LMFDB - Embedded newform 950.2.q.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	950.107
Dual form			950.2.q.c.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73205 + 1.00000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73205 + 1.00000i) q^{9} +(-0.707107 + 0.707107i) q^{12} +(1.93185 - 0.517638i) q^{13} +(1.73205 + 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.448288 - 1.67303i) q^{17} +(-1.41421 - 1.41421i) q^{18} +(-2.59808 + 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(-0.896575 - 3.34607i) q^{23} +(0.866025 - 0.500000i) q^{24} -2.00000 q^{26} +(-3.53553 + 3.53553i) q^{27} +(-0.896575 - 3.34607i) q^{28} +(1.73205 - 3.00000i) q^{29} -10.3923i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.866025 + 1.50000i) q^{34} +(1.00000 + 1.73205i) q^{36} +(2.82843 - 2.82843i) q^{37} +(3.41542 - 2.70831i) q^{38} +2.00000i q^{39} +(6.00000 - 3.46410i) q^{41} +(-3.34607 + 0.896575i) q^{42} +(-3.34607 - 0.896575i) q^{43} +3.46410i q^{46} +(6.69213 - 1.79315i) q^{47} +(-0.965926 + 0.258819i) q^{48} +5.00000i q^{49} +(1.50000 + 0.866025i) q^{51} +(1.93185 + 0.517638i) q^{52} +(4.33013 - 2.50000i) q^{54} +3.46410i q^{56} +(-2.70831 - 3.41542i) q^{57} +(-2.44949 + 2.44949i) q^{58} +(2.59808 + 4.50000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-2.68973 + 10.0382i) q^{62} +(-1.79315 - 6.69213i) q^{63} +1.00000i q^{64} +(2.07055 + 7.72741i) q^{67} +(1.22474 - 1.22474i) q^{68} +3.46410 q^{69} +(12.0000 - 6.92820i) q^{71} +(-0.517638 - 1.93185i) q^{72} +(8.36516 + 2.24144i) q^{73} +(-3.46410 + 2.00000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(0.517638 - 1.93185i) q^{78} +(0.500000 + 0.866025i) q^{81} +(-6.69213 + 1.79315i) q^{82} +(-1.22474 + 1.22474i) q^{83} +3.46410 q^{84} +(3.00000 + 1.73205i) q^{86} +(2.44949 + 2.44949i) q^{87} +(4.33013 - 7.50000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(0.896575 - 3.34607i) q^{92} +(10.0382 + 2.68973i) q^{93} -6.92820 q^{94} +1.00000 q^{96} +(6.76148 + 1.81173i) q^{97} +(1.29410 - 4.82963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^6	$ 8 q + 4 q^{6} + 4 q^{16} + 24 q^{21} - 16 q^{26} + 8 q^{36} + 48 q^{41} + 12 q^{51} + 32 q^{61} + 96 q^{71} - 32 q^{76} + 4 q^{81} + 24 q^{86} - 48 q^{91} + 8 q^{96}+O(q^{100}) $ 8 * q + 4 * q^6 + 4 * q^16 + 24 * q^21 - 16 * q^26 + 8 * q^36 + 48 * q^41 + 12 * q^51 + 32 * q^61 + 96 * q^71 - 32 * q^76 + 4 * q^81 + 24 * q^86 - 48 * q^91 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i	0.850089	+	0.526639i	$0.176548\pi$
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i	−0.999518	+	0.0310384i	$0.990119\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	−2.44949	−	2.44949i	−0.925820	−	0.925820i	−0.997433	+	0.0716124i	$0.977186\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.73205	+	1.00000i	0.577350	+	0.333333i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	1.93185	−	0.517638i	0.535799	−	0.143567i	0.0192343	−	0.999815i	$-0.493877\pi$
$13$	1.93185	−	0.517638i	0.535799	−	0.143567i	0.516565	+	0.856248i	$0.327210\pi$
$14$	1.73205	+	3.00000i	0.462910	+	0.801784i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.448288	−	1.67303i	0.108726	−	0.405770i	−0.890015	−	0.455930i	$-0.849307\pi$
$17$	0.448288	−	1.67303i	0.108726	−	0.405770i	0.998741	+	0.0501604i	$0.0159733\pi$
$18$	−1.41421	−	1.41421i	−0.333333	−	0.333333i
$19$	−2.59808	+	3.50000i	−0.596040	+	0.802955i
$19$	−2.59808	+	3.50000i	−0.596040	+	0.802955i
$20$		0			0
$21$	3.00000	−	1.73205i	0.654654	−	0.377964i
$22$		0			0
$23$	−0.896575	−	3.34607i	−0.186949	−	0.697703i	−0.994205	−	0.107501i	$-0.965715\pi$
$23$	−0.896575	−	3.34607i	−0.186949	−	0.697703i	0.807256	−	0.590201i	$-0.200952\pi$
$24$	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
$28$	−0.896575	−	3.34607i	−0.169437	−	0.632347i
$29$	1.73205	−	3.00000i	0.321634	−	0.557086i	−0.659192	−	0.751975i	$-0.729101\pi$
$29$	1.73205	−	3.00000i	0.321634	−	0.557086i	0.980825	+	0.194889i	$0.0624347\pi$
$30$		0			0
$31$		−	10.3923i		−	1.86651i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$		−	10.3923i		−	1.86651i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	−0.866025	+	1.50000i	−0.148522	+	0.257248i
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	2.82843	−	2.82843i	0.464991	−	0.464991i	−0.435297	−	0.900287i	$-0.643356\pi$
$37$	2.82843	−	2.82843i	0.464991	−	0.464991i	0.900287	+	0.435297i	$0.143356\pi$
$38$	3.41542	−	2.70831i	0.554054	−	0.439346i
$39$			2.00000i			0.320256i
$40$		0			0
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.0480106	−	0.998847i	$-0.484712\pi$
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.889032	+	0.457845i	$0.151379\pi$
$42$	−3.34607	+	0.896575i	−0.516309	+	0.138345i
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.00550783	−	0.999985i	$-0.501753\pi$
$43$	−3.34607	−	0.896575i	−0.510270	−	0.136726i	−0.504762	+	0.863258i	$0.668420\pi$
$44$		0			0
$45$		0			0
$46$			3.46410i			0.510754i
$47$	6.69213	−	1.79315i	0.976148	−	0.261558i	0.264726	−	0.964324i	$-0.414718\pi$
$47$	6.69213	−	1.79315i	0.976148	−	0.261558i	0.711421	+	0.702766i	$0.248052\pi$
$48$	−0.965926	+	0.258819i	−0.139419	+	0.0373573i
$49$			5.00000i			0.714286i
$50$		0			0
$51$	1.50000	+	0.866025i	0.210042	+	0.121268i
$52$	1.93185	+	0.517638i	0.267900	+	0.0717835i
$53$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$53$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$54$	4.33013	−	2.50000i	0.589256	−	0.340207i
$55$		0			0
$56$			3.46410i			0.462910i
$57$	−2.70831	−	3.41542i	−0.358724	−	0.452383i
$58$	−2.44949	+	2.44949i	−0.321634	+	0.321634i
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	0.984102	−	0.177605i	$-0.0568349\pi$
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	−0.645861	+	0.763455i	$0.723502\pi$
$60$		0			0
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−2.68973	+	10.0382i	−0.341596	+	1.27485i
$63$	−1.79315	−	6.69213i	−0.225916	−	0.843129i
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	2.07055	+	7.72741i	0.252958	+	0.944053i	0.969215	+	0.246216i	$0.0791873\pi$
$67$	2.07055	+	7.72741i	0.252958	+	0.944053i	−0.716257	+	0.697837i	$0.754146\pi$
$68$	1.22474	−	1.22474i	0.148522	−	0.148522i
$69$	3.46410			0.417029
$70$		0			0
$71$	12.0000	−	6.92820i	1.42414	−	0.822226i	0.427489	−	0.904021i	$-0.359398\pi$
$71$	12.0000	−	6.92820i	1.42414	−	0.822226i	0.996649	+	0.0817942i	$0.0260650\pi$
$72$	−0.517638	−	1.93185i	−0.0610042	−	0.227671i
$73$	8.36516	+	2.24144i	0.979068	+	0.262341i	0.712652	−	0.701518i	$-0.247494\pi$
$73$	8.36516	+	2.24144i	0.979068	+	0.262341i	0.266416	+	0.963858i	$0.414160\pi$
$74$	−3.46410	+	2.00000i	−0.402694	+	0.232495i
$75$		0			0
$76$	−4.00000	+	1.73205i	−0.458831	+	0.198680i
$77$		0			0
$78$	0.517638	−	1.93185i	0.0586110	−	0.218739i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−6.69213	+	1.79315i	−0.739022	+	0.198020i
$83$	−1.22474	+	1.22474i	−0.134433	+	0.134433i	−0.771121	−	0.636688i	$-0.780304\pi$
$83$	−1.22474	+	1.22474i	−0.134433	+	0.134433i	0.636688	+	0.771121i	$0.280304\pi$
