LMFDB - Embedded newform 950.2.q.d.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
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			107.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	950.107
Dual form			950.2.q.d.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.517638 + 1.93185i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.517638 + 1.93185i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.00000 - 1.73205i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +3.00000 q^{11} +(-1.41421 + 1.41421i) q^{12} +(-1.93185 + 0.517638i) q^{13} +(0.866025 + 1.50000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.707107 + 0.707107i) q^{18} +(-2.59808 + 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(-2.89778 - 0.776457i) q^{22} +(1.34486 + 5.01910i) q^{23} +(1.73205 - 1.00000i) q^{24} +2.00000 q^{26} +(-2.82843 + 2.82843i) q^{27} +(-0.448288 - 1.67303i) q^{28} +3.46410i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.55291 + 5.79555i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-0.707107 + 0.707107i) q^{37} +(3.41542 - 2.70831i) q^{38} -4.00000i q^{39} +(-4.50000 + 2.59808i) q^{41} +(-3.34607 + 0.896575i) q^{42} +(6.69213 + 1.79315i) q^{43} +(2.59808 + 1.50000i) q^{44} -5.19615i q^{46} +(-10.0382 + 2.68973i) q^{47} +(-1.93185 + 0.517638i) q^{48} -4.00000i q^{49} +(-1.93185 - 0.517638i) q^{52} +(-2.89778 + 0.776457i) q^{53} +(3.46410 - 2.00000i) q^{54} +1.73205i q^{56} +(-5.41662 - 6.83083i) q^{57} +(-5.19615 - 9.00000i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.896575 - 3.34607i) q^{62} +(0.448288 + 1.67303i) q^{63} +1.00000i q^{64} +(3.00000 - 5.19615i) q^{66} +(-0.517638 - 1.93185i) q^{67} -10.3923 q^{69} +(-9.00000 + 5.19615i) q^{71} +(0.258819 + 0.965926i) q^{72} +(3.34607 + 0.896575i) q^{73} +(0.866025 - 0.500000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(-3.67423 - 3.67423i) q^{77} +(-1.03528 + 3.86370i) q^{78} +(-1.73205 - 3.00000i) q^{79} +(-5.50000 - 9.52628i) q^{81} +(5.01910 - 1.34486i) q^{82} +3.46410 q^{84} +(-6.00000 - 3.46410i) q^{86} +(-2.12132 - 2.12132i) q^{88} +(-2.59808 + 4.50000i) q^{89} +(3.00000 + 1.73205i) q^{91} +(-1.34486 + 5.01910i) q^{92} +(-6.69213 - 1.79315i) q^{93} +10.3923 q^{94} +2.00000 q^{96} +(7.72741 + 2.07055i) q^{97} +(-1.03528 + 3.86370i) q^{98} +(-2.59808 - 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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
$3$	−0.517638	+	1.93185i	−0.298858	+	1.11536i	0.639246	+	0.769002i	$0.279247\pi$
$3$	−0.517638	+	1.93185i	−0.298858	+	1.11536i	−0.938104	+	0.346353i	$0.887420\pi$
$4$	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	$-0.356148\pi$
$7$	−1.22474	−	1.22474i	−0.462910	−	0.462910i	−0.899608	+	0.436698i	$0.856148\pi$
$8$	−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
$13$	−1.93185	+	0.517638i	−0.535799	+	0.143567i	−0.516565	−	0.856248i	$-0.672790\pi$
$13$	−1.93185	+	0.517638i	−0.535799	+	0.143567i	−0.0192343	+	0.999815i	$0.506123\pi$
$14$	0.866025	+	1.50000i	0.231455	+	0.400892i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$17$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$18$	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
$22$	−2.89778	−	0.776457i	−0.617808	−	0.165541i
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	0.952119	+	0.305727i	$0.0988995\pi$
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	−0.671696	+	0.740827i	$0.734434\pi$
$24$	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
$28$	−0.448288	−	1.67303i	−0.0847184	−	0.316173i
$29$		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	$0.899307\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.55291	+	5.79555i	−0.270328	+	1.00888i
$34$		0			0
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.707107	+	0.707107i	−0.116248	+	0.116248i	−0.762838	−	0.646590i	$-0.776194\pi$
$37$	−0.707107	+	0.707107i	−0.116248	+	0.116248i	0.646590	+	0.762838i	$0.276194\pi$
$38$	3.41542	−	2.70831i	0.554054	−	0.439346i
$39$		−	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	$0.466323\pi$
$42$	−3.34607	+	0.896575i	−0.516309	+	0.138345i
$43$	6.69213	+	1.79315i	1.02054	+	0.273453i	0.730027	−	0.683418i	$-0.239507\pi$
$43$	6.69213	+	1.79315i	1.02054	+	0.273453i	0.290513	+	0.956871i	$0.406174\pi$
$44$	2.59808	+	1.50000i	0.391675	+	0.226134i
$45$		0			0
$46$		−	5.19615i		−	0.766131i
$47$	−10.0382	+	2.68973i	−1.46422	+	0.392337i	−0.900946	−	0.433932i	$-0.857126\pi$
$47$	−10.0382	+	2.68973i	−1.46422	+	0.392337i	−0.563276	+	0.826269i	$0.690459\pi$
$48$	−1.93185	+	0.517638i	−0.278839	+	0.0747146i
$49$		−	4.00000i		−	0.571429i
$50$		0			0
$51$		0			0
$52$	−1.93185	−	0.517638i	−0.267900	−	0.0717835i
$53$	−2.89778	+	0.776457i	−0.398040	+	0.106655i	−0.452286	−	0.891873i	$-0.649391\pi$
$53$	−2.89778	+	0.776457i	−0.398040	+	0.106655i	0.0542455	+	0.998528i	$0.482725\pi$
$54$	3.46410	−	2.00000i	0.471405	−	0.272166i
$55$		0			0
$56$			1.73205i			0.231455i
$57$	−5.41662	−	6.83083i	−0.717449	−	0.904766i
$58$		0			0
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	−0.976034	−	0.217620i	$-0.930171\pi$
$59$	−5.19615	−	9.00000i	−0.676481	−	1.17170i	0.299552	−	0.954080i	$-0.403163\pi$
$60$		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	$0.249096\pi$
$62$	0.896575	−	3.34607i	0.113865	−	0.424951i
