LMFDB - Embedded newform 950.2.q.a.407.1

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			407.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	950.407
Dual form			950.2.q.a.943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.22474 + 2.12132i) q^{6} +(0.775255 + 0.775255i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-2.36603 + 0.633975i) 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} +(1.26795 - 4.73205i) q^{13} +(0.548188 - 0.949490i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.73205 - 0.732051i) q^{17} +(-2.12132 - 2.12132i) q^{18} +(-2.98735 + 3.17423i) q^{19} +(-2.32577 - 1.34278i) q^{21} +(0.375156 + 1.40010i) q^{22} +(-5.01910 - 1.34486i) q^{23} +(-2.12132 - 1.22474i) q^{24} -4.89898 q^{26} +(-1.05902 - 0.283763i) q^{28} +(3.85337 + 6.67423i) q^{29} -0.778539i q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.42953 - 0.918940i) q^{33} +(-1.41421 - 2.44949i) q^{34} +(-1.50000 + 2.59808i) q^{36} +(-3.85337 + 3.85337i) q^{37} +(3.83926 + 2.06400i) q^{38} +12.0000i q^{39} +(-1.50000 - 0.866025i) q^{41} +(-0.695075 + 2.59405i) q^{42} +(2.72670 + 10.1762i) q^{43} +(1.25529 - 0.724745i) q^{44} +5.19615i q^{46} +(-1.79315 + 6.69213i) q^{47} +(-0.633975 + 2.36603i) q^{48} -5.79796i q^{49} +(-6.00000 + 3.46410i) q^{51} +(1.26795 + 4.73205i) q^{52} +(-1.12547 + 4.20030i) q^{53} +1.09638i q^{56} +(5.05575 - 9.40422i) q^{57} +(5.44949 - 5.44949i) q^{58} +(1.73205 - 3.00000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-0.752011 + 0.201501i) q^{62} +(3.17705 + 0.851289i) q^{63} +1.00000i q^{64} +(-1.77526 - 3.07483i) q^{66} +(13.9571 + 3.73980i) q^{67} +(-2.00000 + 2.00000i) q^{68} +12.7279 q^{69} +(-3.00000 - 1.73205i) q^{71} +(2.89778 + 0.776457i) q^{72} +(2.36068 + 8.81017i) q^{73} +(4.71940 + 2.72474i) q^{74} +(1.00000 - 4.24264i) q^{76} +(-1.12372 - 1.12372i) q^{77} +(11.5911 - 3.10583i) q^{78} +(-2.51059 + 4.34847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-0.448288 + 1.67303i) 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} +(5.01910 - 1.34486i) q^{92} +(0.493574 + 1.84204i) q^{93} +6.92820 q^{94} +2.44949 q^{96} +(-3.73980 - 13.9571i) q^{97} +(-5.60040 + 1.50062i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−2.36603	+	0.633975i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−2.36603	+	0.633975i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	−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
$13$	1.26795	−	4.73205i	0.351666	−	1.31243i	−0.532963	−	0.846139i	$-0.678921\pi$
$13$	1.26795	−	4.73205i	0.351666	−	1.31243i	0.884629	−	0.466296i	$-0.154412\pi$
$14$	0.548188	−	0.949490i	0.146509	−	0.253762i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.0881917	−	0.996104i	$-0.471891\pi$
$17$	2.73205	−	0.732051i	0.662620	−	0.177548i	0.574428	+	0.818555i	$0.305225\pi$
$18$	−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
$22$	0.375156	+	1.40010i	0.0799834	+	0.298502i
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.305727	−	0.952119i	$-0.598900\pi$
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.740827	+	0.671696i	$0.765566\pi$
$24$	−2.12132	−	1.22474i	−0.433013	−	0.250000i
$25$		0			0
$26$	−4.89898			−0.960769
$27$		0			0
$28$	−1.05902	−	0.283763i	−0.200136	−	0.0536262i
$29$	3.85337	+	6.67423i	0.715553	+	1.23937i	0.962746	+	0.270408i	$0.0871586\pi$
$29$	3.85337	+	6.67423i	0.715553	+	1.23937i	−0.247193	+	0.968966i	$0.579508\pi$
$30$		0			0
$31$		−	0.778539i		−	0.139830i	−0.997553	−	0.0699149i	$-0.977727\pi$
$31$		−	0.778539i		−	0.139830i	0.997553	−	0.0699149i	$-0.0222728\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.42953	−	0.918940i	0.597004	−	0.159967i
$34$	−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	−0.948942	−	0.315451i	$-0.897844\pi$
$37$	−3.85337	+	3.85337i	−0.633490	+	0.633490i	0.315451	+	0.948942i	$0.397844\pi$
$38$	3.83926	+	2.06400i	0.622810	+	0.334825i
$39$			12.0000i			1.92154i
$40$		0			0
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	0.378275	−	0.925693i	$-0.376517\pi$
$41$	−1.50000	−	0.866025i	−0.234261	−	0.135250i	−0.612536	+	0.790443i	$0.709851\pi$
$42$	−0.695075	+	2.59405i	−0.107252	+	0.400271i
$43$	2.72670	+	10.1762i	0.415818	+	1.55185i	0.783191	+	0.621781i	$0.213591\pi$
$43$	2.72670	+	10.1762i	0.415818	+	1.55185i	−0.367373	+	0.930074i	$0.619743\pi$
$44$	1.25529	−	0.724745i	0.189243	−	0.109259i
$45$		0			0
$46$			5.19615i			0.766131i
$47$	−1.79315	+	6.69213i	−0.261558	+	0.976148i	0.702766	+	0.711421i	$0.251948\pi$
$47$	−1.79315	+	6.69213i	−0.261558	+	0.976148i	−0.964324	+	0.264726i	$0.914718\pi$
$48$	−0.633975	+	2.36603i	−0.0915064	+	0.341506i
$49$		−	5.79796i		−	0.828280i
$50$		0			0
$51$	−6.00000	+	3.46410i	−0.840168	+	0.485071i
$52$	1.26795	+	4.73205i	0.175833	+	0.656217i
$53$	−1.12547	+	4.20030i	−0.154595	+	0.576955i	0.844545	+	0.535485i	$0.179871\pi$
$53$	−1.12547	+	4.20030i	−0.154595	+	0.576955i	−0.999140	+	0.0414708i	$0.986796\pi$
$54$		0			0
$55$		0			0
$56$			1.09638i			0.146509i
$57$	5.05575	−	9.40422i	0.669651	−	1.24562i
$58$	5.44949	−	5.44949i	0.715553	−	0.715553i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	−0.752011	+	0.201501i	−0.0955055	+	0.0255906i
$63$	3.17705	+	0.851289i	0.400271	+	0.107252i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−1.77526	−	3.07483i	−0.218519	−	0.378486i
$67$	13.9571	+	3.73980i	1.70514	+	0.456890i	0.974224	−	0.225583i	$-0.0724286\pi$
$67$	13.9571	+	3.73980i	1.70514	+	0.456890i	0.730911	+	0.682472i	$0.239095\pi$
$68$	−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	0.311305	−	0.950310i	$-0.399234\pi$
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	−0.667340	+	0.744753i	$0.732567\pi$
$72$	2.89778	+	0.776457i	0.341506	+	0.0915064i
$73$	2.36068	+	8.81017i	0.276296	+	1.03115i	0.954968	+	0.296710i	$0.0958894\pi$
$73$	2.36068	+	8.81017i	0.276296	+	1.03115i	−0.678671	+	0.734442i	$0.737444\pi$
