LMFDB - Embedded newform 950.2.q.f.107.5

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	950.107
Dual form			950.2.q.f.293.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.672711 + 2.51059i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.29958 + 2.25093i) q^{6} +(0.692149 + 0.692149i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.25245 - 1.87780i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.672711 + 2.51059i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.29958 + 2.25093i) q^{6} +(0.692149 + 0.692149i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.25245 - 1.87780i) q^{9} +4.06019 q^{11} +(-1.83788 + 1.83788i) q^{12} +(-6.19637 + 1.66031i) q^{13} +(0.489423 + 0.847706i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.670215 + 2.50128i) q^{17} +(-2.65561 - 2.65561i) q^{18} +(-0.843357 + 4.27653i) q^{19} +(-2.20332 + 1.27209i) q^{21} +(3.92185 + 1.05086i) q^{22} +(0.943242 + 3.52023i) q^{23} +(-2.25093 + 1.29958i) q^{24} -6.41495 q^{26} +(1.38871 - 1.38871i) q^{27} +(0.253344 + 0.945493i) q^{28} +(1.89700 - 3.28570i) q^{29} -5.30041i q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.73134 + 10.1935i) q^{33} +(-1.29476 + 2.24258i) q^{34} +(-1.87780 - 3.25245i) q^{36} +(2.58755 - 2.58755i) q^{37} +(-1.92147 + 3.91254i) q^{38} -16.6735i q^{39} +(-7.09414 + 4.09581i) q^{41} +(-2.45748 + 0.658481i) q^{42} +(-4.61022 - 1.23530i) q^{43} +(3.51623 + 2.03010i) q^{44} +3.64441i q^{46} +(6.29637 - 1.68711i) q^{47} +(-2.51059 + 0.672711i) q^{48} -6.04186i q^{49} +(-5.82882 - 3.36527i) q^{51} +(-6.19637 - 1.66031i) q^{52} +(2.10978 - 0.565313i) q^{53} +(1.70082 - 0.981968i) q^{54} +0.978847i q^{56} +(-10.1693 - 4.99419i) q^{57} +(2.68276 - 2.68276i) q^{58} +(2.99735 + 5.19156i) q^{59} +(-4.43800 + 7.68683i) q^{61} +(1.37185 - 5.11980i) q^{62} +(-0.951461 - 3.55090i) q^{63} +1.00000i q^{64} +(-5.27653 + 9.13923i) q^{66} +(-2.47970 - 9.25436i) q^{67} +(-1.83106 + 1.83106i) q^{68} -9.47238 q^{69} +(6.72755 - 3.88415i) q^{71} +(-0.972022 - 3.62764i) q^{72} +(15.0240 + 4.02566i) q^{73} +(3.16909 - 1.82967i) q^{74} +(-2.86864 + 3.28191i) q^{76} +(2.81026 + 2.81026i) q^{77} +(4.31541 - 16.1053i) q^{78} +(3.49356 + 6.05103i) q^{79} +(-3.08112 - 5.33666i) q^{81} +(-7.91249 + 2.12015i) q^{82} +(-4.44010 + 4.44010i) q^{83} -2.54417 q^{84} +(-4.13341 - 2.38642i) q^{86} +(6.97292 + 6.97292i) q^{87} +(2.87099 + 2.87099i) q^{88} +(-1.61923 + 2.80459i) q^{89} +(-5.43800 - 3.13963i) q^{91} +(-0.943242 + 3.52023i) q^{92} +(13.3072 + 3.56564i) q^{93} +6.51848 q^{94} -2.59915 q^{96} +(9.80630 + 2.62759i) q^{97} +(1.56375 - 5.83599i) q^{98} +(-13.2056 - 7.62424i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{6}+O(q^{10}) $ 32 * q + 4 * q^6	$ 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) $ 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * 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
$3$	−0.672711	+	2.51059i	−0.388390	+	1.44949i	0.444364	+	0.895846i	$0.353430\pi$
$3$	−0.672711	+	2.51059i	−0.388390	+	1.44949i	−0.832754	+	0.553644i	$0.813237\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.29958	+	2.25093i	−0.530550	+	0.918940i
$7$	0.692149	+	0.692149i	0.261608	+	0.261608i	0.825707	−	0.564099i	$-0.190776\pi$
$7$	0.692149	+	0.692149i	0.261608	+	0.261608i	−0.564099	+	0.825707i	$0.690776\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−3.25245	−	1.87780i	−1.08415	−	0.625934i
$10$		0			0
$11$	4.06019			1.22419			0.612097	−	0.790783i	$-0.290326\pi$
$11$	4.06019			1.22419			0.612097	+	0.790783i	$0.290326\pi$
$12$	−1.83788	+	1.83788i	−0.530550	+	0.530550i
$13$	−6.19637	+	1.66031i	−1.71856	+	0.460488i	−0.977498	−	0.210945i	$-0.932346\pi$
$13$	−6.19637	+	1.66031i	−1.71856	+	0.460488i	−0.741066	+	0.671433i	$0.765679\pi$
$14$	0.489423	+	0.847706i	0.130804	+	0.226559i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.670215	+	2.50128i	−0.162551	+	0.606649i	0.835789	+	0.549051i	$0.185011\pi$
$17$	−0.670215	+	2.50128i	−0.162551	+	0.606649i	−0.998340	+	0.0575977i	$0.981656\pi$
$18$	−2.65561	−	2.65561i	−0.625934	−	0.625934i
$19$	−0.843357	+	4.27653i	−0.193479	+	0.981104i
$19$	−0.843357	+	4.27653i	−0.193479	+	0.981104i
$20$		0			0
$21$	−2.20332	+	1.27209i	−0.480804	+	0.277592i
$22$	3.92185	+	1.05086i	0.836140	+	0.224043i
$23$	0.943242	+	3.52023i	0.196680	+	0.734018i	0.991826	+	0.127600i	$0.0407274\pi$
$23$	0.943242	+	3.52023i	0.196680	+	0.734018i	−0.795146	+	0.606418i	$0.792606\pi$
$24$	−2.25093	+	1.29958i	−0.459470	+	0.265275i
$25$		0			0
$26$	−6.41495			−1.25808
$27$	1.38871	−	1.38871i	0.267258	−	0.267258i
$28$	0.253344	+	0.945493i	0.0478776	+	0.178681i
$29$	1.89700	−	3.28570i	0.352264	−	0.610139i	−0.634382	−	0.773020i	$-0.718745\pi$
$29$	1.89700	−	3.28570i	0.352264	−	0.610139i	0.986646	+	0.162881i	$0.0520785\pi$
$30$		0			0
$31$		−	5.30041i		−	0.951982i	−0.879450	−	0.475991i	$-0.842090\pi$
$31$		−	5.30041i		−	0.951982i	0.879450	−	0.475991i	$-0.157910\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−2.73134	+	10.1935i	−0.475464	+	1.77446i
$34$	−1.29476	+	2.24258i	−0.222049	+	0.384600i
$35$		0			0
$36$	−1.87780	−	3.25245i	−0.312967	−	0.542075i
$37$	2.58755	−	2.58755i	0.425391	−	0.425391i	−0.461664	−	0.887055i	$-0.652747\pi$
$37$	2.58755	−	2.58755i	0.425391	−	0.425391i	0.887055	+	0.461664i	$0.152747\pi$
$38$	−1.92147	+	3.91254i	−0.311703	+	0.634698i
$39$		−	16.6735i		−	2.66989i
$40$		0			0
$41$	−7.09414	+	4.09581i	−1.10792	+	0.639657i	−0.938290	−	0.345850i	$-0.887590\pi$
$41$	−7.09414	+	4.09581i	−1.10792	+	0.639657i	−0.169630	+	0.985508i	$0.554257\pi$
$42$	−2.45748	+	0.658481i	−0.379198	+	0.101606i
$43$	−4.61022	−	1.23530i	−0.703052	−	0.188382i	−0.110455	−	0.993881i	$-0.535231\pi$
$43$	−4.61022	−	1.23530i	−0.703052	−	0.188382i	−0.592597	+	0.805499i	$0.701897\pi$
$44$	3.51623	+	2.03010i	0.530092	+	0.306049i
$45$		0			0
$46$			3.64441i			0.537338i
$47$	6.29637	−	1.68711i	0.918420	−	0.246090i	0.231510	−	0.972833i	$-0.425633\pi$
$47$	6.29637	−	1.68711i	0.918420	−	0.246090i	0.686910	+	0.726743i	$0.258967\pi$
$48$	−2.51059	+	0.672711i	−0.362373	+	0.0970974i
$49$		−	6.04186i		−	0.863123i
$50$		0			0
$51$	−5.82882	−	3.36527i	−0.816198	−	0.471232i
$52$	−6.19637	−	1.66031i	−0.859282	−	0.230244i
$53$	2.10978	−	0.565313i	0.289800	−	0.0776517i	−0.110990	−	0.993821i	$-0.535402\pi$
$53$	2.10978	−	0.565313i	0.289800	−	0.0776517i	0.400790	+	0.916170i	$0.368736\pi$
$54$	1.70082	−	0.981968i	0.231452	−	0.133629i
$55$		0			0
$56$			0.978847i			0.130804i
$57$	−10.1693	−	4.99419i	−1.34696	−	0.661497i
$58$	2.68276	−	2.68276i	0.352264	−	0.352264i
$59$	2.99735	+	5.19156i	0.390221	+	0.675883i	0.992479	−	0.122419i	$-0.0390652\pi$
$59$	2.99735	+	5.19156i	0.390221	+	0.675883i	−0.602257	+	0.798302i	$0.705732\pi$
$60$		0			0
$61$	−4.43800	+	7.68683i	−0.568227	+	0.984198i	0.428514	+	0.903535i	$0.359037\pi$
$61$	−4.43800	+	7.68683i	−0.568227	+	0.984198i	−0.996741	+	0.0806632i	$0.974296\pi$
$62$	1.37185	−	5.11980i	0.174225	−	0.650216i
$63$	−0.951461	−	3.55090i	−0.119873	−	0.447371i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−5.27653	+	9.13923i	−0.649497	+	1.12496i
$67$	−2.47970	−	9.25436i	−0.302943	−	1.13060i	−0.934701	−	0.355434i	$-0.884333\pi$
$67$	−2.47970	−	9.25436i	−0.302943	−	1.13060i	0.631758	−	0.775166i	$-0.282334\pi$
$68$	−1.83106	+	1.83106i	−0.222049	+	0.222049i
$69$	−9.47238			−1.14034
$70$		0			0
$71$	6.72755	−	3.88415i	0.798414	−	0.460964i	−0.0445025	−	0.999009i	$-0.514170\pi$
$71$	6.72755	−	3.88415i	0.798414	−	0.460964i	0.842916	+	0.538045i	$0.180837\pi$
$72$	−0.972022	−	3.62764i	−0.114554	−	0.427521i
$73$	15.0240	+	4.02566i	1.75842	+	0.471168i	0.986391	−	0.164414i	$-0.0525733\pi$
$73$	15.0240	+	4.02566i	1.75842	+	0.471168i	0.772033	+	0.635583i	$0.219240\pi$
$74$	3.16909	−	1.82967i	0.368399	−	0.212695i
$75$		0			0
$76$	−2.86864	+	3.28191i	−0.329055	+	0.376461i
$77$	2.81026	+	2.81026i	0.320259	+	0.320259i
$78$	4.31541	−	16.1053i	0.488624	−	1.82357i
$79$	3.49356	+	6.05103i	0.393056	+	0.680794i	0.992851	−	0.119360i	$-0.0380844\pi$
