LMFDB - Embedded newform 1638.2.r.z.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			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	1638.757
Dual form			1638.2.r.z.1387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.561553 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.561553 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.280776 - 0.486319i) q^{10} +(-0.780776 - 1.35234i) q^{11} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(2.34233 - 4.05703i) q^{19} +(0.280776 - 0.486319i) q^{20} +(0.780776 - 1.35234i) q^{22} +(-0.438447 - 0.759413i) q^{23} -4.68466 q^{25} +(2.84233 - 2.21837i) q^{26} +(0.500000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} -3.12311 q^{31} +(0.500000 - 0.866025i) q^{32} -5.00000 q^{34} +(-0.280776 + 0.486319i) q^{35} +(-5.40388 - 9.35980i) q^{37} +4.68466 q^{38} +0.561553 q^{40} +(-2.06155 - 3.57071i) q^{41} +(5.56155 - 9.63289i) q^{43} +1.56155 q^{44} +(0.438447 - 0.759413i) q^{46} -4.68466 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.34233 - 4.05703i) q^{50} +(3.34233 + 1.35234i) q^{52} +12.1231 q^{53} +(0.438447 + 0.759413i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(2.43845 - 4.22351i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.56155 - 2.70469i) q^{62} +1.00000 q^{64} +(0.280776 + 2.00514i) q^{65} +(3.56155 + 6.16879i) q^{67} +(-2.50000 - 4.33013i) q^{68} -0.561553 q^{70} +(-2.00000 + 3.46410i) q^{71} -6.56155 q^{73} +(5.40388 - 9.35980i) q^{74} +(2.34233 + 4.05703i) q^{76} -1.56155 q^{77} +5.56155 q^{79} +(0.280776 + 0.486319i) q^{80} +(2.06155 - 3.57071i) q^{82} -6.24621 q^{83} +(1.40388 - 2.43160i) q^{85} +11.1231 q^{86} +(0.780776 + 1.35234i) q^{88} +(1.34233 + 2.32498i) q^{89} +(-3.34233 - 1.35234i) q^{91} +0.876894 q^{92} +(-2.34233 - 4.05703i) q^{94} +(-1.31534 + 2.27824i) q^{95} +(2.12311 - 3.67733i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8} + 3 q^{10} + q^{11} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 10 q^{17} - 3 q^{19} - 3 q^{20} - q^{22} - 10 q^{23} + 6 q^{25} - q^{26} + 2 q^{28} - 2 q^{29} + 4 q^{31} + 2 q^{32} - 20 q^{34} + 3 q^{35} - q^{37} - 6 q^{38} - 6 q^{40} + 14 q^{43} - 2 q^{44} + 10 q^{46} + 6 q^{47} - 2 q^{49} + 3 q^{50} + q^{52} + 32 q^{53} + 10 q^{55} - 2 q^{56} + 2 q^{58} + 18 q^{59} + 2 q^{61} + 2 q^{62} + 4 q^{64} - 3 q^{65} + 6 q^{67} - 10 q^{68} + 6 q^{70} - 8 q^{71} - 18 q^{73} + q^{74} - 3 q^{76} + 2 q^{77} + 14 q^{79} - 3 q^{80} + 8 q^{83} - 15 q^{85} + 28 q^{86} - q^{88} - 7 q^{89} - q^{91} + 20 q^{92} + 3 q^{94} - 30 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8 + 3 * q^10 + q^11 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 10 * q^17 - 3 * q^19 - 3 * q^20 - q^22 - 10 * q^23 + 6 * q^25 - q^26 + 2 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 - 20 * q^34 + 3 * q^35 - q^37 - 6 * q^38 - 6 * q^40 + 14 * q^43 - 2 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^49 + 3 * q^50 + q^52 + 32 * q^53 + 10 * q^55 - 2 * q^56 + 2 * q^58 + 18 * q^59 + 2 * q^61 + 2 * q^62 + 4 * q^64 - 3 * q^65 + 6 * q^67 - 10 * q^68 + 6 * q^70 - 8 * q^71 - 18 * q^73 + q^74 - 3 * q^76 + 2 * q^77 + 14 * q^79 - 3 * q^80 + 8 * q^83 - 15 * q^85 + 28 * q^86 - q^88 - 7 * q^89 - q^91 + 20 * q^92 + 3 * q^94 - 30 * q^95 - 8 * 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
$5$	−0.561553			−0.251134			−0.125567	−	0.992085i	$-0.540075\pi$
$5$	−0.561553			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$		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
$10$	−0.280776	−	0.486319i	−0.0887893	−	0.153788i
$11$	−0.780776	−	1.35234i	−0.235413	−	0.407747i	0.723980	−	0.689821i	$-0.242311\pi$
$11$	−0.780776	−	1.35234i	−0.235413	−	0.407747i	−0.959393	+	0.282074i	$0.908978\pi$
$12$		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
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	0.385499	+	0.922708i	$0.374029\pi$
$17$	−2.50000	+	4.33013i	−0.606339	+	1.05021i	−0.991838	+	0.127502i	$0.959304\pi$
$18$		0			0
$19$	2.34233	−	4.05703i	0.537367	−	0.930747i	−0.461678	−	0.887048i	$-0.652752\pi$
$19$	2.34233	−	4.05703i	0.537367	−	0.930747i	0.999045	−	0.0436994i	$-0.0139144\pi$
$20$	0.280776	−	0.486319i	0.0627835	−	0.108744i
$21$		0			0
$22$	0.780776	−	1.35234i	0.166462	−	0.288321i
$23$	−0.438447	−	0.759413i	−0.0914226	−	0.158349i	0.816687	−	0.577080i	$-0.195808\pi$
$23$	−0.438447	−	0.759413i	−0.0914226	−	0.158349i	−0.908110	+	0.418732i	$0.862475\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$	2.84233	−	2.21837i	0.557427	−	0.435058i
$27$		0			0
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	−3.12311			−0.560926			−0.280463	−	0.959865i	$-0.590488\pi$
$31$	−3.12311			−0.560926			−0.280463	+	0.959865i	$0.590488\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−5.00000			−0.857493
$35$	−0.280776	+	0.486319i	−0.0474599	+	0.0822029i
$36$		0			0
$37$	−5.40388	−	9.35980i	−0.888393	−	1.53874i	−0.841775	−	0.539829i	$-0.818489\pi$
$37$	−5.40388	−	9.35980i	−0.888393	−	1.53874i	−0.0466177	−	0.998913i	$-0.514844\pi$
$38$	4.68466			0.759952
$39$		0			0
$40$	0.561553			0.0887893
$41$	−2.06155	−	3.57071i	−0.321960	−	0.557652i	0.658932	−	0.752202i	$-0.271008\pi$
$41$	−2.06155	−	3.57071i	−0.321960	−	0.557652i	−0.980892	+	0.194551i	$0.937675\pi$
$42$		0			0
$43$	5.56155	−	9.63289i	0.848129	−	1.46900i	−0.0347472	−	0.999396i	$-0.511063\pi$
$43$	5.56155	−	9.63289i	0.848129	−	1.46900i	0.882876	−	0.469606i	$-0.155604\pi$
$44$	1.56155			0.235413
$45$		0			0
$46$	0.438447	−	0.759413i	0.0646455	−	0.111969i
$47$	−4.68466			−0.683328			−0.341664	−	0.939822i	$-0.610990\pi$
$47$	−4.68466			−0.683328			−0.341664	+	0.939822i	$0.610990\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.34233	−	4.05703i	−0.331255	−	0.573751i
$51$		0			0
$52$	3.34233	+	1.35234i	0.463498	+	0.187536i
$53$	12.1231			1.66524			0.832618	−	0.553847i	$-0.186841\pi$
$53$	12.1231			1.66524			0.832618	+	0.553847i	$0.186841\pi$
$54$		0			0
$55$	0.438447	+	0.759413i	0.0591202	+	0.102399i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	2.43845	−	4.22351i	0.317459	−	0.549855i	−0.662498	−	0.749063i	$-0.730504\pi$
$59$	2.43845	−	4.22351i	0.317459	−	0.549855i	0.979957	+	0.199209i	$0.0638372\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−1.56155	−	2.70469i	−0.198317	−	0.343496i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.280776	+	2.00514i	0.0348260	+	0.248708i
$66$		0			0
$67$	3.56155	+	6.16879i	0.435113	+	0.753638i	0.997305	−	0.0733691i	$-0.0233751\pi$
$67$	3.56155	+	6.16879i	0.435113	+	0.753638i	−0.562192	+	0.827007i	$0.690042\pi$
$68$	−2.50000	−	4.33013i	−0.303170	−	0.525105i
$69$		0			0
$70$	−0.561553			−0.0671184
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$		0			0
$73$	−6.56155			−0.767972			−0.383986	−	0.923339i	$-0.625449\pi$
$73$	−6.56155			−0.767972			−0.383986	+	0.923339i	$0.625449\pi$
$74$	5.40388	−	9.35980i	0.628189	−	1.08805i
$75$		0			0
$76$	2.34233	+	4.05703i	0.268684	+	0.465374i
$77$	−1.56155			−0.177955
$78$		0			0
