LMFDB - Embedded newform 350.2.j.b.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,2,Mod(149,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,2,0,-4,0,0,-4,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$2.79476407074$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.2.j.b.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{18} +(1.00000 + 1.73205i) q^{19} +(2.50000 + 0.866025i) q^{21} +6.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -5.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} -2.00000 q^{36} +(-3.46410 + 2.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +9.00000 q^{41} +(-2.59808 + 0.500000i) q^{42} +7.00000i q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(3.46410 + 2.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(2.50000 + 4.33013i) q^{54} +(0.500000 + 2.59808i) q^{56} +2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} -8.00000i q^{62} +(-3.46410 - 4.00000i) q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-4.33013 - 2.50000i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(1.73205 - 1.00000i) q^{72} +(-13.8564 - 8.00000i) q^{73} +(2.00000 - 3.46410i) q^{74} +2.00000 q^{76} +(5.19615 - 15.0000i) q^{77} -4.00000i q^{78} +(1.00000 + 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-7.79423 + 4.50000i) q^{82} -3.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-3.50000 - 6.06218i) q^{86} +(2.59808 + 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} -3.00000i q^{92} +(-6.92820 + 4.00000i) q^{93} +(0.500000 + 0.866025i) q^{96} +14.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{6} - 4 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} + 4 q^{19} + 10 q^{21} - 2 q^{24} - 8 q^{26} + 12 q^{29} - 16 q^{31} - 8 q^{36} - 8 q^{39} + 36 q^{41} - 12 q^{44} - 6 q^{46} + 26 q^{49}+ \cdots - 48 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^6 - 4 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 + 4 * q^19 + 10 * q^21 - 2 * q^24 - 8 * q^26 + 12 * q^29 - 16 * q^31 - 8 * q^36 - 8 * q^39 + 36 * q^41 - 12 * q^44 - 6 * q^46 + 26 * q^49 + 10 * q^54 + 2 * q^56 - 12 * q^59 - 10 * q^61 - 4 * q^64 - 12 * q^66 + 12 * q^69 - 24 * q^71 + 8 * q^74 + 8 * q^76 + 4 * q^79 - 2 * q^81 + 8 * q^84 - 14 * q^86 - 30 * q^89 + 8 * q^91 + 2 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	0.728714	−	0.684819i	$-0.240119\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i	−0.228714	+	0.973494i	$0.573452\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$7$	2.59808	−	0.500000i	0.981981	−	0.188982i
$8$			1.00000i			0.353553i
$9$	−1.00000	−	1.73205i	−0.333333	−	0.577350i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	1.73205	+	1.00000i	0.408248	+	0.235702i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$			6.00000i			1.27920i
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	−0.204046	−	0.978961i	$-0.565409\pi$
$23$	2.59808	−	1.50000i	0.541736	−	0.312772i	0.745782	+	0.666190i	$0.232076\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$		−	5.00000i		−	0.962250i
$28$	0.866025	−	2.50000i	0.163663	−	0.472456i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	5.19615	−	3.00000i	0.904534	−	0.522233i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$	−1.73205	−	1.00000i	−0.280976	−	0.162221i
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$		0			0
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	−2.59808	+	0.500000i	−0.400892	+	0.0771517i
$43$			7.00000i			1.06749i	0.845645	+	0.533745i	$0.179216\pi$
$43$			7.00000i			1.06749i	−0.845645	+	0.533745i	$0.820784\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$	3.46410	+	2.00000i	0.480384	+	0.277350i
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	0.0987002	−	0.995117i	$-0.468532\pi$
$53$	−5.19615	−	3.00000i	−0.713746	−	0.412082i	−0.812447	+	0.583036i	$0.801865\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$			2.00000i			0.264906i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		−	8.00000i		−	1.01600i
$63$	−3.46410	−	4.00000i	−0.436436	−	0.503953i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	0.211604	−	0.977356i	$-0.432131\pi$
$67$	−4.33013	−	2.50000i	−0.529009	−	0.305424i	−0.740613	+	0.671932i	$0.765465\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.73205	−	1.00000i	0.204124	−	0.117851i
$73$	−13.8564	−	8.00000i	−1.62177	−	0.936329i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−13.8564	−	8.00000i	−1.62177	−	0.936329i	−0.635323	−	0.772246i	$-0.719133\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$		0			0
$76$	2.00000			0.229416
$77$	5.19615	−	15.0000i	0.592157	−	1.70941i
$78$		−	4.00000i		−	0.452911i
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−7.79423	+	4.50000i	−0.860729	+	0.496942i
$83$		−	3.00000i		−	0.329293i	−0.986353	−	0.164646i	$-0.947352\pi$
$83$		−	3.00000i		−	0.329293i	0.986353	−	0.164646i	$-0.0526483\pi$
$84$	2.00000	−	1.73205i	0.218218	−	0.188982i
$85$		0			0
$86$	−3.50000	−	6.06218i	−0.377415	−	0.653701i
$87$	2.59808	+	1.50000i	0.278543	+	0.160817i
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$	2.00000	+	10.3923i	0.209657	+	1.08941i
$92$		−	3.00000i		−	0.312772i
$93$	−6.92820	+	4.00000i	−0.718421	+	0.414781i
$94$		0			0
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$	−12.0000			−1.20605
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	0.866025	−	0.500000i	0.0853320	−	0.0492665i	−0.456727	−	0.889607i	$-0.650978\pi$
$103$	0.866025	−	0.500000i	0.0853320	−	0.0492665i	0.542059	+	0.840341i	$0.317645\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	−12.9904	+	7.50000i	−1.25583	+	0.725052i	−0.972261	−	0.233900i	$-0.924851\pi$
$107$	−12.9904	+	7.50000i	−1.25583	+	0.725052i	−0.283567	+	0.958952i	$0.591518\pi$
$108$	−4.33013	−	2.50000i	−0.416667	−	0.240563i
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$	−1.73205	−	2.00000i	−0.163663	−	0.188982i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	6.92820	−	4.00000i	0.640513	−	0.369800i
$118$		−	6.00000i		−	0.552345i
