LMFDB - Embedded newform 525.2.r.c.424.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (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:	$4.19214610612$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.424
Dual form			525.2.r.c.499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.866025 - 0.500000i) q^{12} -3.00000i q^{13} +(2.00000 - 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(2.50000 + 0.866025i) q^{21} +(1.73205 - 1.00000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(1.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +8.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(4.33013 + 2.50000i) q^{32} -2.00000 q^{34} -1.00000 q^{36} +(-6.06218 + 3.50000i) q^{37} +(-0.866025 - 0.500000i) q^{38} +(-1.50000 + 2.59808i) q^{39} +(-2.59808 + 0.500000i) q^{42} -8.00000i q^{43} +(-1.00000 + 1.73205i) q^{46} +(8.66025 - 5.00000i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(2.59808 + 1.50000i) q^{52} +(12.1244 + 7.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 + 7.79423i) q^{56} -1.00000i q^{57} +(-6.92820 + 4.00000i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-3.50000 - 6.06218i) q^{61} +8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} -7.00000 q^{64} +(-4.33013 - 2.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} -2.00000 q^{69} -12.0000 q^{71} +(2.59808 - 1.50000i) q^{72} +(9.52628 + 5.50000i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{76} -3.00000i q^{78} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.0000i q^{83} +(-2.00000 + 1.73205i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-6.92820 - 4.00000i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.50000 + 7.79423i) q^{91} +2.00000i q^{92} +(-6.92820 + 4.00000i) q^{93} +(-5.00000 + 8.66025i) q^{94} +(-2.50000 - 4.33013i) q^{96} -9.00000i q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q - 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{14} + 2 q^{16} + 2 q^{19} + 10 q^{21} - 6 q^{24} + 6 q^{26} + 32 q^{29} + 16 q^{31} - 8 q^{34} - 4 q^{36} - 6 q^{39} - 4 q^{46} + 26 q^{49} - 4 q^{51} + 2 q^{54} + 6 q^{56} + 20 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{69} - 48 q^{71} + 14 q^{74} - 4 q^{76} - 14 q^{79} - 2 q^{81} - 8 q^{84} + 16 q^{86} - 12 q^{89} + 6 q^{91} - 20 q^{94} - 10 q^{96}+O(q^{100}) $ 4 * q - 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^14 + 2 * q^16 + 2 * q^19 + 10 * q^21 - 6 * q^24 + 6 * q^26 + 32 * q^29 + 16 * q^31 - 8 * q^34 - 4 * q^36 - 6 * q^39 - 4 * q^46 + 26 * q^49 - 4 * q^51 + 2 * q^54 + 6 * q^56 + 20 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^69 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 14 * q^79 - 2 * q^81 - 8 * q^84 + 16 * q^86 - 12 * q^89 + 6 * q^91 - 20 * q^94 - 10 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$		−	3.00000i		−	1.06066i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$		−	3.00000i		−	0.832050i	−0.909353	−	0.416025i	$-0.863423\pi$
$13$		−	3.00000i		−	0.832050i	0.909353	−	0.416025i	$-0.136577\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		0			0
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	−0.308431	−	0.951247i	$-0.599804\pi$
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	0.669588	+	0.742732i	$0.266471\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$		0			0
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$		−	1.00000i		−	0.192450i
$28$	0.866025	−	2.50000i	0.163663	−	0.472456i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$	−0.866025	−	0.500000i	−0.140488	−	0.0811107i
$39$	−1.50000	+	2.59808i	−0.240192	+	0.416025i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−2.59808	+	0.500000i	−0.400892	+	0.0771517i
$43$		−	8.00000i		−	1.21999i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$		−	8.00000i		−	1.21999i	0.792406	−	0.609994i	$-0.208828\pi$
$44$		0			0
$45$		0			0
$46$	−1.00000	+	1.73205i	−0.147442	+	0.255377i
$47$	8.66025	−	5.00000i	1.26323	−	0.729325i	0.289530	−	0.957169i	$-0.406501\pi$
$47$	8.66025	−	5.00000i	1.26323	−	0.729325i	0.973698	+	0.227844i	$0.0731676\pi$
$48$		−	1.00000i		−	0.144338i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	2.59808	+	1.50000i	0.360288	+	0.208013i
$53$	12.1244	+	7.00000i	1.66541	+	0.961524i	0.970065	+	0.242846i	$0.0780811\pi$
$53$	12.1244	+	7.00000i	1.66541	+	0.961524i	0.695344	+	0.718677i	$0.255252\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	1.50000	+	7.79423i	0.200446	+	1.04155i
$57$		−	1.00000i		−	0.132453i
$58$	−6.92820	+	4.00000i	−0.909718	+	0.525226i
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$			8.00000i			1.01600i
$63$	−1.73205	−	2.00000i	−0.218218	−	0.251976i
$64$	−7.00000			−0.875000
$65$		0			0
$66$		0			0
$67$	−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	$0.765465\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$	−2.00000			−0.240772
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	2.59808	−	1.50000i	0.306186	−	0.176777i
$73$	9.52628	+	5.50000i	1.11497	+	0.643726i	0.940111	−	0.340868i	$-0.110721\pi$
$73$	9.52628	+	5.50000i	1.11497	+	0.643726i	0.174855	+	0.984594i	$0.444054\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$		0			0
$76$	−1.00000			−0.114708
$77$		0			0
$78$		−	3.00000i		−	0.339683i
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	0.599164	−	0.800626i	$-0.295500\pi$
$79$	−3.50000	−	6.06218i	−0.393781	−	0.682048i	−0.992945	+	0.118578i	$0.962166\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	−6.92820	−	4.00000i	−0.742781	−	0.428845i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	1.50000	+	7.79423i	0.157243	+	0.817057i
$92$			2.00000i			0.208514i
$93$	−6.92820	+	4.00000i	−0.718421	+	0.414781i
$94$	−5.00000	+	8.66025i	−0.515711	+	0.893237i
$95$		0			0
$96$	−2.50000	−	4.33013i	−0.255155	−	0.441942i
$97$		−	9.00000i		−	0.913812i	−0.889515	−	0.456906i	$-0.848958\pi$
$97$		−	9.00000i		−	0.913812i	0.889515	−	0.456906i	$-0.151042\pi$
$98$	−4.33013	+	5.50000i	−0.437409	+	0.555584i
$99$		0			0
$100$		0			0
$101$	8.00000	−	13.8564i	0.796030	−	1.37876i	−0.126153	−	0.992011i	$-0.540263\pi$
$101$	8.00000	−	13.8564i	0.796030	−	1.37876i	0.922183	−	0.386753i	$-0.126403\pi$
$102$	1.73205	+	1.00000i	0.171499	+	0.0990148i
$103$	−11.2583	+	6.50000i	−1.10932	+	0.640464i	−0.938652	−	0.344865i	$-0.887925\pi$
