LMFDB - Embedded newform 168.4.i.c.125.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,4,Mod(125,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.125"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	168.i (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.91232088096$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			125.8
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.65881 + 0.964755i) q^{2} +(5.10794 - 0.953394i) q^{3} +(6.13849 - 5.13019i) q^{4} +17.0023i q^{5} +(-12.6612 + 7.46280i) q^{6} +(-5.04990 + 17.8185i) q^{7} +(-11.3717 + 19.5623i) q^{8} +(25.1821 - 9.73975i) q^{9} +(-16.4031 - 45.2059i) q^{10} -37.8286 q^{11} +(26.4640 - 32.0571i) q^{12} -77.9029 q^{13} +(-3.76378 - 52.2478i) q^{14} +(16.2099 + 86.8468i) q^{15} +(11.3622 - 62.9833i) q^{16} +34.6479 q^{17} +(-57.5578 + 50.1907i) q^{18} +37.7811 q^{19} +(87.2252 + 104.369i) q^{20} +(-8.80655 + 95.8303i) q^{21} +(100.579 - 36.4954i) q^{22} -47.8900i q^{23} +(-39.4353 + 110.765i) q^{24} -164.079 q^{25} +(207.129 - 75.1572i) q^{26} +(119.343 - 73.7585i) q^{27} +(60.4135 + 135.286i) q^{28} -180.790 q^{29} +(-126.885 - 215.270i) q^{30} +163.846i q^{31} +(30.5535 + 178.422i) q^{32} +(-193.226 + 36.0656i) q^{33} +(-92.1220 + 33.4267i) q^{34} +(-302.956 - 85.8600i) q^{35} +(104.613 - 188.976i) q^{36} +159.677i q^{37} +(-100.453 + 36.4496i) q^{38} +(-397.923 + 74.2721i) q^{39} +(-332.605 - 193.345i) q^{40} -81.5544 q^{41} +(-69.0379 - 263.290i) q^{42} +241.294i q^{43} +(-232.211 + 194.068i) q^{44} +(165.598 + 428.154i) q^{45} +(46.2021 + 127.330i) q^{46} +356.246 q^{47} +(-2.01027 - 332.548i) q^{48} +(-291.997 - 179.963i) q^{49} +(436.254 - 158.296i) q^{50} +(176.979 - 33.0331i) q^{51} +(-478.207 + 399.657i) q^{52} +585.689 q^{53} +(-246.150 + 311.246i) q^{54} -643.174i q^{55} +(-291.145 - 301.414i) q^{56} +(192.984 - 36.0203i) q^{57} +(480.686 - 174.418i) q^{58} +172.591i q^{59} +(545.045 + 449.949i) q^{60} +572.943 q^{61} +(-158.072 - 435.636i) q^{62} +(46.3807 + 497.891i) q^{63} +(-253.370 - 444.913i) q^{64} -1324.53i q^{65} +(478.957 - 282.307i) q^{66} +765.089i q^{67} +(212.686 - 177.750i) q^{68} +(-45.6580 - 244.619i) q^{69} +(888.334 - 63.9930i) q^{70} +925.379i q^{71} +(-95.8304 + 603.378i) q^{72} +590.913i q^{73} +(-154.050 - 424.551i) q^{74} +(-838.105 + 156.432i) q^{75} +(231.919 - 193.825i) q^{76} +(191.031 - 674.049i) q^{77} +(986.346 - 581.374i) q^{78} -28.4235 q^{79} +(1070.86 + 193.184i) q^{80} +(539.274 - 490.534i) q^{81} +(216.837 - 78.6800i) q^{82} +2.66288i q^{83} +(437.569 + 633.433i) q^{84} +589.094i q^{85} +(-232.790 - 641.555i) q^{86} +(-923.466 + 172.364i) q^{87} +(430.175 - 740.016i) q^{88} +600.037 q^{89} +(-853.358 - 978.616i) q^{90} +(393.402 - 1388.11i) q^{91} +(-245.685 - 293.972i) q^{92} +(156.210 + 836.917i) q^{93} +(-947.190 + 343.691i) q^{94} +642.367i q^{95} +(326.172 + 882.240i) q^{96} -703.593i q^{97} +(949.984 + 196.781i) q^{98} +(-952.603 + 368.441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) $ 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−2.65881	+	0.964755i	−0.940030	+	0.341092i
$2$	−2.65881	+	0.964755i	−0.940030	+	0.341092i
$3$	5.10794	−	0.953394i	0.983023	−	0.183481i
$3$	5.10794	−	0.953394i	0.983023	−	0.183481i
$4$	6.13849	−	5.13019i	0.767312	−	0.641274i
$5$			17.0023i			1.52073i	0.649494	+	0.760367i	$0.274981\pi$
$5$			17.0023i			1.52073i	−0.649494	+	0.760367i	$0.725019\pi$
$6$	−12.6612	+	7.46280i	−0.861487	+	0.507779i
$7$	−5.04990	+	17.8185i	−0.272669	+	0.962108i
$7$	−5.04990	+	17.8185i	−0.272669	+	0.962108i
$8$	−11.3717	+	19.5623i	−0.502562	+	0.864541i
$9$	25.1821	−	9.73975i	0.932670	−	0.360732i
$10$	−16.4031	−	45.2059i	−0.518711	−	1.42954i
$11$	−37.8286			−1.03689			−0.518443	−	0.855112i	$-0.673488\pi$
$11$	−37.8286			−1.03689			−0.518443	+	0.855112i	$0.673488\pi$
$12$	26.4640	−	32.0571i	0.636624	−	0.771174i
$13$	−77.9029			−1.66203			−0.831015	−	0.556250i	$-0.812240\pi$
$13$	−77.9029			−1.66203			−0.831015	+	0.556250i	$0.812240\pi$
$14$	−3.76378	−	52.2478i	−0.0718508	−	0.997415i
$15$	16.2099	+	86.8468i	0.279025	+	1.49492i
$16$	11.3622	−	62.9833i	0.177535	−	0.984114i
$17$	34.6479			0.494314			0.247157	−	0.968975i	$-0.420504\pi$
$17$	34.6479			0.494314			0.247157	+	0.968975i	$0.420504\pi$
$18$	−57.5578	+	50.1907i	−0.753694	+	0.657225i
$19$	37.7811			0.456189			0.228094	−	0.973639i	$-0.426751\pi$
$19$	37.7811			0.456189			0.228094	+	0.973639i	$0.426751\pi$
$20$	87.2252	+	104.369i	0.975207	+	1.16688i
$21$	−8.80655	+	95.8303i	−0.0915117	+	0.995804i
$22$	100.579	−	36.4954i	0.974705	−	0.353674i
$23$		−	47.8900i		−	0.434163i	−0.976153	−	0.217081i	$-0.930346\pi$
$23$		−	47.8900i		−	0.434163i	0.976153	−	0.217081i	$-0.0696537\pi$
$24$	−39.4353	+	110.765i	−0.335404	+	0.942074i
$25$	−164.079			−1.31263
$26$	207.129	−	75.1572i	1.56236	−	0.566906i
$27$	119.343	−	73.7585i	0.850649	−	0.525734i
$28$	60.4135	+	135.286i	0.407753	+	0.913092i
$29$	−180.790			−1.15765			−0.578826	−	0.815451i	$-0.696489\pi$
$29$	−180.790			−1.15765			−0.578826	+	0.815451i	$0.696489\pi$
$30$	−126.885	−	215.270i	−0.772197	−	1.31009i
$31$			163.846i			0.949280i	0.880180	+	0.474640i	$0.157422\pi$
$31$			163.846i			0.949280i	−0.880180	+	0.474640i	$0.842578\pi$
$32$	30.5535	+	178.422i	0.168786	+	0.985653i
$33$	−193.226	+	36.0656i	−1.01928	+	0.190249i
$34$	−92.1220	+	33.4267i	−0.464670	+	0.168607i
$35$	−302.956	−	85.8600i	−1.46311	−	0.414657i
$36$	104.613	−	188.976i	0.484321	−	0.874891i
$37$			159.677i			0.709481i	0.934965	+	0.354741i	$0.115431\pi$
$37$			159.677i			0.709481i	−0.934965	+	0.354741i	$0.884569\pi$
$38$	−100.453	+	36.4496i	−0.428831	+	0.155603i
$39$	−397.923	+	74.2721i	−1.63381	+	0.304950i
$40$	−332.605	−	193.345i	−1.31474	−	0.764263i
$41$	−81.5544			−0.310650			−0.155325	−	0.987863i	$-0.549642\pi$
$41$	−81.5544			−0.310650			−0.155325	+	0.987863i	$0.549642\pi$
$42$	−69.0379	−	263.290i	−0.253638	−	0.967299i
$43$			241.294i			0.855745i	0.903839	+	0.427873i	$0.140737\pi$
$43$			241.294i			0.855745i	−0.903839	+	0.427873i	$0.859263\pi$
$44$	−232.211	+	194.068i	−0.795616	+	0.664929i
$45$	165.598	+	428.154i	0.548577	+	1.41834i
$46$	46.2021	+	127.330i	0.148090	+	0.408126i
$47$	356.246			1.10561			0.552807	−	0.833309i	$-0.313557\pi$
$47$	356.246			1.10561			0.552807	+	0.833309i	$0.313557\pi$
$48$	−2.01027	−	332.548i	−0.00604496	−	0.999982i
$49$	−291.997	−	179.963i	−0.851303	−	0.524674i
$50$	436.254	−	158.296i	1.23391	−	0.447729i
$51$	176.979	−	33.0331i	0.485923	−	0.0906971i
$52$	−478.207	+	399.657i	−1.27529	+	1.06582i
$53$	585.689			1.51794			0.758968	−	0.651128i	$-0.225704\pi$
$53$	585.689			1.51794			0.758968	+	0.651128i	$0.225704\pi$
$54$	−246.150	+	311.246i	−0.620311	+	0.784356i
$55$		−	643.174i		−	1.57683i
$56$	−291.145	−	301.414i	−0.694749	−	0.719253i
$57$	192.984	−	36.0203i	0.448444	−	0.0837018i
$58$	480.686	−	174.418i	1.08823	−	0.394867i
$59$			172.591i			0.380839i	0.981703	+	0.190419i	$0.0609848\pi$
$59$			172.591i			0.380839i	−0.981703	+	0.190419i	$0.939015\pi$
$60$	545.045	+	449.949i	1.17275	+	0.968136i
$61$	572.943			1.20259			0.601294	−	0.799028i	$-0.294652\pi$
$61$	572.943			1.20259			0.601294	+	0.799028i	$0.294652\pi$
$62$	−158.072	−	435.636i	−0.323792	−	0.892351i
$63$	46.3807	+	497.891i	0.0927527	+	0.995689i
$64$	−253.370	−	444.913i	−0.494862	−	0.868971i
$65$		−	1324.53i		−	2.52750i
$66$	478.957	−	282.307i	0.893265	−	0.526510i
$67$			765.089i			1.39508i	0.716545	+	0.697541i	$0.245723\pi$
$67$			765.089i			1.39508i	−0.716545	+	0.697541i	$0.754277\pi$
$68$	212.686	−	177.750i	0.379293	−	0.316991i
$69$	−45.6580	−	244.619i	−0.0796605	−	0.426792i
$70$	888.334	−	63.9930i	1.51680	−	0.109266i
$71$			925.379i			1.54679i	0.633923	+	0.773396i	$0.281444\pi$
$71$			925.379i			1.54679i	−0.633923	+	0.773396i	$0.718556\pi$
$72$	−95.8304	+	603.378i	−0.156857	+	0.987621i
$73$			590.913i			0.947413i	0.880683	+	0.473706i	$0.157084\pi$
$73$			590.913i			0.947413i	−0.880683	+	0.473706i	$0.842916\pi$
$74$	−154.050	−	424.551i	−0.241999	−	0.666933i
$75$	−838.105	+	156.432i	−1.29035	+	0.240843i
$76$	231.919	−	193.825i	0.350039	−	0.292542i
$77$	191.031	−	674.049i	0.282727	−	0.997597i
$78$	986.346	−	581.374i	1.43182	−	0.843944i
$79$	−28.4235			−0.0404797			−0.0202399	−	0.999795i	$-0.506443\pi$
$79$	−28.4235			−0.0404797			−0.0202399	+	0.999795i	$0.506443\pi$
