LMFDB - Embedded newform 950.2.q.a.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:	no (minimal twist has level 190)
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.a.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.22474 - 2.12132i) q^{6} +(0.775255 + 0.775255i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.22474 - 2.12132i) q^{6} +(0.775255 + 0.775255i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} -1.44949 q^{11} +(-1.73205 + 1.73205i) q^{12} +(4.73205 - 1.26795i) q^{13} +(-0.548188 - 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.732051 + 2.73205i) q^{17} +(2.12132 + 2.12132i) q^{18} +(2.98735 + 3.17423i) q^{19} +(-2.32577 + 1.34278i) q^{21} +(1.40010 + 0.375156i) q^{22} +(1.34486 + 5.01910i) q^{23} +(2.12132 - 1.22474i) q^{24} -4.89898 q^{26} +(0.283763 + 1.05902i) q^{28} +(-3.85337 + 6.67423i) q^{29} +0.778539i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.918940 - 3.42953i) q^{33} +(1.41421 - 2.44949i) q^{34} +(-1.50000 - 2.59808i) q^{36} +(3.85337 - 3.85337i) q^{37} +(-2.06400 - 3.83926i) q^{38} +12.0000i q^{39} +(-1.50000 + 0.866025i) q^{41} +(2.59405 - 0.695075i) q^{42} +(-10.1762 - 2.72670i) q^{43} +(-1.25529 - 0.724745i) q^{44} -5.19615i q^{46} +(6.69213 - 1.79315i) q^{47} +(-2.36603 + 0.633975i) q^{48} -5.79796i q^{49} +(-6.00000 - 3.46410i) q^{51} +(4.73205 + 1.26795i) q^{52} +(-4.20030 + 1.12547i) q^{53} -1.09638i q^{56} +(-9.40422 + 5.05575i) q^{57} +(5.44949 - 5.44949i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(0.201501 - 0.752011i) q^{62} +(-0.851289 - 3.17705i) q^{63} +1.00000i q^{64} +(-1.77526 + 3.07483i) q^{66} +(3.73980 + 13.9571i) q^{67} +(-2.00000 + 2.00000i) q^{68} -12.7279 q^{69} +(-3.00000 + 1.73205i) q^{71} +(0.776457 + 2.89778i) q^{72} +(-8.81017 - 2.36068i) q^{73} +(-4.71940 + 2.72474i) q^{74} +(1.00000 + 4.24264i) q^{76} +(-1.12372 - 1.12372i) q^{77} +(3.10583 - 11.5911i) q^{78} +(2.51059 + 4.34847i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.67303 - 0.448288i) q^{82} +(-12.3485 + 12.3485i) q^{83} -2.68556 q^{84} +(9.12372 + 5.26758i) q^{86} +(-13.3485 - 13.3485i) q^{87} +(1.02494 + 1.02494i) q^{88} +(-6.84072 + 11.8485i) q^{89} +(4.65153 + 2.68556i) q^{91} +(-1.34486 + 5.01910i) q^{92} +(-1.84204 - 0.493574i) q^{93} -6.92820 q^{94} +2.44949 q^{96} +(-13.9571 - 3.73980i) q^{97} +(-1.50062 + 5.60040i) q^{98} +(3.76588 + 2.17423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 16 q^{7}+O(q^{10}) $ 8 * q - 12 * q^3 + 16 * q^7	$ 8 q - 12 q^{3} + 16 q^{7} + 8 q^{11} + 24 q^{13} + 4 q^{16} + 8 q^{17} - 48 q^{21} + 12 q^{22} - 8 q^{28} - 12 q^{33} - 12 q^{36} + 12 q^{38} - 12 q^{41} - 12 q^{42} - 20 q^{43} - 12 q^{48} - 48 q^{51} + 24 q^{52} - 36 q^{53} + 12 q^{57} + 24 q^{58} + 32 q^{61} - 12 q^{62} + 24 q^{63} - 24 q^{66} + 12 q^{67} - 16 q^{68} - 24 q^{71} - 16 q^{73} + 8 q^{76} + 40 q^{77} - 36 q^{81} - 40 q^{83} + 24 q^{86} - 48 q^{87} + 96 q^{91} + 24 q^{93} - 12 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 12 * q^3 + 16 * q^7 + 8 * q^11 + 24 * q^13 + 4 * q^16 + 8 * q^17 - 48 * q^21 + 12 * q^22 - 8 * q^28 - 12 * q^33 - 12 * q^36 + 12 * q^38 - 12 * q^41 - 12 * q^42 - 20 * q^43 - 12 * q^48 - 48 * q^51 + 24 * q^52 - 36 * q^53 + 12 * q^57 + 24 * q^58 + 32 * q^61 - 12 * q^62 + 24 * q^63 - 24 * q^66 + 12 * q^67 - 16 * q^68 - 24 * q^71 - 16 * q^73 + 8 * q^76 + 40 * q^77 - 36 * q^81 - 40 * q^83 + 24 * q^86 - 48 * q^87 + 96 * q^91 + 24 * q^93 - 12 * q^97 - 48 * q^98

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
$3$	−0.633975	+	2.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.633975	+	2.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	1.22474	−	2.12132i	0.500000	−	0.866025i
$7$	0.775255	+	0.775255i	0.293019	+	0.293019i	0.838272	−	0.545253i	$-0.183566\pi$
$7$	0.775255	+	0.775255i	0.293019	+	0.293019i	−0.545253	+	0.838272i	$0.683566\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$		0			0
$11$	−1.44949			−0.437038			−0.218519	−	0.975833i	$-0.570122\pi$
$11$	−1.44949			−0.437038			−0.218519	+	0.975833i	$0.570122\pi$
$12$	−1.73205	+	1.73205i	−0.500000	+	0.500000i
$13$	4.73205	−	1.26795i	1.31243	−	0.351666i	0.466296	−	0.884629i	$-0.345588\pi$
$13$	4.73205	−	1.26795i	1.31243	−	0.351666i	0.846139	+	0.532963i	$0.178921\pi$
$14$	−0.548188	−	0.949490i	−0.146509	−	0.253762i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.732051	+	2.73205i	−0.177548	+	0.662620i	0.818555	+	0.574428i	$0.194775\pi$
$17$	−0.732051	+	2.73205i	−0.177548	+	0.662620i	−0.996104	+	0.0881917i	$0.971891\pi$
$18$	2.12132	+	2.12132i	0.500000	+	0.500000i
$19$	2.98735	+	3.17423i	0.685344	+	0.728219i
$19$	2.98735	+	3.17423i	0.685344	+	0.728219i
$20$		0			0
$21$	−2.32577	+	1.34278i	−0.507524	+	0.293019i
$22$	1.40010	+	0.375156i	0.298502	+	0.0799834i
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	0.952119	+	0.305727i	$0.0988995\pi$
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	−0.671696	+	0.740827i	$0.734434\pi$
$24$	2.12132	−	1.22474i	0.433013	−	0.250000i
$25$		0			0
$26$	−4.89898			−0.960769
$27$		0			0
$28$	0.283763	+	1.05902i	0.0536262	+	0.200136i
$29$	−3.85337	+	6.67423i	−0.715553	+	1.23937i	0.247193	+	0.968966i	$0.420492\pi$
$29$	−3.85337	+	6.67423i	−0.715553	+	1.23937i	−0.962746	+	0.270408i	$0.912841\pi$
$30$		0			0
$31$			0.778539i			0.139830i	0.997553	+	0.0699149i	$0.0222728\pi$
$31$			0.778539i			0.139830i	−0.997553	+	0.0699149i	$0.977727\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.918940	−	3.42953i	0.159967	−	0.597004i
$34$	1.41421	−	2.44949i	0.242536	−	0.420084i
$35$		0			0
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	3.85337	−	3.85337i	0.633490	−	0.633490i	−0.315451	−	0.948942i	$-0.602156\pi$
$37$	3.85337	−	3.85337i	0.633490	−	0.633490i	0.948942	+	0.315451i	$0.102156\pi$
$38$	−2.06400	−	3.83926i	−0.334825	−	0.622810i
$39$			12.0000i			1.92154i
$40$		0			0
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	−0.612536	−	0.790443i	$-0.709851\pi$
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	0.378275	+	0.925693i	$0.376517\pi$
$42$	2.59405	−	0.695075i	0.400271	−	0.107252i
$43$	−10.1762	−	2.72670i	−1.55185	−	0.415818i	−0.621781	−	0.783191i	$-0.713591\pi$
$43$	−10.1762	−	2.72670i	−1.55185	−	0.415818i	−0.930074	+	0.367373i	$0.880257\pi$
$44$	−1.25529	−	0.724745i	−0.189243	−	0.109259i
$45$		0			0
$46$		−	5.19615i		−	0.766131i
$47$	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	$0.248052\pi$
$48$	−2.36603	+	0.633975i	−0.341506	+	0.0915064i
$49$		−	5.79796i		−	0.828280i
$50$		0			0
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	4.73205	+	1.26795i	0.656217	+	0.175833i
$53$	−4.20030	+	1.12547i	−0.576955	+	0.154595i	−0.535485	−	0.844545i	$-0.679871\pi$
$53$	−4.20030	+	1.12547i	−0.576955	+	0.154595i	−0.0414708	+	0.999140i	$0.513204\pi$
$54$		0			0
$55$		0			0
$56$		−	1.09638i		−	0.146509i
$57$	−9.40422	+	5.05575i	−1.24562	+	0.669651i
$58$	5.44949	−	5.44949i	0.715553	−	0.715553i
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	0.730974	−	0.682406i	$-0.239066\pi$
$59$	−1.73205	−	3.00000i	−0.225494	−	0.390567i	−0.956467	+	0.291839i	$0.905733\pi$
$60$		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	$-0.00448323\pi$
$62$	0.201501	−	0.752011i	0.0255906	−	0.0955055i
$63$	−0.851289	−	3.17705i	−0.107252	−	0.400271i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.77526	+	3.07483i	−0.218519	+	0.378486i
$67$	3.73980	+	13.9571i	0.456890	+	1.70514i	0.682472	+	0.730911i	$0.260905\pi$
$67$	3.73980	+	13.9571i	0.456890	+	1.70514i	−0.225583	+	0.974224i	$0.572429\pi$
$68$	−2.00000	+	2.00000i	−0.242536	+	0.242536i
$69$	−12.7279			−1.53226
$70$		0			0
$71$	−3.00000	+	1.73205i	−0.356034	+	0.205557i	−0.667340	−	0.744753i	$-0.732567\pi$
$71$	−3.00000	+	1.73205i	−0.356034	+	0.205557i	0.311305	+	0.950310i	$0.399234\pi$
$72$	0.776457	+	2.89778i	0.0915064	+	0.341506i
$73$	−8.81017	−	2.36068i	−1.03115	−	0.276296i	−0.296710	−	0.954968i	$-0.595889\pi$
$73$	−8.81017	−	2.36068i	−1.03115	−	0.276296i	−0.734442	+	0.678671i	$0.762556\pi$
