LMFDB - Embedded newform 690.3.k.a.277.13

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label			277.13
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.13

$q$-expansion

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(7.06040 + 0.388220i) q^{10} +6.03072 q^{11} +(2.44949 + 2.44949i) q^{12} +(-0.224734 + 0.224734i) q^{13} +12.0925i q^{14} +(0.475470 - 8.64719i) q^{15} -4.00000 q^{16} +(3.58233 + 3.58233i) q^{17} +(3.00000 - 3.00000i) q^{18} +25.3766i q^{19} +(6.67218 + 7.44862i) q^{20} +14.8102 q^{21} +(6.03072 + 6.03072i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(2.74099 - 24.8493i) q^{25} -0.449468 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-12.0925 + 12.0925i) q^{28} -37.7718i q^{29} +(9.12266 - 8.17172i) q^{30} +11.5048 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.38610 - 7.38610i) q^{33} +7.16467i q^{34} +(42.6889 + 2.34727i) q^{35} +6.00000 q^{36} +(20.7844 + 20.7844i) q^{37} +(-25.3766 + 25.3766i) q^{38} +0.550483i q^{39} +(-0.776439 + 14.1208i) q^{40} -24.7818 q^{41} +(14.8102 + 14.8102i) q^{42} +(-19.3473 + 19.3473i) q^{43} +12.0614i q^{44} +(-10.0083 - 11.1729i) q^{45} +6.78233 q^{46} +(5.86417 + 5.86417i) q^{47} +(-4.89898 + 4.89898i) q^{48} +24.1140i q^{49} +(27.5903 - 22.1083i) q^{50} +8.77489 q^{51} +(-0.449468 - 0.449468i) q^{52} +(33.5894 - 33.5894i) q^{53} -7.34847i q^{54} +(22.4603 - 20.1190i) q^{55} -24.1849 q^{56} +(31.0798 + 31.0798i) q^{57} +(37.7718 - 37.7718i) q^{58} -20.0519i q^{59} +(17.2944 + 0.950940i) q^{60} +10.4754 q^{61} +(11.5048 + 11.5048i) q^{62} +(18.1387 - 18.1387i) q^{63} -8.00000i q^{64} +(-0.0872461 + 1.58671i) q^{65} +14.7722 q^{66} +(22.9516 + 22.9516i) q^{67} +(-7.16467 + 7.16467i) q^{68} -8.30662i q^{69} +(40.3416 + 45.0361i) q^{70} +21.4134 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.3312 - 25.3312i) q^{73} +41.5687i q^{74} +(-27.0770 - 33.7910i) q^{75} -50.7531 q^{76} +(36.4632 + 36.4632i) q^{77} +(-0.550483 + 0.550483i) q^{78} -8.78027i q^{79} +(-14.8972 + 13.3444i) q^{80} -9.00000 q^{81} +(-24.7818 - 24.7818i) q^{82} +(-47.9297 + 47.9297i) q^{83} +29.6204i q^{84} +(25.2927 + 1.39073i) q^{85} -38.6945 q^{86} +(-46.2608 - 46.2608i) q^{87} +(-12.0614 + 12.0614i) q^{88} +10.7360i q^{89} +(1.16466 - 21.1812i) q^{90} -2.71759 q^{91} +(6.78233 + 6.78233i) q^{92} +(14.0904 - 14.0904i) q^{93} +11.7283i q^{94} +(84.6586 + 94.5102i) q^{95} -9.79796 q^{96} +(-63.2192 - 63.2192i) q^{97} +(-24.1140 + 24.1140i) q^{98} -18.0922i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) $	$ 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$3$	1.22474	−	1.22474i	0.408248	−	0.408248i
$4$			2.00000i			0.500000i
$5$	3.72431	−	3.33609i	0.744862	−	0.667218i
$5$	3.72431	−	3.33609i	0.744862	−	0.667218i
$6$	2.44949			0.408248
$7$	6.04624	+	6.04624i	0.863748	+	0.863748i	0.991771	−	0.128023i	$-0.0408632\pi$
$7$	6.04624	+	6.04624i	0.863748	+	0.863748i	−0.128023	+	0.991771i	$0.540863\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	7.06040	+	0.388220i	0.706040	+	0.0388220i
$11$	6.03072			0.548247			0.274124	−	0.961694i	$-0.411612\pi$
$11$	6.03072			0.548247			0.274124	+	0.961694i	$0.411612\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−0.224734	+	0.224734i	−0.0172872	+	0.0172872i	−0.715698	−	0.698410i	$-0.753891\pi$
$13$	−0.224734	+	0.224734i	−0.0172872	+	0.0172872i	0.698410	+	0.715698i	$0.253891\pi$
$14$			12.0925i			0.863748i
$15$	0.475470	−	8.64719i	0.0316980	−	0.576479i
$16$	−4.00000			−0.250000
$17$	3.58233	+	3.58233i	0.210725	+	0.210725i	0.804576	−	0.593850i	$-0.202393\pi$
$17$	3.58233	+	3.58233i	0.210725	+	0.210725i	−0.593850	+	0.804576i	$0.702393\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			25.3766i			1.33561i	0.744337	+	0.667804i	$0.232766\pi$
$19$			25.3766i			1.33561i	−0.744337	+	0.667804i	$0.767234\pi$
$20$	6.67218	+	7.44862i	0.333609	+	0.372431i
$21$	14.8102			0.705247
$22$	6.03072	+	6.03072i	0.274124	+	0.274124i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	2.74099	−	24.8493i	0.109639	−	0.993971i
$26$	−0.449468			−0.0172872
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−12.0925	+	12.0925i	−0.431874	+	0.431874i
$29$		−	37.7718i		−	1.30248i	−0.758874	−	0.651238i	$-0.774250\pi$
$29$		−	37.7718i		−	1.30248i	0.758874	−	0.651238i	$-0.225750\pi$
$30$	9.12266	−	8.17172i	0.304089	−	0.272391i
$31$	11.5048			0.371122			0.185561	−	0.982633i	$-0.440590\pi$
$31$	11.5048			0.371122			0.185561	+	0.982633i	$0.440590\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	7.38610	−	7.38610i	0.223821	−	0.223821i
$34$			7.16467i			0.210725i
$35$	42.6889	+	2.34727i	1.21968	+	0.0670648i
$36$	6.00000			0.166667
$37$	20.7844	+	20.7844i	0.561739	+	0.561739i	0.929801	−	0.368062i	$-0.119979\pi$
$37$	20.7844	+	20.7844i	0.561739	+	0.561739i	−0.368062	+	0.929801i	$0.619979\pi$
$38$	−25.3766	+	25.3766i	−0.667804	+	0.667804i
$39$			0.550483i			0.0141150i
$40$	−0.776439	+	14.1208i	−0.0194110	+	0.353020i
$41$	−24.7818			−0.604434			−0.302217	−	0.953239i	$-0.597727\pi$
$41$	−24.7818			−0.604434			−0.302217	+	0.953239i	$0.597727\pi$
$42$	14.8102	+	14.8102i	0.352624	+	0.352624i
$43$	−19.3473	+	19.3473i	−0.449937	+	0.449937i	−0.895333	−	0.445397i	$-0.853063\pi$
$43$	−19.3473	+	19.3473i	−0.449937	+	0.449937i	0.445397	+	0.895333i	$0.353063\pi$
$44$			12.0614i			0.274124i
$45$	−10.0083	−	11.1729i	−0.222406	−	0.248287i
$46$	6.78233			0.147442
$47$	5.86417	+	5.86417i	0.124770	+	0.124770i	0.766734	−	0.641965i	$-0.221880\pi$
$47$	5.86417	+	5.86417i	0.124770	+	0.124770i	−0.641965	+	0.766734i	$0.721880\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			24.1140i			0.492122i
$50$	27.5903	−	22.1083i	0.551805	−	0.442166i
$51$	8.77489			0.172057
$52$	−0.449468	−	0.449468i	−0.00864361	−	0.00864361i
$53$	33.5894	−	33.5894i	0.633763	−	0.633763i	−0.315247	−	0.949010i	$-0.602087\pi$
$53$	33.5894	−	33.5894i	0.633763	−	0.633763i	0.949010	+	0.315247i	$0.102087\pi$
$54$		−	7.34847i		−	0.136083i
$55$	22.4603	−	20.1190i	0.408369	−	0.365801i
$56$	−24.1849			−0.431874
$57$	31.0798	+	31.0798i	0.545260	+	0.545260i
$58$	37.7718	−	37.7718i	0.651238	−	0.651238i
$59$		−	20.0519i		−	0.339863i	−0.985456	−	0.169931i	$-0.945645\pi$
$59$		−	20.0519i		−	0.339863i	0.985456	−	0.169931i	$-0.0543546\pi$
$60$	17.2944	+	0.950940i	0.288240	+	0.0158490i
$61$	10.4754			0.171727			0.0858637	−	0.996307i	$-0.472635\pi$
$61$	10.4754			0.171727			0.0858637	+	0.996307i	$0.472635\pi$
$62$	11.5048	+	11.5048i	0.185561	+	0.185561i
$63$	18.1387	−	18.1387i	0.287916	−	0.287916i
