LMFDB - Embedded newform 168.4.i.c.125.14

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			125.14
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.16

$q$-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} +(51.5700 - 9.19455i) 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} +(-37.6866 + 88.5478i) 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} +(-137.351 - 55.5574i) 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} +(223.474 - 155.394i) 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} +(245.403 + 339.696i) 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} +(14.3877 + 499.840i) 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} +(20.9473 + 117.488i) 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} +(-769.030 + 36.0088i) 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} +(-592.596 + 768.129i) 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	$-0.355797\pi$
$13$	41.0309			0.875379			0.437689	+	0.899126i	$0.355797\pi$
$14$	51.5700	−	9.19455i	0.984475	−	0.175525i
$15$	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	$-0.564977\pi$
$17$	−28.4181			−0.405436			−0.202718	+	0.979237i	$0.564977\pi$
$18$	−72.9225	+	22.6785i	−0.954888	+	0.296965i
$19$	109.654			1.32402			0.662012	−	0.749493i	$-0.269703\pi$
$19$	109.654			1.32402			0.662012	+	0.749493i	$0.269703\pi$
$20$	−16.4180	+	7.91406i	−0.183558	+	0.0884819i
$21$	−37.6866	+	88.5478i	−0.391614	+	0.920130i
$22$	−81.0273	−	50.8916i	−0.785231	−	0.493188i
$23$			142.918i			1.29567i	0.761780	+	0.647835i	$0.224326\pi$
$23$			142.918i			1.29567i	−0.761780	+	0.647835i	$0.775674\pi$
$24$	−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
$28$	−137.351	−	55.5574i	−0.927034	−	0.374977i
$29$	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	$0.117211\pi$
$37$			162.028i			0.719926i	−0.932967	+	0.359963i	$0.882789\pi$
$38$	−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	$-0.588437\pi$
$41$	−144.009			−0.548545			−0.274273	+	0.961652i	$0.588437\pi$
$42$	223.474	−	155.394i	0.821020	−	0.570899i
$43$		−	71.1121i		−	0.252197i	−0.992018	−	0.126099i	$-0.959754\pi$
$43$		−	71.1121i		−	0.252197i	0.992018	−	0.126099i	$-0.0402456\pi$
$44$	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	$-0.307037\pi$
$47$	367.170			1.13951			0.569757	+	0.821813i	$0.307037\pi$
$48$	−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
$56$	245.403	+	339.696i	0.585594	+	0.810604i
$57$	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	$-0.624674\pi$
$61$	−363.737			−0.763472			−0.381736	+	0.924271i	$0.624674\pi$
$62$	−441.449	+	702.855i	−0.904260	+	1.43972i
$63$	14.3877	+	499.840i	0.0287727	+	0.999586i
$64$	−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	$0.161127\pi$
$67$			531.804i			0.969705i	−0.874596	+	0.484852i	$0.838873\pi$
$68$	−98.7182	−	204.794i	−0.176049	−	0.365219i
$69$	310.362	+	674.659i	0.541495	+	1.17709i
$70$	20.9473	+	117.488i	0.0357669	+	0.200608i
$71$			796.705i			1.33171i	0.746081	+	0.665855i	$0.231933\pi$
$71$			796.705i			1.33171i	−0.746081	+	0.665855i	$0.768067\pi$
$72$	−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	$0.777282\pi$
$84$	−769.030	+	36.0088i	−0.998906	+	0.0467724i
$85$		−	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	$-0.929757\pi$
$89$	−1638.53			−1.95150			−0.975750	+	0.218889i	$0.929757\pi$
$90$	−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	$0.977746\pi$
$98$	−592.596	+	768.129i	−0.610829	+	0.791762i
$99$	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
$105$	−201.732	−	85.8588i	−0.187496	−	0.0797996i
$106$	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	$-0.966536\pi$
$109$		−	238.831i		−	0.209871i	0.994479	−	0.104935i	$-0.0334635\pi$
