LMFDB - Embedded newform 819.2.ct.a.316.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(127,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("819.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.ct (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$-1.08105 - 0.911778i$ of defining polynomial
Character	$\chi$	$=$	819.316
Dual form			819.2.ct.a.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713220 - 0.411778i) q^{2} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(0.866025 - 0.500000i) q^{7} +2.73565i q^{8} +O(q^{10})$	\(q+(-0.713220 - 0.411778i) q^{2} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(0.866025 - 0.500000i) q^{7} +2.73565i q^{8} +(-1.30208 + 2.25527i) q^{10} +(-5.14653 - 2.97135i) q^{11} +(-0.0766193 - 3.60474i) q^{13} -0.823556 q^{14} +(-0.195274 + 0.338225i) q^{16} +(1.34982 + 2.33796i) q^{17} +(1.69485 - 0.978524i) q^{19} +(-3.61956 + 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(1.36471 - 2.36374i) q^{23} -4.99883 q^{25} +(-1.42970 + 2.60252i) q^{26} +(-1.14467 - 0.660878i) q^{28} +(-2.99923 + 5.19481i) q^{29} +1.15155i q^{31} +(5.01684 - 2.89647i) q^{32} -2.22331i q^{34} +(-1.58105 - 2.73845i) q^{35} +(-5.63310 - 3.25227i) q^{37} -1.61174 q^{38} +8.65038 q^{40} +(3.23351 + 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} +7.85479i q^{44} +(-1.94667 + 1.12391i) q^{46} +0.456071i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.56527 + 2.05841i) q^{50} +(-4.07561 + 2.46999i) q^{52} -0.399286 q^{53} +(-9.39568 + 16.2738i) q^{55} +(1.36783 + 2.36914i) q^{56} +(4.27822 - 2.47003i) q^{58} +(-4.16200 + 2.40293i) q^{59} +(0.578514 + 1.00201i) q^{61} +(0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-11.3985 + 0.242277i) q^{65} +(-5.43793 - 3.13959i) q^{67} +(1.78413 - 3.09021i) q^{68} +2.60416i q^{70} +(-3.90335 + 2.25360i) q^{71} -8.30575i q^{73} +(2.67843 + 4.63917i) q^{74} +(-2.24018 - 1.29337i) q^{76} -5.94270 q^{77} -7.91410 q^{79} +(1.06950 + 0.617476i) q^{80} +(-1.53747 - 2.66298i) q^{82} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} -5.75769i q^{86} +(8.12857 - 14.0791i) q^{88} +(-3.08423 - 1.78068i) q^{89} +(-1.86872 - 3.08348i) q^{91} -3.60762 q^{92} +(0.187800 - 0.325279i) q^{94} +(-3.09418 - 5.35928i) q^{95} +(-2.96831 + 1.71375i) q^{97} +(-0.713220 + 0.411778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4}+O(q^{10}) $ 12 * q + 4 * q^4	$ 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.713220	−	0.411778i	−0.504323	−	0.291171i	0.226174	−	0.974087i	$-0.427378\pi$
$2$	−0.713220	−	0.411778i	−0.504323	−	0.291171i	−0.730497	+	0.682916i	$0.760712\pi$
$3$		0			0
$3$		0			0
$4$	−0.660878	−	1.14467i	−0.330439	−	0.572337i
$5$		−	3.16209i		−	1.41413i	−0.707148	−	0.707065i	$-0.750019\pi$
$5$		−	3.16209i		−	1.41413i	0.707148	−	0.707065i	$-0.249981\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			2.73565i			0.967199i
$9$		0			0
$10$	−1.30208	+	2.25527i	−0.411754	+	0.713179i
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.998001	−	0.0632025i	$-0.979869\pi$
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.553735	−	0.832693i	$-0.686798\pi$
$12$		0			0
$13$	−0.0766193	−	3.60474i	−0.0212504	−	0.999774i
$13$	−0.0766193	−	3.60474i	−0.0212504	−	0.999774i
$14$	−0.823556			−0.220105
$15$		0			0
$16$	−0.195274	+	0.338225i	−0.0488186	+	0.0845563i
$17$	1.34982	+	2.33796i	0.327380	+	0.567038i	0.981991	−	0.188927i	$-0.0605010\pi$
$17$	1.34982	+	2.33796i	0.327380	+	0.567038i	−0.654611	+	0.755966i	$0.727168\pi$
$18$		0			0
$19$	1.69485	−	0.978524i	0.388826	−	0.224489i	−0.292825	−	0.956166i	$-0.594595\pi$
$19$	1.69485	−	0.978524i	0.388826	−	0.224489i	0.681651	+	0.731677i	$0.261262\pi$
$20$	−3.61956	+	2.08976i	−0.809359	+	0.467284i
$21$		0			0
$22$	2.44707	+	4.23845i	0.521717	+	0.903641i
$23$	1.36471	−	2.36374i	0.284561	−	0.492874i	−0.687941	−	0.725766i	$-0.741485\pi$
$23$	1.36471	−	2.36374i	0.284561	−	0.492874i	0.972503	+	0.232892i	$0.0748188\pi$
$24$		0			0
$25$	−4.99883			−0.999766
$26$	−1.42970	+	2.60252i	−0.280388	+	0.510397i
$27$		0			0
$28$	−1.14467	−	0.660878i	−0.216323	−	0.124894i
$29$	−2.99923	+	5.19481i	−0.556942	+	0.964652i	0.440807	+	0.897602i	$0.354692\pi$
$29$	−2.99923	+	5.19481i	−0.556942	+	0.964652i	−0.997750	+	0.0670505i	$0.978641\pi$
$30$		0			0
$31$			1.15155i			0.206824i	0.994639	+	0.103412i	$0.0329760\pi$
$31$			1.15155i			0.206824i	−0.994639	+	0.103412i	$0.967024\pi$
$32$	5.01684	−	2.89647i	0.886860	−	0.512029i
$33$		0			0
$34$		−	2.22331i		−	0.381294i
$35$	−1.58105	−	2.73845i	−0.267246	−	0.462883i
$36$		0			0
$37$	−5.63310	−	3.25227i	−0.926075	−	0.534670i	−0.0405072	−	0.999179i	$-0.512897\pi$
$37$	−5.63310	−	3.25227i	−0.926075	−	0.534670i	−0.885568	+	0.464509i	$0.846231\pi$
$38$	−1.61174			−0.261459
$39$		0			0
$40$	8.65038			1.36775
$41$	3.23351	+	1.86687i	0.504990	+	0.291556i	0.730772	−	0.682622i	$-0.239160\pi$
$41$	3.23351	+	1.86687i	0.504990	+	0.291556i	−0.225782	+	0.974178i	$0.572494\pi$
$42$		0			0
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	0.999254	+	0.0386258i	$0.0122980\pi$
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	−0.466176	+	0.884692i	$0.654369\pi$
$44$			7.85479i			1.18415i
$45$		0			0
$46$	−1.94667	+	1.12391i	−0.287021	+	0.165712i
$47$			0.456071i			0.0665248i	0.999447	+	0.0332624i	$0.0105897\pi$
$47$			0.456071i			0.0665248i	−0.999447	+	0.0332624i	$0.989410\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	3.56527	+	2.05841i	0.504205	+	0.291103i
$51$		0			0
$52$	−4.07561	+	2.46999i	−0.565186	+	0.342527i
$53$	−0.399286			−0.0548462			−0.0274231	−	0.999624i	$-0.508730\pi$
$53$	−0.399286			−0.0548462			−0.0274231	+	0.999624i	$0.508730\pi$
$54$		0			0
$55$	−9.39568	+	16.2738i	−1.26691	+	2.19436i
$56$	1.36783	+	2.36914i	0.182783	+	0.316590i
$57$		0			0
$58$	4.27822	−	2.47003i	0.561758	−	0.324331i
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	−0.745827	−	0.666140i	$-0.767945\pi$
$59$	−4.16200	+	2.40293i	−0.541846	+	0.312835i	0.203981	+	0.978975i	$0.434612\pi$
$60$		0			0
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	0.900682	−	0.434479i	$-0.143067\pi$
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	−0.826611	+	0.562774i	$0.809734\pi$
$62$	0.474182	−	0.821308i	0.0602212	−	0.104306i
$63$		0			0
$64$	−3.98971			−0.498714
$65$	−11.3985	+	0.242277i	−1.41381	+	0.0300508i
$66$		0			0
$67$	−5.43793	−	3.13959i	−0.664349	−	0.383562i	0.129583	−	0.991569i	$-0.458636\pi$
$67$	−5.43793	−	3.13959i	−0.664349	−	0.383562i	−0.793932	+	0.608007i	$0.791969\pi$
$68$	1.78413	−	3.09021i	0.216358	−	0.374743i
$69$		0			0
$70$			2.60416i			0.311257i
$71$	−3.90335	+	2.25360i	−0.463242	+	0.267453i	−0.713406	−	0.700751i	$-0.752849\pi$
$71$	−3.90335	+	2.25360i	−0.463242	+	0.267453i	0.250165	+	0.968203i	$0.419515\pi$
$72$		0			0
$73$		−	8.30575i		−	0.972115i	−0.873927	−	0.486057i	$-0.838435\pi$
$73$		−	8.30575i		−	0.972115i	0.873927	−	0.486057i	$-0.161565\pi$
$74$	2.67843	+	4.63917i	0.311361	+	0.539293i
$75$		0			0
$76$	−2.24018	−	1.29337i	−0.256966	−	0.148360i
$77$	−5.94270			−0.677233
$78$		0			0
$79$	−7.91410			−0.890405			−0.445203	−	0.895430i	$-0.646868\pi$
$79$	−7.91410			−0.890405			−0.445203	+	0.895430i	$0.646868\pi$
$80$	1.06950	+	0.617476i	0.119574	+	0.0690359i
$81$		0			0
$82$	−1.53747	−	2.66298i	−0.169785	−	0.294077i
$83$			6.19795i			0.680313i	0.940369	+	0.340156i	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		0			0
