LMFDB - Embedded newform 1950.2.bc.a.901.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.a.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.232051 + 0.133975i) q^{11} -1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(4.96410 - 2.86603i) q^{19} -3.00000i q^{21} +(-0.133975 - 0.232051i) q^{22} +(1.73205 - 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-2.59808 - 1.50000i) q^{28} +(-0.732051 + 1.26795i) q^{29} +4.92820i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.232051 + 0.133975i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(5.13397 + 2.96410i) q^{37} -5.73205 q^{38} +(3.46410 + 1.00000i) q^{39} +(-3.46410 - 2.00000i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(3.00000 + 5.19615i) q^{43} +0.267949i q^{44} +(-3.00000 + 1.73205i) q^{46} +6.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(2.59808 - 2.50000i) q^{52} +0.267949 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} +5.73205i q^{57} +(1.26795 - 0.732051i) q^{58} +(-9.92820 + 5.73205i) q^{59} +(0.267949 + 0.464102i) q^{61} +(2.46410 - 4.26795i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +0.267949 q^{66} +(-1.26795 - 0.732051i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(1.73205 + 3.00000i) q^{69} +(-11.1962 + 6.46410i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.92820i q^{73} +(-2.96410 - 5.13397i) q^{74} +(4.96410 + 2.86603i) q^{76} -0.803848 q^{77} +(-2.50000 - 2.59808i) q^{78} +3.07180 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} -9.46410i q^{83} +(2.59808 - 1.50000i) q^{84} -6.00000i q^{86} +(-0.732051 - 1.26795i) q^{87} +(0.133975 - 0.232051i) q^{88} +(-12.2321 - 7.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +3.46410 q^{92} +(-4.26795 - 2.46410i) q^{93} +(3.23205 - 5.59808i) q^{94} +1.00000i q^{96} +(-7.26795 + 4.19615i) q^{97} +(-1.73205 + 1.00000i) q^{98} -0.267949i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} - 4 q^{22} - 4 q^{26} + 4 q^{27} + 4 q^{29} + 6 q^{33} + 2 q^{36} + 24 q^{37} - 16 q^{38} - 6 q^{42} + 12 q^{43} - 12 q^{46} - 2 q^{48} + 4 q^{49} - 16 q^{51} + 8 q^{53} + 6 q^{56} + 12 q^{58} - 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 8 q^{66} - 12 q^{67} - 8 q^{68} - 24 q^{71} + 2 q^{74} + 6 q^{76} - 24 q^{77} - 10 q^{78} + 40 q^{79} - 2 q^{81} + 8 q^{82} + 4 q^{87} + 4 q^{88} - 42 q^{89} + 30 q^{91} - 24 q^{93} + 6 q^{94} - 36 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 - 4 * q^22 - 4 * q^26 + 4 * q^27 + 4 * q^29 + 6 * q^33 + 2 * q^36 + 24 * q^37 - 16 * q^38 - 6 * q^42 + 12 * q^43 - 12 * q^46 - 2 * q^48 + 4 * q^49 - 16 * q^51 + 8 * q^53 + 6 * q^56 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 8 * q^66 - 12 * q^67 - 8 * q^68 - 24 * q^71 + 2 * q^74 + 6 * q^76 - 24 * q^77 - 10 * q^78 + 40 * q^79 - 2 * q^81 + 8 * q^82 + 4 * q^87 + 4 * q^88 - 42 * q^89 + 30 * q^91 - 24 * q^93 + 6 * q^94 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.902867	−	0.429919i	$-0.858542\pi$
$7$	−2.59808	+	1.50000i	−0.981981	+	0.566947i	−0.0791130	+	0.996866i	$0.525209\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	0.534575	−	0.845121i	$-0.320472\pi$
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	−0.464609	+	0.885516i	$0.653805\pi$
$12$	−1.00000			−0.288675
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$14$	3.00000			0.801784
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$			1.00000i			0.235702i
$19$	4.96410	−	2.86603i	1.13884	−	0.657511i	0.192699	−	0.981258i	$-0.438276\pi$
$19$	4.96410	−	2.86603i	1.13884	−	0.657511i	0.946144	+	0.323747i	$0.104943\pi$
$20$		0			0
$21$		−	3.00000i		−	0.654654i
$22$	−0.133975	−	0.232051i	−0.0285635	−	0.0494734i
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	−0.626994	−	0.779024i	$-0.715715\pi$
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	0.988152	+	0.153481i	$0.0490483\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	−2.59808	−	1.50000i	−0.490990	−	0.283473i
$29$	−0.732051	+	1.26795i	−0.135938	+	0.235452i	−0.925956	−	0.377633i	$-0.876738\pi$
$29$	−0.732051	+	1.26795i	−0.135938	+	0.235452i	0.790017	+	0.613085i	$0.210072\pi$
$30$		0			0
$31$			4.92820i			0.885131i	0.896736	+	0.442566i	$0.145932\pi$
$31$			4.92820i			0.885131i	−0.896736	+	0.442566i	$0.854068\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.232051	+	0.133975i	−0.0403949	+	0.0233220i
$34$		−	4.00000i		−	0.685994i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	5.13397	+	2.96410i	0.844020	+	0.487295i	0.858629	−	0.512598i	$-0.171317\pi$
$37$	5.13397	+	2.96410i	0.844020	+	0.487295i	−0.0146085	+	0.999893i	$0.504650\pi$
$38$	−5.73205			−0.929861
$39$	3.46410	+	1.00000i	0.554700	+	0.160128i
$40$		0			0
$41$	−3.46410	−	2.00000i	−0.541002	−	0.312348i	0.204483	−	0.978870i	$-0.434449\pi$
$41$	−3.46410	−	2.00000i	−0.541002	−	0.312348i	−0.745485	+	0.666523i	$0.767782\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$			0.267949i			0.0403949i
$45$		0			0
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$			6.46410i			0.942886i	0.881897	+	0.471443i	$0.156267\pi$
$47$			6.46410i			0.942886i	−0.881897	+	0.471443i	$0.843733\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	1.00000	−	1.73205i	0.142857	−	0.247436i
$50$		0			0
$51$	−4.00000			−0.560112
$52$	2.59808	−	2.50000i	0.360288	−	0.346688i
$53$	0.267949			0.0368057			0.0184028	−	0.999831i	$-0.494142\pi$
$53$	0.267949			0.0368057			0.0184028	+	0.999831i	$0.494142\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	1.50000	+	2.59808i	0.200446	+	0.347183i
$57$			5.73205i			0.759229i
$58$	1.26795	−	0.732051i	0.166490	−	0.0961230i
$59$	−9.92820	+	5.73205i	−1.29254	+	0.746249i	−0.979104	−	0.203359i	$-0.934814\pi$
$59$	−9.92820	+	5.73205i	−1.29254	+	0.746249i	−0.313438	+	0.949609i	$0.601481\pi$
$60$		0			0
$61$	0.267949	+	0.464102i	0.0343074	+	0.0594221i	0.882669	−	0.469995i	$-0.155744\pi$
$61$	0.267949	+	0.464102i	0.0343074	+	0.0594221i	−0.848362	+	0.529417i	$0.822411\pi$
$62$	2.46410	−	4.26795i	0.312941	−	0.542030i
$63$	2.59808	+	1.50000i	0.327327	+	0.188982i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.267949			0.0329823
$67$	−1.26795	−	0.732051i	−0.154905	−	0.0894342i	0.420544	−	0.907272i	$-0.361839\pi$
$67$	−1.26795	−	0.732051i	−0.154905	−	0.0894342i	−0.575449	+	0.817838i	$0.695173\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	1.73205	+	3.00000i	0.208514	+	0.361158i
$70$		0			0
$71$	−11.1962	+	6.46410i	−1.32874	+	0.767148i	−0.985105	−	0.171956i	$-0.944991\pi$
$71$	−11.1962	+	6.46410i	−1.32874	+	0.767148i	−0.343634	+	0.939104i	$0.611658\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			6.92820i			0.810885i	0.914121	+	0.405442i	$0.132883\pi$
$73$			6.92820i			0.810885i	−0.914121	+	0.405442i	$0.867117\pi$
$74$	−2.96410	−	5.13397i	−0.344570	−	0.596812i
$75$		0			0
$76$	4.96410	+	2.86603i	0.569422	+	0.328756i
$77$	−0.803848			−0.0916069
$78$	−2.50000	−	2.59808i	−0.283069	−	0.294174i
$79$	3.07180			0.345604			0.172802	−	0.984957i	$-0.444718\pi$
$79$	3.07180			0.345604			0.172802	+	0.984957i	$0.444718\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.00000	+	3.46410i	0.220863	+	0.382546i
$83$		−	9.46410i		−	1.03882i	−0.854525	−	0.519410i	$-0.826152\pi$
$83$		−	9.46410i		−	1.03882i	0.854525	−	0.519410i	$-0.173848\pi$
$84$	2.59808	−	1.50000i	0.283473	−	0.163663i
$85$		0			0
$86$		−	6.00000i		−	0.646997i
$87$	−0.732051	−	1.26795i	−0.0784841	−	0.135938i
$88$	0.133975	−	0.232051i	0.0142817	−	0.0247367i
$89$	−12.2321	−	7.06218i	−1.29659	−	0.748589i	−0.316780	−	0.948499i	$-0.602602\pi$
$89$	−12.2321	−	7.06218i	−1.29659	−	0.748589i	−0.979814	+	0.199910i	$0.935935\pi$
$90$		0			0
