LMFDB - Embedded newform 2646.2.t.a.2285.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1979,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("2646.1979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.t (of order $6$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2285.8
Root			$1.69547 - 0.354107i$ of defining polynomial
Character	$\chi$	$=$	2646.2285
Dual form			2646.2.t.a.1979.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +(1.55049 + 0.895175i) q^{10} +2.40150i q^{11} +(4.23601 + 2.44566i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.83233 + 3.17369i) q^{17} +(2.61281 - 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +3.76638i q^{23} -1.79465 q^{25} +(2.44566 + 4.23601i) q^{26} +(5.68202 - 3.28052i) q^{29} +(-4.02408 + 2.32330i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.17369 + 1.83233i) q^{34} +(-4.68202 - 8.10950i) q^{37} +3.01701 q^{38} +1.79035i q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 + 1.20075i) q^{44} +(-1.88319 + 3.26178i) q^{46} +(2.56802 - 4.44794i) q^{47} +(-1.55421 - 0.897324i) q^{50} +4.89133i q^{52} +4.29953i q^{55} +6.56103 q^{58} +(7.29501 + 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} -4.64661 q^{62} -1.00000 q^{64} +(7.58394 + 4.37859i) q^{65} +(-0.285115 - 0.493834i) q^{67} -3.66466 q^{68} +5.96254i q^{71} +(10.7226 + 6.19070i) q^{73} -9.36404i q^{74} +(2.61281 + 1.50851i) q^{76} +(-1.51831 + 2.62979i) q^{79} +(-0.895175 + 1.55049i) q^{80} +(-6.99911 + 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} -6.96254i q^{86} -2.40150 q^{88} +(1.87432 + 3.24641i) q^{89} +(-3.26178 + 1.88319i) q^{92} +(4.44794 - 2.56802i) q^{94} +(4.67784 - 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.79035			0.800669			0.400334	−	0.916369i	$-0.368894\pi$
$5$	1.79035			0.800669			0.400334	+	0.916369i	$0.368894\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.55049	+	0.895175i	0.490307	+	0.283079i
$11$			2.40150i			0.724081i	0.932162	+	0.362040i	$0.117920\pi$
$11$			2.40150i			0.724081i	−0.932162	+	0.362040i	$0.882080\pi$
$12$		0			0
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.83233	+	3.17369i	−0.444406	+	0.769734i	−0.998011	−	0.0630460i	$-0.979919\pi$
$17$	−1.83233	+	3.17369i	−0.444406	+	0.769734i	0.553605	+	0.832780i	$0.313252\pi$
$18$		0			0
$19$	2.61281	−	1.50851i	0.599419	−	0.346075i	−0.169394	−	0.985548i	$-0.554181\pi$
$19$	2.61281	−	1.50851i	0.599419	−	0.346075i	0.768813	+	0.639474i	$0.220848\pi$
$20$	0.895175	+	1.55049i	0.200167	+	0.346700i
$21$		0			0
$22$	−1.20075	+	2.07976i	−0.256001	+	0.443407i
$23$			3.76638i			0.785345i	0.919678	+	0.392673i	$0.128449\pi$
$23$			3.76638i			0.785345i	−0.919678	+	0.392673i	$0.871551\pi$
$24$		0			0
$25$	−1.79465			−0.358930
$26$	2.44566	+	4.23601i	0.479634	+	0.830750i
$27$		0			0
$28$		0			0
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.131045	−	0.991376i	$-0.458167\pi$
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.924080	+	0.382200i	$0.124833\pi$
$30$		0			0
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	−0.815763	−	0.578387i	$-0.803682\pi$
$31$	−4.02408	+	2.32330i	−0.722746	+	0.417278i	0.0930163	+	0.995665i	$0.470349\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−3.17369	+	1.83233i	−0.544284	+	0.314242i
$35$		0			0
$36$		0			0
$37$	−4.68202	−	8.10950i	−0.769719	−	1.33319i	−0.937715	−	0.347405i	$-0.887063\pi$
$37$	−4.68202	−	8.10950i	−0.769719	−	1.33319i	0.167996	−	0.985788i	$-0.446271\pi$
$38$	3.01701			0.489424
$39$		0			0
$40$			1.79035i			0.283079i
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	0.356241	+	0.934394i	$0.384058\pi$
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	−0.987330	+	0.158683i	$0.949275\pi$
$42$		0			0
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	−0.999350	−	0.0360419i	$-0.988525\pi$
$43$	−3.48127	−	6.02973i	−0.530888	−	0.919526i	0.468462	−	0.883484i	$-0.344808\pi$
$44$	−2.07976	+	1.20075i	−0.313536	+	0.181020i
$45$		0			0
$46$	−1.88319	+	3.26178i	−0.277661	+	0.480924i
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	−0.615680	−	0.787996i	$-0.711119\pi$
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	0.990265	+	0.139197i	$0.0444520\pi$
$48$		0			0
$49$		0			0
$50$	−1.55421	−	0.897324i	−0.219799	−	0.126901i
$51$		0			0
$52$			4.89133i			0.678305i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$		0			0
$55$			4.29953i			0.579749i
$56$		0			0
$57$		0			0
$58$	6.56103			0.861506
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.745994	+	0.665953i	$0.231975\pi$
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.203735	+	0.979026i	$0.434692\pi$
$60$		0			0
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.972317	−	0.233665i	$-0.0750718\pi$
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.283799	+	0.958884i	$0.408405\pi$
$62$	−4.64661			−0.590120
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.58394	+	4.37859i	0.940672	+	0.543097i
$66$		0			0
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	0.848084	−	0.529862i	$-0.177756\pi$
$67$	−0.285115	−	0.493834i	−0.0348324	−	0.0603315i	−0.882916	+	0.469531i	$0.844423\pi$
$68$	−3.66466			−0.444406
$69$		0			0
$70$		0			0
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$		0			0
$73$	10.7226	+	6.19070i	1.25499	+	0.724567i	0.972096	−	0.234585i	$-0.0753731\pi$
$73$	10.7226	+	6.19070i	1.25499	+	0.724567i	0.282891	+	0.959152i	$0.408706\pi$
$74$		−	9.36404i		−	1.08855i
$75$		0			0
$76$	2.61281	+	1.50851i	0.299710	+	0.173037i
$77$		0			0
$78$		0			0
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	−0.938708	−	0.344713i	$-0.887976\pi$
$79$	−1.51831	+	2.62979i	−0.170824	+	0.295875i	0.767884	+	0.640588i	$0.221309\pi$
$80$	−0.895175	+	1.55049i	−0.100084	+	0.173350i
$81$		0			0
$82$	−6.99911	+	4.04094i	−0.772922	+	0.446247i
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	−0.938297	−	0.345830i	$-0.887597\pi$
$83$	−7.00270	−	12.1290i	−0.768646	−	1.33133i	0.169651	−	0.985504i	$-0.445736\pi$
$84$		0			0
$85$	−3.28052	+	5.68202i	−0.355822	+	0.616302i
$86$		−	6.96254i		−	0.750790i
$87$		0			0
$88$	−2.40150			−0.256001
$89$	1.87432	+	3.24641i	0.198677	+	0.344119i	0.948100	−	0.317973i	$-0.103002\pi$
$89$	1.87432	+	3.24641i	0.198677	+	0.344119i	−0.749423	+	0.662092i	$0.769669\pi$
$90$		0			0
$91$		0			0
$92$	−3.26178	+	1.88319i	−0.340064	+	0.196336i
$93$		0			0
$94$	4.44794	−	2.56802i	0.458770	−	0.264871i
$95$	4.67784	−	2.70075i	0.479936	−	0.277091i
$96$		0			0
