LMFDB - Embedded newform 950.2.q.e.943.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.1
Character	$\chi$	$=$	950.943
Dual form			950.2.q.e.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.61221 - 0.431989i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.834540 - 1.44546i) q^{6} +(2.81008 - 2.81008i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.185481 - 0.107087i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.61221 - 0.431989i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.834540 - 1.44546i) q^{6} +(2.81008 - 2.81008i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.185481 - 0.107087i) q^{9} -5.57889 q^{11} +(1.18022 + 1.18022i) q^{12} +(-0.831890 - 3.10465i) q^{13} +(1.98702 + 3.44163i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.97289 + 1.06453i) q^{17} +(0.151445 - 0.151445i) q^{18} +(0.254973 + 4.35144i) q^{19} +(-5.74435 + 3.31650i) q^{21} +(1.44392 - 5.38879i) q^{22} +(-3.83864 + 1.02856i) q^{23} +(-1.44546 + 0.834540i) q^{24} +3.21417 q^{26} +(3.79342 + 3.79342i) q^{27} +(-3.83864 + 1.02856i) q^{28} +(-2.09440 + 3.62760i) q^{29} +0.573172i q^{31} +(-0.965926 + 0.258819i) q^{32} +(8.99432 + 2.41002i) q^{33} +(-2.05652 + 3.56199i) q^{34} +(0.107087 + 0.185481i) q^{36} +(-7.24641 - 7.24641i) q^{37} +(-4.26916 - 0.879949i) q^{38} +5.36471i q^{39} +(-5.12760 + 2.96042i) q^{41} +(-1.71675 - 6.40699i) q^{42} +(-1.44088 + 5.37742i) q^{43} +(4.83146 + 2.78944i) q^{44} -3.97405i q^{46} +(3.15762 + 11.7844i) q^{47} +(-0.431989 - 1.61221i) q^{48} -8.79306i q^{49} +(-5.94525 - 3.43249i) q^{51} +(-0.831890 + 3.10465i) q^{52} +(-0.981717 - 3.66382i) q^{53} +(-4.64598 + 2.68236i) q^{54} -3.97405i q^{56} +(1.46870 - 7.12556i) q^{57} +(-2.96192 - 2.96192i) q^{58} +(-3.75696 - 6.50724i) q^{59} +(-1.06199 + 1.83942i) q^{61} +(-0.553641 - 0.148348i) q^{62} +(-0.822140 + 0.220292i) q^{63} -1.00000i q^{64} +(-4.65580 + 8.06409i) q^{66} +(-11.4783 + 3.07561i) q^{67} +(-2.90835 - 2.90835i) q^{68} +6.63300 q^{69} +(-4.56561 + 2.63596i) q^{71} +(-0.206877 + 0.0554326i) q^{72} +(3.50990 - 13.0991i) q^{73} +(8.87500 - 5.12398i) q^{74} +(1.95490 - 3.89594i) q^{76} +(-15.6771 + 15.6771i) q^{77} +(-5.18191 - 1.38849i) q^{78} +(-2.48836 - 4.30996i) q^{79} +(-4.15580 - 7.19806i) q^{81} +(-1.53243 - 5.71910i) q^{82} +(-7.30376 - 7.30376i) q^{83} +6.63300 q^{84} +(-4.82126 - 2.78356i) q^{86} +(4.94369 - 4.94369i) q^{87} +(-3.94487 + 3.94487i) q^{88} +(-7.08207 + 12.2665i) q^{89} +(-11.0620 - 6.38664i) q^{91} +(3.83864 + 1.02856i) q^{92} +(0.247604 - 0.924071i) q^{93} -12.2001 q^{94} +1.66908 q^{96} +(-0.619757 + 2.31297i) q^{97} +(8.49345 + 2.27581i) q^{98} +(1.03478 + 0.597429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{6}+O(q^{10}) $ 24 * q - 12 * q^6	$ 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.61221	−	0.431989i	−0.930808	−	0.249409i	−0.238609	−	0.971116i	$-0.576691\pi$
$3$	−1.61221	−	0.431989i	−0.930808	−	0.249409i	−0.692199	+	0.721707i	$0.743358\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	0.834540	−	1.44546i	0.340699	−	0.590109i
$7$	2.81008	−	2.81008i	1.06211	−	1.06211i	0.0641702	−	0.997939i	$-0.479560\pi$
$7$	2.81008	−	2.81008i	1.06211	−	1.06211i	0.997939	−	0.0641702i	$-0.0204401\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.185481	−	0.107087i	−0.0618270	−	0.0356958i
$10$		0			0
$11$	−5.57889			−1.68210			−0.841049	−	0.540959i	$-0.818061\pi$
$11$	−5.57889			−1.68210			−0.841049	+	0.540959i	$0.818061\pi$
$12$	1.18022	+	1.18022i	0.340699	+	0.340699i
$13$	−0.831890	−	3.10465i	−0.230725	−	0.861076i	−0.980030	−	0.198851i	$-0.936279\pi$
$13$	−0.831890	−	3.10465i	−0.230725	−	0.861076i	0.749305	−	0.662225i	$-0.230388\pi$
$14$	1.98702	+	3.44163i	0.531055	+	0.919814i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.97289	+	1.06453i	0.963566	+	0.258187i	0.706109	−	0.708103i	$-0.250449\pi$
$17$	3.97289	+	1.06453i	0.963566	+	0.258187i	0.257457	+	0.966290i	$0.417115\pi$
$18$	0.151445	−	0.151445i	0.0356958	−	0.0356958i
$19$	0.254973	+	4.35144i	0.0584949	+	0.998288i
$19$	0.254973	+	4.35144i	0.0584949	+	0.998288i
$20$		0			0
$21$	−5.74435	+	3.31650i	−1.25352	+	0.723720i
$22$	1.44392	−	5.38879i	0.307845	−	1.14889i
$23$	−3.83864	+	1.02856i	−0.800411	+	0.214469i	−0.635764	−	0.771883i	$-0.719315\pi$
$23$	−3.83864	+	1.02856i	−0.800411	+	0.214469i	−0.164647	+	0.986353i	$0.552648\pi$
$24$	−1.44546	+	0.834540i	−0.295054	+	0.170350i
$25$		0			0
$26$	3.21417			0.630352
$27$	3.79342	+	3.79342i	0.730045	+	0.730045i
$28$	−3.83864	+	1.02856i	−0.725434	+	0.194379i
$29$	−2.09440	+	3.62760i	−0.388920	+	0.673629i	−0.992305	−	0.123821i	$-0.960485\pi$
$29$	−2.09440	+	3.62760i	−0.388920	+	0.673629i	0.603385	+	0.797450i	$0.293818\pi$
$30$		0			0
$31$			0.573172i			0.102945i	0.998674	+	0.0514724i	$0.0163914\pi$
$31$			0.573172i			0.102945i	−0.998674	+	0.0514724i	$0.983609\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	8.99432	+	2.41002i	1.56571	+	0.419531i
$34$	−2.05652	+	3.56199i	−0.352690	+	0.610877i
$35$		0			0
$36$	0.107087	+	0.185481i	0.0178479	+	0.0309135i
$37$	−7.24641	−	7.24641i	−1.19130	−	1.19130i	−0.976702	−	0.214600i	$-0.931155\pi$
$37$	−7.24641	−	7.24641i	−1.19130	−	1.19130i	−0.214600	−	0.976702i	$-0.568845\pi$
$38$	−4.26916	−	0.879949i	−0.692548	−	0.142747i
$39$			5.36471i			0.859041i
$40$		0			0
$41$	−5.12760	+	2.96042i	−0.800797	+	0.462340i	−0.843750	−	0.536737i	$-0.819657\pi$
$41$	−5.12760	+	2.96042i	−0.800797	+	0.462340i	0.0429529	+	0.999077i	$0.486323\pi$
$42$	−1.71675	−	6.40699i	−0.264900	−	0.988620i
$43$	−1.44088	+	5.37742i	−0.219731	+	0.820049i	0.764716	+	0.644368i	$0.222879\pi$
$43$	−1.44088	+	5.37742i	−0.219731	+	0.820049i	−0.984447	+	0.175681i	$0.943787\pi$
$44$	4.83146	+	2.78944i	0.728370	+	0.420524i
$45$		0			0
$46$		−	3.97405i		−	0.585941i
$47$	3.15762	+	11.7844i	0.460587	+	1.71893i	0.671123	+	0.741346i	$0.265812\pi$
$47$	3.15762	+	11.7844i	0.460587	+	1.71893i	−0.210536	+	0.977586i	$0.567521\pi$
$48$	−0.431989	−	1.61221i	−0.0623523	−	0.232702i
$49$		−	8.79306i		−	1.25615i
$50$		0			0
$51$	−5.94525	−	3.43249i	−0.832501	−	0.480645i
$52$	−0.831890	+	3.10465i	−0.115362	+	0.430538i
$53$	−0.981717	−	3.66382i	−0.134849	−	0.503264i	−0.999998	−	0.00174955i	$-0.999443\pi$
$53$	−0.981717	−	3.66382i	−0.134849	−	0.503264i	0.865149	−	0.501514i	$-0.167224\pi$
$54$	−4.64598	+	2.68236i	−0.632237	+	0.365022i
$55$		0			0
$56$		−	3.97405i		−	0.531055i
$57$	1.46870	−	7.12556i	0.194535	−	0.943803i
$58$	−2.96192	−	2.96192i	−0.388920	−	0.388920i
$59$	−3.75696	−	6.50724i	−0.489114	−	0.847170i	0.510808	−	0.859695i	$-0.329346\pi$
$59$	−3.75696	−	6.50724i	−0.489114	−	0.847170i	−0.999922	+	0.0125249i	$0.996013\pi$
$60$		0			0
$61$	−1.06199	+	1.83942i	−0.135974	+	0.235514i	−0.925969	−	0.377599i	$-0.876750\pi$
$61$	−1.06199	+	1.83942i	−0.135974	+	0.235514i	0.789995	+	0.613113i	$0.210083\pi$
$62$	−0.553641	−	0.148348i	−0.0703125	−	0.0188402i
$63$	−0.822140	+	0.220292i	−0.103580	+	0.0277541i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−4.65580	+	8.06409i	−0.573090	+	0.992620i
$67$	−11.4783	+	3.07561i	−1.40230	+	0.375746i	−0.879171	−	0.476506i	$-0.841903\pi$
$67$	−11.4783	+	3.07561i	−1.40230	+	0.375746i	−0.523132	+	0.852252i	$0.675236\pi$
$68$	−2.90835	−	2.90835i	−0.352690	−	0.352690i
$69$	6.63300			0.798520
$70$		0			0
$71$	−4.56561	+	2.63596i	−0.541838	+	0.312830i	−0.745824	−	0.666143i	$-0.767944\pi$
$71$	−4.56561	+	2.63596i	−0.541838	+	0.312830i	0.203985	+	0.978974i	$0.434611\pi$
$72$	−0.206877	+	0.0554326i	−0.0243807	+	0.00653279i
$73$	3.50990	−	13.0991i	0.410802	−	1.53314i	−0.382295	−	0.924041i	$-0.624866\pi$
$73$	3.50990	−	13.0991i	0.410802	−	1.53314i	0.793097	−	0.609095i	$-0.208467\pi$
$74$	8.87500	−	5.12398i	1.03170	−	0.595651i
$75$		0			0
$76$	1.95490	−	3.89594i	0.224243	−	0.446895i
$77$	−15.6771	+	15.6771i	−1.78657	+	1.78657i
$78$	−5.18191	−	1.38849i	−0.586736	−	0.157216i
$79$	−2.48836	−	4.30996i	−0.279962	−	0.484908i	0.691413	−	0.722460i	$-0.256988\pi$
$79$	−2.48836	−	4.30996i	−0.279962	−	0.484908i	−0.971375	+	0.237551i	$0.923655\pi$
