LMFDB - Embedded newform 1950.2.y.h.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1950,2,Mod(49,1950)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1950, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1950.49"); 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.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.h.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.09808 - 0.633975i) q^{11} +1.00000i q^{12} +(3.23205 - 1.59808i) q^{13} +1.26795 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(4.09808 - 2.36603i) q^{19} -1.26795i q^{21} +(-1.09808 + 0.633975i) q^{22} +(7.09808 + 4.09808i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.232051 - 3.59808i) q^{26} -1.00000i q^{27} +(0.633975 - 1.09808i) q^{28} +(-1.50000 + 2.59808i) q^{29} -9.46410i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.633975 + 1.09808i) q^{33} +5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(1.50000 - 2.59808i) q^{37} -4.73205i q^{38} +(-3.59808 - 0.232051i) q^{39} +(5.59808 + 3.23205i) q^{41} +(-1.09808 - 0.633975i) q^{42} +(-3.63397 + 2.09808i) q^{43} +1.26795i q^{44} +(7.09808 - 4.09808i) q^{46} +4.73205 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.69615 - 4.66987i) q^{49} +5.19615 q^{51} +(-3.00000 - 2.00000i) q^{52} -3.00000i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.633975 - 1.09808i) q^{56} -4.73205 q^{57} +(1.50000 + 2.59808i) q^{58} +(12.0000 - 6.92820i) q^{59} +(-7.59808 - 13.1603i) q^{61} +(-8.19615 - 4.73205i) q^{62} +(-0.633975 + 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-3.63397 + 6.29423i) q^{67} +(4.50000 + 2.59808i) q^{68} +(-4.09808 - 7.09808i) q^{69} +(1.90192 - 1.09808i) q^{71} +(-0.500000 - 0.866025i) q^{72} +12.1244 q^{73} +(-1.50000 - 2.59808i) q^{74} +(-4.09808 - 2.36603i) q^{76} -1.60770i q^{77} +(-2.00000 + 3.00000i) q^{78} -8.39230 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.59808 - 3.23205i) q^{82} -5.66025 q^{83} +(-1.09808 + 0.633975i) q^{84} +4.19615i q^{86} +(2.59808 - 1.50000i) q^{87} +(1.09808 + 0.633975i) q^{88} +(8.19615 + 4.73205i) q^{89} +(3.80385 + 2.53590i) q^{91} -8.19615i q^{92} +(-4.73205 + 8.19615i) q^{93} +(2.36603 - 4.09808i) q^{94} -1.00000i q^{96} +(-3.00000 - 5.19615i) q^{97} +(-2.69615 - 4.66987i) q^{98} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 6 q^{11} + 6 q^{13} + 12 q^{14} - 2 q^{16} - 18 q^{17} + 4 q^{18} + 6 q^{19} + 6 q^{22} + 18 q^{23} - 6 q^{26} + 6 q^{28} - 6 q^{29} + 2 q^{32} + 6 q^{33}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 6 * q^11 + 6 * q^13 + 12 * q^14 - 2 * q^16 - 18 * q^17 + 4 * q^18 + 6 * q^19 + 6 * q^22 + 18 * q^23 - 6 * q^26 + 6 * q^28 - 6 * q^29 + 2 * q^32 + 6 * q^33 + 2 * q^36 + 6 * q^37 - 4 * q^39 + 12 * q^41 + 6 * q^42 - 18 * q^43 + 18 * q^46 + 12 * q^47 - 10 * q^49 - 12 * q^52 - 6 * q^56 - 12 * q^57 + 6 * q^58 + 48 * q^59 - 20 * q^61 - 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 + 18 * q^68 - 6 * q^69 + 18 * q^71 - 2 * q^72 - 6 * q^74 - 6 * q^76 - 8 * q^78 + 8 * q^79 - 2 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^88 + 12 * q^89 + 36 * q^91 - 12 * q^93 + 6 * q^94 - 12 * q^97 + 10 * q^98

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−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	+	1.09808i	0.239620	+	0.415034i	0.960605	−	0.277916i	$-0.0896439\pi$
$7$	0.633975	+	1.09808i	0.239620	+	0.415034i	−0.720985	+	0.692950i	$0.756311\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	0.325239	−	0.945632i	$-0.394555\pi$
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	−0.656322	+	0.754481i	$0.727889\pi$
$12$			1.00000i			0.288675i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$14$	1.26795			0.338874
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−4.50000	+	2.59808i	−1.09141	+	0.630126i	−0.933952	−	0.357400i	$-0.883663\pi$
$17$	−4.50000	+	2.59808i	−1.09141	+	0.630126i	−0.157459	+	0.987526i	$0.550330\pi$
$18$	1.00000			0.235702
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$		0			0
$21$		−	1.26795i		−	0.276689i
$22$	−1.09808	+	0.633975i	−0.234111	+	0.135164i
$23$	7.09808	+	4.09808i	1.48005	+	0.854508i	0.999745	−	0.0225928i	$-0.00719212\pi$
$23$	7.09808	+	4.09808i	1.48005	+	0.854508i	0.480306	+	0.877101i	$0.340525\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	0.232051	−	3.59808i	0.0455089	−	0.705641i
$27$		−	1.00000i		−	0.192450i
$28$	0.633975	−	1.09808i	0.119810	−	0.207517i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$		−	9.46410i		−	1.69980i	−0.526942	−	0.849901i	$-0.676661\pi$
$31$		−	9.46410i		−	1.69980i	0.526942	−	0.849901i	$-0.323339\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.633975	+	1.09808i	0.110361	+	0.191151i
$34$			5.19615i			0.891133i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	−0.715981	−	0.698119i	$-0.754020\pi$
$37$	1.50000	−	2.59808i	0.246598	−	0.427121i	0.962580	+	0.270998i	$0.0873538\pi$
$38$		−	4.73205i		−	0.767640i
$39$	−3.59808	−	0.232051i	−0.576153	−	0.0371579i
$40$		0			0
$41$	5.59808	+	3.23205i	0.874273	+	0.504762i	0.868766	−	0.495223i	$-0.164914\pi$
$41$	5.59808	+	3.23205i	0.874273	+	0.504762i	0.00550690	+	0.999985i	$0.498247\pi$
$42$	−1.09808	−	0.633975i	−0.169437	−	0.0978244i
$43$	−3.63397	+	2.09808i	−0.554176	+	0.319954i	−0.750805	−	0.660524i	$-0.770334\pi$
$43$	−3.63397	+	2.09808i	−0.554176	+	0.319954i	0.196629	+	0.980478i	$0.437001\pi$
$44$			1.26795i			0.191151i
$45$		0			0
$46$	7.09808	−	4.09808i	1.04655	−	0.604228i
$47$	4.73205			0.690241			0.345120	−	0.938558i	$-0.387838\pi$
$47$	4.73205			0.690241			0.345120	+	0.938558i	$0.387838\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	2.69615	−	4.66987i	0.385165	−	0.667125i
$50$		0			0
$51$	5.19615			0.727607
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−0.633975	−	1.09808i	−0.0847184	−	0.146737i
$57$	−4.73205			−0.626775
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$	12.0000	−	6.92820i	1.56227	−	0.901975i	0.565240	−	0.824927i	$-0.308784\pi$
$59$	12.0000	−	6.92820i	1.56227	−	0.901975i	0.997027	−	0.0770484i	$-0.0245496\pi$
$60$		0			0
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.686905	−	0.726747i	$-0.741031\pi$
$61$	−7.59808	−	13.1603i	−0.972834	−	1.68500i	−0.285929	−	0.958251i	$-0.592302\pi$
$62$	−8.19615	−	4.73205i	−1.04091	−	0.600971i
$63$	−0.633975	+	1.09808i	−0.0798733	+	0.138345i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	−3.63397	+	6.29423i	−0.443961	+	0.768962i	−0.997979	−	0.0635419i	$-0.979760\pi$
$67$	−3.63397	+	6.29423i	−0.443961	+	0.768962i	0.554019	+	0.832504i	$0.313094\pi$
$68$	4.50000	+	2.59808i	0.545705	+	0.315063i
$69$	−4.09808	−	7.09808i	−0.493350	−	0.854508i
$70$		0			0
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	−0.382878	−	0.923799i	$-0.625067\pi$
$71$	1.90192	−	1.09808i	0.225717	−	0.130318i	0.608595	+	0.793481i	$0.291734\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	12.1244			1.41905			0.709524	−	0.704681i	$-0.248910\pi$
$73$	12.1244			1.41905			0.709524	+	0.704681i	$0.248910\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$		0			0
$76$	−4.09808	−	2.36603i	−0.470082	−	0.271402i
$77$		−	1.60770i		−	0.183214i
$78$	−2.00000	+	3.00000i	−0.226455	+	0.339683i
$79$	−8.39230			−0.944208			−0.472104	−	0.881543i	$-0.656505\pi$
$79$	−8.39230			−0.944208			−0.472104	+	0.881543i	$0.656505\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.59808	−	3.23205i	0.618204	−	0.356920i
$83$	−5.66025			−0.621294			−0.310647	−	0.950525i	$-0.600546\pi$
$83$	−5.66025			−0.621294			−0.310647	+	0.950525i	$0.600546\pi$
$84$	−1.09808	+	0.633975i	−0.119810	+	0.0691723i
$85$		0			0
$86$			4.19615i			0.452483i
$87$	2.59808	−	1.50000i	0.278543	−	0.160817i
