LMFDB - Embedded newform 690.2.i.f.323.12

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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.12
Character	$\chi$	$=$	690.323
Dual form			690.2.i.f.47.12

$q$-expansion

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.396187 - 1.68613i) q^{3} +1.00000i q^{4} +(-2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 + 2.17056i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.68607 - 1.33605i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.396187 - 1.68613i) q^{3} +1.00000i q^{4} +(-2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 + 2.17056i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.68607 - 1.33605i) q^{9} +(-0.965722 - 2.01677i) q^{10} +5.22806i q^{11} +(1.68613 + 0.396187i) q^{12} +(2.60057 + 2.60057i) q^{13} -3.06963 q^{14} +(-2.08868 + 3.26151i) q^{15} -1.00000 q^{16} +(-0.444150 - 0.444150i) q^{17} +(-0.954611 - 2.84407i) q^{18} +2.97966i q^{19} +(0.743206 - 2.10894i) q^{20} +(2.79989 + 4.51979i) q^{21} +(-3.69679 + 3.69679i) q^{22} +(0.707107 - 0.707107i) q^{23} +(0.912127 + 1.47242i) q^{24} +(3.89529 + 3.13476i) q^{25} +3.67776i q^{26} +(-3.31694 + 3.99974i) q^{27} +(-2.17056 - 2.17056i) q^{28} -1.70734 q^{29} +(-3.78315 + 0.829313i) q^{30} -5.25582 q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.81518 + 2.07129i) q^{33} -0.628123i q^{34} +(6.19075 - 2.96441i) q^{35} +(1.33605 - 2.68607i) q^{36} +(-2.75535 + 2.75535i) q^{37} +(-2.10693 + 2.10693i) q^{38} +(5.41521 - 3.35458i) q^{39} +(2.01677 - 0.965722i) q^{40} -6.96597i q^{41} +(-1.21615 + 5.17579i) q^{42} +(7.32093 + 7.32093i) q^{43} -5.22806 q^{44} +(4.67181 + 4.81395i) q^{45} +1.00000 q^{46} +(-6.05572 - 6.05572i) q^{47} +(-0.396187 + 1.68613i) q^{48} -2.42262i q^{49} +(0.537774 + 4.97100i) q^{50} +(-0.924861 + 0.572928i) q^{51} +(-2.60057 + 2.60057i) q^{52} +(-0.302305 + 0.302305i) q^{53} +(-5.17367 + 0.482816i) q^{54} +(3.88553 - 11.0257i) q^{55} -3.06963i q^{56} +(5.02409 + 1.18050i) q^{57} +(-1.20727 - 1.20727i) q^{58} -11.1739 q^{59} +(-3.26151 - 2.08868i) q^{60} -1.40994 q^{61} +(-3.71643 - 3.71643i) q^{62} +(8.73023 - 2.93030i) q^{63} -1.00000i q^{64} +(-3.55169 - 7.41721i) q^{65} +(4.76865 + 7.69790i) q^{66} +(3.64409 - 3.64409i) q^{67} +(0.444150 - 0.444150i) q^{68} +(-0.912127 - 1.47242i) q^{69} +(6.47368 + 2.28137i) q^{70} +4.61412i q^{71} +(2.84407 - 0.954611i) q^{72} +(0.698447 + 0.698447i) q^{73} -3.89665 q^{74} +(6.82888 - 5.32601i) q^{75} -2.97966 q^{76} +(-11.3478 - 11.3478i) q^{77} +(6.20118 + 1.45708i) q^{78} +11.7332i q^{79} +(2.10894 + 0.743206i) q^{80} +(5.42996 + 7.17743i) q^{81} +(4.92569 - 4.92569i) q^{82} +(9.38271 - 9.38271i) q^{83} +(-4.51979 + 2.79989i) q^{84} +(0.606592 + 1.26678i) q^{85} +10.3534i q^{86} +(-0.676425 + 2.87879i) q^{87} +(-3.69679 - 3.69679i) q^{88} -3.53601 q^{89} +(-0.100507 + 6.70745i) q^{90} -11.2894 q^{91} +(0.707107 + 0.707107i) q^{92} +(-2.08229 + 8.86201i) q^{93} -8.56408i q^{94} +(2.21450 - 6.28393i) q^{95} +(-1.47242 + 0.912127i) q^{96} +(-13.1840 + 13.1840i) q^{97} +(1.71305 - 1.71305i) q^{98} +(6.98493 - 14.0429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) $	$ 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	0.396187	−	1.68613i	0.228739	−	0.973488i
$3$	0.396187	−	1.68613i	0.228739	−	0.973488i
$4$			1.00000i			0.500000i
$5$	−2.10894	−	0.743206i	−0.943148	−	0.332372i
$5$	−2.10894	−	0.743206i	−0.943148	−	0.332372i
$6$	1.47242	−	0.912127i	0.601113	−	0.372374i
$7$	−2.17056	+	2.17056i	−0.820393	+	0.820393i	−0.986164	−	0.165771i	$-0.946989\pi$
$7$	−2.17056	+	2.17056i	−0.820393	+	0.820393i	0.165771	+	0.986164i	$0.446989\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.68607	−	1.33605i	−0.895357	−	0.445349i
$10$	−0.965722	−	2.01677i	−0.305388	−	0.637760i
$11$			5.22806i			1.57632i	0.615472	+	0.788159i	$0.288966\pi$
$11$			5.22806i			1.57632i	−0.615472	+	0.788159i	$0.711034\pi$
$12$	1.68613	+	0.396187i	0.486744	+	0.114369i
$13$	2.60057	+	2.60057i	0.721268	+	0.721268i	0.968863	−	0.247596i	$-0.0796405\pi$
$13$	2.60057	+	2.60057i	0.721268	+	0.721268i	−0.247596	+	0.968863i	$0.579641\pi$
$14$	−3.06963			−0.820393
$15$	−2.08868	+	3.26151i	−0.539295	+	0.842117i
$16$	−1.00000			−0.250000
$17$	−0.444150	−	0.444150i	−0.107722	−	0.107722i	0.651191	−	0.758914i	$-0.274270\pi$
$17$	−0.444150	−	0.444150i	−0.107722	−	0.107722i	−0.758914	+	0.651191i	$0.774270\pi$
$18$	−0.954611	−	2.84407i	−0.225004	−	0.670353i
$19$			2.97966i			0.683580i	0.939776	+	0.341790i	$0.111033\pi$
$19$			2.97966i			0.683580i	−0.939776	+	0.341790i	$0.888967\pi$
$20$	0.743206	−	2.10894i	0.166186	−	0.471574i
$21$	2.79989	+	4.51979i	0.610987	+	0.986298i
$22$	−3.69679	+	3.69679i	−0.788159	+	0.788159i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$	0.912127	+	1.47242i	0.186187	+	0.300557i
$25$	3.89529	+	3.13476i	0.779058	+	0.626952i
$26$			3.67776i			0.721268i
$27$	−3.31694	+	3.99974i	−0.638345	+	0.769751i
$28$	−2.17056	−	2.17056i	−0.410196	−	0.410196i
$29$	−1.70734			−0.317044			−0.158522	−	0.987355i	$-0.550673\pi$
$29$	−1.70734			−0.317044			−0.158522	+	0.987355i	$0.550673\pi$
$30$	−3.78315	+	0.829313i	−0.690706	+	0.151411i
$31$	−5.25582			−0.943974			−0.471987	−	0.881606i	$-0.656463\pi$
$31$	−5.25582			−0.943974			−0.471987	+	0.881606i	$0.656463\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	8.81518	+	2.07129i	1.53453	+	0.360565i
$34$		−	0.628123i		−	0.107722i
$35$	6.19075	−	2.96441i	1.04643	−	0.501077i
$36$	1.33605	−	2.68607i	0.222674	−	0.447679i
$37$	−2.75535	+	2.75535i	−0.452977	+	0.452977i	−0.896341	−	0.443365i	$-0.853785\pi$
$37$	−2.75535	+	2.75535i	−0.452977	+	0.452977i	0.443365	+	0.896341i	$0.353785\pi$
$38$	−2.10693	+	2.10693i	−0.341790	+	0.341790i
$39$	5.41521	−	3.35458i	0.867127	−	0.537163i
$40$	2.01677	−	0.965722i	0.318880	−	0.152694i
$41$		−	6.96597i		−	1.08790i	−0.839117	−	0.543951i	$-0.816928\pi$
$41$		−	6.96597i		−	1.08790i	0.839117	−	0.543951i	$-0.183072\pi$
$42$	−1.21615	+	5.17579i	−0.187656	+	0.798642i
$43$	7.32093	+	7.32093i	1.11643	+	1.11643i	0.992261	+	0.124170i	$0.0396268\pi$
$43$	7.32093	+	7.32093i	1.11643	+	1.11643i	0.124170	+	0.992261i	$0.460373\pi$
$44$	−5.22806			−0.788159
$45$	4.67181	+	4.81395i	0.696433	+	0.717622i
$46$	1.00000			0.147442
$47$	−6.05572	−	6.05572i	−0.883318	−	0.883318i	0.110553	−	0.993870i	$-0.464738\pi$
$47$	−6.05572	−	6.05572i	−0.883318	−	0.883318i	−0.993870	+	0.110553i	$0.964738\pi$
$48$	−0.396187	+	1.68613i	−0.0571847	+	0.243372i
$49$		−	2.42262i		−	0.346089i
$50$	0.537774	+	4.97100i	0.0760527	+	0.703005i
$51$	−0.924861	+	0.572928i	−0.129506	+	0.0802260i
$52$	−2.60057	+	2.60057i	−0.360634	+	0.360634i
$53$	−0.302305	+	0.302305i	−0.0415247	+	0.0415247i	−0.727564	−	0.686040i	$-0.759348\pi$
$53$	−0.302305	+	0.302305i	−0.0415247	+	0.0415247i	0.686040	+	0.727564i	$0.259348\pi$
$54$	−5.17367	+	0.482816i	−0.704048	+	0.0657029i
