LMFDB - Embedded newform 950.2.j.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
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 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} -3.00000 q^{11} -1.00000i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} -2.00000i q^{18} +(-3.50000 - 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-2.59808 - 1.50000i) q^{22} +(6.92820 - 4.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} -6.00000 q^{26} +5.00000i q^{27} +(-1.73205 + 1.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} -8.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} +8.00000i q^{37} +(-1.73205 - 4.00000i) q^{38} +6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.73205 - 1.00000i) q^{42} +(-1.50000 - 2.59808i) q^{44} +8.00000 q^{46} +(-5.19615 + 3.00000i) q^{47} +(0.866025 - 0.500000i) q^{48} +3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(-5.19615 - 3.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(1.73205 + 4.00000i) q^{57} -2.00000i q^{58} +(2.50000 - 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(-6.92820 - 4.00000i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-4.33013 + 2.50000i) q^{67} -2.00000i q^{68} -8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.73205 - 1.00000i) q^{72} +(-7.79423 - 4.50000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} -6.00000i q^{77} +(5.19615 + 3.00000i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} +11.0000i q^{83} +2.00000 q^{84} +2.00000i q^{87} -3.00000i q^{88} +(7.00000 + 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(6.92820 + 4.00000i) q^{92} +(6.92820 + 4.00000i) q^{93} -6.00000 q^{94} +1.00000 q^{96} +(12.9904 + 7.50000i) q^{97} +(2.59808 + 1.50000i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9	$ 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9} - 12 q^{11} - 4 q^{14} - 2 q^{16} - 14 q^{19} + 4 q^{21} + 2 q^{24} - 24 q^{26} - 4 q^{29} - 32 q^{31} - 4 q^{34} + 4 q^{36} + 24 q^{39} - 10 q^{41} - 6 q^{44} + 32 q^{46} + 12 q^{49} + 4 q^{51} - 10 q^{54} - 8 q^{56} + 10 q^{59} - 28 q^{61} - 4 q^{64} + 6 q^{66} - 32 q^{69} + 12 q^{71} - 16 q^{74} + 2 q^{76} + 16 q^{79} - 2 q^{81} + 8 q^{84} + 28 q^{89} - 24 q^{91} - 24 q^{94} + 4 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9 - 12 * q^11 - 4 * q^14 - 2 * q^16 - 14 * q^19 + 4 * q^21 + 2 * q^24 - 24 * q^26 - 4 * q^29 - 32 * q^31 - 4 * q^34 + 4 * q^36 + 24 * q^39 - 10 * q^41 - 6 * q^44 + 32 * q^46 + 12 * q^49 + 4 * q^51 - 10 * q^54 - 8 * q^56 + 10 * q^59 - 28 * q^61 - 4 * q^64 + 6 * q^66 - 32 * q^69 + 12 * q^71 - 16 * q^74 + 2 * q^76 + 16 * q^79 - 2 * q^81 + 8 * q^84 + 28 * q^89 - 24 * q^91 - 24 * q^94 + 4 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$			1.00000i			0.353553i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−5.19615	+	3.00000i	−1.44115	+	0.832050i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		−	2.00000i		−	0.471405i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$		0			0
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	6.92820	−	4.00000i	1.44463	−	0.834058i	0.446476	−	0.894795i	$-0.352679\pi$
$23$	6.92820	−	4.00000i	1.44463	−	0.834058i	0.998154	+	0.0607377i	$0.0193453\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−6.00000			−1.17670
$27$			5.00000i			0.962250i
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.59808	+	1.50000i	0.452267	+	0.261116i
$34$	−1.00000	−	1.73205i	−0.171499	−	0.297044i
$35$		0			0
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	−1.73205	−	4.00000i	−0.280976	−	0.648886i
$39$	6.00000			0.960769
$40$		0			0
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	1.73205	−	1.00000i	0.267261	−	0.154303i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$	8.00000			1.17954
$47$	−5.19615	+	3.00000i	−0.757937	+	0.437595i	−0.828554	−	0.559908i	$-0.810836\pi$
$47$	−5.19615	+	3.00000i	−0.757937	+	0.437595i	0.0706177	+	0.997503i	$0.477503\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	3.00000			0.428571
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	−5.19615	−	3.00000i	−0.720577	−	0.416025i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	1.73205	+	4.00000i	0.229416	+	0.529813i
$58$		−	2.00000i		−	0.262613i
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$		0			0
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$	−6.92820	−	4.00000i	−0.879883	−	0.508001i
$63$	3.46410	−	2.00000i	0.436436	−	0.251976i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	−0.740613	−	0.671932i	$-0.765465\pi$
$67$	−4.33013	+	2.50000i	−0.529009	+	0.305424i	0.211604	+	0.977356i	$0.432131\pi$
$68$		−	2.00000i		−	0.242536i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	1.73205	−	1.00000i	0.204124	−	0.117851i
$73$	−7.79423	−	4.50000i	−0.912245	−	0.526685i	−0.0310925	−	0.999517i	$-0.509899\pi$
$73$	−7.79423	−	4.50000i	−0.912245	−	0.526685i	−0.881153	+	0.472831i	$0.843232\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$		−	6.00000i		−	0.683763i
$78$	5.19615	+	3.00000i	0.588348	+	0.339683i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.33013	+	2.50000i	−0.478183	+	0.276079i
$83$			11.0000i			1.20741i	0.797209	+	0.603703i	$0.206309\pi$
$83$			11.0000i			1.20741i	−0.797209	+	0.603703i	$0.793691\pi$
$84$	2.00000			0.218218
$85$		0			0
$86$		0			0
$87$			2.00000i			0.214423i
$88$		−	3.00000i		−	0.319801i
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	0.951584	+	0.307389i	$0.0994552\pi$
$89$	7.00000	+	12.1244i	0.741999	+	1.28518i	−0.209585	+	0.977790i	$0.567211\pi$
$90$		0			0
$91$	−6.00000	−	10.3923i	−0.628971	−	1.08941i
$92$	6.92820	+	4.00000i	0.722315	+	0.417029i
$93$	6.92820	+	4.00000i	0.718421	+	0.414781i
$94$	−6.00000			−0.618853
$95$		0			0
$96$	1.00000			0.102062
$97$	12.9904	+	7.50000i	1.31897	+	0.761510i	0.983563	−	0.180563i	$-0.0577919\pi$
$97$	12.9904	+	7.50000i	1.31897	+	0.761510i	0.335410	+	0.942072i	$0.391125\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$			2.00000i			0.198030i
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	−6.00000			−0.582772
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	−4.33013	+	2.50000i	−0.416667	+	0.240563i
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	−0.991508	−	0.130046i	$-0.958487\pi$
