LMFDB - Embedded newform 168.4.i.c.125.7

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			125.7
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.5

$q$-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} +(30.6172 + 42.5040i) 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} +(42.7826 + 86.2012i) 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} +(-122.411 - 83.4717i) 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} +(-196.914 - 187.918i) 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} +(405.997 + 103.838i) 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} +(-300.715 - 399.522i) 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} +(722.666 - 520.563i) 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} +(704.850 + 309.663i) 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} +(602.743 - 760.193i) 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	$-0.725019\pi$
$5$		−	17.0023i		−	1.52073i	0.649494	−	0.760367i	$-0.274981\pi$
$6$	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	$-0.187760\pi$
$13$	77.9029			1.66203			0.831015	+	0.556250i	$0.187760\pi$
$14$	30.6172	+	42.5040i	0.584485	+	0.811405i
$15$	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	$-0.579496\pi$
$17$	−34.6479			−0.494314			−0.247157	+	0.968975i	$0.579496\pi$
$18$	−57.5578	+	50.1907i	−0.753694	+	0.657225i
$19$	−37.7811			−0.456189			−0.228094	−	0.973639i	$-0.573249\pi$
$19$	−37.7811			−0.456189			−0.228094	+	0.973639i	$0.573249\pi$
$20$	−87.2252	−	104.369i	−0.975207	−	1.16688i
$21$	42.7826	+	86.2012i	0.444568	+	0.895745i
$22$	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
$28$	−122.411	−	83.4717i	−0.826197	−	0.563381i
$29$	−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	$-0.842578\pi$
$31$		−	163.846i		−	0.949280i	0.880180	−	0.474640i	$-0.157422\pi$
$32$	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	$-0.450358\pi$
$41$	81.5544			0.310650			0.155325	+	0.987863i	$0.450358\pi$
$42$	−196.914	−	187.918i	−0.723439	−	0.690388i
$43$			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	$-0.686443\pi$
$47$	−356.246			−1.10561			−0.552807	+	0.833309i	$0.686443\pi$
$48$	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
$56$	405.997	+	103.838i	0.968815	+	0.247786i
$57$	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	$-0.939015\pi$
$59$		−	172.591i		−	0.380839i	0.981703	−	0.190419i	$-0.0609848\pi$
$60$	545.045	+	449.949i	1.17275	+	0.968136i
$61$	−572.943			−1.20259			−0.601294	−	0.799028i	$-0.705348\pi$
$61$	−572.943			−1.20259			−0.601294	+	0.799028i	$0.705348\pi$
$62$	158.072	+	435.636i	0.323792	+	0.892351i
$63$	−300.715	−	399.522i	−0.601373	−	0.798969i
$64$	−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
$70$	722.666	−	520.563i	1.23393	−	0.888846i
$71$			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	$-0.842916\pi$
$73$		−	590.913i		−	0.947413i	0.880683	−	0.473706i	$-0.157084\pi$
$74$	−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	$-0.999440\pi$
$83$		−	2.66288i		−	0.00352155i	0.999998	−	0.00176077i	$-0.000560472\pi$
$84$	704.850	+	309.663i	0.915541	+	0.402226i
$85$			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	$-0.616311\pi$
$89$	−600.037			−0.714649			−0.357324	+	0.933980i	$0.616311\pi$
$90$	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	$0.120040\pi$
$97$			703.593i			0.736485i	−0.929730	+	0.368243i	$0.879960\pi$
$98$	602.743	−	760.193i	0.621288	−	0.783582i
$99$	−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	$0.165263\pi$