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	−0.722323	−	0.691556i	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$		0			0
$99$		0			0
$100$	−0.897324	−	1.55421i	−0.0897324	−	0.155421i
$101$	0.250324			0.0249082			0.0124541	−	0.999922i	$-0.496036\pi$
$101$	0.250324			0.0249082			0.0124541	+	0.999922i	$0.496036\pi$
$102$		0			0
$103$			0.167931i			0.0165468i	0.999966	+	0.00827339i	$0.00263353\pi$
$103$			0.167931i			0.0165468i	−0.999966	+	0.00827339i	$0.997366\pi$
$104$	−2.44566	+	4.23601i	−0.239817	+	0.415375i
$105$		0			0
$106$		0			0
$107$	−6.92024	+	3.99540i	−0.669004	+	0.386250i	−0.795699	−	0.605692i	$-0.792896\pi$
$107$	−6.92024	+	3.99540i	−0.669004	+	0.386250i	0.126695	+	0.991942i	$0.459563\pi$
$108$		0			0
$109$	9.47667	−	16.4141i	0.907700	−	1.57218i	0.0904491	−	0.995901i	$-0.471170\pi$
$109$	9.47667	−	16.4141i	0.907700	−	1.57218i	0.817251	−	0.576282i	$-0.195497\pi$
$110$	−2.14977	+	3.72350i	−0.204972	+	0.355022i
$111$		0			0
$112$		0			0
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	0.546488	−	0.837467i	$-0.315964\pi$
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	−0.452023	+	0.892006i	$0.649298\pi$
$114$		0			0
$115$			6.74314i			0.628801i
$116$	5.68202	+	3.28052i	0.527562	+	0.304588i
$117$		0			0
$118$			14.5900i			1.34312i
$119$		0			0
$120$		0			0
$121$	5.23278			0.475707
$122$	5.66414	+	9.81058i	0.512807	+	0.888208i
$123$		0			0
$124$	−4.02408	−	2.32330i	−0.361373	−	0.208639i
$125$	−12.1648			−1.08805
$126$		0			0
$127$	1.40150			0.124363			0.0621817	−	0.998065i	$-0.480194\pi$
$127$	1.40150			0.124363			0.0621817	+	0.998065i	$0.480194\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	4.37859	+	7.58394i	0.384028	+	0.665156i
$131$	10.4918			0.916671			0.458335	−	0.888779i	$-0.348446\pi$
$131$	10.4918			0.916671			0.458335	+	0.888779i	$0.348446\pi$
$132$		0			0
$133$		0			0
$134$		−	0.570231i		−	0.0492604i
$135$		0			0
$136$	−3.17369	−	1.83233i	−0.272142	−	0.157121i
$137$			4.72056i			0.403305i	0.979457	+	0.201652i	$0.0646311\pi$
$137$			4.72056i			0.403305i	−0.979457	+	0.201652i	$0.935369\pi$
$138$		0			0
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	0.584296	−	0.811540i	$-0.301371\pi$
$139$	2.04707	+	1.18187i	0.173630	+	0.100245i	−0.410666	+	0.911786i	$0.634704\pi$
$140$		0			0
$141$		0			0
$142$	−2.98127	+	5.16371i	−0.250182	+	0.433329i
$143$	−5.87327	+	10.1728i	−0.491148	+	0.850692i
$144$		0			0
$145$	10.1728	−	5.87327i	0.844805	−	0.487749i
$146$	6.19070	+	10.7226i	0.512346	+	0.887410i
$147$		0			0
$148$	4.68202	−	8.10950i	0.384860	−	0.666597i
$149$		−	17.3640i		−	1.42252i	−0.702930	−	0.711259i	$-0.748125\pi$
$149$		−	17.3640i		−	1.42252i	0.702930	−	0.711259i	$-0.251875\pi$
$150$		0			0
$151$	−11.2328			−0.914110			−0.457055	−	0.889438i	$-0.651096\pi$
$151$	−11.2328			−0.914110			−0.457055	+	0.889438i	$0.651096\pi$
$152$	1.50851	+	2.61281i	0.122356	+	0.211927i
$153$		0			0
$154$		0			0
$155$	−7.20451	+	4.15953i	−0.578680	+	0.334101i
$156$		0			0
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.0616014	−	0.998101i	$-0.480379\pi$
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.895181	+	0.445702i	$0.147046\pi$
$158$	−2.62979	+	1.51831i	−0.209215	+	0.120790i
$159$		0			0
$160$	−1.55049	+	0.895175i	−0.122577	+	0.0707698i
$161$		0			0
$162$		0			0
$163$	2.16789	+	3.75489i	0.169802	+	0.294106i	0.938350	−	0.345686i	$-0.112354\pi$
$163$	2.16789	+	3.75489i	0.169802	+	0.294106i	−0.768548	+	0.639792i	$0.779020\pi$
$164$	−8.08188			−0.631088
$165$		0			0
$166$		−	14.0054i		−	1.08703i
$167$	−6.20756	+	10.7518i	−0.480355	+	0.832000i	−0.999746	−	0.0225370i	$-0.992826\pi$
$167$	−6.20756	+	10.7518i	−0.480355	+	0.832000i	0.519391	+	0.854537i	$0.326159\pi$
$168$		0			0
$169$	5.46254	+	9.46139i	0.420195	+	0.727799i
$170$	−5.68202	+	3.28052i	−0.435791	+	0.251604i
$171$		0			0
$172$	3.48127	−	6.02973i	0.265444	−	0.459763i
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	−0.317913	−	0.948120i	$-0.602982\pi$
$173$	8.70908	−	15.0846i	0.662139	−	1.14686i	0.980052	−	0.198739i	$-0.0636846\pi$
$174$		0			0
$175$		0			0
$176$	−2.07976	−	1.20075i	−0.156768	−	0.0905101i
$177$		0			0
$178$			3.74863i			0.280972i
$179$	−11.3640	−	6.56103i	−0.849388	−	0.490395i	0.0110562	−	0.999939i	$-0.496481\pi$
$179$	−11.3640	−	6.56103i	−0.849388	−	0.490395i	−0.860444	+	0.509544i	$0.829814\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$		0			0
$183$		0			0
$184$	−3.76638			−0.277661
$185$	−8.38245	−	14.5188i	−0.616290	−	1.06745i
$186$		0			0
$187$	−7.62164	−	4.40035i	−0.557349	−	0.321786i
$188$	5.13604			0.374584
$189$		0			0
$190$	5.40150			0.391866
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	0.181227	−	0.983441i	$-0.441993\pi$
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	−0.761072	+	0.648668i	$0.775326\pi$
$192$		0			0
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.846923	+	0.531716i	$0.178452\pi$
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.0370176	+	0.999315i	$0.488214\pi$
$194$	−5.51087			−0.395658
$195$		0			0
$196$		0			0
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$		0			0
$199$	−0.155144	−	0.0895727i	−0.0109979	−	0.00634964i	0.494491	−	0.869183i	$-0.335355\pi$
$199$	−0.155144	−	0.0895727i	−0.0109979	−	0.00634964i	−0.505489	+	0.862833i	$0.668688\pi$
$200$		−	1.79465i		−	0.126901i
$201$		0			0
$202$	0.216787	+	0.125162i	0.0152531	+	0.00880637i
$203$		0			0
$204$		0			0
$205$	−7.23469	+	12.5309i	−0.505293	+	0.875193i
$206$	−0.0839657	+	0.145433i	−0.00585017	+	0.0101328i
$207$		0			0
$208$	−4.23601	+	2.44566i	−0.293715	+	0.169576i
$209$	3.62268	+	6.27467i	0.250586	+	0.434028i
$210$		0			0
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	−0.479192	−	0.877710i	$-0.659070\pi$
$211$	7.56103	−	13.0961i	0.520523	−	0.901572i	0.999715	−	0.0238622i	$-0.00759629\pi$
$212$		0			0
$213$		0			0
$214$	−7.99080			−0.546240
$215$	−6.23269	−	10.7953i	−0.425066	−	0.736235i
$216$		0			0
$217$		0			0
$218$	16.4141	−	9.47667i	1.11170	−	0.641841i
$219$		0			0
$220$	−3.72350	+	2.14977i	−0.251039	+	0.144937i
$221$	−15.5236	+	8.96254i	−1.04423	+	0.602885i
$222$		0			0
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	−0.236406	−	0.971654i	$-0.575970\pi$
$223$	7.27049	−	4.19762i	0.486868	−	0.281093i	0.723274	+	0.690561i	$0.242636\pi$
$224$		0			0
$225$		0			0
$226$	0.579764	+	1.00418i	0.0385653	+	0.0667971i
$227$	−2.42522			−0.160967			−0.0804836	−	0.996756i	$-0.525646\pi$
$227$	−2.42522			−0.160967			−0.0804836	+	0.996756i	$0.525646\pi$