$74$	−4.71940	+	2.72474i	−0.548619	+	0.316745i
$75$		0			0
$76$	1.00000	+	4.24264i	0.114708	+	0.486664i
$77$	−1.12372	−	1.12372i	−0.128060	−	0.128060i
$78$	3.10583	−	11.5911i	0.351666	−	1.31243i
$79$	2.51059	+	4.34847i	0.282463	+	0.489241i	0.971991	−	0.235019i	$-0.0755151\pi$
$79$	2.51059	+	4.34847i	0.282463	+	0.489241i	−0.689527	+	0.724260i	$0.742182\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.67303	−	0.448288i	0.184756	−	0.0495051i
$83$	−12.3485	+	12.3485i	−1.35542	+	1.35542i	−0.475946	+	0.879474i	$0.657894\pi$
$83$	−12.3485	+	12.3485i	−1.35542	+	1.35542i	−0.879474	+	0.475946i	$0.842106\pi$
$84$	−2.68556			−0.293019
$85$		0			0
$86$	9.12372	+	5.26758i	0.983836	+	0.568018i
$87$	−13.3485	−	13.3485i	−1.43111	−	1.43111i
$88$	1.02494	+	1.02494i	0.109259	+	0.109259i
$89$	−6.84072	+	11.8485i	−0.725115	+	1.25594i	0.233812	+	0.972282i	$0.424880\pi$
$89$	−6.84072	+	11.8485i	−0.725115	+	1.25594i	−0.958927	+	0.283653i	$0.908453\pi$
$90$		0			0
$91$	4.65153	+	2.68556i	0.487613	+	0.281523i
$92$	−1.34486	+	5.01910i	−0.140212	+	0.523277i
$93$	−1.84204	−	0.493574i	−0.191011	−	0.0511812i
$94$	−6.92820			−0.714590
$95$		0			0
$96$	2.44949			0.250000
$97$	−13.9571	−	3.73980i	−1.41713	−	0.379719i	−0.532667	−	0.846325i	$-0.678810\pi$
$97$	−13.9571	−	3.73980i	−1.41713	−	0.379719i	−0.884466	+	0.466606i	$0.845477\pi$
$98$	−1.50062	+	5.60040i	−0.151586	+	0.565726i
$99$	3.76588	+	2.17423i	0.378486	+	0.218519i
$100$		0			0
$101$	6.34847	−	10.9959i	0.631696	−	1.09413i	−0.355509	−	0.934673i	$-0.615692\pi$
$101$	6.34847	−	10.9959i	0.631696	−	1.09413i	0.987205	−	0.159457i	$-0.0509744\pi$
$102$	4.89898	+	4.89898i	0.485071	+	0.485071i
$103$	−1.34278	−	1.34278i	−0.132308	−	0.132308i	0.637851	−	0.770160i	$-0.279823\pi$
$103$	−1.34278	−	1.34278i	−0.132308	−	0.132308i	−0.770160	+	0.637851i	$0.779823\pi$
$104$	−4.24264	−	2.44949i	−0.416025	−	0.240192i
$105$		0			0
$106$	4.34847			0.422361
$107$	8.66025	−	8.66025i	0.837218	−	0.837218i	−0.151274	−	0.988492i	$-0.548337\pi$
$107$	8.66025	−	8.66025i	0.837218	−	0.837218i	0.988492	+	0.151274i	$0.0483374\pi$
$108$		0			0
$109$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$109$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$110$		0			0
$111$	6.67423	+	11.5601i	0.633490	+	1.09724i
$112$	−0.283763	+	1.05902i	−0.0268131	+	0.100068i
$113$	12.9029	+	12.9029i	1.21380	+	1.21380i	0.969766	+	0.244036i	$0.0784715\pi$
$113$	12.9029	+	12.9029i	1.21380	+	1.21380i	0.244036	+	0.969766i	$0.421528\pi$
$114$	10.3923	−	2.44949i	0.973329	−	0.229416i
$115$		0			0
$116$	−6.67423	+	3.85337i	−0.619687	+	0.357777i
$117$	−14.1962	−	3.80385i	−1.31243	−	0.351666i
$118$	0.896575	+	3.34607i	0.0825365	+	0.308030i
$119$	−2.68556	+	1.55051i	−0.246185	+	0.142135i
$120$		0			0
$121$	−8.89898			−0.808998
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$	−1.09808	−	4.09808i	−0.0990102	−	0.369511i
$124$	−0.389270	+	0.674235i	−0.0349574	+	0.0605481i
$125$		0			0
$126$			3.28913i			0.293019i
$127$	3.59732	+	13.4254i	0.319211	+	1.19131i	0.920005	+	0.391907i	$0.128184\pi$
$127$	3.59732	+	13.4254i	0.319211	+	1.19131i	−0.600794	+	0.799404i	$0.705149\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	12.9029	−	22.3485i	1.13604	−	1.96767i
$130$		0			0
$131$	−3.62372	−	6.27647i	−0.316606	−	0.548378i	0.663171	−	0.748468i	$-0.269210\pi$
$131$	−3.62372	−	6.27647i	−0.316606	−	0.548378i	−0.979778	+	0.200089i	$0.935877\pi$
$132$	2.51059	−	2.51059i	0.218519	−	0.218519i
$133$	−0.144887	+	4.77680i	−0.0125633	+	0.414201i
$134$		−	14.4495i		−	1.24825i
$135$		0			0
$136$	2.44949	−	1.41421i	0.210042	−	0.121268i
$137$	2.73205	−	0.732051i	0.233415	−	0.0625433i	−0.140215	−	0.990121i	$-0.544780\pi$
$137$	2.73205	−	0.732051i	0.233415	−	0.0625433i	0.373630	+	0.927578i	$0.378113\pi$
$138$	12.2942	+	3.29423i	1.04655	+	0.280423i
$139$	14.6349	+	8.44949i	1.24132	+	0.716676i	0.969363	−	0.245633i	$-0.0789958\pi$
$139$	14.6349	+	8.44949i	1.24132	+	0.716676i	0.271957	+	0.962309i	$0.412329\pi$
$140$		0			0
$141$			16.9706i			1.42918i
$142$	3.34607	−	0.896575i	0.280796	−	0.0752389i
$143$	−6.85906	+	1.83788i	−0.573583	+	0.153691i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	7.89898	+	4.56048i	0.653724	+	0.377428i
$147$	13.7181	+	3.67576i	1.13145	+	0.303171i
$148$	5.26380	−	1.41043i	0.432682	−	0.115937i
$149$	5.58542	−	3.22474i	0.457576	−	0.264181i	−0.253449	−	0.967349i	$-0.581565\pi$
$149$	5.58542	−	3.22474i	0.457576	−	0.264181i	0.711024	+	0.703167i	$0.248232\pi$
$150$		0			0
$151$			8.48528i			0.690522i	0.938507	+	0.345261i	$0.112210\pi$
$151$			8.48528i			0.690522i	−0.938507	+	0.345261i	$0.887790\pi$
$152$	0.132150	−	4.35690i	0.0107188	−	0.353391i
$153$	6.00000	−	6.00000i	0.485071	−	0.485071i
$154$	0.794593	+	1.37628i	0.0640301	+	0.110903i
$155$		0			0
$156$	−6.00000	+	10.3923i	−0.480384	+	0.832050i
$157$	1.71089	−	6.38512i	0.136544	−	0.509588i	−0.863443	−	0.504446i	$-0.831697\pi$
$157$	1.71089	−	6.38512i	0.136544	−	0.509588i	0.999987	−	0.00514190i	$-0.00163673\pi$
$158$	−1.29958	−	4.85009i	−0.103389	−	0.385852i
$159$		−	10.6515i		−	0.844721i
$160$		0			0
$161$	−2.84847	+	4.93369i	−0.224491	+	0.388830i
$162$	2.32937	+	8.69333i	0.183013	+	0.683013i
$163$	9.34847	−	9.34847i	0.732229	−	0.732229i	−0.238832	−	0.971061i	$-0.576765\pi$
$163$	9.34847	−	9.34847i	0.732229	−	0.732229i	0.971061	+	0.238832i	$0.0767646\pi$
$164$	−1.73205			−0.135250
$165$		0			0
$166$	15.1237	−	8.73169i	1.17383	−	0.677710i
$167$	1.47448	+	5.50282i	0.114098	+	0.425821i	0.999218	−	0.0395428i	$-0.0125902\pi$
$167$	1.47448	+	5.50282i	0.114098	+	0.425821i	−0.885119	+	0.465364i	$0.845923\pi$
$168$	2.59405	+	0.695075i	0.200136	+	0.0536262i
$169$	9.52628	−	5.50000i	0.732791	−	0.423077i
$170$		0			0
$171$	−3.00000	−	12.7279i	−0.229416	−	0.973329i
$172$	−7.44949	−	7.44949i	−0.568018	−	0.568018i
$173$	0.142483	−	0.531752i	0.0108327	−	0.0404284i	−0.960298	−	0.278977i	$-0.910005\pi$
$173$	0.142483	−	0.531752i	0.0108327	−	0.0404284i	0.971131	+	0.238548i	$0.0766715\pi$
$174$	9.43879	+	16.3485i	0.715553	+	1.23937i
$175$		0			0
$176$	−0.724745	−	1.25529i	−0.0546297	−	0.0946214i
$177$	8.19615	−	2.19615i	0.616061	−	0.165073i
$178$	9.67423	−	9.67423i	0.725115	−	0.725115i
$179$	2.51059			0.187650			0.0938251	−	0.995589i	$-0.470091\pi$
$179$	2.51059			0.187650			0.0938251	+	0.995589i	$0.470091\pi$
$180$		0			0
$181$	18.6742	+	10.7816i	1.38804	+	0.801388i	0.993095	−	0.117314i	$-0.0374285\pi$
$181$	18.6742	+	10.7816i	1.38804	+	0.801388i	0.394950	+	0.918703i	$0.370762\pi$
$182$	−3.79796	−	3.79796i	−0.281523	−	0.281523i
$183$	13.8564	+	13.8564i	1.02430	+	1.02430i
$184$	2.59808	−	4.50000i	0.191533	−	0.331744i
$185$		0			0
$186$	1.65153	+	0.953512i	0.121096	+	0.0699149i
$187$	1.06110	−	3.96008i	0.0775953	−	0.289590i
$188$	6.69213	+	1.79315i	0.488074	+	0.130779i
$189$		0			0
$190$		0			0
$191$	−16.2474			−1.17562			−0.587812	−	0.808998i	$-0.700011\pi$
$191$	−16.2474			−1.17562			−0.587812	+	0.808998i	$0.700011\pi$
$192$	−2.36603	−	0.633975i	−0.170753	−	0.0457532i
$193$	3.45484	−	12.8936i	0.248685	−	0.928104i	−0.722811	−	0.691046i	$-0.757150\pi$
$193$	3.45484	−	12.8936i	0.248685	−	0.928104i	0.971496	−	0.237058i	$-0.0761831\pi$
$194$	12.5136	+	7.22474i	0.898426	+	0.518706i
$195$		0			0
$196$	2.89898	−	5.02118i	0.207070	−	0.358656i
$197$	−5.32577	−	5.32577i	−0.379445	−	0.379445i	0.491457	−	0.870902i	$-0.336465\pi$
$197$	−5.32577	−	5.32577i	−0.379445	−	0.379445i	−0.870902	+	0.491457i	$0.836465\pi$
$198$	−3.07483	−	3.07483i	−0.218519	−	0.218519i
$199$	−8.48528	−	4.89898i	−0.601506	−	0.347279i	0.168128	−	0.985765i	$-0.446228\pi$
$199$	−8.48528	−	4.89898i	−0.601506	−	0.347279i	−0.769634	+	0.638486i	$0.779561\pi$
$200$		0			0
$201$	−35.3939			−2.49649
$202$	−8.97809	+	8.97809i	−0.631696	+	0.631696i
$203$	−8.16158	+	2.18689i	−0.572831	+	0.153490i
$204$	−3.46410	−	6.00000i	−0.242536	−	0.420084i
$205$		0			0
$206$	0.949490	+	1.64456i	0.0661541	+	0.114582i
$207$	4.03459	−	15.0573i	0.280423	−	1.04655i
$208$	3.46410	+	3.46410i	0.240192	+	0.240192i
