LMFDB - Embedded newform 950.2.q.e.407.1

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			407.1
Character	$\chi$	$=$	950.407
Dual form			950.2.q.e.943.1

$q$-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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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	−0.692199	−	0.721707i	$-0.743358\pi$
$3$	−1.61221	+	0.431989i	−0.930808	+	0.249409i	−0.238609	+	0.971116i	$0.576691\pi$
$4$	−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	0.997939	+	0.0641702i	$0.0204401\pi$
$7$	2.81008	+	2.81008i	1.06211	+	1.06211i	0.0641702	+	0.997939i	$0.479560\pi$
$8$	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	0.749305	+	0.662225i	$0.230388\pi$
$13$	−0.831890	+	3.10465i	−0.230725	+	0.861076i	−0.980030	+	0.198851i	$0.936279\pi$
$14$	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	0.257457	−	0.966290i	$-0.417115\pi$
$17$	3.97289	−	1.06453i	0.963566	−	0.258187i	0.706109	+	0.708103i	$0.250449\pi$
$18$	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	−0.164647	−	0.986353i	$-0.552648\pi$
$23$	−3.83864	−	1.02856i	−0.800411	−	0.214469i	−0.635764	+	0.771883i	$0.719315\pi$
$24$	−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	0.603385	−	0.797450i	$-0.293818\pi$
$29$	−2.09440	−	3.62760i	−0.388920	−	0.673629i	−0.992305	+	0.123821i	$0.960485\pi$
$30$		0			0
$31$		−	0.573172i		−	0.102945i	−0.998674	−	0.0514724i	$-0.983609\pi$
$31$		−	0.573172i		−	0.102945i	0.998674	−	0.0514724i	$-0.0163914\pi$
$32$	−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	−0.214600	+	0.976702i	$0.568845\pi$
$37$	−7.24641	+	7.24641i	−1.19130	+	1.19130i	−0.976702	+	0.214600i	$0.931155\pi$
$38$	−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	0.0429529	−	0.999077i	$-0.486323\pi$
$41$	−5.12760	−	2.96042i	−0.800797	−	0.462340i	−0.843750	+	0.536737i	$0.819657\pi$
$42$	−1.71675	+	6.40699i	−0.264900	+	0.988620i
$43$	−1.44088	−	5.37742i	−0.219731	−	0.820049i	−0.984447	−	0.175681i	$-0.943787\pi$
$43$	−1.44088	−	5.37742i	−0.219731	−	0.820049i	0.764716	−	0.644368i	$-0.222879\pi$
$44$	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	−0.210536	−	0.977586i	$-0.567521\pi$
$47$	3.15762	−	11.7844i	0.460587	−	1.71893i	0.671123	−	0.741346i	$-0.265812\pi$
$48$	−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	0.865149	+	0.501514i	$0.167224\pi$
$53$	−0.981717	+	3.66382i	−0.134849	+	0.503264i	−0.999998	+	0.00174955i	$0.999443\pi$
$54$	−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	−0.999922	−	0.0125249i	$-0.996013\pi$
$59$	−3.75696	+	6.50724i	−0.489114	+	0.847170i	0.510808	+	0.859695i	$0.329346\pi$
$60$		0			0
$61$	−1.06199	−	1.83942i	−0.135974	−	0.235514i	0.789995	−	0.613113i	$-0.210083\pi$
$61$	−1.06199	−	1.83942i	−0.135974	−	0.235514i	−0.925969	+	0.377599i	$0.876750\pi$
$62$	−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	−0.523132	−	0.852252i	$-0.675236\pi$
$67$	−11.4783	−	3.07561i	−1.40230	−	0.375746i	−0.879171	+	0.476506i	$0.841903\pi$
$68$	−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	0.203985	−	0.978974i	$-0.434611\pi$
$71$	−4.56561	−	2.63596i	−0.541838	−	0.312830i	−0.745824	+	0.666143i	$0.767944\pi$
$72$	−0.206877	−	0.0554326i	−0.0243807	−	0.00653279i
$73$	3.50990	+	13.0991i	0.410802	+	1.53314i	0.793097	+	0.609095i	$0.208467\pi$
$73$	3.50990	+	13.0991i	0.410802	+	1.53314i	−0.382295	+	0.924041i	$0.624866\pi$
$74$	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	−0.971375	−	0.237551i	$-0.923655\pi$
$79$	−2.48836	+	4.30996i	−0.279962	+	0.484908i	0.691413	+	0.722460i	$0.256988\pi$
$80$		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	−0.983360	−	0.181668i	$-0.941850\pi$
