LMFDB - Embedded newform 168.4.i.c.125.73

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			125.73
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.75

$q$-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} +(-30.6172 - 42.5040i) 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} +(8.80655 + 95.8303i) 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} +(-122.411 - 83.4717i) 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} +(115.868 + 246.298i) 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} +(-405.997 - 103.838i) 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} +(46.3807 - 497.891i) 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} +(722.666 - 520.563i) 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} +(545.687 + 543.074i) 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} +(-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	$0.274981\pi$
$5$			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	$-0.187760\pi$
$13$	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	$-0.420504\pi$
$17$	34.6479			0.494314			0.247157	+	0.968975i	$0.420504\pi$
$18$	76.3507	+	1.60157i	0.999780	+	0.0209718i
$19$	−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
$21$	8.80655	+	95.8303i	0.0915117	+	0.995804i
$22$	100.579	−	36.4954i	0.974705	−	0.353674i
$23$			47.8900i			0.434163i	0.976153	+	0.217081i	$0.0696537\pi$
$23$			47.8900i			0.434163i	−0.976153	+	0.217081i	$0.930346\pi$
$24$	−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
$28$	−122.411	−	83.4717i	−0.826197	−	0.563381i
$29$	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	$0.115431\pi$
$37$			159.677i			0.709481i	−0.934965	+	0.354741i	$0.884569\pi$
$38$	−100.453	+	36.4496i	−0.428831	+	0.155603i
$39$	−397.923	−	74.2721i	−1.63381	−	0.304950i
$40$	332.605	+	193.345i	1.31474	+	0.764263i
$41$	−81.5544			−0.310650			−0.155325	−	0.987863i	$-0.549642\pi$
$41$	−81.5544			−0.310650			−0.155325	+	0.987863i	$0.549642\pi$
$42$	115.868	+	246.298i	0.425685	+	0.904871i
$43$			241.294i			0.855745i	0.903839	+	0.427873i	$0.140737\pi$
$43$			241.294i			0.855745i	−0.903839	+	0.427873i	$0.859263\pi$
$44$	232.211	−	194.068i	0.795616	−	0.664929i
$45$	−165.598	+	428.154i	−0.548577	+	1.41834i
$46$	46.2021	+	127.330i	0.148090	+	0.408126i
$47$	356.246			1.10561			0.552807	−	0.833309i	$-0.313557\pi$
$47$	356.246			1.10561			0.552807	+	0.833309i	$0.313557\pi$
$48$	−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
$56$	−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	$0.0609848\pi$
$59$			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	$-0.705348\pi$
$61$	−572.943			−1.20259			−0.601294	+	0.799028i	$0.705348\pi$
$62$	−158.072	−	435.636i	−0.323792	−	0.892351i
$63$	46.3807	−	497.891i	0.0927527	−	0.995689i
$64$	−253.370	−	444.913i	−0.494862	−	0.868971i
$65$			1324.53i			2.52750i
$66$	−548.545	+	90.5247i	−1.02305	+	0.168831i
$67$			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	$-0.718556\pi$
$71$		−	925.379i		−	1.54679i	0.633923	−	0.773396i	$-0.281444\pi$
$72$	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	$0.999440\pi$
$84$	545.687	+	543.074i	0.708801	+	0.705408i
$85$			589.094i			0.751721i
$86$	232.790	+	641.555i	0.291888	+	0.804426i
$87$	−923.466	−	172.364i	−1.13800	−	0.212407i
$88$	430.175	−	740.016i	0.521100	−	0.896431i
$89$	600.037			0.714649			0.357324	−	0.933980i	$-0.383689\pi$
$89$	600.037			0.714649			0.357324	+	0.933980i	$0.383689\pi$
$90$	−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	$0.879960\pi$
$98$	−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	$-0.834737\pi$