$55$	3.88553	−	11.0257i	0.523924	−	1.48670i
$56$		−	3.06963i		−	0.410196i
$57$	5.02409	+	1.18050i	0.665457	+	0.156361i
$58$	−1.20727	−	1.20727i	−0.158522	−	0.158522i
$59$	−11.1739			−1.45472			−0.727359	−	0.686257i	$-0.759253\pi$
$59$	−11.1739			−1.45472			−0.727359	+	0.686257i	$0.759253\pi$
$60$	−3.26151	−	2.08868i	−0.421059	−	0.269647i
$61$	−1.40994			−0.180525			−0.0902625	−	0.995918i	$-0.528771\pi$
$61$	−1.40994			−0.180525			−0.0902625	+	0.995918i	$0.528771\pi$
$62$	−3.71643	−	3.71643i	−0.471987	−	0.471987i
$63$	8.73023	−	2.93030i	1.09991	−	0.369183i
$64$		−	1.00000i		−	0.125000i
$65$	−3.55169	−	7.41721i	−0.440533	−	0.919991i
$66$	4.76865	+	7.69790i	0.586981	+	0.947546i
$67$	3.64409	−	3.64409i	0.445196	−	0.445196i	−0.448558	−	0.893754i	$-0.648062\pi$
$67$	3.64409	−	3.64409i	0.445196	−	0.445196i	0.893754	+	0.448558i	$0.148062\pi$
$68$	0.444150	−	0.444150i	0.0538611	−	0.0538611i
$69$	−0.912127	−	1.47242i	−0.109807	−	0.177259i
$70$	6.47368	+	2.28137i	0.773752	+	0.272676i
$71$			4.61412i			0.547596i	0.961787	+	0.273798i	$0.0882799\pi$
$71$			4.61412i			0.547596i	−0.961787	+	0.273798i	$0.911720\pi$
$72$	2.84407	−	0.954611i	0.335177	−	0.112502i
$73$	0.698447	+	0.698447i	0.0817471	+	0.0817471i	0.746798	−	0.665051i	$-0.231590\pi$
$73$	0.698447	+	0.698447i	0.0817471	+	0.0817471i	−0.665051	+	0.746798i	$0.731590\pi$
$74$	−3.89665			−0.452977
$75$	6.82888	−	5.32601i	0.788531	−	0.614995i
$76$	−2.97966			−0.341790
$77$	−11.3478	−	11.3478i	−1.29320	−	1.29320i
$78$	6.20118	+	1.45708i	0.702145	+	0.164982i
$79$			11.7332i			1.32009i	0.751225	+	0.660046i	$0.229463\pi$
$79$			11.7332i			1.32009i	−0.751225	+	0.660046i	$0.770537\pi$
$80$	2.10894	+	0.743206i	0.235787	+	0.0830930i
$81$	5.42996	+	7.17743i	0.603329	+	0.797493i
$82$	4.92569	−	4.92569i	0.543951	−	0.543951i
$83$	9.38271	−	9.38271i	1.02989	−	1.02989i	0.0303467	−	0.999539i	$-0.490339\pi$
$83$	9.38271	−	9.38271i	1.02989	−	1.02989i	0.999539	−	0.0303467i	$-0.00966113\pi$
$84$	−4.51979	+	2.79989i	−0.493149	+	0.305493i
$85$	0.606592	+	1.26678i	0.0657942	+	0.137402i
$86$			10.3534i			1.11643i
$87$	−0.676425	+	2.87879i	−0.0725204	+	0.308639i
$88$	−3.69679	−	3.69679i	−0.394080	−	0.394080i
$89$	−3.53601			−0.374816			−0.187408	−	0.982282i	$-0.560009\pi$
$89$	−3.53601			−0.374816			−0.187408	+	0.982282i	$0.560009\pi$
$90$	−0.100507	+	6.70745i	−0.0105944	+	0.707027i
$91$	−11.2894			−1.18345
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$	−2.08229	+	8.86201i	−0.215924	+	0.918947i
$94$		−	8.56408i		−	0.883318i
$95$	2.21450	−	6.28393i	0.227203	−	0.644717i
$96$	−1.47242	+	0.912127i	−0.150278	+	0.0930936i
$97$	−13.1840	+	13.1840i	−1.33863	+	1.33863i	−0.441237	+	0.897391i	$0.645460\pi$
$97$	−13.1840	+	13.1840i	−1.33863	+	1.33863i	−0.897391	+	0.441237i	$0.854540\pi$
$98$	1.71305	−	1.71305i	0.173044	−	0.173044i
$99$	6.98493	−	14.0429i	0.702012	−	1.41137i
$100$	−3.13476	+	3.89529i	−0.313476	+	0.389529i
$101$		−	10.8801i		−	1.08261i	−0.840825	−	0.541306i	$-0.817930\pi$
$101$		−	10.8801i		−	1.08261i	0.840825	−	0.541306i	$-0.182070\pi$
$102$	−1.05910	−	0.248854i	−0.104866	−	0.0246402i
$103$	−2.54969	−	2.54969i	−0.251228	−	0.251228i	0.570246	−	0.821474i	$-0.306848\pi$
$103$	−2.54969	−	2.54969i	−0.251228	−	0.251228i	−0.821474	+	0.570246i	$0.806848\pi$
$104$	−3.67776			−0.360634
$105$	−2.54568	−	11.6129i	−0.248433	−	1.13330i
$106$	−0.427523			−0.0415247
$107$	9.52639	+	9.52639i	0.920950	+	0.920950i	0.997097	−	0.0761462i	$-0.0242616\pi$
$107$	9.52639	+	9.52639i	0.920950	+	0.920950i	−0.0761462	+	0.997097i	$0.524262\pi$
$108$	−3.99974	−	3.31694i	−0.384875	−	0.319172i
$109$		−	8.20451i		−	0.785849i	−0.919571	−	0.392925i	$-0.871463\pi$
$109$		−	8.20451i		−	0.785849i	0.919571	−	0.392925i	$-0.128537\pi$
$110$	10.5438	−	5.04885i	1.00531	−	0.481389i
$111$	3.55425	+	5.73752i	0.337354	+	0.544581i
$112$	2.17056	−	2.17056i	0.205098	−	0.205098i
$113$	0.453030	−	0.453030i	0.0426174	−	0.0426174i	−0.685477	−	0.728094i	$-0.740406\pi$
$113$	0.453030	−	0.453030i	0.0426174	−	0.0426174i	0.728094	+	0.685477i	$0.240406\pi$
$114$	2.71783	+	4.38731i	0.254548	+	0.410909i
$115$	−2.01677	+	0.965722i	−0.188065	+	0.0900541i
$116$		−	1.70734i		−	0.158522i
$117$	−3.51083	−	10.4598i	−0.324576	−	0.967008i
$118$	−7.90115	−	7.90115i	−0.727359	−	0.727359i
$119$	1.92810			0.176749
$120$	−0.829313	−	3.78315i	−0.0757056	−	0.345353i
$121$	−16.3326			−1.48478
$122$	−0.996981	−	0.996981i	−0.0902625	−	0.0902625i
$123$	−11.7455	−	2.75983i	−1.05906	−	0.248845i
$124$		−	5.25582i		−	0.471987i
$125$	−5.88517	−	9.50604i	−0.526386	−	0.850246i
$126$	8.24524	+	4.10117i	0.734545	+	0.365361i
$127$	13.0705	−	13.0705i	1.15982	−	1.15982i	0.175307	−	0.984514i	$-0.443908\pi$
$127$	13.0705	−	13.0705i	1.15982	−	1.15982i	0.984514	−	0.175307i	$-0.0560919\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	15.2445	−	9.44358i	1.34220	−	0.831461i
$130$	2.73333	−	7.75618i	0.239729	−	0.680262i
$131$			3.19088i			0.278788i	0.990237	+	0.139394i	$0.0445155\pi$
$131$			3.19088i			0.278788i	−0.990237	+	0.139394i	$0.955484\pi$
$132$	−2.07129	+	8.81518i	−0.180283	+	0.767263i
$133$	−6.46751	−	6.46751i	−0.560804	−	0.560804i
$134$	5.15352			0.445196
$135$	9.96787	−	5.97006i	0.857897	−	0.513821i
$136$	0.628123			0.0538611
$137$	12.8044	+	12.8044i	1.09396	+	1.09396i	0.995102	+	0.0988556i	$0.0315182\pi$
$137$	12.8044	+	12.8044i	1.09396	+	1.09396i	0.0988556	+	0.995102i	$0.468482\pi$
$138$	0.396187	−	1.68613i	0.0337257	−	0.143533i
$139$			11.9592i			1.01437i	0.861839	+	0.507183i	$0.169313\pi$
$139$			11.9592i			1.01437i	−0.861839	+	0.507183i	$0.830687\pi$
$140$	2.96441	+	6.19075i	0.250538	+	0.523214i
$141$	−12.6099	+	7.81153i	−1.06195	+	0.657850i
$142$	−3.26268	+	3.26268i	−0.273798	+	0.273798i
$143$	−13.5959	+	13.5959i	−1.13695	+	1.13695i
$144$	2.68607	+	1.33605i	0.223839	+	0.111337i
$145$	3.60068	+	1.26890i	0.299020	+	0.105377i
$146$			0.987754i			0.0817471i
$147$	−4.08486	−	0.959812i	−0.336913	−	0.0791640i
$148$	−2.75535	−	2.75535i	−0.226488	−	0.226488i
$149$	−17.1561			−1.40548			−0.702740	−	0.711447i	$-0.748040\pi$
$149$	−17.1561			−1.40548			−0.702740	+	0.711447i	$0.748040\pi$
$150$	8.59481	+	1.06269i	0.701763	+	0.0867682i
$151$	16.9726			1.38121			0.690603	−	0.723234i	$-0.257345\pi$
$151$	16.9726			1.38121			0.690603	+	0.723234i	$0.257345\pi$
$152$	−2.10693	−	2.10693i	−0.170895	−	0.170895i
$153$	0.599613	+	1.78642i	0.0484759	+	0.144424i
$154$		−	16.0482i		−	1.29320i
$155$	11.0842	+	3.90616i	0.890308	+	0.313751i
$156$	3.35458	+	5.41521i	0.268582	+	0.433564i
$157$	11.7841	−	11.7841i	0.940473	−	0.940473i	−0.0578517	−	0.998325i	$-0.518425\pi$
$157$	11.7841	−	11.7841i	0.940473	−	0.940473i	0.998325	+	0.0578517i	$0.0184251\pi$
$158$	−8.29665	+	8.29665i	−0.660046	+	0.660046i
$159$	0.389956	+	0.629494i	0.0309255	+	0.0499221i
$160$	0.965722	+	2.01677i	0.0763470	+	0.159440i
