LMFDB - Embedded newform 525.2.q.b.374.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(299,525)] 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("525.299"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,-2,0,6,0,0,-6,0,-12,0,0,-12,0,10,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.374
Dual form			525.2.q.b.299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.73205 q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} -1.73205 q^{12} -3.46410 q^{13} +(-3.00000 + 3.46410i) q^{14} +(2.50000 + 4.33013i) q^{16} +(-5.19615 - 3.00000i) q^{17} +5.19615 q^{18} +(6.00000 - 3.46410i) q^{19} +(3.00000 - 3.46410i) q^{21} +6.00000i q^{22} +(-0.866025 - 1.50000i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(3.00000 + 5.19615i) q^{26} -5.19615 q^{27} +(2.59808 + 0.500000i) q^{28} -1.73205i q^{29} +(-3.00000 - 1.73205i) q^{31} +(2.59808 - 4.50000i) q^{32} -6.00000i q^{33} +10.3923i q^{34} +(-1.50000 - 2.59808i) q^{36} +(3.46410 - 2.00000i) q^{37} +(-10.3923 - 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +(-7.79423 - 1.50000i) q^{42} -1.00000i q^{43} +(3.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-4.33013 + 7.50000i) q^{48} +(-5.50000 + 4.33013i) q^{49} -10.3923i q^{51} +(1.73205 - 3.00000i) q^{52} +(4.50000 + 7.79423i) q^{54} +(1.50000 + 4.33013i) q^{56} +(10.3923 + 6.00000i) q^{57} +(-2.59808 + 1.50000i) q^{58} +(-4.50000 + 2.59808i) q^{61} +6.00000i q^{62} +(7.79423 + 1.50000i) q^{63} +1.00000 q^{64} +(-9.00000 + 5.19615i) q^{66} +(11.2583 + 6.50000i) q^{67} +(5.19615 - 3.00000i) q^{68} +(1.50000 - 2.59808i) q^{69} +6.92820i q^{71} +(2.59808 - 4.50000i) q^{72} +(1.73205 - 3.00000i) q^{73} +(-6.00000 - 3.46410i) q^{74} +6.92820i q^{76} +(-1.73205 + 9.00000i) q^{77} +(-5.19615 + 9.00000i) q^{78} +(-8.00000 - 13.8564i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 4.50000i) q^{82} +9.00000i q^{83} +(1.50000 + 4.33013i) q^{84} +(-1.50000 + 0.866025i) q^{86} +(2.59808 - 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(1.50000 + 2.59808i) q^{89} +(3.00000 + 8.66025i) q^{91} +1.73205 q^{92} -6.00000i q^{93} +9.00000 q^{96} -10.3923 q^{97} +(11.2583 + 4.50000i) q^{98} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 6 q^{6} - 6 q^{9} - 12 q^{11} - 12 q^{14} + 10 q^{16} + 24 q^{19} + 12 q^{21} - 6 q^{24} + 12 q^{26} - 12 q^{31} - 6 q^{36} - 12 q^{39} - 12 q^{41} + 12 q^{44} - 6 q^{46} - 22 q^{49} + 18 q^{54}+ \cdots + 36 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 6 * q^6 - 6 * q^9 - 12 * q^11 - 12 * q^14 + 10 * q^16 + 24 * q^19 + 12 * q^21 - 6 * q^24 + 12 * q^26 - 12 * q^31 - 6 * q^36 - 12 * q^39 - 12 * q^41 + 12 * q^44 - 6 * q^46 - 22 * q^49 + 18 * q^54 + 6 * q^56 - 18 * q^61 + 4 * q^64 - 36 * q^66 + 6 * q^69 - 24 * q^74 - 32 * q^79 - 18 * q^81 + 6 * q^84 - 6 * q^86 + 6 * q^89 + 12 * q^91 + 36 * q^96 + 36 * q^99

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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	−	1.50000i	−0.612372	−	1.06066i	−0.990839	−	0.135045i	$-0.956882\pi$
$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.50000	−	2.59808i	0.612372	−	1.06066i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	−1.73205			−0.612372
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$	−1.73205			−0.500000
$13$	−3.46410			−0.960769			−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410			−0.960769			−0.480384	+	0.877058i	$0.659503\pi$
$14$	−3.00000	+	3.46410i	−0.801784	+	0.925820i
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$	5.19615			1.22474
$19$	6.00000	−	3.46410i	1.37649	−	0.794719i	0.384759	−	0.923017i	$-0.374285\pi$
$19$	6.00000	−	3.46410i	1.37649	−	0.794719i	0.991736	+	0.128298i	$0.0409513\pi$
$20$		0			0
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$			6.00000i			1.27920i
$23$	−0.866025	−	1.50000i	−0.180579	−	0.312772i	0.761499	−	0.648166i	$-0.224464\pi$
$23$	−0.866025	−	1.50000i	−0.180579	−	0.312772i	−0.942078	+	0.335394i	$0.891130\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$		0			0
$26$	3.00000	+	5.19615i	0.588348	+	1.01905i
$27$	−5.19615			−1.00000
$28$	2.59808	+	0.500000i	0.490990	+	0.0944911i
$29$		−	1.73205i		−	0.321634i	−0.986984	−	0.160817i	$-0.948587\pi$
$29$		−	1.73205i		−	0.321634i	0.986984	−	0.160817i	$-0.0514129\pi$
$30$		0			0
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	2.59808	−	4.50000i	0.459279	−	0.795495i
$33$		−	6.00000i		−	1.04447i
$34$			10.3923i			1.78227i
$35$		0			0
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	−0.187453	−	0.982274i	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$	−10.3923	−	6.00000i	−1.68585	−	0.973329i
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	−7.79423	−	1.50000i	−1.20268	−	0.231455i
$43$		−	1.00000i		−	0.152499i	−0.997089	−	0.0762493i	$-0.975706\pi$
$43$		−	1.00000i		−	0.152499i	0.997089	−	0.0762493i	$-0.0242945\pi$
$44$	3.00000	−	1.73205i	0.452267	−	0.261116i
$45$		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	$0.333333\pi$
$48$	−4.33013	+	7.50000i	−0.625000	+	1.08253i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$		−	10.3923i		−	1.45521i
$52$	1.73205	−	3.00000i	0.240192	−	0.416025i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$		0			0
$56$	1.50000	+	4.33013i	0.200446	+	0.578638i
$57$	10.3923	+	6.00000i	1.37649	+	0.794719i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	−0.759608	−	0.650381i	$-0.774609\pi$
$61$	−4.50000	+	2.59808i	−0.576166	+	0.332650i	0.183442	+	0.983030i	$0.441276\pi$
$62$			6.00000i			0.762001i
$63$	7.79423	+	1.50000i	0.981981	+	0.188982i
$64$	1.00000			0.125000
$65$		0			0
$66$	−9.00000	+	5.19615i	−1.10782	+	0.639602i
$67$	11.2583	+	6.50000i	1.37542	+	0.794101i	0.991605	−	0.129307i	$-0.0412752\pi$
$67$	11.2583	+	6.50000i	1.37542	+	0.794101i	0.383819	+	0.923408i	$0.374609\pi$
$68$	5.19615	−	3.00000i	0.630126	−	0.363803i
$69$	1.50000	−	2.59808i	0.180579	−	0.312772i
$70$		0			0
$71$			6.92820i			0.822226i	0.911584	+	0.411113i	$0.134860\pi$
$71$			6.92820i			0.822226i	−0.911584	+	0.411113i	$0.865140\pi$
$72$	2.59808	−	4.50000i	0.306186	−	0.530330i
$73$	1.73205	−	3.00000i	0.202721	−	0.351123i	−0.746683	−	0.665180i	$-0.768355\pi$
$73$	1.73205	−	3.00000i	0.202721	−	0.351123i	0.949404	+	0.314057i	$0.101688\pi$
$74$	−6.00000	−	3.46410i	−0.697486	−	0.402694i
$75$		0			0
$76$			6.92820i			0.794719i
$77$	−1.73205	+	9.00000i	−0.197386	+	1.02565i
$78$	−5.19615	+	9.00000i	−0.588348	+	1.01905i
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.59808	+	4.50000i	0.286910	+	0.496942i
$83$			9.00000i			0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$			9.00000i			0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	1.50000	+	4.33013i	0.163663	+	0.472456i
$85$		0			0
$86$	−1.50000	+	0.866025i	−0.161749	+	0.0933859i
