LMFDB - Embedded newform 950.2.q.e.107.2

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			107.2
Character	$\chi$	$=$	950.107
Dual form			950.2.q.e.293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.394434 - 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(1.69567 + 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.394434 - 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(1.69567 + 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +4.92692 q^{11} +(1.07761 - 1.07761i) q^{12} +(-3.55219 + 0.951806i) q^{13} +(-1.19902 - 2.07676i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.0410260 + 0.153111i) q^{17} +(-0.479062 - 0.479062i) q^{18} +(0.533033 + 4.32618i) q^{19} +(3.16493 - 1.82727i) q^{21} +(-4.75904 - 1.27518i) q^{22} +(0.620657 + 2.31632i) q^{23} +(-1.31980 + 0.761988i) q^{24} +3.67750 q^{26} +(3.96292 - 3.96292i) q^{27} +(0.620657 + 2.31632i) q^{28} +(-4.62539 + 8.01141i) q^{29} +6.10371i q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.94335 - 7.25267i) q^{33} +(0.0792561 - 0.137276i) q^{34} +(0.338748 + 0.586729i) q^{36} +(-2.44015 + 2.44015i) q^{37} +(0.604829 - 4.31673i) q^{38} +5.60442i q^{39} +(6.51141 - 3.75937i) q^{41} +(-3.53002 + 0.945867i) q^{42} +(6.15257 + 1.64858i) q^{43} +(4.26684 + 2.46346i) q^{44} -2.39804i q^{46} +(-2.62255 + 0.702709i) q^{47} +(1.47205 - 0.394434i) q^{48} -1.24943i q^{49} +(0.209205 + 0.120784i) q^{51} +(-3.55219 - 0.951806i) q^{52} +(6.03648 - 1.61747i) q^{53} +(-4.85357 + 2.80221i) q^{54} -2.39804i q^{56} +(6.57860 + 0.921745i) q^{57} +(6.54129 - 6.54129i) q^{58} +(-1.77358 - 3.07193i) q^{59} +(2.36272 - 4.09236i) q^{61} +(1.57976 - 5.89573i) q^{62} +(0.420493 + 1.56930i) q^{63} +1.00000i q^{64} +(-3.75426 + 6.50256i) q^{66} +(-2.36911 - 8.84162i) q^{67} +(-0.112085 + 0.112085i) q^{68} +3.65455 q^{69} +(3.64869 - 2.10657i) q^{71} +(-0.175349 - 0.654411i) q^{72} +(-3.16211 - 0.847284i) q^{73} +(2.98856 - 1.72545i) q^{74} +(-1.70147 + 4.01310i) q^{76} +(8.35442 + 8.35442i) q^{77} +(1.45053 - 5.41345i) q^{78} +(-7.39795 - 12.8136i) q^{79} +(-3.25426 - 5.63654i) q^{81} +(-7.26254 + 1.94599i) q^{82} +(-2.27867 + 2.27867i) q^{83} +3.65455 q^{84} +(-5.51624 - 3.18480i) q^{86} +(9.96877 + 9.96877i) q^{87} +(-3.48386 - 3.48386i) q^{88} +(3.93005 - 6.80704i) q^{89} +(-7.63728 - 4.40938i) q^{91} +(-0.620657 + 2.31632i) q^{92} +(8.98495 + 2.40751i) q^{93} +2.71506 q^{94} -1.52398 q^{96} +(-16.8877 - 4.52503i) q^{97} +(-0.323375 + 1.20685i) q^{98} +(2.89077 + 1.66898i) 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
$3$	0.394434	−	1.47205i	0.227727	−	0.849887i	−0.753567	−	0.657371i	$-0.771668\pi$
$3$	0.394434	−	1.47205i	0.227727	−	0.849887i	0.981294	−	0.192516i	$-0.0616649\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.761988	+	1.31980i	−0.311080	+	0.538807i
$7$	1.69567	+	1.69567i	0.640902	+	0.640902i	0.950777	−	0.309875i	$-0.100287\pi$
$7$	1.69567	+	1.69567i	0.640902	+	0.640902i	−0.309875	+	0.950777i	$0.600287\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.586729	+	0.338748i	0.195576	+	0.112916i
$10$		0			0
$11$	4.92692			1.48552			0.742761	−	0.669556i	$-0.233516\pi$
$11$	4.92692			1.48552			0.742761	+	0.669556i	$0.233516\pi$
$12$	1.07761	−	1.07761i	0.311080	−	0.311080i
$13$	−3.55219	+	0.951806i	−0.985200	+	0.263983i	−0.715233	−	0.698886i	$-0.753679\pi$
$13$	−3.55219	+	0.951806i	−0.985200	+	0.263983i	−0.269967	+	0.962870i	$0.587013\pi$
$14$	−1.19902	−	2.07676i	−0.320451	−	0.555037i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.0410260	+	0.153111i	−0.00995026	+	0.0371349i	−0.970722	−	0.240204i	$-0.922786\pi$
$17$	−0.0410260	+	0.153111i	−0.00995026	+	0.0371349i	0.960772	+	0.277339i	$0.0894524\pi$
$18$	−0.479062	−	0.479062i	−0.112916	−	0.112916i
$19$	0.533033	+	4.32618i	0.122286	+	0.992495i
$19$	0.533033	+	4.32618i	0.122286	+	0.992495i
$20$		0			0
$21$	3.16493	−	1.82727i	0.690645	−	0.398744i
$22$	−4.75904	−	1.27518i	−1.01463	−	0.271870i
$23$	0.620657	+	2.31632i	0.129416	+	0.482987i	0.999959	−	0.00910610i	$-0.00289860\pi$
$23$	0.620657	+	2.31632i	0.129416	+	0.482987i	−0.870543	+	0.492093i	$0.836232\pi$
$24$	−1.31980	+	0.761988i	−0.269404	+	0.155540i
$25$		0			0
$26$	3.67750			0.721216
$27$	3.96292	−	3.96292i	0.762665	−	0.762665i
$28$	0.620657	+	2.31632i	0.117293	+	0.437744i
$29$	−4.62539	+	8.01141i	−0.858914	+	1.48768i	0.0140525	+	0.999901i	$0.495527\pi$
$29$	−4.62539	+	8.01141i	−0.858914	+	1.48768i	−0.872966	+	0.487781i	$0.837807\pi$
$30$		0			0
$31$			6.10371i			1.09626i	0.836394	+	0.548129i	$0.184660\pi$
$31$			6.10371i			1.09626i	−0.836394	+	0.548129i	$0.815340\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	1.94335	−	7.25267i	0.338293	−	1.26253i
$34$	0.0792561	−	0.137276i	0.0135923	−	0.0235426i
$35$		0			0
$36$	0.338748	+	0.586729i	0.0564580	+	0.0977881i
$37$	−2.44015	+	2.44015i	−0.401159	+	0.401159i	−0.878641	−	0.477483i	$-0.841549\pi$
$37$	−2.44015	+	2.44015i	−0.401159	+	0.401159i	0.477483	+	0.878641i	$0.341549\pi$
$38$	0.604829	−	4.31673i	0.0981162	−	0.700267i
$39$			5.60442i			0.897425i
$40$		0			0
$41$	6.51141	−	3.75937i	1.01691	−	0.587114i	0.103704	−	0.994608i	$-0.466931\pi$
$41$	6.51141	−	3.75937i	1.01691	−	0.587114i	0.913208	+	0.407494i	$0.133597\pi$
$42$	−3.53002	+	0.945867i	−0.544695	+	0.145950i
$43$	6.15257	+	1.64858i	0.938258	+	0.251406i	0.695373	−	0.718649i	$-0.255239\pi$
$43$	6.15257	+	1.64858i	0.938258	+	0.251406i	0.242886	+	0.970055i	$0.421906\pi$
$44$	4.26684	+	2.46346i	0.643250	+	0.371381i
$45$		0			0
$46$		−	2.39804i		−	0.353571i
$47$	−2.62255	+	0.702709i	−0.382538	+	0.102501i	−0.444963	−	0.895549i	$-0.646783\pi$
$47$	−2.62255	+	0.702709i	−0.382538	+	0.102501i	0.0624252	+	0.998050i	$0.480117\pi$
$48$	1.47205	−	0.394434i	0.212472	−	0.0569317i
$49$		−	1.24943i		−	0.178489i
$50$		0			0
$51$	0.209205	+	0.120784i	0.0292945	+	0.0169132i
$52$	−3.55219	−	0.951806i	−0.492600	−	0.131992i
$53$	6.03648	−	1.61747i	0.829174	−	0.222177i	0.180821	−	0.983516i	$-0.442125\pi$
$53$	6.03648	−	1.61747i	0.829174	−	0.222177i	0.648354	+	0.761339i	$0.275458\pi$
$54$	−4.85357	+	2.80221i	−0.660487	+	0.381332i
$55$		0			0
$56$		−	2.39804i		−	0.320451i
$57$	6.57860	+	0.921745i	0.871357	+	0.122088i
$58$	6.54129	−	6.54129i	0.858914	−	0.858914i
$59$	−1.77358	−	3.07193i	−0.230900	−	0.399931i	0.727173	−	0.686454i	$-0.240834\pi$
$59$	−1.77358	−	3.07193i	−0.230900	−	0.399931i	−0.958073	+	0.286523i	$0.907500\pi$
$60$		0			0
$61$	2.36272	−	4.09236i	0.302516	−	0.523973i	−0.674189	−	0.738559i	$-0.735507\pi$
$61$	2.36272	−	4.09236i	0.302516	−	0.523973i	0.976705	+	0.214586i	$0.0688401\pi$
$62$	1.57976	−	5.89573i	0.200629	−	0.748758i
$63$	0.420493	+	1.56930i	0.0529771	+	0.197713i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−3.75426	+	6.50256i	−0.462117	+	0.800410i
$67$	−2.36911	−	8.84162i	−0.289432	−	1.08018i	−0.945539	−	0.325508i	$-0.894465\pi$
$67$	−2.36911	−	8.84162i	−0.289432	−	1.08018i	0.656107	−	0.754668i	$-0.272202\pi$
$68$	−0.112085	+	0.112085i	−0.0135923	+	0.0135923i
$69$	3.65455			0.439956
$70$		0			0
$71$	3.64869	−	2.10657i	0.433020	−	0.250004i	−0.267613	−	0.963527i	$-0.586235\pi$
$71$	3.64869	−	2.10657i	0.433020	−	0.250004i	0.700632	+	0.713523i	$0.252901\pi$
$72$	−0.175349	−	0.654411i	−0.0206651	−	0.0771231i
$73$	−3.16211	−	0.847284i	−0.370097	−	0.0991671i	0.0689769	−	0.997618i	$-0.478027\pi$
$73$	−3.16211	−	0.847284i	−0.370097	−	0.0991671i	−0.439073	+	0.898451i	$0.644693\pi$
$74$	2.98856	−	1.72545i	0.347414	−	0.200579i
$75$		0			0
$76$	−1.70147	+	4.01310i	−0.195172	+	0.460334i
$77$	8.35442	+	8.35442i	0.952074	+	0.952074i
$78$	1.45053	−	5.41345i	0.164240	−	0.612953i
$79$	−7.39795	−	12.8136i	−0.832334	−	1.44165i	−0.896183	−	0.443685i	$-0.853671\pi$
$79$	−7.39795	−	12.8136i	−0.832334	−	1.44165i	0.0638484	−	0.997960i	$-0.479663\pi$
$80$		0			0
$81$	−3.25426	−	5.63654i	−0.361584	−	0.626282i
$82$	−7.26254	+	1.94599i	−0.802013	+	0.214899i
$83$	−2.27867	+	2.27867i	−0.250117	+	0.250117i	−0.821019	−	0.570902i	$-0.806594\pi$
