LMFDB - Embedded newform 168.4.i.c.125.76

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			125.76
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.74

$q$-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} +(14.5008 + 2.39302i) 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} +(36.2462 + 20.3523i) 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} +(76.3507 - 1.60157i) 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} +(76.7365 + 89.0815i) 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} +(-40.6869 + 246.547i) 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} +(204.547 + 69.4015i) 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} +(-30.5876 - 270.467i) 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} +(118.086 + 310.882i) 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} +(388.468 - 80.9730i) 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} +(-346.037 + 616.269i) 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} +(548.545 + 90.5247i) 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} +(476.895 + 381.863i) 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} +(-1129.66 - 186.423i) 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} +(179.608 - 748.629i) 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} +(27.2303 + 1298.14i) 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} +(14.0411 + 940.499i) 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	$0.725019\pi$
$6$	14.5008	+	2.39302i	0.986655	+	0.162825i
$7$	−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	$-0.326512\pi$
$11$	37.8286			1.03689			0.518443	+	0.855112i	$0.326512\pi$
$12$	36.2462	+	20.3523i	0.871947	+	0.489601i
$13$	−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	$-0.579496\pi$
$17$	−34.6479			−0.494314			−0.247157	+	0.968975i	$0.579496\pi$
$18$	76.3507	−	1.60157i	0.999780	−	0.0209718i
$19$	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
$21$	−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	$-0.0696537\pi$
$24$	76.7365	+	89.0815i	0.652657	+	0.757654i
$25$	−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	$-0.303511\pi$
$29$	180.790			1.15765			0.578826	+	0.815451i	$0.303511\pi$
$30$	−40.6869	+	246.547i	−0.247613	+	1.50044i
$31$		−	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
$36$	204.547	+	69.4015i	0.946976	+	0.321303i
$37$		−	159.677i		−	0.709481i	−0.934965	−	0.354741i	$-0.884569\pi$
$37$		−	159.677i		−	0.709481i	0.934965	−	0.354741i	$-0.115431\pi$
$38$	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	$0.450358\pi$
$42$	−30.5876	−	270.467i	−0.112375	−	0.993666i
$43$		−	241.294i		−	0.855745i	−0.903839	−	0.427873i	$-0.859263\pi$
$43$		−	241.294i		−	0.855745i	0.903839	−	0.427873i	$-0.140737\pi$
$44$	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	$0.686443\pi$
$48$	118.086	+	310.882i	0.355087	+	0.934833i
$49$	−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	$-0.774296\pi$
$53$	−585.689			−1.51794			−0.758968	+	0.651128i	$0.774296\pi$
$54$	388.468	−	80.9730i	0.978959	−	0.204056i
$55$			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	$0.939015\pi$
$60$	−346.037	+	616.269i	−0.744552	+	1.32600i
$61$	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
$63$	−300.715	−	399.522i	−0.601373	−	0.798969i
$64$	−253.370	+	444.913i	−0.494862	+	0.868971i
$65$		−	1324.53i		−	2.52750i
$66$	548.545	+	90.5247i	1.02305	+	0.168831i
$67$		−	765.089i		−	1.39508i	−0.716545	−	0.697541i	$-0.754277\pi$
$67$		−	765.089i		−	1.39508i	0.716545	−	0.697541i	$-0.245723\pi$
$68$	−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	$0.718556\pi$
$72$	476.895	+	381.863i	0.780592	+	0.625041i
$73$		−	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
