LMFDB - Embedded newform 168.4.i.c.125.15

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			125.15
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.39518 + 1.50436i) q^{2} +(-4.72061 - 2.17161i) q^{3} +(3.47378 - 7.20645i) q^{4} +2.27823i q^{5} +(14.5736 - 1.90012i) q^{6} +(-13.7109 + 12.4503i) q^{7} +(2.52080 + 22.4866i) q^{8} +(17.5682 + 20.5026i) q^{9} +(-3.42729 - 5.45677i) q^{10} +33.8293 q^{11} +(-32.0479 + 26.4751i) q^{12} -41.0309 q^{13} +(14.1103 - 50.4470i) q^{14} +(4.94743 - 10.7546i) q^{15} +(-39.8658 - 50.0672i) q^{16} +28.4181 q^{17} +(-72.9225 - 22.6785i) q^{18} -109.654 q^{19} +(16.4180 + 7.91406i) q^{20} +(91.7611 - 28.9983i) q^{21} +(-81.0273 + 50.8916i) q^{22} -142.918i q^{23} +(36.9323 - 111.624i) q^{24} +119.810 q^{25} +(98.2764 - 61.7254i) q^{26} +(-38.4090 - 134.936i) q^{27} +(42.0940 + 142.057i) q^{28} +147.654 q^{29} +(4.32890 + 33.2020i) q^{30} -293.446i q^{31} +(170.805 + 59.9472i) q^{32} +(-159.695 - 73.4640i) q^{33} +(-68.0665 + 42.7512i) q^{34} +(-28.3647 - 31.2366i) q^{35} +(208.779 - 55.3830i) q^{36} -162.028i q^{37} +(262.642 - 164.960i) q^{38} +(193.691 + 89.1031i) q^{39} +(-51.2296 + 5.74297i) q^{40} +144.009 q^{41} +(-176.160 + 207.498i) q^{42} +71.1121i q^{43} +(117.515 - 243.789i) q^{44} +(-46.7097 + 40.0245i) q^{45} +(215.000 + 342.314i) q^{46} -367.170 q^{47} +(79.4642 + 322.920i) q^{48} +(32.9788 - 341.411i) q^{49} +(-286.966 + 180.237i) q^{50} +(-134.151 - 61.7130i) q^{51} +(-142.532 + 295.687i) q^{52} -508.040 q^{53} +(294.989 + 265.415i) q^{54} +77.0710i q^{55} +(-314.528 - 276.927i) q^{56} +(517.635 + 238.127i) q^{57} +(-353.658 + 222.125i) q^{58} -202.128i q^{59} +(-60.3164 - 73.0125i) q^{60} +363.737 q^{61} +(441.449 + 702.855i) q^{62} +(-496.141 - 62.3797i) q^{63} +(-499.291 + 113.368i) q^{64} -93.4779i q^{65} +(493.014 - 64.2796i) q^{66} -531.804i q^{67} +(98.7182 - 204.794i) q^{68} +(-310.362 + 674.659i) q^{69} +(114.930 + 32.1465i) q^{70} -796.705i q^{71} +(-416.747 + 446.732i) q^{72} -510.267i q^{73} +(243.749 + 388.087i) q^{74} +(-565.574 - 260.180i) q^{75} +(-380.915 + 790.219i) q^{76} +(-463.831 + 421.186i) q^{77} +(-597.968 + 77.9635i) q^{78} -38.1516 q^{79} +(114.065 - 90.8234i) q^{80} +(-111.715 + 720.389i) q^{81} +(-344.927 + 216.641i) q^{82} +973.913i q^{83} +(109.783 - 762.005i) q^{84} +64.7430i q^{85} +(-106.978 - 170.326i) q^{86} +(-697.016 - 320.647i) q^{87} +(85.2770 + 760.705i) q^{88} +1638.53 q^{89} +(51.6668 - 166.134i) q^{90} +(562.572 - 510.848i) q^{91} +(-1029.93 - 496.464i) q^{92} +(-637.249 + 1385.24i) q^{93} +(879.438 - 552.357i) q^{94} -249.818i q^{95} +(-676.121 - 653.909i) q^{96} +133.473i q^{97} +(434.616 + 867.353i) q^{98} +(594.321 + 693.589i) 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 $

$2$	−2.39518	+	1.50436i	−0.846824	+	0.531873i
$2$	−2.39518	+	1.50436i	−0.846824	+	0.531873i
$3$	−4.72061	−	2.17161i	−0.908481	−	0.417926i
$3$	−4.72061	−	2.17161i	−0.908481	−	0.417926i
$4$	3.47378	−	7.20645i	0.434222	−	0.900806i
$5$			2.27823i			0.203771i	0.994796	+	0.101886i	$0.0324876\pi$
$5$			2.27823i			0.203771i	−0.994796	+	0.101886i	$0.967512\pi$
$6$	14.5736	−	1.90012i	0.991607	−	0.129286i
$7$	−13.7109	+	12.4503i	−0.740320	+	0.672254i
$7$	−13.7109	+	12.4503i	−0.740320	+	0.672254i
$8$	2.52080	+	22.4866i	0.111405	+	0.993775i
$9$	17.5682	+	20.5026i	0.650675	+	0.759356i
$10$	−3.42729	−	5.45677i	−0.108380	−	0.172558i
$11$	33.8293			0.927265			0.463633	−	0.886028i	$-0.346546\pi$
$11$	33.8293			0.927265			0.463633	+	0.886028i	$0.346546\pi$
$12$	−32.0479	+	26.4751i	−0.770953	+	0.636892i
$13$	−41.0309			−0.875379			−0.437689	−	0.899126i	$-0.644203\pi$
$13$	−41.0309			−0.875379			−0.437689	+	0.899126i	$0.644203\pi$
$14$	14.1103	−	50.4470i	0.269367	−	0.963038i
$15$	4.94743	−	10.7546i	0.0851614	−	0.185122i
$16$	−39.8658	−	50.0672i	−0.622903	−	0.782299i
$17$	28.4181			0.405436			0.202718	−	0.979237i	$-0.435023\pi$
$17$	28.4181			0.405436			0.202718	+	0.979237i	$0.435023\pi$
$18$	−72.9225	−	22.6785i	−0.954888	−	0.296965i
$19$	−109.654			−1.32402			−0.662012	−	0.749493i	$-0.730297\pi$
$19$	−109.654			−1.32402			−0.662012	+	0.749493i	$0.730297\pi$
$20$	16.4180	+	7.91406i	0.183558	+	0.0884819i
$21$	91.7611	−	28.9983i	0.953520	−	0.301331i
$22$	−81.0273	+	50.8916i	−0.785231	+	0.493188i
$23$		−	142.918i		−	1.29567i	−0.761780	−	0.647835i	$-0.775674\pi$
$23$		−	142.918i		−	1.29567i	0.761780	−	0.647835i	$-0.224326\pi$
$24$	36.9323	−	111.624i	0.314116	−	0.949385i
$25$	119.810			0.958477
$26$	98.2764	−	61.7254i	0.741292	−	0.465591i
$27$	−38.4090	−	134.936i	−0.273771	−	0.961795i
$28$	42.0940	+	142.057i	0.284107	+	0.958792i
$29$	147.654			0.945471			0.472735	−	0.881204i	$-0.343267\pi$
$29$	147.654			0.945471			0.472735	+	0.881204i	$0.343267\pi$
$30$	4.32890	+	33.2020i	0.0263449	+	0.202061i
$31$		−	293.446i		−	1.70014i	−0.526669	−	0.850071i	$-0.676559\pi$
$31$		−	293.446i		−	1.70014i	0.526669	−	0.850071i	$-0.323441\pi$
$32$	170.805	+	59.9472i	0.943573	+	0.331165i
$33$	−159.695	−	73.4640i	−0.842403	−	0.387529i
$34$	−68.0665	+	42.7512i	−0.343333	+	0.215640i
$35$	−28.3647	−	31.2366i	−0.136986	−	0.150856i
$36$	208.779	−	55.3830i	0.966570	−	0.256403i
$37$		−	162.028i		−	0.719926i	−0.932967	−	0.359963i	$-0.882789\pi$
$37$		−	162.028i		−	0.719926i	0.932967	−	0.359963i	$-0.117211\pi$
$38$	262.642	−	164.960i	1.12122	−	0.704213i
$39$	193.691	+	89.1031i	0.795265	+	0.365844i
$40$	−51.2296	+	5.74297i	−0.202503	+	0.0227011i
$41$	144.009			0.548545			0.274273	−	0.961652i	$-0.411563\pi$
$41$	144.009			0.548545			0.274273	+	0.961652i	$0.411563\pi$
$42$	−176.160	+	207.498i	−0.647194	+	0.762326i
$43$			71.1121i			0.252197i	0.992018	+	0.126099i	$0.0402456\pi$
$43$			71.1121i			0.252197i	−0.992018	+	0.126099i	$0.959754\pi$
$44$	117.515	−	243.789i	0.402639	−	0.835286i
$45$	−46.7097	+	40.0245i	−0.154735	+	0.132589i
$46$	215.000	+	342.314i	0.689132	+	1.09721i
$47$	−367.170			−1.13951			−0.569757	−	0.821813i	$-0.692963\pi$
$47$	−367.170			−1.13951			−0.569757	+	0.821813i	$0.692963\pi$
$48$	79.4642	+	322.920i	0.238952	+	0.971031i
$49$	32.9788	−	341.411i	0.0961480	−	0.995367i
$50$	−286.966	+	180.237i	−0.811662	+	0.509788i
$51$	−134.151	−	61.7130i	−0.368331	−	0.169442i
$52$	−142.532	+	295.687i	−0.380109	+	0.788547i
$53$	−508.040			−1.31669			−0.658345	−	0.752716i	$-0.728743\pi$
$53$	−508.040			−1.31669			−0.658345	+	0.752716i	$0.728743\pi$
$54$	294.989	+	265.415i	0.743389	+	0.668860i
$55$			77.0710i			0.188950i
$56$	−314.528	−	276.927i	−0.750545	−	0.660819i
$57$	517.635	+	238.127i	1.20285	+	0.553345i
$58$	−353.658	+	222.125i	−0.800647	+	0.502870i
$59$		−	202.128i		−	0.446013i	−0.974817	−	0.223007i	$-0.928413\pi$
$59$		−	202.128i		−	0.446013i	0.974817	−	0.223007i	$-0.0715872\pi$
$60$	−60.3164	−	73.0125i	−0.129780	−	0.157098i
$61$	363.737			0.763472			0.381736	−	0.924271i	$-0.375326\pi$
$61$	363.737			0.763472			0.381736	+	0.924271i	$0.375326\pi$
$62$	441.449	+	702.855i	0.904260	+	1.43972i
$63$	−496.141	−	62.3797i	−0.992189	−	0.124748i
$64$	−499.291	+	113.368i	−0.975178	+	0.221423i
$65$		−	93.4779i		−	0.178377i
$66$	493.014	−	64.2796i	0.919483	−	0.119883i
$67$		−	531.804i		−	0.969705i	−0.874596	−	0.484852i	$-0.838873\pi$
$67$		−	531.804i		−	0.969705i	0.874596	−	0.484852i	$-0.161127\pi$
$68$	98.7182	−	204.794i	0.176049	−	0.365219i
$69$	−310.362	+	674.659i	−0.541495	+	1.17709i
$70$	114.930	+	32.1465i	0.196239	+	0.0548892i
$71$		−	796.705i		−	1.33171i	−0.746081	−	0.665855i	$-0.768067\pi$
$71$		−	796.705i		−	1.33171i	0.746081	−	0.665855i	$-0.231933\pi$
$72$	−416.747	+	446.732i	−0.682141	+	0.731221i
$73$		−	510.267i		−	0.818114i	−0.912509	−	0.409057i	$-0.865858\pi$
$73$		−	510.267i		−	0.818114i	0.912509	−	0.409057i	$-0.134142\pi$
$74$	243.749	+	388.087i	0.382909	+	0.609651i
$75$	−565.574	−	260.180i	−0.870758	−	0.400573i
$76$	−380.915	+	790.219i	−0.574920	+	1.19269i
$77$	−463.831	+	421.186i	−0.686473	+	0.623358i
$78$	−597.968	+	77.9635i	−0.868032	+	0.113175i
$79$	−38.1516			−0.0543340			−0.0271670	−	0.999631i	$-0.508649\pi$
$79$	−38.1516			−0.0543340			−0.0271670	+	0.999631i	$0.508649\pi$
$80$	114.065	−	90.8234i	0.159410	−	0.126930i
$81$	−111.715	+	720.389i	−0.153244	+	0.988188i
$82$	−344.927	+	216.641i	−0.464521	+	0.291757i
$83$			973.913i			1.28796i	0.765042	+	0.643981i	$0.222718\pi$