$119$		0			0
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	4.33013	+	2.50000i	0.392031	+	0.226339i
$123$	7.79423	+	4.50000i	0.702782	+	0.405751i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$		0			0
$126$	5.00000	+	1.73205i	0.445435	+	0.154303i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.50000	+	6.06218i	−0.308158	+	0.533745i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		−	6.00000i		−	0.522233i
$133$	3.46410	+	4.00000i	0.300376	+	0.346844i
$134$	5.00000			0.431934
$135$		0			0
$136$		0			0
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$	−2.59808	+	1.50000i	−0.221163	+	0.127688i
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$		0			0
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$	20.7846	+	12.0000i	1.73810	+	1.00349i
$144$	−1.00000	+	1.73205i	−0.0833333	+	0.144338i
$145$		0			0
$146$	16.0000			1.32417
$147$	6.92820	+	1.00000i	0.571429	+	0.0824786i
$148$			4.00000i			0.328798i
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	0.990485	+	0.137619i	$0.0439449\pi$
$149$	7.50000	+	12.9904i	0.614424	+	1.06421i	−0.376061	+	0.926595i	$0.622722\pi$
$150$		0			0
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$	−1.73205	+	1.00000i	−0.140488	+	0.0811107i
$153$		0			0
$154$	3.00000	+	15.5885i	0.241747	+	1.25615i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.999706	+	0.0242497i	$0.00771967\pi$
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.520854	+	0.853646i	$0.325614\pi$
$158$	−1.73205	−	1.00000i	−0.137795	−	0.0795557i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	6.00000	−	5.19615i	0.472866	−	0.409514i
$162$		−	1.00000i		−	0.0785674i
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	−0.358162	−	0.933659i	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	1.50000	+	2.59808i	0.116423	+	0.201650i
$167$		−	3.00000i		−	0.232147i	−0.993241	−	0.116073i	$-0.962969\pi$
$167$		−	3.00000i		−	0.232147i	0.993241	−	0.116073i	$-0.0370308\pi$
$168$	−0.866025	+	2.50000i	−0.0668153	+	0.192879i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	6.06218	+	3.50000i	0.462237	+	0.266872i
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	−6.00000			−0.452267
$177$	−5.19615	+	3.00000i	−0.390567	+	0.225494i
$178$	12.9904	+	7.50000i	0.973670	+	0.562149i
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.0655145	+	0.997852i	$0.520869\pi$
$179$	−12.0000	+	20.7846i	−0.896922	+	1.55351i	−0.831408	+	0.555663i	$0.812464\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	−6.92820	−	8.00000i	−0.513553	−	0.592999i
$183$		−	5.00000i		−	0.369611i
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$		0			0
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$		0			0
$189$	−2.50000	−	12.9904i	−0.181848	−	0.944911i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	1.73205	+	1.00000i	0.124676	+	0.0719816i	0.561041	−	0.827788i	$-0.310401\pi$
$193$	1.73205	+	1.00000i	0.124676	+	0.0719816i	−0.436365	+	0.899770i	$0.643734\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	10.3923	−	6.00000i	0.738549	−	0.426401i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	−2.50000	−	4.33013i	−0.176336	−	0.305424i
$202$		−	15.0000i		−	1.05540i
$203$	7.79423	−	1.50000i	0.547048	−	0.105279i
$204$		0			0
$205$		0			0
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	−5.19615	−	3.00000i	−0.361158	−	0.208514i
$208$	3.46410	−	2.00000i	0.240192	−	0.138675i
$209$	12.0000			0.830057
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$	−5.19615	−	3.00000i	−0.356034	−	0.205557i
$214$	7.50000	−	12.9904i	0.512689	−	0.888004i
$215$		0			0
$216$	5.00000			0.340207
$217$	−6.92820	+	20.0000i	−0.470317	+	1.35769i
$218$			11.0000i			0.745014i
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$		0			0
$221$		0			0
$222$	3.46410	−	2.00000i	0.232495	−	0.134231i
$223$			28.0000i			1.87502i	0.347960	+	0.937509i	$0.386874\pi$
$223$			28.0000i			1.87502i	−0.347960	+	0.937509i	$0.613126\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	0.803523	−	0.595274i	$-0.202957\pi$
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	−0.113761	+	0.993508i	$0.536290\pi$
$228$	1.73205	+	1.00000i	0.114708	+	0.0662266i
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	0.999088	−	0.0426906i	$-0.0135930\pi$
$229$	7.00000	+	12.1244i	0.462573	+	0.801200i	−0.536515	+	0.843891i	$0.680260\pi$
$230$		0			0
$231$	12.0000	−	10.3923i	0.789542	−	0.683763i
$232$			3.00000i			0.196960i
$233$	10.3923	−	6.00000i	0.680823	−	0.393073i	−0.119342	−	0.992853i	$-0.538079\pi$
$233$	10.3923	−	6.00000i	0.680823	−	0.393073i	0.800165	+	0.599780i	$0.204745\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$			2.00000i			0.129914i
$238$		0			0
$239$	−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
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	21.6506	+	12.5000i	1.39176	+	0.803530i
$243$	−13.8564	+	8.00000i	−0.888889	+	0.513200i
$244$	−5.00000			−0.320092
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−6.92820	+	4.00000i	−0.440831	+	0.254514i
$248$	−6.92820	−	4.00000i	−0.439941	−	0.254000i
$249$	1.50000	−	2.59808i	0.0950586	−	0.164646i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$	−5.19615	+	1.00000i	−0.327327	+	0.0629941i
$253$		−	18.0000i		−	1.13165i
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		−	7.00000i		−	0.435801i
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	−18.1865	−	10.5000i	−1.12143	−	0.647458i	−0.179664	−	0.983728i	$-0.557501\pi$
$263$	−18.1865	−	10.5000i	−1.12143	−	0.647458i	−0.941766	+	0.336270i	$0.890834\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	−5.00000	−	1.73205i	−0.306570	−	0.106199i
$267$		−	15.0000i		−	0.917985i
$268$	−4.33013	+	2.50000i	−0.264505	+	0.152712i
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	−0.541533	−	0.840679i	$-0.682156\pi$
$269$	7.50000	−	12.9904i	0.457283	−	0.792038i	0.998816	+	0.0486418i	$0.0154893\pi$
$270$		0			0
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	0.834053	−	0.551684i	$-0.186015\pi$
