LMFDB - Embedded newform 525.2.i.b.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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, 0, 4]))

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{12} -3.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{23} +(1.50000 + 2.59808i) q^{24} +(1.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} -8.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.50000 - 4.33013i) q^{32} +2.00000 q^{34} -1.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.50000 + 2.59808i) q^{39} +(-0.500000 + 2.59808i) q^{42} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{46} +(5.00000 - 8.66025i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-1.50000 - 2.59808i) q^{52} +(7.00000 + 12.1244i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 - 7.79423i) q^{56} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +7.00000 q^{64} +(2.50000 + 4.33013i) q^{67} +(1.00000 - 1.73205i) q^{68} +2.00000 q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} -1.00000 q^{76} -3.00000 q^{78} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.0000 q^{83} +(2.00000 + 1.73205i) q^{84} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(3.00000 - 5.19615i) q^{89} +(1.50000 - 7.79423i) q^{91} -2.00000 q^{92} +(4.00000 - 6.92820i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-2.50000 + 4.33013i) q^{96} +9.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} + q^{4} + 2 q^{6} - q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 + q^4 + 2 * q^6 - q^7 - 6 * q^8 - q^9	$ 2 q - q^{2} - q^{3} + q^{4} + 2 q^{6} - q^{7} - 6 q^{8} - q^{9} + q^{12} - 6 q^{13} - 4 q^{14} + q^{16} - 2 q^{17} - q^{18} - q^{19} + 5 q^{21} - 2 q^{23} + 3 q^{24} + 3 q^{26} + 2 q^{27} - 5 q^{28} - 16 q^{29} + 8 q^{31} - 5 q^{32} + 4 q^{34} - 2 q^{36} - 7 q^{37} - q^{38} + 3 q^{39} - q^{42} - 16 q^{43} - 2 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} - 2 q^{51} - 3 q^{52} + 14 q^{53} - q^{54} + 3 q^{56} + 2 q^{57} + 8 q^{58} - 10 q^{59} - 7 q^{61} - 16 q^{62} - 4 q^{63} + 14 q^{64} + 5 q^{67} + 2 q^{68} + 4 q^{69} - 24 q^{71} + 3 q^{72} + 11 q^{73} - 7 q^{74} - 2 q^{76} - 6 q^{78} + 7 q^{79} - q^{81} + 28 q^{83} + 4 q^{84} + 8 q^{86} + 8 q^{87} + 6 q^{89} + 3 q^{91} - 4 q^{92} + 8 q^{93} + 10 q^{94} - 5 q^{96} + 18 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^3 + q^4 + 2 * q^6 - q^7 - 6 * q^8 - q^9 + q^12 - 6 * q^13 - 4 * q^14 + q^16 - 2 * q^17 - q^18 - q^19 + 5 * q^21 - 2 * q^23 + 3 * q^24 + 3 * q^26 + 2 * q^27 - 5 * q^28 - 16 * q^29 + 8 * q^31 - 5 * q^32 + 4 * q^34 - 2 * q^36 - 7 * q^37 - q^38 + 3 * q^39 - q^42 - 16 * q^43 - 2 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 - 2 * q^51 - 3 * q^52 + 14 * q^53 - q^54 + 3 * q^56 + 2 * q^57 + 8 * q^58 - 10 * q^59 - 7 * q^61 - 16 * q^62 - 4 * q^63 + 14 * q^64 + 5 * q^67 + 2 * q^68 + 4 * q^69 - 24 * q^71 + 3 * q^72 + 11 * q^73 - 7 * q^74 - 2 * q^76 - 6 * q^78 + 7 * q^79 - q^81 + 28 * q^83 + 4 * q^84 + 8 * q^86 + 8 * q^87 + 6 * q^89 + 3 * q^91 - 4 * q^92 + 8 * q^93 + 10 * q^94 - 5 * q^96 + 18 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−3.00000			−1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$		0			0
$26$	1.50000	−	2.59808i	0.294174	−	0.509525i
$27$	1.00000			0.192450
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	2.00000			0.342997
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	1.50000	+	2.59808i	0.240192	+	0.416025i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$		0			0
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	−0.227844	−	0.973698i	$-0.573168\pi$
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	0.957169	−	0.289530i	$-0.0934991\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	−1.50000	−	2.59808i	−0.208013	−	0.360288i
$53$	7.00000	+	12.1244i	0.961524	+	1.66541i	0.718677	+	0.695344i	$0.244748\pi$
$53$	7.00000	+	12.1244i	0.961524	+	1.66541i	0.242846	+	0.970065i	$0.421919\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	1.50000	−	7.79423i	0.200446	−	1.04155i
$57$	1.00000			0.132453
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	−8.00000			−1.01600
$63$	−2.00000	−	1.73205i	−0.251976	−	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$		0			0
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	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	$0.752242\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	−1.00000			−0.114708
$77$		0			0
$78$	−3.00000			−0.339683
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	2.00000	+	1.73205i	0.218218	+	0.188982i
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	4.00000	+	6.92820i	0.428845	+	0.742781i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	1.50000	−	7.79423i	0.157243	−	0.817057i
$92$	−2.00000			−0.208514
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$	5.00000	+	8.66025i	0.515711	+	0.893237i
$95$		0			0
$96$	−2.50000	+	4.33013i	−0.255155	+	0.441942i
$97$	9.00000			0.913812			0.456906	−	0.889515i	$-0.348958\pi$
$97$	9.00000			0.913812			0.456906	+	0.889515i	$0.348958\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$		0			0
$101$	8.00000	+	13.8564i	0.796030	+	1.37876i	0.922183	+	0.386753i	$0.126403\pi$
$101$	8.00000	+	13.8564i	0.796030	+	1.37876i	−0.126153	+	0.992011i	$0.540263\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	9.00000			0.882523
$105$		0			0
$106$	−14.0000			−1.35980
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	0.961645	+	0.274296i	$0.0884447\pi$
