LMFDB - Embedded newform 228.2.c.a.191.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.32
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17379 + 0.788801i) q^{2} +(-0.726100 - 1.57251i) q^{3} +(0.755587 + 1.85178i) q^{4} -2.76393i q^{5} +(0.388103 - 2.41855i) q^{6} -4.18351i q^{7} +(-0.573780 + 2.76962i) q^{8} +(-1.94556 + 2.28359i) q^{9} +O(q^{10})$	\(q+(1.17379 + 0.788801i) q^{2} +(-0.726100 - 1.57251i) q^{3} +(0.755587 + 1.85178i) q^{4} -2.76393i q^{5} +(0.388103 - 2.41855i) q^{6} -4.18351i q^{7} +(-0.573780 + 2.76962i) q^{8} +(-1.94556 + 2.28359i) q^{9} +(2.18019 - 3.24429i) q^{10} -1.17477 q^{11} +(2.36330 - 2.53274i) q^{12} +5.33740 q^{13} +(3.29995 - 4.91058i) q^{14} +(-4.34630 + 2.00689i) q^{15} +(-2.85818 + 2.79836i) q^{16} +6.95552i q^{17} +(-4.08499 + 1.14581i) q^{18} -1.00000i q^{19} +(5.11819 - 2.08839i) q^{20} +(-6.57859 + 3.03764i) q^{21} +(-1.37893 - 0.926656i) q^{22} +2.96927 q^{23} +(4.77186 - 1.10874i) q^{24} -2.63932 q^{25} +(6.26501 + 4.21014i) q^{26} +(5.00364 + 1.40129i) q^{27} +(7.74693 - 3.16100i) q^{28} -3.64543i q^{29} +(-6.68470 - 1.07269i) q^{30} +4.24292i q^{31} +(-5.56226 + 1.03017i) q^{32} +(0.852997 + 1.84733i) q^{33} +(-5.48652 + 8.16435i) q^{34} -11.5629 q^{35} +(-5.69875 - 1.87729i) q^{36} -2.32811 q^{37} +(0.788801 - 1.17379i) q^{38} +(-3.87548 - 8.39310i) q^{39} +(7.65503 + 1.58589i) q^{40} -3.23553i q^{41} +(-10.1180 - 1.62363i) q^{42} +8.22758i q^{43} +(-0.887638 - 2.17541i) q^{44} +(6.31170 + 5.37739i) q^{45} +(3.48532 + 2.34216i) q^{46} -7.26033 q^{47} +(6.47577 + 2.46261i) q^{48} -10.5017 q^{49} +(-3.09802 - 2.08190i) q^{50} +(10.9376 - 5.05040i) q^{51} +(4.03287 + 9.88369i) q^{52} -0.986407i q^{53} +(4.76791 + 5.59170i) q^{54} +3.24697i q^{55} +(11.5867 + 2.40041i) q^{56} +(-1.57251 + 0.726100i) q^{57} +(2.87552 - 4.27898i) q^{58} +2.71307 q^{59} +(-7.00033 - 6.53201i) q^{60} +11.4780 q^{61} +(-3.34682 + 4.98031i) q^{62} +(9.55343 + 8.13925i) q^{63} +(-7.34155 - 3.17830i) q^{64} -14.7522i q^{65} +(-0.455929 + 2.84123i) q^{66} +0.752666i q^{67} +(-12.8801 + 5.25550i) q^{68} +(-2.15599 - 4.66920i) q^{69} +(-13.5725 - 9.12084i) q^{70} -4.98154 q^{71} +(-5.20836 - 6.69873i) q^{72} -5.51948 q^{73} +(-2.73272 - 1.83641i) q^{74} +(1.91641 + 4.15035i) q^{75} +(1.85178 - 0.755587i) q^{76} +4.91464i q^{77} +(2.07146 - 12.9088i) q^{78} +3.62388i q^{79} +(7.73448 + 7.89980i) q^{80} +(-1.42961 - 8.88573i) q^{81} +(2.55219 - 3.79785i) q^{82} +8.74980 q^{83} +(-10.5957 - 9.88690i) q^{84} +19.2246 q^{85} +(-6.48992 + 9.65749i) q^{86} +(-5.73246 + 2.64694i) q^{87} +(0.674057 - 3.25365i) q^{88} -7.44872i q^{89} +(3.16695 + 11.2906i) q^{90} -22.3290i q^{91} +(2.24355 + 5.49844i) q^{92} +(6.67202 - 3.08078i) q^{93} +(-8.52213 - 5.72695i) q^{94} -2.76393 q^{95} +(5.65871 + 7.99869i) q^{96} -3.52257 q^{97} +(-12.3269 - 8.28376i) q^{98} +(2.28557 - 2.68269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.17379	+	0.788801i	0.829998	+	0.557766i
$2$	1.17379	+	0.788801i	0.829998	+	0.557766i
$3$	−0.726100	−	1.57251i	−0.419214	−	0.907887i
$3$	−0.726100	−	1.57251i	−0.419214	−	0.907887i
$4$	0.755587	+	1.85178i	0.377794	+	0.925890i
$5$		−	2.76393i		−	1.23607i	−0.786151	−	0.618034i	$-0.787929\pi$
$5$		−	2.76393i		−	1.23607i	0.786151	−	0.618034i	$-0.212071\pi$
$6$	0.388103	−	2.41855i	0.158442	−	0.987368i
$7$		−	4.18351i		−	1.58122i	−0.612322	−	0.790608i	$-0.709765\pi$
$7$		−	4.18351i		−	1.58122i	0.612322	−	0.790608i	$-0.290235\pi$
$8$	−0.573780	+	2.76962i	−0.202862	+	0.979207i
$9$	−1.94556	+	2.28359i	−0.648519	+	0.761198i
$10$	2.18019	−	3.24429i	0.689437	−	1.02593i
$11$	−1.17477			−0.354205			−0.177103	−	0.984192i	$-0.556672\pi$
$11$	−1.17477			−0.354205			−0.177103	+	0.984192i	$0.556672\pi$
$12$	2.36330	−	2.53274i	0.682227	−	0.731140i
$13$	5.33740			1.48033			0.740164	−	0.672426i	$-0.234748\pi$
$13$	5.33740			1.48033			0.740164	+	0.672426i	$0.234748\pi$
$14$	3.29995	−	4.91058i	0.881949	−	1.31241i
$15$	−4.34630	+	2.00689i	−1.12221	+	0.518177i
$16$	−2.85818	+	2.79836i	−0.714544	+	0.699591i
$17$			6.95552i			1.68696i	0.537159	+	0.843481i	$0.319497\pi$
$17$			6.95552i			1.68696i	−0.537159	+	0.843481i	$0.680503\pi$
$18$	−4.08499	+	1.14581i	−0.962840	+	0.270071i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	5.11819	−	2.08839i	1.14446	−	0.466979i
$21$	−6.57859	+	3.03764i	−1.43557	+	0.662868i
$22$	−1.37893	−	0.926656i	−0.293990	−	0.197564i
$23$	2.96927			0.619136			0.309568	−	0.950877i	$-0.399816\pi$
$23$	2.96927			0.619136			0.309568	+	0.950877i	$0.399816\pi$
$24$	4.77186	−	1.10874i	0.974053	−	0.226321i
$25$	−2.63932			−0.527864
$26$	6.26501	+	4.21014i	1.22867	+	0.825677i
$27$	5.00364	+	1.40129i	0.962951	+	0.269678i
$28$	7.74693	−	3.16100i	1.46403	−	0.597374i
$29$		−	3.64543i		−	0.676939i	−0.940977	−	0.338469i	$-0.890091\pi$
$29$		−	3.64543i		−	0.676939i	0.940977	−	0.338469i	$-0.109909\pi$
$30$	−6.68470	−	1.07269i	−1.22045	−	0.195845i
$31$			4.24292i			0.762050i	0.924565	+	0.381025i	$0.124429\pi$
$31$			4.24292i			0.762050i	−0.924565	+	0.381025i	$0.875571\pi$
$32$	−5.56226	+	1.03017i	−0.983278	+	0.182110i
$33$	0.852997	+	1.84733i	0.148488	+	0.321578i
$34$	−5.48652	+	8.16435i	−0.940930	+	1.40018i
$35$	−11.5629			−1.95449
$36$	−5.69875	−	1.87729i	−0.949792	−	0.312882i
$37$	−2.32811			−0.382738			−0.191369	−	0.981518i	$-0.561293\pi$
$37$	−2.32811			−0.382738			−0.191369	+	0.981518i	$0.561293\pi$
$38$	0.788801	−	1.17379i	0.127960	−	0.190415i
$39$	−3.87548	−	8.39310i	−0.620574	−	1.34397i
$40$	7.65503	+	1.58589i	1.21037	+	0.250751i
$41$		−	3.23553i		−	0.505305i	−0.967557	−	0.252652i	$-0.918697\pi$
$41$		−	3.23553i		−	0.505305i	0.967557	−	0.252652i	$-0.0813029\pi$
$42$	−10.1180	−	1.62363i	−1.56124	−	0.250531i
$43$			8.22758i			1.25469i	0.778740	+	0.627347i	$0.215859\pi$
$43$			8.22758i			1.25469i	−0.778740	+	0.627347i	$0.784141\pi$
$44$	−0.887638	−	2.17541i	−0.133816	−	0.327955i
$45$	6.31170	+	5.37739i	0.940893	+	0.801614i
$46$	3.48532	+	2.34216i	0.513882	+	0.345333i
$47$	−7.26033			−1.05903			−0.529514	−	0.848301i	$-0.677626\pi$
$47$	−7.26033			−1.05903			−0.529514	+	0.848301i	$0.677626\pi$
$48$	6.47577	+	2.46261i	0.934696	+	0.355447i
$49$	−10.5017			−1.50025
$50$	−3.09802	−	2.08190i	−0.438126	−	0.294425i
$51$	10.9376	−	5.05040i	1.53157	−	0.707198i
$52$	4.03287	+	9.88369i	0.559259	+	1.37062i
$53$		−	0.986407i		−	0.135493i	−0.997703	−	0.0677467i	$-0.978419\pi$
$53$		−	0.986407i		−	0.135493i	0.997703	−	0.0677467i	$-0.0215810\pi$
$54$	4.76791	+	5.59170i	0.648830	+	0.760933i
$55$			3.24697i			0.437822i
$56$	11.5867	+	2.40041i	1.54834	+	0.320769i
$57$	−1.57251	+	0.726100i	−0.208284	+	0.0961743i
$58$	2.87552	−	4.27898i	0.377574	−	0.561858i
$59$	2.71307			0.353211			0.176606	−	0.984282i	$-0.443488\pi$
$59$	2.71307			0.353211			0.176606	+	0.984282i	$0.443488\pi$
$60$	−7.00033	−	6.53201i	−0.903739	−	0.843279i
$61$	11.4780			1.46961			0.734805	−	0.678278i	$-0.237274\pi$
$61$	11.4780			1.46961			0.734805	+	0.678278i	$0.237274\pi$
$62$	−3.34682	+	4.98031i	−0.425046	+	0.632500i
$63$	9.55343	+	8.13925i	1.20362	+	1.02545i
$64$	−7.34155	−	3.17830i	−0.917694	−	0.397288i
$65$		−	14.7522i		−	1.82979i
$66$	−0.455929	+	2.84123i	−0.0561210	+	0.349731i
$67$			0.752666i			0.0919528i	0.998943	+	0.0459764i	$0.0146399\pi$
$67$			0.752666i			0.0919528i	−0.998943	+	0.0459764i	$0.985360\pi$
$68$	−12.8801	+	5.25550i	−1.56194	+	0.637324i
$69$	−2.15599	−	4.66920i	−0.259551	−	0.562106i
$70$	−13.5725	−	9.12084i	−1.62222	−	1.09015i
$71$	−4.98154			−0.591200			−0.295600	−	0.955312i	$-0.595520\pi$
$71$	−4.98154			−0.591200			−0.295600	+	0.955312i	$0.595520\pi$
$72$	−5.20836	−	6.69873i	−0.613811	−	0.789453i
$73$	−5.51948			−0.646006			−0.323003	−	0.946398i	$-0.604692\pi$
$73$	−5.51948			−0.646006			−0.323003	+	0.946398i	$0.604692\pi$
$74$	−2.73272	−	1.83641i	−0.317672	−	0.213479i
$75$	1.91641	+	4.15035i	0.221288	+	0.479241i
$76$	1.85178	−	0.755587i	0.212414	−	0.0866718i
$77$			4.91464i			0.560075i
$78$	2.07146	−	12.9088i	0.234546	−	1.46163i
$79$			3.62388i			0.407718i	0.979000	+	0.203859i	$0.0653484\pi$