$80$		0			0
$81$	−4.15580	−	7.19806i	−0.461756	−	0.799784i
$82$	−1.53243	−	5.71910i	−0.169228	−	0.631569i
$83$	−7.30376	−	7.30376i	−0.801692	−	0.801692i	0.181668	−	0.983360i	$-0.441850\pi$
$83$	−7.30376	−	7.30376i	−0.801692	−	0.801692i	−0.983360	+	0.181668i	$0.941850\pi$
$84$	6.63300			0.723720
$85$		0			0
$86$	−4.82126	−	2.78356i	−0.519890	−	0.300159i
$87$	4.94369	−	4.94369i	0.530019	−	0.530019i
$88$	−3.94487	+	3.94487i	−0.420524	+	0.420524i
$89$	−7.08207	+	12.2665i	−0.750698	+	1.30025i	0.196787	+	0.980446i	$0.436949\pi$
$89$	−7.08207	+	12.2665i	−0.750698	+	1.30025i	−0.947485	+	0.319801i	$0.896384\pi$
$90$		0			0
$91$	−11.0620	−	6.38664i	−1.15961	−	0.669502i
$92$	3.83864	+	1.02856i	0.400205	+	0.107235i
$93$	0.247604	−	0.924071i	0.0256754	−	0.0958217i
$94$	−12.2001			−1.25835
$95$		0			0
$96$	1.66908			0.170350
$97$	−0.619757	+	2.31297i	−0.0629268	+	0.234846i	−0.990225	−	0.139476i	$-0.955458\pi$
$97$	−0.619757	+	2.31297i	−0.0629268	+	0.234846i	0.927299	+	0.374323i	$0.122125\pi$
$98$	8.49345	+	2.27581i	0.857968	+	0.229892i
$99$	1.03478	+	0.597429i	0.103999	+	0.0600439i
$100$		0			0
$101$	−0.240729	+	0.416955i	−0.0239534	+	0.0414886i	−0.877754	−	0.479112i	$-0.840959\pi$
$101$	−0.240729	+	0.416955i	−0.0239534	+	0.0414886i	0.853800	+	0.520601i	$0.174292\pi$
$102$	4.85427	−	4.85427i	0.480645	−	0.480645i
$103$	−9.90973	+	9.90973i	−0.976435	+	0.976435i	−0.999729	−	0.0232940i	$-0.992585\pi$
$103$	−9.90973	+	9.90973i	−0.976435	+	0.976435i	0.0232940	+	0.999729i	$0.492585\pi$
$104$	−2.78356	−	1.60709i	−0.272950	−	0.157588i
$105$		0			0
$106$	3.79306			0.368415
$107$	1.75977	+	1.75977i	0.170124	+	0.170124i	0.787034	−	0.616910i	$-0.211616\pi$
$107$	1.75977	+	1.75977i	0.170124	+	0.170124i	−0.616910	+	0.787034i	$0.711616\pi$
$108$	−1.38849	−	5.18191i	−0.133607	−	0.498630i
$109$	−1.33809	−	2.31764i	−0.128166	−	0.221990i	0.794800	−	0.606871i	$-0.207576\pi$
$109$	−1.33809	−	2.31764i	−0.128166	−	0.221990i	−0.922966	+	0.384881i	$0.874242\pi$
$110$		0			0
$111$	8.55233	+	14.8131i	0.811752	+	1.40599i
$112$	3.83864	+	1.02856i	0.362717	+	0.0971897i
$113$	6.56319	−	6.56319i	0.617413	−	0.617413i	−0.327454	−	0.944867i	$-0.606191\pi$
$113$	6.56319	−	6.56319i	0.617413	−	0.617413i	0.944867	+	0.327454i	$0.106191\pi$
$114$	6.50263	+	3.26289i	0.609027	+	0.305598i
$115$		0			0
$116$	3.62760	−	2.09440i	0.336814	−	0.194460i
$117$	−0.178170	+	0.664939i	−0.0164718	+	0.0614737i
$118$	7.25788	−	1.94474i	0.668142	−	0.179028i
$119$	14.1555	−	8.17270i	1.29764	−	0.749190i
$120$		0			0
$121$	20.1240			1.82945
$122$	−1.50188	−	1.50188i	−0.135974	−	0.135974i
$123$	9.54562	−	2.55774i	0.860700	−	0.230624i
$124$	0.286586	−	0.496381i	0.0257362	−	0.0445764i
$125$		0			0
$126$		−	0.851142i		−	0.0758257i
$127$	12.5384	−	3.35965i	1.11260	−	0.298121i	0.344715	−	0.938707i	$-0.387975\pi$
$127$	12.5384	−	3.35965i	1.11260	−	0.298121i	0.767886	+	0.640587i	$0.221309\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	4.64598	−	8.04707i	0.409055	−	0.708505i
$130$		0			0
$131$	4.86636	+	8.42878i	0.425176	+	0.736426i	0.996437	−	0.0843425i	$-0.0268790\pi$
$131$	4.86636	+	8.42878i	0.425176	+	0.736426i	−0.571261	+	0.820768i	$0.693546\pi$
$132$	−6.58430	−	6.58430i	−0.573090	−	0.573090i
$133$	12.9444	+	11.5114i	1.12242	+	0.998163i
$134$		−	11.8833i		−	1.02656i
$135$		0			0
$136$	3.56199	−	2.05652i	0.305438	−	0.176345i
$137$	0.203928	+	0.761069i	0.0174227	+	0.0650225i	0.974090	−	0.226161i	$-0.0726176\pi$
$137$	0.203928	+	0.761069i	0.0174227	+	0.0650225i	−0.956667	+	0.291184i	$0.905951\pi$
$138$	−1.71675	+	6.40699i	−0.146139	+	0.545399i
$139$	12.5016	+	7.21779i	1.06037	+	0.612205i	0.925535	−	0.378663i	$-0.123616\pi$
$139$	12.5016	+	7.21779i	1.06037	+	0.612205i	0.134836	+	0.990868i	$0.456949\pi$
$140$		0			0
$141$		−	20.3630i		−	1.71487i
$142$	−1.36447	−	5.09228i	−0.114504	−	0.427334i
$143$	4.64102	+	17.3205i	0.388101	+	1.44841i
$144$		−	0.214175i		−	0.0178479i
$145$		0			0
$146$	11.7443	+	6.78060i	0.971969	+	0.561167i
$147$	−3.79851	+	14.1762i	−0.313296	+	1.16924i
$148$	2.65237	+	9.89878i	0.218023	+	0.813674i
$149$	−10.9655	+	6.33092i	−0.898327	+	0.518649i	−0.876657	−	0.481116i	$-0.840232\pi$
$149$	−10.9655	+	6.33092i	−0.898327	+	0.518649i	−0.0216699	+	0.999765i	$0.506898\pi$
$150$		0			0
$151$			14.7958i			1.20407i	0.798470	+	0.602034i	$0.205643\pi$
$151$			14.7958i			1.20407i	−0.798470	+	0.602034i	$0.794357\pi$
$152$	3.25722	+	2.89664i	0.264196	+	0.234948i
$153$	−0.622897	−	0.622897i	−0.0503582	−	0.0503582i
$154$	−11.0854	−	19.2004i	−0.893286	−	1.54722i
$155$		0			0
$156$	2.68236	−	4.64598i	0.214760	−	0.371976i
$157$	6.13849	+	1.64480i	0.489905	+	0.131270i	0.495311	−	0.868716i	$-0.335054\pi$
$157$	6.13849	+	1.64480i	0.489905	+	0.131270i	−0.00540611	+	0.999985i	$0.501721\pi$
$158$	4.80713	−	1.28807i	0.382435	−	0.102473i
$159$			6.33092i			0.502075i
$160$		0			0
$161$	−7.89653	+	13.6772i	−0.622334	+	1.07791i
$162$	8.02839	−	2.15120i	0.630770	−	0.169014i
$163$	−13.5793	−	13.5793i	−1.06362	−	1.06362i	−0.997834	−	0.0657815i	$-0.979046\pi$
$163$	−13.5793	−	13.5793i	−1.06362	−	1.06362i	−0.0657815	−	0.997834i	$-0.520954\pi$
$164$	5.92084			0.462340
$165$		0			0
$166$	8.94525	−	5.16454i	0.694286	−	0.400846i
$167$	−2.49101	+	0.667465i	−0.192760	+	0.0516500i	−0.353908	−	0.935280i	$-0.615147\pi$
$167$	−2.49101	+	0.667465i	−0.192760	+	0.0516500i	0.161147	+	0.986930i	$0.448481\pi$
$168$	−1.71675	+	6.40699i	−0.132450	+	0.494310i
$169$	2.31149	−	1.33454i	0.177807	−	0.102657i
$170$		0			0
$171$	0.418692	−	0.834413i	0.0320181	−	0.0638092i
$172$	3.93654	−	3.93654i	0.300159	−	0.300159i
$173$	1.95750	+	0.524511i	0.148826	+	0.0398778i	0.332463	−	0.943116i	$-0.392120\pi$
$173$	1.95750	+	0.524511i	0.148826	+	0.0398778i	−0.183637	+	0.982994i	$0.558787\pi$
$174$	3.49571	+	6.05475i	0.265009	+	0.459010i
$175$		0			0
$176$	−2.78944	−	4.83146i	−0.210262	−	0.364185i
$177$	3.24593	+	12.1140i	0.243979	+	0.910542i
$178$	−10.0156	−	10.0156i	−0.750698	−	0.750698i
$179$	−21.3656			−1.59694			−0.798471	−	0.602034i	$-0.794357\pi$
$179$	−21.3656			−1.59694			−0.798471	+	0.602034i	$0.794357\pi$
$180$		0			0
$181$	2.74435	+	1.58445i	0.203986	+	0.117771i	0.598513	−	0.801113i	$-0.295758\pi$
$181$	2.74435	+	1.58445i	0.203986	+	0.117771i	−0.394527	+	0.918884i	$0.629092\pi$
$182$	9.03208	−	9.03208i	0.669502	−	0.669502i
$183$	2.50676	−	2.50676i	0.185305	−	0.185305i
$184$	−1.98702	+	3.44163i	−0.146485	+	0.253720i
$185$		0			0
$186$	0.828500	+	0.478335i	0.0607485	+	0.0350732i
$187$	−22.1643	−	5.93890i	−1.62081	−	0.434295i
$188$	3.15762	−	11.7844i	0.230293	−	0.859466i
$189$	21.3196			1.55077
$190$		0			0
$191$	18.4130			1.33232			0.666158	−	0.745810i	$-0.267938\pi$
$191$	18.4130			1.33232			0.666158	+	0.745810i	$0.267938\pi$
$192$	−0.431989	+	1.61221i	−0.0311762	+	0.116351i
$193$	−8.25393	−	2.21163i	−0.594131	−	0.159197i	−0.0507904	−	0.998709i	$-0.516174\pi$
$193$	−8.25393	−	2.21163i	−0.594131	−	0.159197i	−0.543340	+	0.839512i	$0.682841\pi$
$194$	−2.07375	−	1.19728i	−0.148886	−	0.0859596i
$195$		0			0
$196$	−4.39653	+	7.61502i	−0.314038	+	0.543930i
$197$	6.38603	−	6.38603i	0.454986	−	0.454986i	−0.442019	−	0.897005i	$-0.645738\pi$
$197$	6.38603	−	6.38603i	0.454986	−	0.454986i	0.897005	+	0.442019i	$0.145738\pi$
$198$	−0.844892	+	0.844892i	−0.0600439	+	0.0600439i
$199$	−12.7686	−	7.37195i	−0.905141	−	0.522584i	−0.0262767	−	0.999655i	$-0.508365\pi$
$199$	−12.7686	−	7.37195i	−0.905141	−	0.522584i	−0.878865	+	0.477071i	$0.841698\pi$
$200$		0			0
$201$	19.8341			1.39899
$202$	−0.340442	−	0.340442i	−0.0239534	−	0.0239534i
$203$	4.30842	+	16.0793i	0.302392	+	1.12854i
$204$	3.43249	+	5.94525i	0.240322	+	0.416250i
$205$		0			0
$206$	−7.00724	−	12.1369i	−0.488217	−	0.845617i
$207$	0.822140	+	0.220292i	0.0571427	+	0.0153113i
$208$	2.27276	−	2.27276i	0.157588	−	0.157588i
$209$	−1.42247	−	24.2762i	−0.0983942	−	1.67922i
$210$		0			0
$211$	−17.0878	+	9.86563i	−1.17637	+	0.679178i	−0.955172	−	0.296051i	$-0.904330\pi$
$211$	−17.0878	+	9.86563i	−1.17637	+	0.679178i	−0.221198	+	0.975229i	$0.570997\pi$