$228$		0			0
$229$			2.01975i			0.133469i	0.997771	+	0.0667344i	$0.0212580\pi$
$229$			2.01975i			0.133469i	−0.997771	+	0.0667344i	$0.978742\pi$
$230$	−3.37157	+	5.83973i	−0.222315	+	0.385061i
$231$		0			0
$232$	3.28052	+	5.68202i	0.215376	+	0.373043i
$233$	11.0236	−	6.36446i	0.722178	−	0.416950i	−0.0933759	−	0.995631i	$-0.529766\pi$
$233$	11.0236	−	6.36446i	0.722178	−	0.416950i	0.815554	+	0.578681i	$0.196432\pi$
$234$		0			0
$235$	4.59766	−	7.96337i	0.299918	−	0.519473i
$236$	−7.29501	+	12.6353i	−0.474864	+	0.822489i
$237$		0			0
$238$		0			0
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.0759814	−	0.997109i	$-0.524209\pi$
$239$	−15.1117	−	8.72474i	−0.977494	−	0.564356i	−0.901513	+	0.432753i	$0.857542\pi$
$240$		0			0
$241$		−	11.4332i		−	0.736476i	−0.929732	−	0.368238i	$-0.879961\pi$
$241$		−	11.4332i		−	0.736476i	0.929732	−	0.368238i	$-0.120039\pi$
$242$	4.53172	+	2.61639i	0.291310	+	0.168188i
$243$		0			0
$244$			11.3283i			0.725219i
$245$		0			0
$246$		0			0
$247$	14.7572			0.938977
$248$	−2.32330	−	4.02408i	−0.147530	−	0.255529i
$249$		0			0
$250$	−10.5350	−	6.08240i	−0.666293	−	0.384685i
$251$	−27.3560			−1.72669			−0.863347	−	0.504611i	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$	1.21374	+	0.700752i	0.0761567	+	0.0439691i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.49673			−0.218120			−0.109060	−	0.994035i	$-0.534784\pi$
$257$	−3.49673			−0.218120			−0.109060	+	0.994035i	$0.534784\pi$
$258$		0			0
$259$		0			0
$260$			8.75718i			0.543097i
$261$		0			0
$262$	9.08614	+	5.24589i	0.561344	+	0.324092i
$263$			9.64348i			0.594643i	0.954777	+	0.297321i	$0.0960932\pi$
$263$			9.64348i			0.594643i	−0.954777	+	0.297321i	$0.903907\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.285115	−	0.493834i	0.0174162	−	0.0301657i
$269$	3.45554	−	5.98517i	0.210688	−	0.364922i	−0.741242	−	0.671238i	$-0.765763\pi$
$269$	3.45554	−	5.98517i	0.210688	−	0.364922i	0.951930	+	0.306316i	$0.0990963\pi$
$270$		0			0
$271$	17.8672	−	10.3156i	1.08535	−	0.626629i	0.153017	−	0.988224i	$-0.451101\pi$
$271$	17.8672	−	10.3156i	1.08535	−	0.626629i	0.932335	+	0.361595i	$0.117768\pi$
$272$	−1.83233	−	3.17369i	−0.111101	−	0.192433i
$273$		0			0
$274$	−2.36028	+	4.08812i	−0.142590	+	0.246973i
$275$		−	4.30986i		−	0.259894i
$276$		0			0
$277$	−15.5144			−0.932168			−0.466084	−	0.884740i	$-0.654336\pi$
$277$	−15.5144			−0.932168			−0.466084	+	0.884740i	$0.654336\pi$
$278$	1.18187	+	2.04707i	0.0708841	+	0.122775i
$279$		0			0
$280$		0			0
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	−0.808275	−	0.588805i	$-0.799599\pi$
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	0.105783	+	0.994389i	$0.466265\pi$
$282$		0			0
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	−0.633629	−	0.773637i	$-0.718435\pi$
$283$	−4.71796	+	2.72392i	−0.280454	+	0.161920i	0.353175	+	0.935557i	$0.385102\pi$
$284$	−5.16371	+	2.98127i	−0.306410	+	0.176906i
$285$		0			0
$286$	−10.1728	+	5.87327i	−0.601530	+	0.347294i
$287$		0			0
$288$		0			0
$289$	1.78512	+	3.09191i	0.105007	+	0.181877i
$290$	11.7465			0.689781
$291$		0			0
$292$			12.3814i			0.724567i
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	−0.248583	−	0.968610i	$-0.579965\pi$
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	0.963133	−	0.269026i	$-0.0867017\pi$
$294$		0			0
$295$	13.0606	+	22.6216i	0.760418	+	1.31708i
$296$	8.10950	−	4.68202i	0.471355	−	0.272137i
$297$		0			0
$298$	8.68202	−	15.0377i	0.502936	−	0.871111i
$299$	−9.21130	+	15.9544i	−0.532703	+	0.922670i
$300$		0			0
$301$		0			0
$302$	−9.72787	−	5.61639i	−0.559776	−	0.323187i
$303$		0			0
$304$			3.01701i			0.173037i
$305$	17.5644	+	10.1408i	1.00573	+	0.580660i
$306$		0			0
$307$		−	31.2223i		−	1.78195i	−0.454053	−	0.890975i	$-0.650022\pi$
$307$		−	31.2223i		−	1.78195i	0.454053	−	0.890975i	$-0.349978\pi$
$308$		0			0
$309$		0			0
$310$	−8.31905			−0.472491
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	0.668889	−	0.743362i	$-0.266770\pi$
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	−0.978215	+	0.207594i	$0.933437\pi$
$312$		0			0
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	0.581458	−	0.813576i	$-0.302482\pi$
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	−0.413849	+	0.910346i	$0.635816\pi$
$314$	13.8431			0.781210
$315$		0			0
$316$	−3.03663			−0.170824
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.885693	−	0.464272i	$-0.153684\pi$
$317$	16.4953	+	9.52357i	0.926468	+	0.534897i	0.0407755	+	0.999168i	$0.487017\pi$
$318$		0			0
$319$	7.87817	+	13.6454i	0.441093	+	0.763995i
$320$	−1.79035			−0.100084
$321$		0			0
$322$		0			0
$323$			11.0563i			0.615191i
$324$		0			0
$325$	−7.60215	−	4.38910i	−0.421692	−	0.243464i
$326$			4.33577i			0.240136i
$327$		0			0
$328$	−6.99911	−	4.04094i	−0.386461	−	0.223123i
$329$		0			0
$330$		0			0
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	−0.867030	−	0.498256i	$-0.833974\pi$
$331$	−0.0366251	+	0.0634366i	−0.00201310	+	0.00348679i	0.865017	+	0.501742i	$0.167307\pi$
$332$	7.00270	−	12.1290i	0.384323	−	0.665667i
$333$		0			0
$334$	−10.7518	+	6.20756i	−0.588313	+	0.339663i
$335$	−0.510456	−	0.884136i	−0.0278892	−	0.0483055i
$336$		0			0
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$			10.9251i			0.594246i
$339$		0			0
$340$	−6.56103			−0.355822
$341$	−5.57943	−	9.66385i	−0.302143	−	0.523327i
$342$		0			0
$343$		0			0
$344$	6.02973	−	3.48127i	0.325101	−	0.187697i
$345$		0			0
$346$	15.0846	−	8.70908i	0.810952	−	0.468203i
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.480556	−	0.876964i	$-0.340435\pi$
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.999751	+	0.0223084i	$0.00710156\pi$
$348$		0			0
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$		0			0
$351$		0			0
$352$	−1.20075	−	2.07976i	−0.0640003	−	0.110852i
$353$	2.15957			0.114943			0.0574713	−	0.998347i	$-0.481696\pi$
$353$	2.15957			0.114943			0.0574713	+	0.998347i	$0.481696\pi$
$354$		0			0
$355$			10.6750i			0.566571i
$356$	−1.87432	+	3.24641i	−0.0993385	+	0.172059i
$357$		0			0
$358$	−6.56103	−	11.3640i	−0.346761	−	0.600608i
$359$	−28.2712	+	16.3224i	−1.49210	+	0.861463i	−0.999959	−	0.00905364i	$-0.997118\pi$
$359$	−28.2712	+	16.3224i	−1.49210	+	0.861463i	−0.492139	+	0.870517i	$0.663785\pi$
$360$		0			0
$361$	−4.94882	+	8.57161i	−0.260464	+	0.451138i
$362$	−6.67887	+	11.5681i	−0.351034	+	0.608008i
$363$		0			0
$364$		0			0
$365$	19.1972	+	11.0835i	1.00483	+	0.580138i
$366$		0			0