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	−0.243276	+	0.969957i	$0.578222\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−0.500000	+	0.866025i	−0.0468293	+	0.0811107i
$115$		0			0
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$	1.50000	−	2.59808i	0.138675	−	0.240192i
$118$	10.0000			0.920575
$119$	5.00000	−	1.73205i	0.458349	−	0.158777i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−3.50000	−	6.06218i	−0.316875	−	0.548844i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$		0			0
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	11.0000			0.976092			0.488046	−	0.872818i	$-0.337710\pi$
$127$	11.0000			0.976092			0.488046	+	0.872818i	$0.337710\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	−7.00000	+	12.1244i	−0.611593	+	1.05931i	0.379379	+	0.925241i	$0.376138\pi$
$131$	−7.00000	+	12.1244i	−0.611593	+	1.05931i	−0.990972	+	0.134069i	$0.957196\pi$
$132$		0			0
$133$	−2.00000	−	1.73205i	−0.173422	−	0.150188i
$134$	−5.00000			−0.431934
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	0.996621	−	0.0821359i	$-0.0261741\pi$
$137$	5.00000	+	8.66025i	0.427179	+	0.739895i	−0.569442	+	0.822031i	$0.692841\pi$
$138$	−1.00000	+	1.73205i	−0.0851257	+	0.147442i
$139$	3.00000			0.254457			0.127228	−	0.991873i	$-0.459392\pi$
$139$	3.00000			0.254457			0.127228	+	0.991873i	$0.459392\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$		0			0
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−11.0000			−0.910366
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$	−7.00000			−0.575396
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	0.885653	−	0.464348i	$-0.153711\pi$
$151$	0.500000	+	0.866025i	0.0406894	+	0.0704761i	−0.844963	+	0.534824i	$0.820378\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$	2.00000			0.161690
$154$		0			0
$155$		0			0
$156$	−1.50000	+	2.59808i	−0.120096	+	0.208013i
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	3.50000	+	6.06218i	0.278445	+	0.482281i
$159$	7.00000	−	12.1244i	0.555136	−	0.961524i
$160$		0			0
$161$	−4.00000	−	3.46410i	−0.315244	−	0.273009i
$162$	1.00000			0.0785674
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	−0.634214	−	0.773158i	$-0.718676\pi$
$163$	4.50000	−	7.79423i	0.352467	−	0.610491i	0.986681	+	0.162667i	$0.0520095\pi$
$164$		0			0
$165$		0			0
$166$	−7.00000	+	12.1244i	−0.543305	+	0.941033i
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$	−7.50000	+	2.59808i	−0.578638	+	0.200446i
$169$	−4.00000			−0.307692
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	−8.00000			−0.606478
$175$		0			0
$176$		0			0
$177$	−5.00000	+	8.66025i	−0.375823	+	0.650945i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	6.00000	+	5.19615i	0.444750	+	0.385164i
$183$	7.00000			0.517455
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$		0			0
$188$	10.0000			0.729325
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	0.737620	−	0.675216i	$-0.235950\pi$
$193$	−3.00000	−	5.19615i	−0.215945	−	0.374027i	−0.953564	+	0.301189i	$0.902616\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$		0			0
$201$	2.50000	−	4.33013i	0.176336	−	0.305424i
$202$	−16.0000			−1.12576
$203$	4.00000	−	20.7846i	0.280745	−	1.45879i
$204$	−2.00000			−0.140028
$205$		0			0
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−1.50000	+	2.59808i	−0.104006	+	0.180144i
$209$		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	$0.555058\pi$
$212$	−7.00000	+	12.1244i	−0.480762	+	0.832704i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	−3.00000			−0.204124
$217$	−20.0000	+	6.92820i	−1.35769	+	0.470317i
$218$	−15.0000			−1.01593
$219$	5.50000	−	9.52628i	0.371656	−	0.643726i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$	−3.50000	+	6.06218i	−0.234905	+	0.406867i
$223$	−15.0000			−1.00447			−0.502237	−	0.864730i	$-0.667490\pi$
$223$	−15.0000			−1.00447			−0.502237	+	0.864730i	$0.667490\pi$
$224$	12.5000	−	4.33013i	0.835191	−	0.289319i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		0			0
$231$		0			0
$232$	24.0000			1.57568
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$	1.50000	+	2.59808i	0.0980581	+	0.169842i
$235$		0			0
$236$	5.00000	−	8.66025i	0.325472	−	0.563735i
$237$	−7.00000			−0.454699
$238$	−1.00000	+	5.19615i	−0.0648204	+	0.336817i
$239$	−28.0000			−1.81117			−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000			−1.81117			−0.905585	+	0.424165i	$0.860568\pi$
$240$		0			0
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	−0.976068	−	0.217465i	$-0.930221\pi$
$241$	−10.5000	−	18.1865i	−0.676364	−	1.17150i	0.299704	−	0.954032i	$-0.403112\pi$
$242$	5.50000	+	9.52628i	0.353553	+	0.612372i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−7.00000			−0.448129
$245$		0			0
$246$		0			0
$247$	1.50000	−	2.59808i	0.0954427	−	0.165312i
$248$	−12.0000	−	20.7846i	−0.762001	−	1.31982i
$249$	−7.00000	−	12.1244i	−0.443607	−	0.768350i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	0.500000	−	2.59808i	0.0314970	−	0.163663i
$253$		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		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$	−8.00000			−0.498058
$259$	−14.0000	−	12.1244i	−0.869918	−	0.753371i
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−7.00000	−	12.1244i	−0.432461	−	0.749045i
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	0.506669	−	0.862141i	$-0.330877\pi$
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	−0.999970	+	0.00771799i	$0.997543\pi$
$264$		0			0
$265$		0			0
$266$	2.50000	−	0.866025i	0.153285	−	0.0530994i
$267$	−6.00000			−0.367194
