LMFDB - Embedded newform 525.2.i.i.151.3

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			151.3
Root			$-0.247087 - 0.427967i$ of defining polynomial
Character	$\chi$	$=$	525.151
Dual form			525.2.i.i.226.3

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.940063	−	0.341000i	$-0.110766\pi$
$2$	0.247087	+	0.427967i	0.174717	+	0.302618i	−0.765347	+	0.643618i	$0.777432\pi$
$3$	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	0.111602	+	0.993753i	$0.464402\pi$
$11$	−2.66927	+	4.62330i	−0.804814	+	1.39398i	−0.916416	+	0.400226i	$0.868932\pi$
$12$	−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	−0.886477	−	0.462772i	$-0.846855\pi$
$17$	−0.175093	+	0.303270i	−0.0424663	+	0.0735538i	0.844011	+	0.536326i	$0.180188\pi$
$18$	0.247087	−	0.427967i	0.0582389	−	0.100873i
$19$	−1.38372	−	2.39668i	−0.317448	−	0.549836i	0.662507	−	0.749056i	$-0.269493\pi$
$19$	−1.38372	−	2.39668i	−0.317448	−	0.549836i	−0.979955	+	0.199220i	$0.936159\pi$
$20$		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	−0.930106	−	0.367292i	$-0.880285\pi$
$23$	−3.75579	−	6.50522i	−0.783137	−	1.35643i	0.146969	−	0.989141i	$-0.453048\pi$
$24$	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	0.448938	+	0.893563i	$0.351803\pi$
$31$	−3.05882	+	5.29802i	−0.549380	+	0.951553i	−0.998317	+	0.0579902i	$0.981531\pi$
$32$	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	0.973716	−	0.227764i	$-0.0731416\pi$
$37$	1.76162	+	3.05121i	0.289608	+	0.501617i	−0.684108	+	0.729381i	$0.739808\pi$
$38$	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	0.984195	+	0.177089i	$0.0566681\pi$
$47$	4.42506	+	7.66443i	0.645461	+	1.11797i	−0.338734	+	0.940882i	$0.609999\pi$
$48$	−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	−0.562725	−	0.826644i	$-0.690247\pi$
$53$	3.16344	−	5.47924i	0.434532	−	0.752631i	0.997257	+	0.0740126i	$0.0235805\pi$
$54$	−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	0.0563553	+	0.998411i	$0.482052\pi$
$59$	−6.42506	+	11.1285i	−0.836471	+	1.44881i	−0.892827	+	0.450400i	$0.851281\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$	−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	−0.957637	−	0.287979i	$-0.907017\pi$
$67$	−1.87790	+	3.25261i	−0.229422	+	0.397370i	0.728215	+	0.685348i	$0.240350\pi$
$68$	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	−0.998338	−	0.0576229i	$-0.981648\pi$
$73$	−3.83853	+	6.64853i	−0.449266	+	0.778152i	0.549072	+	0.835775i	$0.314981\pi$
$74$	−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	0.791916	−	0.610631i	$-0.209084\pi$
$79$	−1.18092	−	2.04541i	−0.132864	−	0.230127i	−0.924779	+	0.380504i	$0.875751\pi$
$80$		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	0.957973	−	0.286859i	$-0.0926111\pi$
$89$	2.17509	+	3.76737i	0.230559	+	0.399341i	−0.727413	+	0.686199i	$0.759278\pi$
$90$		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	−0.904144	−	0.427228i	$-0.859490\pi$
$101$	−0.824907	+	1.42878i	−0.0820813	+	0.142169i	0.822062	+	0.569397i	$0.192823\pi$
$102$	−0.0865263	+	0.149868i	−0.00856738	+	0.0148391i