$84$	3.46410			0.377964
$85$		0			0
$86$	3.00000	+	1.73205i	0.323498	+	0.186772i
$87$	2.44949	+	2.44949i	0.262613	+	0.262613i
$88$		0			0
$89$	4.33013	−	7.50000i	0.458993	−	0.794998i	−0.539915	−	0.841719i	$-0.681544\pi$
$89$	4.33013	−	7.50000i	0.458993	−	0.794998i	0.998908	+	0.0467209i	$0.0148771\pi$
$90$		0			0
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$	0.896575	−	3.34607i	0.0934745	−	0.348851i
$93$	10.0382	+	2.68973i	1.04091	+	0.278912i
$94$	−6.92820			−0.714590
$95$		0			0
$96$	1.00000			0.102062
$97$	6.76148	+	1.81173i	0.686524	+	0.183954i	0.585187	−	0.810898i	$-0.301021\pi$
$97$	6.76148	+	1.81173i	0.686524	+	0.183954i	0.101337	+	0.994852i	$0.467688\pi$
$98$	1.29410	−	4.82963i	0.130723	−	0.487866i
$99$		0			0
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$	−1.22474	−	1.22474i	−0.121268	−	0.121268i
$103$	−2.82843	−	2.82843i	−0.278693	−	0.278693i	0.553894	−	0.832587i	$-0.313141\pi$
$103$	−2.82843	−	2.82843i	−0.278693	−	0.278693i	−0.832587	+	0.553894i	$0.813141\pi$
$104$	−1.73205	−	1.00000i	−0.169842	−	0.0980581i
$105$		0			0
$106$		0			0
$107$	10.6066	−	10.6066i	1.02538	−	1.02538i	0.0257094	−	0.999669i	$-0.491816\pi$
$107$	10.6066	−	10.6066i	1.02538	−	1.02538i	0.999669	−	0.0257094i	$-0.00818447\pi$
$108$	−4.82963	+	1.29410i	−0.464731	+	0.124524i
$109$	−8.66025	−	15.0000i	−0.829502	−	1.43674i	−0.898430	−	0.439118i	$-0.855291\pi$
$109$	−8.66025	−	15.0000i	−0.829502	−	1.43674i	0.0689276	−	0.997622i	$-0.478042\pi$
$110$		0			0
$111$	2.00000	+	3.46410i	0.189832	+	0.328798i
$112$	0.896575	−	3.34607i	0.0847184	−	0.316173i
$113$	−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	$0.889137\pi$
$114$	1.73205	+	4.00000i	0.162221	+	0.374634i
$115$		0			0
$116$	3.00000	−	1.73205i	0.278543	−	0.160817i
$117$	3.86370	+	1.03528i	0.357199	+	0.0957113i
$118$	−1.34486	−	5.01910i	−0.123805	−	0.462045i
$119$	−5.19615	+	3.00000i	−0.476331	+	0.275010i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	1.79315	+	6.69213i	0.161683	+	0.603409i
$124$	5.19615	−	9.00000i	0.466628	−	0.808224i
$125$		0			0
$126$			6.92820i			0.617213i
$127$	−1.03528	−	3.86370i	−0.0918659	−	0.342848i	0.904660	−	0.426135i	$-0.140125\pi$
$127$	−1.03528	−	3.86370i	−0.0918659	−	0.342848i	−0.996526	+	0.0832864i	$0.973458\pi$
$128$	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	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$	14.9372	−	2.20925i	1.29522	−	0.191567i
$134$		−	8.00000i		−	0.691095i
$135$		0			0
$136$	−1.50000	+	0.866025i	−0.128624	+	0.0742611i
$137$	15.0573	−	4.03459i	1.28643	−	0.344698i	0.450127	−	0.892964i	$-0.351379\pi$
$137$	15.0573	−	4.03459i	1.28643	−	0.344698i	0.836304	+	0.548266i	$0.184712\pi$
$138$	−3.34607	−	0.896575i	−0.284836	−	0.0763216i
$139$	−13.8564	−	8.00000i	−1.17529	−	0.678551i	−0.220366	−	0.975417i	$-0.570725\pi$
$139$	−13.8564	−	8.00000i	−1.17529	−	0.678551i	−0.954919	+	0.296866i	$0.904058\pi$
$140$		0			0
$141$			6.92820i			0.583460i
$142$	−13.3843	+	3.58630i	−1.12318	+	0.300956i
$143$		0			0
$144$			2.00000i			0.166667i
$145$		0			0
$146$	−7.50000	−	4.33013i	−0.620704	−	0.358364i
$147$	−4.82963	−	1.29410i	−0.398341	−	0.106735i
$148$	3.86370	−	1.03528i	0.317594	−	0.0850992i
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$			20.7846i			1.69143i	0.533637	+	0.845714i	$0.320825\pi$
$151$			20.7846i			1.69143i	−0.533637	+	0.845714i	$0.679175\pi$
$152$	4.31199	−	0.637756i	0.349749	−	0.0517289i
$153$	2.44949	−	2.44949i	0.198030	−	0.198030i
$154$		0			0
$155$		0			0
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−4.48288	+	16.7303i	−0.357773	+	1.33523i	0.519187	+	0.854661i	$0.326235\pi$
$157$	−4.48288	+	16.7303i	−0.357773	+	1.33523i	−0.876959	+	0.480565i	$0.840432\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.00000	+	10.3923i	−0.472866	+	0.819028i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	−12.2474	+	12.2474i	−0.959294	+	0.959294i	−0.999203	−	0.0399091i	$-0.987293\pi$
$163$	−12.2474	+	12.2474i	−0.959294	+	0.959294i	0.0399091	+	0.999203i	$0.487293\pi$
$164$	6.92820			0.541002
$165$		0			0
$166$	1.50000	−	0.866025i	0.116423	−	0.0672166i
$167$	−4.65874	−	17.3867i	−0.360504	−	1.34542i	−0.873414	−	0.486978i	$-0.838099\pi$
$167$	−4.65874	−	17.3867i	−0.360504	−	1.34542i	0.512910	−	0.858442i	$-0.328568\pi$
$168$	−3.34607	−	0.896575i	−0.258155	−	0.0691723i
$169$	−7.79423	+	4.50000i	−0.599556	+	0.346154i
$170$		0			0
$171$	−8.00000	+	3.46410i	−0.611775	+	0.264906i
$172$	−2.44949	−	2.44949i	−0.186772	−	0.186772i
$173$	−4.65874	+	17.3867i	−0.354198	+	1.32188i	0.527294	+	0.849683i	$0.323207\pi$
$173$	−4.65874	+	17.3867i	−0.354198	+	1.32188i	−0.881491	+	0.472200i	$0.843460\pi$
$174$	−1.73205	−	3.00000i	−0.131306	−	0.227429i
$175$		0			0
$176$		0			0
$177$	−5.01910	+	1.34486i	−0.377258	+	0.101086i
$178$	−6.12372	+	6.12372i	−0.458993	+	0.458993i
$179$	8.66025			0.647298			0.323649	−	0.946177i	$-0.395090\pi$
$179$	8.66025			0.647298			0.323649	+	0.946177i	$0.395090\pi$
$180$		0			0
$181$	−6.00000	−	3.46410i	−0.445976	−	0.257485i	0.260153	−	0.965567i	$-0.416227\pi$
$181$	−6.00000	−	3.46410i	−0.445976	−	0.257485i	−0.706129	+	0.708083i	$0.749560\pi$
$182$	4.89898	+	4.89898i	0.363137	+	0.363137i
$183$	5.65685	+	5.65685i	0.418167	+	0.418167i
$184$	−1.73205	+	3.00000i	−0.127688	+	0.221163i
$185$		0			0
$186$	−9.00000	−	5.19615i	−0.659912	−	0.381000i
$187$		0			0
$188$	6.69213	+	1.79315i	0.488074	+	0.130779i
$189$	17.3205			1.25988
$190$		0			0
$191$	6.00000			0.434145			0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000			0.434145			0.217072	+	0.976156i	$0.430349\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−2.84701	+	10.6252i	−0.204932	+	0.764817i	0.784538	+	0.620081i	$0.212900\pi$
$193$	−2.84701	+	10.6252i	−0.204932	+	0.764817i	−0.989470	+	0.144737i	$0.953766\pi$
$194$	−6.06218	−	3.50000i	−0.435239	−	0.251285i
$195$		0			0
$196$	−2.50000	+	4.33013i	−0.178571	+	0.309295i
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$		0			0
$199$	−3.46410	−	2.00000i	−0.245564	−	0.141776i	0.372168	−	0.928166i	$-0.378615\pi$
$199$	−3.46410	−	2.00000i	−0.245564	−	0.141776i	−0.617731	+	0.786389i	$0.711948\pi$
$200$		0			0
$201$	−8.00000			−0.564276
$202$	4.24264	−	4.24264i	0.298511	−	0.298511i
$203$	−11.5911	+	3.10583i	−0.813536	+	0.217986i
$204$	0.866025	+	1.50000i	0.0606339	+	0.105021i
$205$		0			0
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	1.79315	−	6.69213i	0.124633	−	0.465135i
$208$	1.41421	+	1.41421i	0.0980581	+	0.0980581i
$209$		0			0
$210$		0			0
$211$	−4.50000	+	2.59808i	−0.309793	+	0.178859i	−0.646834	−	0.762631i	$-0.723907\pi$
$211$	−4.50000	+	2.59808i	−0.309793	+	0.178859i	0.337041	+	0.941490i	$0.390574\pi$
$212$		0			0
$213$	3.58630	+	13.3843i	0.245729	+	0.917074i
$214$	−12.9904	+	7.50000i	−0.888004	+	0.512689i
$215$		0			0
$216$	5.00000			0.340207
$217$	−25.4558	+	25.4558i	−1.72806	+	1.72806i
$218$	4.48288	+	16.7303i	0.303619	+	1.13312i
$219$	−4.33013	+	7.50000i	−0.292603	+	0.506803i
$220$		0			0