$79$	5.56155			0.625724			0.312862	−	0.949799i	$-0.398712\pi$
$79$	5.56155			0.625724			0.312862	+	0.949799i	$0.398712\pi$
$80$	0.280776	+	0.486319i	0.0313918	+	0.0543721i
$81$		0			0
$82$	2.06155	−	3.57071i	0.227660	−	0.394319i
$83$	−6.24621			−0.685611			−0.342805	−	0.939406i	$-0.611377\pi$
$83$	−6.24621			−0.685611			−0.342805	+	0.939406i	$0.611377\pi$
$84$		0			0
$85$	1.40388	−	2.43160i	0.152272	−	0.263744i
$86$	11.1231			1.19944
$87$		0			0
$88$	0.780776	+	1.35234i	0.0832310	+	0.144160i
$89$	1.34233	+	2.32498i	0.142287	+	0.246448i	0.928357	−	0.371689i	$-0.121221\pi$
$89$	1.34233	+	2.32498i	0.142287	+	0.246448i	−0.786071	+	0.618137i	$0.787888\pi$
$90$		0			0
$91$	−3.34233	−	1.35234i	−0.350371	−	0.141764i
$92$	0.876894			0.0914226
$93$		0			0
$94$	−2.34233	−	4.05703i	−0.241593	−	0.418451i
$95$	−1.31534	+	2.27824i	−0.134951	+	0.233742i
$96$		0			0
$97$	2.12311	−	3.67733i	0.215569	−	0.373376i	−0.737880	−	0.674932i	$-0.764173\pi$
$97$	2.12311	−	3.67733i	0.215569	−	0.373376i	0.953448	+	0.301556i	$0.0975061\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$		0			0
$100$	2.34233	−	4.05703i	0.234233	−	0.405703i
$101$	−7.71922	−	13.3701i	−0.768091	−	1.33037i	−0.938597	−	0.345017i	$-0.887873\pi$
$101$	−7.71922	−	13.3701i	−0.768091	−	1.33037i	0.170505	−	0.985357i	$-0.445460\pi$
$102$		0			0
$103$	13.3693			1.31732			0.658659	−	0.752442i	$-0.271124\pi$
$103$	13.3693			1.31732			0.658659	+	0.752442i	$0.271124\pi$
$104$	0.500000	+	3.57071i	0.0490290	+	0.350137i
$105$		0			0
$106$	6.06155	+	10.4989i	0.588750	+	1.01975i
$107$	−6.78078	−	11.7446i	−0.655522	−	1.13540i	−0.981763	−	0.190111i	$-0.939115\pi$
$107$	−6.78078	−	11.7446i	−0.655522	−	1.13540i	0.326240	−	0.945287i	$-0.394218\pi$
$108$		0			0
$109$	9.12311			0.873835			0.436918	−	0.899502i	$-0.356070\pi$
$109$	9.12311			0.873835			0.436918	+	0.899502i	$0.356070\pi$
$110$	−0.438447	+	0.759413i	−0.0418043	+	0.0724072i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	−5.96543	+	10.3324i	−0.561181	+	0.971994i	0.436213	+	0.899844i	$0.356319\pi$
$113$	−5.96543	+	10.3324i	−0.561181	+	0.971994i	−0.997394	+	0.0721503i	$0.977014\pi$
$114$		0			0
$115$	0.246211	+	0.426450i	0.0229593	+	0.0397667i
$116$	1.00000			0.0928477
$117$		0			0
$118$	4.87689			0.448955
$119$	2.50000	+	4.33013i	0.229175	+	0.396942i
$120$		0			0
$121$	4.28078	−	7.41452i	0.389161	−	0.674047i
$122$	1.00000			0.0905357
$123$		0			0
$124$	1.56155	−	2.70469i	0.140232	−	0.242888i
$125$	5.43845			0.486430
$126$		0			0
$127$	7.12311	+	12.3376i	0.632073	+	1.09478i	0.987127	+	0.159937i	$0.0511292\pi$
$127$	7.12311	+	12.3376i	0.632073	+	1.09478i	−0.355054	+	0.934846i	$0.615537\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.59612	+	1.24573i	−0.139989	+	0.109258i
$131$	−16.4924			−1.44095			−0.720475	−	0.693481i	$-0.756076\pi$
$131$	−16.4924			−1.44095			−0.720475	+	0.693481i	$0.756076\pi$
$132$		0			0
$133$	−2.34233	−	4.05703i	−0.203106	−	0.351789i
$134$	−3.56155	+	6.16879i	−0.307671	+	0.532902i
$135$		0			0
$136$	2.50000	−	4.33013i	0.214373	−	0.371305i
$137$	7.40388	−	12.8239i	0.632556	−	1.09562i	−0.354471	−	0.935067i	$-0.615339\pi$
$137$	7.40388	−	12.8239i	0.632556	−	1.09562i	0.987027	−	0.160553i	$-0.0513276\pi$
$138$		0			0
$139$	−2.34233	+	4.05703i	−0.198674	+	0.344113i	−0.948099	−	0.317976i	$-0.896997\pi$
$139$	−2.34233	+	4.05703i	−0.198674	+	0.344113i	0.749425	+	0.662089i	$0.230330\pi$
$140$	−0.280776	−	0.486319i	−0.0237299	−	0.0411015i
$141$		0			0
$142$	−4.00000			−0.335673
$143$	−4.43845	+	3.46410i	−0.371162	+	0.289683i
$144$		0			0
$145$	0.280776	+	0.486319i	0.0233172	+	0.0403866i
$146$	−3.28078	−	5.68247i	−0.271519	−	0.470285i
$147$		0			0
$148$	10.8078			0.888393
$149$	1.40388	−	2.43160i	0.115010	−	0.199204i	−0.802773	−	0.596284i	$-0.796643\pi$
$149$	1.40388	−	2.43160i	0.115010	−	0.199204i	0.917784	+	0.397080i	$0.129976\pi$
$150$		0			0
$151$	−21.5616			−1.75465			−0.877327	−	0.479893i	$-0.840676\pi$
$151$	−21.5616			−1.75465			−0.877327	+	0.479893i	$0.840676\pi$
$152$	−2.34233	+	4.05703i	−0.189988	+	0.329069i
$153$		0			0
$154$	−0.780776	−	1.35234i	−0.0629168	−	0.108975i
$155$	1.75379			0.140868
$156$		0			0
$157$	14.8078			1.18179			0.590894	−	0.806749i	$-0.298775\pi$
$157$	14.8078			1.18179			0.590894	+	0.806749i	$0.298775\pi$
$158$	2.78078	+	4.81645i	0.221227	+	0.383176i
$159$		0			0
$160$	−0.280776	+	0.486319i	−0.0221973	+	0.0384469i
$161$	−0.876894			−0.0691090
$162$		0			0
$163$	−3.56155	+	6.16879i	−0.278962	+	0.483177i	−0.971127	−	0.238563i	$-0.923324\pi$
$163$	−3.56155	+	6.16879i	−0.278962	+	0.483177i	0.692165	+	0.721739i	$0.256657\pi$
$164$	4.12311			0.321960
$165$		0			0
$166$	−3.12311	−	5.40938i	−0.242400	−	0.419849i
$167$	−6.24621	−	10.8188i	−0.483346	−	0.837180i	0.516471	−	0.856305i	$-0.327245\pi$
$167$	−6.24621	−	10.8188i	−0.483346	−	0.837180i	−0.999817	+	0.0191244i	$0.993912\pi$
$168$		0			0
$169$	−12.5000	+	3.57071i	−0.961538	+	0.274670i
$170$	2.80776			0.215346
$171$		0			0
$172$	5.56155	+	9.63289i	0.424064	+	0.734501i
$173$	−6.56155	+	11.3649i	−0.498866	+	0.864061i	−0.999999	−	0.00130937i	$-0.999583\pi$
$173$	−6.56155	+	11.3649i	−0.498866	+	0.864061i	0.501134	+	0.865370i	$0.332917\pi$
$174$		0			0
$175$	−2.34233	+	4.05703i	−0.177063	+	0.306683i
$176$	−0.780776	+	1.35234i	−0.0588532	+	0.101937i
$177$		0			0
$178$	−1.34233	+	2.32498i	−0.100612	+	0.174265i
$179$	8.24621	+	14.2829i	0.616351	+	1.06755i	0.990146	+	0.140040i	$0.0447230\pi$
$179$	8.24621	+	14.2829i	0.616351	+	1.06755i	−0.373795	+	0.927511i	$0.621944\pi$
$180$		0			0
$181$	−3.24621			−0.241289			−0.120644	−	0.992696i	$-0.538496\pi$
$181$	−3.24621			−0.241289			−0.120644	+	0.992696i	$0.538496\pi$
$182$	−0.500000	−	3.57071i	−0.0370625	−	0.264679i
$183$		0			0
$184$	0.438447	+	0.759413i	0.0323228	+	0.0559847i
$185$	3.03457	+	5.25602i	0.223106	+	0.386430i
$186$		0			0
$187$	7.80776			0.570960
$188$	2.34233	−	4.05703i	0.170832	−	0.295890i
$189$		0			0
$190$	−2.63068			−0.190850
$191$	11.1231	−	19.2658i	0.804840	−	1.39402i	−0.111560	−	0.993758i	$-0.535585\pi$
$191$	11.1231	−	19.2658i	0.804840	−	1.39402i	0.916399	−	0.400265i	$-0.131082\pi$
$192$		0			0
$193$	−2.18466	−	3.78394i	−0.157255	−	0.272374i	0.776623	−	0.629966i	$-0.216931\pi$
$193$	−2.18466	−	3.78394i	−0.157255	−	0.272374i	−0.933878	+	0.357592i	$0.883598\pi$
$194$	4.24621			0.304860
$195$		0			0
$196$	1.00000			0.0714286
$197$	1.78078	+	3.08440i	0.126875	+	0.219754i	0.922464	−	0.386082i	$-0.126172\pi$
$197$	1.78078	+	3.08440i	0.126875	+	0.219754i	−0.795589	+	0.605836i	$0.792839\pi$
$198$		0			0
$199$	−11.8078	+	20.4516i	−0.837030	+	1.44978i	0.0553365	+	0.998468i	$0.482377\pi$
$199$	−11.8078	+	20.4516i	−0.837030	+	1.44978i	−0.892367	+	0.451311i	$0.850956\pi$
$200$	4.68466			0.331255
$201$		0			0
$202$	7.71922	−	13.3701i	0.543123	−	0.940716i
$203$	−1.00000			−0.0701862
$204$		0			0
$205$	1.15767	+	2.00514i	0.0808552	+	0.140045i
$206$	6.68466	+	11.5782i	0.465742	+	0.806689i
$207$		0			0
$208$	−2.84233	+	2.21837i	−0.197080	+	0.153816i
$209$	−7.31534			−0.506013
$210$		0			0