$103$	5.08070	+	8.80003i	0.500616	+	0.867093i	1.00000		0.000711688i	$0.000226537\pi$
$103$	5.08070	+	8.80003i	0.500616	+	0.867093i	−0.499384	+	0.866381i	$0.666440\pi$
$104$	9.45513			0.927152
$105$		0			0
$106$	3.12658			0.303680
$107$	2.68092	+	4.64349i	0.259174	+	0.448903i	0.966021	−	0.258464i	$-0.0832163\pi$
$107$	2.68092	+	4.64349i	0.259174	+	0.448903i	−0.706847	+	0.707367i	$0.749883\pi$
$108$	−0.877896	+	1.52056i	−0.0844756	+	0.146316i
$109$	0.0529894	−	0.0917803i	0.00507546	−	0.00879096i	−0.863477	−	0.504389i	$-0.831718\pi$
$109$	0.0529894	−	0.0917803i	0.00507546	−	0.00879096i	0.868552	+	0.495598i	$0.165051\pi$
$110$		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	0.992996	−	0.118148i	$-0.0376956\pi$
$131$	4.51159	+	7.81430i	0.394179	+	0.682738i	−0.598817	+	0.800886i	$0.704362\pi$
$132$	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	−0.847650	−	0.530555i	$-0.821984\pi$
$137$	0.417260	−	0.722715i	0.0356489	−	0.0617457i	0.883299	+	0.468809i	$0.155317\pi$
$138$	−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	−0.923145	−	0.384453i	$-0.874390\pi$
$149$	−9.69833	−	16.7980i	−0.794518	−	1.37615i	0.128626	−	0.991693i	$-0.458943\pi$
$150$		0			0
$151$	−9.26359	+	16.0450i	−0.753860	+	1.30572i	0.192078	+	0.981380i	$0.438477\pi$
$151$	−9.26359	+	16.0450i	−0.753860	+	1.30572i	−0.945939	+	0.324345i	$0.894856\pi$
$152$	−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	−0.754232	−	0.656608i	$-0.771991\pi$
$157$	2.39978	−	4.15654i	0.191523	−	0.331728i	0.945755	+	0.324880i	$0.105324\pi$
$158$	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	0.849378	−	0.527785i	$-0.176977\pi$
$163$	−0.413474	−	0.716157i	−0.0323858	−	0.0560938i	−0.881764	+	0.471691i	$0.843644\pi$
$164$	−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	0.999784	−	0.0207644i	$-0.00660998\pi$
$173$	6.33853	+	10.9787i	0.481910	+	0.834692i	−0.517875	+	0.855456i	$0.673277\pi$
$174$	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	−0.999898	−	0.0142942i	$-0.995450\pi$
$179$	−6.52324	+	11.2986i	−0.487570	+	0.844496i	0.512328	+	0.858790i	$0.328783\pi$
$180$		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	0.640614	−	0.767863i	$-0.278680\pi$
$191$	−4.76359	−	8.25078i	−0.344681	−	0.597006i	−0.985296	+	0.170857i	$0.945346\pi$
$192$	−1.36042	+	2.35631i	−0.0981796	+	0.170052i
$193$	7.55299	−	13.0822i	0.543676	−	0.941675i	−0.455013	−	0.890485i	$-0.650365\pi$
$193$	7.55299	−	13.0822i	0.543676	−	0.941675i	0.998689	−	0.0511897i	$-0.0163013\pi$
$194$	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	0.0593348	−	0.998238i	$-0.481102\pi$
$199$	12.6138	−	21.8477i	0.894167	−	1.54874i	0.834832	−	0.550505i	$-0.185565\pi$
$200$		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	−0.529322	−	0.848421i	$-0.677554\pi$
$227$	7.08267	−	12.2675i	0.470093	−	0.814226i	0.999415	+	0.0341954i	$0.0108869\pi$
$228$	−2.42953	+	4.20807i	−0.160900	+	0.278686i
$229$	8.90311	+	15.4206i	0.588334	+	1.01902i	0.994451	+	0.105203i	$0.0335493\pi$
$229$	8.90311	+	15.4206i	0.588334	+	1.01902i	−0.406117	+	0.913821i	$0.633117\pi$
