LMFDB - Embedded newform 1638.2.r.y.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.y.1387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.56155 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.56155 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.780776 - 1.35234i) q^{10} +(-1.28078 - 2.21837i) q^{11} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0615528 - 0.106613i) q^{17} +(1.28078 - 2.21837i) q^{19} +(0.780776 - 1.35234i) q^{20} +(1.28078 - 2.21837i) q^{22} +(-0.561553 - 0.972638i) q^{23} -2.56155 q^{25} +(-3.34233 + 1.35234i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.06155 - 5.30277i) q^{29} +(0.500000 - 0.866025i) q^{32} +0.123106 q^{34} +(0.780776 - 1.35234i) q^{35} +(1.21922 + 2.11176i) q^{37} +2.56155 q^{38} +1.56155 q^{40} +(-5.62311 - 9.73950i) q^{41} +(4.00000 - 6.92820i) q^{43} +2.56155 q^{44} +(0.561553 - 0.972638i) q^{46} +0.315342 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.28078 - 2.21837i) q^{50} +(-2.84233 - 2.21837i) q^{52} -7.00000 q^{53} +(2.00000 + 3.46410i) q^{55} +(0.500000 - 0.866025i) q^{56} +(3.06155 - 5.30277i) q^{58} +(2.56155 - 4.43674i) q^{59} +(5.62311 - 9.73950i) q^{61} +1.00000 q^{64} +(0.780776 - 5.57586i) q^{65} +(-4.56155 - 7.90084i) q^{67} +(0.0615528 + 0.106613i) q^{68} +1.56155 q^{70} +(-5.68466 + 9.84612i) q^{71} -2.43845 q^{73} +(-1.21922 + 2.11176i) q^{74} +(1.28078 + 2.21837i) q^{76} +2.56155 q^{77} -6.56155 q^{79} +(0.780776 + 1.35234i) q^{80} +(5.62311 - 9.73950i) q^{82} +5.12311 q^{83} +(-0.0961180 + 0.166481i) q^{85} +8.00000 q^{86} +(1.28078 + 2.21837i) q^{88} +(1.71922 + 2.97778i) q^{89} +(-2.84233 - 2.21837i) q^{91} +1.12311 q^{92} +(0.157671 + 0.273094i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(0.438447 - 0.759413i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8} + q^{10} - q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} - 8 q^{17} + q^{19} - q^{20} + q^{22} + 6 q^{23} - 2 q^{25} - q^{26} - 2 q^{28} - 4 q^{29} + 2 q^{32} - 16 q^{34} - q^{35} + 9 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 16 q^{43} + 2 q^{44} - 6 q^{46} + 26 q^{47} - 2 q^{49} - q^{50} + q^{52} - 28 q^{53} + 8 q^{55} + 2 q^{56} + 4 q^{58} + 2 q^{59} + 6 q^{61} + 4 q^{64} - q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} + 2 q^{71} - 18 q^{73} - 9 q^{74} + q^{76} + 2 q^{77} - 18 q^{79} - q^{80} + 6 q^{82} + 4 q^{83} - 21 q^{85} + 32 q^{86} + q^{88} + 11 q^{89} + q^{91} - 12 q^{92} + 13 q^{94} - 8 q^{95} + 10 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8 + q^10 - q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 - 8 * q^17 + q^19 - q^20 + q^22 + 6 * q^23 - 2 * q^25 - q^26 - 2 * q^28 - 4 * q^29 + 2 * q^32 - 16 * q^34 - q^35 + 9 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 16 * q^43 + 2 * q^44 - 6 * q^46 + 26 * q^47 - 2 * q^49 - q^50 + q^52 - 28 * q^53 + 8 * q^55 + 2 * q^56 + 4 * q^58 + 2 * q^59 + 6 * q^61 + 4 * q^64 - q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 + 2 * q^71 - 18 * q^73 - 9 * q^74 + q^76 + 2 * q^77 - 18 * q^79 - q^80 + 6 * q^82 + 4 * q^83 - 21 * q^85 + 32 * q^86 + q^88 + 11 * q^89 + q^91 - 12 * q^92 + 13 * q^94 - 8 * q^95 + 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.56155			−0.698348			−0.349174	−	0.937058i	$-0.613538\pi$
$5$	−1.56155			−0.698348			−0.349174	+	0.937058i	$0.613538\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.780776	−	1.35234i	−0.246903	−	0.427649i
$11$	−1.28078	−	2.21837i	−0.386169	−	0.668864i	0.605762	−	0.795646i	$-0.292868\pi$
$11$	−1.28078	−	2.21837i	−0.386169	−	0.668864i	−0.991931	+	0.126782i	$0.959535\pi$
$12$		0			0
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.0615528	−	0.106613i	0.0149287	−	0.0258574i	−0.858465	−	0.512873i	$-0.828581\pi$
$17$	0.0615528	−	0.106613i	0.0149287	−	0.0258574i	0.873393	+	0.487016i	$0.161915\pi$
$18$		0			0
$19$	1.28078	−	2.21837i	0.293830	−	0.508929i	−0.680882	−	0.732393i	$-0.738403\pi$
$19$	1.28078	−	2.21837i	0.293830	−	0.508929i	0.974712	+	0.223464i	$0.0717366\pi$
$20$	0.780776	−	1.35234i	0.174587	−	0.302393i
$21$		0			0
$22$	1.28078	−	2.21837i	0.273062	−	0.472958i
$23$	−0.561553	−	0.972638i	−0.117092	−	0.202809i	0.801522	−	0.597965i	$-0.204024\pi$
$23$	−0.561553	−	0.972638i	−0.117092	−	0.202809i	−0.918614	+	0.395156i	$0.870691\pi$
$24$		0			0
$25$	−2.56155			−0.512311
$26$	−3.34233	+	1.35234i	−0.655485	+	0.265217i
$27$		0			0
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−3.06155	−	5.30277i	−0.568516	−	0.984699i	−0.996713	−	0.0810133i	$-0.974184\pi$
$29$	−3.06155	−	5.30277i	−0.568516	−	0.984699i	0.428197	−	0.903685i	$-0.359149\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	0.123106			0.0211124
$35$	0.780776	−	1.35234i	0.131975	−	0.228588i
$36$		0			0
$37$	1.21922	+	2.11176i	0.200439	+	0.347171i	0.948670	−	0.316268i	$-0.102430\pi$
$37$	1.21922	+	2.11176i	0.200439	+	0.347171i	−0.748231	+	0.663438i	$0.769096\pi$
$38$	2.56155			0.415539
$39$		0			0
$40$	1.56155			0.246903
$41$	−5.62311	−	9.73950i	−0.878182	−	1.52106i	−0.853335	−	0.521364i	$-0.825423\pi$
$41$	−5.62311	−	9.73950i	−0.878182	−	1.52106i	−0.0248471	−	0.999691i	$-0.507910\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	2.56155			0.386169
$45$		0			0
$46$	0.561553	−	0.972638i	0.0827964	−	0.143408i
$47$	0.315342			0.0459973			0.0229986	−	0.999735i	$-0.492679\pi$
$47$	0.315342			0.0459973			0.0229986	+	0.999735i	$0.492679\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−1.28078	−	2.21837i	−0.181129	−	0.313725i
$51$		0			0
$52$	−2.84233	−	2.21837i	−0.394160	−	0.307633i
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$		0			0
$55$	2.00000	+	3.46410i	0.269680	+	0.467099i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	3.06155	−	5.30277i	0.402002	−	0.696287i
$59$	2.56155	−	4.43674i	0.333486	−	0.577614i	−0.649707	−	0.760185i	$-0.725108\pi$
$59$	2.56155	−	4.43674i	0.333486	−	0.577614i	0.983193	+	0.182570i	$0.0584418\pi$
$60$		0			0
$61$	5.62311	−	9.73950i	0.719965	−	1.24702i	−0.241048	−	0.970513i	$-0.577491\pi$
$61$	5.62311	−	9.73950i	0.719965	−	1.24702i	0.961013	−	0.276503i	$-0.0891755\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	0.780776	−	5.57586i	0.0968434	−	0.691600i
$66$		0			0
$67$	−4.56155	−	7.90084i	−0.557282	−	0.965241i	−0.997722	−	0.0674592i	$-0.978511\pi$
$67$	−4.56155	−	7.90084i	−0.557282	−	0.965241i	0.440440	−	0.897782i	$-0.354823\pi$
$68$	0.0615528	+	0.106613i	0.00746437	+	0.0129287i
$69$		0			0
$70$	1.56155			0.186641
$71$	−5.68466	+	9.84612i	−0.674645	+	1.16852i	0.301928	+	0.953331i	$0.402370\pi$
$71$	−5.68466	+	9.84612i	−0.674645	+	1.16852i	−0.976573	+	0.215188i	$0.930963\pi$
$72$		0			0
$73$	−2.43845			−0.285399			−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845			−0.285399			−0.142699	+	0.989766i	$0.545578\pi$
$74$	−1.21922	+	2.11176i	−0.141732	+	0.245487i
$75$		0			0
$76$	1.28078	+	2.21837i	0.146915	+	0.254464i
$77$	2.56155			0.291916
$78$		0			0
$79$	−6.56155			−0.738232			−0.369116	−	0.929383i	$-0.620340\pi$