$209$	−4.33013	−	4.60102i	−0.299521	−	0.318259i
$210$		0			0
$211$	15.8258	−	9.13701i	1.08949	−	0.629018i	0.156050	−	0.987749i	$-0.450124\pi$
$211$	15.8258	−	9.13701i	1.08949	−	0.629018i	0.933441	+	0.358731i	$0.116791\pi$
$212$	−4.20030	−	1.12547i	−0.288478	−	0.0772974i
$213$	−2.19615	−	8.19615i	−0.150478	−	0.561591i
$214$	−10.6066	+	6.12372i	−0.725052	+	0.418609i
$215$		0			0
$216$		0			0
$217$	−0.603566	+	0.603566i	−0.0409728	+	0.0409728i
$218$		0			0
$219$	11.1708	−	19.3485i	0.754856	−	1.30745i
$220$		0			0
$221$			13.8564i			0.932083i
$222$	−3.45484	−	12.8936i	−0.231874	−	0.865364i
$223$	−3.02739	+	11.2984i	−0.202729	+	0.756595i	0.787401	+	0.616442i	$0.211426\pi$
$223$	−3.02739	+	11.2984i	−0.202729	+	0.756595i	−0.990130	+	0.140154i	$0.955240\pi$
$224$	0.548188	−	0.949490i	0.0366274	−	0.0634405i
$225$		0			0
$226$	−9.12372	−	15.8028i	−0.606901	−	1.05118i
$227$	10.9959	−	10.9959i	0.729822	−	0.729822i	−0.240762	−	0.970584i	$-0.577397\pi$
$227$	10.9959	−	10.9959i	0.729822	−	0.729822i	0.970584	+	0.240762i	$0.0773975\pi$
$228$	−10.6722	−	0.323701i	−0.706782	−	0.0214376i
$229$			15.5505i			1.02761i	0.857908	+	0.513803i	$0.171764\pi$
$229$			15.5505i			1.02761i	−0.857908	+	0.513803i	$0.828236\pi$
$230$		0			0
$231$	3.37117	−	1.94635i	0.221807	−	0.128060i
$232$	7.44414	−	1.99465i	0.488732	−	0.130955i
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	0.147543	−	0.989056i	$-0.452863\pi$
$233$	−3.34607	−	0.896575i	−0.219208	−	0.0587366i	−0.366751	+	0.930319i	$0.619530\pi$
$234$	12.7279	+	7.34847i	0.832050	+	0.480384i
$235$		0			0
$236$		−	3.46410i		−	0.225494i
$237$	−11.8802	+	3.18330i	−0.771704	+	0.206778i
$238$	2.99536	−	0.802603i	0.194160	−	0.0520250i
$239$			13.7980i			0.892516i	0.894904	+	0.446258i	$0.147244\pi$
$239$			13.7980i			0.892516i	−0.894904	+	0.446258i	$0.852756\pi$
$240$		0			0
$241$	23.6969	+	13.6814i	1.52645	+	0.881299i	0.999507	+	0.0314005i	$0.00999675\pi$
$241$	23.6969	+	13.6814i	1.52645	+	0.881299i	0.526947	+	0.849898i	$0.323337\pi$
$242$	8.59575	+	2.30323i	0.552556	+	0.148057i
$243$	21.2942	−	5.70577i	1.36603	−	0.366025i
$244$	6.92820	−	4.00000i	0.443533	−	0.256074i
$245$		0			0
$246$			4.24264i			0.270501i
$247$	18.1610	+	11.2328i	1.15556	+	0.714728i
$248$	0.550510	−	0.550510i	0.0349574	−	0.0349574i
$249$	−21.3882	−	37.0454i	−1.35542	−	2.34766i
$250$		0			0
$251$	0.449490	−	0.778539i	0.0283715	−	0.0491410i	−0.851491	−	0.524369i	$-0.824301\pi$
$251$	0.449490	−	0.778539i	0.0283715	−	0.0491410i	0.879863	+	0.475228i	$0.157635\pi$
$252$	0.851289	−	3.17705i	0.0536262	−	0.200136i
$253$	−1.94937	−	7.27513i	−0.122556	−	0.457384i
$254$		−	13.8990i		−	0.872100i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.47185	+	9.22508i	0.154190	+	0.575445i	0.999173	+	0.0406523i	$0.0129436\pi$
$257$	2.47185	+	9.22508i	0.154190	+	0.575445i	−0.844983	+	0.534793i	$0.820390\pi$
$258$	−18.2474	+	18.2474i	−1.13604	+	1.13604i
$259$	5.97469			0.371249
$260$		0			0
$261$	20.0227	−	11.5601i	1.23937	−	0.715553i
$262$	1.87578	+	7.00050i	0.115886	+	0.432492i
$263$	22.3634	+	5.99227i	1.37899	+	0.369499i	0.870754	−	0.491720i	$-0.163631\pi$
$263$	22.3634	+	5.99227i	1.37899	+	0.369499i	0.508235	+	0.861218i	$0.330298\pi$
$264$	−3.07483	+	1.77526i	−0.189243	+	0.109259i
$265$		0			0
$266$	1.37628	−	4.57653i	0.0843849	−	0.280605i
$267$	−23.6969	−	23.6969i	−1.45023	−	1.45023i
$268$	−3.73980	+	13.9571i	−0.228445	+	0.852568i
$269$	−3.46410	−	6.00000i	−0.211210	−	0.365826i	0.740883	−	0.671634i	$-0.234407\pi$
$269$	−3.46410	−	6.00000i	−0.211210	−	0.365826i	−0.952093	+	0.305807i	$0.901074\pi$
$270$		0			0
$271$	−1.65153	−	2.86054i	−0.100323	−	0.173765i	0.811495	−	0.584360i	$-0.198654\pi$
$271$	−1.65153	−	2.86054i	−0.100323	−	0.173765i	−0.911818	+	0.410595i	$0.865321\pi$
$272$	−2.73205	+	0.732051i	−0.165655	+	0.0443871i
$273$	−9.30306	+	9.30306i	−0.563047	+	0.563047i
$274$	−2.82843			−0.170872
$275$		0			0
$276$	−11.0227	−	6.36396i	−0.663489	−	0.383065i
$277$	−13.7980	−	13.7980i	−0.829039	−	0.829039i	0.158345	−	0.987384i	$-0.449384\pi$
$277$	−13.7980	−	13.7980i	−0.829039	−	0.829039i	−0.987384	+	0.158345i	$0.949384\pi$
$278$	−11.9494	−	11.9494i	−0.716676	−	0.716676i
$279$	1.16781	−	2.02270i	0.0699149	−	0.121096i
$280$		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	$0.784449\pi$
$282$	4.39230	−	16.3923i	0.261558	−	0.976148i
$283$	0.614014	+	0.164525i	0.0364994	+	0.00977998i	0.277023	−	0.960863i	$-0.410652\pi$
$283$	0.614014	+	0.164525i	0.0364994	+	0.00977998i	−0.240523	+	0.970643i	$0.577319\pi$
$284$	−3.46410			−0.205557
$285$		0			0
$286$	7.10102			0.419892
$287$	−1.83427	−	0.491492i	−0.108274	−	0.0290119i
$288$	−0.776457	+	2.89778i	−0.0457532	+	0.170753i
$289$	7.79423	+	4.50000i	0.458484	+	0.264706i
$290$		0			0
$291$	17.6969	−	30.6520i	1.03741	−	1.79685i
$292$	−6.44949	−	6.44949i	−0.377428	−	0.377428i
$293$	−19.2669	−	19.2669i	−1.12558	−	1.12558i	−0.990887	−	0.134695i	$-0.956995\pi$
$293$	−19.2669	−	19.2669i	−1.12558	−	1.12558i	−0.134695	−	0.990887i	$-0.543005\pi$
$294$	−12.2993	−	7.10102i	−0.717311	−	0.414140i
$295$		0			0
$296$	−5.44949			−0.316745
$297$		0			0
$298$	−6.22973	+	1.66925i	−0.360878	+	0.0966971i
$299$	12.7279	+	22.0454i	0.736075	+	1.27492i
$300$		0			0
$301$	−5.77526	−	10.0030i	−0.332880	−	0.576565i
$302$	2.19615	−	8.19615i	0.126374	−	0.471636i
$303$	21.9917	+	21.9917i	1.26339	+	1.26339i
$304$	−1.25529	+	4.17423i	−0.0719961	+	0.239409i
$305$		0			0
$306$	−7.34847	+	4.24264i	−0.420084	+	0.242536i
$307$	12.8936	+	3.45484i	0.735878	+	0.197178i	0.607245	−	0.794514i	$-0.292274\pi$
$307$	12.8936	+	3.45484i	0.735878	+	0.197178i	0.128633	+	0.991692i	$0.458941\pi$
$308$	−0.411312	−	1.53504i	−0.0234367	−	0.0874668i
$309$	4.02834	−	2.32577i	0.229164	−	0.132308i
$310$		0			0
$311$	25.7980			1.46287			0.731434	−	0.681912i	$-0.238851\pi$
$311$	25.7980			1.46287			0.731434	+	0.681912i	$0.238851\pi$
$312$	8.48528	−	8.48528i	0.480384	−	0.480384i
$313$	−7.70315	−	28.7486i	−0.435408	−	1.62496i	−0.740088	−	0.672510i	$-0.765216\pi$
$313$	−7.70315	−	28.7486i	−0.435408	−	1.62496i	0.304680	−	0.952455i	$-0.401450\pi$
$314$	−3.30518	+	5.72474i	−0.186522	+	0.323066i
$315$		0			0
$316$			5.02118i			0.282463i
$317$	−3.94633	−	14.7279i	−0.221648	−	0.827202i	−0.983720	−	0.179709i	$-0.942484\pi$
$317$	−3.94633	−	14.7279i	−0.221648	−	0.827202i	0.762072	−	0.647492i	$-0.224182\pi$
$318$	−2.75682	+	10.2886i	−0.154595	+	0.576955i
$319$	5.58542	−	9.67423i	0.312724	−	0.541653i
$320$		0			0
$321$	15.0000	+	25.9808i	0.837218	+	1.45010i
$322$	4.02834	−	4.02834i	0.224491	−	0.224491i
$323$	−10.8591	+	5.83788i	−0.604214	+	0.324828i
$324$		−	9.00000i		−	0.500000i
$325$		0			0
$326$	−11.4495	+	6.61037i	−0.634129	+	0.366114i
$327$		0			0
$328$	1.67303	+	0.448288i	0.0923778	+	0.0247525i
$329$	6.57826	+	3.79796i	0.362671	+	0.209388i
$330$		0			0
$331$		−	4.06767i		−	0.223579i	−0.993732	−	0.111790i	$-0.964342\pi$
$331$		−	4.06767i		−	0.223579i	0.993732	−	0.111790i	$-0.0356583\pi$
$332$	−16.8683	+	4.51985i	−0.925769	+	0.248059i
$333$	−15.7914	+	4.23130i	−0.865364	+	0.231874i
$334$		−	5.69694i		−	0.311723i
$335$		0			0
$336$	−2.32577	−	1.34278i	−0.126881	−	0.0732547i
$337$	17.3867	+	4.65874i	0.947112	+	0.253778i	0.699136	−	0.714988i	$-0.253568\pi$
$337$	17.3867	+	4.65874i	0.947112	+	0.253778i	0.247976	+	0.968766i	$0.420235\pi$
$338$	−10.6252	+	2.84701i	−0.577934	+	0.154857i
$339$	−38.7087	+	22.3485i	−2.10237	+	1.21380i
$340$		0			0
$341$		−	1.12848i		−	0.0611109i
$342$	−0.396451	+	13.0707i	−0.0214376	+	0.706782i
$343$	9.92168	−	9.92168i	0.535721	−	0.535721i
$344$	5.26758	+	9.12372i	0.284009	+	0.491918i
$345$		0			0
$346$	−0.275255	+	0.476756i	−0.0147978	+	0.0256306i
$347$	−2.43463	+	9.08616i	−0.130698	+	0.487771i	−0.999979	−	0.00654796i	$-0.997916\pi$
$347$	−2.43463	+	9.08616i	−0.130698	+	0.487771i	0.869281	+	0.494319i	$0.164582\pi$
$348$	−4.88588	−	18.2343i	−0.261911	−	0.977464i
$349$			19.1010i			1.02245i	0.859446	+	0.511227i	$0.170809\pi$
