LMFDB - Embedded newform 690.2.i.c.47.2

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
Defining polynomial:	$x^{8} - x^{4} + 1$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	690.47
Dual form			690.2.i.c.323.2

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(-2.22474 + 0.224745i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(1.44949 - 1.44949i) q^{13} +3.46410 q^{14} +(-2.92152 + 2.54258i) q^{15} -1.00000 q^{16} +(5.19615 - 5.19615i) q^{17} +(2.70711 - 1.29289i) q^{18} -2.44949i q^{19} +(1.41421 - 1.73205i) q^{20} +(4.89898 - 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(1.00000 + 4.89898i) q^{25} +2.04989i q^{26} +(2.53553 - 4.53553i) q^{27} +(-2.44949 + 2.44949i) q^{28} -9.12096 q^{29} +(0.267949 - 3.86370i) q^{30} -4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} +7.34847i q^{34} +(-0.778539 - 7.70674i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(2.44949 + 2.44949i) q^{37} +(1.73205 + 1.73205i) q^{38} +(2.04989 + 2.89898i) q^{39} +(0.224745 + 2.22474i) q^{40} -8.48528i q^{41} +(-1.01461 + 5.91359i) q^{42} +(-6.89898 + 6.89898i) q^{43} -5.65685 q^{44} +(-3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(2.04989 - 2.04989i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(-4.17121 - 2.75699i) q^{50} +(7.34847 + 10.3923i) q^{51} +(-1.44949 - 1.44949i) q^{52} +(9.43879 + 9.43879i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 - 9.79796i) q^{55} -3.46410i q^{56} +(4.18154 + 0.717439i) q^{57} +(6.44949 - 6.44949i) q^{58} +8.34242 q^{59} +(2.54258 + 2.92152i) q^{60} -8.89898 q^{61} +(3.46410 - 3.46410i) q^{62} +(4.47871 + 9.37769i) q^{63} +1.00000i q^{64} +(4.56048 - 0.460702i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-1.10102 - 1.10102i) q^{67} +(-5.19615 - 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 + 4.89898i) q^{70} -6.14966i q^{71} +(-1.29289 - 2.70711i) q^{72} +(7.89898 - 7.89898i) q^{73} -3.46410 q^{74} +(-8.65597 + 0.272229i) q^{75} -2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-3.49938 - 0.600398i) q^{78} -0.449490i q^{79} +(-1.73205 - 1.41421i) q^{80} +(7.00000 + 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(-3.46410 - 4.89898i) q^{84} +(16.3485 - 1.65153i) q^{85} -9.75663i q^{86} +(2.67147 - 15.5704i) q^{87} +(4.00000 - 4.00000i) q^{88} +2.19275 q^{89} +(6.51727 + 1.58907i) q^{90} -7.10102 q^{91} +(-0.707107 + 0.707107i) q^{92} +(1.43488 - 8.36308i) q^{93} +2.89898i q^{94} +(3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(4.44949 + 4.44949i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q - 8q^{3} - 8q^{6} + O(q^{10}) $	$ 8q - 8q^{3} - 8q^{6} - 8q^{10} + 8q^{12} - 8q^{13} - 8q^{15} - 8q^{16} + 16q^{18} + 32q^{22} + 8q^{25} - 8q^{27} + 16q^{30} + 32q^{33} - 8q^{36} - 8q^{40} - 16q^{43} + 8q^{46} + 8q^{48} + 8q^{52} + 64q^{55} + 32q^{58} + 8q^{60} - 32q^{61} - 64q^{66} - 48q^{67} + 48q^{70} - 16q^{72} + 24q^{73} - 8q^{75} + 8q^{78} + 56q^{81} + 48q^{82} + 72q^{85} - 32q^{87} + 32q^{88} - 8q^{90} - 96q^{91} + 8q^{96} + 16q^{97} + 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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$3$	−0.292893	+	1.70711i	−0.169102	+	0.985599i
$4$		−	1.00000i		−	0.500000i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	−0.997433	+	0.0716124i	$0.977186\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.82843	−	1.00000i	−0.942809	−	0.333333i
$10$	−2.22474	+	0.224745i	−0.703526	+	0.0710706i
$11$		−	5.65685i		−	1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$		−	5.65685i		−	1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$	1.70711	+	0.292893i	0.492799	+	0.0845510i
$13$	1.44949	−	1.44949i	0.402016	−	0.402016i	−0.476927	−	0.878943i	$-0.658249\pi$
$13$	1.44949	−	1.44949i	0.402016	−	0.402016i	0.878943	+	0.476927i	$0.158249\pi$
$14$	3.46410			0.925820
$15$	−2.92152	+	2.54258i	−0.754333	+	0.656492i
$16$	−1.00000			−0.250000
$17$	5.19615	−	5.19615i	1.26025	−	1.26025i	0.309282	−	0.950971i	$-0.399911\pi$
$17$	5.19615	−	5.19615i	1.26025	−	1.26025i	0.950971	−	0.309282i	$-0.100089\pi$
$18$	2.70711	−	1.29289i	0.638071	−	0.304738i
$19$		−	2.44949i		−	0.561951i	−0.959715	−	0.280976i	$-0.909342\pi$
$19$		−	2.44949i		−	0.561951i	0.959715	−	0.280976i	$-0.0906580\pi$
$20$	1.41421	−	1.73205i	0.316228	−	0.387298i
$21$	4.89898	−	3.46410i	1.06904	−	0.755929i
$22$	4.00000	+	4.00000i	0.852803	+	0.852803i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−1.41421	+	1.00000i	−0.288675	+	0.204124i
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$			2.04989i			0.402016i
$27$	2.53553	−	4.53553i	0.487964	−	0.872864i
$28$	−2.44949	+	2.44949i	−0.462910	+	0.462910i
$29$	−9.12096			−1.69372			−0.846859	−	0.531817i	$-0.821510\pi$
$29$	−9.12096			−1.69372			−0.846859	+	0.531817i	$0.821510\pi$
$30$	0.267949	−	3.86370i	0.0489206	−	0.705412i
$31$	−4.89898			−0.879883			−0.439941	−	0.898027i	$-0.645001\pi$
$31$	−4.89898			−0.879883			−0.439941	+	0.898027i	$0.645001\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	9.65685	+	1.65685i	1.68104	+	0.288421i
$34$			7.34847i			1.26025i
$35$	−0.778539	−	7.70674i	−0.131597	−	1.30268i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	2.44949	+	2.44949i	0.402694	+	0.402694i	0.879181	−	0.476488i	$-0.158090\pi$
$37$	2.44949	+	2.44949i	0.402694	+	0.402694i	−0.476488	+	0.879181i	$0.658090\pi$
$38$	1.73205	+	1.73205i	0.280976	+	0.280976i
$39$	2.04989	+	2.89898i	0.328245	+	0.464208i
$40$	0.224745	+	2.22474i	0.0355353	+	0.351763i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$	−1.01461	+	5.91359i	−0.156558	+	0.912487i
$43$	−6.89898	+	6.89898i	−1.05208	+	1.05208i	−0.0535176	+	0.998567i	$0.517043\pi$
$43$	−6.89898	+	6.89898i	−1.05208	+	1.05208i	−0.998567	+	0.0535176i	$0.982957\pi$
$44$	−5.65685			−0.852803
$45$	−3.48477	−	5.73205i	−0.519478	−	0.854484i
$46$	1.00000			0.147442
$47$	2.04989	−	2.04989i	0.299007	−	0.299007i	−0.541618	−	0.840625i	$-0.682188\pi$
$47$	2.04989	−	2.04989i	0.299007	−	0.299007i	0.840625	+	0.541618i	$0.182188\pi$
$48$	0.292893	−	1.70711i	0.0422755	−	0.246400i
$49$			5.00000i			0.714286i
$50$	−4.17121	−	2.75699i	−0.589898	−	0.389898i
$51$	7.34847	+	10.3923i	1.02899	+	1.45521i
$52$	−1.44949	−	1.44949i	−0.201008	−	0.201008i
$53$	9.43879	+	9.43879i	1.29652	+	1.29652i	0.930678	+	0.365840i	$0.119218\pi$
$53$	9.43879	+	9.43879i	1.29652	+	1.29652i	0.365840	+	0.930678i	$0.380782\pi$
$54$	1.41421	+	5.00000i	0.192450	+	0.680414i
$55$	8.00000	−	9.79796i	1.07872	−	1.32116i
$56$		−	3.46410i		−	0.462910i
$57$	4.18154	+	0.717439i	0.553859	+	0.0950271i
$58$	6.44949	−	6.44949i	0.846859	−	0.846859i
$59$	8.34242			1.08609			0.543045	−	0.839704i	$-0.317271\pi$
$59$	8.34242			1.08609			0.543045	+	0.839704i	$0.317271\pi$