$271$	−1.00000	−	1.73205i	−0.0607457	−	0.105215i	−0.894799	+	0.446469i	$0.852681\pi$
$272$		0			0
$273$	−3.46410	+	10.0000i	−0.209657	+	0.605228i
$274$	12.0000			0.724947
$275$		0			0
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$	−6.92820	−	4.00000i	−0.416275	−	0.240337i	0.277207	−	0.960810i	$-0.410591\pi$
$277$	−6.92820	−	4.00000i	−0.416275	−	0.240337i	−0.693482	+	0.720473i	$0.743925\pi$
$278$	−8.66025	+	5.00000i	−0.519408	+	0.299880i
$279$	16.0000			0.957895
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−3.46410	−	2.00000i	−0.205919	−	0.118888i	0.393494	−	0.919327i	$-0.371266\pi$
$283$	−3.46410	−	2.00000i	−0.205919	−	0.118888i	−0.599414	+	0.800439i	$0.704600\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−24.0000			−1.41915
$287$	23.3827	−	4.50000i	1.38024	−	0.265627i
$288$		−	2.00000i		−	0.117851i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	−13.8564	+	8.00000i	−0.810885	+	0.468165i
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$	−6.50000	+	2.59808i	−0.379088	+	0.151523i
$295$		0			0
$296$	−2.00000	−	3.46410i	−0.116248	−	0.201347i
$297$	−25.9808	−	15.0000i	−1.50756	−	0.870388i
$298$	−12.9904	−	7.50000i	−0.752513	−	0.434463i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	3.50000	+	18.1865i	0.201737	+	1.04825i
$302$			4.00000i			0.230174i
$303$	−12.9904	+	7.50000i	−0.746278	+	0.430864i
$304$	1.00000	−	1.73205i	0.0573539	−	0.0993399i
$305$		0			0
$306$		0			0
$307$			5.00000i			0.285365i	0.989769	+	0.142683i	$0.0455728\pi$
$307$			5.00000i			0.285365i	−0.989769	+	0.142683i	$0.954427\pi$
$308$	−10.3923	−	12.0000i	−0.592157	−	0.683763i
$309$	1.00000			0.0568880
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$	−3.46410	−	2.00000i	−0.196116	−	0.113228i
$313$	−6.92820	+	4.00000i	−0.391605	+	0.226093i	−0.682855	−	0.730554i	$-0.739262\pi$
$313$	−6.92820	+	4.00000i	−0.391605	+	0.226093i	0.291250	+	0.956647i	$0.405929\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	2.00000			0.112509
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	−0.178908	−	0.983866i	$-0.557257\pi$
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	0.762598	+	0.646872i	$0.223923\pi$
$318$	5.19615	+	3.00000i	0.291386	+	0.168232i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$	−15.0000			−0.837218
$322$	−2.59808	+	7.50000i	−0.144785	+	0.417959i
$323$		0			0
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	9.52628	−	5.50000i	0.526804	−	0.304151i
$328$			9.00000i			0.496942i
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−2.59808	−	1.50000i	−0.142588	−	0.0823232i
$333$	6.92820	+	4.00000i	0.379663	+	0.219199i
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$		0			0
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$		−	22.0000i		−	1.19842i	−0.800593	−	0.599208i	$-0.795482\pi$
$337$		−	22.0000i		−	1.19842i	0.800593	−	0.599208i	$-0.204518\pi$
$338$	2.59808	−	1.50000i	0.141317	−	0.0815892i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	24.0000	+	41.5692i	1.29967	+	2.25110i
$342$			4.00000i			0.216295i
$343$	15.5885	−	10.0000i	0.841698	−	0.539949i
$344$	−7.00000			−0.377415
$345$		0			0
$346$		0			0
$347$	−7.79423	−	4.50000i	−0.418416	−	0.241573i	0.275983	−	0.961162i	$-0.410997\pi$
$347$	−7.79423	−	4.50000i	−0.418416	−	0.241573i	−0.694399	+	0.719590i	$0.744330\pi$
$348$	2.59808	−	1.50000i	0.139272	−	0.0804084i
$349$	−17.0000			−0.909989			−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000			−0.909989			−0.454995	+	0.890494i	$0.650359\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	5.19615	−	3.00000i	0.276956	−	0.159901i
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	0.355303	−	0.934751i	$-0.384378\pi$
$353$	−5.19615	−	3.00000i	−0.276563	−	0.159674i	−0.631867	+	0.775077i	$0.717711\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$		0			0
$356$	−15.0000			−0.794998
$357$		0			0
$358$		−	24.0000i		−	1.26844i
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−9.52628	+	5.50000i	−0.500690	+	0.289074i
$363$		−	25.0000i		−	1.31216i
$364$	10.0000	+	3.46410i	0.524142	+	0.181568i
$365$		0			0
$366$	2.50000	+	4.33013i	0.130677	+	0.226339i
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.587680	−	0.809093i	$-0.699959\pi$
$368$	−2.59808	−	1.50000i	−0.135434	−	0.0781929i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$		0			0
$371$	−15.0000	−	5.19615i	−0.778761	−	0.269771i
$372$			8.00000i			0.414781i
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	−0.407630	−	0.913147i	$-0.633645\pi$
$373$	3.46410	−	2.00000i	0.179364	−	0.103556i	0.586994	+	0.809591i	$0.300311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			12.0000i			0.618031i
$378$	8.66025	+	10.0000i	0.445435	+	0.514344i
$379$	34.0000			1.74646			0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000			1.74646			0.873231	+	0.487306i	$0.162020\pi$
$380$		0			0
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	−5.19615	−	3.00000i	−0.265858	−	0.153493i
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	−0.129937	−	0.991522i	$-0.541478\pi$
$383$	12.9904	−	7.50000i	0.663777	−	0.383232i	0.793715	+	0.608290i	$0.208144\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−2.00000			−0.101797
$387$	12.1244	−	7.00000i	0.616316	−	0.355830i
$388$	12.1244	+	7.00000i	0.615521	+	0.355371i
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$		0			0
$392$	2.59808	+	6.50000i	0.131223	+	0.328300i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	−0.163876	−	0.986481i	$-0.552400\pi$
$397$	12.1244	−	7.00000i	0.608504	−	0.351320i	0.772380	+	0.635161i	$0.219066\pi$
$398$		−	4.00000i		−	0.200502i
$399$	1.00000	+	5.19615i	0.0500626	+	0.260133i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$	4.33013	+	2.50000i	0.215967	+	0.124689i
$403$	−27.7128	−	16.0000i	−1.38047	−	0.797017i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$	−6.00000	+	5.19615i	−0.297775	+	0.257881i
$407$			24.0000i			1.18964i
$408$		0			0
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	−0.980778	−	0.195127i	$-0.937488\pi$
