LMFDB - Embedded newform 855.2.bs.c.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.2
Root			$0.394508 + 0.683308i$ of defining polynomial
Character	$\chi$	$=$	855.226
Dual form			855.2.bs.c.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0366369 + 0.207778i) q^{2} +(1.83756 + 0.668816i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.843614 + 1.46118i) q^{7} +(-0.417271 + 0.722735i) q^{8} +O(q^{10})$	\(q+(-0.0366369 + 0.207778i) q^{2} +(1.83756 + 0.668816i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.843614 + 1.46118i) q^{7} +(-0.417271 + 0.722735i) q^{8} +(0.0366369 + 0.207778i) q^{10} +(-1.44339 + 2.50003i) q^{11} +(-4.95325 + 4.15627i) q^{13} +(-0.334509 + 0.121751i) q^{14} +(2.86110 + 2.40075i) q^{16} +(-0.518598 + 2.94112i) q^{17} +(-4.34933 + 0.288668i) q^{19} +1.95549 q^{20} +(-0.466570 - 0.391499i) q^{22} +(7.75955 + 2.82424i) q^{23} +(0.766044 - 0.642788i) q^{25} +(-0.682111 - 1.18145i) q^{26} +(0.572926 + 3.24923i) q^{28} +(-1.26021 - 7.14701i) q^{29} +(-2.02800 - 3.51260i) q^{31} +(-1.88224 + 1.57939i) q^{32} +(-0.592100 - 0.215507i) q^{34} +(1.29249 + 1.08453i) q^{35} +7.96989 q^{37} +(0.0993671 - 0.914272i) q^{38} +(-0.144917 + 0.821864i) q^{40} +(-4.17950 - 3.50702i) q^{41} +(5.01011 - 1.82353i) q^{43} +(-4.32437 + 3.62858i) q^{44} +(-0.871103 + 1.50879i) q^{46} +(-0.286452 - 1.62455i) q^{47} +(2.07663 - 3.59683i) q^{49} +(0.105492 + 0.182717i) q^{50} +(-11.8817 + 4.32457i) q^{52} +(1.79663 + 0.653921i) q^{53} +(-0.501285 + 2.84293i) q^{55} -1.40806 q^{56} +1.53116 q^{58} +(-0.616931 + 3.49879i) q^{59} +(7.42370 + 2.70201i) q^{61} +(0.804142 - 0.292684i) q^{62} +(3.47569 + 6.02008i) q^{64} +(-3.23300 + 5.59973i) q^{65} +(0.393370 + 2.23091i) q^{67} +(-2.92002 + 5.05762i) q^{68} +(-0.272695 + 0.228818i) q^{70} +(9.79389 - 3.56469i) q^{71} +(1.08155 + 0.907529i) q^{73} +(-0.291992 + 1.65597i) q^{74} +(-8.18520 - 2.37846i) q^{76} -4.87066 q^{77} +(-1.84675 - 1.54961i) q^{79} +(3.50966 + 1.27741i) q^{80} +(0.881806 - 0.739923i) q^{82} +(-5.70029 - 9.87319i) q^{83} +(0.518598 + 2.94112i) q^{85} +(0.195335 + 1.10780i) q^{86} +(-1.20457 - 2.08638i) q^{88} +(7.74938 - 6.50250i) q^{89} +(-10.2517 - 3.73131i) q^{91} +(12.3697 + 10.3794i) q^{92} +0.348041 q^{94} +(-3.98830 + 1.75882i) q^{95} +(-1.71360 + 9.71828i) q^{97} +(0.671262 + 0.563256i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.0366369	+	0.207778i	−0.0259062	+	0.146921i	−0.995017	−	0.0997037i	$-0.968211\pi$
$2$	−0.0366369	+	0.207778i	−0.0259062	+	0.146921i	0.969111	+	0.246625i	$0.0793216\pi$
$3$		0			0
$3$		0			0
$4$	1.83756	+	0.668816i	0.918778	+	0.334408i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$		0			0
$7$	0.843614	+	1.46118i	0.318856	+	0.552275i	0.980250	−	0.197764i	$-0.0633680\pi$
$7$	0.843614	+	1.46118i	0.318856	+	0.552275i	−0.661394	+	0.750039i	$0.730035\pi$
$8$	−0.417271	+	0.722735i	−0.147528	+	0.255526i
$9$		0			0
$10$	0.0366369	+	0.207778i	0.0115856	+	0.0657053i
$11$	−1.44339	+	2.50003i	−0.435199	+	0.753787i	−0.997312	−	0.0732738i	$-0.976655\pi$
$11$	−1.44339	+	2.50003i	−0.435199	+	0.753787i	0.562113	+	0.827061i	$0.309989\pi$
$12$		0			0
$13$	−4.95325	+	4.15627i	−1.37378	+	1.15274i	−0.402336	+	0.915492i	$0.631802\pi$
$13$	−4.95325	+	4.15627i	−1.37378	+	1.15274i	−0.971449	+	0.237250i	$0.923754\pi$
$14$	−0.334509	+	0.121751i	−0.0894014	+	0.0325394i
$15$		0			0
$16$	2.86110	+	2.40075i	0.715274	+	0.600186i
$17$	−0.518598	+	2.94112i	−0.125778	+	0.713325i	0.855064	+	0.518523i	$0.173518\pi$
$17$	−0.518598	+	2.94112i	−0.125778	+	0.713325i	−0.980842	+	0.194803i	$0.937593\pi$
$18$		0			0
$19$	−4.34933	+	0.288668i	−0.997805	+	0.0662249i
$19$	−4.34933	+	0.288668i	−0.997805	+	0.0662249i
$20$	1.95549			0.437260
$21$		0			0
$22$	−0.466570	−	0.391499i	−0.0994731	−	0.0834678i
$23$	7.75955	+	2.82424i	1.61798	+	0.588896i	0.982995	−	0.183631i	$-0.0587853\pi$
$23$	7.75955	+	2.82424i	1.61798	+	0.588896i	0.634982	+	0.772527i	$0.281008\pi$
$24$		0			0
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−0.682111	−	1.18145i	−0.133773	−	0.231702i
$27$		0			0
$28$	0.572926	+	3.24923i	0.108273	+	0.614046i
$29$	−1.26021	−	7.14701i	−0.234015	−	1.32717i	−0.844677	−	0.535276i	$-0.820208\pi$
$29$	−1.26021	−	7.14701i	−0.234015	−	1.32717i	0.610662	−	0.791891i	$-0.290903\pi$
$30$		0			0
$31$	−2.02800	−	3.51260i	−0.364240	−	0.630882i	0.624414	−	0.781094i	$-0.285338\pi$
$31$	−2.02800	−	3.51260i	−0.364240	−	0.630882i	−0.988654	+	0.150212i	$0.952005\pi$
$32$	−1.88224	+	1.57939i	−0.332736	+	0.279199i
$33$		0			0
$34$	−0.592100	−	0.215507i	−0.101544	−	0.0369591i
$35$	1.29249	+	1.08453i	0.218471	+	0.183319i
$36$		0			0
$37$	7.96989			1.31024			0.655121	−	0.755524i	$-0.272618\pi$
$37$	7.96989			1.31024			0.655121	+	0.755524i	$0.272618\pi$
$38$	0.0993671	−	0.914272i	0.0161195	−	0.148315i
$39$		0			0
$40$	−0.144917	+	0.821864i	−0.0229134	+	0.129948i
$41$	−4.17950	−	3.50702i	−0.652728	−	0.547704i	0.255169	−	0.966896i	$-0.417869\pi$
$41$	−4.17950	−	3.50702i	−0.652728	−	0.547704i	−0.907897	+	0.419192i	$0.862313\pi$
$42$		0			0
$43$	5.01011	−	1.82353i	0.764034	−	0.278086i	0.0695352	−	0.997580i	$-0.477848\pi$
$43$	5.01011	−	1.82353i	0.764034	−	0.278086i	0.694499	+	0.719494i	$0.255626\pi$
$44$	−4.32437	+	3.62858i	−0.651923	+	0.547029i
$45$		0			0
$46$	−0.871103	+	1.50879i	−0.128437	+	0.222460i
$47$	−0.286452	−	1.62455i	−0.0417833	−	0.236965i	0.956763	−	0.290869i	$-0.0939445\pi$
$47$	−0.286452	−	1.62455i	−0.0417833	−	0.236965i	−0.998546	+	0.0539044i	$0.982833\pi$
$48$		0			0
$49$	2.07663	−	3.59683i	0.296662	−	0.513833i
$50$	0.105492	+	0.182717i	0.0149188	+	0.0258401i
$51$		0			0
$52$	−11.8817	+	4.32457i	−1.64769	+	0.599710i
$53$	1.79663	+	0.653921i	0.246787	+	0.0898230i	0.462452	−	0.886644i	$-0.346970\pi$
$53$	1.79663	+	0.653921i	0.246787	+	0.0898230i	−0.215665	+	0.976467i	$0.569192\pi$
$54$		0			0
$55$	−0.501285	+	2.84293i	−0.0675932	+	0.383340i
$56$	−1.40806			−0.188160
$57$		0			0
$58$	1.53116			0.201052
$59$	−0.616931	+	3.49879i	−0.0803175	+	0.455503i	0.917952	+	0.396692i	$0.129842\pi$
$59$	−0.616931	+	3.49879i	−0.0803175	+	0.455503i	−0.998269	+	0.0588110i	$0.981269\pi$
$60$		0			0
$61$	7.42370	+	2.70201i	0.950508	+	0.345956i	0.770307	−	0.637673i	$-0.220103\pi$
$61$	7.42370	+	2.70201i	0.950508	+	0.345956i	0.180201	+	0.983630i	$0.442325\pi$
$62$	0.804142	−	0.292684i	0.102126	−	0.0371709i
$63$		0			0
$64$	3.47569	+	6.02008i	0.434462	+	0.752510i
$65$	−3.23300	+	5.59973i	−0.401005	+	0.694561i
$66$		0			0
$67$	0.393370	+	2.23091i	0.0480578	+	0.272550i	0.999362	−	0.0357028i	$-0.0113670\pi$
$67$	0.393370	+	2.23091i	0.0480578	+	0.272550i	−0.951305	+	0.308252i	$0.900256\pi$
$68$	−2.92002	+	5.05762i	−0.354104	+	0.613326i
$69$		0			0
$70$	−0.272695	+	0.228818i	−0.0325932	+	0.0273490i
$71$	9.79389	−	3.56469i	1.16232	−	0.423050i	0.312395	−	0.949952i	$-0.398869\pi$
$71$	9.79389	−	3.56469i	1.16232	−	0.423050i	0.849926	+	0.526902i	$0.176646\pi$
$72$		0			0
$73$	1.08155	+	0.907529i	0.126586	+	0.106218i	0.703883	−	0.710316i	$-0.251448\pi$
$73$	1.08155	+	0.907529i	0.126586	+	0.106218i	−0.577297	+	0.816534i	$0.695892\pi$
$74$	−0.291992	+	1.65597i	−0.0339434	+	0.192503i
$75$		0			0
$76$	−8.18520	−	2.37846i	−0.938907	−	0.272828i
$77$	−4.87066			−0.555063
$78$		0			0
$79$	−1.84675	−	1.54961i	−0.207776	−	0.174344i	0.532961	−	0.846140i	$-0.321079\pi$
$79$	−1.84675	−	1.54961i	−0.207776	−	0.174344i	−0.740737	+	0.671795i	$0.765524\pi$
$80$	3.50966	+	1.27741i	0.392391	+	0.142819i
$81$		0			0
$82$	0.881806	−	0.739923i	0.0973792	−	0.0817108i
$83$	−5.70029	−	9.87319i	−0.625688	−	1.08372i	−0.988407	−	0.151825i	$-0.951485\pi$
