LMFDB - Embedded newform 429.2.bi.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.319309 + 0.626680i) q^{2} +(1.28422 + 1.16223i) q^{3} +(0.884801 + 1.21782i) q^{4} +(-2.81651 + 1.43508i) q^{5} +(-1.13841 + 0.433681i) q^{6} +(-1.31181 - 0.207770i) q^{7} +(-2.43507 + 0.385677i) q^{8} +(0.298429 + 2.98512i) q^{9} +O(q^{10})$	\(q+(-0.319309 + 0.626680i) q^{2} +(1.28422 + 1.16223i) q^{3} +(0.884801 + 1.21782i) q^{4} +(-2.81651 + 1.43508i) q^{5} +(-1.13841 + 0.433681i) q^{6} +(-1.31181 - 0.207770i) q^{7} +(-2.43507 + 0.385677i) q^{8} +(0.298429 + 2.98512i) q^{9} -2.22328i q^{10} +(3.31378 - 0.137440i) q^{11} +(-0.279118 + 2.59230i) q^{12} +(-0.751447 - 3.52638i) q^{13} +(0.549078 - 0.755741i) q^{14} +(-5.28490 - 1.43048i) q^{15} +(-0.394491 + 1.21412i) q^{16} +(-0.643791 + 1.98138i) q^{17} +(-1.96601 - 0.766157i) q^{18} +(-6.95685 + 1.10186i) q^{19} +(-4.23973 - 2.16025i) q^{20} +(-1.44317 - 1.79145i) q^{21} +(-0.971989 + 2.12056i) q^{22} +8.12614 q^{23} +(-3.57541 - 2.33483i) q^{24} +(2.93432 - 4.03874i) q^{25} +(2.44985 + 0.655088i) q^{26} +(-3.08616 + 4.18039i) q^{27} +(-0.907663 - 1.78139i) q^{28} +(-0.110094 - 0.151532i) q^{29} +(2.58397 - 2.85518i) q^{30} +(3.05796 + 1.55811i) q^{31} +(-4.12154 - 4.12154i) q^{32} +(4.41535 + 3.67488i) q^{33} +(-1.03613 - 1.03613i) q^{34} +(3.99288 - 1.29737i) q^{35} +(-3.37130 + 3.00467i) q^{36} +(9.07548 + 1.43741i) q^{37} +(1.53088 - 4.71155i) q^{38} +(3.13345 - 5.40199i) q^{39} +(6.30491 - 4.58079i) q^{40} +(0.533036 + 3.36546i) q^{41} +(1.58348 - 0.332379i) q^{42} +4.11197i q^{43} +(3.09941 + 3.91399i) q^{44} +(-5.12442 - 7.97934i) q^{45} +(-2.59475 + 5.09249i) q^{46} +(-6.87429 + 1.08878i) q^{47} +(-1.91770 + 1.10070i) q^{48} +(-4.97972 - 1.61801i) q^{49} +(1.59404 + 3.12849i) q^{50} +(-3.12960 + 1.79629i) q^{51} +(3.62963 - 4.03527i) q^{52} +(3.06548 - 0.996034i) q^{53} +(-1.63433 - 3.26887i) q^{54} +(-9.13603 + 5.14264i) q^{55} +3.27448 q^{56} +(-10.2147 - 6.67046i) q^{57} +(0.130116 - 0.0206084i) q^{58} +(-2.28600 + 14.4332i) q^{59} +(-2.93402 - 7.70178i) q^{60} +(-0.834708 + 2.56897i) q^{61} +(-1.95287 + 1.41884i) q^{62} +(0.228736 - 3.97791i) q^{63} +(1.47069 - 0.477857i) q^{64} +(7.17709 + 8.85367i) q^{65} +(-3.71283 + 1.59359i) q^{66} +(2.40554 - 2.40554i) q^{67} +(-2.98261 + 0.969107i) q^{68} +(10.4357 + 9.44447i) q^{69} +(-0.461932 + 2.91652i) q^{70} +(6.67705 - 3.40213i) q^{71} +(-1.87799 - 7.15388i) q^{72} +(14.7391 + 2.33444i) q^{73} +(-3.79868 + 5.22844i) q^{74} +(8.46226 - 1.77626i) q^{75} +(-7.49730 - 7.49730i) q^{76} +(-4.37560 - 0.508209i) q^{77} +(2.38478 + 3.68857i) q^{78} +(2.31156 + 7.11426i) q^{79} +(-0.631272 - 3.98569i) q^{80} +(-8.82188 + 1.78170i) q^{81} +(-2.27927 - 0.740579i) q^{82} +(1.55406 - 0.791832i) q^{83} +(0.904752 - 3.34261i) q^{84} +(-1.03021 - 6.50447i) q^{85} +(-2.57689 - 1.31299i) q^{86} +(0.0347302 - 0.322555i) q^{87} +(-8.01627 + 1.61272i) q^{88} +(2.46422 - 2.46422i) q^{89} +(6.63676 - 0.663493i) q^{90} +(0.253080 + 4.78206i) q^{91} +(7.19002 + 9.89622i) q^{92} +(2.11620 + 5.55502i) q^{93} +(1.51271 - 4.65564i) q^{94} +(18.0128 - 13.0870i) q^{95} +(-0.502764 - 10.0831i) q^{96} +(-5.08335 - 2.59010i) q^{97} +(2.60405 - 2.60405i) q^{98} +(1.39920 + 9.85100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.319309	+	0.626680i	−0.225786	+	0.443130i	−0.975912	−	0.218165i	$-0.929993\pi$
$2$	−0.319309	+	0.626680i	−0.225786	+	0.443130i	0.750126	+	0.661295i	$0.229993\pi$
$3$	1.28422	+	1.16223i	0.741443	+	0.671015i
$3$	1.28422	+	1.16223i	0.741443	+	0.671015i
$4$	0.884801	+	1.21782i	0.442401	+	0.608912i
$5$	−2.81651	+	1.43508i	−1.25958	+	0.641788i	−0.950935	−	0.309390i	$-0.899875\pi$
$5$	−2.81651	+	1.43508i	−1.25958	+	0.641788i	−0.308644	+	0.951178i	$0.599875\pi$
$6$	−1.13841	+	0.433681i	−0.464754	+	0.177050i
$7$	−1.31181	−	0.207770i	−0.495817	−	0.0785297i	−0.0964820	−	0.995335i	$-0.530759\pi$
$7$	−1.31181	−	0.207770i	−0.495817	−	0.0785297i	−0.399335	+	0.916805i	$0.630759\pi$
$8$	−2.43507	+	0.385677i	−0.860928	+	0.136358i
$9$	0.298429	+	2.98512i	0.0994765	+	0.995040i
$10$		−	2.22328i		−	0.703064i
$11$	3.31378	−	0.137440i	0.999141	−	0.0414396i
$11$	3.31378	−	0.137440i	0.999141	−	0.0414396i
$12$	−0.279118	+	2.59230i	−0.0805745	+	0.748332i
$13$	−0.751447	−	3.52638i	−0.208414	−	0.978041i
$13$	−0.751447	−	3.52638i	−0.208414	−	0.978041i
$14$	0.549078	−	0.755741i	0.146747	−	0.201980i
$15$	−5.28490	−	1.43048i	−1.36456	−	0.369348i
$16$	−0.394491	+	1.21412i	−0.0986226	+	0.303529i
$17$	−0.643791	+	1.98138i	−0.156142	+	0.480556i	−0.998275	−	0.0587142i	$-0.981300\pi$
$17$	−0.643791	+	1.98138i	−0.156142	+	0.480556i	0.842133	+	0.539270i	$0.181300\pi$
$18$	−1.96601	−	0.766157i	−0.463392	−	0.180585i
$19$	−6.95685	+	1.10186i	−1.59601	+	0.252783i	−0.890184	−	0.455601i	$-0.849424\pi$
$19$	−6.95685	+	1.10186i	−1.59601	+	0.252783i	−0.705827	+	0.708384i	$0.749424\pi$
$20$	−4.23973	−	2.16025i	−0.948031	−	0.483046i
$21$	−1.44317	−	1.79145i	−0.314926	−	0.390926i
$22$	−0.971989	+	2.12056i	−0.207229	+	0.452105i
$23$	8.12614			1.69442			0.847209	−	0.531260i	$-0.178281\pi$
$23$	8.12614			1.69442			0.847209	+	0.531260i	$0.178281\pi$
$24$	−3.57541	−	2.33483i	−0.729827	−	0.476594i
$25$	2.93432	−	4.03874i	0.586864	−	0.807749i
$26$	2.44985	+	0.655088i	0.480456	+	0.128473i
$27$	−3.08616	+	4.18039i	−0.593931	+	0.804516i
$28$	−0.907663	−	1.78139i	−0.171532	−	0.336651i
$29$	−0.110094	−	0.151532i	−0.0204440	−	0.0281387i	0.798673	−	0.601766i	$-0.205536\pi$
$29$	−0.110094	−	0.151532i	−0.0204440	−	0.0281387i	−0.819117	+	0.573627i	$0.805536\pi$
$30$	2.58397	−	2.85518i	0.471766	−	0.521282i
$31$	3.05796	+	1.55811i	0.549226	+	0.279845i	0.706503	−	0.707710i	$-0.250272\pi$
$31$	3.05796	+	1.55811i	0.549226	+	0.279845i	−0.157277	+	0.987555i	$0.550272\pi$
$32$	−4.12154	−	4.12154i	−0.728591	−	0.728591i
$33$	4.41535	+	3.67488i	0.768613	+	0.639714i
$34$	−1.03613	−	1.03613i	−0.177694	−	0.177694i
$35$	3.99288	−	1.29737i	0.674921	−	0.219295i
$36$	−3.37130	+	3.00467i	−0.561884	+	0.500779i
$37$	9.07548	+	1.43741i	1.49200	+	0.236310i	0.848524	−	0.529157i	$-0.177492\pi$
$37$	9.07548	+	1.43741i	1.49200	+	0.236310i	0.643476	+	0.765467i	$0.277492\pi$
$38$	1.53088	−	4.71155i	0.248341	−	0.764314i
$39$	3.13345	−	5.40199i	0.501753	−	0.865011i
$40$	6.30491	−	4.58079i	0.996894	−	0.724286i
$41$	0.533036	+	3.36546i	0.0832462	+	0.525596i	0.993708	+	0.112003i	$0.0357265\pi$
$41$	0.533036	+	3.36546i	0.0832462	+	0.525596i	−0.910462	+	0.413593i	$0.864273\pi$
$42$	1.58348	−	0.332379i	0.244337	−	0.0512873i
$43$			4.11197i			0.627070i	0.949577	+	0.313535i	$0.101513\pi$
$43$			4.11197i			0.627070i	−0.949577	+	0.313535i	$0.898487\pi$
$44$	3.09941	+	3.91399i	0.467254	+	0.590056i
$45$	−5.12442	−	7.97934i	−0.763903	−	1.18949i
$46$	−2.59475	+	5.09249i	−0.382576	+	0.750847i
$47$	−6.87429	+	1.08878i	−1.00272	+	0.158815i	−0.636141	−	0.771573i	$-0.719470\pi$
$47$	−6.87429	+	1.08878i	−1.00272	+	0.158815i	−0.366577	+	0.930388i	$0.619470\pi$
$48$	−1.91770	+	1.10070i	−0.276796	+	0.158872i
$49$	−4.97972	−	1.61801i	−0.711389	−	0.231144i
$50$	1.59404	+	3.12849i	0.225432	+	0.442435i
$51$	−3.12960	+	1.79629i	−0.438231	+	0.251531i
$52$	3.62963	−	4.03527i	0.503338	−	0.559592i
$53$	3.06548	−	0.996034i	0.421076	−	0.136816i	−0.0908122	−	0.995868i	$-0.528946\pi$
$53$	3.06548	−	0.996034i	0.421076	−	0.136816i	0.511888	+	0.859052i	$0.328946\pi$
$54$	−1.63433	−	3.26887i	−0.222404	−	0.444837i
$55$	−9.13603	+	5.14264i	−1.23190	+	0.693433i
$56$	3.27448			0.437571
$57$	−10.2147	−	6.67046i	−1.35297	−	0.883523i
$58$	0.130116	−	0.0206084i	0.0170851	−	0.00270601i
$59$	−2.28600	+	14.4332i	−0.297611	+	1.87904i	0.155868	+	0.987778i	$0.450183\pi$
$59$	−2.28600	+	14.4332i	−0.297611	+	1.87904i	−0.453479	+	0.891267i	$0.649817\pi$
$60$	−2.93402	−	7.70178i	−0.378780	−	0.994295i
$61$	−0.834708	+	2.56897i	−0.106873	+	0.328923i	−0.990166	−	0.139900i	$-0.955322\pi$
$61$	−0.834708	+	2.56897i	−0.106873	+	0.328923i	0.883292	+	0.468823i	$0.155322\pi$
$62$	−1.95287	+	1.41884i	−0.248015	+	0.180193i
$63$	0.228736	−	3.97791i	0.0288181	−	0.501170i
$64$	1.47069	−	0.477857i	0.183837	−	0.0597322i
$65$	7.17709	+	8.85367i	0.890209	+	1.09816i
$66$	−3.71283	+	1.59359i	−0.457018	+	0.196157i
$67$	2.40554	−	2.40554i	0.293884	−	0.293884i	−0.544729	−	0.838612i	$-0.683367\pi$
$67$	2.40554	−	2.40554i	0.293884	−	0.293884i	0.838612	+	0.544729i	$0.183367\pi$
$68$	−2.98261	+	0.969107i	−0.361694	+	0.117522i
$69$	10.4357	+	9.44447i	1.25632	+	1.13698i
$70$	−0.461932	+	2.91652i	−0.0552114	+	0.348591i
$71$	6.67705	−	3.40213i	0.792421	−	0.403758i	−0.0104249	−	0.999946i	$-0.503318\pi$
$71$	6.67705	−	3.40213i	0.792421	−	0.403758i	0.802845	+	0.596187i	$0.203318\pi$
$72$	−1.87799	−	7.15388i	−0.221323	−	0.843093i
$73$	14.7391	+	2.33444i	1.72508	+	0.273225i	0.938753	−	0.344591i	$-0.111982\pi$
$73$	14.7391	+	2.33444i	1.72508	+	0.273225i	0.786323	+	0.617816i	$0.211982\pi$
$74$	−3.79868	+	5.22844i	−0.441588	+	0.607794i
$75$	8.46226	−	1.77626i	0.977138	−	0.205105i
$76$	−7.49730	−	7.49730i	−0.859999	−	0.859999i
$77$	−4.37560	−	0.508209i	−0.498646	−	0.0579158i
$78$	2.38478	+	3.68857i	0.270023	+	0.417649i
$79$	2.31156	+	7.11426i	0.260071	+	0.800416i	0.992788	+	0.119883i	$0.0382519\pi$
$79$	2.31156	+	7.11426i	0.260071	+	0.800416i	−0.732717	+	0.680533i	$0.761748\pi$