$409$	−6.50000	+	11.2583i	−0.321404	+	0.556689i	0.659374	+	0.751815i	$0.270822\pi$
$410$		0			0
$411$	−6.00000	−	10.3923i	−0.295958	−	0.512615i
$412$		−	1.00000i		−	0.0492665i
$413$	−5.19615	+	15.0000i	−0.255686	+	0.738102i
$414$	6.00000			0.294884
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	8.66025	+	5.00000i	0.424094	+	0.244851i
$418$	−10.3923	+	6.00000i	−0.508304	+	0.293470i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	8.66025	−	5.00000i	0.421575	−	0.243396i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$		0			0
$426$	6.00000			0.290701
$427$	−8.66025	−	10.0000i	−0.419099	−	0.483934i
$428$			15.0000i			0.725052i
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	−4.33013	+	2.50000i	−0.208333	+	0.120281i
$433$			22.0000i			1.05725i	0.848855	+	0.528626i	$0.177293\pi$
$433$			22.0000i			1.05725i	−0.848855	+	0.528626i	$0.822707\pi$
$434$	−4.00000	−	20.7846i	−0.192006	−	0.997693i
$435$		0			0
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	5.19615	+	3.00000i	0.248566	+	0.143509i
$438$	13.8564	+	8.00000i	0.662085	+	0.382255i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	−11.0000	−	8.66025i	−0.523810	−	0.412393i
$442$		0			0
$443$	−18.1865	+	10.5000i	−0.864068	+	0.498870i	−0.865373	−	0.501129i	$-0.832918\pi$
$443$	−18.1865	+	10.5000i	−0.864068	+	0.498870i	0.00130426	+	0.999999i	$0.499585\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$		0			0
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$			15.0000i			0.709476i
$448$	−2.59808	+	0.500000i	−0.122748	+	0.0236228i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	27.0000	−	46.7654i	1.27138	−	2.20210i
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$	3.46410	−	2.00000i	0.162758	−	0.0939682i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.316579	−	0.948566i	$-0.397466\pi$
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.979772	+	0.200118i	$0.0641325\pi$
$458$	−12.1244	−	7.00000i	−0.566534	−	0.327089i
$459$		0			0
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$	−5.19615	+	15.0000i	−0.241747	+	0.697863i
$463$			13.0000i			0.604161i	0.953282	+	0.302081i	$0.0976812\pi$
$463$			13.0000i			0.604161i	−0.953282	+	0.302081i	$0.902319\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−12.9904	+	7.50000i	−0.601123	+	0.347059i	−0.769483	−	0.638667i	$-0.779486\pi$
$467$	−12.9904	+	7.50000i	−0.601123	+	0.347059i	0.168360	+	0.985726i	$0.446153\pi$
$468$		−	8.00000i		−	0.369800i
$469$	−12.5000	−	4.33013i	−0.577196	−	0.199947i
$470$		0			0
$471$	11.0000	+	19.0526i	0.506853	+	0.877896i
$472$	−5.19615	−	3.00000i	−0.239172	−	0.138086i
$473$	36.3731	+	21.0000i	1.67244	+	0.965581i
$474$	−1.00000	−	1.73205i	−0.0459315	−	0.0795557i
$475$		0			0
$476$		0			0
$477$			12.0000i			0.549442i
$478$	10.3923	−	6.00000i	0.475333	−	0.274434i
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		−	2.00000i		−	0.0910975i
$483$	7.79423	−	1.50000i	0.354650	−	0.0682524i
$484$	−25.0000			−1.13636
$485$		0			0
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	0.779936	−	0.625859i	$-0.215252\pi$
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	−0.152042	+	0.988374i	$0.548585\pi$
$488$	4.33013	−	2.50000i	0.196016	−	0.113170i
$489$	4.00000			0.180886
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	7.79423	−	4.50000i	0.351391	−	0.202876i
$493$		0			0
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$		0			0
$496$	8.00000			0.359211
$497$	−15.5885	+	3.00000i	−0.699238	+	0.134568i
$498$			3.00000i			0.134433i
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$	10.3923	−	6.00000i	0.463831	−	0.267793i
$503$		−	21.0000i		−	0.936344i	−0.883637	−	0.468172i	$-0.844913\pi$
$503$		−	21.0000i		−	0.936344i	0.883637	−	0.468172i	$-0.155087\pi$
$504$	4.00000	−	3.46410i	0.178174	−	0.154303i
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$	−2.59808	−	1.50000i	−0.115385	−	0.0666173i
$508$	6.92820	+	4.00000i	0.307389	+	0.177471i
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	0.999220	−	0.0394971i	$-0.0125756\pi$
$509$	10.5000	+	18.1865i	0.465404	+	0.806104i	−0.533815	+	0.845601i	$0.679242\pi$
$510$		0			0
$511$	−40.0000	−	13.8564i	−1.76950	−	0.612971i
$512$		−	1.00000i		−	0.0441942i
$513$	8.66025	−	5.00000i	0.382360	−	0.220755i
$514$		0			0
$515$		0			0
$516$	3.50000	+	6.06218i	0.154079	+	0.266872i
$517$		0			0
$518$	3.46410	−	10.0000i	0.152204	−	0.439375i
$519$		0			0
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	5.19615	+	3.00000i	0.227429	+	0.131306i
$523$	24.2487	−	14.0000i	1.06032	−	0.612177i	0.134801	−	0.990873i	$-0.456961\pi$
$523$	24.2487	−	14.0000i	1.06032	−	0.612177i	0.925521	+	0.378695i	$0.123627\pi$
$524$		0			0
$525$		0			0
$526$	21.0000			0.915644
$527$		0			0
$528$	−5.19615	−	3.00000i	−0.226134	−	0.130558i
$529$	−7.00000	+	12.1244i	−0.304348	+	0.527146i
$530$		0			0
$531$	12.0000			0.520756
$532$	5.19615	−	1.00000i	0.225282	−	0.0433555i
$533$			36.0000i			1.55933i
$534$	7.50000	+	12.9904i	0.324557	+	0.562149i
$535$		0			0
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	−20.7846	+	12.0000i	−0.896922	+	0.517838i
$538$			15.0000i			0.646696i
$539$	6.00000	−	41.5692i	0.258438	−	1.79051i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$	1.73205	+	1.00000i	0.0743980	+	0.0429537i
$543$	9.52628	+	5.50000i	0.408812	+	0.236028i
$544$		0			0
$545$		0			0
$546$	−2.00000	−	10.3923i	−0.0855921	−	0.444750i
$547$		−	19.0000i		−	0.812381i	−0.913788	−	0.406191i	$-0.866857\pi$
$547$		−	19.0000i		−	0.812381i	0.913788	−	0.406191i	$-0.133143\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$			3.00000i			0.127688i
$553$	3.46410	+	4.00000i	0.147309	+	0.170097i
$554$	8.00000			0.339887
$555$		0			0
$556$	5.00000	−	8.66025i	0.212047	−	0.367277i
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	0.792469	−	0.609912i	$-0.208795\pi$
$557$	15.5885	+	9.00000i	0.660504	+	0.381342i	−0.131965	+	0.991254i	$0.542129\pi$
$558$	−13.8564	+	8.00000i	−0.586588	+	0.338667i
$559$	−28.0000			−1.18427
$560$		0			0