$83$	−5.70029	−	9.87319i	−0.625688	−	1.08372i	0.362719	−	0.931898i	$-0.381848\pi$
$84$		0			0
$85$	0.518598	+	2.94112i	0.0562498	+	0.319009i
$86$	0.195335	+	1.10780i	0.0210635	+	0.119457i
$87$		0			0
$88$	−1.20457	−	2.08638i	−0.128408	−	0.222409i
$89$	7.74938	−	6.50250i	0.821433	−	0.689264i	−0.131874	−	0.991266i	$-0.542099\pi$
$89$	7.74938	−	6.50250i	0.821433	−	0.689264i	0.953307	+	0.302002i	$0.0976550\pi$
$90$		0			0
$91$	−10.2517	−	3.73131i	−1.07467	−	0.391148i
$92$	12.3697	+	10.3794i	1.28963	+	1.08213i
$93$		0			0
$94$	0.348041			0.0358977
$95$	−3.98830	+	1.75882i	−0.409191	+	0.180451i
$96$		0			0
$97$	−1.71360	+	9.71828i	−0.173989	+	0.986742i	0.765315	+	0.643656i	$0.222583\pi$
$97$	−1.71360	+	9.71828i	−0.173989	+	0.986742i	−0.939304	+	0.343086i	$0.888528\pi$
$98$	0.671262	+	0.563256i	0.0678077	+	0.0568974i
$99$		0			0
$100$	1.83756	−	0.668816i	0.183756	−	0.0668816i
$101$	−3.19421	+	2.68026i	−0.317836	+	0.266696i	−0.787722	−	0.616031i	$-0.788740\pi$
$101$	−3.19421	+	2.68026i	−0.317836	+	0.266696i	0.469886	+	0.882727i	$0.344295\pi$
$102$		0			0
$103$	6.28180	−	10.8804i	0.618964	−	1.07208i	−0.370711	−	0.928748i	$-0.620886\pi$
$103$	6.28180	−	10.8804i	0.618964	−	1.07208i	0.989675	−	0.143329i	$-0.0457809\pi$
$104$	−0.937034	−	5.31418i	−0.0918837	−	0.521098i
$105$		0			0
$106$	−0.201694	+	0.349344i	−0.0195902	+	0.0339313i
$107$	7.47116	+	12.9404i	0.722264	+	1.25100i	0.960090	+	0.279690i	$0.0902318\pi$
$107$	7.47116	+	12.9404i	0.722264	+	1.25100i	−0.237826	+	0.971308i	$0.576435\pi$
$108$		0			0
$109$	−4.89106	+	1.78020i	−0.468479	+	0.170512i	−0.565463	−	0.824774i	$-0.691303\pi$
$109$	−4.89106	+	1.78020i	−0.468479	+	0.170512i	0.0969843	+	0.995286i	$0.469080\pi$
$110$	−0.572333	−	0.208312i	−0.0545698	−	0.0198618i
$111$		0			0
$112$	−1.09427	+	6.20589i	−0.103398	+	0.586401i
$113$	−8.57064			−0.806258			−0.403129	−	0.915143i	$-0.632077\pi$
$113$	−8.57064			−0.806258			−0.403129	+	0.915143i	$0.632077\pi$
$114$		0			0
$115$	8.25754			0.770019
$116$	2.46433	−	13.9759i	0.228807	−	1.29763i
$117$		0			0
$118$	−0.704370	−	0.256370i	−0.0648425	−	0.0236007i
$119$	−4.73500	+	1.72340i	−0.434057	+	0.157984i
$120$		0			0
$121$	1.33324	+	2.30924i	0.121204	+	0.209931i
$122$	−0.833400	+	1.44349i	−0.0754525	+	0.130688i
$123$		0			0
$124$	−1.37728	−	7.81096i	−0.123684	−	0.701445i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	9.98688	−	8.37999i	0.886192	−	0.743604i	−0.0812503	−	0.996694i	$-0.525891\pi$
$127$	9.98688	−	8.37999i	0.886192	−	0.743604i	0.967443	+	0.253090i	$0.0814469\pi$
$128$	−5.99600	+	2.18236i	−0.529976	+	0.192896i
$129$		0			0
$130$	−1.04505	−	0.876905i	−0.0916574	−	0.0769097i
$131$	−0.0324867	+	0.184241i	−0.00283838	+	0.0160972i	−0.986194	−	0.165594i	$-0.947046\pi$
$131$	−0.0324867	+	0.184241i	−0.00283838	+	0.0160972i	0.983356	+	0.181691i	$0.0581571\pi$
$132$		0			0
$133$	−4.09095	−	6.11164i	−0.354730	−	0.529946i
$134$	−0.477948			−0.0412884
$135$		0			0
$136$	−1.90925	−	1.60205i	−0.163717	−	0.137375i
$137$	2.02559	+	0.737254i	0.173058	+	0.0629879i	0.427096	−	0.904206i	$-0.359537\pi$
$137$	2.02559	+	0.737254i	0.173058	+	0.0629879i	−0.254038	+	0.967194i	$0.581759\pi$
$138$		0			0
$139$	−6.04955	+	5.07617i	−0.513116	+	0.430555i	−0.862224	−	0.506527i	$-0.830929\pi$
$139$	−6.04955	+	5.07617i	−0.513116	+	0.430555i	0.349108	+	0.937082i	$0.386485\pi$
$140$	1.64967	+	2.85732i	0.139423	+	0.241488i
$141$		0			0
$142$	0.381846	+	2.16556i	0.0320438	+	0.181730i
$143$	−3.24131	−	18.3824i	−0.271052	−	1.53721i
$144$		0			0
$145$	−3.62863	−	6.28498i	−0.301342	−	0.521939i
$146$	−0.228189	+	0.191474i	−0.0188851	+	0.0158465i
$147$		0			0
$148$	14.6451	+	5.33039i	1.20382	+	0.438155i
$149$	−13.7096	−	11.5037i	−1.12313	−	0.942421i	−0.124375	−	0.992235i	$-0.539693\pi$
$149$	−13.7096	−	11.5037i	−1.12313	−	0.942421i	−0.998759	+	0.0498141i	$0.984137\pi$
$150$		0			0
$151$	2.93984			0.239241			0.119620	−	0.992820i	$-0.461832\pi$
$151$	2.93984			0.239241			0.119620	+	0.992820i	$0.461832\pi$
$152$	1.60622	−	3.26387i	0.130282	−	0.264735i
$153$		0			0
$154$	0.178446	−	1.01202i	0.0143796	−	0.0815507i
$155$	−3.10708	−	2.60715i	−0.249567	−	0.209411i
$156$		0			0
$157$	−6.35878	+	2.31441i	−0.507486	+	0.184710i	−0.583058	−	0.812431i	$-0.698144\pi$
$157$	−6.35878	+	2.31441i	−0.507486	+	0.184710i	0.0755720	+	0.997140i	$0.475922\pi$
$158$	0.389634	−	0.326942i	0.0309976	−	0.0260101i
$159$		0			0
$160$	−1.22854	+	2.12790i	−0.0971249	+	0.168225i
$161$	2.41933	+	13.7207i	0.190670	+	1.08134i
$162$		0			0
$163$	0.453917	−	0.786207i	0.0355535	−	0.0615805i	−0.847701	−	0.530474i	$-0.822014\pi$
$163$	0.453917	−	0.786207i	0.0355535	−	0.0615805i	0.883255	+	0.468894i	$0.155347\pi$
$164$	−5.33452	−	9.23965i	−0.416556	−	0.721496i
$165$		0			0
$166$	2.26028	−	0.822673i	0.175431	−	0.0638518i
$167$	13.4109	+	4.88117i	1.03777	+	0.377716i	0.804033	−	0.594585i	$-0.202683\pi$
$167$	13.4109	+	4.88117i	1.03777	+	0.377716i	0.233733	+	0.972301i	$0.424906\pi$
$168$		0			0
$169$	5.00268	−	28.3716i	0.384822	−	2.18243i
$170$	−0.630100			−0.0483264
$171$		0			0
$172$	10.4260			0.794971
$173$	−2.44452	+	13.8636i	−0.185854	+	1.05403i	0.739000	+	0.673705i	$0.235298\pi$
$173$	−2.44452	+	13.8636i	−0.185854	+	1.05403i	−0.924854	+	0.380323i	$0.875813\pi$
$174$		0			0
$175$	1.58548	+	0.577066i	0.119851	+	0.0436221i
$176$	−10.1316	+	3.68761i	−0.763699	+	0.277964i
$177$		0			0
$178$	1.06717	+	1.84839i	0.0799875	+	0.138542i
$179$	7.87488	−	13.6397i	0.588596	−	1.01948i	−0.405821	−	0.913953i	$-0.633014\pi$
$179$	7.87488	−	13.6397i	0.588596	−	1.01948i	0.994417	−	0.105525i	$-0.0336524\pi$
$180$		0			0
$181$	0.791542	+	4.48906i	0.0588348	+	0.333669i	0.999991	−	0.00430380i	$-0.00136995\pi$
$181$	0.791542	+	4.48906i	0.0588348	+	0.333669i	−0.941156	+	0.337973i	$0.890259\pi$
$182$	1.15088	−	1.99338i	0.0853087	−	0.147759i
$183$		0			0
$184$	−5.27902	+	4.42962i	−0.389174	+	0.326556i
$185$	7.48925	−	2.72586i	0.550621	−	0.200409i
$186$		0			0
$187$	−6.60433	−	5.54169i	−0.482956	−	0.405249i
$188$	0.560153	−	3.17678i	0.0408533	−	0.231691i
$189$		0			0
$190$	−0.219325	−	0.893121i	−0.0159115	−	0.0647938i
$191$	9.95887			0.720599			0.360299	−	0.932837i	$-0.382675\pi$
$191$	9.95887			0.720599			0.360299	+	0.932837i	$0.382675\pi$
$192$		0			0
$193$	−16.3943	−	13.7564i	−1.18009	−	0.990210i	−0.999978	−	0.00656365i	$-0.997911\pi$
$193$	−16.3943	−	13.7564i	−1.18009	−	0.990210i	−0.180108	−	0.983647i	$-0.557645\pi$
$194$	−1.95647	−	0.712096i	−0.140466	−	0.0511255i
$195$		0			0
$196$	6.22154	−	5.22049i	0.444396	−	0.372892i
$197$	0.683372	+	1.18364i	0.0486883	+	0.0843305i	0.889342	−	0.457242i	$-0.151163\pi$
$197$	0.683372	+	1.18364i	0.0486883	+	0.0843305i	−0.840654	+	0.541572i	$0.817829\pi$
$198$		0			0
$199$	−3.11454	−	17.6634i	−0.220784	−	1.25213i	−0.870583	−	0.492022i	$-0.836258\pi$
$199$	−3.11454	−	17.6634i	−0.220784	−	1.25213i	0.649799	−	0.760106i	$-0.274853\pi$
$200$	0.144917	+	0.821864i	0.0102472	+	0.0581146i
$201$		0			0
$202$	−0.439874	−	0.761885i	−0.0309495	−	0.0536060i
$203$	9.37996	−	7.87072i	0.658344	−	0.552416i
$204$		0			0
$205$	−5.12692	−	1.86604i	−0.358079	−	0.130330i
$206$	2.03057	+	1.70385i	0.141476	+	0.118713i
$207$		0			0
$208$	−24.1499			−1.67449
$209$	5.55611	−	11.2901i	0.384324	−	0.780953i
$210$		0			0
$211$	3.60629	−	20.4523i	0.248267	−	1.40799i	−0.564513	−	0.825424i	$-0.690936\pi$
$211$	3.60629	−	20.4523i	0.248267	−	1.40799i	0.812781	−	0.582570i	$-0.197953\pi$
$212$	2.86406	+	2.40323i	0.196705	+	0.165055i
$213$		0			0
$214$	−2.96246	+	1.07825i	−0.202510	+	0.0737075i
