LMFDB - Embedded newform 950.2.q.b.407.2

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			407.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	950.407
Dual form			950.2.q.b.943.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 1.00000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.500000 - 0.866025i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-1.73205 + 1.00000i) q^{9} -3.00000 q^{11} +(0.707107 - 0.707107i) q^{12} +(0.517638 - 1.93185i) q^{13} +(0.500000 - 0.866025i) q^{16} +(6.69213 - 1.79315i) q^{17} +(-1.41421 - 1.41421i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.776457 - 2.89778i) q^{22} +(-3.34607 - 0.896575i) q^{23} +(0.866025 + 0.500000i) q^{24} +2.00000 q^{26} +(3.53553 - 3.53553i) q^{27} +(-3.46410 - 6.00000i) q^{29} -3.46410i q^{31} +(0.965926 + 0.258819i) q^{32} +(2.89778 - 0.776457i) q^{33} +(3.46410 + 6.00000i) q^{34} +(1.00000 - 1.73205i) q^{36} +(1.41421 - 1.41421i) q^{37} +(-1.60368 - 4.05317i) q^{38} +2.00000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(-0.896575 - 3.34607i) q^{43} +(2.59808 - 1.50000i) q^{44} -3.46410i q^{46} +(1.79315 - 6.69213i) q^{47} +(-0.258819 + 0.965926i) q^{48} -7.00000i q^{49} +(-6.00000 + 3.46410i) q^{51} +(0.517638 + 1.93185i) q^{52} +(-1.55291 + 5.79555i) q^{53} +(4.33013 + 2.50000i) q^{54} +(4.05317 - 1.60368i) q^{57} +(4.89898 - 4.89898i) q^{58} +(-2.59808 + 4.50000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(3.34607 - 0.896575i) q^{62} +1.00000i q^{64} +(1.50000 + 2.59808i) q^{66} +(-0.965926 - 0.258819i) q^{67} +(-4.89898 + 4.89898i) q^{68} +3.46410 q^{69} +(-3.00000 - 1.73205i) q^{71} +(1.93185 + 0.517638i) q^{72} +(-4.03459 - 15.0573i) q^{73} +(1.73205 + 1.00000i) q^{74} +(3.50000 - 2.59808i) q^{76} +(-1.93185 + 0.517638i) q^{78} +(3.46410 - 6.00000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.448288 - 1.67303i) q^{82} +(1.22474 - 1.22474i) q^{83} +(3.00000 - 1.73205i) q^{86} +(4.89898 + 4.89898i) q^{87} +(2.12132 + 2.12132i) q^{88} +(-3.46410 - 6.00000i) q^{89} +(3.34607 - 0.896575i) q^{92} +(0.896575 + 3.34607i) q^{93} +6.92820 q^{94} -1.00000 q^{96} +(0.258819 + 0.965926i) q^{97} +(6.76148 - 1.81173i) q^{98} +(5.19615 - 3.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i	−0.526639	−	0.850089i	$-0.676548\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i	−0.0310384	+	0.999518i	$0.509881\pi$
$4$	−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	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	−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
$13$	0.517638	−	1.93185i	0.143567	−	0.535799i	−0.856248	−	0.516565i	$-0.827210\pi$
$13$	0.517638	−	1.93185i	0.143567	−	0.535799i	0.999815	−	0.0192343i	$-0.00612285\pi$
$14$		0			0
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.69213	−	1.79315i	1.62308	−	0.434903i	0.671176	−	0.741298i	$-0.265790\pi$
$17$	6.69213	−	1.79315i	1.62308	−	0.434903i	0.951904	+	0.306395i	$0.0991229\pi$
$18$	−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
$22$	−0.776457	−	2.89778i	−0.165541	−	0.617808i
$23$	−3.34607	−	0.896575i	−0.697703	−	0.186949i	−0.107501	−	0.994205i	$-0.534285\pi$
$23$	−3.34607	−	0.896575i	−0.697703	−	0.186949i	−0.590201	+	0.807256i	$0.700952\pi$
$24$	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	$-0.944245\pi$
$29$	−3.46410	−	6.00000i	−0.643268	−	1.11417i	0.341431	−	0.939907i	$-0.389088\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	2.89778	−	0.776457i	0.504438	−	0.135164i
$34$	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	$-0.697432\pi$
$37$	1.41421	−	1.41421i	0.232495	−	0.232495i	0.813733	+	0.581238i	$0.197432\pi$
$38$	−1.60368	−	4.05317i	−0.260152	−	0.657511i
$39$			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
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	−0.999985	−	0.00550783i	$-0.998247\pi$
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	0.863258	−	0.504762i	$-0.168420\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$		−	3.46410i		−	0.510754i
$47$	1.79315	−	6.69213i	0.261558	−	0.976148i	−0.702766	−	0.711421i	$-0.748052\pi$
$47$	1.79315	−	6.69213i	0.261558	−	0.976148i	0.964324	−	0.264726i	$-0.0852816\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$		−	7.00000i		−	1.00000i
$50$		0			0
$51$	−6.00000	+	3.46410i	−0.840168	+	0.485071i
$52$	0.517638	+	1.93185i	0.0717835	+	0.267900i
$53$	−1.55291	+	5.79555i	−0.213309	+	0.796081i	0.773446	+	0.633863i	$0.218532\pi$
$53$	−1.55291	+	5.79555i	−0.213309	+	0.796081i	−0.986755	+	0.162218i	$0.948135\pi$
$54$	4.33013	+	2.50000i	0.589256	+	0.340207i
$55$		0			0
$56$		0			0
$57$	4.05317	−	1.60368i	0.536856	−	0.212413i
$58$	4.89898	−	4.89898i	0.643268	−	0.643268i
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	−0.984102	−	0.177605i	$-0.943165\pi$
$59$	−2.59808	+	4.50000i	−0.338241	+	0.585850i	0.645861	+	0.763455i	$0.276498\pi$
$60$		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	$0.662183\pi$
$62$	3.34607	−	0.896575i	0.424951	−	0.113865i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−0.965926	−	0.258819i	−0.118007	−	0.0316198i	0.199332	−	0.979932i	$-0.436123\pi$
$67$	−0.965926	−	0.258819i	−0.118007	−	0.0316198i	−0.317339	+	0.948312i	$0.602789\pi$
$68$	−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	$0.732567\pi$
