LMFDB - Embedded newform 950.2.e.b.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([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("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (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:	$7.58578819202$
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			501.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.b.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +1.00000 q^{12} +(-3.00000 + 5.19615i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 + 1.73205i) q^{21} +(-1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +6.00000 q^{26} -5.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-5.00000 + 8.66025i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.50000 + 6.06218i) q^{34} +(1.00000 + 1.73205i) q^{36} +4.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +6.00000 q^{39} +(-1.00000 - 1.73205i) q^{41} +(1.00000 - 1.73205i) q^{42} +(6.00000 + 10.3923i) q^{43} +2.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -3.00000 q^{49} +(-3.50000 + 6.06218i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(0.500000 - 4.33013i) q^{57} +10.0000 q^{58} +(0.500000 + 0.866025i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(-4.00000 + 6.92820i) q^{67} +7.00000 q^{68} +2.00000 q^{69} +(6.00000 + 10.3923i) q^{71} +(1.00000 - 1.73205i) q^{72} +(1.50000 + 2.59808i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(-3.00000 - 5.19615i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -13.0000 q^{83} -2.00000 q^{84} +(6.00000 - 10.3923i) q^{86} +10.0000 q^{87} +(6.50000 - 11.2583i) q^{89} +(6.00000 - 10.3923i) q^{91} +(-1.00000 - 1.73205i) q^{92} +(1.00000 + 1.73205i) q^{93} +1.00000 q^{96} +(-7.50000 - 12.9904i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 7 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} - 2 q^{23} - q^{24} + 12 q^{26} - 10 q^{27} + 2 q^{28} - 10 q^{29} - 4 q^{31} - q^{32} - 7 q^{34} + 2 q^{36} + 8 q^{37} + q^{38} + 12 q^{39} - 2 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{46} - q^{48} - 6 q^{49} - 7 q^{51} - 6 q^{52} + 5 q^{54} - 4 q^{56} + q^{57} + 20 q^{58} + q^{59} - 8 q^{61} + 2 q^{62} - 4 q^{63} + 2 q^{64} - 8 q^{67} + 14 q^{68} + 4 q^{69} + 12 q^{71} + 2 q^{72} + 3 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{78} + 4 q^{79} - q^{81} - 2 q^{82} - 26 q^{83} - 4 q^{84} + 12 q^{86} + 20 q^{87} + 13 q^{89} + 12 q^{91} - 2 q^{92} + 2 q^{93} + 2 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 6 * q^13 + 2 * q^14 - q^16 - 7 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 - 2 * q^23 - q^24 + 12 * q^26 - 10 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^31 - q^32 - 7 * q^34 + 2 * q^36 + 8 * q^37 + q^38 + 12 * q^39 - 2 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^46 - q^48 - 6 * q^49 - 7 * q^51 - 6 * q^52 + 5 * q^54 - 4 * q^56 + q^57 + 20 * q^58 + q^59 - 8 * q^61 + 2 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^67 + 14 * q^68 + 4 * q^69 + 12 * q^71 + 2 * q^72 + 3 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^78 + 4 * q^79 - q^81 - 2 * q^82 - 26 * q^83 - 4 * q^84 + 12 * q^86 + 20 * q^87 + 13 * q^89 + 12 * q^91 - 2 * q^92 + 2 * q^93 + 2 * q^96 - 15 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	1.00000			0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	1.00000			0.288675
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$	−2.00000			−0.471405
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$		0			0
$21$	1.00000	+	1.73205i	0.218218	+	0.377964i
$22$		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	$0.233529\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	6.00000			1.17670
$27$	−5.00000			−0.962250
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.142605	+	0.989780i	$0.545548\pi$
$29$	−5.00000	+	8.66025i	−0.928477	+	1.60817i	−0.785872	+	0.618389i	$0.787786\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.50000	+	6.06218i	−0.600245	+	1.03965i
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	0.500000	−	4.33013i	0.0811107	−	0.702439i
$39$	6.00000			0.960769
$40$		0			0
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.806914	+	0.590669i	$0.201136\pi$
$43$	6.00000	+	10.3923i	0.914991	+	1.58481i	0.108078	+	0.994142i	$0.465531\pi$
$44$		0			0
$45$		0			0
$46$	2.00000			0.294884
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	−3.50000	+	6.06218i	−0.490098	+	0.848875i
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$	2.50000	+	4.33013i	0.340207	+	0.589256i
$55$		0			0
$56$	−2.00000			−0.267261
$57$	0.500000	−	4.33013i	0.0662266	−	0.573539i
$58$	10.0000			1.31306
$59$	0.500000	+	0.866025i	0.0650945	+	0.112747i	0.896736	−	0.442566i	$-0.145932\pi$
$59$	0.500000	+	0.866025i	0.0650945	+	0.112747i	−0.831641	+	0.555313i	$0.812598\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$	−2.00000	+	3.46410i	−0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	7.00000			0.848875
$69$	2.00000			0.240772
$70$		0			0
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−4.00000	+	1.73205i	−0.458831	+	0.198680i
$77$		0			0
$78$	−3.00000	−	5.19615i	−0.339683	−	0.588348i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	−13.0000			−1.42694			−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000			−1.42694			−0.713468	+	0.700688i	$0.752876\pi$
$84$	−2.00000			−0.218218
$85$		0			0
$86$	6.00000	−	10.3923i	0.646997	−	1.12063i
$87$	10.0000			1.07211
$88$		0			0
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	−0.283164	−	0.959072i	$-0.591384\pi$
$89$	6.50000	−	11.2583i	0.688999	−	1.19338i	0.972162	−	0.234309i	$-0.0752827\pi$
$90$		0			0
$91$	6.00000	−	10.3923i	0.628971	−	1.08941i
$92$	−1.00000	−	1.73205i	−0.104257	−	0.180579i
$93$	1.00000	+	1.73205i	0.103695	+	0.179605i
$94$		0			0
$95$		0			0
