LMFDB - Embedded newform 525.2.i.i.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 3x^{5} + 50x^{4} - 27x^{3} + 53x^{2} + 20x + 16 $ x^8 - x^7 + 8x^6 - 3x^5 + 50x^4 - 27x^3 + 53x^2 + 20x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.3
Root			$-0.247087 + 0.427967i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.i.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247087 - 0.427967i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.87790 + 1.86373i) q^{7} +1.85601 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.247087 - 0.427967i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.87790 + 1.86373i) q^{7} +1.85601 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.66927 - 4.62330i) q^{11} +(-0.877896 + 1.52056i) q^{12} +5.09433 q^{13} +(1.26162 - 0.343173i) q^{14} +(-1.29720 + 2.24681i) q^{16} +(-0.175093 - 0.303270i) q^{17} +(0.247087 + 0.427967i) q^{18} +(-1.38372 + 2.39668i) q^{19} +(-0.675093 + 2.55817i) q^{21} -2.63816 q^{22} +(-3.75579 + 6.50522i) q^{23} +(0.928006 + 1.60735i) q^{24} +(1.25874 - 2.18020i) q^{26} -1.00000 q^{27} +(-1.18532 + 4.49162i) q^{28} +4.00000 q^{29} +(-3.05882 - 5.29802i) q^{31} +(2.49705 + 4.32502i) q^{32} +(2.66927 - 4.62330i) q^{33} -0.173053 q^{34} -1.75579 q^{36} +(1.76162 - 3.05121i) q^{37} +(0.683799 + 1.18437i) q^{38} +(2.54716 + 4.41182i) q^{39} -7.86177 q^{41} +(0.928006 + 0.921008i) q^{42} +1.41726 q^{43} +(4.68668 - 8.11757i) q^{44} +(1.85601 + 3.21471i) q^{46} +(4.42506 - 7.66443i) q^{47} -2.59439 q^{48} +(0.0529894 + 6.99980i) q^{49} +(0.175093 - 0.303270i) q^{51} +(4.47229 + 7.74623i) q^{52} +(3.16344 + 5.47924i) q^{53} +(-0.247087 + 0.427967i) q^{54} +(3.48540 + 3.45911i) q^{56} -2.76745 q^{57} +(0.988347 - 1.71187i) q^{58} +(-6.42506 - 11.1285i) q^{59} +(2.50000 - 4.33013i) q^{61} -3.02317 q^{62} +(-2.55299 + 0.694439i) q^{63} -2.72083 q^{64} +(-1.31908 - 2.28471i) q^{66} +(-1.87790 - 3.25261i) q^{67} +(0.307427 - 0.532479i) q^{68} -7.51159 q^{69} +15.4883 q^{71} +(-0.928006 + 1.60735i) q^{72} +(-3.83853 - 6.64853i) q^{73} +(-0.870545 - 1.50783i) q^{74} -4.85906 q^{76} +(3.60401 - 13.6569i) q^{77} +2.51748 q^{78} +(-1.18092 + 2.04541i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.94254 + 3.36458i) q^{82} -6.87342 q^{83} +(-4.48252 + 1.21929i) q^{84} +(0.350186 - 0.606540i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-4.95419 - 8.58091i) q^{88} +(2.17509 - 3.76737i) q^{89} +(9.56662 + 9.49447i) q^{91} -13.1888 q^{92} +(3.05882 - 5.29802i) q^{93} +(-2.18675 - 3.78756i) q^{94} +(-2.49705 + 4.32502i) q^{96} +5.49993 q^{97} +(3.00877 + 1.70688i) q^{98} +5.33853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	$ 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.247087	−	0.427967i	0.174717	−	0.302618i	−0.765347	−	0.643618i	$-0.777432\pi$
$2$	0.247087	−	0.427967i	0.174717	−	0.302618i	0.940063	+	0.341000i	$0.110766\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.877896	+	1.52056i	0.438948	+	0.760281i
$5$		0			0
$5$		0			0
$6$	0.494173			0.201745
$7$	1.87790	+	1.86373i	0.709778	+	0.704425i
$7$	1.87790	+	1.86373i	0.709778	+	0.704425i
$8$	1.85601			0.656200
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.66927	−	4.62330i	−0.804814	−	1.39398i	−0.916416	−	0.400226i	$-0.868932\pi$
$11$	−2.66927	−	4.62330i	−0.804814	−	1.39398i	0.111602	−	0.993753i	$-0.464402\pi$
$12$	−0.877896	+	1.52056i	−0.253427	+	0.438948i
$13$	5.09433			1.41291			0.706456	−	0.707757i	$-0.250293\pi$
$13$	5.09433			1.41291			0.706456	+	0.707757i	$0.250293\pi$
$14$	1.26162	−	0.343173i	0.337182	−	0.0917169i
$15$		0			0
$16$	−1.29720	+	2.24681i	−0.324299	+	0.561703i
$17$	−0.175093	−	0.303270i	−0.0424663	−	0.0735538i	0.844011	−	0.536326i	$-0.180188\pi$
$17$	−0.175093	−	0.303270i	−0.0424663	−	0.0735538i	−0.886477	+	0.462772i	$0.846855\pi$
$18$	0.247087	+	0.427967i	0.0582389	+	0.100873i
$19$	−1.38372	+	2.39668i	−0.317448	+	0.549836i	−0.979955	−	0.199220i	$-0.936159\pi$
$19$	−1.38372	+	2.39668i	−0.317448	+	0.549836i	0.662507	+	0.749056i	$0.269493\pi$
$20$		0			0
$21$	−0.675093	+	2.55817i	−0.147317	+	0.558239i
$22$	−2.63816			−0.562458
$23$	−3.75579	+	6.50522i	−0.783137	+	1.35643i	0.146969	+	0.989141i	$0.453048\pi$
$23$	−3.75579	+	6.50522i	−0.783137	+	1.35643i	−0.930106	+	0.367292i	$0.880285\pi$
$24$	0.928006	+	1.60735i	0.189429	+	0.328100i
$25$		0			0
$26$	1.25874	−	2.18020i	0.246859	−	0.427573i
$27$	−1.00000			−0.192450
$28$	−1.18532	+	4.49162i	−0.224005	+	0.848837i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−3.05882	−	5.29802i	−0.549380	−	0.951553i	−0.998317	−	0.0579902i	$-0.981531\pi$
$31$	−3.05882	−	5.29802i	−0.549380	−	0.951553i	0.448938	−	0.893563i	$-0.351803\pi$
$32$	2.49705	+	4.32502i	0.441421	+	0.764563i
$33$	2.66927	−	4.62330i	0.464660	−	0.804814i
$34$	−0.173053			−0.0296783
$35$		0			0
$36$	−1.75579			−0.292632
$37$	1.76162	−	3.05121i	0.289608	−	0.501617i	−0.684108	−	0.729381i	$-0.739808\pi$
$37$	1.76162	−	3.05121i	0.289608	−	0.501617i	0.973716	+	0.227764i	$0.0731416\pi$
$38$	0.683799	+	1.18437i	0.110927	+	0.192131i
$39$	2.54716	+	4.41182i	0.407872	+	0.706456i
$40$		0			0
$41$	−7.86177			−1.22780			−0.613901	−	0.789383i	$-0.710401\pi$
$41$	−7.86177			−1.22780			−0.613901	+	0.789383i	$0.710401\pi$
$42$	0.928006	+	0.921008i	0.143194	+	0.142115i
$43$	1.41726			0.216130			0.108065	−	0.994144i	$-0.465535\pi$
$43$	1.41726			0.216130			0.108065	+	0.994144i	$0.465535\pi$
$44$	4.68668	−	8.11757i	0.706543	−	1.22377i
$45$		0			0
$46$	1.85601	+	3.21471i	0.273654	+	0.473983i
$47$	4.42506	−	7.66443i	0.645461	−	1.11797i	−0.338734	−	0.940882i	$-0.609999\pi$
$47$	4.42506	−	7.66443i	0.645461	−	1.11797i	0.984195	−	0.177089i	$-0.0566681\pi$
$48$	−2.59439			−0.374468
$49$	0.0529894	+	6.99980i	0.00756991	+	0.999971i
$50$		0			0
$51$	0.175093	−	0.303270i	0.0245179	−	0.0424663i
$52$	4.47229	+	7.74623i	0.620195	+	1.07421i
$53$	3.16344	+	5.47924i	0.434532	+	0.752631i	0.997257	−	0.0740126i	$-0.0235805\pi$
$53$	3.16344	+	5.47924i	0.434532	+	0.752631i	−0.562725	+	0.826644i	$0.690247\pi$
$54$	−0.247087	+	0.427967i	−0.0336242	+	0.0582389i
$55$		0			0
$56$	3.48540	+	3.45911i	0.465756	+	0.462244i
$57$	−2.76745			−0.366557
$58$	0.988347	−	1.71187i	0.129776	−	0.224779i
$59$	−6.42506	−	11.1285i	−0.836471	−	1.44881i	−0.892827	−	0.450400i	$-0.851281\pi$
$59$	−6.42506	−	11.1285i	−0.836471	−	1.44881i	0.0563553	−	0.998411i	$-0.482052\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	−3.02317			−0.383943
$63$	−2.55299	+	0.694439i	−0.321646	+	0.0874911i
$64$	−2.72083			−0.340104
$65$		0			0
$66$	−1.31908	−	2.28471i	−0.162368	−	0.281229i
$67$	−1.87790	−	3.25261i	−0.229422	−	0.397370i	0.728215	−	0.685348i	$-0.240350\pi$
$67$	−1.87790	−	3.25261i	−0.229422	−	0.397370i	−0.957637	+	0.287979i	$0.907017\pi$
$68$	0.307427	−	0.532479i	0.0372810	−	0.0645726i
$69$	−7.51159			−0.904289
$70$		0			0
$71$	15.4883			1.83812			0.919060	−	0.394117i	$-0.128950\pi$
$71$	15.4883			1.83812			0.919060	+	0.394117i	$0.128950\pi$
$72$	−0.928006	+	1.60735i	−0.109367	+	0.189429i
$73$	−3.83853	−	6.64853i	−0.449266	−	0.778152i	0.549072	−	0.835775i	$-0.314981\pi$
$73$	−3.83853	−	6.64853i	−0.449266	−	0.778152i	−0.998338	+	0.0576229i	$0.981648\pi$
$74$	−0.870545	−	1.50783i	−0.101199	−	0.175282i
$75$		0			0
$76$	−4.85906			−0.557373
$77$	3.60401	−	13.6569i	0.410715	−	1.55635i
$78$	2.51748			0.285048
$79$	−1.18092	+	2.04541i	−0.132864	+	0.230127i	−0.924779	−	0.380504i	$-0.875751\pi$
$79$	−1.18092	+	2.04541i	−0.132864	+	0.230127i	0.791916	+	0.610631i	$0.209084\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.94254	+	3.36458i	−0.214518	+	0.371555i
$83$	−6.87342			−0.754456			−0.377228	−	0.926120i	$-0.623123\pi$
$83$	−6.87342			−0.754456			−0.377228	+	0.926120i	$0.623123\pi$
$84$	−4.48252	+	1.21929i	−0.489083	+	0.133036i
$85$		0			0