$80$	1070.86	+	193.184i	1.49658	+	0.269983i
$81$	539.274	−	490.534i	0.739745	−	0.672887i
$82$	216.837	−	78.6800i	0.292020	−	0.105960i
$83$			2.66288i			0.00352155i	0.999998	+	0.00176077i	$0.000560472\pi$
$83$			2.66288i			0.00352155i	−0.999998	+	0.00176077i	$0.999440\pi$
$84$	437.569	+	633.433i	0.568365	+	0.822776i
$85$			589.094i			0.751721i
$86$	−232.790	−	641.555i	−0.291888	−	0.804426i
$87$	−923.466	+	172.364i	−1.13800	+	0.212407i
$88$	430.175	−	740.016i	0.521100	−	0.896431i
$89$	600.037			0.714649			0.357324	−	0.933980i	$-0.383689\pi$
$89$	600.037			0.714649			0.357324	+	0.933980i	$0.383689\pi$
$90$	−853.358	−	978.616i	−0.999464	−	1.14617i
$91$	393.402	−	1388.11i	0.453184	−	1.59905i
$92$	−245.685	−	293.972i	−0.278417	−	0.333138i
$93$	156.210	+	836.917i	0.174175	+	0.933164i
$94$	−947.190	+	343.691i	−1.03931	+	0.377117i
$95$			642.367i			0.693742i
$96$	326.172	+	882.240i	0.346769	+	0.937951i
$97$		−	703.593i		−	0.736485i	−0.929730	−	0.368243i	$-0.879960\pi$
$97$		−	703.593i		−	0.736485i	0.929730	−	0.368243i	$-0.120040\pi$
$98$	949.984	+	196.781i	0.979213	+	0.202836i
$99$	−952.603	+	368.441i	−0.967073	+	0.374038i
$100$	−1007.20	+	841.757i	−1.00720	+	0.841757i
$101$		−	1007.27i		−	0.992350i	−0.868223	−	0.496175i	$-0.834737\pi$
$101$		−	1007.27i		−	0.992350i	0.868223	−	0.496175i	$-0.165263\pi$
$102$	−438.685	+	258.570i	−0.425846	+	0.251003i
$103$		−	274.314i		−	0.262417i	−0.991355	−	0.131209i	$-0.958114\pi$
$103$		−	274.314i		−	0.262417i	0.991355	−	0.131209i	$-0.0418857\pi$
$104$	885.887	−	1523.96i	0.835273	−	1.43689i
$105$	−1629.34	−	149.732i	−1.51435	−	0.139165i
$106$	−1557.23	+	565.047i	−1.42690	+	0.517756i
$107$	1132.06			1.02281			0.511405	−	0.859340i	$-0.329125\pi$
$107$	1132.06			1.02281			0.511405	+	0.859340i	$0.329125\pi$
$108$	354.189	−	1065.02i	0.315573	−	0.948901i
$109$		−	2168.32i		−	1.90539i	−0.303934	−	0.952693i	$-0.598300\pi$
$109$		−	2168.32i		−	1.90539i	0.303934	−	0.952693i	$-0.401700\pi$
$110$	620.506	+	1710.08i	0.537845	+	1.48227i
$111$	152.235	+	815.622i	0.130176	+	0.697436i
$112$	1064.89	+	520.517i	0.898416	+	0.439145i
$113$		−	42.7131i		−	0.0355585i	−0.999842	−	0.0177793i	$-0.994340\pi$
$113$		−	42.7131i		−	0.0355585i	0.999842	−	0.0177793i	$-0.00565961\pi$
$114$	−478.356	+	281.953i	−0.393001	+	0.231643i
$115$	814.240			0.660246
$116$	−1109.78	+	927.489i	−0.888280	+	0.742373i
$117$	−1961.76	+	758.755i	−1.55012	+	0.599546i
$118$	−166.508	−	458.887i	−0.129901	−	0.358000i
$119$	−174.968	+	617.373i	−0.134784	+	0.475584i
$120$	−1883.26	−	670.491i	−1.43264	−	0.510060i
$121$	100.004			0.0751345
$122$	−1523.34	+	552.750i	−1.13047	+	0.410194i
$123$	−416.575	+	77.7534i	−0.305376	+	0.0569983i
$124$	840.564	+	1005.77i	0.608749	+	0.728394i
$125$		−	664.433i		−	0.475430i
$126$	−603.661	−	1279.05i	−0.426812	−	0.904340i
$127$	−57.0406			−0.0398546			−0.0199273	−	0.999801i	$-0.506343\pi$
$127$	−57.0406			−0.0398546			−0.0199273	+	0.999801i	$0.506343\pi$
$128$	1102.89	+	938.498i	0.761585	+	0.648065i
$129$	230.048	+	1232.52i	0.157013	+	0.841217i
$130$	1277.85	+	3521.67i	0.862113	+	2.37593i
$131$			2244.81i			1.49717i	0.663036	+	0.748587i	$0.269268\pi$
$131$			2244.81i			1.49717i	−0.663036	+	0.748587i	$0.730732\pi$
$132$	−1001.10	+	1212.68i	−0.660107	+	0.799621i
$133$	−190.791	+	673.203i	−0.124389	+	0.438903i
$134$	−738.124	−	2034.22i	−0.475852	−	1.31142i
$135$	1254.07	+	2029.10i	0.799502	+	1.29361i
$136$	−394.005	+	677.793i	−0.248424	+	0.427355i
$137$		−	1244.36i		−	0.776003i	−0.921659	−	0.388002i	$-0.873165\pi$
$137$		−	1244.36i		−	0.776003i	0.921659	−	0.388002i	$-0.126835\pi$
$138$	357.393	+	606.346i	0.220459	+	0.374026i
$139$	502.246			0.306475			0.153237	−	0.988189i	$-0.451030\pi$
$139$	502.246			0.306475			0.153237	+	0.988189i	$0.451030\pi$
$140$	−2300.17	+	1027.17i	−1.38857	+	0.620084i
$141$	1819.69	−	339.643i	1.08684	−	0.202859i
$142$	−892.764	−	2460.40i	−0.527599	−	1.45403i
$143$	2946.96			1.72334
$144$	−327.317	−	1696.72i	−0.189420	−	0.981896i
$145$		−	3073.86i		−	1.76048i
$146$	−570.086	−	1571.12i	−0.323155	−	0.890596i
$147$	−1663.08	−	640.853i	−0.933119	−	0.359569i
$148$	819.176	+	980.179i	0.454972	+	0.544393i
$149$	−2671.10			−1.46863			−0.734313	−	0.678811i	$-0.762496\pi$
$149$	−2671.10			−1.46863			−0.734313	+	0.678811i	$0.762496\pi$
$150$	2077.44	−	1224.49i	1.13082	−	0.666527i
$151$	−1518.45			−0.818345			−0.409172	−	0.912457i	$-0.634183\pi$
$151$	−1518.45			−0.818345			−0.409172	+	0.912457i	$0.634183\pi$
$152$	−429.635	+	739.087i	−0.229263	+	0.394394i
$153$	872.506	−	337.462i	0.461032	−	0.178315i
$154$	142.378	+	1976.46i	0.0745012	+	1.03421i
$155$	−2785.77			−1.44360
$156$	−2061.62	+	2497.34i	−1.05809	+	1.28171i
$157$	1311.73			0.666800			0.333400	−	0.942785i	$-0.391804\pi$
$157$	1311.73			0.666800			0.333400	+	0.942785i	$0.391804\pi$
$158$	75.5727	−	27.4218i	0.0380521	−	0.0138073i
$159$	2991.66	−	558.392i	1.49217	−	0.278512i
$160$	−3033.59	+	519.481i	−1.49892	+	0.256678i
$161$	853.327	+	241.839i	0.417712	+	0.118383i
$162$	−960.580	+	1824.50i	−0.465866	+	0.884855i
$163$		−	3119.89i		−	1.49920i	−0.661894	−	0.749598i	$-0.730247\pi$
$163$		−	3119.89i		−	1.49920i	0.661894	−	0.749598i	$-0.269753\pi$
$164$	−500.621	+	418.390i	−0.238366	+	0.199212i
$165$	−613.198	−	3285.29i	−0.289318	−	1.55006i
$166$	−2.56902	−	7.08007i	−0.00120117	−	0.00331036i
$167$	−3622.79			−1.67868			−0.839342	−	0.543604i	$-0.817059\pi$
$167$	−3622.79			−1.67868			−0.839342	+	0.543604i	$0.817059\pi$
$168$	−1774.52	−	1262.03i	−0.814923	−	0.579569i
$169$	3871.87			1.76234
$170$	−568.332	−	1566.29i	−0.256406	−	0.706640i
$171$	951.408	−	367.979i	0.425474	−	0.164562i
$172$	1237.89	+	1481.18i	0.548767	+	0.656623i
$173$			1901.49i			0.835653i	0.908527	+	0.417826i	$0.137208\pi$
$173$			1901.49i			0.835653i	−0.908527	+	0.417826i	$0.862792\pi$
$174$	2289.03	−	1349.20i	0.997303	−	0.587832i
$175$	828.582	−	2923.64i	0.357914	−	1.26289i
$176$	−429.818	+	2382.57i	−0.184084	+	1.02042i
$177$	164.548	+	881.586i	0.0698766	+	0.374373i
$178$	−1595.38	+	578.888i	−0.671791	+	0.243761i
$179$	1329.17			0.555010			0.277505	−	0.960724i	$-0.410493\pi$
$179$	1329.17			0.555010			0.277505	+	0.960724i	$0.410493\pi$
$180$	3213.04	+	1778.67i	1.33048	+	0.736523i
$181$	2346.73			0.963709			0.481855	−	0.876251i	$-0.339963\pi$
$181$	2346.73			0.963709			0.481855	+	0.876251i	$0.339963\pi$
$182$	293.209	+	4070.26i	0.119418	+	1.65773i
$183$	2926.56	−	546.240i	1.18217	−	0.220652i
$184$	936.839	+	544.589i	0.375352	+	0.218194i
$185$	−2714.89			−1.07893
$186$	−1222.75	−	2074.50i	−0.482025	−	0.817793i
$187$	−1310.68			−0.512548
$188$	2186.82	−	1827.61i	0.848351	−	0.709002i
$189$	711.596	+	2498.98i	0.273868	+	0.961767i
$190$	−619.727	−	1707.93i	−0.236630	−	0.652138i
$191$			2129.66i			0.806791i	0.915026	+	0.403395i	$0.132170\pi$
$191$			2129.66i			0.806791i	−0.915026	+	0.403395i	$0.867830\pi$
$192$	−1718.37	−	2031.03i	−0.645901	−	0.763421i
$193$	878.502			0.327647			0.163824	−	0.986490i	$-0.447617\pi$
$193$	878.502			0.327647			0.163824	+	0.986490i	$0.447617\pi$
$194$	678.795	+	1870.72i	0.251210	+	0.692318i
$195$	−1262.80	−	6765.62i	−0.463748	−	2.48460i
$196$	−2715.67	+	393.298i	−0.989675	+	0.143330i
$197$	3405.38			1.23159			0.615796	−	0.787906i	$-0.288835\pi$
$197$	3405.38			1.23159			0.615796	+	0.787906i	$0.288835\pi$
$198$	2177.33	−	1898.64i	0.781496	−	0.681468i
$199$			2603.72i			0.927503i	0.885965	+	0.463752i	$0.153497\pi$
$199$			2603.72i			0.927503i	−0.885965	+	0.463752i	$0.846503\pi$
$200$	1865.85	−	3209.77i	0.659679	−	1.13482i
$201$	729.431	+	3908.03i	0.255971	+	1.37140i
$202$	971.771	+	2678.14i	0.338483	+	0.932838i
$203$	912.973	−	3221.41i	0.315656	−	1.11379i
$204$	916.920	−	1110.71i	0.314692	−	0.381203i
$205$		−	1386.61i		−	0.472416i
$206$	264.646	+	729.348i	0.0895085	+	0.246680i
$207$	−466.436	−	1205.97i	−0.156616	−	0.404931i
$208$	−885.152	+	4906.59i	−0.295068	+	1.63563i
$209$	−1429.21			−0.473016
$210$	4476.55	−	1173.80i	1.47100	−	0.385715i
$211$		−	987.223i		−	0.322101i	−0.986946	−	0.161050i	$-0.948512\pi$
$211$		−	987.223i		−	0.322101i	0.986946	−	0.161050i	$-0.0514881\pi$
$212$	3595.25	−	3004.70i	1.16473	−	0.973413i
$213$	882.250	+	4726.78i	0.283807	+	1.52053i
$214$	−3009.93	+	1092.16i	−0.961471	+	0.348873i
$215$	−4102.56			−1.30136
$216$	85.7603	+	3173.38i	0.0270151	+	0.999635i
$217$	−2919.50	−	827.408i	−0.913310	−	0.258839i