$96$	1.00000			0.102062
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	−0.942072	−	0.335410i	$-0.891125\pi$
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	0.180563	−	0.983563i	$-0.442208\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$		0			0
$100$		0			0
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$	7.00000			0.693103
$103$	12.0000			1.18240			0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000			1.18240			0.591198	+	0.806527i	$0.298655\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$		0			0
$106$		0			0
$107$	15.0000			1.45010			0.725052	−	0.688694i	$-0.241816\pi$
$107$	15.0000			1.45010			0.725052	+	0.688694i	$0.241816\pi$
$108$	2.50000	−	4.33013i	0.240563	−	0.416667i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	−2.00000	−	3.46410i	−0.189832	−	0.328798i
$112$	1.00000	+	1.73205i	0.0944911	+	0.163663i
$113$	1.00000			0.0940721			0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000			0.0940721			0.0470360	+	0.998893i	$0.485022\pi$
$114$	−4.00000	+	1.73205i	−0.374634	+	0.162221i
$115$		0			0
$116$	−5.00000	−	8.66025i	−0.464238	−	0.804084i
$117$	6.00000	+	10.3923i	0.554700	+	0.960769i
$118$	0.500000	−	0.866025i	0.0460287	−	0.0797241i
$119$	7.00000	+	12.1244i	0.641689	+	1.11144i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	8.00000			0.724286
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	4.00000			0.356348
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.00000	−	10.3923i	0.528271	−	0.914991i
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$		0			0
$133$	−7.00000	−	5.19615i	−0.606977	−	0.450564i
$134$	8.00000			0.691095
$135$		0			0
$136$	−3.50000	−	6.06218i	−0.300123	−	0.519827i
$137$	−7.50000	+	12.9904i	−0.640768	+	1.10984i	0.344493	+	0.938789i	$0.388051\pi$
$137$	−7.50000	+	12.9904i	−0.640768	+	1.10984i	−0.985262	+	0.171054i	$0.945283\pi$
$138$	−1.00000	−	1.73205i	−0.0851257	−	0.147442i
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$		0			0
$144$	−2.00000			−0.166667
$145$		0			0
$146$	1.50000	−	2.59808i	0.124141	−	0.215018i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	−0.981797	−	0.189933i	$-0.939173\pi$
$149$	−8.00000	−	13.8564i	−0.655386	−	1.13516i	0.326411	−	0.945228i	$-0.394160\pi$
$150$		0			0
$151$	−12.0000			−0.976546			−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000			−0.976546			−0.488273	+	0.872691i	$0.662373\pi$
$152$	3.50000	+	2.59808i	0.283887	+	0.210732i
$153$	−14.0000			−1.13183
$154$		0			0
$155$		0			0
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	−3.00000	−	5.19615i	−0.239426	−	0.414698i	0.721124	−	0.692806i	$-0.243626\pi$
$157$	−3.00000	−	5.19615i	−0.239426	−	0.414698i	−0.960550	+	0.278108i	$0.910293\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$		0			0
$160$		0			0
$161$	2.00000	−	3.46410i	0.157622	−	0.273009i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−12.0000			−0.939913			−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000			−0.939913			−0.469956	+	0.882690i	$0.655730\pi$
$164$	2.00000			0.156174
$165$		0			0
$166$	6.50000	+	11.2583i	0.504498	+	0.873816i
$167$	−5.00000	+	8.66025i	−0.386912	+	0.670151i	−0.992032	−	0.125983i	$-0.959791\pi$
$167$	−5.00000	+	8.66025i	−0.386912	+	0.670151i	0.605121	+	0.796134i	$0.293125\pi$
$168$	1.00000	+	1.73205i	0.0771517	+	0.133631i
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$		0			0
$171$	8.00000	−	3.46410i	0.611775	−	0.264906i
$172$	−12.0000			−0.914991
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−5.00000	−	8.66025i	−0.379049	−	0.656532i
$175$		0			0
$176$		0			0
$177$	0.500000	−	0.866025i	0.0375823	−	0.0650945i
$178$	−13.0000			−0.974391
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$		0			0
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	0.207693	+	0.978194i	$0.433404\pi$
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	−0.950988	+	0.309229i	$0.899929\pi$
$182$	−12.0000			−0.889499
$183$	8.00000			0.591377
$184$	−1.00000	+	1.73205i	−0.0737210	+	0.127688i
$185$		0			0
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$		0			0
$188$		0			0
$189$	10.0000			0.727393
$190$		0			0
$191$	−10.0000			−0.723575			−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000			−0.723575			−0.361787	+	0.932261i	$0.617833\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	−7.50000	+	12.9904i	−0.538469	+	0.932655i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$	4.00000			0.284988			0.142494	−	0.989796i	$-0.454488\pi$
$197$	4.00000			0.284988			0.142494	+	0.989796i	$0.454488\pi$
$198$		0			0
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		0			0
$201$	8.00000			0.564276
$202$	2.00000			0.140720
$203$	10.0000	−	17.3205i	0.701862	−	1.21566i
$204$	−3.50000	−	6.06218i	−0.245049	−	0.424437i
$205$		0			0
$206$	−6.00000	−	10.3923i	−0.418040	−	0.724066i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	6.00000			0.416025
$209$		0			0
$210$		0			0
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$		0			0
$213$	6.00000	−	10.3923i	0.411113	−	0.712069i
$214$	−7.50000	−	12.9904i	−0.512689	−	0.888004i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	4.00000			0.271538
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	1.50000	−	2.59808i	0.101361	−	0.175562i
$220$		0			0
$221$	42.0000			2.82523
$222$	−2.00000	+	3.46410i	−0.134231	+	0.232495i
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$		0			0
$226$	−0.500000	−	0.866025i	−0.0332595	−	0.0576072i
$227$	13.0000			0.862840			0.431420	−	0.902151i	$-0.358013\pi$
$227$	13.0000			0.862840			0.431420	+	0.902151i	$0.358013\pi$
$228$	3.50000	+	2.59808i	0.231793	+	0.172062i
$229$	−18.0000			−1.18947			−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000			−1.18947			−0.594737	+	0.803921i	$0.702744\pi$
$230$		0			0
$231$		0			0