$72$	1.93185	+	0.517638i	0.227671	+	0.0610042i
$73$	−4.03459	−	15.0573i	−0.472213	−	1.76232i	−0.631792	−	0.775138i	$-0.717680\pi$
$73$	−4.03459	−	15.0573i	−0.472213	−	1.76232i	0.159579	−	0.987185i	$-0.448986\pi$
$74$	1.73205	+	1.00000i	0.201347	+	0.116248i
$75$		0			0
$76$	3.50000	−	2.59808i	0.401478	−	0.298020i
$77$		0			0
$78$	−1.93185	+	0.517638i	−0.218739	+	0.0586110i
$79$	3.46410	−	6.00000i	0.389742	−	0.675053i	−0.602673	−	0.797988i	$-0.705898\pi$
$79$	3.46410	−	6.00000i	0.389742	−	0.675053i	0.992415	+	0.122936i	$0.0392309\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.448288	−	1.67303i	0.0495051	−	0.184756i
$83$	1.22474	−	1.22474i	0.134433	−	0.134433i	−0.636688	−	0.771121i	$-0.719696\pi$
$83$	1.22474	−	1.22474i	0.134433	−	0.134433i	0.771121	+	0.636688i	$0.219696\pi$
$84$		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	0.621932	−	0.783072i	$-0.286348\pi$
$89$	−3.46410	−	6.00000i	−0.367194	−	0.635999i	−0.989126	+	0.147073i	$0.953015\pi$
$90$		0			0
$91$		0			0
$92$	3.34607	−	0.896575i	0.348851	−	0.0934745i
$93$	0.896575	+	3.34607i	0.0929705	+	0.346971i
$94$	6.92820			0.714590
$95$		0			0
$96$	−1.00000			−0.102062
$97$	0.258819	+	0.965926i	0.0262791	+	0.0980749i	0.977820	−	0.209448i	$-0.0671666\pi$
$97$	0.258819	+	0.965926i	0.0262791	+	0.0980749i	−0.951541	+	0.307523i	$0.900500\pi$
$98$	6.76148	−	1.81173i	0.683013	−	0.183013i
$99$	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	$-0.0860229\pi$
$103$	7.07107	+	7.07107i	0.696733	+	0.696733i	−0.266971	+	0.963704i	$0.586023\pi$
$104$	−1.73205	+	1.00000i	−0.169842	+	0.0980581i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$107$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$108$	−1.29410	+	4.82963i	−0.124524	+	0.464731i
$109$		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	$-0.389137\pi$
$113$	−6.36396	−	6.36396i	−0.598671	−	0.598671i	−0.939959	+	0.341288i	$0.889137\pi$
$114$	2.59808	+	3.50000i	0.243332	+	0.327805i
$115$		0			0
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$	1.03528	+	3.86370i	0.0957113	+	0.357199i
$118$	−5.01910	−	1.34486i	−0.462045	−	0.123805i
$119$		0			0
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	1.67303	+	0.448288i	0.150852	+	0.0404207i
$124$	1.73205	+	3.00000i	0.155543	+	0.269408i
$125$		0			0
$126$		0			0
$127$	−21.2504	−	5.69402i	−1.88567	−	0.505262i	−0.999089	−	0.0426804i	$-0.986410\pi$
$127$	−21.2504	−	5.69402i	−1.88567	−	0.505262i	−0.886576	−	0.462582i	$-0.846923\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	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
$137$	−4.03459	+	15.0573i	−0.344698	+	1.28643i	0.548266	+	0.836304i	$0.315288\pi$
$137$	−4.03459	+	15.0573i	−0.344698	+	1.28643i	−0.892964	+	0.450127i	$0.851379\pi$
$138$	0.896575	+	3.34607i	0.0763216	+	0.284836i
$139$	−4.33013	+	2.50000i	−0.367277	+	0.212047i	−0.672268	−	0.740308i	$-0.734680\pi$
$139$	−4.33013	+	2.50000i	−0.367277	+	0.212047i	0.304991	+	0.952355i	$0.401346\pi$
$140$		0			0
$141$			6.92820i			0.583460i
$142$	0.896575	−	3.34607i	0.0752389	−	0.280796i
$143$	−1.55291	+	5.79555i	−0.129861	+	0.484649i
$144$			2.00000i			0.166667i
$145$		0			0
$146$	13.5000	−	7.79423i	1.11727	−	0.645055i
$147$	1.81173	+	6.76148i	0.149429	+	0.557678i
$148$	−0.517638	+	1.93185i	−0.0425496	+	0.158797i
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.300750	−	0.953703i	$-0.597237\pi$
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.976306	+	0.216394i	$0.930570\pi$
$150$		0			0
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$	3.41542	+	2.70831i	0.277027	+	0.219673i
$153$	−9.79796	+	9.79796i	−0.792118	+	0.792118i
$154$		0			0
$155$		0			0
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−6.69213	+	1.79315i	−0.534090	+	0.143109i	−0.515776	−	0.856723i	$-0.672496\pi$
$157$	−6.69213	+	1.79315i	−0.534090	+	0.143109i	−0.0183138	+	0.999832i	$0.505830\pi$
$158$	6.69213	+	1.79315i	0.532397	+	0.142655i
$159$		−	6.00000i		−	0.475831i
$160$		0			0
$161$		0			0
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−8.57321	+	8.57321i	−0.671506	+	0.671506i	−0.958063	−	0.286557i	$-0.907489\pi$
$163$	−8.57321	+	8.57321i	−0.671506	+	0.671506i	0.286557	+	0.958063i	$0.407489\pi$
$164$	1.73205			0.135250
$165$		0			0
$166$	1.50000	+	0.866025i	0.116423	+	0.0672166i
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$		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
$173$	5.79555	−	1.55291i	0.440628	−	0.118066i	−0.0316829	−	0.999498i	$-0.510087\pi$
$173$	5.79555	−	1.55291i	0.440628	−	0.118066i	0.472311	+	0.881432i	$0.343420\pi$
$174$	−3.46410	+	6.00000i	−0.262613	+	0.454859i
$175$		0			0
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	1.34486	−	5.01910i	0.101086	−	0.377258i
$178$	4.89898	−	4.89898i	0.367194	−	0.367194i
$179$	−22.5167			−1.68297			−0.841487	−	0.540277i	$-0.818319\pi$
$179$	−22.5167			−1.68297			−0.841487	+	0.540277i	$0.818319\pi$
$180$		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
$187$	−20.0764	+	5.37945i	−1.46813	+	0.393385i
$188$	1.79315	+	6.69213i	0.130779	+	0.488074i
$189$		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	$0.834780\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	21.2504	−	5.69402i	1.52963	−	0.409864i	0.606735	−	0.794904i	$-0.292479\pi$