$60$	2.54258	+	2.92152i	0.328246	+	0.377167i
$61$	−8.89898			−1.13940			−0.569699	−	0.821854i	$-0.692940\pi$
$61$	−8.89898			−1.13940			−0.569699	+	0.821854i	$0.692940\pi$
$62$	3.46410	−	3.46410i	0.439941	−	0.439941i
$63$	4.47871	+	9.37769i	0.564265	+	1.18148i
$64$			1.00000i			0.125000i
$65$	4.56048	−	0.460702i	0.565658	−	0.0571430i
$66$	−8.00000	+	5.65685i	−0.984732	+	0.696311i
$67$	−1.10102	−	1.10102i	−0.134511	−	0.134511i	0.636646	−	0.771157i	$-0.280321\pi$
$67$	−1.10102	−	1.10102i	−0.134511	−	0.134511i	−0.771157	+	0.636646i	$0.780321\pi$
$68$	−5.19615	−	5.19615i	−0.630126	−	0.630126i
$69$	1.41421	−	1.00000i	0.170251	−	0.120386i
$70$	6.00000	+	4.89898i	0.717137	+	0.585540i
$71$		−	6.14966i		−	0.729831i	−0.931041	−	0.364915i	$-0.881098\pi$
$71$		−	6.14966i		−	0.729831i	0.931041	−	0.364915i	$-0.118902\pi$
$72$	−1.29289	−	2.70711i	−0.152369	−	0.319036i
$73$	7.89898	−	7.89898i	0.924506	−	0.924506i	−0.0728382	−	0.997344i	$-0.523206\pi$
$73$	7.89898	−	7.89898i	0.924506	−	0.924506i	0.997344	+	0.0728382i	$0.0232057\pi$
$74$	−3.46410			−0.402694
$75$	−8.65597	+	0.272229i	−0.999506	+	0.0314343i
$76$	−2.44949			−0.280976
$77$	−13.8564	+	13.8564i	−1.57908	+	1.57908i
$78$	−3.49938	−	0.600398i	−0.396227	−	0.0679817i
$79$		−	0.449490i		−	0.0505715i	−0.999680	−	0.0252858i	$-0.991950\pi$
$79$		−	0.449490i		−	0.0505715i	0.999680	−	0.0252858i	$-0.00804957\pi$
$80$	−1.73205	−	1.41421i	−0.193649	−	0.158114i
$81$	7.00000	+	5.65685i	0.777778	+	0.628539i
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	0.780449	−	0.625219i	$-0.214990\pi$
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	−0.625219	+	0.780449i	$0.714990\pi$
$84$	−3.46410	−	4.89898i	−0.377964	−	0.534522i
$85$	16.3485	−	1.65153i	1.77324	−	0.179134i
$86$		−	9.75663i		−	1.05208i
$87$	2.67147	−	15.5704i	0.286411	−	1.66933i
$88$	4.00000	−	4.00000i	0.426401	−	0.426401i
$89$	2.19275			0.232431			0.116216	−	0.993224i	$-0.462924\pi$
$89$	2.19275			0.232431			0.116216	+	0.993224i	$0.462924\pi$
$90$	6.51727	+	1.58907i	0.686981	+	0.167503i
$91$	−7.10102			−0.744389
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	1.43488	−	8.36308i	0.148790	−	0.867211i
$94$			2.89898i			0.299007i
$95$	3.46410	−	4.24264i	0.355409	−	0.435286i
$96$	1.00000	+	1.41421i	0.102062	+	0.144338i
$97$	4.44949	+	4.44949i	0.451777	+	0.451777i	0.895944	−	0.444167i	$-0.146500\pi$
$97$	4.44949	+	4.44949i	0.451777	+	0.451777i	−0.444167	+	0.895944i	$0.646500\pi$
$98$	−3.53553	−	3.53553i	−0.357143	−	0.357143i
$99$	−5.65685	+	16.0000i	−0.568535	+	1.60806i
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$			6.29253i			0.626130i	0.949732	+	0.313065i	$0.101356\pi$
$101$			6.29253i			0.626130i	−0.949732	+	0.313065i	$0.898644\pi$
$102$	−12.5446	−	2.15232i	−1.24210	−	0.213111i
$103$	−1.10102	+	1.10102i	−0.108487	+	0.108487i	−0.759267	−	0.650780i	$-0.774442\pi$
$103$	−1.10102	+	1.10102i	−0.108487	+	0.108487i	0.650780	+	0.759267i	$0.274442\pi$
$104$	2.04989			0.201008
$105$	13.3843	+	0.928203i	1.30617	+	0.0905834i
$106$	−13.3485			−1.29652
$107$	0.778539	−	0.778539i	0.0752642	−	0.0752642i	−0.668473	−	0.743737i	$-0.733052\pi$
$107$	0.778539	−	0.778539i	0.0752642	−	0.0752642i	0.743737	+	0.668473i	$0.233052\pi$
$108$	−4.53553	−	2.53553i	−0.436432	−	0.243982i
$109$		−	5.79796i		−	0.555344i	−0.960676	−	0.277672i	$-0.910437\pi$
$109$		−	5.79796i		−	0.555344i	0.960676	−	0.277672i	$-0.0895628\pi$
$110$	1.27135	+	12.5851i	0.121218	+	1.19994i
$111$	−4.89898	+	3.46410i	−0.464991	+	0.328798i
$112$	2.44949	+	2.44949i	0.231455	+	0.231455i
$113$	−2.36773	−	2.36773i	−0.222737	−	0.222737i	0.586913	−	0.809650i	$-0.300343\pi$
$113$	−2.36773	−	2.36773i	−0.222737	−	0.222737i	−0.809650	+	0.586913i	$0.800343\pi$
$114$	−3.46410	+	2.44949i	−0.324443	+	0.229416i
$115$	−0.224745	−	2.22474i	−0.0209576	−	0.207459i
$116$			9.12096i			0.846859i
$117$	−5.54927	+	2.65029i	−0.513030	+	0.245019i
$118$	−5.89898	+	5.89898i	−0.543045	+	0.543045i
$119$	−25.4558			−2.33353
$120$	−3.86370	−	0.267949i	−0.352706	−	0.0244603i
$121$	−21.0000			−1.90909
$122$	6.29253	−	6.29253i	0.569699	−	0.569699i
$123$	14.4853	+	2.48528i	1.30609	+	0.224090i
$124$			4.89898i			0.439941i
$125$	−5.19615	+	9.89949i	−0.464758	+	0.885438i
$126$	−9.79796	−	3.46410i	−0.872872	−	0.308607i
$127$	−8.44949	−	8.44949i	−0.749771	−	0.749771i	0.224665	−	0.974436i	$-0.427871\pi$
$127$	−8.44949	−	8.44949i	−0.749771	−	0.749771i	−0.974436	+	0.224665i	$0.927871\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−9.75663	−	13.7980i	−0.859023	−	1.21484i
$130$	−2.89898	+	3.55051i	−0.254257	+	0.311400i
$131$		−	13.9993i		−	1.22312i	−0.791197	−	0.611561i	$-0.790542\pi$
$131$		−	13.9993i		−	1.22312i	0.791197	−	0.611561i	$-0.209458\pi$
$132$	1.65685	−	9.65685i	0.144211	−	0.840521i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	1.55708			0.134511
$135$	10.8059	−	4.26999i	0.930023	−	0.367502i
$136$	7.34847			0.630126
$137$	−3.28913	+	3.28913i	−0.281009	+	0.281009i	−0.833511	−	0.552502i	$-0.813673\pi$
$137$	−3.28913	+	3.28913i	−0.281009	+	0.281009i	0.552502	+	0.833511i	$0.313673\pi$
$138$	−0.292893	+	1.70711i	−0.0249327	+	0.145319i
$139$		−	10.6969i		−	0.907302i	−0.891179	−	0.453651i	$-0.850121\pi$
$139$		−	10.6969i		−	0.907302i	0.891179	−	0.453651i	$-0.149879\pi$
$140$	−7.70674	+	0.778539i	−0.651339	+	0.0657986i
$141$	2.89898	+	4.09978i	0.244138	+	0.345263i
$142$	4.34847	+	4.34847i	0.364915	+	0.364915i
$143$	−8.19955	−	8.19955i	−0.685681	−	0.685681i
$144$	2.82843	+	1.00000i	0.235702	+	0.0833333i
$145$	−15.7980	−	12.8990i	−1.31195	−	1.07120i
$146$			11.1708i			0.924506i
$147$	−8.53553	−	1.46447i	−0.703999	−	0.120787i
$148$	2.44949	−	2.44949i	0.201347	−	0.201347i
$149$	16.6848			1.36687			0.683437	−	0.730009i	$-0.260484\pi$
$149$	16.6848			1.36687			0.683437	+	0.730009i	$0.260484\pi$
$150$	5.92820	−	6.31319i	0.484036	−	0.515470i
$151$	8.89898			0.724189			0.362094	−	0.932141i	$-0.382062\pi$
$151$	8.89898			0.724189			0.362094	+	0.932141i	$0.382062\pi$
$152$	1.73205	−	1.73205i	0.140488	−	0.140488i
$153$	−19.8931	+	9.50079i	−1.60826	+	0.768093i
$154$		−	19.5959i		−	1.57908i
$155$	−8.48528	−	6.92820i	−0.681554	−	0.556487i
$156$	2.89898	−	2.04989i	0.232104	−	0.164122i
$157$	−3.55051	−	3.55051i	−0.283362	−	0.283362i	0.551087	−	0.834448i	$-0.314213\pi$
$157$	−3.55051	−	3.55051i	−0.283362	−	0.283362i	−0.834448	+	0.551087i	$0.814213\pi$
$158$	0.317837	+	0.317837i	0.0252858	+	0.0252858i
$159$	−18.8776	+	13.3485i	−1.49709	+	1.05860i
$160$	2.22474	−	0.224745i	0.175882	−	0.0177676i
$161$			3.46410i			0.273009i
$162$	−8.94975	+	0.949747i	−0.703159	+	0.0746192i
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	−0.846188	−	0.532884i	$-0.821108\pi$
