LMFDB - Embedded newform 1950.2.bc.d.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 78)
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.d.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.09808 - 2.36603i) q^{11} +1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} +0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-1.09808 + 0.633975i) q^{19} +0.732051i q^{21} +(2.36603 + 4.09808i) q^{22} +(3.09808 - 5.36603i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.633975 - 0.366025i) q^{28} +(-1.23205 + 2.13397i) q^{29} +5.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.09808 + 2.36603i) q^{33} -2.26795i q^{34} +(0.500000 - 0.866025i) q^{36} +(9.06218 + 5.23205i) q^{37} +1.26795 q^{38} +(0.866025 + 3.50000i) q^{39} +(9.86603 + 5.69615i) q^{41} +(0.366025 - 0.633975i) q^{42} +(-3.83013 - 6.63397i) q^{43} -4.73205i q^{44} +(-5.36603 + 3.09808i) q^{46} +8.19615i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-3.46410 - 1.00000i) q^{52} -0.464102 q^{53} +(0.866025 + 0.500000i) q^{54} +(0.366025 + 0.633975i) q^{56} +1.26795i q^{57} +(2.13397 - 1.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +(-0.598076 - 1.03590i) q^{61} +(2.73205 - 4.73205i) q^{62} +(0.633975 + 0.366025i) q^{63} -1.00000 q^{64} +4.73205 q^{66} +(9.63397 + 5.56218i) q^{67} +(-1.13397 + 1.96410i) q^{68} +(-3.09808 - 5.36603i) q^{69} +(-1.09808 + 0.633975i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.73205i q^{73} +(-5.23205 - 9.06218i) q^{74} +(-1.09808 - 0.633975i) q^{76} +3.46410 q^{77} +(1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.69615 - 9.86603i) q^{82} +10.1962i q^{83} +(-0.633975 + 0.366025i) q^{84} +7.66025i q^{86} +(1.23205 + 2.13397i) q^{87} +(-2.36603 + 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} +(0.732051 - 2.53590i) q^{91} +6.19615 q^{92} +(4.73205 + 2.73205i) q^{93} +(4.09808 - 7.09808i) q^{94} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(5.59808 - 3.23205i) q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{22} + 2 q^{23} + 14 q^{26} - 4 q^{27} - 6 q^{28} + 2 q^{29} - 6 q^{33} + 2 q^{36} + 12 q^{37} + 12 q^{38} + 36 q^{41} - 2 q^{42} + 2 q^{43} - 18 q^{46} + 2 q^{48} - 6 q^{49} + 16 q^{51} + 12 q^{53} - 2 q^{56} + 12 q^{58} + 8 q^{61} + 4 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{66} + 42 q^{67} - 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 6 q^{76} + 4 q^{78} - 24 q^{79} - 2 q^{81} - 2 q^{82} - 6 q^{84} - 2 q^{87} - 6 q^{88} - 12 q^{89} - 4 q^{91} + 4 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^22 + 2 * q^23 + 14 * q^26 - 4 * q^27 - 6 * q^28 + 2 * q^29 - 6 * q^33 + 2 * q^36 + 12 * q^37 + 12 * q^38 + 36 * q^41 - 2 * q^42 + 2 * q^43 - 18 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 12 * q^53 - 2 * q^56 + 12 * q^58 + 8 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 6 * q^76 + 4 * q^78 - 24 * q^79 - 2 * q^81 - 2 * q^82 - 6 * q^84 - 2 * q^87 - 6 * q^88 - 12 * q^89 - 4 * q^91 + 4 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^98

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
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	−0.615002	−	0.788526i	$-0.710845\pi$
$7$	−0.633975	+	0.366025i	−0.239620	+	0.138345i	0.375382	+	0.926870i	$0.377511\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.267421	−	0.963580i	$-0.586172\pi$
$11$	−4.09808	−	2.36603i	−1.23562	−	0.713384i	−0.968195	+	0.250196i	$0.919505\pi$
$12$	1.00000			0.288675
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	0.732051			0.195649
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.13397	+	1.96410i	0.275029	+	0.476365i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	1.13397	+	1.96410i	0.275029	+	0.476365i	−0.695113	+	0.718900i	$0.744646\pi$
$18$			1.00000i			0.235702i
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	−0.620641	−	0.784095i	$-0.713128\pi$
$19$	−1.09808	+	0.633975i	−0.251916	+	0.145444i	0.368725	+	0.929538i	$0.379794\pi$
$20$		0			0
$21$			0.732051i			0.159747i
$22$	2.36603	+	4.09808i	0.504438	+	0.873713i
$23$	3.09808	−	5.36603i	0.645994	−	1.11889i	−0.338078	−	0.941118i	$-0.609777\pi$
$23$	3.09808	−	5.36603i	0.645994	−	1.11889i	0.984071	−	0.177775i	$-0.0568901\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	3.50000	−	0.866025i	0.686406	−	0.169842i
$27$	−1.00000			−0.192450
$28$	−0.633975	−	0.366025i	−0.119810	−	0.0691723i
$29$	−1.23205	+	2.13397i	−0.228786	+	0.396269i	−0.957449	−	0.288604i	$-0.906809\pi$
$29$	−1.23205	+	2.13397i	−0.228786	+	0.396269i	0.728663	+	0.684873i	$0.240142\pi$
$30$		0			0
$31$			5.46410i			0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$			5.46410i			0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−4.09808	+	2.36603i	−0.713384	+	0.411872i
$34$		−	2.26795i		−	0.388950i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	9.06218	+	5.23205i	1.48981	+	0.860144i	0.999932	−	0.0116456i	$-0.00370701\pi$
$37$	9.06218	+	5.23205i	1.48981	+	0.860144i	0.489881	+	0.871789i	$0.337040\pi$
$38$	1.26795			0.205689
$39$	0.866025	+	3.50000i	0.138675	+	0.560449i
$40$		0			0
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.998788	+	0.0492283i	$0.0156762\pi$
$41$	9.86603	+	5.69615i	1.54081	+	0.889590i	0.542027	+	0.840361i	$0.317657\pi$
$42$	0.366025	−	0.633975i	0.0564789	−	0.0978244i
$43$	−3.83013	−	6.63397i	−0.584089	−	1.01167i	−0.994988	−	0.0999910i	$-0.968119\pi$
$43$	−3.83013	−	6.63397i	−0.584089	−	1.01167i	0.410899	−	0.911681i	$-0.365215\pi$
$44$		−	4.73205i		−	0.713384i
$45$		0			0
$46$	−5.36603	+	3.09808i	−0.791177	+	0.456786i
$47$			8.19615i			1.19553i	0.801671	+	0.597766i	$0.203945\pi$
$47$			8.19615i			1.19553i	−0.801671	+	0.597766i	$0.796055\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−3.23205	+	5.59808i	−0.461722	+	0.799725i
$50$		0			0
$51$	2.26795			0.317576
$52$	−3.46410	−	1.00000i	−0.480384	−	0.138675i
$53$	−0.464102			−0.0637493			−0.0318746	−	0.999492i	$-0.510148\pi$
$53$	−0.464102			−0.0637493			−0.0318746	+	0.999492i	$0.510148\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	0.366025	+	0.633975i	0.0489122	+	0.0847184i
$57$			1.26795i			0.167944i
$58$	2.13397	−	1.23205i	0.280205	−	0.161776i
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.0241347	−	0.999709i	$-0.492317\pi$
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.877841	+	0.478953i	$0.158984\pi$
$60$		0			0
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	0.825195	−	0.564848i	$-0.191065\pi$
$61$	−0.598076	−	1.03590i	−0.0765758	−	0.132633i	−0.901770	+	0.432215i	$0.857732\pi$
$62$	2.73205	−	4.73205i	0.346971	−	0.600971i
$63$	0.633975	+	0.366025i	0.0798733	+	0.0461149i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.73205			0.582475
$67$	9.63397	+	5.56218i	1.17698	+	0.679528i	0.955313	−	0.295595i	$-0.0955179\pi$
$67$	9.63397	+	5.56218i	1.17698	+	0.679528i	0.221664	+	0.975123i	$0.428851\pi$
$68$	−1.13397	+	1.96410i	−0.137515	+	0.238182i
$69$	−3.09808	−	5.36603i	−0.372965	−	0.645994i
$70$		0			0
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	−0.563742	−	0.825951i	$-0.690639\pi$
$71$	−1.09808	+	0.633975i	−0.130318	+	0.0752389i	0.433424	+	0.901190i	$0.357305\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			9.73205i			1.13905i	0.821974	+	0.569525i	$0.192873\pi$
$73$			9.73205i			1.13905i	−0.821974	+	0.569525i	$0.807127\pi$
$74$	−5.23205	−	9.06218i	−0.608214	−	1.05346i
$75$		0			0
$76$	−1.09808	−	0.633975i	−0.125958	−	0.0727219i
$77$	3.46410			0.394771
$78$	1.00000	−	3.46410i	0.113228	−	0.392232i
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.69615	−	9.86603i	−0.629035	−	1.08952i
$83$			10.1962i			1.11917i	0.828772	+	0.559587i	$0.189040\pi$
$83$			10.1962i			1.11917i	−0.828772	+	0.559587i	$0.810960\pi$
$84$	−0.633975	+	0.366025i	−0.0691723	+	0.0399366i
