LMFDB - Embedded newform 1026.2.e.d.343.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(343,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1026.343");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.e (of order $3$, degree $2$, not 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:	$8.19265124738$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 55x^{8} - 2x^{7} + 70x^{6} - 32x^{5} + 73x^{4} - 18x^{3} + 13x^{2} + 2x + 1 $ x^12 + 8x^10 + 55x^8 - 2x^7 + 70x^6 - 32x^5 + 73x^4 - 18x^3 + 13x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			343.4
Root			$-0.122364 + 0.211941i$ of defining polynomial
Character	$\chi$	$=$	1026.343
Dual form			1026.2.e.d.685.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.573032 + 0.992520i) q^{5} +(0.817447 - 1.41586i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.573032 + 0.992520i) q^{5} +(0.817447 - 1.41586i) q^{7} -1.00000 q^{8} +1.14606 q^{10} +(1.10449 - 1.91303i) q^{11} +(-2.18454 - 3.78373i) q^{13} +(-0.817447 - 1.41586i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.42591 q^{17} -1.00000 q^{19} +(0.573032 - 0.992520i) q^{20} +(-1.10449 - 1.91303i) q^{22} +(2.16859 + 3.75611i) q^{23} +(1.84327 - 3.19264i) q^{25} -4.36908 q^{26} -1.63489 q^{28} +(0.700052 - 1.21253i) q^{29} +(-3.66575 - 6.34926i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.712956 - 1.23488i) q^{34} +1.87369 q^{35} +6.94627 q^{37} +(-0.500000 + 0.866025i) q^{38} +(-0.573032 - 0.992520i) q^{40} +(-2.64018 - 4.57292i) q^{41} +(4.37956 - 7.58562i) q^{43} -2.20898 q^{44} +4.33718 q^{46} +(1.53629 - 2.66093i) q^{47} +(2.16356 + 3.74740i) q^{49} +(-1.84327 - 3.19264i) q^{50} +(-2.18454 + 3.78373i) q^{52} -5.16929 q^{53} +2.53163 q^{55} +(-0.817447 + 1.41586i) q^{56} +(-0.700052 - 1.21253i) q^{58} +(0.653079 + 1.13117i) q^{59} +(0.535684 - 0.927832i) q^{61} -7.33149 q^{62} +1.00000 q^{64} +(2.50362 - 4.33639i) q^{65} +(-3.57079 - 6.18479i) q^{67} +(-0.712956 - 1.23488i) q^{68} +(0.936845 - 1.62266i) q^{70} -12.0806 q^{71} +6.78533 q^{73} +(3.47314 - 6.01565i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-1.80573 - 3.12761i) q^{77} +(-5.40433 + 9.36057i) q^{79} -1.14606 q^{80} -5.28035 q^{82} +(-2.59860 + 4.50091i) q^{83} +(0.817092 + 1.41524i) q^{85} +(-4.37956 - 7.58562i) q^{86} +(-1.10449 + 1.91303i) q^{88} +7.62362 q^{89} -7.14298 q^{91} +(2.16859 - 3.75611i) q^{92} +(-1.53629 - 2.66093i) q^{94} +(-0.573032 - 0.992520i) q^{95} +(-7.77317 + 13.4635i) q^{97} +4.32712 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8} + 6 q^{11} - 6 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 12 q^{26} + 12 q^{28} - 6 q^{29} - 6 q^{31} + 6 q^{32} - 24 q^{35} + 12 q^{37} - 6 q^{38} - 6 q^{41} - 12 q^{43} - 12 q^{44} + 24 q^{46} + 6 q^{47} - 18 q^{49} + 30 q^{50} - 6 q^{52} + 36 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{58} - 12 q^{59} - 12 q^{61} - 12 q^{62} + 12 q^{64} + 6 q^{65} - 18 q^{67} - 12 q^{70} - 36 q^{71} + 48 q^{73} + 6 q^{74} + 6 q^{76} + 6 q^{77} - 18 q^{79} - 12 q^{82} - 12 q^{83} - 36 q^{85} + 12 q^{86} - 6 q^{88} - 12 q^{89} - 24 q^{91} + 12 q^{92} - 6 q^{94} + 18 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8 + 6 * q^11 - 6 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 12 * q^26 + 12 * q^28 - 6 * q^29 - 6 * q^31 + 6 * q^32 - 24 * q^35 + 12 * q^37 - 6 * q^38 - 6 * q^41 - 12 * q^43 - 12 * q^44 + 24 * q^46 + 6 * q^47 - 18 * q^49 + 30 * q^50 - 6 * q^52 + 36 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^58 - 12 * q^59 - 12 * q^61 - 12 * q^62 + 12 * q^64 + 6 * q^65 - 18 * q^67 - 12 * q^70 - 36 * q^71 + 48 * q^73 + 6 * q^74 + 6 * q^76 + 6 * q^77 - 18 * q^79 - 12 * q^82 - 12 * q^83 - 36 * q^85 + 12 * q^86 - 6 * q^88 - 12 * q^89 - 24 * q^91 + 12 * q^92 - 6 * q^94 + 18 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.573032	+	0.992520i	0.256267	+	0.443868i	0.965239	−	0.261369i	$-0.0841739\pi$
$5$	0.573032	+	0.992520i	0.256267	+	0.443868i	−0.708972	+	0.705237i	$0.750841\pi$
$6$		0			0
$7$	0.817447	−	1.41586i	0.308966	−	0.535144i	−0.669171	−	0.743109i	$-0.733350\pi$
$7$	0.817447	−	1.41586i	0.308966	−	0.535144i	0.978136	+	0.207964i	$0.0666838\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.14606			0.362417
$11$	1.10449	−	1.91303i	0.333017	−	0.576802i	−0.650085	−	0.759861i	$-0.725267\pi$
$11$	1.10449	−	1.91303i	0.333017	−	0.576802i	0.983102	+	0.183060i	$0.0586001\pi$
$12$		0			0
$13$	−2.18454	−	3.78373i	−0.605882	−	1.04942i	−0.991911	−	0.126932i	$-0.959487\pi$
$13$	−2.18454	−	3.78373i	−0.605882	−	1.04942i	0.386029	−	0.922486i	$-0.373846\pi$
$14$	−0.817447	−	1.41586i	−0.218472	−	0.378404i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.42591			0.345834			0.172917	−	0.984936i	$-0.444681\pi$
$17$	1.42591			0.345834			0.172917	+	0.984936i	$0.444681\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	0.573032	−	0.992520i	0.128134	−	0.221934i
$21$		0			0
$22$	−1.10449	−	1.91303i	−0.235478	−	0.407860i
$23$	2.16859	+	3.75611i	0.452183	+	0.783204i	0.998521	−	0.0543609i	$-0.0173121\pi$
$23$	2.16859	+	3.75611i	0.452183	+	0.783204i	−0.546339	+	0.837564i	$0.683979\pi$
$24$		0			0
$25$	1.84327	−	3.19264i	0.368654	−	0.638527i
$26$	−4.36908			−0.856847
$27$		0			0
$28$	−1.63489			−0.308966
$29$	0.700052	−	1.21253i	0.129996	−	0.225160i	−0.793679	−	0.608337i	$-0.791837\pi$
$29$	0.700052	−	1.21253i	0.129996	−	0.225160i	0.923675	+	0.383177i	$0.125170\pi$
$30$		0			0
$31$	−3.66575	−	6.34926i	−0.658388	−	1.14036i	−0.981033	−	0.193841i	$-0.937905\pi$
$31$	−3.66575	−	6.34926i	−0.658388	−	1.14036i	0.322645	−	0.946520i	$-0.395428\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	0.712956	−	1.23488i	0.122271	−	0.211779i
$35$	1.87369			0.316712
$36$		0			0
$37$	6.94627			1.14196			0.570980	−	0.820964i	$-0.306563\pi$
$37$	6.94627			1.14196			0.570980	+	0.820964i	$0.306563\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$		0			0
$40$	−0.573032	−	0.992520i	−0.0906042	−	0.156931i
$41$	−2.64018	−	4.57292i	−0.412326	−	0.714170i	0.582818	−	0.812603i	$-0.301950\pi$
$41$	−2.64018	−	4.57292i	−0.412326	−	0.714170i	−0.995144	+	0.0984333i	$0.968617\pi$
$42$		0			0
$43$	4.37956	−	7.58562i	0.667877	−	1.15680i	−0.310620	−	0.950534i	$-0.600537\pi$
$43$	4.37956	−	7.58562i	0.667877	−	1.15680i	0.978497	−	0.206262i	$-0.0661300\pi$
$44$	−2.20898			−0.333017
$45$		0			0
$46$	4.33718			0.639483
$47$	1.53629	−	2.66093i	0.224091	−	0.388137i	−0.731955	−	0.681353i	$-0.761392\pi$
$47$	1.53629	−	2.66093i	0.224091	−	0.388137i	0.956046	+	0.293216i	$0.0947254\pi$
$48$		0			0
$49$	2.16356	+	3.74740i	0.309080	+	0.535343i
$50$	−1.84327	−	3.19264i	−0.260678	−	0.451507i
$51$		0			0
$52$	−2.18454	+	3.78373i	−0.302941	+	0.524709i
$53$	−5.16929			−0.710056			−0.355028	−	0.934856i	$-0.615529\pi$
$53$	−5.16929			−0.710056			−0.355028	+	0.934856i	$0.615529\pi$
$54$		0			0
$55$	2.53163			0.341365
$56$	−0.817447	+	1.41586i	−0.109236	+	0.189202i
$57$		0			0
$58$	−0.700052	−	1.21253i	−0.0919213	−	0.159212i
$59$	0.653079	+	1.13117i	0.0850236	+	0.147265i	0.905401	−	0.424557i	$-0.139570\pi$
$59$	0.653079	+	1.13117i	0.0850236	+	0.147265i	−0.820378	+	0.571822i	$0.806237\pi$
$60$		0			0
$61$	0.535684	−	0.927832i	0.0685873	−	0.118797i	−0.829692	−	0.558221i	$-0.811484\pi$