$88$	1.09808	+	0.633975i	0.117055	+	0.0675819i
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$		0			0
$91$	3.80385	+	2.53590i	0.398752	+	0.265834i
$92$		−	8.19615i		−	0.854508i
$93$	−4.73205	+	8.19615i	−0.490691	+	0.849901i
$94$	2.36603	−	4.09808i	0.244037	−	0.422684i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	−3.00000	−	5.19615i	−0.304604	−	0.527589i	0.672569	−	0.740034i	$-0.265191\pi$
$97$	−3.00000	−	5.19615i	−0.304604	−	0.527589i	−0.977173	+	0.212445i	$0.931857\pi$
$98$	−2.69615	−	4.66987i	−0.272353	−	0.471728i
$99$		−	1.26795i		−	0.127434i
$100$		0			0
$101$	9.69615	−	16.7942i	0.964803	−	1.67109i	0.254660	−	0.967031i	$-0.418036\pi$
$101$	9.69615	−	16.7942i	0.964803	−	1.67109i	0.710143	−	0.704058i	$-0.248630\pi$
$102$	2.59808	−	4.50000i	0.257248	−	0.445566i
$103$			6.19615i			0.610525i	0.952268	+	0.305263i	$0.0987442\pi$
$103$			6.19615i			0.610525i	−0.952268	+	0.305263i	$0.901256\pi$
$104$	−3.23205	+	1.59808i	−0.316929	+	0.156704i
$105$		0			0
$106$	−2.59808	−	1.50000i	−0.252347	−	0.145693i
$107$	1.90192	+	1.09808i	0.183866	+	0.106155i	0.589108	−	0.808054i	$-0.299479\pi$
$107$	1.90192	+	1.09808i	0.183866	+	0.106155i	−0.405242	+	0.914210i	$0.632813\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$		−	4.39230i		−	0.420707i	−0.977625	−	0.210353i	$-0.932539\pi$
$109$		−	4.39230i		−	0.420707i	0.977625	−	0.210353i	$-0.0674614\pi$
$110$		0			0
$111$	−2.59808	+	1.50000i	−0.246598	+	0.142374i
$112$	−1.26795			−0.119810
$113$	−0.696152	+	0.401924i	−0.0654885	+	0.0378098i	−0.532387	−	0.846501i	$-0.678705\pi$
$113$	−0.696152	+	0.401924i	−0.0654885	+	0.0378098i	0.466898	+	0.884311i	$0.345371\pi$
$114$	−2.36603	+	4.09808i	−0.221599	+	0.383820i
$115$		0			0
$116$	3.00000			0.278543
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$		−	13.8564i		−	1.27559i
$119$	−5.70577	−	3.29423i	−0.523047	−	0.301981i
$120$		0			0
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$	−15.1962			−1.37579
$123$	−3.23205	−	5.59808i	−0.291424	−	0.504762i
$124$	−8.19615	+	4.73205i	−0.736036	+	0.424951i
$125$		0			0
$126$	0.633975	+	1.09808i	0.0564789	+	0.0978244i
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	0.338368	−	0.941014i	$-0.390125\pi$
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	−0.645758	+	0.763542i	$0.723458\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.19615			0.369451
$130$		0			0
$131$	−4.39230			−0.383757			−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230			−0.383757			−0.191879	+	0.981419i	$0.561458\pi$
$132$	0.633975	−	1.09808i	0.0551804	−	0.0955753i
$133$	5.19615	+	3.00000i	0.450564	+	0.260133i
$134$	3.63397	+	6.29423i	0.313928	+	0.543739i
$135$		0			0
$136$	4.50000	−	2.59808i	0.385872	−	0.222783i
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$	−8.19615			−0.697703
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$		0			0
$141$	−4.09808	−	2.36603i	−0.345120	−	0.199255i
$142$		−	2.19615i		−	0.184297i
$143$	−4.56218	−	0.294229i	−0.381508	−	0.0246046i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	6.06218	−	10.5000i	0.501709	−	0.868986i
$147$	−4.66987	+	2.69615i	−0.385165	+	0.222375i
$148$	−3.00000			−0.246598
$149$	5.30385	−	3.06218i	0.434508	−	0.250863i	−0.266757	−	0.963764i	$-0.585952\pi$
$149$	5.30385	−	3.06218i	0.434508	−	0.250863i	0.701265	+	0.712900i	$0.252619\pi$
$150$		0			0
$151$			10.7321i			0.873362i	0.899616	+	0.436681i	$0.143846\pi$
$151$			10.7321i			0.873362i	−0.899616	+	0.436681i	$0.856154\pi$
$152$	−4.09808	+	2.36603i	−0.332398	+	0.191910i
$153$	−4.50000	−	2.59808i	−0.363803	−	0.210042i
$154$	−1.39230	−	0.803848i	−0.112195	−	0.0647759i
$155$		0			0
$156$	1.59808	+	3.23205i	0.127948	+	0.258771i
$157$			7.19615i			0.574315i	0.957883	+	0.287158i	$0.0927104\pi$
$157$			7.19615i			0.574315i	−0.957883	+	0.287158i	$0.907290\pi$
$158$	−4.19615	+	7.26795i	−0.333828	+	0.578207i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−1.26795	−	2.19615i	−0.0993134	−	0.172016i	0.812087	−	0.583536i	$-0.198331\pi$
$163$	−1.26795	−	2.19615i	−0.0993134	−	0.172016i	−0.911401	+	0.411520i	$0.864998\pi$
$164$		−	6.46410i		−	0.504762i
$165$		0			0
$166$	−2.83013	+	4.90192i	−0.219660	+	0.380463i
$167$	−4.73205	+	8.19615i	−0.366177	+	0.634237i	−0.988964	−	0.148154i	$-0.952667\pi$
$167$	−4.73205	+	8.19615i	−0.366177	+	0.634237i	0.622787	+	0.782391i	$0.286000\pi$
$168$			1.26795i			0.0978244i
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$		0			0
$171$	4.09808	+	2.36603i	0.313388	+	0.180934i
$172$	3.63397	+	2.09808i	0.277088	+	0.159977i
$173$	−3.80385	+	2.19615i	−0.289201	+	0.166970i	−0.637582	−	0.770383i	$-0.720065\pi$
$173$	−3.80385	+	2.19615i	−0.289201	+	0.166970i	0.348380	+	0.937353i	$0.386732\pi$
$174$		−	3.00000i		−	0.227429i
$175$		0			0
$176$	1.09808	−	0.633975i	0.0827706	−	0.0477876i
$177$	−13.8564			−1.04151
$178$	8.19615	−	4.73205i	0.614328	−	0.354682i
$179$	−1.09808	+	1.90192i	−0.0820741	+	0.142156i	−0.904141	−	0.427235i	$-0.859488\pi$
$179$	−1.09808	+	1.90192i	−0.0820741	+	0.142156i	0.822067	+	0.569391i	$0.192821\pi$
$180$		0			0
$181$	−19.5885			−1.45600			−0.727999	−	0.685578i	$-0.759550\pi$
$181$	−19.5885			−1.45600			−0.727999	+	0.685578i	$0.759550\pi$
$182$	4.09808	−	2.02628i	0.303770	−	0.150198i
$183$			15.1962i			1.12333i
$184$	−7.09808	−	4.09808i	−0.523277	−	0.302114i
$185$		0			0
$186$	4.73205	+	8.19615i	0.346971	+	0.600971i
$187$	6.58846			0.481796
$188$	−2.36603	−	4.09808i	−0.172560	−	0.298883i
$189$	1.09808	−	0.633975i	0.0798733	−	0.0461149i
$190$		0			0
$191$	10.3923	+	18.0000i	0.751961	+	1.30243i	0.946871	+	0.321613i	$0.104225\pi$
$191$	10.3923	+	18.0000i	0.751961	+	1.30243i	−0.194910	+	0.980821i	$0.562442\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	11.5981	−	20.0885i	0.834848	−	1.44600i	−0.0593065	−	0.998240i	$-0.518889\pi$
$193$	11.5981	−	20.0885i	0.834848	−	1.44600i	0.894154	−	0.447759i	$-0.147778\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	−5.39230			−0.385165
$197$	3.46410	−	6.00000i	0.246807	−	0.427482i	−0.715831	−	0.698273i	$-0.753952\pi$
$197$	3.46410	−	6.00000i	0.246807	−	0.427482i	0.962638	+	0.270791i	$0.0872853\pi$
$198$	−1.09808	−	0.633975i	−0.0780369	−	0.0450546i
$199$	11.2942	+	19.5622i	0.800627	+	1.38673i	0.919204	+	0.393781i	$0.128833\pi$
$199$	11.2942	+	19.5622i	0.800627	+	1.38673i	−0.118578	+	0.992945i	$0.537833\pi$
$200$		0			0
$201$	6.29423	−	3.63397i	0.443961	−	0.256321i
$202$	−9.69615	−	16.7942i	−0.682219	−	1.18164i
$203$	−3.80385			−0.266978
$204$	−2.59808	−	4.50000i	−0.181902	−	0.315063i
$205$		0			0
$206$	5.36603	+	3.09808i	0.373869	+	0.215853i
$207$			8.19615i			0.569672i
$208$	−0.232051	+	3.59808i	−0.0160898	+	0.249482i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	12.1962	−	21.1244i	0.839618	−	1.45426i	−0.0505968	−	0.998719i	$-0.516112\pi$
$211$	12.1962	−	21.1244i	0.839618	−	1.45426i	0.890215	−	0.455541i	$-0.150554\pi$
$212$	−2.59808	+	1.50000i	−0.178437	+	0.103020i
$213$	−2.19615			−0.150478
$214$	1.90192	−	1.09808i	0.130013	−	0.0750629i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	10.3923	−	6.00000i	0.705476	−	0.407307i
$218$	−3.80385	−	2.19615i	−0.257629	−	0.148742i
$219$	−10.5000	−	6.06218i	−0.709524	−	0.409644i
$220$		0			0
$221$	−10.3923	+	15.5885i	−0.699062	+	1.04859i
$222$			3.00000i			0.201347i
$223$	−2.53590	+	4.39230i	−0.169816	+	0.294130i	−0.938355	−	0.345673i	$-0.887651\pi$
$223$	−2.53590	+	4.39230i	−0.169816	+	0.294130i	0.768539	+	0.639803i	$0.220984\pi$
$224$	−0.633975	+	1.09808i	−0.0423592	+	0.0733683i
$225$		0			0
$226$			0.803848i			0.0534711i
$227$	10.0981	+	17.4904i	0.670233	+	1.16088i	0.977838	+	0.209363i	$0.0671391\pi$
