LMFDB - Embedded newform 387.2.bc.a.233.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(26,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 17]))

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

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

chi := DirichletCharacter("387.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.bc (of order $42$, degree $12$, 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:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			233.3
Character	$\chi$	$=$	387.233
Dual form			387.2.bc.a.98.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77234 - 0.853513i) q^{2} +(1.16572 + 1.46176i) q^{4} +(-2.24932 + 2.08706i) q^{5} +(-0.712654 - 0.411451i) q^{7} +(0.0570523 + 0.249962i) q^{8} +O(q^{10})$	\(q+(-1.77234 - 0.853513i) q^{2} +(1.16572 + 1.46176i) q^{4} +(-2.24932 + 2.08706i) q^{5} +(-0.712654 - 0.411451i) q^{7} +(0.0570523 + 0.249962i) q^{8} +(5.76789 - 1.77916i) q^{10} +(-1.75064 - 1.39608i) q^{11} +(0.297471 + 0.0917577i) q^{13} +(0.911884 + 1.33749i) q^{14} +(0.944309 - 4.13729i) q^{16} +(4.65851 - 5.02068i) q^{17} +(0.989520 + 0.388358i) q^{19} +(-5.67286 - 0.855046i) q^{20} +(1.91114 + 3.96852i) q^{22} +(0.410979 - 2.72667i) q^{23} +(0.329954 - 4.40293i) q^{25} +(-0.448903 - 0.416521i) q^{26} +(-0.229309 - 1.52137i) q^{28} +(5.21247 - 3.55380i) q^{29} +(-0.0789941 - 1.05410i) q^{31} +(-4.88515 + 6.12578i) q^{32} +(-12.5417 + 4.92224i) q^{34} +(2.46171 - 0.561869i) q^{35} +(-4.34421 + 2.50813i) q^{37} +(-1.42229 - 1.53287i) q^{38} +(-0.650016 - 0.443174i) q^{40} +(4.68214 - 9.72257i) q^{41} +(3.10448 - 5.77600i) q^{43} -4.18645i q^{44} +(-3.05564 + 4.48180i) q^{46} +(-7.96080 + 6.34853i) q^{47} +(-3.16142 - 5.47573i) q^{49} +(-4.34274 + 7.52185i) q^{50} +(0.212639 + 0.541795i) q^{52} +(-1.24334 - 4.03081i) q^{53} +(6.85146 - 0.513446i) q^{55} +(0.0621887 - 0.201611i) q^{56} +(-12.2715 + 1.84963i) q^{58} +(0.0466708 + 0.0106523i) q^{59} +(3.20022 + 0.239823i) q^{61} +(-0.759686 + 1.93565i) q^{62} +(6.23970 - 3.00488i) q^{64} +(-0.860612 + 0.414449i) q^{65} +(1.03874 - 2.64666i) q^{67} +(12.7695 + 0.956945i) q^{68} +(-4.84254 - 1.10528i) q^{70} +(14.8403 - 2.23681i) q^{71} +(2.74477 - 8.89834i) q^{73} +(9.84014 - 0.737416i) q^{74} +(0.585813 + 1.89916i) q^{76} +(0.673176 + 1.71523i) q^{77} +(-1.50477 + 2.60634i) q^{79} +(6.51073 + 11.2769i) q^{80} +(-16.5967 + 13.2354i) q^{82} +(-8.86855 + 13.0078i) q^{83} +21.0157i q^{85} +(-10.4321 + 7.58732i) q^{86} +(0.249091 - 0.517243i) q^{88} +(9.33457 + 6.36420i) q^{89} +(-0.174240 - 0.187786i) q^{91} +(4.46482 - 2.57777i) q^{92} +(19.5278 - 4.45709i) q^{94} +(-3.03627 + 1.19165i) q^{95} +(-4.46477 + 5.59864i) q^{97} +(0.929488 + 12.4032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) $ 168 * q - 24 * q^4 - 6 * q^7	$ 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) $ 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$

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 $

$2$	−1.77234	−	0.853513i	−1.25323	−	0.603525i	−0.314855	−	0.949140i	$-0.601956\pi$
$2$	−1.77234	−	0.853513i	−1.25323	−	0.603525i	−0.938376	+	0.345615i	$0.887670\pi$
$3$		0			0
$3$		0			0
$4$	1.16572	+	1.46176i	0.582858	+	0.730881i
$5$	−2.24932	+	2.08706i	−1.00593	+	0.933363i	−0.997780	−	0.0666036i	$-0.978784\pi$
$5$	−2.24932	+	2.08706i	−1.00593	+	0.933363i	−0.00814675	+	0.999967i	$0.502593\pi$
$6$		0			0
$7$	−0.712654	−	0.411451i	−0.269358	−	0.155514i	0.359238	−	0.933246i	$-0.383037\pi$
$7$	−0.712654	−	0.411451i	−0.269358	−	0.155514i	−0.628596	+	0.777732i	$0.716370\pi$
$8$	0.0570523	+	0.249962i	0.0201710	+	0.0883751i
$9$		0			0
$10$	5.76789	−	1.77916i	1.82397	−	0.562619i
$11$	−1.75064	−	1.39608i	−0.527836	−	0.420935i	0.322974	−	0.946408i	$-0.395317\pi$
$11$	−1.75064	−	1.39608i	−0.527836	−	0.420935i	−0.850811	+	0.525472i	$0.823889\pi$
$12$		0			0
$13$	0.297471	+	0.0917577i	0.0825037	+	0.0254490i	0.335732	−	0.941957i	$-0.391016\pi$
$13$	0.297471	+	0.0917577i	0.0825037	+	0.0254490i	−0.253229	+	0.967406i	$0.581492\pi$
$14$	0.911884	+	1.33749i	0.243711	+	0.357459i
$15$		0			0
$16$	0.944309	−	4.13729i	0.236077	−	1.03432i
$17$	4.65851	−	5.02068i	1.12985	−	1.21769i	0.156674	−	0.987650i	$-0.449923\pi$
$17$	4.65851	−	5.02068i	1.12985	−	1.21769i	0.973180	−	0.230043i	$-0.0738868\pi$
$18$		0			0
$19$	0.989520	+	0.388358i	0.227011	+	0.0890954i	0.476121	−	0.879380i	$-0.342043\pi$
$19$	0.989520	+	0.388358i	0.227011	+	0.0890954i	−0.249109	+	0.968475i	$0.580138\pi$
$20$	−5.67286	−	0.855046i	−1.26849	−	0.191194i
$21$		0			0
$22$	1.91114	+	3.96852i	0.407456	+	0.846092i
$23$	0.410979	−	2.72667i	0.0856950	−	0.568549i	−0.904240	−	0.427025i	$-0.859562\pi$
$23$	0.410979	−	2.72667i	0.0856950	−	0.568549i	0.989935	−	0.141524i	$-0.0452003\pi$
$24$		0			0
$25$	0.329954	−	4.40293i	0.0659907	−	0.880585i
$26$	−0.448903	−	0.416521i	−0.0880371	−	0.0816865i
$27$		0			0
$28$	−0.229309	−	1.52137i	−0.0433353	−	0.287511i
$29$	5.21247	−	3.55380i	0.967931	−	0.659924i	0.0273970	−	0.999625i	$-0.491278\pi$
$29$	5.21247	−	3.55380i	0.967931	−	0.659924i	0.940534	+	0.339701i	$0.110326\pi$
$30$		0			0
$31$	−0.0789941	−	1.05410i	−0.0141878	−	0.189322i	−0.999795	−	0.0202686i	$-0.993548\pi$
$31$	−0.0789941	−	1.05410i	−0.0141878	−	0.189322i	0.985607	−	0.169054i	$-0.0540712\pi$
$32$	−4.88515	+	6.12578i	−0.863580	+	1.08290i
$33$		0			0
$34$	−12.5417	+	4.92224i	−2.15088	+	0.844157i
$35$	2.46171	−	0.561869i	0.416105	−	0.0949732i
$36$		0			0
$37$	−4.34421	+	2.50813i	−0.714184	+	0.412335i	−0.812608	−	0.582810i	$-0.801953\pi$
$37$	−4.34421	+	2.50813i	−0.714184	+	0.412335i	0.0984240	+	0.995145i	$0.468620\pi$
$38$	−1.42229	−	1.53287i	−0.230727	−	0.248664i
$39$		0			0
$40$	−0.650016	−	0.443174i	−0.102777	−	0.0700719i
$41$	4.68214	−	9.72257i	0.731228	−	1.51841i	−0.119518	−	0.992832i	$-0.538135\pi$
$41$	4.68214	−	9.72257i	0.731228	−	1.51841i	0.850745	−	0.525578i	$-0.176151\pi$
$42$		0			0
$43$	3.10448	−	5.77600i	0.473428	−	0.880832i
$43$	3.10448	−	5.77600i	0.473428	−	0.880832i
$44$		−	4.18645i		−	0.631131i
$45$		0			0
$46$	−3.05564	+	4.48180i	−0.450529	+	0.660805i
$47$	−7.96080	+	6.34853i	−1.16120	+	0.926028i	−0.998163	−	0.0605919i	$-0.980701\pi$
$47$	−7.96080	+	6.34853i	−1.16120	+	0.926028i	−0.163039	+	0.986620i	$0.552130\pi$
$48$		0			0
$49$	−3.16142	−	5.47573i	−0.451631	−	0.782248i
$50$	−4.34274	+	7.52185i	−0.614157	+	1.06375i
$51$		0			0
$52$	0.212639	+	0.541795i	0.0294877	+	0.0751335i
$53$	−1.24334	−	4.03081i	−0.170786	−	0.553674i	0.829200	−	0.558952i	$-0.188796\pi$
$53$	−1.24334	−	4.03081i	−0.170786	−	0.553674i	−0.999986	+	0.00527768i	$0.998320\pi$
$54$		0			0
$55$	6.85146	−	0.513446i	0.923850	−	0.0692330i
$56$	0.0621887	−	0.201611i	0.00831032	−	0.0269414i
$57$		0			0
$58$	−12.2715	+	1.84963i	−1.61132	+	0.242868i
$59$	0.0466708	+	0.0106523i	0.00607602	+	0.00138681i	0.225558	−	0.974230i	$-0.427580\pi$
$59$	0.0466708	+	0.0106523i	0.00607602	+	0.00138681i	−0.219482	+	0.975617i	$0.570437\pi$
$60$		0			0
$61$	3.20022	+	0.239823i	0.409746	+	0.0307062i	0.278009	−	0.960578i	$-0.410325\pi$
$61$	3.20022	+	0.239823i	0.409746	+	0.0307062i	0.131737	+	0.991285i	$0.457945\pi$
$62$	−0.759686	+	1.93565i	−0.0964802	+	0.245827i
$63$		0			0
$64$	6.23970	−	3.00488i	0.779963	−	0.375610i
$65$	−0.860612	+	0.414449i	−0.106746	+	0.0514061i
$66$		0			0
$67$	1.03874	−	2.64666i	0.126902	−	0.323341i	−0.853276	−	0.521459i	$-0.825388\pi$
$67$	1.03874	−	2.64666i	0.126902	−	0.323341i	0.980178	+	0.198118i	$0.0634830\pi$
$68$	12.7695	+	0.956945i	1.54853	+	0.116047i
$69$		0			0
$70$	−4.84254	−	1.10528i	−0.578795	−	0.132106i
$71$	14.8403	−	2.23681i	1.76122	−	0.265461i	0.812813	−	0.582525i	$-0.197935\pi$
$71$	14.8403	−	2.23681i	1.76122	−	0.265461i	0.948404	+	0.317065i	$0.102697\pi$