$86$	0.350186	−	0.606540i	0.0377615	−	0.0654049i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	−4.95419	−	8.58091i	−0.528119	−	0.914728i
$89$	2.17509	−	3.76737i	0.230559	−	0.399341i	−0.727413	−	0.686199i	$-0.759278\pi$
$89$	2.17509	−	3.76737i	0.230559	−	0.399341i	0.957973	+	0.286859i	$0.0926111\pi$
$90$		0			0
$91$	9.56662	+	9.49447i	1.00285	+	0.995291i
$92$	−13.1888			−1.37503
$93$	3.05882	−	5.29802i	0.317184	−	0.549380i
$94$	−2.18675	−	3.78756i	−0.225546	−	0.390657i
$95$		0			0
$96$	−2.49705	+	4.32502i	−0.254854	+	0.441421i
$97$	5.49993			0.558433			0.279217	−	0.960228i	$-0.409925\pi$
$97$	5.49993			0.558433			0.279217	+	0.960228i	$0.409925\pi$
$98$	3.00877	+	1.70688i	0.303932	+	0.172421i
$99$	5.33853			0.536543
$100$		0			0
$101$	−0.824907	−	1.42878i	−0.0820813	−	0.142169i	0.822062	−	0.569397i	$-0.192823\pi$
$101$	−0.824907	−	1.42878i	−0.0820813	−	0.142169i	−0.904144	+	0.427228i	$0.859490\pi$
$102$	−0.0865263	−	0.149868i	−0.00856738	−	0.0148391i
$103$	5.08070	−	8.80003i	0.500616	−	0.867093i	−0.499384	−	0.866381i	$-0.666440\pi$
$103$	5.08070	−	8.80003i	0.500616	−	0.867093i	1.00000		0.000711688i	$-0.000226537\pi$
$104$	9.45513			0.927152
$105$		0			0
$106$	3.12658			0.303680
$107$	2.68092	−	4.64349i	0.259174	−	0.448903i	−0.706847	−	0.707367i	$-0.749883\pi$
$107$	2.68092	−	4.64349i	0.259174	−	0.448903i	0.966021	+	0.258464i	$0.0832163\pi$
$108$	−0.877896	−	1.52056i	−0.0844756	−	0.146316i
$109$	0.0529894	+	0.0917803i	0.00507546	+	0.00879096i	0.868552	−	0.495598i	$-0.165051\pi$
$109$	0.0529894	+	0.0917803i	0.00507546	+	0.00879096i	−0.863477	+	0.504389i	$0.831718\pi$
$110$		0			0
$111$	3.52324			0.334411
$112$	−6.62346	+	1.80165i	−0.625858	+	0.170240i
$113$	−4.67707			−0.439981			−0.219991	−	0.975502i	$-0.570603\pi$
$113$	−4.67707			−0.439981			−0.219991	+	0.975502i	$0.570603\pi$
$114$	−0.683799	+	1.18437i	−0.0640436	+	0.110927i
$115$		0			0
$116$	3.51159	+	6.08224i	0.326043	+	0.564722i
$117$	−2.54716	+	4.41182i	−0.235485	+	0.407872i
$118$	−6.35019			−0.584582
$119$	0.236408	−	0.895837i	0.0216715	−	0.0821212i
$120$		0			0
$121$	−8.74997	+	15.1554i	−0.795451	+	1.37776i
$122$	−1.23543	−	2.13983i	−0.111851	−	0.193731i
$123$	−3.93089	−	6.80849i	−0.354436	−	0.613901i
$124$	5.37065	−	9.30223i	0.482298	−	0.835365i
$125$		0			0
$126$	−0.333613	+	1.26418i	−0.0297206	+	0.112622i
$127$	−17.5388			−1.55632			−0.778160	−	0.628066i	$-0.783847\pi$
$127$	−17.5388			−1.55632			−0.778160	+	0.628066i	$0.783847\pi$
$128$	−5.66639	+	9.81447i	−0.500843	+	0.867485i
$129$	0.708630	+	1.22738i	0.0623914	+	0.108065i
$130$		0			0
$131$	4.51159	−	7.81430i	0.394179	−	0.682738i	−0.598817	−	0.800886i	$-0.704362\pi$
$131$	4.51159	−	7.81430i	0.394179	−	0.682738i	0.992996	+	0.118148i	$0.0376956\pi$
$132$	9.37336			0.815846
$133$	−7.06526	+	1.92182i	−0.612636	+	0.166643i
$134$	−1.85601			−0.160335
$135$		0			0
$136$	−0.324975	−	0.562873i	−0.0278664	−	0.0482660i
$137$	0.417260	+	0.722715i	0.0356489	+	0.0617457i	0.883299	−	0.468809i	$-0.155317\pi$
$137$	0.417260	+	0.722715i	0.0356489	+	0.0617457i	−0.847650	+	0.530555i	$0.821984\pi$
$138$	−1.85601	+	3.21471i	−0.157994	+	0.273654i
$139$	−14.3152			−1.21420			−0.607101	−	0.794625i	$-0.707668\pi$
$139$	−14.3152			−1.21420			−0.607101	+	0.794625i	$0.707668\pi$
$140$		0			0
$141$	8.85012			0.745314
$142$	3.82695	−	6.62847i	0.321150	−	0.556249i
$143$	−13.5981	−	23.5526i	−1.13713	−	1.96957i
$144$	−1.29720	−	2.24681i	−0.108100	−	0.187234i
$145$		0			0
$146$	−3.79380			−0.313977
$147$	−6.03551	+	3.54579i	−0.497800	+	0.292452i
$148$	6.18608			0.508492
$149$	−9.69833	+	16.7980i	−0.794518	+	1.37615i	0.128626	+	0.991693i	$0.458943\pi$
$149$	−9.69833	+	16.7980i	−0.794518	+	1.37615i	−0.923145	+	0.384453i	$0.874390\pi$
$150$		0			0
$151$	−9.26359	−	16.0450i	−0.753860	−	1.30572i	−0.945939	−	0.324345i	$-0.894856\pi$
$151$	−9.26359	−	16.0450i	−0.753860	−	1.30572i	0.192078	−	0.981380i	$-0.438477\pi$
$152$	−2.56821	+	4.44827i	−0.208309	+	0.360802i
$153$	0.350186			0.0283109
$154$	−4.95419	−	4.91683i	−0.399220	−	0.396209i
$155$		0			0
$156$	−4.47229	+	7.74623i	−0.358070	+	0.620195i
$157$	2.39978	+	4.15654i	0.191523	+	0.331728i	0.945755	−	0.324880i	$-0.105324\pi$
$157$	2.39978	+	4.15654i	0.191523	+	0.331728i	−0.754232	+	0.656608i	$0.771991\pi$
$158$	0.583579	+	1.01079i	0.0464271	+	0.0804140i
$159$	−3.16344	+	5.47924i	−0.250877	+	0.434532i
$160$		0			0
$161$	−19.1770	+	5.21634i	−1.51136	+	0.411105i
$162$	−0.494173			−0.0388259
$163$	−0.413474	+	0.716157i	−0.0323858	+	0.0560938i	−0.881764	−	0.471691i	$-0.843644\pi$
$163$	−0.413474	+	0.716157i	−0.0323858	+	0.0560938i	0.849378	+	0.527785i	$0.176977\pi$
$164$	−6.90182	−	11.9543i	−0.538942	−	0.933474i
$165$		0			0
$166$	−1.69833	+	2.94160i	−0.131816	+	0.228312i
$167$	4.61485			0.357108			0.178554	−	0.983930i	$-0.442858\pi$
$167$	4.61485			0.357108			0.178554	+	0.983930i	$0.442858\pi$
$168$	−1.25298	+	4.74800i	−0.0966696	+	0.366316i
$169$	12.9522			0.996319
$170$		0			0
$171$	−1.38372	−	2.39668i	−0.105816	−	0.183279i
$172$	1.24421	+	2.15503i	0.0948699	+	0.164320i
$173$	6.33853	−	10.9787i	0.481910	−	0.834692i	−0.517875	−	0.855456i	$-0.673277\pi$
$173$	6.33853	−	10.9787i	0.481910	−	0.834692i	0.999784	+	0.0207644i	$0.00660998\pi$
$174$	1.97669			0.149853
$175$		0			0
$176$	13.8503			1.04400
$177$	6.42506	−	11.1285i	0.482937	−	0.836471i
$178$	−1.07487	−	1.86173i	−0.0805651	−	0.139543i
$179$	−6.52324	−	11.2986i	−0.487570	−	0.844496i	0.512328	−	0.858790i	$-0.328783\pi$
$179$	−6.52324	−	11.2986i	−0.487570	−	0.844496i	−0.999898	+	0.0142942i	$0.995450\pi$
$180$		0			0
$181$	15.0594			1.11935			0.559677	−	0.828711i	$-0.310925\pi$
$181$	15.0594			1.11935			0.559677	+	0.828711i	$0.310925\pi$
$182$	6.42710	−	1.74824i	0.476408	−	0.129588i
$183$	5.00000			0.369611
$184$	−6.97080	+	12.0738i	−0.513894	+	0.890091i
$185$		0			0
$186$	−1.51159	−	2.61814i	−0.110835	−	0.191972i
$187$	−0.934740	+	1.61902i	−0.0683549	+	0.118394i
$188$	15.5390			1.13330
$189$	−1.87790	−	1.86373i	−0.136597	−	0.135567i
$190$		0			0
$191$	−4.76359	+	8.25078i	−0.344681	+	0.597006i	−0.985296	−	0.170857i	$-0.945346\pi$
$191$	−4.76359	+	8.25078i	−0.344681	+	0.597006i	0.640614	+	0.767863i	$0.278680\pi$
$192$	−1.36042	−	2.35631i	−0.0981796	−	0.170052i
$193$	7.55299	+	13.0822i	0.543676	+	0.941675i	0.998689	+	0.0511897i	$0.0163013\pi$
$193$	7.55299	+	13.0822i	0.543676	+	0.941675i	−0.455013	+	0.890485i	$0.650365\pi$
$194$	1.35896	−	2.35379i	0.0975676	−	0.168992i
$195$		0			0
$196$	−10.5971	+	6.22567i	−0.756936	+	0.444691i
$197$	16.8890			1.20329			0.601647	−	0.798762i	$-0.294512\pi$
$197$	16.8890			1.20329			0.601647	+	0.798762i	$0.294512\pi$
$198$	1.31908	−	2.28471i	0.0937430	−	0.162368i
$199$	12.6138	+	21.8477i	0.894167	+	1.54874i	0.834832	+	0.550505i	$0.185565\pi$
$199$	12.6138	+	21.8477i	0.894167	+	1.54874i	0.0593348	+	0.998238i	$0.481102\pi$
$200$		0			0
$201$	1.87790	−	3.25261i	0.132457	−	0.229422i
$202$	−0.815294			−0.0573639
$203$	7.51159	+	7.45494i	0.527210	+	0.523234i
$204$	0.614854			0.0430484
$205$		0			0
$206$	−2.51075	−	4.34874i	−0.174932	−	0.302991i
$207$	−3.75579	−	6.50522i	−0.261046	−	0.452144i
$208$	−6.60834	+	11.4460i	−0.458206	+	0.793636i
$209$	14.7741			1.02195
$210$		0			0
$211$	20.3967			1.40416			0.702082	−	0.712096i	$-0.252254\pi$
$211$	20.3967			1.40416			0.702082	+	0.712096i	$0.252254\pi$
$212$	−5.55434	+	9.62041i	−0.381474	+	0.660732i
$213$	7.74414	+	13.4132i	0.530620	+	0.919060i
$214$	−1.32484	−	2.29469i	−0.0905641	−	0.156862i
$215$		0			0
$216$	−1.85601			−0.126286
$217$	4.12997	−	15.6500i	0.280361	−	1.06239i
$218$	0.0523719			0.00354707
$219$	3.83853	−	6.64853i	0.259384	−	0.449266i
$220$		0			0
$221$	−0.891981	−	1.54496i	−0.0600011	−	0.103925i
$222$	0.870545	−	1.50783i	0.0584272	−	0.101199i
$223$	−22.5738			−1.51165			−0.755827	−	0.654772i	$-0.772765\pi$
$223$	−22.5738			−1.51165			−0.755827	+	0.654772i	$0.772765\pi$
$224$	−3.37149	+	12.7758i	−0.225267	+	0.853618i