$74$	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
$78$	11.5911	−	3.10583i	1.31243	−	0.351666i
$79$	−2.51059	+	4.34847i	−0.282463	+	0.489241i	−0.971991	−	0.235019i	$-0.924485\pi$
$79$	−2.51059	+	4.34847i	−0.282463	+	0.489241i	0.689527	+	0.724260i	$0.257818\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−0.448288	+	1.67303i	−0.0495051	+	0.184756i
$83$	−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	0.958927	+	0.283653i	$0.0915465\pi$
$89$	6.84072	+	11.8485i	0.725115	+	1.25594i	−0.233812	+	0.972282i	$0.575120\pi$
$90$		0			0
$91$	4.65153	−	2.68556i	0.487613	−	0.281523i
$92$	5.01910	−	1.34486i	0.523277	−	0.140212i
$93$	0.493574	+	1.84204i	0.0511812	+	0.191011i
$94$	6.92820			0.714590
$95$		0			0
$96$	2.44949			0.250000
$97$	−3.73980	−	13.9571i	−0.379719	−	1.41713i	−0.846325	−	0.532667i	$-0.821190\pi$
$97$	−3.73980	−	13.9571i	−0.379719	−	1.41713i	0.466606	−	0.884466i	$-0.345477\pi$
$98$	−5.60040	+	1.50062i	−0.565726	+	0.151586i
$99$	−3.76588	+	2.17423i	−0.378486	+	0.218519i
$100$		0			0
$101$	6.34847	+	10.9959i	0.631696	+	1.09413i	0.987205	+	0.159457i	$0.0509744\pi$
$101$	6.34847	+	10.9959i	0.631696	+	1.09413i	−0.355509	+	0.934673i	$0.615692\pi$
$102$	4.89898	+	4.89898i	0.485071	+	0.485071i
$103$	1.34278	+	1.34278i	0.132308	+	0.132308i	0.770160	−	0.637851i	$-0.220177\pi$
$103$	1.34278	+	1.34278i	0.132308	+	0.132308i	−0.637851	+	0.770160i	$0.720177\pi$
$104$	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	−0.988492	−	0.151274i	$-0.951663\pi$
$107$	−8.66025	+	8.66025i	−0.837218	+	0.837218i	0.151274	+	0.988492i	$0.451663\pi$
$108$		0			0
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$		0			0
$111$	6.67423	−	11.5601i	0.633490	−	1.09724i
$112$	1.05902	−	0.283763i	0.100068	−	0.0268131i
$113$	−12.9029	−	12.9029i	−1.21380	−	1.21380i	−0.969766	−	0.244036i	$-0.921528\pi$
$113$	−12.9029	−	12.9029i	−1.21380	−	1.21380i	−0.244036	−	0.969766i	$-0.578472\pi$
$114$	−10.3923	−	2.44949i	−0.973329	−	0.229416i
$115$		0			0
$116$	−6.67423	−	3.85337i	−0.619687	−	0.357777i
$117$	−3.80385	−	14.1962i	−0.351666	−	1.31243i
$118$	−3.34607	−	0.896575i	−0.308030	−	0.0825365i
$119$	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
$123$	4.09808	+	1.09808i	0.369511	+	0.0990102i
$124$	0.389270	+	0.674235i	0.0349574	+	0.0605481i
$125$		0			0
$126$		−	3.28913i		−	0.293019i
$127$	13.4254	+	3.59732i	1.19131	+	0.319211i	0.799404	−	0.600794i	$-0.205149\pi$
$127$	13.4254	+	3.59732i	1.19131	+	0.319211i	0.391907	+	0.920005i	$0.371816\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−12.9029	−	22.3485i	−1.13604	−	1.96767i
$130$		0			0
$131$	−3.62372	+	6.27647i	−0.316606	+	0.548378i	−0.979778	−	0.200089i	$-0.935877\pi$
$131$	−3.62372	+	6.27647i	−0.316606	+	0.548378i	0.663171	+	0.748468i	$0.269210\pi$
$132$	−2.51059	+	2.51059i	−0.218519	+	0.218519i
$133$	−4.77680	+	0.144887i	−0.414201	+	0.0125633i
$134$		−	14.4495i		−	1.24825i
$135$		0			0
$136$	2.44949	+	1.41421i	0.210042	+	0.121268i
$137$	−0.732051	+	2.73205i	−0.0625433	+	0.233415i	−0.990121	−	0.140215i	$-0.955220\pi$
$137$	−0.732051	+	2.73205i	−0.0625433	+	0.233415i	0.927578	+	0.373630i	$0.121887\pi$
$138$	−3.29423	−	12.2942i	−0.280423	−	1.04655i
$139$	−14.6349	+	8.44949i	−1.24132	+	0.716676i	−0.969363	−	0.245633i	$-0.921004\pi$
$139$	−14.6349	+	8.44949i	−1.24132	+	0.716676i	−0.271957	+	0.962309i	$0.587671\pi$
$140$		0			0
$141$		−	16.9706i		−	1.42918i
$142$	−0.896575	+	3.34607i	−0.0752389	+	0.280796i
$143$	−1.83788	+	6.85906i	−0.153691	+	0.573583i
$144$		−	3.00000i		−	0.250000i
$145$		0			0
$146$	7.89898	−	4.56048i	0.653724	−	0.377428i
$147$	3.67576	+	13.7181i	0.303171	+	1.13145i
$148$	1.41043	−	5.26380i	0.115937	−	0.432682i
$149$	−5.58542	−	3.22474i	−0.457576	−	0.264181i	0.253449	−	0.967349i	$-0.418435\pi$
$149$	−5.58542	−	3.22474i	−0.457576	−	0.264181i	−0.711024	+	0.703167i	$0.751768\pi$
$150$		0			0
$151$		−	8.48528i		−	0.690522i	−0.938507	−	0.345261i	$-0.887790\pi$
$151$		−	8.48528i		−	0.690522i	0.938507	−	0.345261i	$-0.112210\pi$
$152$	−4.35690	+	0.132150i	−0.353391	+	0.0107188i
$153$	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
$157$	−6.38512	+	1.71089i	−0.509588	+	0.136544i	−0.504446	−	0.863443i	$-0.668303\pi$
$157$	−6.38512	+	1.71089i	−0.509588	+	0.136544i	−0.00514190	+	0.999987i	$0.501637\pi$
$158$	4.85009	+	1.29958i	0.385852	+	0.103389i
$159$		−	10.6515i		−	0.844721i
$160$		0			0
$161$	−2.84847	−	4.93369i	−0.224491	−	0.388830i
$162$	8.69333	+	2.32937i	0.683013	+	0.183013i
$163$	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
$167$	5.50282	+	1.47448i	0.425821	+	0.114098i	0.465364	−	0.885119i	$-0.345923\pi$
$167$	5.50282	+	1.47448i	0.425821	+	0.114098i	−0.0395428	+	0.999218i	$0.512590\pi$
$168$	−0.695075	−	2.59405i	−0.0536262	−	0.200136i
$169$	−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
$173$	0.531752	−	0.142483i	0.0404284	−	0.0108327i	−0.238548	−	0.971131i	$-0.576671\pi$
$173$	0.531752	−	0.142483i	0.0404284	−	0.0108327i	0.278977	+	0.960298i	$0.410005\pi$
$174$	−9.43879	+	16.3485i	−0.715553	+	1.23937i
$175$		0			0
$176$	−0.724745	+	1.25529i	−0.0546297	+	0.0946214i
$177$	−2.19615	+	8.19615i	−0.165073	+	0.616061i
$178$	9.67423	−	9.67423i	0.725115	−	0.725115i
$179$	−2.51059			−0.187650			−0.0938251	−	0.995589i	$-0.529909\pi$
$179$	−2.51059			−0.187650			−0.0938251	+	0.995589i	$0.529909\pi$
$180$		0			0
$181$	18.6742	−	10.7816i	1.38804	−	0.801388i	0.394950	−	0.918703i	$-0.370762\pi$
$181$	18.6742	−	10.7816i	1.38804	−	0.801388i	0.993095	+	0.117314i	$0.0374285\pi$
$182$	−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
$187$	−3.96008	+	1.06110i	−0.289590	+	0.0775953i
$188$	−1.79315	−	6.69213i	−0.130779	−	0.488074i
$189$		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	$0.700011\pi$
$192$	−0.633975	−	2.36603i	−0.0457532	−	0.170753i
$193$	12.8936	−	3.45484i	0.928104	−	0.248685i	0.237058	−	0.971496i	$-0.423817\pi$
