LMFDB - Embedded newform 168.4.i.c.125.65

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			125.65
Character	$\chi$	$=$	168.125
Dual form			168.4.i.c.125.67

$q$-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} +(-8.03981 + 12.3029i) 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} +(-0.748737 + 41.5625i) 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} +(11.2357 - 75.5365i) 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} +(60.7317 + 100.676i) 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} +(28.0289 + 18.3165i) 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} +(-86.7230 - 197.826i) 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} +(-42.9420 - 268.782i) 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} +(296.917 + 149.774i) 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} +(110.997 + 380.977i) 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} +(94.6889 + 1.70579i) 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} +(271.981 - 416.199i) 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} +(-505.320 - 343.366i) 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} +(329.881 - 504.799i) 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} +(-507.201 - 579.182i) 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} +(-172.090 - 25.5974i) 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} +(936.485 - 87.9343i) 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	$-0.967512\pi$
$5$		−	2.27823i		−	0.203771i	0.994796	−	0.101886i	$-0.0324876\pi$
$6$	−8.03981	+	12.3029i	−0.547040	+	0.837107i
$7$	−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	$-0.653454\pi$
$11$	−33.8293			−0.927265			−0.463633	+	0.886028i	$0.653454\pi$
$12$	−0.748737	+	41.5625i	−0.0180118	+	0.999838i
$13$	−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	$-0.564977\pi$
$17$	−28.4181			−0.405436			−0.202718	+	0.979237i	$0.564977\pi$
$18$	11.2357	−	75.5365i	0.147126	−	0.989118i
$19$	−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
$21$	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	$0.775674\pi$
$24$	60.7317	+	100.676i	0.516534	+	0.856267i
$25$	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	$-0.656733\pi$
$29$	−147.654			−0.945471			−0.472735	+	0.881204i	$0.656733\pi$
$30$	28.0289	+	18.3165i	0.170578	+	0.111471i
$31$		−	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
$36$	−86.7230	−	197.826i	−0.401495	−	0.915861i
$37$		−	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	$-0.588437\pi$
$41$	−144.009			−0.548545			−0.274273	+	0.961652i	$0.588437\pi$
$42$	−42.9420	−	268.782i	−0.157764	−	0.987477i
$43$			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	$-0.307037\pi$
$47$	367.170			1.13951			0.569757	+	0.821813i	$0.307037\pi$
$48$	296.917	+	149.774i	0.892839	+	0.450377i
$49$	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	$-0.271257\pi$
$53$	508.040			1.31669			0.658345	+	0.752716i	$0.271257\pi$
$54$	110.997	+	380.977i	0.279717	+	0.960082i
$55$			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	$0.0715872\pi$
$59$			202.128i			0.446013i	−0.974817	+	0.223007i	$0.928413\pi$
$60$	94.6889	+	1.70579i	0.203738	+	0.00367029i
$61$	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
$63$	14.3877	+	499.840i	0.0287727	+	0.999586i
$64$	−499.291	+	113.368i	−0.975178	+	0.221423i
$65$			93.4779i			0.178377i
$66$	271.981	−	416.199i	0.507251	−	0.776220i
$67$		−	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	$0.231933\pi$
$71$			796.705i			1.33171i	−0.746081	+	0.665855i	$0.768067\pi$
$72$	−505.320	−	343.366i	−0.827118	−	0.562029i
$73$		−	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
$78$	329.881	−	504.799i	0.478867	−	0.732786i
$79$	−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	$-0.777282\pi$
$83$		−	973.913i		−	1.28796i	0.765042	−	0.643981i	$-0.222718\pi$
$84$	−507.201	−	579.182i	−0.658811	−	0.752309i
$85$			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	$0.929757\pi$
$90$	−172.090	−	25.5974i	−0.201554	−	0.0299801i
$91$	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
