LMFDB - Embedded newform 525.2.r.h.499.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 15x^{14} + 158x^{12} - 843x^{10} + 3258x^{8} - 4947x^{6} + 5489x^{4} - 1296x^{2} + 256 $ x^16 - 15x^14 + 158x^12 - 843x^10 + 3258x^8 - 4947x^6 + 5489x^4 - 1296*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.5
Root			$0.427967 + 0.247087i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.h.424.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.427967 + 0.247087i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.877896 - 1.52056i) q^{4} +0.494173 q^{6} +(-1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.427967 + 0.247087i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.877896 - 1.52056i) q^{4} +0.494173 q^{6} +(-1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.66927 - 4.62330i) q^{11} +(-1.52056 - 0.877896i) q^{12} -5.09433i q^{13} +(-1.26162 + 0.343173i) q^{14} +(-1.29720 + 2.24681i) q^{16} +(0.303270 - 0.175093i) q^{17} +(0.427967 - 0.247087i) q^{18} +(1.38372 - 2.39668i) q^{19} +(-0.675093 + 2.55817i) q^{21} -2.63816i q^{22} +(6.50522 + 3.75579i) q^{23} +(-0.928006 - 1.60735i) q^{24} +(1.25874 - 2.18020i) q^{26} -1.00000i q^{27} +(4.49162 + 1.18532i) q^{28} -4.00000 q^{29} +(-3.05882 - 5.29802i) q^{31} +(-4.32502 + 2.49705i) q^{32} +(-4.62330 - 2.66927i) q^{33} +0.173053 q^{34} -1.75579 q^{36} +(3.05121 + 1.76162i) q^{37} +(1.18437 - 0.683799i) q^{38} +(-2.54716 - 4.41182i) q^{39} -7.86177 q^{41} +(-0.921008 + 0.928006i) q^{42} -1.41726i q^{43} +(-4.68668 + 8.11757i) q^{44} +(1.85601 + 3.21471i) q^{46} +(7.66443 + 4.42506i) q^{47} +2.59439i q^{48} +(-0.0529894 - 6.99980i) q^{49} +(0.175093 - 0.303270i) q^{51} +(-7.74623 + 4.47229i) q^{52} +(5.47924 - 3.16344i) q^{53} +(0.247087 - 0.427967i) q^{54} +(3.48540 + 3.45911i) q^{56} -2.76745i q^{57} +(-1.71187 - 0.988347i) q^{58} +(6.42506 + 11.1285i) q^{59} +(2.50000 - 4.33013i) q^{61} -3.02317i q^{62} +(0.694439 + 2.55299i) q^{63} +2.72083 q^{64} +(-1.31908 - 2.28471i) q^{66} +(3.25261 - 1.87790i) q^{67} +(-0.532479 - 0.307427i) q^{68} +7.51159 q^{69} +15.4883 q^{71} +(-1.60735 - 0.928006i) q^{72} +(-6.64853 + 3.83853i) q^{73} +(0.870545 + 1.50783i) q^{74} -4.85906 q^{76} +(13.6569 + 3.60401i) q^{77} -2.51748i q^{78} +(1.18092 - 2.04541i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.36458 - 1.94254i) q^{82} +6.87342i q^{83} +(4.48252 - 1.21929i) q^{84} +(0.350186 - 0.606540i) q^{86} +(-3.46410 + 2.00000i) q^{87} +(-8.58091 + 4.95419i) q^{88} +(-2.17509 + 3.76737i) q^{89} +(9.56662 + 9.49447i) q^{91} -13.1888i q^{92} +(-5.29802 - 3.05882i) q^{93} +(2.18675 + 3.78756i) q^{94} +(-2.49705 + 4.32502i) q^{96} +5.49993i q^{97} +(1.70688 - 3.00877i) q^{98} -5.33853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	$ 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * 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 $

$2$	0.427967	+	0.247087i	0.302618	+	0.174717i	0.643618	−	0.765347i	$-0.277432\pi$
$2$	0.427967	+	0.247087i	0.302618	+	0.174717i	−0.341000	+	0.940063i	$0.610766\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.877896	−	1.52056i	−0.438948	−	0.760281i
$5$		0			0
$5$		0			0
$6$	0.494173			0.201745
$7$	−1.86373	+	1.87790i	−0.704425	+	0.709778i
$7$	−1.86373	+	1.87790i	−0.704425	+	0.709778i
$8$		−	1.85601i		−	0.656200i
$9$	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	$-0.464402\pi$
$12$	−1.52056	−	0.877896i	−0.438948	−	0.253427i
$13$		−	5.09433i		−	1.41291i	−0.707757	−	0.706456i	$-0.750293\pi$
$13$		−	5.09433i		−	1.41291i	0.707757	−	0.706456i	$-0.249707\pi$
$14$	−1.26162	+	0.343173i	−0.337182	+	0.0917169i
$15$		0			0
$16$	−1.29720	+	2.24681i	−0.324299	+	0.561703i
$17$	0.303270	−	0.175093i	0.0735538	−	0.0424663i	−0.462772	−	0.886477i	$-0.653145\pi$
$17$	0.303270	−	0.175093i	0.0735538	−	0.0424663i	0.536326	+	0.844011i	$0.319812\pi$
$18$	0.427967	−	0.247087i	0.100873	−	0.0582389i
$19$	1.38372	−	2.39668i	0.317448	−	0.549836i	−0.662507	−	0.749056i	$-0.730507\pi$
$19$	1.38372	−	2.39668i	0.317448	−	0.549836i	0.979955	+	0.199220i	$0.0638408\pi$
$20$		0			0