$212$	−0.981717	+	3.66382i	−0.0674246	+	0.251632i
$213$	8.49941	−	2.27741i	0.582370	−	0.156046i
$214$	−2.15527	+	1.24435i	−0.147331	+	0.0850619i
$215$		0			0
$216$	5.36471			0.365022
$217$	1.61066	+	1.61066i	0.109339	+	0.109339i
$218$	2.58500	−	0.692648i	0.175078	−	0.0469120i
$219$	−11.3174	+	19.6022i	−0.764756	+	1.32460i
$220$		0			0
$221$		−	13.2200i		−	0.889274i
$222$	−16.5218	+	4.42701i	−1.10887	+	0.297122i
$223$	14.7867	+	3.96208i	0.990190	+	0.265321i	0.717330	−	0.696733i	$-0.245364\pi$
$223$	14.7867	+	3.96208i	0.990190	+	0.265321i	0.272860	+	0.962054i	$0.412030\pi$
$224$	−1.98702	+	3.44163i	−0.132764	+	0.229953i
$225$		0			0
$226$	4.64088	+	8.03824i	0.308707	+	0.534696i
$227$	−14.0408	−	14.0408i	−0.931921	−	0.931921i	0.0659048	−	0.997826i	$-0.479007\pi$
$227$	−14.0408	−	14.0408i	−0.931921	−	0.931921i	−0.997826	+	0.0659048i	$0.979007\pi$
$228$	−4.83471	+	5.43656i	−0.320187	+	0.360045i
$229$		−	15.1988i		−	1.00437i	−0.864762	−	0.502183i	$-0.832531\pi$
$229$		−	15.1988i		−	1.00437i	0.864762	−	0.502183i	$-0.167469\pi$
$230$		0			0
$231$	32.0471	−	18.5024i	2.10854	−	1.21737i
$232$	1.08414	+	4.04606i	0.0711773	+	0.265637i
$233$	−2.07673	+	7.75045i	−0.136051	+	0.507749i	0.863940	+	0.503594i	$0.167989\pi$
$233$	−2.07673	+	7.75045i	−0.136051	+	0.507749i	−0.999991	+	0.00415495i	$0.998677\pi$
$234$	−0.596168	−	0.344198i	−0.0389727	−	0.0225009i
$235$		0			0
$236$			7.51391i			0.489114i
$237$	2.14989	+	8.02349i	0.139650	+	0.521181i
$238$	4.23050	+	15.7884i	0.274223	+	1.02341i
$239$		−	14.6498i		−	0.947614i	−0.880629	−	0.473807i	$-0.842879\pi$
$239$		−	14.6498i		−	0.947614i	0.880629	−	0.473807i	$-0.157121\pi$
$240$		0			0
$241$	12.2118	+	7.05046i	0.786628	+	0.454160i	0.838774	−	0.544479i	$-0.183273\pi$
$241$	12.2118	+	7.05046i	0.786628	+	0.454160i	−0.0521460	+	0.998639i	$0.516606\pi$
$242$	−5.20847	+	19.4383i	−0.334813	+	1.24954i
$243$	−0.574944	−	2.14572i	−0.0368827	−	0.137648i
$244$	1.83942	−	1.06199i	0.117757	−	0.0679870i
$245$		0			0
$246$			9.88236i			0.630076i
$247$	13.2976	−	4.41152i	0.846106	−	0.280698i
$248$	0.405294	+	0.405294i	0.0257362	+	0.0257362i
$249$	8.62003	+	14.9303i	0.546272	+	0.946171i
$250$		0			0
$251$	7.77617	−	13.4687i	0.490827	−	0.850138i	−0.509117	−	0.860697i	$-0.670028\pi$
$251$	7.77617	−	13.4687i	0.490827	−	0.850138i	0.999944	+	0.0105596i	$0.00336127\pi$
$252$	0.822140	+	0.220292i	0.0517899	+	0.0138771i
$253$	21.4153	−	5.73822i	1.34637	−	0.360759i
$254$			12.9807i			0.814481i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.53563	−	1.21532i	0.282925	−	0.0758095i	−0.114566	−	0.993416i	$-0.536548\pi$
$257$	4.53563	−	1.21532i	0.282925	−	0.0758095i	0.397491	+	0.917606i	$0.369881\pi$
$258$	6.57040	+	6.57040i	0.409055	+	0.409055i
$259$	−40.7259			−2.53059
$260$		0			0
$261$	0.776942	−	0.448567i	0.0480915	−	0.0277656i
$262$	−9.40108	+	2.51901i	−0.580801	+	0.155625i
$263$	−5.32590	+	19.8765i	−0.328409	+	1.22564i	0.582431	+	0.812880i	$0.302102\pi$
$263$	−5.32590	+	19.8765i	−0.328409	+	1.22564i	−0.910840	+	0.412759i	$0.864565\pi$
$264$	8.06409	−	4.65580i	0.496310	−	0.286545i
$265$		0			0
$266$	−14.4694	+	9.52393i	−0.887175	+	0.583950i
$267$	16.7168	−	16.7168i	1.02305	−	1.02305i
$268$	11.4783	+	3.07561i	0.701151	+	0.187873i
$269$	4.61436	+	7.99231i	0.281343	+	0.487300i	0.971716	−	0.236154i	$-0.0758869\pi$
$269$	4.61436	+	7.99231i	0.281343	+	0.487300i	−0.690373	+	0.723454i	$0.742554\pi$
$270$		0			0
$271$	−12.5036	−	21.6569i	−0.759541	−	1.31556i	−0.943085	−	0.332552i	$-0.892090\pi$
$271$	−12.5036	−	21.6569i	−0.759541	−	1.31556i	0.183544	−	0.983011i	$-0.441243\pi$
$272$	1.06453	+	3.97289i	0.0645467	+	0.240892i
$273$	15.0753	+	15.0753i	0.912396	+	0.912396i
$274$	−0.787917			−0.0475998
$275$		0			0
$276$	−5.74435	−	3.31650i	−0.345769	−	0.199630i
$277$	11.1332	−	11.1332i	0.668927	−	0.668927i	−0.288541	−	0.957468i	$-0.593170\pi$
$277$	11.1332	−	11.1332i	0.668927	−	0.668927i	0.957468	+	0.288541i	$0.0931700\pi$
$278$	−10.2075	+	10.2075i	−0.612205	+	0.612205i
$279$	0.0613795	−	0.106312i	0.00367470	−	0.00636476i
$280$		0			0
$281$	−16.0185	−	9.24831i	−0.955586	−	0.551708i	−0.0607743	−	0.998152i	$-0.519357\pi$
$281$	−16.0185	−	9.24831i	−0.955586	−	0.551708i	−0.894812	+	0.446444i	$0.852690\pi$
$282$	19.6691	+	5.27032i	1.17128	+	0.313843i
$283$	−3.97901	+	14.8499i	−0.236528	+	0.882733i	0.740927	+	0.671586i	$0.234387\pi$
$283$	−3.97901	+	14.8499i	−0.236528	+	0.882733i	−0.977454	+	0.211147i	$0.932280\pi$
$284$	5.27191			0.312830
$285$		0			0
$286$	−17.9315			−1.06031
$287$	−6.08994	+	22.7280i	−0.359478	+	1.34159i
$288$	0.206877	+	0.0554326i	0.0121904	+	0.00326640i
$289$	−0.0718408	−	0.0414773i	−0.00422593	−	0.00243984i
$290$		0			0
$291$	1.99835	−	3.46125i	0.117146	−	0.202902i
$292$	−9.58922	+	9.58922i	−0.561167	+	0.561167i
$293$	1.79454	−	1.79454i	0.104838	−	0.104838i	−0.652742	−	0.757580i	$-0.726381\pi$
$293$	1.79454	−	1.79454i	0.104838	−	0.104838i	0.757580	+	0.652742i	$0.226381\pi$
$294$	−12.7101	−	7.33816i	−0.741266	−	0.427970i
$295$		0			0
$296$	−10.2480			−0.595651
$297$	−21.1631	−	21.1631i	−1.22801	−	1.22801i
$298$	−3.27713	−	12.2304i	−0.189839	−	0.708488i
$299$	6.38664	+	11.0620i	0.369349	+	0.639731i
$300$		0			0
$301$	11.0620	+	19.1599i	0.637603	+	1.10436i
$302$	−14.2917	−	3.82945i	−0.822394	−	0.220360i
$303$	0.568225	−	0.568225i	0.0326437	−	0.0326437i
$304$	−3.64097	+	2.39653i	−0.208824	+	0.137450i
$305$		0			0
$306$	0.762890	−	0.440454i	0.0436115	−	0.0251791i
$307$	−1.48186	+	5.53039i	−0.0845744	+	0.315636i	−0.995233	−	0.0975232i	$-0.968908\pi$
$307$	−1.48186	+	5.53039i	−0.0845744	+	0.315636i	0.910659	+	0.413159i	$0.135575\pi$
$308$	21.4153	−	5.73822i	1.22025	−	0.326965i
$309$	20.2574	−	11.6956i	1.15240	−	0.665341i
$310$		0			0
$311$	−15.7931			−0.895542			−0.447771	−	0.894148i	$-0.647782\pi$
$311$	−15.7931			−0.895542			−0.447771	+	0.894148i	$0.647782\pi$
$312$	3.79342	+	3.79342i	0.214760	+	0.214760i
$313$	6.27274	−	1.68078i	0.354556	−	0.0950030i	−0.0771446	−	0.997020i	$-0.524580\pi$
$313$	6.27274	−	1.68078i	0.354556	−	0.0950030i	0.431701	+	0.902017i	$0.357914\pi$
$314$	−3.17752	+	5.50362i	−0.179318	+	0.310587i
$315$		0			0
$316$			4.97671i			0.279962i
$317$	−5.96979	+	1.59960i	−0.335297	+	0.0898425i	−0.422539	−	0.906345i	$-0.638861\pi$
$317$	−5.96979	+	1.59960i	−0.335297	+	0.0898425i	0.0872424	+	0.996187i	$0.472195\pi$
$318$	−6.11520	−	1.63856i	−0.342923	−	0.0918860i
$319$	11.6844	−	20.2380i	0.654201	−	1.13311i
$320$		0			0
$321$	−2.07691	−	3.59732i	−0.115922	−	0.200783i
$322$	−11.1674	−	11.1674i	−0.622334	−	0.622334i
$323$	−3.61926	+	17.5592i	−0.201381	+	0.977019i
$324$			8.31160i			0.461756i
$325$		0			0
$326$	16.6312	−	9.60204i	0.921118	−	0.531808i
$327$	1.15608	+	4.31456i	0.0639316	+	0.238596i
$328$	−1.53243	+	5.71910i	−0.0846141	+	0.315784i
$329$	41.9882	+	24.2419i	2.31489	+	1.33650i
$330$		0			0
$331$			29.4402i			1.61818i	0.587686	+	0.809089i	$0.300039\pi$
$331$			29.4402i			1.61818i	−0.587686	+	0.809089i	$0.699961\pi$
$332$	2.67336	+	9.97713i	0.146720	+	0.547566i
$333$	0.568071	+	2.12007i	0.0311301	+	0.116179i
$334$		−	2.57889i		−	0.141110i
$335$		0			0
$336$	−5.74435	−	3.31650i	−0.313380	−	0.180930i
$337$	8.33054	−	31.0900i	0.453793	−	1.69358i	−0.237818	−	0.971310i	$-0.576432\pi$
$337$	8.33054	−	31.0900i	0.453793	−	1.69358i	0.691611	−	0.722270i	$-0.256901\pi$
$338$	0.690809	+	2.57813i	0.0375750	+	0.140232i
$339$	−13.4165	+	7.74599i	−0.728682	+	0.420705i
$340$		0			0
$341$		−	3.19766i		−	0.173163i
$342$	0.697616	+	0.620387i	0.0377227	+	0.0335467i
$343$	−5.03864	−	5.03864i	−0.272061	−	0.272061i
$344$	2.78356	+	4.82126i	0.150079	+	0.259945i
$345$		0			0
$346$	−1.01328	+	1.75505i	−0.0544741	+	0.0943519i
$347$	20.7032	+	5.54741i	1.11141	+	0.297801i	0.767401	−	0.641167i	$-0.221549\pi$
$347$	20.7032	+	5.54741i	1.11141	+	0.297801i	0.344005	+	0.938968i	$0.388216\pi$
$348$	−6.75320	+	1.80951i	−0.362010	+	0.0970002i
$349$		−	18.2359i		−	0.976145i	−0.872803	−	0.488072i	$-0.837700\pi$
$349$		−	18.2359i		−	0.976145i	0.872803	−	0.488072i	$-0.162300\pi$
$350$		0			0
$351$	8.62156	−	14.9330i	0.460185	−	0.797064i