$101$			1007.27i			0.992350i	−0.868223	+	0.496175i	$0.834737\pi$
$102$	−438.685	+	258.570i	−0.425846	+	0.251003i
$103$			274.314i			0.262417i	0.991355	+	0.131209i	$0.0418857\pi$
$103$			274.314i			0.262417i	−0.991355	+	0.131209i	$0.958114\pi$
$104$	−885.887	+	1523.96i	−0.835273	+	1.43689i
$105$	1465.62	−	727.404i	1.36219	−	0.676070i
$106$	−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
$112$	−1179.65	+	115.602i	−0.995233	+	0.0975296i
$113$		−	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
$126$	1184.98	+	772.135i	0.837830	+	0.545931i
$127$	−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	$-0.730732\pi$
$131$		−	2244.81i		−	1.49717i	0.663036	−	0.748587i	$-0.269268\pi$
$132$	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	$-0.548970\pi$
$139$	−502.246			−0.306475			−0.153237	+	0.988189i	$0.548970\pi$
$140$	−1419.21	+	2081.27i	−0.856753	+	1.25643i
$141$	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
$147$	1319.93	−	1197.63i	0.740583	−	0.671964i
$148$	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
$154$	−1158.21	−	1607.87i	−0.606045	−	0.841335i
$155$	−2785.77			−1.44360
$156$	−2061.62	+	2497.34i	−1.05809	+	1.28171i
$157$	−1311.73			−0.666800			−0.333400	−	0.942785i	$-0.608196\pi$
$157$	−1311.73			−0.666800			−0.333400	+	0.942785i	$0.608196\pi$
$158$	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	$-0.182941\pi$
$167$	3622.79			1.67868			0.839342	+	0.543604i	$0.182941\pi$
$168$	−2172.81	−	143.325i	−0.997831	−	0.0658202i
$169$	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	$-0.862792\pi$
$173$		−	1901.49i		−	0.835653i	0.908527	−	0.417826i	$-0.137208\pi$
$174$	−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	$-0.660037\pi$
$181$	−2346.73			−0.963709			−0.481855	+	0.876251i	$0.660037\pi$
$182$	2385.17	+	3311.18i	0.971431	+	1.34858i
$183$	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
$189$	1916.93	+	1754.03i	0.737759	+	0.675064i
$190$	−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
$196$	−869.177	+	2602.70i	−0.316755	+	0.948507i
$197$	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	$-0.846503\pi$
$199$		−	2603.72i		−	0.927503i	0.885965	−	0.463752i	$-0.153497\pi$
$200$	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
$210$	−3195.03	+	3347.99i	−1.04990	+	1.10016i
$211$		−	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	$0.0688949\pi$
$223$			1430.30i			0.429507i	−0.976668	+	0.214754i	$0.931105\pi$
$224$	3024.92	−	1445.43i	0.902282	−	0.431147i
$225$	−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	$-0.737265\pi$
$227$		−	5026.34i		−	1.46965i	0.678258	−	0.734824i	$-0.262735\pi$
$228$	999.839	−	1211.15i	0.290421	−	0.351801i
$229$	4464.57			1.28833			0.644164	−	0.764887i	$-0.277205\pi$
$229$	4464.57			1.28833			0.644164	+	0.764887i	$0.277205\pi$
$230$	2164.91	−	785.543i	0.620651	−	0.225205i
$231$	−1618.41	−	3260.87i	−0.460967	−	0.928786i
$232$	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
$238$	−1060.82	−	1472.67i	−0.288919	−	0.401089i
$239$		−	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	$0.118502\pi$
$241$			2721.77i			0.727489i	−0.931499	+	0.363744i	$0.881498\pi$
$242$	−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	$-0.758972\pi$
$251$		−	5463.02i		−	1.37380i	0.726754	−	0.686898i	$-0.241028\pi$
$252$	−3895.56	−	909.739i	−0.973798	−	0.227413i
$253$			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	$-0.810893\pi$
$257$	−6828.16			−1.65731			−0.828655	+	0.559760i	$0.810893\pi$