$72$		0			0
$73$	2.74477	−	8.89834i	0.321251	−	1.04147i	−0.640594	−	0.767879i	$-0.721312\pi$
$73$	2.74477	−	8.89834i	0.321251	−	1.04147i	0.961846	−	0.273592i	$-0.0882119\pi$
$74$	9.84014	−	0.737416i	1.14389	−	0.0857229i
$75$		0			0
$76$	0.585813	+	1.89916i	0.0671973	+	0.217848i
$77$	0.673176	+	1.71523i	0.0767156	+	0.195468i
$78$		0			0
$79$	−1.50477	+	2.60634i	−0.169300	+	0.293236i	−0.938174	−	0.346164i	$-0.887484\pi$
$79$	−1.50477	+	2.60634i	−0.169300	+	0.293236i	0.768874	+	0.639400i	$0.220817\pi$
$80$	6.51073	+	11.2769i	0.727922	+	1.26080i
$81$		0			0
$82$	−16.5967	+	13.2354i	−1.83280	+	1.46161i
$83$	−8.86855	+	13.0078i	−0.973450	+	1.42779i	−0.0707617	+	0.997493i	$0.522543\pi$
$83$	−8.86855	+	13.0078i	−0.973450	+	1.42779i	−0.902688	+	0.430295i	$0.858409\pi$
$84$		0			0
$85$			21.0157i			2.27947i
$86$	−10.4321	+	7.58732i	−1.12492	+	0.818161i
$87$		0			0
$88$	0.249091	−	0.517243i	0.0265532	−	0.0551383i
$89$	9.33457	+	6.36420i	0.989463	+	0.674604i	0.945904	−	0.324446i	$-0.105178\pi$
$89$	9.33457	+	6.36420i	0.989463	+	0.674604i	0.0435588	+	0.999051i	$0.486130\pi$
$90$		0			0
$91$	−0.174240	−	0.187786i	−0.0182653	−	0.0196853i
$92$	4.46482	−	2.57777i	0.465490	−	0.268751i
$93$		0			0
$94$	19.5278	−	4.45709i	2.01414	−	0.459713i
$95$	−3.03627	+	1.19165i	−0.311515	+	0.122261i
$96$		0			0
$97$	−4.46477	+	5.59864i	−0.453328	+	0.568456i	−0.955001	−	0.296602i	$-0.904147\pi$
$97$	−4.46477	+	5.59864i	−0.453328	+	0.568456i	0.501673	+	0.865057i	$0.332718\pi$
$98$	0.929488	+	12.4032i	0.0938925	+	1.25291i
$99$		0			0
$100$	6.82066	−	4.65025i	0.682066	−	0.465025i
$101$	−0.773444	−	5.13147i	−0.0769605	−	0.510600i	−0.993786	−	0.111311i	$-0.964495\pi$
$101$	−0.773444	−	5.13147i	−0.0769605	−	0.510600i	0.916825	−	0.399289i	$-0.130743\pi$
$102$		0			0
$103$	5.75307	+	5.33807i	0.566867	+	0.525976i	0.910707	−	0.413053i	$-0.135537\pi$
$103$	5.75307	+	5.33807i	0.566867	+	0.525976i	−0.343840	+	0.939028i	$0.611728\pi$
$104$	−0.00596457	+	0.0795916i	−0.000584874	+	0.00780460i
$105$		0			0
$106$	−1.23673	+	8.20516i	−0.120122	+	0.796955i
$107$	2.77803	+	5.76864i	0.268562	+	0.557676i	0.991016	−	0.133744i	$-0.0427000\pi$
$107$	2.77803	+	5.76864i	0.268562	+	0.557676i	−0.722454	+	0.691419i	$0.756986\pi$
$108$		0			0
$109$	10.1948	+	1.53663i	0.976489	+	0.147182i	0.617852	−	0.786295i	$-0.288003\pi$
$109$	10.1948	+	1.53663i	0.976489	+	0.147182i	0.358638	+	0.933477i	$0.383241\pi$
$110$	−12.5813	−	4.93781i	−1.19958	−	0.470801i
$111$		0			0
$112$	−2.37526	+	2.55992i	−0.224441	+	0.241889i
$113$	1.35922	−	5.95512i	0.127864	−	0.560210i	−0.869891	−	0.493244i	$-0.835811\pi$
$113$	1.35922	−	5.95512i	0.127864	−	0.560210i	0.997755	−	0.0669661i	$-0.0213319\pi$
$114$		0			0
$115$	4.76630	+	6.99088i	0.444460	+	0.651903i
$116$	11.2711	+	3.47666i	1.04649	+	0.322800i
$117$		0			0
$118$	−0.0736245	−	0.0587136i	−0.00677769	−	0.00540503i
$119$	−5.38567	+	1.66126i	−0.493703	+	0.152287i
$120$		0			0
$121$	−1.33206	−	5.83614i	−0.121096	−	0.530558i
$122$	−5.46718	−	3.15648i	−0.494975	−	0.285774i
$123$		0			0
$124$	1.44876	−	1.34425i	0.130103	−	0.120718i
$125$	−1.11866	−	1.40276i	−0.100056	−	0.125467i
$126$		0			0
$127$	−5.72217	−	2.75565i	−0.507761	−	0.244525i	0.162421	−	0.986722i	$-0.448070\pi$
$127$	−5.72217	−	2.75565i	−0.507761	−	0.244525i	−0.670182	+	0.742197i	$0.733784\pi$
$128$	2.04677			0.180911
$129$		0			0
$130$	1.87903			0.164802
$131$	−19.4142	−	9.34941i	−1.69623	−	0.816861i	−0.994537	−	0.104382i	$-0.966714\pi$
$131$	−19.4142	−	9.34941i	−1.69623	−	0.816861i	−0.701693	−	0.712479i	$-0.747572\pi$
$132$		0			0
$133$	−0.545395	−	0.683904i	−0.0472917	−	0.0593020i
$134$	−4.09995	+	3.80420i	−0.354182	+	0.328633i
$135$		0			0
$136$	1.52076	+	0.878011i	0.130404	+	0.0752888i
$137$	−2.14808	−	9.41136i	−0.183523	−	0.804067i	−0.979936	−	0.199313i	$-0.936129\pi$
$137$	−2.14808	−	9.41136i	−0.183523	−	0.804067i	0.796413	−	0.604753i	$-0.206728\pi$
$138$		0			0
$139$	17.1836	−	5.30044i	1.45749	−	0.449577i	0.538088	−	0.842888i	$-0.319147\pi$
$139$	17.1836	−	5.30044i	1.45749	−	0.449577i	0.919405	+	0.393311i	$0.128670\pi$
$140$	3.69097	+	2.94345i	0.311944	+	0.248767i
$141$		0			0
$142$	−28.2111	−	8.70198i	−2.36742	−	0.730254i
$143$	−0.392662	−	0.575929i	−0.0328360	−	0.0481616i
$144$		0			0
$145$	−4.30750	+	18.8724i	−0.357718	+	1.56727i
$146$	−12.4595	+	13.4282i	−1.03116	+	1.11132i
$147$		0			0
$148$	−8.73041	−	3.42644i	−0.717636	−	0.281651i
$149$	9.45368	+	1.42491i	0.774476	+	0.116733i	0.524376	−	0.851487i	$-0.324299\pi$
$149$	9.45368	+	1.42491i	0.774476	+	0.116733i	0.250100	+	0.968220i	$0.419537\pi$
$150$		0			0
$151$	−7.27013	−	15.0966i	−0.591635	−	1.22854i	−0.954920	−	0.296864i	$-0.904059\pi$
$151$	−7.27013	−	15.0966i	−0.591635	−	1.22854i	0.363285	−	0.931678i	$-0.381655\pi$
$152$	−0.0406205	+	0.269500i	−0.00329476	+	0.0218593i
$153$		0			0
$154$	0.270871	−	3.61452i	0.0218274	−	0.291267i
$155$	2.37766	+	2.20615i	0.190978	+	0.177202i
$156$		0			0
$157$	1.52072	+	10.0893i	0.121367	+	0.805217i	0.963841	+	0.266479i	$0.0858604\pi$
$157$	1.52072	+	10.0893i	0.121367	+	0.805217i	−0.842474	+	0.538737i	$0.818902\pi$
$158$	4.89150	−	3.33497i	0.389147	−	0.265316i
$159$		0			0
$160$	−1.79664	−	23.9744i	−0.142037	−	1.89535i
$161$	−1.41477	+	1.77407i	−0.111500	+	0.139816i
$162$		0			0
$163$	−6.97799	+	2.73866i	−0.546558	+	0.214508i	−0.622522	−	0.782602i	$-0.713892\pi$
$163$	−6.97799	+	2.73866i	−0.546558	+	0.214508i	0.0759638	+	0.997111i	$0.475797\pi$
$164$	19.6701	−	4.48958i	1.53598	−	0.350577i
$165$		0			0
$166$	26.8204	−	15.4847i	2.08166	−	1.20185i
$167$	−14.9084	−	16.0674i	−1.15365	−	1.24333i	−0.965275	−	0.261236i	$-0.915870\pi$
$167$	−14.9084	−	16.0674i	−1.15365	−	1.24333i	−0.188370	−	0.982098i	$-0.560321\pi$
$168$		0			0
$169$	−10.6610	−	7.26857i	−0.820080	−	0.559121i
$170$	17.9372	−	37.2469i	1.37572	−	2.85671i
$171$		0			0
$172$	12.0621	−	2.19518i	0.919725	−	0.167381i
$173$			17.1303i			1.30239i	0.758910	+	0.651195i	$0.225732\pi$
$173$			17.1303i			1.30239i	−0.758910	+	0.651195i	$0.774268\pi$
$174$		0			0
$175$	−2.04673	+	3.00200i	−0.154718	+	0.226930i
$176$	−7.42914	+	5.92454i	−0.559993	+	0.446579i
$177$		0			0
$178$	−11.1121	−	19.2467i	−0.832886	−	1.44260i
$179$	2.98691	−	5.17348i	0.223252	−	0.386684i	−0.732541	−	0.680722i	$-0.761666\pi$
$179$	2.98691	−	5.17348i	0.223252	−	0.386684i	0.955794	+	0.294038i	$0.0949993\pi$
$180$		0			0
$181$	1.04483	+	2.66218i	0.0776615	+	0.197878i	0.964432	−	0.264332i	$-0.0851516\pi$
$181$	1.04483	+	2.66218i	0.0776615	+	0.197878i	−0.886770	+	0.462211i	$0.847056\pi$
$182$	0.148534	+	0.481537i	0.0110101	+	0.0356939i
$183$		0			0
$184$	0.705011	−	0.0528333i	0.0519741	−	0.00389492i
$185$	4.53689	−	14.7082i	0.333559	−	1.08137i
$186$		0			0
$187$	−15.1646	+	2.28570i	−1.10895	+	0.167147i
$188$	−18.5601	−	4.23621i	−1.35363	−	0.308958i
$189$		0			0
$190$	6.39839	+	0.479493i	0.464188	+	0.0347861i
$191$	6.19737	−	15.7906i	0.448426	−	1.14257i	−0.510742	−	0.859734i	$-0.670629\pi$
$191$	6.19737	−	15.7906i	0.448426	−	1.14257i	0.959168	−	0.282837i	$-0.0912756\pi$
$192$		0			0
$193$	23.6860	−	11.4066i	1.70495	−	0.821063i	0.712053	−	0.702126i	$-0.247766\pi$
$193$	23.6860	−	11.4066i	1.70495	−	0.821063i	0.992902	−	0.118937i	$-0.0379487\pi$
$194$	12.6916	−	6.11195i	0.911203	−	0.438812i
$195$		0			0
$196$	4.31890	−	11.0044i	0.308493	−	0.786028i
$197$	−21.8741	−	1.63924i	−1.55846	−	0.116791i	−0.732600	−	0.680659i	$-0.761693\pi$
$197$	−21.8741	−	1.63924i	−1.55846	−	0.116791i	−0.825865	+	0.563868i	$0.809313\pi$
$198$		0			0
$199$	−14.0160	−	3.19905i	−0.993565	−	0.226775i	−0.305318	−	0.952251i	$-0.598763\pi$
$199$	−14.0160	−	3.19905i	−0.993565	−	0.226775i	−0.688248	+	0.725476i	$0.741620\pi$