$215$	4.08428	−	3.42711i	0.278545	−	0.233727i
$216$		0			0
$217$	3.42170	−	5.92656i	0.232280	−	0.402321i
$218$	−0.190694	−	1.08148i	−0.0129154	−	0.0732469i
$219$		0			0
$220$	−2.82253	+	4.88877i	−0.190295	+	0.329601i
$221$	−9.65533	−	16.7235i	−0.649488	−	1.12495i
$222$		0			0
$223$	−1.83236	+	0.666925i	−0.122704	+	0.0446606i	−0.402642	−	0.915357i	$-0.631908\pi$
$223$	−1.83236	+	0.666925i	−0.122704	+	0.0446606i	0.279938	+	0.960018i	$0.409686\pi$
$224$	−3.89565	−	1.41790i	−0.260289	−	0.0947375i
$225$		0			0
$226$	0.314002	−	1.78079i	0.0208871	−	0.118457i
$227$	−12.6099			−0.836950			−0.418475	−	0.908228i	$-0.637435\pi$
$227$	−12.6099			−0.836950			−0.418475	+	0.908228i	$0.637435\pi$
$228$		0			0
$229$	−6.12765			−0.404926			−0.202463	−	0.979290i	$-0.564895\pi$
$229$	−6.12765			−0.404926			−0.202463	+	0.979290i	$0.564895\pi$
$230$	−0.302531	+	1.71574i	−0.0199483	+	0.113132i
$231$		0			0
$232$	5.69125	+	2.07145i	0.373649	+	0.135997i
$233$	6.20868	−	2.25977i	0.406744	−	0.148043i	−0.130542	−	0.991443i	$-0.541672\pi$
$233$	6.20868	−	2.25977i	0.406744	−	0.148043i	0.537286	+	0.843400i	$0.319450\pi$
$234$		0			0
$235$	−0.824805	−	1.42860i	−0.0538044	−	0.0931919i
$236$	−3.47369	+	6.01660i	−0.226118	+	0.391648i
$237$		0			0
$238$	−0.184609	−	1.04697i	−0.0119664	−	0.0678650i
$239$	−1.10191	+	1.90856i	−0.0712766	+	0.123455i	−0.899461	−	0.437001i	$-0.856041\pi$
$239$	−1.10191	+	1.90856i	−0.0712766	+	0.123455i	0.828184	+	0.560456i	$0.189374\pi$
$240$		0			0
$241$	−0.0956409	+	0.0802523i	−0.00616077	+	0.00516950i	−0.645863	−	0.763453i	$-0.723502\pi$
$241$	−0.0956409	+	0.0802523i	−0.00616077	+	0.00516950i	0.639702	+	0.768623i	$0.279058\pi$
$242$	−0.528656	+	0.192415i	−0.0339833	+	0.0123689i
$243$		0			0
$244$	11.8343	+	9.93017i	0.757615	+	0.635714i
$245$	0.721207	−	4.09017i	0.0460762	−	0.261311i
$246$		0			0
$247$	20.3435	−	19.5068i	1.29443	−	1.24119i
$248$	3.38491			0.214942
$249$		0			0
$250$	0.161623	+	0.135618i	0.0102219	+	0.00857721i
$251$	3.49264	+	1.27122i	0.220453	+	0.0802385i	0.449886	−	0.893086i	$-0.351465\pi$
$251$	3.49264	+	1.27122i	0.220453	+	0.0802385i	−0.229432	+	0.973325i	$0.573687\pi$
$252$		0			0
$253$	−18.2608	+	15.3226i	−1.14804	+	0.963323i
$254$	1.37529	+	2.38207i	0.0862935	+	0.149465i
$255$		0			0
$256$	2.18042	+	12.3658i	0.136276	+	0.772861i
$257$	4.68428	+	26.5659i	0.292198	+	1.65713i	0.678379	+	0.734712i	$0.262683\pi$
$257$	4.68428	+	26.5659i	0.292198	+	1.65713i	−0.386182	+	0.922423i	$0.626206\pi$
$258$		0			0
$259$	6.72351	+	11.6455i	0.417779	+	0.723614i
$260$	−9.68601	+	8.12753i	−0.600701	+	0.504048i
$261$		0			0
$262$	−0.0370911	−	0.0135001i	−0.00229150	−	0.000834036i
$263$	−15.8386	−	13.2902i	−0.976652	−	0.819508i	0.00692932	−	0.999976i	$-0.497794\pi$
$263$	−15.8386	−	13.2902i	−0.976652	−	0.819508i	−0.983581	+	0.180468i	$0.942239\pi$
$264$		0			0
$265$	1.91194			0.117449
$266$	1.41975	−	0.626099i	0.0870502	−	0.0383886i
$267$		0			0
$268$	−0.769230	+	4.36252i	−0.0469882	+	0.266483i
$269$	10.5139	+	8.82218i	0.641042	+	0.537898i	0.904338	−	0.426817i	$-0.140365\pi$
$269$	10.5139	+	8.82218i	0.641042	+	0.537898i	−0.263296	+	0.964715i	$0.584810\pi$
$270$		0			0
$271$	5.05880	−	1.84125i	0.307300	−	0.111848i	−0.183767	−	0.982970i	$-0.558829\pi$
$271$	5.05880	−	1.84125i	0.307300	−	0.111848i	0.491067	+	0.871122i	$0.336607\pi$
$272$	−8.54463	+	7.16979i	−0.518094	+	0.434733i
$273$		0			0
$274$	−0.227397	+	0.393863i	−0.0137375	+	0.0237941i
$275$	0.501285	+	2.84293i	0.0302286	+	0.171435i
$276$		0			0
$277$	−11.3993	+	19.7441i	−0.684916	+	1.18631i	0.288547	+	0.957466i	$0.406828\pi$
$277$	−11.3993	+	19.7441i	−0.684916	+	1.18631i	−0.973463	+	0.228843i	$0.926506\pi$
$278$	−0.833082	−	1.44294i	−0.0499649	−	0.0865418i
$279$		0			0
$280$	−1.32315	+	0.481586i	−0.0790732	+	0.0287803i
$281$	−16.1900	−	5.89267i	−0.965814	−	0.351528i	−0.189505	−	0.981880i	$-0.560688\pi$
$281$	−16.1900	−	5.89267i	−0.965814	−	0.351528i	−0.776309	+	0.630352i	$0.782910\pi$
$282$		0			0
$283$	2.83026	−	16.0512i	0.168242	−	0.954146i	−0.777417	−	0.628986i	$-0.783470\pi$
$283$	2.83026	−	16.0512i	0.168242	−	0.954146i	0.945659	−	0.325161i	$-0.105418\pi$
$284$	20.3809			1.20939
$285$		0			0
$286$	3.93821			0.232871
$287$	1.59851	−	9.06558i	0.0943568	−	0.535124i
$288$		0			0
$289$	7.59356	+	2.76383i	0.446680	+	0.162578i
$290$	1.43882	−	0.523689i	0.0844907	−	0.0307521i
$291$		0			0
$292$	1.38044	+	2.39099i	0.0807841	+	0.139922i
$293$	12.6441	−	21.9002i	0.738675	−	1.27942i	−0.214416	−	0.976742i	$-0.568785\pi$
$293$	12.6441	−	21.9002i	0.738675	−	1.27942i	0.953092	−	0.302681i	$-0.0978817\pi$
$294$		0			0
$295$	0.616931	+	3.49879i	0.0359191	+	0.203707i
$296$	−3.32561	+	5.76012i	−0.193297	+	0.334800i
$297$		0			0
$298$	2.89250	−	2.42710i	0.167558	−	0.140598i
$299$	−50.1733	+	18.2616i	−2.90160	+	1.05609i
$300$		0			0
$301$	6.89110	+	5.78232i	0.397197	+	0.333287i
$302$	−0.107707	+	0.610834i	−0.00619782	+	0.0351496i
$303$		0			0
$304$	−13.1369	−	9.61573i	−0.753451	−	0.551500i
$305$	7.90014			0.452361
$306$		0			0
$307$	13.1982	+	11.0746i	0.753259	+	0.632059i	0.936362	−	0.351035i	$-0.114170\pi$
$307$	13.1982	+	11.0746i	0.753259	+	0.632059i	−0.183104	+	0.983094i	$0.558614\pi$
$308$	−8.95011	−	3.25757i	−0.509980	−	0.185617i
$309$		0			0
$310$	0.655543	−	0.550066i	0.0372323	−	0.0312416i
$311$	12.4862	+	21.6267i	0.708028	+	1.22634i	0.965588	+	0.260078i	$0.0837483\pi$
$311$	12.4862	+	21.6267i	0.708028	+	1.22634i	−0.257560	+	0.966262i	$0.582918\pi$
$312$		0			0
$313$	−2.92827	−	16.6071i	−0.165516	−	0.938687i	−0.948531	−	0.316684i	$-0.897430\pi$
$313$	−2.92827	−	16.6071i	−0.165516	−	0.938687i	0.783015	−	0.622002i	$-0.213681\pi$
$314$	−0.247917	−	1.40601i	−0.0139908	−	0.0793457i
$315$		0			0
$316$	−2.35710	−	4.08263i	−0.132598	−	0.229666i
$317$	−18.4779	+	15.5048i	−1.03782	+	0.870834i	−0.991761	−	0.128104i	$-0.959111\pi$
$317$	−18.4779	+	15.5048i	−1.03782	+	0.870834i	−0.0460593	+	0.998939i	$0.514666\pi$
$318$		0			0
$319$	19.6867	+	7.16538i	1.10224	+	0.401184i
$320$	5.32507	+	4.46827i	0.297681	+	0.249784i
$321$		0			0
$322$	−2.93950			−0.163812
$323$	1.40655	−	12.9416i	0.0782624	−	0.720089i
$324$		0			0
$325$	−1.12281	+	6.36778i	−0.0622823	+	0.353221i
$326$	0.146727	+	0.123118i	0.00812644	+	0.00681889i
$327$		0			0
$328$	4.27863	−	1.55729i	0.236248	−	0.0859872i
$329$	2.13211	−	1.78905i	0.117547	−	0.0986335i
$330$		0			0
$331$	−7.77017	+	13.4583i	−0.427087	+	0.739736i	−0.996613	−	0.0822371i	$-0.973794\pi$
$331$	−7.77017	+	13.4583i	−0.427087	+	0.739736i	0.569526	+	0.821973i	$0.307127\pi$
$332$	−3.87126	−	21.9550i	−0.212463	−	1.20494i
$333$		0			0
$334$	−1.50553	+	2.60766i	−0.0823792	+	0.142685i
$335$	1.13266	+	1.96183i	0.0618841	+	0.107186i
$336$		0			0
$337$	−10.3419	+	3.76416i	−0.563361	+	0.205047i	−0.607973	−	0.793958i	$-0.708017\pi$
$337$	−10.3419	+	3.76416i	−0.563361	+	0.205047i	0.0446119	+	0.999004i	$0.485795\pi$
$338$	5.71172	+	2.07890i	0.310677	+	0.113077i
$339$		0			0
$340$	−1.01411	+	5.75131i	−0.0549979	+	0.311909i
$341$	11.7088			0.634067
$342$		0			0
$343$	18.8181			1.01608
$344$	−0.772645	+	4.38189i	−0.0416582	+	0.236255i
$345$		0			0
$346$	−2.79099	−	1.01584i	−0.150045	−	0.0546118i
$347$	28.6321	−	10.4212i	1.53705	−	0.559441i	0.571716	−	0.820451i	$-0.306278\pi$
$347$	28.6321	−	10.4212i	1.53705	−	0.559441i	0.965336	+	0.261010i	$0.0840555\pi$
$348$		0			0
$349$	−2.80872	−	4.86485i	−0.150347	−	0.260409i	0.781008	−	0.624521i	$-0.214706\pi$
$349$	−2.80872	−	4.86485i	−0.150347	−	0.260409i	−0.931355	+	0.364112i	$0.881373\pi$
$350$	−0.177989	+	0.308285i	−0.00951390	+	0.0164786i
$351$		0			0
