LMFDB - Embedded newform 603.2.u.a.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, degree $10$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			226.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	603.226
Dual form			603.2.u.a.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(1.41542 - 0.909632i) q^{5} +(-0.198939 - 1.38365i) q^{7} +(2.41899 + 5.29684i) q^{8} +O(q^{10})$	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(1.41542 - 0.909632i) q^{5} +(-0.198939 - 1.38365i) q^{7} +(2.41899 + 5.29684i) q^{8} +(-2.76921 - 3.19584i) q^{10} +(3.98926 - 2.56374i) q^{11} +(2.48357 - 5.43826i) q^{13} +(-3.37102 + 0.989821i) q^{14} +(5.04885 - 3.24470i) q^{16} +(-4.13515 - 1.21419i) q^{17} +(-0.661301 + 4.59945i) q^{19} +(-4.75635 + 5.48912i) q^{20} +(-7.80486 - 9.00729i) q^{22} +(0.704273 - 0.812774i) q^{23} +(-0.901106 + 1.97315i) q^{25} +(-14.4174 - 4.23333i) q^{26} +(2.50680 + 5.48912i) q^{28} -2.39011 q^{29} +(-1.12155 - 2.45585i) q^{31} +(-2.25133 - 2.59818i) q^{32} +(-1.54152 + 10.7215i) q^{34} +(-1.54019 - 1.77748i) q^{35} -3.75406 q^{37} +11.6788 q^{38} +(8.24204 + 5.29684i) q^{40} +(0.434813 + 0.127673i) q^{41} +(-4.00098 - 1.17479i) q^{43} +(-13.4055 + 15.4708i) q^{44} +(-2.27389 - 1.46134i) q^{46} +(0.0399670 - 0.0461244i) q^{47} +(4.84154 - 1.42161i) q^{49} +(5.23102 + 1.53597i) q^{50} +(-3.67293 + 25.5458i) q^{52} +(-3.76965 + 1.10687i) q^{53} +(3.31440 - 7.25752i) q^{55} +(6.84774 - 4.40077i) q^{56} +(0.854905 + 5.94600i) q^{58} +(-0.612933 - 1.34214i) q^{59} +(-3.84369 - 2.47019i) q^{61} +(-5.70839 + 3.66856i) q^{62} +(2.20204 - 2.54129i) q^{64} +(-1.43153 - 9.95652i) q^{65} +(8.16797 - 0.533126i) q^{67} +18.6045 q^{68} +(-3.87102 + 4.46740i) q^{70} +(-0.761345 + 0.223551i) q^{71} +(2.64987 + 1.70297i) q^{73} +(1.34277 + 9.33918i) q^{74} +(-2.85475 - 19.8552i) q^{76} +(-4.34094 - 5.00971i) q^{77} +(0.0424701 - 0.0929965i) q^{79} +(4.19474 - 9.18520i) q^{80} +(0.162092 - 1.12738i) q^{82} +(11.6065 - 7.45903i) q^{83} +(-6.95741 + 2.04288i) q^{85} +(-1.49151 + 10.3737i) q^{86} +(23.2297 + 14.9288i) q^{88} +(10.0423 + 11.5895i) q^{89} +(-8.01872 - 2.35451i) q^{91} +(-1.92860 + 4.22305i) q^{92} +(-0.129042 - 0.0829302i) q^{94} +(3.24779 + 7.11167i) q^{95} +16.5271 q^{97} +(-5.26835 - 11.5361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	−0.357685	−	2.48775i	−0.252922	−	1.75911i	−0.580477	−	0.814276i	$-0.697134\pi$
$2$	−0.357685	−	2.48775i	−0.252922	−	1.75911i	0.327556	−	0.944832i	$-0.393775\pi$
$3$		0			0
$3$		0			0
$4$	−4.14200	+	1.21620i	−2.07100	+	0.608100i
$5$	1.41542	−	0.909632i	0.632993	−	0.406800i	−0.184424	−	0.982847i	$-0.559042\pi$
$5$	1.41542	−	0.909632i	0.632993	−	0.406800i	0.817417	+	0.576047i	$0.195405\pi$
$6$		0			0
$7$	−0.198939	−	1.38365i	−0.0751918	−	0.522970i	−0.992254	−	0.124226i	$-0.960355\pi$
$7$	−0.198939	−	1.38365i	−0.0751918	−	0.522970i	0.917062	−	0.398744i	$-0.130554\pi$
$8$	2.41899	+	5.29684i	0.855241	+	1.87272i
$9$		0			0
$10$	−2.76921	−	3.19584i	−0.875702	−	1.01061i
$11$	3.98926	−	2.56374i	1.20281	−	0.772998i	0.223368	−	0.974734i	$-0.428295\pi$
$11$	3.98926	−	2.56374i	1.20281	−	0.772998i	0.979440	+	0.201737i	$0.0646585\pi$
$12$		0			0
$13$	2.48357	−	5.43826i	0.688818	−	1.50830i	−0.164204	−	0.986426i	$-0.552506\pi$
$13$	2.48357	−	5.43826i	0.688818	−	1.50830i	0.853022	−	0.521875i	$-0.174767\pi$
$14$	−3.37102	+	0.989821i	−0.900944	+	0.264541i
$15$		0			0
$16$	5.04885	−	3.24470i	1.26221	−	0.811175i
$17$	−4.13515	−	1.21419i	−1.00292	−	0.294484i	−0.261267	−	0.965267i	$-0.584140\pi$
$17$	−4.13515	−	1.21419i	−1.00292	−	0.294484i	−0.741654	+	0.670783i	$0.765958\pi$
$18$		0			0
$19$	−0.661301	+	4.59945i	−0.151713	+	1.05519i	0.761635	+	0.648006i	$0.224397\pi$
$19$	−0.661301	+	4.59945i	−0.151713	+	1.05519i	−0.913348	+	0.407180i	$0.866512\pi$
$20$	−4.75635	+	5.48912i	−1.06355	+	1.22741i
$21$		0			0
$22$	−7.80486	−	9.00729i	−1.66400	−	1.92036i
$23$	0.704273	−	0.812774i	0.146851	−	0.169475i	−0.677558	−	0.735469i	$-0.736962\pi$
$23$	0.704273	−	0.812774i	0.146851	−	0.169475i	0.824410	+	0.565994i	$0.191507\pi$
$24$		0			0
$25$	−0.901106	+	1.97315i	−0.180221	+	0.394629i
$26$	−14.4174	−	4.23333i	−2.82748	−	0.830224i
$27$		0			0
$28$	2.50680	+	5.48912i	0.473741	+	1.03735i
$29$	−2.39011			−0.443832			−0.221916	−	0.975066i	$-0.571231\pi$
$29$	−2.39011			−0.443832			−0.221916	+	0.975066i	$0.571231\pi$
$30$		0			0
$31$	−1.12155	−	2.45585i	−0.201436	−	0.441084i	0.781774	−	0.623562i	$-0.214315\pi$
$31$	−1.12155	−	2.45585i	−0.201436	−	0.441084i	−0.983210	+	0.182479i	$0.941588\pi$
$32$	−2.25133	−	2.59818i	−0.397983	−	0.459297i
$33$		0			0
$34$	−1.54152	+	10.7215i	−0.264369	+	1.83873i
$35$	−1.54019	−	1.77748i	−0.260340	−	0.300448i
$36$		0			0
$37$	−3.75406			−0.617164			−0.308582	−	0.951198i	$-0.599854\pi$
$37$	−3.75406			−0.617164			−0.308582	+	0.951198i	$0.599854\pi$
$38$	11.6788			1.89456
$39$		0			0
$40$	8.24204	+	5.29684i	1.30318	+	0.837504i
$41$	0.434813	+	0.127673i	0.0679065	+	0.0199391i	0.315509	−	0.948922i	$-0.397825\pi$
$41$	0.434813	+	0.127673i	0.0679065	+	0.0199391i	−0.247603	+	0.968862i	$0.579643\pi$
$42$		0			0
$43$	−4.00098	−	1.17479i	−0.610143	−	0.179154i	−0.0379591	−	0.999279i	$-0.512086\pi$
$43$	−4.00098	−	1.17479i	−0.610143	−	0.179154i	−0.572184	+	0.820125i	$0.693904\pi$
$44$	−13.4055	+	15.4708i	−2.02095	+	2.33231i
$45$		0			0
$46$	−2.27389	−	1.46134i	−0.335267	−	0.215463i
$47$	0.0399670	−	0.0461244i	0.00582979	−	0.00672794i	−0.752827	−	0.658218i	$-0.771310\pi$
$47$	0.0399670	−	0.0461244i	0.00582979	−	0.00672794i	0.758657	+	0.651490i	$0.225856\pi$
$48$		0			0
$49$	4.84154	−	1.42161i	0.691649	−	0.203086i
$50$	5.23102	+	1.53597i	0.739778	+	0.217218i
$51$		0			0
$52$	−3.67293	+	25.5458i	−0.509343	+	3.54256i
$53$	−3.76965	+	1.10687i	−0.517801	+	0.152040i	−0.530183	−	0.847883i	$-0.677877\pi$
$53$	−3.76965	+	1.10687i	−0.517801	+	0.152040i	0.0123821	+	0.999923i	$0.496059\pi$
$54$		0			0
$55$	3.31440	−	7.25752i	0.446913	−	0.978604i
$56$	6.84774	−	4.40077i	0.915067	−	0.588078i
$57$		0			0
$58$	0.854905	+	5.94600i	0.112255	+	0.780748i
$59$	−0.612933	−	1.34214i	−0.0797971	−	0.174731i	0.865528	−	0.500860i	$-0.166983\pi$
$59$	−0.612933	−	1.34214i	−0.0797971	−	0.174731i	−0.945325	+	0.326129i	$0.894256\pi$
$60$		0			0
$61$	−3.84369	−	2.47019i	−0.492134	−	0.316275i	0.270929	−	0.962599i	$-0.412669\pi$
$61$	−3.84369	−	2.47019i	−0.492134	−	0.316275i	−0.763063	+	0.646324i	$0.776305\pi$
$62$	−5.70839	+	3.66856i	−0.724966	+	0.465908i
$63$		0			0
$64$	2.20204	−	2.54129i	0.275255	−	0.317661i
$65$	−1.43153	−	9.95652i	−0.177560	−	1.23495i
$66$		0			0
$67$	8.16797	−	0.533126i	0.997877	−	0.0651317i
$67$	8.16797	−	0.533126i	0.997877	−	0.0651317i
$68$	18.6045			2.25612
$69$		0			0
$70$	−3.87102	+	4.46740i	−0.462676	+	0.533956i
$71$	−0.761345	+	0.223551i	−0.0903551	+	0.0265306i	−0.326598	−	0.945163i	$-0.605902\pi$
$71$	−0.761345	+	0.223551i	−0.0903551	+	0.0265306i	0.236243	+	0.971694i	$0.424084\pi$
$72$		0			0
$73$	2.64987	+	1.70297i	0.310144	+	0.199317i	0.686448	−	0.727179i	$-0.259169\pi$
$73$	2.64987	+	1.70297i	0.310144	+	0.199317i	−0.376304	+	0.926496i	$0.622805\pi$
$74$	1.34277	+	9.33918i	0.156094	+	1.08566i
$75$		0			0
$76$	−2.85475	−	19.8552i	−0.327462	−	2.27755i
$77$	−4.34094	−	5.00971i	−0.494696	−	0.570909i
$78$		0			0
$79$	0.0424701	−	0.0929965i	0.00477826	−	0.0104629i	−0.907228	−	0.420640i	$-0.861806\pi$
$79$	0.0424701	−	0.0929965i	0.00477826	−	0.0104629i	0.912006	+	0.410177i	$0.134533\pi$
