LMFDB - Embedded newform 950.2.q.e.107.1

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			107.1
Character	$\chi$	$=$	950.107
Dual form			950.2.q.e.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.431989 + 1.61221i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.834540 - 1.44546i) q^{6} +(2.81008 + 2.81008i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.185481 + 0.107087i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.431989 + 1.61221i) 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} +(-3.10465 + 0.831890i) q^{13} +(-1.98702 - 3.44163i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.06453 + 3.97289i) q^{17} +(-0.151445 - 0.151445i) q^{18} +(-0.254973 - 4.35144i) q^{19} +(-5.74435 + 3.31650i) q^{21} +(5.38879 + 1.44392i) q^{22} +(1.02856 + 3.83864i) q^{23} +(1.44546 - 0.834540i) q^{24} +3.21417 q^{26} +(-3.79342 + 3.79342i) q^{27} +(1.02856 + 3.83864i) q^{28} +(2.09440 - 3.62760i) q^{29} +0.573172i q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.41002 - 8.99432i) q^{33} +(2.05652 - 3.56199i) q^{34} +(0.107087 + 0.185481i) q^{36} +(7.24641 - 7.24641i) q^{37} +(-0.879949 + 4.26916i) q^{38} -5.36471i q^{39} +(-5.12760 + 2.96042i) q^{41} +(6.40699 - 1.71675i) q^{42} +(5.37742 + 1.44088i) q^{43} +(-4.83146 - 2.78944i) q^{44} -3.97405i q^{46} +(-11.7844 + 3.15762i) q^{47} +(-1.61221 + 0.431989i) q^{48} +8.79306i q^{49} +(-5.94525 - 3.43249i) q^{51} +(-3.10465 - 0.831890i) q^{52} +(-3.66382 + 0.981717i) q^{53} +(4.64598 - 2.68236i) q^{54} -3.97405i q^{56} +(7.12556 + 1.46870i) q^{57} +(-2.96192 + 2.96192i) q^{58} +(3.75696 + 6.50724i) q^{59} +(-1.06199 + 1.83942i) q^{61} +(0.148348 - 0.553641i) q^{62} +(0.220292 + 0.822140i) q^{63} +1.00000i q^{64} +(-4.65580 + 8.06409i) q^{66} +(-3.07561 - 11.4783i) q^{67} +(-2.90835 + 2.90835i) q^{68} -6.63300 q^{69} +(-4.56561 + 2.63596i) q^{71} +(-0.0554326 - 0.206877i) q^{72} +(-13.0991 - 3.50990i) q^{73} +(-8.87500 + 5.12398i) q^{74} +(1.95490 - 3.89594i) q^{76} +(-15.6771 - 15.6771i) q^{77} +(-1.38849 + 5.18191i) q^{78} +(2.48836 + 4.30996i) q^{79} +(-4.15580 - 7.19806i) q^{81} +(5.71910 - 1.53243i) 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} +(-1.02856 + 3.83864i) q^{92} +(-0.924071 - 0.247604i) q^{93} +12.2001 q^{94} +1.66908 q^{96} +(-2.31297 - 0.619757i) q^{97} +(2.27581 - 8.49345i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.431989	+	1.61221i	−0.249409	+	0.930808i	0.721707	+	0.692199i	$0.243358\pi$
$3$	−0.431989	+	1.61221i	−0.249409	+	0.930808i	−0.971116	+	0.238609i	$0.923309\pi$
$4$	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
$13$	−3.10465	+	0.831890i	−0.861076	+	0.230725i	−0.662225	−	0.749305i	$-0.730388\pi$
$13$	−3.10465	+	0.831890i	−0.861076	+	0.230725i	−0.198851	+	0.980030i	$0.563721\pi$
$14$	−1.98702	−	3.44163i	−0.531055	−	0.919814i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.06453	+	3.97289i	−0.258187	+	0.963566i	0.708103	+	0.706109i	$0.249551\pi$
$17$	−1.06453	+	3.97289i	−0.258187	+	0.963566i	−0.966290	+	0.257457i	$0.917115\pi$
$18$	−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
$22$	5.38879	+	1.44392i	1.14889	+	0.307845i
$23$	1.02856	+	3.83864i	0.214469	+	0.800411i	0.986353	+	0.164647i	$0.0526483\pi$
$23$	1.02856	+	3.83864i	0.214469	+	0.800411i	−0.771883	+	0.635764i	$0.780685\pi$
$24$	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
$28$	1.02856	+	3.83864i	0.194379	+	0.725434i
$29$	2.09440	−	3.62760i	0.388920	−	0.673629i	−0.603385	−	0.797450i	$-0.706182\pi$
$29$	2.09440	−	3.62760i	0.388920	−	0.673629i	0.992305	+	0.123821i	$0.0395150\pi$
$30$		0			0
$31$			0.573172i			0.102945i	0.998674	+	0.0514724i	$0.0163914\pi$
$31$			0.573172i			0.102945i	−0.998674	+	0.0514724i	$0.983609\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	2.41002	−	8.99432i	0.419531	−	1.56571i
$34$	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	$-0.431155\pi$
$37$	7.24641	−	7.24641i	1.19130	−	1.19130i	0.976702	−	0.214600i	$-0.0688447\pi$
$38$	−0.879949	+	4.26916i	−0.142747	+	0.692548i
$39$		−	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	$0.486323\pi$
$42$	6.40699	−	1.71675i	0.988620	−	0.264900i
$43$	5.37742	+	1.44088i	0.820049	+	0.219731i	0.644368	−	0.764716i	$-0.277121\pi$
$43$	5.37742	+	1.44088i	0.820049	+	0.219731i	0.175681	+	0.984447i	$0.443787\pi$
$44$	−4.83146	−	2.78944i	−0.728370	−	0.420524i
$45$		0			0
$46$		−	3.97405i		−	0.585941i
$47$	−11.7844	+	3.15762i	−1.71893	+	0.460587i	−0.977586	−	0.210536i	$-0.932479\pi$
$47$	−11.7844	+	3.15762i	−1.71893	+	0.460587i	−0.741346	+	0.671123i	$0.765812\pi$
$48$	−1.61221	+	0.431989i	−0.232702	+	0.0623523i
$49$			8.79306i			1.25615i
$50$		0			0
$51$	−5.94525	−	3.43249i	−0.832501	−	0.480645i
$52$	−3.10465	−	0.831890i	−0.430538	−	0.115362i
$53$	−3.66382	+	0.981717i	−0.503264	+	0.134849i	−0.501514	−	0.865149i	$-0.667224\pi$
$53$	−3.66382	+	0.981717i	−0.503264	+	0.134849i	−0.00174955	+	0.999998i	$0.500557\pi$
$54$	4.64598	−	2.68236i	0.632237	−	0.365022i
$55$		0			0
$56$		−	3.97405i		−	0.531055i
$57$	7.12556	+	1.46870i	0.943803	+	0.194535i
$58$	−2.96192	+	2.96192i	−0.388920	+	0.388920i
$59$	3.75696	+	6.50724i	0.489114	+	0.847170i	0.999922	−	0.0125249i	$-0.00398690\pi$
$59$	3.75696	+	6.50724i	0.489114	+	0.847170i	−0.510808	+	0.859695i	$0.670654\pi$
$60$		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	$0.210083\pi$
$62$	0.148348	−	0.553641i	0.0188402	−	0.0703125i
$63$	0.220292	+	0.822140i	0.0277541	+	0.103580i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−4.65580	+	8.06409i	−0.573090	+	0.992620i
