.817807	−	0.575493i	$-0.804810\pi$
$739$		−	850.579i		−	1.15099i	0.817807	−	0.575493i	$-0.195190\pi$
$740$	−152.581	+	118.059i	−0.206190	+	0.159540i
$741$	463.444			0.625431
$742$	−259.030	−	259.030i	−0.349097	−	0.349097i
$743$	−946.760	+	946.760i	−1.27424	+	1.27424i	−0.330397	+	0.943842i	$0.607183\pi$
$743$	−946.760	+	946.760i	−1.27424	+	1.27424i	−0.943842	+	0.330397i	$0.892817\pi$
$744$			78.5163i			0.105533i
$745$	174.793	−	1370.35i	0.234621	−	1.83939i
$746$	609.395			0.816884
$747$	144.242	+	144.242i	0.193095	+	0.193095i
$748$	−82.3012	+	82.3012i	−0.110028	+	0.110028i
$749$			246.159i			0.328650i
$750$	−284.275	−	113.743i	−0.379034	−	0.151657i
$751$	1016.35			1.35333			0.676666	−	0.736290i	$-0.263424\pi$
$751$	1016.35			1.35333			0.676666	+	0.736290i	$0.263424\pi$
$752$	143.172	+	143.172i	0.190388	+	0.190388i
$753$	−427.075	+	427.075i	−0.567165	+	0.567165i
$754$		−	359.761i		−	0.477136i
$755$	187.301	+	23.8910i	0.248081	+	0.0316437i
$756$	−45.7349			−0.0604959
$757$	−286.507	−	286.507i	−0.378477	−	0.378477i	0.492075	−	0.870553i	$-0.336238\pi$
$757$	−286.507	−	286.507i	−0.378477	−	0.378477i	−0.870553	+	0.492075i	$0.836238\pi$
$758$	−665.410	+	665.410i	−0.877849	+	0.877849i
$759$		−	99.2818i		−	0.130806i
$760$	−240.968	−	311.428i	−0.317063	−	0.409774i
$761$	1051.65			1.38193			0.690964	−	0.722889i	$-0.257186\pi$
$761$	1051.65			1.38193			0.690964	+	0.722889i	$0.257186\pi$
$762$	−5.28361	−	5.28361i	−0.00693388	−	0.00693388i
$763$	20.9741	−	20.9741i	0.0274890	−	0.0274890i
$764$			569.602i			0.745553i
$765$	−57.7637	+	44.6947i	−0.0755081	+	0.0584245i
$766$	−321.311			−0.419466
$767$	−403.425	−	403.425i	−0.525978	−	0.525978i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$		−	1147.01i		−	1.49155i	−0.666195	−	0.745777i	$-0.732078\pi$
$769$		−	1147.01i		−	1.49155i	0.666195	−	0.745777i	$-0.267922\pi$
$770$	47.0603	−	368.945i	0.0611173	−	0.479149i
$771$	417.420			0.541400
$772$	−143.122	−	143.122i	−0.185391	−	0.185391i
$773$	535.350	−	535.350i	0.692561	−	0.692561i	−0.270234	−	0.962795i	$-0.587101\pi$
$773$	535.350	−	535.350i	0.692561	−	0.692561i	0.962795	+	0.270234i	$0.0871009\pi$
$774$			134.599i			0.173901i
$775$	−387.848	−	100.579i	−0.500449	−	0.129780i
$776$	−172.650			−0.222487
$777$	−103.983	−	103.983i	−0.133826	−	0.133826i
$778$	303.465	−	303.465i	0.390058	−	0.390058i
$779$			900.272i

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.95981 + 0.632643i) q^{5} -2.44949 q^{6} +(3.11187 + 3.11187i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(4.32717 + 5.59246i) q^{10} -11.9521 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-6.79511 + 6.79511i) q^{13} +6.22373i q^{14} +(-6.84933 + 5.29968i) q^{15} -4.00000 q^{16} +(-3.44295 - 3.44295i) q^{17} +(3.00000 - 3.00000i) q^{18} +27.8436i q^{19} +(-1.26529 + 9.91963i) q^{20} -7.62248 q^{21} +(-11.9521 - 11.9521i) q^{22} +(3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(24.1995 + 6.27559i) q^{25} -13.5902 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.22373 + 6.22373i) q^{28} +26.4720i q^{29} +(-12.1490 - 1.54965i) q^{30} -16.0271 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.6383 - 14.6383i) q^{33} -6.88590i q^{34} +(13.4656 + 17.4030i) q^{35} +6.00000 q^{36} +(13.6416 + 13.6416i) q^{37} +(-27.8436 + 27.8436i) q^{38} -16.6446i q^{39} +(-11.1849 + 8.65434i) q^{40} +32.3332 q^{41} +(-7.62248 - 7.62248i) q^{42} +(-22.4332 + 22.4332i) q^{43} -23.9043i q^{44} +(1.89793 - 14.8794i) q^{45} +6.78233 q^{46} +(-35.7929 - 35.7929i) q^{47} +(4.89898 - 4.89898i) q^{48} -29.6326i q^{49} +(17.9239 + 30.4751i) q^{50} +8.43348 q^{51} +(-13.5902 - 13.5902i) q^{52} +(-41.6197 + 41.6197i) q^{53} +7.34847i q^{54} +(-59.2803 - 7.56143i) q^{55} -12.4475 q^{56} +(-34.1013 - 34.1013i) q^{57} +(-26.4720 + 26.4720i) q^{58} +59.3699i q^{59} +(-10.5994 - 13.6987i) q^{60} +9.79153 q^{61} +(-16.0271 - 16.0271i) q^{62} +(9.33560 - 9.33560i) q^{63} -8.00000i q^{64} +(-38.0014 + 29.4036i) q^{65} +29.2766 q^{66} +(-35.1732 - 35.1732i) q^{67} +(6.88590 - 6.88590i) q^{68} +8.30662i q^{69} +(-3.93740 + 30.8686i) q^{70} +28.4741 q^{71} +(6.00000 + 6.00000i) q^{72} +(-2.27141 + 2.27141i) q^{73} +27.2833i q^{74} +(-37.3242 + 21.9523i) q^{75} -55.6872 q^{76} +(-37.1934 - 37.1934i) q^{77} +(16.6446 - 16.6446i) q^{78} +21.6053i q^{79} +(-19.8393 - 2.53057i) q^{80} -9.00000 q^{81} +(32.3332 + 32.3332i) q^{82} +(-48.0807 + 48.0807i) q^{83} -15.2450i q^{84} +(-14.8982 - 19.2546i) q^{85} -44.8664 q^{86} +(-32.4215 - 32.4215i) q^{87} +(23.9043 - 23.9043i) q^{88} -113.080i q^{89} +(16.7774 - 12.9815i) q^{90} -42.2909 q^{91} +(6.78233 + 6.78233i) q^{92} +(19.6291 - 19.6291i) q^{93} -71.5858i q^{94} +(-17.6151 + 138.099i) q^{95} +9.79796 q^{96} +(43.1625 + 43.1625i) q^{97} +(29.6326 - 29.6326i) q^{98} +35.8564i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \)	\( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

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