$193$	21.2504	−	5.69402i	1.52963	−	0.409864i	0.922900	+	0.385040i	$0.125812\pi$
$194$	−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	0.395087	−	0.918644i	$-0.370714\pi$
$197$	−7.34847	−	7.34847i	−0.523557	−	0.523557i	−0.918644	+	0.395087i	$0.870714\pi$
$198$	4.24264	+	4.24264i	0.301511	+	0.301511i
$199$	−12.1244	+	7.00000i	−0.859473	+	0.496217i	−0.863836	−	0.503774i	$-0.831945\pi$
$199$	−12.1244	+	7.00000i	−0.859473	+	0.496217i	0.00436292	+	0.999990i	$0.498611\pi$
$200$		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
$207$	6.69213	−	1.79315i	0.465135	−	0.124633i
$208$	−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	$0.783112\pi$
$212$	−1.55291	−	5.79555i	−0.106655	−	0.398040i
$213$	3.34607	+	0.896575i	0.229269	+	0.0614323i
$214$		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
$222$	−1.93185	−	0.517638i	−0.129657	−	0.0347416i
$223$	25.1141	−	6.72930i	1.68176	−	0.450627i	0.713519	−	0.700636i	$-0.247100\pi$
$223$	25.1141	−	6.72930i	1.68176	−	0.450627i	0.968244	+	0.250009i	$0.0804335\pi$
$224$		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	$-0.995442\pi$
$227$	−14.8492	+	14.8492i	−0.985579	+	0.985579i	0.0143186	+	0.999897i	$0.495442\pi$
$228$	−2.70831	+	3.41542i	−0.179362	+	0.226191i
$229$			4.00000i			0.264327i	0.991228	+	0.132164i	$0.0421925\pi$
$229$			4.00000i			0.264327i	−0.991228	+	0.132164i	$0.957808\pi$
$230$		0			0
$231$		0			0
$232$	−1.79315	+	6.69213i	−0.117726	+	0.439360i
$233$	5.82774	+	21.7494i	0.381788	+	1.42485i	0.843168	+	0.537650i	$0.180688\pi$
$233$	5.82774	+	21.7494i	0.381788	+	1.42485i	−0.461380	+	0.887202i	$0.652646\pi$
$234$	−3.46410	+	2.00000i	−0.226455	+	0.130744i
$235$		0			0
$236$		−	5.19615i		−	0.338241i
$237$	−1.79315	+	6.69213i	−0.116478	+	0.434701i
$238$		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	$0.386857\pi$
$242$	−0.517638	−	1.93185i	−0.0332750	−	0.124184i
$243$	−4.14110	+	15.4548i	−0.265652	+	0.991427i
$244$	−6.92820	−	4.00000i	−0.443533	−	0.256074i
$245$		0			0
$246$			1.73205i			0.110432i
$247$	−1.27551	+	8.62398i	−0.0811589	+	0.548731i
$248$	−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
$253$	10.0382	+	2.68973i	0.631096	+	0.169102i
$254$		−	22.0000i		−	1.38040i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.89778	−	0.776457i	−0.180758	−	0.0484341i	0.167304	−	0.985905i	$-0.446494\pi$
$257$	−2.89778	−	0.776457i	−0.180758	−	0.0484341i	−0.348063	+	0.937471i	$0.613160\pi$
$258$	−2.44949	+	2.44949i	−0.152499	+	0.152499i
$259$		0			0
$260$		0			0
$261$	12.0000	+	6.92820i	0.742781	+	0.428845i
$262$	−14.4889	−	3.88229i	−0.895126	−	0.239848i
$263$	1.79315	+	6.69213i	0.110570	+	0.412654i	0.998917	−	0.0465183i	$-0.0148126\pi$
$263$	1.79315	+	6.69213i	0.110570	+	0.412654i	−0.888347	+	0.459173i	$0.848146\pi$
$264$	−2.59808	−	1.50000i	−0.159901	−	0.0923186i
$265$		0			0
$266$		0			0
$267$	4.89898	+	4.89898i	0.299813	+	0.299813i
$268$	0.965926	−	0.258819i	0.0590033	−	0.0158099i
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	−0.740883	−	0.671634i	$-0.765593\pi$
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	0.952093	+	0.305807i	$0.0989263\pi$
$270$		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	$0.00513477\pi$
$272$	1.79315	−	6.69213i	0.108726	−	0.405770i
$273$		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	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$	−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	$0.0989340\pi$
$282$	−6.69213	+	1.79315i	−0.398511	+	0.106781i
$283$	−4.03459	−	15.0573i	−0.239831	−	0.895063i	−0.975911	−	0.218168i	$-0.929992\pi$
$283$	−4.03459	−	15.0573i	−0.239831	−	0.895063i	0.736080	−	0.676895i	$-0.236675\pi$
$284$	3.46410			0.205557
$285$		0			0
$286$	−6.00000			−0.354787
$287$		0			0
$288$	−1.93185	+	0.517638i	−0.113835	+	0.0305021i
$289$	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	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	−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
$298$	4.65874	−	17.3867i	0.269874	−	1.00718i
$299$	−3.46410	+	6.00000i	−0.200334	+	0.346989i
$300$		0			0
$301$		0			0
$302$	−3.34607	+	0.896575i	−0.192544	+	0.0515921i
$303$	−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
$307$	−5.95284	−	22.2163i	−0.339746	−	1.26795i	−0.898631	−	0.438705i	$-0.855437\pi$
$307$	−5.95284	−	22.2163i	−0.339746	−	1.26795i	0.558885	−	0.829245i	$-0.311229\pi$
$308$		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
$313$	8.36516	+	2.24144i	0.472827	+	0.126694i	0.487361	−	0.873201i	$-0.337960\pi$
$313$	8.36516	+	2.24144i	0.472827	+	0.126694i	−0.0145337	+	0.999894i	$0.504626\pi$
$314$	−3.46410	−	6.00000i	−0.195491	−	0.338600i
$315$		0			0
$316$			6.92820i			0.389742i
$317$	17.3867	+	4.65874i	0.976532	+	0.261661i	0.711584	−	0.702601i	$-0.247978\pi$
$317$	17.3867	+	4.65874i	0.976532	+	0.261661i	0.264949	+	0.964262i	$0.414645\pi$
$318$	5.79555	−	1.55291i	0.324999	−	0.0870831i
$319$	10.3923	+	18.0000i	0.581857	+	1.00781i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−28.0812	+	11.1106i	−1.56248	+	0.618212i
$324$			1.00000i			0.0555556i
$325$		0			0
$326$	−10.5000	−	6.06218i	−0.581541	−	0.335753i
$327$		0			0
$328$	0.448288	+	1.67303i	0.0247525	+	0.0923778i
$329$		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	$0.891869\pi$