$218$	2091.90	+	5765.13i	0.649913	+	1.79112i
$219$	563.373	+	3018.35i	0.173832	+	0.931329i
$220$	−3299.61	−	3948.12i	−1.01118	−	1.20992i
$221$	−2699.17			−0.821565
$222$	−1191.64	−	2021.71i	−0.360260	−	0.611209i
$223$		−	1430.30i		−	0.429507i	−0.976668	−	0.214754i	$-0.931105\pi$
$223$		−	1430.30i		−	0.429507i	0.976668	−	0.214754i	$-0.0688949\pi$
$224$	−3333.51	−	356.597i	−0.994327	−	0.106367i
$225$	−4131.85	+	1598.09i	−1.22425	+	0.473508i
$226$	41.2077	+	113.566i	0.0121287	+	0.0334261i
$227$			5026.34i			1.46965i	0.678258	+	0.734824i	$0.262735\pi$
$227$			5026.34i			1.46965i	−0.678258	+	0.734824i	$0.737265\pi$
$228$	999.839	−	1211.15i	0.290421	−	0.351801i
$229$	−4464.57			−1.28833			−0.644164	−	0.764887i	$-0.722795\pi$
$229$	−4464.57			−1.28833			−0.644164	+	0.764887i	$0.722795\pi$
$230$	−2164.91	+	785.543i	−0.620651	+	0.225205i
$231$	333.139	−	3625.13i	0.0948873	−	1.03254i
$232$	2055.89	−	3536.68i	0.581792	−	1.00084i
$233$			2131.34i			0.599265i	0.954055	+	0.299632i	$0.0968641\pi$
$233$			2131.34i			0.599265i	−0.954055	+	0.299632i	$0.903136\pi$
$234$	4483.92	−	3910.00i	1.25266	−	1.09233i
$235$			6057.02i			1.68135i
$236$	885.427	+	1059.45i	0.244222	+	0.292222i
$237$	−145.186	+	27.0988i	−0.0397925	+	0.00742725i
$238$	−130.407	−	1810.28i	−0.0355169	−	0.493037i
$239$		−	6763.79i		−	1.83060i	−0.402774	−	0.915299i	$-0.631954\pi$
$239$		−	6763.79i		−	1.83060i	0.402774	−	0.915299i	$-0.368046\pi$
$240$	5654.08	−	34.1793i	1.52071	−	0.00919277i
$241$		−	2721.77i		−	0.727489i	−0.931499	−	0.363744i	$-0.881498\pi$
$241$		−	2721.77i		−	0.727489i	0.931499	−	0.363744i	$-0.118502\pi$
$242$	−265.891	+	96.4794i	−0.0706287	+	0.0256278i
$243$	2286.91	−	3019.76i	0.603725	−	0.797192i
$244$	3517.01	−	2939.31i	0.922760	−	0.771189i
$245$	3059.79	−	4964.63i	0.797889	−	1.29461i
$246$	1032.58	−	608.624i	0.267621	−	0.157742i
$247$	−2943.26			−0.758199
$248$	−3205.22	−	1863.21i	−0.820692	−	0.477072i
$249$	2.53877	+	13.6018i	0.000646136	+	0.00346177i
$250$	641.015	+	1766.60i	0.162165	+	0.446918i
$251$			5463.02i			1.37380i	0.726754	+	0.686898i	$0.241028\pi$
$251$			5463.02i			1.37380i	−0.726754	+	0.686898i	$0.758972\pi$
$252$	2838.99	+	2818.36i	0.709680	+	0.704524i
$253$			1811.61i			0.450178i
$254$	151.660	−	55.0302i	0.0374645	−	0.0135941i
$255$	561.639	+	3009.06i	0.137926	+	0.738959i
$256$	−3837.80	−	1431.26i	−0.936963	−	0.349430i
$257$	6828.16			1.65731			0.828655	−	0.559760i	$-0.189107\pi$
$257$	6828.16			1.65731			0.828655	+	0.559760i	$0.189107\pi$
$258$	−1800.73	−	3055.08i	−0.434530	−	0.737214i
$259$	−2845.21	−	806.355i	−0.682597	−	0.193453i
$260$	−6795.10	−	8130.62i	−1.62082	−	1.93938i
$261$	−4552.68	+	1760.85i	−1.07971	+	0.417602i
$262$	−2165.69	−	5968.51i	−0.510675	−	1.40739i
$263$		−	665.207i		−	0.155964i	−0.996955	−	0.0779818i	$-0.975152\pi$
$263$		−	665.207i		−	0.155964i	0.996955	−	0.0779818i	$-0.0248476\pi$
$264$	1491.78	−	4190.08i	0.347776	−	0.976825i
$265$			9958.08i			2.30838i
$266$	−142.200	−	1973.98i	−0.0327776	−	0.455010i
$267$	3064.95	−	572.071i	0.702517	−	0.131124i
$268$	3925.06	+	4696.50i	0.894630	+	1.07046i
$269$		−	4857.98i		−	1.10110i	−0.834802	−	0.550550i	$-0.814418\pi$
$269$		−	4857.98i		−	1.10110i	0.834802	−	0.550550i	$-0.185582\pi$
$270$	−5291.90	−	4185.12i	−1.19280	−	0.943328i
$271$			1075.74i			0.241131i	0.992705	+	0.120566i	$0.0384709\pi$
$271$			1075.74i			0.241131i	−0.992705	+	0.120566i	$0.961529\pi$
$272$	393.677	−	2182.24i	0.0877581	−	0.486462i
$273$	686.056	−	7465.46i	0.152095	−	1.65506i
$274$	1200.50	+	3308.50i	0.264689	+	0.729466i
$275$	6206.88			1.36105
$276$	−1535.21	−	1267.36i	−0.334815	−	0.276399i
$277$			6119.99i			1.32749i	0.747959	+	0.663745i	$0.231034\pi$
$277$			6119.99i			1.32749i	−0.747959	+	0.663745i	$0.768966\pi$
$278$	−1335.38	+	484.545i	−0.288095	+	0.104536i
$279$	1595.82	+	4125.99i	0.342435	+	0.885365i
$280$	5124.74	−	4950.15i	1.09379	−	1.05653i
$281$		−	580.494i		−	0.123236i	−0.998100	−	0.0616181i	$-0.980374\pi$
$281$		−	580.494i		−	0.123236i	0.998100	−	0.0616181i	$-0.0196261\pi$
$282$	−4510.52	+	2658.60i	−0.952473	+	0.561408i
$283$	5973.23			1.25467			0.627335	−	0.778750i	$-0.284146\pi$
$283$	5973.23			1.25467			0.627335	+	0.778750i	$0.284146\pi$
$284$	4747.37	+	5680.43i	0.991918	+	1.18687i
$285$	612.429	+	3281.17i	0.127288	+	0.681964i
$286$	−7835.39	+	2843.09i	−1.61999	+	0.587817i
$287$	411.841	−	1453.18i	0.0847046	−	0.298879i
$288$	2507.19	+	4195.46i	0.512978	+	0.858402i
$289$	−3712.52			−0.755653
$290$	2965.52	+	8172.78i	0.600487	+	1.65490i
$291$	−670.801	−	3593.91i	−0.135131	−	0.723982i
$292$	3031.50	+	3627.32i	0.607551	+	0.726961i
$293$			522.434i			0.104167i	0.998643	+	0.0520835i	$0.0165862\pi$
$293$			522.434i			0.104167i	−0.998643	+	0.0520835i	$0.983414\pi$
$294$	5040.07	+	99.4388i	0.999805	+	0.0197258i
$295$	−2934.45			−0.579154
$296$	−3123.66	−	1815.80i	−0.613376	−	0.356558i
$297$	−4514.57	+	2790.18i	−0.882027	+	0.545127i
$298$	7101.95	−	2576.96i	1.38055	−	0.500937i
$299$			3730.77i			0.721591i
$300$	−4342.18	+	5259.90i	−0.835653	+	1.01227i
$301$	−4299.50	−	1218.51i	−0.823319	−	0.233335i
$302$	4037.28	−	1464.94i	0.769269	−	0.279131i
$303$	−960.327	−	5145.08i	−0.182077	−	0.975503i
$304$	429.278	−	2379.58i	0.0809895	−	0.448942i
$305$			9741.37i			1.82882i
$306$	−1994.25	+	1739.00i	−0.372562	+	0.324876i
$307$	7907.97			1.47014			0.735068	−	0.677994i	$-0.237150\pi$
$307$	7907.97			1.47014			0.735068	+	0.677994i	$0.237150\pi$
$308$	−2285.36	−	5117.67i	−0.422794	−	0.946774i
$309$	−261.529	−	1401.18i	−0.0481485	−	0.257962i
$310$	7406.82	−	2687.59i	1.35703	−	0.492402i
$311$	1459.26			0.266068			0.133034	−	0.991111i	$-0.457528\pi$
$311$	1459.26			0.266068			0.133034	+	0.991111i	$0.457528\pi$
$312$	3072.12	−	8628.91i	0.557451	−	1.56576i
$313$		−	5437.91i		−	0.982008i	−0.871157	−	0.491004i	$-0.836630\pi$
$313$		−	5437.91i		−	0.982008i	0.871157	−	0.491004i	$-0.163370\pi$
$314$	−3487.64	+	1265.50i	−0.626812	+	0.227440i
$315$	−8465.31	+	788.579i	−1.51418	+	0.141052i
$316$	−174.478	+	145.818i	−0.0310606	+	0.0259586i
$317$	−7991.76			−1.41597			−0.707984	−	0.706228i	$-0.750395\pi$
$317$	−7991.76			−1.41597			−0.707984	+	0.706228i	$0.750395\pi$
$318$	−7415.54	+	4370.88i	−1.30768	+	0.770776i
$319$	6839.05			1.20035
$320$	7564.56	−	4307.87i	1.32147	−	0.752554i
$321$	5782.51	−	1079.30i	1.00545	−	0.187666i
$322$	−2502.15	+	180.247i	−0.433041	+	0.0311950i
$323$	1309.04			0.225501
$324$	793.797	−	5777.73i	0.136111	−	0.990694i
$325$	12782.2			2.18163
$326$	3009.93	+	8295.19i	0.511364	+	1.40929i
$327$	−2067.26	−	11075.6i	−0.349602	−	1.87304i
$328$	927.411	−	1595.39i	0.156121	−	0.268570i
$329$	−1799.01	+	6347.77i	−0.301467	+	1.06372i
$330$	4799.88	+	8143.37i	0.800681	+	1.35842i
$331$			5913.18i			0.981927i	0.871180	+	0.490963i	$0.163355\pi$
$331$			5913.18i			0.981927i	−0.871180	+	0.490963i	$0.836645\pi$
$332$	13.6611	+	16.3461i	0.00225828	+	0.00270213i
$333$	1555.22	+	4021.01i	0.255932	+	0.661712i
$334$	9632.31	−	3495.11i	1.57801	−	0.572586i
$335$	−13008.3			−2.12155
$336$	5935.65	+	1643.51i	0.963739	+	0.266848i
$337$	−10946.5			−1.76942			−0.884712	−	0.466138i	$-0.845645\pi$
$337$	−10946.5			−1.76942			−0.884712	+	0.466138i	$0.845645\pi$
$338$	−10294.5	+	3735.40i	−1.65665	+	0.601122i
$339$	−40.7224	−	218.176i	−0.00652430	−	0.0349549i
$340$	3022.17	+	3616.15i	0.482059	+	0.576804i
$341$		−	6198.08i		−	0.984296i
$342$	−2174.60	+	1896.26i	−0.343827	+	0.299819i
$343$	4681.23	−	4294.15i	0.736917	−	0.675983i
$344$	−4720.28	−	2743.92i	−0.739827	−	0.430065i
$345$	4159.09	−	776.292i	0.649037	−	0.121142i
$346$	−1834.48	−	5055.70i	−0.285035	−	0.785538i
$347$	1637.21			0.253285			0.126643	−	0.991948i	$-0.459580\pi$
$347$	1637.21			0.253285			0.126643	+	0.991948i	$0.459580\pi$
$348$	−4784.43	+	5795.62i	−0.736989	+	0.892752i
$349$	−4492.59			−0.689062			−0.344531	−	0.938775i	$-0.611962\pi$
$349$	−4492.59			−0.689062			−0.344531	+	0.938775i	$0.611962\pi$
$350$	617.557	+	8572.77i	0.0943137	+	1.30924i
$351$	−9297.15	+	5746.00i	−1.41380	+	0.873786i
$352$	−1155.80	−	6749.46i	−0.175012	−	1.02201i
$353$	1372.22			0.206901			0.103451	−	0.994635i	$-0.467012\pi$
$353$	1372.22			0.206901			0.103451	+	0.994635i	$0.467012\pi$
$354$	−1288.01	−	2185.22i	−0.193382	−	0.328088i
$355$	−15733.6			−2.35226
$356$	3683.32	−	3078.30i	0.548359	−	0.458286i
$357$	−305.128	+	3320.32i	−0.0452355	+	0.492240i
