LMFDB - Embedded newform 950.2.q.b.293.2

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			293.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	950.293
Dual form			950.2.q.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.707107 - 0.707107i) q^{8} +(1.73205 - 1.00000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.707107 - 0.707107i) q^{8} +(1.73205 - 1.00000i) q^{9} -3.00000 q^{11} +(-0.707107 - 0.707107i) q^{12} +(1.93185 + 0.517638i) q^{13} +(0.500000 - 0.866025i) q^{16} +(-1.79315 - 6.69213i) q^{17} +(1.41421 - 1.41421i) q^{18} +(4.33013 - 0.500000i) q^{19} +(-2.89778 + 0.776457i) q^{22} +(0.896575 - 3.34607i) q^{23} +(-0.866025 - 0.500000i) q^{24} +2.00000 q^{26} +(-3.53553 - 3.53553i) q^{27} +(3.46410 + 6.00000i) q^{29} -3.46410i q^{31} +(0.258819 - 0.965926i) q^{32} +(0.776457 + 2.89778i) q^{33} +(-3.46410 - 6.00000i) q^{34} +(1.00000 - 1.73205i) q^{36} +(-1.41421 - 1.41421i) q^{37} +(4.05317 - 1.60368i) q^{38} -2.00000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(3.34607 - 0.896575i) q^{43} +(-2.59808 + 1.50000i) q^{44} -3.46410i q^{46} +(-6.69213 - 1.79315i) q^{47} +(-0.965926 - 0.258819i) q^{48} +7.00000i q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.93185 - 0.517638i) q^{52} +(-5.79555 - 1.55291i) q^{53} +(-4.33013 - 2.50000i) q^{54} +(-1.60368 - 4.05317i) q^{57} +(4.89898 + 4.89898i) q^{58} +(2.59808 - 4.50000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-0.896575 - 3.34607i) q^{62} -1.00000i q^{64} +(1.50000 + 2.59808i) q^{66} +(-0.258819 + 0.965926i) q^{67} +(-4.89898 - 4.89898i) q^{68} -3.46410 q^{69} +(-3.00000 - 1.73205i) q^{71} +(0.517638 - 1.93185i) q^{72} +(15.0573 - 4.03459i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(3.50000 - 2.59808i) q^{76} +(-0.517638 - 1.93185i) q^{78} +(-3.46410 + 6.00000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-1.67303 - 0.448288i) q^{82} +(1.22474 + 1.22474i) q^{83} +(3.00000 - 1.73205i) q^{86} +(4.89898 - 4.89898i) q^{87} +(-2.12132 + 2.12132i) q^{88} +(3.46410 + 6.00000i) q^{89} +(-0.896575 - 3.34607i) q^{92} +(-3.34607 + 0.896575i) q^{93} -6.92820 q^{94} -1.00000 q^{96} +(0.965926 - 0.258819i) q^{97} +(1.81173 + 6.76148i) q^{98} +(-5.19615 + 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{6}+O(q^{10}) $ 8 * q - 4 * q^6	$ 8 q - 4 q^{6} - 24 q^{11} + 4 q^{16} + 16 q^{26} + 8 q^{36} - 12 q^{41} - 48 q^{51} + 32 q^{61} + 12 q^{66} - 24 q^{71} + 28 q^{76} + 4 q^{81} + 24 q^{86} - 8 q^{96}+O(q^{100}) $ 8 * q - 4 * q^6 - 24 * q^11 + 4 * q^16 + 16 * q^26 + 8 * q^36 - 12 * q^41 - 48 * q^51 + 32 * q^61 + 12 * q^66 - 24 * q^71 + 28 * q^76 + 4 * q^81 + 24 * q^86 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i	−0.999518	−	0.0310384i	$-0.990119\pi$
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i	0.850089	−	0.526639i	$-0.176548\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.73205	−	1.00000i	0.577350	−	0.333333i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	1.93185	+	0.517638i	0.535799	+	0.143567i	0.516565	−	0.856248i	$-0.327210\pi$
$13$	1.93185	+	0.517638i	0.535799	+	0.143567i	0.0192343	+	0.999815i	$0.493877\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.79315	−	6.69213i	−0.434903	−	1.62308i	−0.741298	−	0.671176i	$-0.765790\pi$
$17$	−1.79315	−	6.69213i	−0.434903	−	1.62308i	0.306395	−	0.951904i	$-0.400877\pi$
$18$	1.41421	−	1.41421i	0.333333	−	0.333333i
$19$	4.33013	−	0.500000i	0.993399	−	0.114708i
$19$	4.33013	−	0.500000i	0.993399	−	0.114708i
$20$		0			0
$21$		0			0
$22$	−2.89778	+	0.776457i	−0.617808	+	0.165541i
$23$	0.896575	−	3.34607i	0.186949	−	0.697703i	−0.807256	−	0.590201i	$-0.799048\pi$
$23$	0.896575	−	3.34607i	0.186949	−	0.697703i	0.994205	−	0.107501i	$-0.0342850\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	2.00000			0.392232
$27$	−3.53553	−	3.53553i	−0.680414	−	0.680414i
$28$		0			0
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	0.984699	+	0.174265i	$0.0557550\pi$
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	−0.341431	+	0.939907i	$0.610912\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	0.776457	+	2.89778i	0.135164	+	0.504438i
$34$	−3.46410	−	6.00000i	−0.594089	−	1.02899i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	0.581238	−	0.813733i	$-0.302568\pi$
$37$	−1.41421	−	1.41421i	−0.232495	−	0.232495i	−0.813733	+	0.581238i	$0.802568\pi$
$38$	4.05317	−	1.60368i	0.657511	−	0.260152i
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$		0			0
$43$	3.34607	−	0.896575i	0.510270	−	0.136726i	0.00550783	−	0.999985i	$-0.498247\pi$
$43$	3.34607	−	0.896575i	0.510270	−	0.136726i	0.504762	+	0.863258i	$0.331580\pi$
$44$	−2.59808	+	1.50000i	−0.391675	+	0.226134i
$45$		0			0
$46$		−	3.46410i		−	0.510754i
$47$	−6.69213	−	1.79315i	−0.976148	−	0.261558i	−0.264726	−	0.964324i	$-0.585282\pi$
$47$	−6.69213	−	1.79315i	−0.976148	−	0.261558i	−0.711421	+	0.702766i	$0.751948\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$			7.00000i			1.00000i
$50$		0			0
$51$	−6.00000	+	3.46410i	−0.840168	+	0.485071i
$52$	1.93185	−	0.517638i	0.267900	−	0.0717835i
$53$	−5.79555	−	1.55291i	−0.796081	−	0.213309i	−0.162218	−	0.986755i	$-0.551865\pi$
$53$	−5.79555	−	1.55291i	−0.796081	−	0.213309i	−0.633863	+	0.773446i	$0.718532\pi$
$54$	−4.33013	−	2.50000i	−0.589256	−	0.340207i
$55$		0			0
$56$		0			0
$57$	−1.60368	−	4.05317i	−0.212413	−	0.536856i
$58$	4.89898	+	4.89898i	0.643268	+	0.643268i
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	−0.645861	−	0.763455i	$-0.723502\pi$
$59$	2.59808	−	4.50000i	0.338241	−	0.585850i	0.984102	+	0.177605i	$0.0568349\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	−0.896575	−	3.34607i	−0.113865	−	0.424951i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−0.258819	+	0.965926i	−0.0316198	+	0.118007i	−0.979932	−	0.199332i	$-0.936123\pi$
$67$	−0.258819	+	0.965926i	−0.0316198	+	0.118007i	0.948312	+	0.317339i	$0.102789\pi$
$68$	−4.89898	−	4.89898i	−0.594089	−	0.594089i
$69$	−3.46410			−0.417029
$70$		0			0
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	0.311305	−	0.950310i	$-0.399234\pi$
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	−0.667340	+	0.744753i	$0.732567\pi$
$72$	0.517638	−	1.93185i	0.0610042	−	0.227671i
$73$	15.0573	−	4.03459i	1.76232	−	0.472213i	0.775138	−	0.631792i	$-0.217680\pi$
$73$	15.0573	−	4.03459i	1.76232	−	0.472213i	0.987185	+	0.159579i	$0.0510137\pi$
$74$	−1.73205	−	1.00000i	−0.201347	−	0.116248i
$75$		0			0
$76$	3.50000	−	2.59808i	0.401478	−	0.298020i
$77$		0			0
$78$	−0.517638	−	1.93185i	−0.0586110	−	0.218739i
$79$	−3.46410	+	6.00000i	−0.389742	+	0.675053i	−0.992415	−	0.122936i	$-0.960769\pi$
$79$	−3.46410	+	6.00000i	−0.389742	+	0.675053i	0.602673	+	0.797988i	$0.294102\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.67303	−	0.448288i	−0.184756	−	0.0495051i
$83$	1.22474	+	1.22474i	0.134433	+	0.134433i	0.771121	−	0.636688i	$-0.219696\pi$
$83$	1.22474	+	1.22474i	0.134433	+	0.134433i	−0.636688	+	0.771121i	$0.719696\pi$
$84$		0			0
$85$		0			0
$86$	3.00000	−	1.73205i	0.323498	−	0.186772i