$258$	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
$266$	−1156.75	−	1605.85i	−0.266635	−	0.370154i
$267$	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	$0.185582\pi$
$269$			4857.98i			1.10110i	−0.834802	+	0.550550i	$0.814418\pi$
$270$	−5291.90	−	4185.12i	−1.19280	−	0.943328i
$271$		−	1075.74i		−	0.241131i	−0.992705	−	0.120566i	$-0.961529\pi$
$271$		−	1075.74i		−	0.241131i	0.992705	−	0.120566i	$-0.0384709\pi$
$272$	−393.677	+	2182.24i	−0.0877581	+	0.486462i
$273$	3332.89	+	6715.33i	0.738885	+	1.48875i
$274$	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
$280$	1765.49	−	6902.89i	0.376816	−	1.47331i
$281$		−	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	$-0.715854\pi$
$283$	−5973.23			−1.25467			−0.627335	+	0.778750i	$0.715854\pi$
$284$	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	$-0.983414\pi$
$293$		−	522.434i		−	0.104167i	0.998643	−	0.0520835i	$-0.0165862\pi$
$294$	−2354.01	+	4457.67i	−0.466969	+	0.884274i
$295$	−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	$-0.762850\pi$
$307$	−7907.97			−1.47014			−0.735068	+	0.677994i	$0.762850\pi$
$308$	4630.64	+	3157.62i	0.856673	+	0.584163i
$309$	−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	$-0.542472\pi$
$311$	−1459.26			−0.266068			−0.133034	+	0.991111i	$0.542472\pi$
$312$	3072.12	−	8628.91i	0.557451	−	1.56576i
$313$			5437.91i			0.982008i	0.871157	+	0.491004i	$0.163370\pi$
$313$			5437.91i			0.982008i	−0.871157	+	0.491004i	$0.836630\pi$
$314$	3487.64	−	1265.50i	0.626812	−	0.227440i
$315$	−6792.80	+	5112.85i	−1.21502	+	0.914528i
$316$	−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
$322$	2035.51	−	1466.26i	0.352282	−	0.253762i
$323$	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
$336$	5915.35	−	1715.15i	0.960442	−	0.278480i
$337$	−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	$-0.388038\pi$
$349$	4492.59			0.689062			0.344531	+	0.938775i	$0.388038\pi$
$350$	−5023.63	−	6974.01i	−0.767213	−	1.06508i
$351$	−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	$-0.532988\pi$
$353$	−1372.22			−0.206901			−0.103451	+	0.994635i	$0.532988\pi$
$354$	−1288.01	−	2185.22i	−0.193382	−	0.328088i
$355$	15733.6			2.35226
$356$	−3683.32	+	3078.30i	−0.548359	+	0.458286i
$357$	−1482.33	−	2986.69i	−0.219756	−	0.442780i
$358$	−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
$364$	−9536.18	−	6502.69i	−1.37316	−	0.936356i
$365$	−10046.9			−1.44076
$366$	−7254.16	+	4275.76i	−1.03601	+	0.610649i
$367$		−	6151.73i		−	0.874980i	−0.899223	−	0.437490i	$-0.855867\pi$
$367$		−	6151.73i		−	0.874980i	0.899223	−	0.437490i	$-0.144133\pi$
$368$	−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
$378$	−6788.97	−	2814.26i	−0.923775	−	0.382937i
$379$			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	$-0.565476\pi$
$383$	−3061.90			−0.408501			−0.204251	+	0.978919i	$0.565476\pi$
$384$	−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
$392$	−200.000	−	7758.63i	−0.0257692	−	0.999668i
$393$	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	$-0.526972\pi$
$397$	−1338.92			−0.169266			−0.0846329	+	0.996412i	$0.526972\pi$
$398$	2511.96	+	6922.80i	0.316364	+	0.871880i
$399$	−1616.38	−	3256.78i	−0.202807	−	0.408629i
$400$	−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
$406$	−5535.29	−	7684.31i	−0.676630	−	0.939325i
$407$		−	6040.37i		−	0.735652i
$408$	−1366.35	+	3837.77i	−0.165795	+	0.465681i
$409$		−	13294.9i		−	1.60731i	−0.595093	−	0.803657i	$-0.702885\pi$
$409$		−	13294.9i		−	1.60731i	0.595093	−	0.803657i	$-0.297115\pi$
