LMFDB - Embedded newform 690.3.k.a.277.14

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			277.14
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.14

$q$-expansion

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.17412 + 4.81959i) q^{10} +2.27620 q^{11} +(2.44949 + 2.44949i) q^{12} +(6.59512 - 6.59512i) q^{13} -9.27967i q^{14} +(5.90277 - 6.33698i) q^{15} -4.00000 q^{16} +(16.0847 + 16.0847i) q^{17} +(3.00000 - 3.00000i) q^{18} -33.4152i q^{19} +(0.354533 + 9.99371i) q^{20} -11.3652 q^{21} +(2.27620 + 2.27620i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(24.9372 - 1.77155i) q^{25} +13.1902 q^{26} +(-3.67423 - 3.67423i) q^{27} +(9.27967 - 9.27967i) q^{28} +8.75349i q^{29} +(12.2397 - 0.434212i) q^{30} +26.0099 q^{31} +(-4.00000 - 4.00000i) q^{32} +(2.78777 - 2.78777i) q^{33} +32.1694i q^{34} +(-24.0071 - 22.3621i) q^{35} +6.00000 q^{36} +(18.6213 + 18.6213i) q^{37} +(33.4152 - 33.4152i) q^{38} -16.1547i q^{39} +(-9.63918 + 10.3482i) q^{40} +4.34271 q^{41} +(-11.3652 - 11.3652i) q^{42} +(33.4812 - 33.4812i) q^{43} +4.55240i q^{44} +(-0.531799 - 14.9906i) q^{45} +6.78233 q^{46} +(-28.7769 - 28.7769i) q^{47} +(-4.89898 + 4.89898i) q^{48} -5.94385i q^{49} +(26.7087 + 23.1656i) q^{50} +39.3992 q^{51} +(13.1902 + 13.1902i) q^{52} +(-34.3298 + 34.3298i) q^{53} -7.34847i q^{54} +(11.3739 - 0.403494i) q^{55} +18.5593 q^{56} +(-40.9250 - 40.9250i) q^{57} +(-8.75349 + 8.75349i) q^{58} +71.9203i q^{59} +(12.6740 + 11.8055i) q^{60} -71.6157 q^{61} +(26.0099 + 26.0099i) q^{62} +(-13.9195 + 13.9195i) q^{63} -8.00000i q^{64} +(31.7858 - 34.1240i) q^{65} +5.57553 q^{66} +(-80.0034 - 80.0034i) q^{67} +(-32.1694 + 32.1694i) q^{68} -8.30662i q^{69} +(-1.64497 - 46.3692i) q^{70} +103.758 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.17476 - 1.17476i) q^{73} +37.2426i q^{74} +(28.3720 - 32.7113i) q^{75} +66.8303 q^{76} +(-10.5612 - 10.5612i) q^{77} +(16.1547 - 16.1547i) q^{78} +134.376i q^{79} +(-19.9874 + 0.709066i) q^{80} -9.00000 q^{81} +(4.34271 + 4.34271i) q^{82} +(-11.8656 + 11.8656i) q^{83} -22.7305i q^{84} +(83.2241 + 77.5215i) q^{85} +66.9623 q^{86} +(10.7208 + 10.7208i) q^{87} +(-4.55240 + 4.55240i) q^{88} +40.9315i q^{89} +(14.4588 - 15.5224i) q^{90} -61.2005 q^{91} +(6.78233 + 6.78233i) q^{92} +(31.8555 - 31.8555i) q^{93} -57.5539i q^{94} +(-5.92339 - 166.971i) q^{95} -9.79796 q^{96} +(31.1861 + 31.1861i) q^{97} +(5.94385 - 5.94385i) q^{98} -6.82860i 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
$5$	4.99686	−	0.177266i	0.999371	−	0.0354533i
$5$	4.99686	−	0.177266i	0.999371	−	0.0354533i
$6$	2.44949			0.408248
$7$	−4.63984	−	4.63984i	−0.662834	−	0.662834i	0.293213	−	0.956047i	$-0.405275\pi$
$7$	−4.63984	−	4.63984i	−0.662834	−	0.662834i	−0.956047	+	0.293213i	$0.905275\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	5.17412	+	4.81959i	0.517412	+	0.481959i
$11$	2.27620			0.206927			0.103464	−	0.994633i	$-0.467007\pi$
$11$	2.27620			0.206927			0.103464	+	0.994633i	$0.467007\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	6.59512	−	6.59512i	0.507317	−	0.507317i	−0.406385	−	0.913702i	$-0.633211\pi$
$13$	6.59512	−	6.59512i	0.507317	−	0.507317i	0.913702	+	0.406385i	$0.133211\pi$
$14$		−	9.27967i		−	0.662834i
$15$	5.90277	−	6.33698i	0.393518	−	0.422465i
$16$	−4.00000			−0.250000
$17$	16.0847	+	16.0847i	0.946157	+	0.946157i	0.998623	−	0.0524654i	$-0.0167079\pi$
$17$	16.0847	+	16.0847i	0.946157	+	0.946157i	−0.0524654	+	0.998623i	$0.516708\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	33.4152i		−	1.75869i	−0.476183	−	0.879346i	$-0.657980\pi$
$19$		−	33.4152i		−	1.75869i	0.476183	−	0.879346i	$-0.342020\pi$
$20$	0.354533	+	9.99371i	0.0177266	+	0.499686i
$21$	−11.3652			−0.541201
$22$	2.27620	+	2.27620i	0.103464	+	0.103464i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	24.9372	−	1.77155i	0.997486	−	0.0708620i
$26$	13.1902			0.507317
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	9.27967	−	9.27967i	0.331417	−	0.331417i
$29$			8.75349i			0.301844i	0.988546	+	0.150922i	$0.0482243\pi$
$29$			8.75349i			0.301844i	−0.988546	+	0.150922i	$0.951776\pi$
$30$	12.2397	−	0.434212i	0.407992	−	0.0144737i
$31$	26.0099			0.839028			0.419514	−	0.907749i	$-0.362200\pi$
$31$	26.0099			0.839028			0.419514	+	0.907749i	$0.362200\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	2.78777	−	2.78777i	0.0844778	−	0.0844778i
$34$			32.1694i			0.946157i
$35$	−24.0071	−	22.3621i	−0.685917	−	0.638917i
$36$	6.00000			0.166667
$37$	18.6213	+	18.6213i	0.503278	+	0.503278i	0.912455	−	0.409177i	$-0.134184\pi$
$37$	18.6213	+	18.6213i	0.503278	+	0.503278i	−0.409177	+	0.912455i	$0.634184\pi$
$38$	33.4152	−	33.4152i	0.879346	−	0.879346i
$39$		−	16.1547i		−	0.414222i
$40$	−9.63918	+	10.3482i	−0.240980	+	0.258706i
$41$	4.34271			0.105920			0.0529599	−	0.998597i	$-0.483134\pi$
$41$	4.34271			0.105920			0.0529599	+	0.998597i	$0.483134\pi$
$42$	−11.3652	−	11.3652i	−0.270601	−	0.270601i
$43$	33.4812	−	33.4812i	0.778631	−	0.778631i	−0.200967	−	0.979598i	$-0.564408\pi$
$43$	33.4812	−	33.4812i	0.778631	−	0.778631i	0.979598	+	0.200967i	$0.0644083\pi$
$44$			4.55240i			0.103464i
$45$	−0.531799	−	14.9906i	−0.0118178	−	0.333124i
$46$	6.78233			0.147442
$47$	−28.7769	−	28.7769i	−0.612275	−	0.612275i	0.331263	−	0.943538i	$-0.392525\pi$
$47$	−28.7769	−	28.7769i	−0.612275	−	0.612275i	−0.943538	+	0.331263i	$0.892525\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	5.94385i		−	0.121303i
$50$	26.7087	+	23.1656i	0.534174	+	0.463312i
$51$	39.3992			0.772534
$52$	13.1902	+	13.1902i	0.253658	+	0.253658i
$53$	−34.3298	+	34.3298i	−0.647732	+	0.647732i	−0.952444	−	0.304712i	$-0.901440\pi$
$53$	−34.3298	+	34.3298i	−0.647732	+	0.647732i	0.304712	+	0.952444i	$0.401440\pi$
$54$		−	7.34847i		−	0.136083i
$55$	11.3739	−	0.403494i	0.206797	−	0.00733626i
$56$	18.5593			0.331417
$57$	−40.9250	−	40.9250i	−0.717983	−	0.717983i
$58$	−8.75349	+	8.75349i	−0.150922	+	0.150922i
$59$			71.9203i			1.21899i	0.792791	+	0.609494i	$0.208627\pi$
$59$			71.9203i			1.21899i	−0.792791	+	0.609494i	$0.791373\pi$
$60$	12.6740	+	11.8055i	0.211233	+	0.196759i
$61$	−71.6157			−1.17403			−0.587014	−	0.809577i	$-0.699697\pi$
$61$	−71.6157			−1.17403			−0.587014	+	0.809577i	$0.699697\pi$
$62$	26.0099	+	26.0099i	0.419514	+	0.419514i
$63$	−13.9195	+	13.9195i	−0.220945	+	0.220945i
$64$		−	8.00000i		−	0.125000i