$21$	−0.675093	+	2.55817i	−0.147317	+	0.558239i
$22$		−	2.63816i		−	0.562458i
$23$	6.50522	+	3.75579i	1.35643	+	0.783137i	0.989141	−	0.146969i	$-0.0469517\pi$
$23$	6.50522	+	3.75579i	1.35643	+	0.783137i	0.367292	+	0.930106i	$0.380285\pi$
$24$	−0.928006	−	1.60735i	−0.189429	−	0.328100i
$25$		0			0
$26$	1.25874	−	2.18020i	0.246859	−	0.427573i
$27$		−	1.00000i		−	0.192450i
$28$	4.49162	+	1.18532i	0.848837	+	0.224005i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$		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	$-0.351803\pi$
$32$	−4.32502	+	2.49705i	−0.764563	+	0.441421i
$33$	−4.62330	−	2.66927i	−0.804814	−	0.464660i
$34$	0.173053			0.0296783
$35$		0			0
$36$	−1.75579			−0.292632
$37$	3.05121	+	1.76162i	0.501617	+	0.289608i	0.729381	−	0.684108i	$-0.239808\pi$
$37$	3.05121	+	1.76162i	0.501617	+	0.289608i	−0.227764	+	0.973716i	$0.573142\pi$
$38$	1.18437	−	0.683799i	0.192131	−	0.110927i
$39$	−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	$0.710401\pi$
$42$	−0.921008	+	0.928006i	−0.142115	+	0.143194i
$43$		−	1.41726i		−	0.216130i	−0.994144	−	0.108065i	$-0.965535\pi$
$43$		−	1.41726i		−	0.216130i	0.994144	−	0.108065i	$-0.0344655\pi$
$44$	−4.68668	+	8.11757i	−0.706543	+	1.22377i
$45$		0			0
$46$	1.85601	+	3.21471i	0.273654	+	0.473983i
$47$	7.66443	+	4.42506i	1.11797	+	0.645461i	0.940882	−	0.338734i	$-0.109999\pi$
$47$	7.66443	+	4.42506i	1.11797	+	0.645461i	0.177089	+	0.984195i	$0.443332\pi$
$48$			2.59439i			0.374468i
$49$	−0.0529894	−	6.99980i	−0.00756991	−	0.999971i
$50$		0			0
$51$	0.175093	−	0.303270i	0.0245179	−	0.0424663i
$52$	−7.74623	+	4.47229i	−1.07421	+	0.620195i
$53$	5.47924	−	3.16344i	0.752631	−	0.434532i	−0.0740126	−	0.997257i	$-0.523581\pi$
$53$	5.47924	−	3.16344i	0.752631	−	0.434532i	0.826644	+	0.562725i	$0.190247\pi$
$54$	0.247087	−	0.427967i	0.0336242	−	0.0582389i
$55$		0			0
$56$	3.48540	+	3.45911i	0.465756	+	0.462244i
$57$		−	2.76745i		−	0.366557i
$58$	−1.71187	−	0.988347i	−0.224779	−	0.129776i
$59$	6.42506	+	11.1285i	0.836471	+	1.44881i	0.892827	+	0.450400i	$0.148719\pi$
$59$	6.42506	+	11.1285i	0.836471	+	1.44881i	−0.0563553	+	0.998411i	$0.517948\pi$
$60$		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	$0.0629528\pi$
$62$		−	3.02317i		−	0.383943i
$63$	0.694439	+	2.55299i	0.0874911	+	0.321646i
$64$	2.72083			0.340104
$65$		0			0
$66$	−1.31908	−	2.28471i	−0.162368	−	0.281229i
$67$	3.25261	−	1.87790i	0.397370	−	0.229422i	−0.287979	−	0.957637i	$-0.592983\pi$
$67$	3.25261	−	1.87790i	0.397370	−	0.229422i	0.685348	+	0.728215i	$0.259650\pi$
$68$	−0.532479	−	0.307427i	−0.0645726	−	0.0372810i
$69$	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	$0.128950\pi$
$72$	−1.60735	−	0.928006i	−0.189429	−	0.109367i
$73$	−6.64853	+	3.83853i	−0.778152	+	0.449266i	−0.835775	−	0.549072i	$-0.814981\pi$
$73$	−6.64853	+	3.83853i	−0.778152	+	0.449266i	0.0576229	+	0.998338i	$0.481648\pi$
$74$	0.870545	+	1.50783i	0.101199	+	0.175282i
$75$		0			0
$76$	−4.85906			−0.557373
$77$	13.6569	+	3.60401i	1.55635	+	0.410715i
$78$		−	2.51748i		−	0.285048i
$79$	1.18092	−	2.04541i	0.132864	−	0.230127i	−0.791916	−	0.610631i	$-0.790916\pi$
$79$	1.18092	−	2.04541i	0.132864	−	0.230127i	0.924779	+	0.380504i	$0.124249\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.36458	−	1.94254i	−0.371555	−	0.214518i
$83$			6.87342i			0.754456i	0.926120	+	0.377228i	$0.123123\pi$
$83$			6.87342i			0.754456i	−0.926120	+	0.377228i	$0.876877\pi$
$84$	4.48252	−	1.21929i	0.489083	−	0.133036i
$85$		0			0
$86$	0.350186	−	0.606540i	0.0377615	−	0.0654049i
$87$	−3.46410	+	2.00000i	−0.371391	+	0.214423i
$88$	−8.58091	+	4.95419i	−0.914728	+	0.528119i
$89$	−2.17509	+	3.76737i	−0.230559	+	0.399341i	−0.957973	−	0.286859i	$-0.907389\pi$
$89$	−2.17509	+	3.76737i	−0.230559	+	0.399341i	0.727413	+	0.686199i	$0.240722\pi$
$90$		0			0
$91$	9.56662	+	9.49447i	1.00285	+	0.995291i
$92$		−	13.1888i		−	1.37503i
$93$	−5.29802	−	3.05882i	−0.549380	−	0.317184i
$94$	2.18675	+	3.78756i	0.225546	+	0.390657i
$95$		0			0
$96$	−2.49705	+	4.32502i	−0.254854	+	0.441421i
$97$			5.49993i			0.558433i	0.960228	+	0.279217i	$0.0900748\pi$