$91$	7.50000	+	7.79423i	0.786214	+	0.817057i
$92$	3.46410			0.361158
$93$	−4.26795	−	2.46410i	−0.442566	−	0.255515i
$94$	3.23205	−	5.59808i	0.333361	−	0.577397i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−7.26795	+	4.19615i	−0.737948	+	0.426055i	−0.821323	−	0.570464i	$-0.806764\pi$
$97$	−7.26795	+	4.19615i	−0.737948	+	0.426055i	0.0833745	+	0.996518i	$0.473430\pi$
$98$	−1.73205	+	1.00000i	−0.174964	+	0.101015i
$99$		−	0.267949i		−	0.0269299i
$100$		0			0
$101$	−6.19615	+	10.7321i	−0.616540	+	1.06788i	0.373572	+	0.927601i	$0.378133\pi$
$101$	−6.19615	+	10.7321i	−0.616540	+	1.06788i	−0.990112	+	0.140278i	$0.955200\pi$
$102$	3.46410	+	2.00000i	0.342997	+	0.198030i
$103$	11.5885			1.14184			0.570922	−	0.821004i	$-0.306586\pi$
$103$	11.5885			1.14184			0.570922	+	0.821004i	$0.306586\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$		0			0
$106$	−0.232051	−	0.133975i	−0.0225388	−	0.0130128i
$107$	−6.46410	+	11.1962i	−0.624908	+	1.08237i	0.363650	+	0.931536i	$0.381530\pi$
$107$	−6.46410	+	11.1962i	−0.624908	+	1.08237i	−0.988559	+	0.150837i	$0.951803\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	10.3923i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$109$		−	10.3923i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$110$		0			0
$111$	−5.13397	+	2.96410i	−0.487295	+	0.281340i
$112$		−	3.00000i		−	0.283473i
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	−0.997102	−	0.0760733i	$-0.975762\pi$
$113$	−6.00000	−	10.3923i	−0.564433	−	0.977626i	0.432670	−	0.901553i	$-0.357572\pi$
$114$	2.86603	−	4.96410i	0.268428	−	0.464931i
$115$		0			0
$116$	−1.46410			−0.135938
$117$	−2.59808	+	2.50000i	−0.240192	+	0.231125i
$118$	11.4641			1.05536
$119$	−10.3923	−	6.00000i	−0.952661	−	0.550019i
$120$		0			0
$121$	−5.46410	−	9.46410i	−0.496737	−	0.860373i
$122$		−	0.535898i		−	0.0485180i
$123$	3.46410	−	2.00000i	0.312348	−	0.180334i
$124$	−4.26795	+	2.46410i	−0.383273	+	0.221283i
$125$		0			0
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	−6.33013	+	10.9641i	−0.561708	+	0.972907i	0.435640	+	0.900121i	$0.356522\pi$
$127$	−6.33013	+	10.9641i	−0.561708	+	0.972907i	−0.997348	+	0.0727855i	$0.976811\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−6.00000			−0.528271
$130$		0			0
$131$	14.3205			1.25119			0.625594	−	0.780149i	$-0.284857\pi$
$131$	14.3205			1.25119			0.625594	+	0.780149i	$0.284857\pi$
$132$	−0.232051	−	0.133975i	−0.0201974	−	0.0116610i
$133$	−8.59808	+	14.8923i	−0.745548	+	1.29133i
$134$	0.732051	+	1.26795i	0.0632396	+	0.109534i
$135$		0			0
$136$	3.46410	−	2.00000i	0.297044	−	0.171499i
$137$	−11.6603	+	6.73205i	−0.996203	+	0.575158i	−0.907123	−	0.420867i	$-0.861726\pi$
$137$	−11.6603	+	6.73205i	−0.996203	+	0.575158i	−0.0890802	+	0.996024i	$0.528393\pi$
$138$		−	3.46410i		−	0.294884i
$139$	9.89230	+	17.1340i	0.839054	+	1.45328i	0.890686	+	0.454619i	$0.150224\pi$
$139$	9.89230	+	17.1340i	0.839054	+	1.45328i	−0.0516319	+	0.998666i	$0.516442\pi$
$140$		0			0
$141$	−5.59808	−	3.23205i	−0.471443	−	0.272188i
$142$	12.9282			1.08491
$143$	0.267949	−	0.928203i	0.0224070	−	0.0776203i
$144$	1.00000			0.0833333
$145$		0			0
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$	1.00000	+	1.73205i	0.0824786	+	0.142857i
$148$			5.92820i			0.487295i
$149$	16.2679	−	9.39230i	1.33272	−	0.769448i	0.347006	−	0.937863i	$-0.387198\pi$
$149$	16.2679	−	9.39230i	1.33272	−	0.769448i	0.985716	+	0.168415i	$0.0538649\pi$
$150$		0			0
$151$			22.7846i			1.85419i	0.374832	+	0.927093i	$0.377700\pi$
$151$			22.7846i			1.85419i	−0.374832	+	0.927093i	$0.622300\pi$
$152$	−2.86603	−	4.96410i	−0.232465	−	0.402642i
$153$	2.00000	−	3.46410i	0.161690	−	0.280056i
$154$	0.696152	+	0.401924i	0.0560976	+	0.0323879i
$155$		0			0
$156$	0.866025	+	3.50000i	0.0693375	+	0.280224i
$157$	−21.1962			−1.69164			−0.845819	−	0.533471i	$-0.820887\pi$
$157$	−21.1962			−1.69164			−0.845819	+	0.533471i	$0.820887\pi$
$158$	−2.66025	−	1.53590i	−0.211638	−	0.122190i
$159$	−0.133975	+	0.232051i	−0.0106249	+	0.0184028i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	2.53590	−	1.46410i	0.198627	−	0.114677i	−0.397388	−	0.917651i	$-0.630083\pi$
$163$	2.53590	−	1.46410i	0.198627	−	0.114677i	0.596015	+	0.802973i	$0.296750\pi$
$164$		−	4.00000i		−	0.312348i
$165$		0			0
$166$	−4.73205	+	8.19615i	−0.367278	+	0.636145i
$167$	0.401924	+	0.232051i	0.0311018	+	0.0179566i	0.515470	−	0.856907i	$-0.327617\pi$
$167$	0.401924	+	0.232051i	0.0311018	+	0.0179566i	−0.484368	+	0.874864i	$0.660951\pi$
$168$	−3.00000			−0.231455
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$		0			0
$171$	−4.96410	−	2.86603i	−0.379614	−	0.219170i
$172$	−3.00000	+	5.19615i	−0.228748	+	0.396203i
$173$	−1.06218	−	1.83975i	−0.0807559	−	0.139873i	0.822819	−	0.568304i	$-0.192400\pi$
$173$	−1.06218	−	1.83975i	−0.0807559	−	0.139873i	−0.903575	+	0.428430i	$0.859067\pi$
$174$			1.46410i			0.110993i
$175$		0			0
$176$	−0.232051	+	0.133975i	−0.0174915	+	0.0100987i
$177$		−	11.4641i		−	0.861695i
$178$	7.06218	+	12.2321i	0.529333	+	0.916831i
$179$	−4.53590	+	7.85641i	−0.339029	+	0.587215i	−0.984250	−	0.176780i	$-0.943432\pi$
$179$	−4.53590	+	7.85641i	−0.339029	+	0.587215i	0.645221	+	0.763996i	$0.276765\pi$
$180$		0			0
$181$	16.9282			1.25826			0.629132	−	0.777299i	$-0.283411\pi$
$181$	16.9282			1.25826			0.629132	+	0.777299i	$0.283411\pi$
$182$	−2.59808	−	10.5000i	−0.192582	−	0.778312i
$183$	−0.535898			−0.0396147
$184$	−3.00000	−	1.73205i	−0.221163	−	0.127688i
$185$		0			0
$186$	2.46410	+	4.26795i	0.180677	+	0.312941i
$187$			1.07180i			0.0783775i
$188$	−5.59808	+	3.23205i	−0.408282	+	0.235722i
$189$	−2.59808	+	1.50000i	−0.188982	+	0.109109i
$190$		0			0
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	0.988222	+	0.153024i	$0.0489012\pi$
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	−0.361588	+	0.932338i	$0.617765\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	8.53590	+	4.92820i	0.614427	+	0.354740i	0.774696	−	0.632334i	$-0.217903\pi$
$193$	8.53590	+	4.92820i	0.614427	+	0.354740i	−0.160269	+	0.987073i	$0.551236\pi$
$194$	8.39230			0.602532
$195$		0			0
$196$	2.00000			0.142857
$197$	9.86603	+	5.69615i	0.702925	+	0.405834i	0.808436	−	0.588584i	$-0.200314\pi$
$197$	9.86603	+	5.69615i	0.702925	+	0.405834i	−0.105511	+	0.994418i	$0.533648\pi$
$198$	−0.133975	+	0.232051i	−0.00952116	+	0.0164911i
$199$	12.4641	+	21.5885i	0.883557	+	1.53037i	0.847359	+	0.531021i	$0.178191\pi$
$199$	12.4641	+	21.5885i	0.883557	+	1.53037i	0.0361978	+	0.999345i	$0.488475\pi$
$200$		0			0
$201$	1.26795	−	0.732051i	0.0894342	−	0.0516349i
$202$	10.7321	−	6.19615i	0.755104	−	0.435960i
$203$		−	4.39230i		−	0.308279i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$		0			0
$206$	−10.0359	−	5.79423i	−0.699234	−	0.403703i
$207$	−3.46410			−0.240772
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	1.53590			0.106240
$210$		0			0
$211$	4.03590	−	6.99038i	0.277843	−	0.481238i	−0.693006	−	0.720932i	$-0.743714\pi$
$211$	4.03590	−	6.99038i	0.277843	−	0.481238i	0.970848	+	0.239694i	$0.0770473\pi$
$212$	0.133975	+	0.232051i	0.00920141	+	0.0159373i
$213$		−	12.9282i		−	0.885826i
$214$	11.1962	−	6.46410i	0.765353	−	0.441877i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−7.39230	−	12.8038i	−0.501822	−	0.869182i
$218$	−5.19615	+	9.00000i	−0.351928	+	0.609557i
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$		0			0
$221$	10.3923	−	10.0000i	0.699062	−	0.672673i
$222$	5.92820			0.397875
$223$	16.3301	+	9.42820i	1.09355	+	0.631359i	0.934518	−	0.355915i	$-0.115831\pi$
$223$	16.3301	+	9.42820i	1.09355	+	0.631359i	0.159028	+	0.987274i	$0.449164\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$			12.0000i			0.798228i