$367$		−	29.7003i		−	1.55034i	−0.631751	−	0.775171i	$-0.717664\pi$
$367$		−	29.7003i		−	1.55034i	0.631751	−	0.775171i	$-0.282336\pi$
$368$	−3.26178	−	1.88319i	−0.170032	−	0.0981682i
$369$		0			0
$370$		−	16.7649i		−	0.871566i
$371$		0			0
$372$		0			0
$373$	−2.01672			−0.104422			−0.0522109	−	0.998636i	$-0.516627\pi$
$373$	−2.01672			−0.104422			−0.0522109	+	0.998636i	$0.516627\pi$
$374$	−4.40035	−	7.62164i	−0.227537	−	0.394105i
$375$		0			0
$376$	4.44794	+	2.56802i	0.229385	+	0.132436i
$377$	32.0921			1.65283
$378$		0			0
$379$	−18.8709			−0.969332			−0.484666	−	0.874699i	$-0.661059\pi$
$379$	−18.8709			−0.969332			−0.484666	+	0.874699i	$0.661059\pi$
$380$	4.67784	+	2.70075i	0.239968	+	0.138546i
$381$		0			0
$382$	−4.62666	−	8.01361i	−0.236721	−	0.410012i
$383$	0.836511			0.0427437			0.0213719	−	0.999772i	$-0.493197\pi$
$383$	0.836511			0.0427437			0.0213719	+	0.999772i	$0.493197\pi$
$384$		0			0
$385$		0			0
$386$			24.5602i			1.25008i
$387$		0			0
$388$	−4.77256	−	2.75544i	−0.242290	−	0.139886i
$389$		−	24.8219i		−	1.25852i	−0.777195	−	0.629260i	$-0.783358\pi$
$389$		−	24.8219i		−	1.25852i	0.777195	−	0.629260i	$-0.216642\pi$
$390$		0			0
$391$	−11.9533	−	6.90127i	−0.604507	−	0.349012i
$392$		0			0
$393$		0			0
$394$	6.24305	−	10.8133i	0.314520	−	0.544765i
$395$	−2.71831	+	4.70825i	−0.136773	+	0.236898i
$396$		0			0
$397$	−2.62744	+	1.51695i	−0.131867	+	0.0761336i	−0.564482	−	0.825445i	$-0.690924\pi$
$397$	−2.62744	+	1.51695i	−0.131867	+	0.0761336i	0.432615	+	0.901579i	$0.357591\pi$
$398$	−0.0895727	−	0.155144i	−0.00448987	−	0.00777669i
$399$		0			0
$400$	0.897324	−	1.55421i	0.0448662	−	0.0777105i
$401$			13.0771i			0.653038i	0.945191	+	0.326519i	$0.105876\pi$
$401$			13.0771i			0.653038i	−0.945191	+	0.326519i	$0.894124\pi$
$402$		0			0
$403$	−22.7281			−1.13217
$404$	0.125162	+	0.216787i	0.00622705	+	0.0107856i
$405$		0			0
$406$		0			0
$407$	19.4750	−	11.2439i	0.965339	−	0.557339i
$408$		0			0
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	−0.376044	−	0.926602i	$-0.622716\pi$
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	0.614439	+	0.788965i	$0.289382\pi$
$410$	−12.5309	+	7.23469i	−0.618855	+	0.357296i
$411$		0			0
$412$	−0.145433	+	0.0839657i	−0.00716496	+	0.00413669i
$413$		0			0
$414$		0			0
$415$	−12.5373	−	21.7152i	−0.615431	−	1.06596i
$416$	−4.89133			−0.239817
$417$		0			0
$418$			7.24536i			0.354382i
$419$	8.19938	−	14.2017i	0.400566	−	0.693800i	−0.593228	−	0.805034i	$-0.702147\pi$
$419$	8.19938	−	14.2017i	0.400566	−	0.693800i	0.993794	+	0.111234i	$0.0354802\pi$
$420$		0			0
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$	13.0961	−	7.56103i	0.637508	−	0.368065i
$423$		0			0
$424$		0			0
$425$	3.28839	−	5.69566i	0.159510	−	0.276280i
$426$		0			0
$427$		0			0
$428$	−6.92024	−	3.99540i	−0.334502	−	0.193125i
$429$		0			0
$430$		−	12.4654i		−	0.601134i
$431$	−21.6737	−	12.5133i	−1.04398	−	0.602744i	−0.123024	−	0.992404i	$-0.539259\pi$
$431$	−21.6737	−	12.5133i	−1.04398	−	0.602744i	−0.920959	+	0.389660i	$0.872593\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$		0			0
$435$		0			0
$436$	18.9533			0.907700
$437$	5.68161	+	9.84084i	0.271788	+	0.470751i
$438$		0			0
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	0.834507	−	0.550997i	$-0.185752\pi$
$439$	16.2293	+	9.37000i	0.774583	+	0.447206i	−0.0599239	+	0.998203i	$0.519086\pi$
$440$	−4.29953			−0.204972
$441$		0			0
$442$	−17.9251			−0.852609
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	0.475015	−	0.879978i	$-0.342443\pi$
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	−0.524576	+	0.851364i	$0.675776\pi$
$444$		0			0
$445$	3.35568	+	5.81221i	0.159074	+	0.275525i
$446$	8.39524			0.397526
$447$		0			0
$448$		0			0
$449$		−	26.8022i		−	1.26487i	−0.774612	−	0.632436i	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$		0			0
$451$	−16.8084	−	9.70433i	−0.791476	−	0.456959i
$452$			1.15953i			0.0545396i
$453$		0			0
$454$	−2.10030	−	1.21261i	−0.0985719	−	0.0569105i
$455$		0			0
$456$		0			0
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	−0.981291	−	0.192529i	$-0.938331\pi$
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	0.657381	+	0.753559i	$0.271664\pi$
$458$	−1.00987	+	1.74915i	−0.0471883	+	0.0817326i
$459$		0			0
$460$	−5.83973	+	3.37157i	−0.272279	+	0.157200i
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	0.916533	−	0.399959i	$-0.130976\pi$
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	−0.804641	+	0.593761i	$0.797642\pi$
$462$		0			0
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	−0.511041	−	0.859556i	$-0.670740\pi$
$463$	10.5194	−	18.2201i	0.488877	−	0.846760i	0.999918	+	0.0127960i	$0.00407321\pi$
$464$			6.56103i			0.304588i
$465$		0			0
$466$	12.7289			0.589656
$467$	−2.91151	−	5.04288i	−0.134729	−	0.233357i	0.790765	−	0.612120i	$-0.209683\pi$
$467$	−2.91151	−	5.04288i	−0.134729	−	0.233357i	−0.925494	+	0.378763i	$0.876350\pi$
$468$		0			0
$469$		0			0
$470$	7.96337	−	4.59766i	0.367323	−	0.212074i
$471$		0			0
$472$	−12.6353	+	7.29501i	−0.581588	+	0.335780i
$473$	14.4804	−	8.36028i	0.665811	−	0.384406i
$474$		0			0
$475$	−4.68907	+	2.70724i	−0.215149	+	0.124217i
$476$		0			0
$477$		0			0
$478$	−8.72474	−	15.1117i	−0.399060	−	0.691193i
$479$	−26.9561			−1.23166			−0.615828	−	0.787881i	$-0.711178\pi$
$479$	−26.9561			−1.23166			−0.615828	+	0.787881i	$0.711178\pi$
$480$		0			0
$481$		−	45.8026i		−	2.08842i
$482$	5.71659	−	9.90142i	0.260383	−	0.450997i
$483$		0			0
$484$	2.61639	+	4.53172i	0.118927	+	0.205987i
$485$	−8.54455	+	4.93320i	−0.387988	+	0.224005i
$486$		0			0
$487$	6.81338	−	11.8011i	0.308744	−	0.534760i	−0.669344	−	0.742953i	$-0.733425\pi$
$487$	6.81338	−	11.8011i	0.308744	−	0.534760i	0.978088	+	0.208193i	$0.0667581\pi$
$488$	−5.66414	+	9.81058i	−0.256404	+	0.444104i
$489$		0			0
$490$		0			0
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.999637	+	0.0269544i	$0.00858088\pi$
$491$	33.7430	+	19.4815i	1.52280	+	0.879188i	0.523162	+	0.852234i	$0.324752\pi$
$492$		0			0
$493$			24.0440i			1.08289i
$494$	12.7801	+	7.37859i	0.575004	+	0.331979i
$495$		0			0
$496$		−	4.64661i		−	0.208639i
$497$		0			0
$498$		0			0
$499$	26.0097			1.16435			0.582176	−	0.813063i	$-0.302201\pi$
$499$	26.0097			1.16435			0.582176	+	0.813063i	$0.302201\pi$
$500$	−6.08240	−	10.5350i	−0.272013	−	0.471141i
$501$		0			0
$502$	−23.6910	−	13.6780i	−1.05738	−	0.610478i
$503$	10.5271			0.469378			0.234689	−	0.972070i	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$	−7.83319	−	4.52249i	−0.348228	−	0.201049i