$87$	2.59808	−	1.50000i	0.278543	−	0.160817i
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	0.934508	−	0.355942i	$-0.115840\pi$
$89$	1.50000	+	2.59808i	0.159000	+	0.275396i	−0.775509	+	0.631337i	$0.782506\pi$
$90$		0			0
$91$	3.00000	+	8.66025i	0.314485	+	0.907841i
$92$	1.73205			0.180579
$93$		−	6.00000i		−	0.622171i
$94$		0			0
$95$		0			0
$96$	9.00000			0.918559
$97$	−10.3923			−1.05518			−0.527589	−	0.849500i	$-0.676904\pi$
$97$	−10.3923			−1.05518			−0.527589	+	0.849500i	$0.676904\pi$
$98$	11.2583	+	4.50000i	1.13726	+	0.454569i
$99$	9.00000	−	5.19615i	0.904534	−	0.522233i
$100$		0			0
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$	−15.5885	+	9.00000i	−1.54349	+	0.891133i
$103$	2.59808	+	4.50000i	0.255996	+	0.443398i	0.965166	−	0.261640i	$-0.0842633\pi$
$103$	2.59808	+	4.50000i	0.255996	+	0.443398i	−0.709170	+	0.705038i	$0.750930\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$		0			0
$107$	2.59808	+	4.50000i	0.251166	+	0.435031i	0.963847	−	0.266456i	$-0.0858528\pi$
$107$	2.59808	+	4.50000i	0.251166	+	0.435031i	−0.712681	+	0.701488i	$0.752519\pi$
$108$	2.59808	−	4.50000i	0.250000	−	0.433013i
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	8.66025	−	10.0000i	0.818317	−	0.944911i
$113$	6.92820			0.651751			0.325875	−	0.945413i	$-0.394341\pi$
$113$	6.92820			0.651751			0.325875	+	0.945413i	$0.394341\pi$
$114$		−	20.7846i		−	1.94666i
$115$		0			0
$116$	1.50000	+	0.866025i	0.139272	+	0.0804084i
$117$	5.19615	−	9.00000i	0.480384	−	0.832050i
$118$		0			0
$119$	−3.00000	+	15.5885i	−0.275010	+	1.42899i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	7.79423	+	4.50000i	0.705656	+	0.407411i
$123$	−2.59808	−	4.50000i	−0.234261	−	0.405751i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$		0			0
$126$	−4.50000	−	12.9904i	−0.400892	−	1.15728i
$127$		−	16.0000i		−	1.41977i	−0.704317	−	0.709885i	$-0.748747\pi$
$127$		−	16.0000i		−	1.41977i	0.704317	−	0.709885i	$-0.251253\pi$
$128$	−6.06218	−	10.5000i	−0.535826	−	0.928078i
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	5.19615	+	3.00000i	0.452267	+	0.261116i
$133$	−13.8564	−	12.0000i	−1.20150	−	1.04053i
$134$		−	22.5167i		−	1.94514i
$135$		0			0
$136$	9.00000	+	5.19615i	0.771744	+	0.445566i
$137$	10.3923	−	18.0000i	0.887875	−	1.53784i	0.0454914	−	0.998965i	$-0.485515\pi$
$137$	10.3923	−	18.0000i	0.887875	−	1.53784i	0.842383	−	0.538879i	$-0.181152\pi$
$138$	−5.19615			−0.442326
$139$			10.3923i			0.881464i	0.897639	+	0.440732i	$0.145281\pi$
$139$			10.3923i			0.881464i	−0.897639	+	0.440732i	$0.854719\pi$
$140$		0			0
$141$		0			0
$142$	10.3923	−	6.00000i	0.872103	−	0.503509i
$143$	10.3923	+	6.00000i	0.869048	+	0.501745i
$144$	−15.0000			−1.25000
$145$		0			0
$146$	−6.00000			−0.496564
$147$	−11.2583	−	4.50000i	−0.928571	−	0.371154i
$148$			4.00000i			0.328798i
$149$	19.5000	−	11.2583i	1.59750	−	0.922318i	0.605536	−	0.795818i	$-0.292959\pi$
$149$	19.5000	−	11.2583i	1.59750	−	0.922318i	0.991967	−	0.126500i	$-0.0403744\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	−10.3923	+	6.00000i	−0.842927	+	0.486664i
$153$	15.5885	−	9.00000i	1.26025	−	0.727607i
$154$	15.0000	−	5.19615i	1.20873	−	0.418718i
$155$		0			0
$156$	6.00000			0.480384
$157$	1.73205	−	3.00000i	0.138233	−	0.239426i	−0.788595	−	0.614913i	$-0.789191\pi$
$157$	1.73205	−	3.00000i	0.138233	−	0.239426i	0.926828	+	0.375487i	$0.122524\pi$
$158$	−13.8564	+	24.0000i	−1.10236	+	1.90934i
$159$		0			0
$160$		0			0
$161$	−3.00000	+	3.46410i	−0.236433	+	0.273009i
$162$	−7.79423	+	13.5000i	−0.612372	+	1.06066i
$163$	−6.92820	+	4.00000i	−0.542659	+	0.313304i	−0.746156	−	0.665771i	$-0.768103\pi$
$163$	−6.92820	+	4.00000i	−0.542659	+	0.313304i	0.203497	+	0.979076i	$0.434769\pi$
$164$	1.50000	−	2.59808i	0.117130	−	0.202876i
$165$		0			0
$166$	13.5000	−	7.79423i	1.04780	−	0.604949i
$167$			21.0000i			1.62503i	0.582941	+	0.812514i	$0.301902\pi$
$167$			21.0000i			1.62503i	−0.582941	+	0.812514i	$0.698098\pi$
$168$	−5.19615	+	6.00000i	−0.400892	+	0.462910i
$169$	−1.00000			−0.0769231
$170$		0			0
$171$			20.7846i			1.58944i
$172$	0.866025	+	0.500000i	0.0660338	+	0.0381246i
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$	−4.50000	−	2.59808i	−0.341144	−	0.196960i
$175$		0			0
$176$		−	17.3205i		−	1.30558i
$177$		0			0
$178$	2.59808	−	4.50000i	0.194734	−	0.337289i
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	0.797096	−	0.603853i	$-0.206369\pi$
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	−0.124404	+	0.992232i	$0.539702\pi$
$180$		0			0
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$	10.3923	−	12.0000i	0.770329	−	0.889499i
$183$	−7.79423	−	4.50000i	−0.576166	−	0.332650i
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$		0			0
$186$	−9.00000	+	5.19615i	−0.659912	+	0.381000i
$187$	10.3923	+	18.0000i	0.759961	+	1.31629i
$188$		0			0
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$		0			0
$191$	9.00000	−	5.19615i	0.651217	−	0.375980i	−0.137705	−	0.990473i	$-0.543973\pi$
$191$	9.00000	−	5.19615i	0.651217	−	0.375980i	0.788922	+	0.614493i	$0.210639\pi$
$192$	0.866025	+	1.50000i	0.0625000	+	0.108253i
$193$	19.0526	+	11.0000i	1.37143	+	0.791797i	0.991109	−	0.133056i	$-0.0424789\pi$
$193$	19.0526	+	11.0000i	1.37143	+	0.791797i	0.380325	+	0.924853i	$0.375812\pi$
$194$	9.00000	+	15.5885i	0.646162	+	1.11919i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	−3.46410			−0.246807			−0.123404	−	0.992357i	$-0.539381\pi$
$197$	−3.46410			−0.246807			−0.123404	+	0.992357i	$0.539381\pi$
$198$	−15.5885	−	9.00000i	−1.10782	−	0.639602i
$199$	−6.00000	−	3.46410i	−0.425329	−	0.245564i	0.272026	−	0.962290i	$-0.412306\pi$
$199$	−6.00000	−	3.46410i	−0.425329	−	0.245564i	−0.697355	+	0.716726i	$0.745640\pi$
$200$		0			0
$201$			22.5167i			1.58820i
$202$	−25.9808			−1.82800
$203$	−4.33013	+	1.50000i	−0.303915	+	0.105279i
$204$	9.00000	+	5.19615i	0.630126	+	0.363803i
$205$		0			0
$206$	4.50000	−	7.79423i	0.313530	−	0.543050i
$207$	5.19615			0.361158
$208$	−8.66025	−	15.0000i	−0.600481	−	1.04006i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	−10.3923	+	6.00000i	−0.712069	+	0.411113i
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$		0			0
$216$	9.00000			0.612372
$217$	−1.73205	+	9.00000i	−0.117579	+	0.610960i
$218$	8.66025			0.586546
$219$	6.00000			0.405442
$220$		0			0
$221$	18.0000	+	10.3923i	1.21081	+	0.699062i
$222$		−	12.0000i		−	0.805387i
$223$	3.46410			0.231973			0.115987	−	0.993251i	$-0.462997\pi$
$223$	3.46410			0.231973			0.115987	+	0.993251i	$0.462997\pi$
$224$	−13.5000	−	2.59808i	−0.902007	−	0.173591i
$225$		0			0
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$	−10.3923	+	6.00000i	−0.688247	+	0.397360i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$	−15.0000	+	5.19615i	−0.986928	+	0.341882i