$85$	7.39284	−	4.26826i	0.801866	−	0.462958i
$86$		−	5.75769i		−	0.620867i
$87$		0			0
$88$	8.12857	−	14.0791i	0.866509	−	1.50084i
$89$	−3.08423	−	1.78068i	−0.326928	−	0.188752i	0.327549	−	0.944834i	$-0.393778\pi$
$89$	−3.08423	−	1.78068i	−0.326928	−	0.188752i	−0.654476	+	0.756083i	$0.727111\pi$
$90$		0			0
$91$	−1.86872	−	3.08348i	−0.195895	−	0.323237i
$92$	−3.60762			−0.376120
$93$		0			0
$94$	0.187800	−	0.325279i	0.0193701	−	0.0335500i
$95$	−3.09418	−	5.35928i	−0.317457	−	0.549851i
$96$		0			0
$97$	−2.96831	+	1.71375i	−0.301386	+	0.174005i	−0.643065	−	0.765811i	$-0.722338\pi$
$97$	−2.96831	+	1.71375i	−0.301386	+	0.174005i	0.341679	+	0.939817i	$0.389004\pi$
$98$	−0.713220	+	0.411778i	−0.0720461	+	0.0415959i
$99$		0			0
$100$	3.30361	+	5.72203i	0.330361	+	0.572203i
$101$	6.66474	−	11.5437i	0.663167	−	1.14864i	−0.316612	−	0.948555i	$-0.602545\pi$
$101$	6.66474	−	11.5437i	0.663167	−	1.14864i	0.979779	−	0.200084i	$-0.0641214\pi$
$102$		0			0
$103$	−11.6450			−1.14741			−0.573706	−	0.819061i	$-0.694495\pi$
$103$	−11.6450			−1.14741			−0.573706	+	0.819061i	$0.694495\pi$
$104$	9.86130	−	0.209604i	0.966981	−	0.0205533i
$105$		0			0
$106$	0.284779	+	0.164417i	0.0276602	+	0.0159696i
$107$	1.96483	−	3.40318i	0.189947	−	0.328998i	−0.755285	−	0.655396i	$-0.772502\pi$
$107$	1.96483	−	3.40318i	0.189947	−	0.328998i	0.945232	+	0.326398i	$0.105835\pi$
$108$		0			0
$109$		−	11.2533i		−	1.07787i	−0.842346	−	0.538936i	$-0.818826\pi$
$109$		−	11.2533i		−	1.07787i	0.842346	−	0.538936i	$-0.181174\pi$
$110$	13.4024	−	7.73787i	1.27787	−	0.737777i
$111$		0			0
$112$			0.390549i			0.0369034i
$113$	−2.88709	−	5.00059i	−0.271595	−	0.470416i	0.697676	−	0.716414i	$-0.254218\pi$
$113$	−2.88709	−	5.00059i	−0.271595	−	0.470416i	−0.969270	+	0.245998i	$0.920884\pi$
$114$		0			0
$115$	−7.47437	−	4.31533i	−0.696989	−	0.402407i
$116$	7.92849			0.736142
$117$		0			0
$118$	3.95790			0.364354
$119$	2.33796	+	1.34982i	0.214320	+	0.123738i
$120$		0			0
$121$	12.1578	+	21.0580i	1.10526	+	1.91436i
$122$		−	0.952877i		−	0.0862694i
$123$		0			0
$124$	1.31815	−	0.761033i	0.118373	−	0.0683428i
$125$		−	0.00370455i		−	0.000331345i
$126$		0			0
$127$	3.06558	−	5.30975i	0.272027	−	0.471164i	−0.697354	−	0.716727i	$-0.745639\pi$
$127$	3.06558	−	5.30975i	0.272027	−	0.471164i	0.969381	+	0.245563i	$0.0789728\pi$
$128$	−7.18812	−	4.15007i	−0.635346	−	0.366817i
$129$		0			0
$130$	8.22942	+	4.52086i	0.721767	+	0.396506i
$131$	−10.2217			−0.893073			−0.446537	−	0.894765i	$-0.647343\pi$
$131$	−10.2217			−0.893073			−0.446537	+	0.894765i	$0.647343\pi$
$132$		0			0
$133$	0.978524	−	1.69485i	0.0848488	−	0.146962i
$134$	2.58563	+	4.47844i	0.223364	+	0.386878i
$135$		0			0
$136$	−6.39584	+	3.69264i	−0.548439	+	0.316641i
$137$	17.2751	−	9.97376i	1.47591	−	0.852116i	0.476278	−	0.879295i	$-0.341986\pi$
$137$	17.2751	−	9.97376i	1.47591	−	0.852116i	0.999631	+	0.0271788i	$0.00865233\pi$
$138$		0			0
$139$	10.1637	+	17.6041i	0.862077	+	1.49316i	0.869921	+	0.493192i	$0.164170\pi$
$139$	10.1637	+	17.6041i	0.862077	+	1.49316i	−0.00784365	+	0.999969i	$0.502497\pi$
$140$	−2.08976	+	3.61956i	−0.176617	+	0.305909i
$141$		0			0
$142$	3.71193			0.311498
$143$	−10.3166	+	18.7795i	−0.862718	+	1.57042i
$144$		0			0
$145$	16.4265	+	9.48383i	1.36414	+	0.787589i
$146$	−3.42013	+	5.92383i	−0.283052	+	0.490260i
$147$		0			0
$148$			8.59741i			0.706703i
$149$	9.28046	−	5.35808i	0.760285	−	0.438951i	−0.0691132	−	0.997609i	$-0.522017\pi$
$149$	9.28046	−	5.35808i	0.760285	−	0.438951i	0.829398	+	0.558658i	$0.188684\pi$
$150$		0			0
$151$			8.74416i			0.711590i	0.934564	+	0.355795i	$0.115790\pi$
$151$			8.74416i			0.711590i	−0.934564	+	0.355795i	$0.884210\pi$
$152$	2.67690	+	4.63653i	0.217125	+	0.376072i
$153$		0			0
$154$	4.23845	+	2.44707i	0.341544	+	0.197191i
$155$	3.64130			0.292476
$156$		0			0
$157$	6.50734			0.519342			0.259671	−	0.965697i	$-0.416386\pi$
$157$	6.50734			0.519342			0.259671	+	0.965697i	$0.416386\pi$
$158$	5.64449	+	3.25885i	0.449052	+	0.259260i
$159$		0			0
$160$	−9.15891	−	15.8637i	−0.724075	−	1.25414i
$161$		−	2.72941i		−	0.215108i
$162$		0			0
$163$	2.26264	−	1.30634i	0.177224	−	0.102320i	−0.408764	−	0.912640i	$-0.634040\pi$
$163$	2.26264	−	1.30634i	0.177224	−	0.102320i	0.585988	+	0.810320i	$0.300707\pi$
$164$		−	4.93509i		−	0.385366i
$165$		0			0
$166$	2.55218	−	4.42050i	0.198087	−	0.343097i
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	0.624534	−	0.780998i	$-0.285289\pi$
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	−0.364097	+	0.931361i	$0.618622\pi$
$168$		0			0
$169$	−12.9883	+	0.552385i	−0.999097	+	0.0424911i
$170$	−7.03030			−0.539200
$171$		0			0
$172$	4.62036	−	8.00270i	0.352299	−	0.610200i
$173$	−6.98838	−	12.1042i	−0.531317	−	0.920267i	−0.999332	−	0.0365470i	$-0.988364\pi$
$173$	−6.98838	−	12.1042i	−0.531317	−	0.920267i	0.468015	−	0.883720i	$-0.344969\pi$
$174$		0			0
$175$	−4.32911	+	2.49941i	−0.327250	+	0.188938i
$176$	2.00997	−	1.16046i	0.151507	−	0.0874727i
$177$		0			0
$178$	1.46649	+	2.54004i	0.109918	+	0.190384i
$179$	12.6422	−	21.8968i	0.944919	−	1.63665i	0.189005	−	0.981976i	$-0.439474\pi$
$179$	12.6422	−	21.8968i	0.944919	−	1.63665i	0.755914	−	0.654671i	$-0.227193\pi$
$180$		0			0
$181$	−0.864474			−0.0642559			−0.0321279	−	0.999484i	$-0.510228\pi$
$181$	−0.864474			−0.0642559			−0.0321279	+	0.999484i	$0.510228\pi$
$182$	0.0631003	+	2.96870i	0.00467730	+	0.220055i
$183$		0			0
$184$	6.46638	+	3.73336i	0.476708	+	0.275227i
$185$	−10.2840	+	17.8124i	−0.756093	+	1.30959i
$186$		0			0
$187$		−	16.0432i		−	1.17319i
$188$	0.522052	−	0.301407i	0.0380746	−	0.0219824i
$189$		0			0
$190$			5.09647i			0.369737i
$191$	7.33382	+	12.7026i	0.530657	+	0.919125i	0.999360	+	0.0357690i	$0.0113881\pi$
$191$	7.33382	+	12.7026i	0.530657	+	0.919125i	−0.468703	+	0.883356i	$0.655279\pi$
$192$		0			0
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.916503	−	0.400029i	$-0.131000\pi$
$193$	14.2859	+	8.24794i	1.02832	+	0.593700i	0.111816	+	0.993729i	$0.464333\pi$
$194$	2.82275			0.202661
$195$		0			0
$196$	−1.32176			−0.0944111
$197$	−9.53510	−	5.50509i	−0.679348	−	0.392222i	0.120262	−	0.992742i	$-0.461627\pi$
$197$	−9.53510	−	5.50509i	−0.679348	−	0.392222i	−0.799609	+	0.600521i	$0.794960\pi$
$198$		0			0
$199$	−10.6059	−	18.3699i	−0.751829	−	1.30221i	−0.946935	−	0.321425i	$-0.895838\pi$
$199$	−10.6059	−	18.3699i	−0.751829	−	1.30221i	0.195106	−	0.980782i	$-0.437495\pi$
$200$		−	13.6751i		−	0.966972i
$201$		0			0
$202$	−9.50686	+	5.48879i	−0.668901	+	0.386190i
$203$			5.99845i			0.421009i
$204$		0			0
$205$	5.90322	−	10.2247i	0.412299	−	0.714122i
$206$	8.30542	+	4.79514i	0.578666	+	0.334093i
$207$		0			0
$208$	1.23417	+	0.677998i	0.0855746	+	0.0470107i
$209$	−11.6301			−0.804474
$210$		0			0
$211$	8.96788	−	15.5328i	0.617375	−	1.06932i	−0.372588	−	0.927997i	$-0.621530\pi$
$211$	8.96788	−	15.5328i	0.617375	−	1.06932i	0.989963	−	0.141327i	$-0.0451370\pi$
$212$	0.263879	+	0.457052i	0.0181233	+	0.0313905i
$213$		0			0
$214$	−2.80271	+	1.61815i	−0.191589	+	0.110614i
$215$	19.1452	−	11.0535i	1.30569	−	0.753842i
$216$		0			0
$217$	0.575774	+	0.997270i	0.0390861	+	0.0676991i
$218$	−4.63387	+	8.02610i	−0.313845	+	0.543596i
$219$		0			0
$220$	24.8376			1.67455
$221$	8.32431	−	5.04488i	0.559953	−	0.339356i
$222$		0			0