$349$			19.1010i			1.02245i	−0.859446	+	0.511227i	$0.829191\pi$
$350$		0			0
$351$		0			0
$352$	0.375156	+	1.40010i	0.0199959	+	0.0746256i
$353$	1.65153	−	1.65153i	0.0879021	−	0.0879021i	−0.661788	−	0.749691i	$-0.730202\pi$
$353$	1.65153	−	1.65153i	0.0879021	−	0.0879021i	0.749691	+	0.661788i	$0.230202\pi$
$354$	−8.48528			−0.450988
$355$		0			0
$356$	−11.8485	+	6.84072i	−0.627968	+	0.362557i
$357$	−1.96597	−	7.33709i	−0.104050	−	0.388320i
$358$	−2.42504	−	0.649788i	−0.128168	−	0.0343424i
$359$	20.6096	−	11.8990i	1.08774	−	0.628004i	0.154763	−	0.987952i	$-0.450539\pi$
$359$	20.6096	−	11.8990i	1.08774	−	0.628004i	0.932973	+	0.359948i	$0.117205\pi$
$360$		0			0
$361$	−1.15153	+	18.9651i	−0.0606069	+	0.998162i
$362$	−15.2474	−	15.2474i	−0.801388	−	0.801388i
$363$	5.64173	−	21.0552i	0.296114	−	1.10511i
$364$	2.68556	+	4.65153i	0.140762	+	0.243806i
$365$		0			0
$366$	−9.79796	−	16.9706i	−0.512148	−	0.887066i
$367$	14.6123	−	3.91535i	0.762755	−	0.204380i	0.143587	−	0.989638i	$-0.454136\pi$
$367$	14.6123	−	3.91535i	0.762755	−	0.204380i	0.619169	+	0.785258i	$0.287470\pi$
$368$	−3.67423	+	3.67423i	−0.191533	+	0.191533i
$369$	5.19615			0.270501
$370$		0			0
$371$	−4.12883	−	2.38378i	−0.214358	−	0.123760i
$372$	−1.34847	−	1.34847i	−0.0699149	−	0.0699149i
$373$	25.4165	+	25.4165i	1.31602	+	1.31602i	0.916900	+	0.399118i	$0.130684\pi$
$373$	25.4165	+	25.4165i	1.31602	+	1.31602i	0.399118	+	0.916900i	$0.369316\pi$
$374$	−2.04989	+	3.55051i	−0.105997	+	0.183593i
$375$		0			0
$376$	−6.00000	−	3.46410i	−0.309426	−	0.178647i
$377$	−9.77176	+	36.4687i	−0.503271	+	1.87823i
$378$		0			0
$379$	−28.9199			−1.48552			−0.742759	−	0.669559i	$-0.766483\pi$
$379$	−28.9199			−1.48552			−0.742759	+	0.669559i	$0.766483\pi$
$380$		0			0
$381$	−34.0454			−1.74420
$382$	15.6938	+	4.20515i	0.802966	+	0.215154i
$383$	−2.53590	+	9.46410i	−0.129578	+	0.483593i	−0.999961	−	0.00878215i	$-0.997205\pi$
$383$	−2.53590	+	9.46410i	−0.129578	+	0.483593i	0.870383	+	0.492375i	$0.163871\pi$
$384$	2.12132	+	1.22474i	0.108253	+	0.0625000i
$385$		0			0
$386$	−6.67423	+	11.5601i	−0.339710	+	0.588394i
$387$	22.3485	+	22.3485i	1.13604	+	1.13604i
$388$	−10.2173	−	10.2173i	−0.518706	−	0.518706i
$389$	−2.51059	−	1.44949i	−0.127292	−	0.0734920i	0.435002	−	0.900430i	$-0.356748\pi$
$389$	−2.51059	−	1.44949i	−0.127292	−	0.0734920i	−0.562294	+	0.826937i	$0.690081\pi$
$390$		0			0
$391$	−14.6969			−0.743256
$392$	−4.09978	+	4.09978i	−0.207070	+	0.207070i
$393$	17.1476	−	4.59470i	0.864984	−	0.231772i
$394$	3.76588	+	6.52270i	0.189723	+	0.328609i
$395$		0			0
$396$	2.17423	+	3.76588i	0.109259	+	0.189243i
$397$	−2.11389	+	7.88915i	−0.106093	+	0.395945i	−0.998467	−	0.0553522i	$-0.982372\pi$
$397$	−2.11389	+	7.88915i	−0.106093	+	0.395945i	0.892374	+	0.451297i	$0.149039\pi$
$398$	6.92820	+	6.92820i	0.347279	+	0.347279i
$399$	−11.2102	−	3.37117i	−0.561210	−	0.168770i
$400$		0			0
$401$	−15.0000	+	8.66025i	−0.749064	+	0.432472i	−0.825356	−	0.564613i	$-0.809025\pi$
$401$	−15.0000	+	8.66025i	−0.749064	+	0.432472i	0.0762914	+	0.997086i	$0.475692\pi$
$402$	34.1879	+	9.16061i	1.70514	+	0.456890i
$403$	0.987148	+	3.68409i	0.0491733	+	0.183517i
$404$	10.9959	−	6.34847i	0.547065	−	0.315848i
$405$		0			0
$406$	8.44949			0.419341
$407$	−5.58542	+	5.58542i	−0.276859	+	0.276859i
$408$	1.79315	+	6.69213i	0.0887742	+	0.331310i
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	−0.991825	−	0.127609i	$-0.959270\pi$
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	0.606425	+	0.795141i	$0.292603\pi$
$410$		0			0
$411$			6.92820i			0.341743i
$412$	−0.491492	−	1.83427i	−0.0242141	−	0.0903682i
$413$	0.982984	−	3.66855i	0.0483695	−	0.180517i
$414$	−7.79423	+	13.5000i	−0.383065	+	0.663489i
$415$		0			0
$416$	−2.44949	−	4.24264i	−0.120096	−	0.208013i
$417$	−29.2699	+	29.2699i	−1.43335	+	1.43335i
$418$	2.99175	+	5.56496i	0.146331	+	0.272191i
$419$		−	8.34847i		−	0.407849i	−0.978987	−	0.203925i	$-0.934630\pi$
$419$		−	8.34847i		−	0.407849i	0.978987	−	0.203925i	$-0.0653698\pi$
$420$		0			0
$421$	8.32577	−	4.80688i	0.405773	−	0.234273i	−0.283199	−	0.959061i	$-0.591396\pi$
$421$	8.32577	−	4.80688i	0.405773	−	0.234273i	0.688972	+	0.724788i	$0.258062\pi$
$422$	−17.6513	+	4.72966i	−0.859254	+	0.230236i
$423$	−20.0764	−	5.37945i	−0.976148	−	0.261558i
$424$	3.76588	+	2.17423i	0.182888	+	0.105590i
$425$		0			0
$426$			8.48528i			0.411113i
$427$	8.47215	−	2.27010i	0.409996	−	0.109858i
$428$	11.8301	−	3.16987i	0.571831	−	0.153222i
$429$		−	17.3939i		−	0.839784i
$430$		0			0
$431$	20.0227	+	11.5601i	0.964460	+	0.556831i	0.897543	−	0.440927i	$-0.145350\pi$
$431$	20.0227	+	11.5601i	0.964460	+	0.556831i	0.0669170	+	0.997759i	$0.478684\pi$
$432$		0			0
$433$	18.6892	−	5.00775i	0.898145	−	0.240657i	0.219926	−	0.975517i	$-0.429419\pi$
$433$	18.6892	−	5.00775i	0.898145	−	0.240657i	0.678219	+	0.734859i	$0.262752\pi$
$434$	0.739215	−	0.426786i	0.0354834	−	0.0204864i
$435$		0			0
$436$		0			0
$437$	−11.9142	+	19.2627i	−0.569935	+	0.921460i
$438$	−15.7980	+	15.7980i	−0.754856	+	0.754856i
$439$	5.41045	+	9.37117i	0.258227	+	0.447262i	0.965767	−	0.259411i	$-0.0835285\pi$
$439$	5.41045	+	9.37117i	0.258227	+	0.447262i	−0.707540	+	0.706673i	$0.750195\pi$
$440$		0			0
$441$	−8.69694	+	15.0635i	−0.414140	+	0.717311i
$442$	3.58630	−	13.3843i	0.170583	−	0.636624i
$443$	0.806003	+	3.00804i	0.0382944	+	0.142916i	0.982426	−	0.186652i	$-0.0597635\pi$
$443$	0.806003	+	3.00804i	0.0382944	+	0.142916i	−0.944132	+	0.329568i	$0.893097\pi$
$444$			13.3485i			0.633490i
$445$		0			0
$446$	5.84847	−	10.1298i	0.276933	−	0.479662i
$447$	4.08881	+	15.2597i	0.193394	+	0.721757i
$448$	−0.775255	+	0.775255i	−0.0366274	+	0.0366274i
$449$	8.66025			0.408703			0.204351	−	0.978898i	$-0.434492\pi$
$449$	8.66025			0.408703			0.204351	+	0.978898i	$0.434492\pi$
$450$		0			0
$451$	2.17423	−	1.25529i	0.102381	−	0.0591095i
$452$	4.72279	+	17.6257i	0.222141	+	0.829042i
$453$	−20.0764	−	5.37945i	−0.943271	−	0.252749i
$454$	−13.4671	+	7.77526i	−0.632044	+	0.364911i
$455$		0			0
$456$	10.2247	+	3.07483i	0.478818	+	0.143992i
$457$	19.2474	+	19.2474i	0.900358	+	0.900358i	0.995467	−	0.0951092i	$-0.0303200\pi$
$457$	19.2474	+	19.2474i	0.900358	+	0.900358i	−0.0951092	+	0.995467i	$0.530320\pi$
$458$	4.02477	−	15.0206i	0.188065	−	0.701868i
$459$		0			0
$460$		0			0
$461$	8.10102	+	14.0314i	0.377302	+	0.653506i	0.990669	−	0.136292i	$-0.0435185\pi$
$461$	8.10102	+	14.0314i	0.377302	+	0.653506i	−0.613367	+	0.789798i	$0.710185\pi$
$462$	−3.76005	+	1.00750i	−0.174934	+	0.0468733i
$463$	11.2247	−	11.2247i	0.521658	−	0.521658i	−0.396414	−	0.918072i	$-0.629745\pi$
$463$	11.2247	−	11.2247i	0.521658	−	0.521658i	0.918072	+	0.396414i	$0.129745\pi$
$464$	−7.70674			−0.357777
$465$		0			0
$466$	3.00000	+	1.73205i	0.138972	+	0.0802357i
$467$	−23.4495	−	23.4495i	−1.08511	−	1.08511i	−0.996024	−	0.0890893i	$-0.971604\pi$
$467$	−23.4495	−	23.4495i	−1.08511	−	1.08511i	−0.0890893	−	0.996024i	$-0.528396\pi$
$468$	−10.3923	−	10.3923i	−0.480384	−	0.480384i
$469$	−7.92104	+	13.7196i	−0.365760	+	0.633514i
$470$		0			0
$471$	14.0227	+	8.09601i	0.646132	+	0.373045i
$472$	−0.896575	+	3.34607i	−0.0412682	+	0.154015i
$473$	14.7503	+	3.95233i	0.678219	+	0.181728i
$474$	12.2993			0.564927
$475$		0			0
$476$	−3.10102			−0.142135
$477$	12.6009	+	3.37640i	0.576955	+	0.154595i
$478$	3.57117	−	13.3278i	0.163342	−	0.609600i
$479$	−23.7238	−	13.6969i	−1.08397	−	0.625829i	−0.152004	−	0.988380i	$-0.548573\pi$
$479$	−23.7238	−	13.6969i	−1.08397	−	0.625829i	−0.931964	+	0.362551i	$0.881906\pi$
$480$		0			0
$481$	13.3485	−	23.1202i	0.608638	−	1.05419i
$482$	−19.3485	−	19.3485i	−0.881299	−	0.881299i
$483$	−9.86739	−	9.86739i	−0.448982	−	0.448982i
$484$	−7.70674	−	4.44949i	−0.350306	−	0.202250i
$485$		0			0
$486$	−22.0454			−1.00000
$487$	−16.4063	+	16.4063i	−0.743441	+	0.743441i	−0.973239	−	0.229797i	$-0.926194\pi$
$487$	−16.4063	+	16.4063i	−0.743441	+	0.743441i	0.229797	+	0.973239i	$0.426194\pi$
$488$	−7.72741	+	2.07055i	−0.349803	+	0.0937295i
$489$	16.1920	+	28.0454i	0.732229	+	1.26826i