$97$			5.49993i			0.558433i	−0.960228	+	0.279217i	$0.909925\pi$
$98$	1.70688	−	3.00877i	0.172421	−	0.303932i
$99$	−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	$0.859490\pi$
$102$	0.149868	−	0.0865263i	0.0148391	−	0.00856738i
$103$	−8.80003	−	5.08070i	−0.867093	−	0.500616i	−0.000711688	−	1.00000i	$-0.500227\pi$
$103$	−8.80003	−	5.08070i	−0.867093	−	0.500616i	−0.866381	+	0.499384i	$0.833560\pi$
$104$	−9.45513			−0.927152
$105$		0			0
$106$	3.12658			0.303680
$107$	4.64349	+	2.68092i	0.448903	+	0.259174i	0.707367	−	0.706847i	$-0.249883\pi$
$107$	4.64349	+	2.68092i	0.448903	+	0.259174i	−0.258464	+	0.966021i	$0.583216\pi$
$108$	−1.52056	+	0.877896i	−0.146316	+	0.0844756i
$109$	−0.0529894	−	0.0917803i	−0.00507546	−	0.00879096i	0.863477	−	0.504389i	$-0.168282\pi$
$109$	−0.0529894	−	0.0917803i	−0.00507546	−	0.00879096i	−0.868552	+	0.495598i	$0.834949\pi$
$110$		0			0
$111$	3.52324			0.334411
$112$	−1.80165	−	6.62346i	−0.170240	−	0.625858i
$113$			4.67707i			0.439981i	0.975502	+	0.219991i	$0.0706027\pi$
$113$			4.67707i			0.439981i	−0.975502	+	0.219991i	$0.929397\pi$
$114$	0.683799	−	1.18437i	0.0640436	−	0.110927i
$115$		0			0
$116$	3.51159	+	6.08224i	0.326043	+	0.564722i
$117$	−4.41182	−	2.54716i	−0.407872	−	0.235485i
$118$			6.35019i			0.584582i
$119$	−0.236408	+	0.895837i	−0.0216715	+	0.0821212i
$120$		0			0
$121$	−8.74997	+	15.1554i	−0.795451	+	1.37776i
$122$	2.13983	−	1.23543i	0.193731	−	0.111851i
$123$	−6.80849	+	3.93089i	−0.613901	+	0.354436i
$124$	−5.37065	+	9.30223i	−0.482298	+	0.835365i
$125$		0			0
$126$	−0.333613	+	1.26418i	−0.0297206	+	0.112622i
$127$		−	17.5388i		−	1.55632i	−0.628066	−	0.778160i	$-0.716153\pi$
$127$		−	17.5388i		−	1.55632i	0.628066	−	0.778160i	$-0.283847\pi$
$128$	9.81447	+	5.66639i	0.867485	+	0.500843i
$129$	−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	$0.0376956\pi$
$132$			9.37336i			0.815846i
$133$	1.92182	+	7.06526i	0.166643	+	0.612636i
$134$	1.85601			0.160335
$135$		0			0
$136$	−0.324975	−	0.562873i	−0.0278664	−	0.0482660i
$137$	−0.722715	+	0.417260i	−0.0617457	+	0.0356489i	−0.530555	−	0.847650i	$-0.678016\pi$
$137$	−0.722715	+	0.417260i	−0.0617457	+	0.0356489i	0.468809	+	0.883299i	$0.344683\pi$
$138$	3.21471	+	1.85601i	0.273654	+	0.157994i
$139$	14.3152			1.21420			0.607101	−	0.794625i	$-0.292332\pi$
$139$	14.3152			1.21420			0.607101	+	0.794625i	$0.292332\pi$
$140$		0			0
$141$	8.85012			0.745314
$142$	6.62847	+	3.82695i	0.556249	+	0.321150i
$143$	−23.5526	+	13.5981i	−1.96957	+	1.13713i
$144$	1.29720	+	2.24681i	0.108100	+	0.187234i
$145$		0			0
$146$	−3.79380			−0.313977
$147$	−3.54579	−	6.03551i	−0.292452	−	0.497800i
$148$		−	6.18608i		−	0.508492i
$149$	9.69833	−	16.7980i	0.794518	−	1.37615i	−0.128626	−	0.991693i	$-0.541057\pi$
$149$	9.69833	−	16.7980i	0.794518	−	1.37615i	0.923145	−	0.384453i	$-0.125610\pi$
$150$		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	$-0.438477\pi$
$152$	−4.44827	−	2.56821i	−0.360802	−	0.208309i
$153$		−	0.350186i		−	0.0283109i
$154$	4.95419	+	4.91683i	0.399220	+	0.396209i
$155$		0			0
$156$	−4.47229	+	7.74623i	−0.358070	+	0.620195i
$157$	−4.15654	+	2.39978i	−0.331728	+	0.191523i	−0.656608	−	0.754232i	$-0.728009\pi$
$157$	−4.15654	+	2.39978i	−0.331728	+	0.191523i	0.324880	+	0.945755i	$0.394676\pi$
$158$	1.01079	−	0.583579i	0.0804140	−	0.0464271i
$159$	3.16344	−	5.47924i	0.250877	−	0.434532i
$160$		0			0
$161$	−19.1770	+	5.21634i	−1.51136	+	0.411105i
$162$		−	0.494173i		−	0.0388259i
$163$	0.716157	+	0.413474i	0.0560938	+	0.0323858i	0.527785	−	0.849378i	$-0.323023\pi$
$163$	0.716157	+	0.413474i	0.0560938	+	0.0323858i	−0.471691	+	0.881764i	$0.656356\pi$
$164$	6.90182	+	11.9543i	0.538942	+	0.933474i
$165$		0			0
$166$	−1.69833	+	2.94160i	−0.131816	+	0.228312i
$167$			4.61485i			0.357108i	0.983930	+	0.178554i	$0.0571419\pi$
$167$			4.61485i			0.357108i	−0.983930	+	0.178554i	$0.942858\pi$
$168$	4.74800	+	1.25298i	0.366316	+	0.0966696i
$169$	−12.9522			−0.996319
$170$		0			0
$171$	−1.38372	−	2.39668i	−0.105816	−	0.183279i
$172$	−2.15503	+	1.24421i	−0.164320	+	0.0948699i