$78$	−1129.66	−	186.423i	−1.63985	−	0.270619i
$79$	−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	$0.999440\pi$
$84$	179.608	−	748.629i	0.233296	−	0.972406i
$85$		−	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	$0.616311\pi$
$90$	27.2303	+	1298.14i	0.0318925	+	1.52040i
$91$	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
$96$	14.0411	+	940.499i	0.0149278	+	0.999889i
$97$			703.593i			0.736485i	0.929730	+	0.368243i	$0.120040\pi$
$97$			703.593i			0.736485i	−0.929730	+	0.368243i	$0.879960\pi$
$98$	−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	$-0.165263\pi$
$102$	−502.422	−	82.9131i	−0.487718	−	0.0804865i
$103$			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	$-0.670875\pi$
$107$	−1132.06			−1.02281			−0.511405	+	0.859340i	$0.670875\pi$
$108$	1110.98	+	159.485i	0.989853	+	0.142097i
$109$			2168.32i			1.90539i	0.303934	+	0.952693i	$0.401700\pi$
$109$			2168.32i			1.90539i	−0.303934	+	0.952693i	$0.598300\pi$
$110$	−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	$-0.00565961\pi$
$114$	547.857	+	90.4111i	0.450101	+	0.0742788i
$115$	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
$120$	−1514.59	+	1304.70i	−1.15219	+	0.992518i
$121$	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
$126$	−414.101	−	1352.37i	−0.292786	−	0.956178i
$127$	−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	$0.730732\pi$
$132$	1371.14	+	769.900i	0.904110	+	0.507660i
$133$	−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	$-0.126835\pi$
$138$	114.602	−	694.443i	0.0706924	−	0.428369i
$139$	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
$144$	899.567	+	1475.39i	0.520583	+	0.853811i
$145$			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	$-0.237504\pi$
$149$	2671.10			1.46863			0.734313	+	0.678811i	$0.237504\pi$
$150$	−2379.28	−	392.645i	−1.29511	−	0.213729i
$151$	−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
$156$	−2823.68	−	1585.50i	−1.44920	−	0.813730i
$157$	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
$162$	1907.07	−	783.968i	0.924899	−	0.380212i
$163$			3119.89i			1.49920i	0.661894	+	0.749598i	$0.269753\pi$
$163$			3119.89i			1.49920i	−0.661894	+	0.749598i	$0.730247\pi$
$164$	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	$0.182941\pi$
$168$	1199.79	−	1817.18i	0.550985	−	0.834515i
$169$	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	$0.862792\pi$
$174$	2621.61	+	432.635i	1.14220	+	0.188494i
$175$	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	$-0.589507\pi$
$179$	−1329.17			−0.555010			−0.277505	+	0.960724i	$0.589507\pi$
$180$	−1179.99	+	3477.77i	−0.488617	+	1.44010i
$181$	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
$186$	392.088	−	2375.91i	0.154566	−	0.936612i
$187$	−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	$0.867830\pi$
$192$	−870.019	+	2514.15i	−0.327022	+	0.945017i
$193$	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	$-0.711165\pi$
$197$	−3405.38			−1.23159			−0.615796	+	0.787906i	$0.711165\pi$
$198$	2888.24	−	60.5850i	1.03666	−	0.0217454i
$199$		−	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
$204$	−1255.85	−	705.164i	−0.431016	−	0.242017i
$205$			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
$210$	4598.57	−	520.060i	1.51110	−	0.170893i
$211$			987.223i			0.322101i	0.986946	+	0.161050i	$0.0514881\pi$
$211$			987.223i			0.322101i	−0.986946	+	0.161050i	$0.948512\pi$
$212$	−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
$216$	2800.02	+	1495.86i	0.882023	+	0.471207i
$217$	−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
$222$	382.112	−	2315.45i	0.115521	−	0.700013i
$223$			1430.30i			0.429507i	0.976668	+	0.214754i	$0.0688949\pi$
$223$			1430.30i			0.429507i	−0.976668	+	0.214754i	$0.931105\pi$