$163$	−4.00000	+	4.00000i	−0.313304	+	0.313304i	0.532884	+	0.846188i	$0.321108\pi$
$164$	−8.48528			−0.662589
$165$	14.3830	+	16.5266i	1.11972	+	1.28659i
$166$	−2.00000			−0.155230
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	−0.453510	−	0.891251i	$-0.649829\pi$
$167$	5.65685	−	5.65685i	0.437741	−	0.437741i	0.891251	+	0.453510i	$0.149829\pi$
$168$	5.91359	+	1.01461i	0.456243	+	0.0782790i
$169$			8.79796i			0.676766i
$170$	−10.3923	+	12.7279i	−0.797053	+	0.976187i
$171$	−2.44949	+	6.92820i	−0.187317	+	0.529813i
$172$	6.89898	+	6.89898i	0.526042	+	0.526042i
$173$	10.5352	+	10.5352i	0.800974	+	0.800974i	0.983248	−	0.182274i	$-0.0583457\pi$
$173$	10.5352	+	10.5352i	0.800974	+	0.800974i	−0.182274	+	0.983248i	$0.558346\pi$
$174$	9.12096	+	12.8990i	0.691458	+	0.977869i
$175$	9.55051	−	14.4495i	0.721951	−	1.09228i
$176$			5.65685i			0.426401i
$177$	−2.44344	+	14.2414i	−0.183660	+	1.07045i
$178$	−1.55051	+	1.55051i	−0.116216	+	0.116216i
$179$	12.4422			0.929973			0.464987	−	0.885318i	$-0.346059\pi$
$179$	12.4422			0.929973			0.464987	+	0.885318i	$0.346059\pi$
$180$	−5.73205	+	3.48477i	−0.427242	+	0.259739i
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	5.02118	−	5.02118i	0.372195	−	0.372195i
$183$	2.60645	−	15.1915i	0.192674	−	1.12299i
$184$		−	1.00000i		−	0.0737210i
$185$	0.778539	+	7.70674i	0.0572393	+	0.566611i
$186$	4.89898	+	6.92820i	0.359211	+	0.508001i
$187$	−29.3939	−	29.3939i	−2.14949	−	2.14949i
$188$	−2.04989	−	2.04989i	−0.149503	−	0.149503i
$189$	−17.3205	+	4.89898i	−1.25988	+	0.356348i
$190$	0.550510	+	5.44949i	0.0399382	+	0.395348i
$191$		−	23.6130i		−	1.70858i	−0.519797	−	0.854290i	$-0.673992\pi$
$191$		−	23.6130i		−	1.70858i	0.519797	−	0.854290i	$-0.326008\pi$
$192$	−1.70711	−	0.292893i	−0.123200	−	0.0211377i
$193$	−7.89898	+	7.89898i	−0.568581	+	0.568581i	−0.931731	−	0.363150i	$-0.881701\pi$
$193$	−7.89898	+	7.89898i	−0.568581	+	0.568581i	0.363150	+	0.931731i	$0.381701\pi$
$194$	−6.29253			−0.451777
$195$	−0.549266	+	7.92016i	−0.0393337	+	0.567174i
$196$	5.00000			0.357143
$197$	−0.778539	+	0.778539i	−0.0554686	+	0.0554686i	−0.734297	−	0.678828i	$-0.762488\pi$
$197$	−0.778539	+	0.778539i	−0.0554686	+	0.0554686i	0.678828	+	0.734297i	$0.262488\pi$
$198$	−7.31371	−	15.3137i	−0.519763	−	1.08830i
$199$			12.4495i			0.882521i	0.897379	+	0.441260i	$0.145469\pi$
$199$			12.4495i			0.882521i	−0.897379	+	0.441260i	$0.854531\pi$
$200$	−2.75699	+	4.17121i	−0.194949	+	0.294949i
$201$	2.20204	−	1.55708i	0.155320	−	0.109828i
$202$	−4.44949	−	4.44949i	−0.313065	−	0.313065i
$203$	22.3417	+	22.3417i	1.56808	+	1.56808i
$204$	10.3923	−	7.34847i	0.727607	−	0.514496i
$205$	12.0000	−	14.6969i	0.838116	−	1.02648i
$206$		−	1.55708i		−	0.108487i
$207$	1.29289	+	2.70711i	0.0898623	+	0.188157i
$208$	−1.44949	+	1.44949i	−0.100504	+	0.100504i
$209$	−13.8564			−0.958468
$210$	−10.1204	+	8.80776i	−0.698377	+	0.607793i
$211$	−10.6969			−0.736408			−0.368204	−	0.929745i	$-0.620027\pi$
$211$	−10.6969			−0.736408			−0.368204	+	0.929745i	$0.620027\pi$
$212$	9.43879	−	9.43879i	0.648259	−	0.648259i
$213$	10.4981	+	1.80119i	0.719320	+	0.123416i
$214$			1.10102i			0.0752642i
$215$	−21.7060	+	2.19275i	−1.48034	+	0.149544i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	12.0000	+	12.0000i	0.814613	+	0.814613i
$218$	4.09978	+	4.09978i	0.277672	+	0.277672i
$219$	11.1708	+	15.7980i	0.754856	+	1.06753i
$220$	−9.79796	−	8.00000i	−0.660578	−	0.539360i
$221$		−	15.0635i		−	1.01328i
$222$	1.01461	−	5.91359i	0.0680963	−	0.396894i
$223$	−7.55051	+	7.55051i	−0.505620	+	0.505620i	−0.913179	−	0.407559i	$-0.866380\pi$
$223$	−7.55051	+	7.55051i	−0.505620	+	0.505620i	0.407559	+	0.913179i	$0.366380\pi$
$224$	−3.46410			−0.231455
$225$	2.07055	−	14.8564i	0.138037	−	0.990427i
$226$	3.34847			0.222737
$227$	7.70674	−	7.70674i	0.511514	−	0.511514i	−0.403476	−	0.914990i	$-0.632198\pi$
$227$	7.70674	−	7.70674i	0.511514	−	0.511514i	0.914990	+	0.403476i	$0.132198\pi$
$228$	0.717439	−	4.18154i	0.0475136	−	0.276929i
$229$			22.6969i			1.49986i	0.661520	+	0.749928i	$0.269912\pi$
$229$			22.6969i			1.49986i	−0.661520	+	0.749928i	$0.730088\pi$
$230$	1.73205	+	1.41421i	0.114208	+	0.0932505i
$231$	−19.5959	−	27.7128i	−1.28932	−	1.82337i
$232$	−6.44949	−	6.44949i	−0.423430	−	0.423430i
$233$	−10.5352	−	10.5352i	−0.690182	−	0.690182i	0.272090	−	0.962272i	$-0.412285\pi$
$233$	−10.5352	−	10.5352i	−0.690182	−	0.690182i	−0.962272	+	0.272090i	$0.912285\pi$
$234$	2.04989	−	5.79796i	0.134005	−	0.379024i
$235$	6.44949	−	0.651531i	0.420718	−	0.0425012i
$236$		−	8.34242i		−	0.543045i
$237$	0.767327	+	0.131652i	0.0498432	+	0.00855175i
$238$	18.0000	−	18.0000i	1.16677	−	1.16677i
$239$	6.43539			0.416271			0.208135	−	0.978100i	$-0.433261\pi$
$239$	6.43539			0.416271			0.208135	+	0.978100i	$0.433261\pi$
$240$	2.92152	−	2.54258i	0.188583	−	0.164123i
$241$	−18.8990			−1.21739			−0.608695	−	0.793404i	$-0.708307\pi$
$241$	−18.8990			−1.21739			−0.608695	+	0.793404i	$0.708307\pi$
$242$	14.8492	−	14.8492i	0.954545	−	0.954545i
$243$	−11.7071	+	10.2929i	−0.751011	+	0.660289i
$244$			8.89898i			0.569699i
$245$	−7.07107	+	8.66025i	−0.451754	+	0.553283i
$246$	−12.0000	+	8.48528i	−0.765092	+	0.541002i
$247$	−3.55051	−	3.55051i	−0.225914	−	0.225914i
$248$	−3.46410	−	3.46410i	−0.219971	−	0.219971i
$249$	−2.82843	+	2.00000i	−0.179244	+	0.126745i
$250$	−3.32577	−	10.6742i	−0.210340	−	0.675098i
$251$			26.7272i			1.68701i	0.537125	+	0.843503i	$0.319510\pi$
$251$			26.7272i			1.68701i	−0.537125	+	0.843503i	$0.680490\pi$
$252$	9.37769	−	4.47871i	0.590739	−	0.282132i
$253$	−4.00000	+	4.00000i	−0.251478	+	0.251478i
$254$	11.9494			0.749771
$255$	−1.96902	+	28.3923i	−0.123305	+	1.77800i
$256$	1.00000			0.0625000
$257$	18.0990	−	18.0990i	1.12899	−	1.12899i	0.138645	−	0.990342i	$-0.455725\pi$
$257$	18.0990	−	18.0990i	1.12899	−	1.12899i	0.990342	−	0.138645i	$-0.0442748\pi$
$258$	16.6556	+	2.85765i	1.03693	+	0.177910i
$259$		−	12.0000i		−	0.745644i
$260$	−0.460702	−	4.56048i	−0.0285715	−	0.282829i
$261$	25.7980	+	9.12096i	1.59685	+	0.564573i
$262$	9.89898	+	9.89898i	0.611561	+	0.611561i
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	0.510852	−	0.859669i	$-0.329330\pi$
$263$	−5.65685	−	5.65685i	−0.348817	−	0.348817i	−0.859669	+	0.510852i	$0.829330\pi$
$264$	5.65685	+	8.00000i	0.348155	+	0.492366i
$265$	3.00000	+	29.6969i	0.184289	+	1.82427i
$266$		−	8.48528i		−	0.520266i
$267$	−0.642242	+	3.74326i	−0.0393046	+	0.229084i
$268$	−1.10102	+	1.10102i	−0.0672555	+	0.0672555i
$269$	−0.635674			−0.0387578			−0.0193789	−	0.999812i	$-0.506169\pi$
$269$	−0.635674			−0.0387578			−0.0193789	+	0.999812i	$0.506169\pi$
$270$	−4.62158	+	10.6603i	−0.281260	+	0.648762i
$271$	24.4949			1.48796			0.743980	−	0.668202i	$-0.232936\pi$