$232$	−5.00000	+	8.66025i	−0.328266	+	0.568574i
$233$	−6.50000	−	11.2583i	−0.425829	−	0.737558i	0.570668	−	0.821181i	$-0.306684\pi$
$233$	−6.50000	−	11.2583i	−0.425829	−	0.737558i	−0.996497	+	0.0836229i	$0.973351\pi$
$234$	6.00000	−	10.3923i	0.392232	−	0.679366i
$235$		0			0
$236$	−1.00000			−0.0650945
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	7.00000	−	12.1244i	0.453743	−	0.785905i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	5.50000	+	9.52628i	0.353553	+	0.612372i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$		0			0
$246$	2.00000			0.127515
$247$	−24.0000	+	10.3923i	−1.52708	+	0.661247i
$248$	−2.00000			−0.127000
$249$	6.50000	+	11.2583i	0.411921	+	0.713468i
$250$		0			0
$251$	10.0000	−	17.3205i	0.631194	−	1.09326i	−0.356113	−	0.934443i	$-0.615898\pi$
$251$	10.0000	−	17.3205i	0.631194	−	1.09326i	0.987308	−	0.158818i	$-0.0507683\pi$
$252$	−2.00000	−	3.46410i	−0.125988	−	0.218218i
$253$		0			0
$254$	12.0000			0.752947
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$	−12.0000			−0.747087
$259$	−8.00000			−0.497096
$260$		0			0
$261$	10.0000	+	17.3205i	0.618984	+	1.07211i
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	0.565376	−	0.824833i	$-0.308731\pi$
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	−0.997015	+	0.0772134i	$0.975398\pi$
$264$		0			0
$265$		0			0
$266$	−1.00000	+	8.66025i	−0.0613139	+	0.530994i
$267$	−13.0000			−0.795587
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	−0.924337	−	0.381577i	$-0.875381\pi$
$269$	−13.0000	−	22.5167i	−0.792624	−	1.37287i	0.131713	−	0.991288i	$-0.457952\pi$
$270$		0			0
$271$	−13.0000	−	22.5167i	−0.789694	−	1.36779i	−0.926155	−	0.377144i	$-0.876906\pi$
$271$	−13.0000	−	22.5167i	−0.789694	−	1.36779i	0.136461	−	0.990645i	$-0.456427\pi$
$272$	−3.50000	+	6.06218i	−0.212219	+	0.367574i
$273$	−12.0000			−0.726273
$274$	15.0000			0.906183
$275$		0			0
$276$	−1.00000	+	1.73205i	−0.0601929	+	0.104257i
$277$	−22.0000			−1.32185			−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000			−1.32185			−0.660926	+	0.750451i	$0.729836\pi$
$278$		0			0
$279$	−2.00000	+	3.46410i	−0.119737	+	0.207390i
$280$		0			0
$281$	−3.50000	+	6.06218i	−0.208792	+	0.361639i	−0.951334	−	0.308160i	$-0.900287\pi$
$281$	−3.50000	+	6.06218i	−0.208792	+	0.361639i	0.742542	+	0.669800i	$0.233620\pi$
$282$		0			0
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$	−12.0000			−0.712069
$285$		0			0
$286$		0			0
$287$	2.00000	+	3.46410i	0.118056	+	0.204479i
$288$	1.00000	+	1.73205i	0.0589256	+	0.102062i
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	−7.50000	+	12.9904i	−0.439658	+	0.761510i
$292$	−3.00000			−0.175562
$293$	32.0000			1.86946			0.934730	−	0.355359i	$-0.115641\pi$
$293$	32.0000			1.86946			0.934730	+	0.355359i	$0.115641\pi$
$294$	1.50000	−	2.59808i	0.0874818	−	0.151523i
$295$		0			0
$296$	4.00000			0.232495
$297$		0			0
$298$	−8.00000	+	13.8564i	−0.463428	+	0.802680i
$299$	−6.00000	−	10.3923i	−0.346989	−	0.601003i
$300$		0			0
$301$	−12.0000	−	20.7846i	−0.691669	−	1.19800i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$	2.00000			0.114897
$304$	0.500000	−	4.33013i	0.0286770	−	0.248350i
$305$		0			0
$306$	7.00000	+	12.1244i	0.400163	+	0.693103i
$307$	9.50000	+	16.4545i	0.542194	+	0.939107i	0.998778	+	0.0494267i	$0.0157394\pi$
$307$	9.50000	+	16.4545i	0.542194	+	0.939107i	−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$	−6.00000	−	10.3923i	−0.341328	−	0.591198i
$310$		0			0
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$	6.00000			0.339683
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	−0.978553	−	0.205996i	$-0.933957\pi$
$313$	−5.50000	+	9.52628i	−0.310878	+	0.538457i	0.667674	+	0.744453i	$0.267290\pi$
$314$	−3.00000	+	5.19615i	−0.169300	+	0.293236i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−7.50000	−	12.9904i	−0.418609	−	0.725052i
$322$	−4.00000			−0.222911
$323$	3.50000	−	30.3109i	0.194745	−	1.68654i
$324$	1.00000			0.0555556
$325$		0			0
$326$	6.00000	+	10.3923i	0.332309	+	0.575577i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$		0			0
$330$		0			0
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	6.50000	−	11.2583i	0.356734	−	0.617881i
$333$	4.00000	−	6.92820i	0.219199	−	0.379663i
$334$	10.0000			0.547176
$335$		0			0
$336$	1.00000	−	1.73205i	0.0545545	−	0.0944911i
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−11.5000	+	19.9186i	−0.625518	+	1.08343i
$339$	−0.500000	−	0.866025i	−0.0271563	−	0.0470360i
$340$		0			0
$341$		0			0
$342$	−7.00000	−	5.19615i	−0.378517	−	0.280976i
$343$	20.0000			1.07990
$344$	6.00000	+	10.3923i	0.323498	+	0.560316i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	−5.00000	+	8.66025i	−0.268028	+	0.464238i
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$		0			0
$351$	15.0000	−	25.9808i	0.800641	−	1.38675i
$352$		0			0
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$	−1.00000			−0.0531494
$355$		0			0
$356$	6.50000	+	11.2583i	0.344499	+	0.596690i
$357$	7.00000	−	12.1244i	0.370479	−	0.641689i
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	20.0000			1.05118
$363$	5.50000	+	9.52628i	0.288675	+	0.500000i
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$		0			0
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	2.00000			0.104257
$369$	−4.00000			−0.208232
$370$		0			0
$371$		0			0
$372$	−2.00000			−0.103695
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−30.0000	−	51.9615i	−1.54508	−	2.67615i
$378$	−5.00000	−	8.66025i	−0.257172	−	0.445435i
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$	5.00000	+	8.66025i	0.255822	+	0.443097i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	−5.50000	+	9.52628i	−0.279943	+	0.484875i
$387$	24.0000			1.21999
$388$	15.0000			0.761510
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	14.0000			0.708010
