LMFDB - Embedded newform 950.2.q.e.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:	$24$
Relative dimension:	$6$ 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.e.293.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.394434 + 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +O(q^{10})$	\(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	$0.228332\pi$
$3$	−0.394434	+	1.47205i	−0.227727	+	0.849887i	−0.981294	+	0.192516i	$0.938335\pi$
$4$	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	0.309875	−	0.950777i	$-0.399713\pi$
$7$	−1.69567	−	1.69567i	−0.640902	−	0.640902i	−0.950777	+	0.309875i	$0.899713\pi$
$8$	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	0.269967	−	0.962870i	$-0.412987\pi$
$13$	3.55219	−	0.951806i	0.985200	−	0.263983i	0.715233	+	0.698886i	$0.246321\pi$
$14$	−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	−0.960772	−	0.277339i	$-0.910548\pi$
$17$	0.0410260	−	0.153111i	0.00995026	−	0.0371349i	0.970722	+	0.240204i	$0.0772143\pi$
$18$	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	0.870543	−	0.492093i	$-0.163768\pi$
$23$	−0.620657	−	2.31632i	−0.129416	−	0.482987i	−0.999959	+	0.00910610i	$0.997101\pi$
$24$	−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	−0.477483	−	0.878641i	$-0.658451\pi$
$37$	2.44015	−	2.44015i	0.401159	−	0.401159i	0.878641	+	0.477483i	$0.158451\pi$
$38$	−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	−0.242886	−	0.970055i	$-0.578094\pi$
$43$	−6.15257	−	1.64858i	−0.938258	−	0.251406i	−0.695373	+	0.718649i	$0.744761\pi$
$44$	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	−0.0624252	−	0.998050i	$-0.519883\pi$
$47$	2.62255	−	0.702709i	0.382538	−	0.102501i	0.444963	+	0.895549i	$0.353217\pi$
$48$	−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	−0.648354	−	0.761339i	$-0.724542\pi$
$53$	−6.03648	+	1.61747i	−0.829174	+	0.222177i	−0.180821	+	0.983516i	$0.557875\pi$
$54$	−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	$0.105535\pi$
$67$	2.36911	+	8.84162i	0.289432	+	1.08018i	−0.656107	+	0.754668i	$0.727798\pi$
$68$	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	0.439073	−	0.898451i	$-0.355307\pi$
$73$	3.16211	+	0.847284i	0.370097	+	0.0991671i	−0.0689769	+	0.997618i	$0.521973\pi$
$74$	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	−0.570902	−	0.821019i	$-0.693406\pi$
$83$	2.27867	−	2.27867i	0.250117	−	0.250117i	0.821019	+	0.570902i	$0.193406\pi$
$84$	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	0.976564	−	0.215225i	$-0.0690486\pi$
$97$	16.8877	+	4.52503i	1.71468	+	0.459447i	0.738117	+	0.674673i	$0.235715\pi$
$98$	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	0.863219	−	0.504829i	$-0.168445\pi$
$103$	3.63726	+	3.63726i	0.358390	+	0.358390i	−0.504829	+	0.863219i	$0.668445\pi$
$104$	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	$0.515647\pi$
$107$	−10.8399	+	10.8399i	−1.04793	+	1.04793i	−0.998792	+	0.0491359i	$0.984353\pi$
$108$	−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	$-0.911585\pi$
$113$	−13.1375	−	13.1375i	−1.23588	−	1.23588i	−0.274205	−	0.961671i	$-0.588415\pi$
$114$	−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	$-0.968067\pi$
$127$	−2.06655	−	7.71247i	−0.183377	−	0.684371i	0.811596	−	0.584220i	$-0.198599\pi$
$128$	−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	−0.480257	−	0.877128i	$-0.659457\pi$
$137$	−5.35617	+	1.43518i	−0.457608	+	0.122616i	0.0226489	+	0.999743i	$0.492790\pi$
$138$	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	−0.956887	−	0.290459i	$-0.906192\pi$
$157$	0.213396	−	0.796403i	0.0170308	−	0.0635599i	0.973918	+	0.226899i	$0.0728587\pi$
$158$	−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	−0.700598	−	0.713556i	$-0.747083\pi$
$163$	0.165440	−	0.165440i	0.0129583	−	0.0129583i	0.713556	+	0.700598i	$0.247083\pi$
$164$	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	$-0.984108\pi$
$167$	−2.05164	−	7.65682i	−0.158761	−	0.592502i	0.839993	−	0.542597i	$-0.182559\pi$
$168$	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	−0.936201	−	0.351465i	$-0.885684\pi$