$85$		0			0
$86$			7.66025i			0.826026i
$87$	1.23205	+	2.13397i	0.132090	+	0.228786i
$88$	−2.36603	+	4.09808i	−0.252219	+	0.436856i
$89$	2.19615	+	1.26795i	0.232792	+	0.134402i	0.611859	−	0.790967i	$-0.290422\pi$
$89$	2.19615	+	1.26795i	0.232792	+	0.134402i	−0.379068	+	0.925369i	$0.623755\pi$
$90$		0			0
$91$	0.732051	−	2.53590i	0.0767398	−	0.265834i
$92$	6.19615			0.645994
$93$	4.73205	+	2.73205i	0.490691	+	0.283300i
$94$	4.09808	−	7.09808i	0.422684	−	0.732111i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$	5.59808	−	3.23205i	0.565491	−	0.326486i
$99$			4.73205i			0.475589i
$100$		0			0
$101$	−5.96410	+	10.3301i	−0.593450	+	1.02789i	0.400313	+	0.916378i	$0.368901\pi$
$101$	−5.96410	+	10.3301i	−0.593450	+	1.02789i	−0.993764	+	0.111508i	$0.964432\pi$
$102$	−1.96410	−	1.13397i	−0.194475	−	0.112280i
$103$	−18.7321			−1.84572			−0.922862	−	0.385131i	$-0.874156\pi$
$103$	−18.7321			−1.84572			−0.922862	+	0.385131i	$0.874156\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	0.401924	+	0.232051i	0.0390383	+	0.0225388i
$107$	−0.0980762	+	0.169873i	−0.00948139	+	0.0164222i	−0.870727	−	0.491766i	$-0.836351\pi$
$107$	−0.0980762	+	0.169873i	−0.00948139	+	0.0164222i	0.861246	+	0.508189i	$0.169685\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			5.46410i			0.523366i	0.965154	+	0.261683i	$0.0842775\pi$
$109$			5.46410i			0.523366i	−0.965154	+	0.261683i	$0.915723\pi$
$110$		0			0
$111$	9.06218	−	5.23205i	0.860144	−	0.496604i
$112$		−	0.732051i		−	0.0691723i
$113$	−9.33013	−	16.1603i	−0.877705	−	1.52023i	−0.853854	−	0.520513i	$-0.825741\pi$
$113$	−9.33013	−	16.1603i	−0.877705	−	1.52023i	−0.0238510	−	0.999716i	$-0.507593\pi$
$114$	0.633975	−	1.09808i	0.0593772	−	0.102844i
$115$		0			0
$116$	−2.46410			−0.228786
$117$	3.46410	+	1.00000i	0.320256	+	0.0924500i
$118$	−8.00000			−0.736460
$119$	−1.43782	−	0.830127i	−0.131805	−	0.0760976i
$120$		0			0
$121$	5.69615	+	9.86603i	0.517832	+	0.896911i
$122$			1.19615i			0.108295i
$123$	9.86603	−	5.69615i	0.889590	−	0.513605i
$124$	−4.73205	+	2.73205i	−0.424951	+	0.245345i
$125$		0			0
$126$	−0.366025	−	0.633975i	−0.0326081	−	0.0564789i
$127$	−8.92820	+	15.4641i	−0.792250	+	1.37222i	0.132321	+	0.991207i	$0.457757\pi$
$127$	−8.92820	+	15.4641i	−0.792250	+	1.37222i	−0.924571	+	0.381010i	$0.875576\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−7.66025			−0.674448
$130$		0			0
$131$	13.4641			1.17636			0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641			1.17636			0.588182	+	0.808729i	$0.299844\pi$
$132$	−4.09808	−	2.36603i	−0.356692	−	0.205936i
$133$	0.464102	−	0.803848i	0.0402427	−	0.0697024i
$134$	−5.56218	−	9.63397i	−0.480499	−	0.832249i
$135$		0			0
$136$	1.96410	−	1.13397i	0.168420	−	0.0972375i
$137$	1.66987	−	0.964102i	0.142667	−	0.0823688i	−0.426968	−	0.904267i	$-0.640418\pi$
$137$	1.66987	−	0.964102i	0.142667	−	0.0823688i	0.569634	+	0.821898i	$0.307085\pi$
$138$			6.19615i			0.527452i
$139$	4.92820	+	8.53590i	0.418005	+	0.724005i	0.995739	−	0.0922197i	$-0.0293962\pi$
$139$	4.92820	+	8.53590i	0.418005	+	0.724005i	−0.577734	+	0.816225i	$0.696063\pi$
$140$		0			0
$141$	7.09808	+	4.09808i	0.597766	+	0.345120i
$142$	1.26795			0.106404
$143$	16.5622	−	4.09808i	1.38500	−	0.342698i
$144$	1.00000			0.0833333
$145$		0			0
$146$	4.86603	−	8.42820i	0.402715	−	0.697523i
$147$	3.23205	+	5.59808i	0.266575	+	0.461722i
$148$			10.4641i			0.860144i
$149$	−2.42820	+	1.40192i	−0.198926	+	0.114850i	−0.596154	−	0.802870i	$-0.703305\pi$
$149$	−2.42820	+	1.40192i	−0.198926	+	0.114850i	0.397228	+	0.917720i	$0.369972\pi$
$150$		0			0
$151$			3.26795i			0.265942i	0.991120	+	0.132971i	$0.0424517\pi$
$151$			3.26795i			0.265942i	−0.991120	+	0.132971i	$0.957548\pi$
$152$	0.633975	+	1.09808i	0.0514221	+	0.0890657i
$153$	1.13397	−	1.96410i	0.0916764	−	0.158788i
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$		0			0
$156$	−2.59808	+	2.50000i	−0.208013	+	0.200160i
$157$	23.5885			1.88256			0.941282	−	0.337622i	$-0.109622\pi$
$157$	23.5885			1.88256			0.941282	+	0.337622i	$0.109622\pi$
$158$	8.19615	+	4.73205i	0.652051	+	0.376462i
$159$	−0.232051	+	0.401924i	−0.0184028	+	0.0318746i
$160$		0			0
$161$			4.53590i			0.357479i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	5.66025	−	3.26795i	0.443345	−	0.255966i	−0.261670	−	0.965157i	$-0.584273\pi$
$163$	5.66025	−	3.26795i	0.443345	−	0.255966i	0.705016	+	0.709192i	$0.250940\pi$
$164$			11.3923i			0.889590i
$165$		0			0
$166$	5.09808	−	8.83013i	0.395687	−	0.685351i
$167$	−2.19615	−	1.26795i	−0.169943	−	0.0981169i	0.412616	−	0.910905i	$-0.364615\pi$
$167$	−2.19615	−	1.26795i	−0.169943	−	0.0981169i	−0.582559	+	0.812788i	$0.697949\pi$
$168$	0.732051			0.0564789
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	1.09808	+	0.633975i	0.0839720	+	0.0484812i
$172$	3.83013	−	6.63397i	0.292044	−	0.505836i
$173$	8.19615	+	14.1962i	0.623142	+	1.07931i	0.988897	+	0.148602i	$0.0474774\pi$
$173$	8.19615	+	14.1962i	0.623142	+	1.07931i	−0.365755	+	0.930711i	$0.619189\pi$
$174$		−	2.46410i		−	0.186803i
$175$		0			0
$176$	4.09808	−	2.36603i	0.308904	−	0.178346i
$177$		−	8.00000i		−	0.601317i
$178$	−1.26795	−	2.19615i	−0.0950368	−	0.164609i
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	−0.0784298	−	0.996920i	$-0.524991\pi$
$179$	11.0263	−	19.0981i	0.824143	−	1.42746i	0.902573	−	0.430538i	$-0.141676\pi$
$180$		0			0
$181$	−8.80385			−0.654385			−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385			−0.654385			−0.327192	+	0.944958i	$0.606103\pi$
$182$	−1.90192	+	1.83013i	−0.140980	+	0.135658i
$183$	−1.19615			−0.0884221
$184$	−5.36603	−	3.09808i	−0.395589	−	0.228393i
$185$		0			0
$186$	−2.73205	−	4.73205i	−0.200324	−	0.346971i
$187$		−	10.7321i		−	0.784805i
$188$	−7.09808	+	4.09808i	−0.517680	+	0.298883i
$189$	0.633975	−	0.366025i	0.0461149	−	0.0266244i
$190$		0			0
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	0.713052	−	0.701111i	$-0.247312\pi$
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	−0.963706	+	0.266966i	$0.913979\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−7.16025	−	4.13397i	−0.515406	−	0.297570i	0.219647	−	0.975579i	$-0.429510\pi$
$193$	−7.16025	−	4.13397i	−0.515406	−	0.297570i	−0.735053	+	0.678009i	$0.762843\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	−6.46410			−0.461722
$197$	−8.53590	−	4.92820i	−0.608158	−	0.351120i	0.164086	−	0.986446i	$-0.447532\pi$
$197$	−8.53590	−	4.92820i	−0.608158	−	0.351120i	−0.772244	+	0.635326i	$0.780866\pi$
$198$	2.36603	−	4.09808i	0.168146	−	0.291238i
$199$	−1.90192	−	3.29423i	−0.134824	−	0.233522i	0.790706	−	0.612196i	$-0.209714\pi$
$199$	−1.90192	−	3.29423i	−0.134824	−	0.233522i	−0.925530	+	0.378674i	$0.876380\pi$
$200$		0			0
$201$	9.63397	−	5.56218i	0.679528	−	0.392326i
$202$	10.3301	−	5.96410i	0.726825	−	0.419633i
$203$		−	1.80385i		−	0.126605i
$204$	1.13397	+	1.96410i	0.0793941	+	0.137515i
$205$		0			0
$206$	16.2224	+	9.36603i	1.13027	+	0.652562i
$207$	−6.19615			−0.430662
$208$	−0.866025	−	3.50000i	−0.0600481	−	0.242681i
$209$	6.00000			0.415029
$210$		0			0
$211$	2.19615	−	3.80385i	0.151189	−	0.261868i	−0.780476	−	0.625186i	$-0.785023\pi$
$211$	2.19615	−	3.80385i	0.151189	−	0.261868i	0.931665	+	0.363319i	$0.118356\pi$
$212$	−0.232051	−	0.401924i	−0.0159373	−	0.0276042i
$213$			1.26795i			0.0868784i
$214$	0.169873	−	0.0980762i	0.0116123	−	0.00670435i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	2.73205	−	4.73205i	0.185038	−	0.320495i
$219$	8.42820	+	4.86603i	0.569525	+	0.328816i
$220$		0			0
$221$	−7.85641	−	2.26795i	−0.528479	−	0.152559i
$222$	−10.4641			−0.702305
$223$	11.3205	+	6.53590i	0.758077	+	0.437676i	0.828605	−	0.559834i	$-0.189135\pi$
$223$	11.3205	+	6.53590i	0.758077	+	0.437676i	−0.0705277	+	0.997510i	$0.522468\pi$