$211$	5.56155	+	9.63289i	0.382873	+	0.663156i	0.991472	−	0.130323i	$-0.0416013\pi$
$211$	5.56155	+	9.63289i	0.382873	+	0.663156i	−0.608599	+	0.793478i	$0.708268\pi$
$212$	−6.06155	+	10.4989i	−0.416309	+	0.721069i
$213$		0			0
$214$	6.78078	−	11.7446i	0.463524	−	0.802848i
$215$	−3.12311	+	5.40938i	−0.212994	+	0.368916i
$216$		0			0
$217$	−1.56155	+	2.70469i	−0.106005	+	0.183606i
$218$	4.56155	+	7.90084i	0.308947	+	0.535112i
$219$		0			0
$220$	−0.876894			−0.0591202
$221$	16.7116	+	6.76172i	1.12415	+	0.454843i
$222$		0			0
$223$	−8.24621	−	14.2829i	−0.552207	−	0.956451i	−0.998115	−	0.0613719i	$-0.980452\pi$
$223$	−8.24621	−	14.2829i	−0.552207	−	0.956451i	0.445908	−	0.895079i	$-0.352881\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$	−11.9309			−0.793630
$227$	2.43845	−	4.22351i	0.161845	−	0.280324i	−0.773685	−	0.633570i	$-0.781589\pi$
$227$	2.43845	−	4.22351i	0.161845	−	0.280324i	0.935531	+	0.353246i	$0.114922\pi$
$228$		0			0
$229$	2.19224			0.144867			0.0724335	−	0.997373i	$-0.476923\pi$
$229$	2.19224			0.144867			0.0724335	+	0.997373i	$0.476923\pi$
$230$	−0.246211	+	0.426450i	−0.0162347	+	0.0281193i
$231$		0			0
$232$	0.500000	+	0.866025i	0.0328266	+	0.0568574i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	2.63068			0.171607
$236$	2.43845	+	4.22351i	0.158729	+	0.274927i
$237$		0			0
$238$	−2.50000	+	4.33013i	−0.162051	+	0.280680i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$		0			0
$241$	−11.8423	+	20.5115i	−0.762831	+	1.32126i	0.178554	+	0.983930i	$0.442858\pi$
$241$	−11.8423	+	20.5115i	−0.762831	+	1.32126i	−0.941385	+	0.337333i	$0.890475\pi$
$242$	8.56155			0.550357
$243$		0			0
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	0.280776	+	0.486319i	0.0179381	+	0.0310698i
$246$		0			0
$247$	−15.6577	−	6.33527i	−0.996274	−	0.403104i
$248$	3.12311			0.198317
$249$		0			0
$250$	2.71922	+	4.70983i	0.171979	+	0.297876i
$251$	−12.2462	+	21.2111i	−0.772974	+	1.33883i	0.162952	+	0.986634i	$0.447898\pi$
$251$	−12.2462	+	21.2111i	−0.772974	+	1.33883i	−0.935926	+	0.352196i	$0.885435\pi$
$252$		0			0
$253$	−0.684658	+	1.18586i	−0.0430441	+	0.0745546i
$254$	−7.12311	+	12.3376i	−0.446943	+	0.774129i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.6231	−	27.0600i	−0.974543	−	1.68796i	−0.681436	−	0.731877i	$-0.738644\pi$
$257$	−15.6231	−	27.0600i	−0.974543	−	1.68796i	−0.293106	−	0.956080i	$-0.594689\pi$
$258$		0			0
$259$	−10.8078			−0.671562
$260$	−1.87689	−	0.759413i	−0.116400	−	0.0470968i
$261$		0			0
$262$	−8.24621	−	14.2829i	−0.509453	−	0.882398i
$263$	6.24621	+	10.8188i	0.385158	+	0.667113i	0.991791	−	0.127869i	$-0.0408137\pi$
$263$	6.24621	+	10.8188i	0.385158	+	0.667113i	−0.606633	+	0.794982i	$0.707480\pi$
$264$		0			0
$265$	−6.80776			−0.418198
$266$	2.34233	−	4.05703i	0.143617	−	0.248753i
$267$		0			0
$268$	−7.12311			−0.435113
$269$	−6.56155	+	11.3649i	−0.400065	+	0.692933i	−0.993733	−	0.111777i	$-0.964346\pi$
$269$	−6.56155	+	11.3649i	−0.400065	+	0.692933i	0.593668	+	0.804710i	$0.297679\pi$
$270$		0			0
$271$	−2.43845	−	4.22351i	−0.148125	−	0.256560i	0.782409	−	0.622764i	$-0.213990\pi$
$271$	−2.43845	−	4.22351i	−0.148125	−	0.256560i	−0.930535	+	0.366204i	$0.880657\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	14.8078			0.894570
$275$	3.65767	+	6.33527i	0.220566	+	0.382031i
$276$		0			0
$277$	−0.280776	+	0.486319i	−0.0168702	+	0.0292201i	−0.874337	−	0.485319i	$-0.838704\pi$
$277$	−0.280776	+	0.486319i	−0.0168702	+	0.0292201i	0.857467	+	0.514539i	$0.172037\pi$
$278$	−4.68466			−0.280967
$279$		0			0
$280$	0.280776	−	0.486319i	0.0167796	−	0.0290631i
$281$	12.8078			0.764047			0.382024	−	0.924153i	$-0.375227\pi$
$281$	12.8078			0.764047			0.382024	+	0.924153i	$0.375227\pi$
$282$		0			0
$283$	12.2462	+	21.2111i	0.727962	+	1.26087i	0.957743	+	0.287624i	$0.0928655\pi$
$283$	12.2462	+	21.2111i	0.727962	+	1.26087i	−0.229782	+	0.973242i	$0.573801\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$		0			0
$286$	−5.21922	−	2.11176i	−0.308619	−	0.124871i
$287$	−4.12311			−0.243379
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−0.280776	+	0.486319i	−0.0164878	+	0.0285576i
$291$		0			0
$292$	3.28078	−	5.68247i	0.191993	−	0.332541i
$293$	3.84233	−	6.65511i	0.224471	−	0.388796i	−0.731689	−	0.681638i	$-0.761268\pi$
$293$	3.84233	−	6.65511i	0.224471	−	0.388796i	0.956161	+	0.292843i	$0.0946012\pi$
$294$		0			0
$295$	−1.36932	+	2.37173i	−0.0797247	+	0.138087i
$296$	5.40388	+	9.35980i	0.314094	+	0.544027i
$297$		0			0
$298$	2.80776			0.162649
$299$	−2.49242	+	1.94528i	−0.144141	+	0.112498i
$300$		0			0
$301$	−5.56155	−	9.63289i	−0.320563	−	0.555231i
$302$	−10.7808	−	18.6729i	−0.620364	−	1.07450i
$303$		0			0
$304$	−4.68466			−0.268684
$305$	−0.280776	+	0.486319i	−0.0160772	+	0.0278465i
$306$		0			0
$307$	−5.06913			−0.289311			−0.144655	−	0.989482i	$-0.546207\pi$
$307$	−5.06913			−0.289311			−0.144655	+	0.989482i	$0.546207\pi$
$308$	0.780776	−	1.35234i	0.0444889	−	0.0770570i
$309$		0			0
$310$	0.876894	+	1.51883i	0.0498043	+	0.0862635i
$311$	−18.4384			−1.04555			−0.522774	−	0.852471i	$-0.675103\pi$
$311$	−18.4384			−1.04555			−0.522774	+	0.852471i	$0.675103\pi$
$312$		0			0
$313$	−13.6155			−0.769595			−0.384798	−	0.923001i	$-0.625729\pi$
$313$	−13.6155			−0.769595			−0.384798	+	0.923001i	$0.625729\pi$
$314$	7.40388	+	12.8239i	0.417825	+	0.723695i
$315$		0			0
$316$	−2.78078	+	4.81645i	−0.156431	+	0.270946i
$317$	7.43845			0.417785			0.208892	−	0.977939i	$-0.433014\pi$
$317$	7.43845			0.417785			0.208892	+	0.977939i	$0.433014\pi$
$318$		0			0
$319$	−0.780776	+	1.35234i	−0.0437151	+	0.0757168i
$320$	−0.561553			−0.0313918
$321$		0			0
$322$	−0.438447	−	0.759413i	−0.0244337	−	0.0423204i
$323$	11.7116	+	20.2852i	0.651653	+	1.12870i
$324$		0			0
$325$	2.34233	+	16.7276i	0.129929	+	0.927879i
$326$	−7.12311			−0.394512
$327$		0			0
$328$	2.06155	+	3.57071i	0.113830	+	0.197160i
$329$	−2.34233	+	4.05703i	−0.129137	+	0.223671i
$330$		0			0
$331$	5.31534	−	9.20644i	0.292158	−	0.506032i	−0.682162	−	0.731201i	$-0.738960\pi$
$331$	5.31534	−	9.20644i	0.292158	−	0.506032i	0.974320	+	0.225169i	$0.0722935\pi$
$332$	3.12311	−	5.40938i	0.171403	−	0.296878i
$333$		0			0
$334$	6.24621	−	10.8188i	0.341777	−	0.591976i
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$		0			0
$337$	3.49242			0.190244			0.0951222	−	0.995466i	$-0.469676\pi$
$337$	3.49242			0.190244			0.0951222	+	0.995466i	$0.469676\pi$
$338$	−9.34233	−	9.03996i	−0.508156	−	0.491709i
$339$		0			0
$340$	1.40388	+	2.43160i	0.0761362	+	0.131872i
$341$	2.43845	+	4.22351i	0.132049	+	0.228716i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−5.56155	+	9.63289i	−0.299859	+	0.519371i
$345$		0			0
$346$	−13.1231			−0.705503
$347$	−6.34233	+	10.9852i	−0.340474	+	0.589718i	−0.984521	−	0.175268i	$-0.943921\pi$
$347$	−6.34233	+	10.9852i	−0.340474	+	0.589718i	0.644047	+	0.764986i	$0.277254\pi$
$348$		0			0
$349$	−13.2462	−	22.9431i	−0.709053	−	1.22812i	−0.965209	−	0.261481i	$-0.915789\pi$