$352$	5.38879	−	1.44392i	0.287224	−	0.0769613i
$353$	−14.6042	−	14.6042i	−0.777303	−	0.777303i	0.202068	−	0.979371i	$-0.435234\pi$
$353$	−14.6042	−	14.6042i	−0.777303	−	0.777303i	−0.979371	+	0.202068i	$0.935234\pi$
$354$	−12.5413			−0.666563
$355$		0			0
$356$	12.2665	−	7.08207i	0.650124	−	0.375349i
$357$	−26.3522	+	7.06104i	−1.39470	+	0.373710i
$358$	5.52983	−	20.6376i	0.292261	−	1.09073i
$359$	−12.8174	+	7.40015i	−0.676478	+	0.390565i	−0.798527	−	0.601959i	$-0.794387\pi$
$359$	−12.8174	+	7.40015i	−0.676478	+	0.390565i	0.122049	+	0.992524i	$0.461054\pi$
$360$		0			0
$361$	−18.8700	+	2.21900i	−0.993157	+	0.116790i
$362$	−2.24075	+	2.24075i	−0.117771	+	0.117771i
$363$	−32.4440	−	8.69335i	−1.70287	−	0.456282i
$364$	6.38664	+	11.0620i	0.334751	+	0.579806i
$365$		0			0
$366$	1.77255	+	3.07014i	0.0926526	+	0.160479i
$367$	−5.71739	−	21.3376i	−0.298446	−	1.11381i	−0.938442	−	0.345436i	$-0.887731\pi$
$367$	−5.71739	−	21.3376i	−0.298446	−	1.11381i	0.639997	−	0.768378i	$-0.278936\pi$
$368$	−2.81008	−	2.81008i	−0.146485	−	0.146485i
$369$	1.26810			0.0660145
$370$		0			0
$371$	−13.0543	−	7.53691i	−0.677746	−	0.391297i
$372$	−0.676467	+	0.676467i	−0.0350732	+	0.0350732i
$373$	3.26677	−	3.26677i	0.169147	−	0.169147i	−0.617457	−	0.786604i	$-0.711837\pi$
$373$	3.26677	−	3.26677i	0.169147	−	0.169147i	0.786604	+	0.617457i	$0.211837\pi$
$374$	11.4731	−	19.8719i	0.593259	−	1.02755i
$375$		0			0
$376$	10.5656	+	6.10006i	0.544880	+	0.314586i
$377$	13.0048	+	3.48461i	0.669779	+	0.179467i
$378$	−5.51793	+	20.5932i	−0.283811	+	1.05920i
$379$	−24.1730			−1.24168			−0.620841	−	0.783937i	$-0.713209\pi$
$379$	−24.1730			−1.24168			−0.620841	+	0.783937i	$0.713209\pi$
$380$		0			0
$381$	−21.6658			−1.10997
$382$	−4.76563	+	17.7856i	−0.243831	+	0.909989i
$383$	−25.3932	−	6.80409i	−1.29753	−	0.347673i	−0.457016	−	0.889458i	$-0.651082\pi$
$383$	−25.3932	−	6.80409i	−1.29753	−	0.347673i	−0.840517	+	0.541786i	$0.817748\pi$
$384$	−1.44546	−	0.834540i	−0.0737636	−	0.0425874i
$385$		0			0
$386$	4.27255	−	7.40027i	0.217467	−	0.376664i
$387$	0.843109	−	0.843109i	0.0428577	−	0.0428577i
$388$	1.69321	−	1.69321i	0.0859596	−	0.0859596i
$389$	28.8228	+	16.6409i	1.46138	+	0.843726i	0.999075	−	0.0429969i	$-0.0136906\pi$
$389$	28.8228	+	16.6409i	1.46138	+	0.843726i	0.462301	+	0.886723i	$0.347024\pi$
$390$		0			0
$391$	−16.3454			−0.826622
$392$	−6.21763	−	6.21763i	−0.314038	−	0.314038i
$393$	−4.20443	−	15.6912i	−0.212085	−	0.791514i
$394$	4.51561	+	7.82126i	0.227493	+	0.394030i
$395$		0			0
$396$	−0.597429	−	1.03478i	−0.0300219	−	0.0519995i
$397$	−18.3211	−	4.90913i	−0.919510	−	0.246382i	−0.232134	−	0.972684i	$-0.574571\pi$
$397$	−18.3211	−	4.90913i	−0.919510	−	0.246382i	−0.687376	+	0.726302i	$0.741237\pi$
$398$	10.4255	−	10.4255i	0.522584	−	0.522584i
$399$	−15.8962	−	24.1505i	−0.795805	−	1.20904i
$400$		0			0
$401$	25.4303	−	14.6822i	1.26993	−	0.733194i	0.294955	−	0.955511i	$-0.404695\pi$
$401$	25.4303	−	14.6822i	1.26993	−	0.733194i	0.974974	+	0.222317i	$0.0713619\pi$
$402$	−5.13344	+	19.1583i	−0.256033	+	0.955527i
$403$	1.77950	−	0.476816i	0.0886432	−	0.0237519i
$404$	0.416955	−	0.240729i	0.0207443	−	0.0119767i
$405$		0			0
$406$	−16.6465			−0.826150
$407$	40.4269	+	40.4269i	2.00389	+	2.00389i
$408$	−6.63106	+	1.77679i	−0.328286	+	0.0879641i
$409$	1.12100	−	1.94163i	0.0554298	−	0.0960073i	−0.836979	−	0.547235i	$-0.815680\pi$
$409$	1.12100	−	1.94163i	0.0554298	−	0.0960073i	0.892409	+	0.451228i	$0.149014\pi$
$410$		0			0
$411$		−	1.31510i		−	0.0648689i
$412$	13.5369	−	3.62721i	0.666917	−	0.178700i
$413$	−28.8432	−	7.72850i	−1.41928	−	0.380295i
$414$	−0.425571	+	0.737110i	−0.0209157	+	0.0362270i
$415$		0			0
$416$	1.60709	+	2.78356i	0.0787939	+	0.136475i
$417$	−17.0371	−	17.0371i	−0.834312	−	0.834312i
$418$	23.8171	+	4.90914i	1.16493	+	0.240114i
$419$		−	39.9653i		−	1.95243i	−0.216797	−	0.976217i	$-0.569561\pi$
$419$		−	39.9653i		−	1.95243i	0.216797	−	0.976217i	$-0.430439\pi$
$420$		0			0
$421$	−14.8606	+	8.57980i	−0.724264	+	0.418154i	−0.816320	−	0.577600i	$-0.803989\pi$
$421$	−14.8606	+	8.57980i	−0.724264	+	0.418154i	0.0920564	+	0.995754i	$0.470656\pi$
$422$	−5.10683	−	19.0589i	−0.248596	−	0.927774i
$423$	0.676284	−	2.52393i	0.0328820	−	0.122717i
$424$	−3.28489	−	1.89653i	−0.159528	−	0.0921037i
$425$		0			0
$426$			8.79924i			0.426325i
$427$	2.18464	+	8.15320i	0.105722	+	0.394561i
$428$	−0.644122	−	2.40390i	−0.0311348	−	0.116197i
$429$		−	29.9291i		−	1.44499i
$430$		0			0
$431$	17.9452	+	10.3607i	0.864392	+	0.499057i	0.865481	−	0.500942i	$-0.167013\pi$
$431$	17.9452	+	10.3607i	0.864392	+	0.499057i	−0.00108855	+	0.999999i	$0.500346\pi$
$432$	−1.38849	+	5.18191i	−0.0668037	+	0.249315i
$433$	−9.70841	−	36.2323i	−0.466556	−	1.74121i	−0.651678	−	0.758496i	$-0.725934\pi$
$433$	−9.70841	−	36.2323i	−0.466556	−	1.74121i	0.185121	−	0.982716i	$-0.440732\pi$
$434$	−1.97264	+	1.13891i	−0.0946899	+	0.0546693i
$435$		0			0
$436$			2.67618i			0.128166i
$437$	−5.45446	−	16.4413i	−0.260922	−	0.786495i
$438$	−16.0052	−	16.0052i	−0.764756	−	0.764756i
$439$	8.85200	+	15.3321i	0.422483	+	0.731762i	0.996182	−	0.0873044i	$-0.0278253\pi$
$439$	8.85200	+	15.3321i	0.422483	+	0.731762i	−0.573699	+	0.819066i	$0.694492\pi$
$440$		0			0
$441$	−0.941627	+	1.63095i	−0.0448394	+	0.0776641i
$442$	12.7695	+	3.42159i	0.607385	+	0.162748i
$443$	−5.92652	+	1.58801i	−0.281578	+	0.0754485i	−0.396844	−	0.917886i	$-0.629895\pi$
$443$	−5.92652	+	1.58801i	−0.281578	+	0.0754485i	0.115266	+	0.993335i	$0.463228\pi$
$444$		−	17.1047i		−	0.811752i
$445$		0			0
$446$	−7.65416	+	13.2574i	−0.362435	+	0.627755i
$447$	20.4135	−	5.46978i	0.965526	−	0.258712i
$448$	−2.81008	−	2.81008i	−0.132764	−	0.132764i
$449$	−10.8678			−0.512883			−0.256441	−	0.966560i	$-0.582550\pi$
$449$	−10.8678			−0.512883			−0.256441	+	0.966560i	$0.582550\pi$
$450$		0			0
$451$	28.6063	−	16.5159i	1.34702	−	0.777702i
$452$	−8.96549	+	2.40230i	−0.421701	+	0.112994i
$453$	6.39165	−	23.8540i	0.300306	−	1.12076i
$454$	17.1964	−	9.92835i	0.807067	−	0.465961i
$455$		0			0
$456$	−4.00000	−	6.07706i	−0.187317	−	0.284584i
$457$	7.87309	−	7.87309i	0.368288	−	0.368288i	−0.498565	−	0.866852i	$-0.666139\pi$
$457$	7.87309	−	7.87309i	0.368288	−	0.368288i	0.866852	+	0.498565i	$0.166139\pi$
$458$	14.6809	+	3.93374i	0.685994	+	0.183812i
$459$	11.0326	+	19.1091i	0.514959	+	0.891935i
$460$		0			0
$461$	17.3941	+	30.1275i	0.810124	+	1.40318i	0.912776	+	0.408459i	$0.133934\pi$
$461$	17.3941	+	30.1275i	0.810124	+	1.40318i	−0.102652	+	0.994717i	$0.532733\pi$
$462$	9.57754	+	35.7439i	0.445587	+	1.66295i
$463$	−13.5882	−	13.5882i	−0.631497	−	0.631497i	0.316946	−	0.948443i	$-0.397342\pi$
$463$	−13.5882	−	13.5882i	−0.631497	−	0.631497i	−0.948443	+	0.316946i	$0.897342\pi$
$464$	−4.18879			−0.194460
$465$		0			0
$466$	−6.94886	−	4.01193i	−0.321900	−	0.185849i
$467$	24.3519	−	24.3519i	1.12687	−	1.12687i	0.136189	−	0.990683i	$-0.456514\pi$
$467$	24.3519	−	24.3519i	1.12687	−	1.12687i	0.990683	−	0.136189i	$-0.0434856\pi$
$468$	0.486769	−	0.486769i	0.0225009	−	0.0225009i
$469$	−23.6123	+	40.8977i	−1.09032	+	1.88848i
$470$		0			0
$471$	−9.18597	−	5.30353i	−0.423267	−	0.244374i
$472$	−7.25788	−	1.94474i	−0.334071	−	0.0895141i
$473$	8.03848	−	30.0000i	0.369610	−	1.37940i
$474$	−8.30652			−0.381531
$475$		0			0
$476$	−16.3454			−0.749190
$477$	−0.210259	+	0.784698i	−0.00962711	+	0.0359289i
$478$	14.1506	+	3.79164i	0.647233	+	0.173425i
$479$	29.0760	+	16.7870i	1.32852	+	0.767019i	0.985070	−	0.172154i	$-0.0550727\pi$
$479$	29.0760	+	16.7870i	1.32852	+	0.767019i	0.343445	+	0.939173i	$0.388406\pi$
$480$		0			0
$481$	−16.4694	+	28.5258i	−0.750939	+	1.30066i
$482$	−9.97086	+	9.97086i	−0.454160	+	0.454160i
$483$	18.6392	−	18.6392i	0.848115	−	0.848115i
$484$	−17.4279	−	10.0620i	−0.792176	−	0.457363i
$485$		0			0
$486$	2.22141			0.100765
$487$	−23.7780	−	23.7780i	−1.07748	−	1.07748i	−0.996734	−	0.0807490i	$-0.974269\pi$
$487$	−23.7780	−	23.7780i	−1.07748	−	1.07748i	−0.0807490	−	0.996734i	$-0.525731\pi$
$488$	0.549727	+	2.05161i	0.0248850	+	0.0928720i