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	0.999901	−	0.0140665i	$-0.00447764\pi$
$269$	8.00000	+	13.8564i	0.487769	+	0.844840i	−0.512132	+	0.858906i	$0.671144\pi$
$270$		0			0
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	−0.624218	−	0.781251i	$-0.714582\pi$
$271$	6.00000	−	10.3923i	0.364474	−	0.631288i	0.988692	+	0.149963i	$0.0479155\pi$
$272$	−2.00000			−0.121268
$273$	−7.50000	+	2.59808i	−0.453921	+	0.157243i
$274$	−10.0000			−0.604122
$275$		0			0
$276$	1.00000	+	1.73205i	0.0601929	+	0.104257i
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−1.50000	+	2.59808i	−0.0899640	+	0.155822i
$279$	−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	$0.442725\pi$
$282$	5.00000	−	8.66025i	0.297746	−	0.515711i
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	0.997076	+	0.0764162i	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	5.00000			0.294628
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−4.50000	−	7.79423i	−0.263795	−	0.456906i
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−16.0000			−0.934730			−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000			−0.934730			−0.467365	+	0.884064i	$0.654797\pi$
$294$	−6.50000	−	2.59808i	−0.379088	−	0.151523i
$295$		0			0
$296$	10.5000	−	18.1865i	0.610300	−	1.05707i
$297$		0			0
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	4.00000	−	20.7846i	0.230556	−	1.19800i
$302$	−1.00000			−0.0575435
$303$	8.00000	−	13.8564i	0.459588	−	0.796030i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−13.0000			−0.739544
$310$		0			0
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	−4.50000	−	7.79423i	−0.254762	−	0.441261i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	7.00000			0.395033
$315$		0			0
$316$	7.00000			0.393781
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$318$	7.00000	+	12.1244i	0.392541	+	0.679900i
$319$		0			0
$320$		0			0
$321$	6.00000			0.334887
$322$	5.00000	−	1.73205i	0.278639	−	0.0965234i
$323$	2.00000			0.111283
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	4.50000	+	7.79423i	0.249232	+	0.431682i
$327$	7.50000	−	12.9904i	0.414751	−	0.718370i
$328$		0			0
$329$	20.0000	+	17.3205i	1.10264	+	0.954911i
$330$		0			0
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	0.418674	+	0.908137i	$0.362495\pi$
$331$	−10.5000	+	18.1865i	−0.577132	+	0.999622i	−0.995806	+	0.0914858i	$0.970838\pi$
$332$	7.00000	+	12.1244i	0.384175	+	0.665410i
$333$	−3.50000	−	6.06218i	−0.191799	−	0.332205i
$334$	−1.00000	+	1.73205i	−0.0547176	+	0.0947736i
$335$		0			0
$336$	0.500000	−	2.59808i	0.0272772	−	0.141737i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	2.00000	−	3.46410i	0.108786	−	0.188422i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$		0			0
$342$	1.00000			0.0540738
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	24.0000			1.29399
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−5.00000	−	8.66025i	−0.268414	−	0.464907i	0.700038	−	0.714105i	$-0.253166\pi$
$347$	−5.00000	−	8.66025i	−0.268414	−	0.464907i	−0.968452	+	0.249198i	$0.919833\pi$
$348$	−4.00000	+	6.92820i	−0.214423	+	0.371391i
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$		0			0
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	−5.00000	−	8.66025i	−0.265747	−	0.460287i
$355$		0			0
$356$	6.00000			0.317999
$357$	−4.00000	−	3.46410i	−0.211702	−	0.183340i
$358$	−12.0000			−0.634220
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$	−11.0000			−0.577350
$364$	7.50000	−	2.59808i	0.393107	−	0.136176i
$365$		0			0
$366$	−3.50000	+	6.06218i	−0.182948	+	0.316875i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	1.00000	+	1.73205i	0.0521286	+	0.0902894i
$369$		0			0
$370$		0			0
$371$	−35.0000	+	12.1244i	−1.81711	+	0.629465i
$372$	8.00000			0.414781
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$		0			0
$375$		0			0
$376$	−15.0000	+	25.9808i	−0.773566	+	1.33986i
$377$	24.0000			1.23606
$378$	−2.00000	−	1.73205i	−0.102869	−	0.0890871i
$379$	35.0000			1.79783			0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000			1.79783			0.898915	+	0.438124i	$0.144357\pi$
$380$		0			0
$381$	−5.50000	−	9.52628i	−0.281774	−	0.488046i
$382$	4.00000	+	6.92820i	0.204658	+	0.354478i
$383$	−5.00000	+	8.66025i	−0.255488	+	0.442518i	−0.965028	−	0.262147i	$-0.915569\pi$
$383$	−5.00000	+	8.66025i	−0.255488	+	0.442518i	0.709540	+	0.704665i	$0.248903\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	6.00000			0.305392
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	4.50000	+	7.79423i	0.228453	+	0.395692i
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.810326	+	0.585980i	$0.199290\pi$
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.102311	+	0.994753i	$0.467376\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$	19.5000	+	7.79423i	0.984899	+	0.393668i
$393$	14.0000			0.706207
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	11.0000			0.551380
$399$	−0.500000	+	2.59808i	−0.0250313	+	0.130066i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	−12.0000	−	20.7846i	−0.597763	−	1.03536i
$404$	−8.00000	+	13.8564i	−0.398015	+	0.689382i
$405$		0			0
$406$	16.0000	+	13.8564i	0.794067	+	0.687682i
$407$		0			0
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	5.00000	−	8.66025i	0.246632	−	0.427179i
$412$	13.0000			0.640464
$413$	25.0000	−	8.66025i	1.23017	−	0.426143i
$414$	2.00000			0.0982946
$415$		0			0
$416$	7.50000	+	12.9904i	0.367718	+	0.636906i
$417$	−1.50000	−	2.59808i	−0.0734553	−	0.127228i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$	5.00000	+	8.66025i	0.243108	+	0.421076i