$352$	−1.23170	−	6.98532i	−0.0656499	−	0.372319i
$353$	−3.74308	+	6.48321i	−0.199224	+	0.345067i	−0.948277	−	0.317444i	$-0.897176\pi$
$353$	−3.74308	+	6.48321i	−0.199224	+	0.345067i	0.749053	+	0.662510i	$0.230509\pi$
$354$		0			0
$355$	7.98406	−	6.69942i	0.423750	−	0.355568i
$356$	18.5889	−	6.76581i	0.985210	−	0.358587i
$357$		0			0
$358$	2.54552	+	2.13594i	0.134535	+	0.112888i
$359$	4.42550	−	25.0982i	0.233569	−	1.32463i	−0.612038	−	0.790828i	$-0.709650\pi$
$359$	4.42550	−	25.0982i	0.233569	−	1.32463i	0.845607	−	0.533806i	$-0.179239\pi$
$360$		0			0
$361$	18.8333	−	2.51102i	0.991229	−	0.132159i
$362$	−0.961728			−0.0505473
$363$		0			0
$364$	−16.3425	−	13.7130i	−0.856580	−	0.718756i
$365$	1.32672	+	0.482886i	0.0694436	+	0.0252754i
$366$		0			0
$367$	−25.6366	+	21.5117i	−1.33822	+	1.12290i	−0.356141	+	0.934432i	$0.615908\pi$
$367$	−25.6366	+	21.5117i	−1.33822	+	1.12290i	−0.982079	+	0.188468i	$0.939648\pi$
$368$	15.4205	+	26.7091i	0.803850	+	1.39231i
$369$		0			0
$370$	0.291992	+	1.65597i	0.0151800	+	0.0860898i
$371$	0.560167	+	3.17686i	0.0290824	+	0.164935i
$372$		0			0
$373$	5.23935	+	9.07481i	0.271283	+	0.469876i	0.969191	−	0.246312i	$-0.0792187\pi$
$373$	5.23935	+	9.07481i	0.271283	+	0.469876i	−0.697908	+	0.716188i	$0.745885\pi$
$374$	1.39341	−	1.16921i	0.0720513	−	0.0604582i
$375$		0			0
$376$	1.29365	+	0.470849i	0.0667148	+	0.0242822i
$377$	35.9471	+	30.1632i	1.85137	+	1.55348i
$378$		0			0
$379$	−14.2962			−0.734344			−0.367172	−	0.930153i	$-0.619674\pi$
$379$	−14.2962			−0.734344			−0.367172	+	0.930153i	$0.619674\pi$
$380$	−8.50505	+	0.564486i	−0.436300	+	0.0289575i
$381$		0			0
$382$	−0.364862	+	2.06924i	−0.0186680	+	0.105871i
$383$	−28.3295	−	23.7712i	−1.44757	−	1.21465i	−0.934331	−	0.356408i	$-0.884001\pi$
$383$	−28.3295	−	23.7712i	−1.44757	−	1.21465i	−0.513238	−	0.858246i	$-0.671554\pi$
$384$		0			0
$385$	−4.57692	+	1.66586i	−0.233262	+	0.0849003i
$386$	3.45893	−	2.90238i	0.176055	−	0.147727i
$387$		0			0
$388$	−9.64857	+	16.7118i	−0.489832	+	0.848413i
$389$	2.88385	+	16.3551i	0.146217	+	0.829237i	0.966382	+	0.257110i	$0.0827704\pi$
$389$	2.88385	+	16.3551i	0.146217	+	0.829237i	−0.820165	+	0.572127i	$0.806119\pi$
$390$		0			0
$391$	−12.3305	+	21.3571i	−0.623581	+	1.08007i
$392$	1.73304	+	3.00171i	0.0875316	+	0.151609i
$393$		0			0
$394$	−0.270970	+	0.0986252i	−0.0136513	+	0.00496866i
$395$	−2.26537	−	0.824529i	−0.113983	−	0.0414866i
$396$		0			0
$397$	−4.62570	+	26.2337i	−0.232157	+	1.31663i	0.616361	+	0.787464i	$0.288606\pi$
$397$	−4.62570	+	26.2337i	−0.232157	+	1.31663i	−0.848518	+	0.529166i	$0.822505\pi$
$398$	3.78419			0.189684
$399$		0			0
$400$	3.73490			0.186745
$401$	−0.224832	+	1.27508i	−0.0112276	+	0.0636747i	−0.989907	−	0.141720i	$-0.954737\pi$
$401$	−0.224832	+	1.27508i	−0.0112276	+	0.0636747i	0.978679	+	0.205395i	$0.0658478\pi$
$402$		0			0
$403$	24.6445	+	8.96988i	1.22763	+	0.446821i
$404$	−7.66215	+	2.78879i	−0.381206	+	0.138748i
$405$		0			0
$406$	1.29171	+	2.23731i	0.0641066	+	0.111036i
$407$	−11.5037	+	19.9250i	−0.570216	+	0.987643i
$408$		0			0
$409$	4.69402	+	26.6211i	0.232104	+	1.31633i	0.848627	+	0.528992i	$0.177430\pi$
$409$	4.69402	+	26.6211i	0.232104	+	1.31633i	−0.616522	+	0.787337i	$0.711459\pi$
$410$	0.575558	−	0.996896i	0.0284248	−	0.0492332i
$411$		0			0
$412$	18.8201	−	15.7920i	0.927202	−	0.778015i
$413$	−5.63282	+	2.05018i	−0.277173	+	0.100883i
$414$		0			0
$415$	−8.73335	−	7.32815i	−0.428703	−	0.359725i
$416$	2.75884	−	15.6462i	0.135263	−	0.767117i
$417$		0			0
$418$	2.14228	+	1.56807i	0.104782	+	0.0766970i
$419$	4.15498			0.202984			0.101492	−	0.994836i	$-0.467638\pi$
$419$	4.15498			0.202984			0.101492	+	0.994836i	$0.467638\pi$
$420$		0			0
$421$	−20.2274	−	16.9728i	−0.985822	−	0.827203i	−0.000864321	−	1.00000i	$-0.500275\pi$
$421$	−20.2274	−	16.9728i	−0.985822	−	0.827203i	−0.984957	+	0.172797i	$0.944720\pi$
$422$	4.11742	+	1.49862i	0.200433	+	0.0729516i
$423$		0			0
$424$	−1.22230	+	1.02563i	−0.0593599	+	0.0498089i
$425$	1.49324	+	2.58637i	0.0724329	+	0.125458i
$426$		0			0
$427$	2.31461	+	13.1268i	0.112012	+	0.635252i
$428$	5.07391	+	28.7756i	0.245257	+	1.39092i
$429$		0			0
$430$	0.562445	+	0.974183i	0.0271235	+	0.0469793i
$431$	7.44700	−	6.24878i	0.358710	−	0.300993i	−0.445567	−	0.895249i	$-0.646998\pi$
$431$	7.44700	−	6.24878i	0.358710	−	0.300993i	0.804276	+	0.594256i	$0.202553\pi$
$432$		0			0
$433$	0.620049	+	0.225679i	0.0297976	+	0.0108455i	0.356876	−	0.934152i	$-0.383842\pi$
$433$	0.620049	+	0.225679i	0.0297976	+	0.0108455i	−0.327078	+	0.944997i	$0.606064\pi$
$434$	1.10605	+	0.928086i	0.0530921	+	0.0445496i
$435$		0			0
$436$	−10.1782			−0.487449
$437$	−34.5641	−	10.0436i	−1.65342	−	0.480452i
$438$		0			0
$439$	4.72146	−	26.7767i	0.225343	−	1.27798i	−0.636686	−	0.771123i	$-0.719695\pi$
$439$	4.72146	−	26.7767i	0.225343	−	1.27798i	0.862029	−	0.506860i	$-0.169194\pi$
$440$	−1.84551	−	1.54857i	−0.0879813	−	0.0738251i
$441$		0			0
$442$	3.82853	−	1.39347i	0.182104	−	0.0662806i
$443$	−28.9473	+	24.2897i	−1.37533	+	1.15404i	−0.404424	+	0.914572i	$0.632528\pi$
$443$	−28.9473	+	24.2897i	−1.37533	+	1.15404i	−0.970905	+	0.239466i	$0.923028\pi$
$444$		0			0
$445$	5.05805	−	8.76080i	0.239775	−	0.415302i
$446$	−0.0714405	−	0.405159i	−0.00338280	−	0.0191848i
$447$		0			0
$448$	−5.86429	+	10.1572i	−0.277062	+	0.479885i
$449$	−8.27496	−	14.3327i	−0.390520	−	0.676400i	0.601998	−	0.798497i	$-0.294371\pi$
$449$	−8.27496	−	14.3327i	−0.390520	−	0.676400i	−0.992518	+	0.122097i	$0.961038\pi$
$450$		0			0
$451$	14.8003	−	5.38687i	0.696919	−	0.253658i
$452$	−15.7490	−	5.73218i	−0.740772	−	0.269619i
$453$		0			0
$454$	0.461989	−	2.62007i	0.0216822	−	0.122966i
$455$	−10.9096			−0.511451
$456$		0			0
$457$	11.4492			0.535571			0.267785	−	0.963479i	$-0.413708\pi$
$457$	11.4492			0.535571			0.267785	+	0.963479i	$0.413708\pi$
$458$	0.224498	−	1.27319i	0.0104901	−	0.0594923i
$459$		0			0
$460$	15.1737	+	5.52277i	0.707477	+	0.257500i
$461$	−10.1108	+	3.68002i	−0.470905	+	0.171396i	−0.566562	−	0.824019i	$-0.691727\pi$
$461$	−10.1108	+	3.68002i	−0.470905	+	0.171396i	0.0956571	+	0.995414i	$0.469505\pi$
$462$		0			0
$463$	−8.54409	−	14.7988i	−0.397078	−	0.687758i	0.596286	−	0.802772i	$-0.296642\pi$
$463$	−8.54409	−	14.7988i	−0.397078	−	0.687758i	−0.993364	+	0.115013i	$0.963309\pi$
$464$	13.5526	−	23.4737i	0.629162	−	1.08974i
$465$		0			0
$466$	0.242065	+	1.37282i	0.0112134	+	0.0635946i
$467$	15.9280	−	27.5880i	0.737058	−	1.27662i	−0.216756	−	0.976226i	$-0.569548\pi$
$467$	15.9280	−	27.5880i	0.737058	−	1.27662i	0.953815	−	0.300396i	$-0.0971189\pi$
$468$		0			0
$469$	−2.92792	+	2.45682i	−0.135199	+	0.113445i
$470$	0.327051	−	0.119037i	0.0150858	−	0.00549077i
$471$		0			0
$472$	−2.27127	−	1.90582i	−0.104544	−	0.0877225i
$473$	−2.67267	+	15.1575i	−0.122890	+	0.696941i
$474$		0			0
$475$	−3.14623	+	3.01683i	−0.144359	+	0.138422i
$476$	−9.85346			−0.451633
$477$		0			0
$478$	−0.356187	−	0.298877i	−0.0162916	−	0.0136703i
$479$	−3.61807	−	1.31687i	−0.165314	−	0.0601693i	0.258038	−	0.966135i	$-0.416924\pi$
$479$	−3.61807	−	1.31687i	−0.165314	−	0.0601693i	−0.423351	+	0.905966i	$0.639146\pi$
$480$		0			0
$481$	−39.4769	+	33.1250i	−1.79999	+	1.51037i
$482$	−0.0131707	−	0.0228123i	−0.000599909	−	0.00103907i
$483$		0			0
$484$	0.905448	+	5.13505i	0.0411567	+	0.233411i
$485$	1.71360	+	9.71828i	0.0778104	+	0.441284i
$486$		0			0
$487$	−17.7037	−	30.6638i	−0.802233	−	1.38951i	−0.918143	−	0.396249i	$-0.870312\pi$
$487$	−17.7037	−	30.6638i	−0.802233	−	1.38951i	0.115910	−	0.993260i	$-0.463022\pi$
$488$	−5.05053	+	4.23790i	−0.228627	+	0.191841i