$79$			3.62388i			0.407718i	−0.979000	+	0.203859i	$0.934652\pi$
$80$	7.73448	+	7.89980i	0.864742	+	0.883225i
$81$	−1.42961	−	8.88573i	−0.158845	−	0.987303i
$82$	2.55219	−	3.79785i	0.281842	−	0.419402i
$83$	8.74980			0.960416			0.480208	−	0.877155i	$-0.340561\pi$
$83$	8.74980			0.960416			0.480208	+	0.877155i	$0.340561\pi$
$84$	−10.5957	−	9.88690i	−1.15609	−	1.07875i
$85$	19.2246			2.08520
$86$	−6.48992	+	9.65749i	−0.699826	+	1.04139i
$87$	−5.73246	+	2.64694i	−0.614584	+	0.283782i
$88$	0.674057	−	3.25365i	0.0718548	−	0.346840i
$89$		−	7.44872i		−	0.789563i	−0.918775	−	0.394781i	$-0.870820\pi$
$89$		−	7.44872i		−	0.789563i	0.918775	−	0.394781i	$-0.129180\pi$
$90$	3.16695	+	11.2906i	0.333826	+	1.19014i
$91$		−	22.3290i		−	2.34072i
$92$	2.24355	+	5.49844i	0.233906	+	0.573252i
$93$	6.67202	−	3.08078i	0.691856	−	0.319462i
$94$	−8.52213	−	5.72695i	−0.878991	−	0.590690i
$95$	−2.76393			−0.283573
$96$	5.65871	+	7.99869i	0.577540	+	0.816363i
$97$	−3.52257			−0.357663			−0.178831	−	0.983880i	$-0.557232\pi$
$97$	−3.52257			−0.357663			−0.178831	+	0.983880i	$0.557232\pi$
$98$	−12.3269	−	8.28376i	−1.24520	−	0.836786i
$99$	2.28557	−	2.68269i	0.229709	−	0.269620i
$100$	−1.99424	−	4.88744i	−0.199424	−	0.488744i
$101$			8.07416i			0.803409i	0.915769	+	0.401705i	$0.131582\pi$
$101$			8.07416i			0.803409i	−0.915769	+	0.401705i	$0.868418\pi$
$102$	16.8223	+	2.69946i	1.66565	+	0.267286i
$103$			8.33291i			0.821066i	0.911846	+	0.410533i	$0.134657\pi$
$103$			8.33291i			0.821066i	−0.911846	+	0.410533i	$0.865343\pi$
$104$	−3.06250	+	14.7825i	−0.300302	+	1.44955i
$105$	8.39584	+	18.1828i	0.819350	+	1.77446i
$106$	0.778078	−	1.15784i	0.0755736	−	0.112459i
$107$	−3.28319			−0.317398			−0.158699	−	0.987327i	$-0.550730\pi$
$107$	−3.28319			−0.317398			−0.158699	+	0.987327i	$0.550730\pi$
$108$	1.18581	+	10.3244i	0.114105	+	0.993469i
$109$	0.581642			0.0557112			0.0278556	−	0.999612i	$-0.491132\pi$
$109$	0.581642			0.0557112			0.0278556	+	0.999612i	$0.491132\pi$
$110$	−2.56121	+	3.81128i	−0.244202	+	0.363391i
$111$	1.69044	+	3.66096i	0.160449	+	0.347483i
$112$	11.7070	+	11.9572i	1.10620	+	1.12985i
$113$		−	17.0036i		−	1.59957i	−0.600289	−	0.799783i	$-0.704948\pi$
$113$		−	17.0036i		−	1.59957i	0.600289	−	0.799783i	$-0.295052\pi$
$114$	−2.41855	−	0.388103i	−0.226518	−	0.0363491i
$115$		−	8.20687i		−	0.765295i
$116$	6.75053	−	2.75444i	0.626771	−	0.255743i
$117$	−10.3842	+	12.1885i	−0.960021	+	1.12682i
$118$	3.18458	+	2.14007i	0.293165	+	0.197009i
$119$	29.0985			2.66745
$120$	−3.06449	−	13.1891i	−0.279749	−	1.20400i
$121$	−9.61993			−0.874539
$122$	13.4728	+	9.05387i	1.21977	+	0.819699i
$123$	−5.08789	+	2.34932i	−0.458760	+	0.211831i
$124$	−7.85695	+	3.20589i	−0.705575	+	0.287898i
$125$		−	6.52476i		−	0.583592i
$126$	4.79352	+	17.0896i	0.427040	+	1.52246i
$127$			9.10522i			0.807958i	0.914768	+	0.403979i	$0.132373\pi$
$127$			9.10522i			0.807958i	−0.914768	+	0.403979i	$0.867627\pi$
$128$	−6.11043	−	9.52170i	−0.540090	−	0.841607i
$129$	12.9379	−	5.97404i	1.13912	−	0.525985i
$130$	11.6365	−	17.3161i	1.02059	−	1.51872i
$131$	10.6697			0.932220			0.466110	−	0.884727i	$-0.345655\pi$
$131$	10.6697			0.932220			0.466110	+	0.884727i	$0.345655\pi$
$132$	−2.77633	+	2.97538i	−0.241648	+	0.258974i
$133$	−4.18351			−0.362756
$134$	−0.593704	+	0.883476i	−0.0512882	+	0.0763207i
$135$	3.87306	−	13.8297i	0.333340	−	1.19027i
$136$	−19.2641	−	3.99094i	−1.65189	−	0.342221i
$137$			19.9023i			1.70037i	0.526485	+	0.850184i	$0.323510\pi$
$137$			19.9023i			1.70037i	−0.526485	+	0.850184i	$0.676490\pi$
$138$	1.15238	−	7.18133i	0.0980973	−	0.611316i
$139$		−	2.43626i		−	0.206641i	−0.994648	−	0.103320i	$-0.967053\pi$
$139$		−	2.43626i		−	0.206641i	0.994648	−	0.103320i	$-0.0329467\pi$
$140$	−8.73680	−	21.4120i	−0.738394	−	1.80964i
$141$	5.27172	+	11.4169i	0.443959	+	0.961478i
$142$	−5.84730	−	3.92944i	−0.490695	−	0.329751i
$143$	−6.27019			−0.524340
$144$	−0.829579	−	11.9713i	−0.0691316	−	0.997608i
$145$	−10.0757			−0.836743
$146$	−6.47873	−	4.35377i	−0.536184	−	0.360320i
$147$	7.62530	+	16.5140i	0.628924	+	1.36205i
$148$	−1.75909	−	4.31114i	−0.144596	−	0.354374i
$149$			1.95438i			0.160109i	0.996790	+	0.0800544i	$0.0255094\pi$
$149$			1.95438i			0.160109i	−0.996790	+	0.0800544i	$0.974491\pi$
$150$	−1.02433	+	6.38332i	−0.0836359	+	0.521196i
$151$		−	8.89766i		−	0.724081i	−0.932162	−	0.362041i	$-0.882080\pi$
$151$		−	8.89766i		−	0.724081i	0.932162	−	0.362041i	$-0.117920\pi$
$152$	2.76962	+	0.573780i	0.224646	+	0.0465397i
$153$	−15.8836	−	13.5324i	−1.28411	−	1.09403i
$154$	−3.87667	+	5.76877i	−0.312391	+	0.464861i
$155$	11.7271			0.941946
$156$	12.6139	−	13.5183i	1.00992	−	1.08233i
$157$	−5.55963			−0.443707			−0.221854	−	0.975080i	$-0.571211\pi$
$157$	−5.55963			−0.443707			−0.221854	+	0.975080i	$0.571211\pi$
$158$	−2.85852	+	4.25369i	−0.227411	+	0.338405i
$159$	−1.55113	+	0.716230i	−0.123013	+	0.0568007i
$160$	2.84733	+	15.3737i	0.225101	+	1.21540i
$161$		−	12.4220i		−	0.978989i
$162$	5.33100	−	11.5577i	0.418843	−	0.908059i
$163$		−	6.88291i		−	0.539111i	−0.962985	−	0.269556i	$-0.913123\pi$
$163$		−	6.88291i		−	0.539111i	0.962985	−	0.269556i	$-0.0868768\pi$
$164$	5.99149	−	2.44472i	0.467856	−	0.190901i
$165$	5.10589	−	2.35763i	0.397493	−	0.183541i
$166$	10.2705	+	6.90185i	0.797143	+	0.535687i
$167$	−10.0007			−0.773877			−0.386939	−	0.922105i	$-0.626467\pi$
$167$	−10.0007			−0.773877			−0.386939	+	0.922105i	$0.626467\pi$
$168$	−4.63844	−	19.9631i	−0.357863	−	1.54019i
$169$	15.4878			1.19137
$170$	22.5657	+	15.1644i	1.73071	+	1.16305i
$171$	2.28359	+	1.94556i	0.174631	+	0.148781i
$172$	−15.2357	+	6.21665i	−1.16171	+	0.474015i
$173$			2.31071i			0.175680i	0.996135	+	0.0878400i	$0.0279964\pi$
$173$			2.31071i			0.175680i	−0.996135	+	0.0878400i	$0.972004\pi$
$174$	−8.81664	−	1.41480i	−0.668388	−	0.107256i
$175$			11.0416i			0.834667i
$176$	3.35769	−	3.28742i	0.253095	−	0.247799i
$177$	−1.96996	−	4.26632i	−0.148071	−	0.320676i
$178$	5.87556	−	8.74327i	0.440392	−	0.655336i
$179$	−18.3502			−1.37156			−0.685781	−	0.727808i	$-0.740539\pi$
$179$	−18.3502			−1.37156			−0.685781	+	0.727808i	$0.740539\pi$
$180$	−5.18870	+	15.7510i	−0.386743	+	1.17401i
$181$	−5.82511			−0.432977			−0.216489	−	0.976285i	$-0.569460\pi$
$181$	−5.82511			−0.432977			−0.216489	+	0.976285i	$0.569460\pi$
$182$	17.6132	−	26.2097i	1.30557	−	1.94279i
$183$	−8.33419	−	18.0493i	−0.616081	−	1.33424i
$184$	−1.70371	+	8.22375i	−0.125599	+	0.606263i
$185$			6.43473i			0.473091i
$186$	10.2617	+	1.64669i	0.752424	+	0.120741i
$187$		−	8.17111i		−	0.597531i
$188$	−5.48581	−	13.4445i	−0.400094	−	0.980543i
$189$	5.86229	−	20.9327i	0.426419	−	1.52263i
$190$	−3.24429	−	2.18019i	−0.235365	−	0.158168i
$191$	−15.8907			−1.14981			−0.574907	−	0.818219i	$-0.694962\pi$
$191$	−15.8907			−1.14981			−0.574907	+	0.818219i	$0.694962\pi$
$192$	0.332794	+	13.8524i	0.0240173	+	0.999712i
$193$	−8.12243			−0.584665			−0.292333	−	0.956317i	$-0.594431\pi$
$193$	−8.12243			−0.584665			−0.292333	+	0.956317i	$0.594431\pi$
$194$	−4.13477	−	2.77860i	−0.296859	−	0.199492i
$195$	−23.1980	+	10.7116i	−1.66124	+	0.767072i
$196$	−7.93496	−	19.4469i	−0.566783	−	1.38906i
$197$		−	5.70090i		−	0.406172i	−0.979161	−	0.203086i	$-0.934903\pi$
$197$		−	5.70090i		−	0.406172i	0.979161	−	0.203086i	$-0.0650971\pi$
$198$	4.79890	−	1.34606i	0.341043	−	0.0956605i
$199$			19.8828i			1.40945i	0.709479	+	0.704726i	$0.248930\pi$
$199$			19.8828i			1.40945i	−0.709479	+	0.704726i	$0.751070\pi$
$200$	1.51439	−	7.30990i	0.107084	−	0.516888i
$201$	1.18357	−	0.546511i	0.0834828	−	0.0385479i
$202$	−6.36890	+	9.47741i	−0.448115	+	0.666828i
$203$	−15.2507			−1.07039
$204$	17.6166	+	16.4380i	1.23341	+	1.15089i
$205$	−8.94278			−0.624591
$206$	−6.57300	+	9.78112i	−0.457963	+	0.681483i
$207$	−5.77689	+	6.78062i	−0.401522	+	0.471285i
$208$	−15.2552	+	14.9360i	−1.05776	+	1.03562i
$209$			1.17477i			0.0812602i
$210$	−4.48760	+	27.9655i	−0.309674	+	1.92980i
$211$			2.65858i			0.183024i	0.995804	+	0.0915120i	$0.0291700\pi$