$227$	−5.66025	+	3.26795i	−0.375684	+	0.216901i	−0.675939	−	0.736958i	$-0.736262\pi$
$227$	−5.66025	+	3.26795i	−0.375684	+	0.216901i	0.300255	+	0.953859i	$0.402928\pi$
$228$	−4.96410	+	2.86603i	−0.328756	+	0.189807i
$229$			4.53590i			0.299741i	0.988706	+	0.149870i	$0.0478856\pi$
$229$			4.53590i			0.299741i	−0.988706	+	0.149870i	$0.952114\pi$
$230$		0			0
$231$	0.401924	−	0.696152i	0.0264446	−	0.0458035i
$232$	1.26795	+	0.732051i	0.0832449	+	0.0480615i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$	−9.92820	−	5.73205i	−0.646271	−	0.373125i
$237$	−1.53590	+	2.66025i	−0.0997673	+	0.172802i
$238$	6.00000	+	10.3923i	0.388922	+	0.673633i
$239$		−	3.46410i		−	0.224074i	−0.993704	−	0.112037i	$-0.964262\pi$
$239$		−	3.46410i		−	0.224074i	0.993704	−	0.112037i	$-0.0357375\pi$
$240$		0			0
$241$	−21.8205	+	12.5981i	−1.40558	+	0.811513i	−0.994958	−	0.100291i	$-0.968023\pi$
$241$	−21.8205	+	12.5981i	−1.40558	+	0.811513i	−0.410624	+	0.911805i	$0.634689\pi$
$242$			10.9282i			0.702492i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.267949	+	0.464102i	−0.0171537	+	0.0297111i
$245$		0			0
$246$	−4.00000			−0.255031
$247$	−14.3301	−	14.8923i	−0.911804	−	0.947575i
$248$	4.92820			0.312941
$249$	8.19615	+	4.73205i	0.519410	+	0.299882i
$250$		0			0
$251$	−9.76795	−	16.9186i	−0.616547	−	1.06789i	−0.990111	−	0.140287i	$-0.955198\pi$
$251$	−9.76795	−	16.9186i	−0.616547	−	1.06789i	0.373563	−	0.927605i	$-0.378136\pi$
$252$			3.00000i			0.188982i
$253$	0.803848	−	0.464102i	0.0505375	−	0.0291778i
$254$	10.9641	−	6.33013i	0.687949	−	0.397187i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.26795	−	12.5885i	0.453362	−	0.785246i	−0.545230	−	0.838286i	$-0.683558\pi$
$257$	7.26795	−	12.5885i	0.453362	−	0.785246i	0.998592	+	0.0530400i	$0.0168911\pi$
$258$	5.19615	+	3.00000i	0.323498	+	0.186772i
$259$	−17.7846			−1.10508
$260$		0			0
$261$	1.46410			0.0906256
$262$	−12.4019	−	7.16025i	−0.766193	−	0.442362i
$263$	−12.2583	+	21.2321i	−0.755881	+	1.30922i	0.189054	+	0.981967i	$0.439458\pi$
$263$	−12.2583	+	21.2321i	−0.755881	+	1.30922i	−0.944935	+	0.327258i	$0.893875\pi$
$264$	0.133975	+	0.232051i	0.00824557	+	0.0142817i
$265$		0			0
$266$	14.8923	−	8.59808i	0.913106	−	0.527182i
$267$	12.2321	−	7.06218i	0.748589	−	0.432198i
$268$		−	1.46410i		−	0.0894342i
$269$	8.53590	+	14.7846i	0.520443	+	0.901434i	0.999717	+	0.0237685i	$0.00756648\pi$
$269$	8.53590	+	14.7846i	0.520443	+	0.901434i	−0.479275	+	0.877665i	$0.659100\pi$
$270$		0			0
$271$	21.1244	+	12.1962i	1.28321	+	0.740863i	0.977434	−	0.211239i	$-0.0677499\pi$
$271$	21.1244	+	12.1962i	1.28321	+	0.740863i	0.305779	+	0.952103i	$0.401083\pi$
$272$	−4.00000			−0.242536
$273$	−10.5000	+	2.59808i	−0.635489	+	0.157243i
$274$	13.4641			0.813396
$275$		0			0
$276$	−1.73205	+	3.00000i	−0.104257	+	0.180579i
$277$	5.79423	+	10.0359i	0.348141	+	0.602999i	0.985919	−	0.167222i	$-0.0534796\pi$
$277$	5.79423	+	10.0359i	0.348141	+	0.602999i	−0.637778	+	0.770220i	$0.720146\pi$
$278$		−	19.7846i		−	1.18660i
$279$	4.26795	−	2.46410i	0.255515	−	0.147522i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$	3.23205	+	5.59808i	0.192466	+	0.333361i
$283$	−3.19615	+	5.53590i	−0.189992	+	0.329075i	−0.945247	−	0.326355i	$-0.894179\pi$
$283$	−3.19615	+	5.53590i	−0.189992	+	0.329075i	0.755256	+	0.655430i	$0.227513\pi$
$284$	−11.1962	−	6.46410i	−0.664369	−	0.383574i
$285$		0			0
$286$	−0.696152	+	0.669873i	−0.0411644	+	0.0396104i
$287$	12.0000			0.708338
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$		−	8.39230i		−	0.491966i
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	−25.3301	+	14.6244i	−1.47980	+	0.854364i	−0.999738	−	0.0228698i	$-0.992720\pi$
$293$	−25.3301	+	14.6244i	−1.47980	+	0.854364i	−0.480063	+	0.877234i	$0.659386\pi$
$294$		−	2.00000i		−	0.116642i
$295$		0			0
$296$	2.96410	−	5.13397i	0.172285	−	0.298406i
$297$	0.232051	+	0.133975i	0.0134650	+	0.00777399i
$298$	−18.7846			−1.08816
$299$	−12.0000	−	3.46410i	−0.693978	−	0.200334i
$300$		0			0
$301$	−15.5885	−	9.00000i	−0.898504	−	0.518751i
$302$	11.3923	−	19.7321i	0.655553	−	1.13545i
$303$	−6.19615	−	10.7321i	−0.355960	−	0.616540i
$304$			5.73205i			0.328756i
$305$		0			0
$306$	−3.46410	+	2.00000i	−0.198030	+	0.114332i
$307$		−	28.2487i		−	1.61224i	−0.591753	−	0.806120i	$-0.701564\pi$
$307$		−	28.2487i		−	1.61224i	0.591753	−	0.806120i	$-0.298436\pi$
$308$	−0.401924	−	0.696152i	−0.0229017	−	0.0396670i
$309$	−5.79423	+	10.0359i	−0.329622	+	0.570922i
$310$		0			0
$311$	18.9282			1.07332			0.536660	−	0.843799i	$-0.319686\pi$
$311$	18.9282			1.07332			0.536660	+	0.843799i	$0.319686\pi$
$312$	1.00000	−	3.46410i	0.0566139	−	0.196116i
$313$	33.3205			1.88339			0.941693	−	0.336473i	$-0.109234\pi$
$313$	33.3205			1.88339			0.941693	+	0.336473i	$0.109234\pi$
$314$	18.3564	+	10.5981i	1.03591	+	0.598084i
$315$		0			0
$316$	1.53590	+	2.66025i	0.0864010	+	0.149651i
$317$			30.4641i			1.71103i	0.517774	+	0.855517i	$0.326761\pi$
$317$			30.4641i			1.71103i	−0.517774	+	0.855517i	$0.673239\pi$
$318$	0.232051	−	0.133975i	0.0130128	−	0.00751292i
$319$	−0.339746	+	0.196152i	−0.0190221	+	0.0109824i
$320$		0			0
$321$	−6.46410	−	11.1962i	−0.360791	−	0.624908i
$322$	5.19615	−	9.00000i	0.289570	−	0.501550i
$323$	19.8564	+	11.4641i	1.10484	+	0.637880i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−2.92820			−0.162178
$327$	9.00000	+	5.19615i	0.497701	+	0.287348i
$328$	−2.00000	+	3.46410i	−0.110432	+	0.191273i
$329$	−9.69615	−	16.7942i	−0.534566	−	0.925896i
$330$		0			0
$331$	12.4641	−	7.19615i	0.685089	−	0.395536i	−0.116681	−	0.993169i	$-0.537225\pi$
$331$	12.4641	−	7.19615i	0.685089	−	0.395536i	0.801770	+	0.597633i	$0.203892\pi$
$332$	8.19615	−	4.73205i	0.449822	−	0.259705i
$333$		−	5.92820i		−	0.324864i
$334$	−0.232051	−	0.401924i	−0.0126973	−	0.0219923i
$335$		0			0
$336$	2.59808	+	1.50000i	0.141737	+	0.0818317i
$337$	26.3923			1.43768			0.718840	−	0.695175i	$-0.244673\pi$
$337$	26.3923			1.43768			0.718840	+	0.695175i	$0.244673\pi$
$338$	12.9904	+	0.500000i	0.706584	+	0.0271964i
$339$	12.0000			0.651751
$340$		0			0
$341$	−0.660254	+	1.14359i	−0.0357548	+	0.0619291i
$342$	2.86603	+	4.96410i	0.154977	+	0.268428i
$343$		−	15.0000i		−	0.809924i
$344$	5.19615	−	3.00000i	0.280158	−	0.161749i
$345$		0			0
$346$			2.12436i			0.114206i
$347$	2.19615	+	3.80385i	0.117896	+	0.204201i	0.918934	−	0.394412i	$-0.129052\pi$
$347$	2.19615	+	3.80385i	0.117896	+	0.204201i	−0.801038	+	0.598614i	$0.795719\pi$
$348$	0.732051	−	1.26795i	0.0392420	−	0.0679692i
$349$	−9.12436	−	5.26795i	−0.488416	−	0.281987i	0.235501	−	0.971874i	$-0.424327\pi$
$349$	−9.12436	−	5.26795i	−0.488416	−	0.281987i	−0.723917	+	0.689887i	$0.757660\pi$
$350$		0			0
$351$	−0.866025	−	3.50000i	−0.0462250	−	0.186816i
$352$	0.267949			0.0142817
$353$	−6.58846	−	3.80385i	−0.350668	−	0.202458i	0.314311	−	0.949320i	$-0.398226\pi$
$353$	−6.58846	−	3.80385i	−0.350668	−	0.202458i	−0.664980	+	0.746862i	$0.731560\pi$
$354$	−5.73205	+	9.92820i	−0.304655	+	0.527678i
$355$		0			0
$356$		−	14.1244i		−	0.748589i
$357$	10.3923	−	6.00000i	0.550019	−	0.317554i
$358$	7.85641	−	4.53590i	0.415224	−	0.239730i
$359$		−	0.928203i		−	0.0489887i	−0.999700	−	0.0244943i	$-0.992202\pi$
$359$		−	0.928203i		−	0.0489887i	0.999700	−	0.0244943i	$-0.00779757\pi$
$360$		0			0
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	−14.6603	−	8.46410i	−0.770526	−	0.444863i
$363$	10.9282			0.573582
$364$	−3.00000	+	10.3923i	−0.157243	+	0.544705i
$365$		0			0
$366$	0.464102	+	0.267949i	0.0242590	+	0.0140059i
$367$	10.6603	−	18.4641i	0.556461	−	0.963818i	−0.441328	−	0.897346i	$-0.645492\pi$