$225$		0			0
$226$	−1.15564	+	2.00163i	−0.0768721	+	0.133146i
$227$	7.08267	+	12.2675i	0.470093	+	0.814226i	0.999415	−	0.0341954i	$-0.0108869\pi$
$227$	7.08267	+	12.2675i	0.470093	+	0.814226i	−0.529322	+	0.848421i	$0.677554\pi$
$228$	−2.42953	−	4.20807i	−0.160900	−	0.278686i
$229$	8.90311	−	15.4206i	0.588334	−	1.01902i	−0.406117	−	0.913821i	$-0.633117\pi$
$229$	8.90311	−	15.4206i	0.588334	−	1.01902i	0.994451	−	0.105203i	$-0.0335493\pi$
$230$		0			0
$231$	13.6292	−	3.70728i	0.896737	−	0.243921i
$232$	7.42405			0.487413
$233$	−6.82491	+	11.8211i	−0.447115	+	0.774425i	−0.998197	−	0.0600258i	$-0.980882\pi$
$233$	−6.82491	+	11.8211i	−0.447115	+	0.774425i	0.551082	+	0.834451i	$0.314215\pi$
$234$	1.25874	+	2.18020i	0.0822864	+	0.142524i
$235$		0			0
$236$	11.2811	−	19.5394i	0.734335	−	1.27191i
$237$	−2.36184			−0.153418
$238$	−0.324975	−	0.322524i	−0.0210650	−	0.0209061i
$239$	−7.53489			−0.487392			−0.243696	−	0.969852i	$-0.578360\pi$
$239$	−7.53489			−0.487392			−0.243696	+	0.969852i	$0.578360\pi$
$240$		0			0
$241$	−14.2616	−	24.7017i	−0.918667	−	1.59118i	−0.801442	−	0.598073i	$-0.795933\pi$
$241$	−14.2616	−	24.7017i	−0.918667	−	1.59118i	−0.117226	−	0.993105i	$-0.537400\pi$
$242$	4.32400	+	7.48939i	0.277957	+	0.481436i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	8.77896			0.562016
$245$		0			0
$246$	−3.88508			−0.247704
$247$	−7.04914	+	12.2095i	−0.448526	+	0.776869i
$248$	−5.67720	−	9.83320i	−0.360503	−	0.624409i
$249$	−3.43671	−	5.95256i	−0.217793	−	0.377228i
$250$		0			0
$251$	−22.8501			−1.44229			−0.721143	−	0.692786i	$-0.756383\pi$
$251$	−22.8501			−1.44229			−0.721143	+	0.692786i	$0.756383\pi$
$252$	−3.29720	−	3.27233i	−0.207704	−	0.206137i
$253$	40.1008			2.52112
$254$	−4.33361	+	7.50604i	−0.271915	+	0.470971i
$255$		0			0
$256$	0.0793447	+	0.137429i	0.00495904	+	0.00858931i
$257$	−12.5690	+	21.7702i	−0.784036	+	1.35799i	0.145538	+	0.989353i	$0.453509\pi$
$257$	−12.5690	+	21.7702i	−0.784036	+	1.35799i	−0.929574	+	0.368637i	$0.879825\pi$
$258$	0.700372			0.0436033
$259$	8.99479	−	2.44667i	0.558909	−	0.152029i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	−2.22951	−	3.86162i	−0.137739	−	0.238571i
$263$	6.77910	+	11.7417i	0.418017	+	0.724027i	0.995740	−	0.0922061i	$-0.0293919\pi$
$263$	6.77910	+	11.7417i	0.418017	+	0.724027i	−0.577723	+	0.816233i	$0.696059\pi$
$264$	4.95419	−	8.58091i	0.304909	−	0.528119i
$265$		0			0
$266$	−0.923256	+	3.49855i	−0.0566085	+	0.214510i
$267$	4.35019			0.266227
$268$	3.29720	−	5.71091i	0.201408	−	0.348849i
$269$	4.51363	+	7.81783i	0.275201	+	0.476661i	0.970186	−	0.242363i	$-0.0779224\pi$
$269$	4.51363	+	7.81783i	0.275201	+	0.476661i	−0.694985	+	0.719024i	$0.744589\pi$
$270$		0			0
$271$	−2.38819	+	4.13647i	−0.145072	+	0.251273i	−0.929400	−	0.369074i	$-0.879675\pi$
$271$	−2.38819	+	4.13647i	−0.145072	+	0.251273i	0.784328	+	0.620347i	$0.213008\pi$
$272$	0.908520			0.0550871
$273$	−3.43914	+	13.0322i	−0.208146	+	0.788743i
$274$	0.412397			0.0249138
$275$		0			0
$276$	−6.59439	−	11.4218i	−0.396936	−	0.687513i
$277$	−0.935357	−	1.62009i	−0.0562002	−	0.0973416i	0.836557	−	0.547881i	$-0.184565\pi$
$277$	−0.935357	−	1.62009i	−0.0562002	−	0.0973416i	−0.892757	+	0.450539i	$0.851232\pi$
$278$	−3.53710	+	6.12644i	−0.212141	+	0.367439i
$279$	6.11763			0.366253
$280$		0			0
$281$	0.972748			0.0580293			0.0290147	−	0.999579i	$-0.490763\pi$
$281$	0.972748			0.0580293			0.0290147	+	0.999579i	$0.490763\pi$
$282$	2.18675	−	3.78756i	0.130219	−	0.225546i
$283$	12.0899	+	20.9402i	0.718667	+	1.24477i	0.961528	+	0.274707i	$0.0885808\pi$
$283$	12.0899	+	20.9402i	0.718667	+	1.24477i	−0.242861	+	0.970061i	$0.578086\pi$
$284$	13.5971	+	23.5509i	0.806840	+	1.39749i
$285$		0			0
$286$	−13.4396			−0.794703
$287$	−14.7636	−	14.6523i	−0.871467	−	0.864895i
$288$	−4.99411			−0.294280
$289$	8.43868	−	14.6162i	0.496393	−	0.859778i
$290$		0			0
$291$	2.74997	+	4.76308i	0.161206	+	0.279217i
$292$	6.73967	−	11.6734i	0.394409	−	0.683137i
$293$	15.5349			0.907558			0.453779	−	0.891114i	$-0.350076\pi$
$293$	15.5349			0.907558			0.453779	+	0.891114i	$0.350076\pi$
$294$	0.0261859	+	3.45911i	0.00152719	+	0.201740i
$295$		0			0
$296$	3.26959	−	5.66309i	0.190041	−	0.329161i
$297$	2.66927	+	4.62330i	0.154887	+	0.268271i
$298$	4.79266	+	8.30113i	0.277631	+	0.480871i
$299$	−19.1332	+	33.1397i	−1.10650	+	1.91652i
$300$		0			0
$301$	2.66147	+	2.64140i	0.153404	+	0.152248i
$302$	−9.15564			−0.526848
$303$	0.824907	−	1.42878i	0.0473897	−	0.0820813i
$304$	−3.58992	−	6.21793i	−0.205896	−	0.356623i
$305$		0			0
$306$	0.0865263	−	0.149868i	0.00494638	−	0.00856738i
$307$	−3.39395			−0.193703			−0.0968516	−	0.995299i	$-0.530877\pi$
$307$	−3.39395			−0.193703			−0.0968516	+	0.995299i	$0.530877\pi$
$308$	23.9301	−	6.50922i	1.36354	−	0.370897i
$309$	10.1614			0.578062
$310$		0			0
$311$	1.23255	+	2.13485i	0.0698917	+	0.121056i	0.898853	−	0.438249i	$-0.144401\pi$
$311$	1.23255	+	2.13485i	0.0698917	+	0.121056i	−0.828962	+	0.559305i	$0.811068\pi$
$312$	4.72757	+	8.18839i	0.267646	+	0.463576i
$313$	0.237763	−	0.411818i	0.0134392	−	0.0232773i	−0.859228	−	0.511594i	$-0.829055\pi$
$313$	0.237763	−	0.411818i	0.0134392	−	0.0232773i	0.872667	+	0.488316i	$0.162389\pi$
$314$	2.37181			0.133849
$315$		0			0
$316$	−4.14690			−0.233281
$317$	−7.14975	+	12.3837i	−0.401570	+	0.695539i	−0.993916	−	0.110145i	$-0.964869\pi$
$317$	−7.14975	+	12.3837i	−0.401570	+	0.695539i	0.592346	+	0.805684i	$0.298202\pi$
$318$	1.56329	+	2.70769i	0.0876648	+	0.151840i
$319$	−10.6771	−	18.4932i	−0.597801	−	1.03542i
$320$		0			0
$321$	5.36184			0.299269
$322$	−2.50596	+	9.49600i	−0.139652	+	0.529192i
$323$	0.969121			0.0539233
$324$	0.877896	−	1.52056i	0.0487720	−	0.0844756i
$325$		0			0
$326$	0.204328	+	0.353906i	0.0113167	+	0.0196010i
$327$	−0.0529894	+	0.0917803i	−0.00293032	+	0.00507546i
$328$	−14.5915			−0.805683
$329$	22.5943	−	6.14587i	1.24566	−	0.338833i
$330$		0			0
$331$	9.79273	−	16.9615i	0.538257	−	0.932288i	−0.460741	−	0.887535i	$-0.652416\pi$
$331$	9.79273	−	16.9615i	0.538257	−	0.932288i	0.998998	−	0.0447537i	$-0.0142503\pi$
$332$	−6.03415	−	10.4515i	−0.331167	−	0.573598i
$333$	1.76162	+	3.05121i	0.0965361	+	0.167206i
$334$	1.14027	−	1.97500i	0.0623927	−	0.108067i
$335$		0			0
$336$	−4.87200	−	4.83526i	−0.265789	−	0.263785i
$337$	4.38230			0.238719			0.119360	−	0.992851i	$-0.461916\pi$
$337$	4.38230			0.238719			0.119360	+	0.992851i	$0.461916\pi$
$338$	3.20030	−	5.54309i	0.174074	−	0.301504i
$339$	−2.33853	−	4.05046i	−0.127012	−	0.219991i
$340$		0			0
$341$	−16.3296	+	28.2837i	−0.884297	+	1.53165i
$342$	−1.36760			−0.0739512
$343$	−12.9463	+	13.2437i	−0.699032	+	0.715090i
$344$	2.63045			0.141824
$345$		0			0
$346$	−3.13233	−	5.42536i	−0.168395	−	0.291669i
$347$	4.79855	+	8.31134i	0.257600	+	0.446176i	0.965598	−	0.260038i	$-0.0837351\pi$
$347$	4.79855	+	8.31134i	0.257600	+	0.446176i	−0.707999	+	0.706214i	$0.750402\pi$
$348$	−3.51159	+	6.08224i	−0.188241	+	0.326043i
$349$	−19.9007			−1.06526			−0.532629	−	0.846349i	$-0.678796\pi$
$349$	−19.9007			−1.06526			−0.532629	+	0.846349i	$0.678796\pi$
$350$		0			0
$351$	−5.09433			−0.271915
$352$	13.3306	−	23.0893i	0.710523	−	1.23066i
$353$	−13.6983	−	23.7262i	−0.729089	−	1.26282i	−0.957269	−	0.289200i	$-0.906611\pi$
$353$	−13.6983	−	23.7262i	−0.729089	−	1.26282i	0.228180	−	0.973619i	$-0.426722\pi$
$354$	−3.17509	−	5.49942i	−0.168754	−	0.292291i
$355$		0			0
$356$	7.63802			0.404815
$357$	0.894021	−	0.243183i	0.0473166	−	0.0128706i
$358$	−6.44722			−0.340746
$359$	−12.7752	+	22.1274i	−0.674252	+	1.16784i	0.302435	+	0.953170i	$0.402200\pi$
$359$	−12.7752	+	22.1274i	−0.674252	+	1.16784i	−0.976687	+	0.214668i	$0.931133\pi$
$360$		0			0
$361$	5.67062	+	9.82180i	0.298454	+	0.516937i
$362$	3.72097	−	6.44491i	0.195570	−	0.338737i
$363$	−17.4999			−0.918508
$364$	−6.03842	+	22.8818i	−0.316499	+	1.19933i