$230$		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	0.551082	−	0.834451i	$-0.314215\pi$
$233$	−6.82491	−	11.8211i	−0.447115	−	0.774425i	−0.998197	+	0.0600258i	$0.980882\pi$
$234$	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	−0.117226	+	0.993105i	$0.537400\pi$
$241$	−14.2616	+	24.7017i	−0.918667	+	1.59118i	−0.801442	+	0.598073i	$0.795933\pi$
$242$	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	−0.929574	−	0.368637i	$-0.879825\pi$
$257$	−12.5690	−	21.7702i	−0.784036	−	1.35799i	0.145538	−	0.989353i	$-0.453509\pi$
$258$	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	−0.577723	−	0.816233i	$-0.696059\pi$
$263$	6.77910	−	11.7417i	0.418017	−	0.724027i	0.995740	+	0.0922061i	$0.0293919\pi$
$264$	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	−0.694985	−	0.719024i	$-0.744589\pi$
$269$	4.51363	−	7.81783i	0.275201	−	0.476661i	0.970186	+	0.242363i	$0.0779224\pi$
$270$		0			0
$271$	−2.38819	−	4.13647i	−0.145072	−	0.251273i	0.784328	−	0.620347i	$-0.213008\pi$
$271$	−2.38819	−	4.13647i	−0.145072	−	0.251273i	−0.929400	+	0.369074i	$0.879675\pi$
$272$	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	−0.892757	−	0.450539i	$-0.851232\pi$
$277$	−0.935357	+	1.62009i	−0.0562002	+	0.0973416i	0.836557	+	0.547881i	$0.184565\pi$
$278$	−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	−0.242861	−	0.970061i	$-0.578086\pi$
$283$	12.0899	−	20.9402i	0.718667	−	1.24477i	0.961528	−	0.274707i	$-0.0885808\pi$
$284$	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	−0.828962	−	0.559305i	$-0.811068\pi$
$311$	1.23255	−	2.13485i	0.0698917	−	0.121056i	0.898853	+	0.438249i	$0.144401\pi$
$312$	4.72757	−	8.18839i	0.267646	−	0.463576i
$313$	0.237763	+	0.411818i	0.0134392	+	0.0232773i	0.872667	−	0.488316i	$-0.162389\pi$
$313$	0.237763	+	0.411818i	0.0134392	+	0.0232773i	−0.859228	+	0.511594i	$0.829055\pi$
$314$	2.37181			0.133849
$315$		0			0
$316$	−4.14690			−0.233281
$317$	−7.14975	−	12.3837i	−0.401570	−	0.695539i	0.592346	−	0.805684i	$-0.298202\pi$
$317$	−7.14975	−	12.3837i	−0.401570	−	0.695539i	−0.993916	+	0.110145i	$0.964869\pi$
$318$	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	0.998998	+	0.0447537i	$0.0142503\pi$
$331$	9.79273	+	16.9615i	0.538257	+	0.932288i	−0.460741	+	0.887535i	$0.652416\pi$
$332$	−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	−0.707999	−	0.706214i	$-0.750402\pi$
$347$	4.79855	−	8.31134i	0.257600	−	0.446176i	0.965598	+	0.260038i	$0.0837351\pi$
$348$	−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	0.228180	+	0.973619i	$0.426722\pi$
$353$	−13.6983	+	23.7262i	−0.729089	+	1.26282i	−0.957269	+	0.289200i	$0.906611\pi$
$354$	−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	−0.976687	−	0.214668i	$-0.931133\pi$
$359$	−12.7752	−	22.1274i	−0.674252	−	1.16784i	0.302435	−	0.953170i	$-0.402200\pi$
$360$		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	−0.414048	−	0.910255i	$-0.635885\pi$
$367$	11.1357	−	19.2876i	0.581280	−	1.00681i	0.995328	−	0.0965519i	$-0.0307814\pi$
$368$	−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	0.926389	−	0.376569i	$-0.122896\pi$