$61$	0.535684	−	0.927832i	0.0685873	−	0.118797i	0.898280	+	0.439424i	$0.144817\pi$
$62$	−7.33149			−0.931101
$63$		0			0
$64$	1.00000			0.125000
$65$	2.50362	−	4.33639i	0.310536	−	0.537864i
$66$		0			0
$67$	−3.57079	−	6.18479i	−0.436242	−	0.755593i	0.561154	−	0.827711i	$-0.310357\pi$
$67$	−3.57079	−	6.18479i	−0.436242	−	0.755593i	−0.997396	+	0.0721184i	$0.977024\pi$
$68$	−0.712956	−	1.23488i	−0.0864586	−	0.149751i
$69$		0			0
$70$	0.936845	−	1.62266i	0.111974	−	0.193945i
$71$	−12.0806			−1.43370			−0.716849	−	0.697228i	$-0.754416\pi$
$71$	−12.0806			−1.43370			−0.716849	+	0.697228i	$0.754416\pi$
$72$		0			0
$73$	6.78533			0.794163			0.397081	−	0.917783i	$-0.370023\pi$
$73$	6.78533			0.794163			0.397081	+	0.917783i	$0.370023\pi$
$74$	3.47314	−	6.01565i	0.403744	−	0.699305i
$75$		0			0
$76$	0.500000	+	0.866025i	0.0573539	+	0.0993399i
$77$	−1.80573	−	3.12761i	−0.205781	−	0.356424i
$78$		0			0
$79$	−5.40433	+	9.36057i	−0.608034	+	1.05315i	0.383530	+	0.923529i	$0.374708\pi$
$79$	−5.40433	+	9.36057i	−0.608034	+	1.05315i	−0.991564	+	0.129618i	$0.958625\pi$
$80$	−1.14606			−0.128134
$81$		0			0
$82$	−5.28035			−0.583117
$83$	−2.59860	+	4.50091i	−0.285234	+	0.494039i	−0.972666	−	0.232209i	$-0.925405\pi$
$83$	−2.59860	+	4.50091i	−0.285234	+	0.494039i	0.687432	+	0.726249i	$0.258738\pi$
$84$		0			0
$85$	0.817092	+	1.41524i	0.0886261	+	0.153505i
$86$	−4.37956	−	7.58562i	−0.472260	−	0.817978i
$87$		0			0
$88$	−1.10449	+	1.91303i	−0.117739	+	0.203930i
$89$	7.62362			0.808102			0.404051	−	0.914736i	$-0.367602\pi$
$89$	7.62362			0.808102			0.404051	+	0.914736i	$0.367602\pi$
$90$		0			0
$91$	−7.14298			−0.748787
$92$	2.16859	−	3.75611i	0.226091	−	0.391602i
$93$		0			0
$94$	−1.53629	−	2.66093i	−0.158456	−	0.274454i
$95$	−0.573032	−	0.992520i	−0.0587918	−	0.101830i
$96$		0			0
$97$	−7.77317	+	13.4635i	−0.789246	+	1.36701i	0.137184	+	0.990546i	$0.456195\pi$
$97$	−7.77317	+	13.4635i	−0.789246	+	1.36701i	−0.926429	+	0.376468i	$0.877138\pi$
$98$	4.32712			0.437105
$99$		0			0
$100$	−3.68654			−0.368654
$101$	−3.96265	+	6.86352i	−0.394299	+	0.682945i	−0.993011	−	0.118018i	$-0.962346\pi$
$101$	−3.96265	+	6.86352i	−0.394299	+	0.682945i	0.598713	+	0.800964i	$0.295679\pi$
$102$		0			0
$103$	2.17163	+	3.76138i	0.213978	+	0.370620i	0.952956	−	0.303109i	$-0.0980247\pi$
$103$	2.17163	+	3.76138i	0.213978	+	0.370620i	−0.738978	+	0.673729i	$0.764691\pi$
$104$	2.18454	+	3.78373i	0.214212	+	0.371025i
$105$		0			0
$106$	−2.58464	+	4.47673i	−0.251043	+	0.434819i
$107$	4.42033			0.427329			0.213665	−	0.976907i	$-0.431460\pi$
$107$	4.42033			0.427329			0.213665	+	0.976907i	$0.431460\pi$
$108$		0			0
$109$	18.5327			1.77511			0.887554	−	0.460704i	$-0.152403\pi$
$109$	18.5327			1.77511			0.887554	+	0.460704i	$0.152403\pi$
$110$	1.26582	−	2.19246i	0.120691	−	0.209043i
$111$		0			0
$112$	0.817447	+	1.41586i	0.0772415	+	0.133786i
$113$	−5.17058	−	8.95570i	−0.486407	−	0.842482i	0.513471	−	0.858107i	$-0.328359\pi$
$113$	−5.17058	−	8.95570i	−0.486407	−	0.842482i	−0.999878	+	0.0156253i	$0.995026\pi$
$114$		0			0
$115$	−2.48534	+	4.30474i	−0.231759	+	0.401419i
$116$	−1.40010			−0.129996
$117$		0			0
$118$	1.30616			0.120242
$119$	1.16561	−	2.01889i	0.106851	−	0.185071i
$120$		0			0
$121$	3.06020	+	5.30042i	0.278200	+	0.481856i
$122$	−0.535684	−	0.927832i	−0.0484986	−	0.0840020i
$123$		0			0
$124$	−3.66575	+	6.34926i	−0.329194	+	0.570180i
$125$	9.95532			0.890431
$126$		0			0
$127$	8.15572			0.723703			0.361852	−	0.932236i	$-0.382145\pi$
$127$	8.15572			0.723703			0.361852	+	0.932236i	$0.382145\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.50362	−	4.33639i	−0.219582	−	0.380327i
$131$	2.86864	+	4.96864i	0.250635	+	0.434112i	0.963701	−	0.266985i	$-0.0860274\pi$
$131$	2.86864	+	4.96864i	0.250635	+	0.434112i	−0.713066	+	0.701097i	$0.752694\pi$
$132$		0			0
$133$	−0.817447	+	1.41586i	−0.0708816	+	0.122771i
$134$	−7.14158			−0.616939
$135$		0			0
$136$	−1.42591			−0.122271
$137$	−10.5788	+	18.3230i	−0.903808	+	1.56544i	−0.0812995	+	0.996690i	$0.525907\pi$
$137$	−10.5788	+	18.3230i	−0.903808	+	1.56544i	−0.822509	+	0.568752i	$0.807426\pi$
$138$		0			0
$139$	−9.18089	−	15.9018i	−0.778713	−	1.34877i	−0.932684	−	0.360695i	$-0.882540\pi$
$139$	−9.18089	−	15.9018i	−0.778713	−	1.34877i	0.153971	−	0.988075i	$-0.450794\pi$
$140$	−0.936845	−	1.62266i	−0.0791779	−	0.137140i
$141$		0			0
$142$	−6.04028	+	10.4621i	−0.506889	+	0.877957i
$143$	−9.65121			−0.807075
$144$		0			0
$145$	1.60461			0.133255
$146$	3.39266	−	5.87627i	0.280779	−	0.486323i
$147$		0			0
$148$	−3.47314	−	6.01565i	−0.285490	−	0.494483i
$149$	10.1991	+	17.6653i	0.835541	+	1.44720i	0.893589	+	0.448886i	$0.148179\pi$
$149$	10.1991	+	17.6653i	0.835541	+	1.44720i	−0.0580476	+	0.998314i	$0.518488\pi$
$150$		0			0
$151$	7.11165	−	12.3177i	0.578738	−	1.00240i	−0.416887	−	0.908958i	$-0.636879\pi$
$151$	7.11165	−	12.3177i	0.578738	−	1.00240i	0.995624	−	0.0934447i	$-0.0297878\pi$
$152$	1.00000			0.0811107
$153$		0			0
$154$	−3.61145			−0.291019
$155$	4.20118	−	7.27665i	0.337447	−	0.584475i
$156$		0			0
$157$	0.979456	+	1.69647i	0.0781691	+	0.135393i	0.902460	−	0.430774i	$-0.141759\pi$
$157$	0.979456	+	1.69647i	0.0781691	+	0.135393i	−0.824291	+	0.566166i	$0.808426\pi$
$158$	5.40433	+	9.36057i	0.429945	+	0.744687i
$159$		0			0
$160$	−0.573032	+	0.992520i	−0.0453021	+	0.0784656i
$161$	7.09083			0.558836
$162$		0			0
$163$	4.31174			0.337722			0.168861	−	0.985640i	$-0.445991\pi$
$163$	4.31174			0.337722			0.168861	+	0.985640i	$0.445991\pi$
$164$	−2.64018	+	4.57292i	−0.206163	+	0.357085i
$165$		0			0
$166$	2.59860	+	4.50091i	0.201691	+	0.349339i
$167$	2.47885	+	4.29349i	0.191819	+	0.332241i	0.945853	−	0.324595i	$-0.105228\pi$
$167$	2.47885	+	4.29349i	0.191819	+	0.332241i	−0.754034	+	0.656835i	$0.771895\pi$
$168$		0			0
$169$	−3.04442	+	5.27309i	−0.234186	+	0.405622i
$170$	1.63418			0.125336
$171$		0			0
$172$	−8.75912			−0.667877
$173$	−6.55059	+	11.3460i	−0.498032	+	0.862617i	−0.999997	−	0.00227090i	$-0.999277\pi$
$173$	−6.55059	+	11.3460i	−0.498032	+	0.862617i	0.501965	+	0.864888i	$0.332610\pi$
$174$		0			0
$175$	−3.01355	−	5.21962i	−0.227803	−	0.394566i
$176$	1.10449	+	1.91303i	0.0832541	+	0.144200i
$177$		0			0
$178$	3.81181	−	6.60225i	0.285707	−	0.494859i
$179$	12.2984			0.919224			0.459612	−	0.888120i	$-0.347988\pi$
$179$	12.2984			0.919224			0.459612	+	0.888120i	$0.347988\pi$
$180$		0			0
$181$	−1.39563			−0.103736			−0.0518680	−	0.998654i	$-0.516518\pi$
$181$	−1.39563			−0.103736			−0.0518680	+	0.998654i	$0.516518\pi$
$182$	−3.57149	+	6.18600i	−0.264736	+	0.458537i
$183$		0			0
$184$	−2.16859	−	3.75611i	−0.159871	−	0.276904i
$185$	3.98043	+	6.89431i	0.292647	+	0.506880i
$186$		0			0
$187$	1.57491	−	2.72782i	0.115169	−	0.199478i
$188$	−3.07258			−0.224091
$189$		0			0
$190$	−1.14606			−0.0831441
$191$	−0.0522362	+	0.0904757i	−0.00377968	+	0.00654659i	−0.867909	−	0.496723i	$-0.834536\pi$
$191$	−0.0522362	+	0.0904757i	−0.00377968	+	0.00654659i	0.864129	+	0.503270i	$0.167870\pi$
$192$		0			0
$193$	10.4870	+	18.1640i	0.754870	+	1.30747i	0.945439	+	0.325799i	$0.105633\pi$
$193$	10.4870	+	18.1640i	0.754870	+	1.30747i	−0.190570	+	0.981674i	$0.561033\pi$
$194$	7.77317	+	13.4635i	0.558081	+	0.966625i
$195$		0			0
$196$	2.16356	−	3.74740i	0.154540	−	0.267671i