$65$	31.7858	−	34.1240i	0.489012	−	0.524984i
$66$	5.57553			0.0844778
$67$	−80.0034	−	80.0034i	−1.19408	−	1.19408i	−0.975911	−	0.218169i	$-0.929991\pi$
$67$	−80.0034	−	80.0034i	−1.19408	−	1.19408i	−0.218169	−	0.975911i	$-0.570009\pi$
$68$	−32.1694	+	32.1694i	−0.473079	+	0.473079i
$69$		−	8.30662i		−	0.120386i
$70$	−1.64497	−	46.3692i	−0.0234996	−	0.662417i
$71$	103.758			1.46139			0.730694	−	0.682706i	$-0.239197\pi$
$71$	103.758			1.46139			0.730694	+	0.682706i	$0.239197\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	1.17476	−	1.17476i	0.0160926	−	0.0160926i	−0.699015	−	0.715107i	$-0.746378\pi$
$73$	1.17476	−	1.17476i	0.0160926	−	0.0160926i	0.715107	+	0.699015i	$0.246378\pi$
$74$			37.2426i			0.503278i
$75$	28.3720	−	32.7113i	0.378293	−	0.436151i
$76$	66.8303			0.879346
$77$	−10.5612	−	10.5612i	−0.137158	−	0.137158i
$78$	16.1547	−	16.1547i	0.207111	−	0.207111i
$79$			134.376i			1.70096i	0.526008	+	0.850479i	$0.323688\pi$
$79$			134.376i			1.70096i	−0.526008	+	0.850479i	$0.676312\pi$
$80$	−19.9874	+	0.709066i	−0.249843	+	0.00886332i
$81$	−9.00000			−0.111111
$82$	4.34271	+	4.34271i	0.0529599	+	0.0529599i
$83$	−11.8656	+	11.8656i	−0.142959	+	0.142959i	−0.774964	−	0.632005i	$-0.782232\pi$
$83$	−11.8656	+	11.8656i	−0.142959	+	0.142959i	0.632005	+	0.774964i	$0.282232\pi$
$84$		−	22.7305i		−	0.270601i
$85$	83.2241	+	77.5215i	0.979107	+	0.912018i
$86$	66.9623			0.778631
$87$	10.7208	+	10.7208i	0.123227	+	0.123227i
$88$	−4.55240	+	4.55240i	−0.0517319	+	0.0517319i
$89$			40.9315i			0.459905i	0.973202	+	0.229952i	$0.0738570\pi$
$89$			40.9315i			0.459905i	−0.973202	+	0.229952i	$0.926143\pi$
$90$	14.4588	−	15.5224i	0.160653	−	0.172471i
$91$	−61.2005			−0.672533
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	31.8555	−	31.8555i	0.342532	−	0.342532i
$94$		−	57.5539i		−	0.612275i
$95$	−5.92339	−	166.971i	−0.0623514	−	1.75759i
$96$	−9.79796			−0.102062
$97$	31.1861	+	31.1861i	0.321506	+	0.321506i	0.849345	−	0.527839i	$-0.176997\pi$
$97$	31.1861	+	31.1861i	0.321506	+	0.321506i	−0.527839	+	0.849345i	$0.676997\pi$
$98$	5.94385	−	5.94385i	0.0606515	−	0.0606515i
$99$		−	6.82860i		−	0.0689758i
$100$	3.54310	+	49.8743i	0.0354310	+	0.498743i
$101$	44.4799			0.440395			0.220197	−	0.975455i	$-0.429330\pi$
$101$	44.4799			0.440395			0.220197	+	0.975455i	$0.429330\pi$
$102$	39.3992	+	39.3992i	0.386267	+	0.386267i
$103$	87.3328	−	87.3328i	0.847891	−	0.847891i	−0.141979	−	0.989870i	$-0.545346\pi$
$103$	87.3328	−	87.3328i	0.847891	−	0.847891i	0.989870	+	0.141979i	$0.0453465\pi$
$104$			26.3805i			0.253658i
$105$	−56.7904	+	2.01467i	−0.540861	+	0.0191874i
$106$	−68.6596			−0.647732
$107$	15.9149	+	15.9149i	0.148737	+	0.148737i	0.777554	−	0.628817i	$-0.216460\pi$
$107$	15.9149	+	15.9149i	0.148737	+	0.148737i	−0.628817	+	0.777554i	$0.716460\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			40.4073i			0.370709i	0.982672	+	0.185355i	$0.0593434\pi$
$109$			40.4073i			0.370709i	−0.982672	+	0.185355i	$0.940657\pi$
$110$	11.7773	+	10.9704i	0.107067	+	0.0997305i
$111$	45.6127			0.410925
$112$	18.5593	+	18.5593i	0.165708	+	0.165708i
$113$	−44.9394	+	44.9394i	−0.397694	+	0.397694i	−0.877419	−	0.479725i	$-0.840736\pi$
$113$	−44.9394	+	44.9394i	−0.397694	+	0.397694i	0.479725	+	0.877419i	$0.340736\pi$
$114$		−	81.8501i		−	0.717983i
$115$	16.3440	−	17.5463i	0.142122	−	0.152577i
$116$	−17.5070			−0.150922
$117$	−19.7854	−	19.7854i	−0.169106	−	0.169106i
$118$	−71.9203	+	71.9203i	−0.609494	+	0.609494i
$119$		−	149.260i		−	1.25429i
$120$	0.868424	+	24.4795i	0.00723687	+	0.203996i
$121$	−115.819			−0.957181
$122$	−71.6157	−	71.6157i	−0.587014	−	0.587014i
$123$	5.31871	−	5.31871i	0.0432416	−	0.0432416i
$124$			52.0197i			0.419514i
$125$	124.293	−	13.2727i	0.994347	−	0.106182i
$126$	−27.8390			−0.220945
$127$	84.8776	+	84.8776i	0.668328	+	0.668328i	0.957329	−	0.289001i	$-0.0933231\pi$
$127$	84.8776	+	84.8776i	0.668328	+	0.668328i	−0.289001	+	0.957329i	$0.593323\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	82.0117i		−	0.635750i
$130$	65.9097	−	2.33819i	0.506998	−	0.0179860i
$131$	−29.0659			−0.221877			−0.110939	−	0.993827i	$-0.535386\pi$
$131$	−29.0659			−0.221877			−0.110939	+	0.993827i	$0.535386\pi$
$132$	5.57553	+	5.57553i	0.0422389	+	0.0422389i
$133$	−155.041	+	155.041i	−1.16572	+	1.16572i
$134$		−	160.007i		−	1.19408i
$135$	−19.0109	−	17.7083i	−0.140822	−	0.131173i
$136$	−64.3387			−0.473079
$137$	50.3452	+	50.3452i	0.367483	+	0.367483i	0.866558	−	0.499076i	$-0.166327\pi$
$137$	50.3452	+	50.3452i	0.367483	+	0.367483i	−0.499076	+	0.866558i	$0.666327\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			83.2681i			0.599051i	0.954088	+	0.299525i	$0.0968283\pi$
$139$			83.2681i			0.599051i	−0.954088	+	0.299525i	$0.903172\pi$
$140$	44.7242	−	48.0142i	0.319459	−	0.342958i
$141$	−70.4888			−0.499921
$142$	103.758	+	103.758i	0.730694	+	0.730694i
$143$	15.0118	−	15.0118i	0.104978	−	0.104978i
$144$			12.0000i			0.0833333i
$145$	1.55170	+	43.7399i	0.0107014	+	0.301655i
$146$	2.34952			0.0160926
$147$	−7.27970	−	7.27970i	−0.0495218	−	0.0495218i
$148$	−37.2426	+	37.2426i	−0.251639	+	0.251639i
$149$		−	35.8235i		−	0.240426i	−0.992748	−	0.120213i	$-0.961642\pi$
$149$		−	35.8235i		−	0.240426i	0.992748	−	0.120213i	$-0.0383578\pi$
$150$	61.0833	−	4.33939i	0.407222	−	0.0289293i
$151$	−296.868			−1.96602			−0.983008	−	0.183562i	$-0.941237\pi$
$151$	−296.868			−1.96602			−0.983008	+	0.183562i	$0.941237\pi$
$152$	66.8303	+	66.8303i	0.439673	+	0.439673i
$153$	48.2540	−	48.2540i	0.315386	−	0.315386i
$154$		−	21.1224i		−	0.137158i
$155$	129.968	−	4.61068i	0.838501	−	0.0297463i
$156$	32.3094			0.207111
$157$	−171.782	−	171.782i	−1.09415	−	1.09415i	−0.995080	−	0.0990741i	$-0.968412\pi$
$157$	−171.782	−	171.782i	−1.09415	−	1.09415i	−0.0990741	−	0.995080i	$-0.531588\pi$
$158$	−134.376	+	134.376i	−0.850479	+	0.850479i
$159$			84.0905i			0.528871i
$160$	−20.6965	−	19.2784i	−0.129353	−	0.120490i
$161$	−31.4689			−0.195459
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−153.218	+	153.218i	−0.939991	+	0.939991i	−0.998299	−	0.0583080i	$-0.981429\pi$
$163$	−153.218	+	153.218i	−0.939991	+	0.939991i	0.0583080	+	0.998299i	$0.481429\pi$
$164$			8.68542i			0.0529599i
$165$	13.4359	−	14.4242i	0.0814296	−	0.0874197i
$166$	−23.7312			−0.142959
$167$	−125.613	−	125.613i	−0.752174	−	0.752174i	0.222711	−	0.974885i	$-0.428510\pi$