$211$			2.65858i			0.183024i	−0.995804	+	0.0915120i	$0.970830\pi$
$212$	1.82661	−	0.745316i	0.125452	−	0.0511885i
$213$	3.61709	+	7.83350i	0.247839	+	0.536743i
$214$	−3.85379	−	2.58978i	−0.263440	−	0.177034i
$215$	22.7405			1.55089
$216$	−6.75202	+	13.0541i	−0.459417	+	0.888221i
$217$	17.7503			1.20497
$218$	0.682728	+	0.458800i	0.0462402	+	0.0310738i
$219$	4.00769	+	8.67942i	0.270815	+	0.586501i
$220$	−6.01268	+	2.45337i	−0.405375	+	0.165406i
$221$			37.1244i			2.49726i
$222$	−0.903544	+	5.63064i	−0.0606419	+	0.377904i
$223$		−	23.6468i		−	1.58351i	−0.610840	−	0.791754i	$-0.709168\pi$
$223$		−	23.6468i		−	1.58351i	0.610840	−	0.791754i	$-0.290832\pi$
$224$	4.30973	+	23.2697i	0.287956	+	1.55478i
$225$	5.13495	−	6.02714i	0.342330	−	0.401809i
$226$	13.4125	−	19.9588i	0.892184	−	1.32764i
$227$	−11.6284			−0.771807			−0.385904	−	0.922539i	$-0.626110\pi$
$227$	−11.6284			−0.771807			−0.385904	+	0.922539i	$0.626110\pi$
$228$	−2.53274	−	2.36330i	−0.167735	−	0.156514i
$229$	15.0492			0.994479			0.497239	−	0.867613i	$-0.334347\pi$
$229$	15.0492			0.994479			0.497239	+	0.867613i	$0.334347\pi$
$230$	6.47358	−	9.63318i	0.426855	−	0.635193i
$231$	7.72830	−	3.56852i	0.508485	−	0.234791i
$232$	10.0964	+	2.09168i	0.662864	+	0.137325i
$233$			13.8676i			0.908496i	0.890875	+	0.454248i	$0.150092\pi$
$233$			13.8676i			0.908496i	−0.890875	+	0.454248i	$0.849908\pi$
$234$	−21.8032	+	6.11566i	−1.42532	+	0.399793i
$235$			20.0671i			1.30903i
$236$	2.04996	+	5.02400i	0.133441	+	0.327035i
$237$	5.69857	−	2.63130i	0.370162	−	0.170921i
$238$	34.1556	+	22.9529i	2.21398	+	1.48781i
$239$	−3.01695			−0.195150			−0.0975750	−	0.995228i	$-0.531109\pi$
$239$	−3.01695			−0.195150			−0.0975750	+	0.995228i	$0.531109\pi$
$240$	6.80649	−	17.8986i	0.439357	−	1.15535i
$241$	−23.7894			−1.53241			−0.766206	−	0.642596i	$-0.777858\pi$
$241$	−23.7894			−1.53241			−0.766206	+	0.642596i	$0.777858\pi$
$242$	−11.2918	−	7.58820i	−0.725865	−	0.487788i
$243$	−12.9348	+	8.70000i	−0.829770	+	0.558105i
$244$	8.67265	+	21.2548i	0.555209	+	1.36070i
$245$			29.0260i			1.85441i
$246$	−7.82528	−	1.25572i	−0.498922	−	0.0800616i
$247$		−	5.33740i		−	0.339611i
$248$	−11.7513	−	2.43450i	−0.746205	−	0.154591i
$249$	−6.35323	−	13.7591i	−0.402620	−	0.871949i
$250$	5.14673	−	7.65873i	0.325508	−	0.484380i
$251$	−5.69516			−0.359476			−0.179738	−	0.983715i	$-0.557525\pi$
$251$	−5.69516			−0.359476			−0.179738	+	0.983715i	$0.557525\pi$
$252$	−7.85365	+	23.8408i	−0.494734	+	1.50183i
$253$	−3.48820			−0.219301
$254$	−7.18221	+	10.6877i	−0.450652	+	0.670604i
$255$	−13.9590	−	30.2308i	−0.874145	−	1.89313i
$256$	0.338335	−	15.9964i	0.0211459	−	0.999776i
$257$			0.614538i			0.0383338i	0.999816	+	0.0191669i	$0.00610139\pi$
$257$			0.614538i			0.0383338i	−0.999816	+	0.0191669i	$0.993899\pi$
$258$	19.8988	+	3.19314i	1.23884	+	0.198796i
$259$			9.73965i			0.605192i
$260$	27.3178	−	11.1466i	1.69418	−	0.691282i
$261$	8.32468	+	7.09239i	0.515285	+	0.439008i
$262$	12.5241	+	8.41630i	0.773740	+	0.519961i
$263$	26.8492			1.65559			0.827797	−	0.561028i	$-0.189594\pi$
$263$	26.8492			1.65559			0.827797	+	0.561028i	$0.189594\pi$
$264$	−5.60582	+	1.30251i	−0.345014	+	0.0801642i
$265$	−2.72636			−0.167479
$266$	−4.91058	−	3.29995i	−0.301087	−	0.202333i
$267$	−11.7132	+	5.40852i	−0.716834	+	0.330996i
$268$	−1.39377	+	0.568705i	−0.0851382	+	0.0347392i
$269$		−	15.1119i		−	0.921388i	−0.887559	−	0.460694i	$-0.847600\pi$
$269$		−	15.1119i		−	0.921388i	0.887559	−	0.460694i	$-0.152400\pi$
$270$	15.4551	−	13.1782i	0.940565	−	0.801998i
$271$		−	15.8650i		−	0.963731i	−0.876245	−	0.481866i	$-0.839959\pi$
$271$		−	15.8650i		−	0.963731i	0.876245	−	0.481866i	$-0.160041\pi$
$272$	−19.4641	−	19.8801i	−1.18018	−	1.20541i
$273$	−35.1126	+	16.2131i	−2.12511	+	0.981262i
$274$	−15.6990	+	23.3612i	−0.948408	+	1.41130i
$275$	3.10058			0.186972
$276$	7.01730	−	7.52041i	0.422392	−	0.452675i
$277$	−16.2757			−0.977909			−0.488955	−	0.872309i	$-0.662622\pi$
$277$	−16.2757			−0.977909			−0.488955	+	0.872309i	$0.662622\pi$
$278$	1.92172	−	2.85967i	0.115257	−	0.171512i
$279$	−9.68910	−	8.25484i	−0.580071	−	0.494204i
$280$	6.63458	−	32.0249i	0.396492	−	1.91385i
$281$		−	2.53220i		−	0.151059i	−0.997144	−	0.0755293i	$-0.975935\pi$
$281$		−	2.53220i		−	0.151059i	0.997144	−	0.0755293i	$-0.0240646\pi$
$282$	−2.81775	+	17.5595i	−0.167795	+	1.04565i
$283$			2.02399i			0.120314i	0.998189	+	0.0601569i	$0.0191601\pi$
$283$			2.02399i			0.120314i	−0.998189	+	0.0601569i	$0.980840\pi$
$284$	−3.76399	−	9.22471i	−0.223352	−	0.547386i
$285$	2.00689	+	4.34630i	0.118878	+	0.257453i
$286$	−7.35992	−	4.94593i	−0.435201	−	0.292459i
$287$	−13.5359			−0.798996
$288$	8.46921	−	14.7062i	0.499053	−	0.866572i
$289$	−31.3793			−1.84584
$290$	−11.8268	−	7.94773i	−0.694495	−	0.466707i
$291$	2.55774	+	5.53926i	0.149937	+	0.324717i
$292$	−4.17045	−	10.2209i	−0.244057	−	0.598130i
$293$		−	21.0470i		−	1.22958i	−0.788691	−	0.614790i	$-0.789241\pi$
$293$		−	21.0470i		−	1.22958i	0.788691	−	0.614790i	$-0.210759\pi$
$294$	−4.07574	+	25.3989i	−0.237702	+	1.48129i
$295$		−	7.49873i		−	0.436593i
$296$	1.33582	−	6.44796i	0.0776431	−	0.374780i
$297$	−5.87810	−	1.64618i	−0.341082	−	0.0955212i
$298$	−1.54161	+	2.29404i	−0.0893033	+	0.132890i
$299$	15.8482			0.916525
$300$	−6.23752	+	6.68472i	−0.360123	+	0.385942i
$301$	34.4201			1.98394
$302$	7.01848	−	10.4440i	0.403868	−	0.600986i
$303$	12.6967	−	5.86265i	0.729405	−	0.336800i
$304$	2.79836	+	2.85818i	0.160497	+	0.163928i
$305$		−	31.7245i		−	1.81654i
$306$	−7.96973	−	28.4132i	−0.455599	−	1.62428i
$307$		−	13.3500i		−	0.761924i	−0.924591	−	0.380962i	$-0.875593\pi$
$307$		−	13.3500i		−	0.761924i	0.924591	−	0.380962i	$-0.124407\pi$
$308$	−9.10083	+	3.71344i	−0.518568	+	0.211593i
$309$	13.1036	−	6.05052i	0.745436	−	0.344202i
$310$	13.7652	+	9.25037i	0.781813	+	0.525386i
$311$	4.07480			0.231061			0.115530	−	0.993304i	$-0.463143\pi$
$311$	4.07480			0.231061			0.115530	+	0.993304i	$0.463143\pi$
$312$	25.4693	−	5.91781i	1.44192	−	0.335030i
$313$	25.9793			1.46843			0.734217	−	0.678915i	$-0.237549\pi$
$313$	25.9793			1.46843			0.734217	+	0.678915i	$0.237549\pi$
$314$	−6.52587	−	4.38544i	−0.368276	−	0.247485i
$315$	22.4963	−	26.4050i	1.26753	−	1.48775i
$316$	−6.71062	+	2.73815i	−0.377502	+	0.154033i
$317$			4.34318i			0.243937i	0.992534	+	0.121969i	$0.0389207\pi$
$317$			4.34318i			0.243937i	−0.992534	+	0.121969i	$0.961079\pi$
$318$	−2.38567	−	0.382827i	−0.133782	−	0.0214679i
$319$			4.28252i			0.239775i
$320$	−8.78462	+	20.2915i	−0.491075	+	1.13433i
$321$	2.38392	+	5.16284i	0.133058	+	0.288162i
$322$	9.79846	−	14.5808i	0.546047	−	0.812559i
$323$	6.95552			0.387016
$324$	15.3742	−	9.36127i	0.854123	−	0.520070i
$325$	−14.0871			−0.781412
$326$	5.42924	−	8.07912i	0.300698	−	0.447461i
$327$	−0.422330	−	0.914636i	−0.0233549	−	0.0505795i
$328$	8.96117	+	1.85648i	0.494798	+	0.102507i
$329$			30.3736i			1.67455i
$330$	7.85296	+	1.26016i	0.432291	+	0.0693694i
$331$		−	8.69447i		−	0.477891i	−0.971033	−	0.238946i	$-0.923198\pi$
$331$		−	8.69447i		−	0.477891i	0.971033	−	0.238946i	$-0.0768018\pi$
$332$	6.61124	+	16.2027i	0.362839	+	0.889239i
$333$	4.52947	−	5.31645i	0.248213	−	0.291340i
$334$	−11.7388	−	7.88855i	−0.642317	−	0.431643i
$335$	2.08032			0.113660
$336$	10.3023	−	27.0914i	0.562039	−	1.47796i
$337$	17.1029			0.931655			0.465828	−	0.884876i	$-0.345757\pi$
$337$	17.1029			0.931655			0.465828	+	0.884876i	$0.345757\pi$
$338$	18.1795	+	12.2168i	0.988836	+	0.664507i
$339$	−26.7383	+	12.3463i	−1.45223	+	0.670561i
$340$	14.5259	+	35.5997i	0.787775	+	1.93067i
$341$		−	4.98443i		−	0.269922i
$342$	1.14581	+	4.08499i	0.0619585	+	0.220891i
$343$			14.6495i			0.790996i
$344$	−22.7872	−	4.72082i	−1.22861	−	0.254530i
$345$	−12.9054	+	5.95901i	−0.694801	+	0.320822i
$346$	−1.82269	+	2.71230i	−0.0979884	+	0.145814i
$347$	−26.1293			−1.40269			−0.701346	−	0.712821i	$-0.747417\pi$
$347$	−26.1293			−1.40269			−0.701346	+	0.712821i	$0.747417\pi$
$348$	−9.23293	−	8.61526i	−0.494937	−	0.461826i
$349$	24.1577			1.29313			0.646566	−	0.762858i	$-0.276204\pi$