$173$	−10.9787	−	6.33853i	−0.834692	−	0.481910i	0.0207644	−	0.999784i	$-0.493390\pi$
$173$	−10.9787	−	6.33853i	−0.834692	−	0.481910i	−0.855456	+	0.517875i	$0.826723\pi$
$174$	−1.97669			−0.149853
$175$		0			0
$176$	13.8503			1.04400
$177$	11.1285	+	6.42506i	0.836471	+	0.482937i
$178$	−1.86173	+	1.07487i	−0.139543	+	0.0805651i
$179$	6.52324	+	11.2986i	0.487570	+	0.844496i	0.999898	−	0.0142942i	$-0.00455015\pi$
$179$	6.52324	+	11.2986i	0.487570	+	0.844496i	−0.512328	+	0.858790i	$0.671217\pi$
$180$		0			0
$181$	15.0594			1.11935			0.559677	−	0.828711i	$-0.310925\pi$
$181$	15.0594			1.11935			0.559677	+	0.828711i	$0.310925\pi$
$182$	1.74824	+	6.42710i	0.129588	+	0.476408i
$183$		−	5.00000i		−	0.369611i
$184$	6.97080	−	12.0738i	0.513894	−	0.890091i
$185$		0			0
$186$	−1.51159	−	2.61814i	−0.110835	−	0.191972i
$187$	−1.61902	−	0.934740i	−0.118394	−	0.0683549i
$188$		−	15.5390i		−	1.13330i
$189$	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	$0.278680\pi$
$192$	2.35631	−	1.36042i	0.170052	−	0.0981796i
$193$	13.0822	−	7.55299i	0.941675	−	0.543676i	0.0511897	−	0.998689i	$-0.483699\pi$
$193$	13.0822	−	7.55299i	0.941675	−	0.543676i	0.890485	+	0.455013i	$0.150365\pi$
$194$	−1.35896	+	2.35379i	−0.0975676	+	0.168992i
$195$		0			0
$196$	−10.5971	+	6.22567i	−0.756936	+	0.444691i
$197$			16.8890i			1.20329i	0.798762	+	0.601647i	$0.205488\pi$
$197$			16.8890i			1.20329i	−0.798762	+	0.601647i	$0.794512\pi$
$198$	−2.28471	−	1.31908i	−0.162368	−	0.0937430i
$199$	−12.6138	−	21.8477i	−0.894167	−	1.54874i	−0.834832	−	0.550505i	$-0.814435\pi$
$199$	−12.6138	−	21.8477i	−0.894167	−	1.54874i	−0.0593348	−	0.998238i	$-0.518898\pi$
$200$		0			0
$201$	1.87790	−	3.25261i	0.132457	−	0.229422i
$202$		−	0.815294i		−	0.0573639i
$203$	7.45494	−	7.51159i	0.523234	−	0.527210i
$204$	−0.614854			−0.0430484
$205$		0			0
$206$	−2.51075	−	4.34874i	−0.174932	−	0.302991i
$207$	6.50522	−	3.75579i	0.452144	−	0.261046i
$208$	11.4460	+	6.60834i	0.793636	+	0.458206i
$209$	−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	$0.252254\pi$
$212$	−9.62041	−	5.55434i	−0.660732	−	0.381474i
$213$	13.4132	−	7.74414i	0.919060	−	0.530620i
$214$	1.32484	+	2.29469i	0.0905641	+	0.156862i
$215$		0			0
$216$	−1.85601			−0.126286
$217$	15.6500	+	4.12997i	1.06239	+	0.280361i
$218$		−	0.0523719i		−	0.00354707i
$219$	−3.83853	+	6.64853i	−0.259384	+	0.449266i
$220$		0			0
$221$	−0.891981	−	1.54496i	−0.0600011	−	0.103925i
$222$	1.50783	+	0.870545i	0.101199	+	0.0584272i
$223$			22.5738i			1.51165i	0.654772	+	0.755827i	$0.272765\pi$
$223$			22.5738i			1.51165i	−0.654772	+	0.755827i	$0.727235\pi$
$224$	3.37149	−	12.7758i	0.225267	−	0.853618i
$225$		0			0
$226$	−1.15564	+	2.00163i	−0.0768721	+	0.133146i
$227$	−12.2675	+	7.08267i	−0.814226	+	0.470093i	−0.848421	−	0.529322i	$-0.822446\pi$
$227$	−12.2675	+	7.08267i	−0.814226	+	0.470093i	0.0341954	+	0.999415i	$0.489113\pi$
$228$	−4.20807	+	2.42953i	−0.278686	+	0.160900i
$229$	−8.90311	+	15.4206i	−0.588334	+	1.01902i	0.406117	+	0.913821i	$0.366883\pi$
$229$	−8.90311	+	15.4206i	−0.588334	+	1.01902i	−0.994451	+	0.105203i	$0.966451\pi$
$230$		0			0
$231$	13.6292	−	3.70728i	0.896737	−	0.243921i
$232$			7.42405i			0.487413i
$233$	11.8211	+	6.82491i	0.774425	+	0.447115i	0.834451	−	0.551082i	$-0.185785\pi$
$233$	11.8211	+	6.82491i	0.774425	+	0.447115i	−0.0600258	+	0.998197i	$0.519118\pi$
$234$	−1.25874	−	2.18020i	−0.0822864	−	0.142524i
$235$		0			0
$236$	11.2811	−	19.5394i	0.734335	−	1.27191i
$237$		−	2.36184i		−	0.153418i
$238$	−0.322524	+	0.324975i	−0.0209061	+	0.0210650i
$239$	7.53489			0.487392			0.243696	−	0.969852i	$-0.421640\pi$
$239$	7.53489			0.487392			0.243696	+	0.969852i	$0.421640\pi$
$240$		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	$-0.537400\pi$
$242$	−7.48939	+	4.32400i	−0.481436	+	0.277957i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−8.77896			−0.562016
$245$		0			0
$246$	−3.88508			−0.247704
$247$	−12.2095	−	7.04914i	−0.776869	−	0.448526i
$248$	−9.83320	+	5.67720i	−0.624409	+	0.360503i
$249$	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	$0.756383\pi$