$332$	−0.448288	+	1.67303i	−0.0246030	+	0.0918196i
$333$	−1.03528	+	3.86370i	−0.0567328	+	0.211730i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.36465	−	12.5570i	−0.183284	−	0.684025i	−0.994991	−	0.0999609i	$-0.968128\pi$
$337$	−3.36465	−	12.5570i	−0.183284	−	0.684025i	0.811707	−	0.584064i	$-0.198538\pi$
$338$	−2.32937	+	8.69333i	−0.126701	+	0.472855i
$339$	7.79423	+	4.50000i	0.423324	+	0.244406i
$340$		0			0
$341$			10.3923i			0.562775i
$342$	6.83083	+	5.41662i	0.369369	+	0.292897i
$343$		0			0
$344$	−1.73205	+	3.00000i	−0.0933859	+	0.161749i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	31.7876	−	8.51747i	1.70645	−	0.457242i	0.731899	−	0.681413i	$-0.238634\pi$
$347$	31.7876	−	8.51747i	1.70645	−	0.457242i	0.974550	+	0.224171i	$0.0719676\pi$
$348$	−6.69213	−	1.79315i	−0.358736	−	0.0961230i
$349$		−	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
$351$	−5.00000	−	8.66025i	−0.266880	−	0.462250i
$352$	−2.89778	−	0.776457i	−0.154452	−	0.0413853i
$353$	−25.7196	+	25.7196i	−1.36892	+	1.36892i	−0.506933	+	0.861985i	$0.669221\pi$
$353$	−25.7196	+	25.7196i	−1.36892	+	1.36892i	−0.861985	+	0.506933i	$0.830779\pi$
$354$	5.19615			0.276172
$355$		0			0
$356$	6.00000	+	3.46410i	0.317999	+	0.183597i
$357$		0			0
$358$	−5.82774	−	21.7494i	−0.308006	−	1.14949i
$359$	25.9808	+	15.0000i	1.37121	+	0.791670i	0.991081	−	0.133263i	$-0.0425454\pi$
$359$	25.9808	+	15.0000i	1.37121	+	0.791670i	0.380131	+	0.924932i	$0.375879\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	17.1464	+	17.1464i	0.901196	+	0.901196i
$363$	1.93185	−	0.517638i	0.101396	−	0.0271690i
$364$		0			0
$365$		0			0
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	4.48288	−	16.7303i	0.234004	−	0.873316i	−0.744591	−	0.667521i	$-0.767355\pi$
$367$	4.48288	−	16.7303i	0.234004	−	0.873316i	0.978595	−	0.205795i	$-0.0659779\pi$
$368$	−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	−0.981827	−	0.189776i	$-0.939224\pi$
$373$	−22.6274	−	22.6274i	−1.17160	−	1.17160i	−0.189776	−	0.981827i	$-0.560776\pi$
$374$	−10.3923	−	18.0000i	−0.537373	−	0.930758i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	−13.3843	+	3.58630i	−0.689325	+	0.184704i
$378$		0			0
$379$	10.3923			0.533817			0.266908	−	0.963722i	$-0.413998\pi$
$379$	10.3923			0.533817			0.266908	+	0.963722i	$0.413998\pi$
$380$		0			0
$381$	22.0000			1.12709
$382$	−6.21166	−	23.1822i	−0.317816	−	1.18611i
$383$	34.7733	−	9.31749i	1.77683	−	0.476101i	0.786834	−	0.617165i	$-0.211719\pi$
$383$	34.7733	−	9.31749i	1.77683	−	0.476101i	0.990000	+	0.141064i	$0.0450523\pi$
$384$	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	−0.923717	−	0.383076i	$-0.874865\pi$
$389$	−20.7846	+	12.0000i	−1.05382	+	0.608424i	−0.130105	+	0.991500i	$0.541531\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$	−4.94975	+	4.94975i	−0.250000	+	0.250000i
$393$	3.88229	−	14.4889i	0.195835	−	0.730868i
$394$	5.19615	−	9.00000i	0.261778	−	0.453413i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	16.7303	−	4.48288i	0.839671	−	0.224989i	0.186743	−	0.982409i	$-0.440207\pi$
$397$	16.7303	−	4.48288i	0.839671	−	0.224989i	0.652928	+	0.757420i	$0.273540\pi$
$398$	−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	$0.597289\pi$
$402$	0.258819	+	0.965926i	0.0129087	+	0.0481760i
$403$	−6.69213	−	1.79315i	−0.333359	−	0.0893232i
$404$	−10.3923	−	6.00000i	−0.517036	−	0.298511i
$405$		0			0
$406$		0			0
$407$	−4.24264	+	4.24264i	−0.210300	+	0.210300i
$408$	6.69213	+	1.79315i	0.331310	+	0.0887742i
$409$	−9.52628	−	16.5000i	−0.471044	−	0.815872i	0.528407	−	0.848991i	$-0.322789\pi$
$409$	−9.52628	−	16.5000i	−0.471044	−	0.815872i	−0.999451	+	0.0331186i	$0.989456\pi$
$410$		0			0
$411$		−	15.5885i		−	0.768922i
$412$	−9.65926	−	2.58819i	−0.475877	−	0.127511i
$413$		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
$418$	4.81105	+	12.1595i	0.235316	+	0.594741i
$419$			12.0000i			0.586238i	0.956076	+	0.293119i	$0.0946933\pi$
$419$			12.0000i			0.586238i	−0.956076	+	0.293119i	$0.905307\pi$
$420$		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	$0.465437\pi$
$422$	2.68973	−	10.0382i	0.130934	−	0.488652i
$423$	3.58630	+	13.3843i	0.174372	+	0.650765i
$424$	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	$0.359921\pi$
$432$	−1.29410	−	4.82963i	−0.0622622	−	0.232366i
$433$	6.72930	−	25.1141i	0.323389	−	1.20691i	−0.592532	−	0.805547i	$-0.701872\pi$
$433$	6.72930	−	25.1141i	0.323389	−	1.20691i	0.915921	−	0.401358i	$-0.131462\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.9372	+	2.20925i	0.714542	+	0.105683i
$438$	−11.0227	+	11.0227i	−0.526685	+	0.526685i
$439$	−12.1244	+	21.0000i	−0.578664	+	1.00228i	0.416969	+	0.908921i	$0.363092\pi$
$439$	−12.1244	+	21.0000i	−0.578664	+	1.00228i	−0.995633	+	0.0933546i	$0.970241\pi$
$440$		0			0
$441$	7.00000	+	12.1244i	0.333333	+	0.577350i
$442$	13.3843	−	3.58630i	0.636624	−	0.170583i
$443$	21.7494	+	5.82774i	1.03335	+	0.276884i	0.735353	−	0.677684i	$-0.237016\pi$
$443$	21.7494	+	5.82774i	1.03335	+	0.276884i	0.297993	+	0.954568i	$0.403683\pi$
$444$		−	2.00000i		−	0.0949158i
$445$		0			0
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$	17.3867	+	4.65874i	0.822361	+	0.220351i
$448$		0			0
$449$	25.9808			1.22611			0.613054	−	0.790041i	$-0.289941\pi$