$167$	−125.613	−	125.613i	−0.752174	−	0.752174i	−0.974885	+	0.222711i	$0.928510\pi$
$168$	22.7305	−	22.7305i	0.135300	−	0.135300i
$169$			82.0088i			0.485259i
$170$	5.70254	+	160.746i	0.0335444	+	0.945563i
$171$	−100.245			−0.586231
$172$	66.9623	+	66.9623i	0.389316	+	0.389316i
$173$	−125.643	+	125.643i	−0.726262	+	0.726262i	−0.969873	−	0.243611i	$-0.921668\pi$
$173$	−125.643	+	125.643i	−0.726262	+	0.726262i	0.243611	+	0.969873i	$0.421668\pi$
$174$			21.4416i			0.123227i
$175$	−123.924	−	107.485i	−0.708137	−	0.614198i
$176$	−9.10481			−0.0517319
$177$	88.0840	+	88.0840i	0.497650	+	0.497650i
$178$	−40.9315	+	40.9315i	−0.229952	+	0.229952i
$179$			92.2918i			0.515596i	0.966199	+	0.257798i	$0.0829970\pi$
$179$			92.2918i			0.515596i	−0.966199	+	0.257798i	$0.917003\pi$
$180$	29.9811	−	1.06360i	0.166562	−	0.00590888i
$181$	−111.846			−0.617932			−0.308966	−	0.951073i	$-0.599983\pi$
$181$	−111.846			−0.617932			−0.308966	+	0.951073i	$0.599983\pi$
$182$	−61.2005	−	61.2005i	−0.336267	−	0.336267i
$183$	−87.7110	+	87.7110i	−0.479295	+	0.479295i
$184$			13.5647i			0.0737210i
$185$	96.3489	+	89.7470i	0.520805	+	0.485119i
$186$	63.7109			0.342532
$187$	36.6120	+	36.6120i	0.195786	+	0.195786i
$188$	57.5539	−	57.5539i	0.306138	−	0.306138i
$189$			34.0957i			0.180400i
$190$	161.047	−	172.894i	0.847618	−	0.909969i
$191$	−93.7491			−0.490833			−0.245416	−	0.969418i	$-0.578925\pi$
$191$	−93.7491			−0.490833			−0.245416	+	0.969418i	$0.578925\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	−100.013	+	100.013i	−0.518201	+	0.518201i	−0.917027	−	0.398826i	$-0.869418\pi$
$193$	−100.013	+	100.013i	−0.518201	+	0.518201i	0.398826	+	0.917027i	$0.369418\pi$
$194$			62.3722i			0.321506i
$195$	−2.86368	−	80.7226i	−0.0146855	−	0.413962i
$196$	11.8877			0.0606515
$197$	112.363	+	112.363i	0.570371	+	0.570371i	0.932232	−	0.361861i	$-0.117859\pi$
$197$	112.363	+	112.363i	0.570371	+	0.570371i	−0.361861	+	0.932232i	$0.617859\pi$
$198$	6.82860	−	6.82860i	0.0344879	−	0.0344879i
$199$		−	60.0337i		−	0.301677i	−0.988558	−	0.150838i	$-0.951803\pi$
$199$		−	60.0337i		−	0.301677i	0.988558	−	0.150838i	$-0.0481973\pi$
$200$	−46.3312	+	53.4174i	−0.231656	+	0.267087i
$201$	−195.967			−0.974963
$202$	44.4799	+	44.4799i	0.220197	+	0.220197i
$203$	40.6147	−	40.6147i	0.200073	−	0.200073i
$204$			78.7985i			0.386267i
$205$	21.6999	−	0.769817i	0.105853	−	0.00375520i
$206$	174.666			0.847891
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	−26.3805	+	26.3805i	−0.126829	+	0.126829i
$209$		−	76.0596i		−	0.363922i
$210$	−58.8051	−	54.7758i	−0.280024	−	0.260837i
$211$	−72.4262			−0.343252			−0.171626	−	0.985162i	$-0.554902\pi$
$211$	−72.4262			−0.343252			−0.171626	+	0.985162i	$0.554902\pi$
$212$	−68.6596	−	68.6596i	−0.323866	−	0.323866i
$213$	127.078	−	127.078i	0.596609	−	0.596609i
$214$			31.8298i			0.148737i
$215$	161.365	−	173.236i	0.750537	−	0.805747i
$216$	14.6969			0.0680414
$217$	−120.682	−	120.682i	−0.556136	−	0.556136i
$218$	−40.4073	+	40.4073i	−0.185355	+	0.185355i
$219$		−	2.87757i		−	0.0131396i
$220$	0.806988	+	22.7477i	0.00366813	+	0.103399i
$221$	212.161			0.960003
$222$	45.6127	+	45.6127i	0.205463	+	0.205463i
$223$	161.871	−	161.871i	0.725879	−	0.725879i	−0.243917	−	0.969796i	$-0.578432\pi$
$223$	161.871	−	161.871i	0.725879	−	0.725879i	0.969796	+	0.243917i	$0.0784324\pi$
$224$			37.1187i			0.165708i
$225$	−5.31465	−	74.8115i	−0.0236207	−	0.332495i
$226$	−89.8788			−0.397694
$227$	−258.326	−	258.326i	−1.13800	−	1.13800i	−0.988808	−	0.149193i	$-0.952332\pi$
$227$	−258.326	−	258.326i	−1.13800	−	1.13800i	−0.149193	−	0.988808i	$-0.547668\pi$
$228$	81.8501	−	81.8501i	0.358992	−	0.358992i
$229$			210.083i			0.917395i	0.888593	+	0.458697i	$0.151684\pi$
$229$			210.083i			0.917395i	−0.888593	+	0.458697i	$0.848316\pi$
$230$	33.8903	−	1.20228i	0.147349	−	0.00522730i
$231$	−25.8696			−0.111989
$232$	−17.5070	−	17.5070i	−0.0754611	−	0.0754611i
$233$	244.089	−	244.089i	1.04759	−	1.04759i	0.0487828	−	0.998809i	$-0.484466\pi$
$233$	244.089	−	244.089i	1.04759	−	1.04759i	0.998809	−	0.0487828i	$-0.0155342\pi$
$234$		−	39.5707i		−	0.169106i
$235$	−148.895	−	138.693i	−0.633598	−	0.590183i
$236$	−143.841			−0.609494
$237$	164.576	+	164.576i	0.694414	+	0.694414i
$238$	149.260	−	149.260i	0.627145	−	0.627145i
$239$			314.702i			1.31675i	0.752692	+	0.658373i	$0.228755\pi$
$239$			314.702i			1.31675i	−0.752692	+	0.658373i	$0.771245\pi$
$240$	−23.6111	+	25.3479i	−0.0983795	+	0.105616i
$241$	−178.804			−0.741927			−0.370964	−	0.928647i	$-0.620973\pi$
$241$	−178.804			−0.741927			−0.370964	+	0.928647i	$0.620973\pi$
$242$	−115.819	−	115.819i	−0.478591	−	0.478591i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	143.231i		−	0.587014i
$245$	−1.05364	−	29.7006i	−0.00430059	−	0.121227i
$246$	10.6374			0.0432416
$247$	−220.377	−	220.377i	−0.892215	−	0.892215i
$248$	−52.0197	+	52.0197i	−0.209757	+	0.209757i
$249$			29.0646i			0.116725i
$250$	137.566	+	111.021i	0.550264	+	0.444083i
$251$	183.648			0.731664			0.365832	−	0.930681i	$-0.380784\pi$
$251$	183.648			0.731664			0.365832	+	0.930681i	$0.380784\pi$
$252$	−27.8390	−	27.8390i	−0.110472	−	0.110472i
$253$	7.71898	−	7.71898i	0.0305098	−	0.0305098i
$254$			169.755i			0.668328i
$255$	196.872	−	6.98416i	0.772049	−	0.0273889i
$256$	16.0000			0.0625000
$257$	−258.659	−	258.659i	−1.00646	−	1.00646i	−0.999979	−	0.00647714i	$-0.997938\pi$
$257$	−258.659	−	258.659i	−1.00646	−	1.00646i	−0.00647714	−	0.999979i	$-0.502062\pi$
$258$	82.0117	−	82.0117i	0.317875	−	0.317875i
$259$		−	172.800i		−	0.667180i
$260$	68.2479	+	63.5715i	0.262492	+	0.244506i
$261$	26.2605			0.100615
$262$	−29.0659	−	29.0659i	−0.110939	−	0.110939i
$263$	−6.73066	+	6.73066i	−0.0255919	+	0.0255919i	−0.719787	−	0.694195i	$-0.755761\pi$
$263$	−6.73066	+	6.73066i	−0.0255919	+	0.0255919i	0.694195	+	0.719787i	$0.255761\pi$
$264$			11.1511i			0.0422389i
$265$	−165.456	+	177.627i	−0.624361	+	0.670289i
$266$	−310.082			−1.16572
$267$	50.1307	+	50.1307i	0.187755	+	0.187755i
$268$	160.007	−	160.007i	0.597040	−	0.597040i
$269$		−	195.237i		−	0.725787i	−0.931831	−	0.362893i	$-0.881789\pi$
$269$		−	195.237i		−	0.725787i	0.931831	−	0.362893i	$-0.118211\pi$
$270$	−1.30264	−	36.7192i	−0.00482458	−	0.135997i
$271$	−190.383			−0.702522			−0.351261	−	0.936278i	$-0.614247\pi$
$271$	−190.383			−0.702522			−0.351261	+	0.936278i	$0.614247\pi$