$271$	24.4949			1.48796			0.743980	+	0.668202i	$0.232936\pi$
$272$	−5.19615	+	5.19615i	−0.315063	+	0.315063i
$273$	2.07984	−	12.1222i	0.125878	−	0.733669i
$274$		−	4.65153i		−	0.281009i
$275$	27.7128	−	5.65685i	1.67115	−	0.341121i
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	−4.55051	−	4.55051i	−0.273414	−	0.273414i	0.557059	−	0.830473i	$-0.311930\pi$
$277$	−4.55051	−	4.55051i	−0.273414	−	0.273414i	−0.830473	+	0.557059i	$0.811930\pi$
$278$	7.56388	+	7.56388i	0.453651	+	0.453651i
$279$	13.8564	+	4.89898i	0.829561	+	0.293294i
$280$	4.89898	−	6.00000i	0.292770	−	0.358569i
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$	−4.94887	−	0.849091i	−0.294701	−	0.0505627i
$283$	−9.34847	+	9.34847i	−0.555709	+	0.555709i	−0.928083	−	0.372374i	$-0.878544\pi$
$283$	−9.34847	+	9.34847i	−0.555709	+	0.555709i	0.372374	+	0.928083i	$0.378544\pi$
$284$	−6.14966			−0.364915
$285$	6.22803	+	7.15623i	0.368917	+	0.423899i
$286$	11.5959			0.685681
$287$	−20.7846	+	20.7846i	−1.22688	+	1.22688i
$288$	−2.70711	+	1.29289i	−0.159518	+	0.0761845i
$289$		−	37.0000i		−	2.17647i
$290$	20.2918	−	2.04989i	1.19158	−	0.120374i
$291$	−8.89898	+	6.29253i	−0.521667	+	0.368875i
$292$	−7.89898	−	7.89898i	−0.462253	−	0.462253i
$293$	−10.7101	−	10.7101i	−0.625693	−	0.625693i	0.321288	−	0.946981i	$-0.395884\pi$
$293$	−10.7101	−	10.7101i	−0.625693	−	0.625693i	−0.946981	+	0.321288i	$0.895884\pi$
$294$	7.07107	−	5.00000i	0.412393	−	0.291606i
$295$	14.4495	+	11.7980i	0.841282	+	0.686904i
$296$			3.46410i			0.201347i
$297$	−25.6569	−	14.3431i	−1.48876	−	0.832274i
$298$	−11.7980	+	11.7980i	−0.683437	+	0.683437i
$299$	−2.04989			−0.118548
$300$	0.272229	+	8.65597i	0.0157171	+	0.499753i
$301$	33.7980			1.94808
$302$	−6.29253	+	6.29253i	−0.362094	+	0.362094i
$303$	−10.7420	−	1.84304i	−0.617113	−	0.105880i
$304$			2.44949i			0.140488i
$305$	−15.4135	−	12.5851i	−0.882574	−	0.720618i
$306$	7.34847	−	20.7846i	0.420084	−	1.18818i
$307$	6.69694	+	6.69694i	0.382214	+	0.382214i	0.871899	−	0.489685i	$-0.162888\pi$
$307$	6.69694	+	6.69694i	0.382214	+	0.382214i	−0.489685	+	0.871899i	$0.662888\pi$
$308$	13.8564	+	13.8564i	0.789542	+	0.789542i
$309$	−1.55708	−	2.20204i	−0.0885791	−	0.125270i
$310$	10.8990	−	1.10102i	0.619020	−	0.0625338i
$311$			34.1482i			1.93637i	0.250241	+	0.968184i	$0.419490\pi$
$311$			34.1482i			1.93637i	−0.250241	+	0.968184i	$0.580510\pi$
$312$	−0.600398	+	3.49938i	−0.0339909	+	0.198113i
$313$	19.1464	−	19.1464i	1.08222	−	1.08222i	0.0859179	−	0.996302i	$-0.472618\pi$
$313$	19.1464	−	19.1464i	1.08222	−	1.08222i	0.996302	−	0.0859179i	$-0.0273823\pi$
$314$	5.02118			0.283362
$315$	−5.50470	+	22.5765i	−0.310155	+	1.27204i
$316$	−0.449490			−0.0252858
$317$	−6.43539	+	6.43539i	−0.361448	+	0.361448i	−0.864346	−	0.502898i	$-0.832267\pi$
$317$	−6.43539	+	6.43539i	−0.361448	+	0.361448i	0.502898	+	0.864346i	$0.332267\pi$
$318$	3.90968	−	22.7873i	0.219244	−	1.27785i
$319$			51.5959i			2.88882i
$320$	−1.41421	+	1.73205i	−0.0790569	+	0.0968246i
$321$	1.10102	+	1.55708i	0.0614530	+	0.0869076i
$322$	−2.44949	−	2.44949i	−0.136505	−	0.136505i
$323$	−12.7279	−	12.7279i	−0.708201	−	0.708201i
$324$	5.65685	−	7.00000i	0.314270	−	0.388889i
$325$	8.55051	+	5.65153i	0.474297	+	0.313491i
$326$		−	5.65685i		−	0.313304i
$327$	9.89774	+	1.69818i	0.547346	+	0.0939097i
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	−10.0424			−0.553653
$330$	−21.8564	−	1.51575i	−1.20316	−	0.0834393i
$331$	10.6969			0.587957			0.293978	−	0.955812i	$-0.405021\pi$
$331$	10.6969			0.587957			0.293978	+	0.955812i	$0.405021\pi$
$332$	1.41421	−	1.41421i	0.0776151	−	0.0776151i
$333$	−4.47871	−	9.37769i	−0.245432	−	0.513894i
$334$			8.00000i			0.437741i
$335$	−0.349945	−	3.46410i	−0.0191196	−	0.189264i
$336$	−4.89898	+	3.46410i	−0.267261	+	0.188982i
$337$	9.55051	+	9.55051i	0.520249	+	0.520249i	0.917647	−	0.397397i	$-0.130086\pi$
$337$	9.55051	+	9.55051i	0.520249	+	0.520249i	−0.397397	+	0.917647i	$0.630086\pi$
$338$	−6.22110	−	6.22110i	−0.338383	−	0.338383i
$339$	4.73545	−	3.34847i	0.257194	−	0.181864i
$340$	−1.65153	−	16.3485i	−0.0895668	−	0.886620i
$341$			27.7128i			1.50073i
$342$	−3.16693	−	6.63103i	−0.171248	−	0.358565i
$343$	−4.89898	+	4.89898i	−0.264520	+	0.264520i
$344$	−9.75663			−0.526042
$345$	3.86370	+	0.267949i	0.208015	+	0.0144259i
$346$	−14.8990			−0.800974
$347$	−13.9993	+	13.9993i	−0.751520	+	0.751520i	−0.974763	−	0.223243i	$-0.928336\pi$
$347$	−13.9993	+	13.9993i	−0.751520	+	0.751520i	0.223243	+	0.974763i	$0.428336\pi$
$348$	−15.5704	−	2.67147i	−0.834663	−	0.143206i
$349$		−	22.0000i		−	1.17763i	−0.808267	−	0.588817i	$-0.799594\pi$
$349$		−	22.0000i		−	1.17763i	0.808267	−	0.588817i	$-0.200406\pi$
$350$	3.46410	+	16.9706i	0.185164	+	0.907115i
$351$	−2.89898	−	10.2494i	−0.154736	−	0.547075i
$352$	−4.00000	−	4.00000i	−0.213201	−	0.213201i
$353$	2.33562	+	2.33562i	0.124312	+	0.124312i	0.766526	−	0.642213i	$-0.221984\pi$
$353$	2.33562	+	2.33562i	0.124312	+	0.124312i	−0.642213	+	0.766526i	$0.721984\pi$
$354$	−8.34242	−	11.7980i	−0.443394	−	0.627054i
$355$	8.69694	−	10.6515i	0.461586	−	0.565325i
$356$		−	2.19275i		−	0.116216i
$357$	7.45584	−	43.4558i	0.394605	−	2.29993i
$358$	−8.79796	+	8.79796i	−0.464987	+	0.464987i
$359$	12.8708			0.679294			0.339647	−	0.940553i	$-0.389692\pi$
$359$	12.8708			0.679294			0.339647	+	0.940553i	$0.389692\pi$
$360$	1.58907	−	6.51727i	0.0837514	−	0.343490i
$361$	13.0000			0.684211
$362$	−5.65685	+	5.65685i	−0.297318	+	0.297318i
$363$	6.15076	−	35.8492i	0.322831	−	1.88160i
$364$			7.10102i			0.372195i
$365$	24.8523	−	2.51059i	1.30083	−	0.131410i
$366$	8.89898	+	12.5851i	0.465157	+	0.657831i
$367$	0.202041	+	0.202041i	0.0105465	+	0.0105465i	0.712360	−	0.701814i	$-0.247626\pi$
$367$	0.202041	+	0.202041i	0.0105465	+	0.0105465i	−0.701814	+	0.712360i	$0.747626\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	−8.48528	+	24.0000i	−0.441726	+	1.24939i
$370$	−6.00000	−	4.89898i	−0.311925	−	0.254686i
$371$		−	46.2405i		−	2.40068i
$372$	−8.36308	−	1.43488i	−0.433606	−	0.0743950i
$373$	7.55051	−	7.55051i	0.390951	−	0.390951i	−0.484076	−	0.875026i	$-0.660844\pi$
$373$	7.55051	−	7.55051i	0.390951	−	0.390951i	0.875026	+	0.484076i	$0.160844\pi$
$374$	41.5692			2.14949
$375$	−15.3776	−	11.7699i	−0.794095	−	0.607794i
$376$	2.89898			0.149503
$377$	−13.2207	+	13.2207i	−0.680902	+	0.680902i
$378$	8.78335	−	15.7116i	0.451767	−	0.808115i
$379$		−	29.1464i		−	1.49715i	−0.663049	−	0.748576i	$-0.730738\pi$
$379$		−	29.1464i		−	1.49715i	0.663049	−	0.748576i	$-0.269262\pi$
$380$	−4.24264	−	3.46410i	−0.217643	−	0.177705i
$381$	16.8990	−	11.9494i	0.865761	−	0.612185i
$382$	16.6969	+	16.6969i	0.854290	+	0.854290i