$227$	10.0981	+	17.4904i	0.670233	+	1.16088i	−0.307605	+	0.951514i	$0.599528\pi$
$228$	2.36603	+	4.09808i	0.156694	+	0.271402i
$229$			7.85641i			0.519166i	0.965721	+	0.259583i	$0.0835851\pi$
$229$			7.85641i			0.519166i	−0.965721	+	0.259583i	$0.916415\pi$
$230$		0			0
$231$	−0.803848	+	1.39230i	−0.0528893	+	0.0916069i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	3.23205	−	1.59808i	0.211286	−	0.104470i
$235$		0			0
$236$	−12.0000	−	6.92820i	−0.781133	−	0.450988i
$237$	7.26795	+	4.19615i	0.472104	+	0.272569i
$238$	−5.70577	+	3.29423i	−0.369850	+	0.213533i
$239$			6.58846i			0.426172i	0.977033	+	0.213086i	$0.0683514\pi$
$239$			6.58846i			0.426172i	−0.977033	+	0.213086i	$0.931649\pi$
$240$		0			0
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	−0.154068	−	0.988060i	$-0.549237\pi$
$241$	9.69615	−	5.59808i	0.624584	−	0.360604i	0.778652	+	0.627457i	$0.215904\pi$
$242$	−9.39230			−0.603760
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−7.59808	+	13.1603i	−0.486417	+	0.842499i
$245$		0			0
$246$	−6.46410			−0.412136
$247$	9.46410	−	14.1962i	0.602186	−	0.903280i
$248$			9.46410i			0.600971i
$249$	4.90192	+	2.83013i	0.310647	+	0.179352i
$250$		0			0
$251$	8.19615	+	14.1962i	0.517337	+	0.896053i	0.999797	+	0.0201356i	$0.00640979\pi$
$251$	8.19615	+	14.1962i	0.517337	+	0.896053i	−0.482461	+	0.875918i	$0.660257\pi$
$252$	1.26795			0.0798733
$253$	−5.19615	−	9.00000i	−0.326679	−	0.565825i
$254$	−3.46410	+	2.00000i	−0.217357	+	0.125491i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	20.0885	+	11.5981i	1.25308	+	0.723468i	0.971721	−	0.236133i	$-0.0758802\pi$
$257$	20.0885	+	11.5981i	1.25308	+	0.723468i	0.281363	+	0.959601i	$0.409214\pi$
$258$	2.09808	−	3.63397i	0.130621	−	0.226241i
$259$	3.80385			0.236360
$260$		0			0
$261$	−3.00000			−0.185695
$262$	−2.19615	+	3.80385i	−0.135679	+	0.235002i
$263$	7.09808	+	4.09808i	0.437686	+	0.252698i	0.702616	−	0.711570i	$-0.252015\pi$
$263$	7.09808	+	4.09808i	0.437686	+	0.252698i	−0.264930	+	0.964268i	$0.585349\pi$
$264$	−0.633975	−	1.09808i	−0.0390184	−	0.0675819i
$265$		0			0
$266$	5.19615	−	3.00000i	0.318597	−	0.183942i
$267$	−4.73205	−	8.19615i	−0.289597	−	0.501596i
$268$	7.26795			0.443961
$269$	−3.80385	−	6.58846i	−0.231925	−	0.401705i	0.726450	−	0.687220i	$-0.241169\pi$
$269$	−3.80385	−	6.58846i	−0.231925	−	0.401705i	−0.958374	+	0.285514i	$0.907836\pi$
$270$		0			0
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		−	5.19615i		−	0.315063i
$273$	−2.02628	−	4.09808i	−0.122636	−	0.248027i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−4.09808	+	7.09808i	−0.246675	+	0.427254i
$277$	−4.16025	+	2.40192i	−0.249965	+	0.144318i	−0.619748	−	0.784801i	$-0.712765\pi$
$277$	−4.16025	+	2.40192i	−0.249965	+	0.144318i	0.369783	+	0.929118i	$0.379432\pi$
$278$	−4.00000			−0.239904
$279$	8.19615	−	4.73205i	0.490691	−	0.283300i
$280$		0			0
$281$			17.5359i			1.04610i	0.852301	+	0.523052i	$0.175207\pi$
$281$			17.5359i			1.04610i	−0.852301	+	0.523052i	$0.824793\pi$
$282$	−4.09808	+	2.36603i	−0.244037	+	0.140895i
$283$	17.1506	+	9.90192i	1.01950	+	0.588608i	0.913959	−	0.405807i	$-0.133009\pi$
$283$	17.1506	+	9.90192i	1.01950	+	0.588608i	0.105541	+	0.994415i	$0.466343\pi$
$284$	−1.90192	−	1.09808i	−0.112858	−	0.0651588i
$285$		0			0
$286$	−2.53590	+	3.80385i	−0.149951	+	0.224926i
$287$			8.19615i			0.483804i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	5.00000	−	8.66025i	0.294118	−	0.509427i
$290$		0			0
$291$			6.00000i			0.351726i
$292$	−6.06218	−	10.5000i	−0.354762	−	0.614466i
$293$	−1.33013	−	2.30385i	−0.0777069	−	0.134592i	0.824553	−	0.565784i	$-0.191426\pi$
$293$	−1.33013	−	2.30385i	−0.0777069	−	0.134592i	−0.902260	+	0.431192i	$0.858093\pi$
$294$			5.39230i			0.314486i
$295$		0			0
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$	−0.633975	+	1.09808i	−0.0367869	+	0.0637168i
$298$		−	6.12436i		−	0.354774i
$299$	29.4904	+	1.90192i	1.70547	+	0.109991i
$300$		0			0
$301$	−4.60770	−	2.66025i	−0.265583	−	0.153334i
$302$	9.29423	+	5.36603i	0.534823	+	0.308780i
$303$	−16.7942	+	9.69615i	−0.964803	+	0.557029i
$304$			4.73205i			0.271402i
$305$		0			0
$306$	−4.50000	+	2.59808i	−0.257248	+	0.148522i
$307$	−7.26795			−0.414804			−0.207402	−	0.978256i	$-0.566501\pi$
$307$	−7.26795			−0.414804			−0.207402	+	0.978256i	$0.566501\pi$
$308$	−1.39230	+	0.803848i	−0.0793339	+	0.0458035i
$309$	3.09808	−	5.36603i	0.176243	−	0.305263i
$310$		0			0
$311$	8.19615			0.464761			0.232381	−	0.972625i	$-0.425349\pi$
$311$	8.19615			0.464761			0.232381	+	0.972625i	$0.425349\pi$
$312$	3.59808	+	0.232051i	0.203701	+	0.0131373i
$313$			3.60770i			0.203919i	0.994789	+	0.101959i	$0.0325112\pi$
$313$			3.60770i			0.203919i	−0.994789	+	0.101959i	$0.967489\pi$
$314$	6.23205	+	3.59808i	0.351695	+	0.203051i
$315$		0			0
$316$	4.19615	+	7.26795i	0.236052	+	0.408854i
$317$	−18.1244			−1.01797			−0.508983	−	0.860777i	$-0.669978\pi$
$317$	−18.1244			−1.01797			−0.508983	+	0.860777i	$0.669978\pi$
$318$	1.50000	+	2.59808i	0.0841158	+	0.145693i
$319$	3.29423	−	1.90192i	0.184441	−	0.106487i
$320$		0			0
$321$	−1.09808	−	1.90192i	−0.0612886	−	0.106155i
$322$	9.00000	+	5.19615i	0.501550	+	0.289570i
$323$	−12.2942	+	21.2942i	−0.684069	+	1.18484i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−2.53590			−0.140450
$327$	−2.19615	+	3.80385i	−0.121448	+	0.210353i
$328$	−5.59808	−	3.23205i	−0.309102	−	0.178460i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	−10.3923	+	6.00000i	−0.571213	+	0.329790i	−0.757634	−	0.652680i	$-0.773645\pi$
$331$	−10.3923	+	6.00000i	−0.571213	+	0.329790i	0.186421	+	0.982470i	$0.440311\pi$
$332$	2.83013	+	4.90192i	0.155323	+	0.269028i
$333$	3.00000			0.164399
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$		0			0
$336$	1.09808	+	0.633975i	0.0599050	+	0.0345861i
$337$			31.0000i			1.68868i	0.535810	+	0.844339i	$0.320006\pi$
$337$			31.0000i			1.68868i	−0.535810	+	0.844339i	$0.679994\pi$
$338$	−5.00000	−	12.0000i	−0.271964	−	0.652714i
$339$	0.803848			0.0436590
$340$		0			0
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$	4.09808	−	2.36603i	0.221599	−	0.127940i
$343$	15.7128			0.848412
$344$	3.63397	−	2.09808i	0.195931	−	0.113121i
$345$		0			0
$346$			4.39230i			0.236132i
$347$	16.0981	−	9.29423i	0.864190	−	0.498940i	−0.00122316	−	0.999999i	$-0.500389\pi$
$347$	16.0981	−	9.29423i	0.864190	−	0.498940i	0.865413	+	0.501059i	$0.167056\pi$
$348$	−2.59808	−	1.50000i	−0.139272	−	0.0804084i
$349$	8.19615	+	4.73205i	0.438730	+	0.253301i	0.703059	−	0.711132i	$-0.251817\pi$
$349$	8.19615	+	4.73205i	0.438730	+	0.253301i	−0.264329	+	0.964433i	$0.585150\pi$
$350$		0			0
$351$	−1.59808	−	3.23205i	−0.0852990	−	0.172514i
$352$		−	1.26795i		−	0.0675819i
$353$	−17.8923	+	30.9904i	−0.952311	+	1.64945i	−0.211907	+	0.977290i	$0.567967\pi$
$353$	−17.8923	+	30.9904i	−0.952311	+	1.64945i	−0.740404	+	0.672162i	$0.765366\pi$
$354$	−6.92820	+	12.0000i	−0.368230	+	0.637793i
$355$		0			0
$356$		−	9.46410i		−	0.501596i
$357$	3.29423	+	5.70577i	0.174349	+	0.301981i
$358$	1.09808	+	1.90192i	0.0580351	+	0.100520i
$359$			16.0526i			0.847222i	0.905844	+	0.423611i	$0.139238\pi$
$359$			16.0526i			0.847222i	−0.905844	+	0.423611i	$0.860762\pi$
$360$		0			0
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	−9.79423	+	16.9641i	−0.514773	+	0.891613i
$363$			9.39230i			0.492968i
$364$	0.294229	−	4.56218i	0.0154218	−	0.239123i
$365$		0			0
$366$	13.1603	+	7.59808i	0.687897	+	0.397158i
$367$	11.9545	+	6.90192i	0.624019	+	0.360277i	0.778432	−	0.627729i	$-0.216015\pi$
$367$	11.9545	+	6.90192i	0.624019	+	0.360277i	−0.154413	+	0.988006i	$0.549349\pi$
$368$	−7.09808	+	4.09808i	−0.370013	+	0.213627i
