LMFDB - Embedded newform 378.2.u.e.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(43,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("378.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.u (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	378.43
Dual form			378.2.u.e.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.391603 - 1.68720i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.08466 + 0.758756i) q^{5} +(-1.38450 + 1.04075i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.69329 - 1.32143i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.391603 - 1.68720i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.08466 + 0.758756i) q^{5} +(-1.38450 + 1.04075i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.69329 - 1.32143i) q^{9} +(-1.10923 - 1.92124i) q^{10} +(2.50576 - 0.912022i) q^{11} +(1.72957 + 0.0926744i) q^{12} +(0.389713 - 0.327008i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(2.09653 - 3.22012i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.36047 + 2.35640i) q^{17} +(1.21379 + 2.74349i) q^{18} +(3.46049 - 5.99375i) q^{19} +(-0.385230 + 2.18475i) q^{20} +(-1.59357 - 0.678633i) q^{21} +(-2.50576 - 0.912022i) q^{22} +(0.481082 + 2.72835i) q^{23} +(-1.26536 - 1.18274i) q^{24} +(-0.0601097 - 0.0504380i) q^{25} -0.508734 q^{26} +(-3.28421 + 4.02665i) q^{27} +1.00000 q^{28} +(-0.825054 - 0.692302i) q^{29} +(-3.67589 + 1.11913i) q^{30} +(-0.526224 - 2.98436i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.557501 - 4.58487i) q^{33} +(0.472486 - 2.67960i) q^{34} +(1.10923 - 1.92124i) q^{35} +(0.833665 - 2.88184i) q^{36} +(-4.07975 - 7.06633i) q^{37} +(-6.50360 + 2.36712i) q^{38} +(-0.399115 - 0.785581i) q^{39} +(1.69943 - 1.42599i) q^{40} +(-7.78101 + 6.52904i) q^{41} +(0.784526 + 1.54419i) q^{42} +(-4.03397 + 1.46825i) q^{43} +(1.33329 + 2.30932i) q^{44} +(-4.61197 - 4.79828i) q^{45} +(1.38522 - 2.39927i) q^{46} +(-0.0998989 + 0.566555i) q^{47} +(0.209070 + 1.71939i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(0.0136258 + 0.0772755i) q^{50} +(4.50849 - 1.37261i) q^{51} +(0.389713 + 0.327008i) q^{52} +6.87798 q^{53} +(5.10414 - 0.973543i) q^{54} +5.91567 q^{55} +(-0.766044 - 0.642788i) q^{56} +(-8.75752 - 8.18572i) q^{57} +(0.187025 + 1.06067i) q^{58} +(11.6025 + 4.22298i) q^{59} +(3.53525 + 1.50552i) q^{60} +(-2.03502 + 11.5412i) q^{61} +(-1.51520 + 2.62441i) q^{62} +(-1.76904 + 2.42291i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.06054 - 0.386005i) q^{65} +(-2.52003 + 3.87057i) q^{66} +(2.89029 - 2.42524i) q^{67} +(-2.08436 + 1.74899i) q^{68} +(4.79167 + 0.256749i) q^{69} +(-2.08466 + 0.758756i) q^{70} +(6.07749 + 10.5265i) q^{71} +(-2.49104 + 1.67175i) q^{72} +(2.24543 - 3.88920i) q^{73} +(-1.41688 + 8.03553i) q^{74} +(-0.108638 + 0.0816654i) q^{75} +(6.50360 + 2.36712i) q^{76} +(-0.463046 - 2.62606i) q^{77} +(-0.199222 + 0.858336i) q^{78} +(8.77353 + 7.36187i) q^{79} -2.21845 q^{80} +(5.50766 + 7.11798i) q^{81} +10.1574 q^{82} +(-12.1623 - 10.2054i) q^{83} +(0.391603 - 1.68720i) q^{84} +(1.04819 + 5.94457i) q^{85} +(4.03397 + 1.46825i) q^{86} +(-1.49115 + 1.12092i) q^{87} +(0.463046 - 2.62606i) q^{88} +(-4.65877 + 8.06923i) q^{89} +(0.448700 + 6.64022i) q^{90} +(-0.254367 - 0.440576i) q^{91} +(-2.60336 + 0.947547i) q^{92} +(-5.24129 - 0.280841i) q^{93} +(0.440702 - 0.369793i) q^{94} +(11.7618 - 9.86928i) q^{95} +(0.945043 - 1.45151i) q^{96} +(-11.7186 + 4.26523i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-7.95392 - 0.854834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	$ 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) $ 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.391603	−	1.68720i	0.226092	−	0.974106i
$3$	0.391603	−	1.68720i	0.226092	−	0.974106i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	2.08466	+	0.758756i	0.932290	+	0.339326i	0.763117	−	0.646261i	$-0.223668\pi$
$5$	2.08466	+	0.758756i	0.932290	+	0.339326i	0.169173	+	0.985586i	$0.445890\pi$
$6$	−1.38450	+	1.04075i	−0.565219	+	0.424886i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$7$	0.173648	−	0.984808i	0.0656328	−	0.372222i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.69329	−	1.32143i	−0.897765	−	0.440475i
$10$	−1.10923	−	1.92124i	−0.350768	−	0.607548i
$11$	2.50576	−	0.912022i	0.755515	−	0.274985i	0.0645907	−	0.997912i	$-0.479426\pi$
$11$	2.50576	−	0.912022i	0.755515	−	0.274985i	0.690925	+	0.722927i	$0.257204\pi$
$12$	1.72957	+	0.0926744i	0.499284	+	0.0267528i
$13$	0.389713	−	0.327008i	0.108087	−	0.0906956i	−0.587143	−	0.809484i	$-0.699747\pi$
$13$	0.389713	−	0.327008i	0.108087	−	0.0906956i	0.695229	+	0.718788i	$0.255303\pi$
$14$	−0.766044	+	0.642788i	−0.204734	+	0.171792i
$15$	2.09653	−	3.22012i	0.541323	−	0.831430i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.36047	+	2.35640i	0.329962	+	0.571511i	0.982504	−	0.186241i	$-0.0596307\pi$
$17$	1.36047	+	2.35640i	0.329962	+	0.571511i	−0.652542	+	0.757753i	$0.726297\pi$
$18$	1.21379	+	2.74349i	0.286092	+	0.646646i
$19$	3.46049	−	5.99375i	0.793891	−	1.37506i	−0.129649	−	0.991560i	$-0.541385\pi$
$19$	3.46049	−	5.99375i	0.793891	−	1.37506i	0.923541	−	0.383500i	$-0.125282\pi$
$20$	−0.385230	+	2.18475i	−0.0861401	+	0.488525i
$21$	−1.59357	−	0.678633i	−0.347745	−	0.148090i
$22$	−2.50576	−	0.912022i	−0.534230	−	0.194444i
$23$	0.481082	+	2.72835i	0.100313	+	0.568901i	0.992989	+	0.118204i	$0.0377135\pi$
$23$	0.481082	+	2.72835i	0.100313	+	0.568901i	−0.892677	+	0.450697i	$0.851175\pi$
$24$	−1.26536	−	1.18274i	−0.258290	−	0.241426i
$25$	−0.0601097	−	0.0504380i	−0.0120219	−	0.0100876i
$26$	−0.508734			−0.0997709
$27$	−3.28421	+	4.02665i	−0.632047	+	0.774930i
$28$	1.00000			0.188982
$29$	−0.825054	−	0.692302i	−0.153209	−	0.128557i	0.562961	−	0.826483i	$-0.309662\pi$
$29$	−0.825054	−	0.692302i	−0.153209	−	0.128557i	−0.716170	+	0.697926i	$0.754106\pi$
$30$	−3.67589	+	1.11913i	−0.671122	+	0.204323i
$31$	−0.526224	−	2.98436i	−0.0945126	−	0.536008i	−0.994896	−	0.100909i	$-0.967825\pi$
$31$	−0.526224	−	2.98436i	−0.0945126	−	0.536008i	0.900383	−	0.435098i	$-0.143286\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−0.557501	−	4.58487i	−0.0970485	−	0.798124i
$34$	0.472486	−	2.67960i	0.0810307	−	0.459548i
$35$	1.10923	−	1.92124i	0.187493	−	0.324748i
$36$	0.833665	−	2.88184i	0.138944	−	0.480307i
$37$	−4.07975	−	7.06633i	−0.670706	−	1.16170i	−0.977704	−	0.209987i	$-0.932658\pi$
$37$	−4.07975	−	7.06633i	−0.670706	−	1.16170i	0.306998	−	0.951710i	$-0.400676\pi$
$38$	−6.50360	+	2.36712i	−1.05502	+	0.383997i
$39$	−0.399115	−	0.785581i	−0.0639096	−	0.125794i
$40$	1.69943	−	1.42599i	0.268704	−	0.225469i
$41$	−7.78101	+	6.52904i	−1.21519	+	1.01966i	−0.216127	+	0.976365i	$0.569342\pi$
$41$	−7.78101	+	6.52904i	−1.21519	+	1.01966i	−0.999062	+	0.0432993i	$0.986213\pi$
$42$	0.784526	+	1.54419i	0.121055	+	0.238273i
$43$	−4.03397	+	1.46825i	−0.615175	+	0.223905i	−0.630766	−	0.775973i	$-0.717259\pi$
$43$	−4.03397	+	1.46825i	−0.615175	+	0.223905i	0.0155912	+	0.999878i	$0.495037\pi$
$44$	1.33329	+	2.30932i	0.201001	+	0.348143i
$45$	−4.61197	−	4.79828i	−0.687512	−	0.715286i
$46$	1.38522	−	2.39927i	0.204240	−	0.353754i
$47$	−0.0998989	+	0.566555i	−0.0145718	+	0.0826406i	−0.991226	−	0.132175i	$-0.957804\pi$
$47$	−0.0998989	+	0.566555i	−0.0145718	+	0.0826406i	0.976655	+	0.214816i	$0.0689150\pi$
$48$	0.209070	+	1.71939i	0.0301767	+	0.248172i
$49$	−0.939693	−	0.342020i	−0.134242	−	0.0488600i
$50$	0.0136258	+	0.0772755i	0.00192697	+	0.0109284i
$51$	4.50849	−	1.37261i	0.631314	−	0.192204i
$52$	0.389713	+	0.327008i	0.0540434	+	0.0453478i
$53$	6.87798			0.944763			0.472382	−	0.881394i	$-0.343394\pi$
$53$	6.87798			0.944763			0.472382	+	0.881394i	$0.343394\pi$
$54$	5.10414	−	0.973543i	0.694585	−	0.132482i
$55$	5.91567			0.797669
$56$	−0.766044	−	0.642788i	−0.102367	−	0.0858961i
$57$	−8.75752	−	8.18572i	−1.15996	−	1.08422i
$58$	0.187025	+	1.06067i	0.0245575	+	0.139273i
$59$	11.6025	+	4.22298i	1.51052	+	0.549785i	0.958760	−	0.284217i	$-0.0917337\pi$
$59$	11.6025	+	4.22298i	1.51052	+	0.549785i	0.551761	+	0.834002i	$0.313956\pi$
$60$	3.53525	+	1.50552i	0.456399	+	0.194361i
$61$	−2.03502	+	11.5412i	−0.260558	+	1.47770i	0.520835	+	0.853658i	$0.325621\pi$
$61$	−2.03502	+	11.5412i	−0.260558	+	1.47770i	−0.781393	+	0.624040i	$0.785490\pi$
$62$	−1.51520	+	2.62441i	−0.192431	+	0.333300i
$63$	−1.76904	+	2.42291i	−0.222878	+	0.305258i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.06054	−	0.386005i	0.131544	−	0.0478780i
$66$	−2.52003	+	3.87057i	−0.310194	+	0.476434i
$67$	2.89029	−	2.42524i	0.353105	−	0.296290i	−0.448931	−	0.893567i	$-0.648195\pi$
$67$	2.89029	−	2.42524i	0.353105	−	0.296290i	0.802035	+	0.597277i	$0.203751\pi$
$68$	−2.08436	+	1.74899i	−0.252766	+	0.212096i
$69$	4.79167	+	0.256749i	0.576850	+	0.0309090i
$70$	−2.08466	+	0.758756i	−0.249165	+	0.0906886i
$71$	6.07749	+	10.5265i	0.721265	+	1.24927i	0.960493	+	0.278304i	$0.0897724\pi$
$71$	6.07749	+	10.5265i	0.721265	+	1.24927i	−0.239228	+	0.970963i	$0.576894\pi$
$72$	−2.49104	+	1.67175i	−0.293571	+	0.197017i
$73$	2.24543	−	3.88920i	0.262808	−	0.455196i	−0.704179	−	0.710022i	$-0.748685\pi$
$73$	2.24543	−	3.88920i	0.262808	−	0.455196i	0.966987	+	0.254826i	$0.0820182\pi$
$74$	−1.41688	+	8.03553i	−0.164709	+	0.934112i
$75$	−0.108638	+	0.0816654i	−0.0125445	+	0.00942991i
$76$	6.50360	+	2.36712i	0.746014	+	0.271527i
$77$	−0.463046	−	2.62606i	−0.0527690	−	0.299268i
$78$	−0.199222	+	0.858336i	−0.0225574	+	0.0971874i