$161$			3.06963i			0.241921i
$162$	−1.23565	+	8.91477i	−0.0970821	+	0.700411i
$163$	3.78878	+	3.78878i	0.296760	+	0.296760i	0.839743	−	0.542983i	$-0.182705\pi$
$163$	3.78878	+	3.78878i	0.296760	+	0.296760i	−0.542983	+	0.839743i	$0.682705\pi$
$164$	6.96597			0.543951
$165$	−17.0513	−	10.9197i	−1.32744	−	0.850100i
$166$	13.2692			1.02989
$167$	11.5545	+	11.5545i	0.894117	+	0.894117i	0.994908	−	0.100791i	$-0.0321372\pi$
$167$	11.5545	+	11.5545i	0.894117	+	0.894117i	−0.100791	+	0.994908i	$0.532137\pi$
$168$	−5.17579	−	1.21615i	−0.399321	−	0.0938279i
$169$			0.525898i			0.0404537i
$170$	−0.466825	+	1.32468i	−0.0358038	+	0.101598i
$171$	3.98096	−	8.00357i	0.304432	−	0.612048i
$172$	−7.32093	+	7.32093i	−0.558215	+	0.558215i
$173$	6.59928	−	6.59928i	0.501734	−	0.501734i	−0.410242	−	0.911977i	$-0.634556\pi$
$173$	6.59928	−	6.59928i	0.501734	−	0.501734i	0.911977	+	0.410242i	$0.134556\pi$
$174$	−2.51392	+	1.55731i	−0.190580	+	0.118059i
$175$	−15.2591	+	1.65077i	−1.15348	+	0.124786i
$176$		−	5.22806i		−	0.394080i
$177$	−4.42696	+	18.8407i	−0.332751	+	1.41615i
$178$	−2.50034	−	2.50034i	−0.187408	−	0.187408i
$179$	18.4232			1.37702			0.688508	−	0.725229i	$-0.258266\pi$
$179$	18.4232			1.37702			0.688508	+	0.725229i	$0.258266\pi$
$180$	−4.81395	+	4.67181i	−0.358811	+	0.348217i
$181$	4.84965			0.360472			0.180236	−	0.983623i	$-0.442314\pi$
$181$	4.84965			0.360472			0.180236	+	0.983623i	$0.442314\pi$
$182$	−7.98278	−	7.98278i	−0.591723	−	0.591723i
$183$	−0.558602	+	2.37735i	−0.0412931	+	0.175739i
$184$			1.00000i			0.0737210i
$185$	7.85867	−	3.76309i	0.577781	−	0.276668i
$186$	−7.73879	+	4.79398i	−0.567435	+	0.351512i
$187$	2.32204	−	2.32204i	0.169804	−	0.169804i
$188$	6.05572	−	6.05572i	0.441659	−	0.441659i
$189$	−1.48207	−	15.8813i	−0.107804	−	1.15519i
$190$	6.00929	−	2.87752i	0.435960	−	0.208757i
$191$		−	3.19418i		−	0.231123i	−0.993300	−	0.115561i	$-0.963133\pi$
$191$		−	3.19418i		−	0.231123i	0.993300	−	0.115561i	$-0.0368667\pi$
$192$	−1.68613	−	0.396187i	−0.121686	−	0.0285924i
$193$	−1.55053	−	1.55053i	−0.111610	−	0.111610i	0.649096	−	0.760706i	$-0.275147\pi$
$193$	−1.55053	−	1.55053i	−0.111610	−	0.111610i	−0.760706	+	0.649096i	$0.775147\pi$
$194$	−18.6449			−1.33863
$195$	−13.9135	+	3.05001i	−0.996368	+	0.218416i
$196$	2.42262			0.173044
$197$	16.0842	+	16.0842i	1.14595	+	1.14595i	0.987341	+	0.158614i	$0.0507025\pi$
$197$	16.0842	+	16.0842i	1.14595	+	1.14595i	0.158614	+	0.987341i	$0.449298\pi$
$198$	14.8689	−	4.99076i	1.05669	−	0.354678i
$199$			8.97499i			0.636220i	0.948054	+	0.318110i	$0.103048\pi$
$199$			8.97499i			0.636220i	−0.948054	+	0.318110i	$0.896952\pi$
$200$	−4.97100	+	0.537774i	−0.351502	+	0.0380263i
$201$	−4.70067	−	7.58815i	−0.331559	−	0.535227i
$202$	7.69341	−	7.69341i	0.541306	−	0.541306i
$203$	3.70587	−	3.70587i	0.260101	−	0.260101i
$204$	−0.572928	−	0.924861i	−0.0401130	−	0.0647532i
$205$	−5.17715	+	14.6908i	−0.361588	+	1.02605i
$206$		−	3.60580i		−	0.251228i
$207$	−2.84407	+	0.954611i	−0.197676	+	0.0663501i
$208$	−2.60057	−	2.60057i	−0.180317	−	0.180317i
$209$	−15.5778			−1.07754
$210$	6.41147	−	10.0116i	0.442434	−	0.690867i
$211$	−0.301249			−0.0207388			−0.0103694	−	0.999946i	$-0.503301\pi$
$211$	−0.301249			−0.0207388			−0.0103694	+	0.999946i	$0.503301\pi$
$212$	−0.302305	−	0.302305i	−0.0207624	−	0.0207624i
$213$	7.78001	+	1.82806i	0.533078	+	0.125256i
$214$			13.4723i			0.920950i
$215$	−9.99846	−	20.8804i	−0.681890	−	1.42403i
$216$	−0.482816	−	5.17367i	−0.0328515	−	0.352024i
$217$	11.4081	−	11.4081i	0.774430	−	0.774430i
$218$	5.80146	−	5.80146i	0.392925	−	0.392925i
$219$	1.45439	−	0.900957i	0.0982785	−	0.0608810i
$220$	11.0257	+	3.88553i	0.743351	+	0.261962i
$221$		−	2.31008i		−	0.155393i
$222$	−1.54381	+	6.57027i	−0.103613	+	0.440967i
$223$	12.8348	+	12.8348i	0.859480	+	0.859480i	0.991277	−	0.131797i	$-0.0420745\pi$
$223$	12.8348	+	12.8348i	0.859480	+	0.859480i	−0.131797	+	0.991277i	$0.542075\pi$
$224$	3.06963			0.205098
$225$	−6.27483	−	13.6245i	−0.418322	−	0.908299i
$226$	0.640680			0.0426174
$227$	9.96258	+	9.96258i	0.661239	+	0.661239i	0.955672	−	0.294433i	$-0.0951307\pi$
$227$	9.96258	+	9.96258i	0.661239	+	0.661239i	−0.294433	+	0.955672i	$0.595131\pi$
$228$	−1.18050	+	5.02409i	−0.0781806	+	0.332728i
$229$		−	17.6169i		−	1.16416i	−0.813133	−	0.582079i	$-0.802240\pi$
$229$		−	17.6169i		−	1.16416i	0.813133	−	0.582079i	$-0.197760\pi$
$230$	−2.10894	−	0.743206i	−0.139060	−	0.0490056i
$231$	−23.6297	+	14.6380i	−1.55472	+	0.963110i
$232$	1.20727	−	1.20727i	0.0792611	−	0.0792611i
$233$	−1.50132	+	1.50132i	−0.0983549	+	0.0983549i	−0.754572	−	0.656217i	$-0.772156\pi$
$233$	−1.50132	+	1.50132i	−0.0983549	+	0.0983549i	0.656217	+	0.754572i	$0.272156\pi$
$234$	4.91366	−	9.87872i	0.321216	−	0.645792i
$235$	8.27052	+	17.2718i	0.539509	+	1.12669i
$236$		−	11.1739i		−	0.727359i
$237$	19.7838	+	4.64856i	1.28509	+	0.301956i
$238$	1.36338	+	1.36338i	0.0883745	+	0.0883745i
$239$	−24.3097			−1.57246			−0.786232	−	0.617932i	$-0.787971\pi$
$239$	−24.3097			−1.57246			−0.786232	+	0.617932i	$0.787971\pi$
$240$	2.08868	−	3.26151i	0.134824	−	0.210529i
$241$	23.8969			1.53933			0.769667	−	0.638445i	$-0.220422\pi$
$241$	23.8969			1.53933			0.769667	+	0.638445i	$0.220422\pi$
$242$	−11.5489	−	11.5489i	−0.742390	−	0.742390i
$243$	14.2534	−	6.31201i	0.914354	−	0.404915i
$244$		−	1.40994i		−	0.0902625i
$245$	−1.80051	+	5.10918i	−0.115030	+	0.326413i
$246$	−6.35385	−	10.2568i	−0.405107	−	0.653952i
$247$	−7.74879	+	7.74879i	−0.493044	+	0.493044i
$248$	3.71643	−	3.71643i	0.235993	−	0.235993i
$249$	−12.1032	−	19.5378i	−0.767007	−	1.23816i
$250$	2.56034	−	10.8832i	0.161930	−	0.688316i
$251$		−	22.5045i		−	1.42047i	−0.703965	−	0.710234i	$-0.748589\pi$
$251$		−	22.5045i		−	1.42047i	0.703965	−	0.710234i	$-0.251411\pi$
$252$	2.93030	+	8.73023i	0.184592	+	0.549953i
$253$	3.69679	+	3.69679i	0.232415	+	0.232415i
$254$	18.4845			1.15982
$255$	2.37628	−	0.520910i	0.148809	−	0.0326207i
$256$	1.00000			0.0625000
$257$	17.0064	+	17.0064i	1.06083	+	1.06083i	0.998026	+	0.0628062i	$0.0200050\pi$
$257$	17.0064	+	17.0064i	1.06083	+	1.06083i	0.0628062	+	0.998026i	$0.479995\pi$
$258$	17.4571	+	4.10187i	1.08683	+	0.255371i
$259$		−	11.9613i		−	0.743238i
$260$	7.41721	−	3.55169i	0.459996	−	0.220267i
$261$	4.58603	+	2.28108i	0.283868	+	0.141195i
$262$	−2.25629	+	2.25629i	−0.139394	+	0.139394i
$263$	−17.9233	+	17.9233i	−1.10520	+	1.10520i	−0.111428	+	0.993773i	$0.535542\pi$
$263$	−17.9233	+	17.9233i	−1.10520	+	1.10520i	−0.993773	+	0.111428i	$0.964458\pi$
$264$	−7.69790	+	4.76865i	−0.473773	+	0.293490i
$265$	0.862218	−	0.412869i	0.0529656	−	0.0253623i
$266$		−	9.14644i		−	0.560804i
$267$	−1.40092	+	5.96217i	−0.0857350	+	0.364879i
$268$	3.64409	+	3.64409i	0.222598	+	0.222598i
$269$	−17.9945			−1.09714			−0.548571	−	0.836104i	$-0.684828\pi$
$269$	−17.9945			−1.09714			−0.548571	+	0.836104i	$0.684828\pi$