$392$	−3.00000			−0.151523
$393$	−0.500000	+	0.866025i	−0.0252217	+	0.0436852i
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$		0			0
$396$		0			0
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	0.635161	−	0.772380i	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	−16.0000			−0.802008
$399$	−1.00000	+	8.66025i	−0.0500626	+	0.433555i
$400$		0			0
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	−4.00000	−	6.92820i	−0.199502	−	0.345547i
$403$	6.00000	−	10.3923i	0.298881	−	0.517678i
$404$	−1.00000	−	1.73205i	−0.0497519	−	0.0861727i
$405$		0			0
$406$	−20.0000			−0.992583
$407$		0			0
$408$	−3.50000	+	6.06218i	−0.173276	+	0.300123i
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$		0			0
$411$	15.0000			0.739895
$412$	−6.00000	+	10.3923i	−0.295599	+	0.511992i
$413$	−1.00000	−	1.73205i	−0.0492068	−	0.0852286i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$		0			0
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$		0			0
$418$		0			0
$419$	13.0000			0.635092			0.317546	−	0.948243i	$-0.397141\pi$
$419$	13.0000			0.635092			0.317546	+	0.948243i	$0.397141\pi$
$420$		0			0
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	−11.5000	+	19.9186i	−0.559811	+	0.969622i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	8.00000	−	13.8564i	0.387147	−	0.670559i
$428$	−7.50000	+	12.9904i	−0.362526	+	0.627914i
$429$		0			0
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	−0.495388	−	0.868672i	$-0.664974\pi$
$433$	10.5000	−	18.1865i	0.504598	−	0.873989i	0.999986	−	0.00531724i	$-0.00169254\pi$
$434$	−2.00000	−	3.46410i	−0.0960031	−	0.166282i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	−8.00000	+	3.46410i	−0.382692	+	0.165710i
$438$	−3.00000			−0.143346
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$442$	−21.0000	−	36.3731i	−0.998868	−	1.73009i
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	4.00000			0.189832
$445$		0			0
$446$	1.00000	−	1.73205i	0.0473514	−	0.0820150i
$447$	−8.00000	+	13.8564i	−0.378387	+	0.655386i
$448$	−2.00000			−0.0944911
$449$	41.0000			1.93491			0.967455	−	0.253044i	$-0.0814317\pi$
$449$	41.0000			1.93491			0.967455	+	0.253044i	$0.0814317\pi$
$450$		0			0
$451$		0			0
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$	6.00000	+	10.3923i	0.281905	+	0.488273i
$454$	−6.50000	−	11.2583i	−0.305060	−	0.528380i
$455$		0			0
$456$	0.500000	−	4.33013i	0.0234146	−	0.202777i
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	9.00000	+	15.5885i	0.420542	+	0.728401i
$459$	17.5000	+	30.3109i	0.816830	+	1.41479i
$460$		0			0
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	0.841798	−	0.539792i	$-0.181497\pi$
$461$	−1.00000	−	1.73205i	−0.0465746	−	0.0806696i	−0.888373	+	0.459123i	$0.848164\pi$
$462$		0			0
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$	10.0000			0.464238
$465$		0			0
$466$	−6.50000	+	11.2583i	−0.301107	+	0.521532i
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$	−12.0000			−0.554700
$469$	8.00000	−	13.8564i	0.369406	−	0.639829i
$470$		0			0
$471$	−3.00000	+	5.19615i	−0.138233	+	0.239426i
$472$	0.500000	+	0.866025i	0.0230144	+	0.0398621i
$473$		0			0
$474$	−4.00000			−0.183726
$475$		0			0
$476$	−14.0000			−0.641689
$477$		0			0
$478$	3.00000	+	5.19615i	0.137217	+	0.237666i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$	14.0000			0.637683
$483$	−4.00000			−0.182006
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$		0			0
$486$	16.0000			0.725775
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	6.00000	+	10.3923i	0.271329	+	0.469956i
$490$		0			0
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	0.761539	−	0.648119i	$-0.224444\pi$
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	−0.942057	+	0.335453i	$0.891111\pi$
$492$	−1.00000	−	1.73205i	−0.0450835	−	0.0780869i
$493$	70.0000			3.15264
$494$	21.0000	+	15.5885i	0.944835	+	0.701358i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$	6.50000	−	11.2583i	0.291272	−	0.504498i
$499$	16.5000	+	28.5788i	0.738641	+	1.27936i	0.953107	+	0.302633i	$0.0978656\pi$
$499$	16.5000	+	28.5788i	0.738641	+	1.27936i	−0.214466	+	0.976732i	$0.568801\pi$
$500$		0			0
$501$	10.0000			0.446767
$502$	−20.0000			−0.892644
$503$	−4.00000	+	6.92820i	−0.178351	+	0.308913i	−0.941316	−	0.337527i	$-0.890410\pi$
$503$	−4.00000	+	6.92820i	−0.178351	+	0.308913i	0.762965	+	0.646440i	$0.223743\pi$
$504$	−2.00000	+	3.46410i	−0.0890871	+	0.154303i
$505$		0			0
$506$		0			0
$507$	−11.5000	+	19.9186i	−0.510733	+	0.884615i
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−3.00000	−	5.19615i	−0.132712	−	0.229864i
$512$	1.00000			0.0441942
$513$	−17.5000	−	12.9904i	−0.772644	−	0.573539i
$514$	−15.0000			−0.661622
$515$		0			0
$516$	6.00000	+	10.3923i	0.264135	+	0.457496i
$517$		0			0
$518$	4.00000	+	6.92820i	0.175750	+	0.304408i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	10.0000	−	17.3205i	0.437688	−	0.758098i
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	−0.352677	−	0.935745i	$-0.614728\pi$
$523$	14.5000	−	25.1147i	0.634041	−	1.09819i	0.986718	−	0.162446i	$-0.0519382\pi$
$524$	1.00000			0.0436852
$525$		0			0
$526$	−7.00000	+	12.1244i	−0.305215	+	0.528647i
$527$	7.00000	+	12.1244i	0.304925	+	0.528145i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	2.00000			0.0867926
$532$	8.00000	−	3.46410i	0.346844	−	0.150188i
$533$	12.0000			0.519778
$534$	6.50000	+	11.2583i	0.281283	+	0.487196i
$535$		0			0
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	4.50000	+	7.79423i	0.194189	+	0.336346i
$538$	−13.0000	+	22.5167i	−0.560470	+	0.970762i
$539$		0			0
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−13.0000	+	22.5167i	−0.558398	+	0.967173i
$543$	20.0000			0.858282
$544$	7.00000			0.300123
$545$		0			0
$546$	6.00000	+	10.3923i	0.256776	+	0.444750i