$252$	3.27233	−	3.29720i	0.206137	−	0.207704i
$253$		−	40.1008i		−	2.52112i
$254$	4.33361	−	7.50604i	0.271915	−	0.470971i
$255$		0			0
$256$	0.0793447	+	0.137429i	0.00495904	+	0.00858931i
$257$	−21.7702	−	12.5690i	−1.35799	−	0.784036i	−0.368637	−	0.929574i	$-0.620175\pi$
$257$	−21.7702	−	12.5690i	−1.35799	−	0.784036i	−0.989353	+	0.145538i	$0.953509\pi$
$258$		−	0.700372i		−	0.0436033i
$259$	−8.99479	+	2.44667i	−0.558909	+	0.152029i
$260$		0			0
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	3.86162	−	2.22951i	0.238571	−	0.137739i
$263$	11.7417	−	6.77910i	0.724027	−	0.418017i	−0.0922061	−	0.995740i	$-0.529392\pi$
$263$	11.7417	−	6.77910i	0.724027	−	0.418017i	0.816233	+	0.577723i	$0.196059\pi$
$264$	−4.95419	+	8.58091i	−0.304909	+	0.528119i
$265$		0			0
$266$	−0.923256	+	3.49855i	−0.0566085	+	0.214510i
$267$			4.35019i			0.266227i
$268$	−5.71091	−	3.29720i	−0.348849	−	0.201408i
$269$	−4.51363	−	7.81783i	−0.275201	−	0.476661i	0.694985	−	0.719024i	$-0.255411\pi$
$269$	−4.51363	−	7.81783i	−0.275201	−	0.476661i	−0.970186	+	0.242363i	$0.922078\pi$
$270$		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	$0.213008\pi$
$272$			0.908520i			0.0550871i
$273$	13.0322	+	3.43914i	0.788743	+	0.208146i
$274$	−0.412397			−0.0249138
$275$		0			0
$276$	−6.59439	−	11.4218i	−0.396936	−	0.687513i
$277$	1.62009	−	0.935357i	0.0973416	−	0.0562002i	−0.450539	−	0.892757i	$-0.648768\pi$
$277$	1.62009	−	0.935357i	0.0973416	−	0.0562002i	0.547881	+	0.836557i	$0.315435\pi$
$278$	6.12644	+	3.53710i	0.367439	+	0.212141i
$279$	−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	$0.490763\pi$
$282$	3.78756	+	2.18675i	0.225546	+	0.130219i
$283$	20.9402	−	12.0899i	1.24477	−	0.718667i	0.274707	−	0.961528i	$-0.411419\pi$
$283$	20.9402	−	12.0899i	1.24477	−	0.718667i	0.970061	+	0.242861i	$0.0780858\pi$
$284$	−13.5971	−	23.5509i	−0.806840	−	1.39749i
$285$		0			0
$286$	−13.4396			−0.794703
$287$	14.6523	−	14.7636i	0.864895	−	0.871467i
$288$			4.99411i			0.294280i
$289$	−8.43868	+	14.6162i	−0.496393	+	0.859778i
$290$		0			0
$291$	2.74997	+	4.76308i	0.161206	+	0.279217i
$292$	11.6734	+	6.73967i	0.683137	+	0.394409i
$293$		−	15.5349i		−	0.907558i	−0.891114	−	0.453779i	$-0.850076\pi$
$293$		−	15.5349i		−	0.907558i	0.891114	−	0.453779i	$-0.149924\pi$
$294$	−0.0261859	−	3.45911i	−0.00152719	−	0.201740i
$295$		0			0
$296$	3.26959	−	5.66309i	0.190041	−	0.329161i
$297$	−4.62330	+	2.66927i	−0.268271	+	0.154887i
$298$	8.30113	−	4.79266i	0.480871	−	0.277631i
$299$	19.1332	−	33.1397i	1.10650	−	1.91652i
$300$		0			0
$301$	2.66147	+	2.64140i	0.153404	+	0.152248i
$302$		−	9.15564i		−	0.526848i
$303$	−1.42878	−	0.824907i	−0.0820813	−	0.0473897i
$304$	3.58992	+	6.21793i	0.205896	+	0.356623i
$305$		0			0
$306$	0.0865263	−	0.149868i	0.00494638	−	0.00856738i
$307$		−	3.39395i		−	0.193703i	−0.995299	−	0.0968516i	$-0.969123\pi$
$307$		−	3.39395i		−	0.193703i	0.995299	−	0.0968516i	$-0.0308772\pi$
$308$	−6.50922	−	23.9301i	−0.370897	−	1.36354i
$309$	−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	$0.811068\pi$
$312$	−8.18839	+	4.72757i	−0.463576	+	0.267646i
$313$	−0.411818	−	0.237763i	−0.0232773	−	0.0134392i	0.488316	−	0.872667i	$-0.337611\pi$
$313$	−0.411818	−	0.237763i	−0.0232773	−	0.0134392i	−0.511594	+	0.859228i	$0.670945\pi$
$314$	−2.37181			−0.133849
$315$		0			0
$316$	−4.14690			−0.233281
$317$	−12.3837	−	7.14975i	−0.695539	−	0.401570i	0.110145	−	0.993916i	$-0.464869\pi$
$317$	−12.3837	−	7.14975i	−0.695539	−	0.401570i	−0.805684	+	0.592346i	$0.798202\pi$
$318$	2.70769	−	1.56329i	0.151840	−	0.0876648i
$319$	10.6771	+	18.4932i	0.597801	+	1.03542i
$320$		0			0
$321$	5.36184			0.299269
$322$	−9.49600	−	2.50596i	−0.529192	−	0.139652i
$323$		−	0.969121i		−	0.0539233i
$324$	−0.877896	+	1.52056i	−0.0487720	+	0.0844756i
$325$		0			0
$326$	0.204328	+	0.353906i	0.0113167	+	0.0196010i
$327$	−0.0917803	−	0.0529894i	−0.00507546	−	0.00293032i
$328$			14.5915i			0.805683i
$329$	−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	$-0.0142503\pi$
$332$	10.4515	−	6.03415i	0.573598	−	0.331167i