$200$	1.11939	−	0.168721i	0.0791529	−	0.0119304i
$201$		0			0
$202$	−3.00897	+	9.75483i	−0.211710	+	0.686348i
$203$	−5.17690	+	0.387955i	−0.363347	+	0.0272291i
$204$		0			0
$205$	9.75998	+	31.6411i	0.681667	+	2.20991i
$206$	−5.64027	−	14.3712i	−0.392976	−	1.00129i
$207$		0			0
$208$	0.660533	−	1.14408i	0.0457997	−	0.0793274i
$209$	−1.19011	−	2.06133i	−0.0823215	−	0.142585i
$210$		0			0
$211$	−18.5525	+	14.7952i	−1.27721	+	1.01854i	−0.278906	+	0.960319i	$0.589972\pi$
$211$	−18.5525	+	14.7952i	−1.27721	+	1.01854i	−0.998304	+	0.0582218i	$0.981457\pi$
$212$	4.44270	−	6.51624i	0.305126	−	0.447537i
$213$		0			0
$214$		−	12.5951i		−	0.860981i
$215$	5.07193	+	19.4713i	0.345903	+	1.32793i
$216$		0			0
$217$	−0.377416	+	0.783712i	−0.0256207	+	0.0532019i
$218$	−16.7572	−	11.4249i	−1.13494	−	0.773788i
$219$		0			0
$220$	8.73739	+	9.41666i	0.589075	+	0.634871i
$221$	1.84646	−	1.06605i	0.124206	−	0.0717105i
$222$		0			0
$223$	−16.2990	+	3.72013i	−1.09146	+	0.249119i	−0.730122	−	0.683316i	$-0.760537\pi$
$223$	−16.2990	+	3.72013i	−1.09146	+	0.249119i	−0.361338	+	0.932435i	$0.617680\pi$
$224$	6.00188	−	2.35556i	0.401017	−	0.157388i
$225$		0			0
$226$	−7.49176	+	9.39437i	−0.498344	+	0.624904i
$227$	0.305814	+	4.08080i	0.0202976	+	0.270852i	0.998114	+	0.0613884i	$0.0195528\pi$
$227$	0.305814	+	4.08080i	0.0202976	+	0.270852i	−0.977816	+	0.209464i	$0.932828\pi$
$228$		0			0
$229$	12.6976	−	8.65708i	0.839081	−	0.572076i	−0.0657549	−	0.997836i	$-0.520946\pi$
$229$	12.6976	−	8.65708i	0.839081	−	0.572076i	0.904836	+	0.425760i	$0.139993\pi$
$230$	−2.48069	−	16.4583i	−0.163572	−	1.08523i
$231$		0			0
$232$	1.18570	+	1.10017i	0.0778450	+	0.0722296i
$233$	−1.77066	+	23.6278i	−0.116000	+	1.54791i	0.570817	+	0.821077i	$0.306626\pi$
$233$	−1.77066	+	23.6278i	−0.116000	+	1.54791i	−0.686817	+	0.726830i	$0.740993\pi$
$234$		0			0
$235$	4.65661	−	30.8946i	0.303763	−	2.01534i
$236$	0.0388338	+	0.0806392i	0.00252786	+	0.00524916i
$237$		0			0
$238$	10.9631	+	1.65243i	0.710634	+	0.107111i
$239$	−10.7047	−	4.20127i	−0.692427	−	0.271757i	−0.00708063	−	0.999975i	$-0.502254\pi$
$239$	−10.7047	−	4.20127i	−0.692427	−	0.271757i	−0.685346	+	0.728217i	$0.740349\pi$
$240$		0			0
$241$	−0.805081	+	0.867671i	−0.0518598	+	0.0558916i	−0.758449	−	0.651733i	$-0.774042\pi$
$241$	−0.805081	+	0.867671i	−0.0518598	+	0.0558916i	0.706589	+	0.707624i	$0.250233\pi$
$242$	−2.62036	+	11.4805i	−0.168443	+	0.737997i
$243$		0			0
$244$	3.37998	+	4.95753i	0.216381	+	0.317373i
$245$	18.5392	+	5.71860i	1.18443	+	0.365348i
$246$		0			0
$247$	0.258719	+	0.206321i	0.0164619	+	0.0131279i
$248$	0.258979	−	0.0798845i	0.0164452	−	0.00507267i
$249$		0			0
$250$	0.785376	+	3.44096i	0.0496715	+	0.217625i
$251$	4.47296	+	2.58247i	0.282331	+	0.163004i	0.634478	−	0.772941i	$-0.281215\pi$
$251$	4.47296	+	2.58247i	0.282331	+	0.163004i	−0.352147	+	0.935945i	$0.614548\pi$
$252$		0			0
$253$	−4.52613	+	4.19964i	−0.284555	+	0.264029i
$254$	7.78964	+	9.76790i	0.488765	+	0.612892i
$255$		0			0
$256$	−16.1070	−	7.75671i	−1.00669	−	0.484794i
$257$	−4.17240			−0.260267			−0.130133	−	0.991496i	$-0.541541\pi$
$257$	−4.17240			−0.260267			−0.130133	+	0.991496i	$0.541541\pi$
$258$		0			0
$259$	4.12789			0.256495
$260$	−1.60905	−	0.774880i	−0.0997893	−	0.0480560i
$261$		0			0
$262$	26.4288	+	33.1406i	1.63277	+	2.04743i
$263$	−19.8679	+	18.4347i	−1.22511	+	1.13673i	−0.238929	+	0.971037i	$0.576796\pi$
$263$	−19.8679	+	18.4347i	−1.22511	+	1.13673i	−0.986177	+	0.165695i	$0.947013\pi$
$264$		0			0
$265$	11.2092	+	6.47164i	0.688577	+	0.397550i
$266$	0.382903	+	1.67761i	0.0234773	+	0.102861i
$267$		0			0
$268$	5.07966	−	1.56687i	0.310290	−	0.0957117i
$269$	−3.46837	−	2.76594i	−0.211470	−	0.168642i	0.512026	−	0.858970i	$-0.328895\pi$
$269$	−3.46837	−	2.76594i	−0.211470	−	0.168642i	−0.723497	+	0.690328i	$0.757466\pi$
$270$		0			0
$271$	22.8029	+	7.03377i	1.38518	+	0.427271i	0.895667	−	0.444725i	$-0.146699\pi$
$271$	22.8029	+	7.03377i	1.38518	+	0.427271i	0.489512	+	0.871997i	$0.337175\pi$
$272$	−16.3729	−	24.0147i	−0.992754	−	1.45610i
$273$		0			0
$274$	−4.22559	+	18.5135i	−0.255277	+	1.11844i
$275$	−6.72449	+	7.24727i	−0.405502	+	0.437027i
$276$		0			0
$277$	6.53966	+	2.56663i	0.392930	+	0.154214i	0.553576	−	0.832798i	$-0.313263\pi$
$277$	6.53966	+	2.56663i	0.392930	+	0.154214i	−0.160646	+	0.987012i	$0.551358\pi$
$278$	−34.9791	−	5.27225i	−2.09791	−	0.316209i
$279$		0			0
$280$	0.280892	+	0.583279i	0.0167865	+	0.0348576i
$281$	−1.51801	+	10.0714i	−0.0905571	+	0.600807i	0.896817	+	0.442402i	$0.145873\pi$
$281$	−1.51801	+	10.0714i	−0.0905571	+	0.600807i	−0.987374	+	0.158405i	$0.949365\pi$
$282$		0			0
$283$	1.97720	−	26.3839i	0.117532	−	1.56836i	−0.557253	−	0.830343i	$-0.688145\pi$
$283$	1.97720	−	26.3839i	0.117532	−	1.56836i	0.674785	−	0.738015i	$-0.264236\pi$
$284$	20.5692	+	19.0855i	1.22056	+	1.13251i
$285$		0			0
$286$	0.204366	+	1.35588i	0.0120844	+	0.0801750i
$287$	−7.33711	+	5.00235i	−0.433096	+	0.295280i
$288$		0			0
$289$	−2.23510	−	29.8253i	−0.131476	−	1.75443i
$290$	23.7422	−	29.7717i	1.39419	−	1.74826i
$291$		0			0
$292$	16.2069	−	6.36073i	0.948436	−	0.372234i
$293$	23.0210	−	5.25439i	1.34490	−	0.306965i	0.511333	−	0.859383i	$-0.329152\pi$
$293$	23.0210	−	5.25439i	1.34490	−	0.306965i	0.833567	+	0.552418i	$0.186295\pi$
$294$		0			0
$295$	−0.127210	+	0.0734445i	−0.00740643	+	0.00427610i
$296$	−0.874786	−	0.942796i	−0.0508459	−	0.0547989i
$297$		0			0
$298$	−15.5389	−	10.5943i	−0.900146	−	0.613709i
$299$	0.372447	−	0.773394i	0.0215392	−	0.0447265i
$300$		0			0
$301$	−4.58896	+	2.83895i	−0.264503	+	0.163634i
$302$			32.9614i			1.89671i
$303$		0			0
$304$	2.54116	−	3.72720i	0.145746	−	0.213769i
$305$	−7.69884	+	6.13962i	−0.440835	+	0.351554i
$306$		0			0
$307$	−7.48110	−	12.9576i	−0.426969	−	0.739531i	0.569633	−	0.821899i	$-0.307085\pi$
$307$	−7.48110	−	12.9576i	−0.426969	−	0.739531i	−0.996602	+	0.0823675i	$0.973752\pi$
$308$	−1.72252	+	2.98349i	−0.0981496	+	0.170000i
$309$		0			0
$310$	−2.33104	−	5.93940i	−0.132394	−	0.337335i
$311$	6.38993	+	20.7156i	0.362340	+	1.17468i	0.934929	+	0.354834i	$0.115463\pi$
$311$	6.38993	+	20.7156i	0.362340	+	1.17468i	−0.572589	+	0.819842i	$0.694061\pi$
$312$		0			0
$313$	11.7539	−	0.880831i	0.664368	−	0.0497875i	0.261722	−	0.965143i	$-0.415710\pi$
$313$	11.7539	−	0.880831i	0.664368	−	0.0497875i	0.402646	+	0.915356i	$0.368091\pi$
$314$	5.91614	−	19.1797i	0.333867	−	1.08237i
$315$		0			0
$316$	−5.56398	+	0.838635i	−0.312998	+	0.0471769i
$317$	9.42616	+	2.15146i	0.529426	+	0.120838i	0.478874	−	0.877883i	$-0.341045\pi$
$317$	9.42616	+	2.15146i	0.529426	+	0.120838i	0.0505514	+	0.998721i	$0.483902\pi$
$318$		0			0
$319$	−14.0865	−	1.05564i	−0.788694	−	0.0591045i
$320$	−7.76371	+	19.7816i	−0.434004	+	1.10582i
$321$		0			0
$322$	4.02165	−	1.93672i	0.224118	−	0.107929i
$323$	6.55951	−	3.15889i	0.364981	−	0.175766i
$324$		0			0
$325$	0.502154	−	1.27947i	0.0278545	−	0.0709721i
$326$	14.7048	+	1.10197i	0.814425	+	0.0610327i
$327$		0			0
$328$	2.69740	+	0.615665i	0.148939	+	0.0339944i
$329$	8.28540	−	1.24882i	0.456789	−	0.0688499i
$330$		0			0
$331$	−0.374113	+	1.21284i	−0.0205631	+	0.0666639i	−0.965273	−	0.261244i	$-0.915867\pi$
$331$	−0.374113	+	1.21284i	−0.0205631	+	0.0666639i	0.944710	+	0.327908i	$0.106344\pi$
$332$	−29.3525	+	2.19966i	−1.61093	+	0.120722i
$333$		0			0
$334$	12.7089	+	41.2014i	0.695402	+	2.25444i
$335$	3.18730	+	8.12110i	0.174141	+	0.443703i
$336$		0			0
$337$	−7.38338	+	12.7884i	−0.402198	+	0.696628i	−0.993991	−	0.109462i	$-0.965087\pi$
$337$	−7.38338	+	12.7884i	−0.402198	+	0.696628i	0.591793	+	0.806090i	$0.298420\pi$
$338$	12.6911	+	21.9817i	0.690307	+	1.19565i
$339$		0			0
$340$	−30.7200	+	24.4984i	−1.66602	+	1.32861i