$507$		0			0
$508$	0.700752	+	1.21374i	0.0310908	+	0.0538509i
$509$	−0.938871			−0.0416147			−0.0208074	−	0.999784i	$-0.506624\pi$
$509$	−0.938871			−0.0416147			−0.0208074	+	0.999784i	$0.506624\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−3.02826	−	1.74837i	−0.133571	−	0.0771172i
$515$			0.300656i			0.0132485i
$516$		0			0
$517$	10.6818	+	6.16711i	0.469783	+	0.271229i
$518$		0			0
$519$		0			0
$520$	−4.37859	+	7.58394i	−0.192014	+	0.332578i
$521$	19.7527	−	34.2127i	0.865382	−	1.49889i	−0.00128461	−	0.999999i	$-0.500409\pi$
$521$	19.7527	−	34.2127i	0.865382	−	1.49889i	0.866667	−	0.498887i	$-0.166258\pi$
$522$		0			0
$523$	−21.0697	+	12.1646i	−0.921315	+	0.531922i	−0.884054	−	0.467384i	$-0.845197\pi$
$523$	−21.0697	+	12.1646i	−0.921315	+	0.531922i	−0.0372609	+	0.999306i	$0.511863\pi$
$524$	5.24589	+	9.08614i	0.229168	+	0.396930i
$525$		0			0
$526$	−4.82174	+	8.35150i	−0.210238	+	0.364143i
$527$		−	17.0283i		−	0.741763i
$528$		0			0
$529$	8.81436			0.383233
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−34.2349	+	19.7655i	−1.48288	+	0.856141i
$534$		0			0
$535$	−12.3896	+	7.15316i	−0.535651	+	0.309258i
$536$	0.493834	−	0.285115i	0.0213304	−	0.0123151i
$537$		0			0
$538$	5.98517	−	3.45554i	0.258039	−	0.148979i
$539$		0			0
$540$		0			0
$541$	−21.3640	−	37.0036i	−0.918512	−	1.59091i	−0.801677	−	0.597758i	$-0.796058\pi$
$541$	−21.3640	−	37.0036i	−0.918512	−	1.59091i	−0.116835	−	0.993151i	$-0.537275\pi$
$542$	20.6312			0.886187
$543$		0			0
$544$		−	3.66466i		−	0.157121i
$545$	16.9665	−	29.3869i	0.726767	−	1.25880i
$546$		0			0
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	−0.999620	−	0.0275530i	$-0.991229\pi$
$547$	−12.2477	−	21.2136i	−0.523672	−	0.907026i	0.475949	−	0.879473i	$-0.342105\pi$
$548$	−4.08812	+	2.36028i	−0.174636	+	0.100826i
$549$		0			0
$550$	2.15493	−	3.73244i	0.0918864	−	0.159152i
$551$	9.89735	−	17.1427i	0.421641	−	0.730304i
$552$		0			0
$553$		0			0
$554$	−13.4358	−	7.75718i	−0.570834	−	0.329571i
$555$		0			0
$556$			2.36375i			0.100245i
$557$	−2.20344	−	1.27216i	−0.0933627	−	0.0539030i	0.452592	−	0.891718i	$-0.350499\pi$
$557$	−2.20344	−	1.27216i	−0.0933627	−	0.0539030i	−0.545954	+	0.837815i	$0.683833\pi$
$558$		0			0
$559$		−	34.0560i		−	1.44042i
$560$		0			0
$561$		0			0
$562$	−13.5977			−0.573583
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	0.649902	−	0.760018i	$-0.274810\pi$
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	−0.983146	+	0.182823i	$0.941476\pi$
$564$		0			0
$565$	1.79783	+	1.03798i	0.0756354	+	0.0436681i
$566$	−5.44783			−0.228990
$567$		0			0
$568$	−5.96254			−0.250182
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	0.379633	−	0.925137i	$-0.376050\pi$
$569$	−5.52793	−	3.19155i	−0.231743	−	0.133797i	−0.611376	+	0.791340i	$0.709384\pi$
$570$		0			0
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	0.936195	−	0.351480i	$-0.114322\pi$
$571$	3.91188	+	6.77557i	0.163707	+	0.283549i	−0.772488	+	0.635029i	$0.780988\pi$
$572$	−11.7465			−0.491148
$573$		0			0
$574$		0			0
$575$		−	6.75933i		−	0.281884i
$576$		0			0
$577$	−12.4012	−	7.15986i	−0.516270	−	0.298069i	0.219137	−	0.975694i	$-0.429676\pi$
$577$	−12.4012	−	7.15986i	−0.516270	−	0.298069i	−0.735407	+	0.677625i	$0.763009\pi$
$578$			3.57023i			0.148502i
$579$		0			0
$580$	10.1728	+	5.87327i	0.422403	+	0.243874i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−6.19070	+	10.7226i	−0.256173	+	0.443705i
$585$		0			0
$586$	21.1849	−	12.2311i	0.875141	−	0.505263i
$587$	−2.37575	−	4.11492i	−0.0980577	−	0.169841i	0.812823	−	0.582511i	$-0.197930\pi$
$587$	−2.37575	−	4.11492i	−0.0980577	−	0.169841i	−0.910881	+	0.412670i	$0.864596\pi$
$588$		0			0
$589$	−7.00943	+	12.1407i	−0.288819	+	0.500249i
$590$			26.1212i			1.07539i
$591$		0			0
$592$	9.36404			0.384860
$593$	−1.79035	−	3.10098i	−0.0735208	−	0.127342i	0.826921	−	0.562318i	$-0.190090\pi$
$593$	−1.79035	−	3.10098i	−0.0735208	−	0.127342i	−0.900442	+	0.434976i	$0.856757\pi$
$594$		0			0
$595$		0			0
$596$	15.0377	−	8.68202i	0.615968	−	0.355629i
$597$		0			0
$598$	−15.9544	+	9.21130i	−0.652426	+	0.376678i
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	−0.742274	−	0.670096i	$-0.766253\pi$
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	0.209183	+	0.977877i	$0.432920\pi$
$600$		0			0
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$		0			0
$603$		0			0
$604$	−5.61639	−	9.72787i	−0.228528	−	0.395821i
$605$	9.36850			0.380884
$606$		0			0
$607$			24.4832i			0.993741i	0.867825	+	0.496870i	$0.165518\pi$
$607$			24.4832i			0.993741i	−0.867825	+	0.496870i	$0.834482\pi$
$608$	−1.50851	+	2.61281i	−0.0611780	+	0.105963i
$609$		0			0
$610$	10.1408	+	17.5644i	0.410589	+	0.711161i
$611$	21.7563	−	12.5610i	0.880167	−	0.508165i
$612$		0			0
$613$	0.440043	−	0.762177i	0.0177732	−	0.0307840i	−0.857002	−	0.515313i	$-0.827676\pi$
$613$	0.440043	−	0.762177i	0.0177732	−	0.0307840i	0.874775	+	0.484529i	$0.161009\pi$
$614$	15.6111	−	27.0393i	0.630014	−	1.09122i
$615$		0			0
$616$		0			0
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	0.717690	−	0.696362i	$-0.245199\pi$
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	−0.244222	+	0.969719i	$0.578533\pi$
$618$		0			0
$619$			35.4869i			1.42634i	0.700992	+	0.713169i	$0.252741\pi$
$619$			35.4869i			1.42634i	−0.700992	+	0.713169i	$0.747259\pi$
$620$	−7.20451	−	4.15953i	−0.289340	−	0.167051i
$621$		0			0
$622$		−	10.9100i		−	0.437452i
$623$		0			0
$624$		0			0
$625$	−12.8060			−0.512240
$626$	1.71203	+	2.96532i	0.0684263	+	0.118518i
$627$		0			0
$628$	11.9885	+	6.92154i	0.478391	+	0.276199i
$629$	34.3161			1.36827
$630$		0			0
$631$	26.9822			1.07415			0.537073	−	0.843536i	$-0.319530\pi$
$631$	26.9822			1.07415			0.537073	+	0.843536i	$0.319530\pi$
$632$	−2.62979	−	1.51831i	−0.104608	−	0.0603952i
$633$		0			0
$634$	9.52357	+	16.4953i	0.378229	+	0.655112i
$635$	2.50918			0.0995739
$636$		0			0
$637$		0			0
$638$			15.7563i			0.623800i
$639$		0			0
$640$	−1.55049	−	0.895175i	−0.0612884	−	0.0353849i
$641$		−	1.07708i		−	0.0425420i	−0.999774	−	0.0212710i	$-0.993229\pi$
$641$		−	1.07708i		−	0.0425420i	0.999774	−	0.0212710i	$-0.00677128\pi$
$642$		0			0
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.331010	−	0.943627i	$-0.607389\pi$
$643$	−33.3126	−	19.2330i	−1.31372	−	0.758477i	−0.982710	+	0.185150i	$0.940723\pi$
$644$		0			0
$645$		0			0
$646$	−5.52817	+	9.57507i	−0.217503	+	0.376726i