$103$	−11.2583	+	6.50000i	−1.10932	+	0.640464i	−0.170664	+	0.985329i	$0.554591\pi$
$104$	−9.00000			−0.882523
$105$		0			0
$106$	−14.0000			−1.35980
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	0.227345	+	0.973814i	$0.426996\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−7.50000	+	12.9904i	−0.718370	+	1.24425i	0.243276	+	0.969957i	$0.421778\pi$
$109$	−7.50000	+	12.9904i	−0.718370	+	1.24425i	−0.961645	+	0.274296i	$0.911555\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$	−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	$-0.0910696\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$		0			0
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$	2.59808	−	1.50000i	0.240192	−	0.138675i
$118$			10.0000i			0.920575i
$119$	−5.00000	−	1.73205i	−0.458349	−	0.158777i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	6.06218	+	3.50000i	0.548844	+	0.316875i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$		−	11.0000i		−	0.976092i	−0.872818	−	0.488046i	$-0.837710\pi$
$127$		−	11.0000i		−	0.976092i	0.872818	−	0.488046i	$-0.162290\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$		0			0
$133$	−1.73205	−	2.00000i	−0.150188	−	0.173422i
$134$	5.00000			0.431934
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	0.0821359	−	0.996621i	$-0.473826\pi$
$137$	−8.66025	−	5.00000i	−0.739895	−	0.427179i	−0.822031	+	0.569442i	$0.807159\pi$
$138$	1.73205	−	1.00000i	0.147442	−	0.0851257i
$139$	−3.00000			−0.254457			−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000			−0.254457			−0.127228	+	0.991873i	$0.540608\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$	10.3923	−	6.00000i	0.872103	−	0.503509i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−11.0000			−0.910366
$147$	−6.92820	−	1.00000i	−0.571429	−	0.0824786i
$148$		−	7.00000i		−	0.575396i
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	2.59808	−	1.50000i	0.210732	−	0.121666i
$153$			2.00000i			0.161690i
$154$		0			0
$155$		0			0
$156$	−1.50000	−	2.59808i	−0.120096	−	0.208013i
$157$	6.06218	+	3.50000i	0.483814	+	0.279330i	0.722005	−	0.691888i	$-0.243221\pi$
$157$	6.06218	+	3.50000i	0.483814	+	0.279330i	−0.238190	+	0.971219i	$0.576554\pi$
$158$	6.06218	+	3.50000i	0.482281	+	0.278445i
$159$	−7.00000	−	12.1244i	−0.555136	−	0.961524i
$160$		0			0
$161$	−4.00000	+	3.46410i	−0.315244	+	0.273009i
$162$		−	1.00000i		−	0.0785674i
$163$	−7.79423	+	4.50000i	−0.610491	+	0.352467i	−0.773158	−	0.634214i	$-0.781324\pi$
$163$	−7.79423	+	4.50000i	−0.610491	+	0.352467i	0.162667	+	0.986681i	$0.447991\pi$
$164$		0			0
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$	2.59808	−	7.50000i	0.200446	−	0.578638i
$169$	4.00000			0.307692
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	6.92820	+	4.00000i	0.528271	+	0.304997i
$173$	15.5885	−	9.00000i	1.18517	−	0.684257i	0.227964	−	0.973670i	$-0.426793\pi$
$173$	15.5885	−	9.00000i	1.18517	−	0.684257i	0.957205	+	0.289412i	$0.0934598\pi$
$174$	8.00000			0.606478
$175$		0			0
$176$		0			0
$177$	−8.66025	+	5.00000i	−0.650945	+	0.375823i
$178$	5.19615	+	3.00000i	0.389468	+	0.224860i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−5.19615	−	6.00000i	−0.385164	−	0.444750i
$183$			7.00000i			0.517455i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$		0			0
$188$			10.0000i			0.729325i
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$		0			0
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$	6.06218	+	3.50000i	0.437500	+	0.252591i
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	0.301189	−	0.953564i	$-0.402616\pi$
$193$	−5.19615	−	3.00000i	−0.374027	−	0.215945i	−0.675216	+	0.737620i	$0.735950\pi$
$194$	4.50000	+	7.79423i	0.323081	+	0.559593i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$		0			0
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		0			0
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$			16.0000i			1.12576i
$203$	−20.7846	+	4.00000i	−1.45879	+	0.280745i
$204$	2.00000			0.140028
$205$		0			0
$206$	6.50000	−	11.2583i	0.452876	−	0.784405i
$207$	1.73205	+	1.00000i	0.120386	+	0.0695048i
$208$	2.59808	−	1.50000i	0.180144	−	0.104006i
$209$		0			0
$210$		0			0
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−12.1244	+	7.00000i	−0.832704	+	0.480762i
$213$	10.3923	+	6.00000i	0.712069	+	0.411113i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	−3.00000			−0.204124
$217$	−6.92820	+	20.0000i	−0.470317	+	1.35769i
$218$		−	15.0000i		−	1.01593i
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$	−6.06218	+	3.50000i	−0.406867	+	0.234905i
$223$		−	15.0000i		−	1.00447i	−0.864730	−	0.502237i	$-0.832510\pi$
$223$		−	15.0000i		−	1.00447i	0.864730	−	0.502237i	$-0.167490\pi$
$224$	−12.5000	−	4.33013i	−0.835191	−	0.289319i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.948790	−	0.315906i	$-0.102309\pi$
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.200812	+	0.979630i	$0.435642\pi$
$228$	0.866025	+	0.500000i	0.0573539	+	0.0331133i
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	0.996832	−	0.0795401i	$-0.0253452\pi$
$229$	6.50000	+	11.2583i	0.429532	+	0.743971i	−0.567300	+	0.823511i	$0.692012\pi$
$230$		0			0
$231$		0			0
$232$		−	24.0000i		−	1.57568i
$233$	20.7846	−	12.0000i	1.36165	−	0.786146i	0.371802	−	0.928312i	$-0.378740\pi$
$233$	20.7846	−	12.0000i	1.36165	−	0.786146i	0.989843	+	0.142166i	$0.0454066\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$		0			0
$236$	5.00000	+	8.66025i	0.325472	+	0.563735i
$237$			7.00000i			0.454699i
$238$	5.19615	−	1.00000i	0.336817	−	0.0648204i
$239$	28.0000			1.81117			0.905585	−	0.424165i	$-0.139432\pi$
$239$	28.0000			1.81117			0.905585	+	0.424165i	$0.139432\pi$
$240$		0			0
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	0.299704	+	0.954032i	$0.403112\pi$
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	−0.976068	+	0.217465i	$0.930221\pi$
$242$	−9.52628	−	5.50000i	−0.612372	−	0.353553i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	7.00000			0.448129
$245$		0			0
$246$		0			0
$247$	2.59808	−	1.50000i	0.165312	−	0.0954427i
$248$	−20.7846	−	12.0000i	−1.31982	−	0.762001i
$249$	7.00000	−	12.1244i	0.443607	−	0.768350i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	2.59808	−	0.500000i	0.163663	−	0.0314970i
$253$		0			0
$254$	5.50000	+	9.52628i	0.345101	+	0.597732i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		−	8.00000i		−	0.498058i
