LMFDB - Embedded newform 950.2.q.d.943.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	950.943
Dual form			950.2.q.d.407.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.93185 + 0.517638i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.93185 + 0.517638i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +3.00000 q^{11} +(-1.41421 - 1.41421i) q^{12} +(0.517638 + 1.93185i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.707107 - 0.707107i) q^{18} +(2.59808 - 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(0.776457 - 2.89778i) q^{22} +(5.01910 - 1.34486i) q^{23} +(-1.73205 + 1.00000i) q^{24} +2.00000 q^{26} +(-2.82843 - 2.82843i) q^{27} +(-1.67303 + 0.448288i) q^{28} +3.46410i q^{31} +(0.965926 - 0.258819i) q^{32} +(5.79555 + 1.55291i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-0.707107 - 0.707107i) q^{37} +(-2.70831 - 3.41542i) q^{38} +4.00000i q^{39} +(-4.50000 + 2.59808i) q^{41} +(-0.896575 - 3.34607i) q^{42} +(1.79315 - 6.69213i) q^{43} +(-2.59808 - 1.50000i) q^{44} -5.19615i q^{46} +(-2.68973 - 10.0382i) q^{47} +(0.517638 + 1.93185i) q^{48} +4.00000i q^{49} +(0.517638 - 1.93185i) q^{52} +(0.776457 + 2.89778i) q^{53} +(-3.46410 + 2.00000i) q^{54} +1.73205i q^{56} +(6.83083 - 5.41662i) q^{57} +(5.19615 + 9.00000i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(3.34607 + 0.896575i) q^{62} +(1.67303 - 0.448288i) q^{63} -1.00000i q^{64} +(3.00000 - 5.19615i) q^{66} +(1.93185 - 0.517638i) q^{67} +10.3923 q^{69} +(-9.00000 + 5.19615i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(0.896575 - 3.34607i) q^{73} +(-0.866025 + 0.500000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(3.67423 - 3.67423i) q^{77} +(3.86370 + 1.03528i) q^{78} +(1.73205 + 3.00000i) q^{79} +(-5.50000 - 9.52628i) q^{81} +(1.34486 + 5.01910i) q^{82} -3.46410 q^{84} +(-6.00000 - 3.46410i) q^{86} +(-2.12132 + 2.12132i) q^{88} +(2.59808 - 4.50000i) q^{89} +(3.00000 + 1.73205i) q^{91} +(-5.01910 - 1.34486i) q^{92} +(-1.79315 + 6.69213i) q^{93} -10.3923 q^{94} +2.00000 q^{96} +(-2.07055 + 7.72741i) q^{97} +(3.86370 + 1.03528i) q^{98} +(2.59808 + 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{6}+O(q^{10}) $ 8 * q + 8 * q^6	$ 8 q + 8 q^{6} + 24 q^{11} + 4 q^{16} + 24 q^{21} + 16 q^{26} - 4 q^{36} - 36 q^{41} - 16 q^{61} + 24 q^{66} - 72 q^{71} - 32 q^{76} - 44 q^{81} - 48 q^{86} + 24 q^{91} + 16 q^{96}+O(q^{100}) $ 8 * q + 8 * q^6 + 24 * q^11 + 4 * q^16 + 24 * q^21 + 16 * q^26 - 4 * q^36 - 36 * q^41 - 16 * q^61 + 24 * q^66 - 72 * q^71 - 32 * q^76 - 44 * q^81 - 48 * q^86 + 24 * q^91 + 16 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.93185	+	0.517638i	1.11536	+	0.298858i	0.769002	−	0.639246i	$-0.220753\pi$
$3$	1.93185	+	0.517638i	1.11536	+	0.298858i	0.346353	+	0.938104i	$0.387420\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	1.00000	−	1.73205i	0.408248	−	0.707107i
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	−0.436698	−	0.899608i	$-0.643852\pi$
$7$	1.22474	−	1.22474i	0.462910	−	0.462910i	0.899608	+	0.436698i	$0.143852\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$	−1.41421	−	1.41421i	−0.408248	−	0.408248i
$13$	0.517638	+	1.93185i	0.143567	+	0.535799i	0.999815	+	0.0192343i	$0.00612285\pi$
$13$	0.517638	+	1.93185i	0.143567	+	0.535799i	−0.856248	+	0.516565i	$0.827210\pi$
$14$	−0.866025	−	1.50000i	−0.231455	−	0.400892i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$17$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	2.59808	−	3.50000i	0.596040	−	0.802955i
$19$	2.59808	−	3.50000i	0.596040	−	0.802955i
$20$		0			0
$21$	3.00000	−	1.73205i	0.654654	−	0.377964i
$22$	0.776457	−	2.89778i	0.165541	−	0.617808i
$23$	5.01910	−	1.34486i	1.04655	−	0.280423i	0.305727	−	0.952119i	$-0.401100\pi$
$23$	5.01910	−	1.34486i	1.04655	−	0.280423i	0.740827	+	0.671696i	$0.234434\pi$
$24$	−1.73205	+	1.00000i	−0.353553	+	0.204124i
$25$		0			0
$26$	2.00000			0.392232
$27$	−2.82843	−	2.82843i	−0.544331	−	0.544331i
$28$	−1.67303	+	0.448288i	−0.316173	+	0.0847184i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	5.79555	+	1.55291i	1.00888	+	0.270328i
$34$		0			0
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.707107	−	0.707107i	−0.116248	−	0.116248i	0.646590	−	0.762838i	$-0.276194\pi$
$37$	−0.707107	−	0.707107i	−0.116248	−	0.116248i	−0.762838	+	0.646590i	$0.776194\pi$
$38$	−2.70831	−	3.41542i	−0.439346	−	0.554054i
$39$			4.00000i			0.640513i
$40$		0			0
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$	−0.896575	−	3.34607i	−0.138345	−	0.516309i
$43$	1.79315	−	6.69213i	0.273453	−	1.02054i	−0.683418	−	0.730027i	$-0.739507\pi$
$43$	1.79315	−	6.69213i	0.273453	−	1.02054i	0.956871	−	0.290513i	$-0.0938260\pi$
$44$	−2.59808	−	1.50000i	−0.391675	−	0.226134i
$45$		0			0
$46$		−	5.19615i		−	0.766131i
$47$	−2.68973	−	10.0382i	−0.392337	−	1.46422i	−0.826269	−	0.563276i	$-0.809541\pi$
$47$	−2.68973	−	10.0382i	−0.392337	−	1.46422i	0.433932	−	0.900946i	$-0.357126\pi$
$48$	0.517638	+	1.93185i	0.0747146	+	0.278839i
$49$			4.00000i			0.571429i
$50$		0			0
$51$		0			0
$52$	0.517638	−	1.93185i	0.0717835	−	0.267900i
$53$	0.776457	+	2.89778i	0.106655	+	0.398040i	0.998528	−	0.0542455i	$-0.0172754\pi$
$53$	0.776457	+	2.89778i	0.106655	+	0.398040i	−0.891873	+	0.452286i	$0.850609\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$		0			0
$56$			1.73205i			0.231455i
$57$	6.83083	−	5.41662i	0.904766	−	0.717449i
$58$		0			0
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	0.976034	+	0.217620i	$0.0698294\pi$
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	−0.299552	+	0.954080i	$0.596837\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$	3.34607	+	0.896575i	0.424951	+	0.113865i
$63$	1.67303	−	0.448288i	0.210782	−	0.0564789i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	1.93185	−	0.517638i	0.236013	−	0.0632396i	−0.138874	−	0.990310i	$-0.544348\pi$
$67$	1.93185	−	0.517638i	0.236013	−	0.0632396i	0.374887	+	0.927071i	$0.377682\pi$
$68$		0			0
$69$	10.3923			1.25109
$70$		0			0
$71$	−9.00000	+	5.19615i	−1.06810	+	0.616670i	−0.927663	−	0.373419i	$-0.878185\pi$
$71$	−9.00000	+	5.19615i	−1.06810	+	0.616670i	−0.140441	+	0.990089i	$0.544852\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	0.896575	−	3.34607i	0.104936	−	0.391627i	−0.893402	−	0.449259i	$-0.851688\pi$
$73$	0.896575	−	3.34607i	0.104936	−	0.391627i	0.998338	+	0.0576314i	$0.0183548\pi$
$74$	−0.866025	+	0.500000i	−0.100673	+	0.0581238i
$75$		0			0
$76$	−4.00000	+	1.73205i	−0.458831	+	0.198680i
$77$	3.67423	−	3.67423i	0.418718	−	0.418718i
$78$	3.86370	+	1.03528i	0.437478	+	0.117222i
$79$	1.73205	+	3.00000i	0.194871	+	0.337526i	0.946858	−	0.321651i	$-0.104238\pi$
$79$	1.73205	+	3.00000i	0.194871	+	0.337526i	−0.751987	+	0.659178i	$0.770905\pi$
$80$		0			0
$81$	−5.50000	−	9.52628i	−0.611111	−	1.05848i
$82$	1.34486	+	5.01910i	0.148515	+	0.554267i
$83$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$83$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$84$	−3.46410			−0.377964
$85$		0			0
$86$	−6.00000	−	3.46410i	−0.646997	−	0.373544i
$87$		0			0
$88$	−2.12132	+	2.12132i	−0.226134	+	0.226134i
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$	3.00000	+	1.73205i	0.314485	+	0.181568i