$223$	−13.8834	−	8.01558i	−0.929700	−	0.536763i	−0.0429835	−	0.999076i	$-0.513686\pi$
$223$	−13.8834	−	8.01558i	−0.929700	−	0.536763i	−0.886717	+	0.462313i	$0.847020\pi$
$224$	2.89647	−	5.01684i	0.193529	−	0.335201i
$225$		0			0
$226$			4.75536i			0.316322i
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.0508902	−	0.998704i	$-0.483794\pi$
$227$	14.1812	−	8.18751i	0.941239	−	0.543424i	0.890348	+	0.455280i	$0.150461\pi$
$228$		0			0
$229$		−	27.0104i		−	1.78490i	−0.451148	−	0.892449i	$-0.648985\pi$
$229$		−	27.0104i		−	1.78490i	0.451148	−	0.892449i	$-0.351015\pi$
$230$	3.55392	+	6.15556i	0.234338	+	0.405886i
$231$		0			0
$232$	−14.2112	−	8.20484i	−0.933011	−	0.538674i
$233$	11.5681			0.757853			0.378926	−	0.925427i	$-0.376293\pi$
$233$	11.5681			0.757853			0.378926	+	0.925427i	$0.376293\pi$
$234$		0			0
$235$	1.44214			0.0940747
$236$	5.50114	+	3.17609i	0.358094	+	0.206746i
$237$		0			0
$238$	−1.11165	−	1.92544i	−0.0720578	−	0.124808i
$239$		−	14.6731i		−	0.949122i	−0.880223	−	0.474561i	$-0.842607\pi$
$239$		−	14.6731i		−	0.949122i	0.880223	−	0.474561i	$-0.157393\pi$
$240$		0			0
$241$	12.4246	−	7.17334i	0.800338	−	0.462076i	−0.0432510	−	0.999064i	$-0.513772\pi$
$241$	12.4246	−	7.17334i	0.800338	−	0.462076i	0.843589	+	0.536989i	$0.180438\pi$
$242$		−	20.0253i		−	1.28727i
$243$		0			0
$244$	0.764654	−	1.32442i	0.0489519	−	0.0847872i
$245$	−2.73845	−	1.58105i	−0.174953	−	0.101009i
$246$		0			0
$247$	−3.65718	−	6.03453i	−0.232701	−	0.383968i
$248$	−3.15024			−0.200040
$249$		0			0
$250$	−0.00152545	+	0.00264216i	−9.64781e−5	+	0.000167105i
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	0.697469	−	0.716615i	$-0.254309\pi$
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	−0.969341	+	0.245719i	$0.920976\pi$
$252$		0			0
$253$	−14.0470	+	8.11004i	−0.883128	+	0.509874i
$254$	−4.37287	+	2.52468i	−0.274378	+	0.158412i
$255$		0			0
$256$	7.40753	+	12.8302i	0.462970	+	0.801888i
$257$	−5.18197	+	8.97544i	−0.323243	+	0.559873i	−0.981155	−	0.193222i	$-0.938106\pi$
$257$	−5.18197	+	8.97544i	−0.323243	+	0.559873i	0.657912	+	0.753094i	$0.271440\pi$
$258$		0			0
$259$	−6.50454			−0.404172
$260$	7.81035	+	12.8875i	0.484377	+	0.799247i
$261$		0			0
$262$	7.29032	+	4.20907i	0.450397	+	0.260037i
$263$	−11.0413	+	19.1241i	−0.680835	+	1.17924i	0.293891	+	0.955839i	$0.405050\pi$
$263$	−11.0413	+	19.1241i	−0.680835	+	1.17924i	−0.974726	+	0.223403i	$0.928284\pi$
$264$		0			0
$265$			1.26258i			0.0775596i
$266$	−1.39581	+	0.805869i	−0.0855824	+	0.0494110i
$267$		0			0
$268$			8.29954i			0.506975i
$269$	6.46995	+	11.2063i	0.394480	+	0.683259i	0.993035	−	0.117823i	$-0.0375915\pi$
$269$	6.46995	+	11.2063i	0.394480	+	0.683259i	−0.598555	+	0.801082i	$0.704258\pi$
$270$		0			0
$271$	−15.3069	−	8.83745i	−0.929829	−	0.536837i	−0.0430712	−	0.999072i	$-0.513714\pi$
$271$	−15.3069	−	8.83745i	−0.929829	−	0.536837i	−0.886757	+	0.462235i	$0.847048\pi$
$272$	−1.05434			−0.0639289
$273$		0			0
$274$	−16.4279			−0.992446
$275$	25.7266	+	14.8533i	1.55137	+	0.895685i
$276$		0			0
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	−0.998835	−	0.0482562i	$-0.984634\pi$
$277$	−9.00751	−	15.6015i	−0.541209	−	0.937401i	0.457626	−	0.889145i	$-0.348700\pi$
$278$		−	16.7408i		−	1.00405i
$279$		0			0
$280$	7.49145	−	4.32519i	0.447700	−	0.258480i
$281$			2.44178i			0.145665i	0.997344	+	0.0728323i	$0.0232038\pi$
$281$			2.44178i			0.145665i	−0.997344	+	0.0728323i	$0.976796\pi$
$282$		0			0
$283$	−14.3620	+	24.8757i	−0.853732	+	1.47871i	0.0240853	+	0.999710i	$0.492333\pi$
$283$	−14.3620	+	24.8757i	−0.853732	+	1.47871i	−0.877817	+	0.478996i	$0.841001\pi$
$284$	5.15927	+	2.97871i	0.306146	+	0.176754i
$285$		0			0
$286$	15.0910	−	9.14580i	0.892350	−	0.540802i
$287$	3.73374			0.220396
$288$		0			0
$289$	4.85596	−	8.41078i	0.285645	−	0.494752i
$290$	−7.81046	−	13.5281i	−0.458646	−	0.794399i
$291$		0			0
$292$	−9.50738	+	5.48909i	−0.556377	+	0.321225i
$293$	−25.4013	+	14.6654i	−1.48396	+	0.856763i	−0.999834	−	0.0182359i	$-0.994195\pi$
$293$	−25.4013	+	14.6654i	−1.48396	+	0.856763i	−0.484124	+	0.874999i	$0.660862\pi$
$294$		0			0
$295$	7.59829	+	13.1606i	0.442390	+	0.766241i
$296$	8.89708	−	15.4102i	0.517132	−	0.895699i
$297$		0			0
$298$	−8.82535			−0.511239
$299$	−8.62523	−	4.73830i	−0.498810	−	0.274023i
$300$		0			0
$301$	6.05460	+	3.49562i	0.348981	+	0.201484i
$302$	3.60065	−	6.23651i	0.207194	−	0.358871i
$303$		0			0
$304$			0.764323i			0.0438369i
$305$	3.16846	−	1.82931i	0.181426	−	0.104746i
$306$		0			0
$307$			7.06910i			0.403455i	0.979442	+	0.201728i	$0.0646555\pi$
$307$			7.06910i			0.403455i	−0.979442	+	0.201728i	$0.935344\pi$
$308$	3.92740	+	6.80245i	0.223784	+	0.387606i
$309$		0			0
$310$	−2.59705	−	1.49941i	−0.147503	−	0.0851607i
$311$	−22.2686			−1.26274			−0.631368	−	0.775483i	$-0.717506\pi$
$311$	−22.2686			−1.26274			−0.631368	+	0.775483i	$0.717506\pi$
$312$		0			0
$313$	−28.0840			−1.58740			−0.793700	−	0.608309i	$-0.791848\pi$
$313$	−28.0840			−1.58740			−0.793700	+	0.608309i	$0.791848\pi$
$314$	−4.64117	−	2.67958i	−0.261916	−	0.151217i
$315$		0			0
$316$	5.23025	+	9.05906i	0.294225	+	0.509612i
$317$		−	19.5155i		−	1.09610i	−0.836446	−	0.548049i	$-0.815371\pi$
$317$		−	19.5155i		−	1.09610i	0.836446	−	0.548049i	$-0.184629\pi$
$318$		0			0
$319$	30.8712	−	17.8235i	1.72845	−	0.997924i
$320$			12.6158i			0.705247i
$321$		0			0
$322$	−1.12391	+	1.94667i	−0.0626332	+	0.108484i
$323$	4.57550	+	2.64167i	0.254588	+	0.146986i
$324$		0			0
$325$	0.383007	+	18.0195i	0.0212454	+	0.999540i
$326$	−2.15168			−0.119171
$327$		0			0
$328$	−5.10711	+	8.84577i	−0.281993	+	0.488426i
$329$	0.228035	+	0.394969i	0.0125720	+	0.0217753i
$330$		0			0
$331$	13.5367	−	7.81539i	0.744042	−	0.429573i	−0.0794953	−	0.996835i	$-0.525331\pi$
$331$	13.5367	−	7.81539i	0.744042	−	0.429573i	0.823537	+	0.567263i	$0.191998\pi$
$332$	7.09463	−	4.09609i	0.389368	−	0.224802i
$333$		0			0
$334$	−1.60027	−	2.77174i	−0.0875627	−	0.151663i
$335$	−9.92767	+	17.1952i	−0.542407	+	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$	9.49095	+	4.95431i	0.516240	+	0.269479i
$339$		0			0
$340$	−9.77153	−	5.64160i	−0.529936	−	0.305959i
$341$	3.42165	−	5.92647i	0.185293	−	0.320937i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−16.5633	+	9.56281i	−0.893032	+	0.515592i
$345$		0			0
$346$			11.5106i			0.618816i
$347$	−7.97952	−	13.8209i	−0.428363	−	0.741946i	0.568365	−	0.822777i	$-0.307576\pi$
$347$	−7.97952	−	13.8209i	−0.428363	−	0.741946i	−0.996728	+	0.0808303i	$0.974243\pi$
$348$		0			0
$349$	5.90375	+	3.40853i	0.316021	+	0.182455i	0.649617	−	0.760261i	$-0.274929\pi$
$349$	5.90375	+	3.40853i	0.316021	+	0.182455i	−0.333597	+	0.942716i	$0.608262\pi$
$350$	4.11682			0.220053
$351$		0			0
$352$	−34.4257			−1.83490
$353$	−12.1272	−	7.00163i	−0.645465	−	0.372659i	0.141252	−	0.989974i	$-0.454887\pi$
$353$	−12.1272	−	7.00163i	−0.645465	−	0.372659i	−0.786716	+	0.617314i	$0.788221\pi$
$354$		0			0
$355$	7.12608	+	12.3427i	0.378213	+	0.655085i
$356$			4.70725i			0.249484i
$357$		0			0
$358$	−18.0333	+	10.4115i	−0.953088	+	0.550266i
$359$			5.41494i			0.285789i	0.989738	+	0.142895i	$0.0456410\pi$
$359$			5.41494i			0.285789i	−0.989738	+	0.142895i	$0.954359\pi$
$360$		0			0
$361$	−7.58498	+	13.1376i	−0.399210	+	0.691451i
$362$	0.616561	+	0.355972i	0.0324057	+	0.0187094i
$363$		0			0
$364$	−2.29459	+	4.17688i	−0.120269	+	0.218928i
$365$	−26.2636			−1.37470
