LMFDB - Embedded newform 690.3.k.a.277.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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			277.16
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.16

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-7.04634 - 0.590789i) q^{10} -16.7051 q^{11} +(2.44949 + 2.44949i) q^{12} +(-7.41164 + 7.41164i) q^{13} +7.98180i q^{14} +(-0.723566 + 8.62997i) q^{15} -4.00000 q^{16} +(-17.8517 - 17.8517i) q^{17} +(3.00000 - 3.00000i) q^{18} -18.0208i q^{19} +(-6.45555 - 7.63713i) q^{20} +9.77567 q^{21} +(-16.7051 - 16.7051i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(4.16290 - 24.6510i) q^{25} -14.8233 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-7.98180 + 7.98180i) q^{28} +17.7682i q^{29} +(-9.35354 + 7.90641i) q^{30} +2.15176 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-20.4595 + 20.4595i) q^{33} -35.7035i q^{34} +(-28.1212 - 2.35778i) q^{35} +6.00000 q^{36} +(34.1454 + 34.1454i) q^{37} +(18.0208 - 18.0208i) q^{38} +18.1547i q^{39} +(1.18158 - 14.0927i) q^{40} -55.9915 q^{41} +(9.77567 + 9.77567i) q^{42} +(-25.9837 + 25.9837i) q^{43} -33.4103i q^{44} +(9.68333 + 11.4557i) q^{45} +6.78233 q^{46} +(-1.36218 - 1.36218i) q^{47} +(-4.89898 + 4.89898i) q^{48} -17.1454i q^{49} +(28.8139 - 20.4881i) q^{50} -43.7276 q^{51} +(-14.8233 - 14.8233i) q^{52} +(-17.0984 + 17.0984i) q^{53} -7.34847i q^{54} +(63.7897 - 53.9205i) q^{55} -15.9636 q^{56} +(-22.0709 - 22.0709i) q^{57} +(-17.7682 + 17.7682i) q^{58} -72.1392i q^{59} +(-17.2599 - 1.44713i) q^{60} -67.4506 q^{61} +(2.15176 + 2.15176i) q^{62} +(11.9727 - 11.9727i) q^{63} -8.00000i q^{64} +(4.37872 - 52.2250i) q^{65} -40.9191 q^{66} +(29.6984 + 29.6984i) q^{67} +(35.7035 - 35.7035i) q^{68} -8.30662i q^{69} +(-25.7635 - 30.4790i) q^{70} +21.4377 q^{71} +(6.00000 + 6.00000i) q^{72} +(-73.0874 + 73.0874i) q^{73} +68.2909i q^{74} +(-25.0927 - 35.2896i) q^{75} +36.0417 q^{76} +(-66.6685 - 66.6685i) q^{77} +(-18.1547 + 18.1547i) q^{78} +86.1320i q^{79} +(15.2743 - 12.9111i) q^{80} -9.00000 q^{81} +(-55.9915 - 55.9915i) q^{82} +(-105.066 + 105.066i) q^{83} +19.5513i q^{84} +(125.789 + 10.5466i) q^{85} -51.9673 q^{86} +(21.7615 + 21.7615i) q^{87} +(33.4103 - 33.4103i) q^{88} +86.6781i q^{89} +(-1.77237 + 21.1390i) q^{90} -59.1582 q^{91} +(6.78233 + 6.78233i) q^{92} +(2.63536 - 2.63536i) q^{93} -2.72436i q^{94} +(58.1672 + 68.8137i) q^{95} -9.79796 q^{96} +(-42.2382 - 42.2382i) q^{97} +(17.1454 - 17.1454i) q^{98} +50.1154i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

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
$5$	−3.81857	+	3.22778i	−0.763713	+	0.645555i
$5$	−3.81857	+	3.22778i	−0.763713	+	0.645555i
$6$	2.44949			0.408248
$7$	3.99090	+	3.99090i	0.570128	+	0.570128i	0.932164	−	0.362036i	$-0.117918\pi$
$7$	3.99090	+	3.99090i	0.570128	+	0.570128i	−0.362036	+	0.932164i	$0.617918\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−7.04634	−	0.590789i	−0.704634	−	0.0590789i
$11$	−16.7051			−1.51865			−0.759325	−	0.650712i	$-0.774471\pi$
$11$	−16.7051			−1.51865			−0.759325	+	0.650712i	$0.774471\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−7.41164	+	7.41164i	−0.570126	+	0.570126i	−0.932164	−	0.362037i	$-0.882081\pi$
$13$	−7.41164	+	7.41164i	−0.570126	+	0.570126i	0.362037	+	0.932164i	$0.382081\pi$
$14$			7.98180i			0.570128i
$15$	−0.723566	+	8.62997i	−0.0482377	+	0.575332i
$16$	−4.00000			−0.250000
$17$	−17.8517	−	17.8517i	−1.05010	−	1.05010i	−0.998677	−	0.0514253i	$-0.983624\pi$
$17$	−17.8517	−	17.8517i	−1.05010	−	1.05010i	−0.0514253	−	0.998677i	$-0.516376\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$		−	18.0208i		−	0.948465i	−0.880400	−	0.474232i	$-0.842726\pi$
$19$		−	18.0208i		−	0.948465i	0.880400	−	0.474232i	$-0.157274\pi$
$20$	−6.45555	−	7.63713i	−0.322778	−	0.381857i
$21$	9.77567			0.465508
$22$	−16.7051	−	16.7051i	−0.759325	−	0.759325i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	4.16290	−	24.6510i	0.166516	−	0.986039i
$26$	−14.8233			−0.570126
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	−7.98180	+	7.98180i	−0.285064	+	0.285064i
$29$			17.7682i			0.612695i	0.951920	+	0.306347i	$0.0991069\pi$
$29$			17.7682i			0.612695i	−0.951920	+	0.306347i	$0.900893\pi$
$30$	−9.35354	+	7.90641i	−0.311785	+	0.263547i
$31$	2.15176			0.0694117			0.0347059	−	0.999398i	$-0.488951\pi$
$31$	2.15176			0.0694117			0.0347059	+	0.999398i	$0.488951\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−20.4595	+	20.4595i	−0.619986	+	0.619986i
$34$		−	35.7035i		−	1.05010i
$35$	−28.1212	−	2.35778i	−0.803464	−	0.0673652i
$36$	6.00000			0.166667
$37$	34.1454	+	34.1454i	0.922850	+	0.922850i	0.997230	−	0.0743802i	$-0.0236978\pi$
$37$	34.1454	+	34.1454i	0.922850	+	0.922850i	−0.0743802	+	0.997230i	$0.523698\pi$
$38$	18.0208	−	18.0208i	0.474232	−	0.474232i
$39$			18.1547i			0.465506i
$40$	1.18158	−	14.0927i	0.0295395	−	0.352317i
$41$	−55.9915			−1.36565			−0.682823	−	0.730584i	$-0.739248\pi$
$41$	−55.9915			−1.36565			−0.682823	+	0.730584i	$0.739248\pi$
$42$	9.77567	+	9.77567i	0.232754	+	0.232754i
$43$	−25.9837	+	25.9837i	−0.604271	+	0.604271i	−0.941443	−	0.337172i	$-0.890530\pi$
$43$	−25.9837	+	25.9837i	−0.604271	+	0.604271i	0.337172	+	0.941443i	$0.390530\pi$
$44$		−	33.4103i		−	0.759325i
$45$	9.68333	+	11.4557i	0.215185	+	0.254571i
$46$	6.78233			0.147442
$47$	−1.36218	−	1.36218i	−0.0289826	−	0.0289826i	0.692467	−	0.721450i	$-0.256524\pi$
$47$	−1.36218	−	1.36218i	−0.0289826	−	0.0289826i	−0.721450	+	0.692467i	$0.756524\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$		−	17.1454i		−	0.349907i
$50$	28.8139	−	20.4881i	0.576277	−	0.409761i
$51$	−43.7276			−0.857405
$52$	−14.8233	−	14.8233i	−0.285063	−	0.285063i
$53$	−17.0984	+	17.0984i	−0.322612	+	0.322612i	−0.849768	−	0.527156i	$-0.823258\pi$
$53$	−17.0984	+	17.0984i	−0.322612	+	0.322612i	0.527156	+	0.849768i	$0.323258\pi$
$54$		−	7.34847i		−	0.136083i
$55$	63.7897	−	53.9205i	1.15981	−	0.980372i
$56$	−15.9636			−0.285064
$57$	−22.0709	−	22.0709i	−0.387209	−	0.387209i
$58$	−17.7682	+	17.7682i	−0.306347	+	0.306347i
$59$		−	72.1392i		−	1.22270i	−0.791361	−	0.611349i	$-0.790627\pi$
$59$		−	72.1392i		−	1.22270i	0.791361	−	0.611349i	$-0.209373\pi$
$60$	−17.2599	−	1.44713i	−0.287666	−	0.0241189i
$61$	−67.4506			−1.10575			−0.552874	−	0.833265i	$-0.686469\pi$
$61$	−67.4506			−1.10575			−0.552874	+	0.833265i	$0.686469\pi$
$62$	2.15176	+	2.15176i	0.0347059	+	0.0347059i
$63$	11.9727	−	11.9727i	0.190043	−	0.190043i
$64$		−	8.00000i		−	0.125000i
$65$	4.37872	−	52.2250i	0.0673649	−	0.803461i
$66$	−40.9191			−0.619986
$67$	29.6984	+	29.6984i	0.443259	+	0.443259i	0.893106	−	0.449846i	$-0.148521\pi$
$67$	29.6984	+	29.6984i	0.443259	+	0.443259i	−0.449846	+	0.893106i	$0.648521\pi$
$68$	35.7035	−	35.7035i	0.525051	−	0.525051i
$69$		−	8.30662i		−	0.120386i
$70$	−25.7635	−	30.4790i	−0.368050	−	0.435415i
$71$	21.4377			0.301939			0.150969	−	0.988538i	$-0.451760\pi$
$71$	21.4377			0.301939			0.150969	+	0.988538i	$0.451760\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	−73.0874	+	73.0874i	−1.00120	+	1.00120i	−0.00119781	+	0.999999i	$0.500381\pi$
$73$	−73.0874	+	73.0874i	−1.00120	+	1.00120i	−0.999999	+	0.00119781i	$0.999619\pi$
$74$			68.2909i			0.922850i
$75$	−25.0927	−	35.2896i	−0.334569	−	0.470529i
$76$	36.0417			0.474232
$77$	−66.6685	−	66.6685i	−0.865825	−	0.865825i
$78$	−18.1547	+	18.1547i	−0.232753	+	0.232753i
$79$			86.1320i			1.09028i	0.838346	+	0.545139i	$0.183523\pi$
$79$			86.1320i			1.09028i	−0.838346	+	0.545139i	$0.816477\pi$
$80$	15.2743	−	12.9111i	0.190928	−	0.161389i
$81$	−9.00000			−0.111111
$82$	−55.9915	−	55.9915i	−0.682823	−	0.682823i
$83$	−105.066	+	105.066i	−1.26585	+	1.26585i	−0.317640	+	0.948211i	$0.602890\pi$
$83$	−105.066	+	105.066i	−1.26585	+	1.26585i	−0.948211	+	0.317640i	$0.897110\pi$
$84$			19.5513i			0.232754i
$85$	125.789	+	10.5466i	1.47988	+	0.124078i
$86$	−51.9673			−0.604271