$64$		−	8.00000i		−	0.125000i
$65$	−0.0872461	+	1.58671i	−0.00134225	+	0.0244109i
$66$	14.7722			0.223821
$67$	22.9516	+	22.9516i	0.342561	+	0.342561i	0.857329	−	0.514769i	$-0.172122\pi$
$67$	22.9516	+	22.9516i	0.342561	+	0.342561i	−0.514769	+	0.857329i	$0.672122\pi$
$68$	−7.16467	+	7.16467i	−0.105363	+	0.105363i
$69$		−	8.30662i		−	0.120386i
$70$	40.3416	+	45.0361i	0.576309	+	0.643373i
$71$	21.4134			0.301597			0.150799	−	0.988565i	$-0.451815\pi$
$71$	21.4134			0.301597			0.150799	+	0.988565i	$0.451815\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	25.3312	−	25.3312i	0.347002	−	0.347002i	−0.511989	−	0.858992i	$-0.671091\pi$
$73$	25.3312	−	25.3312i	0.347002	−	0.347002i	0.858992	+	0.511989i	$0.171091\pi$
$74$			41.5687i			0.561739i
$75$	−27.0770	−	33.7910i	−0.361027	−	0.450547i
$76$	−50.7531			−0.667804
$77$	36.4632	+	36.4632i	0.473548	+	0.473548i
$78$	−0.550483	+	0.550483i	−0.00705748	+	0.00705748i
$79$		−	8.78027i		−	0.111143i	−0.998455	−	0.0555713i	$-0.982302\pi$
$79$		−	8.78027i		−	0.111143i	0.998455	−	0.0555713i	$-0.0176980\pi$
$80$	−14.8972	+	13.3444i	−0.186216	+	0.166805i
$81$	−9.00000			−0.111111
$82$	−24.7818	−	24.7818i	−0.302217	−	0.302217i
$83$	−47.9297	+	47.9297i	−0.577467	+	0.577467i	−0.934204	−	0.356738i	$-0.883889\pi$
$83$	−47.9297	+	47.9297i	−0.577467	+	0.577467i	0.356738	+	0.934204i	$0.383889\pi$
$84$			29.6204i			0.352624i
$85$	25.2927	+	1.39073i	0.297561	+	0.0163615i
$86$	−38.6945			−0.449937
$87$	−46.2608	−	46.2608i	−0.531733	−	0.531733i
$88$	−12.0614	+	12.0614i	−0.137062	+	0.137062i
$89$			10.7360i			0.120629i	0.998179	+	0.0603145i	$0.0192104\pi$
$89$			10.7360i			0.120629i	−0.998179	+	0.0603145i	$0.980790\pi$
$90$	1.16466	−	21.1812i	0.0129407	−	0.235347i
$91$	−2.71759			−0.0298636
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	14.0904	−	14.0904i	0.151510	−	0.151510i
$94$			11.7283i			0.124770i
$95$	84.6586	+	94.5102i	0.891143	+	0.994845i
$96$	−9.79796			−0.102062
$97$	−63.2192	−	63.2192i	−0.651745	−	0.651745i	0.301668	−	0.953413i	$-0.402456\pi$
$97$	−63.2192	−	63.2192i	−0.651745	−	0.651745i	−0.953413	+	0.301668i	$0.902456\pi$
$98$	−24.1140	+	24.1140i	−0.246061	+	0.246061i
$99$		−	18.0922i		−	0.182749i
$100$	49.6986	+	5.48197i	0.496986	+	0.0548197i
$101$	−6.89640			−0.0682812			−0.0341406	−	0.999417i	$-0.510869\pi$
$101$	−6.89640			−0.0682812			−0.0341406	+	0.999417i	$0.510869\pi$
$102$	8.77489	+	8.77489i	0.0860283	+	0.0860283i
$103$	−88.5287	+	88.5287i	−0.859502	+	0.859502i	−0.991279	−	0.131777i	$-0.957932\pi$
$103$	−88.5287	+	88.5287i	−0.859502	+	0.859502i	0.131777	+	0.991279i	$0.457932\pi$
$104$		−	0.898935i		−	0.00864361i
$105$	55.1578	−	49.4082i	0.525312	−	0.470554i
$106$	67.1788			0.633763
$107$	87.3608	+	87.3608i	0.816456	+	0.816456i	0.985593	−	0.169137i	$-0.0540980\pi$
$107$	87.3608	+	87.3608i	0.816456	+	0.816456i	−0.169137	+	0.985593i	$0.554098\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	8.33514i		−	0.0764692i	−0.999269	−	0.0382346i	$-0.987827\pi$
$109$		−	8.33514i		−	0.0764692i	0.999269	−	0.0382346i	$-0.0121734\pi$
$110$	42.5793	+	2.34124i	0.387085	+	0.0212840i
$111$	50.9111			0.458658
$112$	−24.1849	−	24.1849i	−0.215937	−	0.215937i
$113$	−50.5727	+	50.5727i	−0.447546	+	0.447546i	−0.894538	−	0.446992i	$-0.852495\pi$
$113$	−50.5727	+	50.5727i	−0.447546	+	0.447546i	0.446992	+	0.894538i	$0.352495\pi$
$114$			62.1596i			0.545260i
$115$	1.31652	−	23.9430i	0.0114480	−	0.208200i
$116$	75.5436			0.651238
$117$	0.674201	+	0.674201i	0.00576240	+	0.00576240i
$118$	20.0519	−	20.0519i	0.169931	−	0.169931i
$119$			43.3193i			0.364027i
$120$	16.3434	+	18.2453i	0.136195	+	0.152044i
$121$	−84.6304			−0.699425
$122$	10.4754	+	10.4754i	0.0858637	+	0.0858637i
$123$	−30.3514	+	30.3514i	−0.246759	+	0.246759i
$124$			23.0095i			0.185561i
$125$	−72.6912	−	101.691i	−0.581530	−	0.813525i
$126$	36.2774			0.287916
$127$	−171.315	−	171.315i	−1.34893	−	1.34893i	−0.886822	−	0.462111i	$-0.847092\pi$
$127$	−171.315	−	171.315i	−1.34893	−	1.34893i	−0.462111	−	0.886822i	$-0.652908\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			47.3910i			0.367372i
$130$	−1.67396	+	1.49946i	−0.0128766	+	0.0115343i
$131$	−9.31847			−0.0711333			−0.0355667	−	0.999367i	$-0.511324\pi$
$131$	−9.31847			−0.0711333			−0.0355667	+	0.999367i	$0.511324\pi$
$132$	14.7722	+	14.7722i	0.111911	+	0.111911i
$133$	−153.433	+	153.433i	−1.15363	+	1.15363i
$134$			45.9031i			0.342561i
$135$	−25.9416	−	1.42641i	−0.192160	−	0.0105660i
$136$	−14.3293			−0.105363
$137$	−108.397	−	108.397i	−0.791218	−	0.791218i	0.190474	−	0.981692i	$-0.438997\pi$
$137$	−108.397	−	108.397i	−0.791218	−	0.791218i	−0.981692	+	0.190474i	$0.938997\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$		−	126.720i		−	0.911653i	−0.890069	−	0.455827i	$-0.849344\pi$
$139$		−	126.720i		−	0.911653i	0.890069	−	0.455827i	$-0.150656\pi$
$140$	−4.69454	+	85.3777i	−0.0335324	+	0.609841i
$141$	14.3642			0.101874
$142$	21.4134	+	21.4134i	0.150799	+	0.150799i
$143$	−1.35531	+	1.35531i	−0.00947767	+	0.00947767i
$144$			12.0000i			0.0833333i
$145$	−126.010	−	140.674i	−0.869035	−	0.970165i
$146$	50.6624			0.347002
$147$	29.5334	+	29.5334i	0.200908	+	0.200908i
$148$	−41.5687	+	41.5687i	−0.280870	+	0.280870i
$149$			61.5397i			0.413018i	0.978445	+	0.206509i	$0.0662103\pi$
$149$			61.5397i			0.413018i	−0.978445	+	0.206509i	$0.933790\pi$
$150$	6.71402	−	60.8681i	0.0447601	−	0.405787i
$151$	−100.953			−0.668560			−0.334280	−	0.942474i	$-0.608493\pi$
$151$	−100.953			−0.668560			−0.334280	+	0.942474i	$0.608493\pi$
$152$	−50.7531	−	50.7531i	−0.333902	−	0.333902i
$153$	10.7470	−	10.7470i	0.0702418	−	0.0702418i
$154$			72.9263i			0.473548i
$155$	42.8473	−	38.3810i	0.276434	−	0.247619i
$156$	−1.10097			−0.00705748
$157$	−63.0830	−	63.0830i	−0.401803	−	0.401803i	0.477065	−	0.878868i	$-0.341701\pi$
$157$	−63.0830	−	63.0830i	−0.401803	−	0.401803i	−0.878868	+	0.477065i	$0.841701\pi$
$158$	8.78027	−	8.78027i	0.0555713	−	0.0555713i
$159$		−	82.2769i		−	0.517465i
$160$	−28.2416	−	1.55288i	−0.176510	−	0.00970549i
$161$	41.0076			0.254705
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−35.1517	+	35.1517i	−0.215655	+	0.215655i	−0.806664	−	0.591010i	$-0.798729\pi$
$163$	−35.1517	+	35.1517i	−0.215655	+	0.215655i	0.591010	+	0.806664i	$0.298729\pi$
$164$		−	49.5636i		−	0.302217i
$165$	2.86743	−	52.1488i	0.0173783	−	0.316053i
$166$	−95.8594			−0.577467
$167$	65.9932	+	65.9932i	0.395169	+	0.395169i	0.876525	−	0.481356i	$-0.159856\pi$