$63$	0.448288	+	1.67303i	0.0564789	+	0.210782i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	−0.517638	−	1.93185i	−0.0632396	−	0.236013i	0.927071	−	0.374887i	$-0.122318\pi$
$67$	−0.517638	−	1.93185i	−0.0632396	−	0.236013i	−0.990310	+	0.138874i	$0.955652\pi$
$68$		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	$0.544852\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	3.34607	+	0.896575i	0.391627	+	0.104936i	0.449259	−	0.893402i	$-0.351688\pi$
$73$	3.34607	+	0.896575i	0.391627	+	0.104936i	−0.0576314	+	0.998338i	$0.518355\pi$
$74$	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
$78$	−1.03528	+	3.86370i	−0.117222	+	0.437478i
$79$	−1.73205	−	3.00000i	−0.194871	−	0.337526i	0.751987	−	0.659178i	$-0.229095\pi$
$79$	−1.73205	−	3.00000i	−0.194871	−	0.337526i	−0.946858	+	0.321651i	$0.895762\pi$
$80$		0			0
$81$	−5.50000	−	9.52628i	−0.611111	−	1.05848i
$82$	5.01910	−	1.34486i	0.554267	−	0.148515i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$	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	−0.970235	−	0.242166i	$-0.922142\pi$
$89$	−2.59808	+	4.50000i	−0.275396	+	0.476999i	0.694839	+	0.719165i	$0.255475\pi$
$90$		0			0
$91$	3.00000	+	1.73205i	0.314485	+	0.181568i
$92$	−1.34486	+	5.01910i	−0.140212	+	0.523277i
$93$	−6.69213	−	1.79315i	−0.693942	−	0.185941i
$94$	10.3923			1.07188
$95$		0			0
$96$	2.00000			0.204124
$97$	7.72741	+	2.07055i	0.784599	+	0.210233i	0.628811	−	0.777558i	$-0.283542\pi$
$97$	7.72741	+	2.07055i	0.784599	+	0.210233i	0.155788	+	0.987791i	$0.450208\pi$
$98$	−1.03528	+	3.86370i	−0.104579	+	0.390293i
$99$	−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	0.907584	−	0.419871i	$-0.137925\pi$
$103$	4.94975	+	4.94975i	0.487713	+	0.487713i	−0.419871	+	0.907584i	$0.637925\pi$
$104$	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	−0.881791	−	0.471640i	$-0.843662\pi$
$107$	−4.24264	+	4.24264i	−0.410152	+	0.410152i	0.471640	+	0.881791i	$0.343662\pi$
$108$	−3.86370	+	1.03528i	−0.371785	+	0.0996195i
$109$		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
$112$	0.448288	−	1.67303i	0.0423592	−	0.158087i
$113$	−12.7279	−	12.7279i	−1.19734	−	1.19734i	−0.974959	−	0.222383i	$-0.928617\pi$
$113$	−12.7279	−	12.7279i	−1.19734	−	1.19734i	−0.222383	−	0.974959i	$-0.571383\pi$
$114$	3.46410	+	8.00000i	0.324443	+	0.749269i
$115$		0			0
$116$		0			0
$117$	1.93185	+	0.517638i	0.178600	+	0.0478557i
$118$	2.68973	+	10.0382i	0.247609	+	0.924091i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	2.82843	−	2.82843i	0.256074	−	0.256074i
$123$	−2.68973	−	10.0382i	−0.242524	−	0.905114i
$124$	−1.73205	+	3.00000i	−0.155543	+	0.269408i
$125$		0			0
$126$		−	1.73205i		−	0.154303i
$127$	1.81173	+	6.76148i	0.160765	+	0.599984i	0.998542	+	0.0539720i	$0.0171882\pi$
$127$	1.81173	+	6.76148i	0.160765	+	0.599984i	−0.837777	+	0.546012i	$0.816145\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−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
$133$	7.46859	−	1.10463i	0.647609	−	0.0957833i
$134$			2.00000i			0.172774i
$135$		0			0
$136$		0			0
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$	10.0382	+	2.68973i	0.854508	+	0.228965i
$139$	17.3205	+	10.0000i	1.46911	+	0.848189i	0.999400	−	0.0346338i	$-0.0110265\pi$
$139$	17.3205	+	10.0000i	1.46911	+	0.848189i	0.469706	+	0.882823i	$0.344360\pi$
$140$		0			0
$141$		−	20.7846i		−	1.75038i
$142$	10.0382	−	2.68973i	0.842387	−	0.225717i
$143$	−5.79555	+	1.55291i	−0.484649	+	0.129861i
$144$		−	1.00000i		−	0.0833333i
$145$		0			0
$146$	−3.00000	−	1.73205i	−0.248282	−	0.143346i
$147$	7.72741	+	2.07055i	0.637346	+	0.170776i
$148$	−0.965926	+	0.258819i	−0.0793986	+	0.0212748i
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	−0.697507	−	0.716578i	$-0.745707\pi$
$149$	−5.19615	+	3.00000i	−0.425685	+	0.245770i	0.271821	+	0.962348i	$0.412374\pi$
$150$		0			0
$151$			20.7846i			1.69143i	0.533637	+	0.845714i	$0.320825\pi$
$151$			20.7846i			1.69143i	−0.533637	+	0.845714i	$0.679175\pi$
$152$	4.31199	−	0.637756i	0.349749	−	0.0517289i
$153$		0			0
$154$	2.59808	+	4.50000i	0.209359	+	0.362620i
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	4.93117	−	18.4034i	0.393550	−	1.46875i	−0.430686	−	0.902502i	$-0.641728\pi$
$157$	4.93117	−	18.4034i	0.393550	−	1.46875i	0.824236	−	0.566246i	$-0.191605\pi$
$158$	0.896575	+	3.34607i	0.0713277	+	0.266199i
$159$		−	6.00000i		−	0.475831i
$160$		0			0
$161$	4.50000	−	7.79423i	0.354650	−	0.614271i
$162$	2.84701	+	10.6252i	0.223682	+	0.834793i
$163$	17.1464	−	17.1464i	1.34301	−	1.34301i	0.449966	−	0.893045i	$-0.351436\pi$
$163$	17.1464	−	17.1464i	1.34301	−	1.34301i	0.893045	−	0.449966i	$-0.148564\pi$
$164$	−5.19615			−0.405751
$165$		0			0
$166$		0			0
$167$	5.43520	+	20.2844i	0.420588	+	1.56966i	0.773372	+	0.633952i	$0.218568\pi$
$167$	5.43520	+	20.2844i	0.420588	+	1.56966i	−0.352784	+	0.935705i	$0.614765\pi$
$168$	−3.34607	−	0.896575i	−0.258155	−	0.0691723i
$169$	−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
$173$	3.88229	−	14.4889i	0.295165	−	1.10157i	−0.645922	−	0.763404i	$-0.723527\pi$
$173$	3.88229	−	14.4889i	0.295165	−	1.10157i	0.941086	−	0.338166i	$-0.109807\pi$
$174$		0			0
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	20.0764	−	5.37945i	1.50903	−	0.404344i
$178$	3.67423	−	3.67423i	0.275396	−	0.275396i
$179$	5.19615			0.388379			0.194189	−	0.980964i	$-0.437792\pi$
$179$	5.19615			0.388379			0.194189	+	0.980964i	$0.437792\pi$
$180$		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