$80$	−0.631272	−	3.98569i	−0.0705783	−	0.445614i
$81$	−8.82188	+	1.78170i	−0.980209	+	0.197966i
$82$	−2.27927	−	0.740579i	−0.251703	−	0.0817833i
$83$	1.55406	−	0.791832i	0.170580	−	0.0869148i	−0.366616	−	0.930372i	$-0.619484\pi$
$83$	1.55406	−	0.791832i	0.170580	−	0.0869148i	0.537196	+	0.843458i	$0.319484\pi$
$84$	0.904752	−	3.34261i	0.0987165	−	0.364708i
$85$	−1.03021	−	6.50447i	−0.111742	−	0.705509i
$86$	−2.57689	−	1.31299i	−0.277873	−	0.141583i
$87$	0.0347302	−	0.322555i	0.00372347	−	0.0345815i
$88$	−8.01627	+	1.61272i	−0.854538	+	0.171917i
$89$	2.46422	−	2.46422i	0.261207	−	0.261207i	−0.564338	−	0.825544i	$-0.690868\pi$
$89$	2.46422	−	2.46422i	0.261207	−	0.261207i	0.825544	+	0.564338i	$0.190868\pi$
$90$	6.63676	−	0.663493i	0.699576	−	0.0699383i
$91$	0.253080	+	4.78206i	0.0265300	+	0.501296i
$92$	7.19002	+	9.89622i	0.749612	+	1.03175i
$93$	2.11620	+	5.55502i	0.219440	+	0.576028i
$94$	1.51271	−	4.65564i	0.156024	−	0.480192i
$95$	18.0128	−	13.0870i	1.84807	−	1.34270i
$96$	−0.502764	−	10.0831i	−0.0513131	−	1.02911i
$97$	−5.08335	−	2.59010i	−0.516136	−	0.262984i	0.176463	−	0.984307i	$-0.443534\pi$
$97$	−5.08335	−	2.59010i	−0.516136	−	0.262984i	−0.692599	+	0.721323i	$0.743534\pi$
$98$	2.60405	−	2.60405i	0.263048	−	0.263048i
$99$	1.39920	+	9.85100i	0.140625	+	0.990063i
$100$	7.51477			0.751477
$101$	−2.47008	−	7.60212i	−0.245782	−	0.756439i	−0.995507	−	0.0946893i	$-0.969814\pi$
$101$	−2.47008	−	7.60212i	−0.245782	−	0.756439i	0.749725	−	0.661749i	$-0.230186\pi$
$102$	−0.126391	−	2.53483i	−0.0125146	−	0.250985i
$103$	−2.37944	−	3.27501i	−0.234453	−	0.322697i	0.675538	−	0.737325i	$-0.263912\pi$
$103$	−2.37944	−	3.27501i	−0.234453	−	0.322697i	−0.909991	+	0.414629i	$0.863912\pi$
$104$	3.18987	+	8.29716i	0.312793	+	0.813603i
$105$	6.63557	+	2.97456i	0.647566	+	0.290287i
$106$	−0.354641	+	2.23912i	−0.0344458	+	0.217482i
$107$	7.27672	−	10.0155i	0.703467	−	0.968240i	−0.296446	−	0.955050i	$-0.595801\pi$
$107$	7.27672	−	10.0155i	0.703467	−	0.968240i	0.999913	−	0.0131900i	$-0.00419862\pi$
$108$	−7.82161	−	0.0595839i	−0.752635	−	0.00573346i
$109$	1.37102	−	1.37102i	0.131320	−	0.131320i	−0.638392	−	0.769712i	$-0.720400\pi$
$109$	1.37102	−	1.37102i	0.131320	−	0.131320i	0.769712	+	0.638392i	$0.220400\pi$
$110$	−0.305567	−	7.36746i	−0.0291347	−	0.702460i
$111$	9.98428	+	12.3938i	0.947666	+	1.17636i
$112$	0.769753	−	1.51073i	0.0727349	−	0.142750i
$113$	2.51988	−	3.46832i	0.237051	−	0.326272i	−0.673873	−	0.738847i	$-0.735370\pi$
$113$	2.51988	−	3.46832i	0.237051	−	0.326272i	0.910924	+	0.412575i	$0.135370\pi$
$114$	7.44190	−	4.27142i	0.696997	−	0.400055i
$115$	−22.8873	+	11.6617i	−2.13425	+	1.08746i
$116$	0.0871276	−	0.268151i	0.00808959	−	0.0248972i
$117$	10.3024	−	3.29554i	0.952457	−	0.304672i
$118$	−8.31507	−	6.04125i	−0.765464	−	0.556142i
$119$	1.25620	−	2.46544i	0.115156	−	0.226006i
$120$	13.4208	+	1.44505i	1.22515	+	0.131914i
$121$	10.9622	−	0.910888i	0.996566	−	0.0828080i
$122$	−1.34339	−	1.34339i	−0.121625	−	0.121625i
$123$	−3.22691	+	4.94149i	−0.290961	+	0.445559i
$124$	0.808185	+	5.10268i	0.0725772	+	0.458234i
$125$	0.00387596	−	0.0244719i	0.000346677	−	0.00218883i
$126$	2.41984	+	1.41353i	0.215576	+	0.125927i
$127$	6.81661	+	2.21485i	0.604876	+	0.196536i	0.595414	−	0.803419i	$-0.296988\pi$
$127$	6.81661	+	2.21485i	0.604876	+	0.196536i	0.00946230	+	0.999955i	$0.496988\pi$
$128$	1.65349	−	10.4397i	0.146149	−	0.922748i
$129$	−4.77907	+	5.28067i	−0.420773	+	0.464937i
$130$	−7.84013	+	1.67068i	−0.687625	+	0.146528i
$131$			17.9940i			1.57215i	0.618133	+	0.786074i	$0.287889\pi$
$131$			17.9940i			1.57215i	−0.618133	+	0.786074i	$0.712111\pi$
$132$	−0.568651	+	8.62865i	−0.0494948	+	0.751028i
$133$	9.35499			0.811181
$134$	0.739393	+	2.27562i	0.0638738	+	0.196583i
$135$	2.69298	−	16.2030i	0.231775	−	1.39453i
$136$	0.803501	−	5.07311i	0.0688997	−	0.435015i
$137$	1.41326	+	2.77369i	0.120743	+	0.236972i	0.943465	−	0.331472i	$-0.107545\pi$
$137$	1.41326	+	2.77369i	0.120743	+	0.236972i	−0.822722	+	0.568445i	$0.807545\pi$
$138$	−9.25089	+	3.52416i	−0.787488	+	0.299996i
$139$	9.49017	−	6.89501i	0.804946	−	0.584827i	−0.107415	−	0.994214i	$-0.534257\pi$
$139$	9.49017	−	6.89501i	0.804946	−	0.584827i	0.912361	+	0.409387i	$0.134257\pi$
$140$	5.11287	+	3.71472i	0.432117	+	0.313951i
$141$	−10.0935	−	6.59130i	−0.850026	−	0.555087i
$142$			5.27071i			0.442308i
$143$	−2.97479	−	11.5823i	−0.248765	−	0.968564i
$144$	−3.74201	−	0.815273i	−0.311834	−	0.0679394i
$145$	0.527542	+	0.268796i	0.0438099	+	0.0223223i
$146$	−6.16926	+	8.49126i	−0.510572	+	0.702742i
$147$	−4.51454	−	7.86547i	−0.372353	−	0.648733i
$148$	6.27948	+	12.3242i	0.516170	+	1.01304i
$149$	−4.33561	+	2.20910i	−0.355187	+	0.180977i	−0.622475	−	0.782640i	$-0.713873\pi$
$149$	−4.33561	+	2.20910i	−0.355187	+	0.180977i	0.267288	+	0.963617i	$0.413873\pi$
$150$	−1.58893	+	5.87031i	−0.129736	+	0.479309i
$151$	−1.76500	−	11.1438i	−0.143634	−	0.906867i	−0.949271	−	0.314458i	$-0.898177\pi$
$151$	−1.76500	−	11.1438i	−0.143634	−	0.906867i	0.805638	−	0.592409i	$-0.201823\pi$
$152$	16.5155	−	5.36620i	1.33958	−	0.435256i
$153$	−6.10679	−	1.33049i	−0.493705	−	0.107564i
$154$	1.71565	−	2.57982i	0.138251	−	0.207888i
$155$	−10.8488			−0.871395
$156$	9.35116	−	0.963699i	0.748692	−	0.0771576i
$157$	2.41455	+	1.75428i	0.192702	+	0.140006i	0.679953	−	0.733256i	$-0.262000\pi$
$157$	2.41455	+	1.75428i	0.192702	+	0.140006i	−0.487251	+	0.873262i	$0.662000\pi$
$158$	−5.19646	−	0.823039i	−0.413409	−	0.0654775i
$159$	5.09436	+	2.28367i	0.404009	+	0.181107i
$160$	17.5231	+	5.69359i	1.38532	+	0.450118i
$161$	−10.6599	−	1.68837i	−0.840122	−	0.133062i
$162$	1.70036	−	6.09741i	0.133593	−	0.479057i
$163$	7.72149	−	15.1543i	0.604794	−	1.18697i	−0.362183	−	0.932107i	$-0.617968\pi$
$163$	7.72149	−	15.1543i	0.604794	−	1.18697i	0.966976	−	0.254867i	$-0.0820317\pi$
$164$	−3.62691	+	3.62691i	−0.283214	+	0.283214i
$165$	−17.7096	−	4.01393i	−1.37869	−	0.312484i
$166$			1.22674i			0.0952132i
$167$	20.7653	+	10.5805i	1.60687	+	0.818741i	0.999708	+	0.0241624i	$0.00769188\pi$
$167$	20.7653	+	10.5805i	1.60687	+	0.818741i	0.607161	+	0.794579i	$0.292308\pi$
$168$	4.20515	+	3.80571i	0.324434	+	0.293617i
$169$	−11.8707	+	5.29977i	−0.913127	+	0.407675i
$170$	4.40518	+	1.43133i	0.337862	+	0.109778i
$171$	−5.36530	−	20.4382i	−0.410295	−	1.56295i
$172$	−5.00766	+	3.63828i	−0.381830	+	0.277416i
$173$	15.8465	+	11.5131i	1.20479	+	0.875328i	0.994747	−	0.102365i	$-0.0326411\pi$
$173$	15.8465	+	11.5131i	1.20479	+	0.875328i	0.210038	+	0.977693i	$0.432641\pi$
$174$	0.191049	+	0.124760i	0.0144834	+	0.00945800i
$175$	−4.68840	+	4.68840i	−0.354409	+	0.354409i
$176$	−1.14039	+	4.07753i	−0.0859598	+	0.307355i
$177$	−19.7105	+	15.8785i	−1.48153	+	1.19350i
$178$	0.757428	+	2.33112i	0.0567716	+	0.174725i
$179$	−7.10400	−	5.16136i	−0.530978	−	0.385778i	0.289745	−	0.957104i	$-0.406429\pi$
$179$	−7.10400	−	5.16136i	−0.530978	−	0.385778i	−0.820724	+	0.571326i	$0.806429\pi$
$180$	5.18334	−	13.3008i	0.386343	−	0.991381i
$181$	−7.92298	−	2.57433i	−0.588910	−	0.191349i	−0.000621928	−	1.00000i	$-0.500198\pi$
$181$	−7.92298	−	2.57433i	−0.588910	−	0.191349i	−0.588288	+	0.808651i	$0.700198\pi$
$182$	−3.07763	−	1.36836i	−0.228129	−	0.101429i
$183$	−4.05768	+	2.32899i	−0.299953	+	0.172164i
$184$	−19.7877	+	3.13407i	−1.45877	+	0.231047i
$185$	−27.6239	+	8.97556i	−2.03095	+	0.659897i
$186$	−4.15694	−	0.447587i	−0.304802	−	0.0328187i
$187$	−1.86106	+	6.65434i	−0.136094	+	0.486614i
$188$	−7.40833	−	7.40833i	−0.540308	−	0.540308i
$189$	4.91701	−	4.84266i	0.357660	−	0.352252i
$190$	2.44974	+	15.4670i	0.177723	+	1.12210i
$191$	−14.6452	−	20.1573i	−1.05969	−	1.45853i	−0.880099	−	0.474791i	$-0.842524\pi$
$191$	−14.6452	−	20.1573i	−1.05969	−	1.45853i	−0.179587	−	0.983742i	$-0.557476\pi$
$192$	2.44407	+	1.09562i	0.176386	+	0.0790693i
$193$	−14.2954	+	7.28387i	−1.02900	+	0.524304i	−0.885155	−	0.465295i	$-0.845948\pi$
$193$	−14.2954	+	7.28387i	−1.02900	+	0.524304i	−0.143849	+	0.989600i	$0.545948\pi$
$194$	3.24632	−	2.35859i	0.233072	−	0.169337i
$195$	−1.07308	+	19.7115i	−0.0768447	+	1.41157i
$196$	−2.43561	−	7.49604i	−0.173972	−	0.535432i
$197$	−11.7612	−	11.7612i	−0.837948	−	0.837948i	0.150641	−	0.988589i	$-0.451866\pi$
$197$	−11.7612	−	11.7612i	−0.837948	−	0.837948i	−0.988589	+	0.150641i	$0.951866\pi$
$198$	−6.62020	−	2.26867i	−0.470477	−	0.161227i
$199$		−	18.3497i		−	1.30078i	−0.759601	−	0.650389i	$-0.774606\pi$
$199$		−	18.3497i		−	1.30078i	0.759601	−	0.650389i	$-0.225394\pi$
$200$	−5.58762	+	10.9663i	−0.395105	+	0.775437i
$201$	5.88504	−	0.293439i	0.415099	−	0.0206976i
$202$	5.55281	+	0.879479i	0.390694	+	0.0618799i
$203$	0.112939	+	0.221655i	0.00792676	+	0.0155571i
$204$	−4.95664	−	2.22194i	−0.347034	−	0.155567i
$205$	−6.33100	−	8.71388i	−0.442176	−	0.608604i
$206$	2.81216	−	0.445403i	0.195933	−	0.0310327i
$207$	2.42508	+	24.2575i	0.168555	+	1.68601i
$208$	4.57787	+	0.478777i	0.317418	+	0.0331972i
$209$	−22.9020	+	4.60745i	−1.58416	+	0.318704i
$210$	−3.98290	+	3.20858i	−0.274846	+	0.221413i
$211$	−3.72222	−	11.4558i	−0.256248	−	0.788651i	−0.993581	−	0.113121i	$-0.963915\pi$
$211$	−3.72222	−	11.4558i	−0.256248	−	0.788651i	0.737333	−	0.675529i	$-0.236085\pi$
$212$	3.92533	+	2.85192i	0.269593	+	0.195871i