$167$	65.9932	+	65.9932i	0.395169	+	0.395169i	−0.481356	+	0.876525i	$0.659856\pi$
$168$	−29.6204	+	29.6204i	−0.176312	+	0.176312i
$169$			168.899i			0.999402i
$170$	23.9020	+	26.6834i	0.140600	+	0.156961i
$171$	76.1297			0.445203
$172$	−38.6945	−	38.6945i	−0.224968	−	0.224968i
$173$	153.430	−	153.430i	0.886880	−	0.886880i	−0.107343	−	0.994222i	$-0.534234\pi$
$173$	153.430	−	153.430i	0.886880	−	0.886880i	0.994222	+	0.107343i	$0.0342341\pi$
$174$		−	92.5216i		−	0.531733i
$175$	166.817	−	133.672i	0.953242	−	0.763840i
$176$	−24.1229			−0.137062
$177$	−24.5585	−	24.5585i	−0.138748	−	0.138748i
$178$	−10.7360	+	10.7360i	−0.0603145	+	0.0603145i
$179$		−	17.5087i		−	0.0978139i	−0.998803	−	0.0489069i	$-0.984426\pi$
$179$		−	17.5087i		−	0.0978139i	0.998803	−	0.0489069i	$-0.0155738\pi$
$180$	22.3459	−	20.0165i	0.124144	−	0.111203i
$181$	−345.567			−1.90921			−0.954606	−	0.297871i	$-0.903723\pi$
$181$	−345.567			−1.90921			−0.954606	+	0.297871i	$0.903723\pi$
$182$	−2.71759	−	2.71759i	−0.0149318	−	0.0149318i
$183$	12.8297	−	12.8297i	0.0701074	−	0.0701074i
$184$			13.5647i			0.0737210i
$185$	146.746	+	8.06889i	0.793221	+	0.0436156i
$186$	28.1808			0.151510
$187$	21.6041	+	21.6041i	0.115530	+	0.115530i
$188$	−11.7283	+	11.7283i	−0.0623848	+	0.0623848i
$189$		−	44.4306i		−	0.235082i
$190$	−9.85168	+	179.169i	−0.0518510	+	0.942994i
$191$	109.218			0.571822			0.285911	−	0.958256i	$-0.407704\pi$
$191$	109.218			0.571822			0.285911	+	0.958256i	$0.407704\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	24.0047	−	24.0047i	0.124377	−	0.124377i	−0.642178	−	0.766555i	$-0.721969\pi$
$193$	24.0047	−	24.0047i	0.124377	−	0.124377i	0.766555	+	0.642178i	$0.221969\pi$
$194$		−	126.438i		−	0.651745i
$195$	1.83646	+	2.05017i	0.00941775	+	0.0105137i
$196$	−48.2279			−0.246061
$197$	−141.884	−	141.884i	−0.720223	−	0.720223i	0.248428	−	0.968650i	$-0.420086\pi$
$197$	−141.884	−	141.884i	−0.720223	−	0.720223i	−0.968650	+	0.248428i	$0.920086\pi$
$198$	18.0922	−	18.0922i	0.0913746	−	0.0913746i
$199$		−	176.579i		−	0.887330i	−0.896193	−	0.443665i	$-0.853678\pi$
$199$		−	176.579i		−	0.887330i	0.896193	−	0.443665i	$-0.146322\pi$
$200$	44.2166	+	55.1805i	0.221083	+	0.275903i
$201$	56.2196			0.279700
$202$	−6.89640	−	6.89640i	−0.0341406	−	0.0341406i
$203$	228.377	−	228.377i	1.12501	−	1.12501i
$204$			17.5498i			0.0860283i
$205$	−92.2950	+	82.6743i	−0.450220	+	0.403289i
$206$	−177.057			−0.859502
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	0.898935	−	0.898935i	0.00432180	−	0.00432180i
$209$			153.039i			0.732244i
$210$	104.566	+	5.74961i	0.497933	+	0.0273791i
$211$	−126.385			−0.598980			−0.299490	−	0.954099i	$-0.596817\pi$
$211$	−126.385			−0.598980			−0.299490	+	0.954099i	$0.596817\pi$
$212$	67.1788	+	67.1788i	0.316881	+	0.316881i
$213$	26.2260	−	26.2260i	0.123127	−	0.123127i
$214$			174.722i			0.816456i
$215$	−7.51099	+	136.600i	−0.0349348	+	0.635347i
$216$	14.6969			0.0680414
$217$	69.5605	+	69.5605i	0.320555	+	0.320555i
$218$	8.33514	−	8.33514i	0.0382346	−	0.0382346i
$219$		−	62.0485i		−	0.283326i
$220$	40.2381	+	44.9206i	0.182900	+	0.204184i
$221$	−1.61014			−0.00728571
$222$	50.9111	+	50.9111i	0.229329	+	0.229329i
$223$	100.240	−	100.240i	0.449507	−	0.449507i	−0.445683	−	0.895191i	$-0.647039\pi$
$223$	100.240	−	100.240i	0.449507	−	0.449507i	0.895191	+	0.445683i	$0.147039\pi$
$224$		−	48.3699i		−	0.215937i
$225$	−74.5479	−	8.22296i	−0.331324	−	0.0365465i
$226$	−101.145			−0.447546
$227$	−260.102	−	260.102i	−1.14582	−	1.14582i	−0.987366	−	0.158457i	$-0.949348\pi$
$227$	−260.102	−	260.102i	−1.14582	−	1.14582i	−0.158457	−	0.987366i	$-0.550652\pi$
$228$	−62.1596	+	62.1596i	−0.272630	+	0.272630i
$229$			328.074i			1.43264i	0.697773	+	0.716319i	$0.254174\pi$
$229$			328.074i			1.43264i	−0.697773	+	0.716319i	$0.745826\pi$
$230$	25.2595	−	22.6265i	0.109824	−	0.0983760i
$231$	89.3162			0.386650
$232$	75.5436	+	75.5436i	0.325619	+	0.325619i
$233$	−133.968	+	133.968i	−0.574970	+	0.574970i	−0.933513	−	0.358543i	$-0.883274\pi$
$233$	−133.968	+	133.968i	−0.574970	+	0.574970i	0.358543	+	0.933513i	$0.383274\pi$
$234$			1.34840i			0.00576240i
$235$	41.4034	+	2.27659i	0.176185	+	0.00968760i
$236$	40.1038			0.169931
$237$	−10.7536	−	10.7536i	−0.0453738	−	0.0453738i
$238$	−43.3193	+	43.3193i	−0.182014	+	0.182014i
$239$			28.2933i			0.118382i	0.998247	+	0.0591910i	$0.0188521\pi$
$239$			28.2933i			0.118382i	−0.998247	+	0.0591910i	$0.981148\pi$
$240$	−1.90188	+	34.5888i	−0.00792450	+	0.144120i
$241$	−298.141			−1.23710			−0.618550	−	0.785746i	$-0.712279\pi$
$241$	−298.141			−1.23710			−0.618550	+	0.785746i	$0.712279\pi$
$242$	−84.6304	−	84.6304i	−0.349712	−	0.349712i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$			20.9508i			0.0858637i
$245$	80.4464	+	89.8079i	0.328352	+	0.366563i
$246$	−60.7027			−0.246759
$247$	−5.70297	−	5.70297i	−0.0230890	−	0.0230890i
$248$	−23.0095	+	23.0095i	−0.0927804	+	0.0927804i
$249$			117.403i			0.471499i
$250$	28.9994	−	174.382i	0.115998	−	0.697527i
$251$	−338.924			−1.35030			−0.675148	−	0.737682i	$-0.735920\pi$
$251$	−338.924			−1.35030			−0.675148	+	0.737682i	$0.735920\pi$
$252$	36.2774	+	36.2774i	0.143958	+	0.143958i
$253$	20.4512	−	20.4512i	0.0808347	−	0.0808347i
$254$		−	342.629i		−	1.34893i
$255$	32.6804	−	29.2738i	0.128158	−	0.114799i
$256$	16.0000			0.0625000
$257$	166.864	+	166.864i	0.649277	+	0.649277i	0.952818	−	0.303541i	$-0.0981690\pi$
$257$	166.864	+	166.864i	0.649277	+	0.649277i	−0.303541	+	0.952818i	$0.598169\pi$
$258$	−47.3910	+	47.3910i	−0.183686	+	0.183686i
$259$			251.334i			0.970403i
$260$	−3.17342	−	0.174492i	−0.0122055	−	0.000671124i
$261$	−113.315			−0.434158
$262$	−9.31847	−	9.31847i	−0.0355667	−	0.0355667i
$263$	302.953	−	302.953i	1.15191	−	1.15191i	0.165744	−	0.986169i	$-0.446998\pi$
$263$	302.953	−	302.953i	1.15191	−	1.15191i	0.986169	−	0.165744i	$-0.0530024\pi$
$264$			29.5444i			0.111911i
$265$	13.0401	−	237.155i	0.0492078	−	0.894924i
$266$	−306.865			−1.15363
$267$	13.1488	+	13.1488i	0.0492466	+	0.0492466i
$268$	−45.9031	+	45.9031i	−0.171280	+	0.171280i
$269$			259.411i			0.964354i	0.876074	+	0.482177i	$0.160154\pi$
$269$			259.411i			0.964354i	−0.876074	+	0.482177i	$0.839846\pi$
$270$	−24.5152	−	27.3680i	−0.0907969	−	0.101363i
$271$	−430.196			−1.58744			−0.793719	−	0.608284i	$-0.791858\pi$
$271$	−430.196			−1.58744			−0.793719	+	0.608284i	$0.791858\pi$
$272$	−14.3293	−	14.3293i	−0.0526814	−	0.0526814i
$273$	−3.32835	+	3.32835i	−0.0121918	+	0.0121918i
$274$		−	216.794i		−	0.791218i