$369$			6.46410i			0.336508i
$370$		0			0
$371$	3.29423	−	1.90192i	0.171028	−	0.0987430i
$372$	9.46410			0.490691
$373$	24.2321	−	13.9904i	1.25469	−	0.724394i	0.282651	−	0.959223i	$-0.408786\pi$
$373$	24.2321	−	13.9904i	1.25469	−	0.724394i	0.972037	+	0.234828i	$0.0754528\pi$
$374$	3.29423	−	5.70577i	0.170341	−	0.295038i
$375$		0			0
$376$	−4.73205			−0.244037
$377$	−0.696152	+	10.7942i	−0.0358537	+	0.555931i
$378$		−	1.26795i		−	0.0652163i
$379$	−26.1962	−	15.1244i	−1.34561	−	0.776886i	−0.357982	−	0.933728i	$-0.616535\pi$
$379$	−26.1962	−	15.1244i	−1.34561	−	0.776886i	−0.987624	+	0.156842i	$0.949869\pi$
$380$		0			0
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$	20.7846			1.06343
$383$	−11.6603	−	20.1962i	−0.595811	−	1.03198i	−0.993432	−	0.114425i	$-0.963497\pi$
$383$	−11.6603	−	20.1962i	−0.595811	−	1.03198i	0.397621	−	0.917550i	$-0.369836\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−11.5981	−	20.0885i	−0.590327	−	1.02248i
$387$	−3.63397	−	2.09808i	−0.184725	−	0.106651i
$388$	−3.00000	+	5.19615i	−0.152302	+	0.263795i
$389$	7.39230			0.374805			0.187402	−	0.982283i	$-0.439993\pi$
$389$	7.39230			0.374805			0.187402	+	0.982283i	$0.439993\pi$
$390$		0			0
$391$	−42.5885			−2.15379
$392$	−2.69615	+	4.66987i	−0.136176	+	0.235864i
$393$	3.80385	+	2.19615i	0.191879	+	0.110781i
$394$	−3.46410	−	6.00000i	−0.174519	−	0.302276i
$395$		0			0
$396$	−1.09808	+	0.633975i	−0.0551804	+	0.0318584i
$397$	2.19615	+	3.80385i	0.110222	+	0.190910i	0.915860	−	0.401499i	$-0.131511\pi$
$397$	2.19615	+	3.80385i	0.110222	+	0.190910i	−0.805638	+	0.592408i	$0.798177\pi$
$398$	22.5885			1.13226
$399$	−3.00000	−	5.19615i	−0.150188	−	0.260133i
$400$		0			0
$401$	−18.1865	−	10.5000i	−0.908192	−	0.524345i	−0.0283431	−	0.999598i	$-0.509023\pi$
$401$	−18.1865	−	10.5000i	−0.908192	−	0.524345i	−0.879849	+	0.475253i	$0.842356\pi$
$402$		−	7.26795i		−	0.362492i
$403$	−15.1244	−	30.5885i	−0.753398	−	1.52372i
$404$	−19.3923			−0.964803
$405$		0			0
$406$	−1.90192	+	3.29423i	−0.0943909	+	0.163490i
$407$	−3.29423	+	1.90192i	−0.163289	+	0.0942749i
$408$	−5.19615			−0.257248
$409$	−17.8923	+	10.3301i	−0.884718	+	0.510792i	−0.872211	−	0.489130i	$-0.837314\pi$
$409$	−17.8923	+	10.3301i	−0.884718	+	0.510792i	−0.0125066	+	0.999922i	$0.503981\pi$
$410$		0			0
$411$			9.00000i			0.443937i
$412$	5.36603	−	3.09808i	0.264365	−	0.152631i
$413$	15.2154	+	8.78461i	0.748700	+	0.432262i
$414$	7.09808	+	4.09808i	0.348851	+	0.201409i
$415$		0			0
$416$	3.00000	+	2.00000i	0.147087	+	0.0980581i
$417$			4.00000i			0.195881i
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	−2.19615	+	3.80385i	−0.107289	+	0.185830i	−0.914671	−	0.404199i	$-0.867550\pi$
$419$	−2.19615	+	3.80385i	−0.107289	+	0.185830i	0.807382	+	0.590029i	$0.200884\pi$
$420$		0			0
$421$			6.46410i			0.315041i	0.987516	+	0.157521i	$0.0503500\pi$
$421$			6.46410i			0.315041i	−0.987516	+	0.157521i	$0.949650\pi$
$422$	−12.1962	−	21.1244i	−0.593699	−	1.02832i
$423$	2.36603	+	4.09808i	0.115040	+	0.199255i
$424$			3.00000i			0.145693i
$425$		0			0
$426$	−1.09808	+	1.90192i	−0.0532020	+	0.0921485i
$427$	9.63397	−	16.6865i	0.466221	−	0.807518i
$428$		−	2.19615i		−	0.106155i
$429$	3.80385	+	2.53590i	0.183651	+	0.122434i
$430$		0			0
$431$	33.0788	+	19.0981i	1.59335	+	0.919922i	0.992727	+	0.120391i	$0.0384149\pi$
$431$	33.0788	+	19.0981i	1.59335	+	0.919922i	0.600625	+	0.799531i	$0.294918\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	6.74167	−	3.89230i	0.323984	−	0.187052i	−0.329183	−	0.944266i	$-0.606773\pi$
$433$	6.74167	−	3.89230i	0.323984	−	0.187052i	0.653167	+	0.757214i	$0.273440\pi$
$434$		−	12.0000i		−	0.576018i
$435$		0			0
$436$	−3.80385	+	2.19615i	−0.182171	+	0.105177i
$437$	38.7846			1.85532
$438$	−10.5000	+	6.06218i	−0.501709	+	0.289662i
$439$	7.29423	−	12.6340i	0.348135	−	0.602987i	−0.637784	−	0.770216i	$-0.720149\pi$
$439$	7.29423	−	12.6340i	0.348135	−	0.602987i	0.985918	+	0.167229i	$0.0534819\pi$
$440$		0			0
$441$	5.39230			0.256776
$442$	8.30385	+	16.7942i	0.394974	+	0.798820i
$443$		−	16.3923i		−	0.778822i	−0.921064	−	0.389411i	$-0.872679\pi$
$443$		−	16.3923i		−	0.778822i	0.921064	−	0.389411i	$-0.127321\pi$
$444$	2.59808	+	1.50000i	0.123299	+	0.0711868i
$445$		0			0
$446$	2.53590	+	4.39230i	0.120078	+	0.207982i
$447$	−6.12436			−0.289672
$448$	0.633975	+	1.09808i	0.0299525	+	0.0518792i
$449$	−22.9808	+	13.2679i	−1.08453	+	0.626153i	−0.932115	−	0.362163i	$-0.882038\pi$
$449$	−22.9808	+	13.2679i	−1.08453	+	0.626153i	−0.152415	+	0.988317i	$0.548705\pi$
$450$		0			0
$451$	−4.09808	−	7.09808i	−0.192971	−	0.334235i
$452$	0.696152	+	0.401924i	0.0327443	+	0.0189049i
$453$	5.36603	−	9.29423i	0.252118	−	0.436681i
$454$	20.1962			0.947852
$455$		0			0
$456$	4.73205			0.221599
$457$	15.9904	−	27.6962i	0.747998	−	1.29557i	−0.200782	−	0.979636i	$-0.564348\pi$
$457$	15.9904	−	27.6962i	0.747998	−	1.29557i	0.948781	−	0.315935i	$-0.102318\pi$
$458$	6.80385	+	3.92820i	0.317923	+	0.183553i
$459$	2.59808	+	4.50000i	0.121268	+	0.210042i
$460$		0			0
$461$	−27.6962	+	15.9904i	−1.28994	+	0.744746i	−0.978643	−	0.205567i	$-0.934096\pi$
$461$	−27.6962	+	15.9904i	−1.28994	+	0.744746i	−0.311295	+	0.950313i	$0.600763\pi$
$462$	0.803848	+	1.39230i	0.0373984	+	0.0647759i
$463$	−15.8038			−0.734467			−0.367234	−	0.930129i	$-0.619695\pi$
$463$	−15.8038			−0.734467			−0.367234	+	0.930129i	$0.619695\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	−15.5885	−	9.00000i	−0.722121	−	0.416917i
$467$		−	5.41154i		−	0.250416i	−0.992130	−	0.125208i	$-0.960040\pi$
$467$		−	5.41154i		−	0.250416i	0.992130	−	0.125208i	$-0.0399599\pi$
$468$	0.232051	−	3.59808i	0.0107266	−	0.166321i
$469$	−9.21539			−0.425527
$470$		0			0
$471$	3.59808	−	6.23205i	0.165791	−	0.287158i
$472$	−12.0000	+	6.92820i	−0.552345	+	0.318896i
$473$	5.32051			0.244637
$474$	7.26795	−	4.19615i	0.333828	−	0.192736i
$475$		0			0
$476$			6.58846i			0.301981i
$477$	2.59808	−	1.50000i	0.118958	−	0.0686803i
$478$	5.70577	+	3.29423i	0.260976	+	0.150675i
$479$	−0.588457	−	0.339746i	−0.0268873	−	0.0155234i	0.486496	−	0.873683i	$-0.338275\pi$
$479$	−0.588457	−	0.339746i	−0.0268873	−	0.0155234i	−0.513383	+	0.858159i	$0.671608\pi$
$480$		0			0
$481$	0.696152	−	10.7942i	0.0317418	−	0.492174i
$482$		−	11.1962i		−	0.509971i
$483$	5.19615	−	9.00000i	0.236433	−	0.409514i
$484$	−4.69615	+	8.13397i	−0.213461	+	0.369726i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	7.56218	+	13.0981i	0.342675	+	0.593530i	0.984929	−	0.172962i	$-0.0553337\pi$
$487$	7.56218	+	13.0981i	0.342675	+	0.593530i	−0.642254	+	0.766492i	$0.722000\pi$
$488$	7.59808	+	13.1603i	0.343949	+	0.595737i
$489$			2.53590i			0.114677i
$490$		0			0
$491$	−15.2942	+	26.4904i	−0.690219	+	1.19549i	0.281547	+	0.959547i	$0.409152\pi$
$491$	−15.2942	+	26.4904i	−0.690219	+	1.19549i	−0.971766	+	0.235947i	$0.924181\pi$
$492$	−3.23205	+	5.59808i	−0.145712	+	0.252381i
$493$		−	15.5885i		−	0.702069i
$494$	−7.56218	−	15.2942i	−0.340238	−	0.688120i
$495$		0			0
$496$	8.19615	+	4.73205i	0.368018	+	0.212475i
$497$	2.41154	+	1.39230i	0.108172	+	0.0624534i
$498$	4.90192	−	2.83013i	0.219660	−	0.126821i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	8.19615	−	4.73205i	0.366177	−	0.211412i
$502$	16.3923			0.731624
$503$	−10.9019	+	6.29423i	−0.486093	+	0.280646i	−0.722952	−	0.690898i	$-0.757215\pi$
$503$	−10.9019	+	6.29423i	−0.486093	+	0.280646i	0.236859	+	0.971544i	$0.423882\pi$
$504$	0.633975	−	1.09808i	0.0282395	−	0.0489122i
$505$		0			0
$506$	−10.3923			−0.461994
$507$	−12.0000	+	5.00000i	−0.532939	+	0.222058i
$508$			4.00000i			0.177471i
$509$	−23.0885	−	13.3301i	−1.02338	−	0.590847i	−0.108297	−	0.994119i	$-0.534540\pi$