$224$	−0.366025	+	0.633975i	−0.0244561	+	0.0423592i
$225$		0			0
$226$			18.6603i			1.24126i
$227$	−1.56218	+	0.901924i	−0.103685	+	0.0598628i	−0.550946	−	0.834541i	$-0.685733\pi$
$227$	−1.56218	+	0.901924i	−0.103685	+	0.0598628i	0.447261	+	0.894404i	$0.352400\pi$
$228$	−1.09808	+	0.633975i	−0.0727219	+	0.0419860i
$229$			15.8564i			1.04782i	0.851773	+	0.523910i	$0.175527\pi$
$229$			15.8564i			1.04782i	−0.851773	+	0.523910i	$0.824473\pi$
$230$		0			0
$231$	1.73205	−	3.00000i	0.113961	−	0.197386i
$232$	2.13397	+	1.23205i	0.140102	+	0.0808881i
$233$	19.8564			1.30084			0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564			1.30084			0.650418	+	0.759576i	$0.274594\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	6.92820	+	4.00000i	0.450988	+	0.260378i
$237$	−4.73205	+	8.19615i	−0.307380	+	0.532397i
$238$	0.830127	+	1.43782i	0.0538091	+	0.0932002i
$239$			9.66025i			0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$			9.66025i			0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$		0			0
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.902627	−	0.430424i	$-0.858364\pi$
$241$	−15.2321	+	8.79423i	−0.981183	+	0.566486i	−0.0785557	+	0.996910i	$0.525031\pi$
$242$		−	11.3923i		−	0.732325i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.598076	−	1.03590i	0.0382879	−	0.0663166i
$245$		0			0
$246$	−11.3923			−0.726347
$247$	1.26795	−	4.39230i	0.0806777	−	0.279476i
$248$	5.46410			0.346971
$249$	8.83013	+	5.09808i	0.559587	+	0.323077i
$250$		0			0
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	0.950537	−	0.310611i	$-0.100534\pi$
$251$	3.26795	+	5.66025i	0.206271	+	0.357272i	−0.744266	+	0.667883i	$0.767200\pi$
$252$			0.732051i			0.0461149i
$253$	−25.3923	+	14.6603i	−1.59640	+	0.921682i
$254$	15.4641	−	8.92820i	0.970304	−	0.560205i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.3301	+	23.0885i	−0.831510	+	1.44022i	0.0653297	+	0.997864i	$0.479190\pi$
$257$	−13.3301	+	23.0885i	−0.831510	+	1.44022i	−0.896840	+	0.442355i	$0.854143\pi$
$258$	6.63397	+	3.83013i	0.413013	+	0.238453i
$259$	−7.66025			−0.475985
$260$		0			0
$261$	2.46410			0.152524
$262$	−11.6603	−	6.73205i	−0.720373	−	0.415907i
$263$	14.0263	−	24.2942i	0.864897	−	1.49805i	−0.00225153	−	0.999997i	$-0.500717\pi$
$263$	14.0263	−	24.2942i	0.864897	−	1.49805i	0.867149	−	0.498049i	$-0.165950\pi$
$264$	2.36603	+	4.09808i	0.145619	+	0.252219i
$265$		0			0
$266$	−0.803848	+	0.464102i	−0.0492871	+	0.0284559i
$267$	2.19615	−	1.26795i	0.134402	−	0.0775972i
$268$			11.1244i			0.679528i
$269$	0.732051	+	1.26795i	0.0446339	+	0.0773082i	0.887479	−	0.460848i	$-0.152455\pi$
$269$	0.732051	+	1.26795i	0.0446339	+	0.0773082i	−0.842845	+	0.538156i	$0.819121\pi$
$270$		0			0
$271$	−5.07180	−	2.92820i	−0.308090	−	0.177876i	0.337982	−	0.941153i	$-0.390256\pi$
$271$	−5.07180	−	2.92820i	−0.308090	−	0.177876i	−0.646071	+	0.763277i	$0.723589\pi$
$272$	−2.26795			−0.137515
$273$	−1.83013	−	1.90192i	−0.110764	−	0.115110i
$274$	−1.92820			−0.116487
$275$		0			0
$276$	3.09808	−	5.36603i	0.186482	−	0.322997i
$277$	1.13397	+	1.96410i	0.0681339	+	0.118011i	0.898080	−	0.439832i	$-0.144962\pi$
$277$	1.13397	+	1.96410i	0.0681339	+	0.118011i	−0.829946	+	0.557844i	$0.811629\pi$
$278$		−	9.85641i		−	0.591148i
$279$	4.73205	−	2.73205i	0.283300	−	0.163564i
$280$		0			0
$281$		−	22.3205i		−	1.33153i	−0.746162	−	0.665765i	$-0.768105\pi$
$281$		−	22.3205i		−	1.33153i	0.746162	−	0.665765i	$-0.231895\pi$
$282$	−4.09808	−	7.09808i	−0.244037	−	0.422684i
$283$	−4.16987	+	7.22243i	−0.247873	+	0.429329i	−0.962936	−	0.269732i	$-0.913065\pi$
$283$	−4.16987	+	7.22243i	−0.247873	+	0.429329i	0.715062	+	0.699061i	$0.246398\pi$
$284$	−1.09808	−	0.633975i	−0.0651588	−	0.0376195i
$285$		0			0
$286$	−16.3923	−	4.73205i	−0.969297	−	0.279812i
$287$	−8.33975			−0.492280
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	5.92820	−	10.2679i	0.348718	−	0.603997i
$290$		0			0
$291$			6.00000i			0.351726i
$292$	−8.42820	+	4.86603i	−0.493223	+	0.284763i
$293$	12.5718	−	7.25833i	0.734452	−	0.424036i	−0.0855965	−	0.996330i	$-0.527280\pi$
$293$	12.5718	−	7.25833i	0.734452	−	0.424036i	0.820049	+	0.572294i	$0.193946\pi$
$294$		−	6.46410i		−	0.376994i
$295$		0			0
$296$	5.23205	−	9.06218i	0.304107	−	0.526728i
$297$	4.09808	+	2.36603i	0.237795	+	0.137291i
$298$	2.80385			0.162423
$299$	5.36603	+	21.6865i	0.310325	+	1.25416i
$300$		0			0
$301$	4.85641	+	2.80385i	0.279919	+	0.161611i
$302$	1.63397	−	2.83013i	0.0940247	−	0.162856i
$303$	5.96410	+	10.3301i	0.342629	+	0.593450i
$304$		−	1.26795i		−	0.0727219i
$305$		0			0
$306$	−1.96410	+	1.13397i	−0.112280	+	0.0648250i
$307$		−	8.58846i		−	0.490169i	−0.969502	−	0.245085i	$-0.921184\pi$
$307$		−	8.58846i		−	0.490169i	0.969502	−	0.245085i	$-0.0788157\pi$
$308$	1.73205	+	3.00000i	0.0986928	+	0.170941i
$309$	−9.36603	+	16.2224i	−0.532815	+	0.922862i
$310$		0			0
$311$	−15.6603			−0.888012			−0.444006	−	0.896024i	$-0.646443\pi$
$311$	−15.6603			−0.888012			−0.444006	+	0.896024i	$0.646443\pi$
$312$	3.50000	−	0.866025i	0.198148	−	0.0490290i
$313$	−13.4641			−0.761036			−0.380518	−	0.924774i	$-0.624254\pi$
$313$	−13.4641			−0.761036			−0.380518	+	0.924774i	$0.624254\pi$
$314$	−20.4282	−	11.7942i	−1.15283	−	0.665587i
$315$		0			0
$316$	−4.73205	−	8.19615i	−0.266199	−	0.461070i
$317$			3.33975i			0.187579i	0.995592	+	0.0937894i	$0.0298980\pi$
$317$			3.33975i			0.187579i	−0.995592	+	0.0937894i	$0.970102\pi$
$318$	0.401924	−	0.232051i	0.0225388	−	0.0130128i
$319$	10.0981	−	5.83013i	0.565384	−	0.326424i
$320$		0			0
$321$	0.0980762	+	0.169873i	0.00547408	+	0.00948139i
$322$	2.26795	−	3.92820i	0.126388	−	0.218910i
$323$	−2.49038	−	1.43782i	−0.138569	−	0.0800026i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.53590			−0.361990
$327$	4.73205	+	2.73205i	0.261683	+	0.151083i
$328$	5.69615	−	9.86603i	0.314517	−	0.544760i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.893708	−	0.448649i	$-0.851905\pi$
$331$	−17.3205	+	10.0000i	−0.952021	+	0.549650i	−0.0583130	+	0.998298i	$0.518572\pi$
$332$	−8.83013	+	5.09808i	−0.484616	+	0.279793i
$333$		−	10.4641i		−	0.573429i
$334$	1.26795	+	2.19615i	0.0693791	+	0.120168i
$335$		0			0
$336$	−0.633975	−	0.366025i	−0.0345861	−	0.0199683i
$337$	6.85641			0.373492			0.186746	−	0.982408i	$-0.440206\pi$
$337$	6.85641			0.373492			0.186746	+	0.982408i	$0.440206\pi$
$338$	−6.92820	+	11.0000i	−0.376845	+	0.598321i
$339$	−18.6603			−1.01349
$340$		0			0
$341$	12.9282	−	22.3923i	0.700101	−	1.21261i
$342$	−0.633975	−	1.09808i	−0.0342814	−	0.0593772i
$343$		−	9.85641i		−	0.532196i
$344$	−6.63397	+	3.83013i	−0.357680	+	0.206507i
$345$		0			0
$346$		−	16.3923i		−	0.881256i
$347$	4.43782	+	7.68653i	0.238235	+	0.412635i	0.960208	−	0.279286i	$-0.0900979\pi$
$347$	4.43782	+	7.68653i	0.238235	+	0.412635i	−0.721973	+	0.691921i	$0.756765\pi$
$348$	−1.23205	+	2.13397i	−0.0660449	+	0.114393i
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$349$	16.7321	+	9.66025i	0.895646	+	0.517102i	0.0198610	+	0.999803i	$0.493678\pi$
$350$		0			0
$351$	2.59808	−	2.50000i	0.138675	−	0.133440i
$352$	−4.73205			−0.252219
$353$	−17.1340	−	9.89230i	−0.911949	−	0.526514i	−0.0308916	−	0.999523i	$-0.509835\pi$
$353$	−17.1340	−	9.89230i	−0.911949	−	0.526514i	−0.881058	+	0.473008i	$0.843168\pi$
$354$	−4.00000	+	6.92820i	−0.212598	+	0.368230i
$355$		0			0
$356$			2.53590i			0.134402i
$357$	−1.43782	+	0.830127i	−0.0760976	+	0.0439350i
$358$	−19.0981	+	11.0263i	−1.00936	+	0.582757i
$359$			23.1244i			1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$			23.1244i			1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$		0			0
$361$	−8.69615	+	15.0622i	−0.457692	+	0.792746i
$362$	7.62436	+	4.40192i	0.400727	+	0.231360i
$363$	11.3923			0.597941
$364$	2.56218	−	0.633975i	0.134295	−	0.0332293i