$275$	16.5301	−	149.859i	0.0601096	−	0.544942i
$276$	16.6132			0.0601929
$277$	−171.893	−	171.893i	−0.620553	−	0.620553i	0.325120	−	0.945673i	$-0.394595\pi$
$277$	−171.893	−	171.893i	−0.620553	−	0.620553i	−0.945673	+	0.325120i	$0.894595\pi$
$278$	126.720	−	126.720i	0.455827	−	0.455827i
$279$		−	34.5143i		−	0.123707i
$280$	−90.0723	+	80.6832i	−0.321687	+	0.288154i
$281$	349.790			1.24481			0.622403	−	0.782697i	$-0.286157\pi$
$281$	349.790			1.24481			0.622403	+	0.782697i	$0.286157\pi$
$282$	14.3642	+	14.3642i	0.0509370	+	0.0509370i
$283$	370.808	−	370.808i	1.31028	−	1.31028i	0.389065	−	0.921210i	$-0.372798\pi$
$283$	370.808	−	370.808i	1.31028	−	1.31028i	0.921210	−	0.389065i	$-0.127202\pi$
$284$			42.8268i			0.150799i
$285$	219.436	+	12.0658i	0.769951	+	0.0423361i
$286$	−2.71061			−0.00947767
$287$	−149.836	−	149.836i	−0.522078	−	0.522078i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	263.334i		−	0.911190i
$290$	14.6637	−	266.684i	0.0505646	−	0.919600i
$291$	−154.855			−0.532147
$292$	50.6624	+	50.6624i	0.173501	+	0.173501i
$293$	−50.6461	+	50.6461i	−0.172854	+	0.172854i	−0.788232	−	0.615378i	$-0.789003\pi$
$293$	−50.6461	+	50.6461i	−0.172854	+	0.172854i	0.615378	+	0.788232i	$0.289003\pi$
$294$			59.0669i			0.200908i
$295$	−66.8950	−	74.6795i	−0.226763	−	0.253151i
$296$	−83.1374			−0.280870
$297$	−22.1583	−	22.1583i	−0.0746070	−	0.0746070i
$298$	−61.5397	+	61.5397i	−0.206509	+	0.206509i
$299$			1.52422i			0.00509772i
$300$	67.5821	−	54.1541i	0.225274	−	0.180514i
$301$	−233.956			−0.777264
$302$	−100.953	−	100.953i	−0.334280	−	0.334280i
$303$	−8.44633	+	8.44633i	−0.0278757	+	0.0278757i
$304$		−	101.506i		−	0.333902i
$305$	39.0136	−	34.9468i	0.127913	−	0.114580i
$306$	21.4940			0.0702418
$307$	218.758	+	218.758i	0.712568	+	0.712568i	0.967072	−	0.254504i	$-0.0819121\pi$
$307$	218.758	+	218.758i	0.712568	+	0.712568i	−0.254504	+	0.967072i	$0.581912\pi$
$308$	−72.9263	+	72.9263i	−0.236774	+	0.236774i
$309$			216.850i			0.701781i
$310$	81.2283	+	4.46638i	0.262027	+	0.0144077i
$311$	162.318			0.521924			0.260962	−	0.965349i	$-0.415960\pi$
$311$	162.318			0.521924			0.260962	+	0.965349i	$0.415960\pi$
$312$	−1.10097	−	1.10097i	−0.00352874	−	0.00352874i
$313$	64.2791	−	64.2791i	0.205365	−	0.205365i	−0.596929	−	0.802294i	$-0.703613\pi$
$313$	64.2791	−	64.2791i	0.205365	−	0.205365i	0.802294	+	0.596929i	$0.203613\pi$
$314$		−	126.166i		−	0.401803i
$315$	7.04180	−	128.067i	0.0223549	−	0.406561i
$316$	17.5605			0.0555713
$317$	−340.744	−	340.744i	−1.07490	−	1.07490i	−0.996958	−	0.0779433i	$-0.975165\pi$
$317$	−340.744	−	340.744i	−1.07490	−	1.07490i	−0.0779433	−	0.996958i	$-0.524835\pi$
$318$	82.2769	−	82.2769i	0.258732	−	0.258732i
$319$		−	227.791i		−	0.714079i
$320$	−26.6887	−	29.7945i	−0.0834023	−	0.0931078i
$321$	213.989			0.666633
$322$	41.0076	+	41.0076i	0.127353	+	0.127353i
$323$	−90.9073	+	90.9073i	−0.281447	+	0.281447i
$324$		−	18.0000i		−	0.0555556i
$325$	4.96848	+	6.20047i	0.0152876	+	0.0190784i
$326$	−70.3034			−0.215655
$327$	−10.2084	−	10.2084i	−0.0312184	−	0.0312184i
$328$	49.5636	−	49.5636i	0.151108	−	0.151108i
$329$			70.9123i			0.215539i
$330$	55.0162	−	49.2814i	0.166716	−	0.149338i
$331$	−482.017			−1.45624			−0.728122	−	0.685447i	$-0.759607\pi$
$331$	−482.017			−1.45624			−0.728122	+	0.685447i	$0.759607\pi$
$332$	−95.8594	−	95.8594i	−0.288733	−	0.288733i
$333$	62.3531	−	62.3531i	0.187246	−	0.187246i
$334$			131.986i			0.395169i
$335$	162.047	+	8.91025i	0.483723	+	0.0265978i
$336$	−59.2408			−0.176312
$337$	299.309	+	299.309i	0.888158	+	0.888158i	0.994346	−	0.106188i	$-0.0338646\pi$
$337$	299.309	+	299.309i	0.888158	+	0.888158i	−0.106188	+	0.994346i	$0.533865\pi$
$338$	−168.899	+	168.899i	−0.499701	+	0.499701i
$339$			123.877i			0.365420i
$340$	−2.78146	+	50.5854i	−0.00818077	+	0.148781i
$341$	69.3821			0.203466
$342$	76.1297	+	76.1297i	0.222601	+	0.222601i
$343$	150.467	−	150.467i	0.438679	−	0.438679i
$344$		−	77.3891i		−	0.224968i
$345$	−27.7117	−	30.9365i	−0.0803236	−	0.0896709i
$346$	306.860			0.886880
$347$	−34.8305	−	34.8305i	−0.100376	−	0.100376i	0.655135	−	0.755512i	$-0.272612\pi$
$347$	−34.8305	−	34.8305i	−0.100376	−	0.100376i	−0.755512	+	0.655135i	$0.772612\pi$
$348$	92.5216	−	92.5216i	0.265867	−	0.265867i
$349$			455.518i			1.30521i	0.757699	+	0.652604i	$0.226324\pi$
$349$			455.518i			1.30521i	−0.757699	+	0.652604i	$0.773676\pi$
$350$	300.489	+	33.1453i	0.858541	+	0.0947009i
$351$	1.65145			0.00470498
$352$	−24.1229	−	24.1229i	−0.0685309	−	0.0685309i
$353$	31.7609	−	31.7609i	0.0899741	−	0.0899741i	−0.660687	−	0.750661i	$-0.729735\pi$
$353$	31.7609	−	31.7609i	0.0899741	−	0.0899741i	0.750661	+	0.660687i	$0.229735\pi$
$354$		−	49.1169i		−	0.138748i
$355$	79.7502	−	71.4371i	0.224648	−	0.201231i
$356$	−21.4720			−0.0603145
$357$	53.0550	+	53.0550i	0.148614	+	0.148614i
$358$	17.5087	−	17.5087i	0.0489069	−	0.0489069i
$359$		−	39.3142i		−	0.109510i	−0.998500	−	0.0547551i	$-0.982562\pi$
$359$		−	39.3142i		−	0.109510i	0.998500	−	0.0547551i	$-0.0174378\pi$
$360$	42.3624	+	2.32932i	0.117673	+	0.00647033i
$361$	−282.970			−0.783851
$362$	−345.567	−	345.567i	−0.954606	−	0.954606i
$363$	−103.651	+	103.651i	−0.285539	+	0.285539i
$364$		−	5.43517i		−	0.0149318i
$365$	9.83406	−	178.848i	0.0269426	−	0.489995i
$366$	25.6593			0.0701074
$367$	421.823	+	421.823i	1.14938	+	1.14938i	0.986674	+	0.162708i	$0.0520227\pi$
$367$	421.823	+	421.823i	1.14938	+	1.14938i	0.162708	+	0.986674i	$0.447977\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			74.3453i			0.201478i
$370$	138.677	+	154.815i	0.374803	+	0.418418i
$371$	406.179			1.09482
$372$	28.1808	+	28.1808i	0.0757549	+	0.0757549i
$373$	−324.873	+	324.873i	−0.870973	+	0.870973i	−0.992579	−	0.121605i	$-0.961196\pi$
$373$	−324.873	+	324.873i	−0.870973	+	0.870973i	0.121605	+	0.992579i	$0.461196\pi$
$374$			43.2081i			0.115530i
$375$	−213.573	−	35.5169i	−0.569529	−	0.0947118i
$376$	−23.4567			−0.0623848
$377$	8.48860	+	8.48860i	0.0225162	+	0.0225162i
$378$	44.4306	−	44.4306i	0.117541	−	0.117541i
$379$			188.177i			0.496509i	0.968695	+	0.248255i	$0.0798570\pi$
$379$			188.177i			0.496509i	−0.968695	+	0.248255i	$0.920143\pi$
$380$	−189.020	+	169.317i	−0.497422	+	0.445571i
$381$	−419.633			−1.10140
$382$	109.218	+	109.218i	0.285911	+	0.285911i
$383$	231.954	−	231.954i	0.605624	−	0.605624i	−0.336175	−	0.941799i	$-0.609133\pi$
$383$	231.954	−	231.954i	0.605624	−	0.605624i	0.941799	+	0.336175i	$0.109133\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	257.445	+	14.1557i	0.668687	+	0.0367681i