$365$		0			0
$366$	1.23543	−	2.13983i	0.0645771	−	0.111851i
$367$	11.1357	+	19.2876i	0.581280	+	1.00681i	0.995328	+	0.0965519i	$0.0307814\pi$
$367$	11.1357	+	19.2876i	0.581280	+	1.00681i	−0.414048	+	0.910255i	$0.635885\pi$
$368$	−9.74400	−	16.8771i	−0.507941	−	0.879780i
$369$	3.93089	−	6.80849i	0.204634	−	0.354436i
$370$		0			0
$371$	−4.27123	+	16.1853i	−0.221751	+	0.840296i
$372$	10.7413			0.556910
$373$	2.64738	−	4.58540i	0.137076	−	0.237423i	−0.789312	−	0.613992i	$-0.789563\pi$
$373$	2.64738	−	4.58540i	0.137076	−	0.237423i	0.926389	+	0.376569i	$0.122896\pi$
$374$	0.461924	+	0.800075i	0.0238855	+	0.0413709i
$375$		0			0
$376$	8.21297	−	14.2253i	0.423551	−	0.733612i
$377$	20.3773			1.04948
$378$	−1.26162	+	0.343173i	−0.0648907	+	0.0176509i
$379$	3.10203			0.159341			0.0796704	−	0.996821i	$-0.474613\pi$
$379$	3.10203			0.159341			0.0796704	+	0.996821i	$0.474613\pi$
$380$		0			0
$381$	−8.76942	−	15.1891i	−0.449271	−	0.778160i
$382$	2.35404	+	4.07732i	0.120443	+	0.208614i
$383$	−10.8064	+	18.7171i	−0.552179	+	0.956402i	0.445938	+	0.895064i	$0.352870\pi$
$383$	−10.8064	+	18.7171i	−0.552179	+	0.956402i	−0.998117	+	0.0613379i	$0.980463\pi$
$384$	−11.3328			−0.578323
$385$		0			0
$386$	7.46497			0.379957
$387$	−0.708630	+	1.22738i	−0.0360217	+	0.0623914i
$388$	4.82837	+	8.36298i	0.245123	+	0.424566i
$389$	6.43082	+	11.1385i	0.326055	+	0.564745i	0.981725	−	0.190303i	$-0.0609471\pi$
$389$	6.43082	+	11.1385i	0.326055	+	0.564745i	−0.655670	+	0.755048i	$0.727614\pi$
$390$		0			0
$391$	2.63045			0.133028
$392$	0.0983489	+	12.9917i	0.00496737	+	0.656181i
$393$	9.02317			0.455159
$394$	4.17305	−	7.22794i	0.210235	−	0.364138i
$395$		0			0
$396$	4.68668	+	8.11757i	0.235514	+	0.407923i
$397$	−3.49757	+	6.05797i	−0.175538	+	0.304041i	−0.940347	−	0.340216i	$-0.889500\pi$
$397$	−3.49757	+	6.05797i	−0.175538	+	0.304041i	0.764809	+	0.644257i	$0.222833\pi$
$398$	12.4668			0.624904
$399$	−5.19698	−	5.15778i	−0.260174	−	0.258212i
$400$		0			0
$401$	1.58070	−	2.73785i	0.0789364	−	0.136722i	−0.823855	−	0.566801i	$-0.808181\pi$
$401$	1.58070	−	2.73785i	0.0789364	−	0.136722i	0.902791	+	0.430079i	$0.141514\pi$
$402$	−0.928006	−	1.60735i	−0.0462847	−	0.0801675i
$403$	−15.5826	−	26.9899i	−0.776225	−	1.34446i
$404$	1.44837	−	2.50864i	0.0720589	−	0.124810i
$405$		0			0
$406$	5.04648	−	1.37269i	0.250452	−	0.0681256i
$407$	−18.8089			−0.932324
$408$	0.324975	−	0.562873i	0.0160887	−	0.0278664i
$409$	−1.24753	−	2.16079i	−0.0616866	−	0.106844i	0.833533	−	0.552470i	$-0.186315\pi$
$409$	−1.24753	−	2.16079i	−0.0616866	−	0.106844i	−0.895219	+	0.445626i	$0.852981\pi$
$410$		0			0
$411$	−0.417260	+	0.722715i	−0.0205819	+	0.0356489i
$412$	17.8413			0.878978
$413$	8.67503	−	32.8728i	0.426870	−	1.61757i
$414$	−3.71203			−0.182436
$415$		0			0
$416$	12.7208	+	22.0331i	0.623688	+	1.08026i
$417$	−7.15761	−	12.3973i	−0.350510	−	0.607101i
$418$	3.65048	−	6.32282i	0.178551	−	0.309259i
$419$	−32.6748			−1.59627			−0.798134	−	0.602480i	$-0.794179\pi$
$419$	−32.6748			−1.59627			−0.798134	+	0.602480i	$0.794179\pi$
$420$		0			0
$421$	−26.8774			−1.30992			−0.654961	−	0.755662i	$-0.727315\pi$
$421$	−26.8774			−1.30992			−0.654961	+	0.755662i	$0.727315\pi$
$422$	5.03974	−	8.72909i	0.245331	−	0.424926i
$423$	4.42506	+	7.66443i	0.215154	+	0.372657i
$424$	5.87138	+	10.1695i	0.285140	+	0.493876i
$425$		0			0
$426$	7.65389			0.370832
$427$	12.7649	−	3.47219i	0.617739	−	0.168031i
$428$	9.41428			0.455056
$429$	13.5981	−	23.5526i	0.656523	−	1.13713i
$430$		0			0
$431$	−7.09433	−	12.2877i	−0.341722	−	0.591879i	0.643031	−	0.765840i	$-0.277677\pi$
$431$	−7.09433	−	12.2877i	−0.341722	−	0.591879i	−0.984753	+	0.173961i	$0.944343\pi$
$432$	1.29720	−	2.24681i	0.0624114	−	0.108100i
$433$	29.9717			1.44035			0.720174	−	0.693794i	$-0.244062\pi$
$433$	29.9717			1.44035			0.720174	+	0.693794i	$0.244062\pi$
$434$	−5.67720	−	5.63439i	−0.272514	−	0.270459i
$435$		0			0
$436$	−0.0930383	+	0.161147i	−0.00445573	+	0.00771755i
$437$	−10.3940	−	18.0029i	−0.497210	−	0.861193i
$438$	−1.89690	−	3.28553i	−0.0906374	−	0.156989i
$439$	1.03693	−	1.79602i	0.0494901	−	0.0857193i	−0.840219	−	0.542247i	$-0.817574\pi$
$439$	1.03693	−	1.79602i	0.0494901	−	0.0857193i	0.889709	+	0.456528i	$0.150907\pi$
$440$		0			0
$441$	−6.08850	−	3.45401i	−0.289929	−	0.164477i
$442$	−0.881586			−0.0419328
$443$	−16.0388	+	27.7800i	−0.762025	+	1.31987i	0.179780	+	0.983707i	$0.442461\pi$
$443$	−16.0388	+	27.7800i	−0.762025	+	1.31987i	−0.941805	+	0.336159i	$0.890872\pi$
$444$	3.09304	+	5.35730i	0.146789	+	0.254246i
$445$		0			0
$446$	−5.57768	+	9.66083i	−0.264111	+	0.457454i
$447$	−19.3967			−0.917431
$448$	−5.10944	−	5.07091i	−0.241398	−	0.239578i
$449$	−4.46103			−0.210529			−0.105264	−	0.994444i	$-0.533569\pi$
$449$	−4.46103			−0.210529			−0.105264	+	0.994444i	$0.533569\pi$
$450$		0			0
$451$	20.9852	+	36.3474i	0.988153	+	1.71153i
$452$	−4.10598	−	7.11176i	−0.193129	−	0.334509i
$453$	9.26359	−	16.0450i	0.435242	−	0.753860i
$454$	7.00014			0.328533
$455$		0			0
$456$	−5.13641			−0.240535
$457$	1.13511	−	1.96607i	0.0530983	−	0.0919689i	−0.838255	−	0.545279i	$-0.816424\pi$
$457$	1.13511	−	1.96607i	0.0530983	−	0.0919689i	0.891353	+	0.453310i	$0.149757\pi$
$458$	−4.39968	−	7.62047i	−0.205583	−	0.356081i
$459$	0.175093	+	0.303270i	0.00817264	+	0.0141554i
$460$		0			0
$461$	4.33096			0.201713			0.100856	−	0.994901i	$-0.467842\pi$
$461$	4.33096			0.201713			0.100856	+	0.994901i	$0.467842\pi$
$462$	1.78100	−	6.74887i	0.0828598	−	0.313986i
$463$	−41.7856			−1.94194			−0.970971	−	0.239196i	$-0.923116\pi$
$463$	−41.7856			−1.94194			−0.970971	+	0.239196i	$0.923116\pi$
$464$	−5.18879	+	8.98724i	−0.240883	+	0.417222i
$465$		0			0
$466$	3.37269	+	5.84167i	0.156237	+	0.270610i
$467$	−19.1887	+	33.2357i	−0.887945	+	1.53797i	−0.0456441	+	0.998958i	$0.514534\pi$
$467$	−19.1887	+	33.2357i	−0.887945	+	1.53797i	−0.842301	+	0.539008i	$0.818799\pi$
$468$	−8.94458			−0.413463
$469$	2.53551	−	9.60797i	0.117079	−	0.443655i
$470$		0			0
$471$	−2.39978	+	4.15654i	−0.110576	+	0.191523i
$472$	−11.9250	−	20.6547i	−0.548892	−	0.950709i
$473$	−3.78304	−	6.55242i	−0.173945	−	0.301281i
$474$	−0.583579	+	1.01079i	−0.0268047	+	0.0464271i
$475$		0			0
$476$	1.56972	−	0.426979i	0.0719478	−	0.0195705i
$477$	−6.32688			−0.289688
$478$	−1.86177	+	3.22468i	−0.0851554	+	0.147494i
$479$	−19.0193	−	32.9424i	−0.869015	−	1.50518i	−0.863005	−	0.505196i	$-0.831420\pi$
$479$	−19.0193	−	32.9424i	−0.869015	−	1.50518i	−0.00600999	−	0.999982i	$-0.501913\pi$
$480$		0			0
$481$	8.97426	−	15.5439i	0.409191	−	0.708740i
$482$	−14.0954			−0.642026
$483$	−14.1060	−	13.9996i	−0.641844	−	0.637004i
$484$	−30.7263			−1.39665
$485$		0			0
$486$	−0.247087	−	0.427967i	−0.0112081	−	0.0194130i
$487$	−11.2914	−	19.5572i	−0.511661	−	0.886223i	−0.999909	−	0.0135175i	$-0.995697\pi$
$487$	−11.2914	−	19.5572i	−0.511661	−	0.886223i	0.488248	−	0.872705i	$-0.337636\pi$
$488$	4.64003	−	8.03677i	0.210044	−	0.363808i
$489$	−0.826947			−0.0373959
$490$		0			0
$491$	−0.134148			−0.00605400			−0.00302700	−	0.999995i	$-0.500964\pi$
$491$	−0.134148			−0.00605400			−0.00302700	+	0.999995i	$0.500964\pi$
$492$	6.90182	−	11.9543i	0.311158	−	0.538942i
$493$	−0.700372	−	1.21308i	−0.0315432	−	0.0546344i
$494$	3.48349	+	6.03359i	0.156730	+	0.271464i
$495$		0			0
$496$	15.8715			0.712653
$497$	29.0854	+	28.8660i	1.30466	+	1.29482i
$498$	−3.39666			−0.152208
$499$	7.77768	−	13.4713i	0.348177	−	0.603060i	−0.637749	−	0.770244i	$-0.720134\pi$
$499$	7.77768	−	13.4713i	0.348177	−	0.603060i	0.985926	+	0.167185i	$0.0534676\pi$
$500$		0			0
$501$	2.30743	+	3.99658i	0.103088	+	0.178554i
$502$	−5.64596	+	9.77909i	−0.251992	+	0.436462i
$503$	4.39272			0.195862			0.0979308	−	0.995193i	$-0.468778\pi$
$503$	4.39272			0.195862			0.0979308	+	0.995193i	$0.468778\pi$
$504$	−4.73838	+	1.28889i	−0.211064	+	0.0574116i