$367$	10.6603	−	18.4641i	0.556461	−	0.963818i	0.997788	−	0.0664722i	$-0.0211744\pi$
$368$	1.73205	+	3.00000i	0.0902894	+	0.156386i
$369$			4.00000i			0.208232i
$370$		0			0
$371$	−0.696152	+	0.401924i	−0.0361424	+	0.0208668i
$372$		−	4.92820i		−	0.255515i
$373$	4.53590	+	7.85641i	0.234860	+	0.406789i	0.959232	−	0.282620i	$-0.0912035\pi$
$373$	4.53590	+	7.85641i	0.234860	+	0.406789i	−0.724372	+	0.689409i	$0.757870\pi$
$374$	0.535898	−	0.928203i	0.0277106	−	0.0479962i
$375$		0			0
$376$	6.46410			0.333361
$377$	5.07180	+	1.46410i	0.261211	+	0.0754051i
$378$	3.00000			0.154303
$379$	−8.42820	−	4.86603i	−0.432928	−	0.249951i	0.267665	−	0.963512i	$-0.413748\pi$
$379$	−8.42820	−	4.86603i	−0.432928	−	0.249951i	−0.700593	+	0.713561i	$0.747081\pi$
$380$		0			0
$381$	−6.33013	−	10.9641i	−0.324302	−	0.561708i
$382$		−	17.3205i		−	0.886194i
$383$	−4.14359	+	2.39230i	−0.211728	+	0.122241i	−0.602114	−	0.798410i	$-0.705675\pi$
$383$	−4.14359	+	2.39230i	−0.211728	+	0.122241i	0.390386	+	0.920651i	$0.372341\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−4.92820	−	8.53590i	−0.250839	−	0.434466i
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	−7.26795	−	4.19615i	−0.368974	−	0.213027i
$389$	17.8564			0.905356			0.452678	−	0.891674i	$-0.350469\pi$
$389$	17.8564			0.905356			0.452678	+	0.891674i	$0.350469\pi$
$390$		0			0
$391$	13.8564			0.700749
$392$	−1.73205	−	1.00000i	−0.0874818	−	0.0505076i
$393$	−7.16025	+	12.4019i	−0.361187	+	0.625594i
$394$	−5.69615	−	9.86603i	−0.286968	−	0.497043i
$395$		0			0
$396$	0.232051	−	0.133975i	0.0116610	−	0.00673248i
$397$	5.13397	−	2.96410i	0.257667	−	0.148764i	−0.365603	−	0.930771i	$-0.619137\pi$
$397$	5.13397	−	2.96410i	0.257667	−	0.148764i	0.623270	+	0.782007i	$0.285804\pi$
$398$		−	24.9282i		−	1.24954i
$399$	−8.59808	−	14.8923i	−0.430442	−	0.745548i
$400$		0			0
$401$	−19.1603	−	11.0622i	−0.956817	−	0.552419i	−0.0616254	−	0.998099i	$-0.519628\pi$
$401$	−19.1603	−	11.0622i	−0.956817	−	0.552419i	−0.895192	+	0.445681i	$0.852962\pi$
$402$	−1.46410			−0.0730228
$403$	17.2487	−	4.26795i	0.859220	−	0.212602i
$404$	−12.3923			−0.616540
$405$		0			0
$406$	−2.19615	+	3.80385i	−0.108993	+	0.188782i
$407$	0.794229	+	1.37564i	0.0393685	+	0.0681882i
$408$			4.00000i			0.198030i
$409$	−33.8205	+	19.5263i	−1.67232	+	0.965512i	−0.705980	+	0.708232i	$0.749493\pi$
$409$	−33.8205	+	19.5263i	−1.67232	+	0.965512i	−0.966337	+	0.257280i	$0.917174\pi$
$410$		0			0
$411$		−	13.4641i		−	0.664135i
$412$	5.79423	+	10.0359i	0.285461	+	0.494433i
$413$	17.1962	−	29.7846i	0.846167	−	1.46560i
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$		0			0
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$	−19.7846			−0.968857
$418$	−1.33013	−	0.767949i	−0.0650586	−	0.0375616i
$419$	−4.92820	+	8.53590i	−0.240758	+	0.417006i	−0.960931	−	0.276790i	$-0.910730\pi$
$419$	−4.92820	+	8.53590i	−0.240758	+	0.417006i	0.720172	+	0.693795i	$0.244063\pi$
$420$		0			0
$421$		−	21.8564i		−	1.06522i	−0.846362	−	0.532608i	$-0.821212\pi$
$421$		−	21.8564i		−	1.06522i	0.846362	−	0.532608i	$-0.178788\pi$
$422$	−6.99038	+	4.03590i	−0.340286	+	0.196464i
$423$	5.59808	−	3.23205i	0.272188	−	0.157148i
$424$		−	0.267949i		−	0.0130128i
$425$		0			0
$426$	−6.46410	+	11.1962i	−0.313187	+	0.542455i
$427$	−1.39230	−	0.803848i	−0.0673784	−	0.0389009i
$428$	−12.9282			−0.624908
$429$	0.669873	+	0.696152i	0.0323418	+	0.0336106i
$430$		0			0
$431$	−12.0000	−	6.92820i	−0.578020	−	0.333720i	0.182326	−	0.983238i	$-0.441637\pi$
$431$	−12.0000	−	6.92820i	−0.578020	−	0.333720i	−0.760346	+	0.649518i	$0.774971\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−4.39230	−	7.60770i	−0.211081	−	0.365602i	0.740972	−	0.671536i	$-0.234365\pi$
$433$	−4.39230	−	7.60770i	−0.211081	−	0.365602i	−0.952053	+	0.305933i	$0.901032\pi$
$434$			14.7846i			0.709684i
$435$		0			0
$436$	9.00000	−	5.19615i	0.431022	−	0.248851i
$437$		−	19.8564i		−	0.949861i
$438$	3.46410	+	6.00000i	0.165521	+	0.286691i
$439$	6.66025	−	11.5359i	0.317877	−	0.550578i	−0.662168	−	0.749355i	$-0.730364\pi$
$439$	6.66025	−	11.5359i	0.317877	−	0.550578i	0.980045	+	0.198777i	$0.0636969\pi$
$440$		0			0
$441$	−2.00000			−0.0952381
$442$	−14.0000	+	3.46410i	−0.665912	+	0.164771i
$443$	19.8564			0.943406			0.471703	−	0.881757i	$-0.343639\pi$
$443$	19.8564			0.943406			0.471703	+	0.881757i	$0.343639\pi$
$444$	−5.13397	−	2.96410i	−0.243648	−	0.140670i
$445$		0			0
$446$	−9.42820	−	16.3301i	−0.446438	−	0.773254i
$447$			18.7846i			0.888482i
$448$	2.59808	−	1.50000i	0.122748	−	0.0708683i
$449$	−5.30385	+	3.06218i	−0.250304	+	0.144513i	−0.619903	−	0.784678i	$-0.712828\pi$
$449$	−5.30385	+	3.06218i	−0.250304	+	0.144513i	0.369599	+	0.929191i	$0.379495\pi$
$450$		0			0
$451$	−0.535898	−	0.928203i	−0.0252345	−	0.0437074i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$	−19.7321	−	11.3923i	−0.927093	−	0.535257i
$454$	6.53590			0.306745
$455$		0			0
$456$	5.73205			0.268428
$457$	6.46410	+	3.73205i	0.302378	+	0.174578i	0.643511	−	0.765437i	$-0.277477\pi$
$457$	6.46410	+	3.73205i	0.302378	+	0.174578i	−0.341133	+	0.940015i	$0.610811\pi$
$458$	2.26795	−	3.92820i	0.105974	−	0.183553i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	−10.0526	+	5.80385i	−0.468194	+	0.270312i	−0.715484	−	0.698630i	$-0.753794\pi$
$461$	−10.0526	+	5.80385i	−0.468194	+	0.270312i	0.247289	+	0.968942i	$0.420460\pi$
$462$	−0.696152	+	0.401924i	−0.0323879	+	0.0186992i
$463$		−	40.7846i		−	1.89542i	−0.319131	−	0.947711i	$-0.603391\pi$
$463$		−	40.7846i		−	1.89542i	0.319131	−	0.947711i	$-0.396609\pi$
$464$	−0.732051	−	1.26795i	−0.0339846	−	0.0588631i
$465$		0			0
$466$	15.5885	+	9.00000i	0.722121	+	0.416917i
$467$	−24.3923			−1.12874			−0.564371	−	0.825522i	$-0.690881\pi$
$467$	−24.3923			−1.12874			−0.564371	+	0.825522i	$0.690881\pi$
$468$	−3.46410	−	1.00000i	−0.160128	−	0.0462250i
$469$	4.39230			0.202818
$470$		0			0
$471$	10.5981	−	18.3564i	0.488334	−	0.845819i
$472$	5.73205	+	9.92820i	0.263839	+	0.456983i
$473$			1.60770i			0.0739219i
$474$	2.66025	−	1.53590i	0.122190	−	0.0705461i
$475$		0			0
$476$		−	12.0000i		−	0.550019i
$477$	−0.133975	−	0.232051i	−0.00613428	−	0.0106249i
$478$	−1.73205	+	3.00000i	−0.0792222	+	0.137217i
$479$	−19.2679	−	11.1244i	−0.880375	−	0.508285i	−0.00959301	−	0.999954i	$-0.503054\pi$
$479$	−19.2679	−	11.1244i	−0.880375	−	0.508285i	−0.870782	+	0.491669i	$0.836387\pi$
$480$		0			0
$481$	5.92820	−	20.5359i	0.270303	−	0.936356i
$482$	25.1962			1.14765
$483$	−9.00000	−	5.19615i	−0.409514	−	0.236433i
$484$	5.46410	−	9.46410i	0.248368	−	0.430186i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−18.1865	+	10.5000i	−0.824110	+	0.475800i	−0.851832	−	0.523815i	$-0.824508\pi$
$487$	−18.1865	+	10.5000i	−0.824110	+	0.475800i	0.0277214	+	0.999616i	$0.491175\pi$
$488$	0.464102	−	0.267949i	0.0210089	−	0.0121295i
$489$			2.92820i			0.132418i
$490$		0			0
$491$	−2.69615	+	4.66987i	−0.121676	+	0.210748i	−0.920429	−	0.390911i	$-0.872160\pi$
$491$	−2.69615	+	4.66987i	−0.121676	+	0.210748i	0.798753	+	0.601659i	$0.205493\pi$
$492$	3.46410	+	2.00000i	0.156174	+	0.0901670i
$493$	−5.85641			−0.263759
$494$	4.96410	+	20.0622i	0.223345	+	0.902640i
$495$		0			0
$496$	−4.26795	−	2.46410i	−0.191637	−	0.110641i
$497$	19.3923	−	33.5885i	0.869864	−	1.50665i
$498$	−4.73205	−	8.19615i	−0.212048	−	0.367278i
$499$		−	33.3205i		−	1.49163i	−0.666153	−	0.745815i	$-0.732060\pi$
$499$		−	33.3205i		−	1.49163i	0.666153	−	0.745815i	$-0.267940\pi$
$500$		0			0
$501$	−0.401924	+	0.232051i	−0.0179566	+	0.0103673i
$502$			19.5359i			0.871930i
$503$	1.86603	+	3.23205i	0.0832020	+	0.144110i	0.904624	−	0.426211i	$-0.140152\pi$