$232$			3.00000i			0.196960i
$233$	−1.73205	−	3.00000i	−0.113470	−	0.196537i	0.803697	−	0.595039i	$-0.202863\pi$
$233$	−1.73205	−	3.00000i	−0.113470	−	0.196537i	−0.917167	+	0.398502i	$0.869530\pi$
$234$	−18.0000			−1.17670
$235$		0			0
$236$		0			0
$237$	13.8564	−	24.0000i	0.900070	−	1.55897i
$238$	25.9808	−	9.00000i	1.68408	−	0.583383i
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	−6.00000	−	3.46410i	−0.386494	−	0.223142i	0.294146	−	0.955761i	$-0.404965\pi$
$241$	−6.00000	−	3.46410i	−0.386494	−	0.223142i	−0.680640	+	0.732618i	$0.738298\pi$
$242$	0.866025	−	1.50000i	0.0556702	−	0.0964237i
$243$	7.79423	−	13.5000i	0.500000	−	0.866025i
$244$		−	5.19615i		−	0.332650i
$245$		0			0
$246$	−4.50000	+	7.79423i	−0.286910	+	0.496942i
$247$	−20.7846	+	12.0000i	−1.32249	+	0.763542i
$248$	5.19615	+	3.00000i	0.329956	+	0.190500i
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	−5.19615	+	6.00000i	−0.327327	+	0.377964i
$253$			6.00000i			0.377217i
$254$	−24.0000	+	13.8564i	−1.50589	+	0.869428i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	−2.59808	−	1.50000i	−0.161749	−	0.0933859i
$259$	−8.00000	−	6.92820i	−0.497096	−	0.430498i
$260$		0			0
$261$	4.50000	+	2.59808i	0.278543	+	0.160817i
$262$	−10.3923	+	18.0000i	−0.642039	+	1.11204i
$263$	0.866025	−	1.50000i	0.0534014	−	0.0924940i	−0.838089	−	0.545534i	$-0.816327\pi$
$263$	0.866025	−	1.50000i	0.0534014	−	0.0924940i	0.891490	+	0.453040i	$0.149660\pi$
$264$			10.3923i			0.639602i
$265$		0			0
$266$	−6.00000	+	31.1769i	−0.367884	+	1.91158i
$267$	−2.59808	+	4.50000i	−0.159000	+	0.275396i
$268$	−11.2583	+	6.50000i	−0.687712	+	0.397051i
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	6.00000	−	3.46410i	0.364474	−	0.210429i	−0.306568	−	0.951849i	$-0.599181\pi$
$271$	6.00000	−	3.46410i	0.364474	−	0.210429i	0.671042	+	0.741420i	$0.265847\pi$
$272$		−	30.0000i		−	1.81902i
$273$	−10.3923	+	12.0000i	−0.628971	+	0.726273i
$274$	−36.0000			−2.17484
$275$		0			0
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	−22.5167	−	13.0000i	−1.35290	−	0.781094i	−0.364241	−	0.931305i	$-0.618672\pi$
$277$	−22.5167	−	13.0000i	−1.35290	−	0.781094i	−0.988654	+	0.150210i	$0.952005\pi$
$278$	15.5885	−	9.00000i	0.934934	−	0.539784i
$279$	9.00000	−	5.19615i	0.538816	−	0.311086i
$280$		0			0
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$		0			0
$283$	−15.5885	+	27.0000i	−0.926638	+	1.60498i	−0.137732	+	0.990470i	$0.543981\pi$
$283$	−15.5885	+	27.0000i	−0.926638	+	1.60498i	−0.788906	+	0.614514i	$0.789352\pi$
$284$	−6.00000	−	3.46410i	−0.356034	−	0.205557i
$285$		0			0
$286$		−	20.7846i		−	1.22902i
$287$	2.59808	+	7.50000i	0.153360	+	0.442711i
$288$	7.79423	+	13.5000i	0.459279	+	0.795495i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$		0			0
$291$	−9.00000	−	15.5885i	−0.527589	−	0.913812i
$292$	1.73205	+	3.00000i	0.101361	+	0.175562i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$	3.00000	+	20.7846i	0.174964	+	1.21218i
$295$		0			0
$296$	−6.00000	+	3.46410i	−0.348743	+	0.201347i
$297$	15.5885	+	9.00000i	0.904534	+	0.522233i
$298$	−33.7750	−	19.5000i	−1.95653	−	1.12960i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$	−3.46410			−0.199337
$303$	25.9808			1.49256
$304$	30.0000	+	17.3205i	1.72062	+	0.993399i
$305$		0			0
$306$	−27.0000	−	15.5885i	−1.54349	−	0.891133i
$307$	22.5167			1.28509			0.642547	−	0.766246i	$-0.277878\pi$
$307$	22.5167			1.28509			0.642547	+	0.766246i	$0.277878\pi$
$308$	−6.92820	−	6.00000i	−0.394771	−	0.341882i
$309$	−4.50000	+	7.79423i	−0.255996	+	0.443398i
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	5.19615	+	9.00000i	0.294174	+	0.509525i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−6.00000			−0.338600
$315$		0			0
$316$	16.0000			0.900070
$317$	−8.66025	−	15.0000i	−0.486408	−	0.842484i	0.513470	−	0.858108i	$-0.328360\pi$
$317$	−8.66025	−	15.0000i	−0.486408	−	0.842484i	−0.999878	+	0.0156238i	$0.995027\pi$
$318$		0			0
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$		0			0
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$	7.79423	+	1.50000i	0.434355	+	0.0835917i
$323$	−41.5692			−2.31297
$324$	9.00000			0.500000
$325$		0			0
$326$	12.0000	+	6.92820i	0.664619	+	0.383718i
$327$	−8.66025			−0.478913
$328$	5.19615			0.286910
$329$		0			0
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$	−7.79423	−	4.50000i	−0.427764	−	0.246970i
$333$			12.0000i			0.657596i
$334$	31.5000	−	18.1865i	1.72360	−	0.995123i
$335$		0			0
$336$	22.5000	+	4.33013i	1.22748	+	0.236228i
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$	0.866025	+	1.50000i	0.0471056	+	0.0815892i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	31.1769	−	18.0000i	1.68585	−	0.973329i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$			1.73205i			0.0933859i
$345$		0			0
$346$	−18.0000	−	10.3923i	−0.967686	−	0.558694i
$347$	−9.52628	+	16.5000i	−0.511397	+	0.885766i	0.488515	+	0.872555i	$0.337539\pi$
$347$	−9.52628	+	16.5000i	−0.511397	+	0.885766i	−0.999913	+	0.0132111i	$0.995795\pi$
$348$			3.00000i			0.160817i
$349$		−	8.66025i		−	0.463573i	−0.972767	−	0.231786i	$-0.925543\pi$
$349$		−	8.66025i		−	0.463573i	0.972767	−	0.231786i	$-0.0744570\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$	−15.5885	+	9.00000i	−0.830868	+	0.479702i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$	−3.00000			−0.159000
$357$	−25.9808	+	9.00000i	−1.37505	+	0.476331i
$358$		−	18.0000i		−	0.951330i
$359$	21.0000	−	12.1244i	1.10834	−	0.639899i	0.169939	−	0.985455i	$-0.445643\pi$
$359$	21.0000	−	12.1244i	1.10834	−	0.639899i	0.938398	+	0.345556i	$0.112310\pi$
$360$		0			0
$361$	14.5000	−	25.1147i	0.763158	−	1.32183i
$362$	−7.79423	+	4.50000i	−0.409656	+	0.236515i
$363$	−0.866025	+	1.50000i	−0.0454545	+	0.0787296i
$364$	−9.00000	−	1.73205i	−0.471728	−	0.0907841i
$365$		0			0
$366$			15.5885i			0.814822i
$367$	−7.79423	+	13.5000i	−0.406855	+	0.704694i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−7.79423	+	13.5000i	−0.406855	+	0.704694i	0.587680	+	0.809093i	$0.300041\pi$
$368$	4.33013	−	7.50000i	0.225723	−	0.390965i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$		0			0
$372$	5.19615	+	3.00000i	0.269408	+	0.155543i
$373$	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	$0.300311\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$		0			0
$376$		0			0
$377$			6.00000i			0.309016i
$378$	15.5885	−	18.0000i	0.801784	−	0.925820i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	24.0000	−	13.8564i	1.22956	−	0.709885i
$382$	−15.5885	−	9.00000i	−0.797575	−	0.460480i
$383$	−18.1865	+	10.5000i	−0.929288	+	0.536525i	−0.886586	−	0.462563i	$-0.846930\pi$
$383$	−18.1865	+	10.5000i	−0.929288	+	0.536525i	−0.0427020	+	0.999088i	$0.513597\pi$
$384$	10.5000	−	18.1865i	0.535826	−	0.928078i