$259$	14.0000	−	12.1244i	0.869918	−	0.753371i
$260$		0			0
$261$	4.00000	+	6.92820i	0.247594	+	0.428845i
$262$	12.1244	+	7.00000i	0.749045	+	0.432461i
$263$	−13.8564	−	8.00000i	−0.854423	−	0.493301i	0.00771799	−	0.999970i	$-0.497543\pi$
$263$	−13.8564	−	8.00000i	−0.854423	−	0.493301i	−0.862141	+	0.506669i	$0.830877\pi$
$264$		0			0
$265$		0			0
$266$	2.50000	+	0.866025i	0.153285	+	0.0530994i
$267$			6.00000i			0.367194i
$268$	4.33013	−	2.50000i	0.264505	−	0.152712i
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	−0.999901	−	0.0140665i	$-0.995522\pi$
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	0.512132	+	0.858906i	$0.328856\pi$
$270$		0			0
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$			2.00000i			0.121268i
$273$	2.59808	−	7.50000i	0.157243	−	0.453921i
$274$	10.0000			0.604122
$275$		0			0
$276$	1.00000	−	1.73205i	0.0601929	−	0.104257i
$277$	4.33013	+	2.50000i	0.260172	+	0.150210i	0.624413	−	0.781094i	$-0.285338\pi$
$277$	4.33013	+	2.50000i	0.260172	+	0.150210i	−0.364241	+	0.931305i	$0.618672\pi$
$278$	2.59808	−	1.50000i	0.155822	−	0.0899640i
$279$	8.00000			0.478947
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	8.66025	−	5.00000i	0.515711	−	0.297746i
$283$	16.4545	+	9.50000i	0.978117	+	0.564716i	0.901701	−	0.432360i	$-0.142319\pi$
$283$	16.4545	+	9.50000i	0.978117	+	0.564716i	0.0764162	+	0.997076i	$0.475652\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$			5.00000i			0.294628i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−4.50000	+	7.79423i	−0.263795	+	0.456906i
$292$	−9.52628	+	5.50000i	−0.557483	+	0.321863i
$293$		−	16.0000i		−	0.934730i	−0.884064	−	0.467365i	$-0.845203\pi$
$293$		−	16.0000i		−	0.934730i	0.884064	−	0.467365i	$-0.154797\pi$
$294$	6.50000	−	2.59808i	0.379088	−	0.151523i
$295$		0			0
$296$	10.5000	+	18.1865i	0.610300	+	1.05707i
$297$		0			0
$298$	3.46410	+	2.00000i	0.200670	+	0.115857i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$		0			0
$301$	4.00000	+	20.7846i	0.230556	+	1.19800i
$302$			1.00000i			0.0575435i
$303$	−13.8564	+	8.00000i	−0.796030	+	0.459588i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$		0			0
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$	13.0000			0.739544
$310$		0			0
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$	7.79423	+	4.50000i	0.441261	+	0.254762i
$313$	12.1244	−	7.00000i	0.685309	−	0.395663i	−0.116543	−	0.993186i	$-0.537181\pi$
$313$	12.1244	−	7.00000i	0.685309	−	0.395663i	0.801852	+	0.597522i	$0.203848\pi$
$314$	−7.00000			−0.395033
$315$		0			0
$316$	7.00000			0.393781
$317$	−12.1244	+	7.00000i	−0.680972	+	0.393159i	−0.800221	−	0.599705i	$-0.795285\pi$
$317$	−12.1244	+	7.00000i	−0.680972	+	0.393159i	0.119249	+	0.992864i	$0.461951\pi$
$318$	12.1244	+	7.00000i	0.679900	+	0.392541i
$319$		0			0
$320$		0			0
$321$	6.00000			0.334887
$322$	1.73205	−	5.00000i	0.0965234	−	0.278639i
$323$			2.00000i			0.111283i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	4.50000	−	7.79423i	0.249232	−	0.431682i
$327$	12.9904	−	7.50000i	0.718370	−	0.414751i
$328$		0			0
$329$	−20.0000	+	17.3205i	−1.10264	+	0.954911i
$330$		0			0
$331$	−10.5000	−	18.1865i	−0.577132	−	0.999622i	−0.995806	−	0.0914858i	$-0.970838\pi$
$331$	−10.5000	−	18.1865i	−0.577132	−	0.999622i	0.418674	−	0.908137i	$-0.362495\pi$
$332$	−12.1244	−	7.00000i	−0.665410	−	0.384175i
$333$	−6.06218	−	3.50000i	−0.332205	−	0.191799i
$334$	1.00000	+	1.73205i	0.0547176	+	0.0947736i
$335$		0			0
$336$	0.500000	+	2.59808i	0.0272772	+	0.141737i
$337$			2.00000i			0.108947i	0.998515	+	0.0544735i	$0.0173480\pi$
$337$			2.00000i			0.108947i	−0.998515	+	0.0544735i	$0.982652\pi$
$338$	−3.46410	+	2.00000i	−0.188422	+	0.108786i
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$		0			0
$342$		−	1.00000i		−	0.0540738i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−24.0000			−1.29399
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	0.714105	−	0.700038i	$-0.246834\pi$
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	−0.249198	+	0.968452i	$0.580167\pi$
$348$	6.92820	−	4.00000i	0.371391	−	0.214423i
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$		0			0
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.168397	−	0.985719i	$-0.553859\pi$
$353$	−20.7846	−	12.0000i	−1.10625	−	0.638696i	−0.937856	+	0.347024i	$0.887192\pi$
$354$	5.00000	−	8.66025i	0.265747	−	0.460287i
$355$		0			0
$356$	6.00000			0.317999
$357$	3.46410	+	4.00000i	0.183340	+	0.211702i
$358$		−	12.0000i		−	0.634220i
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	0.924932	+	0.380131i	$0.124121\pi$
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	−0.133263	+	0.991081i	$0.542545\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−19.0526	+	11.0000i	−1.00138	+	0.578147i
$363$		−	11.0000i		−	0.577350i
$364$	−7.50000	−	2.59808i	−0.393107	−	0.136176i
$365$		0			0
$366$	−3.50000	−	6.06218i	−0.182948	−	0.316875i
$367$	−6.92820	−	4.00000i	−0.361649	−	0.208798i	0.308155	−	0.951336i	$-0.400289\pi$
$367$	−6.92820	−	4.00000i	−0.361649	−	0.208798i	−0.669804	+	0.742538i	$0.733622\pi$
$368$	1.73205	+	1.00000i	0.0902894	+	0.0521286i
$369$		0			0
$370$		0			0
$371$	−35.0000	−	12.1244i	−1.81711	−	0.629465i
$372$		−	8.00000i		−	0.414781i
$373$	9.52628	−	5.50000i	0.493252	−	0.284779i	−0.232671	−	0.972556i	$-0.574746\pi$
$373$	9.52628	−	5.50000i	0.493252	−	0.284779i	0.725923	+	0.687776i	$0.241413\pi$
$374$		0			0
$375$		0			0
$376$	−15.0000	−	25.9808i	−0.773566	−	1.33986i
$377$		−	24.0000i		−	1.23606i
$378$	−1.73205	−	2.00000i	−0.0890871	−	0.102869i
$379$	−35.0000			−1.79783			−0.898915	−	0.438124i	$-0.855643\pi$
$379$	−35.0000			−1.79783			−0.898915	+	0.438124i	$0.855643\pi$
$380$		0			0
$381$	−5.50000	+	9.52628i	−0.281774	+	0.488046i
$382$	−6.92820	−	4.00000i	−0.354478	−	0.204658i
$383$	8.66025	−	5.00000i	0.442518	−	0.255488i	−0.262147	−	0.965028i	$-0.584431\pi$
$383$	8.66025	−	5.00000i	0.442518	−	0.255488i	0.704665	+	0.709540i	$0.251097\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	6.00000			0.305392
$387$	6.92820	−	4.00000i	0.352180	−	0.203331i
$388$	7.79423	+	4.50000i	0.395692	+	0.228453i
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.102311	+	0.994753i	$0.532624\pi$
$389$	−18.0000	+	31.1769i	−0.912636	+	1.58073i	−0.810326	+	0.585980i	$0.800710\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$	−7.79423	−	19.5000i	−0.393668	−	0.984899i