$358$	−3534.00	+	1282.32i	−0.521725	+	0.189310i
$359$		−	5118.09i		−	0.752430i	−0.926532	−	0.376215i	$-0.877225\pi$
$359$		−	5118.09i		−	0.752430i	0.926532	−	0.376215i	$-0.122775\pi$
$360$	−10258.8	−	1629.34i	−1.50191	−	0.238538i
$361$	−5431.59			−0.791892
$362$	−6239.51	+	2264.02i	−0.905915	+	0.328714i
$363$	510.814	−	95.3432i	0.0738590	−	0.0137857i
$364$	−4706.39	−	10539.1i	−0.677697	−	1.51759i
$365$	−10046.9			−1.44076
$366$	−7254.16	+	4275.76i	−1.03601	+	0.610649i
$367$			6151.73i			0.874980i	0.899223	+	0.437490i	$0.144133\pi$
$367$			6151.73i			0.874980i	−0.899223	+	0.437490i	$0.855867\pi$
$368$	−3016.27	−	544.137i	−0.427266	−	0.0770791i
$369$	−2053.71	+	794.320i	−0.289734	+	0.112061i
$370$	7218.36	−	2619.20i	1.01423	−	0.368016i
$371$	−2957.67	+	10436.1i	−0.413894	+	1.46042i
$372$	5252.44	+	4336.03i	0.732060	+	0.604334i
$373$		−	12854.7i		−	1.78443i	−0.451614	−	0.892213i	$-0.649152\pi$
$373$		−	12854.7i		−	1.78443i	0.451614	−	0.892213i	$-0.350848\pi$
$374$	3484.85	−	1264.49i	0.481810	−	0.174826i
$375$	−633.466	−	3393.88i	−0.0872321	−	0.467358i
$376$	−4051.12	+	6969.01i	−0.555640	+	0.955849i
$377$	14084.1			1.92405
$378$	−4302.90	−	5957.79i	−0.585495	−	0.810676i
$379$			2284.79i			0.309662i	0.987941	+	0.154831i	$0.0494832\pi$
$379$			2284.79i			0.309662i	−0.987941	+	0.154831i	$0.950517\pi$
$380$	3295.47	+	3943.17i	0.444879	+	0.532316i
$381$	−291.360	+	54.3821i	−0.0391780	+	0.00731255i
$382$	−2054.60	−	5662.36i	−0.275190	−	0.758407i
$383$	3061.90			0.408501			0.204251	−	0.978919i	$-0.434524\pi$
$383$	3061.90			0.408501			0.204251	+	0.978919i	$0.434524\pi$
$384$	6528.27	+	3742.30i	0.867563	+	0.497327i
$385$	11460.4	+	3247.97i	1.51708	+	0.429952i
$386$	−2335.77	+	847.539i	−0.307998	+	0.111758i
$387$	2350.15	+	6076.29i	0.308694	+	0.798128i
$388$	−3609.57	−	4319.00i	−0.472289	−	0.565114i
$389$	2350.30			0.306336			0.153168	−	0.988200i	$-0.451052\pi$
$389$	2350.30			0.306336			0.153168	+	0.988200i	$0.451052\pi$
$390$	9884.71	+	16770.2i	1.28341	+	2.17741i
$391$		−	1659.29i		−	0.214613i
$392$	6841.00	−	3665.66i	0.881435	−	0.472305i
$393$	2140.19	+	11466.3i	0.274703	+	1.47176i
$394$	−9054.25	+	3285.36i	−1.15773	+	0.420086i
$395$		−	483.266i		−	0.0615589i
$396$	−3957.37	+	7148.71i	−0.502186	+	0.907163i
$397$	1338.92			0.169266			0.0846329	−	0.996412i	$-0.473028\pi$
$397$	1338.92			0.169266			0.0846329	+	0.996412i	$0.473028\pi$
$398$	−2511.96	−	6922.80i	−0.316364	−	0.871880i
$399$	−332.721	+	3620.58i	−0.0417466	+	0.454275i
$400$	−1864.30	+	10334.2i	−0.233038	+	1.29178i
$401$		−	7728.45i		−	0.962444i	−0.876599	−	0.481222i	$-0.840193\pi$
$401$		−	7728.45i		−	0.962444i	0.876599	−	0.481222i	$-0.159807\pi$
$402$	−5709.71	−	9686.97i	−0.708394	−	1.20185i
$403$		−	12764.1i		−	1.57773i
$404$	−5167.50	−	6183.14i	−0.636368	−	0.761442i
$405$	8340.23	+	9168.92i	1.02328	+	1.12496i
$406$	680.455	+	9445.90i	0.0831783	+	1.15466i
$407$		−	6040.37i		−	0.735652i
$408$	−1366.35	+	3837.77i	−0.165795	+	0.465681i
$409$			13294.9i			1.60731i	0.595093	+	0.803657i	$0.297115\pi$
$409$			13294.9i			1.60731i	−0.595093	+	0.803657i	$0.702885\pi$
$410$	1337.74	+	3686.74i	0.161138	+	0.444085i
$411$	−1186.36	−	6356.09i	−0.142382	−	0.762829i
$412$	−1407.28	−	1683.87i	−0.168281	−	0.201356i
$413$	−3075.32	−	871.569i	−0.366408	−	0.103843i
$414$	2403.63	+	2756.44i	0.285343	+	0.327226i
$415$	−45.2751			−0.00535534
$416$	−2380.21	−	13899.6i	−0.280527	−	1.63818i
$417$	2565.44	−	478.838i	0.301272	−	0.0562322i
$418$	3799.99	−	1378.84i	0.444649	−	0.161342i
$419$		−	8465.25i		−	0.987003i	−0.869745	−	0.493502i	$-0.835717\pi$
$419$		−	8465.25i		−	0.987003i	0.869745	−	0.493502i	$-0.164283\pi$
$420$	−10769.8	+	7439.69i	−1.25122	+	0.864332i
$421$			1141.45i			0.132140i	0.997815	+	0.0660701i	$0.0210461\pi$
$421$			1141.45i			0.132140i	−0.997815	+	0.0660701i	$0.978954\pi$
$422$	952.429	+	2624.83i	0.109866	+	0.302784i
$423$	8971.03	−	3469.75i	1.03117	−	0.398830i
$424$	−6660.27	+	11457.4i	−0.762857	+	1.31232i
$425$	−5684.99			−0.648853
$426$	−6905.92	−	11716.4i	−0.785429	−	1.33254i
$427$	−2893.31	+	10209.0i	−0.327908	+	1.15702i
$428$	6949.16	−	5807.70i	0.784814	−	0.655901i
$429$	15052.9	−	2809.61i	1.69408	−	0.316199i
$430$	10907.9	−	3957.97i	1.22332	−	0.443884i
$431$			6623.29i			0.740215i	0.928989	+	0.370108i	$0.120679\pi$
$431$			6623.29i			0.740215i	−0.928989	+	0.370108i	$0.879321\pi$
$432$	−3289.55	−	8354.66i	−0.366363	−	0.930472i
$433$			151.928i			0.0168619i	0.999964	+	0.00843095i	$0.00268369\pi$
$433$			151.928i			0.0168619i	−0.999964	+	0.00843095i	$0.997316\pi$
$434$	8560.62	−	616.681i	0.946827	−	0.0682066i
$435$	−2930.59	−	15701.1i	−0.323014	−	1.73059i
$436$	−11123.9	−	13310.2i	−1.22187	−	1.46203i
$437$		−	1809.34i		−	0.198060i
$438$	−4409.86	−	7481.68i	−0.481076	−	0.816184i
$439$			9828.43i			1.06853i	0.845317	+	0.534266i	$0.179412\pi$
$439$			9828.43i			1.06853i	−0.845317	+	0.534266i	$0.820588\pi$
$440$	12582.0	+	7313.98i	1.36323	+	0.792455i
$441$	−9105.89	−	1687.87i	−0.983251	−	0.182255i
$442$	7176.57	−	2604.04i	0.772296	−	0.280230i
$443$	2207.57			0.236760			0.118380	−	0.992968i	$-0.462230\pi$
$443$	2207.57			0.236760			0.118380	+	0.992968i	$0.462230\pi$
$444$	5118.80	+	4225.70i	0.547134	+	0.451673i
$445$			10202.0i			1.08679i
$446$	1379.89	+	3802.90i	0.146502	+	0.403750i
$447$	−13643.8	+	2546.61i	−1.44369	+	0.269465i
$448$	9207.17	−	2267.90i	0.970978	−	0.239170i
$449$		−	7960.02i		−	0.836651i	−0.908297	−	0.418326i	$-0.862617\pi$
$449$		−	7960.02i		−	0.836651i	0.908297	−	0.418326i	$-0.137383\pi$
$450$	9444.02	−	8235.23i	0.989323	−	0.862694i
$451$	3085.09			0.322109
$452$	−219.127	−	262.194i	−0.0228028	−	0.0272845i
$453$	−7756.17	+	1447.68i	−0.804452	+	0.150150i
$454$	−4849.19	−	13364.1i	−0.501286	−	1.38151i
$455$	23601.1	+	6688.75i	2.43173	+	0.689172i
$456$	−1489.91	+	4184.82i	−0.153007	+	0.429764i
$457$	3624.43			0.370993			0.185496	−	0.982645i	$-0.440611\pi$
$457$	3624.43			0.370993			0.185496	+	0.982645i	$0.440611\pi$
$458$	11870.4	−	4307.22i	1.21107	−	0.439439i
$459$	4134.97	−	2555.58i	0.420488	−	0.259878i
$460$	4998.21	−	4177.21i	0.506615	−	0.423399i
$461$			5885.29i			0.594589i	0.954786	+	0.297294i	$0.0960843\pi$
$461$			5885.29i			0.594589i	−0.954786	+	0.297294i	$0.903916\pi$
$462$	2611.61	+	9959.91i	0.262993	+	1.00298i
$463$	13856.2			1.39083			0.695415	−	0.718609i	$-0.255221\pi$
$463$	13856.2			1.39083			0.695415	+	0.718609i	$0.255221\pi$
$464$	−2054.18	+	11386.8i	−0.205524	+	1.13926i
$465$	−14229.5	+	2655.93i	−1.41909	+	0.264873i
$466$	−2056.22	−	5666.82i	−0.204405	−	0.563327i
$467$		−	12318.9i		−	1.22066i	−0.792147	−	0.610330i	$-0.791037\pi$
$467$		−	12318.9i		−	1.22066i	0.792147	−	0.610330i	$-0.208963\pi$
$468$	−8149.68	+	14721.8i	−0.804955	+	1.45409i
$469$	−13632.7	−	3863.62i	−1.34222	−	0.380396i
$470$	−5843.54	−	16104.4i	−0.573494	−	1.58051i
$471$	6700.24	−	1250.60i	0.655480	−	0.122345i
$472$	−3376.29	−	1962.65i	−0.329251	−	0.191395i
$473$		−	9127.83i		−	0.887311i
$474$	359.877	−	212.119i	0.0348728	−	0.0205548i
$475$	−6199.09			−0.598808
$476$	2093.20	+	4687.36i	0.201558	+	0.451355i
$477$	14748.9	−	5704.47i	1.41573	−	0.547567i
$478$	6525.40	+	17983.6i	0.624403	+	1.72082i
$479$	−5683.40			−0.542132			−0.271066	−	0.962561i	$-0.587376\pi$
$479$	−5683.40			−0.542132			−0.271066	+	0.962561i	$0.587376\pi$
$480$	−15000.1	+	5545.68i	−1.42637	+	0.527343i
$481$		−	12439.3i		−	1.17918i
$482$	2625.84	+	7236.67i	0.248141	+	0.683861i
$483$	4589.31	+	421.745i	0.432341	+	0.0397310i
$484$	613.874	−	513.040i	0.0576516	−	0.0481818i
$485$	11962.7			1.12000
$486$	−3167.12	+	10235.3i	−0.295603	+	0.955311i
$487$	3252.77			0.302663			0.151332	−	0.988483i	$-0.451644\pi$
$487$	3252.77			0.302663			0.151332	+	0.988483i	$0.451644\pi$
$488$	−6515.33	+	11208.1i	−0.604375	+	1.03969i
$489$	−2974.49	−	15936.2i	−0.275073	−	1.47374i
$490$	−3345.74	+	16151.9i	−0.308459	+	1.48912i
$491$	−8991.73			−0.826459			−0.413229	−	0.910627i	$-0.635599\pi$
$491$	−8991.73			−0.826459			−0.413229	+	0.910627i	$0.635599\pi$
$492$	−2158.25	+	2614.40i	−0.197767	+	0.239565i
$493$	−6264.00			−0.572244
$494$	7825.56	−	2839.53i	0.712730	−	0.258616i
$495$	−6264.36	−	16196.5i	−0.568812	−	1.47066i
$496$	10319.6	+	1861.66i	0.934200	+	0.168530i
$497$	−16488.9	−	4673.07i	−1.48818	−	0.421762i
$498$	−19.8725	−	33.7153i	−0.00178817	−	0.00303377i