$79$	−6.56155			−0.738232			−0.369116	+	0.929383i	$0.620340\pi$
$80$	0.780776	+	1.35234i	0.0872935	+	0.151197i
$81$		0			0
$82$	5.62311	−	9.73950i	0.620968	−	1.07555i
$83$	5.12311			0.562334			0.281167	−	0.959659i	$-0.409279\pi$
$83$	5.12311			0.562334			0.281167	+	0.959659i	$0.409279\pi$
$84$		0			0
$85$	−0.0961180	+	0.166481i	−0.0104255	+	0.0180574i
$86$	8.00000			0.862662
$87$		0			0
$88$	1.28078	+	2.21837i	0.136531	+	0.236479i
$89$	1.71922	+	2.97778i	0.182237	+	0.315644i	0.942642	−	0.333805i	$-0.108333\pi$
$89$	1.71922	+	2.97778i	0.182237	+	0.315644i	−0.760405	+	0.649449i	$0.774999\pi$
$90$		0			0
$91$	−2.84233	−	2.21837i	−0.297957	−	0.232548i
$92$	1.12311			0.117092
$93$		0			0
$94$	0.157671	+	0.273094i	0.0162625	+	0.0281675i
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$		0			0
$97$	0.438447	−	0.759413i	0.0445176	−	0.0771067i	−0.842908	−	0.538058i	$-0.819158\pi$
$97$	0.438447	−	0.759413i	0.0445176	−	0.0771067i	0.887426	+	0.460951i	$0.152492\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$		0			0
$100$	1.28078	−	2.21837i	0.128078	−	0.221837i
$101$	−2.90388	−	5.02967i	−0.288947	−	0.500471i	0.684612	−	0.728908i	$-0.259972\pi$
$101$	−2.90388	−	5.02967i	−0.288947	−	0.500471i	−0.973559	+	0.228437i	$0.926638\pi$
$102$		0			0
$103$	6.24621			0.615457			0.307729	−	0.951474i	$-0.400431\pi$
$103$	6.24621			0.615457			0.307729	+	0.951474i	$0.400431\pi$
$104$	0.500000	−	3.57071i	0.0490290	−	0.350137i
$105$		0			0
$106$	−3.50000	−	6.06218i	−0.339950	−	0.588811i
$107$	6.96543	+	12.0645i	0.673374	+	1.16632i	0.976941	+	0.213508i	$0.0684889\pi$
$107$	6.96543	+	12.0645i	0.673374	+	1.16632i	−0.303567	+	0.952810i	$0.598178\pi$
$108$		0			0
$109$	−12.2462			−1.17297			−0.586487	−	0.809959i	$-0.699490\pi$
$109$	−12.2462			−1.17297			−0.586487	+	0.809959i	$0.699490\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$		0			0
$112$	1.00000			0.0944911
$113$	0.780776	−	1.35234i	0.0734493	−	0.127218i	−0.826962	−	0.562258i	$-0.809933\pi$
$113$	0.780776	−	1.35234i	0.0734493	−	0.127218i	0.900411	+	0.435041i	$0.143266\pi$
$114$		0			0
$115$	0.876894	+	1.51883i	0.0817708	+	0.141631i
$116$	6.12311			0.568516
$117$		0			0
$118$	5.12311			0.471620
$119$	0.0615528	+	0.106613i	0.00564254	+	0.00977316i
$120$		0			0
$121$	2.21922	−	3.84381i	0.201748	−	0.349437i
$122$	11.2462			1.01818
$123$		0			0
$124$		0			0
$125$	11.8078			1.05612
$126$		0			0
$127$	−6.24621	−	10.8188i	−0.554262	−	0.960009i	−0.997961	−	0.0638334i	$-0.979667\pi$
$127$	−6.24621	−	10.8188i	−0.554262	−	0.960009i	0.443699	−	0.896176i	$-0.353666\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	5.21922	−	2.11176i	0.457756	−	0.185213i
$131$	−14.2462			−1.24470			−0.622349	−	0.782740i	$-0.713821\pi$
$131$	−14.2462			−1.24470			−0.622349	+	0.782740i	$0.713821\pi$
$132$		0			0
$133$	1.28078	+	2.21837i	0.111057	+	0.192357i
$134$	4.56155	−	7.90084i	0.394058	−	0.682529i
$135$		0			0
$136$	−0.0615528	+	0.106613i	−0.00527811	+	0.00914195i
$137$	6.21922	−	10.7720i	0.531344	−	0.920315i	−0.467987	−	0.883736i	$-0.655020\pi$
$137$	6.21922	−	10.7720i	0.531344	−	0.920315i	0.999331	−	0.0365795i	$-0.0116462\pi$
$138$		0			0
$139$	2.71922	−	4.70983i	0.230642	−	0.399483i	−0.727356	−	0.686261i	$-0.759251\pi$
$139$	2.71922	−	4.70983i	0.230642	−	0.399483i	0.957997	+	0.286778i	$0.0925842\pi$
$140$	0.780776	+	1.35234i	0.0659877	+	0.114294i
$141$		0			0
$142$	−11.3693			−0.954092
$143$	8.56155	−	3.46410i	0.715953	−	0.289683i
$144$		0			0
$145$	4.78078	+	8.28055i	0.397022	+	0.687662i
$146$	−1.21922	−	2.11176i	−0.100904	−	0.174770i
$147$		0			0
$148$	−2.43845			−0.200439
$149$	−7.78078	+	13.4767i	−0.637426	+	1.10405i	0.348570	+	0.937283i	$0.386668\pi$
$149$	−7.78078	+	13.4767i	−0.637426	+	1.10405i	−0.985996	+	0.166771i	$0.946666\pi$
$150$		0			0
$151$	−21.9309			−1.78471			−0.892354	−	0.451335i	$-0.850948\pi$
$151$	−21.9309			−1.78471			−0.892354	+	0.451335i	$0.850948\pi$
$152$	−1.28078	+	2.21837i	−0.103885	+	0.179934i
$153$		0			0
$154$	1.28078	+	2.21837i	0.103208	+	0.178761i
$155$		0			0
$156$		0			0
$157$	−1.31534			−0.104976			−0.0524878	−	0.998622i	$-0.516715\pi$
$157$	−1.31534			−0.104976			−0.0524878	+	0.998622i	$0.516715\pi$
$158$	−3.28078	−	5.68247i	−0.261005	−	0.452073i
$159$		0			0
$160$	−0.780776	+	1.35234i	−0.0617258	+	0.106912i
$161$	1.12311			0.0885131
$162$		0			0
$163$	−12.2462	+	21.2111i	−0.959197	+	1.66138i	−0.234741	+	0.972058i	$0.575424\pi$
$163$	−12.2462	+	21.2111i	−0.959197	+	1.66138i	−0.724457	+	0.689320i	$0.757909\pi$
$164$	11.2462			0.878182
$165$		0			0
$166$	2.56155	+	4.43674i	0.198815	+	0.344358i
$167$	6.24621	+	10.8188i	0.483346	+	0.837180i	0.999817	−	0.0191244i	$-0.00608786\pi$
$167$	6.24621	+	10.8188i	0.483346	+	0.837180i	−0.516471	+	0.856305i	$0.672755\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	−0.192236			−0.0147438
$171$		0			0
$172$	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	$0.926793\pi$
$174$		0			0
$175$	1.28078	−	2.21837i	0.0968176	−	0.167693i
$176$	−1.28078	+	2.21837i	−0.0965422	+	0.167216i
$177$		0			0
$178$	−1.71922	+	2.97778i	−0.128861	+	0.223194i
$179$	−0.876894	−	1.51883i	−0.0655422	−	0.113522i	0.831392	−	0.555686i	$-0.187544\pi$
$179$	−0.876894	−	1.51883i	−0.0655422	−	0.113522i	−0.896934	+	0.442164i	$0.854211\pi$
$180$		0			0
$181$	13.2462			0.984583			0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462			0.984583			0.492292	+	0.870430i	$0.336159\pi$
$182$	0.500000	−	3.57071i	0.0370625	−	0.264679i
$183$		0			0
$184$	0.561553	+	0.972638i	0.0413982	+	0.0717038i
$185$	−1.90388	−	3.29762i	−0.139976	−	0.242446i
$186$		0			0
$187$	−0.315342			−0.0230601
$188$	−0.157671	+	0.273094i	−0.0114993	+	0.0199174i
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−2.56155	+	4.43674i	−0.185347	+	0.321031i	−0.943694	−	0.330821i	$-0.892674\pi$
$191$	−2.56155	+	4.43674i	−0.185347	+	0.321031i	0.758346	+	0.651852i	$0.226008\pi$
$192$		0			0
$193$	−0.0615528	−	0.106613i	−0.00443067	−	0.00767414i	0.863802	−	0.503832i	$-0.168077\pi$
$193$	−0.0615528	−	0.106613i	−0.00443067	−	0.00767414i	−0.868232	+	0.496158i	$0.834744\pi$
$194$	0.876894			0.0629573
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.28078	+	10.8786i	0.447487	+	0.775070i	0.998222	−	0.0596103i	$-0.0189858\pi$
$197$	6.28078	+	10.8786i	0.447487	+	0.775070i	−0.550735	+	0.834680i	$0.685652\pi$
$198$		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	$-0.0252700\pi$
$200$	2.56155			0.181129
$201$		0			0
$202$	2.90388	−	5.02967i	0.204316	−	0.353886i
$203$	6.12311			0.429758
$204$		0			0
$205$	8.78078	+	15.2088i	0.613276	+	1.06223i
$206$	3.12311	+	5.40938i	0.217597	+	0.376889i
$207$		0			0
$208$	3.34233	−	1.35234i	0.231749	−	0.0937682i
$209$	−6.56155			−0.453872
$210$		0			0
$211$	−2.56155	−	4.43674i	−0.176345	−	0.305438i	0.764281	−	0.644883i	$-0.223094\pi$
$211$	−2.56155	−	4.43674i	−0.176345	−	0.305438i	−0.940626	+	0.339445i	$0.889761\pi$
$212$	3.50000	−	6.06218i	0.240381	−	0.416352i
$213$		0			0
$214$	−6.96543	+	12.0645i	−0.476147	+	0.824711i