$349$	−13.2462	−	22.9431i	−0.709053	−	1.22812i	0.256155	−	0.966636i	$-0.417544\pi$
$350$	−4.68466			−0.250406
$351$		0			0
$352$	−1.56155			−0.0832310
$353$	5.40388	+	9.35980i	0.287620	+	0.498172i	0.973241	−	0.229786i	$-0.0738028\pi$
$353$	5.40388	+	9.35980i	0.287620	+	0.498172i	−0.685621	+	0.727958i	$0.740469\pi$
$354$		0			0
$355$	1.12311	−	1.94528i	0.0596083	−	0.103245i
$356$	−2.68466			−0.142287
$357$		0			0
$358$	−8.24621	+	14.2829i	−0.435826	+	0.754872i
$359$	29.3693			1.55005			0.775027	−	0.631929i	$-0.217736\pi$
$359$	29.3693			1.55005			0.775027	+	0.631929i	$0.217736\pi$
$360$		0			0
$361$	−1.47301	−	2.55133i	−0.0775270	−	0.134281i
$362$	−1.62311	−	2.81130i	−0.0853085	−	0.147759i
$363$		0			0
$364$	2.84233	−	2.21837i	0.148979	−	0.116274i
$365$	3.68466			0.192864
$366$		0			0
$367$	6.68466	+	11.5782i	0.348936	+	0.604375i	0.986061	−	0.166385i	$-0.0532096\pi$
$367$	6.68466	+	11.5782i	0.348936	+	0.604375i	−0.637124	+	0.770761i	$0.719876\pi$
$368$	−0.438447	+	0.759413i	−0.0228556	+	0.0395871i
$369$		0			0
$370$	−3.03457	+	5.25602i	−0.157760	+	0.273248i
$371$	6.06155	−	10.4989i	0.314700	−	0.545077i
$372$		0			0
$373$	−8.71922	+	15.1021i	−0.451464	+	0.781959i	−0.998477	−	0.0551651i	$-0.982431\pi$
$373$	−8.71922	+	15.1021i	−0.451464	+	0.781959i	0.547013	+	0.837124i	$0.315765\pi$
$374$	3.90388	+	6.76172i	0.201865	+	0.349640i
$375$		0			0
$376$	4.68466			0.241593
$377$	−2.84233	+	2.21837i	−0.146387	+	0.114252i
$378$		0			0
$379$	16.2462	+	28.1393i	0.834512	+	1.44542i	0.894427	+	0.447213i	$0.147584\pi$
$379$	16.2462	+	28.1393i	0.834512	+	1.44542i	−0.0599155	+	0.998203i	$0.519083\pi$
$380$	−1.31534	−	2.27824i	−0.0674756	−	0.116871i
$381$		0			0
$382$	22.2462			1.13822
$383$	10.3423	−	17.9134i	0.528468	−	0.915334i	−0.470981	−	0.882144i	$-0.656100\pi$
$383$	10.3423	−	17.9134i	0.528468	−	0.915334i	0.999449	−	0.0331905i	$-0.0105668\pi$
$384$		0			0
$385$	0.876894			0.0446907
$386$	2.18466	−	3.78394i	0.111196	−	0.192597i
$387$		0			0
$388$	2.12311	+	3.67733i	0.107784	+	0.186688i
$389$	−6.31534			−0.320201			−0.160100	−	0.987101i	$-0.551182\pi$
$389$	−6.31534			−0.320201			−0.160100	+	0.987101i	$0.551182\pi$
$390$		0			0
$391$	4.38447			0.221732
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	−1.78078	+	3.08440i	−0.0897142	+	0.155390i
$395$	−3.12311			−0.157140
$396$		0			0
$397$	5.34233	−	9.25319i	0.268124	−	0.464404i	−0.700254	−	0.713894i	$-0.746930\pi$
$397$	5.34233	−	9.25319i	0.268124	−	0.464404i	0.968377	+	0.249490i	$0.0802630\pi$
$398$	−23.6155			−1.18374
$399$		0			0
$400$	2.34233	+	4.05703i	0.117116	+	0.202852i
$401$	−15.0885	−	26.1341i	−0.753486	−	1.30508i	−0.946124	−	0.323806i	$-0.895038\pi$
$401$	−15.0885	−	26.1341i	−0.753486	−	1.30508i	0.192638	−	0.981270i	$-0.438296\pi$
$402$		0			0
$403$	1.56155	+	11.1517i	0.0777865	+	0.555507i
$404$	15.4384			0.768091
$405$		0			0
$406$	−0.500000	−	0.866025i	−0.0248146	−	0.0429801i
$407$	−8.43845	+	14.6158i	−0.418278	+	0.724479i
$408$		0			0
$409$	17.2808	−	29.9312i	0.854479	−	1.48000i	−0.0226477	−	0.999744i	$-0.507210\pi$
$409$	17.2808	−	29.9312i	0.854479	−	1.48000i	0.877127	−	0.480258i	$-0.159457\pi$
$410$	−1.15767	+	2.00514i	−0.0571733	+	0.0990270i
$411$		0			0
$412$	−6.68466	+	11.5782i	−0.329329	+	0.570415i
$413$	−2.43845	−	4.22351i	−0.119988	−	0.207826i
$414$		0			0
$415$	3.50758			0.172180
$416$	−3.34233	−	1.35234i	−0.163871	−	0.0663041i
$417$		0			0
$418$	−3.65767	−	6.33527i	−0.178903	−	0.309868i
$419$	−13.3693	−	23.1563i	−0.653134	−	1.13126i	−0.982358	−	0.187009i	$-0.940121\pi$
$419$	−13.3693	−	23.1563i	−0.653134	−	1.13126i	0.329224	−	0.944252i	$-0.393213\pi$
$420$		0			0
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	−5.56155	+	9.63289i	−0.270732	+	0.468922i
$423$		0			0
$424$	−12.1231			−0.588750
$425$	11.7116	−	20.2852i	0.568098	−	0.983975i
$426$		0			0
$427$	−0.500000	−	0.866025i	−0.0241967	−	0.0419099i
$428$	13.5616			0.655522
$429$		0			0
$430$	−6.24621			−0.301219
$431$	15.3693	+	26.6204i	0.740314	+	1.28226i	0.952352	+	0.305000i	$0.0986565\pi$
$431$	15.3693	+	26.6204i	0.740314	+	1.28226i	−0.212038	+	0.977261i	$0.568010\pi$
$432$		0			0
$433$	8.84233	−	15.3154i	0.424935	−	0.736009i	−0.571479	−	0.820617i	$-0.693630\pi$
$433$	8.84233	−	15.3154i	0.424935	−	0.736009i	0.996414	+	0.0846072i	$0.0269635\pi$
$434$	−3.12311			−0.149914
$435$		0			0
$436$	−4.56155	+	7.90084i	−0.218459	+	0.378382i
$437$	−4.10795			−0.196510
$438$		0			0
$439$	−2.24621	−	3.89055i	−0.107206	−	0.185686i	0.807431	−	0.589961i	$-0.200857\pi$
$439$	−2.24621	−	3.89055i	−0.107206	−	0.185686i	−0.914637	+	0.404275i	$0.867524\pi$
$440$	−0.438447	−	0.759413i	−0.0209021	−	0.0362036i
$441$		0			0
$442$	2.50000	+	17.8536i	0.118913	+	0.849208i
$443$	−27.4233			−1.30292			−0.651460	−	0.758683i	$-0.725843\pi$
$443$	−27.4233			−1.30292			−0.651460	+	0.758683i	$0.725843\pi$
$444$		0			0
$445$	−0.753789	−	1.30560i	−0.0357330	−	0.0618914i
$446$	8.24621	−	14.2829i	0.390469	−	0.676313i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	−0.571660	−	0.820491i	$-0.693700\pi$
$449$	9.00000	−	15.5885i	0.424736	−	0.735665i	0.996396	+	0.0848262i	$0.0270335\pi$
$450$		0			0
$451$	−3.21922	+	5.57586i	−0.151587	+	0.262557i
$452$	−5.96543	−	10.3324i	−0.280590	−	0.485997i
$453$		0			0
$454$	4.87689			0.228884
$455$	1.87689	+	0.759413i	0.0879902	+	0.0356018i
$456$		0			0
$457$	12.8423	+	22.2436i	0.600739	+	1.04051i	0.992709	+	0.120532i	$0.0384602\pi$
$457$	12.8423	+	22.2436i	0.600739	+	1.04051i	−0.391971	+	0.919978i	$0.628206\pi$
$458$	1.09612	+	1.89853i	0.0512182	+	0.0887126i
$459$		0			0
$460$	−0.492423			−0.0229593
$461$	−3.52699	+	6.10892i	−0.164268	+	0.284521i	−0.936395	−	0.350947i	$-0.885860\pi$
$461$	−3.52699	+	6.10892i	−0.164268	+	0.284521i	0.772127	+	0.635468i	$0.219193\pi$
$462$		0			0
$463$	0.684658			0.0318188			0.0159094	−	0.999873i	$-0.494936\pi$
$463$	0.684658			0.0318188			0.0159094	+	0.999873i	$0.494936\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	7.12311			0.328914
$470$	1.31534	+	2.27824i	0.0606722	+	0.105087i
$471$		0			0
$472$	−2.43845	+	4.22351i	−0.112239	+	0.194403i
$473$	−17.3693			−0.798642
$474$		0			0
$475$	−10.9730	+	19.0058i	−0.503476	+	0.872047i
$476$	−5.00000			−0.229175
$477$		0			0
$478$	−2.00000	−	3.46410i	−0.0914779	−	0.158444i
$479$	0.780776	+	1.35234i	0.0356746	+	0.0617902i	0.883311	−	0.468787i	$-0.155309\pi$
$479$	0.780776	+	1.35234i	0.0356746	+	0.0617902i	−0.847637	+	0.530577i	$0.821975\pi$
$480$		0			0
$481$	−30.7192	+	23.9756i	−1.40068	+	1.09319i
$482$	−23.6847			−1.07881
$483$		0			0
$484$	4.28078	+	7.41452i	0.194581	+	0.337024i
$485$	−1.19224	+	2.06501i	−0.0541366	+	0.0937674i
$486$		0			0
$487$	−5.65767	+	9.79937i	−0.256374	+	0.444052i	−0.965268	−	0.261263i	$-0.915861\pi$
$487$	−5.65767	+	9.79937i	−0.256374	+	0.444052i	0.708894	+	0.705315i	$0.249194\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$		0			0
$490$	−0.280776	+	0.486319i	−0.0126842	+	0.0219697i
$491$	−9.12311	−	15.8017i	−0.411720	−	0.713120i	0.583358	−	0.812215i	$-0.301738\pi$