$270$	11.2698	+	2.82688i	0.685859	+	0.172038i
$271$	−14.0280			−0.852139			−0.426070	−	0.904690i	$-0.640102\pi$
$271$	−14.0280			−0.852139			−0.426070	+	0.904690i	$0.640102\pi$
$272$	0.444150	+	0.444150i	0.0269305	+	0.0269305i
$273$	−4.47270	+	19.0353i	−0.270700	+	1.15207i
$274$			18.1082i			1.09396i
$275$	−16.3887	+	20.3648i	−0.988276	+	1.22804i
$276$	1.47242	−	0.912127i	0.0886293	−	0.0549036i
$277$	−0.994150	+	0.994150i	−0.0597327	+	0.0597327i	−0.736342	−	0.676609i	$-0.763449\pi$
$277$	−0.994150	+	0.994150i	−0.0597327	+	0.0597327i	0.676609	+	0.736342i	$0.263449\pi$
$278$	−8.45642	+	8.45642i	−0.507183	+	0.507183i
$279$	14.1175	+	7.02203i	0.845194	+	0.420398i
$280$	−2.28137	+	6.47368i	−0.136338	+	0.386876i
$281$			15.9968i			0.954291i	0.878824	+	0.477145i	$0.158328\pi$
$281$			15.9968i			0.954291i	−0.878824	+	0.477145i	$0.841672\pi$
$282$	−14.4402	−	3.39298i	−0.859899	−	0.202049i
$283$	21.3172	+	21.3172i	1.26718	+	1.26718i	0.947540	+	0.319636i	$0.103561\pi$
$283$	21.3172	+	21.3172i	1.26718	+	1.26718i	0.319636	+	0.947540i	$0.396439\pi$
$284$	−4.61412			−0.273798
$285$	−9.71816	−	6.22355i	−0.575654	−	0.368651i
$286$	−19.2275			−1.13695
$287$	15.1200	+	15.1200i	0.892507	+	0.892507i
$288$	0.954611	+	2.84407i	0.0562510	+	0.167588i
$289$		−	16.6055i		−	0.976792i
$290$	1.64881	+	3.44331i	0.0968216	+	0.202198i
$291$	17.0065	+	27.4532i	0.996941	+	1.60933i
$292$	−0.698447	+	0.698447i	−0.0408735	+	0.0408735i
$293$	4.08472	−	4.08472i	0.238632	−	0.238632i	−0.577651	−	0.816284i	$-0.696031\pi$
$293$	4.08472	−	4.08472i	0.238632	−	0.238632i	0.816284	+	0.577651i	$0.196031\pi$
$294$	−2.20974	−	3.56712i	−0.128875	−	0.208039i
$295$	23.5651	+	8.30452i	1.37202	+	0.483508i
$296$		−	3.89665i		−	0.226488i
$297$	−20.9109	−	17.3411i	−1.21337	−	1.00623i
$298$	−12.1312	−	12.1312i	−0.702740	−	0.702740i
$299$	3.67776			0.212690
$300$	5.32601	+	6.82888i	0.307497	+	0.394266i
$301$	−31.7810			−1.83182
$302$	12.0014	+	12.0014i	0.690603	+	0.690603i
$303$	−18.3453	−	4.31057i	−1.05391	−	0.247636i
$304$		−	2.97966i		−	0.170895i
$305$	2.97349	+	1.04788i	0.170262	+	0.0600014i
$306$	−0.839202	+	1.68718i	−0.0479740	+	0.0964498i
$307$	15.3903	−	15.3903i	0.878369	−	0.878369i	−0.114997	−	0.993366i	$-0.536686\pi$
$307$	15.3903	−	15.3903i	0.878369	−	0.878369i	0.993366	+	0.114997i	$0.0366858\pi$
$308$	11.3478	−	11.3478i	0.646600	−	0.646600i
$309$	−5.30926	+	3.28895i	−0.302033	+	0.187102i
$310$	5.07567	+	10.5998i	0.288278	+	0.602029i
$311$			19.9984i			1.13401i	0.823715	+	0.567004i	$0.191898\pi$
$311$			19.9984i			1.13401i	−0.823715	+	0.567004i	$0.808102\pi$
$312$	−1.45708	+	6.20118i	−0.0824910	+	0.351073i
$313$	−21.4652	−	21.4652i	−1.21329	−	1.21329i	−0.969939	−	0.243348i	$-0.921754\pi$
$313$	−21.4652	−	21.4652i	−1.21329	−	1.21329i	−0.243348	−	0.969939i	$-0.578246\pi$
$314$	16.6652			0.940473
$315$	−20.5894	−	0.308520i	−1.16008	−	0.0173831i
$316$	−11.7332			−0.660046
$317$	−17.0015	−	17.0015i	−0.954897	−	0.954897i	0.0441291	−	0.999026i	$-0.485949\pi$
$317$	−17.0015	−	17.0015i	−0.954897	−	0.954897i	−0.999026	+	0.0441291i	$0.985949\pi$
$318$	−0.169379	+	0.720860i	−0.00949832	+	0.0404238i
$319$		−	8.92605i		−	0.499763i
$320$	−0.743206	+	2.10894i	−0.0415465	+	0.117894i
$321$	19.8370	−	12.2885i	1.10719	−	0.685877i
$322$	−2.17056	+	2.17056i	−0.120960	+	0.120960i
$323$	1.32341	−	1.32341i	0.0736367	−	0.0736367i
$324$	−7.17743	+	5.42996i	−0.398746	+	0.301664i
$325$	1.97780	+	18.2821i	0.109709	+	1.01411i
$326$			5.35815i			0.296760i
$327$	−13.8339	−	3.25052i	−0.765015	−	0.179754i
$328$	4.92569	+	4.92569i	0.271975	+	0.271975i
$329$	26.2886			1.44933
$330$	−4.33569	−	19.7785i	−0.238672	−	1.08877i
$331$	−33.1267			−1.82081			−0.910404	−	0.413720i	$-0.864229\pi$
$331$	−33.1267			−1.82081			−0.910404	+	0.413720i	$0.864229\pi$
$332$	9.38271	+	9.38271i	0.514943	+	0.514943i
$333$	11.0823	−	3.71979i	0.607309	−	0.203843i
$334$			16.3406i			0.894117i
$335$	−10.3935	+	4.97687i	−0.567857	+	0.271915i
$336$	−2.79989	−	4.51979i	−0.152747	−	0.246575i
$337$	−0.517894	+	0.517894i	−0.0282115	+	0.0282115i	−0.721072	−	0.692860i	$-0.756350\pi$
$337$	−0.517894	+	0.517894i	−0.0282115	+	0.0282115i	0.692860	+	0.721072i	$0.256350\pi$
$338$	−0.371866	+	0.371866i	−0.0202269	+	0.0202269i
$339$	−0.584382	−	0.943351i	−0.0317393	−	0.0512358i
$340$	−1.26678	+	0.606592i	−0.0687009	+	0.0328971i
$341$		−	27.4777i		−	1.48800i
$342$	8.47434	−	2.84441i	0.458240	−	0.153808i
$343$	−9.93545	−	9.93545i	−0.536464	−	0.536464i
$344$	−10.3534			−0.558215
$345$	0.829313	+	3.78315i	0.0446487	+	0.203678i
$346$	9.33280			0.501734
$347$	−15.1025	−	15.1025i	−0.810743	−	0.810743i	0.174003	−	0.984745i	$-0.444330\pi$
$347$	−15.1025	−	15.1025i	−0.810743	−	0.810743i	−0.984745	+	0.174003i	$0.944330\pi$
$348$	−2.87879	−	0.676425i	−0.154319	−	0.0362602i
$349$		−	1.81851i		−	0.0973424i	−0.998815	−	0.0486712i	$-0.984501\pi$
$349$		−	1.81851i		−	0.0973424i	0.998815	−	0.0486712i	$-0.0154986\pi$
$350$	−11.9571	−	9.62255i	−0.639133	−	0.514347i
$351$	−19.0275	+	1.77568i	−1.01561	+	0.0947788i
$352$	3.69679	−	3.69679i	0.197040	−	0.197040i
$353$	−16.7727	+	16.7727i	−0.892723	+	0.892723i	−0.994779	−	0.102056i	$-0.967458\pi$
$353$	−16.7727	+	16.7727i	−0.892723	+	0.892723i	0.102056	+	0.994779i	$0.467458\pi$
$354$	−16.4527	+	10.1920i	−0.874451	+	0.541700i
$355$	3.42925	−	9.73092i	0.182005	−	0.516464i
$356$		−	3.53601i		−	0.187408i
$357$	0.763890	−	3.25103i	0.0404294	−	0.172063i
$358$	13.0272	+	13.0272i	0.688508	+	0.688508i
$359$	−3.97799			−0.209950			−0.104975	−	0.994475i	$-0.533476\pi$
$359$	−3.97799			−0.209950			−0.104975	+	0.994475i	$0.533476\pi$
$360$	−6.70745	−	0.100507i	−0.353514	−	0.00529720i
$361$	10.1217			0.532719
$362$	3.42922	+	3.42922i	0.180236	+	0.180236i
$363$	−6.47076	+	27.5388i	−0.339627	+	1.44541i
$364$		−	11.2894i		−	0.591723i
$365$	−0.953896	−	1.99208i	−0.0499292	−	0.104270i
$366$	−2.07603	+	1.28605i	−0.108516	+	0.0672229i
$367$	−14.9574	+	14.9574i	−0.780770	+	0.780770i	−0.979961	−	0.199191i	$-0.936169\pi$
$367$	−14.9574	+	14.9574i	−0.780770	+	0.780770i	0.199191	+	0.979961i	$0.436169\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$	−9.30686	+	18.7111i	−0.484496	+	0.974061i
$370$	8.21783	+	2.89602i	0.427224	+	0.150557i
$371$		−	1.31234i		−	0.0681332i
$372$	−8.86201	−	2.08229i	−0.459474	−	0.107962i
$373$	−3.78362	−	3.78362i	−0.195909	−	0.195909i	0.602335	−	0.798243i	$-0.294237\pi$
$373$	−3.78362	−	3.78362i	−0.195909	−	0.195909i	−0.798243	+	0.602335i	$0.794237\pi$
$374$	3.28386			0.169804
$375$	−18.3601	+	6.15699i	−0.948109	+	0.317946i
$376$	8.56408			0.441659
$377$	−4.44004	−	4.44004i	−0.228674	−	0.228674i
$378$	10.1818	−	12.2777i	0.523693	−	0.631498i
$379$			0.706517i			0.0362913i	0.999835	+	0.0181457i	$0.00577626\pi$
$379$			0.706517i			0.0362913i	−0.999835	+	0.0181457i	$0.994224\pi$
$380$	6.28393	+	2.21450i	0.322359	+	0.113601i