$373$	2.64738	+	4.58540i	0.137076	+	0.237423i	−0.789312	+	0.613992i	$0.789563\pi$
$374$	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	−0.998117	−	0.0613379i	$-0.980463\pi$
$383$	−10.8064	−	18.7171i	−0.552179	−	0.956402i	0.445938	−	0.895064i	$-0.352870\pi$
$384$	−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	−0.655670	−	0.755048i	$-0.727614\pi$
$389$	6.43082	−	11.1385i	0.326055	−	0.564745i	0.981725	+	0.190303i	$0.0609471\pi$
$390$		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	0.764809	−	0.644257i	$-0.222833\pi$
$397$	−3.49757	−	6.05797i	−0.175538	−	0.304041i	−0.940347	+	0.340216i	$0.889500\pi$
$398$	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	0.902791	−	0.430079i	$-0.141514\pi$
$401$	1.58070	+	2.73785i	0.0789364	+	0.136722i	−0.823855	+	0.566801i	$0.808181\pi$
$402$	−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	−0.895219	−	0.445626i	$-0.852981\pi$
$409$	−1.24753	+	2.16079i	−0.0616866	+	0.106844i	0.833533	+	0.552470i	$0.186315\pi$
$410$		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	−0.984753	−	0.173961i	$-0.944343\pi$
$431$	−7.09433	+	12.2877i	−0.341722	+	0.591879i	0.643031	+	0.765840i	$0.277677\pi$
$432$	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	0.889709	−	0.456528i	$-0.150907\pi$
$439$	1.03693	+	1.79602i	0.0494901	+	0.0857193i	−0.840219	+	0.542247i	$0.817574\pi$
$440$		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	−0.941805	−	0.336159i	$-0.890872\pi$
$443$	−16.0388	−	27.7800i	−0.762025	−	1.31987i	0.179780	−	0.983707i	$-0.442461\pi$
$444$	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	0.891353	−	0.453310i	$-0.149757\pi$
$457$	1.13511	+	1.96607i	0.0530983	+	0.0919689i	−0.838255	+	0.545279i	$0.816424\pi$
$458$	−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	−0.842301	−	0.539008i	$-0.818799\pi$
$467$	−19.1887	−	33.2357i	−0.887945	−	1.53797i	−0.0456441	−	0.998958i	$-0.514534\pi$
$468$	−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	−0.00600999	+	0.999982i	$0.501913\pi$
$479$	−19.0193	+	32.9424i	−0.869015	+	1.50518i	−0.863005	+	0.505196i	$0.831420\pi$
$480$		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	0.488248	+	0.872705i	$0.337636\pi$
$487$	−11.2914	+	19.5572i	−0.511661	+	0.886223i	−0.999909	+	0.0135175i	$0.995697\pi$
$488$	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	0.985926	−	0.167185i	$-0.0534676\pi$
$499$	7.77768	+	13.4713i	0.348177	+	0.603060i	−0.637749	+	0.770244i	$0.720134\pi$
$500$		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	0.841966	−	0.539531i	$-0.181398\pi$
$509$	−1.04377	−	1.80786i	−0.0462642	−	0.0801319i	−0.888230	+	0.459399i	$0.848065\pi$
$510$		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	−0.113081	−	0.993586i	$-0.536072\pi$
$521$	18.3501	−	31.7832i	0.803930	−	1.39245i	0.917011	−	0.398862i	$-0.130595\pi$
$522$	0.988347	−	1.71187i	0.0432588	−	0.0749264i
$523$	−6.31454	−	10.9371i	−0.276116	−	0.478246i	0.694300	−	0.719685i	$-0.255714\pi$
$523$	−6.31454	−	10.9371i	−0.276116	−	0.478246i	−0.970416	+	0.241439i	$0.922381\pi$