$101$		−	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
$105$	−1629.34	+	149.732i	−1.51435	+	0.139165i
$106$	−1557.23	+	565.047i	−1.42690	+	0.517756i
$107$	−1132.06			−1.02281			−0.511405	−	0.859340i	$-0.670875\pi$
$107$	−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	$-0.598300\pi$
$109$		−	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	$0.00565961\pi$
$113$			42.7131i			0.0355585i	−0.999842	+	0.0177793i	$0.994340\pi$
$114$	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
$126$	−357.026	−	1368.54i	−0.252432	−	0.967615i
$127$	−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	$0.126835\pi$
$137$			1244.36i			0.776003i	−0.921659	+	0.388002i	$0.873165\pi$
$138$	−114.602	−	694.443i	−0.0706924	−	0.428369i
$139$	−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
$144$	899.567	−	1475.39i	0.520583	−	0.853811i
$145$			3073.86i			1.76048i
$146$	−570.086	−	1571.12i	−0.323155	−	0.890596i
$147$	1663.08	−	640.853i	0.933119	−	0.359569i
$148$	819.176	+	980.179i	0.454972	+	0.544393i
$149$	2671.10			1.46863			0.734313	−	0.678811i	$-0.237504\pi$
$149$	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
$154$	−1158.21	−	1607.87i	−0.606045	−	0.841335i
$155$	2785.77			1.44360
$156$	−2823.68	+	1585.50i	−1.44920	+	0.813730i
$157$	−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
$162$	1907.07	+	783.968i	0.924899	+	0.380212i
$163$		−	3119.89i		−	1.49920i	−0.661894	−	0.749598i	$-0.730247\pi$
$163$		−	3119.89i		−	1.49920i	0.661894	−	0.749598i	$-0.269753\pi$
$164$	−500.621	+	418.390i	−0.238366	+	0.199212i
$165$	613.198	−	3285.29i	0.289318	−	1.55006i
$166$	2.56902	+	7.08007i	0.00120117	+	0.00331036i
$167$	−3622.79			−1.67868			−0.839342	−	0.543604i	$-0.817059\pi$
$167$	−3622.79			−1.67868			−0.839342	+	0.543604i	$0.817059\pi$
$168$	1974.81	+	917.475i	0.906904	+	0.421338i
$169$	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	$-0.660037\pi$
$181$	−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
$186$	392.088	+	2375.91i	0.154566	+	0.936612i
$187$	1310.68			0.512548
$188$	2186.82	−	1827.61i	0.848351	−	0.709002i
$189$	−711.596	+	2498.98i	−0.273868	+	0.961767i
$190$	−619.727	−	1707.93i	−0.236630	−	0.652138i
$191$		−	2129.66i		−	0.806791i	−0.915026	−	0.403395i	$-0.867830\pi$
$191$		−	2129.66i		−	0.806791i	0.915026	−	0.403395i	$-0.132170\pi$
$192$	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
$196$	−869.177	+	2602.70i	−0.316755	+	0.948507i
$197$	−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
$210$	−4187.64	+	1970.02i	−1.37607	+	0.647354i
$211$		−	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
$216$	−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	$0.931105\pi$
$224$	−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	$0.262735\pi$
$227$			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	$-0.277205\pi$
$229$	4464.57			1.28833			0.644164	+	0.764887i	$0.277205\pi$
$230$	−2164.91	+	785.543i	−0.620651	+	0.225205i
$231$	333.139	+	3625.13i	0.0948873	+	1.03254i
$232$	2055.89	−	3536.68i	0.581792	−	1.00084i
$233$		−	2131.34i		−	0.599265i	−0.954055	−	0.299632i	$-0.903136\pi$
$233$		−	2131.34i		−	0.599265i	0.954055	−	0.299632i	$-0.0968641\pi$
$234$	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
$238$	−1060.82	−	1472.67i	−0.288919	−	0.401089i
$239$			6763.79i			1.83060i	0.402774	+	0.915299i	$0.368046\pi$
$239$			6763.79i			1.83060i	−0.402774	+	0.915299i	$0.631954\pi$
$240$	−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	$0.758972\pi$
$252$	−2269.57	−	3294.25i	−0.567339	−	0.823484i
$253$			1811.61i			0.450178i
$254$	−151.660	+	55.0302i	−0.0374645	+	0.0135941i