$424$	−21.0000	−	36.3731i	−1.01985	−	1.76643i
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−14.0000	−	12.1244i	−0.677507	−	0.586739i
$428$	−6.00000			−0.290021
$429$		0			0
$430$		0			0
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	4.00000	−	20.7846i	0.192006	−	0.997693i
$435$		0			0
$436$	−7.50000	+	12.9904i	−0.359185	+	0.622126i
$437$	−1.00000	−	1.73205i	−0.0478365	−	0.0828552i
$438$	5.50000	+	9.52628i	0.262800	+	0.455183i
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	−0.704405	−	0.709798i	$-0.748786\pi$
$439$	5.50000	−	9.52628i	0.262501	−	0.454665i	0.966906	+	0.255134i	$0.0821195\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	−6.00000			−0.285391
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	−0.928450	−	0.371457i	$-0.878858\pi$
$443$	−3.00000	+	5.19615i	−0.142534	+	0.246877i	0.785916	+	0.618333i	$0.212192\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$		0			0
$446$	7.50000	−	12.9904i	0.355135	−	0.615112i
$447$	−4.00000			−0.189194
$448$	−3.50000	+	18.1865i	−0.165359	+	0.859233i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$		0			0
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	0.500000	−	0.866025i	0.0234920	−	0.0406894i
$454$	20.0000			0.938647
$455$		0			0
$456$	−3.00000			−0.140488
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	−0.828807	−	0.559534i	$-0.810980\pi$
$457$	1.50000	−	2.59808i	0.0701670	−	0.121533i	0.898974	+	0.438001i	$0.144313\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	−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
$463$	33.0000			1.53364			0.766820	−	0.641862i	$-0.221838\pi$
$463$	33.0000			1.53364			0.766820	+	0.641862i	$0.221838\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	1.00000	−	1.73205i	0.0462745	−	0.0801498i	−0.841960	−	0.539539i	$-0.818598\pi$
$467$	1.00000	−	1.73205i	0.0462745	−	0.0801498i	0.888235	+	0.459390i	$0.151932\pi$
$468$	3.00000			0.138675
$469$	−12.5000	+	4.33013i	−0.577196	+	0.199947i
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	15.0000	+	25.9808i	0.690431	+	1.19586i
$473$		0			0
$474$	3.50000	−	6.06218i	0.160760	−	0.278445i
$475$		0			0
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$	−14.0000			−0.641016
$478$	14.0000	−	24.2487i	0.640345	−	1.10911i
$479$	−1.00000	−	1.73205i	−0.0456912	−	0.0791394i	0.842275	−	0.539048i	$-0.181216\pi$
$479$	−1.00000	−	1.73205i	−0.0456912	−	0.0791394i	−0.887967	+	0.459908i	$0.847882\pi$
$480$		0			0
$481$	10.5000	−	18.1865i	0.478759	−	0.829235i
$482$	21.0000			0.956524
$483$	−1.00000	+	5.19615i	−0.0455016	+	0.236433i
$484$	11.0000			0.500000
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$	10.5000	−	18.1865i	0.475313	−	0.823266i
$489$	−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
$493$	8.00000	+	13.8564i	0.360302	+	0.624061i
$494$	1.50000	+	2.59808i	0.0674882	+	0.116893i
$495$		0			0
$496$	8.00000			0.359211
$497$	6.00000	−	31.1769i	0.269137	−	1.39848i
$498$	14.0000			0.627355
$499$	9.50000	−	16.4545i	0.425278	−	0.736604i	−0.571168	−	0.820833i	$-0.693510\pi$
$499$	9.50000	−	16.4545i	0.425278	−	0.736604i	0.996446	+	0.0842294i	$0.0268429\pi$
$500$		0			0
$501$	−1.00000	−	1.73205i	−0.0446767	−	0.0773823i
$502$		0			0
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$	6.00000	+	5.19615i	0.267261	+	0.231455i
$505$		0			0
$506$		0			0
$507$	2.00000	+	3.46410i	0.0888231	+	0.153846i
$508$	5.50000	+	9.52628i	0.244023	+	0.422660i
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	−0.763657	−	0.645622i	$-0.776598\pi$
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	0.940954	+	0.338535i	$0.109931\pi$
$510$		0			0
$511$	−27.5000	+	9.52628i	−1.21653	+	0.421418i
$512$	−11.0000			−0.486136
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$		0			0
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		0			0
$518$	17.5000	−	6.06218i	0.768906	−	0.266357i
$519$	18.0000			0.790112
$520$		0			0
$521$	−17.0000	−	29.4449i	−0.744784	−	1.29000i	−0.950296	−	0.311348i	$-0.899219\pi$
$521$	−17.0000	−	29.4449i	−0.744784	−	1.29000i	0.205512	−	0.978655i	$-0.434114\pi$
$522$	4.00000	+	6.92820i	0.175075	+	0.303239i
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	−14.0000			−0.611593
$525$		0			0
$526$	16.0000			0.697633
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	10.0000			0.433963
$532$	0.500000	−	2.59808i	0.0216777	−	0.112641i
$533$		0			0
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$		0			0
$536$	−7.50000	−	12.9904i	−0.323951	−	0.561099i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	−16.0000			−0.689809
$539$		0			0
$540$		0			0
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	6.00000	+	10.3923i	0.257722	+	0.446388i
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$	−5.00000	+	8.66025i	−0.214373	+	0.371305i
$545$		0			0
$546$	1.50000	−	7.79423i	0.0641941	−	0.333562i
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	−3.50000	−	6.06218i	−0.149376	−	0.258727i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$	−6.00000			−0.255377
$553$	14.0000	+	12.1244i	0.595341	+	0.515580i
$554$	5.00000			0.212430
$555$		0			0
$556$	1.50000	+	2.59808i	0.0636142	+	0.110183i
$557$	2.00000	+	3.46410i	0.0847427	+	0.146779i	0.905282	−	0.424812i	$-0.139660\pi$
$557$	2.00000	+	3.46410i	0.0847427	+	0.146779i	−0.820539	+	0.571591i	$0.806326\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	24.0000			1.01509
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	−0.994228	−	0.107290i	$-0.965783\pi$