$386$	48.0095			0.124377
$387$	58.0418	+	58.0418i	0.149979	+	0.149979i
$388$	126.438	−	126.438i	0.325872	−	0.325872i
$389$			645.912i			1.66044i	0.557435	+	0.830220i	$0.311786\pi$
$389$			645.912i			1.66044i	−0.557435	+	0.830220i	$0.688214\pi$
$390$	−0.213708	+	3.88663i	−0.000547970	+	0.00996572i
$391$	24.2966			0.0621395
$392$	−48.2279	−	48.2279i	−0.123030	−	0.123030i
$393$	−11.4127	+	11.4127i	−0.0290401	+	0.0290401i
$394$		−	283.768i		−	0.720223i
$395$	−29.2918	−	32.7005i	−0.0741564	−	0.0827860i
$396$	36.1843			0.0913746
$397$	−192.099	−	192.099i	−0.483877	−	0.483877i	0.422491	−	0.906367i	$-0.361156\pi$
$397$	−192.099	−	192.099i	−0.483877	−	0.483877i	−0.906367	+	0.422491i	$0.861156\pi$
$398$	176.579	−	176.579i	0.443665	−	0.443665i
$399$			375.832i			0.941935i
$400$	−10.9639	+	99.3971i	−0.0274099	+	0.248493i
$401$	143.800			0.358602			0.179301	−	0.983794i	$-0.442616\pi$
$401$	143.800			0.358602			0.179301	+	0.983794i	$0.442616\pi$
$402$	56.2196	+	56.2196i	0.139850	+	0.139850i
$403$	−2.58551	+	2.58551i	−0.00641566	+	0.00641566i
$404$		−	13.7928i		−	0.0341406i
$405$	−33.5188	+	30.0248i	−0.0827625	+	0.0741354i
$406$	456.754			1.12501
$407$	125.345	+	125.345i	0.307972	+	0.307972i
$408$	−17.5498	+	17.5498i	−0.0430142	+	0.0430142i
$409$		−	174.989i		−	0.427846i	−0.976851	−	0.213923i	$-0.931376\pi$
$409$		−	174.989i		−	0.427846i	0.976851	−	0.213923i	$-0.0686241\pi$
$410$	−174.969	−	9.62077i	−0.426754	−	0.0234653i
$411$	−265.517			−0.646027
$412$	−177.057	−	177.057i	−0.429751	−	0.429751i
$413$	121.239	−	121.239i	0.293556	−	0.293556i
$414$		−	20.3470i		−	0.0491473i
$415$	−18.6073	+	338.403i	−0.0448368	+	0.815429i
$416$	1.79787			0.00432180
$417$	−155.199	−	155.199i	−0.372181	−	0.372181i
$418$	−153.039	+	153.039i	−0.366122	+	0.366122i
$419$			677.602i			1.61719i	0.588366	+	0.808595i	$0.299771\pi$
$419$			677.602i			1.61719i	−0.588366	+	0.808595i	$0.700229\pi$
$420$	98.8163	+	110.316i	0.235277	+	0.262656i
$421$	−647.109			−1.53708			−0.768538	−	0.639805i	$-0.779015\pi$
$421$	−647.109			−1.53708			−0.768538	+	0.639805i	$0.779015\pi$
$422$	−126.385	−	126.385i	−0.299490	−	0.299490i
$423$	17.5925	−	17.5925i	0.0415899	−	0.0415899i
$424$			134.358i			0.316881i
$425$	98.8375	−	79.1993i	0.232559	−	0.186351i
$426$	52.4519			0.123127
$427$	63.3366	+	63.3366i	0.148329	+	0.148329i
$428$	−174.722	+	174.722i	−0.408228	+	0.408228i
$429$			3.31981i			0.00773849i
$430$	−144.111	+	129.089i	−0.335141	+	0.300206i
$431$	79.7599			0.185058			0.0925289	−	0.995710i	$-0.470505\pi$
$431$	79.7599			0.185058			0.0925289	+	0.995710i	$0.470505\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−32.7197	+	32.7197i	−0.0755652	+	0.0755652i	−0.743879	−	0.668314i	$-0.767016\pi$
$433$	−32.7197	+	32.7197i	−0.0755652	+	0.0755652i	0.668314	+	0.743879i	$0.267016\pi$
$434$			139.121i			0.320555i
$435$	−326.620	−	17.9594i	−0.750850	−	0.0412859i
$436$	16.6703			0.0382346
$437$	86.0561	+	86.0561i	0.196925	+	0.196925i
$438$	62.0485	−	62.0485i	0.141663	−	0.141663i
$439$			701.466i			1.59787i	0.601416	+	0.798936i	$0.294603\pi$
$439$			701.466i			1.59787i	−0.601416	+	0.798936i	$0.705397\pi$
$440$	−4.68249	+	85.1587i	−0.0106420	+	0.193542i
$441$	72.3419			0.164041
$442$	−1.61014	−	1.61014i	−0.00364286	−	0.00364286i
$443$	150.926	−	150.926i	0.340691	−	0.340691i	−0.515936	−	0.856627i	$-0.672556\pi$
$443$	150.926	−	150.926i	0.340691	−	0.340691i	0.856627	+	0.515936i	$0.172556\pi$
$444$			101.822i			0.229329i
$445$	35.8162	+	39.9841i	0.0804858	+	0.0898519i
$446$	200.480			0.449507
$447$	75.3704	+	75.3704i	0.168614	+	0.168614i
$448$	48.3699	−	48.3699i	0.107969	−	0.107969i
$449$			233.234i			0.519451i	0.965682	+	0.259726i	$0.0836321\pi$
$449$			233.234i			0.519451i	−0.965682	+	0.259726i	$0.916368\pi$
$450$	−66.3249	−	82.7708i	−0.147389	−	0.183935i
$451$	−149.452			−0.331379
$452$	−101.145	−	101.145i	−0.223773	−	0.223773i
$453$	−123.641	+	123.641i	−0.272938	+	0.272938i
$454$		−	520.204i		−	1.14582i
$455$	−10.1211	+	9.06612i	−0.0222443	+	0.0199255i
$456$	−124.319			−0.272630
$457$	323.809	+	323.809i	0.708554	+	0.708554i	0.966231	−	0.257677i	$-0.0829570\pi$
$457$	323.809	+	323.809i	0.708554	+	0.708554i	−0.257677	+	0.966231i	$0.582957\pi$
$458$	−328.074	+	328.074i	−0.716319	+	0.716319i
$459$		−	26.3247i		−	0.0573522i
$460$	47.8860	+	2.63303i	0.104100	+	0.00572399i
$461$	461.068			1.00015			0.500074	−	0.865983i	$-0.333306\pi$
$461$	461.068			1.00015			0.500074	+	0.865983i	$0.333306\pi$
$462$	89.3162	+	89.3162i	0.193325	+	0.193325i
$463$	168.651	−	168.651i	0.364258	−	0.364258i	−0.501120	−	0.865378i	$-0.667079\pi$
$463$	168.651	−	168.651i	0.364258	−	0.364258i	0.865378	+	0.501120i	$0.167079\pi$
$464$			151.087i			0.325619i
$465$	5.47017	−	99.4839i	0.0117638	−	0.213944i
$466$	−267.936			−0.574970
$467$	616.116	+	616.116i	1.31931	+	1.31931i	0.914325	+	0.404980i	$0.132722\pi$
$467$	616.116	+	616.116i	1.31931	+	1.31931i	0.404980	+	0.914325i	$0.367278\pi$
$468$	−1.34840	+	1.34840i	−0.00288120	+	0.00288120i
$469$			277.541i			0.591772i
$470$	39.1268	+	43.6800i	0.0832486	+	0.0929362i
$471$	−154.521			−0.328070
$472$	40.1038	+	40.1038i	0.0849657	+	0.0849657i
$473$	−116.678	+	116.678i	−0.246677	+	0.246677i
$474$		−	21.5072i		−	0.0453738i
$475$	630.590	+	69.5568i	1.32756	+	0.146435i
$476$	−86.6385			−0.182014
$477$	−100.768	−	100.768i	−0.211254	−	0.211254i
$478$	−28.2933	+	28.2933i	−0.0591910	+	0.0591910i
$479$			465.174i			0.971136i	0.874199	+	0.485568i	$0.161387\pi$
$479$			465.174i			0.971136i	−0.874199	+	0.485568i	$0.838613\pi$
$480$	−36.4906	+	32.6869i	−0.0760222	+	0.0680977i
$481$	−9.34189			−0.0194218
$482$	−298.141	−	298.141i	−0.618550	−	0.618550i
$483$	50.2238	−	50.2238i	0.103983	−	0.103983i
$484$		−	169.261i		−	0.349712i
$485$	−446.353	−	24.5429i	−0.920316	−	0.0506040i
$486$	−22.0454			−0.0453609
$487$	−326.491	−	326.491i	−0.670412	−	0.670412i	0.287399	−	0.957811i	$-0.407209\pi$
$487$	−326.491	−	326.491i	−0.670412	−	0.670412i	−0.957811	+	0.287399i	$0.907209\pi$
$488$	−20.9508	+	20.9508i	−0.0429319	+	0.0429319i
$489$			86.1038i			0.176081i
$490$	−9.36151	+	170.254i	−0.0191051	+	0.347458i
$491$	520.742			1.06057			0.530287	−	0.847818i	$-0.322084\pi$
$491$	520.742			1.06057			0.530287	+	0.847818i	$0.322084\pi$
$492$	−60.7027	−	60.7027i	−0.123379	−	0.123379i
$493$	135.311	−	135.311i	0.274465	−	0.274465i
$494$		−	11.4059i		−	0.0230890i
$495$	−60.3571	−	67.3809i	−0.121934	−	0.136123i
$496$	−46.0191			−0.0927804
$497$	129.471	+	129.471i	0.260504	+	0.260504i