$80$	4.19474	−	9.18520i	0.468986	−	1.02694i
$81$		0			0
$82$	0.162092	−	1.12738i	0.0179001	−	0.124498i
$83$	11.6065	−	7.45903i	1.27398	−	0.818735i	0.283845	−	0.958870i	$-0.408390\pi$
$83$	11.6065	−	7.45903i	1.27398	−	0.818735i	0.990132	+	0.140135i	$0.0447537\pi$
$84$		0			0
$85$	−6.95741	+	2.04288i	−0.754638	+	0.221582i
$86$	−1.49151	+	10.3737i	−0.160833	+	1.11862i
$87$		0			0
$88$	23.2297	+	14.9288i	2.47629	+	1.59142i
$89$	10.0423	+	11.5895i	1.06448	+	1.22848i	0.972545	+	0.232715i	$0.0747610\pi$
$89$	10.0423	+	11.5895i	1.06448	+	1.22848i	0.0919390	+	0.995765i	$0.470694\pi$
$90$		0			0
$91$	−8.01872	−	2.35451i	−0.840590	−	0.246819i
$92$	−1.92860	+	4.22305i	−0.201071	+	0.440283i
$93$		0			0
$94$	−0.129042	−	0.0829302i	−0.0133097	−	0.00855359i
$95$	3.24779	+	7.11167i	0.333216	+	0.729642i
$96$		0			0
$97$	16.5271			1.67808			0.839038	−	0.544073i	$-0.183119\pi$
$97$	16.5271			1.67808			0.839038	+	0.544073i	$0.183119\pi$
$98$	−5.26835	−	11.5361i	−0.532184	−	1.16532i
$99$		0			0
$100$	1.33264	−	9.26870i	0.133264	−	0.926870i
$101$	−1.08597	+	7.55307i	−0.108058	+	0.751559i	0.861687	+	0.507439i	$0.169408\pi$
$101$	−1.08597	+	7.55307i	−0.108058	+	0.751559i	−0.969745	+	0.244119i	$0.921501\pi$
$102$		0			0
$103$	−4.16523	−	9.12058i	−0.410412	−	0.898678i	−0.996108	−	0.0881464i	$-0.971906\pi$
$103$	−4.16523	−	9.12058i	−0.410412	−	0.898678i	0.585695	−	0.810531i	$-0.300822\pi$
$104$	34.8133			3.41372
$105$		0			0
$106$	4.10196	+	8.98205i	0.398418	+	0.872413i
$107$	5.27715	+	3.39142i	0.510161	+	0.327861i	0.770269	−	0.637719i	$-0.220122\pi$
$107$	5.27715	+	3.39142i	0.510161	+	0.327861i	−0.260108	+	0.965580i	$0.583758\pi$
$108$		0			0
$109$	−7.21865	+	15.8066i	−0.691422	+	1.51400i	0.158650	+	0.987335i	$0.449286\pi$
$109$	−7.21865	+	15.8066i	−0.691422	+	1.51400i	−0.850071	+	0.526667i	$0.823441\pi$
$110$	−19.2404	−	5.64950i	−1.83450	−	0.538659i
$111$		0			0
$112$	−5.49394	−	6.34034i	−0.519128	−	0.599106i
$113$	−8.71558	−	5.60116i	−0.819893	−	0.526913i	0.0621587	−	0.998066i	$-0.480202\pi$
$113$	−8.71558	−	5.60116i	−0.819893	−	0.526913i	−0.882051	+	0.471153i	$0.843838\pi$
$114$		0			0
$115$	0.257513	−	1.79104i	0.0240132	−	0.167016i
$116$	9.89982	−	2.90685i	0.919175	−	0.269894i
$117$		0			0
$118$	−3.11967	+	2.00489i	−0.287189	+	0.184565i
$119$	−0.857370	+	5.96314i	−0.0785950	+	0.546640i
$120$		0			0
$121$	4.77187	−	10.4489i	0.433806	−	0.949903i
$122$	−4.77040	+	10.4457i	−0.431891	+	0.945710i
$123$		0			0
$124$	7.63226	+	8.80810i	0.685397	+	0.790991i
$125$	1.71663	+	11.9394i	0.153540	+	1.06789i
$126$		0			0
$127$	−2.95283	−	20.5374i	−0.262021	−	1.82240i	−0.517616	−	0.855613i	$-0.673181\pi$
$127$	−2.95283	−	20.5374i	−0.262021	−	1.82240i	0.255595	−	0.966784i	$-0.417729\pi$
$128$	−12.8940	−	8.28647i	−1.13968	−	0.732428i
$129$		0			0
$130$	−24.2574	+	7.12260i	−2.12751	+	0.624693i
$131$	9.45188	−	10.9080i	0.825814	−	0.953041i	−0.173681	−	0.984802i	$-0.555566\pi$
$131$	9.45188	−	10.9080i	0.825814	−	0.953041i	0.999495	+	0.0317614i	$0.0101117\pi$
$132$		0			0
$133$	6.49558			0.563238
$134$	−4.24785	−	20.1292i	−0.366958	−	1.73890i
$135$		0			0
$136$	−3.57150	−	24.8403i	−0.306254	−	2.13004i
$137$	3.38758	−	3.90948i	0.289421	−	0.334009i	−0.592356	−	0.805676i	$-0.701802\pi$
$137$	3.38758	−	3.90948i	0.289421	−	0.334009i	0.881777	+	0.471667i	$0.156348\pi$
$138$		0			0
$139$	1.19720	−	0.769391i	0.101545	−	0.0652589i	−0.488883	−	0.872349i	$-0.662595\pi$
$139$	1.19720	−	0.769391i	0.101545	−	0.0652589i	0.590428	+	0.807091i	$0.298959\pi$
$140$	8.54124	+	5.48912i	0.721867	+	0.463916i
$141$		0			0
$142$	0.828463	+	1.81408i	0.0695230	+	0.152234i
$143$	−4.03469	−	28.0619i	−0.337397	−	2.34665i
$144$		0			0
$145$	−3.38299	+	2.17412i	−0.280942	+	0.180551i
$146$	3.28875	−	7.20135i	0.272179	−	0.595988i
$147$		0			0
$148$	15.5493	−	4.56569i	1.27815	−	0.375298i
$149$	−1.12719	+	7.83977i	−0.0923429	+	0.642259i	0.890110	+	0.455746i	$0.150628\pi$
$149$	−1.12719	+	7.83977i	−0.0923429	+	0.642259i	−0.982453	+	0.186513i	$0.940281\pi$
$150$		0			0
$151$	9.70547	+	2.84978i	0.789820	+	0.231912i	0.651673	−	0.758500i	$-0.274067\pi$
$151$	9.70547	+	2.84978i	0.789820	+	0.231912i	0.138146	+	0.990412i	$0.455886\pi$
$152$	−25.9622	+	7.62320i	−2.10581	+	0.618323i
$153$		0			0
$154$	−10.9102	+	12.5911i	−0.879172	+	1.01462i
$155$	−3.82138	−	2.45585i	−0.306940	−	0.197259i
$156$		0			0
$157$	−8.01347	+	9.24804i	−0.639545	+	0.738074i	−0.979294	−	0.202442i	$-0.935112\pi$
$157$	−8.01347	+	9.24804i	−0.639545	+	0.738074i	0.339750	+	0.940516i	$0.389658\pi$
$158$	−0.246543	−	0.0723917i	−0.0196139	−	0.00575917i
$159$		0			0
$160$	−5.54996	−	1.62961i	−0.438763	−	0.128832i
$161$	−1.26470	−	0.812774i	−0.0996724	−	0.0640556i
$162$		0			0
$163$	−8.70078			−0.681498			−0.340749	−	0.940154i	$-0.610681\pi$
$163$	−8.70078			−0.681498			−0.340749	+	0.940154i	$0.610681\pi$
$164$	−1.95627			−0.152759
$165$		0			0
$166$	−22.7077	−	26.2061i	−1.76246	−	2.03399i
$167$	2.14398	−	14.9117i	0.165906	−	1.15390i	−0.721332	−	0.692590i	$-0.756470\pi$
$167$	2.14398	−	14.9117i	0.165906	−	1.15390i	0.887238	−	0.461313i	$-0.152621\pi$
$168$		0			0
$169$	−14.8933	−	17.1878i	−1.14564	−	1.32214i
$170$	7.57075	+	16.5776i	0.580650	+	1.27145i
$171$		0			0
$172$	18.0008			1.37255
$173$	−6.61945	−	14.4946i	−0.503267	−	1.10200i	−0.975394	−	0.220471i	$-0.929241\pi$
$173$	−6.61945	−	14.4946i	−0.503267	−	1.10200i	0.472126	−	0.881531i	$-0.343487\pi$
$174$		0			0
$175$	2.90941	+	0.854279i	0.219930	+	0.0645774i
$176$	11.8226	−	25.8879i	0.891163	−	1.95138i
$177$		0			0
$178$	25.2397	−	29.1282i	1.89180	−	2.18325i
$179$	10.7208	+	12.3724i	0.801307	+	0.924757i	0.998452	−	0.0556169i	$-0.0177125\pi$
$179$	10.7208	+	12.3724i	0.801307	+	0.924757i	−0.197145	+	0.980374i	$0.563167\pi$
$180$		0			0
$181$	1.67222	−	1.92985i	0.124295	−	0.143444i	−0.690191	−	0.723627i	$-0.742473\pi$
$181$	1.67222	−	1.92985i	0.124295	−	0.143444i	0.814486	+	0.580183i	$0.197019\pi$
$182$	−2.98926	+	20.7908i	−0.221579	+	1.54111i
$183$		0			0
$184$	6.00876	+	1.76433i	0.442972	+	0.130068i
$185$	−5.31355	+	3.41481i	−0.390660	+	0.251062i
$186$		0			0
$187$	−19.6091	+	5.75774i	−1.43396	+	0.421047i
$188$	−0.109447	+	0.239655i	−0.00798223	+	0.0174787i
$189$		0			0
$190$	16.5304	−	10.6234i	1.19924	−	0.770706i
$191$	−2.04512	−	2.36019i	−0.147980	−	0.170778i	0.676920	−	0.736056i	$-0.263314\pi$
$191$	−2.04512	−	2.36019i	−0.147980	−	0.170778i	−0.824900	+	0.565279i	$0.808769\pi$
$192$		0			0
$193$	8.93875	+	19.5731i	0.643425	+	1.40890i	0.897193	+	0.441639i	$0.145603\pi$
$193$	8.93875	+	19.5731i	0.643425	+	1.40890i	−0.253768	+	0.967265i	$0.581670\pi$
$194$	−5.91151	−	41.1155i	−0.424422	−	2.95192i
$195$		0			0
$196$	−18.3247	+	11.7766i	−1.30891	+	0.841184i
$197$	14.6614	−	4.30498i	1.04458	−	0.306717i	0.285956	−	0.958243i	$-0.407689\pi$
$197$	14.6614	−	4.30498i	1.04458	−	0.306717i	0.758627	+	0.651525i	$0.225871\pi$
$198$		0			0
$199$	2.03198	+	14.1327i	0.144043	+	1.00184i	0.925734	+	0.378176i	$0.123449\pi$
$199$	2.03198	+	14.1327i	0.144043	+	1.00184i	−0.781690	+	0.623667i	$0.785642\pi$
$200$	−12.6312			−0.893161
$201$		0			0
$202$	19.1786			1.34940
$203$	0.475485	+	3.30707i	0.0333725	+	0.232111i
$204$		0			0
$205$	0.731577	−	0.214810i	0.0510955	−	0.0150030i
$206$	−21.1999	+	13.6244i	−1.47707	+	0.949255i
$207$		0			0
$208$	−5.10634	−	35.5154i	−0.354061	−	2.46255i
$209$	9.15370	+	20.0438i	0.633175	+	1.38646i
$210$		0			0
$211$	6.45340	+	7.44762i	0.444270	+	0.512715i	0.933077	−	0.359677i	$-0.117113\pi$