$215$	−6.24621	+	10.8188i	−0.425988	+	0.737833i
$216$		0			0
$217$		0			0
$218$	−6.12311	−	10.6055i	−0.414709	−	0.718297i
$219$		0			0
$220$	−4.00000			−0.269680
$221$	0.349907	+	0.273094i	0.0235373	+	0.0183703i
$222$		0			0
$223$	−4.87689	−	8.44703i	−0.326581	−	0.565655i	0.655250	−	0.755412i	$-0.272563\pi$
$223$	−4.87689	−	8.44703i	−0.326581	−	0.565655i	−0.981831	+	0.189757i	$0.939230\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$		0			0
$226$	1.56155			0.103873
$227$	−5.43845	+	9.41967i	−0.360962	+	0.625205i	−0.988119	−	0.153688i	$-0.950885\pi$
$227$	−5.43845	+	9.41967i	−0.360962	+	0.625205i	0.627157	+	0.778893i	$0.284218\pi$
$228$		0			0
$229$	17.0540			1.12696			0.563479	−	0.826130i	$-0.309462\pi$
$229$	17.0540			1.12696			0.563479	+	0.826130i	$0.309462\pi$
$230$	−0.876894	+	1.51883i	−0.0578207	+	0.100148i
$231$		0			0
$232$	3.06155	+	5.30277i	0.201001	+	0.348144i
$233$	−1.36932			−0.0897069			−0.0448535	−	0.998994i	$-0.514282\pi$
$233$	−1.36932			−0.0897069			−0.0448535	+	0.998994i	$0.514282\pi$
$234$		0			0
$235$	−0.492423			−0.0321221
$236$	2.56155	+	4.43674i	0.166743	+	0.288807i
$237$		0			0
$238$	−0.0615528	+	0.106613i	−0.00398988	+	0.00691067i
$239$	−19.3693			−1.25290			−0.626448	−	0.779463i	$-0.715492\pi$
$239$	−19.3693			−1.25290			−0.626448	+	0.779463i	$0.715492\pi$
$240$		0			0
$241$	0.0961180	−	0.166481i	0.00619150	−	0.0107240i	−0.862913	−	0.505352i	$-0.831363\pi$
$241$	0.0961180	−	0.166481i	0.00619150	−	0.0107240i	0.869105	+	0.494628i	$0.164696\pi$
$242$	4.43845			0.285314
$243$		0			0
$244$	5.62311	+	9.73950i	0.359982	+	0.623508i
$245$	0.780776	+	1.35234i	0.0498820	+	0.0863981i
$246$		0			0
$247$	7.28078	+	5.68247i	0.463265	+	0.361567i
$248$		0			0
$249$		0			0
$250$	5.90388	+	10.2258i	0.373394	+	0.646738i
$251$	−6.80776	+	11.7914i	−0.429702	+	0.744266i	−0.996847	−	0.0793522i	$-0.974715\pi$
$251$	−6.80776	+	11.7914i	−0.429702	+	0.744266i	0.567144	+	0.823618i	$0.308048\pi$
$252$		0			0
$253$	−1.43845	+	2.49146i	−0.0904344	+	0.156637i
$254$	6.24621	−	10.8188i	0.391922	−	0.678829i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1847	−	21.1044i	−0.760058	−	1.31646i	−0.942820	−	0.333302i	$-0.891837\pi$
$257$	−12.1847	−	21.1044i	−0.760058	−	1.31646i	0.182762	−	0.983157i	$-0.441496\pi$
$258$		0			0
$259$	−2.43845			−0.151518
$260$	4.43845	+	3.46410i	0.275261	+	0.214834i
$261$		0			0
$262$	−7.12311	−	12.3376i	−0.440067	−	0.762218i
$263$	2.56155	+	4.43674i	0.157952	+	0.273581i	0.934130	−	0.356933i	$-0.116178\pi$
$263$	2.56155	+	4.43674i	0.157952	+	0.273581i	−0.776178	+	0.630514i	$0.782844\pi$
$264$		0			0
$265$	10.9309			0.671478
$266$	−1.28078	+	2.21837i	−0.0785294	+	0.136017i
$267$		0			0
$268$	9.12311			0.557282
$269$	13.5616	−	23.4893i	0.826862	−	1.43217i	−0.0736251	−	0.997286i	$-0.523457\pi$
$269$	13.5616	−	23.4893i	0.826862	−	1.43217i	0.900488	−	0.434882i	$-0.143210\pi$
$270$		0			0
$271$	11.3693	+	19.6922i	0.690637	+	1.19622i	0.971630	+	0.236508i	$0.0760030\pi$
$271$	11.3693	+	19.6922i	0.690637	+	1.19622i	−0.280993	+	0.959710i	$0.590664\pi$
$272$	−0.123106			−0.00746437
$273$		0			0
$274$	12.4384			0.751434
$275$	3.28078	+	5.68247i	0.197838	+	0.342666i
$276$		0			0
$277$	9.78078	−	16.9408i	0.587670	−	1.01787i	−0.406867	−	0.913487i	$-0.633379\pi$
$277$	9.78078	−	16.9408i	0.587670	−	1.01787i	0.994537	−	0.104387i	$-0.0332879\pi$
$278$	5.43845			0.326176
$279$		0			0
$280$	−0.780776	+	1.35234i	−0.0466603	+	0.0808180i
$281$	−12.9309			−0.771391			−0.385696	−	0.922626i	$-0.626038\pi$
$281$	−12.9309			−0.771391			−0.385696	+	0.922626i	$0.626038\pi$
$282$		0			0
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	0.993626	+	0.112728i	$0.0359589\pi$
$283$	10.0000	+	17.3205i	0.594438	+	1.02960i	−0.399188	+	0.916869i	$0.630708\pi$
$284$	−5.68466	−	9.84612i	−0.337322	−	0.584260i
$285$		0			0
$286$	7.28078	+	5.68247i	0.430521	+	0.336012i
$287$	11.2462			0.663843
$288$		0			0
$289$	8.49242	+	14.7093i	0.499554	+	0.865253i
$290$	−4.78078	+	8.28055i	−0.280737	+	0.486251i
$291$		0			0
$292$	1.21922	−	2.11176i	0.0713497	−	0.123581i
$293$	−3.46543	+	6.00231i	−0.202453	+	0.350659i	−0.949318	−	0.314317i	$-0.898225\pi$
$293$	−3.46543	+	6.00231i	−0.202453	+	0.350659i	0.746865	+	0.664975i	$0.231558\pi$
$294$		0			0
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	−1.21922	−	2.11176i	−0.0708659	−	0.122743i
$297$		0			0
$298$	−15.5616			−0.901457
$299$	3.75379	−	1.51883i	0.217087	−	0.0878360i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	−10.9654	−	18.9927i	−0.630990	−	1.09291i
$303$		0			0
$304$	−2.56155			−0.146915
$305$	−8.78078	+	15.2088i	−0.502786	+	0.870851i
$306$		0			0
$307$	−9.93087			−0.566785			−0.283392	−	0.959004i	$-0.591460\pi$
$307$	−9.93087			−0.566785			−0.283392	+	0.959004i	$0.591460\pi$
$308$	−1.28078	+	2.21837i	−0.0729790	+	0.126403i
$309$		0			0
$310$		0			0
$311$	−21.9309			−1.24359			−0.621793	−	0.783182i	$-0.713595\pi$
$311$	−21.9309			−1.24359			−0.621793	+	0.783182i	$0.713595\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−0.657671	−	1.13912i	−0.0371145	−	0.0642842i
$315$		0			0
$316$	3.28078	−	5.68247i	0.184558	−	0.319664i
$317$	−12.4384			−0.698613			−0.349306	−	0.937009i	$-0.613583\pi$
$317$	−12.4384			−0.698613			−0.349306	+	0.937009i	$0.613583\pi$
$318$		0			0
$319$	−7.84233	+	13.5833i	−0.439086	+	0.760520i
$320$	−1.56155			−0.0872935
$321$		0			0
$322$	0.561553	+	0.972638i	0.0312941	+	0.0542030i
$323$	−0.157671	−	0.273094i	−0.00877304	−	0.0151953i
$324$		0			0
$325$	1.28078	−	9.14657i	0.0710447	−	0.507361i
$326$	−24.4924			−1.35651
$327$		0			0
$328$	5.62311	+	9.73950i	0.310484	+	0.537774i
$329$	−0.157671	+	0.273094i	−0.00869267	+	0.0150561i
$330$		0			0
$331$	−9.68466	+	16.7743i	−0.532317	+	0.922000i	0.466971	+	0.884273i	$0.345345\pi$
$331$	−9.68466	+	16.7743i	−0.532317	+	0.922000i	−0.999288	+	0.0377275i	$0.987988\pi$
$332$	−2.56155	+	4.43674i	−0.140583	+	0.243498i
$333$		0			0
$334$	−6.24621	+	10.8188i	−0.341777	+	0.591976i
$335$	7.12311	+	12.3376i	0.389177	+	0.674074i
$336$		0			0
$337$	−13.4924			−0.734979			−0.367490	−	0.930028i	$-0.619783\pi$
$337$	−13.4924			−0.734979			−0.367490	+	0.930028i	$0.619783\pi$
$338$	−3.15767	−	12.6107i	−0.171755	−	0.685930i
$339$		0			0
$340$	−0.0961180	−	0.166481i	−0.00521273	−	0.00902871i
$341$		0			0
$342$		0			0
$343$	1.00000			0.0539949
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	−18.0000			−0.967686
$347$	7.52699	−	13.0371i	0.404070	−	0.699870i	−0.590143	−	0.807299i	$-0.700929\pi$
$347$	7.52699	−	13.0371i	0.404070	−	0.699870i	0.994213	+	0.107429i	$0.0342619\pi$
$348$		0			0
$349$	9.00000	+	15.5885i	0.481759	+	0.834431i	0.999781	−	0.0209364i	$-0.00666475\pi$
$349$	9.00000	+	15.5885i	0.481759	+	0.834431i	−0.518022	+	0.855367i	$0.673331\pi$
$350$	2.56155			0.136921
$351$		0			0
$352$	−2.56155			−0.136531
$353$	−16.9039	−	29.2784i	−0.899703	−	1.55833i	−0.827874	−	0.560914i	$-0.810450\pi$
$353$	−16.9039	−	29.2784i	−0.899703	−	1.55833i	−0.0718288	−	0.997417i	$-0.522884\pi$