$188$	−10.0382	−	2.68973i	−0.732111	−	0.196168i
$189$	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	$0.165220\pi$
$192$	−1.93185	−	0.517638i	−0.139419	−	0.0373573i
$193$	0.517638	−	1.93185i	0.0372604	−	0.139058i	−0.944790	−	0.327677i	$-0.893734\pi$
$193$	0.517638	−	1.93185i	0.0372604	−	0.139058i	0.982050	+	0.188619i	$0.0604011\pi$
$194$	−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	$-0.190737\pi$
$197$	3.67423	+	3.67423i	0.261778	+	0.261778i	−0.563998	+	0.825776i	$0.690737\pi$
$198$	2.12132	+	2.12132i	0.150756	+	0.150756i
$199$	6.92820	+	4.00000i	0.491127	+	0.283552i	0.725042	−	0.688705i	$-0.241820\pi$
$199$	6.92820	+	4.00000i	0.491127	+	0.283552i	−0.233915	+	0.972257i	$0.575154\pi$
$200$		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
$207$	1.34486	−	5.01910i	0.0934745	−	0.348851i
$208$	−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	$0.0510552\pi$
$212$	−2.89778	−	0.776457i	−0.199020	−	0.0533273i
$213$	−5.37945	−	20.0764i	−0.368594	−	1.37561i
$214$	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
$222$	0.517638	+	1.93185i	0.0347416	+	0.129657i
$223$	−5.95284	+	22.2163i	−0.398632	+	1.48771i	0.416874	+	0.908964i	$0.363126\pi$
$223$	−5.95284	+	22.2163i	−0.398632	+	1.48771i	−0.815506	+	0.578749i	$0.803541\pi$
$224$	−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	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	−1.27551	−	8.62398i	−0.0844729	−	0.571137i
$229$		−	20.0000i		−	1.32164i	−0.750546	−	0.660819i	$-0.770209\pi$
$229$		−	20.0000i		−	1.32164i	0.750546	−	0.660819i	$-0.229791\pi$
$230$		0			0
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$		0			0
$233$	10.0382	+	2.68973i	0.657624	+	0.176210i	0.572174	−	0.820133i	$-0.306100\pi$
$233$	10.0382	+	2.68973i	0.657624	+	0.176210i	0.0854505	+	0.996342i	$0.472767\pi$
$234$	−1.73205	−	1.00000i	−0.113228	−	0.0653720i
$235$		0			0
$236$		−	10.3923i		−	0.676481i
$237$	6.69213	−	1.79315i	0.434701	−	0.116478i
$238$		0			0
$239$		−	24.0000i		−	1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$		−	24.0000i		−	1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$		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	$0.813920\pi$
$242$	1.93185	+	0.517638i	0.124184	+	0.0332750i
$243$	9.65926	−	2.58819i	0.619642	−	0.166032i
$244$	−3.46410	+	2.00000i	−0.221766	+	0.128037i
$245$		0			0
$246$			10.3923i			0.662589i
$247$	3.20736	−	8.10634i	0.204080	−	0.515794i
$248$	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	$0.893120\pi$
$252$	−0.448288	+	1.67303i	−0.0282395	+	0.105391i
$253$	4.03459	+	15.0573i	0.253652	+	0.946644i
$254$		−	7.00000i		−	0.439219i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$257$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$258$	9.79796	−	9.79796i	0.609994	−	0.609994i
$259$	1.73205			0.107624
$260$		0			0
$261$		0			0
$262$	−3.88229	−	14.4889i	−0.239848	−	0.895126i
$263$	−25.0955	−	6.72432i	−1.54745	−	0.414639i	−0.618789	−	0.785557i	$-0.712376\pi$
$263$	−25.0955	−	6.72432i	−1.54745	−	0.414639i	−0.928665	+	0.370918i	$0.879043\pi$
$264$	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
$268$	0.517638	−	1.93185i	0.0316198	−	0.118007i
$269$	−10.3923	−	18.0000i	−0.633630	−	1.09748i	−0.986804	−	0.161922i	$-0.948231\pi$
$269$	−10.3923	−	18.0000i	−0.633630	−	1.09748i	0.353174	−	0.935558i	$-0.385102\pi$
$270$		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	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	−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	$0.512734\pi$
$282$	−5.37945	+	20.0764i	−0.320342	+	1.19553i
$283$	30.1146	+	8.06918i	1.79013	+	0.479663i	0.992368	−	0.123314i	$-0.0393522\pi$
$283$	30.1146	+	8.06918i	1.79013	+	0.479663i	0.797759	+	0.602977i	$0.206019\pi$
$284$	−10.3923			−0.616670
$285$		0			0
$286$	6.00000			0.354787
$287$	8.69333	+	2.32937i	0.513151	+	0.137498i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	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	0.868128	−	0.496341i	$-0.165323\pi$
$293$	6.36396	+	6.36396i	0.371787	+	0.371787i	−0.496341	+	0.868128i	$0.665323\pi$
$294$	−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
$298$	5.79555	−	1.55291i	0.335727	−	0.0899579i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	−6.00000	−	10.3923i	−0.345834	−	0.599002i
$302$	5.37945	−	20.0764i	0.309553	−	1.15527i
$303$	−25.4558	−	25.4558i	−1.46240	−	1.46240i
$304$	−4.33013	−	0.500000i	−0.248350	−	0.0286770i
$305$		0			0
$306$		0			0
$307$	19.3185	+	5.17638i	1.10257	+	0.295432i	0.763809	−	0.645442i	$-0.223327\pi$
$307$	19.3185	+	5.17638i	1.10257	+	0.295432i	0.338757	+	0.940874i	$0.389994\pi$
$308$	−1.34486	−	5.01910i	−0.0766307	−	0.285990i
$309$	−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
$313$	2.68973	+	10.0382i	0.152032	+	0.567392i	0.999341	+	0.0362920i	$0.0115546\pi$
$313$	2.68973	+	10.0382i	0.152032	+	0.567392i	−0.847309	+	0.531100i	$0.821779\pi$
$314$	−9.52628	+	16.5000i	−0.537599	+	0.931149i
$315$		0			0
$316$		−	3.46410i		−	0.194871i
$317$	6.98811	+	26.0800i	0.392492	+	1.46480i	0.826011	+	0.563654i	$0.190605\pi$
$317$	6.98811	+	26.0800i	0.392492	+	1.46480i	−0.433519	+	0.901144i	$0.642728\pi$
$318$	−1.55291	+	5.79555i	−0.0870831	+	0.324999i
$319$		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
$328$	5.01910	+	1.34486i	0.277133	+	0.0742576i
$329$	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
$333$	0.965926	−	0.258819i	0.0529324	−	0.0141832i