$213$	12.5289	+	3.39122i	0.858463	+	0.232362i
$214$	3.95302	+	7.75823i	0.270223	+	0.530342i
$215$	−5.90101	−	11.5814i	−0.402446	−	0.789844i
$216$	5.90273	−	11.3698i	0.401630	−	0.773617i
$217$	−3.68773	−	2.67930i	−0.250340	−	0.181882i
$218$	0.421411	+	1.29697i	0.0285415	+	0.0878418i
$219$	16.2150	+	20.1281i	1.09571	+	1.36013i
$220$	−14.3464	−	6.57587i	−0.967234	−	0.443345i
$221$	7.47088	+	0.781342i	0.502546	+	0.0525588i
$222$	−10.9550	+	2.29950i	−0.735251	+	0.154332i
$223$	18.2828	−	2.89570i	1.22430	−	0.193911i	0.489386	−	0.872067i	$-0.337221\pi$
$223$	18.2828	−	2.89570i	1.22430	−	0.193911i	0.734918	+	0.678156i	$0.237221\pi$
$224$	4.55033	+	6.26300i	0.304032	+	0.418464i
$225$	12.9318	+	7.55401i	0.862121	+	0.503601i
$226$	1.36891	+	2.68663i	0.0910583	+	0.178712i
$227$	−19.2971	−	3.05635i	−1.28079	−	0.202857i	−0.521299	−	0.853374i	$-0.674552\pi$
$227$	−19.2971	−	3.05635i	−1.28079	−	0.202857i	−0.759492	+	0.650517i	$0.774552\pi$
$228$	−0.914555	−	18.3418i	−0.0605679	−	1.21471i
$229$	−1.22333	+	2.40092i	−0.0808397	+	0.158657i	−0.927888	−	0.372859i	$-0.878377\pi$
$229$	−1.22333	+	2.40092i	−0.0808397	+	0.158657i	0.847048	+	0.531516i	$0.178377\pi$
$230$		−	18.0667i		−	1.19128i
$231$	−5.02856	−	5.73811i	−0.330855	−	0.377540i
$232$	0.326530	+	0.326530i	0.0214377	+	0.0214377i
$233$	−1.62782	−	5.00991i	−0.106642	−	0.328210i	0.883470	−	0.468487i	$-0.155201\pi$
$233$	−1.62782	−	5.00991i	−0.106642	−	0.328210i	−0.990112	+	0.140277i	$0.955201\pi$
$234$	−1.22441	+	7.50860i	−0.0800420	+	0.490853i
$235$	17.7990	−	12.9317i	1.16108	−	0.843573i
$236$	−19.5998	+	9.98659i	−1.27584	+	0.650071i
$237$	−5.29987	+	11.8228i	−0.344264	+	0.767975i
$238$	1.14392	+	1.57447i	0.0741495	+	0.102058i
$239$	−0.831255	−	5.24834i	−0.0537694	−	0.339487i	−0.999878	−	0.0156365i	$-0.995023\pi$
$239$	−0.831255	−	5.24834i	−0.0537694	−	0.339487i	0.946108	−	0.323850i	$-0.104977\pi$
$240$	3.82161	−	5.85218i	0.246684	−	0.377757i
$241$	10.8086	+	10.8086i	0.696242	+	0.696242i	0.963598	−	0.267356i	$-0.0861498\pi$
$241$	10.8086	+	10.8086i	0.696242	+	0.696242i	−0.267356	+	0.963598i	$0.586150\pi$
$242$	−2.92950	+	7.16066i	−0.188316	+	0.460304i
$243$	−13.4000	−	7.96499i	−0.859608	−	0.510955i
$244$	−3.86710	+	1.25650i	−0.247566	+	0.0804390i
$245$	16.3474	−	2.58917i	1.04440	−	0.165416i
$246$	−2.06635	−	3.60010i	−0.131746	−	0.229534i
$247$	9.11327	+	23.7045i	0.579863	+	1.50828i
$248$	−8.04729	−	2.61472i	−0.511003	−	0.166035i
$249$	2.91604	+	0.789292i	0.184797	+	0.0500194i
$250$	0.0140984	+	0.0102431i	0.000891661	+	0.000647830i
$251$	−1.73570	−	5.34194i	−0.109556	−	0.337180i	0.881216	−	0.472713i	$-0.156725\pi$
$251$	−1.73570	−	5.34194i	−0.109556	−	0.337180i	−0.990773	+	0.135533i	$0.956725\pi$
$252$	5.04678	−	3.24110i	0.317918	−	0.204170i
$253$	26.9282	−	1.11685i	1.69296	−	0.0702160i
$254$	−3.56461	+	3.56461i	−0.223664	+	0.223664i
$255$	6.23670	−	9.55050i	0.390557	−	0.598075i
$256$	8.51647	+	6.18758i	0.532279	+	0.386724i
$257$	−15.9077	+	11.5576i	−0.992296	+	0.720945i	−0.960423	−	0.278547i	$-0.910147\pi$
$257$	−15.9077	+	11.5576i	−0.992296	+	0.720945i	−0.0318732	+	0.999492i	$0.510147\pi$
$258$	−1.78329	−	4.68111i	−0.111023	−	0.291433i
$259$	−11.6066	−	3.77123i	−0.721202	−	0.234333i
$260$	−4.43192	+	16.5742i	−0.274856	+	1.02789i
$261$	0.419485	−	0.373866i	0.0259655	−	0.0231417i
$262$	−11.2765	−	5.74567i	−0.696665	−	0.354968i
$263$		−	0.855686i		−	0.0527639i	−0.999652	−	0.0263819i	$-0.991601\pi$
$263$		−	0.855686i		−	0.0527639i	0.999652	−	0.0263819i	$-0.00839860\pi$
$264$	−12.1690	−	7.24569i	−0.748950	−	0.445941i
$265$	−7.20454	+	7.20454i	−0.442572	+	0.442572i
$266$	−2.98714	+	5.86258i	−0.183153	+	0.359458i
$267$	6.02859	−	0.300597i	0.368944	−	0.0183962i
$268$	5.05795	+	0.801101i	0.308964	+	0.0489350i
$269$	−5.24489	−	1.70417i	−0.319787	−	0.103905i	0.144725	−	0.989472i	$-0.453770\pi$
$269$	−5.24489	−	1.70417i	−0.319787	−	0.103905i	−0.464512	+	0.885567i	$0.653770\pi$
$270$	9.29418	+	6.86139i	0.565626	+	0.417571i
$271$	7.02710	+	1.11298i	0.426866	+	0.0676089i	0.366171	−	0.930547i	$-0.380668\pi$
$271$	7.02710	+	1.11298i	0.426866	+	0.0676089i	0.0606945	+	0.998156i	$0.480668\pi$
$272$	−2.15166	−	1.56327i	−0.130464	−	0.0947874i
$273$	−5.23286	+	6.43534i	−0.316707	+	0.389485i
$274$	−2.18948			−0.132271
$275$	9.16859	−	13.7868i	0.552887	−	0.831374i
$276$	−2.26816	+	21.0654i	−0.136527	+	1.26799i
$277$	−5.63231	+	1.83005i	−0.338413	+	0.109957i	−0.473293	−	0.880905i	$-0.656935\pi$
$277$	−5.63231	+	1.83005i	−0.338413	+	0.109957i	0.134880	+	0.990862i	$0.456935\pi$
$278$	1.29067	+	8.14894i	0.0774090	+	0.488741i
$279$	−3.73856	+	9.59337i	−0.223822	+	0.574340i
$280$	−9.22259	+	4.69915i	−0.551155	+	0.280828i
$281$	3.99839	+	7.84727i	0.238524	+	0.468129i	0.978975	−	0.203981i	$-0.0653881\pi$
$281$	3.99839	+	7.84727i	0.238524	+	0.468129i	−0.740451	+	0.672110i	$0.765388\pi$
$282$	7.35358	−	4.22073i	0.437899	−	0.251341i
$283$	−6.83518	+	9.40782i	−0.406309	+	0.559237i	−0.962313	−	0.271943i	$-0.912334\pi$
$283$	−6.83518	+	9.40782i	−0.406309	+	0.559237i	0.556004	+	0.831180i	$0.312334\pi$
$284$	10.0511	+	5.12127i	0.596421	+	0.303892i
$285$	38.3425	+	4.12842i	2.27121	+	0.244546i
$286$	8.20830	+	1.83411i	0.485367	+	0.108453i
$287$		−	4.52559i		−	0.267137i
$288$	11.0733	−	13.5333i	0.652500	−	0.797455i
$289$	10.2419	+	7.44116i	0.602463	+	0.437715i
$290$	−0.336898	+	0.244771i	−0.0197833	+	0.0143734i
$291$	−3.51783	−	9.23428i	−0.206219	−	0.541323i
$292$	10.1982	+	20.0151i	0.596804	+	1.17129i
$293$	4.03104	−	25.4510i	0.235496	−	1.48686i	−0.532512	−	0.846423i	$-0.678752\pi$
$293$	4.03104	−	25.4510i	0.235496	−	1.48686i	0.768008	−	0.640441i	$-0.221248\pi$
$294$	6.37067	−	0.317654i	0.371545	−	0.0185259i
$295$	−14.2743	−	43.9318i	−0.831083	−	2.55781i
$296$	−22.6538			−1.31673
$297$	−9.65228	+	14.2770i	−0.560082	+	0.828437i
$298$		−	3.42243i		−	0.198256i
$299$	−6.10637	−	28.6558i	−0.353141	−	1.65721i
$300$	9.65060	+	8.73391i	0.557178	+	0.504253i
$301$	0.854345	−	5.39412i	0.0492436	−	0.310912i
$302$	7.54715	+	2.45222i	0.434290	+	0.141109i
$303$	5.66331	−	12.6336i	0.325349	−	0.725780i
$304$	1.40663	−	8.88110i	0.0806757	−	0.509366i
$305$	−1.33572	−	8.43338i	−0.0764829	−	0.482894i
$306$	2.78375	−	3.40217i	0.159136	−	0.194489i
$307$	−10.6791	−	10.6791i	−0.609487	−	0.609487i	0.333325	−	0.942812i	$-0.391829\pi$
$307$	−10.6791	−	10.6791i	−0.609487	−	0.609487i	−0.942812	+	0.333325i	$0.891829\pi$
$308$	−3.25262	−	5.77837i	−0.185335	−	0.329253i
$309$	0.750614	−	6.97129i	0.0427010	−	0.396583i
$310$	3.46412	−	6.79871i	0.196749	−	0.386141i
$311$	−11.1045	−	8.06787i	−0.629677	−	0.457487i	0.226611	−	0.973985i	$-0.427235\pi$
$311$	−11.1045	−	8.06787i	−0.629677	−	0.457487i	−0.856288	+	0.516498i	$0.827235\pi$
$312$	−5.54674	+	14.3627i	−0.314023	+	0.813130i
$313$	−0.824206	+	2.53664i	−0.0465869	+	0.143380i	−0.971644	−	0.236448i	$-0.924017\pi$
$313$	−0.824206	+	2.53664i	−0.0465869	+	0.143380i	0.925057	+	0.379828i	$0.124017\pi$
$314$	−1.87036	+	0.952995i	−0.105550	+	0.0537806i
$315$	5.06439	+	11.5321i	0.285346	+	0.649758i
$316$	−6.61864	+	9.10978i	−0.372328	+	0.512465i
$317$	−5.00611	+	9.82505i	−0.281171	+	0.551830i	−0.987795	−	0.155760i	$-0.950217\pi$
$317$	−5.00611	+	9.82505i	−0.281171	+	0.551830i	0.706624	+	0.707590i	$0.250217\pi$
$318$	−3.05781	+	2.46334i	−0.171473	+	0.138137i
$319$	−0.385654	−	0.487011i	−0.0215925	−	0.0272674i
$320$	−3.45645	+	3.45645i	−0.193222	+	0.193222i
$321$	20.9853	−	4.40490i	1.17128	−	0.245857i
$322$	4.46189	−	6.14126i	0.248651	−	0.342239i
$323$	2.29555	−	14.4936i	0.127728	−	0.806443i
$324$	−9.97540	−	9.16706i	−0.554189	−	0.509281i
$325$	−16.4471	−	7.31261i	−0.912322	−	0.405631i
$326$	7.03133	+	9.67780i	0.389430	+	0.536004i
$327$	3.35413	−	0.167243i	0.185484	−	0.00924858i
$328$	−2.59596	−	7.98955i	−0.143338	−	0.441149i
$329$	9.24397			0.509637
$330$	8.17029	−	9.81656i	0.449760	−	0.540384i
$331$	−17.7919	+	17.7919i	−0.977933	+	0.977933i	−0.999762	−	0.0218286i	$-0.993051\pi$
$331$	−17.7919	+	17.7919i	−0.977933	+	0.977933i	0.0218286	+	0.999762i	$0.493051\pi$
$332$	2.33934	+	1.19196i	0.128388	+	0.0654171i
$333$	−1.58246	+	27.5204i	−0.0867185	+	1.50811i
$334$	−13.2611	+	9.63477i	−0.725617	+	0.527191i
$335$	−3.32307	+	10.2274i	−0.181559	+	0.558781i
$336$	2.74435	−	1.04547i	0.149716	−	0.0570350i
$337$	8.03930	+	11.0651i	0.437928	+	0.602757i	0.969750	−	0.244100i	$-0.0784924\pi$
$337$	8.03930	+	11.0651i	0.437928	+	0.602757i	−0.531822	+	0.846856i	$0.678492\pi$
$338$	0.469150	−	9.13137i	0.0255184	−	0.496681i
$339$	7.26708	−	1.52539i	0.394694	−	0.0828478i
$340$	7.00978	−	7.00978i	0.380158	−	0.380158i
$341$	10.3476	+	4.74294i	0.560351	+	0.256845i
$342$	14.5214	+	3.16378i	0.785227	+	0.171078i
$343$	14.4801	+	7.37796i	0.781850	+	0.398373i
$344$	−1.58589	−	10.0129i	−0.0855057	−	0.539862i
$345$	−42.9459	−	11.6243i	−2.31213	−	0.625830i
$346$	−12.2750	+	6.25441i	−0.659907	+	0.336239i
$347$	6.48627	+	2.10752i	0.348201	+	0.113137i	0.477896	−	0.878417i	$-0.341400\pi$
$347$	6.48627	+	2.10752i	0.348201	+	0.113137i	−0.129695	+	0.991554i	$0.541400\pi$
$348$	0.423545	−	0.243102i	0.0227044	−	0.0130316i
$349$	−1.37180	−	8.66120i	−0.0734307	−	0.463623i	−0.996815	−	0.0797468i	$-0.974589\pi$
$349$	−1.37180	−	8.66120i	−0.0734307	−	0.463623i	0.923384	−	0.383877i	$-0.125411\pi$