$354$		0			0
$355$	8.87689	−	15.3752i	0.471137	−	0.816033i
$356$	−3.43845			−0.182237
$357$		0			0
$358$	0.876894	−	1.51883i	0.0463453	−	0.0802724i
$359$	1.75379			0.0925614			0.0462807	−	0.998928i	$-0.485263\pi$
$359$	1.75379			0.0925614			0.0462807	+	0.998928i	$0.485263\pi$
$360$		0			0
$361$	6.21922	+	10.7720i	0.327328	+	0.566948i
$362$	6.62311	+	11.4716i	0.348103	+	0.602932i
$363$		0			0
$364$	3.34233	−	1.35234i	0.175186	−	0.0708821i
$365$	3.80776			0.199307
$366$		0			0
$367$	−6.80776	−	11.7914i	−0.355362	−	0.615506i	0.631818	−	0.775117i	$-0.282309\pi$
$367$	−6.80776	−	11.7914i	−0.355362	−	0.615506i	−0.987180	+	0.159611i	$0.948976\pi$
$368$	−0.561553	+	0.972638i	−0.0292730	+	0.0507023i
$369$		0			0
$370$	1.90388	−	3.29762i	0.0989781	−	0.171435i
$371$	3.50000	−	6.06218i	0.181711	−	0.314733i
$372$		0			0
$373$	1.53457	−	2.65794i	0.0794568	−	0.137623i	−0.823559	−	0.567231i	$-0.808015\pi$
$373$	1.53457	−	2.65794i	0.0794568	−	0.137623i	0.903016	+	0.429608i	$0.141348\pi$
$374$	−0.157671	−	0.273094i	−0.00815296	−	0.0141213i
$375$		0			0
$376$	−0.315342			−0.0162625
$377$	20.4654	−	8.28055i	1.05402	−	0.426470i
$378$		0			0
$379$	−18.8078	−	32.5760i	−0.966090	−	1.67332i	−0.706658	−	0.707556i	$-0.749798\pi$
$379$	−18.8078	−	32.5760i	−0.966090	−	1.67332i	−0.259432	−	0.965761i	$-0.583535\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$		0			0
$382$	−5.12311			−0.262121
$383$	−6.40388	+	11.0918i	−0.327223	+	0.566767i	−0.981960	−	0.189090i	$-0.939446\pi$
$383$	−6.40388	+	11.0918i	−0.327223	+	0.566767i	0.654737	+	0.755857i	$0.272780\pi$
$384$		0			0
$385$	−4.00000			−0.203859
$386$	0.0615528	−	0.106613i	0.00313296	−	0.00542644i
$387$		0			0
$388$	0.438447	+	0.759413i	0.0222588	+	0.0385533i
$389$	5.31534			0.269499			0.134749	−	0.990880i	$-0.456977\pi$
$389$	5.31534			0.269499			0.134749	+	0.990880i	$0.456977\pi$
$390$		0			0
$391$	−0.138261			−0.00699214
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	−6.28078	+	10.8786i	−0.316421	+	0.548057i
$395$	10.2462			0.515543
$396$		0			0
$397$	−13.9654	+	24.1888i	−0.700905	+	1.21400i	0.267244	+	0.963629i	$0.413887\pi$
$397$	−13.9654	+	24.1888i	−0.700905	+	1.21400i	−0.968149	+	0.250374i	$0.919446\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	1.28078	+	2.21837i	0.0640388	+	0.110918i
$401$	−0.903882	−	1.56557i	−0.0451377	−	0.0781808i	0.842574	−	0.538581i	$-0.181039\pi$
$401$	−0.903882	−	1.56557i	−0.0451377	−	0.0781808i	−0.887712	+	0.460400i	$0.847706\pi$
$402$		0			0
$403$		0			0
$404$	5.80776			0.288947
$405$		0			0
$406$	3.06155	+	5.30277i	0.151942	+	0.263172i
$407$	3.12311	−	5.40938i	0.154807	−	0.268133i
$408$		0			0
$409$	5.78078	−	10.0126i	0.285841	−	0.495091i	−0.686972	−	0.726684i	$-0.741060\pi$
$409$	5.78078	−	10.0126i	0.285841	−	0.495091i	0.972813	+	0.231593i	$0.0743937\pi$
$410$	−8.78078	+	15.2088i	−0.433652	+	0.751107i
$411$		0			0
$412$	−3.12311	+	5.40938i	−0.153864	+	0.266501i
$413$	2.56155	+	4.43674i	0.126046	+	0.218318i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	2.84233	+	2.21837i	0.139357	+	0.108765i
$417$		0			0
$418$	−3.28078	−	5.68247i	−0.160468	−	0.277939i
$419$	11.6847	+	20.2384i	0.570833	+	0.988712i	0.996481	+	0.0838227i	$0.0267129\pi$
$419$	11.6847	+	20.2384i	0.570833	+	0.988712i	−0.425648	+	0.904889i	$0.639954\pi$
$420$		0			0
$421$	−22.3002			−1.08684			−0.543422	−	0.839459i	$-0.682872\pi$
$421$	−22.3002			−1.08684			−0.543422	+	0.839459i	$0.682872\pi$
$422$	2.56155	−	4.43674i	0.124694	−	0.215977i
$423$		0			0
$424$	7.00000			0.339950
$425$	−0.157671	+	0.273094i	−0.00764816	+	0.0132470i
$426$		0			0
$427$	5.62311	+	9.73950i	0.272121	+	0.471328i
$428$	−13.9309			−0.673374
$429$		0			0
$430$	−12.4924			−0.602438
$431$	9.68466	+	16.7743i	0.466494	+	0.807991i	0.999268	−	0.0382670i	$-0.0121837\pi$
$431$	9.68466	+	16.7743i	0.466494	+	0.807991i	−0.532774	+	0.846258i	$0.678850\pi$
$432$		0			0
$433$	10.6577	−	18.4596i	0.512175	−	0.887113i	−0.487725	−	0.872997i	$-0.662173\pi$
$433$	10.6577	−	18.4596i	0.512175	−	0.887113i	0.999900	−	0.0141160i	$-0.00449340\pi$
$434$		0			0
$435$		0			0
$436$	6.12311	−	10.6055i	0.293244	−	0.507913i
$437$	−2.87689			−0.137621
$438$		0			0
$439$	13.1231	+	22.7299i	0.626332	+	1.08484i	0.988282	+	0.152641i	$0.0487777\pi$
$439$	13.1231	+	22.7299i	0.626332	+	1.08484i	−0.361950	+	0.932197i	$0.617889\pi$
$440$	−2.00000	−	3.46410i	−0.0953463	−	0.165145i
$441$		0			0
$442$	−0.0615528	+	0.439575i	−0.00292777	+	0.0209085i
$443$	27.0540			1.28537			0.642687	−	0.766129i	$-0.277820\pi$
$443$	27.0540			1.28537			0.642687	+	0.766129i	$0.277820\pi$
$444$		0			0
$445$	−2.68466	−	4.64996i	−0.127265	−	0.220429i
$446$	4.87689	−	8.44703i	0.230928	−	0.399978i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−3.31534	+	5.74234i	−0.156461	+	0.270998i	−0.933590	−	0.358343i	$-0.883342\pi$
$449$	−3.31534	+	5.74234i	−0.156461	+	0.270998i	0.777129	+	0.629341i	$0.216675\pi$
$450$		0			0
$451$	−14.4039	+	24.9483i	−0.678252	+	1.17477i
$452$	0.780776	+	1.35234i	0.0367246	+	0.0636089i
$453$		0			0
$454$	−10.8769			−0.510478
$455$	4.43845	+	3.46410i	0.208078	+	0.162400i
$456$		0			0
$457$	−14.4654	−	25.0549i	−0.676665	−	1.17202i	−0.975979	−	0.217863i	$-0.930091\pi$
$457$	−14.4654	−	25.0549i	−0.676665	−	1.17202i	0.299315	−	0.954154i	$-0.403242\pi$
$458$	8.52699	+	14.7692i	0.398440	+	0.690118i
$459$		0			0
$460$	−1.75379			−0.0817708
$461$	3.02699	−	5.24290i	0.140981	−	0.244186i	−0.786885	−	0.617099i	$-0.788308\pi$
$461$	3.02699	−	5.24290i	0.140981	−	0.244186i	0.927866	+	0.372913i	$0.121641\pi$
$462$		0			0
$463$	12.3153			0.572342			0.286171	−	0.958178i	$-0.407617\pi$
$463$	12.3153			0.572342			0.286171	+	0.958178i	$0.407617\pi$
$464$	−3.06155	+	5.30277i	−0.142129	+	0.246175i
$465$		0			0
$466$	−0.684658	−	1.18586i	−0.0317162	−	0.0549341i
$467$	36.9848			1.71145			0.855727	−	0.517427i	$-0.173110\pi$
$467$	36.9848			1.71145			0.855727	+	0.517427i	$0.173110\pi$
$468$		0			0
$469$	9.12311			0.421266
$470$	−0.246211	−	0.426450i	−0.0113569	−	0.0196707i
$471$		0			0
$472$	−2.56155	+	4.43674i	−0.117905	+	0.204217i
$473$	−20.4924			−0.942243
$474$		0			0
$475$	−3.28078	+	5.68247i	−0.150532	+	0.260730i
$476$	−0.123106			−0.00564254
$477$		0			0
$478$	−9.68466	−	16.7743i	−0.442966	−	0.767240i
$479$	−0.965435	−	1.67218i	−0.0441118	−	0.0764040i	0.843126	−	0.537715i	$-0.180712\pi$
$479$	−0.965435	−	1.67218i	−0.0441118	−	0.0764040i	−0.887238	+	0.461311i	$0.847379\pi$
$480$		0			0
$481$	−8.15009	+	3.29762i	−0.371612	+	0.150359i
$482$	0.192236			0.00875611
$483$		0			0
$484$	2.21922	+	3.84381i	0.100874	+	0.174719i
$485$	−0.684658	+	1.18586i	−0.0310887	+	0.0538473i
$486$		0			0
$487$	−11.8423	+	20.5115i	−0.536627	+	0.929466i	0.462456	+	0.886642i	$0.346968\pi$
$487$	−11.8423	+	20.5115i	−0.536627	+	0.929466i	−0.999083	+	0.0428230i	$0.986365\pi$
$488$	−5.62311	+	9.73950i	−0.254546	+	0.440887i
$489$		0			0
$490$	−0.780776	+	1.35234i	−0.0352719	+	0.0610927i