$341$	−1.33333	+	1.95563i	−0.0722037	+	0.105903i
$342$		0			0
$343$			10.9634i			0.591967i
$344$	1.62090	+	0.446468i	0.0873932	+	0.0240720i
$345$		0			0
$346$	14.6209	−	30.3606i	0.786025	−	1.63220i
$347$	−2.15169	−	1.46700i	−0.115509	−	0.0787525i	0.504188	−	0.863594i	$-0.331792\pi$
$347$	−2.15169	−	1.46700i	−0.115509	−	0.0787525i	−0.619697	+	0.784842i	$0.712744\pi$
$348$		0			0
$349$	14.1793	+	15.2816i	0.758999	+	0.818006i	0.987843	−	0.155457i	$-0.0496849\pi$
$349$	14.1793	+	15.2816i	0.758999	+	0.818006i	−0.228844	+	0.973463i	$0.573494\pi$
$350$	6.18974	−	3.57365i	0.330856	−	0.191020i
$351$		0			0
$352$	17.1042	−	3.90393i	0.911658	−	0.208080i
$353$	31.6692	−	12.4293i	1.68558	−	0.661543i	0.687665	−	0.726028i	$-0.258636\pi$
$353$	31.6692	−	12.4293i	1.68558	−	0.661543i	0.997919	+	0.0644856i	$0.0205406\pi$
$354$		0			0
$355$	−28.7122	+	36.0039i	−1.52388	+	1.91089i
$356$	1.57851	+	21.0638i	0.0836610	+	1.11638i
$357$		0			0
$358$	−9.70945	+	6.61979i	−0.513160	+	0.349867i
$359$	−1.81360	−	12.0325i	−0.0957183	−	0.635049i	−0.984323	−	0.176375i	$-0.943563\pi$
$359$	−1.81360	−	12.0325i	−0.0957183	−	0.635049i	0.888605	−	0.458674i	$-0.151675\pi$
$360$		0			0
$361$	−13.0997	−	12.1547i	−0.689456	−	0.639721i
$362$	0.420415	−	5.61005i	0.0220965	−	0.294858i
$363$		0			0
$364$	0.0713842	−	0.473603i	0.00374155	−	0.0248236i
$365$	12.3975	+	25.7437i	0.648916	+	1.34749i
$366$		0			0
$367$	13.5872	+	2.04794i	0.709245	+	0.106901i	0.493750	−	0.869604i	$-0.335626\pi$
$367$	13.5872	+	2.04794i	0.709245	+	0.106901i	0.215494	+	0.976505i	$0.430864\pi$
$368$	−10.8929	−	4.27515i	−0.567832	−	0.222858i
$369$		0			0
$370$	−20.5946	+	22.1957i	−1.07066	+	1.15390i
$371$	−0.772409	+	3.38414i	−0.0401015	+	0.175696i
$372$		0			0
$373$	−8.35905	−	12.2605i	−0.432815	−	0.634824i	0.546429	−	0.837505i	$-0.315987\pi$
$373$	−8.35905	−	12.2605i	−0.432815	−	0.634824i	−0.979245	+	0.202682i	$0.935034\pi$
$374$	28.8277	+	8.89218i	1.49065	+	0.459804i
$375$		0			0
$376$	−2.04107	−	1.62770i	−0.105260	−	0.0839424i
$377$	1.87665	−	0.578869i	0.0966522	−	0.0298133i
$378$		0			0
$379$	−5.48427	−	24.0281i	−0.281708	−	1.23424i	−0.895603	−	0.444855i	$-0.853255\pi$
$379$	−5.48427	−	24.0281i	−0.281708	−	1.23424i	0.613895	−	0.789388i	$-0.289602\pi$
$380$	−5.28134	−	3.04918i	−0.270927	−	0.156420i
$381$		0			0
$382$	−24.4614	+	22.6968i	−1.25155	+	1.16127i
$383$	−13.2367	−	16.5983i	−0.676364	−	0.848134i	0.318650	−	0.947873i	$-0.396771\pi$
$383$	−13.2367	−	16.5983i	−0.676364	−	0.848134i	−0.995014	+	0.0997389i	$0.968199\pi$
$384$		0			0
$385$	−5.09397	−	2.45313i	−0.259613	−	0.125023i
$386$	−51.7152			−2.63224
$387$		0			0
$388$	−13.3885			−0.679700
$389$	27.8284	+	13.4014i	1.41095	+	0.679479i	0.975351	−	0.220660i	$-0.0708210\pi$
$389$	27.8284	+	13.4014i	1.41095	+	0.679479i	0.435603	+	0.900139i	$0.356535\pi$
$390$		0			0
$391$	−11.7752	−	14.7656i	−0.595496	−	0.746728i
$392$	1.18836	−	1.10264i	0.0600213	−	0.0556917i
$393$		0			0
$394$	37.3692	+	21.5751i	1.88263	+	1.08694i
$395$	−2.05488	−	9.00303i	−0.103392	−	0.452992i
$396$		0			0
$397$	−13.5063	+	4.16616i	−0.677864	+	0.209093i	−0.614523	−	0.788899i	$-0.710652\pi$
$397$	−13.5063	+	4.16616i	−0.677864	+	0.209093i	−0.0633407	+	0.997992i	$0.520175\pi$
$398$	22.1106	+	17.6326i	1.10830	+	0.883843i
$399$		0			0
$400$	−17.9046	−	5.52284i	−0.895230	−	0.276142i
$401$	−13.3775	−	19.6212i	−0.668041	−	0.979836i	−0.999341	−	0.0363103i	$-0.988440\pi$
$401$	−13.3775	−	19.6212i	−0.668041	−	0.979836i	0.331300	−	0.943526i	$-0.392513\pi$
$402$		0			0
$403$	0.0732236	−	0.320813i	0.00364753	−	0.0159809i
$404$	6.59936	−	7.11242i	0.328331	−	0.353856i
$405$		0			0
$406$	9.50633	+	3.73096i	0.471791	+	0.185164i
$407$	11.1067	+	1.67407i	0.550539	+	0.0829804i
$408$		0			0
$409$	9.62406	+	19.9846i	0.475879	+	0.988173i	0.991347	+	0.131264i	$0.0419037\pi$
$409$	9.62406	+	19.9846i	0.475879	+	0.988173i	−0.515468	+	0.856909i	$0.672382\pi$
$410$	9.70809	−	64.4090i	0.479448	−	3.18093i
$411$		0			0
$412$	−1.09654	+	14.6323i	−0.0540226	+	0.720881i
$413$	−0.0288772	−	0.0267942i	−0.00142096	−	0.00131845i
$414$		0			0
$415$	−7.19985	−	47.7679i	−0.353427	−	2.34483i
$416$	−2.01528	+	1.37399i	−0.0988071	+	0.0673656i
$417$		0			0
$418$	0.349904	+	4.66914i	0.0171143	+	0.228375i
$419$	−0.367986	+	0.461439i	−0.0179773	+	0.0225428i	−0.790739	−	0.612154i	$-0.790303\pi$
$419$	−0.367986	+	0.461439i	−0.0179773	+	0.0225428i	0.772762	+	0.634696i	$0.218875\pi$
$420$		0			0
$421$	−30.4558	+	11.9530i	−1.48433	+	0.582555i	−0.962689	−	0.270611i	$-0.912774\pi$
$421$	−30.4558	+	11.9530i	−1.48433	+	0.582555i	−0.521638	+	0.853167i	$0.674679\pi$
$422$	45.5092	−	10.3872i	2.21535	−	0.505640i
$423$		0			0
$424$	0.936615	−	0.540755i	0.0454860	−	0.0262614i
$425$	−20.5686	−	22.1677i	−0.997723	−	1.07529i
$426$		0			0
$427$	−2.18197	−	1.48764i	−0.105593	−	0.0719922i
$428$	−5.19398	+	10.7854i	−0.251061	+	0.521333i
$429$		0			0
$430$	7.62985	−	38.8387i	0.367944	−	1.87297i
$431$			38.1626i			1.83823i	0.393990	+	0.919115i	$0.371095\pi$
$431$			38.1626i			1.83823i	−0.393990	+	0.919115i	$0.628905\pi$
$432$		0			0
$433$	18.0819	−	26.5213i	0.868960	−	1.27453i	−0.0914125	−	0.995813i	$-0.529138\pi$
$433$	18.0819	−	26.5213i	0.868960	−	1.27453i	0.960373	−	0.278718i	$-0.0899094\pi$
$434$	1.33782	−	1.06687i	0.0642173	−	0.0512116i
$435$		0			0
$436$	9.63812	+	16.6937i	0.461582	+	0.799484i
$437$	1.46559	−	2.53848i	0.0701089	−	0.121432i
$438$		0			0
$439$	3.80755	+	9.70147i	0.181724	+	0.463026i	0.992487	−	0.122349i	$-0.0390426\pi$
$439$	3.80755	+	9.70147i	0.181724	+	0.463026i	−0.810763	+	0.585375i	$0.800947\pi$
$440$	0.519233	+	1.68331i	0.0247535	+	0.0802488i
$441$		0			0
$442$	−4.18244	+	0.313430i	−0.198938	+	0.0149084i
$443$	−4.27420	+	13.8566i	−0.203073	+	0.658347i	0.795550	+	0.605888i	$0.207182\pi$
$443$	−4.27420	+	13.8566i	−0.203073	+	0.658347i	−0.998623	+	0.0524590i	$0.983294\pi$
$444$		0			0
$445$	−34.2789	+	5.16672i	−1.62498	+	0.244926i
$446$	32.0625	+	7.31805i	1.51820	+	0.346520i
$447$		0			0
$448$	−5.68311	−	0.425890i	−0.268502	−	0.0201214i
$449$	−1.10101	+	2.80533i	−0.0519598	+	0.132392i	−0.954497	−	0.298220i	$-0.903607\pi$
$449$	−1.10101	+	2.80533i	−0.0519598	+	0.132392i	0.902537	+	0.430612i	$0.141702\pi$
$450$		0			0
$451$	−21.7703	+	10.4840i	−1.02512	+	0.493672i
$452$	10.2894	−	4.95513i	0.483974	−	0.233070i
$453$		0			0
$454$	2.94101	−	7.49357i	0.138029	−	0.351691i
$455$	0.783844	+	0.0587410i	0.0367472	+	0.00275382i
$456$		0			0
$457$	−17.2646	−	3.94053i	−0.807604	−	0.184330i	−0.201265	−	0.979537i	$-0.564505\pi$
$457$	−17.2646	−	3.94053i	−0.807604	−	0.184330i	−0.606339	+	0.795206i	$0.707362\pi$
$458$	−29.8934	+	4.50570i	−1.39683	+	0.210538i
$459$		0			0
$460$	−4.66285	+	15.1166i	−0.217406	+	0.704814i
$461$	16.4608	−	1.23357i	0.766657	−	0.0574530i	0.314340	−	0.949310i	$-0.398217\pi$
$461$	16.4608	−	1.23357i	0.766657	−	0.0574530i	0.452317	+	0.891857i	$0.350598\pi$
$462$		0			0
$463$	−3.59347	−	11.6497i	−0.167003	−	0.541409i	0.832926	−	0.553385i	$-0.186664\pi$
$463$	−3.59347	−	11.6497i	−0.167003	−	0.541409i	−0.999928	+	0.0119757i	$0.996188\pi$
$464$	−9.78091	−	24.9214i	−0.454067	−	1.15694i
$465$		0			0
$466$	23.3048	−	40.3651i	1.07957	−	1.86988i
$467$	−12.8067	−	22.1819i	−0.592625	−	1.02646i	−0.993877	−	0.110490i	$-0.964758\pi$
$467$	−12.8067	−	22.1819i	−0.592625	−	1.02646i	0.401252	−	0.915968i	$-0.368575\pi$
$468$		0			0
$469$	−1.82923	+	1.45876i	−0.0844661	+	0.0673595i
$470$	−34.6220	+	50.7811i	−1.59699	+	2.34236i
$471$		0			0
$472$			0.0122737i			0.000564942i
$473$	−13.4986	+	5.77756i	−0.620666	+	0.265653i
$474$		0			0
$475$	2.03641	−	4.22864i	0.0934368	−	0.194023i
$476$	−8.70652	−	5.93601i	−0.399063	−	0.272076i
$477$		0			0
$478$	15.3864	+	16.5826i	0.703759	+	0.758472i