$505$		0			0
$506$	9.90838	−	17.1618i	0.440481	−	0.762936i
$507$	6.47608	+	11.2169i	0.287613	+	0.498160i
$508$	−15.3973	−	26.6689i	−0.683144	−	1.18324i
$509$	−1.04377	+	1.80786i	−0.0462642	+	0.0801319i	−0.888230	−	0.459399i	$-0.848065\pi$
$509$	−1.04377	+	1.80786i	−0.0462642	+	0.0801319i	0.841966	+	0.539531i	$0.181398\pi$
$510$		0			0
$511$	5.18273	−	19.6393i	0.229271	−	0.868790i
$512$	−22.5871			−0.998219
$513$	1.38372	−	2.39668i	0.0610929	−	0.105816i
$514$	6.21129	+	10.7583i	0.273968	+	0.474527i
$515$		0			0
$516$	−1.24421	+	2.15503i	−0.0547732	+	0.0948699i
$517$	−47.2466			−2.07791
$518$	1.17540	−	4.45401i	0.0516440	−	0.195698i
$519$	12.6771			0.556461
$520$		0			0
$521$	18.3501	+	31.7832i	0.803930	+	1.39245i	0.917011	+	0.398862i	$0.130595\pi$
$521$	18.3501	+	31.7832i	0.803930	+	1.39245i	−0.113081	+	0.993586i	$0.536072\pi$
$522$	0.988347	+	1.71187i	0.0432588	+	0.0749264i
$523$	−6.31454	+	10.9371i	−0.276116	+	0.478246i	−0.970416	−	0.241439i	$-0.922381\pi$
$523$	−6.31454	+	10.9371i	−0.276116	+	0.478246i	0.694300	+	0.719685i	$0.255714\pi$
$524$	15.8428			0.692097
$525$		0			0
$526$	6.70010			0.292138
$527$	−1.07115	+	1.85529i	−0.0466602	+	0.0808179i
$528$	6.92513	+	11.9947i	0.301377	+	0.522001i
$529$	−16.7120	−	28.9460i	−0.726607	−	1.25852i
$530$		0			0
$531$	12.8501			0.557648
$532$	−9.12481	−	9.05600i	−0.395611	−	0.392627i
$533$	−40.0504			−1.73478
$534$	1.07487	−	1.86173i	0.0465143	−	0.0805651i
$535$		0			0
$536$	−3.48540	−	6.03689i	−0.150546	−	0.260754i
$537$	6.52324	−	11.2986i	0.281499	−	0.487570i
$538$	4.46103			0.192329
$539$	32.2208	−	18.9293i	1.38785	−	0.815343i
$540$		0			0
$541$	−19.4206	+	33.6374i	−0.834956	+	1.44619i	0.0591098	+	0.998251i	$0.481174\pi$
$541$	−19.4206	+	33.6374i	−0.834956	+	1.44619i	−0.894066	+	0.447935i	$0.852160\pi$
$542$	1.18018	+	2.04414i	0.0506932	+	0.0878031i
$543$	7.52968	+	13.0418i	0.323130	+	0.559677i
$544$	0.874433	−	1.51456i	0.0374910	−	0.0649363i
$545$		0			0
$546$	4.72757	+	4.69191i	0.202321	+	0.200795i
$547$	18.6010			0.795323			0.397662	−	0.917532i	$-0.369822\pi$
$547$	18.6010			0.795323			0.397662	+	0.917532i	$0.369822\pi$
$548$	−0.732622	+	1.26894i	−0.0312961	+	0.0542064i
$549$	2.50000	+	4.33013i	0.106697	+	0.184805i
$550$		0			0
$551$	−5.53489	+	9.58671i	−0.235794	+	0.408408i
$552$	−13.9416			−0.593394
$553$	−6.02975	+	1.64015i	−0.256411	+	0.0697464i
$554$	−0.924457			−0.0392764
$555$		0			0
$556$	−12.5673	−	21.7672i	−0.532972	−	0.923134i
$557$	2.58274	+	4.47344i	0.109434	+	0.189546i	0.915541	−	0.402224i	$-0.131763\pi$
$557$	2.58274	+	4.47344i	0.109434	+	0.189546i	−0.806107	+	0.591770i	$0.798429\pi$
$558$	1.51159	−	2.61814i	0.0639905	−	0.110835i
$559$	7.21998			0.305373
$560$		0			0
$561$	−1.86948			−0.0789295
$562$	0.240353	−	0.416304i	0.0101387	−	0.0175607i
$563$	−6.31908	−	10.9450i	−0.266317	−	0.461275i	0.701590	−	0.712580i	$-0.252474\pi$
$563$	−6.31908	−	10.9450i	−0.266317	−	0.461275i	−0.967908	+	0.251305i	$0.919140\pi$
$564$	7.76949	+	13.4571i	0.327154	+	0.566648i
$565$		0			0
$566$	11.9490			0.502253
$567$	0.675093	−	2.55817i	0.0283512	−	0.107433i
$568$	28.7464			1.20617
$569$	4.39870	−	7.61878i	0.184403	−	0.319396i	−0.758972	−	0.651123i	$-0.774298\pi$
$569$	4.39870	−	7.61878i	0.184403	−	0.319396i	0.943375	+	0.331727i	$0.107631\pi$
$570$		0			0
$571$	19.9516	+	34.5572i	0.834950	+	1.44618i	0.894072	+	0.447924i	$0.147837\pi$
$571$	19.9516	+	34.5572i	0.834950	+	1.44618i	−0.0591220	+	0.998251i	$0.518830\pi$
$572$	23.8755	−	41.3535i	0.998283	−	1.72908i
$573$	−9.52718			−0.398004
$574$	−9.91856	+	2.69795i	−0.413993	+	0.112610i
$575$		0			0
$576$	1.36042	−	2.35631i	0.0566840	−	0.0981796i
$577$	−1.35844	−	2.35289i	−0.0565528	−	0.0979523i	0.836363	−	0.548176i	$-0.184678\pi$
$577$	−1.35844	−	2.35289i	−0.0565528	−	0.0979523i	−0.892916	+	0.450224i	$0.851344\pi$
$578$	−4.17017	−	7.22295i	−0.173456	−	0.300435i
$579$	−7.55299	+	13.0822i	−0.313892	+	0.543676i
$580$		0			0
$581$	−12.9076	−	12.8102i	−0.535497	−	0.531458i
$582$	2.71792			0.112661
$583$	16.8881	−	29.2511i	0.699435	−	1.21146i
$584$	−7.12437	−	12.3398i	−0.294808	−	0.510623i
$585$		0			0
$586$	3.83846	−	6.64842i	0.158566	−	0.274644i
$587$	9.02317			0.372426			0.186213	−	0.982509i	$-0.440379\pi$
$587$	9.02317			0.372426			0.186213	+	0.982509i	$0.440379\pi$
$588$	−10.6901	−	6.06452i	−0.440854	−	0.250097i
$589$	16.9302			0.697597
$590$		0			0
$591$	8.44451	+	14.6263i	0.347361	+	0.601647i
$592$	4.57033	+	7.91605i	0.187840	+	0.325348i
$593$	5.23255	−	9.06305i	0.214875	−	0.372175i	−0.738359	−	0.674408i	$-0.764399\pi$
$593$	5.23255	−	9.06305i	0.214875	−	0.372175i	0.953234	+	0.302233i	$0.0977322\pi$
$594$	2.63816			0.108245
$595$		0			0
$596$	−34.0565			−1.39501
$597$	−12.6138	+	21.8477i	−0.516248	+	0.894167i
$598$	9.45513	+	16.3768i	0.386649	+	0.669696i
$599$	−4.81915	−	8.34701i	−0.196905	−	0.341050i	0.750618	−	0.660736i	$-0.229756\pi$
$599$	−4.81915	−	8.34701i	−0.196905	−	0.341050i	−0.947523	+	0.319686i	$0.896422\pi$
$600$		0			0
$601$	−7.19544			−0.293508			−0.146754	−	0.989173i	$-0.546883\pi$
$601$	−7.19544			−0.293508			−0.146754	+	0.989173i	$0.546883\pi$
$602$	1.78804	−	0.486366i	0.0728752	−	0.0198228i
$603$	3.75579			0.152948
$604$	16.2649	−	28.1717i	0.661811	−	1.14629i
$605$		0			0
$606$	−0.407647	−	0.706065i	−0.0165595	−	0.0286819i
$607$	19.6692	−	34.0681i	0.798348	−	1.38278i	−0.122343	−	0.992488i	$-0.539041\pi$
$607$	19.6692	−	34.0681i	0.798348	−	1.38278i	0.920691	−	0.390292i	$-0.127626\pi$
$608$	−13.8209			−0.560512
$609$	−2.70037	+	10.2327i	−0.109425	+	0.414650i
$610$		0			0
$611$	22.5427	−	39.0451i	0.911980	−	1.57960i
$612$	0.307427	+	0.532479i	0.0124270	+	0.0215242i
$613$	9.77320	+	16.9277i	0.394736	+	0.683703i	0.993067	−	0.117546i	$-0.0375027\pi$
$613$	9.77320	+	16.9277i	0.394736	+	0.683703i	−0.598331	+	0.801249i	$0.704169\pi$
$614$	−0.838601	+	1.45250i	−0.0338432	+	0.0586181i
$615$		0			0
$616$	6.68908	−	25.3474i	0.269511	−	1.02127i
$617$	35.9588			1.44765			0.723824	−	0.689985i	$-0.242383\pi$
$617$	35.9588			1.44765			0.723824	+	0.689985i	$0.242383\pi$
$618$	2.51075	−	4.34874i	0.100997	−	0.174932i
$619$	−4.27972	−	7.41269i	−0.172016	−	0.297941i	0.767108	−	0.641518i	$-0.221695\pi$
$619$	−4.27972	−	7.41269i	−0.172016	−	0.297941i	−0.939125	+	0.343577i	$0.888362\pi$
$620$		0			0
$621$	3.75579	−	6.50522i	0.150715	−	0.261046i
$622$	1.21819			0.0488450
$623$	11.1060	−	3.02094i	0.444952	−	0.121031i
$624$	−13.2167			−0.529091
$625$		0			0
$626$	−0.117496	−	0.203509i	−0.00469609	−	0.00813387i
$627$	7.38705	+	12.7947i	0.295010	+	0.510973i
$628$	−4.21352	+	7.29802i	−0.168138	+	0.291223i
$629$	−1.23379			−0.0491944
$630$		0			0
$631$	−17.5192			−0.697427			−0.348713	−	0.937229i	$-0.613381\pi$
$631$	−17.5192			−0.697427			−0.348713	+	0.937229i	$0.613381\pi$
$632$	−2.19180	+	3.79631i	−0.0871852	+	0.151009i
$633$	10.1983	+	17.6640i	0.405347	+	0.702082i
$634$	3.53321	+	6.11971i	0.140322	+	0.243045i
$635$		0			0
$636$	−11.1087			−0.440488
$637$	0.269945	+	35.6593i	0.0106956	+	1.41287i
$638$	−10.5526			−0.417783
$639$	−7.74414	+	13.4132i	−0.306353	+	0.530620i
$640$		0			0
$641$	−8.14094	−	14.1005i	−0.321548	−	0.556937i	0.659260	−	0.751915i	$-0.270870\pi$
$641$	−8.14094	−	14.1005i	−0.321548	−	0.556937i	−0.980808	+	0.194978i	$0.937536\pi$
$642$	1.32484	−	2.29469i	0.0522872	−	0.0905641i
$643$	−15.7544			−0.621294			−0.310647	−	0.950525i	$-0.600546\pi$
$643$	−15.7544			−0.621294			−0.310647	+	0.950525i	$0.600546\pi$
$644$	−24.7672	−	24.5804i	−0.975963	−	0.968603i
$645$		0			0
$646$	0.239457	−	0.414751i	0.00942131	−	0.0163182i
$647$	−22.7197	−	39.3517i	−0.893203	−	1.54707i	−0.836013	−	0.548710i	$-0.815119\pi$
$647$	−22.7197	−	39.3517i	−0.893203	−	1.54707i	−0.0571903	−	0.998363i	$-0.518214\pi$
$648$	−0.928006	−	1.60735i	−0.0364555	−	0.0631428i
$649$	−34.3004	+	59.4100i	−1.34641	+	2.33205i
$650$		0			0