$366$		0			0
$367$	−15.0159	+	26.0083i	−0.783822	+	1.35762i	0.145878	+	0.989303i	$0.453399\pi$
$367$	−15.0159	+	26.0083i	−0.783822	+	1.35762i	−0.929700	+	0.368317i	$0.879934\pi$
$368$	0.532985	+	0.923157i	0.0277838	+	0.0481229i
$369$		0			0
$370$	14.6695	−	8.46943i	0.762630	−	0.440305i
$371$	−0.345792	+	0.199643i	−0.0179526	+	0.0103649i
$372$		0			0
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	−0.997959	−	0.0638526i	$-0.979661\pi$
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	0.443682	−	0.896184i	$-0.353672\pi$
$374$	−6.60622	+	11.4423i	−0.341599	+	0.591668i
$375$		0			0
$376$	−1.24765			−0.0643427
$377$	18.9557	+	10.4134i	0.976270	+	0.536317i
$378$		0			0
$379$	−8.20693	−	4.73827i	−0.421562	−	0.243389i	0.274184	−	0.961677i	$-0.411592\pi$
$379$	−8.20693	−	4.73827i	−0.421562	−	0.243389i	−0.695745	+	0.718289i	$0.744926\pi$
$380$	−4.08975	+	7.08366i	−0.209800	+	0.363384i
$381$		0			0
$382$		−	12.0796i		−	0.618048i
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	−0.375007	−	0.927022i	$-0.622360\pi$
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	0.615321	+	0.788277i	$0.289026\pi$
$384$		0			0
$385$			18.7914i			0.957696i
$386$	−6.79264	−	11.7652i	−0.345736	−	0.598833i
$387$		0			0
$388$	3.92338	+	2.26516i	0.199179	+	0.114996i
$389$	−10.6422			−0.539580			−0.269790	−	0.962919i	$-0.586954\pi$
$389$	−10.6422			−0.539580			−0.269790	+	0.962919i	$0.586954\pi$
$390$		0			0
$391$	7.36845			0.372638
$392$	2.36914	+	1.36783i	0.119660	+	0.0690856i
$393$		0			0
$394$	4.53375	+	7.85269i	0.228407	+	0.395613i
$395$			25.0251i			1.25915i
$396$		0			0
$397$	32.2035	−	18.5927i	1.61625	−	0.933140i	0.628367	−	0.777917i	$-0.283724\pi$
$397$	32.2035	−	18.5927i	1.61625	−	0.933140i	0.987879	−	0.155223i	$-0.0496097\pi$
$398$			17.4690i			0.875644i
$399$		0			0
$400$	0.976143	−	1.69073i	0.0488072	−	0.0845365i
$401$	0.776487	+	0.448305i	0.0387759	+	0.0223873i	0.519263	−	0.854615i	$-0.326207\pi$
$401$	0.776487	+	0.448305i	0.0387759	+	0.0223873i	−0.480487	+	0.877002i	$0.659540\pi$
$402$		0			0
$403$	4.15103	−	0.0882308i	0.206777	−	0.00439509i
$404$	−17.6183			−0.876545
$405$		0			0
$406$	2.47003	−	4.27822i	0.122586	−	0.212324i
$407$	19.3273	+	33.4758i	0.958016	+	1.65933i
$408$		0			0
$409$	21.2846	−	12.2886i	1.05245	−	0.607635i	0.129119	−	0.991629i	$-0.458785\pi$
$409$	21.2846	−	12.2886i	1.05245	−	0.607635i	0.923335	+	0.383995i	$0.125452\pi$
$410$	−8.42059	+	4.86163i	−0.415863	+	0.240099i
$411$		0			0
$412$	7.69589	+	13.3297i	0.379149	+	0.656706i
$413$	−2.40293	+	4.16200i	−0.118241	+	0.204799i
$414$		0			0
$415$	19.5985			0.962052
$416$	−10.8254	−	17.8624i	−0.530759	−	0.875778i
$417$		0			0
$418$	8.29486	+	4.78904i	0.405715	+	0.234239i
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	−0.944167	−	0.329468i	$-0.893131\pi$
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	0.757411	+	0.652938i	$0.226464\pi$
$420$		0			0
$421$		−	25.0780i		−	1.22223i	−0.791544	−	0.611113i	$-0.790722\pi$
$421$		−	25.0780i		−	1.22223i	0.791544	−	0.611113i	$-0.209278\pi$
$422$	−12.7922	+	7.38555i	−0.622712	+	0.359523i
$423$		0			0
$424$		−	1.09231i		−	0.0530471i
$425$	−6.74753	−	11.6871i	−0.327303	−	0.566906i
$426$		0			0
$427$	1.00201	+	0.578514i	0.0484909	+	0.0279962i
$428$	−5.19405			−0.251064
$429$		0			0
$430$	−18.2063			−0.877987
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	0.329474	−	0.944165i	$-0.393129\pi$
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	−0.652934	+	0.757415i	$0.726462\pi$
$432$		0			0
$433$	17.9880	+	31.1561i	0.864448	+	1.49727i	0.867594	+	0.497273i	$0.165665\pi$
$433$	17.9880	+	31.1561i	0.864448	+	1.49727i	−0.00314644	+	0.999995i	$0.501002\pi$
$434$		−	0.948365i		−	0.0455230i
$435$		0			0
$436$	−12.8814	+	7.43707i	−0.616907	+	0.356171i
$437$		−	5.34160i		−	0.255523i
$438$		0			0
$439$	−14.1175	+	24.4523i	−0.673792	+	1.16704i	0.303028	+	0.952982i	$0.402002\pi$
$439$	−14.1175	+	24.4523i	−0.673792	+	1.16704i	−0.976820	+	0.214061i	$0.931331\pi$
$440$	−44.5194	−	25.7033i	−2.12238	−	1.22536i
$441$		0			0
$442$	−8.01444	+	0.170348i	−0.381208	+	0.00810264i
$443$	−28.7918			−1.36794			−0.683970	−	0.729511i	$-0.739748\pi$
$443$	−28.7918			−1.36794			−0.683970	+	0.729511i	$0.739748\pi$
$444$		0			0
$445$	−5.63068	+	9.75262i	−0.266920	+	0.462319i
$446$	6.60128	+	11.4337i	0.312579	+	0.541404i
$447$		0			0
$448$	−3.45519	+	1.99486i	−0.163243	+	0.0942481i
$449$	25.2795	−	14.5951i	1.19301	−	0.688785i	0.234023	−	0.972231i	$-0.424811\pi$
$449$	25.2795	−	14.5951i	1.19301	−	0.688785i	0.958988	+	0.283446i	$0.0914776\pi$
$450$		0			0
$451$	−11.0942	−	19.2158i	−0.522408	−	0.904836i
$452$	−3.81603	+	6.60955i	−0.179491	+	0.310887i
$453$		0			0
$454$	−13.4858			−0.632918
$455$	−9.75026	+	5.90907i	−0.457099	+	0.277022i
$456$		0			0
$457$	−27.4399	−	15.8424i	−1.28358	−	0.741077i	−0.306081	−	0.952006i	$-0.599018\pi$
$457$	−27.4399	−	15.8424i	−1.28358	−	0.741077i	−0.977501	+	0.210929i	$0.932351\pi$
$458$	−11.1223	+	19.2644i	−0.519711	+	0.900165i
$459$		0			0
$460$			11.4076i			0.531883i
$461$	19.1407	−	11.0509i	0.891471	−	0.514691i	0.0170480	−	0.999855i	$-0.494573\pi$
$461$	19.1407	−	11.0509i	0.891471	−	0.514691i	0.874424	+	0.485163i	$0.161240\pi$
$462$		0			0
$463$			38.8811i			1.80696i	0.428632	+	0.903479i	$0.358996\pi$
$463$			38.8811i			1.80696i	−0.428632	+	0.903479i	$0.641004\pi$
$464$	−1.17134	−	2.02883i	−0.0543783	−	0.0941860i
$465$		0			0
$466$	−8.25062	−	4.76350i	−0.382202	−	0.220665i
$467$	13.2823			0.614632			0.307316	−	0.951607i	$-0.400569\pi$
$467$	13.2823			0.614632			0.307316	+	0.951607i	$0.400569\pi$
$468$		0			0
$469$	−6.27918			−0.289946
$470$	−1.02856	−	0.593841i	−0.0474440	−	0.0273918i
$471$		0			0
$472$	−6.57358	−	11.3858i	−0.302574	−	0.524073i
$473$		−	41.5469i		−	1.91033i
$474$		0			0
$475$	−8.47228	+	4.89147i	−0.388735	+	0.224436i
$476$		−	3.56827i		−	0.163551i
$477$		0			0
$478$	−6.04205	+	10.4651i	−0.276357	+	0.478664i
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	0.362947	−	0.931810i	$-0.381770\pi$
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	−0.625497	+	0.780226i	$0.715104\pi$
$480$		0			0
$481$	−11.2920	+	20.5550i	−0.514870	+	0.937228i
$482$	−11.8153			−0.538172
$483$		0			0
$484$	16.0697	−	27.8335i	0.730439	−	1.26516i
$485$	5.41905	+	9.38607i	0.246066	+	0.426200i
$486$		0			0
$487$	28.9860	−	16.7351i	1.31348	−	0.758338i	0.330809	−	0.943698i	$-0.392678\pi$
$487$	28.9860	−	16.7351i	1.31348	−	0.758338i	0.982671	+	0.185359i	$0.0593449\pi$
$488$	−2.74116	+	1.58261i	−0.124087	+	0.0716415i
$489$		0			0
$490$	1.30208	+	2.25527i	0.0588220	+	0.101883i
$491$	18.6643	−	32.3276i	0.842310	−	1.45892i	−0.0456264	−	0.998959i	$-0.514528\pi$
$491$	18.6643	−	32.3276i	0.842310	−	1.45892i	0.887937	−	0.459966i	$-0.152138\pi$
$492$		0			0
$493$	−16.1937			−0.729327
$494$	0.123490	+	5.80989i	0.00555609	+	0.261399i
$495$		0			0
$496$	−0.389483	−	0.224868i	−0.0174883	−	0.0100969i
$497$	−2.25360	+	3.90335i	−0.101088	+	0.175089i
$498$		0			0
$499$			34.1327i			1.52799i	0.645223	+	0.763994i	$0.276764\pi$
$499$			34.1327i			1.52799i	−0.645223	+	0.763994i	$0.723236\pi$
$500$	−0.00424050	+	0.00244826i	−0.000189641	+	0.000109489i
$501$		0			0
$502$			7.09454i			0.316645i
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	0.984674	−	0.174407i	$-0.0558008\pi$
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	−0.643378	+	0.765549i	$0.722467\pi$