$197$	−21.4751			−1.53004			−0.765018	−	0.644009i	$-0.777270\pi$
$197$	−21.4751			−1.53004			−0.765018	+	0.644009i	$0.777270\pi$
$198$		0			0
$199$	6.38880			0.452890			0.226445	−	0.974024i	$-0.427290\pi$
$199$	6.38880			0.452890			0.226445	+	0.974024i	$0.427290\pi$
$200$	−1.84327	+	3.19264i	−0.130339	+	0.225754i
$201$		0			0
$202$	3.96265	+	6.86352i	0.278811	+	0.482915i
$203$	−1.14451	−	1.98235i	−0.0803289	−	0.139134i
$204$		0			0
$205$	3.02581	−	5.24085i	0.211332	−	0.366037i
$206$	4.34327			0.302610
$207$		0			0
$208$	4.36908			0.302941
$209$	−1.10449	+	1.91303i	−0.0763992	+	0.132327i
$210$		0			0
$211$	0.151291	+	0.262044i	0.0104153	+	0.0180398i	0.871186	−	0.490953i	$-0.163351\pi$
$211$	0.151291	+	0.262044i	0.0104153	+	0.0180398i	−0.860771	+	0.508993i	$0.830018\pi$
$212$	2.58464	+	4.47673i	0.177514	+	0.307463i
$213$		0			0
$214$	2.21016	−	3.82812i	0.151084	−	0.261685i
$215$	10.0385			0.684620
$216$		0			0
$217$	−11.9862			−0.813677
$218$	9.26634	−	16.0498i	0.627595	−	1.08703i
$219$		0			0
$220$	−1.26582	−	2.19246i	−0.0853413	−	0.147816i
$221$	−3.11496	−	5.39527i	−0.209535	−	0.362925i
$222$		0			0
$223$	−10.8305	+	18.7590i	−0.725263	+	1.25619i	0.233602	+	0.972332i	$0.424949\pi$
$223$	−10.8305	+	18.7590i	−0.725263	+	1.25619i	−0.958866	+	0.283860i	$0.908385\pi$
$224$	1.63489			0.109236
$225$		0			0
$226$	−10.3412			−0.687883
$227$	3.75429	−	6.50262i	0.249181	−	0.431594i	−0.714118	−	0.700026i	$-0.753172\pi$
$227$	3.75429	−	6.50262i	0.249181	−	0.431594i	0.963299	+	0.268431i	$0.0865052\pi$
$228$		0			0
$229$	3.05764	+	5.29598i	0.202054	+	0.349968i	0.949190	−	0.314703i	$-0.101905\pi$
$229$	3.05764	+	5.29598i	0.202054	+	0.349968i	−0.747136	+	0.664671i	$0.768572\pi$
$230$	2.48534	+	4.30474i	0.163879	+	0.283846i
$231$		0			0
$232$	−0.700052	+	1.21253i	−0.0459607	+	0.0796062i
$233$	25.3810			1.66277			0.831383	−	0.555700i	$-0.187550\pi$
$233$	25.3810			1.66277			0.831383	+	0.555700i	$0.187550\pi$
$234$		0			0
$235$	3.52137			0.229709
$236$	0.653079	−	1.13117i	0.0425118	−	0.0736326i
$237$		0			0
$238$	−1.16561	−	2.01889i	−0.0755550	−	0.130865i
$239$	3.08704	+	5.34692i	0.199684	+	0.345863i	0.948426	−	0.316999i	$-0.102675\pi$
$239$	3.08704	+	5.34692i	0.199684	+	0.345863i	−0.748742	+	0.662862i	$0.769342\pi$
$240$		0			0
$241$	−5.91630	+	10.2473i	−0.381102	+	0.660089i	−0.991220	−	0.132222i	$-0.957789\pi$
$241$	−5.91630	+	10.2473i	−0.381102	+	0.660089i	0.610118	+	0.792311i	$0.291122\pi$
$242$	6.12040			0.393434
$243$		0			0
$244$	−1.07137			−0.0685873
$245$	−2.47958	+	4.29476i	−0.158414	+	0.274382i
$246$		0			0
$247$	2.18454	+	3.78373i	0.138999	+	0.240753i
$248$	3.66575	+	6.34926i	0.232775	+	0.403178i
$249$		0			0
$250$	4.97766	−	8.62156i	0.314815	−	0.545275i
$251$	29.5694			1.86640			0.933201	−	0.359354i	$-0.117003\pi$
$251$	29.5694			1.86640			0.933201	+	0.359354i	$0.117003\pi$
$252$		0			0
$253$	9.58076			0.602337
$254$	4.07786	−	7.06306i	0.255868	−	0.443176i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.1387	−	24.4889i	−0.881948	−	1.52758i	−0.849172	−	0.528116i	$-0.822899\pi$
$257$	−14.1387	−	24.4889i	−0.881948	−	1.52758i	−0.0327753	−	0.999463i	$-0.510435\pi$
$258$		0			0
$259$	5.67821	−	9.83494i	0.352827	−	0.611114i
$260$	−5.00724			−0.310536
$261$		0			0
$262$	5.73729			0.354451
$263$	−7.44756	+	12.8996i	−0.459236	+	0.795421i	−0.998921	−	0.0464466i	$-0.985210\pi$
$263$	−7.44756	+	12.8996i	−0.459236	+	0.795421i	0.539684	+	0.841867i	$0.318544\pi$
$264$		0			0
$265$	−2.96216	−	5.13062i	−0.181964	−	0.315171i
$266$	0.817447	+	1.41586i	0.0501209	+	0.0868119i
$267$		0			0
$268$	−3.57079	+	6.18479i	−0.218121	+	0.377796i
$269$	28.5720			1.74206			0.871032	−	0.491227i	$-0.163451\pi$
$269$	28.5720			1.74206			0.871032	+	0.491227i	$0.163451\pi$
$270$		0			0
$271$	−17.7114			−1.07589			−0.537947	−	0.842979i	$-0.680800\pi$
$271$	−17.7114			−1.07589			−0.537947	+	0.842979i	$0.680800\pi$
$272$	−0.712956	+	1.23488i	−0.0432293	+	0.0748753i
$273$		0			0
$274$	10.5788	+	18.3230i	0.639089	+	1.10693i
$275$	−4.07175	−	7.05248i	−0.245536	−	0.425280i
$276$		0			0
$277$	−8.37956	+	14.5138i	−0.503479	+	0.872051i	0.496513	+	0.868029i	$0.334614\pi$
$277$	−8.37956	+	14.5138i	−0.503479	+	0.872051i	−0.999992	+	0.00402182i	$0.998720\pi$
$278$	−18.3618			−1.10127
$279$		0			0
$280$	−1.87369			−0.111974
$281$	−2.02850	+	3.51347i	−0.121010	+	0.209596i	−0.920166	−	0.391528i	$-0.871947\pi$
$281$	−2.02850	+	3.51347i	−0.121010	+	0.209596i	0.799156	+	0.601124i	$0.205280\pi$
$282$		0			0
$283$	−9.69303	−	16.7888i	−0.576191	−	0.997992i	−0.995911	−	0.0903385i	$-0.971205\pi$
$283$	−9.69303	−	16.7888i	−0.576191	−	0.997992i	0.419720	−	0.907654i	$-0.362128\pi$
$284$	6.04028	+	10.4621i	0.358425	+	0.620810i
$285$		0			0
$286$	−4.82561	+	8.35820i	−0.285344	+	0.494230i
$287$	−8.63281			−0.509579
$288$		0			0
$289$	−14.9668			−0.880399
$290$	0.802304	−	1.38963i	0.0471129	−	0.0816019i
$291$		0			0
$292$	−3.39266	−	5.87627i	−0.198541	−	0.343882i
$293$	−0.515513	−	0.892896i	−0.0301166	−	0.0521635i	0.850574	−	0.525855i	$-0.176255\pi$
$293$	−0.515513	−	0.892896i	−0.0301166	−	0.0521635i	−0.880691	+	0.473691i	$0.842921\pi$
$294$		0			0
$295$	−0.748470	+	1.29639i	−0.0435776	+	0.0754786i
$296$	−6.94627			−0.403744
$297$		0			0
$298$	20.3982			1.18163
$299$	9.47475	−	16.4107i	0.547939	−	0.949058i
$300$		0			0
$301$	−7.16011	−	12.4017i	−0.412702	−	0.714821i
$302$	−7.11165	−	12.3177i	−0.409229	−	0.708806i
$303$		0			0
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	1.22786			0.0703068
$306$		0			0
$307$	−8.79051			−0.501701			−0.250850	−	0.968026i	$-0.580710\pi$
$307$	−8.79051			−0.501701			−0.250850	+	0.968026i	$0.580710\pi$
$308$	−1.80573	+	3.12761i	−0.102891	+	0.178212i
$309$		0			0
$310$	−4.20118	−	7.27665i	−0.238611	−	0.413286i
$311$	−15.1997	−	26.3266i	−0.861895	−	1.49285i	−0.870098	−	0.492880i	$-0.835944\pi$
$311$	−15.1997	−	26.3266i	−0.861895	−	1.49285i	0.00820248	−	0.999966i	$-0.497389\pi$
$312$		0			0
$313$	−0.531531	+	0.920638i	−0.0300439	+	0.0520375i	−0.880656	−	0.473756i	$-0.842898\pi$
$313$	−0.531531	+	0.920638i	−0.0300439	+	0.0520375i	0.850613	+	0.525793i	$0.176231\pi$
$314$	1.95891			0.110548
$315$		0			0
$316$	10.8087			0.608034
$317$	−8.30479	+	14.3843i	−0.466444	+	0.807904i	−0.999265	−	0.0383233i	$-0.987798\pi$
$317$	−8.30479	+	14.3843i	−0.466444	+	0.807904i	0.532822	+	0.846228i	$0.321132\pi$
$318$		0			0
$319$	−1.54640	−	2.67845i	−0.0865819	−	0.149964i
$320$	0.573032	+	0.992520i	0.0320334	+	0.0554835i
$321$		0			0
$322$	3.54542	−	6.14084i	0.197578	−	0.342216i
$323$	−1.42591			−0.0793398
$324$		0			0
$325$	−16.1068			−0.893443
$326$	2.15587	−	3.73408i	0.119403	−	0.206811i
$327$		0			0
$328$	2.64018	+	4.57292i	0.145779	+	0.252497i
$329$	−2.51167	−	4.35034i	−0.138473	−	0.239842i
$330$		0			0
$331$	−8.36543	+	14.4893i	−0.459805	+	0.796406i	−0.998950	−	0.0458067i	$-0.985414\pi$
$331$	−8.36543	+	14.4893i	−0.459805	+	0.796406i	0.539145	+	0.842213i	$0.318748\pi$
$332$	5.19721			0.285234
$333$		0			0
$334$	4.95770			0.271273
$335$	4.09235	−	7.08816i	0.223589	−	0.387268i
$336$		0			0
$337$	15.7918	+	27.3523i	0.860237	+	1.48997i	0.871700	+	0.490040i	$0.163018\pi$
$337$	15.7918	+	27.3523i	0.860237	+	1.48997i	−0.0114634	+	0.999934i	$0.503649\pi$