$491$	−9.12311	−	15.8017i	−0.411720	−	0.713120i	−0.995078	+	0.0990952i	$0.968405\pi$
$492$		0			0
$493$	5.00000			0.225189
$494$	−2.34233	−	16.7276i	−0.105386	−	0.752609i
$495$		0			0
$496$	1.56155	+	2.70469i	0.0701158	+	0.121444i
$497$	2.00000	+	3.46410i	0.0897123	+	0.155386i
$498$		0			0
$499$	−2.63068			−0.117766			−0.0588828	−	0.998265i	$-0.518754\pi$
$499$	−2.63068			−0.117766			−0.0588828	+	0.998265i	$0.518754\pi$
$500$	−2.71922	+	4.70983i	−0.121607	+	0.210630i
$501$		0			0
$502$	−24.4924			−1.09315
$503$	−6.24621	+	10.8188i	−0.278505	+	0.482384i	−0.971013	−	0.239025i	$-0.923172\pi$
$503$	−6.24621	+	10.8188i	−0.278505	+	0.482384i	0.692509	+	0.721410i	$0.256505\pi$
$504$		0			0
$505$	4.33475	+	7.50801i	0.192894	+	0.334102i
$506$	−1.36932			−0.0608736
$507$		0			0
$508$	−14.2462			−0.632073
$509$	19.8423	+	34.3679i	0.879496	+	1.52333i	0.851895	+	0.523712i	$0.175453\pi$
$509$	19.8423	+	34.3679i	0.879496	+	1.52333i	0.0276006	+	0.999619i	$0.491213\pi$
$510$		0			0
$511$	−3.28078	+	5.68247i	−0.145133	+	0.251378i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.6231	−	27.0600i	0.689106	−	1.19357i
$515$	−7.50758			−0.330823
$516$		0			0
$517$	3.65767	+	6.33527i	0.160864	+	0.278625i
$518$	−5.40388	−	9.35980i	−0.237433	−	0.411246i
$519$		0			0
$520$	−0.280776	−	2.00514i	−0.0123129	−	0.0879314i
$521$	17.0000			0.744784			0.372392	−	0.928076i	$-0.378538\pi$
$521$	17.0000			0.744784			0.372392	+	0.928076i	$0.378538\pi$
$522$		0			0
$523$	−17.9039	−	31.0104i	−0.782882	−	1.35599i	−0.930256	−	0.366911i	$-0.880415\pi$
$523$	−17.9039	−	31.0104i	−0.782882	−	1.35599i	0.147374	−	0.989081i	$-0.452918\pi$
$524$	8.24621	−	14.2829i	0.360237	−	0.623949i
$525$		0			0
$526$	−6.24621	+	10.8188i	−0.272348	+	0.471720i
$527$	7.80776	−	13.5234i	0.340112	−	0.589090i
$528$		0			0
$529$	11.1155	−	19.2527i	0.483284	−	0.837072i
$530$	−3.40388	−	5.89570i	−0.147855	−	0.256093i
$531$		0			0
$532$	4.68466			0.203106
$533$	−11.7192	+	9.14657i	−0.507616	+	0.396182i
$534$		0			0
$535$	3.80776	+	6.59524i	0.164624	+	0.285137i
$536$	−3.56155	−	6.16879i	−0.153836	−	0.266451i
$537$		0			0
$538$	−13.1231			−0.565777
$539$	−0.780776	+	1.35234i	−0.0336304	+	0.0582496i
$540$		0			0
$541$	−2.56155			−0.110130			−0.0550649	−	0.998483i	$-0.517537\pi$
$541$	−2.56155			−0.110130			−0.0550649	+	0.998483i	$0.517537\pi$
$542$	2.43845	−	4.22351i	0.104740	−	0.181415i
$543$		0			0
$544$	2.50000	+	4.33013i	0.107187	+	0.185653i
$545$	−5.12311			−0.219450
$546$		0			0
$547$	26.7386			1.14326			0.571631	−	0.820511i	$-0.306311\pi$
$547$	26.7386			1.14326			0.571631	+	0.820511i	$0.306311\pi$
$548$	7.40388	+	12.8239i	0.316278	+	0.547810i
$549$		0			0
$550$	−3.65767	+	6.33527i	−0.155964	+	0.270137i
$551$	−4.68466			−0.199573
$552$		0			0
$553$	2.78078	−	4.81645i	0.118251	−	0.204816i
$554$	−0.561553			−0.0238581
$555$		0			0
$556$	−2.34233	−	4.05703i	−0.0993369	−	0.172057i
$557$	−13.8693	−	24.0224i	−0.587662	−	1.01786i	−0.994538	−	0.104377i	$-0.966715\pi$
$557$	−13.8693	−	24.0224i	−0.587662	−	1.01786i	0.406876	−	0.913483i	$-0.366618\pi$
$558$		0			0
$559$	−37.1771	−	15.0423i	−1.57242	−	0.636220i
$560$	0.561553			0.0237299
$561$		0			0
$562$	6.40388	+	11.0918i	0.270131	+	0.467881i
$563$	−12.6847	+	21.9705i	−0.534595	+	0.925945i	0.464588	+	0.885527i	$0.346202\pi$
$563$	−12.6847	+	21.9705i	−0.534595	+	0.925945i	−0.999183	+	0.0404182i	$0.987131\pi$
$564$		0			0
$565$	3.34991	−	5.80221i	0.140932	−	0.244101i
$566$	−12.2462	+	21.2111i	−0.514747	+	0.891567i
$567$		0			0
$568$	2.00000	−	3.46410i	0.0839181	−	0.145350i
$569$	−14.8078	−	25.6478i	−0.620774	−	1.07521i	−0.989342	−	0.145611i	$-0.953485\pi$
$569$	−14.8078	−	25.6478i	−0.620774	−	1.07521i	0.368568	−	0.929601i	$-0.379848\pi$
$570$		0			0
$571$	30.2462			1.26576			0.632882	−	0.774248i	$-0.281872\pi$
$571$	30.2462			1.26576			0.632882	+	0.774248i	$0.281872\pi$
$572$	−0.780776	−	5.57586i	−0.0326459	−	0.233138i
$573$		0			0
$574$	−2.06155	−	3.57071i	−0.0860476	−	0.149039i
$575$	2.05398	+	3.55759i	0.0856567	+	0.148362i
$576$		0			0
$577$	43.6847			1.81862			0.909308	−	0.416124i	$-0.136612\pi$
$577$	43.6847			1.81862			0.909308	+	0.416124i	$0.136612\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	−0.561553			−0.0233172
$581$	−3.12311	+	5.40938i	−0.129568	+	0.224419i
$582$		0			0
$583$	−9.46543	−	16.3946i	−0.392018	−	0.678996i
$584$	6.56155			0.271519
$585$		0			0
$586$	7.68466			0.317450
$587$	3.31534	+	5.74234i	0.136839	+	0.237012i	0.926298	−	0.376791i	$-0.122972\pi$
$587$	3.31534	+	5.74234i	0.136839	+	0.237012i	−0.789460	+	0.613803i	$0.789639\pi$
$588$		0			0
$589$	−7.31534	+	12.6705i	−0.301423	+	0.522081i
$590$	−2.73863			−0.112748
$591$		0			0
$592$	−5.40388	+	9.35980i	−0.222098	+	0.384685i
$593$	8.61553			0.353797			0.176899	−	0.984229i	$-0.443394\pi$
$593$	8.61553			0.353797			0.176899	+	0.984229i	$0.443394\pi$
$594$		0			0
$595$	−1.40388	−	2.43160i	−0.0575536	−	0.0996857i
$596$	1.40388	+	2.43160i	0.0575052	+	0.0996020i
$597$		0			0
$598$	−2.93087	−	1.18586i	−0.119852	−	0.0484936i
$599$	31.1231			1.27166			0.635828	−	0.771831i	$-0.280659\pi$
$599$	31.1231			1.27166			0.635828	+	0.771831i	$0.280659\pi$
$600$		0			0
$601$	−4.03457	−	6.98807i	−0.164573	−	0.285049i	0.771930	−	0.635707i	$-0.219291\pi$
$601$	−4.03457	−	6.98807i	−0.164573	−	0.285049i	−0.936504	+	0.350658i	$0.885958\pi$
$602$	5.56155	−	9.63289i	0.226672	−	0.392607i
$603$		0			0
$604$	10.7808	−	18.6729i	0.438664	−	0.759788i
$605$	−2.40388	+	4.16365i	−0.0977317	+	0.169276i
$606$		0			0
$607$	−6.43845	+	11.1517i	−0.261329	+	0.452634i	−0.966595	−	0.256308i	$-0.917494\pi$
$607$	−6.43845	+	11.1517i	−0.261329	+	0.452634i	0.705267	+	0.708942i	$0.250827\pi$
$608$	−2.34233	−	4.05703i	−0.0949940	−	0.164534i
$609$		0			0
$610$	−0.561553			−0.0227366
$611$	2.34233	+	16.7276i	0.0947605	+	0.676725i
$612$		0			0
$613$	8.65009	+	14.9824i	0.349374	+	0.605133i	0.986138	−	0.165925i	$-0.0530609\pi$
$613$	8.65009	+	14.9824i	0.349374	+	0.605133i	−0.636764	+	0.771058i	$0.719728\pi$
$614$	−2.53457	−	4.39000i	−0.102287	−	0.177166i
$615$		0			0
$616$	1.56155			0.0629168
$617$	17.2116	−	29.8114i	0.692915	−	1.20016i	−0.277964	−	0.960592i	$-0.589660\pi$
$617$	17.2116	−	29.8114i	0.692915	−	1.20016i	0.970879	−	0.239572i	$-0.0770071\pi$
$618$		0			0
$619$	16.6847			0.670613			0.335307	−	0.942109i	$-0.391160\pi$
$619$	16.6847			0.670613			0.335307	+	0.942109i	$0.391160\pi$
$620$	−0.876894	+	1.51883i	−0.0352169	+	0.0609975i
$621$		0			0
$622$	−9.21922	−	15.9682i	−0.369657	−	0.640265i
$623$	2.68466			0.107559
$624$		0			0
$625$	20.3693			0.814773
$626$	−6.80776	−	11.7914i	−0.272093	−	0.471279i
$627$		0			0
$628$	−7.40388	+	12.8239i	−0.295447	+	0.511729i
$629$	54.0388			2.15467
$630$		0			0
$631$	−21.9039	+	37.9386i	−0.871980	+	1.51031i	−0.0120342	+	0.999928i	$0.503831\pi$
$631$	−21.9039	+	37.9386i	−0.871980	+	1.51031i	−0.859946	+	0.510386i	$0.829503\pi$
$632$	−5.56155			−0.221227
$633$		0			0
$634$	3.71922	+	6.44188i	0.147709	+	0.255840i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	−2.84233	+	2.21837i	−0.112617	+	0.0878950i