$67$	−3.07561	−	11.4783i	−0.375746	−	1.40230i	−0.852252	−	0.523132i	$-0.824764\pi$
$67$	−3.07561	−	11.4783i	−0.375746	−	1.40230i	0.476506	−	0.879171i	$-0.341903\pi$
$68$	−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	$0.434611\pi$
$72$	−0.0554326	−	0.206877i	−0.00653279	−	0.0243807i
$73$	−13.0991	−	3.50990i	−1.53314	−	0.410802i	−0.609095	−	0.793097i	$-0.708467\pi$
$73$	−13.0991	−	3.50990i	−1.53314	−	0.410802i	−0.924041	+	0.382295i	$0.875134\pi$
$74$	−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
$78$	−1.38849	+	5.18191i	−0.157216	+	0.586736i
$79$	2.48836	+	4.30996i	0.279962	+	0.484908i	0.971375	−	0.237551i	$-0.0763448\pi$
$79$	2.48836	+	4.30996i	0.279962	+	0.484908i	−0.691413	+	0.722460i	$0.743012\pi$
$80$		0			0
$81$	−4.15580	−	7.19806i	−0.461756	−	0.799784i
$82$	5.71910	−	1.53243i	0.631569	−	0.169228i
$83$	−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	−0.196787	−	0.980446i	$-0.563051\pi$
$89$	7.08207	−	12.2665i	0.750698	−	1.30025i	0.947485	−	0.319801i	$-0.103616\pi$
$90$		0			0
$91$	−11.0620	−	6.38664i	−1.15961	−	0.669502i
$92$	−1.02856	+	3.83864i	−0.107235	+	0.400205i
$93$	−0.924071	−	0.247604i	−0.0958217	−	0.0256754i
$94$	12.2001			1.25835
$95$		0			0
$96$	1.66908			0.170350
$97$	−2.31297	−	0.619757i	−0.234846	−	0.0629268i	0.139476	−	0.990225i	$-0.455458\pi$
$97$	−2.31297	−	0.619757i	−0.234846	−	0.0629268i	−0.374323	+	0.927299i	$0.622125\pi$
$98$	2.27581	−	8.49345i	0.229892	−	0.857968i
$99$	−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	$-0.00741537\pi$
$103$	9.90973	+	9.90973i	0.976435	+	0.976435i	−0.0232940	+	0.999729i	$0.507415\pi$
$104$	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	$-0.788384\pi$
$107$	−1.75977	+	1.75977i	−0.170124	+	0.170124i	0.616910	+	0.787034i	$0.288384\pi$
$108$	−5.18191	+	1.38849i	−0.498630	+	0.133607i
$109$	1.33809	+	2.31764i	0.128166	+	0.221990i	0.922966	−	0.384881i	$-0.125758\pi$
$109$	1.33809	+	2.31764i	0.128166	+	0.221990i	−0.794800	+	0.606871i	$0.792424\pi$
$110$		0			0
$111$	8.55233	+	14.8131i	0.811752	+	1.40599i
$112$	−1.02856	+	3.83864i	−0.0971897	+	0.362717i
$113$	−6.56319	−	6.56319i	−0.617413	−	0.617413i	0.327454	−	0.944867i	$-0.393809\pi$
$113$	−6.56319	−	6.56319i	−0.617413	−	0.617413i	−0.944867	+	0.327454i	$0.893809\pi$
$114$	−6.50263	−	3.26289i	−0.609027	−	0.305598i
$115$		0			0
$116$	3.62760	−	2.09440i	0.336814	−	0.194460i
$117$	−0.664939	−	0.178170i	−0.0614737	−	0.0164718i
$118$	−1.94474	−	7.25788i	−0.179028	−	0.668142i
$119$	−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
$123$	−2.55774	−	9.54562i	−0.230624	−	0.860700i
$124$	−0.286586	+	0.496381i	−0.0257362	+	0.0445764i
$125$		0			0
$126$		−	0.851142i		−	0.0758257i
$127$	3.35965	+	12.5384i	0.298121	+	1.11260i	0.938707	+	0.344715i	$0.112025\pi$
$127$	3.35965	+	12.5384i	0.298121	+	1.11260i	−0.640587	+	0.767886i	$0.721309\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−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
$133$	11.5114	−	12.9444i	0.998163	−	1.12242i
$134$			11.8833i			1.02656i
$135$		0			0
$136$	3.56199	−	2.05652i	0.305438	−	0.176345i
$137$	−0.761069	+	0.203928i	−0.0650225	+	0.0174227i	−0.291184	−	0.956667i	$-0.594049\pi$
$137$	−0.761069	+	0.203928i	−0.0650225	+	0.0174227i	0.226161	+	0.974090i	$0.427382\pi$
$138$	6.40699	+	1.71675i	0.545399	+	0.146139i
$139$	−12.5016	−	7.21779i	−1.06037	−	0.612205i	−0.134836	−	0.990868i	$-0.543051\pi$
$139$	−12.5016	−	7.21779i	−1.06037	−	0.612205i	−0.925535	+	0.378663i	$0.876384\pi$
$140$		0			0
$141$		−	20.3630i		−	1.71487i
$142$	5.09228	−	1.36447i	0.427334	−	0.114504i
$143$	17.3205	−	4.64102i	1.44841	−	0.388101i
$144$			0.214175i			0.0178479i
$145$		0			0
$146$	11.7443	+	6.78060i	0.971969	+	0.561167i
$147$	−14.1762	−	3.79851i	−1.16924	−	0.313296i
$148$	9.89878	−	2.65237i	0.813674	−	0.218023i
$149$	10.9655	−	6.33092i	0.898327	−	0.518649i	0.0216699	−	0.999765i	$-0.493102\pi$
$149$	10.9655	−	6.33092i	0.898327	−	0.518649i	0.876657	+	0.481116i	$0.159768\pi$
$150$		0			0
$151$			14.7958i			1.20407i	0.798470	+	0.602034i	$0.205643\pi$
$151$			14.7958i			1.20407i	−0.798470	+	0.602034i	$0.794357\pi$
$152$	−2.89664	+	3.25722i	−0.234948	+	0.264196i
$153$	−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
$157$	−1.64480	+	6.13849i	−0.131270	+	0.489905i	−0.999985	−	0.00540611i	$-0.998279\pi$
$157$	−1.64480	+	6.13849i	−0.131270	+	0.489905i	0.868716	+	0.495311i	$0.164946\pi$
$158$	−1.28807	−	4.80713i	−0.102473	−	0.382435i
$159$		−	6.33092i		−	0.502075i
$160$		0			0
$161$	−7.89653	+	13.6772i	−0.622334	+	1.07791i
$162$	2.15120	+	8.02839i	0.169014	+	0.630770i
$163$	−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
$167$	−0.667465	−	2.49101i	−0.0516500	−	0.192760i	0.935280	−	0.353908i	$-0.115147\pi$
$167$	−0.667465	−	2.49101i	−0.0516500	−	0.192760i	−0.986930	+	0.161147i	$0.948481\pi$
$168$	6.40699	+	1.71675i	0.494310	+	0.132450i
$169$	−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
$173$	0.524511	−	1.95750i	0.0398778	−	0.148826i	−0.943116	−	0.332463i	$-0.892120\pi$
$173$	0.524511	−	1.95750i	0.0398778	−	0.148826i	0.982994	+	0.183637i	$0.0587870\pi$
$174$	−3.49571	−	6.05475i	−0.265009	−	0.459010i
$175$		0			0
$176$	−2.78944	−	4.83146i	−0.210262	−	0.364185i
$177$	−12.1140	+	3.24593i	−0.910542	+	0.243979i
$178$	−10.0156	+	10.0156i	−0.750698	+	0.750698i
$179$	21.3656			1.59694			0.798471	−	0.602034i	$-0.205643\pi$
$179$	21.3656			1.59694			0.798471	+	0.602034i	$0.205643\pi$
$180$		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
$187$	5.93890	−	22.1643i	0.434295	−	1.62081i
$188$	−11.7844	−	3.15762i	−0.859466	−	0.230293i