$79$	8.77353	+	7.36187i	0.987100	+	0.828275i	0.985145	−	0.171723i	$-0.0549334\pi$
$79$	8.77353	+	7.36187i	0.987100	+	0.828275i	0.00195441	+	0.999998i	$0.499378\pi$
$80$	−2.21845			−0.248031
$81$	5.50766	+	7.11798i	0.611963	+	0.790887i
$82$	10.1574			1.12170
$83$	−12.1623	−	10.2054i	−1.33499	−	1.12019i	−0.982883	−	0.184229i	$-0.941021\pi$
$83$	−12.1623	−	10.2054i	−1.33499	−	1.12019i	−0.352106	−	0.935960i	$-0.614534\pi$
$84$	0.391603	−	1.68720i	0.0427274	−	0.184089i
$85$	1.04819	+	5.94457i	0.113692	+	0.644779i
$86$	4.03397	+	1.46825i	0.434994	+	0.158325i
$87$	−1.49115	+	1.12092i	−0.159868	+	0.120176i
$88$	0.463046	−	2.62606i	0.0493609	−	0.279939i
$89$	−4.65877	+	8.06923i	−0.493829	+	0.855337i	−0.999975	−	0.00711123i	$-0.997736\pi$
$89$	−4.65877	+	8.06923i	−0.493829	+	0.855337i	0.506146	+	0.862448i	$0.331070\pi$
$90$	0.448700	+	6.64022i	0.0472971	+	0.699940i
$91$	−0.254367	−	0.440576i	−0.0266649	−	0.0461849i
$92$	−2.60336	+	0.947547i	−0.271419	+	0.0987886i
$93$	−5.24129	−	0.280841i	−0.543497	−	0.0291218i
$94$	0.440702	−	0.369793i	0.0454549	−	0.0381412i
$95$	11.7618	−	9.86928i	1.20673	−	1.01257i
$96$	0.945043	−	1.45151i	0.0964531	−	0.148145i
$97$	−11.7186	+	4.26523i	−1.18985	+	0.433069i	−0.859670	−	0.510850i	$-0.829331\pi$
$97$	−11.7186	+	4.26523i	−1.18985	+	0.433069i	−0.330177	+	0.943919i	$0.607109\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	−7.95392	−	0.854834i	−0.799399	−	0.0859141i
$100$	0.0392338	−	0.0679549i	0.00392338	−	0.00679549i
$101$	−1.55083	+	8.79522i	−0.154314	+	0.875157i	0.805097	+	0.593144i	$0.202113\pi$
$101$	−1.55083	+	8.79522i	−0.154314	+	0.875157i	−0.959410	+	0.282014i	$0.908998\pi$
$102$	−4.33600	−	1.84652i	−0.429328	−	0.182833i
$103$	9.49542	+	3.45605i	0.935612	+	0.340535i	0.764432	−	0.644705i	$-0.223020\pi$
$103$	9.49542	+	3.45605i	0.935612	+	0.340535i	0.171180	+	0.985240i	$0.445242\pi$
$104$	−0.0883407	−	0.501005i	−0.00866252	−	0.0491276i
$105$	−2.80714	−	2.62385i	−0.273948	−	0.256062i
$106$	−5.26884	−	4.42108i	−0.511755	−	0.429413i
$107$	3.50647			0.338984			0.169492	−	0.985532i	$-0.445787\pi$
$107$	3.50647			0.338984			0.169492	+	0.985532i	$0.445787\pi$
$108$	−4.53578	−	2.53510i	−0.436455	−	0.243940i
$109$	14.0792			1.34854			0.674272	−	0.738483i	$-0.264457\pi$
$109$	14.0792			1.34854			0.674272	+	0.738483i	$0.264457\pi$
$110$	−4.53167	−	3.80252i	−0.432077	−	0.362556i
$111$	−13.5200	+	4.11616i	−1.28326	+	0.390688i
$112$	0.173648	+	0.984808i	0.0164082	+	0.0930556i
$113$	2.93854	+	1.06954i	0.276435	+	0.100614i	0.476518	−	0.879165i	$-0.341899\pi$
$113$	2.93854	+	1.06954i	0.276435	+	0.100614i	−0.200083	+	0.979779i	$0.564121\pi$
$114$	1.44697	+	11.8998i	0.135521	+	1.11452i
$115$	−1.06726	+	6.05272i	−0.0995223	+	0.564419i
$116$	0.538516	−	0.932737i	0.0499999	−	0.0866024i
$117$	−1.48173	+	0.365751i	−0.136986	+	0.0338137i
$118$	−6.17358	−	10.6930i	−0.568324	−	0.984366i
$119$	2.55685	−	0.930616i	0.234386	−	0.0853094i
$120$	−1.74043	−	3.42571i	−0.158879	−	0.312723i
$121$	−2.97944	+	2.50004i	−0.270858	+	0.227277i
$122$	8.97745	−	7.53297i	0.812780	−	0.682003i
$123$	7.96873	+	15.6849i	0.718517	+	1.41426i
$124$	2.84765	−	1.03646i	0.255726	−	0.0930767i
$125$	−5.63317	−	9.75694i	−0.503846	−	0.872687i
$126$	2.91258	−	0.718945i	0.259473	−	0.0640487i
$127$	−10.2526	+	17.7580i	−0.909771	+	1.57577i	−0.0953901	+	0.995440i	$0.530410\pi$
$127$	−10.2526	+	17.7580i	−0.909771	+	1.57577i	−0.814381	+	0.580330i	$0.802923\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	0.897509	+	7.38109i	0.0790213	+	0.649869i
$130$	−1.06054	−	0.386005i	−0.0930154	−	0.0338548i
$131$	−1.42716	−	8.09382i	−0.124691	−	0.707160i	−0.981491	−	0.191510i	$-0.938662\pi$
$131$	−1.42716	−	8.09382i	−0.124691	−	0.707160i	0.856799	−	0.515650i	$-0.172450\pi$
$132$	4.41841	−	1.34519i	0.384573	−	0.117083i
$133$	−5.30178	−	4.44872i	−0.459723	−	0.385753i
$134$	−3.77300			−0.325938
$135$	−9.90173	+	5.90230i	−0.852205	+	0.507989i
$136$	2.72094			0.233319
$137$	2.00312	+	1.68082i	0.171138	+	0.143602i	0.724334	−	0.689449i	$-0.242147\pi$
$137$	2.00312	+	1.68082i	0.171138	+	0.143602i	−0.553196	+	0.833051i	$0.686592\pi$
$138$	−3.50560	−	3.27671i	−0.298416	−	0.278932i
$139$	−0.0296573	−	0.168195i	−0.00251550	−	0.0142661i	0.983524	−	0.180777i	$-0.0578611\pi$
$139$	−0.0296573	−	0.168195i	−0.00251550	−	0.0142661i	−0.986040	+	0.166511i	$0.946750\pi$
$140$	2.08466	+	0.758756i	0.176186	+	0.0641265i
$141$	0.916772	+	0.390414i	0.0772061	+	0.0328788i
$142$	2.11069	−	11.9703i	0.177125	−	1.00453i
$143$	0.678288	−	1.17483i	0.0567213	−	0.0982442i
$144$	2.98282	+	0.320574i	0.248569	+	0.0267145i
$145$	−1.19467	−	2.06923i	−0.0992121	−	0.171840i
$146$	−4.22003	+	1.53596i	−0.349252	+	0.127117i
$147$	−0.945043	+	1.45151i	−0.0779459	+	0.119719i
$148$	6.25054	−	5.24482i	0.513791	−	0.431122i
$149$	8.44986	−	7.09027i	0.692239	−	0.580858i	−0.227315	−	0.973821i	$-0.572995\pi$
$149$	8.44986	−	7.09027i	0.692239	−	0.580858i	0.919554	+	0.392963i	$0.128550\pi$
$150$	0.135715	+	0.00727194i	0.0110811	+	0.000593752i
$151$	−2.12578	+	0.773722i	−0.172994	+	0.0629646i	−0.427065	−	0.904221i	$-0.640452\pi$
$151$	−2.12578	+	0.773722i	−0.172994	+	0.0629646i	0.254071	+	0.967186i	$0.418230\pi$
$152$	−3.46049	−	5.99375i	−0.280683	−	0.486157i
$153$	−0.550332	−	8.14424i	−0.0444917	−	0.658423i
$154$	−1.33329	+	2.30932i	−0.107439	+	0.186090i
$155$	1.16740	−	6.62067i	0.0937680	−	0.531785i
$156$	0.704340	−	0.529466i	0.0563924	−	0.0423912i
$157$	−5.57040	−	2.02746i	−0.444566	−	0.161809i	0.110030	−	0.993928i	$-0.464905\pi$
$157$	−5.57040	−	2.02746i	−0.444566	−	0.161809i	−0.554597	+	0.832119i	$0.687127\pi$
$158$	−1.98880	−	11.2790i	−0.158220	−	0.897312i
$159$	2.69344	−	11.6045i	0.213604	−	0.920300i
$160$	1.69943	+	1.42599i	0.134352	+	0.112735i
$161$	2.77044			0.218341
$162$	0.356233	−	8.99295i	0.0279883	−	0.706553i
$163$	−1.43494			−0.112393			−0.0561966	−	0.998420i	$-0.517897\pi$
$163$	−1.43494			−0.112393			−0.0561966	+	0.998420i	$0.517897\pi$
$164$	−7.78101	−	6.52904i	−0.607594	−	0.509832i
$165$	2.31660	−	9.98093i	0.180347	−	0.777014i
$166$	2.75698	+	15.6356i	0.213983	+	1.21356i
$167$	−9.87198	−	3.59311i	−0.763916	−	0.278043i	−0.0694669	−	0.997584i	$-0.522130\pi$
$167$	−9.87198	−	3.59311i	−0.763916	−	0.278043i	−0.694450	+	0.719541i	$0.744352\pi$
$168$	−1.38450	+	1.04075i	−0.106816	+	0.0802959i
$169$	−2.21248	+	12.5476i	−0.170191	+	0.965202i
$170$	3.01814	−	5.22757i	0.231480	−	0.400936i
$171$	−17.2404	+	11.5701i	−1.31841	+	0.884791i
$172$	−2.14643	−	3.71773i	−0.163664	−	0.283474i
$173$	−3.04250	+	1.10738i	−0.231317	+	0.0841925i	−0.455078	−	0.890452i	$-0.650389\pi$
$173$	−3.04250	+	1.10738i	−0.231317	+	0.0841925i	0.223761	+	0.974644i	$0.428166\pi$
$174$	1.86280	+	0.0998133i	0.141219	+	0.00756683i
$175$	−0.0601097	+	0.0504380i	−0.00454386	+	0.00381275i
$176$	−2.04272	+	1.71404i	−0.153975	+	0.129201i
$177$	11.6686	−	17.9221i	0.877066	−	1.34711i
$178$	8.75563	−	3.18679i	0.656262	−	0.238860i
$179$	8.45095	+	14.6375i	0.631653	+	1.09406i	0.987214	+	0.159402i	$0.0509567\pi$
$179$	8.45095	+	14.6375i	0.631653	+	1.09406i	−0.355560	+	0.934653i	$0.615710\pi$
$180$	3.92452	−	5.37512i	0.292517	−	0.400638i
$181$	1.44229	−	2.49811i	0.107204	−	0.185683i	−0.807432	−	0.589960i	$-0.799143\pi$
$181$	1.44229	−	2.49811i	0.107204	−	0.185683i	0.914637	+	0.404277i	$0.132477\pi$
$182$	−0.0883407	+	0.501005i	−0.00654825	+	0.0371370i
$183$	18.6754	+	7.95306i	1.38052	+	0.587907i
$184$	2.60336	+	0.947547i	0.191923	+	0.0698541i
$185$	−3.14328	−	17.8265i	−0.231099	−	1.31063i
$186$	3.83454	+	3.58417i	0.281162	+	0.262804i
$187$	5.55810	+	4.66380i	0.406449	+	0.341051i
$188$	−0.575295			−0.0419577
$189$	3.39518	+	3.93354i	0.246963	+	0.286123i
$190$	−15.3539			−1.11389
$191$	6.39431	+	5.36546i	0.462676	+	0.388231i	0.844115	−	0.536163i	$-0.180127\pi$
$191$	6.39431	+	5.36546i	0.462676	+	0.388231i	−0.381438	+	0.924394i	$0.624571\pi$
$192$	−1.65696	+	0.504462i	−0.119581	+	0.0364064i
$193$	−2.59510	−	14.7176i	−0.186800	−	1.05939i	−0.923621	−	0.383306i	$-0.874785\pi$
$193$	−2.59510	−	14.7176i	−0.186800	−	1.05939i	0.736822	−	0.676087i	$-0.236326\pi$
$194$	11.7186	+	4.26523i	0.841349	+	0.306226i
$195$	−0.235957	−	1.94050i	−0.0168972	−	0.138962i
$196$	0.173648	−	0.984808i	0.0124034	−	0.0703434i
$197$	−3.21739	+	5.57268i	−0.229230	+	0.397037i	−0.957580	−	0.288168i	$-0.906954\pi$
$197$	−3.21739	+	5.57268i	−0.229230	+	0.397037i	0.728350	+	0.685205i	$0.240287\pi$
$198$	5.54358	+	5.76752i	0.393965	+	0.409880i
$199$	−8.12521	−	14.0733i	−0.575981	−	0.997629i	−0.995934	−	0.0900828i	$-0.971287\pi$
$199$	−8.12521	−	14.0733i	−0.575981	−	0.997629i	0.419953	−	0.907546i	$-0.362046\pi$
$200$	−0.0737354	+	0.0268375i	−0.00521388	+	0.00189770i
$201$	−2.96002	−	5.82623i	−0.208784	−	0.410950i
$202$	6.84147	−	5.74067i	0.481364	−	0.403912i
$203$	−0.825054	+	0.692302i	−0.0579074	+	0.0485901i
$204$	2.13465	+	4.20164i	0.149455	+	0.294174i
$205$	−21.1747	+	7.70697i	−1.47891	+	0.538278i
$206$	−5.05241	−	8.75103i	−0.352018	−	0.609713i
$207$	2.30962	−	7.98397i	0.160530	−	0.554924i
$208$	−0.254367	+	0.440576i	−0.0176372	+	0.0305485i
$209$	3.20473	−	18.1749i	0.221676	−	1.25719i
$210$	0.463812	+	3.81438i	0.0320061	+	0.263217i
$211$	11.5432	+	4.20138i	0.794667	+	0.289235i	0.707275	−	0.706939i	$-0.249924\pi$
$211$	11.5432	+	4.20138i	0.794667	+	0.289235i	0.0873923	+	0.996174i	$0.472147\pi$
$212$	1.19435	+	6.77349i	0.0820282	+	0.465205i
$213$	20.1403	−	6.13173i	1.37999	−	0.420139i
$214$	−2.68611	−	2.25392i	−0.183619	−	0.154075i