$83$	−7.30376	+	7.30376i	−0.801692	+	0.801692i	0.181668	+	0.983360i	$0.441850\pi$
$84$	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	−0.947485	−	0.319801i	$-0.896384\pi$
$89$	−7.08207	−	12.2665i	−0.750698	−	1.30025i	0.196787	−	0.980446i	$-0.436949\pi$
$90$		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	0.927299	−	0.374323i	$-0.122125\pi$
$97$	−0.619757	−	2.31297i	−0.0629268	−	0.234846i	−0.990225	+	0.139476i	$0.955458\pi$
$98$	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	0.853800	−	0.520601i	$-0.174292\pi$
$101$	−0.240729	−	0.416955i	−0.0239534	−	0.0414886i	−0.877754	+	0.479112i	$0.840959\pi$
$102$	4.85427	+	4.85427i	0.480645	+	0.480645i
$103$	−9.90973	−	9.90973i	−0.976435	−	0.976435i	0.0232940	−	0.999729i	$-0.492585\pi$
$103$	−9.90973	−	9.90973i	−0.976435	−	0.976435i	−0.999729	+	0.0232940i	$0.992585\pi$
$104$	−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	−0.616910	−	0.787034i	$-0.711616\pi$
$107$	1.75977	−	1.75977i	0.170124	−	0.170124i	0.787034	+	0.616910i	$0.211616\pi$
$108$	−1.38849	+	5.18191i	−0.133607	+	0.498630i
$109$	−1.33809	+	2.31764i	−0.128166	+	0.221990i	−0.922966	−	0.384881i	$-0.874242\pi$
$109$	−1.33809	+	2.31764i	−0.128166	+	0.221990i	0.794800	+	0.606871i	$0.207576\pi$
$110$		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	0.944867	−	0.327454i	$-0.106191\pi$
$113$	6.56319	+	6.56319i	0.617413	+	0.617413i	−0.327454	+	0.944867i	$0.606191\pi$
$114$	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	0.767886	−	0.640587i	$-0.221309\pi$
$127$	12.5384	+	3.35965i	1.11260	+	0.298121i	0.344715	+	0.938707i	$0.387975\pi$
$128$	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	−0.571261	−	0.820768i	$-0.693546\pi$
$131$	4.86636	−	8.42878i	0.425176	−	0.736426i	0.996437	+	0.0843425i	$0.0268790\pi$
$132$	−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	−0.956667	−	0.291184i	$-0.905951\pi$
$137$	0.203928	−	0.761069i	0.0174227	−	0.0650225i	0.974090	+	0.226161i	$0.0726176\pi$
$138$	−1.71675	−	6.40699i	−0.146139	−	0.545399i
$139$	12.5016	−	7.21779i	1.06037	−	0.612205i	0.134836	−	0.990868i	$-0.456949\pi$
$139$	12.5016	−	7.21779i	1.06037	−	0.612205i	0.925535	+	0.378663i	$0.123616\pi$
$140$		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	−0.0216699	−	0.999765i	$-0.506898\pi$
$149$	−10.9655	−	6.33092i	−0.898327	−	0.518649i	−0.876657	+	0.481116i	$0.840232\pi$
$150$		0			0
$151$		−	14.7958i		−	1.20407i	−0.798470	−	0.602034i	$-0.794357\pi$
$151$		−	14.7958i		−	1.20407i	0.798470	−	0.602034i	$-0.205643\pi$
$152$	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	−0.00540611	−	0.999985i	$-0.501721\pi$
$157$	6.13849	−	1.64480i	0.489905	−	0.131270i	0.495311	+	0.868716i	$0.335054\pi$
$158$	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	−0.0657815	+	0.997834i	$0.520954\pi$
$163$	−13.5793	+	13.5793i	−1.06362	+	1.06362i	−0.997834	+	0.0657815i	$0.979046\pi$
$164$	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	0.161147	−	0.986930i	$-0.448481\pi$
$167$	−2.49101	−	0.667465i	−0.192760	−	0.0516500i	−0.353908	+	0.935280i	$0.615147\pi$
$168$	−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	−0.183637	−	0.982994i	$-0.558787\pi$
$173$	1.95750	−	0.524511i	0.148826	−	0.0398778i	0.332463	+	0.943116i	$0.392120\pi$
$174$	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	−0.394527	−	0.918884i	$-0.629092\pi$
$181$	2.74435	−	1.58445i	0.203986	−	0.117771i	0.598513	+	0.801113i	$0.295758\pi$
$182$	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	−0.543340	−	0.839512i	$-0.682841\pi$
$193$	−8.25393	+	2.21163i	−0.594131	+	0.159197i	−0.0507904	+	0.998709i	$0.516174\pi$