$365$		0			0
$366$	1.03590	+	0.598076i	0.0541473	+	0.0312619i
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	−0.991700	−	0.128572i	$-0.958961\pi$
$367$	−7.36603	+	12.7583i	−0.384503	+	0.665979i	0.607197	+	0.794551i	$0.292294\pi$
$368$	3.09808	+	5.36603i	0.161498	+	0.279723i
$369$		−	11.3923i		−	0.593060i
$370$		0			0
$371$	0.294229	−	0.169873i	0.0152756	−	0.00881937i
$372$			5.46410i			0.283300i
$373$	−5.13397	−	8.89230i	−0.265827	−	0.460426i	0.701953	−	0.712223i	$-0.252312\pi$
$373$	−5.13397	−	8.89230i	−0.265827	−	0.460426i	−0.967780	+	0.251797i	$0.918978\pi$
$374$	−5.36603	+	9.29423i	−0.277471	+	0.480593i
$375$		0			0
$376$	8.19615			0.422684
$377$	−2.13397	−	8.62436i	−0.109905	−	0.444177i
$378$	−0.732051			−0.0376526
$379$	1.26795	+	0.732051i	0.0651302	+	0.0376029i	0.532211	−	0.846611i	$-0.321361\pi$
$379$	1.26795	+	0.732051i	0.0651302	+	0.0376029i	−0.467081	+	0.884214i	$0.654694\pi$
$380$		0			0
$381$	8.92820	+	15.4641i	0.457406	+	0.792250i
$382$			6.92820i			0.354478i
$383$	4.73205	−	2.73205i	0.241797	−	0.139601i	−0.374206	−	0.927346i	$-0.622085\pi$
$383$	4.73205	−	2.73205i	0.241797	−	0.139601i	0.616002	+	0.787744i	$0.288751\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	4.13397	+	7.16025i	0.210414	+	0.364447i
$387$	−3.83013	+	6.63397i	−0.194696	+	0.337224i
$388$	−5.19615	−	3.00000i	−0.263795	−	0.152302i
$389$	29.7846			1.51014			0.755070	−	0.655644i	$-0.227603\pi$
$389$	29.7846			1.51014			0.755070	+	0.655644i	$0.227603\pi$
$390$		0			0
$391$	14.0526			0.710668
$392$	5.59808	+	3.23205i	0.282746	+	0.163243i
$393$	6.73205	−	11.6603i	0.339587	−	0.588182i
$394$	4.92820	+	8.53590i	0.248279	+	0.430032i
$395$		0			0
$396$	−4.09808	+	2.36603i	−0.205936	+	0.118897i
$397$	0.339746	−	0.196152i	0.0170514	−	0.00984461i	−0.491450	−	0.870906i	$-0.663533\pi$
$397$	0.339746	−	0.196152i	0.0170514	−	0.00984461i	0.508501	+	0.861061i	$0.330200\pi$
$398$			3.80385i			0.190670i
$399$	−0.464102	−	0.803848i	−0.0232341	−	0.0402427i
$400$		0			0
$401$	−18.9904	−	10.9641i	−0.948334	−	0.547521i	−0.0557713	−	0.998444i	$-0.517762\pi$
$401$	−18.9904	−	10.9641i	−0.948334	−	0.547521i	−0.892563	+	0.450922i	$0.851095\pi$
$402$	−11.1244			−0.554832
$403$	−13.6603	−	14.1962i	−0.680466	−	0.707161i
$404$	−11.9282			−0.593450
$405$		0			0
$406$	−0.901924	+	1.56218i	−0.0447617	+	0.0775296i
$407$	−24.7583	−	42.8827i	−1.22722	−	2.12562i
$408$		−	2.26795i		−	0.112280i
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	−0.773351	−	0.633978i	$-0.781421\pi$
$409$	−12.3564	+	7.13397i	−0.610985	+	0.352752i	0.162366	+	0.986731i	$0.448088\pi$
$410$		0			0
$411$		−	1.92820i		−	0.0951113i
$412$	−9.36603	−	16.2224i	−0.461431	−	0.799222i
$413$	−2.92820	+	5.07180i	−0.144087	+	0.249567i
$414$	5.36603	+	3.09808i	0.263726	+	0.152262i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	9.85641			0.482670
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	−0.708177	−	0.706035i	$-0.750482\pi$
$419$	5.26795	−	9.12436i	0.257356	−	0.445754i	0.965533	+	0.260281i	$0.0838153\pi$
$420$		0			0
$421$		−	32.7128i		−	1.59432i	−0.603765	−	0.797162i	$-0.706333\pi$
$421$		−	32.7128i		−	1.59432i	0.603765	−	0.797162i	$-0.293667\pi$
$422$	−3.80385	+	2.19615i	−0.185168	+	0.106907i
$423$	7.09808	−	4.09808i	0.345120	−	0.199255i
$424$			0.464102i			0.0225388i
$425$		0			0
$426$	0.633975	−	1.09808i	0.0307162	−	0.0532020i
$427$	0.758330	+	0.437822i	0.0366982	+	0.0211877i
$428$	−0.196152			−0.00948139
$429$	4.73205	−	16.3923i	0.228466	−	0.791428i
$430$		0			0
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	0.249694	−	0.968325i	$-0.419670\pi$
$431$	−9.63397	−	5.56218i	−0.464052	−	0.267921i	−0.713747	+	0.700404i	$0.753003\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	7.42820	+	12.8660i	0.356977	+	0.618302i	0.987454	−	0.157906i	$-0.0504742\pi$
$433$	7.42820	+	12.8660i	0.356977	+	0.618302i	−0.630478	+	0.776208i	$0.717141\pi$
$434$			4.00000i			0.192006i
$435$		0			0
$436$	−4.73205	+	2.73205i	−0.226624	+	0.130842i
$437$			7.85641i			0.375823i
$438$	−4.86603	−	8.42820i	−0.232508	−	0.402715i
$439$	−8.83013	+	15.2942i	−0.421439	+	0.729954i	−0.996080	−	0.0884515i	$-0.971808\pi$
$439$	−8.83013	+	15.2942i	−0.421439	+	0.729954i	0.574642	+	0.818405i	$0.305141\pi$
$440$		0			0
$441$	6.46410			0.307814
$442$	5.66987	+	5.89230i	0.269688	+	0.280268i
$443$	−36.3923			−1.72905			−0.864525	−	0.502589i	$-0.832381\pi$
$443$	−36.3923			−1.72905			−0.864525	+	0.502589i	$0.832381\pi$
$444$	9.06218	+	5.23205i	0.430072	+	0.248302i
$445$		0			0
$446$	−6.53590	−	11.3205i	−0.309484	−	0.536042i
$447$			2.80385i			0.132617i
$448$	0.633975	−	0.366025i	0.0299525	−	0.0172931i
$449$	−20.1962	+	11.6603i	−0.953115	+	0.550281i	−0.894047	−	0.447973i	$-0.852146\pi$
$449$	−20.1962	+	11.6603i	−0.953115	+	0.550281i	−0.0590680	+	0.998254i	$0.518813\pi$
$450$		0			0
$451$	−26.9545	−	46.6865i	−1.26924	−	2.19838i
$452$	9.33013	−	16.1603i	0.438852	−	0.760114i
$453$	2.83013	+	1.63397i	0.132971	+	0.0767708i
$454$	1.80385			0.0846588
$455$		0			0
$456$	1.26795			0.0593772
$457$	−16.1603	−	9.33013i	−0.755945	−	0.436445i	0.0718931	−	0.997412i	$-0.477096\pi$
$457$	−16.1603	−	9.33013i	−0.755945	−	0.436445i	−0.827838	+	0.560967i	$0.810429\pi$
$458$	7.92820	−	13.7321i	0.370461	−	0.641657i
$459$	−1.13397	−	1.96410i	−0.0529294	−	0.0916764i
$460$		0			0
$461$	−22.2846	+	12.8660i	−1.03790	+	0.599231i	−0.919237	−	0.393704i	$-0.871193\pi$
$461$	−22.2846	+	12.8660i	−1.03790	+	0.599231i	−0.118661	+	0.992935i	$0.537860\pi$
$462$	−3.00000	+	1.73205i	−0.139573	+	0.0805823i
$463$			28.0526i			1.30371i	0.758342	+	0.651856i	$0.226010\pi$
$463$			28.0526i			1.30371i	−0.758342	+	0.651856i	$0.773990\pi$
$464$	−1.23205	−	2.13397i	−0.0571965	−	0.0990673i
$465$		0			0
$466$	−17.1962	−	9.92820i	−0.796596	−	0.459915i
$467$	−12.5885			−0.582524			−0.291262	−	0.956643i	$-0.594075\pi$
$467$	−12.5885			−0.582524			−0.291262	+	0.956643i	$0.594075\pi$
$468$	0.866025	+	3.50000i	0.0400320	+	0.161788i
$469$	−8.14359			−0.376036
$470$		0			0
$471$	11.7942	−	20.4282i	0.543449	−	0.941282i
$472$	−4.00000	−	6.92820i	−0.184115	−	0.318896i
$473$			36.2487i			1.66672i
$474$	8.19615	−	4.73205i	0.376462	−	0.217350i
$475$		0			0
$476$		−	1.66025i		−	0.0760976i
$477$	0.232051	+	0.401924i	0.0106249	+	0.0184028i
$478$	4.83013	−	8.36603i	0.220925	−	0.382653i
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.127363	−	0.991856i	$-0.540651\pi$
$479$	−22.9808	−	13.2679i	−1.05002	−	0.606228i	−0.922654	+	0.385628i	$0.873985\pi$
$480$		0			0
$481$	−36.6244	+	9.06218i	−1.66993	+	0.413200i
$482$	17.5885			0.801132
$483$	3.92820	+	2.26795i	0.178739	+	0.103195i
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	18.2942	−	10.5622i	0.828991	−	0.478618i	−0.0245163	−	0.999699i	$-0.507805\pi$
$487$	18.2942	−	10.5622i	0.828991	−	0.478618i	0.853507	+	0.521081i	$0.174471\pi$
$488$	−1.03590	+	0.598076i	−0.0468929	+	0.0270736i
$489$		−	6.53590i		−	0.295564i
$490$		0			0
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	−0.800450	−	0.599399i	$-0.795406\pi$
$491$	2.63397	−	4.56218i	0.118870	−	0.205888i	0.919320	+	0.393511i	$0.128740\pi$
$492$	9.86603	+	5.69615i	0.444795	+	0.256802i
$493$	−5.58846			−0.251691
$494$	−3.29423	+	3.16987i	−0.148214	+	0.142619i
$495$		0			0
$496$	−4.73205	−	2.73205i	−0.212475	−	0.122673i
$497$	0.464102	−	0.803848i	0.0208178	−	0.0360575i
$498$	−5.09808	−	8.83013i	−0.228450	−	0.395687i
$499$		−	32.0000i		−	1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$		−	32.0000i		−	1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$		0			0
$501$	−2.19615	+	1.26795i	−0.0981169	+	0.0566478i
$502$		−	6.53590i		−	0.291711i
$503$	−5.49038	−	9.50962i	−0.244804	−	0.424013i	0.717272	−	0.696793i	$-0.245390\pi$