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	−0.855138	−	0.518400i	$-0.826528\pi$
$547$	0.500000	−	0.866025i	0.0213785	−	0.0370286i	0.876517	+	0.481371i	$0.159861\pi$
$548$	−7.50000	−	12.9904i	−0.320384	−	0.554922i
$549$	8.00000	+	13.8564i	0.341432	+	0.591377i
$550$		0			0
$551$	−40.0000	+	17.3205i	−1.70406	+	0.737878i
$552$	2.00000			0.0851257
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$	11.0000	+	19.0526i	0.467345	+	0.809466i
$555$		0			0
$556$		0			0
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	−0.844062	−	0.536246i	$-0.819842\pi$
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	0.886433	+	0.462856i	$0.153175\pi$
$558$	4.00000			0.169334
$559$	−72.0000			−3.04528
$560$		0			0
$561$		0			0
$562$	7.00000			0.295277
$563$	−43.0000			−1.81223			−0.906117	−	0.423027i	$-0.860967\pi$
$563$	−43.0000			−1.81223			−0.906117	+	0.423027i	$0.860967\pi$
$564$		0			0
$565$		0			0
$566$	14.0000	−	24.2487i	0.588464	−	1.01925i
$567$	1.00000	+	1.73205i	0.0419961	+	0.0727393i
$568$	6.00000	+	10.3923i	0.251754	+	0.436051i
$569$	1.00000			0.0419222			0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000			0.0419222			0.0209611	+	0.999780i	$0.493327\pi$
$570$		0			0
$571$	1.00000			0.0418487			0.0209243	−	0.999781i	$-0.493339\pi$
$571$	1.00000			0.0418487			0.0209243	+	0.999781i	$0.493339\pi$
$572$		0			0
$573$	5.00000	+	8.66025i	0.208878	+	0.361787i
$574$	2.00000	−	3.46410i	0.0834784	−	0.144589i
$575$		0			0
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	32.0000			1.33102
$579$	−5.50000	+	9.52628i	−0.228572	+	0.395899i
$580$		0			0
$581$	26.0000			1.07866
$582$	15.0000			0.621770
$583$		0			0
$584$	1.50000	+	2.59808i	0.0620704	+	0.107509i
$585$		0			0
$586$	−16.0000	−	27.7128i	−0.660954	−	1.14481i
$587$	−22.5000	−	38.9711i	−0.928674	−	1.60851i	−0.785543	−	0.618808i	$-0.787616\pi$
$587$	−22.5000	−	38.9711i	−0.928674	−	1.60851i	−0.143132	−	0.989704i	$-0.545717\pi$
$588$	−3.00000			−0.123718
$589$	−7.00000	−	5.19615i	−0.288430	−	0.214104i
$590$		0			0
$591$	−2.00000	−	3.46410i	−0.0822690	−	0.142494i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	7.00000	−	12.1244i	0.287456	−	0.497888i	−0.685746	−	0.727841i	$-0.740524\pi$
$593$	7.00000	−	12.1244i	0.287456	−	0.497888i	0.973202	+	0.229953i	$0.0738573\pi$
$594$		0			0
$595$		0			0
$596$	16.0000			0.655386
$597$	−16.0000			−0.654836
$598$	−6.00000	+	10.3923i	−0.245358	+	0.424973i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−12.0000	+	20.7846i	−0.489083	+	0.847117i
$603$	8.00000	+	13.8564i	0.325785	+	0.564276i
$604$	6.00000	−	10.3923i	0.244137	−	0.422857i
$605$		0			0
$606$	−1.00000	−	1.73205i	−0.0406222	−	0.0703598i
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	−4.00000	+	1.73205i	−0.162221	+	0.0702439i
$609$	−20.0000			−0.810441
$610$		0			0
$611$		0			0
$612$	7.00000	−	12.1244i	0.282958	−	0.490098i
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	0.972056	−	0.234751i	$-0.0754275\pi$
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	−0.689328	+	0.724449i	$0.742094\pi$
$614$	9.50000	−	16.4545i	0.383389	−	0.664049i
$615$		0			0
$616$		0			0
$617$	3.50000	−	6.06218i	0.140905	−	0.244054i	−0.786933	−	0.617039i	$-0.788332\pi$
$617$	3.50000	−	6.06218i	0.140905	−	0.244054i	0.927838	+	0.372985i	$0.121666\pi$
$618$	−6.00000	+	10.3923i	−0.241355	+	0.418040i
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$	5.00000	−	8.66025i	0.200643	−	0.347524i
$622$	−15.0000	−	25.9808i	−0.601445	−	1.04173i
$623$	−13.0000	+	22.5167i	−0.520834	+	0.902111i
$624$	−3.00000	−	5.19615i	−0.120096	−	0.208013i
$625$		0			0
$626$	11.0000			0.439648
$627$		0			0
$628$	6.00000			0.239426
$629$	−14.0000	−	24.2487i	−0.558217	−	0.966859i
$630$		0			0
$631$	−24.0000	+	41.5692i	−0.955425	+	1.65484i	−0.222032	+	0.975039i	$0.571269\pi$
$631$	−24.0000	+	41.5692i	−0.955425	+	1.65484i	−0.733393	+	0.679805i	$0.762064\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−11.5000	+	19.9186i	−0.457084	+	0.791693i
$634$	−24.0000			−0.953162
$635$		0			0
$636$		0			0
$637$	9.00000	−	15.5885i	0.356593	−	0.617637i
$638$		0			0
$639$	24.0000			0.949425
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$	−7.50000	+	12.9904i	−0.296001	+	0.512689i
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$		0			0
$646$	−28.0000	+	12.1244i	−1.10165	+	0.477026i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$		0			0
$650$		0			0
$651$	−2.00000	−	3.46410i	−0.0783862	−	0.135769i
$652$	6.00000	−	10.3923i	0.234978	−	0.406994i
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	−2.00000			−0.0782062
$655$		0			0
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	6.00000			0.234082
$658$		0			0
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	−0.893762	−	0.448542i	$-0.851943\pi$
$659$	−1.50000	+	2.59808i	−0.0584317	+	0.101207i	0.835330	+	0.549749i	$0.185277\pi$
$660$		0			0
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	−0.824506	−	0.565854i	$-0.808547\pi$
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	0.902297	+	0.431116i	$0.141880\pi$
$662$	8.50000	+	14.7224i	0.330362	+	0.572204i
$663$	−21.0000	−	36.3731i	−0.815572	−	1.41261i
$664$	−13.0000			−0.504498
$665$		0			0
$666$	−8.00000			−0.309994
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	−5.00000	−	8.66025i	−0.193456	−	0.335075i
$669$	1.00000	−	1.73205i	0.0386622	−	0.0669650i
$670$		0			0
$671$		0			0
$672$	−2.00000			−0.0771517
$673$	−26.0000			−1.00223			−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000			−1.00223			−0.501113	+	0.865382i	$0.667076\pi$
$674$	11.0000	−	19.0526i	0.423704	−	0.733877i
$675$		0			0
$676$	23.0000			0.884615
$677$	26.0000			0.999261			0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000			0.999261			0.499631	+	0.866239i	$0.333469\pi$