$479$	17.1673	−	9.91154i	0.784394	−	0.452870i	−0.0535914	−	0.998563i	$-0.517067\pi$
$479$	17.1673	−	9.91154i	0.784394	−	0.452870i	0.837985	+	0.545693i	$0.183734\pi$
$480$		0			0
$481$	−1.52242	+	0.347482i	−0.0694163	+	0.0158438i
$482$	2.16744	−	0.850659i	0.0987243	−	0.0387464i
$483$		0			0
$484$	6.97824	−	8.75043i	0.317193	−	0.397747i
$485$	−1.64203	−	21.9114i	−0.0745608	−	0.994945i
$486$		0			0
$487$	12.8825	−	8.78314i	0.583762	−	0.398002i	−0.235118	−	0.971967i	$-0.575548\pi$
$487$	12.8825	−	8.78314i	0.583762	−	0.398002i	0.818880	+	0.573965i	$0.194595\pi$
$488$	0.122633	+	0.813617i	0.00555134	+	0.0368307i
$489$		0			0
$490$	−27.9769	−	25.9588i	−1.26387	−	1.17270i
$491$	−1.95932	+	26.1454i	−0.0884230	+	1.17992i	0.759754	+	0.650211i	$0.225319\pi$
$491$	−1.95932	+	26.1454i	−0.0884230	+	1.17992i	−0.848177	+	0.529713i	$0.822300\pi$
$492$		0			0
$493$	6.43984	−	42.7255i	0.290036	−	1.92426i
$494$	−0.282439	−	0.586491i	−0.0127075	−	0.0263875i
$495$		0			0
$496$	−4.43572	−	0.668577i	−0.199170	−	0.0300200i
$497$	−11.4963	−	4.51197i	−0.515680	−	0.202390i
$498$		0			0
$499$	−2.39166	+	2.57759i	−0.107065	+	0.115389i	−0.784311	−	0.620368i	$-0.786983\pi$
$499$	−2.39166	+	2.57759i	−0.107065	+	0.115389i	0.677245	+	0.735757i	$0.263174\pi$
$500$	0.746457	−	3.27044i	0.0333826	−	0.146259i
$501$		0			0
$502$	−5.72343	−	8.39474i	−0.255449	−	0.374675i
$503$	12.2490	+	3.77833i	0.546158	+	0.168467i	0.555542	−	0.831489i	$-0.312511\pi$
$503$	12.2490	+	3.77833i	0.546158	+	0.168467i	−0.00938414	+	0.999956i	$0.502987\pi$
$504$		0			0
$505$	12.4494	+	9.92808i	0.553992	+	0.441794i
$506$	11.6063	−	3.58006i	0.515962	−	0.159153i
$507$		0			0
$508$	−2.64232	−	11.5768i	−0.117234	−	0.513636i
$509$	−0.438616	−	0.253235i	−0.0194413	−	0.0112244i	0.490248	−	0.871583i	$-0.336906\pi$
$509$	−0.438616	−	0.253235i	−0.0194413	−	0.0112244i	−0.509689	+	0.860359i	$0.670240\pi$
$510$		0			0
$511$	−5.61730	+	5.21210i	−0.248495	+	0.230570i
$512$	19.3743	+	24.2946i	0.856229	+	1.07368i
$513$		0			0
$514$	7.39489	+	3.56119i	0.326175	+	0.157077i
$515$	−24.0814			−1.06115
$516$		0			0
$517$	22.7995			1.00272
$518$	−7.31602	−	3.52321i	−0.321448	−	0.154801i
$519$		0			0
$520$	−0.152697	−	0.191475i	−0.00669619	−	0.00839675i
$521$	3.48915	−	3.23746i	0.152863	−	0.141836i	−0.600034	−	0.799974i	$-0.704846\pi$
$521$	3.48915	−	3.23746i	0.152863	−	0.141836i	0.752897	+	0.658139i	$0.228656\pi$
$522$		0			0
$523$	36.7862	+	21.2385i	1.60855	+	0.928697i	0.989695	+	0.143191i	$0.0457364\pi$
$523$	36.7862	+	21.2385i	1.60855	+	0.928697i	0.618855	+	0.785505i	$0.287597\pi$
$524$	−8.96489	−	39.2778i	−0.391633	−	1.71586i
$525$		0			0
$526$	50.9468	−	15.7150i	2.22139	−	0.685207i
$527$	−5.66030	−	4.51394i	−0.246567	−	0.196630i
$528$		0			0
$529$	14.7124	+	4.53817i	0.639668	+	0.197312i
$530$	−14.3429	−	21.0371i	−0.623015	−	0.913795i
$531$		0			0
$532$	0.363929	−	1.59448i	0.0157783	−	0.0691293i
$533$	2.28492	−	2.46256i	0.0989710	−	0.106665i
$534$		0			0
$535$	−18.2882	−	7.17759i	−0.790668	−	0.310314i
$536$	0.720828	+	0.108647i	0.0311350	+	0.00469285i
$537$		0			0
$538$	3.78637	+	7.86247i	0.163242	+	0.338975i
$539$	−2.11010	+	13.9996i	−0.0908886	+	0.603006i
$540$		0			0
$541$	−2.08004	+	27.7562i	−0.0894279	+	1.19333i	0.754288	+	0.656543i	$0.227982\pi$
$541$	−2.08004	+	27.7562i	−0.0894279	+	1.19333i	−0.843716	+	0.536790i	$0.819637\pi$
$542$	−34.4111	−	31.9288i	−1.47808	−	1.37146i
$543$		0			0
$544$	7.99808	+	53.0638i	0.342915	+	2.27509i
$545$	−26.1385	+	17.8209i	−1.11965	+	0.763365i
$546$		0			0
$547$	−0.556637	−	7.42781i	−0.0238001	−	0.317590i	−0.996379	−	0.0850185i	$-0.972905\pi$
$547$	−0.556637	−	7.42781i	−0.0238001	−	0.317590i	0.972579	−	0.232572i	$-0.0747140\pi$
$548$	11.2531	−	14.1110i	0.480709	−	0.602790i
$549$		0			0
$550$	18.1037	−	7.10518i	0.771944	−	0.302966i
$551$	6.53799	−	1.49225i	0.278528	−	0.0635721i
$552$		0			0
$553$	2.14476	−	1.23828i	0.0912044	−	0.0526569i
$554$	−9.39983	−	10.1306i	−0.399361	−	0.430408i
$555$		0			0
$556$	27.7792	+	18.9395i	1.17810	+	0.803215i
$557$	3.41113	−	7.08328i	0.144534	−	0.300128i	−0.816117	−	0.577887i	$-0.803877\pi$
$557$	3.41113	−	7.08328i	0.144534	−	0.300128i	0.960651	+	0.277759i	$0.0895917\pi$
$558$		0			0
$559$	1.45349	−	1.43334i	0.0614759	−	0.0606236i
$560$		−	10.7154i		−	0.452807i
$561$		0			0
$562$	11.2865	−	16.5542i	0.476091	−	0.698297i
$563$	−6.98838	+	5.57305i	−0.294525	+	0.234876i	−0.759592	−	0.650399i	$-0.774602\pi$
$563$	−6.98838	+	5.57305i	−0.294525	+	0.234876i	0.465067	+	0.885275i	$0.346030\pi$
$564$		0			0
$565$	9.37140	+	16.2317i	0.394258	+	0.682874i
$566$	−26.0232	+	45.0735i	−1.09384	+	1.89458i
$567$		0			0
$568$	1.40579	+	3.58190i	0.0589857	+	0.150293i
$569$	−9.20193	−	29.8319i	−0.385765	−	1.25062i	−0.915452	−	0.402427i	$-0.868167\pi$
$569$	−9.20193	−	29.8319i	−0.385765	−	1.25062i	0.529687	−	0.848193i	$-0.322309\pi$
$570$		0			0
$571$	10.6133	−	0.795357i	0.444153	−	0.0332847i	0.149223	−	0.988804i	$-0.452323\pi$
$571$	10.6133	−	0.795357i	0.444153	−	0.0332847i	0.294930	+	0.955519i	$0.404704\pi$
$572$	0.384139	−	1.24535i	0.0160617	−	0.0520706i
$573$		0			0
$574$	17.2734	−	2.60355i	0.720978	−	0.108670i
$575$	−11.8697	−	2.70918i	−0.495001	−	0.112981i
$576$		0			0
$577$	−1.00892	−	0.0756081i	−0.0420019	−	0.00314760i	0.0537126	−	0.998556i	$-0.482895\pi$
$577$	−1.00892	−	0.0756081i	−0.0420019	−	0.00314760i	−0.0957145	+	0.995409i	$0.530514\pi$
$578$	−21.4949	+	54.7682i	−0.894071	+	2.27806i
$579$		0			0
$580$	−32.6082	+	15.7033i	−1.35398	+	0.652044i
$581$	11.6723	−	5.62107i	0.484247	−	0.233201i
$582$		0			0
$583$	−3.45072	+	8.79228i	−0.142914	+	0.364139i
$584$	2.38085	+	0.178420i	0.0985201	+	0.00738306i
$585$		0			0
$586$	−45.2856	−	10.3361i	−1.87073	−	0.426982i
$587$	18.8346	−	2.83886i	0.777388	−	0.117172i	0.251649	−	0.967819i	$-0.419027\pi$
$587$	18.8346	−	2.83886i	0.777388	−	0.117172i	0.525738	+	0.850646i	$0.323789\pi$
$588$		0			0
$589$	0.331203	−	1.07373i	0.0136470	−	0.0442424i
$590$	0.288144	−	0.0215934i	0.0118627	−	0.000888987i
$591$		0			0
$592$	6.27459	+	20.3417i	0.257884	+	0.836039i
$593$	−1.26040	−	3.21143i	−0.0517582	−	0.131878i	0.902656	−	0.430362i	$-0.141614\pi$
$593$	−1.26040	−	3.21143i	−0.0517582	−	0.131878i	−0.954415	+	0.298484i	$0.903519\pi$
$594$		0			0
$595$	8.64694	−	14.9769i	0.354490	−	0.613994i
$596$	8.93743	+	15.4801i	0.366091	+	0.634089i
$597$		0			0
$598$	−1.32020	+	1.05283i	−0.0539871	+	0.0430533i
$599$	14.4323	−	21.1683i	0.589688	−	0.864913i	−0.409182	−	0.912453i	$-0.634186\pi$
$599$	14.4323	−	21.1683i	0.589688	−	0.864913i	0.998869	+	0.0475401i	$0.0151382\pi$
$600$		0			0
$601$			17.4160i			0.710414i	0.934788	+	0.355207i	$0.115590\pi$
$601$			17.4160i			0.710414i	−0.934788	+	0.355207i	$0.884410\pi$
$602$	10.5563	−	1.11485i	0.430241	−	0.0454377i
$603$		0			0
$604$	13.5927	−	28.2255i	0.553079	−	1.14848i
$605$	15.1766	+	10.3472i	0.617017	+	0.420675i
$606$		0			0
$607$	24.3922	+	26.2885i	0.990047	+	1.06702i	0.997750	+	0.0670467i	$0.0213576\pi$
$607$	24.3922	+	26.2885i	0.990047	+	1.06702i	−0.00770272	+	0.999970i	$0.502452\pi$
$608$	−7.21295	+	4.16440i	−0.292524	+	0.168889i
$609$		0			0
$610$	18.8852	−	4.31042i	0.764639	−	0.174524i
$611$	−2.95063	+	1.15804i	−0.119370	+	0.0468492i
$612$		0			0
$613$	−18.7761	+	23.5444i	−0.758358	+	0.950951i	−0.999811	−	0.0194619i	$-0.993805\pi$
$613$	−18.7761	+	23.5444i	−0.758358	+	0.950951i	0.241453	+	0.970413i	$0.422376\pi$
$614$	2.19952	+	29.3505i	0.0887653	+	1.18449i
$615$		0			0
$616$	−0.390336	+	0.266126i	−0.0157271	+	0.0107225i
$617$	−3.66659	−	24.3262i	−0.147611	−	0.979338i	−0.932881	−	0.360184i	$-0.882714\pi$
$617$	−3.66659	−	24.3262i	−0.147611	−	0.979338i	0.785270	−	0.619154i	$-0.212524\pi$
$618$		0			0