$87$	4.89898	−	4.89898i	0.525226	−	0.525226i
$88$	−2.12132	+	2.12132i	−0.226134	+	0.226134i
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	0.989126	−	0.147073i	$-0.0469852\pi$
$89$	3.46410	+	6.00000i	0.367194	+	0.635999i	−0.621932	+	0.783072i	$0.713652\pi$
$90$		0			0
$91$		0			0
$92$	−0.896575	−	3.34607i	−0.0934745	−	0.348851i
$93$	−3.34607	+	0.896575i	−0.346971	+	0.0929705i
$94$	−6.92820			−0.714590
$95$		0			0
$96$	−1.00000			−0.102062
$97$	0.965926	−	0.258819i	0.0980749	−	0.0262791i	−0.209448	−	0.977820i	$-0.567167\pi$
$97$	0.965926	−	0.258819i	0.0980749	−	0.0262791i	0.307523	+	0.951541i	$0.400500\pi$
$98$	1.81173	+	6.76148i	0.183013	+	0.683013i
$99$	−5.19615	+	3.00000i	−0.522233	+	0.301511i
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	−4.89898	+	4.89898i	−0.485071	+	0.485071i
$103$	−7.07107	+	7.07107i	−0.696733	+	0.696733i	−0.963704	−	0.266971i	$-0.913977\pi$
$103$	−7.07107	+	7.07107i	−0.696733	+	0.696733i	0.266971	+	0.963704i	$0.413977\pi$
$104$	1.73205	−	1.00000i	0.169842	−	0.0980581i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	−4.82963	−	1.29410i	−0.464731	−	0.124524i
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$		0			0
$111$	−1.00000	+	1.73205i	−0.0949158	+	0.164399i
$112$		0			0
$113$	6.36396	−	6.36396i	0.598671	−	0.598671i	−0.341288	−	0.939959i	$-0.610863\pi$
$113$	6.36396	−	6.36396i	0.598671	−	0.598671i	0.939959	+	0.341288i	$0.110863\pi$
$114$	−2.59808	−	3.50000i	−0.243332	−	0.327805i
$115$		0			0
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$	3.86370	−	1.03528i	0.357199	−	0.0957113i
$118$	1.34486	−	5.01910i	0.123805	−	0.462045i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	5.65685	+	5.65685i	0.512148	+	0.512148i
$123$	−0.448288	+	1.67303i	−0.0404207	+	0.150852i
$124$	−1.73205	−	3.00000i	−0.155543	−	0.269408i
$125$		0			0
$126$		0			0
$127$	−5.69402	+	21.2504i	−0.505262	+	1.88567i	−0.0426804	+	0.999089i	$0.513590\pi$
$127$	−5.69402	+	21.2504i	−0.505262	+	1.88567i	−0.462582	+	0.886576i	$0.653077\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−1.73205	−	3.00000i	−0.152499	−	0.264135i
$130$		0			0
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$	2.12132	+	2.12132i	0.184637	+	0.184637i
$133$		0			0
$134$			1.00000i			0.0863868i
$135$		0			0
$136$	−6.00000	−	3.46410i	−0.514496	−	0.297044i
$137$	15.0573	+	4.03459i	1.28643	+	0.344698i	0.836304	−	0.548266i	$-0.184712\pi$
$137$	15.0573	+	4.03459i	1.28643	+	0.344698i	0.450127	+	0.892964i	$0.351379\pi$
$138$	−3.34607	+	0.896575i	−0.284836	+	0.0763216i
$139$	4.33013	−	2.50000i	0.367277	−	0.212047i	−0.304991	−	0.952355i	$-0.598654\pi$
$139$	4.33013	−	2.50000i	0.367277	−	0.212047i	0.672268	+	0.740308i	$0.265320\pi$
$140$		0			0
$141$			6.92820i			0.583460i
$142$	−3.34607	−	0.896575i	−0.280796	−	0.0752389i
$143$	−5.79555	−	1.55291i	−0.484649	−	0.129861i
$144$		−	2.00000i		−	0.166667i
$145$		0			0
$146$	13.5000	−	7.79423i	1.11727	−	0.645055i
$147$	6.76148	−	1.81173i	0.557678	−	0.149429i
$148$	−1.93185	−	0.517638i	−0.158797	−	0.0425496i
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.976306	−	0.216394i	$-0.0694297\pi$
$149$	15.5885	+	9.00000i	1.27706	+	0.737309i	0.300750	+	0.953703i	$0.402763\pi$
$150$		0			0
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$	2.70831	−	3.41542i	0.219673	−	0.277027i
$153$	−9.79796	−	9.79796i	−0.792118	−	0.792118i
$154$		0			0
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	1.79315	+	6.69213i	0.143109	+	0.534090i	0.999832	+	0.0183138i	$0.00582979\pi$
$157$	1.79315	+	6.69213i	0.143109	+	0.534090i	−0.856723	+	0.515776i	$0.827504\pi$
$158$	−1.79315	+	6.69213i	−0.142655	+	0.532397i
$159$			6.00000i			0.475831i
$160$		0			0
$161$		0			0
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−8.57321	−	8.57321i	−0.671506	−	0.671506i	0.286557	−	0.958063i	$-0.407489\pi$
$163$	−8.57321	−	8.57321i	−0.671506	−	0.671506i	−0.958063	+	0.286557i	$0.907489\pi$
$164$	−1.73205			−0.135250
$165$		0			0
$166$	1.50000	+	0.866025i	0.116423	+	0.0672166i
$167$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$167$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$168$		0			0
$169$	−7.79423	−	4.50000i	−0.599556	−	0.346154i
$170$		0			0
$171$	7.00000	−	5.19615i	0.535303	−	0.397360i
$172$	2.44949	−	2.44949i	0.186772	−	0.186772i
$173$	1.55291	+	5.79555i	0.118066	+	0.440628i	0.999498	−	0.0316829i	$-0.0100867\pi$
$173$	1.55291	+	5.79555i	0.118066	+	0.440628i	−0.881432	+	0.472311i	$0.843420\pi$
$174$	3.46410	−	6.00000i	0.262613	−	0.454859i
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	−5.01910	−	1.34486i	−0.377258	−	0.101086i
$178$	4.89898	+	4.89898i	0.367194	+	0.367194i
$179$	22.5167			1.68297			0.841487	−	0.540277i	$-0.181681\pi$
$179$	22.5167			1.68297			0.841487	+	0.540277i	$0.181681\pi$
$180$		0			0
$181$	21.0000	−	12.1244i	1.56092	−	0.901196i	0.563753	−	0.825943i	$-0.309357\pi$
$181$	21.0000	−	12.1244i	1.56092	−	0.901196i	0.997164	−	0.0752530i	$-0.0239764\pi$
$182$		0			0
$183$	5.65685	−	5.65685i	0.418167	−	0.418167i
$184$	−1.73205	−	3.00000i	−0.127688	−	0.221163i
$185$		0			0
$186$	−3.00000	+	1.73205i	−0.219971	+	0.127000i
$187$	5.37945	+	20.0764i	0.393385	+	1.46813i
$188$	−6.69213	+	1.79315i	−0.488074	+	0.130779i
$189$		0			0
$190$		0			0
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	5.69402	+	21.2504i	0.409864	+	1.52963i	0.794904	+	0.606735i	$0.207521\pi$
$193$	5.69402	+	21.2504i	0.409864	+	1.52963i	−0.385040	+	0.922900i	$0.625812\pi$
$194$	0.866025	−	0.500000i	0.0621770	−	0.0358979i
$195$		0			0
$196$	3.50000	+	6.06218i	0.250000	+	0.433013i
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	−0.918644	−	0.395087i	$-0.870714\pi$
$197$	−7.34847	+	7.34847i	−0.523557	+	0.523557i	0.395087	+	0.918644i	$0.370714\pi$
$198$	−4.24264	+	4.24264i	−0.301511	+	0.301511i
$199$	12.1244	−	7.00000i	0.859473	−	0.496217i	−0.00436292	−	0.999990i	$-0.501389\pi$
$199$	12.1244	−	7.00000i	0.859473	−	0.496217i	0.863836	+	0.503774i	$0.168055\pi$
$200$		0			0
$201$	1.00000			0.0705346
$202$	8.48528	+	8.48528i	0.597022	+	0.597022i
$203$		0			0
$204$	−3.46410	+	6.00000i	−0.242536	+	0.420084i
$205$		0			0
$206$	−5.00000	+	8.66025i	−0.348367	+	0.603388i
$207$	−1.79315	−	6.69213i	−0.124633	−	0.465135i
$208$	1.41421	−	1.41421i	0.0980581	−	0.0980581i
$209$	−12.9904	+	1.50000i	−0.898563	+	0.103757i
$210$		0			0
$211$	−9.00000	−	5.19615i	−0.619586	−	0.357718i	0.157122	−	0.987579i	$-0.449778\pi$
$211$	−9.00000	−	5.19615i	−0.619586	−	0.357718i	−0.776708	+	0.629861i	$0.783112\pi$
$212$	−5.79555	+	1.55291i	−0.398040	+	0.106655i
$213$	−0.896575	+	3.34607i	−0.0614323	+	0.229269i
$214$		0			0
$215$		0			0
$216$	−5.00000			−0.340207
$217$		0			0
$218$		0			0
$219$	−7.79423	−	13.5000i	−0.526685	−	0.912245i
$220$		0			0
$221$		−	13.8564i		−	0.932083i
$222$	−0.517638	+	1.93185i	−0.0347416	+	0.129657i
$223$	6.72930	+	25.1141i	0.450627	+	1.68176i	0.700636	+	0.713519i	$0.252900\pi$
$223$	6.72930	+	25.1141i	0.450627	+	1.68176i	−0.250009	+	0.968244i	$0.580434\pi$
$224$		0			0
$225$		0			0
$226$	4.50000	−	7.79423i	0.299336	−	0.518464i