$211$	6.45340	+	7.44762i	0.444270	+	0.512715i	−0.488807	+	0.872392i	$0.662568\pi$
$212$	14.2677	−	9.16930i	0.979910	−	0.629750i
$213$		0			0
$214$	6.54946	−	14.3413i	0.447712	−	0.980352i
$215$	−6.73167	+	1.97660i	−0.459096	+	0.134803i
$216$		0			0
$217$	−3.17491	+	2.04039i	−0.215527	+	0.138511i
$218$	41.9051	+	12.3044i	2.83817	+	0.833362i
$219$		0			0
$220$	−4.90164	+	34.0916i	−0.330468	+	2.29846i
$221$	−16.8730	+	19.4725i	−1.13500	+	1.30986i
$222$		0			0
$223$	16.2386	+	18.7403i	1.08742	+	1.25495i	0.964939	+	0.262475i	$0.0845388\pi$
$223$	16.2386	+	18.7403i	1.08742	+	1.25495i	0.122478	+	0.992471i	$0.460916\pi$
$224$	−3.14709	+	3.63193i	−0.210274	+	0.242669i
$225$		0			0
$226$	−10.8169	+	23.6857i	−0.719529	+	1.57555i
$227$	12.4250	+	3.64830i	0.824675	+	0.242146i	0.666728	−	0.745301i	$-0.267694\pi$
$227$	12.4250	+	3.64830i	0.824675	+	0.242146i	0.157947	+	0.987448i	$0.449513\pi$
$228$		0			0
$229$	1.60467	+	3.51374i	0.106040	+	0.232195i	0.955213	−	0.295920i	$-0.0956263\pi$
$229$	1.60467	+	3.51374i	0.106040	+	0.232195i	−0.849173	+	0.528115i	$0.822899\pi$
$230$	−4.54778			−0.299872
$231$		0			0
$232$	−5.78163	−	12.6600i	−0.379583	−	0.831170i
$233$	12.9682	+	14.9661i	0.849577	+	0.980464i	0.999967	−	0.00816311i	$-0.00259843\pi$
$233$	12.9682	+	14.9661i	0.849577	+	0.980464i	−0.150390	+	0.988627i	$0.548053\pi$
$234$		0			0
$235$	0.0146137	−	0.101640i	0.000953292	−	0.00663029i
$236$	4.17108	+	4.81368i	0.271514	+	0.313344i
$237$		0			0
$238$	15.1415			0.981478
$239$	7.87943			0.509678			0.254839	−	0.966984i	$-0.417978\pi$
$239$	7.87943			0.509678			0.254839	+	0.966984i	$0.417978\pi$
$240$		0			0
$241$	2.38972	+	1.53578i	0.153935	+	0.0989283i	0.615341	−	0.788261i	$-0.289018\pi$
$241$	2.38972	+	1.53578i	0.153935	+	0.0989283i	−0.461406	+	0.887189i	$0.652655\pi$
$242$	−27.7012	−	8.13381i	−1.78070	−	0.522861i
$243$		0			0
$244$	18.9248	+	5.55683i	1.21154	+	0.355739i
$245$	5.55965	−	6.41618i	0.355193	−	0.409915i
$246$		0			0
$247$	23.3706	+	15.0194i	1.48704	+	0.955660i
$248$	10.2952	−	11.8813i	0.653748	−	0.754465i
$249$		0			0
$250$	29.0883	−	8.54109i	1.83971	−	0.540186i
$251$	1.62680	+	0.477671i	0.102683	+	0.0301503i	0.332670	−	0.943043i	$-0.392050\pi$
$251$	1.62680	+	0.477671i	0.102683	+	0.0301503i	−0.229988	+	0.973194i	$0.573869\pi$
$252$		0			0
$253$	0.725785	−	5.04794i	0.0456297	−	0.317362i
$254$	−50.0358	+	14.6918i	−3.13952	+	0.921847i
$255$		0			0
$256$	−13.2090	+	28.9236i	−0.825560	+	1.80772i
$257$	0.349259	−	0.224455i	0.0217862	−	0.0140011i	−0.529702	−	0.848184i	$-0.677696\pi$
$257$	0.349259	−	0.224455i	0.0217862	−	0.0140011i	0.551489	+	0.834182i	$0.314060\pi$
$258$		0			0
$259$	0.746828	+	5.19430i	0.0464056	+	0.322758i
$260$	18.0385	+	39.4989i	1.11870	+	2.44962i
$261$		0			0
$262$	−30.5173	−	19.6123i	−1.88537	−	1.21165i
$263$	17.5459	−	11.2761i	1.08193	−	0.695313i	0.126926	−	0.991912i	$-0.459489\pi$
$263$	17.5459	−	11.2761i	1.08193	−	0.695313i	0.955002	+	0.296599i	$0.0958524\pi$
$264$		0			0
$265$	−4.32877	+	4.99567i	−0.265914	+	0.306882i
$266$	−2.32337	−	16.1594i	−0.142455	−	0.990797i
$267$		0			0
$268$	−33.1834	+	12.1421i	−2.02700	+	0.741697i
$269$	−18.8401			−1.14870			−0.574352	−	0.818609i	$-0.694746\pi$
$269$	−18.8401			−1.14870			−0.574352	+	0.818609i	$0.694746\pi$
$270$		0			0
$271$	11.5562	−	13.3366i	0.701992	−	0.810142i	−0.287028	−	0.957922i	$-0.592667\pi$
$271$	11.5562	−	13.3366i	0.701992	−	0.810142i	0.989020	+	0.147780i	$0.0472128\pi$
$272$	−24.8174	+	7.28705i	−1.50478	+	0.441843i
$273$		0			0
$274$	−10.9375	−	7.02911i	−0.660759	−	0.424644i
$275$	1.46389	+	10.1816i	0.0882761	+	0.613974i
$276$		0			0
$277$	−3.67724	−	25.5758i	−0.220944	−	1.53670i	−0.734479	−	0.678631i	$-0.762574\pi$
$277$	−3.67724	−	25.5758i	−0.220944	−	1.53670i	0.513535	−	0.858068i	$-0.328336\pi$
$278$	−2.34227	−	2.70313i	−0.140480	−	0.162123i
$279$		0			0
$280$	5.68931	−	12.4578i	0.340001	−	0.744499i
$281$	8.28015	−	18.1310i	0.493952	−	1.08160i	−0.484436	−	0.874827i	$-0.660975\pi$
$281$	8.28015	−	18.1310i	0.493952	−	1.08160i	0.978388	−	0.206778i	$-0.0662978\pi$
$282$		0			0
$283$	−0.868714	+	6.04204i	−0.0516397	+	0.359162i	0.947575	+	0.319534i	$0.103526\pi$
$283$	−0.868714	+	6.04204i	−0.0516397	+	0.359162i	−0.999215	+	0.0396280i	$0.987383\pi$
$284$	2.88161	−	1.85190i	0.170992	−	0.109890i
$285$		0			0
$286$	−68.3679	+	20.0746i	−4.04268	+	1.18704i
$287$	0.0901531	−	0.627028i	0.00532157	−	0.0370123i
$288$		0			0
$289$	1.32388	+	0.850806i	0.0778753	+	0.0500474i
$290$	6.61872	+	7.63841i	0.388664	+	0.448543i
$291$		0			0
$292$	−13.0469	−	3.83092i	−0.763513	−	0.224188i
$293$	−7.76451	+	17.0019i	−0.453607	+	0.993262i	0.535291	+	0.844668i	$0.320202\pi$
$293$	−7.76451	+	17.0019i	−0.453607	+	0.993262i	−0.988898	+	0.148594i	$0.952525\pi$
$294$		0			0
$295$	−2.08840	−	1.34214i	−0.121592	−	0.0781422i
$296$	−9.08102	−	19.8847i	−0.527824	−	1.15577i
$297$		0			0
$298$	19.9066			1.15316
$299$	−2.67096	−	5.84860i	−0.154466	−	0.338233i
$300$		0			0
$301$	−0.829552	+	5.76966i	−0.0478146	+	0.332558i
$302$	3.61806	−	25.1641i	0.208196	−	1.44803i
$303$		0			0
$304$	11.5850	+	25.3677i	0.664447	+	1.45494i
$305$	−7.68738			−0.440178
$306$		0			0
$307$	−1.98100	−	4.33778i	−0.113061	−	0.247570i	0.844639	−	0.535336i	$-0.179815\pi$
$307$	−1.98100	−	4.33778i	−0.113061	−	0.247570i	−0.957701	+	0.287766i	$0.907088\pi$
$308$	24.0730	+	15.4708i	1.37169	+	0.881529i
$309$		0			0
$310$	−4.74270	+	10.3851i	−0.269367	+	0.589832i
$311$	4.74712	+	1.39388i	0.269184	+	0.0790397i	0.413539	−	0.910486i	$-0.364292\pi$
$311$	4.74712	+	1.39388i	0.269184	+	0.0790397i	−0.144355	+	0.989526i	$0.546111\pi$
$312$		0			0
$313$	21.8128	+	25.1733i	1.23293	+	1.42288i	0.871436	+	0.490509i	$0.163189\pi$
$313$	21.8128	+	25.1733i	1.23293	+	1.42288i	0.361498	+	0.932373i	$0.382265\pi$
$314$	25.8732	+	16.6277i	1.46011	+	0.938353i
$315$		0			0
$316$	−0.0628086	+	0.436844i	−0.00353326	+	0.0245744i
$317$	8.66687	−	2.54482i	0.486780	−	0.142931i	−0.0291278	−	0.999576i	$-0.509273\pi$
$317$	8.66687	−	2.54482i	0.486780	−	0.142931i	0.515908	+	0.856644i	$0.327455\pi$
$318$		0			0
$319$	−9.53476	+	6.12762i	−0.533844	+	0.343081i
$320$	0.805162	−	5.60002i	0.0450099	−	0.313051i
$321$		0			0
$322$	−1.56962	+	3.43698i	−0.0874714	+	0.191536i
$323$	8.31918	−	18.2165i	0.462891	−	1.01359i
$324$		0			0
$325$	8.49252	+	9.80089i	0.471080	+	0.543655i
$326$	3.11214	+	21.6454i	0.172365	+	1.19883i
$327$		0			0
$328$	0.375545	+	2.61198i	0.0207360	+	0.144222i
$329$	−0.0717710	−	0.0461244i	−0.00395686	−	0.00254292i
$330$		0			0
$331$	11.7600	−	3.45305i	0.646389	−	0.189797i	0.0579258	−	0.998321i	$-0.481551\pi$
$331$	11.7600	−	3.45305i	0.646389	−	0.189797i	0.588463	+	0.808524i	$0.299733\pi$
$332$	−39.0024	+	45.0111i	−2.14053	+	2.47031i
$333$		0			0
$334$	−37.8635			−2.07180
$335$	11.0761	−	8.18444i	0.605153	−	0.447164i
$336$		0			0
$337$	0.0648586	+	0.451102i	0.00353307	+	0.0245731i	0.991512	−	0.130017i	$-0.0415033\pi$
$337$	0.0648586	+	0.451102i	0.00353307	+	0.0245731i	−0.987979	+	0.154590i	$0.950594\pi$
$338$	−37.4320	+	43.1988i	−2.03603	+	2.34970i
$339$		0			0
$340$	26.3331	−	16.9232i	1.42811	−	0.917791i
$341$	−10.7703	−	6.92166i	−0.583245	−	0.374829i
$342$		0			0
$343$	−6.99507	−	15.3171i	−0.377698	−	0.827044i
$344$	−3.45562	−	24.0344i	−0.186314	−	1.29585i
$345$		0			0
$346$	−33.6913	+	21.6521i	−1.81125	+	1.16402i
$347$	−9.43014	+	20.6491i	−0.506236	+	1.10850i	0.468155	+	0.883646i	$0.344919\pi$
$347$	−9.43014	+	20.6491i	−0.506236	+	1.10850i	−0.974392	+	0.224857i	$0.927809\pi$