$79$	3.49356	+	6.05103i	0.393056	+	0.680794i	−0.599795	+	0.800154i	$0.704751\pi$
$80$		0			0
$81$	−3.08112	−	5.33666i	−0.342347	−	0.592962i
$82$	−7.91249	+	2.12015i	−0.873788	+	0.234131i
$83$	−4.44010	+	4.44010i	−0.487365	+	0.487365i	−0.907474	−	0.420109i	$-0.861992\pi$
$83$	−4.44010	+	4.44010i	−0.487365	+	0.487365i	0.420109	+	0.907474i	$0.361992\pi$
$84$	−2.54417			−0.277592
$85$		0			0
$86$	−4.13341	−	2.38642i	−0.445717	−	0.257335i
$87$	6.97292	+	6.97292i	0.747575	+	0.747575i
$88$	2.87099	+	2.87099i	0.306049	+	0.306049i
$89$	−1.61923	+	2.80459i	−0.171638	+	0.297286i	−0.938993	−	0.343937i	$-0.888239\pi$
$89$	−1.61923	+	2.80459i	−0.171638	+	0.297286i	0.767355	+	0.641223i	$0.221573\pi$
$90$		0			0
$91$	−5.43800	−	3.13963i	−0.570057	−	0.329122i
$92$	−0.943242	+	3.52023i	−0.0983398	+	0.367009i
$93$	13.3072	+	3.56564i	1.37989	+	0.369740i
$94$	6.51848			0.672330
$95$		0			0
$96$	−2.59915			−0.265275
$97$	9.80630	+	2.62759i	0.995678	+	0.266791i	0.719634	−	0.694354i	$-0.244310\pi$
$97$	9.80630	+	2.62759i	0.995678	+	0.266791i	0.276044	+	0.961145i	$0.410976\pi$
$98$	1.56375	−	5.83599i	0.157962	−	0.589524i
$99$	−13.2056	−	7.62424i	−1.32721	−	0.766265i
$100$		0			0
$101$	7.18443	−	12.4438i	0.714878	−	1.23820i	−0.248129	−	0.968727i	$-0.579816\pi$
$101$	7.18443	−	12.4438i	0.714878	−	1.23820i	0.963007	−	0.269478i	$-0.0868511\pi$
$102$	−4.75921	−	4.75921i	−0.471232	−	0.471232i
$103$	−5.85218	−	5.85218i	−0.576632	−	0.576632i	0.357341	−	0.933974i	$-0.383683\pi$
$103$	−5.85218	−	5.85218i	−0.576632	−	0.576632i	−0.933974	+	0.357341i	$0.883683\pi$
$104$	−5.55551	−	3.20748i	−0.544763	−	0.314519i
$105$		0			0
$106$	2.18420			0.212148
$107$	−4.37033	+	4.37033i	−0.422496	+	0.422496i	−0.886062	−	0.463566i	$-0.846570\pi$
$107$	−4.37033	+	4.37033i	−0.422496	+	0.422496i	0.463566	+	0.886062i	$0.346570\pi$
$108$	1.89702	−	0.508304i	0.182540	−	0.0489116i
$109$	8.20572	+	14.2127i	0.785965	+	1.36133i	0.928421	+	0.371530i	$0.121167\pi$
$109$	8.20572	+	14.2127i	0.785965	+	1.36133i	−0.142456	+	0.989801i	$0.545500\pi$
$110$		0			0
$111$	4.75561	+	8.23695i	0.451382	+	0.781817i
$112$	−0.253344	+	0.945493i	−0.0239388	+	0.0893407i
$113$	12.9758	+	12.9758i	1.22066	+	1.22066i	0.967398	+	0.253261i	$0.0815033\pi$
$113$	12.9758	+	12.9758i	1.22066	+	1.22066i	0.253261	+	0.967398i	$0.418497\pi$
$114$	−8.53019	−	7.45603i	−0.798926	−	0.698321i
$115$		0			0
$116$	3.28570	−	1.89700i	0.305070	−	0.176132i
$117$	23.2711	+	6.23548i	2.15142	+	0.576470i
$118$	1.55154	+	5.79043i	0.142831	+	0.533052i
$119$	−2.19515	+	1.26737i	−0.201229	+	0.116179i
$120$		0			0
$121$	5.48517			0.498651
$122$	−6.27627	+	6.27627i	−0.568227	+	0.568227i
$123$	−5.51059	−	20.5658i	−0.496873	−	1.85435i
$124$	2.65020	−	4.59029i	0.237995	−	0.412220i
$125$		0			0
$126$		−	3.67616i		−	0.327499i
$127$	0.441398	+	1.64732i	0.0391678	+	0.146176i	0.982741	−	0.184989i	$-0.0592249\pi$
$127$	0.441398	+	1.64732i	0.0391678	+	0.146176i	−0.943573	+	0.331165i	$0.892558\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	6.20269	−	10.7434i	0.546116	−	0.945901i
$130$		0			0
$131$	−6.49083	−	11.2425i	−0.567107	−	0.982258i	−0.996850	−	0.0793067i	$-0.974729\pi$
$131$	−6.49083	−	11.2425i	−0.567107	−	0.982258i	0.429744	−	0.902951i	$-0.358604\pi$
$132$	−7.46215	+	7.46215i	−0.649497	+	0.649497i
$133$	−3.54373	+	2.37627i	−0.307280	+	0.206049i
$134$		−	9.58082i		−	0.827657i
$135$		0			0
$136$	−2.24258	+	1.29476i	−0.192300	+	0.111024i
$137$	−2.06515	+	0.553355i	−0.176438	+	0.0472763i	−0.345956	−	0.938251i	$-0.612445\pi$
$137$	−2.06515	+	0.553355i	−0.176438	+	0.0472763i	0.169519	+	0.985527i	$0.445779\pi$
$138$	−9.14961	−	2.45163i	−0.778867	−	0.208697i
$139$	19.8541	+	11.4628i	1.68400	+	0.972260i	0.958953	+	0.283566i	$0.0915174\pi$
$139$	19.8541	+	11.4628i	1.68400	+	0.972260i	0.725051	+	0.688695i	$0.241816\pi$
$140$		0			0
$141$			16.9425i			1.42682i
$142$	7.50361	−	2.01059i	0.629689	−	0.168725i
$143$	−25.1585	+	6.74119i	−2.10386	+	0.563726i
$144$		−	3.75561i		−	0.312967i
$145$		0			0
$146$	13.4701	+	7.77699i	1.11480	+	0.643628i
$147$	15.1686	+	4.06442i	1.25109	+	0.335228i
$148$	3.53466	−	0.947109i	0.290547	−	0.0778519i
$149$	−8.09426	+	4.67322i	−0.663108	+	0.382845i	−0.793460	−	0.608622i	$-0.791722\pi$
$149$	−8.09426	+	4.67322i	−0.663108	+	0.382845i	0.130352	+	0.991468i	$0.458389\pi$
$150$		0			0
$151$		−	5.03298i		−	0.409578i	−0.978806	−	0.204789i	$-0.934349\pi$
$151$		−	5.03298i		−	0.409578i	0.978806	−	0.204789i	$-0.0656508\pi$
$152$	−3.62031	+	2.42762i	−0.293646	+	0.196906i
$153$	6.87674	−	6.87674i	0.555952	−	0.555952i
$154$	1.98715	+	3.44185i	0.160129	+	0.277352i
$155$		0			0
$156$	8.33673	−	14.4396i	0.667472	−	1.15610i
$157$	−2.73920	+	10.2228i	−0.218612	+	0.815871i	0.766252	+	0.642541i	$0.222120\pi$
$157$	−2.73920	+	10.2228i	−0.218612	+	0.815871i	−0.984864	+	0.173331i	$0.944547\pi$
$158$	1.80840	+	6.74904i	0.143869	+	0.536925i
$159$			5.67708i			0.450222i
$160$		0			0
$161$	−1.78366	+	3.08939i	−0.140572	+	0.243478i
$162$	−1.59491	−	5.95227i	−0.125308	−	0.467655i
$163$	13.6049	−	13.6049i	1.06561	−	1.06561i	0.0679240	−	0.997690i	$-0.478362\pi$
$163$	13.6049	−	13.6049i	1.06561	−	1.06561i	0.997690	−	0.0679240i	$-0.0216375\pi$
$164$	−8.19161			−0.639657
$165$		0			0
$166$	−5.43800	+	3.13963i	−0.422070	+	0.243682i
$167$	−3.69755	−	13.7995i	−0.286125	−	1.06783i	−0.948013	−	0.318231i	$-0.896911\pi$
$167$	−3.69755	−	13.7995i	−0.286125	−	1.06783i	0.661888	−	0.749603i	$-0.269756\pi$
$168$	−2.45748	−	0.658481i	−0.189599	−	0.0508029i
$169$	24.3800	−	14.0758i	1.87539	−	1.08275i
$170$		0			0
$171$	10.7735	−	12.3256i	0.823867	−	0.942559i
$172$	−3.37491	−	3.37491i	−0.257335	−	0.257335i
$173$	2.18254	−	8.14535i	0.165935	−	0.619279i	−0.831984	−	0.554800i	$-0.812795\pi$
$173$	2.18254	−	8.14535i	0.165935	−	0.619279i	0.997919	−	0.0644792i	$-0.0205386\pi$
$174$	4.93060	+	8.54005i	0.373788	+	0.647419i
$175$		0			0
$176$	2.03010	+	3.51623i	0.153024	+	0.265046i
$177$	−15.0502	+	4.03270i	−1.13124	+	0.303116i
$178$	−2.28994	+	2.28994i	−0.171638	+	0.171638i
$179$	−22.1314			−1.65418			−0.827088	−	0.562072i	$-0.810004\pi$
$179$	−22.1314			−1.65418			−0.827088	+	0.562072i	$0.810004\pi$
$180$		0			0
$181$	20.5760	+	11.8796i	1.52941	+	0.883003i	0.999387	+	0.0350164i	$0.0111483\pi$
$181$	20.5760	+	11.8796i	1.52941	+	0.883003i	0.530018	+	0.847986i	$0.322185\pi$
$182$	−4.44010	−	4.44010i	−0.329122	−	0.329122i
$183$	−16.3130	−	16.3130i	−1.20589	−	1.20589i
$184$	−1.82220	+	3.15615i	−0.134335	+	0.232674i
$185$		0			0
$186$	11.9309	+	6.88829i	0.874814	+	0.505074i
$187$	−2.72120	+	10.1557i	−0.198994	+	0.742656i
$188$	6.29637	+	1.68711i	0.459210	+	0.123045i
$189$	1.92239			0.139833
$190$		0			0
$191$	20.0459			1.45047			0.725237	−	0.688499i	$-0.241730\pi$
$191$	20.0459			1.45047			0.725237	+	0.688499i	$0.241730\pi$
$192$	−2.51059	−	0.672711i	−0.181186	−	0.0485487i
$193$	−2.36986	+	8.84445i	−0.170587	+	0.636638i	0.826675	+	0.562680i	$0.190230\pi$
$193$	−2.36986	+	8.84445i	−0.170587	+	0.636638i	−0.997261	+	0.0739577i	$0.976437\pi$
$194$	8.79208	+	5.07611i	0.631235	+	0.364444i
$195$		0			0
$196$	3.02093	−	5.23240i	0.215781	−	0.373743i
$197$	15.3866	+	15.3866i	1.09625	+	1.09625i	0.994845	+	0.101403i	$0.0323331\pi$
$197$	15.3866	+	15.3866i	1.09625	+	1.09625i	0.101403	+	0.994845i	$0.467667\pi$
$198$	−10.7823	−	10.7823i	−0.766265	−	0.766265i
$199$	14.1759	+	8.18443i	1.00490	+	0.580179i	0.909694	−	0.415279i	$-0.136316\pi$
$199$	14.1759	+	8.18443i	1.00490	+	0.580179i	0.0952054	+	0.995458i	$0.469649\pi$
$200$		0			0
$201$	24.9020			1.75645
$202$	10.1603	−	10.1603i	0.714878	−	0.714878i
$203$	3.58720	−	0.961188i	0.251772	−	0.0674622i
$204$	−3.36527	−	5.82882i	−0.235616	−	0.408099i
$205$		0			0
$206$	−4.13812	−	7.16743i	−0.288316	−	0.499378i
$207$	3.54244	−	13.2206i	0.246217	−	0.918894i
$208$	−4.53606	−	4.53606i	−0.314519	−	0.314519i
$209$	−3.42419	+	17.3636i	−0.236856	+	1.20106i
$210$		0			0
$211$	−4.55103	+	2.62754i	−0.313306	+	0.180887i	−0.648405	−	0.761296i	$-0.724564\pi$
$211$	−4.55103	+	2.62754i	−0.313306	+	0.180887i	0.335099	+	0.942183i	$0.391230\pi$