$385$		0			0
$386$		−	38.1051i		−	1.93950i
$387$	2.59808	+	1.50000i	0.132068	+	0.0762493i
$388$	5.19615	−	9.00000i	0.263795	−	0.456906i
$389$	−24.0000	−	13.8564i	−1.21685	−	0.702548i	−0.252606	−	0.967569i	$-0.581288\pi$
$389$	−24.0000	−	13.8564i	−1.21685	−	0.702548i	−0.964242	+	0.265022i	$0.914621\pi$
$390$		0			0
$391$			10.3923i			0.525561i
$392$	9.52628	−	7.50000i	0.481150	−	0.378807i
$393$	10.3923	−	18.0000i	0.524222	−	0.907980i
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$			10.3923i			0.522233i
$397$	−12.1244	−	21.0000i	−0.608504	−	1.05396i	−0.991487	−	0.130204i	$-0.958437\pi$
$397$	−12.1244	−	21.0000i	−0.608504	−	1.05396i	0.382983	−	0.923755i	$-0.374897\pi$
$398$			12.0000i			0.601506i
$399$	6.00000	−	31.1769i	0.300376	−	1.56080i
$400$		0			0
$401$	−16.5000	+	9.52628i	−0.823971	+	0.475720i	−0.851784	−	0.523893i	$-0.824479\pi$
$401$	−16.5000	+	9.52628i	−0.823971	+	0.475720i	0.0278131	+	0.999613i	$0.491146\pi$
$402$	33.7750	−	19.5000i	1.68454	−	0.972572i
$403$	10.3923	+	6.00000i	0.517678	+	0.298881i
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$	6.00000	+	5.19615i	0.297775	+	0.257881i
$407$	−13.8564			−0.686837
$408$			18.0000i			0.891133i
$409$	−19.5000	−	11.2583i	−0.964213	−	0.556689i	−0.0667458	−	0.997770i	$-0.521262\pi$
$409$	−19.5000	−	11.2583i	−0.964213	−	0.556689i	−0.897467	+	0.441081i	$0.854595\pi$
$410$		0			0
$411$	36.0000			1.77575
$412$	−5.19615			−0.255996
$413$		0			0
$414$	−4.50000	−	7.79423i	−0.221163	−	0.383065i
$415$		0			0
$416$	−9.00000	+	15.5885i	−0.441261	+	0.764287i
$417$	−15.5885	+	9.00000i	−0.763370	+	0.440732i
$418$	20.7846	+	36.0000i	1.01661	+	1.76082i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$	17.3205	+	30.0000i	0.843149	+	1.46038i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	18.0000	+	10.3923i	0.872103	+	0.503509i
$427$	10.3923	+	9.00000i	0.502919	+	0.435541i
$428$	−5.19615			−0.251166
$429$			20.7846i			1.00349i
$430$		0			0
$431$	9.00000	+	5.19615i	0.433515	+	0.250290i	0.700843	−	0.713316i	$-0.252807\pi$
$431$	9.00000	+	5.19615i	0.433515	+	0.250290i	−0.267328	+	0.963606i	$0.586141\pi$
$432$	−12.9904	−	22.5000i	−0.625000	−	1.08253i
$433$	−13.8564			−0.665896			−0.332948	−	0.942945i	$-0.608043\pi$
$433$	−13.8564			−0.665896			−0.332948	+	0.942945i	$0.608043\pi$
$434$	15.0000	−	5.19615i	0.720023	−	0.249423i
$435$		0			0
$436$	−2.50000	−	4.33013i	−0.119728	−	0.207375i
$437$	−10.3923	−	6.00000i	−0.497131	−	0.287019i
$438$	−5.19615	−	9.00000i	−0.248282	−	0.430037i
$439$	6.00000	−	3.46410i	0.286364	−	0.165333i	−0.349937	−	0.936773i	$-0.613797\pi$
$439$	6.00000	−	3.46410i	0.286364	−	0.165333i	0.636301	+	0.771441i	$0.280464\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		−	36.0000i		−	1.71235i
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	0.619299	−	0.785155i	$-0.287417\pi$
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	−0.989614	+	0.143751i	$0.954084\pi$
$444$	−6.00000	+	3.46410i	−0.284747	+	0.164399i
$445$		0			0
$446$	−3.00000	−	5.19615i	−0.142054	−	0.246045i
$447$	33.7750	+	19.5000i	1.59750	+	0.922318i
$448$	−0.866025	−	2.50000i	−0.0409159	−	0.118114i
$449$			12.1244i			0.572184i	0.958202	+	0.286092i	$0.0923563\pi$
$449$			12.1244i			0.572184i	−0.958202	+	0.286092i	$0.907644\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$	−3.46410	+	6.00000i	−0.162938	+	0.282216i
$453$	3.46410			0.162758
$454$			20.7846i			0.975470i
$455$		0			0
$456$	−18.0000	−	10.3923i	−0.842927	−	0.486664i
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	−0.653213	−	0.757174i	$-0.726579\pi$
$457$	−6.92820	+	4.00000i	−0.324088	+	0.187112i	0.329125	+	0.944286i	$0.393246\pi$
$458$		0			0
$459$	27.0000	+	15.5885i	1.26025	+	0.727607i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$	20.7846	+	18.0000i	0.966988	+	0.837436i
$463$		−	29.0000i		−	1.34774i	−0.738848	−	0.673872i	$-0.764630\pi$
$463$		−	29.0000i		−	1.34774i	0.738848	−	0.673872i	$-0.235370\pi$
$464$	7.50000	−	4.33013i	0.348179	−	0.201021i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	18.1865	−	10.5000i	0.841572	−	0.485882i	−0.0162260	−	0.999868i	$-0.505165\pi$
$467$	18.1865	−	10.5000i	0.841572	−	0.485882i	0.857798	+	0.513986i	$0.171832\pi$
$468$	5.19615	+	9.00000i	0.240192	+	0.416025i
$469$	6.50000	−	33.7750i	0.300142	−	1.55958i
$470$		0			0
$471$	6.00000			0.276465
$472$		0			0
$473$	−1.73205	+	3.00000i	−0.0796398	+	0.137940i
$474$	−48.0000			−2.20471
$475$		0			0
$476$	−12.0000	−	10.3923i	−0.550019	−	0.476331i
$477$		0			0
$478$	15.5885	−	9.00000i	0.712999	−	0.411650i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		0			0
$481$	−12.0000	+	6.92820i	−0.547153	+	0.315899i
$482$			12.0000i			0.546585i
$483$	−7.79423	−	1.50000i	−0.354650	−	0.0682524i
$484$	−1.00000			−0.0454545
$485$		0			0
$486$	−27.0000			−1.22474
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.972253	−	0.233933i	$-0.0751596\pi$
$487$	27.7128	+	16.0000i	1.25579	+	0.725029i	0.283535	+	0.958962i	$0.408493\pi$
$488$	7.79423	−	4.50000i	0.352828	−	0.203705i
$489$	−12.0000	−	6.92820i	−0.542659	−	0.313304i
$490$		0			0
$491$			38.1051i			1.71966i	0.510581	+	0.859830i	$0.329431\pi$
$491$			38.1051i			1.71966i	−0.510581	+	0.859830i	$0.670569\pi$
$492$	5.19615			0.234261
$493$	−5.19615	+	9.00000i	−0.234023	+	0.405340i
$494$	36.0000	+	20.7846i	1.61972	+	0.935144i
$495$		0			0
$496$		−	17.3205i		−	0.777714i
$497$	17.3205	−	6.00000i	0.776931	−	0.269137i
$498$	23.3827	+	13.5000i	1.04780	+	0.604949i
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	0.665725	−	0.746197i	$-0.268122\pi$
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	−0.979088	+	0.203436i	$0.934789\pi$
$500$		0			0
$501$	−31.5000	+	18.1865i	−1.40732	+	0.812514i
$502$	15.5885	+	27.0000i	0.695747	+	1.20507i
$503$			15.0000i			0.668817i	0.942428	+	0.334408i	$0.108537\pi$
$503$			15.0000i			0.668817i	−0.942428	+	0.334408i	$0.891463\pi$
$504$	−13.5000	−	2.59808i	−0.601338	−	0.115728i
$505$		0			0
$506$	9.00000	−	5.19615i	0.400099	−	0.230997i
$507$	−0.866025	−	1.50000i	−0.0384615	−	0.0666173i
$508$	13.8564	+	8.00000i	0.614779	+	0.354943i
$509$	−22.5000	−	38.9711i	−0.997295	−	1.72737i	−0.562303	−	0.826931i	$-0.690085\pi$
$509$	−22.5000	−	38.9711i	−0.997295	−	1.72737i	−0.434992	−	0.900434i	$-0.643249\pi$
$510$		0			0
$511$	−9.00000	−	1.73205i	−0.398137	−	0.0766214i
$512$	8.66025			0.382733
$513$	−31.1769	+	18.0000i	−1.37649	+	0.794719i
$514$		0			0
$515$		0			0
$516$			1.73205i			0.0762493i
$517$		0			0
$518$	−3.46410	+	18.0000i	−0.152204	+	0.790875i
$519$	18.0000	+	10.3923i	0.790112	+	0.456172i
$520$		0			0
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$		−	9.00000i		−	0.393919i
$523$	−12.1244	−	21.0000i	−0.530161	−	0.918266i	−0.999381	−	0.0351845i	$-0.988798\pi$