$350$	−1.44107	−	4.43517i	−0.0770287	−	0.237070i
$351$	17.0607	+	7.74160i	0.910633	+	0.413216i
$352$	−14.2243	−	13.0914i	−0.758158	−	0.697773i
$353$	19.0009	+	19.0009i	1.01132	+	1.01132i	0.999935	+	0.0113809i	$0.00362273\pi$
$353$	19.0009	+	19.0009i	1.01132	+	1.01132i	0.0113809	+	0.999935i	$0.496377\pi$
$354$	−3.65702	−	17.4223i	−0.194368	−	0.925986i
$355$	−13.9236	+	19.1642i	−0.738990	+	1.01713i
$356$	5.18133	+	0.820642i	0.274610	+	0.0434939i
$357$	4.47865	−	1.70616i	0.237035	−	0.0902994i
$358$	5.50289	−	2.80386i	0.290837	−	0.148189i
$359$	−3.36442	+	21.2421i	−0.177567	+	1.12111i	0.724422	+	0.689357i	$0.242107\pi$
$359$	−3.36442	+	21.2421i	−0.177567	+	1.12111i	−0.901989	+	0.431758i	$0.857893\pi$
$360$	15.5558	+	17.4539i	0.819861	+	0.919900i
$361$	29.1136	−	9.45958i	1.53229	−	0.497873i
$362$	4.14316	−	4.14316i	0.217760	−	0.217760i
$363$	15.1365	+	11.5709i	0.794462	+	0.607313i
$364$	−5.59978	+	4.53938i	−0.293508	+	0.237928i
$365$	−44.8627	+	14.5768i	−2.34822	+	0.762984i
$366$	−0.163873	−	3.28654i	−0.00856578	−	0.171790i
$367$	22.4849	−	16.3362i	1.17370	−	0.852743i	0.182253	−	0.983252i	$-0.441661\pi$
$367$	22.4849	−	16.3362i	1.17370	−	0.852743i	0.991447	+	0.130509i	$0.0416610\pi$
$368$	−3.20569	+	9.86609i	−0.167108	+	0.514305i
$369$	−9.88722	+	2.59553i	−0.514708	+	0.135118i
$370$	3.19578	−	20.1773i	0.166141	−	1.04897i
$371$	−4.22827	+	0.669692i	−0.219521	+	0.0347687i
$372$	−4.89262	+	7.49225i	−0.253670	+	0.388455i
$373$	−12.2291			−0.633199			−0.316600	−	0.948559i	$-0.602541\pi$
$373$	−12.2291			−0.633199			−0.316600	+	0.948559i	$0.602541\pi$
$374$	−3.57589	−	3.29108i	−0.184905	−	0.170178i
$375$	0.0334196	−	0.0269224i	0.00172578	−	0.00139027i
$376$	16.3195	−	5.30252i	0.841613	−	0.273456i
$377$	−0.451628	+	0.502102i	−0.0232600	+	0.0258596i
$378$	1.46475	+	4.62769i	0.0753386	+	0.238023i
$379$	3.85936	+	7.57442i	0.198242	+	0.389072i	0.968631	−	0.248502i	$-0.0799382\pi$
$379$	3.85936	+	7.57442i	0.198242	+	0.389072i	−0.770389	+	0.637574i	$0.779938\pi$
$380$	31.8754	+	10.3569i	1.63517	+	0.531300i
$381$	6.17984	+	10.7668i	0.316603	+	0.551602i
$382$	17.3085	−	2.74140i	0.885581	−	0.140262i
$383$	9.98189	−	19.5906i	0.510051	−	1.00103i	−0.482116	−	0.876108i	$-0.660132\pi$
$383$	9.98189	−	19.5906i	0.510051	−	1.00103i	0.992166	−	0.124923i	$-0.0398685\pi$
$384$	14.2568	−	11.4851i	0.727539	−	0.586097i
$385$	13.0532	−	4.84796i	0.665253	−	0.247075i
$386$		−	11.2844i		−	0.574363i
$387$	−12.2747	+	1.22713i	−0.623959	+	0.0623787i
$388$	−1.34347	−	8.48235i	−0.0682045	−	0.430626i
$389$	2.32354	−	1.68815i	0.117808	−	0.0855927i	−0.527321	−	0.849666i	$-0.676803\pi$
$389$	2.32354	−	1.68815i	0.117808	−	0.0855927i	0.645129	+	0.764073i	$0.276803\pi$
$390$	−12.0101	−	6.96654i	−0.608158	−	0.352764i
$391$	−5.23154	+	16.1010i	−0.264570	+	0.814263i
$392$	12.7500	+	2.01940i	0.643973	+	0.101995i
$393$	−20.9133	+	23.1083i	−1.05494	+	1.16566i
$394$	11.1259	−	3.61503i	0.560516	−	0.182123i
$395$	−16.7201	−	16.7201i	−0.841278	−	0.841278i
$396$	−10.7588	+	10.4202i	−0.540649	+	0.523633i
$397$	1.51018	+	1.51018i	0.0757938	+	0.0757938i	0.743987	−	0.668194i	$-0.232932\pi$
$397$	1.51018	+	1.51018i	0.0757938	+	0.0757938i	−0.668194	+	0.743987i	$0.732932\pi$
$398$	11.4994	+	5.85924i	0.576413	+	0.293697i
$399$	12.0138	+	10.8727i	0.601444	+	0.544315i
$400$	3.74595	+	5.15585i	0.187297	+	0.257793i
$401$	7.35144	+	14.4280i	0.367113	+	0.720500i	0.998488	−	0.0549780i	$-0.0175089\pi$
$401$	7.35144	+	14.4280i	0.367113	+	0.720500i	−0.631374	+	0.775478i	$0.717509\pi$
$402$	−1.69526	+	3.78173i	−0.0845516	+	0.188616i
$403$	3.19658	−	11.9544i	0.159233	−	0.595489i
$404$	7.07252	−	9.73448i	0.351871	−	0.484309i
$405$	22.2900	−	17.6783i	1.10760	−	0.878440i
$406$	−0.174969			−0.00868357
$407$	30.2717	+	3.51594i	1.50051	+	0.174279i
$408$	6.92800	−	5.58112i	0.342987	−	0.276306i
$409$	−19.0072	−	9.68466i	−0.939846	−	0.478875i	−0.0842067	−	0.996448i	$-0.526836\pi$
$409$	−19.0072	−	9.68466i	−0.939846	−	0.478875i	−0.855639	+	0.517573i	$0.826836\pi$
$410$	7.48236	−	1.18509i	0.369527	−	0.0585274i
$411$	−1.40873	+	5.20456i	−0.0694876	+	0.256722i
$412$	1.88306	−	5.79547i	0.0927719	−	0.285523i
$413$	5.99758	−	18.4587i	0.295122	−	0.908291i
$414$	−15.9760	−	6.22590i	−0.785180	−	0.305986i
$415$	−3.24067	+	4.46040i	−0.159078	+	0.218952i
$416$	−11.4370	+	17.6312i	−0.560743	+	0.864441i
$417$	20.2011	+	2.17509i	0.989250	+	0.106515i
$418$	4.42542	−	15.8234i	0.216455	−	0.773949i
$419$		−	21.6446i		−	1.05741i	−0.848807	−	0.528703i	$-0.822679\pi$
$419$		−	21.6446i		−	1.05741i	0.848807	−	0.528703i	$-0.177321\pi$
$420$	2.24867	+	10.7129i	0.109724	+	0.522734i
$421$	−30.9337	+	4.89941i	−1.50761	+	0.238783i	−0.854889	−	0.518812i	$-0.826375\pi$
$421$	−30.9337	+	4.89941i	−1.50761	+	0.238783i	−0.652726	+	0.757594i	$0.726375\pi$
$422$	8.36767	+	1.32531i	0.407332	+	0.0645150i
$423$	−5.30163	−	20.1957i	−0.257774	−	0.981947i
$424$	−7.08051	+	3.60770i	−0.343860	+	0.175205i
$425$	6.11321	+	8.41412i	0.296534	+	0.408145i
$426$	−6.12579	+	6.76873i	−0.296795	+	0.327946i
$427$	1.62873	−	3.19657i	0.0788199	−	0.154693i
$428$	18.6356			0.900787
$429$	9.64110	−	18.3316i	0.465477	−	0.885060i
$430$	9.14207			0.440870
$431$	10.5135	−	20.6340i	0.506419	−	0.993903i	−0.486339	−	0.873770i	$-0.661668\pi$
$431$	10.5135	−	20.6340i	0.506419	−	0.993903i	0.992758	−	0.120133i	$-0.0383320\pi$
$432$	−3.85802	−	5.39608i	−0.185619	−	0.259619i
$433$	−2.49927	−	3.43995i	−0.120107	−	0.165313i	0.744730	−	0.667366i	$-0.232578\pi$
$433$	−2.49927	−	3.43995i	−0.120107	−	0.165313i	−0.864837	+	0.502053i	$0.832578\pi$
$434$	2.85659	−	1.45550i	0.137121	−	0.0698665i
$435$	0.365075	+	0.958319i	0.0175040	+	0.0459479i
$436$	2.88274	+	0.456581i	0.138058	+	0.0218663i
$437$	−56.5324	+	8.95385i	−2.70431	+	0.428321i
$438$	−17.7915	+	3.73451i	−0.850110	+	0.178442i
$439$			27.0196i			1.28957i	0.764363	+	0.644787i	$0.223054\pi$
$439$			27.0196i			1.28957i	−0.764363	+	0.644787i	$0.776946\pi$
$440$	20.2635	−	16.0462i	0.966024	−	0.764975i
$441$	3.34386	−	15.3479i	0.159231	−	0.730854i
$442$	−2.87517	+	4.43236i	−0.136758	+	0.210826i
$443$	−0.409805	+	0.564049i	−0.0194704	+	0.0267988i	−0.818641	−	0.574305i	$-0.805272\pi$
$443$	−0.409805	+	0.564049i	−0.0194704	+	0.0267988i	0.799171	+	0.601104i	$0.205272\pi$
$444$	−6.25934	+	23.1251i	−0.297055	+	1.09747i
$445$	−3.40413	+	10.4768i	−0.161371	+	0.496650i
$446$	−4.02318	+	12.3821i	−0.190503	+	0.586308i
$447$	−8.13536	−	2.20202i	−0.384789	−	0.104152i
$448$	−2.02855	+	0.321291i	−0.0958401	+	0.0151796i
$449$	3.38043	+	1.72242i	0.159532	+	0.0812858i	0.531934	−	0.846786i	$-0.321466\pi$
$449$	3.38043	+	1.72242i	0.159532	+	0.0812858i	−0.372401	+	0.928072i	$0.621466\pi$
$450$	−8.86320	+	5.69204i	−0.417815	+	0.268326i
$451$	2.22891	+	11.0791i	0.104955	+	0.521695i
$452$	6.45341			0.303543
$453$	10.6850	−	16.3624i	0.502025	−	0.768771i
$454$	8.07709	−	11.1172i	0.379076	−	0.521754i
$455$	−7.57545	−	13.1055i	−0.355142	−	0.614396i
$456$	27.4462	+	12.3034i	1.28529	+	0.576162i
$457$	−1.71891	−	3.37354i	−0.0804071	−	0.157808i	0.847302	−	0.531111i	$-0.178225\pi$
$457$	−1.71891	−	3.37354i	−0.0804071	−	0.157808i	−0.927709	+	0.373303i	$0.878225\pi$
$458$	−1.11399	−	1.53327i	−0.0520531	−	0.0716450i
$459$	−6.29611	−	8.80615i	−0.293877	−	0.411036i
$460$	−34.4526	−	17.5545i	−1.60636	−	0.818482i
$461$	27.9247	+	27.9247i	1.30058	+	1.30058i	0.927999	+	0.372584i	$0.121528\pi$
$461$	27.9247	+	27.9247i	1.30058	+	1.30058i	0.372584	+	0.927999i	$0.378472\pi$
$462$	5.20163	−	1.31906i	0.242002	−	0.0613684i
$463$	−15.2044	−	15.2044i	−0.706609	−	0.706609i	0.259212	−	0.965820i	$-0.416537\pi$
$463$	−15.2044	−	15.2044i	−0.706609	−	0.706609i	−0.965820	+	0.259212i	$0.916537\pi$
$464$	0.227408	−	0.0738895i	0.0105572	−	0.00343023i
$465$	−13.9322	−	12.6088i	−0.646090	−	0.584720i
$466$	3.65938	+	0.579590i	0.169518	+	0.0268490i
$467$	11.9693	−	36.8376i	0.553871	−	1.70464i	−0.145034	−	0.989427i	$-0.546329\pi$
$467$	11.9693	−	36.8376i	0.553871	−	1.70464i	0.698905	−	0.715214i	$-0.253671\pi$
$468$	13.1290	+	9.63062i	0.606886	+	0.445176i
$469$	−3.65541	+	2.65581i	−0.168791	+	0.122634i
$470$	2.42067	+	15.2835i	0.111657	+	0.704975i
$471$	1.06193	+	5.05914i	0.0489314	+	0.233113i
$472$		−	36.0276i		−	1.65830i
$473$	0.565147	+	13.6262i	0.0259855	+	0.626531i
$474$	−5.71683	−	7.09646i	−0.262583	−	0.325951i
$475$	−15.9635	+	31.3301i	−0.732456	+	1.43753i
$476$	4.11396	−	0.651587i	0.188563	−	0.0298654i
$477$	3.88811	+	8.85357i	0.178024	+	0.405377i
$478$	3.55446	+	1.15491i	0.162577	+	0.0528245i
$479$	−3.00005	−	5.88794i	−0.137076	−	0.269027i	0.812256	−	0.583301i	$-0.198239\pi$
$479$	−3.00005	−	5.88794i	−0.137076	−	0.269027i	−0.949332	+	0.314274i	$0.898239\pi$
$480$	15.8862	+	27.6777i	0.725100	+	1.26331i
$481$	−1.75088	−	33.0837i	−0.0798333	−	1.50849i
$482$	−10.2248	+	3.32224i	−0.465727	+	0.151324i
$483$	−11.7274	−	14.5576i	−0.533616	−	0.662393i
$484$	10.8087	+	12.5441i	0.491304	+	0.570187i
$485$	18.0343			0.818894
$486$	9.27023	−	5.85419i	0.420506	−	0.265551i
$487$	−2.15242	+	0.340909i	−0.0975353	+	0.0154481i	−0.205011	−	0.978760i	$-0.565723\pi$
$487$	−2.15242	+	0.340909i	−0.0975353	+	0.0154481i	0.107476	+	0.994208i	$0.465723\pi$
$488$	1.04178	−	6.57755i	0.0471592	−	0.297752i
$489$	27.5289	−	10.4872i	1.24490	−	0.474248i