$383$	16.0492	+	16.0492i	0.820074	+	0.820074i	0.986118	−	0.166045i	$-0.0530995\pi$
$383$	16.0492	+	16.0492i	0.820074	+	0.820074i	−0.166045	+	0.986118i	$0.553100\pi$
$384$	1.41421	−	1.00000i	0.0721688	−	0.0510310i
$385$	−43.5959	+	4.40408i	−2.22185	+	0.224453i
$386$		−	11.1708i		−	0.568581i
$387$	26.4122	−	12.6143i	1.34261	−	0.641220i
$388$	4.44949	−	4.44949i	0.225889	−	0.225889i
$389$	31.1127			1.57748			0.788738	−	0.614729i	$-0.210735\pi$
$389$	31.1127			1.57748			0.788738	+	0.614729i	$0.210735\pi$
$390$	−5.21201	−	5.98879i	−0.263920	−	0.303254i
$391$	−7.34847			−0.371628
$392$	−3.53553	+	3.53553i	−0.178571	+	0.178571i
$393$	23.8983	+	4.10029i	1.20551	+	0.206832i
$394$		−	1.10102i		−	0.0554686i
$395$	0.635674	−	0.778539i	0.0319843	−	0.0391726i
$396$	16.0000	+	5.65685i	0.804030	+	0.284268i
$397$	13.4495	+	13.4495i	0.675011	+	0.675011i	0.958867	−	0.283856i	$-0.0916139\pi$
$397$	13.4495	+	13.4495i	0.675011	+	0.675011i	−0.283856	+	0.958867i	$0.591614\pi$
$398$	−8.80312	−	8.80312i	−0.441260	−	0.441260i
$399$	−8.48528	−	12.0000i	−0.424795	−	0.600751i
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$		−	14.7778i		−	0.737969i	−0.929436	−	0.368984i	$-0.879706\pi$
$401$		−	14.7778i		−	0.737969i	0.929436	−	0.368984i	$-0.120294\pi$
$402$	−0.456058	+	2.65810i	−0.0227461	+	0.132574i
$403$	−7.10102	+	7.10102i	−0.353727	+	0.353727i
$404$	6.29253			0.313065
$405$	4.12436	+	19.6975i	0.204941	+	0.978774i
$406$	−31.5959			−1.56808
$407$	13.8564	−	13.8564i	0.686837	−	0.686837i
$408$	−2.15232	+	12.5446i	−0.106556	+	0.621051i
$409$		−	5.79796i		−	0.286691i	−0.989673	−	0.143345i	$-0.954214\pi$
$409$		−	5.79796i		−	0.286691i	0.989673	−	0.143345i	$-0.0457860\pi$
$410$	1.90702	+	18.8776i	0.0941812	+	0.932298i
$411$	−4.65153	−	6.57826i	−0.229443	−	0.324482i
$412$	1.10102	+	1.10102i	0.0542434	+	0.0542434i
$413$	−20.4347	−	20.4347i	−1.00552	−	1.00552i
$414$	−2.82843	−	1.00000i	−0.139010	−	0.0491473i
$415$	0.449490	+	4.44949i	0.0220646	+	0.218417i
$416$		−	2.04989i		−	0.100504i
$417$	18.2608	+	3.13306i	0.894236	+	0.153427i
$418$	9.79796	−	9.79796i	0.479234	−	0.479234i
$419$	−18.2419			−0.891176			−0.445588	−	0.895238i	$-0.647005\pi$
$419$	−18.2419			−0.891176			−0.445588	+	0.895238i	$0.647005\pi$
$420$	0.928203	−	13.3843i	0.0452917	−	0.653085i
$421$	−8.89898			−0.433710			−0.216855	−	0.976204i	$-0.569580\pi$
$421$	−8.89898			−0.433710			−0.216855	+	0.976204i	$0.569580\pi$
$422$	7.56388	−	7.56388i	0.368204	−	0.368204i
$423$	−7.84785	+	3.74807i	−0.381575	+	0.182237i
$424$			13.3485i			0.648259i
$425$	30.6520	+	20.2597i	1.48684	+	0.982739i
$426$	−8.69694	+	6.14966i	−0.421368	+	0.297952i
$427$	21.7980	+	21.7980i	1.05488	+	1.05488i
$428$	−0.778539	−	0.778539i	−0.0376321	−	0.0376321i
$429$	16.3991	−	11.5959i	0.791756	−	0.559856i
$430$	13.7980	−	16.8990i	0.665397	−	0.814941i
$431$		−	5.37113i		−	0.258718i	−0.991598	−	0.129359i	$-0.958708\pi$
$431$		−	5.37113i		−	0.258718i	0.991598	−	0.129359i	$-0.0412920\pi$
$432$	−2.53553	+	4.53553i	−0.121991	+	0.218216i
$433$	14.6515	−	14.6515i	0.704108	−	0.704108i	−0.261182	−	0.965290i	$-0.584112\pi$
$433$	14.6515	−	14.6515i	0.704108	−	0.704108i	0.965290	+	0.261182i	$0.0841123\pi$
$434$	−16.9706			−0.814613
$435$	26.6471	−	23.1908i	1.27763	−	1.11191i
$436$	−5.79796			−0.277672
$437$	−1.73205	+	1.73205i	−0.0828552	+	0.0828552i
$438$	−19.0698	−	3.27186i	−0.911191	−	0.156336i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	12.5851	−	1.27135i	0.599969	−	0.0606092i
$441$	5.00000	−	14.1421i	0.238095	−	0.673435i
$442$	10.6515	+	10.6515i	0.506642	+	0.506642i
$443$	11.3137	+	11.3137i	0.537531	+	0.537531i	0.922803	−	0.385272i	$-0.125893\pi$
$443$	11.3137	+	11.3137i	0.537531	+	0.537531i	−0.385272	+	0.922803i	$0.625893\pi$
$444$	3.46410	+	4.89898i	0.164399	+	0.232495i
$445$	3.79796	+	3.10102i	0.180041	+	0.147002i
$446$		−	10.6780i		−	0.505620i
$447$	−4.88687	+	28.4828i	−0.231141	+	1.34719i
$448$	2.44949	−	2.44949i	0.115728	−	0.115728i
$449$	−26.4415			−1.24785			−0.623925	−	0.781484i	$-0.714463\pi$
$449$	−26.4415			−1.24785			−0.623925	+	0.781484i	$0.714463\pi$
$450$	9.04096	+	11.9692i	0.426195	+	0.564232i
$451$	−48.0000			−2.26023
$452$	−2.36773	+	2.36773i	−0.111368	+	0.111368i
$453$	−2.60645	+	15.1915i	−0.122462	+	0.713759i
$454$			10.8990i			0.511514i
$455$	−12.2993	−	10.0424i	−0.576601	−	0.470793i
$456$	2.44949	+	3.46410i	0.114708	+	0.162221i
$457$	6.44949	+	6.44949i	0.301694	+	0.301694i	0.841677	−	0.539982i	$-0.181569\pi$
$457$	6.44949	+	6.44949i	0.301694	+	0.301694i	−0.539982	+	0.841677i	$0.681569\pi$
$458$	−16.0492	−	16.0492i	−0.749928	−	0.749928i
$459$	−10.3923	−	36.7423i	−0.485071	−	1.71499i
$460$	−2.22474	+	0.224745i	−0.103729	+	0.0104788i
$461$			3.17837i			0.148032i	0.997257	+	0.0740158i	$0.0235815\pi$
$461$			3.17837i			0.148032i	−0.997257	+	0.0740158i	$0.976418\pi$
$462$	33.4523	+	5.73951i	1.55634	+	0.267026i
$463$	−18.0454	+	18.0454i	−0.838641	+	0.838641i	−0.988680	−	0.150039i	$-0.952060\pi$
$463$	−18.0454	+	18.0454i	−0.838641	+	0.838641i	0.150039	+	0.988680i	$0.452060\pi$
$464$	9.12096			0.423430
$465$	14.3125	−	12.4561i	0.663725	−	0.577636i
$466$	14.8990			0.690182
$467$	−10.5352	+	10.5352i	−0.487510	+	0.487510i	−0.907519	−	0.420010i	$-0.862027\pi$
$467$	−10.5352	+	10.5352i	−0.487510	+	0.487510i	0.420010	+	0.907519i	$0.362027\pi$
$468$	2.65029	+	5.54927i	0.122510	+	0.256515i
$469$			5.39388i			0.249066i
$470$	−4.09978	+	5.02118i	−0.189109	+	0.231610i
$471$	7.10102	−	5.02118i	0.327198	−	0.231364i
$472$	5.89898	+	5.89898i	0.271523	+	0.271523i
$473$	39.0265	+	39.0265i	1.79444	+	1.79444i
$474$	−0.635674	+	0.449490i	−0.0291975	+	0.0206457i
$475$	12.0000	−	2.44949i	0.550598	−	0.112390i
$476$			25.4558i			1.16677i
$477$	−17.2581	−	36.1357i	−0.790196	−	1.65454i
$478$	−4.55051	+	4.55051i	−0.208135	+	0.208135i
$479$	−15.1278			−0.691205			−0.345602	−	0.938381i	$-0.612325\pi$
$479$	−15.1278			−0.691205			−0.345602	+	0.938381i	$0.612325\pi$
$480$	−0.267949	+	3.86370i	−0.0122302	+	0.176353i
$481$	7.10102			0.323779
$482$	13.3636	−	13.3636i	0.608695	−	0.608695i
$483$	−5.91359	−	1.01461i	−0.269078	−	0.0461664i
$484$			21.0000i			0.954545i
$485$	1.41421	+	13.9993i	0.0642161	+	0.635674i
$486$	1.00000	−	15.5563i	0.0453609	−	0.705650i
$487$	4.65153	+	4.65153i	0.210781	+	0.210781i	0.804599	−	0.593818i	$-0.202380\pi$
$487$	4.65153	+	4.65153i	0.210781	+	0.210781i	−0.593818	+	0.804599i	$0.702380\pi$
$488$	−6.29253	−	6.29253i	−0.284849	−	0.284849i
$489$	−5.65685	−	8.00000i	−0.255812	−	0.361773i
$490$	−1.12372	−	11.1237i	−0.0507647	−	0.502519i
$491$			11.4566i			0.517028i	0.966008	+	0.258514i	$0.0832328\pi$
$491$			11.4566i			0.517028i	−0.966008	+	0.258514i	$0.916767\pi$
$492$	2.48528	−	14.4853i	0.112045	−	0.653047i