$449$	25.9808			1.22611			0.613054	+	0.790041i	$0.289941\pi$
$450$		0			0
$451$	4.50000	+	2.59808i	0.211897	+	0.122339i
$452$	8.69333	+	2.32937i	0.408900	+	0.109564i
$453$	−0.896575	−	3.34607i	−0.0421248	−	0.157212i
$454$	−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	0.317916	−	0.948119i	$-0.397017\pi$
$457$	−13.4722	−	13.4722i	−0.630203	−	0.630203i	−0.948119	+	0.317916i	$0.897017\pi$
$458$	−3.86370	+	1.03528i	−0.180539	+	0.0483753i
$459$	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	−0.185737	−	0.982599i	$-0.559467\pi$
$463$	17.1464	−	17.1464i	0.796862	−	0.796862i	0.982599	+	0.185737i	$0.0594674\pi$
$464$	−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	0.990147	−	0.140031i	$-0.0447201\pi$
$467$	18.3712	+	18.3712i	0.850117	+	0.850117i	−0.140031	+	0.990147i	$0.544720\pi$
$468$	−2.82843	−	2.82843i	−0.130744	−	0.130744i
$469$		0			0
$470$		0			0
$471$	6.00000	−	3.46410i	0.276465	−	0.159617i
$472$	5.01910	−	1.34486i	0.231023	−	0.0619023i
$473$	2.68973	+	10.0382i	0.123674	+	0.461557i
$474$	−6.92820			−0.318223
$475$		0			0
$476$		0			0
$477$	−3.10583	−	11.5911i	−0.142206	−	0.530720i
$478$		0			0
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.892979	−	0.450098i	$-0.851389\pi$
$479$	−20.7846	+	12.0000i	−0.949673	+	0.548294i	−0.0566937	+	0.998392i	$0.518056\pi$
$480$		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	0.249128	−	0.968471i	$-0.419856\pi$
$487$	26.8701	−	26.8701i	1.21760	−	1.21760i	0.968471	−	0.249128i	$-0.0801440\pi$
$488$	2.07055	−	7.72741i	0.0937295	−	0.349803i
$489$	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	$0.166667\pi$
$492$	−1.67303	+	0.448288i	−0.0754261	+	0.0202104i
$493$	−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
$498$	−1.67303	−	0.448288i	−0.0749704	−	0.0200883i
$499$	26.8468	+	15.5000i	1.20183	+	0.693875i	0.960961	−	0.276683i	$-0.0892352\pi$
$499$	26.8468	+	15.5000i	1.20183	+	0.693875i	0.240866	+	0.970558i	$0.422569\pi$
$500$		0			0
$501$		0			0
$502$	14.8492	−	14.8492i	0.662754	−	0.662754i
$503$	−30.1146	−	8.06918i	−1.34274	−	0.359787i	−0.485292	−	0.874352i	$-0.661287\pi$
$503$	−30.1146	−	8.06918i	−1.34274	−	0.359787i	−0.857451	+	0.514565i	$0.827953\pi$
$504$		0			0
$505$		0			0
$506$			10.3923i			0.461994i
$507$	−8.69333	−	2.32937i	−0.386084	−	0.103451i
$508$	21.2504	−	5.69402i	0.942833	−	0.252631i
$509$	13.8564	+	24.0000i	0.614174	+	1.06378i	0.990529	+	0.137305i	$0.0438442\pi$
$509$	13.8564	+	24.0000i	0.614174	+	1.06378i	−0.376354	+	0.926476i	$0.622822\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−13.5415	+	17.0771i	−0.597874	+	0.753971i
$514$		−	3.00000i		−	0.132324i
$515$		0			0
$516$	−3.00000	−	1.73205i	−0.132068	−	0.0762493i
$517$	−5.37945	+	20.0764i	−0.236588	+	0.882959i
$518$		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	$-0.192716\pi$
$522$	−3.58630	+	13.3843i	−0.156968	+	0.585813i
$523$	5.17638	−	19.3185i	0.226347	−	0.844740i	−0.755513	−	0.655134i	$-0.772612\pi$
$523$	5.17638	−	19.3185i	0.226347	−	0.844740i	0.981860	−	0.189606i	$-0.0607211\pi$
$524$		−	15.0000i		−	0.655278i
$525$		0			0
$526$	−6.00000	+	3.46410i	−0.261612	+	0.151042i
$527$	−6.21166	−	23.1822i	−0.270584	−	1.00983i
$528$	0.776457	−	2.89778i	0.0337910	−	0.126110i
$529$	−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
$537$	21.7494	−	5.82774i	0.938557	−	0.251486i
$538$	6.69213	+	1.79315i	0.288518	+	0.0773082i
$539$			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	$0.721569\pi$
$542$	15.4548	+	4.14110i	0.663841	+	0.177876i
$543$	−17.1464	+	17.1464i	−0.735824	+	0.735824i
$544$	6.92820			0.297044
$545$		0			0
$546$		0			0
$547$	27.0459	+	7.24693i	1.15640	+	0.309856i	0.785527	−	0.618827i	$-0.212392\pi$
$547$	27.0459	+	7.24693i	1.15640	+	0.309856i	0.370873	+	0.928684i	$0.379059\pi$
$548$	−4.03459	−	15.0573i	−0.172349	−	0.643216i
$549$	−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
$557$	8.96575	−	33.4607i	0.379891	−	1.41777i	−0.466174	−	0.884693i	$-0.654368\pi$
$557$	8.96575	−	33.4607i	0.379891	−	1.41777i	0.846065	−	0.533080i	$-0.178966\pi$
$558$	−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	$-0.395916\pi$
$563$	−14.8492	−	14.8492i	−0.625821	−	0.625821i	−0.947014	+	0.321193i	$0.895916\pi$
$564$	−3.46410	−	6.00000i	−0.145865	−	0.252646i
$565$		0			0
$566$	13.5000	−	7.79423i	0.567447	−	0.327616i
$567$		0			0
$568$	0.896575	+	3.34607i	0.0376195	+	0.140398i
$569$	34.6410			1.45223			0.726113	−	0.687575i	$-0.241325\pi$
$569$	34.6410			1.45223			0.726113	+	0.687575i	$0.241325\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−1.55291	−	5.79555i	−0.0649306	−	0.242324i
$573$	23.1822	−	6.21166i	0.968451	−	0.259496i
$574$		0			0
$575$		0			0
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	−13.4722	−	13.4722i	−0.560855	−	0.560855i	0.368695	−	0.929550i	$-0.379805\pi$
$577$	−13.4722	−	13.4722i	−0.560855	−	0.560855i	−0.929550	+	0.368695i	$0.879805\pi$
$578$	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
$583$	4.65874	−	17.3867i	0.192945	−	0.720082i
$584$	−7.79423	+	13.5000i	−0.322527	+	0.558634i
$585$		0			0
$586$		0			0
$587$	−3.34607	+	0.896575i	−0.138107	+	0.0370056i	−0.327210	−	0.944952i	$-0.606109\pi$
$587$	−3.34607	+	0.896575i	−0.138107	+	0.0370056i	0.189103	+	0.981957i	$0.439442\pi$
$588$	−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