$96$	936.485	−	87.9343i	0.995620	−	0.0934871i
$97$			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	$0.0265557\pi$
$101$			169.167i			0.166661i	−0.996522	+	0.0833306i	$0.973444\pi$
$102$	228.476	−	349.625i	0.221789	−	0.339393i
$103$			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	$-0.876264\pi$
$107$	−2048.48			−1.85078			−0.925392	+	0.379012i	$0.876264\pi$
$108$	838.986	+	745.530i	0.747513	+	0.664247i
$109$			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	$0.000112084\pi$
$113$			0.845945i			0.000704246i	−1.00000		0.000352123i	$0.999888\pi$
$114$	881.601	−	1349.07i	0.724294	−	1.10835i
$115$	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
$120$	229.363	−	138.361i	0.174482	−	0.105255i
$121$	−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
$126$	786.403	+	1175.56i	0.556018	+	0.831170i
$127$	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	$0.312720\pi$
$131$			2494.50i			1.66371i	−0.554995	+	0.831854i	$0.687280\pi$
$132$	25.3292	−	1406.03i	0.0167017	−	0.927115i
$133$	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	$-0.0200397\pi$
$138$	−1758.30	−	1149.03i	−1.08461	−	0.708783i
$139$	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
$144$	−1726.88	−	62.2387i	−0.999351	−	0.0360178i
$145$			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	$-0.392263\pi$
$149$	1207.81			0.664078			0.332039	+	0.943266i	$0.392263\pi$
$150$	−963.247	+	1474.01i	−0.524325	+	0.802348i
$151$	−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
$156$	30.7213	−	1705.35i	0.0157672	−	0.875237i
$157$	−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
$162$	−1351.31	−	1557.40i	−0.655361	−	0.755315i
$163$		−	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	$-0.522713\pi$
$167$	−307.719			−0.142587			−0.0712935	+	0.997455i	$0.522713\pi$
$168$	−2086.14	−	624.231i	−0.958030	−	0.286669i
$169$	−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	$0.205778\pi$
$173$			2741.35i			1.20475i	−0.798215	+	0.602373i	$0.794222\pi$
$174$	1187.11	−	1816.57i	0.517210	−	0.791460i
$175$	−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	$-0.548686\pi$
$179$	−729.734			−0.304709			−0.152354	+	0.988326i	$0.548686\pi$
$180$	−450.693	+	197.575i	−0.186626	+	0.0818132i
$181$	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
$186$	3610.23	+	2359.25i	1.42320	+	0.930045i
$187$	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	$-0.142875\pi$
$192$	2110.76	−	1619.43i	0.793392	−	0.608711i
$193$	−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	$-0.476035\pi$
$197$	415.958			0.150435			0.0752177	+	0.997167i	$0.476035\pi$
$198$	−380.094	+	2555.35i	−0.136425	+	0.917175i
$199$		−	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
$204$	21.2777	−	1181.13i	0.00730263	−	0.405370i
$205$			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
$210$	−612.348	+	97.8318i	−0.201219	+	0.0321478i
$211$			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
$216$	3131.07	+	523.539i	0.986307	+	0.164918i
$217$	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
$222$	1993.42	+	1302.68i	0.602655	+	0.393828i
$223$		−	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	$-0.877883\pi$
$227$		−	2560.28i		−	0.748598i	0.927308	−	0.374299i	$-0.122117\pi$
$228$	82.1023	−	4557.51i	0.0238481	−	1.32381i
$229$	−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
$231$	−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	$0.784930\pi$
$234$	−461.009	+	3099.33i	−0.128791	+	0.865853i
$235$		−	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	$-0.979519\pi$
$239$		−	475.148i		−	0.128597i	0.997931	−	0.0642987i	$-0.0204810\pi$
$240$	341.221	−	676.445i	0.0917738	−	0.181935i
$241$		−	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
$246$	1157.80	−	1771.72i	0.300076	−	0.459191i
$247$	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	$-0.728113\pi$
$251$		−	5996.84i		−	1.50804i	0.656853	−	0.754018i	$-0.271887\pi$
$252$	3652.05	+	1632.65i	0.912927	+	0.408124i
$253$		−	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	$0.400722\pi$