$272$	−64.3387	−	64.3387i	−0.236539	−	0.236539i
$273$	−74.9550	+	74.9550i	−0.274561	+	0.274561i
$274$			100.690i			0.367483i
$275$	56.7620	−	4.03240i	0.206407	−	0.0146633i
$276$	16.6132			0.0601929
$277$	361.616	+	361.616i	1.30547	+	1.30547i	0.924647	+	0.380824i	$0.124360\pi$
$277$	361.616	+	361.616i	1.30547	+	1.30547i	0.380824	+	0.924647i	$0.375640\pi$
$278$	−83.2681	+	83.2681i	−0.299525	+	0.299525i
$279$		−	78.0296i		−	0.279676i
$280$	92.7384	−	3.28995i	0.331208	−	0.0117498i
$281$	−259.206			−0.922440			−0.461220	−	0.887286i	$-0.652588\pi$
$281$	−259.206			−0.922440			−0.461220	+	0.887286i	$0.652588\pi$
$282$	−70.4888	−	70.4888i	−0.249960	−	0.249960i
$283$	−283.592	+	283.592i	−1.00209	+	1.00209i	−0.00209570	+	0.999998i	$0.500667\pi$
$283$	−283.592	+	283.592i	−1.00209	+	1.00209i	−0.999998	+	0.00209570i	$0.999333\pi$
$284$			207.517i			0.730694i
$285$	−211.751	−	197.242i	−0.742987	−	0.692077i
$286$	30.0236			0.104978
$287$	−20.1495	−	20.1495i	−0.0702072	−	0.0702072i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			228.434i			0.790428i
$290$	−42.1882	+	45.2916i	−0.145477	+	0.156178i
$291$	76.3900			0.262509
$292$	2.34952	+	2.34952i	0.00804632	+	0.00804632i
$293$	104.580	−	104.580i	0.356927	−	0.356927i	−0.505752	−	0.862679i	$-0.668785\pi$
$293$	104.580	−	104.580i	0.356927	−	0.356927i	0.862679	+	0.505752i	$0.168785\pi$
$294$		−	14.5594i		−	0.0495218i
$295$	12.7490	+	359.375i	0.0432171	+	1.21822i
$296$	−74.4852			−0.251639
$297$	−8.36330	−	8.36330i	−0.0281593	−	0.0281593i
$298$	35.8235	−	35.8235i	0.120213	−	0.120213i
$299$		−	44.7303i		−	0.149600i
$300$	65.4227	+	56.7439i	0.218076	+	0.189146i
$301$	−310.694			−1.03221
$302$	−296.868	−	296.868i	−0.983008	−	0.983008i
$303$	54.4765	−	54.4765i	0.179790	−	0.179790i
$304$			133.661i			0.439673i
$305$	−357.853	+	12.6951i	−1.17329	+	0.0416231i
$306$	96.5081			0.315386
$307$	212.425	+	212.425i	0.691938	+	0.691938i	0.962658	−	0.270720i	$-0.0872618\pi$
$307$	212.425	+	212.425i	0.691938	+	0.691938i	−0.270720	+	0.962658i	$0.587262\pi$
$308$	21.1224	−	21.1224i	0.0685792	−	0.0685792i
$309$		−	213.921i		−	0.692300i
$310$	134.578	+	125.357i	0.434124	+	0.404377i
$311$	−206.221			−0.663089			−0.331545	−	0.943440i	$-0.607570\pi$
$311$	−206.221			−0.663089			−0.331545	+	0.943440i	$0.607570\pi$
$312$	32.3094	+	32.3094i	0.103556	+	0.103556i
$313$	203.838	−	203.838i	0.651240	−	0.651240i	−0.302052	−	0.953292i	$-0.597672\pi$
$313$	203.838	−	203.838i	0.651240	−	0.651240i	0.953292	+	0.302052i	$0.0976716\pi$
$314$		−	343.564i		−	1.09415i
$315$	−67.0863	+	72.0212i	−0.212972	+	0.228639i
$316$	−268.751			−0.850479
$317$	71.5639	+	71.5639i	0.225754	+	0.225754i	0.810916	−	0.585162i	$-0.198969\pi$
$317$	71.5639	+	71.5639i	0.225754	+	0.225754i	−0.585162	+	0.810916i	$0.698969\pi$
$318$	−84.0905	+	84.0905i	−0.264436	+	0.264436i
$319$			19.9247i			0.0624599i
$320$	−1.41813	−	39.9749i	−0.00443166	−	0.124921i
$321$	38.9833			0.121443
$322$	−31.4689	−	31.4689i	−0.0977295	−	0.0977295i
$323$	537.472	−	537.472i	1.66400	−	1.66400i
$324$		−	18.0000i		−	0.0555556i
$325$	152.780	−	176.147i	0.470092	−	0.541991i
$326$	−306.437			−0.939991
$327$	49.4887	+	49.4887i	0.151341	+	0.151341i
$328$	−8.68542	+	8.68542i	−0.0264799	+	0.0264799i
$329$			267.041i			0.811673i
$330$	27.8601	−	0.988355i	0.0844247	−	0.00299501i
$331$	480.713			1.45230			0.726152	−	0.687534i	$-0.241307\pi$
$331$	480.713			1.45230			0.726152	+	0.687534i	$0.241307\pi$
$332$	−23.7312	−	23.7312i	−0.0714794	−	0.0714794i
$333$	55.8639	−	55.8639i	0.167759	−	0.167759i
$334$		−	251.226i		−	0.752174i
$335$	−413.947	−	385.584i	−1.23566	−	1.15100i
$336$	45.4609			0.135300
$337$	−220.766	−	220.766i	−0.655093	−	0.655093i	0.299122	−	0.954215i	$-0.403306\pi$
$337$	−220.766	−	220.766i	−0.655093	−	0.655093i	−0.954215	+	0.299122i	$0.903306\pi$
$338$	−82.0088	+	82.0088i	−0.242630	+	0.242630i
$339$			110.079i			0.324716i
$340$	−155.043	+	166.448i	−0.456009	+	0.489553i
$341$	59.2037			0.173618
$342$	−100.245	−	100.245i	−0.293115	−	0.293115i
$343$	−254.930	+	254.930i	−0.743237	+	0.743237i
$344$			133.925i			0.389316i
$345$	−1.47249	−	41.5070i	−0.00426807	−	0.120310i
$346$	−251.287			−0.726262
$347$	229.061	+	229.061i	0.660118	+	0.660118i	0.955408	−	0.295290i	$-0.0954163\pi$
$347$	229.061	+	229.061i	0.660118	+	0.660118i	−0.295290	+	0.955408i	$0.595416\pi$
$348$	−21.4416	+	21.4416i	−0.0616137	+	0.0616137i
$349$			498.993i			1.42978i	0.699237	+	0.714890i	$0.253523\pi$
$349$			498.993i			1.42978i	−0.699237	+	0.714890i	$0.746477\pi$
$350$	−16.4394	−	231.409i	−0.0469697	−	0.661167i
$351$	−48.4640			−0.138074
$352$	−9.10481	−	9.10481i	−0.0258659	−	0.0258659i
$353$	99.5617	−	99.5617i	0.282044	−	0.282044i	−0.551879	−	0.833924i	$-0.686089\pi$
$353$	99.5617	−	99.5617i	0.282044	−	0.282044i	0.833924	+	0.551879i	$0.186089\pi$
$354$			176.168i			0.497650i
$355$	518.466	−	18.3929i	1.46047	−	0.0518110i
$356$	−81.8630			−0.229952
$357$	−182.806	−	182.806i	−0.512062	−	0.512062i
$358$	−92.2918	+	92.2918i	−0.257798	+	0.257798i
$359$			320.098i			0.891639i	0.895123	+	0.445819i	$0.147088\pi$
$359$			320.098i			0.891639i	−0.895123	+	0.445819i	$0.852912\pi$
$360$	31.0447	+	28.9175i	0.0862354	+	0.0803265i
$361$	−755.573			−2.09300
$362$	−111.846	−	111.846i	−0.308966	−	0.308966i
$363$	−141.849	+	141.849i	−0.390768	+	0.390768i
$364$		−	122.401i		−	0.336267i
$365$	5.66187	−	6.07836i	0.0155120	−	0.0166531i
$366$	−175.422			−0.479295
$367$	114.617	+	114.617i	0.312308	+	0.312308i	0.845803	−	0.533495i	$-0.179122\pi$
$367$	114.617	+	114.617i	0.312308	+	0.312308i	−0.533495	+	0.845803i	$0.679122\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	13.0281i		−	0.0353066i
$370$	6.60186	+	186.096i	0.0178429	+	0.502962i
$371$	318.569			0.858677
$372$	63.7109	+	63.7109i	0.171266	+	0.171266i
$373$	444.902	−	444.902i	1.19277	−	1.19277i	0.216480	−	0.976287i	$-0.430542\pi$
$373$	444.902	−	444.902i	1.19277	−	1.19277i	0.976287	−	0.216480i	$-0.0694576\pi$
$374$			73.2239i			0.195786i
$375$	135.972	−	168.483i	0.362592	−	0.449289i
$376$	115.108			0.306138
$377$	57.7303	+	57.7303i	0.153131	+	0.153131i
$378$	−34.0957	+	34.0957i	−0.0902002	+	0.0902002i
$379$			255.776i			0.674870i	0.941349	+	0.337435i	$0.109559\pi$
$379$			255.776i			0.674870i	−0.941349	+	0.337435i	$0.890441\pi$
$380$	333.942	−	11.8468i	0.878794	−	0.0311757i
$381$	207.907			0.545687