$381$	−16.8602	−	27.2170i	−0.863776	−	1.39437i
$382$	2.25863	−	2.25863i	0.115561	−	0.115561i
$383$	−22.6285	+	22.6285i	−1.15626	+	1.15626i	−0.170991	+	0.985273i	$0.554697\pi$
$383$	−22.6285	+	22.6285i	−1.15626	+	1.15626i	−0.985273	+	0.170991i	$0.945303\pi$
$384$	−0.912127	−	1.47242i	−0.0465468	−	0.0751392i
$385$	15.4981	+	32.3656i	0.789856	+	1.64950i
$386$		−	2.19279i		−	0.111610i
$387$	−9.88343	−	29.4456i	−0.502403	−	1.49681i
$388$	−13.1840	−	13.1840i	−0.669314	−	0.669314i
$389$	−28.6741			−1.45384			−0.726918	−	0.686724i	$-0.759048\pi$
$389$	−28.6741			−1.45384			−0.726918	+	0.686724i	$0.759048\pi$
$390$	−11.9950	−	7.68166i	−0.607392	−	0.388976i
$391$	−0.628123			−0.0317655
$392$	1.71305	+	1.71305i	0.0865222	+	0.0865222i
$393$	5.38024	+	1.26419i	0.271397	+	0.0637697i
$394$			22.7465i			1.14595i
$395$	8.72021	−	24.7447i	0.438762	−	1.24504i
$396$	14.0429	+	6.98493i	0.705684	+	0.351006i
$397$	−4.16145	+	4.16145i	−0.208857	+	0.208857i	−0.803782	−	0.594924i	$-0.797182\pi$
$397$	−4.16145	+	4.16145i	−0.208857	+	0.208857i	0.594924	+	0.803782i	$0.297182\pi$
$398$	−6.34628	+	6.34628i	−0.318110	+	0.318110i
$399$	−13.4674	+	8.34272i	−0.674214	+	0.417658i
$400$	−3.89529	−	3.13476i	−0.194764	−	0.156738i
$401$			7.43533i			0.371303i	0.982616	+	0.185651i	$0.0594395\pi$
$401$			7.43533i			0.371303i	−0.982616	+	0.185651i	$0.940560\pi$
$402$	2.04176	−	8.68950i	0.101834	−	0.433393i
$403$	−13.6681	−	13.6681i	−0.680858	−	0.680858i
$404$	10.8801			0.541306
$405$	−6.11716	−	19.1724i	−0.303964	−	0.952683i
$406$	5.24089			0.260101
$407$	−14.4051	−	14.4051i	−0.714036	−	0.714036i
$408$	0.248854	−	1.05910i	0.0123201	−	0.0524331i
$409$			14.4432i			0.714170i	0.934072	+	0.357085i	$0.116229\pi$
$409$			14.4432i			0.714170i	−0.934072	+	0.357085i	$0.883771\pi$
$410$	−14.0488	+	6.72719i	−0.693821	+	0.332232i
$411$	26.6629	−	16.5170i	1.31518	−	0.814724i
$412$	2.54969	−	2.54969i	0.125614	−	0.125614i
$413$	24.2536	−	24.2536i	1.19344	−	1.19344i
$414$	−2.68607	−	1.33605i	−0.132013	−	0.0656631i
$415$	−26.7609	+	12.8143i	−1.31364	+	0.629030i
$416$		−	3.67776i		−	0.180317i
$417$	20.1648	+	4.73808i	0.987472	+	0.232025i
$418$	−11.0152	−	11.0152i	−0.538770	−	0.538770i
$419$	4.96433			0.242523			0.121262	−	0.992621i	$-0.461306\pi$
$419$	4.96433			0.242523			0.121262	+	0.992621i	$0.461306\pi$
$420$	11.6129	−	2.54568i	0.566650	−	0.124217i
$421$	−38.1579			−1.85970			−0.929851	−	0.367938i	$-0.880064\pi$
$421$	−38.1579			−1.85970			−0.929851	+	0.367938i	$0.880064\pi$
$422$	−0.213015	−	0.213015i	−0.0103694	−	0.0103694i
$423$	8.17537	+	24.3568i	0.397500	+	1.18427i
$424$		−	0.427523i		−	0.0207624i
$425$	−0.337788	−	3.12240i	−0.0163851	−	0.151458i
$426$	4.20867	+	6.79393i	0.203911	+	0.329167i
$427$	3.06036	−	3.06036i	0.148101	−	0.148101i
$428$	−9.52639	+	9.52639i	−0.460475	+	0.460475i
$429$	17.5380	+	28.3110i	0.846740	+	1.36687i
$430$	7.69468	−	21.8346i	0.371070	−	1.05296i
$431$			28.1762i			1.35720i	0.734508	+	0.678600i	$0.237413\pi$
$431$			28.1762i			1.35720i	−0.734508	+	0.678600i	$0.762587\pi$
$432$	3.31694	−	3.99974i	0.159586	−	0.192438i
$433$	13.8540	+	13.8540i	0.665781	+	0.665781i	0.956737	−	0.290956i	$-0.0939732\pi$
$433$	13.8540	+	13.8540i	0.665781	+	0.665781i	−0.290956	+	0.956737i	$0.593973\pi$
$434$	16.1334			0.774430
$435$	3.56608	−	5.56849i	0.170980	−	0.266988i
$436$	8.20451			0.392925
$437$	2.10693	+	2.10693i	0.100788	+	0.100788i
$438$	1.66548	+	0.391335i	0.0795798	+	0.0186987i
$439$		−	13.6748i		−	0.652661i	−0.945256	−	0.326330i	$-0.894188\pi$
$439$		−	13.6748i		−	0.652661i	0.945256	−	0.326330i	$-0.105812\pi$
$440$	5.04885	+	10.5438i	0.240694	+	0.502657i
$441$	−3.23674	+	6.50734i	−0.154130	+	0.309873i
$442$	1.63348	−	1.63348i	0.0776965	−	0.0776965i
$443$	24.2823	−	24.2823i	1.15369	−	1.15369i	0.167879	−	0.985808i	$-0.446308\pi$
$443$	24.2823	−	24.2823i	1.15369	−	1.15369i	0.985808	−	0.167879i	$-0.0536919\pi$
$444$	−5.73752	+	3.55425i	−0.272290	+	0.168677i
$445$	7.45724	+	2.62798i	0.353507	+	0.124578i
$446$			18.1511i			0.859480i
$447$	−6.79701	+	28.9274i	−0.321488	+	1.36822i
$448$	2.17056	+	2.17056i	0.102549	+	0.102549i
$449$	15.3176			0.722883			0.361442	−	0.932395i	$-0.382285\pi$
$449$	15.3176			0.722883			0.361442	+	0.932395i	$0.382285\pi$
$450$	5.19699	−	14.0709i	0.244988	−	0.663310i
$451$	36.4185			1.71488
$452$	0.453030	+	0.453030i	0.0213087	+	0.0213087i
$453$	6.72431	−	28.6179i	0.315936	−	1.34459i
$454$			14.0892i			0.661239i
$455$	23.8086	+	8.39032i	1.11616	+	0.393344i
$456$	−4.38731	+	2.71783i	−0.205454	+	0.127274i
$457$	0.783829	−	0.783829i	0.0366660	−	0.0366660i	−0.688536	−	0.725202i	$-0.741746\pi$
$457$	0.783829	−	0.783829i	0.0366660	−	0.0366660i	0.725202	+	0.688536i	$0.241746\pi$
$458$	12.4570	−	12.4570i	0.582079	−	0.582079i
$459$	3.24970	−	0.303268i	0.151683	−	0.0141553i
$460$	−0.965722	−	2.01677i	−0.0450270	−	0.0940326i
$461$			29.9101i			1.39305i	0.717531	+	0.696527i	$0.245272\pi$
$461$			29.9101i			1.39305i	−0.717531	+	0.696527i	$0.754728\pi$
$462$	−27.0593	−	6.35809i	−1.25891	−	0.295805i
$463$	12.8240	+	12.8240i	0.595982	+	0.595982i	0.939241	−	0.343259i	$-0.111531\pi$
$463$	12.8240	+	12.8240i	0.595982	+	0.595982i	−0.343259	+	0.939241i	$0.611531\pi$
$464$	1.70734			0.0792611
$465$	10.9777	−	17.1419i	0.509080	−	0.794937i
$466$	−2.12319			−0.0983549
$467$	27.4406	+	27.4406i	1.26980	+	1.26980i	0.946192	+	0.323607i	$0.104895\pi$
$467$	27.4406	+	27.4406i	1.26980	+	1.26980i	0.323607	+	0.946192i	$0.395105\pi$
$468$	10.4598	−	3.51083i	0.483504	−	0.162288i
$469$			15.8194i			0.730472i
$470$	−6.36488	+	18.0612i	−0.293590	+	0.833100i
$471$	−15.2008	−	24.5382i	−0.700417	−	1.13066i
$472$	7.90115	−	7.90115i	0.363680	−	0.363680i
$473$	−38.2742	+	38.2742i	−1.75985	+	1.75985i
$474$	10.7022	+	17.2763i	0.491568	+	0.793525i
$475$	−9.34051	+	11.6066i	−0.428572	+	0.532548i
$476$			1.92810i			0.0883745i
$477$	1.21590	−	0.408118i	0.0556724	−	0.0186865i
$478$	−17.1895	−	17.1895i	−0.786232	−	0.786232i
$479$	15.9073			0.726824			0.363412	−	0.931629i	$-0.381612\pi$
$479$	15.9073			0.726824			0.363412	+	0.931629i	$0.381612\pi$
$480$	3.78315	−	0.829313i	0.172676	−	0.0378528i
$481$	−14.3309			−0.653435
$482$	16.8977	+	16.8977i	0.769667	+	0.769667i
$483$	5.17579	+	1.21615i	0.235507	+	0.0553367i
$484$		−	16.3326i		−	0.742390i
$485$	37.6026	−	18.0058i	1.70745	−	0.817602i
$486$	14.5419	+	5.61539i	0.659635	+	0.254719i
$487$	17.8486	−	17.8486i	0.808797	−	0.808797i	−0.175655	−	0.984452i	$-0.556204\pi$
$487$	17.8486	−	17.8486i	0.808797	−	0.808797i	0.984452	+	0.175655i	$0.0562042\pi$
$488$	0.996981	−	0.996981i	0.0451312	−	0.0451312i
$489$	7.88945	−	4.88731i	0.356773	−	0.221012i
$490$	−4.88588	+	2.33958i	−0.220722	+	0.105691i
$491$		−	12.5148i		−	0.564787i	−0.959299	−	0.282393i	$-0.908872\pi$
$491$		−	12.5148i		−	0.564787i	0.959299	−	0.282393i	$-0.0911283\pi$
$492$	2.75983	−	11.7455i	0.124423	−	0.529530i