$393$			14.0000i			0.706207i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	−0.772380	−	0.635161i	$-0.780934\pi$
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	0.163876	+	0.986481i	$0.447600\pi$
$398$			11.0000i			0.551380i
$399$	0.500000	+	2.59808i	0.0250313	+	0.130066i
$400$		0			0
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$	−4.33013	−	2.50000i	−0.215967	−	0.124689i
$403$	−20.7846	−	12.0000i	−1.03536	−	0.597763i
$404$	8.00000	+	13.8564i	0.398015	+	0.689382i
$405$		0			0
$406$	16.0000	−	13.8564i	0.794067	−	0.687682i
$407$		0			0
$408$	−5.19615	+	3.00000i	−0.257248	+	0.148522i
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$	5.00000	+	8.66025i	0.246632	+	0.427179i
$412$		−	13.0000i		−	0.640464i
$413$	−8.66025	+	25.0000i	−0.426143	+	1.23017i
$414$	−2.00000			−0.0982946
$415$		0			0
$416$	7.50000	−	12.9904i	0.367718	−	0.636906i
$417$	2.59808	+	1.50000i	0.127228	+	0.0734553i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$	4.33013	−	2.50000i	0.210787	−	0.121698i
$423$	8.66025	+	5.00000i	0.421076	+	0.243108i
$424$	21.0000	−	36.3731i	1.01985	−	1.76643i
$425$		0			0
$426$	−12.0000			−0.581402
$427$	12.1244	+	14.0000i	0.586739	+	0.677507i
$428$		−	6.00000i		−	0.290021i
$429$		0			0
$430$		0			0
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	−0.840936	−	0.541135i	$-0.817995\pi$
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	0.889104	+	0.457705i	$0.151328\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	2.00000i		−	0.0961139i	−0.998845	−	0.0480569i	$-0.984697\pi$
$433$		−	2.00000i		−	0.0961139i	0.998845	−	0.0480569i	$-0.0153029\pi$
$434$	−4.00000	−	20.7846i	−0.192006	−	0.997693i
$435$		0			0
$436$	−7.50000	−	12.9904i	−0.359185	−	0.622126i
$437$	1.73205	+	1.00000i	0.0828552	+	0.0478365i
$438$	9.52628	+	5.50000i	0.455183	+	0.262800i
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	0.704405	−	0.709798i	$-0.251214\pi$
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	−0.966906	+	0.255134i	$0.917881\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$			6.00000i			0.285391i
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	−0.371457	−	0.928450i	$-0.621142\pi$
$443$	5.19615	−	3.00000i	0.246877	−	0.142534i	0.618333	+	0.785916i	$0.287808\pi$
$444$	−3.50000	+	6.06218i	−0.166103	+	0.287698i
$445$		0			0
$446$	7.50000	+	12.9904i	0.355135	+	0.615112i
$447$			4.00000i			0.189194i
$448$	18.1865	−	3.50000i	0.859233	−	0.165359i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$		0			0
$452$	5.19615	+	3.00000i	0.244406	+	0.141108i
$453$	−0.866025	+	0.500000i	−0.0406894	+	0.0234920i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	−3.00000			−0.140488
$457$	2.59808	−	1.50000i	0.121533	−	0.0701670i	−0.438001	−	0.898974i	$-0.644313\pi$
$457$	2.59808	−	1.50000i	0.121533	−	0.0701670i	0.559534	+	0.828807i	$0.310980\pi$
$458$	−11.2583	−	6.50000i	−0.526067	−	0.303725i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$			33.0000i			1.53364i	0.641862	+	0.766820i	$0.278162\pi$
$463$			33.0000i			1.53364i	−0.641862	+	0.766820i	$0.721838\pi$
$464$	4.00000	+	6.92820i	0.185695	+	0.321634i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	1.73205	−	1.00000i	0.0801498	−	0.0462745i	−0.459390	−	0.888235i	$-0.651932\pi$
$467$	1.73205	−	1.00000i	0.0801498	−	0.0462745i	0.539539	+	0.841960i	$0.318598\pi$
$468$			3.00000i			0.138675i
$469$	12.5000	+	4.33013i	0.577196	+	0.199947i
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−25.9808	−	15.0000i	−1.19586	−	0.690431i
$473$		0			0
$474$	−3.50000	−	6.06218i	−0.160760	−	0.278445i
$475$		0			0
$476$	4.00000	−	3.46410i	0.183340	−	0.158777i
$477$			14.0000i			0.641016i
$478$	−24.2487	+	14.0000i	−1.10911	+	0.640345i
$479$	1.00000	−	1.73205i	0.0456912	−	0.0791394i	−0.842275	−	0.539048i	$-0.818784\pi$
$479$	1.00000	−	1.73205i	0.0456912	−	0.0791394i	0.887967	+	0.459908i	$0.152118\pi$
$480$		0			0
$481$	10.5000	+	18.1865i	0.478759	+	0.829235i
$482$		−	21.0000i		−	0.956524i
$483$	5.19615	−	1.00000i	0.236433	−	0.0455016i
$484$	−11.0000			−0.500000
$485$		0			0
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	6.92820	+	4.00000i	0.313947	+	0.181257i	0.648691	−	0.761052i	$-0.275317\pi$
$487$	6.92820	+	4.00000i	0.313947	+	0.181257i	−0.334744	+	0.942309i	$0.608650\pi$
$488$	−18.1865	+	10.5000i	−0.823266	+	0.475313i
$489$	9.00000			0.406994
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	13.8564	+	8.00000i	0.624061	+	0.360302i
$494$	−1.50000	+	2.59808i	−0.0674882	+	0.116893i
$495$		0			0
$496$	8.00000			0.359211
$497$	31.1769	−	6.00000i	1.39848	−	0.269137i
$498$			14.0000i			0.627355i
$499$	−9.50000	−	16.4545i	−0.425278	−	0.736604i	0.571168	−	0.820833i	$-0.306490\pi$
$499$	−9.50000	−	16.4545i	−0.425278	−	0.736604i	−0.996446	+	0.0842294i	$0.973157\pi$
$500$		0			0
$501$	−1.00000	+	1.73205i	−0.0446767	+	0.0773823i
$502$		0			0
$503$			40.0000i			1.78351i	0.452517	+	0.891756i	$0.350526\pi$
$503$			40.0000i			1.78351i	−0.452517	+	0.891756i	$0.649474\pi$
$504$	−6.00000	+	5.19615i	−0.267261	+	0.231455i
$505$		0			0
$506$		0			0
$507$	−3.46410	−	2.00000i	−0.153846	−	0.0888231i
$508$	9.52628	+	5.50000i	0.422660	+	0.244023i
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	0.763657	−	0.645622i	$-0.223402\pi$
$509$	−4.00000	−	6.92820i	−0.177297	−	0.307087i	−0.940954	+	0.338535i	$0.890069\pi$
$510$		0			0
$511$	−27.5000	−	9.52628i	−1.21653	−	0.421418i
$512$			11.0000i			0.486136i
$513$	0.866025	−	0.500000i	0.0382360	−	0.0220755i
$514$		0			0
$515$		0			0
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$		0			0
$518$	−6.06218	+	17.5000i	−0.266357	+	0.768906i
$519$	−18.0000			−0.790112
$520$		0			0
$521$	−17.0000	+	29.4449i	−0.744784	+	1.29000i	0.205512	+	0.978655i	$0.434114\pi$
$521$	−17.0000	+	29.4449i	−0.744784	+	1.29000i	−0.950296	+	0.311348i	$0.899219\pi$
$522$	−6.92820	−	4.00000i	−0.303239	−	0.175075i
$523$	−13.8564	+	8.00000i	−0.605898	+	0.349816i	−0.771358	−	0.636401i	$-0.780422\pi$
$523$	−13.8564	+	8.00000i	−0.605898	+	0.349816i	0.165460	+	0.986216i	$0.447089\pi$
$524$	14.0000			0.611593
$525$		0			0
$526$	16.0000			0.697633
$527$	13.8564	−	8.00000i	0.603595	−	0.348485i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	10.0000			0.433963
$532$	2.59808	−	0.500000i	0.112641	−	0.0216777i