$382$	−93.7491	−	93.7491i	−0.245416	−	0.245416i
$383$	336.758	−	336.758i	0.879265	−	0.879265i	−0.114194	−	0.993458i	$-0.536428\pi$
$383$	336.758	−	336.758i	0.879265	−	0.879265i	0.993458	+	0.114194i	$0.0364285\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−54.6450	−	50.9007i	−0.141935	−	0.132210i
$386$	−200.026			−0.518201
$387$	−100.443	−	100.443i	−0.259544	−	0.259544i
$388$	−62.3722	+	62.3722i	−0.160753	+	0.160753i
$389$			459.806i			1.18202i	0.806664	+	0.591011i	$0.201271\pi$
$389$			459.806i			1.18202i	−0.806664	+	0.591011i	$0.798729\pi$
$390$	77.8589	−	83.5863i	0.199638	−	0.214324i
$391$	109.092			0.279007
$392$	11.8877	+	11.8877i	0.0303258	+	0.0303258i
$393$	−35.5984	+	35.5984i	−0.0905811	+	0.0905811i
$394$			224.726i			0.570371i
$395$	23.8203	+	671.456i	0.0603046	+	1.69989i
$396$	13.6572			0.0344879
$397$	76.9931	+	76.9931i	0.193937	+	0.193937i	0.797395	−	0.603458i	$-0.206211\pi$
$397$	76.9931	+	76.9931i	0.193937	+	0.193937i	−0.603458	+	0.797395i	$0.706211\pi$
$398$	60.0337	−	60.0337i	0.150838	−	0.150838i
$399$			379.771i			0.951807i
$400$	−99.7486	+	7.08620i	−0.249372	+	0.0177155i
$401$	50.6120			0.126215			0.0631073	−	0.998007i	$-0.479899\pi$
$401$	50.6120			0.126215			0.0631073	+	0.998007i	$0.479899\pi$
$402$	−195.967	−	195.967i	−0.487481	−	0.487481i
$403$	171.538	−	171.538i	0.425653	−	0.425653i
$404$			88.9598i			0.220197i
$405$	−44.9717	+	1.59540i	−0.111041	+	0.00393925i
$406$	81.2295			0.200073
$407$	42.3858	+	42.3858i	0.104142	+	0.104142i
$408$	−78.7985	+	78.7985i	−0.193134	+	0.193134i
$409$			570.317i			1.39442i	0.716867	+	0.697210i	$0.245575\pi$
$409$			570.317i			1.39442i	−0.716867	+	0.697210i	$0.754425\pi$
$410$	22.4697	+	20.9301i	0.0548042	+	0.0510490i
$411$	123.320			0.300049
$412$	174.666	+	174.666i	0.423945	+	0.423945i
$413$	333.698	−	333.698i	0.807986	−	0.807986i
$414$		−	20.3470i		−	0.0491473i
$415$	−57.1873	+	61.3940i	−0.137801	+	0.147937i
$416$	−52.7610			−0.126829
$417$	101.982	+	101.982i	0.244561	+	0.244561i
$418$	76.0596	−	76.0596i	0.181961	−	0.181961i
$419$			230.287i			0.549610i	0.961500	+	0.274805i	$0.0886133\pi$
$419$			230.287i			0.549610i	−0.961500	+	0.274805i	$0.911387\pi$
$420$	−4.02935	−	113.581i	−0.00959368	−	0.270431i
$421$	506.694			1.20355			0.601774	−	0.798666i	$-0.294461\pi$
$421$	506.694			1.20355			0.601774	+	0.798666i	$0.294461\pi$
$422$	−72.4262	−	72.4262i	−0.171626	−	0.171626i
$423$	−86.3308	+	86.3308i	−0.204092	+	0.204092i
$424$		−	137.319i		−	0.323866i
$425$	429.601	+	372.611i	1.01083	+	0.876732i
$426$	254.155			0.596609
$427$	332.285	+	332.285i	0.778185	+	0.778185i
$428$	−31.8298	+	31.8298i	−0.0743686	+	0.0743686i
$429$		−	36.7713i		−	0.0857140i
$430$	334.601	−	11.8702i	0.778142	−	0.0276050i
$431$	693.838			1.60983			0.804916	−	0.593389i	$-0.202210\pi$
$431$	693.838			1.60983			0.804916	+	0.593389i	$0.202210\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	203.719	−	203.719i	0.470482	−	0.470482i	−0.431589	−	0.902070i	$-0.642047\pi$
$433$	203.719	−	203.719i	0.470482	−	0.470482i	0.902070	+	0.431589i	$0.142047\pi$
$434$		−	241.363i		−	0.556136i
$435$	55.4707	+	51.6698i	0.127519	+	0.118781i
$436$	−80.8147			−0.185355
$437$	−113.316	−	113.316i	−0.259305	−	0.259305i
$438$	2.87757	−	2.87757i	0.00656979	−	0.00656979i
$439$		−	719.749i		−	1.63952i	−0.572708	−	0.819759i	$-0.694107\pi$
$439$		−	719.749i		−	1.63952i	0.572708	−	0.819759i	$-0.305893\pi$
$440$	−21.9407	+	23.5547i	−0.0498653	+	0.0535334i
$441$	−17.8316			−0.0404344
$442$	212.161	+	212.161i	0.480002	+	0.480002i
$443$	257.483	−	257.483i	0.581225	−	0.581225i	−0.354015	−	0.935240i	$-0.615184\pi$
$443$	257.483	−	257.483i	0.581225	−	0.581225i	0.935240	+	0.354015i	$0.115184\pi$
$444$			91.2254i			0.205463i
$445$	7.25578	+	204.529i	0.0163051	+	0.459615i
$446$	323.742			0.725879
$447$	−43.8746	−	43.8746i	−0.0981535	−	0.0981535i
$448$	−37.1187	+	37.1187i	−0.0828542	+	0.0828542i
$449$			520.870i			1.16007i	0.814593	+	0.580033i	$0.196960\pi$
$449$			520.870i			1.16007i	−0.814593	+	0.580033i	$0.803040\pi$
$450$	69.4968	−	80.1261i	0.154437	−	0.178058i
$451$	9.88489			0.0219177
$452$	−89.8788	−	89.8788i	−0.198847	−	0.198847i
$453$	−363.588	+	363.588i	−0.802623	+	0.802623i
$454$		−	516.653i		−	1.13800i
$455$	−305.810	+	10.8488i	−0.672111	+	0.0238435i
$456$	163.700			0.358992
$457$	−274.247	−	274.247i	−0.600103	−	0.600103i	0.340237	−	0.940340i	$-0.389493\pi$
$457$	−274.247	−	274.247i	−0.600103	−	0.600103i	−0.940340	+	0.340237i	$0.889493\pi$
$458$	−210.083	+	210.083i	−0.458697	+	0.458697i
$459$		−	118.198i		−	0.257511i
$460$	35.0926	+	32.6881i	0.0762883	+	0.0710610i
$461$	−72.7050			−0.157712			−0.0788558	−	0.996886i	$-0.525127\pi$
$461$	−72.7050			−0.157712			−0.0788558	+	0.996886i	$0.525127\pi$
$462$	−25.8696	−	25.8696i	−0.0559947	−	0.0559947i
$463$	455.202	−	455.202i	0.983158	−	0.983158i	−0.0167027	−	0.999861i	$-0.505317\pi$
$463$	455.202	−	455.202i	0.983158	−	0.983158i	0.999861	+	0.0167027i	$0.00531687\pi$
$464$		−	35.0139i		−	0.0754611i
$465$	153.530	−	164.824i	0.330173	−	0.354460i
$466$	488.178			1.04759
$467$	−569.865	−	569.865i	−1.22027	−	1.22027i	−0.967536	−	0.252733i	$-0.918671\pi$
$467$	−569.865	−	569.865i	−1.22027	−	1.22027i	−0.252733	−	0.967536i	$-0.581329\pi$
$468$	39.5707	−	39.5707i	0.0845528	−	0.0845528i
$469$			742.405i			1.58295i
$470$	−10.2024	−	287.588i	−0.0217072	−	0.611890i
$471$	−420.779			−0.893373
$472$	−143.841	−	143.841i	−0.304747	−	0.304747i
$473$	76.2099	−	76.2099i	0.161120	−	0.161120i
$474$			329.152i			0.694414i
$475$	−59.1966	−	833.279i	−0.124624	−	1.75427i
$476$	298.521			0.627145
$477$	102.989	+	102.989i	0.215911	+	0.215911i
$478$	−314.702	+	314.702i	−0.658373	+	0.658373i
$479$		−	681.451i		−	1.42265i	−0.702861	−	0.711327i	$-0.748095\pi$
$479$		−	681.451i		−	1.42265i	0.702861	−	0.711327i	$-0.251905\pi$
$480$	−48.9590	+	1.73685i	−0.101998	+	0.00361844i
$481$	245.619			0.510643
$482$	−178.804	−	178.804i	−0.370964	−	0.370964i
$483$	−38.5414	+	38.5414i	−0.0797958	+	0.0797958i
$484$		−	231.638i		−	0.478591i
$485$	161.361	+	150.304i	0.332703	+	0.309906i
$486$	−22.0454			−0.0453609
$487$	457.067	+	457.067i	0.938535	+	0.938535i	0.998217	−	0.0596820i	$-0.0190087\pi$
$487$	457.067	+	457.067i	0.938535	+	0.938535i	−0.0596820	+	0.998217i	$0.519009\pi$
$488$	143.231	−	143.231i	0.293507	−	0.293507i
$489$			375.307i			0.767499i
$490$	28.6469	−	30.7542i	0.0584631	−	0.0627637i