$338$	3.04442	+	5.27309i	0.165594	+	0.286818i
$339$		0			0
$340$	0.817092	−	1.41524i	0.0443130	−	0.0767524i
$341$	−16.1951			−0.877016
$342$		0			0
$343$	18.5186			0.999913
$344$	−4.37956	+	7.58562i	−0.236130	+	0.408989i
$345$		0			0
$346$	6.55059	+	11.3460i	0.352162	+	0.609962i
$347$	17.2828	+	29.9347i	0.927789	+	1.60698i	0.787013	+	0.616936i	$0.211626\pi$
$347$	17.2828	+	29.9347i	0.927789	+	1.60698i	0.140776	+	0.990042i	$0.455040\pi$
$348$		0			0
$349$	−2.51645	+	4.35862i	−0.134703	+	0.233312i	−0.925484	−	0.378787i	$-0.876341\pi$
$349$	−2.51645	+	4.35862i	−0.134703	+	0.233312i	0.790781	+	0.612099i	$0.209675\pi$
$350$	−6.02710			−0.322162
$351$		0			0
$352$	2.20898			0.117739
$353$	−0.814604	+	1.41094i	−0.0433570	+	0.0750966i	−0.886890	−	0.461982i	$-0.847139\pi$
$353$	−0.814604	+	1.41094i	−0.0433570	+	0.0750966i	0.843533	+	0.537078i	$0.180472\pi$
$354$		0			0
$355$	−6.92254	−	11.9902i	−0.367410	−	0.636373i
$356$	−3.81181	−	6.60225i	−0.202026	−	0.349918i
$357$		0			0
$358$	6.14919	−	10.6507i	0.324995	−	0.562908i
$359$	−2.96052			−0.156250			−0.0781252	−	0.996944i	$-0.524893\pi$
$359$	−2.96052			−0.156250			−0.0781252	+	0.996944i	$0.524893\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$	−0.697813	+	1.20865i	−0.0366762	+	0.0635251i
$363$		0			0
$364$	3.57149	+	6.18600i	0.187197	+	0.324234i
$365$	3.88821	+	6.73457i	0.203518	+	0.352504i
$366$		0			0
$367$	14.1162	−	24.4500i	0.736862	−	1.27628i	−0.217040	−	0.976163i	$-0.569640\pi$
$367$	14.1162	−	24.4500i	0.736862	−	1.27628i	0.953902	−	0.300119i	$-0.0970265\pi$
$368$	−4.33718			−0.226091
$369$		0			0
$370$	7.96086			0.413866
$371$	−4.22562	+	7.31898i	−0.219383	+	0.379983i
$372$		0			0
$373$	4.93227	+	8.54294i	0.255383	+	0.442336i	0.964999	−	0.262252i	$-0.0844651\pi$
$373$	4.93227	+	8.54294i	0.255383	+	0.442336i	−0.709616	+	0.704588i	$0.751132\pi$
$374$	−1.57491	−	2.72782i	−0.0814365	−	0.141052i
$375$		0			0
$376$	−1.53629	+	2.66093i	−0.0792281	+	0.137227i
$377$	−6.11716			−0.315050
$378$		0			0
$379$	−4.36079			−0.223999			−0.111999	−	0.993708i	$-0.535725\pi$
$379$	−4.36079			−0.223999			−0.111999	+	0.993708i	$0.535725\pi$
$380$	−0.573032	+	0.992520i	−0.0293959	+	0.0509152i
$381$		0			0
$382$	0.0522362	+	0.0904757i	0.00267263	+	0.00462914i
$383$	−16.6855	−	28.9001i	−0.852588	−	1.47673i	−0.878864	−	0.477072i	$-0.841698\pi$
$383$	−16.6855	−	28.9001i	−0.852588	−	1.47673i	0.0262761	−	0.999655i	$-0.491635\pi$
$384$		0			0
$385$	2.06947	−	3.58444i	0.105470	−	0.182680i
$386$	20.9740			1.06755
$387$		0			0
$388$	15.5463			0.789246
$389$	−6.61771	+	11.4622i	−0.335531	+	0.581157i	−0.983587	−	0.180436i	$-0.942249\pi$
$389$	−6.61771	+	11.4622i	−0.335531	+	0.581157i	0.648056	+	0.761593i	$0.275582\pi$
$390$		0			0
$391$	3.09222	+	5.35588i	0.156380	+	0.270859i
$392$	−2.16356	−	3.74740i	−0.109276	−	0.189272i
$393$		0			0
$394$	−10.7375	+	18.5980i	−0.540949	+	0.936952i
$395$	−12.3874			−0.623278
$396$		0			0
$397$	27.6615			1.38829			0.694145	−	0.719835i	$-0.255783\pi$
$397$	27.6615			1.38829			0.694145	+	0.719835i	$0.255783\pi$
$398$	3.19440	−	5.53286i	0.160121	−	0.277337i
$399$		0			0
$400$	1.84327	+	3.19264i	0.0921635	+	0.159632i
$401$	3.90931	+	6.77112i	0.195221	+	0.338133i	0.946973	−	0.321313i	$-0.104124\pi$
$401$	3.90931	+	6.77112i	0.195221	+	0.338133i	−0.751752	+	0.659446i	$0.770791\pi$
$402$		0			0
$403$	−16.0159	+	27.7404i	−0.797810	+	1.38185i
$404$	7.92531			0.394299
$405$		0			0
$406$	−2.28902			−0.113602
$407$	7.67209	−	13.2885i	0.380292	−	0.658684i
$408$		0			0
$409$	−9.80320	−	16.9796i	−0.484737	−	0.839589i	0.515109	−	0.857125i	$-0.327751\pi$
$409$	−9.80320	−	16.9796i	−0.484737	−	0.839589i	−0.999846	+	0.0175352i	$0.994418\pi$
$410$	−3.02581	−	5.24085i	−0.149434	−	0.258827i
$411$		0			0
$412$	2.17163	−	3.76138i	0.106989	−	0.185310i
$413$	2.13543			0.105078
$414$		0			0
$415$	−5.95633			−0.292385
$416$	2.18454	−	3.78373i	0.107106	−	0.185513i
$417$		0			0
$418$	1.10449	+	1.91303i	0.0540224	+	0.0935696i
$419$	6.59852	+	11.4290i	0.322359	+	0.558342i	0.980974	−	0.194138i	$-0.0621909\pi$
$419$	6.59852	+	11.4290i	0.322359	+	0.558342i	−0.658615	+	0.752480i	$0.728858\pi$
$420$		0			0
$421$	15.1960	−	26.3202i	0.740606	−	1.28277i	−0.211613	−	0.977353i	$-0.567872\pi$
$421$	15.1960	−	26.3202i	0.740606	−	1.28277i	0.952220	−	0.305414i	$-0.0987949\pi$
$422$	0.302582			0.0147295
$423$		0			0
$424$	5.16929			0.251043
$425$	2.62834	−	4.55242i	0.127493	−	0.220825i
$426$		0			0
$427$	−0.875787	−	1.51691i	−0.0423823	−	0.0734083i
$428$	−2.21016	−	3.82812i	−0.106832	−	0.185039i
$429$		0			0
$430$	5.01925	−	8.69360i	0.242050	−	0.419243i
$431$	12.2675			0.590903			0.295452	−	0.955358i	$-0.404530\pi$
$431$	12.2675			0.590903			0.295452	+	0.955358i	$0.404530\pi$
$432$		0			0
$433$	−3.30259			−0.158712			−0.0793561	−	0.996846i	$-0.525286\pi$
$433$	−3.30259			−0.158712			−0.0793561	+	0.996846i	$0.525286\pi$
$434$	−5.99311	+	10.3804i	−0.287678	+	0.498273i
$435$		0			0
$436$	−9.26634	−	16.0498i	−0.443777	−	0.768644i
$437$	−2.16859	−	3.75611i	−0.103738	−	0.179679i
$438$		0			0
$439$	−10.4785	+	18.1493i	−0.500112	+	0.866220i	0.499888	+	0.866090i	$0.333375\pi$
$439$	−10.4785	+	18.1493i	−0.500112	+	0.866220i	−1.00000		0.000129598i	$0.999959\pi$
$440$	−2.53163			−0.120691
$441$		0			0
$442$	−6.22992			−0.296327
$443$	17.4811	−	30.2782i	0.830554	−	1.43856i	−0.0670450	−	0.997750i	$-0.521357\pi$
$443$	17.4811	−	30.2782i	0.830554	−	1.43856i	0.897599	−	0.440812i	$-0.145310\pi$
$444$		0			0
$445$	4.36857	+	7.56659i	0.207090	+	0.358691i
$446$	10.8305	+	18.7590i	0.512838	+	0.888262i
$447$		0			0
$448$	0.817447	−	1.41586i	0.0386207	−	0.0668931i
$449$	−12.8844			−0.608055			−0.304027	−	0.952663i	$-0.598331\pi$
$449$	−12.8844			−0.608055			−0.304027	+	0.952663i	$0.598331\pi$
$450$		0			0
$451$	−11.6642			−0.549246
$452$	−5.17058	+	8.95570i	−0.243204	+	0.421241i
$453$		0			0
$454$	−3.75429	−	6.50262i	−0.176198	−	0.305183i
$455$	−4.09315	−	7.08954i	−0.191890	−	0.332363i
$456$		0			0
$457$	1.35841	−	2.35284i	0.0635439	−	0.110061i	−0.832503	−	0.554020i	$-0.813093\pi$
$457$	1.35841	−	2.35284i	0.0635439	−	0.110061i	0.896047	+	0.443959i	$0.146426\pi$
$458$	6.11527			0.285748
$459$		0			0
$460$	4.97069			0.231759
$461$	−1.83407	+	3.17670i	−0.0854211	+	0.147954i	−0.905571	−	0.424196i	$-0.860557\pi$
$461$	−1.83407	+	3.17670i	−0.0854211	+	0.147954i	0.820149	+	0.572149i	$0.193890\pi$
$462$		0			0
$463$	−6.14975	−	10.6517i	−0.285803	−	0.495025i	0.687001	−	0.726657i	$-0.258927\pi$
$463$	−6.14975	−	10.6517i	−0.285803	−	0.495025i	−0.972804	+	0.231632i	$0.925594\pi$
$464$	0.700052	+	1.21253i	0.0324991	+	0.0562901i
$465$		0			0
$466$	12.6905	−	21.9806i	0.587877	−	1.01823i
$467$	−17.4976			−0.809693			−0.404847	−	0.914385i	$-0.632675\pi$
$467$	−17.4976			−0.809693			−0.404847	+	0.914385i	$0.632675\pi$
$468$		0			0
$469$	−11.6757			−0.539135
$470$	1.76069	−	3.04960i	0.0812144	−	0.140667i
$471$		0			0
$472$	−0.653079	−	1.13117i	−0.0300604	−	0.0520661i
$473$	−9.67437	−	16.7565i	−0.444828	−	0.770465i
$474$		0			0
$475$	−1.84327	+	3.19264i	−0.0845750	+	0.146488i
$476$	−2.33121			−0.106851
$477$		0			0
$478$	6.17409			0.282396
$479$	−5.75981	+	9.97628i	−0.263172	+	0.455828i	−0.967083	−	0.254461i	$-0.918102\pi$
$479$	−5.75981	+	9.97628i	−0.263172	+	0.455828i	0.703911	+	0.710288i	$0.251435\pi$