$638$	−1.56155			−0.0618225
$639$		0			0
$640$	−0.280776	−	0.486319i	−0.0110987	−	0.0192234i
$641$	4.03457	−	6.98807i	0.159356	−	0.276012i	−0.775281	−	0.631617i	$-0.782392\pi$
$641$	4.03457	−	6.98807i	0.159356	−	0.276012i	0.934637	+	0.355604i	$0.115725\pi$
$642$		0			0
$643$	11.2192	−	19.4323i	0.442443	−	0.766334i	−0.555427	−	0.831565i	$-0.687445\pi$
$643$	11.2192	−	19.4323i	0.442443	−	0.766334i	0.997870	+	0.0652314i	$0.0207786\pi$
$644$	0.438447	−	0.759413i	0.0172772	−	0.0299251i
$645$		0			0
$646$	−11.7116	+	20.2852i	−0.460789	+	0.798109i
$647$	−0.0961180	−	0.166481i	−0.00377879	−	0.00654505i	0.864130	−	0.503269i	$-0.167869\pi$
$647$	−0.0961180	−	0.166481i	−0.00377879	−	0.00654505i	−0.867909	+	0.496724i	$0.834536\pi$
$648$		0			0
$649$	−7.61553			−0.298936
$650$	−13.3153	+	10.3923i	−0.522271	+	0.407620i
$651$		0			0
$652$	−3.56155	−	6.16879i	−0.139481	−	0.241588i
$653$	0.903882	+	1.56557i	0.0353716	+	0.0612655i	0.883169	−	0.469054i	$-0.155405\pi$
$653$	0.903882	+	1.56557i	0.0353716	+	0.0612655i	−0.847798	+	0.530320i	$0.822072\pi$
$654$		0			0
$655$	9.26137			0.361872
$656$	−2.06155	+	3.57071i	−0.0804901	+	0.139413i
$657$		0			0
$658$	−4.68466			−0.182627
$659$	−20.3423	+	35.2339i	−0.792425	+	1.37252i	0.132037	+	0.991245i	$0.457848\pi$
$659$	−20.3423	+	35.2339i	−0.792425	+	1.37252i	−0.924462	+	0.381275i	$0.875485\pi$
$660$		0			0
$661$	−5.40388	−	9.35980i	−0.210187	−	0.364054i	0.741586	−	0.670858i	$-0.234074\pi$
$661$	−5.40388	−	9.35980i	−0.210187	−	0.364054i	−0.951773	+	0.306804i	$0.900741\pi$
$662$	10.6307			0.413173
$663$		0			0
$664$	6.24621			0.242400
$665$	1.31534	+	2.27824i	0.0510068	+	0.0883463i
$666$		0			0
$667$	−0.438447	+	0.759413i	−0.0169767	+	0.0294046i
$668$	12.4924			0.483346
$669$		0			0
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	−1.56155			−0.0602831
$672$		0			0
$673$	−12.6231	−	21.8639i	−0.486585	−	0.842790i	0.513296	−	0.858212i	$-0.328424\pi$
$673$	−12.6231	−	21.8639i	−0.486585	−	0.842790i	−0.999881	+	0.0154217i	$0.995091\pi$
$674$	1.74621	+	3.02453i	0.0672615	+	0.116500i
$675$		0			0
$676$	3.15767	−	12.6107i	0.121449	−	0.485026i
$677$	49.6155			1.90688			0.953440	−	0.301583i	$-0.0975151\pi$
$677$	49.6155			1.90688			0.953440	+	0.301583i	$0.0975151\pi$
$678$		0			0
$679$	−2.12311	−	3.67733i	−0.0814773	−	0.141123i
$680$	−1.40388	+	2.43160i	−0.0538364	+	0.0932474i
$681$		0			0
$682$	−2.43845	+	4.22351i	−0.0933730	+	0.161727i
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$		0			0
$685$	−4.15767	+	7.20130i	−0.158856	+	0.275147i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$		0			0
$688$	−11.1231			−0.424064
$689$	−6.06155	−	43.2881i	−0.230927	−	1.64915i
$690$		0			0
$691$	−2.24621	−	3.89055i	−0.0854499	−	0.148004i	0.820133	−	0.572173i	$-0.193899\pi$
$691$	−2.24621	−	3.89055i	−0.0854499	−	0.148004i	−0.905583	+	0.424169i	$0.860566\pi$
$692$	−6.56155	−	11.3649i	−0.249433	−	0.432030i
$693$		0			0
$694$	−12.6847			−0.481503
$695$	1.31534	−	2.27824i	0.0498937	−	0.0864185i
$696$		0			0
$697$	20.6155			0.780869
$698$	13.2462	−	22.9431i	0.501376	−	0.868410i
$699$		0			0
$700$	−2.34233	−	4.05703i	−0.0885317	−	0.153341i
$701$	28.0540			1.05958			0.529792	−	0.848128i	$-0.322270\pi$
$701$	28.0540			1.05958			0.529792	+	0.848128i	$0.322270\pi$
$702$		0			0
$703$	−50.6307			−1.90957
$704$	−0.780776	−	1.35234i	−0.0294266	−	0.0509684i
$705$		0			0
$706$	−5.40388	+	9.35980i	−0.203378	+	0.352261i
$707$	−15.4384			−0.580623
$708$		0			0
$709$	16.6501	−	28.8388i	0.625307	−	1.08306i	−0.363174	−	0.931721i	$-0.618307\pi$
$709$	16.6501	−	28.8388i	0.625307	−	1.08306i	0.988481	−	0.151343i	$-0.0483597\pi$
$710$	2.24621			0.0842988
$711$		0			0
$712$	−1.34233	−	2.32498i	−0.0503059	−	0.0871324i
$713$	1.36932	+	2.37173i	0.0512813	+	0.0888219i
$714$		0			0
$715$	2.49242	−	1.94528i	0.0932113	−	0.0727492i
$716$	−16.4924			−0.616351
$717$		0			0
$718$	14.6847	+	25.4346i	0.548027	+	0.949210i
$719$	−3.46543	+	6.00231i	−0.129239	+	0.223848i	−0.923382	−	0.383883i	$-0.874587\pi$
$719$	−3.46543	+	6.00231i	−0.129239	+	0.223848i	0.794143	+	0.607731i	$0.207920\pi$
$720$		0			0
$721$	6.68466	−	11.5782i	0.248950	−	0.431194i
$722$	1.47301	−	2.55133i	0.0548198	−	0.0949508i
$723$		0			0
$724$	1.62311	−	2.81130i	0.0603222	−	0.104481i
$725$	2.34233	+	4.05703i	0.0869919	+	0.150674i
$726$		0			0
$727$	33.7538			1.25186			0.625929	−	0.779880i	$-0.284720\pi$
$727$	33.7538			1.25186			0.625929	+	0.779880i	$0.284720\pi$
$728$	3.34233	+	1.35234i	0.123875	+	0.0501212i
$729$		0			0
$730$	1.84233	+	3.19101i	0.0681877	+	0.118104i
$731$	27.8078	+	48.1645i	1.02851	+	1.78143i
$732$		0			0
$733$	−8.61553			−0.318222			−0.159111	−	0.987261i	$-0.550863\pi$
$733$	−8.61553			−0.318222			−0.159111	+	0.987261i	$0.550863\pi$
$734$	−6.68466	+	11.5782i	−0.246735	+	0.427358i
$735$		0			0
$736$	−0.876894			−0.0323228
$737$	5.56155	−	9.63289i	0.204862	−	0.354832i
$738$		0			0
$739$	−11.3153	−	19.5987i	−0.416242	−	0.720952i	0.579316	−	0.815103i	$-0.303320\pi$
$739$	−11.3153	−	19.5987i	−0.416242	−	0.720952i	−0.995558	+	0.0941513i	$0.969986\pi$
$740$	−6.06913			−0.223106
$741$		0			0
$742$	12.1231			0.445053
$743$	16.6847	+	28.8987i	0.612101	+	1.06019i	0.990886	+	0.134705i	$0.0430086\pi$
$743$	16.6847	+	28.8987i	0.612101	+	1.06019i	−0.378785	+	0.925485i	$0.623658\pi$
$744$		0			0
$745$	−0.788354	+	1.36547i	−0.0288831	+	0.0500269i
$746$	−17.4384			−0.638467
$747$		0			0
$748$	−3.90388	+	6.76172i	−0.142740	+	0.247233i
$749$	−13.5616			−0.495528
$750$		0			0
$751$	−9.90388	−	17.1540i	−0.361398	−	0.625959i	0.626793	−	0.779186i	$-0.284367\pi$
$751$	−9.90388	−	17.1540i	−0.361398	−	0.625959i	−0.988191	+	0.153226i	$0.951034\pi$
$752$	2.34233	+	4.05703i	0.0854160	+	0.147945i
$753$		0			0
$754$	−3.34233	−	1.35234i	−0.121720	−	0.0492495i
$755$	12.1080			0.440653
$756$		0			0
$757$	−0.561553	−	0.972638i	−0.0204100	−	0.0353511i	0.855640	−	0.517571i	$-0.173164\pi$
$757$	−0.561553	−	0.972638i	−0.0204100	−	0.0353511i	−0.876050	+	0.482220i	$0.839830\pi$
$758$	−16.2462	+	28.1393i	−0.590089	+	1.02206i
$759$		0			0
$760$	1.31534	−	2.27824i	0.0477125	−	0.0826404i
$761$	−4.75379	+	8.23380i	−0.172325	+	0.298475i	−0.939232	−	0.343283i	$-0.888461\pi$
$761$	−4.75379	+	8.23380i	−0.172325	+	0.298475i	0.766907	+	0.641758i	$0.221795\pi$
$762$		0			0
$763$	4.56155	−	7.90084i	0.165139	−	0.286030i
$764$	11.1231	+	19.2658i	0.402420	+	0.697012i
$765$		0			0
$766$	20.6847			0.747367
$767$	−16.3002	−	6.59524i	−0.588566	−	0.238140i
$768$		0			0
$769$	−21.4924	−	37.2260i	−0.775037	−	1.34240i	−0.934774	−	0.355243i	$-0.884398\pi$
$769$	−21.4924	−	37.2260i	−0.775037	−	1.34240i	0.159737	−	0.987160i	$-0.448935\pi$
$770$	0.438447	+	0.759413i	0.0158005	+	0.0273673i
$771$		0			0
$772$	4.36932			0.157255
$773$	−3.24621	+	5.62260i	−0.116758	+	0.202231i	−0.918481	−	0.395465i	$-0.870584\pi$
$773$	−3.24621	+	5.62260i	−0.116758	+	0.202231i	0.801723	+	0.597696i	$0.203917\pi$
$774$		0			0
$775$	14.6307			0.525550