$489$	16.0266	+	27.7588i	0.724746	+	1.25530i
$490$		0			0
$491$	−0.0205143	−	0.0355318i	−0.000925798	−	0.00160353i	0.865562	−	0.500802i	$-0.166961\pi$
$491$	−0.0205143	−	0.0355318i	−0.000925798	−	0.00160353i	−0.866488	+	0.499198i	$0.833628\pi$
$492$	−9.54562	−	2.55774i	−0.430350	−	0.115312i
$493$	−12.1825	+	12.1825i	−0.548672	+	0.548672i
$494$	0.819529	+	13.9863i	0.0368724	+	0.629272i
$495$		0			0
$496$	−0.496381	+	0.286586i	−0.0222882	+	0.0128681i
$497$	−5.42248	+	20.2370i	−0.243231	+	0.907751i
$498$	−16.6526	+	4.46205i	−0.746221	+	0.199949i
$499$	−17.8866	+	10.3269i	−0.800716	+	0.462293i	−0.843721	−	0.536781i	$-0.819640\pi$
$499$	−17.8866	+	10.3269i	−0.800716	+	0.462293i	0.0430056	+	0.999075i	$0.486307\pi$
$500$		0			0
$501$	4.30437			0.192305
$502$	10.9972	+	10.9972i	0.490827	+	0.490827i
$503$	−12.0196	+	3.22065i	−0.535928	+	0.143602i	−0.516624	−	0.856212i	$-0.672812\pi$
$503$	−12.0196	+	3.22065i	−0.535928	+	0.143602i	−0.0193038	+	0.999814i	$0.506145\pi$
$504$	−0.425571	+	0.737110i	−0.0189564	+	0.0328335i
$505$		0			0
$506$			22.1708i			0.985611i
$507$	−4.30311	+	1.15301i	−0.191108	+	0.0512072i
$508$	−12.5384	−	3.35965i	−0.556301	−	0.149060i
$509$	−8.59703	+	14.8905i	−0.381057	+	0.660009i	−0.991214	−	0.132271i	$-0.957773\pi$
$509$	−8.59703	+	14.8905i	−0.381057	+	0.660009i	0.610157	+	0.792281i	$0.291106\pi$
$510$		0			0
$511$	−26.9464	−	46.6726i	−1.19204	−	2.06467i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−15.5396	+	17.4741i	−0.686091	+	0.771499i
$514$			4.69563i			0.207116i
$515$		0			0
$516$	−8.04707	+	4.64598i	−0.354252	+	0.204528i
$517$	−17.6160	−	65.7439i	−0.774752	−	2.89141i
$518$	10.5406	−	39.3382i	0.463129	−	1.72842i
$519$	−2.92931	−	1.69124i	−0.128583	−	0.0742372i
$520$		0			0
$521$		−	7.98939i		−	0.350022i	−0.984567	−	0.175011i	$-0.944004\pi$
$521$		−	7.98939i		−	0.350022i	0.984567	−	0.175011i	$-0.0559961\pi$
$522$	0.232196	+	0.866566i	0.0101629	+	0.0379286i
$523$	−3.94272	−	14.7144i	−0.172403	−	0.643417i	−0.996979	−	0.0776662i	$-0.975253\pi$
$523$	−3.94272	−	14.7144i	−0.172403	−	0.643417i	0.824576	−	0.565751i	$-0.191414\pi$
$524$		−	9.73272i		−	0.425176i
$525$		0			0
$526$	−17.8208	−	10.2889i	−0.777024	−	0.448615i
$527$	−0.610159	+	2.27715i	−0.0265790	+	0.0991940i
$528$	2.41002	+	8.99432i	0.104883	+	0.391427i
$529$	−6.24139	+	3.60347i	−0.271365	+	0.156673i
$530$		0			0
$531$			1.60929i			0.0698373i
$532$	−5.45446	−	16.4413i	−0.236481	−	0.712822i
$533$	13.4567	+	13.4567i	0.582874	+	0.582874i
$534$	11.8205	+	20.4738i	0.511525	+	0.885987i
$535$		0			0
$536$	−5.94163	+	10.2912i	−0.256639	+	0.444512i
$537$	34.4458	+	9.22972i	1.48645	+	0.398292i
$538$	−8.91427	+	2.38857i	−0.384321	+	0.102979i
$539$			49.0555i			2.11297i
$540$		0			0
$541$	2.38687	−	4.13418i	0.102620	−	0.177742i	−0.810144	−	0.586232i	$-0.800611\pi$
$541$	2.38687	−	4.13418i	0.102620	−	0.177742i	0.912763	+	0.408489i	$0.133944\pi$
$542$	24.1551	−	6.47235i	1.03755	−	0.278011i
$543$	−3.73999	−	3.73999i	−0.160498	−	0.160498i
$544$	−4.11303			−0.176345
$545$		0			0
$546$	−18.4633	+	10.6598i	−0.790158	+	0.456198i
$547$	4.22997	−	1.13342i	0.180860	−	0.0484614i	−0.167252	−	0.985914i	$-0.553489\pi$
$547$	4.22997	−	1.13342i	0.180860	−	0.0484614i	0.348113	+	0.937453i	$0.386823\pi$
$548$	0.203928	−	0.761069i	0.00871137	−	0.0325113i
$549$	0.393958	−	0.227452i	0.0168137	−	0.00970742i
$550$		0			0
$551$	−16.3193	−	8.18869i	−0.695225	−	0.348850i
$552$	4.69024	−	4.69024i	0.199630	−	0.199630i
$553$	−19.1038	−	5.11884i	−0.812375	−	0.217675i
$554$	7.87234	+	13.6353i	0.334464	+	0.579308i
$555$		0			0
$556$	−7.21779	−	12.5016i	−0.306103	−	0.530185i
$557$	9.53737	+	35.5939i	0.404111	+	1.50816i	0.805689	+	0.592339i	$0.201795\pi$
$557$	9.53737	+	35.5939i	0.404111	+	1.50816i	−0.401578	+	0.915825i	$0.631538\pi$
$558$	0.0868038	+	0.0868038i	0.00367470	+	0.00367470i
$559$	17.8937			0.756822
$560$		0			0
$561$	33.1679	+	19.1495i	1.40035	+	0.808491i
$562$	13.0791	−	13.0791i	0.551708	−	0.551708i
$563$	16.9569	−	16.9569i	0.714648	−	0.714648i	−0.252856	−	0.967504i	$-0.581370\pi$
$563$	16.9569	−	16.9569i	0.714648	−	0.714648i	0.967504	+	0.252856i	$0.0813698\pi$
$564$	−10.1815	+	17.6348i	−0.428718	+	0.742561i
$565$		0			0
$566$	−13.3140	−	7.68686i	−0.559630	−	0.323103i
$567$	−31.9052	−	8.54898i	−1.33989	−	0.359023i
$568$	−1.36447	+	5.09228i	−0.0572519	+	0.213667i
$569$	−20.7088			−0.868160			−0.434080	−	0.900874i	$-0.642927\pi$
$569$	−20.7088			−0.868160			−0.434080	+	0.900874i	$0.642927\pi$
$570$		0			0
$571$	44.7544			1.87291			0.936457	−	0.350782i	$-0.114084\pi$
$571$	44.7544			1.87291			0.936457	+	0.350782i	$0.114084\pi$
$572$	4.64102	−	17.3205i	0.194051	−	0.724207i
$573$	−29.6855	−	7.95421i	−1.24013	−	0.332292i
$574$	−20.3773	−	11.7649i	−0.850534	−	0.491056i
$575$		0			0
$576$	−0.107087	+	0.185481i	−0.00446198	+	0.00772837i
$577$	−0.691973	+	0.691973i	−0.0288072	+	0.0288072i	−0.721364	−	0.692556i	$-0.756484\pi$
$577$	−0.691973	+	0.691973i	−0.0288072	+	0.0288072i	0.692556	+	0.721364i	$0.256484\pi$
$578$	0.0586577	−	0.0586577i	0.00243984	−	0.00243984i
$579$	12.3516	+	7.13122i	0.513316	+	0.296363i
$580$		0			0
$581$	−41.0483			−1.70297
$582$	2.82610	+	2.82610i	0.117146	+	0.117146i
$583$	5.47689	+	20.4400i	0.226829	+	0.846539i
$584$	−6.78060	−	11.7443i	−0.280583	−	0.485985i
$585$		0			0
$586$	1.26893	+	2.19785i	0.0524190	+	0.0907923i
$587$	−15.1350	−	4.05541i	−0.624689	−	0.167385i	−0.0674303	−	0.997724i	$-0.521480\pi$
$587$	−15.1350	−	4.05541i	−0.624689	−	0.167385i	−0.557258	+	0.830339i	$0.688147\pi$
$588$	10.3777	−	10.3777i	0.427970	−	0.427970i
$589$	−2.49412	+	0.146144i	−0.102768	+	0.00602174i
$590$		0			0
$591$	−13.0543	+	7.53691i	−0.536982	+	0.310027i
$592$	2.65237	−	9.89878i	0.109012	−	0.406837i
$593$	−15.0573	+	4.03459i	−0.618329	+	0.165681i	−0.554368	−	0.832272i	$-0.687040\pi$
$593$	−15.0573	+	4.03459i	−0.618329	+	0.165681i	−0.0639609	+	0.997952i	$0.520373\pi$
$594$	25.9194	−	14.9646i	1.06349	−	0.614003i
$595$		0			0
$596$	12.6618			0.518649
$597$	17.4010	+	17.4010i	0.712176	+	0.712176i
$598$	−12.3380	+	3.30597i	−0.504540	+	0.135191i
$599$	13.8776	−	24.0366i	0.567022	−	0.982110i	−0.429837	−	0.902907i	$-0.641429\pi$
$599$	13.8776	−	24.0366i	0.567022	−	0.982110i	0.996858	−	0.0792037i	$-0.0252378\pi$
$600$		0			0
$601$			5.35237i			0.218328i	0.994024	+	0.109164i	$0.0348173\pi$
$601$			5.35237i			0.218328i	−0.994024	+	0.109164i	$0.965183\pi$
$602$	−21.3701	+	5.72611i	−0.870981	+	0.233379i
$603$	2.45837	+	0.658719i	0.100113	+	0.0268251i
$604$	7.39792	−	12.8136i	0.301017	−	0.521377i
$605$		0			0
$606$	0.401796	+	0.695931i	0.0163218	+	0.0282703i
$607$	18.0625	+	18.0625i	0.733133	+	0.733133i	0.971239	−	0.238106i	$-0.0765265\pi$
$607$	18.0625	+	18.0625i	0.733133	+	0.733133i	−0.238106	+	0.971239i	$0.576527\pi$
$608$	−1.37252	−	4.13717i	−0.0556630	−	0.167784i
$609$		−	27.7843i		−	1.12588i
$610$		0			0
$611$	33.9597	−	19.6067i	1.37386	−	0.793200i
$612$	0.227996	+	0.850893i	0.00921619	+	0.0343953i
$613$	−3.50245	+	13.0713i	−0.141463	+	0.527946i	0.858425	+	0.512940i	$0.171444\pi$
$613$	−3.50245	+	13.0713i	−0.141463	+	0.527946i	−0.999887	+	0.0150066i	$0.995223\pi$
$614$	−4.95841	−	2.86274i	−0.200105	−	0.115531i
$615$		0			0
$616$			22.1708i			0.893286i
$617$	−2.12136	−	7.91702i	−0.0854027	−	0.318727i	0.909987	−	0.414636i	$-0.136091\pi$
$617$	−2.12136	−	7.91702i	−0.0854027	−	0.318727i	−0.995390	+	0.0959086i	$0.969424\pi$
$618$	6.05411	+	22.5942i	0.243532	+	0.908873i
$619$		−	25.0072i		−	1.00513i	−0.864541	−	0.502563i	$-0.832391\pi$
$619$		−	25.0072i		−	1.00513i	0.864541	−	0.502563i	$-0.167609\pi$
$620$		0			0
$621$	−18.4633	−	10.6598i	−0.740908	−	0.427764i
$622$	4.08755	−	15.2549i	0.163896	−	0.611667i
$623$	14.5687	+	54.3710i	0.583681	+	2.17833i
$624$	−4.64598	+	2.68236i	−0.185988	+	0.107380i
$625$		0			0
$626$			6.49402i			0.259553i
$627$	−8.19374	+	39.7527i	−0.327226	+	1.58757i
$628$	−4.49369	−	4.49369i	−0.179318	−	0.179318i
$629$	−21.0751	−	36.5032i	−0.840320	−	1.45548i
$630$		0			0
$631$	−14.1667	+	24.5374i	−0.563966	+	0.976817i	0.433179	+	0.901308i	$0.357392\pi$