$489$		0			0
$490$	0.823425	+	0.299702i	0.0371985	+	0.0135392i
$491$	−15.5179	−	13.0210i	−0.700311	−	0.587631i	0.221551	−	0.975149i	$-0.428888\pi$
$491$	−15.5179	−	13.0210i	−0.700311	−	0.587631i	−0.921862	+	0.387518i	$0.873333\pi$
$492$		0			0
$493$	21.6737			0.976136
$494$	3.30777	+	4.94162i	0.148824	+	0.222334i
$495$		0			0
$496$	2.63055	−	14.9186i	0.118115	−	0.669866i
$497$	13.4709	+	11.3034i	0.604253	+	0.507029i
$498$		0			0
$499$	−0.553880	+	0.201596i	−0.0247951	+	0.00902467i	−0.354388	−	0.935099i	$-0.615311\pi$
$499$	−0.553880	+	0.201596i	−0.0247951	+	0.00902467i	0.329593	+	0.944123i	$0.393089\pi$
$500$	1.49799	−	1.25696i	0.0669921	−	0.0562131i
$501$		0			0
$502$	−0.392091	+	0.679121i	−0.0174999	+	0.0303107i
$503$	1.97091	+	11.1776i	0.0878787	+	0.498385i	0.996698	+	0.0811953i	$0.0258738\pi$
$503$	1.97091	+	11.1776i	0.0878787	+	0.498385i	−0.908820	+	0.417190i	$0.863015\pi$
$504$		0			0
$505$	−2.08487	+	3.61111i	−0.0927757	+	0.160692i
$506$	−2.51468	−	4.35556i	−0.111791	−	0.193628i
$507$		0			0
$508$	23.9561	−	8.71931i	1.06288	−	0.386857i
$509$	11.1499	+	4.05822i	0.494209	+	0.179877i	0.577088	−	0.816682i	$-0.304189\pi$
$509$	11.1499	+	4.05822i	0.494209	+	0.179877i	−0.0828785	+	0.996560i	$0.526411\pi$
$510$		0			0
$511$	−0.413654	+	2.34595i	−0.0182990	+	0.103779i
$512$	−15.4108			−0.681069
$513$		0			0
$514$	−5.69143			−0.251038
$515$	2.18165	−	12.3727i	0.0961349	−	0.545208i
$516$		0			0
$517$	4.47488	+	1.62872i	0.196805	+	0.0716312i
$518$	−2.66600	+	0.970346i	−0.117137	+	0.0426346i
$519$		0			0
$520$	−2.69808	−	4.67321i	−0.118319	−	0.204934i
$521$	−12.2611	+	21.2368i	−0.537166	+	0.930400i	0.461889	+	0.886938i	$0.347172\pi$
$521$	−12.2611	+	21.2368i	−0.537166	+	0.930400i	−0.999055	+	0.0434617i	$0.986161\pi$
$522$		0			0
$523$	3.68721	+	20.9112i	0.161230	+	0.914382i	0.952867	+	0.303390i	$0.0981184\pi$
$523$	3.68721	+	20.9112i	0.161230	+	0.914382i	−0.791636	+	0.610993i	$0.790770\pi$
$524$	−0.182919	+	0.316826i	−0.00799087	+	0.0138406i
$525$		0			0
$526$	3.34169	−	2.80401i	0.145705	−	0.122261i
$527$	11.3827	−	4.14296i	0.495838	−	0.180470i
$528$		0			0
$529$	34.6152	+	29.0456i	1.50501	+	1.26285i
$530$	−0.0700475	+	0.397259i	−0.00304267	+	0.0172558i
$531$		0			0
$532$	−3.42979	−	13.9666i	−0.148700	−	0.605528i
$533$	35.2782			1.52807
$534$		0			0
$535$	11.4465	+	9.60474i	0.494874	+	0.415249i
$536$	−1.77650	−	0.646594i	−0.0767332	−	0.0279286i
$537$		0			0
$538$	−2.21825	+	1.86134i	−0.0956357	+	0.0802479i
$539$	5.99478	+	10.3833i	0.258214	+	0.447239i
$540$		0			0
$541$	2.57449	+	14.6006i	0.110686	+	0.627730i	0.988796	+	0.149272i	$0.0476930\pi$
$541$	2.57449	+	14.6006i	0.110686	+	0.627730i	−0.878110	+	0.478458i	$0.841196\pi$
$542$	0.197233	+	1.11857i	0.00847190	+	0.0480465i
$543$		0			0
$544$	−3.66903	−	6.35495i	−0.157308	−	0.272466i
$545$	−3.98723	+	3.34568i	−0.170794	+	0.143313i
$546$		0			0
$547$	−7.48131	−	2.72298i	−0.319878	−	0.116426i	0.177091	−	0.984195i	$-0.443331\pi$
$547$	−7.48131	−	2.72298i	−0.319878	−	0.116426i	−0.496969	+	0.867769i	$0.665554\pi$
$548$	3.22905	+	2.70949i	0.137938	+	0.115744i
$549$		0			0
$550$	−0.609064			−0.0259706
$551$	7.54419	+	30.7209i	0.321393	+	1.30876i
$552$		0			0
$553$	0.706315	−	4.00571i	0.0300355	−	0.170340i
$554$	−3.68476	−	3.09188i	−0.156551	−	0.131362i
$555$		0			0
$556$	−14.5114	+	5.28172i	−0.615421	+	0.223995i
$557$	6.20896	−	5.20994i	0.263082	−	0.220752i	−0.501699	−	0.865042i	$-0.667292\pi$
$557$	6.20896	−	5.20994i	0.263082	−	0.220752i	0.764781	+	0.644290i	$0.222847\pi$
$558$		0			0
$559$	−17.2372	+	29.8558i	−0.729057	+	1.26276i
$560$	1.09427	+	6.20589i	0.0462411	+	0.262247i
$561$		0			0
$562$	1.81752	−	3.14804i	0.0766675	−	0.132792i
$563$	4.14912	+	7.18648i	0.174864	+	0.302874i	0.940114	−	0.340859i	$-0.110718\pi$
$563$	4.14912	+	7.18648i	0.174864	+	0.302874i	−0.765250	+	0.643733i	$0.777385\pi$
$564$		0			0
$565$	−8.05377	+	2.93133i	−0.338825	+	0.123322i
$566$	3.23141	+	1.17614i	0.135826	+	0.0494367i
$567$		0			0
$568$	−1.51039	+	8.56583i	−0.0633745	+	0.359414i
$569$	7.28643			0.305463			0.152732	−	0.988268i	$-0.451193\pi$
$569$	7.28643			0.305463			0.152732	+	0.988268i	$0.451193\pi$
$570$		0			0
$571$	−20.6974			−0.866159			−0.433080	−	0.901356i	$-0.642573\pi$
$571$	−20.6974			−0.866159			−0.433080	+	0.901356i	$0.642573\pi$
$572$	6.33834	−	35.9465i	0.265019	−	1.50300i
$573$		0			0
$574$	1.82507	+	0.664270i	0.0761768	+	0.0277261i
$575$	7.75955	−	2.82424i	0.323595	−	0.117779i
$576$		0			0
$577$	−7.29547	−	12.6361i	−0.303715	−	0.526049i	0.673260	−	0.739406i	$-0.264894\pi$
$577$	−7.29547	−	12.6361i	−0.303715	−	0.526049i	−0.976974	+	0.213357i	$0.931560\pi$
$578$	−0.852469	+	1.47652i	−0.0354580	+	0.0614151i
$579$		0			0
$580$	−2.46433	−	13.9759i	−0.102326	−	0.580317i
$581$	9.61769	−	16.6583i	0.399009	−	0.691104i
$582$		0			0
$583$	−4.22807	+	3.54777i	−0.175109	+	0.146934i
$584$	−1.10720	+	0.402989i	−0.0458164	+	0.0166758i
$585$		0			0
$586$	4.08715	+	3.42952i	0.168838	+	0.141672i
$587$	1.82464	−	10.3481i	0.0753110	−	0.427110i	−0.923719	−	0.383071i	$-0.874866\pi$
$587$	1.82464	−	10.3481i	0.0753110	−	0.427110i	0.999030	−	0.0440388i	$-0.0140225\pi$
$588$		0			0
$589$	9.83443	+	14.6920i	0.405220	+	0.605375i
$590$	−0.749575			−0.0308595
$591$		0			0
$592$	22.8026	+	19.1337i	0.937183	+	0.786389i
$593$	22.8495	+	8.31653i	0.938316	+	0.341519i	0.765501	−	0.643435i	$-0.222491\pi$
$593$	22.8495	+	8.31653i	0.938316	+	0.341519i	0.172815	+	0.984954i	$0.444714\pi$
$594$		0			0
$595$	−3.86001	+	3.23893i	−0.158245	+	0.132783i
$596$	−17.4983	−	30.3079i	−0.716757	−	1.24146i
$597$		0			0
$598$	−1.95617	−	11.0940i	−0.0799936	−	0.453666i
$599$	6.58292	+	37.3336i	0.268971	+	1.52541i	0.757484	+	0.652854i	$0.226428\pi$
$599$	6.58292	+	37.3336i	0.268971	+	1.52541i	−0.488513	+	0.872557i	$0.662461\pi$
$600$		0			0
$601$	−12.9738	−	22.4713i	−0.529213	−	0.916623i	−0.999420	−	0.0340669i	$-0.989154\pi$
$601$	−12.9738	−	22.4713i	−0.529213	−	0.916623i	0.470207	−	0.882556i	$-0.344179\pi$
$602$	−1.45391	+	1.21998i	−0.0592569	+	0.0497225i
$603$		0			0
$604$	5.40211	+	1.96621i	0.219809	+	0.0800039i
$605$	2.04264	+	1.71398i	0.0830453	+	0.0696833i
$606$		0			0
$607$	−11.5300			−0.467988			−0.233994	−	0.972238i	$-0.575180\pi$
$607$	−11.5300			−0.467988			−0.233994	+	0.972238i	$0.575180\pi$
$608$	7.73056	−	7.41261i	0.313516	−	0.300621i
$609$		0			0
$610$	−0.289437	+	1.64148i	−0.0117190	+	0.0664615i
$611$	8.17093	+	6.85623i	0.330561	+	0.277373i
$612$		0			0
$613$	−21.2917	+	7.74954i	−0.859963	+	0.313001i	−0.734096	−	0.679046i	$-0.762394\pi$
$613$	−21.2917	+	7.74954i	−0.859963	+	0.313001i	−0.125868	+	0.992047i	$0.540171\pi$
$614$	−2.78459	+	2.33655i	−0.112377	+	0.0942956i
$615$		0			0
$616$	2.03239	−	3.52020i	0.0818872	−	0.141833i
$617$	−1.03785	−	5.88595i	−0.0417823	−	0.236959i	0.956764	−	0.290867i	$-0.0939436\pi$
$617$	−1.03785	−	5.88595i	−0.0417823	−	0.236959i	−0.998546	+	0.0539072i	$0.982832\pi$
$618$		0			0
$619$	17.1031	−	29.6234i	0.687431	−	1.19067i	−0.285235	−	0.958458i	$-0.592072\pi$
$619$	17.1031	−	29.6234i	0.687431	−	1.19067i	0.972666	−	0.232208i	$-0.0745951\pi$
$620$	−3.96573	−	6.86884i	−0.159268	−	0.275859i
$621$		0			0
$622$	−4.95103	+	1.80203i	−0.198518	+	0.0722547i
$623$	16.0388	+	5.83766i	0.642582	+	0.233881i
$624$		0			0
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	3.55787			0.142201
$627$		0			0
$628$	−13.2325			−0.528035
$629$	−4.13317	+	23.4404i	−0.164800	+	0.934629i
$630$		0			0
$631$	13.3916	+	4.87414i	0.533111	+	0.194036i	0.594527	−	0.804076i	$-0.297339\pi$