$92$	−5.01910	−	1.34486i	−0.523277	−	0.140212i
$93$	−1.79315	+	6.69213i	−0.185941	+	0.693942i
$94$	−10.3923			−1.07188
$95$		0			0
$96$	2.00000			0.204124
$97$	−2.07055	+	7.72741i	−0.210233	+	0.784599i	0.777558	+	0.628811i	$0.216458\pi$
$97$	−2.07055	+	7.72741i	−0.210233	+	0.784599i	−0.987791	+	0.155788i	$0.950208\pi$
$98$	3.86370	+	1.03528i	0.390293	+	0.104579i
$99$	2.59808	+	1.50000i	0.261116	+	0.150756i
$100$		0			0
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	4.94975	−	4.94975i	0.487713	−	0.487713i	−0.419871	−	0.907584i	$-0.637925\pi$
$103$	4.94975	−	4.94975i	0.487713	−	0.487713i	0.907584	+	0.419871i	$0.137925\pi$
$104$	−1.73205	−	1.00000i	−0.169842	−	0.0980581i
$105$		0			0
$106$	3.00000			0.291386
$107$	−4.24264	−	4.24264i	−0.410152	−	0.410152i	0.471640	−	0.881791i	$-0.343662\pi$
$107$	−4.24264	−	4.24264i	−0.410152	−	0.410152i	−0.881791	+	0.471640i	$0.843662\pi$
$108$	1.03528	+	3.86370i	0.0996195	+	0.371785i
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$		0			0
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	1.67303	+	0.448288i	0.158087	+	0.0423592i
$113$	−12.7279	+	12.7279i	−1.19734	+	1.19734i	−0.222383	+	0.974959i	$0.571383\pi$
$113$	−12.7279	+	12.7279i	−1.19734	+	1.19734i	−0.974959	+	0.222383i	$0.928617\pi$
$114$	−3.46410	−	8.00000i	−0.324443	−	0.749269i
$115$		0			0
$116$		0			0
$117$	−0.517638	+	1.93185i	−0.0478557	+	0.178600i
$118$	10.0382	−	2.68973i	0.924091	−	0.247609i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	2.82843	+	2.82843i	0.256074	+	0.256074i
$123$	−10.0382	+	2.68973i	−0.905114	+	0.242524i
$124$	1.73205	−	3.00000i	0.155543	−	0.269408i
$125$		0			0
$126$		−	1.73205i		−	0.154303i
$127$	−6.76148	+	1.81173i	−0.599984	+	0.160765i	−0.546012	−	0.837777i	$-0.683855\pi$
$127$	−6.76148	+	1.81173i	−0.599984	+	0.160765i	−0.0539720	+	0.998542i	$0.517188\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	6.92820	−	12.0000i	0.609994	−	1.05654i
$130$		0			0
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$	−4.24264	−	4.24264i	−0.369274	−	0.369274i
$133$	−1.10463	−	7.46859i	−0.0957833	−	0.647609i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$		0			0
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$	2.68973	−	10.0382i	0.228965	−	0.854508i
$139$	−17.3205	−	10.0000i	−1.46911	−	0.848189i	−0.469706	−	0.882823i	$-0.655640\pi$
$139$	−17.3205	−	10.0000i	−1.46911	−	0.848189i	−0.999400	+	0.0346338i	$0.988974\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$	2.68973	+	10.0382i	0.225717	+	0.842387i
$143$	1.55291	+	5.79555i	0.129861	+	0.484649i
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	−3.00000	−	1.73205i	−0.248282	−	0.143346i
$147$	−2.07055	+	7.72741i	−0.170776	+	0.637346i
$148$	0.258819	+	0.965926i	0.0212748	+	0.0793986i
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	−0.271821	−	0.962348i	$-0.587626\pi$
$149$	5.19615	−	3.00000i	0.425685	−	0.245770i	0.697507	+	0.716578i	$0.254293\pi$
$150$		0			0
$151$			20.7846i			1.69143i	0.533637	+	0.845714i	$0.320825\pi$
$151$			20.7846i			1.69143i	−0.533637	+	0.845714i	$0.679175\pi$
$152$	0.637756	+	4.31199i	0.0517289	+	0.349749i
$153$		0			0
$154$	−2.59808	−	4.50000i	−0.209359	−	0.362620i
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	18.4034	+	4.93117i	1.46875	+	0.393550i	0.902502	−	0.430686i	$-0.141728\pi$
$157$	18.4034	+	4.93117i	1.46875	+	0.393550i	0.566246	+	0.824236i	$0.308395\pi$
$158$	3.34607	−	0.896575i	0.266199	−	0.0713277i
$159$			6.00000i			0.475831i
$160$		0			0
$161$	4.50000	−	7.79423i	0.354650	−	0.614271i
$162$	−10.6252	+	2.84701i	−0.834793	+	0.223682i
$163$	−17.1464	−	17.1464i	−1.34301	−	1.34301i	−0.893045	−	0.449966i	$-0.851436\pi$
$163$	−17.1464	−	17.1464i	−1.34301	−	1.34301i	−0.449966	−	0.893045i	$-0.648564\pi$
$164$	5.19615			0.405751
$165$		0			0
$166$		0			0
$167$	−20.2844	+	5.43520i	−1.56966	+	0.420588i	−0.935705	−	0.352784i	$-0.885235\pi$
$167$	−20.2844	+	5.43520i	−1.56966	+	0.420588i	−0.633952	+	0.773372i	$0.718568\pi$
$168$	−0.896575	+	3.34607i	−0.0691723	+	0.258155i
$169$	7.79423	−	4.50000i	0.599556	−	0.346154i
$170$		0			0
$171$	4.00000	−	1.73205i	0.305888	−	0.132453i
$172$	−4.89898	+	4.89898i	−0.373544	+	0.373544i
$173$	−14.4889	−	3.88229i	−1.10157	−	0.295165i	−0.338166	−	0.941086i	$-0.609807\pi$
$173$	−14.4889	−	3.88229i	−1.10157	−	0.295165i	−0.763404	+	0.645922i	$0.776473\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	5.37945	+	20.0764i	0.404344	+	1.50903i
$178$	−3.67423	−	3.67423i	−0.275396	−	0.275396i
$179$	−5.19615			−0.388379			−0.194189	−	0.980964i	$-0.562208\pi$
$179$	−5.19615			−0.388379			−0.194189	+	0.980964i	$0.562208\pi$
$180$		0			0
$181$	−18.0000	−	10.3923i	−1.33793	−	0.772454i	−0.351429	−	0.936214i	$-0.614304\pi$
$181$	−18.0000	−	10.3923i	−1.33793	−	0.772454i	−0.986500	+	0.163760i	$0.947638\pi$
$182$	2.44949	−	2.44949i	0.181568	−	0.181568i
$183$	−5.65685	+	5.65685i	−0.418167	+	0.418167i
$184$	−2.59808	+	4.50000i	−0.191533	+	0.331744i
$185$		0			0
$186$	6.00000	+	3.46410i	0.439941	+	0.254000i
$187$		0			0
$188$	−2.68973	+	10.0382i	−0.196168	+	0.732111i
$189$	−6.92820			−0.503953
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	0.517638	−	1.93185i	0.0373573	−	0.139419i
$193$	−1.93185	−	0.517638i	−0.139058	−	0.0372604i	0.188619	−	0.982050i	$-0.439599\pi$
$193$	−1.93185	−	0.517638i	−0.139058	−	0.0372604i	−0.327677	+	0.944790i	$0.606266\pi$
$194$	6.92820	+	4.00000i	0.497416	+	0.287183i
$195$		0			0
$196$	2.00000	−	3.46410i	0.142857	−	0.247436i
$197$	−3.67423	+	3.67423i	−0.261778	+	0.261778i	−0.825776	−	0.563998i	$-0.809263\pi$
$197$	−3.67423	+	3.67423i	−0.261778	+	0.261778i	0.563998	+	0.825776i	$0.309263\pi$
$198$	2.12132	−	2.12132i	0.150756	−	0.150756i
$199$	−6.92820	−	4.00000i	−0.491127	−	0.283552i	0.233915	−	0.972257i	$-0.424846\pi$
$199$	−6.92820	−	4.00000i	−0.491127	−	0.283552i	−0.725042	+	0.688705i	$0.758180\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	12.7279	+	12.7279i	0.895533	+	0.895533i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	5.01910	+	1.34486i	0.348851	+	0.0934745i
$208$	−1.41421	+	1.41421i	−0.0980581	+	0.0980581i
$209$	7.79423	−	10.5000i	0.539138	−	0.726300i
$210$		0			0
$211$	19.5000	−	11.2583i	1.34244	−	0.775055i	0.355271	−	0.934763i	$-0.384389\pi$
$211$	19.5000	−	11.2583i	1.34244	−	0.775055i	0.987164	+	0.159708i	$0.0510552\pi$
$212$	0.776457	−	2.89778i	0.0533273	−	0.199020i
$213$	−20.0764	+	5.37945i	−1.37561	+	0.368594i
$214$	−5.19615	+	3.00000i	−0.355202	+	0.205076i
$215$		0			0
$216$	4.00000			0.272166
$217$	4.24264	+	4.24264i	0.288009	+	0.288009i
$218$		0			0
$219$	3.46410	−	6.00000i	0.234082	−	0.405442i
$220$		0			0
$221$		0			0
$222$	−1.93185	+	0.517638i	−0.129657	+	0.0347416i
$223$	22.2163	+	5.95284i	1.48771	+	0.398632i	0.908964	−	0.416874i	$-0.136874\pi$
$223$	22.2163	+	5.95284i	1.48771	+	0.398632i	0.578749	+	0.815506i	$0.303541\pi$
$224$	0.866025	−	1.50000i	0.0578638	−	0.100223i
$225$		0			0
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$227$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$228$	−8.62398	+	1.27551i	−0.571137	+	0.0844729i
$229$			20.0000i			1.32164i	0.750546	+	0.660819i	$0.229791\pi$