$348$		0			0
$349$	−30.9301	+	9.08190i	−1.65565	+	0.486143i	−0.970267	−	0.242038i	$-0.922184\pi$
$349$	−30.9301	+	9.08190i	−1.65565	+	0.486143i	−0.685385	+	0.728181i	$0.740366\pi$
$350$	1.08458	−	7.54345i	0.0579735	−	0.403215i
$351$		0			0
$352$	−15.6422	−	4.59297i	−0.833733	−	0.244806i
$353$	−31.2724	+	9.18239i	−1.66446	+	0.488729i	−0.972441	−	0.233150i	$-0.925097\pi$
$353$	−31.2724	+	9.18239i	−1.66446	+	0.488729i	−0.692019	+	0.721880i	$0.743278\pi$
$354$		0			0
$355$	−0.874270	+	1.00896i	−0.0464015	+	0.0535501i
$356$	−55.6904	−	35.7900i	−2.95159	−	1.89687i
$357$		0			0
$358$	26.9449	−	31.0960i	1.42408	−	1.64348i
$359$	−30.2671	−	8.88721i	−1.59743	−	0.469049i	−0.642603	−	0.766199i	$-0.722146\pi$
$359$	−30.2671	−	8.88721i	−1.59743	−	0.469049i	−0.954831	+	0.297150i	$0.903964\pi$
$360$		0			0
$361$	−2.48725	−	0.730323i	−0.130908	−	0.0384380i
$362$	−5.39912	−	3.46980i	−0.283771	−	0.182369i
$363$		0			0
$364$	36.0771			1.89095
$365$	5.29974			0.277401
$366$		0			0
$367$	12.7025	+	14.6595i	0.663065	+	0.765218i	0.983275	−	0.182129i	$-0.0582987\pi$
$367$	12.7025	+	14.6595i	0.663065	+	0.765218i	−0.320209	+	0.947347i	$0.603753\pi$
$368$	0.918561	−	6.38873i	0.0478833	−	0.333036i
$369$		0			0
$370$	10.3958	+	11.9974i	0.540452	+	0.623715i
$371$	2.28145	+	4.99567i	0.118447	+	0.259362i
$372$		0			0
$373$	17.4411			0.903065			0.451533	−	0.892255i	$-0.350877\pi$
$373$	17.4411			0.903065			0.451533	+	0.892255i	$0.350877\pi$
$374$	21.3377	+	46.7231i	1.10335	+	2.41599i
$375$		0			0
$376$	0.340993	+	0.100125i	0.0175854	+	0.00516354i
$377$	−5.93599	+	12.9980i	−0.305719	+	0.669431i
$378$		0			0
$379$	14.0280	−	16.1892i	0.720570	−	0.831582i	−0.270806	−	0.962634i	$-0.587290\pi$
$379$	14.0280	−	16.1892i	0.720570	−	0.831582i	0.991375	+	0.131052i	$0.0418356\pi$
$380$	−22.1016	−	25.5066i	−1.13379	−	1.30846i
$381$		0			0
$382$	−5.14008	+	5.93196i	−0.262989	+	0.303506i
$383$	−5.36042	+	37.2825i	−0.273904	+	1.90505i	0.132204	+	0.991223i	$0.457795\pi$
$383$	−5.36042	+	37.2825i	−0.273904	+	1.90505i	−0.406108	+	0.913825i	$0.633114\pi$
$384$		0			0
$385$	−10.7012	−	3.14216i	−0.545385	−	0.160139i
$386$	45.4959	−	29.2384i	2.31568	−	1.48820i
$387$		0			0
$388$	−68.4554	+	20.1003i	−3.47530	+	1.02044i
$389$	8.33248	−	18.2456i	0.422473	−	0.925088i	−0.572015	−	0.820243i	$-0.693838\pi$
$389$	8.33248	−	18.2456i	0.422473	−	0.925088i	0.994489	−	0.104845i	$-0.0334346\pi$
$390$		0			0
$391$	−3.89913	+	2.50582i	−0.197188	+	0.126725i
$392$	19.2416	+	22.2060i	0.971850	+	1.12157i
$393$		0			0
$394$	−15.9539	−	34.9342i	−0.803747	−	1.75996i
$395$	−0.0244798	−	0.170261i	−0.00123171	−	0.00856675i
$396$		0			0
$397$	−9.96399	+	6.40347i	−0.500078	+	0.321381i	−0.766248	−	0.642546i	$-0.777878\pi$
$397$	−9.96399	+	6.40347i	−0.500078	+	0.321381i	0.266169	+	0.963926i	$0.414242\pi$
$398$	34.4320	−	10.1101i	1.72592	−	0.506776i
$399$		0			0
$400$	1.85272	+	12.8859i	0.0926359	+	0.644297i
$401$	−23.7298			−1.18501			−0.592505	−	0.805567i	$-0.701861\pi$
$401$	−23.7298			−1.18501			−0.592505	+	0.805567i	$0.701861\pi$
$402$		0			0
$403$	−16.1410			−0.804040
$404$	−4.68797	−	32.6056i	−0.233235	−	1.62219i
$405$		0			0
$406$	8.05710	−	2.36578i	0.399867	−	0.117412i
$407$	−14.9759	+	9.62445i	−0.742329	+	0.477066i
$408$		0			0
$409$	−3.55246	−	24.7079i	−0.175658	−	1.22173i	−0.866669	−	0.498884i	$-0.833744\pi$
$409$	−3.55246	−	24.7079i	−0.175658	−	1.22173i	0.691011	−	0.722844i	$-0.257166\pi$
$410$	−0.796070	−	1.74315i	−0.0393151	−	0.0860880i
$411$		0			0
$412$	28.3448	+	32.7117i	1.39645	+	1.61159i
$413$	−1.73511	+	1.11509i	−0.0853791	+	0.0548698i
$414$		0			0
$415$	9.64301	−	21.1153i	0.473357	−	1.03651i
$416$	−19.7209	+	5.79058i	−0.966897	+	0.283906i
$417$		0			0
$418$	46.5900	−	29.9415i	2.27879	−	1.46449i
$419$	3.07342	+	0.902437i	0.150146	+	0.0440869i	0.355942	−	0.934508i	$-0.384160\pi$
$419$	3.07342	+	0.902437i	0.150146	+	0.0440869i	−0.205796	+	0.978595i	$0.565978\pi$
$420$		0			0
$421$	1.59845	−	11.1175i	0.0779038	−	0.541833i	−0.913073	−	0.407797i	$-0.866297\pi$
$421$	1.59845	−	11.1175i	0.0779038	−	0.541833i	0.990976	−	0.134036i	$-0.0427937\pi$
$422$	16.2196	−	18.7184i	0.789556	−	0.911196i
$423$		0			0
$424$	−14.9816	−	17.2897i	−0.727572	−	0.839663i
$425$	6.12198	−	7.06514i	0.296960	−	0.342710i
$426$		0			0
$427$	−2.65322	+	5.80974i	−0.128398	+	0.281153i
$428$	−25.9826	−	7.62918i	−1.25592	−	0.368770i
$429$		0			0
$430$	7.32511	+	16.0398i	0.353248	+	0.773506i
$431$	0.299510			0.0144269			0.00721345	−	0.999974i	$-0.497704\pi$
$431$	0.299510			0.0144269			0.00721345	+	0.999974i	$0.497704\pi$
$432$		0			0
$433$	−2.96890	−	6.50098i	−0.142676	−	0.312417i	0.824781	−	0.565452i	$-0.191298\pi$
$433$	−2.96890	−	6.50098i	−0.142676	−	0.312417i	−0.967457	+	0.253035i	$0.918571\pi$
$434$	6.21162	+	7.16859i	0.298167	+	0.344103i
$435$		0			0
$436$	10.6756	−	74.2505i	0.511269	−	3.55595i
$437$	3.27258	+	3.77676i	0.156549	+	0.180667i
$438$		0			0
$439$	−18.1442			−0.865976			−0.432988	−	0.901400i	$-0.642541\pi$
$439$	−18.1442			−0.865976			−0.432988	+	0.901400i	$0.642541\pi$
$440$	46.4594			2.21487
$441$		0			0
$442$	54.4780	+	35.0109i	2.59125	+	1.66530i
$443$	22.0835	+	6.48430i	1.04922	+	0.308078i	0.760502	−	0.649336i	$-0.224953\pi$
$443$	22.0835	+	6.48430i	1.04922	+	0.308078i	0.288717	+	0.957414i	$0.406771\pi$
$444$		0			0
$445$	24.7562	+	7.26907i	1.17356	+	0.344587i
$446$	40.8131	−	47.1008i	1.93256	−	2.23029i
$447$		0			0
$448$	−3.95432	−	2.54129i	−0.186824	−	0.120065i
$449$	−17.1388	+	19.7792i	−0.808830	+	0.933440i	−0.998831	−	0.0483442i	$-0.984606\pi$
$449$	−17.1388	+	19.7792i	−0.808830	+	0.933440i	0.190001	+	0.981784i	$0.439151\pi$
$450$		0			0
$451$	2.06190	−	0.605430i	0.0970913	−	0.0285086i
$452$	42.9121	+	12.6001i	2.01841	+	0.592660i
$453$		0			0
$454$	4.63185	−	32.2152i	0.217384	−	1.51194i
$455$	−13.4915	+	3.96148i	−0.632493	+	0.185717i
$456$		0			0
$457$	6.12614	−	13.4144i	0.286569	−	0.627498i	−0.710526	−	0.703671i	$-0.751543\pi$
$457$	6.12614	−	13.4144i	0.286569	−	0.627498i	0.997095	+	0.0761730i	$0.0242701\pi$
$458$	8.16736	−	5.24885i	0.381636	−	0.245262i
$459$		0			0
$460$	1.11165	+	7.73168i	0.0518309	+	0.360492i
$461$	0.236239	+	0.517290i	0.0110027	+	0.0240926i	0.915054	−	0.403332i	$-0.132148\pi$
$461$	0.236239	+	0.517290i	0.0110027	+	0.0240926i	−0.904051	+	0.427425i	$0.859421\pi$
$462$		0			0
$463$	−22.0263	−	14.1554i	−1.02365	−	0.657859i	−0.0827576	−	0.996570i	$-0.526373\pi$
$463$	−22.0263	−	14.1554i	−1.02365	−	0.657859i	−0.940890	+	0.338711i	$0.890009\pi$
$464$	−12.0673	+	7.75518i	−0.560210	+	0.360025i
$465$		0			0
$466$	32.5935	−	37.6149i	1.50987	−	1.74248i
$467$	−3.29307	−	22.9038i	−0.152385	−	1.05986i	−0.912207	−	0.409730i	$-0.865623\pi$
$467$	−3.29307	−	22.9038i	−0.152385	−	1.05986i	0.759822	−	0.650131i	$-0.225286\pi$
$468$		0			0
$469$	−2.36258	−	11.1955i	−0.109094	−	0.516962i
$470$	−0.258084			−0.0119045
$471$		0			0
$472$	5.62640	−	6.49322i	0.258976	−	0.298874i
$473$	−18.9728	+	5.57092i	−0.872371	+	0.256151i
$474$		0			0
$475$	−8.47949	−	5.44943i	−0.389065	−	0.250037i
$476$	−3.70115	−	25.7421i	−0.169642	−	1.17989i
$477$		0			0
$478$	−2.81835	−	19.6021i	−0.128909	−	0.896579i
$479$	8.55421	+	9.87209i	0.390852	+	0.451067i	0.916739	−	0.399487i	$-0.130812\pi$
$479$	8.55421	+	9.87209i	0.390852	+	0.451067i	−0.525887	+	0.850555i	$0.676266\pi$
$480$		0			0
$481$	−9.32347	+	20.4155i	−0.425113	+	0.930869i
$482$	2.96588	−	6.49437i	0.135092	−	0.295810i
$483$		0			0