$212$	2.10978	+	0.565313i	0.144900	+	0.0388259i
$213$	5.22582	+	19.5030i	0.358068	+	1.33633i
$214$	−5.35254	+	3.09029i	−0.365892	+	0.211248i
$215$		0			0
$216$	1.96394			0.133629
$217$	3.66867	−	3.66867i	0.249046	−	0.249046i
$218$	4.24759	+	15.8522i	0.287683	+	1.07365i
$219$	−20.2136	+	35.0110i	−1.36591	+	2.36582i
$220$		0			0
$221$		−	16.6116i		−	1.11742i
$222$	2.46168	+	9.18712i	0.165217	+	0.616599i
$223$	2.37092	−	8.84840i	0.158769	−	0.592533i	−0.839984	−	0.542610i	$-0.817436\pi$
$223$	2.37092	−	8.84840i	0.158769	−	0.592533i	0.998753	−	0.0499222i	$-0.0158973\pi$
$224$	−0.489423	+	0.847706i	−0.0327010	+	0.0566398i
$225$		0			0
$226$	9.17527	+	15.8920i	0.610330	+	1.05712i
$227$	−11.1279	+	11.1279i	−0.738587	+	0.738587i	−0.972304	−	0.233718i	$-0.924911\pi$
$227$	−11.1279	+	11.1279i	−0.738587	+	0.738587i	0.233718	+	0.972304i	$0.424911\pi$
$228$	−6.30977	−	9.40975i	−0.417875	−	0.623176i
$229$		−	2.80109i		−	0.185101i	−0.995708	−	0.0925505i	$-0.970498\pi$
$229$		−	2.80109i		−	0.185101i	0.995708	−	0.0925505i	$-0.0295020\pi$
$230$		0			0
$231$	−8.94590	+	5.16492i	−0.588597	+	0.339827i
$232$	3.66472	−	0.981960i	0.240601	−	0.0644688i
$233$	15.6343	+	4.18919i	1.02424	+	0.274443i	0.731566	−	0.681771i	$-0.238790\pi$
$233$	15.6343	+	4.18919i	1.02424	+	0.274443i	0.292669	+	0.956214i	$0.405456\pi$
$234$	20.8643	+	12.0460i	1.36394	+	0.787473i
$235$		0			0
$236$			5.99469i			0.390221i
$237$	−17.5418	+	4.70031i	−1.13946	+	0.305318i
$238$	−2.44837	+	0.656038i	−0.158704	+	0.0425246i
$239$		−	19.6954i		−	1.27399i	−0.770868	−	0.636995i	$-0.780177\pi$
$239$		−	19.6954i		−	1.27399i	0.770868	−	0.636995i	$-0.219823\pi$
$240$		0			0
$241$	−8.42316	−	4.86311i	−0.542584	−	0.313261i	0.203542	−	0.979066i	$-0.434755\pi$
$241$	−8.42316	−	4.86311i	−0.542584	−	0.313261i	−0.746125	+	0.665806i	$0.768088\pi$
$242$	5.29826	+	1.41967i	0.340585	+	0.0912596i
$243$	21.1619	−	5.67032i	1.35754	−	0.363751i
$244$	−7.68683	+	4.43800i	−0.492099	+	0.284114i
$245$		0			0
$246$		−	21.2913i		−	1.35748i
$247$	−1.87463	−	27.8992i	−0.119280	−	1.77518i
$248$	3.74796	−	3.74796i	0.237995	−	0.237995i
$249$	−8.16038	−	14.1342i	−0.517143	−	0.895718i
$250$		0			0
$251$	9.67141	−	16.7514i	0.610454	−	1.05734i	−0.380710	−	0.924695i	$-0.624320\pi$
$251$	9.67141	−	16.7514i	0.610454	−	1.05734i	0.991164	−	0.132643i	$-0.0423464\pi$
$252$	0.951461	−	3.55090i	0.0599364	−	0.223686i
$253$	3.82974	+	14.2928i	0.240774	+	0.898581i
$254$			1.70543i			0.107008i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.62352	−	24.7193i	−0.413164	−	1.54195i	−0.788486	−	0.615053i	$-0.789135\pi$
$257$	−6.62352	−	24.7193i	−0.413164	−	1.54195i	0.375322	−	0.926895i	$-0.377532\pi$
$258$	8.77192	−	8.77192i	0.546116	−	0.546116i
$259$	3.58194			0.222571
$260$		0			0
$261$	−12.3398	+	7.12439i	−0.763814	+	0.440988i
$262$	−3.35990	−	12.5393i	−0.207575	−	0.774682i
$263$	−17.7432	−	4.75428i	−1.09409	−	0.293161i	−0.333736	−	0.942667i	$-0.608309\pi$
$263$	−17.7432	−	4.75428i	−1.09409	−	0.293161i	−0.760357	+	0.649505i	$0.774976\pi$
$264$	−9.13923	+	5.27653i	−0.562480	+	0.324748i
$265$		0			0
$266$	−4.03800	+	1.37812i	−0.247586	+	0.0844978i
$267$	−5.95190	−	5.95190i	−0.364250	−	0.364250i
$268$	2.47970	−	9.25436i	0.151472	−	0.565300i
$269$	6.23569	+	10.8005i	0.380197	+	0.658520i	0.991090	−	0.133193i	$-0.0425229\pi$
$269$	6.23569	+	10.8005i	0.380197	+	0.658520i	−0.610893	+	0.791713i	$0.709190\pi$
$270$		0			0
$271$	11.3878	+	19.7242i	0.691757	+	1.19816i	0.971262	+	0.238014i	$0.0764963\pi$
$271$	11.3878	+	19.7242i	0.691757	+	1.19816i	−0.279505	+	0.960144i	$0.590170\pi$
$272$	−2.50128	+	0.670215i	−0.151662	+	0.0406378i
$273$	11.5405	−	11.5405i	0.698464	−	0.698464i
$274$	−2.13800			−0.129161
$275$		0			0
$276$	−8.20332	−	4.73619i	−0.493782	−	0.285085i
$277$	−16.8767	−	16.8767i	−1.01402	−	1.01402i	−0.999900	−	0.0141198i	$-0.995505\pi$
$277$	−16.8767	−	16.8767i	−1.01402	−	1.01402i	−0.0141198	−	0.999900i	$-0.504495\pi$
$278$	16.2108	+	16.2108i	0.972260	+	0.972260i
$279$	−9.95312	+	17.2393i	−0.595878	+	1.03209i
$280$		0			0
$281$	−6.50771	−	3.75723i	−0.388217	−	0.224137i	0.293170	−	0.956060i	$-0.405290\pi$
$281$	−6.50771	−	3.75723i	−0.388217	−	0.224137i	−0.681388	+	0.731923i	$0.738623\pi$
$282$	−4.38505	+	16.3652i	−0.261126	+	0.974536i
$283$	−17.7563	−	4.75780i	−1.05550	−	0.282822i	−0.310980	−	0.950417i	$-0.600657\pi$
$283$	−17.7563	−	4.75780i	−1.05550	−	0.282822i	−0.744525	+	0.667595i	$0.767324\pi$
$284$	7.76831			0.460964
$285$		0			0
$286$	−26.0459			−1.54013
$287$	−7.74512	−	2.07530i	−0.457180	−	0.122501i
$288$	0.972022	−	3.62764i	0.0572770	−	0.213761i
$289$	8.91524	+	5.14721i	0.524426	+	0.302777i
$290$		0			0
$291$	−13.1936	+	22.8520i	−0.773423	+	1.33961i
$292$	10.9983	+	10.9983i	0.643628	+	0.643628i
$293$	−22.0621	−	22.0621i	−1.28888	−	1.28888i	−0.935468	−	0.353412i	$-0.885021\pi$
$293$	−22.0621	−	22.0621i	−1.28888	−	1.28888i	−0.353412	−	0.935468i	$-0.614979\pi$
$294$	13.5998	+	7.85186i	0.793158	+	0.457930i
$295$		0			0
$296$	3.65935			0.212695
$297$	5.63844	−	5.63844i	0.327175	−	0.327175i
$298$	−9.02797	+	2.41904i	−0.522976	+	0.140131i
$299$	−11.6893	−	20.2465i	−0.676013	−	1.17089i
$300$		0			0
$301$	−2.33594	−	4.04597i	−0.134642	−	0.233206i
$302$	1.30263	−	4.86148i	0.0749579	−	0.279747i
$303$	26.4083	+	26.4083i	1.51711	+	1.51711i
$304$	−4.12527	+	1.40790i	−0.236600	+	0.0807486i
$305$		0			0
$306$	8.42226	−	4.86259i	0.481468	−	0.277976i
$307$	0.321015	+	0.0860156i	0.0183213	+	0.00490917i	0.267968	−	0.963428i	$-0.413648\pi$
$307$	0.321015	+	0.0860156i	0.0183213	+	0.00490917i	−0.249647	+	0.968337i	$0.580315\pi$
$308$	1.02863	+	3.83889i	0.0586114	+	0.218741i
$309$	18.6293	−	10.7556i	1.05978	−	0.611865i
$310$		0			0
$311$	−2.54536			−0.144334			−0.0721670	−	0.997393i	$-0.522991\pi$
$311$	−2.54536			−0.144334			−0.0721670	+	0.997393i	$0.522991\pi$
$312$	11.7899	−	11.7899i	0.667472	−	0.667472i
$313$	−8.27488	−	30.8823i	−0.467724	−	1.74557i	−0.647697	−	0.761898i	$-0.724268\pi$
$313$	−8.27488	−	30.8823i	−0.467724	−	1.74557i	0.179973	−	0.983671i	$-0.442399\pi$
$314$	−5.29173	+	9.16555i	−0.298630	+	0.517242i
$315$		0			0
$316$			6.98712i			0.393056i
$317$	−2.71482	−	10.1318i	−0.152479	−	0.569061i	−0.999308	−	0.0371950i	$-0.988158\pi$
$317$	−2.71482	−	10.1318i	−0.152479	−	0.569061i	0.846829	−	0.531866i	$-0.178509\pi$
$318$	−1.46934	+	5.48364i	−0.0823963	+	0.307507i
$319$	7.70219	−	13.3406i	0.431240	−	0.746929i
$320$		0			0
$321$	−8.03214	−	13.9121i	−0.448310	−	0.776496i
$322$	−2.52247	+	2.52247i	−0.140572	+	0.140572i
$323$	−10.1316	−	4.97567i	−0.563735	−	0.276853i
$324$		−	6.16224i		−	0.342347i
$325$		0			0
$326$	16.6625	−	9.62009i	0.922849	−	0.532807i
$327$	−41.2024	+	11.0401i	−2.27850	+	0.610522i
$328$	−7.91249	−	2.12015i	−0.436894	−	0.117065i
$329$	5.52576	+	3.19030i	0.304645	+	0.175887i
$330$		0			0
$331$			11.8080i			0.649028i	0.945881	+	0.324514i	$0.105201\pi$
$331$			11.8080i			0.649028i	−0.945881	+	0.324514i	$0.894799\pi$
$332$	−6.06530	+	1.62519i	−0.332876	+	0.0891940i
$333$	−13.2748	+	3.55697i	−0.727454	+	0.194921i
$334$		−	14.2863i		−	0.781709i
$335$		0			0
$336$	−2.20332	−	1.27209i	−0.120201	−	0.0693980i
$337$	−9.19272	−	2.46318i	−0.500759	−	0.134178i	−0.000406983	−	1.00000i	$-0.500130\pi$
$337$	−9.19272	−	2.46318i	−0.500759	−	0.134178i	−0.500352	+	0.865822i	$0.666796\pi$
$338$	27.1924	−	7.28618i	1.47907	−	0.396316i
$339$	−41.3058	+	23.8479i	−2.24343	+	1.29524i
$340$		0			0
$341$		−	21.5207i		−	1.16541i
$342$	13.5965	−	9.11720i	0.735212	−	0.493001i
$343$	9.02691	−	9.02691i	0.487407	−	0.487407i
$344$	−2.38642	−	4.13341i	−0.128667	−	0.222858i
$345$		0			0
$346$	4.21634	−	7.30292i	0.226672	−	0.392607i
$347$	2.76338	−	10.3131i	0.148346	−	0.553634i	−0.851238	−	0.524780i	$-0.824148\pi$
$347$	2.76338	−	10.3131i	0.148346	−	0.553634i	0.999584	−	0.0288540i	$-0.00918580\pi$
$348$	2.55227	+	9.52519i	0.136816	+	0.510604i
$349$			1.19891i			0.0641763i	0.999485	+	0.0320882i	$0.0102157\pi$
$349$			1.19891i			0.0641763i	−0.999485	+	0.0320882i	$0.989784\pi$