$229$			20.0000i			1.32164i	−0.750546	+	0.660819i	$0.770209\pi$
$230$		0			0
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$		0			0
$233$	2.68973	−	10.0382i	0.176210	−	0.657624i	−0.820133	−	0.572174i	$-0.806100\pi$
$233$	2.68973	−	10.0382i	0.176210	−	0.657624i	0.996342	−	0.0854505i	$-0.0272330\pi$
$234$	1.73205	+	1.00000i	0.113228	+	0.0653720i
$235$		0			0
$236$		−	10.3923i		−	0.676481i
$237$	1.79315	+	6.69213i	0.116478	+	0.434701i
$238$		0			0
$239$			24.0000i			1.55243i	0.630468	+	0.776215i	$0.282863\pi$
$239$			24.0000i			1.55243i	−0.630468	+	0.776215i	$0.717137\pi$
$240$		0			0
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	0.0609515	−	0.998141i	$-0.480586\pi$
$241$	−12.0000	−	6.92820i	−0.772988	−	0.446285i	−0.833939	+	0.551856i	$0.813920\pi$
$242$	−0.517638	+	1.93185i	−0.0332750	+	0.124184i
$243$	−2.58819	−	9.65926i	−0.166032	−	0.619642i
$244$	3.46410	−	2.00000i	0.221766	−	0.128037i
$245$		0			0
$246$			10.3923i			0.662589i
$247$	8.10634	+	3.20736i	0.515794	+	0.204080i
$248$	−2.44949	−	2.44949i	−0.155543	−	0.155543i
$249$		0			0
$250$		0			0
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	0.186722	+	0.982413i	$0.440214\pi$
$251$	−12.0000	+	20.7846i	−0.757433	+	1.31191i	−0.944156	+	0.329500i	$0.893120\pi$
$252$	−1.67303	−	0.448288i	−0.105391	−	0.0282395i
$253$	15.0573	−	4.03459i	0.946644	−	0.253652i
$254$			7.00000i			0.439219i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$257$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$258$	−9.79796	−	9.79796i	−0.609994	−	0.609994i
$259$	−1.73205			−0.107624
$260$		0			0
$261$		0			0
$262$	14.4889	−	3.88229i	0.895126	−	0.239848i
$263$	−6.72432	+	25.0955i	−0.414639	+	1.54745i	0.370918	+	0.928665i	$0.379043\pi$
$263$	−6.72432	+	25.0955i	−0.414639	+	1.54745i	−0.785557	+	0.618789i	$0.787624\pi$
$264$	−5.19615	+	3.00000i	−0.319801	+	0.184637i
$265$		0			0
$266$	−7.50000	−	0.866025i	−0.459855	−	0.0530994i
$267$	7.34847	−	7.34847i	0.449719	−	0.449719i
$268$	−1.93185	−	0.517638i	−0.118007	−	0.0316198i
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	0.986804	+	0.161922i	$0.0517692\pi$
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	−0.353174	+	0.935558i	$0.614898\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$		0			0
$273$	4.89898	+	4.89898i	0.296500	+	0.296500i
$274$		0			0
$275$		0			0
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$277$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$278$	−14.1421	+	14.1421i	−0.848189	+	0.848189i
$279$	−1.73205	+	3.00000i	−0.103695	+	0.179605i
$280$		0			0
$281$	13.5000	+	7.79423i	0.805342	+	0.464965i	0.845336	−	0.534235i	$-0.179400\pi$
$281$	13.5000	+	7.79423i	0.805342	+	0.464965i	−0.0399934	+	0.999200i	$0.512734\pi$
$282$	−20.0764	−	5.37945i	−1.19553	−	0.320342i
$283$	8.06918	−	30.1146i	0.479663	−	1.79013i	−0.123314	−	0.992368i	$-0.539352\pi$
$283$	8.06918	−	30.1146i	0.479663	−	1.79013i	0.602977	−	0.797759i	$-0.293981\pi$
$284$	10.3923			0.616670
$285$		0			0
$286$	6.00000			0.354787
$287$	−2.32937	+	8.69333i	−0.137498	+	0.513151i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	−14.7224	−	8.50000i	−0.866025	−	0.500000i
$290$		0			0
$291$	−8.00000	+	13.8564i	−0.468968	+	0.812277i
$292$	−2.44949	+	2.44949i	−0.143346	+	0.143346i
$293$	6.36396	−	6.36396i	0.371787	−	0.371787i	−0.496341	−	0.868128i	$-0.665323\pi$
$293$	6.36396	−	6.36396i	0.371787	−	0.371787i	0.868128	+	0.496341i	$0.165323\pi$
$294$	6.92820	+	4.00000i	0.404061	+	0.233285i
$295$		0			0
$296$	1.00000			0.0581238
$297$	−8.48528	−	8.48528i	−0.492366	−	0.492366i
$298$	−1.55291	−	5.79555i	−0.0899579	−	0.335727i
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	−6.00000	−	10.3923i	−0.345834	−	0.599002i
$302$	20.0764	+	5.37945i	1.15527	+	0.309553i
$303$	−25.4558	+	25.4558i	−1.46240	+	1.46240i
$304$	4.33013	+	0.500000i	0.248350	+	0.0286770i
$305$		0			0
$306$		0			0
$307$	−5.17638	+	19.3185i	−0.295432	+	1.10257i	0.645442	+	0.763809i	$0.276673\pi$
$307$	−5.17638	+	19.3185i	−0.295432	+	1.10257i	−0.940874	+	0.338757i	$0.889994\pi$
$308$	−5.01910	+	1.34486i	−0.285990	+	0.0766307i
$309$	12.1244	−	7.00000i	0.689730	−	0.398216i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−2.82843	−	2.82843i	−0.160128	−	0.160128i
$313$	10.0382	−	2.68973i	0.567392	−	0.152032i	0.0362920	−	0.999341i	$-0.488445\pi$
$313$	10.0382	−	2.68973i	0.567392	−	0.152032i	0.531100	+	0.847309i	$0.321779\pi$
$314$	9.52628	−	16.5000i	0.537599	−	0.931149i
$315$		0			0
$316$		−	3.46410i		−	0.194871i
$317$	−26.0800	+	6.98811i	−1.46480	+	0.392492i	−0.901144	−	0.433519i	$-0.857272\pi$
$317$	−26.0800	+	6.98811i	−1.46480	+	0.392492i	−0.563654	+	0.826011i	$0.690605\pi$
$318$	5.79555	+	1.55291i	0.324999	+	0.0870831i
$319$		0			0
$320$		0			0
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$	−6.36396	−	6.36396i	−0.354650	−	0.354650i
$323$		0			0
$324$			11.0000i			0.611111i
$325$		0			0
$326$	−21.0000	+	12.1244i	−1.16308	+	0.671506i
$327$		0			0
$328$	1.34486	−	5.01910i	0.0742576	−	0.277133i
$329$	−15.5885	−	9.00000i	−0.859419	−	0.496186i
$330$		0			0
$331$		−	19.0526i		−	1.04722i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$		−	19.0526i		−	1.04722i	0.851957	−	0.523612i	$-0.175416\pi$
$332$		0			0
$333$	−0.258819	−	0.965926i	−0.0141832	−	0.0529324i
$334$			21.0000i			1.14907i
$335$		0			0
$336$	3.00000	+	1.73205i	0.163663	+	0.0944911i
$337$	0.517638	−	1.93185i	0.0281975	−	0.105235i	−0.950393	−	0.311052i	$-0.899319\pi$
$337$	0.517638	−	1.93185i	0.0281975	−	0.105235i	0.978590	+	0.205817i	$0.0659853\pi$
$338$	−2.32937	−	8.69333i	−0.126701	−	0.472855i
$339$	−31.1769	+	18.0000i	−1.69330	+	0.977626i
$340$		0			0
$341$			10.3923i			0.562775i
$342$	−0.637756	−	4.31199i	−0.0344859	−	0.233166i
$343$	13.4722	+	13.4722i	0.727430	+	0.727430i
$344$	3.46410	+	6.00000i	0.186772	+	0.323498i
$345$		0			0
$346$	−7.50000	+	12.9904i	−0.403202	+	0.698367i
$347$	10.0382	+	2.68973i	0.538879	+	0.144392i	0.517985	−	0.855390i	$-0.326682\pi$
$347$	10.0382	+	2.68973i	0.538879	+	0.144392i	0.0208935	+	0.999782i	$0.493349\pi$
$348$		0			0
$349$			4.00000i			0.214115i	0.994253	+	0.107058i	$0.0341429\pi$
$349$			4.00000i			0.214115i	−0.994253	+	0.107058i	$0.965857\pi$
$350$		0			0
$351$	4.00000	−	6.92820i	0.213504	−	0.369800i
$352$	2.89778	−	0.776457i	0.154452	−	0.0413853i
$353$	−7.34847	−	7.34847i	−0.391120	−	0.391120i	0.483967	−	0.875086i	$-0.339196\pi$
$353$	−7.34847	−	7.34847i	−0.391120	−	0.391120i	−0.875086	+	0.483967i	$0.839196\pi$
$354$	20.7846			1.10469
$355$		0			0
$356$	−4.50000	+	2.59808i	−0.238500	+	0.137698i
$357$		0			0
$358$	−1.34486	+	5.01910i	−0.0710782	+	0.265268i
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	−0.630814	−	0.775934i	$-0.717279\pi$
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	0.356572	+	0.934268i	$0.383946\pi$
$360$		0			0
$361$	−5.50000	−	18.1865i	−0.289474	−	0.957186i
$362$	−14.6969	+	14.6969i	−0.772454	+	0.772454i
$363$	−3.86370	−	1.03528i	−0.202792	−	0.0543379i
$364$	−1.73205	−	3.00000i	−0.0907841	−	0.157243i
$365$		0			0
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	0.896575	+	3.34607i	0.0468009	+	0.174663i	0.985370	−	0.170427i	$-0.0545148\pi$