$83$	−2.27867	+	2.27867i	−0.250117	+	0.250117i	0.570902	+	0.821019i	$0.306594\pi$
$84$	3.65455			0.398744
$85$		0			0
$86$	−5.51624	−	3.18480i	−0.594832	−	0.343426i
$87$	9.96877	+	9.96877i	1.06876	+	1.06876i
$88$	−3.48386	−	3.48386i	−0.371381	−	0.371381i
$89$	3.93005	−	6.80704i	0.416584	−	0.721545i	−0.579009	−	0.815321i	$-0.696561\pi$
$89$	3.93005	−	6.80704i	0.416584	−	0.721545i	0.995593	+	0.0937763i	$0.0298938\pi$
$90$		0			0
$91$	−7.63728	−	4.40938i	−0.800604	−	0.462229i
$92$	−0.620657	+	2.31632i	−0.0647080	+	0.241494i
$93$	8.98495	+	2.40751i	0.931696	+	0.249647i
$94$	2.71506			0.280037
$95$		0			0
$96$	−1.52398			−0.155540
$97$	−16.8877	−	4.52503i	−1.71468	−	0.459447i	−0.738117	−	0.674673i	$-0.764285\pi$
$97$	−16.8877	−	4.52503i	−1.71468	−	0.459447i	−0.976564	+	0.215225i	$0.930951\pi$
$98$	−0.323375	+	1.20685i	−0.0326658	+	0.121910i
$99$	2.89077	+	1.66898i	0.290533	+	0.167739i
$100$		0			0
$101$	3.87897	−	6.71857i	0.385972	−	0.668523i	−0.605932	−	0.795517i	$-0.707200\pi$
$101$	3.87897	−	6.71857i	0.385972	−	0.668523i	0.991903	+	0.126994i	$0.0405329\pi$
$102$	−0.170815	−	0.170815i	−0.0169132	−	0.0169132i
$103$	−3.63726	−	3.63726i	−0.358390	−	0.358390i	0.504829	−	0.863219i	$-0.331555\pi$
$103$	−3.63726	−	3.63726i	−0.358390	−	0.358390i	−0.863219	+	0.504829i	$0.831555\pi$
$104$	3.18480	+	1.83875i	0.312296	+	0.180304i
$105$		0			0
$106$	−6.24943			−0.606998
$107$	10.8399	−	10.8399i	1.04793	−	1.04793i	0.0491359	−	0.998792i	$-0.484353\pi$
$107$	10.8399	−	10.8399i	1.04793	−	1.04793i	0.998792	−	0.0491359i	$-0.0156468\pi$
$108$	5.41345	−	1.45053i	0.520910	−	0.139577i
$109$	4.50461	+	7.80221i	0.431463	+	0.747316i	0.997000	−	0.0774073i	$-0.0246642\pi$
$109$	4.50461	+	7.80221i	0.431463	+	0.747316i	−0.565536	+	0.824723i	$0.691331\pi$
$110$		0			0
$111$	2.62954	+	4.55450i	0.249585	+	0.432294i
$112$	−0.620657	+	2.31632i	−0.0586466	+	0.218872i
$113$	13.1375	+	13.1375i	1.23588	+	1.23588i	0.961671	+	0.274205i	$0.0884146\pi$
$113$	13.1375	+	13.1375i	1.23588	+	1.23588i	0.274205	+	0.961671i	$0.411585\pi$
$114$	−6.11587	−	2.59300i	−0.572804	−	0.242857i
$115$		0			0
$116$	−8.01141	+	4.62539i	−0.743841	+	0.429457i
$117$	−2.40659	−	0.644845i	−0.222490	−	0.0596159i
$118$	0.918072	+	3.42629i	0.0845154	+	0.315416i
$119$	−0.329192	+	0.190059i	−0.0301770	+	0.0174227i
$120$		0			0
$121$	13.2746			1.20678
$122$	−3.34140	+	3.34140i	−0.302516	+	0.302516i
$123$	−2.96564	−	11.0679i	−0.267403	−	0.997962i
$124$	−3.05185	+	5.28596i	−0.274064	+	0.474694i
$125$		0			0
$126$		−	1.62466i		−	0.144736i
$127$	2.06655	+	7.71247i	0.183377	+	0.684371i	0.994972	+	0.100151i	$0.0319327\pi$
$127$	2.06655	+	7.71247i	0.183377	+	0.684371i	−0.811596	+	0.584220i	$0.801401\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.85357	−	8.40663i	0.427333	−	0.740162i
$130$		0			0
$131$	9.21772	+	15.9656i	0.805356	+	1.39492i	0.916051	+	0.401062i	$0.131359\pi$
$131$	9.21772	+	15.9656i	0.805356	+	1.39492i	−0.110695	+	0.993854i	$0.535308\pi$
$132$	5.30932	−	5.30932i	0.462117	−	0.462117i
$133$	−6.43192	+	8.23962i	−0.557718	+	0.714465i
$134$			9.15352i			0.790744i
$135$		0			0
$136$	0.137276	−	0.0792561i	0.0117713	−	0.00679616i
$137$	5.35617	−	1.43518i	0.457608	−	0.122616i	−0.0226489	−	0.999743i	$-0.507210\pi$
$137$	5.35617	−	1.43518i	0.457608	−	0.122616i	0.480257	+	0.877128i	$0.340543\pi$
$138$	−3.53002	−	0.945867i	−0.300496	−	0.0805176i
$139$	−5.00828	−	2.89153i	−0.424797	−	0.245256i	0.272331	−	0.962204i	$-0.412206\pi$
$139$	−5.00828	−	2.89153i	−0.424797	−	0.245256i	−0.697127	+	0.716947i	$0.745539\pi$
$140$		0			0
$141$			4.13769i			0.348456i
$142$	−4.06958	+	1.09044i	−0.341512	+	0.0915078i
$143$	−17.5014	+	4.68947i	−1.46354	+	0.392153i
$144$			0.677496i			0.0564580i
$145$		0			0
$146$	2.83507	+	1.63683i	0.234632	+	0.135465i
$147$	−1.83921	−	0.492816i	−0.151696	−	0.0406468i
$148$	−3.33331	+	0.893158i	−0.273996	+	0.0734171i
$149$	16.4960	−	9.52398i	1.35141	−	0.780235i	0.362959	−	0.931805i	$-0.381766\pi$
$149$	16.4960	−	9.52398i	1.35141	−	0.780235i	0.988446	+	0.151570i	$0.0484330\pi$
$150$		0			0
$151$		−	10.5073i		−	0.855072i	−0.903998	−	0.427536i	$-0.859382\pi$
$151$		−	10.5073i		−	0.855072i	0.903998	−	0.427536i	$-0.140618\pi$
$152$	2.68216	−	3.43599i	0.217552	−	0.278695i
$153$	−0.0759372	+	0.0759372i	−0.00613916	+	0.00613916i
$154$	−5.90747	−	10.2320i	−0.476037	−	0.824521i
$155$		0			0
$156$	−2.80221	+	4.85357i	−0.224356	+	0.388596i
$157$	−0.213396	+	0.796403i	−0.0170308	+	0.0635599i	−0.973918	−	0.226899i	$-0.927141\pi$
$157$	−0.213396	+	0.796403i	−0.0170308	+	0.0635599i	0.956887	+	0.290459i	$0.0938079\pi$
$158$	3.82946	+	14.2917i	0.304655	+	1.13699i
$159$		−	9.52398i		−	0.755300i
$160$		0			0
$161$	−2.87529	+	4.98014i	−0.226604	+	0.392490i
$162$	1.68453	+	6.28674i	0.132349	+	0.493933i
$163$	−0.165440	+	0.165440i	−0.0129583	+	0.0129583i	−0.713556	−	0.700598i	$-0.752917\pi$
$163$	−0.165440	+	0.165440i	−0.0129583	+	0.0129583i	0.700598	+	0.713556i	$0.252917\pi$
$164$	7.51873			0.587114
$165$		0			0
$166$	2.79080	−	1.61127i	0.216608	−	0.125059i
$167$	2.05164	+	7.65682i	0.158761	+	0.592502i	0.998754	+	0.0499057i	$0.0158921\pi$
$167$	2.05164	+	7.65682i	0.158761	+	0.592502i	−0.839993	+	0.542597i	$0.817441\pi$
$168$	−3.53002	−	0.945867i	−0.272347	−	0.0729752i
$169$	0.453777	−	0.261988i	0.0349059	−	0.0201529i
$170$		0			0
$171$	−1.15274	+	2.71886i	−0.0881523	+	0.207916i
$172$	4.50399	+	4.50399i	0.343426	+	0.343426i
$173$	−0.661662	+	2.46935i	−0.0503052	+	0.187742i	−0.986506	−	0.163723i	$-0.947650\pi$
$173$	−0.661662	+	2.46935i	−0.0503052	+	0.187742i	0.936201	+	0.351465i	$0.114316\pi$
$174$	−7.04899	−	12.2092i	−0.534382	−	0.925577i
$175$		0			0
$176$	2.46346	+	4.26684i	0.185690	+	0.321625i
$177$	−5.22159	+	1.39912i	−0.392479	+	0.105164i
$178$	−5.55792	+	5.55792i	−0.416584	+	0.416584i
$179$	−21.3316			−1.59440			−0.797200	−	0.603715i	$-0.793686\pi$
$179$	−21.3316			−1.59440			−0.797200	+	0.603715i	$0.793686\pi$
$180$		0			0
$181$	−6.16493	−	3.55933i	−0.458236	−	0.264563i	0.253066	−	0.967449i	$-0.418561\pi$
$181$	−6.16493	−	3.55933i	−0.458236	−	0.264563i	−0.711302	+	0.702886i	$0.751894\pi$
$182$	6.23581	+	6.23581i	0.462229	+	0.462229i
$183$	−5.09221	−	5.09221i	−0.376427	−	0.376427i
$184$	1.19902	−	2.07676i	0.0883928	−	0.153101i
$185$		0			0
$186$	−8.05569	−	4.65095i	−0.590672	−	0.341024i
$187$	−0.202132	+	0.754366i	−0.0147813	+	0.0551647i
$188$	−2.62255	−	0.702709i	−0.191269	−	0.0512503i
$189$	13.4396			0.977586
$190$		0			0
$191$	−25.8767			−1.87237			−0.936185	−	0.351508i	$-0.885669\pi$
$191$	−25.8767			−1.87237			−0.936185	+	0.351508i	$0.885669\pi$
$192$	1.47205	+	0.394434i	0.106236	+	0.0284658i
$193$	−3.15797	+	11.7857i	−0.227316	+	0.848354i	0.754148	+	0.656705i	$0.228050\pi$
$193$	−3.15797	+	11.7857i	−0.227316	+	0.848354i	−0.981463	+	0.191649i	$0.938616\pi$
$194$	15.1411	+	8.74169i	1.08706	+	0.627617i
$195$		0			0
$196$	0.624713	−	1.08203i	0.0446223	−	0.0772881i
$197$	6.95348	+	6.95348i	0.495415	+	0.495415i	0.910007	−	0.414592i	$-0.136076\pi$
$197$	6.95348	+	6.95348i	0.495415	+	0.495415i	−0.414592	+	0.910007i	$0.636076\pi$
$198$	−2.36030	−	2.36030i	−0.167739	−	0.167739i
$199$	−22.8221	−	13.1763i	−1.61782	−	0.934046i	−0.987484	−	0.157721i	$-0.949585\pi$
$199$	−22.8221	−	13.1763i	−1.61782	−	0.934046i	−0.630332	−	0.776326i	$-0.717081\pi$
$200$		0			0
$201$	−13.9497			−0.983939
$202$	−5.48569	+	5.48569i	−0.385972	+	0.385972i
$203$	−21.4278	+	5.74157i	−1.50394	+	0.402979i
$204$	0.120784	+	0.209205i	0.00845660	+	0.0146473i
$205$		0			0
$206$	2.57193	+	4.45471i	0.179195	+	0.310374i
$207$	−0.420493	+	1.56930i	−0.0292263	+	0.109074i
$208$	−2.60038	−	2.60038i	−0.180304	−	0.180304i
$209$	2.62621	+	21.3148i	0.181659	+	1.47437i
$210$		0			0
$211$	−12.3233	+	7.11485i	−0.848370	+	0.489807i	−0.860100	−	0.510125i	$-0.829599\pi$
$211$	−12.3233	+	7.11485i	−0.848370	+	0.489807i	0.0117307	+	0.999931i	$0.496266\pi$
$212$	6.03648	+	1.61747i	0.414587	+	0.111088i
$213$	−1.66181	−	6.20195i	−0.113865	−	0.424951i