$350$		0			0
$351$	−6.29928	+	10.9107i	−0.336230	+	0.582368i
$352$	1.05086	+	3.92185i	0.0560108	+	0.209035i
$353$	−7.40047	+	7.40047i	−0.393888	+	0.393888i	−0.876071	−	0.482183i	$-0.839844\pi$
$353$	−7.40047	+	7.40047i	−0.393888	+	0.393888i	0.482183	+	0.876071i	$0.339844\pi$
$354$	−15.5811			−0.828128
$355$		0			0
$356$	−2.80459	+	1.61923i	−0.148643	+	0.0858190i
$357$	−1.70514	−	6.36368i	−0.0902458	−	0.336802i
$358$	−21.3773	−	5.72802i	−1.12982	−	0.302735i
$359$	20.5473	−	11.8630i	1.08444	−	0.626104i	0.152352	−	0.988326i	$-0.451315\pi$
$359$	20.5473	−	11.8630i	1.08444	−	0.626104i	0.932092	+	0.362223i	$0.117982\pi$
$360$		0			0
$361$	−17.5775	−	7.21329i	−0.925132	−	0.379647i
$362$	16.8003	+	16.8003i	0.883003	+	0.883003i
$363$	−3.68993	+	13.7710i	−0.193671	+	0.722790i
$364$	−3.13963	−	5.43800i	−0.164561	−	0.285028i
$365$		0			0
$366$	−11.5350	−	19.9793i	−0.602946	−	1.04433i
$367$	21.8299	−	5.84931i	1.13951	−	0.305332i	0.360758	−	0.932659i	$-0.382518\pi$
$367$	21.8299	−	5.84931i	1.13951	−	0.305332i	0.778755	+	0.627328i	$0.215851\pi$
$368$	−2.57698	+	2.57698i	−0.134335	+	0.134335i
$369$	30.7645			1.60153
$370$		0			0
$371$	1.85156	+	1.06900i	0.0961283	+	0.0554997i
$372$	9.74152	+	9.74152i	0.505074	+	0.505074i
$373$	−0.559369	−	0.559369i	−0.0289630	−	0.0289630i	0.692477	−	0.721440i	$-0.256519\pi$
$373$	−0.559369	−	0.559369i	−0.0289630	−	0.0289630i	−0.721440	+	0.692477i	$0.756519\pi$
$374$	−5.25696	+	9.10532i	−0.271831	+	0.470825i
$375$		0			0
$376$	5.64517	+	3.25924i	0.291127	+	0.168083i
$377$	−6.29923	+	23.5090i	−0.324427	+	1.21078i
$378$	1.85689	+	0.497552i	0.0955080	+	0.0255913i
$379$	−4.94607			−0.254063			−0.127031	−	0.991899i	$-0.540545\pi$
$379$	−4.94607			−0.254063			−0.127031	+	0.991899i	$0.540545\pi$
$380$		0			0
$381$	−4.43268			−0.227093
$382$	19.3629	+	5.18827i	0.990692	+	0.265455i
$383$	0.543765	−	2.02936i	0.0277851	−	0.103695i	−0.950641	−	0.310294i	$-0.899573\pi$
$383$	0.543765	−	2.02936i	0.0277851	−	0.103695i	0.978426	+	0.206598i	$0.0662393\pi$
$384$	−2.25093	−	1.29958i	−0.114867	−	0.0663188i
$385$		0			0
$386$	−4.57823	+	7.92972i	−0.233026	+	0.403612i
$387$	12.6748	+	12.6748i	0.644298	+	0.644298i
$388$	7.17871	+	7.17871i	0.364444	+	0.364444i
$389$	−9.32130	−	5.38166i	−0.472609	−	0.272861i	0.244722	−	0.969593i	$-0.421303\pi$
$389$	−9.32130	−	5.38166i	−0.472609	−	0.272861i	−0.717331	+	0.696732i	$0.754637\pi$
$390$		0			0
$391$	−9.43724			−0.477261
$392$	4.27224	−	4.27224i	0.215781	−	0.215781i
$393$	32.5916	−	8.73291i	1.64403	−	0.440517i
$394$	10.8800	+	18.8446i	0.548124	+	0.949379i
$395$		0			0
$396$	−7.62424	−	13.2056i	−0.383133	−	0.663605i
$397$	−7.04871	+	26.3061i	−0.353765	+	1.32027i	0.528267	+	0.849078i	$0.322842\pi$
$397$	−7.04871	+	26.3061i	−0.353765	+	1.32027i	−0.882032	+	0.471189i	$0.843825\pi$
$398$	11.5745	+	11.5745i	0.580179	+	0.580179i
$399$	−3.58194	−	10.4954i	−0.179321	−	0.525427i
$400$		0			0
$401$	−20.6419	+	11.9176i	−1.03081	+	0.595137i	−0.917216	−	0.398391i	$-0.869569\pi$
$401$	−20.6419	+	11.9176i	−1.03081	+	0.595137i	−0.113592	+	0.993528i	$0.536236\pi$
$402$	24.0535	+	6.44512i	1.19968	+	0.321453i
$403$	8.80033	+	32.8433i	0.438376	+	1.63604i
$404$	12.4438	−	7.18443i	0.619102	−	0.357439i
$405$		0			0
$406$	3.71375			0.184310
$407$	10.5060	−	10.5060i	0.520761	−	0.520761i
$408$	−1.74199	−	6.50120i	−0.0862415	−	0.321858i
$409$	−7.00979	+	12.1413i	−0.346612	+	0.600349i	−0.985645	−	0.168830i	$-0.946001\pi$
$409$	−7.00979	+	12.1413i	−0.346612	+	0.600349i	0.639033	+	0.769179i	$0.279335\pi$
$410$		0			0
$411$		−	5.55699i		−	0.274106i
$412$	−2.14205	−	7.99423i	−0.105531	−	0.393847i
$413$	−1.51872	+	5.66794i	−0.0747314	+	0.278901i
$414$	6.84348	−	11.8533i	0.336339	−	0.582555i
$415$		0			0
$416$	−3.20748	−	5.55551i	−0.157259	−	0.272381i
$417$	−42.1344	+	42.1344i	−2.06333	+	2.06333i
$418$	−7.80153	+	15.8857i	−0.381585	+	0.776993i
$419$			9.42497i			0.460440i	0.973139	+	0.230220i	$0.0739446\pi$
$419$			9.42497i			0.460440i	−0.973139	+	0.230220i	$0.926055\pi$
$420$		0			0
$421$	8.68770	−	5.01585i	0.423413	−	0.244457i	−0.273124	−	0.961979i	$-0.588057\pi$
$421$	8.68770	−	5.01585i	0.423413	−	0.244457i	0.696536	+	0.717522i	$0.254723\pi$
$422$	−5.07601	+	1.36011i	−0.247096	+	0.0662093i
$423$	−23.6467	−	6.33611i	−1.14974	−	0.308072i
$424$	1.89157	+	1.09210i	0.0918630	+	0.0530371i
$425$		0			0
$426$			20.1910i			0.978259i
$427$	−8.39219	+	2.24868i	−0.406127	+	0.108821i
$428$	−5.96998	+	1.59965i	−0.288570	+	0.0773221i
$429$		−	67.6974i		−	3.26846i
$430$		0			0
$431$	21.8815	+	12.6333i	1.05400	+	0.608525i	0.923766	−	0.382959i	$-0.125095\pi$
$431$	21.8815	+	12.6333i	1.05400	+	0.608525i	0.130231	+	0.991484i	$0.458428\pi$
$432$	1.89702	+	0.508304i	0.0912702	+	0.0244558i
$433$	−13.5640	+	3.63446i	−0.651843	+	0.174661i	−0.569562	−	0.821948i	$-0.692887\pi$
$433$	−13.5640	+	3.63446i	−0.651843	+	0.174661i	−0.0822811	+	0.996609i	$0.526221\pi$
$434$	4.49319	−	2.59414i	0.215680	−	0.124523i
$435$		0			0
$436$			16.4114i			0.785965i
$437$	−15.8499	+	1.06500i	−0.758202	+	0.0509459i
$438$	−28.5863	+	28.5863i	−1.36591	+	1.36591i
$439$	−20.5693	−	35.6271i	−0.981719	−	1.70039i	−0.655695	−	0.755026i	$-0.727624\pi$
$439$	−20.5693	−	35.6271i	−0.981719	−	1.70039i	−0.326024	−	0.945362i	$-0.605709\pi$
$440$		0			0
$441$	−11.3454	+	19.6508i	−0.540258	+	0.935754i
$442$	4.29940	−	16.0456i	0.204501	−	0.763210i
$443$	1.29279	+	4.82475i	0.0614222	+	0.229231i	0.989813	−	0.142375i	$-0.0454740\pi$
$443$	1.29279	+	4.82475i	0.0614222	+	0.229231i	−0.928391	+	0.371606i	$0.878807\pi$
$444$			9.51121i			0.451382i
$445$		0			0
$446$	4.58027	−	7.93326i	0.216882	−	0.375651i
$447$	−6.28745	−	23.4651i	−0.297386	−	1.10986i
$448$	−0.692149	+	0.692149i	−0.0327010	+	0.0327010i
$449$	−17.0495			−0.804617			−0.402308	−	0.915504i	$-0.631792\pi$
$449$	−17.0495			−0.804617			−0.402308	+	0.915504i	$0.631792\pi$
$450$		0			0
$451$	−28.8036	+	16.6298i	−1.35631	+	0.783065i
$452$	4.74947	+	17.7253i	0.223396	+	0.833726i
$453$	12.6357	+	3.38574i	0.593679	+	0.159076i
$454$	−13.6289	+	7.86864i	−0.639635	+	0.369293i
$455$		0			0
$456$	−3.65935	−	10.7222i	−0.171365	−	0.502113i
$457$	23.8079	+	23.8079i	1.11369	+	1.11369i	0.992648	+	0.121040i	$0.0386228\pi$
$457$	23.8079	+	23.8079i	1.11369	+	1.11369i	0.121040	+	0.992648i	$0.461377\pi$
$458$	0.724975	−	2.70564i	0.0338758	−	0.126426i
$459$	2.54282	+	4.40429i	0.118689	+	0.205575i
$460$		0			0
$461$	10.5118	+	18.2069i	0.489582	+	0.847980i	0.999928	−	0.0119887i	$-0.00381620\pi$
$461$	10.5118	+	18.2069i	0.489582	+	0.847980i	−0.510347	+	0.859969i	$0.670483\pi$
$462$	−9.97786	+	2.67356i	−0.464212	+	0.124385i
$463$	10.5959	−	10.5959i	0.492433	−	0.492433i	−0.416639	−	0.909072i	$-0.636792\pi$
$463$	10.5959	−	10.5959i	0.492433	−	0.492433i	0.909072	+	0.416639i	$0.136792\pi$
$464$	3.79400			0.176132
$465$		0			0
$466$	14.0173	+	8.09290i	0.649339	+	0.374896i
$467$	16.5651	+	16.5651i	0.766540	+	0.766540i	0.977496	−	0.210956i	$-0.0676576\pi$
$467$	16.5651	+	16.5651i	0.766540	+	0.766540i	−0.210956	+	0.977496i	$0.567658\pi$
$468$	17.0356	+	17.0356i	0.787473	+	0.787473i
$469$	4.68908	−	8.12172i	0.216522	−	0.375026i
$470$		0			0
$471$	−23.8227	−	13.7540i	−1.09769	−	0.633752i
$472$	−1.55154	+	5.79043i	−0.0714155	+	0.266526i
$473$	−18.7184	−	5.01557i	−0.860672	−	0.230616i
$474$	−18.1606			−0.834145
$475$		0			0
$476$	−2.53474			−0.116179
$477$	−7.92349	−	2.12309i	−0.362792	−	0.0972097i
$478$	5.09755	−	19.0243i	0.233156	−	0.870152i
$479$	−23.8426	−	13.7656i	−1.08940	−	0.628964i	−0.155982	−	0.987760i	$-0.549854\pi$
$479$	−23.8426	−	13.7656i	−1.08940	−	0.628964i	−0.933416	+	0.358796i	$0.883188\pi$
$480$		0			0
$481$	−11.7373	+	20.3296i	−0.535174	+	0.926948i
$482$	−6.87748	−	6.87748i	−0.313261	−	0.313261i
$483$	−6.55630	−	6.55630i	−0.298322	−	0.298322i
$484$	4.75029	+	2.74258i	0.215922	+	0.124663i
$485$		0			0
$486$	21.9084			0.993787
$487$	27.4827	−	27.4827i	1.24536	−	1.24536i	0.287615	−	0.957746i	$-0.407138\pi$
$487$	27.4827	−	27.4827i	1.24536	−	1.24536i	0.957746	−	0.287615i	$-0.0928623\pi$