$221$		−	3.46410i		−	0.233021i
$222$	−1.03528	−	3.86370i	−0.0694832	−	0.259315i
$223$	0.517638	−	1.93185i	0.0346636	−	0.129366i	−0.946426	−	0.322921i	$-0.895335\pi$
$223$	0.517638	−	1.93185i	0.0346636	−	0.129366i	0.981089	+	0.193555i	$0.0620018\pi$
$224$	−1.73205	+	3.00000i	−0.115728	+	0.200446i
$225$		0			0
$226$	4.50000	+	7.79423i	0.299336	+	0.518464i
$227$	19.0919	−	19.0919i	1.26717	−	1.26717i	0.319631	−	0.947542i	$-0.396441\pi$
$227$	19.0919	−	19.0919i	1.26717	−	1.26717i	0.947542	−	0.319631i	$-0.103559\pi$
$228$	−0.637756	−	4.31199i	−0.0422365	−	0.285569i
$229$			22.0000i			1.45380i	0.686743	+	0.726900i	$0.259040\pi$
$229$			22.0000i			1.45380i	−0.686743	+	0.726900i	$0.740960\pi$
$230$		0			0
$231$		0			0
$232$	−3.34607	+	0.896575i	−0.219680	+	0.0588631i
$233$	21.7494	+	5.82774i	1.42485	+	0.381788i	0.887202	−	0.461380i	$-0.152646\pi$
$233$	21.7494	+	5.82774i	1.42485	+	0.381788i	0.537650	+	0.843168i	$0.319312\pi$
$234$	−3.46410	−	2.00000i	−0.226455	−	0.130744i
$235$		0			0
$236$			5.19615i			0.338241i
$237$		0			0
$238$	5.79555	−	1.55291i	0.375670	−	0.100660i
$239$			18.0000i			1.16432i	0.813073	+	0.582162i	$0.197793\pi$
$239$			18.0000i			1.16432i	−0.813073	+	0.582162i	$0.802207\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	10.6252	+	2.84701i	0.683013	+	0.183013i
$243$	−15.4548	+	4.14110i	−0.991427	+	0.265652i
$244$	6.92820	−	4.00000i	0.443533	−	0.256074i
$245$		0			0
$246$		−	6.92820i		−	0.441726i
$247$	−3.20736	+	8.10634i	−0.204080	+	0.515794i
$248$	−7.34847	+	7.34847i	−0.466628	+	0.466628i
$249$	−0.866025	−	1.50000i	−0.0548821	−	0.0950586i
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	1.79315	−	6.69213i	0.112958	−	0.421565i
$253$		0			0
$254$			4.00000i			0.250982i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.32937	−	8.69333i	−0.145302	−	0.542275i	−0.999742	−	0.0227244i	$-0.992766\pi$
$257$	−2.32937	−	8.69333i	−0.145302	−	0.542275i	0.854440	−	0.519551i	$-0.173901\pi$
$258$	−2.44949	+	2.44949i	−0.152499	+	0.152499i
$259$	−13.8564			−0.860995
$260$		0			0
$261$	6.00000	−	3.46410i	0.371391	−	0.214423i
$262$	3.88229	+	14.4889i	0.239848	+	0.895126i
$263$	−23.4225	−	6.27603i	−1.44429	−	0.386996i	−0.550257	−	0.834996i	$-0.685470\pi$
$263$	−23.4225	−	6.27603i	−1.44429	−	0.386996i	−0.894034	+	0.447999i	$0.852137\pi$
$264$		0			0
$265$		0			0
$266$	−15.0000	−	1.73205i	−0.919709	−	0.106199i
$267$	6.12372	+	6.12372i	0.374766	+	0.374766i
$268$	−2.07055	+	7.72741i	−0.126479	+	0.472026i
$269$	−12.1244	−	21.0000i	−0.739235	−	1.28039i	−0.952840	−	0.303473i	$-0.901854\pi$
$269$	−12.1244	−	21.0000i	−0.739235	−	1.28039i	0.213605	−	0.976920i	$-0.431479\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$	1.67303	−	0.448288i	0.101443	−	0.0271814i
$273$	4.89898	−	4.89898i	0.296500	−	0.296500i
$274$	−15.5885			−0.941733
$275$		0			0
$276$	3.00000	+	1.73205i	0.180579	+	0.104257i
$277$	17.1464	+	17.1464i	1.03023	+	1.03023i	0.999529	+	0.0307004i	$0.00977377\pi$
$277$	17.1464	+	17.1464i	1.03023	+	1.03023i	0.0307004	+	0.999529i	$0.490226\pi$
$278$	11.3137	+	11.3137i	0.678551	+	0.678551i
$279$	10.3923	−	18.0000i	0.622171	−	1.07763i
$280$		0			0
$281$	−10.5000	−	6.06218i	−0.626377	−	0.361639i	0.152970	−	0.988231i	$-0.451116\pi$
$281$	−10.5000	−	6.06218i	−0.626377	−	0.361639i	−0.779348	+	0.626592i	$0.784449\pi$
$282$	1.79315	−	6.69213i	0.106781	−	0.398511i
$283$	−3.34607	−	0.896575i	−0.198903	−	0.0532959i	0.157992	−	0.987440i	$-0.449498\pi$
$283$	−3.34607	−	0.896575i	−0.198903	−	0.0532959i	−0.356895	+	0.934144i	$0.616165\pi$
$284$	13.8564			0.822226
$285$		0			0
$286$		0			0
$287$	−23.1822	−	6.21166i	−1.36840	−	0.366663i
$288$	0.517638	−	1.93185i	0.0305021	−	0.113835i
$289$	12.1244	+	7.00000i	0.713197	+	0.411765i
$290$		0			0
$291$	−3.50000	+	6.06218i	−0.205174	+	0.355371i
$292$	6.12372	+	6.12372i	0.358364	+	0.358364i
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	4.33013	+	2.50000i	0.252538	+	0.145803i
$295$		0			0
$296$	−4.00000			−0.232495
$297$		0			0
$298$		0			0
$299$	−3.46410	−	6.00000i	−0.200334	−	0.346989i
$300$		0			0
$301$	6.00000	+	10.3923i	0.345834	+	0.599002i
$302$	5.37945	−	20.0764i	0.309553	−	1.15527i
$303$	−4.24264	−	4.24264i	−0.243733	−	0.243733i
$304$	−4.33013	−	0.500000i	−0.248350	−	0.0286770i
$305$		0			0
$306$	−3.00000	+	1.73205i	−0.171499	+	0.0990148i
$307$	−10.6252	−	2.84701i	−0.606411	−	0.162487i	−0.0574685	−	0.998347i	$-0.518303\pi$
$307$	−10.6252	−	2.84701i	−0.606411	−	0.162487i	−0.548943	+	0.835860i	$0.684970\pi$
$308$		0			0
$309$	3.46410	−	2.00000i	0.197066	−	0.113776i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$	1.41421	−	1.41421i	0.0800641	−	0.0800641i
$313$	−4.93117	−	18.4034i	−0.278726	−	1.04022i	−0.953303	−	0.302015i	$-0.902341\pi$
$313$	−4.93117	−	18.4034i	−0.278726	−	1.04022i	0.674577	−	0.738204i	$-0.264326\pi$
$314$	8.66025	−	15.0000i	0.488726	−	0.846499i
$315$		0			0
$316$		0			0
$317$	3.10583	+	11.5911i	0.174441	+	0.651022i	0.996646	+	0.0818309i	$0.0260767\pi$
$317$	3.10583	+	11.5911i	0.174441	+	0.651022i	−0.822206	+	0.569191i	$0.807257\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	7.50000	+	12.9904i	0.418609	+	0.725052i
$322$	8.48528	−	8.48528i	0.472866	−	0.472866i
$323$	4.69093	+	5.91567i	0.261010	+	0.329157i
$324$			1.00000i			0.0555556i
$325$		0			0
$326$	15.0000	−	8.66025i	0.830773	−	0.479647i
$327$	16.7303	−	4.48288i	0.925189	−	0.247904i
$328$	−6.69213	−	1.79315i	−0.369511	−	0.0990102i
$329$	−20.7846	−	12.0000i	−1.14589	−	0.661581i
$330$		0			0
$331$		−	5.19615i		−	0.285606i	−0.989751	−	0.142803i	$-0.954388\pi$
$331$		−	5.19615i		−	0.285606i	0.989751	−	0.142803i	$-0.0456116\pi$
$332$	−1.67303	+	0.448288i	−0.0918196	+	0.0246030i
$333$	7.72741	−	2.07055i	0.423459	−	0.113466i
$334$			18.0000i			0.984916i
$335$		0			0
$336$	3.00000	+	1.73205i	0.163663	+	0.0944911i
$337$	−21.2504	−	5.69402i	−1.15758	−	0.310173i	−0.371582	−	0.928400i	$-0.621184\pi$
$337$	−21.2504	−	5.69402i	−1.15758	−	0.310173i	−0.785999	+	0.618227i	$0.787851\pi$
$338$	8.69333	−	2.32937i	0.472855	−	0.126701i
$339$	7.79423	−	4.50000i	0.423324	−	0.244406i
$340$		0			0
$341$		0			0
$342$	8.62398	−	1.27551i	0.466332	−	0.0689718i
$343$	−4.89898	+	4.89898i	−0.264520	+	0.264520i
$344$	1.73205	+	3.00000i	0.0933859	+	0.161749i
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	−0.896575	+	3.34607i	−0.0481307	+	0.179626i	−0.985807	−	0.167885i	$-0.946306\pi$
$347$	−0.896575	+	3.34607i	−0.0481307	+	0.179626i	0.937676	+	0.347511i	$0.112973\pi$
$348$	0.896575	+	3.34607i	0.0480615	+	0.179368i
$349$		−	28.0000i		−	1.49881i	−0.662114	−	0.749403i	$-0.730341\pi$
$349$		−	28.0000i		−	1.49881i	0.662114	−	0.749403i	$-0.269659\pi$
$350$		0			0
$351$	−5.00000	+	8.66025i	−0.266880	+	0.462250i
$352$		0			0
$353$	−3.67423	+	3.67423i	−0.195560	+	0.195560i	−0.798093	−	0.602534i	$-0.794158\pi$
$353$	−3.67423	+	3.67423i	−0.195560	+	0.195560i	0.602534	+	0.798093i	$0.294158\pi$
$354$	5.19615			0.276172
$355$		0			0
$356$	7.50000	−	4.33013i	0.397499	−	0.229496i