$490$	−3.59729	+	11.0713i	−0.162509	+	0.500151i
$491$	−30.1386	+	21.8970i	−1.36013	+	0.988196i	−0.361698	+	0.932295i	$0.617803\pi$
$491$	−30.1386	+	21.8970i	−1.36013	+	0.988196i	−0.998436	+	0.0559003i	$0.982197\pi$
$492$	−8.87304	+	0.442427i	−0.400028	+	0.0199461i
$493$	0.371120	−	0.120584i	0.0167144	−	0.00543084i
$494$	−17.7651	−	1.85796i	−0.799288	−	0.0835936i
$495$	−18.0778	−	25.7374i	−0.812539	−	1.15681i
$496$	−3.09807	+	3.09807i	−0.139107	+	0.139107i
$497$	−9.46588	+	3.07565i	−0.424603	+	0.137962i
$498$	−1.42575	+	1.57540i	−0.0638895	+	0.0705952i
$499$	3.03316	−	19.1506i	0.135783	−	0.857301i	−0.821933	−	0.569585i	$-0.807104\pi$
$499$	3.03316	−	19.1506i	0.135783	−	0.857301i	0.957716	−	0.287716i	$-0.0928959\pi$
$500$	0.0332319	−	0.0169325i	0.00148618	−	0.000757245i
$501$	14.3702	+	37.7218i	0.642015	+	1.68528i
$502$	3.90191	+	0.618002i	0.174151	+	0.0275828i
$503$	23.3070	−	32.0793i	1.03921	−	1.43034i	0.141400	−	0.989952i	$-0.454839\pi$
$503$	23.3070	−	32.0793i	1.03921	−	1.43034i	0.897806	−	0.440392i	$-0.145161\pi$
$504$	0.977201	+	9.77472i	0.0435280	+	0.435400i
$505$	17.8666	+	17.8666i	0.795055	+	0.795055i
$506$	−7.89852	+	17.2320i	−0.351132	+	0.766056i
$507$	−21.4041	−	6.99040i	−0.950588	−	0.310455i
$508$	3.33405	+	10.2611i	0.147924	+	0.455264i
$509$	5.20163	+	32.8418i	0.230558	+	1.45569i	0.782940	+	0.622097i	$0.213719\pi$
$509$	5.20163	+	32.8418i	0.230558	+	1.45569i	−0.552382	+	0.833591i	$0.686281\pi$
$510$	3.99367	+	6.95798i	0.176843	+	0.308104i
$511$	−18.8498	−	6.12467i	−0.833866	−	0.270939i
$512$	12.2386	−	6.23586i	0.540873	−	0.275589i
$513$	16.8637	−	32.4828i	0.744552	−	1.43415i
$514$	−2.16345	−	13.6595i	−0.0954258	−	0.602495i
$515$	11.4016	+	5.80941i	0.502415	+	0.255993i
$516$	−10.6594	−	1.14773i	−0.469256	−	0.0505258i
$517$	−22.6302	+	4.55278i	−0.995276	+	0.200231i
$518$	6.06946	−	6.06946i	0.266677	−	0.266677i
$519$	6.96937	+	33.2027i	0.305922	+	1.45744i
$520$	−20.8914	−	18.7913i	−0.916148	−	0.824052i
$521$	14.2661	+	19.6356i	0.625008	+	0.860250i	0.997706	−	0.0677027i	$-0.0215669\pi$
$521$	14.2661	+	19.6356i	0.625008	+	0.860250i	−0.372697	+	0.927953i	$0.621567\pi$
$522$	0.100349	+	0.382262i	0.00439215	+	0.0167311i
$523$	−2.04035	+	6.27956i	−0.0892184	+	0.274586i	−0.985704	−	0.168487i	$-0.946112\pi$
$523$	−2.04035	+	6.27956i	−0.0892184	+	0.274586i	0.896485	+	0.443073i	$0.146112\pi$
$524$	−21.9136	+	15.9212i	−0.957300	+	0.695519i
$525$	−11.4699	+	0.571912i	−0.500589	+	0.0249603i
$526$	0.536241	+	0.273228i	0.0233812	+	0.0119133i
$527$	−5.05590	+	5.05590i	−0.220239	+	0.220239i
$528$	−6.20354	+	3.91104i	−0.269975	+	0.170206i
$529$	43.0342			1.87105
$530$	−2.21446	−	6.81542i	−0.0961902	−	0.296043i
$531$	−43.7671	−	2.51668i	−1.89933	−	0.109215i
$532$	8.27731	+	11.3927i	0.358867	+	0.493938i
$533$	11.4673	−	4.40865i	0.496705	−	0.190960i
$534$	−1.73661	+	3.87398i	−0.0751503	+	0.167643i
$535$	−6.12180	+	38.6515i	−0.264669	+	1.67105i
$536$	−4.92990	+	6.78543i	−0.212939	+	0.293086i
$537$	−3.12438	−	14.8848i	−0.134827	−	0.642327i
$538$	2.74271	−	2.74271i	0.118247	−	0.118247i
$539$	−16.7241	−	4.67731i	−0.720356	−	0.201466i
$540$	22.1151	−	11.0568i	0.951684	−	0.475810i
$541$	−7.32798	+	14.3820i	−0.315054	+	0.618329i	−0.993177	−	0.116620i	$-0.962794\pi$
$541$	−7.32798	+	14.3820i	−0.315054	+	0.618329i	0.678122	+	0.734949i	$0.262794\pi$
$542$	−2.94130	+	4.04835i	−0.126340	+	0.173892i
$543$	−7.18285	−	12.5143i	−0.308246	−	0.537042i
$544$	10.8197	−	5.51294i	0.463893	−	0.236365i
$545$	−1.89396	+	5.82901i	−0.0811283	+	0.249687i
$546$	−2.36200	−	5.33419i	−0.101084	−	0.228282i
$547$	5.15418	+	3.74473i	0.220377	+	0.160113i	0.692496	−	0.721421i	$-0.256511\pi$
$547$	5.15418	+	3.74473i	0.220377	+	0.160113i	−0.472120	+	0.881535i	$0.656511\pi$
$548$	−2.12741	+	4.17527i	−0.0908783	+	0.178359i
$549$	−7.91778	−	1.72505i	−0.337922	−	0.0736233i
$550$	5.71228	+	10.1480i	0.243573	+	0.432713i
$551$	0.932876	+	0.932876i	0.0397418	+	0.0397418i
$552$	−29.0543	−	18.9731i	−1.23663	−	0.807550i
$553$	−1.55420	−	9.81282i	−0.0660912	−	0.417284i
$554$	0.651595	−	4.11401i	0.0276836	−	0.174788i
$555$	−45.9068	−	20.5789i	−1.94864	−	0.873525i
$556$	16.7938	+	5.45665i	0.712217	+	0.231413i
$557$	0.118630	−	0.749001i	0.00502652	−	0.0317362i	−0.985048	−	0.172282i	$-0.944886\pi$
$557$	0.118630	−	0.749001i	0.00502652	−	0.0317362i	0.990074	+	0.140546i	$0.0448858\pi$
$558$	−4.81822	−	5.40613i	−0.203971	−	0.228860i
$559$	14.5004	−	3.08993i	0.613300	−	0.130690i
$560$			5.35963i			0.226486i
$561$	−10.1239	+	6.38264i	−0.427431	+	0.269475i
$562$	−6.19445			−0.261297
$563$	−10.1522	−	31.2452i	−0.427863	−	1.31683i	−0.900226	−	0.435423i	$-0.856599\pi$
$563$	−10.1522	−	31.2452i	−0.427863	−	1.31683i	0.472363	−	0.881404i	$-0.343401\pi$
$564$	−0.903702	−	18.1241i	−0.0380527	−	0.763162i
$565$	−2.11994	+	13.3848i	−0.0891867	+	0.563102i
$566$	−3.71315	−	7.28748i	−0.156076	−	0.306315i
$567$	11.9428	−	0.504321i	0.501551	−	0.0211795i
$568$	−14.9470	+	10.8596i	−0.627161	+	0.455659i
$569$	−16.3385	−	11.8706i	−0.684944	−	0.497641i	0.190050	−	0.981774i	$-0.439135\pi$
$569$	−16.3385	−	11.8706i	−0.684944	−	0.497641i	−0.874994	+	0.484133i	$0.839135\pi$
$570$	−14.8303	+	22.7102i	−0.621173	+	0.951226i
$571$		−	26.3358i		−	1.10212i	−0.834465	−	0.551060i	$-0.814223\pi$
$571$		−	26.3358i		−	1.10212i	0.834465	−	0.551060i	$-0.185777\pi$
$572$	11.4732	−	13.8708i	0.479717	−	0.579969i
$573$	4.61994	−	42.9075i	0.193001	−	1.79249i
$574$	2.83609	+	1.44506i	0.118376	+	0.0603157i
$575$	23.8447	−	32.8194i	0.994393	−	1.36866i
$576$	1.86536	+	4.24759i	0.0777233	+	0.176983i
$577$	10.6688	+	20.9388i	0.444150	+	0.871693i	0.999205	+	0.0398794i	$0.0126974\pi$
$577$	10.6688	+	20.9388i	0.444150	+	0.871693i	−0.555055	+	0.831814i	$0.687303\pi$
$578$	−7.93355	+	4.04234i	−0.329992	+	0.168139i
$579$	−26.8239	−	7.26051i	−1.11476	−	0.301736i
$580$	0.139423	+	0.880284i	0.00578924	+	0.0365518i
$581$	−2.20315	+	0.715845i	−0.0914019	+	0.0296983i
$582$	6.91022	+	0.744038i	0.286438	+	0.0308414i
$583$	10.0214	−	3.72195i	0.415044	−	0.154147i
$584$	−36.7910			−1.52242
$585$	−24.2874	+	24.0667i	−1.00416	+	0.995035i
$586$	14.6625	+	10.6529i	0.605701	+	0.440068i
$587$	17.5465	+	2.77909i	0.724220	+	0.114705i	0.507652	−	0.861562i	$-0.330514\pi$
$587$	17.5465	+	2.77909i	0.724220	+	0.114705i	0.216568	+	0.976268i	$0.430514\pi$
$588$	5.58429	−	12.4573i	0.230292	−	0.513730i
$589$	−22.9906	−	7.47010i	−0.947311	−	0.307800i
$590$	32.0891	+	5.08242i	1.32109	+	0.209240i
$591$	−1.43468	−	28.7731i	−0.0590149	−	1.18357i
$592$	−5.32538	+	10.4516i	−0.218872	+	0.429560i
$593$	22.3269	−	22.3269i	0.916854	−	0.916854i	−0.0799451	−	0.996799i	$-0.525474\pi$
$593$	22.3269	−	22.3269i	0.916854	−	0.916854i	0.996799	+	0.0799451i	$0.0254745\pi$
$594$	−5.86506	−	10.6077i	−0.240646	−	0.435238i
$595$			8.74667i			0.358578i
$596$	−6.52646	−	3.32540i	−0.267334	−	0.136214i
$597$	21.3267	−	23.5651i	0.872843	−	0.964454i
$598$	19.9079	+	5.32334i	0.814093	+	0.217687i
$599$	19.2557	+	6.25656i	0.786767	+	0.255636i	0.674727	−	0.738068i	$-0.264262\pi$
$599$	19.2557	+	6.25656i	0.786767	+	0.255636i	0.112040	+	0.993704i	$0.464262\pi$
$600$	−19.9212	+	7.58903i	−0.813278	+	0.309821i
$601$	9.59371	−	6.97024i	0.391335	−	0.284322i	−0.374667	−	0.927159i	$-0.622243\pi$
$601$	9.59371	−	6.97024i	0.391335	−	0.284322i	0.766003	+	0.642838i	$0.222243\pi$
$602$	3.10759	+	2.25779i	0.126656	+	0.0920208i
$603$	7.89871	+	6.46295i	0.321661	+	0.263191i
$604$	12.0095	−	12.0095i	0.488659	−	0.488659i
$605$	−29.5680	+	18.2972i	−1.20211	+	0.743887i
$606$	6.10886	+	7.58310i	0.248155	+	0.308042i
$607$	13.6115	+	41.8919i	0.552474	+	1.70034i	0.702521	+	0.711663i	$0.252057\pi$
$607$	13.6115	+	41.8919i	0.552474	+	1.70034i	−0.150047	+	0.988679i	$0.547943\pi$
$608$	33.2142	+	24.1316i	1.34702	+	0.978664i
$609$	−0.112577	+	0.415915i	−0.00456184	+	0.0168537i
$610$	5.71154	+	1.85579i	0.231253	+	0.0751388i
$611$	9.00512	+	23.4232i	0.364308	+	0.947600i
$612$	−3.78300	−	8.61422i	−0.152919	−	0.348209i
$613$	−11.5561	+	1.83030i	−0.466745	+	0.0739252i	−0.385378	−	0.922759i	$-0.625929\pi$
$613$	−11.5561	+	1.83030i	−0.466745	+	0.0739252i	−0.0813678	+	0.996684i	$0.525929\pi$
$614$	10.1023	−	3.28243i	0.407695	−	0.132468i
$615$	1.99717	−	18.5486i	0.0805337	−	0.747952i
$616$	10.8509	−	0.450043i	0.437195	−	0.0181328i
$617$	5.82073	+	5.82073i	0.234334	+	0.234334i	0.814499	−	0.580165i	$-0.197012\pi$
$617$	5.82073	+	5.82073i	0.234334	+	0.234334i	−0.580165	+	0.814499i	$0.697012\pi$
$618$	4.12909	+	2.69639i	0.166096	+	0.108465i
$619$	−1.94357	−	12.2712i	−0.0781187	−	0.493222i	−0.995465	−	0.0951313i	$-0.969673\pi$
$619$	−1.94357	−	12.2712i	−0.0781187	−	0.493222i	0.917346	−	0.398091i	$-0.130327\pi$
$620$	−9.59902	−	13.2119i	−0.385506	−	0.530603i
$621$	−25.0785	+	33.9704i	−1.00637	+	1.36319i
$622$	8.60173	−	4.38280i	0.344898	−	0.175734i
$623$	−3.74457	+	2.72059i	−0.150023	+	0.108998i
$624$	5.32253	+	5.93541i	0.213072	+	0.237606i
$625$	7.73752	+	23.8136i	0.309501	+	0.952545i
$626$	−1.32649	−	1.32649i	−0.0530171	−	0.0530171i
$627$	−34.7661	−	20.7005i	−1.38842	−	0.826698i
$628$			4.49269i			0.179278i
$629$	−8.69078	+	17.0566i	−0.346524	+	0.680092i
$630$	−8.84402	−	0.508545i	−0.352354	−	0.0202609i
$631$	22.5559	+	3.57250i	0.897935	+	0.142219i	0.588306	−	0.808638i	$-0.299795\pi$