$488$	−8.57355	+	2.29728i	−0.388106	+	0.103993i
$489$	25.0041	+	43.3084i	1.13072	+	1.95847i
$490$		0			0
$491$	7.13782	+	12.3631i	0.322125	+	0.557937i	0.980926	−	0.194380i	$-0.0622695\pi$
$491$	7.13782	+	12.3631i	0.322125	+	0.557937i	−0.658801	+	0.752317i	$0.728936\pi$
$492$	5.51059	−	20.5658i	0.248436	−	0.927177i
$493$	6.94705	+	6.94705i	0.312879	+	0.312879i
$494$	5.41009	−	27.4338i	0.243412	−	1.23430i
$495$		0			0
$496$	4.59029	−	2.65020i	0.206110	−	0.118998i
$497$	7.34488	+	1.96806i	0.329463	+	0.0882794i
$498$	−4.22412	−	15.7646i	−0.189287	−	0.706431i
$499$	11.3242	−	6.53800i	0.506939	−	0.292681i	−0.224636	−	0.974443i	$-0.572119\pi$
$499$	11.3242	−	6.53800i	0.506939	−	0.292681i	0.731574	+	0.681762i	$0.238786\pi$
$500$		0			0
$501$	37.1322			1.65894
$502$	13.6774	−	13.6774i	0.610454	−	0.610454i
$503$	1.71058	+	6.38395i	0.0762708	+	0.284646i	0.993518	−	0.113671i	$-0.0362609\pi$
$503$	1.71058	+	6.38395i	0.0762708	+	0.284646i	−0.917248	+	0.398317i	$0.869594\pi$
$504$	1.83808	−	3.18365i	0.0818746	−	0.141811i
$505$		0			0
$506$			14.7970i			0.657807i
$507$	18.9379	+	70.6772i	0.841062	+	3.13888i
$508$	−0.441398	+	1.64732i	−0.0195839	+	0.0730881i
$509$	−4.67550	+	8.09820i	−0.207238	+	0.358946i	−0.950843	−	0.309672i	$-0.899781\pi$
$509$	−4.67550	+	8.09820i	−0.207238	+	0.358946i	0.743606	+	0.668618i	$0.233114\pi$
$510$		0			0
$511$	7.61248	+	13.1852i	0.336756	+	0.583279i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	4.76770	+	7.11005i	0.210499	+	0.313917i
$514$		−	25.5913i		−	1.12878i
$515$		0			0
$516$	10.7434	−	6.20269i	0.472950	−	0.273058i
$517$	25.5645	−	6.84998i	1.12432	−	0.301262i
$518$	3.45989	+	0.927075i	0.152019	+	0.0407333i
$519$	18.9814	+	10.9589i	0.833192	+	0.481043i
$520$		0			0
$521$		−	13.8328i		−	0.606025i	−0.952987	−	0.303012i	$-0.902008\pi$
$521$		−	13.8328i		−	0.606025i	0.952987	−	0.303012i	$-0.0979924\pi$
$522$	−13.7633	+	3.68785i	−0.602401	+	0.161413i
$523$	5.15867	−	1.38226i	0.225573	−	0.0604421i	−0.144262	−	0.989540i	$-0.546081\pi$
$523$	5.15867	−	1.38226i	0.225573	−	0.0604421i	0.369835	+	0.929097i	$0.379414\pi$
$524$		−	12.9817i		−	0.567107i
$525$		0			0
$526$	−15.9081	−	9.18456i	−0.693627	−	0.400466i
$527$	13.2578	+	3.55241i	0.577518	+	0.154746i
$528$	−10.1935	+	2.73134i	−0.443614	+	0.118866i
$529$	8.41629	−	4.85915i	0.365926	−	0.211267i
$530$		0			0
$531$		−	22.5137i		−	0.977012i
$532$	−4.25710	+	0.286047i	−0.184568	+	0.0124017i
$533$	37.1576	−	37.1576i	1.60948	−	1.60948i
$534$	−4.20863	−	7.28956i	−0.182125	−	0.315450i
$535$		0			0
$536$	4.79041	−	8.29723i	0.206914	−	0.358386i
$537$	14.8880	−	55.5628i	0.642465	−	2.39771i
$538$	3.22783	+	12.0464i	0.139162	+	0.519359i
$539$		−	24.5311i		−	1.05663i
$540$		0			0
$541$	−7.28570	+	12.6192i	−0.313237	+	0.542542i	−0.979061	−	0.203567i	$-0.934747\pi$
$541$	−7.28570	+	12.6192i	−0.313237	+	0.542542i	0.665824	+	0.746109i	$0.268080\pi$
$542$	5.89473	+	21.9995i	0.253201	+	0.944957i
$543$	−43.6665	+	43.6665i	−1.87391	+	1.87391i
$544$	−2.58951			−0.111024
$545$		0			0
$546$	14.1342	−	8.16038i	0.604888	−	0.349232i
$547$	−2.61139	−	9.74585i	−0.111655	−	0.416703i	0.887360	−	0.461078i	$-0.152537\pi$
$547$	−2.61139	−	9.74585i	−0.111655	−	0.416703i	−0.999015	+	0.0443750i	$0.985870\pi$
$548$	−2.06515	−	0.553355i	−0.0882188	−	0.0236381i
$549$	28.8687	−	16.6674i	1.23209	−	0.711346i
$550$		0			0
$551$	12.4516	+	10.8836i	0.530455	+	0.463657i
$552$	−6.69798	−	6.69798i	−0.285085	−	0.285085i
$553$	−1.77015	+	6.60628i	−0.0752743	+	0.280928i
$554$	−11.9336	−	20.6696i	−0.507010	−	0.878167i
$555$		0			0
$556$	11.4628	+	19.8541i	0.486130	+	0.842002i
$557$	6.39366	−	1.71318i	0.270908	−	0.0725896i	−0.120807	−	0.992676i	$-0.538548\pi$
$557$	6.39366	−	1.71318i	0.270908	−	0.0725896i	0.391716	+	0.920086i	$0.371882\pi$
$558$	−14.0758	+	14.0758i	−0.595878	+	0.595878i
$559$	30.6176			1.29499
$560$		0			0
$561$	−23.6661	−	13.6636i	−0.999185	−	0.576880i
$562$	−5.31352	−	5.31352i	−0.224137	−	0.224137i
$563$	−22.8598	−	22.8598i	−0.963424	−	0.963424i	0.0359305	−	0.999354i	$-0.488561\pi$
$563$	−22.8598	−	22.8598i	−0.963424	−	0.963424i	−0.999354	+	0.0359305i	$0.988561\pi$
$564$	−8.47127	+	14.6727i	−0.356705	+	0.617831i
$565$		0			0
$566$	−15.9199	−	9.19135i	−0.669163	−	0.386341i
$567$	1.56117	−	5.82636i	0.0655629	−	0.244684i
$568$	7.50361	+	2.01059i	0.314844	+	0.0843623i
$569$	−30.3121			−1.27075			−0.635375	−	0.772203i	$-0.719155\pi$
$569$	−30.3121			−1.27075			−0.635375	+	0.772203i	$0.719155\pi$
$570$		0			0
$571$	−3.70241			−0.154941			−0.0774706	−	0.996995i	$-0.524684\pi$
$571$	−3.70241			−0.154941			−0.0774706	+	0.996995i	$0.524684\pi$
$572$	−25.1585	−	6.74119i	−1.05193	−	0.281863i
$573$	−13.4851	+	50.3272i	−0.563349	+	2.10245i
$574$	−6.94408	−	4.00917i	−0.289840	−	0.167339i
$575$		0			0
$576$	1.87780	−	3.25245i	0.0782418	−	0.135519i
$577$	9.61846	+	9.61846i	0.400422	+	0.400422i	0.878382	−	0.477960i	$-0.158624\pi$
$577$	9.61846	+	9.61846i	0.400422	+	0.400422i	−0.477960	+	0.878382i	$0.658624\pi$
$578$	7.27926	+	7.27926i	0.302777	+	0.302777i
$579$	−20.6106	−	11.8995i	−0.856546	−	0.494527i
$580$		0			0
$581$	−6.14643			−0.254997
$582$	−18.6586	+	18.6586i	−0.773423	+	0.773423i
$583$	8.56610	−	2.29528i	0.354772	−	0.0950608i
$584$	7.77699	+	13.4701i	0.321814	+	0.557398i
$585$		0			0
$586$	−15.6002	−	27.0204i	−0.644440	−	1.11620i
$587$	1.73848	−	6.48809i	0.0717546	−	0.267792i	−0.920723	−	0.390216i	$-0.872400\pi$
$587$	1.73848	−	6.48809i	0.0717546	−	0.267792i	0.992478	+	0.122424i	$0.0390669\pi$
$588$	11.1042	+	11.1042i	0.457930	+	0.457930i
$589$	22.6674	+	4.47014i	0.933993	+	0.184189i
$590$		0			0
$591$	−48.9801	+	28.2787i	−2.01477	+	1.16323i
$592$	3.53466	+	0.947109i	0.145274	+	0.0389259i
$593$	−7.45574	−	27.8252i	−0.306171	−	1.14264i	−0.931933	−	0.362630i	$-0.881879\pi$
$593$	−7.45574	−	27.8252i	−0.306171	−	1.14264i	0.625762	−	0.780014i	$-0.284788\pi$
$594$	6.90565	−	3.98698i	0.283342	−	0.163588i
$595$		0			0
$596$	−9.34645			−0.382845
$597$	−30.0840	+	30.0840i	−1.23126	+	1.23126i
$598$	−6.05085	−	22.5821i	−0.247438	−	0.923450i
$599$	−10.8725	+	18.8318i	−0.444239	+	0.769445i	−0.997999	−	0.0632314i	$-0.979859\pi$
$599$	−10.8725	+	18.8318i	−0.444239	+	0.769445i	0.553759	+	0.832677i	$0.313193\pi$
$600$		0			0
$601$		−	44.2703i		−	1.80582i	−0.429827	−	0.902911i	$-0.641425\pi$
$601$		−	44.2703i		−	1.80582i	0.429827	−	0.902911i	$-0.358575\pi$
$602$	−1.20917	−	4.51270i	−0.0492822	−	0.183924i
$603$	−9.31277	+	34.7557i	−0.379245	+	1.41536i
$604$	2.51649	−	4.35868i	0.102394	−	0.177352i
$605$		0			0
$606$	18.6735	+	32.3434i	0.758557	+	1.31386i
$607$	−1.55155	+	1.55155i	−0.0629754	+	0.0629754i	−0.737893	−	0.674918i	$-0.764179\pi$
$607$	−1.55155	+	1.55155i	−0.0629754	+	0.0629754i	0.674918	+	0.737893i	$0.264179\pi$
$608$	−4.34909	+	0.292229i	−0.176379	+	0.0118514i
$609$			9.65260i			0.391143i
$610$		0			0
$611$	−36.2135	+	20.9079i	−1.46504	+	0.845842i
$612$	9.39381	−	2.51706i	0.379722	−	0.101746i
$613$	−4.46673	−	1.19686i	−0.180409	−	0.0483406i	0.167483	−	0.985875i	$-0.446436\pi$
$613$	−4.46673	−	1.19686i	−0.180409	−	0.0483406i	−0.347893	+	0.937534i	$0.613103\pi$
$614$	0.287814	+	0.166169i	0.0116152	+	0.00670605i
$615$		0			0
$616$			3.97431i			0.160129i
$617$	6.29373	−	1.68640i	0.253376	−	0.0678919i	−0.129895	−	0.991528i	$-0.541464\pi$
$617$	6.29373	−	1.68640i	0.253376	−	0.0678919i	0.383271	+	0.923636i	$0.374797\pi$
$618$	20.7782	−	5.56751i	0.835823	−	0.223958i
$619$			20.5352i			0.825379i	0.910872	+	0.412690i	$0.135411\pi$
$619$			20.5352i			0.825379i	−0.910872	+	0.412690i	$0.864589\pi$
$620$		0			0
$621$	6.19847	+	3.57869i	0.248736	+	0.143608i
$622$	−2.45863	−	0.658787i	−0.0985820	−	0.0264150i
$623$	−3.06194	+	0.820445i	−0.122674	+	0.0328704i
$624$	14.4396	−	8.33673i	0.578048	−	0.333736i
$625$		0			0
$626$		−	31.9717i		−	1.27785i
$627$	−41.2893	−	20.2774i	−1.64894	−	0.809801i
$628$	−7.48364	+	7.48364i	−0.298630	+	0.298630i
$629$	4.73796	+	8.20639i	0.188915	+	0.327210i
$630$		0			0
$631$	4.10736	−	7.11416i	0.163512	−	0.283210i	−0.772614	−	0.634876i	$-0.781051\pi$