$333$	3.05121	−	1.76162i	0.167206	−	0.0965361i
$334$	−1.14027	+	1.97500i	−0.0623927	+	0.108067i
$335$		0			0
$336$	−4.87200	−	4.83526i	−0.265789	−	0.263785i
$337$			4.38230i			0.238719i	0.992851	+	0.119360i	$0.0380841\pi$
$337$			4.38230i			0.238719i	−0.992851	+	0.119360i	$0.961916\pi$
$338$	−5.54309	−	3.20030i	−0.301504	−	0.174074i
$339$	2.33853	+	4.05046i	0.127012	+	0.219991i
$340$		0			0
$341$	−16.3296	+	28.2837i	−0.884297	+	1.53165i
$342$		−	1.36760i		−	0.0739512i
$343$	13.2437	+	12.9463i	0.715090	+	0.699032i
$344$	−2.63045			−0.141824
$345$		0			0
$346$	−3.13233	−	5.42536i	−0.168395	−	0.291669i
$347$	−8.31134	+	4.79855i	−0.446176	+	0.257600i	−0.706214	−	0.707999i	$-0.749598\pi$
$347$	−8.31134	+	4.79855i	−0.446176	+	0.257600i	0.260038	+	0.965598i	$0.416265\pi$
$348$	6.08224	+	3.51159i	0.326043	+	0.188241i
$349$	19.9007			1.06526			0.532629	−	0.846349i	$-0.321204\pi$
$349$	19.9007			1.06526			0.532629	+	0.846349i	$0.321204\pi$
$350$		0			0
$351$	−5.09433			−0.271915
$352$	23.0893	+	13.3306i	1.23066	+	0.710523i
$353$	−23.7262	+	13.6983i	−1.26282	+	0.729089i	−0.973619	−	0.228180i	$-0.926722\pi$
$353$	−23.7262	+	13.6983i	−1.26282	+	0.729089i	−0.289200	+	0.957269i	$0.593389\pi$
$354$	3.17509	+	5.49942i	0.168754	+	0.292291i
$355$		0			0
$356$	7.63802			0.404815
$357$	0.243183	+	0.894021i	0.0128706	+	0.0473166i
$358$			6.44722i			0.340746i
$359$	12.7752	−	22.1274i	0.674252	−	1.16784i	−0.302435	−	0.953170i	$-0.597800\pi$
$359$	12.7752	−	22.1274i	0.674252	−	1.16784i	0.976687	−	0.214668i	$-0.0688670\pi$
$360$		0			0
$361$	5.67062	+	9.82180i	0.298454	+	0.516937i
$362$	6.44491	+	3.72097i	0.338737	+	0.195570i
$363$			17.4999i			0.918508i
$364$	6.03842	−	22.8818i	0.316499	−	1.19933i
$365$		0			0
$366$	1.23543	−	2.13983i	0.0645771	−	0.111851i
$367$	−19.2876	+	11.1357i	−1.00681	+	0.581280i	−0.910255	−	0.414048i	$-0.864115\pi$
$367$	−19.2876	+	11.1357i	−1.00681	+	0.581280i	−0.0965519	+	0.995328i	$0.530781\pi$
$368$	−16.8771	+	9.74400i	−0.879780	+	0.507941i
$369$	−3.93089	+	6.80849i	−0.204634	+	0.354436i
$370$		0			0
$371$	−4.27123	+	16.1853i	−0.221751	+	0.840296i
$372$			10.7413i			0.556910i
$373$	−4.58540	−	2.64738i	−0.237423	−	0.137076i	0.376569	−	0.926389i	$-0.377104\pi$
$373$	−4.58540	−	2.64738i	−0.237423	−	0.137076i	−0.613992	+	0.789312i	$0.710437\pi$
$374$	−0.461924	−	0.800075i	−0.0238855	−	0.0413709i
$375$		0			0
$376$	8.21297	−	14.2253i	0.423551	−	0.733612i
$377$			20.3773i			1.04948i
$378$	0.343173	+	1.26162i	0.0176509	+	0.0648907i
$379$	−3.10203			−0.159341			−0.0796704	−	0.996821i	$-0.525387\pi$
$379$	−3.10203			−0.159341			−0.0796704	+	0.996821i	$0.525387\pi$
$380$		0			0
$381$	−8.76942	−	15.1891i	−0.449271	−	0.778160i
$382$	−4.07732	+	2.35404i	−0.208614	+	0.120443i
$383$	18.7171	+	10.8064i	0.956402	+	0.552179i	0.895064	−	0.445938i	$-0.147130\pi$
$383$	18.7171	+	10.8064i	0.956402	+	0.552179i	0.0613379	+	0.998117i	$0.480463\pi$
$384$	11.3328			0.578323
$385$		0			0
$386$	7.46497			0.379957
$387$	−1.22738	−	0.708630i	−0.0623914	−	0.0360217i
$388$	8.36298	−	4.82837i	0.424566	−	0.245123i
$389$	−6.43082	−	11.1385i	−0.326055	−	0.564745i	0.655670	−	0.755048i	$-0.272386\pi$
$389$	−6.43082	−	11.1385i	−0.326055	−	0.564745i	−0.981725	+	0.190303i	$0.939053\pi$
$390$		0			0
$391$	2.63045			0.133028
$392$	−12.9917	+	0.0983489i	−0.656181	+	0.00496737i
$393$		−	9.02317i		−	0.455159i
$394$	−4.17305	+	7.22794i	−0.210235	+	0.364138i
$395$		0			0
$396$	4.68668	+	8.11757i	0.235514	+	0.407923i
$397$	−6.05797	−	3.49757i	−0.304041	−	0.175538i	0.340216	−	0.940347i	$-0.389500\pi$
$397$	−6.05797	−	3.49757i	−0.304041	−	0.175538i	−0.644257	+	0.764809i	$0.722833\pi$
$398$		−	12.4668i		−	0.624904i
$399$	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	$0.141514\pi$
$402$	1.60735	−	0.928006i	0.0801675	−	0.0462847i
$403$	−26.9899	+	15.5826i	−1.34446	+	0.776225i
$404$	−1.44837	+	2.50864i	−0.0720589	+	0.124810i
$405$		0			0
$406$	5.04648	−	1.37269i	0.250452	−	0.0681256i
$407$		−	18.8089i		−	0.932324i
$408$	−0.562873	−	0.324975i	−0.0278664	−	0.0160887i
$409$	1.24753	+	2.16079i	0.0616866	+	0.106844i	0.895219	−	0.445626i	$-0.147019\pi$