$524$	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	−0.894066	−	0.447935i	$-0.852160\pi$
$541$	−19.4206	−	33.6374i	−0.834956	−	1.44619i	0.0591098	−	0.998251i	$-0.481174\pi$
$542$	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	−0.806107	−	0.591770i	$-0.798429\pi$
$557$	2.58274	−	4.47344i	0.109434	−	0.189546i	0.915541	+	0.402224i	$0.131763\pi$
$558$	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	−0.967908	−	0.251305i	$-0.919140\pi$
$563$	−6.31908	+	10.9450i	−0.266317	+	0.461275i	0.701590	+	0.712580i	$0.252474\pi$
$564$	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	0.943375	−	0.331727i	$-0.107631\pi$
$569$	4.39870	+	7.61878i	0.184403	+	0.319396i	−0.758972	+	0.651123i	$0.774298\pi$
$570$		0			0
$571$	19.9516	−	34.5572i	0.834950	−	1.44618i	−0.0591220	−	0.998251i	$-0.518830\pi$
$571$	19.9516	−	34.5572i	0.834950	−	1.44618i	0.894072	−	0.447924i	$-0.147837\pi$
$572$	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	−0.892916	−	0.450224i	$-0.851344\pi$
$577$	−1.35844	+	2.35289i	−0.0565528	+	0.0979523i	0.836363	+	0.548176i	$0.184678\pi$
$578$	−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	0.953234	−	0.302233i	$-0.0977322\pi$
$593$	5.23255	+	9.06305i	0.214875	+	0.372175i	−0.738359	+	0.674408i	$0.764399\pi$
$594$	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	−0.947523	−	0.319686i	$-0.896422\pi$
$599$	−4.81915	+	8.34701i	−0.196905	+	0.341050i	0.750618	+	0.660736i	$0.229756\pi$
$600$		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	0.920691	+	0.390292i	$0.127626\pi$
$607$	19.6692	+	34.0681i	0.798348	+	1.38278i	−0.122343	+	0.992488i	$0.539041\pi$
$608$	−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	−0.598331	−	0.801249i	$-0.704169\pi$
$613$	9.77320	−	16.9277i	0.394736	−	0.683703i	0.993067	+	0.117546i	$0.0375027\pi$
$614$	−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	−0.939125	−	0.343577i	$-0.888362\pi$
$619$	−4.27972	+	7.41269i	−0.172016	+	0.297941i	0.767108	+	0.641518i	$0.221695\pi$
$620$		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	−0.980808	−	0.194978i	$-0.937536\pi$
$641$	−8.14094	+	14.1005i	−0.321548	+	0.556937i	0.659260	+	0.751915i	$0.270870\pi$
$642$	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	−0.0571903	+	0.998363i	$0.518214\pi$
$647$	−22.7197	+	39.3517i	−0.893203	+	1.54707i	−0.836013	+	0.548710i	$0.815119\pi$
$648$	−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	0.615394	−	0.788220i	$-0.288997\pi$
$653$	−9.58070	−	16.5943i	−0.374922	−	0.649384i	−0.990315	+	0.138836i	$0.955664\pi$
$654$	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	−0.764174	−	0.645010i	$-0.776853\pi$
$661$	4.53801	−	7.86006i	0.176508	−	0.305721i	0.940682	+	0.339289i	$0.110186\pi$
$662$	−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	0.882765	−	0.469814i	$-0.155679\pi$
$677$	0.897966	+	1.55532i	0.0345116	+	0.0597759i	−0.848254	+	0.529590i	$0.822346\pi$
$678$	−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	−0.0324893	−	0.999472i	$-0.510343\pi$
$683$	22.1965	−	38.4454i	0.849324	−	1.47107i	0.881813	−	0.471599i	$-0.156323\pi$