$491$	−8.24621	−	14.2829i	−0.372146	−	0.644576i	0.617749	−	0.786375i	$-0.288045\pi$
$491$	−8.24621	−	14.2829i	−0.372146	−	0.644576i	−0.989895	+	0.141799i	$0.954711\pi$
$492$		0			0
$493$	−0.753789			−0.0339489
$494$	−1.28078	+	9.14657i	−0.0576249	+	0.411524i
$495$		0			0
$496$		0			0
$497$	−5.68466	−	9.84612i	−0.254992	−	0.441659i
$498$		0			0
$499$	30.2462			1.35401			0.677003	−	0.735980i	$-0.263278\pi$
$499$	30.2462			1.35401			0.677003	+	0.735980i	$0.263278\pi$
$500$	−5.90388	+	10.2258i	−0.264030	+	0.457313i
$501$		0			0
$502$	−13.6155			−0.607691
$503$	−14.2462	+	24.6752i	−0.635207	+	1.10021i	0.351264	+	0.936276i	$0.385752\pi$
$503$	−14.2462	+	24.6752i	−0.635207	+	1.10021i	−0.986471	+	0.163935i	$0.947581\pi$
$504$		0			0
$505$	4.53457	+	7.85410i	0.201786	+	0.349503i
$506$	−2.87689			−0.127894
$507$		0			0
$508$	12.4924			0.554262
$509$	−20.9039	−	36.2066i	−0.926548	−	1.60483i	−0.789052	−	0.614326i	$-0.789428\pi$
$509$	−20.9039	−	36.2066i	−0.926548	−	1.60483i	−0.137496	−	0.990502i	$-0.543906\pi$
$510$		0			0
$511$	1.21922	−	2.11176i	0.0539353	−	0.0934186i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.1847	−	21.1044i	0.537442	−	0.930877i
$515$	−9.75379			−0.429803
$516$		0			0
$517$	−0.403882	−	0.699544i	−0.0177627	−	0.0307659i
$518$	−1.21922	−	2.11176i	−0.0535696	−	0.0927853i
$519$		0			0
$520$	−0.780776	+	5.57586i	−0.0342393	+	0.244518i
$521$	−25.8769			−1.13369			−0.566844	−	0.823825i	$-0.691836\pi$
$521$	−25.8769			−1.13369			−0.566844	+	0.823825i	$0.691836\pi$
$522$		0			0
$523$	8.40388	+	14.5560i	0.367476	+	0.636487i	0.989170	−	0.146773i	$-0.0468886\pi$
$523$	8.40388	+	14.5560i	0.367476	+	0.636487i	−0.621694	+	0.783260i	$0.713555\pi$
$524$	7.12311	−	12.3376i	0.311174	−	0.538970i
$525$		0			0
$526$	−2.56155	+	4.43674i	−0.111689	+	0.193451i
$527$		0			0
$528$		0			0
$529$	10.8693	−	18.8262i	0.472579	−	0.818531i
$530$	5.46543	+	9.46641i	0.237403	+	0.411195i
$531$		0			0
$532$	−2.56155			−0.111057
$533$	37.5885	−	15.2088i	1.62814	−	0.658764i
$534$		0			0
$535$	−10.8769	−	18.8393i	−0.470249	−	0.814495i
$536$	4.56155	+	7.90084i	0.197029	+	0.341264i
$537$		0			0
$538$	27.1231			1.16936
$539$	−1.28078	+	2.21837i	−0.0551669	+	0.0955520i
$540$		0			0
$541$	19.1771			0.824487			0.412244	−	0.911074i	$-0.364745\pi$
$541$	19.1771			0.824487			0.412244	+	0.911074i	$0.364745\pi$
$542$	−11.3693	+	19.6922i	−0.488354	+	0.845854i
$543$		0			0
$544$	−0.0615528	−	0.106613i	−0.00263906	−	0.00457098i
$545$	19.1231			0.819144
$546$		0			0
$547$	−33.6155			−1.43730			−0.718648	−	0.695374i	$-0.755239\pi$
$547$	−33.6155			−1.43730			−0.718648	+	0.695374i	$0.755239\pi$
$548$	6.21922	+	10.7720i	0.265672	+	0.460158i
$549$		0			0
$550$	−3.28078	+	5.68247i	−0.139893	+	0.242301i
$551$	−15.6847			−0.668189
$552$		0			0
$553$	3.28078	−	5.68247i	0.139513	−	0.241643i
$554$	19.5616			0.831091
$555$		0			0
$556$	2.71922	+	4.70983i	0.115321	+	0.199741i
$557$	6.06155	+	10.4989i	0.256836	+	0.444853i	0.965393	−	0.260801i	$-0.0839866\pi$
$557$	6.06155	+	10.4989i	0.256836	+	0.444853i	−0.708556	+	0.705654i	$0.750653\pi$
$558$		0			0
$559$	22.7386	+	17.7470i	0.961742	+	0.750616i
$560$	−1.56155			−0.0659877
$561$		0			0
$562$	−6.46543	−	11.1985i	−0.272728	−	0.472379i
$563$	−2.87689	+	4.98293i	−0.121247	+	0.210005i	−0.920260	−	0.391309i	$-0.872023\pi$
$563$	−2.87689	+	4.98293i	−0.121247	+	0.210005i	0.799013	+	0.601314i	$0.205356\pi$
$564$		0			0
$565$	−1.21922	+	2.11176i	−0.0512931	+	0.0888423i
$566$	−10.0000	+	17.3205i	−0.420331	+	0.728035i
$567$		0			0
$568$	5.68466	−	9.84612i	0.238523	−	0.413134i
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	0.537874	−	0.843025i	$-0.319228\pi$
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	−0.999018	+	0.0443003i	$0.985894\pi$
$570$		0			0
$571$	−21.1231			−0.883974			−0.441987	−	0.897021i	$-0.645726\pi$
$571$	−21.1231			−0.883974			−0.441987	+	0.897021i	$0.645726\pi$
$572$	−1.28078	+	9.14657i	−0.0535520	+	0.382437i
$573$		0			0
$574$	5.62311	+	9.73950i	0.234704	+	0.406519i
$575$	1.43845	+	2.49146i	0.0599874	+	0.103901i
$576$		0			0
$577$	−35.5616			−1.48045			−0.740223	−	0.672361i	$-0.765280\pi$
$577$	−35.5616			−1.48045			−0.740223	+	0.672361i	$0.765280\pi$
$578$	−8.49242	+	14.7093i	−0.353238	+	0.611827i
$579$		0			0
$580$	−9.56155			−0.397022
$581$	−2.56155	+	4.43674i	−0.106271	+	0.184067i
$582$		0			0
$583$	8.96543	+	15.5286i	0.371310	+	0.643128i
$584$	2.43845			0.100904
$585$		0			0
$586$	−6.93087			−0.286312
$587$	1.12311	+	1.94528i	0.0463555	+	0.0802901i	0.888272	−	0.459317i	$-0.151906\pi$
$587$	1.12311	+	1.94528i	0.0463555	+	0.0802901i	−0.841917	+	0.539608i	$0.818573\pi$
$588$		0			0
$589$		0			0
$590$	−8.00000			−0.329355
$591$		0			0
$592$	1.21922	−	2.11176i	0.0501098	−	0.0867927i
$593$	33.9848			1.39559			0.697795	−	0.716297i	$-0.254165\pi$
$593$	33.9848			1.39559			0.697795	+	0.716297i	$0.254165\pi$
$594$		0			0
$595$	−0.0961180	−	0.166481i	−0.00394045	−	0.00682506i
$596$	−7.78078	−	13.4767i	−0.318713	−	0.552027i
$597$		0			0
$598$	3.19224	+	2.49146i	0.130540	+	0.101884i
$599$	−23.8617			−0.974964			−0.487482	−	0.873133i	$-0.662085\pi$
$599$	−23.8617			−0.974964			−0.487482	+	0.873133i	$0.662085\pi$
$600$		0			0
$601$	−14.1501	−	24.5087i	−0.577194	−	0.999730i	−0.995799	−	0.0915616i	$-0.970814\pi$
$601$	−14.1501	−	24.5087i	−0.577194	−	0.999730i	0.418605	−	0.908168i	$-0.362519\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$		0			0
$604$	10.9654	−	18.9927i	0.446177	−	0.772802i
$605$	−3.46543	+	6.00231i	−0.140890	+	0.244029i
$606$		0			0
$607$	24.4924	−	42.4221i	0.994117	−	1.72186i	0.403256	−	0.915087i	$-0.367878\pi$
$607$	24.4924	−	42.4221i	0.994117	−	1.72186i	0.590861	−	0.806774i	$-0.298788\pi$
$608$	−1.28078	−	2.21837i	−0.0519423	−	0.0899668i
$609$		0			0
$610$	−17.5616			−0.711046
$611$	−0.157671	+	1.12599i	−0.00637868	+	0.0455529i
$612$		0			0
$613$	−10.7808	−	18.6729i	−0.435431	−	0.754189i	0.561899	−	0.827206i	$-0.310071\pi$
$613$	−10.7808	−	18.6729i	−0.435431	−	0.754189i	−0.997331	+	0.0730162i	$0.976738\pi$
$614$	−4.96543	−	8.60039i	−0.200389	−	0.347083i
$615$		0			0
$616$	−2.56155			−0.103208
$617$	11.5885	−	20.0719i	0.466537	−	0.808066i	−0.532732	−	0.846284i	$-0.678835\pi$
$617$	11.5885	−	20.0719i	0.466537	−	0.808066i	0.999269	+	0.0382179i	$0.0121681\pi$
$618$		0			0
$619$	2.06913			0.0831654			0.0415827	−	0.999135i	$-0.486760\pi$
$619$	2.06913			0.0831654			0.0415827	+	0.999135i	$0.486760\pi$
$620$		0			0
$621$		0			0
$622$	−10.9654	−	18.9927i	−0.439674	−	0.761537i
$623$	−3.43845			−0.137758
$624$		0			0
$625$	−5.63068			−0.225227
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$		0			0
$628$	0.657671	−	1.13912i	0.0262439	−	0.0454558i
$629$	0.300187			0.0119692
$630$		0			0
$631$	5.03457	−	8.72012i	0.200423	−	0.347143i	−0.748242	−	0.663426i	$-0.769102\pi$
$631$	5.03457	−	8.72012i	0.200423	−	0.347143i	0.948665	+	0.316283i	$0.102435\pi$
$632$	6.56155			0.261005
$633$		0			0
$634$	−6.21922	−	10.7720i	−0.246997	−	0.427811i
$635$	9.75379	+	16.8941i	0.387067	+	0.670420i