$631$	22.5559	+	3.57250i	0.897935	+	0.142219i	0.309629	+	0.950857i	$0.399795\pi$
$632$	−8.37263	−	16.4322i	−0.333045	−	0.653638i
$633$	8.53418	−	19.0378i	0.339203	−	0.756686i
$634$	−4.55866	−	6.27446i	−0.181048	−	0.249191i
$635$	−22.3775	+	3.54425i	−0.888025	+	0.140649i
$636$	1.72638	+	8.22464i	0.0684556	+	0.326128i
$637$	−1.96371	+	18.7762i	−0.0778051	+	0.743941i
$638$	0.428343	−	0.0861746i	0.0169583	−	0.00341168i
$639$	12.1484	+	18.9165i	0.480583	+	0.748326i
$640$	10.3248	+	31.7764i	0.408122	+	1.25607i
$641$	13.9828	+	10.1591i	0.552288	+	0.401261i	0.828628	−	0.559799i	$-0.189122\pi$
$641$	13.9828	+	10.1591i	0.552288	+	0.401261i	−0.276340	+	0.961060i	$0.589122\pi$
$642$	−3.94034	+	14.5576i	−0.155513	+	0.574542i
$643$	−11.5243	−	22.6177i	−0.454475	−	0.891957i	−0.998597	−	0.0529510i	$-0.983137\pi$
$643$	−11.5243	−	22.6177i	−0.454475	−	0.891957i	0.544122	−	0.839006i	$-0.316863\pi$
$644$	−7.37580	−	14.4758i	−0.290647	−	0.570427i
$645$	5.88209	−	21.7314i	0.231607	−	0.855672i
$646$	8.34983	+	6.06650i	0.328520	+	0.238683i
$647$	0.969034	+	2.98238i	0.0380967	+	0.117249i	0.968296	−	0.249805i	$-0.0803664\pi$
$647$	0.969034	+	2.98238i	0.0380967	+	0.117249i	−0.930200	+	0.367054i	$0.880366\pi$
$648$	20.7947	−	7.74095i	0.816895	−	0.304093i
$649$	−5.59159	+	48.1426i	−0.219489	+	1.88976i
$650$	9.83438	−	7.97209i	0.385736	−	0.312691i
$651$	−1.62189	−	7.72681i	−0.0635668	−	0.302837i
$652$	25.2872	−	4.00510i	0.990324	−	0.156852i
$653$	−13.8282	−	19.0329i	−0.541140	−	0.744815i	0.447637	−	0.894215i	$-0.352266\pi$
$653$	−13.8282	−	19.0329i	−0.541140	−	0.744815i	−0.988777	+	0.149400i	$0.952266\pi$
$654$	−0.966197	+	2.15537i	−0.0377813	+	0.0842816i
$655$	−25.8229	−	50.6803i	−1.00898	−	1.98024i
$656$	−4.29634	−	0.680473i	−0.167744	−	0.0265680i
$657$	−2.57001	+	44.6945i	−0.100265	+	1.74370i
$658$	−2.95169	+	5.79301i	−0.115069	+	0.225835i
$659$			24.6688i			0.960962i	0.877005	+	0.480481i	$0.159538\pi$
$659$			24.6688i			0.960962i	−0.877005	+	0.480481i	$0.840462\pi$
$660$	−10.7812	−	25.1187i	−0.419658	−	0.977744i
$661$	−6.56885	−	6.56885i	−0.255499	−	0.255499i	0.567722	−	0.823220i	$-0.307825\pi$
$661$	−6.56885	−	6.56885i	−0.255499	−	0.255499i	−0.823220	+	0.567722i	$0.807825\pi$
$662$	−5.46872	−	16.8310i	−0.212548	−	0.654154i
$663$	8.68613	+	9.68632i	0.337341	+	0.376185i
$664$	−3.47885	+	2.52753i	−0.135006	+	0.0980873i
$665$	−26.3484	+	13.4252i	−1.02175	+	0.520606i
$666$	−16.7412	−	9.77921i	−0.648707	−	0.378937i
$667$	−0.894642	−	1.23137i	−0.0346407	−	0.0476788i
$668$	5.48804	+	34.6501i	0.212339	+	1.34065i
$669$	26.8445	+	17.5301i	1.03787	+	0.677753i
$670$	−5.34820	−	5.34820i	−0.206619	−	0.206619i
$671$	−2.41296	+	8.62770i	−0.0931512	+	0.333069i
$672$	−1.43544	+	13.3316i	−0.0553734	+	0.514278i
$673$	19.4689	−	6.32582i	0.750469	−	0.243842i	0.0912863	−	0.995825i	$-0.470902\pi$
$673$	19.4689	−	6.32582i	0.750469	−	0.243842i	0.659183	+	0.751982i	$0.270902\pi$
$674$	−9.50132	+	1.50486i	−0.365977	+	0.0579651i
$675$	7.82775	+	24.7308i	0.301290	+	0.951888i
$676$	−16.9574	−	9.76713i	−0.652206	−	0.375659i
$677$	−42.7968	−	13.9055i	−1.64481	−	0.534432i	−0.667206	−	0.744873i	$-0.732510\pi$
$677$	−42.7968	−	13.9055i	−1.64481	−	0.534432i	−0.977607	+	0.210441i	$0.932510\pi$
$678$	−1.36452	+	5.04120i	−0.0524039	+	0.193606i
$679$	6.13024	+	4.45388i	0.235257	+	0.170924i
$680$	5.01725	+	15.4415i	0.192403	+	0.592155i
$681$	−21.2294	−	26.3527i	−0.813513	−	1.00984i
$682$	−6.27638	+	4.97014i	−0.240335	+	0.190316i
$683$	−8.75685	+	8.75685i	−0.335071	+	0.335071i	−0.854509	−	0.519437i	$-0.826142\pi$
$683$	−8.75685	+	8.75685i	−0.335071	+	0.335071i	0.519437	+	0.854509i	$0.326142\pi$
$684$	20.1429	−	24.6177i	0.770184	−	0.941283i
$685$	−7.96093	−	5.78396i	−0.304172	−	0.220994i
$686$	−9.24724	+	6.71851i	−0.353061	+	0.256514i
$687$	−4.36144	+	1.66151i	−0.166399	+	0.0633904i
$688$	−4.99241	−	1.62213i	−0.190334	−	0.0618433i
$689$	−5.81594	−	10.0616i	−0.221569	−	0.383315i
$690$	20.9977	−	23.2016i	0.799370	−	0.883269i
$691$	34.7713	+	17.7169i	1.32276	+	0.673981i	0.965593	−	0.260058i	$-0.0837416\pi$
$691$	34.7713	+	17.7169i	1.32276	+	0.673981i	0.357170	+	0.934039i	$0.383742\pi$
$692$			29.4851i			1.12085i
$693$	0.211258	−	13.2133i	0.00802504	−	0.501933i
$694$	−3.39186	+	3.39186i	−0.128753	+	0.128753i
$695$	−16.8342	+	33.0390i	−0.638558	+	1.25324i
$696$	0.0398316	+	0.798839i	0.00150981	+	0.0302799i
$697$	−7.01143	−	1.11050i	−0.265577	−	0.0420632i
$698$	5.86583	+	1.90592i	0.222025	+	0.0721402i
$699$	3.73221	−	8.32571i	0.141165	−	0.314907i
$700$	−9.85794	−	1.56134i	−0.372595	−	0.0590133i
$701$	16.1400	+	11.7264i	0.609601	+	0.442901i	0.849274	−	0.527953i	$-0.177040\pi$
$701$	16.1400	+	11.7264i	0.609601	+	0.442901i	−0.239673	+	0.970854i	$0.577040\pi$
$702$	−10.2991	+	8.21963i	−0.388716	+	0.310230i
$703$	−64.7206			−2.44098
$704$	4.80787	−	1.78564i	0.181204	−	0.0672990i
$705$	37.8875	+	4.07943i	1.42692	+	0.153640i
$706$	−17.9746	+	5.84032i	−0.676485	+	0.219803i
$707$	1.66078	+	10.4857i	0.0624599	+	0.394357i
$708$	−36.7771	−	9.95456i	−1.38217	−	0.374115i
$709$	5.17551	−	2.63705i	0.194370	−	0.0990366i	−0.354097	−	0.935209i	$-0.615212\pi$
$709$	5.17551	−	2.63705i	0.194370	−	0.0990366i	0.548467	+	0.836172i	$0.315212\pi$
$710$	−7.56389	−	14.8450i	−0.283868	−	0.557122i
$711$	−20.5471	+	9.02339i	−0.770575	+	0.338404i
$712$	−5.05015	+	6.95094i	−0.189263	+	0.260497i
$713$	24.8494	+	12.6614i	0.930619	+	0.474174i
$714$	−0.360860	+	3.35147i	−0.0135049	+	0.125426i
$715$	25.0001	+	28.3527i	0.934951	+	1.06033i
$716$		−	13.2182i		−	0.493988i
$717$	5.03228	−	7.70612i	0.187934	−	0.287790i
$718$	−12.2377	−	8.89121i	−0.456707	−	0.331817i
$719$	1.85976	−	1.35119i	0.0693573	−	0.0503910i	−0.552566	−	0.833469i	$-0.686351\pi$
$719$	1.85976	−	1.35119i	0.0693573	−	0.0503910i	0.621924	+	0.783078i	$0.286351\pi$
$720$	11.7094	−	3.07387i	0.436383	−	0.114556i
$721$	2.44092	+	4.79057i	0.0909045	+	0.178410i
$722$	−3.36811	+	21.2654i	−0.125348	+	0.791418i
$723$	1.31848	+	26.4427i	0.0490349	+	0.983414i
$724$	−3.87518	−	11.9266i	−0.144020	−	0.443247i
$725$	−0.935050			−0.0347269
$726$	−12.0845	+	5.79108i	−0.448497	+	0.214927i
$727$		−	32.4779i		−	1.20454i	−0.798293	−	0.602269i	$-0.794263\pi$
$727$		−	32.4779i		−	1.20454i	0.798293	−	0.602269i	$-0.205737\pi$
$728$	−2.46060	−	11.5470i	−0.0911959	−	0.427962i
$729$	−7.95128	−	25.8027i	−0.294492	−	0.955654i
$730$	5.19011	−	32.7691i	0.192095	−	1.21284i
$731$	−8.14739	−	2.64725i	−0.301342	−	0.0979120i
$732$	−6.42654	−	2.88086i	−0.237532	−	0.106480i
$733$	−1.83465	+	11.5835i	−0.0677643	+	0.427847i	0.930361	+	0.366645i	$0.119494\pi$
$733$	−1.83465	+	11.5835i	−0.0677643	+	0.427847i	−0.998125	+	0.0612024i	$0.980506\pi$
$734$	3.05795	+	19.3071i	0.112871	+	0.712639i
$735$	24.0028	+	15.6744i	0.885357	+	0.578159i
$736$	−33.4922	−	33.4922i	−1.23454	−	1.23454i
$737$	7.64081	−	8.30204i	0.281453	−	0.305810i
$738$	1.53052	−	7.02490i	0.0563391	−	0.258590i
$739$	11.3429	−	22.2616i	0.417254	−	0.818907i	−0.582726	−	0.812668i	$-0.698014\pi$
$739$	11.3429	−	22.2616i	0.417254	−	0.818907i	0.999981	−	0.00623890i	$-0.00198592\pi$
$740$	−35.3724	−	25.6995i	−1.30031	−	0.944733i
$741$	−15.8467	+	41.0334i	−0.582143	+	1.50740i
$742$	0.930443	−	2.86361i	0.0341576	−	0.105126i
$743$	−10.7778	+	5.49155i	−0.395398	+	0.201465i	−0.640373	−	0.768064i	$-0.721220\pi$
$743$	−10.7778	+	5.49155i	−0.395398	+	0.201465i	0.244975	+	0.969529i	$0.421220\pi$
$744$	−7.29555	−	12.7107i	−0.267468	−	0.465997i
$745$	9.04103	−	12.4439i	0.331238	−	0.455910i
$746$	3.90487	−	7.66374i	0.142967	−	0.280589i
$747$	2.82749	+	4.40274i	0.103452	+	0.161088i
$748$	−9.75049	+	3.62133i	−0.356513	+	0.132409i
$749$	−11.6266	+	11.6266i	−0.424827	+	0.424827i
$750$	0.00620056	+	0.0295400i	0.000226412	+	0.00107865i
$751$	−15.2682	+	21.0149i	−0.557145	+	0.766845i	−0.990960	−	0.134157i	$-0.957167\pi$
$751$	−15.2682	+	21.0149i	−0.557145	+	0.766845i	0.433815	+	0.901002i	$0.357167\pi$
$752$	1.38994	−	8.77571i	0.0506857	−	0.320017i
$753$	3.97956	−	8.87750i	0.145023	−	0.323514i
$754$	−0.170448	−	0.443352i	−0.00620736	−	0.0161459i
$755$	20.9633	+	28.8536i	0.762934	+	1.05009i
$756$	10.2481	+	1.70326i	0.372719	+	0.0619470i
$757$	−8.72023	−	26.8381i	−0.316942	−	0.975448i	−0.974948	−	0.222434i	$-0.928600\pi$
$757$	−8.72023	−	26.8381i	−0.316942	−	0.975448i	0.658006	−	0.753013i	$-0.271400\pi$
$758$	−5.97907			−0.217169
$759$	35.8797	+	29.8626i	1.30235	+	1.08394i
$760$	−38.8150	+	38.8150i	−1.40797	+	1.40797i
$761$	−6.27403	−	3.19678i	−0.227434	−	0.115883i	0.336561	−	0.941662i	$-0.390736\pi$
$761$	−6.27403	−	3.19678i	−0.227434	−	0.115883i	−0.563995	+	0.825778i	$0.690736\pi$
$762$	−8.72064	+	0.434828i	−0.315915	+	0.0157521i
$763$	−2.08337	+	1.51366i	−0.0754231	+	0.0547981i
$764$	11.5900	−	35.6705i	0.419313	−	1.29051i
$765$	19.1092	−	5.01642i	0.690894	−	0.181369i
$766$	9.08970	+	12.5109i	0.328424	+	0.452037i
$767$	52.6148	−	2.78452i	1.89981	−	0.100543i
$768$	3.74559	+	17.8443i	0.135157	+	0.643901i
$769$	−14.2900	+	14.2900i	−0.515309	+	0.515309i	−0.916148	−	0.400839i	$-0.868719\pi$
$769$	−14.2900	+	14.2900i	−0.515309	+	0.515309i	0.400839	+	0.916148i	$0.368719\pi$
$770$	−1.12989	+	9.72819i	−0.0407185	+	0.350579i
$771$	−33.8616	−	3.64596i	−1.21950	−	0.131306i
$772$	−21.5191	−	10.9645i	−0.774488	−	0.394621i