$498$	−117.403	+	117.403i	−0.235750	+	0.235750i
$499$		−	153.945i		−	0.308506i	−0.988031	−	0.154253i	$-0.950703\pi$
$499$		−	153.945i		−	0.308506i	0.988031	−	0.154253i	$-0.0492971\pi$
$500$	203.381	−	145.382i	0.406763	−	0.290765i
$501$	161.650			0.322654
$502$	−338.924	−	338.924i	−0.675148	−	0.675148i
$503$	413.457	−	413.457i	0.821982	−	0.821982i	−0.164410	−	0.986392i	$-0.552572\pi$
$503$	413.457	−	413.457i	0.821982	−	0.821982i	0.986392	+	0.164410i	$0.0525721\pi$
$504$			72.5548i			0.143958i
$505$	−25.6843	+	23.0070i	−0.0508601	+	0.0455585i
$506$	40.9023			0.0808347
$507$	206.858	+	206.858i	0.408004	+	0.408004i
$508$	342.629	−	342.629i	0.674467	−	0.674467i
$509$			528.261i			1.03784i	0.854823	+	0.518920i	$0.173666\pi$
$509$			528.261i			1.03784i	−0.854823	+	0.518920i	$0.826334\pi$
$510$	61.9542	+	3.40658i	0.121479	+	0.00667957i
$511$	306.317			0.599445
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	93.2395	−	93.2395i	0.181753	−	0.181753i
$514$			333.729i			0.649277i
$515$	−34.3686	+	625.048i	−0.0667351	+	1.21369i
$516$	−94.7819			−0.183686
$517$	35.3652	+	35.3652i	0.0684046	+	0.0684046i
$518$	−251.334	+	251.334i	−0.485201	+	0.485201i
$519$		−	375.826i		−	0.724134i
$520$	−2.99893	−	3.34791i	−0.00576717	−	0.00643830i
$521$	630.082			1.20937			0.604685	−	0.796464i	$-0.293299\pi$
$521$	630.082			1.20937			0.604685	+	0.796464i	$0.293299\pi$
$522$	−113.315	−	113.315i	−0.217079	−	0.217079i
$523$	325.068	−	325.068i	0.621545	−	0.621545i	−0.324381	−	0.945927i	$-0.605156\pi$
$523$	325.068	−	325.068i	0.621545	−	0.621545i	0.945927	+	0.324381i	$0.105156\pi$
$524$		−	18.6369i		−	0.0355667i
$525$	40.5945	−	368.023i	0.0773229	−	0.700996i
$526$	605.906			1.15191
$527$	41.2139	+	41.2139i	0.0782047	+	0.0782047i
$528$	−29.5444	+	29.5444i	−0.0559553	+	0.0559553i
$529$		−	23.0000i		−	0.0434783i
$530$	250.195	−	224.115i	0.472066	−	0.422858i
$531$	−60.1557			−0.113288
$532$	−306.865	−	306.865i	−0.576815	−	0.576815i
$533$	5.56930	−	5.56930i	0.0104490	−	0.0104490i
$534$			26.2977i			0.0492466i
$535$	616.802	+	33.9152i	1.15290	+	0.0633928i
$536$	−91.8063			−0.171280
$537$	−21.4437	−	21.4437i	−0.0399323	−	0.0399323i
$538$	−259.411	+	259.411i	−0.482177	+	0.482177i
$539$			145.425i			0.269804i
$540$	2.85282	−	51.8832i	0.00528300	−	0.0960799i
$541$	242.869			0.448926			0.224463	−	0.974483i	$-0.427937\pi$
$541$	242.869			0.448926			0.224463	+	0.974483i	$0.427937\pi$
$542$	−430.196	−	430.196i	−0.793719	−	0.793719i
$543$	−423.232	+	423.232i	−0.779433	+	0.779433i
$544$		−	28.6587i		−	0.0526814i
$545$	−27.8068	−	31.0426i	−0.0510216	−	0.0569590i
$546$	−6.65670			−0.0121918
$547$	139.082	+	139.082i	0.254263	+	0.254263i	0.822716	−	0.568453i	$-0.192458\pi$
$547$	139.082	+	139.082i	0.254263	+	0.254263i	−0.568453	+	0.822716i	$0.692458\pi$
$548$	216.794	−	216.794i	0.395609	−	0.395609i
$549$		−	31.4261i		−	0.0572425i
$550$	166.389	−	133.329i	0.302526	−	0.242416i
$551$	958.518			1.73960
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	53.0876	−	53.0876i	0.0959992	−	0.0959992i
$554$		−	343.787i		−	0.620553i
$555$	189.609	−	169.844i	0.341637	−	0.306025i
$556$	253.440			0.455827
$557$	−501.877	−	501.877i	−0.901036	−	0.901036i	0.0944902	−	0.995526i	$-0.469878\pi$
$557$	−501.877	−	501.877i	−0.901036	−	0.901036i	−0.995526	+	0.0944902i	$0.969878\pi$
$558$	34.5143	−	34.5143i	0.0618536	−	0.0618536i
$559$		−	8.69597i		−	0.0155563i
$560$	−170.755	−	9.38907i	−0.304920	−	0.0167662i
$561$	52.9189			0.0943296
$562$	349.790	+	349.790i	0.622403	+	0.622403i
$563$	592.906	−	592.906i	1.05312	−	1.05312i	0.0546116	−	0.998508i	$-0.482608\pi$
$563$	592.906	−	592.906i	1.05312	−	1.05312i	0.998508	−	0.0546116i	$-0.0173921\pi$
$564$			28.7285i			0.0509370i
$565$	−19.6333	+	357.064i	−0.0347492	+	0.631971i
$566$	741.616			1.31028
$567$	−54.4161	−	54.4161i	−0.0959720	−	0.0959720i
$568$	−42.8268	+	42.8268i	−0.0753993	+	0.0753993i
$569$			204.295i			0.359043i	0.983754	+	0.179521i	$0.0574549\pi$
$569$			204.295i			0.359043i	−0.983754	+	0.179521i	$0.942545\pi$
$570$	207.370	+	231.502i	0.363807	+	0.406144i
$571$	106.932			0.187271			0.0936357	−	0.995607i	$-0.470151\pi$
$571$	106.932			0.187271			0.0936357	+	0.995607i	$0.470151\pi$
$572$	−2.71061	−	2.71061i	−0.00473884	−	0.00473884i
$573$	133.764	−	133.764i	0.233445	−	0.233445i
$574$		−	299.673i		−	0.522078i
$575$	−74.9729	−	93.5632i	−0.130388	−	0.162719i
$576$	−24.0000			−0.0416667
$577$	−258.933	−	258.933i	−0.448757	−	0.448757i	0.446184	−	0.894941i	$-0.352783\pi$
$577$	−258.933	−	258.933i	−0.448757	−	0.448757i	−0.894941	+	0.446184i	$0.852783\pi$
$578$	263.334	−	263.334i	0.455595	−	0.455595i
$579$		−	58.7993i		−	0.101553i
$580$	281.348	−	252.020i	0.485082	−	0.434518i
$581$	−579.589			−0.997571
$582$	−154.855	−	154.855i	−0.266074	−	0.266074i
$583$	202.568	−	202.568i	0.347459	−	0.347459i
$584$			101.325i			0.173501i
$585$	4.76013	+	0.261738i	0.00813698	+	0.000447416i
$586$	−101.292			−0.172854
$587$	−668.767	−	668.767i	−1.13930	−	1.13930i	−0.988577	−	0.150719i	$-0.951841\pi$
$587$	−668.767	−	668.767i	−1.13930	−	1.13930i	−0.150719	−	0.988577i	$-0.548159\pi$
$588$	−59.0669	+	59.0669i	−0.100454	+	0.100454i
$589$			291.952i			0.495673i
$590$	7.78454	−	141.574i	0.0131941	−	0.239957i
$591$	−347.543			−0.588059
$592$	−83.1374	−	83.1374i	−0.140435	−	0.140435i
$593$	31.4468	−	31.4468i	0.0530300	−	0.0530300i	−0.680094	−	0.733124i	$-0.738061\pi$
$593$	31.4468	−	31.4468i	0.0530300	−	0.0530300i	0.733124	+	0.680094i	$0.238061\pi$
$594$		−	44.3166i		−	0.0746070i
$595$	144.517	+	161.334i	0.242886	+	0.271150i
$596$	−123.079			−0.206509
$597$	−216.264	−	216.264i	−0.362251	−	0.362251i
$598$	−1.52422	+	1.52422i	−0.00254886	+	0.00254886i
$599$			789.984i			1.31884i	0.751776	+	0.659419i	$0.229198\pi$
$599$			789.984i			1.31884i	−0.751776	+	0.659419i	$0.770802\pi$
$600$	121.736	+	13.4280i	0.202894	+	0.0223801i
$601$	490.719			0.816503			0.408252	−	0.912869i	$-0.366139\pi$
$601$	490.719			0.816503			0.408252	+	0.912869i	$0.366139\pi$
$602$	−233.956	−	233.956i	−0.388632	−	0.388632i
$603$	68.8547	−	68.8547i	0.114187	−	0.114187i
$604$		−	201.905i		−	0.334280i
$605$	−315.190	+	282.335i	−0.520975	+	0.466669i
$606$	−16.8927			−0.0278757
$607$	268.721	+	268.721i	0.442703	+	0.442703i	0.892920	−	0.450216i	$-0.148653\pi$
$607$	268.721	+	268.721i	0.442703	+	0.442703i	−0.450216	+	0.892920i	$0.648653\pi$
$608$	101.506	−	101.506i	0.166951	−	0.166951i
$609$		−	559.408i		−	0.918567i
$610$	73.9604	+	4.06675i	0.121247	+	0.00666680i
$611$	−2.63575			−0.00431384