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	0.608377	+	0.793648i	$0.291821\pi$
$110$		0			0
$111$	4.00000	−	6.92820i	0.379663	−	0.657596i
$112$	−1.73205	−	1.00000i	−0.163663	−	0.0944911i
$113$			13.0000i			1.22294i	0.791269	+	0.611469i	$0.209421\pi$
$113$			13.0000i			1.22294i	−0.791269	+	0.611469i	$0.790579\pi$
$114$	−0.500000	+	4.33013i	−0.0468293	+	0.405554i
$115$		0			0
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$	4.33013	−	2.50000i	0.398621	−	0.230144i
$119$	2.00000	−	3.46410i	0.183340	−	0.317554i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		−	14.0000i		−	1.26750i
$123$	4.33013	−	2.50000i	0.390434	−	0.225417i
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$		0			0
$126$	4.00000			0.356348
$127$	5.19615	−	3.00000i	0.461084	−	0.266207i	−0.251416	−	0.967879i	$-0.580896\pi$
$127$	5.19615	−	3.00000i	0.461084	−	0.266207i	0.712500	+	0.701672i	$0.247563\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$			3.00000i			0.261116i
$133$	5.19615	−	7.00000i	0.450564	−	0.606977i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−2.59808	+	1.50000i	−0.221969	+	0.128154i	−0.606861	−	0.794808i	$-0.707572\pi$
$137$	−2.59808	+	1.50000i	−0.221969	+	0.128154i	0.384893	+	0.922961i	$0.374238\pi$
$138$	−6.92820	−	4.00000i	−0.589768	−	0.340503i
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$	15.5885	−	9.00000i	1.30357	−	0.752618i
$144$	2.00000			0.166667
$145$		0			0
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$	−2.59808	−	1.50000i	−0.214286	−	0.123718i
$148$	−6.92820	+	4.00000i	−0.569495	+	0.328798i
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	2.59808	−	3.50000i	0.210732	−	0.283887i
$153$			4.00000i			0.323381i
$154$	3.00000	−	5.19615i	0.241747	−	0.418718i
$155$		0			0
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	6.92820	−	4.00000i	0.551178	−	0.318223i
$159$	6.00000			0.475831
$160$		0			0
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$		−	3.00000i		−	0.234978i	−0.993074	−	0.117489i	$-0.962515\pi$
$163$		−	3.00000i		−	0.234978i	0.993074	−	0.117489i	$-0.0374845\pi$
$164$	−5.00000			−0.390434
$165$		0			0
$166$	−5.50000	+	9.52628i	−0.426883	+	0.739383i
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	−0.207385	−	0.978259i	$-0.566495\pi$
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	0.743505	+	0.668730i	$0.233162\pi$
$168$	1.73205	+	1.00000i	0.133631	+	0.0771517i
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$		0			0
$171$	−1.00000	+	8.66025i	−0.0764719	+	0.662266i
$172$		0			0
$173$	−15.5885	−	9.00000i	−1.18517	−	0.684257i	−0.227964	−	0.973670i	$-0.573207\pi$
$173$	−15.5885	−	9.00000i	−1.18517	−	0.684257i	−0.957205	+	0.289412i	$0.906540\pi$
$174$	−1.00000	+	1.73205i	−0.0758098	+	0.131306i
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−4.33013	+	2.50000i	−0.325472	+	0.187912i
$178$			14.0000i			1.04934i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$		0			0
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$		−	12.0000i		−	0.889499i
$183$			14.0000i			1.03491i
$184$	4.00000	+	6.92820i	0.294884	+	0.510754i
$185$		0			0
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	5.19615	+	3.00000i	0.379980	+	0.219382i
$188$	−5.19615	−	3.00000i	−0.378968	−	0.218797i
$189$	−10.0000			−0.727393
$190$		0			0
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	8.66025	+	5.00000i	0.623379	+	0.359908i	0.778183	−	0.628037i	$-0.216141\pi$
$193$	8.66025	+	5.00000i	0.623379	+	0.359908i	−0.154805	+	0.987945i	$0.549475\pi$
$194$	7.50000	+	12.9904i	0.538469	+	0.932655i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$			6.00000i			0.426401i
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	−0.932075	−	0.362267i	$-0.882003\pi$
$199$	−11.0000	−	19.0526i	−0.779769	−	1.35060i	0.152305	−	0.988334i	$-0.451330\pi$
$200$		0			0
$201$	5.00000			0.352673
$202$			10.0000i			0.703598i
$203$	3.46410	−	2.00000i	0.243132	−	0.140372i
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$		0			0
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−13.8564	−	8.00000i	−0.963087	−	0.556038i
$208$		−	6.00000i		−	0.416025i
$209$	10.5000	+	7.79423i	0.726300	+	0.539138i
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$	−5.19615	+	3.00000i	−0.356034	+	0.205557i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$	−5.00000			−0.340207
$217$		−	16.0000i		−	1.08615i
$218$	−6.92820	+	4.00000i	−0.469237	+	0.270914i
$219$	4.50000	+	7.79423i	0.304082	+	0.526685i
$220$		0			0
$221$	12.0000			0.807207
$222$	6.92820	−	4.00000i	0.464991	−	0.268462i
$223$	−13.8564	−	8.00000i	−0.927894	−	0.535720i	−0.0417488	−	0.999128i	$-0.513293\pi$
$223$	−13.8564	−	8.00000i	−0.927894	−	0.535720i	−0.886145	+	0.463409i	$0.846626\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$		0			0
$226$	−6.50000	+	11.2583i	−0.432374	+	0.748893i
$227$		−	7.00000i		−	0.464606i	−0.972643	−	0.232303i	$-0.925374\pi$
$227$		−	7.00000i		−	0.464606i	0.972643	−	0.232303i	$-0.0746261\pi$
$228$	−2.59808	+	3.50000i	−0.172062	+	0.231793i
$229$	24.0000			1.58596			0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000			1.58596			0.792982	+	0.609245i	$0.208527\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	1.73205	−	1.00000i	0.113715	−	0.0656532i
$233$	9.52628	+	5.50000i	0.624087	+	0.360317i	0.778459	−	0.627696i	$-0.216002\pi$
$233$	9.52628	+	5.50000i	0.624087	+	0.360317i	−0.154371	+	0.988013i	$0.549335\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$		0			0
$236$	5.00000			0.325472
$237$	−6.92820	+	4.00000i	−0.450035	+	0.259828i
$238$	3.46410	−	2.00000i	0.224544	−	0.129641i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	−1.73205	−	1.00000i	−0.111340	−	0.0642824i
$243$	13.8564	−	8.00000i	0.888889	−	0.513200i
$244$	7.00000	−	12.1244i	0.448129	−	0.776182i
$245$		0			0
$246$	5.00000			0.318788
$247$	25.9808	+	3.00000i	1.65312	+	0.190885i
$248$		−	8.00000i		−	0.508001i
$249$	5.50000	−	9.52628i	0.348548	−	0.603703i
$250$		0			0
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	0.999088	+	0.0426905i	$0.0135929\pi$
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	−0.462573	+	0.886581i	$0.653074\pi$
$252$	3.46410	+	2.00000i	0.218218	+	0.125988i
$253$	−20.7846	+	12.0000i	−1.30672	+	0.754434i
$254$	6.00000			0.376473