$490$		0			0
$491$	−10.1742	−	17.6223i	−0.459157	−	0.795283i	0.539760	−	0.841819i	$-0.318515\pi$
$491$	−10.1742	−	17.6223i	−0.459157	−	0.795283i	−0.998917	+	0.0465362i	$0.985182\pi$
$492$	1.09808	−	4.09808i	0.0495051	−	0.184756i
$493$	−15.4135	−	15.4135i	−0.694188	−	0.694188i
$494$	−14.6349	−	15.5505i	−0.658457	−	0.699651i
$495$		0			0
$496$	−0.674235	+	0.389270i	−0.0302740	+	0.0174787i
$497$	−3.66855	−	0.982984i	−0.164557	−	0.0440929i
$498$	11.0713	+	41.3188i	0.496118	+	1.85154i
$499$	18.4008	−	10.6237i	0.823734	−	0.475583i	−0.0279682	−	0.999609i	$-0.508904\pi$
$499$	18.4008	−	10.6237i	0.823734	−	0.475583i	0.851703	+	0.524026i	$0.175570\pi$
$500$		0			0
$501$	−13.9546			−0.623445
$502$	−0.635674	+	0.635674i	−0.0283715	+	0.0283715i
$503$	−1.08977	−	4.06706i	−0.0485903	−	0.181341i	0.937366	−	0.348347i	$-0.113257\pi$
$503$	−1.08977	−	4.06706i	−0.0485903	−	0.181341i	−0.985956	+	0.167006i	$0.946590\pi$
$504$	−1.64456	+	2.84847i	−0.0732547	+	0.126881i
$505$		0			0
$506$			7.53177i			0.334828i
$507$	6.97372	+	26.0263i	0.309714	+	1.15587i
$508$	−3.59732	+	13.4254i	−0.159605	+	0.595655i
$509$	10.7816	−	18.6742i	0.477885	−	0.827721i	−0.521794	−	0.853072i	$-0.674737\pi$
$509$	10.7816	−	18.6742i	0.477885	−	0.827721i	0.999679	+	0.0253508i	$0.00807027\pi$
$510$		0			0
$511$	−5.00000	−	8.66025i	−0.221187	−	0.383107i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	9.55051i		−	0.421255i
$515$		0			0
$516$	22.3485	−	12.9029i	0.983836	−	0.568018i
$517$	−9.70017	+	2.59915i	−0.426613	+	0.114311i
$518$	−5.77111	−	1.54636i	−0.253568	−	0.0679433i
$519$	1.16781	+	0.674235i	0.0512611	+	0.0295956i
$520$		0			0
$521$		−	35.8481i		−	1.57054i	−0.619156	−	0.785268i	$-0.712525\pi$
$521$		−	35.8481i		−	1.57054i	0.619156	−	0.785268i	$-0.287475\pi$
$522$	−22.3324	+	5.98396i	−0.977464	+	0.261911i
$523$	−0.824487	+	0.220921i	−0.0360523	+	0.00966019i	−0.276800	−	0.960928i	$-0.589274\pi$
$523$	−0.824487	+	0.220921i	−0.0360523	+	0.00966019i	0.240748	+	0.970588i	$0.422607\pi$
$524$		−	7.24745i		−	0.316606i
$525$		0			0
$526$	−20.0505	−	11.5762i	−0.874244	−	0.504745i
$527$	−2.12701	−	0.569930i	−0.0926539	−	0.0248265i
$528$	3.42953	−	0.918940i	0.149251	−	0.0399917i
$529$	−3.46410	+	2.00000i	−0.150613	+	0.0869565i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	−2.51387	+	4.06438i	−0.108990	+	0.176213i
$533$	−6.00000	+	6.00000i	−0.259889	+	0.259889i
$534$	16.7563	+	29.0227i	0.725115	+	1.25594i
$535$		0			0
$536$	7.22474	−	12.5136i	0.312061	−	0.540506i
$537$	−1.59165	+	5.94012i	−0.0686848	+	0.256335i
$538$	1.79315	+	6.69213i	0.0773082	+	0.288518i
$539$			8.40408i			0.361989i
$540$		0			0
$541$	7.22474	−	12.5136i	0.310616	−	0.538003i	−0.667880	−	0.744269i	$-0.732798\pi$
$541$	7.22474	−	12.5136i	0.310616	−	0.538003i	0.978496	+	0.206266i	$0.0661313\pi$
$542$	0.854895	+	3.19051i	0.0367209	+	0.137044i
$543$	−37.3485	+	37.3485i	−1.60278	+	1.60278i
$544$	2.82843			0.121268
$545$		0			0
$546$	11.3939	−	6.57826i	0.487613	−	0.281523i
$547$	−4.65874	−	17.3867i	−0.199193	−	0.743400i	−0.991141	−	0.132811i	$-0.957600\pi$
$547$	−4.65874	−	17.3867i	−0.199193	−	0.743400i	0.791948	−	0.610589i	$-0.209067\pi$
$548$	2.73205	+	0.732051i	0.116707	+	0.0312717i
$549$	−20.7846	+	12.0000i	−0.887066	+	0.512148i
$550$		0			0
$551$	−32.6969	+	7.70674i	−1.39294	+	0.328318i
$552$	9.00000	+	9.00000i	0.383065	+	0.383065i
$553$	−1.42483	+	5.31752i	−0.0605897	+	0.226124i
$554$	9.75663	+	16.8990i	0.414520	+	0.717969i
$555$		0			0
$556$	8.44949	+	14.6349i	0.358338	+	0.620660i
$557$	40.3978	−	10.8245i	1.71171	−	0.458651i	0.735866	−	0.677127i	$-0.236775\pi$
$557$	40.3978	−	10.8245i	1.71171	−	0.458651i	0.975842	+	0.218477i	$0.0701087\pi$
$558$	−1.65153	+	1.65153i	−0.0699149	+	0.0699149i
$559$	−51.6116			−2.18294
$560$		0			0
$561$	8.69694	+	5.02118i	0.367185	+	0.211994i
$562$	8.57321	+	8.57321i	0.361639	+	0.361639i
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	0.967623	−	0.252399i	$-0.0812196\pi$
$563$	16.9706	+	16.9706i	0.715224	+	0.715224i	−0.252399	+	0.967623i	$0.581220\pi$
$564$	−8.48528	+	14.6969i	−0.357295	+	0.618853i
$565$		0			0
$566$	−0.550510	−	0.317837i	−0.0231397	−	0.0133597i
$567$	2.55387	−	9.53116i	0.107252	−	0.400271i
$568$	3.34607	+	0.896575i	0.140398	+	0.0376195i
$569$	15.2385			0.638832			0.319416	−	0.947615i	$-0.396513\pi$
$569$	15.2385			0.638832			0.319416	+	0.947615i	$0.396513\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	−6.85906	−	1.83788i	−0.286792	−	0.0768456i
$573$	10.3005	−	38.4419i	0.430308	−	1.60593i
$574$	1.64456	+	0.949490i	0.0686428	+	0.0396309i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−5.24745	−	5.24745i	−0.218454	−	0.218454i	0.589393	−	0.807847i	$-0.299367\pi$
$577$	−5.24745	−	5.24745i	−0.218454	−	0.218454i	−0.807847	+	0.589393i	$0.799367\pi$
$578$	−6.36396	−	6.36396i	−0.264706	−	0.264706i
$579$	28.3164	+	16.3485i	1.17679	+	0.679419i
$580$		0			0
$581$	−19.1464			−0.794328
$582$	−25.0273	+	25.0273i	−1.03741	+	1.03741i
$583$	6.08829	−	1.63135i	0.252151	−	0.0675637i
$584$	4.56048	+	7.89898i	0.188714	+	0.326862i
$585$		0			0
$586$	13.6237	+	23.5970i	0.562791	+	0.974782i
$587$	3.58630	−	13.3843i	0.148023	−	0.552428i	−0.851580	−	0.524225i	$-0.824355\pi$
$587$	3.58630	−	13.3843i	0.148023	−	0.552428i	0.999602	−	0.0282024i	$-0.00897830\pi$
$588$	10.0424	+	10.0424i	0.414140	+	0.414140i
$589$	−2.47127	+	2.32577i	−0.101827	+	0.0958315i
$590$		0			0
$591$	15.9773	−	9.22450i	0.657218	−	0.379445i
$592$	5.26380	+	1.41043i	0.216341	+	0.0579684i
$593$	10.6147	+	39.6147i	0.435895	+	1.62678i	0.738915	+	0.673798i	$0.235338\pi$
$593$	10.6147	+	39.6147i	0.435895	+	1.62678i	−0.303020	+	0.952984i	$0.597995\pi$
$594$		0			0
$595$		0			0
$596$	6.44949			0.264181
$597$	16.9706	−	16.9706i	0.694559	−	0.694559i
$598$	−6.58846	−	24.5885i	−0.269422	−	1.00550i
$599$	14.6349	−	25.3485i	0.597968	−	1.03571i	−0.395153	−	0.918615i	$-0.629308\pi$
$599$	14.6349	−	25.3485i	0.597968	−	1.03571i	0.993121	−	0.117095i	$-0.0373582\pi$
$600$		0			0
$601$		−	0.174973i		−	0.00713728i	−0.999994	−	0.00356864i	$-0.998864\pi$
$601$		−	0.174973i		−	0.00713728i	0.999994	−	0.00356864i	$-0.00113594\pi$
$602$	2.98949	+	11.1569i	0.121843	+	0.454723i
$603$	11.2194	−	41.8714i	0.456890	−	1.70514i
$604$	−4.24264	+	7.34847i	−0.172631	+	0.299005i
$605$		0			0
$606$	−15.5505	−	26.9343i	−0.631696	−	1.09413i
$607$	1.34278	−	1.34278i	0.0545018	−	0.0545018i	−0.679331	−	0.733832i	$-0.737730\pi$
$607$	1.34278	−	1.34278i	0.0545018	−	0.0545018i	0.733832	+	0.679331i	$0.237730\pi$
$608$	2.29289	−	3.70711i	0.0929891	−	0.150343i
$609$		−	20.6969i		−	0.838682i
$610$		0			0
$611$	29.3939	−	16.9706i	1.18915	−	0.686555i
$612$	8.19615	−	2.19615i	0.331310	−	0.0887742i
$613$	−43.1918	−	11.5732i	−1.74450	−	0.467438i	−0.761063	−	0.648678i	$-0.775322\pi$
$613$	−43.1918	−	11.5732i	−1.74450	−	0.467438i	−0.983439	+	0.181240i	$0.941989\pi$
$614$	−11.5601	−	6.67423i	−0.466528	−	0.269350i
$615$		0			0
$616$			1.58919i			0.0640301i
$617$	31.4806	−	8.43520i	1.26736	−	0.339589i	0.438342	−	0.898808i	$-0.355566\pi$
$617$	31.4806	−	8.43520i	1.26736	−	0.339589i	0.829020	+	0.559220i	$0.188899\pi$
$618$	−4.49303	+	1.20390i	−0.180736	+	0.0484282i
$619$		−	19.0454i		−	0.765500i	−0.923852	−	0.382750i	$-0.874977\pi$
$619$		−	19.0454i		−	0.765500i	0.923852	−	0.382750i	$-0.125023\pi$
$620$		0			0
$621$		0			0
$622$	−24.9189	−	6.67700i	−0.999157	−	0.267723i
$623$	−14.4889	+	3.88229i	−0.580485	+	0.155540i
$624$	−10.3923	+	6.00000i	−0.416025	+	0.240192i
$625$		0			0
$626$			29.7627i			1.18956i
$627$	13.6313	−	7.32826i	0.544383	−	0.292663i
$628$	4.67423	−	4.67423i	0.186522	−	0.186522i
$629$	7.70674	+	13.3485i	0.307288	+	0.532238i
$630$		0			0
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	−0.885244	−	0.465128i	$-0.846008\pi$
$631$	−1.00000	+	1.73205i	−0.0398094	+	0.0689519i	0.845434	+	0.534080i	$0.179342\pi$
$632$	1.29958	−	4.85009i	0.0516944	−	0.192926i
$633$	11.5853	+	43.2368i	0.460473	+	1.71851i
$634$			15.2474i			0.605554i
$635$		0			0