$215$	−9.52351			−0.649498
$216$	1.84508	+	4.85754i	0.125542	+	0.330514i
$217$	−3.03040			−0.205717
$218$	−10.7853	−	9.04995i	−0.730473	−	0.612940i
$219$	−5.68254	−	5.31151i	−0.383991	−	0.358919i
$220$	1.02725	+	5.82580i	0.0692569	+	0.392775i
$221$	1.30075	+	0.473436i	0.0874981	+	0.0318467i
$222$	13.0027	+	5.53730i	0.872684	+	0.371640i
$223$	3.13418	−	17.7748i	0.209880	−	1.19029i	−0.679693	−	0.733497i	$-0.737887\pi$
$223$	3.13418	−	17.7748i	0.209880	−	1.19029i	0.889573	−	0.456793i	$-0.151002\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	0.0952429	+	0.215275i	0.00634953	+	0.0143517i
$226$	−1.56357	−	2.70818i	−0.104007	−	0.180145i
$227$	−18.8434	+	6.85844i	−1.25068	+	0.455211i	−0.880632	−	0.473801i	$-0.842881\pi$
$227$	−18.8434	+	6.85844i	−1.25068	+	0.455211i	−0.370049	+	0.929012i	$0.620659\pi$
$228$	6.54063	−	10.0459i	0.433164	−	0.665306i
$229$	−11.8690	+	9.95926i	−0.784325	+	0.658127i	−0.944334	−	0.328989i	$-0.893292\pi$
$229$	−11.8690	+	9.95926i	−0.784325	+	0.658127i	0.160009	+	0.987116i	$0.448848\pi$
$230$	4.70818	−	3.95063i	0.310448	−	0.260497i
$231$	−4.61203	−	0.247123i	−0.303449	−	0.0162595i
$232$	−1.01208	+	0.368366i	−0.0664462	+	0.0241844i
$233$	1.88856	+	3.27108i	0.123723	+	0.214295i	0.921233	−	0.389011i	$-0.127183\pi$
$233$	1.88856	+	3.27108i	0.123723	+	0.214295i	−0.797510	+	0.603306i	$0.793850\pi$
$234$	1.37017	+	0.672254i	0.0895708	+	0.0439466i
$235$	−0.638133	+	1.10528i	−0.0416272	+	0.0721004i
$236$	−2.14406	+	12.1596i	−0.139567	+	0.791521i
$237$	15.8567	−	11.9198i	1.03000	−	0.774273i
$238$	−2.55685	−	0.930616i	−0.165736	−	0.0603229i
$239$	−3.47238	−	19.6928i	−0.224609	−	1.27382i	−0.863430	−	0.504468i	$-0.831689\pi$
$239$	−3.47238	−	19.6928i	−0.224609	−	1.27382i	0.638821	−	0.769355i	$-0.279422\pi$
$240$	−0.868753	+	3.74298i	−0.0560778	+	0.241608i
$241$	−23.0167	−	19.3133i	−1.48264	−	1.24408i	−0.903310	−	0.428988i	$-0.858870\pi$
$241$	−23.0167	−	19.3133i	−1.48264	−	1.24408i	−0.579329	−	0.815094i	$-0.696685\pi$
$242$	3.88938			0.250019
$243$	14.1663	−	6.50511i	0.908767	−	0.417303i
$244$	−11.7192			−0.750247
$245$	−1.69943	−	1.42599i	−0.108573	−	0.0911034i
$246$	3.97766	−	17.1375i	0.253607	−	1.09265i
$247$	−0.611405	−	3.46745i	−0.0389027	−	0.220628i
$248$	−2.84765	−	1.03646i	−0.180826	−	0.0658152i
$249$	−21.9814	+	16.5238i	−1.39301	+	1.04716i
$250$	−1.95638	+	11.0952i	−0.123732	+	0.701721i
$251$	−5.50656	+	9.53764i	−0.347571	+	0.602010i	−0.985817	−	0.167822i	$-0.946327\pi$
$251$	−5.50656	+	9.53764i	−0.347571	+	0.602010i	0.638247	+	0.769832i	$0.279660\pi$
$252$	−2.69329	−	1.32143i	−0.169662	−	0.0832420i
$253$	3.69380	+	6.39784i	0.232227	+	0.402229i
$254$	19.2686	−	7.01319i	1.20902	−	0.440047i
$255$	10.4402	+	0.559408i	0.653788	+	0.0350315i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−9.94427	+	8.34423i	−0.620307	+	0.520499i	−0.897900	−	0.440200i	$-0.854908\pi$
$257$	−9.94427	+	8.34423i	−0.620307	+	0.520499i	0.277593	+	0.960699i	$0.410463\pi$
$258$	4.05694	−	6.23115i	0.252574	−	0.387934i
$259$	−7.66742	+	2.79071i	−0.476430	+	0.173406i
$260$	0.564301	+	0.977398i	0.0349965	+	0.0606156i
$261$	1.30729	+	2.95482i	0.0809190	+	0.182899i
$262$	−4.10934	+	7.11759i	−0.253876	+	0.439726i
$263$	3.93572	−	22.3206i	0.242687	−	1.37635i	−0.583116	−	0.812389i	$-0.698167\pi$
$263$	3.93572	−	22.3206i	0.242687	−	1.37635i	0.825803	−	0.563958i	$-0.190722\pi$
$264$	−4.24937	−	1.80963i	−0.261530	−	0.111375i
$265$	14.3383	+	5.21871i	0.880793	+	0.320583i
$266$	1.20182	+	6.81584i	0.0736881	+	0.417906i
$267$	11.7900	+	11.0202i	0.721538	+	0.674427i
$268$	2.89029	+	2.42524i	0.176552	+	0.148145i
$269$	9.85551			0.600901			0.300450	−	0.953797i	$-0.402863\pi$
$269$	9.85551			0.600901			0.300450	+	0.953797i	$0.402863\pi$
$270$	11.3791	+	1.84328i	0.692509	+	0.112179i
$271$	21.6284			1.31383			0.656917	−	0.753963i	$-0.271860\pi$
$271$	21.6284			1.31383			0.656917	+	0.753963i	$0.271860\pi$
$272$	−2.08436	−	1.74899i	−0.126383	−	0.106048i
$273$	−0.842952	+	0.256637i	−0.0510178	+	0.0155324i
$274$	−0.454071	−	2.57516i	−0.0274314	−	0.155571i
$275$	−0.196621	−	0.0715642i	−0.0118567	−	0.00431548i
$276$	0.579217	+	4.76346i	0.0348647	+	0.286727i
$277$	−1.75472	+	9.95148i	−0.105431	+	0.597927i	0.885617	+	0.464417i	$0.153736\pi$
$277$	−1.75472	+	9.95148i	−0.105431	+	0.597927i	−0.991047	+	0.133510i	$0.957375\pi$
$278$	−0.0853948	+	0.147908i	−0.00512164	+	0.00887094i
$279$	−2.52634	+	8.73313i	−0.151248	+	0.522839i
$280$	−1.10923	−	1.92124i	−0.0662890	−	0.114816i
$281$	−24.0925	+	8.76896i	−1.43724	+	0.523112i	−0.938997	−	0.343926i	$-0.888243\pi$
$281$	−24.0925	+	8.76896i	−1.43724	+	0.523112i	−0.498242	+	0.867038i	$0.666021\pi$
$282$	−0.451334	−	0.888364i	−0.0268766	−	0.0529013i
$283$	−18.1917	+	15.2647i	−1.08139	+	0.907391i	−0.996035	−	0.0889595i	$-0.971646\pi$
$283$	−18.1917	+	15.2647i	−1.08139	+	0.907391i	−0.0853517	+	0.996351i	$0.527201\pi$
$284$	−9.31125	+	7.81307i	−0.552521	+	0.463620i
$285$	−12.0455	−	23.7093i	−0.713515	−	1.40442i
$286$	−1.27477	+	0.463977i	−0.0753784	+	0.0274355i
$287$	5.07869	+	8.79655i	0.299786	+	0.519244i
$288$	−2.07891	−	2.16290i	−0.122501	−	0.127450i
$289$	4.79825	−	8.31081i	0.282250	−	0.488871i
$290$	−0.414905	+	2.35304i	−0.0243641	+	0.138175i
$291$	2.60725	+	21.4420i	0.152840	+	1.25695i
$292$	4.22003	+	1.53596i	0.246958	+	0.0898855i
$293$	1.70707	+	9.68130i	0.0997284	+	0.565588i	0.993195	+	0.116459i	$0.0371544\pi$
$293$	1.70707	+	9.68130i	0.0997284	+	0.565588i	−0.893467	+	0.449129i	$0.851734\pi$
$294$	1.65696	−	0.504462i	0.0966359	−	0.0294208i
$295$	20.9832	+	17.6070i	1.22169	+	1.02512i
$296$	−8.15950			−0.474261
$297$	−4.55706	+	13.0851i	−0.264427	+	0.759275i
$298$	−11.0305			−0.638980
$299$	1.07968	+	0.905956i	0.0624393	+	0.0523928i
$300$	−0.0992895	−	0.0928067i	−0.00573248	−	0.00535820i
$301$	0.745448	+	4.22764i	0.0429669	+	0.243677i
$302$	2.12578	+	0.773722i	0.122325	+	0.0445227i
$303$	14.2320	+	6.06081i	0.817607	+	0.348184i
$304$	−1.20182	+	6.81584i	−0.0689289	+	0.390915i
$305$	−12.9993	+	22.5154i	−0.744336	+	1.28923i
$306$	−4.81344	+	6.59260i	−0.275166	+	0.376874i
$307$	3.49893	+	6.06032i	0.199694	+	0.345880i	0.948429	−	0.316989i	$-0.102672\pi$
$307$	3.49893	+	6.06032i	0.199694	+	0.345880i	−0.748735	+	0.662869i	$0.769338\pi$
$308$	2.50576	−	0.912022i	0.142779	−	0.0519673i
$309$	9.54949	−	14.6673i	0.543251	−	0.834393i
$310$	−5.14997	+	4.32134i	−0.292498	+	0.245435i
$311$	−12.7575	+	10.7048i	−0.723409	+	0.607012i	−0.928326	−	0.371767i	$-0.878752\pi$
$311$	−12.7575	+	10.7048i	−0.723409	+	0.607012i	0.204917	+	0.978779i	$0.434308\pi$
$312$	−0.879890	−	0.0471466i	−0.0498140	−	0.00266915i
$313$	−23.1418	+	8.42293i	−1.30805	+	0.476092i	−0.899611	−	0.436693i	$-0.856150\pi$
$313$	−23.1418	+	8.42293i	−1.30805	+	0.476092i	−0.408441	+	0.912785i	$0.633927\pi$
$314$	2.96395	+	5.13371i	0.167265	+	0.289712i
$315$	−5.52625	+	3.70869i	−0.311369	+	0.208961i
$316$	−5.72652	+	9.91862i	−0.322142	+	0.557966i
$317$	1.07860	−	6.11702i	0.0605800	−	0.343566i	−0.939420	−	0.342769i	$-0.888635\pi$
$317$	1.07860	−	6.11702i	0.0605800	−	0.343566i	1.00000		0.000797024i	$-0.000253701\pi$
$318$	−9.52255	+	7.15828i	−0.533998	+	0.401416i
$319$	−2.69878	−	0.982277i	−0.151103	−	0.0549969i
$320$	−0.385230	−	2.18475i	−0.0215350	−	0.122131i
$321$	1.37315	−	5.91612i	0.0766415	−	0.330206i
$322$	−2.12228	−	1.78081i	−0.118270	−	0.0992404i
$323$	18.8316			1.04782
$324$	−6.05345	+	6.66001i	−0.336303	+	0.370001i
$325$	−0.0399191			−0.00221431
$326$	1.09923	+	0.922361i	0.0608806	+	0.0510849i
$327$	5.51347	−	23.7545i	0.304895	−	1.31363i
$328$	1.76381	+	10.0031i	0.0973902	+	0.552327i
$329$	0.540601	+	0.196763i	0.0298043	+	0.0108479i
$330$	−8.19023	+	6.15675i	−0.450857	+	0.338918i
$331$	−3.62837	+	20.5775i	−0.199433	+	1.13104i	0.706529	+	0.707685i	$0.250260\pi$
$331$	−3.62837	+	20.5775i	−0.199433	+	1.13104i	−0.905962	+	0.423359i	$0.860851\pi$
$332$	7.93840	−	13.7497i	0.435676	−	0.754613i
$333$	1.65032	+	24.4228i	0.0904372	+	1.33836i
$334$	5.25277	+	9.09806i	0.287419	+	0.497824i
$335$	7.86544	−	2.86279i	0.429735	−	0.156411i
$336$	1.72957	+	0.0926744i	0.0943558	+	0.00505581i
$337$	25.5557	−	21.4437i	1.39211	−	1.16812i	0.427627	−	0.903955i	$-0.359350\pi$
$337$	25.5557	−	21.4437i	1.39211	−	1.16812i	0.964479	−	0.264160i	$-0.0850947\pi$
$338$	9.76032	−	8.18988i	0.530891	−	0.445471i
$339$	2.95528	−	4.53908i	0.160509	−	0.246529i
$340$	−5.67224	+	2.06453i	−0.307620	+	0.111965i
$341$	−4.04040	−	6.99817i	−0.218800	−	0.378972i
$342$	20.6441	+	2.21869i	1.11630	+	0.119973i
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	−0.745448	+	4.22764i	−0.0401918	+	0.227939i
$345$	9.79422	+	4.17094i	0.527303	+	0.224556i
$346$	3.04250	+	1.10738i	0.163566	+	0.0595331i
$347$	−5.99210	−	33.9829i	−0.321673	−	1.82430i	−0.532094	−	0.846685i	$-0.678595\pi$
$347$	−5.99210	−	33.9829i	−0.321673	−	1.82430i	0.210422	−	0.977611i	$-0.432516\pi$
$348$	−1.36283	−	1.27385i	−0.0730553	−	0.0682854i
$349$	−0.434392	−	0.364498i	−0.0232525	−	0.0195111i	0.631087	−	0.775712i	$-0.282609\pi$
$349$	−0.434392	−	0.364498i	−0.0232525	−	0.0195111i	−0.654340	+	0.756201i	$0.727053\pi$
$350$	0.0784676			0.00419427
$351$	0.0368470	+	2.64320i	0.00196675	+	0.141084i
$352$	2.66658			0.142129
$353$	17.6820	+	14.8370i	0.941118	+	0.789692i	0.977780	−	0.209636i	$-0.0672278\pi$
$353$	17.6820	+	14.8370i	0.941118	+	0.789692i	−0.0366613	+	0.999328i	$0.511672\pi$
$354$	−20.4588	+	6.22867i	−1.08737	+	0.331050i
$355$	4.68246	+	26.5556i	0.248519	+	1.40942i