$651$	15.6182	−	4.24832i	0.612127	−	0.166505i
$652$	−1.45195			−0.0568627
$653$	−9.58070	+	16.5943i	−0.374922	+	0.649384i	−0.990315	−	0.138836i	$-0.955664\pi$
$653$	−9.58070	+	16.5943i	−0.374922	+	0.649384i	0.615394	+	0.788220i	$0.288997\pi$
$654$	0.0261859	+	0.0453554i	0.00102395	+	0.00177354i
$655$		0			0
$656$	10.1983	−	17.6639i	0.398175	−	0.689660i
$657$	7.67707			0.299511
$658$	2.95251	−	11.1882i	0.115101	−	0.436160i
$659$	−8.76258			−0.341342			−0.170671	−	0.985328i	$-0.554593\pi$
$659$	−8.76258			−0.341342			−0.170671	+	0.985328i	$0.554593\pi$
$660$		0			0
$661$	4.53801	+	7.86006i	0.176508	+	0.305721i	0.940682	−	0.339289i	$-0.110186\pi$
$661$	4.53801	+	7.86006i	0.176508	+	0.305721i	−0.764174	+	0.645010i	$0.776853\pi$
$662$	−4.83930	−	8.38192i	−0.188085	−	0.325773i
$663$	0.891981	−	1.54496i	0.0346417	−	0.0600011i
$664$	−12.7572			−0.495074
$665$		0			0
$666$	1.74109			0.0674659
$667$	−15.0232	+	26.0209i	−0.581699	+	1.00753i
$668$	4.05136	+	7.01717i	0.156752	+	0.271502i
$669$	−11.2869	−	19.5495i	−0.436377	−	0.755827i
$670$		0			0
$671$	−26.6927			−1.03046
$672$	−12.7499	+	3.46810i	−0.491838	+	0.133785i
$673$	−18.3460			−0.707185			−0.353593	−	0.935400i	$-0.615040\pi$
$673$	−18.3460			−0.707185			−0.353593	+	0.935400i	$0.615040\pi$
$674$	1.08281	−	1.87548i	0.0417082	−	0.0722407i
$675$		0			0
$676$	11.3706	+	19.6945i	0.437333	+	0.757482i
$677$	0.897966	−	1.55532i	0.0345116	−	0.0597759i	−0.848254	−	0.529590i	$-0.822346\pi$
$677$	0.897966	−	1.55532i	0.0345116	−	0.0597759i	0.882765	+	0.469814i	$0.155679\pi$
$678$	−2.31128			−0.0887642
$679$	10.3283	+	10.2504i	0.396364	+	0.393375i
$680$		0			0
$681$	−7.08267	+	12.2675i	−0.271409	+	0.470093i
$682$	8.06965	+	13.9770i	0.309003	+	0.535209i
$683$	22.1965	+	38.4454i	0.849324	+	1.47107i	0.881813	+	0.471599i	$0.156323\pi$
$683$	22.1965	+	38.4454i	0.849324	+	1.47107i	−0.0324893	+	0.999472i	$0.510343\pi$
$684$	2.42953	−	4.20807i	0.0928954	−	0.160900i
$685$		0			0
$686$	2.46900	+	8.81290i	0.0942667	+	0.336478i
$687$	17.8062			0.679349
$688$	−1.83846	+	3.18431i	−0.0700908	+	0.121401i
$689$	16.1156	+	27.9130i	0.613955	+	1.06340i
$690$		0			0
$691$	−21.5962	+	37.4058i	−0.821559	+	1.42298i	0.0829614	+	0.996553i	$0.473562\pi$
$691$	−21.5962	+	37.4058i	−0.821559	+	1.42298i	−0.904521	+	0.426430i	$0.859771\pi$
$692$	22.2583			0.846134
$693$	10.0252	+	9.94961i	0.380826	+	0.377954i
$694$	4.74263			0.180028
$695$		0			0
$696$	3.71203	+	6.42942i	0.140704	+	0.243706i
$697$	1.37654	+	2.38424i	0.0521402	+	0.0903095i
$698$	−4.91719	+	8.51683i	−0.186118	+	0.322367i
$699$	−13.6498			−0.516283
$700$		0			0
$701$	−9.69616			−0.366219			−0.183109	−	0.983093i	$-0.558616\pi$
$701$	−9.69616			−0.366219			−0.183109	+	0.983093i	$0.558616\pi$
$702$	−1.25874	+	2.18020i	−0.0475081	+	0.0822864i
$703$	4.87519	+	8.44407i	0.183871	+	0.318474i
$704$	7.26263	+	12.5792i	0.273721	+	0.474098i
$705$		0			0
$706$	−13.5387			−0.509536
$707$	1.11378	−	4.22051i	0.0418879	−	0.158729i
$708$	22.5621			0.847937
$709$	−9.07685	+	15.7216i	−0.340888	+	0.590435i	−0.984598	−	0.174834i	$-0.944061\pi$
$709$	−9.07685	+	15.7216i	−0.340888	+	0.590435i	0.643710	+	0.765270i	$0.277394\pi$
$710$		0			0
$711$	−1.18092	−	2.04541i	−0.0442879	−	0.0767090i
$712$	4.03700	−	6.99229i	0.151293	−	0.262047i
$713$	45.9531			1.72096
$714$	0.116827	−	0.442699i	0.00437213	−	0.0165676i
$715$		0			0
$716$	11.4535	−	19.8380i	0.428036	−	0.741380i
$717$	−3.76745	−	6.52541i	−0.140698	−	0.243696i
$718$	6.31319	+	10.9348i	0.235606	+	0.408082i
$719$	17.5904	−	30.4675i	0.656011	−	1.13624i	−0.325628	−	0.945498i	$-0.605576\pi$
$719$	17.5904	−	30.4675i	0.656011	−	1.13624i	0.981639	−	0.190747i	$-0.0610910\pi$
$720$		0			0
$721$	25.9419	−	7.05647i	0.966128	−	0.262797i
$722$	5.60454			0.208579
$723$	14.2616	−	24.7017i	0.530393	−	0.918667i
$724$	13.2206	+	22.8987i	0.491338	+	0.851023i
$725$		0			0
$726$	−4.32400	+	7.48939i	−0.160479	+	0.277957i
$727$	−4.79075			−0.177679			−0.0888396	−	0.996046i	$-0.528316\pi$
$727$	−4.79075			−0.177679			−0.0888396	+	0.996046i	$0.528316\pi$
$728$	17.7558	+	17.6219i	0.658072	+	0.653109i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.248152	−	0.429812i	−0.00917825	−	0.0158972i
$732$	4.38948	+	7.60281i	0.162240	+	0.281008i
$733$	6.06214	−	10.4999i	0.223910	−	0.387824i	−0.732082	−	0.681217i	$-0.761451\pi$
$733$	6.06214	−	10.4999i	0.223910	−	0.387824i	0.955992	+	0.293393i	$0.0947844\pi$
$734$	11.0060			0.406237
$735$		0			0
$736$	−37.5136			−1.38277
$737$	−10.0252	+	17.3642i	−0.369283	+	0.639618i
$738$	−1.94254	−	3.36458i	−0.0715058	−	0.123852i
$739$	16.4581	+	28.5063i	0.605422	+	1.04862i	0.991985	+	0.126359i	$0.0403291\pi$
$739$	16.4581	+	28.5063i	0.605422	+	1.04862i	−0.386562	+	0.922263i	$0.626338\pi$
$740$		0			0
$741$	−14.0983			−0.517913
$742$	5.87138	+	5.82711i	0.215545	+	0.213920i
$743$	−38.8112			−1.42385			−0.711923	−	0.702258i	$-0.752175\pi$
$743$	−38.8112			−1.42385			−0.711923	+	0.702258i	$0.752175\pi$
$744$	5.67720	−	9.83320i	0.208136	−	0.360503i
$745$		0			0
$746$	−1.30827	−	2.26598i	−0.0478990	−	0.0829635i
$747$	3.43671	−	5.95256i	0.125743	−	0.217793i
$748$	−3.28242			−0.120017
$749$	13.6887	−	3.72347i	0.500175	−	0.136053i
$750$		0			0
$751$	15.0341	−	26.0398i	0.548602	−	0.950206i	−0.449769	−	0.893145i	$-0.648494\pi$
$751$	15.0341	−	26.0398i	0.548602	−	0.950206i	0.998371	−	0.0570610i	$-0.0181729\pi$
$752$	11.4803	+	19.8845i	0.418645	+	0.725115i
$753$	−11.4251	−	19.7888i	−0.416352	−	0.721143i
$754$	5.03496	−	8.72081i	0.183362	−	0.317593i
$755$		0			0
$756$	1.18532	−	4.49162i	0.0431098	−	0.163359i
$757$	7.17713			0.260857			0.130429	−	0.991458i	$-0.458365\pi$
$757$	7.17713			0.260857			0.130429	+	0.991458i	$0.458365\pi$
$758$	0.766471	−	1.32757i	0.0278395	−	0.0482194i
$759$	20.0504	+	34.7284i	0.727784	+	1.26056i
$760$		0			0
$761$	3.80431	−	6.58926i	0.137906	−	0.238860i	−0.788798	−	0.614653i	$-0.789296\pi$
$761$	3.80431	−	6.58926i	0.137906	−	0.238860i	0.926704	+	0.375792i	$0.122629\pi$
$762$	−8.66723			−0.313980
$763$	−0.0715455	+	0.271112i	−0.00259012	+	0.00981491i
$764$	−16.7278			−0.605189
$765$		0			0
$766$	5.34021	+	9.24952i	0.192950	+	0.334199i
$767$	−32.7313	−	56.6923i	−1.18186	−	2.04704i
$768$	−0.0793447	+	0.137429i	−0.00286310	+	0.00495904i
$769$	50.2712			1.81283			0.906413	−	0.422393i	$-0.138810\pi$
$769$	50.2712			1.81283			0.906413	+	0.422393i	$0.138810\pi$
$770$		0			0
$771$	−25.1381			−0.905326
$772$	−13.2615	+	22.9696i	−0.477291	+	0.826693i
$773$	13.5505	+	23.4701i	0.487377	+	0.844162i	0.999895	−	0.0145147i	$-0.00462032\pi$
$773$	13.5505	+	23.4701i	0.487377	+	0.844162i	−0.512517	+	0.858677i	$0.671287\pi$
$774$	0.350186	+	0.606540i	0.0125872	+	0.0218016i
$775$		0			0
$776$	10.2079			0.366444
$777$	6.61628	+	6.56638i	0.237358	+	0.235568i
$778$	6.35588			0.227869
$779$	10.8785	−	18.8421i	0.389763	−	0.675090i
$780$		0			0
$781$	−41.3423	−	71.6070i	−1.47935	−	2.56230i
$782$	0.649950	−	1.12575i	0.0232422	−	0.0402566i
$783$	−4.00000			−0.142948
$784$	−15.7960	−	8.96106i	−0.564141	−	0.320038i
$785$		0			0
$786$	2.22951	−	3.86162i	0.0795238	−	0.137739i
$787$	17.1750	+	29.7480i	0.612224	+	1.06040i	0.990865	+	0.134859i	$0.0430581\pi$
$787$	17.1750	+	29.7480i	0.612224	+	1.06040i	−0.378641	+	0.925543i	$0.623609\pi$
$788$	14.8268	+	25.6808i	0.528183	+	0.914840i
$789$	−6.77910	+	11.7417i	−0.241342	+	0.418017i
$790$		0			0
$791$	−8.78304	−	8.71681i	−0.312289	−	0.309934i
$792$	9.90838			0.352079
$793$	12.7358	−	22.0591i	0.452262	−	0.783341i
$794$	1.72841	+	2.99369i	0.0613388	+	0.106242i
$795$		0			0
$796$	−22.1472	+	38.3600i	−0.784986	+	1.35964i
$797$	16.5581			0.586517			0.293258	−	0.956033i	$-0.405260\pi$
$797$	16.5581			0.586517			0.293258	+	0.956033i	$0.405260\pi$
$798$	−3.49146	+	0.949713i	−0.123596	+	0.0336195i
$799$	−3.09919			−0.109641
$800$		0			0
$801$	2.17509	+	3.76737i	0.0768531	+	0.133114i