$214$	−13.2761	+	7.66493i	−0.907532	+	0.523964i
$215$		0			0
$216$	−5.60442			−0.381332
$217$	−10.3499	+	10.3499i	−0.702594	+	0.702594i
$218$	−2.33176	−	8.70223i	−0.157926	−	0.589390i
$219$	−2.49449	+	4.32058i	−0.168562	+	0.291957i
$220$		0			0
$221$		−	0.582928i		−	0.0392120i
$222$	−1.36115	−	5.07989i	−0.0913545	−	0.340940i
$223$	−4.43506	+	16.5519i	−0.296994	+	1.10840i	0.642628	+	0.766179i	$0.277844\pi$
$223$	−4.43506	+	16.5519i	−0.296994	+	1.10840i	−0.939621	+	0.342216i	$0.888822\pi$
$224$	1.19902	−	2.07676i	0.0801127	−	0.138759i
$225$		0			0
$226$	−9.28965	−	16.0901i	−0.617938	−	1.07030i
$227$	15.3513	−	15.3513i	1.01890	−	1.01890i	0.0190821	−	0.999818i	$-0.493926\pi$
$227$	15.3513	−	15.3513i	1.01890	−	1.01890i	0.999818	−	0.0190821i	$-0.00607439\pi$
$228$	5.23636	+	4.08755i	0.346787	+	0.270705i
$229$		−	29.5542i		−	1.95299i	−0.215531	−	0.976497i	$-0.569148\pi$
$229$		−	29.5542i		−	1.95299i	0.215531	−	0.976497i	$-0.430852\pi$
$230$		0			0
$231$	15.5934	−	9.00284i	1.02597	−	0.592343i
$232$	8.93557	−	2.39428i	0.586649	−	0.157192i
$233$	−4.45603	−	1.19399i	−0.291924	−	0.0782209i	0.109885	−	0.993944i	$-0.464952\pi$
$233$	−4.45603	−	1.19399i	−0.291924	−	0.0782209i	−0.401809	+	0.915723i	$0.631618\pi$
$234$	2.15769	+	1.24574i	0.141053	+	0.0814369i
$235$		0			0
$236$		−	3.54716i		−	0.230900i
$237$	−21.7803	+	5.83601i	−1.41478	+	0.379089i
$238$	0.367166	−	0.0983818i	0.0237998	−	0.00637714i
$239$			6.46056i			0.417899i	0.977926	+	0.208949i	$0.0670044\pi$
$239$			6.46056i			0.417899i	−0.977926	+	0.208949i	$0.932996\pi$
$240$		0			0
$241$	0.597834	+	0.345160i	0.0385099	+	0.0222337i	0.519131	−	0.854694i	$-0.326256\pi$
$241$	0.597834	+	0.345160i	0.0385099	+	0.0222337i	−0.480621	+	0.876928i	$0.659589\pi$
$242$	−12.8222	−	3.43571i	−0.824244	−	0.220856i
$243$	6.65951	−	1.78441i	0.427208	−	0.114470i
$244$	4.09236	−	2.36272i	0.261986	−	0.151258i
$245$		0			0
$246$			11.4584i			0.730559i
$247$	−6.01112	−	14.8601i	−0.382479	−	0.945524i
$248$	4.31597	−	4.31597i	0.274064	−	0.274064i
$249$	2.45553	+	4.25311i	0.155613	+	0.269530i
$250$		0			0
$251$	4.81477	−	8.33943i	0.303906	−	0.526380i	−0.673111	−	0.739541i	$-0.735043\pi$
$251$	4.81477	−	8.33943i	0.303906	−	0.526380i	0.977017	+	0.213161i	$0.0683759\pi$
$252$	−0.420493	+	1.56930i	−0.0264886	+	0.0988566i
$253$	3.05793	+	11.4123i	0.192250	+	0.717488i
$254$		−	7.98454i		−	0.500994i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.797277	−	2.97548i	−0.0497328	−	0.185605i	0.936591	−	0.350424i	$-0.113963\pi$
$257$	−0.797277	−	2.97548i	−0.0497328	−	0.185605i	−0.986324	+	0.164819i	$0.947296\pi$
$258$	−6.86398	+	6.86398i	−0.427333	+	0.427333i
$259$	−8.27538			−0.514207
$260$		0			0
$261$	−5.42770	+	3.13368i	−0.335966	+	0.193970i
$262$	−4.77144	−	17.8073i	−0.294781	−	1.10014i
$263$	−15.2486	−	4.08585i	−0.940269	−	0.251944i	−0.244041	−	0.969765i	$-0.578473\pi$
$263$	−15.2486	−	4.08585i	−0.940269	−	0.251944i	−0.696228	+	0.717821i	$0.745140\pi$
$264$	−6.50256	+	3.75426i	−0.400205	+	0.231058i
$265$		0			0
$266$	8.34533	−	6.29415i	0.511685	−	0.385919i
$267$	−8.47015	−	8.47015i	−0.518364	−	0.518364i
$268$	2.36911	−	8.84162i	0.144716	−	0.540088i
$269$	8.43845	+	14.6158i	0.514502	+	0.891143i	0.999858	+	0.0168267i	$0.00535637\pi$
$269$	8.43845	+	14.6158i	0.514502	+	0.891143i	−0.485357	+	0.874316i	$0.661310\pi$
$270$		0			0
$271$	−7.71404	−	13.3611i	−0.468594	−	0.811629i	0.530761	−	0.847521i	$-0.321906\pi$
$271$	−7.71404	−	13.3611i	−0.468594	−	0.811629i	−0.999356	+	0.0358922i	$0.988573\pi$
$272$	−0.153111	+	0.0410260i	−0.00928372	+	0.00248757i
$273$	−9.50323	+	9.50323i	−0.575161	+	0.575161i
$274$	−5.54511			−0.334993
$275$		0			0
$276$	3.16493	+	1.82727i	0.190507	+	0.109989i
$277$	20.0894	+	20.0894i	1.20706	+	1.20706i	0.971976	+	0.235081i	$0.0755354\pi$
$277$	20.0894	+	20.0894i	1.20706	+	1.20706i	0.235081	+	0.971976i	$0.424465\pi$
$278$	4.08924	+	4.08924i	0.245256	+	0.245256i
$279$	−2.06762	+	3.58122i	−0.123785	+	0.214402i
$280$		0			0
$281$	−24.2579	−	14.0053i	−1.44711	−	0.835488i	−0.448799	−	0.893633i	$-0.648148\pi$
$281$	−24.2579	−	14.0053i	−1.44711	−	0.835488i	−0.998308	+	0.0581450i	$0.981481\pi$
$282$	1.07091	−	3.99670i	0.0637719	−	0.238000i
$283$	26.3092	+	7.04953i	1.56392	+	0.419051i	0.933902	−	0.357530i	$-0.116381\pi$
$283$	26.3092	+	7.04953i	1.56392	+	0.419051i	0.630017	+	0.776581i	$0.283048\pi$
$284$	4.21314			0.250004
$285$		0			0
$286$	18.1187			1.07138
$287$	17.4158	+	4.66656i	1.02802	+	0.275458i
$288$	0.175349	−	0.654411i	0.0103325	−	0.0385615i
$289$	14.7007	+	8.48744i	0.864745	+	0.499261i
$290$		0			0
$291$	−13.3221	+	23.0746i	−0.780957	+	1.35266i
$292$	−2.31482	−	2.31482i	−0.135465	−	0.135465i
$293$	−11.1535	−	11.1535i	−0.651593	−	0.651593i	0.301783	−	0.953377i	$-0.402418\pi$
$293$	−11.1535	−	11.1535i	−0.651593	−	0.651593i	−0.953377	+	0.301783i	$0.902418\pi$
$294$	1.64899	+	0.952047i	0.0961713	+	0.0555245i
$295$		0			0
$296$	3.45090			0.200579
$297$	19.5250	−	19.5250i	1.13296	−	1.13296i
$298$	−18.3989	+	4.92997i	−1.06582	+	0.285586i
$299$	−4.40938	−	7.63728i	−0.255001	−	0.441675i
$300$		0			0
$301$	7.63728	+	13.2281i	0.440205	+	0.762458i
$302$	−2.71949	+	10.1493i	−0.156489	+	0.584025i
$303$	−8.36006	−	8.36006i	−0.480273	−	0.480273i
$304$	−3.48007	+	2.62471i	−0.199596	+	0.150538i
$305$		0			0
$306$	0.0930037	−	0.0536957i	0.00531667	−	0.00306958i
$307$	−23.1893	−	6.21356i	−1.32349	−	0.354627i	−0.473203	−	0.880954i	$-0.656902\pi$
$307$	−23.1893	−	6.21356i	−1.32349	−	0.354627i	−0.850282	+	0.526327i	$0.823569\pi$
$308$	3.05793	+	11.4123i	0.174242	+	0.650279i
$309$	−6.78888	+	3.91956i	−0.386206	+	0.222976i
$310$		0			0
$311$	−5.75057			−0.326085			−0.163043	−	0.986619i	$-0.552131\pi$
$311$	−5.75057			−0.326085			−0.163043	+	0.986619i	$0.552131\pi$
$312$	3.96292	−	3.96292i	0.224356	−	0.224356i
$313$	0.366236	+	1.36681i	0.0207009	+	0.0772567i	0.975504	−	0.219984i	$-0.0706004\pi$
$313$	0.366236	+	1.36681i	0.0207009	+	0.0772567i	−0.954803	+	0.297240i	$0.903934\pi$
$314$	0.412249	−	0.714035i	0.0232645	−	0.0402953i
$315$		0			0
$316$		−	14.7959i		−	0.832334i
$317$	−5.38496	−	20.0969i	−0.302450	−	1.12876i	−0.935119	−	0.354335i	$-0.884707\pi$
$317$	−5.38496	−	20.0969i	−0.302450	−	1.12876i	0.632669	−	0.774422i	$-0.281959\pi$
$318$	−2.46499	+	9.19945i	−0.138230	+	0.515880i
$319$	−22.7889	+	39.4716i	−1.27594	+	2.20999i
$320$		0			0
$321$	−11.6812	−	20.2324i	−0.651980	−	1.12926i
$322$	4.06627	−	4.06627i	0.226604	−	0.226604i
$323$	−0.684255	−	0.0958728i	−0.0380730	−	0.00533450i
$324$		−	6.50851i		−	0.361584i
$325$		0			0
$326$	0.202622	−	0.116984i	0.0112222	−	0.00647914i
$327$	13.2620	−	3.55354i	0.733390	−	0.196511i
$328$	−7.26254	−	1.94599i	−0.401007	−	0.107449i
$329$	−5.63853	−	3.25541i	−0.310862	−	0.179476i
$330$		0			0
$331$		−	2.19600i		−	0.120703i	−0.998177	−	0.0603516i	$-0.980778\pi$
$331$		−	2.19600i		−	0.120703i	0.998177	−	0.0603516i	$-0.0192222\pi$
$332$	−3.11273	+	0.834053i	−0.170833	+	0.0457746i
$333$	−2.25830	+	0.605111i	−0.123754	+	0.0331599i
$334$		−	7.92692i		−	0.433742i
$335$		0			0
$336$	3.16493	+	1.82727i	0.172661	+	0.0996860i
$337$	−26.2167	−	7.02475i	−1.42812	−	0.382663i	−0.539761	−	0.841818i	$-0.681485\pi$
$337$	−26.2167	−	7.02475i	−1.42812	−	0.382663i	−0.888356	+	0.459156i	$0.848152\pi$
$338$	−0.506122	+	0.135615i	−0.0275294	+	0.00737649i
$339$	24.5210	−	14.1572i	1.33180	−	0.768914i
$340$		0			0
$341$			30.0725i			1.62852i
$342$	1.81715	−	2.32787i	0.0982605	−	0.125877i
$343$	13.9883	−	13.9883i	0.755296	−	0.755296i
$344$	−3.18480	−	5.51624i	−0.171713	−	0.297416i
$345$		0			0
$346$	1.27823	−	2.21396i	0.0687182	−	0.119023i
$347$	−4.52390	+	16.8834i	−0.242856	+	0.906350i	0.731593	+	0.681742i	$0.238777\pi$
$347$	−4.52390	+	16.8834i	−0.242856	+	0.906350i	−0.974449	+	0.224609i	$0.927890\pi$
$348$	3.64882	+	13.6176i	0.195598	+	0.729980i
$349$		−	10.0383i		−	0.537337i	−0.963233	−	0.268669i	$-0.913416\pi$
$349$		−	10.0383i		−	0.537337i	0.963233	−	0.268669i	$-0.0865837\pi$
$350$		0			0
$351$	−10.3051	+	17.8490i	−0.550046	+	0.952708i