$409$	1.24753	+	2.16079i	0.0616866	+	0.106844i	−0.833533	+	0.552470i	$0.813685\pi$
$410$		0			0
$411$	−0.417260	+	0.722715i	−0.0205819	+	0.0356489i
$412$			17.8413i			0.878978i
$413$	−32.8728	−	8.67503i	−1.61757	−	0.426870i
$414$	3.71203			0.182436
$415$		0			0
$416$	12.7208	+	22.0331i	0.623688	+	1.08026i
$417$	12.3973	−	7.15761i	0.607101	−	0.350510i
$418$	−6.32282	−	3.65048i	−0.309259	−	0.178551i
$419$	32.6748			1.59627			0.798134	−	0.602480i	$-0.205821\pi$
$419$	32.6748			1.59627			0.798134	+	0.602480i	$0.205821\pi$
$420$		0			0
$421$	−26.8774			−1.30992			−0.654961	−	0.755662i	$-0.727315\pi$
$421$	−26.8774			−1.30992			−0.654961	+	0.755662i	$0.727315\pi$
$422$	8.72909	+	5.03974i	0.424926	+	0.245331i
$423$	7.66443	−	4.42506i	0.372657	−	0.215154i
$424$	−5.87138	−	10.1695i	−0.285140	−	0.493876i
$425$		0			0
$426$	7.65389			0.370832
$427$	3.47219	+	12.7649i	0.168031	+	0.617739i
$428$		−	9.41428i		−	0.455056i
$429$	−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	$0.944343\pi$
$432$	2.24681	+	1.29720i	0.108100	+	0.0624114i
$433$		−	29.9717i		−	1.44035i	−0.693794	−	0.720174i	$-0.744062\pi$
$433$		−	29.9717i		−	1.44035i	0.693794	−	0.720174i	$-0.255938\pi$
$434$	5.67720	+	5.63439i	0.272514	+	0.270459i
$435$		0			0
$436$	−0.0930383	+	0.161147i	−0.00445573	+	0.00771755i
$437$	18.0029	−	10.3940i	0.861193	−	0.497210i
$438$	−3.28553	+	1.89690i	−0.156989	+	0.0906374i
$439$	−1.03693	+	1.79602i	−0.0494901	+	0.0857193i	−0.889709	−	0.456528i	$-0.849093\pi$
$439$	−1.03693	+	1.79602i	−0.0494901	+	0.0857193i	0.840219	+	0.542247i	$0.182426\pi$
$440$		0			0
$441$	−6.08850	−	3.45401i	−0.289929	−	0.164477i
$442$		−	0.881586i		−	0.0419328i
$443$	27.7800	+	16.0388i	1.31987	+	0.762025i	0.983707	−	0.179780i	$-0.0575387\pi$
$443$	27.7800	+	16.0388i	1.31987	+	0.762025i	0.336159	+	0.941805i	$0.390872\pi$
$444$	−3.09304	−	5.35730i	−0.146789	−	0.254246i
$445$		0			0
$446$	−5.57768	+	9.66083i	−0.264111	+	0.457454i
$447$		−	19.3967i		−	0.917431i
$448$	−5.07091	+	5.10944i	−0.239578	+	0.241398i
$449$	4.46103			0.210529			0.105264	−	0.994444i	$-0.466431\pi$
$449$	4.46103			0.210529			0.105264	+	0.994444i	$0.466431\pi$
$450$		0			0
$451$	20.9852	+	36.3474i	0.988153	+	1.71153i
$452$	7.11176	−	4.10598i	0.334509	−	0.193129i
$453$	−16.0450	−	9.26359i	−0.753860	−	0.435242i
$454$	−7.00014			−0.328533
$455$		0			0
$456$	−5.13641			−0.240535
$457$	1.96607	+	1.13511i	0.0919689	+	0.0530983i	0.545279	−	0.838255i	$-0.316424\pi$
$457$	1.96607	+	1.13511i	0.0919689	+	0.0530983i	−0.453310	+	0.891353i	$0.649757\pi$
$458$	−7.62047	+	4.39968i	−0.356081	+	0.205583i
$459$	−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	$0.467842\pi$
$462$	6.74887	+	1.78100i	0.313986	+	0.0828598i
$463$			41.7856i			1.94194i	0.239196	+	0.970971i	$0.423116\pi$
$463$			41.7856i			1.94194i	−0.239196	+	0.970971i	$0.576884\pi$
$464$	5.18879	−	8.98724i	0.240883	−	0.417222i
$465$		0			0
$466$	3.37269	+	5.84167i	0.156237	+	0.270610i
$467$	−33.2357	−	19.1887i	−1.53797	−	0.887945i	−0.998958	−	0.0456441i	$-0.985466\pi$
$467$	−33.2357	−	19.1887i	−1.53797	−	0.887945i	−0.539008	−	0.842301i	$-0.681201\pi$
$468$			8.94458i			0.413463i
$469$	−2.53551	+	9.60797i	−0.117079	+	0.443655i
$470$		0			0
$471$	−2.39978	+	4.15654i	−0.110576	+	0.191523i
$472$	20.6547	−	11.9250i	0.950709	−	0.548892i
$473$	−6.55242	+	3.78304i	−0.301281	+	0.173945i
$474$	0.583579	−	1.01079i	0.0268047	−	0.0464271i
$475$		0			0
$476$	1.56972	−	0.426979i	0.0719478	−	0.0195705i
$477$		−	6.32688i		−	0.289688i
$478$	3.22468	+	1.86177i	0.147494	+	0.0851554i
$479$	19.0193	+	32.9424i	0.869015	+	1.50518i	0.863005	+	0.505196i	$0.168580\pi$
$479$	19.0193	+	32.9424i	0.869015	+	1.50518i	0.00600999	+	0.999982i	$0.498087\pi$
$480$		0			0
$481$	8.97426	−	15.5439i	0.409191	−	0.708740i
$482$		−	14.0954i		−	0.642026i
$483$	−13.9996	+	14.1060i	−0.637004	+	0.641844i
$484$	30.7263			1.39665
$485$		0			0
$486$	−0.247087	−	0.427967i	−0.0112081	−	0.0194130i
$487$	19.5572	−	11.2914i	0.886223	−	0.511661i	0.0135175	−	0.999909i	$-0.495697\pi$