$194$	−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	0.897005	−	0.442019i	$-0.145738\pi$
$197$	6.38603	+	6.38603i	0.454986	+	0.454986i	−0.442019	+	0.897005i	$0.645738\pi$
$198$	−0.844892	−	0.844892i	−0.0600439	−	0.0600439i
$199$	−12.7686	+	7.37195i	−0.905141	+	0.522584i	−0.878865	−	0.477071i	$-0.841698\pi$
$199$	−12.7686	+	7.37195i	−0.905141	+	0.522584i	−0.0262767	+	0.999655i	$0.508365\pi$
$200$		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	−0.221198	−	0.975229i	$-0.570997\pi$
$211$	−17.0878	−	9.86563i	−1.17637	−	0.679178i	−0.955172	+	0.296051i	$0.904330\pi$
$212$	−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	0.272860	−	0.962054i	$-0.412030\pi$
$223$	14.7867	−	3.96208i	0.990190	−	0.265321i	0.717330	+	0.696733i	$0.245364\pi$
$224$	−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	−0.997826	−	0.0659048i	$-0.979007\pi$
$227$	−14.0408	+	14.0408i	−0.931921	+	0.931921i	0.0659048	+	0.997826i	$0.479007\pi$
$228$	−4.83471	−	5.43656i	−0.320187	−	0.360045i
$229$			15.1988i			1.00437i	0.864762	+	0.502183i	$0.167469\pi$
$229$			15.1988i			1.00437i	−0.864762	+	0.502183i	$0.832531\pi$
$230$		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	−0.999991	−	0.00415495i	$-0.998677\pi$
$233$	−2.07673	−	7.75045i	−0.136051	−	0.507749i	0.863940	−	0.503594i	$-0.167989\pi$
$234$	−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	$0.157121\pi$
$239$			14.6498i			0.947614i	−0.880629	+	0.473807i	$0.842879\pi$
$240$		0			0
$241$	12.2118	−	7.05046i	0.786628	−	0.454160i	−0.0521460	−	0.998639i	$-0.516606\pi$
$241$	12.2118	−	7.05046i	0.786628	−	0.454160i	0.838774	+	0.544479i	$0.183273\pi$
$242$	−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	0.999944	−	0.0105596i	$-0.00336127\pi$
$251$	7.77617	+	13.4687i	0.490827	+	0.850138i	−0.509117	+	0.860697i	$0.670028\pi$
$252$	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	0.397491	−	0.917606i	$-0.369881\pi$
$257$	4.53563	+	1.21532i	0.282925	+	0.0758095i	−0.114566	+	0.993416i	$0.536548\pi$
$258$	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	−0.910840	−	0.412759i	$-0.864565\pi$
$263$	−5.32590	−	19.8765i	−0.328409	−	1.22564i	0.582431	−	0.812880i	$-0.302102\pi$
$264$	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	−0.690373	−	0.723454i	$-0.742554\pi$
$269$	4.61436	−	7.99231i	0.281343	−	0.487300i	0.971716	+	0.236154i	$0.0758869\pi$
$270$		0			0
$271$	−12.5036	+	21.6569i	−0.759541	+	1.31556i	0.183544	+	0.983011i	$0.441243\pi$
$271$	−12.5036	+	21.6569i	−0.759541	+	1.31556i	−0.943085	+	0.332552i	$0.892090\pi$
$272$	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	0.957468	−	0.288541i	$-0.0931700\pi$
$277$	11.1332	+	11.1332i	0.668927	+	0.668927i	−0.288541	+	0.957468i	$0.593170\pi$
$278$	−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	−0.894812	−	0.446444i	$-0.852690\pi$
$281$	−16.0185	+	9.24831i	−0.955586	+	0.551708i	−0.0607743	+	0.998152i	$0.519357\pi$
$282$	19.6691	−	5.27032i	1.17128	−	0.313843i
$283$	−3.97901	−	14.8499i	−0.236528	−	0.882733i	−0.977454	−	0.211147i	$-0.932280\pi$
$283$	−3.97901	−	14.8499i	−0.236528	−	0.882733i	0.740927	−	0.671586i	$-0.234387\pi$
$284$	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	0.757580	−	0.652742i	$-0.226381\pi$
$293$	1.79454	+	1.79454i	0.104838	+	0.104838i	−0.652742	+	0.757580i	$0.726381\pi$
$294$	−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	0.910659	−	0.413159i	$-0.135575\pi$
$307$	−1.48186	−	5.53039i	−0.0845744	−	0.315636i	−0.995233	+	0.0975232i	$0.968908\pi$
$308$	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	0.431701	−	0.902017i	$-0.357914\pi$
$313$	6.27274	+	1.68078i	0.354556	+	0.0950030i	−0.0771446	+	0.997020i	$0.524580\pi$