$334$		−	21.0000i		−	1.14907i
$335$		0			0
$336$	3.00000	+	1.73205i	0.163663	+	0.0944911i
$337$	−1.93185	−	0.517638i	−0.105235	−	0.0281975i	0.205817	−	0.978590i	$-0.434015\pi$
$337$	−1.93185	−	0.517638i	−0.105235	−	0.0281975i	−0.311052	+	0.950393i	$0.600681\pi$
$338$	8.69333	−	2.32937i	0.472855	−	0.126701i
$339$	31.1769	−	18.0000i	1.69330	−	0.977626i
$340$		0			0
$341$			10.3923i			0.562775i
$342$	−4.31199	+	0.637756i	−0.233166	+	0.0344859i
$343$	−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
$347$	2.68973	−	10.0382i	0.144392	−	0.538879i	−0.855390	−	0.517985i	$-0.826682\pi$
$347$	2.68973	−	10.0382i	0.144392	−	0.538879i	0.999782	−	0.0208935i	$-0.00665108\pi$
$348$		0			0
$349$		−	4.00000i		−	0.214115i	−0.994253	−	0.107058i	$-0.965857\pi$
$349$		−	4.00000i		−	0.214115i	0.994253	−	0.107058i	$-0.0341429\pi$
$350$		0			0
$351$	4.00000	−	6.92820i	0.213504	−	0.369800i
$352$	−0.776457	−	2.89778i	−0.0413853	−	0.154452i
$353$	7.34847	−	7.34847i	0.391120	−	0.391120i	−0.483967	−	0.875086i	$-0.660804\pi$
$353$	7.34847	−	7.34847i	0.391120	−	0.391120i	0.875086	+	0.483967i	$0.160804\pi$
$354$	−20.7846			−1.10469
$355$		0			0
$356$	−4.50000	+	2.59808i	−0.238500	+	0.137698i
$357$		0			0
$358$	−5.01910	−	1.34486i	−0.265268	−	0.0710782i
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	−0.356572	−	0.934268i	$-0.616054\pi$
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	0.630814	+	0.775934i	$0.282721\pi$
$360$		0			0
$361$	−5.50000	−	18.1865i	−0.289474	−	0.957186i
$362$	14.6969	+	14.6969i	0.772454	+	0.772454i
$363$	1.03528	−	3.86370i	0.0543379	−	0.202792i
$364$	1.73205	+	3.00000i	0.0907841	+	0.157243i
$365$		0			0
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	3.34607	−	0.896575i	0.174663	−	0.0468009i	−0.170427	−	0.985370i	$-0.554515\pi$
$367$	3.34607	−	0.896575i	0.174663	−	0.0468009i	0.345091	+	0.938569i	$0.387848\pi$
$368$	−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	0.989335	+	0.145655i	$0.0465290\pi$
$373$	21.9203	+	21.9203i	1.13499	+	1.13499i	0.145655	+	0.989335i	$0.453471\pi$
$374$		0			0
$375$		0			0
$376$	9.00000	+	5.19615i	0.464140	+	0.267971i
$377$		0			0
$378$	−6.69213	−	1.79315i	−0.344206	−	0.0922297i
$379$	3.46410			0.177939			0.0889695	−	0.996034i	$-0.471643\pi$
$379$	3.46410			0.177939			0.0889695	+	0.996034i	$0.471643\pi$
$380$		0			0
$381$	−14.0000			−0.717242
$382$	−23.1822	−	6.21166i	−1.18611	−	0.317816i
$383$	−6.21166	+	23.1822i	−0.317401	+	1.18456i	0.604333	+	0.796732i	$0.293440\pi$
$383$	−6.21166	+	23.1822i	−0.317401	+	1.18456i	−0.921733	+	0.387824i	$0.873227\pi$
$384$	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	0.983290	−	0.182047i	$-0.0582724\pi$
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.333987	+	0.942578i	$0.391606\pi$
$390$		0			0
$391$		0			0
$392$	−2.82843	+	2.82843i	−0.142857	+	0.142857i
$393$	−28.9778	+	7.76457i	−1.46174	+	0.391671i
$394$	−2.59808	−	4.50000i	−0.130889	−	0.226707i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	0.448288	−	1.67303i	0.0224989	−	0.0839671i	−0.953764	−	0.300558i	$-0.902827\pi$
$397$	0.448288	−	1.67303i	0.0224989	−	0.0839671i	0.976262	+	0.216591i	$0.0694938\pi$
$398$	−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	$0.159650\pi$
$402$	−3.86370	−	1.03528i	−0.192704	−	0.0516349i
$403$	−1.79315	−	6.69213i	−0.0893232	−	0.333359i
$404$	−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	$0.522565\pi$
$409$	−18.1865	+	31.5000i	−0.899266	+	1.55757i	−0.828434	+	0.560087i	$0.810768\pi$
$410$		0			0
$411$		0			0
$412$	1.81173	+	6.76148i	0.0892577	+	0.333114i
$413$	−4.65874	+	17.3867i	−0.229242	+	0.855542i
$414$	−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
$418$	10.2462	−	8.12493i	0.501160	−	0.397403i
$419$			9.00000i			0.439679i	0.975536	+	0.219839i	$0.0705533\pi$
$419$			9.00000i			0.439679i	−0.975536	+	0.219839i	$0.929447\pi$
$420$		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	$0.251835\pi$
$422$	−21.7494	+	5.82774i	−1.05875	+	0.283690i
$423$	10.0382	+	2.68973i	0.488074	+	0.130779i
$424$	2.59808	+	1.50000i	0.126174	+	0.0728464i
$425$		0			0
$426$			20.7846i			1.00702i
$427$	6.69213	−	1.79315i	0.323855	−	0.0867767i
$428$	−5.79555	+	1.55291i	−0.280139	+	0.0750629i
$429$		−	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	$0.747193\pi$
$432$	−3.86370	−	1.03528i	−0.185893	−	0.0498097i
$433$	27.0459	−	7.24693i	1.29974	−	0.348265i	0.458391	−	0.888751i	$-0.348426\pi$
$433$	27.0459	−	7.24693i	1.29974	−	0.348265i	0.841353	+	0.540485i	$0.181759\pi$
$434$	−5.19615	+	3.00000i	−0.249423	+	0.144005i
$435$		0			0
$436$		0			0
$437$	−21.0609	−	8.33298i	−1.00748	−	0.398620i
$438$	4.89898	−	4.89898i	0.234082	−	0.234082i
$439$	12.1244	+	21.0000i	0.578664	+	1.00228i	0.995633	+	0.0933546i	$0.0297590\pi$
$439$	12.1244	+	21.0000i	0.578664	+	1.00228i	−0.416969	+	0.908921i	$0.636908\pi$
$440$		0			0
$441$	−2.00000	+	3.46410i	−0.0952381	+	0.164957i
$442$		0			0
$443$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$443$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$444$		−	2.00000i		−	0.0949158i
$445$		0			0
$446$	11.5000	−	19.9186i	0.544541	−	0.943172i
$447$	−3.10583	−	11.5911i	−0.146901	−	0.548241i
$448$	1.22474	−	1.22474i	0.0578638	−	0.0578638i
$449$	−5.19615			−0.245222			−0.122611	−	0.992455i	$-0.539127\pi$
$449$	−5.19615			−0.245222			−0.122611	+	0.992455i	$0.539127\pi$
$450$		0			0