$631$	13.3916	+	4.87414i	0.533111	+	0.194036i	−0.0614161	+	0.998112i	$0.519562\pi$
$632$	1.89055	−	0.688105i	0.0752021	−	0.0273713i
$633$		0			0
$634$	−2.54458	−	4.40735i	−0.101058	−	0.175038i
$635$	6.51847	−	11.2903i	0.258678	−	0.448043i
$636$		0			0
$637$	4.66333	+	26.4471i	0.184768	+	1.04787i
$638$	−2.21007	+	3.82795i	−0.0874975	+	0.151550i
$639$		0			0
$640$	−4.88798	+	4.10150i	−0.193214	+	0.162126i
$641$	−37.3475	+	13.5934i	−1.47514	+	0.536906i	−0.949490	−	0.313797i	$-0.898399\pi$
$641$	−37.3475	+	13.5934i	−1.47514	+	0.536906i	−0.525647	+	0.850703i	$0.676177\pi$
$642$		0			0
$643$	12.1851	+	10.2245i	0.480532	+	0.403214i	0.850619	−	0.525783i	$-0.176228\pi$
$643$	12.1851	+	10.2245i	0.480532	+	0.403214i	−0.370087	+	0.928997i	$0.620672\pi$
$644$	−4.73096	+	26.8306i	−0.186426	+	1.05727i
$645$		0			0
$646$	2.63745	+	0.766390i	0.103769	+	0.0301532i
$647$	−18.8549			−0.741262			−0.370631	−	0.928780i	$-0.620858\pi$
$647$	−18.8549			−0.741262			−0.370631	+	0.928780i	$0.620858\pi$
$648$		0			0
$649$	−7.85659	−	6.59246i	−0.308398	−	0.258777i
$650$	−1.28195	−	0.466592i	−0.0502822	−	0.0183012i
$651$		0			0
$652$	1.35993	−	1.14111i	0.0532588	−	0.0446894i
$653$	−21.2626	−	36.8279i	−0.832070	−	1.44119i	−0.896394	−	0.443259i	$-0.853822\pi$
$653$	−21.2626	−	36.8279i	−0.832070	−	1.44119i	0.0643232	−	0.997929i	$-0.479511\pi$
$654$		0			0
$655$	0.0324867	+	0.184241i	0.00126936	+	0.00719890i
$656$	−3.53850	−	20.0678i	−0.138155	−	0.783517i
$657$		0			0
$658$	0.293612	+	0.508551i	0.0114462	+	0.0198254i
$659$	35.1057	−	29.4572i	1.36752	−	1.14749i	0.393945	−	0.919134i	$-0.371110\pi$
$659$	35.1057	−	29.4572i	1.36752	−	1.14749i	0.973578	−	0.228354i	$-0.0733344\pi$
$660$		0			0
$661$	43.3834	+	15.7903i	1.68742	+	0.614170i	0.994296	−	0.106652i	$-0.0340131\pi$
$661$	43.3834	+	15.7903i	1.68742	+	0.614170i	0.693121	+	0.720822i	$0.256235\pi$
$662$	−2.51167	−	2.10754i	−0.0976189	−	0.0819120i
$663$		0			0
$664$	9.51427			0.369225
$665$	−5.93454	−	4.34387i	−0.230132	−	0.168448i
$666$		0			0
$667$	10.4062	−	59.0167i	0.402931	−	2.28514i
$668$	21.3787	+	17.9388i	0.827166	+	0.694074i
$669$		0			0
$670$	−0.449124	+	0.163468i	−0.0173512	+	0.00631531i
$671$	−17.4704	+	14.6594i	−0.674437	+	0.565920i
$672$		0			0
$673$	−2.74410	+	4.75292i	−0.105777	+	0.183212i	−0.914056	−	0.405589i	$-0.867066\pi$
$673$	−2.74410	+	4.75292i	−0.105777	+	0.183212i	0.808278	+	0.588801i	$0.200400\pi$
$674$	−0.403213	−	2.28674i	−0.0155312	−	0.0880818i
$675$		0			0
$676$	28.1681	−	48.7885i	1.08339	−	1.87648i
$677$	−14.7154	−	25.4878i	−0.565557	−	0.979574i	−0.996998	−	0.0774324i	$-0.975328\pi$
$677$	−14.7154	−	25.4878i	−0.565557	−	0.979574i	0.431440	−	0.902141i	$-0.358006\pi$
$678$		0			0
$679$	−15.6458	+	5.69460i	−0.600430	+	0.218539i
$680$	−2.34204	−	0.852434i	−0.0898133	−	0.0326894i
$681$		0			0
$682$	−0.428975	+	2.43284i	−0.0164263	+	0.0931581i
$683$	27.4543			1.05051			0.525254	−	0.850945i	$-0.323970\pi$
$683$	27.4543			1.05051			0.525254	+	0.850945i	$0.323970\pi$
$684$		0			0
$685$	2.15559			0.0823608
$686$	−0.689437	+	3.90999i	−0.0263228	+	0.149284i
$687$		0			0
$688$	18.7122	+	6.81069i	0.713397	+	0.259655i
$689$	−11.6170	+	4.22826i	−0.442574	+	0.161084i
$690$		0			0
$691$	−1.71390	−	2.96856i	−0.0651997	−	0.112929i	0.831583	−	0.555401i	$-0.187435\pi$
$691$	−1.71390	−	2.96856i	−0.0651997	−	0.112929i	−0.896783	+	0.442471i	$0.854102\pi$
$692$	−13.7641	+	23.8402i	−0.523233	+	0.906267i
$693$		0			0
$694$	1.11631	+	6.33094i	0.0423747	+	0.240319i
$695$	−3.94856	+	6.83911i	−0.149777	+	0.259422i
$696$		0			0
$697$	12.4820	−	10.4737i	0.472790	−	0.396718i
$698$	1.11371	−	0.405358i	0.0421546	−	0.0153430i
$699$		0			0
$700$	2.52745	+	2.12078i	0.0955286	+	0.0801580i
$701$	0.566267	−	3.21146i	0.0213876	−	0.121295i	−0.972245	−	0.233966i	$-0.924829\pi$
$701$	0.566267	−	3.21146i	0.0213876	−	0.121295i	0.993632	+	0.112671i	$0.0359406\pi$
$702$		0			0
$703$	−34.6637	+	2.30065i	−1.30737	+	0.0867707i
$704$	−20.0672			−0.756309
$705$		0			0
$706$	−1.20994	−	1.01526i	−0.0455365	−	0.0382097i
$707$	−6.61103	−	2.40622i	−0.248634	−	0.0904952i
$708$		0			0
$709$	−13.1285	+	11.0161i	−0.493052	+	0.413720i	−0.855118	−	0.518433i	$-0.826516\pi$
$709$	−13.1285	+	11.0161i	−0.493052	+	0.413720i	0.362067	+	0.932152i	$0.382071\pi$
$710$	1.09948	+	1.90436i	0.0412628	+	0.0714693i
$711$		0			0
$712$	1.46599	+	8.31406i	0.0549404	+	0.311583i
$713$	−5.81593	−	32.9838i	−0.217808	−	1.23525i
$714$		0			0
$715$	−9.33298	−	16.1652i	−0.349034	−	0.604544i
$716$	23.5930	−	19.7968i	0.881710	−	0.739843i
$717$		0			0
$718$	5.05273	+	1.83904i	0.188566	+	0.0686325i
$719$	−4.76900	−	4.00167i	−0.177854	−	0.149237i	0.549515	−	0.835484i	$-0.314813\pi$
$719$	−4.76900	−	4.00167i	−0.177854	−	0.149237i	−0.727369	+	0.686247i	$0.759257\pi$
$720$		0			0
$721$	21.1977			0.789442
$722$	−0.168259	+	4.00516i	−0.00626197	+	0.149056i
$723$		0			0
$724$	−1.54785	+	8.77829i	−0.0575253	+	0.326242i
$725$	−5.55939	−	4.66488i	−0.206471	−	0.173249i
$726$		0			0
$727$	39.7667	−	14.4739i	1.47487	−	0.536807i	0.525449	−	0.850825i	$-0.323897\pi$
$727$	39.7667	−	14.4739i	1.47487	−	0.536807i	0.949417	+	0.314017i	$0.101675\pi$
$728$	6.97449	−	5.85229i	0.258492	−	0.216900i
$729$		0			0
$730$	−0.148940	+	0.257972i	−0.00551252	+	0.00954796i
$731$	2.76498	+	15.6810i	0.102266	+	0.579982i
$732$		0			0
$733$	11.3815	−	19.7134i	0.420386	−	0.728129i	−0.575591	−	0.817737i	$-0.695228\pi$
$733$	11.3815	−	19.7134i	0.420386	−	0.728129i	0.995977	+	0.0896082i	$0.0285615\pi$
$734$	−3.53041	−	6.11485i	−0.130310	−	0.225703i
$735$		0			0
$736$	−19.0659	+	6.93941i	−0.702778	+	0.255790i
$737$	−6.14514	−	2.23665i	−0.226359	−	0.0823879i
$738$		0			0
$739$	3.11567	−	17.6698i	0.114612	−	0.649996i	−0.872330	−	0.488918i	$-0.837392\pi$
$739$	3.11567	−	17.6698i	0.114612	−	0.649996i	0.986942	−	0.161078i	$-0.0514971\pi$
$740$	15.5850			0.572916
$741$		0			0
$742$	−0.680606			−0.0249858
$743$	3.00948	−	17.0676i	0.110407	−	0.626150i	−0.878515	−	0.477715i	$-0.841465\pi$
$743$	3.00948	−	17.0676i	0.110407	−	0.626150i	0.988922	−	0.148435i	$-0.0474237\pi$
$744$		0			0
$745$	−16.8173	−	6.12100i	−0.616138	−	0.224256i
$746$	−2.07750	+	0.756149i	−0.0760628	+	0.0276846i
$747$		0			0
$748$	−8.42945	−	14.6002i	−0.308211	−	0.533838i
$749$	−12.6055	+	21.8334i	−0.460597	+	0.797777i
$750$		0			0
$751$	−0.379642	−	2.15305i	−0.0138533	−	0.0785661i	0.977097	−	0.212793i	$-0.0682560\pi$
$751$	−0.379642	−	2.15305i	−0.0138533	−	0.0785661i	−0.990951	+	0.134227i	$0.957145\pi$
$752$	3.08056	−	5.33569i	0.112337	−	0.194573i
$753$		0			0
$754$	−7.58424	+	6.36394i	−0.276202	+	0.231761i
$755$	2.76254	−	1.00548i	0.100539	−	0.0365933i
$756$		0			0
$757$	−11.9799	−	10.0523i	−0.435417	−	0.365358i	0.398574	−	0.917136i	$-0.369505\pi$
$757$	−11.9799	−	10.0523i	−0.435417	−	0.365358i	−0.833991	+	0.551778i	$0.813950\pi$
$758$	0.523767	−	2.97043i	0.0190241	−	0.107891i
$759$		0			0
$760$	0.393045	−	3.61639i	0.0142573	−	0.131180i
$761$	−26.2993			−0.953349			−0.476675	−	0.879080i	$-0.658158\pi$
$761$	−26.2993			−0.953349			−0.476675	+	0.879080i	$0.658158\pi$
$762$		0			0
$763$	−6.72737	−	5.64493i	−0.243547	−	0.204360i
$764$	18.3000	+	6.66065i	0.662070	+	0.240974i
$765$		0			0
$766$	5.97705	−	5.01534i	0.215960	−	0.181212i
$767$	−11.4861	−	19.8945i	−0.414739	−	0.718349i
$768$		0			0
$769$	0.0147166	+	0.0834622i	0.000530695	+	0.00300972i	0.985072	−	0.172143i	$-0.0550692\pi$
$769$	0.0147166	+	0.0834622i	0.000530695	+	0.00300972i	−0.984541	+	0.175153i	$0.943958\pi$
$770$	−0.178446	−	1.01202i	−0.00643075	−	0.0364706i
$771$		0			0
$772$	−20.9249	−	36.2430i	−0.753104	−	1.30441i