$314$	−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	0.0872424	−	0.996187i	$-0.472195\pi$
$317$	−5.96979	−	1.59960i	−0.335297	−	0.0898425i	−0.422539	+	0.906345i	$0.638861\pi$
$318$	−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	$-0.699961\pi$
$331$		−	29.4402i		−	1.61818i	0.587686	−	0.809089i	$-0.300039\pi$
$332$	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	0.691611	+	0.722270i	$0.256901\pi$
$337$	8.33054	+	31.0900i	0.453793	+	1.69358i	−0.237818	+	0.971310i	$0.576432\pi$
$338$	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	0.344005	−	0.938968i	$-0.388216\pi$
$347$	20.7032	−	5.54741i	1.11141	−	0.297801i	0.767401	+	0.641167i	$0.221549\pi$
$348$	−6.75320	−	1.80951i	−0.362010	−	0.0970002i
$349$			18.2359i			0.976145i	0.872803	+	0.488072i	$0.162300\pi$
$349$			18.2359i			0.976145i	−0.872803	+	0.488072i	$0.837700\pi$
$350$		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	−0.979371	−	0.202068i	$-0.935234\pi$
$353$	−14.6042	+	14.6042i	−0.777303	+	0.777303i	0.202068	+	0.979371i	$0.435234\pi$
$354$	−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	0.122049	−	0.992524i	$-0.461054\pi$
$359$	−12.8174	−	7.40015i	−0.676478	−	0.390565i	−0.798527	+	0.601959i	$0.794387\pi$
$360$		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	0.639997	+	0.768378i	$0.278936\pi$
$367$	−5.71739	+	21.3376i	−0.298446	+	1.11381i	−0.938442	+	0.345436i	$0.887731\pi$
$368$	−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	0.786604	−	0.617457i	$-0.211837\pi$
$373$	3.26677	+	3.26677i	0.169147	+	0.169147i	−0.617457	+	0.786604i	$0.711837\pi$
$374$	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	−0.840517	−	0.541786i	$-0.817748\pi$
$383$	−25.3932	+	6.80409i	−1.29753	+	0.347673i	−0.457016	+	0.889458i	$0.651082\pi$
$384$	−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	0.462301	−	0.886723i	$-0.347024\pi$
$389$	28.8228	−	16.6409i	1.46138	−	0.843726i	0.999075	+	0.0429969i	$0.0136906\pi$
$390$		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	−0.687376	−	0.726302i	$-0.741237\pi$
$397$	−18.3211	+	4.90913i	−0.919510	+	0.246382i	−0.232134	+	0.972684i	$0.574571\pi$
$398$	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	0.974974	−	0.222317i	$-0.0713619\pi$
$401$	25.4303	+	14.6822i	1.26993	+	0.733194i	0.294955	+	0.955511i	$0.404695\pi$
$402$	−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	0.892409	−	0.451228i	$-0.149014\pi$
$409$	1.12100	+	1.94163i	0.0554298	+	0.0960073i	−0.836979	+	0.547235i	$0.815680\pi$
$410$		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	$0.430439\pi$
$419$			39.9653i			1.95243i	−0.216797	+	0.976217i	$0.569561\pi$
$420$		0			0
$421$	−14.8606	−	8.57980i	−0.724264	−	0.418154i	0.0920564	−	0.995754i	$-0.470656\pi$
$421$	−14.8606	−	8.57980i	−0.724264	−	0.418154i	−0.816320	+	0.577600i	$0.803989\pi$
$422$	−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	−0.00108855	−	0.999999i	$-0.500346\pi$
$431$	17.9452	−	10.3607i	0.864392	−	0.499057i	0.865481	+	0.500942i	$0.167013\pi$
$432$	−1.38849	−	5.18191i	−0.0668037	−	0.249315i
$433$	−9.70841	+	36.2323i	−0.466556	+	1.74121i	0.185121	+	0.982716i	$0.440732\pi$
$433$	−9.70841	+	36.2323i	−0.466556	+	1.74121i	−0.651678	+	0.758496i	$0.725934\pi$
$434$	−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	−0.573699	−	0.819066i	$-0.694492\pi$
$439$	8.85200	−	15.3321i	0.422483	−	0.731762i	0.996182	+	0.0873044i	$0.0278253\pi$
$440$		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	0.115266	−	0.993335i	$-0.463228\pi$
$443$	−5.92652	−	1.58801i	−0.281578	−	0.0754485i	−0.396844	+	0.917886i	$0.629895\pi$
$444$			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	0.866852	−	0.498565i	$-0.166139\pi$