$493$	−47.3939	+	47.3939i	−2.13451	+	2.13451i
$494$	5.02118			0.225914
$495$	−32.4254	+	19.7128i	−1.45741	+	0.886025i
$496$	4.89898			0.219971
$497$	−15.0635	+	15.0635i	−0.675692	+	0.675692i
$498$	0.585786	−	3.41421i	0.0262497	−	0.152995i
$499$		−	14.2020i		−	0.635771i	−0.948129	−	0.317885i	$-0.897027\pi$
$499$		−	14.2020i		−	0.635771i	0.948129	−	0.317885i	$-0.102973\pi$
$500$	9.89949	+	5.19615i	0.442719	+	0.232379i
$501$	8.00000	+	11.3137i	0.357414	+	0.505459i
$502$	−18.8990	−	18.8990i	−0.843503	−	0.843503i
$503$	18.8776	+	18.8776i	0.841710	+	0.841710i	0.989081	−	0.147371i	$-0.0470812\pi$
$503$	18.8776	+	18.8776i	0.841710	+	0.841710i	−0.147371	+	0.989081i	$0.547081\pi$
$504$	−3.46410	+	9.79796i	−0.154303	+	0.436436i
$505$	−8.89898	+	10.8990i	−0.395999	+	0.484998i
$506$		−	5.65685i		−	0.251478i
$507$	−15.0191	−	2.57686i	−0.667020	−	0.114442i
$508$	−8.44949	+	8.44949i	−0.374885	+	0.374885i
$509$	42.4906			1.88336			0.941682	−	0.336504i	$-0.109245\pi$
$509$	42.4906			1.88336			0.941682	+	0.336504i	$0.109245\pi$
$510$	−18.6841	−	21.4687i	−0.827345	−	0.950650i
$511$	−38.6969			−1.71185
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−11.1097	−	6.21076i	−0.490507	−	0.274212i
$514$			25.5959i			1.12899i
$515$	−3.46410	+	0.349945i	−0.152647	+	0.0154204i
$516$	−13.7980	+	9.75663i	−0.607421	+	0.429512i
$517$	−11.5959	−	11.5959i	−0.509988	−	0.509988i
$518$	8.48528	+	8.48528i	0.372822	+	0.372822i
$519$	−21.0703	+	14.8990i	−0.924885	+	0.653993i
$520$	3.55051	+	2.89898i	0.155700	+	0.127129i
$521$		−	42.4906i		−	1.86155i	−0.365595	−	0.930774i	$-0.619134\pi$
$521$		−	42.4906i		−	1.86155i	0.365595	−	0.930774i	$-0.380866\pi$
$522$	−24.6914	+	11.7924i	−1.08071	+	0.516140i
$523$	2.24745	−	2.24745i	0.0982741	−	0.0982741i	−0.656260	−	0.754534i	$-0.727863\pi$
$523$	2.24745	−	2.24745i	0.0982741	−	0.0982741i	0.754534	+	0.656260i	$0.227863\pi$
$524$	−13.9993			−0.611561
$525$	21.8695	+	20.5359i	0.954465	+	0.896260i
$526$	8.00000			0.348817
$527$	−25.4558	+	25.4558i	−1.10887	+	1.10887i
$528$	−9.65685	−	1.65685i	−0.420261	−	0.0721053i
$529$			1.00000i			0.0434783i
$530$	−23.1202	−	18.8776i	−1.00428	−	0.819990i
$531$	−23.5959	−	8.34242i	−1.02398	−	0.362030i
$532$	6.00000	+	6.00000i	0.260133	+	0.260133i
$533$	−12.2993	−	12.2993i	−0.532743	−	0.532743i
$534$	−2.19275	−	3.10102i	−0.0948897	−	0.134194i
$535$	2.44949	−	0.247449i	0.105901	−	0.0106981i
$536$		−	1.55708i		−	0.0672555i
$537$	−3.64423	+	21.2402i	−0.157260	+	0.916580i
$538$	0.449490	−	0.449490i	0.0193789	−	0.0193789i
$539$	28.2843			1.21829
$540$	−4.26999	−	10.8059i	−0.183751	−	0.465011i
$541$	−10.6969			−0.459897			−0.229949	−	0.973203i	$-0.573856\pi$
$541$	−10.6969			−0.459897			−0.229949	+	0.973203i	$0.573856\pi$
$542$	−17.3205	+	17.3205i	−0.743980	+	0.743980i
$543$	−2.34315	+	13.6569i	−0.100554	+	0.586072i
$544$		−	7.34847i		−	0.315063i
$545$	8.19955	−	10.0424i	0.351230	−	0.430167i
$546$	7.10102	+	10.0424i	0.303896	+	0.429773i
$547$	27.5959	+	27.5959i	1.17992	+	1.17992i	0.979765	+	0.200151i	$0.0641433\pi$
$547$	27.5959	+	27.5959i	1.17992	+	1.17992i	0.200151	+	0.979765i	$0.435857\pi$
$548$	3.28913	+	3.28913i	0.140505	+	0.140505i
$549$	25.1701	+	8.89898i	1.07423	+	0.379799i
$550$	−15.5959	+	23.5959i	−0.665012	+	1.00613i
$551$			22.3417i			0.951788i
$552$	1.70711	+	0.292893i	0.0726593	+	0.0124664i
$553$	−1.10102	+	1.10102i	−0.0468202	+	0.0468202i
$554$	6.43539			0.273414
$555$	−13.3843	−	0.928203i	−0.568130	−	0.0394000i
$556$	−10.6969			−0.453651
$557$	−23.9309	+	23.9309i	−1.01398	+	1.01398i	−0.0140828	+	0.999901i	$0.504483\pi$
$557$	−23.9309	+	23.9309i	−1.01398	+	1.01398i	−0.999901	+	0.0140828i	$0.995517\pi$
$558$	−13.2621	+	6.33386i	−0.561428	+	0.268134i
$559$			20.0000i			0.845910i
$560$	0.778539	+	7.70674i	0.0328993	+	0.325669i
$561$	58.7878	−	41.5692i	2.48202	−	1.75505i
$562$	−4.00000	−	4.00000i	−0.168730	−	0.168730i
$563$	1.12848	+	1.12848i	0.0475599	+	0.0475599i	0.730487	−	0.682927i	$-0.239293\pi$
$563$	1.12848	+	1.12848i	0.0475599	+	0.0475599i	−0.682927	+	0.730487i	$0.739293\pi$
$564$	4.09978	−	2.89898i	0.172632	−	0.122069i
$565$	−0.752551	−	7.44949i	−0.0316601	−	0.313402i
$566$		−	13.2207i		−	0.555709i
$567$	−3.29002	−	31.0028i	−0.138168	−	1.30200i
$568$	4.34847	−	4.34847i	0.182458	−	0.182458i
$569$	−10.0424			−0.420998			−0.210499	−	0.977594i	$-0.567509\pi$
$569$	−10.0424			−0.420998			−0.210499	+	0.977594i	$0.567509\pi$
$570$	−9.46410	−	0.656339i	−0.396408	−	0.0274910i
$571$	26.4495			1.10688			0.553438	−	0.832890i	$-0.313315\pi$
$571$	26.4495			1.10688			0.553438	+	0.832890i	$0.313315\pi$
$572$	−8.19955	+	8.19955i	−0.342841	+	0.342841i
$573$	40.3100	+	6.91610i	1.68397	+	0.288924i
$574$		−	29.3939i		−	1.22688i
$575$	2.75699	−	4.17121i	0.114975	−	0.173951i
$576$	1.00000	−	2.82843i	0.0416667	−	0.117851i
$577$	18.7980	+	18.7980i	0.782569	+	0.782569i	0.980264	−	0.197694i	$-0.0633454\pi$
$577$	18.7980	+	18.7980i	0.782569	+	0.782569i	−0.197694	+	0.980264i	$0.563345\pi$
$578$	26.1630	+	26.1630i	1.08824	+	1.08824i
$579$	−11.1708	−	15.7980i	−0.464244	−	0.656541i
$580$	−12.8990	+	15.7980i	−0.535601	+	0.655975i
$581$		−	6.92820i		−	0.287430i
$582$	1.84304	−	10.7420i	0.0763964	−	0.445271i
$583$	53.3939	−	53.3939i	2.21135	−	2.21135i
$584$	11.1708			0.462253
$585$	−13.3597	−	3.25742i	−0.552355	−	0.134678i
$586$	15.1464			0.625693
$587$	0.142865	−	0.142865i	0.00589665	−	0.00589665i	−0.704152	−	0.710049i	$-0.748673\pi$
$587$	0.142865	−	0.142865i	0.00589665	−	0.00589665i	0.710049	+	0.704152i	$0.248673\pi$
$588$	−1.46447	+	8.53553i	−0.0603936	+	0.351999i
$589$			12.0000i			0.494451i
$590$	−18.5597	+	1.87492i	−0.764093	+	0.0771890i
$591$	−1.10102	−	1.55708i	−0.0452899	−	0.0640496i
$592$	−2.44949	−	2.44949i	−0.100673	−	0.100673i
$593$	2.68556	+	2.68556i	0.110283	+	0.110283i	0.760095	−	0.649812i	$-0.225152\pi$
$593$	2.68556	+	2.68556i	0.110283	+	0.110283i	−0.649812	+	0.760095i	$0.725152\pi$
$594$	28.2843	−	8.00000i	1.16052	−	0.328244i
$595$	−44.0908	−	36.0000i	−1.80755	−	1.47586i
$596$		−	16.6848i		−	0.683437i
$597$	−21.2526	−	3.64637i	−0.869811	−	0.149236i
$598$	1.44949	−	1.44949i	0.0592740	−	0.0592740i
$599$	−17.4634			−0.713534			−0.356767	−	0.934193i	$-0.616121\pi$
$599$	−17.4634			−0.713534			−0.356767	+	0.934193i	$0.616121\pi$
$600$	−6.31319	−	5.92820i	−0.257735	−	0.242018i
$601$	−35.7980			−1.46023			−0.730115	−	0.683325i	$-0.760533\pi$
$601$	−35.7980			−1.46023			−0.730115	+	0.683325i	$0.760533\pi$
$602$	−23.8988	+	23.8988i	−0.974041	+	0.974041i
$603$	2.01314	+	4.21518i	0.0819812	+	0.171655i
$604$		−	8.89898i		−	0.362094i
$605$	−36.3731	−	29.6985i	−1.47878	−	1.20742i
$606$	8.89898	−	6.29253i	0.361496	−	0.255617i
$607$	7.34847	+	7.34847i	0.298265	+	0.298265i	0.840334	−	0.542069i	$-0.182359\pi$