$503$	−5.49038	−	9.50962i	−0.244804	−	0.424013i	−0.962076	+	0.272780i	$0.912057\pi$
$504$	0.366025	−	0.633975i	0.0163041	−	0.0282395i
$505$		0			0
$506$	29.3205			1.30346
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	−17.8564			−0.792250
$509$	8.89230	+	5.13397i	0.394144	+	0.227559i	0.683954	−	0.729525i	$-0.260259\pi$
$509$	8.89230	+	5.13397i	0.394144	+	0.227559i	−0.289810	+	0.957084i	$0.593592\pi$
$510$		0			0
$511$	−3.56218	−	6.16987i	−0.157581	−	0.272939i
$512$			1.00000i			0.0441942i
$513$	1.09808	−	0.633975i	0.0484812	−	0.0279907i
$514$	23.0885	−	13.3301i	1.01839	−	0.587967i
$515$		0			0
$516$	−3.83013	−	6.63397i	−0.168612	−	0.292044i
$517$	19.3923	−	33.5885i	0.852873	−	1.47722i
$518$	6.63397	+	3.83013i	0.291480	+	0.168286i
$519$	16.3923			0.719542
$520$		0			0
$521$	−17.4449			−0.764273			−0.382137	−	0.924106i	$-0.624812\pi$
$521$	−17.4449			−0.764273			−0.382137	+	0.924106i	$0.624812\pi$
$522$	−2.13397	−	1.23205i	−0.0934015	−	0.0539254i
$523$	18.2224	−	31.5622i	0.796811	−	1.38012i	−0.124871	−	0.992173i	$-0.539852\pi$
$523$	18.2224	−	31.5622i	0.796811	−	1.38012i	0.921683	−	0.387945i	$-0.126815\pi$
$524$	6.73205	+	11.6603i	0.294091	+	0.509381i
$525$		0			0
$526$	−24.2942	+	14.0263i	−1.05928	+	0.611575i
$527$	−10.7321	+	6.19615i	−0.467495	+	0.269909i
$528$		−	4.73205i		−	0.205936i
$529$	−7.69615	−	13.3301i	−0.334615	−	0.579571i
$530$		0			0
$531$	−6.92820	−	4.00000i	−0.300658	−	0.173585i
$532$	0.928203			0.0402427
$533$	−39.8731	+	9.86603i	−1.72709	+	0.427345i
$534$	−2.53590			−0.109739
$535$		0			0
$536$	5.56218	−	9.63397i	0.240249	−	0.416124i
$537$	−11.0263	−	19.0981i	−0.475819	−	0.824143i
$538$		−	1.46410i		−	0.0631219i
$539$	26.4904	−	15.2942i	1.14102	−	0.658769i
$540$		0			0
$541$			40.3205i			1.73351i	0.498731	+	0.866757i	$0.333800\pi$
$541$			40.3205i			1.73351i	−0.498731	+	0.866757i	$0.666200\pi$
$542$	2.92820	+	5.07180i	0.125777	+	0.217852i
$543$	−4.40192	+	7.62436i	−0.188905	+	0.327192i
$544$	1.96410	+	1.13397i	0.0842102	+	0.0486188i
$545$		0			0
$546$	0.633975	+	2.56218i	0.0271316	+	0.109651i
$547$	−6.19615			−0.264928			−0.132464	−	0.991188i	$-0.542289\pi$
$547$	−6.19615			−0.264928			−0.132464	+	0.991188i	$0.542289\pi$
$548$	1.66987	+	0.964102i	0.0713334	+	0.0411844i
$549$	−0.598076	+	1.03590i	−0.0255253	+	0.0442111i
$550$		0			0
$551$		−	3.12436i		−	0.133102i
$552$	−5.36603	+	3.09808i	−0.228393	+	0.131863i
$553$	6.00000	−	3.46410i	0.255146	−	0.147309i
$554$		−	2.26795i		−	0.0963559i
$555$		0			0
$556$	−4.92820	+	8.53590i	−0.209002	+	0.362003i
$557$	−26.3038	−	15.1865i	−1.11453	−	0.643474i	−0.174531	−	0.984652i	$-0.555841\pi$
$557$	−26.3038	−	15.1865i	−1.11453	−	0.643474i	−0.939999	+	0.341178i	$0.889174\pi$
$558$	−5.46410			−0.231314
$559$	26.5359	+	7.66025i	1.12235	+	0.323994i
$560$		0			0
$561$	−9.29423	−	5.36603i	−0.392403	−	0.226554i
$562$	−11.1603	+	19.3301i	−0.470767	+	0.815392i
$563$	−10.5359	−	18.2487i	−0.444035	−	0.769091i	0.553949	−	0.832550i	$-0.313120\pi$
$563$	−10.5359	−	18.2487i	−0.444035	−	0.769091i	−0.997984	+	0.0634589i	$0.979787\pi$
$564$			8.19615i			0.345120i
$565$		0			0
$566$	7.22243	−	4.16987i	0.303581	−	0.175273i
$567$		−	0.732051i		−	0.0307432i
$568$	0.633975	+	1.09808i	0.0266010	+	0.0460743i
$569$	−19.3205	+	33.4641i	−0.809958	+	1.40289i	0.102935	+	0.994688i	$0.467177\pi$
$569$	−19.3205	+	33.4641i	−0.809958	+	1.40289i	−0.912893	+	0.408200i	$0.866157\pi$
$570$		0			0
$571$	24.0526			1.00657			0.503284	−	0.864121i	$-0.332125\pi$
$571$	24.0526			1.00657			0.503284	+	0.864121i	$0.332125\pi$
$572$	11.8301	+	12.2942i	0.494642	+	0.514048i
$573$	−6.92820			−0.289430
$574$	7.22243	+	4.16987i	0.301458	+	0.174047i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$			0.267949i			0.0111549i	0.999984	+	0.00557744i	$0.00177536\pi$
$577$			0.267949i			0.0111549i	−0.999984	+	0.00557744i	$0.998225\pi$
$578$	−10.2679	+	5.92820i	−0.427090	+	0.246581i
$579$	−7.16025	+	4.13397i	−0.297570	+	0.171802i
$580$		0			0
$581$	−3.73205	−	6.46410i	−0.154832	−	0.268176i
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	1.90192	+	1.09808i	0.0787696	+	0.0454777i
$584$	9.73205			0.402715
$585$		0			0
$586$	−14.5167			−0.599678
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	0.185999	−	0.982550i	$-0.440448\pi$
$587$	−13.8564	−	8.00000i	−0.571915	−	0.330195i	−0.757914	+	0.652355i	$0.773781\pi$
$588$	−3.23205	+	5.59808i	−0.133288	+	0.230861i
$589$	−3.46410	−	6.00000i	−0.142736	−	0.247226i
$590$		0			0
$591$	−8.53590	+	4.92820i	−0.351120	+	0.202719i
$592$	−9.06218	+	5.23205i	−0.372453	+	0.215036i
$593$			36.8564i			1.51351i	0.653698	+	0.756756i	$0.273217\pi$
$593$			36.8564i			1.51351i	−0.653698	+	0.756756i	$0.726783\pi$
$594$	−2.36603	−	4.09808i	−0.0970792	−	0.168146i
$595$		0			0
$596$	−2.42820	−	1.40192i	−0.0994631	−	0.0574250i
$597$	−3.80385			−0.155681
$598$	6.19615	−	21.4641i	0.253380	−	0.877732i
$599$	−9.46410			−0.386693			−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410			−0.386693			−0.193346	+	0.981131i	$0.561934\pi$
$600$		0			0
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	−0.799218	−	0.601041i	$-0.794753\pi$
$601$	2.96410	−	5.13397i	0.120908	−	0.209419i	0.920126	+	0.391622i	$0.128086\pi$
$602$	−2.80385	−	4.85641i	−0.114276	−	0.197932i
$603$		−	11.1244i		−	0.453019i
$604$	−2.83013	+	1.63397i	−0.115156	+	0.0664855i
$605$		0			0
$606$		−	11.9282i		−	0.484550i
$607$	0.392305	+	0.679492i	0.0159232	+	0.0275797i	0.873877	−	0.486147i	$-0.161598\pi$
$607$	0.392305	+	0.679492i	0.0159232	+	0.0275797i	−0.857954	+	0.513726i	$0.828265\pi$
$608$	−0.633975	+	1.09808i	−0.0257111	+	0.0445329i
$609$	−1.56218	−	0.901924i	−0.0633026	−	0.0365478i
$610$		0			0
$611$	−20.4904	−	21.2942i	−0.828952	−	0.861472i
$612$	2.26795			0.0916764
$613$	−9.86603	−	5.69615i	−0.398485	−	0.230065i	0.287345	−	0.957827i	$-0.407227\pi$
$613$	−9.86603	−	5.69615i	−0.398485	−	0.230065i	−0.685830	+	0.727762i	$0.740561\pi$
$614$	−4.29423	+	7.43782i	−0.173301	+	0.300166i
$615$		0			0
$616$		−	3.46410i		−	0.139573i
$617$	30.5263	−	17.6244i	1.22894	−	0.709530i	0.262133	−	0.965032i	$-0.415574\pi$
$617$	30.5263	−	17.6244i	1.22894	−	0.709530i	0.966809	+	0.255502i	$0.0822407\pi$
$618$	16.2224	−	9.36603i	0.652562	−	0.376757i
$619$			10.5359i			0.423474i	0.977327	+	0.211737i	$0.0679119\pi$
$619$			10.5359i			0.423474i	−0.977327	+	0.211737i	$0.932088\pi$
$620$		0			0
$621$	−3.09808	+	5.36603i	−0.124322	+	0.215331i
$622$	13.5622	+	7.83013i	0.543794	+	0.313959i
$623$	−1.85641			−0.0743754
$624$	−3.46410	−	1.00000i	−0.138675	−	0.0400320i
$625$		0			0
$626$	11.6603	+	6.73205i	0.466037	+	0.269067i
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	11.7942	+	20.4282i	0.470641	+	0.815174i
$629$			23.7321i			0.946259i
$630$		0			0
$631$	41.3205	−	23.8564i	1.64494	−	0.949709i	0.665904	−	0.746037i	$-0.268046\pi$
$631$	41.3205	−	23.8564i	1.64494	−	0.949709i	0.979039	−	0.203671i	$-0.0652874\pi$
$632$			9.46410i			0.376462i
$633$	−2.19615	−	3.80385i	−0.0872892	−	0.151189i
$634$	1.66987	−	2.89230i	0.0663191	−	0.114868i
$635$		0			0
$636$	−0.464102			−0.0184028
$637$	−5.59808	−	22.6244i	−0.221804	−	0.896410i
$638$	−11.6603			−0.461634
$639$	1.09808	+	0.633975i	0.0434392	+	0.0250796i
$640$		0			0
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	0.999885	+	0.0151806i	$0.00483233\pi$
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	−0.486796	+	0.873516i	$0.661834\pi$
$642$		−	0.196152i		−	0.00774152i
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$	−3.92820	+	2.26795i	−0.154793	+	0.0893697i
$645$		0			0
$646$	1.43782	+	2.49038i	0.0565704	+	0.0979827i
$647$	−13.1244	+	22.7321i	−0.515972	+	0.893689i	0.483856	+	0.875147i	$0.339236\pi$
$647$	−13.1244	+	22.7321i	−0.515972	+	0.893689i	−0.999828	+	0.0185417i	$0.994098\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−37.8564			−1.48599