$523$	−12.1244	−	21.0000i	−0.530161	−	0.918266i	0.469220	−	0.883081i	$-0.344535\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	−3.00000			−0.130806
$527$	10.3923	+	18.0000i	0.452696	+	0.784092i
$528$	25.9808	−	15.0000i	1.13067	−	0.652791i
$529$	10.0000	−	17.3205i	0.434783	−	0.753066i
$530$		0			0
$531$		0			0
$532$	17.3205	−	6.00000i	0.750939	−	0.260133i
$533$	10.3923			0.450141
$534$	9.00000			0.389468
$535$		0			0
$536$	−19.5000	−	11.2583i	−0.842272	−	0.486286i
$537$			18.0000i			0.776757i
$538$	5.19615			0.224022
$539$	24.0000	−	3.46410i	1.03375	−	0.149209i
$540$		0			0
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−14.5000	−	25.1147i	−0.623404	−	1.07977i	0.365444	−	0.930834i	$-0.380917\pi$
$542$	−10.3923	−	6.00000i	−0.446388	−	0.257722i
$543$	7.79423	−	4.50000i	0.334482	−	0.193113i
$544$	−27.0000	+	15.5885i	−1.15762	+	0.668350i
$545$		0			0
$546$	27.0000	+	5.19615i	1.15549	+	0.222375i
$547$		−	1.00000i		−	0.0427569i	−0.999771	−	0.0213785i	$-0.993195\pi$
$547$		−	1.00000i		−	0.0427569i	0.999771	−	0.0213785i	$-0.00680549\pi$
$548$	10.3923	+	18.0000i	0.443937	+	0.768922i
$549$		−	15.5885i		−	0.665299i
$550$		0			0
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$	−2.59808	+	4.50000i	−0.110581	+	0.191533i
$553$	−27.7128	+	32.0000i	−1.17847	+	1.36078i
$554$			45.0333i			1.91328i
$555$		0			0
$556$	−9.00000	−	5.19615i	−0.381685	−	0.220366i
$557$	8.66025	−	15.0000i	0.366947	−	0.635570i	−0.622140	−	0.782906i	$-0.713736\pi$
$557$	8.66025	−	15.0000i	0.366947	−	0.635570i	0.989087	+	0.147336i	$0.0470698\pi$
$558$	−15.5885	−	9.00000i	−0.659912	−	0.381000i
$559$			3.46410i			0.146516i
$560$		0			0
$561$	−18.0000	+	31.1769i	−0.759961	+	1.31629i
$562$	10.3923	−	6.00000i	0.438373	−	0.253095i
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	0.831614	−	0.555354i	$-0.187417\pi$
$563$	18.1865	+	10.5000i	0.766471	+	0.442522i	−0.0651433	+	0.997876i	$0.520750\pi$
$564$		0			0
$565$		0			0
$566$	54.0000			2.26979
$567$	−15.5885	+	18.0000i	−0.654654	+	0.755929i
$568$		−	12.0000i		−	0.503509i
$569$	−6.00000	+	3.46410i	−0.251533	+	0.145223i	−0.620466	−	0.784233i	$-0.713057\pi$
$569$	−6.00000	+	3.46410i	−0.251533	+	0.145223i	0.368933	+	0.929456i	$0.379723\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−10.3923	+	6.00000i	−0.434524	+	0.250873i
$573$	15.5885	+	9.00000i	0.651217	+	0.375980i
$574$	9.00000	−	10.3923i	0.375653	−	0.433766i
$575$		0			0
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$	−12.1244	+	21.0000i	−0.504744	+	0.874241i	0.495241	+	0.868755i	$0.335080\pi$
$577$	−12.1244	+	21.0000i	−0.504744	+	0.874241i	−0.999985	+	0.00548605i	$0.998254\pi$
$578$	16.4545	−	28.5000i	0.684416	−	1.18544i
$579$			38.1051i			1.58359i
$580$		0			0
$581$	22.5000	−	7.79423i	0.933457	−	0.323359i
$582$	−15.5885	+	27.0000i	−0.646162	+	1.11919i
$583$		0			0
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$		0			0
$586$	−36.0000	+	20.7846i	−1.48715	+	0.858604i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	9.52628	−	7.50000i	0.392857	−	0.309295i
$589$	−24.0000			−0.988903
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	17.3205	+	10.0000i	0.711868	+	0.410997i
$593$	−41.5692	+	24.0000i	−1.70704	+	0.985562i	−0.768864	+	0.639413i	$0.779178\pi$
$593$	−41.5692	+	24.0000i	−1.70704	+	0.985562i	−0.938179	+	0.346149i	$0.887489\pi$
$594$		−	31.1769i		−	1.27920i
$595$		0			0
$596$			22.5167i			0.922318i
$597$		−	12.0000i		−	0.491127i
$598$	5.19615	−	9.00000i	0.212486	−	0.368037i
$599$	12.0000	+	6.92820i	0.490307	+	0.283079i	0.724702	−	0.689063i	$-0.241978\pi$
$599$	12.0000	+	6.92820i	0.490307	+	0.283079i	−0.234395	+	0.972141i	$0.575311\pi$
$600$		0			0
$601$			20.7846i			0.847822i	0.905704	+	0.423911i	$0.139343\pi$
$601$			20.7846i			0.847822i	−0.905704	+	0.423911i	$0.860657\pi$
$602$	3.46410	+	3.00000i	0.141186	+	0.122271i
$603$	−33.7750	+	19.5000i	−1.37542	+	0.794101i
$604$	1.00000	+	1.73205i	0.0406894	+	0.0704761i
$605$		0			0
$606$	−22.5000	−	38.9711i	−0.914000	−	1.58309i
$607$	−0.866025	−	1.50000i	−0.0351509	−	0.0608831i	0.847915	−	0.530133i	$-0.177858\pi$
$607$	−0.866025	−	1.50000i	−0.0351509	−	0.0608831i	−0.883066	+	0.469249i	$0.844525\pi$
$608$		−	36.0000i		−	1.45999i
$609$	−6.00000	−	5.19615i	−0.243132	−	0.210559i
$610$		0			0
$611$		0			0
$612$			18.0000i			0.727607i
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	0.534570	−	0.845124i	$-0.320473\pi$
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	−0.464614	+	0.885514i	$0.653807\pi$
$614$	−19.5000	−	33.7750i	−0.786956	−	1.36305i
$615$		0			0
$616$	3.00000	−	15.5885i	0.120873	−	0.628077i
$617$	34.6410			1.39459			0.697297	−	0.716782i	$-0.254386\pi$
$617$	34.6410			1.39459			0.697297	+	0.716782i	$0.254386\pi$
$618$	15.5885			0.627060
$619$	21.0000	+	12.1244i	0.844061	+	0.487319i	0.858643	−	0.512575i	$-0.171308\pi$
$619$	21.0000	+	12.1244i	0.844061	+	0.487319i	−0.0145814	+	0.999894i	$0.504642\pi$
$620$		0			0
$621$	4.50000	+	7.79423i	0.180579	+	0.312772i
$622$	−41.5692			−1.66677
$623$	5.19615	−	6.00000i	0.208179	−	0.240385i
$624$	15.0000	−	25.9808i	0.600481	−	1.04006i
$625$		0			0
$626$		0			0
$627$	−20.7846	−	36.0000i	−0.830057	−	1.43770i
$628$	1.73205	+	3.00000i	0.0691164	+	0.119713i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	13.8564	+	24.0000i	0.551178	+	0.954669i
$633$	−17.3205	−	30.0000i	−0.688428	−	1.19239i
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$		0			0
$636$		0			0
$637$	19.0526	−	15.0000i	0.754890	−	0.594322i
$638$	10.3923			0.411435
$639$	−18.0000	−	10.3923i	−0.712069	−	0.411113i
$640$		0			0
$641$	10.5000	+	6.06218i	0.414725	+	0.239442i	0.692818	−	0.721113i	$-0.256369\pi$
$641$	10.5000	+	6.06218i	0.414725	+	0.239442i	−0.278093	+	0.960554i	$0.589702\pi$
$642$	15.5885			0.615227
$643$	−17.3205			−0.683054			−0.341527	−	0.939872i	$-0.610944\pi$
$643$	−17.3205			−0.683054			−0.341527	+	0.939872i	$0.610944\pi$
$644$	−1.50000	−	4.33013i	−0.0591083	−	0.170631i
$645$		0			0
$646$	36.0000	+	62.3538i	1.41640	+	2.45328i
$647$	−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	$0.685449\pi$
$648$	7.79423	+	13.5000i	0.306186	+	0.530330i
$649$		0			0
$650$		0			0
$651$	−15.0000	+	5.19615i	−0.587896	+	0.203653i
$652$		−	8.00000i		−	0.313304i
$653$	15.5885	+	27.0000i	0.610023	+	1.05659i	0.991236	+	0.132104i	$0.0421733\pi$
$653$	15.5885	+	27.0000i	0.610023	+	1.05659i	−0.381212	+	0.924487i	$0.624493\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$		0			0
$656$	−7.50000	−	12.9904i	−0.292826	−	0.507189i
$657$	5.19615	+	9.00000i	0.202721	+	0.351123i
$658$		0			0
$659$		−	41.5692i		−	1.61931i	−0.586908	−	0.809653i	$-0.699655\pi$
$659$		−	41.5692i		−	1.61931i	0.586908	−	0.809653i	$-0.300345\pi$
$660$		0			0
$661$	28.5000	+	16.4545i	1.10852	+	0.640005i	0.938446	−	0.345426i	$-0.112266\pi$