$87$	21.7615	+	21.7615i	0.250132	+	0.250132i
$88$	33.4103	−	33.4103i	0.379662	−	0.379662i
$89$			86.6781i			0.973911i	0.873427	+	0.486955i	$0.161893\pi$
$89$			86.6781i			0.973911i	−0.873427	+	0.486955i	$0.838107\pi$
$90$	−1.77237	+	21.1390i	−0.0196930	+	0.234878i
$91$	−59.1582			−0.650090
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	2.63536	−	2.63536i	0.0283372	−	0.0283372i
$94$		−	2.72436i		−	0.0289826i
$95$	58.1672	+	68.8137i	0.612287	+	0.724355i
$96$	−9.79796			−0.102062
$97$	−42.2382	−	42.2382i	−0.435445	−	0.435445i	0.455031	−	0.890476i	$-0.349628\pi$
$97$	−42.2382	−	42.2382i	−0.435445	−	0.435445i	−0.890476	+	0.455031i	$0.849628\pi$
$98$	17.1454	−	17.1454i	0.174954	−	0.174954i
$99$			50.1154i			0.506216i
$100$	49.3019	+	8.32581i	0.493019	+	0.0832581i
$101$	61.6323			0.610221			0.305111	−	0.952317i	$-0.401307\pi$
$101$	61.6323			0.610221			0.305111	+	0.952317i	$0.401307\pi$
$102$	−43.7276	−	43.7276i	−0.428702	−	0.428702i
$103$	10.6060	−	10.6060i	0.102971	−	0.102971i	−0.653744	−	0.756715i	$-0.726803\pi$
$103$	10.6060	−	10.6060i	0.102971	−	0.102971i	0.756715	+	0.653744i	$0.226803\pi$
$104$		−	29.6466i		−	0.285063i
$105$	−37.3290	+	31.5537i	−0.355515	+	0.300511i
$106$	−34.1969			−0.322612
$107$	11.9686	+	11.9686i	0.111856	+	0.111856i	0.760819	−	0.648964i	$-0.224797\pi$
$107$	11.9686	+	11.9686i	0.111856	+	0.111856i	−0.648964	+	0.760819i	$0.724797\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			36.7920i			0.337541i	0.985655	+	0.168771i	$0.0539797\pi$
$109$			36.7920i			0.337541i	−0.985655	+	0.168771i	$0.946020\pi$
$110$	117.710	+	9.86922i	1.07009	+	0.0897202i
$111$	83.6389			0.753504
$112$	−15.9636	−	15.9636i	−0.142532	−	0.142532i
$113$	45.2853	−	45.2853i	0.400755	−	0.400755i	−0.477744	−	0.878499i	$-0.658545\pi$
$113$	45.2853	−	45.2853i	0.400755	−	0.400755i	0.878499	+	0.477744i	$0.158545\pi$
$114$		−	44.1418i		−	0.387209i
$115$	−2.00346	+	23.8953i	−0.0174214	+	0.207785i
$116$	−35.5363			−0.306347
$117$	22.2349	+	22.2349i	0.190042	+	0.190042i
$118$	72.1392	−	72.1392i	0.611349	−	0.611349i
$119$		−	142.489i		−	1.19739i
$120$	−15.8128	−	18.7071i	−0.131773	−	0.155892i
$121$	158.062			1.30630
$122$	−67.4506	−	67.4506i	−0.552874	−	0.552874i
$123$	−68.5753	+	68.5753i	−0.557523	+	0.557523i
$124$			4.30353i			0.0347059i
$125$	63.6715	+	107.568i	0.509372	+	0.860546i
$126$	23.9454			0.190043
$127$	107.150	+	107.150i	0.843701	+	0.843701i	0.989338	−	0.145637i	$-0.0465231\pi$
$127$	107.150	+	107.150i	0.843701	+	0.843701i	−0.145637	+	0.989338i	$0.546523\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			63.6467i			0.493385i
$130$	56.6037	−	47.8462i	0.435413	−	0.368048i
$131$	160.837			1.22776			0.613881	−	0.789399i	$-0.289608\pi$
$131$	160.837			1.22776			0.613881	+	0.789399i	$0.289608\pi$
$132$	−40.9191	−	40.9191i	−0.309993	−	0.309993i
$133$	71.9193	−	71.9193i	0.540747	−	0.540747i
$134$			59.3968i			0.443259i
$135$	25.8899	+	2.17070i	0.191777	+	0.0160792i
$136$	71.4069			0.525051
$137$	−185.661	−	185.661i	−1.35519	−	1.35519i	−0.879748	−	0.475441i	$-0.842288\pi$
$137$	−185.661	−	185.661i	−1.35519	−	1.35519i	−0.475441	−	0.879748i	$-0.657712\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			130.439i			0.938412i	0.883089	+	0.469206i	$0.155460\pi$
$139$			130.439i			0.938412i	−0.883089	+	0.469206i	$0.844540\pi$
$140$	4.71556	−	56.2425i	0.0336826	−	0.401732i
$141$	−3.33665			−0.0236642
$142$	21.4377	+	21.4377i	0.150969	+	0.150969i
$143$	123.812	−	123.812i	0.865822	−	0.865822i
$144$			12.0000i			0.0833333i
$145$	−57.3517	−	67.8489i	−0.395529	−	0.467923i
$146$	−146.175			−1.00120
$147$	−20.9988	−	20.9988i	−0.142849	−	0.142849i
$148$	−68.2909	+	68.2909i	−0.461425	+	0.461425i
$149$			5.80879i			0.0389852i	0.999810	+	0.0194926i	$0.00620507\pi$
$149$			5.80879i			0.0389852i	−0.999810	+	0.0194926i	$0.993795\pi$
$150$	10.1970	−	60.3823i	0.0679800	−	0.402549i
$151$	−118.863			−0.787173			−0.393587	−	0.919288i	$-0.628766\pi$
$151$	−118.863			−0.787173			−0.393587	+	0.919288i	$0.628766\pi$
$152$	36.0417	+	36.0417i	0.237116	+	0.237116i
$153$	−53.5552	+	53.5552i	−0.350034	+	0.350034i
$154$		−	133.337i		−	0.865825i
$155$	−8.21665	+	6.94541i	−0.0530107	+	0.0448091i
$156$	−36.3095			−0.232753
$157$	16.2859	+	16.2859i	0.103732	+	0.103732i	0.757068	−	0.653336i	$-0.226631\pi$
$157$	16.2859	+	16.2859i	0.103732	+	0.103732i	−0.653336	+	0.757068i	$0.726631\pi$
$158$	−86.1320	+	86.1320i	−0.545139	+	0.545139i
$159$			41.8824i			0.263412i
$160$	28.1854	+	2.36316i	0.176159	+	0.0147697i
$161$	27.0676			0.168122
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	126.235	−	126.235i	0.774448	−	0.774448i	−0.204432	−	0.978881i	$-0.565535\pi$
$163$	126.235	−	126.235i	0.774448	−	0.774448i	0.978881	+	0.204432i	$0.0655349\pi$
$164$		−	111.983i		−	0.682823i
$165$	12.0873	−	144.165i	0.0732562	−	0.873727i
$166$	−210.131			−1.26585
$167$	72.1438	+	72.1438i	0.431999	+	0.431999i	0.889308	−	0.457309i	$-0.151187\pi$
$167$	72.1438	+	72.1438i	0.431999	+	0.431999i	−0.457309	+	0.889308i	$0.651187\pi$
$168$	−19.5513	+	19.5513i	−0.116377	+	0.116377i
$169$			59.1352i			0.349912i
$170$	115.243	+	136.336i	0.677899	+	0.801977i
$171$	−54.0625			−0.316155
$172$	−51.9673	−	51.9673i	−0.302136	−	0.302136i
$173$	−109.972	+	109.972i	−0.635679	+	0.635679i	−0.949487	−	0.313808i	$-0.898395\pi$
$173$	−109.972	+	109.972i	−0.635679	+	0.635679i	0.313808	+	0.949487i	$0.398395\pi$
$174$			43.5229i			0.250132i
$175$	114.993	−	81.7658i	0.657104	−	0.467233i
$176$	66.8206			0.379662
$177$	−88.3521	−	88.3521i	−0.499165	−	0.499165i
$178$	−86.6781	+	86.6781i	−0.486955	+	0.486955i
$179$		−	4.73899i		−	0.0264748i	−0.999912	−	0.0132374i	$-0.995786\pi$
$179$		−	4.73899i		−	0.0264748i	0.999912	−	0.0132374i	$-0.00421372\pi$
$180$	−22.9114	+	19.3667i	−0.127286	+	0.107593i
$181$	39.1292			0.216183			0.108092	−	0.994141i	$-0.465526\pi$
$181$	39.1292			0.216183			0.108092	+	0.994141i	$0.465526\pi$
$182$	−59.1582	−	59.1582i	−0.325045	−	0.325045i
$183$	−82.6098	+	82.6098i	−0.451420	+	0.451420i
$184$			13.5647i			0.0737210i
$185$	−240.601	−	20.1728i	−1.30054	−	0.109042i
$186$	5.27072			0.0283372
$187$	298.216	+	298.216i	1.59474	+	1.59474i
$188$	2.72436	−	2.72436i	0.0144913	−	0.0144913i
$189$		−	29.3270i		−	0.155169i
$190$	−10.6465	+	126.981i	−0.0560343	+	0.668321i
$191$	−230.340			−1.20597			−0.602984	−	0.797753i	$-0.706022\pi$
$191$	−230.340			−1.20597			−0.602984	+	0.797753i	$0.706022\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	187.139	−	187.139i	0.969631	−	0.969631i	−0.0299208	−	0.999552i	$-0.509526\pi$
$193$	187.139	−	187.139i	0.969631	−	0.969631i	0.999552	+	0.0299208i	$0.00952551\pi$
$194$		−	84.4763i		−	0.435445i
$195$	−58.5994	−	69.3251i	−0.300510	−	0.355513i
$196$	34.2909			0.174954
$197$	87.8443	+	87.8443i	0.445910	+	0.445910i	0.893992	−	0.448082i	$-0.147893\pi$
$197$	87.8443	+	87.8443i	0.445910	+	0.445910i	−0.448082	+	0.893992i	$0.647893\pi$
$198$	−50.1154	+	50.1154i	−0.253108	+	0.253108i
$199$		−	211.873i		−	1.06469i	−0.846528	−	0.532344i	$-0.821311\pi$
$199$		−	211.873i		−	1.06469i	0.846528	−	0.532344i	$-0.178689\pi$
$200$	40.9761	+	57.6277i	0.204881	+	0.288139i
$201$	72.7459			0.361920
$202$	61.6323	+	61.6323i	0.305111	+	0.305111i
$203$	−70.9109	+	70.9109i	−0.349315	+	0.349315i
$204$		−	87.4553i		−	0.428702i
$205$	213.807	−	180.728i	1.04296	−	0.881601i
$206$	21.2120			0.102971
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	29.6466	−	29.6466i	0.142532	−	0.142532i
$209$			301.041i			1.44039i
$210$	−68.8827	−	5.77536i	−0.328013	−	0.0275017i
$211$	103.501			0.490527			0.245264	−	0.969456i	$-0.421125\pi$
$211$	103.501			0.490527			0.245264	+	0.969456i	$0.421125\pi$
$212$	−34.1969	−	34.1969i	−0.161306	−	0.161306i
$213$	26.2557	−	26.2557i	0.123266	−	0.123266i
$214$			23.9371i			0.111856i
$215$	15.3509	−	183.090i	0.0713994	−	0.851580i
$216$	14.6969			0.0680414
$217$	8.58747	+	8.58747i	0.0395736	+	0.0395736i
$218$	−36.7920	+	36.7920i	−0.168771	+	0.168771i