$410$	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	$0.164283\pi$
$419$			8465.25i			0.987003i	−0.869745	+	0.493502i	$0.835717\pi$
$420$	5264.98	−	11984.1i	0.611678	−	1.39229i
$421$			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	$-0.997316\pi$
$433$		−	151.928i		−	0.0168619i	0.999964	−	0.00843095i	$-0.00268369\pi$
$434$	6964.12	−	5016.51i	0.770250	−	0.554840i
$435$	−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	$-0.820588\pi$
$439$		−	9828.43i		−	1.06853i	0.845317	−	0.534266i	$-0.179412\pi$
$440$	−12582.0	−	7313.98i	−1.36323	−	0.792455i
$441$	−5600.30	+	7375.83i	−0.604718	+	0.796439i
$442$	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
$448$	−6648.19	+	6761.43i	−0.701111	+	0.713053i
$449$		−	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	$-0.903916\pi$
$461$		−	5885.29i		−	0.594589i	0.954786	−	0.297294i	$-0.0960843\pi$
$462$	7448.97	+	7108.66i	0.750125	+	0.715854i
$463$	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	$0.208963\pi$
$467$			12318.9i			1.22066i	−0.792147	+	0.610330i	$0.791037\pi$
$468$	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
$476$	4241.28	+	2892.12i	0.408401	+	0.278487i
$477$	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	$-0.412624\pi$
$479$	5683.40			0.542132			0.271066	+	0.962561i	$0.412624\pi$
$480$	−15000.1	+	5545.68i	−1.42637	+	0.527343i
$481$			12439.3i			1.17918i
$482$	−2625.84	−	7236.67i	−0.248141	−	0.683861i
$483$	4128.17	−	2048.86i	0.388899	−	0.193015i
$484$	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
$490$	−12925.0	−	10248.0i	−1.19162	−	0.944814i
$491$	−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	$-0.526645\pi$
$503$	−1886.42			−0.167220			−0.0836098	+	0.996499i	$0.526645\pi$
$504$	11235.2	−	1339.44i	0.992968	−	0.118380i
$505$	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	$0.156789\pi$
$509$			10860.9i			0.945781i	−0.881121	+	0.472891i	$0.843211\pi$
$510$	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
$518$	−6786.92	+	4888.87i	−0.575676	+	0.414681i
$519$	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	$-0.405883\pi$
$521$	6930.38			0.582774			0.291387	+	0.956605i	$0.405883\pi$
$522$	10405.9	−	9073.98i	0.872516	−	0.760838i
$523$	−9140.75			−0.764239			−0.382119	−	0.924113i	$-0.624806\pi$
$523$	−9140.75			−0.764239			−0.382119	+	0.924113i	$0.624806\pi$
$524$	−11516.3	−	13779.7i	−0.960099	−	1.14880i
$525$	−7019.73	−	14143.8i	−0.583554	−	1.17578i
$526$	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
$532$	4624.83	+	3153.66i	0.376902	+	0.257008i
$533$	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
$546$	−15340.2	−	14639.3i	−1.20238	−	1.14745i
$547$		−	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
$560$	1965.49	+	20056.7i	0.148317	+	1.51348i
$561$	−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	$-0.866899\pi$
$563$		−	10849.1i		−	0.812139i	0.913842	−	0.406070i	$-0.133101\pi$
$564$	9427.69	−	11420.2i	0.703861	−	0.852622i
$565$	−726.222			−0.0540750
$566$	15881.6	−	5762.70i	1.17943	−	0.427958i
$567$	−11463.9	−	7131.91i	−0.849095	−	0.528240i
$568$	−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
$574$	2496.97	+	3466.39i	0.181570	+	0.252063i
$575$			7857.73i			0.569896i
$576$	−10713.7	−	8736.09i	−0.775009	−	0.631951i
$577$		−	3778.32i		−	0.272606i	−0.990667	−	0.136303i	$-0.956478\pi$
$577$		−	3778.32i		−	0.272606i	0.990667	−	0.136303i	$-0.0435220\pi$
$578$	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	$-0.979678\pi$
$587$		−	1814.70i		−	0.127599i	0.997963	−	0.0637997i	$-0.0203219\pi$