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	−0.416775	−	0.909010i	$-0.636840\pi$
$257$	2.59808	−	1.50000i	0.162064	−	0.0935674i	0.578838	+	0.815442i	$0.303506\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−6.06218	+	3.50000i	−0.374523	+	0.216231i
$263$	−22.5167	−	13.0000i	−1.38844	−	0.801614i	−0.395298	−	0.918553i	$-0.629359\pi$
$263$	−22.5167	−	13.0000i	−1.38844	−	0.801614i	−0.993139	+	0.116939i	$0.962692\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	8.00000	−	3.46410i	0.490511	−	0.212398i
$267$		−	14.0000i		−	0.856786i
$268$	−4.33013	−	2.50000i	−0.264505	−	0.152712i
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	0.0243472	+	0.999704i	$0.492249\pi$
$269$	−14.0000	+	24.2487i	−0.853595	+	1.47847i	−0.877942	+	0.478766i	$0.841084\pi$
$270$		0			0
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	−0.310204	−	0.950670i	$-0.600397\pi$
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	0.978406	−	0.206691i	$-0.0662693\pi$
$272$	1.73205	−	1.00000i	0.105021	−	0.0606339i
$273$			12.0000i			0.726273i
$274$	−3.00000			−0.181237
$275$		0			0
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$		−	14.0000i		−	0.841178i	−0.907251	−	0.420589i	$-0.861823\pi$
$277$		−	14.0000i		−	0.841178i	0.907251	−	0.420589i	$-0.138177\pi$
$278$			9.00000i			0.539784i
$279$	8.00000	+	13.8564i	0.478947	+	0.829561i
$280$		0			0
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$	5.19615	+	3.00000i	0.309426	+	0.178647i
$283$	−25.1147	−	14.5000i	−1.49292	−	0.861936i	−0.492949	−	0.870058i	$-0.664081\pi$
$283$	−25.1147	−	14.5000i	−1.49292	−	0.861936i	−0.999967	+	0.00812260i	$0.997414\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	18.0000			1.06436
$287$	−8.66025	−	5.00000i	−0.511199	−	0.295141i
$288$	1.73205	+	1.00000i	0.102062	+	0.0589256i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$		−	9.00000i		−	0.526685i
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$	−1.50000	−	2.59808i	−0.0874818	−	0.151523i
$295$		0			0
$296$	−8.00000			−0.464991
$297$		−	15.0000i		−	0.870388i
$298$	3.46410	−	2.00000i	0.200670	−	0.115857i
$299$	−24.0000	+	41.5692i	−1.38796	+	2.40401i
$300$		0			0
$301$		0			0
$302$	10.3923	+	6.00000i	0.598010	+	0.345261i
$303$		−	10.0000i		−	0.574485i
$304$	4.00000	−	1.73205i	0.229416	−	0.0993399i
$305$		0			0
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	4.33013	+	2.50000i	0.247133	+	0.142683i	0.618451	−	0.785823i	$-0.287761\pi$
$307$	4.33013	+	2.50000i	0.247133	+	0.142683i	−0.371318	+	0.928506i	$0.621094\pi$
$308$	5.19615	−	3.00000i	0.296078	−	0.170941i
$309$	−3.00000	+	5.19615i	−0.170664	+	0.295599i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$			6.00000i			0.339683i
$313$	−11.2583	+	6.50000i	−0.636358	+	0.367402i	−0.783210	−	0.621757i	$-0.786419\pi$
$313$	−11.2583	+	6.50000i	−0.636358	+	0.367402i	0.146852	+	0.989158i	$0.453086\pi$
$314$		0			0
$315$		0			0
$316$	8.00000			0.450035
$317$	−25.9808	+	15.0000i	−1.45922	+	0.842484i	−0.998973	−	0.0453045i	$-0.985574\pi$
$317$	−25.9808	+	15.0000i	−1.45922	+	0.842484i	−0.460252	+	0.887788i	$0.652241\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$		0			0
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$			16.0000i			0.891645i
$323$	3.46410	+	8.00000i	0.192748	+	0.445132i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	1.50000	−	2.59808i	0.0830773	−	0.143894i
$327$	6.92820	−	4.00000i	0.383131	−	0.221201i
$328$	−4.33013	−	2.50000i	−0.239091	−	0.138039i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	−9.52628	+	5.50000i	−0.522823	+	0.301852i
$333$	13.8564	−	8.00000i	0.759326	−	0.438397i
$334$	8.00000			0.437741
$335$		0			0
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	−16.4545	−	9.50000i	−0.896333	−	0.517498i	−0.0203242	−	0.999793i	$-0.506470\pi$
$337$	−16.4545	−	9.50000i	−0.896333	−	0.517498i	−0.876009	+	0.482295i	$0.839803\pi$
$338$	19.9186	−	11.5000i	1.08343	−	0.625518i
$339$	6.50000	−	11.2583i	0.353032	−	0.611469i
$340$		0			0
$341$	24.0000			1.29967
$342$	−5.19615	+	7.00000i	−0.280976	+	0.378517i
$343$			20.0000i			1.07990i
$344$		0			0
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.972147	−	0.234372i	$-0.0753034\pi$
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.283101	+	0.959090i	$0.408637\pi$
$348$	−1.73205	+	1.00000i	−0.0928477	+	0.0536056i
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$		0			0
$351$	−15.0000	−	25.9808i	−0.800641	−	1.38675i
$352$	2.59808	−	1.50000i	0.138478	−	0.0799503i
$353$			21.0000i			1.11772i	0.829263	+	0.558859i	$0.188761\pi$
$353$			21.0000i			1.11772i	−0.829263	+	0.558859i	$0.811239\pi$
$354$	−5.00000			−0.265747
$355$		0			0
$356$	−7.00000	+	12.1244i	−0.370999	+	0.642590i
$357$	−3.46410	+	2.00000i	−0.183340	+	0.105851i
$358$	−2.59808	−	1.50000i	−0.137313	−	0.0792775i
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$			16.0000i			0.840941i
$363$	1.73205	+	1.00000i	0.0909091	+	0.0524864i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$		0			0
$366$	−7.00000	+	12.1244i	−0.365896	+	0.633750i
$367$	−24.2487	+	14.0000i	−1.26577	+	0.730794i	−0.974185	−	0.225750i	$-0.927517\pi$
$367$	−24.2487	+	14.0000i	−1.26577	+	0.730794i	−0.291587	+	0.956544i	$0.594183\pi$
$368$			8.00000i			0.417029i
$369$	10.0000			0.520579
$370$		0			0
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$			8.00000i			0.414781i
$373$			24.0000i			1.24267i	0.783544	+	0.621336i	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	10.3923	+	6.00000i	0.535231	+	0.309016i
$378$	−8.66025	−	5.00000i	−0.445435	−	0.257172i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$	−3.46410	−	2.00000i	−0.177239	−	0.102329i
$383$	5.19615	+	3.00000i	0.265511	+	0.153293i	0.626846	−	0.779143i	$-0.284346\pi$
$383$	5.19615	+	3.00000i	0.265511	+	0.153293i	−0.361335	+	0.932436i	$0.617679\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	5.00000	+	8.66025i	0.254493	+	0.440795i
$387$		0			0
$388$			15.0000i			0.761510i
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$			3.00000i			0.151523i
$393$	6.06218	−	3.50000i	0.305796	−	0.176552i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−13.8564	−	8.00000i	−0.695433	−	0.401508i	0.110211	−	0.993908i	$-0.464847\pi$
$397$	−13.8564	−	8.00000i	−0.695433	−	0.401508i	−0.805644	+	0.592400i	$0.798181\pi$