$773$	0.00879051	−	0.00737611i	0.000316173	−	0.000265300i	−0.642630	−	0.766177i	$-0.722157\pi$
$773$	0.00879051	−	0.00737611i	0.000316173	−	0.000265300i	0.642946	+	0.765912i	$0.277712\pi$
$774$		0			0
$775$	−3.81140	−	1.38724i	−0.136909	−	0.0498310i
$776$	−6.30871	−	5.29364i	−0.226470	−	0.190030i
$777$		0			0
$778$	−3.50389			−0.125621
$779$	19.1904	+	14.0467i	0.687567	+	0.503275i
$780$		0			0
$781$	−5.22461	+	29.6302i	−0.186951	+	1.06025i
$782$	−3.98578	−	3.34447i	−0.142531	−	0.119598i
$783$		0			0
$784$	14.5765	−	5.30542i	0.520590	−	0.189479i
$785$	−5.18373	+	4.34966i	−0.185015	+	0.155246i
$786$		0			0
$787$	−15.0534	+	26.0733i	−0.536596	+	0.929411i	0.462488	+	0.886625i	$0.346957\pi$
$787$	−15.0534	+	26.0733i	−0.536596	+	0.929411i	−0.999084	+	0.0427861i	$0.986377\pi$
$788$	0.464101	+	2.63205i	0.0165329	+	0.0937628i
$789$		0			0
$790$	0.254316	−	0.440488i	0.00904814	−	0.0156718i
$791$	−7.23031	−	12.5233i	−0.257080	−	0.445276i
$792$		0			0
$793$	−48.0017	+	17.4712i	−1.70459	+	0.620421i
$794$	−5.28131	−	1.92224i	−0.187427	−	0.0682178i
$795$		0			0
$796$	6.09044	−	34.5406i	0.215870	−	1.22426i
$797$	−38.2339			−1.35432			−0.677158	−	0.735838i	$-0.736789\pi$
$797$	−38.2339			−1.35432			−0.677158	+	0.735838i	$0.736789\pi$
$798$		0			0
$799$	4.92654			0.174288
$800$	−0.426669	+	2.41976i	−0.0150850	+	0.0855514i
$801$		0			0
$802$	−0.256698	−	0.0934304i	−0.00906431	−	0.00329914i
$803$	−3.82995	+	1.39399i	−0.135156	+	0.0491927i
$804$		0			0
$805$	6.96617	+	12.0658i	0.245525	+	0.425262i
$806$	−2.76665	+	4.79197i	−0.0974509	+	0.168790i
$807$		0			0
$808$	−0.604267	−	3.42697i	−0.0212580	−	0.120560i
$809$	1.85001	−	3.20432i	0.0650431	−	0.112658i	−0.831670	−	0.555270i	$-0.812615\pi$
$809$	1.85001	−	3.20432i	0.0650431	−	0.112658i	0.896713	+	0.442612i	$0.145948\pi$
$810$		0			0
$811$	31.3508	−	26.3064i	1.10088	−	0.923744i	0.103392	−	0.994641i	$-0.467030\pi$
$811$	31.3508	−	26.3064i	1.10088	−	0.923744i	0.997484	+	0.0708964i	$0.0225860\pi$
$812$	22.5002	−	8.18942i	0.789604	−	0.287392i
$813$		0			0
$814$	−3.71851	−	3.12020i	−0.130334	−	0.109363i
$815$	0.157644	−	0.894042i	0.00552202	−	0.0313169i
$816$		0			0
$817$	−21.2642	+	9.37739i	−0.743940	+	0.328073i
$818$	−5.70327			−0.199410
$819$		0			0
$820$	−8.17295	−	6.85792i	−0.285412	−	0.239489i
$821$	16.3884	+	5.96489i	0.571959	+	0.208176i	0.611776	−	0.791031i	$-0.290455\pi$
$821$	16.3884	+	5.96489i	0.571959	+	0.208176i	−0.0398170	+	0.999207i	$0.512677\pi$
$822$		0			0
$823$	−4.98291	+	4.18116i	−0.173693	+	0.145746i	−0.725490	−	0.688233i	$-0.758387\pi$
$823$	−4.98291	+	4.18116i	−0.173693	+	0.145746i	0.551797	+	0.833979i	$0.313942\pi$
$824$	5.24243	+	9.08016i	0.182629	+	0.316322i
$825$		0			0
$826$	−0.219613	−	1.24549i	−0.00764133	−	0.0433361i
$827$	−0.281701	−	1.59761i	−0.00979571	−	0.0555542i	0.979518	−	0.201356i	$-0.0645349\pi$
$827$	−0.281701	−	1.59761i	−0.00979571	−	0.0555542i	−0.989314	+	0.145802i	$0.953424\pi$
$828$		0			0
$829$	−16.3252	−	28.2760i	−0.566996	−	0.982066i	−0.996861	−	0.0791727i	$-0.974772\pi$
$829$	−16.3252	−	28.2760i	−0.566996	−	0.982066i	0.429865	−	0.902893i	$-0.358561\pi$
$830$	1.84259	−	1.54612i	0.0639574	−	0.0536666i
$831$		0			0
$832$	−42.2371	−	15.3730i	−1.46431	−	0.532964i
$833$	9.50176	+	7.97292i	0.329216	+	0.276245i
$834$		0			0
$835$	14.2716			0.493888
$836$	17.7607	−	17.0302i	0.614265	−	0.589001i
$837$		0			0
$838$	−0.152226	+	0.863314i	−0.00525854	+	0.0298227i
$839$	8.85542	+	7.43058i	0.305723	+	0.256532i	0.782722	−	0.622372i	$-0.213831\pi$
$839$	8.85542	+	7.43058i	0.305723	+	0.256532i	−0.476999	+	0.878904i	$0.658275\pi$
$840$		0			0
$841$	−22.2406	+	8.09491i	−0.766916	+	0.279135i
$842$	4.26764	−	3.58098i	0.147073	−	0.123409i
$843$		0			0
$844$	20.3056	−	35.1703i	0.698947	−	1.21061i
$845$	−5.00268	−	28.3716i	−0.172097	−	0.976013i
$846$		0			0
$847$	−2.24948	+	3.89622i	−0.0772931	+	0.133876i
$848$	3.57044	+	6.18419i	0.122610	+	0.212366i
$849$		0			0
$850$	−0.592100	+	0.215507i	−0.0203089	+	0.00739182i
$851$	61.8427	+	22.5089i	2.11994	+	0.771596i
$852$		0			0
$853$	8.28547	−	46.9892i	0.283689	−	1.60888i	−0.426242	−	0.904609i	$-0.640163\pi$
$853$	8.28547	−	46.9892i	0.283689	−	1.60888i	0.709931	−	0.704271i	$-0.248726\pi$
$854$	−2.81227			−0.0962339
$855$		0			0
$856$	−12.4700			−0.426216
$857$	6.69167	−	37.9503i	0.228583	−	1.29636i	−0.627132	−	0.778913i	$-0.715772\pi$
$857$	6.69167	−	37.9503i	0.228583	−	1.29636i	0.855716	−	0.517447i	$-0.173117\pi$
$858$		0			0
$859$	−18.0347	−	6.56408i	−0.615335	−	0.223964i	0.0155009	−	0.999880i	$-0.495066\pi$
$859$	−18.0347	−	6.56408i	−0.615335	−	0.223964i	−0.630836	+	0.775916i	$0.717288\pi$
$860$	9.79719	−	3.56589i	0.334081	−	0.121596i
$861$		0			0
$862$	1.02553	+	1.77626i	0.0349295	+	0.0604997i
$863$	−4.58397	+	7.93967i	−0.156040	+	0.270269i	−0.933437	−	0.358741i	$-0.883206\pi$
$863$	−4.58397	+	7.93967i	−0.156040	+	0.270269i	0.777397	+	0.629010i	$0.216540\pi$
$864$		0			0
$865$	2.44452	+	13.8636i	0.0831163	+	0.471376i
$866$	−0.0696079	+	0.120564i	−0.00236537	+	0.00409695i
$867$		0			0
$868$	10.2513	−	8.60190i	0.347953	−	0.291967i
$869$	6.53965	−	2.38024i	0.221842	−	0.0807440i
$870$		0			0
$871$	−11.2207	−	9.41533i	−0.380201	−	0.319026i
$872$	0.754286	−	4.27777i	0.0255434	−	0.144864i
$873$		0			0
$874$	3.35317	−	6.81370i	0.113423	−	0.230477i
$875$	1.68723			0.0570387
$876$		0			0
$877$	−2.78066	−	2.33325i	−0.0938961	−	0.0787882i	0.594631	−	0.803999i	$-0.297298\pi$
$877$	−2.78066	−	2.33325i	−0.0938961	−	0.0787882i	−0.688527	+	0.725210i	$0.741743\pi$
$878$	5.39064	+	1.96203i	0.181925	+	0.0662154i
$879$		0			0
$880$	−8.25937	+	6.93043i	−0.278423	+	0.233625i
$881$	−4.17191	−	7.22596i	−0.140555	−	0.243449i	0.787151	−	0.616761i	$-0.211555\pi$
$881$	−4.17191	−	7.22596i	−0.140555	−	0.243449i	−0.927706	+	0.373312i	$0.878222\pi$
$882$		0			0
$883$	4.89899	+	27.7836i	0.164864	+	0.934991i	0.949204	+	0.314660i	$0.101891\pi$
$883$	4.89899	+	27.7836i	0.164864	+	0.934991i	−0.784340	+	0.620331i	$0.786998\pi$
$884$	−6.55725	−	37.1880i	−0.220544	−	1.25077i
$885$		0			0
$886$	−3.98633	−	6.90452i	−0.133923	−	0.231962i
$887$	6.77332	−	5.68349i	0.227426	−	0.190833i	−0.521953	−	0.852974i	$-0.674796\pi$
$887$	6.77332	−	5.68349i	0.227426	−	0.190833i	0.749379	+	0.662141i	$0.230352\pi$
$888$		0			0
$889$	20.6698	+	7.52318i	0.693242	+	0.252319i
$890$	1.63499	+	1.37192i	0.0548051	+	0.0459869i
$891$		0			0
$892$	−3.81312			−0.127673
$893$	1.71483	+	6.98301i	0.0573846	+	0.233678i
$894$		0			0
$895$	2.73492	−	15.5105i	0.0914182	−	0.518458i
$896$	−8.24714	−	6.92017i	−0.275517	−	0.231187i
$897$		0			0
$898$	3.28118	−	1.19425i	0.109495	−	0.0398528i
$899$	−22.5489	+	18.9208i	−0.752048	+	0.631043i
$900$		0			0
$901$	−2.85499	+	4.94498i	−0.0951134	+	0.164741i
$902$	0.577037	+	3.27254i	0.0192132	+	0.108964i
$903$		0			0
$904$	3.57628	−	6.19431i	0.118945	−	0.206020i
$905$	2.27915	+	3.94761i	0.0757616	+	0.131223i
$906$		0			0
$907$	−3.97425	+	1.44651i	−0.131963	+	0.0480305i	−0.407157	−	0.913358i	$-0.633480\pi$
$907$	−3.97425	+	1.44651i	−0.131963	+	0.0480305i	0.275195	+	0.961389i	$0.411258\pi$
$908$	−23.1714	−	8.43371i	−0.768971	−	0.279882i
$909$		0			0
$910$	0.399695	−	2.26678i	0.0132498	−	0.0751432i
$911$	−10.1182			−0.335231			−0.167616	−	0.985852i	$-0.553607\pi$
$911$	−10.1182			−0.335231			−0.167616	+	0.985852i	$0.553607\pi$
$912$		0			0
$913$	32.9110			1.08920
$914$	−0.419463	+	2.37890i	−0.0138746	+	0.0786869i
$915$		0			0
$916$	−11.2599	−	4.09826i	−0.372037	−	0.135410i
$917$	−0.296616	+	0.107959i	−0.00979513	+	0.00356513i
$918$		0			0
$919$	23.9378	+	41.4616i	0.789637	+	1.36769i	0.926190	+	0.377058i	$0.123064\pi$