$457$	7.87309	+	7.87309i	0.368288	+	0.368288i	−0.498565	+	0.866852i	$0.666139\pi$
$458$	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	−0.102652	−	0.994717i	$-0.532733\pi$
$461$	17.3941	−	30.1275i	0.810124	−	1.40318i	0.912776	−	0.408459i	$-0.133934\pi$
$462$	9.57754	−	35.7439i	0.445587	−	1.66295i
$463$	−13.5882	+	13.5882i	−0.631497	+	0.631497i	−0.948443	−	0.316946i	$-0.897342\pi$
$463$	−13.5882	+	13.5882i	−0.631497	+	0.631497i	0.316946	+	0.948443i	$0.397342\pi$
$464$	−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	0.990683	+	0.136189i	$0.0434856\pi$
$467$	24.3519	+	24.3519i	1.12687	+	1.12687i	0.136189	+	0.990683i	$0.456514\pi$
$468$	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	0.343445	−	0.939173i	$-0.388406\pi$
$479$	29.0760	−	16.7870i	1.32852	−	0.767019i	0.985070	+	0.172154i	$0.0550727\pi$
$480$		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	−0.0807490	+	0.996734i	$0.525731\pi$
$487$	−23.7780	+	23.7780i	−1.07748	+	1.07748i	−0.996734	+	0.0807490i	$0.974269\pi$
$488$	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	−0.866488	−	0.499198i	$-0.833628\pi$
$491$	−0.0205143	+	0.0355318i	−0.000925798	+	0.00160353i	0.865562	+	0.500802i	$0.166961\pi$
$492$	−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	0.0430056	−	0.999075i	$-0.486307\pi$
$499$	−17.8866	−	10.3269i	−0.800716	−	0.462293i	−0.843721	+	0.536781i	$0.819640\pi$
$500$		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	−0.0193038	−	0.999814i	$-0.506145\pi$
$503$	−12.0196	−	3.22065i	−0.535928	−	0.143602i	−0.516624	+	0.856212i	$0.672812\pi$
$504$	−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	0.610157	−	0.792281i	$-0.291106\pi$
$509$	−8.59703	−	14.8905i	−0.381057	−	0.660009i	−0.991214	+	0.132271i	$0.957773\pi$
$510$		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	$0.0559961\pi$
$521$			7.98939i			0.350022i	−0.984567	+	0.175011i	$0.944004\pi$
$522$	0.232196	−	0.866566i	0.0101629	−	0.0379286i
$523$	−3.94272	+	14.7144i	−0.172403	+	0.643417i	0.824576	+	0.565751i	$0.191414\pi$
$523$	−3.94272	+	14.7144i	−0.172403	+	0.643417i	−0.996979	+	0.0776662i	$0.975253\pi$
$524$			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	0.912763	−	0.408489i	$-0.133944\pi$
$541$	2.38687	+	4.13418i	0.102620	+	0.177742i	−0.810144	+	0.586232i	$0.800611\pi$
$542$	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	0.348113	−	0.937453i	$-0.386823\pi$
$547$	4.22997	+	1.13342i	0.180860	+	0.0484614i	−0.167252	+	0.985914i	$0.553489\pi$
$548$	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	−0.401578	−	0.915825i	$-0.631538\pi$
$557$	9.53737	−	35.5939i	0.404111	−	1.50816i	0.805689	−	0.592339i	$-0.201795\pi$
$558$	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	0.967504	−	0.252856i	$-0.0813698\pi$
$563$	16.9569	+	16.9569i	0.714648	+	0.714648i	−0.252856	+	0.967504i	$0.581370\pi$
$564$	−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	0.692556	−	0.721364i	$-0.256484\pi$
$577$	−0.691973	−	0.691973i	−0.0288072	−	0.0288072i	−0.721364	+	0.692556i	$0.756484\pi$
$578$	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	−0.557258	−	0.830339i	$-0.688147\pi$
$587$	−15.1350	+	4.05541i	−0.624689	+	0.167385i	−0.0674303	+	0.997724i	$0.521480\pi$
$588$	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	−0.0639609	−	0.997952i	$-0.520373\pi$
$593$	−15.0573	−	4.03459i	−0.618329	−	0.165681i	−0.554368	+	0.832272i	$0.687040\pi$
$594$	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	0.996858	+	0.0792037i	$0.0252378\pi$
$599$	13.8776	+	24.0366i	0.567022	+	0.982110i	−0.429837	+	0.902907i	$0.641429\pi$
$600$		0			0