$83$			973.913i			1.28796i	−0.765042	+	0.643981i	$0.777282\pi$
$84$	109.783	−	762.005i	0.142598	−	0.989781i
$85$			64.7430i			0.0826161i
$86$	−106.978	−	170.326i	−0.134137	−	0.213567i
$87$	−697.016	−	320.647i	−0.858942	−	0.395137i
$88$	85.2770	+	760.705i	0.103302	+	0.921493i
$89$	1638.53			1.95150			0.975750	−	0.218889i	$-0.0702433\pi$
$89$	1638.53			1.95150			0.975750	+	0.218889i	$0.0702433\pi$
$90$	51.6668	−	166.134i	0.0605128	−	0.194579i
$91$	562.572	−	510.848i	0.648061	−	0.588477i
$92$	−1029.93	−	496.464i	−1.16715	−	0.562609i
$93$	−637.249	+	1385.24i	−0.710534	+	1.54455i
$94$	879.438	−	552.357i	0.964969	−	0.606077i
$95$		−	249.818i		−	0.269798i
$96$	−676.121	−	653.909i	−0.718815	−	0.695201i
$97$			133.473i			0.139713i	0.997557	+	0.0698565i	$0.0222541\pi$
$97$			133.473i			0.139713i	−0.997557	+	0.0698565i	$0.977746\pi$
$98$	434.616	+	867.353i	0.447989	+	0.894039i
$99$	594.321	+	693.589i	0.603348	+	0.704125i
$100$	416.192	−	863.402i	0.416192	−	0.863402i
$101$		−	169.167i		−	0.166661i	−0.996522	−	0.0833306i	$-0.973444\pi$
$101$		−	169.167i		−	0.166661i	0.996522	−	0.0833306i	$-0.0265557\pi$
$102$	414.154	−	53.9977i	0.402033	−	0.0524173i
$103$			939.850i			0.899089i	0.893258	+	0.449544i	$0.148414\pi$
$103$			939.850i			0.899089i	−0.893258	+	0.449544i	$0.851586\pi$
$104$	−103.431	−	922.644i	−0.0975215	−	0.869930i
$105$	66.0649	+	209.053i	0.0614026	+	0.194300i
$106$	1216.85	−	764.277i	1.11501	−	0.700312i
$107$	2048.48			1.85078			0.925392	−	0.379012i	$-0.123736\pi$
$107$	2048.48			1.85078			0.925392	+	0.379012i	$0.123736\pi$
$108$	−1105.83	−	191.945i	−0.985268	−	0.171018i
$109$			238.831i			0.209871i	0.994479	+	0.104935i	$0.0334635\pi$
$109$			238.831i			0.209871i	−0.994479	+	0.104935i	$0.966536\pi$
$110$	−115.943	−	184.599i	−0.100497	−	0.160007i
$111$	−351.862	+	764.871i	−0.300876	+	0.654039i
$112$	1169.95	+	190.125i	0.987052	+	0.160403i
$113$		−	0.845945i		−	0.000704246i	−1.00000		0.000352123i	$-0.999888\pi$
$113$		−	0.845945i		−	0.000704246i	1.00000		0.000352123i	$-0.000112084\pi$
$114$	−1598.06	+	208.356i	−1.31291	+	0.171178i
$115$	325.600			0.264020
$116$	512.917	−	1064.06i	0.410544	−	0.851685i
$117$	−720.840	−	841.241i	−0.569587	−	0.664725i
$118$	304.074	+	484.132i	0.237223	+	0.377695i
$119$	−389.639	+	353.815i	−0.300152	+	0.272556i
$120$	254.306	+	84.1403i	0.193457	+	0.0640077i
$121$	−186.578			−0.140179
$122$	−871.216	+	547.194i	−0.646527	+	0.406070i
$123$	−679.808	−	312.730i	−0.498343	−	0.229252i
$124$	−2114.70	−	1019.36i	−1.53150	−	0.738239i
$125$			557.733i			0.399081i
$126$	1282.19	−	596.966i	0.906559	−	0.422079i
$127$	46.6406			0.0325881			0.0162940	−	0.999867i	$-0.494813\pi$
$127$	46.6406			0.0325881			0.0162940	+	0.999867i	$0.494813\pi$
$128$	1025.34	−	1022.65i	0.708035	−	0.706177i
$129$	154.428	−	335.692i	0.105400	−	0.229117i
$130$	140.625	+	223.896i	0.0948739	+	0.151054i
$131$		−	2494.50i		−	1.66371i	−0.554995	−	0.831854i	$-0.687280\pi$
$131$		−	2494.50i		−	1.66371i	0.554995	−	0.831854i	$-0.312720\pi$
$132$	−1084.16	+	895.635i	−0.714878	+	0.590568i
$133$	1503.46	−	1365.23i	0.980202	−	0.890081i
$134$	800.027	+	1273.77i	0.515760	+	0.821169i
$135$	307.416	−	87.5046i	0.195986	−	0.0557866i
$136$	71.6365	+	639.026i	0.0451675	+	0.402912i
$137$			201.774i			0.125830i	0.998019	+	0.0629151i	$0.0200397\pi$
$137$			201.774i			0.125830i	−0.998019	+	0.0629151i	$0.979960\pi$
$138$	−271.560	−	2082.83i	−0.167513	−	1.28480i
$139$	309.414			0.188807			0.0944034	−	0.995534i	$-0.469906\pi$
$139$	309.414			0.188807			0.0944034	+	0.995534i	$0.469906\pi$
$140$	−323.638	+	95.8998i	−0.195374	+	0.0578929i
$141$	1733.26	+	797.349i	1.03523	+	0.476233i
$142$	1198.53	+	1908.25i	0.708301	+	1.12772i
$143$	−1388.05			−0.811709
$144$	326.137	−	1696.94i	0.188737	−	0.982028i
$145$			336.390i			0.192660i
$146$	767.628	+	1222.18i	0.435133	+	0.692798i
$147$	−897.091	+	1540.05i	−0.503339	+	0.864089i
$148$	−1167.65	−	562.850i	−0.648514	−	0.312608i
$149$	−1207.81			−0.664078			−0.332039	−	0.943266i	$-0.607737\pi$
$149$	−1207.81			−0.664078			−0.332039	+	0.943266i	$0.607737\pi$
$150$	1746.06	−	227.652i	0.950433	−	0.123918i
$151$	−2555.54			−1.37726			−0.688631	−	0.725112i	$-0.741788\pi$
$151$	−2555.54			−1.37726			−0.688631	+	0.725112i	$0.741788\pi$
$152$	−276.417	−	2465.75i	−0.147503	−	1.31578i
$153$	499.256	+	582.646i	0.263807	+	0.307870i
$154$	477.342	−	1706.59i	0.249775	−	0.892991i
$155$	668.537			0.346440
$156$	1314.95	−	1086.30i	0.674876	−	0.557522i
$157$	−38.2182			−0.0194276			−0.00971382	−	0.999953i	$-0.503092\pi$
$157$	−38.2182			−0.0194276			−0.00971382	+	0.999953i	$0.503092\pi$
$158$	91.3799	−	57.3939i	0.0460114	−	0.0288988i
$159$	2398.25	+	1103.26i	1.19619	+	0.550280i
$160$	−136.574	+	389.133i	−0.0674819	+	0.192273i
$161$	1779.37	+	1959.54i	0.871020	+	0.959211i
$162$	−816.151	−	1893.52i	−0.395820	−	0.918328i
$163$		−	2887.96i		−	1.38775i	−0.720097	−	0.693873i	$-0.755903\pi$
$163$		−	2887.96i		−	1.38775i	0.720097	−	0.693873i	$-0.244097\pi$
$164$	500.254	−	1037.79i	0.238190	−	0.494133i
$165$	167.368	−	363.822i	0.0789672	−	0.171657i
$166$	−1465.12	−	2332.70i	−0.685032	−	1.09068i
$167$	307.719			0.142587			0.0712935	−	0.997455i	$-0.477287\pi$
$167$	307.719			0.142587			0.0712935	+	0.997455i	$0.477287\pi$
$168$	883.384	+	1990.29i	0.405682	+	0.914014i
$169$	−513.464			−0.233712
$170$	−97.3971	−	155.071i	−0.0439413	−	0.0699613i
$171$	−1926.43	−	2248.20i	−0.861509	−	1.00541i
$172$	512.465	+	247.027i	0.227181	+	0.109510i
$173$		−	2741.35i		−	1.20475i	−0.798215	−	0.602373i	$-0.794222\pi$
$173$		−	2741.35i		−	1.20475i	0.798215	−	0.602373i	$-0.205778\pi$
$174$	2151.85	−	280.559i	0.937535	−	0.122237i
$175$	−1642.70	+	1491.67i	−0.709580	+	0.644341i
$176$	−1348.63	−	1693.74i	−0.577596	−	0.725399i
$177$	−438.942	+	954.165i	−0.186401	+	0.405195i
$178$	−3924.57	+	2464.94i	−1.65258	+	1.03795i
$179$	729.734			0.304709			0.152354	−	0.988326i	$-0.451314\pi$
$179$	729.734			0.304709			0.152354	+	0.988326i	$0.451314\pi$
$180$	126.175	+	475.647i	0.0522475	+	0.196959i
$181$	2056.86			0.844671			0.422336	−	0.906440i	$-0.361210\pi$
$181$	2056.86			0.844671			0.422336	+	0.906440i	$0.361210\pi$
$182$	−578.958	+	2069.89i	−0.235798	+	0.843023i
$183$	−1717.06	−	789.895i	−0.693600	−	0.319075i
$184$	3213.73	−	360.268i	1.28761	−	0.144344i
$185$	369.138			0.146700
$186$	−557.580	−	4276.56i	−0.219805	−	1.68587i
$187$	961.365			0.375946
$188$	−1275.47	+	2645.99i	−0.494802	+	1.02648i
$189$	2206.62	+	1371.89i	0.849249	+	0.527993i
$190$	375.818	+	598.360i	0.143498	+	0.228471i
$191$			2290.89i			0.867868i	0.900945	+	0.433934i	$0.142875\pi$
$191$			2290.89i			0.867868i	−0.900945	+	0.433934i	$0.857125\pi$
$192$	2603.15	+	549.097i	0.978469	+	0.206394i
$193$	−3149.48			−1.17464			−0.587318	−	0.809356i	$-0.699816\pi$
$193$	−3149.48			−1.17464			−0.587318	+	0.809356i	$0.699816\pi$
$194$	−200.793	−	319.693i	−0.0743096	−	0.118312i
$195$	−202.997	+	441.272i	−0.0745485	+	0.162052i
$196$	−2345.80	−	1423.64i	−0.854883	−	0.518821i
$197$	−415.958			−0.150435			−0.0752177	−	0.997167i	$-0.523965\pi$
$197$	−415.958			−0.150435			−0.0752177	+	0.997167i	$0.523965\pi$
$198$	−2466.92	−	767.196i	−0.885435	−	0.275365i
$199$		−	1202.25i		−	0.428266i	−0.976804	−	0.214133i	$-0.931307\pi$
$199$		−	1202.25i		−	0.428266i	0.976804	−	0.214133i	$-0.0686927\pi$
$200$	302.017	+	2694.11i	0.106779	+	0.952511i
$201$	−1154.87	+	2510.44i	−0.405265	+	0.880958i
$202$	254.489	+	405.186i	0.0886426	+	0.141133i
$203$	−2024.47	+	1838.34i	−0.699951	+	0.635597i
$204$	−910.741	+	752.373i	−0.312572	+	0.258219i
$205$			328.085i			0.111778i
$206$	−1413.88	−	2251.11i	−0.478201	−	0.761370i
$207$	2930.19	−	2510.81i	0.983876	−	0.843061i
$208$	1635.73	+	2054.30i	0.545276	+	0.684808i
$209$	−3709.53			−1.22772
$210$	−472.729	−	401.334i	−0.155340	−	0.131879i
$211$			4107.87i			1.34027i	0.742239	+	0.670135i	$0.233764\pi$
$211$			4107.87i			1.34027i	−0.742239	+	0.670135i	$0.766236\pi$
$212$	−1764.82	+	3661.16i	−0.571736	+	1.18608i
$213$	−1730.13	+	3760.93i	−0.556557	+	1.20983i
$214$	−4906.47	+	3081.66i	−1.56729	+	0.984382i
$215$	−162.010			−0.0513906
$216$	2937.43	−	1203.83i	0.925308	−	0.379215i
$217$	3653.49	+	4023.41i	1.14293	+	1.25865i
$218$	−359.289	−	572.044i	−0.111624	−	0.177723i