$636$		0			0
$637$	3.34233	−	1.35234i	0.132428	−	0.0535818i
$638$	−15.6847			−0.620962
$639$		0			0
$640$	−0.780776	−	1.35234i	−0.0308629	−	0.0534561i
$641$	4.21922	−	7.30791i	0.166649	−	0.288645i	−0.770590	−	0.637331i	$-0.780039\pi$
$641$	4.21922	−	7.30791i	0.166649	−	0.288645i	0.937240	+	0.348686i	$0.113372\pi$
$642$		0			0
$643$	−23.8423	+	41.2961i	−0.940250	+	1.62856i	−0.175256	+	0.984523i	$0.556075\pi$
$643$	−23.8423	+	41.2961i	−0.940250	+	1.62856i	−0.764994	+	0.644037i	$0.777258\pi$
$644$	−0.561553	+	0.972638i	−0.0221283	+	0.0383273i
$645$		0			0
$646$	0.157671	−	0.273094i	0.00620347	−	0.0107447i
$647$	−4.47301	−	7.74748i	−0.175852	−	0.304585i	0.764604	−	0.644501i	$-0.222935\pi$
$647$	−4.47301	−	7.74748i	−0.175852	−	0.304585i	−0.940456	+	0.339916i	$0.889601\pi$
$648$		0			0
$649$	−13.1231			−0.515127
$650$	8.56155	−	3.46410i	0.335812	−	0.135873i
$651$		0			0
$652$	−12.2462	−	21.2111i	−0.479599	−	0.830689i
$653$	10.2808	+	17.8068i	0.402318	+	0.696835i	0.994005	−	0.109333i	$-0.0348713\pi$
$653$	10.2808	+	17.8068i	0.402318	+	0.696835i	−0.591687	+	0.806168i	$0.701538\pi$
$654$		0			0
$655$	22.2462			0.869231
$656$	−5.62311	+	9.73950i	−0.219545	+	0.380264i
$657$		0			0
$658$	−0.315342			−0.0122933
$659$	1.03457	−	1.79192i	0.0403009	−	0.0698033i	−0.845171	−	0.534495i	$-0.820502\pi$
$659$	1.03457	−	1.79192i	0.0403009	−	0.0698033i	0.885472	+	0.464692i	$0.153835\pi$
$660$		0			0
$661$	10.0270	+	17.3673i	0.390005	+	0.675508i	0.992450	−	0.122653i	$-0.0391401\pi$
$661$	10.0270	+	17.3673i	0.390005	+	0.675508i	−0.602445	+	0.798160i	$0.705807\pi$
$662$	−19.3693			−0.752810
$663$		0			0
$664$	−5.12311			−0.198815
$665$	−2.00000	−	3.46410i	−0.0775567	−	0.134332i
$666$		0			0
$667$	−3.43845	+	5.95557i	−0.133137	+	0.230600i
$668$	−12.4924			−0.483346
$669$		0			0
$670$	−7.12311	+	12.3376i	−0.275190	+	0.476642i
$671$	−28.8078			−1.11211
$672$		0			0
$673$	1.37689	+	2.38485i	0.0530754	+	0.0919293i	0.891342	−	0.453331i	$-0.149764\pi$
$673$	1.37689	+	2.38485i	0.0530754	+	0.0919293i	−0.838267	+	0.545260i	$0.816431\pi$
$674$	−6.74621	−	11.6848i	−0.259854	−	0.450081i
$675$		0			0
$676$	9.34233	−	9.03996i	0.359320	−	0.347691i
$677$	24.7386			0.950783			0.475391	−	0.879774i	$-0.342306\pi$
$677$	24.7386			0.950783			0.475391	+	0.879774i	$0.342306\pi$
$678$		0			0
$679$	0.438447	+	0.759413i	0.0168261	+	0.0291436i
$680$	0.0961180	−	0.166481i	0.00368596	−	0.00638426i
$681$		0			0
$682$		0			0
$683$	20.2462	−	35.0675i	0.774700	−	1.34182i	−0.160263	−	0.987074i	$-0.551234\pi$
$683$	20.2462	−	35.0675i	0.774700	−	1.34182i	0.934963	−	0.354745i	$-0.115432\pi$
$684$		0			0
$685$	−9.71165	+	16.8211i	−0.371063	+	0.642700i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−8.00000			−0.304997
$689$	3.50000	−	24.9950i	0.133339	−	0.952234i
$690$		0			0
$691$	16.4924	+	28.5657i	0.627401	+	1.08669i	0.988071	+	0.153997i	$0.0492148\pi$
$691$	16.4924	+	28.5657i	0.627401	+	1.08669i	−0.360670	+	0.932694i	$0.617452\pi$
$692$	−9.00000	−	15.5885i	−0.342129	−	0.592584i
$693$		0			0
$694$	15.0540			0.571441
$695$	−4.24621	+	7.35465i	−0.161068	+	0.278978i
$696$		0			0
$697$	−1.38447			−0.0524406
$698$	−9.00000	+	15.5885i	−0.340655	+	0.590032i
$699$		0			0
$700$	1.28078	+	2.21837i	0.0484088	+	0.0838465i
$701$	39.3002			1.48435			0.742174	−	0.670207i	$-0.233795\pi$
$701$	39.3002			1.48435			0.742174	+	0.670207i	$0.233795\pi$
$702$		0			0
$703$	6.24621			0.235580
$704$	−1.28078	−	2.21837i	−0.0482711	−	0.0836080i
$705$		0			0
$706$	16.9039	−	29.2784i	0.636186	−	1.10191i
$707$	5.80776			0.218423
$708$		0			0
$709$	19.1501	−	33.1689i	0.719197	−	1.24569i	−0.242122	−	0.970246i	$-0.577843\pi$
$709$	19.1501	−	33.1689i	0.719197	−	1.24569i	0.961318	−	0.275440i	$-0.0888234\pi$
$710$	17.7538			0.666288
$711$		0			0
$712$	−1.71922	−	2.97778i	−0.0644306	−	0.111597i
$713$		0			0
$714$		0			0
$715$	−13.3693	+	5.40938i	−0.499984	+	0.202299i
$716$	1.75379			0.0655422
$717$		0			0
$718$	0.876894	+	1.51883i	0.0327254	+	0.0566821i
$719$	0.403882	−	0.699544i	0.0150623	−	0.0260886i	−0.858396	−	0.512988i	$-0.828539\pi$
$719$	0.403882	−	0.699544i	0.0150623	−	0.0260886i	0.873458	+	0.486899i	$0.161872\pi$
$720$		0			0
$721$	−3.12311	+	5.40938i	−0.116311	+	0.201456i
$722$	−6.21922	+	10.7720i	−0.231456	+	0.400893i
$723$		0			0
$724$	−6.62311	+	11.4716i	−0.246146	+	0.426337i
$725$	7.84233	+	13.5833i	0.291257	+	0.504472i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	2.84233	+	2.21837i	0.105344	+	0.0822183i
$729$		0			0
$730$	1.90388	+	3.29762i	0.0704658	+	0.122050i
$731$	−0.492423	−	0.852901i	−0.0182129	−	0.0315457i
$732$		0			0
$733$	−28.8617			−1.06603			−0.533016	−	0.846105i	$-0.678942\pi$
$733$	−28.8617			−1.06603			−0.533016	+	0.846105i	$0.678942\pi$
$734$	6.80776	−	11.7914i	0.251279	−	0.435228i
$735$		0			0
$736$	−1.12311			−0.0413982
$737$	−11.6847	+	20.2384i	−0.430410	+	0.745492i
$738$		0			0
$739$	−7.68466	−	13.3102i	−0.282685	−	0.489624i	0.689360	−	0.724419i	$-0.257892\pi$
$739$	−7.68466	−	13.3102i	−0.282685	−	0.489624i	−0.972045	+	0.234794i	$0.924558\pi$
$740$	3.80776			0.139976
$741$		0			0
$742$	7.00000			0.256978
$743$	−2.24621	−	3.89055i	−0.0824055	−	0.142731i	0.821877	−	0.569665i	$-0.192927\pi$
$743$	−2.24621	−	3.89055i	−0.0824055	−	0.142731i	−0.904283	+	0.426934i	$0.859594\pi$
$744$		0			0
$745$	12.1501	−	21.0446i	0.445145	−	0.771014i
$746$	3.06913			0.112369
$747$		0			0
$748$	0.157671	−	0.273094i	0.00576501	−	0.00998530i
$749$	−13.9309			−0.509023
$750$		0			0
$751$	20.4039	+	35.3406i	0.744548	+	1.28960i	0.950406	+	0.311013i	$0.100668\pi$
$751$	20.4039	+	35.3406i	0.744548	+	1.28960i	−0.205857	+	0.978582i	$0.565998\pi$
$752$	−0.157671	−	0.273094i	−0.00574966	−	0.00995871i
$753$		0			0
$754$	17.4039	+	13.5833i	0.633812	+	0.494675i
$755$	34.2462			1.24635
$756$		0			0
$757$	−26.3693	−	45.6730i	−0.958409	−	1.66001i	−0.726366	−	0.687308i	$-0.758792\pi$
$757$	−26.3693	−	45.6730i	−0.958409	−	1.66001i	−0.232043	−	0.972706i	$-0.574541\pi$
$758$	18.8078	−	32.5760i	0.683129	−	1.18321i
$759$		0			0
$760$	2.00000	−	3.46410i	0.0725476	−	0.125656i
$761$	25.4924	−	44.1542i	0.924100	−	1.60059i	0.131097	−	0.991370i	$-0.458150\pi$
$761$	25.4924	−	44.1542i	0.924100	−	1.60059i	0.793003	−	0.609218i	$-0.208517\pi$
$762$		0			0
$763$	6.12311	−	10.6055i	0.221671	−	0.383946i
$764$	−2.56155	−	4.43674i	−0.0926737	−	0.160516i
$765$		0			0
$766$	−12.8078			−0.462763
$767$	14.5616	+	11.3649i	0.525787	+	0.410364i
$768$		0			0
$769$	−2.43845	−	4.22351i	−0.0879327	−	0.152304i	0.818704	−	0.574215i	$-0.194693\pi$
$769$	−2.43845	−	4.22351i	−0.0879327	−	0.152304i	−0.906637	+	0.421911i	$0.861359\pi$
$770$	−2.00000	−	3.46410i	−0.0720750	−	0.124838i
$771$		0			0
$772$	0.123106			0.00443067
$773$	10.3693	−	17.9602i	0.372958	−	0.645983i	−0.617061	−	0.786915i	$-0.711677\pi$
$773$	10.3693	−	17.9602i	0.372958	−	0.645983i	0.990019	+	0.140933i	$0.0450101\pi$
$774$		0			0
$775$		0			0
$776$	−0.438447	+	0.759413i	−0.0157393	+	0.0272613i
$777$		0			0