$631$	4.10736	−	7.11416i	0.163512	−	0.283210i	0.936126	+	0.351666i	$0.114385\pi$
$632$	−1.80840	+	6.74904i	−0.0719343	+	0.268462i
$633$	−3.53514	−	13.1933i	−0.140509	−	0.524388i
$634$		−	10.4893i		−	0.416581i
$635$		0			0
$636$	−2.83854	+	4.91649i	−0.112555	+	0.194952i
$637$	10.0314	+	37.4376i	0.397457	+	1.48333i
$638$	10.8925	−	10.8925i	0.431240	−	0.431240i
$639$	−29.1747			−1.15413
$640$		0			0
$641$	−31.7676	+	18.3410i	−1.25474	+	0.724427i	−0.972048	−	0.234782i	$-0.924562\pi$
$641$	−31.7676	+	18.3410i	−1.25474	+	0.724427i	−0.282697	+	0.959209i	$0.591229\pi$
$642$	−4.15774	−	15.5169i	−0.164093	−	0.612403i
$643$	−21.2398	−	5.69120i	−0.837617	−	0.224439i	−0.185583	−	0.982629i	$-0.559417\pi$
$643$	−21.2398	−	5.69120i	−0.837617	−	0.224439i	−0.652034	+	0.758190i	$0.726084\pi$
$644$	−3.08939	+	1.78366i	−0.121739	+	0.0702860i
$645$		0			0
$646$	−8.49854	−	7.42837i	−0.334371	−	0.292265i
$647$	−23.8745	−	23.8745i	−0.938605	−	0.938605i	0.0596164	−	0.998221i	$-0.481012\pi$
$647$	−23.8745	−	23.8745i	−0.938605	−	0.938605i	−0.998221	+	0.0596164i	$0.981012\pi$
$648$	1.59491	−	5.95227i	0.0626538	−	0.233827i
$649$	12.1698	+	21.0787i	0.477707	+	0.827412i
$650$		0			0
$651$	6.74258	+	11.6785i	0.264263	+	0.457716i
$652$	18.5846	−	4.97972i	0.727828	−	0.195021i
$653$	−7.20619	+	7.20619i	−0.282000	+	0.282000i	−0.833906	−	0.551906i	$-0.813901\pi$
$653$	−7.20619	+	7.20619i	−0.282000	+	0.282000i	0.551906	+	0.833906i	$0.313901\pi$
$654$	−42.6559			−1.66798
$655$		0			0
$656$	−7.09414	−	4.09581i	−0.276980	−	0.159914i
$657$	−41.3053	−	41.3053i	−1.61148	−	1.61148i
$658$	4.51176	+	4.51176i	0.175887	+	0.175887i
$659$	−16.5619	+	28.6860i	−0.645159	+	1.11745i	0.339106	+	0.940748i	$0.389875\pi$
$659$	−16.5619	+	28.6860i	−0.645159	+	1.11745i	−0.984265	+	0.176700i	$0.943458\pi$
$660$		0			0
$661$	−2.47962	−	1.43161i	−0.0964461	−	0.0556832i	0.451001	−	0.892523i	$-0.351067\pi$
$661$	−2.47962	−	1.43161i	−0.0964461	−	0.0556832i	−0.547447	+	0.836840i	$0.684400\pi$
$662$	−3.05615	+	11.4057i	−0.118780	+	0.443295i
$663$	41.7049	+	11.1748i	1.61968	+	0.433993i
$664$	−6.27926			−0.243682
$665$		0			0
$666$	−13.7431			−0.532533
$667$	13.3557	+	3.57866i	0.517137	+	0.138566i
$668$	3.69755	−	13.7995i	0.143063	−	0.533917i
$669$	20.6198	+	11.9048i	0.797206	+	0.460267i
$670$		0			0
$671$	−18.0191	+	31.2100i	−0.695620	+	1.20485i
$672$	−1.79900	−	1.79900i	−0.0693980	−	0.0693980i
$673$	−1.80376	−	1.80376i	−0.0695298	−	0.0695298i	0.671487	−	0.741017i	$-0.265656\pi$
$673$	−1.80376	−	1.80376i	−0.0695298	−	0.0695298i	−0.741017	+	0.671487i	$0.765656\pi$
$674$	−8.24197	−	4.75850i	−0.317469	−	0.183291i
$675$		0			0
$676$	28.1516			1.08275
$677$	−31.0474	+	31.0474i	−1.19325	+	1.19325i	−0.217100	+	0.976149i	$0.569660\pi$
$677$	−31.0474	+	31.0474i	−1.19325	+	1.19325i	−0.976149	+	0.217100i	$0.930340\pi$
$678$	−46.0707	+	12.3446i	−1.76933	+	0.474092i
$679$	4.96874	+	8.60610i	0.190683	+	0.330272i
$680$		0			0
$681$	−20.4518	−	35.4236i	−0.783715	−	1.35743i
$682$	5.56996	−	20.7874i	0.213285	−	0.795990i
$683$	−19.8744	−	19.8744i	−0.760472	−	0.760472i	0.215936	−	0.976408i	$-0.430720\pi$
$683$	−19.8744	−	19.8744i	−0.760472	−	0.760472i	−0.976408	+	0.215936i	$0.930720\pi$
$684$	15.4929	−	5.28751i	0.592385	−	0.202173i
$685$		0			0
$686$	11.0557	−	6.38299i	0.422107	−	0.243704i
$687$	7.03238	+	1.88432i	0.268302	+	0.0718914i
$688$	−1.23530	−	4.61022i	−0.0470955	−	0.175763i
$689$	−12.1344	+	7.00578i	−0.462282	+	0.266899i
$690$		0			0
$691$	−24.0602			−0.915293			−0.457646	−	0.889134i	$-0.651307\pi$
$691$	−24.0602			−0.915293			−0.457646	+	0.889134i	$0.651307\pi$
$692$	5.96281	−	5.96281i	0.226672	−	0.226672i
$693$	−3.86311	−	14.4173i	−0.146748	−	0.547669i
$694$	5.33843	−	9.24644i	0.202644	−	0.350990i
$695$		0			0
$696$			9.86120i			0.373788i
$697$	−5.49014	−	20.4895i	−0.207954	−	0.776095i
$698$	−0.310301	+	1.15806i	−0.0117451	+	0.0438332i
$699$	−21.0347	+	36.4331i	−0.795605	+	1.37803i
$700$		0			0
$701$	−20.8449	−	36.1044i	−0.787300	−	1.36364i	−0.927616	−	0.373536i	$-0.878145\pi$
$701$	−20.8449	−	36.1044i	−0.787300	−	1.36364i	0.140316	−	0.990107i	$-0.455188\pi$
$702$	−8.90852	+	8.90852i	−0.336230	+	0.336230i
$703$	8.88352	+	13.2480i	0.335048	+	0.499657i
$704$			4.06019i			0.153024i
$705$		0			0
$706$	−9.06369	+	5.23293i	−0.341117	+	0.196944i
$707$	13.5857	−	3.64027i	0.510942	−	0.136906i
$708$	−15.0502	−	4.03270i	−0.565622	−	0.151558i
$709$	3.82826	+	2.21025i	0.143773	+	0.0830075i	0.570161	−	0.821533i	$-0.306881\pi$
$709$	3.82826	+	2.21025i	0.143773	+	0.0830075i	−0.426388	+	0.904540i	$0.640214\pi$
$710$		0			0
$711$		−	26.2409i		−	0.984110i
$712$	−3.12811	+	0.838175i	−0.117231	+	0.0314119i
$713$	18.6586	−	4.99957i	0.698772	−	0.187235i
$714$		−	6.58817i		−	0.246556i
$715$		0			0
$716$	−19.1663	−	11.0657i	−0.716279	−	0.413544i
$717$	49.4471	+	13.2493i	1.84664	+	0.494805i
$718$	22.9175	−	6.14072i	0.855273	−	0.229170i
$719$	−12.9608	+	7.48293i	−0.483357	+	0.279066i	−0.721814	−	0.692087i	$-0.756692\pi$
$719$	−12.9608	+	7.48293i	−0.483357	+	0.279066i	0.238458	+	0.971153i	$0.423358\pi$
$720$		0			0
$721$		−	8.10116i		−	0.301703i
$722$	−15.1116	−	11.5169i	−0.562396	−	0.428614i
$723$	17.8756	−	17.8756i	0.664802	−	0.664802i
$724$	11.8796	+	20.5760i	0.441501	+	0.764703i
$725$		0			0
$726$	−7.12840	+	12.3467i	−0.264560	+	0.458231i
$727$	11.4901	−	42.8815i	0.426143	−	1.59039i	−0.335272	−	0.942121i	$-0.608828\pi$
$727$	11.4901	−	42.8815i	0.426143	−	1.59039i	0.761415	−	0.648265i	$-0.224505\pi$
$728$	−1.62519	−	6.06530i	−0.0602336	−	0.224795i
$729$			38.4567i			1.42432i
$730$		0			0
$731$	6.17967	−	10.7035i	0.228563	−	0.395884i
$732$	−5.97097	−	22.2840i	−0.220694	−	0.823640i
$733$	6.32317	−	6.32317i	0.233552	−	0.233552i	−0.580622	−	0.814173i	$-0.697190\pi$
$733$	6.32317	−	6.32317i	0.233552	−	0.233552i	0.814173	+	0.580622i	$0.197190\pi$
$734$	22.6000			0.834182
$735$		0			0
$736$	−3.15615	+	1.82220i	−0.116337	+	0.0671673i
$737$	−10.0681	−	37.5745i	−0.370862	−	1.38407i
$738$	29.7162	+	7.96243i	1.09387	+	0.293101i
$739$	11.8968	−	6.86864i	0.437632	−	0.252667i	−0.264961	−	0.964259i	$-0.585359\pi$
$739$	11.8968	−	6.86864i	0.437632	−	0.252667i	0.702593	+	0.711592i	$0.252026\pi$
$740$		0			0
$741$	71.3046	+	14.0617i	2.61944	+	0.516568i
$742$	1.51179	+	1.51179i	0.0554997	+	0.0554997i
$743$	5.62480	−	20.9920i	0.206354	−	0.770123i	−0.782679	−	0.622426i	$-0.786147\pi$
$743$	5.62480	−	20.9920i	0.206354	−	0.770123i	0.989033	−	0.147697i	$-0.0471861\pi$
$744$	6.88829	+	11.9309i	0.252537	+	0.437407i
$745$		0			0
$746$	−0.395534	−	0.685084i	−0.0144815	−	0.0250827i
$747$	22.7789	−	6.10358i	0.833435	−	0.223318i
$748$	−7.43446	+	7.43446i	−0.271831	+	0.271831i
$749$	−6.04984			−0.221056
$750$		0			0
$751$	−9.49288	−	5.48071i	−0.346400	−	0.199994i	0.316699	−	0.948526i	$-0.397426\pi$
$751$	−9.49288	−	5.48071i	−0.346400	−	0.199994i	−0.663099	+	0.748532i	$0.730759\pi$
$752$	4.60926	+	4.60926i	0.168083	+	0.168083i
$753$	35.5498	+	35.5498i	1.29551	+	1.29551i
$754$	−12.1692	+	21.0776i	−0.443175	+	0.767602i
$755$		0			0
$756$	1.66484	+	0.961196i	0.0605496	+	0.0349584i
$757$	−11.7776	+	43.9547i	−0.428065	+	1.59756i	0.329072	+	0.944305i	$0.393264\pi$
$757$	−11.7776	+	43.9547i	−0.428065	+	1.59756i	−0.757137	+	0.653256i	$0.773402\pi$
$758$	−4.77754	−	1.28014i	−0.173528	−	0.0464967i
$759$	−38.4597			−1.39600
$760$		0			0
$761$	52.2387			1.89365			0.946826	−	0.321746i	$-0.104270\pi$
$761$	52.2387			1.89365			0.946826	+	0.321746i	$0.104270\pi$
$762$	−4.28164	−	1.14726i	−0.155108	−	0.0415610i
$763$	−4.15774	+	15.5169i	−0.150520	+	0.561750i
$764$	17.3603	+	10.0230i	0.628074	+	0.362618i
$765$		0			0
$766$	1.05047	−	1.81947i	0.0379552	−	0.0657403i
$767$	−27.1923	−	27.1923i	−0.981856	−	0.981856i
$768$	−1.83788	−	1.83788i	−0.0663188	−	0.0663188i
$769$	−23.2102	−	13.4004i	−0.836982	−	0.483232i	0.0192555	−	0.999815i	$-0.493870\pi$
$769$	−23.2102	−	13.4004i	−0.836982	−	0.483232i	−0.856237	+	0.516583i	$0.827204\pi$
$770$		0			0
$771$	66.5158			2.39551
$772$	−6.47459	+	6.47459i	−0.233026	+	0.233026i