$533$		0			0
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	10.3923	−	6.00000i	0.448461	−	0.258919i
$538$		−	16.0000i		−	0.689809i
$539$		0			0
$540$		0			0
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$	−10.3923	−	6.00000i	−0.446388	−	0.257722i
$543$	−19.0526	−	11.0000i	−0.817624	−	0.472055i
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$		0			0
$546$	1.50000	+	7.79423i	0.0641941	+	0.333562i
$547$			12.0000i			0.513083i	0.966533	+	0.256541i	$0.0825830\pi$
$547$			12.0000i			0.513083i	−0.966533	+	0.256541i	$0.917417\pi$
$548$	8.66025	−	5.00000i	0.369948	−	0.213589i
$549$	3.50000	−	6.06218i	0.149376	−	0.258727i
$550$		0			0
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$			6.00000i			0.255377i
$553$	12.1244	+	14.0000i	0.515580	+	0.595341i
$554$	−5.00000			−0.212430
$555$		0			0
$556$	1.50000	−	2.59808i	0.0636142	−	0.110183i
$557$	−3.46410	−	2.00000i	−0.146779	−	0.0847427i	0.424812	−	0.905282i	$-0.360340\pi$
$557$	−3.46410	−	2.00000i	−0.146779	−	0.0847427i	−0.571591	+	0.820539i	$0.693674\pi$
$558$	−6.92820	+	4.00000i	−0.293294	+	0.169334i
$559$	−24.0000			−1.01509
$560$		0			0
$561$		0			0
$562$	−5.19615	+	3.00000i	−0.219186	+	0.126547i
$563$	−24.2487	−	14.0000i	−1.02196	−	0.590030i	−0.107290	−	0.994228i	$-0.534217\pi$
$563$	−24.2487	−	14.0000i	−1.02196	−	0.590030i	−0.914671	+	0.404198i	$0.867551\pi$
$564$	5.00000	−	8.66025i	0.210538	−	0.364662i
$565$		0			0
$566$	−19.0000			−0.798630
$567$	0.866025	−	2.50000i	0.0363696	−	0.104990i
$568$			36.0000i			1.51053i
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		0			0
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	−0.832931	−	0.553377i	$-0.813339\pi$
$571$	1.50000	−	2.59808i	0.0627730	−	0.108726i	0.895704	+	0.444651i	$0.146672\pi$
$572$		0			0
$573$		−	8.00000i		−	0.334205i
$574$		0			0
$575$		0			0
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	0.463513	−	0.886090i	$-0.346589\pi$
$577$	−1.73205	−	1.00000i	−0.0721062	−	0.0416305i	−0.535620	+	0.844459i	$0.679922\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	3.00000	+	5.19615i	0.124676	+	0.215945i
$580$		0			0
$581$	−7.00000	−	36.3731i	−0.290409	−	1.50901i
$582$		−	9.00000i		−	0.373062i
$583$		0			0
$584$	16.5000	−	28.5788i	0.682775	−	1.18260i
$585$		0			0
$586$	8.00000	+	13.8564i	0.330477	+	0.572403i
$587$			6.00000i			0.247647i	0.992304	+	0.123823i	$0.0395156\pi$
$587$			6.00000i			0.247647i	−0.992304	+	0.123823i	$0.960484\pi$
$588$	4.33013	−	5.50000i	0.178571	−	0.226816i
$589$	8.00000			0.329634
$590$		0			0
$591$	−6.00000	+	10.3923i	−0.246807	+	0.427482i
$592$	−6.06218	−	3.50000i	−0.249154	−	0.143849i
$593$	36.3731	−	21.0000i	1.49366	−	0.862367i	0.493689	−	0.869638i	$-0.335648\pi$
$593$	36.3731	−	21.0000i	1.49366	−	0.862367i	0.999974	+	0.00727173i	$0.00231468\pi$
$594$		0			0
$595$		0			0
$596$	4.00000			0.163846
$597$	−9.52628	+	5.50000i	−0.389885	+	0.225100i
$598$	5.19615	+	3.00000i	0.212486	+	0.122679i
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	−0.468173	−	0.883637i	$-0.655088\pi$
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	0.999338	−	0.0363689i	$-0.0115791\pi$
$600$		0			0
$601$	−45.0000			−1.83559			−0.917794	−	0.397057i	$-0.870032\pi$
$601$	−45.0000			−1.83559			−0.917794	+	0.397057i	$0.870032\pi$
$602$	−13.8564	−	16.0000i	−0.564745	−	0.652111i
$603$		−	5.00000i		−	0.203616i
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$		0			0
$606$	8.00000	−	13.8564i	0.324978	−	0.562878i
$607$	37.2391	−	21.5000i	1.51149	−	0.872658i	0.511578	−	0.859237i	$-0.329061\pi$
$607$	37.2391	−	21.5000i	1.51149	−	0.872658i	0.999910	−	0.0134214i	$-0.00427228\pi$
$608$			5.00000i			0.202777i
$609$	20.0000	+	6.92820i	0.810441	+	0.280745i
$610$		0			0
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$	−1.73205	−	1.00000i	−0.0700140	−	0.0404226i
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	0.391381	−	0.920229i	$-0.371998\pi$
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	−0.601251	+	0.799060i	$0.705331\pi$
$614$	−6.00000	−	10.3923i	−0.242140	−	0.419399i
$615$		0			0
$616$		0			0
$617$			24.0000i			0.966204i	0.875564	+	0.483102i	$0.160490\pi$
$617$			24.0000i			0.966204i	−0.875564	+	0.483102i	$0.839510\pi$
$618$	−11.2583	+	6.50000i	−0.452876	+	0.261468i
$619$	−6.00000	+	10.3923i	−0.241160	+	0.417702i	−0.961045	−	0.276392i	$-0.910861\pi$
$619$	−6.00000	+	10.3923i	−0.241160	+	0.417702i	0.719885	+	0.694094i	$0.244195\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$			30.0000i			1.20289i
$623$	10.3923	+	12.0000i	0.416359	+	0.480770i
$624$	−3.00000			−0.120096
$625$		0			0
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$		0			0
$628$	−6.06218	+	3.50000i	−0.241907	+	0.139665i
$629$	−14.0000			−0.558217
$630$		0			0
$631$	45.0000			1.79142			0.895711	−	0.444637i	$-0.146667\pi$
$631$	45.0000			1.79142			0.895711	+	0.444637i	$0.146667\pi$
$632$	−18.1865	+	10.5000i	−0.723421	+	0.417668i
$633$	4.33013	+	2.50000i	0.172107	+	0.0993661i
$634$	7.00000	−	12.1244i	0.278006	−	0.481520i
$635$		0			0
$636$	14.0000			0.555136
$637$	−7.79423	−	19.5000i	−0.308819	−	0.772618i
$638$		0			0
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$		0			0
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	−0.999556	−	0.0297987i	$-0.990513\pi$
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	0.525584	+	0.850741i	$0.323847\pi$
$642$	−5.19615	+	3.00000i	−0.205076	+	0.118401i
$643$		−	29.0000i		−	1.14365i	−0.820376	−	0.571824i	$-0.806236\pi$
$643$		−	29.0000i		−	1.14365i	0.820376	−	0.571824i	$-0.193764\pi$
$644$	−1.00000	−	5.19615i	−0.0394055	−	0.204757i
$645$		0			0
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$	10.3923	+	6.00000i	0.408564	+	0.235884i	0.690172	−	0.723645i	$-0.257535\pi$
$647$	10.3923	+	6.00000i	0.408564	+	0.235884i	−0.281609	+	0.959529i	$0.590868\pi$
$648$	2.59808	+	1.50000i	0.102062	+	0.0589256i
$649$		0			0
$650$		0			0
$651$	16.0000	−	13.8564i	0.627089	−	0.543075i
$652$		−	9.00000i		−	0.352467i
$653$	38.1051	−	22.0000i	1.49117	−	0.860927i	0.491220	−	0.871036i	$-0.336551\pi$
$653$	38.1051	−	22.0000i	1.49117	−	0.860927i	0.999949	+	0.0101092i	$0.00321793\pi$
$654$	−7.50000	+	12.9904i	−0.293273	+	0.507964i
$655$		0			0
$656$		0			0
$657$			11.0000i			0.429151i
$658$	8.66025	−	25.0000i	0.337612	−	0.974601i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	0.739014	+	0.673690i	$0.235292\pi$