$224$	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	$0.737265\pi$
$228$	1369.42	+	768.934i	0.397772	+	0.223350i
$229$	−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
$231$	−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	$0.903136\pi$
$234$	−5947.95	+	124.767i	−1.66166	+	0.0348558i
$235$		−	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	$-0.368046\pi$
$240$	−5285.72	+	2007.73i	−1.42163	+	0.539993i
$241$			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
$246$	1182.60	+	195.161i	0.306505	+	0.0505815i
$247$	−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	$0.758972\pi$
$252$	203.689	−	3995.19i	0.0509174	−	0.998703i
$253$		−	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	$0.810893\pi$
$258$	577.423	−	3498.96i	0.139336	−	0.844325i
$259$	−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	$-0.0248476\pi$
$264$	2902.83	+	3369.83i	0.676731	+	0.785601i
$265$		−	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	$-0.185582\pi$
$270$	1376.73	+	6604.86i	0.310315	+	1.48874i
$271$		−	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
$276$	974.671	−	1735.83i	0.212566	−	0.378567i
$277$		−	6119.99i		−	1.32749i	−0.747959	−	0.663745i	$-0.768966\pi$
$277$		−	6119.99i		−	1.32749i	0.747959	−	0.663745i	$-0.231034\pi$
$278$	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	$-0.0196261\pi$
$282$	−5165.86	−	852.506i	−1.09086	−	0.180021i
$283$	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
$288$	968.387	+	4790.63i	0.198135	+	0.980175i
$289$	−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	$0.983414\pi$
$294$	−4664.85	+	1910.86i	−0.925372	+	0.379059i
$295$	−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
$300$	−5947.23	−	3339.39i	−1.14455	−	0.642665i
$301$	−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
$306$	−2645.39	+	55.4908i	−0.494206	+	0.0103667i
$307$	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	$-0.542472\pi$
$311$	−1459.26			−0.266068			−0.133034	+	0.991111i	$0.542472\pi$
$312$	−5978.00	−	6939.71i	−1.08474	−	1.25924i
$313$			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	$-0.249605\pi$
$317$	7991.76			1.41597			0.707984	+	0.706228i	$0.249605\pi$
$318$	−8492.97	−	1401.57i	−1.49768	−	0.247157i
$319$	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
$324$	5826.87	−	244.561i	0.999120	−	0.0419344i
$325$	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
$330$	−1539.13	+	9326.55i	−0.256746	+	1.55579i
$331$		−	5913.18i		−	0.981927i	−0.871180	−	0.490963i	$-0.836645\pi$
$331$		−	5913.18i		−	0.981927i	0.871180	−	0.490963i	$-0.163355\pi$
$332$	−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
$336$	4943.13	−	3674.03i	0.802589	−	0.596532i
$337$	−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
$342$	2884.62	−	60.5090i	0.456089	−	0.00956711i
$343$	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	$-0.540420\pi$
$347$	−1637.21			−0.253285			−0.126643	+	0.991948i	$0.540420\pi$
$348$	6552.95	+	3679.50i	1.00941	+	0.566787i
$349$	−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	$-0.532988\pi$
$353$	−1372.22			−0.206901			−0.103451	+	0.994635i	$0.532988\pi$
$354$	−413.015	+	2502.71i	−0.0620099	+	0.375756i
$355$	−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	$-0.122775\pi$
$360$	−6492.55	+	8108.32i	−0.950521	+	1.18707i
$361$	−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
$366$	8308.14	+	1371.07i	1.18654	+	0.195811i
$367$		−	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
$372$	3334.65	−	5938.80i	0.464768	−	0.827722i
$373$			12854.7i			1.78443i	0.451614	+	0.892213i	$0.350848\pi$
$373$			12854.7i			1.78443i	−0.451614	+	0.892213i	$0.649152\pi$
$374$	−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