$258$	−874.885	−	571.727i	−0.211116	−	0.137962i
$259$	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	$-0.293190\pi$
$264$	−2054.51	−	3405.80i	−0.478964	−	0.793986i
$265$		−	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	$0.101493\pi$
$269$			2766.06i			0.626950i	−0.949597	+	0.313475i	$0.898507\pi$
$270$	867.954	−	252.876i	0.195637	−	0.0569983i
$271$		−	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
$276$	−5940.02	−	107.008i	−1.29546	−	0.0233374i
$277$			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	$0.168862\pi$
$281$			4766.56i			1.01192i	−0.862557	+	0.505960i	$0.831138\pi$
$282$	−2951.97	+	4517.25i	−0.623360	+	0.953896i
$283$	−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
$288$	−4229.82	+	2448.78i	−0.865431	+	0.501027i
$289$	−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	$0.164487\pi$
$293$			4955.76i			0.988118i	−0.869428	+	0.494059i	$0.835513\pi$
$294$	3935.20	+	3150.61i	0.780632	+	0.624991i
$295$	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
$300$	−89.7059	+	4979.59i	−0.0172639	+	0.958322i
$301$	−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
$306$	−319.296	+	2146.60i	−0.0596502	+	0.401024i
$307$	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	$-0.358725\pi$
$311$	4710.11			0.858798			0.429399	+	0.903115i	$0.358725\pi$
$312$	−2491.88	−	4130.83i	−0.452163	−	0.749558i
$313$			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	$-0.229125\pi$
$317$	8487.77			1.50385			0.751926	+	0.659248i	$0.229125\pi$
$318$	−4084.54	+	6250.36i	−0.720282	+	1.10221i
$319$	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
$324$	−5579.52	−	1697.40i	−0.956708	−	0.291050i
$325$	−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
$330$	−948.197	−	619.636i	−0.158171	−	0.103363i
$331$		−	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
$336$	−5935.74	+	1643.17i	−0.963754	+	0.266792i
$337$	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
$342$	−1232.04	+	8282.91i	−0.194799	+	1.30962i
$343$	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	$-0.576846\pi$
$347$	−3090.79			−0.478162			−0.239081	+	0.971000i	$0.576846\pi$
$348$	110.554	−	6136.86i	0.0170296	−	0.945317i
$349$	−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	$-0.483331\pi$
$353$	694.292			0.104684			0.0523420	+	0.998629i	$0.483331\pi$
$354$	−2486.76	−	1625.07i	−0.373361	−	0.243987i
$355$	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	$-0.0788705\pi$
$360$	−782.267	+	1151.23i	−0.114525	+	0.168543i
$361$	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
$366$	−2924.38	+	4475.03i	−0.417650	+	0.639108i
$367$		−	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
$372$	12196.3	+	219.713i	1.69987	+	0.0306226i
$373$		−	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
$378$	−6265.16	−	3841.61i	−0.852500	−	0.522727i
$379$			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	$-0.906477\pi$
$383$	−14348.5			−1.91429			−0.957147	+	0.289603i	$0.906477\pi$
$384$	2619.44	−	7054.19i	0.348107	−	0.937455i
$385$	−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	$-0.552759\pi$
$389$	−2531.67			−0.329977			−0.164988	+	0.986296i	$0.552759\pi$
$390$	−1150.05	−	751.544i	−0.149321	−	0.0975793i
$391$		−	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
$396$	2933.78	+	6692.32i	0.372293	+	0.849246i
$397$	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
$399$	−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	$0.869080\pi$
$402$	6542.74	+	4275.60i	0.811746	+	0.530467i
$403$			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
$408$	−1725.88	−	2861.02i	−0.209421	−	0.347161i
$409$		−	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
$414$	10795.5	+	1605.78i	1.28157	+	0.190627i
$415$	−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	$-0.948907\pi$
$419$		−	2741.55i		−	0.319651i	0.987145	−	0.159825i	$-0.0510931\pi$
$420$	−1319.51	+	1155.52i	−0.153299	+	0.134247i
$421$			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
$426$	−9801.78	−	6405.35i	−1.11478	−	0.728499i
$427$	−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	$-0.0225915\pi$