$601$		−	5.35237i		−	0.218328i	−0.994024	−	0.109164i	$-0.965183\pi$
$601$		−	5.35237i		−	0.218328i	0.994024	−	0.109164i	$-0.0348173\pi$
$602$	−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	−0.238106	−	0.971239i	$-0.576527\pi$
$607$	18.0625	−	18.0625i	0.733133	−	0.733133i	0.971239	+	0.238106i	$0.0765265\pi$
$608$	−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	−0.999887	−	0.0150066i	$-0.995223\pi$
$613$	−3.50245	−	13.0713i	−0.141463	−	0.527946i	0.858425	−	0.512940i	$-0.171444\pi$
$614$	−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	−0.995390	−	0.0959086i	$-0.969424\pi$
$617$	−2.12136	+	7.91702i	−0.0854027	+	0.318727i	0.909987	+	0.414636i	$0.136091\pi$
$618$	6.05411	−	22.5942i	0.243532	−	0.908873i
$619$			25.0072i			1.00513i	0.864541	+	0.502563i	$0.167609\pi$
$619$			25.0072i			1.00513i	−0.864541	+	0.502563i	$0.832391\pi$
$620$		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	−0.997145	−	0.0755096i	$-0.975942\pi$
$631$	−14.1667	−	24.5374i	−0.563966	−	0.976817i	0.433179	−	0.901308i	$-0.357392\pi$
$632$	−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	0.846846	−	0.531838i	$-0.178499\pi$
$641$	20.4996	+	11.8354i	0.809684	+	0.467471i	−0.0371624	+	0.999309i	$0.511832\pi$
$642$	4.01229	+	1.07509i	0.158353	+	0.0424304i
$643$	−2.66769	−	9.95594i	−0.105203	−	0.392624i	0.893165	−	0.449729i	$-0.148480\pi$
$643$	−2.66769	−	9.95594i	−0.105203	−	0.392624i	−0.998368	+	0.0571053i	$0.981813\pi$
$644$	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	0.601547	−	0.798837i	$-0.294551\pi$
$647$	−5.01831	−	5.01831i	−0.197290	−	0.197290i	−0.798837	+	0.601547i	$0.794551\pi$
$648$	−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	−0.415328	−	0.909672i	$-0.636333\pi$
$653$	12.6324	−	12.6324i	0.494344	−	0.494344i	0.909672	+	0.415328i	$0.136333\pi$
$654$	−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	0.768842	−	0.639439i	$-0.220833\pi$
$659$	−4.34736	−	7.52985i	−0.169349	−	0.293321i	−0.938191	+	0.346117i	$0.887500\pi$
$660$		0			0
$661$	−31.8131	+	18.3673i	−1.23739	+	0.714406i	−0.968559	−	0.248782i	$-0.919970\pi$
$661$	−31.8131	+	18.3673i	−1.23739	+	0.714406i	−0.268828	+	0.963188i	$0.586636\pi$
$662$	−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	0.658171	−	0.752868i	$-0.271330\pi$
$673$	−2.45665	−	2.45665i	−0.0946967	−	0.0946967i	−0.752868	+	0.658171i	$0.771330\pi$
$674$	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	−0.957265	−	0.289212i	$-0.906607\pi$
$677$	−17.3822	+	17.3822i	−0.668053	+	0.668053i	0.289212	+	0.957265i	$0.406607\pi$
$678$	−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	0.998336	−	0.0576691i	$-0.0183669\pi$
$683$	24.5836	+	24.5836i	0.940667	+	0.940667i	−0.0576691	+	0.998336i	$0.518367\pi$
$684$	−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	−0.252840	+	0.967508i	$0.581365\pi$
$701$	−25.5314	+	44.2216i	−0.964307	+	1.67023i	−0.711467	+	0.702720i	$0.751969\pi$
$702$	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	−0.0443465	−	0.999016i	$-0.514121\pi$
$709$	21.2658	−	12.2778i	0.798654	−	0.461103i	0.843000	+	0.537913i	$0.180787\pi$
$710$		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	0.0662111	−	0.997806i	$-0.478909\pi$
$719$	−20.5077	−	11.8401i	−0.764808	−	0.441562i	−0.831020	+	0.556243i	$0.812242\pi$
$720$		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	−0.280559	−	0.959837i	$-0.590520\pi$
$727$	−1.17593	+	0.315088i	−0.0436127	+	0.0116860i	0.236947	+	0.971523i	$0.423853\pi$
$728$	−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	0.0494669	−	0.998776i	$-0.484248\pi$
$733$	28.3801	−	28.3801i	1.04824	−	1.04824i	0.998776	−	0.0494669i	$-0.0157522\pi$