$378$	−3404.54	−	6513.01i	−0.463256	−	0.886225i
$379$		−	2284.79i		−	0.309662i	−0.987941	−	0.154831i	$-0.950517\pi$
$379$		−	2284.79i		−	0.309662i	0.987941	−	0.154831i	$-0.0494832\pi$
$380$	−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	$0.565476\pi$
$384$	−4738.75	+	5845.28i	−0.629748	+	0.776799i
$385$	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	$-0.548948\pi$
$389$	−2350.30			−0.306336			−0.153168	+	0.988200i	$0.548948\pi$
$390$	3169.63	−	19206.8i	0.411540	−	2.49378i
$391$			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
$396$	7737.73	+	2625.36i	0.981907	+	0.333155i
$397$	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
$399$	−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	$-0.159807\pi$
$402$	1830.88	−	11094.4i	0.227154	−	1.37647i
$403$			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
$408$	−2658.76	−	3086.48i	−0.322618	−	0.374519i
$409$		−	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
$414$	−76.6989	−	3656.43i	−0.00910518	−	0.434067i
$415$	−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	$-0.164283\pi$
$420$	12728.4	+	3053.75i	1.47877	+	0.354781i
$421$		−	1141.45i		−	0.132140i	−0.997815	−	0.0660701i	$-0.978954\pi$
$421$		−	1141.45i		−	0.132140i	0.997815	−	0.0660701i	$-0.0210461\pi$
$422$	−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
$426$	−2214.45	+	13418.7i	−0.251856	+	1.52615i
$427$	−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	$0.879321\pi$
$432$	6001.56	+	6678.54i	0.668403	+	0.743800i
$433$		−	151.928i		−	0.0168619i	−0.999964	−	0.00843095i	$-0.997316\pi$
$433$		−	151.928i		−	0.0168619i	0.999964	−	0.00843095i	$-0.00268369\pi$
$434$	−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
$438$	1414.07	−	8568.71i	0.154262	−	0.934769i
$439$		−	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	$-0.537770\pi$
$443$	−2207.57			−0.236760			−0.118380	+	0.992968i	$0.537770\pi$
$444$	3249.80	−	5787.69i	0.347362	−	0.618630i
$445$		−	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	$-0.137383\pi$
$450$	−12527.5	+	262.783i	−1.31234	+	0.0275283i
$451$	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
$456$	2899.19	+	3365.60i	0.297735	+	0.345633i
$457$	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	$0.903916\pi$
$462$	−1157.09	−	10231.4i	−0.116521	−	1.03032i
$463$	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	$-0.208963\pi$
$468$	−15934.8	−	5406.58i	−1.57390	−	0.534016i
$469$	−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
$474$	−412.164	−	68.0182i	−0.0399395	−	0.00659109i
$475$	−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	$-0.412624\pi$
$479$	5683.40			0.542132			0.271066	+	0.962561i	$0.412624\pi$
$480$	−15990.7	+	238.732i	−1.52056	+	0.0227012i
$481$			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
$486$	8993.78	−	5822.65i	0.839436	−	0.543458i
$487$	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	$-0.364401\pi$
$491$	8991.73			0.826459			0.413229	+	0.910627i	$0.364401\pi$
$492$	2956.03	+	1659.82i	0.270870	+	0.152094i
$493$	−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
$498$	−6.37232	+	38.6139i	−0.000573395	+	0.00347455i
$499$			10529.3i			0.944599i	0.881438	+	0.472300i	$0.156576\pi$
$499$			10529.3i			0.944599i	−0.881438	+	0.472300i	$0.843424\pi$
$500$	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	$0.526645\pi$
$504$	4395.95	−	10425.9i	0.388514	−	0.921443i
$505$	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	$-0.156789\pi$
$510$	1409.72	−	8542.34i	0.122399	−	0.741689i
$511$	−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
$516$	4910.90	−	8745.99i	0.418973	−	0.746164i
$517$	−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	$-0.405883\pi$