$227$	14.8492	+	14.8492i	0.985579	+	0.985579i	0.999897	−	0.0143186i	$-0.00455792\pi$
$227$	14.8492	+	14.8492i	0.985579	+	0.985579i	−0.0143186	+	0.999897i	$0.504558\pi$
$228$	−3.41542	−	2.70831i	−0.226191	−	0.179362i
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	6.69213	+	1.79315i	0.439360	+	0.117726i
$233$	−21.7494	+	5.82774i	−1.42485	+	0.381788i	−0.887202	−	0.461380i	$-0.847354\pi$
$233$	−21.7494	+	5.82774i	−1.42485	+	0.381788i	−0.537650	+	0.843168i	$0.680688\pi$
$234$	3.46410	−	2.00000i	0.226455	−	0.130744i
$235$		0			0
$236$		−	5.19615i		−	0.338241i
$237$	6.69213	+	1.79315i	0.434701	+	0.116478i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	−0.637883	−	0.770133i	$-0.720190\pi$
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	0.348013	+	0.937490i	$0.386857\pi$
$242$	−1.93185	+	0.517638i	−0.124184	+	0.0332750i
$243$	−15.4548	−	4.14110i	−0.991427	−	0.265652i
$244$	6.92820	+	4.00000i	0.443533	+	0.256074i
$245$		0			0
$246$			1.73205i			0.110432i
$247$	8.62398	+	1.27551i	0.548731	+	0.0811589i
$248$	−2.44949	−	2.44949i	−0.155543	−	0.155543i
$249$	0.866025	−	1.50000i	0.0548821	−	0.0950586i
$250$		0			0
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	−0.979889	−	0.199543i	$-0.936054\pi$
$251$	−10.5000	−	18.1865i	−0.662754	−	1.14792i	0.317135	−	0.948380i	$-0.397279\pi$
$252$		0			0
$253$	−2.68973	+	10.0382i	−0.169102	+	0.631096i
$254$			22.0000i			1.38040i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.776457	+	2.89778i	−0.0484341	+	0.180758i	−0.985905	−	0.167304i	$-0.946494\pi$
$257$	−0.776457	+	2.89778i	−0.0484341	+	0.180758i	0.937471	+	0.348063i	$0.113160\pi$
$258$	−2.44949	−	2.44949i	−0.152499	−	0.152499i
$259$		0			0
$260$		0			0
$261$	12.0000	+	6.92820i	0.742781	+	0.428845i
$262$	−3.88229	+	14.4889i	−0.239848	+	0.895126i
$263$	−6.69213	+	1.79315i	−0.412654	+	0.110570i	−0.459173	−	0.888347i	$-0.651854\pi$
$263$	−6.69213	+	1.79315i	−0.412654	+	0.110570i	0.0465183	+	0.998917i	$0.485187\pi$
$264$	2.59808	+	1.50000i	0.159901	+	0.0923186i
$265$		0			0
$266$		0			0
$267$	4.89898	−	4.89898i	0.299813	−	0.299813i
$268$	0.258819	+	0.965926i	0.0158099	+	0.0590033i
$269$	−3.46410	+	6.00000i	−0.211210	+	0.365826i	−0.952093	−	0.305807i	$-0.901074\pi$
$269$	−3.46410	+	6.00000i	−0.211210	+	0.365826i	0.740883	+	0.671634i	$0.234407\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−6.69213	−	1.79315i	−0.405770	−	0.108726i
$273$		0			0
$274$	15.5885			0.941733
$275$		0			0
$276$	−3.00000	+	1.73205i	−0.180579	+	0.104257i
$277$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$277$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$278$	3.53553	−	3.53553i	0.212047	−	0.212047i
$279$	−3.46410	−	6.00000i	−0.207390	−	0.359211i
$280$		0			0
$281$	19.5000	−	11.2583i	1.16327	−	0.671616i	0.211186	−	0.977446i	$-0.432267\pi$
$281$	19.5000	−	11.2583i	1.16327	−	0.671616i	0.952086	+	0.305830i	$0.0989340\pi$
$282$	1.79315	+	6.69213i	0.106781	+	0.398511i
$283$	15.0573	−	4.03459i	0.895063	−	0.239831i	0.218168	−	0.975911i	$-0.429992\pi$
$283$	15.0573	−	4.03459i	0.895063	−	0.239831i	0.676895	+	0.736080i	$0.263325\pi$
$284$	−3.46410			−0.205557
$285$		0			0
$286$	−6.00000			−0.354787
$287$		0			0
$288$	−0.517638	−	1.93185i	−0.0305021	−	0.113835i
$289$	−26.8468	+	15.5000i	−1.57922	+	0.911765i
$290$		0			0
$291$	−0.500000	−	0.866025i	−0.0293105	−	0.0507673i
$292$	11.0227	−	11.0227i	0.645055	−	0.645055i
$293$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$293$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$294$	6.06218	−	3.50000i	0.353553	−	0.204124i
$295$		0			0
$296$	−2.00000			−0.116248
$297$	10.6066	+	10.6066i	0.615457	+	0.615457i
$298$	17.3867	+	4.65874i	1.00718	+	0.269874i
$299$	3.46410	−	6.00000i	0.200334	−	0.346989i
$300$		0			0
$301$		0			0
$302$	0.896575	+	3.34607i	0.0515921	+	0.192544i
$303$	8.48528	−	8.48528i	0.487467	−	0.487467i
$304$	1.73205	−	4.00000i	0.0993399	−	0.229416i
$305$		0			0
$306$	−12.0000	−	6.92820i	−0.685994	−	0.396059i
$307$	−22.2163	+	5.95284i	−1.26795	+	0.339746i	−0.829245	−	0.558885i	$-0.811229\pi$
$307$	−22.2163	+	5.95284i	−1.26795	+	0.339746i	−0.438705	+	0.898631i	$0.644563\pi$
$308$		0			0
$309$	8.66025	+	5.00000i	0.492665	+	0.284440i
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$	−1.41421	−	1.41421i	−0.0800641	−	0.0800641i
$313$	−2.24144	+	8.36516i	−0.126694	+	0.472827i	−0.999894	−	0.0145337i	$-0.995374\pi$
$313$	−2.24144	+	8.36516i	−0.126694	+	0.472827i	0.873201	+	0.487361i	$0.162040\pi$
$314$	3.46410	+	6.00000i	0.195491	+	0.338600i
$315$		0			0
$316$			6.92820i			0.389742i
$317$	4.65874	−	17.3867i	0.261661	−	0.976532i	−0.702601	−	0.711584i	$-0.747978\pi$
$317$	4.65874	−	17.3867i	0.261661	−	0.976532i	0.964262	−	0.264949i	$-0.0853551\pi$
$318$	1.55291	+	5.79555i	0.0870831	+	0.324999i
$319$	−10.3923	−	18.0000i	−0.581857	−	1.00781i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.1106	−	28.0812i	−0.618212	−	1.56248i
$324$		−	1.00000i		−	0.0555556i
$325$		0			0
$326$	−10.5000	−	6.06218i	−0.581541	−	0.335753i
$327$		0			0
$328$	−1.67303	+	0.448288i	−0.0923778	+	0.0247525i
$329$		0			0
$330$		0			0
$331$			12.1244i			0.666415i	0.942854	+	0.333207i	$0.108131\pi$
$331$			12.1244i			0.666415i	−0.942854	+	0.333207i	$0.891869\pi$
$332$	1.67303	+	0.448288i	0.0918196	+	0.0246030i
$333$	−3.86370	−	1.03528i	−0.211730	−	0.0567328i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.5570	+	3.36465i	−0.684025	+	0.183284i	−0.584064	−	0.811707i	$-0.698538\pi$
$337$	−12.5570	+	3.36465i	−0.684025	+	0.183284i	−0.0999609	+	0.994991i	$0.531872\pi$
$338$	−8.69333	−	2.32937i	−0.472855	−	0.126701i
$339$	−7.79423	−	4.50000i	−0.423324	−	0.244406i
$340$		0			0
$341$			10.3923i			0.562775i
$342$	5.41662	−	6.83083i	0.292897	−	0.369369i
$343$		0			0
$344$	1.73205	−	3.00000i	0.0933859	−	0.161749i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−8.51747	−	31.7876i	−0.457242	−	1.70645i	−0.681413	−	0.731899i	$-0.738634\pi$
$347$	−8.51747	−	31.7876i	−0.457242	−	1.70645i	0.224171	−	0.974550i	$-0.428032\pi$
$348$	1.79315	−	6.69213i	0.0961230	−	0.358736i
$349$			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
$351$	−5.00000	−	8.66025i	−0.266880	−	0.462250i
$352$	−0.776457	+	2.89778i	−0.0413853	+	0.154452i
$353$	−25.7196	−	25.7196i	−1.36892	−	1.36892i	−0.861985	−	0.506933i	$-0.830779\pi$
$353$	−25.7196	−	25.7196i	−1.36892	−	1.36892i	−0.506933	−	0.861985i	$-0.669221\pi$
$354$	−5.19615			−0.276172
$355$		0			0
$356$	6.00000	+	3.46410i	0.317999	+	0.183597i
$357$		0			0
$358$	21.7494	−	5.82774i	1.14949	−	0.308006i
$359$	−25.9808	−	15.0000i	−1.37121	−	0.791670i	−0.380131	−	0.924932i	$-0.624121\pi$
$359$	−25.9808	−	15.0000i	−1.37121	−	0.791670i	−0.991081	+	0.133263i	$0.957455\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	17.1464	−	17.1464i	0.901196	−	0.901196i
$363$	0.517638	+	1.93185i	0.0271690	+	0.101396i
$364$		0			0
$365$		0			0
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	−16.7303	−	4.48288i	−0.873316	−	0.234004i	−0.205795	−	0.978595i	$-0.565978\pi$