$504$		0			0
$505$	−36.5022	−	21.0745i	−1.62433	−	0.937805i
$506$	13.3581			0.593842
$507$		0			0
$508$	−8.10390			−0.359553
$509$	16.0189	+	9.24851i	0.710025	+	0.409933i	0.811070	−	0.584949i	$-0.198885\pi$
$509$	16.0189	+	9.24851i	0.710025	+	0.409933i	−0.101046	+	0.994882i	$0.532219\pi$
$510$		0			0
$511$	−4.15288	−	7.19299i	−0.183712	−	0.318199i
$512$			4.39924i			0.194421i
$513$		0			0
$514$	7.39178	−	4.26765i	0.326037	−	0.188238i
$515$			36.8224i			1.62259i
$516$		0			0
$517$	1.35515	−	2.34718i	0.0595992	−	0.103229i
$518$	4.63917	+	2.67843i	0.203833	+	0.117683i
$519$		0			0
$520$	−0.662786	−	31.1824i	−0.0290651	−	1.36744i
$521$	−23.5865			−1.03334			−0.516671	−	0.856184i	$-0.672829\pi$
$521$	−23.5865			−1.03334			−0.516671	+	0.856184i	$0.672829\pi$
$522$		0			0
$523$	−6.15294	+	10.6572i	−0.269049	+	0.466007i	−0.968617	−	0.248560i	$-0.920043\pi$
$523$	−6.15294	+	10.6572i	−0.269049	+	0.466007i	0.699567	+	0.714567i	$0.253376\pi$
$524$	6.75529	+	11.7005i	0.295106	+	0.511139i
$525$		0			0
$526$	15.7498	−	9.09312i	0.686722	−	0.396479i
$527$	−2.69227	+	1.55438i	−0.117277	+	0.0677101i
$528$		0			0
$529$	7.77515	+	13.4670i	0.338050	+	0.585520i
$530$	0.519902	−	0.900497i	0.0225831	−	0.0391151i
$531$		0			0
$532$	−2.58674			−0.112149
$533$	6.48183	−	11.7990i	0.280759	−	0.511072i
$534$		0			0
$535$	−10.7612	−	6.21297i	−0.465246	−	0.268610i
$536$	8.58883	−	14.8763i	0.370981	−	0.642558i
$537$		0			0
$538$		−	10.6567i		−	0.459444i
$539$	−5.14653	+	2.97135i	−0.221677	+	0.127985i
$540$		0			0
$541$		−	19.4411i		−	0.835838i	−0.908484	−	0.417919i	$-0.862760\pi$
$541$		−	19.4411i		−	0.835838i	0.908484	−	0.417919i	$-0.137240\pi$
$542$	7.27813	+	12.6061i	0.312623	+	0.541478i
$543$		0			0
$544$	13.5437	+	7.81944i	0.580680	+	0.335256i
$545$	−35.5841			−1.52425
$546$		0			0
$547$	40.2163			1.71953			0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163			1.71953			0.859763	+	0.510693i	$0.170611\pi$
$548$	−22.8334	−	13.1829i	−0.975395	−	0.563145i
$549$		0			0
$550$	−12.2325	−	21.1873i	−0.521595	−	0.903429i
$551$			11.7393i			0.500109i
$552$		0			0
$553$	−6.85381	+	3.95705i	−0.291454	+	0.168271i
$554$			14.8364i			0.630337i
$555$		0			0
$556$	13.4340	−	23.2683i	0.569727	−	0.986797i
$557$	−6.89702	−	3.98199i	−0.292236	−	0.168722i	0.346714	−	0.937971i	$-0.387297\pi$
$557$	−6.89702	−	3.98199i	−0.292236	−	0.168722i	−0.638950	+	0.769248i	$0.720631\pi$
$558$		0			0
$559$	21.5574	−	13.0647i	0.911781	−	0.552578i
$560$	1.23495			0.0521862
$561$		0			0
$562$	1.00547	−	1.74153i	0.0424133	−	0.0734620i
$563$	0.711981	+	1.23319i	0.0300064	+	0.0519726i	0.880639	−	0.473789i	$-0.157114\pi$
$563$	0.711981	+	1.23319i	0.0300064	+	0.0519726i	−0.850632	+	0.525761i	$0.823781\pi$
$564$		0			0
$565$	−15.8123	+	9.12924i	−0.665229	+	0.384070i
$566$	20.4865	−	11.8279i	0.861113	−	0.497164i
$567$		0			0
$568$	−6.16506	−	10.6782i	−0.258680	−	0.448047i
$569$	9.25946	−	16.0379i	0.388177	−	0.672342i	−0.604028	−	0.796963i	$-0.706438\pi$
$569$	9.25946	−	16.0379i	0.388177	−	0.672342i	0.992204	+	0.124622i	$0.0397717\pi$
$570$		0			0
$571$	−4.35766			−0.182362			−0.0911812	−	0.995834i	$-0.529064\pi$
$571$	−4.35766			−0.182362			−0.0911812	+	0.995834i	$0.529064\pi$
$572$	28.3145	−	0.601828i	1.18389	−	0.0251637i
$573$		0			0
$574$	−2.66298	−	1.53747i	−0.111151	−	0.0641729i
$575$	−6.82194	+	11.8159i	−0.284494	+	0.492759i
$576$		0			0
$577$		−	9.56416i		−	0.398161i	−0.979983	−	0.199081i	$-0.936204\pi$
$577$		−	9.56416i		−	0.398161i	0.979983	−	0.199081i	$-0.0637955\pi$
$578$	−6.92674	+	3.99916i	−0.288115	+	0.166343i
$579$		0			0
$580$		−	25.0706i		−	1.04100i
$581$	3.09897	+	5.36758i	0.128567	+	0.222685i
$582$		0			0
$583$	2.05494	+	1.18642i	0.0851068	+	0.0491364i
$584$	22.7216			0.940228
$585$		0			0
$586$	24.1556			0.997859
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	0.541595	−	0.840640i	$-0.317821\pi$
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	−0.457218	+	0.889355i	$0.651154\pi$
$588$		0			0
$589$	1.12682	+	1.95171i	0.0464297	+	0.0804186i
$590$		−	12.5152i		−	0.515244i
$591$		0			0
$592$	2.20000	−	1.27017i	0.0904194	−	0.0522037i
$593$			40.4292i			1.66023i	0.557594	+	0.830114i	$0.311725\pi$
$593$			40.4292i			1.66023i	−0.557594	+	0.830114i	$0.688275\pi$
$594$		0			0
$595$	4.26826	−	7.39284i	0.174982	−	0.303077i
$596$	−12.2665	−	7.08207i	−0.502455	−	0.290093i
$597$		0			0
$598$	4.20056	+	6.93114i	0.171774	+	0.283435i
$599$	38.5873			1.57663			0.788316	−	0.615270i	$-0.210953\pi$
$599$	38.5873			1.57663			0.788316	+	0.615270i	$0.210953\pi$
$600$		0			0
$601$	−4.08115	+	7.06877i	−0.166474	+	0.288341i	−0.937178	−	0.348852i	$-0.886571\pi$
$601$	−4.08115	+	7.06877i	−0.166474	+	0.288341i	0.770704	+	0.637193i	$0.219905\pi$
$602$	−2.87884	−	4.98630i	−0.117333	−	0.203226i
$603$		0			0
$604$	10.0092	−	5.77882i	0.407269	−	0.235137i
$605$	66.5872	−	38.4442i	2.70716	−	1.56298i
$606$		0			0
$607$	−3.79263	−	6.56902i	−0.153938	−	0.266628i	0.778734	−	0.627354i	$-0.215862\pi$
$607$	−3.79263	−	6.56902i	−0.153938	−	0.266628i	−0.932672	+	0.360726i	$0.882529\pi$
$608$	5.66853	−	9.81819i	0.229889	−	0.398180i
$609$		0			0
$610$	−3.01308			−0.121996
$611$	1.64402	−	0.0349438i	0.0665098	−	0.00141368i
$612$		0			0
$613$	−13.4908	−	7.78892i	−0.544889	−	0.314592i	0.202169	−	0.979351i	$-0.435201\pi$
$613$	−13.4908	−	7.78892i	−0.544889	−	0.314592i	−0.747058	+	0.664759i	$0.768534\pi$
$614$	2.91090	−	5.04183i	0.117474	−	0.203472i
$615$		0			0
$616$		−	16.2571i		−	0.655019i
$617$	−20.6709	+	11.9343i	−0.832177	+	0.480458i	−0.854598	−	0.519291i	$-0.826196\pi$
$617$	−20.6709	+	11.9343i	−0.832177	+	0.480458i	0.0224202	+	0.999749i	$0.492863\pi$
$618$		0			0
$619$			19.4963i			0.783622i	0.920046	+	0.391811i	$0.128151\pi$
$619$			19.4963i			0.783622i	−0.920046	+	0.391811i	$0.871849\pi$
$620$	−2.40646	−	4.16810i	−0.0966456	−	0.167395i
$621$		0			0
$622$	15.8824	+	9.16972i	0.636827	+	0.367672i
$623$	−3.56136			−0.142683
$624$		0			0
$625$	−25.0059			−1.00023
$626$	20.0301	+	11.5644i	0.800562	+	0.462205i
$627$		0			0
$628$	−4.30055	−	7.44878i	−0.171611	−	0.297239i
$629$		−	17.5599i		−	0.700161i
$630$		0			0
$631$	−22.2239	+	12.8309i	−0.884718	+	0.510792i	−0.872211	−	0.489130i	$-0.837314\pi$
$631$	−22.2239	+	12.8309i	−0.884718	+	0.510792i	−0.0125066	+	0.999922i	$0.503981\pi$
$632$		−	21.6502i		−	0.861199i
$633$		0			0
$634$	−8.03604	+	13.9188i	−0.319152	+	0.552788i
$635$	−16.7899	−	9.69366i	−0.666287	−	0.384681i
$636$		0			0
$637$	−3.16010	−	1.73601i	−0.125208	−	0.0687834i
$638$	−29.3573			−1.16227
$639$		0			0
$640$	−13.1229	+	22.7295i	−0.518728	+	0.898463i
$641$	0.553020	+	0.957859i	0.0218430	+	0.0378332i	0.876740	−	0.480964i	$-0.159713\pi$
$641$	0.553020	+	0.957859i	0.0218430	+	0.0378332i	−0.854897	+	0.518797i	$0.826380\pi$
$642$		0			0
$643$	10.9437	−	6.31833i	0.431576	−	0.249171i	−0.268442	−	0.963296i	$-0.586509\pi$
$643$	10.9437	−	6.31833i	0.431576	−	0.249171i	0.700018	+	0.714125i	$0.253175\pi$
$644$	−3.12429	+	1.80381i	−0.123114	+	0.0710801i
$645$		0			0
$646$	−2.17556	−	3.76818i	−0.0855962	−	0.148257i
$647$	−12.8574	+	22.2697i	−0.505477	+	0.875512i	0.494503	+	0.869176i	$0.335350\pi$
$647$	−12.8574	+	22.2697i	−0.505477	+	0.875512i	−0.999980	+	0.00633579i	$0.997983\pi$
$648$		0			0
$649$	28.5598			1.12107
$650$	7.14685	−	13.0096i	0.280323	−	0.510277i
$651$		0			0