$588$	1958.30	−	14123.1i	0.137345	−	0.990523i
$589$			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	$-0.389880\pi$
$593$	9793.33			0.678185			0.339093	+	0.940753i	$0.389880\pi$
$594$	−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	$-0.810665\pi$
$601$		−	16512.2i		−	1.12071i	0.828252	−	0.560355i	$-0.189335\pi$
$602$	−10256.0	+	7387.75i	−0.694356	+	0.500170i
$603$	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	$-0.918910\pi$
$607$		−	7537.39i		−	0.504009i	0.967726	−	0.252004i	$-0.0810898\pi$
$608$	−1154.35	−	6741.00i	−0.0769982	−	0.449644i
$609$	−7734.68	−	15584.3i	−0.514655	−	1.03696i
$610$	−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
$616$	−15358.3	−	3928.06i	−1.00455	−	0.256926i
$617$		−	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	$-0.367167\pi$
$619$	12483.7			0.810602			0.405301	+	0.914183i	$0.367167\pi$
$620$	−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
$630$	13128.1	−	20147.5i	0.830215	−	1.27412i
$631$	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	$-0.423270\pi$
$643$	7784.75			0.477450			0.238725	+	0.971087i	$0.423270\pi$
$644$	−3997.46	+	5862.26i	−0.244599	+	0.358704i
$645$	−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	$-0.632287\pi$
$647$	−13288.6			−0.807463			−0.403732	+	0.914877i	$0.632287\pi$
$648$	3463.54	+	16127.7i	0.209970	+	0.977708i
$649$			6528.89i			0.394887i
$650$	33985.5	−	12331.7i	2.05080	−	0.744138i
$651$	14123.8	−	7009.78i	0.850313	−	0.422020i
$652$	−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
$658$	−10907.3	−	15141.9i	−0.646215	−	0.897101i
$659$	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	$-0.558309\pi$
$661$	−6191.40			−0.364323			−0.182162	+	0.983269i	$0.558309\pi$
$662$	−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
$672$	−14073.1	+	10267.1i	−0.807857	+	0.589379i
$673$	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	$0.101808\pi$
$677$			11076.8i			0.628826i	−0.949286	+	0.314413i	$0.898192\pi$
$678$	−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
$686$	−16589.3	−	6901.07i	−0.923297	−	0.384088i
$687$	−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	$-0.541298\pi$
$691$	−4700.10			−0.258756			−0.129378	+	0.991595i	$0.541298\pi$
$692$	−9755.03	−	11672.3i	−0.535882	−	0.641206i
$693$	11375.6	+	15113.4i	0.623556	+	0.828440i
$694$	−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
$700$	20085.1	+	13696.0i	1.08449	+	0.739512i
$701$	−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
$714$	6822.64	+	6510.94i	0.357606	+	0.341269i
$715$			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	$-0.542133\pi$
$719$	−5088.93			−0.263957			−0.131979	+	0.991253i	$0.542133\pi$
$720$	−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	$-0.986060\pi$
$727$		−	1716.37i		−	0.0875609i	0.999041	−	0.0437804i	$-0.0139402\pi$
$728$	31628.4	+	8089.32i	1.61020	+	0.411827i
$729$	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	$-0.519962\pi$
$733$	−2487.51			−0.125346			−0.0626728	+	0.998034i	$0.519962\pi$
$734$	5934.91	+	16356.3i	0.298449	+	0.822508i
$735$	−20362.5	−	22441.8i	−1.02188	−	1.12623i
$736$	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
$742$	17932.1	+	24894.1i	0.887210	+	1.23166i
$743$		−	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
$756$	20765.6	+	932.888i	0.998992	+	0.0448794i
$757$			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	$-0.681146\pi$
$761$	−22624.8			−1.07772			−0.538862	+	0.842394i	$0.681146\pi$