$219$			179.027i			0.817474i
$220$	107.841	+	127.579i	0.490186	+	0.579906i
$221$	264.621			1.19738
$222$	83.6389	+	83.6389i	0.376752	+	0.376752i
$223$	158.145	−	158.145i	0.709170	−	0.709170i	−0.257191	−	0.966361i	$-0.582797\pi$
$223$	158.145	−	158.145i	0.709170	−	0.709170i	0.966361	+	0.257191i	$0.0827969\pi$
$224$		−	31.9272i		−	0.142532i
$225$	−73.9529	−	12.4887i	−0.328680	−	0.0555054i
$226$	90.5707			0.400755
$227$	45.6136	+	45.6136i	0.200941	+	0.200941i	0.800403	−	0.599462i	$-0.204619\pi$
$227$	45.6136	+	45.6136i	0.200941	+	0.200941i	−0.599462	+	0.800403i	$0.704619\pi$
$228$	44.1418	−	44.1418i	0.193605	−	0.193605i
$229$			178.009i			0.777334i	0.921378	+	0.388667i	$0.127064\pi$
$229$			178.009i			0.777334i	−0.921378	+	0.388667i	$0.872936\pi$
$230$	−25.8988	+	21.8919i	−0.112603	+	0.0951820i
$231$	−163.304			−0.706943
$232$	−35.5363	−	35.5363i	−0.153174	−	0.153174i
$233$	194.951	−	194.951i	0.836702	−	0.836702i	−0.151722	−	0.988423i	$-0.548482\pi$
$233$	194.951	−	194.951i	0.836702	−	0.836702i	0.988423	+	0.151722i	$0.0484817\pi$
$234$			44.4698i			0.190042i
$235$	9.59839	+	0.804762i	0.0408442	+	0.00342452i
$236$	144.278			0.611349
$237$	105.490	+	105.490i	0.445104	+	0.445104i
$238$	142.489	−	142.489i	0.598693	−	0.598693i
$239$			82.5568i			0.345426i	0.984972	+	0.172713i	$0.0552533\pi$
$239$			82.5568i			0.345426i	−0.984972	+	0.172713i	$0.944747\pi$
$240$	2.89426	−	34.5199i	0.0120594	−	0.143833i
$241$	108.909			0.451904			0.225952	−	0.974138i	$-0.427451\pi$
$241$	108.909			0.451904			0.225952	+	0.974138i	$0.427451\pi$
$242$	158.062	+	158.062i	0.653148	+	0.653148i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	134.901i		−	0.552874i
$245$	55.3417	+	65.4710i	0.225884	+	0.267229i
$246$	−137.151			−0.557523
$247$	133.564	+	133.564i	0.540744	+	0.540744i
$248$	−4.30353	+	4.30353i	−0.0173529	+	0.0173529i
$249$			257.357i			1.03356i
$250$	−43.8968	+	171.240i	−0.175587	+	0.684959i
$251$	−421.149			−1.67788			−0.838941	−	0.544222i	$-0.816825\pi$
$251$	−421.149			−1.67788			−0.838941	+	0.544222i	$0.816825\pi$
$252$	23.9454	+	23.9454i	0.0950214	+	0.0950214i
$253$	−56.6499	+	56.6499i	−0.223913	+	0.223913i
$254$			214.300i			0.843701i
$255$	166.977	−	141.143i	0.654812	−	0.553502i
$256$	16.0000			0.0625000
$257$	−93.7588	−	93.7588i	−0.364820	−	0.364820i	0.500764	−	0.865584i	$-0.333053\pi$
$257$	−93.7588	−	93.7588i	−0.364820	−	0.364820i	−0.865584	+	0.500764i	$0.833053\pi$
$258$	−63.6467	+	63.6467i	−0.246693	+	0.246693i
$259$			272.542i			1.05229i
$260$	104.450	+	8.75743i	0.401731	+	0.0336824i
$261$	53.3045			0.204232
$262$	160.837	+	160.837i	0.613881	+	0.613881i
$263$	−237.440	+	237.440i	−0.902815	+	0.902815i	−0.995679	−	0.0928643i	$-0.970398\pi$
$263$	−237.440	+	237.440i	−0.902815	+	0.902815i	0.0928643	+	0.995679i	$0.470398\pi$
$264$		−	81.8381i		−	0.309993i
$265$	10.1016	−	120.481i	0.0381191	−	0.454647i
$266$	143.839			0.540747
$267$	106.159	+	106.159i	0.397597	+	0.397597i
$268$	−59.3968	+	59.3968i	−0.221630	+	0.221630i
$269$			66.0224i			0.245436i	0.992442	+	0.122718i	$0.0391611\pi$
$269$			66.0224i			0.245436i	−0.992442	+	0.122718i	$0.960839\pi$
$270$	23.7192	+	28.0606i	0.0878490	+	0.103928i
$271$	−301.309			−1.11184			−0.555920	−	0.831236i	$-0.687634\pi$
$271$	−301.309			−1.11184			−0.555920	+	0.831236i	$0.687634\pi$
$272$	71.4069	+	71.4069i	0.262526	+	0.262526i
$273$	−72.4537	+	72.4537i	−0.265398	+	0.265398i
$274$		−	371.322i		−	1.35519i
$275$	−69.5419	+	411.798i	−0.252880	+	1.49745i
$276$	16.6132			0.0601929
$277$	−237.920	−	237.920i	−0.858918	−	0.858918i	0.132293	−	0.991211i	$-0.457766\pi$
$277$	−237.920	−	237.920i	−0.858918	−	0.858918i	−0.991211	+	0.132293i	$0.957766\pi$
$278$	−130.439	+	130.439i	−0.469206	+	0.469206i
$279$		−	6.45529i		−	0.0231372i
$280$	60.9581	−	51.5269i	0.217707	−	0.184025i
$281$	−307.240			−1.09338			−0.546691	−	0.837334i	$-0.684113\pi$
$281$	−307.240			−1.09338			−0.546691	+	0.837334i	$0.684113\pi$
$282$	−3.33665	−	3.33665i	−0.0118321	−	0.0118321i
$283$	74.7029	−	74.7029i	0.263968	−	0.263968i	−0.562696	−	0.826664i	$-0.690236\pi$
$283$	74.7029	−	74.7029i	0.263968	−	0.263968i	0.826664	+	0.562696i	$0.190236\pi$
$284$			42.8753i			0.150969i
$285$	155.519	+	13.0393i	0.545682	+	0.0457518i
$286$	247.625			0.865822
$287$	−223.456	−	223.456i	−0.778594	−	0.778594i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$			348.369i			1.20543i
$290$	10.4972	−	125.201i	0.0361974	−	0.431726i
$291$	−103.462			−0.355539
$292$	−146.175	−	146.175i	−0.500599	−	0.500599i
$293$	10.2341	−	10.2341i	0.0349285	−	0.0349285i	−0.689427	−	0.724355i	$-0.742138\pi$
$293$	10.2341	−	10.2341i	0.0349285	−	0.0349285i	0.724355	+	0.689427i	$0.242138\pi$
$294$		−	41.9976i		−	0.142849i
$295$	232.849	+	275.468i	0.789320	+	0.933791i
$296$	−136.582			−0.461425
$297$	61.3786	+	61.3786i	0.206662	+	0.206662i
$298$	−5.80879	+	5.80879i	−0.0194926	+	0.0194926i
$299$			50.2682i			0.168121i
$300$	70.5793	−	50.1853i	0.235264	−	0.167284i
$301$	−207.396			−0.689024
$302$	−118.863	−	118.863i	−0.393587	−	0.393587i
$303$	75.4839	−	75.4839i	0.249122	−	0.249122i
$304$			72.0833i			0.237116i
$305$	257.565	−	217.716i	0.844475	−	0.713822i
$306$	−107.110			−0.350034
$307$	370.463	+	370.463i	1.20672	+	1.20672i	0.972083	+	0.234638i	$0.0753906\pi$
$307$	370.463	+	370.463i	1.20672	+	1.20672i	0.234638	+	0.972083i	$0.424609\pi$
$308$	133.337	−	133.337i	0.432913	−	0.432913i
$309$		−	25.9793i		−	0.0840754i
$310$	−15.1621	−	1.27124i	−0.0489099	−	0.00410077i
$311$	−121.488			−0.390637			−0.195319	−	0.980740i	$-0.562574\pi$
$311$	−121.488			−0.390637			−0.195319	+	0.980740i	$0.562574\pi$
$312$	−36.3095	−	36.3095i	−0.116377	−	0.116377i
$313$	424.047	−	424.047i	1.35478	−	1.35478i	0.474560	−	0.880223i	$-0.342607\pi$
$313$	424.047	−	424.047i	1.35478	−	1.35478i	0.880223	−	0.474560i	$-0.157393\pi$
$314$			32.5719i			0.103732i
$315$	−7.07334	+	84.3637i	−0.0224551	+	0.267821i
$316$	−172.264			−0.545139
$317$	302.071	+	302.071i	0.952906	+	0.952906i	0.998940	−	0.0460337i	$-0.0146582\pi$
$317$	302.071	+	302.071i	0.952906	+	0.952906i	−0.0460337	+	0.998940i	$0.514658\pi$
$318$	−41.8824	+	41.8824i	−0.131706	+	0.131706i
$319$		−	296.820i		−	0.930469i
$320$	25.8222	+	30.5485i	0.0806944	+	0.0954642i
$321$	29.3168			0.0913297
$322$	27.0676	+	27.0676i	0.0840609	+	0.0840609i
$323$	−321.703	+	321.703i	−0.995985	+	0.995985i
$324$		−	18.0000i		−	0.0555556i
$325$	151.850	+	213.558i	0.467231	+	0.657102i
$326$	252.470			0.774448
$327$	45.0608	+	45.0608i	0.137801	+	0.137801i
$328$	111.983	−	111.983i	0.341412	−	0.341412i
$329$		−	10.8726i		−	0.0330476i
$330$	156.252	−	132.078i	0.473492	−	0.400235i
$331$	−578.605			−1.74805			−0.874026	−	0.485879i	$-0.838499\pi$
$331$	−578.605			−1.74805			−0.874026	+	0.485879i	$0.838499\pi$
$332$	−210.131	−	210.131i	−0.632926	−	0.632926i
$333$	102.436	−	102.436i	0.307617	−	0.307617i
$334$			144.288i			0.431999i
$335$	−209.265	−	17.5455i	−0.624672	−	0.0523746i
$336$	−39.1027			−0.116377
$337$	−141.241	−	141.241i	−0.419113	−	0.419113i	0.465785	−	0.884898i	$-0.345772\pi$
$337$	−141.241	−	141.241i	−0.419113	−	0.419113i	−0.884898	+	0.465785i	$0.845772\pi$
$338$	−59.1352	+	59.1352i	−0.174956	+	0.174956i
$339$		−	110.926i		−	0.327215i
$340$	−21.0932	+	251.579i	−0.0620389	+	0.739938i
$341$	−35.9455			−0.105412
$342$	−54.0625	−	54.0625i	−0.158077	−	0.158077i
$343$	263.980	−	263.980i	0.769620	−	0.769620i
$344$		−	103.935i		−	0.302136i
$345$	26.8119	+	31.7194i	0.0777157	+	0.0919403i
$346$	−219.945			−0.635679
$347$	−351.519	−	351.519i	−1.01302	−	1.01302i	−0.999914	−	0.0131089i	$-0.995827\pi$
$347$	−351.519	−	351.519i	−1.01302	−	1.01302i	−0.0131089	−	0.999914i	$-0.504173\pi$
$348$	−43.5229	+	43.5229i	−0.125066	+	0.125066i
$349$			579.696i			1.66102i	0.557003	+	0.830510i	$0.311951\pi$
$349$			579.696i			1.66102i	−0.557003	+	0.830510i	$0.688049\pi$
$350$	196.759	+	33.2275i	0.562169	+	0.0949356i
$351$	54.4642			0.155169
$352$	66.8206	+	66.8206i	0.189831	+	0.189831i