$503$	1.86603	+	3.23205i	0.0832020	+	0.144110i	−0.821422	+	0.570321i	$0.806819\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	−0.928203			−0.0412637
$507$	0.500000	−	12.9904i	0.0222058	−	0.576923i
$508$	−12.6603			−0.561708
$509$	25.3923	+	14.6603i	1.12549	+	0.649804i	0.942798	−	0.333365i	$-0.108184\pi$
$509$	25.3923	+	14.6603i	1.12549	+	0.649804i	0.182696	+	0.983169i	$0.441517\pi$
$510$		0			0
$511$	−10.3923	−	18.0000i	−0.459728	−	0.796273i
$512$			1.00000i			0.0441942i
$513$	4.96410	−	2.86603i	0.219170	−	0.126538i
$514$	−12.5885	+	7.26795i	−0.555253	+	0.320575i
$515$		0			0
$516$	−3.00000	−	5.19615i	−0.132068	−	0.228748i
$517$	−0.866025	+	1.50000i	−0.0380878	+	0.0659699i
$518$	15.4019	+	8.89230i	0.676722	+	0.390705i
$519$	2.12436			0.0932489
$520$		0			0
$521$	−6.60770			−0.289488			−0.144744	−	0.989469i	$-0.546236\pi$
$521$	−6.60770			−0.289488			−0.144744	+	0.989469i	$0.546236\pi$
$522$	−1.26795	−	0.732051i	−0.0554966	−	0.0320410i
$523$	−20.8564	+	36.1244i	−0.911987	+	1.57961i	−0.100733	+	0.994913i	$0.532119\pi$
$523$	−20.8564	+	36.1244i	−0.911987	+	1.57961i	−0.811254	+	0.584694i	$0.801214\pi$
$524$	7.16025	+	12.4019i	0.312797	+	0.541781i
$525$		0			0
$526$	21.2321	−	12.2583i	0.925761	−	0.534489i
$527$	−17.0718	+	9.85641i	−0.743659	+	0.429352i
$528$		−	0.267949i		−	0.0116610i
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$		0			0
$531$	9.92820	+	5.73205i	0.430847	+	0.248750i
$532$	−17.1962			−0.745548
$533$	−4.00000	+	13.8564i	−0.173259	+	0.600188i
$534$	−14.1244			−0.611221
$535$		0			0
$536$	−0.732051	+	1.26795i	−0.0316198	+	0.0547671i
$537$	−4.53590	−	7.85641i	−0.195738	−	0.339029i
$538$		−	17.0718i		−	0.736017i
$539$	0.464102	−	0.267949i	0.0199903	−	0.0115414i
$540$		0			0
$541$		−	14.7846i		−	0.635640i	−0.948151	−	0.317820i	$-0.897049\pi$
$541$		−	14.7846i		−	0.635640i	0.948151	−	0.317820i	$-0.102951\pi$
$542$	−12.1962	−	21.1244i	−0.523870	−	0.907369i
$543$	−8.46410	+	14.6603i	−0.363229	+	0.629132i
$544$	3.46410	+	2.00000i	0.148522	+	0.0857493i
$545$		0			0
$546$	10.3923	+	3.00000i	0.444750	+	0.128388i
$547$	5.32051			0.227488			0.113744	−	0.993510i	$-0.463716\pi$
$547$	5.32051			0.227488			0.113744	+	0.993510i	$0.463716\pi$
$548$	−11.6603	−	6.73205i	−0.498101	−	0.287579i
$549$	0.267949	−	0.464102i	0.0114358	−	0.0198074i
$550$		0			0
$551$			8.39230i			0.357524i
$552$	3.00000	−	1.73205i	0.127688	−	0.0737210i
$553$	−7.98076	+	4.60770i	−0.339377	+	0.195939i
$554$		−	11.5885i		−	0.492346i
$555$		0			0
$556$	−9.89230	+	17.1340i	−0.419527	+	0.726642i
$557$	19.5788	+	11.3038i	0.829582	+	0.478959i	0.853710	−	0.520749i	$-0.174347\pi$
$557$	19.5788	+	11.3038i	0.829582	+	0.478959i	−0.0241275	+	0.999709i	$0.507681\pi$
$558$	−4.92820			−0.208627
$559$	15.5885	−	15.0000i	0.659321	−	0.634432i
$560$		0			0
$561$	−0.928203	−	0.535898i	−0.0391888	−	0.0226256i
$562$	−3.46410	+	6.00000i	−0.146124	+	0.253095i
$563$	−7.66025	−	13.2679i	−0.322841	−	0.559177i	0.658232	−	0.752815i	$-0.271305\pi$
$563$	−7.66025	−	13.2679i	−0.322841	−	0.559177i	−0.981073	+	0.193638i	$0.937971\pi$
$564$		−	6.46410i		−	0.272188i
$565$		0			0
$566$	5.53590	−	3.19615i	0.232691	−	0.134344i
$567$		−	3.00000i		−	0.125988i
$568$	6.46410	+	11.1962i	0.271228	+	0.469780i
$569$	8.16025	−	14.1340i	0.342096	−	0.592527i	−0.642726	−	0.766096i	$-0.722197\pi$
$569$	8.16025	−	14.1340i	0.342096	−	0.592527i	0.984822	+	0.173569i	$0.0555300\pi$
$570$		0			0
$571$	10.8564			0.454326			0.227163	−	0.973857i	$-0.427055\pi$
$571$	10.8564			0.454326			0.227163	+	0.973857i	$0.427055\pi$
$572$	0.937822	−	0.232051i	0.0392123	−	0.00970253i
$573$	−17.3205			−0.723575
$574$	−10.3923	−	6.00000i	−0.433766	−	0.250435i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	9.32051i		−	0.388018i	−0.981000	−	0.194009i	$-0.937851\pi$
$577$		−	9.32051i		−	0.388018i	0.981000	−	0.194009i	$-0.0621491\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	−8.53590	+	4.92820i	−0.354740	+	0.204809i
$580$		0			0
$581$	14.1962	+	24.5885i	0.588956	+	1.02010i
$582$	−4.19615	+	7.26795i	−0.173936	+	0.301266i
$583$	0.0621778	+	0.0358984i	0.00257514	+	0.00148676i
$584$	6.92820			0.286691
$585$		0			0
$586$	29.2487			1.20825
$587$	7.73205	+	4.46410i	0.319136	+	0.184253i	0.651007	−	0.759071i	$-0.274347\pi$
$587$	7.73205	+	4.46410i	0.319136	+	0.184253i	−0.331871	+	0.943325i	$0.607680\pi$
$588$	−1.00000	+	1.73205i	−0.0412393	+	0.0714286i
$589$	14.1244	+	24.4641i	0.581984	+	1.00803i
$590$		0			0
$591$	−9.86603	+	5.69615i	−0.405834	+	0.234308i
$592$	−5.13397	+	2.96410i	−0.211005	+	0.121824i
$593$		−	44.7846i		−	1.83908i	−0.392992	−	0.919542i	$-0.628560\pi$
$593$		−	44.7846i		−	1.83908i	0.392992	−	0.919542i	$-0.371440\pi$
$594$	−0.133975	−	0.232051i	−0.00549704	−	0.00952116i
$595$		0			0
$596$	16.2679	+	9.39230i	0.666361	+	0.384724i
$597$	−24.9282			−1.02024
$598$	8.66025	+	9.00000i	0.354144	+	0.368037i
$599$	28.9282			1.18197			0.590987	−	0.806681i	$-0.298738\pi$
$599$	28.9282			1.18197			0.590987	+	0.806681i	$0.298738\pi$
$600$		0			0
$601$	−15.3564	+	26.5981i	−0.626401	+	1.08496i	0.361867	+	0.932230i	$0.382139\pi$
$601$	−15.3564	+	26.5981i	−0.626401	+	1.08496i	−0.988268	+	0.152729i	$0.951194\pi$
$602$	9.00000	+	15.5885i	0.366813	+	0.635338i
$603$			1.46410i			0.0596228i
$604$	−19.7321	+	11.3923i	−0.802886	+	0.463546i
$605$		0			0
$606$			12.3923i			0.503403i
$607$	−10.7224	−	18.5718i	−0.435210	−	0.753806i	0.562103	−	0.827067i	$-0.309993\pi$
$607$	−10.7224	−	18.5718i	−0.435210	−	0.753806i	−0.997313	+	0.0732615i	$0.976659\pi$
$608$	2.86603	−	4.96410i	0.116233	−	0.201321i
$609$	3.80385	+	2.19615i	0.154140	+	0.0889926i
$610$		0			0
$611$	22.6244	−	5.59808i	0.915283	−	0.226474i
$612$	4.00000			0.161690
$613$	−38.9711	−	22.5000i	−1.57403	−	0.908766i	−0.995667	−	0.0929864i	$-0.970359\pi$
$613$	−38.9711	−	22.5000i	−1.57403	−	0.908766i	−0.578362	−	0.815780i	$-0.696308\pi$
$614$	−14.1244	+	24.4641i	−0.570013	+	0.987291i
$615$		0			0
$616$			0.803848i			0.0323879i
$617$	30.7128	−	17.7321i	1.23645	−	0.713865i	0.268084	−	0.963395i	$-0.413609\pi$
$617$	30.7128	−	17.7321i	1.23645	−	0.713865i	0.968367	+	0.249530i	$0.0802761\pi$
$618$	10.0359	−	5.79423i	0.403703	−	0.233078i
$619$		−	2.51666i		−	0.101153i	−0.998720	−	0.0505766i	$-0.983894\pi$
$619$		−	2.51666i		−	0.101153i	0.998720	−	0.0505766i	$-0.0161059\pi$
$620$		0			0
$621$	1.73205	−	3.00000i	0.0695048	−	0.120386i
$622$	−16.3923	−	9.46410i	−0.657272	−	0.379476i
$623$	42.3731			1.69764
$624$	−2.59808	+	2.50000i	−0.104006	+	0.100080i
$625$		0			0
$626$	−28.8564	−	16.6603i	−1.15333	−	0.665878i
$627$	−0.767949	+	1.33013i	−0.0306689	+	0.0531202i
$628$	−10.5981	−	18.3564i	−0.422909	−	0.732500i
$629$			23.7128i			0.945492i
$630$		0			0
$631$	−6.92820	+	4.00000i	−0.275807	+	0.159237i	−0.631524	−	0.775356i	$-0.717570\pi$
$631$	−6.92820	+	4.00000i	−0.275807	+	0.159237i	0.355716	+	0.934594i	$0.384237\pi$
$632$		−	3.07180i		−	0.122190i
$633$	4.03590	+	6.99038i	0.160413	+	0.277843i
$634$	15.2321	−	26.3827i	0.604942	−	1.04779i
$635$		0			0
$636$	−0.267949			−0.0106249
$637$	−6.92820	−	2.00000i	−0.274505	−	0.0792429i
$638$	0.392305			0.0155315
$639$	11.1962	+	6.46410i	0.442913	+	0.255716i
$640$		0			0
$641$	−7.23205	−	12.5263i	−0.285649	−	0.494758i	0.687117	−	0.726546i	$-0.258876\pi$
$641$	−7.23205	−	12.5263i	−0.285649	−	0.494758i	−0.972766	+	0.231788i	$0.925542\pi$
$642$			12.9282i			0.510235i
$643$	−11.0718	+	6.39230i	−0.436629	+	0.252088i	−0.702167	−	0.712013i	$-0.747784\pi$
$643$	−11.0718	+	6.39230i	−0.436629	+	0.252088i	0.265538	+	0.964100i	$0.414451\pi$
$644$	−9.00000	+	5.19615i	−0.354650	+	0.204757i
$645$		0			0