$219$	−1108.10	+	2408.77i	−0.341911	+	0.743240i
$220$	555.408	+	267.727i	0.170207	+	0.0820462i
$221$	−1166.02			−0.354910
$222$	−307.872	−	2361.33i	−0.0930767	−	0.713884i
$223$		−	3886.29i		−	1.16702i	−0.812106	−	0.583509i	$-0.801679\pi$
$223$		−	3886.29i		−	1.16702i	0.812106	−	0.583509i	$-0.198321\pi$
$224$	−3088.26	+	1304.65i	−0.921173	+	0.389153i
$225$	2104.84	+	2456.41i	0.623657	+	0.727826i
$226$	1.27261	+	2.02619i	0.000374570	+	0.000596373i
$227$			2560.28i			0.748598i	0.927308	+	0.374299i	$0.122117\pi$
$227$			2560.28i			0.748598i	−0.927308	+	0.374299i	$0.877883\pi$
$228$	3514.20	−	2903.11i	1.02076	−	0.843261i
$229$	−1212.09			−0.349770			−0.174885	−	0.984589i	$-0.555955\pi$
$229$	−1212.09			−0.349770			−0.174885	+	0.984589i	$0.555955\pi$
$230$	−779.870	+	489.821i	−0.223579	+	0.140425i
$231$	3104.21	−	980.993i	0.884166	−	0.279414i
$232$	372.207	+	3320.23i	0.105330	+	0.939585i
$233$		−	4448.69i		−	1.25083i	−0.780292	−	0.625415i	$-0.784930\pi$
$233$		−	4448.69i		−	1.25083i	0.780292	−	0.625415i	$-0.215070\pi$
$234$	2992.08	+	930.518i	0.835889	+	0.259957i
$235$		−	836.497i		−	0.232200i
$236$	−1456.62	−	702.146i	−0.401772	−	0.193669i
$237$	180.099	+	82.8503i	0.0493614	+	0.0227076i
$238$	400.988	−	1433.61i	0.109211	−	0.390450i
$239$			475.148i			0.128597i	0.997931	+	0.0642987i	$0.0204810\pi$
$239$			475.148i			0.128597i	−0.997931	+	0.0642987i	$0.979519\pi$
$240$	−735.687	+	181.038i	−0.197868	+	0.0486914i
$241$		−	7311.01i		−	1.95412i	−0.212960	−	0.977061i	$-0.568310\pi$
$241$		−	7311.01i		−	1.95412i	0.212960	−	0.977061i	$-0.431690\pi$
$242$	446.888	−	280.682i	0.118707	−	0.0745574i
$243$	2091.77	−	3158.07i	0.552209	−	0.833706i
$244$	1263.54	−	2621.25i	0.331516	−	0.687740i
$245$	777.813	+	75.1332i	0.202827	+	0.0195922i
$246$	2098.72	−	273.633i	0.543942	−	0.0709195i
$247$	4499.22			1.15902
$248$	6598.58	−	739.719i	1.68956	−	0.189404i
$249$	2114.96	−	4597.46i	0.538273	−	1.17009i
$250$	−839.034	−	1335.87i	−0.212261	−	0.337952i
$251$			5996.84i			1.50804i	0.656853	+	0.754018i	$0.271887\pi$
$251$			5996.84i			1.50804i	−0.656853	+	0.754018i	$0.728113\pi$
$252$	−2173.02	+	3358.72i	−0.543203	+	0.839601i
$253$		−	4834.81i		−	1.20143i
$254$	−111.713	+	70.1645i	−0.0275964	+	0.0173327i
$255$	140.597	−	305.626i	0.0345274	−	0.0750551i
$256$	−917.442	+	3991.93i	−0.223985	+	0.974593i
$257$	−2528.53			−0.613719			−0.306859	−	0.951755i	$-0.599278\pi$
$257$	−2528.53			−0.613719			−0.306859	+	0.951755i	$0.599278\pi$
$258$	135.121	+	1036.36i	0.0326057	+	0.250081i
$259$	2017.30	+	2221.56i	0.483974	+	0.532976i
$260$	−673.644	−	324.721i	−0.160683	−	0.0774552i
$261$	2594.02	+	3027.29i	0.615194	+	0.717949i
$262$	3752.64	+	5974.78i	0.884882	+	1.40887i
$263$			6792.30i			1.59251i	0.604958	+	0.796257i	$0.293190\pi$
$263$			6792.30i			1.59251i	−0.604958	+	0.796257i	$0.706810\pi$
$264$	1249.39	−	3776.18i	0.291269	−	0.880332i
$265$		−	1157.43i		−	0.268304i
$266$	−1547.26	+	5531.74i	−0.356648	+	1.27508i
$267$	−7734.84	−	3558.24i	−1.77290	−	0.815583i
$268$	−3832.42	−	1847.37i	−0.873516	−	0.421067i
$269$		−	2766.06i		−	0.626950i	−0.949597	−	0.313475i	$-0.898507\pi$
$269$		−	2766.06i		−	0.626950i	0.949597	−	0.313475i	$-0.101493\pi$
$270$	−604.677	+	672.054i	−0.136294	+	0.151481i
$271$		−	923.677i		−	0.207046i	−0.994627	−	0.103523i	$-0.966989\pi$
$271$		−	923.677i		−	0.207046i	0.994627	−	0.103523i	$-0.0330115\pi$
$272$	−1132.91	−	1422.81i	−0.252547	−	0.317172i
$273$	−3765.04	+	1189.83i	−0.834691	+	0.263779i
$274$	−303.542	−	483.286i	−0.0669257	−	0.106556i
$275$	4053.08			0.888763
$276$	3783.77	+	4580.22i	0.825203	+	0.998901i
$277$			3713.69i			0.805537i	0.915302	+	0.402768i	$0.131952\pi$
$277$			3713.69i			0.805537i	−0.915302	+	0.402768i	$0.868048\pi$
$278$	−741.102	+	465.472i	−0.159886	+	0.100421i
$279$	6016.40	−	5155.32i	1.29101	−	1.10624i
$280$	630.903	−	716.567i	0.134656	−	0.152939i
$281$		−	4766.56i		−	1.01192i	−0.862557	−	0.505960i	$-0.831138\pi$
$281$		−	4766.56i		−	1.01192i	0.862557	−	0.505960i	$-0.168862\pi$
$282$	−5350.98	+	697.665i	−1.12995	+	0.147324i
$283$	−8241.05			−1.73102			−0.865512	−	0.500888i	$-0.833007\pi$
$283$	−8241.05			−1.73102			−0.865512	+	0.500888i	$0.833007\pi$
$284$	−5741.41	−	2767.57i	−1.19961	−	0.578258i
$285$	−542.507	+	1179.29i	−0.112756	+	0.245106i
$286$	3324.62	−	2088.13i	0.687374	−	0.431726i
$287$	−1974.49	+	1792.95i	−0.406099	+	0.368762i
$288$	1771.66	+	4555.12i	0.362487	+	0.931989i
$289$	−4105.41			−0.835622
$290$	−506.053	−	805.714i	−0.102470	−	0.163149i
$291$	289.852	−	630.075i	0.0583898	−	0.126927i
$292$	−3677.22	−	1772.55i	−0.736961	−	0.355243i
$293$		−	4955.76i		−	0.988118i	−0.869428	−	0.494059i	$-0.835513\pi$
$293$		−	4955.76i		−	0.988118i	0.869428	−	0.494059i	$-0.164487\pi$
$294$	−168.101	−	5038.25i	−0.0333464	−	0.999444i
$295$	460.494			0.0908847
$296$	3643.46	−	408.441i	0.715445	−	0.0802033i
$297$	−1299.35	−	4564.79i	−0.253858	−	0.891839i
$298$	2892.92	−	1816.99i	0.562357	−	0.353205i
$299$			5864.05i			1.13420i
$300$	−3839.65	+	3171.97i	−0.738941	+	0.610447i
$301$	−885.369	−	975.012i	−0.169541	−	0.186707i
$302$	6120.97	−	3844.46i	1.16630	−	0.732529i
$303$	−367.365	+	798.572i	−0.0696521	+	0.151408i
$304$	4371.46	+	5490.09i	0.824738	+	1.03578i
$305$			828.678i			0.155574i
$306$	−2072.32	−	644.479i	−0.387146	−	0.120400i
$307$	6152.25			1.14374			0.571869	−	0.820345i	$-0.306219\pi$
$307$	6152.25			1.14374			0.571869	+	0.820345i	$0.306219\pi$
$308$	1424.01	+	4805.68i	0.263443	+	0.889055i
$309$	2040.99	−	4436.66i	0.375753	−	0.816805i
$310$	−1601.27	+	1005.72i	−0.293374	+	0.184262i
$311$	−4710.11			−0.858798			−0.429399	−	0.903115i	$-0.641275\pi$
$311$	−4710.11			−0.858798			−0.429399	+	0.903115i	$0.641275\pi$
$312$	−1515.37	+	4580.05i	−0.274970	+	0.831071i
$313$			6006.89i			1.08476i	0.840134	+	0.542379i	$0.182476\pi$
$313$			6006.89i			1.08476i	−0.840134	+	0.542379i	$0.817524\pi$
$314$	91.5394	−	57.4940i	0.0164518	−	0.0103330i
$315$	142.115	−	1130.32i	0.0254200	−	0.202179i
$316$	−132.530	+	274.937i	−0.0235930	+	0.0489444i
$317$	−8487.77			−1.50385			−0.751926	−	0.659248i	$-0.770875\pi$
$317$	−8487.77			−1.50385			−0.751926	+	0.659248i	$0.770875\pi$
$318$	−7403.96	+	965.334i	−1.30564	+	0.170230i
$319$	4995.03			0.876702
$320$	−258.280	−	1137.50i	−0.0451196	−	0.198713i
$321$	−9670.06	−	4448.49i	−1.68140	−	0.773491i
$322$	−7209.78	−	2016.61i	−1.24778	−	0.349011i
$323$	−3116.17			−0.536806
$324$	4803.38	+	3307.54i	0.823624	+	0.567136i
$325$	−4915.90			−0.839031
$326$	4344.55	+	6917.19i	0.738105	+	1.17518i
$327$	518.648	−	1127.43i	0.0877104	−	0.190663i
$328$	363.017	+	3238.26i	0.0611106	+	0.545131i
$329$	5034.23	−	4571.38i	0.843606	−	0.766044i
$330$	146.444	+	1123.20i	0.0244287	+	0.187364i
$331$		−	10975.0i		−	1.82247i	−0.411885	−	0.911236i	$-0.635130\pi$
$331$		−	10975.0i		−	1.82247i	0.411885	−	0.911236i	$-0.364870\pi$
$332$	7018.45	+	3383.15i	1.16020	+	0.559261i
$333$	3322.00	−	2846.55i	0.546680	−	0.468438i
$334$	−737.043	+	462.922i	−0.120746	+	0.0758382i
$335$	1211.57			0.197598
$336$	−5109.99	−	3438.18i	−0.829681	−	0.558238i
$337$	1629.69			0.263427			0.131714	−	0.991288i	$-0.457952\pi$
$337$	1629.69			0.263427			0.131714	+	0.991288i	$0.457952\pi$
$338$	1229.84	−	772.438i	0.197913	−	0.124305i
$339$	−1.83706	+	3.99337i	−0.000294323	+	0.000639794i
$340$	466.567	+	224.903i	0.0744211	+	0.0358737i
$341$		−	9927.06i		−	1.57648i
$342$	7996.27	+	2486.79i	1.26430	+	0.393188i
$343$	3798.51	+	5091.65i	0.597960	+	0.801526i
$344$	−1599.07	+	179.260i	−0.250628	+	0.0280960i
$345$	−1537.03	−	707.076i	−0.239857	−	0.110341i
$346$	4123.99	+	6566.03i	0.640772	+	1.02021i
$347$	3090.79			0.478162			0.239081	−	0.971000i	$-0.423154\pi$
$347$	3090.79			0.478162			0.239081	+	0.971000i	$0.423154\pi$
$348$	−4732.00	+	3909.15i	−0.728913	+	0.602163i
$349$	−8418.13			−1.29115			−0.645576	−	0.763696i	$-0.723383\pi$
$349$	−8418.13			−1.29115			−0.645576	+	0.763696i	$0.723383\pi$
$350$	1690.55	−	6044.04i	0.258182	−	0.923050i
$351$	1575.96	+	5536.55i	0.239653	+	0.841935i
$352$	5778.21	+	2027.97i	0.874942	+	0.307078i
$353$	−694.292			−0.104684			−0.0523420	−	0.998629i	$-0.516669\pi$
$353$	−694.292			−0.104684			−0.0523420	+	0.998629i	$0.516669\pi$
$354$	−384.066	−	2945.73i	−0.0576635	−	0.442270i
$355$	1815.08			0.271364