$193$	12.8936	−	3.45484i	0.928104	−	0.248685i	0.691046	+	0.722811i	$0.257150\pi$
$194$	−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	$-0.553772\pi$
$199$	8.48528	−	4.89898i	0.601506	−	0.347279i	0.769634	+	0.638486i	$0.220439\pi$
$200$		0			0
$201$	−35.3939			−2.49649
$202$	8.97809	−	8.97809i	0.631696	−	0.631696i
$203$	−2.18689	+	8.16158i	−0.153490	+	0.572831i
$204$	3.46410	−	6.00000i	0.242536	−	0.420084i
$205$		0			0
$206$	0.949490	−	1.64456i	0.0661541	−	0.114582i
$207$	−15.0573	+	4.03459i	−1.04655	+	0.280423i
$208$	−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	0.933441	−	0.358731i	$-0.116791\pi$
$211$	15.8258	+	9.13701i	1.08949	+	0.629018i	0.156050	+	0.987749i	$0.450124\pi$
$212$	−1.12547	−	4.20030i	−0.0772974	−	0.288478i
$213$	8.19615	+	2.19615i	0.561591	+	0.150478i
$214$	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
$222$	−12.8936	−	3.45484i	−0.865364	−	0.231874i
$223$	−11.2984	+	3.02739i	−0.756595	+	0.202729i	−0.616442	−	0.787401i	$-0.711426\pi$
$223$	−11.2984	+	3.02739i	−0.756595	+	0.202729i	−0.140154	+	0.990130i	$0.544760\pi$
$224$	−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	−0.970584	−	0.240762i	$-0.922603\pi$
$227$	−10.9959	+	10.9959i	−0.729822	+	0.729822i	0.240762	+	0.970584i	$0.422603\pi$
$228$	0.323701	+	10.6722i	0.0214376	+	0.706782i
$229$			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
$232$	−1.99465	+	7.44414i	−0.130955	+	0.488732i
$233$	0.896575	+	3.34607i	0.0587366	+	0.219208i	0.989056	−	0.147543i	$-0.0471366\pi$
$233$	0.896575	+	3.34607i	0.0587366	+	0.219208i	−0.930319	+	0.366751i	$0.880470\pi$
$234$	−12.7279	+	7.34847i	−0.832050	+	0.480384i
$235$		0			0
$236$			3.46410i			0.225494i
$237$	3.18330	−	11.8802i	0.206778	−	0.771704i
$238$	0.802603	−	2.99536i	0.0520250	−	0.194160i
$239$			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	0.526947	−	0.849898i	$-0.323337\pi$
$241$	23.6969	−	13.6814i	1.52645	−	0.881299i	0.999507	−	0.0314005i	$-0.00999675\pi$
$242$	2.30323	+	8.59575i	0.148057	+	0.552556i
$243$	5.70577	−	21.2942i	0.366025	−	1.36603i
$244$	−6.92820	−	4.00000i	−0.443533	−	0.256074i
$245$		0			0
$246$		−	4.24264i		−	0.270501i
$247$	11.2328	+	18.1610i	0.714728	+	1.15556i
$248$	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	0.879863	−	0.475228i	$-0.157635\pi$
$251$	0.449490	+	0.778539i	0.0283715	+	0.0491410i	−0.851491	+	0.524369i	$0.824301\pi$
$252$	−3.17705	+	0.851289i	−0.200136	+	0.0536262i
$253$	7.27513	+	1.94937i	0.457384	+	0.122556i
$254$		−	13.8990i		−	0.872100i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.22508	+	2.47185i	0.575445	+	0.154190i	0.534793	−	0.844983i	$-0.320390\pi$
$257$	9.22508	+	2.47185i	0.575445	+	0.154190i	0.0406523	+	0.999173i	$0.487056\pi$
$258$	−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
$262$	7.00050	+	1.87578i	0.432492	+	0.115886i
$263$	−5.99227	−	22.3634i	−0.369499	−	1.37899i	−0.861218	−	0.508235i	$-0.830298\pi$
$263$	−5.99227	−	22.3634i	−0.369499	−	1.37899i	0.491720	−	0.870754i	$-0.336369\pi$
$264$	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
$268$	−13.9571	+	3.73980i	−0.852568	+	0.228445i
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	−0.740883	−	0.671634i	$-0.765593\pi$
$269$	3.46410	−	6.00000i	0.211210	−	0.365826i	0.952093	+	0.305807i	$0.0989263\pi$
$270$		0			0
$271$	−1.65153	+	2.86054i	−0.100323	+	0.173765i	−0.911818	−	0.410595i	$-0.865321\pi$
$271$	−1.65153	+	2.86054i	−0.100323	+	0.173765i	0.811495	+	0.584360i	$0.198654\pi$
$272$	0.732051	−	2.73205i	0.0443871	−	0.165655i
$273$	−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	−0.779348	−	0.626592i	$-0.784449\pi$
$281$	−10.5000	+	6.06218i	−0.626377	+	0.361639i	0.152970	+	0.988231i	$0.451116\pi$
$282$	−16.3923	+	4.39230i	−0.976148	+	0.261558i
$283$	−0.164525	−	0.614014i	−0.00977998	−	0.0364994i	0.960863	−	0.277023i	$-0.0893477\pi$
$283$	−0.164525	−	0.614014i	−0.00977998	−	0.0364994i	−0.970643	+	0.240523i	$0.922681\pi$
$284$	3.46410			0.205557
$285$		0			0
$286$	7.10102			0.419892
$287$	−0.491492	−	1.83427i	−0.0290119	−	0.108274i
$288$	−2.89778	+	0.776457i	−0.170753	+	0.0457532i
$289$	−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	$0.0430053\pi$
$293$	19.2669	+	19.2669i	1.12558	+	1.12558i	0.134695	+	0.990887i	$0.456995\pi$
$294$	12.2993	−	7.10102i	0.717311	−	0.414140i
$295$		0			0
$296$	−5.44949			−0.316745
$297$		0			0
$298$	−1.66925	+	6.22973i	−0.0966971	+	0.360878i
$299$	−12.7279	+	22.0454i	−0.736075	+	1.27492i
$300$		0			0
$301$	−5.77526	+	10.0030i	−0.332880	+	0.576565i
$302$	−8.19615	+	2.19615i	−0.471636	+	0.126374i
$303$	−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
$307$	3.45484	+	12.8936i	0.197178	+	0.735878i	0.991692	+	0.128633i	$0.0410589\pi$
$307$	3.45484	+	12.8936i	0.197178	+	0.735878i	−0.794514	+	0.607245i	$0.792274\pi$
$308$	1.53504	+	0.411312i	0.0874668	+	0.0234367i
$309$	−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
$313$	28.7486	+	7.70315i	1.62496	+	0.435408i	0.952455	−	0.304680i	$-0.0985495\pi$
$313$	28.7486	+	7.70315i	1.62496	+	0.435408i	0.672510	+	0.740088i	$0.265216\pi$
$314$	3.30518	+	5.72474i	0.186522	+	0.323066i
$315$		0			0
$316$		−	5.02118i		−	0.282463i
$317$	−14.7279	−	3.94633i	−0.827202	−	0.221648i	−0.179709	−	0.983720i	$-0.557516\pi$
$317$	−14.7279	−	3.94633i	−0.827202	−	0.221648i	−0.647492	+	0.762072i	$0.724182\pi$
$318$	−10.2886	+	2.75682i	−0.576955	+	0.154595i
$319$	−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
$323$	−5.83788	+	10.8591i	−0.324828	+	0.604214i
$324$		−	9.00000i		−	0.500000i
$325$		0			0
$326$	−11.4495	−	6.61037i	−0.634129	−	0.366114i
$327$		0			0
$328$	−0.448288	−	1.67303i	−0.0247525	−	0.0923778i
$329$	−6.57826	+	3.79796i	−0.362671	+	0.209388i
$330$		0			0
$331$			4.06767i			0.223579i	0.993732	+	0.111790i	$0.0356583\pi$
$331$			4.06767i			0.223579i	−0.993732	+	0.111790i	$0.964342\pi$
$332$	4.51985	−	16.8683i	0.248059	−	0.925769i
$333$	−4.23130	+	15.7914i	−0.231874	+	0.865364i