$762$	−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	$-0.906778\pi$
$769$		−	12312.9i		−	0.577393i	0.957421	−	0.288697i	$-0.0932219\pi$
$770$	−27337.5	+	19692.2i	−1.27945	+	0.921632i
$771$	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	$-0.856410\pi$
$773$		−	18738.9i		−	0.871916i	0.899967	−	0.435958i	$-0.143590\pi$
$774$	−12110.7	−	13888.4i	−0.562417	−	0.644970i
$775$			26883.7i			1.24606i
$776$	−13763.9	−	8001.04i	−0.636722	−	0.370130i
$777$	−13764.4	+	6831.42i	−0.635514	+	0.315413i
$778$	−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
$784$	8016.94	+	20435.7i	0.365203	+	0.930928i
$785$			22302.5i			1.01403i
$786$	−16752.6	−	28422.0i	−0.760234	−	1.28980i
$787$	−7115.83			−0.322302			−0.161151	−	0.986930i	$-0.551521\pi$
$787$	−7115.83			−0.322302			−0.161151	+	0.986930i	$0.551521\pi$
$788$	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	$-0.912035\pi$
$797$		−	12278.2i		−	0.545693i	0.962058	−	0.272846i	$-0.0879650\pi$
$798$	7439.63	+	7099.74i	0.330025	+	0.314947i
$799$	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	$-0.786364\pi$
$811$	−36172.6			−1.56621			−0.783103	+	0.621892i	$0.786364\pi$
$812$	22130.7	+	15090.9i	0.956449	+	0.652200i
$813$	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
$819$	−23426.5	−	31123.9i	−0.999499	−	1.32791i
$820$	−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
$826$	7335.82	−	5284.26i	0.309014	−	0.222594i
$827$	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	$-0.303520\pi$
$829$	27630.7			1.15760			0.578802	+	0.815468i	$0.303520\pi$
$830$	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	$-0.212418\pi$
$839$	38177.4			1.57095			0.785476	+	0.618892i	$0.212418\pi$
$840$	−2436.86	+	36942.8i	−0.100095	+	1.51744i
$841$	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	$-0.464472\pi$
$853$	5549.77			0.222767			0.111384	+	0.993777i	$0.464472\pi$
$854$	−17541.9	−	24352.4i	−0.702894	−	0.975786i
$855$	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	$-0.350116\pi$
$857$	22763.4			0.907332			0.453666	+	0.891172i	$0.350116\pi$
$858$	−37312.1	+	21992.6i	−1.48463	+	0.875074i
$859$	672.946			0.0267295			0.0133647	−	0.999911i	$-0.495746\pi$
$859$	672.946			0.0267295			0.0133647	+	0.999911i	$0.495746\pi$
$860$	25183.6	−	21046.9i	0.998550	−	0.834529i
$861$	3489.11	+	7030.09i	0.138105	+	0.278263i
$862$	−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
$868$	−13676.5	+	20056.6i	−0.534807	+	0.784292i
$869$	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	$-0.490089\pi$
$881$	1628.16			0.0622635			0.0311317	+	0.999515i	$0.490089\pi$
$882$	7774.23	−	25013.8i	0.296794	−	0.954942i
$883$		−	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	$-0.267660\pi$
$887$	35230.3			1.33362			0.666808	+	0.745230i	$0.267660\pi$
$888$	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
$896$	11153.1	−	24391.2i	0.415848	−	0.909434i
$897$	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
$903$	−20799.9	+	10323.2i	−0.766529	+	0.380437i
$904$	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
$910$	56297.8	−	40553.4i	2.05083	−	1.47729i
$911$		−	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
$924$	−26663.5	−	11714.1i	−0.949312	−	0.417063i
$925$		−	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	$-0.631873\pi$
$929$	−22796.3			−0.805083			−0.402542	+	0.915402i	$0.631873\pi$
$930$	−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	$0.208034\pi$
$937$			34878.2i			1.21603i	−0.793925	+	0.608016i	$0.791966\pi$
$938$	−32519.3	+	23424.9i	−1.13198	+	0.815404i