$480$		0			0
$481$	−15.1744	−	26.2828i	−0.691893	−	1.19839i
$482$	5.91630	+	10.2473i	0.269480	+	0.466753i
$483$		0			0
$484$	3.06020	−	5.30042i	0.139100	−	0.240928i
$485$	−17.8171			−0.809032
$486$		0			0
$487$	−31.3219			−1.41933			−0.709666	−	0.704538i	$-0.751154\pi$
$487$	−31.3219			−1.41933			−0.709666	+	0.704538i	$0.751154\pi$
$488$	−0.535684	+	0.927832i	−0.0242493	+	0.0420010i
$489$		0			0
$490$	2.47958	+	4.29476i	0.112016	+	0.194017i
$491$	−18.1009	−	31.3517i	−0.816883	−	1.41488i	−0.907968	−	0.419040i	$-0.862367\pi$
$491$	−18.1009	−	31.3517i	−0.816883	−	1.41488i	0.0910845	−	0.995843i	$-0.470967\pi$
$492$		0			0
$493$	0.998212	−	1.72895i	0.0449572	−	0.0778682i
$494$	4.36908			0.196574
$495$		0			0
$496$	7.33149			0.329194
$497$	−9.87521	+	17.1044i	−0.442964	+	0.767236i
$498$		0			0
$499$	6.93596	+	12.0134i	0.310496	+	0.537795i	0.978470	−	0.206390i	$-0.0661714\pi$
$499$	6.93596	+	12.0134i	0.310496	+	0.537795i	−0.667974	+	0.744185i	$0.732838\pi$
$500$	−4.97766	−	8.62156i	−0.222608	−	0.385568i
$501$		0			0
$502$	14.7847	−	25.6078i	0.659873	−	1.14293i
$503$	1.02490			0.0456982			0.0228491	−	0.999739i	$-0.492726\pi$
$503$	1.02490			0.0456982			0.0228491	+	0.999739i	$0.492726\pi$
$504$		0			0
$505$	−9.08290			−0.404184
$506$	4.79038	−	8.29719i	0.212958	−	0.368855i
$507$		0			0
$508$	−4.07786	−	7.06306i	−0.180926	−	0.313373i
$509$	1.94719	+	3.37264i	0.0863078	+	0.149490i	0.905948	−	0.423389i	$-0.139160\pi$
$509$	1.94719	+	3.37264i	0.0863078	+	0.149490i	−0.819640	+	0.572879i	$0.805826\pi$
$510$		0			0
$511$	5.54664	−	9.60707i	0.245369	−	0.424992i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−28.2774			−1.24726
$515$	−2.48883	+	4.31078i	−0.109671	+	0.189956i
$516$		0			0
$517$	−3.39364	−	5.87795i	−0.149252	−	0.258512i
$518$	−5.67821	−	9.83494i	−0.249486	−	0.432123i
$519$		0			0
$520$	−2.50362	+	4.33639i	−0.109791	+	0.190163i
$521$	−30.3308			−1.32882			−0.664408	−	0.747370i	$-0.731316\pi$
$521$	−30.3308			−1.32882			−0.664408	+	0.747370i	$0.731316\pi$
$522$		0			0
$523$	13.5519			0.592582			0.296291	−	0.955098i	$-0.404250\pi$
$523$	13.5519			0.592582			0.296291	+	0.955098i	$0.404250\pi$
$524$	2.86864	−	4.96864i	0.125317	−	0.217056i
$525$		0			0
$526$	7.44756	+	12.8996i	0.324729	+	0.562447i
$527$	−5.22703	−	9.05348i	−0.227693	−	0.394376i
$528$		0			0
$529$	2.09441	−	3.62763i	0.0910615	−	0.157723i
$530$	−5.92433			−0.257336
$531$		0			0
$532$	1.63489			0.0708816
$533$	−11.5351	+	19.9794i	−0.499642	+	0.865405i
$534$		0			0
$535$	2.53299	+	4.38726i	0.109511	+	0.189678i
$536$	3.57079	+	6.18479i	0.154235	+	0.267142i
$537$		0			0
$538$	14.2860	−	24.7441i	0.615913	−	1.06679i
$539$	9.55854			0.411715
$540$		0			0
$541$	6.78464			0.291694			0.145847	−	0.989307i	$-0.453409\pi$
$541$	6.78464			0.291694			0.145847	+	0.989307i	$0.453409\pi$
$542$	−8.85572	+	15.3386i	−0.380386	+	0.658848i
$543$		0			0
$544$	0.712956	+	1.23488i	0.0305677	+	0.0529448i
$545$	10.6198	+	18.3940i	0.454902	+	0.787914i
$546$		0			0
$547$	15.5510	−	26.9351i	0.664913	−	1.15166i	−0.314396	−	0.949292i	$-0.601802\pi$
$547$	15.5510	−	26.9351i	0.664913	−	1.15166i	0.979309	−	0.202371i	$-0.0648648\pi$
$548$	21.1576			0.903808
$549$		0			0
$550$	−8.14350			−0.347240
$551$	−0.700052	+	1.21253i	−0.0298232	+	0.0516553i
$552$		0			0
$553$	8.83550	+	15.3035i	0.375724	+	0.650773i
$554$	8.37956	+	14.5138i	0.356013	+	0.616633i
$555$		0			0
$556$	−9.18089	+	15.9018i	−0.389356	+	0.674385i
$557$	−23.6478			−1.00199			−0.500995	−	0.865450i	$-0.667033\pi$
$557$	−23.6478			−1.00199			−0.500995	+	0.865450i	$0.667033\pi$
$558$		0			0
$559$	−38.2693			−1.61862
$560$	−0.936845	+	1.62266i	−0.0395889	+	0.0685701i
$561$		0			0
$562$	2.02850	+	3.51347i	0.0855673	+	0.148207i
$563$	−16.1173	−	27.9160i	−0.679263	−	1.17652i	−0.975203	−	0.221311i	$-0.928966\pi$
$563$	−16.1173	−	27.9160i	−0.679263	−	1.17652i	0.295940	−	0.955206i	$-0.404367\pi$
$564$		0			0
$565$	5.92581	−	10.2638i	0.249301	−	0.431801i
$566$	−19.3861			−0.814857
$567$		0			0
$568$	12.0806			0.506889
$569$	14.5117	−	25.1350i	0.608361	−	1.05371i	−0.383150	−	0.923686i	$-0.625161\pi$
$569$	14.5117	−	25.1350i	0.608361	−	1.05371i	0.991511	−	0.130026i	$-0.0415060\pi$
$570$		0			0
$571$	9.28675	+	16.0851i	0.388638	+	0.673141i	0.992267	−	0.124124i	$-0.0396122\pi$
$571$	9.28675	+	16.0851i	0.388638	+	0.673141i	−0.603628	+	0.797266i	$0.706279\pi$
$572$	4.82561	+	8.35820i	0.201769	+	0.349474i
$573$		0			0
$574$	−4.31641	+	7.47623i	−0.180163	+	0.312052i
$575$	15.9892			0.666796
$576$		0			0
$577$	−9.63391			−0.401065			−0.200533	−	0.979687i	$-0.564267\pi$
$577$	−9.63391			−0.401065			−0.200533	+	0.979687i	$0.564267\pi$
$578$	−7.48339	+	12.9616i	−0.311268	+	0.539132i
$579$		0			0
$580$	−0.802304	−	1.38963i	−0.0333138	−	0.0577013i
$581$	4.24844	+	7.35851i	0.176255	+	0.305283i
$582$		0			0
$583$	−5.70943	+	9.88902i	−0.236460	+	0.409561i
$584$	−6.78533			−0.280779
$585$		0			0
$586$	−1.03103			−0.0425913
$587$	−12.8763	+	22.3024i	−0.531461	+	0.920518i	0.467865	+	0.883800i	$0.345024\pi$
$587$	−12.8763	+	22.3024i	−0.531461	+	0.920518i	−0.999326	+	0.0367175i	$0.988310\pi$
$588$		0			0
$589$	3.66575	+	6.34926i	0.151044	+	0.261617i
$590$	0.748470	+	1.29639i	0.0308140	+	0.0533714i
$591$		0			0
$592$	−3.47314	+	6.01565i	−0.142745	+	0.247242i
$593$	23.1785			0.951825			0.475913	−	0.879493i	$-0.342118\pi$
$593$	23.1785			0.951825			0.475913	+	0.879493i	$0.342118\pi$
$594$		0			0
$595$	2.67172			0.109530
$596$	10.1991	−	17.6653i	0.417771	−	0.723600i
$597$		0			0
$598$	−9.47475	−	16.4107i	−0.387451	−	0.671085i
$599$	−22.3463	−	38.7049i	−0.913045	−	1.58144i	−0.809738	−	0.586791i	$-0.800391\pi$
$599$	−22.3463	−	38.7049i	−0.913045	−	1.58144i	−0.103307	−	0.994650i	$-0.532942\pi$
$600$		0			0
$601$	24.1800	−	41.8810i	0.986323	−	1.70836i	0.350422	−	0.936592i	$-0.386038\pi$
$601$	24.1800	−	41.8810i	0.986323	−	1.70836i	0.635901	−	0.771770i	$-0.280629\pi$
$602$	−14.3202			−0.583649
$603$		0			0
$604$	−14.2233			−0.578738
$605$	−3.50718	+	6.07462i	−0.142587	+	0.246968i
$606$		0			0
$607$	−13.4826	−	23.3525i	−0.547240	−	0.947848i	−0.998462	−	0.0554365i	$-0.982345\pi$
$607$	−13.4826	−	23.3525i	−0.547240	−	0.947848i	0.451222	−	0.892412i	$-0.350988\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	0.613928	−	1.06335i	0.0248572	−	0.0430540i
$611$	−13.4243			−0.543091
$612$		0			0
$613$	14.7376			0.595248			0.297624	−	0.954683i	$-0.403806\pi$
$613$	14.7376			0.595248			0.297624	+	0.954683i	$0.403806\pi$
$614$	−4.39525	+	7.61280i	−0.177378	+	0.307228i
$615$		0			0
$616$	1.80573	+	3.12761i	0.0727547	+	0.126015i
$617$	7.57298	+	13.1168i	0.304877	+	0.528062i	0.977234	−	0.212165i	$-0.0680514\pi$
$617$	7.57298	+	13.1168i	0.304877	+	0.528062i	−0.672357	+	0.740227i	$0.734718\pi$
$618$		0			0
$619$	0.730870	−	1.26590i	0.0293761	−	0.0508810i	−0.850964	−	0.525225i	$-0.823981\pi$
$619$	0.730870	−	1.26590i	0.0293761	−	0.0508810i	0.880340	+	0.474344i	$0.157315\pi$
$620$	−8.40235			−0.337447
$621$		0			0
$622$	−30.3994			−1.21890
$623$	6.23190	−	10.7940i	0.249676	−	0.432451i
$624$		0			0
$625$	−3.51164	−	6.08233i	−0.140465	−	0.243293i
$626$	0.531531	+	0.920638i	0.0212442	+	0.0367961i
$627$		0			0
$628$	0.979456	−	1.69647i	0.0390845	−	0.0676964i