$110$	115.943	−	184.599i	0.100497	−	0.160007i
$111$	351.862	+	764.871i	0.300876	+	0.654039i
$112$	−76.7561	−	1182.81i	−0.0647569	−	0.997901i
$113$			0.845945i			0.000704246i	1.00000		0.000352123i	$0.000112084\pi$
$113$			0.845945i			0.000704246i	−1.00000		0.000352123i	$0.999888\pi$
$114$	−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
$126$	717.480	−	1218.85i	0.507287	−	0.861777i
$127$	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	$-0.979960\pi$
$137$		−	201.774i		−	0.125830i	0.998019	−	0.0629151i	$-0.0200397\pi$
$138$	271.560	−	2082.83i	0.167513	−	1.28480i
$139$	−309.414			−0.188807			−0.0944034	−	0.995534i	$-0.530094\pi$
$139$	−309.414			−0.188807			−0.0944034	+	0.995534i	$0.530094\pi$
$140$	126.573	−	312.918i	0.0764095	−	0.188903i
$141$	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
$147$	−585.731	−	1683.28i	−0.328642	−	0.944455i
$148$	−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
$154$	1744.58	−	311.045i	0.912870	−	0.162758i
$155$	668.537			0.346440
$156$	1314.95	+	1086.30i	0.674876	+	0.557522i
$157$	38.2182			0.0194276			0.00971382	−	0.999953i	$-0.496908\pi$
$157$	38.2182			0.0194276			0.00971382	+	0.999953i	$0.496908\pi$
$158$	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	$0.244097\pi$
$163$			2887.96i			1.38775i	−0.720097	+	0.693873i	$0.755903\pi$
$164$	−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	$-0.522713\pi$
$167$	−307.719			−0.142587			−0.0712935	+	0.997455i	$0.522713\pi$
$168$	1896.14	+	1070.65i	0.870774	+	0.491683i
$169$	−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	$-0.638790\pi$
$181$	−2056.86			−0.844671			−0.422336	+	0.906440i	$0.638790\pi$
$182$	2115.96	−	377.261i	0.861789	−	0.153651i
$183$	−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
$189$	1153.38	+	2328.30i	0.443893	+	0.896080i
$190$	375.818	−	598.360i	0.143498	−	0.228471i
$191$		−	2290.89i		−	0.867868i	−0.900945	−	0.433934i	$-0.857125\pi$
$191$		−	2290.89i		−	0.867868i	0.900945	−	0.433934i	$-0.142875\pi$
$192$	−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
$196$	2574.92	−	948.325i	0.938382	−	0.345600i
$197$	−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
$210$	354.023	+	509.126i	0.116333	+	0.167300i
$211$		−	4107.87i		−	1.34027i	−0.742239	−	0.670135i	$-0.766236\pi$
$211$		−	4107.87i		−	1.34027i	0.742239	−	0.670135i	$-0.233764\pi$
$212$	−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	$-0.198321\pi$
$224$	−1595.53	+	2948.51i	−0.475919	+	0.879489i
$225$	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	$-0.444045\pi$
$229$	1212.09			0.349770			0.174885	+	0.984589i	$0.444045\pi$
$230$	779.870	+	489.821i	0.223579	+	0.140425i
$231$	−1274.91	+	2995.51i	−0.363130	+	0.853204i
$232$	372.207	−	3320.23i	0.105330	−	0.939585i
$233$			4448.69i			1.25083i	0.780292	+	0.625415i	$0.215070\pi$
$233$			4448.69i			1.25083i	−0.780292	+	0.625415i	$0.784930\pi$
$234$	−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
$238$	−1465.52	+	261.292i	−0.399141	+	0.0711640i
$239$		−	475.148i		−	0.128597i	−0.997931	−	0.0642987i	$-0.979519\pi$
$239$		−	475.148i		−	0.128597i	0.997931	−	0.0642987i	$-0.0204810\pi$
$240$	−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	$0.728113\pi$
$252$	−3552.09	+	1840.02i	−0.887939	+	0.459961i
$253$			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	$-0.400722\pi$
$257$	2528.53			0.613719			0.306859	+	0.951755i	$0.400722\pi$
$258$	−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	$-0.706810\pi$
$263$		−	6792.30i		−	1.59251i	0.604958	−	0.796257i	$-0.293190\pi$
$264$	−1249.39	−	3776.18i	−0.291269	−	0.880332i
$265$		−	1157.43i		−	0.268304i
$266$	5654.88	−	1008.22i	1.30347	−	0.232399i