$563$	−14.0000	−	24.2487i	−0.590030	−	1.02196i	0.404198	−	0.914671i	$-0.367551\pi$
$564$	−5.00000	−	8.66025i	−0.210538	−	0.364662i
$565$		0			0
$566$	−19.0000			−0.798630
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	36.0000			1.51053
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	−0.963948	−	0.266090i	$-0.914268\pi$
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	0.712415	+	0.701758i	$0.247601\pi$
$570$		0			0
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$		0			0
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−3.00000	+	5.19615i	−0.124676	+	0.215945i
$580$		0			0
$581$	−7.00000	+	36.3731i	−0.290409	+	1.50901i
$582$	9.00000			0.373062
$583$		0			0
$584$	−16.5000	−	28.5788i	−0.682775	−	1.18260i
$585$		0			0
$586$	8.00000	−	13.8564i	0.330477	−	0.572403i
$587$	−6.00000			−0.247647			−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000			−0.247647			−0.123823	+	0.992304i	$0.539516\pi$
$588$	−5.50000	+	4.33013i	−0.226816	+	0.178571i
$589$	−8.00000			−0.329634
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	0.00727173	+	0.999974i	$0.497685\pi$
$593$	−21.0000	+	36.3731i	−0.862367	+	1.49366i	−0.869638	+	0.493689i	$0.835648\pi$
$594$		0			0
$595$		0			0
$596$	4.00000			0.163846
$597$	−5.50000	+	9.52628i	−0.225100	+	0.389885i
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−13.0000	−	22.5167i	−0.531166	−	0.920006i	−0.999338	−	0.0363689i	$-0.988421\pi$
$599$	−13.0000	−	22.5167i	−0.531166	−	0.920006i	0.468173	−	0.883637i	$-0.344912\pi$
$600$		0			0
$601$	−45.0000			−1.83559			−0.917794	−	0.397057i	$-0.870032\pi$
$601$	−45.0000			−1.83559			−0.917794	+	0.397057i	$0.870032\pi$
$602$	16.0000	+	13.8564i	0.652111	+	0.564745i
$603$	−5.00000			−0.203616
$604$	−0.500000	+	0.866025i	−0.0203447	+	0.0352381i
$605$		0			0
$606$	8.00000	+	13.8564i	0.324978	+	0.562878i
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	5.00000			0.202777
$609$	−20.0000	+	6.92820i	−0.810441	+	0.280745i
$610$		0			0
$611$	−15.0000	+	25.9808i	−0.606835	+	1.05107i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	−0.920229	+	0.391381i	$0.871998\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$		0			0
$616$		0			0
$617$	−24.0000			−0.966204			−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000			−0.966204			−0.483102	+	0.875564i	$0.660490\pi$
$618$	6.50000	−	11.2583i	0.261468	−	0.452876i
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	0.961045	−	0.276392i	$-0.0891387\pi$
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	−0.719885	+	0.694094i	$0.755805\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$	−30.0000			−1.20289
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$	3.00000			0.120096
$625$		0			0
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$		0			0
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	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	$0.146667\pi$
$632$	−10.5000	+	18.1865i	−0.417668	+	0.723421i
$633$	2.50000	+	4.33013i	0.0993661	+	0.172107i
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$		0			0
$636$	14.0000			0.555136
$637$	19.5000	+	7.79423i	0.772618	+	0.308819i
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$	−3.00000	+	5.19615i	−0.118401	+	0.205076i
$643$	−29.0000			−1.14365			−0.571824	−	0.820376i	$-0.693764\pi$
$643$	−29.0000			−1.14365			−0.571824	+	0.820376i	$0.693764\pi$
$644$	1.00000	−	5.19615i	0.0394055	−	0.204757i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	0.723645	−	0.690172i	$-0.242465\pi$
$647$	−6.00000	−	10.3923i	−0.235884	−	0.408564i	−0.959529	+	0.281609i	$0.909132\pi$
$648$	1.50000	+	2.59808i	0.0589256	+	0.102062i
$649$		0			0
$650$		0			0
$651$	16.0000	+	13.8564i	0.627089	+	0.543075i
$652$	9.00000			0.352467
$653$	−22.0000	+	38.1051i	−0.860927	+	1.49117i	0.0101092	+	0.999949i	$0.496782\pi$
$653$	−22.0000	+	38.1051i	−0.860927	+	1.49117i	−0.871036	+	0.491220i	$0.836551\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$		0			0
$656$		0			0
$657$	−11.0000			−0.429151
$658$	−25.0000	+	8.66025i	−0.974601	+	0.337612i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	0.739014	−	0.673690i	$-0.235292\pi$
$661$	−5.50000	−	9.52628i	−0.213925	−	0.370529i	−0.952940	+	0.303160i	$0.901958\pi$
$662$	−10.5000	−	18.1865i	−0.408094	−	0.706840i
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$	−42.0000			−1.62992
$665$		0			0
$666$	7.00000			0.271244
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$	1.00000	+	1.73205i	0.0386912	+	0.0670151i
$669$	7.50000	+	12.9904i	0.289967	+	0.502237i
$670$		0			0
$671$		0			0
$672$	−10.0000	−	8.66025i	−0.385758	−	0.334077i
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	1.00000	−	1.73205i	0.0385186	−	0.0667161i
$675$		0			0
$676$	−2.00000	−	3.46410i	−0.0769231	−	0.133235i
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	−0.699580	−	0.714554i	$-0.746630\pi$
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	0.968612	+	0.248577i	$0.0799630\pi$
$678$	−6.00000			−0.230429
$679$	−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		0.866025	−	0.500000i	$-0.166667\pi$
$683$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	13.0000			0.495981
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−21.0000	−	36.3731i	−0.800036	−	1.38570i
$690$		0			0
$691$	7.50000	−	12.9904i	0.285313	−	0.494177i	−0.687372	−	0.726306i	$-0.741236\pi$
$691$	7.50000	−	12.9904i	0.285313	−	0.494177i	0.972685	+	0.232128i	$0.0745690\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	10.0000			0.379595