$631$	−14.1667	+	24.5374i	−0.563966	+	0.976817i	−0.997145	+	0.0755096i	$0.975942\pi$
$632$	−4.80713	−	1.28807i	−0.191218	−	0.0512366i
$633$	31.8109	−	8.52370i	1.26437	−	0.338786i
$634$		−	6.18038i		−	0.245454i
$635$		0			0
$636$	3.16546	−	5.48274i	0.125519	−	0.217405i
$637$	−27.2994	+	7.31486i	−1.08164	+	0.289825i
$638$	16.5242	+	16.5242i	0.654201	+	0.654201i
$639$	1.12911			0.0446670
$640$		0			0
$641$	20.4996	−	11.8354i	0.809684	−	0.467471i	−0.0371624	−	0.999309i	$-0.511832\pi$
$641$	20.4996	−	11.8354i	0.809684	−	0.467471i	0.846846	+	0.531838i	$0.178499\pi$
$642$	4.01229	−	1.07509i	0.158353	−	0.0424304i
$643$	−2.66769	+	9.95594i	−0.105203	+	0.392624i	−0.998368	−	0.0571053i	$-0.981813\pi$
$643$	−2.66769	+	9.95594i	−0.105203	+	0.392624i	0.893165	+	0.449729i	$0.148480\pi$
$644$	13.6772	−	7.89653i	0.538957	−	0.311167i
$645$		0			0
$646$	−16.0241	−	8.04059i	−0.630461	−	0.316353i
$647$	−5.01831	+	5.01831i	−0.197290	+	0.197290i	−0.798837	−	0.601547i	$-0.794551\pi$
$647$	−5.01831	+	5.01831i	−0.197290	+	0.197290i	0.601547	+	0.798837i	$0.294551\pi$
$648$	−8.02839	−	2.15120i	−0.315385	−	0.0845072i
$649$	20.9596	+	36.3031i	0.822737	+	1.42502i
$650$		0			0
$651$	−1.90092	−	3.29250i	−0.0745031	−	0.129043i
$652$	4.97038	+	18.5497i	0.194655	+	0.726463i
$653$	12.6324	+	12.6324i	0.494344	+	0.494344i	0.909672	−	0.415328i	$-0.136333\pi$
$653$	12.6324	+	12.6324i	0.494344	+	0.494344i	−0.415328	+	0.909672i	$0.636333\pi$
$654$	−4.46676			−0.174664
$655$		0			0
$656$	−5.12760	−	2.96042i	−0.200199	−	0.115585i
$657$	−2.05377	+	2.05377i	−0.0801252	+	0.0801252i
$658$	−34.2833	+	34.2833i	−1.33650	+	1.33650i
$659$	−4.34736	+	7.52985i	−0.169349	+	0.293321i	−0.938191	−	0.346117i	$-0.887500\pi$
$659$	−4.34736	+	7.52985i	−0.169349	+	0.293321i	0.768842	+	0.639439i	$0.220833\pi$
$660$		0			0
$661$	−31.8131	−	18.3673i	−1.23739	−	0.714406i	−0.268828	−	0.963188i	$-0.586636\pi$
$661$	−31.8131	−	18.3673i	−1.23739	−	0.714406i	−0.968559	+	0.248782i	$0.919970\pi$
$662$	−28.4370	−	7.61968i	−1.10524	−	0.296147i
$663$	−5.71090	+	21.3134i	−0.221793	+	0.827743i
$664$	−10.3291			−0.400846
$665$		0			0
$666$	−2.19486			−0.0850490
$667$	4.30842	−	16.0793i	0.166823	−	0.622591i
$668$	2.49101	+	0.667465i	0.0963802	+	0.0258250i
$669$	−22.1276	−	12.7754i	−0.855503	−	0.493925i
$670$		0			0
$671$	5.92473	−	10.2619i	0.228722	−	0.396158i
$672$	4.69024	−	4.69024i	0.180930	−	0.180930i
$673$	−2.45665	+	2.45665i	−0.0946967	+	0.0946967i	−0.752868	−	0.658171i	$-0.771330\pi$
$673$	−2.45665	+	2.45665i	−0.0946967	+	0.0946967i	0.658171	+	0.752868i	$0.271330\pi$
$674$	27.8745	+	16.0934i	1.07369	+	0.619893i
$675$		0			0
$676$	−2.66908			−0.102657
$677$	−17.3822	−	17.3822i	−0.668053	−	0.668053i	0.289212	−	0.957265i	$-0.406607\pi$
$677$	−17.3822	−	17.3822i	−0.668053	−	0.668053i	−0.957265	+	0.289212i	$0.906607\pi$
$678$	−4.00962	−	14.9641i	−0.153989	−	0.574693i
$679$	4.75805	+	8.24118i	0.182597	+	0.316267i
$680$		0			0
$681$	16.5712	+	28.7022i	0.635010	+	1.09987i
$682$	3.08870	+	0.827616i	0.118273	+	0.0316910i
$683$	24.5836	−	24.5836i	0.940667	−	0.940667i	−0.0576691	−	0.998336i	$-0.518367\pi$
$683$	24.5836	−	24.5836i	0.940667	−	0.940667i	0.998336	+	0.0576691i	$0.0183669\pi$
$684$	−0.779804	+	0.513277i	−0.0298166	+	0.0196256i
$685$		0			0
$686$	6.17105	−	3.56286i	0.235612	−	0.136031i
$687$	−6.56572	+	24.5036i	−0.250498	+	0.934871i
$688$	−5.37742	+	1.44088i	−0.205012	+	0.0549329i
$689$	−10.5582	+	6.09578i	−0.402236	+	0.232231i
$690$		0			0
$691$	15.0377			0.572062			0.286031	−	0.958220i	$-0.407664\pi$
$691$	15.0377			0.572062			0.286031	+	0.958220i	$0.407664\pi$
$692$	−1.43299	−	1.43299i	−0.0544741	−	0.0544741i
$693$	4.58663	−	1.22898i	0.174232	−	0.0466852i
$694$	−10.7168	+	18.5620i	−0.406803	+	0.704604i
$695$		0			0
$696$		−	6.99143i		−	0.265009i
$697$	−23.5228	+	6.30293i	−0.890991	+	0.238740i
$698$	17.6145	+	4.71979i	0.666719	+	0.178647i
$699$	6.69623	−	11.5982i	0.253275	−	0.438684i
$700$		0			0
$701$	−25.5314	−	44.2216i	−0.964307	−	1.67023i	−0.711467	−	0.702720i	$-0.751969\pi$
$701$	−25.5314	−	44.2216i	−0.964307	−	1.67023i	−0.252840	−	0.967508i	$-0.581365\pi$
$702$	12.1927	+	12.1927i	0.460185	+	0.460185i
$703$	29.6846	−	33.3799i	1.11958	−	1.25895i
$704$			5.57889i			0.210262i
$705$		0			0
$706$	17.8864	−	10.3267i	0.673164	−	0.388652i
$707$	0.495208	+	1.84814i	0.0186242	+	0.0695066i
$708$	3.24593	−	12.1140i	0.121990	−	0.455271i
$709$	21.2658	+	12.2778i	0.798654	+	0.461103i	0.843000	−	0.537913i	$-0.180787\pi$
$709$	21.2658	+	12.2778i	0.798654	+	0.461103i	−0.0443465	+	0.999016i	$0.514121\pi$
$710$		0			0
$711$			1.06589i			0.0399739i
$712$	3.66595	+	13.6815i	0.137387	+	0.512736i
$713$	−0.589541	−	2.20020i	−0.0220785	−	0.0823981i
$714$		−	27.2818i		−	1.02099i
$715$		0			0
$716$	18.5032	+	10.6828i	0.691496	+	0.399235i
$717$	−6.32854	+	23.6184i	−0.236344	+	0.882047i
$718$	−3.83060	−	14.2960i	−0.142957	−	0.533522i
$719$	−20.5077	+	11.8401i	−0.764808	+	0.441562i	−0.831020	−	0.556243i	$-0.812242\pi$
$719$	−20.5077	+	11.8401i	−0.764808	+	0.441562i	0.0662111	+	0.997806i	$0.478909\pi$
$720$		0			0
$721$			55.6942i			2.07416i
$722$	2.74052	−	18.8013i	0.101992	−	0.699713i
$723$	−16.6421	−	16.6421i	−0.618928	−	0.618928i
$724$	−1.58445	−	2.74435i	−0.0588856	−	0.101993i
$725$		0			0
$726$	16.7943	−	29.0885i	0.623293	−	1.07958i
$727$	−1.17593	−	0.315088i	−0.0436127	−	0.0116860i	0.236947	−	0.971523i	$-0.423853\pi$
$727$	−1.17593	−	0.315088i	−0.0436127	−	0.0116860i	−0.280559	+	0.959837i	$0.590520\pi$
$728$	−12.3380	+	3.30597i	−0.457278	+	0.122527i
$729$			28.6425i			1.06083i
$730$		0			0
$731$	−11.4489	+	19.8300i	−0.423452	+	0.733440i
$732$	−3.42430	+	0.917538i	−0.126566	+	0.0339132i
$733$	28.3801	+	28.3801i	1.04824	+	1.04824i	0.998776	+	0.0494669i	$0.0157522\pi$
$733$	28.3801	+	28.3801i	1.04824	+	1.04824i	0.0494669	+	0.998776i	$0.484248\pi$
$734$	22.0903			0.815368
$735$		0			0
$736$	3.44163	−	1.98702i	0.126860	−	0.0732427i
$737$	64.0364	−	17.1585i	2.35881	−	0.632041i
$738$	−0.328208	+	1.22489i	−0.0120815	+	0.0450887i
$739$	27.8620	−	16.0861i	1.02492	−	0.591738i	0.109395	−	0.993998i	$-0.465109\pi$
$739$	27.8620	−	16.0861i	1.02492	−	0.591738i	0.915525	+	0.402261i	$0.131775\pi$
$740$		0			0
$741$	−23.3442	+	1.36786i	−0.857571	+	0.0502496i
$742$	10.6588	−	10.6588i	0.391297	−	0.391297i
$743$	−2.13174	−	0.571198i	−0.0782059	−	0.0209552i	0.219504	−	0.975612i	$-0.429556\pi$
$743$	−2.13174	−	0.571198i	−0.0782059	−	0.0209552i	−0.297710	+	0.954656i	$0.596223\pi$
$744$	−0.478335	−	0.828500i	−0.0175366	−	0.0303743i
$745$		0			0
$746$	2.30996	+	4.00096i	0.0845736	+	0.146486i
$747$	0.572567	+	2.13685i	0.0209491	+	0.0781833i
$748$	16.2254	+	16.2254i	0.593259	+	0.593259i
$749$	9.89020			0.361380
$750$		0			0
$751$	−29.4090	−	16.9793i	−1.07315	−	0.619584i	−0.144110	−	0.989562i	$-0.546032\pi$
$751$	−29.4090	−	16.9793i	−1.07315	−	0.619584i	−0.929041	+	0.369978i	$0.879365\pi$
$752$	−8.62678	+	8.62678i	−0.314586	+	0.314586i
$753$	−18.3551	+	18.3551i	−0.668898	+	0.668898i
$754$	−6.73176	+	11.6597i	−0.245156	+	0.424623i
$755$		0			0
$756$	−18.4633	−	10.6598i	−0.671505	−	0.387694i
$757$	−45.1229	−	12.0906i	−1.64002	−	0.439442i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	−45.1229	−	12.0906i	−1.64002	−	0.439442i	−0.956795	+	0.290765i	$0.906090\pi$
$758$	6.25642	−	23.3493i	0.227243	−	0.848084i
$759$	−37.0048			−1.34319
$760$		0			0
$761$	3.34210			0.121151			0.0605756	−	0.998164i	$-0.480706\pi$
$761$	3.34210			0.121151			0.0605756	+	0.998164i	$0.480706\pi$
$762$	5.60752	−	20.9275i	0.203139	−	0.758125i
$763$	−10.2729	−	2.75262i	−0.371904	−	0.0996514i
$764$	−15.9461	−	9.20649i	−0.576910	−	0.333079i
$765$		0			0
$766$	13.1445	−	22.7669i	0.474930	−	0.822603i
$767$	−17.0774	+	17.0774i	−0.616627	+	0.616627i
$768$	1.18022	−	1.18022i	0.0425874	−	0.0425874i
$769$	−29.7858	−	17.1968i	−1.07410	−	0.620134i	−0.144803	−	0.989460i	$-0.546255\pi$
$769$	−29.7858	−	17.1968i	−1.07410	−	0.620134i	−0.929300	+	0.369327i	$0.879588\pi$
$770$		0			0
$771$	−7.83738			−0.282256