$432$	8287.07	−	3456.30i	0.922944	−	0.384934i
$433$			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
$438$	6277.77	+	4102.45i	0.684848	+	0.447541i
$439$			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	$-0.382011\pi$
$443$	6755.15			0.724485			0.362242	+	0.932084i	$0.382011\pi$
$444$	6734.29	+	121.316i	0.719809	+	0.0129672i
$445$			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	$0.111991\pi$
$449$			6557.46i			0.689233i	−0.938744	+	0.344617i	$0.888009\pi$
$450$	1346.14	−	9050.00i	0.141017	−	0.948047i
$451$	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
$456$	−6659.51	−	11039.6i	−0.683903	−	1.13372i
$457$	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	$0.255395\pi$
$461$			14233.2i			1.43798i	−0.695022	+	0.718988i	$0.744605\pi$
$462$	1452.70	+	9092.72i	0.146289	+	0.915653i
$463$	−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	$-0.850656\pi$
$467$		−	9126.22i		−	0.904307i	0.891940	−	0.452153i	$-0.149344\pi$
$468$	3558.32	+	8116.98i	0.351460	+	0.801726i
$469$	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
$474$	306.731	−	469.375i	0.0297229	−	0.0454834i
$475$	−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	$-0.181294\pi$
$479$	17657.1			1.68429			0.842143	+	0.539254i	$0.181294\pi$
$480$	−200.335	−	2133.53i	−0.0190500	−	0.202879i
$481$			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
$486$	9761.05	+	4417.38i	0.911050	+	0.412297i
$487$	−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	$-0.606722\pi$
$491$	−7159.61			−0.658063			−0.329031	+	0.944319i	$0.606722\pi$
$492$	107.824	−	5985.35i	0.00988029	−	0.548456i
$493$	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
$498$	11982.0	+	7830.07i	1.07816	+	0.704566i
$499$			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	$-0.862087\pi$
$503$	−20477.4			−1.81520			−0.907599	+	0.419839i	$0.862087\pi$
$504$	11203.4	−	1583.53i	0.990158	−	0.139952i
$505$	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	$-0.698130\pi$
$509$		−	18659.8i		−	1.62491i	0.583022	−	0.812457i	$-0.301870\pi$
$510$	−796.527	−	520.522i	−0.0691585	−	0.0451943i
$511$	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
$516$	−2955.59	−	53.2442i	−0.252157	−	0.00454253i
$517$	−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	$-0.763110\pi$
$521$	−17496.1			−1.47125			−0.735623	+	0.677391i	$0.763110\pi$
$522$	−1658.99	+	11153.3i	−0.139103	+	0.935182i
$523$	−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
$525$	4515.22	−	10608.9i	0.375353	−	0.881923i
$526$	−10218.1	−	16268.8i	−0.847016	−	1.34858i
$527$			8339.17i			0.689298i
$528$	−10044.5	−	5066.77i	−0.827898	−	0.417619i
$529$	−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
$534$	13173.4	−	20158.6i	1.06755	−	1.63361i
$535$			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
$540$	1698.49	−	1911.40i	0.135354	−	0.152322i
$541$		−	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
$546$	1761.95	+	11028.4i	0.138103	+	0.864416i
$547$		−	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
$552$	−14388.4	+	8679.65i	−1.10944	+	0.669258i
$553$	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	$-0.408656\pi$
$557$	7441.55			0.566084			0.283042	+	0.959108i	$0.408656\pi$
$558$	−22165.8	−	3297.05i	−1.68164	−	0.250135i
$559$		−	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	$0.183493\pi$
$563$			14562.5i			1.09012i	−0.838397	+	0.545059i	$0.816507\pi$
$564$	−274.913	+	15260.5i	−0.0205247	+	1.13933i
$565$	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	$-0.248934\pi$
$570$	−3073.49	−	2008.49i	−0.225850	−	0.147590i
$571$		−	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
$576$	−6447.31	+	12228.5i	−0.466385	+	0.884582i
$577$		−	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
$582$	−1642.11	−	1073.10i	−0.116955	−	0.0764286i
$583$	−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	$-0.945671\pi$
$587$		−	4831.23i		−	0.339704i	0.985470	−	0.169852i	$-0.0543290\pi$
$588$	14165.2	+	1626.31i	0.993474	+	0.114061i
$589$			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	$0.492972\pi$