$499$		−	10529.3i		−	0.944599i	−0.881438	−	0.472300i	$-0.843424\pi$
$499$		−	10529.3i		−	0.944599i	0.881438	−	0.472300i	$-0.156576\pi$
$500$	−3408.67	−	4078.62i	−0.304881	−	0.364803i
$501$	−18505.0	+	3453.95i	−1.65019	+	0.308006i
$502$	−5270.48	−	14525.1i	−0.468592	−	1.29141i
$503$	1886.42			0.167220			0.0836098	−	0.996499i	$-0.473355\pi$
$503$	1886.42			0.167220			0.0836098	+	0.996499i	$0.473355\pi$
$504$	−10267.3	−	4754.55i	−0.907428	−	0.420207i
$505$	17126.0			1.50910
$506$	−1747.76	−	4816.72i	−0.153552	−	0.423181i
$507$	19777.3	−	3691.41i	1.73242	−	0.323356i
$508$	−350.143	+	292.629i	−0.0305809	+	0.0255577i
$509$		−	10860.9i		−	0.945781i	−0.881121	−	0.472891i	$-0.843211\pi$
$509$		−	10860.9i		−	0.945781i	0.881121	−	0.472891i	$-0.156789\pi$
$510$	−4396.29	−	7458.66i	−0.381708	−	0.647598i
$511$	−10529.2	−	2984.05i	−0.911513	−	0.258330i
$512$	11584.8	+	102.914i	0.999961	+	0.00888324i
$513$	4508.90	−	2786.68i	0.388057	−	0.239834i
$514$	−18154.7	+	6587.50i	−1.55792	+	0.565296i
$515$	4663.97			0.399067
$516$	7735.20	+	6385.60i	0.659929	+	0.544788i
$517$	−13476.3			−1.14640
$518$	8342.79	−	600.990i	0.707647	−	0.0509768i
$519$	1812.87	+	9712.71i	0.153326	+	0.821466i
$520$	25910.9	+	15062.1i	2.18513	+	1.27023i
$521$	−6930.38			−0.582774			−0.291387	−	0.956605i	$-0.594117\pi$
$521$	−6930.38			−0.582774			−0.291387	+	0.956605i	$0.594117\pi$
$522$	10405.9	−	9073.98i	0.872516	−	0.760838i
$523$	9140.75			0.764239			0.382119	−	0.924113i	$-0.375194\pi$
$523$	9140.75			0.764239			0.382119	+	0.924113i	$0.375194\pi$
$524$	11516.3	+	13779.7i	0.960099	+	1.14880i
$525$	1444.97	−	15723.7i	0.120121	−	1.30712i
$526$	641.762	+	1768.66i	0.0531980	+	0.146610i
$527$			5676.93i			0.469243i
$528$	76.0459	+	12579.8i	0.00626794	+	1.03687i
$529$	9873.55			0.811503
$530$	−9607.10	−	26476.6i	−0.787370	−	2.16994i
$531$	1681.00	+	4346.21i	0.137381	+	0.355197i
$532$	2282.49	+	5111.25i	0.186012	+	0.416543i
$533$	6353.33			0.516310
$534$	−7597.20	+	4477.95i	−0.615661	+	0.362884i
$535$			19247.7i			1.55542i
$536$	−14966.9	−	8700.35i	−1.20611	−	0.701116i
$537$	6789.31	−	1267.22i	0.545587	−	0.101834i
$538$	4686.76	+	12916.4i	0.375577	+	1.03507i
$539$	11045.8	+	6807.76i	0.882705	+	0.544027i
$540$	18107.8	+	6022.04i	1.44303	+	0.479903i
$541$		−	1327.06i		−	0.105461i	−0.998609	−	0.0527307i	$-0.983207\pi$
$541$		−	1327.06i		−	0.105461i	0.998609	−	0.0527307i	$-0.0167925\pi$
$542$	−1037.83	−	2860.19i	−0.0822481	−	0.226671i
$543$	11987.0	−	2237.36i	0.947348	−	0.176822i
$544$	1058.61	+	6181.95i	0.0834333	+	0.487222i
$545$	36866.4			2.89759
$546$	5378.25	+	20511.1i	0.421553	+	1.60768i
$547$		−	6943.34i		−	0.542735i	−0.962476	−	0.271367i	$-0.912524\pi$
$547$		−	6943.34i		−	0.542735i	0.962476	−	0.271367i	$-0.0874758\pi$
$548$	−6383.78	−	7638.47i	−0.497631	−	0.595437i
$549$	14427.9	−	5580.33i	1.12162	−	0.433811i
$550$	−16502.9	+	5988.12i	−1.27943	+	0.464244i
$551$	−6830.47			−0.528108
$552$	5304.53	+	1888.55i	0.409014	+	0.145620i
$553$	143.536	−	506.465i	0.0110376	−	0.0389459i
$554$	−5904.29	−	16271.9i	−0.452797	−	1.24788i
$555$	−13867.5	+	2588.36i	−1.06062	+	0.197963i
$556$	3083.04	−	2576.62i	0.235162	−	0.196534i
$557$	12038.4			0.915770			0.457885	−	0.889012i	$-0.348607\pi$
$557$	12038.4			0.915770			0.457885	+	0.889012i	$0.348607\pi$
$558$	−8223.56	−	9430.64i	−0.623891	−	0.715467i
$559$		−	18797.5i		−	1.42227i
$560$	−8850.00	+	18105.6i	−0.667823	+	1.36625i
$561$	−6694.88	+	1249.59i	−0.503847	+	0.0940427i
$562$	560.035	+	1543.42i	0.0420349	+	0.115846i
$563$			10849.1i			0.812139i	0.913842	+	0.406070i	$0.133101\pi$
$563$			10849.1i			0.812139i	−0.913842	+	0.406070i	$0.866899\pi$
$564$	9427.69	−	11420.2i	0.703861	−	0.852622i
$565$	726.222			0.0540750
$566$	−15881.6	+	5762.70i	−1.17943	+	0.427958i
$567$	6017.30	+	12086.2i	0.445684	+	0.895190i
$568$	−18102.6	−	10523.1i	−1.33727	−	0.777359i
$569$			10335.0i			0.761450i	0.924688	+	0.380725i	$0.124326\pi$
$569$			10335.0i			0.761450i	−0.924688	+	0.380725i	$0.875674\pi$
$570$	−4793.86	−	8133.16i	−0.352268	−	0.597650i
$571$		−	2025.81i		−	0.148472i	−0.997241	−	0.0742360i	$-0.976348\pi$
$571$		−	2025.81i		−	0.148472i	0.997241	−	0.0742360i	$-0.0236518\pi$
$572$	18089.9	−	15118.5i	1.32234	−	1.10513i
$573$	2030.41	+	10878.2i	0.148030	+	0.793094i
$574$	306.953	+	4261.04i	0.0223205	+	0.309847i
$575$			7857.73i			0.569896i
$576$	−10713.7	−	8736.09i	−0.775009	−	0.631951i
$577$			3778.32i			0.272606i	0.990667	+	0.136303i	$0.0435220\pi$
$577$			3778.32i			0.272606i	−0.990667	+	0.136303i	$0.956478\pi$
$578$	9870.88	−	3581.68i	0.710337	−	0.257748i
$579$	4487.33	−	837.558i	0.322085	−	0.0601170i
$580$	−15769.5	−	18868.8i	−1.12895	−	1.35084i
$581$	−47.4484	−	13.4473i	−0.00338811	−	0.000960217i
$582$	5250.78	+	8908.35i	0.373972	+	0.634473i
$583$	−22155.8			−1.57393
$584$	−11559.6	−	6719.67i	−0.819077	−	0.476134i
$585$	−12900.6	−	33354.4i	−0.911751	−	2.35733i
$586$	−504.021	−	1389.05i	−0.0355306	−	0.0979200i
$587$			1814.70i			0.127599i	0.997963	+	0.0637997i	$0.0203219\pi$
$587$			1814.70i			0.127599i	−0.997963	+	0.0637997i	$0.979678\pi$
$588$	−13496.5	+	4598.04i	−0.946575	+	0.322483i
$589$			6190.30i			0.433051i
$590$	7802.14	−	2831.03i	0.544422	−	0.197545i
$591$	17394.5	−	3246.67i	1.21068	−	0.225973i
$592$	10057.0	+	1814.29i	0.698211	+	0.125958i
$593$	−9793.33			−0.678185			−0.339093	−	0.940753i	$-0.610120\pi$
$593$	−9793.33			−0.678185			−0.339093	+	0.940753i	$0.610120\pi$
$594$	9311.52	−	11774.0i	0.643192	−	0.813288i
$595$	−10496.8	−	2974.87i	−0.723236	−	0.204971i
$596$	−16396.6	+	13703.3i	−1.12689	+	0.941792i
$597$	2482.37	+	13299.7i	0.170179	+	0.911757i
$598$	−3599.28	−	9919.39i	−0.246129	−	0.678317i
$599$			10824.1i			0.738332i	0.929363	+	0.369166i	$0.120357\pi$
$599$			10824.1i			0.738332i	−0.929363	+	0.369166i	$0.879643\pi$
$600$	6470.50	−	18174.2i	0.440262	−	1.23660i
$601$			16512.2i			1.12071i	0.828252	+	0.560355i	$0.189335\pi$
$601$			16512.2i			1.12071i	−0.828252	+	0.560355i	$0.810665\pi$
$602$	12607.1	−	908.178i	0.853533	−	0.0614860i
$603$	7451.78	+	19266.5i	0.503250	+	1.30115i
$604$	−9321.03	+	7789.97i	−0.627926	+	0.524783i
$605$			1700.30i			0.114260i
$606$	7517.07	+	12753.3i	0.503895	+	0.854897i
$607$			7537.39i			0.504009i	0.967726	+	0.252004i	$0.0810898\pi$
$607$			7537.39i			0.504009i	−0.967726	+	0.252004i	$0.918910\pi$
$608$	1154.35	+	6741.00i	0.0769982	+	0.449644i
$609$	1592.14	−	17325.2i	0.105939	−	1.15279i
$610$	−9398.03	−	25900.4i	−0.623796	−	1.71914i
$611$	−27752.6			−1.83756
$612$	3624.63	−	6547.63i	0.239407	−	0.432471i
$613$		−	10916.9i		−	0.719297i	−0.933088	−	0.359648i	$-0.882897\pi$
$613$		−	10916.9i		−	0.719297i	0.933088	−	0.359648i	$-0.117103\pi$
$614$	−21025.7	+	7629.25i	−1.38197	+	0.501452i
$615$	−1321.99	−	7082.74i	−0.0866792	−	0.464396i
$616$	11013.6	+	11402.1i	0.720376	+	0.745784i
$617$		−	27154.5i		−	1.77180i	−0.463881	−	0.885898i	$-0.653543\pi$
$617$		−	27154.5i		−	1.77180i	0.463881	−	0.885898i	$-0.346457\pi$
$618$	2047.15	+	3473.15i	0.133250	+	0.226069i
$619$	−12483.7			−0.810602			−0.405301	−	0.914183i	$-0.632833\pi$
$619$	−12483.7			−0.810602			−0.405301	+	0.914183i	$0.632833\pi$
$620$	−17100.4	+	14291.5i	−1.10769	+	0.925745i
$621$	−3532.29	−	5715.32i	−0.228254	−	0.369320i
$622$	−3879.89	+	1407.83i	−0.250112	+	0.0907537i
$623$	−3030.12	+	10691.7i	−0.194863	+	0.687569i
$624$	156.606	+	25906.4i	0.0100469	+	1.66200i
$625$	−9212.97			−0.589630
$626$	5246.25	+	14458.3i	0.334956	+	0.923117i
$627$	−7300.31	+	1362.60i	−0.464986	+	0.0867894i
$628$	8052.06	−	6729.44i	0.511643	−	0.427601i
$629$			5532.48i			0.350707i
$630$	21746.8	−	10263.6i	1.37526	−	0.649068i
$631$	5011.50			0.316172			0.158086	−	0.987425i	$-0.449468\pi$
$631$	5011.50			0.316172			0.158086	+	0.987425i	$0.449468\pi$
$632$	323.224	−	556.031i	0.0203436	−	0.0349964i
$633$	−941.212	−	5042.68i	−0.0590992	−	0.316632i
$634$	21248.5	−	7710.09i	1.33105	−	0.482976i
$635$		−	969.822i		−	0.0606082i
$636$	15499.7	−	18775.5i	0.966354	−	1.17059i
$637$	22747.4	+	14019.7i	1.41489	+	0.872023i
$638$	−18183.7	+	6598.01i	−1.12837	+	0.409432i
$639$	9012.96	+	23303.0i	0.557977	+	1.44265i
$640$	−15956.7	+	18751.7i	−0.985534	+	1.15817i
$641$			20433.1i			1.25906i	0.776975	+	0.629531i	$0.216753\pi$
$641$			20433.1i			1.25906i	−0.776975	+	0.629531i	$0.783247\pi$
$642$	−14333.3	+	8448.35i	−0.881137	+	0.519361i