$619$	19.6993	+	18.2783i	0.791783	+	0.734667i	0.968343	−	0.249623i	$-0.0803065\pi$
$619$	19.6993	+	18.2783i	0.791783	+	0.734667i	−0.176560	+	0.984290i	$0.556497\pi$
$620$	−0.453184	+	6.04732i	−0.0182003	+	0.242866i
$621$		0			0
$622$	6.35595	−	42.1690i	0.254851	−	1.69082i
$623$	−4.03376	−	8.37619i	−0.161609	−	0.335585i
$624$		0			0
$625$	27.2737	+	4.11084i	1.09095	+	0.164434i
$626$	−21.5836	−	8.47095i	−0.862655	−	0.338567i
$627$		0			0
$628$	−12.9755	+	13.9842i	−0.517778	+	0.558032i
$629$	−7.64503	+	33.4951i	−0.304827	+	1.33554i
$630$		0			0
$631$	−2.35935	−	3.46053i	−0.0939242	−	0.137761i	0.776401	−	0.630240i	$-0.217043\pi$
$631$	−2.35935	−	3.46053i	−0.0939242	−	0.137761i	−0.870325	+	0.492478i	$0.836091\pi$
$632$	−0.737337	−	0.227438i	−0.0293297	−	0.00904701i
$633$		0			0
$634$	−14.8700	−	11.8585i	−0.590564	−	0.470959i
$635$	18.6222	−	5.74419i	0.739000	−	0.227951i
$636$		0			0
$637$	−0.437989	−	1.91896i	−0.0173538	−	0.0760319i
$638$	24.0651	+	13.8940i	0.952746	+	0.550068i
$639$		0			0
$640$	−4.60384	+	4.27174i	−0.181983	+	0.168855i
$641$	12.7758	+	16.0203i	0.504612	+	0.632764i	0.967263	−	0.253777i	$-0.0816730\pi$
$641$	12.7758	+	16.0203i	0.504612	+	0.632764i	−0.462651	+	0.886541i	$0.653102\pi$
$642$		0			0
$643$	12.0920	+	5.82320i	0.476862	+	0.229644i	0.656846	−	0.754025i	$-0.271890\pi$
$643$	12.0920	+	5.82320i	0.476862	+	0.229644i	−0.179984	+	0.983670i	$0.557605\pi$
$644$	−4.24250			−0.167178
$645$		0			0
$646$	−14.3218			−0.563484
$647$	−12.5771	−	6.05682i	−0.494457	−	0.238118i	0.170000	−	0.985444i	$-0.445623\pi$
$647$	−12.5771	−	6.05682i	−0.494457	−	0.238118i	−0.664458	+	0.747326i	$0.731337\pi$
$648$		0			0
$649$	−0.0668320	−	0.0838047i	−0.00262339	−	0.00328962i
$650$	−1.98203	+	1.83905i	−0.0777416	+	0.0721336i
$651$		0			0
$652$	−12.1376	−	7.00766i	−0.475346	−	0.274441i
$653$	−1.58174	−	6.93005i	−0.0618982	−	0.271194i	0.934503	−	0.355955i	$-0.115844\pi$
$653$	−1.58174	−	6.93005i	−0.0618982	−	0.271194i	−0.996401	+	0.0847612i	$0.972987\pi$
$654$		0			0
$655$	63.1816	−	19.4890i	2.46871	−	0.761497i
$656$	−35.8037	−	28.5525i	−1.39790	−	1.11479i
$657$		0			0
$658$	−15.7504	−	4.85836i	−0.614015	−	0.189399i
$659$	−12.0038	−	17.6064i	−0.467603	−	0.685847i	0.517913	−	0.855433i	$-0.326709\pi$
$659$	−12.0038	−	17.6064i	−0.467603	−	0.685847i	−0.985515	+	0.169586i	$0.945757\pi$
$660$		0			0
$661$	2.80070	−	12.2706i	0.108934	−	0.477273i	−0.890804	−	0.454388i	$-0.849858\pi$
$661$	2.80070	−	12.2706i	0.108934	−	0.477273i	0.999738	−	0.0228845i	$-0.00728500\pi$
$662$	1.69823	−	1.83026i	0.0660036	−	0.0711350i
$663$		0			0
$664$	−3.75743	−	1.47468i	−0.145816	−	0.0572287i
$665$	2.65412	+	0.400044i	0.102922	+	0.0155130i
$666$		0			0
$667$	−7.54781	−	15.6732i	−0.292252	−	0.606868i
$668$	6.10779	−	40.5226i	0.236318	−	1.56786i
$669$		0			0
$670$	1.28250	−	17.1137i	0.0495472	−	0.661161i
$671$	−5.26760	−	4.88762i	−0.203354	−	0.188685i
$672$		0			0
$673$	−0.430482	−	2.85606i	−0.0165939	−	0.110093i	0.979001	−	0.203858i	$-0.0653480\pi$
$673$	−0.430482	−	2.85606i	−0.0165939	−	0.110093i	−0.995594	+	0.0937646i	$0.970110\pi$
$674$	24.0009	−	16.3635i	0.924480	−	0.630300i
$675$		0			0
$676$	−1.80282	−	24.0570i	−0.0693393	−	0.925269i
$677$	9.08406	−	11.3911i	0.349129	−	0.437794i	−0.575998	−	0.817451i	$-0.695387\pi$
$677$	9.08406	−	11.3911i	0.349129	−	0.437794i	0.925127	+	0.379657i	$0.123958\pi$
$678$		0			0
$679$	5.48540	−	2.15286i	0.210510	−	0.0826192i
$680$	−5.25314	+	1.19899i	−0.201449	+	0.0459794i
$681$		0			0
$682$	4.03226	−	2.32803i	0.154403	−	0.0891448i
$683$	14.0177	+	15.1075i	0.536374	+	0.578074i	0.941851	−	0.336032i	$-0.109085\pi$
$683$	14.0177	+	15.1075i	0.536374	+	0.578074i	−0.405477	+	0.914105i	$0.632894\pi$
$684$		0			0
$685$	24.4738	+	16.6860i	0.935097	+	0.637538i
$686$	9.35739	−	19.4308i	0.357267	−	0.741872i
$687$		0			0
$688$	−20.9654	−	18.2984i	−0.799298	−	0.697622i
$689$		−	1.31313i		−	0.0500265i
$690$		0			0
$691$	−19.7977	+	29.0379i	−0.753141	+	1.10466i	0.237925	+	0.971284i	$0.423533\pi$
$691$	−19.7977	+	29.0379i	−0.753141	+	1.10466i	−0.991066	+	0.133372i	$0.957420\pi$
$692$	−25.0404	+	19.9690i	−0.951892	+	0.759109i
$693$		0			0
$694$	2.56142	+	4.43651i	0.0972301	+	0.168408i
$695$	−27.5891	+	47.7856i	−1.04651	+	1.81261i
$696$		0			0
$697$	−27.0021	−	68.8002i	−1.02278	−	2.60599i
$698$	−12.0874	−	39.1864i	−0.457515	−	1.48323i
$699$		0			0
$700$	−6.77412	+	0.507650i	−0.256038	+	0.0191874i
$701$	0.286844	−	0.929926i	0.0108340	−	0.0351228i	−0.949994	−	0.312267i	$-0.898912\pi$
$701$	0.286844	−	0.929926i	0.0108340	−	0.0351228i	0.960828	+	0.277144i	$0.0893879\pi$
$702$		0			0
$703$	−5.27274	+	0.794738i	−0.198865	+	0.0299741i
$704$	−15.1185	−	3.45070i	−0.569800	−	0.130053i
$705$		0			0
$706$	−66.7371	−	5.00125i	−2.51168	−	0.188225i
$707$	−1.56015	+	3.97519i	−0.0586754	+	0.149503i
$708$		0			0
$709$	18.1080	−	8.72037i	0.680061	−	0.327500i	−0.0617666	−	0.998091i	$-0.519673\pi$
$709$	18.1080	−	8.72037i	0.680061	−	0.327500i	0.741828	+	0.670590i	$0.233959\pi$
$710$	81.6174	−	39.3049i	3.06305	−	1.47509i
$711$		0			0
$712$	−1.05825	+	2.69639i	−0.0396597	+	0.101051i
$713$	−2.90665	−	0.217823i	−0.108855	−	0.00815755i
$714$		0			0
$715$	2.08522	+	0.475939i	0.0779829	+	0.0177991i
$716$	11.0443	−	1.66466i	0.412744	−	0.0622112i
$717$		0			0
$718$	−7.05555	+	22.8735i	−0.263311	+	0.853632i
$719$	−26.0818	+	1.95456i	−0.972686	+	0.0728927i	−0.551583	−	0.834120i	$-0.685976\pi$
$719$	−26.0818	+	1.95456i	−0.972686	+	0.0728927i	−0.421103	+	0.907013i	$0.638357\pi$
$720$		0			0
$721$	−1.90359	−	6.17130i	−0.0708936	−	0.229831i
$722$	12.8428	+	32.7230i	0.477960	+	1.21782i
$723$		0			0
$724$	−2.67350	+	4.63064i	−0.0993598	+	0.172096i
$725$	−13.9272	−	24.1227i	−0.517245	−	0.895894i
$726$		0			0
$727$	21.2433	−	16.9410i	0.787870	−	0.628305i	−0.144626	−	0.989486i	$-0.546198\pi$
$727$	21.2433	−	16.9410i	0.787870	−	0.628305i	0.932496	+	0.361181i	$0.117626\pi$
$728$	0.0369987	−	0.0542671i	0.00137126	−	0.00201127i
$729$		0			0
$730$		−	56.2080i		−	2.08035i
$731$	−14.5372	−	42.4942i	−0.537679	−	1.57170i
$732$		0			0
$733$	−1.13551	+	2.35790i	−0.0419409	+	0.0870911i	−0.920886	−	0.389831i	$-0.872533\pi$
$733$	−1.13551	+	2.35790i	−0.0419409	+	0.0870911i	0.878946	+	0.476922i	$0.158248\pi$
$734$	−22.3331	−	15.2265i	−0.824330	−	0.562019i
$735$		0			0
$736$	14.6953	+	15.8377i	0.541675	+	0.583786i
$737$	−5.51342	+	3.18317i	−0.203089	+	0.117254i
$738$		0			0
$739$	−48.2687	+	11.0170i	−1.77559	+	0.405267i	−0.979748	−	0.200234i	$-0.935830\pi$
$739$	−48.2687	+	11.0170i	−1.77559	+	0.405267i	−0.795844	+	0.605501i	$0.792973\pi$
$740$	26.7887	−	10.5138i	0.984771	−	0.386494i
$741$		0			0
$742$	4.25738	−	5.33858i	0.156293	−	0.195986i
$743$	1.45109	+	19.3634i	0.0532353	+	0.710376i	0.958421	+	0.285359i	$0.0921128\pi$
$743$	1.45109	+	19.3634i	0.0532353	+	0.710376i	−0.905185	+	0.425017i	$0.860268\pi$
$744$		0			0
$745$	−24.2382	+	16.5253i	−0.888020	+	0.605442i
$746$	4.35059	+	28.8643i	0.159286	+	1.05680i
$747$		0			0
$748$	−21.0188	−	19.5026i	−0.768524	−	0.713086i
$749$	0.393738	−	5.25407i	0.0143869	−	0.191979i
$750$		0			0
$751$	−2.87545	+	19.0774i	−0.104927	+	0.696142i	0.873081	+	0.487575i	$0.162118\pi$
$751$	−2.87545	+	19.0774i	−0.104927	+	0.696142i	−0.978008	+	0.208568i	$0.933120\pi$
$752$	18.7482	+	38.9311i	0.683677	+	1.41967i
$753$		0			0
$754$	−3.82012	−	0.575791i	−0.139121	−	0.0209691i
$755$	47.8604	+	18.7838i	1.74182	+	0.683613i
$756$		0			0
$757$	−12.8863	+	13.8882i	−0.468362	+	0.504774i	−0.922415	−	0.386200i	$-0.873787\pi$
$757$	−12.8863	+	13.8882i	−0.468362	+	0.504774i	0.454053	+	0.890975i	$0.349978\pi$
$758$	−10.7884	+	47.2669i	−0.391851	+	1.71681i
$759$		0			0
$760$	−0.471094	−	0.690968i	−0.0170884	−	0.0250640i