$357$	−1.55291	−	5.79555i	−0.0821889	−	0.306733i
$358$	−8.36516	−	2.24144i	−0.442113	−	0.118464i
$359$	−10.3923	+	6.00000i	−0.548485	+	0.316668i	−0.748511	−	0.663123i	$-0.769231\pi$
$359$	−10.3923	+	6.00000i	−0.548485	+	0.316668i	0.200026	+	0.979791i	$0.435897\pi$
$360$		0			0
$361$	−5.50000	−	18.1865i	−0.289474	−	0.957186i
$362$	4.89898	+	4.89898i	0.257485	+	0.257485i
$363$	2.84701	−	10.6252i	0.149429	−	0.557678i
$364$	−3.46410	−	6.00000i	−0.181568	−	0.314485i
$365$		0			0
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	−26.7685	+	7.17260i	−1.39731	+	0.374407i	−0.877376	−	0.479803i	$-0.840708\pi$
$367$	−26.7685	+	7.17260i	−1.39731	+	0.374407i	−0.519929	+	0.854209i	$0.674042\pi$
$368$	2.44949	−	2.44949i	0.127688	−	0.127688i
$369$	13.8564			0.721336
$370$		0			0
$371$		0			0
$372$	7.34847	+	7.34847i	0.381000	+	0.381000i
$373$	−7.07107	−	7.07107i	−0.366126	−	0.366126i	0.499936	−	0.866062i	$-0.333357\pi$
$373$	−7.07107	−	7.07107i	−0.366126	−	0.366126i	−0.866062	+	0.499936i	$0.833357\pi$
$374$		0			0
$375$		0			0
$376$	−6.00000	−	3.46410i	−0.309426	−	0.178647i
$377$	1.79315	−	6.69213i	0.0923520	−	0.344662i
$378$	−16.7303	−	4.48288i	−0.860515	−	0.230574i
$379$	−5.19615			−0.266908			−0.133454	−	0.991055i	$-0.542607\pi$
$379$	−5.19615			−0.266908			−0.133454	+	0.991055i	$0.542607\pi$
$380$		0			0
$381$	4.00000			0.204926
$382$	−5.79555	−	1.55291i	−0.296526	−	0.0794540i
$383$	−6.21166	+	23.1822i	−0.317401	+	1.18456i	0.604333	+	0.796732i	$0.293440\pi$
$383$	−6.21166	+	23.1822i	−0.317401	+	1.18456i	−0.921733	+	0.387824i	$0.873227\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	5.50000	−	9.52628i	0.279943	−	0.484875i
$387$	−4.89898	−	4.89898i	−0.249029	−	0.249029i
$388$	4.94975	+	4.94975i	0.251285	+	0.251285i
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.983290	−	0.182047i	$-0.0582724\pi$
$389$	25.9808	+	15.0000i	1.31728	+	0.760530i	0.333987	+	0.942578i	$0.391606\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	14.4889	−	3.88229i	0.730868	−	0.195835i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.06918	+	30.1146i	−0.404980	+	1.51141i	0.399111	+	0.916903i	$0.369319\pi$
$397$	−8.06918	+	30.1146i	−0.404980	+	1.51141i	−0.804092	+	0.594505i	$0.797348\pi$
$398$	2.82843	+	2.82843i	0.141776	+	0.141776i
$399$	−1.73205	+	15.0000i	−0.0867110	+	0.750939i
$400$		0			0
$401$	−30.0000	+	17.3205i	−1.49813	+	0.864945i	−0.999998	−	0.00215698i	$-0.999313\pi$
$401$	−30.0000	+	17.3205i	−1.49813	+	0.864945i	−0.498131	+	0.867102i	$0.665980\pi$
$402$	7.72741	+	2.07055i	0.385408	+	0.103270i
$403$	−5.37945	−	20.0764i	−0.267970	−	1.00008i
$404$	−5.19615	+	3.00000i	−0.258518	+	0.149256i
$405$		0			0
$406$	12.0000			0.595550
$407$		0			0
$408$	−0.448288	−	1.67303i	−0.0221936	−	0.0828275i
$409$	−3.46410	+	6.00000i	−0.171289	+	0.296681i	−0.938871	−	0.344270i	$-0.888126\pi$
$409$	−3.46410	+	6.00000i	−0.171289	+	0.296681i	0.767582	+	0.640951i	$0.221460\pi$
$410$		0			0
$411$			15.5885i			0.768922i
$412$	−1.03528	−	3.86370i	−0.0510044	−	0.190351i
$413$	4.65874	−	17.3867i	0.229242	−	0.855542i
$414$	−3.46410	+	6.00000i	−0.170251	+	0.294884i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	11.3137	−	11.3137i	0.554035	−	0.554035i
$418$		0			0
$419$			21.0000i			1.02592i	0.858413	+	0.512959i	$0.171451\pi$
$419$			21.0000i			1.02592i	−0.858413	+	0.512959i	$0.828549\pi$
$420$		0			0
$421$	33.0000	−	19.0526i	1.60832	−	0.928565i	0.618576	−	0.785725i	$-0.287710\pi$
$421$	33.0000	−	19.0526i	1.60832	−	0.928565i	0.989746	−	0.142840i	$-0.0456234\pi$
$422$	5.01910	−	1.34486i	0.244326	−	0.0654669i
$423$	13.3843	+	3.58630i	0.650765	+	0.174372i
$424$		0			0
$425$		0			0
$426$		−	13.8564i		−	0.671345i
$427$	−26.7685	+	7.17260i	−1.29542	+	0.347107i
$428$	14.4889	−	3.88229i	0.700347	−	0.187657i
$429$		0			0
$430$		0			0
$431$	21.0000	+	12.1244i	1.01153	+	0.584010i	0.911641	−	0.410988i	$-0.134816\pi$
$431$	21.0000	+	12.1244i	1.01153	+	0.584010i	0.0998939	+	0.994998i	$0.468150\pi$
$432$	−4.82963	−	1.29410i	−0.232366	−	0.0622622i
$433$	33.8074	−	9.05867i	1.62468	−	0.435332i	0.672308	−	0.740271i	$-0.265303\pi$
$433$	33.8074	−	9.05867i	1.62468	−	0.435332i	0.952372	+	0.304939i	$0.0986362\pi$
$434$	31.1769	−	18.0000i	1.49654	−	0.864028i
$435$		0			0
$436$		−	17.3205i		−	0.829502i
$437$	14.0406	+	5.55532i	0.671653	+	0.265747i
$438$	6.12372	−	6.12372i	0.292603	−	0.292603i
$439$	3.46410	+	6.00000i	0.165333	+	0.286364i	0.936773	−	0.349937i	$-0.113797\pi$
$439$	3.46410	+	6.00000i	0.165333	+	0.286364i	−0.771441	+	0.636301i	$0.780464\pi$
$440$		0			0
$441$	−5.00000	+	8.66025i	−0.238095	+	0.412393i
$442$	−0.896575	+	3.34607i	−0.0426457	+	0.159156i
$443$	−6.27603	−	23.4225i	−0.298183	−	1.11283i	−0.938656	−	0.344854i	$-0.887928\pi$
$443$	−6.27603	−	23.4225i	−0.298183	−	1.11283i	0.640473	−	0.767980i	$-0.278738\pi$
$444$			4.00000i			0.189832i
$445$		0			0
$446$	−1.00000	+	1.73205i	−0.0473514	+	0.0820150i
$447$		0			0
$448$	2.44949	−	2.44949i	0.115728	−	0.115728i
$449$	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
$451$		0			0
$452$	−2.32937	−	8.69333i	−0.109564	−	0.408900i
$453$	−20.0764	−	5.37945i	−0.943271	−	0.252749i
$454$	−23.3827	+	13.5000i	−1.09740	+	0.633586i
$455$		0			0
$456$	−0.500000	+	4.33013i	−0.0234146	+	0.202777i
$457$	−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	$0.897017\pi$
$458$	5.69402	−	21.2504i	0.266064	−	0.992964i
$459$	4.33013	+	7.50000i	0.202113	+	0.350070i
$460$		0			0
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	0.576685	−	0.816967i	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$		0			0
$463$	7.34847	−	7.34847i	0.341512	−	0.341512i	−0.515423	−	0.856936i	$-0.672365\pi$
$463$	7.34847	−	7.34847i	0.341512	−	0.341512i	0.856936	+	0.515423i	$0.172365\pi$
$464$	3.46410			0.160817
$465$		0			0
$466$	−19.5000	−	11.2583i	−0.903320	−	0.521532i
$467$	25.7196	+	25.7196i	1.19016	+	1.19016i	0.977021	+	0.213142i	$0.0683696\pi$
$467$	25.7196	+	25.7196i	1.19016	+	1.19016i	0.213142	+	0.977021i	$0.431630\pi$
$468$	2.82843	+	2.82843i	0.130744	+	0.130744i
$469$	13.8564	−	24.0000i	0.639829	−	1.10822i
$470$		0			0
$471$	−15.0000	−	8.66025i	−0.691164	−	0.399043i
$472$	1.34486	−	5.01910i	0.0619023	−	0.231023i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−6.00000			−0.275010
$477$		0			0
$478$	4.65874	−	17.3867i	0.213086	−	0.795248i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	4.00000	−	6.92820i	0.182384	−	0.315899i
$482$		0			0
$483$	−8.48528	−	8.48528i	−0.386094	−	0.386094i
$484$	−9.52628	−	5.50000i	−0.433013	−	0.250000i
$485$		0			0
$486$	16.0000			0.725775
$487$	11.3137	−	11.3137i	0.512673	−	0.512673i	−0.402671	−	0.915345i	$-0.631918\pi$
$487$	11.3137	−	11.3137i	0.512673	−	0.512673i	0.915345	+	0.402671i	$0.131918\pi$
$488$	−7.72741	+	2.07055i	−0.349803	+	0.0937295i
$489$	−8.66025	−	15.0000i	−0.391630	−	0.678323i
$490$		0			0
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	0.998815	+	0.0486647i	$0.0154966\pi$
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	−0.457263	+	0.889332i	$0.651170\pi$