$267$	−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
$273$	−1546.32	+	3633.20i	−0.342811	+	0.805462i
$274$	−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	$-0.868048\pi$
$277$		−	3713.69i		−	0.805537i	0.915302	−	0.402768i	$-0.131952\pi$
$278$	741.102	+	465.472i	0.159886	+	0.100421i
$279$	−6016.40	−	5155.32i	−1.29101	−	1.10624i
$280$	−773.907	+	559.084i	−0.165178	+	0.119327i
$281$			4766.56i			1.01192i	0.862557	+	0.505960i	$0.168862\pi$
$281$			4766.56i			1.01192i	−0.862557	+	0.505960i	$0.831138\pi$
$282$	−5350.98	−	697.665i	−1.12995	−	0.147324i
$283$	8241.05			1.73102			0.865512	−	0.500888i	$-0.166993\pi$
$283$	8241.05			1.73102			0.865512	+	0.500888i	$0.166993\pi$
$284$	−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	$-0.164487\pi$
$294$	−1129.34	+	4912.92i	−0.224029	+	0.974583i
$295$	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	$-0.693781\pi$
$307$	−6152.25			−1.14374			−0.571869	+	0.820345i	$0.693781\pi$
$308$	−4646.50	−	1879.47i	−0.859607	−	0.347703i
$309$	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	$-0.358725\pi$
$311$	4710.11			0.858798			0.429399	+	0.903115i	$0.358725\pi$
$312$	−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
$315$	−1138.75	+	32.7785i	−0.203687	+	0.00586305i
$316$	−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
$322$	1314.07	+	7370.27i	0.227422	+	1.27556i
$323$	−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	$0.364870\pi$
$331$			10975.0i			1.82247i	−0.411885	+	0.911236i	$0.635130\pi$
$332$	−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
$336$	−2930.93	−	5416.89i	−0.475880	−	0.879510i
$337$	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	$-0.276617\pi$
$349$	8418.13			1.29115			0.645576	+	0.763696i	$0.276617\pi$
$350$	6178.58	−	1101.60i	0.943597	−	0.168237i
$351$	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	$-0.483331\pi$
$353$	694.292			0.104684			0.0523420	+	0.998629i	$0.483331\pi$
$354$	−384.066	+	2945.73i	−0.0576635	+	0.442270i
$355$	−1815.08			−0.271364
$356$	−5691.87	−	11808.0i	−0.847384	−	1.75792i
$357$	1070.98	−	2516.36i	0.158774	−	0.373053i
$358$	−1747.84	−	1097.79i	−0.258035	−	0.162066i
$359$		−	3336.44i		−	0.490503i	−0.969460	−	0.245251i	$-0.921129\pi$
$359$		−	3336.44i		−	0.490503i	0.969460	−	0.245251i	$-0.0788705\pi$
$360$	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
$364$	−5635.65	−	2279.57i	−0.811506	−	0.328247i
$365$	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	$0.0350788\pi$
$373$			1584.56i			0.219960i	−0.993934	+	0.109980i	$0.964921\pi$
$374$	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
$378$	740.073	−	7311.80i	0.100702	−	0.994917i
$379$		−	1454.58i		−	0.197142i	−0.995130	−	0.0985711i	$-0.968573\pi$
$379$		−	1454.58i		−	0.197142i	0.995130	−	0.0985711i	$-0.0314272\pi$
$380$	−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	$-0.906477\pi$
$383$	−14348.5			−1.91429			−0.957147	+	0.289603i	$0.906477\pi$
$384$	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
$392$	−7594.02	−	1602.21i	−0.978460	−	0.206438i
$393$	−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	$-0.645062\pi$
$397$	−6962.76			−0.880229			−0.440115	+	0.897942i	$0.645062\pi$
$398$	−1808.62	+	2879.60i	−0.227783	+	0.362666i
$399$	−4132.50	+	9709.66i	−0.518506	+	1.21827i
$400$	−4776.30	+	5998.53i	−0.597038	+	0.749816i
$401$			6420.79i			0.799598i	0.916603	+	0.399799i	$0.130920\pi$
$401$			6420.79i			0.799598i	−0.916603	+	0.399799i	$0.869080\pi$
$402$	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
$406$	7614.51	−	1357.61i	0.930792	−	0.165954i
$407$			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	$0.948907\pi$
$420$	−82.0364	−	1752.03i	−0.00953087	−	0.203548i