$173$	0.661662	−	2.46935i	0.0503052	−	0.187742i	0.986506	+	0.163723i	$0.0523504\pi$
$174$	−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	$-0.771950\pi$
$193$	3.15797	−	11.7857i	0.227316	−	0.848354i	0.981463	−	0.191649i	$-0.0613837\pi$
$194$	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	0.414592	−	0.910007i	$-0.363924\pi$
$197$	−6.95348	−	6.95348i	−0.495415	−	0.495415i	−0.910007	+	0.414592i	$0.863924\pi$
$198$	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	$-0.722156\pi$
$223$	4.43506	−	16.5519i	0.296994	−	1.10840i	0.939621	−	0.342216i	$-0.111178\pi$
$224$	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	$0.506074\pi$
$227$	−15.3513	+	15.3513i	−1.01890	+	1.01890i	−0.999818	+	0.0190821i	$0.993926\pi$
$228$	−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	0.401809	−	0.915723i	$-0.368382\pi$
$233$	4.45603	+	1.19399i	0.291924	+	0.0782209i	−0.109885	+	0.993944i	$0.535048\pi$
$234$	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	0.986324	−	0.164819i	$-0.0527041\pi$
$257$	0.797277	+	2.97548i	0.0497328	+	0.185605i	−0.936591	+	0.350424i	$0.886037\pi$
$258$	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	0.696228	−	0.717821i	$-0.254860\pi$
$263$	15.2486	+	4.08585i	0.940269	+	0.251944i	0.244041	+	0.969765i	$0.421527\pi$
$264$	−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	$-0.924465\pi$
$277$	−20.0894	−	20.0894i	−1.20706	−	1.20706i	−0.235081	−	0.971976i	$-0.575535\pi$
$278$	−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	−0.630017	−	0.776581i	$-0.716952\pi$
$283$	−26.3092	−	7.04953i	−1.56392	−	0.419051i	−0.933902	+	0.357530i	$0.883619\pi$
$284$	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	0.953377	−	0.301783i	$-0.0975819\pi$
$293$	11.1535	+	11.1535i	0.651593	+	0.651593i	−0.301783	+	0.953377i	$0.597582\pi$
$294$	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	0.850282	−	0.526327i	$-0.176431\pi$
$307$	23.1893	+	6.21356i	1.32349	+	0.354627i	0.473203	+	0.880954i	$0.343098\pi$
$308$	−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	0.954803	−	0.297240i	$-0.0960663\pi$
$313$	−0.366236	−	1.36681i	−0.0207009	−	0.0772567i	−0.975504	+	0.219984i	$0.929400\pi$
$314$	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	$0.115293\pi$
$317$	5.38496	+	20.0969i	0.302450	+	1.12876i	−0.632669	+	0.774422i	$0.718041\pi$
$318$	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	0.888356	−	0.459156i	$-0.151848\pi$
$337$	26.2167	+	7.02475i	1.42812	+	0.382663i	0.539761	+	0.841818i	$0.318515\pi$
$338$	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	$-0.761223\pi$
$347$	4.52390	−	16.8834i	0.242856	−	0.906350i	0.974449	−	0.224609i	$-0.0721104\pi$
$348$	−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	−0.998726	−	0.0504691i	$-0.983928\pi$
$353$	−17.8161	+	17.8161i	−0.948257	+	0.948257i	0.0504691	+	0.998726i	$0.483928\pi$
$354$	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	0.739615	−	0.673030i	$-0.235007\pi$
$367$	32.8864	−	8.81188i	1.71666	−	0.459977i	0.977041	+	0.213053i	$0.0683408\pi$
$368$	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	$-0.971739\pi$
$373$	−20.9496	−	20.9496i	−1.08473	−	1.08473i	−0.0886693	−	0.996061i	$-0.528261\pi$
$374$	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	$0.175294\pi$
$383$	−2.88615	+	10.7713i	−0.147475	+	0.550385i	−0.999633	+	0.0270998i	$0.991373\pi$
$384$	−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	$-0.578328\pi$
$397$	9.01205	−	33.6334i	0.452302	−	1.68801i	0.695902	−	0.718137i	$-0.255005\pi$
$398$	−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	−0.462579	−	0.886578i	$-0.653076\pi$
$433$	−8.73743	+	2.34119i	−0.419894	+	0.112510i	0.0426844	+	0.999089i	$0.486409\pi$
$434$	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	$0.0671486\pi$
$443$	4.96093	+	18.5144i	0.235701	+	0.879647i	−0.742131	+	0.670255i	$0.766185\pi$
$444$			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	0.464301	−	0.885677i	$-0.346305\pi$
$457$	−9.00799	−	9.00799i	−0.421376	−	0.421376i	−0.885677	+	0.464301i	$0.846305\pi$
$458$	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	−0.922686	−	0.385553i	$-0.874011\pi$