$636$	5.32577	−	9.22450i	0.211180	−	0.365775i
$637$	−7.35152	−	27.4362i	−0.291278	−	1.08706i
$638$	−7.89898	+	7.89898i	−0.312724	+	0.312724i
$639$	10.3923			0.411113
$640$		0			0
$641$	−22.3485	+	12.9029i	−0.882711	+	0.509634i	−0.871551	−	0.490304i	$-0.836886\pi$
$641$	−22.3485	+	12.9029i	−0.882711	+	0.509634i	−0.0111600	+	0.999938i	$0.503552\pi$
$642$	−7.76457	−	28.9778i	−0.306443	−	1.14366i
$643$	29.5006	+	7.90465i	1.16339	+	0.311729i	0.788319	−	0.615267i	$-0.210952\pi$
$643$	29.5006	+	7.90465i	1.16339	+	0.311729i	0.375070	+	0.926996i	$0.377619\pi$
$644$	−4.93369	+	2.84847i	−0.194415	+	0.112245i
$645$		0			0
$646$	12.0000	−	2.82843i	0.472134	−	0.111283i
$647$	10.3258	+	10.3258i	0.405948	+	0.405948i	0.880323	−	0.474375i	$-0.157326\pi$
$647$	10.3258	+	10.3258i	0.405948	+	0.405948i	−0.474375	+	0.880323i	$0.657326\pi$
$648$	−2.32937	+	8.69333i	−0.0915064	+	0.341506i
$649$	2.51059	+	4.34847i	0.0985493	+	0.170692i
$650$		0			0
$651$	−1.04541	−	1.81070i	−0.0409728	−	0.0709669i
$652$	12.7702	−	3.42178i	0.500121	−	0.134007i
$653$	10.0227	−	10.0227i	0.392219	−	0.392219i	−0.483259	−	0.875478i	$-0.660547\pi$
$653$	10.0227	−	10.0227i	0.392219	−	0.392219i	0.875478	+	0.483259i	$0.160547\pi$
$654$		0			0
$655$		0			0
$656$	−1.50000	−	0.866025i	−0.0585652	−	0.0338126i
$657$	19.3485	+	19.3485i	0.754856	+	0.754856i
$658$	−5.37113	−	5.37113i	−0.209388	−	0.209388i
$659$	−1.43027	+	2.47730i	−0.0557153	+	0.0965018i	−0.892538	−	0.450972i	$-0.851077\pi$
$659$	−1.43027	+	2.47730i	−0.0557153	+	0.0965018i	0.836823	+	0.547474i	$0.184411\pi$
$660$		0			0
$661$	−33.0681	−	19.0919i	−1.28620	−	0.742588i	−0.308226	−	0.951313i	$-0.599735\pi$
$661$	−33.0681	−	19.0919i	−1.28620	−	0.742588i	−0.977974	+	0.208725i	$0.933069\pi$
$662$	−1.05279	+	3.92907i	−0.0409178	+	0.152707i
$663$	−32.7846	−	8.78461i	−1.27325	−	0.341166i
$664$	17.4634			0.677710
$665$		0			0
$666$	16.3485			0.633490
$667$	−38.6809	−	10.3645i	−1.49773	−	0.401316i
$668$	−1.47448	+	5.50282i	−0.0570492	+	0.212910i
$669$	−24.8130	−	14.3258i	−0.959324	−	0.553866i
$670$		0			0
$671$	−5.79796	+	10.0424i	−0.223828	+	0.387681i
$672$	1.89898	+	1.89898i	0.0732547	+	0.0732547i
$673$	3.11416	+	3.11416i	0.120042	+	0.120042i	0.764576	−	0.644534i	$-0.222949\pi$
$673$	3.11416	+	3.11416i	0.120042	+	0.120042i	−0.644534	+	0.764576i	$0.722949\pi$
$674$	−15.5885	−	9.00000i	−0.600445	−	0.346667i
$675$		0			0
$676$	11.0000			0.423077
$677$	9.22450	−	9.22450i	0.354526	−	0.354526i	−0.507264	−	0.861791i	$-0.669343\pi$
$677$	9.22450	−	9.22450i	0.354526	−	0.354526i	0.861791	+	0.507264i	$0.169343\pi$
$678$	43.1739	−	11.5684i	1.65808	−	0.444282i
$679$	−7.92104	−	13.7196i	−0.303982	−	0.526512i
$680$		0			0
$681$	19.0454	+	32.9876i	0.729822	+	1.26409i
$682$	−0.292073	+	1.09003i	−0.0111841	+	0.0417395i
$683$	−25.8058	−	25.8058i	−0.987431	−	0.987431i	0.0124909	−	0.999922i	$-0.496024\pi$
$683$	−25.8058	−	25.8058i	−0.987431	−	0.987431i	−0.999922	+	0.0124909i	$0.996024\pi$
$684$	3.76588	−	12.5227i	0.143992	−	0.478818i
$685$		0			0
$686$	−12.1515	+	7.01569i	−0.463948	+	0.267860i
$687$	−36.7929	−	9.85863i	−1.40374	−	0.376130i
$688$	−2.72670	−	10.1762i	−0.103955	−	0.387964i
$689$	−18.4490	+	10.6515i	−0.702851	+	0.405791i
$690$		0			0
$691$	6.55051			0.249193			0.124597	−	0.992207i	$-0.460236\pi$
$691$	6.55051			0.249193			0.124597	+	0.992207i	$0.460236\pi$
$692$	0.389270	−	0.389270i	0.0147978	−	0.0147978i
$693$	1.23393	+	4.60511i	0.0468733	+	0.174934i
$694$	4.70334	−	8.14643i	0.178536	−	0.309234i
$695$		0			0
$696$			18.8776i			0.715553i
$697$	−1.26795	−	4.73205i	−0.0480270	−	0.179239i
$698$	4.94371	−	18.4502i	0.187122	−	0.698349i
$699$	4.24264	−	7.34847i	0.160471	−	0.277945i
$700$		0			0
$701$	−4.67423	−	8.09601i	−0.176543	−	0.305782i	0.764151	−	0.645038i	$-0.223158\pi$
$701$	−4.67423	−	8.09601i	−0.176543	−	0.305782i	−0.940694	+	0.339255i	$0.889825\pi$
$702$		0			0
$703$	23.7429	+	0.720152i	0.895479	+	0.0271611i
$704$		−	1.44949i		−	0.0546297i
$705$		0			0
$706$	−2.02270	+	1.16781i	−0.0761255	+	0.0439511i
$707$	13.4463	−	3.60292i	0.505700	−	0.135502i
$708$	8.19615	+	2.19615i	0.308030	+	0.0825365i
$709$	−23.1202	−	13.3485i	−0.868298	−	0.501312i	−0.00151596	−	0.999999i	$-0.500483\pi$
$709$	−23.1202	−	13.3485i	−0.868298	−	0.501312i	−0.866782	+	0.498687i	$0.833816\pi$
$710$		0			0
$711$		−	15.0635i		−	0.564927i
$712$	13.2153	−	3.54102i	0.495262	−	0.132705i
$713$	−3.90756	+	1.04703i	−0.146339	+	0.0392115i
$714$			7.59592i			0.284270i
$715$		0			0
$716$	2.17423	+	1.25529i	0.0812550	+	0.0469126i
$717$	−32.6463	−	8.74756i	−1.21920	−	0.326683i
$718$	−22.9871	+	6.15937i	−0.857870	+	0.229865i
$719$	−22.7310	+	13.1237i	−0.847722	+	0.489432i	−0.859881	−	0.510494i	$-0.829463\pi$
$719$	−22.7310	+	13.1237i	−0.847722	+	0.489432i	0.0121598	+	0.999926i	$0.496129\pi$
$720$		0			0
$721$		−	2.08200i		−	0.0775376i
$722$	6.02082	−	18.0208i	0.224072	−	0.670665i
$723$	−47.3939	+	47.3939i	−1.76260	+	1.76260i
$724$	10.7816	+	18.6742i	0.400694	+	0.694022i
$725$		0			0
$726$	−10.8990	+	18.8776i	−0.404499	+	0.700613i
$727$	−5.45340	+	20.3524i	−0.202256	+	0.754828i	0.788013	+	0.615659i	$0.211110\pi$
$727$	−5.45340	+	20.3524i	−0.202256	+	0.754828i	−0.990269	+	0.139170i	$0.955557\pi$
$728$	−1.39015	−	5.18811i	−0.0515224	−	0.192284i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	14.8990	−	25.8058i	0.551059	−	0.954462i
$732$	5.07180	+	18.9282i	0.187459	+	0.699607i
$733$	−12.0227	+	12.0227i	−0.444069	+	0.444069i	−0.893377	−	0.449308i	$-0.851671\pi$
$733$	−12.0227	+	12.0227i	−0.444069	+	0.444069i	0.449308	+	0.893377i	$0.351671\pi$
$734$	−15.1278			−0.558376
$735$		0			0
$736$	4.50000	−	2.59808i	0.165872	−	0.0957664i
$737$	−5.42081	−	20.2307i	−0.199678	−	0.745208i
$738$	−5.01910	−	1.34486i	−0.184756	−	0.0495051i
$739$	38.4069	−	22.1742i	1.41282	−	0.815692i	0.417167	−	0.908830i	$-0.363023\pi$
$739$	38.4069	−	22.1742i	1.41282	−	0.815692i	0.995653	+	0.0931373i	$0.0296895\pi$
$740$		0			0
$741$	−38.0908	+	35.8481i	−1.39930	+	1.31691i
$742$	3.37117	+	3.37117i	0.123760	+	0.123760i
$743$	12.7579	−	47.6132i	0.468043	−	1.74676i	−0.178555	−	0.983930i	$-0.557142\pi$
$743$	12.7579	−	47.6132i	0.468043	−	1.74676i	0.646598	−	0.762831i	$-0.276191\pi$
$744$	0.953512	+	1.65153i	0.0349574	+	0.0605481i
$745$		0			0
$746$	−17.9722	−	31.1288i	−0.658009	−	1.13970i
$747$	50.6050	−	13.5596i	1.85154	−	0.496118i
$748$	2.89898	−	2.89898i	0.105997	−	0.105997i
$749$	13.4278			0.490642
$750$		0			0
$751$	−38.0227	−	21.9524i	−1.38747	−	0.801055i	−0.394439	−	0.918922i	$-0.629061\pi$
$751$	−38.0227	−	21.9524i	−1.38747	−	0.801055i	−0.993029	+	0.117867i	$0.962394\pi$
$752$	4.89898	+	4.89898i	0.178647	+	0.178647i
$753$	1.55708	+	1.55708i	0.0567431	+	0.0567431i
$754$	18.8776	−	32.6969i	0.687481	−	1.19075i
$755$		0			0
$756$		0			0
$757$	−0.172835	+	0.645028i	−0.00628179	+	0.0234440i	−0.968996	−	0.247078i	$-0.920530\pi$
$757$	−0.172835	+	0.645028i	−0.00628179	+	0.0234440i	0.962714	+	0.270522i	$0.0871963\pi$
$758$	27.9345	+	7.48503i	1.01463	+	0.271869i
$759$	18.4490			0.669656
$760$		0			0
$761$	−8.79796			−0.318926			−0.159463	−	0.987204i	$-0.550976\pi$
$761$	−8.79796			−0.318926			−0.159463	+	0.987204i	$0.550976\pi$
$762$	32.8853	+	8.81160i	1.19131	+	0.319211i
$763$		0			0
$764$	−14.0707	−	8.12372i	−0.509060	−	0.293906i
$765$		0			0
$766$	4.89898	−	8.48528i	0.177007	−	0.306586i
$767$	−12.0000	−	12.0000i	−0.433295	−	0.433295i
$768$	−1.73205	−	1.73205i	−0.0625000	−	0.0625000i
$769$	37.7552	+	21.7980i	1.36149	+	0.786055i	0.989822	−	0.142313i	$-0.0454538\pi$
$769$	37.7552	+	21.7980i	1.36149	+	0.786055i	0.371665	+	0.928367i	$0.378787\pi$
$770$		0			0
$771$	−23.3939			−0.842510
$772$	9.43879	−	9.43879i	0.339710	−	0.339710i
$773$	−7.39081	+	1.98036i	−0.265829	+	0.0712287i	−0.389272	−	0.921123i	$-0.627273\pi$
$773$	−7.39081	+	1.98036i	−0.265829	+	0.0712287i	0.123443	+	0.992352i	$0.460607\pi$
$774$	−15.8028	−	27.3712i	−0.568018	−	0.983836i
$775$		0			0
$776$	7.22474	+	12.5136i	0.259353	+	0.449213i
$777$	−3.78780	+	14.1363i	−0.135887	+	0.507136i