$650$		0			0
$651$	−4.00000			−0.156772
$652$	5.66025	+	3.26795i	0.221673	+	0.127983i
$653$	−5.26795	+	9.12436i	−0.206151	+	0.357064i	−0.950499	−	0.310728i	$-0.899427\pi$
$653$	−5.26795	+	9.12436i	−0.206151	+	0.357064i	0.744348	+	0.667792i	$0.232760\pi$
$654$	−2.73205	−	4.73205i	−0.106832	−	0.185038i
$655$		0			0
$656$	−9.86603	+	5.69615i	−0.385204	+	0.222397i
$657$	8.42820	−	4.86603i	0.328816	−	0.189842i
$658$			6.00000i			0.233904i
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	−0.950205	−	0.311627i	$-0.899126\pi$
$659$	−19.1244	−	33.1244i	−0.744979	−	1.29034i	0.205225	−	0.978715i	$-0.434207\pi$
$660$		0			0
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	0.649776	−	0.760126i	$-0.274863\pi$
$661$	8.13397	+	4.69615i	0.316375	+	0.182659i	−0.333401	+	0.942785i	$0.608196\pi$
$662$	20.0000			0.777322
$663$	−5.89230	+	5.66987i	−0.228838	+	0.220200i
$664$	10.1962			0.395687
$665$		0			0
$666$	−5.23205	+	9.06218i	−0.202738	+	0.351152i
$667$	7.63397	+	13.2224i	0.295589	+	0.511975i
$668$		−	2.53590i		−	0.0981169i
$669$	11.3205	−	6.53590i	0.437676	−	0.252692i
$670$		0			0
$671$			5.66025i			0.218512i
$672$	0.366025	+	0.633975i	0.0141197	+	0.0244561i
$673$	−7.03590	+	12.1865i	−0.271214	+	0.469756i	−0.969173	−	0.246381i	$-0.920758\pi$
$673$	−7.03590	+	12.1865i	−0.271214	+	0.469756i	0.697959	+	0.716138i	$0.254092\pi$
$674$	−5.93782	−	3.42820i	−0.228716	−	0.132049i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	38.5359			1.48105			0.740527	−	0.672026i	$-0.234576\pi$
$677$	38.5359			1.48105			0.740527	+	0.672026i	$0.234576\pi$
$678$	16.1603	+	9.33013i	0.620631	+	0.358321i
$679$	2.19615	−	3.80385i	0.0842806	−	0.145978i
$680$		0			0
$681$			1.80385i			0.0691236i
$682$	−22.3923	+	12.9282i	−0.857446	+	0.495046i
$683$	32.7846	−	18.9282i	1.25447	−	0.724268i	0.282475	−	0.959275i	$-0.408845\pi$
$683$	32.7846	−	18.9282i	1.25447	−	0.724268i	0.971994	+	0.235007i	$0.0755114\pi$
$684$			1.26795i			0.0484812i
$685$		0			0
$686$	−4.92820	+	8.53590i	−0.188160	+	0.325902i
$687$	13.7321	+	7.92820i	0.523910	+	0.302480i
$688$	7.66025			0.292044
$689$	1.20577	−	1.16025i	0.0459362	−	0.0442022i
$690$		0			0
$691$	22.8109	+	13.1699i	0.867767	+	0.501006i	0.866606	−	0.498994i	$-0.166297\pi$
$691$	22.8109	+	13.1699i	0.867767	+	0.501006i	0.00116153	+	0.999999i	$0.499630\pi$
$692$	−8.19615	+	14.1962i	−0.311571	+	0.539657i
$693$	−1.73205	−	3.00000i	−0.0657952	−	0.113961i
$694$		−	8.87564i		−	0.336915i
$695$		0			0
$696$	2.13397	−	1.23205i	0.0808881	−	0.0467008i
$697$			25.8372i			0.978653i
$698$	−9.66025	−	16.7321i	−0.365646	−	0.633317i
$699$	9.92820	−	17.1962i	0.375519	−	0.650418i
$700$		0			0
$701$	−31.3205			−1.18296			−0.591480	−	0.806320i	$-0.701456\pi$
$701$	−31.3205			−1.18296			−0.591480	+	0.806320i	$0.701456\pi$
$702$	−3.50000	+	0.866025i	−0.132099	+	0.0326860i
$703$	−13.2679			−0.500410
$704$	4.09808	+	2.36603i	0.154452	+	0.0891729i
$705$		0			0
$706$	9.89230	+	17.1340i	0.372302	+	0.644846i
$707$		−	8.73205i		−	0.328403i
$708$	6.92820	−	4.00000i	0.260378	−	0.150329i
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.343707	−	0.939077i	$-0.388317\pi$
$709$	35.3827	−	20.4282i	1.32882	−	0.767197i	0.985118	+	0.171880i	$0.0549841\pi$
$710$		0			0
$711$	4.73205	+	8.19615i	0.177466	+	0.307380i
$712$	1.26795	−	2.19615i	0.0475184	−	0.0823043i
$713$	29.3205	+	16.9282i	1.09806	+	0.633966i
$714$	1.66025			0.0621334
$715$		0			0
$716$	22.0526			0.824143
$717$	8.36603	+	4.83013i	0.312435	+	0.180384i
$718$	11.5622	−	20.0263i	0.431497	−	0.747374i
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	0.575737	−	0.817635i	$-0.304715\pi$
$719$	−11.2679	−	19.5167i	−0.420224	−	0.727849i	−0.995961	+	0.0897860i	$0.971382\pi$
$720$		0			0
$721$	11.8756	−	6.85641i	0.442272	−	0.255346i
$722$	15.0622	−	8.69615i	0.560556	−	0.323637i
$723$			17.5885i			0.654122i
$724$	−4.40192	−	7.62436i	−0.163596	−	0.283357i
$725$		0			0
$726$	−9.86603	−	5.69615i	−0.366163	−	0.211404i
$727$	20.9808			0.778133			0.389067	−	0.921210i	$-0.372798\pi$
$727$	20.9808			0.778133			0.389067	+	0.921210i	$0.372798\pi$
$728$	−2.53590	−	0.732051i	−0.0939866	−	0.0271316i
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.68653	−	15.0455i	0.321283	−	0.556479i
$732$	−0.598076	−	1.03590i	−0.0221055	−	0.0382879i
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$	12.7583	−	7.36603i	0.470919	−	0.271885i
$735$		0			0
$736$		−	6.19615i		−	0.228393i
$737$	−26.3205	−	45.5885i	−0.969528	−	1.67927i
$738$	−5.69615	+	9.86603i	−0.209678	+	0.363173i
$739$	9.46410	+	5.46410i	0.348143	+	0.201000i	0.663867	−	0.747851i	$-0.268914\pi$
$739$	9.46410	+	5.46410i	0.348143	+	0.201000i	−0.315724	+	0.948851i	$0.602247\pi$
$740$		0			0
$741$	−3.16987	−	3.29423i	−0.116448	−	0.121017i
$742$	−0.339746			−0.0124725
$743$	23.9090	+	13.8038i	0.877135	+	0.506414i	0.869713	−	0.493558i	$-0.164304\pi$
$743$	23.9090	+	13.8038i	0.877135	+	0.506414i	0.00742221	+	0.999972i	$0.497637\pi$
$744$	2.73205	−	4.73205i	0.100162	−	0.173485i
$745$		0			0
$746$			10.2679i			0.375936i
$747$	8.83013	−	5.09808i	0.323077	−	0.186529i
$748$	9.29423	−	5.36603i	0.339831	−	0.196201i
$749$		−	0.143594i		−	0.00524679i
$750$		0			0
$751$	7.95448	−	13.7776i	0.290263	−	0.502751i	−0.683609	−	0.729849i	$-0.739590\pi$
$751$	7.95448	−	13.7776i	0.290263	−	0.502751i	0.973872	+	0.227098i	$0.0729238\pi$
$752$	−7.09808	−	4.09808i	−0.258840	−	0.149441i
$753$	6.53590			0.238181
$754$	−2.46410	+	8.53590i	−0.0897373	+	0.310859i
$755$		0			0
$756$	0.633975	+	0.366025i	0.0230574	+	0.0133122i
$757$	3.53590	−	6.12436i	0.128514	−	0.222593i	−0.794587	−	0.607151i	$-0.792312\pi$
$757$	3.53590	−	6.12436i	0.128514	−	0.222593i	0.923101	+	0.384557i	$0.125646\pi$
$758$	−0.732051	−	1.26795i	−0.0265893	−	0.0460540i
$759$			29.3205i			1.06427i
$760$		0			0
$761$	−20.1962	+	11.6603i	−0.732110	+	0.422684i	−0.819194	−	0.573517i	$-0.805579\pi$
$761$	−20.1962	+	11.6603i	−0.732110	+	0.422684i	0.0870836	+	0.996201i	$0.472245\pi$
$762$		−	17.8564i		−	0.646869i
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	3.46410	−	6.00000i	0.125327	−	0.217072i
$765$		0			0
$766$	−5.46410			−0.197426
$767$	−8.00000	+	27.7128i	−0.288863	+	1.00065i
$768$	−1.00000			−0.0360844
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	0.226270	−	0.974065i	$-0.427347\pi$
$769$	−13.9808	−	8.07180i	−0.504159	−	0.291076i	−0.730429	+	0.682988i	$0.760680\pi$
$770$		0			0
$771$	13.3301	+	23.0885i	0.480073	+	0.831510i
$772$		−	8.26795i		−	0.297570i
$773$	−30.3731	+	17.5359i	−1.09244	+	0.630722i	−0.934226	−	0.356682i	$-0.883908\pi$
$773$	−30.3731	+	17.5359i	−1.09244	+	0.630722i	−0.158217	+	0.987404i	$0.550575\pi$
$774$	6.63397	−	3.83013i	0.238453	−	0.137671i
$775$		0			0
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−3.83013	+	6.63397i	−0.137405	+	0.237993i
$778$	−25.7942	−	14.8923i	−0.924768	−	0.533915i
$779$	−14.4449			−0.517541
$780$		0			0
$781$	6.00000			0.214697
$782$	−12.1699	−	7.02628i	−0.435194	−	0.251259i
$783$	1.23205	−	2.13397i	0.0440299	−	0.0762620i
$784$	−3.23205	−	5.59808i	−0.115430	−	0.199931i
$785$		0			0
$786$	−11.6603	+	6.73205i	−0.415907	+	0.240124i
$787$	−34.0526	+	19.6603i	−1.21384	+	0.700812i	−0.963594	−	0.267369i	$-0.913846\pi$
$787$	−34.0526	+	19.6603i	−1.21384	+	0.700812i	−0.250248	+	0.968182i	$0.580512\pi$
$788$		−	9.85641i		−	0.351120i
$789$	−14.0263	−	24.2942i	−0.499349	−	0.864897i
$790$		0			0
$791$	11.8301	+	6.83013i	0.420631	+	0.242851i
$792$	4.73205			0.168146
$793$	4.14359	+	1.19615i	0.147143	+	0.0424766i
$794$	−0.392305			−0.0139224
$795$		0			0
$796$	1.90192	−	3.29423i	0.0674119	−	0.116761i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$			0.928203i			0.0328580i
$799$	−16.0981	+	9.29423i	−0.569509	+	0.328806i
$800$		0			0