$353$	381.406	−	381.406i	1.08047	−	1.08047i	0.0840038	−	0.996465i	$-0.473229\pi$
$353$	381.406	−	381.406i	1.08047	−	1.08047i	0.996465	−	0.0840038i	$-0.0267708\pi$
$354$		−	176.704i		−	0.499165i
$355$	−81.8611	+	69.1960i	−0.230595	+	0.194918i
$356$	−173.356			−0.486955
$357$	−174.513	−	174.513i	−0.488831	−	0.488831i
$358$	4.73899	−	4.73899i	0.0132374	−	0.0132374i
$359$			713.563i			1.98764i	0.111002	+	0.993820i	$0.464594\pi$
$359$			713.563i			1.98764i	−0.111002	+	0.993820i	$0.535406\pi$
$360$	−42.2781	−	3.54474i	−0.117439	−	0.00984649i
$361$	36.2497			0.100415
$362$	39.1292	+	39.1292i	0.108092	+	0.108092i
$363$	193.585	−	193.585i	0.533293	−	0.533293i
$364$		−	118.316i		−	0.325045i
$365$	43.1792	−	514.999i	0.118299	−	1.41096i
$366$	−165.220			−0.451420
$367$	−501.508	−	501.508i	−1.36651	−	1.36651i	−0.865366	−	0.501140i	$-0.832914\pi$
$367$	−501.508	−	501.508i	−1.36651	−	1.36651i	−0.501140	−	0.865366i	$-0.667086\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			167.975i			0.455215i
$370$	−220.428	−	260.773i	−0.595751	−	0.704793i
$371$	−136.476			−0.367861
$372$	5.27072	+	5.27072i	0.0141686	+	0.0141686i
$373$	432.197	−	432.197i	1.15871	−	1.15871i	0.173952	−	0.984754i	$-0.444346\pi$
$373$	432.197	−	432.197i	1.15871	−	1.15871i	0.984754	−	0.173952i	$-0.0556538\pi$
$374$			596.432i			1.59474i
$375$	209.725	+	53.7624i	0.559267	+	0.143366i
$376$	5.44872			0.0144913
$377$	−131.691	−	131.691i	−0.349313	−	0.349313i
$378$	29.3270	−	29.3270i	0.0775847	−	0.0775847i
$379$			132.672i			0.350059i	0.984563	+	0.175029i	$0.0560020\pi$
$379$			132.672i			0.350059i	−0.984563	+	0.175029i	$0.943998\pi$
$380$	−137.627	+	116.334i	−0.362178	+	0.306143i
$381$	262.463			0.688879
$382$	−230.340	−	230.340i	−0.602984	−	0.602984i
$383$	−387.528	+	387.528i	−1.01182	+	1.01182i	−0.0118921	+	0.999929i	$0.503785\pi$
$383$	−387.528	+	387.528i	−1.01182	+	1.01182i	−0.999929	+	0.0118921i	$0.996215\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	469.769	+	39.3871i	1.22018	+	0.102304i
$386$	374.278			0.969631
$387$	77.9510	+	77.9510i	0.201424	+	0.201424i
$388$	84.4763	−	84.4763i	0.217722	−	0.217722i
$389$			141.741i			0.364374i	0.983264	+	0.182187i	$0.0583175\pi$
$389$			141.741i			0.364374i	−0.983264	+	0.182187i	$0.941682\pi$
$390$	10.7256	−	127.925i	0.0275016	−	0.328012i
$391$	−121.076			−0.309658
$392$	34.2909	+	34.2909i	0.0874768	+	0.0874768i
$393$	196.984	−	196.984i	0.501231	−	0.501231i
$394$			175.689i			0.445910i
$395$	−278.015	−	328.901i	−0.703835	−	0.832660i
$396$	−100.231			−0.253108
$397$	−57.7135	−	57.7135i	−0.145374	−	0.145374i	0.630674	−	0.776048i	$-0.282779\pi$
$397$	−57.7135	−	57.7135i	−0.145374	−	0.145374i	−0.776048	+	0.630674i	$0.782779\pi$
$398$	211.873	−	211.873i	0.532344	−	0.532344i
$399$		−	176.166i		−	0.441518i
$400$	−16.6516	+	98.6039i	−0.0416290	+	0.246510i
$401$	409.746			1.02181			0.510906	−	0.859637i	$-0.329310\pi$
$401$	409.746			1.02181			0.510906	+	0.859637i	$0.329310\pi$
$402$	72.7459	+	72.7459i	0.180960	+	0.180960i
$403$	−15.9481	+	15.9481i	−0.0395734	+	0.0395734i
$404$			123.265i			0.305111i
$405$	34.3671	−	29.0500i	0.0848570	−	0.0717284i
$406$	−141.822			−0.349315
$407$	−570.404	−	570.404i	−1.40149	−	1.40149i
$408$	87.4553	−	87.4553i	0.214351	−	0.214351i
$409$		−	664.563i		−	1.62485i	−0.583066	−	0.812424i	$-0.698147\pi$
$409$		−	664.563i		−	1.62485i	0.583066	−	0.812424i	$-0.301853\pi$
$410$	394.535	+	33.0792i	0.962281	+	0.0806809i
$411$	−454.774			−1.10651
$412$	21.2120	+	21.2120i	0.0514855	+	0.0514855i
$413$	287.900	−	287.900i	0.697095	−	0.697095i
$414$		−	20.3470i		−	0.0491473i
$415$	62.0717	−	740.329i	0.149570	−	1.78392i
$416$	59.2931			0.142532
$417$	159.755	+	159.755i	0.383105	+	0.383105i
$418$	−301.041	+	301.041i	−0.720193	+	0.720193i
$419$		−	287.529i		−	0.686226i	−0.939294	−	0.343113i	$-0.888519\pi$
$419$		−	287.529i		−	0.686226i	0.939294	−	0.343113i	$-0.111481\pi$
$420$	−63.1074	−	74.6581i	−0.150256	−	0.177757i
$421$	−363.794			−0.864118			−0.432059	−	0.901845i	$-0.642213\pi$
$421$	−363.794			−0.864118			−0.432059	+	0.901845i	$0.642213\pi$
$422$	103.501	+	103.501i	0.245264	+	0.245264i
$423$	−4.08654	+	4.08654i	−0.00966085	+	0.00966085i
$424$		−	68.3938i		−	0.161306i
$425$	−514.378	+	365.748i	−1.21030	+	0.860582i
$426$	52.5113			0.123266
$427$	−269.189	−	269.189i	−0.630419	−	0.630419i
$428$	−23.9371	+	23.9371i	−0.0559278	+	0.0559278i
$429$		−	303.277i		−	0.706940i
$430$	198.441	−	167.739i	0.461490	−	0.390091i
$431$	−833.171			−1.93311			−0.966556	−	0.256456i	$-0.917445\pi$
$431$	−833.171			−1.93311			−0.966556	+	0.256456i	$0.917445\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	−365.422	+	365.422i	−0.843930	+	0.843930i	−0.989367	−	0.145437i	$-0.953541\pi$
$433$	−365.422	+	365.422i	−0.843930	+	0.843930i	0.145437	+	0.989367i	$0.453541\pi$
$434$			17.1749i			0.0395736i
$435$	−153.339	−	12.8564i	−0.352503	−	0.0295550i
$436$	−73.5840			−0.168771
$437$	−61.1116	−	61.1116i	−0.139843	−	0.139843i
$438$	−179.027	+	179.027i	−0.408737	+	0.408737i
$439$		−	134.041i		−	0.305332i	−0.988278	−	0.152666i	$-0.951214\pi$
$439$		−	134.041i		−	0.305332i	0.988278	−	0.152666i	$-0.0487859\pi$
$440$	−19.7384	+	235.420i	−0.0448601	+	0.535046i
$441$	−51.4363			−0.116636
$442$	264.621	+	264.621i	0.598691	+	0.598691i
$443$	423.762	−	423.762i	0.956572	−	0.956572i	−0.0425232	−	0.999095i	$-0.513540\pi$
$443$	423.762	−	423.762i	0.956572	−	0.956572i	0.999095	+	0.0425232i	$0.0135396\pi$
$444$			167.278i			0.376752i
$445$	−279.778	−	330.986i	−0.628714	−	0.743789i
$446$	316.290			0.709170
$447$	7.11428	+	7.11428i	0.0159156	+	0.0159156i
$448$	31.9272	−	31.9272i	0.0712661	−	0.0712661i
$449$			78.0600i			0.173853i	0.996215	+	0.0869265i	$0.0277045\pi$
$449$			78.0600i			0.173853i	−0.996215	+	0.0869265i	$0.972295\pi$
$450$	−61.4642	−	86.4416i	−0.136587	−	0.192092i
$451$	935.346			2.07394
$452$	90.5707	+	90.5707i	0.200378	+	0.200378i
$453$	−145.577	+	145.577i	−0.321362	+	0.321362i
$454$			91.2271i			0.200941i
$455$	225.900	−	190.950i	0.496483	−	0.419669i
$456$	88.2837			0.193605
$457$	142.520	+	142.520i	0.311860	+	0.311860i	0.845630	−	0.533770i	$-0.179225\pi$
$457$	142.520	+	142.520i	0.311860	+	0.311860i	−0.533770	+	0.845630i	$0.679225\pi$
$458$	−178.009	+	178.009i	−0.388667	+	0.388667i
$459$			131.183i			0.285802i
$460$	−47.7906	−	4.00693i	−0.103893	−	0.00871071i
$461$	602.901			1.30781			0.653905	−	0.756576i	$-0.273129\pi$
$461$	602.901			1.30781			0.653905	+	0.756576i	$0.273129\pi$
$462$	−163.304	−	163.304i	−0.353472	−	0.353472i
$463$	−170.407	+	170.407i	−0.368049	+	0.368049i	−0.866765	−	0.498716i	$-0.833805\pi$
$463$	−170.407	+	170.407i	−0.368049	+	0.368049i	0.498716	+	0.866765i	$0.333805\pi$
$464$		−	71.0726i		−	0.153174i
$465$	−1.55694	+	18.5697i	−0.00334827	+	0.0399348i
$466$	389.903			0.836702
$467$	−466.315	−	466.315i	−0.998533	−	0.998533i	0.00146594	−	0.999999i	$-0.499533\pi$
$467$	−466.315	−	466.315i	−0.998533	−	0.998533i	−0.999999	+	0.00146594i	$0.999533\pi$
$468$	−44.4698	+	44.4698i	−0.0950210	+	0.0950210i
$469$			237.046i			0.505430i
$470$	8.79363	+	10.4032i	0.0187099	+	0.0221344i
$471$	39.8922			0.0846969
$472$	144.278	+	144.278i	0.305675	+	0.305675i
$473$	434.061	−	434.061i	0.917676	−	0.917676i
$474$			210.979i			0.445104i
$475$	−444.231	−	75.0190i	−0.935223	−	0.157935i
$476$	284.978			0.598693
$477$	51.2953	+	51.2953i	0.107537	+	0.107537i
$478$	−82.5568	+	82.5568i	−0.172713	+	0.172713i
$479$			538.427i			1.12406i	0.827115	+	0.562032i	$0.189980\pi$
$479$			538.427i			1.12406i	−0.827115	+	0.562032i	$0.810020\pi$
$480$	37.4142	−	31.6256i	0.0779462	−	0.0658867i
$481$	−506.147			−1.05228
$482$	108.909	+	108.909i	0.225952	+	0.225952i
$483$	33.1509	−	33.1509i	0.0686354	−	0.0686354i
$484$			316.124i			0.653148i
$485$	297.625	+	24.9539i	0.613659	+	0.0514512i
$486$	−22.0454			−0.0453609
$487$	−174.119	−	174.119i	−0.357533	−	0.357533i	0.505370	−	0.862903i	$-0.331356\pi$
$487$	−174.119	−	174.119i	−0.357533	−	0.357533i	−0.862903	+	0.505370i	$0.831356\pi$