$594$	−3754.94	−	12888.2i	−0.259372	−	0.890251i
$595$	−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	$0.880424\pi$
$600$	7276.25	+	12062.0i	0.495086	+	0.820712i
$601$			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
$606$	−2081.25	−	1360.07i	−0.139513	−	0.0911703i
$607$		−	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
$612$	2464.50	+	5621.84i	0.162780	+	0.371323i
$613$		−	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	$0.0935897\pi$
$617$			8883.01i			0.579605i	−0.957086	+	0.289803i	$0.906410\pi$
$618$	−11562.9	−	7556.21i	−0.752633	−	0.491837i
$619$	−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
$624$	−12182.8	−	6145.38i	−0.781572	−	0.394250i
$625$	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
$630$	2678.20	−	1791.61i	0.169369	−	0.113301i
$631$	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
$636$	−380.388	+	21115.4i	−0.0237160	+	1.31648i
$637$	−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	$-0.177684\pi$
$642$	16469.4	−	25202.2i	1.01245	−	1.54930i
$643$	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	$-0.239257\pi$
$647$	24046.1			1.46113			0.730565	+	0.682843i	$0.239257\pi$
$648$	−15917.5	+	4328.04i	−0.964965	+	0.262379i
$649$		−	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	$-0.657659\pi$
$653$	−15862.2			−0.950593			−0.475296	+	0.879826i	$0.657659\pi$
$654$	−2938.32	−	1920.16i	−0.175684	−	0.114808i
$655$	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	$-0.660620\pi$
$659$	−16357.6			−0.966922			−0.483461	+	0.875366i	$0.660620\pi$
$660$	−3203.26	−	57.7059i	−0.188919	−	0.00340333i
$661$	−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
$666$	−12239.0	−	1820.49i	−0.712092	−	0.105920i
$667$		−	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
$672$	−11745.3	+	12865.2i	−0.674231	+	0.738521i
$673$	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	$-0.986066\pi$
$677$		−	1541.71i		−	0.0875227i	0.999042	−	0.0437613i	$-0.0139341\pi$
$678$	−10.4076	−	6.80124i	−0.000589529	−	0.000385251i
$679$	−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	$-0.242547\pi$
$683$	25827.4			1.44694			0.723468	+	0.690357i	$0.242547\pi$
$684$	9509.56	+	21692.5i	0.531589	+	1.21262i
$685$	−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
$690$	−2617.76	+	4005.82i	−0.144430	+	0.221013i
$691$	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
$693$	−486.726	−	16909.2i	−0.0266799	−	0.926881i
$694$	−7403.00	+	4649.67i	−0.404919	+	0.254322i
$695$		−	704.917i		−	0.0384734i
$696$	−8967.28	−	14865.2i	−0.488368	−	0.809575i
$697$	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	$-0.606346\pi$
$701$	−12172.2			−0.655829			−0.327914	+	0.944707i	$0.606346\pi$
$702$	−4554.29	−	15631.8i	−0.244859	−	0.840436i
$703$			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
$708$	−8400.93	−	151.340i	−0.445941	−	0.00803351i
$709$		−	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
$714$	1220.33	+	7638.29i	0.0639632	+	0.400358i
$715$		−	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	$0.582880\pi$
$720$	−141.794	+	3934.23i	−0.00733938	+	0.203639i
$721$	−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
$726$	1500.05	−	2295.45i	0.0766835	−	0.117345i
$727$		−	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
$732$	−272.343	+	15117.8i	−0.0137515	+	0.763348i
$733$	−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
$735$	3834.91	−	1334.43i	0.192453	−	0.0669677i
$736$	8567.53	−	24411.1i	0.429081	−	1.22256i
$737$			17990.6i			0.899174i
$738$	−1618.03	+	10877.9i	−0.0807054	+	0.542576i
$739$		−	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	$0.0809454\pi$
$743$			10189.8i			0.503131i	−0.967840	+	0.251565i	$0.919055\pi$
$744$	29542.9	−	17821.5i	1.45577	−	0.878181i
$745$		−	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
$750$	6861.74	+	4484.07i	0.334074	+	0.218313i
$751$	−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
$756$	−20785.4	+	223.741i	−0.999942	+	0.0107637i
$757$			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	$-0.360258\pi$
$761$	17846.0			0.850089			0.425045	+	0.905172i	$0.360258\pi$