$352$	−1.27518	−	4.75904i	−0.0679674	−	0.253658i
$353$	17.8161	−	17.8161i	0.948257	−	0.948257i	−0.0504691	−	0.998726i	$-0.516072\pi$
$353$	17.8161	−	17.8161i	0.948257	−	0.948257i	0.998726	+	0.0504691i	$0.0160716\pi$
$354$	5.40579			0.287314
$355$		0			0
$356$	6.80704	−	3.93005i	0.360772	−	0.208292i
$357$	0.149932	+	0.559552i	0.00793522	+	0.0296146i
$358$	20.6048	+	5.52103i	1.08900	+	0.291795i
$359$	−4.17542	+	2.41068i	−0.220370	+	0.127231i	−0.606122	−	0.795372i	$-0.707276\pi$
$359$	−4.17542	+	2.41068i	−0.220370	+	0.127231i	0.385752	+	0.922603i	$0.373942\pi$
$360$		0			0
$361$	−18.4318	+	4.61200i	−0.970092	+	0.242737i
$362$	5.03365	+	5.03365i	0.264563	+	0.264563i
$363$	5.23594	−	19.5408i	0.274815	−	1.02562i
$364$	−4.40938	−	7.63728i	−0.231114	−	0.400302i
$365$		0			0
$366$	3.60074	+	6.23666i	0.188213	+	0.325995i
$367$	−32.8864	+	8.81188i	−1.71666	+	0.459977i	−0.977041	−	0.213053i	$-0.931659\pi$
$367$	−32.8864	+	8.81188i	−1.71666	+	0.459977i	−0.739615	+	0.673030i	$0.764993\pi$
$368$	−1.69567	+	1.69567i	−0.0883928	+	0.0883928i
$369$	5.09391			0.265178
$370$		0			0
$371$	12.9786	+	7.49317i	0.673813	+	0.389026i
$372$	6.57744	+	6.57744i	0.341024	+	0.341024i
$373$	20.9496	+	20.9496i	1.08473	+	1.08473i	0.996061	+	0.0886693i	$0.0282614\pi$
$373$	20.9496	+	20.9496i	1.08473	+	1.08473i	0.0886693	+	0.996061i	$0.471739\pi$
$374$	0.390489	−	0.676346i	0.0201917	−	0.0349730i
$375$		0			0
$376$	2.35131	+	1.35753i	0.121260	+	0.0700093i
$377$	8.80495	−	32.8605i	0.453478	−	1.69240i
$378$	−12.9816	−	3.47842i	−0.667704	−	0.178911i
$379$	33.6580			1.72890			0.864448	−	0.502723i	$-0.167668\pi$
$379$	33.6580			1.72890			0.864448	+	0.502723i	$0.167668\pi$
$380$		0			0
$381$	12.1682			0.623398
$382$	24.9949	+	6.69737i	1.27885	+	0.342668i
$383$	2.88615	−	10.7713i	0.147475	−	0.550385i	−0.852157	−	0.523285i	$-0.824706\pi$
$383$	2.88615	−	10.7713i	0.147475	−	0.550385i	0.999633	−	0.0270998i	$-0.00862718\pi$
$384$	−1.31980	−	0.761988i	−0.0673509	−	0.0388850i
$385$		0			0
$386$	6.10074	−	10.5668i	0.310519	−	0.537835i
$387$	3.05144	+	3.05144i	0.155113	+	0.155113i
$388$	−12.3626	−	12.3626i	−0.627617	−	0.627617i
$389$	−4.69447	−	2.71035i	−0.238019	−	0.137420i	0.376247	−	0.926519i	$-0.377214\pi$
$389$	−4.69447	−	2.71035i	−0.238019	−	0.137420i	−0.614266	+	0.789099i	$0.710548\pi$
$390$		0			0
$391$	−0.380118			−0.0192234
$392$	−0.883477	+	0.883477i	−0.0446223	+	0.0446223i
$393$	27.1378	−	7.27156i	1.36892	−	0.366802i
$394$	−4.91686	−	8.51624i	−0.247708	−	0.429042i
$395$		0			0
$396$	1.66898	+	2.89077i	0.0838696	+	0.145266i
$397$	−9.01205	+	33.6334i	−0.452302	+	1.68801i	0.243600	+	0.969876i	$0.421672\pi$
$397$	−9.01205	+	33.6334i	−0.452302	+	1.68801i	−0.695902	+	0.718137i	$0.744995\pi$
$398$	18.6342	+	18.6342i	0.934046	+	0.934046i
$399$	9.59214	+	12.7181i	0.480208	+	0.636701i
$400$		0			0
$401$	6.24689	−	3.60665i	0.311955	−	0.180107i	−0.335846	−	0.941917i	$-0.609022\pi$
$401$	6.24689	−	3.60665i	0.311955	−	0.180107i	0.647801	+	0.761810i	$0.275689\pi$
$402$	13.4744	+	3.61046i	0.672043	+	0.180073i
$403$	−5.80954	−	21.6815i	−0.289394	−	1.08003i
$404$	6.71857	−	3.87897i	0.334261	−	0.192986i
$405$		0			0
$406$	22.1837			1.10096
$407$	−12.0224	+	12.0224i	−0.595930	+	0.595930i
$408$	−0.0625226	−	0.233338i	−0.00309533	−	0.0115519i
$409$	−0.332992	+	0.576760i	−0.0164654	+	0.0285189i	−0.874141	−	0.485673i	$-0.838575\pi$
$409$	−0.332992	+	0.576760i	−0.0164654	+	0.0285189i	0.857675	+	0.514192i	$0.171908\pi$
$410$		0			0
$411$		−	8.45062i		−	0.416838i
$412$	−1.33133	−	4.96859i	−0.0655898	−	0.244785i
$413$	2.20157	−	8.21637i	0.108332	−	0.404301i
$414$	0.812330	−	1.40700i	0.0399238	−	0.0691501i
$415$		0			0
$416$	1.83875	+	3.18480i	0.0901520	+	0.156148i
$417$	−6.23191	+	6.23191i	−0.305178	+	0.305178i
$418$	2.97994	−	21.2682i	0.145754	−	1.04026i
$419$		−	10.2471i		−	0.500605i	−0.968168	−	0.250302i	$-0.919470\pi$
$419$		−	10.2471i		−	0.500605i	0.968168	−	0.250302i	$-0.0805300\pi$
$420$		0			0
$421$	23.5062	−	13.5713i	1.14562	−	0.661426i	0.197806	−	0.980241i	$-0.436618\pi$
$421$	23.5062	−	13.5713i	1.14562	−	0.661426i	0.947817	+	0.318816i	$0.103285\pi$
$422$	13.7448	−	3.68292i	0.669088	−	0.179282i
$423$	−1.77676	−	0.476083i	−0.0863893	−	0.0231479i
$424$	−5.41216	−	3.12471i	−0.262838	−	0.151749i
$425$		0			0
$426$			6.42073i			0.311085i
$427$	10.9457	−	2.93288i	0.529698	−	0.141932i
$428$	14.8075	−	3.96766i	0.715748	−	0.191784i
$429$			27.6125i			1.33315i
$430$		0			0
$431$	11.7908	+	6.80742i	0.567943	+	0.327902i	0.756327	−	0.654194i	$-0.226992\pi$
$431$	11.7908	+	6.80742i	0.567943	+	0.327902i	−0.188385	+	0.982095i	$0.560325\pi$
$432$	5.41345	+	1.45053i	0.260455	+	0.0697887i
$433$	8.73743	−	2.34119i	0.419894	−	0.112510i	−0.0426844	−	0.999089i	$-0.513591\pi$
$433$	8.73743	−	2.34119i	0.419894	−	0.112510i	0.462579	+	0.886578i	$0.346924\pi$
$434$	12.6759	−	7.31845i	0.608464	−	0.351297i
$435$		0			0
$436$			9.00921i			0.431463i
$437$	−9.69002	+	3.91976i	−0.463536	+	0.187507i
$438$	3.52774	−	3.52774i	0.168562	−	0.168562i
$439$	−0.957449	−	1.65835i	−0.0456965	−	0.0791487i	0.842272	−	0.539052i	$-0.181217\pi$
$439$	−0.957449	−	1.65835i	−0.0456965	−	0.0791487i	−0.887969	+	0.459903i	$0.847884\pi$
$440$		0			0
$441$	0.423240	−	0.733074i	0.0201543	−	0.0349083i
$442$	−0.150873	+	0.563065i	−0.00717629	+	0.0267823i
$443$	−4.96093	−	18.5144i	−0.235701	−	0.879647i	−0.977832	−	0.209392i	$-0.932851\pi$
$443$	−4.96093	−	18.5144i	−0.235701	−	0.879647i	0.742131	−	0.670255i	$-0.233815\pi$
$444$			5.25909i			0.249585i
$445$		0			0
$446$	8.56788	−	14.8400i	0.405701	−	0.702694i
$447$	−7.51316	−	28.0395i	−0.355360	−	1.32622i
$448$	−1.69567	+	1.69567i	−0.0801127	+	0.0801127i
$449$	−20.7974			−0.981488			−0.490744	−	0.871304i	$-0.663275\pi$
$449$	−20.7974			−0.981488			−0.490744	+	0.871304i	$0.663275\pi$
$450$		0			0
$451$	32.0812	−	18.5221i	1.51065	−	0.872172i
$452$	4.80867	+	17.9462i	0.226181	+	0.844119i
$453$	−15.4672	−	4.14444i	−0.726715	−	0.194723i
$454$	−18.8014	+	10.8550i	−0.882393	+	0.509450i
$455$		0			0
$456$	−4.00000	−	5.30354i	−0.187317	−	0.248361i
$457$	9.00799	+	9.00799i	0.421376	+	0.421376i	0.885677	−	0.464301i	$-0.153695\pi$
$457$	9.00799	+	9.00799i	0.421376	+	0.421376i	−0.464301	+	0.885677i	$0.653695\pi$
$458$	−7.64918	+	28.5471i	−0.357423	+	1.33392i
$459$	0.444184	+	0.769350i	0.0207328	+	0.0359102i
$460$		0			0
$461$	0.295626	+	0.512039i	0.0137687	+	0.0238480i	0.872828	−	0.488029i	$-0.162284\pi$
$461$	0.295626	+	0.512039i	0.0137687	+	0.0238480i	−0.859059	+	0.511877i	$0.828950\pi$
$462$	−17.3921	+	4.66021i	−0.809156	+	0.216813i
$463$	11.5577	−	11.5577i	0.537133	−	0.537133i	−0.385553	−	0.922686i	$-0.625989\pi$
$463$	11.5577	−	11.5577i	0.537133	−	0.537133i	0.922686	+	0.385553i	$0.125989\pi$
$464$	−9.25078			−0.429457
$465$		0			0
$466$	3.99517	+	2.30661i	0.185073	+	0.106852i
$467$	21.0087	+	21.0087i	0.972166	+	0.972166i	0.999623	−	0.0274570i	$-0.00874093\pi$
$467$	21.0087	+	21.0087i	0.972166	+	0.972166i	−0.0274570	+	0.999623i	$0.508741\pi$
$468$	−1.76175	−	1.76175i	−0.0814369	−	0.0814369i
$469$	10.9752	−	19.0097i	0.506789	−	0.877785i
$470$		0			0
$471$	1.08817	+	0.628257i	0.0501404	+	0.0289486i
$472$	−0.918072	+	3.42629i	−0.0422577	+	0.157708i
$473$	30.3132	+	8.12241i	1.39380	+	0.373469i
$474$	22.5486			1.03569
$475$		0			0
$476$	−0.380118			−0.0174227
$477$	4.08969	+	1.09583i	0.187254	+	0.0501746i
$478$	1.67212	−	6.24042i	0.0764808	−	0.285430i
$479$	0.940715	+	0.543122i	0.0429824	+	0.0248159i	0.521337	−	0.853351i	$-0.325433\pi$
$479$	0.940715	+	0.543122i	0.0429824	+	0.0248159i	−0.478355	+	0.878167i	$0.658767\pi$
$480$		0			0
$481$	6.34533	−	10.9904i	0.289322	−	0.501121i
$482$	−0.488130	−	0.488130i	−0.0222337	−	0.0222337i
$483$	6.19690	+	6.19690i	0.281969	+	0.281969i
$484$	11.4961	+	6.63728i	0.522550	+	0.301694i
$485$		0			0
$486$	−6.89443			−0.312738
$487$	−7.21190	+	7.21190i	−0.326803	+	0.326803i	−0.851369	−	0.524567i	$-0.824227\pi$
$487$	−7.21190	+	7.21190i	−0.326803	+	0.326803i	0.524567	+	0.851369i	$0.324227\pi$