$612$	21.4940	+	21.4940i	0.0351209	+	0.0351209i
$613$	754.006	−	754.006i	1.23003	−	1.23003i	0.266073	−	0.963953i	$-0.414274\pi$
$613$	754.006	−	754.006i	1.23003	−	1.23003i	0.963953	−	0.266073i	$-0.0857261\pi$
$614$			437.517i			0.712568i
$615$	−11.7830	+	214.293i	−0.0191593	+	0.348444i
$616$	−145.853			−0.236774
$617$	−577.903	−	577.903i	−0.936634	−	0.936634i	0.0614748	−	0.998109i	$-0.480420\pi$
$617$	−577.903	−	577.903i	−0.936634	−	0.936634i	−0.998109	+	0.0614748i	$0.980420\pi$
$618$	−216.850	+	216.850i	−0.350890	+	0.350890i
$619$			71.5819i			0.115641i	0.998327	+	0.0578206i	$0.0184151\pi$
$619$			71.5819i			0.115641i	−0.998327	+	0.0578206i	$0.981585\pi$
$620$	76.7619	+	85.6947i	0.123810	+	0.138217i
$621$	−24.9199			−0.0401286
$622$	162.318	+	162.318i	0.260962	+	0.260962i
$623$	−64.9123	+	64.9123i	−0.104193	+	0.104193i
$624$		−	2.20193i		−	0.00352874i
$625$	−609.974	−	136.223i	−0.975958	−	0.217957i
$626$	128.558			0.205365
$627$	187.434	+	187.434i	0.298937	+	0.298937i
$628$	126.166	−	126.166i	0.200901	−	0.200901i
$629$			148.913i			0.236746i
$630$	135.108	−	121.025i	0.214458	−	0.192103i
$631$	568.739			0.901330			0.450665	−	0.892693i	$-0.351187\pi$
$631$	568.739			0.901330			0.450665	+	0.892693i	$0.351187\pi$
$632$	17.5605	+	17.5605i	0.0277857	+	0.0277857i
$633$	−154.789	+	154.789i	−0.244533	+	0.244533i
$634$		−	681.487i		−	1.07490i
$635$	−1209.55	−	66.5077i	−1.90480	−	0.104736i
$636$	164.554			0.258732
$637$	−5.41922	−	5.41922i	−0.00850741	−	0.00850741i
$638$	227.791	−	227.791i	0.357039	−	0.357039i
$639$		−	64.2402i		−	0.100532i
$640$	3.10576	−	56.4832i	0.00485275	−	0.0882550i
$641$	−1051.81			−1.64089			−0.820445	−	0.571726i	$-0.806274\pi$
$641$	−1051.81			−1.64089			−0.820445	+	0.571726i	$0.806274\pi$
$642$	213.989	+	213.989i	0.333317	+	0.333317i
$643$	−64.6780	+	64.6780i	−0.100588	+	0.100588i	−0.755610	−	0.655022i	$-0.772659\pi$
$643$	−64.6780	+	64.6780i	−0.100588	+	0.100588i	0.655022	+	0.755610i	$0.272659\pi$
$644$			82.0151i			0.127353i
$645$	158.101	+	176.499i	0.245117	+	0.273641i
$646$	−181.815			−0.281447
$647$	682.188	+	682.188i	1.05439	+	1.05439i	0.998433	+	0.0559524i	$0.0178195\pi$
$647$	682.188	+	682.188i	1.05439	+	1.05439i	0.0559524	+	0.998433i	$0.482181\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	120.927i		−	0.186329i
$650$	−1.23198	+	11.1689i	−0.00189536	+	0.0171830i
$651$	170.388			0.261732
$652$	−70.3034	−	70.3034i	−0.107827	−	0.107827i
$653$	−740.977	+	740.977i	−1.13473	+	1.13473i	−0.145346	+	0.989381i	$0.546429\pi$
$653$	−740.977	+	740.977i	−1.13473	+	1.13473i	−0.989381	+	0.145346i	$0.953571\pi$
$654$		−	20.4168i		−	0.0312184i
$655$	−34.7049	+	31.0873i	−0.0529845	+	0.0474615i
$656$	99.1271			0.151108
$657$	−75.9935	−	75.9935i	−0.115667	−	0.115667i
$658$	−70.9123	+	70.9123i	−0.107770	+	0.107770i
$659$		−	985.952i		−	1.49613i	−0.663623	−	0.748067i	$-0.730982\pi$
$659$		−	985.952i		−	1.49613i	0.663623	−	0.748067i	$-0.269018\pi$
$660$	104.298	+	5.73485i	0.158027	+	0.00868917i
$661$	649.680			0.982875			0.491438	−	0.870913i	$-0.336472\pi$
$661$	649.680			0.982875			0.491438	+	0.870913i	$0.336472\pi$
$662$	−482.017	−	482.017i	−0.728122	−	0.728122i
$663$	−1.97201	+	1.97201i	−0.00297438	+	0.00297438i
$664$		−	191.719i		−	0.288733i
$665$	−59.5656	+	1083.30i	−0.0895723	+	1.62902i
$666$	124.706			0.187246
$667$	−128.090	−	128.090i	−0.192040	−	0.192040i
$668$	−131.986	+	131.986i	−0.197584	+	0.197584i
$669$		−	245.537i		−	0.367021i
$670$	153.137	+	170.958i	0.228563	+	0.255160i
$671$	63.1741			0.0941492
$672$	−59.2408	−	59.2408i	−0.0881559	−	0.0881559i
$673$	634.795	−	634.795i	0.943232	−	0.943232i	−0.0552411	−	0.998473i	$-0.517593\pi$
$673$	634.795	−	634.795i	0.943232	−	0.943232i	0.998473	+	0.0552411i	$0.0175927\pi$
$674$			598.618i			0.888158i
$675$	−101.373	+	81.2311i	−0.150182	+	0.120342i
$676$	−337.798			−0.499701
$677$	−500.696	−	500.696i	−0.739580	−	0.739580i	0.232916	−	0.972497i	$-0.425173\pi$
$677$	−500.696	−	500.696i	−0.739580	−	0.739580i	−0.972497	+	0.232916i	$0.925173\pi$
$678$	−123.877	+	123.877i	−0.182710	+	0.182710i
$679$		−	764.477i		−	1.12589i
$680$	−53.3669	+	47.8040i	−0.0784807	+	0.0702999i
$681$	−637.117			−0.935560
$682$	69.3821	+	69.3821i	0.101733	+	0.101733i
$683$	−457.846	+	457.846i	−0.670345	+	0.670345i	−0.957796	−	0.287450i	$-0.907192\pi$
$683$	−457.846	+	457.846i	−0.670345	+	0.670345i	0.287450	+	0.957796i	$0.407192\pi$
$684$			152.259i			0.222601i
$685$	−765.325	−	42.0818i	−1.11726	−	0.0614333i
$686$	300.934			0.438679
$687$	401.807	+	401.807i	0.584872	+	0.584872i
$688$	77.3891	−	77.3891i	0.112484	−	0.112484i
$689$			15.0974i			0.0219120i
$690$	3.22479	−	58.6481i	0.00467361	−	0.0849973i
$691$	182.546			0.264176			0.132088	−	0.991238i	$-0.457832\pi$
$691$	182.546			0.264176			0.132088	+	0.991238i	$0.457832\pi$
$692$	306.860	+	306.860i	0.443440	+	0.443440i
$693$	109.390	−	109.390i	0.157849	−	0.157849i
$694$		−	69.6610i		−	0.100376i
$695$	−422.749	−	471.944i	−0.608272	−	0.679056i
$696$	185.043			0.265867
$697$	−88.7766	−	88.7766i	−0.127370	−	0.127370i
$698$	−455.518	+	455.518i	−0.652604	+	0.652604i
$699$			328.153i			0.469461i
$700$	267.344	+	333.635i	0.381920	+	0.476621i
$701$	336.087			0.479440			0.239720	−	0.970842i	$-0.422944\pi$
$701$	336.087			0.479440			0.239720	+	0.970842i	$0.422944\pi$
$702$	1.65145	+	1.65145i	0.00235249	+	0.00235249i
$703$	−527.436	+	527.436i	−0.750264	+	0.750264i
$704$		−	48.2458i		−	0.0685309i
$705$	53.4969	−	47.9204i	0.0758821	−	0.0679722i
$706$	63.5217			0.0899741
$707$	−41.6973	−	41.6973i	−0.0589777	−	0.0589777i
$708$	49.1169	−	49.1169i	0.0693742	−	0.0693742i
$709$		−	607.338i		−	0.856612i	−0.903634	−	0.428306i	$-0.859110\pi$
$709$		−	607.338i		−	0.856612i	0.903634	−	0.428306i	$-0.140890\pi$
$710$	151.187	+	8.31310i	0.212940	+	0.0117086i
$711$	−26.3408			−0.0370475
$712$	−21.4720	−	21.4720i	−0.0301572	−	0.0301572i
$713$	39.0146	−	39.0146i	0.0547189	−	0.0547189i
$714$			106.110i			0.148614i
$715$	−0.526157	+	9.56901i	−0.000735884	+	0.0133832i
$716$	35.0174			0.0489069
$717$	34.6521	+	34.6521i	0.0483293	+	0.0483293i
$718$	39.3142	−	39.3142i	0.0547551	−	0.0547551i
$719$		−	916.546i		−	1.27475i	−0.770553	−	0.637376i	$-0.780020\pi$
$719$		−	916.546i		−	1.27475i	0.770553	−	0.637376i	$-0.219980\pi$
$720$	40.0331	+	44.6917i	0.0556015	+	0.0620719i
$721$	−1070.53			−1.48479
$722$	−282.970	−	282.970i	−0.391926	−	0.391926i
$723$	−365.147	+	365.147i	−0.505044	+	0.505044i
$724$		−	691.135i		−	0.954606i
$725$	−938.602	−	103.532i	−1.29462	−	0.142803i