$762$	−374.982	+	573.815i	−0.0178270	+	0.0272797i
$763$	−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
$768$	−4338.04	−	20836.7i	−0.203822	−	0.979008i
$769$			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	$-0.706159\pi$
$773$		−	34278.9i		−	1.59499i	0.603328	−	0.797493i	$-0.293841\pi$
$774$	5371.56	+	798.991i	0.249453	+	0.0371048i
$775$		−	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
$780$	−3885.17	−	69.9903i	−0.178348	−	0.00321289i
$781$		−	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
$786$	−30689.6	−	20055.3i	−1.39270	−	0.910114i
$787$	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
$792$	17094.6	+	11615.8i	0.766958	+	0.521150i
$793$	−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	$0.0762343\pi$
$797$			10674.8i			0.474428i	−0.971457	+	0.237214i	$0.923766\pi$
$798$	4708.78	+	29473.2i	0.208884	+	1.30744i
$799$	−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
$804$	22103.1	+	398.181i	0.969547	+	0.0174661i
$805$	−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	$-0.347037\pi$
$810$	−3548.12	+	3078.59i	−0.153912	+	0.133544i
$811$	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
$816$	−8437.82	−	4256.31i	−0.361989	−	0.182599i
$817$		−	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	$-0.549998\pi$
$821$	−7359.71			−0.312857			−0.156429	+	0.987689i	$0.549998\pi$
$822$	2482.41	+	1622.23i	0.105333	+	0.0688341i
$823$	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	$-0.233009\pi$
$827$	35380.2			1.48765			0.743827	+	0.668373i	$0.233009\pi$
$828$	28272.9	−	12394.3i	1.18665	−	0.520206i
$829$	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
$834$	−2487.63	+	3806.69i	−0.103285	+	0.158052i
$835$			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	$0.678851\pi$
$840$	−1422.14	+	4752.70i	−0.0584149	+	0.195219i
$841$	−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
$846$	4125.39	−	27734.7i	0.167652	−	1.12711i
$847$	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
$852$	−33113.0	−	596.522i	−1.33149	−	0.0239865i
$853$	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	$-0.390180\pi$
$857$	16970.1			0.676414			0.338207	+	0.941072i	$0.390180\pi$
$858$	−11159.6	+	17077.0i	−0.444037	+	0.679487i
$859$	−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
$861$	−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	$0.757126\pi$
$864$	14649.5	−	20745.2i	0.576835	−	0.816860i
$865$	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
$870$	−4138.57	−	2704.51i	−0.161277	−	0.105392i
$871$			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
$876$	21208.0	+	382.056i	0.817981	+	0.0147357i
$877$		−	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	$-0.213986\pi$
$881$	40919.7			1.56484			0.782418	+	0.622754i	$0.213986\pi$
$882$	−25418.4	−	6327.08i	−0.970389	−	0.241546i
$883$			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	$-0.606175\pi$
$887$	−17298.4			−0.654817			−0.327409	+	0.944883i	$0.606175\pi$
$888$	16312.3	−	9840.25i	0.616449	−	0.371866i
$889$	−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
$894$	−9710.56	+	14859.6i	−0.363277	+	0.555904i
$895$			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
$900$	−10390.2	−	23701.5i	−0.384824	−	0.877832i
$901$	−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
$906$	20546.0	−	31440.5i	0.753417	−	1.15292i
$907$		−	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	$-0.758238\pi$
$911$		−	37866.6i		−	1.37714i	0.725168	−	0.688571i	$-0.241762\pi$
$912$	−32558.3	−	16423.4i	−1.18214	−	0.596310i
$913$			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
$918$	−3154.31	−	10826.7i	−0.113407	−	0.389252i
$919$	−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
$924$	17158.2	+	19593.3i	0.610892	+	0.697590i
$925$		−	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	$0.480320\pi$
$930$	5374.91	−	8224.95i	0.189516	−	0.290007i
$931$	−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
$936$	20733.7	+	14088.6i	0.724041	+	0.491988i
$937$			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	$0.116259\pi$