$939$	−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	$0.206107\pi$
$941$			34823.7i			1.20640i	−0.797591	+	0.603198i	$0.793893\pi$
$942$	−16608.1	+	9789.19i	−0.574440	+	0.338587i
$943$		−	3905.64i		−	0.134873i
$944$	−10870.4	−	1961.02i	−0.374789	−	0.0676122i
$945$	29822.6	−	32592.3i	1.02659	−	1.12193i
$946$	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
$952$	−14066.9	−	3597.78i	−0.478899	−	0.122484i
$953$			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
$966$	−8999.36	+	9430.19i	−0.299741	+	0.314090i
$967$	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	$-0.952134\pi$
$971$		−	9065.66i		−	0.299620i	0.988715	−	0.149810i	$-0.0478661\pi$
$972$	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
$980$	44252.0	+	14778.0i	1.44243	+	0.481701i
$981$	−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	$-0.620794\pi$
$983$	−22834.0			−0.740886			−0.370443	+	0.928855i	$0.620794\pi$
$984$	3216.12	−	9033.36i	0.104193	−	0.292656i
$985$		−	57899.4i		−	1.87292i
$986$	−16654.8	+	6043.23i	−0.537927	+	0.195188i
$987$	−15241.2	−	30708.9i	−0.491521	−	0.990349i
$988$	−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
$994$	−39332.3	+	28332.5i	−1.25507	+	0.904077i
$995$	−44269.4			−1.41049
$996$	85.3641	+	70.4703i	0.00271573	+	0.00224190i
$997$	−17170.3			−0.545427			−0.272713	−	0.962095i	$-0.587921\pi$
$997$	−17170.3			−0.545427			−0.272713	+	0.962095i	$0.587921\pi$
$998$	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.125.7	yes	80
3.2	odd	2	inner	168.4.i.c.125.73	yes	80
4.3	odd	2		672.4.i.c.209.74		80
7.6	odd	2	inner	168.4.i.c.125.8	yes	80
8.3	odd	2		672.4.i.c.209.7		80
8.5	even	2	inner	168.4.i.c.125.76	yes	80
12.11	even	2		672.4.i.c.209.75		80
21.20	even	2	inner	168.4.i.c.125.74	yes	80
24.5	odd	2	inner	168.4.i.c.125.6	yes	80
24.11	even	2		672.4.i.c.209.6		80
28.27	even	2		672.4.i.c.209.8		80
56.13	odd	2	inner	168.4.i.c.125.75	yes	80
56.27	even	2		672.4.i.c.209.73		80
84.83	odd	2		672.4.i.c.209.5		80
168.83	odd	2		672.4.i.c.209.76		80
168.125	even	2	inner	168.4.i.c.125.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.5	✓	80	168.125	even	2	inner
168.4.i.c.125.6	yes	80	24.5	odd	2	inner
168.4.i.c.125.7	yes	80	1.1	even	1	trivial
168.4.i.c.125.8	yes	80	7.6	odd	2	inner
168.4.i.c.125.73	yes	80	3.2	odd	2	inner
168.4.i.c.125.74	yes	80	21.20	even	2	inner
168.4.i.c.125.75	yes	80	56.13	odd	2	inner
168.4.i.c.125.76	yes	80	8.5	even	2	inner
672.4.i.c.209.5		80	84.83	odd	2
672.4.i.c.209.6		80	24.11	even	2
672.4.i.c.209.7		80	8.3	odd	2
672.4.i.c.209.8		80	28.27	even	2
672.4.i.c.209.73		80	56.27	even	2
672.4.i.c.209.74		80	4.3	odd	2
672.4.i.c.209.75		80	12.11	even	2
672.4.i.c.209.76		80	168.83	odd	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} +(30.6172 + 42.5040i) 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} +(42.7826 + 86.2012i) 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} +(-122.411 - 83.4717i) 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} +(-196.914 - 187.918i) 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} +(405.997 + 103.838i) 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} +(-300.715 - 399.522i) 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} +(722.666 - 520.563i) 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} +(704.850 + 309.663i) 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} +(602.743 - 760.193i) 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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