$661$	28.5000	+	16.4545i	1.10852	+	0.640005i	0.170075	+	0.985431i	$0.445599\pi$
$662$	−8.66025	+	15.0000i	−0.336590	+	0.582992i
$663$			36.0000i			1.39812i
$664$		−	15.5885i		−	0.604949i
$665$		0			0
$666$	18.0000	−	10.3923i	0.697486	−	0.402694i
$667$	−2.59808	+	1.50000i	−0.100598	+	0.0580802i
$668$	−18.1865	−	10.5000i	−0.703658	−	0.406257i
$669$	3.00000	+	5.19615i	0.115987	+	0.200895i
$670$		0			0
$671$	18.0000			0.694882
$672$	−7.79423	−	22.5000i	−0.300669	−	0.867956i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	−48.0000	+	27.7128i	−1.84889	+	1.06746i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	5.19615	−	3.00000i	0.199704	−	0.115299i	−0.396813	−	0.917899i	$-0.629884\pi$
$677$	5.19615	−	3.00000i	0.199704	−	0.115299i	0.596518	+	0.802600i	$0.296551\pi$
$678$	10.3923	−	18.0000i	0.399114	−	0.691286i
$679$	9.00000	+	25.9808i	0.345388	+	0.997050i
$680$		0			0
$681$		−	20.7846i		−	0.796468i
$682$	10.3923	−	18.0000i	0.397942	−	0.689256i
$683$	19.9186	−	34.5000i	0.762163	−	1.32011i	−0.179570	−	0.983745i	$-0.557471\pi$
$683$	19.9186	−	34.5000i	0.762163	−	1.32011i	0.941733	−	0.336361i	$-0.109196\pi$
$684$	−18.0000	−	10.3923i	−0.688247	−	0.397360i
$685$		0			0
$686$	1.50000	−	32.0429i	0.0572703	−	1.22341i
$687$		0			0
$688$	4.33013	−	2.50000i	0.165085	−	0.0953116i
$689$		0			0
$690$		0			0
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$			12.0000i			0.456172i
$693$	−20.7846	−	18.0000i	−0.789542	−	0.683763i
$694$	33.0000			1.25266
$695$		0			0
$696$	−4.50000	+	2.59808i	−0.170572	+	0.0984798i
$697$	15.5885	+	9.00000i	0.590455	+	0.340899i
$698$	−12.9904	+	7.50000i	−0.491693	+	0.283879i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$		0			0
$701$		−	25.9808i		−	0.981280i	−0.871362	−	0.490640i	$-0.836763\pi$
$701$		−	25.9808i		−	0.981280i	0.871362	−	0.490640i	$-0.163237\pi$
$702$	−15.5885	−	27.0000i	−0.588348	−	1.01905i
$703$	13.8564	−	24.0000i	0.522604	−	0.905177i
$704$	−3.00000	−	1.73205i	−0.113067	−	0.0652791i
$705$		0			0
$706$		0			0
$707$	−38.9711	−	7.50000i	−1.46566	−	0.282067i
$708$		0			0
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	0.987421	−	0.158114i	$-0.0505412\pi$
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$710$		0			0
$711$	48.0000			1.80014
$712$	−2.59808	−	4.50000i	−0.0973670	−	0.168645i
$713$			6.00000i			0.224702i
$714$	36.0000	+	31.1769i	1.34727	+	1.16677i
$715$		0			0
$716$	−9.00000	+	5.19615i	−0.336346	+	0.194189i
$717$	−15.5885	+	9.00000i	−0.582162	+	0.336111i
$718$	−36.3731	−	21.0000i	−1.35743	−	0.783713i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$		0			0
$721$	9.00000	−	10.3923i	0.335178	−	0.387030i
$722$	−50.2295			−1.86935
$723$		−	12.0000i		−	0.446285i
$724$	4.50000	+	2.59808i	0.167241	+	0.0965567i
$725$		0			0
$726$	3.00000			0.111340
$727$	−5.19615			−0.192715			−0.0963573	−	0.995347i	$-0.530719\pi$
$727$	−5.19615			−0.192715			−0.0963573	+	0.995347i	$0.530719\pi$
$728$	−5.19615	−	15.0000i	−0.192582	−	0.555937i
$729$	27.0000			1.00000
$730$		0			0
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$	7.79423	−	4.50000i	0.288083	−	0.166325i
$733$	8.66025	+	15.0000i	0.319874	+	0.554038i	0.980461	−	0.196711i	$-0.0630262\pi$
$733$	8.66025	+	15.0000i	0.319874	+	0.554038i	−0.660588	+	0.750749i	$0.729693\pi$
$734$	27.0000			0.996588
$735$		0			0
$736$	−9.00000			−0.331744
$737$	−22.5167	−	39.0000i	−0.829412	−	1.43658i
$738$	−15.5885			−0.573819
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	−0.269913	−	0.962885i	$-0.586995\pi$
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	0.968839	−	0.247691i	$-0.0796718\pi$
$740$		0			0
$741$	−36.0000	−	20.7846i	−1.32249	−	0.763542i
$742$		0			0
$743$	46.7654			1.71566			0.857828	−	0.513938i	$-0.171814\pi$
$743$	46.7654			1.71566			0.857828	+	0.513938i	$0.171814\pi$
$744$			10.3923i			0.381000i
$745$		0			0
$746$	−6.00000	−	3.46410i	−0.219676	−	0.126830i
$747$	−23.3827	−	13.5000i	−0.855528	−	0.493939i
$748$	−20.7846			−0.759961
$749$	9.00000	−	10.3923i	0.328853	−	0.379727i
$750$		0			0
$751$	10.0000	+	17.3205i	0.364905	+	0.632034i	0.988761	−	0.149505i	$-0.0477681\pi$
$751$	10.0000	+	17.3205i	0.364905	+	0.632034i	−0.623856	+	0.781540i	$0.714435\pi$
$752$		0			0
$753$	−15.5885	−	27.0000i	−0.568075	−	0.983935i
$754$	9.00000	−	5.19615i	0.327761	−	0.189233i
$755$		0			0
$756$	−13.5000	−	2.59808i	−0.490990	−	0.0944911i
$757$			22.0000i			0.799604i	0.916602	+	0.399802i	$0.130921\pi$
$757$			22.0000i			0.799604i	−0.916602	+	0.399802i	$0.869079\pi$
$758$	13.8564	+	24.0000i	0.503287	+	0.871719i
$759$	−9.00000	+	5.19615i	−0.326679	+	0.188608i
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	−41.5692	−	24.0000i	−1.50589	−	0.869428i
$763$	12.9904	+	2.50000i	0.470283	+	0.0905061i
$764$			10.3923i			0.375980i
$765$		0			0
$766$	31.5000	+	18.1865i	1.13814	+	0.657106i
$767$		0			0
$768$	−32.9090			−1.18750
$769$			41.5692i			1.49902i	0.661991	+	0.749512i	$0.269712\pi$
$769$			41.5692i			1.49902i	−0.661991	+	0.749512i	$0.730288\pi$
$770$		0			0
$771$		0			0
$772$	−19.0526	+	11.0000i	−0.685717	+	0.395899i
$773$	−15.5885	−	9.00000i	−0.560678	−	0.323708i	0.192740	−	0.981250i	$-0.438263\pi$
$773$	−15.5885	−	9.00000i	−0.560678	−	0.323708i	−0.753418	+	0.657542i	$0.771596\pi$
$774$		−	5.19615i		−	0.186772i
$775$		0			0
$776$	18.0000			0.646162
$777$	3.46410	−	18.0000i	0.124274	−	0.645746i
$778$			48.0000i			1.72088i
$779$	−18.0000	+	10.3923i	−0.644917	+	0.372343i
$780$		0			0
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$	15.5885	−	9.00000i	0.557442	−	0.321839i
$783$			9.00000i			0.321634i
$784$	−32.5000	−	12.9904i	−1.16071	−	0.463942i
$785$		0			0
$786$	−36.0000			−1.28408
$787$	12.9904	−	22.5000i	0.463057	−	0.802038i	−0.536054	−	0.844183i	$-0.680086\pi$
$787$	12.9904	−	22.5000i	0.463057	−	0.802038i	0.999112	+	0.0421450i	$0.0134192\pi$
$788$	1.73205	−	3.00000i	0.0617018	−	0.106871i
$789$	3.00000			0.106803
$790$		0			0
$791$	−6.00000	−	17.3205i	−0.213335	−	0.615846i
$792$	−15.5885	+	9.00000i	−0.553912	+	0.319801i
$793$	15.5885	−	9.00000i	0.553562	−	0.319599i
$794$	−21.0000	+	36.3731i	−0.745262	+	1.29083i
$795$		0			0
$796$	6.00000	−	3.46410i	0.212664	−	0.122782i
$797$			12.0000i			0.425062i	0.977154	+	0.212531i	$0.0681706\pi$
$797$			12.0000i			0.425062i	−0.977154	+	0.212531i	$0.931829\pi$
$798$	−51.9615	+	18.0000i	−1.83942	+	0.637193i
$799$		0			0
$800$		0			0
$801$	−9.00000			−0.317999
$802$	28.5788	+	16.5000i	1.00915	+	0.582635i
$803$	−10.3923	+	6.00000i	−0.366736	+	0.211735i
$804$	−19.5000	−	11.2583i	−0.687712	−	0.397051i
$805$		0			0
$806$		−	20.7846i		−	0.732107i
$807$	−5.19615			−0.182913
$808$	−12.9904	+	22.5000i	−0.457000	+	0.791547i
$809$	−16.5000	−	9.52628i	−0.580109	−	0.334926i	0.181068	−	0.983471i	$-0.442045\pi$