$421$		−	5647.52i		−	0.653784i	−0.945062	−	0.326892i	$-0.893999\pi$
$421$		−	5647.52i		−	0.653784i	0.945062	−	0.326892i	$-0.106001\pi$
$422$	−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	$-0.977408\pi$
$431$		−	1269.04i		−	0.141828i	0.997482	−	0.0709139i	$-0.0225915\pi$
$432$	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	$0.813473\pi$
$434$	−2698.10	−	15133.0i	−0.298417	−	1.67375i
$435$	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
$441$	−6420.44	−	6674.14i	−0.693277	−	0.720671i
$442$	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
$448$	8257.22	−	4661.95i	0.870796	−	0.491644i
$449$			6557.46i			0.689233i	0.938744	+	0.344617i	$0.111991\pi$
$449$			6557.46i			0.689233i	−0.938744	+	0.344617i	$0.888009\pi$
$450$	−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	$-0.255395\pi$
$462$	7559.98	−	5256.86i	0.761304	−	0.529375i
$463$	−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
$476$	3903.26	+	1578.84i	0.375853	+	0.152029i
$477$	−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	$-0.181294\pi$
$479$	17657.1			1.68429			0.842143	+	0.539254i	$0.181294\pi$
$480$	1489.76	+	1540.36i	0.141662	+	0.146474i
$481$			6648.16i			0.630208i
$482$	−10998.4	+	17511.2i	−1.03934	+	1.65480i
$483$	−12655.1	−	5386.09i	−1.19219	−	0.507403i
$484$	−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
$490$	−1749.97	−	1350.07i	−0.161338	−	0.124469i
$491$	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	$-0.705210\pi$
$499$		−	17819.0i		−	1.59858i	0.600947	−	0.799289i	$-0.294790\pi$
$500$	−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	$-0.862087\pi$
$503$	−20477.4			−1.81520			−0.907599	+	0.419839i	$0.862087\pi$
$504$	11276.0	+	936.468i	0.996569	+	0.0827651i
$505$	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
$518$	1489.78	+	8355.79i	0.126365	+	0.708749i
$519$	−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	$-0.763110\pi$
$521$	−17496.1			−1.47125			−0.735623	+	0.677391i	$0.763110\pi$
$522$	−10767.3	+	3348.56i	−0.902819	+	0.280771i
$523$	1593.34			0.133216			0.0666079	−	0.997779i	$-0.478782\pi$
$523$	1593.34			0.133216			0.0666079	+	0.997779i	$0.478782\pi$
$524$	17976.5	−	8665.34i	1.49868	−	0.722419i
$525$	−4515.22	+	10608.9i	−0.375353	+	0.881923i
$526$	−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
$532$	−15061.2	−	6092.12i	−1.22742	−	0.496479i
$533$	−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	$0.110902\pi$
$541$			8592.00i			0.682807i	−0.939917	+	0.341404i	$0.889098\pi$
$542$	−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
$546$	9169.36	−	6375.94i	0.718704	−	0.499753i
$547$			468.066i			0.0365870i	0.999833	+	0.0182935i	$0.00582332\pi$
$547$			468.066i			0.0365870i	−0.999833	+	0.0182935i	$0.994177\pi$
$548$	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
$560$	2694.71	−	174.868i	0.203343	−	0.0131956i
$561$	−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
$567$	10500.8	+	8486.32i	0.777764	+	0.628557i
$568$	17915.2	+	2008.34i	1.32342	+	0.148359i
$569$		−	19130.4i		−	1.40947i	−0.709470	−	0.704735i	$-0.751066\pi$
$569$		−	19130.4i		−	1.40947i	0.709470	−	0.704735i	$-0.248934\pi$
$570$	474.683	−	3640.75i	0.0348812	−	0.267534i
$571$			13903.0i			1.01896i	0.860483	+	0.509479i	$0.170162\pi$
$571$			13903.0i			1.01896i	−0.860483	+	0.509479i	$0.829838\pi$
$572$	4821.76	+	10002.9i	0.352462	+	0.731192i
$573$	−4974.91	−	10814.4i	−0.362705	−	0.788441i
$574$	−7426.52	+	1324.09i	−0.540029	+	0.0962833i
$575$			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	$0.945671\pi$
$588$	10095.8	−	10068.4i	0.708067	−	0.706145i
$589$		−	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	$-0.492972\pi$
$593$	637.576			0.0441519			0.0220760	+	0.999756i	$0.492972\pi$