$367$	−16.7303	−	4.48288i	−0.873316	−	0.234004i	−0.667521	+	0.744591i	$0.732645\pi$
$368$	−2.44949	−	2.44949i	−0.127688	−	0.127688i
$369$	−3.46410			−0.180334
$370$		0			0
$371$		0			0
$372$	−2.44949	+	2.44949i	−0.127000	+	0.127000i
$373$	22.6274	−	22.6274i	1.17160	−	1.17160i	0.189776	−	0.981827i	$-0.439224\pi$
$373$	22.6274	−	22.6274i	1.17160	−	1.17160i	0.981827	−	0.189776i	$-0.0607761\pi$
$374$	10.3923	+	18.0000i	0.537373	+	0.930758i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	3.58630	+	13.3843i	0.184704	+	0.689325i
$378$		0			0
$379$	−10.3923			−0.533817			−0.266908	−	0.963722i	$-0.586002\pi$
$379$	−10.3923			−0.533817			−0.266908	+	0.963722i	$0.586002\pi$
$380$		0			0
$381$	22.0000			1.12709
$382$	−23.1822	+	6.21166i	−1.18611	+	0.317816i
$383$	9.31749	+	34.7733i	0.476101	+	1.77683i	0.617165	+	0.786834i	$0.288281\pi$
$383$	9.31749	+	34.7733i	0.476101	+	1.77683i	−0.141064	+	0.990000i	$0.545052\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	11.0000	+	19.0526i	0.559885	+	0.969750i
$387$	4.89898	−	4.89898i	0.249029	−	0.249029i
$388$	0.707107	−	0.707107i	0.0358979	−	0.0358979i
$389$	20.7846	−	12.0000i	1.05382	−	0.608424i	0.130105	−	0.991500i	$-0.458469\pi$
$389$	20.7846	−	12.0000i	1.05382	−	0.608424i	0.923717	+	0.383076i	$0.125135\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$	14.4889	+	3.88229i	0.730868	+	0.195835i
$394$	−5.19615	+	9.00000i	−0.261778	+	0.453413i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−4.48288	−	16.7303i	−0.224989	−	0.839671i	−0.982409	−	0.186743i	$-0.940207\pi$
$397$	−4.48288	−	16.7303i	−0.224989	−	0.839671i	0.757420	−	0.652928i	$-0.226460\pi$
$398$	9.89949	−	9.89949i	0.496217	−	0.496217i
$399$		0			0
$400$		0			0
$401$	7.50000	+	4.33013i	0.374532	+	0.216236i	0.675437	−	0.737418i	$-0.263955\pi$
$401$	7.50000	+	4.33013i	0.374532	+	0.216236i	−0.300904	+	0.953654i	$0.597289\pi$
$402$	0.965926	−	0.258819i	0.0481760	−	0.0129087i
$403$	1.79315	−	6.69213i	0.0893232	−	0.333359i
$404$	10.3923	+	6.00000i	0.517036	+	0.298511i
$405$		0			0
$406$		0			0
$407$	4.24264	+	4.24264i	0.210300	+	0.210300i
$408$	−1.79315	+	6.69213i	−0.0887742	+	0.331310i
$409$	9.52628	+	16.5000i	0.471044	+	0.815872i	0.999451	−	0.0331186i	$-0.0105439\pi$
$409$	9.52628	+	16.5000i	0.471044	+	0.815872i	−0.528407	+	0.848991i	$0.677211\pi$
$410$		0			0
$411$		−	15.5885i		−	0.768922i
$412$	−2.58819	+	9.65926i	−0.127511	+	0.475877i
$413$		0			0
$414$	−3.46410	−	6.00000i	−0.170251	−	0.294884i
$415$		0			0
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−3.53553	−	3.53553i	−0.173136	−	0.173136i
$418$	−12.1595	+	4.81105i	−0.594741	+	0.235316i
$419$		−	12.0000i		−	0.586238i	−0.956076	−	0.293119i	$-0.905307\pi$
$419$		−	12.0000i		−	0.586238i	0.956076	−	0.293119i	$-0.0946933\pi$
$420$		0			0
$421$	21.0000	+	12.1244i	1.02348	+	0.590905i	0.915109	−	0.403206i	$-0.132104\pi$
$421$	21.0000	+	12.1244i	1.02348	+	0.590905i	0.108368	+	0.994111i	$0.465437\pi$
$422$	−10.0382	−	2.68973i	−0.488652	−	0.130934i
$423$	−13.3843	+	3.58630i	−0.650765	+	0.174372i
$424$	−5.19615	+	3.00000i	−0.252347	+	0.145693i
$425$		0			0
$426$			3.46410i			0.167836i
$427$		0			0
$428$		0			0
$429$			6.00000i			0.289683i
$430$		0			0
$431$	−3.00000	+	1.73205i	−0.144505	+	0.0834300i	−0.570509	−	0.821291i	$-0.693254\pi$
$431$	−3.00000	+	1.73205i	−0.144505	+	0.0834300i	0.426004	+	0.904721i	$0.359921\pi$
$432$	−4.82963	+	1.29410i	−0.232366	+	0.0622622i
$433$	25.1141	+	6.72930i	1.20691	+	0.323389i	0.805547	−	0.592532i	$-0.201872\pi$
$433$	25.1141	+	6.72930i	1.20691	+	0.323389i	0.401358	+	0.915921i	$0.368538\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.20925	−	14.9372i	0.105683	−	0.714542i
$438$	−11.0227	−	11.0227i	−0.526685	−	0.526685i
$439$	12.1244	−	21.0000i	0.578664	−	1.00228i	−0.416969	−	0.908921i	$-0.636908\pi$
$439$	12.1244	−	21.0000i	0.578664	−	1.00228i	0.995633	−	0.0933546i	$-0.0297590\pi$
$440$		0			0
$441$	7.00000	+	12.1244i	0.333333	+	0.577350i
$442$	−3.58630	−	13.3843i	−0.170583	−	0.636624i
$443$	−5.82774	+	21.7494i	−0.276884	+	1.03335i	0.677684	+	0.735353i	$0.262984\pi$
$443$	−5.82774	+	21.7494i	−0.276884	+	1.03335i	−0.954568	+	0.297993i	$0.903683\pi$
$444$			2.00000i			0.0949158i
$445$		0			0
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$	4.65874	−	17.3867i	0.220351	−	0.822361i
$448$		0			0
$449$	−25.9808			−1.22611			−0.613054	−	0.790041i	$-0.710059\pi$
$449$	−25.9808			−1.22611			−0.613054	+	0.790041i	$0.710059\pi$
$450$		0			0
$451$	4.50000	+	2.59808i	0.211897	+	0.122339i
$452$	2.32937	−	8.69333i	0.109564	−	0.408900i
$453$	3.34607	−	0.896575i	0.157212	−	0.0421248i
$454$	18.1865	+	10.5000i	0.853536	+	0.492789i
$455$		0			0
$456$	−4.00000	−	1.73205i	−0.187317	−	0.0811107i
$457$	−13.4722	+	13.4722i	−0.630203	+	0.630203i	−0.948119	−	0.317916i	$-0.897017\pi$
$457$	−13.4722	+	13.4722i	−0.630203	+	0.630203i	0.317916	+	0.948119i	$0.397017\pi$
$458$	−1.03528	−	3.86370i	−0.0483753	−	0.180539i
$459$	−17.3205	+	30.0000i	−0.808452	+	1.40028i
$460$		0			0
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	17.1464	+	17.1464i	0.796862	+	0.796862i	0.982599	−	0.185737i	$-0.0594674\pi$
$463$	17.1464	+	17.1464i	0.796862	+	0.796862i	−0.185737	+	0.982599i	$0.559467\pi$
$464$	6.92820			0.321634
$465$		0			0
$466$	−19.5000	+	11.2583i	−0.903320	+	0.521532i
$467$	18.3712	−	18.3712i	0.850117	−	0.850117i	−0.140031	−	0.990147i	$-0.544720\pi$
$467$	18.3712	−	18.3712i	0.850117	−	0.850117i	0.990147	+	0.140031i	$0.0447201\pi$
$468$	2.82843	−	2.82843i	0.130744	−	0.130744i
$469$		0			0
$470$		0			0
$471$	6.00000	−	3.46410i	0.276465	−	0.159617i
$472$	−1.34486	−	5.01910i	−0.0619023	−	0.231023i
$473$	−10.0382	+	2.68973i	−0.461557	+	0.123674i
$474$	6.92820			0.318223
$475$		0			0
$476$		0			0
$477$	−11.5911	+	3.10583i	−0.530720	+	0.142206i
$478$		0			0
$479$	20.7846	−	12.0000i	0.949673	−	0.548294i	0.0566937	−	0.998392i	$-0.481944\pi$
$479$	20.7846	−	12.0000i	0.949673	−	0.548294i	0.892979	+	0.450098i	$0.148611\pi$
$480$		0			0
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	−3.67423	+	3.67423i	−0.167357	+	0.167357i
$483$		0			0
$484$	−1.73205	+	1.00000i	−0.0787296	+	0.0454545i
$485$		0			0
$486$	−16.0000			−0.725775
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.968471	−	0.249128i	$-0.919856\pi$
$487$	−26.8701	−	26.8701i	−1.21760	−	1.21760i	−0.249128	−	0.968471i	$-0.580144\pi$
$488$	7.72741	+	2.07055i	0.349803	+	0.0937295i
$489$	−6.06218	+	10.5000i	−0.274141	+	0.474826i
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	0.448288	+	1.67303i	0.0202104	+	0.0754261i
$493$	33.9411	−	33.9411i	1.52863	−	1.52863i
$494$	8.66025	−	1.00000i	0.389643	−	0.0449921i
$495$		0			0
$496$	−3.00000	−	1.73205i	−0.134704	−	0.0777714i
$497$		0			0
$498$	0.448288	−	1.67303i	0.0200883	−	0.0749704i
$499$	−26.8468	−	15.5000i	−1.20183	−	0.693875i	−0.240866	−	0.970558i	$-0.577431\pi$
$499$	−26.8468	−	15.5000i	−1.20183	−	0.693875i	−0.960961	+	0.276683i	$0.910765\pi$
$500$		0			0
$501$		0			0
$502$	−14.8492	−	14.8492i	−0.662754	−	0.662754i
$503$	8.06918	−	30.1146i	0.359787	−	1.34274i	−0.514565	−	0.857451i	$-0.672047\pi$