$652$	−2.99066	−	1.72666i	−0.117123	−	0.0676211i
$653$	12.6303	−	21.8764i	0.494263	−	0.856089i	−0.505715	−	0.862701i	$-0.668771\pi$
$653$	12.6303	−	21.8764i	0.494263	−	0.856089i	0.999978	+	0.00661158i	$0.00210455\pi$
$654$		0			0
$655$			32.3219i			1.26292i
$656$	−1.26285	+	0.729104i	−0.0493058	+	0.0284667i
$657$		0			0
$658$		−	0.375600i		−	0.0146424i
$659$	11.4882	+	19.8982i	0.447517	+	0.775123i	0.998224	−	0.0595764i	$-0.0189750\pi$
$659$	11.4882	+	19.8982i	0.447517	+	0.775123i	−0.550707	+	0.834699i	$0.685642\pi$
$660$		0			0
$661$	26.3554	+	15.2163i	1.02511	+	0.591845i	0.915579	−	0.402138i	$-0.131733\pi$
$661$	26.3554	+	15.2163i	1.02511	+	0.591845i	0.109528	+	0.993984i	$0.465066\pi$
$662$	−12.8728			−0.500316
$663$		0			0
$664$	−16.9554			−0.657998
$665$	−5.35928	−	3.09418i	−0.207824	−	0.119987i
$666$		0			0
$667$	8.18613	+	14.1788i	0.316968	+	0.549005i
$668$		−	5.13665i		−	0.198743i
$669$		0			0
$670$	14.1612	−	8.17600i	0.547096	−	0.315866i
$671$		−	6.87586i		−	0.265440i
$672$		0			0
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	−0.742468	−	0.669881i	$-0.766345\pi$
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	0.951368	+	0.308056i	$0.0996784\pi$
$674$	−15.5126	−	8.95620i	−0.597523	−	0.344980i
$675$		0			0
$676$	9.21595	+	14.5023i	0.354460	+	0.557779i
$677$	18.1209			0.696442			0.348221	−	0.937412i	$-0.386786\pi$
$677$	18.1209			0.696442			0.348221	+	0.937412i	$0.386786\pi$
$678$		0			0
$679$	−1.71375	+	2.96831i	−0.0657679	+	0.113913i
$680$	11.6765	+	20.2242i	0.447772	+	0.775564i
$681$		0			0
$682$	−4.88078	+	2.81792i	−0.186895	+	0.107904i
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.971855	−	0.235580i	$-0.924301\pi$
$683$	−32.7662	+	18.9176i	−1.25376	+	0.723861i	−0.281909	+	0.959441i	$0.590968\pi$
$684$		0			0
$685$	−31.5380	−	54.6254i	−1.20500	−	2.08713i
$686$	−0.411778	+	0.713220i	−0.0157218	+	0.0272309i
$687$		0			0
$688$	−2.73042			−0.104096
$689$	0.0305930	+	1.43932i	0.00116550	+	0.0548338i
$690$		0			0
$691$	26.0034	+	15.0131i	0.989216	+	0.571124i	0.905040	−	0.425327i	$-0.139841\pi$
$691$	26.0034	+	15.0131i	0.989216	+	0.571124i	0.0841761	+	0.996451i	$0.473174\pi$
$692$	−9.23693	+	15.9988i	−0.351135	+	0.608184i
$693$		0			0
$694$			13.1432i			0.498907i
$695$	55.6658	−	32.1387i	2.11152	−	1.21909i
$696$		0			0
$697$			10.0798i			0.381798i
$698$	−2.80712	−	4.86207i	−0.106251	−	0.184032i
$699$		0			0
$700$	5.72203	+	3.30361i	0.216272	+	0.124865i
$701$	−0.116177			−0.00438796			−0.00219398	−	0.999998i	$-0.500698\pi$
$701$	−0.116177			−0.00438796			−0.00219398	+	0.999998i	$0.500698\pi$
$702$		0			0
$703$	−12.7297			−0.480110
$704$	20.5332	+	11.8548i	0.773873	+	0.446796i
$705$		0			0
$706$	5.76624	+	9.98741i	0.217015	+	0.375881i
$707$		−	13.3295i		−	0.501307i
$708$		0			0
$709$	5.82829	−	3.36497i	0.218886	−	0.126374i	−0.386548	−	0.922269i	$-0.626333\pi$
$709$	5.82829	−	3.36497i	0.218886	−	0.126374i	0.605434	+	0.795895i	$0.292999\pi$
$710$		−	11.7375i		−	0.440499i
$711$		0			0
$712$	4.87132	−	8.43738i	0.182561	−	0.316204i
$713$	2.72196	+	1.57153i	0.101938	+	0.0588541i
$714$		0			0
$715$	59.3826	+	32.6221i	2.22078	+	1.22000i
$716$	−33.4197			−1.24895
$717$		0			0
$718$	2.22975	−	3.86204i	0.0832136	−	0.144130i
$719$	−23.4039	−	40.5367i	−0.872818	−	1.51177i	−0.859069	−	0.511860i	$-0.828957\pi$
$719$	−23.4039	−	40.5367i	−0.872818	−	1.51177i	−0.0137492	−	0.999905i	$-0.504377\pi$
$720$		0			0
$721$	−10.0848	+	5.82248i	−0.375579	+	0.216840i
$722$	10.8195	−	6.24666i	0.402661	−	0.232476i
$723$		0			0
$724$	0.571312	+	0.989541i	0.0212326	+	0.0367760i
$725$	14.9926	−	25.9680i	0.556812	−	0.964426i
$726$		0			0
$727$	13.3362			0.494611			0.247305	−	0.968938i	$-0.420455\pi$
$727$	13.3362			0.494611			0.247305	+	0.968938i	$0.420455\pi$
$728$	8.43534	−	5.11217i	0.312634	−	0.189470i
$729$		0			0
$730$	18.7317	+	10.8148i	0.693291	+	0.400272i
$731$	−9.43694	+	16.3453i	−0.349038	+	0.604551i
$732$		0			0
$733$		−	29.4612i		−	1.08817i	−0.839029	−	0.544087i	$-0.816876\pi$
$733$		−	29.4612i		−	1.08817i	0.839029	−	0.544087i	$-0.183124\pi$
$734$	21.4193	−	12.3664i	0.790599	−	0.456453i
$735$		0			0
$736$		−	15.8113i		−	0.582814i
$737$	18.6576	+	32.3160i	0.687263	+	1.19037i
$738$		0			0
$739$	−10.4184	−	6.01509i	−0.383249	−	0.221269i	0.295982	−	0.955193i	$-0.404353\pi$
$739$	−10.4184	−	6.01509i	−0.383249	−	0.221269i	−0.679231	+	0.733925i	$0.737686\pi$
$740$	27.1858			0.999370
$741$		0			0
$742$	0.328834			0.0120719
$743$	18.9509	+	10.9413i	0.695242	+	0.401398i	0.805573	−	0.592497i	$-0.201858\pi$
$743$	18.9509	+	10.9413i	0.695242	+	0.401398i	−0.110331	+	0.993895i	$0.535191\pi$
$744$		0			0
$745$	−16.9427	−	29.3457i	−0.620734	−	1.07514i
$746$			17.6321i			0.645558i
$747$		0			0
$748$	−18.3642	+	10.6026i	−0.671461	+	0.387668i
$749$		−	3.92966i		−	0.143587i
$750$		0			0
$751$	17.3746	−	30.0937i	0.634008	−	1.09813i	−0.352717	−	0.935730i	$-0.614742\pi$
$751$	17.3746	−	30.0937i	0.634008	−	1.09813i	0.986724	−	0.162403i	$-0.0519245\pi$
$752$	−0.154255	−	0.0890590i	−0.00562509	−	0.00324765i
$753$		0			0
$754$	−9.23160	−	15.2326i	−0.336195	−	0.554739i
$755$	27.6498			1.00628
$756$		0			0
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	0.122481	+	0.992471i	$0.460915\pi$
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	−0.920745	+	0.390164i	$0.872418\pi$
$758$	3.90223	+	6.75887i	0.141736	+	0.245493i
$759$		0			0
$760$	14.6611	−	8.46461i	0.531815	−	0.307044i
$761$	−0.122449	+	0.0706957i	−0.00443876	+	0.00256272i	−0.502218	−	0.864741i	$-0.667482\pi$
$761$	−0.122449	+	0.0706957i	−0.00443876	+	0.00256272i	0.497779	+	0.867304i	$0.334149\pi$
$762$		0			0
$763$	−5.62666	−	9.74566i	−0.203699	−	0.352817i
$764$	9.69352	−	16.7897i	0.350699	−	0.607429i
$765$		0			0
$766$	−4.47241			−0.161595
$767$	8.98082	+	14.8188i	0.324279	+	0.535076i
$768$		0			0
$769$	11.8200	+	6.82429i	0.426241	+	0.246090i	0.697744	−	0.716347i	$-0.254187\pi$
$769$	11.8200	+	6.82429i	0.426241	+	0.246090i	−0.271503	+	0.962438i	$0.587521\pi$
$770$	7.73787	−	13.4024i	0.278853	−	0.482988i
$771$		0			0
$772$		−	21.8035i		−	0.784726i
$773$	−15.2328	+	8.79469i	−0.547887	+	0.316323i	−0.748269	−	0.663395i	$-0.769115\pi$
$773$	−15.2328	+	8.79469i	−0.547887	+	0.316323i	0.200382	+	0.979718i	$0.435782\pi$
$774$		0			0
$775$		−	5.75639i		−	0.206776i
$776$	−4.68824	−	8.12026i	−0.168298	−	0.291500i
$777$		0			0
$778$	7.59022	+	4.38221i	0.272123	+	0.157110i
$779$	7.30711			0.261804
$780$		0			0
$781$	26.7849			0.958439
$782$	−5.25533	−	3.03416i	−0.187930	−	0.108501i
$783$		0			0
$784$	0.195274	+	0.338225i	0.00697409	+	0.0120795i
$785$		−	20.5768i		−	0.734418i
$786$		0			0
$787$	2.57075	−	1.48422i	0.0916374	−	0.0529069i	−0.453481	−	0.891266i	$-0.649818\pi$
$787$	2.57075	−	1.48422i	0.0916374	−	0.0529069i	0.545118	+	0.838359i	$0.316485\pi$
$788$			14.5528i			0.518421i
$789$		0			0
$790$	10.3048	−	17.8484i	0.366628	−	0.635018i
$791$	−5.00059	−	2.88709i	−0.177800	−	0.102653i
$792$		0			0
$793$	3.56768	−	2.16216i	0.126692	−	0.0767807i
$794$	−30.6242			−1.08681
$795$		0			0
$796$	−14.0184	+	24.2805i	−0.496867	+	0.860600i
$797$	−4.72611	−	8.18586i	−0.167407	−	0.289958i	0.770100	−	0.637923i	$-0.220206\pi$
$797$	−4.72611	−	8.18586i	−0.167407	−	0.289958i	−0.937508	+	0.347965i	$0.886873\pi$
$798$		0			0
$799$	−1.06628	+	0.615614i	−0.0377221	+	0.0217789i
$800$	−25.0783	+	14.4790i	−0.886652	+	0.511909i