$398$		−	22.0000i		−	1.10276i
$399$	−8.00000	+	3.46410i	−0.400501	+	0.173422i
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	4.33013	+	2.50000i	0.215967	+	0.124689i
$403$	41.5692	−	24.0000i	2.07071	−	1.19553i
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$		0			0
$406$	4.00000			0.198517
$407$		−	24.0000i		−	1.18964i
$408$	−1.73205	+	1.00000i	−0.0857493	+	0.0495074i
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$		0			0
$411$	3.00000			0.147979
$412$	5.19615	−	3.00000i	0.255996	−	0.147799i
$413$	8.66025	+	5.00000i	0.426143	+	0.246034i
$414$	−8.00000	−	13.8564i	−0.393179	−	0.681005i
$415$		0			0
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$		−	9.00000i		−	0.440732i
$418$	5.19615	+	12.0000i	0.254152	+	0.586939i
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	3.46410	−	2.00000i	0.168630	−	0.0973585i
$423$	10.3923	+	6.00000i	0.505291	+	0.291730i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$		0			0
$426$	−6.00000			−0.290701
$427$	24.2487	−	14.0000i	1.17348	−	0.677507i
$428$	10.3923	−	6.00000i	0.502331	−	0.290021i
$429$	−18.0000			−0.869048
$430$		0			0
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	−4.33013	−	2.50000i	−0.208333	−	0.120281i
$433$	−25.9808	+	15.0000i	−1.24856	+	0.720854i	−0.970821	−	0.239804i	$-0.922917\pi$
$433$	−25.9808	+	15.0000i	−1.24856	+	0.720854i	−0.277734	+	0.960658i	$0.589584\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$		0			0
$436$	−8.00000			−0.383131
$437$	−34.6410	−	4.00000i	−1.65710	−	0.191346i
$438$			9.00000i			0.430037i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$442$	10.3923	+	6.00000i	0.494312	+	0.285391i
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$	8.00000			0.379663
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	−3.46410	+	2.00000i	−0.163846	+	0.0945968i
$448$		−	2.00000i		−	0.0944911i
$449$	−29.0000			−1.36859			−0.684297	−	0.729203i	$-0.739891\pi$
$449$	−29.0000			−1.36859			−0.684297	+	0.729203i	$0.739891\pi$
$450$		0			0
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$	−11.2583	+	6.50000i	−0.529547	+	0.305734i
$453$	−10.3923	−	6.00000i	−0.488273	−	0.281905i
$454$	3.50000	−	6.06218i	0.164263	−	0.284512i
$455$		0			0
$456$	−4.00000	+	1.73205i	−0.187317	+	0.0811107i
$457$			13.0000i			0.608114i	0.952654	+	0.304057i	$0.0983414\pi$
$457$			13.0000i			0.608114i	−0.952654	+	0.304057i	$0.901659\pi$
$458$	20.7846	+	12.0000i	0.971201	+	0.560723i
$459$	5.00000	−	8.66025i	0.233380	−	0.404226i
$460$		0			0
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$	−5.19615	+	3.00000i	−0.241747	+	0.139573i
$463$		−	34.0000i		−	1.58011i	−0.613033	−	0.790057i	$-0.710051\pi$
$463$		−	34.0000i		−	1.58011i	0.613033	−	0.790057i	$-0.289949\pi$
$464$	2.00000			0.0928477
$465$		0			0
$466$	5.50000	+	9.52628i	0.254783	+	0.441296i
$467$			7.00000i			0.323921i	0.986797	+	0.161961i	$0.0517818\pi$
$467$			7.00000i			0.323921i	−0.986797	+	0.161961i	$0.948218\pi$
$468$			12.0000i			0.554700i
$469$	−5.00000	−	8.66025i	−0.230879	−	0.399893i
$470$		0			0
$471$		0			0
$472$	4.33013	+	2.50000i	0.199310	+	0.115072i
$473$		0			0
$474$	−8.00000			−0.367452
$475$		0			0
$476$	4.00000			0.183340
$477$	10.3923	+	6.00000i	0.475831	+	0.274721i
$478$	−10.3923	−	6.00000i	−0.475333	−	0.274434i
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−24.0000	−	41.5692i	−1.09431	−	1.89539i
$482$			19.0000i			0.865426i
$483$		−	16.0000i		−	0.728025i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$	16.0000			0.725775
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$	12.1244	−	7.00000i	0.548844	−	0.316875i
$489$	−1.50000	+	2.59808i	−0.0678323	+	0.117489i
$490$		0			0
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$	4.33013	+	2.50000i	0.195217	+	0.112709i
$493$			4.00000i			0.180151i
$494$	21.0000	+	15.5885i	0.944835	+	0.701358i
$495$		0			0
$496$	4.00000	−	6.92820i	0.179605	−	0.311086i
$497$	10.3923	+	6.00000i	0.466159	+	0.269137i
$498$	9.52628	−	5.50000i	0.426883	−	0.246461i
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	−0.214466	−	0.976732i	$-0.568801\pi$
$499$	16.5000	−	28.5788i	0.738641	−	1.27936i	0.953107	−	0.302633i	$-0.0978656\pi$
$500$		0			0
$501$	−8.00000			−0.357414
$502$			17.0000i			0.758747i
$503$	−3.46410	+	2.00000i	−0.154457	+	0.0891756i	−0.575236	−	0.817987i	$-0.695090\pi$
$503$	−3.46410	+	2.00000i	−0.154457	+	0.0891756i	0.420780	+	0.907163i	$0.361757\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$		0			0
$506$	−24.0000			−1.06693
$507$	−19.9186	+	11.5000i	−0.884615	+	0.510733i
$508$	5.19615	+	3.00000i	0.230542	+	0.133103i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$		0			0
$511$	9.00000	−	15.5885i	0.398137	−	0.689593i
$512$		−	1.00000i		−	0.0441942i
$513$	12.9904	−	17.5000i	0.573539	−	0.772644i
$514$	3.00000			0.132324
$515$		0			0
$516$		0			0
$517$	15.5885	−	9.00000i	0.685580	−	0.395820i
$518$	−13.8564	−	8.00000i	−0.608816	−	0.351500i
$519$	9.00000	+	15.5885i	0.395056	+	0.684257i
$520$		0			0
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	−3.46410	+	2.00000i	−0.151620	+	0.0875376i
$523$	−6.92820	+	4.00000i	−0.302949	+	0.174908i	−0.643767	−	0.765222i	$-0.722629\pi$
$523$	−6.92820	+	4.00000i	−0.302949	+	0.174908i	0.340818	+	0.940129i	$0.389296\pi$
$524$	−7.00000			−0.305796
$525$		0			0
$526$	−13.0000	−	22.5167i	−0.566827	−	0.981773i
$527$	13.8564	+	8.00000i	0.603595	+	0.348485i
$528$	−2.59808	+	1.50000i	−0.113067	+	0.0652791i
$529$	20.5000	−	35.5070i	0.891304	−	1.54378i
$530$		0			0
$531$	−10.0000			−0.433963
$532$	8.66025	+	1.00000i	0.375470	+	0.0433555i
$533$		−	30.0000i		−	1.29944i
$534$	7.00000	−	12.1244i	0.302920	−	0.524672i
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	2.59808	+	1.50000i	0.112115	+	0.0647298i
$538$	−24.2487	+	14.0000i	−1.04544	+	0.603583i
$539$	−9.00000			−0.387657
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	19.0526	−	11.0000i	0.818377	−	0.472490i
$543$		−	16.0000i		−	0.686626i
$544$	2.00000			0.0857493
$545$		0			0
$546$	−6.00000	+	10.3923i	−0.256776	+	0.444750i
$547$	−6.92820	+	4.00000i	−0.296229	+	0.171028i	−0.640747	−	0.767752i	$-0.721375\pi$
$547$	−6.92820	+	4.00000i	−0.296229	+	0.171028i	0.344519	+	0.938779i	$0.388042\pi$
$548$	−2.59808	−	1.50000i	−0.110984	−	0.0640768i