$488$	−4.56443	+	1.22304i	−0.206622	+	0.0553642i
$489$	0.178281	+	0.308791i	0.00806213	+	0.0139640i
$490$		0			0
$491$	11.8502	+	20.5251i	0.534790	+	0.926284i	0.999173	+	0.0406496i	$0.0129427\pi$
$491$	11.8502	+	20.5251i	0.534790	+	0.926284i	−0.464383	+	0.885634i	$0.653724\pi$
$492$	2.96564	−	11.0679i	0.133702	−	0.498981i
$493$	−1.03687	−	1.03687i	−0.0466985	−	0.0466985i
$494$	1.96023	+	15.9095i	0.0881948	+	0.715803i
$495$		0			0
$496$	−5.28596	+	3.05185i	−0.237347	+	0.137032i
$497$	9.75901	+	2.61492i	0.437751	+	0.117295i
$498$	−1.27108	−	4.74372i	−0.0569583	−	0.212571i
$499$	−24.0371	+	13.8778i	−1.07605	+	0.621256i	−0.929828	−	0.367996i	$-0.880044\pi$
$499$	−24.0371	+	13.8778i	−1.07605	+	0.621256i	−0.146220	+	0.989252i	$0.546711\pi$
$500$		0			0
$501$	12.0804			0.539714
$502$	−6.80912	+	6.80912i	−0.303906	+	0.303906i
$503$	−8.25311	−	30.8010i	−0.367988	−	1.37335i	−0.863324	−	0.504649i	$-0.831622\pi$
$503$	−8.25311	−	30.8010i	−0.367988	−	1.37335i	0.495336	−	0.868701i	$-0.335045\pi$
$504$	0.812330	−	1.40700i	0.0361840	−	0.0626726i
$505$		0			0
$506$		−	11.8149i		−	0.525238i
$507$	−0.206674	−	0.771318i	−0.00917872	−	0.0342555i
$508$	−2.06655	+	7.71247i	−0.0916883	+	0.342185i
$509$	1.49048	−	2.58159i	0.0660644	−	0.114427i	−0.831101	−	0.556121i	$-0.812289\pi$
$509$	1.49048	−	2.58159i	0.0660644	−	0.114427i	0.897166	+	0.441694i	$0.145622\pi$
$510$		0			0
$511$	−3.92517	−	6.79859i	−0.173639	−	0.300752i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	19.2567	+	15.0320i	0.850204	+	0.663677i
$514$			3.08044i			0.135872i
$515$		0			0
$516$	8.40663	−	4.85357i	0.370081	−	0.213666i
$517$	−12.9211	+	3.46219i	−0.568268	+	0.152267i
$518$	7.99340	+	2.14182i	0.351210	+	0.0941064i
$519$	3.37403	+	1.94800i	0.148103	+	0.0855075i
$520$		0			0
$521$			34.7368i			1.52185i	0.648841	+	0.760924i	$0.275254\pi$
$521$			34.7368i			1.52185i	−0.648841	+	0.760924i	$0.724746\pi$
$522$	6.05381	−	1.62211i	0.264968	−	0.0709980i
$523$	−19.9879	+	5.35573i	−0.874008	+	0.234190i	−0.667820	−	0.744323i	$-0.732773\pi$
$523$	−19.9879	+	5.35573i	−0.874008	+	0.234190i	−0.206188	+	0.978512i	$0.566106\pi$
$524$			18.4354i			0.805356i
$525$		0			0
$526$	13.6715	+	7.89325i	0.596106	+	0.344162i
$527$	−0.934545	−	0.250411i	−0.0407094	−	0.0109081i
$528$	7.25267	−	1.94335i	0.315632	−	0.0845733i
$529$	14.9384	−	8.62471i	0.649497	−	0.374988i
$530$		0			0
$531$		−	2.40319i		−	0.104289i
$532$	−9.69002	+	3.91976i	−0.420116	+	0.169943i
$533$	−19.5516	+	19.5516i	−0.846873	+	0.846873i
$534$	5.98930	+	10.3738i	0.259182	+	0.448917i
$535$		0			0
$536$	−4.57676	+	7.92718i	−0.197686	+	0.342402i
$537$	−8.41392	+	31.4012i	−0.363087	+	1.35506i
$538$	−4.36806	−	16.3018i	−0.188321	−	0.702822i
$539$		−	6.15582i		−	0.265150i
$540$		0			0
$541$	−5.13245	+	8.88966i	−0.220661	+	0.382196i	−0.955009	−	0.296577i	$-0.904155\pi$
$541$	−5.13245	+	8.88966i	−0.220661	+	0.382196i	0.734348	+	0.678773i	$0.237488\pi$
$542$	3.99308	+	14.9024i	0.171517	+	0.640112i
$543$	−7.67116	+	7.67116i	−0.329201	+	0.329201i
$544$	0.158512			0.00679616
$545$		0			0
$546$	11.6390	−	6.71980i	0.498104	−	0.287581i
$547$	−6.66414	−	24.8709i	−0.284938	−	1.06340i	−0.948884	−	0.315624i	$-0.897786\pi$
$547$	−6.66414	−	24.8709i	−0.284938	−	1.06340i	0.663946	−	0.747780i	$-0.268880\pi$
$548$	5.35617	+	1.43518i	0.228804	+	0.0613079i
$549$	2.77256	−	1.60074i	0.118330	−	0.0683178i
$550$		0			0
$551$	−37.1243	−	15.7400i	−1.58155	−	0.670544i
$552$	−2.58416	−	2.58416i	−0.109989	−	0.109989i
$553$	9.18318	−	34.2721i	0.390509	−	1.45740i
$554$	−14.2054	−	24.6044i	−0.603528	−	1.04534i
$555$		0			0
$556$	−2.89153	−	5.00828i	−0.122628	−	0.212398i
$557$	−25.7129	+	6.88975i	−1.08949	+	0.291928i	−0.758478	−	0.651698i	$-0.774057\pi$
$557$	−25.7129	+	6.88975i	−1.08949	+	0.291928i	−0.331012	+	0.943626i	$0.607390\pi$
$558$	2.92405	−	2.92405i	0.123785	−	0.123785i
$559$	−23.4242			−0.990739
$560$		0			0
$561$	1.03074	+	0.595096i	0.0435177	+	0.0251250i
$562$	19.8065	+	19.8065i	0.835488	+	0.835488i
$563$	−13.4241	−	13.4241i	−0.565758	−	0.565758i	0.365179	−	0.930937i	$-0.381008\pi$
$563$	−13.4241	−	13.4241i	−0.565758	−	0.565758i	−0.930937	+	0.365179i	$0.881008\pi$
$564$	−2.06884	+	3.58334i	−0.0871140	+	0.150886i
$565$		0			0
$566$	−23.5882	−	13.6186i	−0.991485	−	0.572434i
$567$	4.03956	−	15.0758i	0.169645	−	0.633125i
$568$	−4.06958	−	1.09044i	−0.170756	−	0.0457539i
$569$	30.1939			1.26579			0.632897	−	0.774236i	$-0.281866\pi$
$569$	30.1939			1.26579			0.632897	+	0.774236i	$0.281866\pi$
$570$		0			0
$571$	24.7196			1.03448			0.517242	−	0.855839i	$-0.326959\pi$
$571$	24.7196			1.03448			0.517242	+	0.855839i	$0.326959\pi$
$572$	−17.5014	−	4.68947i	−0.731768	−	0.196077i
$573$	−10.2066	+	38.0917i	−0.426389	+	1.59130i
$574$	−15.6146	−	9.01509i	−0.651741	−	0.376283i
$575$		0			0
$576$	−0.338748	+	0.586729i	−0.0141145	+	0.0244470i
$577$	−26.4463	−	26.4463i	−1.10098	−	1.10098i	−0.994293	−	0.106682i	$-0.965977\pi$
$577$	−26.4463	−	26.4463i	−1.10098	−	1.10098i	−0.106682	−	0.994293i	$-0.534023\pi$
$578$	−12.0030	−	12.0030i	−0.499261	−	0.499261i
$579$	16.1035	+	9.29738i	0.669240	+	0.386386i
$580$		0			0
$581$	−7.72775			−0.320601
$582$	18.8403	−	18.8403i	0.780957	−	0.780957i
$583$	29.7413	−	7.96915i	1.23176	−	0.330048i
$584$	1.63683	+	2.83507i	0.0677324	+	0.117316i
$585$		0			0
$586$	7.88670	+	13.6602i	0.325797	+	0.564296i
$587$	9.78854	−	36.5313i	0.404016	−	1.50781i	−0.401846	−	0.915707i	$-0.631631\pi$
$587$	9.78854	−	36.5313i	0.404016	−	1.50781i	0.805863	−	0.592103i	$-0.201702\pi$
$588$	−1.34640	−	1.34640i	−0.0555245	−	0.0555245i
$589$	−26.4058	+	3.25348i	−1.08803	+	0.134057i
$590$		0			0
$591$	12.9786	−	7.49317i	0.533866	−	0.308228i
$592$	−3.33331	−	0.893158i	−0.136998	−	0.0367086i
$593$	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	$0.812960\pi$
$594$	−23.9131	+	13.8063i	−0.981168	+	0.566478i
$595$		0			0
$596$	19.0480			0.780235
$597$	−28.3980	+	28.3980i	−1.16225	+	1.16225i
$598$	2.28246	+	8.51827i	0.0933369	+	0.348338i
$599$	−4.80824	+	8.32811i	−0.196459	+	0.340277i	−0.947378	−	0.320117i	$-0.896278\pi$
$599$	−4.80824	+	8.32811i	−0.196459	+	0.340277i	0.750919	+	0.660395i	$0.229611\pi$
$600$		0			0
$601$			18.0184i			0.734987i	0.930026	+	0.367494i	$0.119784\pi$
$601$			18.0184i			0.734987i	−0.930026	+	0.367494i	$0.880216\pi$
$602$	−3.95334	−	14.7541i	−0.161126	−	0.601332i
$603$	1.60506	−	5.99016i	0.0653631	−	0.243938i
$604$	5.25365	−	9.09959i	0.213768	−	0.370257i
$605$		0			0
$606$	5.91146	+	10.2389i	0.240136	+	0.415929i
$607$	24.8718	−	24.8718i	1.00952	−	1.00952i	0.00956121	−	0.999954i	$-0.496957\pi$
$607$	24.8718	−	24.8718i	1.00952	−	1.00952i	0.999954	−	0.00956121i	$-0.00304347\pi$
$608$	4.04081	−	1.63457i	0.163877	−	0.0662905i
$609$			33.8074i			1.36995i
$610$		0			0
$611$	8.64694	−	4.99231i	0.349818	−	0.201967i
$612$	−0.103732	+	0.0277949i	−0.00419312	+	0.00112354i
$613$	25.3338	+	6.78817i	1.02322	+	0.274172i	0.731144	−	0.682223i	$-0.238987\pi$
$613$	25.3338	+	6.78817i	1.02322	+	0.274172i	0.292078	+	0.956394i	$0.405653\pi$
$614$	20.7910	+	12.0037i	0.839056	+	0.484429i
$615$		0			0
$616$		−	11.8149i		−	0.476037i
$617$	1.77179	−	0.474750i	0.0713296	−	0.0191127i	−0.222978	−	0.974824i	$-0.571578\pi$
$617$	1.77179	−	0.474750i	0.0713296	−	0.0191127i	0.294307	+	0.955711i	$0.404911\pi$
$618$	7.57201	−	2.02891i	0.304591	−	0.0816149i
$619$			15.4281i			0.620107i	0.950719	+	0.310053i	$0.100347\pi$
$619$			15.4281i			0.620107i	−0.950719	+	0.310053i	$0.899653\pi$
$620$		0			0
$621$	11.6390	+	6.71980i	0.467058	+	0.269656i
$622$	5.55463	+	1.48836i	0.222720	+	0.0596777i
$623$	18.2065	−	4.87842i	0.729429	−	0.195450i
$624$	−4.85357	+	2.80221i	−0.194298	+	0.112178i
$625$		0			0
$626$		−	1.41503i		−	0.0565558i
$627$	32.4122	+	4.54136i	1.29442	+	0.181365i
$628$	−0.583007	+	0.583007i	−0.0232645	+	0.0232645i
$629$	−0.273505	−	0.473724i	−0.0109053	−	0.0188886i
$630$		0			0
$631$	1.10364	−	1.91156i	0.0439351	−	0.0760979i	−0.843222	−	0.537566i	$-0.819344\pi$