$778$	2.65767	+	4.60322i	0.0952821	+	0.165033i
$779$	−28.8078			−1.03215
$780$		0			0
$781$	29.1231			1.04211
$782$	−0.0691303	−	0.119737i	−0.00247209	−	0.00428179i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	2.05398			0.0733095
$786$		0			0
$787$	0.0885405	−	0.153357i	0.00315613	−	0.00546657i	−0.864443	−	0.502731i	$-0.832329\pi$
$787$	0.0885405	−	0.153357i	0.00315613	−	0.00546657i	0.867599	+	0.497264i	$0.165662\pi$
$788$	−12.5616			−0.447487
$789$		0			0
$790$	5.12311	+	8.87348i	0.182272	+	0.315704i
$791$	0.780776	+	1.35234i	0.0277612	+	0.0480838i
$792$		0			0
$793$	31.9654	+	24.9483i	1.13513	+	0.885939i
$794$	−27.9309			−0.991229
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	25.2462	−	43.7277i	0.894267	−	1.54892i	0.0595571	−	0.998225i	$-0.481031\pi$
$797$	25.2462	−	43.7277i	0.894267	−	1.54892i	0.834710	−	0.550690i	$-0.185636\pi$
$798$		0			0
$799$	0.0194102	−	0.0336194i	0.000686682	−	0.00118937i
$800$	−1.28078	+	2.21837i	−0.0452823	+	0.0784312i
$801$		0			0
$802$	0.903882	−	1.56557i	0.0319172	−	0.0552822i
$803$	3.12311	+	5.40938i	0.110212	+	0.190893i
$804$		0			0
$805$	−1.75379			−0.0618129
$806$		0			0
$807$		0			0
$808$	2.90388	+	5.02967i	0.102158	+	0.176943i
$809$	4.46543	+	7.73436i	0.156996	+	0.271926i	0.933784	−	0.357837i	$-0.116486\pi$
$809$	4.46543	+	7.73436i	0.156996	+	0.271926i	−0.776788	+	0.629762i	$0.783152\pi$
$810$		0			0
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	−3.06155	+	5.30277i	−0.107439	+	0.186091i
$813$		0			0
$814$	6.24621			0.218930
$815$	19.1231	−	33.1222i	0.669853	−	1.16022i
$816$		0			0
$817$	−10.2462	−	17.7470i	−0.358470	−	0.620887i
$818$	11.5616			0.404240
$819$		0			0
$820$	−17.5616			−0.613276
$821$	13.6501	+	23.6427i	0.476392	+	0.825134i	0.999634	−	0.0270494i	$-0.00861116\pi$
$821$	13.6501	+	23.6427i	0.476392	+	0.825134i	−0.523243	+	0.852184i	$0.675278\pi$
$822$		0			0
$823$	19.1231	−	33.1222i	0.666590	−	1.15457i	−0.312262	−	0.949996i	$-0.601087\pi$
$823$	19.1231	−	33.1222i	0.666590	−	1.15457i	0.978852	−	0.204571i	$-0.0655799\pi$
$824$	−6.24621			−0.217597
$825$		0			0
$826$	−2.56155	+	4.43674i	−0.0891278	+	0.154374i
$827$	−34.2462			−1.19086			−0.595429	−	0.803408i	$-0.703018\pi$
$827$	−34.2462			−1.19086			−0.595429	+	0.803408i	$0.703018\pi$
$828$		0			0
$829$	0.184658	+	0.319838i	0.00641345	+	0.0111084i	0.869214	−	0.494436i	$-0.164625\pi$
$829$	0.184658	+	0.319838i	0.00641345	+	0.0111084i	−0.862801	+	0.505544i	$0.831292\pi$
$830$	−4.00000	−	6.92820i	−0.138842	−	0.240481i
$831$		0			0
$832$	−0.500000	+	3.57071i	−0.0173344	+	0.123792i
$833$	−0.123106			−0.00426536
$834$		0			0
$835$	−9.75379	−	16.8941i	−0.337544	−	0.584643i
$836$	3.28078	−	5.68247i	0.113468	−	0.196532i
$837$		0			0
$838$	−11.6847	+	20.2384i	−0.403640	+	0.699125i
$839$	9.12311	−	15.8017i	0.314965	−	0.545535i	−0.664465	−	0.747319i	$-0.731341\pi$
$839$	9.12311	−	15.8017i	0.314965	−	0.545535i	0.979430	+	0.201784i	$0.0646740\pi$
$840$		0			0
$841$	−4.24621	+	7.35465i	−0.146421	+	0.253609i
$842$	−11.1501	−	19.3125i	−0.384258	−	0.665554i
$843$		0			0
$844$	5.12311			0.176345
$845$	19.5194	+	5.57586i	0.671488	+	0.191815i
$846$		0			0
$847$	2.21922	+	3.84381i	0.0762534	+	0.132075i
$848$	3.50000	+	6.06218i	0.120190	+	0.208176i
$849$		0			0
$850$	−0.315342			−0.0108161
$851$	1.36932	−	2.37173i	0.0469396	−	0.0813017i
$852$		0			0
$853$	30.3693			1.03983			0.519913	−	0.854219i	$-0.325964\pi$
$853$	30.3693			1.03983			0.519913	+	0.854219i	$0.325964\pi$
$854$	−5.62311	+	9.73950i	−0.192419	+	0.333279i
$855$		0			0
$856$	−6.96543	−	12.0645i	−0.238074	−	0.412356i
$857$	−16.4384			−0.561527			−0.280763	−	0.959777i	$-0.590588\pi$
$857$	−16.4384			−0.561527			−0.280763	+	0.959777i	$0.590588\pi$
$858$		0			0
$859$	17.9309			0.611793			0.305897	−	0.952065i	$-0.401044\pi$
$859$	17.9309			0.611793			0.305897	+	0.952065i	$0.401044\pi$
$860$	−6.24621	−	10.8188i	−0.212994	−	0.368916i
$861$		0			0
$862$	−9.68466	+	16.7743i	−0.329861	+	0.571336i
$863$	−41.1231			−1.39985			−0.699923	−	0.714218i	$-0.746783\pi$
$863$	−41.1231			−1.39985			−0.699923	+	0.714218i	$0.746783\pi$
$864$		0			0
$865$	14.0540	−	24.3422i	0.477849	−	0.827660i
$866$	21.3153			0.724325
$867$		0			0
$868$		0			0
$869$	8.40388	+	14.5560i	0.285082	+	0.493777i
$870$		0			0
$871$	30.4924	−	12.3376i	1.03320	−	0.418043i
$872$	12.2462			0.414709
$873$		0			0
$874$	−1.43845	−	2.49146i	−0.0486562	−	0.0842750i
$875$	−5.90388	+	10.2258i	−0.199588	+	0.345696i
$876$		0			0
$877$	14.2732	−	24.7219i	0.481972	−	0.834799i	−0.517814	−	0.855493i	$-0.673254\pi$
$877$	14.2732	−	24.7219i	0.481972	−	0.834799i	0.999786	+	0.0206937i	$0.00658747\pi$
$878$	−13.1231	+	22.7299i	−0.442883	+	0.767096i
$879$		0			0
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	9.97301	+	17.2738i	0.335999	+	0.581968i	0.983676	−	0.179947i	$-0.0575927\pi$
$881$	9.97301	+	17.2738i	0.335999	+	0.581968i	−0.647677	+	0.761915i	$0.724259\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	−0.411460	+	0.166481i	−0.0138389	+	0.00559937i
$885$		0			0
$886$	13.5270	+	23.4294i	0.454448	+	0.787127i
$887$	−4.47301	−	7.74748i	−0.150189	−	0.260135i	0.781108	−	0.624396i	$-0.214655\pi$
$887$	−4.47301	−	7.74748i	−0.150189	−	0.260135i	−0.931297	+	0.364261i	$0.881322\pi$
$888$		0			0
$889$	12.4924			0.418982
$890$	2.68466	−	4.64996i	0.0899900	−	0.155867i
$891$		0			0
$892$	9.75379			0.326581
$893$	0.403882	−	0.699544i	0.0135154	−	0.0234094i
$894$		0			0
$895$	1.36932	+	2.37173i	0.0457712	+	0.0792781i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−6.63068			−0.221269
$899$		0			0
$900$		0			0
$901$	−0.430870	+	0.746288i	−0.0143544	+	0.0248625i
$902$	−28.8078			−0.959194
$903$		0			0
$904$	−0.780776	+	1.35234i	−0.0259682	+	0.0449783i
$905$	−20.6847			−0.687581
$906$		0			0
$907$	0.561553	+	0.972638i	0.0186461	+	0.0322959i	0.875198	−	0.483765i	$-0.160731\pi$
$907$	0.561553	+	0.972638i	0.0186461	+	0.0322959i	−0.856552	+	0.516061i	$0.827398\pi$
$908$	−5.43845	−	9.41967i	−0.180481	−	0.312603i
$909$		0			0
$910$	−0.780776	+	5.57586i	−0.0258825	+	0.184838i
$911$	−13.6155			−0.451103			−0.225551	−	0.974231i	$-0.572418\pi$
$911$	−13.6155			−0.451103			−0.225551	+	0.974231i	$0.572418\pi$
$912$		0			0
$913$	−6.56155	−	11.3649i	−0.217156	−	0.376125i
$914$	14.4654	−	25.0549i	0.478474	−	0.828741i
$915$		0			0
$916$	−8.52699	+	14.7692i	−0.281740	+	0.487987i
$917$	7.12311	−	12.3376i	0.235226	−	0.407423i
$918$		0			0
$919$	22.9654	−	39.7773i	0.757560	−	1.31213i	−0.186532	−	0.982449i	$-0.559725\pi$
$919$	22.9654	−	39.7773i	0.757560	−	1.31213i	0.944092	−	0.329683i	$-0.106942\pi$
$920$	−0.876894	−	1.51883i	−0.0289104	−	0.0500742i
$921$		0			0
$922$	6.05398			0.199377
$923$	−32.3153	−	25.2213i	−1.06367	−	0.830171i
$924$		0			0
$925$	−3.12311	−	5.40938i	−0.102687	−	0.177859i
$926$	6.15767	+	10.6654i	0.202354	+	0.350487i
$927$		0			0
$928$	−6.12311			−0.201001
$929$	−1.37689	+	2.38485i	−0.0451744	+	0.0782444i	−0.887729	−	0.460367i	$-0.847718\pi$
$929$	−1.37689	+	2.38485i	−0.0451744	+	0.0782444i	0.842554	+	0.538612i	$0.181051\pi$