$493$	0.758313	+	0.758313i	0.0341527	+	0.0341527i
$494$	−10.9584			−0.493044
$495$	−25.1676	+	24.4245i	−1.13120	+	1.09780i
$496$	5.25582			0.235993
$497$	−10.0152	−	10.0152i	−0.449243	−	0.449243i
$498$	5.25707	−	22.3735i	0.235575	−	1.00258i
$499$			26.3804i			1.18095i	0.807056	+	0.590474i	$0.201059\pi$
$499$			26.3804i			1.18095i	−0.807056	+	0.590474i	$0.798941\pi$
$500$	9.50604	−	5.88517i	0.425123	−	0.263193i
$501$	24.0602	−	14.9047i	1.07493	−	0.665893i
$502$	15.9131	−	15.9131i	0.710234	−	0.710234i
$503$	−9.48821	+	9.48821i	−0.423059	+	0.423059i	−0.886255	−	0.463197i	$-0.846702\pi$
$503$	−9.48821	+	9.48821i	−0.423059	+	0.423059i	0.463197	+	0.886255i	$0.346702\pi$
$504$	−4.10117	+	8.24524i	−0.182681	+	0.367272i
$505$	−8.08618	+	22.9456i	−0.359830	+	1.02106i
$506$			5.22806i			0.232415i
$507$	0.886733	+	0.208354i	0.0393812	+	0.00925334i
$508$	13.0705	+	13.0705i	0.579911	+	0.579911i
$509$	14.3787			0.637323			0.318662	−	0.947869i	$-0.396767\pi$
$509$	14.3787			0.637323			0.318662	+	0.947869i	$0.396767\pi$
$510$	2.04863	+	1.31195i	0.0907147	+	0.0580940i
$511$	−3.03204			−0.134129
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−11.9179	−	9.88333i	−0.526186	−	0.436360i
$514$			24.0507i			1.06083i
$515$	3.48221	+	7.27210i	0.153444	+	0.320447i
$516$	9.44358	+	15.2445i	0.415730	+	0.671101i
$517$	31.6596	−	31.6596i	1.39239	−	1.39239i
$518$	8.45790	−	8.45790i	0.371619	−	0.371619i
$519$	−8.51270	−	13.7418i	−0.373666	−	0.603198i
$520$	7.75618	+	2.73333i	0.340131	+	0.119865i
$521$		−	12.6632i		−	0.554784i	−0.960757	−	0.277392i	$-0.910530\pi$
$521$		−	12.6632i		−	0.554784i	0.960757	−	0.277392i	$-0.0894701\pi$
$522$	1.62984	+	4.85578i	0.0713363	+	0.212532i
$523$	−9.41837	−	9.41837i	−0.411836	−	0.411836i	0.470541	−	0.882378i	$-0.344059\pi$
$523$	−9.41837	−	9.41837i	−0.411836	−	0.411836i	−0.882378	+	0.470541i	$0.844059\pi$
$524$	−3.19088			−0.139394
$525$	−3.26206	+	26.3829i	−0.142368	+	1.15144i
$526$	−25.3474			−1.10520
$527$	2.33437	+	2.33437i	0.101687	+	0.101687i
$528$	−8.81518	−	2.07129i	−0.383632	−	0.0901413i
$529$		−	1.00000i		−	0.0434783i
$530$	0.901622	+	0.317738i	0.0391640	+	0.0138017i
$531$	30.0139	+	14.9289i	1.30249	+	0.647858i
$532$	6.46751	−	6.46751i	0.280402	−	0.280402i
$533$	18.1155	−	18.1155i	0.784668	−	0.784668i
$534$	−5.20649	+	3.22529i	−0.225307	+	0.139572i
$535$	−13.0105	−	27.1707i	−0.562495	−	1.17469i
$536$			5.15352i			0.222598i
$537$	7.29904	−	31.0639i	0.314977	−	1.34051i
$538$	−12.7240	−	12.7240i	−0.548571	−	0.548571i
$539$	12.6656			0.545546
$540$	5.97006	+	9.96787i	0.256911	+	0.428949i
$541$	9.84624			0.423323			0.211661	−	0.977343i	$-0.432113\pi$
$541$	9.84624			0.423323			0.211661	+	0.977343i	$0.432113\pi$
$542$	−9.91928	−	9.91928i	−0.426070	−	0.426070i
$543$	1.92137	−	8.17714i	0.0824538	−	0.350915i
$544$			0.628123i			0.0269305i
$545$	−6.09764	+	17.3028i	−0.261194	+	0.741173i
$546$	−16.6227	+	10.2973i	−0.711385	+	0.440685i
$547$	−24.2038	+	24.2038i	−1.03488	+	1.03488i	−0.0355120	+	0.999369i	$0.511306\pi$
$547$	−24.2038	+	24.2038i	−1.03488	+	1.03488i	−0.999369	+	0.0355120i	$0.988694\pi$
$548$	−12.8044	+	12.8044i	−0.546979	+	0.546979i
$549$	3.78721	+	1.88375i	0.161634	+	0.0803966i
$550$	−25.9886	+	2.81151i	−1.10816	+	0.119883i
$551$		−	5.08727i		−	0.216725i
$552$	1.68613	+	0.396187i	0.0717665	+	0.0168629i
$553$	−25.4676	−	25.4676i	−1.08299	−	1.08299i
$554$	−1.40594			−0.0597327
$555$	−3.23155	−	14.7416i	−0.137171	−	0.625748i
$556$	−11.9592			−0.507183
$557$	−19.7073	−	19.7073i	−0.835026	−	0.835026i	0.153174	−	0.988199i	$-0.451051\pi$
$557$	−19.7073	−	19.7073i	−0.835026	−	0.835026i	−0.988199	+	0.153174i	$0.951051\pi$
$558$	5.01727	+	14.9479i	0.212398	+	0.632796i
$559$			38.0771i			1.61049i
$560$	−6.19075	+	2.96441i	−0.261607	+	0.125269i
$561$	−2.99530	−	4.83523i	−0.126462	−	0.204143i
$562$	−11.3115	+	11.3115i	−0.477145	+	0.477145i
$563$	6.01209	−	6.01209i	0.253379	−	0.253379i	−0.568975	−	0.822355i	$-0.692660\pi$
$563$	6.01209	−	6.01209i	0.253379	−	0.253379i	0.822355	+	0.568975i	$0.192660\pi$
$564$	−7.81153	−	12.6099i	−0.328925	−	0.530974i
$565$	−1.29211	+	0.618719i	−0.0543594	+	0.0260297i
$566$			30.1471i			1.26718i
$567$	−27.3650	−	3.79300i	−1.14922	−	0.159291i
$568$	−3.26268	−	3.26268i	−0.136899	−	0.136899i
$569$	−1.31647			−0.0551895			−0.0275947	−	0.999619i	$-0.508785\pi$
$569$	−1.31647			−0.0551895			−0.0275947	+	0.999619i	$0.508785\pi$
$570$	−2.47107	−	11.2725i	−0.103502	−	0.472153i
$571$	17.5617			0.734934			0.367467	−	0.930036i	$-0.380225\pi$
$571$	17.5617			0.734934			0.367467	+	0.930036i	$0.380225\pi$
$572$	−13.5959	−	13.5959i	−0.568474	−	0.568474i
$573$	−5.38581	−	1.26549i	−0.224995	−	0.0528668i
$574$			21.3829i			0.892507i
$575$	4.97100	−	0.537774i	0.207305	−	0.0224267i
$576$	−1.33605	+	2.68607i	−0.0556686	+	0.111920i
$577$	16.0820	−	16.0820i	0.669504	−	0.669504i	−0.288097	−	0.957601i	$-0.593023\pi$
$577$	16.0820	−	16.0820i	0.669504	−	0.669504i	0.957601	+	0.288097i	$0.0930225\pi$
$578$	11.7418	−	11.7418i	0.488396	−	0.488396i
$579$	−3.22871	+	2.00010i	−0.134180	+	0.0831214i
$580$	−1.26890	+	3.60068i	−0.0526883	+	0.149510i
$581$			40.7314i			1.68982i
$582$	−7.38688	+	31.4378i	−0.306196	+	1.30314i
$583$	−1.58046	−	1.58046i	−0.0654562	−	0.0654562i
$584$	−0.987754			−0.0408735
$585$	−0.369642	+	24.6684i	−0.0152828	+	1.01991i
$586$	5.77667			0.238632
$587$	−9.61314	−	9.61314i	−0.396777	−	0.396777i	0.480318	−	0.877095i	$-0.340521\pi$
$587$	−9.61314	−	9.61314i	−0.396777	−	0.396777i	−0.877095	+	0.480318i	$0.840521\pi$
$588$	0.959812	−	4.08486i	0.0395820	−	0.168457i
$589$		−	15.6605i		−	0.645282i
$590$	10.7909	+	22.5353i	0.444254	+	0.927762i
$591$	33.4925	−	20.7478i	1.37770	−	0.853448i
$592$	2.75535	−	2.75535i	0.113244	−	0.113244i
$593$	12.3638	−	12.3638i	0.507719	−	0.507719i	−0.406106	−	0.913826i	$-0.633114\pi$
$593$	12.3638	−	12.3638i	0.507719	−	0.507719i	0.913826	+	0.406106i	$0.133114\pi$
$594$	−2.52419	−	27.0483i	−0.103569	−	1.10980i
$595$	−4.06626	−	1.43298i	−0.166701	−	0.0587464i
$596$		−	17.1561i		−	0.702740i
$597$	15.1330	+	3.55578i	0.619353	+	0.145528i
$598$	2.60057	+	2.60057i	0.106345	+	0.106345i
$599$	48.6613			1.98825			0.994123	−	0.108255i	$-0.0345263\pi$
$599$	48.6613			1.98825			0.994123	+	0.108255i	$0.0345263\pi$
$600$	−1.06269	+	8.59481i	−0.0433841	+	0.350881i
$601$	−28.4823			−1.16182			−0.580909	−	0.813969i	$-0.697303\pi$
$601$	−28.4823			−1.16182			−0.580909	+	0.813969i	$0.697303\pi$
$602$	−22.4725	−	22.4725i	−0.915912	−	0.915912i
$603$	−14.6570	+	4.91961i	−0.596877	+	0.200342i
$604$			16.9726i			0.690603i
$605$	34.4445	+	12.1385i	1.40037	+	0.493499i
$606$	−9.92406	−	16.0201i	−0.403137	−	0.650773i
$607$	10.2267	−	10.2267i	0.415088	−	0.415088i	−0.468419	−	0.883507i	$-0.655176\pi$
$607$	10.2267	−	10.2267i	0.415088	−	0.415088i	0.883507	+	0.468419i	$0.155176\pi$
$608$	2.10693	−	2.10693i	0.0854475	−	0.0854475i