$349$	24.1577			1.29313			0.646566	+	0.762858i	$0.276204\pi$
$350$	−8.70963	+	12.9606i	−0.465549	+	0.692772i
$351$	26.7064	+	7.47922i	1.42548	+	0.399211i
$352$	6.53435	−	1.21021i	0.348282	−	0.0645044i
$353$			33.8754i			1.80301i	0.432771	+	0.901504i	$0.357536\pi$
$353$			33.8754i			1.80301i	−0.432771	+	0.901504i	$0.642464\pi$
$354$	1.05295	−	6.56168i	0.0559636	−	0.348749i
$355$			13.7686i			0.730763i
$356$	13.7934	−	5.62816i	0.731048	−	0.298292i
$357$	−21.1284	−	45.7575i	−1.11823	−	2.42175i
$358$	−21.5394	−	14.4747i	−1.13839	−	0.765011i
$359$	3.94534			0.208227			0.104114	−	0.994565i	$-0.466799\pi$
$359$	3.94534			0.208227			0.104114	+	0.994565i	$0.466799\pi$
$360$	−18.5148	+	14.3955i	−0.975818	+	0.758712i
$361$	−1.00000			−0.0526316
$362$	−6.83749	−	4.59485i	−0.359370	−	0.241500i
$363$	6.98503	+	15.1274i	0.366619	+	0.793983i
$364$	41.3485	−	16.8715i	2.16725	−	0.884309i
$365$			15.2555i			0.798507i
$366$	4.45465	−	27.7602i	0.232848	−	1.45105i
$367$			28.8056i			1.50364i	0.659368	+	0.751820i	$0.270824\pi$
$367$			28.8056i			1.50364i	−0.659368	+	0.751820i	$0.729176\pi$
$368$	−8.48671	+	8.30910i	−0.442400	+	0.433142i
$369$	7.38864	+	6.29491i	0.384637	+	0.327700i
$370$	−5.07572	+	7.55305i	−0.263874	+	0.392664i
$371$	−4.12664			−0.214244
$372$	10.7462	+	10.0273i	0.557166	+	0.519892i
$373$	28.6012			1.48092			0.740458	−	0.672103i	$-0.234609\pi$
$373$	28.6012			1.48092			0.740458	+	0.672103i	$0.234609\pi$
$374$	6.44537	−	9.59120i	0.333282	−	0.495949i
$375$	−10.2602	+	4.73763i	−0.529836	+	0.244650i
$376$	4.16583	−	20.1083i	0.214836	−	1.03701i
$377$		−	19.4571i		−	1.00209i
$378$	23.3929	−	19.9466i	1.20320	−	1.02594i
$379$		−	18.3029i		−	0.940155i	−0.882625	−	0.470078i	$-0.844226\pi$
$379$		−	18.3029i		−	0.940155i	0.882625	−	0.470078i	$-0.155774\pi$
$380$	−2.08839	−	5.11819i	−0.107132	−	0.262558i
$381$	14.3180	−	6.61130i	0.733535	−	0.338707i
$382$	−18.6525	−	12.5346i	−0.954343	−	0.641327i
$383$	34.6420			1.77012			0.885061	−	0.465475i	$-0.154117\pi$
$383$	34.6420			1.77012			0.885061	+	0.465475i	$0.154117\pi$
$384$	−10.5362	+	16.5224i	−0.537671	+	0.843155i
$385$	13.5837			0.692291
$386$	−9.53407	−	6.40698i	−0.485271	−	0.326107i
$387$	−18.7885	−	16.0072i	−0.955071	−	0.813693i
$388$	−2.66161	−	6.52302i	−0.135123	−	0.331156i
$389$			3.81008i			0.193179i	0.995324	+	0.0965894i	$0.0307934\pi$
$389$			3.81008i			0.193179i	−0.995324	+	0.0965894i	$0.969207\pi$
$390$	−35.6789	−	5.72537i	−1.80667	−	0.289915i
$391$			20.6528i			1.04446i
$392$	6.02568	−	29.0857i	0.304343	−	1.46905i
$393$	−7.74730	−	16.7782i	−0.390799	−	0.846350i
$394$	4.49687	−	6.69168i	0.226549	−	0.337122i
$395$	10.0161			0.503967
$396$	6.69470	+	2.20537i	0.336421	+	0.110824i
$397$	−28.4710			−1.42892			−0.714460	−	0.699676i	$-0.753328\pi$
$397$	−28.4710			−1.42892			−0.714460	+	0.699676i	$0.753328\pi$
$398$	−15.6835	+	23.3383i	−0.786145	+	1.16984i
$399$	3.03764	+	6.57859i	0.152072	+	0.329342i
$400$	7.54364	−	7.38577i	0.377182	−	0.369289i
$401$			38.9284i			1.94399i	0.234997	+	0.971996i	$0.424492\pi$
$401$			38.9284i			1.94399i	−0.234997	+	0.971996i	$0.575508\pi$
$402$	1.82036	+	0.292112i	0.0907913	+	0.0145692i
$403$			22.6461i			1.12808i
$404$	−14.9516	+	6.10073i	−0.743868	+	0.303523i
$405$	−24.5596	+	3.95134i	−1.22037	+	0.196344i
$406$	−17.9012	−	12.0297i	−0.888419	−	0.597026i
$407$	2.73498			0.135568
$408$	7.71190	+	33.1908i	0.381796	+	1.64319i
$409$	34.0334			1.68284			0.841422	−	0.540379i	$-0.181719\pi$
$409$	34.0334			1.68284			0.841422	+	0.540379i	$0.181719\pi$
$410$	−10.4970	−	7.05407i	−0.518409	−	0.348376i
$411$	31.2965	−	14.4511i	1.54374	−	0.712818i
$412$	−15.4307	+	6.29624i	−0.760217	+	0.310194i
$413$		−	11.3501i		−	0.558503i
$414$	−12.1294	+	3.40223i	−0.596130	+	0.167211i
$415$		−	24.1839i		−	1.18714i
$416$	−29.6880	+	5.49844i	−1.45557	+	0.269583i
$417$	−3.83104	+	1.76897i	−0.187607	+	0.0866267i
$418$	−0.926656	+	1.37893i	−0.0453242	+	0.0674458i
$419$	20.7742			1.01488			0.507442	−	0.861686i	$-0.330591\pi$
$419$	20.7742			1.01488			0.507442	+	0.861686i	$0.330591\pi$
$420$	−27.3267	+	29.2859i	−1.33341	+	1.42901i
$421$	−24.0255			−1.17093			−0.585465	−	0.810698i	$-0.699088\pi$
$421$	−24.0255			−1.17093			−0.585465	+	0.810698i	$0.699088\pi$
$422$	−2.09709	+	3.12062i	−0.102085	+	0.151910i
$423$	14.1254	−	16.5796i	0.686800	−	0.806130i
$424$	2.73197	+	0.565981i	0.132676	+	0.0274865i
$425$		−	18.3578i		−	0.890486i
$426$	−1.93335	+	12.0481i	−0.0936710	+	0.583732i
$427$		−	48.0184i		−	2.32377i
$428$	−2.48074	−	6.07975i	−0.119911	−	0.293876i
$429$	4.55279	+	9.85992i	0.219811	+	0.476042i
$430$	26.6926	+	17.9377i	1.28723	+	0.865032i
$431$	9.00062			0.433545			0.216772	−	0.976222i	$-0.430447\pi$
$431$	9.00062			0.433545			0.216772	+	0.976222i	$0.430447\pi$
$432$	−18.2226	+	9.99687i	−0.876734	+	0.480975i
$433$	18.2435			0.876726			0.438363	−	0.898798i	$-0.355558\pi$
$433$	18.2435			0.876726			0.438363	+	0.898798i	$0.355558\pi$
$434$	20.8352	+	14.0014i	1.00012	+	0.672090i
$435$	7.31597	+	15.8441i	0.350774	+	0.759668i
$436$	0.439481	+	1.07707i	0.0210473	+	0.0515824i
$437$		−	2.96927i		−	0.142040i
$438$	−2.14212	+	13.3491i	−0.102355	+	0.637846i
$439$		−	4.60360i		−	0.219718i	−0.993947	−	0.109859i	$-0.964960\pi$
$439$		−	4.60360i		−	0.219718i	0.993947	−	0.109859i	$-0.0350399\pi$
$440$	−8.99287	−	1.86305i	−0.428718	−	0.0888174i
$441$	20.4317	−	23.9817i	0.972938	−	1.14198i
$442$	−29.2837	+	43.5764i	−1.39289	+	2.07272i
$443$	−5.45278			−0.259069			−0.129535	−	0.991575i	$-0.541348\pi$
$443$	−5.45278			−0.259069			−0.129535	+	0.991575i	$0.541348\pi$
$444$	−5.50203	+	5.89650i	−0.261115	+	0.279835i
$445$	−20.5878			−0.975953
$446$	18.6526	−	27.7565i	0.883227	−	1.31431i
$447$	3.07327	−	1.41907i	0.145361	−	0.0671198i
$448$	−13.2965	+	30.7134i	−0.628198	+	1.45107i
$449$		−	14.0583i		−	0.663452i	−0.943376	−	0.331726i	$-0.892369\pi$
$449$		−	14.0583i		−	0.663452i	0.943376	−	0.331726i	$-0.107631\pi$
$450$	10.7816	−	3.02417i	0.508249	−	0.142561i
$451$			3.80099i			0.178982i
$452$	31.4870	−	12.8477i	1.48102	−	0.604306i
$453$	−13.9916	+	6.46059i	−0.657384	+	0.303545i
$454$	−13.6494	−	9.17253i	−0.640599	−	0.430488i
$455$	−61.7159			−2.89329
$456$	−1.10874	−	4.77186i	−0.0519217	−	0.223463i
$457$	−20.0892			−0.939733			−0.469867	−	0.882737i	$-0.655698\pi$
$457$	−20.0892			−0.939733			−0.469867	+	0.882737i	$0.655698\pi$
$458$	17.6647	+	11.8708i	0.825415	+	0.554687i
$459$	−9.74668	+	34.8029i	−0.454936	+	1.62446i
$460$	15.1973	−	6.20101i	0.708578	−	0.289123i
$461$		−	22.8317i		−	1.06338i	−0.846940	−	0.531689i	$-0.821558\pi$
$461$		−	22.8317i		−	1.06338i	0.846940	−	0.531689i	$-0.178442\pi$
$462$	11.8863	+	1.90738i	0.553000	+	0.0887395i
$463$			0.535795i			0.0249005i	0.999922	+	0.0124503i	$0.00396314\pi$
$463$			0.535795i			0.0249005i	−0.999922	+	0.0124503i	$0.996037\pi$
$464$	10.2012	+	10.4193i	0.473580	+	0.483703i
$465$	−8.51507	−	18.4410i	−0.394877	−	0.855181i
$466$	−10.9388	+	16.2777i	−0.506728	+	0.754050i
$467$	24.2781			1.12346			0.561728	−	0.827322i	$-0.310137\pi$
$467$	24.2781			1.12346			0.561728	+	0.827322i	$0.310137\pi$
$468$	−30.4165	−	10.0198i	−1.40600	−	0.463167i
$469$	3.14878			0.145397
$470$	−15.8289	+	23.5546i	−0.730133	+	1.08649i
$471$	4.03685	+	8.74257i	0.186008	+	0.402836i
$472$	−1.55670	+	7.51415i	−0.0716531	+	0.345867i
$473$		−	9.66547i		−	0.444419i
$474$	8.76452	+	1.40644i	0.402568	+	0.0645997i
$475$			2.63932i			0.121100i
$476$	21.9864	+	53.8839i	1.00775	+	2.46977i
$477$	2.25255	+	1.91911i	0.103137	+	0.0878701i
$478$	−3.54127	−	2.37977i	−0.161974	−	0.108848i
$479$	7.90911			0.361376			0.180688	−	0.983540i	$-0.442167\pi$
$479$	7.90911			0.361376			0.180688	+	0.983540i	$0.442167\pi$
$480$	22.1078	−	15.6403i	1.00908	−	0.713878i
$481$	−12.4260			−0.566578
$482$	−27.9239	−	18.7651i	−1.27190	−	0.854727i
$483$	−19.5336	+	9.01959i	−0.888811	+	0.410406i
$484$	−7.26869	−	17.8140i	−0.330395	−	0.809727i
$485$			9.73614i			0.442095i
$486$	−22.0454	+	0.00900123i	−1.00000	+	0.000408304i
$487$			30.2541i			1.37094i	0.728099	+	0.685472i	$0.240404\pi$