$778$	2.04989	+	2.04989i	0.0734920	+	0.0734920i
$779$	−7.22999	−	2.17423i	−0.259041	−	0.0779000i
$780$		0			0
$781$	4.34847	−	2.51059i	0.155600	−	0.0898360i
$782$	14.1962	+	3.80385i	0.507653	+	0.136025i
$783$		0			0
$784$	5.02118	−	2.89898i	0.179328	−	0.103535i
$785$		0			0
$786$	−17.7526			−0.633213
$787$	−16.3670	+	16.3670i	−0.583420	+	0.583420i	−0.935842	−	0.352421i	$-0.885358\pi$
$787$	−16.3670	+	16.3670i	−0.583420	+	0.583420i	0.352421	+	0.935842i	$0.385358\pi$
$788$	−1.94937	−	7.27513i	−0.0694433	−	0.259166i
$789$	−28.3557	+	49.1135i	−1.00949	+	1.74849i
$790$		0			0
$791$			20.0061i			0.711334i
$792$	−1.12547	−	4.20030i	−0.0399917	−	0.149251i
$793$	10.1436	−	37.8564i	0.360210	−	1.34432i
$794$	4.08372	−	7.07321i	0.144926	−	0.251019i
$795$		0			0
$796$	−4.89898	−	8.48528i	−0.173640	−	0.300753i
$797$	−9.65309	+	9.65309i	−0.341930	+	0.341930i	−0.857093	−	0.515163i	$-0.827732\pi$
$797$	−9.65309	+	9.65309i	−0.341930	+	0.341930i	0.515163	+	0.857093i	$0.327732\pi$
$798$	9.95567	+	6.15771i	0.352427	+	0.217981i
$799$			19.5959i			0.693254i
$800$		0			0
$801$	35.5454	−	20.5222i	1.25594	−	0.725115i
$802$	16.7303	−	4.48288i	0.590768	−	0.158296i
$803$	12.7702	+	3.42178i	0.450652	+	0.120752i
$804$	−30.6520	−	17.6969i	−1.08101	−	0.624123i
$805$		0			0
$806$		−	3.81405i		−	0.134344i
$807$	16.3923	−	4.39230i	0.577036	−	0.154616i
$808$	−12.2643	+	3.28621i	−0.431457	+	0.115608i
$809$		−	18.2020i		−	0.639950i	−0.947426	−	0.319975i	$-0.896326\pi$
$809$		−	18.2020i		−	0.639950i	0.947426	−	0.319975i	$-0.103674\pi$
$810$		0			0
$811$	6.52270	+	3.76588i	0.229043	+	0.132238i	0.610131	−	0.792301i	$-0.291117\pi$
$811$	6.52270	+	3.76588i	0.229043	+	0.132238i	−0.381087	+	0.924539i	$0.624450\pi$
$812$	−8.16158	−	2.18689i	−0.286415	−	0.0767448i
$813$	7.81513	−	2.09406i	0.274088	−	0.0734418i
$814$	6.84072	−	3.94949i	0.239767	−	0.138430i
$815$		0			0
$816$		−	6.92820i		−	0.242536i
$817$	−21.7446	−	40.4472i	−0.760748	−	1.41507i
$818$	11.0227	−	11.0227i	0.385400	−	0.385400i
$819$	−8.05669	−	13.9546i	−0.281523	−	0.487613i
$820$		0			0
$821$	1.24745	−	2.16064i	0.0435363	−	0.0754070i	−0.843436	−	0.537229i	$-0.819471\pi$
$821$	1.24745	−	2.16064i	0.0435363	−	0.0754070i	0.886972	+	0.461822i	$0.152804\pi$
$822$	1.79315	−	6.69213i	0.0625433	−	0.233415i
$823$	−3.21197	−	11.9872i	−0.111962	−	0.417848i	0.887080	−	0.461616i	$-0.152730\pi$
$823$	−3.21197	−	11.9872i	−0.111962	−	0.417848i	−0.999042	+	0.0437682i	$0.986064\pi$
$824$			1.89898i			0.0661541i
$825$		0			0
$826$	−1.89898	+	3.28913i	−0.0660739	+	0.114443i
$827$	−9.22465	−	34.4269i	−0.320773	−	1.19714i	−0.918494	−	0.395436i	$-0.870594\pi$
$827$	−9.22465	−	34.4269i	−0.320773	−	1.19714i	0.597721	−	0.801704i	$-0.296073\pi$
$828$	11.0227	−	11.0227i	0.383065	−	0.383065i
$829$	41.5692			1.44376			0.721879	−	0.692019i	$-0.243279\pi$
$829$	41.5692			1.44376			0.721879	+	0.692019i	$0.243279\pi$
$830$		0			0
$831$	41.3939	−	23.8988i	1.43594	−	0.829039i
$832$	1.26795	+	4.73205i	0.0439582	+	0.164054i
$833$	15.8403	+	4.24440i	0.548835	+	0.147060i
$834$	35.8481	−	20.6969i	1.24132	−	0.716676i
$835$		0			0
$836$	−1.44949	−	6.14966i	−0.0501317	−	0.212691i
$837$		0			0
$838$	−2.16074	+	8.06400i	−0.0746416	+	0.278566i
$839$	−7.49245	−	12.9773i	−0.258668	−	0.448026i	0.707217	−	0.706996i	$-0.249950\pi$
$839$	−7.49245	−	12.9773i	−0.258668	−	0.448026i	−0.965885	+	0.258970i	$0.916617\pi$
$840$		0			0
$841$	−15.1969	−	26.3219i	−0.524032	−	0.907651i
$842$	−9.28618	+	2.48823i	−0.320023	+	0.0857499i
$843$	21.0000	−	21.0000i	0.723278	−	0.723278i
$844$	18.2740			0.629018
$845$		0			0
$846$	18.0000	+	10.3923i	0.618853	+	0.357295i
$847$	−6.89898	−	6.89898i	−0.237052	−	0.237052i
$848$	−3.07483	−	3.07483i	−0.105590	−	0.105590i
$849$	−0.778539	+	1.34847i	−0.0267194	+	0.0462793i
$850$		0			0
$851$	24.5227	+	14.1582i	0.840627	+	0.485336i
$852$	2.19615	−	8.19615i	0.0752389	−	0.280796i
$853$	−29.2246	−	7.83070i	−1.00063	−	0.268118i	−0.278921	−	0.960314i	$-0.589977\pi$
$853$	−29.2246	−	7.83070i	−1.00063	−	0.268118i	−0.721710	+	0.692196i	$0.756643\pi$
$854$	−8.77101			−0.300138
$855$		0			0
$856$	−12.2474			−0.418609
$857$	37.3784	+	10.0155i	1.27682	+	0.342123i	0.832640	−	0.553814i	$-0.186828\pi$
$857$	37.3784	+	10.0155i	1.27682	+	0.342123i	0.444181	+	0.895937i	$0.353495\pi$
$858$	−4.50187	+	16.8012i	−0.153691	+	0.573583i
$859$	−8.35847	−	4.82577i	−0.285187	−	0.164653i	0.350582	−	0.936532i	$-0.385984\pi$
$859$	−8.35847	−	4.82577i	−0.285187	−	0.164653i	−0.635769	+	0.771879i	$0.719317\pi$
$860$		0			0
$861$	2.32577	−	4.02834i	0.0792619	−	0.137286i
$862$	−16.3485	−	16.3485i	−0.556831	−	0.556831i
$863$	21.7774	+	21.7774i	0.741313	+	0.741313i	0.972831	−	0.231518i	$-0.0743692\pi$
$863$	21.7774	+	21.7774i	0.741313	+	0.741313i	−0.231518	+	0.972831i	$0.574369\pi$
$864$		0			0
$865$		0			0
$866$	−19.3485			−0.657488
$867$	−15.5885	+	15.5885i	−0.529412	+	0.529412i
$868$	−0.824487	+	0.220921i	−0.0279849	+	0.00749854i
$869$	−3.63907	−	6.30306i	−0.123447	−	0.213817i
$870$		0			0
$871$	35.3939	+	61.3040i	1.19928	+	2.07721i
$872$		0			0
$873$	30.6520	+	30.6520i	1.03741	+	1.03741i
$874$	16.4938	−	15.5227i	0.557911	−	0.525063i
$875$		0			0
$876$	19.3485	−	11.1708i	0.653724	−	0.377428i
$877$	−17.3329	−	4.64435i	−0.585292	−	0.156829i	−0.0459914	−	0.998942i	$-0.514645\pi$
$877$	−17.3329	−	4.64435i	−0.585292	−	0.156829i	−0.539301	+	0.842113i	$0.681311\pi$
$878$	−2.80065	−	10.4522i	−0.0945175	−	0.352744i
$879$	57.8006	−	33.3712i	1.94956	−	1.12558i
$880$		0			0
$881$	45.2929			1.52596			0.762978	−	0.646425i	$-0.223737\pi$
$881$	45.2929			1.52596			0.762978	+	0.646425i	$0.223737\pi$
$882$	12.2993	−	12.2993i	0.414140	−	0.414140i
$883$	5.16133	+	19.2624i	0.173693	+	0.648230i	0.996771	+	0.0803014i	$0.0255883\pi$
$883$	5.16133	+	19.2624i	0.173693	+	0.648230i	−0.823078	+	0.567928i	$0.807745\pi$
$884$	−6.92820	+	12.0000i	−0.233021	+	0.403604i
$885$		0			0
$886$		−	3.11416i		−	0.104622i
$887$	1.42483	+	5.31752i	0.0478410	+	0.178545i	0.985712	−	0.168439i	$-0.0538726\pi$
$887$	1.42483	+	5.31752i	0.0478410	+	0.178545i	−0.937871	+	0.346984i	$0.887206\pi$
$888$	3.45484	−	12.8936i	0.115937	−	0.432682i
$889$	−7.61926	+	13.1969i	−0.255542	+	0.442611i
$890$		0			0
$891$	6.52270	+	11.2977i	0.218519	+	0.378486i
$892$	−8.27098	+	8.27098i	−0.276933	+	0.276933i
$893$	25.6836	+	15.8856i	0.859469	+	0.531592i
$894$		−	15.7980i		−	0.528363i
$895$		0			0
$896$	0.949490	−	0.548188i	0.0317202	−	0.0183137i
$897$	−60.2292	+	16.1384i	−2.01099	+	0.538844i
$898$	−8.36516	−	2.24144i	−0.279149	−	0.0747978i
$899$	−5.19615	−	3.00000i	−0.173301	−	0.100056i
$900$		0			0
$901$		−	12.2993i		−	0.409750i
$902$	−2.42504	+	0.649788i	−0.0807451	+	0.0216356i
$903$	27.3288	−	7.32273i	0.909446	−	0.243685i
$904$		−	18.2474i		−	0.606901i
$905$		0			0
$906$	18.0000	+	10.3923i	0.598010	+	0.345261i
$907$	18.1037	+	4.85088i	0.601124	+	0.161071i	0.546532	−	0.837438i	$-0.315948\pi$
$907$	18.1037	+	4.85088i	0.601124	+	0.161071i	0.0545918	+	0.998509i	$0.482614\pi$
$908$	15.0206	−	4.02477i	0.498477	−	0.133567i
$909$	−32.9876	+	19.0454i	−1.09413	+	0.631696i
$910$		0			0
$911$			39.6622i			1.31407i	0.753861	+	0.657034i	$0.228189\pi$
$911$			39.6622i			1.31407i	−0.753861	+	0.657034i	$0.771811\pi$
$912$	−9.08052	−	5.61642i	−0.300686	−	0.185978i
$913$	17.8990	−	17.8990i	0.592370	−	0.592370i
$914$	−13.6100	−	23.5732i	−0.450179	−	0.779733i
$915$		0			0
$916$	−7.77526	+	13.4671i	−0.256902	+	0.444967i
$917$	2.05656	−	7.67518i	0.0679135	−	0.253457i
$918$		0			0
$919$			34.0908i			1.12455i	0.826950	+	0.562276i	$0.190074\pi$
$919$			34.0908i			1.12455i	−0.826950	+	0.562276i	$0.809926\pi$
$920$		0			0
$921$	−16.3485	+	28.3164i	−0.538700	+	0.933056i
$922$	−4.19340	−	15.6500i	−0.138102	−	0.515404i
$923$	−12.0000	+	12.0000i	−0.394985	+	0.394985i
$924$	3.89270			0.128060
$925$		0			0
$926$	−13.7474	+	7.93709i	−0.451769	+	0.260829i
$927$	1.47448	+	5.50282i	0.0484282	+	0.180736i
$928$	7.44414	+	1.99465i	0.244366	+	0.0654776i