$594$	−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	$0.119576\pi$
$599$			10757.3i			0.733774i	−0.930266	+	0.366887i	$0.880424\pi$
$600$	−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	$0.993580\pi$
$602$	−653.844	−	3667.25i	−0.0442669	−	0.248282i
$603$	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
$609$	−5564.58	+	13074.4i	−0.370259	+	0.869955i
$610$	−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	$0.238127\pi$
$613$			20648.4i			1.36049i	−0.732983	+	0.680247i	$0.761873\pi$
$614$	14735.7	+	9255.22i	0.968544	+	0.608323i
$615$	−712.472	−	1548.76i	−0.0467149	−	0.101548i
$616$	8301.80	+	11491.7i	0.543001	+	0.751645i
$617$			8883.01i			0.579605i	0.957086	+	0.289803i	$0.0935897\pi$
$617$			8883.01i			0.579605i	−0.957086	+	0.289803i	$0.906410\pi$
$618$	1785.82	−	13697.0i	0.116240	−	0.891543i
$619$	20038.9			1.30118			0.650589	−	0.759430i	$-0.274522\pi$
$619$	20038.9			1.30118			0.650589	+	0.759430i	$0.274522\pi$
$620$	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
$630$	2776.82	+	1634.59i	0.175605	+	0.103371i
$631$	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	$-0.822316\pi$
$641$		−	17191.8i		−	1.05934i	0.848205	−	0.529668i	$-0.177684\pi$
$642$	−29853.7	−	3892.34i	−1.83525	−	0.239281i
$643$	−6251.36			−0.383405			−0.191703	−	0.981453i	$-0.561401\pi$
$643$	−6251.36			−0.383405			−0.191703	+	0.981453i	$0.561401\pi$
$644$	7940.14	−	19629.9i	0.485847	−	1.20113i
$645$	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	$-0.239257\pi$
$647$	24046.1			1.46113			0.730565	+	0.682843i	$0.239257\pi$
$648$	−16480.7	+	696.122i	−0.999109	+	0.0422010i
$649$		−	6837.84i		−	0.413573i
$650$	−11774.5	−	7395.30i	−0.710512	−	0.446258i
$651$	25984.0	+	11059.0i	1.56435	+	0.665799i
$652$	−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
$658$	18934.9	−	3375.96i	1.12182	−	0.200013i
$659$	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	$-0.485019\pi$
$661$	1599.08			0.0940954			0.0470477	+	0.998893i	$0.485019\pi$
$662$	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
$672$	−1128.86	+	17383.6i	−0.0648017	+	0.997898i
$673$	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
$686$	−1438.41	−	17909.8i	−0.0800563	−	0.996790i
$687$	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	$-0.698934\pi$
$691$	−21254.8			−1.17015			−0.585073	+	0.810981i	$0.698934\pi$
$692$	19755.4	−	9522.84i	1.08524	−	0.523127i
$693$	486.726	+	16909.2i	0.0266799	+	0.926881i
$694$	−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
$700$	−16456.0	−	6656.31i	−0.888541	−	0.359407i
$701$	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	$0.229691\pi$
$709$			24941.7i			1.32117i	−0.750753	+	0.660583i	$0.770309\pi$
$710$	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
$714$	−6350.72	+	4415.99i	−0.332871	+	0.231463i
$715$			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	$-0.582880\pi$
$719$	−9926.70			−0.514887			−0.257443	+	0.966293i	$0.582880\pi$
$720$	−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	$-0.156587\pi$
$728$	10069.1	+	13938.1i	0.512617	+	0.709586i
$729$	−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	$-0.477591\pi$
$733$	2791.96			0.140687			0.0703434	+	0.997523i	$0.477591\pi$
$734$	−13352.7	+	21259.6i	−0.671468	+	1.06908i
$735$	3834.91	−	1334.43i	0.192453	−	0.0669677i
$736$	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	$0.0637203\pi$
$739$			7989.50i			0.397698i	−0.980030	+	0.198849i	$0.936280\pi$
$740$	−1282.30	−	2660.17i	−0.0637005	−	0.132148i
$741$	21239.1	−	9770.55i	1.05295	−	0.484386i
$742$	−26199.6	+	4671.20i	−1.29625	+	0.231112i
$743$			10189.8i			0.503131i	0.967840	+	0.251565i	$0.0809454\pi$