$773$	−19.5043	+	5.22617i	−0.701522	+	0.187972i	−0.591912	−	0.806002i	$-0.701627\pi$
$773$	−19.5043	+	5.22617i	−0.701522	+	0.187972i	−0.109610	+	0.993975i	$0.534960\pi$
$774$	8.96247	+	15.5234i	0.322149	+	0.557979i
$775$		0			0
$776$	5.07611	+	8.79208i	0.182222	+	0.315617i
$777$	−2.40961	+	8.99279i	−0.0864443	+	0.322614i
$778$	−7.61081	−	7.61081i	−0.272861	−	0.272861i
$779$	−11.5330	−	33.7926i	−0.413211	−	1.21074i
$780$		0			0
$781$	27.3152	−	15.7704i	0.977413	−	0.564310i
$782$	−9.11567	−	2.44254i	−0.325976	−	0.0873449i
$783$	−1.92851	−	7.19728i	−0.0689192	−	0.257210i
$784$	5.23240	−	3.02093i	0.186872	−	0.107890i
$785$		0			0
$786$	33.7414			1.20351
$787$	11.1138	−	11.1138i	0.396163	−	0.396163i	−0.480714	−	0.876877i	$-0.659623\pi$
$787$	11.1138	−	11.1138i	0.396163	−	0.396163i	0.876877	+	0.480714i	$0.159623\pi$
$788$	5.63188	+	21.0185i	0.200627	+	0.748752i
$789$	23.8721	−	41.3477i	0.849869	−	1.47202i
$790$		0			0
$791$			17.9624i			0.638668i
$792$	−3.94660	−	14.7289i	−0.140236	−	0.523369i
$793$	14.7369	−	54.9989i	0.523323	−	1.95307i
$794$	−13.6171	+	23.5854i	−0.483251	+	0.837016i
$795$		0			0
$796$	8.18443	+	14.1759i	0.290090	+	0.502450i
$797$	20.9141	−	20.9141i	0.740817	−	0.740817i	−0.231918	−	0.972735i	$-0.574500\pi$
$797$	20.9141	−	20.9141i	0.740817	−	0.740817i	0.972735	+	0.231918i	$0.0745002\pi$
$798$	−0.743481	−	11.0648i	−0.0263189	−	0.391691i
$799$			16.8797i			0.597160i
$800$		0			0
$801$	10.5329	−	6.08119i	0.372163	−	0.214868i
$802$	−23.0231	+	6.16901i	−0.812972	+	0.217835i
$803$	61.0003	+	16.3450i	2.15265	+	0.576802i
$804$	21.5658	+	12.4510i	0.760567	+	0.439114i
$805$		0			0
$806$			34.0019i			1.19767i
$807$	−31.3105	+	8.38963i	−1.10218	+	0.295329i
$808$	13.8793	−	3.71894i	0.488271	−	0.130832i
$809$		−	28.7975i		−	1.01246i	−0.862397	−	0.506232i	$-0.831038\pi$
$809$		−	28.7975i		−	1.01246i	0.862397	−	0.506232i	$-0.168962\pi$
$810$		0			0
$811$	−12.8987	−	7.44709i	−0.452936	−	0.261503i	0.256134	−	0.966641i	$-0.417551\pi$
$811$	−12.8987	−	7.44709i	−0.452936	−	0.261503i	−0.709069	+	0.705139i	$0.750885\pi$
$812$	3.58720	+	0.961188i	0.125886	+	0.0337311i
$813$	−57.1800	+	15.3213i	−2.00539	+	0.537342i
$814$	12.8671	−	7.42883i	0.450992	−	0.260380i
$815$		0			0
$816$		−	6.73054i		−	0.235616i
$817$	9.17088	−	18.6740i	0.320848	−	0.653319i
$818$	−9.91334	+	9.91334i	−0.346612	+	0.346612i
$819$	11.7912	+	20.4230i	0.412018	+	0.713636i
$820$		0			0
$821$	7.93981	−	13.7521i	0.277101	−	0.479953i	−0.693562	−	0.720397i	$-0.743960\pi$
$821$	7.93981	−	13.7521i	0.277101	−	0.479953i	0.970663	+	0.240444i	$0.0772929\pi$
$822$	1.43825	−	5.36764i	0.0501649	−	0.187218i
$823$	−9.91792	−	37.0142i	−0.345717	−	1.29023i	−0.891772	−	0.452484i	$-0.850538\pi$
$823$	−9.91792	−	37.0142i	−0.345717	−	1.29023i	0.546056	−	0.837749i	$-0.316129\pi$
$824$		−	8.27623i		−	0.288316i
$825$		0			0
$826$	−2.93394	+	5.08174i	−0.102085	+	0.176816i
$827$	9.91742	+	37.0123i	0.344862	+	1.28704i	0.892773	+	0.450507i	$0.148757\pi$
$827$	9.91742	+	37.0123i	0.344862	+	1.28704i	−0.547911	+	0.836537i	$0.684577\pi$
$828$	9.67814	−	9.67814i	0.336339	−	0.336339i
$829$	26.7511			0.929103			0.464552	−	0.885546i	$-0.346215\pi$
$829$	26.7511			0.929103			0.464552	+	0.885546i	$0.346215\pi$
$830$		0			0
$831$	53.7235	−	31.0173i	1.86365	−	1.07598i
$832$	−1.66031	−	6.19637i	−0.0575610	−	0.214820i
$833$	15.1124	+	4.04934i	0.523612	+	0.140301i
$834$	−51.6039	+	29.7935i	−1.78690	+	1.03167i
$835$		0			0
$836$	−11.6472	+	13.3252i	−0.402827	+	0.460861i
$837$	−7.36074	−	7.36074i	−0.254424	−	0.254424i
$838$	−2.43936	+	9.10383i	−0.0842664	+	0.314486i
$839$	23.6809	+	41.0166i	0.817557	+	1.41605i	0.907477	+	0.420101i	$0.138005\pi$
$839$	23.6809	+	41.0166i	0.817557	+	1.41605i	−0.0899203	+	0.995949i	$0.528661\pi$
$840$		0			0
$841$	7.30278	+	12.6488i	0.251820	+	0.436165i
$842$	9.68987	−	2.59639i	0.333935	−	0.0894776i
$843$	13.8107	−	13.8107i	0.475665	−	0.475665i
$844$	−5.25507			−0.180887
$845$		0			0
$846$	−21.2010	−	12.2404i	−0.728906	−	0.420834i
$847$	3.79655	+	3.79655i	0.130451	+	0.130451i
$848$	1.54446	+	1.54446i	0.0530371	+	0.0530371i
$849$	23.8898	−	41.3783i	0.819894	−	1.42010i
$850$		0			0
$851$	11.5494	+	6.66808i	0.395910	+	0.228579i
$852$	−5.22582	+	19.5030i	−0.179034	+	0.668163i
$853$	24.1369	+	6.46746i	0.826431	+	0.221441i	0.647156	−	0.762358i	$-0.275958\pi$
$853$	24.1369	+	6.46746i	0.826431	+	0.221441i	0.179275	+	0.983799i	$0.442625\pi$
$854$	−8.68824			−0.297305
$855$		0			0
$856$	−6.18058			−0.211248
$857$	−6.37021	−	1.70689i	−0.217602	−	0.0583064i	0.148371	−	0.988932i	$-0.452597\pi$
$857$	−6.37021	−	1.70689i	−0.217602	−	0.0583064i	−0.365973	+	0.930625i	$0.619264\pi$
$858$	17.5214	−	65.3907i	0.598170	−	2.23240i
$859$	−19.4181	−	11.2110i	−0.662536	−	0.382515i	0.130706	−	0.991421i	$-0.458275\pi$
$859$	−19.4181	−	11.2110i	−0.662536	−	0.382515i	−0.793243	+	0.608906i	$0.791609\pi$
$860$		0			0
$861$	10.4204	−	18.0487i	0.355128	−	0.615099i
$862$	17.8662	+	17.8662i	0.608525	+	0.608525i
$863$	−4.87502	−	4.87502i	−0.165948	−	0.165948i	0.619248	−	0.785196i	$-0.287438\pi$
$863$	−4.87502	−	4.87502i	−0.165948	−	0.165948i	−0.785196	+	0.619248i	$0.787438\pi$
$864$	1.70082	+	0.981968i	0.0578630	+	0.0334072i
$865$		0			0
$866$	−14.0425			−0.477182
$867$	−18.9199	+	18.9199i	−0.642554	+	0.642554i
$868$	5.01150	−	1.34283i	0.170101	−	0.0455786i
$869$	14.1845	+	24.5683i	0.481177	+	0.833424i
$870$		0			0
$871$	30.7303	+	53.2264i	1.04126	+	1.80351i
$872$	−4.24759	+	15.8522i	−0.143842	+	0.536824i
$873$	−26.9604	−	26.9604i	−0.912471	−	0.912471i
$874$	−15.5854	−	3.07353i	−0.527185	−	0.103964i
$875$		0			0
$876$	−35.0110	+	20.2136i	−1.18291	+	0.682954i
$877$	10.2557	+	2.74801i	0.346311	+	0.0927936i	0.427782	−	0.903882i	$-0.359295\pi$
$877$	10.2557	+	2.74801i	0.346311	+	0.0927936i	−0.0814712	+	0.996676i	$0.525962\pi$
$878$	−10.6475	−	39.7368i	−0.359334	−	1.34105i
$879$	70.2302	−	40.5474i	2.36881	−	1.36763i
$880$		0			0
$881$	−28.8251			−0.971141			−0.485571	−	0.874197i	$-0.661388\pi$
$881$	−28.8251			−0.971141			−0.485571	+	0.874197i	$0.661388\pi$
$882$	−16.0448	+	16.0448i	−0.540258	+	0.540258i
$883$	3.81104	+	14.2230i	0.128252	+	0.478642i	0.999935	−	0.0114284i	$-0.00363785\pi$
$883$	3.81104	+	14.2230i	0.128252	+	0.478642i	−0.871683	+	0.490070i	$0.836971\pi$
$884$	8.30580	−	14.3861i	0.279354	−	0.483856i
$885$		0			0
$886$			4.99494i			0.167808i
$887$	10.3265	+	38.5389i	0.346729	+	1.29401i	0.890579	+	0.454828i	$0.150299\pi$
$887$	10.3265	+	38.5389i	0.346729	+	1.29401i	−0.543851	+	0.839182i	$0.683034\pi$
$888$	−2.46168	+	9.18712i	−0.0826087	+	0.308300i
$889$	−0.834679	+	1.44571i	−0.0279942	+	0.0484874i
$890$		0			0
$891$	−12.5100	−	21.6679i	−0.419099	−	0.725901i
$892$	6.47748	−	6.47748i	0.216882	−	0.216882i
$893$	1.90489	+	28.3495i	0.0637446	+	0.948679i
$894$		−	24.2929i		−	0.812475i
$895$		0			0
$896$	−0.847706	+	0.489423i	−0.0283199	+	0.0163505i
$897$	58.6943	−	15.7271i	1.95975	−	0.525113i
$898$	−16.4686	−	4.41274i	−0.549564	−	0.147255i
$899$	−17.4156	−	10.0549i	−0.580842	−	0.335349i
$900$		0			0
$901$			5.65602i			0.188429i
$902$	−32.1262	+	8.60820i	−1.06969	+	0.286622i
$903$	11.7292	−	3.14283i	0.390323	−	0.104587i
$904$			18.3505i			0.610330i
$905$		0			0
$906$	11.3289	+	6.54074i	0.376377	+	0.217302i
$907$	−8.64927	−	2.31756i	−0.287194	−	0.0769534i	0.112346	−	0.993669i	$-0.464164\pi$
$907$	−8.64927	−	2.31756i	−0.287194	−	0.0769534i	−0.399540	+	0.916716i	$0.630830\pi$
$908$	−15.2010	+	4.07311i	−0.504464	+	0.135171i
$909$	−46.7340	+	26.9819i	−1.55007	+	0.894933i
$910$		0			0
$911$		−	7.56630i		−	0.250683i	−0.992114	−	0.125341i	$-0.959997\pi$
$911$		−	7.56630i		−	0.250683i	0.992114	−	0.125341i	$-0.0400026\pi$
$912$	−0.759548	−	11.3040i	−0.0251511	−	0.374312i
$913$	−18.0277	+	18.0277i	−0.596629	+	0.596629i
$914$	16.8347	+	29.1586i	0.556844	+	0.964481i
$915$		0			0
$916$	1.40054	−	2.42581i	0.0462753	−	0.0801511i
$917$	3.28883	−	12.2741i	0.108607	−	0.405326i
$918$	1.31626	+	4.91234i	0.0434430	+	0.162132i
$919$		−	36.8353i		−	1.21508i	−0.794287	−	0.607542i	$-0.792156\pi$