$367$	0.896575	+	3.34607i	0.0468009	+	0.174663i	−0.938569	+	0.345091i	$0.887848\pi$
$368$	3.67423	+	3.67423i	0.191533	+	0.191533i
$369$	−5.19615			−0.270501
$370$		0			0
$371$	4.50000	+	2.59808i	0.233628	+	0.134885i
$372$	4.89898	−	4.89898i	0.254000	−	0.254000i
$373$	21.9203	−	21.9203i	1.13499	−	1.13499i	0.145655	−	0.989335i	$-0.453471\pi$
$373$	21.9203	−	21.9203i	1.13499	−	1.13499i	0.989335	−	0.145655i	$-0.0465290\pi$
$374$		0			0
$375$		0			0
$376$	9.00000	+	5.19615i	0.464140	+	0.267971i
$377$		0			0
$378$	−1.79315	+	6.69213i	−0.0922297	+	0.344206i
$379$	−3.46410			−0.177939			−0.0889695	−	0.996034i	$-0.528357\pi$
$379$	−3.46410			−0.177939			−0.0889695	+	0.996034i	$0.528357\pi$
$380$		0			0
$381$	−14.0000			−0.717242
$382$	6.21166	−	23.1822i	0.317816	−	1.18611i
$383$	23.1822	+	6.21166i	1.18456	+	0.317401i	0.796732	−	0.604333i	$-0.206560\pi$
$383$	23.1822	+	6.21166i	1.18456	+	0.317401i	0.387824	+	0.921733i	$0.373227\pi$
$384$	−1.73205	−	1.00000i	−0.0883883	−	0.0510310i
$385$		0			0
$386$	−1.00000	+	1.73205i	−0.0508987	+	0.0881591i
$387$	4.89898	−	4.89898i	0.249029	−	0.249029i
$388$	5.65685	−	5.65685i	0.287183	−	0.287183i
$389$	−25.9808	−	15.0000i	−1.31728	−	0.760530i	−0.333987	−	0.942578i	$-0.608394\pi$
$389$	−25.9808	−	15.0000i	−1.31728	−	0.760530i	−0.983290	+	0.182047i	$0.941728\pi$
$390$		0			0
$391$		0			0
$392$	−2.82843	−	2.82843i	−0.142857	−	0.142857i
$393$	7.76457	+	28.9778i	0.391671	+	1.46174i
$394$	2.59808	+	4.50000i	0.130889	+	0.226707i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	1.67303	+	0.448288i	0.0839671	+	0.0224989i	0.300558	−	0.953764i	$-0.402827\pi$
$397$	1.67303	+	0.448288i	0.0839671	+	0.0224989i	−0.216591	+	0.976262i	$0.569494\pi$
$398$	−5.65685	+	5.65685i	−0.283552	+	0.283552i
$399$	1.73205	−	15.0000i	0.0867110	−	0.750939i
$400$		0			0
$401$	18.0000	−	10.3923i	0.898877	−	0.518967i	0.0220414	−	0.999757i	$-0.492983\pi$
$401$	18.0000	−	10.3923i	0.898877	−	0.518967i	0.876836	+	0.480790i	$0.159650\pi$
$402$	1.03528	−	3.86370i	0.0516349	−	0.192704i
$403$	−6.69213	+	1.79315i	−0.333359	+	0.0893232i
$404$	15.5885	−	9.00000i	0.775555	−	0.447767i
$405$		0			0
$406$		0			0
$407$	−2.12132	−	2.12132i	−0.105150	−	0.105150i
$408$		0			0
$409$	18.1865	−	31.5000i	0.899266	−	1.55757i	0.0708321	−	0.997488i	$-0.477435\pi$
$409$	18.1865	−	31.5000i	0.899266	−	1.55757i	0.828434	−	0.560087i	$-0.189232\pi$
$410$		0			0
$411$		0			0
$412$	−6.76148	+	1.81173i	−0.333114	+	0.0892577i
$413$	17.3867	+	4.65874i	0.855542	+	0.229242i
$414$	2.59808	−	4.50000i	0.127688	−	0.221163i
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−28.2843	−	28.2843i	−1.38509	−	1.38509i
$418$	−8.12493	−	10.2462i	−0.397403	−	0.501160i
$419$		−	9.00000i		−	0.439679i	−0.975536	−	0.219839i	$-0.929447\pi$
$419$		−	9.00000i		−	0.439679i	0.975536	−	0.219839i	$-0.0705533\pi$
$420$		0			0
$421$	9.00000	−	5.19615i	0.438633	−	0.253245i	−0.264385	−	0.964417i	$-0.585169\pi$
$421$	9.00000	−	5.19615i	0.438633	−	0.253245i	0.703018	+	0.711172i	$0.251835\pi$
$422$	−5.82774	−	21.7494i	−0.283690	−	1.05875i
$423$	2.68973	−	10.0382i	0.130779	−	0.488074i
$424$	−2.59808	−	1.50000i	−0.126174	−	0.0728464i
$425$		0			0
$426$			20.7846i			1.00702i
$427$	1.79315	+	6.69213i	0.0867767	+	0.323855i
$428$	1.55291	+	5.79555i	0.0750629	+	0.280139i
$429$			12.0000i			0.579365i
$430$		0			0
$431$	−9.00000	−	5.19615i	−0.433515	−	0.250290i	0.267328	−	0.963606i	$-0.413859\pi$
$431$	−9.00000	−	5.19615i	−0.433515	−	0.250290i	−0.700843	+	0.713316i	$0.747193\pi$
$432$	1.03528	−	3.86370i	0.0498097	−	0.185893i
$433$	−7.24693	−	27.0459i	−0.348265	−	1.29974i	−0.888751	−	0.458391i	$-0.848426\pi$
$433$	−7.24693	−	27.0459i	−0.348265	−	1.29974i	0.540485	−	0.841353i	$-0.318241\pi$
$434$	5.19615	−	3.00000i	0.249423	−	0.144005i
$435$		0			0
$436$		0			0
$437$	8.33298	−	21.0609i	0.398620	−	1.00748i
$438$	−4.89898	−	4.89898i	−0.234082	−	0.234082i
$439$	−12.1244	−	21.0000i	−0.578664	−	1.00228i	−0.995633	−	0.0933546i	$-0.970241\pi$
$439$	−12.1244	−	21.0000i	−0.578664	−	1.00228i	0.416969	−	0.908921i	$-0.363092\pi$
$440$		0			0
$441$	−2.00000	+	3.46410i	−0.0952381	+	0.164957i
$442$		0			0
$443$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$443$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$444$			2.00000i			0.0949158i
$445$		0			0
$446$	11.5000	−	19.9186i	0.544541	−	0.943172i
$447$	11.5911	−	3.10583i	0.548241	−	0.146901i
$448$	−1.22474	−	1.22474i	−0.0578638	−	0.0578638i
$449$	5.19615			0.245222			0.122611	−	0.992455i	$-0.460873\pi$
$449$	5.19615			0.245222			0.122611	+	0.992455i	$0.460873\pi$
$450$		0			0
$451$	−13.5000	+	7.79423i	−0.635690	+	0.367016i
$452$	17.3867	−	4.65874i	0.817800	−	0.219129i
$453$	−10.7589	+	40.1528i	−0.505497	+	1.88654i
$454$		0			0
$455$		0			0
$456$	−1.00000	+	8.66025i	−0.0468293	+	0.405554i
$457$	26.9444	−	26.9444i	1.26041	−	1.26041i	0.309509	−	0.950897i	$-0.399835\pi$
$457$	26.9444	−	26.9444i	1.26041	−	1.26041i	0.950897	−	0.309509i	$-0.100165\pi$
$458$	19.3185	+	5.17638i	0.902695	+	0.241876i
$459$		0			0
$460$		0			0
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	0.576685	−	0.816967i	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$	−2.68973	−	10.0382i	−0.125137	−	0.467019i
$463$	23.2702	+	23.2702i	1.08146	+	1.08146i	0.996374	+	0.0850817i	$0.0271151\pi$
$463$	23.2702	+	23.2702i	1.08146	+	1.08146i	0.0850817	+	0.996374i	$0.472885\pi$
$464$		0			0
$465$		0			0
$466$	−9.00000	−	5.19615i	−0.416917	−	0.240707i
$467$	29.3939	−	29.3939i	1.36019	−	1.36019i	0.486513	−	0.873673i	$-0.338269\pi$
$467$	29.3939	−	29.3939i	1.36019	−	1.36019i	0.873673	−	0.486513i	$-0.161731\pi$
$468$	1.41421	−	1.41421i	0.0653720	−	0.0653720i
$469$	1.73205	−	3.00000i	0.0799787	−	0.138527i
$470$		0			0
$471$	33.0000	+	19.0526i	1.52056	+	0.877896i
$472$	−10.0382	−	2.68973i	−0.462045	−	0.123805i
$473$	5.37945	−	20.0764i	0.247348	−	0.923113i
$474$	6.92820			0.318223
$475$		0			0
$476$		0			0
$477$	−0.776457	+	2.89778i	−0.0355515	+	0.132680i
$478$	23.1822	+	6.21166i	1.06033	+	0.284115i
$479$	−5.19615	−	3.00000i	−0.237418	−	0.137073i	0.376571	−	0.926388i	$-0.377103\pi$
$479$	−5.19615	−	3.00000i	−0.237418	−	0.137073i	−0.613990	+	0.789314i	$0.710436\pi$
$480$		0			0
$481$	1.00000	−	1.73205i	0.0455961	−	0.0789747i
$482$	−9.79796	+	9.79796i	−0.446285	+	0.446285i
$483$	12.7279	−	12.7279i	0.579141	−	0.579141i
$484$	1.73205	+	1.00000i	0.0787296	+	0.0454545i
$485$		0			0
$486$	−10.0000			−0.453609
$487$	−17.6777	−	17.6777i	−0.801052	−	0.801052i	0.182208	−	0.983260i	$-0.441675\pi$
$487$	−17.6777	−	17.6777i	−0.801052	−	0.801052i	−0.983260	+	0.182208i	$0.941675\pi$
$488$	−1.03528	−	3.86370i	−0.0468648	−	0.174902i
$489$	−24.2487	−	42.0000i	−1.09656	−	1.89931i
$490$		0			0
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	0.999552	−	0.0299272i	$-0.00952753\pi$
$491$	10.5000	+	18.1865i	0.473858	+	0.820747i	−0.525694	+	0.850674i	$0.676194\pi$
$492$	10.0382	+	2.68973i	0.452557	+	0.121262i
$493$		0			0
$494$	5.19615	−	7.00000i	0.233786	−	0.314945i
$495$		0			0
$496$	−3.00000	+	1.73205i	−0.134704	+	0.0777714i
$497$	−4.65874	+	17.3867i	−0.208973	+	0.779899i
$498$		0			0
$499$	6.06218	−	3.50000i	0.271380	−	0.156682i	−0.358134	−	0.933670i	$-0.616587\pi$