$189$	−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	$0.267938\pi$
$192$	−1.61221	−	0.431989i	−0.116351	−	0.0311762i
$193$	−2.21163	+	8.25393i	−0.159197	+	0.594131i	0.839512	+	0.543340i	$0.182841\pi$
$193$	−2.21163	+	8.25393i	−0.159197	+	0.594131i	−0.998709	+	0.0507904i	$0.983826\pi$
$194$	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	$-0.158302\pi$
$199$	12.7686	+	7.37195i	0.905141	+	0.522584i	0.0262767	+	0.999655i	$0.491635\pi$
$200$		0			0
$201$	19.8341			1.39899
$202$	0.340442	−	0.340442i	0.0239534	−	0.0239534i
$203$	16.0793	−	4.30842i	1.12854	−	0.302392i
$204$	−3.43249	−	5.94525i	−0.240322	−	0.416250i
$205$		0			0
$206$	−7.00724	−	12.1369i	−0.488217	−	0.845617i
$207$	−0.220292	+	0.822140i	−0.0153113	+	0.0571427i
$208$	−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	$0.570997\pi$
$212$	−3.66382	−	0.981717i	−0.251632	−	0.0674246i
$213$	−2.27741	−	8.49941i	−0.156046	−	0.582370i
$214$	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
$218$	−0.692648	−	2.58500i	−0.0469120	−	0.175078i
$219$	11.3174	−	19.6022i	0.764756	−	1.32460i
$220$		0			0
$221$		−	13.2200i		−	0.889274i
$222$	−4.42701	−	16.5218i	−0.297122	−	1.10887i
$223$	3.96208	−	14.7867i	0.265321	−	0.990190i	−0.696733	−	0.717330i	$-0.745364\pi$
$223$	3.96208	−	14.7867i	0.265321	−	0.990190i	0.962054	−	0.272860i	$-0.0879695\pi$
$224$	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	$-0.520993\pi$
$227$	14.0408	−	14.0408i	0.931921	−	0.931921i	0.997826	+	0.0659048i	$0.0209934\pi$
$228$	5.43656	+	4.83471i	0.360045	+	0.320187i
$229$			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
$232$	−4.04606	+	1.08414i	−0.265637	+	0.0711773i
$233$	7.75045	+	2.07673i	0.507749	+	0.136051i	0.503594	−	0.863940i	$-0.332011\pi$
$233$	7.75045	+	2.07673i	0.507749	+	0.136051i	0.00415495	+	0.999991i	$0.498677\pi$
$234$	0.596168	+	0.344198i	0.0389727	+	0.0225009i
$235$		0			0
$236$			7.51391i			0.489114i
$237$	−8.02349	+	2.14989i	−0.521181	+	0.139650i
$238$	15.7884	−	4.23050i	1.02341	−	0.274223i
$239$			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	0.838774	−	0.544479i	$-0.183273\pi$
$241$	12.2118	+	7.05046i	0.786628	+	0.454160i	−0.0521460	+	0.998639i	$0.516606\pi$
$242$	−19.4383	−	5.20847i	−1.24954	−	0.334813i
$243$	−2.14572	+	0.574944i	−0.137648	+	0.0368827i
$244$	−1.83942	+	1.06199i	−0.117757	+	0.0679870i
$245$		0			0
$246$			9.88236i			0.630076i
$247$	4.41152	+	13.2976i	0.280698	+	0.846106i
$248$	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	$0.00336127\pi$
$252$	−0.220292	+	0.822140i	−0.0138771	+	0.0517899i
$253$	−5.73822	−	21.4153i	−0.360759	−	1.34637i
$254$		−	12.9807i		−	0.814481i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.21532	+	4.53563i	0.0758095	+	0.282925i	0.993416	−	0.114566i	$-0.0365477\pi$
$257$	1.21532	+	4.53563i	0.0758095	+	0.282925i	−0.917606	+	0.397491i	$0.869881\pi$
$258$	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
$262$	−2.51901	−	9.40108i	−0.155625	−	0.580801i
$263$	19.8765	+	5.32590i	1.22564	+	0.328409i	0.812880	−	0.582431i	$-0.197898\pi$
$263$	19.8765	+	5.32590i	1.22564	+	0.328409i	0.412759	+	0.910840i	$0.364565\pi$
$264$	−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
$268$	3.07561	−	11.4783i	0.187873	−	0.701151i
$269$	−4.61436	−	7.99231i	−0.281343	−	0.487300i	0.690373	−	0.723454i	$-0.257446\pi$
$269$	−4.61436	−	7.99231i	−0.281343	−	0.487300i	−0.971716	+	0.236154i	$0.924113\pi$
$270$		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	$-0.441243\pi$
$272$	−3.97289	+	1.06453i	−0.240892	+	0.0645467i
$273$	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	−0.0607743	−	0.998152i	$-0.519357\pi$
$281$	−16.0185	−	9.24831i	−0.955586	−	0.551708i	−0.894812	+	0.446444i	$0.852690\pi$
$282$	−5.27032	+	19.6691i	−0.313843	+	1.17128i
$283$	14.8499	+	3.97901i	0.882733	+	0.236528i	0.671586	−	0.740927i	$-0.265613\pi$
$283$	14.8499	+	3.97901i	0.882733	+	0.236528i	0.211147	+	0.977454i	$0.432280\pi$
$284$	−5.27191			−0.312830
$285$		0			0
$286$	−17.9315			−1.06031
$287$	−22.7280	−	6.08994i	−1.34159	−	0.359478i
$288$	0.0554326	−	0.206877i	0.00326640	−	0.0121904i
$289$	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	$-0.273619\pi$
$293$	−1.79454	−	1.79454i	−0.104838	−	0.104838i	−0.757580	+	0.652742i	$0.773619\pi$
$294$	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
$298$	−12.2304	+	3.27713i	−0.708488	+	0.189839i
$299$	−6.38664	−	11.0620i	−0.369349	−	0.639731i
$300$		0			0
$301$	11.0620	+	19.1599i	0.637603	+	1.10436i
$302$	3.82945	−	14.2917i	0.220360	−	0.822394i
$303$	−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
$307$	−5.53039	−	1.48186i	−0.315636	−	0.0845744i	0.0975232	−	0.995233i	$-0.468908\pi$
$307$	−5.53039	−	1.48186i	−0.315636	−	0.0845744i	−0.413159	+	0.910659i	$0.635575\pi$
$308$	−5.73822	−	21.4153i	−0.326965	−	1.22025i
$309$	−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
$313$	−1.68078	−	6.27274i	−0.0950030	−	0.354556i	0.902017	−	0.431701i	$-0.142086\pi$
$313$	−1.68078	−	6.27274i	−0.0950030	−	0.354556i	−0.997020	+	0.0771446i	$0.975420\pi$
$314$	3.17752	−	5.50362i	0.179318	−	0.310587i
$315$		0			0
$316$			4.97671i			0.279962i
$317$	−1.59960	−	5.96979i	−0.0898425	−	0.335297i	0.906345	−	0.422539i	$-0.138861\pi$
$317$	−1.59960	−	5.96979i	−0.0898425	−	0.335297i	−0.996187	+	0.0872424i	$0.972195\pi$
$318$	−1.63856	+	6.11520i	−0.0918860	+	0.342923i
$319$	−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
$323$	17.5592	+	3.61926i	0.977019	+	0.201381i
$324$		−	8.31160i		−	0.461756i
$325$		0			0
$326$	16.6312	−	9.60204i	0.921118	−	0.531808i
$327$	−4.31456	+	1.15608i	−0.238596	+	0.0639316i