$334$		−	5.69694i		−	0.311723i
$335$		0			0
$336$	−2.32577	+	1.34278i	−0.126881	+	0.0732547i
$337$	4.65874	+	17.3867i	0.253778	+	0.947112i	0.968766	+	0.247976i	$0.0797653\pi$
$337$	4.65874	+	17.3867i	0.253778	+	0.947112i	−0.714988	+	0.699136i	$0.753568\pi$
$338$	−2.84701	+	10.6252i	−0.154857	+	0.577934i
$339$	38.7087	+	22.3485i	2.10237	+	1.21380i
$340$		0			0
$341$			1.12848i			0.0611109i
$342$	13.0707	−	0.396451i	0.706782	−	0.0214376i
$343$	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
$347$	9.08616	−	2.43463i	0.487771	−	0.130698i	−0.00654796	−	0.999979i	$-0.502084\pi$
$347$	9.08616	−	2.43463i	0.487771	−	0.130698i	0.494319	+	0.869281i	$0.335418\pi$
$348$	18.2343	+	4.88588i	0.977464	+	0.261911i
$349$			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
$352$	1.40010	+	0.375156i	0.0746256	+	0.0199959i
$353$	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
$357$	−7.33709	−	1.96597i	−0.388320	−	0.104050i
$358$	0.649788	+	2.42504i	0.0343424	+	0.128168i
$359$	−20.6096	−	11.8990i	−1.08774	−	0.628004i	−0.154763	−	0.987952i	$-0.549461\pi$
$359$	−20.6096	−	11.8990i	−1.08774	−	0.628004i	−0.932973	+	0.359948i	$0.882795\pi$
$360$		0			0
$361$	−1.15153	−	18.9651i	−0.0606069	−	0.998162i
$362$	−15.2474	−	15.2474i	−0.801388	−	0.801388i
$363$	21.0552	−	5.64173i	1.10511	−	0.296114i
$364$	−2.68556	+	4.65153i	−0.140762	+	0.243806i
$365$		0			0
$366$	−9.79796	+	16.9706i	−0.512148	+	0.887066i
$367$	−3.91535	+	14.6123i	−0.204380	+	0.762755i	0.785258	+	0.619169i	$0.212530\pi$
$367$	−3.91535	+	14.6123i	−0.204380	+	0.762755i	−0.989638	+	0.143587i	$0.954136\pi$
$368$	−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	$-0.869316\pi$
$373$	−25.4165	−	25.4165i	−1.31602	−	1.31602i	−0.399118	−	0.916900i	$-0.630684\pi$
$374$	2.04989	+	3.55051i	0.105997	+	0.183593i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$	36.4687	−	9.77176i	1.87823	−	0.503271i
$378$		0			0
$379$	28.9199			1.48552			0.742759	−	0.669559i	$-0.233517\pi$
$379$	28.9199			1.48552			0.742759	+	0.669559i	$0.233517\pi$
$380$		0			0
$381$	−34.0454			−1.74420
$382$	4.20515	+	15.6938i	0.215154	+	0.802966i
$383$	−9.46410	+	2.53590i	−0.483593	+	0.129578i	−0.492375	−	0.870383i	$-0.663871\pi$
$383$	−9.46410	+	2.53590i	−0.483593	+	0.129578i	0.00878215	+	0.999961i	$0.497205\pi$
$384$	−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	$-0.643252\pi$
$389$	2.51059	−	1.44949i	0.127292	−	0.0734920i	0.562294	+	0.826937i	$0.309919\pi$
$390$		0			0
$391$	−14.6969			−0.743256
$392$	4.09978	−	4.09978i	0.207070	−	0.207070i
$393$	4.59470	−	17.1476i	0.231772	−	0.864984i
$394$	−3.76588	+	6.52270i	−0.189723	+	0.328609i
$395$		0			0
$396$	2.17423	−	3.76588i	0.109259	−	0.189243i
$397$	7.88915	−	2.11389i	0.395945	−	0.106093i	−0.0553522	−	0.998467i	$-0.517628\pi$
$397$	7.88915	−	2.11389i	0.395945	−	0.106093i	0.451297	+	0.892374i	$0.350961\pi$
$398$	−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	0.0762914	−	0.997086i	$-0.475692\pi$
$401$	−15.0000	−	8.66025i	−0.749064	−	0.432472i	−0.825356	+	0.564613i	$0.809025\pi$
$402$	9.16061	+	34.1879i	0.456890	+	1.70514i
$403$	−3.68409	−	0.987148i	−0.183517	−	0.0491733i
$404$	−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
$408$	−6.69213	−	1.79315i	−0.331310	−	0.0887742i
$409$	7.79423	+	13.5000i	0.385400	+	0.667532i	0.991825	−	0.127609i	$-0.0407302\pi$
$409$	7.79423	+	13.5000i	0.385400	+	0.667532i	−0.606425	+	0.795141i	$0.707397\pi$
$410$		0			0
$411$		−	6.92820i		−	0.341743i
$412$	−1.83427	−	0.491492i	−0.0903682	−	0.0242141i
$413$	3.66855	−	0.982984i	0.180517	−	0.0483695i
$414$	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
$418$	−5.56496	−	2.99175i	−0.272191	−	0.146331i
$419$		−	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	0.688972	−	0.724788i	$-0.258062\pi$
$421$	8.32577	+	4.80688i	0.405773	+	0.234273i	−0.283199	+	0.959061i	$0.591396\pi$
$422$	4.72966	−	17.6513i	0.230236	−	0.859254i
$423$	5.37945	+	20.0764i	0.261558	+	0.976148i
$424$	−3.76588	+	2.17423i	−0.182888	+	0.105590i
$425$		0			0
$426$		−	8.48528i		−	0.411113i
$427$	−2.27010	+	8.47215i	−0.109858	+	0.409996i
$428$	3.16987	−	11.8301i	0.153222	−	0.571831i
$429$		−	17.3939i		−	0.839784i
$430$		0			0
$431$	20.0227	−	11.5601i	0.964460	−	0.556831i	0.0669170	−	0.997759i	$-0.478684\pi$
$431$	20.0227	−	11.5601i	0.964460	−	0.556831i	0.897543	+	0.440927i	$0.145350\pi$
$432$		0			0
$433$	5.00775	−	18.6892i	0.240657	−	0.898145i	−0.734859	−	0.678219i	$-0.762752\pi$
$433$	5.00775	−	18.6892i	0.240657	−	0.898145i	0.975517	−	0.219926i	$-0.0705814\pi$
$434$	−0.739215	−	0.426786i	−0.0354834	−	0.0204864i
$435$		0			0
$436$		0			0
$437$	19.2627	−	11.9142i	0.921460	−	0.569935i
$438$	−15.7980	+	15.7980i	−0.754856	+	0.754856i
$439$	−5.41045	+	9.37117i	−0.258227	+	0.447262i	−0.965767	−	0.259411i	$-0.916471\pi$
$439$	−5.41045	+	9.37117i	−0.258227	+	0.447262i	0.707540	+	0.706673i	$0.249805\pi$
$440$		0			0
$441$	−8.69694	−	15.0635i	−0.414140	−	0.717311i
$442$	−13.3843	+	3.58630i	−0.636624	+	0.170583i
$443$	−3.00804	−	0.806003i	−0.142916	−	0.0382944i	0.186652	−	0.982426i	$-0.440236\pi$
$443$	−3.00804	−	0.806003i	−0.142916	−	0.0382944i	−0.329568	+	0.944132i	$0.606903\pi$
$444$			13.3485i			0.633490i
$445$		0			0
$446$	5.84847	+	10.1298i	0.276933	+	0.479662i
$447$	15.2597	+	4.08881i	0.721757	+	0.193394i
$448$	−0.775255	+	0.775255i	−0.0366274	+	0.0366274i
$449$	−8.66025			−0.408703			−0.204351	−	0.978898i	$-0.565508\pi$
$449$	−8.66025			−0.408703			−0.204351	+	0.978898i	$0.565508\pi$
$450$		0			0
$451$	2.17423	+	1.25529i	0.102381	+	0.0591095i
$452$	17.6257	+	4.72279i	0.829042	+	0.222141i
$453$	5.37945	+	20.0764i	0.252749	+	0.943271i
$454$	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	$0.530320\pi$
$458$	15.0206	−	4.02477i	0.701868	−	0.188065i
$459$		0			0
$460$		0			0
$461$	8.10102	−	14.0314i	0.377302	−	0.653506i	−0.613367	−	0.789798i	$-0.710185\pi$