$643$	−7784.75			−0.477450			−0.238725	−	0.971087i	$-0.576730\pi$
$643$	−7784.75			−0.477450			−0.238725	+	0.971087i	$0.576730\pi$
$644$	6478.82	−	2893.20i	0.396431	−	0.177031i
$645$	−20955.6	+	3911.36i	−1.27927	+	0.238775i
$646$	−3480.47	+	1262.90i	−0.211977	+	0.0769166i
$647$	13288.6			0.807463			0.403732	−	0.914877i	$-0.367713\pi$
$647$	13288.6			0.807463			0.403732	+	0.914877i	$0.367713\pi$
$648$	3463.54	+	16127.7i	0.209970	+	0.977708i
$649$		−	6528.89i		−	0.394887i
$650$	−33985.5	+	12331.7i	−2.05080	+	0.744138i
$651$	−15701.4	−	1442.92i	−0.945297	−	0.0868702i
$652$	−16005.7	−	19151.4i	−0.961395	−	1.15035i
$653$	−6596.26			−0.395301			−0.197651	−	0.980273i	$-0.563331\pi$
$653$	−6596.26			−0.395301			−0.197651	+	0.980273i	$0.563331\pi$
$654$	16181.7	+	27453.6i	0.967515	+	1.64147i
$655$	−38167.0			−2.27680
$656$	−926.641	+	5136.57i	−0.0551513	+	0.305715i
$657$	5755.35	+	14880.4i	0.341762	+	0.883623i
$658$	−1340.83	−	18613.1i	−0.0794393	−	1.10276i
$659$	8372.03			0.494883			0.247442	−	0.968903i	$-0.420410\pi$
$659$	8372.03			0.494883			0.247442	+	0.968903i	$0.420410\pi$
$660$	−20618.3	−	17020.9i	−1.21601	−	1.00385i
$661$	6191.40			0.364323			0.182162	−	0.983269i	$-0.441691\pi$
$661$	6191.40			0.364323			0.182162	+	0.983269i	$0.441691\pi$
$662$	−5704.77	−	15722.0i	−0.334928	−	0.923040i
$663$	−13787.2	+	2573.37i	−0.807618	+	0.150741i
$664$	−52.0921	−	30.2814i	−0.00304452	−	0.00176980i
$665$	−11446.0	−	3243.89i	−0.667455	−	0.189162i
$666$	−8014.31	−	9190.68i	−0.466289	−	0.534732i
$667$			8658.04i			0.502610i
$668$	−22238.5	+	18585.6i	−1.28807	+	1.07650i
$669$	−1363.64	−	7305.90i	−0.0788063	−	0.422216i
$670$	34586.5	−	12549.8i	1.99432	−	0.723644i
$671$	−21673.7			−1.24695
$672$	−17367.3	+	1356.67i	−0.996963	+	0.0778789i
$673$	1317.91			0.0754855			0.0377428	−	0.999287i	$-0.487983\pi$
$673$	1317.91			0.0754855			0.0377428	+	0.999287i	$0.487983\pi$
$674$	29104.7	−	10560.7i	1.66331	−	0.603537i
$675$	−19581.6	+	12102.2i	−1.11659	+	0.690096i
$676$	23767.4	−	19863.4i	1.35227	−	1.13014i
$677$		−	11076.8i		−	0.628826i	−0.949286	−	0.314413i	$-0.898192\pi$
$677$		−	11076.8i		−	0.628826i	0.949286	−	0.314413i	$-0.101808\pi$
$678$	318.759	+	540.800i	0.0180559	+	0.0306332i
$679$	12537.0	+	3553.08i	0.708578	+	0.200817i
$680$	−11524.1	−	6698.99i	−0.649893	−	0.377786i
$681$	4792.08	+	25674.2i	0.269652	+	1.44470i
$682$	5979.63	+	16479.5i	0.335736	+	0.925268i
$683$	−31967.1			−1.79090			−0.895451	−	0.445161i	$-0.853147\pi$
$683$	−31967.1			−1.79090			−0.895451	+	0.445161i	$0.853147\pi$
$684$	3952.41	−	7139.74i	0.220942	−	0.399115i
$685$	21156.9			1.18009
$686$	−8303.67	+	15933.5i	−0.462151	+	0.886801i
$687$	−22804.8	+	4256.50i	−1.26646	+	0.236383i
$688$	15197.5	+	2741.64i	0.842151	+	0.151925i
$689$	−45626.9			−2.52285
$690$	−10309.3	+	6076.51i	−0.568794	+	0.335259i
$691$	4700.10			0.258756			0.129378	−	0.991595i	$-0.458702\pi$
$691$	4700.10			0.258756			0.129378	+	0.991595i	$0.458702\pi$
$692$	9755.03	+	11672.3i	0.535882	+	0.641206i
$693$	−1754.52	−	18834.5i	−0.0961740	−	1.03242i
$694$	−4353.02	+	1579.50i	−0.238095	+	0.0863936i
$695$			8539.35i			0.466066i
$696$	7129.52	−	20025.2i	0.388281	−	1.09059i
$697$	−2825.69			−0.153559
$698$	11944.9	−	4334.25i	0.647739	−	0.235034i
$699$	2032.01	+	10886.8i	0.109954	+	0.589091i
$700$	−9912.58	−	22197.5i	−0.535229	−	1.19855i
$701$	−22855.2			−1.23143			−0.615714	−	0.787970i	$-0.711132\pi$
$701$	−22855.2			−1.23143			−0.615714	+	0.787970i	$0.711132\pi$
$702$	19175.8	−	24247.0i	1.03098	−	1.30362i
$703$			6032.79i			0.323657i
$704$	9584.62	+	16830.5i	0.513116	+	0.901025i
$705$	5774.72	+	30938.9i	0.308494	+	1.65280i
$706$	−3648.47	+	1323.86i	−0.194493	+	0.0705724i
$707$	17948.1	+	5086.62i	0.954748	+	0.270583i
$708$	5532.78	+	4567.45i	0.293693	+	0.242451i
$709$			20814.1i			1.10252i	0.834333	+	0.551261i	$0.185853\pi$
$709$			20814.1i			1.10252i	−0.834333	+	0.551261i	$0.814147\pi$
$710$	41832.6	−	15179.1i	2.21119	−	0.802338i
$711$	−715.764	+	276.838i	−0.0377542	+	0.0146023i
$712$	−6823.43	+	11738.1i	−0.359156	+	0.617843i
$713$	7846.60			0.412142
$714$	−2392.02	−	9122.45i	−0.125377	−	0.478150i
$715$			50105.2i			2.62074i
$716$	8159.09	−	6818.89i	0.425865	−	0.355913i
$717$	−6448.55	−	34549.0i	−0.335880	−	1.79952i
$718$	4937.70	+	13608.0i	0.256648	+	0.707306i
$719$	5088.93			0.263957			0.131979	−	0.991253i	$-0.457867\pi$
$719$	5088.93			0.263957			0.131979	+	0.991253i	$0.457867\pi$
$720$	28848.1	−	5565.15i	1.49320	−	0.288057i
$721$	4887.86	+	1385.26i	0.252474	+	0.0715530i
$722$	14441.5	−	5240.15i	0.744402	−	0.270108i
$723$	−2594.92	−	13902.7i	−0.133480	−	0.715139i
$724$	14405.4	−	12039.2i	0.739465	−	0.618002i
$725$	29663.9			1.51957
$726$	−1266.17	+	746.310i	−0.0647274	+	0.0381517i
$727$			1716.37i			0.0875609i	0.999041	+	0.0437804i	$0.0139402\pi$
$727$			1716.37i			0.0875609i	−0.999041	+	0.0437804i	$0.986060\pi$
$728$	22681.1	+	23481.0i	1.15469	+	1.19542i
$729$	8802.37	−	17605.1i	0.447207	−	0.894431i
$730$	26712.7	−	9692.79i	1.35436	−	0.491433i
$731$			8360.34i			0.423007i
$732$	15162.4	−	18366.9i	0.765596	−	0.927405i
$733$	2487.51			0.125346			0.0626728	−	0.998034i	$-0.480038\pi$
$733$	2487.51			0.125346			0.0626728	+	0.998034i	$0.480038\pi$
$734$	−5934.91	−	16356.3i	−0.298449	−	0.822508i
$735$	10896.0	−	28276.2i	0.546809	−	1.41902i
$736$	8544.63	−	1463.21i	0.427934	−	0.0732806i
$737$		−	28942.3i		−	1.44654i
$738$	4694.09	−	4093.27i	0.234135	−	0.204167i
$739$		−	16167.7i		−	0.804786i	−0.915467	−	0.402393i	$-0.868179\pi$
$739$		−	16167.7i		−	0.804786i	0.915467	−	0.402393i	$-0.131821\pi$
$740$	−16665.3	+	13927.9i	−0.827877	+	0.691891i
$741$	−15034.0	+	2806.09i	−0.745328	+	0.139115i
$742$	−2204.40	−	30601.0i	−0.109065	−	1.51401i
$743$		−	6261.24i		−	0.309156i	−0.987981	−	0.154578i	$-0.950598\pi$
$743$		−	6261.24i		−	0.309156i	0.987981	−	0.154578i	$-0.0494017\pi$
$744$	−18148.4	−	6461.33i	−0.894292	−	0.318392i
$745$		−	45415.0i		−	2.23339i
$746$	12401.6	+	34178.2i	0.608654	+	1.67741i
$747$	25.9358	+	67.0568i	0.00127033	+	0.00328444i
$748$	−8045.61	+	6724.05i	−0.393284	+	0.328684i
$749$	−5716.80	+	20171.6i	−0.278888	+	0.984053i
$750$	4958.53	+	8412.54i	0.241413	+	0.409576i
$751$	26131.4			1.26971			0.634853	−	0.772633i	$-0.281061\pi$
$751$	26131.4			1.26971			0.634853	+	0.772633i	$0.281061\pi$
$752$	4047.76	−	22437.6i	0.196285	−	1.08805i
$753$	5208.41	+	27904.8i	0.252065	+	1.35047i
$754$	−37446.9	+	13587.7i	−1.80867	+	0.656280i
$755$		−	25817.3i		−	1.24448i
$756$	17188.4	+	11689.3i	0.826898	+	0.562351i
$757$			2301.88i			0.110519i	0.998472	+	0.0552596i	$0.0175987\pi$
$757$			2301.88i			0.110519i	−0.998472	+	0.0552596i	$0.982401\pi$
$758$	−2204.26	−	6074.81i	−0.105623	−	0.291091i
$759$	1727.18	+	9253.60i	0.0825989	+	0.442535i
$760$	−12566.2	−	7304.80i	−0.599768	−	0.348648i
$761$	22624.8			1.07772			0.538862	−	0.842394i	$-0.318854\pi$
$761$	22624.8			1.07772			0.538862	+	0.842394i	$0.318854\pi$
$762$	722.204	−	425.682i	0.0343342	−	0.0202373i
$763$	38636.1	+	10949.8i	1.83319	+	0.519540i
$764$	10925.6	+	13072.9i	0.517374	+	0.619060i
$765$	5737.63	+	14834.6i	0.271169	+	0.701107i
$766$	−8141.01	+	2953.99i	−0.384003	+	0.139337i
$767$		−	13445.4i		−	0.632965i
$768$	−20967.8	−	3651.87i	−0.985170	−	0.171583i
$769$			12312.9i			0.577393i	0.957421	+	0.288697i	$0.0932219\pi$
$769$			12312.9i			0.577393i	−0.957421	+	0.288697i	$0.906778\pi$
$770$	−33604.4	+	2420.76i	−1.57275	+	0.113297i
$771$	34877.8	−	6509.92i	1.62917	−	0.304084i
$772$	5392.68	−	4506.88i	0.251408	−	0.210112i
$773$			18738.9i			0.871916i	0.899967	+	0.435958i	$0.143590\pi$
$773$			18738.9i			0.871916i	−0.899967	+	0.435958i	$0.856410\pi$
$774$	−12110.7	−	13888.4i	−0.562417	−	0.644970i
$775$		−	26883.7i		−	1.24606i
$776$	13763.9	+	8001.04i	0.636722	+	0.370130i
$777$	−15301.9	−	1406.21i	−0.706504	−	0.0649258i
$778$	−6248.98	+	2267.46i	−0.287965	+	0.104489i
$779$	−3081.22			−0.141715
$780$	−42460.6	−	35052.3i	−1.94915	−	1.60907i
$781$		−	35005.8i		−	1.60385i
$782$	1600.80	+	4411.72i	0.0732029	+	0.201743i
$783$	−21576.0	+	13334.8i	−0.984756	+	0.608618i
$784$	−14652.4	+	16346.2i	−0.667475	+	0.744632i
$785$			22302.5i			1.01403i
$786$	−16752.6	−	28422.0i	−0.760234	−	1.28980i
$787$	7115.83			0.322302			0.161151	−	0.986930i	$-0.448479\pi$
$787$	7115.83			0.322302			0.161151	+	0.986930i	$0.448479\pi$
$788$	20903.9	−	17470.3i	0.945015	−	0.789788i