$521$	6930.38			0.582774			0.291387	+	0.956605i	$0.405883\pi$
$522$	13803.5	−	289.548i	1.15740	−	0.0242781i
$523$	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
$525$	7019.73	+	14143.8i	0.583554	+	1.17578i
$526$	641.762	−	1768.66i	0.0531980	−	0.146610i
$527$			5676.93i			0.469243i
$528$	4467.01	+	11760.2i	0.368185	+	0.969316i
$529$	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
$534$	−8701.02	−	1435.90i	−0.705112	−	0.116362i
$535$		−	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
$540$	−2711.62	+	18889.2i	−0.216091	+	1.50530i
$541$			1327.06i			0.105461i	0.998609	+	0.0527307i	$0.0167925\pi$
$541$			1327.06i			0.105461i	−0.998609	+	0.0527307i	$0.983207\pi$
$542$	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
$546$	2382.86	+	21070.2i	0.186771	+	1.65150i
$547$			6943.34i			0.542735i	0.962476	+	0.271367i	$0.0874758\pi$
$547$			6943.34i			0.542735i	−0.962476	+	0.271367i	$0.912524\pi$
$548$	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
$552$	4266.11	−	3674.91i	0.328945	−	0.283359i
$553$	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	$-0.651393\pi$
$557$	−12038.4			−0.915770			−0.457885	+	0.889012i	$0.651393\pi$
$558$	−262.411	−	12509.8i	−0.0199081	−	0.949071i
$559$			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	$0.866899\pi$
$564$	−12912.6	−	7250.44i	−0.964037	−	0.541309i
$565$	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	$0.875674\pi$
$570$	−1537.20	+	9314.84i	−0.112958	+	0.684484i
$571$			2025.81i			0.148472i	0.997241	+	0.0742360i	$0.0236518\pi$
$571$			2025.81i			0.148472i	−0.997241	+	0.0742360i	$0.976348\pi$
$572$	−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
$576$	−2047.03	+	13671.6i	−0.148078	+	0.988976i
$577$		−	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
$582$	−1683.71	+	10202.7i	−0.119918	+	0.726657i
$583$	−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	$0.979678\pi$
$588$	−14246.4	+	580.157i	−0.999172	+	0.0406892i
$589$		−	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	$0.389880\pi$
$594$	14695.2	−	3063.10i	1.01507	−	0.211583i
$595$	−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	$0.879643\pi$
$600$	−12590.8	−	14616.4i	−0.856698	−	0.994520i
$601$		−	16512.2i		−	1.12071i	−0.828252	−	0.560355i	$-0.810665\pi$
$601$		−	16512.2i		−	1.12071i	0.828252	−	0.560355i	$-0.189335\pi$
$602$	−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
$606$	2410.42	−	14606.3i	0.161579	−	0.979107i
$607$		−	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
$612$	−7087.11	−	2404.61i	−0.468104	−	0.158825i
$613$			10916.9i			0.719297i	0.933088	+	0.359648i	$0.117103\pi$
$613$			10916.9i			0.719297i	−0.933088	+	0.359648i	$0.882897\pi$
$614$	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	$-0.346457\pi$
$618$	−656.439	+	3977.77i	−0.0427279	+	0.258915i
$619$	−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
$624$	−9199.21	−	24218.6i	−0.590165	−	1.55372i
$625$	−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
$630$	22993.4	−	7040.68i	1.45409	−	0.445250i
$631$	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
$636$	−21229.0	−	11920.1i	−1.32356	−	0.743182i
$637$	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	$0.783247\pi$
$642$	−16415.8	−	2709.05i	−1.00916	−	0.166538i
$643$	−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	$-0.632287\pi$
$647$	−13288.6			−0.807463			−0.403732	+	0.914877i	$0.632287\pi$
$648$	15728.5	+	4971.26i	0.953506	+	0.301373i
$649$			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	$-0.436669\pi$
$653$	6596.26			0.395301			0.197651	+	0.980273i	$0.436669\pi$
$654$	−5188.83	+	31442.3i	−0.310244	+	1.87996i
$655$	−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	$-0.579590\pi$