$809$	−16.5000	−	9.52628i	−0.580109	−	0.334926i	−0.761177	+	0.648544i	$0.775378\pi$
$810$		0			0
$811$			45.0333i			1.58133i	0.612247	+	0.790667i	$0.290266\pi$
$811$			45.0333i			1.58133i	−0.612247	+	0.790667i	$0.709734\pi$
$812$	0.866025	−	4.50000i	0.0303915	−	0.157919i
$813$	10.3923	+	6.00000i	0.364474	+	0.210429i
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$		0			0
$816$	45.0000	−	25.9808i	1.57532	−	0.909509i
$817$	−3.46410	−	6.00000i	−0.121194	−	0.209913i
$818$			39.0000i			1.36360i
$819$	−27.0000	−	5.19615i	−0.943456	−	0.181568i
$820$		0			0
$821$	36.0000	−	20.7846i	1.25641	−	0.725388i	0.284034	−	0.958814i	$-0.408327\pi$
$821$	36.0000	−	20.7846i	1.25641	−	0.725388i	0.972375	+	0.233426i	$0.0749938\pi$
$822$	−31.1769	−	54.0000i	−1.08742	−	1.88347i
$823$	19.9186	+	11.5000i	0.694318	+	0.400865i	0.805228	−	0.592966i	$-0.202043\pi$
$823$	19.9186	+	11.5000i	0.694318	+	0.400865i	−0.110910	+	0.993831i	$0.535376\pi$
$824$	−4.50000	−	7.79423i	−0.156765	−	0.271525i
$825$		0			0
$826$		0			0
$827$	22.5167			0.782981			0.391491	−	0.920182i	$-0.371960\pi$
$827$	22.5167			0.782981			0.391491	+	0.920182i	$0.371960\pi$
$828$	−2.59808	+	4.50000i	−0.0902894	+	0.156386i
$829$	12.0000	+	6.92820i	0.416777	+	0.240626i	0.693698	−	0.720266i	$-0.255980\pi$
$829$	12.0000	+	6.92820i	0.416777	+	0.240626i	−0.276920	+	0.960893i	$0.589314\pi$
$830$		0			0
$831$		−	45.0333i		−	1.56219i
$832$	−3.46410			−0.120096
$833$	41.5692	−	6.00000i	1.44029	−	0.207888i
$834$	27.0000	+	15.5885i	0.934934	+	0.539784i
$835$		0			0
$836$	12.0000	−	20.7846i	0.415029	−	0.718851i
$837$	15.5885	+	9.00000i	0.538816	+	0.311086i
$838$		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
$841$	26.0000			0.896552
$842$	−30.3109	−	52.5000i	−1.04458	−	1.80927i
$843$	−10.3923	+	6.00000i	−0.357930	+	0.206651i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$		0			0
$846$		0			0
$847$	1.73205	−	2.00000i	0.0595140	−	0.0687208i
$848$		0			0
$849$	−54.0000			−1.85328
$850$		0			0
$851$	−6.00000	−	3.46410i	−0.205677	−	0.118748i
$852$		−	12.0000i		−	0.411113i
$853$	−20.7846			−0.711651			−0.355826	−	0.934552i	$-0.615800\pi$
$853$	−20.7846			−0.711651			−0.355826	+	0.934552i	$0.615800\pi$
$854$	4.50000	−	23.3827i	0.153987	−	0.800139i
$855$		0			0
$856$	−4.50000	−	7.79423i	−0.153807	−	0.266401i
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.969599	−	0.244701i	$-0.0786899\pi$
$857$	36.3731	+	21.0000i	1.24248	+	0.717346i	0.272882	+	0.962048i	$0.412023\pi$
$858$	31.1769	−	18.0000i	1.06436	−	0.614510i
$859$	−24.0000	+	13.8564i	−0.818869	+	0.472774i	−0.850026	−	0.526740i	$-0.823414\pi$
$859$	−24.0000	+	13.8564i	−0.818869	+	0.472774i	0.0311570	+	0.999515i	$0.490081\pi$
$860$		0			0
$861$	−9.00000	+	10.3923i	−0.306719	+	0.354169i
$862$		−	18.0000i		−	0.613082i
$863$	−4.33013	−	7.50000i	−0.147399	−	0.255303i	0.782866	−	0.622190i	$-0.213757\pi$
$863$	−4.33013	−	7.50000i	−0.147399	−	0.255303i	−0.930265	+	0.366887i	$0.880424\pi$
$864$	−13.5000	+	23.3827i	−0.459279	+	0.795495i
$865$		0			0
$866$	12.0000	+	20.7846i	0.407777	+	0.706290i
$867$	−16.4545	+	28.5000i	−0.558824	+	0.967911i
$868$	−6.92820	−	6.00000i	−0.235159	−	0.203653i
$869$			55.4256i			1.88019i
$870$		0			0
$871$	−39.0000	−	22.5167i	−1.32146	−	0.762948i
$872$	4.33013	−	7.50000i	0.146637	−	0.253982i
$873$	15.5885	−	27.0000i	0.527589	−	0.913812i
$874$			20.7846i			0.703050i
$875$		0			0
$876$	−3.00000	+	5.19615i	−0.101361	+	0.175562i
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.0471555	−	0.998888i	$-0.484984\pi$
$877$	27.7128	−	16.0000i	0.935795	−	0.540282i	0.888640	+	0.458606i	$0.151651\pi$
$878$	−10.3923	−	6.00000i	−0.350723	−	0.202490i
$879$	36.0000	−	20.7846i	1.21425	−	0.701047i
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	−28.5788	+	22.5000i	−0.962300	+	0.757614i
$883$			20.0000i			0.673054i	0.941674	+	0.336527i	$0.109252\pi$
$883$			20.0000i			0.673054i	−0.941674	+	0.336527i	$0.890748\pi$
$884$	−18.0000	+	10.3923i	−0.605406	+	0.349531i
$885$		0			0
$886$	−13.5000	+	23.3827i	−0.453541	+	0.785557i
$887$	7.79423	−	4.50000i	0.261705	−	0.151095i	−0.363407	−	0.931630i	$-0.618387\pi$
$887$	7.79423	−	4.50000i	0.261705	−	0.151095i	0.625112	+	0.780535i	$0.285053\pi$
$888$	−10.3923	−	6.00000i	−0.348743	−	0.201347i
$889$	−40.0000	+	13.8564i	−1.34156	+	0.464729i
$890$		0			0
$891$			31.1769i			1.04447i
$892$	−1.73205	+	3.00000i	−0.0579934	+	0.100447i
$893$		0			0
$894$		−	67.5500i		−	2.25921i
$895$		0			0
$896$	−21.0000	+	24.2487i	−0.701561	+	0.810093i
$897$	−5.19615	+	9.00000i	−0.173494	+	0.300501i
$898$	18.1865	−	10.5000i	0.606892	−	0.350390i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$		0			0
$901$		0			0
$902$		−	18.0000i		−	0.599334i
$903$	−3.46410	−	3.00000i	−0.115278	−	0.0998337i
$904$	−12.0000			−0.399114
$905$		0			0
$906$	−3.00000	−	5.19615i	−0.0996683	−	0.172631i
$907$	−32.0429	−	18.5000i	−1.06397	−	0.614282i	−0.137441	−	0.990510i	$-0.543888\pi$
$907$	−32.0429	−	18.5000i	−1.06397	−	0.614282i	−0.926527	+	0.376228i	$0.877221\pi$
$908$	10.3923	−	6.00000i	0.344881	−	0.199117i
$909$	22.5000	+	38.9711i	0.746278	+	1.29259i
$910$		0			0
$911$			24.2487i			0.803396i	0.915772	+	0.401698i	$0.131580\pi$
$911$			24.2487i			0.803396i	−0.915772	+	0.401698i	$0.868420\pi$
$912$			60.0000i			1.98680i
$913$	15.5885	−	27.0000i	0.515903	−	0.893570i
$914$	12.0000	+	6.92820i	0.396925	+	0.229165i
$915$		0			0
$916$		0			0
$917$	−20.7846	+	24.0000i	−0.686368	+	0.792550i
$918$		−	54.0000i		−	1.78227i
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	19.5000	+	33.7750i	0.642547	+	1.11292i
$922$	25.9808	+	45.0000i	0.855631	+	1.48200i
$923$		−	24.0000i		−	0.789970i
$924$	3.00000	−	15.5885i	0.0986928	−	0.512823i
$925$		0			0
$926$	−43.5000	+	25.1147i	−1.42950	+	0.825321i
$927$	−15.5885			−0.511992
$928$	−7.79423	−	4.50000i	−0.255858	−	0.147720i
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	−18.0000	+	45.0333i	−0.589926	+	1.47591i
$932$	3.46410			0.113470
$933$	41.5692			1.36092
$934$	−31.5000	−	18.1865i	−1.03071	−	0.595082i
$935$		0			0
$936$	−9.00000	+	15.5885i	−0.294174	+	0.509525i
$937$	−48.4974			−1.58434			−0.792171	−	0.610299i	$-0.791049\pi$
$937$	−48.4974			−1.58434			−0.792171	+	0.610299i	$0.791049\pi$
$938$	−56.2917	+	19.5000i	−1.83799	+	0.636698i
$939$		0			0
$940$		0			0
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	−5.19615	−	9.00000i	−0.169300	−	0.293236i
$943$	2.59808	+	4.50000i	0.0846050	+	0.146540i
$944$		0			0
$945$		0			0
$946$	6.00000			0.195077
$947$	−12.9904	−	22.5000i	−0.422131	−	0.731152i	0.574017	−	0.818843i	$-0.305384\pi$
$947$	−12.9904	−	22.5000i	−0.422131	−	0.731152i	−0.996148	+	0.0876916i	$0.972051\pi$
$948$	13.8564	+	24.0000i	0.450035	+	0.779484i
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$		0			0