$499$	6.06218	−	3.50000i	0.271380	−	0.156682i	0.629515	+	0.776989i	$0.283254\pi$
$500$		0			0
$501$	−42.0000			−1.87642
$502$	16.9706	+	16.9706i	0.757433	+	0.757433i
$503$	5.01910	−	1.34486i	0.223791	−	0.0599645i	−0.145181	−	0.989405i	$-0.546377\pi$
$503$	5.01910	−	1.34486i	0.223791	−	0.0599645i	0.368972	+	0.929441i	$0.379710\pi$
$504$	−0.866025	+	1.50000i	−0.0385758	+	0.0668153i
$505$		0			0
$506$		−	15.5885i		−	0.692991i
$507$	17.3867	−	4.65874i	0.772169	−	0.206902i
$508$	6.76148	+	1.81173i	0.299992	+	0.0803827i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	−3.00000	−	5.19615i	−0.132712	−	0.229864i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−17.2480	+	2.55103i	−0.761516	+	0.112631i
$514$		0			0
$515$		0			0
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	−8.06918	−	30.1146i	−0.354882	−	1.32444i
$518$	−0.448288	+	1.67303i	−0.0196966	+	0.0735088i
$519$	−25.9808	−	15.0000i	−1.14043	−	0.658427i
$520$		0			0
$521$		−	20.7846i		−	0.910590i	−0.890341	−	0.455295i	$-0.849534\pi$
$521$		−	20.7846i		−	0.910590i	0.890341	−	0.455295i	$-0.150466\pi$
$522$		0			0
$523$	−7.24693	−	27.0459i	−0.316886	−	1.18264i	−0.922221	−	0.386664i	$-0.873627\pi$
$523$	−7.24693	−	27.0459i	−0.316886	−	1.18264i	0.605334	−	0.795971i	$-0.293039\pi$
$524$		−	15.0000i		−	0.655278i
$525$		0			0
$526$	22.5000	+	12.9904i	0.981047	+	0.566408i
$527$		0			0
$528$	1.55291	+	5.79555i	0.0675819	+	0.252219i
$529$	3.46410	−	2.00000i	0.150613	−	0.0869565i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	−2.77766	+	7.02030i	−0.120427	+	0.304369i
$533$	−7.34847	−	7.34847i	−0.318298	−	0.318298i
$534$	−5.19615	−	9.00000i	−0.224860	−	0.389468i
$535$		0			0
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	−10.0382	−	2.68973i	−0.433180	−	0.116070i
$538$	20.0764	−	5.37945i	0.865555	−	0.231925i
$539$			12.0000i			0.516877i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−1.93185	+	0.517638i	−0.0829801	+	0.0222345i
$543$	−29.3939	−	29.3939i	−1.26141	−	1.26141i
$544$		0			0
$545$		0			0
$546$	6.00000	−	3.46410i	0.256776	−	0.148250i
$547$	21.2504	−	5.69402i	0.908600	−	0.243459i	0.225894	−	0.974152i	$-0.427470\pi$
$547$	21.2504	−	5.69402i	0.908600	−	0.243459i	0.682706	+	0.730693i	$0.260803\pi$
$548$		0			0
$549$	−3.46410	+	2.00000i	−0.147844	+	0.0853579i
$550$		0			0
$551$		0			0
$552$	−7.34847	+	7.34847i	−0.312772	+	0.312772i
$553$	5.79555	+	1.55291i	0.246452	+	0.0660366i
$554$		0			0
$555$		0			0
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−1.34486	−	5.01910i	−0.0569837	−	0.212666i	0.931563	−	0.363579i	$-0.118445\pi$
$557$	−1.34486	−	5.01910i	−0.0569837	−	0.212666i	−0.988547	+	0.150913i	$0.951779\pi$
$558$	2.44949	+	2.44949i	0.103695	+	0.103695i
$559$	13.8564			0.586064
$560$		0			0
$561$		0			0
$562$	11.0227	−	11.0227i	0.464965	−	0.464965i
$563$	−16.9706	+	16.9706i	−0.715224	+	0.715224i	−0.967623	−	0.252399i	$-0.918780\pi$
$563$	−16.9706	+	16.9706i	−0.715224	+	0.715224i	0.252399	+	0.967623i	$0.418780\pi$
$564$	−10.3923	+	18.0000i	−0.437595	+	0.757937i
$565$		0			0
$566$	−27.0000	−	15.5885i	−1.13489	−	0.655232i
$567$	−18.4034	−	4.93117i	−0.772868	−	0.207089i
$568$	2.68973	−	10.0382i	0.112858	−	0.421193i
$569$	−5.19615			−0.217834			−0.108917	−	0.994051i	$-0.534738\pi$
$569$	−5.19615			−0.217834			−0.108917	+	0.994051i	$0.534738\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	1.55291	−	5.79555i	0.0649306	−	0.242324i
$573$	46.3644	+	12.4233i	1.93690	+	0.518991i
$574$	7.79423	+	4.50000i	0.325325	+	0.187826i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−7.34847	+	7.34847i	−0.305921	+	0.305921i	−0.843325	−	0.537404i	$-0.819405\pi$
$577$	−7.34847	+	7.34847i	−0.305921	+	0.305921i	0.537404	+	0.843325i	$0.319405\pi$
$578$	−12.0208	+	12.0208i	−0.500000	+	0.500000i
$579$	−3.46410	−	2.00000i	−0.143963	−	0.0831172i
$580$		0			0
$581$		0			0
$582$	11.3137	+	11.3137i	0.468968	+	0.468968i
$583$	2.32937	+	8.69333i	0.0964727	+	0.360041i
$584$	1.73205	+	3.00000i	0.0716728	+	0.124141i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−20.0764	−	5.37945i	−0.828641	−	0.222034i	−0.180520	−	0.983571i	$-0.557778\pi$
$587$	−20.0764	−	5.37945i	−0.828641	−	0.222034i	−0.648121	+	0.761537i	$0.724445\pi$
$588$	5.65685	−	5.65685i	0.233285	−	0.233285i
$589$	12.1244	+	9.00000i	0.499575	+	0.370839i
$590$		0			0
$591$	−9.00000	+	5.19615i	−0.370211	+	0.213741i
$592$	0.258819	−	0.965926i	0.0106374	−	0.0396993i
$593$	−40.1528	+	10.7589i	−1.64888	+	0.441815i	−0.959298	−	0.282395i	$-0.908871\pi$
$593$	−40.1528	+	10.7589i	−1.64888	+	0.441815i	−0.689579	+	0.724210i	$0.742204\pi$
$594$	−10.3923	+	6.00000i	−0.426401	+	0.246183i
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−11.3137	−	11.3137i	−0.463039	−	0.463039i
$598$	10.0382	−	2.68973i	0.410492	−	0.109991i
$599$	−10.3923	+	18.0000i	−0.424618	+	0.735460i	−0.996385	−	0.0849563i	$-0.972925\pi$
$599$	−10.3923	+	18.0000i	−0.424618	+	0.735460i	0.571767	+	0.820416i	$0.306258\pi$
$600$		0			0
$601$			22.5167i			0.918474i	0.888314	+	0.459237i	$0.151877\pi$
$601$			22.5167i			0.918474i	−0.888314	+	0.459237i	$0.848123\pi$
$602$	−11.5911	+	3.10583i	−0.472418	+	0.126584i
$603$	1.93185	+	0.517638i	0.0786711	+	0.0210799i
$604$	10.3923	−	18.0000i	0.422857	−	0.732410i
$605$		0			0
$606$	18.0000	+	31.1769i	0.731200	+	1.26648i
$607$	7.77817	+	7.77817i	0.315706	+	0.315706i	0.847115	−	0.531409i	$-0.178337\pi$
$607$	7.77817	+	7.77817i	0.315706	+	0.315706i	−0.531409	+	0.847115i	$0.678337\pi$
$608$	1.60368	−	4.05317i	0.0650379	−	0.164378i
$609$		0			0
$610$		0			0
$611$	18.0000	−	10.3923i	0.728202	−	0.420428i
$612$		0			0
$613$	1.34486	−	5.01910i	0.0543185	−	0.202719i	−0.933434	−	0.358750i	$-0.883203\pi$
$613$	1.34486	−	5.01910i	0.0543185	−	0.202719i	0.987752	+	0.156030i	$0.0498698\pi$
$614$	17.3205	+	10.0000i	0.698999	+	0.403567i
$615$		0			0
$616$			5.19615i			0.209359i
$617$	−8.06918	−	30.1146i	−0.324853	−	1.21237i	−0.914460	−	0.404677i	$-0.867384\pi$
$617$	−8.06918	−	30.1146i	−0.324853	−	1.21237i	0.589607	−	0.807690i	$-0.299283\pi$
$618$	−3.62347	−	13.5230i	−0.145757	−	0.543973i
$619$			31.0000i			1.24600i	0.782224	+	0.622998i	$0.214085\pi$
$619$			31.0000i			1.24600i	−0.782224	+	0.622998i	$0.785915\pi$
$620$		0			0
$621$	−18.0000	−	10.3923i	−0.722315	−	0.417029i
$622$		0			0
$623$	−2.32937	−	8.69333i	−0.0933243	−	0.348291i
$624$	−3.46410	+	2.00000i	−0.138675	+	0.0800641i
$625$		0			0
$626$		−	10.3923i		−	0.415360i
$627$	20.4925	−	16.2499i	0.818391	−	0.648957i
$628$	−13.4722	−	13.4722i	−0.537599	−	0.537599i
$629$		0			0
$630$		0			0
$631$	13.0000	−	22.5167i	0.517522	−	0.896374i	−0.482271	−	0.876022i	$-0.660188\pi$
$631$	13.0000	−	22.5167i	0.517522	−	0.896374i	0.999793	−	0.0203520i	$-0.00647871\pi$
$632$	−3.34607	−	0.896575i	−0.133099	−	0.0356639i
$633$	43.4988	−	11.6555i	1.72892	−	0.463264i
$634$			27.0000i			1.07231i
$635$		0			0
$636$	3.00000	−	5.19615i	0.118958	−	0.206041i
$637$	−7.72741	+	2.07055i	−0.306171	+	0.0820383i
$638$		0			0
$639$	−10.3923			−0.411113
$640$		0			0
$641$	18.0000	−	10.3923i	0.710957	−	0.410471i	−0.100458	−	0.994941i	$-0.532031\pi$
$641$	18.0000	−	10.3923i	0.710957	−	0.410471i	0.811415	+	0.584470i	$0.198698\pi$