$659$	−8372.03			−0.494883			−0.247442	+	0.968903i	$0.579590\pi$
$660$	−13090.1	+	23312.6i	−0.772016	+	1.37491i
$661$	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
$666$	−255.734	−	12191.5i	−0.0148791	−	0.709325i
$667$		−	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
$672$	16687.4	−	4999.62i	0.957930	−	0.287001i
$673$	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	$-0.101808\pi$
$678$	102.213	−	619.375i	0.00578980	−	0.0350840i
$679$	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	$-0.146853\pi$
$683$	31967.1			1.79090			0.895451	+	0.445161i	$0.146853\pi$
$684$	7728.02	+	2622.07i	0.432000	+	0.146575i
$685$	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
$690$	11807.1	+	1948.50i	0.651435	+	0.107504i
$691$	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
$693$	−11375.6	−	15113.4i	−0.623556	−	0.828440i
$694$	−4353.02	−	1579.50i	−0.238095	−	0.0863936i
$695$			8539.35i			0.466066i
$696$	13873.2	+	16105.1i	0.755550	+	0.877099i
$697$	−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	$-0.288868\pi$
$701$	22855.2			1.23143			0.615714	+	0.787970i	$0.288868\pi$
$702$	−30262.8	+	6308.03i	−1.62706	+	0.339147i
$703$		−	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
$708$	−3512.63	+	6255.77i	−0.186459	+	0.332071i
$709$		−	20814.1i		−	1.10252i	−0.834333	−	0.551261i	$-0.814147\pi$
$709$		−	20814.1i		−	1.10252i	0.834333	−	0.551261i	$-0.185853\pi$
$710$	−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
$714$	1059.79	+	9371.11i	0.0555488	+	0.491183i
$715$		−	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	$0.542133\pi$
$720$	−25085.0	+	15294.7i	−1.29842	+	0.791668i
$721$	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
$726$	1450.14	+	239.312i	0.0741318	+	0.0122337i
$727$		−	1716.37i		−	0.0875609i	−0.999041	−	0.0437804i	$-0.986060\pi$
$727$		−	1716.37i		−	0.0875609i	0.999041	−	0.0437804i	$-0.0139402\pi$
$728$	−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
$732$	20767.0	+	11660.7i	1.04859	+	0.588788i
$733$	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
$735$	−20362.5	−	22441.8i	−1.02188	−	1.12623i
$736$	8544.63	+	1463.21i	0.427934	+	0.0732806i
$737$		−	28942.3i		−	1.44654i
$738$	6226.74	−	130.615i	0.310582	−	0.00651490i
$739$			16167.7i			0.804786i	0.915467	+	0.402393i	$0.131821\pi$
$739$			16167.7i			0.804786i	−0.915467	+	0.402393i	$0.868179\pi$
$740$	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	$-0.0494017\pi$
$744$	14595.7	−	12573.0i	0.719225	−	0.619554i
$745$			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
$750$	1590.00	−	9634.81i	0.0774116	−	0.469085i
$751$	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
$756$	−2768.56	−	20601.4i	−0.133190	−	0.991091i
$757$		−	2301.88i		−	0.110519i	−0.998472	−	0.0552596i	$-0.982401\pi$
$757$		−	2301.88i		−	0.110519i	0.998472	−	0.0552596i	$-0.0175987\pi$
$758$	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	$0.681146\pi$
$762$	−827.134	−	136.499i	−0.0393227	−	0.00648931i
$763$	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
$768$	−18238.7	+	10969.7i	−0.856943	+	0.515412i
$769$		−	12312.9i		−	0.577393i	−0.957421	−	0.288697i	$-0.906778\pi$
$769$		−	12312.9i		−	0.577393i	0.957421	−	0.288697i	$-0.0932219\pi$
$770$	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	$0.856410\pi$
$774$	−386.449	−	18423.0i	−0.0179465	−	0.855557i
$775$			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
$780$	26957.3	−	48009.1i	1.23747	−	2.20385i
$781$			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
$786$	−5371.88	+	32551.5i	−0.243777	+	1.47719i
$787$	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
$792$	18040.3	+	14445.3i	0.809385	+	0.648097i
$793$	−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	$0.912035\pi$