$356$	5691.87	−	11808.0i	0.847384	−	1.75792i
$357$	2607.68	−	824.077i	0.386591	−	0.122170i
$358$	−1747.84	+	1097.79i	−0.258035	+	0.162066i
$359$			3336.44i			0.490503i	0.969460	+	0.245251i	$0.0788705\pi$
$359$			3336.44i			0.490503i	−0.969460	+	0.245251i	$0.921129\pi$
$360$	−1017.76	−	949.447i	−0.149002	−	0.139001i
$361$	5165.10			0.753040
$362$	−4926.56	+	3094.27i	−0.715288	+	0.449258i
$363$	880.762	+	405.175i	0.127350	+	0.0585845i
$364$	−1727.15	−	5828.71i	−0.248702	−	0.839307i
$365$	1162.51			0.166708
$366$	5300.96	−	691.143i	0.757064	−	0.0987066i
$367$		−	8875.98i		−	1.26246i	−0.775596	−	0.631229i	$-0.782551\pi$
$367$		−	8875.98i		−	1.26246i	0.775596	−	0.631229i	$-0.217449\pi$
$368$	−7155.49	+	5697.53i	−1.01360	+	0.807077i
$369$	2529.98	+	2952.55i	0.356925	+	0.416541i
$370$	−884.151	+	555.318i	−0.124229	+	0.0780259i
$371$	6965.69	−	6325.26i	0.974773	−	0.885151i
$372$	7769.00	+	9404.32i	1.08281	+	1.31073i
$373$		−	1584.56i		−	0.219960i	−0.993934	−	0.109980i	$-0.964921\pi$
$373$		−	1584.56i		−	0.219960i	0.993934	−	0.109980i	$-0.0350788\pi$
$374$	−2302.64	+	1446.24i	−0.318360	+	0.199956i
$375$	1211.18	−	2632.84i	0.166787	−	0.362558i
$376$	−925.563	−	8256.38i	−0.126947	−	1.13242i
$377$	−6058.37			−0.827645
$378$	−7349.08	+	33.6292i	−0.999990	+	0.00457592i
$379$			1454.58i			0.197142i	0.995130	+	0.0985711i	$0.0314272\pi$
$379$			1454.58i			0.197142i	−0.995130	+	0.0985711i	$0.968573\pi$
$380$	−1800.30	−	867.812i	−0.243036	−	0.117152i
$381$	−220.172	−	101.285i	−0.0296056	−	0.0136194i
$382$	−3446.33	−	5487.09i	−0.461595	−	0.734931i
$383$	14348.5			1.91429			0.957147	−	0.289603i	$-0.0935233\pi$
$383$	14348.5			1.91429			0.957147	+	0.289603i	$0.0935233\pi$
$384$	−7061.05	+	2600.90i	−0.938367	+	0.345642i
$385$	−959.559	−	1056.71i	−0.127022	−	0.139883i
$386$	7543.58	−	4737.97i	0.994710	−	0.624757i
$387$	−1457.98	+	1249.31i	−0.191508	+	0.164099i
$388$	961.869	+	463.656i	0.125854	+	0.0606665i
$389$	2531.67			0.329977			0.164988	−	0.986296i	$-0.447241\pi$
$389$	2531.67			0.329977			0.164988	+	0.986296i	$0.447241\pi$
$390$	−177.619	−	1362.31i	−0.0230617	−	0.176880i
$391$		−	4061.46i		−	0.525311i
$392$	7760.29	−	119.051i	0.999882	−	0.0153393i
$393$	−5417.09	+	11775.6i	−0.695307	+	1.51145i
$394$	996.294	−	625.752i	0.127392	−	0.0800126i
$395$		−	86.9181i		−	0.0110717i
$396$	7062.85	−	1873.57i	0.896267	−	0.237753i
$397$	6962.76			0.880229			0.440115	−	0.897942i	$-0.354938\pi$
$397$	6962.76			0.880229			0.440115	+	0.897942i	$0.354938\pi$
$398$	1808.62	+	2879.60i	0.227783	+	0.362666i
$399$	−10062.0	+	3179.79i	−1.26248	+	0.398969i
$400$	−4776.30	−	5998.53i	−0.597038	−	0.749816i
$401$		−	6420.79i		−	0.799598i	−0.916603	−	0.399799i	$-0.869080\pi$
$401$		−	6420.79i		−	0.799598i	0.916603	−	0.399799i	$-0.130920\pi$
$402$	−1010.49	−	7750.30i	−0.125370	−	0.961566i
$403$			12040.3i			1.48827i
$404$	−1219.10	−	587.649i	−0.150129	−	0.0723679i
$405$	−1641.21	−	254.512i	−0.201364	−	0.0312267i
$406$	2083.44	−	7448.70i	0.254678	−	0.910524i
$407$		−	5481.30i		−	0.667563i
$408$	1049.55	−	3172.15i	0.127354	−	0.384914i
$409$		−	650.008i		−	0.0785840i	−0.999228	−	0.0392920i	$-0.987490\pi$
$409$		−	650.008i		−	0.0785840i	0.999228	−	0.0392920i	$-0.0125102\pi$
$410$	−493.559	−	785.822i	−0.0594516	−	0.0946561i
$411$	438.175	−	952.497i	0.0525878	−	0.114314i
$412$	6772.98	+	3264.83i	0.809904	+	0.390404i
$413$	2516.56	+	2771.36i	0.299834	+	0.330193i
$414$	−3241.16	+	10421.9i	−0.384768	+	1.23722i
$415$	−2218.80			−0.262449
$416$	−7008.28	−	2459.69i	−0.825984	−	0.289895i
$417$	−1460.62	−	671.926i	−0.171527	−	0.0789074i
$418$	8885.00	−	5580.49i	1.03966	−	0.652992i
$419$			2741.55i			0.319651i	0.987145	+	0.159825i	$0.0510931\pi$
$419$			2741.55i			0.319651i	−0.987145	+	0.159825i	$0.948907\pi$
$420$	1736.02	+	250.110i	0.201689	+	0.0290575i
$421$			5647.52i			0.653784i	0.945062	+	0.326892i	$0.106001\pi$
$421$			5647.52i			0.653784i	−0.945062	+	0.326892i	$0.893999\pi$
$422$	−6179.73	−	9839.08i	−0.712854	−	1.13497i
$423$	−6450.52	−	7527.94i	−0.741454	−	0.865298i
$424$	−1280.67	−	11424.1i	−0.146686	−	1.30849i
$425$	3404.76			0.388601
$426$	−1513.83	−	11610.8i	−0.172172	−	1.32053i
$427$	−4987.17	+	4528.65i	−0.565214	+	0.513247i
$428$	7115.95	−	14762.2i	0.803651	−	1.66720i
$429$	6552.42	+	3014.30i	0.737422	+	0.339234i
$430$	388.043	−	243.722i	0.0435188	−	0.0273333i
$431$			1269.04i			0.141828i	0.997482	+	0.0709139i	$0.0225915\pi$
$431$			1269.04i			0.141828i	−0.997482	+	0.0709139i	$0.977408\pi$
$432$	−5224.66	+	7302.36i	−0.581879	+	0.813275i
$433$			9965.68i			1.10605i	0.833164	+	0.553026i	$0.186527\pi$
$433$			9965.68i			1.10605i	−0.833164	+	0.553026i	$0.813473\pi$
$434$	−14803.4	−	4140.61i	−1.63730	−	0.457962i
$435$	730.507	−	1587.96i	0.0805176	−	0.175028i
$436$	1721.13	+	829.646i	0.189053	+	0.0911304i
$437$			15671.6i			1.71550i
$438$	−969.567	−	7436.43i	−0.105771	−	0.811247i
$439$			17103.9i			1.85951i	0.368180	+	0.929754i	$0.379981\pi$
$439$			17103.9i			1.85951i	−0.368180	+	0.929754i	$0.620019\pi$
$440$	−1733.06	+	194.281i	−0.187774	+	0.0210499i
$441$	7579.20	−	5321.83i	0.818399	−	0.574650i
$442$	2792.83	−	1754.12i	0.300546	−	0.188767i
$443$	−6755.15			−0.724485			−0.362242	−	0.932084i	$-0.617989\pi$
$443$	−6755.15			−0.724485			−0.362242	+	0.932084i	$0.617989\pi$
$444$	4289.71	+	5192.66i	0.458515	+	0.555029i
$445$			3732.94i			0.397659i
$446$	5846.40	+	9308.36i	0.620706	+	0.988260i
$447$	5701.59	+	2622.89i	0.603302	+	0.277536i
$448$	5434.27	−	7770.72i	0.573091	−	0.819491i
$449$		−	6557.46i		−	0.689233i	−0.938744	−	0.344617i	$-0.888009\pi$
$449$		−	6557.46i		−	0.689233i	0.938744	−	0.344617i	$-0.111991\pi$
$450$	−8736.82	−	2717.10i	−0.915239	−	0.284634i
$451$	4871.71			0.508647
$452$	−6.09626	−	2.93862i	−0.000634389	−	0.000305799i
$453$	12063.7	+	5549.63i	1.25122	+	0.575594i
$454$	−3851.59	−	6132.33i	−0.398159	−	0.633931i
$455$	1163.83	+	1281.67i	0.119915	+	0.132056i
$456$	−4049.79	+	12240.1i	−0.415897	+	1.25701i
$457$	428.629			0.0438740			0.0219370	−	0.999759i	$-0.493017\pi$
$457$	428.629			0.0438740			0.0219370	+	0.999759i	$0.493017\pi$
$458$	2903.18	−	1823.43i	0.296193	−	0.186033i
$459$	−1091.51	−	3834.63i	−0.110996	−	0.389946i
$460$	1131.06	−	2346.42i	0.114643	−	0.237831i
$461$		−	14233.2i		−	1.43798i	−0.695022	−	0.718988i	$-0.744605\pi$
$461$		−	14233.2i		−	1.43798i	0.695022	−	0.718988i	$-0.255395\pi$
$462$	−5959.38	+	7019.52i	−0.600120	+	0.706878i
$463$	−6905.29			−0.693123			−0.346562	−	0.938027i	$-0.612651\pi$
$463$	−6905.29			−0.693123			−0.346562	+	0.938027i	$0.612651\pi$
$464$	−5886.34	−	7392.61i	−0.588936	−	0.739641i
$465$	−3155.90	−	1451.80i	−0.314734	−	0.144786i
$466$	6692.45	+	10655.4i	0.665283	+	1.05923i
$467$			9126.22i			0.904307i	0.891940	+	0.452153i	$0.149344\pi$
$467$			9126.22i			0.904307i	−0.891940	+	0.452153i	$0.850656\pi$
$468$	−8566.40	+	2272.41i	−0.846115	+	0.224450i
$469$	6621.13	+	7291.52i	0.651888	+	0.717892i
$470$	1258.40	+	2003.56i	0.123501	+	0.196633i
$471$	180.413	+	82.9949i	0.0176496	+	0.00811933i
$472$	4545.16	−	509.524i	0.443237	−	0.0496881i
$473$			2405.67i			0.233854i
$474$	−556.006	+	72.4924i	−0.0538780	+	0.00702465i
$475$	−13137.7			−1.26905
$476$	1196.23	+	4036.98i	0.115187	+	0.388729i
$477$	−8925.36	−	10416.1i	−0.856738	−	0.999837i
$478$	−714.796	−	1138.06i	−0.0683975	−	0.108899i
$479$	−17657.1			−1.68429			−0.842143	−	0.539254i	$-0.818706\pi$
$479$	−17657.1			−1.68429			−0.842143	+	0.539254i	$0.818706\pi$
$480$	1489.76	−	1540.36i	0.141662	−	0.146474i
$481$			6648.16i			0.630208i
$482$	10998.4	+	17511.2i	1.03934	+	1.65480i
$483$	−4144.38	−	13114.3i	−0.390426	−	1.23545i
$484$	−648.131	+	1344.57i	−0.0608688	+	0.126274i
$485$	−304.083			−0.0284695
$486$	−259.263	+	10710.9i	−0.0241984	+	0.999707i
$487$	−9567.19			−0.890206			−0.445103	−	0.895479i	$-0.646833\pi$
$487$	−9567.19			−0.890206			−0.445103	+	0.895479i	$0.646833\pi$
$488$	916.911	+	8179.20i	0.0850545	+	0.758720i
$489$	−6271.53	+	13632.9i	−0.579976	+	1.26074i
$490$	−1976.03	+	990.156i	−0.182179	+	0.0912872i
$491$	7159.61			0.658063			0.329031	−	0.944319i	$-0.393278\pi$
$491$	7159.61			0.658063			0.329031	+	0.944319i	$0.393278\pi$
$492$	−4615.17	+	3812.64i	−0.422903	+	0.349364i
$493$	4196.05			0.383327
$494$	−10776.4	+	6768.47i	−0.981488	+	0.616453i