$549$	−14.0000	+	24.2487i	−0.597505	+	1.03491i
$550$		0			0
$551$	−1.00000	+	8.66025i	−0.0426014	+	0.368939i
$552$		−	8.00000i		−	0.340503i
$553$	13.8564	+	8.00000i	0.589234	+	0.340195i
$554$	7.00000	−	12.1244i	0.297402	−	0.515115i
$555$		0			0
$556$	−4.50000	+	7.79423i	−0.190843	+	0.330549i
$557$	−34.6410	+	20.0000i	−1.46779	+	0.847427i	−0.999349	−	0.0360693i	$-0.988516\pi$
$557$	−34.6410	+	20.0000i	−1.46779	+	0.847427i	−0.468438	+	0.883497i	$0.655183\pi$
$558$			16.0000i			0.677334i
$559$		0			0
$560$		0			0
$561$	−3.00000	−	5.19615i	−0.126660	−	0.219382i
$562$		−	7.00000i		−	0.295277i
$563$			23.0000i			0.969334i	0.874699	+	0.484667i	$0.161059\pi$
$563$			23.0000i			0.969334i	−0.874699	+	0.484667i	$0.838941\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	−14.5000	−	25.1147i	−0.609480	−	1.05565i
$567$	−1.73205	−	1.00000i	−0.0727393	−	0.0419961i
$568$	5.19615	+	3.00000i	0.218026	+	0.125877i
$569$	−34.0000			−1.42535			−0.712677	−	0.701492i	$-0.752517\pi$
$569$	−34.0000			−1.42535			−0.712677	+	0.701492i	$0.752517\pi$
$570$		0			0
$571$	−29.0000			−1.21361			−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000			−1.21361			−0.606806	+	0.794850i	$0.707550\pi$
$572$	15.5885	+	9.00000i	0.651786	+	0.376309i
$573$	3.46410	+	2.00000i	0.144715	+	0.0835512i
$574$	−5.00000	−	8.66025i	−0.208696	−	0.361472i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$			7.00000i			0.291414i	0.989328	+	0.145707i	$0.0465456\pi$
$577$			7.00000i			0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$578$		−	13.0000i		−	0.540729i
$579$	−5.00000	−	8.66025i	−0.207793	−	0.359908i
$580$		0			0
$581$	−22.0000			−0.912714
$582$		−	15.0000i		−	0.621770i
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$	4.50000	−	7.79423i	0.186211	−	0.322527i
$585$		0			0
$586$	11.0000	−	19.0526i	0.454406	−	0.787054i
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$		−	3.00000i		−	0.123718i
$589$	28.0000	+	20.7846i	1.15372	+	0.856415i
$590$		0			0
$591$	4.00000	−	6.92820i	0.164538	−	0.284988i
$592$	−6.92820	−	4.00000i	−0.284747	−	0.164399i
$593$	11.2583	−	6.50000i	0.462324	−	0.266923i	−0.250697	−	0.968066i	$-0.580660\pi$
$593$	11.2583	−	6.50000i	0.462324	−	0.266923i	0.713021	+	0.701143i	$0.247326\pi$
$594$	7.50000	−	12.9904i	0.307729	−	0.533002i
$595$		0			0
$596$	4.00000			0.163846
$597$			22.0000i			0.900400i
$598$	−41.5692	+	24.0000i	−1.69989	+	0.981433i
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.660006	+	0.751260i	$0.270554\pi$
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.320607	+	0.947212i	$0.396113\pi$
$600$		0			0
$601$	−37.0000			−1.50926			−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000			−1.50926			−0.754631	+	0.656150i	$0.772184\pi$
$602$		0			0
$603$	8.66025	+	5.00000i	0.352673	+	0.203616i
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$		0			0
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$		−	14.0000i		−	0.568242i	−0.958788	−	0.284121i	$-0.908298\pi$
$607$		−	14.0000i		−	0.568242i	0.958788	−	0.284121i	$-0.0917018\pi$
$608$	4.33013	+	0.500000i	0.175610	+	0.0202777i
$609$	−4.00000			−0.162088
$610$		0			0
$611$	18.0000	−	31.1769i	0.728202	−	1.26128i
$612$	−3.46410	+	2.00000i	−0.140028	+	0.0808452i
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.231127	−	0.972924i	$-0.574241\pi$
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.958140	+	0.286300i	$0.907575\pi$
$614$	2.50000	+	4.33013i	0.100892	+	0.174750i
$615$		0			0
$616$	6.00000			0.241747
$617$	16.4545	−	9.50000i	0.662433	−	0.382456i	−0.130771	−	0.991413i	$-0.541745\pi$
$617$	16.4545	−	9.50000i	0.662433	−	0.382456i	0.793203	+	0.608957i	$0.208412\pi$
$618$	−5.19615	+	3.00000i	−0.209020	+	0.120678i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	20.0000	+	34.6410i	0.802572	+	1.39010i
$622$	−20.7846	−	12.0000i	−0.833387	−	0.481156i
$623$	−24.2487	+	14.0000i	−0.971504	+	0.560898i
$624$	−3.00000	+	5.19615i	−0.120096	+	0.208013i
$625$		0			0
$626$	−13.0000			−0.519584
$627$	−5.19615	−	12.0000i	−0.207514	−	0.479234i
$628$		0			0
$629$	8.00000	−	13.8564i	0.318981	−	0.552491i
$630$		0			0
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	0.993241	+	0.116071i	$0.0370299\pi$
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	−0.396100	+	0.918207i	$0.629637\pi$
$632$	6.92820	+	4.00000i	0.275589	+	0.159111i
$633$	−3.46410	+	2.00000i	−0.137686	+	0.0794929i
$634$	−30.0000			−1.19145
$635$		0			0
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	−15.5885	+	9.00000i	−0.617637	+	0.356593i
$638$			6.00000i			0.237542i
$639$	−12.0000			−0.474713
$640$		0			0
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	−0.995400	−	0.0958109i	$-0.969456\pi$
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	0.580674	+	0.814136i	$0.302789\pi$
$642$	−10.3923	+	6.00000i	−0.410152	+	0.236801i
$643$	−4.33013	−	2.50000i	−0.170764	−	0.0985904i	0.412182	−	0.911101i	$-0.364767\pi$
$643$	−4.33013	−	2.50000i	−0.170764	−	0.0985904i	−0.582946	+	0.812511i	$0.698100\pi$
$644$	−8.00000	+	13.8564i	−0.315244	+	0.546019i
$645$		0			0
$646$	−1.00000	+	8.66025i	−0.0393445	+	0.340733i
$647$			6.00000i			0.235884i	0.993020	+	0.117942i	$0.0376297\pi$
$647$			6.00000i			0.235884i	−0.993020	+	0.117942i	$0.962370\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−7.50000	+	12.9904i	−0.294401	+	0.509917i
$650$		0			0
$651$	−8.00000	+	13.8564i	−0.313545	+	0.543075i
$652$	2.59808	−	1.50000i	0.101749	−	0.0587445i
$653$			36.0000i			1.40879i	0.709809	+	0.704394i	$0.248781\pi$
$653$			36.0000i			1.40879i	−0.709809	+	0.704394i	$0.751219\pi$
$654$	8.00000			0.312825
$655$		0			0
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$			18.0000i			0.702247i
$658$		−	12.0000i		−	0.467809i
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−14.7224	−	8.50000i	−0.572204	−	0.330362i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$	−11.0000			−0.426883
$665$		0			0
$666$	16.0000			0.619987
$667$	−13.8564	−	8.00000i	−0.536522	−	0.309761i
$668$	6.92820	+	4.00000i	0.268060	+	0.154765i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	21.0000	+	36.3731i	0.810696	+	1.40417i
$672$			2.00000i			0.0771517i
$673$		−	26.0000i		−	1.00223i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$		−	26.0000i		−	1.00223i	0.865382	−	0.501113i	$-0.167076\pi$