$647$	4.47605	−	7.75275i	0.175972	−	0.304792i	−0.764525	−	0.644594i	$-0.777027\pi$
$647$	4.47605	−	7.75275i	0.175972	−	0.304792i	0.940497	+	0.339802i	$0.110360\pi$
$648$		0			0
$649$	−30.3438	+	17.5190i	−1.19110	+	0.687680i
$650$	−4.38910	−	7.60215i	−0.172155	−	0.298181i
$651$		0			0
$652$	−2.16789	+	3.75489i	−0.0849010	+	0.147053i
$653$		−	11.3846i		−	0.445513i	−0.974874	−	0.222757i	$-0.928494\pi$
$653$		−	11.3846i		−	0.445513i	0.974874	−	0.222757i	$-0.0715055\pi$
$654$		0			0
$655$	18.7839			0.733949
$656$	−4.04094	−	6.99911i	−0.157772	−	0.273269i
$657$		0			0
$658$		0			0
$659$	−31.4373	+	18.1503i	−1.22462	+	0.707036i	−0.965900	−	0.258915i	$-0.916635\pi$
$659$	−31.4373	+	18.1503i	−1.22462	+	0.707036i	−0.258723	+	0.965952i	$0.583302\pi$
$660$		0			0
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.963886	−	0.266315i	$-0.914194\pi$
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$662$	−0.0634366	+	0.0366251i	−0.00246553	+	0.00142348i
$663$		0			0
$664$	12.1290	−	7.00270i	0.470698	−	0.271757i
$665$		0			0
$666$		0			0
$667$	12.3557	+	21.4007i	0.478414	+	0.828637i
$668$	−12.4151			−0.480355
$669$		0			0
$670$		−	1.02091i		−	0.0394413i
$671$	−13.6025	+	23.5602i	−0.525117	+	0.909530i
$672$		0			0
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$	1.93364	−	1.11639i	0.0744811	−	0.0430017i
$675$		0			0
$676$	−5.46254	+	9.46139i	−0.210098	+	0.363900i
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	−0.675889	−	0.737004i	$-0.736240\pi$
$677$	7.81408	−	13.5344i	0.300320	−	0.520169i	0.976208	+	0.216835i	$0.0695733\pi$
$678$		0			0
$679$		0			0
$680$	−5.68202	−	3.28052i	−0.217896	−	0.125802i
$681$		0			0
$682$		−	11.1589i		−	0.427294i
$683$	9.63996	+	5.56563i	0.368863	+	0.212963i	0.672961	−	0.739678i	$-0.265022\pi$
$683$	9.63996	+	5.56563i	0.368863	+	0.212963i	−0.304099	+	0.952640i	$0.598355\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$		0			0
$687$		0			0
$688$	6.96254			0.265444
$689$		0			0
$690$		0			0
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	0.548988	−	0.835830i	$-0.315013\pi$
$691$	2.61903	+	1.51210i	0.0996324	+	0.0575228i	−0.449356	+	0.893353i	$0.648346\pi$
$692$	17.4182			0.662139
$693$		0			0
$694$	31.8409			1.20867
$695$	3.66497	+	2.11597i	0.139020	+	0.0802633i
$696$		0			0
$697$	−14.8087	−	25.6494i	−0.560919	−	0.971540i
$698$	14.7354			0.557745
$699$		0			0
$700$		0			0
$701$		−	50.1486i		−	1.89409i	−0.321103	−	0.947044i	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$		0			0
$703$	−24.4664	−	14.1257i	−0.922769	−	0.532761i
$704$		−	2.40150i		−	0.0905101i
$705$		0			0
$706$	1.87025	+	1.07979i	0.0703876	+	0.0406383i
$707$		0			0
$708$		0			0
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$	−5.33751	+	9.24484i	−0.200313	+	0.346953i
$711$		0			0
$712$	−3.24641	+	1.87432i	−0.121664	+	0.0702429i
$713$	−8.75046	−	15.1562i	−0.327707	−	0.567605i
$714$		0			0
$715$	−10.5152	+	18.2129i	−0.393246	+	0.681123i
$716$		−	13.1221i		−	0.490395i
$717$		0			0
$718$	−32.6448			−1.21829
$719$	17.1580	+	29.7186i	0.639887	+	1.10832i	0.985457	+	0.169924i	$0.0543521\pi$
$719$	17.1580	+	29.7186i	0.639887	+	1.10832i	−0.345571	+	0.938393i	$0.612315\pi$
$720$		0			0
$721$		0			0
$722$	−8.57161	+	4.94882i	−0.319002	+	0.184176i
$723$		0			0
$724$	−11.5681	+	6.67887i	−0.429927	+	0.248218i
$725$	−10.1972	+	5.88737i	−0.378716	+	0.218651i
$726$		0			0
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$727$	−19.4757	+	11.2443i	−0.722315	+	0.417029i	0.0932892	+	0.995639i	$0.470262\pi$
$728$		0			0
$729$		0			0
$730$	11.0835	+	19.1972i	0.410220	+	0.710521i
$731$	25.5154			0.943720
$732$		0			0
$733$			31.1845i			1.15182i	0.817512	+	0.575912i	$0.195353\pi$
$733$			31.1845i			1.15182i	−0.817512	+	0.575912i	$0.804647\pi$
$734$	14.8501	−	25.7212i	0.548129	−	0.949387i
$735$		0			0
$736$	−1.88319	−	3.26178i	−0.0694154	−	0.120231i
$737$	1.18595	−	0.684706i	0.0436849	−	0.0252215i
$738$		0			0
$739$	−2.04314	+	3.53882i	−0.0751581	+	0.130178i	−0.901155	−	0.433497i	$-0.857279\pi$
$739$	−2.04314	+	3.53882i	−0.0751581	+	0.130178i	0.825997	+	0.563675i	$0.190613\pi$
$740$	8.38245	−	14.5188i	0.308145	−	0.533723i
$741$		0			0
$742$		0			0
$743$	1.78246	+	1.02910i	0.0653921	+	0.0377542i	0.532340	−	0.846531i	$-0.321313\pi$
$743$	1.78246	+	1.02910i	0.0653921	+	0.0377542i	−0.466947	+	0.884285i	$0.654646\pi$
$744$		0			0
$745$		−	31.0877i		−	1.13897i
$746$	−1.74653	−	1.00836i	−0.0639450	−	0.0369187i
$747$		0			0
$748$		−	8.80071i		−	0.321786i
$749$		0			0
$750$		0			0
$751$	23.8105			0.868859			0.434429	−	0.900706i	$-0.356950\pi$
$751$	23.8105			0.868859			0.434429	+	0.900706i	$0.356950\pi$
$752$	2.56802	+	4.44794i	0.0936461	+	0.162200i
$753$		0			0
$754$	27.7926	+	16.0461i	1.01215	+	0.584363i
$755$	−20.1106			−0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$	−16.3427	−	9.43544i	−0.593592	−	0.342711i
$759$		0			0
$760$	2.70075	+	4.67784i	0.0979666	+	0.169683i
$761$	−27.8735			−1.01041			−0.505207	−	0.862998i	$-0.668584\pi$
$761$	−27.8735			−1.01041			−0.505207	+	0.862998i	$0.668584\pi$
$762$		0			0
$763$		0			0
$764$		−	9.25333i		−	0.334774i
$765$		0			0
$766$	0.724440	+	0.418256i	0.0261751	+	0.0151122i
$767$			71.3645i			2.57682i
$768$		0			0
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	0.607800	−	0.794090i	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$		0			0
$771$		0			0
$772$	−12.2801	+	21.2698i	−0.441970	+	0.765515i
$773$	1.07077	−	1.85462i	0.0385128	−	0.0667061i	−0.846127	−	0.532982i	$-0.821071\pi$
$773$	1.07077	−	1.85462i	0.0385128	−	0.0667061i	0.884639	+	0.466276i	$0.154405\pi$
$774$		0			0
$775$	7.22181	−	4.16951i	0.259415	−	0.149773i
$776$	−2.75544	−	4.77256i	−0.0989144	−	0.171325i
$777$		0			0
$778$	12.4109	−	21.4964i	0.444954	−	0.770682i
$779$			24.3831i			0.873615i
$780$		0			0
$781$	−14.3191			−0.512376
$782$	−6.90127	−	11.9533i	−0.246789	−	0.427451i
$783$		0			0
$784$		0			0
$785$	21.4635	−	12.3920i	0.766066	−	0.442288i
$786$		0			0
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	−0.189170	−	0.981944i	$-0.560580\pi$
$787$	15.8961	−	9.17759i	0.566633	−	0.327146i	0.755804	+	0.654798i	$0.227247\pi$
$788$	10.8133	−	6.24305i	0.385207	−	0.222400i
$789$		0			0
$790$	−4.70825	+	2.71831i	−0.167512	+	0.0967131i
$791$		0			0
$792$		0			0
$793$	27.7052	+	47.9868i	0.983839	+	1.70406i
$794$	−3.03390			−0.107669
$795$		0			0
$796$		−	0.179145i		−	0.00634964i
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	−0.557660	−	0.830069i	$-0.688301\pi$