$773$	−2.92103	−	18.4427i	−0.105062	−	0.663336i	−0.982867	−	0.184317i	$-0.940993\pi$
$773$	−2.92103	−	18.4427i	−0.105062	−	0.663336i	0.877805	−	0.479019i	$-0.159007\pi$
$774$	3.15041	−	8.08416i	0.113239	−	0.290579i
$775$	15.2658	−	7.77834i	0.548365	−	0.279406i
$776$	13.3773	+	4.34654i	0.480216	+	0.156032i
$777$	−10.5224	−	18.3327i	−0.377489	−	0.657682i
$778$	0.316002	+	1.99516i	0.0113292	+	0.0715299i
$779$	−7.41650	−	22.8256i	−0.265724	−	0.817814i
$780$	−24.9546	+	16.1339i	−0.893518	+	0.577687i
$781$	21.6587	−	12.1916i	0.775008	−	0.436249i
$782$	−8.41970	−	8.41970i	−0.301088	−	0.301088i
$783$	0.973230	+	0.00741392i	0.0347804	+	0.000264952i
$784$	3.92891	−	5.40767i	0.140318	−	0.193131i
$785$	−9.31813	−	1.47585i	−0.332578	−	0.0526752i
$786$	−7.80368	−	20.4846i	−0.278348	−	0.730662i
$787$	44.0466	−	22.4429i	1.57009	−	0.800001i	0.570321	−	0.821422i	$-0.306819\pi$
$787$	44.0466	−	22.4429i	1.57009	−	0.800001i	0.999771	+	0.0214207i	$0.00681895\pi$
$788$	3.91674	−	24.7293i	0.139528	−	0.880945i
$789$	0.994506	−	1.09889i	0.0354054	−	0.0391214i
$790$	15.8170	−	5.13925i	0.562744	−	0.182846i
$791$	−4.02622	+	4.02622i	−0.143156	+	0.143156i
$792$	−7.20647	−	23.4483i	−0.256071	−	0.833197i
$793$	9.68638	+	1.01305i	0.343974	+	0.0359745i
$794$	−1.42861	+	0.464185i	−0.0506996	+	0.0164733i
$795$	−17.6256	+	0.878844i	−0.625114	+	0.0311694i
$796$	22.3468	−	16.2359i	0.792060	−	0.575465i
$797$	−14.2664	+	43.9074i	−0.505341	+	1.55528i	0.294855	+	0.955542i	$0.404729\pi$
$797$	−14.2664	+	43.9074i	−0.505341	+	1.55528i	−0.800196	+	0.599738i	$0.795271\pi$
$798$	−10.6498	+	4.05709i	−0.377000	+	0.143619i
$799$	2.26831	−	14.3216i	0.0802471	−	0.506660i
$800$	−28.7397	+	4.55193i	−1.01610	+	0.160935i
$801$	8.09138	+	6.62059i	0.285895	+	0.233927i
$802$	−11.3891			−0.402164
$803$	49.1628	+	5.71007i	1.73492	+	0.201504i
$804$	5.56445	+	6.90731i	0.196243	+	0.243602i
$805$	32.4468	−	10.5426i	1.14360	−	0.371577i
$806$	6.47086	+	5.82037i	0.227926	+	0.205014i
$807$	−4.75494	−	8.28431i	−0.167382	−	0.291621i
$808$	8.94678	+	17.5590i	0.314747	+	0.617725i
$809$	23.8242	+	7.74094i	0.837613	+	0.272157i	0.696249	−	0.717800i	$-0.254851\pi$
$809$	23.8242	+	7.74094i	0.837613	+	0.272157i	0.141365	+	0.989958i	$0.454851\pi$
$810$	3.96121	+	19.6135i	0.139183	+	0.689149i
$811$	26.9000	−	4.26054i	0.944586	−	0.149608i	0.334903	−	0.942253i	$-0.391297\pi$
$811$	26.9000	−	4.26054i	0.944586	−	0.149608i	0.609683	+	0.792645i	$0.291297\pi$
$812$	−0.170008	+	0.333660i	−0.00596613	+	0.0117092i
$813$	7.73078	+	9.59644i	0.271130	+	0.336562i
$814$	−11.8694	+	17.8480i	−0.416022	+	0.625571i
$815$			53.7630i			1.88324i
$816$	−0.946314	−	4.50832i	−0.0331276	−	0.157823i
$817$	−4.53080	−	28.6064i	−0.158513	−	1.00081i
$818$	12.1384	−	8.81903i	0.424408	−	0.308350i
$819$	−14.1995	+	2.18258i	−0.496170	+	0.0762656i
$820$	5.01029	−	15.4201i	0.174967	−	0.538493i
$821$	−13.5264	−	2.14236i	−0.472073	−	0.0747690i	−0.0841347	−	0.996454i	$-0.526813\pi$
$821$	−13.5264	−	2.14236i	−0.472073	−	0.0747690i	−0.387938	+	0.921685i	$0.626813\pi$
$822$	−2.81177	−	2.54469i	−0.0980718	−	0.0887562i
$823$	−32.4396	+	10.5403i	−1.13077	+	0.367411i	−0.813870	−	0.581047i	$-0.802643\pi$
$823$	−32.4396	+	10.5403i	−1.13077	+	0.367411i	−0.316904	+	0.948458i	$0.602643\pi$
$824$	7.05720	+	7.05720i	0.245849	+	0.245849i
$825$	27.7979	−	7.04919i	0.967799	−	0.245421i
$826$	9.65259	+	9.65259i	0.335856	+	0.335856i
$827$	35.8008	+	18.2414i	1.24492	+	0.634317i	0.947294	−	0.320367i	$-0.103806\pi$
$827$	35.8008	+	18.2414i	1.24492	+	0.634317i	0.297623	+	0.954683i	$0.403806\pi$
$828$	−27.3957	+	24.4164i	−0.952066	+	0.848529i
$829$	−20.6338	−	28.3999i	−0.716640	−	0.986371i	−0.999629	−	0.0272475i	$-0.991326\pi$
$829$	−20.6338	−	28.3999i	−0.716640	−	0.986371i	0.282988	−	0.959123i	$-0.408674\pi$
$830$	−1.76047	−	3.45511i	−0.0611067	−	0.119929i
$831$	−9.36006	−	4.19588i	−0.324697	−	0.145553i
$832$	−2.79025	−	4.82713i	−0.0967346	−	0.167351i
$833$	6.41180	−	8.82508i	0.222156	−	0.305771i
$834$	−7.81347	+	11.9651i	−0.270558	+	0.414316i
$835$	−73.6695			−2.54944
$836$	−25.8748	−	23.8139i	−0.894898	−	0.823622i
$837$	−15.9509	+	7.97490i	−0.551342	+	0.275653i
$838$	13.5642	+	6.91131i	0.468568	+	0.238747i
$839$	0.492717	−	0.0780387i	0.0170105	−	0.00269420i	−0.147923	−	0.988999i	$-0.547259\pi$
$839$	0.492717	−	0.0780387i	0.0170105	−	0.00269420i	0.164934	+	0.986305i	$0.447259\pi$
$840$	−17.3053	−	4.68407i	−0.597090	−	0.161616i
$841$	8.95065	−	27.5473i	0.308643	−	0.949906i
$842$	6.80704	−	20.9499i	0.234586	−	0.721982i
$843$	−3.98556	+	14.7247i	−0.137270	+	0.507144i
$844$	10.6577	−	14.6691i	0.366855	−	0.504932i
$845$	25.8282	−	31.9622i	0.888516	−	1.09953i
$846$	14.3491	+	3.12624i	0.493331	+	0.107482i
$847$	−14.5696	−	1.08271i	−0.500617	−	0.0372024i
$848$			4.11477i			0.141302i
$849$	−19.7119	+	4.13762i	−0.676512	+	0.142003i
$850$	−7.22496	+	1.14432i	−0.247814	+	0.0392499i
$851$	73.7486	+	11.6806i	2.52807	+	0.400407i
$852$	6.95564	+	18.2585i	0.238296	+	0.625526i
$853$	−33.3766	+	17.0062i	−1.14279	+	0.582281i	−0.919741	−	0.392526i	$-0.871601\pi$
$853$	−33.3766	+	17.0062i	−1.14279	+	0.582281i	−0.223050	+	0.974807i	$0.571601\pi$
$854$	1.48315	+	2.04139i	0.0507525	+	0.0698548i
$855$	44.4419	+	49.8647i	1.51988	+	1.70534i
$856$	−13.8566	+	27.1950i	−0.473608	+	0.929507i
$857$	−40.1443			−1.37130			−0.685652	−	0.727929i	$-0.740483\pi$
$857$	−40.1443			−1.37130			−0.685652	+	0.727929i	$0.740483\pi$
$858$	8.40958	+	11.8953i	0.287098	+	0.406100i
$859$	13.9289			0.475248			0.237624	−	0.971357i	$-0.423631\pi$
$859$	13.9289			0.475248			0.237624	+	0.971357i	$0.423631\pi$
$860$	8.88288	−	17.4336i	0.302904	−	0.594482i
$861$	5.25978	−	5.81184i	0.179253	−	0.198067i
$862$	9.57382	+	13.1772i	0.326086	+	0.448818i
$863$	13.1637	−	6.70722i	0.448096	−	0.228316i	−0.215355	−	0.976536i	$-0.569091\pi$
$863$	13.1637	−	6.70722i	0.448096	−	0.228316i	0.663451	+	0.748219i	$0.269091\pi$
$864$	29.9493	−	4.50991i	1.01890	−	0.153430i
$865$	−61.1540	−	9.68584i	−2.07930	−	0.329328i
$866$	2.95378	−	0.467833i	0.100374	−	0.0158976i
$867$	4.50444	+	21.4595i	0.152979	+	0.728803i
$868$		−	6.86166i		−	0.232900i
$869$	8.63778	+	23.2574i	0.293017	+	0.788952i
$870$	−0.717131	−	0.0772150i	−0.0243130	−	0.00261784i
$871$	−10.2905	−	6.67521i	−0.348680	−	0.226181i
$872$	−2.80976	+	3.86730i	−0.0951504	+	0.130963i
$873$	6.21473	−	15.9474i	0.210337	−	0.539737i
$874$	12.4401	−	38.2867i	0.420793	−	1.29507i
$875$	−0.0101690	+	0.0312971i	−0.000343777	+	0.00105804i
$876$	−10.1655	+	37.5564i	−0.343460	+	1.26891i
$877$	6.69782	−	1.06083i	0.226169	−	0.0358217i	−0.0423211	−	0.999104i	$-0.513475\pi$
$877$	6.69782	−	1.06083i	0.226169	−	0.0358217i	0.268490	+	0.963282i	$0.413475\pi$
$878$	−16.9326	−	8.62760i	−0.571448	−	0.291167i
$879$	34.7567	−	27.9996i	1.17232	−	0.944403i
$880$	−2.63968	−	13.1209i	−0.0889838	−	0.442307i
$881$	9.55941			0.322065			0.161032	−	0.986949i	$-0.448518\pi$
$881$	9.55941			0.322065			0.161032	+	0.986949i	$0.448518\pi$
$882$	8.55051	+	6.99626i	0.287911	+	0.235576i
$883$	−23.7875	+	32.7407i	−0.800514	+	1.10181i	0.192205	+	0.981355i	$0.438436\pi$
$883$	−23.7875	+	32.7407i	−0.800514	+	1.10181i	−0.992718	+	0.120458i	$0.961564\pi$
$884$	5.65871	+	9.78955i	0.190323	+	0.329258i
$885$	32.7277	−	73.0081i	1.10013	−	2.45414i
$886$	−0.222623	−	0.436923i	−0.00747917	−	0.0146787i
$887$	−3.46193	−	4.76493i	−0.116240	−	0.159991i	0.746932	−	0.664900i	$-0.231526\pi$
$887$	−3.46193	−	4.76493i	−0.116240	−	0.159991i	−0.863172	+	0.504909i	$0.831526\pi$
$888$	−29.0924	−	26.3290i	−0.976278	−	0.883544i
$889$	−8.48191	−	4.32175i	−0.284474	−	0.144947i
$890$	−5.47865	−	5.47865i	−0.183645	−	0.183645i
$891$	−28.9889	+	7.11661i	−0.971163	+	0.238416i
$892$	19.7031	+	19.7031i	0.659708	+	0.659708i
$893$	46.6237	−	15.1490i	1.56020	−	0.506941i
$894$	3.97766	−	4.39514i	0.133033	−	0.146996i
$895$	27.4154	+	4.34218i	0.916397	+	0.145143i
$896$	−4.33812	+	13.3513i	−0.144926	+	0.446037i
$897$	25.4628	−	43.8974i	0.850180	−	1.46569i
$898$	−2.15881	+	1.56846i	−0.0720403	+	0.0523403i
$899$	−0.100561	−	0.634918i	−0.00335390	−	0.0211757i
$900$	2.24263	+	22.4325i	0.0747543	+	0.747750i
$901$			6.71513i			0.223713i
$902$	−7.65477	−	2.14085i	−0.254876	−	0.0712825i
$903$	7.36639	−	5.93428i	0.245138	−	0.197480i
$904$	−4.79844	+	9.41748i	−0.159594	+	0.313221i
$905$	26.0095	−	4.11950i	0.864584	−	0.136937i
$906$	6.84214	+	11.9207i	0.227315	+	0.396040i
$907$	22.0599	+	7.16770i	0.732488	+	0.238000i	0.651429	−	0.758710i	$-0.274170\pi$
$907$	22.0599	+	7.16770i	0.732488	+	0.238000i	0.0810587	+	0.996709i	$0.474170\pi$
$908$	−13.3520	−	26.2047i	−0.443100	−	0.869633i
$909$	21.9561	−	9.64217i	0.728237	−	0.319811i
$910$	10.6319	−	0.562668i	0.352443	−	0.0186523i
$911$	24.8422	−	8.07171i	0.823057	−	0.267428i	0.132939	−	0.991124i	$-0.457558\pi$
$911$	24.8422	−	8.07171i	0.823057	−	0.267428i	0.690118	+	0.723697i	$0.257558\pi$
$912$	12.1283	−	9.77044i	0.401609	−	0.323531i
$913$	5.04097	−	2.83754i	0.166832	−	0.0939090i
$914$	2.66300			0.0880841
$915$	8.08621	−	12.3827i	0.267322	−	0.409360i
$916$	−4.00630	+	0.634535i	−0.132372	+	0.0209656i
$917$	3.73863	−	23.6048i	0.123460	−	0.779498i
$918$	7.52905	−	1.13376i	0.248496	−	0.0374197i
$919$	4.14814	−	12.7667i	0.136834	−	0.421133i	−0.859036	−	0.511915i	$-0.828936\pi$