$255$	561.639	−	3009.06i	0.137926	−	0.738959i
$256$	−3837.80	−	1431.26i	−0.936963	−	0.349430i
$257$	6828.16			1.65731			0.828655	−	0.559760i	$-0.189107\pi$
$257$	6828.16			1.65731			0.828655	+	0.559760i	$0.189107\pi$
$258$	−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	$0.0248476\pi$
$263$			665.207i			0.155964i	−0.996955	+	0.0779818i	$0.975152\pi$
$264$	−2902.83	+	3369.83i	−0.676731	+	0.785601i
$265$		−	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	$-0.814418\pi$
$269$		−	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
$273$	686.056	+	7465.46i	0.152095	+	1.65506i
$274$	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	$0.231034\pi$
$277$			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	$0.0196261\pi$
$281$			580.494i			0.123236i	−0.998100	+	0.0616181i	$0.980374\pi$
$282$	−5165.86	+	852.506i	−1.09086	+	0.180021i
$283$	−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
$288$	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	$0.983414\pi$
$294$	3803.54	−	3308.37i	0.754513	−	0.656285i
$295$	−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	$-0.762850\pi$
$307$	−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	$-0.457528\pi$
$311$	1459.26			0.266068			0.133034	+	0.991111i	$0.457528\pi$
$312$	−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
$315$	8465.31	+	788.579i	1.51418	+	0.141052i
$316$	−174.478	+	145.818i	−0.0310606	+	0.0259586i
$317$	7991.76			1.41597			0.707984	−	0.706228i	$-0.249605\pi$
$317$	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
$322$	2035.51	−	1466.26i	0.352282	−	0.253762i
$323$	−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	$0.163355\pi$
$331$			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
$336$	6135.77	+	534.181i	0.996232	+	0.0867321i
$337$	−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	$-0.388038\pi$
$349$	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	$-0.467012\pi$
$353$	1372.22			0.206901			0.103451	+	0.994635i	$0.467012\pi$
$354$	−413.015	−	2502.71i	−0.0620099	−	0.375756i
$355$	15733.6			2.35226
$356$	3683.32	−	3078.30i	0.548359	−	0.458286i
$357$	305.128	+	3320.32i	0.0452355	+	0.492240i
$358$	−3534.00	+	1282.32i	−0.521725	+	0.189310i
$359$			5118.09i			0.752430i	0.926532	+	0.376215i	$0.122775\pi$
$359$			5118.09i			0.752430i	−0.926532	+	0.376215i	$0.877225\pi$
$360$	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
$364$	−9536.18	−	6502.69i	−1.37316	−	0.936356i
$365$	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	$-0.649152\pi$
$373$		−	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
$378$	518.908	+	7330.82i	0.0706078	+	0.997504i
$379$			2284.79i			0.309662i	0.987941	+	0.154831i	$0.0494832\pi$
$379$			2284.79i			0.309662i	−0.987941	+	0.154831i	$0.950517\pi$
$380$	−3295.47	−	3943.17i	−0.444879	−	0.532316i
$381$	291.360	+	54.3821i	0.0391780	+	0.00731255i
$382$	−2054.60	−	5662.36i	−0.275190	−	0.758407i
$383$	3061.90			0.408501			0.204251	−	0.978919i	$-0.434524\pi$
$383$	3061.90			0.408501			0.204251	+	0.978919i	$0.434524\pi$
$384$	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
$392$	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
$396$	7737.73	−	2625.36i	0.981907	−	0.333155i
$397$	−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
$399$	−332.721	−	3620.58i	−0.0417466	−	0.454275i
$400$	−1864.30	+	10334.2i	−0.233038	+	1.29178i
$401$			7728.45i			0.962444i	0.876599	+	0.481222i	$0.159807\pi$
$401$			7728.45i			0.962444i	−0.876599	+	0.481222i	$0.840193\pi$
$402$	−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
$406$	−5535.29	−	7684.31i	−0.676630	−	0.939325i