$492$	−1.79315	+	6.69213i	−0.0808415	+	0.301705i
$493$	−4.24264	−	4.24264i	−0.191079	−	0.191079i
$494$	5.19615	−	7.00000i	0.233786	−	0.314945i
$495$		0			0
$496$	9.00000	−	5.19615i	0.404112	−	0.233314i
$497$	−46.3644	−	12.4233i	−2.07973	−	0.557262i
$498$	0.448288	+	1.67303i	0.0200883	+	0.0749704i
$499$	−26.8468	+	15.5000i	−1.20183	+	0.693875i	−0.960961	−	0.276683i	$-0.910765\pi$
$499$	−26.8468	+	15.5000i	−1.20183	+	0.693875i	−0.240866	+	0.970558i	$0.577431\pi$
$500$		0			0
$501$	18.0000			0.804181
$502$	8.48528	−	8.48528i	0.378717	−	0.378717i
$503$	−10.7589	−	40.1528i	−0.479716	−	1.79032i	−0.602760	−	0.797923i	$-0.705932\pi$
$503$	−10.7589	−	40.1528i	−0.479716	−	1.79032i	0.123044	−	0.992401i	$-0.460734\pi$
$504$	−3.46410	+	6.00000i	−0.154303	+	0.267261i
$505$		0			0
$506$		0			0
$507$	−2.32937	−	8.69333i	−0.103451	−	0.386084i
$508$	1.03528	−	3.86370i	0.0459330	−	0.171424i
$509$	−12.1244	+	21.0000i	−0.537403	+	0.930809i	0.461640	+	0.887067i	$0.347261\pi$
$509$	−12.1244	+	21.0000i	−0.537403	+	0.930809i	−0.999043	+	0.0437414i	$0.986072\pi$
$510$		0			0
$511$	−15.0000	−	25.9808i	−0.663561	−	1.14932i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.18878	−	21.5600i	−0.140788	−	0.951895i
$514$			9.00000i			0.396973i
$515$		0			0
$516$	3.00000	−	1.73205i	0.132068	−	0.0762493i
$517$		0			0
$518$	13.3843	+	3.58630i	0.588071	+	0.157573i
$519$	−15.5885	−	9.00000i	−0.684257	−	0.395056i
$520$		0			0
$521$		−	20.7846i		−	0.910590i	−0.890341	−	0.455295i	$-0.849534\pi$
$521$		−	20.7846i		−	0.910590i	0.890341	−	0.455295i	$-0.150466\pi$
$522$	−6.69213	+	1.79315i	−0.292907	+	0.0784841i
$523$	28.0118	−	7.50575i	1.22487	−	0.328204i	0.412292	−	0.911052i	$-0.364728\pi$
$523$	28.0118	−	7.50575i	1.22487	−	0.328204i	0.812581	+	0.582848i	$0.198062\pi$
$524$		−	15.0000i		−	0.655278i
$525$		0			0
$526$	21.0000	+	12.1244i	0.915644	+	0.528647i
$527$	−17.3867	−	4.65874i	−0.757375	−	0.202938i
$528$		0			0
$529$	9.52628	−	5.50000i	0.414186	−	0.239130i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	14.0406	+	5.55532i	0.608737	+	0.240854i
$533$	9.79796	−	9.79796i	0.424397	−	0.424397i
$534$	−4.33013	−	7.50000i	−0.187383	−	0.324557i
$535$		0			0
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$	−2.24144	+	8.36516i	−0.0967252	+	0.360983i
$538$	6.27603	+	23.4225i	0.270579	+	1.00981i
$539$		0			0
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	0.517638	+	1.93185i	0.0222345	+	0.0829801i
$543$	4.89898	−	4.89898i	0.210235	−	0.210235i
$544$	−1.73205			−0.0742611
$545$		0			0
$546$	−6.00000	+	3.46410i	−0.256776	+	0.148250i
$547$	1.81173	+	6.76148i	0.0774641	+	0.289100i	0.993781	−	0.111355i	$-0.0355189\pi$
$547$	1.81173	+	6.76148i	0.0774641	+	0.289100i	−0.916317	+	0.400455i	$0.868852\pi$
$548$	15.0573	+	4.03459i	0.643216	+	0.172349i
$549$	13.8564	−	8.00000i	0.591377	−	0.341432i
$550$		0			0
$551$	6.00000	+	13.8564i	0.255609	+	0.590303i
$552$	−2.44949	−	2.44949i	−0.104257	−	0.104257i
$553$		0			0
$554$	−12.1244	−	21.0000i	−0.515115	−	0.892205i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	23.4225	−	6.27603i	0.992441	−	0.265924i	0.274166	−	0.961682i	$-0.411598\pi$
$557$	23.4225	−	6.27603i	0.992441	−	0.265924i	0.718276	+	0.695759i	$0.244932\pi$
$558$	−14.6969	+	14.6969i	−0.622171	+	0.622171i
$559$	−6.92820			−0.293032
$560$		0			0
$561$		0			0
$562$	8.57321	+	8.57321i	0.361639	+	0.361639i
$563$	−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
$566$	3.00000	+	1.73205i	0.126099	+	0.0728035i
$567$	0.896575	−	3.34607i	0.0376526	−	0.140522i
$568$	−13.3843	−	3.58630i	−0.561591	−	0.150478i
$569$	39.8372			1.67006			0.835030	−	0.550204i	$-0.185450\pi$
$569$	39.8372			1.67006			0.835030	+	0.550204i	$0.185450\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$		0			0
$573$	−1.55291	+	5.79555i	−0.0648739	+	0.242113i
$574$	20.7846	+	12.0000i	0.867533	+	0.500870i
$575$		0			0
$576$	−1.00000	+	1.73205i	−0.0416667	+	0.0721688i
$577$	29.3939	+	29.3939i	1.22368	+	1.22368i	0.966313	+	0.257370i	$0.0828560\pi$
$577$	29.3939	+	29.3939i	1.22368	+	1.22368i	0.257370	+	0.966313i	$0.417144\pi$
$578$	−9.89949	−	9.89949i	−0.411765	−	0.411765i
$579$	−9.52628	−	5.50000i	−0.395899	−	0.228572i
$580$		0			0
$581$	6.00000			0.248922
$582$	4.94975	−	4.94975i	0.205174	−	0.205174i
$583$		0			0
$584$	−4.33013	−	7.50000i	−0.179182	−	0.310352i
$585$		0			0
$586$		0			0
$587$	−7.62089	+	28.4416i	−0.314548	+	1.17391i	0.609862	+	0.792508i	$0.291225\pi$
$587$	−7.62089	+	28.4416i	−0.314548	+	1.17391i	−0.924410	+	0.381401i	$0.875442\pi$
$588$	−3.53553	−	3.53553i	−0.145803	−	0.145803i
$589$	36.3731	+	27.0000i	1.49873	+	1.11252i
$590$		0			0
$591$		0			0
$592$	3.86370	+	1.03528i	0.158797	+	0.0425496i
$593$	−5.37945	−	20.0764i	−0.220908	−	0.824439i	−0.984003	−	0.178153i	$-0.942988\pi$
$593$	−5.37945	−	20.0764i	−0.220908	−	0.824439i	0.763095	−	0.646286i	$-0.223679\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.82843	−	2.82843i	0.115760	−	0.115760i
$598$	1.79315	+	6.69213i	0.0733274	+	0.273662i
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	0.430784	+	0.902455i	$0.358237\pi$
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	−0.996941	+	0.0781581i	$0.975096\pi$
$600$		0			0
$601$		−	22.5167i		−	0.918474i	−0.888314	−	0.459237i	$-0.848123\pi$
$601$		−	22.5167i		−	0.918474i	0.888314	−	0.459237i	$-0.151877\pi$
$602$	−3.10583	−	11.5911i	−0.126584	−	0.472418i
$603$	−4.14110	+	15.4548i	−0.168639	+	0.629369i
$604$	−10.3923	+	18.0000i	−0.422857	+	0.732410i
$605$		0			0
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$	24.0416	−	24.0416i	0.975820	−	0.975820i	−0.0238948	−	0.999714i	$-0.507607\pi$
$607$	24.0416	−	24.0416i	0.975820	−	0.975820i	0.999714	+	0.0238948i	$0.00760667\pi$
$608$	4.05317	+	1.60368i	0.164378	+	0.0650379i
$609$		−	12.0000i		−	0.486265i
$610$		0			0
$611$	12.0000	−	6.92820i	0.485468	−	0.280285i
$612$	3.34607	−	0.896575i	0.135257	−	0.0362419i
$613$	−3.34607	−	0.896575i	−0.135146	−	0.0362123i	0.190612	−	0.981665i	$-0.438953\pi$
$613$	−3.34607	−	0.896575i	−0.135146	−	0.0362123i	−0.325758	+	0.945453i	$0.605620\pi$
$614$	9.52628	+	5.50000i	0.384449	+	0.221962i
$615$		0			0
$616$		0			0
$617$	−41.8258	+	11.2072i	−1.68384	+	0.451185i	−0.968790	−	0.247884i	$-0.920265\pi$
$617$	−41.8258	+	11.2072i	−1.68384	+	0.451185i	−0.715054	+	0.699069i	$0.753598\pi$
$618$	−3.86370	+	1.03528i	−0.155421	+	0.0416449i
$619$			44.0000i			1.76851i	0.467005	+	0.884255i	$0.345333\pi$
$619$			44.0000i			1.76851i	−0.467005	+	0.884255i	$0.654667\pi$
$620$		0			0
$621$	15.0000	+	8.66025i	0.601929	+	0.347524i
$622$	−28.9778	−	7.76457i	−1.16190	−	0.311331i
$623$	−28.9778	+	7.76457i	−1.16097	+	0.311081i
$624$	−1.73205	+	1.00000i	−0.0693375	+	0.0400320i
$625$		0			0
$626$			19.0526i			0.761493i
$627$		0			0
$628$	−12.2474	+	12.2474i	−0.488726	+	0.488726i
$629$	−3.46410	−	6.00000i	−0.138123	−	0.239236i
$630$		0			0
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	−0.775356	−	0.631524i	$-0.782430\pi$