$678$	−0.500000	+	0.866025i	−0.0192024	+	0.0332595i
$679$	15.0000	+	25.9808i	0.575647	+	0.997050i
$680$		0			0
$681$	−6.50000	−	11.2583i	−0.249081	−	0.431420i
$682$		0			0
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$	−1.00000	+	8.66025i	−0.0382360	+	0.331133i
$685$		0			0
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	9.00000	+	15.5885i	0.343371	+	0.594737i
$688$	6.00000	−	10.3923i	0.228748	−	0.396203i
$689$		0			0
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$		0			0
$696$	10.0000			0.379049
$697$	−7.00000	+	12.1244i	−0.265144	+	0.459243i
$698$	−8.00000	−	13.8564i	−0.302804	−	0.524473i
$699$	−6.50000	+	11.2583i	−0.245853	+	0.425829i
$700$		0			0
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	0.998585	−	0.0531839i	$-0.0169370\pi$
$701$	12.0000	+	20.7846i	0.453234	+	0.785024i	−0.545351	+	0.838208i	$0.683604\pi$
$702$	−30.0000			−1.13228
$703$	14.0000	+	10.3923i	0.528020	+	0.391953i
$704$		0			0
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$	2.00000	−	3.46410i	0.0752177	−	0.130281i
$708$	0.500000	+	0.866025i	0.0187912	+	0.0325472i
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	−0.473768	−	0.880650i	$-0.657106\pi$
$709$	14.0000	−	24.2487i	0.525781	−	0.910679i	0.999549	−	0.0300298i	$-0.00956021\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	6.50000	−	11.2583i	0.243598	−	0.421924i
$713$	2.00000	−	3.46410i	0.0749006	−	0.129732i
$714$	−14.0000			−0.523937
$715$		0			0
$716$	4.50000	−	7.79423i	0.168173	−	0.291284i
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	12.0000	−	20.7846i	0.447836	−	0.775675i
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	−0.993305	−	0.115524i	$-0.963145\pi$
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	0.396605	−	0.917989i	$-0.370188\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	13.0000	−	13.8564i	0.483810	−	0.515682i
$723$	14.0000			0.520666
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$		0			0
$726$	5.50000	−	9.52628i	0.204124	−	0.353553i
$727$	7.00000	+	12.1244i	0.259616	+	0.449667i	0.966139	−	0.258022i	$-0.0830708\pi$
$727$	7.00000	+	12.1244i	0.259616	+	0.449667i	−0.706523	+	0.707690i	$0.749737\pi$
$728$	6.00000	−	10.3923i	0.222375	−	0.385164i
$729$	13.0000			0.481481
$730$		0			0
$731$	42.0000	−	72.7461i	1.55343	−	2.69061i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	−6.00000			−0.221615			−0.110808	−	0.993842i	$-0.535344\pi$
$733$	−6.00000			−0.221615			−0.110808	+	0.993842i	$0.535344\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	−1.00000	−	1.73205i	−0.0368605	−	0.0638442i
$737$		0			0
$738$	2.00000	+	3.46410i	0.0736210	+	0.127515i
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$		0			0
$741$	21.0000	+	15.5885i	0.771454	+	0.572656i
$742$		0			0
$743$	−13.0000	−	22.5167i	−0.476924	−	0.826056i	0.522727	−	0.852500i	$-0.324915\pi$
$743$	−13.0000	−	22.5167i	−0.476924	−	0.826056i	−0.999650	+	0.0264443i	$0.991582\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$		0			0
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	−13.0000	+	22.5167i	−0.475645	+	0.823842i
$748$		0			0
$749$	−30.0000			−1.09618
$750$		0			0
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	−0.525193	−	0.850983i	$-0.676007\pi$
$751$	13.0000	−	22.5167i	0.474377	−	0.821645i	0.999570	+	0.0293387i	$0.00934013\pi$
$752$		0			0
$753$	−20.0000			−0.728841
$754$	−30.0000	+	51.9615i	−1.09254	+	1.89233i
$755$		0			0
$756$	−5.00000	+	8.66025i	−0.181848	+	0.314970i
$757$	−16.0000	−	27.7128i	−0.581530	−	1.00724i	−0.995298	−	0.0968571i	$-0.969121\pi$
$757$	−16.0000	−	27.7128i	−0.581530	−	1.00724i	0.413768	−	0.910382i	$-0.364212\pi$
$758$	0.500000	+	0.866025i	0.0181608	+	0.0314555i
$759$		0			0
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$	−6.00000	−	10.3923i	−0.217357	−	0.376473i
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	5.00000	−	8.66025i	0.180894	−	0.313317i
$765$		0			0
$766$	6.00000	−	10.3923i	0.216789	−	0.375489i
$767$	−6.00000			−0.216647
$768$	1.00000			0.0360844
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$		0			0
$771$	−15.0000			−0.540212
$772$	11.0000			0.395899
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$	−12.0000	−	20.7846i	−0.431331	−	0.747087i
$775$		0			0
$776$	−7.50000	−	12.9904i	−0.269234	−	0.466328i
$777$	4.00000	+	6.92820i	0.143499	+	0.248548i
$778$	18.0000			0.645331
$779$	1.00000	−	8.66025i	0.0358287	−	0.310286i
$780$		0			0
$781$		0			0
$782$	−7.00000	−	12.1244i	−0.250319	−	0.433566i
$783$	25.0000	−	43.3013i	0.893427	−	1.54746i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	1.00000			0.0356688
$787$	−29.0000			−1.03374			−0.516869	−	0.856064i	$-0.672903\pi$
$787$	−29.0000			−1.03374			−0.516869	+	0.856064i	$0.672903\pi$
$788$	−2.00000	+	3.46410i	−0.0712470	+	0.123404i
$789$	−7.00000	+	12.1244i	−0.249207	+	0.431638i
$790$		0			0
$791$	−2.00000			−0.0711118
$792$		0			0
$793$	−24.0000	−	41.5692i	−0.852265	−	1.47617i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−8.00000			−0.283375			−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000			−0.283375			−0.141687	+	0.989911i	$0.545253\pi$
$798$	8.00000	−	3.46410i	0.283197	−	0.122628i
$799$		0			0
$800$		0			0
$801$	−13.0000	−	22.5167i	−0.459332	−	0.795587i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$		0			0
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$	−12.0000			−0.422682
$807$	−13.0000	+	22.5167i	−0.457622	+	0.792624i
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	45.0000			1.58212			0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000			1.58212			0.791058	+	0.611741i	$0.209531\pi$
$810$		0			0
$811$	−22.0000	+	38.1051i	−0.772524	+	1.33805i	0.163651	+	0.986518i	$0.447673\pi$
$811$	−22.0000	+	38.1051i	−0.772524	+	1.33805i	−0.936175	+	0.351533i	$0.885660\pi$