$919$	4.14814	−	12.7667i	0.136834	−	0.421133i	0.995871	+	0.0907813i	$0.0289364\pi$
$920$	51.2346	−	37.2241i	1.68916	−	1.22724i
$921$	−1.30268	−	26.1258i	−0.0429249	−	0.860876i
$922$	−26.4164	+	8.58322i	−0.869979	+	0.282673i
$923$	−17.0146	−	20.9893i	−0.560044	−	0.690871i
$924$	2.53874	−	11.2010i	0.0835184	−	0.368486i
$925$	32.4357	−	32.4357i	1.06648	−	1.06648i
$926$	14.3832	−	4.67339i	0.472661	−	0.153577i
$927$	9.06622	−	8.08027i	0.297774	−	0.265391i
$928$	−0.170786	+	1.07830i	−0.00560633	+	0.0353970i
$929$	−8.84879	+	4.50868i	−0.290319	+	0.147925i	−0.593085	−	0.805140i	$-0.702090\pi$
$929$	−8.84879	+	4.50868i	−0.290319	+	0.147925i	0.302765	+	0.953065i	$0.402090\pi$
$930$	12.3504	−	4.70492i	0.404985	−	0.154280i
$931$	36.4260	+	5.76931i	1.19381	+	0.189081i
$932$	4.66089	−	6.41517i	0.152673	−	0.210136i
$933$	−4.88381	−	23.2669i	−0.159889	−	0.761724i
$934$	19.2635	+	19.2635i	0.630320	+	0.630320i
$935$	−4.30785	−	21.4128i	−0.140882	−	0.700272i
$936$	−23.8161	+	11.9983i	−0.778452	+	0.392176i
$937$	5.07793	+	15.6283i	0.165889	+	0.510554i	0.999101	−	0.0424004i	$-0.0135005\pi$
$937$	5.07793	+	15.6283i	0.165889	+	0.510554i	−0.833212	+	0.552954i	$0.813501\pi$
$938$	−0.497137	−	3.13880i	−0.0162321	−	0.102485i
$939$	−4.00663	+	2.29968i	−0.130751	+	0.0750474i
$940$	31.4971	+	10.2340i	1.02732	+	0.333798i
$941$	2.13221	−	1.08642i	0.0695081	−	0.0354161i	−0.418891	−	0.908037i	$-0.637581\pi$
$941$	2.13221	−	1.08642i	0.0695081	−	0.0354161i	0.488399	+	0.872620i	$0.337581\pi$
$942$	−3.50955	−	0.949939i	−0.114347	−	0.0309507i
$943$	4.33153	+	27.3482i	0.141054	+	0.890580i
$944$	−16.6218	−	8.46923i	−0.540994	−	0.275650i
$945$	−6.89917	+	20.6957i	−0.224430	+	0.673231i
$946$	−8.71969	−	3.99679i	−0.283502	−	0.129947i
$947$	−19.4322	+	19.4322i	−0.631462	+	0.631462i	−0.948435	−	0.316973i	$-0.897334\pi$
$947$	−19.4322	+	19.4322i	−0.631462	+	0.631462i	0.316973	+	0.948435i	$0.397334\pi$
$948$	−19.0875	+	4.00654i	−0.619932	+	0.130126i
$949$	−2.84352	−	53.7296i	−0.0923046	−	1.74414i
$950$	−14.5367	−	20.0080i	−0.471632	−	0.649145i
$951$	−17.8479	+	6.79923i	−0.578759	+	0.220480i
$952$	−2.10808	+	6.48800i	−0.0683233	+	0.210277i
$953$	5.60048	−	4.06898i	0.181417	−	0.131807i	−0.493370	−	0.869819i	$-0.664235\pi$
$953$	5.60048	−	4.06898i	0.181417	−	0.131807i	0.674788	+	0.738012i	$0.264235\pi$
$954$	−6.78986	−	0.390428i	−0.219830	−	0.0126406i
$955$	70.1756	+	35.7562i	2.27083	+	1.15704i
$956$	5.65606	−	5.65606i	0.182930	−	0.182930i
$957$	0.0707563	−	1.07365i	0.00228723	−	0.0347061i
$958$	4.64780			0.150163
$959$	−1.27764	−	3.93218i	−0.0412573	−	0.126977i
$960$	−8.45604	+	0.421634i	−0.272918	+	0.0136082i
$961$	−11.2979	−	15.5502i	−0.364449	−	0.501621i
$962$	21.2920	+	9.46669i	0.686480	+	0.305218i
$963$	32.0692	+	18.7330i	1.03342	+	0.603661i
$964$	−3.59951	+	22.7264i	−0.115932	+	0.731969i
$965$	29.8101	−	41.0301i	0.959621	−	1.32081i
$966$	12.8676	−	2.70096i	0.414009	−	0.0869021i
$967$	14.0527	−	14.0527i	0.451903	−	0.451903i	−0.444083	−	0.895986i	$-0.646470\pi$
$967$	14.0527	−	14.0527i	0.451903	−	0.451903i	0.895986	+	0.444083i	$0.146470\pi$
$968$	−26.3425	+	6.44596i	−0.846679	+	0.207181i
$969$	19.7929	−	15.9449i	0.635839	−	0.512224i
$970$	−5.75851	+	11.3017i	−0.184895	+	0.362876i
$971$	−23.8513	+	32.8286i	−0.765426	+	1.05352i	0.231317	+	0.972878i	$0.425696\pi$
$971$	−23.8513	+	32.8286i	−0.765426	+	1.05352i	−0.996743	+	0.0806401i	$0.974304\pi$
$972$	−2.15633	−	23.3662i	−0.0691645	−	0.749472i
$973$	−13.8819	+	7.07317i	−0.445032	+	0.226755i
$974$	0.473645	−	1.45773i	0.0151766	−	0.0467087i
$975$	−12.6227	−	28.5064i	−0.404251	−	0.912934i
$976$	−2.78974	−	2.02687i	−0.0892975	−	0.0648784i
$977$	−10.9770	+	21.5435i	−0.351184	+	0.689238i	−0.997255	−	0.0740391i	$-0.976411\pi$
$977$	−10.9770	+	21.5435i	−0.351184	+	0.689238i	0.646071	+	0.763277i	$0.276411\pi$
$978$	−2.21810	+	20.6004i	−0.0709269	+	0.658730i
$979$	7.82719	−	8.50455i	0.250158	−	0.271807i
$980$	17.6173	+	17.6173i	0.562766	+	0.562766i
$981$	4.50181	+	3.68350i	0.143732	+	0.117605i
$982$	−4.09885	−	25.8791i	−0.130800	−	0.825836i
$983$	5.65592	−	35.7101i	0.180396	−	1.13897i	−0.716780	−	0.697300i	$-0.754385\pi$
$983$	5.65592	−	35.7101i	0.180396	−	1.13897i	0.897175	−	0.441674i	$-0.145615\pi$
$984$	5.95194	−	13.2774i	0.189741	−	0.423269i
$985$	50.0036	+	16.2471i	1.59325	+	0.517677i
$986$	−0.0429344	+	0.271077i	−0.00136731	+	0.00863286i
$987$	11.8713	+	10.7437i	0.377867	+	0.341974i
$988$	−20.8045	+	32.0721i	−0.661878	+	1.02035i
$989$			33.4145i			1.06252i
$990$	21.9016	−	3.11082i	0.696077	−	0.0988684i
$991$	−32.1022			−1.01976			−0.509880	−	0.860245i	$-0.670310\pi$
$991$	−32.1022			−1.01976			−0.509880	+	0.860245i	$0.670310\pi$
$992$	−6.18170	−	19.0253i	−0.196269	−	0.604054i
$993$	−43.5271	+	2.17034i	−1.38129	+	0.0688738i
$994$	1.09510	−	6.91416i	0.0347343	−	0.219304i
$995$	26.3334	+	51.6821i	0.834824	+	1.63843i
$996$	1.61890	+	4.24959i	0.0512967	+	0.134654i
$997$	3.20325	−	2.32730i	0.101448	−	0.0737062i	−0.535905	−	0.844278i	$-0.680029\pi$
$997$	3.20325	−	2.32730i	0.101448	−	0.0737062i	0.637353	+	0.770572i	$0.280029\pi$
$998$	11.0328	+	8.01580i	0.349237	+	0.253736i
$999$	−34.0173	+	33.5029i	−1.07626	+	1.05999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.20	✓	416
3.2	odd	2	inner	429.2.bi.a.5.33	yes	416
11.9	even	5	inner	429.2.bi.a.317.33	yes	416
13.8	odd	4	inner	429.2.bi.a.203.20	yes	416
33.20	odd	10	inner	429.2.bi.a.317.20	yes	416
39.8	even	4	inner	429.2.bi.a.203.33	yes	416
143.86	odd	20	inner	429.2.bi.a.86.33	yes	416
429.86	even	20	inner	429.2.bi.a.86.20	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.20	✓	416	1.1	even	1	trivial
429.2.bi.a.5.33	yes	416	3.2	odd	2	inner
429.2.bi.a.86.20	yes	416	429.86	even	20	inner
429.2.bi.a.86.33	yes	416	143.86	odd	20	inner
429.2.bi.a.203.20	yes	416	13.8	odd	4	inner
429.2.bi.a.203.33	yes	416	39.8	even	4	inner
429.2.bi.a.317.20	yes	416	33.20	odd	10	inner
429.2.bi.a.317.33	yes	416	11.9	even	5	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.319309 + 0.626680i) q^{2} +(1.28422 + 1.16223i) q^{3} +(0.884801 + 1.21782i) q^{4} +(-2.81651 + 1.43508i) q^{5} +(-1.13841 + 0.433681i) q^{6} +(-1.31181 - 0.207770i) q^{7} +(-2.43507 + 0.385677i) q^{8} +(0.298429 + 2.98512i) q^{9} +O(q^{10})\)	\(q+(-0.319309 + 0.626680i) q^{2} +(1.28422 + 1.16223i) q^{3} +(0.884801 + 1.21782i) q^{4} +(-2.81651 + 1.43508i) q^{5} +(-1.13841 + 0.433681i) q^{6} +(-1.31181 - 0.207770i) q^{7} +(-2.43507 + 0.385677i) q^{8} +(0.298429 + 2.98512i) q^{9} -2.22328i q^{10} +(3.31378 - 0.137440i) q^{11} +(-0.279118 + 2.59230i) q^{12} +(-0.751447 - 3.52638i) q^{13} +(0.549078 - 0.755741i) q^{14} +(-5.28490 - 1.43048i) q^{15} +(-0.394491 + 1.21412i) q^{16} +(-0.643791 + 1.98138i) q^{17} +(-1.96601 - 0.766157i) q^{18} +(-6.95685 + 1.10186i) q^{19} +(-4.23973 - 2.16025i) q^{20} +(-1.44317 - 1.79145i) q^{21} +(-0.971989 + 2.12056i) q^{22} +8.12614 q^{23} +(-3.57541 - 2.33483i) q^{24} +(2.93432 - 4.03874i) q^{25} +(2.44985 + 0.655088i) q^{26} +(-3.08616 + 4.18039i) q^{27} +(-0.907663 - 1.78139i) q^{28} +(-0.110094 - 0.151532i) q^{29} +(2.58397 - 2.85518i) q^{30} +(3.05796 + 1.55811i) q^{31} +(-4.12154 - 4.12154i) q^{32} +(4.41535 + 3.67488i) q^{33} +(-1.03613 - 1.03613i) q^{34} +(3.99288 - 1.29737i) q^{35} +(-3.37130 + 3.00467i) q^{36} +(9.07548 + 1.43741i) q^{37} +(1.53088 - 4.71155i) q^{38} +(3.13345 - 5.40199i) q^{39} +(6.30491 - 4.58079i) q^{40} +(0.533036 + 3.36546i) q^{41} +(1.58348 - 0.332379i) q^{42} +4.11197i q^{43} +(3.09941 + 3.91399i) q^{44} +(-5.12442 - 7.97934i) q^{45} +(-2.59475 + 5.09249i) q^{46} +(-6.87429 + 1.08878i) q^{47} +(-1.91770 + 1.10070i) q^{48} +(-4.97972 - 1.61801i) q^{49} +(1.59404 + 3.12849i) q^{50} +(-3.12960 + 1.79629i) q^{51} +(3.62963 - 4.03527i) q^{52} +(3.06548 - 0.996034i) q^{53} +(-1.63433 - 3.26887i) q^{54} +(-9.13603 + 5.14264i) q^{55} +3.27448 q^{56} +(-10.2147 - 6.67046i) q^{57} +(0.130116 - 0.0206084i) q^{58} +(-2.28600 + 14.4332i) q^{59} +(-2.93402 - 7.70178i) q^{60} +(-0.834708 + 2.56897i) q^{61} +(-1.95287 + 1.41884i) q^{62} +(0.228736 - 3.97791i) q^{63} +(1.47069 - 0.477857i) q^{64} +(7.17709 + 8.85367i) q^{65} +(-3.71283 + 1.59359i) q^{66} +(2.40554 - 2.40554i) q^{67} +(-2.98261 + 0.969107i) q^{68} +(10.4357 + 9.44447i) q^{69} +(-0.461932 + 2.91652i) q^{70} +(6.67705 - 3.40213i) q^{71} +(-1.87799 - 7.15388i) q^{72} +(14.7391 + 2.33444i) q^{73} +(-3.79868 + 5.22844i) q^{74} +(8.46226 - 1.77626i) q^{75} +(-7.49730 - 7.49730i) q^{76} +(-4.37560 - 0.508209i) q^{77} +(2.38478 + 3.68857i) q^{78} +(2.31156 + 7.11426i) q^{79} +(-0.631272 - 3.98569i) q^{80} +(-8.82188 + 1.78170i) q^{81} +(-2.27927 - 0.740579i) q^{82} +(1.55406 - 0.791832i) q^{83} +(0.904752 - 3.34261i) q^{84} +(-1.03021 - 6.50447i) q^{85} +(-2.57689 - 1.31299i) q^{86} +(0.0347302 - 0.322555i) q^{87} +(-8.01627 + 1.61272i) q^{88} +(2.46422 - 2.46422i) q^{89} +(6.63676 - 0.663493i) q^{90} +(0.253080 + 4.78206i) q^{91} +(7.19002 + 9.89622i) q^{92} +(2.11620 + 5.55502i) q^{93} +(1.51271 - 4.65564i) q^{94} +(18.0128 - 13.0870i) q^{95} +(-0.502764 - 10.0831i) q^{96} +(-5.08335 - 2.59010i) q^{97} +(2.60405 - 2.60405i) q^{98} +(1.39920 + 9.85100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

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