$503$	8.06918	−	30.1146i	0.359787	−	1.34274i	0.874352	−	0.485292i	$-0.161287\pi$
$504$		0			0
$505$		0			0
$506$			10.3923i			0.461994i
$507$	−2.32937	+	8.69333i	−0.103451	+	0.386084i
$508$	5.69402	+	21.2504i	0.252631	+	0.942833i
$509$	−13.8564	−	24.0000i	−0.614174	−	1.06378i	−0.990529	−	0.137305i	$-0.956156\pi$
$509$	−13.8564	−	24.0000i	−0.614174	−	1.06378i	0.376354	−	0.926476i	$-0.377178\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−17.0771	−	13.5415i	−0.753971	−	0.597874i
$514$			3.00000i			0.132324i
$515$		0			0
$516$	−3.00000	−	1.73205i	−0.132068	−	0.0762493i
$517$	20.0764	+	5.37945i	0.882959	+	0.236588i
$518$		0			0
$519$	5.19615	−	3.00000i	0.228086	−	0.131685i
$520$		0			0
$521$		−	25.9808i		−	1.13824i	−0.822255	−	0.569119i	$-0.807284\pi$
$521$		−	25.9808i		−	1.13824i	0.822255	−	0.569119i	$-0.192716\pi$
$522$	13.3843	+	3.58630i	0.585813	+	0.156968i
$523$	19.3185	+	5.17638i	0.844740	+	0.226347i	0.655134	−	0.755513i	$-0.272612\pi$
$523$	19.3185	+	5.17638i	0.844740	+	0.226347i	0.189606	+	0.981860i	$0.439279\pi$
$524$			15.0000i			0.655278i
$525$		0			0
$526$	−6.00000	+	3.46410i	−0.261612	+	0.151042i
$527$	−23.1822	+	6.21166i	−1.00983	+	0.270584i
$528$	2.89778	+	0.776457i	0.126110	+	0.0337910i
$529$	9.52628	+	5.50000i	0.414186	+	0.239130i
$530$		0			0
$531$		−	10.3923i		−	0.450988i
$532$		0			0
$533$	−2.44949	−	2.44949i	−0.106099	−	0.106099i
$534$	3.46410	−	6.00000i	0.149906	−	0.259645i
$535$		0			0
$536$	0.500000	+	0.866025i	0.0215967	+	0.0374066i
$537$	−5.82774	−	21.7494i	−0.251486	−	0.938557i
$538$	−1.79315	+	6.69213i	−0.0773082	+	0.288518i
$539$		−	21.0000i		−	0.904534i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	4.14110	−	15.4548i	0.177876	−	0.663841i
$543$	−17.1464	−	17.1464i	−0.735824	−	0.735824i
$544$	−6.92820			−0.297044
$545$		0			0
$546$		0			0
$547$	7.24693	−	27.0459i	0.309856	−	1.15640i	−0.618827	−	0.785527i	$-0.712392\pi$
$547$	7.24693	−	27.0459i	0.309856	−	1.15640i	0.928684	−	0.370873i	$-0.120941\pi$
$548$	15.0573	−	4.03459i	0.643216	−	0.172349i
$549$	13.8564	+	8.00000i	0.591377	+	0.341432i
$550$		0			0
$551$	18.0000	+	24.2487i	0.766826	+	1.03303i
$552$	−2.44949	+	2.44949i	−0.104257	+	0.104257i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−33.4607	−	8.96575i	−1.41777	−	0.379891i	−0.533080	−	0.846065i	$-0.678966\pi$
$557$	−33.4607	−	8.96575i	−1.41777	−	0.379891i	−0.884693	+	0.466174i	$0.845632\pi$
$558$	−4.89898	−	4.89898i	−0.207390	−	0.207390i
$559$	6.92820			0.293032
$560$		0			0
$561$	18.0000	−	10.3923i	0.759961	−	0.438763i
$562$	15.9217	−	15.9217i	0.671616	−	0.671616i
$563$	14.8492	−	14.8492i	0.625821	−	0.625821i	−0.321193	−	0.947014i	$-0.604084\pi$
$563$	14.8492	−	14.8492i	0.625821	−	0.625821i	0.947014	+	0.321193i	$0.104084\pi$
$564$	3.46410	+	6.00000i	0.145865	+	0.252646i
$565$		0			0
$566$	13.5000	−	7.79423i	0.567447	−	0.327616i
$567$		0			0
$568$	−3.34607	+	0.896575i	−0.140398	+	0.0376195i
$569$	−34.6410			−1.45223			−0.726113	−	0.687575i	$-0.758675\pi$
$569$	−34.6410			−1.45223			−0.726113	+	0.687575i	$0.758675\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−5.79555	+	1.55291i	−0.242324	+	0.0649306i
$573$	6.21166	+	23.1822i	0.259496	+	0.968451i
$574$		0			0
$575$		0			0
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	−0.929550	−	0.368695i	$-0.879805\pi$
$577$	−13.4722	+	13.4722i	−0.560855	+	0.560855i	0.368695	+	0.929550i	$0.379805\pi$
$578$	−21.9203	+	21.9203i	−0.911765	+	0.911765i
$579$	19.0526	−	11.0000i	0.791797	−	0.457144i
$580$		0			0
$581$		0			0
$582$	−0.707107	−	0.707107i	−0.0293105	−	0.0293105i
$583$	17.3867	+	4.65874i	0.720082	+	0.192945i
$584$	7.79423	−	13.5000i	0.322527	−	0.558634i
$585$		0			0
$586$		0			0
$587$	0.896575	+	3.34607i	0.0370056	+	0.138107i	0.981957	−	0.189103i	$-0.0605581\pi$
$587$	0.896575	+	3.34607i	0.0370056	+	0.138107i	−0.944952	+	0.327210i	$0.893891\pi$
$588$	4.94975	−	4.94975i	0.204124	−	0.204124i
$589$	−1.73205	−	15.0000i	−0.0713679	−	0.618064i
$590$		0			0
$591$	9.00000	+	5.19615i	0.370211	+	0.213741i
$592$	−1.93185	+	0.517638i	−0.0793986	+	0.0212748i
$593$	1.34486	−	5.01910i	0.0552269	−	0.206110i	−0.932799	−	0.360397i	$-0.882641\pi$
$593$	1.34486	−	5.01910i	0.0552269	−	0.206110i	0.988026	+	0.154287i	$0.0493080\pi$
$594$	12.9904	+	7.50000i	0.533002	+	0.307729i
$595$		0			0
$596$	18.0000			0.737309
$597$	−9.89949	−	9.89949i	−0.405159	−	0.405159i
$598$	1.79315	−	6.69213i	0.0733274	−	0.273662i
$599$	8.66025	+	15.0000i	0.353848	+	0.612883i	0.986920	−	0.161210i	$-0.0515395\pi$
$599$	8.66025	+	15.0000i	0.353848	+	0.612883i	−0.633072	+	0.774093i	$0.718206\pi$
$600$		0			0
$601$		−	22.5167i		−	0.918474i	−0.888314	−	0.459237i	$-0.848123\pi$
$601$		−	22.5167i		−	0.918474i	0.888314	−	0.459237i	$-0.151877\pi$
$602$		0			0
$603$	0.517638	+	1.93185i	0.0210799	+	0.0786711i
$604$	1.73205	+	3.00000i	0.0704761	+	0.122068i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	28.2843	+	28.2843i	1.14802	+	1.14802i	0.986941	+	0.161082i	$0.0514984\pi$
$607$	28.2843	+	28.2843i	1.14802	+	1.14802i	0.161082	+	0.986941i	$0.448502\pi$
$608$	0.637756	−	4.31199i	0.0258644	−	0.174874i
$609$		0			0
$610$		0			0
$611$	−12.0000	−	6.92820i	−0.485468	−	0.280285i
$612$	−13.3843	−	3.58630i	−0.541027	−	0.144968i
$613$	−36.8067	+	9.86233i	−1.48661	+	0.398336i	−0.908591	−	0.417688i	$-0.862841\pi$
$613$	−36.8067	+	9.86233i	−1.48661	+	0.398336i	−0.578019	+	0.816024i	$0.696174\pi$
$614$	−19.9186	+	11.5000i	−0.803849	+	0.464102i
$615$		0			0
$616$		0			0
$617$	−18.4034	−	4.93117i	−0.740891	−	0.198521i	−0.131417	−	0.991327i	$-0.541953\pi$
$617$	−18.4034	−	4.93117i	−0.740891	−	0.198521i	−0.609474	+	0.792806i	$0.708619\pi$
$618$	9.65926	+	2.58819i	0.388552	+	0.104112i
$619$			28.0000i			1.12542i	0.826656	+	0.562708i	$0.190240\pi$
$619$			28.0000i			1.12542i	−0.826656	+	0.562708i	$0.809760\pi$
$620$		0			0
$621$	−15.0000	+	8.66025i	−0.601929	+	0.347524i
$622$	−17.3867	+	4.65874i	−0.697142	+	0.186799i
$623$		0			0
$624$	−1.73205	−	1.00000i	−0.0693375	−	0.0400320i
$625$		0			0
$626$			8.66025i			0.346133i
$627$	4.81105	+	12.1595i	0.192135	+	0.485604i
$628$	4.89898	+	4.89898i	0.195491	+	0.195491i
$629$	−6.92820	+	12.0000i	−0.276246	+	0.478471i
$630$		0			0
$631$	4.00000	+	6.92820i	0.159237	+	0.275807i	0.934594	−	0.355716i	$-0.115763\pi$
$631$	4.00000	+	6.92820i	0.159237	+	0.275807i	−0.775356	+	0.631524i	$0.782430\pi$
$632$	1.79315	+	6.69213i	0.0713277	+	0.266199i
$633$	−2.68973	+	10.0382i	−0.106907	+	0.398982i
$634$		−	18.0000i		−	0.714871i
$635$		0			0
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−3.62347	+	13.5230i	−0.143567	+	0.535799i
$638$	−14.6969	−	14.6969i	−0.581857	−	0.581857i
$639$	−6.92820			−0.274075
$640$		0			0
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.372690	−	0.927956i	$-0.621564\pi$
$641$	−34.5000	−	19.9186i	−1.36267	−	0.786737i	−0.989978	+	0.141219i	$0.954898\pi$
$642$		0			0
$643$	38.4797	−	10.3106i	1.51749	−	0.406611i	0.598577	−	0.801065i	$-0.295733\pi$
$643$	38.4797	−	10.3106i	1.51749	−	0.406611i	0.918916	+	0.394454i	$0.129066\pi$