$951$	15.0000	−	25.9808i	0.486408	−	0.842484i
$952$	5.19615	−	27.0000i	0.168408	−	0.875075i
$953$	6.92820			0.224427			0.112213	−	0.993684i	$-0.464206\pi$
$953$	6.92820			0.224427			0.112213	+	0.993684i	$0.464206\pi$
$954$		0			0
$955$		0			0
$956$	−9.00000	−	5.19615i	−0.291081	−	0.168056i
$957$	−10.3923			−0.335936
$958$	10.3923			0.335760
$959$	−54.0000	−	10.3923i	−1.74375	−	0.335585i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$	20.7846	+	12.0000i	0.670123	+	0.386896i
$963$	−15.5885			−0.502331
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$		0			0
$966$	4.50000	+	12.9904i	0.144785	+	0.417959i
$967$			23.0000i			0.739630i	0.929105	+	0.369815i	$0.120579\pi$
$967$			23.0000i			0.739630i	−0.929105	+	0.369815i	$0.879421\pi$
$968$	−0.866025	−	1.50000i	−0.0278351	−	0.0482118i
$969$	−36.0000	−	62.3538i	−1.15649	−	2.00309i
$970$		0			0
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$	7.79423	+	13.5000i	0.250000	+	0.433013i
$973$	25.9808	−	9.00000i	0.832905	−	0.288527i
$974$		−	55.4256i		−	1.77595i
$975$		0			0
$976$	−22.5000	−	12.9904i	−0.720207	−	0.415812i
$977$	12.1244	−	21.0000i	0.387893	−	0.671850i	−0.604273	−	0.796777i	$-0.706537\pi$
$977$	12.1244	−	21.0000i	0.387893	−	0.671850i	0.992166	+	0.124928i	$0.0398698\pi$
$978$			24.0000i			0.767435i
$979$		−	10.3923i		−	0.332140i
$980$		0			0
$981$	−7.50000	−	12.9904i	−0.239457	−	0.414751i
$982$	57.1577	−	33.0000i	1.82397	−	1.05307i
$983$	49.3634	+	28.5000i	1.57445	+	0.909009i	0.995613	+	0.0935651i	$0.0298263\pi$
$983$	49.3634	+	28.5000i	1.57445	+	0.909009i	0.578836	+	0.815444i	$0.303507\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$		0			0
$986$	18.0000			0.573237
$987$		0			0
$988$		−	24.0000i		−	0.763542i
$989$	−1.50000	+	0.866025i	−0.0476972	+	0.0275380i
$990$		0			0
$991$	−17.0000	+	29.4449i	−0.540023	+	0.935347i	0.458879	+	0.888499i	$0.348251\pi$
$991$	−17.0000	+	29.4449i	−0.540023	+	0.935347i	−0.998902	+	0.0468483i	$0.985082\pi$
$992$	−15.5885	+	9.00000i	−0.494934	+	0.285750i
$993$	8.66025	−	15.0000i	0.274825	−	0.476011i
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$		0			0
$996$		−	15.5885i		−	0.493939i
$997$	−3.46410	+	6.00000i	−0.109709	+	0.190022i	−0.915652	−	0.401971i	$-0.868325\pi$
$997$	−3.46410	+	6.00000i	−0.109709	+	0.190022i	0.805943	+	0.591993i	$0.201659\pi$
$998$	−12.1244	+	21.0000i	−0.383790	+	0.664743i
$999$	−18.0000	+	10.3923i	−0.569495	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.b.374.1		4
3.2	odd	2		525.2.q.a.374.2		4
5.2	odd	4		525.2.t.e.101.1		2
5.3	odd	4		105.2.s.a.101.1	yes	2
5.4	even	2	inner	525.2.q.b.374.2		4
7.5	odd	6		525.2.q.a.299.1		4
15.2	even	4		525.2.t.a.101.1		2
15.8	even	4		105.2.s.b.101.1	yes	2
15.14	odd	2		525.2.q.a.374.1		4
21.5	even	6	inner	525.2.q.b.299.2		4
35.3	even	12		735.2.b.a.146.1		2
35.12	even	12		525.2.t.a.26.1		2
35.13	even	4		735.2.s.c.521.1		2
35.18	odd	12		735.2.b.b.146.1		2
35.19	odd	6		525.2.q.a.299.2		4
35.23	odd	12		735.2.s.e.656.1		2
35.33	even	12		105.2.s.b.26.1	yes	2
105.23	even	12		735.2.s.c.656.1		2
105.38	odd	12		735.2.b.b.146.2		2
105.47	odd	12		525.2.t.e.26.1		2
105.53	even	12		735.2.b.a.146.2		2
105.68	odd	12		105.2.s.a.26.1	✓	2
105.83	odd	4		735.2.s.e.521.1		2
105.89	even	6	inner	525.2.q.b.299.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.a.26.1	✓	2	105.68	odd	12
105.2.s.a.101.1	yes	2	5.3	odd	4
105.2.s.b.26.1	yes	2	35.33	even	12
105.2.s.b.101.1	yes	2	15.8	even	4
525.2.q.a.299.1		4	7.5	odd	6
525.2.q.a.299.2		4	35.19	odd	6
525.2.q.a.374.1		4	15.14	odd	2
525.2.q.a.374.2		4	3.2	odd	2
525.2.q.b.299.1		4	105.89	even	6	inner
525.2.q.b.299.2		4	21.5	even	6	inner
525.2.q.b.374.1		4	1.1	even	1	trivial
525.2.q.b.374.2		4	5.4	even	2	inner
525.2.t.a.26.1		2	35.12	even	12
525.2.t.a.101.1		2	15.2	even	4
525.2.t.e.26.1		2	105.47	odd	12
525.2.t.e.101.1		2	5.2	odd	4
735.2.b.a.146.1		2	35.3	even	12
735.2.b.a.146.2		2	105.53	even	12
735.2.b.b.146.1		2	35.18	odd	12
735.2.b.b.146.2		2	105.38	odd	12
735.2.s.c.521.1		2	35.13	even	4
735.2.s.c.656.1		2	105.23	even	12
735.2.s.e.521.1		2	105.83	odd	4
735.2.s.e.656.1		2	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{6} +(-0.866025 - 2.50000i) q^{7} -1.73205 q^{8} +(-1.50000 + 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{11} -1.73205 q^{12} -3.46410 q^{13} +(-3.00000 + 3.46410i) q^{14} +(2.50000 + 4.33013i) q^{16} +(-5.19615 - 3.00000i) q^{17} +5.19615 q^{18} +(6.00000 - 3.46410i) q^{19} +(3.00000 - 3.46410i) q^{21} +6.00000i q^{22} +(-0.866025 - 1.50000i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(3.00000 + 5.19615i) q^{26} -5.19615 q^{27} +(2.59808 + 0.500000i) q^{28} -1.73205i q^{29} +(-3.00000 - 1.73205i) q^{31} +(2.59808 - 4.50000i) q^{32} -6.00000i q^{33} +10.3923i q^{34} +(-1.50000 - 2.59808i) q^{36} +(3.46410 - 2.00000i) q^{37} +(-10.3923 - 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +(-7.79423 - 1.50000i) q^{42} -1.00000i q^{43} +(3.00000 - 1.73205i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-4.33013 + 7.50000i) q^{48} +(-5.50000 + 4.33013i) q^{49} -10.3923i q^{51} +(1.73205 - 3.00000i) q^{52} +(4.50000 + 7.79423i) q^{54} +(1.50000 + 4.33013i) q^{56} +(10.3923 + 6.00000i) q^{57} +(-2.59808 + 1.50000i) q^{58} +(-4.50000 + 2.59808i) q^{61} +6.00000i q^{62} +(7.79423 + 1.50000i) q^{63} +1.00000 q^{64} +(-9.00000 + 5.19615i) q^{66} +(11.2583 + 6.50000i) q^{67} +(5.19615 - 3.00000i) q^{68} +(1.50000 - 2.59808i) q^{69} +6.92820i q^{71} +(2.59808 - 4.50000i) q^{72} +(1.73205 - 3.00000i) q^{73} +(-6.00000 - 3.46410i) q^{74} +6.92820i q^{76} +(-1.73205 + 9.00000i) q^{77} +(-5.19615 + 9.00000i) q^{78} +(-8.00000 - 13.8564i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.59808 + 4.50000i) q^{82} +9.00000i q^{83} +(1.50000 + 4.33013i) q^{84} +(-1.50000 + 0.866025i) q^{86} +(2.59808 - 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(1.50000 + 2.59808i) q^{89} +(3.00000 + 8.66025i) q^{91} +1.73205 q^{92} -6.00000i q^{93} +9.00000 q^{96} -10.3923 q^{97} +(11.2583 + 4.50000i) q^{98} +(9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 6 q^{6} - 6 q^{9} - 12 q^{11} - 12 q^{14} + 10 q^{16} + 24 q^{19} + 12 q^{21} - 6 q^{24} + 12 q^{26} - 12 q^{31} - 6 q^{36} - 12 q^{39} - 12 q^{41} + 12 q^{44} - 6 q^{46} - 22 q^{49} + 18 q^{54}+ \cdots + 36 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 6 * q^6 - 6 * q^9 - 12 * q^11 - 12 * q^14 + 10 * q^16 + 24 * q^19 + 12 * q^21 - 6 * q^24 + 12 * q^26 - 12 * q^31 - 6 * q^36 - 12 * q^39 - 12 * q^41 + 12 * q^44 - 6 * q^46 - 22 * q^49 + 18 * q^54 + 6 * q^56 - 18 * q^61 + 4 * q^64 - 36 * q^66 + 6 * q^69 - 24 * q^74 - 32 * q^79 - 18 * q^81 + 6 * q^84 - 6 * q^86 + 6 * q^89 + 12 * q^91 + 36 * q^96 + 36 * q^99

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