$487$			30.2541i			1.37094i	−0.728099	+	0.685472i	$0.759596\pi$
$488$	−6.58587	+	31.7897i	−0.298128	+	1.43905i
$489$	−10.8234	+	4.99768i	−0.489452	+	0.226003i
$490$	−22.8958	+	34.0706i	−1.03432	+	1.53915i
$491$	40.0162			1.80590			0.902952	−	0.429742i	$-0.141395\pi$
$491$	40.0162			1.80590			0.902952	+	0.429742i	$0.141395\pi$
$492$	−8.19476	−	7.64654i	−0.369449	−	0.344733i
$493$	25.3559			1.14197
$494$	4.21014	−	6.26501i	0.189423	−	0.281876i
$495$	−7.41477	−	6.31717i	−0.333269	−	0.283936i
$496$	−11.8732	−	12.1270i	−0.533123	−	0.544518i
$497$			20.8403i			0.934815i
$498$	3.39582	−	21.1618i	0.152170	−	0.948284i
$499$		−	21.9968i		−	0.984711i	−0.870394	−	0.492356i	$-0.836136\pi$
$499$		−	21.9968i		−	0.984711i	0.870394	−	0.492356i	$-0.163864\pi$
$500$	12.0824	−	4.93003i	0.540342	−	0.220477i
$501$	7.26150	+	15.7262i	0.324420	+	0.702593i
$502$	−6.68495	−	4.49235i	−0.298364	−	0.200503i
$503$	−38.2086			−1.70364			−0.851819	−	0.523836i	$-0.824500\pi$
$503$	−38.2086			−1.70364			−0.851819	+	0.523836i	$0.824500\pi$
$504$	−28.0242	+	21.7892i	−1.24830	+	0.970568i
$505$	22.3164			0.993068
$506$	−4.09443	−	2.75149i	−0.182020	−	0.122319i
$507$	−11.2457	−	24.3547i	−0.499440	−	1.08163i
$508$	−16.8609	+	6.87979i	−0.748080	+	0.305241i
$509$		−	40.3946i		−	1.79046i	−0.445607	−	0.895229i	$-0.647012\pi$
$509$		−	40.3946i		−	1.79046i	0.445607	−	0.895229i	$-0.352988\pi$
$510$	7.46111	−	46.4956i	0.330384	−	2.05886i
$511$			23.0908i			1.02147i
$512$	13.0151	−	18.5096i	0.575193	−	0.818018i
$513$	1.40129	−	5.00364i	0.0618683	−	0.220916i
$514$	−0.484748	+	0.721341i	−0.0213813	+	0.0318170i
$515$	23.0316			1.01489
$516$	20.8383	+	19.4443i	0.917357	+	0.855987i
$517$	8.52918			0.375113
$518$	−7.68264	+	11.4323i	−0.337556	+	0.502308i
$519$	3.63361	−	1.67781i	0.159498	−	0.0736475i
$520$	40.8580	+	8.46453i	1.79174	+	0.371194i
$521$		−	32.2318i		−	1.41210i	−0.708161	−	0.706051i	$-0.750475\pi$
$521$		−	32.2318i		−	1.41210i	0.708161	−	0.706051i	$-0.249525\pi$
$522$	4.17698	+	14.8915i	0.182821	+	0.651784i
$523$			27.1152i			1.18566i	0.805326	+	0.592832i	$0.201990\pi$
$523$			27.1152i			1.18566i	−0.805326	+	0.592832i	$0.798010\pi$
$524$	8.06192	+	19.7580i	0.352187	+	0.863133i
$525$	17.3630	−	8.01731i	0.757784	−	0.349904i
$526$	31.5155	+	21.1787i	1.37414	+	0.923434i
$527$	−29.5117			−1.28555
$528$	−7.60751	−	2.89299i	−0.331074	−	0.125901i
$529$	−14.1834			−0.616670
$530$	−3.20019	−	2.15055i	−0.139007	−	0.0934141i
$531$	−5.27843	+	6.19554i	−0.229064	+	0.268864i
$532$	−3.16100	−	7.74693i	−0.137047	−	0.335872i
$533$		−	17.2693i		−	0.748017i
$534$	−18.0151	−	2.89087i	−0.779589	−	0.125100i
$535$			9.07452i			0.392326i
$536$	−2.08460	−	0.431865i	−0.0900409	−	0.0186537i
$537$	13.3241	+	28.8559i	0.574978	+	1.24522i
$538$	11.9203	−	17.7383i	0.513919	−	0.764751i
$539$	12.3371			0.531395
$540$	28.5360	−	3.27750i	1.22799	−	0.141041i
$541$	−3.09585			−0.133101			−0.0665506	−	0.997783i	$-0.521199\pi$
$541$	−3.09585			−0.133101			−0.0665506	+	0.997783i	$0.521199\pi$
$542$	12.5143	−	18.6223i	0.537537	−	0.799895i
$543$	4.22961	+	9.16003i	0.181510	+	0.393095i
$544$	−7.16539	−	38.6884i	−0.307213	−	1.65875i
$545$		−	1.60762i		−	0.0688628i
$546$	−54.0039	−	8.66596i	−2.31115	−	0.370869i
$547$			8.26344i			0.353319i	0.984272	+	0.176660i	$0.0565292\pi$
$547$			8.26344i			0.353319i	−0.984272	+	0.176660i	$0.943471\pi$
$548$	−36.8547	+	15.0379i	−1.57435	+	0.642389i
$549$	−22.3312	+	26.2112i	−0.953071	+	1.11866i
$550$	3.63945	+	2.44574i	0.155186	+	0.104287i
$551$	−3.64543			−0.155300
$552$	14.1690	−	3.29216i	0.603071	−	0.140124i
$553$	15.1605			0.644690
$554$	−19.1043	−	12.8382i	−0.811663	−	0.545445i
$555$	10.1187	−	4.67226i	0.429513	−	0.198326i
$556$	4.51142	−	1.84081i	0.191327	−	0.0780676i
$557$			37.7264i			1.59852i	0.600987	+	0.799258i	$0.294774\pi$
$557$			37.7264i			1.59852i	−0.600987	+	0.799258i	$0.705226\pi$
$558$	−4.86159	−	17.3323i	−0.205808	−	0.733733i
$559$			43.9139i			1.85736i
$560$	33.0489	−	32.3573i	1.39657	−	1.36734i
$561$	−12.8491	+	5.93304i	−0.542490	+	0.250493i
$562$	1.99740	−	2.97229i	0.0842554	−	0.125378i
$563$	32.3887			1.36502			0.682510	−	0.730876i	$-0.260888\pi$
$563$	32.3887			1.36502			0.682510	+	0.730876i	$0.260888\pi$
$564$	−17.1584	+	18.3885i	−0.722498	+	0.774298i
$565$	−46.9969			−1.97717
$566$	−1.59653	+	2.37575i	−0.0671070	+	0.0998602i
$567$	−37.1735	+	5.98077i	−1.56114	+	0.251169i
$568$	2.85831	−	13.7969i	0.119932	−	0.578907i
$569$		−	11.3341i		−	0.475148i	−0.971369	−	0.237574i	$-0.923648\pi$
$569$		−	11.3341i		−	0.475148i	0.971369	−	0.237574i	$-0.0763522\pi$
$570$	−1.07269	+	6.68470i	−0.0449300	+	0.279991i
$571$		−	8.93991i		−	0.374124i	−0.982348	−	0.187062i	$-0.940104\pi$
$571$		−	8.93991i		−	0.374124i	0.982348	−	0.187062i	$-0.0598965\pi$
$572$	−4.73768	−	11.6110i	−0.198092	−	0.485481i
$573$	11.5383	+	24.9883i	0.482018	+	1.04390i
$574$	−15.8883	−	10.6771i	−0.663165	−	0.445653i
$575$	−7.83686			−0.326820
$576$	21.5414	−	10.5816i	0.897557	−	0.440898i
$577$	7.06738			0.294219			0.147109	−	0.989120i	$-0.453003\pi$
$577$	7.06738			0.294219			0.147109	+	0.989120i	$0.453003\pi$
$578$	−36.8328	−	24.7520i	−1.53204	−	1.02955i
$579$	5.89770	+	12.7726i	0.245100	+	0.530810i
$580$	−7.61308	−	18.6580i	−0.316116	−	0.774731i
$581$		−	36.6048i		−	1.51862i
$582$	−1.36712	+	8.51950i	−0.0566688	+	0.353145i
$583$			1.15880i			0.0479924i
$584$	3.16697	−	15.2868i	0.131050	−	0.632574i
$585$	33.6881	+	28.7013i	1.39283	+	1.18665i
$586$	16.6019	−	24.7049i	0.685818	−	1.02055i
$587$	−21.9172			−0.904619			−0.452310	−	0.891861i	$-0.649400\pi$
$587$	−21.9172			−0.904619			−0.452310	+	0.891861i	$0.649400\pi$
$588$	−24.8188	+	26.5982i	−1.02351	+	1.09689i
$589$	4.24292			0.174826
$590$	5.91500	−	8.80197i	0.243517	−	0.362371i
$591$	−8.96470	+	4.13942i	−0.368758	+	0.170273i
$592$	6.65414	−	6.51489i	0.273483	−	0.267760i
$593$			10.7284i			0.440561i	0.975437	+	0.220280i	$0.0706972\pi$
$593$			10.7284i			0.440561i	−0.975437	+	0.220280i	$0.929303\pi$
$594$	−5.60117	−	6.56893i	−0.229819	−	0.269526i
$595$		−	80.4262i		−	3.29715i
$596$	−3.61908	+	1.47670i	−0.148243	+	0.0604881i
$597$	31.2658	−	14.4369i	1.27962	−	0.590862i
$598$	18.6025	+	12.5011i	0.760714	+	0.511207i
$599$	40.0465			1.63625			0.818127	−	0.575037i	$-0.195012\pi$
$599$	40.0465			1.63625			0.818127	+	0.575037i	$0.195012\pi$
$600$	−12.5945	+	2.92633i	−0.514167	+	0.119467i
$601$	−15.1928			−0.619728			−0.309864	−	0.950781i	$-0.600284\pi$
$601$	−15.1928			−0.619728			−0.309864	+	0.950781i	$0.600284\pi$
$602$	40.4021	+	27.1506i	1.64667	+	1.10658i
$603$	−1.71878	−	1.46436i	−0.0699943	−	0.0596332i
$604$	16.4765	−	6.72296i	0.670419	−	0.273553i
$605$			26.5888i			1.08099i
$606$	19.5278	+	3.13360i	0.793261	+	0.127294i
$607$		−	23.3212i		−	0.946577i	−0.880908	−	0.473288i	$-0.843067\pi$
$607$		−	23.3212i		−	0.946577i	0.880908	−	0.473288i	$-0.156933\pi$
$608$	1.03017	+	5.56226i	0.0417790	+	0.225579i
$609$	11.0735	+	23.9818i	0.448721	+	0.971791i
$610$	25.0243	−	37.2380i	1.01320	−	1.50772i
$611$	−38.7513			−1.56771
$612$	13.0575	−	39.6378i	0.527819	−	1.60226i
$613$	−39.5194			−1.59618			−0.798088	−	0.602541i	$-0.794155\pi$
$613$	−39.5194			−1.59618			−0.798088	+	0.602541i	$0.794155\pi$
$614$	10.5305	−	15.6701i	0.424976	−	0.632396i
$615$	6.49335	+	14.0626i	0.261837	+	0.567058i
$616$	−13.6117	−	2.81992i	−0.548429	−	0.113618i
$617$			29.2956i			1.17940i	0.807623	+	0.589699i	$0.200754\pi$
$617$			29.2956i			1.17940i	−0.807623	+	0.589699i	$0.799246\pi$
$618$	20.1535	+	3.23402i	0.810695	+	0.130092i
$619$			19.2306i			0.772942i	0.922302	+	0.386471i	$0.126306\pi$
$619$			19.2306i			0.772942i	−0.922302	+	0.386471i	$0.873694\pi$
$620$	8.86087	+	21.7161i	0.355861	+	0.872138i
$621$	14.8572	+	4.16080i	0.596198	+	0.166967i
$622$	4.78298	+	3.21420i	0.191780	+	0.128878i
$623$	−31.1618			−1.24847
$624$	34.5637	+	13.1439i	1.38366	+	0.526179i
$625$	−31.2306			−1.24922
$626$	30.4943	+	20.4925i	1.21880	+	0.819043i
$627$	1.84733	−	0.852997i	0.0737751	−	0.0340654i
$628$	−4.20079	−	10.2952i	−0.167630	−	0.410824i