$644$		0			0
$645$		0			0
$646$	−18.0000	−	24.2487i	−0.708201	−	0.954053i
$647$	7.34847	−	7.34847i	0.288898	−	0.288898i	−0.547746	−	0.836644i	$-0.684514\pi$
$647$	7.34847	−	7.34847i	0.288898	−	0.288898i	0.836644	+	0.547746i	$0.184514\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−7.79423	+	13.5000i	−0.305950	+	0.529921i
$650$		0			0
$651$		0			0
$652$	−11.7112	−	3.13801i	−0.458647	−	0.122894i
$653$	4.89898	+	4.89898i	0.191712	+	0.191712i	0.796435	−	0.604724i	$-0.206716\pi$
$653$	4.89898	+	4.89898i	0.191712	+	0.191712i	−0.604724	+	0.796435i	$0.706716\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	+	0.866025i	−0.0585652	+	0.0338126i
$657$	22.0454	−	22.0454i	0.860073	−	0.860073i
$658$		0			0
$659$	−1.73205	−	3.00000i	−0.0674711	−	0.116863i	0.830316	−	0.557292i	$-0.188160\pi$
$659$	−1.73205	−	3.00000i	−0.0674711	−	0.116863i	−0.897787	+	0.440429i	$0.854826\pi$
$660$		0			0
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	−0.378754	−	0.925497i	$-0.623647\pi$
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	0.612127	+	0.790759i	$0.290314\pi$
$662$	3.13801	+	11.7112i	0.121962	+	0.455170i
$663$	−13.3843	+	3.58630i	−0.519802	+	0.139280i
$664$	1.73205			0.0672166
$665$		0			0
$666$	−4.00000			−0.154997
$667$	23.1822	−	6.21166i	0.897619	−	0.240516i
$668$		0			0
$669$	22.5167	−	13.0000i	0.870544	−	0.502609i
$670$		0			0
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$		0			0
$673$	−1.41421	+	1.41421i	−0.0545139	+	0.0545139i	−0.733838	−	0.679324i	$-0.762273\pi$
$673$	−1.41421	+	1.41421i	−0.0545139	+	0.0545139i	0.679324	+	0.733838i	$0.262273\pi$
$674$	−11.2583	+	6.50000i	−0.433655	+	0.250371i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	12.7279	+	12.7279i	0.489174	+	0.489174i	0.908045	−	0.418872i	$-0.137574\pi$
$677$	12.7279	+	12.7279i	0.489174	+	0.489174i	−0.418872	+	0.908045i	$0.637574\pi$
$678$	−8.69333	−	2.32937i	−0.333865	−	0.0894590i
$679$		0			0
$680$		0			0
$681$	10.5000	−	18.1865i	0.402361	−	0.696909i
$682$	2.68973	+	10.0382i	0.102995	+	0.384382i
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	−0.525879	−	0.850559i	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$	3.46410	−	8.00000i	0.132453	−	0.305888i
$685$		0			0
$686$		0			0
$687$	−3.86370	+	1.03528i	−0.147409	+	0.0394982i
$688$	0.896575	−	3.34607i	0.0341816	−	0.127568i
$689$	−10.3923	−	6.00000i	−0.395915	−	0.228582i
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$	4.24264	+	4.24264i	0.161281	+	0.161281i
$693$		0			0
$694$	−16.4545	−	28.5000i	−0.624604	−	1.08185i
$695$		0			0
$696$		−	6.92820i		−	0.262613i
$697$	−3.10583	+	11.5911i	−0.117642	+	0.439045i
$698$	1.03528	+	3.86370i	0.0391858	+	0.146243i
$699$	11.2583	+	19.5000i	0.425829	+	0.737558i
$700$		0			0
$701$	−12.0000	+	20.7846i	−0.453234	+	0.785024i	−0.998585	−	0.0531839i	$-0.983063\pi$
$701$	−12.0000	+	20.7846i	−0.453234	+	0.785024i	0.545351	+	0.838208i	$0.316396\pi$
$702$	−7.07107	−	7.07107i	−0.266880	−	0.266880i
$703$	−6.83083	−	5.41662i	−0.257630	−	0.204292i
$704$			3.00000i			0.113067i
$705$		0			0
$706$	−31.5000	−	18.1865i	−1.18552	−	0.684459i
$707$		0			0
$708$	−5.01910	+	1.34486i	−0.188629	+	0.0505431i
$709$	29.4449	−	17.0000i	1.10583	−	0.638448i	0.168080	−	0.985773i	$-0.446243\pi$
$709$	29.4449	−	17.0000i	1.10583	−	0.638448i	0.937745	+	0.347325i	$0.112910\pi$
$710$		0			0
$711$			13.8564i			0.519656i
$712$	6.69213	+	1.79315i	0.250798	+	0.0672012i
$713$	−11.5911	−	3.10583i	−0.434090	−	0.116314i
$714$		0			0
$715$		0			0
$716$	19.5000	−	11.2583i	0.728749	−	0.420744i
$717$		0			0
$718$	−28.9778	−	7.76457i	−1.08144	−	0.289771i
$719$	5.19615	+	3.00000i	0.193784	+	0.111881i	0.593753	−	0.804648i	$-0.297646\pi$
$719$	5.19615	+	3.00000i	0.193784	+	0.111881i	−0.399969	+	0.916529i	$0.630979\pi$
$720$		0			0
$721$		0			0
$722$	16.7489	−	8.97073i	0.623330	−	0.333856i
$723$	3.67423	+	3.67423i	0.136646	+	0.136646i
$724$	12.1244	−	21.0000i	0.450598	−	0.780459i
$725$		0			0
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	1.79315	+	6.69213i	0.0665043	+	0.248197i	0.991173	−	0.132575i	$-0.0423247\pi$
$727$	1.79315	+	6.69213i	0.0665043	+	0.248197i	−0.924669	+	0.380773i	$0.875658\pi$
$728$		0			0
$729$			13.0000i			0.481481i
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	2.07055	−	7.72741i	0.0765298	−	0.285613i
$733$	−22.0454	−	22.0454i	−0.814266	−	0.814266i	0.171005	−	0.985270i	$-0.445299\pi$
$733$	−22.0454	−	22.0454i	−0.814266	−	0.814266i	−0.985270	+	0.171005i	$0.945299\pi$
$734$	−17.3205			−0.639312
$735$		0			0
$736$	−3.00000	−	1.73205i	−0.110581	−	0.0638442i
$737$	0.776457	−	2.89778i	0.0286012	−	0.106741i
$738$	−3.34607	+	0.896575i	−0.123170	+	0.0330034i
$739$	−9.52628	−	5.50000i	−0.350430	−	0.202321i	0.314445	−	0.949276i	$-0.398182\pi$
$739$	−9.52628	−	5.50000i	−0.350430	−	0.202321i	−0.664875	+	0.746955i	$0.731515\pi$
$740$		0			0
$741$	−1.00000	−	8.66025i	−0.0367359	−	0.318142i
$742$		0			0
$743$	−1.55291	−	5.79555i	−0.0569709	−	0.212618i	0.931572	−	0.363556i	$-0.118437\pi$
$743$	−1.55291	−	5.79555i	−0.0569709	−	0.212618i	−0.988543	+	0.150938i	$0.951771\pi$
$744$	−1.73205	+	3.00000i	−0.0635001	+	0.109985i
$745$		0			0
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$	3.34607	+	0.896575i	0.122426	+	0.0328040i
$748$	14.6969	+	14.6969i	0.537373	+	0.537373i
$749$		0			0
$750$		0			0
$751$	15.0000	−	8.66025i	0.547358	−	0.316017i	−0.200698	−	0.979653i	$-0.564321\pi$
$751$	15.0000	−	8.66025i	0.547358	−	0.316017i	0.748056	+	0.663636i	$0.230988\pi$
$752$	−4.89898	+	4.89898i	−0.178647	+	0.178647i
$753$	−14.8492	+	14.8492i	−0.541136	+	0.541136i
$754$	6.92820	+	12.0000i	0.252310	+	0.437014i
$755$		0			0
$756$		0			0
$757$	9.86233	+	36.8067i	0.358452	+	1.33776i	0.876084	+	0.482159i	$0.160147\pi$
$757$	9.86233	+	36.8067i	0.358452	+	1.33776i	−0.517631	+	0.855604i	$0.673186\pi$
$758$	−10.0382	+	2.68973i	−0.364604	+	0.0976953i
$759$	10.3923			0.377217
$760$		0			0
$761$	15.0000			0.543750			0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000			0.543750			0.271875	+	0.962333i	$0.412356\pi$
$762$	21.2504	−	5.69402i	0.769820	−	0.206273i
$763$		0			0
$764$	−20.7846	+	12.0000i	−0.751961	+	0.434145i
$765$		0			0
$766$	18.0000	+	31.1769i	0.650366	+	1.12647i
$767$	7.34847	−	7.34847i	0.265338	−	0.265338i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	−0.702416	−	0.711767i	$-0.747895\pi$
$769$	−12.1244	+	7.00000i	−0.437215	+	0.252426i	0.265200	+	0.964193i	$0.414562\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	15.5563	+	15.5563i	0.559885	+	0.559885i
$773$	46.3644	+	12.4233i	1.66761	+	0.446836i	0.964466	−	0.264209i	$-0.0851107\pi$
$773$	46.3644	+	12.4233i	1.66761	+	0.446836i	0.703147	+	0.711044i	$0.251777\pi$
$774$	3.46410	−	6.00000i	0.124515	−	0.215666i
$775$		0			0
$776$	0.500000	−	0.866025i	0.0179490	−	0.0310885i
$777$		0			0
$778$	16.9706	−	16.9706i	0.608424	−	0.608424i
$779$	−6.92820	−	3.00000i	−0.248229	−	0.107486i
$780$		0			0
$781$	9.00000	+	5.19615i	0.322045	+	0.185933i
$782$	−23.1822	+	6.21166i	−0.828994	+	0.222128i
$783$	8.96575	−	33.4607i	0.320410	−	1.19579i