$495$	−1580.16	+	1354.00i	−0.143480	+	0.122945i
$496$	−14692.0	+	11698.4i	−1.33002	+	1.05902i
$497$	9919.23	+	10923.6i	0.895248	+	0.985892i
$498$	1850.55	+	14193.4i	0.166516	+	1.27715i
$499$			17819.0i			1.59858i	0.600947	+	0.799289i	$0.294790\pi$
$499$			17819.0i			1.59858i	−0.600947	+	0.799289i	$0.705210\pi$
$500$	4019.27	+	1937.44i	0.359495	+	0.173290i
$501$	−1452.62	−	668.246i	−0.129538	−	0.0595909i
$502$	−9021.43	−	14363.5i	−0.802084	−	1.27704i
$503$	20477.4			1.81520			0.907599	−	0.419839i	$-0.137913\pi$
$503$	20477.4			1.81520			0.907599	+	0.419839i	$0.137913\pi$
$504$	152.030	−	11313.8i	0.0134364	−	0.999910i
$505$	385.402			0.0339607
$506$	7273.32	+	11580.2i	0.639009	+	1.01740i
$507$	2423.86	+	1115.04i	0.212323	+	0.0976742i
$508$	162.019	−	336.113i	0.0141505	−	0.0293555i
$509$			18659.8i			1.62491i	0.583022	+	0.812457i	$0.301870\pi$
$509$			18659.8i			1.62491i	−0.583022	+	0.812457i	$0.698130\pi$
$510$	123.019	+	943.539i	0.0106811	+	0.0819227i
$511$	6353.00	+	6996.24i	0.549980	+	0.605666i
$512$	−3807.88	−	10941.6i	−0.328684	−	0.944440i
$513$	4211.72	+	14796.3i	0.362479	+	1.27344i
$514$	6056.30	−	3803.84i	0.519712	−	0.326420i
$515$	−2141.19			−0.183208
$516$	−1882.70	−	2278.99i	−0.160623	−	0.194432i
$517$	−12421.1			−1.05663
$518$	−8173.84	−	2286.27i	−0.693316	−	0.193924i
$519$	−5953.15	+	12940.8i	−0.503495	+	1.09449i
$520$	2102.00	−	235.639i	0.177267	−	0.0198721i
$521$	17496.1			1.47125			0.735623	−	0.677391i	$-0.236890\pi$
$521$	17496.1			1.47125			0.735623	+	0.677391i	$0.236890\pi$
$522$	−10767.3	−	3348.56i	−0.902819	−	0.280771i
$523$	−1593.34			−0.133216			−0.0666079	−	0.997779i	$-0.521218\pi$
$523$	−1593.34			−0.133216			−0.0666079	+	0.997779i	$0.521218\pi$
$524$	−17976.5	−	8665.34i	−1.49868	−	0.722419i
$525$	10993.9	−	3474.28i	0.913927	−	0.288819i
$526$	−10218.1	−	16268.8i	−0.847016	−	1.34858i
$527$		−	8339.17i		−	0.689298i
$528$	2688.22	+	10924.2i	0.221571	+	0.900404i
$529$	−8258.51			−0.678763
$530$	1741.20	+	2772.26i	0.142704	+	0.227206i
$531$	4144.15	−	3551.03i	0.338683	−	0.290210i
$532$	−4615.79	−	15577.1i	−0.376165	−	1.26946i
$533$	−5908.80			−0.480185
$534$	23879.2	−	3113.39i	1.93512	−	0.252302i
$535$			4666.91i			0.377136i
$536$	11958.4	−	1340.57i	0.963668	−	0.108030i
$537$	−3444.79	−	1584.70i	−0.276822	−	0.127346i
$538$	4161.16	+	6625.20i	0.333458	+	0.530916i
$539$	1115.65	−	11549.7i	0.0891547	−	0.922969i
$540$	437.296	−	2519.35i	0.0348486	−	0.200769i
$541$		−	8592.00i		−	0.682807i	−0.939917	−	0.341404i	$-0.889098\pi$
$541$		−	8592.00i		−	0.682807i	0.939917	−	0.341404i	$-0.110902\pi$
$542$	1389.55	+	2212.37i	0.110122	+	0.175331i
$543$	−9709.64	−	4466.70i	−0.767368	−	0.353010i
$544$	4853.95	+	1703.59i	0.382558	+	0.134266i
$545$	−544.113			−0.0427656
$546$	7228.02	−	8513.84i	0.566540	−	0.667324i
$547$		−	468.066i		−	0.0365870i	−0.999833	−	0.0182935i	$-0.994177\pi$
$547$		−	468.066i		−	0.0365870i	0.999833	−	0.0182935i	$-0.00582332\pi$
$548$	1454.08	+	700.919i	0.113349	+	0.0546383i
$549$	6390.22	+	7457.57i	0.496772	+	0.579747i
$550$	−9707.85	+	6097.31i	−0.752626	+	0.472709i
$551$	−16190.9			−1.25183
$552$	−15953.1	−	5278.29i	−1.23009	−	0.406990i
$553$	523.093	−	475.000i	0.0402246	−	0.0365263i
$554$	−5586.74	−	8894.94i	−0.428443	−	0.682148i
$555$	−1742.55	−	801.623i	−0.133274	−	0.0613099i
$556$	1074.84	−	2229.78i	0.0819841	−	0.170078i
$557$	−7441.55			−0.566084			−0.283042	−	0.959108i	$-0.591344\pi$
$557$	−7441.55			−0.566084			−0.283042	+	0.959108i	$0.591344\pi$
$558$	−6654.89	+	21398.8i	−0.504882	+	1.62345i
$559$		−	2917.79i		−	0.220768i
$560$	−433.149	+	2665.41i	−0.0326855	+	0.201133i
$561$	−4538.22	−	2087.71i	−0.341540	−	0.157118i
$562$	7170.65	+	11416.8i	0.538213	+	0.856918i
$563$		−	14562.5i		−	1.09012i	−0.838397	−	0.545059i	$-0.816507\pi$
$563$		−	14562.5i		−	1.09012i	0.838397	−	0.545059i	$-0.183493\pi$
$564$	11767.0	−	9720.86i	0.878512	−	0.725748i
$565$	1.92726			0.000143505
$566$	19738.8	−	12397.5i	1.46587	−	0.920685i
$567$	−7437.37	−	11268.1i	−0.550864	−	0.834595i
$568$	17915.2	−	2008.34i	1.32342	−	0.148359i
$569$			19130.4i			1.40947i	0.709470	+	0.704735i	$0.248934\pi$
$569$			19130.4i			1.40947i	−0.709470	+	0.704735i	$0.751066\pi$
$570$	−474.683	−	3640.75i	−0.0348812	−	0.267534i
$571$		−	13903.0i		−	1.01896i	−0.860483	−	0.509479i	$-0.829838\pi$
$571$		−	13903.0i		−	1.01896i	0.860483	−	0.509479i	$-0.170162\pi$
$572$	−4821.76	+	10002.9i	−0.352462	+	0.731192i
$573$	4974.91	−	10814.4i	0.362705	−	0.788441i
$574$	2032.00	−	7264.80i	0.147760	−	0.528270i
$575$		−	17122.9i		−	1.24187i
$576$	−11096.0	−	8245.09i	−0.802663	−	0.596433i
$577$		−	20711.2i		−	1.49431i	−0.664648	−	0.747157i	$-0.731418\pi$
$577$		−	20711.2i		−	1.49431i	0.664648	−	0.747157i	$-0.268582\pi$
$578$	9833.20	−	6176.03i	0.707625	−	0.444445i
$579$	14867.5	+	6839.45i	1.06713	+	0.490911i
$580$	2424.18	+	1168.54i	0.173549	+	0.0836571i
$581$	−12125.5	−	13353.2i	−0.865838	−	0.953504i
$582$	253.615	+	1945.19i	0.0180630	+	0.138540i
$583$	−17186.6			−1.22092
$584$	11474.2	−	1286.28i	0.813021	−	0.0911418i
$585$	1916.54	−	1642.24i	0.135452	−	0.116065i
$586$	7455.27	+	11869.9i	0.525553	+	0.836762i
$587$			4831.23i			0.339704i	0.985470	+	0.169852i	$0.0543290\pi$
$587$			4831.23i			0.339704i	−0.985470	+	0.169852i	$0.945671\pi$
$588$	7981.99	+	11814.6i	0.559816	+	0.828617i
$589$			32177.6i			2.25103i
$590$	−1102.97	+	692.750i	−0.0769633	+	0.0483391i
$591$	1963.57	+	903.298i	0.136668	+	0.0628709i
$592$	−8112.29	+	6459.38i	−0.563198	+	0.448444i
$593$	−637.576			−0.0441519			−0.0220760	−	0.999756i	$-0.507028\pi$
$593$	−637.576			−0.0441519			−0.0220760	+	0.999756i	$0.507028\pi$
$594$	9979.29	+	8978.81i	0.689319	+	0.620210i
$595$	−806.072	−	887.687i	−0.0555390	−	0.0611624i
$596$	−4195.66	+	8704.02i	−0.288357	+	0.598205i
$597$	−2610.81	+	5675.33i	−0.178984	+	0.389072i
$598$	−8821.67	−	14045.5i	−0.603252	−	0.960470i
$599$		−	10757.3i		−	0.733774i	−0.930266	−	0.366887i	$-0.880424\pi$
$599$		−	10757.3i		−	0.733774i	0.930266	−	0.366887i	$-0.119576\pi$
$600$	4424.85	−	13373.7i	0.301073	−	0.909964i
$601$			594.275i			0.0403344i	0.999797	+	0.0201672i	$0.00641985\pi$
$601$			594.275i			0.0403344i	−0.999797	+	0.0201672i	$0.993580\pi$
$602$	3587.39	+	1003.41i	0.242876	+	0.0679336i
$603$	10903.4	−	9342.86i	0.736351	−	0.630963i
$604$	−8877.36	+	18416.3i	−0.598038	+	1.24065i
$605$		−	425.068i		−	0.0285644i
$606$	−321.437	−	2465.38i	−0.0215470	−	0.165262i
$607$		−	1028.34i		−	0.0687628i	−0.999409	−	0.0343814i	$-0.989054\pi$
$607$		−	1028.34i		−	0.0687628i	0.999409	−	0.0343814i	$-0.0109461\pi$
$608$	−18729.5	−	6573.48i	−1.24931	−	0.438470i
$609$	13548.9	−	4281.71i	0.901525	−	0.284900i
$610$	−1246.63	−	1984.83i	−0.0827454	−	0.131743i
$611$	15065.3			0.997507
$612$	5933.11	−	1573.88i	0.391882	−	0.103955i
$613$		−	20648.4i		−	1.36049i	−0.732983	−	0.680247i	$-0.761873\pi$
$613$		−	20648.4i		−	1.36049i	0.732983	−	0.680247i	$-0.238127\pi$
$614$	−14735.7	+	9255.22i	−0.968544	+	0.608323i
$615$	712.472	−	1548.76i	0.0467149	−	0.101548i
$616$	−10640.2	−	9368.24i	−0.695954	−	0.612755i
$617$		−	8883.01i		−	0.579605i	−0.957086	−	0.289803i	$-0.906410\pi$
$617$		−	8883.01i		−	0.579605i	0.957086	−	0.289803i	$-0.0935897\pi$
$618$	1785.82	+	13697.0i	0.116240	+	0.891543i
$619$	−20038.9			−1.30118			−0.650589	−	0.759430i	$-0.725478\pi$
$619$	−20038.9			−1.30118			−0.650589	+	0.759430i	$0.725478\pi$
$620$	2322.35	−	4817.78i	0.150432	−	0.312075i
$621$	−19284.8	+	5489.33i	−1.24617	+	0.354717i
$622$	11281.6	−	7085.73i	0.727251	−	0.456771i
$623$	−22465.7	+	20400.2i	−1.44473	+	1.31190i
$624$	−3260.49	−	13249.7i	−0.209173	−	0.850021i
$625$	13705.6			0.877156
$626$	−9036.55	−	14387.6i	−0.576954	−	0.918600i
$627$	17511.2	+	8055.66i	1.11536	+	0.513097i
$628$	−132.761	+	275.417i	−0.00843591	+	0.0175005i
$629$		−	4604.54i		−	0.291884i
$630$	1360.03	+	2921.12i	0.0860076	+	0.184731i
$631$	24780.4			1.56338			0.781689	−	0.623669i	$-0.214359\pi$
$631$	24780.4			1.56338			0.781689	+	0.623669i	$0.214359\pi$
$632$	−96.1727	−	857.898i	−0.00605307	−	0.0539958i
$633$	8920.68	−	19391.6i	0.560134	−	1.21761i
$634$	20329.7	−	12768.7i	1.27350	−	0.799858i
$635$			106.258i			0.00664051i
$636$	16281.6	−	13450.4i	1.01511	−	0.838590i
$637$	−1353.15	+	14008.4i	−0.0841659	+	0.871323i