$484$	−7.05707	+	49.0830i	−0.320776	+	2.23105i
$485$	23.3927	−	15.0336i	1.06221	−	0.682641i
$486$		0			0
$487$	10.2422	−	3.00738i	0.464118	−	0.136277i	−0.0413093	−	0.999146i	$-0.513153\pi$
$487$	10.2422	−	3.00738i	0.464118	−	0.136277i	0.505428	+	0.862869i	$0.331335\pi$
$488$	3.78637	−	26.3348i	0.171401	−	1.19212i
$489$		0			0
$490$	−17.9505	−	11.5361i	−0.810921	−	0.521147i
$491$	−12.7969	−	14.7684i	−0.577515	−	0.666488i	0.389553	−	0.921004i	$-0.372629\pi$
$491$	−12.7969	−	14.7684i	−0.577515	−	0.666488i	−0.967069	+	0.254516i	$0.918084\pi$
$492$		0			0
$493$	9.88344	+	2.90204i	0.445128	+	0.130701i
$494$	29.0052	−	63.5125i	1.30501	−	2.85756i
$495$		0			0
$496$	−13.6310	−	8.76013i	−0.612051	−	0.393341i
$497$	0.460777	+	1.00896i	0.0206687	+	0.0452581i
$498$		0			0
$499$	−33.0146			−1.47794			−0.738968	−	0.673741i	$-0.764686\pi$
$499$	−33.0146			−1.47794			−0.738968	+	0.673741i	$0.764686\pi$
$500$	−21.6310	−	47.3652i	−0.967367	−	2.11824i
$501$		0			0
$502$	0.606447	−	4.21793i	0.0270670	−	0.188255i
$503$	3.76047	−	26.1547i	0.167671	−	1.16618i	−0.716010	−	0.698090i	$-0.754034\pi$
$503$	3.76047	−	26.1547i	0.167671	−	1.16618i	0.883681	−	0.468089i	$-0.155057\pi$
$504$		0			0
$505$	5.33342	+	11.6786i	0.237334	+	0.519689i
$506$	−12.8177			−0.569814
$507$		0			0
$508$	37.2082	+	81.4745i	1.65085	+	3.61485i
$509$	8.14286	+	5.23310i	0.360926	+	0.231953i	0.708518	−	0.705693i	$-0.249364\pi$
$509$	8.14286	+	5.23310i	0.360926	+	0.231953i	−0.347592	+	0.937646i	$0.613001\pi$
$510$		0			0
$511$	1.82915	−	4.00527i	0.0809167	−	0.177183i
$512$	47.2669	+	13.8788i	2.08892	+	0.613363i
$513$		0			0
$514$	−0.683314	−	0.788586i	−0.0301397	−	0.0347830i
$515$	−14.1919	−	9.12058i	−0.625370	−	0.401901i
$516$		0			0
$517$	0.0411878	−	0.286468i	0.00181144	−	0.0125988i
$518$	12.6550	−	3.71585i	0.556030	−	0.163265i
$519$		0			0
$520$	49.2753	−	31.6673i	2.16086	−	1.38870i
$521$	−3.13475	+	21.8027i	−0.137336	+	0.955192i	0.798309	+	0.602249i	$0.205728\pi$
$521$	−3.13475	+	21.8027i	−0.137336	+	0.955192i	−0.935645	+	0.352944i	$0.885181\pi$
$522$		0			0
$523$	−1.54962	+	3.39320i	−0.0677603	+	0.148374i	−0.940482	−	0.339844i	$-0.889626\pi$
$523$	−1.54962	+	3.39320i	−0.0677603	+	0.148374i	0.872722	+	0.488218i	$0.162353\pi$
$524$	−25.8833	+	56.6765i	−1.13072	+	2.47593i
$525$		0			0
$526$	−34.3281	−	39.6167i	−1.49677	−	1.72737i
$527$	1.65590	+	11.5171i	0.0721323	+	0.501692i
$528$		0			0
$529$	3.10864	+	21.6211i	0.135158	+	0.940046i
$530$	13.9763	+	8.98205i	0.607093	+	0.390155i
$531$		0			0
$532$	−26.9047	+	7.89993i	−1.16647	+	0.342506i
$533$	1.77421	−	2.04754i	0.0768494	−	0.0886889i
$534$		0			0
$535$	10.5543			0.456302
$536$	22.5821	+	41.9748i	0.975398	+	1.81304i
$537$		0			0
$538$	6.73884	+	46.8696i	0.290532	+	2.02069i
$539$	15.6696	−	18.0836i	0.674935	−	0.778917i
$540$		0			0
$541$	−15.5932	+	10.0212i	−0.670406	+	0.430844i	−0.831072	−	0.556165i	$-0.812272\pi$
$541$	−15.5932	+	10.0212i	−0.670406	+	0.430844i	0.160666	+	0.987009i	$0.448636\pi$
$542$	−37.3117	−	23.9788i	−1.60268	−	1.02998i
$543$		0			0
$544$	6.15492	+	13.4774i	0.263890	+	0.577839i
$545$	4.16084	+	28.9393i	0.178231	+	1.23962i
$546$		0			0
$547$	−0.379566	+	0.243932i	−0.0162291	+	0.0104298i	−0.548730	−	0.836000i	$-0.684889\pi$
$547$	−0.379566	+	0.243932i	−0.0162291	+	0.0104298i	0.532501	+	0.846429i	$0.321252\pi$
$548$	−9.27665	+	20.3130i	−0.396279	+	0.867730i
$549$		0			0
$550$	24.8057	−	7.28362i	1.05772	−	0.310574i
$551$	1.58058	−	10.9932i	0.0673349	−	0.468325i
$552$		0			0
$553$	−0.137123	−	0.0402631i	−0.00583108	−	0.00171216i
$554$	−62.3110	+	18.2962i	−2.64734	+	0.777329i
$555$		0			0
$556$	−4.02305	+	4.64285i	−0.170615	+	0.196901i
$557$	13.8580	+	8.90601i	0.587183	+	0.377360i	0.800240	−	0.599680i	$-0.204706\pi$
$557$	13.8580	+	8.90601i	0.587183	+	0.377360i	−0.213057	+	0.977040i	$0.568342\pi$
$558$		0			0
$559$	−16.3255	+	18.8407i	−0.690496	+	0.796875i
$560$	−13.5436	−	3.97675i	−0.572321	−	0.168049i
$561$		0			0
$562$	−48.0672	−	14.1138i	−2.02759	−	0.595355i
$563$	−19.5088	−	12.5376i	−0.822199	−	0.528395i	0.0605910	−	0.998163i	$-0.480701\pi$
$563$	−19.5088	−	12.5376i	−0.822199	−	0.528395i	−0.882790	+	0.469767i	$0.844338\pi$
$564$		0			0
$565$	−17.4312			−0.733334
$566$	15.3418			0.644866
$567$		0			0
$568$	−3.02580	−	3.49196i	−0.126960	−	0.146519i
$569$	−1.25675	+	8.74088i	−0.0526857	+	0.366437i	0.946374	+	0.323074i	$0.104716\pi$
$569$	−1.25675	+	8.74088i	−0.0526857	+	0.366437i	−0.999059	+	0.0433629i	$0.986193\pi$
$570$		0			0
$571$	−4.61681	−	5.32808i	−0.193207	−	0.222973i	0.650878	−	0.759183i	$-0.274401\pi$
$571$	−4.61681	−	5.32808i	−0.193207	−	0.222973i	−0.844085	+	0.536210i	$0.819856\pi$
$572$	50.8405	+	111.325i	2.12575	+	4.65474i
$573$		0			0
$574$	−1.59214			−0.0664546
$575$	0.969098	+	2.12203i	0.0404142	+	0.0884947i
$576$		0			0
$577$	−6.51507	−	1.91300i	−0.271226	−	0.0796392i	0.143291	−	0.989681i	$-0.454231\pi$
$577$	−6.51507	−	1.91300i	−0.271226	−	0.0796392i	−0.414517	+	0.910041i	$0.636050\pi$
$578$	1.64306	−	3.59781i	0.0683425	−	0.149649i
$579$		0			0
$580$	11.3682	−	13.1196i	0.472038	−	0.544761i
$581$	−12.6297	−	14.5754i	−0.523967	−	0.604690i
$582$		0			0
$583$	−12.2004	+	14.0800i	−0.505288	+	0.583134i
$584$	−2.61035	+	18.1554i	−0.108017	+	0.751275i
$585$		0			0
$586$	45.0738	+	13.2349i	1.86198	+	0.546727i
$587$	−13.9744	+	8.98081i	−0.576786	+	0.370678i	−0.796273	−	0.604938i	$-0.793198\pi$
$587$	−13.9744	+	8.98081i	−0.576786	+	0.370678i	0.219487	+	0.975615i	$0.429562\pi$
$588$		0			0
$589$	12.0372	−	3.53445i	0.495986	−	0.145635i
$590$	−2.59191	+	5.67550i	−0.106707	+	0.233657i
$591$		0			0
$592$	−18.9537	+	12.1808i	−0.778992	+	0.500628i
$593$	7.07633	+	8.16652i	0.290590	+	0.335359i	0.882208	−	0.470859i	$-0.156056\pi$
$593$	7.07633	+	8.16652i	0.290590	+	0.335359i	−0.591618	+	0.806218i	$0.701511\pi$
$594$		0			0
$595$	4.21073	+	9.22021i	0.172623	+	0.377992i
$596$	−4.86592	−	33.8432i	−0.199316	−	1.38627i
$597$		0			0
$598$	−13.5945	+	8.73666i	−0.555921	+	0.357269i
$599$	−14.1801	+	4.16365i	−0.579382	+	0.170122i	−0.558276	−	0.829655i	$-0.688537\pi$
$599$	−14.1801	+	4.16365i	−0.579382	+	0.170122i	−0.0211062	+	0.999777i	$0.506719\pi$
$600$		0			0
$601$	0.204537	+	1.42259i	0.00834326	+	0.0580286i	0.993568	−	0.113239i	$-0.0361227\pi$
$601$	0.204537	+	1.42259i	0.00834326	+	0.0580286i	−0.985224	+	0.171268i	$0.945214\pi$
$602$	14.6502			0.597098
$603$		0			0
$604$	−43.6660			−1.77674
$605$	−2.75051	−	19.1302i	−0.111824	−	0.777754i
$606$		0			0
$607$	2.48263	−	0.728966i	0.100767	−	0.0295878i	−0.230960	−	0.972963i	$-0.574187\pi$
$607$	2.48263	−	0.728966i	0.100767	−	0.0295878i	0.331727	+	0.943375i	$0.392369\pi$
$608$	13.4390	−	8.63672i	0.545023	−	0.350265i
$609$		0			0
$610$	2.74966	+	19.1243i	0.111331	+	0.774321i
$611$	−0.151576	−	0.331904i	−0.00613209	−	0.0134274i
$612$		0			0
$613$	−10.2699	−	11.8522i	−0.414799	−	0.478704i	0.509446	−	0.860502i	$-0.329850\pi$
$613$	−10.2699	−	11.8522i	−0.414799	−	0.478704i	−0.924246	+	0.381799i	$0.875305\pi$
$614$	−10.0828	+	6.47980i	−0.406907	+	0.261503i
$615$		0			0
$616$	16.0350	−	35.1117i	0.646067	−	1.41469i
$617$	1.67778	−	0.492640i	0.0675448	−	0.0198329i	−0.247786	−	0.968815i	$-0.579703\pi$
$617$	1.67778	−	0.492640i	0.0675448	−	0.0198329i	0.315330	+	0.948982i	$0.397885\pi$
$618$		0			0
$619$	17.4799	−	11.2337i	0.702578	−	0.451520i	−0.139959	−	0.990157i	$-0.544697\pi$
$619$	17.4799	−	11.2337i	0.702578	−	0.451520i	0.842538	+	0.538638i	$0.181061\pi$