$407$			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	$-0.164283\pi$
$420$	−9233.53	+	9277.94i	−1.07274	+	1.07790i
$421$			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
$426$	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	$-0.879321\pi$
$431$		−	6623.29i		−	0.740215i	0.928989	−	0.370108i	$-0.120679\pi$
$432$	−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	$-0.00268369\pi$
$434$	−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
$438$	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
$441$	−9105.89	+	1687.87i	−0.983251	+	0.182255i
$442$	7176.57	−	2604.04i	0.772296	−	0.280230i
$443$	−2207.57			−0.236760			−0.118380	−	0.992968i	$-0.537770\pi$
$443$	−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
$448$	−6648.19	+	6761.43i	−0.701111	+	0.713053i
$449$			7960.02i			0.836651i	0.908297	+	0.418326i	$0.137383\pi$
$449$			7960.02i			0.836651i	−0.908297	+	0.418326i	$0.862617\pi$
$450$	−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	$0.903916\pi$
$462$	4383.11	+	9317.11i	0.441387	+	0.938249i
$463$	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
$476$	−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	$-0.587376\pi$
$479$	−5683.40			−0.542132			−0.271066	+	0.962561i	$0.587376\pi$
$480$	−15990.7	−	238.732i	−1.52056	−	0.0227012i
$481$			12439.3i			1.17918i
$482$	2625.84	+	7236.67i	0.248141	+	0.683861i
$483$	−4589.31	+	421.745i	−0.432341	+	0.0397310i
$484$	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
$490$	−12925.0	−	10248.0i	−1.19162	−	0.944814i
$491$	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	$-0.843424\pi$
$499$		−	10529.3i		−	0.944599i	0.881438	−	0.472300i	$-0.156576\pi$
$500$	−3408.67	−	4078.62i	−0.304881	−	0.364803i
$501$	18505.0	+	3453.95i	1.65019	+	0.308006i
$502$	5270.48	+	14525.1i	0.468592	+	1.29141i
$503$	1886.42			0.167220			0.0836098	−	0.996499i	$-0.473355\pi$
$503$	1886.42			0.167220			0.0836098	+	0.996499i	$0.473355\pi$
$504$	−9212.49	−	6569.18i	−0.814200	−	0.580584i
$505$	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
$518$	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	$-0.594117\pi$
$521$	−6930.38			−0.582774			−0.291387	+	0.956605i	$0.594117\pi$
$522$	13803.5	+	289.548i	1.15740	+	0.0242781i
$523$	−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
$525$	−1444.97	−	15723.7i	−0.120121	−	1.30712i
$526$	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
$532$	4624.83	+	3153.66i	0.376902	+	0.257008i
$533$	−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	$-0.983207\pi$
$541$		−	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
$546$	9026.43	+	19187.3i	0.707501	+	1.50392i
$547$		−	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
$552$	−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
$560$	−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	$0.133101\pi$
$563$			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
$567$	6017.30	−	12086.2i	0.445684	−	0.895190i
$568$	−18102.6	−	10523.1i	−1.33727	−	0.777359i
$569$		−	10335.0i		−	0.761450i	−0.924688	−	0.380725i	$-0.875674\pi$
$569$		−	10335.0i		−	0.761450i	0.924688	−	0.380725i	$-0.124326\pi$
$570$	1537.20	+	9314.84i	0.112958	+	0.684484i
$571$		−	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
$576$	−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	$0.979678\pi$
$588$	6921.10	−	12465.8i	0.485411	−	0.874286i
$589$			6190.30i			0.433051i
$590$	−7802.14	+	2831.03i	−0.544422	+	0.197545i
$591$	17394.5	+	3246.67i	1.21068	+	0.225973i
$592$	10057.0	+	1814.29i	0.698211	+	0.125958i
$593$	−9793.33			−0.678185			−0.339093	−	0.940753i	$-0.610120\pi$