$646$	−11.4641	−	19.8564i	−0.451049	−	0.781240i
$647$	−17.8660	+	30.9449i	−0.702386	+	1.21657i	0.265241	+	0.964182i	$0.414549\pi$
$647$	−17.8660	+	30.9449i	−0.702386	+	1.21657i	−0.967627	+	0.252386i	$0.918785\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−3.07180			−0.120579
$650$		0			0
$651$	14.7846			0.579455
$652$	2.53590	+	1.46410i	0.0993134	+	0.0573386i
$653$	−0.794229	+	1.37564i	−0.0310806	+	0.0538331i	−0.881147	−	0.472842i	$-0.843228\pi$
$653$	−0.794229	+	1.37564i	−0.0310806	+	0.0538331i	0.850067	+	0.526675i	$0.176562\pi$
$654$	−5.19615	−	9.00000i	−0.203186	−	0.351928i
$655$		0			0
$656$	3.46410	−	2.00000i	0.135250	−	0.0780869i
$657$	6.00000	−	3.46410i	0.234082	−	0.135147i
$658$			19.3923i			0.755991i
$659$	19.8564	+	34.3923i	0.773496	+	1.33973i	0.935636	+	0.352966i	$0.114827\pi$
$659$	19.8564	+	34.3923i	0.773496	+	1.33973i	−0.162140	+	0.986768i	$0.551840\pi$
$660$		0			0
$661$	−18.7128	−	10.8038i	−0.727844	−	0.420221i	0.0897889	−	0.995961i	$-0.471381\pi$
$661$	−18.7128	−	10.8038i	−0.727844	−	0.420221i	−0.817633	+	0.575740i	$0.804714\pi$
$662$	−14.3923			−0.559373
$663$	3.46410	+	14.0000i	0.134535	+	0.543715i
$664$	−9.46410			−0.367278
$665$		0			0
$666$	−2.96410	+	5.13397i	−0.114857	+	0.198937i
$667$	2.53590	+	4.39230i	0.0981904	+	0.170071i
$668$			0.464102i			0.0179566i
$669$	−16.3301	+	9.42820i	−0.631359	+	0.364515i
$670$		0			0
$671$			0.143594i			0.00554337i
$672$	−1.50000	−	2.59808i	−0.0578638	−	0.100223i
$673$	−8.39230	+	14.5359i	−0.323500	+	0.560318i	−0.981208	−	0.192955i	$-0.938193\pi$
$673$	−8.39230	+	14.5359i	−0.323500	+	0.560318i	0.657708	+	0.753273i	$0.271526\pi$
$674$	−22.8564	−	13.1962i	−0.880396	−	0.508297i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	−10.9282			−0.420005			−0.210002	−	0.977701i	$-0.567347\pi$
$677$	−10.9282			−0.420005			−0.210002	+	0.977701i	$0.567347\pi$
$678$	−10.3923	−	6.00000i	−0.399114	−	0.230429i
$679$	12.5885	−	21.8038i	0.483101	−	0.836755i
$680$		0			0
$681$		−	6.53590i		−	0.250456i
$682$	1.14359	−	0.660254i	0.0437905	−	0.0252824i
$683$	−35.7846	+	20.6603i	−1.36926	+	0.790543i	−0.990834	−	0.135089i	$-0.956868\pi$
$683$	−35.7846	+	20.6603i	−1.36926	+	0.790543i	−0.378427	+	0.925631i	$0.623535\pi$
$684$		−	5.73205i		−	0.219170i
$685$		0			0
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	−3.92820	−	2.26795i	−0.149870	−	0.0865277i
$688$	−6.00000			−0.228748
$689$	−0.232051	−	0.937822i	−0.00884043	−	0.0357282i
$690$		0			0
$691$	13.0359	+	7.52628i	0.495909	+	0.286313i	0.727023	−	0.686614i	$-0.240904\pi$
$691$	13.0359	+	7.52628i	0.495909	+	0.286313i	−0.231114	+	0.972927i	$0.574237\pi$
$692$	1.06218	−	1.83975i	0.0403779	−	0.0699366i
$693$	0.401924	+	0.696152i	0.0152678	+	0.0264446i
$694$		−	4.39230i		−	0.166730i
$695$		0			0
$696$	−1.26795	+	0.732051i	−0.0480615	+	0.0277483i
$697$		−	16.0000i		−	0.606043i
$698$	5.26795	+	9.12436i	0.199395	+	0.345362i
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	−4.39230			−0.165895			−0.0829475	−	0.996554i	$-0.526433\pi$
$701$	−4.39230			−0.165895			−0.0829475	+	0.996554i	$0.526433\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	33.9808			1.28161
$704$	−0.232051	−	0.133975i	−0.00874574	−	0.00504936i
$705$		0			0
$706$	3.80385	+	6.58846i	0.143160	+	0.247960i
$707$		−	37.1769i		−	1.39818i
$708$	9.92820	−	5.73205i	0.373125	−	0.215424i
$709$	−23.6603	+	13.6603i	−0.888579	+	0.513022i	−0.873478	−	0.486864i	$-0.838141\pi$
$709$	−23.6603	+	13.6603i	−0.888579	+	0.513022i	−0.0151019	+	0.999886i	$0.504807\pi$
$710$		0			0
$711$	−1.53590	−	2.66025i	−0.0576007	−	0.0997673i
$712$	−7.06218	+	12.2321i	−0.264666	+	0.458415i
$713$	14.7846	+	8.53590i	0.553688	+	0.319672i
$714$	−12.0000			−0.449089
$715$		0			0
$716$	−9.07180			−0.339029
$717$	3.00000	+	1.73205i	0.112037	+	0.0646846i
$718$	−0.464102	+	0.803848i	−0.0173201	+	0.0299993i
$719$	−8.00000	−	13.8564i	−0.298350	−	0.516757i	0.677409	−	0.735607i	$-0.263103\pi$
$719$	−8.00000	−	13.8564i	−0.298350	−	0.516757i	−0.975759	+	0.218850i	$0.929769\pi$
$720$		0			0
$721$	−30.1077	+	17.3827i	−1.12127	+	0.647365i
$722$	−12.0000	+	6.92820i	−0.446594	+	0.257841i
$723$		−	25.1962i		−	0.937055i
$724$	8.46410	+	14.6603i	0.314566	+	0.544844i
$725$		0			0
$726$	−9.46410	−	5.46410i	−0.351246	−	0.202792i
$727$	4.66025			0.172839			0.0864196	−	0.996259i	$-0.472457\pi$
$727$	4.66025			0.172839			0.0864196	+	0.996259i	$0.472457\pi$
$728$	7.79423	−	7.50000i	0.288873	−	0.277968i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	−0.267949	−	0.464102i	−0.00990369	−	0.0171537i
$733$			20.8564i			0.770349i	0.922844	+	0.385174i	$0.125859\pi$
$733$			20.8564i			0.770349i	−0.922844	+	0.385174i	$0.874141\pi$
$734$	−18.4641	+	10.6603i	−0.681522	+	0.393477i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$	−0.196152	−	0.339746i	−0.00722537	−	0.0125147i
$738$	2.00000	−	3.46410i	0.0736210	−	0.127515i
$739$	31.0359	+	17.9186i	1.14167	+	0.659146i	0.946845	−	0.321691i	$-0.104251\pi$
$739$	31.0359	+	17.9186i	1.14167	+	0.659146i	0.194829	+	0.980837i	$0.437585\pi$
$740$		0			0
$741$	20.0622	−	4.96410i	0.737003	−	0.182361i
$742$	0.803848			0.0295102
$743$	9.46410	+	5.46410i	0.347204	+	0.200458i	0.663453	−	0.748218i	$-0.269090\pi$
$743$	9.46410	+	5.46410i	0.347204	+	0.200458i	−0.316249	+	0.948676i	$0.602424\pi$
$744$	−2.46410	+	4.26795i	−0.0903383	+	0.156471i
$745$		0			0
$746$		−	9.07180i		−	0.332142i
$747$	−8.19615	+	4.73205i	−0.299882	+	0.173137i
$748$	−0.928203	+	0.535898i	−0.0339385	+	0.0195944i
$749$		−	38.7846i		−	1.41716i
$750$		0			0
$751$	10.5885	−	18.3397i	0.386378	−	0.669227i	−0.605581	−	0.795784i	$-0.707059\pi$
$751$	10.5885	−	18.3397i	0.386378	−	0.669227i	0.991959	+	0.126557i	$0.0403926\pi$
$752$	−5.59808	−	3.23205i	−0.204141	−	0.117861i
$753$	19.5359			0.711928
$754$	−3.66025	−	3.80385i	−0.133299	−	0.138528i
$755$		0			0
$756$	−2.59808	−	1.50000i	−0.0944911	−	0.0545545i
$757$	10.8660	−	18.8205i	0.394932	−	0.684043i	−0.598160	−	0.801377i	$-0.704101\pi$
$757$	10.8660	−	18.8205i	0.394932	−	0.684043i	0.993093	+	0.117334i	$0.0374347\pi$
$758$	4.86603	+	8.42820i	0.176742	+	0.306126i
$759$			0.928203i			0.0336916i
$760$		0			0
$761$	6.91154	−	3.99038i	0.250543	−	0.144651i	−0.369470	−	0.929243i	$-0.620461\pi$
$761$	6.91154	−	3.99038i	0.250543	−	0.144651i	0.620013	+	0.784592i	$0.287127\pi$
$762$			12.6603i			0.458633i
$763$	15.5885	+	27.0000i	0.564340	+	0.977466i
$764$	−8.66025	+	15.0000i	−0.313317	+	0.542681i
$765$		0			0
$766$	4.78461			0.172875
$767$	28.6603	+	29.7846i	1.03486	+	1.07546i
$768$	1.00000			0.0360844
$769$	13.6077	+	7.85641i	0.490706	+	0.283309i	0.724867	−	0.688889i	$-0.241901\pi$
$769$	13.6077	+	7.85641i	0.490706	+	0.283309i	−0.234161	+	0.972198i	$0.575234\pi$
$770$		0			0
$771$	7.26795	+	12.5885i	0.261749	+	0.453362i
$772$			9.85641i			0.354740i
$773$	28.2391	−	16.3038i	1.01569	−	0.586409i	0.102837	−	0.994698i	$-0.467208\pi$
$773$	28.2391	−	16.3038i	1.01569	−	0.586409i	0.912852	+	0.408290i	$0.133875\pi$
$774$	−5.19615	+	3.00000i	−0.186772	+	0.107833i
$775$		0			0
$776$	4.19615	+	7.26795i	0.150633	+	0.260904i
$777$	8.89230	−	15.4019i	0.319010	−	0.552541i
$778$	−15.4641	−	8.92820i	−0.554415	−	0.320092i
$779$	−22.9282			−0.821488
$780$		0			0
$781$	−3.46410			−0.123955
$782$	−12.0000	−	6.92820i	−0.429119	−	0.247752i
$783$	−0.732051	+	1.26795i	−0.0261614	+	0.0453128i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$		0			0
$786$	12.4019	−	7.16025i	0.442362	−	0.255398i
$787$	−1.26795	+	0.732051i	−0.0451975	+	0.0260948i	−0.522428	−	0.852683i	$-0.674974\pi$
$787$	−1.26795	+	0.732051i	−0.0451975	+	0.0260948i	0.477231	+	0.878778i	$0.341641\pi$