$620$	18.8149	+	5.52457i	0.755626	+	0.221872i
$621$		0			0
$622$	1.76966	−	12.3082i	0.0709568	−	0.493515i
$623$	14.0379	−	16.2006i	0.562418	−	0.649065i
$624$		0			0
$625$	6.18768	+	7.14097i	0.247507	+	0.285639i
$626$	54.8230	−	63.2691i	2.19117	−	2.52874i
$627$		0			0
$628$	21.9443	−	48.0514i	0.875674	−	1.91746i
$629$	15.5236	+	4.55814i	0.618966	+	0.181745i
$630$		0			0
$631$	−2.49035	−	5.45311i	−0.0991393	−	0.217085i	0.853563	−	0.520989i	$-0.174437\pi$
$631$	−2.49035	−	5.45311i	−0.0991393	−	0.217085i	−0.952702	+	0.303905i	$0.901710\pi$
$632$	0.595322			0.0236806
$633$		0			0
$634$	−9.43090	−	20.6508i	−0.374549	−	0.820148i
$635$	−22.8609	−	26.3829i	−0.907208	−	1.04697i
$636$		0			0
$637$	4.29325	−	29.8602i	0.170105	−	1.18310i
$638$	18.6545	+	21.5284i	0.738537	+	0.852317i
$639$		0			0
$640$	−25.7880			−1.01936
$641$	−21.2829			−0.840625			−0.420313	−	0.907379i	$-0.638080\pi$
$641$	−21.2829			−0.840625			−0.420313	+	0.907379i	$0.638080\pi$
$642$		0			0
$643$	24.4006	+	15.6813i	0.962267	+	0.618412i	0.924625	−	0.380880i	$-0.124379\pi$
$643$	24.4006	+	15.6813i	0.962267	+	0.618412i	0.0376427	+	0.999291i	$0.488015\pi$
$644$	6.22689	+	1.82838i	0.245374	+	0.0720483i
$645$		0			0
$646$	−48.2937	−	14.1803i	−1.90009	−	0.557917i
$647$	−27.3198	+	31.5287i	−1.07405	+	1.23952i	−0.104529	+	0.994522i	$0.533334\pi$
$647$	−27.3198	+	31.5287i	−1.07405	+	1.23952i	−0.969523	+	0.245000i	$0.921212\pi$
$648$		0			0
$649$	−5.88604	−	3.78273i	−0.231047	−	0.148485i
$650$	21.3446	−	24.6329i	0.837203	−	0.966183i
$651$		0			0
$652$	36.0386	−	10.5819i	1.41138	−	0.414419i
$653$	−23.1581	−	6.79982i	−0.906245	−	0.266098i	−0.204786	−	0.978807i	$-0.565650\pi$
$653$	−23.1581	−	6.79982i	−0.906245	−	0.266098i	−0.701460	+	0.712709i	$0.747468\pi$
$654$		0			0
$655$	3.45602	−	24.0371i	0.135038	−	0.939209i
$656$	2.60957	−	0.766239i	0.101887	−	0.0299166i
$657$		0			0
$658$	−0.0890748	+	0.195047i	−0.00347250	+	0.00760371i
$659$	−16.1770	+	10.3963i	−0.630167	+	0.404984i	−0.816371	−	0.577527i	$-0.804018\pi$
$659$	−16.1770	+	10.3963i	−0.630167	+	0.404984i	0.186204	+	0.982511i	$0.440381\pi$
$660$		0			0
$661$	1.68794	+	11.7399i	0.0656534	+	0.456630i	0.995956	+	0.0898377i	$0.0286348\pi$
$661$	1.68794	+	11.7399i	0.0656534	+	0.456630i	−0.930303	+	0.366792i	$0.880456\pi$
$662$	−12.7967	−	28.0209i	−0.497359	−	1.08906i
$663$		0			0
$664$	67.5852	+	43.4344i	2.62282	+	1.68558i
$665$	9.19394	−	5.90859i	0.356526	−	0.229125i
$666$		0			0
$667$	−1.68329	+	1.94262i	−0.0651771	+	0.0752184i
$668$	9.25527	+	64.3718i	0.358097	+	2.49062i
$669$		0			0
$670$	−24.3227	−	24.6272i	−0.939666	−	0.951433i
$671$	−21.6664			−0.836423
$672$		0			0
$673$	−30.2700	+	34.9334i	−1.16682	+	1.34658i	−0.240138	+	0.970739i	$0.577193\pi$
$673$	−30.2700	+	34.9334i	−1.16682	+	1.34658i	−0.926683	+	0.375844i	$0.877353\pi$
$674$	1.09903	−	0.322705i	0.0423331	−	0.0124301i
$675$		0			0
$676$	82.5920	+	53.0787i	3.17662	+	2.04149i
$677$	−2.47426	−	17.2089i	−0.0950935	−	0.661390i	−0.980492	−	0.196558i	$-0.937024\pi$
$677$	−2.47426	−	17.2089i	−0.0950935	−	0.661390i	0.885399	−	0.464832i	$-0.153885\pi$
$678$		0			0
$679$	−3.28789	−	22.8677i	−0.126177	−	0.877584i
$680$	−27.6507	−	31.9106i	−1.06036	−	1.22372i
$681$		0			0
$682$	−13.3670	+	29.2697i	−0.511850	+	1.12079i
$683$	16.9669	−	37.1524i	0.649222	−	1.42160i	−0.243012	−	0.970023i	$-0.578136\pi$
$683$	16.9669	−	37.1524i	0.649222	−	1.42160i	0.892234	−	0.451574i	$-0.149137\pi$
$684$		0			0
$685$	1.23865	−	8.61499i	0.0473263	−	0.329162i
$686$	−35.6031	+	22.8807i	−1.35933	+	0.873589i
$687$		0			0
$688$	−24.0122	+	7.05062i	−0.915457	+	0.268802i
$689$	−3.34274	+	23.2493i	−0.127348	+	0.885727i
$690$		0			0
$691$	25.6402	+	16.4779i	0.975397	+	0.626850i	0.928218	−	0.372037i	$-0.121340\pi$
$691$	25.6402	+	16.4779i	0.975397	+	0.626850i	0.0471793	+	0.998886i	$0.484977\pi$
$692$	45.0461	+	51.9859i	1.71239	+	1.97621i
$693$		0			0
$694$	54.7430	+	16.0740i	2.07802	+	0.610160i
$695$	0.994666	−	2.17801i	0.0377298	−	0.0826168i
$696$		0			0
$697$	−1.64300	−	1.05589i	−0.0622330	−	0.0399947i
$698$	33.6568	+	73.6981i	1.27393	+	2.78951i
$699$		0			0
$700$	−13.0897			−0.494746
$701$	13.2483	+	29.0097i	0.500382	+	1.09568i	0.976345	+	0.216218i	$0.0693722\pi$
$701$	13.2483	+	29.0097i	0.500382	+	1.09568i	−0.475964	+	0.879465i	$0.657901\pi$
$702$		0			0
$703$	2.48256	−	17.2666i	0.0936317	−	0.651223i
$704$	2.26930	−	15.7833i	0.0855275	−	0.594857i
$705$		0			0
$706$	34.0292	+	74.5135i	1.28071	+	2.80435i
$707$	10.6668			0.401168
$708$		0			0
$709$	−6.06057	−	13.2708i	−0.227610	−	0.498395i	0.761027	−	0.648720i	$-0.224695\pi$
$709$	−6.06057	−	13.2708i	−0.227610	−	0.498395i	−0.988637	+	0.150325i	$0.951968\pi$
$710$	2.82276	+	1.81408i	0.105936	+	0.0680812i
$711$		0			0
$712$	−37.0953	+	81.2273i	−1.39020	+	3.04412i
$713$	−2.78593	−	0.818022i	−0.104334	−	0.0306352i
$714$		0			0
$715$	−31.2367	−	36.0491i	−1.16819	−	1.34816i
$716$	−59.4527	−	38.2079i	−2.22185	−	1.42790i
$717$		0			0
$718$	−11.2831	+	78.4758i	−0.421082	+	2.92869i
$719$	32.5892	−	9.56905i	1.21537	−	0.356865i	0.389661	−	0.920959i	$-0.372592\pi$
$719$	32.5892	−	9.56905i	1.21537	−	0.356865i	0.825711	+	0.564093i	$0.190774\pi$
$720$		0			0
$721$	−11.7911	+	7.57765i	−0.439122	+	0.282207i
$722$	−0.927211	+	6.44890i	−0.0345072	+	0.240003i
$723$		0			0
$724$	−4.57926	+	10.0272i	−0.170187	+	0.372658i
$725$	2.15374	−	4.71603i	0.0799878	−	0.175149i
$726$		0			0
$727$	19.4939	+	22.4971i	0.722988	+	0.834372i	0.991663	−	0.128859i	$-0.0411313\pi$
$727$	19.4939	+	22.4971i	0.722988	+	0.834372i	−0.268675	+	0.963231i	$0.586586\pi$
$728$	−6.92571	−	48.1694i	−0.256684	−	1.78528i
$729$		0			0
$730$	−1.89564	−	13.1844i	−0.0701607	−	0.487978i
$731$	15.1182	+	9.71589i	0.559167	+	0.359355i
$732$		0			0
$733$	−21.8888	+	6.42713i	−0.808481	+	0.237392i	−0.659749	−	0.751486i	$-0.729337\pi$
$733$	−21.8888	+	6.42713i	−0.808481	+	0.237392i	−0.148732	+	0.988877i	$0.547519\pi$
$734$	31.9257	−	36.8442i	1.17840	−	1.35994i
$735$		0			0
$736$	−3.69729			−0.136284
$737$	31.2174	−	23.0674i	1.14991	−	0.849697i
$738$		0			0
$739$	−6.99859	−	48.6762i	−0.257447	−	1.79058i	−0.550859	−	0.834598i	$-0.685700\pi$
$739$	−6.99859	−	48.6762i	−0.257447	−	1.79058i	0.293412	−	0.955986i	$-0.405209\pi$
$740$	17.8556	−	20.6065i	0.656386	−	0.757510i
$741$		0			0
$742$	11.6120	−	7.46255i	0.426288	−	0.273959i
$743$	35.6835	+	22.9324i	1.30910	+	0.841308i	0.994172	−	0.107808i	$-0.0343832\pi$
$743$	35.6835	+	22.9324i	1.30910	+	0.841308i	0.314928	+	0.949115i	$0.398020\pi$
$744$		0			0
$745$	5.53587	+	12.1219i	0.202818	+	0.444110i
$746$	−6.23842	−	43.3892i	−0.228405	−	1.58859i
$747$		0			0
$748$	74.2181	−	47.6971i	2.71368	−	1.74398i
$749$	3.64270	−	7.97640i	0.133101	−	0.291451i
$750$		0			0
$751$	−36.8957	+	10.8336i	−1.34634	+	0.395322i	−0.873929	−	0.486053i	$-0.838436\pi$
$751$	−36.8957	+	10.8336i	−1.34634	+	0.395322i	−0.472416	+	0.881376i	$0.656618\pi$
$752$	0.0521277	−	0.362556i	0.00190090	−	0.0132211i
$753$		0			0
$754$	34.4591	+	10.1181i	1.25493	+	0.368479i
$755$	16.3295	−	4.79478i	0.594292	−	0.174500i
$756$		0			0
$757$	11.5444	−	13.3230i	0.419588	−	0.484231i	−0.506123	−	0.862461i	$-0.668922\pi$
$757$	11.5444	−	13.3230i	0.419588	−	0.484231i	0.925712	+	0.378230i	$0.123467\pi$
$758$	−45.2923	−	29.1076i	−1.64509	−	1.05723i
$759$		0			0
$760$	−29.8130	+	34.4061i	−1.08143	+	1.24804i
$761$	−21.0384	−	6.17743i	−0.762642	−	0.223932i	−0.122793	−	0.992432i	$-0.539185\pi$
$761$	−21.0384	−	6.17743i	−0.762642	−	0.223932i	−0.639849	+	0.768501i	$0.721003\pi$