$802$	−0.781140	−	1.35297i	−0.0275830	−	0.0477752i
$803$	−20.4921	+	35.4934i	−0.723152	+	1.25254i
$804$	6.59439			0.232566
$805$		0			0
$806$	−15.4010			−0.542478
$807$	−4.51363	+	7.81783i	−0.158887	+	0.275201i
$808$	−1.53104	−	2.65184i	−0.0538617	−	0.0932912i
$809$	4.27903	+	7.41150i	0.150443	+	0.260574i	0.931390	−	0.364022i	$-0.118597\pi$
$809$	4.27903	+	7.41150i	0.150443	+	0.260574i	−0.780948	+	0.624597i	$0.785263\pi$
$810$		0			0
$811$	21.4277			0.752429			0.376215	−	0.926533i	$-0.377226\pi$
$811$	21.4277			0.752429			0.376215	+	0.926533i	$0.377226\pi$
$812$	−4.74129	+	17.9665i	−0.166387	+	0.630500i
$813$	−4.77639			−0.167515
$814$	−4.64743	+	8.04959i	−0.162893	+	0.282138i
$815$		0			0
$816$	0.454260	+	0.786802i	0.0159023	+	0.0275436i
$817$	−1.96110	+	3.39672i	−0.0686100	+	0.118836i
$818$	−1.23300			−0.0431107
$819$	−13.0058	+	3.53770i	−0.454458	+	0.123617i
$820$		0			0
$821$	7.56010	−	13.0945i	0.263849	−	0.457001i	−0.703412	−	0.710782i	$-0.748341\pi$
$821$	7.56010	−	13.0945i	0.263849	−	0.457001i	0.967262	+	0.253782i	$0.0816745\pi$
$822$	0.206199	+	0.357147i	0.00719201	+	0.0124569i
$823$	12.3522	+	21.3946i	0.430569	+	0.745768i	0.996922	−	0.0783949i	$-0.0249795\pi$
$823$	12.3522	+	21.3946i	0.430569	+	0.745768i	−0.566353	+	0.824163i	$0.691646\pi$
$824$	9.42984	−	16.3330i	0.328504	−	0.568986i
$825$		0			0
$826$	−11.9250	−	11.8351i	−0.414924	−	0.411794i
$827$	28.8578			1.00348			0.501742	−	0.865017i	$-0.332693\pi$
$827$	28.8578			1.00348			0.501742	+	0.865017i	$0.332693\pi$
$828$	6.59439	−	11.4218i	0.229171	−	0.396936i
$829$	0.434740	+	0.752992i	0.0150991	+	0.0261525i	0.873476	−	0.486867i	$-0.161860\pi$
$829$	0.434740	+	0.752992i	0.0150991	+	0.0261525i	−0.858377	+	0.513019i	$0.828527\pi$
$830$		0			0
$831$	0.935357	−	1.62009i	0.0324472	−	0.0562002i
$832$	−13.8608			−0.480537
$833$	2.11355	−	1.24169i	0.0732302	−	0.0430219i
$834$	−7.07420			−0.244960
$835$		0			0
$836$	12.9701	+	22.4649i	0.448581	+	0.776966i
$837$	3.05882	+	5.29802i	0.105728	+	0.183127i
$838$	−8.07350	+	13.9837i	−0.278895	+	0.483059i
$839$	21.7235			0.749980			0.374990	−	0.927029i	$-0.377646\pi$
$839$	21.7235			0.749980			0.374990	+	0.927029i	$0.377646\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−6.64104	+	11.5026i	−0.228865	+	0.396406i
$843$	0.486374	+	0.842425i	0.0167516	+	0.0290147i
$844$	17.9062	+	31.0144i	0.616355	+	1.06756i
$845$		0			0
$846$	4.37349			0.150364
$847$	−44.6771	+	12.1526i	−1.53512	+	0.417569i
$848$	−16.4144			−0.563673
$849$	−12.0899	+	20.9402i	−0.414923	+	0.718667i
$850$		0			0
$851$	13.2326	+	22.9195i	0.453606	+	0.785669i
$852$	−13.5971	+	23.5509i	−0.465829	+	0.806840i
$853$	0.670546			0.0229591			0.0114795	−	0.999934i	$-0.496346\pi$
$853$	0.670546			0.0229591			0.0114795	+	0.999934i	$0.496346\pi$
$854$	1.66806	−	6.32090i	0.0570800	−	0.216297i
$855$		0			0
$856$	4.97582	−	8.61837i	0.170070	−	0.294570i
$857$	−12.2442	−	21.2076i	−0.418254	−	0.724437i	0.577510	−	0.816384i	$-0.304025\pi$
$857$	−12.2442	−	21.2076i	−0.418254	−	0.724437i	−0.995764	+	0.0919463i	$0.970691\pi$
$858$	−6.71982	−	11.6391i	−0.229411	−	0.397352i
$859$	−4.79970	+	8.31332i	−0.163764	+	0.283647i	−0.936215	−	0.351426i	$-0.885697\pi$
$859$	−4.79970	+	8.31332i	−0.163764	+	0.283647i	0.772452	+	0.635073i	$0.219030\pi$
$860$		0			0
$861$	5.30743	−	20.1118i	0.180877	−	0.685407i
$862$	−7.01165			−0.238818
$863$	14.7519	−	25.5511i	0.502162	−	0.869770i	−0.497835	−	0.867272i	$-0.665872\pi$
$863$	14.7519	−	25.5511i	0.502162	−	0.869770i	0.999997	−	0.00249807i	$-0.000795160\pi$
$864$	−2.49705	−	4.32502i	−0.0849515	−	0.147140i
$865$		0			0
$866$	7.40561	−	12.8269i	0.251653	−	0.435875i
$867$	16.8774			0.573186
$868$	27.4224	−	7.45917i	0.930777	−	0.253181i
$869$	12.6088			0.427723
$870$		0			0
$871$	−9.56662	−	16.5699i	−0.324152	−	0.561448i
$872$	0.0983489	+	0.170345i	0.00333052	+	0.00576862i
$873$	−2.74997	+	4.76308i	−0.0930722	+	0.161206i
$874$	−10.2728			−0.347484
$875$		0			0
$876$	13.4793			0.455425
$877$	2.65383	−	4.59656i	0.0896134	−	0.155215i	−0.817734	−	0.575596i	$-0.804770\pi$
$877$	2.65383	−	4.59656i	0.0896134	−	0.155215i	0.907348	+	0.420381i	$0.138104\pi$
$878$	−0.512424	−	0.887545i	−0.0172935	−	0.0299532i
$879$	7.76745	+	13.4536i	0.261989	+	0.453779i
$880$		0			0
$881$	49.2817			1.66034			0.830172	−	0.557507i	$-0.188242\pi$
$881$	49.2817			1.66034			0.830172	+	0.557507i	$0.188242\pi$
$882$	−2.98259	+	1.75223i	−0.100429	+	0.0590008i
$883$	−6.02862			−0.202879			−0.101440	−	0.994842i	$-0.532345\pi$
$883$	−6.02862			−0.202879			−0.101440	+	0.994842i	$0.532345\pi$
$884$	1.56613	−	2.71262i	0.0526748	−	0.0912354i
$885$		0			0
$886$	7.92593	+	13.7281i	0.266277	+	0.461205i
$887$	−3.99243	+	6.91509i	−0.134053	+	0.232186i	−0.925235	−	0.379394i	$-0.876132\pi$
$887$	−3.99243	+	6.91509i	−0.134053	+	0.232186i	0.791183	+	0.611580i	$0.209466\pi$
$888$	6.53918			0.219440
$889$	−32.9361	−	32.6877i	−1.10464	−	1.09631i
$890$		0			0
$891$	−2.66927	+	4.62330i	−0.0894238	+	0.154887i
$892$	−19.8175	−	34.3248i	−0.663537	−	1.14928i
$893$	12.2461	+	21.2109i	0.409801	+	0.709795i
$894$	−4.79266	+	8.30113i	−0.160290	+	0.277631i
$895$		0			0
$896$	−28.9325	+	7.86992i	−0.966565	+	0.262916i
$897$	−38.2665			−1.27768
$898$	−1.10226	+	1.90917i	−0.0367829	+	0.0637099i
$899$	−12.2353	−	21.1921i	−0.408069	−	0.706796i
$900$		0			0
$901$	1.10779	−	1.91875i	0.0369059	−	0.0639229i
$902$	20.7406			0.690587
$903$	−0.956782	+	3.62560i	−0.0318397	+	0.120652i
$904$	−8.68069			−0.288716
$905$		0			0
$906$	−4.57782	−	7.92902i	−0.152088	−	0.263424i
$907$	−1.26554	−	2.19198i	−0.0420216	−	0.0727836i	0.844250	−	0.535950i	$-0.180047\pi$
$907$	−1.26554	−	2.19198i	−0.0420216	−	0.0727836i	−0.886271	+	0.463167i	$0.846713\pi$
$908$	−12.4357	+	21.5393i	−0.412693	+	0.714806i
$909$	1.64981			0.0547209
$910$		0			0
$911$	1.41047			0.0467309			0.0233655	−	0.999727i	$-0.492562\pi$
$911$	1.41047			0.0467309			0.0233655	+	0.999727i	$0.492562\pi$
$912$	3.58992	−	6.21793i	0.118874	−	0.205896i
$913$	18.3470	+	31.7779i	0.607197	+	1.05170i
$914$	−0.560942	−	0.971580i	−0.0185543	−	0.0321370i
$915$		0			0
$916$	31.2640			1.03299
$917$	23.0361	−	6.26604i	0.760718	−	0.206923i
$918$	0.173053			0.00571159
$919$	−23.3418	+	40.4292i	−0.769975	+	1.33364i	0.167601	+	0.985855i	$0.446398\pi$
$919$	−23.3418	+	40.4292i	−0.769975	+	1.33364i	−0.937576	+	0.347780i	$0.886935\pi$
$920$		0			0
$921$	−1.69698	−	2.93925i	−0.0559173	−	0.0968516i
$922$	1.07012	−	1.85351i	0.0352426	−	0.0610420i
$923$	78.9023			2.59710
$924$	17.6022	+	17.4694i	0.579070	+	0.574703i
$925$		0			0
$926$	−10.3247	+	17.8829i	−0.339290	+	0.587667i
$927$	5.08070	+	8.80003i	0.166872	+	0.289031i
$928$	9.98821	+	17.3001i	0.327879	+	0.567903i
$929$	8.91923	−	15.4486i	0.292631	−	0.506851i	−0.681800	−	0.731538i	$-0.738803\pi$
$929$	8.91923	−	15.4486i	0.292631	−	0.506851i	0.974431	+	0.224687i	$0.0721361\pi$
$930$		0			0
$931$	−16.8496	−	9.55878i	−0.552223	−	0.313277i
$932$	−23.9662			−0.785040
$933$	−1.23255	+	2.13485i	−0.0403520	+	0.0698917i
$934$	9.48252	+	16.4242i	0.310278	+	0.537416i
$935$		0			0
$936$	−4.72757	+	8.18839i	−0.154525	+	0.267646i
$937$	−0.343849			−0.0112330			−0.00561652	−	0.999984i	$-0.501788\pi$
$937$	−0.343849			−0.0112330			−0.00561652	+	0.999984i	$0.501788\pi$
$938$	−3.48540	−	3.45911i	−0.113802	−	0.112944i
$939$	0.475526			0.0155182
$940$		0			0
$941$	23.0737	+	39.9649i	0.752182	+	1.30282i	0.946763	+	0.321931i	$0.104332\pi$
$941$	23.0737	+	39.9649i	0.752182	+	1.30282i	−0.194581	+	0.980886i	$0.562335\pi$
$942$	1.18591	+	2.05405i	0.0386389	+	0.0669246i
$943$	29.5272	−	51.1426i	0.961537	−	1.66543i
$944$	33.3383			1.08507
$945$		0			0
$946$	−3.73896			−0.121564
$947$	13.8309	−	23.9558i	0.449444	−	0.778459i	−0.548906	−	0.835884i	$-0.684956\pi$
$947$	13.8309	−	23.9558i	0.449444	−	0.778459i	0.998350	+	0.0574248i	$0.0182889\pi$
$948$	−2.07345	−	3.59132i	−0.0673425	−	0.116641i