$684$	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	−0.904521	−	0.426430i	$-0.859771\pi$
$691$	−21.5962	−	37.4058i	−0.821559	−	1.42298i	0.0829614	−	0.996553i	$-0.473562\pi$
$692$	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	0.643710	−	0.765270i	$-0.277394\pi$
$709$	−9.07685	−	15.7216i	−0.340888	−	0.590435i	−0.984598	+	0.174834i	$0.944061\pi$
$710$		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	0.981639	+	0.190747i	$0.0610910\pi$
$719$	17.5904	+	30.4675i	0.656011	+	1.13624i	−0.325628	+	0.945498i	$0.605576\pi$
$720$		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	0.955992	−	0.293393i	$-0.0947844\pi$
$733$	6.06214	+	10.4999i	0.223910	+	0.387824i	−0.732082	+	0.681217i	$0.761451\pi$
$734$	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	−0.386562	−	0.922263i	$-0.626338\pi$
$739$	16.4581	−	28.5063i	0.605422	−	1.04862i	0.991985	−	0.126359i	$-0.0403291\pi$
$740$		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	0.998371	+	0.0570610i	$0.0181729\pi$
$751$	15.0341	+	26.0398i	0.548602	+	0.950206i	−0.449769	+	0.893145i	$0.648494\pi$
$752$	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	0.926704	−	0.375792i	$-0.122629\pi$
$761$	3.80431	+	6.58926i	0.137906	+	0.238860i	−0.788798	+	0.614653i	$0.789296\pi$
$762$	−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	−0.512517	−	0.858677i	$-0.671287\pi$
$773$	13.5505	−	23.4701i	0.487377	−	0.844162i	0.999895	+	0.0145147i	$0.00462032\pi$
$774$	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	−0.378641	−	0.925543i	$-0.623609\pi$
$787$	17.1750	−	29.7480i	0.612224	−	1.06040i	0.990865	−	0.134859i	$-0.0430581\pi$
$788$	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	−0.780948	−	0.624597i	$-0.785263\pi$
$809$	4.27903	−	7.41150i	0.150443	−	0.260574i	0.931390	+	0.364022i	$0.118597\pi$
$810$		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	0.967262	−	0.253782i	$-0.0816745\pi$
$821$	7.56010	+	13.0945i	0.263849	+	0.457001i	−0.703412	+	0.710782i	$0.748341\pi$
$822$	0.206199	−	0.357147i	0.00719201	−	0.0124569i
$823$	12.3522	−	21.3946i	0.430569	−	0.745768i	−0.566353	−	0.824163i	$-0.691646\pi$
$823$	12.3522	−	21.3946i	0.430569	−	0.745768i	0.996922	+	0.0783949i	$0.0249795\pi$
$824$	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	−0.858377	−	0.513019i	$-0.828527\pi$
$829$	0.434740	−	0.752992i	0.0150991	−	0.0261525i	0.873476	+	0.486867i	$0.161860\pi$
$830$		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	−0.995764	−	0.0919463i	$-0.970691\pi$
$857$	−12.2442	+	21.2076i	−0.418254	+	0.724437i	0.577510	+	0.816384i	$0.304025\pi$
$858$	−6.71982	+	11.6391i	−0.229411	+	0.397352i
$859$	−4.79970	−	8.31332i	−0.163764	−	0.283647i	0.772452	−	0.635073i	$-0.219030\pi$
$859$	−4.79970	−	8.31332i	−0.163764	−	0.283647i	−0.936215	+	0.351426i	$0.885697\pi$
$860$		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	0.999997	+	0.00249807i	$0.000795160\pi$
$863$	14.7519	+	25.5511i	0.502162	+	0.869770i	−0.497835	+	0.867272i	$0.665872\pi$
$864$	−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	0.907348	−	0.420381i	$-0.138104\pi$