$941$			20620.2i			0.714345i	−0.934038	+	0.357173i	$0.883741\pi$
$942$	307.267	−	470.194i	0.0106277	−	0.0162630i
$943$		−	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	$-0.483692\pi$
$947$	2984.78			0.102421			0.0512103	+	0.998688i	$0.483692\pi$
$948$	28.5655	−	1585.67i	0.000978654	−	0.0543252i
$949$			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	$0.00892849\pi$
$953$			1650.21i			0.0560920i	−0.999607	+	0.0280460i	$0.991072\pi$
$954$	5708.16	−	38375.5i	0.193720	−	1.30236i
$955$	−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
$960$	−3689.44	−	4808.81i	−0.124038	−	0.161670i
$961$	−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
$966$	38413.8	−	6137.18i	1.27944	−	0.204410i
$967$	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	$-0.986964\pi$
$971$		−	2477.59i		−	0.0818841i	0.999162	−	0.0409421i	$-0.0130359\pi$
$972$	30024.8	−	4103.76i	0.990788	−	0.135420i
$973$	−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	$0.849129\pi$
$978$	35530.3	+	23218.7i	1.16169	+	0.759153i
$979$	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	$-0.852850\pi$
$983$	−55169.7			−1.79007			−0.895035	+	0.445996i	$0.852850\pi$
$984$	−8745.89	−	14498.2i	−0.283342	−	0.469701i
$985$		−	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
$990$	5821.67	+	865.943i	0.186894	+	0.0277995i
$991$	−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
$996$	40478.2	+	729.204i	1.28775	+	0.0231985i
$997$	−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.125.65	yes	80
3.2	odd	2	inner	168.4.i.c.125.15	yes	80
4.3	odd	2		672.4.i.c.209.65		80
7.6	odd	2	inner	168.4.i.c.125.66	yes	80
8.3	odd	2		672.4.i.c.209.16		80
8.5	even	2	inner	168.4.i.c.125.14	yes	80
12.11	even	2		672.4.i.c.209.68		80
21.20	even	2	inner	168.4.i.c.125.16	yes	80
24.5	odd	2	inner	168.4.i.c.125.68	yes	80
24.11	even	2		672.4.i.c.209.13		80
28.27	even	2		672.4.i.c.209.15		80
56.13	odd	2	inner	168.4.i.c.125.13	✓	80
56.27	even	2		672.4.i.c.209.66		80
84.83	odd	2		672.4.i.c.209.14		80
168.83	odd	2		672.4.i.c.209.67		80
168.125	even	2	inner	168.4.i.c.125.67	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.i.c.125.13	✓	80	56.13	odd	2	inner
168.4.i.c.125.14	yes	80	8.5	even	2	inner
168.4.i.c.125.15	yes	80	3.2	odd	2	inner
168.4.i.c.125.16	yes	80	21.20	even	2	inner
168.4.i.c.125.65	yes	80	1.1	even	1	trivial
168.4.i.c.125.66	yes	80	7.6	odd	2	inner
168.4.i.c.125.67	yes	80	168.125	even	2	inner
168.4.i.c.125.68	yes	80	24.5	odd	2	inner
672.4.i.c.209.13		80	24.11	even	2
672.4.i.c.209.14		80	84.83	odd	2
672.4.i.c.209.15		80	28.27	even	2
672.4.i.c.209.16		80	8.3	odd	2
672.4.i.c.209.65		80	4.3	odd	2
672.4.i.c.209.66		80	56.27	even	2
672.4.i.c.209.67		80	168.83	odd	2
672.4.i.c.209.68		80	12.11	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} +(-8.03981 + 12.3029i) 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} +(-0.748737 + 41.5625i) 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} +(11.2357 - 75.5365i) 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} +(60.7317 + 100.676i) 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} +(28.0289 + 18.3165i) 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} +(-86.7230 - 197.826i) 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} +(-42.9420 - 268.782i) 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} +(296.917 + 149.774i) 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} +(110.997 + 380.977i) 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} +(94.6889 + 1.70579i) 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} +(271.981 - 416.199i) 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} +(-505.320 - 343.366i) 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} +(329.881 - 504.799i) 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} +(-507.201 - 579.182i) 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} +(-172.090 - 25.5974i) 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} +(936.485 - 87.9343i) 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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