$592$	−0.517638	−	1.93185i	−0.0212748	−	0.0793986i
$593$	−5.01910	−	1.34486i	−0.206110	−	0.0552269i	0.154287	−	0.988026i	$-0.450692\pi$
$593$	−5.01910	−	1.34486i	−0.206110	−	0.0552269i	−0.360397	+	0.932799i	$0.617359\pi$
$594$	−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
$598$	−6.69213	−	1.79315i	−0.273662	−	0.0733274i
$599$	−8.66025	−	15.0000i	−0.353848	−	0.612883i	0.633072	−	0.774093i	$-0.281794\pi$
$599$	−8.66025	−	15.0000i	−0.353848	−	0.612883i	−0.986920	+	0.161210i	$0.948460\pi$
$600$		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
$603$	1.93185	−	0.517638i	0.0786711	−	0.0210799i
$604$	−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	−0.161082	+	0.986941i	$0.551498\pi$
$607$	−28.2843	+	28.2843i	−1.14802	+	1.14802i	−0.986941	+	0.161082i	$0.948502\pi$
$608$	−4.31199	−	0.637756i	−0.174874	−	0.0258644i
$609$		0			0
$610$		0			0
$611$	−12.0000	−	6.92820i	−0.485468	−	0.280285i
$612$	3.58630	−	13.3843i	0.144968	−	0.541027i
$613$	9.86233	+	36.8067i	0.398336	+	1.48661i	0.816024	+	0.578019i	$0.196174\pi$
$613$	9.86233	+	36.8067i	0.398336	+	1.48661i	−0.417688	+	0.908591i	$0.637159\pi$
$614$	19.9186	−	11.5000i	0.803849	−	0.464102i
$615$		0			0
$616$		0			0
$617$	4.93117	−	18.4034i	0.198521	−	0.740891i	−0.792806	−	0.609474i	$-0.791381\pi$
$617$	4.93117	−	18.4034i	0.198521	−	0.740891i	0.991327	−	0.131417i	$-0.0419527\pi$
$618$	2.58819	−	9.65926i	0.104112	−	0.388552i
$619$		−	28.0000i		−	1.12542i	−0.826656	−	0.562708i	$-0.809760\pi$
$619$		−	28.0000i		−	1.12542i	0.826656	−	0.562708i	$-0.190240\pi$
$620$		0			0
$621$	−15.0000	+	8.66025i	−0.601929	+	0.347524i
$622$	−4.65874	−	17.3867i	−0.186799	−	0.697142i
$623$		0			0
$624$	1.73205	+	1.00000i	0.0693375	+	0.0400320i
$625$		0			0
$626$			8.66025i			0.346133i
$627$	−12.1595	+	4.81105i	−0.485604	+	0.192135i
$628$	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	$0.782430\pi$
$632$	−6.69213	+	1.79315i	−0.266199	+	0.0713277i
$633$	10.0382	+	2.68973i	0.398982	+	0.106907i
$634$			18.0000i			0.714871i
$635$		0			0
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−13.5230	−	3.62347i	−0.535799	−	0.143567i
$638$	−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
$643$	−10.3106	−	38.4797i	−0.406611	−	1.51749i	−0.801065	−	0.598577i	$-0.795733\pi$
$643$	−10.3106	−	38.4797i	−0.406611	−	1.51749i	0.394454	−	0.918916i	$-0.370934\pi$
$644$		0			0
$645$		0			0
$646$	−18.0000	−	24.2487i	−0.708201	−	0.954053i
$647$	7.34847	+	7.34847i	0.288898	+	0.288898i	0.836644	−	0.547746i	$-0.184514\pi$
$647$	7.34847	+	7.34847i	0.288898	+	0.288898i	−0.547746	+	0.836644i	$0.684514\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	7.79423	−	13.5000i	0.305950	−	0.529921i
$650$		0			0
$651$		0			0
$652$	3.13801	−	11.7112i	0.122894	−	0.458647i
$653$	4.89898	−	4.89898i	0.191712	−	0.191712i	−0.604724	−	0.796435i	$-0.706716\pi$
$653$	4.89898	−	4.89898i	0.191712	−	0.191712i	0.796435	+	0.604724i	$0.206716\pi$
$654$		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	0.897787	−	0.440429i	$-0.145174\pi$
$659$	1.73205	+	3.00000i	0.0674711	+	0.116863i	−0.830316	+	0.557292i	$0.811840\pi$
$660$		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	$0.290314\pi$
$662$	−11.7112	+	3.13801i	−0.455170	+	0.121962i
$663$	3.58630	+	13.3843i	0.139280	+	0.519802i
$664$	−1.73205			−0.0672166
$665$		0			0
$666$	−4.00000			−0.154997
$667$	6.21166	+	23.1822i	0.240516	+	0.897619i
$668$		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	$-0.237727\pi$
$673$	1.41421	+	1.41421i	0.0545139	+	0.0545139i	−0.679324	+	0.733838i	$0.737727\pi$
$674$	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	$-0.862426\pi$
$677$	−12.7279	+	12.7279i	−0.489174	+	0.489174i	0.418872	+	0.908045i	$0.362426\pi$
$678$	−2.32937	+	8.69333i	−0.0894590	+	0.333865i
$679$		0			0
$680$		0			0
$681$	10.5000	−	18.1865i	0.402361	−	0.696909i
$682$	−10.0382	+	2.68973i	−0.384382	+	0.102995i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$	−3.46410	+	8.00000i	−0.132453	+	0.305888i
$685$		0			0
$686$		0			0
$687$	−1.03528	−	3.86370i	−0.0394982	−	0.147409i
$688$	−3.34607	−	0.896575i	−0.127568	−	0.0341816i
$689$	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
$697$	−11.5911	−	3.10583i	−0.439045	−	0.117642i
$698$	3.86370	−	1.03528i	0.146243	−	0.0391858i
$699$	−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
$703$	−5.41662	+	6.83083i	−0.204292	+	0.257630i
$704$		−	3.00000i		−	0.113067i
$705$		0			0
$706$	−31.5000	−	18.1865i	−1.18552	−	0.684459i
$707$		0			0
$708$	1.34486	+	5.01910i	0.0505431	+	0.188629i
$709$	−29.4449	+	17.0000i	−1.10583	+	0.638448i	−0.937745	−	0.347325i	$-0.887090\pi$
$709$	−29.4449	+	17.0000i	−1.10583	+	0.638448i	−0.168080	+	0.985773i	$0.553757\pi$
$710$		0			0
$711$			13.8564i			0.519656i
$712$	−1.79315	+	6.69213i	−0.0672012	+	0.250798i
$713$	−3.10583	+	11.5911i	−0.116314	+	0.434090i
$714$		0			0
$715$		0			0
$716$	19.5000	−	11.2583i	0.728749	−	0.420744i
$717$		0			0
$718$	−7.76457	+	28.9778i	−0.289771	+	1.08144i
$719$	−5.19615	−	3.00000i	−0.193784	−	0.111881i	0.399969	−	0.916529i	$-0.369021\pi$
$719$	−5.19615	−	3.00000i	−0.193784	−	0.111881i	−0.593753	+	0.804648i	$0.702354\pi$
$720$		0			0
$721$		0			0
$722$	8.97073	+	16.7489i	0.333856	+	0.623330i