$801$		−	2.53590i		−	0.0896016i
$802$	10.9641	+	18.9904i	0.387156	+	0.670574i
$803$	23.0263	−	39.8827i	0.812580	−	1.40743i
$804$	9.63397	+	5.56218i	0.339764	+	0.196163i
$805$		0			0
$806$	4.73205	+	19.1244i	0.166679	+	0.673627i
$807$	1.46410			0.0515388
$808$	10.3301	+	5.96410i	0.363413	+	0.209816i
$809$	11.2058	−	19.4090i	0.393974	−	0.682383i	−0.598996	−	0.800752i	$-0.704433\pi$
$809$	11.2058	−	19.4090i	0.393974	−	0.682383i	0.992970	+	0.118369i	$0.0377667\pi$
$810$		0			0
$811$			45.1769i			1.58638i	0.608977	+	0.793188i	$0.291580\pi$
$811$			45.1769i			1.58638i	−0.608977	+	0.793188i	$0.708420\pi$
$812$	1.56218	−	0.901924i	0.0548217	−	0.0316513i
$813$	−5.07180	+	2.92820i	−0.177876	+	0.102697i
$814$			49.5167i			1.73556i
$815$		0			0
$816$	−1.13397	+	1.96410i	−0.0396971	+	0.0687573i
$817$	8.41154	+	4.85641i	0.294283	+	0.169904i
$818$	14.2679			0.498867
$819$	−2.56218	+	0.633975i	−0.0895297	+	0.0221529i
$820$		0			0
$821$	11.1962	+	6.46410i	0.390748	+	0.225599i	0.682484	−	0.730900i	$-0.260900\pi$
$821$	11.1962	+	6.46410i	0.390748	+	0.225599i	−0.291736	+	0.956499i	$0.594233\pi$
$822$	−0.964102	+	1.66987i	−0.0336269	+	0.0582435i
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	0.959177	+	0.282806i	$0.0912654\pi$
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	−0.234671	+	0.972075i	$0.575401\pi$
$824$			18.7321i			0.652562i
$825$		0			0
$826$	5.07180	−	2.92820i	0.176470	−	0.101885i
$827$		−	33.4641i		−	1.16366i	−0.813310	−	0.581830i	$-0.802337\pi$
$827$		−	33.4641i		−	1.16366i	0.813310	−	0.581830i	$-0.197663\pi$
$828$	−3.09808	−	5.36603i	−0.107666	−	0.186482i
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	−0.741338	−	0.671132i	$-0.765808\pi$
$829$	6.06218	−	10.5000i	0.210548	−	0.364680i	0.951886	+	0.306452i	$0.0991418\pi$
$830$		0			0
$831$	2.26795			0.0786743
$832$	2.59808	−	2.50000i	0.0900721	−	0.0866719i
$833$	−14.6603			−0.507948
$834$	−8.53590	−	4.92820i	−0.295574	−	0.170650i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		−	5.46410i		−	0.188867i
$838$	−9.12436	+	5.26795i	−0.315196	+	0.181978i
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	−0.273433	−	0.961891i	$-0.588159\pi$
$839$	12.2487	−	7.07180i	0.422872	−	0.244146i	0.696306	+	0.717745i	$0.254826\pi$
$840$		0			0
$841$	11.4641	+	19.8564i	0.395314	+	0.684704i
$842$	−16.3564	+	28.3301i	−0.563679	+	0.976321i
$843$	−19.3301	−	11.1603i	−0.665765	−	0.384380i
$844$	4.39230			0.151189
$845$		0			0
$846$	−8.19615			−0.281790
$847$	−7.22243	−	4.16987i	−0.248166	−	0.143279i
$848$	0.232051	−	0.401924i	0.00796866	−	0.0138021i
$849$	4.16987	+	7.22243i	0.143110	+	0.247873i
$850$		0			0
$851$	56.1506	−	32.4186i	1.92482	−	1.11129i
$852$	−1.09808	+	0.633975i	−0.0376195	+	0.0217196i
$853$		−	8.17691i		−	0.279972i	−0.990153	−	0.139986i	$-0.955294\pi$
$853$		−	8.17691i		−	0.279972i	0.990153	−	0.139986i	$-0.0447058\pi$
$854$	−0.437822	−	0.758330i	−0.0149820	−	0.0259495i
$855$		0			0
$856$	0.169873	+	0.0980762i	0.00580614	+	0.00335218i
$857$	−19.4449			−0.664224			−0.332112	−	0.943240i	$-0.607761\pi$
$857$	−19.4449			−0.664224			−0.332112	+	0.943240i	$0.607761\pi$
$858$	−12.2942	+	11.8301i	−0.419718	+	0.403874i
$859$	−22.8756			−0.780507			−0.390253	−	0.920707i	$-0.627613\pi$
$859$	−22.8756			−0.780507			−0.390253	+	0.920707i	$0.627613\pi$
$860$		0			0
$861$	−4.16987	+	7.22243i	−0.142109	+	0.246140i
$862$	5.56218	+	9.63397i	0.189449	+	0.328134i
$863$			7.12436i			0.242516i	0.992621	+	0.121258i	$0.0386928\pi$
$863$			7.12436i			0.242516i	−0.992621	+	0.121258i	$0.961307\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$		−	14.8564i		−	0.504841i
$867$	−5.92820	−	10.2679i	−0.201332	−	0.348718i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	38.7846	+	22.3923i	1.31568	+	0.759607i
$870$		0			0
$871$	−38.9352	+	9.63397i	−1.31927	+	0.326435i
$872$	5.46410			0.185038
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	3.92820	−	6.80385i	0.132873	−	0.230144i
$875$		0			0
$876$			9.73205i			0.328816i
$877$	8.72243	−	5.03590i	0.294536	−	0.170050i	−0.345450	−	0.938437i	$-0.612274\pi$
$877$	8.72243	−	5.03590i	0.294536	−	0.170050i	0.639985	+	0.768387i	$0.278940\pi$
$878$	15.2942	−	8.83013i	0.516155	−	0.298002i
$879$		−	14.5167i		−	0.489635i
$880$		0			0
$881$	25.9186	−	44.8923i	0.873219	−	1.51246i	0.0145717	−	0.999894i	$-0.495362\pi$
$881$	25.9186	−	44.8923i	0.873219	−	1.51246i	0.858648	−	0.512566i	$-0.171305\pi$
$882$	−5.59808	−	3.23205i	−0.188497	−	0.108829i
$883$	29.0718			0.978344			0.489172	−	0.872187i	$-0.337299\pi$
$883$	29.0718			0.978344			0.489172	+	0.872187i	$0.337299\pi$
$884$	−1.96410	−	7.93782i	−0.0660599	−	0.266978i
$885$		0			0
$886$	31.5167	+	18.1962i	1.05882	+	0.611312i
$887$	5.07180	−	8.78461i	0.170294	−	0.294958i	−0.768228	−	0.640176i	$-0.778862\pi$
$887$	5.07180	−	8.78461i	0.170294	−	0.294958i	0.938523	+	0.345217i	$0.112195\pi$
$888$	−5.23205	−	9.06218i	−0.175576	−	0.304107i
$889$		−	13.0718i		−	0.438414i
$890$		0			0
$891$	4.09808	−	2.36603i	0.137291	−	0.0792648i
$892$			13.0718i			0.437676i
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$	1.40192	−	2.42820i	0.0468873	−	0.0812113i
$895$		0			0
$896$	−0.732051			−0.0244561
$897$	21.4641	+	6.19615i	0.716665	+	0.206884i
$898$	23.3205			0.778215
$899$	−11.6603	−	6.73205i	−0.388891	−	0.224526i
$900$		0			0
$901$	−0.526279	−	0.911543i	−0.0175329	−	0.0303679i
$902$			53.9090i			1.79497i
$903$	4.85641	−	2.80385i	0.161611	−	0.0933062i
$904$	−16.1603	+	9.33013i	−0.537482	+	0.310315i
$905$		0			0
$906$	−1.63397	−	2.83013i	−0.0542852	−	0.0940247i
$907$	−7.80385	+	13.5167i	−0.259123	+	0.448813i	−0.966007	−	0.258516i	$-0.916767\pi$
$907$	−7.80385	+	13.5167i	−0.259123	+	0.448813i	0.706885	+	0.707329i	$0.250100\pi$
$908$	−1.56218	−	0.901924i	−0.0518427	−	0.0299314i
$909$	11.9282			0.395634
$910$		0			0
$911$	−9.46410			−0.313560			−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410			−0.313560			−0.156780	+	0.987634i	$0.550111\pi$
$912$	−1.09808	−	0.633975i	−0.0363609	−	0.0209930i
$913$	24.1244	−	41.7846i	0.798400	−	1.38287i
$914$	9.33013	+	16.1603i	0.308613	+	0.534534i
$915$		0			0
$916$	−13.7321	+	7.92820i	−0.453720	+	0.261955i
$917$	−8.53590	+	4.92820i	−0.281880	+	0.162744i
$918$			2.26795i			0.0748535i
$919$	28.9808	+	50.1962i	0.955987	+	1.65582i	0.732093	+	0.681205i	$0.238544\pi$
$919$	28.9808	+	50.1962i	0.955987	+	1.65582i	0.223894	+	0.974613i	$0.428123\pi$
$920$		0			0
$921$	−7.43782	−	4.29423i	−0.245085	−	0.141500i
$922$	25.7321			0.847440
$923$	1.26795	−	4.39230i	0.0417351	−	0.144574i
$924$	3.46410			0.113961
$925$		0			0
$926$	14.0263	−	24.2942i	0.460932	−	0.798358i
$927$	9.36603	+	16.2224i	0.307621	+	0.532815i
$928$			2.46410i			0.0808881i
$929$	−8.00962	+	4.62436i	−0.262787	+	0.151720i	−0.625605	−	0.780140i	$-0.715148\pi$
$929$	−8.00962	+	4.62436i	−0.262787	+	0.151720i	0.362818	+	0.931860i	$0.381815\pi$
$930$		0			0
$931$		−	8.19615i		−	0.268618i
$932$	9.92820	+	17.1962i	0.325209	+	0.563279i
$933$	−7.83013	+	13.5622i	−0.256347	+	0.444006i
$934$	10.9019	+	6.29423i	0.356722	+	0.205953i
$935$		0			0
$936$	1.00000	−	3.46410i	0.0326860	−	0.113228i
$937$	−43.2487			−1.41287			−0.706437	−	0.707776i	$-0.749699\pi$
$937$	−43.2487			−1.41287			−0.706437	+	0.707776i	$0.749699\pi$
$938$	7.05256	+	4.07180i	0.230274	+	0.132949i
$939$	−6.73205	+	11.6603i	−0.219692	+	0.380518i
$940$		0			0
$941$			56.6410i			1.84644i	0.384267	+	0.923222i	$0.374454\pi$
$941$			56.6410i			1.84644i	−0.384267	+	0.923222i	$0.625546\pi$
$942$	−20.4282	+	11.7942i	−0.665587	+	0.384277i
$943$	61.1314	−	35.2942i	1.99071	−	1.14934i
$944$			8.00000i			0.260378i
$945$		0			0
$946$	18.1244	−	31.3923i	0.589274	−	1.02065i
$947$	30.2487	+	17.4641i	0.982951	+	0.567507i	0.903160	−	0.429305i	$-0.141241\pi$