$812$	10.0000	+	17.3205i	0.350931	+	0.607831i
$813$	−13.0000	+	22.5167i	−0.455930	+	0.789694i
$814$		0			0
$815$		0			0
$816$	7.00000			0.245049
$817$	−6.00000	+	51.9615i	−0.209913	+	1.81790i
$818$	2.00000			0.0699284
$819$	−12.0000	−	20.7846i	−0.419314	−	0.726273i
$820$		0			0
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$	−7.50000	−	12.9904i	−0.261593	−	0.453092i
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$	12.0000			0.418040
$825$		0			0
$826$	−1.00000	+	1.73205i	−0.0347945	+	0.0602658i
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	0.362441	+	0.932007i	$0.381944\pi$
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	−0.988362	+	0.152121i	$0.951390\pi$
$828$	−4.00000			−0.139010
$829$	−30.0000			−1.04194			−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000			−1.04194			−0.520972	+	0.853574i	$0.674430\pi$
$830$		0			0
$831$	11.0000	+	19.0526i	0.381586	+	0.660926i
$832$	−3.00000	+	5.19615i	−0.104006	+	0.180144i
$833$	10.5000	+	18.1865i	0.363803	+	0.630126i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	10.0000			0.345651
$838$	−6.50000	−	11.2583i	−0.224539	−	0.388913i
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$	7.00000			0.241093
$844$	23.0000			0.791693
$845$		0			0
$846$		0			0
$847$	22.0000			0.755929
$848$		0			0
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$		0			0
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$	6.00000	+	10.3923i	0.205557	+	0.356034i
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	0.946232	+	0.323489i	$0.104856\pi$
$853$	22.0000	+	38.1051i	0.753266	+	1.30469i	−0.192966	+	0.981205i	$0.561811\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$	15.0000			0.512689
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	−0.570064	−	0.821600i	$-0.693082\pi$
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	0.996559	+	0.0828900i	$0.0264150\pi$
$860$		0			0
$861$	2.00000	−	3.46410i	0.0681598	−	0.118056i
$862$	30.0000			1.02180
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	−21.0000			−0.713609
$867$	32.0000			1.08678
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$		0			0
$870$		0			0
$871$	−24.0000	−	41.5692i	−0.813209	−	1.40852i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−30.0000			−1.01535
$874$	7.00000	+	5.19615i	0.236779	+	0.175762i
$875$		0			0
$876$	1.50000	+	2.59808i	0.0506803	+	0.0877809i
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	−16.0000	−	27.7128i	−0.539667	−	0.934730i
$880$		0			0
$881$	−37.0000			−1.24656			−0.623281	−	0.781998i	$-0.714201\pi$
$881$	−37.0000			−1.24656			−0.623281	+	0.781998i	$0.714201\pi$
$882$	6.00000			0.202031
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	−0.954424	−	0.298455i	$-0.903529\pi$
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	0.735681	+	0.677328i	$0.236862\pi$
$884$	−21.0000	+	36.3731i	−0.706306	+	1.22336i
$885$		0			0
$886$	36.0000			1.20944
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	−0.529340	−	0.848410i	$-0.677561\pi$
$887$	14.0000	−	24.2487i	0.470074	−	0.814192i	0.999414	+	0.0342175i	$0.0108939\pi$
$888$	−2.00000	−	3.46410i	−0.0671156	−	0.116248i
$889$	12.0000	−	20.7846i	0.402467	−	0.697093i
$890$		0			0
$891$		0			0
$892$	−2.00000			−0.0669650
$893$		0			0
$894$	16.0000			0.535120
$895$		0			0
$896$	1.00000	+	1.73205i	0.0334077	+	0.0578638i
$897$	−6.00000	+	10.3923i	−0.200334	+	0.346989i
$898$	−20.5000	−	35.5070i	−0.684094	−	1.18489i
$899$	10.0000	−	17.3205i	0.333519	−	0.577671i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−12.0000	+	20.7846i	−0.399335	+	0.691669i
$904$	1.00000			0.0332595
$905$		0			0
$906$	6.00000	−	10.3923i	0.199337	−	0.345261i
$907$	26.5000	+	45.8993i	0.879918	+	1.52406i	0.851430	+	0.524469i	$0.175736\pi$
$907$	26.5000	+	45.8993i	0.879918	+	1.52406i	0.0284883	+	0.999594i	$0.490931\pi$
$908$	−6.50000	+	11.2583i	−0.215710	+	0.373621i
$909$	2.00000	+	3.46410i	0.0663358	+	0.114897i
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$	−4.00000	+	1.73205i	−0.132453	+	0.0573539i
$913$		0			0
$914$	−5.50000	−	9.52628i	−0.181924	−	0.315101i
$915$		0			0
$916$	9.00000	−	15.5885i	0.297368	−	0.515057i
$917$	1.00000	+	1.73205i	0.0330229	+	0.0571974i
$918$	17.5000	−	30.3109i	0.577586	−	1.00041i
$919$	56.0000			1.84727			0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000			1.84727			0.923635	+	0.383274i	$0.125203\pi$
$920$		0			0
$921$	9.50000	−	16.4545i	0.313036	−	0.542194i
$922$	−1.00000	+	1.73205i	−0.0329332	+	0.0570421i
$923$	−72.0000			−2.36991
$924$		0			0
$925$		0			0
$926$	11.0000	+	19.0526i	0.361482	+	0.626106i
$927$	12.0000	−	20.7846i	0.394132	−	0.682656i
$928$	−5.00000	−	8.66025i	−0.164133	−	0.284287i
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	0.889583	−	0.456774i	$-0.150995\pi$
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	−0.840369	+	0.542014i	$0.817662\pi$
$930$		0			0
$931$	−10.5000	−	7.79423i	−0.344124	−	0.255446i
$932$	13.0000			0.425829
$933$	−15.0000	−	25.9808i	−0.491078	−	0.850572i
$934$	−11.5000	−	19.9186i	−0.376291	−	0.651756i
$935$		0			0
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$	−0.500000	+	0.866025i	−0.0163343	+	0.0282918i	−0.874077	−	0.485787i	$-0.838533\pi$
$937$	−0.500000	+	0.866025i	−0.0163343	+	0.0282918i	0.857743	+	0.514079i	$0.171866\pi$
$938$	−16.0000			−0.522419
$939$	11.0000			0.358971
$940$		0			0
$941$	−22.0000	+	38.1051i	−0.717180	+	1.24219i	0.244933	+	0.969540i	$0.421234\pi$
$941$	−22.0000	+	38.1051i	−0.717180	+	1.24219i	−0.962113	+	0.272651i	$0.912099\pi$
$942$	6.00000			0.195491
$943$	4.00000			0.130258
$944$	0.500000	−	0.866025i	0.0162736	−	0.0281867i
$945$		0			0
$946$		0			0
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	−0.885720	−	0.464220i	$-0.846335\pi$
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	0.0408333	−	0.999166i	$-0.486999\pi$