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	0.997691	+	0.0679130i	$0.0216340\pi$
$798$		0			0
$799$	9.41094	+	16.3002i	0.332935	+	0.576660i
$800$	1.55421	−	0.897324i	0.0549497	−	0.0317252i
$801$		0			0
$802$	−6.53854	+	11.3251i	−0.230884	+	0.399903i
$803$	−14.8670	+	25.7504i	−0.524645	+	0.908712i
$804$		0			0
$805$		0			0
$806$	−19.6831	−	11.3640i	−0.693307	−	0.400281i
$807$		0			0
$808$			0.250324i			0.00880637i
$809$	−32.7237	−	18.8930i	−1.15050	−	0.664244i	−0.201494	−	0.979490i	$-0.564580\pi$
$809$	−32.7237	−	18.8930i	−1.15050	−	0.664244i	−0.949010	+	0.315246i	$0.897913\pi$
$810$		0			0
$811$		−	36.5165i		−	1.28227i	−0.767429	−	0.641134i	$-0.778464\pi$
$811$		−	36.5165i		−	1.28227i	0.767429	−	0.641134i	$-0.221536\pi$
$812$		0			0
$813$		0			0
$814$	22.4878			0.788196
$815$	3.88128	+	6.72257i	0.135955	+	0.235481i
$816$		0			0
$817$	−18.1918	−	10.5030i	−0.636449	−	0.367454i
$818$	5.56709			0.194649
$819$		0			0
$820$	−14.4694			−0.505293
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	0.400547	−	0.916276i	$-0.368820\pi$
$821$	−5.52142	−	3.18779i	−0.192699	−	0.111255i	−0.593245	+	0.805022i	$0.702154\pi$
$822$		0			0
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	0.510888	−	0.859647i	$-0.329317\pi$
$823$	−14.0293	−	24.2995i	−0.489032	−	0.847028i	−0.999920	+	0.0126187i	$0.995983\pi$
$824$	−0.167931			−0.00585017
$825$		0			0
$826$		0			0
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$		0			0
$829$	44.9680	+	25.9623i	1.56180	+	0.901708i	0.997075	+	0.0764314i	$0.0243526\pi$
$829$	44.9680	+	25.9623i	1.56180	+	0.901708i	0.564729	+	0.825276i	$0.308981\pi$
$830$		−	25.0746i		−	0.870351i
$831$		0			0
$832$	−4.23601	−	2.44566i	−0.146857	−	0.0847881i
$833$		0			0
$834$		0			0
$835$	−11.1137	+	19.2495i	−0.384606	+	0.666156i
$836$	−3.62268	+	6.27467i	−0.125293	+	0.217014i
$837$		0			0
$838$	14.2017	−	8.19938i	0.490591	−	0.283243i
$839$	−3.33038	−	5.76838i	−0.114977	−	0.199147i	0.802793	−	0.596257i	$-0.203346\pi$
$839$	−3.33038	−	5.76838i	−0.114977	−	0.199147i	−0.917771	+	0.397111i	$0.870013\pi$
$840$		0			0
$841$	7.02357	−	12.1652i	0.242192	−	0.419489i
$842$		−	15.4578i		−	0.532712i
$843$		0			0
$844$	15.1221			0.520523
$845$	9.77985	+	16.9392i	0.336437	+	0.582726i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	5.69566	−	3.28839i	0.195360	−	0.112791i
$851$	30.5435	−	17.6343i	1.04702	−	0.604495i
$852$		0			0
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	−0.133281	−	0.991078i	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$		0			0
$855$		0			0
$856$	−3.99540	−	6.92024i	−0.136560	−	0.236529i
$857$	15.2966			0.522522			0.261261	−	0.965268i	$-0.415862\pi$
$857$	15.2966			0.522522			0.261261	+	0.965268i	$0.415862\pi$
$858$		0			0
$859$			4.25646i			0.145229i	0.997360	+	0.0726143i	$0.0231342\pi$
$859$			4.25646i			0.145229i	−0.997360	+	0.0726143i	$0.976866\pi$
$860$	6.23269	−	10.7953i	0.212533	−	0.368118i
$861$		0			0
$862$	−12.5133	−	21.6737i	−0.426204	−	0.738208i
$863$	20.4922	−	11.8312i	0.697562	−	0.402738i	−0.108876	−	0.994055i	$-0.534725\pi$
$863$	20.4922	−	11.8312i	0.697562	−	0.402738i	0.806439	+	0.591317i	$0.201392\pi$
$864$		0			0
$865$	15.5923	−	27.0067i	0.530154	−	0.918254i
$866$	1.12584	−	1.95001i	0.0382576	−	0.0662641i
$867$		0			0
$868$		0			0
$869$	−6.31546	−	3.64623i	−0.214237	−	0.123690i
$870$		0			0
$871$		−	2.78919i		−	0.0945079i
$872$	16.4141	+	9.47667i	0.555851	+	0.320920i
$873$		0			0
$874$			11.3632i			0.384367i
$875$		0			0
$876$		0			0
$877$	−20.3923			−0.688599			−0.344300	−	0.938860i	$-0.611884\pi$
$877$	−20.3923			−0.688599			−0.344300	+	0.938860i	$0.611884\pi$
$878$	9.37000	+	16.2293i	0.316222	+	0.547713i
$879$		0			0
$880$	−3.72350	−	2.14977i	−0.125519	−	0.0724686i
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		0			0
$883$	−24.8311			−0.835632			−0.417816	−	0.908532i	$-0.637204\pi$
$883$	−24.8311			−0.835632			−0.417816	+	0.908532i	$0.637204\pi$
$884$	−15.5236	−	8.96254i	−0.522114	−	0.301443i
$885$		0			0
$886$	−0.602256	−	1.04314i	−0.0202332	−	0.0350449i
$887$	9.72119			0.326405			0.163203	−	0.986593i	$-0.447818\pi$
$887$	9.72119			0.326405			0.163203	+	0.986593i	$0.447818\pi$
$888$		0			0
$889$		0			0
$890$			6.71136i			0.224965i
$891$		0			0
$892$	7.27049	+	4.19762i	0.243434	+	0.140547i
$893$		−	15.4955i		−	0.518537i
$894$		0			0
$895$	−20.3456	−	11.7465i	−0.680079	−	0.392644i
$896$		0			0
$897$		0			0
$898$	13.4011	−	23.2114i	0.447200	−	0.774573i
$899$	−15.2433	+	26.4021i	−0.508392	+	0.880560i
$900$		0			0
$901$		0			0
$902$	−9.70433	−	16.8084i	−0.323119	−	0.559658i
$903$		0			0
$904$	−0.579764	+	1.00418i	−0.0192827	+	0.0333985i
$905$			23.9150i			0.794963i
$906$		0			0
$907$	−16.0863			−0.534136			−0.267068	−	0.963678i	$-0.586055\pi$
$907$	−16.0863			−0.534136			−0.267068	+	0.963678i	$0.586055\pi$
$908$	−1.21261	−	2.10030i	−0.0402418	−	0.0697009i
$909$		0			0
$910$		0			0
$911$	−27.0087	+	15.5935i	−0.894838	+	0.516635i	−0.875522	−	0.483179i	$-0.839482\pi$
$911$	−27.0087	+	15.5935i	−0.894838	+	0.516635i	−0.0193161	+	0.999813i	$0.506149\pi$
$912$		0			0
$913$	29.1279	−	16.8170i	0.963993	−	0.556562i
$914$	−11.9934	+	6.92442i	−0.396708	+	0.229039i
$915$		0			0
$916$	−1.74915	+	1.00987i	−0.0577936	+	0.0333672i
$917$		0			0
$918$		0			0
$919$	−12.8832	−	22.3143i	−0.424977	−	0.736082i	0.571441	−	0.820643i	$-0.306385\pi$
$919$	−12.8832	−	22.3143i	−0.424977	−	0.736082i	−0.996418	+	0.0845609i	$0.973051\pi$
$920$	−6.74314			−0.222315
$921$		0			0
$922$			4.80483i			0.158239i
$923$	−14.5824	+	25.2574i	−0.479984	+	0.831357i
$924$		0			0
$925$	8.40258	+	14.5537i	0.276275	+	0.478522i
$926$	18.2201	−	10.5194i	0.598750	−	0.345689i
$927$		0			0
$928$	−3.28052	+	5.68202i	−0.107688	+	0.186521i
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.0682329	+	0.997669i	$0.521736\pi$
$929$	−27.3744	+	47.4138i	−0.898124	+	1.55560i	−0.829891	+	0.557926i	$0.811597\pi$
$930$		0			0
$931$		0			0
$932$	11.0236	+	6.36446i	0.361089	+	0.208475i
$933$		0			0
$934$		−	5.82302i		−	0.190535i
$935$	−13.6454	−	7.87817i	−0.446252	−	0.257644i
$936$		0			0
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$		0			0
$939$		0			0
$940$	9.19531			0.299918
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	0.998712	+	0.0507297i	$0.0161547\pi$
$941$	16.6658	+	28.8660i	0.543289	+	0.941005i	−0.455423	+	0.890275i	$0.650512\pi$
$942$		0			0
$943$	−26.3613	−	15.2197i	−0.858443	−	0.495622i
$944$	−14.5900			−0.474864
$945$		0			0