$561$		0			0
$562$	5.19615	−	3.00000i	0.219186	−	0.126547i
$563$	23.3827	+	13.5000i	0.985463	+	0.568957i	0.903915	−	0.427712i	$-0.140680\pi$
$563$	23.3827	+	13.5000i	0.985463	+	0.568957i	0.0815478	+	0.996669i	$0.474014\pi$
$564$		0			0
$565$		0			0
$566$	4.00000			0.168133
$567$	−0.866025	+	2.50000i	−0.0363696	+	0.104990i
$568$		−	6.00000i		−	0.251754i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	−0.538642	−	0.842535i	$-0.681062\pi$
$571$	11.0000	−	19.0526i	0.460336	−	0.797325i	0.998978	+	0.0452101i	$0.0143957\pi$
$572$	20.7846	−	12.0000i	0.869048	−	0.501745i
$573$			6.00000i			0.250654i
$574$	−18.0000	+	15.5885i	−0.751305	+	0.650650i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−22.5167	−	13.0000i	−0.937381	−	0.541197i	−0.0482425	−	0.998836i	$-0.515362\pi$
$577$	−22.5167	−	13.0000i	−0.937381	−	0.541197i	−0.889138	+	0.457639i	$0.848695\pi$
$578$	14.7224	+	8.50000i	0.612372	+	0.353553i
$579$	1.00000	+	1.73205i	0.0415586	+	0.0719816i
$580$		0			0
$581$	−1.50000	−	7.79423i	−0.0622305	−	0.323359i
$582$		−	14.0000i		−	0.580319i
$583$	−31.1769	+	18.0000i	−1.29122	+	0.745484i
$584$	8.00000	−	13.8564i	0.331042	−	0.573382i
$585$		0			0
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$			12.0000i			0.495293i	0.968850	+	0.247647i	$0.0796572\pi$
$587$			12.0000i			0.495293i	−0.968850	+	0.247647i	$0.920343\pi$
$588$	4.33013	−	5.50000i	0.178571	−	0.226816i
$589$	−16.0000			−0.659269
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	3.46410	+	2.00000i	0.142374	+	0.0821995i
$593$	−5.19615	+	3.00000i	−0.213380	+	0.123195i	−0.602881	−	0.797831i	$-0.705981\pi$
$593$	−5.19615	+	3.00000i	−0.213380	+	0.123195i	0.389501	+	0.921026i	$0.372647\pi$
$594$	30.0000			1.23091
$595$		0			0
$596$	15.0000			0.614424
$597$	−3.46410	+	2.00000i	−0.141776	+	0.0818546i
$598$	−10.3923	−	6.00000i	−0.424973	−	0.245358i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	−46.0000			−1.87638			−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000			−1.87638			−0.938190	+	0.346122i	$0.887498\pi$
$602$	−12.1244	−	14.0000i	−0.494152	−	0.570597i
$603$			10.0000i			0.407231i
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$		0			0
$606$	7.50000	−	12.9904i	0.304667	−	0.527698i
$607$	19.9186	−	11.5000i	0.808470	−	0.466771i	−0.0379540	−	0.999279i	$-0.512084\pi$
$607$	19.9186	−	11.5000i	0.808470	−	0.466771i	0.846424	+	0.532509i	$0.178751\pi$
$608$			2.00000i			0.0811107i
$609$	7.50000	+	2.59808i	0.303915	+	0.105279i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−13.8564	−	8.00000i	−0.559655	−	0.323117i	0.193352	−	0.981129i	$-0.438064\pi$
$613$	−13.8564	−	8.00000i	−0.559655	−	0.323117i	−0.753007	+	0.658012i	$0.771397\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$		0			0
$616$	15.0000	+	5.19615i	0.604367	+	0.209359i
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$	−0.866025	+	0.500000i	−0.0348367	+	0.0201129i
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	−0.690365	−	0.723462i	$-0.742550\pi$
$619$	7.00000	−	12.1244i	0.281354	−	0.487319i	0.971718	+	0.236143i	$0.0758832\pi$
$620$		0			0
$621$	−7.50000	−	12.9904i	−0.300965	−	0.521286i
$622$			18.0000i			0.721734i
$623$	−25.9808	−	30.0000i	−1.04090	−	1.20192i
$624$	4.00000			0.160128
$625$		0			0
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	10.3923	+	6.00000i	0.415029	+	0.239617i
$628$	19.0526	−	11.0000i	0.760280	−	0.438948i
$629$		0			0
$630$		0			0
$631$	14.0000			0.557331			0.278666	−	0.960388i	$-0.410108\pi$
$631$	14.0000			0.557331			0.278666	+	0.960388i	$0.410108\pi$
$632$	−1.73205	+	1.00000i	−0.0688973	+	0.0397779i
$633$	−8.66025	−	5.00000i	−0.344214	−	0.198732i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	10.3923	+	26.0000i	0.411758	+	1.03016i
$638$			18.0000i			0.712627i
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$641$	1.50000	−	2.59808i	0.0592464	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$642$	12.9904	−	7.50000i	0.512689	−	0.296001i
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$	−1.50000	−	7.79423i	−0.0591083	−	0.307136i
$645$		0			0
$646$		0			0
$647$	−2.59808	−	1.50000i	−0.102141	−	0.0589711i	0.448059	−	0.894004i	$-0.352115\pi$
$647$	−2.59808	−	1.50000i	−0.102141	−	0.0589711i	−0.550200	+	0.835033i	$0.685449\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$		0			0
$651$	−16.0000	+	13.8564i	−0.627089	+	0.543075i
$652$		−	4.00000i		−	0.156652i
$653$	41.5692	−	24.0000i	1.62673	−	0.939193i	0.641669	−	0.766982i	$-0.278242\pi$
$653$	41.5692	−	24.0000i	1.62673	−	0.939193i	0.985060	−	0.172211i	$-0.0550911\pi$
$654$	−5.50000	+	9.52628i	−0.215067	+	0.372507i
$655$		0			0
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$			32.0000i			1.24844i
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	0.123974	+	0.992286i	$0.460436\pi$
$661$	−20.5000	+	35.5070i	−0.797358	+	1.38106i	−0.921331	+	0.388778i	$0.872897\pi$
$662$	−24.2487	−	14.0000i	−0.942453	−	0.544125i
$663$		0			0
$664$	3.00000			0.116423
$665$		0			0
$666$	−8.00000			−0.309994
$667$	7.79423	−	4.50000i	0.301794	−	0.174241i
$668$	−2.59808	−	1.50000i	−0.100523	−	0.0580367i
$669$	−14.0000	+	24.2487i	−0.541271	+	0.937509i
$670$		0			0
$671$	−30.0000			−1.15814
$672$	1.73205	+	2.00000i	0.0668153	+	0.0771517i
$673$		−	8.00000i		−	0.308377i	−0.988041	−	0.154189i	$-0.950724\pi$
$673$		−	8.00000i		−	0.308377i	0.988041	−	0.154189i	$-0.0492764\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	−0.286820	−	0.957984i	$-0.592598\pi$
$677$	10.3923	−	6.00000i	0.399409	−	0.230599i	0.686229	+	0.727386i	$0.259265\pi$
$678$			6.00000i			0.230429i
$679$	7.00000	+	36.3731i	0.268635	+	1.39587i
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	−41.5692	−	24.0000i	−1.59177	−	0.919007i
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	0.641651	−	0.766997i	$-0.278250\pi$
$683$	7.79423	+	4.50000i	0.298238	+	0.172188i	−0.343413	+	0.939184i	$0.611583\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$			14.0000i			0.534133i