$947$	30.2487	+	17.4641i	0.982951	+	0.567507i	0.0797913	+	0.996812i	$0.474575\pi$
$948$	−9.46410			−0.307380
$949$	−24.3301	−	25.2846i	−0.789789	−	0.820773i
$950$		0			0
$951$	2.89230	+	1.66987i	0.0937894	+	0.0541493i
$952$	−0.830127	+	1.43782i	−0.0269046	+	0.0466001i
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	0.976969	+	0.213383i	$0.0684483\pi$
$953$	20.7846	+	36.0000i	0.673280	+	1.16615i	−0.303689	+	0.952771i	$0.598218\pi$
$954$		−	0.464102i		−	0.0150258i
$955$		0			0
$956$	−8.36603	+	4.83013i	−0.270577	+	0.156217i
$957$		−	11.6603i		−	0.376922i
$958$	13.2679	+	22.9808i	0.428668	+	0.742475i
$959$	−0.705771	+	1.22243i	−0.0227905	+	0.0394744i
$960$		0			0
$961$	1.14359			0.0368901
$962$	36.2487	+	10.4641i	1.16871	+	0.337376i
$963$	0.196152			0.00632092
$964$	−15.2321	−	8.79423i	−0.490591	−	0.283243i
$965$		0			0
$966$	−2.26795	−	3.92820i	−0.0729701	−	0.126388i
$967$		−	18.8756i		−	0.607000i	−0.952831	−	0.303500i	$-0.901845\pi$
$967$		−	18.8756i		−	0.607000i	0.952831	−	0.303500i	$-0.0981552\pi$
$968$	9.86603	−	5.69615i	0.317106	−	0.183081i
$969$	−2.49038	+	1.43782i	−0.0800026	+	0.0461895i
$970$		0			0
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	0.974474	−	0.224500i	$-0.0720748\pi$
$971$	9.12436	+	15.8038i	0.292815	+	0.507170i	−0.681660	+	0.731669i	$0.738741\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−6.24871	−	3.60770i	−0.200324	−	0.115657i
$974$	−21.1244			−0.676868
$975$		0			0
$976$	1.19615			0.0382879
$977$	−27.7750	−	16.0359i	−0.888601	−	0.513034i	−0.0151161	−	0.999886i	$-0.504812\pi$
$977$	−27.7750	−	16.0359i	−0.888601	−	0.513034i	−0.873485	+	0.486852i	$0.838145\pi$
$978$	−3.26795	+	5.66025i	−0.104497	+	0.180995i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	4.73205	−	2.73205i	0.151083	−	0.0872277i
$982$	−4.56218	+	2.63397i	−0.145585	+	0.0840535i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	−5.69615	−	9.86603i	−0.181587	−	0.314517i
$985$		0			0
$986$	4.83975	+	2.79423i	0.154129	+	0.0889864i
$987$	−6.00000			−0.190982
$988$	4.43782	−	1.09808i	0.141186	−	0.0349345i
$989$	−47.4641			−1.50927
$990$		0			0
$991$	4.29423	−	7.43782i	0.136411	−	0.236270i	−0.789725	−	0.613461i	$-0.789777\pi$
$991$	4.29423	−	7.43782i	0.136411	−	0.236270i	0.926135	+	0.377191i	$0.123110\pi$
$992$	2.73205	+	4.73205i	0.0867427	+	0.150243i
$993$			20.0000i			0.634681i
$994$	−0.803848	+	0.464102i	−0.0254965	+	0.0147204i
$995$		0			0
$996$			10.1962i			0.323077i
$997$	19.3301	+	33.4808i	0.612191	+	1.06035i	0.990870	+	0.134818i	$0.0430451\pi$
$997$	19.3301	+	33.4808i	0.612191	+	1.06035i	−0.378679	+	0.925528i	$0.623622\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$	−9.06218	−	5.23205i	−0.286715	−	0.165535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.d.901.1		4
5.2	odd	4		1950.2.y.g.199.1		4
5.3	odd	4		1950.2.y.b.199.2		4
5.4	even	2		78.2.i.a.43.2	✓	4
13.10	even	6	inner	1950.2.bc.d.751.1		4
15.14	odd	2		234.2.l.c.199.1		4
20.19	odd	2		624.2.bv.e.433.1		4
60.59	even	2		1872.2.by.h.433.2		4
65.4	even	6		1014.2.b.e.337.3		4
65.9	even	6		1014.2.b.e.337.2		4
65.19	odd	12		1014.2.a.i.1.2		2
65.23	odd	12		1950.2.y.g.49.1		4
65.24	odd	12		1014.2.e.g.991.1		4
65.29	even	6		1014.2.i.a.361.1		4
65.34	odd	4		1014.2.e.g.529.1		4
65.44	odd	4		1014.2.e.i.529.2		4
65.49	even	6		78.2.i.a.49.2	yes	4
65.54	odd	12		1014.2.e.i.991.2		4
65.59	odd	12		1014.2.a.k.1.1		2
65.62	odd	12		1950.2.y.b.49.2		4
65.64	even	2		1014.2.i.a.823.1		4
195.59	even	12		3042.2.a.p.1.2		2
195.74	odd	6		3042.2.b.i.1351.3		4
195.134	odd	6		3042.2.b.i.1351.2		4
195.149	even	12		3042.2.a.y.1.1		2
195.179	odd	6		234.2.l.c.127.1		4
260.19	even	12		8112.2.a.bj.1.2		2
260.59	even	12		8112.2.a.bp.1.1		2
260.179	odd	6		624.2.bv.e.49.2		4
780.179	even	6		1872.2.by.h.1297.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	5.4	even	2
78.2.i.a.49.2	yes	4	65.49	even	6
234.2.l.c.127.1		4	195.179	odd	6
234.2.l.c.199.1		4	15.14	odd	2
624.2.bv.e.49.2		4	260.179	odd	6
624.2.bv.e.433.1		4	20.19	odd	2
1014.2.a.i.1.2		2	65.19	odd	12
1014.2.a.k.1.1		2	65.59	odd	12
1014.2.b.e.337.2		4	65.9	even	6
1014.2.b.e.337.3		4	65.4	even	6
1014.2.e.g.529.1		4	65.34	odd	4
1014.2.e.g.991.1		4	65.24	odd	12
1014.2.e.i.529.2		4	65.44	odd	4
1014.2.e.i.991.2		4	65.54	odd	12
1014.2.i.a.361.1		4	65.29	even	6
1014.2.i.a.823.1		4	65.64	even	2
1872.2.by.h.433.2		4	60.59	even	2
1872.2.by.h.1297.1		4	780.179	even	6
1950.2.y.b.49.2		4	65.62	odd	12
1950.2.y.b.199.2		4	5.3	odd	4
1950.2.y.g.49.1		4	65.23	odd	12
1950.2.y.g.199.1		4	5.2	odd	4
1950.2.bc.d.751.1		4	13.10	even	6	inner
1950.2.bc.d.901.1		4	1.1	even	1	trivial
3042.2.a.p.1.2		2	195.59	even	12
3042.2.a.y.1.1		2	195.149	even	12
3042.2.b.i.1351.2		4	195.134	odd	6
3042.2.b.i.1351.3		4	195.74	odd	6
8112.2.a.bj.1.2		2	260.19	even	12
8112.2.a.bp.1.1		2	260.59	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.09808 - 2.36603i) q^{11} +1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} +0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-1.09808 + 0.633975i) q^{19} +0.732051i q^{21} +(2.36603 + 4.09808i) q^{22} +(3.09808 - 5.36603i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.633975 - 0.366025i) q^{28} +(-1.23205 + 2.13397i) q^{29} +5.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.09808 + 2.36603i) q^{33} -2.26795i q^{34} +(0.500000 - 0.866025i) q^{36} +(9.06218 + 5.23205i) q^{37} +1.26795 q^{38} +(0.866025 + 3.50000i) q^{39} +(9.86603 + 5.69615i) q^{41} +(0.366025 - 0.633975i) q^{42} +(-3.83013 - 6.63397i) q^{43} -4.73205i q^{44} +(-5.36603 + 3.09808i) q^{46} +8.19615i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-3.46410 - 1.00000i) q^{52} -0.464102 q^{53} +(0.866025 + 0.500000i) q^{54} +(0.366025 + 0.633975i) q^{56} +1.26795i q^{57} +(2.13397 - 1.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +(-0.598076 - 1.03590i) q^{61} +(2.73205 - 4.73205i) q^{62} +(0.633975 + 0.366025i) q^{63} -1.00000 q^{64} +4.73205 q^{66} +(9.63397 + 5.56218i) q^{67} +(-1.13397 + 1.96410i) q^{68} +(-3.09808 - 5.36603i) q^{69} +(-1.09808 + 0.633975i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.73205i q^{73} +(-5.23205 - 9.06218i) q^{74} +(-1.09808 - 0.633975i) q^{76} +3.46410 q^{77} +(1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.69615 - 9.86603i) q^{82} +10.1962i q^{83} +(-0.633975 + 0.366025i) q^{84} +7.66025i q^{86} +(1.23205 + 2.13397i) q^{87} +(-2.36603 + 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} +(0.732051 - 2.53590i) q^{91} +6.19615 q^{92} +(4.73205 + 2.73205i) q^{93} +(4.09808 - 7.09808i) q^{94} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(5.59808 - 3.23205i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{22} + 2 q^{23} + 14 q^{26} - 4 q^{27} - 6 q^{28} + 2 q^{29} - 6 q^{33} + 2 q^{36} + 12 q^{37} + 12 q^{38} + 36 q^{41} - 2 q^{42} + 2 q^{43} - 18 q^{46} + 2 q^{48} - 6 q^{49} + 16 q^{51} + 12 q^{53} - 2 q^{56} + 12 q^{58} + 8 q^{61} + 4 q^{62} + 6 q^{63} - 4 q^{64} + 12 q^{66} + 42 q^{67} - 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 6 q^{76} + 4 q^{78} - 24 q^{79} - 2 q^{81} - 2 q^{82} - 6 q^{84} - 2 q^{87} - 6 q^{88} - 12 q^{89} - 4 q^{91} + 4 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^22 + 2 * q^23 + 14 * q^26 - 4 * q^27 - 6 * q^28 + 2 * q^29 - 6 * q^33 + 2 * q^36 + 12 * q^37 + 12 * q^38 + 36 * q^41 - 2 * q^42 + 2 * q^43 - 18 * q^46 + 2 * q^48 - 6 * q^49 + 16 * q^51 + 12 * q^53 - 2 * q^56 + 12 * q^58 + 8 * q^61 + 4 * q^62 + 6 * q^63 - 4 * q^64 + 12 * q^66 + 42 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^71 - 14 * q^74 + 6 * q^76 + 4 * q^78 - 24 * q^79 - 2 * q^81 - 2 * q^82 - 6 * q^84 - 2 * q^87 - 6 * q^88 - 12 * q^89 - 4 * q^91 + 4 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^98

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