$629$	9.90477			0.394929
$630$		0			0
$631$	−8.53126			−0.339624			−0.169812	−	0.985476i	$-0.554316\pi$
$631$	−8.53126			−0.339624			−0.169812	+	0.985476i	$0.554316\pi$
$632$	5.40433	−	9.36057i	0.214973	−	0.372344i
$633$		0			0
$634$	8.30479	+	14.3843i	0.329826	+	0.571275i
$635$	4.67349	+	8.09472i	0.185462	+	0.321229i
$636$		0			0
$637$	9.45277	−	16.3727i	0.374532	−	0.648709i
$638$	−3.09280			−0.122445
$639$		0			0
$640$	1.14606			0.0453021
$641$	−4.52036	+	7.82949i	−0.178543	+	0.309246i	−0.941382	−	0.337343i	$-0.890472\pi$
$641$	−4.52036	+	7.82949i	−0.178543	+	0.309246i	0.762838	+	0.646589i	$0.223805\pi$
$642$		0			0
$643$	9.39572	+	16.2739i	0.370531	+	0.641779i	0.989647	−	0.143521i	$-0.0458424\pi$
$643$	9.39572	+	16.2739i	0.370531	+	0.641779i	−0.619116	+	0.785299i	$0.712509\pi$
$644$	−3.54542	−	6.14084i	−0.139709	−	0.241983i
$645$		0			0
$646$	−0.712956	+	1.23488i	−0.0280509	+	0.0485855i
$647$	−28.8633			−1.13473			−0.567367	−	0.823465i	$-0.692038\pi$
$647$	−28.8633			−1.13473			−0.567367	+	0.823465i	$0.692038\pi$
$648$		0			0
$649$	2.88528			0.113257
$650$	−8.05339	+	13.9489i	−0.315880	+	0.547120i
$651$		0			0
$652$	−2.15587	−	3.73408i	−0.0844304	−	0.146238i
$653$	−23.8280	−	41.2713i	−0.932461	−	1.61507i	−0.779100	−	0.626900i	$-0.784324\pi$
$653$	−23.8280	−	41.2713i	−0.932461	−	1.61507i	−0.153361	−	0.988170i	$-0.549010\pi$
$654$		0			0
$655$	−3.28765	+	5.69437i	−0.128459	+	0.222498i
$656$	5.28035			0.206163
$657$		0			0
$658$	−5.02334			−0.195830
$659$	24.8385	−	43.0216i	0.967571	−	1.67588i	0.265027	−	0.964241i	$-0.414619\pi$
$659$	24.8385	−	43.0216i	0.967571	−	1.67588i	0.702544	−	0.711641i	$-0.252048\pi$
$660$		0			0
$661$	9.00134	+	15.5908i	0.350111	+	0.606411i	0.986269	−	0.165149i	$-0.0528104\pi$
$661$	9.00134	+	15.5908i	0.350111	+	0.606411i	−0.636157	+	0.771559i	$0.719477\pi$
$662$	8.36543	+	14.4893i	0.325132	+	0.563144i
$663$		0			0
$664$	2.59860	−	4.50091i	0.100845	−	0.174669i
$665$	−1.87369			−0.0726586
$666$		0			0
$667$	6.07251			0.235129
$668$	2.47885	−	4.29349i	0.0959096	−	0.166120i
$669$		0			0
$670$	−4.09235	−	7.08816i	−0.158101	−	0.273840i
$671$	−1.18332	−	2.04956i	−0.0456814	−	0.0791226i
$672$		0			0
$673$	−8.33566	+	14.4378i	−0.321316	+	0.556536i	−0.980760	−	0.195218i	$-0.937458\pi$
$673$	−8.33566	+	14.4378i	−0.321316	+	0.556536i	0.659444	+	0.751754i	$0.270792\pi$
$674$	31.5837			1.21656
$675$		0			0
$676$	6.08883			0.234186
$677$	−21.8921	+	37.9182i	−0.841380	+	1.45731i	0.0473478	+	0.998878i	$0.484923\pi$
$677$	−21.8921	+	37.9182i	−0.841380	+	1.45731i	−0.888728	+	0.458435i	$0.848410\pi$
$678$		0			0
$679$	12.7083	+	22.0114i	0.487700	+	0.844721i
$680$	−0.817092	−	1.41524i	−0.0313341	−	0.0542722i
$681$		0			0
$682$	−8.09757	+	14.0254i	−0.310072	+	0.537060i
$683$	−33.3197			−1.27494			−0.637472	−	0.770474i	$-0.720020\pi$
$683$	−33.3197			−1.27494			−0.637472	+	0.770474i	$0.720020\pi$
$684$		0			0
$685$	−24.2480			−0.926467
$686$	9.25932	−	16.0376i	0.353522	−	0.612319i
$687$		0			0
$688$	4.37956	+	7.58562i	0.166969	+	0.289199i
$689$	11.2925	+	19.5592i	0.430210	+	0.745146i
$690$		0			0
$691$	25.0713	−	43.4248i	0.953757	−	1.65196i	0.216570	−	0.976267i	$-0.430513\pi$
$691$	25.0713	−	43.4248i	0.953757	−	1.65196i	0.737187	−	0.675689i	$-0.236154\pi$
$692$	13.1012			0.498032
$693$		0			0
$694$	34.5656			1.31209
$695$	10.5219	−	18.2244i	0.399117	−	0.691292i
$696$		0			0
$697$	−3.76466	−	6.52057i	−0.142597	−	0.246984i
$698$	2.51645	+	4.35862i	0.0952491	+	0.164976i
$699$		0			0
$700$	−3.01355	+	5.21962i	−0.113901	+	0.197283i
$701$	38.8954			1.46906			0.734529	−	0.678578i	$-0.237403\pi$
$701$	38.8954			1.46906			0.734529	+	0.678578i	$0.237403\pi$
$702$		0			0
$703$	−6.94627			−0.261984
$704$	1.10449	−	1.91303i	0.0416271	−	0.0721002i
$705$		0			0
$706$	0.814604	+	1.41094i	0.0306580	+	0.0531013i
$707$	6.47851	+	11.2211i	0.243650	+	0.422014i
$708$		0			0
$709$	20.2895	−	35.1425i	0.761989	−	1.31980i	−0.179835	−	0.983697i	$-0.557556\pi$
$709$	20.2895	−	35.1425i	0.761989	−	1.31980i	0.941824	−	0.336107i	$-0.109110\pi$
$710$	−13.8451			−0.519597
$711$		0			0
$712$	−7.62362			−0.285707
$713$	15.8990	−	27.5379i	0.595423	−	1.03130i
$714$		0			0
$715$	−5.53045	−	9.57902i	−0.206827	−	0.358235i
$716$	−6.14919	−	10.6507i	−0.229806	−	0.398036i
$717$		0			0
$718$	−1.48026	+	2.56389i	−0.0552429	+	0.0956835i
$719$	−31.4899			−1.17437			−0.587187	−	0.809451i	$-0.699765\pi$
$719$	−31.4899			−1.17437			−0.587187	+	0.809451i	$0.699765\pi$
$720$		0			0
$721$	7.10078			0.264447
$722$	0.500000	−	0.866025i	0.0186081	−	0.0322301i
$723$		0			0
$724$	0.697813	+	1.20865i	0.0259340	+	0.0449190i
$725$	−2.58077	−	4.47002i	−0.0958474	−	0.166013i
$726$		0			0
$727$	1.31306	−	2.27429i	0.0486987	−	0.0843487i	−0.840649	−	0.541581i	$-0.817826\pi$
$727$	1.31306	−	2.27429i	0.0486987	−	0.0843487i	0.889347	+	0.457232i	$0.151159\pi$
$728$	7.14298			0.264736
$729$		0			0
$730$	7.77641			0.287818
$731$	6.24486	−	10.8164i	0.230975	−	0.400060i
$732$		0			0
$733$	4.04043	+	6.99824i	0.149237	+	0.258486i	0.930946	−	0.365158i	$-0.118985\pi$
$733$	4.04043	+	6.99824i	0.149237	+	0.258486i	−0.781709	+	0.623644i	$0.785652\pi$
$734$	−14.1162	−	24.4500i	−0.521040	−	0.902468i
$735$		0			0
$736$	−2.16859	+	3.75611i	−0.0799354	+	0.138452i
$737$	−15.7756			−0.581103
$738$		0			0
$739$	46.0684			1.69465			0.847326	−	0.531073i	$-0.178211\pi$
$739$	46.0684			1.69465			0.847326	+	0.531073i	$0.178211\pi$
$740$	3.98043	−	6.89431i	0.146324	−	0.253440i
$741$		0			0
$742$	4.22562	+	7.31898i	0.155127	+	0.268688i
$743$	18.0871	+	31.3277i	0.663550	+	1.14930i	0.979676	+	0.200585i	$0.0642844\pi$
$743$	18.0871	+	31.3277i	0.663550	+	1.14930i	−0.316126	+	0.948717i	$0.602382\pi$
$744$		0			0
$745$	−11.6888	+	20.2456i	−0.428244	+	0.741741i
$746$	9.86453			0.361166
$747$		0			0
$748$	−3.14981			−0.115169
$749$	3.61338	−	6.25856i	0.132030	−	0.228683i
$750$		0			0
$751$	11.3308	+	19.6256i	0.413468	+	0.716148i	0.995266	−	0.0971851i	$-0.0309839\pi$
$751$	11.3308	+	19.6256i	0.413468	+	0.716148i	−0.581798	+	0.813333i	$0.697651\pi$
$752$	1.53629	+	2.66093i	0.0560227	+	0.0970342i
$753$		0			0
$754$	−3.05858	+	5.29762i	−0.111387	+	0.192928i
$755$	16.3008			0.593247
$756$		0			0
$757$	6.45466			0.234599			0.117299	−	0.993097i	$-0.462576\pi$
$757$	6.45466			0.234599			0.117299	+	0.993097i	$0.462576\pi$
$758$	−2.18039	+	3.77655i	−0.0791955	+	0.137171i
$759$		0			0
$760$	0.573032	+	0.992520i	0.0207860	+	0.0360025i
$761$	3.73318	+	6.46606i	0.135328	+	0.234394i	0.925723	−	0.378203i	$-0.123458\pi$
$761$	3.73318	+	6.46606i	0.135328	+	0.234394i	−0.790395	+	0.612598i	$0.790125\pi$
$762$		0			0
$763$	15.1495	−	26.2397i	0.548448	−	0.949939i
$764$	0.104472			0.00377968
$765$		0			0
$766$	−33.3710			−1.20574
$767$	2.85335	−	4.94215i	0.103029	−	0.178451i
$768$		0			0
$769$	12.4774	+	21.6115i	0.449947	+	0.779331i	0.998382	−	0.0568620i	$-0.0181095\pi$
$769$	12.4774	+	21.6115i	0.449947	+	0.779331i	−0.548435	+	0.836193i	$0.684776\pi$
$770$	−2.06947	−	3.58444i	−0.0745787	−	0.129174i
$771$		0			0
$772$	10.4870	−	18.1640i	0.377435	−	0.653736i
$773$	52.8951			1.90250			0.951252	−	0.308414i	$-0.0997982\pi$
$773$	52.8951			1.90250			0.951252	+	0.308414i	$0.0997982\pi$
$774$		0			0
$775$	−27.0278			−0.970869