$761$	0.863483	+	0.266349i	0.0313013	+	0.00965516i	0.310366	−	0.950617i	$-0.399548\pi$
$761$	0.863483	+	0.266349i	0.0313013	+	0.00965516i	−0.279065	+	0.960272i	$0.590024\pi$
$762$		0			0
$763$	−6.63315	−	5.28976i	−0.240136	−	0.191502i
$764$	30.3065	−	9.34833i	1.09645	−	0.338211i
$765$		0			0
$766$	9.29304	+	40.7155i	0.335771	+	1.47111i
$767$	0.0129058	+	0.00745116i	0.000466001	+	0.000269046i
$768$		0			0
$769$	−17.3142	+	16.0653i	−0.624367	+	0.579328i	−0.927594	−	0.373590i	$-0.878127\pi$
$769$	−17.3142	+	16.0653i	−0.624367	+	0.579328i	0.303226	+	0.952919i	$0.401936\pi$
$770$	6.93446	+	8.69554i	0.249901	+	0.313366i
$771$		0			0
$772$	44.2848	+	21.3265i	1.59385	+	0.767556i
$773$	−8.97914			−0.322957			−0.161479	−	0.986876i	$-0.551626\pi$
$773$	−8.97914			−0.322957			−0.161479	+	0.986876i	$0.551626\pi$
$774$		0			0
$775$	−4.66720			−0.167651
$776$	−1.65418	−	0.796609i	−0.0593814	−	0.0285966i
$777$		0			0
$778$	−37.8829	−	47.5037i	−1.35817	−	1.70309i
$779$	8.40891	−	7.80233i	0.301280	−	0.279547i
$780$		0			0
$781$	−29.1027	−	16.8024i	−1.04138	−	0.601239i
$782$	8.26695	+	36.2199i	0.295625	+	1.29522i
$783$		0			0
$784$	−25.6400	+	7.90890i	−0.915716	+	0.282461i
$785$	−24.4777	−	19.5203i	−0.873646	−	0.696709i
$786$		0			0
$787$	2.29444	+	0.707742i	0.0817880	+	0.0252283i	0.335379	−	0.942083i	$-0.391136\pi$
$787$	2.29444	+	0.707742i	0.0817880	+	0.0252283i	−0.253591	+	0.967311i	$0.581612\pi$
$788$	−23.1028	−	33.8856i	−0.823004	−	1.20712i
$789$		0			0
$790$	−4.04226	+	17.7103i	−0.143817	+	0.630103i
$791$	−3.41889	+	3.68469i	−0.121562	+	0.131012i
$792$		0			0
$793$	0.929968	+	0.364985i	0.0330241	+	0.0129610i
$794$	27.4937	+	4.14400i	0.975714	+	0.147065i
$795$		0			0
$796$	−11.6624	−	24.2172i	−0.413362	−	0.858356i
$797$	−4.15539	+	27.5692i	−0.147192	+	0.976552i	0.786272	+	0.617880i	$0.212008\pi$
$797$	−4.15539	+	27.5692i	−0.147192	+	0.976552i	−0.933464	+	0.358672i	$0.883230\pi$
$798$		0			0
$799$	−5.21155	+	69.5433i	−0.184371	+	2.46026i
$800$	25.3595	+	23.5302i	0.896593	+	0.831917i
$801$		0			0
$802$	6.96251	+	46.1933i	0.245855	+	1.63114i
$803$	−17.2279	+	11.7458i	−0.607961	+	0.414500i
$804$		0			0
$805$	−0.520319	−	6.94318i	−0.0183388	−	0.244715i
$806$	−0.403595	+	0.506092i	−0.0142160	+	0.0178263i
$807$		0			0
$808$	1.23855	−	0.486094i	0.0435719	−	0.0171007i
$809$	15.8010	−	3.60647i	0.555532	−	0.126797i	0.0644677	−	0.997920i	$-0.479465\pi$
$809$	15.8010	−	3.60647i	0.555532	−	0.126797i	0.491065	+	0.871123i	$0.336608\pi$
$810$		0			0
$811$	18.2267	−	10.5232i	0.640025	−	0.369519i	−0.144599	−	0.989490i	$-0.546189\pi$
$811$	18.2267	−	10.5232i	0.640025	−	0.369519i	0.784624	+	0.619972i	$0.212856\pi$
$812$	−6.60189	−	7.11515i	−0.231681	−	0.249693i
$813$		0			0
$814$	−18.2560	−	12.4467i	−0.639872	−	0.436257i
$815$	9.97997	−	20.7236i	0.349583	−	0.725917i
$816$		0			0
$817$	5.31510	−	4.50982i	0.185952	−	0.157779i
$818$		−	43.6336i		−	1.52561i
$819$		0			0
$820$	−34.8744	+	51.1513i	−1.21787	+	1.78628i
$821$	18.4456	−	14.7099i	0.643757	−	0.513379i	−0.246320	−	0.969188i	$-0.579222\pi$
$821$	18.4456	−	14.7099i	0.643757	−	0.513379i	0.890077	+	0.455809i	$0.150650\pi$
$822$		0			0
$823$	10.3171	+	17.8697i	0.359630	+	0.622898i	0.987899	−	0.155098i	$-0.0495694\pi$
$823$	10.3171	+	17.8697i	0.359630	+	0.622898i	−0.628269	+	0.777997i	$0.716236\pi$
$824$	−1.00609	+	1.74260i	−0.0350488	+	0.0607064i
$825$		0			0
$826$	0.0283110	+	0.0721354i	0.000985067	+	0.00250991i
$827$	−14.5153	−	47.0576i	−0.504748	−	1.63635i	−0.746041	−	0.665900i	$-0.768048\pi$
$827$	−14.5153	−	47.0576i	−0.504748	−	1.63635i	0.241293	−	0.970452i	$-0.422428\pi$
$828$		0			0
$829$	−8.95721	+	0.671250i	−0.311097	+	0.0233135i	−0.229364	−	0.973341i	$-0.573665\pi$
$829$	−8.95721	+	0.671250i	−0.311097	+	0.0233135i	−0.0817330	+	0.996654i	$0.526045\pi$
$830$	−28.0099	+	90.8059i	−0.972239	+	3.15192i
$831$		0			0
$832$	2.13185	−	0.321325i	0.0739087	−	0.0111399i
$833$	−42.2194	−	9.63630i	−1.46282	−	0.333878i
$834$		0			0
$835$	67.0674	+	5.02601i	2.32096	+	0.173932i
$836$	1.62584	−	4.14258i	0.0562309	−	0.143274i
$837$		0			0
$838$	1.04604	−	0.503746i	0.0361348	−	0.0174016i
$839$	30.9761	−	14.9173i	1.06941	−	0.515002i	0.185495	−	0.982645i	$-0.440611\pi$
$839$	30.9761	−	14.9173i	1.06941	−	0.515002i	0.883917	+	0.467643i	$0.154897\pi$
$840$		0			0
$841$	3.94542	−	10.0528i	0.136049	−	0.346647i
$842$	64.1801	+	4.80963i	2.21179	+	0.165751i
$843$		0			0
$844$	−43.2540	−	9.87244i	−1.48886	−	0.339823i
$845$	39.1500	−	5.90092i	1.34680	−	0.202998i
$846$		0			0
$847$	−1.45199	+	4.70722i	−0.0498908	+	0.161742i
$848$	−17.8507	+	1.33773i	−0.612996	+	0.0459377i
$849$		0			0
$850$	17.5341	+	56.8441i	0.601414	+	1.94974i
$851$	5.05346	+	12.8760i	0.173230	+	0.441384i
$852$		0			0
$853$	−27.1774	+	47.0726i	−0.930535	+	1.61173i	−0.148127	+	0.988968i	$0.547324\pi$
$853$	−27.1774	+	47.0726i	−0.930535	+	1.61173i	−0.782408	+	0.622766i	$0.786009\pi$
$854$	2.59747	+	4.49895i	0.0888836	+	0.153951i
$855$		0			0
$856$	−1.28345	+	1.02352i	−0.0438674	+	0.0349831i
$857$	11.2570	−	16.5110i	0.384532	−	0.564005i	−0.584358	−	0.811496i	$-0.698654\pi$
$857$	11.2570	−	16.5110i	0.384532	−	0.564005i	0.968890	+	0.247491i	$0.0796060\pi$
$858$		0			0
$859$			23.9608i			0.817533i	0.912639	+	0.408767i	$0.134041\pi$
$859$			23.9608i			0.817533i	−0.912639	+	0.408767i	$0.865959\pi$
$860$	−22.5500	+	30.1120i	−0.768949	+	1.02681i
$861$		0			0
$862$	32.5723	−	67.6371i	1.10942	−	2.30373i
$863$	11.6554	+	7.94653i	0.396755	+	0.270503i	0.745220	−	0.666819i	$-0.232345\pi$
$863$	11.6554	+	7.94653i	0.396755	+	0.270503i	−0.348465	+	0.937322i	$0.613297\pi$
$864$		0			0
$865$	−35.7520	−	38.5314i	−1.21560	−	1.31011i
$866$	−54.6835	+	31.5715i	−1.85822	+	1.07284i
$867$		0			0
$868$	−1.58556	+	0.361894i	−0.0538174	+	0.0122835i
$869$	6.27297	−	2.46196i	0.212796	−	0.0835162i
$870$		0			0
$871$	0.551846	−	0.691993i	0.0186986	−	0.0234473i
$872$	0.197541	+	2.63600i	0.00668957	+	0.0892661i
$873$		0			0
$874$	−4.76415	+	3.24815i	−0.161150	+	0.109870i
$875$	0.220053	+	1.45996i	0.00743915	+	0.0493556i
$876$		0			0
$877$	14.4685	+	13.4248i	0.488567	+	0.453324i	0.885578	−	0.464490i	$-0.153762\pi$
$877$	14.4685	+	13.4248i	0.488567	+	0.453324i	−0.397012	+	0.917813i	$0.629953\pi$
$878$	1.53207	−	20.4441i	0.0517049	−	0.689954i
$879$		0			0
$880$	4.34562	−	28.8313i	0.146491	−	0.971903i
$881$	4.40828	+	9.15389i	0.148519	+	0.308402i	0.961934	−	0.273281i	$-0.0881088\pi$
$881$	4.40828	+	9.15389i	0.148519	+	0.308402i	−0.813416	+	0.581683i	$0.802394\pi$
$882$		0			0
$883$	44.8671	+	6.76263i	1.50990	+	0.227581i	0.851207	−	0.524831i	$-0.175871\pi$
$883$	44.8671	+	6.76263i	1.50990	+	0.227581i	0.658693	+	0.752412i	$0.271110\pi$
$884$	3.71076	+	1.45637i	0.124806	+	0.0489829i
$885$		0			0
$886$	19.4021	−	20.9105i	0.651826	−	0.702502i
$887$	−8.58244	+	37.6021i	−0.288170	+	1.26256i	0.598864	+	0.800851i	$0.295619\pi$
$887$	−8.58244	+	37.6021i	−0.288170	+	1.26256i	−0.887034	+	0.461705i	$0.847238\pi$
$888$		0			0
$889$	2.94411	+	4.31822i	0.0987424	+	0.144828i
$890$	65.1637	+	20.1003i	2.18429	+	0.673765i
$891$		0			0
$892$	−24.4379	−	19.4886i	−0.818242	−	0.652527i
$893$	−10.3429	+	3.19035i	−0.346111	+	0.106761i
$894$		0			0
$895$	4.07887	+	17.8707i	0.136341	+	0.597351i
$896$	−1.45864	−	0.842145i	−0.0487297	−	0.0281341i
$897$		0			0
$898$	4.34574	−	4.03226i	0.145019	−	0.134558i
$899$	−4.15782	−	5.21374i	−0.138671	−	0.173888i
$900$		0			0
$901$	−26.0295	−	12.5351i	−0.867168	−	0.417606i
$902$	47.5325			1.58266
$903$		0			0
$904$	1.56610			0.0520878
$905$	−7.90629	−	3.80747i	−0.262814	−	0.126565i
$906$		0			0
$907$	−5.07579	−	6.36483i	−0.168539	−	0.211341i	0.690388	−	0.723439i	$-0.257440\pi$
$907$	−5.07579	−	6.36483i	−0.168539	−	0.211341i	−0.858927	+	0.512098i	$0.828868\pi$