$743$			10189.8i			0.503131i	−0.967840	+	0.251565i	$0.919055\pi$
$744$	−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
$756$	−12772.2	+	16399.7i	−0.614446	+	0.788959i
$757$		−	3586.57i		−	0.172201i	−0.996286	−	0.0861004i	$-0.972559\pi$
$757$		−	3586.57i		−	0.172201i	0.996286	−	0.0861004i	$-0.0274406\pi$
$758$	−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	$-0.360258\pi$
$761$	17846.0			0.850089			0.425045	+	0.905172i	$0.360258\pi$
$762$	−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	$0.873969\pi$
$770$	708.633	+	3974.55i	0.0331654	+	0.186017i
$771$	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
$777$	−14347.2	−	6106.29i	−0.662425	−	0.281933i
$778$	−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
$784$	15778.8	+	15261.8i	0.718784	+	0.695233i
$785$			87.0698i			0.00395880i
$786$	−4739.84	+	36353.9i	−0.215095	+	1.64974i
$787$	−17734.8			−0.803273			−0.401636	−	0.915799i	$-0.631558\pi$
$787$	−17734.8			−0.803273			−0.401636	+	0.915799i	$0.631558\pi$
$788$	−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	$-0.0762343\pi$
$798$	24505.0	−	17039.6i	1.08705	−	0.755884i
$799$	−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	$-0.652963\pi$
$809$		−	40808.4i		−	1.77348i	0.462265	−	0.886742i	$-0.347037\pi$
$810$	−4313.88	−	1859.38i	−0.187129	−	0.0806568i
$811$	−18140.2			−0.785436			−0.392718	−	0.919659i	$-0.628465\pi$
$811$	−18140.2			−0.785436			−0.392718	+	0.919659i	$0.628465\pi$
$812$	−20280.5	−	8203.27i	−0.876483	−	0.354530i
$813$	−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
$819$	590.341	+	20508.9i	0.0251870	+	0.875017i
$820$	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
$826$	−1858.47	−	10423.7i	−0.0782864	−	0.439089i
$827$	−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	$-0.713062\pi$
$829$	−29620.3			−1.24096			−0.620479	+	0.784223i	$0.713062\pi$
$830$	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	$-0.678851\pi$
$839$	−25895.0			−1.06555			−0.532774	+	0.846257i	$0.678851\pi$
$840$	−2439.20	+	4319.84i	−0.100191	+	0.177439i
$841$	−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	$-0.768243\pi$
$853$	−37192.4			−1.49290			−0.746449	+	0.665442i	$0.768243\pi$
$854$	−18757.9	+	3344.40i	−0.751619	+	0.134008i
$855$	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	$-0.390180\pi$
$857$	16970.1			0.676414			0.338207	+	0.941072i	$0.390180\pi$
$858$	−20228.8	−	2637.45i	−0.804896	−	0.104943i
$859$	31307.1			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$859$	31307.1			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$860$	562.786	+	1167.51i	0.0223149	+	0.0462929i
$861$	5427.20	−	12751.6i	0.214818	−	0.504733i
$862$	−1909.11	+	3039.59i	−0.0754343	+	0.120103i
$863$			35041.9i			1.38220i	0.722759	+	0.691101i	$0.242874\pi$
$863$			35041.9i			1.38220i	−0.722759	+	0.691101i	$0.757126\pi$
$864$	−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
$868$	−16303.1	+	40305.1i	−0.637514	+	1.57609i
$869$	−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	$0.120997\pi$
$877$			19272.8i			0.742070i	−0.928619	+	0.371035i	$0.879003\pi$
$878$	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	$-0.213986\pi$
$881$	40919.7			1.56484			0.782418	+	0.622754i	$0.213986\pi$
$882$	5337.78	+	25644.4i	0.203778	+	0.979017i
$883$		−	31577.4i		−	1.20347i	−0.798696	−	0.601735i	$-0.794476\pi$
$883$		−	31577.4i		−	1.20347i	0.798696	−	0.601735i	$-0.205524\pi$
$884$	−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	$-0.606175\pi$
$887$	−17298.4			−0.654817			−0.327409	+	0.944883i	$0.606175\pi$
$888$	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
$896$	−26790.8	−	1255.65i	−0.998903	−	0.0468172i
$897$	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