$638$	−11964.0	+	7514.34i	−0.742412	+	0.466294i
$639$	16334.5	−	13996.7i	1.01124	−	0.866511i
$640$	2329.84	+	2335.97i	0.143899	+	0.144277i
$641$			17191.8i			1.05934i	0.848205	+	0.529668i	$0.177684\pi$
$641$			17191.8i			1.05934i	−0.848205	+	0.529668i	$0.822316\pi$
$642$	29853.7	−	3892.34i	1.83525	−	0.239281i
$643$	6251.36			0.383405			0.191703	−	0.981453i	$-0.438599\pi$
$643$	6251.36			0.383405			0.191703	+	0.981453i	$0.438599\pi$
$644$	20302.4	−	6015.98i	1.24228	−	0.368110i
$645$	764.784	+	351.822i	0.0466874	+	0.0214775i
$646$	7463.80	−	4687.86i	0.454581	−	0.285513i
$647$	−24046.1			−1.46113			−0.730565	−	0.682843i	$-0.760743\pi$
$647$	−24046.1			−1.46113			−0.730565	+	0.682843i	$0.760743\pi$
$648$	−16480.7	−	696.122i	−0.999109	−	0.0422010i
$649$		−	6837.84i		−	0.413573i
$650$	11774.5	−	7395.30i	0.710512	−	0.446258i
$651$	−8509.43	−	26926.9i	−0.512305	−	1.62112i
$652$	−20812.0	−	10032.1i	−1.25009	−	0.602590i
$653$	15862.2			0.950593			0.475296	−	0.879826i	$-0.342341\pi$
$653$	15862.2			0.950593			0.475296	+	0.879826i	$0.342341\pi$
$654$	453.807	+	3480.63i	0.0271334	+	0.208109i
$655$	5683.05			0.339016
$656$	−5741.01	−	7210.10i	−0.341690	−	0.429127i
$657$	10461.8	−	8964.49i	0.621240	−	0.532326i
$658$	−5180.87	+	18522.6i	−0.306948	+	1.09740i
$659$	16357.6			0.966922			0.483461	−	0.875366i	$-0.339380\pi$
$659$	16357.6			0.966922			0.483461	+	0.875366i	$0.339380\pi$
$660$	−2040.46	−	2469.96i	−0.120341	−	0.145672i
$661$	−1599.08			−0.0940954			−0.0470477	−	0.998893i	$-0.514981\pi$
$661$	−1599.08			−0.0940954			−0.0470477	+	0.998893i	$0.514981\pi$
$662$	16510.3	+	26287.0i	0.969324	+	1.54331i
$663$	5504.33	+	2532.14i	0.322429	+	0.148326i
$664$	−21899.9	+	2455.04i	−1.27994	+	0.143485i
$665$	3110.32	+	3425.24i	0.181373	+	0.199737i
$666$	−3674.55	+	11815.5i	−0.213793	+	0.687449i
$667$		−	21102.4i		−	1.22502i
$668$	1068.95	−	2217.56i	0.0619144	−	0.128443i
$669$	−8439.50	+	18345.6i	−0.487728	+	1.06021i
$670$	−2901.93	+	1822.65i	−0.167331	+	0.105097i
$671$	12305.0			0.707941
$672$	17411.6	+	547.769i	0.999506	+	0.0314444i
$673$	22120.1			1.26696			0.633481	−	0.773758i	$-0.281625\pi$
$673$	22120.1			1.26696			0.633481	+	0.773758i	$0.281625\pi$
$674$	−3903.41	+	2451.65i	−0.223077	+	0.140110i
$675$	−4601.77	−	16166.6i	−0.262403	−	0.921859i
$676$	−1783.66	+	3700.25i	−0.101483	+	0.210529i
$677$			1541.71i			0.0875227i	0.999042	+	0.0437613i	$0.0139341\pi$
$677$			1541.71i			0.0875227i	−0.999042	+	0.0437613i	$0.986066\pi$
$678$	−1.60739	−	12.3285i	−9.10495e−5	−	0.000698336i
$679$	−1661.79	−	1830.04i	−0.0939227	−	0.103432i
$680$	−1455.85	+	163.204i	−0.0821018	+	0.00920383i
$681$	5559.93	−	12086.1i	0.312859	−	0.680087i
$682$	14933.9	+	23777.1i	0.838489	+	1.33500i
$683$	−25827.4			−1.44694			−0.723468	−	0.690357i	$-0.757453\pi$
$683$	−25827.4			−1.44694			−0.723468	+	0.690357i	$0.757453\pi$
$684$	−22893.6	+	6072.99i	−1.27976	+	0.339483i
$685$	−459.689			−0.0256406
$686$	−16757.8	−	6481.09i	−0.932677	−	0.360713i
$687$	5721.81	+	2632.19i	0.317759	+	0.146178i
$688$	3560.38	−	2834.94i	0.197294	−	0.157094i
$689$	20845.3			1.15260
$690$	4745.16	−	618.677i	0.261805	−	0.0341343i
$691$	21254.8			1.17015			0.585073	−	0.810981i	$-0.301066\pi$
$691$	21254.8			1.17015			0.585073	+	0.810981i	$0.301066\pi$
$692$	−19755.4	−	9522.84i	−1.08524	−	0.523127i
$693$	−16784.1	−	2110.26i	−0.920022	−	0.115674i
$694$	−7403.00	+	4649.67i	−0.404919	+	0.254322i
$695$			704.917i			0.0384734i
$696$	5453.20	−	16481.8i	0.296987	−	0.897615i
$697$	4092.45			0.222400
$698$	20162.9	−	12663.9i	1.09338	−	0.686729i
$699$	−9660.81	+	21000.5i	−0.522755	+	1.13635i
$700$	5043.26	+	17019.8i	0.272311	+	0.918981i
$701$	12172.2			0.655829			0.327914	−	0.944707i	$-0.393654\pi$
$701$	12172.2			0.655829			0.327914	+	0.944707i	$0.393654\pi$
$702$	−12103.7	−	10890.2i	−0.650747	−	0.585506i
$703$			17767.1i			0.953200i
$704$	−16890.7	+	3835.18i	−0.904249	+	0.205318i
$705$	−1816.55	+	3948.77i	−0.0970426	+	0.210950i
$706$	1662.96	−	1044.47i	0.0886489	−	0.0556786i
$707$	2106.19	+	2319.44i	0.112039	+	0.123383i
$708$	5351.35	+	6477.77i	0.284062	+	0.343855i
$709$		−	24941.7i		−	1.32117i	−0.750753	−	0.660583i	$-0.770309\pi$
$709$		−	24941.7i		−	1.32117i	0.750753	−	0.660583i	$-0.229691\pi$
$710$	−4347.44	+	2730.54i	−0.229798	+	0.144331i
$711$	−670.256	−	782.207i	−0.0353538	−	0.0412589i
$712$	4130.40	+	36844.8i	0.217407	+	1.93935i
$713$	−41938.6			−2.20282
$714$	−5006.14	+	5896.71i	−0.262395	+	0.309074i
$715$		−	3162.29i		−	0.165403i
$716$	2534.93	−	5258.79i	0.132311	−	0.274484i
$717$	1031.84	−	2242.99i	0.0537442	−	0.116828i
$718$	−5019.22	−	7991.37i	−0.260885	−	0.415370i
$719$	9926.70			0.514887			0.257443	−	0.966293i	$-0.417120\pi$
$719$	9926.70			0.514887			0.257443	+	0.966293i	$0.417120\pi$
$720$	3866.03	+	743.016i	0.200109	+	0.0384591i
$721$	−11701.4	−	12886.2i	−0.604416	−	0.665613i
$722$	−12371.3	+	7770.19i	−0.637692	+	0.400522i
$723$	−15876.6	+	34512.4i	−0.816679	+	1.77528i
$724$	7145.08	−	14822.7i	0.366775	−	0.760885i
$725$	17690.4			0.906212
$726$	−2719.11	+	354.520i	−0.139003	+	0.0181232i
$727$		−	18517.3i		−	0.944659i	−0.881422	−	0.472330i	$-0.843413\pi$
$727$		−	18517.3i		−	0.944659i	0.881422	−	0.472330i	$-0.156587\pi$
$728$	12905.4	+	11362.6i	0.657011	+	0.578467i
$729$	−16732.5	+	10365.5i	−0.850099	+	0.526623i
$730$	−2784.41	+	1748.83i	−0.141172	+	0.0886675i
$731$			2020.87i			0.102250i
$732$	−11657.0	+	9629.99i	−0.588601	+	0.486249i
$733$	−2791.96			−0.140687			−0.0703434	−	0.997523i	$-0.522409\pi$
$733$	−2791.96			−0.140687			−0.0703434	+	0.997523i	$0.522409\pi$
$734$	13352.7	+	21259.6i	0.671468	+	1.06908i
$735$	−3508.59	−	2043.78i	−0.176076	−	0.102566i
$736$	8567.53	−	24411.1i	0.429081	−	1.22256i
$737$		−	17990.6i		−	0.899174i
$738$	−10501.5	−	3265.89i	−0.523800	−	0.162899i
$739$		−	7989.50i		−	0.397698i	−0.980030	−	0.198849i	$-0.936280\pi$
$739$		−	7989.50i		−	0.397698i	0.980030	−	0.198849i	$-0.0637203\pi$
$740$	1282.30	−	2660.17i	0.0637005	−	0.132148i
$741$	−21239.1	−	9770.55i	−1.05295	−	0.484386i
$742$	−7168.59	+	25629.1i	−0.354673	+	1.26802i
$743$		−	10189.8i		−	0.503131i	−0.967840	−	0.251565i	$-0.919055\pi$
$743$		−	10189.8i		−	0.503131i	0.967840	−	0.251565i	$-0.0809454\pi$
$744$	−32755.7	−	10837.6i	−1.61409	−	0.534041i
$745$		−	2751.67i		−	0.135320i
$746$	2383.75	+	3795.30i	0.116991	+	0.186268i
$747$	−19967.8	+	17109.9i	−0.978022	+	0.838044i
$748$	3339.57	−	6928.03i	0.163244	−	0.338655i
$749$	−28086.5	+	25504.2i	−1.37017	+	1.24420i
$750$	1059.76	+	8128.17i	0.0515958	+	0.395732i
$751$	−7615.28			−0.370020			−0.185010	−	0.982737i	$-0.559232\pi$
$751$	−7615.28			−0.370020			−0.185010	+	0.982737i	$0.559232\pi$
$752$	14637.5	+	18383.1i	0.709807	+	0.891442i
$753$	13022.8	−	28308.7i	0.630248	−	1.37002i
$754$	14510.9	−	9114.00i	0.700870	−	0.440202i
$755$		−	5822.10i		−	0.280646i
$756$	17551.8	−	11136.2i	0.844381	−	0.535743i
$757$			3586.57i			0.172201i	0.996286	+	0.0861004i	$0.0274406\pi$
$757$			3586.57i			0.172201i	−0.996286	+	0.0861004i	$0.972559\pi$
$758$	−2188.22	−	3483.99i	−0.104855	−	0.166945i
$759$	−10499.3	+	22823.2i	−0.502110	+	1.09148i
$760$	5617.55	−	629.743i	0.268118	−	0.0300568i
$761$	−17846.0			−0.850089			−0.425045	−	0.905172i	$-0.639742\pi$
$761$	−17846.0			−0.850089			−0.425045	+	0.905172i	$0.639742\pi$
$762$	679.721	−	88.6226i	0.0323146	−	0.00421320i
$763$	−2973.53	−	3274.60i	−0.141086	−	0.155371i
$764$	16509.2	+	7958.03i	0.781780	+	0.376847i
$765$	−1327.40	+	1137.42i	−0.0627351	+	0.0537562i
$766$	−34367.3	+	21585.4i	−1.62107	+	1.01816i
$767$			8293.49i			0.390431i
$768$	12999.8	−	16852.0i	0.610794	−	0.791790i
$769$			16449.0i			0.771346i	0.922636	+	0.385673i	$0.126031\pi$
$769$			16449.0i			0.771346i	−0.922636	+	0.385673i	$0.873969\pi$
$770$	3888.00	+	1087.49i	0.181966	+	0.0508969i
$771$	11936.2	+	5490.99i	0.557552	+	0.256489i
$772$	−10940.6	+	22696.6i	−0.510053	+	1.05812i
$773$			34278.9i			1.59499i	0.603328	+	0.797493i	$0.293841\pi$
$773$			34278.9i			1.59499i	−0.603328	+	0.797493i	$0.706159\pi$
$774$	1612.71	−	5185.67i	0.0748937	−	0.240820i
$775$		−	35157.6i		−	1.62955i
$776$	−3001.36	+	336.460i	−0.138843	+	0.0155647i
$777$	−4698.54	−	14867.9i	−0.216936	−	0.686464i
$778$	−6063.82	+	3808.56i	−0.279432	+	0.175506i