$356$	−8.75563	−	3.18679i	−0.464047	−	0.168899i
$357$	−0.568867	−	4.67834i	−0.0301076	−	0.247604i
$358$	2.93498	−	16.6451i	0.155119	−	0.879722i
$359$	10.8943	−	18.8695i	0.574979	−	0.995893i	−0.421065	−	0.907031i	$-0.638343\pi$
$359$	10.8943	−	18.8695i	0.574979	−	0.995893i	0.996044	−	0.0888625i	$-0.0283232\pi$
$360$	−6.46142	+	1.59494i	−0.340547	+	0.0840610i
$361$	−14.4500	−	25.0282i	−0.760527	−	1.31727i
$362$	−2.71061	+	0.986582i	−0.142467	+	0.0518536i
$363$	3.05132	+	6.00593i	0.160153	+	0.315230i
$364$	0.389713	−	0.327008i	0.0204265	−	0.0171399i
$365$	7.63191	−	6.40394i	0.399473	−	0.335197i
$366$	−9.19404	−	18.0967i	−0.480580	−	0.945929i
$367$	30.1835	−	10.9859i	1.57556	−	0.573459i	0.601331	−	0.799000i	$-0.294637\pi$
$367$	30.1835	−	10.9859i	1.57556	−	0.573459i	0.974234	+	0.225541i	$0.0724150\pi$
$368$	−1.38522	−	2.39927i	−0.0722096	−	0.125071i
$369$	29.5842	−	7.30260i	1.54009	−	0.380158i
$370$	−9.05073	+	15.6763i	−0.470525	+	0.814973i
$371$	1.19435	−	6.77349i	0.0620075	−	0.351662i
$372$	−0.633567	−	5.21043i	−0.0328489	−	0.270148i
$373$	−32.3084	−	11.7593i	−1.67286	−	0.608873i	−0.680560	−	0.732693i	$-0.738263\pi$
$373$	−32.3084	−	11.7593i	−1.67286	−	0.608873i	−0.992305	+	0.123820i	$0.960485\pi$
$374$	−1.25992	−	7.14536i	−0.0651489	−	0.369478i
$375$	−18.6679	+	5.68344i	−0.964005	+	0.293492i
$376$	0.440702	+	0.369793i	0.0227275	+	0.0190706i
$377$	−0.547922			−0.0282194
$378$	−0.0724288	−	5.19565i	−0.00372534	−	0.267235i
$379$	13.4012			0.688371			0.344186	−	0.938902i	$-0.388155\pi$
$379$	13.4012			0.688371			0.344186	+	0.938902i	$0.388155\pi$
$380$	11.7618	+	9.86928i	0.603365	+	0.506284i
$381$	25.9464	+	24.2523i	1.32927	+	1.24248i
$382$	−1.44947	−	8.22037i	−0.0741615	−	0.420591i
$383$	−22.6494	−	8.24370i	−1.15733	−	0.421234i	−0.309187	−	0.951001i	$-0.600057\pi$
$383$	−22.6494	−	8.24370i	−1.15733	−	0.421234i	−0.848143	+	0.529768i	$0.822279\pi$
$384$	1.59357	+	0.678633i	0.0813214	+	0.0346314i
$385$	1.02725	−	5.82580i	0.0523533	−	0.296910i
$386$	−7.47230	+	12.9424i	−0.380330	+	0.658751i
$387$	12.8048	+	1.37618i	0.650907	+	0.0699551i
$388$	−6.23536	−	10.8000i	−0.316552	−	0.548285i
$389$	18.5791	−	6.76224i	0.941998	−	0.342859i	0.175044	−	0.984561i	$-0.443993\pi$
$389$	18.5791	−	6.76224i	0.941998	−	0.342859i	0.766955	+	0.641701i	$0.221771\pi$
$390$	−1.06658	+	1.63818i	−0.0540082	+	0.0829525i
$391$	−5.77460	+	4.84546i	−0.292034	+	0.245046i
$392$	−0.766044	+	0.642788i	−0.0386911	+	0.0324657i
$393$	−14.2148	−	0.761662i	−0.717041	−	0.0384207i
$394$	6.04671	−	2.20082i	0.304629	−	0.110876i
$395$	12.7040	+	22.0040i	0.639208	+	1.10714i
$396$	−0.539337	−	7.98152i	−0.0271027	−	0.401087i
$397$	−6.16453	+	10.6773i	−0.309389	+	0.535878i	−0.978229	−	0.207529i	$-0.933458\pi$
$397$	−6.16453	+	10.6773i	−0.309389	+	0.535878i	0.668840	+	0.743407i	$0.266791\pi$
$398$	−2.82186	+	16.0035i	−0.141447	+	0.802185i
$399$	−9.58209	+	7.20304i	−0.479704	+	0.360603i
$400$	0.0737354	+	0.0268375i	0.00368677	+	0.00134187i
$401$	4.19678	+	23.8011i	0.209577	+	1.18857i	0.890072	+	0.455819i	$0.150654\pi$
$401$	4.19678	+	23.8011i	0.209577	+	1.18857i	−0.680495	+	0.732753i	$0.738235\pi$
$402$	−1.47752	+	6.36581i	−0.0736920	+	0.317498i
$403$	−1.18099	−	0.990965i	−0.0588291	−	0.0493635i
$404$	−8.93090			−0.444329
$405$	6.08082	+	19.0176i	0.302158	+	0.944990i
$406$	1.07703			0.0534522
$407$	−16.6675	−	13.9857i	−0.826179	−	0.693246i
$408$	1.06553	−	4.59077i	0.0527515	−	0.227277i
$409$	−2.34815	−	13.3170i	−0.116109	−	0.658485i	−0.986195	−	0.165586i	$-0.947048\pi$
$409$	−2.34815	−	13.3170i	−0.116109	−	0.658485i	0.870087	−	0.492899i	$-0.164063\pi$
$410$	21.1747	+	7.70697i	1.04575	+	0.380620i
$411$	3.62031	−	2.72145i	0.178577	−	0.134239i
$412$	−1.75468	+	9.95130i	−0.0864470	+	0.490265i
$413$	6.17358	−	10.6930i	0.303782	−	0.526166i
$414$	−6.90127	+	4.63148i	−0.339179	+	0.227625i
$415$	−17.6110	−	30.5031i	−0.864488	−	1.49734i
$416$	0.478053	−	0.173997i	0.0234385	−	0.00853091i
$417$	−0.295393	−	0.0158278i	−0.0144654	−	0.000775092i
$418$	−14.1376	+	11.8629i	−0.691493	+	0.580231i
$419$	−19.9572	+	16.7461i	−0.974974	+	0.818100i	−0.983324	−	0.181865i	$-0.941787\pi$
$419$	−19.9572	+	16.7461i	−0.974974	+	0.818100i	0.00834951	+	0.999965i	$0.497342\pi$
$420$	2.09653	−	3.22012i	0.102300	−	0.157126i
$421$	30.7645	−	11.1974i	1.49937	−	0.545727i	0.543474	−	0.839426i	$-0.317109\pi$
$421$	30.7645	−	11.1974i	1.49937	−	0.545727i	0.955898	+	0.293699i	$0.0948864\pi$
$422$	−6.14201	−	10.6383i	−0.298988	−	0.517863i
$423$	1.01772	−	1.39389i	0.0494831	−	0.0677733i
$424$	3.43899	−	5.95651i	0.167012	−	0.289274i
$425$	0.0370748	−	0.210262i	0.00179839	−	0.0101992i
$426$	−19.3698	−	8.24877i	−0.938469	−	0.399654i
$427$	11.0125	+	4.00821i	0.532931	+	0.193971i
$428$	0.608893	+	3.45320i	0.0294319	+	0.166917i
$429$	−1.71655	−	1.60448i	−0.0828760	−	0.0774648i
$430$	7.29543	+	6.12160i	0.351817	+	0.295210i
$431$	−17.4443			−0.840262			−0.420131	−	0.907463i	$-0.638016\pi$
$431$	−17.4443			−0.840262			−0.420131	+	0.907463i	$0.638016\pi$
$432$	1.70896	−	4.90708i	0.0822222	−	0.236092i
$433$	28.5484			1.37195			0.685975	−	0.727625i	$-0.259376\pi$
$433$	28.5484			1.37195			0.685975	+	0.727625i	$0.259376\pi$
$434$	2.32142	+	1.94790i	0.111432	+	0.0935024i
$435$	−3.95905	+	1.20533i	−0.189822	+	0.0577913i
$436$	2.44483	+	13.8653i	0.117086	+	0.664029i
$437$	18.0178	+	6.55796i	0.861910	+	0.313710i
$438$	0.938904	+	7.72152i	0.0448626	+	0.368949i
$439$	4.25196	−	24.1141i	0.202935	−	1.15090i	−0.697721	−	0.716370i	$-0.745802\pi$
$439$	4.25196	−	24.1141i	0.202935	−	1.15090i	0.900656	−	0.434533i	$-0.143086\pi$
$440$	2.95784	−	5.12312i	0.141009	−	0.244235i
$441$	2.07891	+	2.16290i	0.0989959	+	0.102995i
$442$	−0.692116	−	1.19878i	−0.0329206	−	0.0570202i
$443$	4.81866	−	1.75385i	0.228941	−	0.0833279i	−0.225002	−	0.974358i	$-0.572239\pi$
$443$	4.81866	−	1.75385i	0.228941	−	0.0833279i	0.453944	+	0.891030i	$0.350017\pi$
$444$	−6.40134	−	12.5998i	−0.303794	−	0.597960i
$445$	−15.8345	+	13.2868i	−0.750629	+	0.629853i
$446$	−13.8264	+	11.6017i	−0.654697	+	0.549356i
$447$	−8.65373	−	17.0332i	−0.409307	−	0.805642i
$448$	−0.939693	+	0.342020i	−0.0443963	+	0.0161589i
$449$	7.28240	+	12.6135i	0.343678	+	0.595268i	0.985113	−	0.171910i	$-0.0549938\pi$
$449$	7.28240	+	12.6135i	0.343678	+	0.595268i	−0.641435	+	0.767178i	$0.721661\pi$
$450$	0.0654157	−	0.226131i	0.00308373	−	0.0106599i
$451$	−13.5427	+	23.4567i	−0.637701	+	1.10453i
$452$	−0.543021	+	3.07963i	−0.0255416	+	0.144853i
$453$	0.472961	+	3.88962i	0.0222216	+	0.182750i
$454$	18.8434	+	6.85844i	0.884365	+	0.321883i
$455$	−0.195980	−	1.11146i	−0.00918767	−	0.0521058i
$456$	−11.4678	+	3.49138i	−0.537029	+	0.163499i
$457$	−25.6964	−	21.5618i	−1.20202	−	1.00862i	−0.999570	−	0.0293271i	$-0.990664\pi$
$457$	−25.6964	−	21.5618i	−1.20202	−	1.00862i	−0.202455	−	0.979292i	$-0.564892\pi$
$458$	15.4939			0.723981
$459$	−13.9565	−	2.26079i	−0.651433	−	0.105525i
$460$	−6.14609			−0.286563
$461$	19.0352	+	15.9724i	0.886557	+	0.743909i	0.967516	−	0.252808i	$-0.0813541\pi$
$461$	19.0352	+	15.9724i	0.886557	+	0.743909i	−0.0809598	+	0.996717i	$0.525799\pi$
$462$	3.37417	+	3.15386i	0.156981	+	0.146731i
$463$	−4.45487	−	25.2648i	−0.207035	−	1.17416i	−0.894205	−	0.447658i	$-0.852258\pi$
$463$	−4.45487	−	25.2648i	−0.207035	−	1.17416i	0.687169	−	0.726497i	$-0.258853\pi$
$464$	1.01208	+	0.368366i	0.0469846	+	0.0171010i
$465$	−10.7132	−	4.56232i	−0.496815	−	0.211572i
$466$	0.655889	−	3.71973i	0.0303835	−	0.172313i
$467$	−10.0986	+	17.4912i	−0.467305	+	0.809397i	−0.999302	−	0.0373497i	$-0.988108\pi$
$467$	−10.0986	+	17.4912i	−0.467305	+	0.809397i	0.531997	+	0.846746i	$0.321442\pi$
$468$	−0.617494	−	1.39570i	−0.0285437	−	0.0645165i
$469$	−1.88650	−	3.26752i	−0.0871105	−	0.150880i
$470$	1.19930	−	0.436508i	0.0553194	−	0.0201346i
$471$	−5.60212	+	8.60442i	−0.258132	+	0.396471i
$472$	9.45847	−	7.93660i	0.435361	−	0.365312i
$473$	−8.76909	+	7.35814i	−0.403203	+	0.338328i
$474$	−19.8088	−	1.06140i	−0.909849	−	0.0487519i
$475$	−0.510322	+	0.185742i	−0.0234152	+	0.00852242i
$476$	1.36047	+	2.35640i	0.0623570	+	0.108005i
$477$	−18.5244	−	9.08875i	−0.848175	−	0.416145i
$478$	−9.99831	+	17.3176i	−0.457312	+	0.792088i
$479$	6.42099	−	36.4153i	0.293383	−	1.66386i	−0.380321	−	0.924855i	$-0.624187\pi$
$479$	6.42099	−	36.4153i	0.293383	−	1.66386i	0.673704	−	0.739002i	$-0.264702\pi$
$480$	3.07144	−	2.30886i	0.140191	−	0.105385i
$481$	−3.90067	−	1.41973i	−0.177855	−	0.0647341i
$482$	5.21747	+	29.5898i	0.237649	+	1.34778i
$483$	1.08491	−	4.67429i	0.0493653	−	0.212688i
$484$	−2.97944	−	2.50004i	−0.135429	−	0.113638i
$485$	−27.6657			−1.25623
$486$	−15.0334	−	4.12270i	−0.681929	−	0.187010i
$487$	24.3122			1.10169			0.550846	−	0.834607i	$-0.314305\pi$
$487$	24.3122			1.10169			0.550846	+	0.834607i	$0.314305\pi$
$488$	8.97745	+	7.53297i	0.406390	+	0.341002i
$489$	−0.561927	+	2.42103i	−0.0254112	+	0.109483i
$490$	0.385230	+	2.18475i	0.0174029	+	0.0986969i
$491$	−36.2577	−	13.1967i	−1.63629	−	0.595560i	−0.649903	−	0.760017i	$-0.725191\pi$
$491$	−36.2577	−	13.1967i	−1.63629	−	0.595560i	−0.986384	+	0.164457i	$0.947413\pi$
$492$	−14.0629	+	10.5713i	−0.634003	+	0.476592i
$493$	0.508882	−	2.88601i	0.0229189	−	0.129980i
$494$	−1.76047	+	3.04922i	−0.0792073	+	0.137191i
$495$	−15.9326	−	7.81712i	−0.716119	−	0.351354i
$496$	1.51520	+	2.62441i	0.0680345	+	0.117839i
$497$	11.4219	−	4.15725i	0.512344	−	0.186478i
$498$	27.4600	+	1.47137i	1.23051	+	0.0659338i