$695$		0			0
$696$	−12.0000	−	20.7846i	−0.454859	−	0.787839i
$697$		0			0
$698$	11.0000	−	19.0526i	0.416356	−	0.721150i
$699$	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	$0.278071\pi$
$702$	1.50000	−	2.59808i	0.0566139	−	0.0980581i
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$		0			0
$705$		0			0
$706$	24.0000			0.903252
$707$	−40.0000	+	13.8564i	−1.50435	+	0.521124i
$708$	−10.0000			−0.375823
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$		0			0
$711$	3.50000	+	6.06218i	0.131260	+	0.227349i
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	−16.0000			−0.599205
$714$	5.00000	−	1.73205i	0.187120	−	0.0648204i
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	14.0000	+	24.2487i	0.522840	+	0.905585i
$718$	−15.0000	−	25.9808i	−0.559795	−	0.969593i
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	−0.826319	−	0.563202i	$-0.809569\pi$
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	0.900907	+	0.434013i	$0.142903\pi$
$720$		0			0
$721$	26.0000	+	22.5167i	0.968291	+	0.838564i
$722$	−18.0000			−0.669891
$723$	−10.5000	+	18.1865i	−0.390499	+	0.676364i
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$		0			0
$726$	5.50000	−	9.52628i	0.204124	−	0.353553i
$727$	43.0000			1.59478			0.797391	−	0.603463i	$-0.206213\pi$
$727$	43.0000			1.59478			0.797391	+	0.603463i	$0.206213\pi$
$728$	−4.50000	+	23.3827i	−0.166781	+	0.866620i
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$	3.50000	+	6.06218i	0.129364	+	0.224065i
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	−0.423802	−	0.905755i	$-0.639305\pi$
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	0.996308	−	0.0858539i	$-0.0273618\pi$
$734$	−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	0.825877	+	0.563850i	$0.190680\pi$
$739$	24.5000	+	42.4352i	0.901247	+	1.56101i	0.0753699	+	0.997156i	$0.475986\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$	7.00000	−	36.3731i	0.256978	−	1.33530i
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$	−12.0000	+	20.7846i	−0.439941	+	0.762001i
$745$		0			0
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$	−7.00000	+	12.1244i	−0.256117	+	0.443607i
$748$		0			0
$749$	−12.0000	−	10.3923i	−0.438470	−	0.379727i
$750$		0			0
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	−0.995903	−	0.0904254i	$-0.971177\pi$
$751$	−11.5000	+	19.9186i	−0.419641	+	0.726839i	0.576262	+	0.817265i	$0.304511\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$		0			0
$754$	−12.0000	+	20.7846i	−0.437014	+	0.756931i
$755$		0			0
$756$	−2.50000	+	0.866025i	−0.0909241	+	0.0314970i
$757$	−43.0000			−1.56286			−0.781431	−	0.623992i	$-0.785510\pi$
$757$	−43.0000			−1.56286			−0.781431	+	0.623992i	$0.785510\pi$
$758$	−17.5000	+	30.3109i	−0.635629	+	1.10094i
$759$		0			0
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	11.0000			0.398488
$763$	−37.5000	+	12.9904i	−1.35759	+	0.470283i
$764$	8.00000			0.289430
$765$		0			0
$766$	−5.00000	−	8.66025i	−0.180657	−	0.312908i
$767$	15.0000	+	25.9808i	0.541619	+	0.938111i
$768$	8.50000	−	14.7224i	0.306717	−	0.531250i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$		0			0
$772$	3.00000	−	5.19615i	0.107972	−	0.187014i
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	−0.868804	−	0.495156i	$-0.835111\pi$
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	0.00558380	−	0.999984i	$-0.498223\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	−27.0000			−0.969244
$777$	−3.50000	+	18.1865i	−0.125562	+	0.652438i
$778$	−36.0000			−1.29066
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−2.00000	+	3.46410i	−0.0715199	+	0.123876i
$783$	−8.00000			−0.285897
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$	−7.00000	+	12.1244i	−0.249682	+	0.432461i
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	0.976812	−	0.214097i	$-0.0686810\pi$
$787$	8.50000	+	14.7224i	0.302992	+	0.524798i	−0.673820	+	0.738896i	$0.735348\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$	−8.00000	+	13.8564i	−0.284808	+	0.493301i
$790$		0			0
$791$	3.00000	−	15.5885i	0.106668	−	0.554262i
$792$		0			0
$793$	10.5000	−	18.1865i	0.372866	−	0.645823i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$		0			0
$796$	5.50000	−	9.52628i	0.194942	−	0.337650i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$	−2.00000	−	1.73205i	−0.0707992	−	0.0613139i
$799$	−20.0000			−0.707549
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	6.00000	+	10.3923i	0.211867	+	0.366965i
$803$		0			0
$804$	5.00000			0.176336
$805$		0			0
$806$	24.0000			0.845364
$807$	8.00000	−	13.8564i	0.281613	−	0.487769i
$808$	−24.0000	−	41.5692i	−0.844317	−	1.46240i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$		0			0
$811$	3.00000			0.105344			0.0526721	−	0.998612i	$-0.483226\pi$
$811$	3.00000			0.105344			0.0526721	+	0.998612i	$0.483226\pi$
$812$	20.0000	−	6.92820i	0.701862	−	0.243132i
$813$	−12.0000			−0.420858
$814$		0			0
$815$		0			0
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	5.00000			0.174821
$819$	6.00000	+	5.19615i	0.209657	+	0.181568i
$820$		0			0
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	0.819159	−	0.573567i	$-0.194441\pi$
$823$	−2.50000	−	4.33013i	−0.0871445	−	0.150939i	−0.906303	+	0.422628i	$0.861108\pi$
$824$	−19.5000	+	33.7750i	−0.679315	+	1.17661i
$825$		0			0
$826$	−5.00000	+	25.9808i	−0.173972	+	0.903986i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$	1.00000	−	1.73205i	0.0347524	−	0.0601929i
$829$	7.50000	+	12.9904i	0.260486	+	0.451175i	0.966371	−	0.257152i	$-0.0827840\pi$