$451$	−13.5000	+	7.79423i	−0.635690	+	0.367016i
$452$	−4.65874	−	17.3867i	−0.219129	−	0.817800i
$453$	−40.1528	−	10.7589i	−1.88654	−	0.505497i
$454$		0			0
$455$		0			0
$456$	−1.00000	+	8.66025i	−0.0468293	+	0.405554i
$457$	−26.9444	−	26.9444i	−1.26041	−	1.26041i	−0.950897	−	0.309509i	$-0.899835\pi$
$457$	−26.9444	−	26.9444i	−1.26041	−	1.26041i	−0.309509	−	0.950897i	$-0.600165\pi$
$458$	−5.17638	+	19.3185i	−0.241876	+	0.902695i
$459$		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	$0.971013\pi$
$462$	−10.0382	+	2.68973i	−0.467019	+	0.125137i
$463$	−23.2702	+	23.2702i	−1.08146	+	1.08146i	−0.0850817	+	0.996374i	$0.527115\pi$
$463$	−23.2702	+	23.2702i	−1.08146	+	1.08146i	−0.996374	+	0.0850817i	$0.972885\pi$
$464$		0			0
$465$		0			0
$466$	−9.00000	−	5.19615i	−0.416917	−	0.240707i
$467$	−29.3939	−	29.3939i	−1.36019	−	1.36019i	−0.873673	−	0.486513i	$-0.838269\pi$
$467$	−29.3939	−	29.3939i	−1.36019	−	1.36019i	−0.486513	−	0.873673i	$-0.661731\pi$
$468$	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
$472$	−2.68973	+	10.0382i	−0.123805	+	0.462045i
$473$	20.0764	+	5.37945i	0.923113	+	0.247348i
$474$	−6.92820			−0.318223
$475$		0			0
$476$		0			0
$477$	2.89778	+	0.776457i	0.132680	+	0.0355515i
$478$	−6.21166	+	23.1822i	−0.284115	+	1.06033i
$479$	5.19615	+	3.00000i	0.237418	+	0.137073i	0.613990	−	0.789314i	$-0.289564\pi$
$479$	5.19615	+	3.00000i	0.237418	+	0.137073i	−0.376571	+	0.926388i	$0.622897\pi$
$480$		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	−0.983260	−	0.182208i	$-0.941675\pi$
$487$	−17.6777	+	17.6777i	−0.801052	+	0.801052i	0.182208	+	0.983260i	$0.441675\pi$
$488$	3.86370	−	1.03528i	0.174902	−	0.0468648i
$489$	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	$0.676194\pi$
$492$	2.68973	−	10.0382i	0.121262	−	0.452557i
$493$		0			0
$494$	−5.19615	+	7.00000i	−0.233786	+	0.314945i
$495$		0			0
$496$	−3.00000	+	1.73205i	−0.134704	+	0.0777714i
$497$	17.3867	+	4.65874i	0.779899	+	0.208973i
$498$		0			0
$499$	−6.06218	+	3.50000i	−0.271380	+	0.156682i	−0.629515	−	0.776989i	$-0.716746\pi$
$499$	−6.06218	+	3.50000i	−0.271380	+	0.156682i	0.358134	+	0.933670i	$0.383413\pi$
$500$		0			0
$501$	−42.0000			−1.87642
$502$	16.9706	−	16.9706i	0.757433	−	0.757433i
$503$	1.34486	+	5.01910i	0.0599645	+	0.223791i	0.989405	−	0.145181i	$-0.0463765\pi$
$503$	1.34486	+	5.01910i	0.0599645	+	0.223791i	−0.929441	+	0.368972i	$0.879710\pi$
$504$	0.866025	−	1.50000i	0.0385758	−	0.0668153i
$505$		0			0
$506$		−	15.5885i		−	0.692991i
$507$	−4.65874	−	17.3867i	−0.206902	−	0.772169i
$508$	−1.81173	+	6.76148i	−0.0803827	+	0.299992i
$509$		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
$513$	−2.55103	−	17.2480i	−0.112631	−	0.761516i
$514$		0			0
$515$		0			0
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	−30.1146	+	8.06918i	−1.32444	+	0.354882i
$518$	−1.67303	−	0.448288i	−0.0735088	−	0.0196966i
$519$	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
$523$	27.0459	−	7.24693i	1.18264	−	0.316886i	0.386664	−	0.922221i	$-0.373627\pi$
$523$	27.0459	−	7.24693i	1.18264	−	0.316886i	0.795971	+	0.605334i	$0.206961\pi$
$524$			15.0000i			0.655278i
$525$		0			0
$526$	22.5000	+	12.9904i	0.981047	+	0.566408i
$527$		0			0
$528$	−5.79555	+	1.55291i	−0.252219	+	0.0675819i
$529$	−3.46410	+	2.00000i	−0.150613	+	0.0869565i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	7.02030	+	2.77766i	0.304369	+	0.120427i
$533$	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
$537$	−2.68973	+	10.0382i	−0.116070	+	0.433180i
$538$	5.37945	+	20.0764i	0.231925	+	0.865555i
$539$		−	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	$0.0977023\pi$
$542$	0.517638	+	1.93185i	0.0222345	+	0.0829801i
$543$	29.3939	−	29.3939i	1.26141	−	1.26141i
$544$		0			0
$545$		0			0
$546$	6.00000	−	3.46410i	0.256776	−	0.148250i
$547$	−5.69402	−	21.2504i	−0.243459	−	0.908600i	−0.974152	−	0.225894i	$-0.927470\pi$
$547$	−5.69402	−	21.2504i	−0.243459	−	0.908600i	0.730693	−	0.682706i	$-0.239197\pi$
$548$		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
$553$	−1.55291	+	5.79555i	−0.0660366	+	0.246452i
$554$		0			0
$555$		0			0
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−5.01910	+	1.34486i	−0.212666	+	0.0569837i	−0.363579	−	0.931563i	$-0.618445\pi$
$557$	−5.01910	+	1.34486i	−0.212666	+	0.0569837i	0.150913	+	0.988547i	$0.451779\pi$
$558$	−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	0.252399	−	0.967623i	$-0.418780\pi$
$563$	−16.9706	−	16.9706i	−0.715224	−	0.715224i	−0.967623	+	0.252399i	$0.918780\pi$
$564$	10.3923	−	18.0000i	0.437595	−	0.757937i
$565$		0			0
$566$	−27.0000	−	15.5885i	−1.13489	−	0.655232i
$567$	−4.93117	+	18.4034i	−0.207089	+	0.772868i
$568$	10.0382	+	2.68973i	0.421193	+	0.112858i
$569$	5.19615			0.217834			0.108917	−	0.994051i	$-0.465262\pi$
$569$	5.19615			0.217834			0.108917	+	0.994051i	$0.465262\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	−5.79555	−	1.55291i	−0.242324	−	0.0649306i
$573$	−12.4233	+	46.3644i	−0.518991	+	1.93690i
$574$	−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	$-0.180595\pi$
$577$	7.34847	+	7.34847i	0.305921	+	0.305921i	−0.537404	+	0.843325i	$0.680595\pi$
$578$	−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
$583$	−8.69333	+	2.32937i	−0.360041	+	0.0964727i
$584$	−1.73205	−	3.00000i	−0.0716728	−	0.124141i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−5.37945	+	20.0764i	−0.222034	+	0.828641i	0.761537	+	0.648121i	$0.224445\pi$