$461$	8.10102	−	14.0314i	0.377302	−	0.653506i	0.990669	+	0.136292i	$0.0435185\pi$
$462$	1.00750	−	3.76005i	0.0468733	−	0.174934i
$463$	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
$472$	3.34607	−	0.896575i	0.154015	−	0.0412682i
$473$	−3.95233	−	14.7503i	−0.181728	−	0.678219i
$474$	−12.2993			−0.564927
$475$		0			0
$476$	−3.10102			−0.142135
$477$	3.37640	+	12.6009i	0.154595	+	0.576955i
$478$	13.3278	−	3.57117i	0.609600	−	0.163342i
$479$	23.7238	−	13.6969i	1.08397	−	0.625829i	0.152004	−	0.988380i	$-0.451427\pi$
$479$	23.7238	−	13.6969i	1.08397	−	0.625829i	0.931964	+	0.362551i	$0.118094\pi$
$480$		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	−0.229797	−	0.973239i	$-0.573806\pi$
$487$	16.4063	−	16.4063i	0.743441	−	0.743441i	0.973239	+	0.229797i	$0.0738063\pi$
$488$	−2.07055	+	7.72741i	−0.0937295	+	0.349803i
$489$	−16.1920	+	28.0454i	−0.732229	+	1.26826i
$490$		0			0
$491$	−10.1742	+	17.6223i	−0.459157	+	0.795283i	−0.998917	−	0.0465362i	$-0.985182\pi$
$491$	−10.1742	+	17.6223i	−0.459157	+	0.795283i	0.539760	+	0.841819i	$0.318515\pi$
$492$	−4.09808	+	1.09808i	−0.184756	+	0.0495051i
$493$	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
$497$	−0.982984	−	3.66855i	−0.0440929	−	0.164557i
$498$	−41.3188	−	11.0713i	−1.85154	−	0.496118i
$499$	−18.4008	−	10.6237i	−0.823734	−	0.475583i	0.0279682	−	0.999609i	$-0.491096\pi$
$499$	−18.4008	−	10.6237i	−0.823734	−	0.475583i	−0.851703	+	0.524026i	$0.824430\pi$
$500$		0			0
$501$	−13.9546			−0.623445
$502$	0.635674	−	0.635674i	0.0283715	−	0.0283715i
$503$	4.06706	+	1.08977i	0.181341	+	0.0485903i	0.348347	−	0.937366i	$-0.386743\pi$
$503$	4.06706	+	1.08977i	0.181341	+	0.0485903i	−0.167006	+	0.985956i	$0.553410\pi$
$504$	1.64456	+	2.84847i	0.0732547	+	0.126881i
$505$		0			0
$506$		−	7.53177i		−	0.334828i
$507$	26.0263	+	6.97372i	1.15587	+	0.309714i
$508$	−13.4254	+	3.59732i	−0.595655	+	0.159605i
$509$	−10.7816	−	18.6742i	−0.477885	−	0.827721i	0.521794	−	0.853072i	$-0.325263\pi$
$509$	−10.7816	−	18.6742i	−0.477885	−	0.827721i	−0.999679	+	0.0253508i	$0.991930\pi$
$510$		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
$517$	2.59915	−	9.70017i	0.114311	−	0.426613i
$518$	1.54636	+	5.77111i	0.0679433	+	0.253568i
$519$	−1.16781	+	0.674235i	−0.0512611	+	0.0295956i
$520$		0			0
$521$			35.8481i			1.57054i	0.619156	+	0.785268i	$0.287475\pi$
$521$			35.8481i			1.57054i	−0.619156	+	0.785268i	$0.712525\pi$
$522$	5.98396	−	22.3324i	0.261911	−	0.977464i
$523$	−0.220921	+	0.824487i	−0.00966019	+	0.0360523i	−0.970588	−	0.240748i	$-0.922607\pi$
$523$	−0.220921	+	0.824487i	−0.00966019	+	0.0360523i	0.960928	+	0.276800i	$0.0892740\pi$
$524$		−	7.24745i		−	0.316606i
$525$		0			0
$526$	−20.0505	+	11.5762i	−0.874244	+	0.504745i
$527$	−0.569930	−	2.12701i	−0.0248265	−	0.0926539i
$528$	0.918940	−	3.42953i	0.0399917	−	0.149251i
$529$	3.46410	+	2.00000i	0.150613	+	0.0869565i
$530$		0			0
$531$		−	10.3923i		−	0.450988i
$532$	4.06438	−	2.51387i	0.176213	−	0.108990i
$533$	−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
$537$	5.94012	−	1.59165i	0.256335	−	0.0686848i
$538$	−6.69213	−	1.79315i	−0.288518	−	0.0773082i
$539$			8.40408i			0.361989i
$540$		0			0
$541$	7.22474	+	12.5136i	0.310616	+	0.538003i	0.978496	−	0.206266i	$-0.0661313\pi$
$541$	7.22474	+	12.5136i	0.310616	+	0.538003i	−0.667880	+	0.744269i	$0.732798\pi$
$542$	3.19051	+	0.854895i	0.137044	+	0.0367209i
$543$	−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
$547$	−17.3867	−	4.65874i	−0.743400	−	0.199193i	−0.132811	−	0.991141i	$-0.542400\pi$
$547$	−17.3867	−	4.65874i	−0.743400	−	0.199193i	−0.610589	+	0.791948i	$0.709067\pi$
$548$	−0.732051	−	2.73205i	−0.0312717	−	0.116707i
$549$	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
$553$	−5.31752	+	1.42483i	−0.226124	+	0.0605897i
$554$	−9.75663	+	16.8990i	−0.414520	+	0.717969i
$555$		0			0
$556$	8.44949	−	14.6349i	0.358338	−	0.620660i
$557$	−10.8245	+	40.3978i	−0.458651	+	1.71171i	0.218477	+	0.975842i	$0.429891\pi$
$557$	−10.8245	+	40.3978i	−0.458651	+	1.71171i	−0.677127	+	0.735866i	$0.736775\pi$
$558$	−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	0.252399	−	0.967623i	$-0.418780\pi$
$563$	−16.9706	−	16.9706i	−0.715224	−	0.715224i	−0.967623	+	0.252399i	$0.918780\pi$
$564$	8.48528	+	14.6969i	0.357295	+	0.618853i
$565$		0			0
$566$	−0.550510	+	0.317837i	−0.0231397	+	0.0133597i
$567$	−9.53116	+	2.55387i	−0.400271	+	0.107252i
$568$	−0.896575	−	3.34607i	−0.0376195	−	0.140398i
$569$	−15.2385			−0.638832			−0.319416	−	0.947615i	$-0.603487\pi$
$569$	−15.2385			−0.638832			−0.319416	+	0.947615i	$0.603487\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	−1.83788	−	6.85906i	−0.0768456	−	0.286792i
$573$	38.4419	−	10.3005i	1.60593	−	0.430308i
$574$	−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
$583$	1.63135	−	6.08829i	0.0675637	−	0.252151i
$584$	−4.56048	+	7.89898i	−0.188714	+	0.326862i
$585$		0			0
$586$	13.6237	−	23.5970i	0.562791	−	0.974782i
$587$	−13.3843	+	3.58630i	−0.552428	+	0.148023i	−0.524225	−	0.851580i	$-0.675645\pi$
$587$	−13.3843	+	3.58630i	−0.552428	+	0.148023i	−0.0282024	+	0.999602i	$0.508978\pi$
$588$	−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
$592$	1.41043	+	5.26380i	0.0579684	+	0.216341i
$593$	−39.6147	−	10.6147i	−1.62678	−	0.435895i	−0.673798	−	0.738915i	$-0.735338\pi$
$593$	−39.6147	−	10.6147i	−1.62678	−	0.435895i	−0.952984	+	0.303020i	$0.902005\pi$
$594$		0			0
$595$		0			0
$596$	6.44949			0.264181
$597$	−16.9706	+	16.9706i	−0.694559	+	0.694559i
$598$	24.5885	+	6.58846i	1.00550	+	0.269422i
$599$	−14.6349	−	25.3485i	−0.597968	−	1.03571i	−0.993121	−	0.117095i	$-0.962642\pi$
$599$	−14.6349	−	25.3485i	−0.597968	−	1.03571i	0.395153	−	0.918615i	$-0.370692\pi$
$600$		0			0
$601$			0.174973i			0.00713728i	0.999994	+	0.00356864i	$0.00113594\pi$
$601$			0.174973i			0.00713728i	−0.999994	+	0.00356864i	$0.998864\pi$
$602$	11.1569	+	2.98949i	0.454723	+	0.121843i