$463$	−11.5577	+	11.5577i	−0.537133	+	0.537133i	0.385553	+	0.922686i	$0.374011\pi$
$464$	−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	0.0274570	−	0.999623i	$-0.491259\pi$
$467$	−21.0087	−	21.0087i	−0.972166	−	0.972166i	−0.999623	+	0.0274570i	$0.991259\pi$
$468$	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	−0.524567	−	0.851369i	$-0.675773\pi$
$487$	7.21190	−	7.21190i	0.326803	−	0.326803i	0.851369	+	0.524567i	$0.175773\pi$
$488$	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	$0.168378\pi$
$503$	8.25311	+	30.8010i	0.367988	+	1.37335i	−0.495336	+	0.868701i	$0.664955\pi$
$504$	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	0.206188	−	0.978512i	$-0.433894\pi$
$523$	19.9879	−	5.35573i	0.874008	−	0.234190i	0.667820	+	0.744323i	$0.267227\pi$
$524$			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	$0.102214\pi$
$547$	6.66414	+	24.8709i	0.284938	+	1.06340i	−0.663946	+	0.747780i	$0.731120\pi$
$548$	−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	0.331012	−	0.943626i	$-0.392610\pi$
$557$	25.7129	−	6.88975i	1.08949	−	0.291928i	0.758478	+	0.651698i	$0.225943\pi$
$558$	−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	0.930937	−	0.365179i	$-0.118992\pi$
$563$	13.4241	+	13.4241i	0.565758	+	0.565758i	−0.365179	+	0.930937i	$0.618992\pi$
$564$	−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	$0.0340227\pi$
$577$	26.4463	+	26.4463i	1.10098	+	1.10098i	0.106682	+	0.994293i	$0.465977\pi$
$578$	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	$0.368369\pi$
$587$	−9.78854	+	36.5313i	−0.404016	+	1.50781i	−0.805863	+	0.592103i	$0.798298\pi$
$588$	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	$-0.979627\pi$
$593$	−4.03459	−	15.0573i	−0.165681	−	0.618329i	0.832272	−	0.554368i	$-0.187040\pi$
$594$	−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	$0.503043\pi$
$607$	−24.8718	+	24.8718i	−1.00952	+	1.00952i	−0.999954	+	0.00956121i	$0.996957\pi$
$608$	−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	−0.292078	−	0.956394i	$-0.594347\pi$
$613$	−25.3338	−	6.78817i	−1.02322	−	0.274172i	−0.731144	+	0.682223i	$0.761013\pi$
$614$	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	−0.294307	−	0.955711i	$-0.595089\pi$
$617$	−1.77179	+	0.474750i	−0.0713296	+	0.0191127i	0.222978	+	0.974824i	$0.428422\pi$
$618$	−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	0.961357	−	0.275306i	$-0.0887793\pi$
$643$	41.9986	+	11.2535i	1.65626	+	0.443794i	0.694906	+	0.719101i	$0.255446\pi$
$644$	−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	0.749813	−	0.661650i	$-0.230144\pi$
$647$	2.24253	+	2.24253i	0.0881628	+	0.0881628i	−0.661650	+	0.749813i	$0.730144\pi$
$648$	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	$0.611979\pi$
$653$	−32.7942	+	32.7942i	−1.28334	+	1.28334i	−0.938757	+	0.344581i	$0.888021\pi$
$654$	−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	0.638449	−	0.769664i	$-0.279576\pi$
$673$	−3.40401	−	3.40401i	−0.131215	−	0.131215i	−0.769664	+	0.638449i	$0.779576\pi$
$674$	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	$0.579109\pi$
$677$	−31.6199	+	31.6199i	−1.21525	+	1.21525i	−0.969276	+	0.245977i	$0.920891\pi$
$678$	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	0.981973	−	0.189022i	$-0.0605316\pi$
$683$	20.7232	+	20.7232i	0.792951	+	0.792951i	−0.189022	+	0.981973i	$0.560532\pi$
$684$	−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	$-0.737031\pi$
$727$	7.46505	−	27.8600i	0.276863	−	1.03327i	0.954582	−	0.297947i	$-0.0963020\pi$
$728$	−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	−0.208993	−	0.977917i	$-0.567018\pi$
$733$	20.8178	−	20.8178i	0.768925	−	0.768925i	0.977917	+	0.208993i	$0.0670184\pi$
$734$	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	−0.883071	−	0.469239i	$-0.844528\pi$
$743$	3.17038	−	11.8320i	0.116310	−	0.434075i	0.999382	+	0.0351632i	$0.0111951\pi$
$744$	−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	$0.220699\pi$
$757$	−5.95712	+	22.2323i	−0.216515	+	0.808045i	−0.985628	+	0.168932i	$0.945968\pi$