$688$	6.06218	−	3.50000i	0.231118	−	0.133436i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$	−31.1769	+	6.00000i	−1.18431	+	0.227921i
$694$	9.00000			0.341635
$695$		0			0
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$		0			0
$698$	14.7224	−	8.50000i	0.557252	−	0.321730i
$699$	12.0000			0.453882
$700$		0			0
$701$	−3.00000			−0.113308			−0.0566542	−	0.998394i	$-0.518043\pi$
$701$	−3.00000			−0.113308			−0.0566542	+	0.998394i	$0.518043\pi$
$702$	−17.3205	+	10.0000i	−0.653720	+	0.377426i
$703$	−6.92820	−	4.00000i	−0.261302	−	0.150863i
$704$	−3.00000	+	5.19615i	−0.113067	+	0.195837i
$705$		0			0
$706$	6.00000			0.225813
$707$	−12.9904	+	37.5000i	−0.488554	+	1.41033i
$708$			6.00000i			0.225494i
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	0.413114	−	0.910679i	$-0.364441\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	12.9904	−	7.50000i	0.486835	−	0.281074i
$713$			24.0000i			0.898807i
$714$		0			0
$715$		0			0
$716$	12.0000	+	20.7846i	0.448461	+	0.776757i
$717$	−10.3923	−	6.00000i	−0.388108	−	0.224074i
$718$	−20.7846	−	12.0000i	−0.775675	−	0.447836i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	2.00000	−	1.73205i	0.0744839	−	0.0645049i
$722$			15.0000i			0.558242i
$723$	−1.73205	+	1.00000i	−0.0644157	+	0.0371904i
$724$	5.50000	−	9.52628i	0.204406	−	0.354041i
$725$		0			0
$726$	12.5000	+	21.6506i	0.463919	+	0.803530i
$727$		−	19.0000i		−	0.704671i	−0.935874	−	0.352335i	$-0.885388\pi$
$727$		−	19.0000i		−	0.704671i	0.935874	−	0.352335i	$-0.114612\pi$
$728$	−10.3923	+	2.00000i	−0.385164	+	0.0741249i
$729$	−13.0000			−0.481481
$730$		0			0
$731$		0			0
$732$	−4.33013	−	2.50000i	−0.160046	−	0.0924027i
$733$	29.4449	−	17.0000i	1.08757	−	0.627909i	0.154642	−	0.987971i	$-0.450578\pi$
$733$	29.4449	−	17.0000i	1.08757	−	0.627909i	0.932929	+	0.360061i	$0.117244\pi$
$734$	35.0000			1.29187
$735$		0			0
$736$	3.00000			0.110581
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$	15.5885	+	9.00000i	0.573819	+	0.331295i
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	−0.521475	−	0.853266i	$-0.674618\pi$
$739$	13.0000	−	22.5167i	0.478213	−	0.828289i	0.999688	+	0.0249776i	$0.00795146\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$	15.5885	−	3.00000i	0.572270	−	0.110133i
$743$		−	39.0000i		−	1.43077i	−0.698730	−	0.715386i	$-0.746251\pi$
$743$		−	39.0000i		−	1.43077i	0.698730	−	0.715386i	$-0.253749\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$		0			0
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$	−5.19615	+	3.00000i	−0.190117	+	0.109764i
$748$		0			0
$749$	−30.0000	+	25.9808i	−1.09618	+	0.949316i
$750$		0			0
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$		0			0
$753$	−10.3923	−	6.00000i	−0.378717	−	0.218652i
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$		0			0
$756$	−12.5000	−	4.33013i	−0.454621	−	0.157485i
$757$		−	28.0000i		−	1.01768i	−0.860862	−	0.508839i	$-0.830075\pi$
$757$		−	28.0000i		−	1.01768i	0.860862	−	0.508839i	$-0.169925\pi$
$758$	−29.4449	+	17.0000i	−1.06949	+	0.617468i
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		−	8.00000i		−	0.289809i
$763$	9.52628	−	27.5000i	0.344874	−	0.995567i
$764$	6.00000			0.217072
$765$		0			0
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	−20.7846	−	12.0000i	−0.750489	−	0.433295i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$		0			0
$772$	1.73205	−	1.00000i	0.0623379	−	0.0359908i
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	0.301326	−	0.953521i	$-0.402571\pi$
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	−0.675111	+	0.737716i	$0.735904\pi$
$774$	−7.00000	+	12.1244i	−0.251610	+	0.435801i
$775$		0			0
$776$	−14.0000			−0.502571
$777$	−10.3923	+	2.00000i	−0.372822	+	0.0717496i
$778$		−	30.0000i		−	1.07555i
$779$	9.00000	+	15.5885i	0.322458	+	0.558514i
$780$		0			0
$781$	−18.0000	+	31.1769i	−0.644091	+	1.11560i
$782$		0			0
$783$		−	15.0000i		−	0.536056i
$784$	−5.50000	−	4.33013i	−0.196429	−	0.154647i
$785$		0			0
$786$		0			0
$787$	37.2391	+	21.5000i	1.32743	+	0.766392i	0.984902	−	0.173115i	$-0.0553833\pi$
$787$	37.2391	+	21.5000i	1.32743	+	0.766392i	0.342529	+	0.939507i	$0.388717\pi$
$788$	−5.19615	−	3.00000i	−0.185105	−	0.106871i
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$		0			0
$791$	−3.00000	−	15.5885i	−0.106668	−	0.554262i
$792$		−	12.0000i		−	0.426401i
$793$	17.3205	−	10.0000i	0.615069	−	0.355110i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$		−	48.0000i		−	1.70025i	−0.526583	−	0.850124i	$-0.676527\pi$
$797$		−	48.0000i		−	1.70025i	0.526583	−	0.850124i	$-0.323473\pi$
$798$	−3.46410	−	4.00000i	−0.122628	−	0.141598i
$799$		0			0
$800$		0			0
$801$	−15.0000	+	25.9808i	−0.529999	+	0.917985i
$802$	12.9904	+	7.50000i	0.458706	+	0.264834i
$803$	−83.1384	+	48.0000i	−2.93389	+	1.69388i
$804$	−5.00000			−0.176336
$805$		0			0
$806$	32.0000			1.12715
$807$	12.9904	−	7.50000i	0.457283	−	0.264013i
$808$	−12.9904	−	7.50000i	−0.457000	−	0.263849i
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	−0.620274	−	0.784385i	$-0.712979\pi$
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	0.989434	+	0.144981i	$0.0463120\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	2.59808	−	7.50000i	0.0911746	−	0.263198i
$813$		−	2.00000i		−	0.0701431i
$814$	−12.0000	−	20.7846i	−0.420600	−	0.728500i
$815$		0			0
$816$		0			0
$817$	−12.1244	+	7.00000i	−0.424178	+	0.244899i
$818$		−	13.0000i		−	0.454534i
$819$	16.0000	−	13.8564i	0.559085	−	0.484182i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	10.3923	+	6.00000i	0.362473	+	0.209274i
$823$	−16.4545	−	9.50000i	−0.573567	−	0.331149i	0.185006	−	0.982737i	$-0.440770\pi$
$823$	−16.4545	−	9.50000i	−0.573567	−	0.331149i	−0.758573	+	0.651588i	$0.774103\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$		0			0
$826$	−3.00000	−	15.5885i	−0.104383	−	0.542392i
$827$			15.0000i			0.521601i	0.965393	+	0.260801i	$0.0839865\pi$
$827$			15.0000i			0.521601i	−0.965393	+	0.260801i	$0.916014\pi$
$828$	−5.19615	+	3.00000i	−0.180579	+	0.104257i