$509$	−23.0885	−	13.3301i	−1.02338	−	0.590847i	−0.915081	+	0.403271i	$0.867873\pi$
$510$		0			0
$511$	7.68653	+	13.3135i	0.340032	+	0.588953i
$512$	−1.00000			−0.0441942
$513$	−2.36603	−	4.09808i	−0.104463	−	0.180934i
$514$	20.0885	−	11.5981i	0.886064	−	0.511569i
$515$		0			0
$516$	−2.09808	−	3.63397i	−0.0923627	−	0.159977i
$517$	−5.19615	−	3.00000i	−0.228527	−	0.131940i
$518$	1.90192	−	3.29423i	0.0835657	−	0.144740i
$519$	4.39230			0.192801
$520$		0			0
$521$	−29.1962			−1.27911			−0.639553	−	0.768747i	$-0.720881\pi$
$521$	−29.1962			−1.27911			−0.639553	+	0.768747i	$0.720881\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	28.2224	+	16.2942i	1.23408	+	0.712497i	0.967878	−	0.251420i	$-0.0808976\pi$
$523$	28.2224	+	16.2942i	1.23408	+	0.712497i	0.266203	+	0.963917i	$0.414231\pi$
$524$	2.19615	+	3.80385i	0.0959394	+	0.166172i
$525$		0			0
$526$	7.09808	−	4.09808i	0.309491	−	0.178685i
$527$	24.5885	+	42.5885i	1.07109	+	1.85518i
$528$	−1.26795			−0.0551804
$529$	22.0885	+	38.2583i	0.960368	+	1.66341i
$530$		0			0
$531$	12.0000	+	6.92820i	0.520756	+	0.300658i
$532$		−	6.00000i		−	0.260133i
$533$	23.2583	+	1.50000i	1.00743	+	0.0649722i
$534$	−9.46410			−0.409552
$535$		0			0
$536$	3.63397	−	6.29423i	0.156964	−	0.271869i
$537$	1.90192	−	1.09808i	0.0820741	−	0.0473855i
$538$	−7.60770			−0.327991
$539$	−5.92116	+	3.41858i	−0.255042	+	0.147249i
$540$		0			0
$541$		−	10.8564i		−	0.466753i	−0.972386	−	0.233377i	$-0.925022\pi$
$541$		−	10.8564i		−	0.466753i	0.972386	−	0.233377i	$-0.0749775\pi$
$542$		0			0
$543$	16.9641	+	9.79423i	0.727999	+	0.420311i
$544$	−4.50000	−	2.59808i	−0.192936	−	0.111392i
$545$		0			0
$546$	−4.56218	−	0.294229i	−0.195243	−	0.0125918i
$547$			4.19615i			0.179415i	0.995968	+	0.0897073i	$0.0285931\pi$
$547$			4.19615i			0.179415i	−0.995968	+	0.0897073i	$0.971407\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	7.59808	−	13.1603i	0.324278	−	0.561666i
$550$		0			0
$551$			14.1962i			0.604776i
$552$	4.09808	+	7.09808i	0.174426	+	0.302114i
$553$	−5.32051	−	9.21539i	−0.226251	−	0.391878i
$554$			4.80385i			0.204096i
$555$		0			0
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	12.8660	−	22.2846i	0.545151	−	0.944229i	−0.453446	−	0.891284i	$-0.649806\pi$
$557$	12.8660	−	22.2846i	0.545151	−	0.944229i	0.998597	−	0.0529457i	$-0.0168610\pi$
$558$		−	9.46410i		−	0.400647i
$559$	−8.39230	+	12.5885i	−0.354957	+	0.532435i
$560$		0			0
$561$	−5.70577	−	3.29423i	−0.240898	−	0.139082i
$562$	15.1865	+	8.76795i	0.640605	+	0.369854i
$563$	−28.3923	+	16.3923i	−1.19659	+	0.690853i	−0.959794	−	0.280705i	$-0.909432\pi$
$563$	−28.3923	+	16.3923i	−1.19659	+	0.690853i	−0.236799	+	0.971559i	$0.576098\pi$
$564$			4.73205i			0.199255i
$565$		0			0
$566$	17.1506	−	9.90192i	0.720895	−	0.416209i
$567$	−1.26795			−0.0532489
$568$	−1.90192	+	1.09808i	−0.0798029	+	0.0460743i
$569$	−4.39230	+	7.60770i	−0.184135	+	0.318931i	−0.943285	−	0.331985i	$-0.892282\pi$
$569$	−4.39230	+	7.60770i	−0.184135	+	0.318931i	0.759150	+	0.650916i	$0.225615\pi$
$570$		0			0
$571$	24.1962			1.01258			0.506289	−	0.862364i	$-0.331017\pi$
$571$	24.1962			1.01258			0.506289	+	0.862364i	$0.331017\pi$
$572$	2.02628	+	4.09808i	0.0847230	+	0.171349i
$573$		−	20.7846i		−	0.868290i
$574$	7.09808	+	4.09808i	0.296268	+	0.171050i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−19.7321			−0.821456			−0.410728	−	0.911758i	$-0.634725\pi$
$577$	−19.7321			−0.821456			−0.410728	+	0.911758i	$0.634725\pi$
$578$	−5.00000	−	8.66025i	−0.207973	−	0.360219i
$579$	−20.0885	+	11.5981i	−0.834848	+	0.482000i
$580$		0			0
$581$	−3.58846	−	6.21539i	−0.148874	−	0.257858i
$582$	5.19615	+	3.00000i	0.215387	+	0.124354i
$583$	−1.90192	+	3.29423i	−0.0787696	+	0.136433i
$584$	−12.1244			−0.501709
$585$		0			0
$586$	−2.66025			−0.109894
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$	4.66987	+	2.69615i	0.192582	+	0.111187i
$589$	−22.3923	−	38.7846i	−0.922659	−	1.59809i
$590$		0			0
$591$	−6.00000	+	3.46410i	−0.246807	+	0.142494i
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	−19.1436			−0.786133			−0.393067	−	0.919510i	$-0.628586\pi$
$593$	−19.1436			−0.786133			−0.393067	+	0.919510i	$0.628586\pi$
$594$	0.633975	+	1.09808i	0.0260123	+	0.0450546i
$595$		0			0
$596$	−5.30385	−	3.06218i	−0.217254	−	0.125432i
$597$		−	22.5885i		−	0.924484i
$598$	16.3923	−	24.5885i	0.670331	−	1.00550i
$599$	−16.3923			−0.669771			−0.334886	−	0.942259i	$-0.608698\pi$
$599$	−16.3923			−0.669771			−0.334886	+	0.942259i	$0.608698\pi$
$600$		0			0
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	−0.590632	−	0.806941i	$-0.701121\pi$
$601$	9.89230	−	17.1340i	0.403516	−	0.698909i	0.994147	+	0.108032i	$0.0344548\pi$
$602$	−4.60770	+	2.66025i	−0.187796	+	0.108424i
$603$	−7.26795			−0.295974
$604$	9.29423	−	5.36603i	0.378177	−	0.218340i
$605$		0			0
$606$			19.3923i			0.787759i
$607$	−6.24871	+	3.60770i	−0.253627	+	0.146432i	−0.621424	−	0.783474i	$-0.713446\pi$
$607$	−6.24871	+	3.60770i	−0.253627	+	0.146432i	0.367797	+	0.929906i	$0.380112\pi$
$608$	4.09808	+	2.36603i	0.166199	+	0.0959550i
$609$	3.29423	+	1.90192i	0.133489	+	0.0770698i
$610$		0			0
$611$	15.2942	−	7.56218i	0.618738	−	0.305933i
$612$			5.19615i			0.210042i
$613$	−6.57180	+	11.3827i	−0.265432	+	0.459742i	−0.967677	−	0.252194i	$-0.918848\pi$
$613$	−6.57180	+	11.3827i	−0.265432	+	0.459742i	0.702244	+	0.711936i	$0.252181\pi$
$614$	−3.63397	+	6.29423i	−0.146655	+	0.254014i
$615$		0			0
$616$			1.60770i			0.0647759i
$617$	−15.6962	−	27.1865i	−0.631903	−	1.09449i	−0.987162	−	0.159721i	$-0.948941\pi$
$617$	−15.6962	−	27.1865i	−0.631903	−	1.09449i	0.355259	−	0.934768i	$-0.384393\pi$
$618$	−3.09808	−	5.36603i	−0.124623	−	0.215853i
$619$			28.3923i			1.14118i	0.821234	+	0.570592i	$0.193286\pi$
$619$			28.3923i			1.14118i	−0.821234	+	0.570592i	$0.806714\pi$
$620$		0			0
$621$	4.09808	−	7.09808i	0.164450	−	0.284836i
$622$	4.09808	−	7.09808i	0.164318	−	0.284607i
$623$			12.0000i			0.480770i
$624$	2.00000	−	3.00000i	0.0800641	−	0.120096i
$625$		0			0
$626$	3.12436	+	1.80385i	0.124874	+	0.0720962i
$627$	5.19615	+	3.00000i	0.207514	+	0.119808i
$628$	6.23205	−	3.59808i	0.248686	−	0.143579i
$629$			15.5885i			0.621552i
$630$		0			0
$631$	−1.60770	+	0.928203i	−0.0640013	+	0.0369512i	−0.531659	−	0.846958i	$-0.678431\pi$
$631$	−1.60770	+	0.928203i	−0.0640013	+	0.0369512i	0.467658	+	0.883910i	$0.345098\pi$
$632$	8.39230			0.333828
$633$	−21.1244	+	12.1962i	−0.839618	+	0.484754i
$634$	−9.06218	+	15.6962i	−0.359905	+	0.623374i
$635$		0			0
$636$	3.00000			0.118958
$637$	1.25129	−	19.4019i	0.0495779	−	0.768732i
$638$		−	3.80385i		−	0.150596i
$639$	1.90192	+	1.09808i	0.0752389	+	0.0434392i
$640$		0			0
$641$	−20.5981	−	35.6769i	−0.813575	−	1.40915i	−0.910347	−	0.413847i	$-0.864185\pi$
$641$	−20.5981	−	35.6769i	−0.813575	−	1.40915i	0.0967715	−	0.995307i	$-0.469148\pi$
$642$	−2.19615			−0.0866752
$643$	13.8564	+	24.0000i	0.546443	+	0.946468i	0.998515	+	0.0544858i	$0.0173519\pi$
$643$	13.8564	+	24.0000i	0.546443	+	0.946468i	−0.452071	+	0.891982i	$0.649315\pi$
$644$	9.00000	−	5.19615i	0.354650	−	0.204757i
$645$		0			0
$646$	12.2942	+	21.2942i	0.483710	+	0.837810i
$647$	−42.5885	−	24.5885i	−1.67433	−	0.966672i	−0.965172	−	0.261618i	$-0.915744\pi$
$647$	−42.5885	−	24.5885i	−1.67433	−	0.966672i	−0.709153	−	0.705054i	$-0.750923\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−17.5692			−0.689652
$650$		0			0
$651$	−12.0000			−0.470317
$652$	−1.26795	+	2.19615i	−0.0496567	+	0.0860080i
$653$	11.4115	+	6.58846i	0.446568	+	0.257826i	0.706380	−	0.707833i	$-0.250327\pi$
$653$	11.4115	+	6.58846i	0.446568	+	0.257826i	−0.259812	+	0.965659i	$0.583660\pi$