$798$	−1155.63	−	10218.6i	−0.0512644	−	0.453299i
$799$	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
$804$	15571.3	−	27731.5i	0.683033	−	1.21644i
$805$	−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	$-0.0642497\pi$
$810$	13329.3	+	32424.6i	0.578201	+	1.40653i
$811$	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
$816$	−4091.41	−	10771.4i	−0.175525	−	0.462101i
$817$		−	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	$-0.548780\pi$
$821$	−7181.84			−0.305296			−0.152648	+	0.988281i	$0.548780\pi$
$822$	2977.77	−	18044.2i	0.126352	−	0.765648i
$823$	−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	$-0.536296\pi$
$827$	−5411.98			−0.227561			−0.113781	+	0.993506i	$0.536296\pi$
$828$	3323.64	−	9795.74i	0.139498	−	0.411142i
$829$	−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
$834$	7282.98	+	1201.89i	0.302385	+	0.0499016i
$835$			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	$0.212418\pi$
$840$	30896.3	+	20399.2i	1.26908	+	0.837902i
$841$	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
$846$	−27199.7	+	570.552i	−1.10537	+	0.0231867i
$847$	−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
$852$	−18833.6	+	33541.4i	−0.757310	+	1.34872i
$853$	−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	$-0.350116\pi$
$857$	22763.4			0.907332			0.453666	+	0.891172i	$0.350116\pi$
$858$	−42733.3	−	7052.14i	−1.70034	−	0.280602i
$859$	−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
$861$	−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	$-0.277108\pi$
$864$	9513.82	+	23547.0i	0.374614	+	0.927181i
$865$	−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
$870$	−7355.80	+	44573.4i	−0.286650	+	1.73699i
$871$			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
$876$	12026.4	−	21418.3i	0.463854	−	0.826093i
$877$		−	5911.60i		−	0.227617i	−0.993503	−	0.113809i	$-0.963695\pi$
$877$		−	5911.60i		−	0.227617i	0.993503	−	0.113809i	$-0.0363051\pi$
$878$	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	$0.490089\pi$
$882$	−22006.0	+	14208.0i	−0.840113	+	0.542412i
$883$			13348.7i			0.508743i	0.967107	+	0.254371i	$0.0818686\pi$
$883$			13348.7i			0.508743i	−0.967107	+	0.254371i	$0.918131\pi$
$884$	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	$0.267660\pi$
$888$	14224.3	−	12253.1i	0.537541	−	0.463048i
$889$	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
$894$	38733.2	+	6392.01i	1.44903	+	0.239128i
$895$		−	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
$900$	−33561.8	−	11387.3i	−1.24303	−	0.421753i
$901$	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
$906$	−22018.8	−	3633.70i	−0.807424	−	0.133247i
$907$		−	41269.7i		−	1.51085i	−0.655237	−	0.755423i	$-0.727431\pi$
$907$		−	41269.7i		−	1.51085i	0.655237	−	0.755423i	$-0.272569\pi$
$908$	−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	$-0.0694228\pi$
$912$	4461.41	+	11745.5i	0.161987	+	0.426461i
$913$			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
$918$	−13459.6	+	2805.54i	−0.483914	+	0.100868i
$919$	−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
$924$	6794.32	−	28319.6i	0.241901	−	1.00827i
$925$			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	$0.631873\pi$
$930$	40395.9	+	6666.41i	1.42434	+	0.235054i
$931$	−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
$936$	−37151.5	−	29748.2i	−1.29737	−	1.03884i
$937$			34878.2i			1.21603i	0.793925	+	0.608016i	$0.208034\pi$
$937$			34878.2i			1.21603i	−0.793925	+	0.608016i	$0.791966\pi$
$938$	−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	$-0.206107\pi$
$942$	19021.2	+	3139.00i	0.657901	+	0.108571i
$943$		−	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	$-0.778671\pi$