$723$	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
$727$	−6.69213	+	1.79315i	−0.248197	+	0.0665043i	−0.380773	−	0.924669i	$-0.624342\pi$
$727$	−6.69213	+	1.79315i	−0.248197	+	0.0665043i	0.132575	+	0.991173i	$0.457675\pi$
$728$		0			0
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	7.72741	+	2.07055i	0.285613	+	0.0765298i
$733$	−22.0454	+	22.0454i	−0.814266	+	0.814266i	−0.985270	−	0.171005i	$-0.945299\pi$
$733$	−22.0454	+	22.0454i	−0.814266	+	0.814266i	0.171005	+	0.985270i	$0.445299\pi$
$734$	17.3205			0.639312
$735$		0			0
$736$	−3.00000	−	1.73205i	−0.110581	−	0.0638442i
$737$	2.89778	+	0.776457i	0.106741	+	0.0286012i
$738$	0.896575	+	3.34607i	0.0330034	+	0.123170i
$739$	9.52628	+	5.50000i	0.350430	+	0.202321i	0.664875	−	0.746955i	$-0.268485\pi$
$739$	9.52628	+	5.50000i	0.350430	+	0.202321i	−0.314445	+	0.949276i	$0.601818\pi$
$740$		0			0
$741$	−1.00000	−	8.66025i	−0.0367359	−	0.318142i
$742$		0			0
$743$	−5.79555	+	1.55291i	−0.212618	+	0.0569709i	−0.363556	−	0.931572i	$-0.618437\pi$
$743$	−5.79555	+	1.55291i	−0.212618	+	0.0569709i	0.150938	+	0.988543i	$0.451771\pi$
$744$	1.73205	−	3.00000i	0.0635001	−	0.109985i
$745$		0			0
$746$	16.0000	−	27.7128i	0.585802	−	1.01464i
$747$	−0.896575	+	3.34607i	−0.0328040	+	0.122426i
$748$	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
$757$	−36.8067	+	9.86233i	−1.33776	+	0.358452i	−0.855604	−	0.517631i	$-0.826814\pi$
$757$	−36.8067	+	9.86233i	−1.33776	+	0.358452i	−0.482159	+	0.876084i	$0.660147\pi$
$758$	2.68973	+	10.0382i	0.0976953	+	0.364604i
$759$	−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	$0.412356\pi$
$762$	5.69402	+	21.2504i	0.206273	+	0.769820i
$763$		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	−0.265200	−	0.964193i	$-0.585438\pi$
$769$	12.1244	−	7.00000i	0.437215	−	0.252426i	0.702416	+	0.711767i	$0.252105\pi$
$770$		0			0
$771$	3.00000			0.108042
$772$	−15.5563	+	15.5563i	−0.559885	+	0.559885i
$773$	12.4233	−	46.3644i	0.446836	−	1.66761i	−0.264209	−	0.964466i	$-0.585111\pi$
$773$	12.4233	−	46.3644i	0.446836	−	1.66761i	0.711044	−	0.703147i	$-0.248223\pi$
$774$	−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
$782$	−6.21166	−	23.1822i	−0.222128	−	0.828994i
$783$	−33.4607	−	8.96575i	−1.19579	−	0.320410i
$784$	−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	$-0.563668\pi$
$787$	21.9203	−	21.9203i	0.781375	−	0.781375i	0.980063	+	0.198688i	$0.0636681\pi$
$788$	10.0382	+	2.68973i	0.357596	+	0.0958175i
$789$	−3.46410	−	6.00000i	−0.123325	−	0.213606i
$790$		0			0
$791$		0			0
$792$	−5.79555	−	1.55291i	−0.205936	−	0.0551804i
$793$	15.4548	−	4.14110i	0.548817	−	0.147055i
$794$	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	−0.469726	+	0.882812i	$0.655647\pi$
$797$	−38.1838	+	38.1838i	−1.35254	+	1.35254i	−0.882812	+	0.469726i	$0.844353\pi$
$798$		0			0
$799$		−	48.0000i		−	1.69812i
$800$		0			0
$801$	12.0000	+	6.92820i	0.423999	+	0.244796i
$802$	−2.24144	+	8.36516i	−0.0791480	+	0.295384i
$803$	12.1038	+	45.1719i	0.427133	+	1.59408i
$804$	−0.866025	+	0.500000i	−0.0305424	+	0.0176336i
$805$		0			0
$806$		−	6.92820i		−	0.244036i
$807$	−1.79315	+	6.69213i	−0.0631219	+	0.235574i
$808$	3.10583	−	11.5911i	0.109263	−	0.407774i
$809$			3.00000i			0.105474i	0.998608	+	0.0527372i	$0.0167946\pi$
$809$			3.00000i			0.105474i	−0.998608	+	0.0527372i	$0.983205\pi$
$810$		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
$813$	−4.14110	+	15.4548i	−0.145235	+	0.542024i
$814$	−5.19615	−	3.00000i	−0.182125	−	0.105150i
$815$		0			0
$816$			6.92820i			0.242536i
$817$	5.55532	+	14.0406i	0.194356	+	0.491218i
$818$	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	$-0.428503\pi$
$822$	15.0573	−	4.03459i	0.525183	−	0.140722i
$823$	43.4988	+	11.6555i	1.51627	+	0.406285i	0.918513	−	0.395390i	$-0.129390\pi$
$823$	43.4988	+	11.6555i	1.51627	+	0.406285i	0.597761	+	0.801674i	$0.296057\pi$
$824$		−	10.0000i		−	0.348367i
$825$		0			0
$826$		0			0
$827$	−31.8756	−	8.54103i	−1.10842	−	0.297001i	−0.342232	−	0.939615i	$-0.611183\pi$
$827$	−31.8756	−	8.54103i	−1.10842	−	0.297001i	−0.766189	+	0.642615i	$0.777850\pi$
$828$	−4.89898	+	4.89898i	−0.170251	+	0.170251i
$829$	−41.5692			−1.44376			−0.721879	−	0.692019i	$-0.756721\pi$
$829$	−41.5692			−1.44376			−0.721879	+	0.692019i	$0.756721\pi$
$830$		0			0
$831$		0			0
$832$	1.93185	+	0.517638i	0.0669749	+	0.0179459i
$833$	−12.5521	−	46.8449i	−0.434903	−	1.62308i
$834$	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
$838$	−11.5911	+	3.10583i	−0.400408	+	0.107289i
$839$	−13.8564	+	24.0000i	−0.478376	+	0.828572i	−0.999693	−	0.0247915i	$-0.992108\pi$
$839$	−13.8564	+	24.0000i	−0.478376	+	0.828572i	0.521316	+	0.853363i	$0.325441\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$	−6.27603	+	23.4225i	−0.216286	+	0.807191i
$843$	−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
$852$	−3.34607	+	0.896575i	−0.114634	+	0.0307162i
$853$	13.4486	+	50.1910i	0.460472	+	1.71851i	0.671481	+	0.741022i	$0.265659\pi$
$853$	13.4486	+	50.1910i	0.460472	+	1.71851i	−0.211008	+	0.977484i	$0.567675\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.98811	+	26.0800i	0.238709	+	0.890876i	0.976442	+	0.215782i	$0.0692301\pi$
$857$	6.98811	+	26.0800i	0.238709	+	0.890876i	−0.737732	+	0.675094i	$0.764103\pi$