$587$	−5.37945	+	20.0764i	−0.222034	+	0.828641i	−0.983571	+	0.180520i	$0.942222\pi$
$588$	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
$592$	−0.965926	−	0.258819i	−0.0396993	−	0.0106374i
$593$	−10.7589	−	40.1528i	−0.441815	−	1.64888i	−0.724210	−	0.689579i	$-0.757796\pi$
$593$	−10.7589	−	40.1528i	−0.441815	−	1.64888i	0.282395	−	0.959298i	$-0.408871\pi$
$594$	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
$598$	2.68973	+	10.0382i	0.109991	+	0.410492i
$599$	10.3923	−	18.0000i	0.424618	−	0.735460i	−0.571767	−	0.820416i	$-0.693742\pi$
$599$	10.3923	−	18.0000i	0.424618	−	0.735460i	0.996385	+	0.0849563i	$0.0270751\pi$
$600$		0			0
$601$			22.5167i			0.918474i	0.888314	+	0.459237i	$0.151877\pi$
$601$			22.5167i			0.918474i	−0.888314	+	0.459237i	$0.848123\pi$
$602$	3.10583	+	11.5911i	0.126584	+	0.472418i
$603$	−0.517638	+	1.93185i	−0.0210799	+	0.0786711i
$604$	−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	−0.531409	−	0.847115i	$-0.678337\pi$
$607$	7.77817	−	7.77817i	0.315706	−	0.315706i	0.847115	+	0.531409i	$0.178337\pi$
$608$	4.05317	+	1.60368i	0.164378	+	0.0650379i
$609$		0			0
$610$		0			0
$611$	18.0000	−	10.3923i	0.728202	−	0.420428i
$612$		0			0
$613$	5.01910	+	1.34486i	0.202719	+	0.0543185i	0.358750	−	0.933434i	$-0.383203\pi$
$613$	5.01910	+	1.34486i	0.202719	+	0.0543185i	−0.156030	+	0.987752i	$0.549870\pi$
$614$	−17.3205	−	10.0000i	−0.698999	−	0.403567i
$615$		0			0
$616$			5.19615i			0.209359i
$617$	−30.1146	+	8.06918i	−1.21237	+	0.324853i	−0.807690	−	0.589607i	$-0.799283\pi$
$617$	−30.1146	+	8.06918i	−1.21237	+	0.324853i	−0.404677	+	0.914460i	$0.632616\pi$
$618$	13.5230	−	3.62347i	0.543973	−	0.145757i
$619$		−	31.0000i		−	1.24600i	−0.782224	−	0.622998i	$-0.785915\pi$
$619$		−	31.0000i		−	1.24600i	0.782224	−	0.622998i	$-0.214085\pi$
$620$		0			0
$621$	−18.0000	−	10.3923i	−0.722315	−	0.417029i
$622$		0			0
$623$	8.69333	−	2.32937i	0.348291	−	0.0933243i
$624$	3.46410	−	2.00000i	0.138675	−	0.0800641i
$625$		0			0
$626$		−	10.3923i		−	0.415360i
$627$	−16.2499	−	20.4925i	−0.648957	−	0.818391i
$628$	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	$-0.00647871\pi$
$632$	−0.896575	+	3.34607i	−0.0356639	+	0.133099i
$633$	11.6555	+	43.4988i	0.463264	+	1.72892i
$634$		−	27.0000i		−	1.07231i
$635$		0			0
$636$	3.00000	−	5.19615i	0.118958	−	0.206041i
$637$	2.07055	+	7.72741i	0.0820383	+	0.306171i
$638$		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	$0.198698\pi$
$642$	3.10583	+	11.5911i	0.122577	+	0.457465i
$643$	−33.4607	−	8.96575i	−1.31956	−	0.353575i	−0.470747	−	0.882268i	$-0.656015\pi$
$643$	−33.4607	−	8.96575i	−1.31956	−	0.353575i	−0.848813	+	0.528694i	$0.822682\pi$
$644$	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	$-0.282569\pi$
$647$	−3.67423	−	3.67423i	−0.144449	−	0.144449i	−0.775633	+	0.631184i	$0.782569\pi$
$648$	−2.84701	+	10.6252i	−0.111841	+	0.417397i
$649$	−15.5885	−	27.0000i	−0.611900	−	1.05984i
$650$		0			0
$651$	6.00000	+	10.3923i	0.235159	+	0.407307i
$652$	23.4225	−	6.27603i	0.917294	−	0.245788i
$653$	11.0227	−	11.0227i	0.431352	−	0.431352i	−0.457736	−	0.889088i	$-0.651340\pi$
$653$	11.0227	−	11.0227i	0.431352	−	0.431352i	0.889088	+	0.457736i	$0.151340\pi$
$654$		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	−0.673333	−	0.739339i	$-0.735138\pi$
$659$	7.79423	−	13.5000i	0.303620	−	0.525885i	0.976953	+	0.213454i	$0.0684713\pi$
$660$		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	$0.731446\pi$
$662$	−4.93117	+	18.4034i	−0.191655	+	0.715267i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.00000			−0.0387492
$667$		0			0
$668$	−5.43520	+	20.2844i	−0.210294	+	0.784829i
$669$	−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	0.992714	−	0.120492i	$-0.0384471\pi$
$673$	22.6274	+	22.6274i	0.872223	+	0.872223i	−0.120492	+	0.992714i	$0.538447\pi$
$674$	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	−0.995153	−	0.0983348i	$-0.968648\pi$
$677$	−23.3345	+	23.3345i	−0.896819	+	0.896819i	0.0983348	+	0.995153i	$0.468648\pi$
$678$	−34.7733	+	9.31749i	−1.33546	+	0.357836i
$679$	−6.92820	−	12.0000i	−0.265880	−	0.460518i
$680$		0			0
$681$		0			0
$682$	2.68973	−	10.0382i	0.102995	−	0.384382i
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	0.0256307	−	0.999671i	$-0.491841\pi$
$683$	−25.4558	−	25.4558i	−0.974041	−	0.974041i	−0.999671	+	0.0256307i	$0.991841\pi$
$684$	4.33013	+	0.500000i	0.165567	+	0.0191180i
$685$		0			0
$686$	16.5000	−	9.52628i	0.629973	−	0.363715i
$687$	38.6370	+	10.3528i	1.47409	+	0.394982i
$688$	1.79315	+	6.69213i	0.0683632	+	0.255135i
$689$	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
$693$	1.34486	+	5.01910i	0.0510871	+	0.190660i
$694$	−5.19615	+	9.00000i	−0.197243	+	0.341635i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−1.03528	+	3.86370i	−0.0391858	+	0.146243i
$699$	−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
$703$	−0.637756	−	4.31199i	−0.0240534	−	0.162630i
$704$			3.00000i			0.113067i
$705$		0			0
$706$	−9.00000	+	5.19615i	−0.338719	+	0.195560i
$707$	30.1146	−	8.06918i	1.13258	−	0.303473i
$708$	20.0764	+	5.37945i	0.754517	+	0.202172i
$709$	−27.7128	−	16.0000i	−1.04078	−	0.600893i	−0.120723	−	0.992686i	$-0.538521\pi$
$709$	−27.7128	−	16.0000i	−1.04078	−	0.600893i	−0.920053	+	0.391794i	$0.871855\pi$
$710$		0			0
$711$			3.46410i			0.129914i
$712$	5.01910	−	1.34486i	0.188099	−	0.0504009i