$762$		0			0
$763$	23.3069	+	6.84353i	0.843767	+	0.247752i
$764$	11.3414	+	7.28865i	0.410316	+	0.263694i
$765$		0			0
$766$	94.6671			3.42046
$767$	−8.82114			−0.318513
$768$		0			0
$769$	2.51426	+	2.90161i	0.0906664	+	0.104635i	0.799270	−	0.600972i	$-0.205220\pi$
$769$	2.51426	+	2.90161i	0.0906664	+	0.104635i	−0.708603	+	0.705607i	$0.750674\pi$
$770$	−3.98926	+	27.7459i	−0.143763	+	0.999894i
$771$		0			0
$772$	−60.8291	−	70.2006i	−2.18929	−	2.52657i
$773$	−0.245766	−	0.538153i	−0.00883960	−	0.0193560i	0.905161	−	0.425070i	$-0.139750\pi$
$773$	−0.245766	−	0.538153i	−0.00883960	−	0.0193560i	−0.914000	+	0.405713i	$0.867023\pi$
$774$		0			0
$775$	5.85638			0.210368
$776$	39.9789	+	87.5416i	1.43516	+	3.14256i
$777$		0			0
$778$	−48.3709	−	14.2030i	−1.73418	−	0.509202i
$779$	−0.874767	+	1.91547i	−0.0313418	+	0.0686289i
$780$		0			0
$781$	−2.46408	+	2.84370i	−0.0881717	+	0.101756i
$782$	7.62853	+	8.80380i	0.272796	+	0.314823i
$783$		0			0
$784$	19.8316	−	22.8868i	0.708270	−	0.817387i
$785$	−2.93008	+	20.3791i	−0.104579	+	0.727362i
$786$		0			0
$787$	27.9995	+	8.22139i	0.998073	+	0.293061i	0.739665	−	0.672975i	$-0.234984\pi$
$787$	27.9995	+	8.22139i	0.998073	+	0.293061i	0.258408	+	0.966036i	$0.416802\pi$
$788$	−55.4919	+	35.6625i	−1.97682	+	1.27042i
$789$		0			0
$790$	−0.414811	+	0.121799i	−0.0147583	+	0.00433343i
$791$	−6.01618	+	13.1736i	−0.213911	+	0.468399i
$792$		0			0
$793$	−22.9796	+	14.7681i	−0.816029	+	0.524430i
$794$	19.4942	+	22.4975i	0.691824	+	0.798408i
$795$		0			0
$796$	−25.6047	−	56.0665i	−0.907535	−	1.98722i
$797$	−2.98441	−	20.7570i	−0.105713	−	0.735251i	−0.971877	−	0.235490i	$-0.924330\pi$
$797$	−2.98441	−	20.7570i	−0.105713	−	0.735251i	0.866164	−	0.499761i	$-0.166579\pi$
$798$		0			0
$799$	−0.221273	+	0.142204i	−0.00782809	+	0.00503081i
$800$	7.15528	−	2.10098i	0.252977	−	0.0742808i
$801$		0			0
$802$	8.48780	+	59.0340i	0.299715	+	2.08456i
$803$	14.9370			0.527115
$804$		0			0
$805$	−2.52940			−0.0891497
$806$	5.77339	+	40.1548i	0.203359	+	1.41439i
$807$		0			0
$808$	−42.6344	+	12.5186i	−1.49987	+	0.440402i
$809$	44.8077	−	28.7962i	1.57535	−	1.01242i	0.597824	−	0.801628i	$-0.296032\pi$
$809$	44.8077	−	28.7962i	1.57535	−	1.01242i	0.977531	−	0.210792i	$-0.0676041\pi$
$810$		0			0
$811$	1.83380	+	12.7544i	0.0643934	+	0.447866i	0.996355	+	0.0853081i	$0.0271875\pi$
$811$	1.83380	+	12.7544i	0.0643934	+	0.447866i	−0.931961	+	0.362558i	$0.881903\pi$
$812$	−5.99152	−	13.1196i	−0.210261	−	0.460407i
$813$		0			0
$814$	29.2999	+	33.8139i	1.02696	+	1.18518i
$815$	−12.3152	+	7.91451i	−0.431383	+	0.277233i
$816$		0			0
$817$	8.04925	−	17.6254i	0.281608	−	0.616635i
$818$	−60.1966	+	17.6753i	−2.10472	+	0.618003i
$819$		0			0
$820$	−2.76894	+	1.77949i	−0.0966955	+	0.0621424i
$821$	37.4807	+	11.0053i	1.30808	+	0.384088i	0.860179	−	0.509993i	$-0.170352\pi$
$821$	37.4807	+	11.0053i	1.30808	+	0.384088i	0.447906	+	0.894081i	$0.352170\pi$
$822$		0			0
$823$	5.90993	−	41.1044i	0.206007	−	1.43281i	−0.580012	−	0.814608i	$-0.696952\pi$
$823$	5.90993	−	41.1044i	0.206007	−	1.43281i	0.786019	−	0.618203i	$-0.212139\pi$
$824$	38.2346	−	44.1251i	1.33197	−	1.53717i
$825$		0			0
$826$	3.39469	+	3.91768i	0.118116	+	0.136313i
$827$	−24.8524	+	28.6812i	−0.864203	+	0.997343i	0.135775	+	0.990740i	$0.456647\pi$
$827$	−24.8524	+	28.6812i	−0.864203	+	0.997343i	−0.999978	+	0.00660356i	$0.997898\pi$
$828$		0			0
$829$	−3.51398	+	7.69455i	−0.122046	+	0.267243i	−0.960787	−	0.277287i	$-0.910565\pi$
$829$	−3.51398	+	7.69455i	−0.122046	+	0.267243i	0.838741	+	0.544530i	$0.183292\pi$
$830$	−55.9787	−	16.4368i	−1.94305	−	0.570531i
$831$		0			0
$832$	−8.35126	−	18.2867i	−0.289528	−	0.633978i
$833$	−21.7466			−0.753475
$834$		0			0
$835$	−10.5295	−	23.0565i	−0.364390	−	0.797903i
$836$	−62.2919	−	71.8887i	−2.15441	−	2.48632i
$837$		0			0
$838$	1.14573	−	7.96870i	0.0395784	−	0.275274i
$839$	−14.6757	−	16.9367i	−0.506661	−	0.584718i	0.443579	−	0.896235i	$-0.353708\pi$
$839$	−14.6757	−	16.9367i	−0.506661	−	0.584718i	−0.950241	+	0.311517i	$0.899163\pi$
$840$		0			0
$841$	−23.2874			−0.803014
$842$	−28.2293			−0.972846
$843$		0			0
$844$	−35.7878	−	22.9994i	−1.23187	−	0.791672i
$845$	−36.7148	−	10.7804i	−1.26303	−	0.370859i
$846$		0			0
$847$	−15.4070	−	4.52389i	−0.529389	−	0.155443i
$848$	−15.4409	+	17.8198i	−0.530244	+	0.611934i
$849$		0			0
$850$	−19.7661	−	12.7029i	−0.677971	−	0.435705i
$851$	−2.64388	+	3.05120i	−0.0906312	+	0.104594i
$852$		0			0
$853$	−23.2811	+	6.83594i	−0.797128	+	0.234058i	−0.654840	−	0.755767i	$-0.727264\pi$
$853$	−23.2811	+	6.83594i	−0.797128	+	0.234058i	−0.142288	+	0.989825i	$0.545446\pi$
$854$	15.4022	+	4.52250i	0.527053	+	0.154757i
$855$		0			0
$856$	−5.19845	+	36.1560i	−0.177679	+	1.23579i
$857$	−9.68490	+	2.84374i	−0.330830	+	0.0971404i	−0.442929	−	0.896557i	$-0.646061\pi$
$857$	−9.68490	+	2.84374i	−0.330830	+	0.0971404i	0.112099	+	0.993697i	$0.464243\pi$
$858$		0			0
$859$	−7.50346	+	16.4303i	−0.256015	+	0.560594i	−0.993377	−	0.114904i	$-0.963344\pi$
$859$	−7.50346	+	16.4303i	−0.256015	+	0.560594i	0.737362	+	0.675498i	$0.236071\pi$
$860$	25.4787	−	16.3741i	0.868815	−	0.558353i
$861$		0			0
$862$	−0.107130	−	0.745108i	−0.00364887	−	0.0253785i
$863$	−3.35916	−	7.35553i	−0.114347	−	0.250385i	0.843802	−	0.536654i	$-0.180312\pi$
$863$	−3.35916	−	7.35553i	−0.114347	−	0.250385i	−0.958149	+	0.286269i	$0.907585\pi$
$864$		0			0
$865$	−22.5540	−	14.4946i	−0.766859	−	0.492830i
$866$	−15.1109	+	9.71120i	−0.513490	+	0.330000i
$867$		0			0
$868$	10.6690	−	12.3126i	0.362128	−	0.417918i
$869$	−0.0689948	−	0.479870i	−0.00234049	−	0.0162785i
$870$		0			0
$871$	17.3864	−	45.7436i	0.589117	−	1.54996i
$872$	−101.187			−3.42663
$873$		0			0
$874$	8.22509	−	9.49226i	0.278218	−	0.321081i
$875$	16.1784	−	4.75042i	0.546931	−	0.160593i
$876$		0			0
$877$	35.4297	+	22.7693i	1.19638	+	0.768865i	0.978326	−	0.207072i	$-0.0663935\pi$
$877$	35.4297	+	22.7693i	1.19638	+	0.768865i	0.218052	+	0.975937i	$0.430030\pi$
$878$	6.48992	+	45.1384i	0.219024	+	1.52335i
$879$		0			0
$880$	−6.81457	−	47.3964i	−0.229719	−	1.59773i
$881$	17.0479	+	19.6743i	0.574359	+	0.662846i	0.966382	−	0.257110i	$-0.0827702\pi$
$881$	17.0479	+	19.6743i	0.574359	+	0.662846i	−0.392023	+	0.919955i	$0.628225\pi$
$882$		0			0
$883$	−6.71513	+	14.7041i	−0.225982	+	0.494832i	−0.988329	−	0.152337i	$-0.951320\pi$
$883$	−6.71513	+	14.7041i	−0.225982	+	0.494832i	0.762346	+	0.647169i	$0.224047\pi$
$884$	46.2055	−	101.176i	1.55406	−	3.40291i
$885$		0			0
$886$	8.23241	−	57.2577i	0.276573	−	1.92361i
$887$	−2.42642	+	1.55937i	−0.0814714	+	0.0523585i	−0.580742	−	0.814087i	$-0.697238\pi$
$887$	−2.42642	+	1.55937i	−0.0814714	+	0.0523585i	0.499271	+	0.866446i	$0.333601\pi$
$888$		0			0
$889$	−27.8291	+	8.17135i	−0.933357	+	0.274058i
$890$	9.22875	−	64.1874i	0.309348	−	2.15157i
$891$		0			0
$892$	−90.0523	−	57.8731i	−3.01517	−	1.93774i
$893$	0.185717	+	0.214328i	0.00621477	+	0.00717223i
$894$		0			0
$895$	26.4287	+	7.76015i	0.883413	+	0.259393i
$896$	−8.90045	+	19.4893i	−0.297343	+	0.651091i
$897$		0			0
$898$	55.3362	+	35.5624i	1.84659	+	1.18673i
$899$	2.68062	+	5.86974i	0.0894037	+	0.195767i
$900$		0			0
$901$	16.9320			0.564086
$902$	−2.24367	−	4.91296i	−0.0747062	−	0.163584i
$903$		0			0
$904$	8.58560	−	59.7142i	0.285553	−	1.98606i
$905$	0.611438	−	4.25264i	0.0203249	−	0.141363i
$906$		0			0
$907$	−2.66205	−	5.82908i	−0.0883920	−	0.193551i	0.860273	−	0.509833i	$-0.170293\pi$