$726$	−207.301			−0.285539
$727$	246.536	+	246.536i	0.339114	+	0.339114i	0.856034	−	0.516920i	$-0.172922\pi$
$727$	246.536	+	246.536i	0.339114	+	0.339114i	−0.516920	+	0.856034i	$0.672922\pi$
$728$	5.43517	−	5.43517i	0.00746590	−	0.00746590i
$729$			27.0000i			0.0370370i
$730$	188.682	−	169.014i	0.258469	−	0.231526i
$731$	−138.617			−0.189626
$732$	25.6593	+	25.6593i	0.0350537	+	0.0350537i
$733$	730.190	−	730.190i	0.996166	−	0.996166i	−0.00382636	−	0.999993i	$-0.501218\pi$
$733$	730.190	−	730.190i	0.996166	−	0.996166i	0.999993	+	0.00382636i	$0.00121797\pi$
$734$			843.646i			1.14938i
$735$	208.518	+	11.4655i	0.283698	+	0.0155993i
$736$	−27.1293			−0.0368605
$737$	138.414	+	138.414i	0.187808	+	0.187808i
$738$	−74.3453	+	74.3453i	−0.100739	+	0.100739i
$739$		−	865.300i		−	1.17091i	−0.810706	−	0.585453i	$-0.800917\pi$
$739$		−	865.300i		−	1.17091i	0.810706	−	0.585453i	$-0.199083\pi$
$740$	−16.1378	+	293.492i	−0.0218078	+	0.396611i
$741$	−13.9694			−0.0188521
$742$	406.179	+	406.179i	0.547411	+	0.547411i
$743$	791.656	−	791.656i	1.06549	−	1.06549i	0.0677859	−	0.997700i	$-0.478407\pi$
$743$	791.656	−	791.656i	1.06549	−	1.06549i	0.997700	−	0.0677859i	$-0.0215935\pi$
$744$			56.3616i			0.0757549i
$745$	205.302	+	229.193i	0.275573	+	0.307641i
$746$	−649.746			−0.870973
$747$	143.789	+	143.789i	0.192489	+	0.192489i
$748$	−43.2081	+	43.2081i	−0.0577648	+	0.0577648i
$749$			1056.41i			1.41042i
$750$	−178.056	−	249.090i	−0.237408	−	0.332120i
$751$	1140.21			1.51825			0.759125	−	0.650944i	$-0.225627\pi$
$751$	1140.21			1.51825			0.759125	+	0.650944i	$0.225627\pi$
$752$	−23.4567	−	23.4567i	−0.0311924	−	0.0311924i
$753$	−415.096	+	415.096i	−0.551256	+	0.551256i
$754$			16.9772i			0.0225162i
$755$	−375.979	+	336.787i	−0.497985	+	0.446075i
$756$	88.8612			0.117541
$757$	171.242	+	171.242i	0.226212	+	0.226212i	0.811108	−	0.584896i	$-0.198865\pi$
$757$	171.242	+	171.242i	0.226212	+	0.226212i	−0.584896	+	0.811108i	$0.698865\pi$
$758$	−188.177	+	188.177i	−0.248255	+	0.248255i
$759$		−	50.0949i		−	0.0660012i
$760$	−358.338	−	19.7034i	−0.471497	−	0.0259255i
$761$	82.4693			0.108370			0.0541848	−	0.998531i	$-0.482744\pi$
$761$	82.4693			0.108370			0.0541848	+	0.998531i	$0.482744\pi$
$762$	−419.633	−	419.633i	−0.550700	−	0.550700i
$763$	50.3962	−	50.3962i	0.0660501	−	0.0660501i
$764$			218.436i			0.285911i
$765$	4.17220	−	75.8781i	0.00545385	−	0.0991871i
$766$	463.908			0.605624
$767$	4.50634	+	4.50634i	0.00587528	+	0.00587528i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			643.087i			0.836264i	0.908386	+	0.418132i	$0.137315\pi$
$769$			643.087i			0.836264i	−0.908386	+	0.418132i	$0.862685\pi$
$770$	243.289	+	271.600i	0.315960	+	0.352728i
$771$	408.732			0.530133
$772$	48.0095	+	48.0095i	0.0621884	+	0.0621884i
$773$	−815.269	+	815.269i	−1.05468	+	1.05468i	−0.0562666	+	0.998416i	$0.517920\pi$
$773$	−815.269	+	815.269i	−1.05468	+	1.05468i	−0.998416	+	0.0562666i	$0.982080\pi$
$774$			116.084i			0.149979i
$775$	31.5344	−	285.885i	0.0406896	−	0.368884i
$776$	252.877			0.325872
$777$	307.820	+	307.820i	0.396165	+	0.396165i
$778$	−645.912	+	645.912i	−0.830220	+	0.830220i
$779$		−	628.876i		−	0.807287i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(3.72431 - 3.33609i) q^{5} +2.44949 q^{6} +(6.04624 + 6.04624i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(7.06040 + 0.388220i) q^{10} +6.03072 q^{11} +(2.44949 + 2.44949i) q^{12} +(-0.224734 + 0.224734i) q^{13} +12.0925i q^{14} +(0.475470 - 8.64719i) q^{15} -4.00000 q^{16} +(3.58233 + 3.58233i) q^{17} +(3.00000 - 3.00000i) q^{18} +25.3766i q^{19} +(6.67218 + 7.44862i) q^{20} +14.8102 q^{21} +(6.03072 + 6.03072i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(2.74099 - 24.8493i) q^{25} -0.449468 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-12.0925 + 12.0925i) q^{28} -37.7718i q^{29} +(9.12266 - 8.17172i) q^{30} +11.5048 q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.38610 - 7.38610i) q^{33} +7.16467i q^{34} +(42.6889 + 2.34727i) q^{35} +6.00000 q^{36} +(20.7844 + 20.7844i) q^{37} +(-25.3766 + 25.3766i) q^{38} +0.550483i q^{39} +(-0.776439 + 14.1208i) q^{40} -24.7818 q^{41} +(14.8102 + 14.8102i) q^{42} +(-19.3473 + 19.3473i) q^{43} +12.0614i q^{44} +(-10.0083 - 11.1729i) q^{45} +6.78233 q^{46} +(5.86417 + 5.86417i) q^{47} +(-4.89898 + 4.89898i) q^{48} +24.1140i q^{49} +(27.5903 - 22.1083i) q^{50} +8.77489 q^{51} +(-0.449468 - 0.449468i) q^{52} +(33.5894 - 33.5894i) q^{53} -7.34847i q^{54} +(22.4603 - 20.1190i) q^{55} -24.1849 q^{56} +(31.0798 + 31.0798i) q^{57} +(37.7718 - 37.7718i) q^{58} -20.0519i q^{59} +(17.2944 + 0.950940i) q^{60} +10.4754 q^{61} +(11.5048 + 11.5048i) q^{62} +(18.1387 - 18.1387i) q^{63} -8.00000i q^{64} +(-0.0872461 + 1.58671i) q^{65} +14.7722 q^{66} +(22.9516 + 22.9516i) q^{67} +(-7.16467 + 7.16467i) q^{68} -8.30662i q^{69} +(40.3416 + 45.0361i) q^{70} +21.4134 q^{71} +(6.00000 + 6.00000i) q^{72} +(25.3312 - 25.3312i) q^{73} +41.5687i q^{74} +(-27.0770 - 33.7910i) q^{75} -50.7531 q^{76} +(36.4632 + 36.4632i) q^{77} +(-0.550483 + 0.550483i) q^{78} -8.78027i q^{79} +(-14.8972 + 13.3444i) q^{80} -9.00000 q^{81} +(-24.7818 - 24.7818i) q^{82} +(-47.9297 + 47.9297i) q^{83} +29.6204i q^{84} +(25.2927 + 1.39073i) q^{85} -38.6945 q^{86} +(-46.2608 - 46.2608i) q^{87} +(-12.0614 + 12.0614i) q^{88} +10.7360i q^{89} +(1.16466 - 21.1812i) q^{90} -2.71759 q^{91} +(6.78233 + 6.78233i) q^{92} +(14.0904 - 14.0904i) q^{93} +11.7283i q^{94} +(84.6586 + 94.5102i) q^{95} -9.79796 q^{96} +(-63.2192 - 63.2192i) q^{97} +(-24.1140 + 24.1140i) q^{98} -18.0922i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} + O(q^{10}) \)	\( 40q + 40q^{2} - 8q^{5} - 8q^{7} - 80q^{8} - 16q^{10} + 32q^{11} + 16q^{13} + 24q^{15} - 160q^{16} - 48q^{17} + 120q^{18} - 16q^{20} - 96q^{21} + 32q^{22} + 32q^{26} + 16q^{28} + 24q^{30} + 152q^{31} - 160q^{32} - 24q^{33} + 48q^{35} + 240q^{36} + 216q^{37} + 16q^{38} - 168q^{41} - 96q^{42} - 48q^{43} + 24q^{45} - 232q^{47} - 40q^{50} + 32q^{52} + 8q^{53} - 272q^{55} + 32q^{56} - 136q^{58} - 64q^{61} + 152q^{62} - 24q^{63} + 416q^{65} - 48q^{66} - 32q^{67} + 96q^{68} + 88q^{70} - 104q^{71} + 240q^{72} + 480q^{73} - 216q^{75} + 32q^{76} + 280q^{77} - 192q^{78} + 32q^{80} - 360q^{81} - 168q^{82} - 576q^{83} - 208q^{85} - 96q^{86} + 24q^{87} - 64q^{88} + 144q^{91} + 96q^{93} + 168q^{95} + 24q^{97} + 176q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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