$642$	−11.5911	+	3.10583i	−0.457465	+	0.122577i
$643$	−8.96575	+	33.4607i	−0.353575	+	1.31956i	0.528694	+	0.848813i	$0.322682\pi$
$643$	−8.96575	+	33.4607i	−0.353575	+	1.31956i	−0.882268	+	0.470747i	$0.843985\pi$
$644$	−7.79423	+	4.50000i	−0.307136	+	0.177325i
$645$		0			0
$646$		0			0
$647$	3.67423	−	3.67423i	0.144449	−	0.144449i	−0.631184	−	0.775633i	$-0.717431\pi$
$647$	3.67423	−	3.67423i	0.144449	−	0.144449i	0.775633	+	0.631184i	$0.217431\pi$
$648$	10.6252	+	2.84701i	0.417397	+	0.111841i
$649$	15.5885	+	27.0000i	0.611900	+	1.05984i
$650$		0			0
$651$	6.00000	+	10.3923i	0.235159	+	0.407307i
$652$	6.27603	+	23.4225i	0.245788	+	0.917294i
$653$	−11.0227	−	11.0227i	−0.431352	−	0.431352i	0.457736	−	0.889088i	$-0.348660\pi$
$653$	−11.0227	−	11.0227i	−0.431352	−	0.431352i	−0.889088	+	0.457736i	$0.848660\pi$
$654$		0			0
$655$		0			0
$656$	−4.50000	−	2.59808i	−0.175695	−	0.101438i
$657$	2.44949	−	2.44949i	0.0955637	−	0.0955637i
$658$	−12.7279	+	12.7279i	−0.496186	+	0.496186i
$659$	−7.79423	+	13.5000i	−0.303620	+	0.525885i	−0.976953	−	0.213454i	$-0.931529\pi$
$659$	−7.79423	+	13.5000i	−0.303620	+	0.525885i	0.673333	+	0.739339i	$0.264862\pi$
$660$		0			0
$661$	−9.00000	−	5.19615i	−0.350059	−	0.202107i	0.314652	−	0.949207i	$-0.398112\pi$
$661$	−9.00000	−	5.19615i	−0.350059	−	0.202107i	−0.664711	+	0.747100i	$0.731446\pi$
$662$	−18.4034	−	4.93117i	−0.715267	−	0.191655i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.00000			−0.0387492
$667$		0			0
$668$	20.2844	+	5.43520i	0.784829	+	0.210294i
$669$	39.8372	+	23.0000i	1.54019	+	0.889231i
$670$		0			0
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$	2.44949	−	2.44949i	0.0944911	−	0.0944911i
$673$	22.6274	−	22.6274i	0.872223	−	0.872223i	−0.120492	−	0.992714i	$-0.538447\pi$
$673$	22.6274	−	22.6274i	0.872223	−	0.872223i	0.992714	+	0.120492i	$0.0384471\pi$
$674$	−1.73205	−	1.00000i	−0.0667161	−	0.0385186i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−23.3345	−	23.3345i	−0.896819	−	0.896819i	0.0983348	−	0.995153i	$-0.468648\pi$
$677$	−23.3345	−	23.3345i	−0.896819	−	0.896819i	−0.995153	+	0.0983348i	$0.968648\pi$
$678$	9.31749	+	34.7733i	0.357836	+	1.33546i
$679$	6.92820	+	12.0000i	0.265880	+	0.460518i
$680$		0			0
$681$		0			0
$682$	10.0382	+	2.68973i	0.384382	+	0.102995i
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	−0.999671	−	0.0256307i	$-0.991841\pi$
$683$	−25.4558	+	25.4558i	−0.974041	+	0.974041i	0.0256307	+	0.999671i	$0.491841\pi$
$684$	−4.33013	−	0.500000i	−0.165567	−	0.0191180i
$685$		0			0
$686$	16.5000	−	9.52628i	0.629973	−	0.363715i
$687$	−10.3528	+	38.6370i	−0.394982	+	1.47409i
$688$	6.69213	−	1.79315i	0.255135	−	0.0683632i
$689$	−5.19615	+	3.00000i	−0.197958	+	0.114291i
$690$		0			0
$691$	−17.0000			−0.646710			−0.323355	−	0.946278i	$-0.604811\pi$
$691$	−17.0000			−0.646710			−0.323355	+	0.946278i	$0.604811\pi$
$692$	10.6066	+	10.6066i	0.403202	+	0.403202i
$693$	5.01910	−	1.34486i	0.190660	−	0.0510871i
$694$	5.19615	−	9.00000i	0.197243	−	0.341635i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	3.86370	+	1.03528i	0.146243	+	0.0391858i
$699$	10.3923	−	18.0000i	0.393073	−	0.680823i
$700$		0			0
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	0.730186	−	0.683248i	$-0.239433\pi$
$701$	−6.00000	−	10.3923i	−0.226617	−	0.392512i	−0.956803	+	0.290736i	$0.906100\pi$
$702$	−5.65685	−	5.65685i	−0.213504	−	0.213504i
$703$	−4.31199	+	0.637756i	−0.162630	+	0.0240534i
$704$		−	3.00000i		−	0.113067i
$705$		0			0
$706$	−9.00000	+	5.19615i	−0.338719	+	0.195560i
$707$	8.06918	+	30.1146i	0.303473	+	1.13258i
$708$	5.37945	−	20.0764i	0.202172	−	0.754517i
$709$	27.7128	+	16.0000i	1.04078	+	0.600893i	0.920053	−	0.391794i	$-0.128145\pi$
$709$	27.7128	+	16.0000i	1.04078	+	0.600893i	0.120723	+	0.992686i	$0.461479\pi$
$710$		0			0
$711$			3.46410i			0.129914i
$712$	1.34486	+	5.01910i	0.0504009	+	0.188099i
$713$	4.65874	+	17.3867i	0.174471	+	0.651136i
$714$		0			0
$715$		0			0
$716$	4.50000	+	2.59808i	0.168173	+	0.0970947i
$717$	−12.4233	+	46.3644i	−0.463957	+	1.73151i
$718$	1.55291	+	5.79555i	0.0579542	+	0.216288i
$719$	−15.5885	+	9.00000i	−0.581351	+	0.335643i	−0.761670	−	0.647965i	$-0.775620\pi$
$719$	−15.5885	+	9.00000i	−0.581351	+	0.335643i	0.180319	+	0.983608i	$0.442287\pi$
$720$		0			0
$721$		−	12.1244i		−	0.451535i
$722$	−18.9903	+	0.605571i	−0.706748	+	0.0225370i
$723$	−19.5959	−	19.5959i	−0.728780	−	0.728780i
$724$	10.3923	+	18.0000i	0.386227	+	0.668965i
$725$		0			0
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$	23.4225	+	6.27603i	0.868691	+	0.232765i	0.665522	−	0.746379i	$-0.268209\pi$
$727$	23.4225	+	6.27603i	0.868691	+	0.232765i	0.203169	+	0.979144i	$0.434876\pi$
$728$	−3.34607	+	0.896575i	−0.124013	+	0.0332293i
$729$			13.0000i			0.481481i
$730$		0			0
$731$		0			0
$732$	7.72741	−	2.07055i	0.285613	−	0.0765298i
$733$	−33.0681	−	33.0681i	−1.22140	−	1.22140i	−0.967135	−	0.254264i	$-0.918167\pi$
$733$	−33.0681	−	33.0681i	−1.22140	−	1.22140i	−0.254264	−	0.967135i	$-0.581833\pi$
$734$	3.46410			0.127862
$735$		0			0
$736$	4.50000	−	2.59808i	0.165872	−	0.0957664i
$737$	5.79555	−	1.55291i	0.213482	−	0.0572023i
$738$	−1.34486	+	5.01910i	−0.0495051	+	0.184756i
$739$	14.7224	−	8.50000i	0.541573	−	0.312678i	−0.204143	−	0.978941i	$-0.565441\pi$
$739$	14.7224	−	8.50000i	0.541573	−	0.312678i	0.745716	+	0.666264i	$0.232107\pi$
$740$		0			0
$741$	14.0000	+	10.3923i	0.514303	+	0.381771i
$742$	3.67423	−	3.67423i	0.134885	−	0.134885i
$743$	20.2844	+	5.43520i	0.744164	+	0.199398i	0.610928	−	0.791686i	$-0.290796\pi$
$743$	20.2844	+	5.43520i	0.744164	+	0.199398i	0.133236	+	0.991084i	$0.457463\pi$
$744$	−3.46410	−	6.00000i	−0.127000	−	0.219971i
$745$		0			0
$746$	−15.5000	−	26.8468i	−0.567495	−	0.982931i
$747$		0			0
$748$		0			0
$749$	−10.3923			−0.379727
$750$		0			0
$751$	39.0000	+	22.5167i	1.42313	+	0.821645i	0.996565	−	0.0828123i	$-0.0263902\pi$
$751$	39.0000	+	22.5167i	1.42313	+	0.821645i	0.426565	+	0.904457i	$0.359724\pi$
$752$	7.34847	−	7.34847i	0.267971	−	0.267971i
$753$	−33.9411	+	33.9411i	−1.23688	+	1.23688i
$754$		0			0
$755$		0			0
$756$	6.00000	+	3.46410i	0.218218	+	0.125988i
$757$	21.7494	+	5.82774i	0.790496	+	0.211813i	0.631407	−	0.775451i	$-0.282478\pi$
$757$	21.7494	+	5.82774i	0.790496	+	0.211813i	0.159089	+	0.987264i	$0.449144\pi$
$758$	−0.896575	+	3.34607i	−0.0325651	+	0.121535i
$759$	31.1769			1.13165
$760$		0			0
$761$	21.0000			0.761249			0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000			0.761249			0.380625	+	0.924730i	$0.375709\pi$
$762$	−3.62347	+	13.5230i	−0.131264	+	0.489885i
$763$		0			0
$764$	−20.7846	−	12.0000i	−0.751961	−	0.434145i
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	−14.6969	+	14.6969i	−0.530676	+	0.530676i
$768$	−1.41421	+	1.41421i	−0.0510310	+	0.0510310i
$769$	−29.4449	−	17.0000i	−1.06181	−	0.613036i	−0.135877	−	0.990726i	$-0.543385\pi$
$769$	−29.4449	−	17.0000i	−1.06181	−	0.613036i	−0.925932	+	0.377690i	$0.876718\pi$
$770$		0			0
$771$		0			0
$772$	1.41421	+	1.41421i	0.0508987	+	0.0508987i
$773$	5.43520	+	20.2844i	0.195491	+	0.729581i	0.992139	+	0.125138i	$0.0399374\pi$
$773$	5.43520	+	20.2844i	0.195491	+	0.729581i	−0.796649	+	0.604443i	$0.793396\pi$