$631$	1.10364	−	1.91156i	0.0439351	−	0.0760979i	0.887157	+	0.461468i	$0.152677\pi$
$632$	−3.82946	+	14.2917i	−0.152328	+	0.568495i
$633$	5.61268	+	20.9468i	0.223084	+	0.832561i
$634$			20.8059i			0.826307i
$635$		0			0
$636$	4.76199	−	8.24801i	0.188825	−	0.327055i
$637$	1.18921	+	4.43819i	0.0471182	+	0.175848i
$638$	32.2284	−	32.2284i	1.27594	−	1.27594i
$639$	2.85439			0.112918
$640$		0			0
$641$	−11.6878	+	6.74793i	−0.461639	+	0.266527i	−0.712733	−	0.701435i	$-0.752543\pi$
$641$	−11.6878	+	6.74793i	−0.461639	+	0.266527i	0.251094	+	0.967963i	$0.419210\pi$
$642$	6.04662	+	22.5663i	0.238641	+	0.890621i
$643$	−41.9986	−	11.2535i	−1.65626	−	0.443794i	−0.694906	−	0.719101i	$-0.744554\pi$
$643$	−41.9986	−	11.2535i	−1.65626	−	0.443794i	−0.961357	+	0.275306i	$0.911221\pi$
$644$	−4.98014	+	2.87529i	−0.196245	+	0.113302i
$645$		0			0
$646$	0.636126	+	0.269704i	0.0250280	+	0.0106114i
$647$	−2.24253	−	2.24253i	−0.0881628	−	0.0881628i	0.661650	−	0.749813i	$-0.269856\pi$
$647$	−2.24253	−	2.24253i	−0.0881628	−	0.0881628i	−0.749813	+	0.661650i	$0.769856\pi$
$648$	−1.68453	+	6.28674i	−0.0661745	+	0.246966i
$649$	−8.73828	−	15.1352i	−0.343008	−	0.594107i
$650$		0			0
$651$	11.1531	+	19.3178i	0.437126	+	0.757125i
$652$	−0.225996	+	0.0605553i	−0.00885067	+	0.00237153i
$653$	32.7942	−	32.7942i	1.28334	−	1.28334i	0.344581	−	0.938757i	$-0.388021\pi$
$653$	32.7942	−	32.7942i	1.28334	−	1.28334i	0.938757	−	0.344581i	$-0.111979\pi$
$654$	−13.7298			−0.536879
$655$		0			0
$656$	6.51141	+	3.75937i	0.254228	+	0.146779i
$657$	−1.56828	−	1.56828i	−0.0611845	−	0.0611845i
$658$	4.60384	+	4.60384i	0.179476	+	0.179476i
$659$	19.3919	−	33.5878i	0.755402	−	1.30840i	−0.189772	−	0.981828i	$-0.560775\pi$
$659$	19.3919	−	33.5878i	0.755402	−	1.30840i	0.945174	−	0.326567i	$-0.105892\pi$
$660$		0			0
$661$	22.2873	+	12.8676i	0.866877	+	0.500492i	0.866309	−	0.499508i	$-0.166486\pi$
$661$	22.2873	+	12.8676i	0.866877	+	0.500492i	0.000568016		1.00000i	$0.499819\pi$
$662$	−0.568368	+	2.12118i	−0.0220902	+	0.0824419i
$663$	−0.858098	−	0.229927i	−0.0333258	−	0.00892961i
$664$	3.22253			0.125059
$665$		0			0
$666$	2.33797			0.0905945
$667$	−21.4278	−	5.74157i	−0.829688	−	0.222314i
$668$	−2.05164	+	7.65682i	−0.0793803	+	0.296251i
$669$	22.6158	+	13.0572i	0.874378	+	0.504822i
$670$		0			0
$671$	11.6410	−	20.1627i	0.449394	−	0.778373i
$672$	−2.58416	−	2.58416i	−0.0996860	−	0.0996860i
$673$	3.40401	+	3.40401i	0.131215	+	0.131215i	0.769664	−	0.638449i	$-0.220424\pi$
$673$	3.40401	+	3.40401i	0.131215	+	0.131215i	−0.638449	+	0.769664i	$0.720424\pi$
$674$	23.5053	+	13.5708i	0.905390	+	0.522727i
$675$		0			0
$676$	0.523976			0.0201529
$677$	31.6199	−	31.6199i	1.21525	−	1.21525i	0.245977	−	0.969276i	$-0.420891\pi$
$677$	31.6199	−	31.6199i	1.21525	−	1.21525i	0.969276	−	0.245977i	$-0.0791089\pi$
$678$	−27.3496	+	7.32831i	−1.05036	+	0.281442i
$679$	−20.9629	−	36.3088i	−0.804482	−	1.39340i
$680$		0			0
$681$	−16.5428	−	28.6529i	−0.633920	−	1.09798i
$682$	7.78333	−	29.0478i	0.298039	−	1.11230i
$683$	−20.7232	−	20.7232i	−0.792951	−	0.792951i	0.189022	−	0.981973i	$-0.439468\pi$
$683$	−20.7232	−	20.7232i	−0.792951	−	0.792951i	−0.981973	+	0.189022i	$0.939468\pi$
$684$	−2.35773	+	1.77823i	−0.0901502	+	0.0679924i
$685$		0			0
$686$	−17.1321	+	9.89121i	−0.654106	+	0.377648i
$687$	−43.5052	−	11.6572i	−1.65983	−	0.444749i
$688$	1.64858	+	6.15257i	0.0628514	+	0.234565i
$689$	−19.9032	+	11.4911i	−0.758252	+	0.437777i
$690$		0			0
$691$	−39.3446			−1.49674			−0.748369	−	0.663282i	$-0.769163\pi$
$691$	−39.3446			−1.49674			−0.748369	+	0.663282i	$0.769163\pi$
$692$	−1.80769	+	1.80769i	−0.0687182	+	0.0687182i
$693$	2.07173	+	7.73182i	0.0786987	+	0.293708i
$694$	8.73951	−	15.1373i	0.331747	−	0.574603i
$695$		0			0
$696$		−	14.0980i		−	0.534382i
$697$	0.308463	+	1.15120i	0.0116839	+	0.0436049i
$698$	−2.59810	+	9.69625i	−0.0983396	+	0.367008i
$699$	−3.51522	+	6.08854i	−0.132958	+	0.230290i
$700$		0			0
$701$	0.708055	+	1.22639i	0.0267429	+	0.0463200i	0.879087	−	0.476661i	$-0.158153\pi$
$701$	0.708055	+	1.22639i	0.0267429	+	0.0463200i	−0.852344	+	0.522981i	$0.824820\pi$
$702$	14.5736	−	14.5736i	0.550046	−	0.550046i
$703$	−11.8572	−	9.25587i	−0.447204	−	0.349092i
$704$			4.92692i			0.185690i
$705$		0			0
$706$	−21.8202	+	12.5979i	−0.821214	+	0.474128i
$707$	17.9699	−	4.81502i	0.675828	−	0.181087i
$708$	−5.22159	−	1.39912i	−0.196239	−	0.0525822i
$709$	−42.6724	−	24.6369i	−1.60259	−	0.925258i	−0.990966	−	0.134113i	$-0.957181\pi$
$709$	−42.6724	−	24.6369i	−1.60259	−	0.925258i	−0.611629	−	0.791145i	$-0.709485\pi$
$710$		0			0
$711$		−	10.0242i		−	0.375935i
$712$	−7.59227	+	2.03434i	−0.284532	+	0.0762402i
$713$	−14.1382	+	3.78831i	−0.529478	+	0.141873i
$714$		−	0.579291i		−	0.0216794i
$715$		0			0
$716$	−18.4737	−	10.6658i	−0.690395	−	0.398600i
$717$	9.51025	+	2.54826i	0.355167	+	0.0951667i
$718$	4.65707	−	1.24786i	0.173800	−	0.0465697i
$719$	−25.3850	+	14.6561i	−0.946702	+	0.546578i	−0.892055	−	0.451927i	$-0.850737\pi$
$719$	−25.3850	+	14.6561i	−0.946702	+	0.546578i	−0.0546469	+	0.998506i	$0.517403\pi$
$720$		0			0
$721$		−	12.3352i		−	0.459385i
$722$	18.9974	+	0.315640i	0.707009	+	0.0117469i
$723$	0.743898	−	0.743898i	0.0276659	−	0.0276659i
$724$	−3.55933	−	6.16493i	−0.132281	−	0.229118i
$725$		0			0
$726$	−10.1151	+	17.5198i	−0.375405	+	0.650220i
$727$	−7.46505	+	27.8600i	−0.276863	+	1.03327i	0.677719	+	0.735321i	$0.262969\pi$
$727$	−7.46505	+	27.8600i	−0.276863	+	1.03327i	−0.954582	+	0.297947i	$0.903698\pi$
$728$	2.28246	+	8.51827i	0.0845938	+	0.315708i
$729$		−	30.0325i		−	1.11231i
$730$		0			0
$731$	−0.504831	+	0.874392i	−0.0186718	+	0.0323406i
$732$	−1.86388	−	6.95609i	−0.0688909	−	0.257104i
$733$	−20.8178	+	20.8178i	−0.768925	+	0.768925i	−0.977917	−	0.208993i	$-0.932982\pi$
$733$	−20.8178	+	20.8178i	−0.768925	+	0.768925i	0.208993	+	0.977917i	$0.432982\pi$
$734$	34.0465			1.25668
$735$		0			0
$736$	2.07676	−	1.19902i	0.0765504	−	0.0441964i
$737$	−11.6724	−	43.5620i	−0.429958	−	1.60463i
$738$	−4.92034	−	1.31840i	−0.181120	−	0.0485310i
$739$	6.92621	−	3.99885i	0.254785	−	0.147100i	−0.367168	−	0.930154i	$-0.619673\pi$
$739$	6.92621	−	3.99885i	0.254785	−	0.147100i	0.621953	+	0.783054i	$0.286339\pi$
$740$		0			0
$741$	−24.2457	+	2.98734i	−0.890690	+	0.109743i
$742$	−10.5969	−	10.5969i	−0.389026	−	0.389026i
$743$	−3.17038	+	11.8320i	−0.116310	+	0.434075i	−0.999382	−	0.0351632i	$-0.988805\pi$
$743$	−3.17038	+	11.8320i	−0.116310	+	0.434075i	0.883071	+	0.469239i	$0.155472\pi$
$744$	−4.65095	−	8.05569i	−0.170512	−	0.295336i
$745$		0			0
$746$	−14.8136	−	25.6579i	−0.542365	−	0.939404i
$747$	−2.10886	+	0.565067i	−0.0771592	+	0.0206747i
$748$	−0.552234	+	0.552234i	−0.0201917	+	0.0201917i
$749$	36.7616			1.34324
$750$		0			0
$751$	−25.3395	−	14.6298i	−0.924652	−	0.533848i	−0.0395361	−	0.999218i	$-0.512588\pi$
$751$	−25.3395	−	14.6298i	−0.924652	−	0.533848i	−0.885116	+	0.465370i	$0.845921\pi$
$752$	−1.91984	−	1.91984i	−0.0700093	−	0.0700093i
$753$	−10.3769	−	10.3769i	−0.378156	−	0.378156i
$754$	−17.0099	+	29.4619i	−0.619463	+	1.07294i
$755$		0			0
$756$	11.6390	+	6.71980i	0.423307	+	0.244397i
$757$	5.95712	−	22.2323i	0.216515	−	0.808045i	−0.769113	−	0.639113i	$-0.779301\pi$
$757$	5.95712	−	22.2323i	0.216515	−	0.808045i	0.985628	−	0.168932i	$-0.0540318\pi$
$758$	−32.5111	−	8.71133i	−1.18086	−	0.316410i
$759$	18.0057			0.653565
$760$		0			0
$761$	−43.2641			−1.56832			−0.784162	−	0.620556i	$-0.786907\pi$
$761$	−43.2641			−1.56832			−0.784162	+	0.620556i	$0.786907\pi$
$762$	−11.7536	−	3.14937i	−0.425789	−	0.114090i
$763$	−5.59163	+	20.8683i	−0.202431	+	0.755482i
$764$	−22.4099	−	12.9383i	−0.810760	−	0.468093i
$765$		0			0
$766$	−5.57561	+	9.65724i	−0.201455	+	0.348930i
$767$	9.22397	+	9.22397i	0.333058	+	0.333058i
$768$	1.07761	+	1.07761i	0.0388850	+	0.0388850i
$769$	−12.8970	−	7.44607i	−0.465076	−	0.268512i	0.249100	−	0.968478i	$-0.419865\pi$
$769$	−12.8970	−	7.44607i	−0.465076	−	0.268512i	−0.714176	+	0.699966i	$0.753199\pi$