$491$	−2.82990			−0.00576355			−0.00288178	−	0.999996i	$-0.500917\pi$
$491$	−2.82990			−0.00576355			−0.00288178	+	0.999996i	$0.500917\pi$
$492$	10.6374	+	10.6374i	0.0216208	+	0.0216208i
$493$	−140.797	+	140.797i	−0.285592	+	0.285592i
$494$		−	440.754i		−	0.892215i
$495$	−1.21048	−	34.1216i	−0.00244542	−	0.0689324i
$496$	−104.039			−0.209757
$497$	−481.422	−	481.422i	−0.968657	−	0.968657i
$498$	−29.0646	+	29.0646i	−0.0583627	+	0.0583627i
$499$			562.240i			1.12673i	0.826207	+	0.563367i	$0.190494\pi$
$499$			562.240i			1.12673i	−0.826207	+	0.563367i	$0.809506\pi$
$500$	26.5454	+	248.587i	0.0530908	+	0.497173i
$501$	−307.688			−0.614147
$502$	183.648	+	183.648i	0.365832	+	0.365832i
$503$	−516.973	+	516.973i	−1.02778	+	1.02778i	−0.0281756	+	0.999603i	$0.508970\pi$
$503$	−516.973	+	516.973i	−1.02778	+	1.02778i	−0.999603	+	0.0281756i	$0.991030\pi$
$504$		−	55.6780i		−	0.110472i
$505$	222.260	−	7.88479i	0.440118	−	0.0156134i
$506$	15.4380			0.0305098
$507$	100.440	+	100.440i	0.198106	+	0.198106i
$508$	−169.755	+	169.755i	−0.334164	+	0.334164i
$509$			347.014i			0.681756i	0.940108	+	0.340878i	$0.110724\pi$
$509$			347.014i			0.681756i	−0.940108	+	0.340878i	$0.889276\pi$
$510$	203.857	+	189.888i	0.399719	+	0.372330i
$511$	−10.9014			−0.0213335
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−122.775	+	122.775i	−0.239328	+	0.239328i
$514$		−	517.318i		−	1.00646i
$515$	420.908	−	451.871i	0.817297	−	0.877418i
$516$	164.023			0.317875
$517$	−65.5021	−	65.5021i	−0.126697	−	0.126697i
$518$	172.800	−	172.800i	0.333590	−	0.333590i
$519$			307.762i			0.592990i
$520$	4.67637	+	131.819i	0.00899302	+	0.253499i
$521$	910.660			1.74791			0.873954	−	0.486010i	$-0.161548\pi$
$521$	910.660			1.74791			0.873954	+	0.486010i	$0.161548\pi$
$522$	26.2605	+	26.2605i	0.0503074	+	0.0503074i
$523$	595.957	−	595.957i	1.13950	−	1.13950i	0.150957	−	0.988540i	$-0.451765\pi$
$523$	595.957	−	595.957i	1.13950	−	1.13950i	0.988540	−	0.150957i	$-0.0482355\pi$
$524$		−	58.1319i		−	0.110939i
$525$	−283.416	+	20.1341i	−0.539841	+	0.0383506i
$526$	−13.4613			−0.0255919
$527$	418.360	+	418.360i	0.793853	+	0.793853i
$528$	−11.1511	+	11.1511i	−0.0211194	+	0.0211194i
$529$		−	23.0000i		−	0.0434783i
$530$	−343.082	+	12.1710i	−0.647325	+	0.0229642i
$531$	215.761			0.406329
$532$	−310.082	−	310.082i	−0.582860	−	0.582860i
$533$	28.6407	−	28.6407i	0.0537349	−	0.0537349i
$534$			100.261i			0.187755i
$535$	82.3456	+	76.7032i	0.153917	+	0.143370i
$536$	320.014			0.597040
$537$	113.034	+	113.034i	0.210491	+	0.210491i
$538$	195.237	−	195.237i	0.362893	−	0.362893i
$539$		−	13.5294i		−	0.0251009i
$540$	35.4166	−	38.0219i	0.0655863	−	0.0704109i
$541$	−876.710			−1.62054			−0.810268	−	0.586059i	$-0.800679\pi$
$541$	−876.710			−1.62054			−0.810268	+	0.586059i	$0.800679\pi$
$542$	−190.383	−	190.383i	−0.351261	−	0.351261i
$543$	−136.983	+	136.983i	−0.252270	+	0.252270i
$544$		−	128.677i		−	0.236539i
$545$	7.16286	+	201.910i	0.0131429	+	0.370476i
$546$	−149.910			−0.274561
$547$	−628.878	−	628.878i	−1.14969	−	1.14969i	−0.986614	−	0.163071i	$-0.947860\pi$
$547$	−628.878	−	628.878i	−1.14969	−	1.14969i	−0.163071	−	0.986614i	$-0.552140\pi$
$548$	−100.690	+	100.690i	−0.183741	+	0.183741i
$549$			214.847i			0.391343i
$550$	60.7944	+	52.7296i	0.110535	+	0.0958720i
$551$	292.499			0.530852
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	623.481	−	623.481i	1.12745	−	1.12745i
$554$			723.231i			1.30547i
$555$	227.920	−	8.08560i	0.410667	−	0.0145686i
$556$	−166.536			−0.299525
$557$	628.139	+	628.139i	1.12772	+	1.12772i	0.990547	+	0.137170i	$0.0438008\pi$
$557$	628.139	+	628.139i	1.12772	+	1.12772i	0.137170	+	0.990547i	$0.456199\pi$
$558$	78.0296	−	78.0296i	0.139838	−	0.139838i
$559$		−	441.624i		−	0.790026i
$560$	96.0283	+	89.4484i	0.171479	+	0.159729i
$561$	89.6806			0.159859
$562$	−259.206	−	259.206i	−0.461220	−	0.461220i
$563$	318.946	−	318.946i	0.566511	−	0.566511i	−0.364638	−	0.931149i	$-0.618807\pi$
$563$	318.946	−	318.946i	0.566511	−	0.566511i	0.931149	+	0.364638i	$0.118807\pi$
$564$		−	140.978i		−	0.249960i
$565$	−216.590	+	232.522i	−0.383344	+	0.411543i
$566$	−567.185			−1.00209
$567$	41.7585	+	41.7585i	0.0736482	+	0.0736482i
$568$	−207.517	+	207.517i	−0.365347	+	0.365347i
$569$			496.154i			0.871976i	0.899952	+	0.435988i	$0.143601\pi$
$569$			496.154i			0.871976i	−0.899952	+	0.435988i	$0.856399\pi$
$570$	−14.5093	−	408.993i	−0.0254549	−	0.717532i
$571$	−623.806			−1.09248			−0.546240	−	0.837629i	$-0.683941\pi$
$571$	−623.806			−1.09248			−0.546240	+	0.837629i	$0.683941\pi$
$572$	30.0236	+	30.0236i	0.0524889	+	0.0524889i
$573$	−114.819	+	114.819i	−0.200382	+	0.200382i
$574$		−	40.2989i		−	0.0702072i
$575$	78.5584	−	90.5736i	0.136623	−	0.157519i
$576$	−24.0000			−0.0416667
$577$	299.545	+	299.545i	0.519143	+	0.519143i	0.917312	−	0.398169i	$-0.130354\pi$
$577$	299.545	+	299.545i	0.519143	+	0.519143i	−0.398169	+	0.917312i	$0.630354\pi$
$578$	−228.434	+	228.434i	−0.395214	+	0.395214i
$579$			244.980i			0.423109i
$580$	−87.4798	+	3.10340i	−0.150827	+	0.00535069i
$581$	110.109			0.189516
$582$	76.3900	+	76.3900i	0.131254	+	0.131254i
$583$	−78.1416	+	78.1416i	−0.134034	+	0.134034i
$584$			4.69905i			0.00804632i
$585$	−102.372	−	95.3573i	−0.174995	−	0.163004i
$586$	209.159			0.356927
$587$	−76.2399	−	76.2399i	−0.129881	−	0.129881i	0.639178	−	0.769059i	$-0.279275\pi$
$587$	−76.2399	−	76.2399i	−0.129881	−	0.129881i	−0.769059	+	0.639178i	$0.779275\pi$
$588$	14.5594	−	14.5594i	0.0247609	−	0.0247609i
$589$		−	869.124i		−	1.47559i
$590$	−346.626	+	372.124i	−0.587502	+	0.630719i
$591$	275.232			0.465706
$592$	−74.4852	−	74.4852i	−0.125820	−	0.125820i
$593$	312.744	−	312.744i	0.527393	−	0.527393i	−0.392401	−	0.919794i	$-0.628356\pi$
$593$	312.744	−	312.744i	0.527393	−	0.527393i	0.919794	+	0.392401i	$0.128356\pi$
$594$		−	16.7266i		−	0.0281593i
$595$	−26.4589	−	745.833i	−0.0444687	−	1.25350i
$596$	71.6470			0.120213
$597$	−73.5259	−	73.5259i	−0.123159	−	0.123159i
$598$	44.7303	−	44.7303i	0.0747998	−	0.0747998i
$599$		−	822.073i		−	1.37241i	−0.727408	−	0.686205i	$-0.759275\pi$
$599$		−	822.073i		−	1.37241i	0.727408	−	0.686205i	$-0.240725\pi$
$600$	8.67879	+	122.167i	0.0144646	+	0.203611i
$601$	−70.4421			−0.117208			−0.0586040	−	0.998281i	$-0.518665\pi$
$601$	−70.4421			−0.117208			−0.0586040	+	0.998281i	$0.518665\pi$