$499$	20.5338	−	17.2299i	0.919219	−	0.771316i	−0.0546313	−	0.998507i	$-0.517398\pi$
$499$	20.5338	−	17.2299i	0.919219	−	0.771316i	0.973850	+	0.227190i	$0.0729539\pi$
$500$	8.63052	−	7.24186i	0.385968	−	0.323866i
$501$	−9.92819	+	15.2489i	−0.443559	+	0.681272i
$502$	10.3489	−	3.76671i	0.461896	−	0.168116i
$503$	−16.1919	−	28.0452i	−0.721962	−	1.25047i	−0.960212	−	0.279271i	$-0.909907\pi$
$503$	−16.1919	−	28.0452i	−0.721962	−	1.25047i	0.238250	−	0.971204i	$-0.423426\pi$
$504$	1.21379	+	2.74349i	0.0540663	+	0.122205i
$505$	−9.90639	+	17.1584i	−0.440829	+	0.763538i
$506$	1.28284	−	7.27536i	0.0570293	−	0.323429i
$507$	20.3039	+	8.64659i	0.901730	+	0.384009i
$508$	−19.2686	−	7.01319i	−0.854905	−	0.311160i
$509$	−3.26683	−	18.5271i	−0.144800	−	0.821201i	−0.967528	−	0.252765i	$-0.918660\pi$
$509$	−3.26683	−	18.5271i	−0.144800	−	0.821201i	0.822728	−	0.568435i	$-0.192451\pi$
$510$	−7.63804	−	7.13933i	−0.338218	−	0.316135i
$511$	−3.44020	−	2.88667i	−0.152185	−	0.127699i
$512$	−1.00000			−0.0441942
$513$	12.7698	+	33.6190i	0.563798	+	1.48431i
$514$	12.9813			0.572582
$515$	17.1725	+	14.4094i	0.756709	+	0.634954i
$516$	−7.11310	+	2.16559i	−0.313137	+	0.0953346i
$517$	0.266388	+	1.51076i	0.0117157	+	0.0664432i
$518$	7.66742	+	2.79071i	0.336887	+	0.122617i
$519$	0.676919	+	5.56696i	0.0297134	+	0.244362i
$520$	0.195980	−	1.11146i	0.00859428	−	0.0487406i
$521$	−8.42532	+	14.5931i	−0.369120	+	0.639334i	−0.989428	−	0.145024i	$-0.953674\pi$
$521$	−8.42532	+	14.5931i	−0.369120	+	0.639334i	0.620308	+	0.784358i	$0.287007\pi$
$522$	0.897884	−	3.10383i	0.0392993	−	0.135851i
$523$	−10.3417	−	17.9124i	−0.452213	−	0.783255i	0.546310	−	0.837583i	$-0.316032\pi$
$523$	−10.3417	−	17.9124i	−0.452213	−	0.783255i	−0.998523	+	0.0543273i	$0.982699\pi$
$524$	7.72303	−	2.81095i	0.337382	−	0.122797i
$525$	0.0615599	+	0.121169i	0.00268669	+	0.00528824i
$526$	−17.3623	+	14.5687i	−0.757034	+	0.635227i
$527$	6.31645	−	5.30013i	0.275149	−	0.230877i
$528$	2.09200	+	4.11769i	0.0910426	+	0.179200i
$529$	14.4005	−	5.24134i	0.626107	−	0.227884i
$530$	−7.62924	−	13.2142i	−0.331393	−	0.573989i
$531$	−25.6687	−	26.7056i	−1.11393	−	1.15892i
$532$	3.46049	−	5.99375i	0.150031	−	0.259862i
$533$	−0.897310	+	5.08890i	−0.0388668	+	0.220425i
$534$	−1.94802	−	16.0205i	−0.0842991	−	0.693273i
$535$	7.30982	+	2.66056i	0.316031	+	0.115026i
$536$	−0.655175	−	3.71568i	−0.0282992	−	0.160493i
$537$	28.0058	−	8.52636i	1.20854	−	0.367940i
$538$	−7.54976	−	6.33500i	−0.325493	−	0.273121i
$539$	−2.66658			−0.114858
$540$	−7.53205	−	8.72637i	−0.324128	−	0.375523i
$541$	28.8967			1.24237			0.621184	−	0.783665i	$-0.286652\pi$
$541$	28.8967			1.24237			0.621184	+	0.783665i	$0.286652\pi$
$542$	−16.5683	−	13.9025i	−0.711671	−	0.597163i
$543$	−3.65001	−	3.41169i	−0.156637	−	0.146410i
$544$	0.472486	+	2.67960i	0.0202577	+	0.114887i
$545$	29.3504	+	10.6827i	1.25723	+	0.457596i
$546$	0.810701	+	0.345244i	0.0346948	+	0.0147751i
$547$	1.53128	−	8.68429i	0.0654726	−	0.371314i	−0.934413	−	0.356191i	$-0.884075\pi$
$547$	1.53128	−	8.68429i	0.0654726	−	0.371314i	0.999886	−	0.0151223i	$-0.00481376\pi$
$548$	−1.30744	+	2.26456i	−0.0558512	+	0.0967372i
$549$	20.7317	−	28.3947i	0.884809	−	1.21186i
$550$	0.104620	+	0.181207i	0.00446101	+	0.00772669i
$551$	−7.00458	+	2.54946i	−0.298405	+	0.108611i
$552$	2.61819	−	4.02134i	0.111437	−	0.171159i
$553$	8.77353	−	7.36187i	0.373089	−	0.313059i
$554$	7.74088	−	6.49537i	0.328878	−	0.275962i
$555$	−31.3077	−	1.67754i	−1.32894	−	0.0712077i
$556$	0.160490	−	0.0584135i	0.00680628	−	0.00247728i
$557$	−6.13331	−	10.6232i	−0.259877	−	0.450119i	0.706332	−	0.707881i	$-0.250349\pi$
$557$	−6.13331	−	10.6232i	−0.259877	−	0.450119i	−0.966209	+	0.257761i	$0.917015\pi$
$558$	7.54884	−	5.06607i	0.319568	−	0.214464i
$559$	−1.09196	+	1.89133i	−0.0461851	+	0.0799949i
$560$	−0.385230	+	2.18475i	−0.0162790	+	0.0923225i
$561$	10.0453	−	7.55127i	0.424115	−	0.318815i
$562$	24.0925	+	8.76896i	1.01628	+	0.369896i
$563$	1.56562	+	8.87905i	0.0659828	+	0.374207i	0.999862	+	0.0166183i	$0.00529002\pi$
$563$	1.56562	+	8.87905i	0.0659828	+	0.374207i	−0.933879	+	0.357589i	$0.883599\pi$
$564$	−0.225287	+	0.970638i	−0.00948631	+	0.0408713i
$565$	5.31436	+	4.45927i	0.223577	+	0.187603i
$566$	23.7476			0.998188
$567$	7.96624	−	4.18797i	0.334551	−	0.175878i
$568$	12.1550			0.510011
$569$	22.8409	+	19.1658i	0.957542	+	0.803473i	0.980552	−	0.196262i	$-0.0628803\pi$
$569$	22.8409	+	19.1658i	0.957542	+	0.803473i	−0.0230092	+	0.999735i	$0.507325\pi$
$570$	−6.01263	+	25.9051i	−0.251841	+	1.08504i
$571$	−2.73539	−	15.5132i	−0.114473	−	0.649206i	−0.987010	−	0.160659i	$-0.948638\pi$
$571$	−2.73539	−	15.5132i	−0.114473	−	0.649206i	0.872537	−	0.488547i	$-0.162473\pi$
$572$	1.27477	+	0.463977i	0.0533006	+	0.0193998i
$573$	11.5566	−	8.68736i	0.482786	−	0.362920i
$574$	1.76381	−	10.0031i	0.0736200	−	0.417520i
$575$	0.108695	−	0.188265i	0.00453289	−	0.00785120i
$576$	0.202258	+	2.99317i	0.00842742	+	0.124716i
$577$	4.03590	+	6.99038i	0.168017	+	0.291013i	0.937722	−	0.347385i	$-0.112930\pi$
$577$	4.03590	+	6.99038i	0.168017	+	0.291013i	−0.769706	+	0.638399i	$0.779597\pi$
$578$	−9.01776	+	3.28219i	−0.375089	+	0.136521i
$579$	−25.8477	−	1.38498i	−1.07420	−	0.0575579i
$580$	1.83034	−	1.53584i	0.0760009	−	0.0637723i
$581$	−12.1623	+	10.2054i	−0.504579	+	0.423392i
$582$	11.7854	−	18.1014i	0.488519	−	0.750328i
$583$	17.2346	−	6.27287i	0.713783	−	0.259796i
$584$	−2.24543	−	3.88920i	−0.0929165	−	0.160936i
$585$	−3.36642	−	0.361800i	−0.139184	−	0.0149586i
$586$	4.91533	−	8.51359i	0.203050	−	0.351693i
$587$	0.705537	−	4.00130i	0.0291206	−	0.165151i	−0.966779	−	0.255612i	$-0.917723\pi$
$587$	0.705537	−	4.00130i	0.0291206	−	0.165151i	0.995900	+	0.0904610i	$0.0288341\pi$
$588$	−1.59357	−	0.678633i	−0.0657176	−	0.0279864i
$589$	−19.7085	−	7.17331i	−0.812075	−	0.295571i
$590$	−4.75650	−	26.9754i	−0.195822	−	1.11056i
$591$	8.14229	+	7.61066i	0.334929	+	0.313061i
$592$	6.25054	+	5.24482i	0.256895	+	0.215561i
$593$	−13.6140			−0.559060			−0.279530	−	0.960137i	$-0.590179\pi$
$593$	−13.6140			−0.559060			−0.279530	+	0.960137i	$0.590179\pi$
$594$	11.9019	−	7.09455i	0.488339	−	0.291093i
$595$	6.03627			0.247463
$596$	8.44986	+	7.09027i	0.346120	+	0.290429i
$597$	−26.9263	+	8.19773i	−1.10202	+	0.335511i
$598$	−0.244743	−	1.38801i	−0.0100083	−	0.0567597i
$599$	−11.3280	−	4.12304i	−0.462848	−	0.168463i	0.100062	−	0.994981i	$-0.468096\pi$
$599$	−11.3280	−	4.12304i	−0.462848	−	0.168463i	−0.562910	+	0.826518i	$0.690318\pi$
$600$	0.0164052	+	0.134916i	0.000669741	+	0.00550793i
$601$	1.98408	−	11.2523i	0.0809321	−	0.458989i	−0.917228	−	0.398362i	$-0.869579\pi$
$601$	1.98408	−	11.2523i	0.0809321	−	0.458989i	0.998160	−	0.0606271i	$-0.0193101\pi$
$602$	2.14643	−	3.71773i	0.0874820	−	0.151523i
$603$	−10.9892	+	2.71258i	−0.447513	+	0.110465i
$604$	−1.13111	−	1.95913i	−0.0460240	−	0.0797160i
$605$	−8.10804	+	2.95109i	−0.329639	+	0.119979i
$606$	−7.00653	−	13.7910i	−0.284621	−	0.560221i
$607$	17.5561	−	14.7313i	0.712580	−	0.597925i	−0.212742	−	0.977108i	$-0.568239\pi$
$607$	17.5561	−	14.7313i	0.712580	−	0.597925i	0.925322	+	0.379183i	$0.123795\pi$
$608$	5.30178	−	4.44872i	0.215016	−	0.180420i
$609$	0.844960	+	1.66314i	0.0342395	+	0.0673938i
$610$	24.4306	−	8.89203i	0.989168	−	0.360028i
$611$	0.146336	+	0.253461i	0.00592012	+	0.0102540i
$612$	7.92495	−	1.95620i	0.320347	−	0.0790749i
$613$	−17.0358	+	29.5069i	−0.688069	+	1.19177i	0.284393	+	0.958708i	$0.408208\pi$
$613$	−17.0358	+	29.5069i	−0.688069	+	1.19177i	−0.972462	+	0.233063i	$0.925125\pi$
$614$	1.21516	−	6.89154i	0.0490400	−	0.278120i
$615$	4.71112	+	38.7441i	0.189971	+	1.56231i
$616$	−2.50576	−	0.912022i	−0.100960	−	0.0367464i
$617$	3.00568	+	17.0460i	0.121004	+	0.686248i	0.983601	+	0.180357i	$0.0577252\pi$
$617$	3.00568	+	17.0460i	0.121004	+	0.686248i	−0.862597	+	0.505891i	$0.831164\pi$
$618$	−16.7433	+	5.09750i	−0.673514	+	0.205051i
$619$	−4.92863	−	4.13561i	−0.198098	−	0.166224i	0.538343	−	0.842726i	$-0.319051\pi$
$619$	−4.92863	−	4.13561i	−0.198098	−	0.166224i	−0.736441	+	0.676502i	$0.763495\pi$
$620$	6.72280			0.269994
$621$	−12.5661	−	7.02334i	−0.504261	−	0.281837i
$622$	16.6537			0.667752
$623$	7.13765	+	5.98920i	0.285964	+	0.239952i
$624$	0.643730	+	0.601699i	0.0257698	+	0.0240872i
$625$	−4.27201	−	24.2278i	−0.170880	−	0.969110i
$626$	23.1418	+	8.42293i	0.924932	+	0.336648i
$627$	−29.4098	−	12.5244i	−1.17451	−	0.500176i
$628$	1.02937	−	5.83784i	0.0410763	−	0.232955i
$629$	11.1007	−	19.2270i	0.442616	−	0.766633i
$630$	6.61725	+	0.711178i	0.263638	+	0.0283340i
$631$	13.5848	+	23.5296i	0.540802	+	0.936697i	0.998858	+	0.0477735i	$0.0152126\pi$
$631$	13.5848	+	23.5296i	0.540802	+	0.936697i	−0.458056	+	0.888923i	$0.651454\pi$
$632$	10.7623	−	3.91717i	0.428103	−	0.155817i
$633$	11.6089	−	17.8304i	0.461414	−	0.708696i
$634$	−4.75820	+	3.99260i	−0.188972	+	0.158566i
$635$	−34.8472	+	29.2403i	−1.38287	+	1.16037i
$636$	11.8959	+	0.637413i	0.471705	+	0.0252751i
$637$	−0.478053	+	0.173997i	−0.0189412	+	0.00689402i
$638$	1.43599	+	2.48721i	0.0568515	+	0.0984697i
$639$	−2.45844	−	36.3820i	−0.0972545	−	1.43925i
$640$	−1.10923	+	1.92124i	−0.0438460	+	0.0759435i
$641$	−6.01959	+	34.1388i	−0.237760	+	1.34840i	0.598964	+	0.800776i	$0.295579\pi$
$641$	−6.01959	+	34.1388i	−0.237760	+	1.34840i	−0.836723	+	0.547626i	$0.815532\pi$
$642$	−4.85470	+	3.64937i	−0.191600	+	0.144029i
$643$	14.1438	+	5.14791i	0.557775	+	0.203014i	0.605498	−	0.795847i	$-0.292974\pi$