$779$	−15791.2			−0.726287
$780$	2474.84	+	2995.77i	0.113607	+	0.137520i
$781$		−	26952.0i		−	1.23485i
$782$	6109.91	+	9727.92i	0.279399	+	0.444846i
$783$	−5671.24	−	19923.8i	−0.258842	−	0.909349i
$784$	−18408.2	+	11959.5i	−0.838566	+	0.544800i
$785$		−	87.0698i		−	0.00395880i
$786$	−4739.84	−	36353.9i	−0.215095	−	1.64974i
$787$	17734.8			0.803273			0.401636	−	0.915799i	$-0.368442\pi$
$787$	17734.8			0.803273			0.401636	+	0.915799i	$0.368442\pi$
$788$	−1444.94	+	2997.58i	−0.0653224	+	0.135513i
$789$	14750.2	−	32063.8i	0.665554	−	1.44677i
$790$	130.757	+	208.185i	0.00588874	+	0.00937579i
$791$	10.5323	+	11.5987i	0.000473433	+	0.000521368i
$792$	−14098.3	+	15112.6i	−0.632526	+	0.678036i
$793$	−14924.5			−0.668327
$794$	−16677.1	+	10474.5i	−0.745399	+	0.468170i
$795$	−2513.49	+	5463.78i	−0.112131	+	0.243749i
$796$	−8663.93	−	4176.34i	−0.385785	−	0.185963i
$797$		−	10674.8i		−	0.474428i	−0.971457	−	0.237214i	$-0.923766\pi$
$797$		−	10674.8i		−	0.474428i	0.971457	−	0.237214i	$-0.0762343\pi$
$798$	19316.8	−	22753.1i	0.856900	−	1.00934i
$799$	−10434.3			−0.462000
$800$	20464.1	+	7182.26i	0.904393	+	0.317414i
$801$	28786.0	+	33594.1i	1.26979	+	1.48188i
$802$	9659.20	+	15378.9i	0.425285	+	0.677119i
$803$		−	17262.0i		−	0.758608i
$804$	14079.6	+	17043.2i	0.617597	+	0.747597i
$805$	−4464.27	+	4053.82i	−0.195460	+	0.177489i
$806$	−18113.1	−	28838.8i	−0.791570	−	1.26030i
$807$	−6006.79	+	13057.5i	−0.262019	+	0.569572i
$808$	3803.99	−	426.438i	0.165624	−	0.0185669i
$809$			40808.4i			1.77348i	0.462265	+	0.886742i	$0.347037\pi$
$809$			40808.4i			1.77348i	−0.462265	+	0.886742i	$0.652963\pi$
$810$	4313.88	−	1859.38i	0.187129	−	0.0806568i
$811$	18140.2			0.785436			0.392718	−	0.919659i	$-0.371535\pi$
$811$	18140.2			0.785436			0.392718	+	0.919659i	$0.371535\pi$
$812$	6215.34	+	20975.2i	0.268615	+	0.906510i
$813$	−2005.87	+	4360.32i	−0.0865299	+	0.188097i
$814$	8245.87	+	13128.7i	0.355059	+	0.565308i
$815$	6579.45			0.282783
$816$	2258.22	+	9176.78i	0.0968795	+	0.393691i
$817$		−	7797.76i		−	0.333915i
$818$	977.849	+	1556.89i	0.0417967	+	0.0665468i
$819$	20357.1	+	2559.49i	0.868541	+	0.109201i
$820$	2364.33	+	1139.69i	0.100690	+	0.0485364i
$821$	7359.71			0.312857			0.156429	−	0.987689i	$-0.450002\pi$
$821$	7359.71			0.312857			0.156429	+	0.987689i	$0.450002\pi$
$822$	383.394	+	2940.58i	0.0162681	+	0.124774i
$823$	23969.6			1.01522			0.507611	−	0.861586i	$-0.330529\pi$
$823$	23969.6			1.01522			0.507611	+	0.861586i	$0.330529\pi$
$824$	−21134.0	+	2369.18i	−0.893492	+	0.100163i
$825$	−19133.0	−	8801.70i	−0.807424	−	0.371437i
$826$	−10196.7	−	2852.08i	−0.429528	−	0.120141i
$827$	−35380.2			−1.48765			−0.743827	−	0.668373i	$-0.766991\pi$
$827$	−35380.2			−1.48765			−0.743827	+	0.668373i	$0.766991\pi$
$828$	−7915.22	−	29838.3i	−0.332214	−	1.25236i
$829$	29620.3			1.24096			0.620479	−	0.784223i	$-0.286938\pi$
$829$	29620.3			1.24096			0.620479	+	0.784223i	$0.286938\pi$
$830$	5314.42	−	3337.88i	0.222248	−	0.139590i
$831$	8064.67	−	17530.8i	0.336655	−	0.731815i
$832$	20486.4	−	4651.61i	0.853650	−	0.193829i
$833$	937.194	−	9702.25i	0.0389818	−	0.403557i
$834$	4509.27	−	587.922i	0.187222	−	0.0244102i
$835$			701.056i			0.0290551i
$836$	−12886.1	+	26732.6i	−0.533104	+	1.10594i
$837$	−39596.4	+	11270.9i	−1.63519	+	0.465449i
$838$	−4124.30	−	6566.52i	−0.170014	−	0.270688i
$839$	25895.0			1.06555			0.532774	−	0.846257i	$-0.321149\pi$
$839$	25895.0			1.06555			0.532774	+	0.846257i	$0.321149\pi$
$840$	−4534.35	+	2012.55i	−0.186250	+	0.0826663i
$841$	−2587.32			−0.106085
$842$	−8495.92	−	13526.8i	−0.347730	−	0.553640i
$843$	−10351.1	+	22501.1i	−0.422908	+	0.919309i
$844$	29603.1	+	14269.8i	1.20732	+	0.581975i
$845$		−	1169.79i		−	0.0476237i
$846$	26774.9	+	8326.84i	1.08811	+	0.338396i
$847$	2558.16	−	2322.96i	0.103777	−	0.0942359i
$848$	20253.4	+	25436.1i	0.820170	+	1.03005i
$849$	38902.8	+	17896.3i	1.57260	+	0.723441i
$850$	−8155.03	+	5122.01i	−0.329077	+	0.206686i
$851$	−23156.7			−0.932787
$852$	21092.8	+	25532.7i	0.848156	+	1.02669i
$853$	37192.4			1.49290			0.746449	−	0.665442i	$-0.231757\pi$
$853$	37192.4			1.49290			0.746449	+	0.665442i	$0.231757\pi$
$854$	5132.44	−	18349.5i	0.205654	−	0.735252i
$855$	5121.93	−	4388.86i	0.204873	−	0.175551i
$856$	5163.81	+	46063.2i	0.206186	+	1.83926i
$857$	−16970.1			−0.676414			−0.338207	−	0.941072i	$-0.609820\pi$
$857$	−16970.1			−0.676414			−0.338207	+	0.941072i	$0.609820\pi$
$858$	−20228.8	+	2637.45i	−0.804896	+	0.104943i
$859$	−31307.1			−1.24352			−0.621760	−	0.783208i	$-0.713582\pi$
$859$	−31307.1			−1.24352			−0.621760	+	0.783208i	$0.713582\pi$
$860$	−562.786	+	1167.51i	−0.0223149	+	0.0462929i
$861$	13214.4	−	4176.01i	0.523049	−	0.165294i
$862$	−1909.11	−	3039.59i	−0.0754343	−	0.120103i
$863$		−	35041.9i		−	1.38220i	−0.722759	−	0.691101i	$-0.757126\pi$
$863$		−	35041.9i		−	1.38220i	0.722759	−	0.691101i	$-0.242874\pi$
$864$	1528.60	−	25350.3i	0.0601899	−	0.998187i
$865$	6245.43			0.245493
$866$	−14992.0	−	23869.6i	−0.588279	−	0.936631i
$867$	19380.0	+	8915.35i	0.759147	+	0.349228i
$868$	41685.9	−	12352.3i	1.63008	−	0.483023i
$869$	−1290.64			−0.0503821
$870$	639.179	+	4902.41i	0.0249083	+	0.191043i
$871$			21820.4i			0.848859i
$872$	−5370.50	+	602.047i	−0.208564	+	0.0233806i
$873$	−2736.55	+	2344.89i	−0.106092	+	0.0909078i
$874$	−23575.8	−	37536.2i	−0.912428	−	1.45273i
$875$	−6943.96	−	7647.03i	−0.268284	−	0.295448i
$876$	13509.4	+	16353.0i	0.521050	+	0.630727i
$877$		−	19272.8i		−	0.742070i	−0.928619	−	0.371035i	$-0.879003\pi$
$877$		−	19272.8i		−	0.742070i	0.928619	−	0.371035i	$-0.120997\pi$
$878$	−25730.5	−	40966.9i	−0.989023	−	1.57468i
$879$	−10762.0	+	23394.2i	−0.412961	+	0.897686i
$880$	3858.72	−	3072.49i	0.147815	−	0.117697i
$881$	−40919.7			−1.56484			−0.782418	−	0.622754i	$-0.786014\pi$
$881$	−40919.7			−1.56484			−0.782418	+	0.622754i	$0.786014\pi$
$882$	−10147.6	+	24148.6i	−0.387399	+	0.921912i
$883$			31577.4i			1.20347i	0.798696	+	0.601735i	$0.205524\pi$
$883$			31577.4i			1.20347i	−0.798696	+	0.601735i	$0.794476\pi$
$884$	−4050.50	+	8402.87i	−0.154110	+	0.319705i
$885$	−2173.81	−	1000.01i	−0.0825670	−	0.0379831i
$886$	16179.8	−	10162.2i	0.613511	−	0.385334i
$887$	17298.4			0.654817			0.327409	−	0.944883i	$-0.393825\pi$
$887$	17298.4			0.654817			0.327409	+	0.944883i	$0.393825\pi$
$888$	−18086.3	−	5984.07i	−0.683487	−	0.226140i
$889$	−639.486	+	580.691i	−0.0241256	+	0.0219075i
$890$	−5615.70	−	8941.07i	−0.211504	−	0.336748i
$891$	−3779.23	+	24370.3i	−0.142098	+	0.916313i
$892$	−28006.3	−	13500.1i	−1.05126	−	0.506745i
$893$	40261.8			1.50875
$894$	−17602.1	+	2294.98i	−0.658505	+	0.0858563i
$895$			1662.50i			0.0620909i
$896$	−1326.05	+	26787.4i	−0.0494422	+	0.998777i
$897$	12734.4	−	27681.9i	0.474013	−	1.03040i
$898$	9864.81	+	15706.3i	0.366585	+	0.583659i
$899$		−	43328.4i		−	1.60743i
$900$	25013.8	−	6635.42i	0.926435	−	0.245756i
$901$	−14437.5			−0.533833
$902$	−11668.6	+	7328.83i	−0.430735	+	0.270536i
$903$	2062.13	+	6525.32i	0.0759949	+	0.240475i
$904$	19.0224	−	2.13246i	0.000699863	−	7.84565e-5i
$905$			4686.01i			0.172120i
$906$	−37243.4	+	4855.82i	−1.36570	+	0.178061i
$907$		−	28199.6i		−	1.03236i	−0.856480	−	0.516181i	$-0.827353\pi$
$907$		−	28199.6i		−	1.03236i	0.856480	−	0.516181i	$-0.172647\pi$
$908$	18450.5	+	8893.83i	0.674341	+	0.325058i
$909$	3468.37	−	2971.97i	0.126555	−	0.108442i
$910$	−4715.68	−	1319.00i	−0.171784	−	0.0480489i
$911$			37866.6i			1.37714i	0.725168	+	0.688571i	$0.241762\pi$
$911$			37866.6i			1.37714i	−0.725168	+	0.688571i	$0.758238\pi$
$912$	−8713.61	−	35409.6i	−0.316378	−	1.28567i
$913$			32946.8i			1.19428i
$914$	−1026.64	+	644.815i	−0.0371536	+	0.0233354i
$915$	1799.56	−	3911.86i	0.0650183	−	0.141336i
$916$	−4210.54	+	8734.88i	−0.151878	+	0.315075i
$917$	31057.4	+	34201.9i	1.11844	+	1.23168i
$918$	8383.05	+	7542.60i	0.301396	+	0.271180i
$919$	−47333.4			−1.69901			−0.849503	−	0.527584i	$-0.823098\pi$
$919$	−47333.4			−1.69901			−0.849503	+	0.527584i	$0.823098\pi$
$920$	820.773	+	7321.62i	0.0294131	+	0.262377i
$921$	−29042.3	−	13360.3i	−1.03906	−	0.477998i
$922$	21412.0	+	34091.1i	0.764821	+	1.21771i
$923$			32689.5i			1.16575i
$924$	3713.87	−	25778.1i	0.132227	−	0.917789i
$925$		−	19412.5i		−	0.690033i
$926$	16539.4	−	10388.1i	0.586954	−	0.368654i