$488$	134.901	−	134.901i	0.276437	−	0.276437i
$489$		−	309.211i		−	0.632334i
$490$	−10.1293	+	120.813i	−0.0206721	+	0.246557i
$491$	498.635			1.01555			0.507775	−	0.861490i	$-0.330468\pi$
$491$	498.635			1.01555			0.507775	+	0.861490i	$0.330468\pi$
$492$	−137.151	−	137.151i	−0.278761	−	0.278761i
$493$	317.192	−	317.192i	0.643392	−	0.643392i
$494$			267.128i			0.540744i
$495$	−161.761	−	191.369i	−0.326791	−	0.386604i
$496$	−8.60705			−0.0173529
$497$	85.5556	+	85.5556i	0.172144	+	0.172144i
$498$	−257.357	+	257.357i	−0.516782	+	0.516782i
$499$		−	281.223i		−	0.563574i	−0.959477	−	0.281787i	$-0.909073\pi$
$499$		−	281.223i		−	0.563574i	0.959477	−	0.281787i	$-0.0909272\pi$
$500$	−215.137	+	127.343i	−0.430273	+	0.254686i
$501$	176.716			0.352726
$502$	−421.149	−	421.149i	−0.838941	−	0.838941i
$503$	44.0788	−	44.0788i	0.0876318	−	0.0876318i	−0.661932	−	0.749564i	$-0.730263\pi$
$503$	44.0788	−	44.0788i	0.0876318	−	0.0876318i	0.749564	+	0.661932i	$0.230263\pi$
$504$			47.8908i			0.0950214i
$505$	−235.347	+	198.935i	−0.466034	+	0.393932i
$506$	−113.300			−0.223913
$507$	72.4255	+	72.4255i	0.142851	+	0.142851i
$508$	−214.300	+	214.300i	−0.421851	+	0.421851i
$509$		−	126.037i		−	0.247617i	−0.992306	−	0.123808i	$-0.960489\pi$
$509$		−	126.037i		−	0.247617i	0.992306	−	0.123808i	$-0.0395108\pi$
$510$	308.120	+	25.8338i	0.604157	+	0.0506546i
$511$	−583.369			−1.14162
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−66.2128	+	66.2128i	−0.129070	+	0.129070i
$514$		−	187.518i		−	0.364820i
$515$	−6.26592	+	74.7336i	−0.0121668	+	0.145114i
$516$	−127.293			−0.246693
$517$	22.7554	+	22.7554i	0.0440143	+	0.0440143i
$518$	−272.542	+	272.542i	−0.526143	+	0.526143i
$519$			269.376i			0.519029i
$520$	95.6925	+	113.207i	0.184024	+	0.217706i
$521$	−237.283			−0.455437			−0.227719	−	0.973727i	$-0.573127\pi$
$521$	−237.283			−0.455437			−0.227719	+	0.973727i	$0.573127\pi$
$522$	53.3045	+	53.3045i	0.102116	+	0.102116i
$523$	−700.159	+	700.159i	−1.33874	+	1.33874i	−0.441449	+	0.897286i	$0.645535\pi$
$523$	−700.159	+	700.159i	−1.33874	+	1.33874i	−0.897286	+	0.441449i	$0.854465\pi$
$524$			321.673i			0.613881i
$525$	40.6952	−	240.980i	0.0775146	−	0.459009i
$526$	−474.880			−0.902815
$527$	−38.4127	−	38.4127i	−0.0728894	−	0.0728894i
$528$	81.8381	−	81.8381i	0.154996	−	0.154996i
$529$		−	23.0000i		−	0.0434783i
$530$	130.583	−	110.380i	0.246383	−	0.208264i
$531$	−216.418			−0.407566
$532$	143.839	+	143.839i	0.270373	+	0.270373i
$533$	414.989	−	414.989i	0.778591	−	0.778591i
$534$			212.317i			0.397597i
$535$	−84.3345	−	7.07089i	−0.157635	−	0.0132166i
$536$	−118.794			−0.221630
$537$	−5.80405	−	5.80405i	−0.0108083	−	0.0108083i
$538$	−66.0224	+	66.0224i	−0.122718	+	0.122718i
$539$			286.417i			0.531386i
$540$	−4.34140	+	51.7798i	−0.00803962	+	0.0958886i
$541$	−150.854			−0.278842			−0.139421	−	0.990233i	$-0.544524\pi$
$541$	−150.854			−0.278842			−0.139421	+	0.990233i	$0.544524\pi$
$542$	−301.309	−	301.309i	−0.555920	−	0.555920i
$543$	47.9233	−	47.9233i	0.0882565	−	0.0882565i
$544$			142.814i			0.262526i
$545$	−118.756	−	140.493i	−0.217902	−	0.257785i
$546$	−144.907			−0.265398
$547$	124.017	+	124.017i	0.226722	+	0.226722i	0.811322	−	0.584600i	$-0.198748\pi$
$547$	124.017	+	124.017i	0.226722	+	0.226722i	−0.584600	+	0.811322i	$0.698748\pi$
$548$	371.322	−	371.322i	0.677594	−	0.677594i
$549$			202.352i			0.368583i
$550$	−481.340	+	342.256i	−0.875163	+	0.622284i
$551$	320.197			0.581120
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	−343.744	+	343.744i	−0.621598	+	0.621598i
$554$		−	475.841i		−	0.858918i
$555$	−319.381	+	269.968i	−0.575461	+	0.486428i
$556$	−260.878			−0.469206
$557$	−772.395	−	772.395i	−1.38671	−	1.38671i	−0.832139	−	0.554567i	$-0.812884\pi$
$557$	−772.395	−	772.395i	−1.38671	−	1.38671i	−0.554567	−	0.832139i	$-0.687116\pi$
$558$	6.45529	−	6.45529i	0.0115686	−	0.0115686i
$559$		−	385.163i		−	0.689021i
$560$	112.485	+	9.43112i	0.200866	+	0.0168413i
$561$	730.477			1.30210
$562$	−307.240	−	307.240i	−0.546691	−	0.546691i
$563$	−169.515	+	169.515i	−0.301093	+	0.301093i	−0.841441	−	0.540349i	$-0.818292\pi$
$563$	−169.515	+	169.515i	−0.301093	+	0.301093i	0.540349	+	0.841441i	$0.318292\pi$
$564$		−	6.67329i		−	0.0118321i
$565$	−26.7541	+	319.096i	−0.0473524	+	0.564772i
$566$	149.406			0.263968
$567$	−35.9181	−	35.9181i	−0.0633476	−	0.0633476i
$568$	−42.8753	+	42.8753i	−0.0754847	+	0.0754847i
$569$			755.411i			1.32761i	0.747905	+	0.663805i	$0.231060\pi$
$569$			755.411i			1.32761i	−0.747905	+	0.663805i	$0.768940\pi$
$570$	142.480	+	168.559i	0.249965	+	0.295717i
$571$	300.261			0.525851			0.262926	−	0.964816i	$-0.415313\pi$
$571$	300.261			0.525851			0.262926	+	0.964816i	$0.415313\pi$
$572$	247.625	+	247.625i	0.432911	+	0.432911i
$573$	−282.108	+	282.108i	−0.492334	+	0.492334i
$574$		−	446.913i		−	0.778594i
$575$	−69.4784	−	97.7126i	−0.120832	−	0.169935i
$576$	−24.0000			−0.0416667
$577$	693.168	+	693.168i	1.20133	+	1.20133i	0.973762	+	0.227569i	$0.0730778\pi$
$577$	693.168	+	693.168i	1.20133	+	1.20133i	0.227569	+	0.973762i	$0.426922\pi$
$578$	−348.369	+	348.369i	−0.602715	+	0.602715i
$579$		−	458.395i		−	0.791701i
$580$	135.698	−	114.703i	0.233962	−	0.197764i
$581$	−838.613			−1.44340
$582$	−103.462	−	103.462i	−0.177770	−	0.177770i
$583$	285.632	−	285.632i	0.489935	−	0.489935i
$584$		−	292.350i		−	0.500599i
$585$	−156.675	−	13.1362i	−0.267820	−	0.0224550i
$586$	20.4681			0.0349285
$587$	233.532	+	233.532i	0.397839	+	0.397839i	0.877470	−	0.479631i	$-0.159229\pi$
$587$	233.532	+	233.532i	0.397839	+	0.397839i	−0.479631	+	0.877470i	$0.659229\pi$
$588$	41.9976	−	41.9976i	0.0714245	−	0.0714245i
$589$		−	38.7766i		−	0.0658346i
$590$	−42.6191	+	508.318i	−0.0722357	+	0.861555i
$591$	215.174			0.364084
$592$	−136.582	−	136.582i	−0.230712	−	0.230712i
$593$	582.754	−	582.754i	0.982722	−	0.982722i	−0.0171309	−	0.999853i	$-0.505453\pi$
$593$	582.754	−	582.754i	0.982722	−	0.982722i	0.999853	+	0.0171309i	$0.00545322\pi$
$594$			122.757i			0.206662i
$595$	459.923	+	544.104i	0.772979	+	0.914460i
$596$	−11.6176			−0.0194926
$597$	−259.490	−	259.490i	−0.434657	−	0.434657i
$598$	−50.2682	+	50.2682i	−0.0840605	+	0.0840605i
$599$		−	573.521i		−	0.957465i	−0.877961	−	0.478732i	$-0.841096\pi$
$599$		−	573.521i		−	0.957465i	0.877961	−	0.478732i	$-0.158904\pi$
$600$	120.765	+	20.3940i	0.201274	+	0.0339900i
$601$	−847.669			−1.41043			−0.705215	−	0.708993i	$-0.749150\pi$
$601$	−847.669			−1.41043			−0.705215	+	0.708993i	$0.749150\pi$
$602$	−207.396	−	207.396i	−0.344512	−	0.344512i
$603$	89.0951	−	89.0951i	0.147753	−	0.147753i
$604$		−	237.726i		−	0.393587i
$605$	−603.569	+	510.188i	−0.997635	+	0.843286i
$606$	150.968			0.249122
$607$	−700.957	−	700.957i	−1.15479	−	1.15479i	−0.985580	−	0.169208i	$-0.945879\pi$
$607$	−700.957	−	700.957i	−1.15479	−	1.15479i	−0.169208	−	0.985580i	$-0.554121\pi$
$608$	−72.0833	+	72.0833i	−0.118558	+	0.118558i
$609$			173.696i			0.285214i
$610$	475.280	+	39.8491i	0.779148	+	0.0653264i
$611$	20.1920			0.0330474
$612$	−107.110	−	107.110i	−0.175017	−	0.175017i
$613$	−342.192	+	342.192i	−0.558225	+	0.558225i	−0.928802	−	0.370577i	$-0.879160\pi$
$613$	−342.192	+	342.192i	−0.558225	+	0.558225i	0.370577	+	0.928802i	$0.379160\pi$
$614$			740.927i			1.20672i
$615$	40.5136	−	483.205i	0.0658757	−	0.785700i
$616$	266.674			0.432913
$617$	−57.6784	−	57.6784i	−0.0934820	−	0.0934820i	0.658819	−	0.752301i	$-0.271056\pi$
$617$	−57.6784	−	57.6784i	−0.0934820	−	0.0934820i	−0.752301	+	0.658819i	$0.771056\pi$
$618$	25.9793	−	25.9793i	0.0420377	−	0.0420377i
$619$		−	706.959i		−	1.14210i	−0.820916	−	0.571050i	$-0.806536\pi$
$619$		−	706.959i		−	1.14210i	0.820916	−	0.571050i	$-0.193464\pi$
$620$	−13.8908	−	16.4333i	−0.0224046	−	0.0265053i
$621$	−24.9199			−0.0401286
$622$	−121.488	−	121.488i	−0.195319	−	0.195319i
$623$	−345.923	+	345.923i	−0.555254	+	0.555254i
$624$		−	72.6189i		−	0.116377i