$629$		−	16.1932i		−	0.645665i
$630$	47.2344	−	13.2490i	1.88186	−	0.527851i
$631$		−	25.3952i		−	1.01097i	−0.862837	−	0.505483i	$-0.831314\pi$
$631$		−	25.3952i		−	1.01097i	0.862837	−	0.505483i	$-0.168686\pi$
$632$	−10.0367	−	2.07931i	−0.399240	−	0.0827105i
$633$	4.18063	−	1.93039i	0.166165	−	0.0767262i
$634$	−3.42590	+	5.09800i	−0.136060	+	0.202467i
$635$	25.1662			0.998691
$636$	−2.49832	−	2.33118i	−0.0990646	−	0.0924373i
$637$	−56.0519			−2.22086
$638$	−3.37806	+	5.02680i	−0.133739	+	0.199013i
$639$	9.69187	−	11.3758i	0.383404	−	0.450020i
$640$	−26.3173	+	16.8888i	−1.04028	+	0.667588i
$641$		−	9.12220i		−	0.360305i	−0.983639	−	0.180153i	$-0.942341\pi$
$641$		−	9.12220i		−	0.360305i	0.983639	−	0.180153i	$-0.0576592\pi$
$642$	−1.27421	+	7.94056i	−0.0502893	+	0.313389i
$643$			10.3186i			0.406924i	0.979083	+	0.203462i	$0.0652194\pi$
$643$			10.3186i			0.406924i	−0.979083	+	0.203462i	$0.934781\pi$
$644$	23.0028	−	9.38589i	0.906436	−	0.369856i
$645$	−16.5118	−	35.7595i	−0.650153	−	1.40803i
$646$	8.16435	+	5.48652i	0.321222	+	0.215864i
$647$	9.86134			0.387689			0.193845	−	0.981032i	$-0.437904\pi$
$647$	9.86134			0.387689			0.193845	+	0.981032i	$0.437904\pi$
$648$	25.4303	+	1.13899i	0.998998	+	0.0447439i
$649$	−3.18722			−0.125109
$650$	−16.5354	−	11.1119i	−0.648570	−	0.435845i
$651$	−12.8885	−	27.9124i	−0.505139	−	1.09397i
$652$	12.7456	−	5.20064i	0.499158	−	0.203673i
$653$			29.8606i			1.16853i	0.811561	+	0.584267i	$0.198618\pi$
$653$			29.8606i			1.16853i	−0.811561	+	0.584267i	$0.801382\pi$
$654$	0.225737	−	1.40673i	0.00882700	−	0.0550075i
$655$		−	29.4904i		−	1.15229i
$656$	9.05418	+	9.24771i	0.353506	+	0.361062i
$657$	10.7385	−	12.6042i	0.418947	−	0.491738i
$658$	−23.9587	+	35.6524i	−0.934008	+	1.38987i
$659$	−24.6316			−0.959510			−0.479755	−	0.877403i	$-0.659274\pi$
$659$	−24.6316			−0.959510			−0.479755	+	0.877403i	$0.659274\pi$
$660$	8.22375	+	7.67358i	0.320109	+	0.298694i
$661$	−3.07287			−0.119521			−0.0597604	−	0.998213i	$-0.519034\pi$
$661$	−3.07287			−0.119521			−0.0597604	+	0.998213i	$0.519034\pi$
$662$	6.85820	−	10.2055i	0.266552	−	0.396649i
$663$	58.3784	−	26.9560i	2.26723	−	1.04689i
$664$	−5.02047	+	24.2336i	−0.194832	+	0.940446i
$665$			11.5629i			0.448391i
$666$	9.51028	−	2.66758i	0.368516	−	0.103366i
$667$		−	10.8243i		−	0.419118i
$668$	−7.55640	−	18.5191i	−0.292366	−	0.716525i
$669$	−37.1848	+	17.1699i	−1.43765	+	0.663829i
$670$	2.44187	+	1.64096i	0.0943375	+	0.0633957i
$671$	−13.4840			−0.520543
$672$	33.4626	−	23.6732i	1.29085	−	0.913215i
$673$	−21.3800			−0.824140			−0.412070	−	0.911152i	$-0.635194\pi$
$673$	−21.3800			−0.824140			−0.412070	+	0.911152i	$0.635194\pi$
$674$	20.0753	+	13.4908i	0.773272	+	0.519646i
$675$	−13.2062	−	3.69844i	−0.508307	−	0.142353i
$676$	11.7024	+	28.6800i	0.450093	+	1.10308i
$677$		−	18.5680i		−	0.713628i	−0.934175	−	0.356814i	$-0.883863\pi$
$677$		−	18.5680i		−	0.713628i	0.934175	−	0.356814i	$-0.116137\pi$
$678$	−41.1241	−	6.59915i	−1.57936	−	0.253439i
$679$			14.7367i			0.565542i
$680$	−11.0307	+	53.2447i	−0.423008	+	2.04184i
$681$	8.44341	+	18.2858i	0.323552	+	0.700714i
$682$	3.93172	−	5.85070i	0.150553	−	0.224035i
$683$	−38.1270			−1.45889			−0.729445	−	0.684039i	$-0.760222\pi$
$683$	−38.1270			−1.45889			−0.729445	+	0.684039i	$0.760222\pi$
$684$	−1.87729	+	5.69875i	−0.0717800	+	0.217897i
$685$	55.0086			2.10177
$686$	−11.5555	+	17.1955i	−0.441191	+	0.656525i
$687$	−10.9272	−	23.6650i	−0.416899	−	0.902875i
$688$	−23.0237	−	23.5159i	−0.877772	−	0.896534i
$689$		−	5.26485i		−	0.200575i
$690$	−19.8487	−	3.18511i	−0.755628	−	0.121255i
$691$		−	21.9646i		−	0.835572i	−0.908545	−	0.417786i	$-0.862806\pi$
$691$		−	21.9646i		−	0.835572i	0.908545	−	0.417786i	$-0.137194\pi$
$692$	−4.27892	+	1.74594i	−0.162660	+	0.0663708i
$693$	−11.2230	−	9.56171i	−0.426328	−	0.363219i
$694$	−30.6704	−	20.6108i	−1.16423	−	0.782374i
$695$	−6.73366			−0.255422
$696$	−4.04185	−	17.3955i	−0.153206	−	0.659374i
$697$	22.5048			0.852430
$698$	28.3562	+	19.0556i	1.07330	+	0.721265i
$699$	21.8069	−	10.0693i	0.824812	−	0.380854i
$700$	−20.4466	+	8.34290i	−0.772810	+	0.315332i
$701$		−	24.1206i		−	0.911024i	−0.890230	−	0.455512i	$-0.849456\pi$
$701$		−	24.1206i		−	0.911024i	0.890230	−	0.455512i	$-0.150544\pi$
$702$	25.4482	+	29.8451i	0.960481	+	1.12643i
$703$			2.32811i			0.0878062i
$704$	8.62460	+	3.73376i	0.325052	+	0.140721i
$705$	31.5556	−	14.5707i	1.18845	−	0.548764i
$706$	−26.7210	+	39.7628i	−1.00566	+	1.49649i
$707$	33.7783			1.27036
$708$	6.41180	−	6.87150i	0.240970	−	0.258247i
$709$	10.3421			0.388405			0.194203	−	0.980961i	$-0.437788\pi$
$709$	10.3421			0.388405			0.194203	+	0.980961i	$0.437788\pi$
$710$	−10.8607	+	16.1615i	−0.407595	+	0.606532i
$711$	−8.27546	−	7.05046i	−0.310354	−	0.264413i
$712$	20.6301	+	4.27393i	0.773146	+	0.160172i
$713$			12.5984i			0.471813i
$714$	11.2932	−	70.3760i	0.422637	−	2.63376i
$715$			17.3304i			0.648120i
$716$	−13.8652	−	33.9806i	−0.518167	−	1.26991i
$717$	2.19060	+	4.74417i	0.0818096	+	0.177174i
$718$	4.63102	+	3.11209i	0.172828	+	0.116142i
$719$	−12.9147			−0.481639			−0.240819	−	0.970570i	$-0.577416\pi$
$719$	−12.9147			−0.481639			−0.240819	+	0.970570i	$0.577416\pi$
$720$	−33.0878	+	2.29290i	−1.23311	+	0.0854513i
$721$	34.8608			1.29828
$722$	−1.17379	−	0.788801i	−0.0436841	−	0.0293561i
$723$	17.2735	+	37.4090i	0.642408	+	1.39126i
$724$	−4.40138	−	10.7868i	−0.163576	−	0.400889i
$725$			9.62145i			0.357332i
$726$	−3.73352	+	23.2663i	−0.138564	+	0.863492i
$727$			44.6126i			1.65459i	0.561768	+	0.827295i	$0.310121\pi$
$727$			44.6126i			1.65459i	−0.561768	+	0.827295i	$0.689879\pi$
$728$	61.8429	+	12.8120i	2.29205	+	0.474843i
$729$	23.0728	+	14.0231i	0.854548	+	0.519373i
$730$	−12.0335	+	17.9068i	−0.445380	+	0.662759i
$731$	−57.2271			−2.11662
$732$	27.1261	−	29.0709i	1.00261	−	1.07449i
$733$	−3.57344			−0.131988			−0.0659939	−	0.997820i	$-0.521022\pi$
$733$	−3.57344			−0.131988			−0.0659939	+	0.997820i	$0.521022\pi$
$734$	−22.7219	+	33.8119i	−0.838680	+	1.24802i
$735$	45.6436	−	21.0758i	1.68359	−	0.777393i
$736$	−16.5159	+	3.05886i	−0.608783	+	0.112751i
$737$		−	0.884206i		−	0.0325702i
$738$	3.70731	+	13.2171i	0.136468	+	0.486528i
$739$		−	45.8217i		−	1.68558i	−0.538244	−	0.842789i	$-0.680912\pi$
$739$		−	45.8217i		−	1.68558i	0.538244	−	0.842789i	$-0.319088\pi$
$740$	−11.9157	+	4.86200i	−0.438030	+	0.178731i
$741$	−8.39310	+	3.87548i	−0.308328	+	0.142369i
$742$	−4.84382	−	3.25509i	−0.177822	−	0.119498i
$743$	−34.7031			−1.27313			−0.636567	−	0.771221i	$-0.719646\pi$
$743$	−34.7031			−1.27313			−0.636567	+	0.771221i	$0.719646\pi$
$744$	4.70431	+	20.2466i	0.172468	+	0.742277i
$745$	5.40177			0.197905
$746$	33.5720	+	22.5607i	1.22916	+	0.826005i
$747$	−17.0232	+	19.9810i	−0.622848	+	0.731067i
$748$	15.1311	−	6.17398i	0.553247	−	0.225743i
$749$			13.7352i			0.501875i
$750$	−15.7804	−	2.53228i	−0.576220	−	0.0924656i
$751$		−	2.72028i		−	0.0992644i	−0.998768	−	0.0496322i	$-0.984195\pi$
$751$		−	2.72028i		−	0.0992644i	0.998768	−	0.0496322i	$-0.0158049\pi$
$752$	20.7513	−	20.3170i	0.756722	−	0.740886i
$753$	4.13526	+	8.95569i	0.150697	+	0.326363i
$754$	15.3478	−	22.8386i	0.558933	−	0.831734i
$755$	−24.5925			−0.895014
$756$	43.1923	−	4.96085i	1.57089	−	0.180424i
$757$	−2.28675			−0.0831132			−0.0415566	−	0.999136i	$-0.513232\pi$
$757$	−2.28675			−0.0831132			−0.0415566	+	0.999136i	$0.513232\pi$
$758$	14.4373	−	21.4838i	0.524387	−	0.780327i
$759$	2.53278	+	5.48522i	0.0919341	+	0.199101i
$760$	1.58589	−	7.65503i	0.0575263	−	0.277677i
$761$		−	18.6061i		−	0.674472i	−0.941420	−	0.337236i	$-0.890508\pi$
$761$		−	18.6061i		−	0.674472i	0.941420	−	0.337236i	$-0.109492\pi$
$762$	22.0214	+	3.53376i	0.797752	+	0.128015i
$763$		−	2.43330i		−	0.0880915i
$764$	−12.0068	−	29.4262i	−0.434392	−	1.06460i
$765$	−37.4026	+	43.9012i	−1.35229	+	1.58725i
$766$	40.6626	+	27.3256i	1.46920	+	0.987314i
$767$	14.4807			0.522868
$768$	−25.4002	+	11.0830i	−0.916549	+	0.399922i
$769$	−54.9617			−1.98197			−0.990985	−	0.133974i	$-0.957226\pi$