$643$	14.1438	+	5.14791i	0.557775	+	0.203014i	−0.0477223	+	0.998861i	$0.515196\pi$
$644$	0.481082	+	2.72835i	0.0189573	+	0.107512i
$645$	−3.72944	+	16.0681i	−0.146846	+	0.632680i
$646$	−14.4258	−	12.1047i	−0.567576	−	0.476253i
$647$	4.60492			0.181038			0.0905191	−	0.995895i	$-0.471147\pi$
$647$	4.60492			0.181038			0.0905191	+	0.995895i	$0.471147\pi$
$648$	8.91818	−	1.21079i	0.350339	−	0.0475642i
$649$	32.9246			1.29240
$650$	0.0305798	+	0.0256595i	0.00119944	+	0.00100645i
$651$	−1.18672	+	5.11290i	−0.0465110	+	0.200390i
$652$	−0.249175	−	1.41314i	−0.00975843	−	0.0553428i
$653$	−16.2197	−	5.90350i	−0.634727	−	0.231022i	0.00456056	−	0.999990i	$-0.498548\pi$
$653$	−16.2197	−	5.90350i	−0.634727	−	0.231022i	−0.639287	+	0.768968i	$0.720771\pi$
$654$	−19.4926	+	14.6530i	−0.762223	+	0.572978i
$655$	3.16608	−	17.9558i	0.123709	−	0.701590i
$656$	5.07869	−	8.79655i	0.198290	−	0.343448i
$657$	−11.1869	+	7.50758i	−0.436442	+	0.292899i
$658$	−0.287648	−	0.498220i	−0.0112137	−	0.0194226i
$659$	−21.5107	+	7.82924i	−0.837937	+	0.304984i	−0.725112	−	0.688631i	$-0.758212\pi$
$659$	−21.5107	+	7.82924i	−0.837937	+	0.304984i	−0.112825	+	0.993615i	$0.535990\pi$
$660$	10.2316	+	0.548232i	0.398263	+	0.0213399i
$661$	33.7035	−	28.2806i	1.31092	−	1.09999i	0.322768	−	0.946478i	$-0.395387\pi$
$661$	33.7035	−	28.2806i	1.31092	−	1.09999i	0.988147	−	0.153510i	$-0.0490578\pi$
$662$	16.0065	−	13.4310i	0.622109	−	0.522012i
$663$	1.30816	−	2.00923i	0.0508047	−	0.0780322i
$664$	−14.9193	+	5.43019i	−0.578982	+	0.210732i
$665$	−7.67694	−	13.2968i	−0.297699	−	0.515630i
$666$	14.4344	−	19.7698i	0.559323	−	0.766062i
$667$	1.49193	−	2.58409i	0.0577676	−	0.100056i
$668$	1.82427	−	10.3459i	0.0705830	−	0.400296i
$669$	−28.7623	−	12.2487i	−1.11202	−	0.473561i
$670$	−7.86544	−	2.86279i	−0.303868	−	0.110599i
$671$	5.42654	+	30.7754i	0.209489	+	1.18807i
$672$	−1.26536	−	1.18274i	−0.0488122	−	0.0456251i
$673$	31.9086	+	26.7745i	1.22999	+	1.03208i	0.998240	+	0.0593051i	$0.0188885\pi$
$673$	31.9086	+	26.7745i	1.22999	+	1.03208i	0.231747	+	0.972776i	$0.425556\pi$
$674$	−33.3605			−1.28500
$675$	0.400509	−	0.0763916i	0.0154156	−	0.00294031i
$676$	−12.7412			−0.490046
$677$	29.9503	+	25.1313i	1.15108	+	0.965873i	0.999744	−	0.0226086i	$-0.00719714\pi$
$677$	29.9503	+	25.1313i	1.15108	+	0.965873i	0.151339	+	0.988482i	$0.451642\pi$
$678$	−5.18154	+	1.57752i	−0.198996	+	0.0605843i
$679$	2.16552	+	12.2813i	0.0831049	+	0.471311i
$680$	5.67224	+	2.06453i	0.217520	+	0.0791710i
$681$	4.19243	+	34.4784i	0.160654	+	1.32122i
$682$	−1.40322	+	7.95803i	−0.0537319	+	0.304729i
$683$	17.6462	−	30.5641i	0.675212	−	1.16950i	−0.301195	−	0.953563i	$-0.597385\pi$
$683$	17.6462	−	30.5641i	0.675212	−	1.16950i	0.976407	−	0.215939i	$-0.0692813\pi$
$684$	−14.3881	−	14.9694i	−0.550144	−	0.572368i
$685$	2.90050	+	5.02382i	0.110823	+	0.191950i
$686$	0.939693	−	0.342020i	0.0358776	−	0.0130584i
$687$	12.1553	+	23.9254i	0.463755	+	0.912813i
$688$	3.28852	−	2.75940i	0.125374	−	0.105201i
$689$	2.68044	−	2.24915i	0.102116	−	0.0856859i
$690$	−4.82177	−	9.49073i	−0.183562	−	0.361306i
$691$	14.4844	−	5.27188i	0.551011	−	0.200552i	−0.0514845	−	0.998674i	$-0.516395\pi$
$691$	14.4844	−	5.27188i	0.551011	−	0.200552i	0.602496	+	0.798122i	$0.294173\pi$
$692$	−1.61888	−	2.80398i	−0.0615406	−	0.106591i
$693$	−2.22303	+	7.68464i	−0.0844460	+	0.291915i
$694$	−17.2536	+	29.8840i	−0.654936	+	1.13438i
$695$	0.0657933	−	0.373133i	0.00249568	−	0.0141537i
$696$	0.225175	+	1.85183i	0.00853524	+	0.0701936i
$697$	−25.9709	−	9.45262i	−0.983716	−	0.358043i
$698$	0.0984686	+	0.558443i	0.00372709	+	0.0211374i
$699$	6.25853	−	1.90541i	0.236719	−	0.0720693i
$700$	−0.0601097	−	0.0504380i	−0.00227193	−	0.00190638i
$701$	34.8669			1.31690			0.658452	−	0.752623i	$-0.271212\pi$
$701$	34.8669			1.31690			0.658452	+	0.752623i	$0.271212\pi$
$702$	1.67079	−	2.04849i	0.0630599	−	0.0773154i
$703$	−56.4717			−2.12987
$704$	−2.04272	−	1.71404i	−0.0769877	−	0.0646004i
$705$	1.61493	+	1.50949i	0.0608218	+	0.0568506i
$706$	−4.00819	−	22.7316i	−0.150850	−	0.855513i
$707$	8.39230	+	3.05455i	0.315625	+	0.114878i
$708$	19.6760	+	8.37919i	0.739470	+	0.314909i
$709$	−6.64152	+	37.6660i	−0.249428	+	1.41457i	0.560553	+	0.828118i	$0.310589\pi$
$709$	−6.64152	+	37.6660i	−0.249428	+	1.41457i	−0.809981	+	0.586456i	$0.800523\pi$
$710$	13.4826	−	23.3526i	0.505994	−	0.876407i
$711$	−13.9015	−	31.4213i	−0.521348	−	1.17839i
$712$	4.65877	+	8.06923i	0.174595	+	0.302407i
$713$	7.88924	−	2.87145i	0.295454	−	0.107537i
$714$	−2.57140	+	3.94948i	−0.0962324	+	0.147806i
$715$	2.30541	−	1.93447i	0.0862175	−	0.0723451i
$716$	−12.9476	+	10.8643i	−0.483874	+	0.406019i
$717$	−34.5856	−	1.85318i	−1.29162	−	0.0692081i
$718$	−20.4746	+	7.45214i	−0.764105	+	0.278111i
$719$	−18.0202	−	31.2119i	−0.672039	−	1.16401i	−0.977325	−	0.211746i	$-0.932085\pi$
$719$	−18.0202	−	31.2119i	−0.672039	−	1.16401i	0.305285	−	0.952261i	$-0.401248\pi$
$720$	5.97495	+	2.93152i	0.222673	+	0.109251i
$721$	5.05241	−	8.75103i	0.188162	−	0.325905i
$722$	−5.01844	+	28.4610i	−0.186767	+	1.05921i
$723$	−41.5989	+	31.2707i	−1.54708	+	1.16297i
$724$	2.71061	+	0.986582i	0.100739	+	0.0366660i
$725$	0.0146754	+	0.0832281i	0.000545029	+	0.00309102i
$726$	1.52309	−	6.56216i	0.0565272	−	0.243545i
$727$	−1.63645	−	1.37314i	−0.0606924	−	0.0509270i	0.611937	−	0.790907i	$-0.290391\pi$
$727$	−1.63645	−	1.37314i	−0.0606924	−	0.0509270i	−0.672629	+	0.739980i	$0.734835\pi$
$728$	−0.508734			−0.0188549
$729$	−5.42787	−	26.4488i	−0.201032	−	0.979585i
$730$	−9.96276			−0.368738
$731$	−8.94787	−	7.50815i	−0.330949	−	0.277699i
$732$	−4.58929	+	19.7727i	−0.169625	+	0.730820i
$733$	0.625807	+	3.54913i	0.0231147	+	0.131090i	0.994181	−	0.107718i	$-0.0343544\pi$
$733$	0.625807	+	3.54913i	0.0231147	+	0.131090i	−0.971067	+	0.238808i	$0.923243\pi$
$734$	−30.1835	−	10.9859i	−1.11409	−	0.405497i
$735$	−3.07144	+	2.30886i	−0.113292	+	0.0851637i
$736$	−0.481082	+	2.72835i	−0.0177329	+	0.100568i
$737$	5.03050	−	8.71308i	0.185301	−	0.320950i
$738$	−27.3568	−	13.4222i	−1.00702	−	0.494079i
$739$	−6.43087	−	11.1386i	−0.236563	−	0.409740i	0.723162	−	0.690678i	$-0.242688\pi$
$739$	−6.43087	−	11.1386i	−0.236563	−	0.409740i	−0.959726	+	0.280938i	$0.909354\pi$
$740$	17.0098	−	6.19106i	0.625293	−	0.227588i
$741$	−6.08971	−	0.326301i	−0.223711	−	0.0119870i
$742$	−5.26884	+	4.42108i	−0.193425	+	0.162303i
$743$	10.7609	−	9.02947i	0.394779	−	0.331259i	−0.423692	−	0.905806i	$-0.639266\pi$
$743$	10.7609	−	9.02947i	0.394779	−	0.331259i	0.818472	+	0.574547i	$0.194822\pi$
$744$	−2.86386	+	4.39867i	−0.104994	+	0.161263i
$745$	22.9949	−	8.36946i	0.842468	−	0.306633i
$746$	17.1909	+	29.7756i	0.629405	+	1.09016i
$747$	19.2710	+	43.5578i	0.705091	+	1.59370i
$748$	−3.62779	+	6.28352i	−0.132645	+	0.229748i
$749$	0.608893	−	3.45320i	0.0222485	−	0.126177i
$750$	17.9537	+	7.64571i	0.655575	+	0.279182i
$751$	−29.9096	−	10.8862i	−1.09142	−	0.397243i	−0.267271	−	0.963622i	$-0.586122\pi$
$751$	−29.9096	−	10.8862i	−1.09142	−	0.397243i	−0.824145	+	0.566379i	$0.808344\pi$
$752$	−0.0998989	−	0.566555i	−0.00364294	−	0.0206601i
$753$	13.9355	+	13.0256i	0.507839	+	0.474681i
$754$	0.419733	+	0.352198i	0.0152858	+	0.0128263i
$755$	−5.01861			−0.182646
$756$	−3.28421	+	4.02665i	−0.119446	+	0.146448i
$757$	−28.5352			−1.03713			−0.518565	−	0.855038i	$-0.673533\pi$
$757$	−28.5352			−1.03713			−0.518565	+	0.855038i	$0.673533\pi$
$758$	−10.2659	−	8.61410i	−0.372874	−	0.312878i
$759$	12.2409	−	3.72676i	0.444318	−	0.135273i
$760$	−2.66617	−	15.1206i	−0.0967123	−	0.548482i
$761$	−22.0460	−	8.02410i	−0.799168	−	0.290873i	−0.0900265	−	0.995939i	$-0.528695\pi$
$761$	−22.0460	−	8.02410i	−0.799168	−	0.290873i	−0.709142	+	0.705066i	$0.750917\pi$
$762$	−4.28703	−	35.2564i	−0.155303	−	1.27720i
$763$	2.44483	−	13.8653i	0.0885088	−	0.501959i
$764$	−4.17359	+	7.22887i	−0.150995	+	0.261531i
$765$	5.03223	−	17.3956i	0.181941	−	0.628938i
$766$	12.0515	+	20.8738i	0.435438	+	0.754201i
$767$	5.90260	−	2.14837i	0.213131	−	0.0775732i
$768$	−0.784526	−	1.54419i	−0.0283092	−	0.0557211i
$769$	−19.5315	+	16.3888i	−0.704322	+	0.590997i	−0.923000	−	0.384801i	$-0.874270\pi$
$769$	−19.5315	+	16.3888i	−0.704322	+	0.590997i	0.218677	+	0.975797i	$0.429826\pi$
$770$	−4.53167	+	3.80252i	−0.163310	+	0.137033i
$771$	10.1842	+	20.0456i	0.366775	+	0.721925i
$772$	14.0433	−	5.11136i	0.505431	−	0.183962i
$773$	20.1300	+	34.8662i	0.724027	+	1.25405i	0.959373	+	0.282139i	$0.0910441\pi$
$773$	20.1300	+	34.8662i	0.724027	+	1.25405i	−0.235347	+	0.971911i	$0.575623\pi$
$774$	−8.92449	−	9.28501i	−0.320784	−	0.333743i
$775$	−0.118894	+	0.205931i	−0.00427081	+	0.00739725i
$776$	−2.16552	+	12.2813i	−0.0777375	+	0.440871i
$777$	1.70591	+	14.0293i	0.0611991	+	0.503299i
$778$	−18.5791	−	6.76224i	−0.666093	−	0.242438i
$779$	12.2073	+	69.2311i	0.437372	+	2.48046i
$780$	1.87005	−	0.569337i	0.0669585	−	0.0203855i
$781$	24.8292	+	20.8341i	0.888457	+	0.745504i
$782$	7.53820			0.269566
$783$	5.49732	−	1.04854i	0.196458	−	0.0374716i
$784$	1.00000			0.0357143
$785$	−10.0741	−	8.45314i	−0.359559	−	0.301706i
$786$	10.3996	+	9.72055i	0.370940	+	0.346721i
$787$	−3.47714	−	19.7198i	−0.123947	−	0.702936i	−0.981928	−	0.189255i	$-0.939393\pi$
$787$	−3.47714	−	19.7198i	−0.123947	−	0.702936i	0.857981	−	0.513681i	$-0.171718\pi$
$788$	−6.04671	−	2.20082i	−0.215405	−	0.0784011i
$789$	−36.1181	−	15.3812i	−1.28584	−	0.547584i
$790$	4.41206	−	25.0220i	0.156974	−	0.890243i