$625$	−590.340	−	205.239i	−0.944545	−	0.328383i
$626$	848.094			1.35478
$627$	368.698	+	368.698i	0.588035	+	0.588035i
$628$	−32.5719	+	32.5719i	−0.0518660	+	0.0518660i
$629$		−	1219.11i		−	1.93817i
$630$	−91.4371	+	77.2904i	−0.145138	+	0.122683i
$631$	−209.729			−0.332376			−0.166188	−	0.986094i	$-0.553146\pi$
$631$	−209.729			−0.332376			−0.166188	+	0.986094i	$0.553146\pi$
$632$	−172.264	−	172.264i	−0.272569	−	0.272569i
$633$	126.763	−	126.763i	0.200257	−	0.200257i
$634$			604.142i			0.952906i
$635$	−755.016	−	63.3031i	−1.18900	−	0.0996899i
$636$	−83.7649			−0.131706
$637$	127.076	+	127.076i	0.199491	+	0.199491i
$638$	296.820	−	296.820i	0.465234	−	0.465234i
$639$		−	64.3130i		−	0.100646i
$640$	−4.72631	+	56.3708i	−0.00738487	+	0.0880793i
$641$	199.911			0.311873			0.155937	−	0.987767i	$-0.450160\pi$
$641$	199.911			0.311873			0.155937	+	0.987767i	$0.450160\pi$
$642$	29.3168	+	29.3168i	0.0456649	+	0.0456649i
$643$	396.479	−	396.479i	0.616607	−	0.616607i	−0.328052	−	0.944660i	$-0.606392\pi$
$643$	396.479	−	396.479i	0.616607	−	0.616607i	0.944660	+	0.328052i	$0.106392\pi$
$644$			54.1352i			0.0840609i
$645$	−205.437	−	243.039i	−0.318508	−	0.376805i
$646$	−643.406			−0.995985
$647$	−326.847	−	326.847i	−0.505173	−	0.505173i	0.407868	−	0.913041i	$-0.366272\pi$
$647$	−326.847	−	326.847i	−0.505173	−	0.505173i	−0.913041	+	0.407868i	$0.866272\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			1205.10i			1.85685i
$650$	−61.7079	+	365.408i	−0.0949352	+	0.562166i
$651$	21.0349			0.0323117
$652$	252.470	+	252.470i	0.387224	+	0.387224i
$653$	810.388	−	810.388i	1.24102	−	1.24102i	0.281446	−	0.959577i	$-0.409186\pi$
$653$	810.388	−	810.388i	1.24102	−	1.24102i	0.959577	−	0.281446i	$-0.0908141\pi$
$654$			90.1216i			0.137801i
$655$	−614.166	+	519.145i	−0.937658	+	0.792588i
$656$	223.966			0.341412
$657$	219.262	+	219.262i	0.333732	+	0.333732i
$658$	10.8726	−	10.8726i	0.0165238	−	0.0165238i
$659$			1229.80i			1.86615i	0.359676	+	0.933077i	$0.382887\pi$
$659$			1229.80i			1.86615i	−0.359676	+	0.933077i	$0.617113\pi$
$660$	288.330	+	24.1746i	0.436863	+	0.0366281i
$661$	−267.953			−0.405376			−0.202688	−	0.979243i	$-0.564968\pi$
$661$	−267.953			−0.405376			−0.202688	+	0.979243i	$0.564968\pi$
$662$	−578.605	−	578.605i	−0.874026	−	0.874026i
$663$	324.094	−	324.094i	0.488829	−	0.488829i
$664$		−	420.263i		−	0.632926i
$665$	−42.4892	+	506.768i	−0.0638935	+	0.762057i
$666$	204.873			0.307617
$667$	60.2547	+	60.2547i	0.0903369	+	0.0903369i
$668$	−144.288	+	144.288i	−0.216000	+	0.216000i
$669$		−	387.374i		−	0.579035i
$670$	−191.720	−	226.811i	−0.286149	−	0.338523i
$671$	1126.77			1.67924
$672$	−39.1027	−	39.1027i	−0.0581885	−	0.0581885i
$673$	−473.159	+	473.159i	−0.703060	+	0.703060i	−0.965066	−	0.262006i	$-0.915616\pi$
$673$	−473.159	+	473.159i	−0.703060	+	0.703060i	0.262006	+	0.965066i	$0.415616\pi$
$674$		−	282.482i		−	0.419113i
$675$	−105.869	+	75.2780i	−0.156843	+	0.111523i
$676$	−118.270			−0.174956
$677$	−477.245	−	477.245i	−0.704941	−	0.704941i	0.260526	−	0.965467i	$-0.416104\pi$
$677$	−477.245	−	477.245i	−0.704941	−	0.704941i	−0.965467	+	0.260526i	$0.916104\pi$
$678$	110.926	−	110.926i	0.163608	−	0.163608i
$679$		−	337.136i		−	0.496519i
$680$	−272.672	+	230.486i	−0.400989	+	0.338950i
$681$	111.730			0.164067
$682$	−35.9455	−	35.9455i	−0.0527060	−	0.0527060i
$683$	−841.661	+	841.661i	−1.23230	+	1.23230i	−0.269221	+	0.963078i	$0.586766\pi$
$683$	−841.661	+	841.661i	−1.23230	+	1.23230i	−0.963078	+	0.269221i	$0.913234\pi$
$684$		−	108.125i		−	0.158077i
$685$	1308.23	+	109.686i	1.90983	+	0.160126i
$686$	527.960			0.769620
$687$	218.016	+	218.016i	0.317345	+	0.317345i
$688$	103.935	−	103.935i	0.151068	−	0.151068i
$689$		−	253.455i		−	0.367859i
$690$	−4.90746	+	58.5313i	−0.00711227	+	0.0848280i
$691$	−621.298			−0.899129			−0.449565	−	0.893248i	$-0.648421\pi$
$691$	−621.298			−0.899129			−0.449565	+	0.893248i	$0.648421\pi$
$692$	−219.945	−	219.945i	−0.317839	−	0.317839i
$693$	−200.006	+	200.006i	−0.288608	+	0.288608i
$694$		−	703.038i		−	1.01302i
$695$	−421.029	−	498.091i	−0.605797	−	0.716678i
$696$	−87.0458			−0.125066
$697$	999.546	+	999.546i	1.43407	+	1.43407i
$698$	−579.696	+	579.696i	−0.830510	+	0.830510i
$699$		−	477.532i		−	0.683164i
$700$	163.532	+	229.987i	0.233617	+	0.328552i
$701$	1084.61			1.54724			0.773619	−	0.633651i	$-0.218444\pi$
$701$	1084.61			1.54724			0.773619	+	0.633651i	$0.218444\pi$
$702$	54.4642	+	54.4642i	0.0775843	+	0.0775843i
$703$	615.329	−	615.329i	0.875290	−	0.875290i
$704$			133.641i			0.189831i
$705$	12.7412	−	10.7700i	0.0180726	−	0.0152765i
$706$	762.811			1.08047
$707$	245.968	+	245.968i	0.347904	+	0.347904i
$708$	176.704	−	176.704i	0.249582	−	0.249582i
$709$			1187.52i			1.67492i	0.546500	+	0.837459i	$0.315960\pi$
$709$			1187.52i			1.67492i	−0.546500	+	0.837459i	$0.684040\pi$
$710$	−151.057	−	12.6651i	−0.212757	−	0.0178382i
$711$	258.396			0.363426
$712$	−173.356	−	173.356i	−0.243478	−	0.243478i
$713$	7.29699	−	7.29699i	0.0102342	−	0.0102342i
$714$		−	349.025i		−	0.488831i
$715$	−73.1471	+	872.425i	−0.102304	+	1.22018i
$716$	9.47797			0.0132374
$717$	101.111	+	101.111i	0.141019	+	0.141019i
$718$	−713.563	+	713.563i	−0.993820	+	0.993820i
$719$			311.822i			0.433689i	0.976206	+	0.216844i	$0.0695764\pi$
$719$			311.822i			0.433689i	−0.976206	+	0.216844i	$0.930424\pi$
$720$	−38.7333	−	45.8228i	−0.0537963	−	0.0636428i
$721$	84.6550			0.117413
$722$	36.2497	+	36.2497i	0.0502074	+	0.0502074i
$723$	133.386	−	133.386i	0.184489	−	0.184489i
$724$			78.2584i			0.108092i
$725$	438.002	+	73.9671i	0.604141	+	0.102024i
$726$	387.171			0.533293
$727$	319.511	+	319.511i	0.439493	+	0.439493i	0.891841	−	0.452348i	$-0.149414\pi$
$727$	319.511	+	319.511i	0.439493	+	0.439493i	−0.452348	+	0.891841i	$0.649414\pi$
$728$	118.316	−	118.316i	0.162523	−	0.162523i
$729$			27.0000i			0.0370370i
$730$	558.178	−	471.820i	0.764628	−	0.646328i
$731$	927.707			1.26909
$732$	−165.220	−	165.220i	−0.225710	−	0.225710i
$733$	−623.340	+	623.340i	−0.850396	+	0.850396i	−0.990182	−	0.139786i	$-0.955359\pi$
$733$	−623.340	+	623.340i	−0.850396	+	0.850396i	0.139786	+	0.990182i	$0.455359\pi$
$734$		−	1003.02i		−	1.36651i
$735$	147.965	+	12.4059i	0.201313	+	0.0168787i
$736$	−27.1293			−0.0368605
$737$	−496.116	−	496.116i	−0.673156	−	0.673156i
$738$	−167.975	+	167.975i	−0.227608	+	0.227608i
$739$			744.713i			1.00773i	0.863782	+	0.503865i	$0.168089\pi$
$739$			744.713i			1.00773i	−0.863782	+	0.503865i	$0.831911\pi$
$740$	40.3455	−	481.201i	0.0545210	−	0.650272i
$741$	327.163			0.441516
$742$	−136.476	−	136.476i	−0.183930	−	0.183930i
$743$	542.987	−	542.987i	0.730803	−	0.730803i	−0.239976	−	0.970779i	$-0.577139\pi$
$743$	542.987	−	542.987i	0.730803	−	0.730803i	0.970779	+	0.239976i	$0.0771394\pi$
$744$			10.5414i			0.0141686i
$745$	−18.7495	−	22.1812i	−0.0251671	−	0.0297735i
$746$	864.395			1.15871
$747$	315.197	+	315.197i	0.421950	+	0.421950i
$748$	−596.432	+	596.432i	−0.797368	+	0.797368i
$749$			95.5306i			0.127544i
$750$	155.963	+	263.487i	0.207950	+	0.351317i
$751$	−581.183			−0.773879			−0.386940	−	0.922105i	$-0.626468\pi$
$751$	−581.183			−0.773879			−0.386940	+	0.922105i	$0.626468\pi$
$752$	5.44872	+	5.44872i	0.00724564	+	0.00724564i
$753$	−515.800	+	515.800i	−0.684993	+	0.684993i
$754$		−	263.382i		−	0.349313i
$755$	453.887	−	383.664i	0.601175	−	0.508164i
$756$	58.6540			0.0775847
$757$	448.860	+	448.860i	0.592946	+	0.592946i	0.938426	−	0.345480i	$-0.112284\pi$
$757$	448.860	+	448.860i	0.592946	+	0.592946i	−0.345480	+	0.938426i	$0.612284\pi$
$758$	−132.672	+	132.672i	−0.175029	+	0.175029i
$759$			138.763i			0.182824i
$760$	−253.962	−	21.2930i	−0.334160	−	0.0280171i
$761$	450.906			0.592518			0.296259	−	0.955108i	$-0.404261\pi$
$761$	450.906			0.592518			0.296259	+	0.955108i	$0.404261\pi$
$762$	262.463	+	262.463i	0.344440	+	0.344440i
$763$	−146.833	+	146.833i	−0.192442	+	0.192442i
$764$		−	460.680i		−	0.602984i