$593$	−9793.33			−0.678185			−0.339093	+	0.940753i	$0.610120\pi$
$594$	−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	$-0.879643\pi$
$599$		−	10824.1i		−	0.738332i	0.929363	−	0.369166i	$-0.120357\pi$
$600$	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	$-0.189335\pi$
$602$	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
$606$	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
$609$	1592.14	+	17325.2i	0.105939	+	1.15279i
$610$	−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	$-0.882897\pi$
$613$		−	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	$0.346457\pi$
$617$			27154.5i			1.77180i	−0.463881	+	0.885898i	$0.653543\pi$
$618$	−656.439	−	3977.77i	−0.0427279	−	0.258915i
$619$	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
$624$	−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
$630$	23268.4	−	6070.27i	1.47148	−	0.383882i
$631$	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	$-0.783247\pi$
$641$		−	20433.1i		−	1.25906i	0.776975	−	0.629531i	$-0.216753\pi$
$642$	16415.8	−	2709.05i	1.00916	−	0.166538i
$643$	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	$-0.367713\pi$
$647$	13288.6			0.807463			0.403732	+	0.914877i	$0.367713\pi$
$648$	15728.5	−	4971.26i	0.953506	−	0.301373i
$649$			6528.89i			0.394887i
$650$	−33985.5	+	12331.7i	−2.05080	+	0.744138i
$651$	15701.4	−	1442.92i	0.945297	−	0.0868702i
$652$	−16005.7	−	19151.4i	−0.961395	−	1.15035i
$653$	6596.26			0.395301			0.197651	−	0.980273i	$-0.436669\pi$
$653$	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
$658$	−10907.3	−	15141.9i	−0.646215	−	0.897101i
$659$	−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	$-0.558309\pi$
$661$	−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
$666$	−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
$672$	16829.2	−	4499.23i	0.966071	−	0.258276i
$673$	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
$686$	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
$690$	11807.1	−	1948.50i	0.651435	−	0.107504i
$691$	−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
$693$	1754.52	−	18834.5i	0.0961740	−	1.03242i
$694$	−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
$700$	20085.1	+	13696.0i	1.08449	+	0.739512i
$701$	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	$0.185853\pi$
$709$			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
$714$	4014.57	+	8533.70i	0.210422	+	0.447291i
$715$			50105.2i			2.62074i
$716$	−8159.09	+	6818.89i	−0.425865	+	0.355913i
$717$	6448.55	−	34549.0i	0.335880	−	1.79952i
$718$	4937.70	+	13608.0i	0.256648	+	0.707306i
$719$	5088.93			0.263957			0.131979	−	0.991253i	$-0.457867\pi$
$719$	5088.93			0.263957			0.131979	+	0.991253i	$0.457867\pi$
$720$	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	$-0.0139402\pi$
$728$	−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
$732$	20767.0	−	11660.7i	1.04859	−	0.588788i
$733$	−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
$735$	10896.0	+	28276.2i	0.546809	+	1.41902i
$736$	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	$-0.868179\pi$
$739$		−	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	$0.0494017\pi$
$743$			6261.24i			0.309156i	−0.987981	+	0.154578i	$0.950598\pi$
$744$	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
$756$	8452.12	+	18990.6i	0.406615	+	0.913600i
$757$			2301.88i			0.110519i	0.998472	+	0.0552596i	$0.0175987\pi$
$757$			2301.88i			0.110519i	−0.998472	+	0.0552596i	$0.982401\pi$
$758$	2204.26	+	6074.81i	0.105623	+	0.291091i
$759$	1727.18	−	9253.60i	0.0825989	−	0.442535i
$760$	−12566.2	−	7304.80i	−0.599768	−	0.348648i