$789$	−634.204	−	3397.84i	−0.0286163	−	0.153316i
$790$	466.234	+	1284.91i	0.0209973	+	0.0578672i
$791$	761.083	+	215.697i	0.0342111	+	0.00969570i
$792$	3625.13	−	22824.9i	0.162643	−	1.02405i
$793$	−44634.0			−1.99874
$794$	−3559.93	+	1291.73i	−0.159115	+	0.0577353i
$795$	9493.96	+	50865.2i	0.423542	+	2.26919i
$796$	13357.6	+	15982.9i	0.594784	+	0.711684i
$797$			12278.2i			0.545693i	0.962058	+	0.272846i	$0.0879650\pi$
$797$			12278.2i			0.545693i	−0.962058	+	0.272846i	$0.912035\pi$
$798$	−2608.33	−	9947.41i	−0.115707	−	0.441271i
$799$	12343.2			0.546521
$800$	−5013.19	−	29275.3i	−0.221554	−	1.29380i
$801$	15110.2	−	5844.21i	0.666531	−	0.257796i
$802$	7456.06	+	20548.4i	0.328282	+	0.904726i
$803$		−	22353.4i		−	0.982360i
$804$	24526.6	+	20247.3i	1.07585	+	0.888143i
$805$	−4111.83	+	14508.5i	−0.180029	+	0.635228i
$806$	12314.2	+	33937.3i	0.538152	+	1.48311i
$807$	−4631.57	−	24814.3i	−0.202031	−	1.08241i
$808$	19704.6	+	11454.4i	0.857927	+	0.498718i
$809$		−	9226.15i		−	0.400957i	−0.979698	−	0.200479i	$-0.935750\pi$
$809$		−	9226.15i		−	0.400957i	0.979698	−	0.200479i	$-0.0642497\pi$
$810$	−31020.8	−	16332.1i	−1.34563	−	0.708458i
$811$	36172.6			1.56621			0.783103	−	0.621892i	$-0.213636\pi$
$811$	36172.6			1.56621			0.783103	+	0.621892i	$0.213636\pi$
$812$	−10922.2	−	24458.3i	−0.472036	−	1.05704i
$813$	1025.60	+	5494.82i	0.0442430	+	0.237038i
$814$	5827.48	+	16060.2i	0.250925	+	0.691534i
$815$	53045.4			2.27988
$816$	−69.6517	−	11522.1i	−0.00298811	−	0.494305i
$817$			9116.38i			0.390381i
$818$	−12826.3	−	35348.6i	−0.548243	−	1.51092i
$819$	−3613.19	−	38787.2i	−0.154158	−	1.65486i
$820$	−7113.60	−	8511.72i	−0.302948	−	0.362491i
$821$	7181.84			0.305296			0.152648	−	0.988281i	$-0.451220\pi$
$821$	7181.84			0.305296			0.152648	+	0.988281i	$0.451220\pi$
$822$	9286.37	+	15755.1i	0.394038	+	0.668517i
$823$	−2266.38			−0.0959916			−0.0479958	−	0.998848i	$-0.515283\pi$
$823$	−2266.38			−0.0959916			−0.0479958	+	0.998848i	$0.515283\pi$
$824$	5366.22	+	3119.41i	0.226870	+	0.131881i
$825$	31704.4	−	5917.60i	1.33794	−	0.249726i
$826$	9017.52	−	649.596i	0.379854	−	0.0273636i
$827$	5411.98			0.227561			0.113781	−	0.993506i	$-0.463704\pi$
$827$	5411.98			0.227561			0.113781	+	0.993506i	$0.463704\pi$
$828$	−9050.07	−	5009.92i	−0.379845	−	0.210274i
$829$	−27630.7			−1.15760			−0.578802	−	0.815468i	$-0.696480\pi$
$829$	−27630.7			−1.15760			−0.578802	+	0.815468i	$0.696480\pi$
$830$	120.378	−	43.6794i	0.00503418	−	0.00182667i
$831$	5834.76	+	31260.5i	0.243569	+	1.30495i
$832$	19738.2	+	34660.0i	0.822476	+	1.44426i
$833$	−10117.1	−	6235.34i	−0.420811	−	0.259354i
$834$	−6359.05	+	3748.16i	−0.264024	+	0.155621i
$835$		−	61595.9i		−	2.55283i
$836$	−8773.19	+	7332.11i	−0.362951	+	0.303333i
$837$	12085.1	+	19553.9i	0.499069	+	0.807504i
$838$	8166.89	+	22507.4i	0.336659	+	0.927812i
$839$	−38177.4			−1.57095			−0.785476	−	0.618892i	$-0.787582\pi$
$839$	−38177.4			−1.57095			−0.785476	+	0.618892i	$0.787582\pi$
$840$	21457.4	−	30170.9i	0.881370	−	1.23928i
$841$	8296.14			0.340159
$842$	−1101.22	−	3034.90i	−0.0450720	−	0.124216i
$843$	−553.439	−	2965.13i	−0.0226115	−	0.121144i
$844$	−5064.64	−	6060.06i	−0.206555	−	0.247152i
$845$			65830.7i			2.68005i
$846$	−20504.8	+	17880.2i	−0.833296	+	0.726638i
$847$	−505.010	+	1781.92i	−0.0204868	+	0.0722875i
$848$	6654.74	−	36888.6i	0.269487	−	1.49382i
$849$	30510.9	−	5694.84i	1.23337	−	0.230208i
$850$	15115.3	−	5484.62i	0.609941	−	0.221319i
$851$	7646.94			0.308030
$852$	29665.0	+	24489.2i	1.19285	+	0.984725i
$853$	−5549.77			−0.222767			−0.111384	−	0.993777i	$-0.535528\pi$
$853$	−5549.77			−0.222767			−0.111384	+	0.993777i	$0.535528\pi$
$854$	−2156.43	−	29935.0i	−0.0864070	−	1.19948i
$855$	6256.50	+	16176.1i	0.250255	+	0.647032i
$856$	−12873.5	+	22145.8i	−0.514025	+	0.884261i
$857$	−22763.4			−0.907332			−0.453666	−	0.891172i	$-0.649884\pi$
$857$	−22763.4			−0.907332			−0.453666	+	0.891172i	$0.649884\pi$
$858$	−37312.1	+	21992.6i	−1.48463	+	0.875074i
$859$	−672.946			−0.0267295			−0.0133647	−	0.999911i	$-0.504254\pi$
$859$	−672.946			−0.0267295			−0.0133647	+	0.999911i	$0.504254\pi$
$860$	−25183.6	+	21046.9i	−0.998550	+	0.834529i
$861$	718.212	−	7815.38i	0.0284281	−	0.309347i
$862$	−6389.86	−	17610.0i	−0.252482	−	0.695824i
$863$		−	38773.2i		−	1.52938i	−0.644397	−	0.764691i	$-0.722892\pi$
$863$		−	38773.2i		−	1.52938i	0.644397	−	0.764691i	$-0.277108\pi$
$864$	16806.5	+	19039.8i	0.661769	+	0.749708i
$865$	−32329.8			−1.27081
$866$	−146.574	−	403.948i	−0.00575147	−	0.0158507i
$867$	−18963.4	+	3539.50i	−0.742825	+	0.138648i
$868$	−22166.1	+	9898.53i	−0.866780	+	0.387072i
$869$	1075.22			0.0419729
$870$	22939.6	+	38918.8i	0.893936	+	1.51663i
$871$		−	59602.7i		−	2.31867i
$872$	42417.3	+	24657.4i	1.64728	+	0.957575i
$873$	−6852.83	−	17717.9i	−0.265674	−	0.686898i
$874$	1745.57	+	4810.68i	0.0675569	+	0.186183i
$875$	11839.2	+	3355.32i	0.457415	+	0.129635i
$876$	18943.0	+	15637.9i	0.730620	+	0.603146i
$877$			5911.60i			0.227617i	0.993503	+	0.113809i	$0.0363051\pi$
$877$			5911.60i			0.227617i	−0.993503	+	0.113809i	$0.963695\pi$
$878$	−9482.03	−	26131.9i	−0.364468	−	1.00445i
$879$	498.085	+	2668.56i	0.0191126	+	0.102399i
$880$	−40509.3	−	7307.90i	−1.55178	−	0.279942i
$881$	−1628.16			−0.0622635			−0.0311317	−	0.999515i	$-0.509911\pi$
$881$	−1628.16			−0.0622635			−0.0311317	+	0.999515i	$0.509911\pi$
$882$	25839.2	−	4297.24i	0.986451	−	0.164054i
$883$		−	13348.7i		−	0.508743i	−0.967107	−	0.254371i	$-0.918131\pi$
$883$		−	13348.7i		−	0.508743i	0.967107	−	0.254371i	$-0.0818686\pi$
$884$	−16568.8	+	13847.3i	−0.630397	+	0.526848i
$885$	−14989.0	+	2797.69i	−0.569322	+	0.106264i
$886$	−5869.50	+	2129.76i	−0.222562	+	0.0807571i
$887$	−35230.3			−1.33362			−0.666808	−	0.745230i	$-0.732340\pi$
$887$	−35230.3			−1.33362			−0.666808	+	0.745230i	$0.732340\pi$
$888$	−17686.6	−	6296.92i	−0.668384	−	0.237963i
$889$	288.049	−	1016.38i	0.0108671	−	0.0383444i
$890$	−9842.45	−	27125.2i	−0.370696	−	1.02162i
$891$	−20400.0	+	18556.2i	−0.767032	+	0.697708i
$892$	−7337.73	−	8779.90i	−0.275432	−	0.329566i
$893$	13459.4			0.504369
$894$	33819.4	−	19933.9i	1.26520	−	0.745738i
$895$			22598.9i			0.844022i
$896$	−22292.1	+	14912.6i	−0.831169	+	0.556020i
$897$	3556.89	+	19056.5i	0.132398	+	0.709341i
$898$	7679.47	+	21164.1i	0.285375	+	0.786477i
$899$		−	29621.8i		−	1.09894i
$900$	−17164.8	+	31007.0i	−0.635735	+	1.14841i
$901$	20292.9			0.750337
$902$	−8202.65	+	2976.36i	−0.302792	+	0.109869i
$903$	−23123.3	−	2124.97i	−0.852154	−	0.0783107i
$904$	835.568	+	485.720i	0.0307418	+	0.0178704i
$905$			39899.9i			1.46554i
$906$	19225.5	−	11331.9i	0.704994	−	0.415538i
$907$			41269.7i			1.51085i	0.655237	+	0.755423i	$0.272569\pi$
$907$			41269.7i			1.51085i	−0.655237	+	0.755423i	$0.727431\pi$
$908$	25786.1	+	30854.2i	0.942447	+	1.12768i
$909$	−9810.58	−	25365.2i	−0.357972	−	0.925535i
$910$	−69203.8	+	4985.24i	−2.52097	+	0.181603i
$911$		−	11899.0i		−	0.432747i	−0.976311	−	0.216373i	$-0.930577\pi$
$911$		−	11899.0i		−	0.432747i	0.976311	−	0.216373i	$-0.0694228\pi$
$912$	−75.9504	−	12564.0i	−0.00275764	−	0.456181i
$913$		−	100.733i		−	0.00365145i
$914$	−9636.66	+	3496.69i	−0.348744	+	0.126543i
$915$	9287.36	+	49758.3i	0.335552	+	1.79777i
$916$	−27405.8	+	22904.1i	−0.988550	+	0.826172i
$917$	−39999.1	−	11336.1i	−1.44044	−	0.408233i
$918$	−8528.58	+	10784.0i	−0.306629	+	0.387718i
$919$	−19268.9			−0.691647			−0.345823	−	0.938300i	$-0.612400\pi$
$919$	−19268.9			−0.691647			−0.345823	+	0.938300i	$0.612400\pi$
$920$	−9259.29	+	15928.4i	−0.331815	+	0.570810i
$921$	40393.4	−	7539.40i	1.44518	−	0.269741i
$922$	−5677.87	−	15647.9i	−0.202810	−	0.558931i
$923$		−	72089.7i		−	2.57081i
$924$	−16552.6	−	23961.9i	−0.589331	−	0.853126i
$925$		−	26199.7i		−	0.931287i
$926$	−36841.0	+	13367.9i	−1.30742	+	0.474401i
$927$	−2671.75	−	6907.80i	−0.0946621	−	0.244748i
$928$	−5523.78	−	32257.0i	−0.195395	−	1.14104i
$929$	22796.3			0.805083			0.402542	−	0.915402i	$-0.368127\pi$
$929$	22796.3			0.805083			0.402542	+	0.915402i	$0.368127\pi$
$930$	35271.3	−	20789.6i	1.24365	−	0.733031i
$931$	−11032.0	−	6799.21i	−0.388355	−	0.239350i
$932$	10934.2	+	13083.2i	0.384293	+	0.459823i
$933$	7453.81	−	1391.25i	0.261551	−	0.0488183i
$934$	11884.7	+	32753.4i	0.416358	+	1.14746i
$935$		−	22284.6i		−	0.779449i