$903$	6296.82	+	2679.97i	0.232054	+	0.0987640i
$904$	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	$0.172647\pi$
$907$			28199.6i			1.03236i	−0.856480	+	0.516181i	$0.827353\pi$
$908$	−18450.5	+	8893.83i	−0.674341	+	0.325058i
$909$	−3468.37	−	2971.97i	−0.126555	−	0.108442i
$910$	859.487	+	4820.65i	0.0313096	+	0.175608i
$911$		−	37866.6i		−	1.37714i	−0.725168	−	0.688571i	$-0.758238\pi$
$911$		−	37866.6i		−	1.37714i	0.725168	−	0.688571i	$-0.241762\pi$
$912$	−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
$924$	−26015.8	+	1218.15i	−0.926251	+	0.0433704i
$925$			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	$-0.480320\pi$
$929$	3499.09			0.123575			0.0617877	+	0.998089i	$0.480320\pi$
$930$	−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	$0.967791\pi$
$938$	4889.70	+	27425.1i	0.170207	+	0.954650i
$939$	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
$945$	−5304.41	+	2627.66i	−0.182595	+	0.0904526i
$946$	−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
$952$	−6973.88	−	9653.53i	−0.237421	−	0.328648i
$953$			1650.21i			0.0560920i	0.999607	+	0.0280460i	$0.00892849\pi$
$953$			1650.21i			0.0560920i	−0.999607	+	0.0280460i	$0.991072\pi$
$954$	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
$966$	22208.5	+	31938.5i	0.739697	+	1.06377i
$967$	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	$0.150871\pi$
$977$			27876.8i			0.912853i	−0.889761	+	0.456427i	$0.849129\pi$
$978$	5487.46	−	42088.0i	0.179417	−	1.37610i
$979$	−55430.2			−1.80956
$980$	2160.50	+	5866.26i	0.0704232	+	0.191215i
$981$	−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	$-0.852850\pi$
$983$	−55169.7			−1.79007			−0.895035	+	0.445996i	$0.852850\pi$
$984$	5318.57	+	16074.9i	0.172307	+	0.520781i
$985$		−	947.648i		−	0.0306544i
$986$	10050.3	+	6312.38i	0.324611	+	0.203882i
$987$	−13837.4	+	32512.1i	−0.446250	+	1.04850i
$988$	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
$994$	7325.34	+	41086.0i	0.233748	+	1.31104i
$995$	2739.00			0.0872683
$996$	−25784.4	+	31211.9i	−0.820293	+	0.992958i
$997$	3203.48			0.101760			0.0508802	−	0.998705i	$-0.483797\pi$
$997$	3203.48			0.101760			0.0508802	+	0.998705i	$0.483797\pi$
$998$	−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.125.14	yes	80
3.2	odd	2	inner	168.4.i.c.125.68	yes	80
4.3	odd	2		672.4.i.c.209.16		80
7.6	odd	2	inner	168.4.i.c.125.13	✓	80
8.3	odd	2		672.4.i.c.209.65		80
8.5	even	2	inner	168.4.i.c.125.65	yes	80
12.11	even	2		672.4.i.c.209.13		80
21.20	even	2	inner	168.4.i.c.125.67	yes	80
24.5	odd	2	inner	168.4.i.c.125.15	yes	80
24.11	even	2		672.4.i.c.209.68		80
28.27	even	2		672.4.i.c.209.66		80
56.13	odd	2	inner	168.4.i.c.125.66	yes	80
56.27	even	2		672.4.i.c.209.15		80
84.83	odd	2		672.4.i.c.209.67		80
168.83	odd	2		672.4.i.c.209.14		80
168.125	even	2	inner	168.4.i.c.125.16	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.39518 - 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} +(51.5700 - 9.19455i) 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} +(-37.6866 + 88.5478i) 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} +(-137.351 - 55.5574i) 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} +(223.474 - 155.394i) 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} +(245.403 + 339.696i) 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} +(14.3877 + 499.840i) 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} +(20.9473 + 117.488i) 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} +(-769.030 + 36.0088i) 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} +(-592.596 + 768.129i) 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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