$949$	−19.5547	−	33.8698i	−0.634774	−	1.09946i
$950$		0			0
$951$	−14.2995			−0.463693
$952$	0.438777	−	1.66268i	0.0142208	−	0.0538879i
$953$	4.24907			0.137641			0.0688204	−	0.997629i	$-0.478076\pi$
$953$	4.24907			0.137641			0.0688204	+	0.997629i	$0.478076\pi$
$954$	−1.56329	+	2.70769i	−0.0506133	+	0.0876648i
$955$		0			0
$956$	−6.61485	−	11.4573i	−0.213940	−	0.370554i
$957$	10.6771	−	18.4932i	0.345141	−	0.597801i
$958$	−18.7977			−0.607325
$959$	−0.563379	+	2.13485i	−0.0181924	+	0.0689378i
$960$		0			0
$961$	−3.21271	+	5.56458i	−0.103636	+	0.179503i
$962$	−4.43484	−	7.68137i	−0.142985	−	0.247657i
$963$	2.68092	+	4.64349i	0.0863914	+	0.149634i
$964$	25.0403	−	43.3711i	0.806495	−	1.39689i
$965$		0			0
$966$	−9.47676	+	2.57777i	−0.304910	+	0.0829385i
$967$	59.6146			1.91708			0.958538	−	0.284965i	$-0.0919820\pi$
$967$	59.6146			1.91708			0.958538	+	0.284965i	$0.0919820\pi$
$968$	−16.2400	+	28.1286i	−0.521975	+	0.904087i
$969$	0.484560	+	0.839283i	0.0155663	+	0.0269617i
$970$		0			0
$971$	0.475617	−	0.823793i	0.0152633	−	0.0264368i	−0.858293	−	0.513160i	$-0.828475\pi$
$971$	0.475617	−	0.823793i	0.0152633	−	0.0264368i	0.873556	+	0.486723i	$0.161808\pi$
$972$	1.75579			0.0563171
$973$	−26.8825	−	26.6798i	−0.861814	−	0.855314i
$974$	−11.1598			−0.357583
$975$		0			0
$976$	6.48598	+	11.2341i	0.207611	+	0.359593i
$977$	11.5253	+	19.9624i	0.368726	+	0.638653i	0.989367	−	0.145443i	$-0.0464606\pi$
$977$	11.5253	+	19.9624i	0.368726	+	0.638653i	−0.620640	+	0.784095i	$0.713127\pi$
$978$	−0.204328	+	0.353906i	−0.00653368	+	0.0113167i
$979$	−23.2236			−0.742230
$980$		0			0
$981$	−0.105979			−0.00338364
$982$	−0.0331461	+	0.0574108i	−0.00105774	+	0.00183205i
$983$	−15.9174	−	27.5698i	−0.507687	−	0.879339i	−0.999960	−	0.00889883i	$-0.997167\pi$
$983$	−15.9174	−	27.5698i	−0.507687	−	0.879339i	0.492274	−	0.870441i	$-0.336166\pi$
$984$	−7.29577	−	12.6367i	−0.232581	−	0.402842i
$985$		0			0
$986$	−0.692210			−0.0220445
$987$	16.6196	+	16.4943i	0.529008	+	0.525018i
$988$	−24.7536			−0.787518
$989$	−5.32293	+	9.21959i	−0.169259	+	0.293166i
$990$		0			0
$991$	4.05306	+	7.02010i	0.128750	+	0.223001i	0.923192	−	0.384338i	$-0.125570\pi$
$991$	4.05306	+	7.02010i	0.128750	+	0.223001i	−0.794443	+	0.607339i	$0.792237\pi$
$992$	15.2760	−	26.4589i	0.485015	−	0.840071i
$993$	19.5855			0.621525
$994$	19.5403	−	5.31516i	0.619781	−	0.168587i
$995$		0			0
$996$	6.03415	−	10.4515i	0.191199	−	0.331167i
$997$	−14.1235	−	24.4625i	−0.447294	−	0.774737i	0.550914	−	0.834562i	$-0.314279\pi$
$997$	−14.1235	−	24.4625i	−0.447294	−	0.774737i	−0.998209	+	0.0598251i	$0.980946\pi$
$998$	−3.84352	−	6.65717i	−0.121665	−	0.210729i
$999$	−1.76162	+	3.05121i	−0.0557352	+	0.0965361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.i.226.3	yes	8
5.2	odd	4		525.2.r.h.499.5		16
5.3	odd	4		525.2.r.h.499.4		16
5.4	even	2		525.2.i.j.226.2	yes	8
7.2	even	3		3675.2.a.bw.1.2		4
7.4	even	3	inner	525.2.i.i.151.3	✓	8
7.5	odd	6		3675.2.a.bx.1.2		4
35.4	even	6		525.2.i.j.151.2	yes	8
35.9	even	6		3675.2.a.br.1.3		4
35.18	odd	12		525.2.r.h.424.5		16
35.19	odd	6		3675.2.a.bq.1.3		4
35.32	odd	12		525.2.r.h.424.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.3	✓	8	7.4	even	3	inner
525.2.i.i.226.3	yes	8	1.1	even	1	trivial
525.2.i.j.151.2	yes	8	35.4	even	6
525.2.i.j.226.2	yes	8	5.4	even	2
525.2.r.h.424.4		16	35.32	odd	12
525.2.r.h.424.5		16	35.18	odd	12
525.2.r.h.499.4		16	5.3	odd	4
525.2.r.h.499.5		16	5.2	odd	4
3675.2.a.bq.1.3		4	35.19	odd	6
3675.2.a.br.1.3		4	35.9	even	6
3675.2.a.bw.1.2		4	7.2	even	3
3675.2.a.bx.1.2		4	7.5	odd	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247087 - 0.427967i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.87790 + 1.86373i) q^{7} +1.85601 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.247087 - 0.427967i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.877896 + 1.52056i) q^{4} +0.494173 q^{6} +(1.87790 + 1.86373i) q^{7} +1.85601 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.66927 - 4.62330i) q^{11} +(-0.877896 + 1.52056i) q^{12} +5.09433 q^{13} +(1.26162 - 0.343173i) q^{14} +(-1.29720 + 2.24681i) q^{16} +(-0.175093 - 0.303270i) q^{17} +(0.247087 + 0.427967i) q^{18} +(-1.38372 + 2.39668i) q^{19} +(-0.675093 + 2.55817i) q^{21} -2.63816 q^{22} +(-3.75579 + 6.50522i) q^{23} +(0.928006 + 1.60735i) q^{24} +(1.25874 - 2.18020i) q^{26} -1.00000 q^{27} +(-1.18532 + 4.49162i) q^{28} +4.00000 q^{29} +(-3.05882 - 5.29802i) q^{31} +(2.49705 + 4.32502i) q^{32} +(2.66927 - 4.62330i) q^{33} -0.173053 q^{34} -1.75579 q^{36} +(1.76162 - 3.05121i) q^{37} +(0.683799 + 1.18437i) q^{38} +(2.54716 + 4.41182i) q^{39} -7.86177 q^{41} +(0.928006 + 0.921008i) q^{42} +1.41726 q^{43} +(4.68668 - 8.11757i) q^{44} +(1.85601 + 3.21471i) q^{46} +(4.42506 - 7.66443i) q^{47} -2.59439 q^{48} +(0.0529894 + 6.99980i) q^{49} +(0.175093 - 0.303270i) q^{51} +(4.47229 + 7.74623i) q^{52} +(3.16344 + 5.47924i) q^{53} +(-0.247087 + 0.427967i) q^{54} +(3.48540 + 3.45911i) q^{56} -2.76745 q^{57} +(0.988347 - 1.71187i) q^{58} +(-6.42506 - 11.1285i) q^{59} +(2.50000 - 4.33013i) q^{61} -3.02317 q^{62} +(-2.55299 + 0.694439i) q^{63} -2.72083 q^{64} +(-1.31908 - 2.28471i) q^{66} +(-1.87790 - 3.25261i) q^{67} +(0.307427 - 0.532479i) q^{68} -7.51159 q^{69} +15.4883 q^{71} +(-0.928006 + 1.60735i) q^{72} +(-3.83853 - 6.64853i) q^{73} +(-0.870545 - 1.50783i) q^{74} -4.85906 q^{76} +(3.60401 - 13.6569i) q^{77} +2.51748 q^{78} +(-1.18092 + 2.04541i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.94254 + 3.36458i) q^{82} -6.87342 q^{83} +(-4.48252 + 1.21929i) q^{84} +(0.350186 - 0.606540i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-4.95419 - 8.58091i) q^{88} +(2.17509 - 3.76737i) q^{89} +(9.56662 + 9.49447i) q^{91} -13.1888 q^{92} +(3.05882 - 5.29802i) q^{93} +(-2.18675 - 3.78756i) q^{94} +(-2.49705 + 4.32502i) q^{96} +5.49993 q^{97} +(3.00877 + 1.70688i) q^{98} +5.33853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9	\( 8 q - q^{2} + 4 q^{3} - 7 q^{4} - 2 q^{6} + q^{7} + 6 q^{8} - 4 q^{9} - 8 q^{11} + 7 q^{12} - 14 q^{13} - 12 q^{14} - 17 q^{16} + 6 q^{17} - q^{18} - 3 q^{19} + 2 q^{21} - 24 q^{22} - 2 q^{23} + 3 q^{24} + 19 q^{26} - 8 q^{27} + 15 q^{28} + 32 q^{29} - 9 q^{31} - 17 q^{32} + 8 q^{33} + 28 q^{34} + 14 q^{36} - 8 q^{37} - 27 q^{38} - 7 q^{39} + 8 q^{41} + 3 q^{42} + 10 q^{43} - 26 q^{44} + 6 q^{46} - 6 q^{47} - 34 q^{48} - 21 q^{49} - 6 q^{51} + 35 q^{52} + 6 q^{53} + q^{54} - 21 q^{56} - 6 q^{57} - 4 q^{58} - 10 q^{59} + 20 q^{61} + 88 q^{62} + q^{63} + 42 q^{64} - 12 q^{66} - q^{67} - 8 q^{68} - 4 q^{69} + 44 q^{71} - 3 q^{72} - 4 q^{73} + 21 q^{74} - 46 q^{76} + 32 q^{77} + 38 q^{78} - 8 q^{79} - 4 q^{81} + 8 q^{82} + 4 q^{83} - 18 q^{84} - 12 q^{86} + 16 q^{87} - 28 q^{88} + 10 q^{89} + 21 q^{91} - 132 q^{92} + 9 q^{93} - 22 q^{94} + 17 q^{96} - 24 q^{97} + 67 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 - 7 * q^4 - 2 * q^6 + q^7 + 6 * q^8 - 4 * q^9 - 8 * q^11 + 7 * q^12 - 14 * q^13 - 12 * q^14 - 17 * q^16 + 6 * q^17 - q^18 - 3 * q^19 + 2 * q^21 - 24 * q^22 - 2 * q^23 + 3 * q^24 + 19 * q^26 - 8 * q^27 + 15 * q^28 + 32 * q^29 - 9 * q^31 - 17 * q^32 + 8 * q^33 + 28 * q^34 + 14 * q^36 - 8 * q^37 - 27 * q^38 - 7 * q^39 + 8 * q^41 + 3 * q^42 + 10 * q^43 - 26 * q^44 + 6 * q^46 - 6 * q^47 - 34 * q^48 - 21 * q^49 - 6 * q^51 + 35 * q^52 + 6 * q^53 + q^54 - 21 * q^56 - 6 * q^57 - 4 * q^58 - 10 * q^59 + 20 * q^61 + 88 * q^62 + q^63 + 42 * q^64 - 12 * q^66 - q^67 - 8 * q^68 - 4 * q^69 + 44 * q^71 - 3 * q^72 - 4 * q^73 + 21 * q^74 - 46 * q^76 + 32 * q^77 + 38 * q^78 - 8 * q^79 - 4 * q^81 + 8 * q^82 + 4 * q^83 - 18 * q^84 - 12 * q^86 + 16 * q^87 - 28 * q^88 + 10 * q^89 + 21 * q^91 - 132 * q^92 + 9 * q^93 - 22 * q^94 + 17 * q^96 - 24 * q^97 + 67 * q^98 + 16 * q^99

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