$662$	18.1865	+	10.5000i	0.706840	+	0.408094i
$663$	−5.19615	+	3.00000i	−0.201802	+	0.116510i
$664$	42.0000			1.62992
$665$		0			0
$666$	7.00000			0.271244
$667$	13.8564	−	8.00000i	0.536522	−	0.309761i
$668$	1.73205	+	1.00000i	0.0670151	+	0.0386912i
$669$	−7.50000	+	12.9904i	−0.289967	+	0.502237i
$670$		0			0
$671$		0			0
$672$	8.66025	+	10.0000i	0.334077	+	0.385758i
$673$		−	1.00000i		−	0.0385472i	−0.999814	−	0.0192736i	$-0.993865\pi$
$673$		−	1.00000i		−	0.0385472i	0.999814	−	0.0192736i	$-0.00613535\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$		0			0
$676$	−2.00000	+	3.46410i	−0.0769231	+	0.133235i
$677$	12.1244	−	7.00000i	0.465977	−	0.269032i	−0.248577	−	0.968612i	$-0.579963\pi$
$677$	12.1244	−	7.00000i	0.465977	−	0.269032i	0.714554	+	0.699580i	$0.246630\pi$
$678$		−	6.00000i		−	0.230429i
$679$	4.50000	+	23.3827i	0.172694	+	0.897345i
$680$		0			0
$681$	−10.0000	−	17.3205i	−0.383201	−	0.663723i
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$		0			0
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		−	13.0000i		−	0.495981i
$688$	6.92820	−	4.00000i	0.264135	−	0.152499i
$689$	21.0000	−	36.3731i	0.800036	−	1.38570i
$690$		0			0
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	0.972685	−	0.232128i	$-0.0745690\pi$
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	−0.687372	+	0.726306i	$0.741236\pi$
$692$			18.0000i			0.684257i
$693$		0			0
$694$	−10.0000			−0.379595
$695$		0			0
$696$	−12.0000	+	20.7846i	−0.454859	+	0.787839i
$697$		0			0
$698$	−19.0526	+	11.0000i	−0.721150	+	0.416356i
$699$	−24.0000			−0.907763
$700$		0			0
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$	2.59808	−	1.50000i	0.0980581	−	0.0566139i
$703$	−6.06218	−	3.50000i	−0.228639	−	0.132005i
$704$		0			0
$705$		0			0
$706$	24.0000			0.903252
$707$	−13.8564	+	40.0000i	−0.521124	+	1.50435i
$708$		−	10.0000i		−	0.375823i
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$		0			0
$711$	3.50000	−	6.06218i	0.131260	−	0.227349i
$712$	−15.5885	+	9.00000i	−0.584202	+	0.337289i
$713$		−	16.0000i		−	0.599205i
$714$	−5.00000	−	1.73205i	−0.187120	−	0.0648204i
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−24.2487	−	14.0000i	−0.905585	−	0.522840i
$718$	−25.9808	−	15.0000i	−0.969593	−	0.559795i
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	0.826319	−	0.563202i	$-0.190431\pi$
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	−0.900907	+	0.434013i	$0.857097\pi$
$720$		0			0
$721$	26.0000	−	22.5167i	0.968291	−	0.838564i
$722$			18.0000i			0.669891i
$723$	18.1865	−	10.5000i	0.676364	−	0.390499i
$724$	−11.0000	+	19.0526i	−0.408812	+	0.708083i
$725$		0			0
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$		−	43.0000i		−	1.59478i	−0.603463	−	0.797391i	$-0.706213\pi$
$727$		−	43.0000i		−	1.59478i	0.603463	−	0.797391i	$-0.293787\pi$
$728$	23.3827	−	4.50000i	0.866620	−	0.166781i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$	−6.06218	−	3.50000i	−0.224065	−	0.129364i
$733$	−26.8468	+	15.5000i	−0.991609	+	0.572506i	−0.905755	−	0.423802i	$-0.860695\pi$
$733$	−26.8468	+	15.5000i	−0.991609	+	0.572506i	−0.0858539	+	0.996308i	$0.527362\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	10.0000			0.368605
$737$		0			0
$738$		0			0
$739$	−24.5000	+	42.4352i	−0.901247	+	1.56101i	−0.0753699	+	0.997156i	$0.524014\pi$
$739$	−24.5000	+	42.4352i	−0.901247	+	1.56101i	−0.825877	+	0.563850i	$0.809320\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$	36.3731	−	7.00000i	1.33530	−	0.256978i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	12.0000	+	20.7846i	0.439941	+	0.762001i
$745$		0			0
$746$	−5.50000	+	9.52628i	−0.201369	+	0.348782i
$747$	−12.1244	+	7.00000i	−0.443607	+	0.256117i
$748$		0			0
$749$	12.0000	−	10.3923i	0.438470	−	0.379727i
$750$		0			0
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	0.576262	−	0.817265i	$-0.304511\pi$
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	−0.995903	+	0.0904254i	$0.971177\pi$
$752$	8.66025	+	5.00000i	0.315807	+	0.182331i
$753$		0			0
$754$	12.0000	+	20.7846i	0.437014	+	0.756931i
$755$		0			0
$756$	−2.50000	−	0.866025i	−0.0909241	−	0.0314970i
$757$			43.0000i			1.56286i	0.623992	+	0.781431i	$0.285510\pi$
$757$			43.0000i			1.56286i	−0.623992	+	0.781431i	$0.714490\pi$
$758$	30.3109	−	17.5000i	1.10094	−	0.635629i
$759$		0			0
$760$		0			0
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$		−	11.0000i		−	0.398488i
$763$	12.9904	−	37.5000i	0.470283	−	1.35759i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−5.00000	+	8.66025i	−0.180657	+	0.312908i
$767$	−25.9808	−	15.0000i	−0.938111	−	0.541619i
$768$	−14.7224	+	8.50000i	−0.531250	+	0.306717i
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$		0			0
$771$		0			0
$772$	5.19615	−	3.00000i	0.187014	−	0.107972i
$773$	−41.5692	−	24.0000i	−1.49514	−	0.863220i	−0.495156	−	0.868804i	$-0.664889\pi$
$773$	−41.5692	−	24.0000i	−1.49514	−	0.863220i	−0.999984	+	0.00558380i	$0.998223\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$		0			0
$776$	−27.0000			−0.969244
$777$	−18.1865	+	3.50000i	−0.652438	+	0.125562i
$778$		−	36.0000i		−	1.29066i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−3.46410	+	2.00000i	−0.123876	+	0.0715199i
$783$		−	8.00000i		−	0.285897i
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$	−7.00000	−	12.1244i	−0.249682	−	0.432461i
$787$	−14.7224	−	8.50000i	−0.524798	−	0.302992i	0.214097	−	0.976812i	$-0.431319\pi$
$787$	−14.7224	−	8.50000i	−0.524798	−	0.302992i	−0.738896	+	0.673820i	$0.764652\pi$
$788$	10.3923	+	6.00000i	0.370211	+	0.213741i
$789$	8.00000	+	13.8564i	0.284808	+	0.493301i
$790$		0			0
$791$	3.00000	+	15.5885i	0.106668	+	0.554262i
$792$		0			0
$793$	−18.1865	+	10.5000i	−0.645823	+	0.372866i
$794$	7.00000	−	12.1244i	0.248421	−	0.430277i
$795$		0			0
$796$	5.50000	+	9.52628i	0.194942	+	0.337650i
$797$		−	30.0000i		−	1.06265i	−0.847167	−	0.531327i	$-0.821693\pi$
$797$		−	30.0000i		−	1.06265i	0.847167	−	0.531327i	$-0.178307\pi$
$798$	−1.73205	−	2.00000i	−0.0613139	−	0.0707992i
$799$	20.0000			0.707549
$800$		0			0
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−10.3923	−	6.00000i	−0.366965	−	0.211867i
$803$		0			0
$804$	−5.00000			−0.176336
$805$		0			0
$806$	24.0000			0.845364
$807$	13.8564	−	8.00000i	0.487769	−	0.281613i
$808$	−41.5692	−	24.0000i	−1.46240	−	0.844317i