$328$	5.71910	+	1.53243i	0.315784	+	0.0846141i
$329$	−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	$0.699961\pi$
$332$	−9.97713	+	2.67336i	−0.547566	+	0.146720i
$333$	2.12007	−	0.568071i	0.116179	−	0.0311301i
$334$			2.57889i			0.141110i
$335$		0			0
$336$	−5.74435	−	3.31650i	−0.313380	−	0.180930i
$337$	31.0900	+	8.33054i	1.69358	+	0.453793i	0.971310	−	0.237818i	$-0.0764322\pi$
$337$	31.0900	+	8.33054i	1.69358	+	0.453793i	0.722270	+	0.691611i	$0.243099\pi$
$338$	2.57813	−	0.690809i	0.140232	−	0.0375750i
$339$	13.4165	−	7.74599i	0.728682	−	0.420705i
$340$		0			0
$341$		−	3.19766i		−	0.173163i
$342$	−0.620387	+	0.697616i	−0.0335467	+	0.0377227i
$343$	−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
$347$	−5.54741	+	20.7032i	−0.297801	+	1.11141i	0.641167	+	0.767401i	$0.278451\pi$
$347$	−5.54741	+	20.7032i	−0.297801	+	1.11141i	−0.938968	+	0.344005i	$0.888216\pi$
$348$	1.80951	+	6.75320i	0.0970002	+	0.362010i
$349$			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
$352$	1.44392	+	5.38879i	0.0769613	+	0.287224i
$353$	−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
$357$	−7.06104	−	26.3522i	−0.373710	−	1.39470i
$358$	−20.6376	−	5.52983i	−1.09073	−	0.292261i
$359$	12.8174	−	7.40015i	0.676478	−	0.390565i	−0.122049	−	0.992524i	$-0.538946\pi$
$359$	12.8174	−	7.40015i	0.676478	−	0.390565i	0.798527	+	0.601959i	$0.205613\pi$
$360$		0			0
$361$	−18.8700	+	2.21900i	−0.993157	+	0.116790i
$362$	−2.24075	−	2.24075i	−0.117771	−	0.117771i
$363$	−8.69335	+	32.4440i	−0.456282	+	1.70287i
$364$	−6.38664	−	11.0620i	−0.334751	−	0.579806i
$365$		0			0
$366$	1.77255	+	3.07014i	0.0926526	+	0.160479i
$367$	21.3376	−	5.71739i	1.11381	−	0.298446i	0.345436	−	0.938442i	$-0.387731\pi$
$367$	21.3376	−	5.71739i	1.11381	−	0.298446i	0.768378	+	0.639997i	$0.221064\pi$
$368$	−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	$-0.288163\pi$
$373$	−3.26677	−	3.26677i	−0.169147	−	0.169147i	−0.786604	+	0.617457i	$0.788163\pi$
$374$	−11.4731	+	19.8719i	−0.593259	+	1.02755i
$375$		0			0
$376$	10.5656	+	6.10006i	0.544880	+	0.314586i
$377$	−3.48461	+	13.0048i	−0.179467	+	0.669779i
$378$	20.5932	+	5.51793i	1.05920	+	0.283811i
$379$	24.1730			1.24168			0.620841	−	0.783937i	$-0.286791\pi$
$379$	24.1730			1.24168			0.620841	+	0.783937i	$0.286791\pi$
$380$		0			0
$381$	−21.6658			−1.10997
$382$	−17.7856	−	4.76563i	−0.909989	−	0.243831i
$383$	−6.80409	+	25.3932i	−0.347673	+	1.29753i	0.541786	+	0.840517i	$0.317748\pi$
$383$	−6.80409	+	25.3932i	−0.347673	+	1.29753i	−0.889458	+	0.457016i	$0.848918\pi$
$384$	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	$-0.652976\pi$
$389$	−28.8228	−	16.6409i	−1.46138	−	0.843726i	−0.999075	+	0.0429969i	$0.986309\pi$
$390$		0			0
$391$	−16.3454			−0.826622
$392$	6.21763	−	6.21763i	0.314038	−	0.314038i
$393$	−15.6912	+	4.20443i	−0.791514	+	0.212085i
$394$	−4.51561	−	7.82126i	−0.227493	−	0.394030i
$395$		0			0
$396$	−0.597429	−	1.03478i	−0.0300219	−	0.0519995i
$397$	4.90913	−	18.3211i	0.246382	−	0.919510i	−0.726302	−	0.687376i	$-0.758763\pi$
$397$	4.90913	−	18.3211i	0.246382	−	0.919510i	0.972684	−	0.232134i	$-0.0745708\pi$
$398$	−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	$0.0713619\pi$
$402$	−19.1583	−	5.13344i	−0.955527	−	0.256033i
$403$	−0.476816	−	1.77950i	−0.0237519	−	0.0886432i
$404$	−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
$408$	1.77679	+	6.63106i	0.0879641	+	0.328286i
$409$	−1.12100	+	1.94163i	−0.0554298	+	0.0960073i	−0.892409	−	0.451228i	$-0.850986\pi$
$409$	−1.12100	+	1.94163i	−0.0554298	+	0.0960073i	0.836979	+	0.547235i	$0.184320\pi$
$410$		0			0
$411$		−	1.31510i		−	0.0648689i
$412$	3.62721	+	13.5369i	0.178700	+	0.666917i
$413$	−7.72850	+	28.8432i	−0.380295	+	1.41928i
$414$	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
$418$	4.90914	−	23.8171i	0.240114	−	1.16493i
$419$			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	−0.816320	−	0.577600i	$-0.803989\pi$
$421$	−14.8606	+	8.57980i	−0.724264	+	0.418154i	0.0920564	+	0.995754i	$0.470656\pi$
$422$	19.0589	−	5.10683i	0.927774	−	0.248596i
$423$	−2.52393	−	0.676284i	−0.122717	−	0.0328820i
$424$	3.28489	+	1.89653i	0.159528	+	0.0921037i
$425$		0			0
$426$			8.79924i			0.426325i
$427$	−8.15320	+	2.18464i	−0.394561	+	0.105722i
$428$	−2.40390	+	0.644122i	−0.116197	+	0.0311348i
$429$			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	$0.500346\pi$
$432$	−5.18191	−	1.38849i	−0.249315	−	0.0668037i
$433$	−36.2323	+	9.70841i	−1.74121	+	0.466556i	−0.982716	−	0.185121i	$-0.940732\pi$
$433$	−36.2323	+	9.70841i	−1.74121	+	0.466556i	−0.758496	+	0.651678i	$0.774066\pi$
$434$	1.97264	−	1.13891i	0.0946899	−	0.0546693i
$435$		0			0
$436$			2.67618i			0.128166i
$437$	16.4413	−	5.45446i	0.786495	−	0.260922i
$438$	−16.0052	+	16.0052i	−0.764756	+	0.764756i
$439$	−8.85200	−	15.3321i	−0.422483	−	0.731762i	0.573699	−	0.819066i	$-0.305508\pi$
$439$	−8.85200	−	15.3321i	−0.422483	−	0.731762i	−0.996182	+	0.0873044i	$0.972175\pi$
$440$		0			0
$441$	−0.941627	+	1.63095i	−0.0448394	+	0.0776641i
$442$	−3.42159	+	12.7695i	−0.162748	+	0.607385i
$443$	1.58801	+	5.92652i	0.0754485	+	0.281578i	0.993335	−	0.115266i	$-0.0367721\pi$
$443$	1.58801	+	5.92652i	0.0754485	+	0.281578i	−0.917886	+	0.396844i	$0.870105\pi$
$444$			17.1047i			0.811752i
$445$		0			0
$446$	−7.65416	+	13.2574i	−0.362435	+	0.627755i
$447$	5.46978	+	20.4135i	0.258712	+	0.965526i
$448$	−2.81008	+	2.81008i	−0.132764	+	0.132764i
$449$	10.8678			0.512883			0.256441	−	0.966560i	$-0.417450\pi$
$449$	10.8678			0.512883			0.256441	+	0.966560i	$0.417450\pi$
$450$		0			0