$674$	−9.50000	−	16.4545i	−0.365926	−	0.633803i
$675$		0			0
$676$	23.0000			0.884615
$677$		−	2.00000i		−	0.0768662i	−0.999261	−	0.0384331i	$-0.987763\pi$
$677$		−	2.00000i		−	0.0768662i	0.999261	−	0.0384331i	$-0.0122367\pi$
$678$	11.2583	−	6.50000i	0.432374	−	0.249631i
$679$	−15.0000	+	25.9808i	−0.575647	+	0.997050i
$680$		0			0
$681$	−3.50000	+	6.06218i	−0.134120	+	0.232303i
$682$	20.7846	+	12.0000i	0.795884	+	0.459504i
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$	−8.00000	+	3.46410i	−0.305888	+	0.132453i
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−20.7846	−	12.0000i	−0.792982	−	0.457829i
$688$		0			0
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$		−	18.0000i		−	0.684257i
$693$	−10.3923	+	6.00000i	−0.394771	+	0.227921i
$694$	13.5000	+	23.3827i	0.512453	+	0.887595i
$695$		0			0
$696$	−2.00000			−0.0758098
$697$	8.66025	−	5.00000i	0.328031	−	0.189389i
$698$	−13.8564	−	8.00000i	−0.524473	−	0.302804i
$699$	−5.50000	−	9.52628i	−0.208029	−	0.360317i
$700$		0			0
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	−0.130843	−	0.991403i	$-0.541768\pi$
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	0.924002	−	0.382389i	$-0.124898\pi$
$702$		−	30.0000i		−	1.13228i
$703$	20.7846	−	28.0000i	0.783906	−	1.05604i
$704$	3.00000			0.113067
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	−17.3205	+	10.0000i	−0.651405	+	0.376089i
$708$	−4.33013	−	2.50000i	−0.162736	−	0.0939558i
$709$	10.0000	+	17.3205i	0.375558	+	0.650485i	0.990410	−	0.138157i	$-0.0441178\pi$
$709$	10.0000	+	17.3205i	0.375558	+	0.650485i	−0.614852	+	0.788642i	$0.710784\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$	−12.1244	+	7.00000i	−0.454379	+	0.262336i
$713$	−55.4256	+	32.0000i	−2.07571	+	1.19841i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$	10.3923	+	6.00000i	0.388108	+	0.224074i
$718$	20.7846	−	12.0000i	0.775675	−	0.447836i
$719$	25.0000	−	43.3013i	0.932343	−	1.61486i	0.153037	−	0.988220i	$-0.451094\pi$
$719$	25.0000	−	43.3013i	0.932343	−	1.61486i	0.779305	−	0.626644i	$-0.215572\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$	−4.33013	+	18.5000i	−0.161151	+	0.688499i
$723$		−	19.0000i		−	0.706618i
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$		0			0
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	−6.92820	−	4.00000i	−0.256953	−	0.148352i	0.365991	−	0.930618i	$-0.380730\pi$
$727$	−6.92820	−	4.00000i	−0.256953	−	0.148352i	−0.622944	+	0.782267i	$0.714063\pi$
$728$	10.3923	−	6.00000i	0.385164	−	0.222375i
$729$	−13.0000			−0.481481
$730$		0			0
$731$		0			0
$732$	−12.1244	+	7.00000i	−0.448129	+	0.258727i
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$	12.9904	−	7.50000i	0.478507	−	0.276266i
$738$	8.66025	+	5.00000i	0.318788	+	0.184053i
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	−0.816373	−	0.577524i	$-0.804019\pi$
$739$	2.50000	−	4.33013i	0.0919640	−	0.159286i	0.908337	+	0.418238i	$0.137352\pi$
$740$		0			0
$741$	−21.0000	−	15.5885i	−0.771454	−	0.572656i
$742$		−	12.0000i		−	0.440534i
$743$	3.46410	+	2.00000i	0.127086	+	0.0733729i	0.562195	−	0.827005i	$-0.309957\pi$
$743$	3.46410	+	2.00000i	0.127086	+	0.0733729i	−0.435110	+	0.900378i	$0.643290\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$		0			0
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	19.0526	−	11.0000i	0.697097	−	0.402469i
$748$			6.00000i			0.219382i
$749$	24.0000			0.876941
$750$		0			0
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$		−	6.00000i		−	0.218797i
$753$		−	17.0000i		−	0.619514i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$		0			0
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	−29.4449	−	17.0000i	−1.07019	−	0.617876i	−0.141958	−	0.989873i	$-0.545340\pi$
$757$	−29.4449	−	17.0000i	−1.07019	−	0.617876i	−0.928234	+	0.371997i	$0.878673\pi$
$758$	24.2487	+	14.0000i	0.880753	+	0.508503i
$759$	24.0000			0.871145
$760$		0			0
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$	−5.19615	−	3.00000i	−0.188237	−	0.108679i
$763$	−13.8564	−	8.00000i	−0.501636	−	0.289619i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$		0			0
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$			30.0000i			1.08324i
$768$			1.00000i			0.0360844i
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$			10.0000i			0.359908i
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.888220	−	0.459418i	$-0.848058\pi$
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.0462427	+	0.998930i	$0.514725\pi$
$774$		0			0
$775$		0			0
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$	13.8564	+	8.00000i	0.497096	+	0.286998i
$778$		0			0
$779$	20.0000	−	8.66025i	0.716574	−	0.310286i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	−13.8564	−	8.00000i	−0.495504	−	0.286079i
$783$	8.66025	−	5.00000i	0.309492	−	0.178685i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$		0			0
$786$	7.00000			0.249682
$787$		−	1.00000i		−	0.0356462i	−0.999841	−	0.0178231i	$-0.994326\pi$
$787$		−	1.00000i		−	0.0356462i	0.999841	−	0.0178231i	$-0.00567356\pi$
$788$	−6.92820	+	4.00000i	−0.246807	+	0.142494i
$789$	13.0000	+	22.5167i	0.462812	+	0.801614i
$790$		0			0
$791$	−26.0000			−0.924454
$792$	−5.19615	+	3.00000i	−0.184637	+	0.106600i
$793$	72.7461	+	42.0000i	2.58329	+	1.49146i
$794$	−8.00000	−	13.8564i	−0.283909	−	0.491745i
$795$		0			0
$796$	11.0000	−	19.0526i	0.389885	−	0.675300i
$797$		−	28.0000i		−	0.991811i	−0.868377	−	0.495905i	$-0.834836\pi$
$797$		−	28.0000i		−	0.991811i	0.868377	−	0.495905i	$-0.165164\pi$
$798$	−8.66025	−	1.00000i	−0.306570	−	0.0353996i
$799$	12.0000			0.424529
$800$		0			0
$801$	14.0000	−	24.2487i	0.494666	−	0.856786i
$802$	2.59808	−	1.50000i	0.0917413	−	0.0529668i
$803$	23.3827	+	13.5000i	0.825157	+	0.476405i
$804$	2.50000	+	4.33013i	0.0881682	+	0.152712i
$805$		0			0
$806$	48.0000			1.69073
$807$	24.2487	−	14.0000i	0.853595	−	0.492823i
$808$	−8.66025	+	5.00000i	−0.304667	+	0.175899i
$809$	51.0000			1.79306			0.896532	−	0.442978i	$-0.146078\pi$
$809$	51.0000			1.79306			0.896532	+	0.442978i	$0.146078\pi$
$810$		0			0
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	0.635303	−	0.772263i	$-0.280875\pi$
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	−0.986451	+	0.164057i	$0.947542\pi$