$631$	4.00000	−	6.92820i	0.159237	−	0.275807i	0.934594	+	0.355716i	$0.115763\pi$
$632$		0			0
$633$	−1.34486	−	5.01910i	−0.0534535	−	0.199491i
$634$		−	12.0000i		−	0.476581i
$635$		0			0
$636$		0			0
$637$	2.58819	+	9.65926i	0.102548	+	0.382714i
$638$		0			0
$639$	27.7128			1.09630
$640$		0			0
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	−0.692818	−	0.721113i	$-0.743631\pi$
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	0.278093	+	0.960554i	$0.410298\pi$
$642$	−3.88229	−	14.4889i	−0.153222	−	0.571831i
$643$	8.36516	+	2.24144i	0.329890	+	0.0883937i	0.419962	−	0.907541i	$-0.362043\pi$
$643$	8.36516	+	2.24144i	0.329890	+	0.0883937i	−0.0900726	+	0.995935i	$0.528710\pi$
$644$	−10.3923	+	6.00000i	−0.409514	+	0.236433i
$645$		0			0
$646$	−3.00000	−	6.92820i	−0.118033	−	0.272587i
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$		0			0
$650$		0			0
$651$	−18.0000	−	31.1769i	−0.705476	−	1.22192i
$652$	−16.7303	+	4.48288i	−0.655210	+	0.175563i
$653$	−34.2929	+	34.2929i	−1.34198	+	1.34198i	−0.447899	+	0.894084i	$0.647828\pi$
$653$	−34.2929	+	34.2929i	−1.34198	+	1.34198i	−0.894084	+	0.447899i	$0.852172\pi$
$654$	−17.3205			−0.677285
$655$		0			0
$656$	6.00000	+	3.46410i	0.234261	+	0.135250i
$657$	12.2474	+	12.2474i	0.477818	+	0.477818i
$658$	16.9706	+	16.9706i	0.661581	+	0.661581i
$659$	−0.866025	+	1.50000i	−0.0337356	+	0.0584317i	−0.882400	−	0.470500i	$-0.844074\pi$
$659$	−0.866025	+	1.50000i	−0.0337356	+	0.0584317i	0.848665	+	0.528931i	$0.177407\pi$
$660$		0			0
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	0.378754	−	0.925497i	$-0.376353\pi$
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	−0.612127	+	0.790759i	$0.709686\pi$
$662$	−1.34486	+	5.01910i	−0.0522696	+	0.195073i
$663$	3.34607	+	0.896575i	0.129950	+	0.0348201i
$664$	1.73205			0.0672166
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−11.5911	−	3.10583i	−0.448810	−	0.120258i
$668$	4.65874	−	17.3867i	0.180252	−	0.672710i
$669$	1.73205	+	1.00000i	0.0669650	+	0.0386622i
$670$		0			0
$671$		0			0
$672$	−2.44949	−	2.44949i	−0.0944911	−	0.0944911i
$673$	32.5269	+	32.5269i	1.25382	+	1.25382i	0.953994	+	0.299827i	$0.0969288\pi$
$673$	32.5269	+	32.5269i	1.25382	+	1.25382i	0.299827	+	0.953994i	$0.403071\pi$
$674$	19.0526	+	11.0000i	0.733877	+	0.423704i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	21.2132	−	21.2132i	0.815290	−	0.815290i	−0.170132	−	0.985421i	$-0.554419\pi$
$677$	21.2132	−	21.2132i	0.815290	−	0.815290i	0.985421	+	0.170132i	$0.0544193\pi$
$678$	−8.69333	+	2.32937i	−0.333865	+	0.0894590i
$679$	−12.1244	−	21.0000i	−0.465290	−	0.805906i
$680$		0			0
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$		0			0
$683$	23.3345	+	23.3345i	0.892871	+	0.892871i	0.994792	−	0.101922i	$-0.0324991\pi$
$683$	23.3345	+	23.3345i	0.892871	+	0.892871i	−0.101922	+	0.994792i	$0.532499\pi$
$684$	−8.66025	−	1.00000i	−0.331133	−	0.0382360i
$685$		0			0
$686$	6.00000	−	3.46410i	0.229081	−	0.132260i
$687$	−21.2504	−	5.69402i	−0.810752	−	0.217240i
$688$	−0.896575	−	3.34607i	−0.0341816	−	0.127568i
$689$		0			0
$690$		0			0
$691$	43.0000			1.63580			0.817899	−	0.575362i	$-0.195139\pi$
$691$	43.0000			1.63580			0.817899	+	0.575362i	$0.195139\pi$
$692$	−12.7279	+	12.7279i	−0.483843	+	0.483843i
$693$		0			0
$694$	1.73205	−	3.00000i	0.0657477	−	0.113878i
$695$		0			0
$696$		−	3.46410i		−	0.131306i
$697$	−3.10583	−	11.5911i	−0.117642	−	0.439045i
$698$	−7.24693	+	27.0459i	−0.274300	+	1.02370i
$699$	−11.2583	+	19.5000i	−0.425829	+	0.737558i
$700$		0			0
$701$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$701$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$702$	7.07107	−	7.07107i	0.266880	−	0.266880i
$703$	2.55103	+	17.2480i	0.0962138	+	0.650519i
$704$		0			0
$705$		0			0
$706$	4.50000	−	2.59808i	0.169360	−	0.0977799i
$707$	20.0764	−	5.37945i	0.755050	−	0.202315i
$708$	−5.01910	−	1.34486i	−0.188629	−	0.0505431i
$709$	−6.92820	−	4.00000i	−0.260194	−	0.150223i	0.364229	−	0.931309i	$-0.381333\pi$
$709$	−6.92820	−	4.00000i	−0.260194	−	0.150223i	−0.624423	+	0.781086i	$0.714666\pi$
$710$		0			0
$711$		0			0
$712$	−8.36516	+	2.24144i	−0.313498	+	0.0840015i
$713$	−34.7733	+	9.31749i	−1.30227	+	0.348943i
$714$			6.00000i			0.224544i
$715$		0			0
$716$	7.50000	+	4.33013i	0.280288	+	0.161824i
$717$	−17.3867	−	4.65874i	−0.649317	−	0.173984i
$718$	11.5911	−	3.10583i	0.432576	−	0.115908i
$719$	31.1769	−	18.0000i	1.16270	−	0.671287i	0.210752	−	0.977539i	$-0.432409\pi$
$719$	31.1769	−	18.0000i	1.16270	−	0.671287i	0.951950	+	0.306253i	$0.0990753\pi$
$720$		0			0
$721$			13.8564i			0.516040i
$722$	0.605571	+	18.9903i	0.0225370	+	0.706748i
$723$		0			0
$724$	−3.46410	−	6.00000i	−0.128742	−	0.222988i
$725$		0			0
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	2.68973	−	10.0382i	0.0997564	−	0.372296i	−0.897941	−	0.440115i	$-0.854938\pi$
$727$	2.68973	−	10.0382i	0.0997564	−	0.372296i	0.997698	+	0.0678194i	$0.0216042\pi$
$728$	1.79315	+	6.69213i	0.0664586	+	0.248027i
$729$		−	13.0000i		−	0.481481i
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$	2.07055	+	7.72741i	0.0765298	+	0.285613i
$733$	−7.34847	+	7.34847i	−0.271422	+	0.271422i	−0.829672	−	0.558251i	$-0.811473\pi$
$733$	−7.34847	+	7.34847i	−0.271422	+	0.271422i	0.558251	+	0.829672i	$0.311473\pi$
$734$	27.7128			1.02290
$735$		0			0
$736$	−3.00000	+	1.73205i	−0.110581	+	0.0638442i
$737$		0			0
$738$	−13.3843	−	3.58630i	−0.492681	−	0.132014i
$739$	21.6506	−	12.5000i	0.796431	−	0.459820i	−0.0457903	−	0.998951i	$-0.514581\pi$
$739$	21.6506	−	12.5000i	0.796431	−	0.459820i	0.842222	+	0.539131i	$0.181247\pi$
$740$		0			0
$741$	−7.00000	−	5.19615i	−0.257151	−	0.190885i
$742$		0			0
$743$	−1.55291	+	5.79555i	−0.0569709	+	0.212618i	−0.988543	−	0.150938i	$-0.951771\pi$
$743$	−1.55291	+	5.79555i	−0.0569709	+	0.212618i	0.931572	+	0.363556i	$0.118437\pi$
$744$	−5.19615	−	9.00000i	−0.190500	−	0.329956i
$745$		0			0
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$	−3.34607	+	0.896575i	−0.122426	+	0.0328040i
$748$		0			0
$749$	−51.9615			−1.89863
$750$		0			0
$751$	−9.00000	−	5.19615i	−0.328415	−	0.189610i	0.326722	−	0.945120i	$-0.394056\pi$
$751$	−9.00000	−	5.19615i	−0.328415	−	0.189610i	−0.655137	+	0.755510i	$0.727389\pi$
$752$	4.89898	+	4.89898i	0.178647	+	0.178647i
$753$	−8.48528	−	8.48528i	−0.309221	−	0.309221i
$754$	−3.46410	+	6.00000i	−0.126155	+	0.218507i
$755$		0			0
$756$	15.0000	+	8.66025i	0.545545	+	0.314970i
$757$	8.96575	−	33.4607i	0.325866	−	1.21615i	−0.587573	−	0.809171i	$-0.699916\pi$
$757$	8.96575	−	33.4607i	0.325866	−	1.21615i	0.913439	−	0.406977i	$-0.133417\pi$
$758$	5.01910	+	1.34486i	0.182302	+	0.0488476i
$759$		0			0
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$	−3.86370	−	1.03528i	−0.139967	−	0.0375041i
$763$	−15.5291	+	57.9555i	−0.562193	+	2.09813i
$764$	5.19615	+	3.00000i	0.187990	+	0.108536i
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	7.34847	+	7.34847i	0.265338	+	0.265338i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	0.0958377	−	0.995397i	$-0.469447\pi$