$765$	31.6398	−	377.368i	0.0413593	−	0.493292i
$766$	−775.055			−1.01182
$767$	534.670	+	534.670i	0.697092	+	0.697092i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$		−	968.892i		−	1.25994i	−0.776620	−	0.629969i	$-0.783068\pi$
$769$		−	968.892i		−	1.25994i	0.776620	−	0.629969i	$-0.216932\pi$
$770$	430.382	+	509.157i	0.558938	+	0.661242i
$771$	−229.661			−0.297875
$772$	374.278	+	374.278i	0.484816	+	0.484816i
$773$	1017.80	−	1017.80i	1.31669	−	1.31669i	0.400306	−	0.916382i	$-0.368904\pi$
$773$	1017.80	−	1017.80i	1.31669	−	1.31669i	0.916382	−	0.400306i	$-0.131096\pi$
$774$			155.902i			0.201424i
$775$	8.95759	−	53.0431i	0.0115582	−	0.0684427i
$776$	168.953			0.217722
$777$	333.794	+	333.794i	0.429594	+	0.429594i
$778$	−141.741	+	141.741i	−0.182187	+	0.182187i
$779$			1009.01i			1.29527i
$780$	138.650	−	117.199i	0.177757	−	0.150255i
$781$	−358.119			−0.458539
$782$	−121.076	−	121.076i	−0.154829	−	0.154829i
$783$	65.2844	−	65.2844i	0.0833772	−	0.0833772i
$784$			68.5818i			0.0874768i
$785$	−114.756	−	9.62155i	−0.146186	−	0.0122568i
$786$	393.968			0.501231
$787$	70.1269	+	70.1269i	0.0891066	+	0.0891066i	0.750255	−	0.661148i	$-0.229931\pi$
$787$	70.1269	+	70.1269i	0.0891066	+	0.0891066i	−0.661148	+	0.750255i	$0.729931\pi$
$788$	−175.689	+	175.689i	−0.222955	+	0.222955i
$789$			581.607i			0.737145i
$790$	50.8858	−	606.915i	0.0644125	−	0.768247i
$791$	361.459			0.456964
$792$	−100.231	−	100.231i	−0.126554	−	0.126554i
$793$	499.920	−	499.920i	0.630416	−	0.630416i
$794$		−	115.427i		−	0.145374i
$795$	−135.187	−	159.931i	−0.170047	−	0.201171i
$796$	423.746			0.532344
$797$	−585.608	−	585.608i	−0.734766	−	0.734766i	0.236794	−	0.971560i	$-0.423903\pi$
$797$	−585.608	−	585.608i	−0.734766	−	0.734766i	−0.971560	+	0.236794i	$0.923903\pi$
$798$	176.166	−	176.166i	0.220759	−	0.220759i
$799$			48.6346i			0.0608693i
$800$	−115.255	+	81.9523i	−0.144069	+	0.102440i
$801$	260.034			0.324637
$802$	409.746	+	409.746i	0.510906	+	0.510906i
$803$	1220.94	−	1220.94i	1.52047	−	1.52047i
$804$			145.492i			0.180960i
$805$	−103.359	+	87.3682i	−0.128397	+	0.108532i
$806$	−31.8962			−0.0395734
$807$	80.8605	+	80.8605i	0.100199	+	0.100199i
$808$	−123.265	+	123.265i	−0.152555	+	0.152555i
$809$			9.59843i			0.0118646i	0.999982	+	0.00593228i	$0.00188831\pi$
$809$			9.59843i			0.0118646i	−0.999982	+	0.00593228i	$0.998112\pi$
$810$	63.4171	+	5.31710i	0.0782927	+	0.00656433i
$811$	−1230.65			−1.51745			−0.758723	−	0.651413i	$-0.774176\pi$
$811$	−1230.65			−1.51745			−0.758723	+	0.651413i	$0.774176\pi$
$812$	−141.822	−	141.822i	−0.174657	−	0.174657i
$813$	−369.026	+	369.026i	−0.453907	+	0.453907i
$814$		−	1140.81i		−	1.40149i
$815$	−74.5783	+	889.496i	−0.0915071	+	1.09141i
$816$	174.911			0.214351
$817$	468.247	+	468.247i	0.573130	+	0.573130i
$818$	664.563	−	664.563i	0.812424	−	0.812424i
$819$			177.475i			0.216697i
$820$	361.456	+	427.615i	0.440800	+	0.521481i
$821$	621.813			0.757384			0.378692	−	0.925523i	$-0.376374\pi$
$821$	621.813			0.757384			0.378692	+	0.925523i	$0.376374\pi$
$822$	−454.774	−	454.774i	−0.553253	−	0.553253i
$823$	−1062.95	+	1062.95i	−1.29155	+	1.29155i	−0.357726	+	0.933827i	$0.616448\pi$
$823$	−1062.95	+	1062.95i	−1.29155	+	1.29155i	−0.933827	+	0.357726i	$0.883552\pi$
$824$			42.4240i			0.0514855i
$825$	419.176	+	589.519i	0.508092	+	0.714568i
$826$	575.801			0.697095
$827$	−23.8942	−	23.8942i	−0.0288926	−	0.0288926i	0.692513	−	0.721406i	$-0.256504\pi$
$827$	−23.8942	−	23.8942i	−0.0288926	−	0.0288926i	−0.721406	+	0.692513i	$0.756504\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$		−	183.615i		−	0.221489i	−0.993849	−	0.110745i	$-0.964676\pi$
$829$		−	183.615i		−	0.221489i	0.993849	−	0.110745i	$-0.0353235\pi$
$830$	802.400	−	678.257i	0.966748	−	0.817177i
$831$	−582.783			−0.701304
$832$	59.2931	+	59.2931i	0.0712658	+	0.0712658i
$833$	−306.076	+	306.076i	−0.367438	+	0.367438i
$834$			319.510i			0.383105i
$835$	−508.350	−	42.6218i	−0.608803	−	0.0510441i
$836$	−602.081			−0.720193
$837$	−7.90608	−	7.90608i	−0.00944574	−	0.00944574i
$838$	287.529	−	287.529i	0.343113	−	0.343113i
$839$			662.013i			0.789050i	0.918885	+	0.394525i	$0.129091\pi$
$839$			662.013i			0.789050i	−0.918885	+	0.394525i	$0.870909\pi$
$840$	11.5507	−	137.765i	0.0137509	−	0.164006i
$841$	525.293			0.624605
$842$	−363.794	−	363.794i	−0.432059	−	0.432059i
$843$	−376.291	+	376.291i	−0.446371	+	0.446371i
$844$			207.002i			0.245264i
$845$	−190.875	−	225.812i	−0.225888	−	0.267233i
$846$	−8.17308			−0.00966085
$847$	630.809	+	630.809i	0.744756	+	0.744756i
$848$	68.3938	−	68.3938i	0.0806530	−	0.0806530i
$849$		−	182.984i		−	0.215529i
$850$	−880.125	−	148.630i	−1.03544	−	0.174859i
$851$	231.586			0.272134
$852$	52.5113	+	52.5113i	0.0616330	+	0.0616330i
$853$	603.569	−	603.569i	0.707584	−	0.707584i	−0.258443	−	0.966027i	$-0.583209\pi$
$853$	603.569	−	603.569i	0.707584	−	0.707584i	0.966027	+	0.258443i	$0.0832094\pi$
$854$		−	538.377i		−	0.630419i
$855$	206.441	−	174.502i	0.241452	−	0.204096i
$856$	−47.8742			−0.0559278
$857$	−192.933	−	192.933i	−0.225126	−	0.225126i	0.585527	−	0.810653i	$-0.300888\pi$
$857$	−192.933	−	192.933i	−0.225126	−	0.225126i	−0.810653	+	0.585527i	$0.800888\pi$
$858$	303.277	−	303.277i	0.353470	−	0.353470i
$859$		−	173.638i		−	0.202140i	−0.994879	−	0.101070i	$-0.967773\pi$
$859$		−	173.638i		−	0.202140i	0.994879	−	0.101070i	$-0.0322265\pi$
$860$	366.180	+	30.7017i	0.425790	+	0.0356997i
$861$	−547.354			−0.635719
$862$	−833.171	−	833.171i	−0.966556	−	0.966556i
$863$	41.1471	−	41.1471i	0.0476792	−	0.0476792i	−0.682865	−	0.730544i	$-0.739266\pi$
$863$	41.1471	−	41.1471i	0.0476792	−	0.0476792i	0.730544	+	0.682865i	$0.239266\pi$
$864$			29.3939i			0.0340207i
$865$	64.9705	−	774.904i	0.0751104	−	0.895842i
$866$	−730.843			−0.843930
$867$	426.663	+	426.663i	0.492114	+	0.492114i
$868$	−17.1749	+	17.1749i	−0.0197868	+	0.0197868i
$869$		−	1438.85i		−	1.65575i
$870$	−140.482	−	166.195i	−0.161474	−	0.191029i
$871$	−440.227			−0.505428
$872$	−73.5840	−	73.5840i	−0.0843853	−	0.0843853i
$873$	−126.714	+	126.714i	−0.145148	+	0.145148i
$874$		−	122.223i		−	0.139843i
$875$	−175.188	+	683.401i	−0.200214	+	0.781029i
$876$	−358.054			−0.408737
$877$	−796.431	−	796.431i	−0.908132	−	0.908132i	0.0879899	−	0.996121i	$-0.471956\pi$
$877$	−796.431	−	796.431i	−0.908132	−	0.908132i	−0.996121	+	0.0879899i	$0.971956\pi$
$878$	134.041	−	134.041i	0.152666	−	0.152666i
$879$		−	25.0682i		−	0.0285190i
$880$	−255.159	+	215.682i	−0.289953	+	0.245093i
$881$	−664.288			−0.754016			−0.377008	−	0.926210i	$-0.623047\pi$
$881$	−664.288			−0.754016			−0.377008	+	0.926210i	$0.623047\pi$
$882$	−51.4363	−	51.4363i	−0.0583178	−	0.0583178i
$883$	133.496	−	133.496i	0.151185	−	0.151185i	−0.627462	−	0.778647i	$-0.715906\pi$
$883$	133.496	−	133.496i	0.151185	−	0.151185i	0.778647	+	0.627462i	$0.215906\pi$
$884$			529.243i			0.598691i
$885$	622.560	+	52.1975i	0.703457	+	0.0589802i
$886$	847.523			0.956572
$887$	807.222	+	807.222i	0.910059	+	0.910059i	0.996276	−	0.0862178i	$-0.0274781\pi$
$887$	807.222	+	807.222i	0.910059	+	0.910059i	−0.0862178	+	0.996276i	$0.527478\pi$
$888$	−167.278	+	167.278i	−0.188376	+	0.188376i
$889$			855.250i			0.962036i
$890$	51.2085	−	610.764i	0.0575376	−	0.686251i
$891$	150.346			0.168739
$892$	316.290	+	316.290i	0.354585	+	0.354585i
$893$	−24.5476	+	24.5476i	−0.0274889	+	0.0274889i
$894$			14.2286i			0.0159156i
$895$	15.2964	+	18.0961i	0.0170909	+	0.0202191i
$896$	63.8544			0.0712661
$897$	61.5657	+	61.5657i	0.0686351	+	0.0686351i
$898$	−78.0600	+	78.0600i	−0.0869265	+	0.0869265i
$899$			38.2329i			0.0425282i
$900$	24.9774	−	147.906i	0.0277527	−	0.164340i
$901$	610.474			0.677551
$902$	935.346	+	935.346i	1.03697	+	1.03697i
$903$	−254.008	+	254.008i	−0.281293	+	0.281293i
$904$			181.141i			0.200378i
$905$	−149.417	+	126.300i	−0.165102	+	0.139558i
$906$	−291.154			−0.321362
$907$	304.935	+	304.935i	0.336201	+	0.336201i	0.854936	−	0.518734i	$-0.173597\pi$