$603$	41.8714	−	11.2194i	1.70514	−	0.456890i
$604$	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	−0.733832	−	0.679331i	$-0.762270\pi$
$607$	−1.34278	+	1.34278i	−0.0545018	+	0.0545018i	0.679331	+	0.733832i	$0.262270\pi$
$608$	3.70711	−	2.29289i	0.150343	−	0.0929891i
$609$		−	20.6969i		−	0.838682i
$610$		0			0
$611$	29.3939	+	16.9706i	1.18915	+	0.686555i
$612$	−2.19615	+	8.19615i	−0.0887742	+	0.331310i
$613$	11.5732	+	43.1918i	0.467438	+	1.74450i	0.648678	+	0.761063i	$0.275322\pi$
$613$	11.5732	+	43.1918i	0.467438	+	1.74450i	−0.181240	+	0.983439i	$0.558011\pi$
$614$	11.5601	−	6.67423i	0.466528	−	0.269350i
$615$		0			0
$616$		−	1.58919i		−	0.0640301i
$617$	−8.43520	+	31.4806i	−0.339589	+	1.26736i	0.559220	+	0.829020i	$0.311101\pi$
$617$	−8.43520	+	31.4806i	−0.339589	+	1.26736i	−0.898808	+	0.438342i	$0.855566\pi$
$618$	−1.20390	+	4.49303i	−0.0484282	+	0.180736i
$619$		−	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
$622$	−6.67700	−	24.9189i	−0.267723	−	0.999157i
$623$	−3.88229	+	14.4889i	−0.155540	+	0.580485i
$624$	10.3923	+	6.00000i	0.416025	+	0.240192i
$625$		0			0
$626$		−	29.7627i		−	1.18956i
$627$	−7.32826	+	13.6313i	−0.292663	+	0.544383i
$628$	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	0.845434	−	0.534080i	$-0.179342\pi$
$631$	−1.00000	−	1.73205i	−0.0398094	−	0.0689519i	−0.885244	+	0.465128i	$0.846008\pi$
$632$	−4.85009	+	1.29958i	−0.192926	+	0.0516944i
$633$	−43.2368	−	11.5853i	−1.71851	−	0.460473i
$634$			15.2474i			0.605554i
$635$		0			0
$636$	5.32577	+	9.22450i	0.211180	+	0.365775i
$637$	−27.4362	−	7.35152i	−1.08706	−	0.291278i
$638$	−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	−0.0111600	−	0.999938i	$-0.503552\pi$
$641$	−22.3485	−	12.9029i	−0.882711	−	0.509634i	−0.871551	+	0.490304i	$0.836886\pi$
$642$	−28.9778	−	7.76457i	−1.14366	−	0.306443i
$643$	−7.90465	−	29.5006i	−0.311729	−	1.16339i	−0.926996	−	0.375070i	$-0.877619\pi$
$643$	−7.90465	−	29.5006i	−0.311729	−	1.16339i	0.615267	−	0.788319i	$-0.289048\pi$
$644$	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	$0.657326\pi$
$648$	−8.69333	+	2.32937i	−0.341506	+	0.0915064i
$649$	−2.51059	+	4.34847i	−0.0985493	+	0.170692i
$650$		0			0
$651$	−1.04541	+	1.81070i	−0.0409728	+	0.0709669i
$652$	−3.42178	+	12.7702i	−0.134007	+	0.500121i
$653$	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	$-0.148923\pi$
$659$	1.43027	+	2.47730i	0.0557153	+	0.0965018i	−0.836823	+	0.547474i	$0.815589\pi$
$660$		0			0
$661$	−33.0681	+	19.0919i	−1.28620	+	0.742588i	−0.977974	−	0.208725i	$-0.933069\pi$
$661$	−33.0681	+	19.0919i	−1.28620	+	0.742588i	−0.308226	+	0.951313i	$0.599735\pi$
$662$	3.92907	−	1.05279i	0.152707	−	0.0409178i
$663$	8.78461	+	32.7846i	0.341166	+	1.27325i
$664$	−17.4634			−0.677710
$665$		0			0
$666$	16.3485			0.633490
$667$	−10.3645	−	38.6809i	−0.401316	−	1.49773i
$668$	−5.50282	+	1.47448i	−0.212910	+	0.0570492i
$669$	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	0.644534	−	0.764576i	$-0.277051\pi$
$673$	−3.11416	−	3.11416i	−0.120042	−	0.120042i	−0.764576	+	0.644534i	$0.777051\pi$
$674$	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	−0.861791	−	0.507264i	$-0.830657\pi$
$677$	−9.22450	+	9.22450i	−0.354526	+	0.354526i	0.507264	+	0.861791i	$0.330657\pi$
$678$	11.5684	−	43.1739i	0.444282	−	1.65808i
$679$	7.92104	−	13.7196i	0.303982	−	0.526512i
$680$		0			0
$681$	19.0454	−	32.9876i	0.729822	−	1.26409i
$682$	1.09003	−	0.292073i	0.0417395	−	0.0111841i
$683$	25.8058	+	25.8058i	0.987431	+	0.987431i	0.999922	−	0.0124909i	$-0.00397608\pi$
$683$	25.8058	+	25.8058i	0.987431	+	0.987431i	−0.0124909	+	0.999922i	$0.503976\pi$
$684$	−3.76588	−	12.5227i	−0.143992	−	0.478818i
$685$		0			0
$686$	−12.1515	−	7.01569i	−0.463948	−	0.267860i
$687$	−9.85863	−	36.7929i	−0.376130	−	1.40374i
$688$	10.1762	+	2.72670i	0.387964	+	0.103955i
$689$	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
$693$	−4.60511	−	1.23393i	−0.174934	−	0.0468733i
$694$	−4.70334	−	8.14643i	−0.178536	−	0.309234i
$695$		0			0
$696$		−	18.8776i		−	0.715553i
$697$	−4.73205	−	1.26795i	−0.179239	−	0.0480270i
$698$	18.4502	−	4.94371i	0.698349	−	0.187122i
$699$	−4.24264	−	7.34847i	−0.160471	−	0.277945i
$700$		0			0
$701$	−4.67423	+	8.09601i	−0.176543	+	0.305782i	−0.940694	−	0.339255i	$-0.889825\pi$
$701$	−4.67423	+	8.09601i	−0.176543	+	0.305782i	0.764151	+	0.645038i	$0.223158\pi$
$702$		0			0
$703$	−0.720152	−	23.7429i	−0.0271611	−	0.895479i
$704$		−	1.44949i		−	0.0546297i
$705$		0			0
$706$	−2.02270	−	1.16781i	−0.0761255	−	0.0439511i
$707$	−3.60292	+	13.4463i	−0.135502	+	0.505700i
$708$	−2.19615	−	8.19615i	−0.0825365	−	0.308030i
$709$	23.1202	−	13.3485i	0.868298	−	0.501312i	0.00151596	−	0.999999i	$-0.499517\pi$
$709$	23.1202	−	13.3485i	0.868298	−	0.501312i	0.866782	+	0.498687i	$0.166184\pi$
$710$		0			0
$711$			15.0635i			0.564927i
$712$	−3.54102	+	13.2153i	−0.132705	+	0.495262i
$713$	−1.04703	+	3.90756i	−0.0392115	+	0.146339i
$714$			7.59592i			0.284270i
$715$		0			0
$716$	2.17423	−	1.25529i	0.0812550	−	0.0469126i
$717$	−8.74756	−	32.6463i	−0.326683	−	1.21920i
$718$	−6.15937	+	22.9871i	−0.229865	+	0.857870i
$719$	22.7310	+	13.1237i	0.847722	+	0.489432i	0.859881	−	0.510494i	$-0.170537\pi$
$719$	22.7310	+	13.1237i	0.847722	+	0.489432i	−0.0121598	+	0.999926i	$0.503871\pi$
$720$		0			0
$721$			2.08200i			0.0775376i
$722$	−18.0208	+	6.02082i	−0.670665	+	0.224072i
$723$	−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
$727$	20.3524	−	5.45340i	0.754828	−	0.202256i	0.139170	−	0.990269i	$-0.455557\pi$
$727$	20.3524	−	5.45340i	0.754828	−	0.202256i	0.615659	+	0.788013i	$0.288890\pi$
$728$	5.18811	+	1.39015i	0.192284	+	0.0515224i
$729$			27.0000i			1.00000i
$730$		0			0
$731$	14.8990	+	25.8058i	0.551059	+	0.954462i
$732$	18.9282	+	5.07180i	0.699607	+	0.187459i
$733$	−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