$877$	2.65383	+	4.59656i	0.0896134	+	0.155215i	−0.817734	+	0.575596i	$0.804770\pi$
$878$	−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	0.791183	−	0.611580i	$-0.209466\pi$
$887$	−3.99243	−	6.91509i	−0.134053	−	0.232186i	−0.925235	+	0.379394i	$0.876132\pi$
$888$	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	−0.886271	−	0.463167i	$-0.846713\pi$
$907$	−1.26554	+	2.19198i	−0.0420216	+	0.0727836i	0.844250	+	0.535950i	$0.180047\pi$
$908$	−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	−0.937576	−	0.347780i	$-0.886935\pi$
$919$	−23.3418	−	40.4292i	−0.769975	−	1.33364i	0.167601	−	0.985855i	$-0.446398\pi$
$920$		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	0.974431	−	0.224687i	$-0.0721361\pi$
$929$	8.91923	+	15.4486i	0.292631	+	0.506851i	−0.681800	+	0.731538i	$0.738803\pi$
$930$		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	−0.194581	−	0.980886i	$-0.562335\pi$
$941$	23.0737	−	39.9649i	0.752182	−	1.30282i	0.946763	−	0.321931i	$-0.104332\pi$
$942$	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	0.998350	−	0.0574248i	$-0.0182889\pi$
$947$	13.8309	+	23.9558i	0.449444	+	0.778459i	−0.548906	+	0.835884i	$0.684956\pi$
$948$	−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	0.873556	−	0.486723i	$-0.161808\pi$
$971$	0.475617	+	0.823793i	0.0152633	+	0.0264368i	−0.858293	+	0.513160i	$0.828475\pi$
$972$	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	−0.620640	−	0.784095i	$-0.713127\pi$
$977$	11.5253	−	19.9624i	0.368726	−	0.638653i	0.989367	+	0.145443i	$0.0464606\pi$
$978$	−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	0.492274	+	0.870441i	$0.336166\pi$
$983$	−15.9174	+	27.5698i	−0.507687	+	0.879339i	−0.999960	+	0.00889883i	$0.997167\pi$
$984$	−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	−0.794443	−	0.607339i	$-0.792237\pi$
$991$	4.05306	−	7.02010i	0.128750	−	0.223001i	0.923192	+	0.384338i	$0.125570\pi$
$992$	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	−0.998209	−	0.0598251i	$-0.980946\pi$
$997$	−14.1235	+	24.4625i	−0.447294	+	0.774737i	0.550914	+	0.834562i	$0.314279\pi$
$998$	−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.151.3	✓	8
5.2	odd	4		525.2.r.h.424.4		16
5.3	odd	4		525.2.r.h.424.5		16
5.4	even	2		525.2.i.j.151.2	yes	8
7.2	even	3	inner	525.2.i.i.226.3	yes	8
7.3	odd	6		3675.2.a.bx.1.2		4
7.4	even	3		3675.2.a.bw.1.2		4
35.2	odd	12		525.2.r.h.499.5		16
35.4	even	6		3675.2.a.br.1.3		4
35.9	even	6		525.2.i.j.226.2	yes	8
35.23	odd	12		525.2.r.h.499.4		16
35.24	odd	6		3675.2.a.bq.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.3	✓	8	1.1	even	1	trivial
525.2.i.i.226.3	yes	8	7.2	even	3	inner
525.2.i.j.151.2	yes	8	5.4	even	2
525.2.i.j.226.2	yes	8	35.9	even	6
525.2.r.h.424.4		16	5.2	odd	4
525.2.r.h.424.5		16	5.3	odd	4
525.2.r.h.499.4		16	35.23	odd	12
525.2.r.h.499.5		16	35.2	odd	12
3675.2.a.bq.1.3		4	35.24	odd	6
3675.2.a.br.1.3		4	35.4	even	6
3675.2.a.bw.1.2		4	7.4	even	3
3675.2.a.bx.1.2		4	7.3	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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