$908$	−5.60867	+	5.20408i	−0.186130	+	0.172704i
$909$		0			0
$910$	−1.33910	−	0.773129i	−0.0443907	−	0.0256290i
$911$	−12.0428	−	52.7631i	−0.398997	−	1.74812i	−0.631358	−	0.775491i	$-0.717502\pi$
$911$	−12.0428	−	52.7631i	−0.398997	−	1.74812i	0.232361	−	0.972630i	$-0.425355\pi$
$912$		0			0
$913$	33.6856	−	10.3906i	1.11483	−	0.343879i
$914$	27.2354	+	21.7195i	0.900867	+	0.718418i
$915$		0			0
$916$	27.4564	+	8.46918i	0.907185	+	0.279829i
$917$	9.98881	+	14.6509i	0.329860	+	0.483815i
$918$		0			0
$919$	6.08632	−	26.6659i	0.200769	−	0.879628i	−0.769701	−	0.638405i	$-0.779594\pi$
$919$	6.08632	−	26.6659i	0.200769	−	0.879628i	0.970470	−	0.241223i	$-0.0775484\pi$
$920$	−1.47553	+	1.59024i	−0.0486468	+	0.0524287i
$921$		0			0
$922$	−30.2270	−	11.8632i	−0.995473	−	0.390694i
$923$	4.61980	+	0.696323i	0.152063	+	0.0229197i
$924$		0			0
$925$	9.60974	+	19.9548i	0.315966	+	0.656111i
$926$	−3.57436	+	23.7143i	−0.117461	+	0.779301i
$927$		0			0
$928$	−3.69387	+	49.2913i	−0.121257	+	1.61806i
$929$	−24.3838	−	22.6248i	−0.800006	−	0.742297i	0.169983	−	0.985447i	$-0.445629\pi$
$929$	−24.3838	−	22.6248i	−0.800006	−	0.742297i	−0.969989	+	0.243150i	$0.921819\pi$
$930$		0			0
$931$	−1.00174	−	6.64611i	−0.0328307	−	0.217817i
$932$	−36.6023	+	24.9550i	−1.19895	+	0.817429i
$933$		0			0
$934$	3.76531	+	50.2446i	0.123205	+	1.64405i
$935$	29.3397	−	36.7909i	0.959512	−	1.20319i
$936$		0			0
$937$	−6.17020	+	2.42162i	−0.201572	+	0.0791110i	−0.463979	−	0.885846i	$-0.653579\pi$
$937$	−6.17020	+	2.42162i	−0.201572	+	0.0791110i	0.262408	+	0.964957i	$0.415484\pi$
$938$	4.48709	−	1.02415i	0.146509	−	0.0334397i
$939$		0			0
$940$	50.5888	−	29.2074i	1.65002	−	0.952642i
$941$	9.09211	+	9.79896i	0.296394	+	0.319437i	0.863638	−	0.504113i	$-0.168181\pi$
$941$	9.09211	+	9.79896i	0.296394	+	0.319437i	−0.567243	+	0.823550i	$0.691990\pi$
$942$		0			0
$943$	−24.5859	−	16.7624i	−0.800628	−	0.545859i
$944$	0.0881433	−	0.183031i	0.00286882	−	0.00595717i
$945$		0			0
$946$	28.8553	+	1.28144i	0.938167	+	0.0416631i
$947$			22.9740i			0.746556i	0.927720	+	0.373278i	$0.121766\pi$
$947$			22.9740i			0.746556i	−0.927720	+	0.373278i	$0.878234\pi$
$948$		0			0
$949$	1.63298	−	2.39515i	0.0530088	−	0.0777497i
$950$	−7.21840	+	5.75648i	−0.234196	+	0.186765i
$951$		0			0
$952$	−0.722517	−	1.25144i	−0.0234169	−	0.0405593i
$953$	−4.78625	+	8.29003i	−0.155042	+	0.268541i	−0.933074	−	0.359684i	$-0.882885\pi$
$953$	−4.78625	+	8.29003i	−0.155042	+	0.268541i	0.778032	+	0.628224i	$0.216218\pi$
$954$		0			0
$955$	19.0162	+	48.4525i	0.615350	+	1.56789i
$956$	−6.33734	−	20.5451i	−0.204964	−	0.664478i
$957$		0			0
$958$	−38.8859	+	2.91409i	−1.25635	+	0.0941501i
$959$	−2.34147	+	7.59087i	−0.0756101	+	0.245122i
$960$		0			0
$961$	29.5489	−	4.45377i	0.953189	−	0.143670i
$962$	2.99482	+	0.683548i	0.0965569	+	0.0220385i
$963$		0			0
$964$	−2.20682	−	0.165379i	−0.0710770	−	0.00532649i
$965$	−29.4711	+	75.0912i	−0.948709	+	2.41727i
$966$		0			0
$967$	−31.5699	+	15.2033i	−1.01522	+	0.488905i	−0.866077	−	0.499911i	$-0.833366\pi$
$967$	−31.5699	+	15.2033i	−1.01522	+	0.488905i	−0.149144	+	0.988815i	$0.547652\pi$
$968$	1.38282	−	0.665930i	0.0444454	−	0.0214038i
$969$		0			0
$970$	−15.7914	+	40.2359i	−0.507032	+	1.29190i
$971$	36.2858	+	2.71924i	1.16447	+	0.0872647i	0.642903	−	0.765948i	$-0.277730\pi$
$971$	36.2858	+	2.71924i	1.16447	+	0.0872647i	0.521564	+	0.853212i	$0.325349\pi$
$972$		0			0
$973$	−14.4268	−	3.29283i	−0.462503	−	0.105563i
$974$	−30.3286	+	4.57131i	−0.971793	+	0.146474i
$975$		0			0
$976$	4.01421	−	13.0138i	0.128492	−	0.416560i
$977$	−0.127560	+	0.00955932i	−0.00408101	+	0.000305830i	−0.0767704	−	0.997049i	$-0.524461\pi$
$977$	−0.127560	+	0.00955932i	−0.00408101	+	0.000305830i	0.0726894	+	0.997355i	$0.476842\pi$
$978$		0			0
$979$	−7.45646	−	24.1733i	−0.238310	−	0.772581i
$980$	13.2523	+	33.7662i	0.423328	+	1.07862i
$981$		0			0
$982$	25.7880	−	44.6661i	0.822927	−	1.42535i
$983$	9.51767	+	16.4851i	0.303566	+	0.525793i	0.976941	−	0.213509i	$-0.0684892\pi$
$983$	9.51767	+	16.4851i	0.303566	+	0.525793i	−0.673375	+	0.739301i	$0.735156\pi$
$984$		0			0
$985$	52.6230	−	41.9655i	1.67671	−	1.33713i
$986$	−47.8803	+	70.2276i	−1.52482	+	2.23650i
$987$		0			0
$988$			0.618698i			0.0196834i
$989$	−14.4734	−	10.8387i	−0.460226	−	0.344650i
$990$		0			0
$991$	−14.7442	+	30.6167i	−0.468366	+	0.972573i	0.524283	+	0.851544i	$0.324334\pi$
$991$	−14.7442	+	30.6167i	−0.468366	+	0.972573i	−0.992649	+	0.121029i	$0.961381\pi$
$992$	6.84310	+	4.66554i	0.217269	+	0.148131i
$993$		0			0
$994$	16.5243	+	17.8090i	0.524120	+	0.564867i
$995$	38.2030	−	22.0565i	1.21112	−	0.699239i
$996$		0			0
$997$	31.6465	−	7.22312i	1.00226	−	0.228758i	0.310254	−	0.950654i	$-0.399586\pi$
$997$	31.6465	−	7.22312i	1.00226	−	0.228758i	0.692002	+	0.721895i	$0.256729\pi$
$998$	6.43883	−	2.52705i	0.203818	−	0.0799925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.bc.a.233.3	yes	168
3.2	odd	2	inner	387.2.bc.a.233.12	yes	168
43.12	odd	42	inner	387.2.bc.a.98.12	yes	168
129.98	even	42	inner	387.2.bc.a.98.3	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.bc.a.98.3	✓	168	129.98	even	42	inner
387.2.bc.a.98.12	yes	168	43.12	odd	42	inner
387.2.bc.a.233.3	yes	168	1.1	even	1	trivial
387.2.bc.a.233.12	yes	168	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77234 - 0.853513i) q^{2} +(1.16572 + 1.46176i) q^{4} +(-2.24932 + 2.08706i) q^{5} +(-0.712654 - 0.411451i) q^{7} +(0.0570523 + 0.249962i) q^{8} +O(q^{10})\)	\(q+(-1.77234 - 0.853513i) q^{2} +(1.16572 + 1.46176i) q^{4} +(-2.24932 + 2.08706i) q^{5} +(-0.712654 - 0.411451i) q^{7} +(0.0570523 + 0.249962i) q^{8} +(5.76789 - 1.77916i) q^{10} +(-1.75064 - 1.39608i) q^{11} +(0.297471 + 0.0917577i) q^{13} +(0.911884 + 1.33749i) q^{14} +(0.944309 - 4.13729i) q^{16} +(4.65851 - 5.02068i) q^{17} +(0.989520 + 0.388358i) q^{19} +(-5.67286 - 0.855046i) q^{20} +(1.91114 + 3.96852i) q^{22} +(0.410979 - 2.72667i) q^{23} +(0.329954 - 4.40293i) q^{25} +(-0.448903 - 0.416521i) q^{26} +(-0.229309 - 1.52137i) q^{28} +(5.21247 - 3.55380i) q^{29} +(-0.0789941 - 1.05410i) q^{31} +(-4.88515 + 6.12578i) q^{32} +(-12.5417 + 4.92224i) q^{34} +(2.46171 - 0.561869i) q^{35} +(-4.34421 + 2.50813i) q^{37} +(-1.42229 - 1.53287i) q^{38} +(-0.650016 - 0.443174i) q^{40} +(4.68214 - 9.72257i) q^{41} +(3.10448 - 5.77600i) q^{43} -4.18645i q^{44} +(-3.05564 + 4.48180i) q^{46} +(-7.96080 + 6.34853i) q^{47} +(-3.16142 - 5.47573i) q^{49} +(-4.34274 + 7.52185i) q^{50} +(0.212639 + 0.541795i) q^{52} +(-1.24334 - 4.03081i) q^{53} +(6.85146 - 0.513446i) q^{55} +(0.0621887 - 0.201611i) q^{56} +(-12.2715 + 1.84963i) q^{58} +(0.0466708 + 0.0106523i) q^{59} +(3.20022 + 0.239823i) q^{61} +(-0.759686 + 1.93565i) q^{62} +(6.23970 - 3.00488i) q^{64} +(-0.860612 + 0.414449i) q^{65} +(1.03874 - 2.64666i) q^{67} +(12.7695 + 0.956945i) q^{68} +(-4.84254 - 1.10528i) q^{70} +(14.8403 - 2.23681i) q^{71} +(2.74477 - 8.89834i) q^{73} +(9.84014 - 0.737416i) q^{74} +(0.585813 + 1.89916i) q^{76} +(0.673176 + 1.71523i) q^{77} +(-1.50477 + 2.60634i) q^{79} +(6.51073 + 11.2769i) q^{80} +(-16.5967 + 13.2354i) q^{82} +(-8.86855 + 13.0078i) q^{83} +21.0157i q^{85} +(-10.4321 + 7.58732i) q^{86} +(0.249091 - 0.517243i) q^{88} +(9.33457 + 6.36420i) q^{89} +(-0.174240 - 0.187786i) q^{91} +(4.46482 - 2.57777i) q^{92} +(19.5278 - 4.45709i) q^{94} +(-3.03627 + 1.19165i) q^{95} +(-4.46477 + 5.59864i) q^{97} +(0.929488 + 12.4032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) \) 168 * q - 24 * q^4 - 6 * q^7	\( 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) \) 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Introduction

L-functions

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