$713$	−17.3867	+	4.65874i	−0.651136	+	0.174471i
$714$		0			0
$715$		0			0
$716$	4.50000	+	2.59808i	0.168173	+	0.0970947i
$717$	46.3644	+	12.4233i	1.73151	+	0.463957i
$718$	−5.79555	+	1.55291i	−0.216288	+	0.0579542i
$719$	15.5885	−	9.00000i	0.581351	−	0.335643i	−0.180319	−	0.983608i	$-0.557713\pi$
$719$	15.5885	−	9.00000i	0.581351	−	0.335643i	0.761670	+	0.647965i	$0.224380\pi$
$720$		0			0
$721$		−	12.1244i		−	0.451535i
$722$	0.605571	+	18.9903i	0.0225370	+	0.706748i
$723$	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
$727$	6.27603	−	23.4225i	0.232765	−	0.868691i	−0.746379	−	0.665522i	$-0.768209\pi$
$727$	6.27603	−	23.4225i	0.232765	−	0.868691i	0.979144	−	0.203169i	$-0.0651242\pi$
$728$	−0.896575	−	3.34607i	−0.0332293	−	0.124013i
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$		0			0
$732$	−2.07055	−	7.72741i	−0.0765298	−	0.285613i
$733$	33.0681	−	33.0681i	1.22140	−	1.22140i	0.254264	−	0.967135i	$-0.418167\pi$
$733$	33.0681	−	33.0681i	1.22140	−	1.22140i	0.967135	−	0.254264i	$-0.0818331\pi$
$734$	−3.46410			−0.127862
$735$		0			0
$736$	4.50000	−	2.59808i	0.165872	−	0.0957664i
$737$	−1.55291	−	5.79555i	−0.0572023	−	0.213482i
$738$	−5.01910	−	1.34486i	−0.184756	−	0.0495051i
$739$	−14.7224	+	8.50000i	−0.541573	+	0.312678i	−0.745716	−	0.666264i	$-0.767893\pi$
$739$	−14.7224	+	8.50000i	−0.541573	+	0.312678i	0.204143	+	0.978941i	$0.434559\pi$
$740$		0			0
$741$	14.0000	+	10.3923i	0.514303	+	0.381771i
$742$	−3.67423	−	3.67423i	−0.134885	−	0.134885i
$743$	−5.43520	+	20.2844i	−0.199398	+	0.744164i	0.791686	+	0.610928i	$0.209204\pi$
$743$	−5.43520	+	20.2844i	−0.199398	+	0.744164i	−0.991084	+	0.133236i	$0.957463\pi$
$744$	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
$757$	5.82774	−	21.7494i	0.211813	−	0.790496i	−0.775451	−	0.631407i	$-0.782478\pi$
$757$	5.82774	−	21.7494i	0.211813	−	0.790496i	0.987264	−	0.159089i	$-0.0508557\pi$
$758$	−3.34607	−	0.896575i	−0.121535	−	0.0325651i
$759$	−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	$0.375709\pi$
$762$	13.5230	+	3.62347i	0.489885	+	0.131264i
$763$		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	0.925932	−	0.377690i	$-0.123282\pi$
$769$	29.4449	+	17.0000i	1.06181	+	0.613036i	0.135877	+	0.990726i	$0.456615\pi$
$770$		0			0
$771$		0			0
$772$	1.41421	−	1.41421i	0.0508987	−	0.0508987i
$773$	−20.2844	+	5.43520i	−0.729581	+	0.195491i	−0.604443	−	0.796649i	$-0.706604\pi$
$773$	−20.2844	+	5.43520i	−0.729581	+	0.195491i	−0.125138	+	0.992139i	$0.539937\pi$
$774$	3.46410	+	6.00000i	0.124515	+	0.215666i
$775$		0			0
$776$	−4.00000	−	6.92820i	−0.143592	−	0.248708i
$777$	−0.896575	+	3.34607i	−0.0321645	+	0.120039i
$778$	−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	−0.476101	−	0.879391i	$-0.657950\pi$
$787$	11.3137	−	11.3137i	0.403290	−	0.403290i	0.879391	+	0.476101i	$0.157950\pi$
$788$	1.34486	+	5.01910i	0.0479088	+	0.178798i
$789$	25.9808	−	45.0000i	0.924940	−	1.60204i
$790$		0			0
$791$			31.1769i			1.10852i
$792$	0.776457	+	2.89778i	0.0275902	+	0.102968i
$793$	2.07055	−	7.72741i	0.0735275	−	0.274408i
$794$	−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	−0.493845	−	0.869550i	$-0.664409\pi$
$797$	10.6066	−	10.6066i	0.375705	−	0.375705i	0.869550	+	0.493845i	$0.164409\pi$
$798$	5.55532	−	14.0406i	0.196656	−	0.497032i
$799$		0			0
$800$		0			0
$801$	4.50000	−	2.59808i	0.159000	−	0.0917985i
$802$	−20.0764	+	5.37945i	−0.708922	+	0.189955i
$803$	10.0382	+	2.68973i	0.354240	+	0.0949184i
$804$	3.46410	+	2.00000i	0.122169	+	0.0705346i
$805$		0			0
$806$			6.92820i			0.244036i
$807$	40.1528	−	10.7589i	1.41344	−	0.378731i
$808$	17.3867	−	4.65874i	0.611661	−	0.163894i
$809$			42.0000i			1.47664i	0.674450	+	0.738321i	$0.264381\pi$
$809$			42.0000i			1.47664i	−0.674450	+	0.738321i	$0.735619\pi$
$810$		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
$813$	3.86370	−	1.03528i	0.135506	−	0.0363087i
$814$	2.59808	−	1.50000i	0.0910625	−	0.0525750i
$815$		0			0
$816$		0			0
$817$	−23.6627	+	18.7637i	−0.827853	+	0.656459i
$818$	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
$823$	−1.34486	−	5.01910i	−0.0468790	−	0.174955i	0.938517	−	0.345233i	$-0.112200\pi$
$823$	−1.34486	−	5.01910i	−0.0468790	−	0.174955i	−0.985396	+	0.170278i	$0.945533\pi$
$824$		−	7.00000i		−	0.243857i
$825$		0			0
$826$	9.00000	−	15.5885i	0.313150	−	0.542392i
$827$	−9.31749	−	34.7733i	−0.324001	−	1.20919i	−0.915313	−	0.402744i	$-0.868056\pi$
$827$	−9.31749	−	34.7733i	−0.324001	−	1.20919i	0.591312	−	0.806443i	$-0.298610\pi$
$828$	3.67423	−	3.67423i	0.127688	−	0.127688i
$829$	−27.7128			−0.962506			−0.481253	−	0.876582i	$-0.659818\pi$
$829$	−27.7128			−0.962506			−0.481253	+	0.876582i	$0.659818\pi$
$830$		0			0
$831$		0			0
$832$	−0.517638	−	1.93185i	−0.0179459	−	0.0669749i
$833$		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
$838$	2.32937	−	8.69333i	0.0804668	−	0.300306i
$839$		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
$842$	−10.0382	+	2.68973i	−0.345939	+	0.0926941i
$843$	−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
$852$	5.37945	−	20.0764i	0.184297	−	0.687806i
$853$	13.3843	+	3.58630i	0.458268	+	0.122793i	0.480566	−	0.876959i	$-0.340431\pi$
$853$	13.3843	+	3.58630i	0.458268	+	0.122793i	−0.0222973	+	0.999751i	$0.507098\pi$
$854$	−6.92820			−0.237078
$855$		0			0
$856$	6.00000			0.205076
$857$	46.3644	+	12.4233i	1.58378	+	0.424372i	0.940093	−	0.340917i	$-0.110738\pi$