$791$	1.56357	−	2.70818i	0.0555940	−	0.0962917i
$792$	−4.71727	+	6.46088i	−0.167621	+	0.229577i
$793$	2.98098	+	5.16321i	0.105858	+	0.183351i
$794$	11.5855	−	4.21679i	0.411155	−	0.149648i
$795$	14.4199	−	22.1479i	0.511422	−	0.785505i
$796$	12.4485	−	10.4456i	0.441227	−	0.370234i
$797$	3.78113	−	3.17275i	0.133935	−	0.112384i	−0.573359	−	0.819304i	$-0.694360\pi$
$797$	3.78113	−	3.17275i	0.133935	−	0.112384i	0.707294	+	0.706919i	$0.249916\pi$
$798$	11.9703	+	0.641398i	0.423745	+	0.0227053i
$799$	−1.47094	+	0.535379i	−0.0520381	+	0.0189403i
$800$	−0.0392338	−	0.0679549i	−0.00138712	−	0.00240257i
$801$	23.2103	−	15.5766i	0.820097	−	0.550372i
$802$	12.0842	−	20.9304i	0.426706	−	0.739077i
$803$	2.07947	−	11.7933i	0.0733830	−	0.416176i
$804$	5.22371	−	3.92676i	0.184226	−	0.138486i
$805$	5.77544	+	2.10209i	0.203558	+	0.0740889i
$806$	0.267708	+	1.51825i	0.00942960	+	0.0534779i
$807$	3.85945	−	16.6282i	0.135859	−	0.585341i
$808$	6.84147	+	5.74067i	0.240682	+	0.201956i
$809$	−50.1518			−1.76324			−0.881622	−	0.471956i	$-0.843548\pi$
$809$	−50.1518			−1.76324			−0.881622	+	0.471956i	$0.843548\pi$
$810$	7.56607	−	18.4770i	0.265845	−	0.649215i
$811$	−2.73188			−0.0959293			−0.0479647	−	0.998849i	$-0.515273\pi$
$811$	−2.73188			−0.0959293			−0.0479647	+	0.998849i	$0.515273\pi$
$812$	−0.825054	−	0.692302i	−0.0289537	−	0.0242951i
$813$	8.46976	−	36.4915i	0.297048	−	1.27981i
$814$	3.77822	+	21.4274i	0.132427	+	0.751028i
$815$	−2.99137	−	1.08877i	−0.104783	−	0.0381379i
$816$	−3.76713	+	2.83183i	−0.131876	+	0.0991337i
$817$	−5.15923	+	29.2595i	−0.180499	+	1.02366i
$818$	−6.76124	+	11.7108i	−0.236401	+	0.409459i
$819$	0.102896	+	1.52273i	0.00359546	+	0.0532084i
$820$	−11.2668	−	19.5147i	−0.393455	−	0.681484i
$821$	−34.7317	+	12.6413i	−1.21215	+	0.441185i	−0.867448	−	0.497528i	$-0.834241\pi$
$821$	−34.7317	+	12.6413i	−1.21215	+	0.441185i	−0.344698	+	0.938714i	$0.612019\pi$
$822$	−4.52263	−	0.242333i	−0.157745	−	0.00845235i
$823$	−22.3531	+	18.7565i	−0.779181	+	0.653811i	−0.943042	−	0.332673i	$-0.892050\pi$
$823$	−22.3531	+	18.7565i	−0.779181	+	0.653811i	0.163861	+	0.986483i	$0.447605\pi$
$824$	7.74074	−	6.49525i	0.269661	−	0.226273i
$825$	−0.197741	+	0.303714i	−0.00688444	+	0.0105740i
$826$	−11.6025	+	4.22298i	−0.403704	+	0.146936i
$827$	2.81479	+	4.87536i	0.0978799	+	0.169533i	0.910807	−	0.412833i	$-0.135461\pi$
$827$	2.81479	+	4.87536i	0.0978799	+	0.169533i	−0.812927	+	0.582366i	$0.802127\pi$
$828$	8.26374	+	0.888131i	0.287185	+	0.0308647i
$829$	−15.7885	+	27.3465i	−0.548357	+	0.949782i	0.450030	+	0.893013i	$0.351413\pi$
$829$	−15.7885	+	27.3465i	−0.548357	+	0.949782i	−0.998387	+	0.0567689i	$0.981920\pi$
$830$	−6.11622	+	34.6868i	−0.212297	+	1.20400i
$831$	16.1030	+	6.85759i	0.558607	+	0.237887i
$832$	−0.478053	−	0.173997i	−0.0165735	−	0.00603227i
$833$	−0.472486	−	2.67960i	−0.0163707	−	0.0928427i
$834$	0.216110	+	0.201999i	0.00748327	+	0.00699467i
$835$	−17.8535	−	14.9808i	−0.617844	−	0.518433i
$836$	18.4553			0.638291
$837$	13.7452	+	7.68237i	0.475105	+	0.265541i
$838$	26.0523			0.899962
$839$	20.6630	+	17.3383i	0.713365	+	0.598584i	0.925541	−	0.378647i	$-0.123611\pi$
$839$	20.6630	+	17.3383i	0.713365	+	0.598584i	−0.212176	+	0.977231i	$0.568055\pi$
$840$	−3.67589	+	1.11913i	−0.126830	+	0.0386135i
$841$	−4.83437	−	27.4171i	−0.166702	−	0.945416i
$842$	−30.7645	−	11.1974i	−1.06022	−	0.385887i
$843$	5.36029	+	44.0829i	0.184618	+	1.51829i
$844$	−2.13310	+	12.0974i	−0.0734243	+	0.416410i
$845$	−14.1329	+	24.4788i	−0.486185	+	0.842098i
$846$	−1.67559	+	0.413605i	−0.0576081	+	0.0142200i
$847$	1.94469	+	3.36830i	0.0668203	+	0.115736i
$848$	−6.46319	+	2.35241i	−0.221947	+	0.0807820i
$849$	18.6306	+	36.6708i	0.639402	+	1.25854i
$850$	−0.163555	+	0.137239i	−0.00560988	+	0.00470725i
$851$	17.3167	−	14.5305i	0.593610	−	0.498098i
$852$	9.53590	+	18.7696i	0.326695	+	0.643035i
$853$	−5.63136	+	2.04965i	−0.192814	+	0.0701786i	−0.436622	−	0.899645i	$-0.643825\pi$
$853$	−5.63136	+	2.04965i	−0.192814	+	0.0701786i	0.243808	+	0.969823i	$0.421603\pi$
$854$	−5.85961	−	10.1491i	−0.200512	−	0.347297i
$855$	−44.7194	+	11.0386i	−1.52937	+	0.377512i
$856$	1.75324	−	3.03669i	0.0599244	−	0.103792i
$857$	−5.48675	+	31.1169i	−0.187424	+	1.06293i	0.735378	+	0.677657i	$0.237005\pi$
$857$	−5.48675	+	31.1169i	−0.187424	+	1.06293i	−0.922802	+	0.385275i	$0.874106\pi$
$858$	0.283620	+	2.33248i	0.00968262	+	0.0796295i
$859$	−2.08254	−	0.757981i	−0.0710552	−	0.0258620i	0.306248	−	0.951952i	$-0.400926\pi$
$859$	−2.08254	−	0.757981i	−0.0710552	−	0.0258620i	−0.377303	+	0.926090i	$0.623149\pi$
$860$	−1.65374	−	9.37883i	−0.0563921	−	0.319815i
$861$	16.8304	−	5.12402i	0.573578	−	0.174626i
$862$	13.3631	+	11.2130i	0.455149	+	0.381915i
$863$	16.1340			0.549209			0.274604	−	0.961557i	$-0.411453\pi$
$863$	16.1340			0.549209			0.274604	+	0.961557i	$0.411453\pi$
$864$	−4.46335	+	2.66055i	−0.151846	+	0.0905137i
$865$	−7.18282			−0.244223
$866$	−21.8694	−	18.3506i	−0.743151	−	0.623578i
$867$	−12.1430	−	11.3501i	−0.412398	−	0.385471i
$868$	−0.526224	−	2.98436i	−0.0178612	−	0.101296i
$869$	28.6986	+	10.4454i	0.973532	+	0.354337i
$870$	3.80758	+	1.62149i	0.129089	+	0.0549736i
$871$	0.333310	−	1.89029i	0.0112938	−	0.0640501i
$872$	7.03961	−	12.1930i	0.238391	−	0.412906i
$873$	37.1979	+	3.99778i	1.25896	+	0.135304i
$874$	−9.58709	−	16.6053i	−0.324288	−	0.561684i
$875$	−10.5869	+	3.85332i	−0.357902	+	0.130266i
$876$	4.24406	−	6.51854i	0.143393	−	0.220241i
$877$	−10.1286	+	8.49894i	−0.342020	+	0.286989i	−0.797576	−	0.603218i	$-0.793885\pi$
$877$	−10.1286	+	8.49894i	−0.342020	+	0.286989i	0.455556	+	0.890207i	$0.349440\pi$
$878$	−18.7574	+	15.7393i	−0.633032	+	0.531177i
$879$	17.0028	+	0.911050i	0.573490	+	0.0307290i
$880$	−5.55891	+	2.02328i	−0.187391	+	0.0682047i
$881$	−18.2273	−	31.5706i	−0.614094	−	1.06364i	−0.990543	−	0.137204i	$-0.956188\pi$
$881$	−18.2273	−	31.5706i	−0.614094	−	1.06364i	0.376449	−	0.926437i	$-0.377145\pi$
$882$	−0.202258	−	2.99317i	−0.00681039	−	0.100785i
$883$	−6.07840	+	10.5281i	−0.204555	+	0.354299i	−0.949991	−	0.312278i	$-0.898908\pi$
$883$	−6.07840	+	10.5281i	−0.204555	+	0.354299i	0.745436	+	0.666577i	$0.232241\pi$
$884$	−0.240370	+	1.36320i	−0.00808450	+	0.0458495i
$885$	37.9236	−	28.5079i	1.27479	−	0.958282i
$886$	−4.81866	−	1.75385i	−0.161886	−	0.0589217i
$887$	8.83107	+	50.0835i	0.296518	+	1.68164i	0.660967	+	0.750415i	$0.270146\pi$
$887$	8.83107	+	50.0835i	0.296518	+	1.68164i	−0.364449	+	0.931223i	$0.618743\pi$
$888$	−3.19528	+	13.7667i	−0.107227	+	0.461980i
$889$	15.7079	+	13.1805i	0.526826	+	0.442059i
$890$	20.6705			0.692878
$891$	20.2926	+	12.8128i	0.679829	+	0.429246i
$892$	18.0490			0.604326
$893$	3.05009	+	2.55933i	0.102067	+	0.0856447i
$894$	−4.31958	+	18.6107i	−0.144468	+	0.622434i
$895$	6.51112	+	36.9264i	0.217643	+	1.23431i
$896$	0.939693	+	0.342020i	0.0313929	+	0.0114261i
$897$	1.95133	−	1.46686i	0.0651532	−	0.0489769i
$898$	2.52915	−	14.3435i	0.0843989	−	0.478650i
$899$	−1.63192	+	2.82657i	−0.0544275	+	0.0942713i
$900$	−0.195466	+	0.131178i	−0.00651552	+	0.00437260i
$901$	9.35728	+	16.2073i	0.311736	+	0.539943i
$902$	25.4520	−	9.26376i	0.847458	−	0.308449i
$903$	7.42480	+	0.397839i	0.247082	+	0.0132392i
$904$	2.39552	−	2.01008i	0.0796739	−	0.0668544i
$905$	4.90214	−	4.11338i	0.162953	−	0.136733i
$906$	2.13789	−	3.28363i	0.0710266	−	0.109091i
$907$	−13.7094	+	4.98983i	−0.455215	+	0.165685i	−0.559443	−	0.828869i	$-0.688985\pi$
$907$	−13.7094	+	4.98983i	−0.455215	+	0.165685i	0.104228	+	0.994553i	$0.466763\pi$
$908$	−10.0264	−	17.3662i	−0.332737	−	0.576317i
$909$	15.7991	−	21.6388i	0.524023	−	0.717714i
$910$	−0.564301	+	0.977398i	−0.0187064	+	0.0324004i
$911$	−0.946643	+	5.36868i	−0.0313637	+	0.177872i	−0.996466	−	0.0840025i	$-0.973230\pi$
$911$	−0.946643	+	5.36868i	−0.0313637	+	0.177872i	0.965102	+	0.261875i	$0.0843407\pi$
$912$	11.0291	+	4.69681i	0.365209	+	0.155527i
$913$	−39.7835	−	14.4800i	−1.31664	−	0.479218i
$914$	5.82489	+	33.0346i	0.192670	+	1.09269i
$915$	32.8975	+	30.7495i	1.08756	+	1.01655i
$916$	−11.8690	−	9.95926i	−0.392162	−	0.329063i
$917$	−8.21868			−0.271405
$918$	9.23808	+	10.7029i	0.304902	+	0.353249i
$919$	9.93376			0.327684			0.163842	−	0.986487i	$-0.447611\pi$
$919$	9.93376			0.327684			0.163842	+	0.986487i	$0.447611\pi$
$920$	4.70818	+	3.95063i	0.155224	+	0.130249i
$921$	11.5952	−	3.53015i	0.382074	−	0.116322i
$922$	−4.31492	−	24.4712i	−0.142104	−	0.805915i
$923$	5.81073	+	2.11493i	0.191262	+	0.0696138i
$924$	−0.557501	−	4.58487i	−0.0183404	−	0.150831i
$925$	−0.111179	+	0.630529i	−0.00365555	+	0.0207317i
$926$	−12.8273	+	22.2175i	−0.421531	+	0.730113i
$927$	−21.0070	−	21.8557i	−0.689962	−	0.717834i
$928$	−0.538516	−	0.932737i	−0.0176776	−	0.0306186i
$929$	24.1046	−	8.77334i	0.790845	−	0.287844i	0.0851576	−	0.996367i	$-0.472861\pi$
$929$	24.1046	−	8.77334i	0.790845	−	0.287844i	0.705687	+	0.708524i	$0.250638\pi$
$930$	5.27422	+	10.3813i	0.172948	+	0.340415i
$931$	−5.30178	+	4.44872i	−0.173759	+	0.145801i
$932$	−2.89344	+	2.42788i	−0.0947777	+	0.0795279i
$933$	13.0653	+	25.7164i	0.427737	+	0.841918i
$934$	18.9791	−	6.90782i	0.621014	−	0.226031i
$935$	8.04809	+	13.9397i	0.263201	+	0.455877i
$936$	−0.424114	+	1.46609i	−0.0138626	+	0.0479206i
$937$	−0.553406	+	0.958528i	−0.0180790	+	0.0313137i	−0.874923	−	0.484261i	$-0.839088\pi$
$937$	−0.553406	+	0.958528i	−0.0180790	+	0.0313137i	0.856844	+	0.515575i	$0.172422\pi$
$938$	−0.655175	+	3.71568i	−0.0213922	+	0.121321i
$939$	5.14877	+	42.3433i	0.168024	+	1.38182i