$451$	28.6063	−	16.5159i	1.34702	−	0.777702i
$452$	−2.40230	−	8.96549i	−0.112994	−	0.421701i
$453$	−23.8540	−	6.39165i	−1.12076	−	0.300306i
$454$	−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	$0.666139\pi$
$458$	3.93374	−	14.6809i	0.183812	−	0.685994i
$459$	−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	$0.532733\pi$
$462$	−35.7439	+	9.57754i	−1.66295	+	0.445587i
$463$	−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
$472$	1.94474	−	7.25788i	0.0895141	−	0.334071i
$473$	−30.0000	−	8.03848i	−1.37940	−	0.369610i
$474$	8.30652			0.381531
$475$		0			0
$476$	−16.3454			−0.749190
$477$	−0.784698	−	0.210259i	−0.0359289	−	0.00962711i
$478$	3.79164	−	14.1506i	0.173425	−	0.647233i
$479$	−29.0760	−	16.7870i	−1.32852	−	0.767019i	−0.343445	−	0.939173i	$-0.611594\pi$
$479$	−29.0760	−	16.7870i	−1.32852	−	0.767019i	−0.985070	+	0.172154i	$0.944927\pi$
$480$		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	$-0.474269\pi$
$487$	23.7780	−	23.7780i	1.07748	−	1.07748i	0.996734	−	0.0807490i	$-0.0257312\pi$
$488$	2.05161	−	0.549727i	0.0928720	−	0.0248850i
$489$	−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	$0.833628\pi$
$492$	2.55774	−	9.54562i	0.115312	−	0.430350i
$493$	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
$497$	−20.2370	−	5.42248i	−0.907751	−	0.243231i
$498$	4.46205	+	16.6526i	0.199949	+	0.746221i
$499$	17.8866	−	10.3269i	0.800716	−	0.462293i	−0.0430056	−	0.999075i	$-0.513693\pi$
$499$	17.8866	−	10.3269i	0.800716	−	0.462293i	0.843721	+	0.536781i	$0.180360\pi$
$500$		0			0
$501$	4.30437			0.192305
$502$	−10.9972	+	10.9972i	−0.490827	+	0.490827i
$503$	3.22065	+	12.0196i	0.143602	+	0.535928i	0.999814	+	0.0193038i	$0.00614497\pi$
$503$	3.22065	+	12.0196i	0.143602	+	0.535928i	−0.856212	+	0.516624i	$0.827188\pi$
$504$	0.425571	−	0.737110i	0.0189564	−	0.0328335i
$505$		0			0
$506$			22.1708i			0.985611i
$507$	−1.15301	−	4.30311i	−0.0512072	−	0.191108i
$508$	−3.35965	+	12.5384i	−0.149060	+	0.556301i
$509$	8.59703	−	14.8905i	0.381057	−	0.660009i	−0.610157	−	0.792281i	$-0.708894\pi$
$509$	8.59703	−	14.8905i	0.381057	−	0.660009i	0.991214	+	0.132271i	$0.0422270\pi$
$510$		0			0
$511$	−26.9464	−	46.6726i	−1.19204	−	2.06467i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	17.4741	+	15.5396i	0.771499	+	0.686091i
$514$		−	4.69563i		−	0.207116i
$515$		0			0
$516$	−8.04707	+	4.64598i	−0.354252	+	0.204528i
$517$	65.7439	−	17.6160i	2.89141	−	0.774752i
$518$	−39.3382	−	10.5406i	−1.72842	−	0.463129i
$519$	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	$-0.0559961\pi$
$522$	−0.866566	+	0.232196i	−0.0379286	+	0.0101629i
$523$	−14.7144	+	3.94272i	−0.643417	+	0.172403i	−0.565751	−	0.824576i	$-0.691414\pi$
$523$	−14.7144	+	3.94272i	−0.643417	+	0.172403i	−0.0776662	+	0.996979i	$0.524747\pi$
$524$			9.73272i			0.425176i
$525$		0			0
$526$	−17.8208	−	10.2889i	−0.777024	−	0.448615i
$527$	−2.27715	−	0.610159i	−0.0991940	−	0.0265790i
$528$	8.99432	−	2.41002i	0.391427	−	0.104883i
$529$	6.24139	−	3.60347i	0.271365	−	0.156673i
$530$		0			0
$531$			1.60929i			0.0698373i
$532$	16.4413	−	5.45446i	0.712822	−	0.236481i
$533$	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
$537$	−9.22972	+	34.4458i	−0.398292	+	1.48645i
$538$	2.38857	+	8.91427i	0.102979	+	0.384321i
$539$		−	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	$0.133944\pi$
$542$	6.47235	+	24.1551i	0.278011	+	1.03755i
$543$	−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
$547$	1.13342	+	4.22997i	0.0484614	+	0.180860i	0.985914	−	0.167252i	$-0.0534894\pi$
$547$	1.13342	+	4.22997i	0.0484614	+	0.180860i	−0.937453	+	0.348113i	$0.886823\pi$
$548$	−0.761069	−	0.203928i	−0.0325113	−	0.00871137i
$549$	−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
$553$	−5.11884	+	19.1038i	−0.217675	+	0.812375i
$554$	−7.87234	−	13.6353i	−0.334464	−	0.579308i
$555$		0			0
$556$	−7.21779	−	12.5016i	−0.306103	−	0.530185i
$557$	−35.5939	+	9.53737i	−1.50816	+	0.404111i	−0.915825	−	0.401578i	$-0.868462\pi$
$557$	−35.5939	+	9.53737i	−1.50816	+	0.404111i	−0.592339	+	0.805689i	$0.701795\pi$
$558$	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	$-0.418630\pi$
$563$	−16.9569	−	16.9569i	−0.714648	−	0.714648i	−0.967504	+	0.252856i	$0.918630\pi$
$564$	10.1815	−	17.6348i	0.428718	−	0.742561i
$565$		0			0
$566$	−13.3140	−	7.68686i	−0.559630	−	0.323103i
$567$	8.54898	−	31.9052i	0.359023	−	1.33989i
$568$	5.09228	+	1.36447i	0.213667	+	0.0572519i
$569$	20.7088			0.868160			0.434080	−	0.900874i	$-0.357073\pi$
$569$	20.7088			0.868160			0.434080	+	0.900874i	$0.357073\pi$
$570$		0			0
$571$	44.7544			1.87291			0.936457	−	0.350782i	$-0.114084\pi$
$571$	44.7544			1.87291			0.936457	+	0.350782i	$0.114084\pi$
$572$	17.3205	+	4.64102i	0.724207	+	0.194051i
$573$	−7.95421	+	29.6855i	−0.332292	+	1.24013i
$574$	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
$583$	20.4400	−	5.47689i	0.846539	−	0.226829i
$584$	6.78060	+	11.7443i	0.280583	+	0.485985i
$585$		0			0
$586$	1.26893	+	2.19785i	0.0524190	+	0.0907923i
$587$	4.05541	−	15.1350i	0.167385	−	0.624689i	−0.830339	−	0.557258i	$-0.811853\pi$
$587$	4.05541	−	15.1350i	0.167385	−	0.624689i	0.997724	−	0.0674303i	$-0.0214800\pi$
$588$	−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
$592$	9.89878	+	2.65237i	0.406837	+	0.109012i
$593$	4.03459	+	15.0573i	0.165681	+	0.618329i	0.997952	+	0.0639609i	$0.0203733\pi$
$593$	4.03459	+	15.0573i	0.165681	+	0.618329i	−0.832272	+	0.554368i	$0.812960\pi$
$594$	−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
$598$	3.30597	+	12.3380i	0.135191	+	0.504540i