$734$	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	0.915525	−	0.402261i	$-0.131775\pi$
$739$	27.8620	+	16.0861i	1.02492	+	0.591738i	0.109395	+	0.993998i	$0.465109\pi$
$740$		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	−0.297710	−	0.954656i	$-0.596223\pi$
$743$	−2.13174	+	0.571198i	−0.0782059	+	0.0209552i	0.219504	+	0.975612i	$0.429556\pi$
$744$	−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	−0.929041	−	0.369978i	$-0.879365\pi$
$751$	−29.4090	+	16.9793i	−1.07315	+	0.619584i	−0.144110	+	0.989562i	$0.546032\pi$
$752$	−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	−0.956795	−	0.290765i	$-0.906090\pi$
$757$	−45.1229	+	12.0906i	−1.64002	+	0.439442i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	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	−0.929300	−	0.369327i	$-0.879588\pi$
$769$	−29.7858	+	17.1968i	−1.07410	+	0.620134i	−0.144803	+	0.989460i	$0.546255\pi$
$770$		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	−0.924390	−	0.381448i	$-0.875425\pi$
$773$	1.85944	−	6.93953i	0.0668794	−	0.249597i	0.991270	+	0.131851i	$0.0420920\pi$
$774$	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	−0.395429	−	0.918497i	$-0.629404\pi$
$787$	14.6739	−	14.6739i	0.523068	−	0.523068i	0.918497	+	0.395429i	$0.129404\pi$
$788$	−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	−0.912168	−	0.409816i	$-0.865593\pi$
$797$	−14.1820	+	14.1820i	−0.502353	+	0.502353i	0.409816	+	0.912168i	$0.365593\pi$
$798$	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	$-0.814897\pi$
$809$		−	31.2471i		−	1.09859i	0.835629	−	0.549294i	$-0.185103\pi$
$810$		0			0
$811$	−9.51809	+	5.49527i	−0.334225	+	0.192965i	−0.657716	−	0.753266i	$-0.728477\pi$
$811$	−9.51809	+	5.49527i	−0.334225	+	0.192965i	0.323490	+	0.946232i	$0.395144\pi$
$812$	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	−0.982622	−	0.185618i	$-0.940571\pi$
$821$	−18.6836	−	32.3609i	−0.652061	−	1.12940i	0.330562	−	0.943784i	$-0.392762\pi$
$822$	1.27028	−	0.340372i	0.0443063	−	0.0118718i
$823$	45.0785	+	12.0787i	1.57134	+	0.421039i	0.936231	−	0.351386i	$-0.114289\pi$
$823$	45.0785	+	12.0787i	1.57134	+	0.421039i	0.635107	+	0.772424i	$0.280956\pi$
$824$		−	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	0.465929	−	0.884822i	$-0.345720\pi$
$827$	12.2802	+	3.29047i	0.427024	+	0.114421i	−0.0389046	+	0.999243i	$0.512387\pi$
$828$	−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	−0.999453	−	0.0330579i	$-0.989475\pi$
$839$	−13.6456	+	23.6348i	−0.471098	+	0.815965i	0.528356	+	0.849023i	$0.322809\pi$
$840$		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	0.946875	−	0.321602i	$-0.104221\pi$
$853$	−0.991372	−	3.69985i	−0.0339439	−	0.126680i	−0.980819	+	0.194922i	$0.937555\pi$
$854$	−8.44081			−0.288839
$855$		0			0
$856$	2.48870			0.0850619
$857$	2.91119	+	10.8647i	0.0994443	+	0.371131i	0.997656	−	0.0684325i	$-0.0217998\pi$
$857$	2.91119	+	10.8647i	0.0994443	+	0.371131i	−0.898211	+	0.439564i	$0.855133\pi$
$858$	28.9093	−	7.74623i	0.986948	−	0.264452i
$859$	−34.1982	+	19.7443i	−1.16683	+	0.673668i	−0.952931	−	0.303188i	$-0.901949\pi$
$859$	−34.1982	+	19.7443i	−1.16683	+	0.673668i	−0.213897	+	0.976856i	$0.568616\pi$
$860$		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	0.946325	−	0.323215i	$-0.104764\pi$
$863$	18.3050	+	18.3050i	0.623110	+	0.623110i	−0.323215	+	0.946325i	$0.604764\pi$
$864$	−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	−0.901903	−	0.431939i	$-0.857830\pi$
$877$	−9.97410	−	37.2238i	−0.336801	−	1.25696i	0.565102	−	0.825021i	$-0.308837\pi$
$878$	−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	0.832486	−	0.554046i	$-0.186917\pi$