$801$		0			0
$802$	−0.369204	−	0.639481i	−0.0130371	−	0.0225809i
$803$	−24.6793	+	42.7458i	−0.870913	+	1.50847i
$804$		0			0
$805$	−8.63066			−0.304191
$806$	−2.99693	−	1.64637i	−0.105562	−	0.0579911i
$807$		0			0
$808$	31.5795	+	18.2324i	1.11096	+	0.641414i
$809$	−0.581273	+	1.00679i	−0.0204365	+	0.0353970i	−0.876063	−	0.482197i	$-0.839839\pi$
$809$	−0.581273	+	1.00679i	−0.0204365	+	0.0353970i	0.855626	+	0.517594i	$0.173172\pi$
$810$		0			0
$811$		−	19.5561i		−	0.686706i	−0.939206	−	0.343353i	$-0.888437\pi$
$811$		−	19.5561i		−	0.686706i	0.939206	−	0.343353i	$-0.111563\pi$
$812$	6.86627	−	3.96424i	0.240959	−	0.139118i
$813$		0			0
$814$		−	31.8342i		−	1.11579i
$815$	−4.13075	−	7.15467i	−0.144694	−	0.250617i
$816$		0			0
$817$	11.8491	+	6.84111i	0.414549	+	0.239340i
$818$	−20.2408			−0.707702
$819$		0			0
$820$	−15.6052			−0.544958
$821$	−10.9283	−	6.30945i	−0.381400	−	0.220201i	0.297027	−	0.954869i	$-0.404005\pi$
$821$	−10.9283	−	6.30945i	−0.381400	−	0.220201i	−0.678427	+	0.734668i	$0.737338\pi$
$822$		0			0
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	0.803095	−	0.595851i	$-0.203185\pi$
$823$	−3.28404	−	5.68812i	−0.114474	−	0.198275i	−0.917570	+	0.397575i	$0.869852\pi$
$824$		−	31.8565i		−	1.10978i
$825$		0			0
$826$	3.42764	−	1.97895i	0.119263	−	0.0688564i
$827$		−	17.3050i		−	0.601754i	−0.953663	−	0.300877i	$-0.902721\pi$
$827$		−	17.3050i		−	0.601754i	0.953663	−	0.300877i	$-0.0972794\pi$
$828$		0			0
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	−0.896800	−	0.442437i	$-0.854114\pi$
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	0.831561	+	0.555433i	$0.187447\pi$
$830$	−13.9780	−	8.07022i	−0.485185	−	0.280122i
$831$		0			0
$832$	0.305689	+	14.3819i	0.0105979	+	0.498602i
$833$	2.69964			0.0935371
$834$		0			0
$835$	6.14432	−	10.6423i	0.212633	−	0.368291i
$836$	7.68610	+	13.3127i	0.265829	+	0.460430i
$837$		0			0
$838$	5.45298	−	3.14828i	0.188370	−	0.108756i
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.392766	−	0.919638i	$-0.371518\pi$
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.992813	+	0.119674i	$0.0381849\pi$
$840$		0			0
$841$	−3.49071	−	6.04609i	−0.120369	−	0.208486i
$842$	−10.3266	+	17.8861i	−0.355877	+	0.616396i
$843$		0			0
$844$	−23.7067			−0.816018
$845$	1.74669	+	41.0701i	0.0600880	+	1.41285i
$846$		0			0
$847$	21.0580	+	12.1578i	0.723560	+	0.417748i
$848$	0.0779704	−	0.135049i	0.00267751	−	0.00463759i
$849$		0			0
$850$			11.1139i			0.381205i
$851$	−15.3751	+	8.87679i	−0.527050	+	0.304293i
$852$		0			0
$853$			15.3103i			0.524215i	0.965039	+	0.262107i	$0.0844174\pi$
$853$			15.3103i			0.524215i	−0.965039	+	0.262107i	$0.915583\pi$
$854$	−0.476438	−	0.825215i	−0.0163034	−	0.0282383i
$855$		0			0
$856$	9.30993	+	5.37509i	0.318207	+	0.183717i
$857$	2.59248			0.0885574			0.0442787	−	0.999019i	$-0.485901\pi$
$857$	2.59248			0.0885574			0.0442787	+	0.999019i	$0.485901\pi$
$858$		0			0
$859$	−13.7738			−0.469955			−0.234978	−	0.972001i	$-0.575502\pi$
$859$	−13.7738			−0.469955			−0.234978	+	0.972001i	$0.575502\pi$
$860$	−25.3053	−	14.6100i	−0.862903	−	0.498197i
$861$		0			0
$862$	3.19294	+	5.53034i	0.108752	+	0.188364i
$863$			29.7592i			1.01302i	0.862235	+	0.506508i	$0.169064\pi$
$863$			29.7592i			1.01302i	−0.862235	+	0.506508i	$0.830936\pi$
$864$		0			0
$865$	−38.2747	+	22.0979i	−1.30138	+	0.751351i
$866$		−	29.6282i		−	1.00681i
$867$		0			0
$868$	0.761033	−	1.31815i	0.0258311	−	0.0447408i
$869$	40.7301	+	23.5155i	1.38167	+	0.797710i
$870$		0			0
$871$	−10.9007	+	19.8429i	−0.369358	+	0.672350i
$872$	30.7852			1.04252
$873$		0			0
$874$	−2.19955	+	3.80974i	−0.0744009	+	0.128866i
$875$	−0.00185228	−	0.00320824i	−6.26183e−5	−	0.000108458i
$876$		0			0
$877$	−1.24995	+	0.721660i	−0.0422079	+	0.0243687i	−0.520955	−	0.853584i	$-0.674424\pi$
$877$	−1.24995	+	0.721660i	−0.0422079	+	0.0243687i	0.478748	+	0.877953i	$0.341091\pi$
$878$	20.1378	−	11.6266i	0.679618	−	0.392378i
$879$		0			0
$880$	−3.66947	−	6.35571i	−0.123698	−	0.214251i
$881$	17.9402	−	31.0733i	0.604420	−	1.04689i	−0.387723	−	0.921776i	$-0.626738\pi$
$881$	17.9402	−	31.0733i	0.604420	−	1.04689i	0.992143	−	0.125110i	$-0.0399284\pi$
$882$		0			0
$883$	10.5626			0.355458			0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626			0.355458			0.177729	+	0.984079i	$0.443125\pi$
$884$	−11.2761	−	6.19456i	−0.379256	−	0.208346i
$885$		0			0
$886$	20.5349	+	11.8558i	0.689883	+	0.398304i
$887$	6.11401	−	10.5898i	0.205288	−	0.355570i	−0.744936	−	0.667136i	$-0.767520\pi$
$887$	6.11401	−	10.5898i	0.205288	−	0.355570i	0.950225	+	0.311566i	$0.100853\pi$
$888$		0			0
$889$		−	6.13117i		−	0.205633i
$890$	8.03183	−	4.63718i	0.269228	−	0.155439i
$891$		0			0
$892$			21.1893i			0.709469i
$893$	0.446276	+	0.772973i	0.0149341	+	0.0258666i
$894$		0			0
$895$	−69.2399	−	39.9757i	−2.31443	−	1.33624i
$896$	−8.30013			−0.277288
$897$		0			0
$898$	−24.0398			−0.802217
$899$	−5.98208	−	3.45375i	−0.199513	−	0.115189i
$900$		0			0
$901$	−0.538965	−	0.933515i	−0.0179555	−	0.0310999i
$902$			18.2735i			0.608440i
$903$		0			0
$904$	13.6799	−	7.89807i	0.454985	−	0.262686i
$905$			2.73355i			0.0908662i
$906$		0			0
$907$	2.26278	−	3.91924i	0.0751343	−	0.130136i	−0.826010	−	0.563655i	$-0.809395\pi$
$907$	2.26278	−	3.91924i	0.0751343	−	0.130136i	0.901145	+	0.433519i	$0.142728\pi$
$908$	−18.7441	−	10.8219i	−0.622044	−	0.359137i
$909$		0			0
$910$	9.38731	−	0.199529i	0.311186	−	0.00661432i
$911$	57.2723			1.89751			0.948757	−	0.316006i	$-0.102342\pi$
$911$	57.2723			1.89751			0.948757	+	0.316006i	$0.102342\pi$
$912$		0			0
$913$	18.4163	−	31.8979i	0.609489	−	1.05567i
$914$	13.0471	+	22.5983i	0.431560	+	0.747484i
$915$		0			0
$916$	−30.9181	+	17.8506i	−1.02156	+	0.589800i
$917$	−8.85224	+	5.11084i	−0.292327	+	0.168775i
$918$		0			0
$919$	20.3775	+	35.2949i	0.672193	+	1.16427i	0.977281	+	0.211948i	$0.0679809\pi$
$919$	20.3775	+	35.2949i	0.672193	+	1.16427i	−0.305088	+	0.952324i	$0.598686\pi$
$920$	11.8052	−	20.4473i	0.389207	−	0.674127i
$921$		0			0
$922$	−18.2021			−0.599453
$923$	8.42270	+	13.8979i	0.277236	+	0.457454i
$924$		0			0
$925$	28.1589	+	16.2575i	0.925858	+	0.534545i
$926$	16.0104	−	27.7308i	0.526134	−	0.911291i
$927$		0			0
$928$			34.7487i			1.14068i
$929$	−45.2751	+	26.1396i	−1.48543	+	0.857611i	−0.999862	−	0.0165897i	$-0.994719\pi$
$929$	−45.2751	+	26.1396i	−1.48543	+	0.857611i	−0.485564	+	0.874201i	$0.661386\pi$
$930$		0			0
$931$		−	1.95705i		−	0.0641397i
$932$	−7.64511	−	13.2417i	−0.250424	−	0.433747i
$933$		0			0
$934$	−9.47322	−	5.46937i	−0.309973	−	0.178963i
$935$	−50.7300			−1.65905
$936$		0			0
$937$	−6.38634			−0.208633			−0.104316	−	0.994544i	$-0.533265\pi$
$937$	−6.38634			−0.208633			−0.104316	+	0.994544i	$0.533265\pi$
$938$	4.47844	+	2.58563i	0.146226	+	0.0844238i
$939$		0			0
$940$	−0.953077	−	1.65078i	−0.0310859	−	0.0538424i
$941$		−	25.3711i		−	0.827073i	−0.910488	−	0.413536i	$-0.864293\pi$
$941$		−	25.3711i		−	0.827073i	0.910488	−	0.413536i	$-0.135707\pi$
$942$		0			0
$943$	8.82560	−	5.09546i	0.287401	−	0.165931i
$944$		−	1.87692i		−	0.0610887i
$945$		0			0
$946$	−17.1081	+	29.6321i	−0.556232	+	0.963422i
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	0.0656800	−	0.997841i	$-0.479078\pi$
$947$	−23.5612	−	13.6031i	−0.765635	−	0.442040i	−0.831315	+	0.555801i	$0.812412\pi$
$948$		0			0
$949$	−29.9401	+	0.636381i	−0.971895	+	0.0206578i