$769$	−19.9186	−	11.5000i	−0.718283	−	0.414701i	−0.814120	+	0.580696i	$0.802780\pi$
$770$		0			0
$771$	9.00000			0.324127
$772$	−7.77817	+	7.77817i	−0.279943	+	0.279943i
$773$	17.3867	−	4.65874i	0.625355	−	0.167563i	0.0677939	−	0.997699i	$-0.478404\pi$
$773$	17.3867	−	4.65874i	0.625355	−	0.167563i	0.557561	+	0.830136i	$0.311737\pi$
$774$	3.46410	+	6.00000i	0.124515	+	0.215666i
$775$		0			0
$776$	−3.50000	−	6.06218i	−0.125643	−	0.217620i
$777$	3.58630	−	13.3843i	0.128658	−	0.480158i
$778$	−21.2132	−	21.2132i	−0.760530	−	0.760530i
$779$	−3.46410	+	30.0000i	−0.124114	+	1.07486i
$780$		0			0
$781$		0			0
$782$	5.79555	+	1.55291i	0.207249	+	0.0555321i
$783$	4.48288	+	16.7303i	0.160205	+	0.597893i
$784$	−4.33013	+	2.50000i	−0.154647	+	0.0892857i
$785$		0			0
$786$	−15.0000			−0.535032
$787$	−9.19239	+	9.19239i	−0.327673	+	0.327673i	−0.851701	−	0.524028i	$-0.824429\pi$
$787$	−9.19239	+	9.19239i	−0.327673	+	0.327673i	0.524028	+	0.851701i	$0.324429\pi$
$788$		0			0
$789$	12.1244	−	21.0000i	0.431638	−	0.747620i
$790$		0			0
$791$			31.1769i			1.10852i
$792$		0			0
$793$	4.14110	−	15.4548i	0.147055	−	0.548817i
$794$	15.5885	−	27.0000i	0.553214	−	0.958194i
$795$		0			0
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	8.48528	−	8.48528i	0.300564	−	0.300564i	−0.540670	−	0.841235i	$-0.681829\pi$
$797$	8.48528	−	8.48528i	0.300564	−	0.300564i	0.841235	+	0.540670i	$0.181829\pi$
$798$	5.55532	−	14.0406i	0.196656	−	0.497032i
$799$		−	12.0000i		−	0.424529i
$800$		0			0
$801$	15.0000	−	8.66025i	0.529999	−	0.305995i
$802$	33.4607	−	8.96575i	1.18154	−	0.316592i
$803$		0			0
$804$	−6.92820	−	4.00000i	−0.244339	−	0.141069i
$805$		0			0
$806$			20.7846i			0.732107i
$807$	23.4225	−	6.27603i	0.824510	−	0.220927i
$808$	5.79555	−	1.55291i	0.203887	−	0.0546313i
$809$			51.0000i			1.79306i	0.442978	+	0.896532i	$0.353922\pi$
$809$			51.0000i			1.79306i	−0.442978	+	0.896532i	$0.646078\pi$
$810$		0			0
$811$	−15.0000	−	8.66025i	−0.526721	−	0.304103i	0.212959	−	0.977061i	$-0.431690\pi$
$811$	−15.0000	−	8.66025i	−0.526721	−	0.304103i	−0.739680	+	0.672958i	$0.765023\pi$
$812$	−11.5911	−	3.10583i	−0.406768	−	0.108993i
$813$	1.93185	−	0.517638i	0.0677530	−	0.0181544i
$814$		0			0
$815$		0			0
$816$			1.73205i			0.0606339i
$817$	11.8313	−	9.38186i	0.413926	−	0.328230i
$818$	4.89898	−	4.89898i	0.171289	−	0.171289i
$819$	−6.92820	−	12.0000i	−0.242091	−	0.419314i
$820$		0			0
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$	4.03459	−	15.0573i	0.140722	−	0.525183i
$823$	7.17260	+	26.7685i	0.250021	+	0.933092i	0.970793	+	0.239919i	$0.0771210\pi$
$823$	7.17260	+	26.7685i	0.250021	+	0.933092i	−0.720772	+	0.693173i	$0.756212\pi$
$824$			4.00000i			0.139347i
$825$		0			0
$826$	−9.00000	+	15.5885i	−0.313150	+	0.542392i
$827$	−9.31749	−	34.7733i	−0.324001	−	1.20919i	−0.915313	−	0.402744i	$-0.868056\pi$
$827$	−9.31749	−	34.7733i	−0.324001	−	1.20919i	0.591312	−	0.806443i	$-0.298610\pi$
$828$	4.89898	−	4.89898i	0.170251	−	0.170251i
$829$	−45.0333			−1.56407			−0.782036	−	0.623233i	$-0.785819\pi$
$829$	−45.0333			−1.56407			−0.782036	+	0.623233i	$0.785819\pi$
$830$		0			0
$831$	−21.0000	+	12.1244i	−0.728482	+	0.420589i
$832$	0.517638	+	1.93185i	0.0179459	+	0.0669749i
$833$	8.36516	+	2.24144i	0.289836	+	0.0776612i
$834$	−13.8564	+	8.00000i	−0.479808	+	0.277017i
$835$		0			0
$836$		0			0
$837$	36.7423	+	36.7423i	1.27000	+	1.27000i
$838$	5.43520	−	20.2844i	0.187756	−	0.700714i
$839$	−24.2487	−	42.0000i	−0.837158	−	1.45000i	−0.892261	−	0.451520i	$-0.850882\pi$
$839$	−24.2487	−	42.0000i	−0.837158	−	1.45000i	0.0551024	−	0.998481i	$-0.482451\pi$
$840$		0			0
$841$	8.50000	+	14.7224i	0.293103	+	0.507670i
$842$	−36.8067	+	9.86233i	−1.26844	+	0.339878i
$843$	8.57321	−	8.57321i	0.295277	−	0.295277i
$844$	−5.19615			−0.178859
$845$		0			0
$846$	−12.0000	−	6.92820i	−0.412568	−	0.238197i
$847$	26.9444	+	26.9444i	0.925820	+	0.925820i
$848$		0			0
$849$	1.73205	−	3.00000i	0.0594438	−	0.102960i
$850$		0			0
$851$	−12.0000	−	6.92820i	−0.411355	−	0.237496i
$852$	−3.58630	+	13.3843i	−0.122865	+	0.458537i
$853$	20.0764	+	5.37945i	0.687403	+	0.184189i	0.585581	−	0.810614i	$-0.300866\pi$
$853$	20.0764	+	5.37945i	0.687403	+	0.184189i	0.101821	+	0.994803i	$0.467533\pi$
$854$	27.7128			0.948313
$855$		0			0
$856$	−15.0000			−0.512689
$857$	−28.9778	−	7.76457i	−0.989862	−	0.265233i	−0.272669	−	0.962108i	$-0.587907\pi$
$857$	−28.9778	−	7.76457i	−0.989862	−	0.265233i	−0.717193	+	0.696875i	$0.754573\pi$
$858$		0			0
$859$	0.866025	+	0.500000i	0.0295484	+	0.0170598i	0.514701	−	0.857369i	$-0.327903\pi$
$859$	0.866025	+	0.500000i	0.0295484	+	0.0170598i	−0.485153	+	0.874429i	$0.661236\pi$
$860$		0			0
$861$	12.0000	−	20.7846i	0.408959	−	0.708338i
$862$	−17.1464	−	17.1464i	−0.584010	−	0.584010i
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$	4.33013	+	2.50000i	0.147314	+	0.0850517i
$865$		0			0
$866$	−35.0000			−1.18935
$867$	−9.89949	+	9.89949i	−0.336204	+	0.336204i
$868$	−34.7733	+	9.31749i	−1.18028	+	0.316256i
$869$		0			0
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$	−4.48288	+	16.7303i	−0.151809	+	0.566560i
$873$	9.89949	+	9.89949i	0.335047	+	0.335047i
$874$	−12.1244	−	9.00000i	−0.410112	−	0.304430i
$875$		0			0
$876$	−7.50000	+	4.33013i	−0.253402	+	0.146301i
$877$	−1.93185	−	0.517638i	−0.0652340	−	0.0174794i	0.226054	−	0.974115i	$-0.427417\pi$
$877$	−1.93185	−	0.517638i	−0.0652340	−	0.0174794i	−0.291288	+	0.956635i	$0.594084\pi$
$878$	−1.79315	−	6.69213i	−0.0605159	−	0.225848i
$879$		0			0
$880$		0			0
$881$	−45.0000			−1.51609			−0.758044	−	0.652203i	$-0.773845\pi$
$881$	−45.0000			−1.51609			−0.758044	+	0.652203i	$0.773845\pi$
$882$	7.07107	−	7.07107i	0.238095	−	0.238095i
$883$	−0.448288	−	1.67303i	−0.0150861	−	0.0563020i	0.957972	−	0.286860i	$-0.0926115\pi$
$883$	−0.448288	−	1.67303i	−0.0150861	−	0.0563020i	−0.973059	+	0.230558i	$0.925945\pi$
$884$	1.73205	−	3.00000i	0.0582552	−	0.100901i
$885$		0			0
$886$			24.2487i			0.814651i
$887$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$887$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$888$	1.03528	−	3.86370i	0.0347416	−	0.129657i
$889$	−6.92820	+	12.0000i	−0.232364	+	0.402467i
$890$		0			0
$891$		0			0
$892$	1.41421	−	1.41421i	0.0473514	−	0.0473514i
$893$	−11.1106	+	28.0812i	−0.371803	+	0.939702i
$894$		0			0
$895$		0			0
$896$	−3.00000	+	1.73205i	−0.100223	+	0.0578638i
$897$	6.69213	−	1.79315i	0.223444	−	0.0598716i
$898$	−25.0955	−	6.72432i	−0.837447	−	0.224393i
$899$	−31.1769	−	18.0000i	−1.03981	−	0.600334i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−11.5911	+	3.10583i	−0.385728	+	0.103356i
$904$			9.00000i			0.299336i
$905$		0			0
$906$	18.0000	+	10.3923i	0.598010	+	0.345261i
$907$	35.7393	+	9.57630i	1.18670	+	0.317976i	0.797582	−	0.603211i	$-0.206112\pi$
$907$	35.7393	+	9.57630i	1.18670	+	0.317976i	0.389121	+	0.921187i	$0.372779\pi$
$908$	26.0800	−	6.98811i	0.865495	−	0.231909i