$758$	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	0.0755831	−	0.997140i	$-0.475918\pi$
$773$	17.7830	−	4.76494i	0.639610	−	0.171383i	0.564027	+	0.825757i	$0.309252\pi$
$774$	−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	−0.123934	−	0.992290i	$-0.539551\pi$
$787$	24.3605	−	24.3605i	0.868357	−	0.868357i	0.992290	+	0.123934i	$0.0395510\pi$
$788$	−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	$0.513080\pi$
$797$	−29.3671	+	29.3671i	−1.04024	+	1.04024i	−0.999156	+	0.0410799i	$0.986920\pi$
$798$	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	$0.0977519\pi$
$823$	7.99972	+	29.8554i	0.278853	+	1.04069i	−0.674362	+	0.738401i	$0.735581\pi$
$824$			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	$-0.991177\pi$
$827$	−4.24980	−	15.8605i	−0.147780	−	0.551523i	0.851836	−	0.523809i	$-0.175489\pi$
$828$	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	0.676038	−	0.736866i	$-0.263695\pi$
$853$	26.0832	+	6.98897i	0.893072	+	0.239298i	0.217033	+	0.976164i	$0.430362\pi$
$854$	−11.3318			−0.387766
$855$		0			0
$856$	−15.3299			−0.523964
$857$	2.36739	+	0.634339i	0.0808683	+	0.0216686i	0.299026	−	0.954245i	$-0.403338\pi$
$857$	2.36739	+	0.634339i	0.0808683	+	0.0216686i	−0.218158	+	0.975913i	$0.570005\pi$
$858$	−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	0.471281	−	0.881983i	$-0.343792\pi$
$863$	−12.0651	−	12.0651i	−0.410702	−	0.410702i	−0.881983	+	0.471281i	$0.843792\pi$
$864$	−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	0.0473710	−	0.998877i	$-0.484916\pi$
$877$	−12.1727	−	3.26167i	−0.411043	−	0.110139i	−0.458414	+	0.888739i	$0.651582\pi$
$878$	−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	$-0.800501\pi$
$883$	−11.9386	−	44.5556i	−0.401767	−	1.49941i	0.408174	−	0.912904i	$-0.366166\pi$
$884$	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	0.922641	−	0.385661i	$-0.126027\pi$
$887$	−2.06155	−	7.69380i	−0.0692200	−	0.258333i	−0.991861	+	0.127328i	$0.959360\pi$
$888$	−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	0.00630979	−	0.999980i	$-0.497992\pi$
$907$	−14.7033	−	3.93974i	−0.488216	−	0.130817i	−0.494526	+	0.869163i	$0.664658\pi$
$908$	−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	−0.785687	−	0.618624i	$-0.787690\pi$
$937$	−35.4102	+	9.48813i	−1.15680	+	0.309964i	−0.371113	+	0.928588i	$0.621024\pi$
$938$	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	$-0.603072\pi$
$947$	13.2752	−	49.5438i	0.431387	−	1.60996i	0.749567	−	0.661928i	$-0.230262\pi$
$948$	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	−0.887616	−	0.460585i	$-0.847640\pi$
$953$	3.43821	−	12.8316i	0.111374	−	0.415655i	0.998990	+	0.0449297i	$0.0143064\pi$
$954$	−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	$-0.801849\pi$
$967$	5.68120	−	21.2025i	0.182695	−	0.681827i	0.995112	−	0.0987505i	$-0.0314846\pi$
$968$	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	$0.511639\pi$
$977$	−32.3787	+	32.3787i	−1.03589	+	1.03589i	−0.999332	+	0.0365554i	$0.988361\pi$
$978$	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	−0.932393	−	0.361446i	$-0.882283\pi$
$983$	1.74968	−	6.52989i	0.0558061	−	0.208271i	0.988199	+	0.153175i	$0.0489498\pi$
$984$	−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	−0.186507	−	0.982454i	$-0.559717\pi$
$997$	4.52157	−	1.21155i	0.143200	−	0.0383702i	0.329707	+	0.944083i	$0.393050\pi$
$998$	−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.107.5	yes	24
5.2	odd	4	inner	950.2.q.e.943.2	yes	24
5.3	odd	4	inner	950.2.q.e.943.5	yes	24
5.4	even	2	inner	950.2.q.e.107.2	✓	24
19.8	odd	6	inner	950.2.q.e.407.5	yes	24
95.8	even	12	inner	950.2.q.e.293.5	yes	24
95.27	even	12	inner	950.2.q.e.293.2	yes	24
95.84	odd	6	inner	950.2.q.e.407.2	yes	24

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.394434 + 1.47205i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.761988 + 1.31980i) q^{6} +(-1.69567 - 1.69567i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.586729 + 0.338748i) q^{9} +O(q^{10})\)	\(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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