$609$	−4.78036	−	7.71679i	−0.193710	−	0.312700i
$610$	1.36161	+	2.84354i	0.0551302	+	0.115132i
$611$		−	31.4966i		−	1.27422i
$612$	−1.78642	+	0.599613i	−0.0722119	+	0.0242379i
$613$	4.21128	+	4.21128i	0.170092	+	0.170092i	0.787020	−	0.616928i	$-0.211623\pi$
$613$	4.21128	+	4.21128i	0.170092	+	0.170092i	−0.616928	+	0.787020i	$0.711623\pi$
$614$	21.7651			0.878369
$615$	22.7196	+	14.5497i	0.916141	+	0.586700i
$616$	16.0482			0.646600
$617$	1.18781	+	1.18781i	0.0478194	+	0.0478194i	0.730612	−	0.682793i	$-0.239235\pi$
$617$	1.18781	+	1.18781i	0.0478194	+	0.0478194i	−0.682793	+	0.730612i	$0.739235\pi$
$618$	−6.07986	−	1.42857i	−0.244568	−	0.0574657i
$619$		−	9.65709i		−	0.388151i	−0.980987	−	0.194076i	$-0.937829\pi$
$619$		−	9.65709i		−	0.388151i	0.980987	−	0.194076i	$-0.0621707\pi$
$620$	−3.90616	+	11.0842i	−0.156875	+	0.445154i
$621$	0.482816	+	5.17367i	0.0193747	+	0.207612i
$622$	−14.1410	+	14.1410i	−0.567004	+	0.567004i
$623$	7.67510	−	7.67510i	0.307497	−	0.307497i
$624$	−5.41521	+	3.35458i	−0.216782	+	0.134291i
$625$	5.34654	+	24.4216i	0.213862	+	0.976864i
$626$		−	30.3564i		−	1.21329i
$627$	−6.17173	+	26.2662i	−0.246475	+	1.04897i
$628$	11.7841	+	11.7841i	0.470237	+	0.470237i
$629$	2.44758			0.0975913
$630$	−14.3407	−	14.7771i	−0.571349	−	0.588732i
$631$	−20.1398			−0.801754			−0.400877	−	0.916132i	$-0.631295\pi$
$631$	−20.1398			−0.801754			−0.400877	+	0.916132i	$0.631295\pi$
$632$	−8.29665	−	8.29665i	−0.330023	−	0.330023i
$633$	−0.119351	+	0.507945i	−0.00474377	+	0.0201890i
$634$		−	24.0437i		−	0.954897i
$635$	−37.2791	+	17.8509i	−1.47938	+	0.708391i
$636$	−0.629494	+	0.389956i	−0.0249611	+	0.0154627i
$637$	6.30019	−	6.30019i	0.249623	−	0.249623i
$638$	6.31167	−	6.31167i	0.249881	−	0.249881i
$639$	6.16468	−	12.3939i	0.243871	−	0.490294i
$640$	−2.01677	+	0.965722i	−0.0797200	+	0.0381735i
$641$		−	7.77971i		−	0.307280i	−0.988127	−	0.153640i	$-0.950900\pi$
$641$		−	7.77971i		−	0.307280i	0.988127	−	0.153640i	$-0.0490996\pi$
$642$	22.7161	+	5.33757i	0.896534	+	0.210657i
$643$	−22.1643	−	22.1643i	−0.874075	−	0.874075i	0.118838	−	0.992914i	$-0.462083\pi$
$643$	−22.1643	−	22.1643i	−0.874075	−	0.874075i	−0.992914	+	0.118838i	$0.962083\pi$
$644$	−3.06963			−0.120960
$645$	−39.1683	+	8.58617i	−1.54225	+	0.338080i
$646$	1.87159			0.0736367
$647$	7.24949	+	7.24949i	0.285007	+	0.285007i	0.835102	−	0.550095i	$-0.185409\pi$
$647$	7.24949	+	7.24949i	0.285007	+	0.285007i	−0.550095	+	0.835102i	$0.685409\pi$
$648$	−8.91477	−	1.23565i	−0.350205	−	0.0485410i
$649$		−	58.4178i		−	2.29310i
$650$	−11.5289	+	14.3259i	−0.452200	+	0.561909i
$651$	−14.7157	−	23.7552i	−0.576756	−	0.931040i
$652$	−3.78878	+	3.78878i	−0.148380	+	0.148380i
$653$	18.2696	−	18.2696i	0.714944	−	0.714944i	−0.252621	−	0.967565i	$-0.581293\pi$
$653$	18.2696	−	18.2696i	0.714944	−	0.714944i	0.967565	+	0.252621i	$0.0812926\pi$
$654$	−7.48356	−	12.0805i	−0.292630	−	0.472385i
$655$	2.37148	−	6.72938i	0.0926615	−	0.262939i
$656$			6.96597i			0.271975i
$657$	−0.942921	−	2.80924i	−0.0367868	−	0.109599i
$658$	18.5888	+	18.5888i	0.724667	+	0.724667i
$659$	23.0114			0.896399			0.448199	−	0.893934i	$-0.352066\pi$
$659$	23.0114			0.896399			0.448199	+	0.893934i	$0.352066\pi$
$660$	10.9197	−	17.0513i	0.425050	−	0.663722i
$661$	−21.2264			−0.825611			−0.412806	−	0.910819i	$-0.635451\pi$
$661$	−21.2264			−0.825611			−0.412806	+	0.910819i	$0.635451\pi$
$662$	−23.4241	−	23.4241i	−0.910404	−	0.910404i
$663$	−3.89510	−	0.915226i	−0.151273	−	0.0355444i
$664$			13.2692i			0.514943i
$665$	8.83292	+	18.4463i	0.342526	+	0.715317i
$666$	10.4667	+	5.20611i	0.405576	+	0.201733i
$667$	−1.20727	+	1.20727i	−0.0467456	+	0.0467456i
$668$	−11.5545	+	11.5545i	−0.447058	+	0.447058i
$669$	26.7261	−	16.5561i	1.03329	−	0.640097i
$670$	−10.8685	−	3.83013i	−0.419886	−	0.147971i
$671$		−	7.37127i		−	0.284565i
$672$	1.21615	−	5.17579i	0.0469139	−	0.199661i
$673$	−2.23113	−	2.23113i	−0.0860038	−	0.0860038i	0.662796	−	0.748800i	$-0.269370\pi$
$673$	−2.23113	−	2.23113i	−0.0860038	−	0.0860038i	−0.748800	+	0.662796i	$0.769370\pi$
$674$	−0.732413			−0.0282115
$675$	−25.4587	+	5.18234i	−0.979904	+	0.199468i
$676$	−0.525898			−0.0202269
$677$	−8.73195	−	8.73195i	−0.335596	−	0.335596i	0.519111	−	0.854707i	$-0.326263\pi$
$677$	−8.73195	−	8.73195i	−0.335596	−	0.335596i	−0.854707	+	0.519111i	$0.826263\pi$
$678$	0.253829	−	1.08027i	0.00974826	−	0.0414876i
$679$		−	57.2330i		−	2.19640i
$680$	−1.32468	−	0.466825i	−0.0507990	−	0.0179019i
$681$	20.7453	−	12.8512i	0.794960	−	0.492457i
$682$	19.4297	−	19.4297i	0.744002	−	0.744002i
$683$	7.60796	−	7.60796i	0.291110	−	0.291110i	−0.546408	−	0.837519i	$-0.684005\pi$
$683$	7.60796	−	7.60796i	0.291110	−	0.291110i	0.837519	+	0.546408i	$0.184005\pi$
$684$	8.00357	+	3.98096i	0.306024	+	0.152216i
$685$	−17.4875	−	36.5202i	−0.668163	−	1.39536i
$686$		−	14.0509i		−	0.536464i
$687$	−29.7044	−	6.97959i	−1.13329	−	0.266288i
$688$	−7.32093	−	7.32093i	−0.279108	−	0.279108i
$689$	−1.57233			−0.0599009
$690$	−2.08868	+	3.26151i	−0.0795147	+	0.124163i
$691$	48.5623			1.84740			0.923698	−	0.383120i	$-0.125151\pi$
$691$	48.5623			1.84740			0.923698	+	0.383120i	$0.125151\pi$
$692$	6.59928	+	6.59928i	0.250867	+	0.250867i
$693$	15.3198	+	45.6421i	0.581951	+	1.73380i
$694$		−	21.3581i		−	0.810743i
$695$	8.88815	−	25.2213i	0.337147	−	0.956697i
$696$	−1.55731	−	2.51392i	−0.0590296	−	0.0952898i
$697$	−3.09394	+	3.09394i	−0.117191	+	0.117191i
$698$	1.28588	−	1.28588i	0.0486712	−	0.0486712i
$699$	1.93662	+	3.12623i	0.0732497	+	0.118245i
$700$	−1.65077	−	15.2591i	−0.0623931	−	0.576740i
$701$		−	18.5789i		−	0.701715i	−0.936429	−	0.350858i	$-0.885890\pi$
$701$		−	18.5789i		−	0.701715i	0.936429	−	0.350858i	$-0.114110\pi$
$702$	−14.7101	−	12.1989i	−0.555196	−	0.460417i
$703$	−8.21000	−	8.21000i	−0.309646	−	0.309646i
$704$	5.22806			0.197040
$705$	32.3992	−	7.10230i	1.22023	−	0.267488i
$706$	−23.7202			−0.892723
$707$	23.6159	+	23.6159i	0.888168	+	0.888168i
$708$	−18.8407	−	4.42696i	−0.708076	−	0.166375i
$709$			40.6579i			1.52694i	0.645844	+	0.763469i	$0.276505\pi$
$709$			40.6579i			1.52694i	−0.645844	+	0.763469i	$0.723495\pi$
$710$	9.30564	−	4.45596i	0.349235	−	0.167229i
$711$	15.6761	−	31.5163i	0.587901	−	1.18195i
$712$	2.50034	−	2.50034i	0.0937041	−	0.0937041i
$713$	−3.71643	+	3.71643i	−0.139181	+	0.139181i
$714$	2.83898	−	1.75868i	0.106246	−	0.0658168i
$715$	38.7776	−	18.5684i	1.45020	−	0.694420i
$716$			18.4232i			0.688508i
$717$	−9.63119	+	40.9893i	−0.359683	+	1.53077i
$718$	−2.81286	−	2.81286i	−0.104975	−	0.104975i
$719$	−20.2760			−0.756166			−0.378083	−	0.925772i	$-0.623417\pi$
$719$	−20.2760			−0.756166			−0.378083	+	0.925772i	$0.623417\pi$
$720$	−4.67181	−	4.81395i	−0.174108	−	0.179405i
$721$	11.0685			0.412212
$722$	7.15709	+	7.15709i	0.266359	+	0.266359i
$723$	9.46765	−	40.2933i	0.352106	−	1.49852i
$724$			4.84965i			0.180236i