$784$	6.06218	+	3.50000i	0.216506	+	0.125000i
$785$		0			0
$786$	15.0000			0.535032
$787$	−21.9203	−	21.9203i	−0.781375	−	0.781375i	0.198688	−	0.980063i	$-0.436332\pi$
$787$	−21.9203	−	21.9203i	−0.781375	−	0.781375i	−0.980063	+	0.198688i	$0.936332\pi$
$788$	−2.68973	+	10.0382i	−0.0958175	+	0.357596i
$789$	3.46410	+	6.00000i	0.123325	+	0.213606i
$790$		0			0
$791$		0			0
$792$	−1.55291	+	5.79555i	−0.0551804	+	0.205936i
$793$	4.14110	+	15.4548i	0.147055	+	0.548817i
$794$	−8.66025	−	15.0000i	−0.307341	−	0.532330i
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	38.1838	+	38.1838i	1.35254	+	1.35254i	0.882812	+	0.469726i	$0.155647\pi$
$797$	38.1838	+	38.1838i	1.35254	+	1.35254i	0.469726	+	0.882812i	$0.344353\pi$
$798$		0			0
$799$			48.0000i			1.69812i
$800$		0			0
$801$	12.0000	+	6.92820i	0.423999	+	0.244796i
$802$	8.36516	+	2.24144i	0.295384	+	0.0791480i
$803$	−45.1719	+	12.1038i	−1.59408	+	0.427133i
$804$	0.866025	−	0.500000i	0.0305424	−	0.0176336i
$805$		0			0
$806$		−	6.92820i		−	0.244036i
$807$	6.69213	+	1.79315i	0.235574	+	0.0631219i
$808$	11.5911	+	3.10583i	0.407774	+	0.109263i
$809$		−	3.00000i		−	0.105474i	−0.998608	−	0.0527372i	$-0.983205\pi$
$809$		−	3.00000i		−	0.105474i	0.998608	−	0.0527372i	$-0.0167946\pi$
$810$		0			0
$811$	−9.00000	+	5.19615i	−0.316033	+	0.182462i	−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−9.00000	+	5.19615i	−0.316033	+	0.182462i	0.333590	+	0.942718i	$0.391740\pi$
$812$		0			0
$813$	−15.4548	−	4.14110i	−0.542024	−	0.145235i
$814$	5.19615	+	3.00000i	0.182125	+	0.105150i
$815$		0			0
$816$			6.92820i			0.242536i
$817$	14.0406	−	5.55532i	0.491218	−	0.194356i
$818$	13.4722	+	13.4722i	0.471044	+	0.471044i
$819$		0			0
$820$		0			0
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	−0.955636	−	0.294549i	$-0.904831\pi$
$821$	−21.0000	−	36.3731i	−0.732905	−	1.26943i	0.222731	−	0.974880i	$-0.428503\pi$
$822$	−4.03459	−	15.0573i	−0.140722	−	0.525183i
$823$	−11.6555	+	43.4988i	−0.406285	+	1.51627i	0.395390	+	0.918513i	$0.370610\pi$
$823$	−11.6555	+	43.4988i	−0.406285	+	1.51627i	−0.801674	+	0.597761i	$0.796057\pi$
$824$			10.0000i			0.348367i
$825$		0			0
$826$		0			0
$827$	−8.54103	+	31.8756i	−0.297001	+	1.10842i	0.642615	+	0.766189i	$0.277850\pi$
$827$	−8.54103	+	31.8756i	−0.297001	+	1.10842i	−0.939615	+	0.342232i	$0.888817\pi$
$828$	−4.89898	−	4.89898i	−0.170251	−	0.170251i
$829$	41.5692			1.44376			0.721879	−	0.692019i	$-0.243279\pi$
$829$	41.5692			1.44376			0.721879	+	0.692019i	$0.243279\pi$
$830$		0			0
$831$		0			0
$832$	0.517638	−	1.93185i	0.0179459	−	0.0669749i
$833$	46.8449	−	12.5521i	1.62308	−	0.434903i
$834$	−4.33013	−	2.50000i	−0.149940	−	0.0865679i
$835$		0			0
$836$	−10.5000	+	7.79423i	−0.363150	+	0.269569i
$837$	−12.2474	+	12.2474i	−0.423334	+	0.423334i
$838$	−3.10583	−	11.5911i	−0.107289	−	0.400408i
$839$	13.8564	−	24.0000i	0.478376	−	0.828572i	−0.521316	−	0.853363i	$-0.674559\pi$
$839$	13.8564	−	24.0000i	0.478376	−	0.828572i	0.999693	+	0.0247915i	$0.00789218\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$	23.4225	+	6.27603i	0.807191	+	0.216286i
$843$	−15.9217	−	15.9217i	−0.548372	−	0.548372i
$844$	−10.3923			−0.357718
$845$		0			0
$846$	−12.0000	+	6.92820i	−0.412568	+	0.238197i
$847$		0			0
$848$	−4.24264	+	4.24264i	−0.145693	+	0.145693i
$849$	−7.79423	−	13.5000i	−0.267497	−	0.463319i
$850$		0			0
$851$	−6.00000	+	3.46410i	−0.205677	+	0.118748i
$852$	0.896575	+	3.34607i	0.0307162	+	0.114634i
$853$	−50.1910	+	13.4486i	−1.71851	+	0.460472i	−0.977484	−	0.211008i	$-0.932325\pi$
$853$	−50.1910	+	13.4486i	−1.71851	+	0.460472i	−0.741022	+	0.671481i	$0.765659\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.0800	−	6.98811i	0.890876	−	0.238709i	0.215782	−	0.976442i	$-0.430770\pi$
$857$	26.0800	−	6.98811i	0.890876	−	0.238709i	0.675094	+	0.737732i	$0.264103\pi$
$858$	1.55291	+	5.79555i	0.0530156	+	0.197857i
$859$	−4.33013	+	2.50000i	−0.147742	+	0.0852989i	−0.572049	−	0.820220i	$-0.693851\pi$
$859$	−4.33013	+	2.50000i	−0.147742	+	0.0852989i	0.424307	+	0.905519i	$0.360518\pi$
$860$		0			0
$861$		0			0
$862$	−2.44949	+	2.44949i	−0.0834300	+	0.0834300i
$863$	−29.6985	+	29.6985i	−1.01095	+	1.01095i	−0.0110088	+	0.999939i	$0.503504\pi$
$863$	−29.6985	+	29.6985i	−1.01095	+	1.01095i	−0.999939	+	0.0110088i	$0.996496\pi$
$864$	−4.33013	+	2.50000i	−0.147314	+	0.0850517i
$865$		0			0
$866$	26.0000			0.883516
$867$	21.9203	+	21.9203i	0.744453	+	0.744453i
$868$		0			0
$869$	10.3923	−	18.0000i	0.352535	−	0.610608i
$870$		0			0
$871$	−1.00000	+	1.73205i	−0.0338837	+	0.0586883i
$872$		0			0
$873$	1.41421	−	1.41421i	0.0478639	−	0.0478639i
$874$	−1.73205	−	15.0000i	−0.0585875	−	0.507383i
$875$		0			0
$876$	−13.5000	−	7.79423i	−0.456123	−	0.263343i
$877$	−19.3185	+	5.17638i	−0.652340	+	0.174794i	−0.569787	−	0.821793i	$-0.692974\pi$
$877$	−19.3185	+	5.17638i	−0.652340	+	0.174794i	−0.0825533	+	0.996587i	$0.526307\pi$
$878$	6.27603	−	23.4225i	0.211806	−	0.790470i
$879$		0			0
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$	9.89949	+	9.89949i	0.333333	+	0.333333i
$883$	−10.3106	+	38.4797i	−0.346980	+	1.29495i	0.543302	+	0.839537i	$0.317174\pi$
$883$	−10.3106	+	38.4797i	−0.346980	+	1.29495i	−0.890282	+	0.455409i	$0.849493\pi$
$884$	−6.92820	−	12.0000i	−0.233021	−	0.403604i
$885$		0			0
$886$			22.5167i			0.756462i
$887$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$887$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$888$	0.517638	+	1.93185i	0.0173708	+	0.0648287i
$889$		0			0
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	18.3848	+	18.3848i	0.615568	+	0.615568i
$893$	−29.8744	−	4.41851i	−0.999707	−	0.147860i
$894$		−	18.0000i		−	0.602010i
$895$		0			0
$896$		0			0
$897$	−6.69213	−	1.79315i	−0.223444	−	0.0598716i
$898$	−25.0955	+	6.72432i	−0.837447	+	0.224393i
$899$	20.7846	−	12.0000i	0.693206	−	0.400222i
$900$		0			0
$901$			41.5692i			1.38487i
$902$	5.01910	+	1.34486i	0.167118	+	0.0447790i
$903$		0			0
$904$		−	9.00000i		−	0.299336i
$905$		0			0
$906$	3.00000	−	1.73205i	0.0996683	−	0.0575435i
$907$	−16.4207	+	4.39992i	−0.545242	+	0.146097i	−0.520917	−	0.853607i	$-0.674410\pi$
$907$	−16.4207	+	4.39992i	−0.545242	+	0.146097i	−0.0243242	+	0.999704i	$0.507743\pi$
$908$	20.2844	+	5.43520i	0.673163	+	0.180373i
$909$	20.7846	+	12.0000i	0.689382	+	0.398015i
$910$		0			0
$911$		−	10.3923i		−	0.344312i	−0.985070	−	0.172156i	$-0.944927\pi$
$911$		−	10.3923i		−	0.344312i	0.985070	−	0.172156i	$-0.0550734\pi$
$912$	−4.31199	−	0.637756i	−0.142784	−	0.0211182i
$913$	−3.67423	−	3.67423i	−0.121599	−	0.121599i
$914$	−9.52628	+	16.5000i	−0.315101	+	0.545771i
$915$		0			0
$916$	−2.00000	−	3.46410i	−0.0660819	−	0.114457i
$917$		0			0
$918$	−8.96575	+	33.4607i	−0.295914	+	1.10437i
$919$			38.0000i			1.25350i	0.779219	+	0.626752i	$0.215616\pi$
$919$			38.0000i			1.25350i	−0.779219	+	0.626752i	$0.784384\pi$
$920$		0			0
$921$	11.5000	+	19.9186i	0.378938	+	0.656340i
$922$	−7.76457	+	28.9778i	−0.255713	+	0.954332i
$923$	−4.89898	−	4.89898i	−0.161252	−	0.161252i
$924$		0			0
$925$		0			0