$927$	−19269.4	+	16511.5i	−0.682729	+	0.585015i
$928$	25220.0	+	8851.44i	0.892120	+	0.313107i
$929$	−3499.09			−0.123575			−0.0617877	−	0.998089i	$-0.519680\pi$
$929$	−3499.09			−0.123575			−0.0617877	+	0.998089i	$0.519680\pi$
$930$	9742.98	−	1270.30i	0.343532	−	0.0447900i
$931$	−3616.27	+	37437.2i	−0.127302	+	1.31789i
$932$	−32059.2	−	15453.7i	−1.12675	−	0.543138i
$933$	22234.6	+	10228.5i	0.780201	+	0.358914i
$934$	−13729.2	−	21859.0i	−0.480977	−	0.765789i
$935$			2190.21i			0.0766070i
$936$	17099.5	−	18329.8i	0.597132	−	0.640095i
$937$			5794.61i			0.202029i	0.994885	+	0.101015i	$0.0322089\pi$
$937$			5794.61i			0.202029i	−0.994885	+	0.101015i	$0.967791\pi$
$938$	−26827.9	−	7503.92i	−0.933862	−	0.261206i
$939$	13044.6	−	28356.2i	0.453349	−	0.985483i
$940$	−6028.17	−	2905.80i	−0.209167	−	0.100826i
$941$		−	20620.2i		−	0.714345i	−0.934038	−	0.357173i	$-0.883741\pi$
$941$		−	20620.2i		−	0.714345i	0.934038	−	0.357173i	$-0.116259\pi$
$942$	−556.976	+	72.6189i	−0.0192646	+	0.00251173i
$943$		−	20581.4i		−	0.710734i
$944$	−10120.0	+	8057.98i	−0.348916	+	0.277823i
$945$	−3125.49	+	5027.19i	−0.107590	+	0.173052i
$946$	−3619.01	−	5762.02i	−0.124381	−	0.198033i
$947$	−2984.78			−0.102421			−0.0512103	−	0.998688i	$-0.516308\pi$
$947$	−2984.78			−0.102421			−0.0512103	+	0.998688i	$0.516308\pi$
$948$	1222.68	−	1010.07i	0.0418890	−	0.0346049i
$949$			20936.7i			0.716159i
$950$	31467.1	−	19763.8i	1.07466	−	0.674972i
$951$	40067.4	+	18432.1i	1.36622	+	0.628499i
$952$	−8938.28	−	7869.73i	−0.304298	−	0.267920i
$953$		−	1650.21i		−	0.0560920i	−0.999607	−	0.0280460i	$-0.991072\pi$
$953$		−	1650.21i		−	0.0560920i	0.999607	−	0.0280460i	$-0.00892849\pi$
$954$	37047.5	+	11521.6i	1.25729	+	0.391011i
$955$	−5219.17			−0.176846
$956$	3424.13	+	1650.56i	0.115841	+	0.0558398i
$957$	−23579.6	−	10847.3i	−0.796467	−	0.366397i
$958$	42291.9	−	26562.7i	1.42629	−	0.895827i
$959$	−2512.16	−	2766.51i	−0.0845899	−	0.0931547i
$960$	−1250.97	+	5930.57i	−0.0420572	+	0.199384i
$961$	−56319.3			−1.89048
$962$	−10001.3	−	15923.5i	−0.335191	−	0.533676i
$963$	35988.1	+	41999.2i	1.20426	+	1.40540i
$964$	−52686.4	−	25396.8i	−1.76028	−	0.848523i
$965$		−	7175.25i		−	0.239357i
$966$	29655.2	+	25176.5i	0.987723	+	0.838550i
$967$	19631.7			0.652858			0.326429	−	0.945222i	$-0.394155\pi$
$967$	19631.7			0.652858			0.326429	+	0.945222i	$0.394155\pi$
$968$	−470.327	−	4195.50i	−0.0156166	−	0.139306i
$969$	14710.2	+	6767.11i	0.487678	+	0.224346i
$970$	728.334	−	457.452i	0.0241087	−	0.0151422i
$971$			2477.59i			0.0818841i	0.999162	+	0.0409421i	$0.0130359\pi$
$971$			2477.59i			0.0818841i	−0.999162	+	0.0409421i	$0.986964\pi$
$972$	−15492.2	−	26044.6i	−0.511226	−	0.859447i
$973$	−4242.35	+	3852.31i	−0.139778	+	0.126926i
$974$	22915.1	−	14392.5i	0.753848	−	0.473477i
$975$	23206.0	+	10675.4i	0.762244	+	0.350653i
$976$	−14500.7	−	18211.3i	−0.475569	−	0.597264i
$977$		−	27876.8i		−	0.912853i	−0.889761	−	0.456427i	$-0.849129\pi$
$977$		−	27876.8i		−	0.912853i	0.889761	−	0.456427i	$-0.150871\pi$
$978$	−5487.46	−	42088.0i	−0.179417	−	1.37610i
$979$	55430.2			1.80956
$980$	3243.39	−	5344.27i	0.105721	−	0.174201i
$981$	−4896.67	+	4195.84i	−0.159367	+	0.136558i
$982$	−17148.6	+	10770.7i	−0.557263	+	0.350006i
$983$	55169.7			1.79007			0.895035	−	0.445996i	$-0.147150\pi$
$983$	55169.7			1.79007			0.895035	+	0.445996i	$0.147150\pi$
$984$	5318.57	−	16074.9i	0.172307	−	0.520781i
$985$		−	947.648i		−	0.0306544i
$986$	−10050.3	+	6312.38i	−0.324611	+	0.203882i
$987$	−33691.9	+	10647.3i	−1.08655	+	0.343371i
$988$	15629.3	−	32423.4i	0.503273	−	1.04405i
$989$	10163.2			0.326765
$990$	1747.85	−	5620.21i	0.0561114	−	0.180426i
$991$	−24768.7			−0.793949			−0.396975	−	0.917830i	$-0.629940\pi$
$991$	−24768.7			−0.793949			−0.396975	+	0.917830i	$0.629940\pi$
$992$	17591.3	−	50122.0i	0.563027	−	1.60421i
$993$	−23833.3	+	51808.4i	−0.761659	+	1.65568i
$994$	−40191.4	−	11241.7i	−1.28249	−	0.358719i
$995$	2739.00			0.0872683
$996$	−25784.4	−	31211.9i	−0.820293	−	0.992958i
$997$	−3203.48			−0.101760			−0.0508802	−	0.998705i	$-0.516203\pi$
$997$	−3203.48			−0.101760			−0.0508802	+	0.998705i	$0.516203\pi$
$998$	−26806.3	−	42679.8i	−0.850240	−	1.35371i
$999$	−21863.5	+	6223.34i	−0.692421	+	0.197095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.4.i.c.125.15	yes	80
3.2	odd	2	inner	168.4.i.c.125.65	yes	80
4.3	odd	2		672.4.i.c.209.68		80
7.6	odd	2	inner	168.4.i.c.125.16	yes	80
8.3	odd	2		672.4.i.c.209.13		80
8.5	even	2	inner	168.4.i.c.125.68	yes	80
12.11	even	2		672.4.i.c.209.65		80
21.20	even	2	inner	168.4.i.c.125.66	yes	80
24.5	odd	2	inner	168.4.i.c.125.14	yes	80
24.11	even	2		672.4.i.c.209.16		80
28.27	even	2		672.4.i.c.209.14		80
56.13	odd	2	inner	168.4.i.c.125.67	yes	80
56.27	even	2		672.4.i.c.209.67		80
84.83	odd	2		672.4.i.c.209.15		80
168.83	odd	2		672.4.i.c.209.66		80
168.125	even	2	inner	168.4.i.c.125.13	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.13	✓	80	168.125	even	2	inner
168.4.i.c.125.14	yes	80	24.5	odd	2	inner
168.4.i.c.125.15	yes	80	1.1	even	1	trivial
168.4.i.c.125.16	yes	80	7.6	odd	2	inner
168.4.i.c.125.65	yes	80	3.2	odd	2	inner
168.4.i.c.125.66	yes	80	21.20	even	2	inner
168.4.i.c.125.67	yes	80	56.13	odd	2	inner
168.4.i.c.125.68	yes	80	8.5	even	2	inner
672.4.i.c.209.13		80	8.3	odd	2
672.4.i.c.209.14		80	28.27	even	2
672.4.i.c.209.15		80	84.83	odd	2
672.4.i.c.209.16		80	24.11	even	2
672.4.i.c.209.65		80	12.11	even	2
672.4.i.c.209.66		80	168.83	odd	2
672.4.i.c.209.67		80	56.27	even	2
672.4.i.c.209.68		80	4.3	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+(-2.39518 + 1.50436i) q^{2} +(-4.72061 - 2.17161i) q^{3} +(3.47378 - 7.20645i) q^{4} +2.27823i q^{5} +(14.5736 - 1.90012i) q^{6} +(-13.7109 + 12.4503i) q^{7} +(2.52080 + 22.4866i) q^{8} +(17.5682 + 20.5026i) q^{9} +(-3.42729 - 5.45677i) q^{10} +33.8293 q^{11} +(-32.0479 + 26.4751i) q^{12} -41.0309 q^{13} +(14.1103 - 50.4470i) q^{14} +(4.94743 - 10.7546i) q^{15} +(-39.8658 - 50.0672i) q^{16} +28.4181 q^{17} +(-72.9225 - 22.6785i) q^{18} -109.654 q^{19} +(16.4180 + 7.91406i) q^{20} +(91.7611 - 28.9983i) q^{21} +(-81.0273 + 50.8916i) q^{22} -142.918i q^{23} +(36.9323 - 111.624i) q^{24} +119.810 q^{25} +(98.2764 - 61.7254i) q^{26} +(-38.4090 - 134.936i) q^{27} +(42.0940 + 142.057i) q^{28} +147.654 q^{29} +(4.32890 + 33.2020i) q^{30} -293.446i q^{31} +(170.805 + 59.9472i) q^{32} +(-159.695 - 73.4640i) q^{33} +(-68.0665 + 42.7512i) q^{34} +(-28.3647 - 31.2366i) q^{35} +(208.779 - 55.3830i) q^{36} -162.028i q^{37} +(262.642 - 164.960i) q^{38} +(193.691 + 89.1031i) q^{39} +(-51.2296 + 5.74297i) q^{40} +144.009 q^{41} +(-176.160 + 207.498i) q^{42} +71.1121i q^{43} +(117.515 - 243.789i) q^{44} +(-46.7097 + 40.0245i) q^{45} +(215.000 + 342.314i) q^{46} -367.170 q^{47} +(79.4642 + 322.920i) q^{48} +(32.9788 - 341.411i) q^{49} +(-286.966 + 180.237i) q^{50} +(-134.151 - 61.7130i) q^{51} +(-142.532 + 295.687i) q^{52} -508.040 q^{53} +(294.989 + 265.415i) q^{54} +77.0710i q^{55} +(-314.528 - 276.927i) q^{56} +(517.635 + 238.127i) q^{57} +(-353.658 + 222.125i) q^{58} -202.128i q^{59} +(-60.3164 - 73.0125i) q^{60} +363.737 q^{61} +(441.449 + 702.855i) q^{62} +(-496.141 - 62.3797i) q^{63} +(-499.291 + 113.368i) q^{64} -93.4779i q^{65} +(493.014 - 64.2796i) q^{66} -531.804i q^{67} +(98.7182 - 204.794i) q^{68} +(-310.362 + 674.659i) q^{69} +(114.930 + 32.1465i) q^{70} -796.705i q^{71} +(-416.747 + 446.732i) q^{72} -510.267i q^{73} +(243.749 + 388.087i) q^{74} +(-565.574 - 260.180i) q^{75} +(-380.915 + 790.219i) q^{76} +(-463.831 + 421.186i) q^{77} +(-597.968 + 77.9635i) q^{78} -38.1516 q^{79} +(114.065 - 90.8234i) q^{80} +(-111.715 + 720.389i) q^{81} +(-344.927 + 216.641i) q^{82} +973.913i q^{83} +(109.783 - 762.005i) q^{84} +64.7430i q^{85} +(-106.978 - 170.326i) q^{86} +(-697.016 - 320.647i) q^{87} +(85.2770 + 760.705i) q^{88} +1638.53 q^{89} +(51.6668 - 166.134i) q^{90} +(562.572 - 510.848i) q^{91} +(-1029.93 - 496.464i) q^{92} +(-637.249 + 1385.24i) q^{93} +(879.438 - 552.357i) q^{94} -249.818i q^{95} +(-676.121 - 653.909i) q^{96} +133.473i q^{97} +(434.616 + 867.353i) q^{98} +(594.321 + 693.589i) 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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