$774$	−3.46410	−	6.00000i	−0.124515	−	0.215666i
$775$		0			0
$776$	−4.00000	−	6.92820i	−0.143592	−	0.248708i
$777$	−3.34607	−	0.896575i	−0.120039	−	0.0321645i
$778$	−21.2132	+	21.2132i	−0.760530	+	0.760530i
$779$	−2.59808	+	22.5000i	−0.0930857	+	0.806146i
$780$		0			0
$781$	−27.0000	+	15.5885i	−0.966136	+	0.557799i
$782$		0			0
$783$		0			0
$784$	−3.46410	+	2.00000i	−0.123718	+	0.0714286i
$785$		0			0
$786$	30.0000			1.07006
$787$	11.3137	+	11.3137i	0.403290	+	0.403290i	0.879391	−	0.476101i	$-0.157950\pi$
$787$	11.3137	+	11.3137i	0.403290	+	0.403290i	−0.476101	+	0.879391i	$0.657950\pi$
$788$	5.01910	−	1.34486i	0.178798	−	0.0479088i
$789$	−25.9808	+	45.0000i	−0.924940	+	1.60204i
$790$		0			0
$791$			31.1769i			1.10852i
$792$	−2.89778	+	0.776457i	−0.102968	+	0.0275902i
$793$	−7.72741	−	2.07055i	−0.274408	−	0.0735275i
$794$	0.866025	−	1.50000i	0.0307341	−	0.0532330i
$795$		0			0
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	10.6066	+	10.6066i	0.375705	+	0.375705i	0.869550	−	0.493845i	$-0.164409\pi$
$797$	10.6066	+	10.6066i	0.375705	+	0.375705i	−0.493845	+	0.869550i	$0.664409\pi$
$798$	−14.0406	−	5.55532i	−0.497032	−	0.196656i
$799$		0			0
$800$		0			0
$801$	4.50000	−	2.59808i	0.159000	−	0.0917985i
$802$	−5.37945	−	20.0764i	−0.189955	−	0.708922i
$803$	2.68973	−	10.0382i	0.0949184	−	0.354240i
$804$	−3.46410	−	2.00000i	−0.122169	−	0.0705346i
$805$		0			0
$806$			6.92820i			0.244036i
$807$	10.7589	+	40.1528i	0.378731	+	1.41344i
$808$	−4.65874	−	17.3867i	−0.163894	−	0.611661i
$809$		−	42.0000i		−	1.47664i	−0.674450	−	0.738321i	$-0.735619\pi$
$809$		−	42.0000i		−	1.47664i	0.674450	−	0.738321i	$-0.264381\pi$
$810$		0			0
$811$	−40.5000	−	23.3827i	−1.42215	−	0.821077i	−0.425665	−	0.904881i	$-0.639960\pi$
$811$	−40.5000	−	23.3827i	−1.42215	−	0.821077i	−0.996482	+	0.0838036i	$0.973293\pi$
$812$		0			0
$813$	−1.03528	−	3.86370i	−0.0363087	−	0.135506i
$814$	−2.59808	+	1.50000i	−0.0910625	+	0.0525750i
$815$		0			0
$816$		0			0
$817$	−18.7637	−	23.6627i	−0.656459	−	0.827853i
$818$	−25.7196	−	25.7196i	−0.899266	−	0.899266i
$819$	1.73205	+	3.00000i	0.0605228	+	0.104828i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	−5.01910	+	1.34486i	−0.174955	+	0.0468790i	−0.345233	−	0.938517i	$-0.612200\pi$
$823$	−5.01910	+	1.34486i	−0.174955	+	0.0468790i	0.170278	+	0.985396i	$0.445533\pi$
$824$			7.00000i			0.243857i
$825$		0			0
$826$	9.00000	−	15.5885i	0.313150	−	0.542392i
$827$	34.7733	−	9.31749i	1.20919	−	0.324001i	0.402744	−	0.915313i	$-0.368056\pi$
$827$	34.7733	−	9.31749i	1.20919	−	0.324001i	0.806443	+	0.591312i	$0.201390\pi$
$828$	−3.67423	−	3.67423i	−0.127688	−	0.127688i
$829$	27.7128			0.962506			0.481253	−	0.876582i	$-0.340182\pi$
$829$	27.7128			0.962506			0.481253	+	0.876582i	$0.340182\pi$
$830$		0			0
$831$		0			0
$832$	1.93185	−	0.517638i	0.0669749	−	0.0179459i
$833$		0			0
$834$	−34.6410	+	20.0000i	−1.19952	+	0.692543i
$835$		0			0
$836$	−12.0000	+	5.19615i	−0.415029	+	0.179713i
$837$	9.79796	−	9.79796i	0.338667	−	0.338667i
$838$	−8.69333	−	2.32937i	−0.300306	−	0.0804668i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−2.68973	−	10.0382i	−0.0926941	−	0.345939i
$843$	22.0454	+	22.0454i	0.759284	+	0.759284i
$844$	−22.5167			−0.775055
$845$		0			0
$846$	−9.00000	−	5.19615i	−0.309426	−	0.178647i
$847$	−2.44949	+	2.44949i	−0.0841655	+	0.0841655i
$848$	−2.12132	+	2.12132i	−0.0728464	+	0.0728464i
$849$	31.1769	−	54.0000i	1.06999	−	1.85328i
$850$		0			0
$851$	−4.50000	−	2.59808i	−0.154258	−	0.0890609i
$852$	20.0764	+	5.37945i	0.687806	+	0.184297i
$853$	3.58630	−	13.3843i	0.122793	−	0.458268i	−0.876959	−	0.480566i	$-0.840431\pi$
$853$	3.58630	−	13.3843i	0.122793	−	0.458268i	0.999751	+	0.0222973i	$0.00709804\pi$
$854$	6.92820			0.237078
$855$		0			0
$856$	6.00000			0.205076
$857$	−12.4233	+	46.3644i	−0.424372	+	1.58378i	0.340917	+	0.940093i	$0.389262\pi$
$857$	−12.4233	+	46.3644i	−0.424372	+	1.58378i	−0.765290	+	0.643686i	$0.777404\pi$
$858$	11.5911	+	3.10583i	0.395714	+	0.106031i
$859$	9.52628	+	5.50000i	0.325032	+	0.187658i	0.653633	−	0.756811i	$-0.273244\pi$
$859$	9.52628	+	5.50000i	0.325032	+	0.187658i	−0.328601	+	0.944469i	$0.606577\pi$
$860$		0			0
$861$	−9.00000	+	15.5885i	−0.306719	+	0.531253i
$862$	−7.34847	+	7.34847i	−0.250290	+	0.250290i
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	−0.864201	−	0.503148i	$-0.832175\pi$
$863$	−10.6066	+	10.6066i	−0.361053	+	0.361053i	0.503148	+	0.864201i	$0.332175\pi$
$864$	−3.46410	−	2.00000i	−0.117851	−	0.0680414i
$865$		0			0
$866$	−28.0000			−0.951479
$867$	−24.0416	−	24.0416i	−0.816497	−	0.816497i
$868$	−1.55291	−	5.79555i	−0.0527093	−	0.196714i
$869$	5.19615	+	9.00000i	0.176267	+	0.305304i
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$		0			0
$873$	−5.65685	+	5.65685i	−0.191456	+	0.191456i
$874$	−18.1865	−	13.5000i	−0.615169	−	0.456644i
$875$		0			0
$876$	−6.00000	+	3.46410i	−0.202721	+	0.117041i
$877$	−12.1645	+	45.3985i	−0.410766	+	1.53300i	0.382402	+	0.923996i	$0.375097\pi$
$877$	−12.1645	+	45.3985i	−0.410766	+	1.53300i	−0.793168	+	0.609003i	$0.791570\pi$
$878$	−23.4225	+	6.27603i	−0.790470	+	0.211806i
$879$	15.5885	−	9.00000i	0.525786	−	0.303562i
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	2.82843	+	2.82843i	0.0952381	+	0.0952381i
$883$	36.8067	−	9.86233i	1.23864	−	0.331894i	0.420705	−	0.907198i	$-0.361783\pi$
$883$	36.8067	−	9.86233i	1.23864	−	0.331894i	0.817940	+	0.575304i	$0.195116\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$887$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$888$	1.93185	+	0.517638i	0.0648287	+	0.0173708i
$889$	−6.06218	+	10.5000i	−0.203319	+	0.352159i
$890$		0			0
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$	−16.2635	−	16.2635i	−0.544541	−	0.544541i
$893$	−42.1218	−	16.6660i	−1.40955	−	0.557705i
$894$		−	12.0000i		−	0.401340i
$895$		0			0
$896$	−1.50000	+	0.866025i	−0.0501115	+	0.0289319i
$897$	5.37945	+	20.0764i	0.179615	+	0.670331i
$898$	1.34486	−	5.01910i	0.0448787	−	0.167489i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	4.03459	+	15.0573i	0.134337	+	0.501353i
$903$	−6.21166	−	23.1822i	−0.206711	−	0.771456i
$904$		−	18.0000i		−	0.598671i
$905$		0			0
$906$	36.0000	+	20.7846i	1.19602	+	0.690522i
$907$	−11.3880	+	42.5007i	−0.378134	+	1.41121i	0.470578	+	0.882358i	$0.344045\pi$
$907$	−11.3880	+	42.5007i	−0.378134	+	1.41121i	−0.848712	+	0.528856i	$0.822621\pi$
$908$		0			0
$909$	−15.5885	+	9.00000i	−0.517036	+	0.298511i
$910$		0			0
$911$		−	31.1769i		−	1.03294i	−0.856306	−	0.516469i	$-0.827246\pi$
$911$		−	31.1769i		−	1.03294i	0.856306	−	0.516469i	$-0.172754\pi$
$912$	8.10634	+	3.20736i	0.268428	+	0.106206i
$913$		0			0
$914$	−19.0526	−	33.0000i	−0.630203	−	1.09154i
$915$		0			0
$916$	10.0000	−	17.3205i	0.330409	−	0.572286i
$917$	25.0955	+	6.72432i	0.828726	+	0.222056i
$918$		0			0
$919$		−	46.0000i		−	1.51740i	−0.651440	−	0.758700i	$-0.725835\pi$
$919$		−	46.0000i		−	1.51740i	0.651440	−	0.758700i	$-0.274165\pi$
$920$		0			0
$921$	−20.0000	+	34.6410i	−0.659022	+	1.14146i
$922$	−17.3867	+	4.65874i	−0.572599	+	0.153428i
$923$	−14.6969	−	14.6969i	−0.483756	−	0.483756i
$924$	−10.3923			−0.341882