$926$	21.0000	+	12.1244i	0.690103	+	0.398431i
$927$	−5.17638	+	19.3185i	−0.170015	+	0.634503i
$928$	6.69213	−	1.79315i	0.219680	−	0.0588631i
$929$	−2.59808	−	1.50000i	−0.0852401	−	0.0492134i	0.456774	−	0.889583i	$-0.349005\pi$
$929$	−2.59808	−	1.50000i	−0.0852401	−	0.0492134i	−0.542014	+	0.840369i	$0.682338\pi$
$930$		0			0
$931$	3.50000	+	30.3109i	0.114708	+	0.993399i
$932$	−15.9217	+	15.9217i	−0.521532	+	0.521532i
$933$	4.65874	+	17.3867i	0.152520	+	0.569214i
$934$	12.9904	−	22.5000i	0.425058	−	0.736222i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	31.7876	+	8.51747i	1.03846	+	0.278254i	0.737474	−	0.675376i	$-0.236019\pi$
$937$	31.7876	+	8.51747i	1.03846	+	0.278254i	0.300983	+	0.953630i	$0.402685\pi$
$938$		0			0
$939$	8.66025			0.282617
$940$		0			0
$941$	−3.00000	+	1.73205i	−0.0977972	+	0.0564632i	−0.548101	−	0.836412i	$-0.684649\pi$
$941$	−3.00000	+	1.73205i	−0.0977972	+	0.0564632i	0.450304	+	0.892875i	$0.351316\pi$
$942$	4.89898	−	4.89898i	0.159617	−	0.159617i
$943$	−4.24264	+	4.24264i	−0.138159	+	0.138159i
$944$	−2.59808	−	4.50000i	−0.0845602	−	0.146463i
$945$		0			0
$946$	−9.00000	+	5.19615i	−0.292615	+	0.168941i
$947$	6.27603	+	23.4225i	0.203944	+	0.761128i	0.989769	+	0.142679i	$0.0455717\pi$
$947$	6.27603	+	23.4225i	0.203944	+	0.761128i	−0.785825	+	0.618448i	$0.787762\pi$
$948$	6.69213	−	1.79315i	0.217350	−	0.0582388i
$949$	31.1769			1.01205
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−3.88229	−	14.4889i	−0.125760	−	0.469341i	0.874106	−	0.485735i	$-0.161448\pi$
$953$	−3.88229	−	14.4889i	−0.125760	−	0.469341i	−0.999866	+	0.0163940i	$0.994781\pi$
$954$	−10.3923	+	6.00000i	−0.336463	+	0.194257i
$955$		0			0
$956$		0			0
$957$	−14.6969	+	14.6969i	−0.475085	+	0.475085i
$958$	16.9706	−	16.9706i	0.548294	−	0.548294i
$959$		0			0
$960$		0			0
$961$	19.0000			0.612903
$962$	−2.82843	−	2.82843i	−0.0911922	−	0.0911922i
$963$		0			0
$964$	−2.59808	+	4.50000i	−0.0836784	+	0.144935i
$965$		0			0
$966$		0			0
$967$	−2.68973	−	10.0382i	−0.0864958	−	0.322807i	0.909097	−	0.416583i	$-0.136773\pi$
$967$	−2.68973	−	10.0382i	−0.0864958	−	0.322807i	−0.995593	+	0.0937769i	$0.970106\pi$
$968$	−1.41421	+	1.41421i	−0.0454545	+	0.0454545i
$969$	−24.2487	+	18.0000i	−0.778981	+	0.578243i
$970$		0			0
$971$	37.5000	+	21.6506i	1.20343	+	0.694802i	0.961317	−	0.275445i	$-0.0888254\pi$
$971$	37.5000	+	21.6506i	1.20343	+	0.694802i	0.242116	+	0.970247i	$0.422159\pi$
$972$	−15.4548	+	4.14110i	−0.495713	+	0.132826i
$973$		0			0
$974$	−32.9090	−	19.0000i	−1.05447	−	0.608799i
$975$		0			0
$976$	8.00000			0.256074
$977$	−6.36396	−	6.36396i	−0.203601	−	0.203601i	0.597940	−	0.801541i	$-0.295986\pi$
$977$	−6.36396	−	6.36396i	−0.203601	−	0.203601i	−0.801541	+	0.597940i	$0.795986\pi$
$978$	−3.13801	+	11.7112i	−0.100343	+	0.374484i
$979$	−10.3923	−	18.0000i	−0.332140	−	0.575282i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.5291	+	57.9555i	0.495303	+	1.84849i	0.528328	+	0.849040i	$0.322819\pi$
$983$	15.5291	+	57.9555i	0.495303	+	1.84849i	−0.0330251	+	0.999455i	$0.510514\pi$
$984$	0.866025	+	1.50000i	0.0276079	+	0.0478183i
$985$		0			0
$986$	24.0000	−	41.5692i	0.764316	−	1.32383i
$987$		0			0
$988$	8.10634	−	3.20736i	0.257897	−	0.102040i
$989$		−	12.0000i		−	0.381578i
$990$		0			0
$991$	42.0000	+	24.2487i	1.33417	+	0.770286i	0.985936	−	0.167121i	$-0.0534469\pi$
$991$	42.0000	+	24.2487i	1.33417	+	0.770286i	0.348238	+	0.937406i	$0.386780\pi$
$992$	−3.34607	−	0.896575i	−0.106238	−	0.0284663i
$993$	11.7112	−	3.13801i	0.371645	−	0.0995819i
$994$		0			0
$995$		0			0
$996$		−	1.73205i		−	0.0548821i
$997$	13.3843	+	3.58630i	0.423884	+	0.113579i	0.464454	−	0.885597i	$-0.346251\pi$
$997$	13.3843	+	3.58630i	0.423884	+	0.113579i	−0.0405699	+	0.999177i	$0.512917\pi$
$998$	−29.9437	−	8.02339i	−0.947851	−	0.253976i
$999$			10.0000i			0.316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.b.293.2	yes	8
5.2	odd	4	inner	950.2.q.b.407.2	yes	8
5.3	odd	4	inner	950.2.q.b.407.1	yes	8
5.4	even	2	inner	950.2.q.b.293.1	yes	8
19.12	odd	6	inner	950.2.q.b.943.2	yes	8
95.12	even	12	inner	950.2.q.b.107.2	yes	8
95.69	odd	6	inner	950.2.q.b.943.1	yes	8
95.88	even	12	inner	950.2.q.b.107.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.b.107.1	✓	8	95.88	even	12	inner
950.2.q.b.107.2	yes	8	95.12	even	12	inner
950.2.q.b.293.1	yes	8	5.4	even	2	inner
950.2.q.b.293.2	yes	8	1.1	even	1	trivial
950.2.q.b.407.1	yes	8	5.3	odd	4	inner
950.2.q.b.407.2	yes	8	5.2	odd	4	inner
950.2.q.b.943.1	yes	8	95.69	odd	6	inner
950.2.q.b.943.2	yes	8	19.12	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.707107 - 0.707107i) q^{8} +(1.73205 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(0.707107 - 0.707107i) q^{8} +(1.73205 - 1.00000i) q^{9} -3.00000 q^{11} +(-0.707107 - 0.707107i) q^{12} +(1.93185 + 0.517638i) q^{13} +(0.500000 - 0.866025i) q^{16} +(-1.79315 - 6.69213i) q^{17} +(1.41421 - 1.41421i) q^{18} +(4.33013 - 0.500000i) q^{19} +(-2.89778 + 0.776457i) q^{22} +(0.896575 - 3.34607i) q^{23} +(-0.866025 - 0.500000i) q^{24} +2.00000 q^{26} +(-3.53553 - 3.53553i) q^{27} +(3.46410 + 6.00000i) q^{29} -3.46410i q^{31} +(0.258819 - 0.965926i) q^{32} +(0.776457 + 2.89778i) q^{33} +(-3.46410 - 6.00000i) q^{34} +(1.00000 - 1.73205i) q^{36} +(-1.41421 - 1.41421i) q^{37} +(4.05317 - 1.60368i) q^{38} -2.00000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(3.34607 - 0.896575i) q^{43} +(-2.59808 + 1.50000i) q^{44} -3.46410i q^{46} +(-6.69213 - 1.79315i) q^{47} +(-0.965926 - 0.258819i) q^{48} +7.00000i q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.93185 - 0.517638i) q^{52} +(-5.79555 - 1.55291i) q^{53} +(-4.33013 - 2.50000i) q^{54} +(-1.60368 - 4.05317i) q^{57} +(4.89898 + 4.89898i) q^{58} +(2.59808 - 4.50000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-0.896575 - 3.34607i) q^{62} -1.00000i q^{64} +(1.50000 + 2.59808i) q^{66} +(-0.258819 + 0.965926i) q^{67} +(-4.89898 - 4.89898i) q^{68} -3.46410 q^{69} +(-3.00000 - 1.73205i) q^{71} +(0.517638 - 1.93185i) q^{72} +(15.0573 - 4.03459i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(3.50000 - 2.59808i) q^{76} +(-0.517638 - 1.93185i) q^{78} +(-3.46410 + 6.00000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-1.67303 - 0.448288i) q^{82} +(1.22474 + 1.22474i) q^{83} +(3.00000 - 1.73205i) q^{86} +(4.89898 - 4.89898i) q^{87} +(-2.12132 + 2.12132i) q^{88} +(3.46410 + 6.00000i) q^{89} +(-0.896575 - 3.34607i) q^{92} +(-3.34607 + 0.896575i) q^{93} -6.92820 q^{94} -1.00000 q^{96} +(0.965926 - 0.258819i) q^{97} +(1.81173 + 6.76148i) q^{98} +(-5.19615 + 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{6}+O(q^{10}) \) 8 * q - 4 * q^6	\( 8 q - 4 q^{6} - 24 q^{11} + 4 q^{16} + 16 q^{26} + 8 q^{36} - 12 q^{41} - 48 q^{51} + 32 q^{61} + 12 q^{66} - 24 q^{71} + 28 q^{76} + 4 q^{81} + 24 q^{86} - 8 q^{96}+O(q^{100}) \) 8 * q - 4 * q^6 - 24 * q^11 + 4 * q^16 + 16 * q^26 + 8 * q^36 - 12 * q^41 - 48 * q^51 + 32 * q^61 + 12 * q^66 - 24 * q^71 + 28 * q^76 + 4 * q^81 + 24 * q^86 - 8 * q^96

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