$947$	−44753.6			−1.53569			−0.767844	+	0.640637i	$0.778671\pi$
$948$	−1030.24	−	578.485i	−0.0352962	−	0.0198189i
$949$			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	$0.845747\pi$
$954$	−44717.8	+	938.019i	−1.51760	+	0.0318339i
$955$	−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
$960$	−42746.4	−	14792.3i	−1.43712	−	0.497313i
$961$	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
$966$	−12952.7	+	1464.84i	−0.431413	+	0.0487892i
$967$	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	$0.952134\pi$
$972$	29530.1	−	6804.51i	0.974464	−	0.224542i
$973$	−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	$0.575324\pi$
$978$	−7465.97	+	45241.0i	−0.244106	+	1.47919i
$979$	−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	$-0.620794\pi$
$983$	−22834.0			−0.740886			−0.370443	+	0.928855i	$0.620794\pi$
$984$	6258.20	+	7264.99i	0.202748	+	0.235365i
$985$		−	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
$990$	1030.09	+	49106.8i	0.0330690	+	1.57648i
$991$	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
$996$	−54.1957	+	96.5190i	−0.00172415	+	0.00307060i
$997$	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.125.76	yes	80
3.2	odd	2	inner	168.4.i.c.125.6	yes	80
4.3	odd	2		672.4.i.c.209.7		80
7.6	odd	2	inner	168.4.i.c.125.75	yes	80
8.3	odd	2		672.4.i.c.209.74		80
8.5	even	2	inner	168.4.i.c.125.7	yes	80
12.11	even	2		672.4.i.c.209.6		80
21.20	even	2	inner	168.4.i.c.125.5	✓	80
24.5	odd	2	inner	168.4.i.c.125.73	yes	80
24.11	even	2		672.4.i.c.209.75		80
28.27	even	2		672.4.i.c.209.73		80
56.13	odd	2	inner	168.4.i.c.125.8	yes	80
56.27	even	2		672.4.i.c.209.8		80
84.83	odd	2		672.4.i.c.209.76		80
168.83	odd	2		672.4.i.c.209.5		80
168.125	even	2	inner	168.4.i.c.125.74	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.5	✓	80	21.20	even	2	inner
168.4.i.c.125.6	yes	80	3.2	odd	2	inner
168.4.i.c.125.7	yes	80	8.5	even	2	inner
168.4.i.c.125.8	yes	80	56.13	odd	2	inner
168.4.i.c.125.73	yes	80	24.5	odd	2	inner
168.4.i.c.125.74	yes	80	168.125	even	2	inner
168.4.i.c.125.75	yes	80	7.6	odd	2	inner
168.4.i.c.125.76	yes	80	1.1	even	1	trivial
672.4.i.c.209.5		80	168.83	odd	2
672.4.i.c.209.6		80	12.11	even	2
672.4.i.c.209.7		80	4.3	odd	2
672.4.i.c.209.8		80	56.27	even	2
672.4.i.c.209.73		80	28.27	even	2
672.4.i.c.209.74		80	8.3	odd	2
672.4.i.c.209.75		80	24.11	even	2
672.4.i.c.209.76		80	84.83	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} +(14.5008 + 2.39302i) 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} +(36.2462 + 20.3523i) 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} +(76.3507 - 1.60157i) 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} +(76.7365 + 89.0815i) 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} +(-40.6869 + 246.547i) 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} +(204.547 + 69.4015i) 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} +(-30.5876 - 270.467i) 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} +(118.086 + 310.882i) 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} +(388.468 - 80.9730i) 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} +(-346.037 + 616.269i) 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} +(548.545 + 90.5247i) 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} +(476.895 + 381.863i) 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} +(-1129.66 - 186.423i) 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} +(179.608 - 748.629i) 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} +(27.2303 + 1298.14i) 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} +(14.0411 + 940.499i) 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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