$812$	3.46410	+	2.00000i	0.121566	+	0.0701862i
$813$	−19.0526	+	11.0000i	−0.668202	+	0.385787i
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$		0			0
$816$	−2.00000			−0.0700140
$817$		0			0
$818$		−	19.0000i		−	0.664319i
$819$	−12.0000	+	20.7846i	−0.419314	+	0.726273i
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	2.59808	+	1.50000i	0.0906183	+	0.0523185i
$823$	−1.73205	+	1.00000i	−0.0603755	+	0.0348578i	−0.529884	−	0.848070i	$-0.677765\pi$
$823$	−1.73205	+	1.00000i	−0.0603755	+	0.0348578i	0.469508	+	0.882928i	$0.344431\pi$
$824$	6.00000			0.209020
$825$		0			0
$826$	5.00000	+	8.66025i	0.173972	+	0.301329i
$827$	23.3827	−	13.5000i	0.813096	−	0.469441i	−0.0349341	−	0.999390i	$-0.511122\pi$
$827$	23.3827	−	13.5000i	0.813096	−	0.469441i	0.848030	+	0.529949i	$0.177789\pi$
$828$		−	16.0000i		−	0.556038i
$829$	−48.0000			−1.66711			−0.833554	−	0.552437i	$-0.813698\pi$
$829$	−48.0000			−1.66711			−0.833554	+	0.552437i	$0.813698\pi$
$830$		0			0
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$	5.19615	−	3.00000i	0.180144	−	0.104006i
$833$	−5.19615	−	3.00000i	−0.180036	−	0.103944i
$834$	4.50000	−	7.79423i	0.155822	−	0.269892i
$835$		0			0
$836$	−1.50000	+	12.9904i	−0.0518786	+	0.449282i
$837$		−	40.0000i		−	1.38260i
$838$	−24.2487	−	14.0000i	−0.837658	−	0.483622i
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	−0.233973	−	0.972243i	$-0.575173\pi$
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	0.958974	−	0.283495i	$-0.0914938\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	6.92820	−	4.00000i	0.238762	−	0.137849i
$843$			7.00000i			0.241093i
$844$	4.00000			0.137686
$845$		0			0
$846$	6.00000	+	10.3923i	0.206284	+	0.357295i
$847$		−	4.00000i		−	0.137442i
$848$		−	6.00000i		−	0.206041i
$849$	14.5000	+	25.1147i	0.497639	+	0.861936i
$850$		0			0
$851$	32.0000	+	55.4256i	1.09695	+	1.89997i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$	−8.66025	−	5.00000i	−0.296521	−	0.171197i	0.344358	−	0.938839i	$-0.388097\pi$
$853$	−8.66025	−	5.00000i	−0.296521	−	0.171197i	−0.640879	+	0.767642i	$0.721430\pi$
$854$	28.0000			0.958140
$855$		0			0
$856$	12.0000			0.410152
$857$	12.9904	+	7.50000i	0.443743	+	0.256195i	0.705184	−	0.709024i	$-0.250864\pi$
$857$	12.9904	+	7.50000i	0.443743	+	0.256195i	−0.261441	+	0.965219i	$0.584198\pi$
$858$	−15.5885	−	9.00000i	−0.532181	−	0.307255i
$859$	11.5000	+	19.9186i	0.392375	+	0.679613i	0.992762	−	0.120096i	$-0.0383202\pi$
$859$	11.5000	+	19.9186i	0.392375	+	0.679613i	−0.600387	+	0.799709i	$0.704987\pi$
$860$		0			0
$861$	5.00000	+	8.66025i	0.170400	+	0.295141i
$862$			6.00000i			0.204361i
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	−30.0000			−1.01944
$867$			13.0000i			0.441503i
$868$	13.8564	−	8.00000i	0.470317	−	0.271538i
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	15.0000	−	25.9808i	0.508256	−	0.880325i
$872$	−6.92820	−	4.00000i	−0.234619	−	0.135457i
$873$		−	30.0000i		−	1.01535i
$874$	−28.0000	−	20.7846i	−0.947114	−	0.703050i
$875$		0			0
$876$	−4.50000	+	7.79423i	−0.152041	+	0.263343i
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.939155	−	0.343495i	$-0.111611\pi$
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.172102	+	0.985079i	$0.444944\pi$
$878$	−6.92820	+	4.00000i	−0.233816	+	0.134993i
$879$	−11.0000	+	19.0526i	−0.371021	+	0.642627i
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$		−	6.00000i		−	0.202031i
$883$	−19.9186	+	11.5000i	−0.670314	+	0.387006i	−0.796196	−	0.605039i	$-0.793157\pi$
$883$	−19.9186	+	11.5000i	−0.670314	+	0.387006i	0.125882	+	0.992045i	$0.459824\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	9.00000			0.302361
$887$	3.46410	−	2.00000i	0.116313	−	0.0671534i	−0.440715	−	0.897647i	$-0.645275\pi$
$887$	3.46410	−	2.00000i	0.116313	−	0.0671534i	0.557028	+	0.830494i	$0.311942\pi$
$888$	6.92820	+	4.00000i	0.232495	+	0.134231i
$889$	6.00000	+	10.3923i	0.201234	+	0.348547i
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		−	16.0000i		−	0.535720i
$893$	25.9808	+	3.00000i	0.869413	+	0.100391i
$894$	−4.00000			−0.133780
$895$		0			0
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$	41.5692	−	24.0000i	1.38796	−	0.801337i
$898$	−25.1147	−	14.5000i	−0.838090	−	0.483871i
$899$	8.00000	+	13.8564i	0.266815	+	0.462137i
$900$		0			0
$901$	12.0000			0.399778
$902$	12.9904	−	7.50000i	0.432532	−	0.249723i
$903$		0			0
$904$	−13.0000			−0.432374
$905$		0			0
$906$	−6.00000	−	10.3923i	−0.199337	−	0.345261i
$907$	−40.7032	−	23.5000i	−1.35153	−	0.780305i	−0.363064	−	0.931764i	$-0.618269\pi$
$907$	−40.7032	−	23.5000i	−1.35153	−	0.780305i	−0.988463	+	0.151460i	$0.951603\pi$
$908$	6.06218	−	3.50000i	0.201180	−	0.116152i
$909$	10.0000	−	17.3205i	0.331679	−	0.574485i
$910$		0			0
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	−4.33013	−	0.500000i	−0.143385	−	0.0165567i
$913$		−	33.0000i		−	1.09214i
$914$	−6.50000	+	11.2583i	−0.215001	+	0.372392i
$915$		0			0
$916$	12.0000	+	20.7846i	0.396491	+	0.686743i
$917$	−12.1244	−	7.00000i	−0.400381	−	0.231160i
$918$	8.66025	−	5.00000i	0.285831	−	0.165025i
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$		0			0
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$	19.0526	−	11.0000i	0.627463	−	0.362266i
$923$			36.0000i			1.18495i
$924$	−6.00000			−0.197386
$925$		0			0
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	−10.3923	+	6.00000i	−0.341328	+	0.197066i
$928$	1.73205	+	1.00000i	0.0568574	+	0.0328266i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$		0			0
$931$	−10.5000	−	7.79423i	−0.344124	−	0.255446i
$932$			11.0000i			0.360317i
$933$	20.7846	+	12.0000i	0.680458	+	0.392862i
$934$	−3.50000	+	6.06218i	−0.114523	+	0.198361i
$935$		0			0
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	30.3109	−	17.5000i	0.990214	−	0.571700i	0.0848755	−	0.996392i	$-0.472951\pi$
$937$	30.3109	−	17.5000i	0.990214	−	0.571700i	0.905338	+	0.424691i	$0.139617\pi$
$938$		−	10.0000i		−	0.326512i
$939$	13.0000			0.424239
$940$		0			0
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$			40.0000i			1.30258i
$944$	2.50000	+	4.33013i	0.0813681	+	0.140934i
$945$		0			0
$946$		0			0
$947$	45.0333	+	26.0000i	1.46339	+	0.844886i	0.999166	−	0.0408333i	$-0.0130013\pi$
$947$	45.0333	+	26.0000i	1.46339	+	0.844886i	0.464220	+	0.885720i	$0.346335\pi$