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$		−	4.00000i		−	0.138675i
$833$		0			0
$834$	−10.0000			−0.346272
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	34.6410	+	20.0000i	1.19737	+	0.691301i
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−14.7224	+	8.50000i	−0.507369	+	0.292929i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	−5.00000	+	8.66025i	−0.172107	+	0.298098i
$845$		0			0
$846$		0			0
$847$	−43.3013	−	50.0000i	−1.48785	−	1.71802i
$848$			6.00000i			0.206041i
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$	−5.19615	+	3.00000i	−0.178017	+	0.102778i
$853$			46.0000i			1.57501i	0.616308	+	0.787505i	$0.288628\pi$
$853$			46.0000i			1.57501i	−0.616308	+	0.787505i	$0.711372\pi$
$854$	12.5000	+	4.33013i	0.427741	+	0.148174i
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	−5.19615	−	3.00000i	−0.177497	−	0.102478i	0.408619	−	0.912705i	$-0.366010\pi$
$857$	−5.19615	−	3.00000i	−0.177497	−	0.102478i	−0.586116	+	0.810227i	$0.699344\pi$
$858$	−20.7846	−	12.0000i	−0.709575	−	0.409673i
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	0.998549	+	0.0538535i	$0.0171504\pi$
$859$	16.0000	+	27.7128i	0.545913	+	0.945549i	−0.452636	+	0.891695i	$0.649516\pi$
$860$		0			0
$861$	22.5000	+	7.79423i	0.766798	+	0.265627i
$862$		−	30.0000i		−	1.02180i
$863$	−23.3827	+	13.5000i	−0.795956	+	0.459545i	−0.842055	−	0.539392i	$-0.818654\pi$
$863$	−23.3827	+	13.5000i	−0.795956	+	0.459545i	0.0460992	+	0.998937i	$0.485321\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	−11.0000	−	19.0526i	−0.373795	−	0.647432i
$867$		−	17.0000i		−	0.577350i
$868$	13.8564	+	16.0000i	0.470317	+	0.543075i
$869$	12.0000			0.407072
$870$		0			0
$871$	10.0000	−	17.3205i	0.338837	−	0.586883i
$872$	9.52628	+	5.50000i	0.322601	+	0.186254i
$873$	24.2487	−	14.0000i	0.820695	−	0.473828i
$874$	−6.00000			−0.202953
$875$		0			0
$876$	−16.0000			−0.540590
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	−0.470471	−	0.882415i	$-0.655916\pi$
$877$	1.73205	−	1.00000i	0.0584872	−	0.0337676i	0.528958	+	0.848648i	$0.322583\pi$
$878$	24.2487	+	14.0000i	0.818354	+	0.472477i
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$		0			0
$881$	57.0000			1.92038			0.960189	−	0.279350i	$-0.0901189\pi$
$881$	57.0000			1.92038			0.960189	+	0.279350i	$0.0901189\pi$
$882$	13.8564	+	2.00000i	0.466569	+	0.0673435i
$883$			52.0000i			1.74994i	0.484178	+	0.874970i	$0.339119\pi$
$883$			52.0000i			1.74994i	−0.484178	+	0.874970i	$0.660881\pi$
$884$		0			0
$885$		0			0
$886$	10.5000	−	18.1865i	0.352754	−	0.610989i
$887$	−18.1865	+	10.5000i	−0.610644	+	0.352555i	−0.773217	−	0.634141i	$-0.781354\pi$
$887$	−18.1865	+	10.5000i	−0.610644	+	0.352555i	0.162573	+	0.986696i	$0.448021\pi$
$888$		−	4.00000i		−	0.134231i
$889$	4.00000	+	20.7846i	0.134156	+	0.697093i
$890$		0			0
$891$	3.00000	+	5.19615i	0.100504	+	0.174078i
$892$	24.2487	+	14.0000i	0.811907	+	0.468755i
$893$		0			0
$894$	−7.50000	−	12.9904i	−0.250838	−	0.434463i
$895$		0			0
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$			12.0000i			0.400668i
$898$	−7.79423	+	4.50000i	−0.260097	+	0.150167i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$		0			0
$902$			54.0000i			1.79800i
$903$	−6.06218	+	17.5000i	−0.201737	+	0.582364i
$904$	6.00000			0.199557
$905$		0			0
$906$	−2.00000	+	3.46410i	−0.0664455	+	0.115087i
$907$	21.6506	+	12.5000i	0.718898	+	0.415056i	0.814347	−	0.580379i	$-0.197095\pi$
$907$	21.6506	+	12.5000i	0.718898	+	0.415056i	−0.0954492	+	0.995434i	$0.530429\pi$
$908$	10.3923	−	6.00000i	0.344881	−	0.199117i
$909$	30.0000			0.995037
$910$		0			0
$911$	18.0000			0.596367			0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000			0.596367			0.298183	+	0.954509i	$0.403619\pi$
$912$	1.73205	−	1.00000i	0.0573539	−	0.0331133i
$913$	−15.5885	−	9.00000i	−0.515903	−	0.297857i
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	14.0000			0.462573
$917$		0			0
$918$		0			0
$919$	7.00000	+	12.1244i	0.230909	+	0.399946i	0.958076	−	0.286515i	$-0.0924968\pi$
$919$	7.00000	+	12.1244i	0.230909	+	0.399946i	−0.727167	+	0.686461i	$0.759163\pi$
$920$		0			0
$921$	−2.50000	+	4.33013i	−0.0823778	+	0.142683i
$922$	−15.5885	+	9.00000i	−0.513378	+	0.296399i
$923$		−	24.0000i		−	0.789970i
$924$	−3.00000	−	15.5885i	−0.0986928	−	0.512823i
$925$		0			0
$926$	−6.50000	−	11.2583i	−0.213603	−	0.369972i
$927$	−1.73205	−	1.00000i	−0.0568880	−	0.0328443i
$928$	2.59808	+	1.50000i	0.0852860	+	0.0492399i
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$	11.0000	+	8.66025i	0.360510	+	0.283828i
$932$		−	12.0000i		−	0.393073i
$933$	15.5885	−	9.00000i	0.510343	−	0.294647i
$934$	7.50000	−	12.9904i	0.245407	−	0.425058i
$935$		0			0
$936$	4.00000	+	6.92820i	0.130744	+	0.226455i
$937$		−	28.0000i		−	0.914720i	−0.889282	−	0.457360i	$-0.848795\pi$
$937$		−	28.0000i		−	0.914720i	0.889282	−	0.457360i	$-0.151205\pi$
$938$	12.9904	−	2.50000i	0.424151	−	0.0816279i
$939$	−8.00000			−0.261070
$940$		0			0
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	−0.812975	−	0.582298i	$-0.802154\pi$
$941$	3.00000	−	5.19615i	0.0977972	−	0.169390i	0.910773	+	0.412908i	$0.135487\pi$
$942$	−19.0526	−	11.0000i	−0.620766	−	0.358399i
$943$	23.3827	−	13.5000i	0.761445	−	0.439620i
$944$	6.00000			0.195283
$945$		0			0
$946$	−42.0000			−1.36554
$947$	−2.59808	+	1.50000i	−0.0844261	+	0.0487435i	−0.541619	−	0.840624i	$-0.682188\pi$
$947$	−2.59808	+	1.50000i	−0.0844261	+	0.0487435i	0.457193	+	0.889368i	$0.348855\pi$
$948$	1.73205	+	1.00000i	0.0562544	+	0.0324785i
$949$	32.0000	−	55.4256i	1.03876	−	1.79919i
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$		−	60.0000i		−	1.94359i	−0.235826	−	0.971795i	$-0.575780\pi$
$953$		−	60.0000i		−	1.94359i	0.235826	−	0.971795i	$-0.424220\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$		0			0
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$	15.5885	−	9.00000i	0.503903	−	0.290929i
$958$			12.0000i			0.387702i
$959$	−30.0000	−	10.3923i	−0.968751	−	0.335585i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	13.8564	+	8.00000i	0.446748	+	0.257930i