$654$	2.19615	+	3.80385i	0.0858764	+	0.148742i
$655$		0			0
$656$	−5.59808	+	3.23205i	−0.218568	+	0.126190i
$657$	6.06218	+	10.5000i	0.236508	+	0.409644i
$658$	6.00000			0.233904
$659$	−18.5885	−	32.1962i	−0.724103	−	1.25418i	−0.959342	−	0.282246i	$-0.908920\pi$
$659$	−18.5885	−	32.1962i	−0.724103	−	1.25418i	0.235238	−	0.971938i	$-0.424413\pi$
$660$		0			0
$661$	−7.79423	−	4.50000i	−0.303160	−	0.175030i	0.340701	−	0.940172i	$-0.389335\pi$
$661$	−7.79423	−	4.50000i	−0.303160	−	0.175030i	−0.643862	+	0.765142i	$0.722669\pi$
$662$			12.0000i			0.466393i
$663$	16.7942	−	8.30385i	0.652234	−	0.322495i
$664$	5.66025			0.219660
$665$		0			0
$666$	1.50000	−	2.59808i	0.0581238	−	0.100673i
$667$	−21.2942	+	12.2942i	−0.824516	+	0.476034i
$668$	9.46410			0.366177
$669$	4.39230	−	2.53590i	0.169816	−	0.0980435i
$670$		0			0
$671$			19.2679i			0.743831i
$672$	1.09808	−	0.633975i	0.0423592	−	0.0244561i
$673$	−0.866025	−	0.500000i	−0.0333828	−	0.0192736i	0.483216	−	0.875501i	$-0.339469\pi$
$673$	−0.866025	−	0.500000i	−0.0333828	−	0.0192736i	−0.516599	+	0.856228i	$0.672802\pi$
$674$	26.8468	+	15.5000i	1.03410	+	0.597038i
$675$		0			0
$676$	−12.8923	−	1.66987i	−0.495858	−	0.0642259i
$677$		−	16.3923i		−	0.630007i	−0.949090	−	0.315004i	$-0.897994\pi$
$677$		−	16.3923i		−	0.630007i	0.949090	−	0.315004i	$-0.102006\pi$
$678$	0.401924	−	0.696152i	0.0154358	−	0.0267356i
$679$	3.80385	−	6.58846i	0.145978	−	0.252842i
$680$		0			0
$681$		−	20.1962i		−	0.773918i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	13.8564	+	24.0000i	0.530201	+	0.918334i	0.999379	+	0.0352311i	$0.0112167\pi$
$683$	13.8564	+	24.0000i	0.530201	+	0.918334i	−0.469179	+	0.883103i	$0.655450\pi$
$684$		−	4.73205i		−	0.180934i
$685$		0			0
$686$	7.85641	−	13.6077i	0.299959	−	0.519544i
$687$	3.92820	−	6.80385i	0.149870	−	0.259583i
$688$		−	4.19615i		−	0.159977i
$689$	−4.79423	−	9.69615i	−0.182646	−	0.369394i
$690$		0			0
$691$	22.0981	+	12.7583i	0.840650	+	0.485350i	0.857485	−	0.514509i	$-0.172026\pi$
$691$	22.0981	+	12.7583i	0.840650	+	0.485350i	−0.0168348	+	0.999858i	$0.505359\pi$
$692$	3.80385	+	2.19615i	0.144601	+	0.0834852i
$693$	1.39230	−	0.803848i	0.0528893	−	0.0305356i
$694$		−	18.5885i		−	0.705608i
$695$		0			0
$696$	−2.59808	+	1.50000i	−0.0984798	+	0.0568574i
$697$	−33.5885			−1.27225
$698$	8.19615	−	4.73205i	0.310229	−	0.179111i
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$		0			0
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	−3.59808	−	0.232051i	−0.135801	−	0.00875819i
$703$		−	14.1962i		−	0.535418i
$704$	−1.09808	−	0.633975i	−0.0413853	−	0.0238938i
$705$		0			0
$706$	17.8923	+	30.9904i	0.673386	+	1.16634i
$707$	24.5885			0.924744
$708$	6.92820	+	12.0000i	0.260378	+	0.450988i
$709$	39.1865	−	22.6244i	1.47168	−	0.849676i	0.472188	−	0.881498i	$-0.343464\pi$
$709$	39.1865	−	22.6244i	1.47168	−	0.849676i	0.999494	+	0.0318226i	$0.0101311\pi$
$710$		0			0
$711$	−4.19615	−	7.26795i	−0.157368	−	0.272569i
$712$	−8.19615	−	4.73205i	−0.307164	−	0.177341i
$713$	38.7846	−	67.1769i	1.45250	−	2.51580i
$714$	6.58846			0.246567
$715$		0			0
$716$	2.19615			0.0820741
$717$	3.29423	−	5.70577i	0.123025	−	0.213086i
$718$	13.9019	+	8.02628i	0.518815	+	0.299538i
$719$	−15.8038	−	27.3731i	−0.589384	−	1.02084i	−0.994313	−	0.106495i	$-0.966037\pi$
$719$	−15.8038	−	27.3731i	−0.589384	−	1.02084i	0.404929	−	0.914348i	$-0.367296\pi$
$720$		0			0
$721$	−6.80385	+	3.92820i	−0.253389	+	0.146294i
$722$	−1.69615	−	2.93782i	−0.0631243	−	0.109334i
$723$	−11.1962			−0.416389
$724$	9.79423	+	16.9641i	0.364000	+	0.630466i
$725$		0			0
$726$	8.13397	+	4.69615i	0.301880	+	0.174291i
$727$			13.8038i			0.511956i	0.966683	+	0.255978i	$0.0823975\pi$
$727$			13.8038i			0.511956i	−0.966683	+	0.255978i	$0.917602\pi$
$728$	−3.80385	−	2.53590i	−0.140980	−	0.0939866i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	10.9019	−	18.8827i	0.403222	−	0.698401i
$732$	13.1603	−	7.59808i	0.486417	−	0.280833i
$733$	−20.3205			−0.750555			−0.375278	−	0.926912i	$-0.622453\pi$
$733$	−20.3205			−0.750555			−0.375278	+	0.926912i	$0.622453\pi$
$734$	11.9545	−	6.90192i	0.441248	−	0.254755i
$735$		0			0
$736$			8.19615i			0.302114i
$737$	7.98076	−	4.60770i	0.293975	−	0.169727i
$738$	5.59808	+	3.23205i	0.206068	+	0.118973i
$739$	−4.39230	−	2.53590i	−0.161574	−	0.0932845i	0.417033	−	0.908891i	$-0.363070\pi$
$739$	−4.39230	−	2.53590i	−0.161574	−	0.0932845i	−0.578607	+	0.815607i	$0.696403\pi$
$740$		0			0
$741$	−15.2942	+	7.56218i	−0.561848	+	0.277804i
$742$		−	3.80385i		−	0.139644i
$743$	−8.19615	+	14.1962i	−0.300688	+	0.520806i	−0.976292	−	0.216458i	$-0.930550\pi$
$743$	−8.19615	+	14.1962i	−0.300688	+	0.520806i	0.675604	+	0.737264i	$0.263883\pi$
$744$	4.73205	−	8.19615i	0.173485	−	0.300486i
$745$		0			0
$746$		−	27.9808i		−	1.02445i
$747$	−2.83013	−	4.90192i	−0.103549	−	0.179352i
$748$	−3.29423	−	5.70577i	−0.120449	−	0.208624i
$749$			2.78461i			0.101747i
$750$		0			0
$751$	13.4904	−	23.3660i	0.492271	−	0.852638i	−0.507689	−	0.861540i	$-0.669500\pi$
$751$	13.4904	−	23.3660i	0.492271	−	0.852638i	0.999960	+	0.00890181i	$0.00283357\pi$
$752$	−2.36603	+	4.09808i	−0.0862801	+	0.149441i
$753$		−	16.3923i		−	0.597369i
$754$	9.00000	+	6.00000i	0.327761	+	0.218507i
$755$		0			0
$756$	−1.09808	−	0.633975i	−0.0399366	−	0.0230574i
$757$	19.7321	+	11.3923i	0.717174	+	0.414060i	0.813712	−	0.581269i	$-0.197444\pi$
$757$	19.7321	+	11.3923i	0.717174	+	0.414060i	−0.0965379	+	0.995329i	$0.530777\pi$
$758$	−26.1962	+	15.1244i	−0.951487	+	0.549341i
$759$			10.3923i			0.377217i
$760$		0			0
$761$	14.1962	−	8.19615i	0.514610	−	0.297110i	−0.220117	−	0.975474i	$-0.570644\pi$
$761$	14.1962	−	8.19615i	0.514610	−	0.297110i	0.734727	+	0.678363i	$0.237310\pi$
$762$	4.00000			0.144905
$763$	4.82309	−	2.78461i	0.174607	−	0.100810i
$764$	10.3923	−	18.0000i	0.375980	−	0.651217i
$765$		0			0
$766$	−23.3205			−0.842604
$767$	27.7128	−	41.5692i	1.00065	−	1.50098i
$768$			1.00000i			0.0360844i
$769$	18.8038	+	10.8564i	0.678084	+	0.391492i	0.799133	−	0.601155i	$-0.205292\pi$
$769$	18.8038	+	10.8564i	0.678084	+	0.391492i	−0.121049	+	0.992647i	$0.538626\pi$
$770$		0			0
$771$	−11.5981	−	20.0885i	−0.417695	−	0.723468i
$772$	−23.1962			−0.834848
$773$	−4.60770	−	7.98076i	−0.165727	−	0.287048i	0.771186	−	0.636610i	$-0.219664\pi$
$773$	−4.60770	−	7.98076i	−0.165727	−	0.287048i	−0.936913	+	0.349562i	$0.886330\pi$
$774$	−3.63397	+	2.09808i	−0.130621	+	0.0754138i
$775$		0			0
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−3.29423	−	1.90192i	−0.118180	−	0.0682311i
$778$	3.69615	−	6.40192i	0.132513	−	0.229520i
$779$	30.5885			1.09595
$780$		0			0
$781$	−2.78461			−0.0996412
$782$	−21.2942	+	36.8827i	−0.761480	+	1.31892i
$783$	2.59808	+	1.50000i	0.0928477	+	0.0536056i
$784$	2.69615	+	4.66987i	0.0962912	+	0.166781i
$785$		0			0
$786$	3.80385	−	2.19615i	0.135679	−	0.0783342i
$787$	−10.7321	−	18.5885i	−0.382556	−	0.662607i	0.608871	−	0.793270i	$-0.291623\pi$
$787$	−10.7321	−	18.5885i	−0.382556	−	0.662607i	−0.991427	+	0.130663i	$0.958290\pi$
$788$	−6.92820			−0.246807
$789$	−4.09808	−	7.09808i	−0.145895	−	0.252698i
$790$		0			0
$791$	−0.882686	−	0.509619i	−0.0313847	−	0.0181200i
$792$			1.26795i			0.0450546i
$793$	−45.5885	−	30.3923i	−1.61889	−	1.07926i
$794$	4.39230			0.155877
$795$		0			0
$796$	11.2942	−	19.5622i	0.400313	−	0.693363i
$797$	−5.19615	+	3.00000i	−0.184057	+	0.106265i	−0.589197	−	0.807989i	$-0.700556\pi$
$797$	−5.19615	+	3.00000i	−0.184057	+	0.106265i	0.405140	+	0.914255i	$0.367223\pi$
$798$	−6.00000			−0.212398
$799$	−21.2942	+	12.2942i	−0.753336	+	0.434939i
$800$		0			0
$801$			9.46410i			0.334398i
$802$	−18.1865	+	10.5000i	−0.642189	+	0.370768i