$925$		0			0
$926$	28.5000	−	16.4545i	0.936568	−	0.540728i
$927$	6.76148	−	1.81173i	0.222076	−	0.0595051i
$928$		0			0
$929$	18.1865	−	10.5000i	0.596681	−	0.344494i	−0.171054	−	0.985262i	$-0.554717\pi$
$929$	18.1865	−	10.5000i	0.596681	−	0.344494i	0.767735	+	0.640768i	$0.221384\pi$
$930$		0			0
$931$	14.0000	+	10.3923i	0.458831	+	0.340594i
$932$	−7.34847	+	7.34847i	−0.240707	+	0.240707i
$933$		0			0
$934$	−20.7846	−	36.0000i	−0.680093	−	1.17796i
$935$		0			0
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$	9.86233	+	36.8067i	0.322188	+	1.20242i	0.917108	+	0.398638i	$0.130517\pi$
$937$	9.86233	+	36.8067i	0.322188	+	1.20242i	−0.594920	+	0.803785i	$0.702816\pi$
$938$	−2.44949	−	2.44949i	−0.0799787	−	0.0799787i
$939$	20.7846			0.678280
$940$		0			0
$941$	36.0000	+	20.7846i	1.17357	+	0.677559i	0.954517	−	0.298155i	$-0.0963712\pi$
$941$	36.0000	+	20.7846i	1.17357	+	0.677559i	0.219049	+	0.975714i	$0.429705\pi$
$942$	26.9444	−	26.9444i	0.877896	−	0.877896i
$943$	−19.0919	+	19.0919i	−0.621717	+	0.621717i
$944$	−5.19615	+	9.00000i	−0.169120	+	0.292925i
$945$		0			0
$946$	−18.0000	−	10.3923i	−0.585230	−	0.337883i
$947$	−40.1528	−	10.7589i	−1.30479	−	0.349617i	−0.461531	−	0.887124i	$-0.652700\pi$
$947$	−40.1528	−	10.7589i	−1.30479	−	0.349617i	−0.843259	+	0.537507i	$0.819366\pi$
$948$	1.79315	−	6.69213i	0.0582388	−	0.217350i
$949$	6.92820			0.224899
$950$		0			0
$951$	−54.0000			−1.75107
$952$		0			0
$953$	34.7733	+	9.31749i	1.12642	+	0.301823i	0.773478	−	0.633823i	$-0.218515\pi$
$953$	34.7733	+	9.31749i	1.12642	+	0.301823i	0.352940	+	0.935646i	$0.385182\pi$
$954$	2.59808	+	1.50000i	0.0841158	+	0.0485643i
$955$		0			0
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	−4.24264	+	4.24264i	−0.137073	+	0.137073i
$959$		0			0
$960$		0			0
$961$	19.0000			0.612903
$962$	−1.41421	−	1.41421i	−0.0455961	−	0.0455961i
$963$	−1.55291	−	5.79555i	−0.0500420	−	0.186759i
$964$	6.92820	+	12.0000i	0.223142	+	0.386494i
$965$		0			0
$966$	−9.00000	−	15.5885i	−0.289570	−	0.501550i
$967$	−36.8067	−	9.86233i	−1.18362	−	0.317151i	−0.387261	−	0.921970i	$-0.626579\pi$
$967$	−36.8067	−	9.86233i	−1.18362	−	0.317151i	−0.796363	+	0.604819i	$0.793245\pi$
$968$	1.41421	−	1.41421i	0.0454545	−	0.0454545i
$969$		0			0
$970$		0			0
$971$	9.00000	−	5.19615i	0.288824	−	0.166752i	−0.348588	−	0.937276i	$-0.613339\pi$
$971$	9.00000	−	5.19615i	0.288824	−	0.166752i	0.637411	+	0.770524i	$0.280005\pi$
$972$	−2.58819	+	9.65926i	−0.0830162	+	0.309821i
$973$	−33.4607	+	8.96575i	−1.07270	+	0.287429i
$974$	−21.6506	+	12.5000i	−0.693731	+	0.400526i
$975$		0			0
$976$	−4.00000			−0.128037
$977$	33.9411	+	33.9411i	1.08587	+	1.08587i	0.995949	+	0.0899242i	$0.0286625\pi$
$977$	33.9411	+	33.9411i	1.08587	+	1.08587i	0.0899242	+	0.995949i	$0.471338\pi$
$978$	−46.8449	+	12.5521i	−1.49794	+	0.401371i
$979$	7.79423	−	13.5000i	0.249105	−	0.431462i
$980$		0			0
$981$		0			0
$982$	20.2844	−	5.43520i	0.647303	−	0.173444i
$983$	20.2844	+	5.43520i	0.646973	+	0.173356i	0.567360	−	0.823470i	$-0.307965\pi$
$983$	20.2844	+	5.43520i	0.646973	+	0.173356i	0.0796132	+	0.996826i	$0.474631\pi$
$984$	5.19615	−	9.00000i	0.165647	−	0.286910i
$985$		0			0
$986$		0			0
$987$	−25.4558	−	25.4558i	−0.810268	−	0.810268i
$988$	−5.41662	−	6.83083i	−0.172326	−	0.217318i
$989$		−	36.0000i		−	1.14473i
$990$		0			0
$991$	−6.00000	+	3.46410i	−0.190596	+	0.110041i	−0.592262	−	0.805746i	$-0.701765\pi$
$991$	−6.00000	+	3.46410i	−0.190596	+	0.110041i	0.401665	+	0.915786i	$0.368431\pi$
$992$	0.896575	+	3.34607i	0.0284663	+	0.106238i
$993$	9.86233	−	36.8067i	0.312972	−	1.16803i
$994$	15.5885	+	9.00000i	0.494436	+	0.285463i
$995$		0			0
$996$		0			0
$997$	−2.24144	−	8.36516i	−0.0709871	−	0.264927i	0.921306	−	0.388837i	$-0.127123\pi$
$997$	−2.24144	−	8.36516i	−0.0709871	−	0.264927i	−0.992293	+	0.123910i	$0.960457\pi$
$998$	−1.81173	−	6.76148i	−0.0573494	−	0.214031i
$999$			4.00000i			0.126554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.d.943.2	yes	8
5.2	odd	4	inner	950.2.q.d.107.2	yes	8
5.3	odd	4	inner	950.2.q.d.107.1	✓	8
5.4	even	2	inner	950.2.q.d.943.1	yes	8
19.8	odd	6	inner	950.2.q.d.293.2	yes	8
95.8	even	12	inner	950.2.q.d.407.1	yes	8
95.27	even	12	inner	950.2.q.d.407.2	yes	8
95.84	odd	6	inner	950.2.q.d.293.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.d.107.1	✓	8	5.3	odd	4	inner
950.2.q.d.107.2	yes	8	5.2	odd	4	inner
950.2.q.d.293.1	yes	8	95.84	odd	6	inner
950.2.q.d.293.2	yes	8	19.8	odd	6	inner
950.2.q.d.407.1	yes	8	95.8	even	12	inner
950.2.q.d.407.2	yes	8	95.27	even	12	inner
950.2.q.d.943.1	yes	8	5.4	even	2	inner
950.2.q.d.943.2	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.93185 + 0.517638i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.93185 + 0.517638i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(1.22474 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +3.00000 q^{11} +(-1.41421 - 1.41421i) q^{12} +(0.517638 + 1.93185i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.707107 - 0.707107i) q^{18} +(2.59808 - 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(0.776457 - 2.89778i) q^{22} +(5.01910 - 1.34486i) q^{23} +(-1.73205 + 1.00000i) q^{24} +2.00000 q^{26} +(-2.82843 - 2.82843i) q^{27} +(-1.67303 + 0.448288i) q^{28} +3.46410i q^{31} +(0.965926 - 0.258819i) q^{32} +(5.79555 + 1.55291i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-0.707107 - 0.707107i) q^{37} +(-2.70831 - 3.41542i) q^{38} +4.00000i q^{39} +(-4.50000 + 2.59808i) q^{41} +(-0.896575 - 3.34607i) q^{42} +(1.79315 - 6.69213i) q^{43} +(-2.59808 - 1.50000i) q^{44} -5.19615i q^{46} +(-2.68973 - 10.0382i) q^{47} +(0.517638 + 1.93185i) q^{48} +4.00000i q^{49} +(0.517638 - 1.93185i) q^{52} +(0.776457 + 2.89778i) q^{53} +(-3.46410 + 2.00000i) q^{54} +1.73205i q^{56} +(6.83083 - 5.41662i) q^{57} +(5.19615 + 9.00000i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(3.34607 + 0.896575i) q^{62} +(1.67303 - 0.448288i) q^{63} -1.00000i q^{64} +(3.00000 - 5.19615i) q^{66} +(1.93185 - 0.517638i) q^{67} +10.3923 q^{69} +(-9.00000 + 5.19615i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(0.896575 - 3.34607i) q^{73} +(-0.866025 + 0.500000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(3.67423 - 3.67423i) q^{77} +(3.86370 + 1.03528i) q^{78} +(1.73205 + 3.00000i) q^{79} +(-5.50000 - 9.52628i) q^{81} +(1.34486 + 5.01910i) q^{82} -3.46410 q^{84} +(-6.00000 - 3.46410i) q^{86} +(-2.12132 + 2.12132i) q^{88} +(2.59808 - 4.50000i) q^{89} +(3.00000 + 1.73205i) q^{91} +(-5.01910 - 1.34486i) q^{92} +(-1.79315 + 6.69213i) q^{93} -10.3923 q^{94} +2.00000 q^{96} +(-2.07055 + 7.72741i) q^{97} +(3.86370 + 1.03528i) q^{98} +(2.59808 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{6}+O(q^{10}) \) 8 * q + 8 * q^6	\( 8 q + 8 q^{6} + 24 q^{11} + 4 q^{16} + 24 q^{21} + 16 q^{26} - 4 q^{36} - 36 q^{41} - 16 q^{61} + 24 q^{66} - 72 q^{71} - 32 q^{76} - 44 q^{81} - 48 q^{86} + 24 q^{91} + 16 q^{96}+O(q^{100}) \) 8 * q + 8 * q^6 + 24 * q^11 + 4 * q^16 + 24 * q^21 + 16 * q^26 - 4 * q^36 - 36 * q^41 - 16 * q^61 + 24 * q^66 - 72 * q^71 - 32 * q^76 - 44 * q^81 - 48 * q^86 + 24 * q^91 + 16 * q^96

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