$948$	2.00000	+	3.46410i	0.0649570	+	0.112509i
$949$	−18.0000			−0.584305
$950$		0			0
$951$	−24.0000			−0.778253
$952$	7.00000	+	12.1244i	0.226871	+	0.392953i
$953$	1.00000	+	1.73205i	0.0323932	+	0.0561066i	0.881768	−	0.471684i	$-0.156354\pi$
$953$	1.00000	+	1.73205i	0.0323932	+	0.0561066i	−0.849374	+	0.527791i	$0.823020\pi$
$954$		0			0
$955$		0			0
$956$	3.00000	−	5.19615i	0.0970269	−	0.168056i
$957$		0			0
$958$	24.0000			0.775405
$959$	15.0000	−	25.9808i	0.484375	−	0.838963i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	24.0000			0.773791
$963$	15.0000	−	25.9808i	0.483368	−	0.837218i
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$		0			0
$966$	2.00000	+	3.46410i	0.0643489	+	0.111456i
$967$	−6.00000	−	10.3923i	−0.192947	−	0.334194i	0.753279	−	0.657702i	$-0.228471\pi$
$967$	−6.00000	−	10.3923i	−0.192947	−	0.334194i	−0.946226	+	0.323508i	$0.895138\pi$
$968$	−11.0000			−0.353553
$969$	−28.0000	+	12.1244i	−0.899490	+	0.389490i
$970$		0			0
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	0.960173	+	0.279406i	$0.0901376\pi$
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	−0.238114	+	0.971237i	$0.576529\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$		0			0
$974$	−10.0000	−	17.3205i	−0.320421	−	0.554985i
$975$		0			0
$976$	8.00000			0.256074
$977$	−42.0000			−1.34370			−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000			−1.34370			−0.671850	+	0.740688i	$0.734500\pi$
$978$	6.00000	−	10.3923i	0.191859	−	0.332309i
$979$		0			0
$980$		0			0
$981$	4.00000			0.127710
$982$	−4.00000	+	6.92820i	−0.127645	+	0.221088i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$		0			0
$986$	−35.0000	−	60.6218i	−1.11463	−	1.93059i
$987$		0			0
$988$	3.00000	−	25.9808i	0.0954427	−	0.826558i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	8.50000	+	14.7224i	0.269739	+	0.467202i
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$		0			0
$996$	−13.0000			−0.411921
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	−0.985961	−	0.166978i	$-0.946599\pi$
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	0.637587	+	0.770378i	$0.279933\pi$
$998$	16.5000	−	28.5788i	0.522298	−	0.904647i
$999$	−20.0000			−0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.b.501.1	yes	2
5.2	odd	4		950.2.j.b.349.2		4
5.3	odd	4		950.2.j.b.349.1		4
5.4	even	2		950.2.e.g.501.1	yes	2
19.11	even	3	inner	950.2.e.b.201.1	✓	2
95.49	even	6		950.2.e.g.201.1	yes	2
95.68	odd	12		950.2.j.b.49.2		4
95.87	odd	12		950.2.j.b.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.e.b.201.1	✓	2	19.11	even	3	inner
950.2.e.b.501.1	yes	2	1.1	even	1	trivial
950.2.e.g.201.1	yes	2	95.49	even	6
950.2.e.g.501.1	yes	2	5.4	even	2
950.2.j.b.49.1		4	95.87	odd	12
950.2.j.b.49.2		4	95.68	odd	12
950.2.j.b.349.1		4	5.3	odd	4
950.2.j.b.349.2		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +1.00000 q^{12} +(-3.00000 + 5.19615i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} -2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} +(1.00000 + 1.73205i) q^{21} +(-1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +6.00000 q^{26} -5.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-5.00000 + 8.66025i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.50000 + 6.06218i) q^{34} +(1.00000 + 1.73205i) q^{36} +4.00000 q^{37} +(0.500000 - 4.33013i) q^{38} +6.00000 q^{39} +(-1.00000 - 1.73205i) q^{41} +(1.00000 - 1.73205i) q^{42} +(6.00000 + 10.3923i) q^{43} +2.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -3.00000 q^{49} +(-3.50000 + 6.06218i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.50000 + 4.33013i) q^{54} -2.00000 q^{56} +(0.500000 - 4.33013i) q^{57} +10.0000 q^{58} +(0.500000 + 0.866025i) q^{59} +(-4.00000 + 6.92820i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(-4.00000 + 6.92820i) q^{67} +7.00000 q^{68} +2.00000 q^{69} +(6.00000 + 10.3923i) q^{71} +(1.00000 - 1.73205i) q^{72} +(1.50000 + 2.59808i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-4.00000 + 1.73205i) q^{76} +(-3.00000 - 5.19615i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -13.0000 q^{83} -2.00000 q^{84} +(6.00000 - 10.3923i) q^{86} +10.0000 q^{87} +(6.50000 - 11.2583i) q^{89} +(6.00000 - 10.3923i) q^{91} +(-1.00000 - 1.73205i) q^{92} +(1.00000 + 1.73205i) q^{93} +1.00000 q^{96} +(-7.50000 - 12.9904i) q^{97} +(1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{16} - 7 q^{17} - 4 q^{18} + 7 q^{19} + 2 q^{21} - 2 q^{23} - q^{24} + 12 q^{26} - 10 q^{27} + 2 q^{28} - 10 q^{29} - 4 q^{31} - q^{32} - 7 q^{34} + 2 q^{36} + 8 q^{37} + q^{38} + 12 q^{39} - 2 q^{41} + 2 q^{42} + 12 q^{43} + 4 q^{46} - q^{48} - 6 q^{49} - 7 q^{51} - 6 q^{52} + 5 q^{54} - 4 q^{56} + q^{57} + 20 q^{58} + q^{59} - 8 q^{61} + 2 q^{62} - 4 q^{63} + 2 q^{64} - 8 q^{67} + 14 q^{68} + 4 q^{69} + 12 q^{71} + 2 q^{72} + 3 q^{73} - 4 q^{74} - 8 q^{76} - 6 q^{78} + 4 q^{79} - q^{81} - 2 q^{82} - 26 q^{83} - 4 q^{84} + 12 q^{86} + 20 q^{87} + 13 q^{89} + 12 q^{91} - 2 q^{92} + 2 q^{93} + 2 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^12 - 6 * q^13 + 2 * q^14 - q^16 - 7 * q^17 - 4 * q^18 + 7 * q^19 + 2 * q^21 - 2 * q^23 - q^24 + 12 * q^26 - 10 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^31 - q^32 - 7 * q^34 + 2 * q^36 + 8 * q^37 + q^38 + 12 * q^39 - 2 * q^41 + 2 * q^42 + 12 * q^43 + 4 * q^46 - q^48 - 6 * q^49 - 7 * q^51 - 6 * q^52 + 5 * q^54 - 4 * q^56 + q^57 + 20 * q^58 + q^59 - 8 * q^61 + 2 * q^62 - 4 * q^63 + 2 * q^64 - 8 * q^67 + 14 * q^68 + 4 * q^69 + 12 * q^71 + 2 * q^72 + 3 * q^73 - 4 * q^74 - 8 * q^76 - 6 * q^78 + 4 * q^79 - q^81 - 2 * q^82 - 26 * q^83 - 4 * q^84 + 12 * q^86 + 20 * q^87 + 13 * q^89 + 12 * q^91 - 2 * q^92 + 2 * q^93 + 2 * q^96 - 15 * q^97 + 3 * q^98

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