$607$	7.34847	+	7.34847i	0.298265	+	0.298265i	−0.542069	+	0.840334i	$0.682359\pi$
$608$	−1.73205	−	1.73205i	−0.0702439	−	0.0702439i
$609$	−44.6834	+	31.5959i	−1.81066	+	1.28033i
$610$	19.7980	−	2.00000i	0.801596	−	0.0809776i
$611$		−	5.94258i		−	0.240411i
$612$	9.50079	+	19.8931i	0.384047	+	0.804131i
$613$	−11.3485	+	11.3485i	−0.458360	+	0.458360i	−0.898117	−	0.439757i	$-0.855065\pi$
$613$	−11.3485	+	11.3485i	−0.458360	+	0.458360i	0.439757	+	0.898117i	$0.355065\pi$
$614$	−9.47090			−0.382214
$615$	21.5745	+	24.7899i	0.869969	+	0.999626i
$616$	−19.5959			−0.789542
$617$	−12.7600	+	12.7600i	−0.513699	+	0.513699i	−0.915658	−	0.401958i	$-0.868330\pi$
$617$	−12.7600	+	12.7600i	−0.513699	+	0.513699i	0.401958	+	0.915658i	$0.368330\pi$
$618$	2.65810	+	0.456058i	0.106924	+	0.0183453i
$619$		−	14.0454i		−	0.564533i	−0.959336	−	0.282266i	$-0.908914\pi$
$619$		−	14.0454i		−	0.564533i	0.959336	−	0.282266i	$-0.0910862\pi$
$620$	−6.92820	+	8.48528i	−0.278243	+	0.340777i
$621$	−5.00000	+	1.41421i	−0.200643	+	0.0567504i
$622$	−24.1464	−	24.1464i	−0.968184	−	0.968184i
$623$	−5.37113	−	5.37113i	−0.215190	−	0.215190i
$624$	−2.04989	−	2.89898i	−0.0820612	−	0.116052i
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$			27.0771i			1.08222i
$627$	4.05845	−	23.6544i	0.162079	−	0.944664i
$628$	−3.55051	+	3.55051i	−0.141681	+	0.141681i
$629$	25.4558			1.01499
$630$	−12.0716	−	19.8564i	−0.480943	−	0.791098i
$631$	19.5505			0.778294			0.389147	−	0.921176i	$-0.372770\pi$
$631$	19.5505			0.778294			0.389147	+	0.921176i	$0.372770\pi$
$632$	0.317837	−	0.317837i	0.0126429	−	0.0126429i
$633$	3.13306	−	18.2608i	0.124528	−	0.725802i
$634$		−	9.10102i		−	0.361448i
$635$	−2.68556	−	26.5843i	−0.106573	−	1.05497i
$636$	13.3485	+	18.8776i	0.529301	+	0.748545i
$637$	7.24745	+	7.24745i	0.287154	+	0.287154i
$638$	−36.4838	−	36.4838i	−1.44441	−	1.44441i
$639$	−6.14966	+	17.3939i	−0.243277	+	0.688091i
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$			13.5065i			0.533473i	0.963769	+	0.266737i	$0.0859454\pi$
$641$			13.5065i			0.533473i	−0.963769	+	0.266737i	$0.914055\pi$
$642$	−1.87956	−	0.322481i	−0.0741803	−	0.0127273i
$643$	−13.1010	+	13.1010i	−0.516654	+	0.516654i	−0.916557	−	0.399903i	$-0.869044\pi$
$643$	−13.1010	+	13.1010i	−0.516654	+	0.516654i	0.399903	+	0.916557i	$0.369044\pi$
$644$	3.46410			0.136505
$645$	2.61428	−	37.6967i	0.102937	−	1.48431i
$646$	18.0000			0.708201
$647$	−13.6493	+	13.6493i	−0.536610	+	0.536610i	−0.922532	−	0.385921i	$-0.873884\pi$
$647$	−13.6493	+	13.6493i	−0.536610	+	0.536610i	0.385921	+	0.922532i	$0.373884\pi$
$648$	0.949747	+	8.94975i	0.0373096	+	0.351579i
$649$		−	47.1918i		−	1.85244i
$650$	−10.0424	+	2.04989i	−0.393894	+	0.0804032i
$651$	−24.0000	+	16.9706i	−0.940634	+	0.665129i
$652$	4.00000	+	4.00000i	0.156652	+	0.156652i
$653$	−9.26382	−	9.26382i	−0.362521	−	0.362521i	0.502219	−	0.864740i	$-0.332517\pi$
$653$	−9.26382	−	9.26382i	−0.362521	−	0.362521i	−0.864740	+	0.502219i	$0.832517\pi$
$654$	−8.19955	+	5.79796i	−0.320628	+	0.226718i
$655$	19.7980	−	24.2474i	0.773570	−	0.947426i
$656$			8.48528i			0.331295i
$657$	−30.2407	+	14.4427i	−1.17980	+	0.563464i
$658$	7.10102	−	7.10102i	0.276827	−	0.276827i
$659$	4.09978			0.159705			0.0798523	−	0.996807i	$-0.474555\pi$
$659$	4.09978			0.159705			0.0798523	+	0.996807i	$0.474555\pi$
$660$	16.5266	−	14.3830i	0.643297	−	0.559858i
$661$	7.10102			0.276198			0.138099	−	0.990418i	$-0.455901\pi$
$661$	7.10102			0.276198			0.138099	+	0.990418i	$0.455901\pi$
$662$	−7.56388	+	7.56388i	−0.293978	+	0.293978i
$663$	25.7151	+	4.41201i	0.998691	+	0.171348i
$664$			2.00000i			0.0776151i
$665$	−18.8776	+	1.90702i	−0.732041	+	0.0739512i
$666$	9.79796	+	3.46410i	0.379663	+	0.134231i
$667$	6.44949	+	6.44949i	0.249725	+	0.249725i
$668$	−5.65685	−	5.65685i	−0.218870	−	0.218870i
$669$	−10.6780	−	15.1010i	−0.412837	−	0.583839i
$670$	2.69694	+	2.20204i	0.104192	+	0.0850723i
$671$			50.3402i			1.94336i
$672$	1.01461	−	5.91359i	0.0391395	−	0.228122i
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	−0.646918	−	0.762560i	$-0.723942\pi$
$673$	3.00000	−	3.00000i	0.115642	−	0.115642i	0.762560	+	0.646918i	$0.223942\pi$
$674$	−13.5065			−0.520249
$675$	24.7550	+	7.88599i	0.952821	+	0.303532i
$676$	8.79796			0.338383
$677$	22.6595	−	22.6595i	0.870876	−	0.870876i	−0.121692	−	0.992568i	$-0.538832\pi$
$677$	22.6595	−	22.6595i	0.870876	−	0.870876i	0.992568	+	0.121692i	$0.0388319\pi$
$678$	−0.980744	+	5.71619i	−0.0376652	+	0.219529i
$679$		−	21.7980i		−	0.836529i
$680$	12.7279	+	10.3923i	0.488094	+	0.398527i
$681$	10.8990	+	15.4135i	0.417650	+	0.590646i
$682$	−19.5959	−	19.5959i	−0.750366	−	0.750366i
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	0.783603	−	0.621262i	$-0.213380\pi$
$683$	4.24264	+	4.24264i	0.162340	+	0.162340i	−0.621262	+	0.783603i	$0.713380\pi$
$684$	6.92820	+	2.44949i	0.264906	+	0.0936586i
$685$	−10.3485	+	1.04541i	−0.395395	+	0.0399430i
$686$		−	6.92820i		−	0.264520i
$687$	−38.7461	−	6.64778i	−1.47826	−	0.253629i
$688$	6.89898	−	6.89898i	0.263021	−	0.263021i
$689$	27.3629			1.04244
$690$	−2.92152	+	2.54258i	−0.111220	+	0.0967944i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	10.5352	−	10.5352i	0.400487	−	0.400487i
$693$	53.0482	−	25.3354i	2.01514	−	0.962413i
$694$		−	19.7980i		−	0.751520i
$695$	15.1278	−	18.5276i	0.573828	−	0.702793i
$696$	12.8990	−	9.12096i	0.488935	−	0.345729i
$697$	−44.0908	−	44.0908i	−1.67006	−	1.67006i
$698$	15.5563	+	15.5563i	0.588817	+	0.588817i
$699$	21.0703	−	14.8990i	0.796953	−	0.563531i
$700$	−14.4495	−	9.55051i	−0.546139	−	0.360975i
$701$			43.0621i			1.62643i	0.581962	+	0.813216i	$0.302285\pi$
$701$			43.0621i			1.62643i	−0.581962	+	0.813216i	$0.697715\pi$
$702$	9.29734	+	5.19756i	0.350905	+	0.196169i
$703$	6.00000	−	6.00000i	0.226294	−	0.226294i
$704$	5.65685			0.213201
$705$	−0.776779	+	11.2008i	−0.0292552	+	0.421846i
$706$	−3.30306			−0.124312
$707$	15.4135	−	15.4135i	0.579684	−	0.579684i
$708$	14.2414	+	2.44344i	0.535224	+	0.0918300i
$709$		−	7.10102i		−	0.266684i	−0.991070	−	0.133342i	$-0.957429\pi$
$709$		−	7.10102i		−	0.266684i	0.991070	−	0.133342i	$-0.0425709\pi$
$710$	1.38211	+	13.6814i	0.0518695	+	0.513455i
$711$	−0.449490	+	1.27135i	−0.0168572	+	0.0476793i
$712$	1.55051	+	1.55051i	0.0581078	+	0.0581078i
$713$	3.46410	+	3.46410i	0.129732	+	0.129732i
$714$	25.4558	+	36.0000i	0.952661	+	1.34727i
$715$	−2.60612	−	25.7980i	−0.0974635	−	0.964789i
$716$		−	12.4422i		−	0.464987i
$717$	−1.88488	+	10.9859i	−0.0703922	+	0.410276i
$718$	−9.10102	+	9.10102i	−0.339647	+	0.339647i
$719$	−32.8769			−1.22610			−0.613050	−	0.790044i	$-0.710058\pi$
$719$	−32.8769			−1.22610			−0.613050	+	0.790044i	$0.710058\pi$