$907$	304.935	+	304.935i	0.336201	+	0.336201i	−0.518734	+	0.854936i	$0.673597\pi$
$908$	−91.2271	+	91.2271i	−0.100470	+	0.100470i
$909$		−	184.897i		−	0.203407i
$910$	416.849	+	34.9500i	0.458076	+	0.0384066i
$911$	73.7746			0.0809820			0.0404910	−	0.999180i	$-0.487108\pi$
$911$	73.7746			0.0809820			0.0404910	+	0.999180i	$0.487108\pi$
$912$	88.2837	+	88.2837i	0.0968023	+	0.0968023i
$913$	1755.14	−	1755.14i	1.92238	−	1.92238i
$914$			285.040i			0.311860i
$915$	48.8050	−	582.097i	0.0533388	−	0.636172i
$916$	−356.019			−0.388667
$917$	641.883	+	641.883i	0.699982	+	0.699982i
$918$	−131.183	+	131.183i	−0.142901	+	0.142901i
$919$			1532.20i			1.66724i	0.552336	+	0.833621i	$0.313736\pi$
$919$			1532.20i			1.66724i	−0.552336	+	0.833621i	$0.686264\pi$
$920$	−43.7837	−	51.7976i	−0.0475910	−	0.0563017i
$921$	907.446			0.985284
$922$	602.901	+	602.901i	0.653905	+	0.653905i
$923$	−158.888	+	158.888i	−0.172143	+	0.172143i
$924$		−	326.608i		−	0.353472i
$925$	983.862	−	699.574i	1.06364	−	0.756296i
$926$	−340.814			−0.368049
$927$	−31.8180	−	31.8180i	−0.0343237	−	0.0343237i
$928$	71.0726	−	71.0726i	0.0765869	−	0.0765869i
$929$		−	161.499i		−	0.173842i	−0.996215	−	0.0869209i	$-0.972297\pi$
$929$		−	161.499i		−	0.173842i	0.996215	−	0.0869209i	$-0.0277027\pi$
$930$	−20.1266	+	17.0127i	−0.0216415	+	0.0182932i
$931$	−308.975			−0.331875
$932$	389.903	+	389.903i	0.418351	+	0.418351i
$933$	−148.792	+	148.792i	−0.159477	+	0.159477i
$934$		−	932.630i		−	0.998533i
$935$	−2101.33	−	176.183i	−2.24741	−	0.188431i
$936$	−88.9397			−0.0950210
$937$	−408.190	−	408.190i	−0.435635	−	0.435635i	0.454905	−	0.890540i	$-0.349673\pi$
$937$	−408.190	−	408.190i	−0.435635	−	0.435635i	−0.890540	+	0.454905i	$0.849673\pi$
$938$	−237.046	+	237.046i	−0.252715	+	0.252715i
$939$		−	1038.70i		−	1.10618i
$940$	−1.60952	+	19.1968i	−0.00171226	+	0.0204221i
$941$	1212.70			1.28873			0.644367	−	0.764716i	$-0.277121\pi$
$941$	1212.70			1.28873			0.644367	+	0.764716i	$0.277121\pi$
$942$	39.8922	+	39.8922i	0.0423484	+	0.0423484i
$943$	−189.876	+	189.876i	−0.201354	+	0.201354i
$944$			288.557i			0.305675i
$945$	94.6610	+	111.987i	0.100170	+	0.118505i
$946$	868.121			0.917676
$947$	1226.11	+	1226.11i	1.29473	+	1.29473i	0.931826	+	0.362906i	$0.118215\pi$
$947$	1226.11	+	1226.11i	1.29473	+	1.29473i	0.362906	+	0.931826i	$0.381785\pi$
$948$	−210.979	+	210.979i	−0.222552	+	0.222552i
$949$		−	1083.39i		−	1.14162i
$950$	−369.212	−	519.250i	−0.388644	−	0.546579i
$951$	739.920			0.778045
$952$	284.978	+	284.978i	0.299347	+	0.299347i
$953$	395.986	−	395.986i	0.415515	−	0.415515i	−0.468140	−	0.883655i	$-0.655076\pi$
$953$	395.986	−	395.986i	0.415515	−	0.415515i	0.883655	+	0.468140i	$0.155076\pi$
$954$			102.591i			0.107537i
$955$	879.568	−	743.486i	0.921014	−	0.778519i
$956$	−165.114			−0.172713
$957$	−363.528	−	363.528i	−0.379862	−	0.379862i
$958$	−538.427	+	538.427i	−0.562032	+	0.562032i
$959$		−	1481.91i		−	1.54526i
$960$	69.0398	+	5.78853i	0.0719165	+	0.00602972i
$961$	−956.370			−0.995182
$962$	−506.147	−	506.147i	−0.526141	−	0.526141i
$963$	35.9057	−	35.9057i	0.0372852	−	0.0372852i
$964$			217.818i			0.225952i
$965$	−110.560	+	1318.64i	−0.114570	+	1.36647i
$966$	66.3018			0.0686354
$967$	342.304	+	342.304i	0.353986	+	0.353986i	0.861590	−	0.507605i	$-0.169469\pi$
$967$	342.304	+	342.304i	0.353986	+	0.353986i	−0.507605	+	0.861590i	$0.669469\pi$
$968$	−316.124	+	316.124i	−0.326574	+	0.326574i
$969$			788.008i			0.813218i
$970$	272.671	+	322.578i	0.281104	+	0.332555i
$971$	−1017.40			−1.04779			−0.523895	−	0.851783i	$-0.675521\pi$
$971$	−1017.40			−1.04779			−0.523895	+	0.851783i	$0.675521\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	−520.570	+	520.570i	−0.535015	+	0.535015i
$974$		−	348.237i		−	0.357533i
$975$	447.532	+	75.5764i	0.459007	+	0.0775143i
$976$	269.803			0.276437
$977$	1088.93	+	1088.93i	1.11457	+	1.11457i	0.992525	+	0.122045i	$0.0389453\pi$
$977$	1088.93	+	1088.93i	1.11457	+	1.11457i	0.122045	+	0.992525i	$0.461055\pi$
$978$	309.211	−	309.211i	0.316167	−	0.316167i
$979$		−	1447.97i		−	1.47903i
$980$	−130.942	+	110.683i	−0.133614	+	0.112942i
$981$	110.376			0.112514
$982$	498.635	+	498.635i	0.507775	+	0.507775i
$983$	−513.566	+	513.566i	−0.522448	+	0.522448i	−0.918310	−	0.395862i	$-0.870446\pi$
$983$	−513.566	+	513.566i	−0.522448	+	0.522448i	0.395862	+	0.918310i	$0.370446\pi$
$984$		−	274.301i		−	0.278761i
$985$	−618.981	−	51.8975i	−0.628407	−	0.0526878i
$986$	634.385			0.643392
$987$	−13.3162	−	13.3162i	−0.0134916	−	0.0134916i
$988$	−267.128	+	267.128i	−0.270372	+	0.270372i
$989$			176.230i			0.178190i
$990$	29.6077	−	353.131i	0.0299067	−	0.356698i
$991$	164.713			0.166209			0.0831046	−	0.996541i	$-0.473516\pi$
$991$	164.713			0.166209			0.0831046	+	0.996541i	$0.473516\pi$
$992$	−8.60705	−	8.60705i	−0.00867647	−	0.00867647i
$993$	−708.644	+	708.644i	−0.713639	+	0.713639i
$994$			171.111i			0.172144i
$995$	683.879	+	809.051i	0.687316	+	0.813117i
$996$	−514.714			−0.516782
$997$	4.65005	+	4.65005i	0.00466404	+	0.00466404i	0.709435	−	0.704771i	$-0.248950\pi$
$997$	4.65005	+	4.65005i	0.00466404	+	0.00466404i	−0.704771	+	0.709435i	$0.748950\pi$
$998$	281.223	−	281.223i	0.281787	−	0.281787i
$999$		−	250.917i		−	0.251168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.16	✓	40
5.3	odd	4	inner	690.3.k.a.553.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.16	✓	40	1.1	even	1	trivial
690.3.k.a.553.16	yes	40	5.3	odd	4	inner

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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-3.81857 + 3.22778i) q^{5} +2.44949 q^{6} +(3.99090 + 3.99090i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-7.04634 - 0.590789i) q^{10} -16.7051 q^{11} +(2.44949 + 2.44949i) q^{12} +(-7.41164 + 7.41164i) q^{13} +7.98180i q^{14} +(-0.723566 + 8.62997i) q^{15} -4.00000 q^{16} +(-17.8517 - 17.8517i) q^{17} +(3.00000 - 3.00000i) q^{18} -18.0208i q^{19} +(-6.45555 - 7.63713i) q^{20} +9.77567 q^{21} +(-16.7051 - 16.7051i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(4.16290 - 24.6510i) q^{25} -14.8233 q^{26} +(-3.67423 - 3.67423i) q^{27} +(-7.98180 + 7.98180i) q^{28} +17.7682i q^{29} +(-9.35354 + 7.90641i) q^{30} +2.15176 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-20.4595 + 20.4595i) q^{33} -35.7035i q^{34} +(-28.1212 - 2.35778i) q^{35} +6.00000 q^{36} +(34.1454 + 34.1454i) q^{37} +(18.0208 - 18.0208i) q^{38} +18.1547i q^{39} +(1.18158 - 14.0927i) q^{40} -55.9915 q^{41} +(9.77567 + 9.77567i) q^{42} +(-25.9837 + 25.9837i) q^{43} -33.4103i q^{44} +(9.68333 + 11.4557i) q^{45} +6.78233 q^{46} +(-1.36218 - 1.36218i) q^{47} +(-4.89898 + 4.89898i) q^{48} -17.1454i q^{49} +(28.8139 - 20.4881i) q^{50} -43.7276 q^{51} +(-14.8233 - 14.8233i) q^{52} +(-17.0984 + 17.0984i) q^{53} -7.34847i q^{54} +(63.7897 - 53.9205i) q^{55} -15.9636 q^{56} +(-22.0709 - 22.0709i) q^{57} +(-17.7682 + 17.7682i) q^{58} -72.1392i q^{59} +(-17.2599 - 1.44713i) q^{60} -67.4506 q^{61} +(2.15176 + 2.15176i) q^{62} +(11.9727 - 11.9727i) q^{63} -8.00000i q^{64} +(4.37872 - 52.2250i) q^{65} -40.9191 q^{66} +(29.6984 + 29.6984i) q^{67} +(35.7035 - 35.7035i) q^{68} -8.30662i q^{69} +(-25.7635 - 30.4790i) q^{70} +21.4377 q^{71} +(6.00000 + 6.00000i) q^{72} +(-73.0874 + 73.0874i) q^{73} +68.2909i q^{74} +(-25.0927 - 35.2896i) q^{75} +36.0417 q^{76} +(-66.6685 - 66.6685i) q^{77} +(-18.1547 + 18.1547i) q^{78} +86.1320i q^{79} +(15.2743 - 12.9111i) q^{80} -9.00000 q^{81} +(-55.9915 - 55.9915i) q^{82} +(-105.066 + 105.066i) q^{83} +19.5513i q^{84} +(125.789 + 10.5466i) q^{85} -51.9673 q^{86} +(21.7615 + 21.7615i) q^{87} +(33.4103 - 33.4103i) q^{88} +86.6781i q^{89} +(-1.77237 + 21.1390i) q^{90} -59.1582 q^{91} +(6.78233 + 6.78233i) q^{92} +(2.63536 - 2.63536i) q^{93} -2.72436i q^{94} +(58.1672 + 68.8137i) q^{95} -9.79796 q^{96} +(-42.2382 - 42.2382i) q^{97} +(17.1454 - 17.1454i) q^{98} +50.1154i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more