$803$	−13.3135	−	7.68653i	−0.469822	−	0.271252i
$804$	−6.29423	−	3.63397i	−0.221980	−	0.128160i
$805$		0			0
$806$	−34.0526	−	2.19615i	−1.19945	−	0.0773562i
$807$			7.60770i			0.267804i
$808$	−9.69615	+	16.7942i	−0.341109	+	0.590819i
$809$	−18.4019	+	31.8731i	−0.646977	+	1.12060i	0.336864	+	0.941553i	$0.390634\pi$
$809$	−18.4019	+	31.8731i	−0.646977	+	1.12060i	−0.983841	+	0.179044i	$0.942700\pi$
$810$		0			0
$811$			16.3923i			0.575612i	0.957689	+	0.287806i	$0.0929258\pi$
$811$			16.3923i			0.575612i	−0.957689	+	0.287806i	$0.907074\pi$
$812$	1.90192	+	3.29423i	0.0667444	+	0.115605i
$813$		0			0
$814$			3.80385i			0.133325i
$815$		0			0
$816$	−2.59808	+	4.50000i	−0.0909509	+	0.157532i
$817$	−9.92820	+	17.1962i	−0.347344	+	0.601617i
$818$			20.6603i			0.722369i
$819$	−0.294229	+	4.56218i	−0.0102812	+	0.159415i
$820$		0			0
$821$	24.8038	+	14.3205i	0.865660	+	0.499789i	0.865904	−	0.500211i	$-0.166744\pi$
$821$	24.8038	+	14.3205i	0.865660	+	0.499789i	−0.000243419		1.00000i	$0.500077\pi$
$822$	7.79423	+	4.50000i	0.271855	+	0.156956i
$823$	−27.7128	+	16.0000i	−0.966008	+	0.557725i	−0.898017	−	0.439961i	$-0.854992\pi$
$823$	−27.7128	+	16.0000i	−0.966008	+	0.557725i	−0.0679910	+	0.997686i	$0.521659\pi$
$824$		−	6.19615i		−	0.215853i
$825$		0			0
$826$	15.2154	−	8.78461i	0.529411	−	0.305656i
$827$	−44.1051			−1.53369			−0.766843	−	0.641835i	$-0.778173\pi$
$827$	−44.1051			−1.53369			−0.766843	+	0.641835i	$0.778173\pi$
$828$	7.09808	−	4.09808i	0.246675	−	0.142418i
$829$	−19.9904	+	34.6244i	−0.694295	+	1.20255i	0.276123	+	0.961122i	$0.410950\pi$
$829$	−19.9904	+	34.6244i	−0.694295	+	1.20255i	−0.970418	+	0.241431i	$0.922383\pi$
$830$		0			0
$831$	4.80385			0.166644
$832$	3.23205	−	1.59808i	0.112051	−	0.0554033i
$833$			28.0192i			0.970809i
$834$	3.46410	+	2.00000i	0.119952	+	0.0692543i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$	−9.46410			−0.327127
$838$	2.19615	+	3.80385i	0.0758648	+	0.131402i
$839$	10.3923	−	6.00000i	0.358782	−	0.207143i	−0.309764	−	0.950813i	$-0.600250\pi$
$839$	10.3923	−	6.00000i	0.358782	−	0.207143i	0.668546	+	0.743670i	$0.266917\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	5.59808	+	3.23205i	0.192922	+	0.111384i
$843$	8.76795	−	15.1865i	0.301984	−	0.523052i
$844$	−24.3923			−0.839618
$845$		0			0
$846$	4.73205			0.162691
$847$	5.95448	−	10.3135i	0.204598	−	0.354375i
$848$	2.59808	+	1.50000i	0.0892183	+	0.0515102i
$849$	−9.90192	−	17.1506i	−0.339833	−	0.588608i
$850$		0			0
$851$	21.2942	−	12.2942i	0.729957	−	0.421441i
$852$	1.09808	+	1.90192i	0.0376195	+	0.0651588i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	−9.63397	−	16.6865i	−0.329668	−	0.571001i
$855$		0			0
$856$	−1.90192	−	1.09808i	−0.0650064	−	0.0375315i
$857$		−	18.3731i		−	0.627612i	−0.949487	−	0.313806i	$-0.898396\pi$
$857$		−	18.3731i		−	0.627612i	0.949487	−	0.313806i	$-0.101604\pi$
$858$	4.09808	−	2.02628i	0.139906	−	0.0691760i
$859$	20.5885			0.702469			0.351235	−	0.936288i	$-0.385762\pi$
$859$	20.5885			0.702469			0.351235	+	0.936288i	$0.385762\pi$
$860$		0			0
$861$	4.09808	−	7.09808i	0.139662	−	0.241902i
$862$	33.0788	−	19.0981i	1.12667	−	0.650483i
$863$	−49.5167			−1.68557			−0.842783	−	0.538253i	$-0.819085\pi$
$863$	−49.5167			−1.68557			−0.842783	+	0.538253i	$0.819085\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	7.78461i		−	0.264532i
$867$	−8.66025	+	5.00000i	−0.294118	+	0.169809i
$868$	−10.3923	−	6.00000i	−0.352738	−	0.203653i
$869$	9.21539	+	5.32051i	0.312611	+	0.180486i
$870$		0			0
$871$	−1.68653	+	26.1506i	−0.0571460	+	0.886080i
$872$			4.39230i			0.148742i
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$	19.3923	−	33.5885i	0.655954	−	1.13615i
$875$		0			0
$876$			12.1244i			0.409644i
$877$	−11.3038	−	19.5788i	−0.381704	−	0.661130i	0.609602	−	0.792708i	$-0.291329\pi$
$877$	−11.3038	−	19.5788i	−0.381704	−	0.661130i	−0.991306	+	0.131577i	$0.957996\pi$
$878$	−7.29423	−	12.6340i	−0.246168	−	0.426376i
$879$			2.66025i			0.0897281i
$880$		0			0
$881$	−6.99038	+	12.1077i	−0.235512	+	0.407919i	−0.959421	−	0.281976i	$-0.909010\pi$
$881$	−6.99038	+	12.1077i	−0.235512	+	0.407919i	0.723909	+	0.689895i	$0.242343\pi$
$882$	2.69615	−	4.66987i	0.0907842	−	0.157243i
$883$			16.7846i			0.564847i	0.959290	+	0.282424i	$0.0911383\pi$
$883$			16.7846i			0.564847i	−0.959290	+	0.282424i	$0.908862\pi$
$884$	18.6962	+	1.20577i	0.628820	+	0.0405545i
$885$		0			0
$886$	−14.1962	−	8.19615i	−0.476929	−	0.275355i
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.401813	−	0.915722i	$-0.631620\pi$
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.993945	+	0.109881i	$0.964953\pi$
$888$	2.59808	−	1.50000i	0.0871857	−	0.0503367i
$889$		−	5.07180i		−	0.170103i
$890$		0			0
$891$	1.09808	−	0.633975i	0.0367869	−	0.0212389i
$892$	5.07180			0.169816
$893$	19.3923	−	11.1962i	0.648939	−	0.374665i
$894$	−3.06218	+	5.30385i	−0.102415	+	0.177387i
$895$		0			0
$896$	1.26795			0.0423592
$897$	−24.5885	−	16.3923i	−0.820985	−	0.547323i
$898$			26.5359i			0.885514i
$899$	24.5885	+	14.1962i	0.820071	+	0.473468i
$900$		0			0
$901$	7.79423	+	13.5000i	0.259663	+	0.449750i
$902$	−8.19615			−0.272902
$903$	2.66025	+	4.60770i	0.0885277	+	0.153334i
$904$	0.696152	−	0.401924i	0.0231537	−	0.0133678i
$905$		0			0
$906$	−5.36603	−	9.29423i	−0.178274	−	0.308780i
$907$	18.3397	+	10.5885i	0.608961	+	0.351584i	0.772559	−	0.634943i	$-0.218977\pi$
$907$	18.3397	+	10.5885i	0.608961	+	0.351584i	−0.163598	+	0.986527i	$0.552310\pi$
$908$	10.0981	−	17.4904i	0.335116	−	0.580439i
$909$	19.3923			0.643202
$910$		0			0
$911$	−25.1769			−0.834148			−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769			−0.834148			−0.417074	+	0.908872i	$0.636944\pi$
$912$	2.36603	−	4.09808i	0.0783469	−	0.135701i
$913$	6.21539	+	3.58846i	0.205699	+	0.118761i
$914$	−15.9904	−	27.6962i	−0.528915	−	0.916107i
$915$		0			0
$916$	6.80385	−	3.92820i	0.224805	−	0.129791i
$917$	−2.78461	−	4.82309i	−0.0919559	−	0.159272i
$918$	5.19615			0.171499
$919$	5.80385	+	10.0526i	0.191451	+	0.331603i	0.945731	−	0.324949i	$-0.105347\pi$
$919$	5.80385	+	10.0526i	0.191451	+	0.331603i	−0.754280	+	0.656553i	$0.772014\pi$
$920$		0			0
$921$	6.29423	+	3.63397i	0.207402	+	0.119744i
$922$			31.9808i			1.05323i
$923$	4.39230	−	6.58846i	0.144574	−	0.216862i
$924$	1.60770			0.0528893
$925$		0			0
$926$	−7.90192	+	13.6865i	−0.259673	+	0.449767i
$927$	−5.36603	+	3.09808i	−0.176243	+	0.101754i
$928$	−3.00000			−0.0984798
$929$	−47.9711	+	27.6962i	−1.57388	+	0.908681i	−0.578196	+	0.815898i	$0.696243\pi$
$929$	−47.9711	+	27.6962i	−1.57388	+	0.908681i	−0.995686	+	0.0927833i	$0.970424\pi$
$930$		0			0
$931$		−	25.5167i		−	0.836275i
$932$	−15.5885	+	9.00000i	−0.510617	+	0.294805i
$933$	−7.09808	−	4.09808i	−0.232381	−	0.134165i
$934$	−4.68653	−	2.70577i	−0.153348	−	0.0885355i
$935$		0			0
$936$	−3.00000	−	2.00000i	−0.0980581	−	0.0653720i
$937$		−	15.3923i		−	0.502845i	−0.967877	−	0.251422i	$-0.919102\pi$
$937$		−	15.3923i		−	0.502845i	0.967877	−	0.251422i	$-0.0808983\pi$
$938$	−4.60770	+	7.98076i	−0.150447	+	0.260581i
$939$	1.80385	−	3.12436i	0.0588663	−	0.101959i
$940$		0			0
$941$			38.7846i			1.26434i	0.774829	+	0.632171i	$0.217836\pi$
$941$			38.7846i			1.26434i	−0.774829	+	0.632171i	$0.782164\pi$
$942$	−3.59808	−	6.23205i	−0.117232	−	0.203051i
$943$	26.4904	+	45.8827i	0.862645	+	1.49415i
$944$			13.8564i			0.450988i
$945$		0			0
$946$	2.66025	−	4.60770i	0.0864923	−	0.149809i
$947$	−14.5359	+	25.1769i	−0.472353	+	0.818140i	−0.999499	−	0.0316348i	$-0.989929\pi$
$947$	−14.5359	+	25.1769i	−0.472353	+	0.818140i	0.527146	+	0.849775i	$0.323262\pi$
$948$		−	8.39230i		−	0.272569i