$737$	−20.2307	−	5.42081i	−0.745208	−	0.199678i
$738$	1.34486	+	5.01910i	0.0495051	+	0.184756i
$739$	−38.4069	−	22.1742i	−1.41282	−	0.815692i	−0.417167	−	0.908830i	$-0.636977\pi$
$739$	−38.4069	−	22.1742i	−1.41282	−	0.815692i	−0.995653	+	0.0931373i	$0.970310\pi$
$740$		0			0
$741$	−38.0908	−	35.8481i	−1.39930	−	1.31691i
$742$	3.37117	+	3.37117i	0.123760	+	0.123760i
$743$	47.6132	−	12.7579i	1.74676	−	0.468043i	0.762831	−	0.646598i	$-0.223809\pi$
$743$	47.6132	−	12.7579i	1.74676	−	0.468043i	0.983930	+	0.178555i	$0.0571423\pi$
$744$	−0.953512	+	1.65153i	−0.0349574	+	0.0605481i
$745$		0			0
$746$	−17.9722	+	31.1288i	−0.658009	+	1.13970i
$747$	−13.5596	+	50.6050i	−0.496118	+	1.85154i
$748$	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	−0.993029	−	0.117867i	$-0.962394\pi$
$751$	−38.0227	+	21.9524i	−1.38747	+	0.801055i	−0.394439	+	0.918922i	$0.629061\pi$
$752$	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
$757$	0.645028	−	0.172835i	0.0234440	−	0.00628179i	−0.247078	−	0.968996i	$-0.579470\pi$
$757$	0.645028	−	0.172835i	0.0234440	−	0.00628179i	0.270522	+	0.962714i	$0.412804\pi$
$758$	−7.48503	−	27.9345i	−0.271869	−	1.01463i
$759$	−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	$0.550976\pi$
$762$	8.81160	+	32.8853i	0.319211	+	1.19131i
$763$		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	$-0.954546\pi$
$769$	−37.7552	+	21.7980i	−1.36149	+	0.786055i	−0.371665	+	0.928367i	$0.621213\pi$
$770$		0			0
$771$	−23.3939			−0.842510
$772$	−9.43879	+	9.43879i	−0.339710	+	0.339710i
$773$	−1.98036	+	7.39081i	−0.0712287	+	0.265829i	−0.992352	−	0.123443i	$-0.960607\pi$
$773$	−1.98036	+	7.39081i	−0.0712287	+	0.265829i	0.921123	+	0.389272i	$0.127273\pi$
$774$	15.8028	−	27.3712i	0.568018	−	0.983836i
$775$		0			0
$776$	7.22474	−	12.5136i	0.259353	−	0.449213i
$777$	14.1363	−	3.78780i	0.507136	−	0.135887i
$778$	−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
$782$	3.80385	+	14.1962i	0.136025	+	0.507653i
$783$		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	−0.352421	−	0.935842i	$-0.614642\pi$
$787$	16.3670	−	16.3670i	0.583420	−	0.583420i	0.935842	+	0.352421i	$0.114642\pi$
$788$	7.27513	+	1.94937i	0.259166	+	0.0694433i
$789$	28.3557	+	49.1135i	1.00949	+	1.74849i
$790$		0			0
$791$		−	20.0061i		−	0.711334i
$792$	−4.20030	−	1.12547i	−0.149251	−	0.0399917i
$793$	37.8564	−	10.1436i	1.34432	−	0.360210i
$794$	−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	−0.515163	−	0.857093i	$-0.672268\pi$
$797$	9.65309	−	9.65309i	0.341930	−	0.341930i	0.857093	+	0.515163i	$0.172268\pi$
$798$	−6.15771	−	9.95567i	−0.217981	−	0.352427i
$799$			19.5959i			0.693254i
$800$		0			0
$801$	35.5454	+	20.5222i	1.25594	+	0.725115i
$802$	−4.48288	+	16.7303i	−0.158296	+	0.590768i
$803$	−3.42178	−	12.7702i	−0.120752	−	0.450652i
$804$	30.6520	−	17.6969i	1.08101	−	0.624123i
$805$		0			0
$806$			3.81405i			0.134344i
$807$	−4.39230	+	16.3923i	−0.154616	+	0.577036i
$808$	−3.28621	+	12.2643i	−0.115608	+	0.431457i
$809$		−	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	−0.381087	−	0.924539i	$-0.624450\pi$
$811$	6.52270	−	3.76588i	0.229043	−	0.132238i	0.610131	+	0.792301i	$0.291117\pi$
$812$	−2.18689	−	8.16158i	−0.0767448	−	0.286415i
$813$	2.09406	−	7.81513i	0.0734418	−	0.274088i
$814$	−6.84072	−	3.94949i	−0.239767	−	0.138430i
$815$		0			0
$816$			6.92820i			0.242536i
$817$	−40.4472	−	21.7446i	−1.41507	−	0.760748i
$818$	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	0.886972	−	0.461822i	$-0.152804\pi$
$821$	1.24745	+	2.16064i	0.0435363	+	0.0754070i	−0.843436	+	0.537229i	$0.819471\pi$
$822$	−6.69213	+	1.79315i	−0.233415	+	0.0625433i
$823$	11.9872	+	3.21197i	0.417848	+	0.111962i	0.461616	−	0.887080i	$-0.347270\pi$
$823$	11.9872	+	3.21197i	0.417848	+	0.111962i	−0.0437682	+	0.999042i	$0.513936\pi$
$824$			1.89898i			0.0661541i
$825$		0			0
$826$	−1.89898	−	3.28913i	−0.0660739	−	0.114443i
$827$	−34.4269	−	9.22465i	−1.19714	−	0.320773i	−0.395436	−	0.918494i	$-0.629406\pi$
$827$	−34.4269	−	9.22465i	−1.19714	−	0.320773i	−0.801704	+	0.597721i	$0.796073\pi$
$828$	11.0227	−	11.0227i	0.383065	−	0.383065i
$829$	−41.5692			−1.44376			−0.721879	−	0.692019i	$-0.756721\pi$
$829$	−41.5692			−1.44376			−0.721879	+	0.692019i	$0.756721\pi$
$830$		0			0
$831$	41.3939	+	23.8988i	1.43594	+	0.829039i
$832$	4.73205	+	1.26795i	0.164054	+	0.0439582i
$833$	−4.24440	−	15.8403i	−0.147060	−	0.548835i
$834$	−35.8481	−	20.6969i	−1.24132	−	0.716676i
$835$		0			0
$836$	−1.44949	+	6.14966i	−0.0501317	+	0.212691i
$837$		0			0
$838$	−8.06400	+	2.16074i	−0.278566	+	0.0746416i
$839$	7.49245	−	12.9773i	0.258668	−	0.448026i	−0.707217	−	0.706996i	$-0.750050\pi$
$839$	7.49245	−	12.9773i	0.258668	−	0.448026i	0.965885	+	0.258970i	$0.0833831\pi$
$840$		0			0
$841$	−15.1969	+	26.3219i	−0.524032	+	0.907651i
$842$	2.48823	−	9.28618i	0.0857499	−	0.320023i
$843$	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
$852$	−8.19615	+	2.19615i	−0.280796	+	0.0752389i
$853$	7.83070	+	29.2246i	0.268118	+	1.00063i	0.960314	+	0.278921i	$0.0899767\pi$
$853$	7.83070	+	29.2246i	0.268118	+	1.00063i	−0.692196	+	0.721710i	$0.743357\pi$
$854$	8.77101			0.300138
$855$		0			0
$856$	−12.2474			−0.418609
$857$	10.0155	+	37.3784i	0.342123	+	1.27682i	0.895937	+	0.444181i	$0.146505\pi$
$857$	10.0155	+	37.3784i	0.342123	+	1.27682i	−0.553814	+	0.832640i	$0.686828\pi$
$858$	−16.8012	+	4.50187i	−0.573583	+	0.153691i
$859$	8.35847	−	4.82577i	0.285187	−	0.164653i	−0.350582	−	0.936532i	$-0.614016\pi$
$859$	8.35847	−	4.82577i	0.285187	−	0.164653i	0.635769	+	0.771879i	$0.280683\pi$
$860$		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	0.231518	−	0.972831i	$-0.425631\pi$
$863$	−21.7774	−	21.7774i	−0.741313	−	0.741313i	−0.972831	+	0.231518i	$0.925631\pi$
$864$		0			0
$865$		0			0
$866$	−19.3485			−0.657488
$867$	15.5885	−	15.5885i	0.529412	−	0.529412i
$868$	−0.220921	+	0.824487i	−0.00749854	+	0.0279849i