$788$			11.3923i			0.405834i
$789$	−12.2583	−	21.2321i	−0.436408	−	0.755881i
$790$		0			0
$791$	31.1769	+	18.0000i	1.10852	+	0.640006i
$792$	−0.267949			−0.00952116
$793$	1.39230	−	1.33975i	0.0494422	−	0.0475758i
$794$	−5.92820			−0.210384
$795$		0			0
$796$	−12.4641	+	21.5885i	−0.441778	+	0.765183i
$797$	−5.07180	−	8.78461i	−0.179652	−	0.311167i	0.762109	−	0.647449i	$-0.224164\pi$
$797$	−5.07180	−	8.78461i	−0.179652	−	0.311167i	−0.941761	+	0.336282i	$0.890831\pi$
$798$			17.1962i			0.608737i
$799$	−22.3923	+	12.9282i	−0.792183	+	0.457367i
$800$		0			0
$801$			14.1244i			0.499060i
$802$	11.0622	+	19.1603i	0.390619	+	0.676572i
$803$	−0.928203	+	1.60770i	−0.0327556	+	0.0567343i
$804$	1.26795	+	0.732051i	0.0447171	+	0.0258174i
$805$		0			0
$806$	−17.0718	−	4.92820i	−0.601328	−	0.173589i
$807$	−17.0718			−0.600956
$808$	10.7321	+	6.19615i	0.377552	+	0.217980i
$809$	3.39230	−	5.87564i	0.119267	−	0.206577i	−0.800210	−	0.599719i	$-0.795279\pi$
$809$	3.39230	−	5.87564i	0.119267	−	0.206577i	0.919477	+	0.393143i	$0.128612\pi$
$810$		0			0
$811$		−	23.5885i		−	0.828303i	−0.910208	−	0.414151i	$-0.864078\pi$
$811$		−	23.5885i		−	0.828303i	0.910208	−	0.414151i	$-0.135922\pi$
$812$	3.80385	−	2.19615i	0.133489	−	0.0770698i
$813$	−21.1244	+	12.1962i	−0.740863	+	0.427738i
$814$		−	1.58846i		−	0.0556754i
$815$		0			0
$816$	2.00000	−	3.46410i	0.0700140	−	0.121268i
$817$	29.7846	+	17.1962i	1.04203	+	0.601617i
$818$	39.0526			1.36544
$819$	3.00000	−	10.3923i	0.104828	−	0.363137i
$820$		0			0
$821$	−12.7128	−	7.33975i	−0.443680	−	0.256159i	0.261477	−	0.965210i	$-0.415790\pi$
$821$	−12.7128	−	7.33975i	−0.443680	−	0.256159i	−0.705157	+	0.709051i	$0.749124\pi$
$822$	−6.73205	+	11.6603i	−0.234807	+	0.406698i
$823$	−4.20577	−	7.28461i	−0.146604	−	0.253926i	0.783366	−	0.621560i	$-0.213501\pi$
$823$	−4.20577	−	7.28461i	−0.146604	−	0.253926i	−0.929970	+	0.367635i	$0.880168\pi$
$824$		−	11.5885i		−	0.403703i
$825$		0			0
$826$	−29.7846	+	17.1962i	−1.03634	+	0.598331i
$827$			46.4974i			1.61687i	0.588583	+	0.808437i	$0.299686\pi$
$827$			46.4974i			1.61687i	−0.588583	+	0.808437i	$0.700314\pi$
$828$	−1.73205	−	3.00000i	−0.0601929	−	0.104257i
$829$	2.33975	−	4.05256i	0.0812627	−	0.140751i	−0.822530	−	0.568722i	$-0.807438\pi$
$829$	2.33975	−	4.05256i	0.0812627	−	0.140751i	0.903793	+	0.427971i	$0.140771\pi$
$830$		0			0
$831$	−11.5885			−0.401999
$832$	0.866025	+	3.50000i	0.0300240	+	0.121341i
$833$	8.00000			0.277184
$834$	17.1340	+	9.89230i	0.593301	+	0.342543i
$835$		0			0
$836$	0.767949	+	1.33013i	0.0265601	+	0.0460034i
$837$			4.92820i			0.170344i
$838$	8.53590	−	4.92820i	0.294868	−	0.170242i
$839$	16.6077	−	9.58846i	0.573361	−	0.331030i	−0.185129	−	0.982714i	$-0.559270\pi$
$839$	16.6077	−	9.58846i	0.573361	−	0.331030i	0.758491	+	0.651684i	$0.225937\pi$
$840$		0			0
$841$	13.4282	+	23.2583i	0.463041	+	0.802011i
$842$	−10.9282	+	18.9282i	−0.376611	+	0.652309i
$843$	6.00000	+	3.46410i	0.206651	+	0.119310i
$844$	8.07180			0.277843
$845$		0			0
$846$	−6.46410			−0.222240
$847$	28.3923	+	16.3923i	0.975571	+	0.563246i
$848$	−0.133975	+	0.232051i	−0.00460071	+	0.00796866i
$849$	−3.19615	−	5.53590i	−0.109692	−	0.189992i
$850$		0			0
$851$	17.7846	−	10.2679i	0.609649	−	0.351981i
$852$	11.1962	−	6.46410i	0.383574	−	0.221456i
$853$		−	24.6410i		−	0.843692i	−0.906667	−	0.421846i	$-0.861382\pi$
$853$		−	24.6410i		−	0.843692i	0.906667	−	0.421846i	$-0.138618\pi$
$854$	0.803848	+	1.39230i	0.0275071	+	0.0476437i
$855$		0			0
$856$	11.1962	+	6.46410i	0.382677	+	0.220938i
$857$	28.9282			0.988169			0.494084	−	0.869414i	$-0.335503\pi$
$857$	28.9282			0.988169			0.494084	+	0.869414i	$0.335503\pi$
$858$	−0.232051	−	0.937822i	−0.00792208	−	0.0320167i
$859$	−6.07180			−0.207167			−0.103584	−	0.994621i	$-0.533031\pi$
$859$	−6.07180			−0.207167			−0.103584	+	0.994621i	$0.533031\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	6.92820	+	12.0000i	0.235976	+	0.408722i
$863$			2.92820i			0.0996772i	0.998757	+	0.0498386i	$0.0158707\pi$
$863$			2.92820i			0.0996772i	−0.998757	+	0.0498386i	$0.984129\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$			8.78461i			0.298513i
$867$	0.500000	+	0.866025i	0.0169809	+	0.0294118i
$868$	7.39230	−	12.8038i	0.250911	−	0.434591i
$869$	0.712813	+	0.411543i	0.0241805	+	0.0139606i
$870$		0			0
$871$	−1.46410	+	5.07180i	−0.0496092	+	0.171851i
$872$	−10.3923			−0.351928
$873$	7.26795	+	4.19615i	0.245983	+	0.142018i
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$		0			0
$876$		−	6.92820i		−	0.234082i
$877$	−18.8038	+	10.8564i	−0.634961	+	0.366595i	−0.782671	−	0.622436i	$-0.786143\pi$
$877$	−18.8038	+	10.8564i	−0.634961	+	0.366595i	0.147710	+	0.989031i	$0.452810\pi$
$878$	−11.5359	+	6.66025i	−0.389318	+	0.224773i
$879$		−	29.2487i		−	0.986535i
$880$		0			0
$881$	−19.5526	+	33.8660i	−0.658742	+	1.14098i	0.322199	+	0.946672i	$0.395578\pi$
$881$	−19.5526	+	33.8660i	−0.658742	+	1.14098i	−0.980941	+	0.194303i	$0.937755\pi$
$882$	1.73205	+	1.00000i	0.0583212	+	0.0336718i
$883$	13.3205			0.448271			0.224135	−	0.974558i	$-0.428044\pi$
$883$	13.3205			0.448271			0.224135	+	0.974558i	$0.428044\pi$
$884$	13.8564	+	4.00000i	0.466041	+	0.134535i
$885$		0			0
$886$	−17.1962	−	9.92820i	−0.577716	−	0.333545i
$887$	27.8660	−	48.2654i	0.935650	−	1.62059i	0.162178	−	0.986762i	$-0.448148\pi$
$887$	27.8660	−	48.2654i	0.935650	−	1.62059i	0.773472	−	0.633831i	$-0.218519\pi$
$888$	2.96410	+	5.13397i	0.0994687	+	0.172285i
$889$		−	37.9808i		−	1.27383i
$890$		0			0
$891$	−0.232051	+	0.133975i	−0.00777399	+	0.00448832i
$892$			18.8564i			0.631359i
$893$	18.5263	+	32.0885i	0.619958	+	1.07380i
$894$	9.39230	−	16.2679i	0.314126	−	0.544082i
$895$		0			0
$896$	−3.00000			−0.100223
$897$	9.00000	−	8.66025i	0.300501	−	0.289157i
$898$	6.12436			0.204372
$899$	−6.24871	−	3.60770i	−0.208406	−	0.120323i
$900$		0			0
$901$	0.535898	+	0.928203i	0.0178534	+	0.0309229i
$902$			1.07180i			0.0356869i
$903$	15.5885	−	9.00000i	0.518751	−	0.299501i
$904$	−10.3923	+	6.00000i	−0.345643	+	0.199557i
$905$		0			0
$906$	11.3923	+	19.7321i	0.378484	+	0.655553i
$907$	10.4641	−	18.1244i	0.347455	−	0.601809i	−0.638342	−	0.769753i	$-0.720379\pi$
$907$	10.4641	−	18.1244i	0.347455	−	0.601809i	0.985797	+	0.167944i	$0.0537127\pi$
$908$	−5.66025	−	3.26795i	−0.187842	−	0.108451i
$909$	12.3923			0.411027
$910$		0			0
$911$	12.7846			0.423573			0.211787	−	0.977316i	$-0.432072\pi$
$911$	12.7846			0.423573			0.211787	+	0.977316i	$0.432072\pi$
$912$	−4.96410	−	2.86603i	−0.164378	−	0.0949036i
$913$	1.26795	−	2.19615i	0.0419630	−	0.0726820i
$914$	−3.73205	−	6.46410i	−0.123445	−	0.213813i
$915$		0			0
$916$	−3.92820	+	2.26795i	−0.129791	+	0.0749352i
$917$	−37.2058	+	21.4808i	−1.22864	+	0.709357i
$918$		−	4.00000i		−	0.132020i
$919$	23.9808	+	41.5359i	0.791052	+	1.37014i	0.925316	+	0.379197i	$0.123800\pi$
$919$	23.9808	+	41.5359i	0.791052	+	1.37014i	−0.134264	+	0.990946i	$0.542867\pi$
$920$		0			0
$921$	24.4641	+	14.1244i	0.806120	+	0.465413i
$922$	11.6077			0.382279
$923$	32.3205	+	33.5885i	1.06384	+	1.10558i
$924$	0.803848			0.0264446
$925$		0			0
$926$	−20.3923	+	35.3205i	−0.670133	+	1.16070i
$927$	−5.79423	−	10.0359i	−0.190307	−	0.329622i
$928$			1.46410i			0.0480615i
$929$	50.1051	−	28.9282i	1.64390	−	0.949104i	0.664466	−	0.747319i	$-0.268659\pi$
$929$	50.1051	−	28.9282i	1.64390	−	0.949104i	0.979430	−	0.201785i	$-0.0646742\pi$
$930$		0			0
$931$		−	11.4641i		−	0.375721i
$932$	−9.00000	−	15.5885i	−0.294805	−	0.510617i
$933$	−9.46410	+	16.3923i	−0.309841	+	0.536660i
$934$	21.1244	+	12.1962i	0.691210	+	0.399070i
$935$		0			0