$936$	7465.47	−	47004.9i	0.260701	−	1.64146i
$937$		−	34878.2i		−	1.21603i	−0.793925	−	0.608016i	$-0.791966\pi$
$937$		−	34878.2i		−	1.21603i	0.793925	−	0.608016i	$-0.208034\pi$
$938$	39974.2	−	2879.63i	1.39148	−	0.100238i
$939$	−5184.46	−	27776.5i	−0.180180	−	0.965337i
$940$	31073.7	+	37181.0i	1.07820	+	1.29012i
$941$		−	34823.7i		−	1.20640i	−0.797591	−	0.603198i	$-0.793893\pi$
$941$		−	34823.7i		−	1.20640i	0.797591	−	0.603198i	$-0.206107\pi$
$942$	−16608.1	+	9789.19i	−0.574440	+	0.338587i
$943$			3905.64i			0.134873i
$944$	10870.4	+	1961.02i	0.374789	+	0.0676122i
$945$	−42488.5	+	12098.8i	−1.46259	+	0.416480i
$946$	8806.12	+	24269.1i	0.302655	+	0.834099i
$947$	44753.6			1.53569			0.767844	−	0.640637i	$-0.221329\pi$
$947$	44753.6			1.53569			0.767844	+	0.640637i	$0.221329\pi$
$948$	−752.200	+	911.177i	−0.0257704	+	0.0312169i
$949$		−	46033.8i		−	1.57463i
$950$	16482.2	−	5980.60i	0.562897	−	0.204249i
$951$	−40821.4	+	7619.29i	−1.39193	+	0.259803i
$952$	−10087.6	−	10443.4i	−0.343424	−	0.355537i
$953$			27410.7i			0.931709i	0.884861	+	0.465854i	$0.154253\pi$
$953$			27410.7i			0.931709i	−0.884861	+	0.465854i	$0.845747\pi$
$954$	−33711.0	+	29396.1i	−1.14406	+	0.997625i
$955$	−36209.2			−1.22691
$956$	−34699.5	−	41519.5i	−1.17392	−	1.40464i
$957$	34933.4	−	6520.30i	1.17998	−	0.220242i
$958$	15111.1	−	5483.09i	0.509620	−	0.184917i
$959$	22172.5	+	6283.87i	0.746599	+	0.211592i
$960$	34532.2	−	29216.3i	1.16096	−	0.982243i
$961$	2945.36			0.0988674
$962$	12000.9	+	33073.8i	0.402209	+	1.10846i
$963$	28507.7	−	11026.0i	0.953943	−	0.368960i
$964$	−13963.2	−	16707.6i	−0.466520	−	0.558211i
$965$			14936.6i			0.498264i
$966$	−12609.0	+	3306.22i	−0.419965	+	0.110120i
$967$	19242.8			0.639923			0.319961	−	0.947431i	$-0.396330\pi$
$967$	19242.8			0.639923			0.319961	+	0.947431i	$0.396330\pi$
$968$	−1137.21	+	1956.31i	−0.0377598	+	0.0649569i
$969$	6686.48	−	1248.03i	0.221672	−	0.0413750i
$970$	−31806.6	+	11541.1i	−1.05283	+	0.382023i
$971$			9065.66i			0.299620i	0.988715	+	0.149810i	$0.0478661\pi$
$971$			9065.66i			0.299620i	−0.988715	+	0.149810i	$0.952134\pi$
$972$	−1453.78	−	30269.1i	−0.0479733	−	0.998849i
$973$	−2536.29	+	8949.27i	−0.0835661	+	0.294862i
$974$	−8648.48	+	3138.13i	−0.284512	+	0.103236i
$975$	65290.9	−	12186.5i	2.14460	−	0.400287i
$976$	6509.92	−	36085.9i	0.213501	−	1.18348i
$977$			59374.1i			1.94426i	0.234435	+	0.972132i	$0.424676\pi$
$977$			59374.1i			1.94426i	−0.234435	+	0.972132i	$0.575324\pi$
$978$	23283.1	+	39501.7i	0.761260	+	1.29154i
$979$	−22698.6			−0.741010
$980$	−6686.98	−	46172.7i	−0.217967	−	1.50503i
$981$	−21118.9	−	54602.7i	−0.687333	−	1.77710i
$982$	23907.3	−	8674.82i	0.776896	−	0.281899i
$983$	22834.0			0.740886			0.370443	−	0.928855i	$-0.379206\pi$
$983$	22834.0			0.740886			0.370443	+	0.928855i	$0.379206\pi$
$984$	3216.12	−	9033.36i	0.104193	−	0.292656i
$985$			57899.4i			1.87292i
$986$	16654.8	−	6043.23i	0.537927	−	0.195188i
$987$	−3137.30	+	34139.2i	−0.101177	+	1.10098i
$988$	−18067.2	+	15099.5i	−0.581775	+	0.486214i
$989$	11555.6			0.371533
$990$	32281.3	+	37019.7i	1.03633	+	1.18845i
$991$	33338.9			1.06866			0.534331	−	0.845275i	$-0.320563\pi$
$991$	33338.9			1.06866			0.534331	+	0.845275i	$0.320563\pi$
$992$	−29233.8	+	5006.08i	−0.935660	+	0.160225i
$993$	5637.59	+	30204.2i	0.180165	+	0.965257i
$994$	48349.0	−	3482.92i	1.54279	−	0.111138i
$995$	−44269.4			−1.41049
$996$	85.3641	+	70.4703i	0.00271573	+	0.00224190i
$997$	17170.3			0.545427			0.272713	−	0.962095i	$-0.412079\pi$
$997$	17170.3			0.545427			0.272713	+	0.962095i	$0.412079\pi$
$998$	10158.2	+	27995.3i	0.322196	+	0.887951i
$999$	11777.6	+	19056.3i	0.372999	+	0.603519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.8	yes	80
3.2	odd	2	inner	168.4.i.c.125.74	yes	80
4.3	odd	2		672.4.i.c.209.8		80
7.6	odd	2	inner	168.4.i.c.125.7	yes	80
8.3	odd	2		672.4.i.c.209.73		80
8.5	even	2	inner	168.4.i.c.125.75	yes	80
12.11	even	2		672.4.i.c.209.5		80
21.20	even	2	inner	168.4.i.c.125.73	yes	80
24.5	odd	2	inner	168.4.i.c.125.5	✓	80
24.11	even	2		672.4.i.c.209.76		80
28.27	even	2		672.4.i.c.209.74		80
56.13	odd	2	inner	168.4.i.c.125.76	yes	80
56.27	even	2		672.4.i.c.209.7		80
84.83	odd	2		672.4.i.c.209.75		80
168.83	odd	2		672.4.i.c.209.6		80
168.125	even	2	inner	168.4.i.c.125.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.5	✓	80	24.5	odd	2	inner
168.4.i.c.125.6	yes	80	168.125	even	2	inner
168.4.i.c.125.7	yes	80	7.6	odd	2	inner
168.4.i.c.125.8	yes	80	1.1	even	1	trivial
168.4.i.c.125.73	yes	80	21.20	even	2	inner
168.4.i.c.125.74	yes	80	3.2	odd	2	inner
168.4.i.c.125.75	yes	80	8.5	even	2	inner
168.4.i.c.125.76	yes	80	56.13	odd	2	inner
672.4.i.c.209.5		80	12.11	even	2
672.4.i.c.209.6		80	168.83	odd	2
672.4.i.c.209.7		80	56.27	even	2
672.4.i.c.209.8		80	4.3	odd	2
672.4.i.c.209.73		80	8.3	odd	2
672.4.i.c.209.74		80	28.27	even	2
672.4.i.c.209.75		80	84.83	odd	2
672.4.i.c.209.76		80	24.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	168.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65881 + 0.964755i) q^{2} +(5.10794 - 0.953394i) q^{3} +(6.13849 - 5.13019i) q^{4} +17.0023i q^{5} +(-12.6612 + 7.46280i) q^{6} +(-5.04990 + 17.8185i) q^{7} +(-11.3717 + 19.5623i) q^{8} +(25.1821 - 9.73975i) q^{9} +(-16.4031 - 45.2059i) q^{10} -37.8286 q^{11} +(26.4640 - 32.0571i) q^{12} -77.9029 q^{13} +(-3.76378 - 52.2478i) q^{14} +(16.2099 + 86.8468i) q^{15} +(11.3622 - 62.9833i) q^{16} +34.6479 q^{17} +(-57.5578 + 50.1907i) q^{18} +37.7811 q^{19} +(87.2252 + 104.369i) q^{20} +(-8.80655 + 95.8303i) q^{21} +(100.579 - 36.4954i) q^{22} -47.8900i q^{23} +(-39.4353 + 110.765i) q^{24} -164.079 q^{25} +(207.129 - 75.1572i) q^{26} +(119.343 - 73.7585i) q^{27} +(60.4135 + 135.286i) q^{28} -180.790 q^{29} +(-126.885 - 215.270i) q^{30} +163.846i q^{31} +(30.5535 + 178.422i) q^{32} +(-193.226 + 36.0656i) q^{33} +(-92.1220 + 33.4267i) q^{34} +(-302.956 - 85.8600i) q^{35} +(104.613 - 188.976i) q^{36} +159.677i q^{37} +(-100.453 + 36.4496i) q^{38} +(-397.923 + 74.2721i) q^{39} +(-332.605 - 193.345i) q^{40} -81.5544 q^{41} +(-69.0379 - 263.290i) q^{42} +241.294i q^{43} +(-232.211 + 194.068i) q^{44} +(165.598 + 428.154i) q^{45} +(46.2021 + 127.330i) q^{46} +356.246 q^{47} +(-2.01027 - 332.548i) q^{48} +(-291.997 - 179.963i) q^{49} +(436.254 - 158.296i) q^{50} +(176.979 - 33.0331i) q^{51} +(-478.207 + 399.657i) q^{52} +585.689 q^{53} +(-246.150 + 311.246i) q^{54} -643.174i q^{55} +(-291.145 - 301.414i) q^{56} +(192.984 - 36.0203i) q^{57} +(480.686 - 174.418i) q^{58} +172.591i q^{59} +(545.045 + 449.949i) q^{60} +572.943 q^{61} +(-158.072 - 435.636i) q^{62} +(46.3807 + 497.891i) q^{63} +(-253.370 - 444.913i) q^{64} -1324.53i q^{65} +(478.957 - 282.307i) q^{66} +765.089i q^{67} +(212.686 - 177.750i) q^{68} +(-45.6580 - 244.619i) q^{69} +(888.334 - 63.9930i) q^{70} +925.379i q^{71} +(-95.8304 + 603.378i) q^{72} +590.913i q^{73} +(-154.050 - 424.551i) q^{74} +(-838.105 + 156.432i) q^{75} +(231.919 - 193.825i) q^{76} +(191.031 - 674.049i) q^{77} +(986.346 - 581.374i) q^{78} -28.4235 q^{79} +(1070.86 + 193.184i) q^{80} +(539.274 - 490.534i) q^{81} +(216.837 - 78.6800i) q^{82} +2.66288i q^{83} +(437.569 + 633.433i) q^{84} +589.094i q^{85} +(-232.790 - 641.555i) q^{86} +(-923.466 + 172.364i) q^{87} +(430.175 - 740.016i) q^{88} +600.037 q^{89} +(-853.358 - 978.616i) q^{90} +(393.402 - 1388.11i) q^{91} +(-245.685 - 293.972i) q^{92} +(156.210 + 836.917i) q^{93} +(-947.190 + 343.691i) q^{94} +642.367i q^{95} +(326.172 + 882.240i) q^{96} -703.593i q^{97} +(949.984 + 196.781i) q^{98} +(-952.603 + 368.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 28 q^{4} + 64 q^{7} + 104 q^{9} - 8 q^{15} - 892 q^{16} + 692 q^{18} + 128 q^{22} - 976 q^{25} + 612 q^{28} - 332 q^{30} + 1544 q^{36} + 568 q^{39} + 780 q^{42} + 208 q^{46} - 4048 q^{49} - 1448 q^{57}+ \cdots - 2072 q^{88}+O(q^{100}) \) 80 * q + 28 * q^4 + 64 * q^7 + 104 * q^9 - 8 * q^15 - 892 * q^16 + 692 * q^18 + 128 * q^22 - 976 * q^25 + 612 * q^28 - 332 * q^30 + 1544 * q^36 + 568 * q^39 + 780 * q^42 + 208 * q^46 - 4048 * q^49 - 1448 * q^57 - 1760 * q^58 + 4156 * q^60 - 2152 * q^63 + 2764 * q^64 + 1968 * q^70 - 2740 * q^72 - 3620 * q^78 + 4992 * q^79 + 1568 * q^81 + 2484 * q^84 - 2072 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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