$963$	25.9808	+	15.0000i	0.837218	+	0.483368i
$964$	1.00000	+	1.73205i	0.0322078	+	0.0557856i
$965$		0			0
$966$	−6.00000	+	5.19615i	−0.193047	+	0.167183i
$967$			35.0000i			1.12552i	0.826619	+	0.562762i	$0.190261\pi$
$967$			35.0000i			1.12552i	−0.826619	+	0.562762i	$0.809739\pi$
$968$	21.6506	−	12.5000i	0.695878	−	0.401765i
$969$		0			0
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$			16.0000i			0.513200i
$973$	25.9808	−	5.00000i	0.832905	−	0.160293i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	−2.50000	+	4.33013i	−0.0800230	+	0.138604i
$977$	5.19615	+	3.00000i	0.166240	+	0.0959785i	0.580812	−	0.814038i	$-0.302735\pi$
$977$	5.19615	+	3.00000i	0.166240	+	0.0959785i	−0.414572	+	0.910017i	$0.636069\pi$
$978$	−3.46410	+	2.00000i	−0.110770	+	0.0639529i
$979$	−90.0000			−2.87641
$980$		0			0
$981$	−22.0000			−0.702406
$982$		0			0
$983$	33.7750	+	19.5000i	1.07725	+	0.621953i	0.930155	−	0.367168i	$-0.119673\pi$
$983$	33.7750	+	19.5000i	1.07725	+	0.621953i	0.147100	+	0.989122i	$0.453006\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$		0			0
$986$		0			0
$987$		0			0
$988$			8.00000i			0.254514i
$989$	10.5000	+	18.1865i	0.333881	+	0.578298i
$990$		0			0
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	−0.553308	−	0.832977i	$-0.686635\pi$
$991$	14.0000	−	24.2487i	0.444725	−	0.770286i	0.998033	+	0.0626908i	$0.0199682\pi$
$992$	−6.92820	+	4.00000i	−0.219971	+	0.127000i
$993$			28.0000i			0.888553i
$994$	12.0000	−	10.3923i	0.380617	−	0.329624i
$995$		0			0
$996$	−1.50000	−	2.59808i	−0.0475293	−	0.0823232i
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	0.295567	−	0.955322i	$-0.404491\pi$
$997$	−12.1244	−	7.00000i	−0.383982	−	0.221692i	−0.679549	+	0.733630i	$0.737825\pi$
$998$	19.0526	+	11.0000i	0.603098	+	0.348199i
$999$	10.0000	+	17.3205i	0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.j.b.249.1		4
5.2	odd	4		350.2.e.e.151.1		2
5.3	odd	4		70.2.e.c.11.1	✓	2
5.4	even	2	inner	350.2.j.b.249.2		4
7.2	even	3	inner	350.2.j.b.149.2		4
7.3	odd	6		2450.2.c.l.99.1		2
7.4	even	3		2450.2.c.g.99.1		2
15.8	even	4		630.2.k.b.361.1		2
20.3	even	4		560.2.q.g.81.1		2
35.2	odd	12		350.2.e.e.51.1		2
35.3	even	12		490.2.a.b.1.1		1
35.4	even	6		2450.2.c.g.99.2		2
35.9	even	6	inner	350.2.j.b.149.1		4
35.13	even	4		490.2.e.h.361.1		2
35.17	even	12		2450.2.a.bc.1.1		1
35.18	odd	12		490.2.a.c.1.1		1
35.23	odd	12		70.2.e.c.51.1	yes	2
35.24	odd	6		2450.2.c.l.99.2		2
35.32	odd	12		2450.2.a.w.1.1		1
35.33	even	12		490.2.e.h.471.1		2
105.23	even	12		630.2.k.b.541.1		2
105.38	odd	12		4410.2.a.bd.1.1		1
105.53	even	12		4410.2.a.bm.1.1		1
140.3	odd	12		3920.2.a.bc.1.1		1
140.23	even	12		560.2.q.g.401.1		2
140.123	even	12		3920.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.c.11.1	✓	2	5.3	odd	4
70.2.e.c.51.1	yes	2	35.23	odd	12
350.2.e.e.51.1		2	35.2	odd	12
350.2.e.e.151.1		2	5.2	odd	4
350.2.j.b.149.1		4	35.9	even	6	inner
350.2.j.b.149.2		4	7.2	even	3	inner
350.2.j.b.249.1		4	1.1	even	1	trivial
350.2.j.b.249.2		4	5.4	even	2	inner
490.2.a.b.1.1		1	35.3	even	12
490.2.a.c.1.1		1	35.18	odd	12
490.2.e.h.361.1		2	35.13	even	4
490.2.e.h.471.1		2	35.33	even	12
560.2.q.g.81.1		2	20.3	even	4
560.2.q.g.401.1		2	140.23	even	12
630.2.k.b.361.1		2	15.8	even	4
630.2.k.b.541.1		2	105.23	even	12
2450.2.a.w.1.1		1	35.32	odd	12
2450.2.a.bc.1.1		1	35.17	even	12
2450.2.c.g.99.1		2	7.4	even	3
2450.2.c.g.99.2		2	35.4	even	6
2450.2.c.l.99.1		2	7.3	odd	6
2450.2.c.l.99.2		2	35.24	odd	6
3920.2.a.p.1.1		1	140.123	even	12
3920.2.a.bc.1.1		1	140.3	odd	12
4410.2.a.bd.1.1		1	105.38	odd	12
4410.2.a.bm.1.1		1	105.53	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.00000 - 1.73205i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{18} +(1.00000 + 1.73205i) q^{19} +(2.50000 + 0.866025i) q^{21} +6.00000i q^{22} +(2.59808 - 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -5.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +3.00000 q^{29} +(-4.00000 + 6.92820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} -2.00000 q^{36} +(-3.46410 + 2.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +9.00000 q^{41} +(-2.59808 + 0.500000i) q^{42} +7.00000i q^{43} +(-3.00000 - 5.19615i) q^{44} +(-1.50000 + 2.59808i) q^{46} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(3.46410 + 2.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(2.50000 + 4.33013i) q^{54} +(0.500000 + 2.59808i) q^{56} +2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-2.50000 - 4.33013i) q^{61} -8.00000i q^{62} +(-3.46410 - 4.00000i) q^{63} -1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(-4.33013 - 2.50000i) q^{67} +3.00000 q^{69} -6.00000 q^{71} +(1.73205 - 1.00000i) q^{72} +(-13.8564 - 8.00000i) q^{73} +(2.00000 - 3.46410i) q^{74} +2.00000 q^{76} +(5.19615 - 15.0000i) q^{77} -4.00000i q^{78} +(1.00000 + 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-7.79423 + 4.50000i) q^{82} -3.00000i q^{83} +(2.00000 - 1.73205i) q^{84} +(-3.50000 - 6.06218i) q^{86} +(2.59808 + 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} -3.00000i q^{92} +(-6.92820 + 4.00000i) q^{93} +(0.500000 + 0.866025i) q^{96} +14.0000i q^{97} +(-4.33013 + 5.50000i) q^{98} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{6} - 4 q^{9} + 12 q^{11} - 8 q^{14} - 2 q^{16} + 4 q^{19} + 10 q^{21} - 2 q^{24} - 8 q^{26} + 12 q^{29} - 16 q^{31} - 8 q^{36} - 8 q^{39} + 36 q^{41} - 12 q^{44} - 6 q^{46} + 26 q^{49}+ \cdots - 48 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^6 - 4 * q^9 + 12 * q^11 - 8 * q^14 - 2 * q^16 + 4 * q^19 + 10 * q^21 - 2 * q^24 - 8 * q^26 + 12 * q^29 - 16 * q^31 - 8 * q^36 - 8 * q^39 + 36 * q^41 - 12 * q^44 - 6 * q^46 + 26 * q^49 + 10 * q^54 + 2 * q^56 - 12 * q^59 - 10 * q^61 - 4 * q^64 - 12 * q^66 + 12 * q^69 - 24 * q^71 + 8 * q^74 + 8 * q^76 + 4 * q^79 - 2 * q^81 + 8 * q^84 - 14 * q^86 - 30 * q^89 + 8 * q^91 + 2 * q^96 - 48 * q^99

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