$772$	6.04230	+	6.04230i	0.217467	+	0.217467i
$773$	1.85944	+	6.93953i	0.0668794	+	0.249597i	0.991270	−	0.131851i	$-0.0420920\pi$
$773$	1.85944	+	6.93953i	0.0668794	+	0.249597i	−0.924390	+	0.381448i	$0.875425\pi$
$774$	0.596168	+	1.03259i	0.0214288	+	0.0371158i
$775$		0			0
$776$	1.19728	+	2.07375i	0.0429798	+	0.0744432i
$777$	65.6586	+	17.5932i	2.35549	+	0.631151i
$778$	−23.5338	+	23.5338i	−0.843726	+	0.843726i
$779$	−14.1895	−	21.5576i	−0.508391	−	0.772381i
$780$		0			0
$781$	25.4710	−	14.7057i	0.911425	−	0.526211i
$782$	4.23050	−	15.7884i	0.151282	−	0.564593i
$783$	−21.7060	+	5.81610i	−0.775708	+	0.207850i
$784$	7.61502	−	4.39653i	0.271965	−	0.157019i
$785$		0			0
$786$	16.2447			0.579428
$787$	14.6739	+	14.6739i	0.523068	+	0.523068i	0.918497	−	0.395429i	$-0.129404\pi$
$787$	14.6739	+	14.6739i	0.523068	+	0.523068i	−0.395429	+	0.918497i	$0.629404\pi$
$788$	−8.72348	+	2.33745i	−0.310761	+	0.0832682i
$789$	17.1729	−	29.7443i	0.611372	−	1.05893i
$790$		0			0
$791$		−	36.8862i		−	1.31152i
$792$	1.15414	−	0.309252i	0.0410107	−	0.0109888i
$793$	6.59423	+	1.76692i	0.234168	+	0.0627452i
$794$	9.48370	−	16.4263i	0.336564	−	0.582946i
$795$		0			0
$796$	7.37195	+	12.7686i	0.261292	+	0.452571i
$797$	−14.1820	−	14.1820i	−0.502353	−	0.502353i	0.409816	−	0.912168i	$-0.365593\pi$
$797$	−14.1820	−	14.1820i	−0.502353	−	0.502353i	−0.912168	+	0.409816i	$0.865593\pi$
$798$	27.4419	−	9.10393i	0.971432	−	0.322275i
$799$			50.1795i			1.77522i
$800$		0			0
$801$	2.62718	−	1.51680i	0.0928268	−	0.0535936i
$802$	7.60007	+	28.3638i	0.268368	+	1.00156i
$803$	−19.5813	+	73.0785i	−0.691010	+	2.57888i
$804$	−17.1768	−	9.91705i	−0.605780	−	0.349747i
$805$		0			0
$806$			1.84227i			0.0648914i
$807$	−3.98671	−	14.8786i	−0.140339	−	0.523752i
$808$	0.124611	+	0.465053i	0.00438378	+	0.0163605i
$809$			31.2471i			1.09859i	0.835629	+	0.549294i	$0.185103\pi$
$809$			31.2471i			1.09859i	−0.835629	+	0.549294i	$0.814897\pi$
$810$		0			0
$811$	−9.51809	−	5.49527i	−0.334225	−	0.192965i	0.323490	−	0.946232i	$-0.395144\pi$
$811$	−9.51809	−	5.49527i	−0.334225	−	0.192965i	−0.657716	+	0.753266i	$0.728477\pi$
$812$	4.30842	−	16.0793i	0.151196	−	0.564271i
$813$	10.8029	+	40.3168i	0.378873	+	1.41397i
$814$	−49.5126	+	28.5861i	−1.73542	+	1.00194i
$815$		0			0
$816$		−	6.86498i		−	0.240322i
$817$	−23.7669	−	4.89878i	−0.831498	−	0.171386i
$818$	1.58533	+	1.58533i	0.0554298	+	0.0554298i
$819$	1.36786	+	2.36920i	0.0477969	+	0.0827866i
$820$		0			0
$821$	−18.6836	+	32.3609i	−0.652061	+	1.12940i	0.330562	+	0.943784i	$0.392762\pi$
$821$	−18.6836	+	32.3609i	−0.652061	+	1.12940i	−0.982622	+	0.185618i	$0.940571\pi$
$822$	1.27028	+	0.340372i	0.0443063	+	0.0118718i
$823$	45.0785	−	12.0787i	1.57134	−	0.421039i	0.635107	−	0.772424i	$-0.280956\pi$
$823$	45.0785	−	12.0787i	1.57134	−	0.421039i	0.936231	+	0.351386i	$0.114289\pi$
$824$			14.0145i			0.488217i
$825$		0			0
$826$	14.9303	−	25.8601i	0.519492	−	0.899787i
$827$	12.2802	−	3.29047i	0.427024	−	0.114421i	−0.0389046	−	0.999243i	$-0.512387\pi$
$827$	12.2802	−	3.29047i	0.427024	−	0.114421i	0.465929	+	0.884822i	$0.345720\pi$
$828$	−0.601848	−	0.601848i	−0.0209157	−	0.0209157i
$829$	47.6024			1.65330			0.826650	−	0.562716i	$-0.190244\pi$
$829$	47.6024			1.65330			0.826650	+	0.562716i	$0.190244\pi$
$830$		0			0
$831$	−22.7584	+	13.1396i	−0.789479	+	0.455806i
$832$	−3.10465	+	0.831890i	−0.107635	+	0.0288406i
$833$	9.36049	−	34.9338i	0.324322	−	1.21039i
$834$	20.8661	−	12.0471i	0.722535	−	0.417156i
$835$		0			0
$836$	−10.9062	+	21.7350i	−0.377198	+	0.751721i
$837$	−2.17428	+	2.17428i	−0.0751543	+	0.0751543i
$838$	38.6035	+	10.3438i	1.33354	+	0.357320i
$839$	−13.6456	−	23.6348i	−0.471098	−	0.815965i	0.528356	−	0.849023i	$-0.322809\pi$
$839$	−13.6456	−	23.6348i	−0.471098	−	0.815965i	−0.999453	+	0.0330579i	$0.989475\pi$
$840$		0			0
$841$	5.72700	+	9.91946i	0.197483	+	0.342050i
$842$	−4.44123	−	16.5749i	−0.153055	−	0.571209i
$843$	21.8300	+	21.8300i	0.751866	+	0.751866i
$844$	19.7313			0.679178
$845$		0			0
$846$	2.26289	+	1.30648i	0.0777997	+	0.0449177i
$847$	56.5499	−	56.5499i	1.94308	−	1.94308i
$848$	2.68210	−	2.68210i	0.0921037	−	0.0921037i
$849$	12.8300	−	22.2222i	0.440323	−	0.762663i
$850$		0			0
$851$	35.2697	+	20.3630i	1.20903	+	0.698033i
$852$	−8.49941	−	2.27741i	−0.291185	−	0.0780228i
$853$	−0.991372	+	3.69985i	−0.0339439	+	0.126680i	−0.980819	−	0.194922i	$-0.937555\pi$
$853$	−0.991372	+	3.69985i	−0.0339439	+	0.126680i	0.946875	+	0.321602i	$0.104221\pi$
$854$	−8.44081			−0.288839
$855$		0			0
$856$	2.48870			0.0850619
$857$	2.91119	−	10.8647i	0.0994443	−	0.371131i	−0.898211	−	0.439564i	$-0.855133\pi$
$857$	2.91119	−	10.8647i	0.0994443	−	0.371131i	0.997656	+	0.0684325i	$0.0217998\pi$
$858$	28.9093	+	7.74623i	0.986948	+	0.264452i
$859$	−34.1982	−	19.7443i	−1.16683	−	0.673668i	−0.213897	−	0.976856i	$-0.568616\pi$
$859$	−34.1982	−	19.7443i	−1.16683	−	0.673668i	−0.952931	+	0.303188i	$0.901949\pi$
$860$		0			0
$861$	19.6365	−	34.0114i	0.669210	−	1.15911i
$862$	−14.6522	+	14.6522i	−0.499057	+	0.499057i
$863$	18.3050	−	18.3050i	0.623110	−	0.623110i	−0.323215	−	0.946325i	$-0.604764\pi$
$863$	18.3050	−	18.3050i	0.623110	−	0.623110i	0.946325	+	0.323215i	$0.104764\pi$
$864$	−4.64598	−	2.68236i	−0.158059	−	0.0912556i
$865$		0			0
$866$	37.5104			1.27466
$867$	0.0979044	+	0.0979044i	0.00332501	+	0.00332501i
$868$	−0.589541	−	2.20020i	−0.0200103	−	0.0746796i
$869$	13.8823	+	24.0448i	0.470923	+	0.815663i
$870$		0			0
$871$	19.0974	+	33.0777i	0.647092	+	1.12080i
$872$	−2.58500	−	0.692648i	−0.0875390	−	0.0234560i
$873$	0.362643	−	0.362643i	0.0122736	−	0.0122736i
$874$	17.2928	−	1.01328i	0.584938	−	0.0342746i
$875$		0			0
$876$	19.6022	−	11.3174i	0.662298	−	0.382378i
$877$	−9.97410	+	37.2238i	−0.336801	+	1.25696i	0.565102	+	0.825021i	$0.308837\pi$
$877$	−9.97410	+	37.2238i	−0.336801	+	1.25696i	−0.901903	+	0.431939i	$0.857830\pi$
$878$	−17.1008	+	4.58213i	−0.577123	+	0.154640i
$879$	−3.66839	+	2.11794i	−0.123732	+	0.0714365i
$880$		0			0
$881$	14.5894			0.491530			0.245765	−	0.969329i	$-0.420961\pi$
$881$	14.5894			0.491530			0.245765	+	0.969329i	$0.420961\pi$
$882$	−1.33166	−	1.33166i	−0.0448394	−	0.0448394i
$883$	37.9291	−	10.1631i	1.27642	−	0.342015i	0.443931	−	0.896061i	$-0.353583\pi$
$883$	37.9291	−	10.1631i	1.27642	−	0.342015i	0.832486	+	0.554046i	$0.186917\pi$
$884$	−6.61000	+	11.4489i	−0.222319	+	0.385067i
$885$		0			0
$886$		−	6.13559i		−	0.206129i
$887$	−29.7648	+	7.97545i	−0.999404	+	0.267789i	−0.721196	−	0.692731i	$-0.756407\pi$
$887$	−29.7648	+	7.97545i	−0.999404	+	0.267789i	−0.278208	+	0.960521i	$0.589740\pi$
$888$	16.5218	+	4.42701i	0.554437	+	0.148561i
$889$	25.7929	−	44.6747i	0.865067	−	1.49834i
$890$		0			0
$891$	23.1848	+	40.1572i	0.776718	+	1.34532i
$892$	−10.8246	−	10.8246i	−0.362435	−	0.362435i
$893$	−50.4740	+	16.7449i	−1.68905	+	0.560347i
$894$			21.1336i			0.706814i
$895$		0			0
$896$	3.44163	−	1.98702i	0.114977	−	0.0663818i
$897$	−5.51793	−	20.5932i	−0.184238	−	0.687586i
$898$	2.81279	−	10.4975i	0.0938640	−	0.350305i
$899$	−2.07924	−	1.20045i	−0.0693465	−	0.0400372i
$900$		0			0
$901$		−	15.6010i		−	0.519744i
$902$	8.54924	+	31.9062i	0.284659	+	1.06236i
$903$	−9.55733	−	35.6684i	−0.318048	−	1.18697i
$904$		−	9.28176i		−	0.308707i
$905$		0			0
$906$	21.3869	+	12.3477i	0.710531	+	0.410225i
$907$	−13.4281	+	50.1145i	−0.445874	+	1.66402i	0.267744	+	0.963490i	$0.413722\pi$
$907$	−13.4281	+	50.1145i	−0.445874	+	1.66402i	−0.713618	+	0.700535i	$0.752945\pi$
$908$	5.13929	+	19.1801i	0.170553	+	0.636514i
$909$	0.0893013	−	0.0515582i	0.00296194	−	0.00171008i
$910$		0			0
$911$		−	25.5121i		−	0.845254i	−0.906304	−	0.422627i	$-0.861108\pi$
$911$		−	25.5121i		−	0.845254i	0.906304	−	0.422627i	$-0.138892\pi$
$912$	6.90527	−	2.29084i	0.228656	−	0.0758574i
$913$	40.7469	+	40.7469i	1.34852	+	1.34852i
$914$	5.56711	+	9.64252i	0.184144	+	0.318946i
$915$		0			0
$916$	−7.59940	+	13.1625i	−0.251091	+	0.434903i
$917$	37.3604	+	10.0107i	1.23375	+	0.330582i
$918$	−21.3134	+	5.71090i	−0.703447	+	0.188488i