$776$	−2.12311	+	3.67733i	−0.0762151	+	0.132008i
$777$		0			0
$778$	−3.15767	−	5.46925i	−0.113208	−	0.196082i
$779$	−19.3153			−0.692044
$780$		0			0
$781$	6.24621			0.223507
$782$	2.19224	+	3.79706i	0.0783942	+	0.135783i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−8.31534			−0.296787
$786$		0			0
$787$	9.90388	−	17.1540i	0.353035	−	0.611475i	−0.633744	−	0.773543i	$-0.718483\pi$
$787$	9.90388	−	17.1540i	0.353035	−	0.611475i	0.986780	+	0.162067i	$0.0518162\pi$
$788$	−3.56155			−0.126875
$789$		0			0
$790$	−1.56155	−	2.70469i	−0.0555576	−	0.0962285i
$791$	5.96543	+	10.3324i	0.212106	+	0.367379i
$792$		0			0
$793$	−3.34233	−	1.35234i	−0.118690	−	0.0480232i
$794$	10.6847			0.379184
$795$		0			0
$796$	−11.8078	−	20.4516i	−0.418515	−	0.724889i
$797$	25.0540	−	43.3948i	0.887457	−	1.53712i	0.0445863	−	0.999006i	$-0.485803\pi$
$797$	25.0540	−	43.3948i	0.887457	−	1.53712i	0.842871	−	0.538116i	$-0.180864\pi$
$798$		0			0
$799$	11.7116	−	20.2852i	0.414328	−	0.717638i
$800$	−2.34233	+	4.05703i	−0.0828138	+	0.143438i
$801$		0			0
$802$	15.0885	−	26.1341i	0.532795	−	0.922828i
$803$	5.12311	+	8.87348i	0.180790	+	0.313138i
$804$		0			0
$805$	0.492423			0.0173556
$806$	−8.87689	+	6.92820i	−0.312675	+	0.244036i
$807$		0			0
$808$	7.71922	+	13.3701i	0.271561	+	0.470358i
$809$	8.96543	+	15.5286i	0.315208	+	0.545956i	0.979482	−	0.201533i	$-0.0645924\pi$
$809$	8.96543	+	15.5286i	0.315208	+	0.545956i	−0.664274	+	0.747489i	$0.731259\pi$
$810$		0			0
$811$	22.2462			0.781170			0.390585	−	0.920567i	$-0.372273\pi$
$811$	22.2462			0.781170			0.390585	+	0.920567i	$0.372273\pi$
$812$	0.500000	−	0.866025i	0.0175466	−	0.0303915i
$813$		0			0
$814$	−16.8769			−0.591535
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−26.0540	−	45.1268i	−0.911513	−	1.57879i
$818$	34.5616			1.20842
$819$		0			0
$820$	−2.31534			−0.0808552
$821$	−20.4654	−	35.4472i	−0.714249	−	1.23711i	−0.963249	−	0.268611i	$-0.913435\pi$
$821$	−20.4654	−	35.4472i	−0.714249	−	1.23711i	0.249000	−	0.968503i	$-0.419898\pi$
$822$		0			0
$823$	1.12311	−	1.94528i	0.0391490	−	0.0678081i	−0.845787	−	0.533521i	$-0.820869\pi$
$823$	1.12311	−	1.94528i	0.0391490	−	0.0678081i	0.884936	+	0.465713i	$0.154202\pi$
$824$	−13.3693			−0.465742
$825$		0			0
$826$	2.43845	−	4.22351i	0.0848444	−	0.146955i
$827$	44.4924			1.54715			0.773577	−	0.633703i	$-0.218466\pi$
$827$	44.4924			1.54715			0.773577	+	0.633703i	$0.218466\pi$
$828$		0			0
$829$	22.5540	+	39.0646i	0.783332	+	1.35677i	0.929991	+	0.367584i	$0.119815\pi$
$829$	22.5540	+	39.0646i	0.783332	+	1.35677i	−0.146659	+	0.989187i	$0.546852\pi$
$830$	1.75379	+	3.03765i	0.0608749	+	0.105438i
$831$		0			0
$832$	−0.500000	−	3.57071i	−0.0173344	−	0.123792i
$833$	5.00000			0.173240
$834$		0			0
$835$	3.50758	+	6.07530i	0.121385	+	0.210245i
$836$	3.65767	−	6.33527i	0.126503	−	0.219110i
$837$		0			0
$838$	13.3693	−	23.1563i	0.461835	−	0.799922i
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	−0.788680	−	0.614804i	$-0.789235\pi$
$839$	4.00000	−	6.92820i	0.138095	−	0.239188i	0.926776	+	0.375615i	$0.122569\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	6.28078	+	10.8786i	0.216450	+	0.374902i
$843$		0			0
$844$	−11.1231			−0.382873
$845$	7.01941	−	2.00514i	0.241475	−	0.0689791i
$846$		0			0
$847$	−4.28078	−	7.41452i	−0.147089	−	0.254766i
$848$	−6.06155	−	10.4989i	−0.208155	−	0.360534i
$849$		0			0
$850$	23.4233			0.803412
$851$	−4.73863	+	8.20755i	−0.162438	+	0.281351i
$852$		0			0
$853$	24.3693			0.834390			0.417195	−	0.908817i	$-0.363013\pi$
$853$	24.3693			0.834390			0.417195	+	0.908817i	$0.363013\pi$
$854$	0.500000	−	0.866025i	0.0171096	−	0.0296348i
$855$		0			0
$856$	6.78078	+	11.7446i	0.231762	+	0.401424i
$857$	−31.3002			−1.06919			−0.534597	−	0.845107i	$-0.679537\pi$
$857$	−31.3002			−1.06919			−0.534597	+	0.845107i	$0.679537\pi$
$858$		0			0
$859$	−16.1922			−0.552472			−0.276236	−	0.961090i	$-0.589087\pi$
$859$	−16.1922			−0.552472			−0.276236	+	0.961090i	$0.589087\pi$
$860$	−3.12311	−	5.40938i	−0.106497	−	0.184458i
$861$		0			0
$862$	−15.3693	+	26.6204i	−0.523481	+	0.906696i
$863$	48.1080			1.63761			0.818807	−	0.574069i	$-0.194636\pi$
$863$	48.1080			1.63761			0.818807	+	0.574069i	$0.194636\pi$
$864$		0			0
$865$	3.68466	−	6.38202i	0.125282	−	0.216995i
$866$	17.6847			0.600949
$867$		0			0
$868$	−1.56155	−	2.70469i	−0.0530026	−	0.0918031i
$869$	−4.34233	−	7.52113i	−0.147303	−	0.255137i
$870$		0			0
$871$	20.2462	−	15.8017i	0.686017	−	0.535420i
$872$	−9.12311			−0.308947
$873$		0			0
$874$	−2.05398	−	3.55759i	−0.0694768	−	0.120337i
$875$	2.71922	−	4.70983i	0.0919265	−	0.159221i
$876$		0			0
$877$	22.6501	−	39.2311i	0.764839	−	1.32474i	−0.175492	−	0.984481i	$-0.556152\pi$
$877$	22.6501	−	39.2311i	0.764839	−	1.32474i	0.940331	−	0.340260i	$-0.110515\pi$
$878$	2.24621	−	3.89055i	0.0758060	−	0.131300i
$879$		0			0
$880$	0.438447	−	0.759413i	0.0147801	−	0.0255998i
$881$	0.911460	+	1.57869i	0.0307079	+	0.0531876i	0.880971	−	0.473170i	$-0.156891\pi$
$881$	0.911460	+	1.57869i	0.0307079	+	0.0531876i	−0.850263	+	0.526358i	$0.823557\pi$
$882$		0			0
$883$	8.87689			0.298731			0.149366	−	0.988782i	$-0.452277\pi$
$883$	8.87689			0.298731			0.149366	+	0.988782i	$0.452277\pi$
$884$	−14.2116	+	11.0918i	−0.477989	+	0.373059i
$885$		0			0
$886$	−13.7116	−	23.7493i	−0.460652	−	0.797872i
$887$	4.78078	+	8.28055i	0.160523	+	0.278034i	0.935056	−	0.354499i	$-0.115349\pi$
$887$	4.78078	+	8.28055i	0.160523	+	0.278034i	−0.774534	+	0.632533i	$0.782015\pi$
$888$		0			0
$889$	14.2462			0.477803
$890$	0.753789	−	1.30560i	0.0252671	−	0.0437638i
$891$		0			0
$892$	16.4924			0.552207
$893$	−10.9730	+	19.0058i	−0.367198	+	0.636005i
$894$		0			0
$895$	−4.63068	−	8.02058i	−0.154787	−	0.268098i
$896$	1.00000			0.0334077
$897$		0			0
$898$	18.0000			0.600668
$899$	1.56155	+	2.70469i	0.0520807	+	0.0902064i
$900$		0			0
$901$	−30.3078	+	52.4946i	−1.00970	+	1.74885i
$902$	−6.43845			−0.214377
$903$		0			0
$904$	5.96543	−	10.3324i	0.198407	−	0.343652i
$905$	1.82292			0.0605959
$906$		0			0
$907$	−15.5616	−	26.9534i	−0.516713	−	0.894973i	−0.999812	−	0.0194071i	$-0.993822\pi$
$907$	−15.5616	−	26.9534i	−0.516713	−	0.894973i	0.483099	−	0.875566i	$-0.339511\pi$
$908$	2.43845	+	4.22351i	0.0809227	+	0.140162i
$909$		0			0
$910$	0.280776	+	2.00514i	0.00930765	+	0.0664699i
$911$	54.7386			1.81357			0.906786	−	0.421591i	$-0.138528\pi$
$911$	54.7386			1.81357			0.906786	+	0.421591i	$0.138528\pi$
$912$		0			0
$913$	4.87689	+	8.44703i	0.161402	+	0.279556i
$914$	−12.8423	+	22.2436i	−0.424786	+	0.735752i
$915$		0			0
$916$	−1.09612	+	1.89853i	−0.0362168	+	0.0627293i
$917$	−8.24621	+	14.2829i	−0.272314	+	0.471661i
$918$		0			0
$919$	−1.21922	+	2.11176i	−0.0402185	+	0.0696604i	−0.885434	−	0.464765i	$-0.846139\pi$
$919$	−1.21922	+	2.11176i	−0.0402185	+	0.0696604i	0.845215	+	0.534426i	$0.179472\pi$
$920$	−0.246211	−	0.426450i	−0.00811734	−	0.0140597i
$921$		0			0
$922$	−7.05398			−0.232310
$923$	13.3693	+	5.40938i	0.440056	+	0.178052i
$924$		0			0
$925$	25.3153	+	43.8475i	0.832363	+	1.44170i