$949$	39.1865	−	19.3756i	1.27205	−	0.628960i
$950$		0			0
$951$	15.6962	+	9.06218i	0.508983	+	0.293861i
$952$	5.70577	+	3.29423i	0.184925	+	0.106767i
$953$	−20.7846	+	12.0000i	−0.673280	+	0.388718i	−0.797318	−	0.603559i	$-0.793749\pi$
$953$	−20.7846	+	12.0000i	−0.673280	+	0.388718i	0.124039	+	0.992277i	$0.460415\pi$
$954$		−	3.00000i		−	0.0971286i
$955$		0			0
$956$	5.70577	−	3.29423i	0.184538	−	0.106543i
$957$	−3.80385			−0.122961
$958$	−0.588457	+	0.339746i	−0.0190122	+	0.0109767i
$959$	5.70577	−	9.88269i	0.184249	−	0.319129i
$960$		0			0
$961$	−58.5692			−1.88933
$962$	−9.00000	−	6.00000i	−0.290172	−	0.193448i
$963$			2.19615i			0.0707700i
$964$	−9.69615	−	5.59808i	−0.312292	−	0.180302i
$965$		0			0
$966$	−5.19615	−	9.00000i	−0.167183	−	0.289570i
$967$	−39.1244			−1.25815			−0.629077	−	0.777343i	$-0.716567\pi$
$967$	−39.1244			−1.25815			−0.629077	+	0.777343i	$0.716567\pi$
$968$	4.69615	+	8.13397i	0.150940	+	0.261436i
$969$	21.2942	−	12.2942i	0.684069	−	0.394948i
$970$		0			0
$971$	−24.5885	−	42.5885i	−0.789081	−	1.36673i	−0.926530	−	0.376220i	$-0.877224\pi$
$971$	−24.5885	−	42.5885i	−0.789081	−	1.36673i	0.137449	−	0.990509i	$-0.456110\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	2.53590	−	4.39230i	0.0812972	−	0.140811i
$974$	15.1244			0.484616
$975$		0			0
$976$	15.1962			0.486417
$977$	−5.42820	+	9.40192i	−0.173664	+	0.300794i	−0.939698	−	0.342005i	$-0.888894\pi$
$977$	−5.42820	+	9.40192i	−0.173664	+	0.300794i	0.766034	+	0.642800i	$0.222227\pi$
$978$	2.19615	+	1.26795i	0.0702252	+	0.0405445i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	3.80385	−	2.19615i	0.121448	−	0.0701178i
$982$	15.2942	+	26.4904i	0.488058	+	0.845342i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$	3.23205	+	5.59808i	0.103034	+	0.178460i
$985$		0			0
$986$	−13.5000	−	7.79423i	−0.429928	−	0.248219i
$987$		−	6.00000i		−	0.190982i
$988$	−17.0263	−	1.09808i	−0.541678	−	0.0349345i
$989$	−34.3923			−1.09361
$990$		0			0
$991$	21.6865	−	37.5622i	0.688895	−	1.19320i	−0.283300	−	0.959031i	$-0.591429\pi$
$991$	21.6865	−	37.5622i	0.688895	−	1.19320i	0.972196	−	0.234171i	$-0.0752374\pi$
$992$	8.19615	−	4.73205i	0.260228	−	0.150243i
$993$	12.0000			0.380808
$994$	2.41154	−	1.39230i	0.0764895	−	0.0441612i
$995$		0			0
$996$		−	5.66025i		−	0.179352i
$997$	2.42820	−	1.40192i	0.0769020	−	0.0443994i	−0.461056	−	0.887371i	$-0.652529\pi$
$997$	2.42820	−	1.40192i	0.0769020	−	0.0443994i	0.537958	+	0.842972i	$0.319196\pi$
$998$		0			0
$999$	−2.59808	−	1.50000i	−0.0821995	−	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.h.199.1		4
5.2	odd	4		1950.2.bc.c.901.2		4
5.3	odd	4		78.2.i.b.43.1	✓	4
5.4	even	2		1950.2.y.a.199.2		4
13.10	even	6		1950.2.y.a.49.2		4
15.8	even	4		234.2.l.a.199.2		4
20.3	even	4		624.2.bv.d.433.1		4
60.23	odd	4		1872.2.by.k.433.1		4
65.3	odd	12		1014.2.i.f.361.2		4
65.8	even	4		1014.2.e.j.529.2		4
65.18	even	4		1014.2.e.h.529.1		4
65.23	odd	12		78.2.i.b.49.1	yes	4
65.28	even	12		1014.2.e.h.991.1		4
65.33	even	12		1014.2.a.h.1.2		2
65.38	odd	4		1014.2.i.f.823.2		4
65.43	odd	12		1014.2.b.d.337.2		4
65.48	odd	12		1014.2.b.d.337.3		4
65.49	even	6	inner	1950.2.y.h.49.1		4
65.58	even	12		1014.2.a.j.1.1		2
65.62	odd	12		1950.2.bc.c.751.2		4
65.63	even	12		1014.2.e.j.991.2		4
195.23	even	12		234.2.l.a.127.2		4
195.98	odd	12		3042.2.a.v.1.1		2
195.113	even	12		3042.2.b.l.1351.2		4
195.173	even	12		3042.2.b.l.1351.3		4
195.188	odd	12		3042.2.a.s.1.2		2
260.23	even	12		624.2.bv.d.49.1		4
260.123	odd	12		8112.2.a.bx.1.1		2
260.163	odd	12		8112.2.a.bq.1.2		2
780.23	odd	12		1872.2.by.k.1297.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.1	✓	4	5.3	odd	4
78.2.i.b.49.1	yes	4	65.23	odd	12
234.2.l.a.127.2		4	195.23	even	12
234.2.l.a.199.2		4	15.8	even	4
624.2.bv.d.49.1		4	260.23	even	12
624.2.bv.d.433.1		4	20.3	even	4
1014.2.a.h.1.2		2	65.33	even	12
1014.2.a.j.1.1		2	65.58	even	12
1014.2.b.d.337.2		4	65.43	odd	12
1014.2.b.d.337.3		4	65.48	odd	12
1014.2.e.h.529.1		4	65.18	even	4
1014.2.e.h.991.1		4	65.28	even	12
1014.2.e.j.529.2		4	65.8	even	4
1014.2.e.j.991.2		4	65.63	even	12
1014.2.i.f.361.2		4	65.3	odd	12
1014.2.i.f.823.2		4	65.38	odd	4
1872.2.by.k.433.1		4	60.23	odd	4
1872.2.by.k.1297.1		4	780.23	odd	12
1950.2.y.a.49.2		4	13.10	even	6
1950.2.y.a.199.2		4	5.4	even	2
1950.2.y.h.49.1		4	65.49	even	6	inner
1950.2.y.h.199.1		4	1.1	even	1	trivial
1950.2.bc.c.751.2		4	65.62	odd	12
1950.2.bc.c.901.2		4	5.2	odd	4
3042.2.a.s.1.2		2	195.188	odd	12
3042.2.a.v.1.1		2	195.98	odd	12
3042.2.b.l.1351.2		4	195.113	even	12
3042.2.b.l.1351.3		4	195.173	even	12
8112.2.a.bq.1.2		2	260.163	odd	12
8112.2.a.bx.1.1		2	260.123	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(0.633975 + 1.09808i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.09808 - 0.633975i) q^{11} +1.00000i q^{12} +(3.23205 - 1.59808i) q^{13} +1.26795 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-4.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(4.09808 - 2.36603i) q^{19} -1.26795i q^{21} +(-1.09808 + 0.633975i) q^{22} +(7.09808 + 4.09808i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.232051 - 3.59808i) q^{26} -1.00000i q^{27} +(0.633975 - 1.09808i) q^{28} +(-1.50000 + 2.59808i) q^{29} -9.46410i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.633975 + 1.09808i) q^{33} +5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(1.50000 - 2.59808i) q^{37} -4.73205i q^{38} +(-3.59808 - 0.232051i) q^{39} +(5.59808 + 3.23205i) q^{41} +(-1.09808 - 0.633975i) q^{42} +(-3.63397 + 2.09808i) q^{43} +1.26795i q^{44} +(7.09808 - 4.09808i) q^{46} +4.73205 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.69615 - 4.66987i) q^{49} +5.19615 q^{51} +(-3.00000 - 2.00000i) q^{52} -3.00000i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.633975 - 1.09808i) q^{56} -4.73205 q^{57} +(1.50000 + 2.59808i) q^{58} +(12.0000 - 6.92820i) q^{59} +(-7.59808 - 13.1603i) q^{61} +(-8.19615 - 4.73205i) q^{62} +(-0.633975 + 1.09808i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-3.63397 + 6.29423i) q^{67} +(4.50000 + 2.59808i) q^{68} +(-4.09808 - 7.09808i) q^{69} +(1.90192 - 1.09808i) q^{71} +(-0.500000 - 0.866025i) q^{72} +12.1244 q^{73} +(-1.50000 - 2.59808i) q^{74} +(-4.09808 - 2.36603i) q^{76} -1.60770i q^{77} +(-2.00000 + 3.00000i) q^{78} -8.39230 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.59808 - 3.23205i) q^{82} -5.66025 q^{83} +(-1.09808 + 0.633975i) q^{84} +4.19615i q^{86} +(2.59808 - 1.50000i) q^{87} +(1.09808 + 0.633975i) q^{88} +(8.19615 + 4.73205i) q^{89} +(3.80385 + 2.53590i) q^{91} -8.19615i q^{92} +(-4.73205 + 8.19615i) q^{93} +(2.36603 - 4.09808i) q^{94} -1.00000i q^{96} +(-3.00000 - 5.19615i) q^{97} +(-2.69615 - 4.66987i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{7} - 4 q^{8} + 2 q^{9} + 6 q^{11} + 6 q^{13} + 12 q^{14} - 2 q^{16} - 18 q^{17} + 4 q^{18} + 6 q^{19} + 6 q^{22} + 18 q^{23} - 6 q^{26} + 6 q^{28} - 6 q^{29} + 2 q^{32} + 6 q^{33}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^7 - 4 * q^8 + 2 * q^9 + 6 * q^11 + 6 * q^13 + 12 * q^14 - 2 * q^16 - 18 * q^17 + 4 * q^18 + 6 * q^19 + 6 * q^22 + 18 * q^23 - 6 * q^26 + 6 * q^28 - 6 * q^29 + 2 * q^32 + 6 * q^33 + 2 * q^36 + 6 * q^37 - 4 * q^39 + 12 * q^41 + 6 * q^42 - 18 * q^43 + 18 * q^46 + 12 * q^47 - 10 * q^49 - 12 * q^52 - 6 * q^56 - 12 * q^57 + 6 * q^58 + 48 * q^59 - 20 * q^61 - 12 * q^62 - 6 * q^63 + 4 * q^64 + 12 * q^66 - 18 * q^67 + 18 * q^68 - 6 * q^69 + 18 * q^71 - 2 * q^72 - 6 * q^74 - 6 * q^76 - 8 * q^78 + 8 * q^79 - 2 * q^81 + 12 * q^82 + 12 * q^83 + 6 * q^84 - 6 * q^88 + 12 * q^89 + 36 * q^91 - 12 * q^93 + 6 * q^94 - 12 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more