$602$	−310.694	−	310.694i	−0.516103	−	0.516103i
$603$	−240.010	+	240.010i	−0.398027	+	0.398027i
$604$		−	593.737i		−	0.983008i
$605$	−578.730	+	20.5308i	−0.956579	+	0.0339352i
$606$	108.953			0.179790
$607$	66.6471	+	66.6471i	0.109797	+	0.109797i	0.759871	−	0.650074i	$-0.225262\pi$
$607$	66.6471	+	66.6471i	0.109797	+	0.109797i	−0.650074	+	0.759871i	$0.725262\pi$
$608$	−133.661	+	133.661i	−0.219837	+	0.219837i
$609$		−	99.4854i		−	0.163359i
$610$	−370.549	−	345.158i	−0.607457	−	0.565833i
$611$	−379.575			−0.621235
$612$	96.5081	+	96.5081i	0.157693	+	0.157693i
$613$	182.027	−	182.027i	0.296945	−	0.296945i	−0.542871	−	0.839816i	$-0.682663\pi$
$613$	182.027	−	182.027i	0.296945	−	0.296945i	0.839816	+	0.542871i	$0.182663\pi$
$614$			424.850i			0.691938i
$615$	25.6340	−	27.5197i	0.0416813	−	0.0447474i
$616$	42.2448			0.0685792
$617$	−312.757	−	312.757i	−0.506900	−	0.506900i	0.406674	−	0.913573i	$-0.366689\pi$
$617$	−312.757	−	312.757i	−0.506900	−	0.506900i	−0.913573	+	0.406674i	$0.866689\pi$
$618$	213.921	−	213.921i	0.346150	−	0.346150i
$619$		−	779.683i		−	1.25958i	−0.776764	−	0.629792i	$-0.783140\pi$
$619$		−	779.683i		−	1.25958i	0.776764	−	0.629792i	$-0.216860\pi$
$620$	9.22135	+	259.935i	0.0148732	+	0.419250i
$621$	−24.9199			−0.0401286
$622$	−206.221	−	206.221i	−0.331545	−	0.331545i
$623$	189.915	−	189.915i	0.304840	−	0.304840i
$624$			64.6187i			0.103556i
$625$	618.723	−	88.3548i	0.989957	−	0.141368i
$626$	407.676			0.651240
$627$	−93.1537	−	93.1537i	−0.148570	−	0.148570i
$628$	343.564	−	343.564i	0.547077	−	0.547077i
$629$			599.035i			0.952361i
$630$	−139.108	+	4.93492i	−0.220806	+	0.00783321i
$631$	286.619			0.454230			0.227115	−	0.973868i	$-0.427071\pi$
$631$	286.619			0.454230			0.227115	+	0.973868i	$0.427071\pi$
$632$	−268.751	−	268.751i	−0.425240	−	0.425240i
$633$	−88.7037	+	88.7037i	−0.140132	+	0.140132i
$634$			143.128i			0.225754i
$635$	439.167	+	409.075i	0.691602	+	0.644213i
$636$	−168.181			−0.264436
$637$	−39.2004	−	39.2004i	−0.0615391	−	0.0615391i
$638$	−19.9247	+	19.9247i	−0.0312299	+	0.0312299i
$639$		−	311.275i		−	0.487129i
$640$	38.5567	−	41.3930i	0.0602449	−	0.0646765i
$641$	328.082			0.511829			0.255914	−	0.966699i	$-0.417623\pi$
$641$	328.082			0.511829			0.255914	+	0.966699i	$0.417623\pi$
$642$	38.9833	+	38.9833i	0.0607217	+	0.0607217i
$643$	159.578	−	159.578i	0.248177	−	0.248177i	−0.572045	−	0.820222i	$-0.693850\pi$
$643$	159.578	−	159.578i	0.248177	−	0.248177i	0.820222	+	0.572045i	$0.193850\pi$
$644$		−	62.9378i		−	0.0977295i
$645$	−14.5379	−	409.801i	−0.0225394	−	0.635350i
$646$	1074.94			1.66400
$647$	127.452	+	127.452i	0.196989	+	0.196989i	0.798708	−	0.601719i	$-0.205517\pi$
$647$	127.452	+	127.452i	0.196989	+	0.196989i	−0.601719	+	0.798708i	$0.705517\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			163.705i			0.252242i
$650$	328.927	−	23.3672i	0.506042	−	0.0359495i
$651$	−295.608			−0.454083
$652$	−306.437	−	306.437i	−0.469995	−	0.469995i
$653$	−902.017	+	902.017i	−1.38134	+	1.38134i	−0.539105	+	0.842238i	$0.681238\pi$
$653$	−902.017	+	902.017i	−1.38134	+	1.38134i	−0.842238	+	0.539105i	$0.818762\pi$
$654$			98.9773i			0.151341i
$655$	−145.238	+	5.15241i	−0.221738	+	0.00786628i
$656$	−17.3708			−0.0264799
$657$	−3.52429	−	3.52429i	−0.00536421	−	0.00536421i
$658$	−267.041	+	267.041i	−0.405837	+	0.405837i
$659$		−	723.945i		−	1.09855i	−0.835641	−	0.549276i	$-0.814904\pi$
$659$		−	723.945i		−	1.09855i	0.835641	−	0.549276i	$-0.185096\pi$
$660$	28.8485	+	26.8718i	0.0437098	+	0.0407148i
$661$	38.6236			0.0584321			0.0292160	−	0.999573i	$-0.490699\pi$
$661$	38.6236			0.0584321			0.0292160	+	0.999573i	$0.490699\pi$
$662$	480.713	+	480.713i	0.726152	+	0.726152i
$663$	259.843	−	259.843i	0.391920	−	0.391920i
$664$		−	47.4623i		−	0.0714794i
$665$	−747.233	+	802.201i	−1.12366	+	1.20632i
$666$	111.728			0.167759
$667$	29.6845	+	29.6845i	0.0445045	+	0.0445045i
$668$	251.226	−	251.226i	0.376087	−	0.376087i
$669$		−	396.502i		−	0.592678i
$670$	−28.3638	−	799.531i	−0.0423341	−	1.19333i
$671$	−163.012			−0.242939
$672$	45.4609	+	45.4609i	0.0676502	+	0.0676502i
$673$	−691.238	+	691.238i	−1.02710	+	1.02710i	−0.0274776	+	0.999622i	$0.508747\pi$
$673$	−691.238	+	691.238i	−1.02710	+	1.02710i	−0.999622	+	0.0274776i	$0.991253\pi$
$674$		−	441.533i		−	0.655093i
$675$	−98.1340	−	85.1159i	−0.145384	−	0.126098i
$676$	−164.018			−0.242630
$677$	242.001	+	242.001i	0.357460	+	0.357460i	0.862876	−	0.505416i	$-0.168661\pi$
$677$	242.001	+	242.001i	0.357460	+	0.357460i	−0.505416	+	0.862876i	$0.668661\pi$
$678$	−110.079	+	110.079i	−0.162358	+	0.162358i
$679$		−	289.397i		−	0.426210i
$680$	−321.491	+	11.4051i	−0.472781	+	0.0167722i
$681$	−632.768			−0.929174
$682$	59.2037	+	59.2037i	0.0868090	+	0.0868090i
$683$	−166.819	+	166.819i	−0.244245	+	0.244245i	−0.818604	−	0.574359i	$-0.805251\pi$
$683$	−166.819	+	166.819i	−0.244245	+	0.244245i	0.574359	+	0.818604i	$0.305251\pi$
$684$		−	200.491i		−	0.293115i
$685$	260.492	+	242.643i	0.380280	+	0.354223i
$686$	−509.861			−0.743237
$687$	257.299	+	257.299i	0.374525	+	0.374525i
$688$	−133.925	+	133.925i	−0.194658	+	0.194658i
$689$			452.818i			0.657211i
$690$	40.0345	−	42.9795i	0.0580210	−	0.0622891i
$691$	230.554			0.333653			0.166827	−	0.985986i	$-0.446648\pi$
$691$	230.554			0.333653			0.166827	+	0.985986i	$0.446648\pi$
$692$	−251.287	−	251.287i	−0.363131	−	0.363131i
$693$	−31.6836	+	31.6836i	−0.0457195	+	0.0457195i
$694$			458.122i			0.660118i
$695$	14.7606	+	416.079i	0.0212383	+	0.598674i
$696$	−42.8832			−0.0616137
$697$	69.8511	+	69.8511i	0.100217	+	0.100217i
$698$	−498.993	+	498.993i	−0.714890	+	0.714890i
$699$		−	597.893i		−	0.855355i
$700$	214.969	−	247.848i	0.307099	−	0.354069i
$701$	−569.921			−0.813012			−0.406506	−	0.913648i	$-0.633253\pi$
$701$	−569.921			−0.813012			−0.406506	+	0.913648i	$0.633253\pi$
$702$	−48.4640	−	48.4640i	−0.0690371	−	0.0690371i
$703$	622.234	−	622.234i	0.885112	−	0.885112i
$704$		−	18.2096i		−	0.0258659i
$705$	−352.222	+	12.4953i	−0.499606	+	0.0177238i
$706$	199.123			0.282044
$707$	−206.379	−	206.379i	−0.291909	−	0.291909i
$708$	−176.168	+	176.168i	−0.248825	+	0.248825i
$709$			1007.05i			1.42039i	0.704008	+	0.710193i	$0.251392\pi$
$709$			1007.05i			1.42039i	−0.704008	+	0.710193i	$0.748608\pi$
$710$	536.859	+	500.073i	0.756140	+	0.704329i
$711$	403.127			0.566986
$712$	−81.8630	−	81.8630i	−0.114976	−	0.114976i