$919$		−	36.8353i		−	1.21508i	0.794287	−	0.607542i	$-0.207844\pi$
$920$		0			0
$921$	−0.431900	+	0.748073i	−0.0142316	+	0.0246498i
$922$	5.44129	+	20.3072i	0.179199	+	0.668781i
$923$	−35.2375	+	35.2375i	−1.15986	+	1.15986i
$924$	−10.3298			−0.339827
$925$		0			0
$926$	12.9773	−	7.49242i	0.426459	−	0.246216i
$927$	8.04468	+	30.0232i	0.264222	+	0.986090i
$928$	3.66472	+	0.981960i	0.120300	+	0.0322344i
$929$	−19.9031	+	11.4911i	−0.653000	+	0.377010i	−0.789605	−	0.613616i	$-0.789714\pi$
$929$	−19.9031	+	11.4911i	−0.653000	+	0.377010i	0.136605	+	0.990626i	$0.456381\pi$
$930$		0			0
$931$	25.8382	+	5.09544i	0.846813	+	0.166996i
$932$	11.4451	+	11.4451i	0.374896	+	0.374896i
$933$	1.71229	−	6.39035i	0.0560579	−	0.209211i
$934$	11.7133	+	20.2880i	0.383270	+	0.663843i
$935$		0			0
$936$	12.0460	+	20.8643i	0.393736	+	0.681971i
$937$	17.3834	−	4.65787i	0.567891	−	0.152166i	0.0365618	−	0.999331i	$-0.488359\pi$
$937$	17.3834	−	4.65787i	0.567891	−	0.152166i	0.531329	+	0.847165i	$0.321693\pi$
$938$	6.63136	−	6.63136i	0.216522	−	0.216522i
$939$	83.0993			2.71184
$940$		0			0
$941$	35.2478	+	20.3503i	1.14905	+	0.663402i	0.948655	−	0.316314i	$-0.102445\pi$
$941$	35.2478	+	20.3503i	1.14905	+	0.663402i	0.200391	+	0.979716i	$0.435779\pi$
$942$	−19.4511	−	19.4511i	−0.633752	−	0.633752i
$943$	−21.1097	−	21.1097i	−0.687425	−	0.687425i
$944$	−2.99735	+	5.19156i	−0.0975553	+	0.168971i
$945$		0			0
$946$	−16.7824	−	9.68934i	−0.545644	−	0.315028i
$947$	1.29365	−	4.82795i	0.0420378	−	0.156887i	−0.941716	−	0.336408i	$-0.890788\pi$
$947$	1.29365	−	4.82795i	0.0420378	−	0.156887i	0.983754	+	0.179520i	$0.0574546\pi$
$948$	−17.5418	−	4.70031i	−0.569731	−	0.152659i
$949$	−99.7780			−3.23893
$950$		0			0
$951$	27.2632			0.884070
$952$	−2.44837	−	0.656038i	−0.0793520	−	0.0212623i
$953$	−3.67220	+	13.7048i	−0.118954	+	0.443943i	−0.999552	−	0.0299208i	$-0.990474\pi$
$953$	−3.67220	+	13.7048i	−0.118954	+	0.443943i	0.880598	+	0.473864i	$0.157141\pi$
$954$	−7.10401	−	4.10150i	−0.230001	−	0.132791i
$955$		0			0
$956$	9.84771	−	17.0567i	0.318498	−	0.551654i
$957$	28.3114	+	28.3114i	0.915178	+	0.915178i
$958$	−19.4674	−	19.4674i	−0.628964	−	0.628964i
$959$	−1.81240	−	1.04639i	−0.0585253	−	0.0337896i
$960$		0			0
$961$	2.90566			0.0937309
$962$	−16.5990	+	16.5990i	−0.535174	+	0.535174i
$963$	22.4209	−	6.00766i	0.722503	−	0.193594i
$964$	−4.86311	−	8.42316i	−0.156630	−	0.271292i
$965$		0			0
$966$	−4.63600	−	8.02979i	−0.149161	−	0.258354i
$967$	−3.51103	+	13.1033i	−0.112907	+	0.421375i	−0.999122	−	0.0418998i	$-0.986659\pi$
$967$	−3.51103	+	13.1033i	−0.112907	+	0.421375i	0.886215	+	0.463275i	$0.153326\pi$
$968$	3.87860	+	3.87860i	0.124663	+	0.124663i
$969$	19.3075	−	22.0890i	0.620245	−	0.709602i
$970$		0			0
$971$	39.7699	−	22.9611i	1.27628	−	0.736858i	0.300114	−	0.953903i	$-0.402975\pi$
$971$	39.7699	−	22.9611i	1.27628	−	0.736858i	0.976162	+	0.217045i	$0.0696418\pi$
$972$	21.1619	+	5.67032i	0.678769	+	0.181876i
$973$	5.80806	+	21.6760i	0.186198	+	0.694900i
$974$	33.6593	−	19.4332i	1.07851	−	0.622680i
$975$		0			0
$976$	−8.87599			−0.284114
$977$	−18.3304	+	18.3304i	−0.586440	+	0.586440i	−0.936665	−	0.350225i	$-0.886105\pi$
$977$	−18.3304	+	18.3304i	−0.586440	+	0.586440i	0.350225	+	0.936665i	$0.386105\pi$
$978$	12.9431	+	48.3042i	0.413874	+	1.54460i
$979$	−6.57438	+	11.3872i	−0.210118	+	0.363935i
$980$		0			0
$981$		−	61.6349i		−	1.96785i
$982$	3.69480	+	13.7892i	0.117906	+	0.440031i
$983$	14.1246	−	52.7139i	0.450506	−	1.68131i	−0.250468	−	0.968125i	$-0.580584\pi$
$983$	14.1246	−	52.7139i	0.450506	−	1.68131i	0.700974	−	0.713187i	$-0.252749\pi$
$984$	10.6456	−	18.4388i	0.339370	−	0.587807i
$985$		0			0
$986$	4.91231	+	8.50836i	0.156440	+	0.270962i
$987$	−11.7268	+	11.7268i	−0.373267	+	0.373267i
$988$	12.3261	−	25.0988i	0.392146	−	0.798498i
$989$		−	17.3942i		−	0.553103i
$990$		0			0
$991$	46.9277	−	27.0937i	1.49071	−	0.860661i	0.490764	−	0.871292i	$-0.336718\pi$
$991$	46.9277	−	27.0937i	1.49071	−	0.860661i	0.999943	+	0.0106317i	$0.00338423\pi$
$992$	5.11980	−	1.37185i	0.162554	−	0.0435562i
$993$	−29.6451	−	7.94339i	−0.940760	−	0.252076i
$994$	6.58524	+	3.80199i	0.208871	+	0.120592i
$995$		0			0
$996$		−	16.3208i		−	0.517143i
$997$	41.3388	−	11.0767i	1.30921	−	0.350803i	0.464287	−	0.885685i	$-0.346311\pi$
$997$	41.3388	−	11.0767i	1.30921	−	0.350803i	0.844927	+	0.534882i	$0.179644\pi$
$998$	12.6305	−	3.38432i	0.399810	−	0.107129i
$999$		−	7.18672i		−	0.227378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.f.107.5	yes	32
5.2	odd	4	inner	950.2.q.f.943.4	yes	32
5.3	odd	4	inner	950.2.q.f.943.5	yes	32
5.4	even	2	inner	950.2.q.f.107.4	✓	32
19.8	odd	6	inner	950.2.q.f.407.5	yes	32
95.8	even	12	inner	950.2.q.f.293.5	yes	32
95.27	even	12	inner	950.2.q.f.293.4	yes	32
95.84	odd	6	inner	950.2.q.f.407.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.f.107.4	✓	32	5.4	even	2	inner
950.2.q.f.107.5	yes	32	1.1	even	1	trivial
950.2.q.f.293.4	yes	32	95.27	even	12	inner
950.2.q.f.293.5	yes	32	95.8	even	12	inner
950.2.q.f.407.4	yes	32	95.84	odd	6	inner
950.2.q.f.407.5	yes	32	19.8	odd	6	inner
950.2.q.f.943.4	yes	32	5.2	odd	4	inner
950.2.q.f.943.5	yes	32	5.3	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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.672711 + 2.51059i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.29958 + 2.25093i) q^{6} +(0.692149 + 0.692149i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.25245 - 1.87780i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.672711 + 2.51059i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.29958 + 2.25093i) q^{6} +(0.692149 + 0.692149i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.25245 - 1.87780i) q^{9} +4.06019 q^{11} +(-1.83788 + 1.83788i) q^{12} +(-6.19637 + 1.66031i) q^{13} +(0.489423 + 0.847706i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.670215 + 2.50128i) q^{17} +(-2.65561 - 2.65561i) q^{18} +(-0.843357 + 4.27653i) q^{19} +(-2.20332 + 1.27209i) q^{21} +(3.92185 + 1.05086i) q^{22} +(0.943242 + 3.52023i) q^{23} +(-2.25093 + 1.29958i) q^{24} -6.41495 q^{26} +(1.38871 - 1.38871i) q^{27} +(0.253344 + 0.945493i) q^{28} +(1.89700 - 3.28570i) q^{29} -5.30041i q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.73134 + 10.1935i) q^{33} +(-1.29476 + 2.24258i) q^{34} +(-1.87780 - 3.25245i) q^{36} +(2.58755 - 2.58755i) q^{37} +(-1.92147 + 3.91254i) q^{38} -16.6735i q^{39} +(-7.09414 + 4.09581i) q^{41} +(-2.45748 + 0.658481i) q^{42} +(-4.61022 - 1.23530i) q^{43} +(3.51623 + 2.03010i) q^{44} +3.64441i q^{46} +(6.29637 - 1.68711i) q^{47} +(-2.51059 + 0.672711i) q^{48} -6.04186i q^{49} +(-5.82882 - 3.36527i) q^{51} +(-6.19637 - 1.66031i) q^{52} +(2.10978 - 0.565313i) q^{53} +(1.70082 - 0.981968i) q^{54} +0.978847i q^{56} +(-10.1693 - 4.99419i) q^{57} +(2.68276 - 2.68276i) q^{58} +(2.99735 + 5.19156i) q^{59} +(-4.43800 + 7.68683i) q^{61} +(1.37185 - 5.11980i) q^{62} +(-0.951461 - 3.55090i) q^{63} +1.00000i q^{64} +(-5.27653 + 9.13923i) q^{66} +(-2.47970 - 9.25436i) q^{67} +(-1.83106 + 1.83106i) q^{68} -9.47238 q^{69} +(6.72755 - 3.88415i) q^{71} +(-0.972022 - 3.62764i) q^{72} +(15.0240 + 4.02566i) q^{73} +(3.16909 - 1.82967i) q^{74} +(-2.86864 + 3.28191i) q^{76} +(2.81026 + 2.81026i) q^{77} +(4.31541 - 16.1053i) q^{78} +(3.49356 + 6.05103i) q^{79} +(-3.08112 - 5.33666i) q^{81} +(-7.91249 + 2.12015i) q^{82} +(-4.44010 + 4.44010i) q^{83} -2.54417 q^{84} +(-4.13341 - 2.38642i) q^{86} +(6.97292 + 6.97292i) q^{87} +(2.87099 + 2.87099i) q^{88} +(-1.61923 + 2.80459i) q^{89} +(-5.43800 - 3.13963i) q^{91} +(-0.943242 + 3.52023i) q^{92} +(13.3072 + 3.56564i) q^{93} +6.51848 q^{94} -2.59915 q^{96} +(9.80630 + 2.62759i) q^{97} +(1.56375 - 5.83599i) q^{98} +(-13.2056 - 7.62424i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{6}+O(q^{10}) \) 32 * q + 4 * q^6	\( 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) \) 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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