$769$	−54.9617			−1.98197			−0.990985	+	0.133974i	$0.957226\pi$
$770$	15.9445	+	10.7148i	0.574600	+	0.386136i
$771$	0.966365	−	0.446216i	0.0348028	−	0.0160701i
$772$	−6.13721	−	15.0410i	−0.220883	−	0.541336i
$773$			12.1156i			0.435769i	0.975975	+	0.217884i	$0.0699156\pi$
$773$			12.1156i			0.435769i	−0.975975	+	0.217884i	$0.930084\pi$
$774$	−9.42727	−	33.6095i	−0.338856	−	1.20807i
$775$		−	11.1984i		−	0.402259i
$776$	2.02118	−	9.75616i	0.0725561	−	0.350226i
$777$	15.3157	−	7.07196i	0.549446	−	0.253705i
$778$	−3.00540	+	4.47225i	−0.107749	+	0.160338i
$779$	−3.23553			−0.115925
$780$	−37.3636	−	34.8640i	−1.33783	−	1.24833i
$781$	5.85214			0.209406
$782$	−16.2910	+	24.2422i	−0.582564	+	0.866899i
$783$	5.10829	−	18.2404i	0.182555	−	0.651859i
$784$	30.0158	−	29.3876i	1.07199	−	1.04956i
$785$			15.3665i			0.548452i
$786$	4.14095	−	25.8053i	0.147703	−	0.920444i
$787$		−	50.6014i		−	1.80375i	−0.432002	−	0.901873i	$-0.642193\pi$
$787$		−	50.6014i		−	1.80375i	0.432002	−	0.901873i	$-0.357807\pi$
$788$	10.5568	−	4.30752i	0.376071	−	0.153449i
$789$	−19.4952	−	42.2206i	−0.694048	−	1.50309i
$790$	11.7569	+	7.90074i	0.418292	+	0.281096i
$791$	−71.1348			−2.52926
$792$	6.11860	+	7.86944i	0.217415	+	0.279628i
$793$	61.2628			2.17551
$794$	−33.4191	−	22.4580i	−1.18600	−	0.797004i
$795$	1.97961	+	4.28722i	0.0702095	+	0.152052i
$796$	−36.8185	+	15.0232i	−1.30500	+	0.532482i
$797$			52.5966i			1.86307i	0.363654	+	0.931534i	$0.381529\pi$
$797$			52.5966i			1.86307i	−0.363654	+	0.931534i	$0.618471\pi$
$798$	−1.62363	+	10.1180i	−0.0574758	+	0.358174i
$799$		−	50.4994i		−	1.78654i
$800$	14.6806	−	2.71895i	0.519037	−	0.0961295i
$801$	17.0099	+	14.4919i	0.601014	+	0.512047i
$802$	−30.7068	+	45.6940i	−1.08429	+	1.61351i
$803$	6.48409			0.228819
$804$	1.90631	+	1.77878i	0.0672304	+	0.0627327i
$805$	−34.3335			−1.21010
$806$	−17.8633	+	26.5819i	−0.629208	+	0.936308i
$807$	−23.7636	+	10.9727i	−0.836517	+	0.386259i
$808$	−22.3623	−	4.63280i	−0.786704	−	0.162981i
$809$		−	16.6197i		−	0.584318i	−0.956370	−	0.292159i	$-0.905626\pi$
$809$		−	16.6197i		−	0.584318i	0.956370	−	0.292159i	$-0.0943736\pi$
$810$	−31.9447	−	14.7345i	−1.12242	−	0.517719i
$811$			25.9759i			0.912137i	0.889945	+	0.456068i	$0.150743\pi$
$811$			25.9759i			0.912137i	−0.889945	+	0.456068i	$0.849257\pi$
$812$	−11.5232	−	28.2409i	−0.404385	−	0.991060i
$813$	−24.9479	+	11.5196i	−0.874959	+	0.404010i
$814$	3.21030	+	2.15735i	0.112521	+	0.0756152i
$815$	−19.0239			−0.666378
$816$	−17.1287	+	45.0423i	−0.599626	+	1.57680i
$817$	8.22758			0.287847
$818$	39.9482	+	26.8456i	1.39676	+	0.938633i
$819$	50.9905	+	43.4424i	1.78175	+	1.51800i
$820$	−6.75705	−	16.5601i	−0.235967	−	0.578302i
$821$		−	25.4822i		−	0.889336i	−0.895696	−	0.444668i	$-0.853322\pi$
$821$		−	25.4822i		−	0.889336i	0.895696	−	0.444668i	$-0.146678\pi$
$822$	48.1347	+	7.72414i	1.67889	+	0.269410i
$823$			6.91043i			0.240882i	0.992720	+	0.120441i	$0.0384309\pi$
$823$			6.91043i			0.240882i	−0.992720	+	0.120441i	$0.961569\pi$
$824$	−23.0790	−	4.78126i	−0.803994	−	0.166563i
$825$	−2.25133	−	4.87569i	−0.0783813	−	0.169750i
$826$	8.95299	−	13.3227i	0.311514	−	0.463557i
$827$	34.3866			1.19574			0.597870	−	0.801593i	$-0.296014\pi$
$827$	34.3866			1.19574			0.597870	+	0.801593i	$0.296014\pi$
$828$	−16.9212	−	5.57419i	−0.588051	−	0.193716i
$829$	−39.8092			−1.38263			−0.691315	−	0.722553i	$-0.742969\pi$
$829$	−39.8092			−1.38263			−0.691315	+	0.722553i	$0.742969\pi$
$830$	19.0762	−	28.3869i	0.662146	−	0.985323i
$831$	11.8178	+	25.5936i	0.409953	+	0.887832i
$832$	−39.1848	−	16.9639i	−1.35849	−	0.588117i
$833$		−	73.0449i		−	2.53086i
$834$	−5.89221	−	0.945519i	−0.204031	−	0.0327406i
$835$			27.6412i			0.956565i
$836$	−2.17541	+	0.887638i	−0.0752380	+	0.0306996i
$837$	−5.94554	+	21.2300i	−0.205508	+	0.733817i
$838$	24.3846	+	16.3867i	0.842352	+	0.566068i
$839$	48.4574			1.67293			0.836467	−	0.548018i	$-0.184617\pi$
$839$	48.4574			1.67293			0.836467	+	0.548018i	$0.184617\pi$
$840$	−55.1767	+	12.8203i	−1.90378	+	0.442343i
$841$	15.7109			0.541754
$842$	−28.2009	−	18.9513i	−0.971869	−	0.653105i
$843$	−3.98191	+	1.83863i	−0.137144	+	0.0633259i
$844$	−4.92310	+	2.00879i	−0.169460	+	0.0691453i
$845$		−	42.8073i		−	1.47262i
$846$	29.6583	−	8.31898i	1.01967	−	0.286012i
$847$			40.2450i			1.38284i
$848$	2.76032	+	2.81932i	0.0947899	+	0.0968160i
$849$	3.18274	−	1.46962i	0.109231	−	0.0504372i
$850$	14.4807	−	21.5483i	0.496683	−	0.739102i
$851$	−6.91279			−0.236967
$852$	−11.7729	+	12.6170i	−0.403333	+	0.432250i
$853$	41.2494			1.41235			0.706176	−	0.708037i	$-0.250419\pi$
$853$	41.2494			1.41235			0.706176	+	0.708037i	$0.250419\pi$
$854$	37.8769	−	56.3637i	1.29612	−	1.92873i
$855$	5.37739	−	6.31170i	0.183903	−	0.215856i
$856$	1.88383	−	9.09318i	0.0643880	−	0.310799i
$857$			18.4966i			0.631832i	0.948787	+	0.315916i	$0.102312\pi$
$857$			18.4966i			0.631832i	−0.948787	+	0.315916i	$0.897688\pi$
$858$	−2.43348	+	15.1648i	−0.0830775	+	0.517716i
$859$			56.8196i			1.93866i	0.245765	+	0.969329i	$0.420961\pi$
$859$			56.8196i			1.93866i	−0.245765	+	0.969329i	$0.579039\pi$
$860$	17.1824	+	42.1103i	0.585915	+	1.43595i
$861$	9.82838	+	21.2852i	0.334950	+	0.725399i
$862$	10.5649	+	7.09969i	0.359841	+	0.241817i
$863$	24.7624			0.842923			0.421461	−	0.906846i	$-0.361517\pi$
$863$	24.7624			0.842923			0.421461	+	0.906846i	$0.361517\pi$
$864$	−29.2751	−	2.63971i	−0.995959	−	0.0898048i
$865$	6.38664			0.217152
$866$	21.4141	+	14.3905i	0.727681	+	0.489008i
$867$	22.7845	+	49.3442i	0.773802	+	1.67582i
$868$	13.4119	+	32.8696i	0.455229	+	1.11567i
$869$		−	4.25720i		−	0.144416i
$870$	−3.91041	+	24.3686i	−0.132575	+	0.826173i
$871$			4.01728i			0.136120i
$872$	−0.333735	+	1.61093i	−0.0113017	+	0.0545528i
$873$	6.85336	−	8.04412i	0.231951	−	0.272252i
$874$	2.34216	−	3.48532i	0.0792249	−	0.117893i
$875$	−27.2964			−0.922786
$876$	−13.0442	+	13.9794i	−0.440723	+	0.472321i
$877$	39.3072			1.32731			0.663655	−	0.748039i	$-0.269004\pi$
$877$	39.3072			1.32731			0.663655	+	0.748039i	$0.269004\pi$
$878$	3.63133	−	5.40369i	0.122551	−	0.182366i
$879$	−33.0966	+	15.2822i	−1.11632	+	0.515457i
$880$	−9.08620	−	9.28041i	−0.306296	−	0.312843i
$881$		−	42.1263i		−	1.41927i	−0.704570	−	0.709635i	$-0.748860\pi$
$881$		−	42.1263i		−	1.41927i	0.704570	−	0.709635i	$-0.251140\pi$
$882$	42.8994	−	12.0330i	1.44450	−	0.405173i
$883$		−	28.0654i		−	0.944476i	−0.881471	−	0.472238i	$-0.843446\pi$
$883$		−	28.0654i		−	0.944476i	0.881471	−	0.472238i	$-0.156554\pi$
$884$	−68.7462	+	28.0507i	−2.31219	+	0.943448i
$885$	−11.7918	+	5.44483i	−0.396377	+	0.183026i
$886$	−6.40044	−	4.30115i	−0.215027	−	0.144500i
$887$	2.73938			0.0919795			0.0459898	−	0.998942i	$-0.485356\pi$
$887$	2.73938			0.0919795			0.0459898	+	0.998942i	$0.485356\pi$
$888$	−11.1094	+	2.58127i	−0.372807	+	0.0866219i
$889$	38.0918			1.27756
$890$	−24.1658	−	16.2396i	−0.810040	−	0.544354i
$891$	1.67945	+	10.4386i	0.0562638	+	0.349708i
$892$	43.7887	−	17.8672i	1.46615	−	0.598239i
$893$			7.26033i			0.242958i
$894$	4.72676	+	0.758499i	0.158086	+	0.0253680i
$895$			50.7188i			1.69534i
$896$	−39.8341	+	25.5630i	−1.33076	+	0.854000i
$897$	−11.5074	−	24.9214i	−0.384220	−	0.832102i
$898$	11.0892	−	16.5016i	0.370051	−	0.550664i
$899$	15.4672			0.515862
$900$	15.0408	+	4.95477i	0.501361	+	0.165159i
$901$	6.86097			0.228572
$902$	−2.99822	+	4.46158i	−0.0998298	+	0.148554i
$903$	−24.9924	−	54.1259i	−0.831696	−	1.80120i
$904$	47.0935	+	9.75635i	1.56631	+	0.324491i
$905$			16.1002i			0.535189i
$906$	−21.5194	−	3.45320i	−0.714935	−	0.114725i
$907$		−	42.3789i		−	1.40717i	−0.710612	−	0.703584i	$-0.751582\pi$
$907$		−	42.3789i		−	1.40717i	0.710612	−	0.703584i	$-0.248418\pi$
$908$	−8.78631	−	21.5333i	−0.291584	−	0.714608i
$909$	−18.4381	−	15.7088i	−0.611554	−	0.521026i
$910$	−72.4418	−	48.6816i	−2.40142	−	1.61378i
$911$	52.4108			1.73645			0.868224	−	0.496173i	$-0.165262\pi$
$911$	52.4108			1.73645			0.868224	+	0.496173i	$0.165262\pi$
$912$	2.46261	−	6.47577i	0.0815452	−	0.214434i
$913$	−10.2790			−0.340184
$914$	−23.5806	−	15.8464i	−0.779977	−	0.524152i