$725$	−6.65057	−	5.35209i	−0.246996	−	0.198772i
$726$	−24.0484	+	14.8974i	−0.892520	+	0.552894i
$727$	36.0659	−	36.0659i	1.33761	−	1.33761i	0.439239	−	0.898370i	$-0.355248\pi$
$727$	36.0659	−	36.0659i	1.33761	−	1.33761i	0.898370	−	0.439239i	$-0.144752\pi$
$728$	7.98278	−	7.98278i	0.295861	−	0.295861i
$729$	−4.99586	−	26.5338i	−0.185032	−	0.982733i
$730$	0.734105	−	2.08312i	0.0271704	−	0.0770996i
$731$		−	6.50318i		−	0.240529i
$732$	−2.37735	−	0.558602i	−0.0878694	−	0.0206465i
$733$	−13.8202	−	13.8202i	−0.510462	−	0.510462i	0.404206	−	0.914668i	$-0.367548\pi$
$733$	−13.8202	−	13.8202i	−0.510462	−	0.510462i	−0.914668	+	0.404206i	$0.867548\pi$
$734$	−21.1530			−0.780770
$735$	7.90140	+	5.06008i	0.291447	+	0.186644i
$736$	−1.00000			−0.0368605
$737$	19.0515	+	19.0515i	0.701771	+	0.701771i
$738$	−19.8117	+	6.64980i	−0.729278	+	0.244782i
$739$			18.0843i			0.665240i	0.943061	+	0.332620i	$0.107933\pi$
$739$			18.0843i			0.665240i	−0.943061	+	0.332620i	$0.892067\pi$
$740$	3.76309	+	7.85867i	0.138334	+	0.288891i
$741$	9.99550	+	16.1354i	0.367194	+	0.592751i
$742$	0.927963	−	0.927963i	0.0340666	−	0.0340666i
$743$	−14.2366	+	14.2366i	−0.522291	+	0.522291i	−0.918263	−	0.395972i	$-0.870408\pi$
$743$	−14.2366	+	14.2366i	−0.522291	+	0.522291i	0.395972	+	0.918263i	$0.370408\pi$
$744$	−4.79398	−	7.73879i	−0.175756	−	0.283718i
$745$	36.1812	+	12.7505i	1.32558	+	0.467142i
$746$		−	5.35085i		−	0.195909i
$747$	−37.7384	+	12.6669i	−1.38077	+	0.463457i
$748$	2.32204	+	2.32204i	0.0849022	+	0.0849022i
$749$	−41.3551			−1.51108
$750$	−17.3362	−	8.62887i	−0.633027	−	0.315082i
$751$	9.75271			0.355882			0.177941	−	0.984041i	$-0.443056\pi$
$751$	9.75271			0.355882			0.177941	+	0.984041i	$0.443056\pi$
$752$	6.05572	+	6.05572i	0.220829	+	0.220829i
$753$	−37.9454	−	8.91598i	−1.38281	−	0.324916i
$754$		−	6.27917i		−	0.228674i
$755$	−35.7942	−	12.6141i	−1.30268	−	0.459074i
$756$	15.8813	−	1.48207i	0.577596	−	0.0539022i
$757$	20.1653	−	20.1653i	0.732920	−	0.732920i	−0.238277	−	0.971197i	$-0.576583\pi$
$757$	20.1653	−	20.1653i	0.732920	−	0.732920i	0.971197	+	0.238277i	$0.0765827\pi$
$758$	−0.499583	+	0.499583i	−0.0181457	+	0.0181457i
$759$	7.69790	−	4.76865i	0.279416	−	0.173091i
$760$	2.87752	+	6.00929i	0.104379	+	0.217980i
$761$		−	1.55390i		−	0.0563288i	−0.999603	−	0.0281644i	$-0.991034\pi$
$761$		−	1.55390i		−	0.0563288i	0.999603	−	0.0281644i	$-0.00896620\pi$
$762$	7.32333	−	31.1673i	0.265296	−	1.12907i
$763$	17.8083	+	17.8083i	0.644705	+	0.644705i
$764$	3.19418			0.115561
$765$	0.0631309	−	4.21310i	0.00228250	−	0.152325i
$766$	−32.0016			−1.15626
$767$	−29.0585	−	29.0585i	−1.04924	−	1.04924i
$768$	0.396187	−	1.68613i	0.0142962	−	0.0608430i
$769$			26.7080i			0.963116i	0.876414	+	0.481558i	$0.159929\pi$
$769$			26.7080i			0.963116i	−0.876414	+	0.481558i	$0.840071\pi$
$770$	−11.9271	+	33.8447i	−0.429824	+	1.21968i
$771$	35.4128	−	21.9373i	1.27536	−	0.790053i
$772$	1.55053	−	1.55053i	0.0558050	−	0.0558050i
$773$	−4.61426	+	4.61426i	−0.165963	+	0.165963i	−0.785202	−	0.619239i	$-0.787441\pi$
$773$	−4.61426	+	4.61426i	−0.165963	+	0.165963i	0.619239	+	0.785202i	$0.287441\pi$
$774$	13.8326	−	27.8098i	0.497201	−	0.999604i
$775$	−20.4730	−	16.4758i	−0.735410	−	0.591827i
$776$		−	18.6449i		−	0.669314i
$777$	−20.1683	−	4.73891i	−0.723533	−	0.170007i

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.396187 - 1.68613i) q^{3} +1.00000i q^{4} +(-2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 + 2.17056i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.68607 - 1.33605i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.396187 - 1.68613i) q^{3} +1.00000i q^{4} +(-2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 + 2.17056i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.68607 - 1.33605i) q^{9} +(-0.965722 - 2.01677i) q^{10} +5.22806i q^{11} +(1.68613 + 0.396187i) q^{12} +(2.60057 + 2.60057i) q^{13} -3.06963 q^{14} +(-2.08868 + 3.26151i) q^{15} -1.00000 q^{16} +(-0.444150 - 0.444150i) q^{17} +(-0.954611 - 2.84407i) q^{18} +2.97966i q^{19} +(0.743206 - 2.10894i) q^{20} +(2.79989 + 4.51979i) q^{21} +(-3.69679 + 3.69679i) q^{22} +(0.707107 - 0.707107i) q^{23} +(0.912127 + 1.47242i) q^{24} +(3.89529 + 3.13476i) q^{25} +3.67776i q^{26} +(-3.31694 + 3.99974i) q^{27} +(-2.17056 - 2.17056i) q^{28} -1.70734 q^{29} +(-3.78315 + 0.829313i) q^{30} -5.25582 q^{31} +(-0.707107 - 0.707107i) q^{32} +(8.81518 + 2.07129i) q^{33} -0.628123i q^{34} +(6.19075 - 2.96441i) q^{35} +(1.33605 - 2.68607i) q^{36} +(-2.75535 + 2.75535i) q^{37} +(-2.10693 + 2.10693i) q^{38} +(5.41521 - 3.35458i) q^{39} +(2.01677 - 0.965722i) q^{40} -6.96597i q^{41} +(-1.21615 + 5.17579i) q^{42} +(7.32093 + 7.32093i) q^{43} -5.22806 q^{44} +(4.67181 + 4.81395i) q^{45} +1.00000 q^{46} +(-6.05572 - 6.05572i) q^{47} +(-0.396187 + 1.68613i) q^{48} -2.42262i q^{49} +(0.537774 + 4.97100i) q^{50} +(-0.924861 + 0.572928i) q^{51} +(-2.60057 + 2.60057i) q^{52} +(-0.302305 + 0.302305i) q^{53} +(-5.17367 + 0.482816i) q^{54} +(3.88553 - 11.0257i) q^{55} -3.06963i q^{56} +(5.02409 + 1.18050i) q^{57} +(-1.20727 - 1.20727i) q^{58} -11.1739 q^{59} +(-3.26151 - 2.08868i) q^{60} -1.40994 q^{61} +(-3.71643 - 3.71643i) q^{62} +(8.73023 - 2.93030i) q^{63} -1.00000i q^{64} +(-3.55169 - 7.41721i) q^{65} +(4.76865 + 7.69790i) q^{66} +(3.64409 - 3.64409i) q^{67} +(0.444150 - 0.444150i) q^{68} +(-0.912127 - 1.47242i) q^{69} +(6.47368 + 2.28137i) q^{70} +4.61412i q^{71} +(2.84407 - 0.954611i) q^{72} +(0.698447 + 0.698447i) q^{73} -3.89665 q^{74} +(6.82888 - 5.32601i) q^{75} -2.97966 q^{76} +(-11.3478 - 11.3478i) q^{77} +(6.20118 + 1.45708i) q^{78} +11.7332i q^{79} +(2.10894 + 0.743206i) q^{80} +(5.42996 + 7.17743i) q^{81} +(4.92569 - 4.92569i) q^{82} +(9.38271 - 9.38271i) q^{83} +(-4.51979 + 2.79989i) q^{84} +(0.606592 + 1.26678i) q^{85} +10.3534i q^{86} +(-0.676425 + 2.87879i) q^{87} +(-3.69679 - 3.69679i) q^{88} -3.53601 q^{89} +(-0.100507 + 6.70745i) q^{90} -11.2894 q^{91} +(0.707107 + 0.707107i) q^{92} +(-2.08229 + 8.86201i) q^{93} -8.56408i q^{94} +(2.21450 - 6.28393i) q^{95} +(-1.47242 + 0.912127i) q^{96} +(-13.1840 + 13.1840i) q^{97} +(1.71305 - 1.71305i) q^{98} +(6.98493 - 14.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} + O(q^{10}) \)	\( 32q + 4q^{3} + 12q^{6} + 8q^{7} - 4q^{12} - 12q^{15} - 32q^{16} + 8q^{18} - 40q^{22} + 32q^{25} + 4q^{27} + 8q^{28} - 20q^{30} + 8q^{31} + 8q^{33} + 20q^{36} - 16q^{37} + 8q^{40} - 8q^{42} - 80q^{43} - 4q^{45} + 32q^{46} - 4q^{48} + 36q^{51} + 12q^{57} - 16q^{58} - 4q^{60} + 8q^{61} + 44q^{63} + 52q^{66} + 64q^{67} + 64q^{70} - 8q^{72} - 56q^{73} - 68q^{75} - 8q^{76} + 60q^{78} - 44q^{81} - 48q^{85} - 60q^{87} - 40q^{88} - 64q^{90} + 40q^{91} + 92q^{93} - 12q^{96} - 40q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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