$761$	22624.8			1.07772			0.538862	−	0.842394i	$-0.318854\pi$
$761$	22624.8			1.07772			0.538862	+	0.842394i	$0.318854\pi$
$762$	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	$-0.0932219\pi$
$770$	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	$0.143590\pi$
$773$			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
$777$	−15301.9	+	1406.21i	−0.706504	+	0.0649258i
$778$	−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
$784$	8016.94	+	20435.7i	0.365203	+	0.930928i
$785$		−	22302.5i		−	1.01403i
$786$	−5371.88	−	32551.5i	−0.243777	−	1.47719i
$787$	−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
$792$	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	$0.912035\pi$
$798$	−4377.61	−	9305.42i	−0.194193	−	0.412792i
$799$	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	$0.0642497\pi$
$809$			9226.15i			0.400957i	−0.979698	+	0.200479i	$0.935750\pi$
$810$	−13329.3	+	32424.6i	−0.578201	+	1.40653i
$811$	−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
$816$	−4091.41	+	10771.4i	−0.175525	+	0.462101i
$817$		−	9116.38i		−	0.390381i
$818$	−12826.3	−	35348.6i	−0.548243	−	1.51092i
$819$	3613.19	−	38787.2i	0.154158	−	1.65486i
$820$	−7113.60	−	8511.72i	−0.302948	−	0.362491i
$821$	−7181.84			−0.305296			−0.152648	−	0.988281i	$-0.548780\pi$
$821$	−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
$826$	7335.82	−	5284.26i	0.309014	−	0.222594i
$827$	−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	$-0.303520\pi$
$829$	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
$834$	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	$-0.787582\pi$
$839$	−38177.4			−1.57095			−0.785476	+	0.618892i	$0.787582\pi$
$840$	−15599.2	+	33576.3i	−0.640743	+	1.37916i
$841$	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	$-0.464472\pi$
$853$	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	$-0.649884\pi$
$857$	−22763.4			−0.907332			−0.453666	+	0.891172i	$0.649884\pi$
$858$	−42733.3	+	7052.14i	−1.70034	+	0.280602i
$859$	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
$861$	−718.212	−	7815.38i	−0.0284281	−	0.309347i
$862$	−6389.86	−	17610.0i	−0.252482	−	0.695824i
$863$			38773.2i			1.52938i	0.644397	+	0.764691i	$0.277108\pi$
$863$			38773.2i			1.52938i	−0.644397	+	0.764691i	$0.722892\pi$
$864$	−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
$868$	−13676.5	+	20056.6i	−0.534807	+	0.784292i
$869$	−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	$0.0363051\pi$
$877$			5911.60i			0.227617i	−0.993503	+	0.113809i	$0.963695\pi$
$878$	−9482.03	−	26131.9i	−0.364468	−	1.00445i
$879$	498.085	−	2668.56i	0.0191126	−	0.102399i
$880$	40509.3	+	7307.90i	1.55178	+	0.279942i
$881$	−1628.16			−0.0622635			−0.0311317	−	0.999515i	$-0.509911\pi$
$881$	−1628.16			−0.0622635			−0.0311317	+	0.999515i	$0.509911\pi$
$882$	−22582.4	+	13272.7i	−0.862119	+	0.506705i
$883$		−	13348.7i		−	0.508743i	−0.967107	−	0.254371i	$-0.918131\pi$
$883$		−	13348.7i		−	0.508743i	0.967107	−	0.254371i	$-0.0818686\pi$
$884$	16568.8	−	13847.3i	0.630397	−	0.526848i
$885$	14989.0	+	2797.69i	0.569322	+	0.106264i
$886$	−5869.50	+	2129.76i	−0.222562	+	0.0807571i
$887$	−35230.3			−1.33362			−0.666808	−	0.745230i	$-0.732340\pi$
$887$	−35230.3			−1.33362			−0.666808	+	0.745230i	$0.732340\pi$
$888$	−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
$896$	−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
$900$	−33561.8	+	11387.3i	−1.24303	+	0.421753i
$901$	−20292.9			−0.750337
$902$	−8202.65	+	2976.36i	−0.302792	+	0.109869i
$903$	−23123.3	+	2124.97i	−0.852154	+	0.0783107i
$904$	835.568	+	485.720i	0.0307418	+	0.0178704i