$915$	−49.8870	+	23.0351i	−1.64921	+	0.761518i
$916$	11.3710	+	27.8678i	0.375708	+	0.920778i
$917$		−	44.6369i		−	1.47404i
$918$	−38.8932	+	33.1633i	−1.28367	+	1.09455i
$919$		−	5.60095i		−	0.184758i	−0.995724	−	0.0923792i	$-0.970553\pi$
$919$		−	5.60095i		−	0.184758i	0.995724	−	0.0923792i	$-0.0294472\pi$
$920$	22.7299	+	4.70894i	0.749382	+	0.155249i
$921$	−20.9930	+	9.69342i	−0.691741	+	0.319409i
$922$	18.0096	−	26.7997i	0.593116	−	0.882601i
$923$	−26.5885			−0.875170
$924$	12.4475	+	11.6148i	0.409493	+	0.382098i
$925$	6.14462			0.202034
$926$	−0.422635	+	0.628913i	−0.0138887	+	0.0206674i
$927$	−19.0290	−	16.2122i	−0.624994	−	0.532477i
$928$	3.75542	+	20.2768i	0.123278	+	0.665619i
$929$			20.7574i			0.681028i	0.940239	+	0.340514i	$0.110601\pi$
$929$			20.7574i			0.681028i	−0.940239	+	0.340514i	$0.889399\pi$
$930$	4.55133	−	28.3626i	0.149244	−	0.930048i
$931$			10.5017i			0.344180i
$932$	−25.6797	+	10.4782i	−0.841167	+	0.343224i
$933$	−2.95871	−	6.40765i	−0.0968638	−	0.209777i
$934$	28.4975	+	19.1506i	0.932467	+	0.626626i
$935$	−22.5844			−0.738588
$936$	−27.7991	−	35.7538i	−0.908642	−	1.16865i
$937$	−38.4234			−1.25524			−0.627619	−	0.778521i	$-0.715970\pi$
$937$	−38.4234			−1.25524			−0.627619	+	0.778521i	$0.715970\pi$
$938$	3.69603	+	2.48376i	0.120679	+	0.0810977i
$939$	−18.8635	−	40.8526i	−0.615588	−	1.33317i
$940$	−37.1598	+	15.1624i	−1.21202	+	0.494543i
$941$		−	56.1048i		−	1.82897i	−0.404625	−	0.914483i	$-0.632598\pi$
$941$		−	56.1048i		−	1.82897i	0.404625	−	0.914483i	$-0.367402\pi$
$942$	−2.15771	+	13.4462i	−0.0703019	+	0.438102i
$943$		−	9.60717i		−	0.312853i
$944$	−7.75442	+	7.59214i	−0.252385	+	0.247103i
$945$	−57.8567	−	16.2030i	−1.88208	−	0.527083i
$946$	7.62413	−	11.3453i	0.247882	−	0.368867i
$947$	−5.69875			−0.185184			−0.0925922	−	0.995704i	$-0.529515\pi$
$947$	−5.69875			−0.185184			−0.0925922	+	0.995704i	$0.529515\pi$
$948$	9.17835	+	8.56432i	0.298099	+	0.278156i
$949$	−29.4596			−0.956301
$950$	−2.08190	+	3.09802i	−0.0675457	+	0.100513i
$951$	6.82968	−	3.15358i	0.221468	−	0.102262i
$952$	−16.6961	+	80.5916i	−0.541125	+	2.61199i
$953$			15.9430i			0.516443i	0.966086	+	0.258222i	$0.0831365\pi$
$953$			15.9430i			0.516443i	−0.966086	+	0.258222i	$0.916864\pi$
$954$	1.13024	+	4.02946i	0.0365928	+	0.130459i
$955$			43.9209i			1.42125i
$956$	−2.27957	−	5.58672i	−0.0737264	−	0.180687i
$957$	6.73430	−	3.10954i	0.217689	−	0.100517i
$958$	9.28367	+	6.23871i	0.299942	+	0.201564i
$959$	83.2614			2.68865
$960$	38.2871	−	0.919820i	1.23571	−	0.0296871i
$961$	12.9977			0.419279
$962$	−14.5856	−	9.80166i	−0.470259	−	0.316018i
$963$	6.38764	−	7.49748i	0.205839	−	0.241603i
$964$	−17.9750	−	44.0528i	−0.578935	−	1.41884i
$965$			22.4498i			0.722686i
$966$	−30.0431	−	4.82100i	−0.966622	−	0.155113i
$967$		−	2.98611i		−	0.0960269i	−0.998847	−	0.0480134i	$-0.984711\pi$
$967$		−	2.98611i		−	0.0960269i	0.998847	−	0.0480134i	$-0.0152890\pi$
$968$	5.51973	−	26.6435i	0.177411	−	0.856355i
$969$	−5.05040	−	10.9376i	−0.162242	−	0.351367i
$970$	−7.67987	+	11.4282i	−0.246586	+	0.366938i
$971$	32.7704			1.05165			0.525826	−	0.850592i	$-0.323756\pi$
$971$	32.7704			1.05165			0.525826	+	0.850592i	$0.323756\pi$
$972$	−25.8839	−	17.3789i	−0.830226	−	0.557427i
$973$	−10.1921			−0.326744
$974$	−23.8645	+	35.5121i	−0.764666	+	1.13788i
$975$	10.2286	+	22.1521i	0.327579	+	0.709434i
$976$	−32.8062	+	32.1197i	−1.05010	+	1.02813i
$977$			20.8446i			0.666878i	0.942772	+	0.333439i	$0.108209\pi$
$977$			20.8446i			0.666878i	−0.942772	+	0.333439i	$0.891791\pi$
$978$	−16.6467	−	2.67128i	−0.532301	−	0.0854180i
$979$			8.75050i			0.279667i
$980$	−53.7498	+	21.9317i	−1.71697	+	0.700583i
$981$	−1.13162	+	1.32823i	−0.0361298	+	0.0424073i
$982$	46.9707	+	31.5648i	1.49890	+	1.00727i
$983$	55.3829			1.76644			0.883221	−	0.468957i	$-0.155370\pi$
$983$	55.3829			1.76644			0.883221	+	0.468957i	$0.155370\pi$
$984$	−3.58737	−	15.4395i	−0.114361	−	0.492193i
$985$	−15.7569			−0.502056
$986$	29.7626	+	20.0007i	0.947833	+	0.636952i
$987$	47.7627	−	22.0543i	1.52030	−	0.701995i
$988$	9.88369	−	4.03287i	0.314442	−	0.128303i
$989$			24.4299i			0.776827i
$990$	−3.72042	−	13.2638i	−0.118243	−	0.421552i
$991$		−	18.7212i		−	0.594698i	−0.954769	−	0.297349i	$-0.903897\pi$
$991$		−	18.7212i		−	0.594698i	0.954769	−	0.297349i	$-0.0961026\pi$
$992$	−4.37094	−	23.6002i	−0.138777	−	0.749307i
$993$	−13.6721	+	6.31305i	−0.433872	+	0.200339i
$994$	−16.4388	+	24.4622i	−0.521408	+	0.775894i
$995$	54.9546			1.74218
$996$	20.6785	−	22.1610i	0.655222	−	0.702198i
$997$	−25.0833			−0.794395			−0.397198	−	0.917733i	$-0.630017\pi$
$997$	−25.0833			−0.794395			−0.397198	+	0.917733i	$0.630017\pi$
$998$	17.3511	−	25.8197i	0.549239	−	0.817309i
$999$	−11.6490	−	3.26234i	−0.368558	−	0.103216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.32	yes	36
3.2	odd	2	inner	228.2.c.a.191.5	✓	36
4.3	odd	2	inner	228.2.c.a.191.6	yes	36
12.11	even	2	inner	228.2.c.a.191.31	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.5	✓	36	3.2	odd	2	inner
228.2.c.a.191.6	yes	36	4.3	odd	2	inner
228.2.c.a.191.31	yes	36	12.11	even	2	inner
228.2.c.a.191.32	yes	36	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17379 + 0.788801i) q^{2} +(-0.726100 - 1.57251i) q^{3} +(0.755587 + 1.85178i) q^{4} -2.76393i q^{5} +(0.388103 - 2.41855i) q^{6} -4.18351i q^{7} +(-0.573780 + 2.76962i) q^{8} +(-1.94556 + 2.28359i) q^{9} +O(q^{10})\)	\(q+(1.17379 + 0.788801i) q^{2} +(-0.726100 - 1.57251i) q^{3} +(0.755587 + 1.85178i) q^{4} -2.76393i q^{5} +(0.388103 - 2.41855i) q^{6} -4.18351i q^{7} +(-0.573780 + 2.76962i) q^{8} +(-1.94556 + 2.28359i) q^{9} +(2.18019 - 3.24429i) q^{10} -1.17477 q^{11} +(2.36330 - 2.53274i) q^{12} +5.33740 q^{13} +(3.29995 - 4.91058i) q^{14} +(-4.34630 + 2.00689i) q^{15} +(-2.85818 + 2.79836i) q^{16} +6.95552i q^{17} +(-4.08499 + 1.14581i) q^{18} -1.00000i q^{19} +(5.11819 - 2.08839i) q^{20} +(-6.57859 + 3.03764i) q^{21} +(-1.37893 - 0.926656i) q^{22} +2.96927 q^{23} +(4.77186 - 1.10874i) q^{24} -2.63932 q^{25} +(6.26501 + 4.21014i) q^{26} +(5.00364 + 1.40129i) q^{27} +(7.74693 - 3.16100i) q^{28} -3.64543i q^{29} +(-6.68470 - 1.07269i) q^{30} +4.24292i q^{31} +(-5.56226 + 1.03017i) q^{32} +(0.852997 + 1.84733i) q^{33} +(-5.48652 + 8.16435i) q^{34} -11.5629 q^{35} +(-5.69875 - 1.87729i) q^{36} -2.32811 q^{37} +(0.788801 - 1.17379i) q^{38} +(-3.87548 - 8.39310i) q^{39} +(7.65503 + 1.58589i) q^{40} -3.23553i q^{41} +(-10.1180 - 1.62363i) q^{42} +8.22758i q^{43} +(-0.887638 - 2.17541i) q^{44} +(6.31170 + 5.37739i) q^{45} +(3.48532 + 2.34216i) q^{46} -7.26033 q^{47} +(6.47577 + 2.46261i) q^{48} -10.5017 q^{49} +(-3.09802 - 2.08190i) q^{50} +(10.9376 - 5.05040i) q^{51} +(4.03287 + 9.88369i) q^{52} -0.986407i q^{53} +(4.76791 + 5.59170i) q^{54} +3.24697i q^{55} +(11.5867 + 2.40041i) q^{56} +(-1.57251 + 0.726100i) q^{57} +(2.87552 - 4.27898i) q^{58} +2.71307 q^{59} +(-7.00033 - 6.53201i) q^{60} +11.4780 q^{61} +(-3.34682 + 4.98031i) q^{62} +(9.55343 + 8.13925i) q^{63} +(-7.34155 - 3.17830i) q^{64} -14.7522i q^{65} +(-0.455929 + 2.84123i) q^{66} +0.752666i q^{67} +(-12.8801 + 5.25550i) q^{68} +(-2.15599 - 4.66920i) q^{69} +(-13.5725 - 9.12084i) q^{70} -4.98154 q^{71} +(-5.20836 - 6.69873i) q^{72} -5.51948 q^{73} +(-2.73272 - 1.83641i) q^{74} +(1.91641 + 4.15035i) q^{75} +(1.85178 - 0.755587i) q^{76} +4.91464i q^{77} +(2.07146 - 12.9088i) q^{78} +3.62388i q^{79} +(7.73448 + 7.89980i) q^{80} +(-1.42961 - 8.88573i) q^{81} +(2.55219 - 3.79785i) q^{82} +8.74980 q^{83} +(-10.5957 - 9.88690i) q^{84} +19.2246 q^{85} +(-6.48992 + 9.65749i) q^{86} +(-5.73246 + 2.64694i) q^{87} +(0.674057 - 3.25365i) q^{88} -7.44872i q^{89} +(3.16695 + 11.2906i) q^{90} -22.3290i q^{91} +(2.24355 + 5.49844i) q^{92} +(6.67202 - 3.08078i) q^{93} +(-8.52213 - 5.72695i) q^{94} -2.76393 q^{95} +(5.65871 + 7.99869i) q^{96} -3.52257 q^{97} +(-12.3269 - 8.28376i) q^{98} +(2.28557 - 2.68269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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