$776$	7.77317	−	13.4635i	0.279041	−	0.483312i
$777$		0			0
$778$	6.61771	+	11.4622i	0.237256	+	0.410940i
$779$	2.64018	+	4.57292i	0.0945941	+	0.163842i
$780$		0			0
$781$	−13.3429	+	23.1105i	−0.477445	+	0.826960i
$782$	6.18444			0.221155
$783$		0			0
$784$	−4.32712			−0.154540
$785$	−1.12252	+	1.94426i	−0.0400644	+	0.0693936i
$786$		0			0
$787$	−18.3515	−	31.7858i	−0.654161	−	1.13304i	−0.982103	−	0.188343i	$-0.939688\pi$
$787$	−18.3515	−	31.7858i	−0.654161	−	1.13304i	0.327942	−	0.944698i	$-0.393645\pi$
$788$	10.7375	+	18.5980i	0.382509	+	0.662525i
$789$		0			0
$790$	−6.19370	+	10.7278i	−0.220362	+	0.381678i
$791$	−16.9067			−0.601133
$792$		0			0
$793$	−4.68089			−0.166223
$794$	13.8307	−	23.9555i	0.490835	−	0.850151i
$795$		0			0
$796$	−3.19440	−	5.53286i	−0.113222	−	0.196107i
$797$	−6.58912	−	11.4127i	−0.233398	−	0.404258i	0.725408	−	0.688320i	$-0.241651\pi$
$797$	−6.58912	−	11.4127i	−0.233398	−	0.404258i	−0.958806	+	0.284062i	$0.908318\pi$
$798$		0			0
$799$	2.19061	−	3.79425i	0.0774983	−	0.134231i
$800$	3.68654			0.130339
$801$		0			0
$802$	7.81861			0.276085
$803$	7.49433	−	12.9806i	0.264469	−	0.458074i
$804$		0			0
$805$	4.06327	+	7.03779i	0.143212	+	0.248050i
$806$	16.0159	+	27.7404i	0.564137	+	0.977114i
$807$		0			0
$808$	3.96265	−	6.86352i	0.139406	−	0.241458i
$809$	53.7680			1.89038			0.945191	−	0.326519i	$-0.105876\pi$
$809$	53.7680			1.89038			0.945191	+	0.326519i	$0.105876\pi$
$810$		0			0
$811$	−26.3479			−0.925200			−0.462600	−	0.886567i	$-0.653083\pi$
$811$	−26.3479			−0.925200			−0.462600	+	0.886567i	$0.653083\pi$
$812$	−1.14451	+	1.98235i	−0.0401644	+	0.0695669i
$813$		0			0
$814$	−7.67209	−	13.2885i	−0.268907	−	0.465760i
$815$	2.47076	+	4.27949i	0.0865471	+	0.149904i
$816$		0			0
$817$	−4.37956	+	7.58562i	−0.153221	+	0.265387i
$818$	−19.6064			−0.685522
$819$		0			0
$820$	−6.05161			−0.211332
$821$	16.0585	−	27.8142i	0.560447	−	0.970722i	−0.437011	−	0.899456i	$-0.643963\pi$
$821$	16.0585	−	27.8142i	0.560447	−	0.970722i	0.997457	−	0.0712657i	$-0.0227038\pi$
$822$		0			0
$823$	25.8298	+	44.7386i	0.900372	+	1.55949i	0.827012	+	0.562184i	$0.190039\pi$
$823$	25.8298	+	44.7386i	0.900372	+	1.55949i	0.0733601	+	0.997306i	$0.476628\pi$
$824$	−2.17163	−	3.76138i	−0.0756525	−	0.131034i
$825$		0			0
$826$	1.06771	−	1.84934i	0.0371505	−	0.0643466i
$827$	−10.0857			−0.350713			−0.175357	−	0.984505i	$-0.556108\pi$
$827$	−10.0857			−0.350713			−0.175357	+	0.984505i	$0.556108\pi$
$828$		0			0
$829$	15.4641			0.537092			0.268546	−	0.963267i	$-0.413457\pi$
$829$	15.4641			0.537092			0.268546	+	0.963267i	$0.413457\pi$
$830$	−2.97816	+	5.15833i	−0.103374	+	0.179048i
$831$		0			0
$832$	−2.18454	−	3.78373i	−0.0757352	−	0.131177i
$833$	3.08505	+	5.34346i	0.106891	+	0.185140i
$834$		0			0
$835$	−2.84092	+	4.92061i	−0.0983140	+	0.170285i
$836$	2.20898			0.0763992
$837$		0			0
$838$	13.1970			0.455884
$839$	−12.1835	+	21.1024i	−0.420621	+	0.728537i	−0.996000	−	0.0893500i	$-0.971521\pi$
$839$	−12.1835	+	21.1024i	−0.420621	+	0.728537i	0.575380	+	0.817887i	$0.304854\pi$
$840$		0			0
$841$	13.5199	+	23.4171i	0.466202	+	0.807485i
$842$	−15.1960	−	26.3202i	−0.523688	−	0.907054i
$843$		0			0
$844$	0.151291	−	0.262044i	0.00520765	−	0.00901991i
$845$	−6.97819			−0.240057
$846$		0			0
$847$	10.0062			0.343817
$848$	2.58464	−	4.47673i	0.0887570	−	0.153732i
$849$		0			0
$850$	−2.62834	−	4.55242i	−0.0901513	−	0.156147i
$851$	15.0636	+	26.0910i	0.516375	+	0.894387i
$852$		0			0
$853$	−13.5908	+	23.5400i	−0.465341	+	0.805994i	−0.999217	−	0.0395686i	$-0.987402\pi$
$853$	−13.5908	+	23.5400i	−0.465341	+	0.805994i	0.533876	+	0.845563i	$0.320735\pi$
$854$	−1.75157			−0.0599376
$855$		0			0
$856$	−4.42033			−0.151084
$857$	−21.9284	+	37.9811i	−0.749060	+	1.29741i	0.199214	+	0.979956i	$0.436161\pi$
$857$	−21.9284	+	37.9811i	−0.749060	+	1.29741i	−0.948274	+	0.317454i	$0.897172\pi$
$858$		0			0
$859$	26.5531	+	45.9913i	0.905979	+	1.56920i	0.819597	+	0.572940i	$0.194197\pi$
$859$	26.5531	+	45.9913i	0.905979	+	1.56920i	0.0863825	+	0.996262i	$0.472469\pi$
$860$	−5.01925	−	8.69360i	−0.171155	−	0.296449i
$861$		0			0
$862$	6.13373	−	10.6239i	0.208916	−	0.361853i
$863$	−9.08908			−0.309396			−0.154698	−	0.987962i	$-0.549440\pi$
$863$	−9.08908			−0.309396			−0.154698	+	0.987962i	$0.549440\pi$
$864$		0			0
$865$	−15.0148			−0.510518
$866$	−1.65129	+	2.86012i	−0.0561133	+	0.0971910i
$867$		0			0
$868$	5.99311	+	10.3804i	0.203419	+	0.352333i
$869$	11.9381	+	20.6773i	0.404971	+	0.701431i
$870$		0			0
$871$	−15.6011	+	27.0218i	−0.528622	+	0.915600i
$872$	−18.5327			−0.627595
$873$		0			0
$874$	−4.33718			−0.146707
$875$	8.13795	−	14.0953i	0.275113	−	0.476509i
$876$		0			0
$877$	−4.63591	−	8.02963i	−0.156544	−	0.271141i	0.777076	−	0.629406i	$-0.216702\pi$
$877$	−4.63591	−	8.02963i	−0.156544	−	0.271141i	−0.933620	+	0.358265i	$0.883369\pi$
$878$	10.4785	+	18.1493i	0.353633	+	0.612510i
$879$		0			0
$880$	−1.26582	+	2.19246i	−0.0426707	+	0.0739078i
$881$	−0.681963			−0.0229759			−0.0114880	−	0.999934i	$-0.503657\pi$
$881$	−0.681963			−0.0229759			−0.0114880	+	0.999934i	$0.503657\pi$
$882$		0			0
$883$	−1.29612			−0.0436179			−0.0218090	−	0.999762i	$-0.506943\pi$
$883$	−1.29612			−0.0436179			−0.0218090	+	0.999762i	$0.506943\pi$
$884$	−3.11496	+	5.39527i	−0.104767	+	0.181462i
$885$		0			0
$886$	−17.4811	−	30.2782i	−0.587291	−	1.01722i
$887$	10.7287	+	18.5826i	0.360234	+	0.623943i	0.987999	−	0.154460i	$-0.0493636\pi$
$887$	10.7287	+	18.5826i	0.360234	+	0.623943i	−0.627765	+	0.778403i	$0.716030\pi$
$888$		0			0
$889$	6.66687	−	11.5474i	0.223600	−	0.387286i
$890$	8.73715			0.292870
$891$		0			0
$892$	21.6610			0.725263
$893$	−1.53629	+	2.66093i	−0.0514100	+	0.0890447i
$894$		0			0
$895$	7.04736	+	12.2064i	0.235567	+	0.408015i
$896$	−0.817447	−	1.41586i	−0.0273090	−	0.0473005i
$897$		0			0
$898$	−6.44222	+	11.1583i	−0.214980	+	0.372356i
$899$	−10.2649			−0.342352
$900$		0			0
$901$	−7.37094			−0.245562
$902$	−5.83210	+	10.1015i	−0.194188	+	0.336343i
$903$		0			0
$904$	5.17058	+	8.95570i	0.171971	+	0.297862i
$905$	−0.799737	−	1.38519i	−0.0265842	−	0.0460451i
$906$		0			0
$907$	1.98110	−	3.43137i	0.0657814	−	0.113937i	−0.831259	−	0.555885i	$-0.812379\pi$
$907$	1.98110	−	3.43137i	0.0657814	−	0.113937i	0.897040	+	0.441949i	$0.145713\pi$
$908$	−7.50858			−0.249181
$909$		0			0
$910$	−8.18630			−0.271373
$911$	−8.58261	+	14.8655i	−0.284355	+	0.492517i	−0.972452	−	0.233101i	$-0.925113\pi$
$911$	−8.58261	+	14.8655i	−0.284355	+	0.492517i	0.688098	+	0.725618i	$0.258446\pi$
$912$		0			0
$913$	5.74027	+	9.94244i	0.189975	+	0.329047i
$914$	−1.35841	−	2.35284i	−0.0449323	−	0.0778250i
$915$		0			0
$916$	3.05764	−	5.29598i	0.101027	−	0.174984i
$917$	9.37986			0.309750
$918$		0			0
$919$	−1.23791			−0.0408350			−0.0204175	−	0.999792i	$-0.506500\pi$
$919$	−1.23791			−0.0408350			−0.0204175	+	0.999792i	$0.506500\pi$
$920$	2.48534	−	4.30474i	0.0819394	−	0.141923i
$921$		0			0
$922$	1.83407	+	3.17670i	0.0604018	+	0.104619i
$923$	26.3904	+	45.7096i	0.868652	+	1.50455i
$924$		0			0
$925$	12.8039	−	22.1769i	0.420988	−	0.729173i
$926$	−12.2995			−0.404186
$927$		0			0
$928$	1.40010			0.0459607
$929$	18.4485	−	31.9538i	0.605276	−	1.04837i	−0.386731	−	0.922192i	$-0.626396\pi$