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	21.7128			0.709327			0.354663	−	0.934994i	$-0.384595\pi$
$937$	21.7128			0.709327			0.354663	+	0.934994i	$0.384595\pi$
$938$	−3.80385	−	2.19615i	−0.124200	−	0.0717069i
$939$	−16.6603	+	28.8564i	−0.543687	+	0.941693i
$940$		0			0
$941$			60.4974i			1.97216i	0.166273	+	0.986080i	$0.446827\pi$
$941$			60.4974i			1.97216i	−0.166273	+	0.986080i	$0.553173\pi$
$942$	−18.3564	+	10.5981i	−0.598084	+	0.345304i
$943$	−12.0000	+	6.92820i	−0.390774	+	0.225613i
$944$		−	11.4641i		−	0.373125i
$945$		0			0
$946$	0.803848	−	1.39230i	0.0261353	−	0.0452677i
$947$	−29.7846	−	17.1962i	−0.967870	−	0.558800i	−0.0692836	−	0.997597i	$-0.522071\pi$
$947$	−29.7846	−	17.1962i	−0.967870	−	0.558800i	−0.898586	+	0.438797i	$0.855405\pi$
$948$	−3.07180			−0.0997673
$949$	24.2487	−	6.00000i	0.787146	−	0.194768i
$950$		0			0
$951$	−26.3827	−	15.2321i	−0.855517	−	0.493933i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−26.6603	−	46.1769i	−0.863610	−	1.49582i	−0.868420	−	0.495829i	$-0.834864\pi$
$953$	−26.6603	−	46.1769i	−0.863610	−	1.49582i	0.00481009	−	0.999988i	$-0.498469\pi$
$954$			0.267949i			0.00867518i
$955$		0			0
$956$	3.00000	−	1.73205i	0.0970269	−	0.0560185i
$957$		−	0.392305i		−	0.0126814i
$958$	11.1244	+	19.2679i	0.359412	+	0.622519i
$959$	20.1962	−	34.9808i	0.652168	−	1.12959i
$960$		0			0
$961$	6.71281			0.216542
$962$	−15.4019	+	14.8205i	−0.496578	+	0.477832i
$963$	12.9282			0.416606
$964$	−21.8205	−	12.5981i	−0.702791	−	0.405757i
$965$		0			0
$966$	5.19615	+	9.00000i	0.167183	+	0.289570i
$967$		−	1.14359i		−	0.0367755i	−0.999831	−	0.0183877i	$-0.994147\pi$
$967$		−	1.14359i		−	0.0367755i	0.999831	−	0.0183877i	$-0.00585333\pi$
$968$	−9.46410	+	5.46410i	−0.304188	+	0.175623i
$969$	−19.8564	+	11.4641i	−0.637880	+	0.368280i
$970$		0			0
$971$	20.6962	+	35.8468i	0.664171	+	1.15038i	0.979509	+	0.201399i	$0.0645487\pi$
$971$	20.6962	+	35.8468i	0.664171	+	1.15038i	−0.315338	+	0.948979i	$0.602118\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−51.4019	−	29.6769i	−1.64787	−	0.951398i
$974$	21.0000			0.672883
$975$		0			0
$976$	−0.535898			−0.0171537
$977$	4.73205	+	2.73205i	0.151392	+	0.0874060i	0.573782	−	0.819008i	$-0.305476\pi$
$977$	4.73205	+	2.73205i	0.151392	+	0.0874060i	−0.422391	+	0.906414i	$0.638809\pi$
$978$	1.46410	−	2.53590i	0.0468168	−	0.0810891i
$979$	−1.89230	−	3.27757i	−0.0604783	−	0.104752i
$980$		0			0
$981$	−9.00000	+	5.19615i	−0.287348	+	0.165900i
$982$	4.66987	−	2.69615i	0.149022	−	0.0860377i
$983$			46.1769i			1.47281i	0.676538	+	0.736407i	$0.263479\pi$
$983$			46.1769i			1.47281i	−0.676538	+	0.736407i	$0.736521\pi$
$984$	−2.00000	−	3.46410i	−0.0637577	−	0.110432i
$985$		0			0
$986$	5.07180	+	2.92820i	0.161519	+	0.0932530i
$987$	19.3923			0.617264
$988$	5.73205	−	19.8564i	0.182361	−	0.631716i
$989$	20.7846			0.660912
$990$		0			0
$991$	−19.5885	+	33.9282i	−0.622248	+	1.07776i	0.366818	+	0.930293i	$0.380447\pi$
$991$	−19.5885	+	33.9282i	−0.622248	+	1.07776i	−0.989066	+	0.147472i	$0.952886\pi$
$992$	2.46410	+	4.26795i	0.0782353	+	0.135508i
$993$			14.3923i			0.456726i
$994$	−33.5885	+	19.3923i	−1.06536	+	0.615087i
$995$		0			0
$996$			9.46410i			0.299882i
$997$	30.9904	+	53.6769i	0.981475	+	1.69996i	0.656659	+	0.754188i	$0.271969\pi$
$997$	30.9904	+	53.6769i	0.981475	+	1.69996i	0.324817	+	0.945777i	$0.394697\pi$
$998$	−16.6603	+	28.8564i	−0.527371	+	0.913434i
$999$	5.13397	+	2.96410i	0.162432	+	0.0937800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.a.901.1		4
5.2	odd	4		1950.2.y.e.199.2		4
5.3	odd	4		1950.2.y.d.199.1		4
5.4	even	2		390.2.bb.a.121.2	✓	4
13.10	even	6	inner	1950.2.bc.a.751.1		4
15.14	odd	2		1170.2.bs.d.901.1		4
65.4	even	6		5070.2.b.p.1351.3		4
65.9	even	6		5070.2.b.p.1351.2		4
65.19	odd	12		5070.2.a.ba.1.1		2
65.23	odd	12		1950.2.y.e.49.2		4
65.49	even	6		390.2.bb.a.361.2	yes	4
65.59	odd	12		5070.2.a.be.1.2		2
65.62	odd	12		1950.2.y.d.49.1		4
195.179	odd	6		1170.2.bs.d.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.a.121.2	✓	4	5.4	even	2
390.2.bb.a.361.2	yes	4	65.49	even	6
1170.2.bs.d.361.1		4	195.179	odd	6
1170.2.bs.d.901.1		4	15.14	odd	2
1950.2.y.d.49.1		4	65.62	odd	12
1950.2.y.d.199.1		4	5.3	odd	4
1950.2.y.e.49.2		4	65.23	odd	12
1950.2.y.e.199.2		4	5.2	odd	4
1950.2.bc.a.751.1		4	13.10	even	6	inner
1950.2.bc.a.901.1		4	1.1	even	1	trivial
5070.2.a.ba.1.1		2	65.19	odd	12
5070.2.a.be.1.2		2	65.59	odd	12
5070.2.b.p.1351.2		4	65.9	even	6
5070.2.b.p.1351.3		4	65.4	even	6

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.232051 + 0.133975i) q^{11} -1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(4.96410 - 2.86603i) q^{19} -3.00000i q^{21} +(-0.133975 - 0.232051i) q^{22} +(1.73205 - 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-2.59808 - 1.50000i) q^{28} +(-0.732051 + 1.26795i) q^{29} +4.92820i q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.232051 + 0.133975i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(5.13397 + 2.96410i) q^{37} -5.73205 q^{38} +(3.46410 + 1.00000i) q^{39} +(-3.46410 - 2.00000i) q^{41} +(-1.50000 + 2.59808i) q^{42} +(3.00000 + 5.19615i) q^{43} +0.267949i q^{44} +(-3.00000 + 1.73205i) q^{46} +6.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.00000 - 1.73205i) q^{49} -4.00000 q^{51} +(2.59808 - 2.50000i) q^{52} +0.267949 q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.50000 + 2.59808i) q^{56} +5.73205i q^{57} +(1.26795 - 0.732051i) q^{58} +(-9.92820 + 5.73205i) q^{59} +(0.267949 + 0.464102i) q^{61} +(2.46410 - 4.26795i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +0.267949 q^{66} +(-1.26795 - 0.732051i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(1.73205 + 3.00000i) q^{69} +(-11.1962 + 6.46410i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.92820i q^{73} +(-2.96410 - 5.13397i) q^{74} +(4.96410 + 2.86603i) q^{76} -0.803848 q^{77} +(-2.50000 - 2.59808i) q^{78} +3.07180 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.00000 + 3.46410i) q^{82} -9.46410i q^{83} +(2.59808 - 1.50000i) q^{84} -6.00000i q^{86} +(-0.732051 - 1.26795i) q^{87} +(0.133975 - 0.232051i) q^{88} +(-12.2321 - 7.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +3.46410 q^{92} +(-4.26795 - 2.46410i) q^{93} +(3.23205 - 5.59808i) q^{94} +1.00000i q^{96} +(-7.26795 + 4.19615i) q^{97} +(-1.73205 + 1.00000i) q^{98} -0.267949i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 6 q^{11} - 4 q^{12} + 12 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} - 4 q^{22} - 4 q^{26} + 4 q^{27} + 4 q^{29} + 6 q^{33} + 2 q^{36} + 24 q^{37} - 16 q^{38} - 6 q^{42} + 12 q^{43} - 12 q^{46} - 2 q^{48} + 4 q^{49} - 16 q^{51} + 8 q^{53} + 6 q^{56} + 12 q^{58} - 12 q^{59} + 8 q^{61} - 4 q^{62} - 4 q^{64} + 8 q^{66} - 12 q^{67} - 8 q^{68} - 24 q^{71} + 2 q^{74} + 6 q^{76} - 24 q^{77} - 10 q^{78} + 40 q^{79} - 2 q^{81} + 8 q^{82} + 4 q^{87} + 4 q^{88} - 42 q^{89} + 30 q^{91} - 24 q^{93} + 6 q^{94} - 36 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 6 * q^11 - 4 * q^12 + 12 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 - 4 * q^22 - 4 * q^26 + 4 * q^27 + 4 * q^29 + 6 * q^33 + 2 * q^36 + 24 * q^37 - 16 * q^38 - 6 * q^42 + 12 * q^43 - 12 * q^46 - 2 * q^48 + 4 * q^49 - 16 * q^51 + 8 * q^53 + 6 * q^56 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 8 * q^66 - 12 * q^67 - 8 * q^68 - 24 * q^71 + 2 * q^74 + 6 * q^76 - 24 * q^77 - 10 * q^78 + 40 * q^79 - 2 * q^81 + 8 * q^82 + 4 * q^87 + 4 * q^88 - 42 * q^89 + 30 * q^91 - 24 * q^93 + 6 * q^94 - 36 * q^97

Introduction

L-functions

Modular forms

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Database

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