$720$	3.48477	+	5.73205i	0.129870	+	0.213621i
$721$	5.39388			0.200878
$722$	−9.19239	+	9.19239i	−0.342105	+	0.342105i
$723$	5.53538	−	32.2626i	0.205863	−	1.19986i
$724$		−	8.00000i		−	0.297318i
$725$	−9.12096	−	44.6834i	−0.338744	−	1.65950i
$726$	21.0000	+	29.6985i	0.779383	+	1.10221i
$727$	−0.247449	−	0.247449i	−0.00917736	−	0.00917736i	0.702503	−	0.711681i	$-0.252066\pi$
$727$	−0.247449	−	0.247449i	−0.00917736	−	0.00917736i	−0.711681	+	0.702503i	$0.752066\pi$
$728$	−5.02118	−	5.02118i	−0.186097	−	0.186097i
$729$	−14.1421	−	23.0000i	−0.523783	−	0.851852i
$730$	−15.7980	+	19.3485i	−0.584709	+	0.716119i
$731$			71.6963i			2.65178i
$732$	−15.1915	−	2.60645i	−0.561494	−	0.0963372i
$733$	9.14643	−	9.14643i	0.337831	−	0.337831i	−0.517719	−	0.855550i	$-0.673219\pi$
$733$	9.14643	−	9.14643i	0.337831	−	0.337831i	0.855550	+	0.517719i	$0.173219\pi$
$734$	−0.285729			−0.0105465
$735$	−12.7129	−	14.6076i	−0.468923	−	0.538809i
$736$	−1.00000			−0.0368605
$737$	−6.22831	+	6.22831i	−0.229423	+	0.229423i
$738$	−10.9706	−	22.9706i	−0.403832	−	0.845558i
$739$			1.30306i			0.0479339i	0.999713	+	0.0239669i	$0.00762965\pi$
$739$			1.30306i			0.0479339i	−0.999713	+	0.0239669i	$0.992370\pi$
$740$	7.70674	−	0.778539i	0.283305	−	0.0286197i
$741$	7.10102	−	5.02118i	0.260863	−	0.184458i
$742$	32.6969	+	32.6969i	1.20034	+	1.20034i
$743$	17.6062	+	17.6062i	0.645910	+	0.645910i	0.952002	−	0.306092i	$-0.0990215\pi$
$743$	17.6062	+	17.6062i	0.645910	+	0.645910i	−0.306092	+	0.952002i	$0.599021\pi$
$744$	6.92820	−	4.89898i	0.254000	−	0.179605i
$745$	28.8990	+	23.5959i	1.05878	+	0.864488i
$746$			10.6780i			0.390951i
$747$	−2.58579	−	5.41421i	−0.0946090	−	0.198096i
$748$	−29.3939	+	29.3939i	−1.07475	+	1.07475i
$749$	−3.81405			−0.139362
$750$	19.1962	−	2.55103i	0.700944	−	0.0931503i
$751$	−17.7526			−0.647800			−0.323900	−	0.946091i	$-0.604994\pi$
$751$	−17.7526			−0.647800			−0.323900	+	0.946091i	$0.604994\pi$
$752$	−2.04989	+	2.04989i	−0.0747517	+	0.0747517i
$753$	−45.6262	−	7.82821i	−1.66271	−	0.285276i
$754$		−	18.6969i		−	0.680902i
$755$	15.4135	+	12.5851i	0.560954	+	0.458017i
$756$	4.89898	+	17.3205i	0.178174	+	0.629941i
$757$	−10.6515	−	10.6515i	−0.387136	−	0.387136i	0.486528	−	0.873665i	$-0.338263\pi$
$757$	−10.6515	−	10.6515i	−0.387136	−	0.387136i	−0.873665	+	0.486528i	$0.838263\pi$
$758$	20.6096	+	20.6096i	0.748576	+	0.748576i
$759$	−5.65685	−	8.00000i	−0.205331	−	0.290382i
$760$	5.44949	−	0.550510i	0.197674	−	0.0199691i
$761$		−	14.4279i		−	0.523010i	−0.965202	−	0.261505i	$-0.915781\pi$
$761$		−	14.4279i		−	0.523010i	0.965202	−	0.261505i	$-0.0842187\pi$
$762$	−3.49989	+	20.3989i	−0.126788	+	0.738973i
$763$	−14.2020	+	14.2020i	−0.514148	+	0.514148i
$764$	−23.6130			−0.854290
$765$	−47.8920	−	11.6772i	−1.73154	−	0.422191i
$766$	−22.6969			−0.820074
$767$	12.0922	−	12.0922i	0.436626	−	0.436626i
$768$	−0.292893	+	1.70711i	−0.0105689	+	0.0615999i
$769$		−	0.696938i		−	0.0251322i	−0.999921	−	0.0125661i	$-0.996000\pi$
$769$		−	0.696938i		−	0.0251322i	0.999921	−	0.0125661i	$-0.00400003\pi$
$770$	27.7128	−	33.9411i	0.998700	−	1.22315i
$771$	25.5959	+	36.1981i	0.921814	+	1.30364i
$772$	7.89898	+	7.89898i	0.284290	+	0.284290i
$773$	−18.2740	−	18.2740i	−0.657271	−	0.657271i	0.297463	−	0.954733i	$-0.403860\pi$
$773$	−18.2740	−	18.2740i	−0.657271	−	0.657271i	−0.954733	+	0.297463i	$0.903860\pi$
$774$	−9.75663	+	27.5959i	−0.350695	+	0.991915i
$775$	−4.89898	−	24.0000i	−0.175977	−

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.292893 + 1.70711i) q^{3} -1.00000i q^{4} +(1.73205 + 1.41421i) q^{5} +(-1.00000 - 1.41421i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.82843 - 1.00000i) q^{9} +(-2.22474 + 0.224745i) q^{10} -5.65685i q^{11} +(1.70711 + 0.292893i) q^{12} +(1.44949 - 1.44949i) q^{13} +3.46410 q^{14} +(-2.92152 + 2.54258i) q^{15} -1.00000 q^{16} +(5.19615 - 5.19615i) q^{17} +(2.70711 - 1.29289i) q^{18} -2.44949i q^{19} +(1.41421 - 1.73205i) q^{20} +(4.89898 - 3.46410i) q^{21} +(4.00000 + 4.00000i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-1.41421 + 1.00000i) q^{24} +(1.00000 + 4.89898i) q^{25} +2.04989i q^{26} +(2.53553 - 4.53553i) q^{27} +(-2.44949 + 2.44949i) q^{28} -9.12096 q^{29} +(0.267949 - 3.86370i) q^{30} -4.89898 q^{31} +(0.707107 - 0.707107i) q^{32} +(9.65685 + 1.65685i) q^{33} +7.34847i q^{34} +(-0.778539 - 7.70674i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(2.44949 + 2.44949i) q^{37} +(1.73205 + 1.73205i) q^{38} +(2.04989 + 2.89898i) q^{39} +(0.224745 + 2.22474i) q^{40} -8.48528i q^{41} +(-1.01461 + 5.91359i) q^{42} +(-6.89898 + 6.89898i) q^{43} -5.65685 q^{44} +(-3.48477 - 5.73205i) q^{45} +1.00000 q^{46} +(2.04989 - 2.04989i) q^{47} +(0.292893 - 1.70711i) q^{48} +5.00000i q^{49} +(-4.17121 - 2.75699i) q^{50} +(7.34847 + 10.3923i) q^{51} +(-1.44949 - 1.44949i) q^{52} +(9.43879 + 9.43879i) q^{53} +(1.41421 + 5.00000i) q^{54} +(8.00000 - 9.79796i) q^{55} -3.46410i q^{56} +(4.18154 + 0.717439i) q^{57} +(6.44949 - 6.44949i) q^{58} +8.34242 q^{59} +(2.54258 + 2.92152i) q^{60} -8.89898 q^{61} +(3.46410 - 3.46410i) q^{62} +(4.47871 + 9.37769i) q^{63} +1.00000i q^{64} +(4.56048 - 0.460702i) q^{65} +(-8.00000 + 5.65685i) q^{66} +(-1.10102 - 1.10102i) q^{67} +(-5.19615 - 5.19615i) q^{68} +(1.41421 - 1.00000i) q^{69} +(6.00000 + 4.89898i) q^{70} -6.14966i q^{71} +(-1.29289 - 2.70711i) q^{72} +(7.89898 - 7.89898i) q^{73} -3.46410 q^{74} +(-8.65597 + 0.272229i) q^{75} -2.44949 q^{76} +(-13.8564 + 13.8564i) q^{77} +(-3.49938 - 0.600398i) q^{78} -0.449490i q^{79} +(-1.73205 - 1.41421i) q^{80} +(7.00000 + 5.65685i) q^{81} +(6.00000 + 6.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(-3.46410 - 4.89898i) q^{84} +(16.3485 - 1.65153i) q^{85} -9.75663i q^{86} +(2.67147 - 15.5704i) q^{87} +(4.00000 - 4.00000i) q^{88} +2.19275 q^{89} +(6.51727 + 1.58907i) q^{90} -7.10102 q^{91} +(-0.707107 + 0.707107i) q^{92} +(1.43488 - 8.36308i) q^{93} +2.89898i q^{94} +(3.46410 - 4.24264i) q^{95} +(1.00000 + 1.41421i) q^{96} +(4.44949 + 4.44949i) q^{97} +(-3.53553 - 3.53553i) q^{98} +(-5.65685 + 16.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q - 8q^{3} - 8q^{6} + O(q^{10}) \)	\( 8q - 8q^{3} - 8q^{6} - 8q^{10} + 8q^{12} - 8q^{13} - 8q^{15} - 8q^{16} + 16q^{18} + 32q^{22} + 8q^{25} - 8q^{27} + 16q^{30} + 32q^{33} - 8q^{36} - 8q^{40} - 16q^{43} + 8q^{46} + 8q^{48} + 8q^{52} + 64q^{55} + 32q^{58} + 8q^{60} - 32q^{61} - 64q^{66} - 48q^{67} + 48q^{70} - 16q^{72} + 24q^{73} - 8q^{75} + 8q^{78} + 56q^{81} + 48q^{82} + 72q^{85} - 32q^{87} + 32q^{88} - 8q^{90} - 96q^{91} + 8q^{96} + 16q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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