$929$	41.9103	−	24.1969i	1.37503	−	0.793876i	0.383477	−	0.923551i	$-0.374727\pi$
$929$	41.9103	−	24.1969i	1.37503	−	0.793876i	0.991557	+	0.129675i	$0.0413933\pi$
$930$		0			0
$931$	18.4041	−	17.3205i	0.603169	−	0.567657i
$932$	−2.44949	−	2.44949i	−0.0802357	−	0.0802357i
$933$	−16.3553	+	61.0386i	−0.535447	+	1.99831i
$934$	16.5813	+	28.7196i	0.542556	+	0.939735i
$935$		0			0
$936$	7.34847	+	12.7279i	0.240192	+	0.416025i
$937$	−49.7909	+	13.3414i	−1.62660	+	0.435846i	−0.952931	−	0.303188i	$-0.901949\pi$
$937$	−49.7909	+	13.3414i	−1.62660	+	0.435846i	−0.673668	+	0.739034i	$0.735282\pi$
$938$	11.2020	−	11.2020i	0.365760	−	0.365760i
$939$	72.9034			2.37911
$940$		0			0
$941$	8.62883	+	4.98186i	0.281292	+	0.162404i	0.634008	−	0.773326i	$-0.281409\pi$
$941$	8.62883	+	4.98186i	0.281292	+	0.162404i	−0.352716	+	0.935730i	$0.614742\pi$
$942$	−11.4495	−	11.4495i	−0.373045	−	0.373045i
$943$	−6.36396	−	6.36396i	−0.207239	−	0.207239i
$944$	1.73205	−	3.00000i	0.0563735	−	0.0976417i
$945$		0			0
$946$	−13.2247	−	7.63531i	−0.429974	−	0.248245i
$947$	−2.92820	+	10.9282i	−0.0951538	+	0.355119i	−0.997043	−	0.0768492i	$-0.975514\pi$
$947$	−2.92820	+	10.9282i	−0.0951538	+	0.355119i	0.901889	+	0.431968i	$0.142181\pi$
$948$	−11.8802	−	3.18330i	−0.385852	−	0.103389i
$949$	−44.6834			−1.45048
$950$		0			0
$951$	37.3485			1.21111
$952$	2.99536	+	0.802603i	0.0970800	+	0.0260125i
$953$	1.96597	−	7.33709i	0.0636840	−	0.237672i	−0.926746	−	0.375689i	$-0.877406\pi$
$953$	1.96597	−	7.33709i	0.0636840	−	0.237672i	0.990430	+	0.138017i	$0.0440728\pi$
$954$	−11.2977	−	6.52270i	−0.365775	−	0.211180i
$955$		0			0
$956$	−6.89898	+	11.9494i	−0.223129	+	0.386471i
$957$	19.3485	+	19.3485i	0.625447	+	0.625447i
$958$	19.3704	+	19.3704i	0.625829	+	0.625829i
$959$	2.68556	+	1.55051i	0.0867213	+	0.0500686i
$960$		0			0
$961$	30.3939			0.980448
$962$	−18.8776	+	18.8776i	−0.608638	+	0.608638i
$963$	−35.4904	+	9.50962i	−1.14366	+	0.306443i
$964$	13.6814	+	23.6969i	0.440649	+	0.763227i
$965$		0			0
$966$	6.97730	+	12.0850i	0.224491	+	0.388830i
$967$	0.732051	−	2.73205i	0.0235412	−	0.0878568i	−0.953156	−	0.302480i	$-0.902186\pi$
$967$	0.732051	−	2.73205i	0.0235412	−	0.0878568i	0.976697	+	0.214623i	$0.0688522\pi$
$968$	6.29253	+	6.29253i	0.202250	+	0.202250i
$969$	−6.92820	−	29.3939i	−0.222566	−	0.944267i
$970$		0			0
$971$	16.0454	−	9.26382i	0.514922	−	0.297290i	−0.219933	−	0.975515i	$-0.570584\pi$
$971$	16.0454	−	9.26382i	0.514922	−	0.297290i	0.734854	+	0.678225i	$0.237250\pi$
$972$	21.2942	+	5.70577i	0.683013	+	0.183013i
$973$	4.79531	+	17.8963i	0.153730	+	0.573730i
$974$	20.0936	−	11.6010i	0.643839	−	0.371721i
$975$		0			0
$976$	8.00000			0.256074
$977$	25.6308	−	25.6308i	0.820002	−	0.820002i	−0.166106	−	0.986108i	$-0.553119\pi$
$977$	25.6308	−	25.6308i	0.820002	−	0.820002i	0.986108	+	0.166106i	$0.0531192\pi$
$978$	−8.38161	−	31.2806i	−0.268014	−	1.00024i
$979$	9.91555	−	17.1742i	0.316902	−	0.548891i
$980$		0			0
$981$		0			0
$982$	5.26657	+	19.6551i	0.168063	+	0.627220i
$983$	−10.2220	+	38.1491i	−0.326032	+	1.21677i	0.587238	+	0.809414i	$0.300215\pi$
$983$	−10.2220	+	38.1491i	−0.326032	+	1.21677i	−0.913270	+	0.407354i	$0.866451\pi$
$984$	−2.12132	+	3.67423i	−0.0676252	+	0.117130i
$985$		0			0
$986$	10.8990	+	18.8776i	0.347094	+	0.601185i
$987$	−13.1565	+	13.1565i	−0.418777	+	0.418777i
$988$	10.1115	+	18.8084i	0.321690	+	0.598376i
$989$		−	54.7423i		−	1.74071i
$990$		0			0
$991$	−41.0227	+	23.6845i	−1.30313	+	0.752362i	−0.980940	−	0.194313i	$-0.937752\pi$
$991$	−41.0227	+	23.6845i	−1.30313	+	0.752362i	−0.322190	+	0.946675i	$0.604419\pi$
$992$	0.752011	−	0.201501i	0.0238764	−	0.00639765i
$993$	9.62421	+	2.57880i	0.305415	+	0.0818357i
$994$	3.28913	+	1.89898i	0.104325	+	0.0602320i
$995$		0			0
$996$		−	42.7764i		−	1.35542i
$997$	39.5078	−	10.5861i	1.25122	−	0.335264i	0.428414	−	0.903582i	$-0.359072\pi$
$997$	39.5078	−	10.5861i	1.25122	−	0.335264i	0.822809	+	0.568318i	$0.192406\pi$
$998$	−20.5235	+	5.49924i	−0.649659	+	0.174076i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.a.107.1		8
5.2	odd	4		190.2.m.a.183.2	yes	8
5.3	odd	4	inner	950.2.q.a.943.1		8
5.4	even	2		190.2.m.a.107.2	yes	8
19.8	odd	6	inner	950.2.q.a.407.1		8
95.8	even	12	inner	950.2.q.a.293.1		8
95.27	even	12		190.2.m.a.103.2	yes	8
95.84	odd	6		190.2.m.a.27.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.a.27.2	✓	8	95.84	odd	6
190.2.m.a.103.2	yes	8	95.27	even	12
190.2.m.a.107.2	yes	8	5.4	even	2
190.2.m.a.183.2	yes	8	5.2	odd	4
950.2.q.a.107.1		8	1.1	even	1	trivial
950.2.q.a.293.1		8	95.8	even	12	inner
950.2.q.a.407.1		8	19.8	odd	6	inner
950.2.q.a.943.1		8	5.3	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.22474 - 2.12132i) q^{6} +(0.775255 + 0.775255i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.22474 - 2.12132i) q^{6} +(0.775255 + 0.775255i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.59808 - 1.50000i) q^{9} -1.44949 q^{11} +(-1.73205 + 1.73205i) q^{12} +(4.73205 - 1.26795i) q^{13} +(-0.548188 - 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.732051 + 2.73205i) q^{17} +(2.12132 + 2.12132i) q^{18} +(2.98735 + 3.17423i) q^{19} +(-2.32577 + 1.34278i) q^{21} +(1.40010 + 0.375156i) q^{22} +(1.34486 + 5.01910i) q^{23} +(2.12132 - 1.22474i) q^{24} -4.89898 q^{26} +(0.283763 + 1.05902i) q^{28} +(-3.85337 + 6.67423i) q^{29} +0.778539i q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.918940 - 3.42953i) q^{33} +(1.41421 - 2.44949i) q^{34} +(-1.50000 - 2.59808i) q^{36} +(3.85337 - 3.85337i) q^{37} +(-2.06400 - 3.83926i) q^{38} +12.0000i q^{39} +(-1.50000 + 0.866025i) q^{41} +(2.59405 - 0.695075i) q^{42} +(-10.1762 - 2.72670i) q^{43} +(-1.25529 - 0.724745i) q^{44} -5.19615i q^{46} +(6.69213 - 1.79315i) q^{47} +(-2.36603 + 0.633975i) q^{48} -5.79796i q^{49} +(-6.00000 - 3.46410i) q^{51} +(4.73205 + 1.26795i) q^{52} +(-4.20030 + 1.12547i) q^{53} -1.09638i q^{56} +(-9.40422 + 5.05575i) q^{57} +(5.44949 - 5.44949i) q^{58} +(-1.73205 - 3.00000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(0.201501 - 0.752011i) q^{62} +(-0.851289 - 3.17705i) q^{63} +1.00000i q^{64} +(-1.77526 + 3.07483i) q^{66} +(3.73980 + 13.9571i) q^{67} +(-2.00000 + 2.00000i) q^{68} -12.7279 q^{69} +(-3.00000 + 1.73205i) q^{71} +(0.776457 + 2.89778i) q^{72} +(-8.81017 - 2.36068i) q^{73} +(-4.71940 + 2.72474i) q^{74} +(1.00000 + 4.24264i) q^{76} +(-1.12372 - 1.12372i) q^{77} +(3.10583 - 11.5911i) q^{78} +(2.51059 + 4.34847i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(1.67303 - 0.448288i) q^{82} +(-12.3485 + 12.3485i) q^{83} -2.68556 q^{84} +(9.12372 + 5.26758i) q^{86} +(-13.3485 - 13.3485i) q^{87} +(1.02494 + 1.02494i) q^{88} +(-6.84072 + 11.8485i) q^{89} +(4.65153 + 2.68556i) q^{91} +(-1.34486 + 5.01910i) q^{92} +(-1.84204 - 0.493574i) q^{93} -6.92820 q^{94} +2.44949 q^{96} +(-13.9571 - 3.73980i) q^{97} +(-1.50062 + 5.60040i) q^{98} +(3.76588 + 2.17423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 16 q^{7}+O(q^{10}) \) 8 * q - 12 * q^3 + 16 * q^7	\( 8 q - 12 q^{3} + 16 q^{7} + 8 q^{11} + 24 q^{13} + 4 q^{16} + 8 q^{17} - 48 q^{21} + 12 q^{22} - 8 q^{28} - 12 q^{33} - 12 q^{36} + 12 q^{38} - 12 q^{41} - 12 q^{42} - 20 q^{43} - 12 q^{48} - 48 q^{51} + 24 q^{52} - 36 q^{53} + 12 q^{57} + 24 q^{58} + 32 q^{61} - 12 q^{62} + 24 q^{63} - 24 q^{66} + 12 q^{67} - 16 q^{68} - 24 q^{71} - 16 q^{73} + 8 q^{76} + 40 q^{77} - 36 q^{81} - 40 q^{83} + 24 q^{86} - 48 q^{87} + 96 q^{91} + 24 q^{93} - 12 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 12 * q^3 + 16 * q^7 + 8 * q^11 + 24 * q^13 + 4 * q^16 + 8 * q^17 - 48 * q^21 + 12 * q^22 - 8 * q^28 - 12 * q^33 - 12 * q^36 + 12 * q^38 - 12 * q^41 - 12 * q^42 - 20 * q^43 - 12 * q^48 - 48 * q^51 + 24 * q^52 - 36 * q^53 + 12 * q^57 + 24 * q^58 + 32 * q^61 - 12 * q^62 + 24 * q^63 - 24 * q^66 + 12 * q^67 - 16 * q^68 - 24 * q^71 - 16 * q^73 + 8 * q^76 + 40 * q^77 - 36 * q^81 - 40 * q^83 + 24 * q^86 - 48 * q^87 + 96 * q^91 + 24 * q^93 - 12 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more