$905$		−	39899.9i		−	1.46554i
$906$	22018.8	−	3633.70i	0.807424	−	0.133247i
$907$			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	$0.0694228\pi$
$911$			11899.0i			0.432747i	−0.976311	+	0.216373i	$0.930577\pi$
$912$	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
$924$	20642.6	+	20543.8i	0.734947	+	0.731428i
$925$		−	26199.7i		−	0.931287i
$926$	36841.0	−	13367.9i	1.30742	−	0.474401i
$927$	−2671.75	+	6907.80i	−0.0946621	+	0.244748i
$928$	−5523.78	−	32257.0i	−0.195395	−	1.14104i
$929$	22796.3			0.805083			0.402542	−	0.915402i	$-0.368127\pi$
$929$	22796.3			0.805083			0.402542	+	0.915402i	$0.368127\pi$
$930$	−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	$0.791966\pi$
$938$	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	$-0.793893\pi$
$941$		−	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
$945$	−42488.5	−	12098.8i	−1.46259	−	0.416480i
$946$	8806.12	+	24269.1i	0.302655	+	0.834099i
$947$	−44753.6			−1.53569			−0.767844	−	0.640637i	$-0.778671\pi$
$947$	−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
$952$	−14066.9	−	3597.78i	−0.478899	−	0.122484i
$953$		−	27410.7i		−	0.931709i	−0.884861	−	0.465854i	$-0.845747\pi$
$953$		−	27410.7i		−	0.931709i	0.884861	−	0.465854i	$-0.154253\pi$
$954$	−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
$966$	−11795.2	+	5548.90i	−0.392862	+	0.184817i
$967$	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	$-0.575324\pi$
$977$		−	59374.1i		−	1.94426i	0.234435	−	0.972132i	$-0.424676\pi$
$978$	7465.97	+	45241.0i	0.244106	+	1.47919i
$979$	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	$-0.379206\pi$
$983$	22834.0			0.740886			0.370443	+	0.928855i	$0.379206\pi$
$984$	6258.20	−	7264.99i	0.202748	−	0.235365i
$985$		−	57899.4i		−	1.87292i
$986$	16654.8	−	6043.23i	0.537927	−	0.195188i
$987$	3137.30	+	34139.2i	0.101177	+	1.10098i
$988$	−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
$994$	−39332.3	+	28332.5i	−1.25507	+	0.904077i
$995$	44269.4			1.41049
$996$	−54.1957	−	96.5190i	−0.00172415	−	0.00307060i
$997$	−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.125.73	yes	80
3.2	odd	2	inner	168.4.i.c.125.7	yes	80
4.3	odd	2		672.4.i.c.209.75		80
7.6	odd	2	inner	168.4.i.c.125.74	yes	80
8.3	odd	2		672.4.i.c.209.6		80
8.5	even	2	inner	168.4.i.c.125.6	yes	80
12.11	even	2		672.4.i.c.209.74		80
21.20	even	2	inner	168.4.i.c.125.8	yes	80
24.5	odd	2	inner	168.4.i.c.125.76	yes	80
24.11	even	2		672.4.i.c.209.7		80
28.27	even	2		672.4.i.c.209.5		80
56.13	odd	2	inner	168.4.i.c.125.5	✓	80
56.27	even	2		672.4.i.c.209.76		80
84.83	odd	2		672.4.i.c.209.8		80
168.83	odd	2		672.4.i.c.209.73		80
168.125	even	2	inner	168.4.i.c.125.75	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.65881 - 0.964755i) q^{2} +(-5.10794 - 0.953394i) q^{3} +(6.13849 - 5.13019i) q^{4} +17.0023i q^{5} +(-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} +(-30.6172 - 42.5040i) 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} +(8.80655 + 95.8303i) 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} +(-122.411 - 83.4717i) 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} +(115.868 + 246.298i) 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} +(-405.997 - 103.838i) 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} +(46.3807 - 497.891i) 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} +(722.666 - 520.563i) 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} +(545.687 + 543.074i) 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} +(-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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