$770$		0			0
$771$	−4.69452			−0.169069
$772$	−8.62774	+	8.62774i	−0.310519	+	0.310519i
$773$	−17.7830	+	4.76494i	−0.639610	+	0.171383i	−0.564027	−	0.825757i	$-0.690748\pi$
$773$	−17.7830	+	4.76494i	−0.639610	+	0.171383i	−0.0755831	+	0.997140i	$0.524082\pi$
$774$	−2.15769	−	3.73723i	−0.0775567	−	0.134332i
$775$		0			0
$776$	8.74169	+	15.1411i	0.313808	+	0.543532i
$777$	−3.26409	+	12.1818i	−0.117099	+	0.437018i
$778$	3.83302	+	3.83302i	0.137420	+	0.137420i
$779$	19.7345	+	26.1657i	0.707062	+	0.937484i
$780$		0			0
$781$	17.9768	−	10.3789i	0.643261	−	0.371387i
$782$	0.367166	+	0.0983818i	0.0131298	+	0.00351813i
$783$	13.4185	+	50.0787i	0.479539	+	1.78967i
$784$	1.08203	−	0.624713i	0.0386441	−	0.0223112i
$785$		0			0
$786$	−28.0952			−1.00212
$787$	−24.3605	+	24.3605i	−0.868357	+	0.868357i	−0.992290	−	0.123934i	$-0.960449\pi$
$787$	−24.3605	+	24.3605i	−0.868357	+	0.868357i	0.123934	+	0.992290i	$0.460449\pi$
$788$	2.54515	+	9.49864i	0.0906673	+	0.338375i
$789$	−12.0291	+	20.8351i	−0.428248	+	0.741748i
$790$		0			0
$791$			44.5538i			1.58415i
$792$	−0.863930	−	3.22423i	−0.0306984	−	0.114568i
$793$	−4.49771	+	16.7857i	−0.159718	+	0.596077i
$794$	17.4099	−	30.1549i	0.617856	−	1.07016i
$795$		0			0
$796$	−13.1763	−	22.8221i	−0.467023	−	0.808908i
$797$	29.3671	−	29.3671i	1.04024	−	1.04024i	0.0410799	−	0.999156i	$-0.486920\pi$
$797$	29.3671	−	29.3671i	1.04024	−	1.04024i	0.999156	−	0.0410799i	$-0.0130798\pi$
$798$	−5.97362	−	14.7674i	−0.211464	−	0.522759i
$799$		−	0.430370i		−	0.0152254i
$800$		0			0
$801$	4.61174	−	2.66259i	0.162948	−	0.0940780i
$802$	−6.96750	+	1.86694i	−0.246031	+	0.0659238i
$803$	−15.5794	−	4.17450i	−0.549787	−	0.147315i
$804$	−12.0808	−	6.97487i	−0.426058	−	0.245985i
$805$		0			0
$806$			22.4464i			0.790639i
$807$	24.8436	−	6.65683i	0.874537	−	0.234331i
$808$	−7.49359	+	2.00790i	−0.263624	+	0.0706377i
$809$			46.8264i			1.64633i	0.567803	+	0.823165i	$0.307794\pi$
$809$			46.8264i			1.64633i	−0.567803	+	0.823165i	$0.692206\pi$
$810$		0			0
$811$	14.4298	+	8.33106i	0.506700	+	0.292543i	0.731476	−	0.681867i	$-0.238832\pi$
$811$	14.4298	+	8.33106i	0.506700	+	0.292543i	−0.224776	+	0.974410i	$0.572165\pi$
$812$	−21.4278	−	5.74157i	−0.751969	−	0.201489i
$813$	−22.7109	+	6.08536i	−0.796505	+	0.213423i
$814$	14.7244	−	8.50115i	0.516091	−	0.297965i
$815$		0			0
$816$			0.241569i			0.00845660i
$817$	−3.85252	+	27.4959i	−0.134783	+	0.961960i
$818$	0.470922	−	0.470922i	0.0164654	−	0.0164654i
$819$	−2.98734	−	5.17422i	−0.104386	−	0.180802i
$820$		0			0
$821$	3.66783	−	6.35288i	0.128008	−	0.221717i	−0.794897	−	0.606745i	$-0.792475\pi$
$821$	3.66783	−	6.35288i	0.128008	−	0.221717i	0.922905	+	0.385028i	$0.125808\pi$
$822$	−2.18718	+	8.16267i	−0.0762867	+	0.284706i
$823$	−7.99972	−	29.8554i	−0.278853	−	1.04069i	−0.953215	−	0.302292i	$-0.902248\pi$
$823$	−7.99972	−	29.8554i	−0.278853	−	1.04069i	0.674362	−	0.738401i	$-0.264419\pi$
$824$			5.14386i			0.179195i
$825$		0			0
$826$	−4.25311	+	7.36660i	−0.147984	+	0.256317i
$827$	4.24980	+	15.8605i	0.147780	+	0.551523i	0.999616	+	0.0277138i	$0.00882271\pi$
$827$	4.24980	+	15.8605i	0.147780	+	0.551523i	−0.851836	+	0.523809i	$0.824511\pi$
$828$	−1.14881	+	1.14881i	−0.0399238	+	0.0399238i
$829$	46.5326			1.61614			0.808071	−	0.589084i	$-0.200511\pi$
$829$	46.5326			1.61614			0.808071	+	0.589084i	$0.200511\pi$
$830$		0			0
$831$	37.4966	−	21.6486i	1.30074	−	0.750983i
$832$	−0.951806	−	3.55219i	−0.0329979	−	0.123150i
$833$	0.191301	+	0.0512589i	0.00662818	+	0.00177602i
$834$	7.63250	−	4.40663i	0.264292	−	0.152589i
$835$		0			0
$836$	−8.38302	+	19.7722i	−0.289933	+	0.683837i
$837$	24.1885	+	24.1885i	0.836077	+	0.836077i
$838$	−2.65215	+	9.89796i	−0.0916170	+	0.341919i
$839$	1.39526	+	2.41666i	0.0481697	+	0.0834323i	0.889105	−	0.457703i	$-0.151328\pi$
$839$	1.39526	+	2.41666i	0.0481697	+	0.0834323i	−0.840935	+	0.541136i	$0.817995\pi$
$840$		0			0
$841$	−28.2885	−	48.9971i	−0.975465	−	1.68956i
$842$	−26.2178	+	7.02503i	−0.903524	+	0.242099i
$843$	−30.1847	+	30.1847i	−1.03962	+	1.03962i
$844$	−14.2297			−0.489807
$845$		0			0
$846$	1.59300	+	0.919721i	0.0547686	+	0.0316207i
$847$	22.5092	+	22.5092i	0.773426	+	0.773426i
$848$	4.41901	+	4.41901i	0.151749	+	0.151749i
$849$	20.7545	−	35.9478i	0.712292	−	1.23373i
$850$		0			0
$851$	−7.16669	−	4.13769i	−0.245671	−	0.141838i
$852$	1.66181	−	6.20195i	0.0569326	−	0.212475i
$853$	−26.0832	−	6.98897i	−0.893072	−	0.239298i	−0.217033	−	0.976164i	$-0.569638\pi$
$853$	−26.0832	−	6.98897i	−0.893072	−	0.239298i	−0.676038	+	0.736866i	$0.736305\pi$
$854$	−11.3318			−0.387766
$855$		0			0
$856$	−15.3299			−0.523964
$857$	−2.36739	−	0.634339i	−0.0808683	−	0.0216686i	0.218158	−	0.975913i	$-0.429995\pi$
$857$	−2.36739	−	0.634339i	−0.0808683	−	0.0216686i	−0.299026	+	0.954245i	$0.596662\pi$
$858$	7.14665	−	26.6716i	0.243982	−	0.910555i
$859$	18.7669	+	10.8351i	0.640318	+	0.369688i	0.784737	−	0.619829i	$-0.212798\pi$
$859$	18.7669	+	10.8351i	0.640318	+	0.369688i	−0.144419	+	0.989517i	$0.546131\pi$
$860$		0			0
$861$	13.7388	−	23.7963i	0.468217	−	0.810975i
$862$	−9.62714	−	9.62714i	−0.327902	−	0.327902i
$863$	12.0651	+	12.0651i	0.410702	+	0.410702i	0.881983	−	0.471281i	$-0.156208\pi$
$863$	12.0651	+	12.0651i	0.410702	+	0.410702i	−0.471281	+	0.881983i	$0.656208\pi$
$864$	−4.85357	−	2.80221i	−0.165122	−	0.0953331i
$865$		0			0
$866$	−9.04565			−0.307384
$867$	18.2924	−	18.2924i	0.621241	−	0.621241i
$868$	−14.1382	+	3.78831i	−0.479881	+	0.128584i
$869$	−36.4491	−	63.1317i	−1.23645	−	2.14160i
$870$		0			0
$871$	16.8310	+	29.1522i	0.570297	+	0.987784i
$872$	2.33176	−	8.70223i	0.0789632	−	0.294695i
$873$	−8.37563	−	8.37563i	−0.283472	−	0.283472i
$874$	10.3743	−	1.27823i	0.350917	−	0.0432368i
$875$		0			0
$876$	−4.32058	+	2.49449i	−0.145979	+	0.0842808i
$877$	12.1727	+	3.26167i	0.411043	+	0.110139i	0.458414	−	0.888739i	$-0.348418\pi$
$877$	12.1727	+	3.26167i	0.411043	+	0.110139i	−0.0473710	+	0.998877i	$0.515084\pi$
$878$	0.495612	+	1.84965i	0.0167261	+	0.0624226i
$879$	−20.8178	+	12.0191i	−0.702166	+	0.405396i
$880$		0			0
$881$	25.1454			0.847171			0.423585	−	0.905856i	$-0.360771\pi$
$881$	25.1454			0.847171			0.423585	+	0.905856i	$0.360771\pi$
$882$	−0.598552	+	0.598552i	−0.0201543	+	0.0201543i
$883$	11.9386	+	44.5556i	0.401767	+	1.49941i	0.809941	+	0.586511i	$0.199499\pi$
$883$	11.9386	+	44.5556i	0.401767	+	1.49941i	−0.408174	+	0.912904i	$0.633834\pi$
$884$	0.291464	−	0.504831i	0.00980300	−	0.0169793i
$885$		0			0
$886$			19.1676i			0.643946i
$887$	2.06155	+	7.69380i	0.0692200	+	0.258333i	0.991861	−	0.127328i	$-0.0406401\pi$
$887$	2.06155	+	7.69380i	0.0692200	+	0.258333i	−0.922641	+	0.385661i	$0.873973\pi$
$888$	1.36115	−	5.07989i	0.0456773	−	0.170470i
$889$	−9.57360	+	16.5820i	−0.321088	+	0.556141i
$890$		0			0
$891$	−16.0335	−	27.7708i	−0.537141	−	0.930356i
$892$	−12.1168	+	12.1168i	−0.405701	+	0.405701i
$893$	−4.43795	−	10.9711i	−0.148510	−	0.367132i
$894$			29.0286i			0.970863i
$895$		0			0
$896$	2.07676	−	1.19902i	0.0693797	−	0.0400564i
$897$	−12.9816	+	3.47842i	−0.433445	+	0.116141i
$898$	20.0887	+	5.38275i	0.670369	+	0.179625i
$899$	−48.8993	−	28.2320i	−1.63088	−	0.941591i
$900$		0			0
$901$			0.990610i			0.0330020i
$902$	−35.7820	+	9.58774i	−1.19141	+	0.319237i
$903$	22.4849	−	6.02480i	0.748250	−	0.200493i
$904$		−	18.5793i		−	0.617938i
$905$		0			0
$906$	13.8676	+	8.00644i	0.460719	+	0.265996i
$907$	14.7033	+	3.93974i	0.488216	+	0.130817i	0.494526	−	0.869163i	$-0.335342\pi$
$907$	14.7033	+	3.93974i	0.488216	+	0.130817i	−0.00630979	+	0.999980i	$0.502008\pi$
$908$	20.9702	−	5.61896i	0.695922	−	0.186472i
$909$	4.55180	−	2.62799i	0.150974	−	0.0871648i
$910$		0			0
$911$			12.4861i			0.413682i	0.978375	+	0.206841i	$0.0663183\pi$
$911$			12.4861i			0.413682i	−0.978375	+	0.206841i	$0.933682\pi$
$912$	2.49105	+	6.15811i	0.0824867	+	0.203915i
$913$	−11.2269	+	11.2269i	−0.371555	+	0.371555i
$914$	−6.36961	−	11.0325i	−0.210688	−	0.364922i
$915$		0			0