$883$	37.9291	+	10.1631i	1.27642	+	0.342015i	0.443931	+	0.896061i	$0.353583\pi$
$884$	−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	−0.278208	−	0.960521i	$-0.589740\pi$
$887$	−29.7648	−	7.97545i	−0.999404	−	0.267789i	−0.721196	+	0.692731i	$0.756407\pi$
$888$	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	−0.713618	−	0.700535i	$-0.752945\pi$
$907$	−13.4281	−	50.1145i	−0.445874	−	1.66402i	0.267744	−	0.963490i	$-0.413722\pi$
$908$	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	$0.138892\pi$
$911$			25.5121i			0.845254i	−0.906304	+	0.422627i	$0.861108\pi$
$912$	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	$0.0570707\pi$
$919$			10.8124i			0.356667i	−0.983970	+	0.178334i	$0.942929\pi$
$920$		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	0.0819935	−	0.996633i	$-0.473871\pi$
$929$	−22.5585	−	13.0241i	−0.740119	−	0.427308i	−0.822113	+	0.569325i	$0.807205\pi$
$930$		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	−0.861682	−	0.507449i	$-0.830589\pi$
$937$	4.23284	−	15.7972i	0.138281	−	0.516071i	0.999963	−	0.00862262i	$-0.00274470\pi$
$938$	−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	0.124241	−	0.992252i	$-0.460350\pi$
$941$	32.0769	−	18.5196i	1.04568	−	0.603722i	0.921436	+	0.388530i	$0.127017\pi$
$942$	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	−0.556673	−	0.830732i	$-0.687922\pi$
$947$	−19.1841	+	5.14037i	−0.623400	+	0.167039i	−0.0667269	+	0.997771i	$0.521256\pi$
$948$	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	−0.847040	−	0.531529i	$-0.821618\pi$
$953$	−40.5899	+	10.8760i	−1.31483	+	0.352309i	−0.467794	+	0.883837i	$0.654951\pi$
$954$	−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	0.565030	−	0.825070i	$-0.308865\pi$
$967$	45.6155	−	12.2226i	1.46690	−	0.393053i	0.901865	+	0.432017i	$0.142198\pi$
$968$	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	−0.0641799	−	0.997938i	$-0.520443\pi$
$971$	−29.9303	−	17.2803i	−0.960510	−	0.554551i	−0.896330	+	0.443388i	$0.853776\pi$
$972$	−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	−0.985825	−	0.167777i	$-0.946341\pi$
$977$	−25.5697	+	25.5697i	−0.818048	+	0.818048i	0.167777	+	0.985825i	$0.446341\pi$
$978$	−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	−0.799674	−	0.600434i	$-0.794995\pi$
$983$	−37.3724	+	10.0139i	−1.19200	+	0.319394i	−0.392321	+	0.919828i	$0.628328\pi$
$984$	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	0.396297	−	0.918122i	$-0.370295\pi$
$991$	−6.31720	−	3.64723i	−0.200672	−	0.115858i	−0.596969	+	0.802264i	$0.703628\pi$
$992$	−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	−0.686463	−	0.727165i	$-0.740838\pi$
$997$	8.57629	−	32.0072i	0.271614	−	1.01368i	0.958077	−	0.286512i	$-0.0924958\pi$
$998$	−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.407.1	yes	24
5.2	odd	4	inner	950.2.q.e.293.6	yes	24
5.3	odd	4	inner	950.2.q.e.293.1	yes	24
5.4	even	2	inner	950.2.q.e.407.6	yes	24
19.12	odd	6	inner	950.2.q.e.107.1	✓	24
95.12	even	12	inner	950.2.q.e.943.6	yes	24
95.69	odd	6	inner	950.2.q.e.107.6	yes	24
95.88	even	12	inner	950.2.q.e.943.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.1	✓	24	19.12	odd	6	inner
950.2.q.e.107.6	yes	24	95.69	odd	6	inner
950.2.q.e.293.1	yes	24	5.3	odd	4	inner
950.2.q.e.293.6	yes	24	5.2	odd	4	inner
950.2.q.e.407.1	yes	24	1.1	even	1	trivial
950.2.q.e.407.6	yes	24	5.4	even	2	inner
950.2.q.e.943.1	yes	24	95.88	even	12	inner
950.2.q.e.943.6	yes	24	95.12	even	12	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

Varieties

Fields

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Database

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