$858$	5.79555	−	1.55291i	0.197857	−	0.0530156i
$859$	4.33013	−	2.50000i	0.147742	−	0.0852989i	−0.424307	−	0.905519i	$-0.639482\pi$
$859$	4.33013	−	2.50000i	0.147742	−	0.0852989i	0.572049	+	0.820220i	$0.306149\pi$
$860$		0			0
$861$		0			0
$862$	−2.44949	−	2.44949i	−0.0834300	−	0.0834300i
$863$	29.6985	+	29.6985i	1.01095	+	1.01095i	0.999939	+	0.0110088i	$0.00350427\pi$
$863$	29.6985	+	29.6985i	1.01095	+	1.01095i	0.0110088	+	0.999939i	$0.496496\pi$
$864$	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
$877$	−5.17638	−	19.3185i	−0.174794	−	0.652340i	−0.996587	−	0.0825533i	$-0.973693\pi$
$877$	−5.17638	−	19.3185i	−0.174794	−	0.652340i	0.821793	−	0.569787i	$-0.192974\pi$
$878$	−23.4225	−	6.27603i	−0.790470	−	0.211806i
$879$		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
$883$	38.4797	+	10.3106i	1.29495	+	0.346980i	0.839537	−	0.543302i	$-0.182826\pi$
$883$	38.4797	+	10.3106i	1.29495	+	0.346980i	0.455409	+	0.890282i	$0.349493\pi$
$884$	6.92820	+	12.0000i	0.233021	+	0.403604i
$885$		0			0
$886$			22.5167i			0.756462i
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$	1.93185	−	0.517638i	0.0648287	−	0.0173708i
$889$		0			0
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	−18.3848	+	18.3848i	−0.615568	+	0.615568i
$893$	−4.41851	+	29.8744i	−0.147860	+	0.999707i
$894$			18.0000i			0.602010i
$895$		0			0
$896$		0			0
$897$	1.79315	−	6.69213i	0.0598716	−	0.223444i
$898$	6.72432	+	25.0955i	0.224393	+	0.837447i
$899$	−20.7846	+	12.0000i	−0.693206	+	0.400222i
$900$		0			0
$901$			41.5692i			1.38487i
$902$	−1.34486	+	5.01910i	−0.0447790	+	0.167118i
$903$		0			0
$904$			9.00000i			0.299336i
$905$		0			0
$906$	3.00000	−	1.73205i	0.0996683	−	0.0575435i
$907$	−4.39992	−	16.4207i	−0.146097	−	0.545242i	−0.999704	−	0.0243242i	$-0.992257\pi$
$907$	−4.39992	−	16.4207i	−0.146097	−	0.545242i	0.853607	−	0.520917i	$-0.174410\pi$
$908$	5.43520	−	20.2844i	0.180373	−	0.673163i
$909$	−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	$-0.0550734\pi$
$912$	0.637756	−	4.31199i	0.0211182	−	0.142784i
$913$	−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
$918$	33.4607	+	8.96575i	1.10437	+	0.295914i
$919$		−	38.0000i		−	1.25350i	−0.779219	−	0.626752i	$-0.784384\pi$
$919$		−	38.0000i		−	1.25350i	0.779219	−	0.626752i	$-0.215616\pi$
$920$		0			0
$921$	11.5000	+	19.9186i	0.378938	+	0.656340i
$922$	−28.9778	−	7.76457i	−0.954332	−	0.255713i
$923$	−4.89898	+	4.89898i	−0.161252	+	0.161252i
$924$		0			0
$925$		0			0
$926$	21.0000	+	12.1244i	0.690103	+	0.398431i
$927$	−19.3185	−	5.17638i	−0.634503	−	0.170015i
$928$	−1.79315	−	6.69213i	−0.0588631	−	0.219680i
$929$	2.59808	+	1.50000i	0.0852401	+	0.0492134i	0.542014	−	0.840369i	$-0.317662\pi$
$929$	2.59808	+	1.50000i	0.0852401	+	0.0492134i	−0.456774	+	0.889583i	$0.650995\pi$
$930$		0			0
$931$	3.50000	+	30.3109i	0.114708	+	0.993399i
$932$	−15.9217	−	15.9217i	−0.521532	−	0.521532i
$933$	17.3867	−	4.65874i	0.569214	−	0.152520i
$934$	−12.9904	+	22.5000i	−0.425058	+	0.736222i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	−8.51747	+	31.7876i	−0.278254	+	1.03846i	0.675376	+	0.737474i	$0.263981\pi$
$937$	−8.51747	+	31.7876i	−0.278254	+	1.03846i	−0.953630	+	0.300983i	$0.902685\pi$
$938$		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
$947$	−23.4225	+	6.27603i	−0.761128	+	0.203944i	−0.618448	−	0.785825i	$-0.712238\pi$
$947$	−23.4225	+	6.27603i	−0.761128	+	0.203944i	−0.142679	+	0.989769i	$0.545572\pi$
$948$	−1.79315	−	6.69213i	−0.0582388	−	0.217350i
$949$	−31.1769			−1.01205
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−14.4889	+	3.88229i	−0.469341	+	0.125760i	−0.485735	−	0.874106i	$-0.661448\pi$
$953$	−14.4889	+	3.88229i	−0.469341	+	0.125760i	0.0163940	+	0.999866i	$0.494781\pi$
$954$	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
$967$	10.0382	−	2.68973i	0.322807	−	0.0864958i	−0.0937769	−	0.995593i	$-0.529894\pi$
$967$	10.0382	−	2.68973i	0.322807	−	0.0864958i	0.416583	+	0.909097i	$0.363227\pi$
$968$	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	$0.422159\pi$
$972$	−4.14110	−	15.4548i	−0.132826	−	0.495713i
$973$		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	$-0.704014\pi$
$977$	6.36396	−	6.36396i	0.203601	−	0.203601i	0.801541	+	0.597940i	$0.204014\pi$
$978$	11.7112	+	3.13801i	0.374484	+	0.100343i
$979$	10.3923	+	18.0000i	0.332140	+	0.575282i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	57.9555	−	15.5291i	1.84849	−	0.495303i	0.849040	−	0.528328i	$-0.177181\pi$
$983$	57.9555	−	15.5291i	1.84849	−	0.495303i	0.999455	+	0.0330251i	$0.0105141\pi$
$984$	−0.866025	−	1.50000i	−0.0276079	−	0.0478183i
$985$		0			0
$986$	24.0000	−	41.5692i	0.764316	−	1.32383i
$987$		0			0
$988$	−3.20736	−	8.10634i	−0.102040	−	0.257897i
$989$			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	$0.386780\pi$
$992$	0.896575	−	3.34607i	0.0284663	−	0.106238i
$993$	−3.13801	−	11.7112i	−0.0995819	−	0.371645i
$994$		0			0
$995$		0			0
$996$		−	1.73205i		−	0.0548821i
$997$	−3.58630	+	13.3843i	−0.113579	+	0.423884i	−0.999177	−	0.0405699i	$-0.987083\pi$
$997$	−3.58630	+	13.3843i	−0.113579	+	0.423884i	0.885597	+	0.464454i	$0.153749\pi$
$998$	−8.02339	+	29.9437i	−0.253976	+	0.947851i
$999$		−	10.0000i		−	0.316386i

Twists

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more