$857$	46.3644	+	12.4233i	1.58378	+	0.424372i	0.643686	+	0.765290i	$0.277404\pi$
$858$	−3.10583	+	11.5911i	−0.106031	+	0.395714i
$859$	−9.52628	−	5.50000i	−0.325032	−	0.187658i	0.328601	−	0.944469i	$-0.393423\pi$
$859$	−9.52628	−	5.50000i	−0.325032	−	0.187658i	−0.653633	+	0.756811i	$0.726756\pi$
$860$		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	0.503148	−	0.864201i	$-0.332175\pi$
$863$	−10.6066	−	10.6066i	−0.361053	−	0.361053i	−0.864201	+	0.503148i	$0.832175\pi$
$864$	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
$868$	5.79555	−	1.55291i	0.196714	−	0.0527093i
$869$	−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
$877$	45.3985	+	12.1645i	1.53300	+	0.410766i	0.923996	−	0.382402i	$-0.124903\pi$
$877$	45.3985	+	12.1645i	1.53300	+	0.410766i	0.609003	+	0.793168i	$0.291570\pi$
$878$	−6.27603	−	23.4225i	−0.211806	−	0.790470i
$879$	−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
$883$	9.86233	+	36.8067i	0.331894	+	1.23864i	0.907198	+	0.420705i	$0.138217\pi$
$883$	9.86233	+	36.8067i	0.331894	+	1.23864i	−0.575304	+	0.817940i	$0.695116\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$887$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$888$	−0.517638	+	1.93185i	−0.0173708	+	0.0648287i
$889$	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
$893$	16.6660	−	42.1218i	0.557705	−	1.40955i
$894$			12.0000i			0.401340i
$895$		0			0
$896$	−1.50000	+	0.866025i	−0.0501115	+	0.0289319i
$897$	20.0764	−	5.37945i	0.670331	−	0.179615i
$898$	5.01910	+	1.34486i	0.167489	+	0.0448787i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	15.0573	−	4.03459i	0.501353	−	0.134337i
$903$	23.1822	−	6.21166i	0.771456	−	0.206711i
$904$			18.0000i			0.598671i
$905$		0			0
$906$	36.0000	+	20.7846i	1.19602	+	0.690522i
$907$	42.5007	+	11.3880i	1.41121	+	0.378134i	0.882358	−	0.470578i	$-0.155955\pi$
$907$	42.5007	+	11.3880i	1.41121	+	0.378134i	0.528856	+	0.848712i	$0.322621\pi$
$908$		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	$-0.172754\pi$
$912$	3.20736	−	8.10634i	0.106206	−	0.268428i
$913$		0			0
$914$	19.0526	+	33.0000i	0.630203	+	1.09154i
$915$		0			0
$916$	10.0000	−	17.3205i	0.330409	−	0.572286i
$917$	6.72432	−	25.0955i	0.222056	−	0.828726i
$918$		0			0
$919$			46.0000i			1.51740i	0.651440	+	0.758700i	$0.274165\pi$
$919$			46.0000i			1.51740i	−0.651440	+	0.758700i	$0.725835\pi$
$920$		0			0
$921$	−20.0000	+	34.6410i	−0.659022	+	1.14146i
$922$	4.65874	+	17.3867i	0.153428	+	0.572599i
$923$	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
$927$	−1.81173	−	6.76148i	−0.0595051	−	0.222076i
$928$		0			0
$929$	−18.1865	+	10.5000i	−0.596681	+	0.344494i	−0.767735	−	0.640768i	$-0.778616\pi$
$929$	−18.1865	+	10.5000i	−0.596681	+	0.344494i	0.171054	+	0.985262i	$0.445283\pi$
$930$		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
$937$	36.8067	−	9.86233i	1.20242	−	0.322188i	0.398638	−	0.917108i	$-0.369483\pi$
$937$	36.8067	−	9.86233i	1.20242	−	0.322188i	0.803785	+	0.594920i	$0.202816\pi$
$938$	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
$947$	−10.7589	+	40.1528i	−0.349617	+	1.30479i	0.537507	+	0.843259i	$0.319366\pi$
$947$	−10.7589	+	40.1528i	−0.349617	+	1.30479i	−0.887124	+	0.461531i	$0.847300\pi$
$948$	6.69213	+	1.79315i	0.217350	+	0.0582388i
$949$	−6.92820			−0.224899
$950$		0			0
$951$	−54.0000			−1.75107
$952$		0			0
$953$	−9.31749	+	34.7733i	−0.301823	+	1.12642i	0.633823	+	0.773478i	$0.281485\pi$
$953$	−9.31749	+	34.7733i	−0.301823	+	1.12642i	−0.935646	+	0.352940i	$0.885182\pi$
$954$	−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
$963$	5.79555	−	1.55291i	0.186759	−	0.0500420i
$964$	−6.92820	−	12.0000i	−0.223142	−	0.386494i
$965$		0			0
$966$	−9.00000	−	15.5885i	−0.289570	−	0.501550i
$967$	−9.86233	+	36.8067i	−0.317151	+	1.18362i	0.604819	+	0.796363i	$0.293245\pi$
$967$	−9.86233	+	36.8067i	−0.317151	+	1.18362i	−0.921970	+	0.387261i	$0.873421\pi$
$968$	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	$0.280005\pi$
$972$	9.65926	+	2.58819i	0.309821	+	0.0830162i
$973$	−8.96575	−	33.4607i	−0.287429	−	1.07270i
$974$	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	0.0899242	−	0.995949i	$-0.471338\pi$
$977$	33.9411	−	33.9411i	1.08587	−	1.08587i	0.995949	−	0.0899242i	$-0.0286625\pi$
$978$	−12.5521	−	46.8449i	−0.401371	−	1.49794i
$979$	−7.79423	+	13.5000i	−0.249105	+	0.431462i
$980$		0			0
$981$		0			0
$982$	−5.43520	−	20.2844i	−0.173444	−	0.647303i
$983$	−5.43520	+	20.2844i	−0.173356	+	0.646973i	0.823470	+	0.567360i	$0.192035\pi$
$983$	−5.43520	+	20.2844i	−0.173356	+	0.646973i	−0.996826	+	0.0796132i	$0.974631\pi$
$984$	−5.19615	+	9.00000i	−0.165647	+	0.286910i
$985$		0			0
$986$		0			0
$987$	−25.4558	+	25.4558i	−0.810268	+	0.810268i
$988$	6.83083	−	5.41662i	0.217318	−	0.172326i
$989$			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	$0.368431\pi$
$992$	3.34607	−	0.896575i	0.106238	−	0.0284663i
$993$	36.8067	+	9.86233i	1.16803	+	0.312972i
$994$	−15.5885	−	9.00000i	−0.494436	−	0.285463i
$995$		0			0
$996$		0			0
$997$	−8.36516	+	2.24144i	−0.264927	+	0.0709871i	−0.388837	−	0.921306i	$-0.627123\pi$
$997$	−8.36516	+	2.24144i	−0.264927	+	0.0709871i	0.123910	+	0.992293i	$0.460457\pi$
$998$	6.76148	−	1.81173i	0.214031	−	0.0573494i
$999$		−	4.00000i		−	0.126554i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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