$950$	8.05681			0.261397
$951$		0			0
$952$	−3.69264	+	6.39584i	−0.119679	+	0.207290i
$953$	−13.2939	−	23.0258i	−0.430633	−	0.745878i	0.566295	−	0.824203i	$-0.308376\pi$
$953$	−13.2939	−	23.0258i	−0.430633	−	0.745878i	−0.996928	+	0.0783248i	$0.975043\pi$
$954$		0			0
$955$	40.1667	−	23.1902i	1.29976	−	0.750418i
$956$	−16.7959	+	9.69711i	−0.543218	+	0.313627i
$957$		0			0
$958$	2.73220	+	4.73230i	0.0882732	+	0.152894i
$959$	9.97376	−	17.2751i	0.322070	−	0.557841i
$960$		0			0
$961$	29.6739			0.957224
$962$	16.5178	−	10.0105i	0.532554	−	0.322751i
$963$		0			0
$964$	−16.4223	−	9.48141i	−0.528926	−	0.305376i
$965$	26.0808	−	45.1732i	0.839569	−	1.45418i
$966$		0			0
$967$		−	35.2467i		−	1.13346i	−0.823904	−	0.566729i	$-0.808209\pi$
$967$		−	35.2467i		−	1.13346i	0.823904	−	0.566729i	$-0.191791\pi$
$968$	−57.6073	+	33.2596i	−1.85157	+	1.06900i
$969$		0			0
$970$		−	8.92578i		−	0.286590i
$971$	18.4891	+	32.0241i	0.593344	+	1.02770i	0.993778	+	0.111377i	$0.0355261\pi$
$971$	18.4891	+	32.0241i	0.593344	+	1.02770i	−0.400434	+	0.916326i	$0.631141\pi$
$972$		0			0
$973$	17.6041	+	10.1637i	0.564362	+	0.325834i
$974$	−27.5645			−0.883224
$975$		0			0
$976$	−0.451876			−0.0144642
$977$	21.4363	+	12.3762i	0.685807	+	0.395951i	0.802039	−	0.597271i	$-0.203748\pi$
$977$	21.4363	+	12.3762i	0.685807	+	0.395951i	−0.116232	+	0.993222i	$0.537082\pi$
$978$		0			0
$979$	10.5820	+	18.3286i	0.338204	+	0.585786i
$980$			4.17951i			0.133510i
$981$		0			0
$982$	−26.6236	+	15.3711i	−0.849593	+	0.490513i
$983$			4.55736i			0.145357i	0.997355	+	0.0726786i	$0.0231547\pi$
$983$			4.55736i			0.145357i	−0.997355	+	0.0726786i	$0.976845\pi$
$984$		0			0
$985$	−17.4076	+	30.1509i	−0.554652	+	0.960686i
$986$	11.5497	+	6.66820i	0.367816	+	0.212359i
$987$		0			0
$988$	−4.49062	+	8.17436i	−0.142866	+	0.260061i
$989$	19.0820			0.606773
$990$		0			0
$991$	13.5982	−	23.5527i	0.431960	−	0.748176i	−0.565082	−	0.825034i	$-0.691156\pi$
$991$	13.5982	−	23.5527i	0.431960	−	0.748176i	0.997042	+	0.0768584i	$0.0244890\pi$
$992$	3.33543	+	5.77713i	0.105900	+	0.183424i
$993$		0			0
$994$	3.21462	−	1.85596i	0.101962	−	0.0588676i
$995$	−58.0873	+	33.5367i	−1.84149	+	1.06319i
$996$		0			0
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	0.999700	−	0.0244727i	$-0.00779070\pi$
$997$	15.1137	+	26.1777i	0.478656	+	0.829057i	−0.521044	+	0.853530i	$0.674457\pi$
$998$	14.0551	−	24.3441i	0.444906	−	0.770600i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.ct.a.316.3		12
3.2	odd	2		91.2.q.a.43.4	yes	12
12.11	even	2		1456.2.cc.c.225.6		12
13.10	even	6	inner	819.2.ct.a.127.3		12
21.2	odd	6		637.2.k.h.459.3		12
21.5	even	6		637.2.k.g.459.3		12
21.11	odd	6		637.2.u.h.30.3		12
21.17	even	6		637.2.u.i.30.3		12
21.20	even	2		637.2.q.h.589.4		12
39.17	odd	6		1183.2.c.i.337.8		12
39.20	even	12		1183.2.a.m.1.5		6
39.23	odd	6		91.2.q.a.36.4	✓	12
39.32	even	12		1183.2.a.p.1.2		6
39.35	odd	6		1183.2.c.i.337.5		12
156.23	even	6		1456.2.cc.c.673.6		12
273.20	odd	12		8281.2.a.by.1.5		6
273.23	odd	6		637.2.u.h.361.3		12
273.62	even	6		637.2.q.h.491.4		12
273.101	even	6		637.2.k.g.569.4		12
273.179	odd	6		637.2.k.h.569.4		12
273.188	odd	12		8281.2.a.ch.1.2		6
273.257	even	6		637.2.u.i.361.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	39.23	odd	6
91.2.q.a.43.4	yes	12	3.2	odd	2
637.2.k.g.459.3		12	21.5	even	6
637.2.k.g.569.4		12	273.101	even	6
637.2.k.h.459.3		12	21.2	odd	6
637.2.k.h.569.4		12	273.179	odd	6
637.2.q.h.491.4		12	273.62	even	6
637.2.q.h.589.4		12	21.20	even	2
637.2.u.h.30.3		12	21.11	odd	6
637.2.u.h.361.3		12	273.23	odd	6
637.2.u.i.30.3		12	21.17	even	6
637.2.u.i.361.3		12	273.257	even	6
819.2.ct.a.127.3		12	13.10	even	6	inner
819.2.ct.a.316.3		12	1.1	even	1	trivial
1183.2.a.m.1.5		6	39.20	even	12
1183.2.a.p.1.2		6	39.32	even	12
1183.2.c.i.337.5		12	39.35	odd	6
1183.2.c.i.337.8		12	39.17	odd	6
1456.2.cc.c.225.6		12	12.11	even	2
1456.2.cc.c.673.6		12	156.23	even	6
8281.2.a.by.1.5		6	273.20	odd	12
8281.2.a.ch.1.2		6	273.188	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.ct (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.713220 - 0.411778i) q^{2} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(0.866025 - 0.500000i) q^{7} +2.73565i q^{8} +O(q^{10})\)	\(q+(-0.713220 - 0.411778i) q^{2} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(0.866025 - 0.500000i) q^{7} +2.73565i q^{8} +(-1.30208 + 2.25527i) q^{10} +(-5.14653 - 2.97135i) q^{11} +(-0.0766193 - 3.60474i) q^{13} -0.823556 q^{14} +(-0.195274 + 0.338225i) q^{16} +(1.34982 + 2.33796i) q^{17} +(1.69485 - 0.978524i) q^{19} +(-3.61956 + 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(1.36471 - 2.36374i) q^{23} -4.99883 q^{25} +(-1.42970 + 2.60252i) q^{26} +(-1.14467 - 0.660878i) q^{28} +(-2.99923 + 5.19481i) q^{29} +1.15155i q^{31} +(5.01684 - 2.89647i) q^{32} -2.22331i q^{34} +(-1.58105 - 2.73845i) q^{35} +(-5.63310 - 3.25227i) q^{37} -1.61174 q^{38} +8.65038 q^{40} +(3.23351 + 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} +7.85479i q^{44} +(-1.94667 + 1.12391i) q^{46} +0.456071i q^{47} +(0.500000 - 0.866025i) q^{49} +(3.56527 + 2.05841i) q^{50} +(-4.07561 + 2.46999i) q^{52} -0.399286 q^{53} +(-9.39568 + 16.2738i) q^{55} +(1.36783 + 2.36914i) q^{56} +(4.27822 - 2.47003i) q^{58} +(-4.16200 + 2.40293i) q^{59} +(0.578514 + 1.00201i) q^{61} +(0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-11.3985 + 0.242277i) q^{65} +(-5.43793 - 3.13959i) q^{67} +(1.78413 - 3.09021i) q^{68} +2.60416i q^{70} +(-3.90335 + 2.25360i) q^{71} -8.30575i q^{73} +(2.67843 + 4.63917i) q^{74} +(-2.24018 - 1.29337i) q^{76} -5.94270 q^{77} -7.91410 q^{79} +(1.06950 + 0.617476i) q^{80} +(-1.53747 - 2.66298i) q^{82} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} -5.75769i q^{86} +(8.12857 - 14.0791i) q^{88} +(-3.08423 - 1.78068i) q^{89} +(-1.86872 - 3.08348i) q^{91} -3.60762 q^{92} +(0.187800 - 0.325279i) q^{94} +(-3.09418 - 5.35928i) q^{95} +(-2.96831 + 1.71375i) q^{97} +(-0.713220 + 0.411778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4}+O(q^{10}) \) 12 * q + 4 * q^4	\( 12 q + 4 q^{4} + 12 q^{10} - 6 q^{11} + 4 q^{13} + 8 q^{14} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} + 12 q^{23} - 20 q^{25} + 42 q^{26} - 8 q^{29} - 36 q^{32} - 6 q^{35} - 42 q^{37} - 4 q^{38} + 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 6 q^{49} + 18 q^{50} + 2 q^{52} + 44 q^{53} - 6 q^{55} + 12 q^{56} - 12 q^{58} - 18 q^{59} + 14 q^{61} + 4 q^{62} - 52 q^{64} - 60 q^{65} - 24 q^{67} + 8 q^{68} + 24 q^{71} - 6 q^{74} - 18 q^{76} - 8 q^{77} - 56 q^{79} + 72 q^{80} + 14 q^{82} - 48 q^{85} - 14 q^{88} + 12 q^{89} + 14 q^{91} - 24 q^{92} + 4 q^{94} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 12 * q^10 - 6 * q^11 + 4 * q^13 + 8 * q^14 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 + 12 * q^23 - 20 * q^25 + 42 * q^26 - 8 * q^29 - 36 * q^32 - 6 * q^35 - 42 * q^37 - 4 * q^38 + 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 6 * q^49 + 18 * q^50 + 2 * q^52 + 44 * q^53 - 6 * q^55 + 12 * q^56 - 12 * q^58 - 18 * q^59 + 14 * q^61 + 4 * q^62 - 52 * q^64 - 60 * q^65 - 24 * q^67 + 8 * q^68 + 24 * q^71 - 6 * q^74 - 18 * q^76 - 8 * q^77 - 56 * q^79 + 72 * q^80 + 14 * q^82 - 48 * q^85 - 14 * q^88 + 12 * q^89 + 14 * q^91 - 24 * q^92 + 4 * q^94 + 22 * q^95 + 6 * q^97

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