$948$	−6.92820	−	4.00000i	−0.225018	−	0.129914i
$949$	54.0000			1.75291
$950$		0			0
$951$	30.0000			0.972817
$952$	3.46410	+	2.00000i	0.112272	+	0.0648204i
$953$	−6.06218	−	3.50000i	−0.196373	−	0.113376i	0.398589	−	0.917129i	$-0.369500\pi$
$953$	−6.06218	−	3.50000i	−0.196373	−	0.113376i	−0.594963	+	0.803753i	$0.702833\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$		0			0
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		−	6.00000i		−	0.193952i
$958$			12.0000i			0.387702i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$		0			0
$961$	33.0000			1.06452
$962$		−	48.0000i		−	1.54758i
$963$	−20.7846	+	12.0000i	−0.669775	+	0.386695i
$964$	−9.50000	+	16.4545i	−0.305974	+	0.529963i
$965$		0			0
$966$	8.00000	−	13.8564i	0.257396	−	0.445823i
$967$	46.7654	+	27.0000i	1.50387	+	0.868261i	0.999990	+	0.00448958i	$0.00142908\pi$
$967$	46.7654	+	27.0000i	1.50387	+	0.868261i	0.503883	+	0.863772i	$0.331904\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	1.00000	−	8.66025i	0.0321246	−	0.278207i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	13.8564	+	8.00000i	0.444444	+	0.256600i
$973$	−15.5885	+	9.00000i	−0.499743	+	0.288527i
$974$	−2.00000	+	3.46410i	−0.0640841	+	0.110997i
$975$		0			0
$976$	14.0000			0.448129
$977$			33.0000i			1.05576i	0.849318	+	0.527882i	$0.177014\pi$
$977$			33.0000i			1.05576i	−0.849318	+	0.527882i	$0.822986\pi$
$978$	−2.59808	+	1.50000i	−0.0830773	+	0.0479647i
$979$	−21.0000	−	36.3731i	−0.671163	−	1.16249i
$980$		0			0
$981$	16.0000			0.510841
$982$	−17.3205	+	10.0000i	−0.552720	+	0.319113i
$983$	31.1769	+	18.0000i	0.994389	+	0.574111i	0.906583	−	0.422027i	$-0.138681\pi$
$983$	31.1769	+	18.0000i	0.994389	+	0.574111i	0.0878058	+	0.996138i	$0.472015\pi$
$984$	2.50000	+	4.33013i	0.0796971	+	0.138039i
$985$		0			0
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$			12.0000i			0.381964i
$988$	10.3923	+	24.0000i	0.330623	+	0.763542i
$989$		0			0
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	6.92820	−	4.00000i	0.219971	−	0.127000i
$993$	14.7224	+	8.50000i	0.467202	+	0.269739i
$994$	6.00000	+	10.3923i	0.190308	+	0.329624i
$995$		0			0
$996$	11.0000			0.348548
$997$	1.73205	−	1.00000i	0.0548546	−	0.0316703i	−0.472322	−	0.881426i	$-0.656584\pi$
$997$	1.73205	−	1.00000i	0.0548546	−	0.0316703i	0.527176	+	0.849756i	$0.323251\pi$
$998$	28.5788	−	16.5000i	0.904647	−	0.522298i
$999$	−40.0000			−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.a.49.2		4
5.2	odd	4		950.2.e.a.201.1		2
5.3	odd	4		190.2.e.b.11.1	✓	2
5.4	even	2	inner	950.2.j.a.49.1		4
15.8	even	4		1710.2.l.b.1531.1		2
19.7	even	3	inner	950.2.j.a.349.1		4
20.3	even	4		1520.2.q.e.961.1		2
95.7	odd	12		950.2.e.a.501.1		2
95.8	even	12		3610.2.a.i.1.1		1
95.64	even	6	inner	950.2.j.a.349.2		4
95.68	odd	12		3610.2.a.a.1.1		1
95.83	odd	12		190.2.e.b.121.1	yes	2
285.83	even	12		1710.2.l.b.1261.1		2
380.83	even	12		1520.2.q.e.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.b.11.1	✓	2	5.3	odd	4
190.2.e.b.121.1	yes	2	95.83	odd	12
950.2.e.a.201.1		2	5.2	odd	4
950.2.e.a.501.1		2	95.7	odd	12
950.2.j.a.49.1		4	5.4	even	2	inner
950.2.j.a.49.2		4	1.1	even	1	trivial
950.2.j.a.349.1		4	19.7	even	3	inner
950.2.j.a.349.2		4	95.64	even	6	inner
1520.2.q.e.881.1		2	380.83	even	12
1520.2.q.e.961.1		2	20.3	even	4
1710.2.l.b.1261.1		2	285.83	even	12
1710.2.l.b.1531.1		2	15.8	even	4
3610.2.a.a.1.1		1	95.68	odd	12
3610.2.a.i.1.1		1	95.8	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} +2.00000i q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} -3.00000 q^{11} -1.00000i q^{12} +(-5.19615 + 3.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} -2.00000i q^{18} +(-3.50000 - 2.59808i) q^{19} +(1.00000 - 1.73205i) q^{21} +(-2.59808 - 1.50000i) q^{22} +(6.92820 - 4.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} -6.00000 q^{26} +5.00000i q^{27} +(-1.73205 + 1.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} -8.00000 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.59808 + 1.50000i) q^{33} +(-1.00000 - 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{36} +8.00000i q^{37} +(-1.73205 - 4.00000i) q^{38} +6.00000 q^{39} +(-2.50000 + 4.33013i) q^{41} +(1.73205 - 1.00000i) q^{42} +(-1.50000 - 2.59808i) q^{44} +8.00000 q^{46} +(-5.19615 + 3.00000i) q^{47} +(0.866025 - 0.500000i) q^{48} +3.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(-5.19615 - 3.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(1.73205 + 4.00000i) q^{57} -2.00000i q^{58} +(2.50000 - 4.33013i) q^{59} +(-7.00000 - 12.1244i) q^{61} +(-6.92820 - 4.00000i) q^{62} +(3.46410 - 2.00000i) q^{63} -1.00000 q^{64} +(1.50000 + 2.59808i) q^{66} +(-4.33013 + 2.50000i) q^{67} -2.00000i q^{68} -8.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(1.73205 - 1.00000i) q^{72} +(-7.79423 - 4.50000i) q^{73} +(-4.00000 + 6.92820i) q^{74} +(0.500000 - 4.33013i) q^{76} -6.00000i q^{77} +(5.19615 + 3.00000i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} +11.0000i q^{83} +2.00000 q^{84} +2.00000i q^{87} -3.00000i q^{88} +(7.00000 + 12.1244i) q^{89} +(-6.00000 - 10.3923i) q^{91} +(6.92820 + 4.00000i) q^{92} +(6.92820 + 4.00000i) q^{93} -6.00000 q^{94} +1.00000 q^{96} +(12.9904 + 7.50000i) q^{97} +(2.59808 + 1.50000i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9	\( 4 q + 2 q^{4} - 2 q^{6} - 4 q^{9} - 12 q^{11} - 4 q^{14} - 2 q^{16} - 14 q^{19} + 4 q^{21} + 2 q^{24} - 24 q^{26} - 4 q^{29} - 32 q^{31} - 4 q^{34} + 4 q^{36} + 24 q^{39} - 10 q^{41} - 6 q^{44} + 32 q^{46} + 12 q^{49} + 4 q^{51} - 10 q^{54} - 8 q^{56} + 10 q^{59} - 28 q^{61} - 4 q^{64} + 6 q^{66} - 32 q^{69} + 12 q^{71} - 16 q^{74} + 2 q^{76} + 16 q^{79} - 2 q^{81} + 8 q^{84} + 28 q^{89} - 24 q^{91} - 24 q^{94} + 4 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^6 - 4 * q^9 - 12 * q^11 - 4 * q^14 - 2 * q^16 - 14 * q^19 + 4 * q^21 + 2 * q^24 - 24 * q^26 - 4 * q^29 - 32 * q^31 - 4 * q^34 + 4 * q^36 + 24 * q^39 - 10 * q^41 - 6 * q^44 + 32 * q^46 + 12 * q^49 + 4 * q^51 - 10 * q^54 - 8 * q^56 + 10 * q^59 - 28 * q^61 - 4 * q^64 + 6 * q^66 - 32 * q^69 + 12 * q^71 - 16 * q^74 + 2 * q^76 + 16 * q^79 - 2 * q^81 + 8 * q^84 + 28 * q^89 - 24 * q^91 - 24 * q^94 + 4 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more