$869$	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
$877$	−4.64435	−	17.3329i	−0.156829	−	0.585292i	−0.998942	−	0.0459914i	$-0.985355\pi$
$877$	−4.64435	−	17.3329i	−0.156829	−	0.585292i	0.842113	−	0.539301i	$-0.181311\pi$
$878$	10.4522	+	2.80065i	0.352744	+	0.0945175i
$879$	−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
$883$	−19.2624	−	5.16133i	−0.648230	−	0.173693i	−0.0803014	−	0.996771i	$-0.525588\pi$
$883$	−19.2624	−	5.16133i	−0.648230	−	0.173693i	−0.567928	+	0.823078i	$0.692255\pi$
$884$	6.92820	+	12.0000i	0.233021	+	0.403604i
$885$		0			0
$886$			3.11416i			0.104622i
$887$	5.31752	+	1.42483i	0.178545	+	0.0478410i	0.346984	−	0.937871i	$-0.387206\pi$
$887$	5.31752	+	1.42483i	0.178545	+	0.0478410i	−0.168439	+	0.985712i	$0.553873\pi$
$888$	12.8936	−	3.45484i	0.432682	−	0.115937i
$889$	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
$893$	−15.8856	−	25.6836i	−0.531592	−	0.859469i
$894$		−	15.7980i		−	0.528363i
$895$		0			0
$896$	0.949490	+	0.548188i	0.0317202	+	0.0183137i
$897$	16.1384	−	60.2292i	0.538844	−	2.01099i
$898$	2.24144	+	8.36516i	0.0747978	+	0.279149i
$899$	5.19615	−	3.00000i	0.173301	−	0.100056i
$900$		0			0
$901$			12.2993i			0.409750i
$902$	0.649788	−	2.42504i	0.0216356	−	0.0807451i
$903$	7.32273	−	27.3288i	0.243685	−	0.909446i
$904$		−	18.2474i		−	0.606901i
$905$		0			0
$906$	18.0000	−	10.3923i	0.598010	−	0.345261i
$907$	4.85088	+	18.1037i	0.161071	+	0.601124i	0.998509	+	0.0545918i	$0.0173857\pi$
$907$	4.85088	+	18.1037i	0.161071	+	0.601124i	−0.837438	+	0.546532i	$0.815948\pi$
$908$	4.02477	−	15.0206i	0.133567	−	0.498477i
$909$	32.9876	+	19.0454i	1.09413	+	0.631696i
$910$		0			0
$911$		−	39.6622i		−	1.31407i	−0.753861	−	0.657034i	$-0.771811\pi$
$911$		−	39.6622i		−	1.31407i	0.753861	−	0.657034i	$-0.228189\pi$
$912$	−5.61642	−	9.08052i	−0.185978	−	0.300686i
$913$	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
$917$	−7.67518	+	2.05656i	−0.253457	+	0.0679135i
$918$		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
$922$	−15.6500	−	4.19340i	−0.515404	−	0.138102i
$923$	−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
$927$	5.50282	+	1.47448i	0.180736	+	0.0484282i
$928$	−1.99465	−	7.44414i	−0.0654776	−	0.244366i
$929$	−41.9103	−	24.1969i	−1.37503	−	0.793876i	−0.383477	−	0.923551i	$-0.625273\pi$
$929$	−41.9103	−	24.1969i	−1.37503	−	0.793876i	−0.991557	+	0.129675i	$0.958607\pi$
$930$		0			0
$931$	18.4041	+	17.3205i	0.603169	+	0.567657i
$932$	−2.44949	−	2.44949i	−0.0802357	−	0.0802357i
$933$	−61.0386	+	16.3553i	−1.99831	+	0.535447i
$934$	−16.5813	+	28.7196i	−0.542556	+	0.939735i
$935$		0			0
$936$	7.34847	−	12.7279i	0.240192	−	0.416025i
$937$	13.3414	−	49.7909i	0.435846	−	1.62660i	−0.303188	−	0.952931i	$-0.598051\pi$
$937$	13.3414	−	49.7909i	0.435846	−	1.62660i	0.739034	−	0.673668i	$-0.235282\pi$
$938$	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	−0.352716	−	0.935730i	$-0.614742\pi$
$941$	8.62883	−	4.98186i	0.281292	−	0.162404i	0.634008	+	0.773326i	$0.281409\pi$
$942$	−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
$947$	10.9282	−	2.92820i	0.355119	−	0.0951538i	−0.0768492	−	0.997043i	$-0.524486\pi$
$947$	10.9282	−	2.92820i	0.355119	−	0.0951538i	0.431968	+	0.901889i	$0.357819\pi$
$948$	3.18330	+	11.8802i	0.103389	+	0.385852i
$949$	44.6834			1.45048
$950$		0			0
$951$	37.3485			1.21111
$952$	0.802603	+	2.99536i	0.0260125	+	0.0970800i
$953$	7.33709	−	1.96597i	0.237672	−	0.0636840i	−0.138017	−	0.990430i	$-0.544073\pi$
$953$	7.33709	−	1.96597i	0.237672	−	0.0636840i	0.375689	+	0.926746i	$0.377406\pi$
$954$	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
$963$	−9.50962	+	35.4904i	−0.306443	+	1.14366i
$964$	−13.6814	+	23.6969i	−0.440649	+	0.763227i
$965$		0			0
$966$	6.97730	−	12.0850i	0.224491	−	0.388830i
$967$	−2.73205	+	0.732051i	−0.0878568	+	0.0235412i	−0.302480	−	0.953156i	$-0.597814\pi$
$967$	−2.73205	+	0.732051i	−0.0878568	+	0.0235412i	0.214623	+	0.976697i	$0.431148\pi$
$968$	−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	0.734854	−	0.678225i	$-0.237250\pi$
$971$	16.0454	+	9.26382i	0.514922	+	0.297290i	−0.219933	+	0.975515i	$0.570584\pi$
$972$	5.70577	+	21.2942i	0.183013	+	0.683013i
$973$	−17.8963	−	4.79531i	−0.573730	−	0.153730i
$974$	−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	−0.986108	−	0.166106i	$-0.946881\pi$
$977$	−25.6308	+	25.6308i	−0.820002	+	0.820002i	0.166106	+	0.986108i	$0.446881\pi$
$978$	31.2806	+	8.38161i	1.00024	+	0.268014i
$979$	−9.91555	−	17.1742i	−0.316902	−	0.548891i
$980$		0			0
$981$		0			0
$982$	19.6551	+	5.26657i	0.627220	+	0.168063i
$983$	−38.1491	+	10.2220i	−1.21677	+	0.326032i	−0.809414	−	0.587238i	$-0.800215\pi$
$983$	−38.1491	+	10.2220i	−1.21677	+	0.326032i	−0.407354	+	0.913270i	$0.633549\pi$
$984$	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
$988$	−18.8084	−	10.1115i	−0.598376	−	0.321690i
$989$		−	54.7423i		−	1.74071i
$990$		0			0
$991$	−41.0227	−	23.6845i	−1.30313	−	0.752362i	−0.322190	−	0.946675i	$-0.604419\pi$
$991$	−41.0227	−	23.6845i	−1.30313	−	0.752362i	−0.980940	+	0.194313i	$0.937752\pi$
$992$	−0.201501	+	0.752011i	−0.00639765	+	0.0238764i
$993$	−2.57880	−	9.62421i	−0.0818357	−	0.305415i
$994$	−3.28913	+	1.89898i	−0.104325	+	0.0602320i
$995$		0			0
$996$			42.7764i			1.35542i
$997$	−10.5861	+	39.5078i	−0.335264	+	1.25122i	0.568318	+	0.822809i	$0.307594\pi$
$997$	−10.5861	+	39.5078i	−0.335264	+	1.25122i	−0.903582	+	0.428414i	$0.859072\pi$
$998$	−5.49924	+	20.5235i	−0.174076	+	0.649659i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.a.27.2	✓	8	5.4	even	2
190.2.m.a.103.2	yes	8	5.2	odd	4
190.2.m.a.107.2	yes	8	95.69	odd	6
190.2.m.a.183.2	yes	8	95.12	even	12
950.2.q.a.107.1		8	19.12	odd	6	inner
950.2.q.a.293.1		8	5.3	odd	4	inner
950.2.q.a.407.1		8	1.1	even	1	trivial
950.2.q.a.943.1		8	95.88	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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