$829$	7.50000	+	12.9904i	0.260486	+	0.451175i	−0.705885	+	0.708326i	$0.749451\pi$
$830$		0			0
$831$	−2.50000	+	4.33013i	−0.0867240	+	0.150210i
$832$	−21.0000			−0.728044
$833$	2.00000	+	13.8564i	0.0692959	+	0.480096i
$834$	3.00000			0.103882
$835$		0			0
$836$		0			0
$837$	4.00000	+	6.92820i	0.138260	+	0.239474i
$838$	−12.0000	+	20.7846i	−0.414533	+	0.717992i
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	17.5000	−	30.3109i	0.603090	−	1.04458i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$		0			0
$846$	−10.0000			−0.343807
$847$	22.0000	+	19.0526i	0.755929	+	0.654654i
$848$	14.0000			0.480762
$849$	9.50000	−	16.4545i	0.326039	−	0.564716i
$850$		0			0
$851$	−7.00000	−	12.1244i	−0.239957	−	0.415618i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$	17.5000	−	6.06218i	0.598838	−	0.207443i
$855$		0			0
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.0438309	−	0.999039i	$-0.486044\pi$
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.843278	−	0.537478i	$-0.180623\pi$
$860$		0			0
$861$		0			0
$862$	−2.00000			−0.0681203
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−13.0000			−0.441503
$868$	−16.0000	−	13.8564i	−0.543075	−	0.470317i
$869$		0			0
$870$		0			0
$871$	−7.50000	−	12.9904i	−0.254128	−	0.440162i
$872$	−22.5000	−	38.9711i	−0.761946	−	1.31973i
$873$	−4.50000	+	7.79423i	−0.152302	+	0.263795i
$874$	2.00000			0.0676510
$875$		0			0
$876$	11.0000			0.371656
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	−0.992225	−	0.124459i	$-0.960280\pi$
$877$	−11.5000	+	19.9186i	−0.388327	+	0.672603i	0.603897	+	0.797062i	$0.293614\pi$
$878$	5.50000	+	9.52628i	0.185616	+	0.321496i
$879$	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	$0.435209\pi$
$882$	1.00000	+	6.92820i	0.0336718	+	0.233285i
$883$	31.0000			1.04323			0.521617	−	0.853180i	$-0.325329\pi$
$883$	31.0000			1.04323			0.521617	+	0.853180i	$0.325329\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	−29.0000	+	50.2295i	−0.973725	+	1.68654i	−0.289644	+	0.957135i	$0.593537\pi$
$887$	−29.0000	+	50.2295i	−0.973725	+	1.68654i	−0.684081	+	0.729406i	$0.739796\pi$
$888$	−21.0000			−0.704714
$889$	−5.50000	+	28.5788i	−0.184464	+	0.958503i
$890$		0			0
$891$		0			0
$892$	−7.50000	−	12.9904i	−0.251119	−	0.434950i
$893$	5.00000	+	8.66025i	0.167319	+	0.289804i
$894$	2.00000	−	3.46410i	0.0668900	−	0.115857i
$895$		0			0
$896$	6.00000	+	5.19615i	0.200446	+	0.173591i
$897$	−6.00000			−0.200334
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$	−32.0000	−	55.4256i	−1.06726	−	1.84855i
$900$		0			0
$901$	14.0000	−	24.2487i	0.466408	−	0.807842i
$902$		0			0
$903$	−20.0000	+	6.92820i	−0.665558	+	0.230556i
$904$	18.0000			0.598671
$905$		0			0
$906$	0.500000	+	0.866025i	0.0166114	+	0.0287718i
$907$	−0.500000	−	0.866025i	−0.0166022	−	0.0287559i	0.857605	−	0.514309i	$-0.171952\pi$
$907$	−0.500000	−	0.866025i	−0.0166022	−	0.0287559i	−0.874207	+	0.485553i	$0.838618\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	−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	$0.147496\pi$
$912$	0.500000	−	0.866025i	0.0165567	−	0.0286770i
$913$		0			0
$914$	1.50000	+	2.59808i	0.0496156	+	0.0859367i
$915$		0			0
$916$	−13.0000			−0.429532
$917$	−28.0000	−	24.2487i	−0.924641	−	0.800763i
$918$	2.00000			0.0660098
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$		0			0
$921$	6.00000	+	10.3923i	0.197707	+	0.342438i
$922$	1.00000	−	1.73205i	0.0329332	−	0.0570421i
$923$	36.0000			1.18495
$924$		0			0
$925$		0			0
$926$	−16.5000	+	28.5788i	−0.542224	+	0.939159i
$927$	6.50000	+	11.2583i	0.213488	+	0.369772i
$928$	20.0000	+	34.6410i	0.656532	+	1.13715i
$929$	22.0000	−	38.1051i	0.721797	−	1.25019i	−0.238482	−	0.971147i	$-0.576650\pi$
$929$	22.0000	−	38.1051i	0.721797	−	1.25019i	0.960279	−	0.279042i	$-0.0900167\pi$
$930$		0			0
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$	−24.0000			−0.786146
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	1.00000	+	1.73205i	0.0327210	+	0.0566744i
$935$		0			0
$936$	−4.50000	+	7.79423i	−0.147087	+	0.254762i
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	2.50000	−	12.9904i	0.0816279	−	0.424151i
$939$	14.0000			0.456873
$940$		0			0
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	−0.973568	−	0.228395i	$-0.926652\pi$
$941$	−21.0000	−	36.3731i	−0.684580	−	1.18573i	0.288988	−	0.957333i	$-0.406681\pi$
$942$	−3.50000	−	6.06218i	−0.114036	−	0.197516i
$943$		0			0
$944$	−10.0000			−0.325472
$945$		0			0
$946$		0			0
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	−0.630082	−	0.776528i	$-0.716979\pi$
$947$	11.0000	−	19.0526i	0.357452	−	0.619125i	0.987534	+	0.157403i	$0.0503122\pi$
$948$	−3.50000	−	6.06218i	−0.113675	−	0.196890i
$949$	−16.5000	−	28.5788i	−0.535613	−	0.927708i
$950$		0			0
$951$	14.0000			0.453981
$952$	−15.0000	+	5.19615i	−0.486153	+	0.168408i
$953$	−20.0000			−0.647864			−0.323932	−	0.946080i	$-0.605005\pi$
$953$	−20.0000			−0.647864			−0.323932	+	0.946080i	$0.605005\pi$
$954$	7.00000	−	12.1244i	0.226633	−	0.392541i
$955$		0			0
$956$	−14.0000	−	24.2487i	−0.452792	−	0.784259i
$957$		0			0
$958$	2.00000			0.0646171
$959$	−25.0000	+	8.66025i	−0.807292	+	0.279654i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	10.5000	+	18.1865i	0.338534	+	0.586357i
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$	10.5000	−	18.1865i	0.338182	−	0.585749i
$965$		0			0
$966$	−4.00000	−	3.46410i	−0.128698	−	0.111456i
$967$	−23.0000			−0.739630			−0.369815	−	0.929105i	$-0.620579\pi$
$967$	−23.0000			−0.739630			−0.369815	+	0.929105i	$0.620579\pi$