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	3.00000			0.105344			0.0526721	−	0.998612i	$-0.483226\pi$
$811$	3.00000			0.105344			0.0526721	+	0.998612i	$0.483226\pi$
$812$	6.92820	−	20.0000i	0.243132	−	0.701862i
$813$		−	12.0000i		−	0.420858i
$814$		0			0
$815$		0			0
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	6.92820	−	4.00000i	0.242387	−	0.139942i
$818$			5.00000i			0.174821i
$819$	−6.00000	+	5.19615i	−0.209657	+	0.181568i
$820$		0			0
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	0.891891	+	0.452250i	$0.149379\pi$
$821$	24.0000	+	41.5692i	0.837606	+	1.45078i	−0.0542853	+	0.998525i	$0.517288\pi$
$822$	−8.66025	−	5.00000i	−0.302061	−	0.174395i
$823$	−4.33013	−	2.50000i	−0.150939	−	0.0871445i	0.422628	−	0.906303i	$-0.361108\pi$
$823$	−4.33013	−	2.50000i	−0.150939	−	0.0871445i	−0.573567	+	0.819159i	$0.694441\pi$
$824$	19.5000	+	33.7750i	0.679315	+	1.17661i
$825$		0			0
$826$	−5.00000	−	25.9808i	−0.173972	−	0.903986i
$827$			24.0000i			0.834562i	0.908778	+	0.417281i	$0.137017\pi$
$827$			24.0000i			0.834562i	−0.908778	+	0.417281i	$0.862983\pi$
$828$	−1.73205	+	1.00000i	−0.0601929	+	0.0347524i
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	−0.966371	−	0.257152i	$-0.917216\pi$
$829$	−7.50000	+	12.9904i	−0.260486	+	0.451175i	0.705885	+	0.708326i	$0.250549\pi$
$830$		0			0
$831$	−2.50000	−	4.33013i	−0.0867240	−	0.150210i
$832$			21.0000i			0.728044i
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$	−3.00000			−0.103882
$835$		0			0
$836$		0			0
$837$	−6.92820	−	4.00000i	−0.239474	−	0.138260i
$838$	20.7846	−	12.0000i	0.717992	−	0.414533i
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	30.3109	−	17.5000i	1.04458	−	0.603090i
$843$	−5.19615	−	3.00000i	−0.178965	−	0.103325i
$844$	2.50000	−	4.33013i	0.0860535	−	0.149049i
$845$		0			0
$846$	−10.0000			−0.343807
$847$	−19.0526	−	22.0000i	−0.654654	−	0.755929i
$848$			14.0000i			0.480762i
$849$	−9.50000	−	16.4545i	−0.326039	−	0.564716i
$850$		0			0
$851$	−7.00000	+	12.1244i	−0.239957	+	0.415618i
$852$	−10.3923	+	6.00000i	−0.356034	+	0.205557i
$853$		−	6.00000i		−	0.205436i	−0.994711	−	0.102718i	$-0.967246\pi$
$853$		−	6.00000i		−	0.205436i	0.994711	−	0.102718i	$-0.0327539\pi$
$854$	−17.5000	−	6.06218i	−0.598838	−	0.207443i
$855$		0			0
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	0.742030	−	0.670366i	$-0.233863\pi$
$857$	15.5885	+	9.00000i	0.532492	+	0.307434i	−0.209539	+	0.977800i	$0.567196\pi$
$858$		0			0
$859$	−26.0000	−	45.0333i	−0.887109	−	1.53652i	−0.843278	−	0.537478i	$-0.819377\pi$
$859$	−26.0000	−	45.0333i	−0.887109	−	1.53652i	−0.0438309	−	0.999039i	$-0.513956\pi$
$860$		0			0
$861$		0			0
$862$			2.00000i			0.0681203i
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	−0.408946	−	0.912558i	$-0.634104\pi$
$863$	5.19615	−	3.00000i	0.176879	−	0.102121i	0.585826	+	0.810437i	$0.300770\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$			13.0000i			0.441503i
$868$	−13.8564	−	16.0000i	−0.470317	−	0.543075i
$869$		0			0
$870$		0			0
$871$	−7.50000	+	12.9904i	−0.254128	+	0.440162i
$872$	38.9711	+	22.5000i	1.31973	+	0.761946i
$873$	7.79423	−	4.50000i	0.263795	−	0.152302i
$874$	−2.00000			−0.0676510
$875$		0			0
$876$	11.0000			0.371656
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	−0.797062	−	0.603897i	$-0.793614\pi$
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	0.124459	+	0.992225i	$0.460280\pi$
$878$	9.52628	+	5.50000i	0.321496	+	0.185616i
$879$	−8.00000	+	13.8564i	−0.269833	+	0.467365i
$880$		0			0
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$	−6.92820	−	1.00000i	−0.233285	−	0.0336718i
$883$			31.0000i			1.04323i	0.853180	+	0.521617i	$0.174671\pi$
$883$			31.0000i			1.04323i	−0.853180	+	0.521617i	$0.825329\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	−50.2295	+	29.0000i	−1.68654	+	0.973725i	−0.729406	+	0.684081i	$0.760204\pi$
$887$	−50.2295	+	29.0000i	−1.68654	+	0.973725i	−0.957135	+	0.289644i	$0.906463\pi$
$888$		−	21.0000i		−	0.704714i
$889$	5.50000	+	28.5788i	0.184464	+	0.958503i
$890$		0			0
$891$		0			0
$892$	12.9904	+	7.50000i	0.434950	+	0.251119i
$893$	8.66025	+	5.00000i	0.289804	+	0.167319i
$894$	−2.00000	−	3.46410i	−0.0668900	−	0.115857i
$895$		0			0
$896$	6.00000	−	5.19615i	0.200446	−	0.173591i
$897$			6.00000i			0.200334i
$898$	5.19615	−	3.00000i	0.173398	−	0.100111i
$899$	32.0000	−	55.4256i	1.06726	−	1.84855i
$900$		0			0
$901$	14.0000	+	24.2487i	0.466408	+	0.807842i
$902$		0			0
$903$	6.92820	−	20.0000i	0.230556	−	0.665558i
$904$	−18.0000			−0.598671
$905$		0			0
$906$	0.500000	−	0.866025i	0.0166114	−	0.0287718i
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	0.514309	−	0.857605i	$-0.328048\pi$
$907$	0.866025	+	0.500000i	0.0287559	+	0.0166022i	−0.485553	+	0.874207i	$0.661382\pi$
$908$	−17.3205	+	10.0000i	−0.574801	+	0.331862i
$909$	16.0000			0.530687
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	0.866025	−	0.500000i	0.0286770	−	0.0165567i
$913$		0			0
$914$	−1.50000	+	2.59808i	−0.0496156	+	0.0859367i
$915$		0			0
$916$	−13.0000			−0.429532
$917$	24.2487	+	28.0000i	0.800763	+	0.924641i
$918$			2.00000i			0.0660098i
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	0.993208	−	0.116348i	$-0.0371189\pi$
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	−0.597365	+	0.801970i	$0.703786\pi$
$920$		0			0
$921$	6.00000	−	10.3923i	0.197707	−	0.342438i
$922$	1.73205	−	1.00000i	0.0570421	−	0.0329332i
$923$			36.0000i			1.18495i
$924$		0			0
$925$		0			0
$926$	−16.5000	−	28.5788i	−0.542224	−	0.939159i
$927$	−11.2583	−	6.50000i	−0.369772	−	0.213488i
$928$	34.6410	+	20.0000i	1.13715	+	0.656532i
$929$	−22.0000	−	38.1051i	−0.721797	−	1.25019i	−0.960279	−	0.279042i	$-0.909983\pi$
$929$	−22.0000	−	38.1051i	−0.721797	−	1.25019i	0.238482	−	0.971147i	$-0.423350\pi$
$930$		0			0
$931$	5.50000	+	4.33013i	0.180255	+	0.141914i
$932$			24.0000i			0.786146i
$933$	−25.9808	+	15.0000i	−0.850572	+	0.491078i
$934$	−1.00000	+	1.73205i	−0.0327210	+	0.0566744i
$935$		0			0
$936$	−4.50000	−	7.79423i	−0.147087	−	0.254762i
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$	−12.9904	+	2.50000i	−0.424151	+	0.0816279i
$939$	−14.0000			−0.456873
$940$		0			0
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	0.288988	+	0.957333i	$0.406681\pi$