$919$		−	10.8124i		−	0.356667i	−0.983970	−	0.178334i	$-0.942929\pi$
$919$		−	10.8124i		−	0.356667i	0.983970	−	0.178334i	$-0.0570707\pi$
$920$		0			0
$921$	4.77814	−	8.27598i	0.157445	−	0.272703i
$922$	−33.6028	+	9.00385i	−1.10665	+	0.296526i
$923$	11.9818	+	11.9818i	0.394386	+	0.394386i
$924$	−37.0048			−1.21737
$925$		0			0
$926$	16.6421	−	9.60831i	0.546893	−	0.315749i
$927$	2.89927	−	0.776858i	0.0952247	−	0.0255154i
$928$	1.08414	−	4.04606i	0.0355886	−	0.132819i
$929$	−22.5585	+	13.0241i	−0.740119	+	0.427308i	−0.822113	−	0.569325i	$-0.807205\pi$
$929$	−22.5585	+	13.0241i	−0.740119	+	0.427308i	0.0819935	+	0.996633i	$0.473871\pi$
$930$		0			0
$931$	38.2624	−	2.24200i	1.25400	−	0.0734785i
$932$	5.67372	−	5.67372i	0.185849	−	0.185849i
$933$	25.4617	+	6.82244i	0.833578	+	0.223357i
$934$	17.2194	+	29.8249i	0.563436	+	0.975900i
$935$		0			0
$936$	0.344198	+	0.596168i	0.0112505	+	0.0194864i
$937$	4.23284	+	15.7972i	0.138281	+	0.516071i	0.999963	+	0.00862262i	$0.00274470\pi$
$937$	4.23284	+	15.7972i	0.138281	+	0.516071i	−0.861682	+	0.507449i	$0.830589\pi$
$938$	−33.3929	−	33.3929i	−1.09032	−	1.09032i
$939$	−10.8390			−0.353718
$940$		0			0
$941$	32.0769	+	18.5196i	1.04568	+	0.603722i	0.921436	−	0.388530i	$-0.127017\pi$
$941$	32.0769	+	18.5196i	1.04568	+	0.603722i	0.124241	+	0.992252i	$0.460350\pi$
$942$	7.50032	−	7.50032i	0.244374	−	0.244374i
$943$	16.6380	−	16.6380i	0.541809	−	0.541809i
$944$	3.75696	−	6.50724i	0.122278	−	0.211793i
$945$		0			0
$946$	26.8973	+	15.5292i	0.874506	+	0.504896i
$947$	−19.1841	−	5.14037i	−0.623400	−	0.167039i	−0.0667269	−	0.997771i	$-0.521256\pi$
$947$	−19.1841	−	5.14037i	−0.623400	−	0.167039i	−0.556673	+	0.830732i	$0.687922\pi$
$948$	2.14989	−	8.02349i	0.0698251	−	0.260591i
$949$	−43.5881			−1.41493
$950$		0			0
$951$	10.3155			0.334505
$952$	4.23050	−	15.7884i	0.137111	−	0.511706i
$953$	−40.5899	−	10.8760i	−1.31483	−	0.352309i	−0.467794	−	0.883837i	$-0.654951\pi$
$953$	−40.5899	−	10.8760i	−1.31483	−	0.352309i	−0.847040	+	0.531529i	$0.821618\pi$
$954$	−0.703541	−	0.406190i	−0.0227780	−	0.0131509i
$955$		0			0
$956$	−7.32488	+	12.6871i	−0.236904	+	0.410329i
$957$	−27.5803	+	27.5803i	−0.891543	+	0.891543i
$958$	−23.7404	+	23.7404i	−0.767019	+	0.767019i
$959$	2.71172	+	1.56561i	0.0875659	+	0.0505562i
$960$		0			0
$961$	30.6715			0.989402
$962$	−23.2912	−	23.2912i	−0.750939	−	0.750939i
$963$	−0.137955	−	0.514854i	−0.00444553	−	0.0165909i
$964$	−7.05046	−	12.2118i	−0.227080	−	0.393314i
$965$		0			0
$966$	13.1799	+	22.8283i	0.424057	+	0.734489i
$967$	45.6155	+	12.2226i	1.46690	+	0.393053i	0.901865	−	0.432017i	$-0.142198\pi$
$967$	45.6155	+	12.2226i	1.46690	+	0.393053i	0.565030	+	0.825070i	$0.308865\pi$
$968$	14.2298	−	14.2298i	0.457363	−	0.457363i
$969$	13.4204	−	26.7455i	0.431125	−	0.859191i
$970$		0			0
$971$	−29.9303	+	17.2803i	−0.960510	+	0.554551i	−0.896330	−	0.443388i	$-0.853776\pi$
$971$	−29.9303	+	17.2803i	−0.960510	+	0.554551i	−0.0641799	+	0.997938i	$0.520443\pi$
$972$	−0.574944	+	2.14572i	−0.0184413	+	0.0688240i
$973$	55.4130	−	14.8479i	1.77646	−	0.476001i
$974$	29.1220	−	16.8136i	0.933128	−	0.538742i
$975$		0			0
$976$	−2.12398			−0.0679870
$977$	−25.5697	−	25.5697i	−0.818048	−	0.818048i	0.167777	−	0.985825i	$-0.446341\pi$
$977$	−25.5697	−	25.5697i	−0.818048	−	0.818048i	−0.985825	+	0.167777i	$0.946341\pi$
$978$	−30.9609	+	8.29596i	−0.990022	+	0.265276i
$979$	39.5101	−	68.4335i	1.26275	−	2.18714i
$980$		0			0
$981$			0.573172i			0.0183000i
$982$	0.0396306	−	0.0106190i	0.00126466	−	0.000338866i
$983$	−37.3724	−	10.0139i	−1.19200	−	0.319394i	−0.392321	−	0.919828i	$-0.628328\pi$
$983$	−37.3724	−	10.0139i	−1.19200	−	0.319394i	−0.799674	+	0.600434i	$0.794995\pi$
$984$	4.94118	−	8.55837i	0.157519	−	0.272831i
$985$		0			0
$986$	−8.61432	−	14.9204i	−0.274336	−	0.475164i
$987$	−57.2215	−	57.2215i	−1.82138	−	1.82138i
$988$	−13.7218	−	2.82831i	−0.436549	−	0.0899805i
$989$		−	22.1240i		−	0.703502i
$990$		0			0
$991$	−6.31720	+	3.64723i	−0.200672	+	0.115858i	−0.596969	−	0.802264i	$-0.703628\pi$
$991$	−6.31720	+	3.64723i	−0.200672	+	0.115858i	0.396297	+	0.918122i	$0.370295\pi$
$992$	−0.148348	−	0.553641i	−0.00471005	−	0.0175781i
$993$	12.7178	−	47.4636i	0.403589	−	1.50621i
$994$	−18.1440	−	10.4754i	−0.575491	−	0.332260i
$995$		0			0
$996$		−	17.2401i		−	0.546272i
$997$	8.57629	+	32.0072i	0.271614	+	1.01368i	0.958077	+	0.286512i	$0.0924958\pi$
$997$	8.57629	+	32.0072i	0.271614	+	1.01368i	−0.686463	+	0.727165i	$0.740838\pi$
$998$	−5.34557	−	19.9499i	−0.169211	−	0.631505i
$999$		−	54.9774i		−	1.73941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.e.943.1	yes	24
5.2	odd	4	inner	950.2.q.e.107.1	✓	24
5.3	odd	4	inner	950.2.q.e.107.6	yes	24
5.4	even	2	inner	950.2.q.e.943.6	yes	24
19.8	odd	6	inner	950.2.q.e.293.1	yes	24
95.8	even	12	inner	950.2.q.e.407.6	yes	24
95.27	even	12	inner	950.2.q.e.407.1	yes	24
95.84	odd	6	inner	950.2.q.e.293.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.1	✓	24	5.2	odd	4	inner
950.2.q.e.107.6	yes	24	5.3	odd	4	inner
950.2.q.e.293.1	yes	24	19.8	odd	6	inner
950.2.q.e.293.6	yes	24	95.84	odd	6	inner
950.2.q.e.407.1	yes	24	95.27	even	12	inner
950.2.q.e.407.6	yes	24	95.8	even	12	inner
950.2.q.e.943.1	yes	24	1.1	even	1	trivial
950.2.q.e.943.6	yes	24	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.61221 - 0.431989i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.834540 - 1.44546i) q^{6} +(2.81008 - 2.81008i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.185481 - 0.107087i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.61221 - 0.431989i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.834540 - 1.44546i) q^{6} +(2.81008 - 2.81008i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.185481 - 0.107087i) q^{9} -5.57889 q^{11} +(1.18022 + 1.18022i) q^{12} +(-0.831890 - 3.10465i) q^{13} +(1.98702 + 3.44163i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.97289 + 1.06453i) q^{17} +(0.151445 - 0.151445i) q^{18} +(0.254973 + 4.35144i) q^{19} +(-5.74435 + 3.31650i) q^{21} +(1.44392 - 5.38879i) q^{22} +(-3.83864 + 1.02856i) q^{23} +(-1.44546 + 0.834540i) q^{24} +3.21417 q^{26} +(3.79342 + 3.79342i) q^{27} +(-3.83864 + 1.02856i) q^{28} +(-2.09440 + 3.62760i) q^{29} +0.573172i q^{31} +(-0.965926 + 0.258819i) q^{32} +(8.99432 + 2.41002i) q^{33} +(-2.05652 + 3.56199i) q^{34} +(0.107087 + 0.185481i) q^{36} +(-7.24641 - 7.24641i) q^{37} +(-4.26916 - 0.879949i) q^{38} +5.36471i q^{39} +(-5.12760 + 2.96042i) q^{41} +(-1.71675 - 6.40699i) q^{42} +(-1.44088 + 5.37742i) q^{43} +(4.83146 + 2.78944i) q^{44} -3.97405i q^{46} +(3.15762 + 11.7844i) q^{47} +(-0.431989 - 1.61221i) q^{48} -8.79306i q^{49} +(-5.94525 - 3.43249i) q^{51} +(-0.831890 + 3.10465i) q^{52} +(-0.981717 - 3.66382i) q^{53} +(-4.64598 + 2.68236i) q^{54} -3.97405i q^{56} +(1.46870 - 7.12556i) q^{57} +(-2.96192 - 2.96192i) q^{58} +(-3.75696 - 6.50724i) q^{59} +(-1.06199 + 1.83942i) q^{61} +(-0.553641 - 0.148348i) q^{62} +(-0.822140 + 0.220292i) q^{63} -1.00000i q^{64} +(-4.65580 + 8.06409i) q^{66} +(-11.4783 + 3.07561i) q^{67} +(-2.90835 - 2.90835i) q^{68} +6.63300 q^{69} +(-4.56561 + 2.63596i) q^{71} +(-0.206877 + 0.0554326i) q^{72} +(3.50990 - 13.0991i) q^{73} +(8.87500 - 5.12398i) q^{74} +(1.95490 - 3.89594i) q^{76} +(-15.6771 + 15.6771i) q^{77} +(-5.18191 - 1.38849i) q^{78} +(-2.48836 - 4.30996i) q^{79} +(-4.15580 - 7.19806i) q^{81} +(-1.53243 - 5.71910i) q^{82} +(-7.30376 - 7.30376i) q^{83} +6.63300 q^{84} +(-4.82126 - 2.78356i) q^{86} +(4.94369 - 4.94369i) q^{87} +(-3.94487 + 3.94487i) q^{88} +(-7.08207 + 12.2665i) q^{89} +(-11.0620 - 6.38664i) q^{91} +(3.83864 + 1.02856i) q^{92} +(0.247604 - 0.924071i) q^{93} -12.2001 q^{94} +1.66908 q^{96} +(-0.619757 + 2.31297i) q^{97} +(8.49345 + 2.27581i) q^{98} +(1.03478 + 0.597429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{6}+O(q^{10}) \) 24 * q - 12 * q^6	\( 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

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Database

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