$929$	18.4485	−	31.9538i	0.605276	−	1.04837i	0.992008	−	0.126177i	$-0.0402708\pi$
$930$		0			0
$931$	−2.16356	−	3.74740i	−0.0709079	−	0.122816i
$932$	−12.6905	−	21.9806i	−0.415691	−	0.719999i
$933$		0			0
$934$	−8.74881	+	15.1534i	−0.286270	+	0.495834i
$935$	3.60988			0.118056
$936$		0			0
$937$	−29.7583			−0.972162			−0.486081	−	0.873914i	$-0.661574\pi$
$937$	−29.7583			−0.972162			−0.486081	+	0.873914i	$0.661574\pi$
$938$	−5.83786	+	10.1115i	−0.190613	+	0.330151i
$939$		0			0
$940$	−1.76069	−	3.04960i	−0.0574272	−	0.0994669i
$941$	14.4325	+	24.9978i	0.470486	+	0.814905i	0.999430	−	0.0337510i	$-0.0107453\pi$
$941$	14.4325	+	24.9978i	0.470486	+	0.814905i	−0.528944	+	0.848656i	$0.677412\pi$
$942$		0			0
$943$	11.4509	−	19.8336i	0.372894	−	0.645871i
$944$	−1.30616			−0.0425118
$945$		0			0
$946$	−19.3487			−0.629082
$947$	18.0124	−	31.1983i	0.585323	−	1.01381i	−0.409512	−	0.912305i	$-0.634301\pi$
$947$	18.0124	−	31.1983i	0.585323	−	1.01381i	0.994835	−	0.101504i	$-0.0323656\pi$
$948$		0			0
$949$	−14.8228	−	25.6739i	−0.481169	−	0.833409i
$950$	1.84327	+	3.19264i	0.0598036	+	0.103583i
$951$		0			0
$952$	−1.16561	+	2.01889i	−0.0377775	+	0.0654326i
$953$	3.29871			0.106856			0.0534278	−	0.998572i	$-0.482985\pi$
$953$	3.29871			0.106856			0.0534278	+	0.998572i	$0.482985\pi$
$954$		0			0
$955$	−0.119732			−0.00387443
$956$	3.08704	−	5.34692i	0.0998421	−	0.172932i
$957$		0			0
$958$	5.75981	+	9.97628i	0.186091	+	0.322319i
$959$	17.2952	+	29.9562i	0.558492	+	0.967336i
$960$		0			0
$961$	−11.3754	+	19.7028i	−0.366949	+	0.635574i
$962$	−30.3488			−0.978484
$963$		0			0
$964$	11.8326			0.381102
$965$	−12.0187	+	20.8171i	−0.386897	+	0.670125i
$966$		0			0
$967$	−25.8504	−	44.7743i	−0.831294	−	1.43984i	−0.897013	−	0.442005i	$-0.854267\pi$
$967$	−25.8504	−	44.7743i	−0.831294	−	1.43984i	0.0657191	−	0.997838i	$-0.479066\pi$
$968$	−3.06020	−	5.30042i	−0.0983585	−	0.170362i
$969$		0			0
$970$	−8.90854	+	15.4300i	−0.286036	+	0.495429i
$971$	4.38750			0.140801			0.0704007	−	0.997519i	$-0.477572\pi$
$971$	4.38750			0.140801			0.0704007	+	0.997519i	$0.477572\pi$
$972$		0			0
$973$	−30.0195			−0.962382
$974$	−15.6610	+	27.1256i	−0.501810	+	0.869160i
$975$		0			0
$976$	0.535684	+	0.927832i	0.0171468	+	0.0296992i
$977$	24.6775	+	42.7426i	0.789502	+	1.36746i	0.926273	+	0.376854i	$0.122994\pi$
$977$	24.6775	+	42.7426i	0.789502	+	1.36746i	−0.136771	+	0.990603i	$0.543672\pi$
$978$		0			0
$979$	8.42022	−	14.5843i	0.269111	−	0.466115i
$980$	4.95916			0.158414
$981$		0			0
$982$	−36.2018			−1.15525
$983$	−26.2273	+	45.4270i	−0.836520	+	1.44890i	0.0562663	+	0.998416i	$0.482080\pi$
$983$	−26.2273	+	45.4270i	−0.836520	+	1.44890i	−0.892787	+	0.450480i	$0.851253\pi$
$984$		0			0
$985$	−12.3059	−	21.3144i	−0.392098	−	0.679134i
$986$	−0.998212	−	1.72895i	−0.0317895	−	0.0550611i
$987$		0			0
$988$	2.18454	−	3.78373i	0.0694994	−	0.120377i
$989$	37.9899			1.20801
$990$		0			0
$991$	−16.9358			−0.537985			−0.268992	−	0.963142i	$-0.586691\pi$
$991$	−16.9358			−0.537985			−0.268992	+	0.963142i	$0.586691\pi$
$992$	3.66575	−	6.34926i	0.116388	−	0.201589i
$993$		0			0
$994$	9.87521	+	17.1044i	0.313223	+	0.542518i
$995$	3.66098	+	6.34101i	0.116061	+	0.201024i
$996$		0			0
$997$	−29.9924	+	51.9483i	−0.949868	+	1.64522i	−0.204171	+	0.978935i	$0.565450\pi$
$997$	−29.9924	+	51.9483i	−0.949868	+	1.64522i	−0.745697	+	0.666285i	$0.767884\pi$
$998$	13.8719			0.439108
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.e.d.343.4		12
3.2	odd	2		342.2.e.c.115.3	✓	12
9.2	odd	6		3078.2.a.x.1.4		6
9.4	even	3	inner	1026.2.e.d.685.4		12
9.5	odd	6		342.2.e.c.229.3	yes	12
9.7	even	3		3078.2.a.v.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.e.c.115.3	✓	12	3.2	odd	2
342.2.e.c.229.3	yes	12	9.5	odd	6
1026.2.e.d.343.4		12	1.1	even	1	trivial
1026.2.e.d.685.4		12	9.4	even	3	inner
3078.2.a.v.1.3		6	9.7	even	3
3078.2.a.x.1.4		6	9.2	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:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1026.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.573032 + 0.992520i) q^{5} +(0.817447 - 1.41586i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.573032 + 0.992520i) q^{5} +(0.817447 - 1.41586i) q^{7} -1.00000 q^{8} +1.14606 q^{10} +(1.10449 - 1.91303i) q^{11} +(-2.18454 - 3.78373i) q^{13} +(-0.817447 - 1.41586i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.42591 q^{17} -1.00000 q^{19} +(0.573032 - 0.992520i) q^{20} +(-1.10449 - 1.91303i) q^{22} +(2.16859 + 3.75611i) q^{23} +(1.84327 - 3.19264i) q^{25} -4.36908 q^{26} -1.63489 q^{28} +(0.700052 - 1.21253i) q^{29} +(-3.66575 - 6.34926i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.712956 - 1.23488i) q^{34} +1.87369 q^{35} +6.94627 q^{37} +(-0.500000 + 0.866025i) q^{38} +(-0.573032 - 0.992520i) q^{40} +(-2.64018 - 4.57292i) q^{41} +(4.37956 - 7.58562i) q^{43} -2.20898 q^{44} +4.33718 q^{46} +(1.53629 - 2.66093i) q^{47} +(2.16356 + 3.74740i) q^{49} +(-1.84327 - 3.19264i) q^{50} +(-2.18454 + 3.78373i) q^{52} -5.16929 q^{53} +2.53163 q^{55} +(-0.817447 + 1.41586i) q^{56} +(-0.700052 - 1.21253i) q^{58} +(0.653079 + 1.13117i) q^{59} +(0.535684 - 0.927832i) q^{61} -7.33149 q^{62} +1.00000 q^{64} +(2.50362 - 4.33639i) q^{65} +(-3.57079 - 6.18479i) q^{67} +(-0.712956 - 1.23488i) q^{68} +(0.936845 - 1.62266i) q^{70} -12.0806 q^{71} +6.78533 q^{73} +(3.47314 - 6.01565i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-1.80573 - 3.12761i) q^{77} +(-5.40433 + 9.36057i) q^{79} -1.14606 q^{80} -5.28035 q^{82} +(-2.59860 + 4.50091i) q^{83} +(0.817092 + 1.41524i) q^{85} +(-4.37956 - 7.58562i) q^{86} +(-1.10449 + 1.91303i) q^{88} +7.62362 q^{89} -7.14298 q^{91} +(2.16859 - 3.75611i) q^{92} +(-1.53629 - 2.66093i) q^{94} +(-0.573032 - 0.992520i) q^{95} +(-7.77317 + 13.4635i) q^{97} +4.32712 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8} + 6 q^{11} - 6 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{19} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 12 q^{26} + 12 q^{28} - 6 q^{29} - 6 q^{31} + 6 q^{32} - 24 q^{35} + 12 q^{37} - 6 q^{38} - 6 q^{41} - 12 q^{43} - 12 q^{44} + 24 q^{46} + 6 q^{47} - 18 q^{49} + 30 q^{50} - 6 q^{52} + 36 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{58} - 12 q^{59} - 12 q^{61} - 12 q^{62} + 12 q^{64} + 6 q^{65} - 18 q^{67} - 12 q^{70} - 36 q^{71} + 48 q^{73} + 6 q^{74} + 6 q^{76} + 6 q^{77} - 18 q^{79} - 12 q^{82} - 12 q^{83} - 36 q^{85} + 12 q^{86} - 6 q^{88} - 12 q^{89} - 24 q^{91} + 12 q^{92} - 6 q^{94} + 18 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 6 * q^7 - 12 * q^8 + 6 * q^11 - 6 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^19 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 12 * q^26 + 12 * q^28 - 6 * q^29 - 6 * q^31 + 6 * q^32 - 24 * q^35 + 12 * q^37 - 6 * q^38 - 6 * q^41 - 12 * q^43 - 12 * q^44 + 24 * q^46 + 6 * q^47 - 18 * q^49 + 30 * q^50 - 6 * q^52 + 36 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^58 - 12 * q^59 - 12 * q^61 - 12 * q^62 + 12 * q^64 + 6 * q^65 - 18 * q^67 - 12 * q^70 - 36 * q^71 + 48 * q^73 + 6 * q^74 + 6 * q^76 + 6 * q^77 - 18 * q^79 - 12 * q^82 - 12 * q^83 - 36 * q^85 + 12 * q^86 - 6 * q^88 - 12 * q^89 - 24 * q^91 + 12 * q^92 - 6 * q^94 + 18 * q^97 - 36 * q^98

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