$909$	−10.3923	+	6.00000i	−0.344691	+	0.199007i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	1.60368	−	4.05317i	0.0531032	−	0.134214i
$913$		0			0
$914$	9.52628	+	16.5000i	0.315101	+	0.545771i
$915$		0			0
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$	−13.4486	+	50.1910i	−0.444113	+	1.65745i
$918$	−2.24144	−	8.36516i	−0.0739785	−	0.276092i
$919$		−	32.0000i		−	1.05558i	−0.849374	−	0.527791i	$-0.823020\pi$
$919$		−	32.0000i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$920$		0			0
$921$	5.50000	−	9.52628i	0.181231	−	0.313902i
$922$	4.65874	+	17.3867i	0.153428	+	0.572599i
$923$	19.5959	−	19.5959i	0.645007	−	0.645007i
$924$		0			0
$925$		0			0
$926$	−9.00000	+	5.19615i	−0.295758	+	0.170756i
$927$	−2.07055	−	7.72741i	−0.0680059	−	0.253801i
$928$	−3.34607	−	0.896575i	−0.109840	−	0.0294315i
$929$	18.1865	−	10.5000i	0.596681	−	0.344494i	−0.171054	−	0.985262i	$-0.554717\pi$
$929$	18.1865	−	10.5000i	0.596681	−	0.344494i	0.767735	+	0.640768i	$0.221384\pi$
$930$		0			0
$931$	−17.5000	−	12.9904i	−0.573539	−	0.425743i
$932$	15.9217	+	15.9217i	0.521532	+	0.521532i
$933$	−7.76457	+	28.9778i	−0.254201	+	0.948690i
$934$	−18.1865	−	31.5000i	−0.595082	−	1.03071i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−41.8258	+	11.2072i	−1.36639	+	0.366123i	−0.866159	−	0.499769i	$-0.833418\pi$
$937$	−41.8258	+	11.2072i	−1.36639	+	0.366123i	−0.500231	+	0.865892i	$0.666752\pi$
$938$	−19.5959	+	19.5959i	−0.639829	+	0.639829i
$939$	19.0526			0.621757
$940$		0			0
$941$	12.0000	+	6.92820i	0.391189	+	0.225853i	0.682675	−	0.730722i	$-0.260816\pi$
$941$	12.0000	+	6.92820i	0.391189	+	0.225853i	−0.291486	+	0.956575i	$0.594150\pi$
$942$	12.2474	+	12.2474i	0.399043	+	0.399043i
$943$	−16.9706	−	16.9706i	−0.552638	−	0.552638i
$944$	−2.59808	+	4.50000i	−0.0845602	+	0.146463i
$945$		0			0
$946$		0			0
$947$	15.2418	−	56.8831i	0.495291	−	1.84845i	−0.0331004	−	0.999452i	$-0.510538\pi$
$947$	15.2418	−	56.8831i	0.495291	−	1.84845i	0.528392	−	0.849001i	$-0.322795\pi$
$948$		0			0
$949$	17.3205			0.562247
$950$		0			0
$951$	−12.0000			−0.389127
$952$	5.79555	+	1.55291i	0.187835	+	0.0503302i
$953$	1.55291	−	5.79555i	0.0503038	−	0.187736i	−0.936202	−	0.351462i	$-0.885685\pi$
$953$	1.55291	−	5.79555i	0.0503038	−	0.187736i	0.986506	+	0.163726i	$0.0523512\pi$
$954$		0			0
$955$		0			0
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$		0			0
$958$		0			0
$959$	−46.7654	−	27.0000i	−1.51013	−	0.871875i
$960$		0			0
$961$	−77.0000			−2.48387
$962$	−5.65685	+	5.65685i	−0.182384	+	0.182384i
$963$	28.9778	−	7.76457i	0.933796	−	0.250210i
$964$		0			0
$965$		0			0
$966$	6.00000	+	10.3923i	0.193047	+	0.334367i
$967$	−7.17260	+	26.7685i	−0.230655	+	0.860818i	0.749404	+	0.662113i	$0.230340\pi$
$967$	−7.17260	+	26.7685i	−0.230655	+	0.860818i	−0.980059	+	0.198705i	$0.936327\pi$
$968$	7.77817	+	7.77817i	0.250000	+	0.250000i
$969$	−6.92820	+	3.00000i	−0.222566	+	0.0963739i
$970$		0			0
$971$	25.5000	−	14.7224i	0.818334	−	0.472465i	−0.0315077	−	0.999504i	$-0.510031\pi$
$971$	25.5000	−	14.7224i	0.818334	−	0.472465i	0.849842	+	0.527038i	$0.176698\pi$
$972$	−15.4548	−	4.14110i	−0.495713	−	0.132826i
$973$	14.3452	+	53.5370i	0.459886	+	1.71632i
$974$	−13.8564	+	8.00000i	−0.443988	+	0.256337i
$975$		0			0
$976$	8.00000			0.256074
$977$	−4.24264	+	4.24264i	−0.135734	+	0.135734i	−0.771709	−	0.635975i	$-0.780598\pi$
$977$	−4.24264	+	4.24264i	−0.135734	+	0.135734i	0.635975	+	0.771709i	$0.280598\pi$
$978$	4.48288	+	16.7303i	0.143347	+	0.534977i
$979$		0			0
$980$		0			0
$981$		−	34.6410i		−	1.10600i
$982$	−6.21166	−	23.1822i	−0.198222	−	0.739774i
$983$	−15.5291	+	57.9555i	−0.495303	+	1.84849i	0.0330251	+	0.999455i	$0.489486\pi$
$983$	−15.5291	+	57.9555i	−0.495303	+	1.84849i	−0.528328	+	0.849040i	$0.677181\pi$
$984$	3.46410	−	6.00000i	0.110432	−	0.191273i
$985$		0			0
$986$	3.00000	+	5.19615i	0.0955395	+	0.165479i
$987$	16.9706	−	16.9706i	0.540179	−	0.540179i
$988$	−6.83083	+	5.41662i	−0.217318	+	0.172326i
$989$			12.0000i			0.381578i
$990$		0			0
$991$	−42.0000	+	24.2487i	−1.33417	+	0.770286i	−0.985936	−	0.167121i	$-0.946553\pi$
$991$	−42.0000	+	24.2487i	−1.33417	+	0.770286i	−0.348238	+	0.937406i	$0.613220\pi$
$992$	−10.0382	+	2.68973i	−0.318713	+	0.0853989i
$993$	5.01910	+	1.34486i	0.159276	+	0.0426779i
$994$	41.5692	+	24.0000i	1.31850	+	0.761234i
$995$		0			0
$996$		−	1.73205i		−	0.0548821i
$997$	23.4225	−	6.27603i	0.741797	−	0.198764i	0.131920	−	0.991260i	$-0.457886\pi$
$997$	23.4225	−	6.27603i	0.741797	−	0.198764i	0.609876	+	0.792497i	$0.291219\pi$
$998$	29.9437	−	8.02339i	0.947851	−	0.253976i
$999$			20.0000i			0.632772i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73205 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.44949 - 2.44949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73205 + 1.00000i) q^{9} +(-0.707107 + 0.707107i) q^{12} +(1.93185 - 0.517638i) q^{13} +(1.73205 + 3.00000i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.448288 - 1.67303i) q^{17} +(-1.41421 - 1.41421i) q^{18} +(-2.59808 + 3.50000i) q^{19} +(3.00000 - 1.73205i) q^{21} +(-0.896575 - 3.34607i) q^{23} +(0.866025 - 0.500000i) q^{24} -2.00000 q^{26} +(-3.53553 + 3.53553i) q^{27} +(-0.896575 - 3.34607i) q^{28} +(1.73205 - 3.00000i) q^{29} -10.3923i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.866025 + 1.50000i) q^{34} +(1.00000 + 1.73205i) q^{36} +(2.82843 - 2.82843i) q^{37} +(3.41542 - 2.70831i) q^{38} +2.00000i q^{39} +(6.00000 - 3.46410i) q^{41} +(-3.34607 + 0.896575i) q^{42} +(-3.34607 - 0.896575i) q^{43} +3.46410i q^{46} +(6.69213 - 1.79315i) q^{47} +(-0.965926 + 0.258819i) q^{48} +5.00000i q^{49} +(1.50000 + 0.866025i) q^{51} +(1.93185 + 0.517638i) q^{52} +(4.33013 - 2.50000i) q^{54} +3.46410i q^{56} +(-2.70831 - 3.41542i) q^{57} +(-2.44949 + 2.44949i) q^{58} +(2.59808 + 4.50000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-2.68973 + 10.0382i) q^{62} +(-1.79315 - 6.69213i) q^{63} +1.00000i q^{64} +(2.07055 + 7.72741i) q^{67} +(1.22474 - 1.22474i) q^{68} +3.46410 q^{69} +(12.0000 - 6.92820i) q^{71} +(-0.517638 - 1.93185i) q^{72} +(8.36516 + 2.24144i) q^{73} +(-3.46410 + 2.00000i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(0.517638 - 1.93185i) q^{78} +(0.500000 + 0.866025i) q^{81} +(-6.69213 + 1.79315i) q^{82} +(-1.22474 + 1.22474i) q^{83} +3.46410 q^{84} +(3.00000 + 1.73205i) q^{86} +(2.44949 + 2.44949i) q^{87} +(4.33013 - 7.50000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(0.896575 - 3.34607i) q^{92} +(10.0382 + 2.68973i) q^{93} -6.92820 q^{94} +1.00000 q^{96} +(6.76148 + 1.81173i) q^{97} +(1.29410 - 4.82963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^6	\( 8 q + 4 q^{6} + 4 q^{16} + 24 q^{21} - 16 q^{26} + 8 q^{36} + 48 q^{41} + 12 q^{51} + 32 q^{61} + 96 q^{71} - 32 q^{76} + 4 q^{81} + 24 q^{86} - 48 q^{91} + 8 q^{96}+O(q^{100}) \) 8 * q + 4 * q^6 + 4 * q^16 + 24 * q^21 - 16 * q^26 + 8 * q^36 + 48 * q^41 + 12 * q^51 + 32 * q^61 + 96 * q^71 - 32 * q^76 + 4 * q^81 + 24 * q^86 - 48 * q^91 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more