$599$	−13.8776	+	24.0366i	−0.567022	+	0.982110i	0.429837	+	0.902907i	$0.358571\pi$
$599$	−13.8776	+	24.0366i	−0.567022	+	0.982110i	−0.996858	+	0.0792037i	$0.974762\pi$
$600$		0			0
$601$			5.35237i			0.218328i	0.994024	+	0.109164i	$0.0348173\pi$
$601$			5.35237i			0.218328i	−0.994024	+	0.109164i	$0.965183\pi$
$602$	−5.72611	−	21.3701i	−0.233379	−	0.870981i
$603$	0.658719	−	2.45837i	0.0268251	−	0.100113i
$604$	−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	$-0.923473\pi$
$607$	−18.0625	+	18.0625i	−0.733133	+	0.733133i	0.238106	+	0.971239i	$0.423473\pi$
$608$	−4.13717	+	1.37252i	−0.167784	+	0.0556630i
$609$			27.7843i			1.12588i
$610$		0			0
$611$	33.9597	−	19.6067i	1.37386	−	0.793200i
$612$	−0.850893	+	0.227996i	−0.0343953	+	0.00921619i
$613$	13.0713	+	3.50245i	0.527946	+	0.141463i	0.512940	−	0.858425i	$-0.328556\pi$
$613$	13.0713	+	3.50245i	0.527946	+	0.141463i	0.0150066	+	0.999887i	$0.495223\pi$
$614$	4.95841	+	2.86274i	0.200105	+	0.115531i
$615$		0			0
$616$			22.1708i			0.893286i
$617$	7.91702	−	2.12136i	0.318727	−	0.0854027i	−0.0959086	−	0.995390i	$-0.530576\pi$
$617$	7.91702	−	2.12136i	0.318727	−	0.0854027i	0.414636	+	0.909987i	$0.363909\pi$
$618$	22.5942	−	6.05411i	0.908873	−	0.243532i
$619$			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
$622$	15.2549	+	4.08755i	0.611667	+	0.163896i
$623$	54.3710	−	14.5687i	2.17833	−	0.583681i
$624$	4.64598	−	2.68236i	0.185988	−	0.107380i
$625$		0			0
$626$			6.49402i			0.259553i
$627$	−39.7527	−	8.19374i	−1.58757	−	0.327226i
$628$	−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	$0.975942\pi$
$632$	1.28807	−	4.80713i	0.0512366	−	0.191218i
$633$	−8.52370	−	31.8109i	−0.338786	−	1.26437i
$634$			6.18038i			0.245454i
$635$		0			0
$636$	3.16546	−	5.48274i	0.125519	−	0.217405i
$637$	−7.31486	−	27.2994i	−0.289825	−	1.08164i
$638$	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	$0.178499\pi$
$642$	1.07509	+	4.01229i	0.0424304	+	0.158353i
$643$	9.95594	+	2.66769i	0.392624	+	0.105203i	0.449729	−	0.893165i	$-0.351520\pi$
$643$	9.95594	+	2.66769i	0.392624	+	0.105203i	−0.0571053	+	0.998368i	$0.518187\pi$
$644$	−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	$0.794551\pi$
$648$	−2.15120	+	8.02839i	−0.0845072	+	0.315385i
$649$	−20.9596	−	36.3031i	−0.822737	−	1.42502i
$650$		0			0
$651$	−1.90092	−	3.29250i	−0.0745031	−	0.129043i
$652$	−18.5497	+	4.97038i	−0.726463	+	0.194655i
$653$	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	$-0.779167\pi$
$659$	4.34736	−	7.52985i	0.169349	−	0.293321i	0.938191	+	0.346117i	$0.112500\pi$
$660$		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	$0.919970\pi$
$662$	7.61968	−	28.4370i	0.296147	−	1.10524i
$663$	21.3134	+	5.71090i	0.827743	+	0.221793i
$664$	10.3291			0.400846
$665$		0			0
$666$	−2.19486			−0.0850490
$667$	16.0793	+	4.30842i	0.622591	+	0.166823i
$668$	0.667465	−	2.49101i	0.0258250	−	0.0963802i
$669$	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	$-0.228670\pi$
$673$	2.45665	+	2.45665i	0.0946967	+	0.0946967i	−0.658171	+	0.752868i	$0.728670\pi$
$674$	−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	$-0.593393\pi$
$677$	17.3822	−	17.3822i	0.668053	−	0.668053i	0.957265	+	0.289212i	$0.0933932\pi$
$678$	−14.9641	+	4.00962i	−0.574693	+	0.153989i
$679$	−4.75805	−	8.24118i	−0.182597	−	0.316267i
$680$		0			0
$681$	16.5712	+	28.7022i	0.635010	+	1.09987i
$682$	−0.827616	+	3.08870i	−0.0316910	+	0.118273i
$683$	−24.5836	−	24.5836i	−0.940667	−	0.940667i	0.0576691	−	0.998336i	$-0.481633\pi$
$683$	−24.5836	−	24.5836i	−0.940667	−	0.940667i	−0.998336	+	0.0576691i	$0.981633\pi$
$684$	0.779804	−	0.513277i	0.0298166	−	0.0196256i
$685$		0			0
$686$	6.17105	−	3.56286i	0.235612	−	0.136031i
$687$	−24.5036	−	6.56572i	−0.934871	−	0.250498i
$688$	1.44088	+	5.37742i	0.0549329	+	0.205012i
$689$	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
$693$	−1.22898	−	4.58663i	−0.0466852	−	0.174232i
$694$	10.7168	−	18.5620i	0.406803	−	0.704604i
$695$		0			0
$696$		−	6.99143i		−	0.265009i
$697$	−6.30293	−	23.5228i	−0.238740	−	0.890991i
$698$	4.71979	−	17.6145i	0.178647	−	0.666719i
$699$	−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
$703$	−33.3799	−	29.6846i	−1.25895	−	1.11958i
$704$		−	5.57889i		−	0.210262i
$705$		0			0
$706$	17.8864	−	10.3267i	0.673164	−	0.388652i
$707$	−1.84814	+	0.495208i	−0.0695066	+	0.0186242i
$708$	−12.1140	−	3.24593i	−0.455271	−	0.121990i
$709$	−21.2658	−	12.2778i	−0.798654	−	0.461103i	0.0443465	−	0.999016i	$-0.485879\pi$
$709$	−21.2658	−	12.2778i	−0.798654	−	0.461103i	−0.843000	+	0.537913i	$0.819213\pi$
$710$		0			0
$711$			1.06589i			0.0399739i
$712$	−13.6815	+	3.66595i	−0.512736	+	0.137387i
$713$	−2.20020	+	0.589541i	−0.0823981	+	0.0220785i
$714$			27.2818i			1.02099i
$715$		0			0
$716$	18.5032	+	10.6828i	0.691496	+	0.399235i
$717$	−23.6184	−	6.32854i	−0.882047	−	0.236344i
$718$	−14.2960	+	3.83060i	−0.533522	+	0.142957i
$719$	20.5077	−	11.8401i	0.764808	−	0.441562i	−0.0662111	−	0.997806i	$-0.521091\pi$
$719$	20.5077	−	11.8401i	0.764808	−	0.441562i	0.831020	+	0.556243i	$0.187758\pi$
$720$		0			0
$721$			55.6942i			2.07416i
$722$	18.8013	+	2.74052i	0.699713	+	0.101992i
$723$	−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
$727$	0.315088	−	1.17593i	0.0116860	−	0.0436127i	−0.959837	−	0.280559i	$-0.909480\pi$
$727$	0.315088	−	1.17593i	0.0116860	−	0.0436127i	0.971523	+	0.236947i	$0.0761467\pi$
$728$	3.30597	+	12.3380i	0.122527	+	0.457278i
$729$		−	28.6425i		−	1.06083i
$730$		0			0
$731$	−11.4489	+	19.8300i	−0.423452	+	0.733440i
$732$	−0.917538	−	3.42430i	−0.0339132	−	0.126566i