$940$	−1.19930	−	0.436508i	−0.0391167	−	0.0142373i
$941$	−1.72777	−	9.79867i	−0.0563237	−	0.319427i	0.943609	−	0.331063i	$-0.107407\pi$
$941$	−1.72777	−	9.79867i	−0.0563237	−	0.319427i	−0.999932	+	0.0116356i	$0.996296\pi$
$942$	9.82229	−	2.99040i	0.320027	−	0.0974325i
$943$	−21.5568	−	18.0883i	−0.701987	−	0.589037i
$944$	−12.3472			−0.401866
$945$	4.09322	+	10.7762i	0.133152	+	0.350551i
$946$	11.4472			0.372182
$947$	−16.4379	−	13.7930i	−0.534159	−	0.448213i	0.335376	−	0.942084i	$-0.391137\pi$
$947$	−16.4379	−	13.7930i	−0.534159	−	0.448213i	−0.869535	+	0.493872i	$0.835581\pi$
$948$	14.4922	+	13.5459i	0.470684	+	0.439952i
$949$	−0.396726	−	2.24994i	−0.0128783	−	0.0730362i
$950$	0.510322	+	0.185742i	0.0165570	+	0.00602626i
$951$	−9.89826	−	4.21525i	−0.320973	−	0.136689i
$952$	0.472486	−	2.67960i	0.0153134	−	0.0868464i
$953$	8.93437	−	15.4748i	0.289413	−	0.501277i	−0.684257	−	0.729241i	$-0.739873\pi$
$953$	8.93437	−	15.4748i	0.289413	−	0.501277i	0.973670	+	0.227964i	$0.0732067\pi$
$954$	8.34840	+	18.8697i	0.270289	+	0.610928i
$955$	9.25891	+	16.0369i	0.299611	+	0.518942i
$956$	18.7907	−	6.83925i	0.607734	−	0.221197i
$957$	−2.71415	+	4.16873i	−0.0877360	+	0.134756i
$958$	−28.3260	+	23.7684i	−0.915173	+	0.767921i
$959$	2.00312	−	1.68082i	0.0646841	−	0.0542764i
$960$	−3.83697	−	0.205594i	−0.123838	−	0.00663551i
$961$	20.5010	−	7.46174i	0.661321	−	0.240701i
$962$	2.07551	+	3.59488i	0.0669170	+	0.115904i
$963$	−9.44396	−	4.63355i	−0.304327	−	0.149314i
$964$	15.0231	−	26.0208i	0.483862	−	0.838074i
$965$	5.75712	−	32.6502i	0.185328	−	1.05105i
$966$	−3.83567	+	2.88335i	−0.123411	+	0.0927702i
$967$	−51.8408	−	18.8685i	−1.66709	−	0.606770i	−0.675635	−	0.737236i	$-0.736130\pi$
$967$	−51.8408	−	18.8685i	−1.66709	−	0.606770i	−0.991453	+	0.130466i	$0.958353\pi$
$968$	0.675383	+	3.83029i	0.0217076	+	0.123110i
$969$	7.37450	−	31.7726i	0.236903	−	1.02068i
$970$	21.1931	+	17.7832i	0.680471	+	0.570983i
$971$	−1.29047			−0.0414132			−0.0207066	−	0.999786i	$-0.506592\pi$
$971$	−1.29047			−0.0414132			−0.0207066	+	0.999786i	$0.506592\pi$
$972$	8.86624	+	12.8215i	0.284385	+	0.411249i
$973$	−0.170790			−0.00547526
$974$	−18.6242	−	15.6276i	−0.596759	−	0.500741i
$975$	−0.0156324	+	0.0673516i	−0.000500639	+	0.00215698i
$976$	−2.03502	−	11.5412i	−0.0651395	−	0.369424i
$977$	7.32936	+	2.66767i	0.234487	+	0.0853463i	0.456591	−	0.889677i	$-0.349070\pi$
$977$	7.32936	+	2.66767i	0.234487	+	0.0853463i	−0.222104	+	0.975023i	$0.571292\pi$
$978$	1.98667	−	1.49342i	0.0635267	−	0.0477542i
$979$	−4.31445	+	24.4685i	−0.137890	+	0.782016i
$980$	1.10923	−	1.92124i	0.0354329	−	0.0613716i
$981$	−37.9195	−	18.6047i	−1.21068	−	0.594001i
$982$	19.2923	+	33.4153i	0.615643	+	1.06632i
$983$	36.9055	−	13.4325i	1.17710	−	0.428431i	0.321926	−	0.946765i	$-0.395670\pi$
$983$	36.9055	−	13.4325i	1.17710	−	0.428431i	0.855178	+	0.518334i	$0.173448\pi$
$984$	17.5679	+	0.941330i	0.560044	+	0.0300085i
$985$	−10.9355	+	9.17596i	−0.348433	+	0.292370i
$986$	−2.24492	+	1.88371i	−0.0714928	+	0.0599896i
$987$	0.543679	−	0.835049i	0.0173055	−	0.0265799i
$988$	3.30860	−	1.20423i	0.105261	−	0.0383117i
$989$	−5.94656	−	10.2997i	−0.189090	−	0.327513i
$990$	7.18036	+	16.2296i	0.228207	+	0.515810i
$991$	7.14803	−	12.3808i	0.227065	−	0.393288i	−0.729872	−	0.683584i	$-0.760420\pi$
$991$	7.14803	−	12.3808i	0.227065	−	0.393288i	0.956937	+	0.290296i	$0.0937538\pi$
$992$	0.526224	−	2.98436i	0.0167076	−	0.0947536i
$993$	33.2975	+	14.1800i	1.05667	+	0.449989i
$994$	−11.4219	−	4.15725i	−0.362282	−	0.131860i
$995$	−6.26016	−	35.5031i	−0.198460	−	1.12552i
$996$	−20.0898	−	18.7781i	−0.636570	−	0.595007i
$997$	−27.0795	−	22.7224i	−0.857615	−	0.719624i	0.103838	−	0.994594i	$-0.466888\pi$
$997$	−27.0795	−	22.7224i	−0.857615	−	0.719624i	−0.961453	+	0.274970i	$0.911332\pi$
$998$	−26.8050			−0.848496
$999$	41.8524	+	6.77961i	1.32415	+	0.214497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.u.e.43.4	✓	36
27.22	even	9	inner	378.2.u.e.211.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.u.e.43.4	✓	36	1.1	even	1	trivial
378.2.u.e.211.4	yes	36	27.22	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.391603 - 1.68720i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.08466 + 0.758756i) q^{5} +(-1.38450 + 1.04075i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.69329 - 1.32143i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.391603 - 1.68720i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.08466 + 0.758756i) q^{5} +(-1.38450 + 1.04075i) q^{6} +(0.173648 - 0.984808i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.69329 - 1.32143i) q^{9} +(-1.10923 - 1.92124i) q^{10} +(2.50576 - 0.912022i) q^{11} +(1.72957 + 0.0926744i) q^{12} +(0.389713 - 0.327008i) q^{13} +(-0.766044 + 0.642788i) q^{14} +(2.09653 - 3.22012i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.36047 + 2.35640i) q^{17} +(1.21379 + 2.74349i) q^{18} +(3.46049 - 5.99375i) q^{19} +(-0.385230 + 2.18475i) q^{20} +(-1.59357 - 0.678633i) q^{21} +(-2.50576 - 0.912022i) q^{22} +(0.481082 + 2.72835i) q^{23} +(-1.26536 - 1.18274i) q^{24} +(-0.0601097 - 0.0504380i) q^{25} -0.508734 q^{26} +(-3.28421 + 4.02665i) q^{27} +1.00000 q^{28} +(-0.825054 - 0.692302i) q^{29} +(-3.67589 + 1.11913i) q^{30} +(-0.526224 - 2.98436i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-0.557501 - 4.58487i) q^{33} +(0.472486 - 2.67960i) q^{34} +(1.10923 - 1.92124i) q^{35} +(0.833665 - 2.88184i) q^{36} +(-4.07975 - 7.06633i) q^{37} +(-6.50360 + 2.36712i) q^{38} +(-0.399115 - 0.785581i) q^{39} +(1.69943 - 1.42599i) q^{40} +(-7.78101 + 6.52904i) q^{41} +(0.784526 + 1.54419i) q^{42} +(-4.03397 + 1.46825i) q^{43} +(1.33329 + 2.30932i) q^{44} +(-4.61197 - 4.79828i) q^{45} +(1.38522 - 2.39927i) q^{46} +(-0.0998989 + 0.566555i) q^{47} +(0.209070 + 1.71939i) q^{48} +(-0.939693 - 0.342020i) q^{49} +(0.0136258 + 0.0772755i) q^{50} +(4.50849 - 1.37261i) q^{51} +(0.389713 + 0.327008i) q^{52} +6.87798 q^{53} +(5.10414 - 0.973543i) q^{54} +5.91567 q^{55} +(-0.766044 - 0.642788i) q^{56} +(-8.75752 - 8.18572i) q^{57} +(0.187025 + 1.06067i) q^{58} +(11.6025 + 4.22298i) q^{59} +(3.53525 + 1.50552i) q^{60} +(-2.03502 + 11.5412i) q^{61} +(-1.51520 + 2.62441i) q^{62} +(-1.76904 + 2.42291i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.06054 - 0.386005i) q^{65} +(-2.52003 + 3.87057i) q^{66} +(2.89029 - 2.42524i) q^{67} +(-2.08436 + 1.74899i) q^{68} +(4.79167 + 0.256749i) q^{69} +(-2.08466 + 0.758756i) q^{70} +(6.07749 + 10.5265i) q^{71} +(-2.49104 + 1.67175i) q^{72} +(2.24543 - 3.88920i) q^{73} +(-1.41688 + 8.03553i) q^{74} +(-0.108638 + 0.0816654i) q^{75} +(6.50360 + 2.36712i) q^{76} +(-0.463046 - 2.62606i) q^{77} +(-0.199222 + 0.858336i) q^{78} +(8.77353 + 7.36187i) q^{79} -2.21845 q^{80} +(5.50766 + 7.11798i) q^{81} +10.1574 q^{82} +(-12.1623 - 10.2054i) q^{83} +(0.391603 - 1.68720i) q^{84} +(1.04819 + 5.94457i) q^{85} +(4.03397 + 1.46825i) q^{86} +(-1.49115 + 1.12092i) q^{87} +(0.463046 - 2.62606i) q^{88} +(-4.65877 + 8.06923i) q^{89} +(0.448700 + 6.64022i) q^{90} +(-0.254367 - 0.440576i) q^{91} +(-2.60336 + 0.947547i) q^{92} +(-5.24129 - 0.280841i) q^{93} +(0.440702 - 0.369793i) q^{94} +(11.7618 - 9.86928i) q^{95} +(0.945043 - 1.45151i) q^{96} +(-11.7186 + 4.26523i) q^{97} +(0.500000 + 0.866025i) q^{98} +(-7.95392 - 0.854834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9}+O(q^{10}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9	\( 36 q + 3 q^{3} + 3 q^{5} + 6 q^{6} + 18 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{13} - 6 q^{15} + 6 q^{18} - 15 q^{19} - 6 q^{20} + 3 q^{21} - 3 q^{24} - 3 q^{25} - 18 q^{26} - 30 q^{27} + 36 q^{28} - 6 q^{29} - 9 q^{30} + 60 q^{33} + 9 q^{34} + 3 q^{35} - 27 q^{37} + 15 q^{38} + 6 q^{39} - 3 q^{40} - 9 q^{41} - 6 q^{43} + 9 q^{44} + 42 q^{45} - 9 q^{46} + 36 q^{47} + 3 q^{48} - 15 q^{50} - 36 q^{51} + 9 q^{52} - 42 q^{53} - 27 q^{54} + 30 q^{55} - 18 q^{57} - 21 q^{58} + 12 q^{59} + 24 q^{60} + 3 q^{61} + 18 q^{62} + 12 q^{63} - 18 q^{64} - 84 q^{65} + 18 q^{66} - 69 q^{67} + 9 q^{68} - 48 q^{69} - 3 q^{70} + 12 q^{71} + 6 q^{72} - 12 q^{73} + 9 q^{75} - 15 q^{76} + 9 q^{77} - 48 q^{78} - 51 q^{79} - 6 q^{80} - 69 q^{81} + 15 q^{83} + 3 q^{84} - 12 q^{85} + 6 q^{86} + 84 q^{87} - 9 q^{88} - 3 q^{89} + 6 q^{90} - 9 q^{91} + 18 q^{92} - 21 q^{93} + 9 q^{94} - 75 q^{95} - 42 q^{97} + 18 q^{98} + 39 q^{99}+O(q^{100}) \) 36 * q + 3 * q^3 + 3 * q^5 + 6 * q^6 + 18 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^13 - 6 * q^15 + 6 * q^18 - 15 * q^19 - 6 * q^20 + 3 * q^21 - 3 * q^24 - 3 * q^25 - 18 * q^26 - 30 * q^27 + 36 * q^28 - 6 * q^29 - 9 * q^30 + 60 * q^33 + 9 * q^34 + 3 * q^35 - 27 * q^37 + 15 * q^38 + 6 * q^39 - 3 * q^40 - 9 * q^41 - 6 * q^43 + 9 * q^44 + 42 * q^45 - 9 * q^46 + 36 * q^47 + 3 * q^48 - 15 * q^50 - 36 * q^51 + 9 * q^52 - 42 * q^53 - 27 * q^54 + 30 * q^55 - 18 * q^57 - 21 * q^58 + 12 * q^59 + 24 * q^60 + 3 * q^61 + 18 * q^62 + 12 * q^63 - 18 * q^64 - 84 * q^65 + 18 * q^66 - 69 * q^67 + 9 * q^68 - 48 * q^69 - 3 * q^70 + 12 * q^71 + 6 * q^72 - 12 * q^73 + 9 * q^75 - 15 * q^76 + 9 * q^77 - 48 * q^78 - 51 * q^79 - 6 * q^80 - 69 * q^81 + 15 * q^83 + 3 * q^84 - 12 * q^85 + 6 * q^86 + 84 * q^87 - 9 * q^88 - 3 * q^89 + 6 * q^90 - 9 * q^91 + 18 * q^92 - 21 * q^93 + 9 * q^94 - 75 * q^95 - 42 * q^97 + 18 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

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