$907$	−2.66205	−	5.82908i	−0.0883920	−	0.193551i	−0.948665	+	0.316282i	$0.897566\pi$
$908$	−55.9013			−1.85515
$909$		0			0
$910$	14.6809	+	32.1467i	0.486667	+	1.06565i
$911$	−2.41146	−	1.54975i	−0.0798952	−	0.0513455i	0.500083	−	0.865977i	$-0.333303\pi$
$911$	−2.41146	−	1.54975i	−0.0798952	−	0.0513455i	−0.579979	+	0.814632i	$0.696939\pi$
$912$		0			0
$913$	27.1783	−	59.5121i	0.899469	−	1.96956i
$914$	−35.5629	−	10.4422i	−1.17632	−	0.345398i
$915$		0			0
$916$	−10.9200	−	12.6023i	−0.360806	−	0.416392i
$917$	−16.9733	−	10.9080i	−0.560506	−	0.360215i
$918$		0			0
$919$	−1.79235	+	12.4661i	−0.0591241	+	0.411217i	0.938669	+	0.344819i	$0.112060\pi$
$919$	−1.79235	+	12.4661i	−0.0591241	+	0.411217i	−0.997793	+	0.0663979i	$0.978849\pi$
$920$	10.1098	−	2.96850i	0.333310	−	0.0978686i
$921$		0			0
$922$	1.20239	−	0.772731i	0.0395987	−	0.0254485i
$923$	−0.675125	+	4.69560i	−0.0222220	+	0.154557i
$924$		0			0
$925$	3.38281	−	7.40731i	0.111226	−	0.243551i
$926$	−27.3368	+	59.8592i	−0.898342	+	1.96709i
$927$		0			0
$928$	5.38093	+	6.20992i	0.176638	+	0.203851i
$929$	6.63359	+	46.1377i	0.217641	+	1.51373i	0.746711	+	0.665149i	$0.231632\pi$
$929$	6.63359	+	46.1377i	0.217641	+	1.51373i	−0.529070	+	0.848578i	$0.677459\pi$
$930$		0			0
$931$	3.33688	+	23.2085i	0.109362	+	0.760629i
$932$	−71.9162	−	46.2177i	−2.35569	−	1.51391i
$933$		0			0
$934$	−55.8011	+	16.3847i	−1.82587	+	0.536123i
$935$	−22.5175	+	25.9866i	−0.736402	+	0.849853i
$936$		0			0
$937$	−51.8841			−1.69498			−0.847490	−	0.530811i	$-0.821887\pi$
$937$	−51.8841			−1.69498			−0.847490	+	0.530811i	$0.821887\pi$
$938$	−27.0067	+	9.88201i	−0.881801	+	0.322659i
$939$		0			0
$940$	0.0630853	+	0.438768i	0.00205762	+	0.0143110i
$941$	12.2835	−	14.1759i	0.400431	−	0.462122i	−0.519345	−	0.854564i	$-0.673824\pi$
$941$	12.2835	−	14.1759i	0.400431	−	0.462122i	0.919777	+	0.392442i	$0.128370\pi$
$942$		0			0
$943$	0.409997	−	0.263489i	0.0133513	−	0.00858037i
$944$	−7.44944	−	4.78746i	−0.242459	−	0.155819i
$945$		0			0
$946$	20.6454	+	45.2071i	0.671239	+	1.46981i
$947$	−6.49525	−	45.1754i	−0.211067	−	1.46800i	−0.769602	−	0.638523i	$-0.779546\pi$
$947$	−6.49525	−	45.1754i	−0.211067	−	1.46800i	0.558535	−	0.829481i	$-0.311364\pi$
$948$		0			0
$949$	15.8423	−	10.1812i	0.514263	−	0.330497i
$950$	−10.5239	+	23.0441i	−0.341439	+	0.747648i
$951$		0			0
$952$	−33.6598	+	9.88340i	−1.09092	+	0.320323i
$953$	−2.66697	+	18.5492i	−0.0863917	+	0.600868i	0.899930	+	0.436035i	$0.143618\pi$
$953$	−2.66697	+	18.5492i	−0.0863917	+	0.600868i	−0.986322	+	0.164833i	$0.947292\pi$
$954$		0			0
$955$	−5.04160	−	1.48035i	−0.163142	−	0.0479029i
$956$	−32.6366	+	9.58297i	−1.05554	+	0.309935i
$957$		0			0
$958$	21.4996	−	24.8119i	0.694621	−	0.801635i
$959$	−6.08327	−	3.90948i	−0.196439	−	0.126244i
$960$		0			0
$961$	15.5274	−	17.9195i	0.500883	−	0.578049i
$962$	54.1237	+	15.8922i	1.74502	+	0.512384i
$963$		0			0
$964$	−11.7660	−	3.45482i	−0.378959	−	0.111272i
$965$	30.4564	+	19.5731i	0.980425	+	0.630081i
$966$		0			0
$967$	50.8675			1.63579			0.817895	−	0.575367i	$-0.195141\pi$
$967$	50.8675			1.63579			0.817895	+	0.575367i	$0.195141\pi$
$968$	66.8894			2.14991
$969$		0			0
$970$	−45.7672	−	52.8181i	−1.46950	−	1.69589i
$971$	−2.57572	+	17.9145i	−0.0826588	+	0.574904i	0.905834	+	0.423634i	$0.139246\pi$
$971$	−2.57572	+	17.9145i	−0.0826588	+	0.574904i	−0.988492	+	0.151271i	$0.951663\pi$
$972$		0			0
$973$	−1.30274	−	1.50344i	−0.0417638	−	0.0481980i
$974$	−11.1451	−	24.4044i	−0.357112	−	0.781967i
$975$		0			0
$976$	−27.4213			−0.877733
$977$	10.4661	+	22.9176i	0.334840	+	0.733198i	0.999908	−	0.0135852i	$-0.00432443\pi$
$977$	10.4661	+	22.9176i	0.334840	+	0.733198i	−0.665067	+	0.746783i	$0.731597\pi$
$978$		0			0
$979$	69.7738	+	20.4874i	2.22998	+	0.654782i
$980$	−15.2247	+	33.3375i	−0.486336	+	1.06493i
$981$		0			0
$982$	−32.1629	+	37.1179i	−1.02636	+	1.18448i
$983$	2.07004	+	2.38895i	0.0660239	+	0.0761957i	0.787801	−	0.615930i	$-0.211220\pi$
$983$	2.07004	+	2.38895i	0.0660239	+	0.0761957i	−0.721777	+	0.692126i	$0.756674\pi$
$984$		0			0
$985$	16.8361	−	19.4298i	0.536441	−	0.619086i
$986$	3.68440	−	25.6256i	0.117335	−	0.816085i
$987$		0			0
$988$	−115.068	−	33.7869i	−3.66079	−	1.07490i
$989$	−3.77262	+	2.42452i	−0.119962	+	0.0770952i
$990$		0			0
$991$	−3.58696	+	1.05323i	−0.113944	+	0.0334569i	−0.338207	−	0.941072i	$-0.609820\pi$
$991$	−3.58696	+	1.05323i	−0.113944	+	0.0334569i	0.224264	+	0.974529i	$0.428002\pi$
$992$	−3.85575	+	8.44292i	−0.122420	+	0.268063i
$993$		0			0
$994$	2.34524	−	1.50719i	0.0743864	−	0.0478052i
$995$	15.7317	+	18.1553i	0.498728	+	0.575563i
$996$		0			0
$997$	8.71422	+	19.0815i	0.275982	+	0.604317i	0.995972	−	0.0896682i	$-0.0285807\pi$
$997$	8.71422	+	19.0815i	0.275982	+	0.604317i	−0.719989	+	0.693985i	$0.755853\pi$
$998$	11.8088	+	82.1322i	0.373802	+	2.59985i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.a.226.1		10
3.2	odd	2		67.2.e.b.25.1	✓	10
67.59	even	11	inner	603.2.u.a.595.1		10
201.59	odd	22		67.2.e.b.59.1	yes	10
201.107	odd	22		4489.2.a.i.1.1		5
201.161	even	22		4489.2.a.h.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.25.1	✓	10	3.2	odd	2
67.2.e.b.59.1	yes	10	201.59	odd	22
603.2.u.a.226.1		10	1.1	even	1	trivial
603.2.u.a.595.1		10	67.59	even	11	inner
4489.2.a.h.1.5		5	201.161	even	22
4489.2.a.i.1.1		5	201.107	odd	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(1.41542 - 0.909632i) q^{5} +(-0.198939 - 1.38365i) q^{7} +(2.41899 + 5.29684i) q^{8} +O(q^{10})\)	\(q+(-0.357685 - 2.48775i) q^{2} +(-4.14200 + 1.21620i) q^{4} +(1.41542 - 0.909632i) q^{5} +(-0.198939 - 1.38365i) q^{7} +(2.41899 + 5.29684i) q^{8} +(-2.76921 - 3.19584i) q^{10} +(3.98926 - 2.56374i) q^{11} +(2.48357 - 5.43826i) q^{13} +(-3.37102 + 0.989821i) q^{14} +(5.04885 - 3.24470i) q^{16} +(-4.13515 - 1.21419i) q^{17} +(-0.661301 + 4.59945i) q^{19} +(-4.75635 + 5.48912i) q^{20} +(-7.80486 - 9.00729i) q^{22} +(0.704273 - 0.812774i) q^{23} +(-0.901106 + 1.97315i) q^{25} +(-14.4174 - 4.23333i) q^{26} +(2.50680 + 5.48912i) q^{28} -2.39011 q^{29} +(-1.12155 - 2.45585i) q^{31} +(-2.25133 - 2.59818i) q^{32} +(-1.54152 + 10.7215i) q^{34} +(-1.54019 - 1.77748i) q^{35} -3.75406 q^{37} +11.6788 q^{38} +(8.24204 + 5.29684i) q^{40} +(0.434813 + 0.127673i) q^{41} +(-4.00098 - 1.17479i) q^{43} +(-13.4055 + 15.4708i) q^{44} +(-2.27389 - 1.46134i) q^{46} +(0.0399670 - 0.0461244i) q^{47} +(4.84154 - 1.42161i) q^{49} +(5.23102 + 1.53597i) q^{50} +(-3.67293 + 25.5458i) q^{52} +(-3.76965 + 1.10687i) q^{53} +(3.31440 - 7.25752i) q^{55} +(6.84774 - 4.40077i) q^{56} +(0.854905 + 5.94600i) q^{58} +(-0.612933 - 1.34214i) q^{59} +(-3.84369 - 2.47019i) q^{61} +(-5.70839 + 3.66856i) q^{62} +(2.20204 - 2.54129i) q^{64} +(-1.43153 - 9.95652i) q^{65} +(8.16797 - 0.533126i) q^{67} +18.6045 q^{68} +(-3.87102 + 4.46740i) q^{70} +(-0.761345 + 0.223551i) q^{71} +(2.64987 + 1.70297i) q^{73} +(1.34277 + 9.33918i) q^{74} +(-2.85475 - 19.8552i) q^{76} +(-4.34094 - 5.00971i) q^{77} +(0.0424701 - 0.0929965i) q^{79} +(4.19474 - 9.18520i) q^{80} +(0.162092 - 1.12738i) q^{82} +(11.6065 - 7.45903i) q^{83} +(-6.95741 + 2.04288i) q^{85} +(-1.49151 + 10.3737i) q^{86} +(23.2297 + 14.9288i) q^{88} +(10.0423 + 11.5895i) q^{89} +(-8.01872 - 2.35451i) q^{91} +(-1.92860 + 4.22305i) q^{92} +(-0.129042 - 0.0829302i) q^{94} +(3.24779 + 7.11167i) q^{95} +16.5271 q^{97} +(-5.26835 - 11.5361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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