$733$	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
$737$	17.1585	+	64.0364i	0.632041	+	2.35881i
$738$	1.22489	+	0.328208i	0.0450887	+	0.0120815i
$739$	−27.8620	+	16.0861i	−1.02492	+	0.591738i	−0.915525	−	0.402261i	$-0.868225\pi$
$739$	−27.8620	+	16.0861i	−1.02492	+	0.591738i	−0.109395	+	0.993998i	$0.534891\pi$
$740$		0			0
$741$	−23.3442	+	1.36786i	−0.857571	+	0.0502496i
$742$	10.6588	+	10.6588i	0.391297	+	0.391297i
$743$	−0.571198	+	2.13174i	−0.0209552	+	0.0782059i	−0.975612	−	0.219504i	$-0.929556\pi$
$743$	−0.571198	+	2.13174i	−0.0209552	+	0.0782059i	0.954656	+	0.297710i	$0.0962228\pi$
$744$	0.478335	+	0.828500i	0.0175366	+	0.0303743i
$745$		0			0
$746$	2.30996	+	4.00096i	0.0845736	+	0.146486i
$747$	−2.13685	+	0.572567i	−0.0781833	+	0.0209491i
$748$	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
$757$	12.0906	−	45.1229i	0.439442	−	1.64002i	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	12.0906	−	45.1229i	0.439442	−	1.64002i	0.730207	−	0.683226i	$-0.239424\pi$
$758$	−23.3493	−	6.25642i	−0.848084	−	0.227243i
$759$	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	$0.480706\pi$
$762$	20.9275	+	5.60752i	0.758125	+	0.203139i
$763$	−2.75262	+	10.2729i	−0.0996514	+	0.371904i
$764$	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	$-0.120412\pi$
$769$	29.7858	+	17.1968i	1.07410	+	0.620134i	0.144803	+	0.989460i	$0.453745\pi$
$770$		0			0
$771$	−7.83738			−0.282256
$772$	−6.04230	+	6.04230i	−0.217467	+	0.217467i
$773$	6.93953	−	1.85944i	0.249597	−	0.0668794i	−0.131851	−	0.991270i	$-0.542092\pi$
$773$	6.93953	−	1.85944i	0.249597	−	0.0668794i	0.381448	+	0.924390i	$0.375425\pi$
$774$	−0.596168	−	1.03259i	−0.0214288	−	0.0371158i
$775$		0			0
$776$	1.19728	+	2.07375i	0.0429798	+	0.0744432i
$777$	−17.5932	+	65.6586i	−0.631151	+	2.35549i
$778$	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
$782$	15.7884	+	4.23050i	0.564593	+	0.151282i
$783$	5.81610	+	21.7060i	0.207850	+	0.775708i
$784$	−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	$-0.870596\pi$
$787$	−14.6739	+	14.6739i	−0.523068	+	0.523068i	0.395429	+	0.918497i	$0.370596\pi$
$788$	2.33745	+	8.72348i	0.0832682	+	0.310761i
$789$	−17.1729	+	29.7443i	−0.611372	+	1.05893i
$790$		0			0
$791$		−	36.8862i		−	1.31152i
$792$	0.309252	+	1.15414i	0.0109888	+	0.0410107i
$793$	1.76692	−	6.59423i	0.0627452	−	0.234168i
$794$	−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	$-0.634407\pi$
$797$	14.1820	−	14.1820i	0.502353	−	0.502353i	0.912168	+	0.409816i	$0.134407\pi$
$798$	−9.10393	−	27.4419i	−0.322275	−	0.971432i
$799$		−	50.1795i		−	1.77522i
$800$		0			0
$801$	2.62718	−	1.51680i	0.0928268	−	0.0535936i
$802$	−28.3638	+	7.60007i	−1.00156	+	0.268368i
$803$	73.0785	+	19.5813i	2.57888	+	0.691010i
$804$	17.1768	+	9.91705i	0.605780	+	0.349747i
$805$		0			0
$806$			1.84227i			0.0648914i
$807$	14.8786	−	3.98671i	0.523752	−	0.140339i
$808$	0.465053	−	0.124611i	0.0163605	−	0.00438378i
$809$		−	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	0.323490	−	0.946232i	$-0.395144\pi$
$811$	−9.51809	−	5.49527i	−0.334225	−	0.192965i	−0.657716	+	0.753266i	$0.728477\pi$
$812$	16.0793	+	4.30842i	0.564271	+	0.151196i
$813$	40.3168	−	10.8029i	1.41397	−	0.378873i
$814$	49.5126	−	28.5861i	1.73542	−	1.00194i
$815$		0			0
$816$		−	6.86498i		−	0.240322i
$817$	4.89878	−	23.7669i	0.171386	−	0.831498i
$818$	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	$0.940571\pi$
$822$	−0.340372	+	1.27028i	−0.0118718	+	0.0443063i
$823$	−12.0787	−	45.0785i	−0.421039	−	1.57134i	−0.772424	−	0.635107i	$-0.780956\pi$
$823$	−12.0787	−	45.0785i	−0.421039	−	1.57134i	0.351386	−	0.936231i	$-0.385711\pi$
$824$		−	14.0145i		−	0.488217i
$825$		0			0
$826$	14.9303	−	25.8601i	0.519492	−	0.899787i
$827$	3.29047	+	12.2802i	0.114421	+	0.427024i	0.999243	−	0.0389046i	$-0.0123869\pi$
$827$	3.29047	+	12.2802i	0.114421	+	0.427024i	−0.884822	+	0.465929i	$0.845720\pi$
$828$	−0.601848	+	0.601848i	−0.0209157	+	0.0209157i
$829$	−47.6024			−1.65330			−0.826650	−	0.562716i	$-0.809756\pi$
$829$	−47.6024			−1.65330			−0.826650	+	0.562716i	$0.809756\pi$
$830$		0			0
$831$	−22.7584	+	13.1396i	−0.789479	+	0.455806i
$832$	−0.831890	−	3.10465i	−0.0288406	−	0.107635i
$833$	−34.9338	−	9.36049i	−1.21039	−	0.324322i
$834$	−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
$838$	10.3438	−	38.6035i	0.357320	−	1.33354i
$839$	13.6456	+	23.6348i	0.471098	+	0.815965i	0.999453	−	0.0330579i	$-0.0105246\pi$
$839$	13.6456	+	23.6348i	0.471098	+	0.815965i	−0.528356	+	0.849023i	$0.677191\pi$
$840$		0			0
$841$	5.72700	+	9.91946i	0.197483	+	0.342050i
$842$	16.5749	−	4.44123i	0.571209	−	0.153055i
$843$	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
$852$	2.27741	−	8.49941i	0.0780228	−	0.291185i
$853$	3.69985	+	0.991372i	0.126680	+	0.0339439i	0.321602	−	0.946875i	$-0.395779\pi$
$853$	3.69985	+	0.991372i	0.126680	+	0.0339439i	−0.194922	+	0.980819i	$0.562445\pi$
$854$	8.44081			0.288839
$855$		0			0
$856$	2.48870			0.0850619
$857$	10.8647	+	2.91119i	0.371131	+	0.0994443i	0.439564	−	0.898211i	$-0.355133\pi$
$857$	10.8647	+	2.91119i	0.371131	+	0.0994443i	−0.0684325	+	0.997656i	$0.521800\pi$
$858$	7.74623	−	28.9093i	0.264452	−	0.986948i
$859$	34.1982	+	19.7443i	1.16683	+	0.673668i	0.952931	−	0.303188i	$-0.0980509\pi$
$859$	34.1982	+	19.7443i	1.16683	+	0.673668i	0.213897	+	0.976856i	$0.431384\pi$
$860$		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	$-0.395236\pi$
$863$	−18.3050	−	18.3050i	−0.623110	−	0.623110i	−0.946325	+	0.323215i	$0.895236\pi$
$864$	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