$919$	23.9378	+	41.4616i	0.789637	+	1.36769i	−0.136553	+	0.990633i	$0.543602\pi$
$920$	−3.44563	+	5.96801i	−0.113599	+	0.196760i
$921$		0			0
$922$	−0.394201	−	2.23562i	−0.0129823	−	0.0736263i
$923$	−33.6958	+	58.3629i	−1.10911	+	1.92104i
$924$		0			0
$925$	6.10529	−	5.12295i	0.200741	−	0.168441i
$926$	3.38790	−	1.23309i	0.111333	−	0.0405220i
$927$		0			0
$928$	13.6599	+	11.4620i	0.448408	+	0.376259i
$929$	3.75604	−	21.3015i	0.123232	−	0.698881i	−0.859111	−	0.511789i	$-0.828983\pi$
$929$	3.75604	−	21.3015i	0.123232	−	0.698881i	0.982342	−	0.187092i	$-0.0599061\pi$
$930$		0			0
$931$	−7.99367	+	16.2433i	−0.261982	+	0.532351i
$932$	12.9202			0.423214
$933$		0			0
$934$	5.14864	+	4.32023i	0.168469	+	0.141362i
$935$	−8.10141	−	2.94867i	−0.264944	−	0.0964319i
$936$		0			0
$937$	27.6414	−	23.1939i	0.903006	−	0.757712i	−0.0677696	−	0.997701i	$-0.521588\pi$
$937$	27.6414	−	23.1939i	0.903006	−	0.757712i	0.970776	+	0.239989i	$0.0771438\pi$
$938$	−0.403203	−	0.698368i	−0.0131651	−	0.0228025i
$939$		0			0
$940$	−0.560153	−	3.17678i	−0.0182702	−	0.103615i
$941$	8.41858	+	47.7441i	0.274438	+	1.55641i	0.740742	+	0.671789i	$0.234474\pi$
$941$	8.41858	+	47.7441i	0.274438	+	1.55641i	−0.466305	+	0.884624i	$0.654415\pi$
$942$		0			0
$943$	−22.5264	−	39.0168i	−0.733559	−	1.27056i
$944$	−10.1648	+	8.52928i	−0.330836	+	0.277604i
$945$		0			0
$946$	−3.05148	−	1.11065i	−0.0992120	−	0.0361102i
$947$	−26.9727	−	22.6328i	−0.876495	−	0.735466i	0.0889606	−	0.996035i	$-0.471645\pi$
$947$	−26.9727	−	22.6328i	−0.876495	−	0.735466i	−0.965455	+	0.260569i	$0.916090\pi$
$948$		0			0
$949$	−9.12913			−0.296344
$950$	−0.511563	−	0.764245i	−0.0165973	−	0.0247954i
$951$		0			0
$952$	0.730219	−	4.14128i	0.0236665	−	0.134220i
$953$	−34.1607	−	28.6643i	−1.10657	−	0.928527i	−0.108725	−	0.994072i	$-0.534677\pi$
$953$	−34.1607	−	28.6643i	−1.10657	−	0.928527i	−0.997850	+	0.0655452i	$0.979121\pi$
$954$		0			0
$955$	9.35828	−	3.40613i	0.302827	−	0.110220i
$956$	−3.30130	+	2.77012i	−0.106772	+	0.0895920i
$957$		0			0
$958$	0.406172	−	0.703510i	0.0131228	−	0.0227294i
$959$	0.631553	+	3.58171i	0.0203939	+	0.115660i
$960$		0			0
$961$	7.27442	−	12.5997i	0.234659	−	0.406441i
$962$	−5.43635	−	9.41604i	−0.175275	−	0.303585i
$963$		0			0
$964$	−0.229419	+	0.0835019i	−0.00738910	+	0.00268941i
$965$	−20.1106	−	7.31965i	−0.647382	−	0.235628i
$966$		0			0
$967$	0.469769	−	2.66419i	0.0151067	−	0.0856746i	−0.976322	−	0.216321i	$-0.930594\pi$
$967$	0.469769	−	2.66419i	0.0151067	−	0.0856746i	0.991429	+	0.130647i	$0.0417053\pi$
$968$	−2.22529			−0.0715236
$969$		0			0
$970$	−2.08203			−0.0668499
$971$	1.24026	−	7.03387i	0.0398019	−	0.225728i	−0.958418	−	0.285368i	$-0.907884\pi$
$971$	1.24026	−	7.03387i	0.0398019	−	0.225728i	0.998220	+	0.0596403i	$0.0189954\pi$
$972$		0			0
$973$	−12.5207	−	4.55716i	−0.401395	−	0.146096i
$974$	7.01988	−	2.55503i	0.224932	−	0.0818684i
$975$		0			0
$976$	14.7531	+	25.5531i	0.472235	+	0.817935i
$977$	−14.4495	+	25.0272i	−0.462280	+	0.800692i	−0.999074	−	0.0430210i	$-0.986302\pi$
$977$	−14.4495	+	25.0272i	−0.462280	+	0.800692i	0.536794	+	0.843713i	$0.319635\pi$
$978$		0			0
$979$	5.07105	+	28.7593i	0.162071	+	0.919152i
$980$	4.06082	−	7.03355i	0.129718	−	0.224679i
$981$		0			0
$982$	3.27402	−	2.74722i	0.104478	−	0.0876675i
$983$	9.71738	−	3.53684i	0.309936	−	0.112808i	−0.182369	−	0.983230i	$-0.558377\pi$
$983$	9.71738	−	3.53684i	0.309936	−	0.112808i	0.492305	+	0.870423i	$0.336154\pi$
$984$		0			0
$985$	1.04699	+	0.878526i	0.0333598	+	0.0279922i
$986$	−0.794059	+	4.50333i	−0.0252880	+	0.143415i
$987$		0			0
$988$	50.4289	−	22.2388i	1.60436	−	0.707511i
$989$	44.0262			1.39995
$990$		0			0
$991$	24.2226	+	20.3251i	0.769455	+	0.645650i	0.940569	−	0.339602i	$-0.110292\pi$
$991$	24.2226	+	20.3251i	0.769455	+	0.645650i	−0.171114	+	0.985251i	$0.554737\pi$
$992$	9.36494	+	3.40856i	0.297337	+	0.108222i
$993$		0			0
$994$	−2.84214	+	2.38484i	−0.0901473	+	0.0756426i
$995$	−8.96796	−	15.5330i	−0.284304	−	0.492428i
$996$		0			0
$997$	1.36787	+	7.75758i	0.0433209	+	0.245685i	0.998777	−	0.0494495i	$-0.0157467\pi$
$997$	1.36787	+	7.75758i	0.0433209	+	0.245685i	−0.955456	+	0.295134i	$0.904636\pi$
$998$	−0.0215948	−	0.122470i	−0.000683571	−	0.00387672i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.226.2		18
3.2	odd	2		95.2.k.a.36.2	✓	18
15.2	even	4		475.2.u.b.74.4		36
15.8	even	4		475.2.u.b.74.3		36
15.14	odd	2		475.2.l.c.226.2		18
19.9	even	9	inner	855.2.bs.c.541.2		18
57.35	odd	18		1805.2.a.v.1.4		9
57.41	even	18		1805.2.a.s.1.6		9
57.47	odd	18		95.2.k.a.66.2	yes	18
285.47	even	36		475.2.u.b.199.3		36
285.104	odd	18		475.2.l.c.351.2		18
285.149	odd	18		9025.2.a.cc.1.6		9
285.218	even	36		475.2.u.b.199.4		36
285.269	even	18		9025.2.a.cf.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.2	✓	18	3.2	odd	2
95.2.k.a.66.2	yes	18	57.47	odd	18
475.2.l.c.226.2		18	15.14	odd	2
475.2.l.c.351.2		18	285.104	odd	18
475.2.u.b.74.3		36	15.8	even	4
475.2.u.b.74.4		36	15.2	even	4
475.2.u.b.199.3		36	285.47	even	36
475.2.u.b.199.4		36	285.218	even	36
855.2.bs.c.226.2		18	1.1	even	1	trivial
855.2.bs.c.541.2		18	19.9	even	9	inner
1805.2.a.s.1.6		9	57.41	even	18
1805.2.a.v.1.4		9	57.35	odd	18
9025.2.a.cc.1.6		9	285.149	odd	18
9025.2.a.cf.1.4		9	285.269	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0366369 + 0.207778i) q^{2} +(1.83756 + 0.668816i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.843614 + 1.46118i) q^{7} +(-0.417271 + 0.722735i) q^{8} +O(q^{10})\)	\(q+(-0.0366369 + 0.207778i) q^{2} +(1.83756 + 0.668816i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.843614 + 1.46118i) q^{7} +(-0.417271 + 0.722735i) q^{8} +(0.0366369 + 0.207778i) q^{10} +(-1.44339 + 2.50003i) q^{11} +(-4.95325 + 4.15627i) q^{13} +(-0.334509 + 0.121751i) q^{14} +(2.86110 + 2.40075i) q^{16} +(-0.518598 + 2.94112i) q^{17} +(-4.34933 + 0.288668i) q^{19} +1.95549 q^{20} +(-0.466570 - 0.391499i) q^{22} +(7.75955 + 2.82424i) q^{23} +(0.766044 - 0.642788i) q^{25} +(-0.682111 - 1.18145i) q^{26} +(0.572926 + 3.24923i) q^{28} +(-1.26021 - 7.14701i) q^{29} +(-2.02800 - 3.51260i) q^{31} +(-1.88224 + 1.57939i) q^{32} +(-0.592100 - 0.215507i) q^{34} +(1.29249 + 1.08453i) q^{35} +7.96989 q^{37} +(0.0993671 - 0.914272i) q^{38} +(-0.144917 + 0.821864i) q^{40} +(-4.17950 - 3.50702i) q^{41} +(5.01011 - 1.82353i) q^{43} +(-4.32437 + 3.62858i) q^{44} +(-0.871103 + 1.50879i) q^{46} +(-0.286452 - 1.62455i) q^{47} +(2.07663 - 3.59683i) q^{49} +(0.105492 + 0.182717i) q^{50} +(-11.8817 + 4.32457i) q^{52} +(1.79663 + 0.653921i) q^{53} +(-0.501285 + 2.84293i) q^{55} -1.40806 q^{56} +1.53116 q^{58} +(-0.616931 + 3.49879i) q^{59} +(7.42370 + 2.70201i) q^{61} +(0.804142 - 0.292684i) q^{62} +(3.47569 + 6.02008i) q^{64} +(-3.23300 + 5.59973i) q^{65} +(0.393370 + 2.23091i) q^{67} +(-2.92002 + 5.05762i) q^{68} +(-0.272695 + 0.228818i) q^{70} +(9.79389 - 3.56469i) q^{71} +(1.08155 + 0.907529i) q^{73} +(-0.291992 + 1.65597i) q^{74} +(-8.18520 - 2.37846i) q^{76} -4.87066 q^{77} +(-1.84675 - 1.54961i) q^{79} +(3.50966 + 1.27741i) q^{80} +(0.881806 - 0.739923i) q^{82} +(-5.70029 - 9.87319i) q^{83} +(0.518598 + 2.94112i) q^{85} +(0.195335 + 1.10780i) q^{86} +(-1.20457 - 2.08638i) q^{88} +(7.74938 - 6.50250i) q^{89} +(-10.2517 - 3.73131i) q^{91} +(12.3697 + 10.3794i) q^{92} +0.348041 q^{94} +(-3.98830 + 1.75882i) q^{95} +(-1.71360 + 9.71828i) q^{97} +(0.671262 + 0.563256i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Introduction

L-functions

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