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	−0.973568	+	0.228395i	$0.926652\pi$
$942$	6.06218	+	3.50000i	0.197516	+	0.114036i
$943$		0			0
$944$	10.0000			0.325472
$945$		0			0
$946$		0			0
$947$	19.0526	−	11.0000i	0.619125	−	0.357452i	−0.157403	−	0.987534i	$-0.550312\pi$
$947$	19.0526	−	11.0000i	0.619125	−	0.357452i	0.776528	+	0.630082i	$0.216979\pi$
$948$	−6.06218	−	3.50000i	−0.196890	−	0.113675i
$949$	16.5000	−	28.5788i	0.535613	−	0.927708i
$950$		0			0
$951$	14.0000			0.453981
$952$	−5.19615	+	15.0000i	−0.168408	+	0.486153i
$953$		−	20.0000i		−	0.647864i	−0.946080	−	0.323932i	$-0.894995\pi$
$953$		−	20.0000i		−	0.647864i	0.946080	−	0.323932i	$-0.105005\pi$
$954$	−7.00000	−	12.1244i	−0.226633	−	0.392541i
$955$		0			0
$956$	−14.0000	+	24.2487i	−0.452792	+	0.784259i
$957$		0			0
$958$			2.00000i			0.0646171i
$959$	25.0000	+	8.66025i	0.807292	+	0.279654i
$960$		0			0
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−18.1865	−	10.5000i	−0.586357	−	0.338534i
$963$	−5.19615	−	3.00000i	−0.167444	−	0.0966736i
$964$	−10.5000	−	18.1865i	−0.338182	−	0.585749i
$965$		0			0
$966$	−4.00000	+	3.46410i	−0.128698	+	0.111456i
$967$			23.0000i			0.739630i	0.929105	+	0.369815i	$0.120579\pi$
$967$			23.0000i			0.739630i	−0.929105	+	0.369815i	$0.879421\pi$
$968$	28.5788	−	16.5000i	0.918559	−	0.530330i
$969$	1.00000	−	1.73205i	0.0321246	−	0.0556415i
$970$		0			0
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	0.794678	−	0.607032i	$-0.207640\pi$
$971$	−4.00000	−	6.92820i	−0.128366	−	0.222337i	−0.923044	+	0.384695i	$0.874307\pi$
$972$			1.00000i			0.0320750i
$973$	7.79423	−	1.50000i	0.249871	−	0.0480878i
$974$	−8.00000			−0.256337
$975$		0			0
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	−34.6410	−	20.0000i	−1.10826	−	0.639857i	−0.169885	−	0.985464i	$-0.554340\pi$
$977$	−34.6410	−	20.0000i	−1.10826	−	0.639857i	−0.938379	+	0.345607i	$0.887673\pi$
$978$	−7.79423	+	4.50000i	−0.249232	+	0.143894i
$979$		0			0
$980$		0			0
$981$	−15.0000			−0.478913
$982$	5.19615	−	3.00000i	0.165816	−	0.0957338i
$983$	19.0526	+	11.0000i	0.607682	+	0.350846i	0.772058	−	0.635552i	$-0.219228\pi$
$983$	19.0526	+	11.0000i	0.607682	+	0.350846i	−0.164376	+	0.986398i	$0.552561\pi$
$984$		0			0
$985$		0			0
$986$	−16.0000			−0.509544
$987$	25.9808	−	5.00000i	0.826977	−	0.159152i
$988$			3.00000i			0.0954427i
$989$	−8.00000	−	13.8564i	−0.254385	−	0.440608i
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$	34.6410	−	20.0000i	1.09985	−	0.635001i
$993$			21.0000i			0.666415i
$994$	−24.0000	+	20.7846i	−0.761234	+	0.659248i
$995$		0			0
$996$	7.00000	+	12.1244i	0.221803	+	0.384175i
$997$	−32.0429	−	18.5000i	−1.01481	−	0.585901i	−0.102214	−	0.994762i	$-0.532593\pi$
$997$	−32.0429	−	18.5000i	−1.01481	−	0.585901i	−0.912596	+	0.408862i	$0.865926\pi$
$998$	16.4545	+	9.50000i	0.520858	+	0.300717i
$999$	3.50000	+	6.06218i	0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.c.424.1		4
5.2	odd	4		525.2.i.b.151.1	✓	2
5.3	odd	4		525.2.i.d.151.1	yes	2
5.4	even	2	inner	525.2.r.c.424.2		4
7.2	even	3	inner	525.2.r.c.499.2		4
35.2	odd	12		525.2.i.b.226.1	yes	2
35.3	even	12		3675.2.a.g.1.1		1
35.9	even	6	inner	525.2.r.c.499.1		4
35.17	even	12		3675.2.a.k.1.1		1
35.18	odd	12		3675.2.a.e.1.1		1
35.23	odd	12		525.2.i.d.226.1	yes	2
35.32	odd	12		3675.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.b.151.1	✓	2	5.2	odd	4
525.2.i.b.226.1	yes	2	35.2	odd	12
525.2.i.d.151.1	yes	2	5.3	odd	4
525.2.i.d.226.1	yes	2	35.23	odd	12
525.2.r.c.424.1		4	1.1	even	1	trivial
525.2.r.c.424.2		4	5.4	even	2	inner
525.2.r.c.499.1		4	35.9	even	6	inner
525.2.r.c.499.2		4	7.2	even	3	inner
3675.2.a.e.1.1		1	35.18	odd	12
3675.2.a.g.1.1		1	35.3	even	12
3675.2.a.k.1.1		1	35.17	even	12
3675.2.a.m.1.1		1	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -3.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.866025 - 0.500000i) q^{12} -3.00000i q^{13} +(2.00000 - 1.73205i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(2.50000 + 0.866025i) q^{21} +(1.73205 - 1.00000i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(1.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(0.866025 - 2.50000i) q^{28} +8.00000 q^{29} +(4.00000 - 6.92820i) q^{31} +(4.33013 + 2.50000i) q^{32} -2.00000 q^{34} -1.00000 q^{36} +(-6.06218 + 3.50000i) q^{37} +(-0.866025 - 0.500000i) q^{38} +(-1.50000 + 2.59808i) q^{39} +(-2.59808 + 0.500000i) q^{42} -8.00000i q^{43} +(-1.00000 + 1.73205i) q^{46} +(8.66025 - 5.00000i) q^{47} -1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(2.59808 + 1.50000i) q^{52} +(12.1244 + 7.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(1.50000 + 7.79423i) q^{56} -1.00000i q^{57} +(-6.92820 + 4.00000i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-3.50000 - 6.06218i) q^{61} +8.00000i q^{62} +(-1.73205 - 2.00000i) q^{63} -7.00000 q^{64} +(-4.33013 - 2.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} -2.00000 q^{69} -12.0000 q^{71} +(2.59808 - 1.50000i) q^{72} +(9.52628 + 5.50000i) q^{73} +(3.50000 - 6.06218i) q^{74} -1.00000 q^{76} -3.00000i q^{78} +(-3.50000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} +14.0000i q^{83} +(-2.00000 + 1.73205i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-6.92820 - 4.00000i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(1.50000 + 7.79423i) q^{91} +2.00000i q^{92} +(-6.92820 + 4.00000i) q^{93} +(-5.00000 + 8.66025i) q^{94} +(-2.50000 - 4.33013i) q^{96} -9.00000i q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q - 2 q^{4} + 4 q^{6} + 2 q^{9} + 8 q^{14} + 2 q^{16} + 2 q^{19} + 10 q^{21} - 6 q^{24} + 6 q^{26} + 32 q^{29} + 16 q^{31} - 8 q^{34} - 4 q^{36} - 6 q^{39} - 4 q^{46} + 26 q^{49} - 4 q^{51} + 2 q^{54} + 6 q^{56} + 20 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{69} - 48 q^{71} + 14 q^{74} - 4 q^{76} - 14 q^{79} - 2 q^{81} - 8 q^{84} + 16 q^{86} - 12 q^{89} + 6 q^{91} - 20 q^{94} - 10 q^{96}+O(q^{100}) \) 4 * q - 2 * q^4 + 4 * q^6 + 2 * q^9 + 8 * q^14 + 2 * q^16 + 2 * q^19 + 10 * q^21 - 6 * q^24 + 6 * q^26 + 32 * q^29 + 16 * q^31 - 8 * q^34 - 4 * q^36 - 6 * q^39 - 4 * q^46 + 26 * q^49 - 4 * q^51 + 2 * q^54 + 6 * q^56 + 20 * q^59 - 14 * q^61 - 28 * q^64 - 8 * q^69 - 48 * q^71 + 14 * q^74 - 4 * q^76 - 14 * q^79 - 2 * q^81 - 8 * q^84 + 16 * q^86 - 12 * q^89 + 6 * q^91 - 20 * q^94 - 10 * q^96

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