$868$	−2.20020	+	0.589541i	−0.0746796	+	0.0200103i
$869$	−13.8823	−	24.0448i	−0.470923	−	0.815663i
$870$		0			0
$871$	19.0974	+	33.0777i	0.647092	+	1.12080i
$872$	0.692648	−	2.58500i	0.0234560	−	0.0875390i
$873$	−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
$877$	−37.2238	−	9.97410i	−1.25696	−	0.336801i	−0.431939	−	0.901903i	$-0.642170\pi$
$877$	−37.2238	−	9.97410i	−1.25696	−	0.336801i	−0.825021	+	0.565102i	$0.808837\pi$
$878$	4.58213	+	17.1008i	0.154640	+	0.577123i
$879$	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
$883$	−10.1631	−	37.9291i	−0.342015	−	1.27642i	−0.896061	−	0.443931i	$-0.853583\pi$
$883$	−10.1631	−	37.9291i	−0.342015	−	1.27642i	0.554046	−	0.832486i	$-0.313083\pi$
$884$	6.61000	−	11.4489i	0.222319	−	0.385067i
$885$		0			0
$886$		−	6.13559i		−	0.206129i
$887$	−7.97545	−	29.7648i	−0.267789	−	0.999404i	−0.960521	−	0.278208i	$-0.910260\pi$
$887$	−7.97545	−	29.7648i	−0.267789	−	0.999404i	0.692731	−	0.721196i	$-0.256407\pi$
$888$	4.42701	−	16.5218i	0.148561	−	0.554437i
$889$	−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
$893$	16.7449	+	50.4740i	0.560347	+	1.68905i
$894$		−	21.1336i		−	0.706814i
$895$		0			0
$896$	3.44163	−	1.98702i	0.114977	−	0.0663818i
$897$	20.5932	−	5.51793i	0.687586	−	0.184238i
$898$	−10.4975	−	2.81279i	−0.350305	−	0.0938640i
$899$	2.07924	+	1.20045i	0.0693465	+	0.0400372i
$900$		0			0
$901$		−	15.6010i		−	0.519744i
$902$	−31.9062	+	8.54924i	−1.06236	+	0.284659i
$903$	−35.6684	+	9.55733i	−1.18697	+	0.318048i
$904$			9.28176i			0.308707i
$905$		0			0
$906$	21.3869	+	12.3477i	0.710531	+	0.410225i
$907$	−50.1145	−	13.4281i	−1.66402	−	0.445874i	−0.700535	−	0.713618i	$-0.747055\pi$
$907$	−50.1145	−	13.4281i	−1.66402	−	0.445874i	−0.963490	+	0.267744i	$0.913722\pi$
$908$	19.1801	−	5.13929i	0.636514	−	0.170553i
$909$	−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	$-0.138892\pi$
$912$	2.29084	+	6.90527i	0.0758574	+	0.228656i
$913$	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
$917$	−10.0107	+	37.3604i	−0.330582	+	1.23375i
$918$	5.71090	+	21.3134i	0.188488	+	0.703447i
$919$			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
$922$	−9.00385	−	33.6028i	−0.296526	−	1.10665i
$923$	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
$927$	0.776858	+	2.89927i	0.0255154	+	0.0952247i
$928$	−4.04606	−	1.08414i	−0.132819	−	0.0355886i
$929$	22.5585	−	13.0241i	0.740119	−	0.427308i	−0.0819935	−	0.996633i	$-0.526129\pi$
$929$	22.5585	−	13.0241i	0.740119	−	0.427308i	0.822113	+	0.569325i	$0.192795\pi$
$930$		0			0
$931$	38.2624	−	2.24200i	1.25400	−	0.0734785i
$932$	5.67372	+	5.67372i	0.185849	+	0.185849i
$933$	6.82244	−	25.4617i	0.223357	−	0.833578i
$934$	−17.2194	−	29.8249i	−0.563436	−	0.975900i
$935$		0			0
$936$	0.344198	+	0.596168i	0.0112505	+	0.0194864i
$937$	−15.7972	+	4.23284i	−0.516071	+	0.138281i	−0.507449	−	0.861682i	$-0.669411\pi$
$937$	−15.7972	+	4.23284i	−0.516071	+	0.138281i	−0.00862262	+	0.999963i	$0.502745\pi$
$938$	−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
$947$	5.14037	−	19.1841i	0.167039	−	0.623400i	−0.830732	−	0.556673i	$-0.812078\pi$
$947$	5.14037	−	19.1841i	0.167039	−	0.623400i	0.997771	−	0.0667269i	$-0.0212556\pi$
$948$	−8.02349	−	2.14989i	−0.260591	−	0.0698251i
$949$	43.5881			1.41493
$950$		0			0
$951$	10.3155			0.334505
$952$	15.7884	+	4.23050i	0.511706	+	0.137111i
$953$	−10.8760	+	40.5899i	−0.352309	+	1.31483i	0.531529	+	0.847040i	$0.321618\pi$
$953$	−10.8760	+	40.5899i	−0.352309	+	1.31483i	−0.883837	+	0.467794i	$0.845049\pi$
$954$	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
$963$	−0.514854	+	0.137955i	−0.0165909	+	0.00444553i
$964$	7.05046	+	12.2118i	0.227080	+	0.393314i
$965$		0			0
$966$	13.1799	+	22.8283i	0.424057	+	0.734489i
$967$	−12.2226	+	45.6155i	−0.393053	+	1.46690i	0.432017	+	0.901865i	$0.357802\pi$
$967$	−12.2226	+	45.6155i	−0.393053	+	1.46690i	−0.825070	+	0.565030i	$0.808865\pi$
$968$	−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	$0.520443\pi$
$972$	−2.14572	−	0.574944i	−0.0688240	−	0.0184413i
$973$	−14.8479	−	55.4130i	−0.476001	−	1.77646i
$974$	−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	$-0.553659\pi$
$977$	25.5697	−	25.5697i	0.818048	−	0.818048i	0.985825	+	0.167777i	$0.0536588\pi$
$978$	8.29596	+	30.9609i	0.265276	+	0.990022i
$979$	−39.5101	+	68.4335i	−1.26275	+	2.18714i
$980$		0			0
$981$			0.573172i			0.0183000i
$982$	0.0106190	+	0.0396306i	0.000338866	+	0.00126466i
$983$	−10.0139	+	37.3724i	−0.319394	+	1.19200i	0.600434	+	0.799674i	$0.294995\pi$
$983$	−10.0139	+	37.3724i	−0.319394	+	1.19200i	−0.919828	+	0.392321i	$0.871672\pi$
$984$	−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
$988$	−2.82831	+	13.7218i	−0.0899805	+	0.436549i
$989$			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	$0.370295\pi$
$992$	0.553641	−	0.148348i	0.0175781	−	0.00471005i
$993$	−47.4636	−	12.7178i	−1.50621	−	0.403589i
$994$	18.1440	+	10.4754i	0.575491	+	0.332260i
$995$		0			0
$996$		−	17.2401i		−	0.546272i
$997$	−32.0072	+	8.57629i	−1.01368	+	0.271614i	−0.727165	−	0.686463i	$-0.759162\pi$
$997$	−32.0072	+	8.57629i	−1.01368	+	0.271614i	−0.286512	+	0.958077i	$0.592496\pi$
$998$	−19.9499	+	5.34557i	−0.631505	+	0.169211i
$999$			54.9774i			1.73941i

Twists

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

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

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

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Representations

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Database

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