$968$	−16.5000	+	28.5788i	−0.530330	+	0.918559i
$969$	−1.00000	−	1.73205i	−0.0321246	−	0.0556415i
$970$		0			0
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	−0.923044	−	0.384695i	$-0.874307\pi$
$971$	−4.00000	+	6.92820i	−0.128366	+	0.222337i	0.794678	+	0.607032i	$0.207640\pi$
$972$	−1.00000			−0.0320750
$973$	−1.50000	+	7.79423i	−0.0480878	+	0.249871i
$974$	8.00000			0.256337
$975$		0			0
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	20.0000	+	34.6410i	0.639857	+	1.10826i	0.985464	+	0.169885i	$0.0543396\pi$
$977$	20.0000	+	34.6410i	0.639857	+	1.10826i	−0.345607	+	0.938379i	$0.612327\pi$
$978$	4.50000	−	7.79423i	0.143894	−	0.249232i
$979$		0			0
$980$		0			0
$981$	−15.0000			−0.478913
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	11.0000	+	19.0526i	0.350846	+	0.607682i	0.986398	−	0.164376i	$-0.0525609\pi$
$983$	11.0000	+	19.0526i	0.350846	+	0.607682i	−0.635552	+	0.772058i	$0.719228\pi$
$984$		0			0
$985$		0			0
$986$	−16.0000			−0.509544
$987$	5.00000	−	25.9808i	0.159152	−	0.826977i
$988$	3.00000			0.0954427
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$	20.0000	−	34.6410i	0.635001	−	1.09985i
$993$	21.0000			0.666415
$994$	24.0000	+	20.7846i	0.761234	+	0.659248i
$995$		0			0
$996$	7.00000	−	12.1244i	0.221803	−	0.384175i
$997$	18.5000	+	32.0429i	0.585901	+	1.01481i	0.994762	+	0.102214i	$0.0325925\pi$
$997$	18.5000	+	32.0429i	0.585901	+	1.01481i	−0.408862	+	0.912596i	$0.634074\pi$
$998$	9.50000	+	16.4545i	0.300717	+	0.520858i
$999$	−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.i.b.226.1	yes	2
5.2	odd	4		525.2.r.c.499.1		4
5.3	odd	4		525.2.r.c.499.2		4
5.4	even	2		525.2.i.d.226.1	yes	2
7.2	even	3		3675.2.a.m.1.1		1
7.4	even	3	inner	525.2.i.b.151.1	✓	2
7.5	odd	6		3675.2.a.k.1.1		1
35.4	even	6		525.2.i.d.151.1	yes	2
35.9	even	6		3675.2.a.e.1.1		1
35.18	odd	12		525.2.r.c.424.1		4
35.19	odd	6		3675.2.a.g.1.1		1
35.32	odd	12		525.2.r.c.424.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.b.151.1	✓	2	7.4	even	3	inner
525.2.i.b.226.1	yes	2	1.1	even	1	trivial
525.2.i.d.151.1	yes	2	35.4	even	6
525.2.i.d.226.1	yes	2	5.4	even	2
525.2.r.c.424.1		4	35.18	odd	12
525.2.r.c.424.2		4	35.32	odd	12
525.2.r.c.499.1		4	5.2	odd	4
525.2.r.c.499.2		4	5.3	odd	4
3675.2.a.e.1.1		1	35.9	even	6
3675.2.a.g.1.1		1	35.19	odd	6
3675.2.a.k.1.1		1	7.5	odd	6
3675.2.a.m.1.1		1	7.2	even	3

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{12} -3.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{23} +(1.50000 + 2.59808i) q^{24} +(1.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} -8.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.50000 - 4.33013i) q^{32} +2.00000 q^{34} -1.00000 q^{36} +(-3.50000 + 6.06218i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.50000 + 2.59808i) q^{39} +(-0.500000 + 2.59808i) q^{42} -8.00000 q^{43} +(-1.00000 - 1.73205i) q^{46} +(5.00000 - 8.66025i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-1.50000 - 2.59808i) q^{52} +(7.00000 + 12.1244i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 - 7.79423i) q^{56} +1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-3.50000 + 6.06218i) q^{61} -8.00000 q^{62} +(-2.00000 - 1.73205i) q^{63} +7.00000 q^{64} +(2.50000 + 4.33013i) q^{67} +(1.00000 - 1.73205i) q^{68} +2.00000 q^{69} -12.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} -1.00000 q^{76} -3.00000 q^{78} +(3.50000 - 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +14.0000 q^{83} +(2.00000 + 1.73205i) q^{84} +(4.00000 - 6.92820i) q^{86} +(4.00000 + 6.92820i) q^{87} +(3.00000 - 5.19615i) q^{89} +(1.50000 - 7.79423i) q^{91} -2.00000 q^{92} +(4.00000 - 6.92820i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-2.50000 + 4.33013i) q^{96} +9.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} + q^{4} + 2 q^{6} - q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 + q^4 + 2 * q^6 - q^7 - 6 * q^8 - q^9	\( 2 q - q^{2} - q^{3} + q^{4} + 2 q^{6} - q^{7} - 6 q^{8} - q^{9} + q^{12} - 6 q^{13} - 4 q^{14} + q^{16} - 2 q^{17} - q^{18} - q^{19} + 5 q^{21} - 2 q^{23} + 3 q^{24} + 3 q^{26} + 2 q^{27} - 5 q^{28} - 16 q^{29} + 8 q^{31} - 5 q^{32} + 4 q^{34} - 2 q^{36} - 7 q^{37} - q^{38} + 3 q^{39} - q^{42} - 16 q^{43} - 2 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} - 2 q^{51} - 3 q^{52} + 14 q^{53} - q^{54} + 3 q^{56} + 2 q^{57} + 8 q^{58} - 10 q^{59} - 7 q^{61} - 16 q^{62} - 4 q^{63} + 14 q^{64} + 5 q^{67} + 2 q^{68} + 4 q^{69} - 24 q^{71} + 3 q^{72} + 11 q^{73} - 7 q^{74} - 2 q^{76} - 6 q^{78} + 7 q^{79} - q^{81} + 28 q^{83} + 4 q^{84} + 8 q^{86} + 8 q^{87} + 6 q^{89} + 3 q^{91} - 4 q^{92} + 8 q^{93} + 10 q^{94} - 5 q^{96} + 18 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^3 + q^4 + 2 * q^6 - q^7 - 6 * q^8 - q^9 + q^12 - 6 * q^13 - 4 * q^14 + q^16 - 2 * q^17 - q^18 - q^19 + 5 * q^21 - 2 * q^23 + 3 * q^24 + 3 * q^26 + 2 * q^27 - 5 * q^28 - 16 * q^29 + 8 * q^31 - 5 * q^32 + 4 * q^34 - 2 * q^36 - 7 * q^37 - q^38 + 3 * q^39 - q^42 - 16 * q^43 - 2 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 - 2 * q^51 - 3 * q^52 + 14 * q^53 - q^54 + 3 * q^56 + 2 * q^57 + 8 * q^58 - 10 * q^59 - 7 * q^61 - 16 * q^62 - 4 * q^63 + 14 * q^64 + 5 * q^67 + 2 * q^68 + 4 * q^69 - 24 * q^71 + 3 * q^72 + 11 * q^73 - 7 * q^74 - 2 * q^76 - 6 * q^78 + 7 * q^79 - q^81 + 28 * q^83 + 4 * q^84 + 8 * q^86 + 8 * q^87 + 6 * q^89 + 3 * q^91 - 4 * q^92 + 8 * q^93 + 10 * q^94 - 5 * q^96 + 18 * q^97 + 11 * q^98

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