$926$	0.342329	+	0.592932i	0.0112496	+	0.0194849i
$927$		0			0
$928$	−1.00000			−0.0328266
$929$	17.3078	−	29.9779i	0.567849	−	0.983544i	−0.428929	−	0.903338i	$-0.641109\pi$
$929$	17.3078	−	29.9779i	0.567849	−	0.983544i	0.996778	−	0.0802057i	$-0.0255577\pi$
$930$		0			0
$931$	−4.68466			−0.153533
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$		0			0
$934$	−14.0000	−	24.2487i	−0.458094	−	0.793442i
$935$	−4.38447			−0.143388
$936$		0			0
$937$	9.43845			0.308341			0.154170	−	0.988044i	$-0.450730\pi$
$937$	9.43845			0.308341			0.154170	+	0.988044i	$0.450730\pi$
$938$	3.56155	+	6.16879i	0.116289	+	0.201418i
$939$		0			0
$940$	−1.31534	+	2.27824i	−0.0429017	+	0.0743079i
$941$	−28.6307			−0.933334			−0.466667	−	0.884433i	$-0.654545\pi$
$941$	−28.6307			−0.933334			−0.466667	+	0.884433i	$0.654545\pi$
$942$		0			0
$943$	−1.80776	+	3.13114i	−0.0588689	+	0.101964i
$944$	−4.87689			−0.158729
$945$		0			0
$946$	−8.68466	−	15.0423i	−0.282363	−	0.489066i
$947$	−6.34233	−	10.9852i	−0.206098	−	0.356972i	0.744384	−	0.667752i	$-0.232743\pi$
$947$	−6.34233	−	10.9852i	−0.206098	−	0.356972i	−0.950482	+	0.310780i	$0.899410\pi$
$948$		0			0
$949$	3.28078	+	23.4294i	0.106499	+	0.760551i
$950$	−21.9460			−0.712023
$951$		0			0
$952$	−2.50000	−	4.33013i	−0.0810255	−	0.140340i
$953$	−1.63068	+	2.82443i	−0.0528230	+	0.0914921i	−0.891228	−	0.453556i	$-0.850155\pi$
$953$	−1.63068	+	2.82443i	−0.0528230	+	0.0914921i	0.838405	+	0.545048i	$0.183489\pi$
$954$		0			0
$955$	−6.24621	+	10.8188i	−0.202123	+	0.350087i
$956$	2.00000	−	3.46410i	0.0646846	−	0.112037i
$957$		0			0
$958$	−0.780776	+	1.35234i	−0.0252257	+	0.0436923i
$959$	−7.40388	−	12.8239i	−0.239084	−	0.414105i
$960$		0			0
$961$	−21.2462			−0.685362
$962$	−36.1231	−	14.6158i	−1.16466	−	0.471233i
$963$		0			0
$964$	−11.8423	−	20.5115i	−0.381416	−	0.660631i
$965$	1.22680	+	2.12488i	0.0394921	+	0.0684024i
$966$		0			0
$967$	28.4924			0.916255			0.458127	−	0.888887i	$-0.348520\pi$
$967$	28.4924			0.916255			0.458127	+	0.888887i	$0.348520\pi$
$968$	−4.28078	+	7.41452i	−0.137589	+	0.238312i
$969$		0			0
$970$	−2.38447			−0.0765608
$971$	−9.56155	+	16.5611i	−0.306845	+	0.531471i	−0.977670	−	0.210144i	$-0.932607\pi$
$971$	−9.56155	+	16.5611i	−0.306845	+	0.531471i	0.670826	+	0.741615i	$0.265940\pi$
$972$		0			0
$973$	2.34233	+	4.05703i	0.0750916	+	0.130063i
$974$	−11.3153			−0.362567
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	−17.5270	−	30.3576i	−0.560738	−	0.971227i	−0.997432	−	0.0716167i	$-0.977184\pi$
$977$	−17.5270	−	30.3576i	−0.560738	−	0.971227i	0.436694	−	0.899610i	$-0.356149\pi$
$978$		0			0
$979$	2.09612	−	3.63058i	0.0669922	−	0.116034i
$980$	−0.561553			−0.0179381
$981$		0			0
$982$	9.12311	−	15.8017i	0.291130	−	0.504252i
$983$	27.2311			0.868536			0.434268	−	0.900784i	$-0.357007\pi$
$983$	27.2311			0.868536			0.434268	+	0.900784i	$0.357007\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	2.50000	+	4.33013i	0.0796162	+	0.137899i
$987$		0			0
$988$	13.3153	−	10.3923i	0.423617	−	0.330623i
$989$	−9.75379			−0.310152
$990$		0			0
$991$	2.78078	+	4.81645i	0.0883343	+	0.152999i	0.906807	−	0.421546i	$-0.138512\pi$
$991$	2.78078	+	4.81645i	0.0883343	+	0.152999i	−0.818473	+	0.574545i	$0.805179\pi$
$992$	−1.56155	+	2.70469i	−0.0495794	+	0.0858740i
$993$		0			0
$994$	−2.00000	+	3.46410i	−0.0634361	+	0.109875i
$995$	6.63068	−	11.4847i	0.210207	−	0.364089i
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	−1.31534	−	2.27824i	−0.0416364	−	0.0721164i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.i.211.2	✓	4	3.2	odd	2
546.2.l.i.295.2	yes	4	39.35	odd	6
1638.2.r.z.757.1		4	1.1	even	1	trivial
1638.2.r.z.1387.1		4	13.9	even	3	inner
7098.2.a.bq.1.1		2	39.23	odd	6
7098.2.a.bw.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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.561553 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.561553 q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.280776 - 0.486319i) q^{10} +(-0.780776 - 1.35234i) q^{11} +(-0.500000 - 3.57071i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} +(2.34233 - 4.05703i) q^{19} +(0.280776 - 0.486319i) q^{20} +(0.780776 - 1.35234i) q^{22} +(-0.438447 - 0.759413i) q^{23} -4.68466 q^{25} +(2.84233 - 2.21837i) q^{26} +(0.500000 + 0.866025i) q^{28} +(-0.500000 - 0.866025i) q^{29} -3.12311 q^{31} +(0.500000 - 0.866025i) q^{32} -5.00000 q^{34} +(-0.280776 + 0.486319i) q^{35} +(-5.40388 - 9.35980i) q^{37} +4.68466 q^{38} +0.561553 q^{40} +(-2.06155 - 3.57071i) q^{41} +(5.56155 - 9.63289i) q^{43} +1.56155 q^{44} +(0.438447 - 0.759413i) q^{46} -4.68466 q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.34233 - 4.05703i) q^{50} +(3.34233 + 1.35234i) q^{52} +12.1231 q^{53} +(0.438447 + 0.759413i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.500000 - 0.866025i) q^{58} +(2.43845 - 4.22351i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-1.56155 - 2.70469i) q^{62} +1.00000 q^{64} +(0.280776 + 2.00514i) q^{65} +(3.56155 + 6.16879i) q^{67} +(-2.50000 - 4.33013i) q^{68} -0.561553 q^{70} +(-2.00000 + 3.46410i) q^{71} -6.56155 q^{73} +(5.40388 - 9.35980i) q^{74} +(2.34233 + 4.05703i) q^{76} -1.56155 q^{77} +5.56155 q^{79} +(0.280776 + 0.486319i) q^{80} +(2.06155 - 3.57071i) q^{82} -6.24621 q^{83} +(1.40388 - 2.43160i) q^{85} +11.1231 q^{86} +(0.780776 + 1.35234i) q^{88} +(1.34233 + 2.32498i) q^{89} +(-3.34233 - 1.35234i) q^{91} +0.876894 q^{92} +(-2.34233 - 4.05703i) q^{94} +(-1.31534 + 2.27824i) q^{95} +(2.12311 - 3.67733i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 6 q^{5} + 2 q^{7} - 4 q^{8} + 3 q^{10} + q^{11} - 2 q^{13} + 4 q^{14} - 2 q^{16} - 10 q^{17} - 3 q^{19} - 3 q^{20} - q^{22} - 10 q^{23} + 6 q^{25} - q^{26} + 2 q^{28} - 2 q^{29} + 4 q^{31} + 2 q^{32} - 20 q^{34} + 3 q^{35} - q^{37} - 6 q^{38} - 6 q^{40} + 14 q^{43} - 2 q^{44} + 10 q^{46} + 6 q^{47} - 2 q^{49} + 3 q^{50} + q^{52} + 32 q^{53} + 10 q^{55} - 2 q^{56} + 2 q^{58} + 18 q^{59} + 2 q^{61} + 2 q^{62} + 4 q^{64} - 3 q^{65} + 6 q^{67} - 10 q^{68} + 6 q^{70} - 8 q^{71} - 18 q^{73} + q^{74} - 3 q^{76} + 2 q^{77} + 14 q^{79} - 3 q^{80} + 8 q^{83} - 15 q^{85} + 28 q^{86} - q^{88} - 7 q^{89} - q^{91} + 20 q^{92} + 3 q^{94} - 30 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 + 2 * q^7 - 4 * q^8 + 3 * q^10 + q^11 - 2 * q^13 + 4 * q^14 - 2 * q^16 - 10 * q^17 - 3 * q^19 - 3 * q^20 - q^22 - 10 * q^23 + 6 * q^25 - q^26 + 2 * q^28 - 2 * q^29 + 4 * q^31 + 2 * q^32 - 20 * q^34 + 3 * q^35 - q^37 - 6 * q^38 - 6 * q^40 + 14 * q^43 - 2 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^49 + 3 * q^50 + q^52 + 32 * q^53 + 10 * q^55 - 2 * q^56 + 2 * q^58 + 18 * q^59 + 2 * q^61 + 2 * q^62 + 4 * q^64 - 3 * q^65 + 6 * q^67 - 10 * q^68 + 6 * q^70 - 8 * q^71 - 18 * q^73 + q^74 - 3 * q^76 + 2 * q^77 + 14 * q^79 - 3 * q^80 + 8 * q^83 - 15 * q^85 + 28 * q^86 - q^88 - 7 * q^89 - q^91 + 20 * q^92 + 3 * q^94 - 30 * q^95 - 8 * q^97 + 2 * q^98

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