$916$	14.7771	−	25.5947i	0.488249	−	0.845671i
$917$	−11.4421	+	42.7024i	−0.377851	+	1.41016i
$918$	−0.229927	−	0.858098i	−0.00758871	−	0.0283215i
$919$			5.76604i			0.190204i	0.995468	+	0.0951021i	$0.0303177\pi$
$919$			5.76604i			0.190204i	−0.995468	+	0.0951021i	$0.969682\pi$
$920$		0			0
$921$	−18.2933	+	31.6850i	−0.602786	+	1.04406i
$922$	−0.153027	−	0.571105i	−0.00503968	−	0.0188083i
$923$	−10.9558	+	10.9558i	−0.360614	+	0.360614i
$924$	18.0057			0.592343
$925$		0			0
$926$	−14.1553	+	8.17255i	−0.465171	+	0.268567i
$927$	−0.901970	−	3.36620i	−0.0296246	−	0.110560i
$928$	8.93557	+	2.39428i	0.293324	+	0.0785961i
$929$	−6.29795	+	3.63613i	−0.206629	+	0.119297i	−0.599744	−	0.800192i	$-0.704731\pi$
$929$	−6.29795	+	3.63613i	−0.206629	+	0.119297i	0.393115	+	0.919489i	$0.371398\pi$
$930$		0			0
$931$	5.40524	−	0.665985i	0.177150	−	0.0218268i
$932$	−3.26204	−	3.26204i	−0.106852	−	0.106852i
$933$	−2.26822	+	8.46512i	−0.0742583	+	0.277136i
$934$	−14.8554	−	25.7303i	−0.486083	−	0.841920i
$935$		0			0
$936$	1.24574	+	2.15769i	0.0407184	+	0.0705264i
$937$	35.4102	−	9.48813i	1.15680	−	0.309964i	0.371113	−	0.928588i	$-0.378976\pi$
$937$	35.4102	−	9.48813i	1.15680	−	0.309964i	0.785687	+	0.618624i	$0.212310\pi$
$938$	−15.5213	+	15.5213i	−0.506789	+	0.506789i
$939$	2.15647			0.0703736
$940$		0			0
$941$	41.6812	+	24.0646i	1.35877	+	0.784485i	0.989458	−	0.144822i	$-0.0462608\pi$
$941$	41.6812	+	24.0646i	1.35877	+	0.784485i	0.369310	+	0.929306i	$0.379594\pi$
$942$	−0.888490	−	0.888490i	−0.0289486	−	0.0289486i
$943$	12.7493	+	12.7493i	0.415173	+	0.415173i
$944$	1.77358	−	3.07193i	0.0577251	−	0.0999828i
$945$		0			0
$946$	−27.1781	−	15.6913i	−0.883636	−	0.510168i
$947$	−13.2752	+	49.5438i	−0.431387	+	1.60996i	0.318180	+	0.948030i	$0.396928\pi$
$947$	−13.2752	+	49.5438i	−0.431387	+	1.60996i	−0.749567	+	0.661928i	$0.769738\pi$
$948$	−21.7803	−	5.83601i	−0.707390	−	0.189545i
$949$	12.0388			0.390798
$950$		0			0
$951$	−31.7077			−1.02819
$952$	0.367166	+	0.0983818i	0.0118999	+	0.00318857i
$953$	−3.43821	+	12.8316i	−0.111374	+	0.415655i	−0.998990	−	0.0449297i	$-0.985694\pi$
$953$	−3.43821	+	12.8316i	−0.111374	+	0.415655i	0.887616	+	0.460585i	$0.152360\pi$
$954$	−3.66672	−	2.11698i	−0.118714	−	0.0685398i
$955$		0			0
$956$	−3.23028	+	5.59501i	−0.104475	+	0.180955i
$957$	49.1154	+	49.1154i	1.58767	+	1.58767i
$958$	−0.768091	−	0.768091i	−0.0248159	−	0.0248159i
$959$	11.5159	+	6.64869i	0.371867	+	0.214697i
$960$		0			0
$961$	−6.25523			−0.201782
$962$	−8.97365	+	8.97365i	−0.289322	+	0.289322i
$963$	10.0320	−	2.68807i	0.323278	−	0.0866220i
$964$	0.345160	+	0.597834i	0.0111168	+	0.0192549i
$965$		0			0
$966$	−4.38187	−	7.58962i	−0.140984	−	0.244192i
$967$	−5.68120	+	21.2025i	−0.182695	+	0.681827i	0.812417	+	0.583077i	$0.198151\pi$
$967$	−5.68120	+	21.2025i	−0.182695	+	0.681827i	−0.995112	+	0.0987505i	$0.968515\pi$
$968$	−9.38653	−	9.38653i	−0.301694	−	0.301694i
$969$	−0.411023	+	0.969441i	−0.0132040	+	0.0311429i
$970$		0			0
$971$	−10.7469	+	6.20472i	−0.344884	+	0.199119i	−0.662430	−	0.749124i	$-0.730475\pi$
$971$	−10.7469	+	6.20472i	−0.344884	+	0.199119i	0.317546	+	0.948243i	$0.397141\pi$
$972$	6.65951	+	1.78441i	0.213604	+	0.0572350i
$973$	−3.58930	−	13.3955i	−0.115068	−	0.429438i
$974$	8.83274	−	5.09959i	0.283019	−	0.163401i
$975$		0			0
$976$	4.72545			0.151258
$977$	32.3787	−	32.3787i	1.03589	−	1.03589i	0.0365554	−	0.999332i	$-0.488361\pi$
$977$	32.3787	−	32.3787i	1.03589	−	1.03589i	0.999332	−	0.0365554i	$-0.0116385\pi$
$978$	−0.0922849	−	0.344412i	−0.00295095	−	0.0110131i
$979$	19.3630	−	33.5377i	0.618845	−	1.07187i
$980$		0			0
$981$			6.10371i			0.194876i
$982$	−6.13409	−	22.8928i	−0.195747	−	0.730537i
$983$	−1.74968	+	6.52989i	−0.0558061	+	0.208271i	−0.988199	−	0.153175i	$-0.951050\pi$
$983$	−1.74968	+	6.52989i	−0.0558061	+	0.208271i	0.932393	+	0.361446i	$0.117717\pi$
$984$	−5.72919	+	9.92324i	−0.182640	+	0.316341i
$985$		0			0
$986$	0.733181	+	1.26991i	0.0233492	+	0.0404421i
$987$	−7.01614	+	7.01614i	−0.223326	+	0.223326i
$988$	2.22426	−	15.8748i	0.0707630	−	0.505044i
$989$			15.2746i			0.485702i
$990$		0			0
$991$	20.3856	−	11.7696i	0.647568	−	0.373874i	−0.139956	−	0.990158i	$-0.544696\pi$
$991$	20.3856	−	11.7696i	0.647568	−	0.373874i	0.787524	+	0.616284i	$0.211363\pi$
$992$	5.89573	−	1.57976i	0.187190	−	0.0501573i
$993$	−3.23262	−	0.866179i	−0.102584	−	0.0274874i
$994$	−8.74969	−	5.05163i	−0.277523	−	0.160228i
$995$		0			0
$996$			4.91106i			0.155613i
$997$	−4.52157	+	1.21155i	−0.143200	+	0.0383702i	−0.329707	−	0.944083i	$-0.606950\pi$
$997$	−4.52157	+	1.21155i	−0.143200	+	0.0383702i	0.186507	+	0.982454i	$0.440283\pi$
$998$	26.8099	−	7.18369i	0.848652	−	0.227396i
$999$			19.3403i			0.611899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.e.107.2	✓	24
5.2	odd	4	inner	950.2.q.e.943.5	yes	24
5.3	odd	4	inner	950.2.q.e.943.2	yes	24
5.4	even	2	inner	950.2.q.e.107.5	yes	24
19.8	odd	6	inner	950.2.q.e.407.2	yes	24
95.8	even	12	inner	950.2.q.e.293.2	yes	24
95.27	even	12	inner	950.2.q.e.293.5	yes	24
95.84	odd	6	inner	950.2.q.e.407.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.2	✓	24	1.1	even	1	trivial
950.2.q.e.107.5	yes	24	5.4	even	2	inner
950.2.q.e.293.2	yes	24	95.8	even	12	inner
950.2.q.e.293.5	yes	24	95.27	even	12	inner
950.2.q.e.407.2	yes	24	19.8	odd	6	inner
950.2.q.e.407.5	yes	24	95.84	odd	6	inner
950.2.q.e.943.2	yes	24	5.3	odd	4	inner
950.2.q.e.943.5	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.394434 - 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(1.69567 + 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.394434 - 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(1.69567 + 1.69567i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +4.92692 q^{11} +(1.07761 - 1.07761i) q^{12} +(-3.55219 + 0.951806i) q^{13} +(-1.19902 - 2.07676i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.0410260 + 0.153111i) q^{17} +(-0.479062 - 0.479062i) q^{18} +(0.533033 + 4.32618i) q^{19} +(3.16493 - 1.82727i) q^{21} +(-4.75904 - 1.27518i) q^{22} +(0.620657 + 2.31632i) q^{23} +(-1.31980 + 0.761988i) q^{24} +3.67750 q^{26} +(3.96292 - 3.96292i) q^{27} +(0.620657 + 2.31632i) q^{28} +(-4.62539 + 8.01141i) q^{29} +6.10371i q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.94335 - 7.25267i) q^{33} +(0.0792561 - 0.137276i) q^{34} +(0.338748 + 0.586729i) q^{36} +(-2.44015 + 2.44015i) q^{37} +(0.604829 - 4.31673i) q^{38} +5.60442i q^{39} +(6.51141 - 3.75937i) q^{41} +(-3.53002 + 0.945867i) q^{42} +(6.15257 + 1.64858i) q^{43} +(4.26684 + 2.46346i) q^{44} -2.39804i q^{46} +(-2.62255 + 0.702709i) q^{47} +(1.47205 - 0.394434i) q^{48} -1.24943i q^{49} +(0.209205 + 0.120784i) q^{51} +(-3.55219 - 0.951806i) q^{52} +(6.03648 - 1.61747i) q^{53} +(-4.85357 + 2.80221i) q^{54} -2.39804i q^{56} +(6.57860 + 0.921745i) q^{57} +(6.54129 - 6.54129i) q^{58} +(-1.77358 - 3.07193i) q^{59} +(2.36272 - 4.09236i) q^{61} +(1.57976 - 5.89573i) q^{62} +(0.420493 + 1.56930i) q^{63} +1.00000i q^{64} +(-3.75426 + 6.50256i) q^{66} +(-2.36911 - 8.84162i) q^{67} +(-0.112085 + 0.112085i) q^{68} +3.65455 q^{69} +(3.64869 - 2.10657i) q^{71} +(-0.175349 - 0.654411i) q^{72} +(-3.16211 - 0.847284i) q^{73} +(2.98856 - 1.72545i) q^{74} +(-1.70147 + 4.01310i) q^{76} +(8.35442 + 8.35442i) q^{77} +(1.45053 - 5.41345i) q^{78} +(-7.39795 - 12.8136i) q^{79} +(-3.25426 - 5.63654i) q^{81} +(-7.26254 + 1.94599i) q^{82} +(-2.27867 + 2.27867i) q^{83} +3.65455 q^{84} +(-5.51624 - 3.18480i) q^{86} +(9.96877 + 9.96877i) q^{87} +(-3.48386 - 3.48386i) q^{88} +(3.93005 - 6.80704i) q^{89} +(-7.63728 - 4.40938i) q^{91} +(-0.620657 + 2.31632i) q^{92} +(8.98495 + 2.40751i) q^{93} +2.71506 q^{94} -1.52398 q^{96} +(-16.8877 - 4.52503i) q^{97} +(-0.323375 + 1.20685i) q^{98} +(2.89077 + 1.66898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{6}+O(q^{10}) \) 24 * q - 12 * q^6	\( 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

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