$930$		0			0
$931$	−2.56155			−0.0839515
$932$	0.684658	−	1.18586i	0.0224267	−	0.0388442i
$933$		0			0
$934$	18.4924	+	32.0298i	0.605091	+	1.04805i
$935$	0.492423			0.0161039
$936$		0			0
$937$	−34.4384			−1.12506			−0.562528	−	0.826779i	$-0.690171\pi$
$937$	−34.4384			−1.12506			−0.562528	+	0.826779i	$0.690171\pi$
$938$	4.56155	+	7.90084i	0.148940	+	0.257972i
$939$		0			0
$940$	0.246211	−	0.426450i	0.00803053	−	0.0139093i
$941$	10.6307			0.346550			0.173275	−	0.984873i	$-0.444565\pi$
$941$	10.6307			0.346550			0.173275	+	0.984873i	$0.444565\pi$
$942$		0			0
$943$	−6.31534	+	10.9385i	−0.205656	+	0.356206i
$944$	−5.12311			−0.166743
$945$		0			0
$946$	−10.2462	−	17.7470i	−0.333133	−	0.577003i
$947$	29.2808	+	50.7158i	0.951497	+	1.64804i	0.742187	+	0.670192i	$0.233788\pi$
$947$	29.2808	+	50.7158i	0.951497	+	1.64804i	0.209310	+	0.977849i	$0.432878\pi$
$948$		0			0
$949$	1.21922	−	8.70700i	0.0395777	−	0.282641i
$950$	−6.56155			−0.212885
$951$		0			0
$952$	−0.0615528	−	0.106613i	−0.00199494	−	0.00345533i
$953$	6.43845	−	11.1517i	0.208562	−	0.361240i	−0.742700	−	0.669624i	$-0.766455\pi$
$953$	6.43845	−	11.1517i	0.208562	−	0.361240i	0.951262	+	0.308385i	$0.0997884\pi$
$954$		0			0
$955$	4.00000	−	6.92820i	0.129437	−	0.224191i
$956$	9.68466	−	16.7743i	0.313224	−	0.542520i
$957$		0			0
$958$	0.965435	−	1.67218i	0.0311918	−	0.0540258i
$959$	6.21922	+	10.7720i	0.200829	+	0.347846i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−6.93087	−	5.40938i	−0.223460	−	0.174405i
$963$		0			0
$964$	0.0961180	+	0.166481i	0.00309575	+	0.00536200i
$965$	0.0961180	+	0.166481i	0.00309415	+	0.00535922i
$966$		0			0
$967$	−28.4924			−0.916255			−0.458127	−	0.888887i	$-0.651480\pi$
$967$	−28.4924			−0.916255			−0.458127	+	0.888887i	$0.651480\pi$
$968$	−2.21922	+	3.84381i	−0.0713285	+	0.123545i
$969$		0			0
$970$	−1.36932			−0.0439661
$971$	20.8078	−	36.0401i	0.667753	−	1.15658i	−0.310778	−	0.950482i	$-0.600590\pi$
$971$	20.8078	−	36.0401i	0.667753	−	1.15658i	0.978531	−	0.206100i	$-0.0660771\pi$
$972$		0			0
$973$	2.71922	+	4.70983i	0.0871743	+	0.150990i
$974$	−23.6847			−0.758905
$975$		0			0
$976$	−11.2462			−0.359982
$977$	−20.5885	−	35.6604i	−0.658686	−	1.14088i	−0.980956	−	0.194230i	$-0.937779\pi$
$977$	−20.5885	−	35.6604i	−0.658686	−	1.14088i	0.322270	−	0.946648i	$-0.395554\pi$
$978$		0			0
$979$	4.40388	−	7.62775i	0.140749	−	0.243784i
$980$	−1.56155			−0.0498820
$981$		0			0
$982$	8.24621	−	14.2829i	0.263147	−	0.455784i
$983$	−18.7386			−0.597670			−0.298835	−	0.954305i	$-0.596598\pi$
$983$	−18.7386			−0.597670			−0.298835	+	0.954305i	$0.596598\pi$
$984$		0			0
$985$	−9.80776	−	16.9875i	−0.312501	−	0.541268i
$986$	−0.376894	−	0.652800i	−0.0120028	−	0.0207894i
$987$		0			0
$988$	−8.56155	+	3.46410i	−0.272379	+	0.110208i
$989$	−8.98485			−0.285701
$990$		0			0
$991$	14.3348	+	24.8285i	0.455358	+	0.788704i	0.998709	−	0.0508022i	$-0.0161778\pi$
$991$	14.3348	+	24.8285i	0.455358	+	0.788704i	−0.543350	+	0.839506i	$0.682844\pi$
$992$		0			0
$993$		0			0
$994$	5.68466	−	9.84612i	0.180306	−	0.312300i
$995$	−12.4924	+	21.6375i	−0.396036	+	0.685955i
$996$		0			0
$997$	20.9924	−	36.3599i	0.664837	−	1.15153i	−0.314493	−	0.949260i	$-0.601834\pi$
$997$	20.9924	−	36.3599i	0.664837	−	1.15153i	0.979330	−	0.202271i	$-0.0648322\pi$
$998$	15.1231	+	26.1940i	0.478714	+	0.829156i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.y.757.1		4
3.2	odd	2		546.2.l.l.211.2	✓	4
13.9	even	3	inner	1638.2.r.y.1387.1		4
39.23	odd	6		7098.2.a.bi.1.1		2
39.29	odd	6		7098.2.a.bt.1.2		2
39.35	odd	6		546.2.l.l.295.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.l.211.2	✓	4	3.2	odd	2
546.2.l.l.295.2	yes	4	39.35	odd	6
1638.2.r.y.757.1		4	1.1	even	1	trivial
1638.2.r.y.1387.1		4	13.9	even	3	inner
7098.2.a.bi.1.1		2	39.23	odd	6
7098.2.a.bt.1.2		2	39.29	odd	6

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.56155 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.56155 q^{5} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.780776 - 1.35234i) q^{10} +(-1.28078 - 2.21837i) q^{11} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0615528 - 0.106613i) q^{17} +(1.28078 - 2.21837i) q^{19} +(0.780776 - 1.35234i) q^{20} +(1.28078 - 2.21837i) q^{22} +(-0.561553 - 0.972638i) q^{23} -2.56155 q^{25} +(-3.34233 + 1.35234i) q^{26} +(-0.500000 - 0.866025i) q^{28} +(-3.06155 - 5.30277i) q^{29} +(0.500000 - 0.866025i) q^{32} +0.123106 q^{34} +(0.780776 - 1.35234i) q^{35} +(1.21922 + 2.11176i) q^{37} +2.56155 q^{38} +1.56155 q^{40} +(-5.62311 - 9.73950i) q^{41} +(4.00000 - 6.92820i) q^{43} +2.56155 q^{44} +(0.561553 - 0.972638i) q^{46} +0.315342 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-1.28078 - 2.21837i) q^{50} +(-2.84233 - 2.21837i) q^{52} -7.00000 q^{53} +(2.00000 + 3.46410i) q^{55} +(0.500000 - 0.866025i) q^{56} +(3.06155 - 5.30277i) q^{58} +(2.56155 - 4.43674i) q^{59} +(5.62311 - 9.73950i) q^{61} +1.00000 q^{64} +(0.780776 - 5.57586i) q^{65} +(-4.56155 - 7.90084i) q^{67} +(0.0615528 + 0.106613i) q^{68} +1.56155 q^{70} +(-5.68466 + 9.84612i) q^{71} -2.43845 q^{73} +(-1.21922 + 2.11176i) q^{74} +(1.28078 + 2.21837i) q^{76} +2.56155 q^{77} -6.56155 q^{79} +(0.780776 + 1.35234i) q^{80} +(5.62311 - 9.73950i) q^{82} +5.12311 q^{83} +(-0.0961180 + 0.166481i) q^{85} +8.00000 q^{86} +(1.28078 + 2.21837i) q^{88} +(1.71922 + 2.97778i) q^{89} +(-2.84233 - 2.21837i) q^{91} +1.12311 q^{92} +(0.157671 + 0.273094i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(0.438447 - 0.759413i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 2 q^{7} - 4 q^{8} + q^{10} - q^{11} - 2 q^{13} - 4 q^{14} - 2 q^{16} - 8 q^{17} + q^{19} - q^{20} + q^{22} + 6 q^{23} - 2 q^{25} - q^{26} - 2 q^{28} - 4 q^{29} + 2 q^{32} - 16 q^{34} - q^{35} + 9 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} + 16 q^{43} + 2 q^{44} - 6 q^{46} + 26 q^{47} - 2 q^{49} - q^{50} + q^{52} - 28 q^{53} + 8 q^{55} + 2 q^{56} + 4 q^{58} + 2 q^{59} + 6 q^{61} + 4 q^{64} - q^{65} - 10 q^{67} - 8 q^{68} - 2 q^{70} + 2 q^{71} - 18 q^{73} - 9 q^{74} + q^{76} + 2 q^{77} - 18 q^{79} - q^{80} + 6 q^{82} + 4 q^{83} - 21 q^{85} + 32 q^{86} + q^{88} + 11 q^{89} + q^{91} - 12 q^{92} + 13 q^{94} - 8 q^{95} + 10 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 2 * q^7 - 4 * q^8 + q^10 - q^11 - 2 * q^13 - 4 * q^14 - 2 * q^16 - 8 * q^17 + q^19 - q^20 + q^22 + 6 * q^23 - 2 * q^25 - q^26 - 2 * q^28 - 4 * q^29 + 2 * q^32 - 16 * q^34 - q^35 + 9 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 + 16 * q^43 + 2 * q^44 - 6 * q^46 + 26 * q^47 - 2 * q^49 - q^50 + q^52 - 28 * q^53 + 8 * q^55 + 2 * q^56 + 4 * q^58 + 2 * q^59 + 6 * q^61 + 4 * q^64 - q^65 - 10 * q^67 - 8 * q^68 - 2 * q^70 + 2 * q^71 - 18 * q^73 - 9 * q^74 + q^76 + 2 * q^77 - 18 * q^79 - q^80 + 6 * q^82 + 4 * q^83 - 21 * q^85 + 32 * q^86 + q^88 + 11 * q^89 + q^91 - 12 * q^92 + 13 * q^94 - 8 * q^95 + 10 * q^97 + 2 * q^98

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