$713$	88.2038	−	88.2038i	0.123708	−	0.123708i
$714$		−	365.612i		−	0.512062i
$715$	72.3508	−	77.6730i	0.101190	−	0.108634i
$716$	−184.584			−0.257798
$717$	385.430	+	385.430i	0.537559	+	0.537559i
$718$	−320.098	+	320.098i	−0.445819	+	0.445819i
$719$			1131.87i			1.57423i	0.616806	+	0.787115i	$0.288426\pi$
$719$			1131.87i			1.57423i	−0.616806	+	0.787115i	$0.711574\pi$
$720$	2.12720	+	59.9623i	0.00295444	+	0.0832809i
$721$	−810.419			−1.12402
$722$	−755.573	−	755.573i	−1.04650	−	1.04650i
$723$	−218.990	+	218.990i	−0.302891	+	0.302891i
$724$		−	223.692i		−	0.308966i
$725$	15.5072	+	218.287i	0.0213893	+	0.301086i
$726$	−283.697			−0.390768
$727$	745.476	+	745.476i	1.02541	+	1.02541i	0.999669	+	0.0257448i	$0.00819574\pi$
$727$	745.476	+	745.476i	1.02541	+	1.02541i	0.0257448	+	0.999669i	$0.491804\pi$
$728$	122.401	−	122.401i	0.168133	−	0.168133i
$729$			27.0000i			0.0370370i
$730$	11.7402	−	0.416492i	0.0160825	−	0.000570537i
$731$	1077.07			1.47342
$732$	−175.422	−	175.422i	−0.239647	−	0.239647i
$733$	917.155	−	917.155i	1.25123	−	1.25123i	0.296067	−	0.955167i	$-0.404325\pi$
$733$	917.155	−	917.155i	1.25123	−	1.25123i	0.955167	−	0.296067i	$-0.0956753\pi$
$734$			229.234i			0.312308i
$735$	−37.6661	−	35.0852i	−0.0512463	−	0.0477349i
$736$	−27.1293			−0.0368605
$737$	−182.104	−	182.104i	−0.247088	−	0.247088i
$738$	13.0281	−	13.0281i	0.0176533	−	0.0176533i
$739$			413.291i			0.559257i	0.960108	+	0.279629i	$0.0902114\pi$
$739$			413.291i			0.559257i	−0.960108	+	0.279629i	$0.909789\pi$
$740$	−179.494	+	192.698i	−0.242560	+	0.260402i
$741$	−539.811			−0.728490
$742$	318.569	+	318.569i	0.429339	+	0.429339i
$743$	674.486	−	674.486i	0.907788	−	0.907788i	−0.0883055	−	0.996093i	$-0.528145\pi$
$743$	674.486	−	674.486i	0.907788	−	0.907788i	0.996093	+	0.0883055i	$0.0281452\pi$
$744$			127.422i			0.171266i
$745$	−6.35030	−	179.005i	−0.00852389	−	0.240275i
$746$	889.804			1.19277
$747$	35.5968	+	35.5968i	0.0476529	+	0.0476529i
$748$	−73.2239	+	73.2239i	−0.0978930	+	0.0978930i
$749$		−	147.685i		−	0.197176i
$750$	304.455	−	32.5113i	0.405940	−	0.0433485i
$751$	233.606			0.311060			0.155530	−	0.987831i	$-0.450291\pi$
$751$	233.606			0.311060			0.155530	+	0.987831i	$0.450291\pi$
$752$	115.108	+	115.108i	0.153069	+	0.153069i
$753$	224.922	−	224.922i	0.298701	−	0.298701i
$754$			115.461i			0.153131i
$755$	−1483.41	+	52.6248i	−1.96478	+	0.0697017i
$756$	−68.1914			−0.0902002
$757$	0.636656	+	0.636656i	0.000841026	+	0.000841026i	0.707527	−	0.706686i	$-0.249811\pi$
$757$	0.636656	+	0.636656i	0.000841026	+	0.000841026i	−0.706686	+	0.707527i	$0.749811\pi$
$758$	−255.776	+	255.776i	−0.337435	+	0.337435i
$759$		−	18.9076i		−	0.0249111i
$760$	345.788	+	322.095i	0.454985	+	0.423809i
$761$	−400.232			−0.525929			−0.262964	−	0.964806i	$-0.584700\pi$
$761$	−400.232			−0.525929			−0.262964	+	0.964806i	$0.584700\pi$
$762$	207.907	+	207.907i	0.272844	+	0.272844i
$763$	187.483	−	187.483i	0.245719	−	0.245719i
$764$		−	187.498i		−	0.245416i
$765$	232.565	−	249.672i	0.304006	−	0.326369i
$766$	673.517			0.879265
$767$	474.323	+	474.323i	0.618413	+	0.618413i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	818.791i		−	1.06475i	−0.846509	−	0.532374i	$-0.821300\pi$
$769$		−	818.791i		−	1.06475i	0.846509	−	0.532374i	$-0.178700\pi$
$770$	−3.74429	−	105.546i	−0.00486272	−	0.137072i
$771$	−633.583			−0.821768
$772$	−200.026	−	200.026i	−0.259100	−	0.259100i
$773$	−836.271	+	836.271i	−1.08185	+	1.08185i	−0.0855136	+	0.996337i	$0.527253\pi$
$773$	−836.271	+	836.271i	−1.08185	+	1.08185i	−0.996337	+	0.0855136i	$0.972747\pi$
$774$		−	200.887i		−	0.259544i
$775$	648.612	−	46.0778i	0.836919	−	0.0594552i
$776$	−124.744			−0.160753
$777$	−211.635	−	211.635i	−0.272375	−	0.272375i
$778$	−459.806	+	459.806i	−0.591011	+	0.591011i
$779$		−	145.112i		−

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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(4.99686 - 0.177266i) q^{5} +2.44949 q^{6} +(-4.63984 - 4.63984i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(5.17412 + 4.81959i) q^{10} +2.27620 q^{11} +(2.44949 + 2.44949i) q^{12} +(6.59512 - 6.59512i) q^{13} -9.27967i q^{14} +(5.90277 - 6.33698i) q^{15} -4.00000 q^{16} +(16.0847 + 16.0847i) q^{17} +(3.00000 - 3.00000i) q^{18} -33.4152i q^{19} +(0.354533 + 9.99371i) q^{20} -11.3652 q^{21} +(2.27620 + 2.27620i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(24.9372 - 1.77155i) q^{25} +13.1902 q^{26} +(-3.67423 - 3.67423i) q^{27} +(9.27967 - 9.27967i) q^{28} +8.75349i q^{29} +(12.2397 - 0.434212i) q^{30} +26.0099 q^{31} +(-4.00000 - 4.00000i) q^{32} +(2.78777 - 2.78777i) q^{33} +32.1694i q^{34} +(-24.0071 - 22.3621i) q^{35} +6.00000 q^{36} +(18.6213 + 18.6213i) q^{37} +(33.4152 - 33.4152i) q^{38} -16.1547i q^{39} +(-9.63918 + 10.3482i) q^{40} +4.34271 q^{41} +(-11.3652 - 11.3652i) q^{42} +(33.4812 - 33.4812i) q^{43} +4.55240i q^{44} +(-0.531799 - 14.9906i) q^{45} +6.78233 q^{46} +(-28.7769 - 28.7769i) q^{47} +(-4.89898 + 4.89898i) q^{48} -5.94385i q^{49} +(26.7087 + 23.1656i) q^{50} +39.3992 q^{51} +(13.1902 + 13.1902i) q^{52} +(-34.3298 + 34.3298i) q^{53} -7.34847i q^{54} +(11.3739 - 0.403494i) q^{55} +18.5593 q^{56} +(-40.9250 - 40.9250i) q^{57} +(-8.75349 + 8.75349i) q^{58} +71.9203i q^{59} +(12.6740 + 11.8055i) q^{60} -71.6157 q^{61} +(26.0099 + 26.0099i) q^{62} +(-13.9195 + 13.9195i) q^{63} -8.00000i q^{64} +(31.7858 - 34.1240i) q^{65} +5.57553 q^{66} +(-80.0034 - 80.0034i) q^{67} +(-32.1694 + 32.1694i) q^{68} -8.30662i q^{69} +(-1.64497 - 46.3692i) q^{70} +103.758 q^{71} +(6.00000 + 6.00000i) q^{72} +(1.17476 - 1.17476i) q^{73} +37.2426i q^{74} +(28.3720 - 32.7113i) q^{75} +66.8303 q^{76} +(-10.5612 - 10.5612i) q^{77} +(16.1547 - 16.1547i) q^{78} +134.376i q^{79} +(-19.9874 + 0.709066i) q^{80} -9.00000 q^{81} +(4.34271 + 4.34271i) q^{82} +(-11.8656 + 11.8656i) q^{83} -22.7305i q^{84} +(83.2241 + 77.5215i) q^{85} +66.9623 q^{86} +(10.7208 + 10.7208i) q^{87} +(-4.55240 + 4.55240i) q^{88} +40.9315i q^{89} +(14.4588 - 15.5224i) q^{90} -61.2005 q^{91} +(6.78233 + 6.78233i) q^{92} +(31.8555 - 31.8555i) q^{93} -57.5539i q^{94} +(-5.92339 - 166.971i) q^{95} -9.79796 q^{96} +(31.1861 + 31.1861i) q^{97} +(5.94385 - 5.94385i) q^{98} -6.82860i 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

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