$946$	16.7206			0.543632
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	0.389004	−	0.921236i	$-0.372819\pi$
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	−0.603312	+	0.797505i	$0.706153\pi$
$948$		0			0
$949$	30.2808	+	52.4478i	0.982955	+	1.70253i
$950$	−5.41447			−0.175669
$951$		0			0
$952$		0			0
$953$			55.7861i			1.80709i	0.428495	+	0.903544i	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$	−14.3472	−	8.28334i	−0.464264	−	0.268043i
$956$		−	17.4495i		−	0.564356i
$957$		0			0
$958$	−23.3447	−	13.4781i	−0.754232	−	0.435456i
$959$		0			0
$960$		0			0
$961$	−4.70451	+	8.14845i	−0.151758	+	0.262853i
$962$	22.9013	−	39.6662i	0.738367	−	1.27889i
$963$		0			0
$964$	9.90142	−	5.71659i	0.318903	−	0.184119i
$965$	21.9857	+	38.0803i	0.707744	+	1.22585i
$966$		0			0
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	−0.996775	−	0.0802517i	$-0.974428\pi$
$967$	−13.3369	+	23.1003i	−0.428887	+	0.742855i	0.567887	+	0.823106i	$0.307761\pi$
$968$			5.23278i			0.168188i
$969$		0			0
$970$	−9.86639			−0.316791
$971$	4.29971	+	7.44731i	0.137984	+	0.238996i	0.926733	−	0.375719i	$-0.122604\pi$
$971$	4.29971	+	7.44731i	0.137984	+	0.238996i	−0.788749	+	0.614715i	$0.789271\pi$
$972$		0			0
$973$		0			0
$974$	11.8011	−	6.81338i	0.378132	−	0.218315i
$975$		0			0
$976$	−9.81058	+	5.66414i	−0.314029	+	0.181305i
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	−0.690542	−	0.723293i	$-0.742628\pi$
$977$	−12.7973	+	7.38854i	−0.409423	+	0.236380i	0.281119	+	0.959673i	$0.409295\pi$
$978$		0			0
$979$	−7.79627	+	4.50118i	−0.249170	+	0.143858i
$980$		0			0
$981$		0			0
$982$	19.4815	+	33.7430i	0.621680	+	1.07678i
$983$	−20.5135			−0.654280			−0.327140	−	0.944976i	$-0.606085\pi$
$983$	−20.5135			−0.654280			−0.327140	+	0.944976i	$0.606085\pi$
$984$		0			0
$985$		−	22.3545i		−	0.712273i
$986$	−12.0220	+	20.8227i	−0.382858	+	0.663130i
$987$		0			0
$988$	7.37859	+	12.7801i	0.234744	+	0.406589i
$989$	22.7103	−	13.1118i	0.722145	−	0.416931i
$990$		0			0
$991$	4.64647	−	8.04792i	0.147600	−	0.255651i	−0.782740	−	0.622349i	$-0.786179\pi$
$991$	4.64647	−	8.04792i	0.147600	−	0.255651i	0.930340	+	0.366698i	$0.119512\pi$
$992$	2.32330	−	4.02408i	0.0737650	−	0.127765i
$993$		0			0
$994$		0			0
$995$	−0.277763	−	0.160366i	−0.00880567	−	0.00508396i
$996$		0			0
$997$			0.0199668i			0.000632354i	1.00000		0.000316177i	$0.000100642\pi$
$997$			0.0199668i			0.000632354i	−1.00000		0.000316177i	$0.999899\pi$
$998$	22.5250	+	13.0048i	0.713018	+	0.411661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.t.a.2285.8		16
3.2	odd	2		882.2.t.b.815.3		16
7.2	even	3		2646.2.l.b.1097.1		16
7.3	odd	6		378.2.m.a.125.4		16
7.4	even	3		378.2.m.a.125.1		16
7.5	odd	6		2646.2.l.b.1097.4		16
7.6	odd	2	inner	2646.2.t.a.2285.5		16
9.2	odd	6		2646.2.l.b.521.8		16
9.7	even	3		882.2.l.a.227.2		16
21.2	odd	6		882.2.l.a.509.7		16
21.5	even	6		882.2.l.a.509.6		16
21.11	odd	6		126.2.m.a.41.5	✓	16
21.17	even	6		126.2.m.a.41.8	yes	16
21.20	even	2		882.2.t.b.815.2		16
28.3	even	6		3024.2.cc.b.881.6		16
28.11	odd	6		3024.2.cc.b.881.3		16
63.2	odd	6	inner	2646.2.t.a.1979.5		16
63.4	even	3		1134.2.d.a.1133.6		16
63.11	odd	6		378.2.m.a.251.4		16
63.16	even	3		882.2.t.b.803.2		16
63.20	even	6		2646.2.l.b.521.5		16
63.25	even	3		126.2.m.a.83.8	yes	16
63.31	odd	6		1134.2.d.a.1133.3		16
63.32	odd	6		1134.2.d.a.1133.11		16
63.34	odd	6		882.2.l.a.227.3		16
63.38	even	6		378.2.m.a.251.1		16
63.47	even	6	inner	2646.2.t.a.1979.8		16
63.52	odd	6		126.2.m.a.83.5	yes	16
63.59	even	6		1134.2.d.a.1133.14		16
63.61	odd	6		882.2.t.b.803.3		16
84.11	even	6		1008.2.cc.b.545.8		16
84.59	odd	6		1008.2.cc.b.545.1		16
252.11	even	6		3024.2.cc.b.2897.6		16
252.115	even	6		1008.2.cc.b.209.8		16
252.151	odd	6		1008.2.cc.b.209.1		16
252.227	odd	6		3024.2.cc.b.2897.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	21.11	odd	6
126.2.m.a.41.8	yes	16	21.17	even	6
126.2.m.a.83.5	yes	16	63.52	odd	6
126.2.m.a.83.8	yes	16	63.25	even	3
378.2.m.a.125.1		16	7.4	even	3
378.2.m.a.125.4		16	7.3	odd	6
378.2.m.a.251.1		16	63.38	even	6
378.2.m.a.251.4		16	63.11	odd	6
882.2.l.a.227.2		16	9.7	even	3
882.2.l.a.227.3		16	63.34	odd	6
882.2.l.a.509.6		16	21.5	even	6
882.2.l.a.509.7		16	21.2	odd	6
882.2.t.b.803.2		16	63.16	even	3
882.2.t.b.803.3		16	63.61	odd	6
882.2.t.b.815.2		16	21.20	even	2
882.2.t.b.815.3		16	3.2	odd	2
1008.2.cc.b.209.1		16	252.151	odd	6
1008.2.cc.b.209.8		16	252.115	even	6
1008.2.cc.b.545.1		16	84.59	odd	6
1008.2.cc.b.545.8		16	84.11	even	6
1134.2.d.a.1133.3		16	63.31	odd	6
1134.2.d.a.1133.6		16	63.4	even	3
1134.2.d.a.1133.11		16	63.32	odd	6
1134.2.d.a.1133.14		16	63.59	even	6
2646.2.l.b.521.5		16	63.20	even	6
2646.2.l.b.521.8		16	9.2	odd	6
2646.2.l.b.1097.1		16	7.2	even	3
2646.2.l.b.1097.4		16	7.5	odd	6
2646.2.t.a.1979.5		16	63.2	odd	6	inner
2646.2.t.a.1979.8		16	63.47	even	6	inner
2646.2.t.a.2285.5		16	7.6	odd	2	inner
2646.2.t.a.2285.8		16	1.1	even	1	trivial
3024.2.cc.b.881.3		16	28.11	odd	6
3024.2.cc.b.881.6		16	28.3	even	6
3024.2.cc.b.2897.3		16	252.227	odd	6
3024.2.cc.b.2897.6		16	252.11	even	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +(1.55049 + 0.895175i) q^{10} +2.40150i q^{11} +(4.23601 + 2.44566i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.83233 + 3.17369i) q^{17} +(2.61281 - 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +3.76638i q^{23} -1.79465 q^{25} +(2.44566 + 4.23601i) q^{26} +(5.68202 - 3.28052i) q^{29} +(-4.02408 + 2.32330i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.17369 + 1.83233i) q^{34} +(-4.68202 - 8.10950i) q^{37} +3.01701 q^{38} +1.79035i q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 + 1.20075i) q^{44} +(-1.88319 + 3.26178i) q^{46} +(2.56802 - 4.44794i) q^{47} +(-1.55421 - 0.897324i) q^{50} +4.89133i q^{52} +4.29953i q^{55} +6.56103 q^{58} +(7.29501 + 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} -4.64661 q^{62} -1.00000 q^{64} +(7.58394 + 4.37859i) q^{65} +(-0.285115 - 0.493834i) q^{67} -3.66466 q^{68} +5.96254i q^{71} +(10.7226 + 6.19070i) q^{73} -9.36404i q^{74} +(2.61281 + 1.50851i) q^{76} +(-1.51831 + 2.62979i) q^{79} +(-0.895175 + 1.55049i) q^{80} +(-6.99911 + 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} -6.96254i q^{86} -2.40150 q^{88} +(1.87432 + 3.24641i) q^{89} +(-3.26178 + 1.88319i) q^{92} +(4.44794 - 2.56802i) q^{94} +(4.67784 - 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Introduction

L-functions

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