$487$	19.5572	−	11.2914i	0.886223	−	0.511661i	0.872705	+	0.488248i	$0.162364\pi$
$488$	−8.03677	−	4.64003i	−0.363808	−	0.210044i
$489$	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	$0.500964\pi$
$492$	11.9543	+	6.90182i	0.538942	+	0.311158i
$493$	−1.21308	+	0.700372i	−0.0546344	+	0.0315432i
$494$	−3.48349	−	6.03359i	−0.156730	−	0.271464i
$495$		0			0
$496$	15.8715			0.712653
$497$	−28.8660	+	29.0854i	−1.29482	+	1.30466i
$498$			3.39666i			0.152208i
$499$	−7.77768	+	13.4713i	−0.348177	+	0.603060i	−0.985926	−	0.167185i	$-0.946532\pi$
$499$	−7.77768	+	13.4713i	−0.348177	+	0.603060i	0.637749	+	0.770244i	$0.279866\pi$
$500$		0			0
$501$	2.30743	+	3.99658i	0.103088	+	0.178554i
$502$	−9.77909	−	5.64596i	−0.436462	−	0.251992i
$503$		−	4.39272i		−	0.195862i	−0.995193	−	0.0979308i	$-0.968778\pi$
$503$		−	4.39272i		−	0.195862i	0.995193	−	0.0979308i	$-0.0312224\pi$
$504$	4.73838	−	1.28889i	0.211064	−	0.0574116i
$505$		0			0
$506$	9.90838	−	17.1618i	0.440481	−	0.762936i
$507$	−11.2169	+	6.47608i	−0.498160	+	0.287613i
$508$	−26.6689	+	15.3973i	−1.18324	+	0.683144i
$509$	1.04377	−	1.80786i	0.0462642	−	0.0801319i	−0.841966	−	0.539531i	$-0.818602\pi$
$509$	1.04377	−	1.80786i	0.0462642	−	0.0801319i	0.888230	+	0.459399i	$0.151935\pi$
$510$		0			0
$511$	5.18273	−	19.6393i	0.229271	−	0.868790i
$512$		−	22.5871i		−	0.998219i
$513$	−2.39668	−	1.38372i	−0.105816	−	0.0610929i
$514$	−6.21129	−	10.7583i	−0.273968	−	0.474527i
$515$		0			0
$516$	−1.24421	+	2.15503i	−0.0547732	+	0.0948699i
$517$		−	47.2466i		−	2.07791i
$518$	−4.45401	−	1.17540i	−0.195698	−	0.0516440i
$519$	−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	$0.536072\pi$
$522$	−1.71187	+	0.988347i	−0.0749264	+	0.0432588i
$523$	10.9371	+	6.31454i	0.478246	+	0.276116i	0.719685	−	0.694300i	$-0.244286\pi$
$523$	10.9371	+	6.31454i	0.478246	+	0.276116i	−0.241439	+	0.970416i	$0.577619\pi$
$524$	−15.8428			−0.692097
$525$		0			0
$526$	6.70010			0.292138
$527$	−1.85529	−	1.07115i	−0.0808179	−	0.0466602i
$528$	11.9947	−	6.92513i	0.522001	−	0.301377i
$529$	16.7120	+	28.9460i	0.726607	+	1.25852i
$530$		0			0
$531$	12.8501			0.557648
$532$	9.05600	−	9.12481i	0.392627	−	0.395611i
$533$			40.0504i			1.73478i
$534$	−1.07487	+	1.86173i	−0.0465143	+	0.0805651i
$535$		0			0
$536$	−3.48540	−	6.03689i	−0.150546	−	0.260754i
$537$	11.2986	+	6.52324i	0.487570	+	0.281499i
$538$		−	4.46103i		−	0.192329i
$539$	−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	$0.852160\pi$
$542$	−2.04414	+	1.18018i	−0.0878031	+	0.0506932i
$543$	13.0418	−	7.52968i	0.559677	−	0.323130i
$544$	−0.874433	+	1.51456i	−0.0374910	+	0.0649363i
$545$		0			0
$546$	4.72757	+	4.69191i	0.202321	+	0.200795i
$547$			18.6010i			0.795323i	0.917532	+	0.397662i	$0.130178\pi$
$547$			18.6010i			0.795323i	−0.917532	+	0.397662i	$0.869822\pi$
$548$	1.26894	+	0.732622i	0.0542064	+	0.0312961i
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$		0			0
$551$	−5.53489	+	9.58671i	−0.235794	+	0.408408i
$552$		−	13.9416i		−	0.593394i
$553$	1.64015	+	6.02975i	0.0697464	+	0.256411i
$554$	0.924457			0.0392764
$555$		0			0
$556$	−12.5673	−	21.7672i	−0.532972	−	0.923134i
$557$	−4.47344	+	2.58274i	−0.189546	+	0.109434i	−0.591770	−	0.806107i	$-0.701571\pi$
$557$	−4.47344	+	2.58274i	−0.189546	+	0.109434i	0.402224	+	0.915541i	$0.368237\pi$
$558$	−2.61814	−	1.51159i	−0.110835	−	0.0639905i
$559$	−7.21998			−0.305373
$560$		0			0
$561$	−1.86948			−0.0789295
$562$	0.416304	+	0.240353i	0.0175607	+	0.0101387i
$563$	−10.9450	+	6.31908i	−0.461275	+	0.266317i	−0.712580	−	0.701590i	$-0.752474\pi$
$563$	−10.9450	+	6.31908i	−0.461275	+	0.266317i	0.251305	+	0.967908i	$0.419140\pi$
$564$	−7.76949	−	13.4571i	−0.327154	−	0.566648i
$565$		0			0
$566$	11.9490			0.502253
$567$	2.55817	+	0.675093i	0.107433	+	0.0283512i
$568$		−	28.7464i		−	1.20617i
$569$	−4.39870	+	7.61878i	−0.184403	+	0.319396i	−0.943375	−	0.331727i	$-0.892369\pi$
$569$	−4.39870	+	7.61878i	−0.184403	+	0.319396i	0.758972	+	0.651123i	$0.225702\pi$
$570$		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	$0.518830\pi$
$572$	41.3535	+	23.8755i	1.72908	+	0.998283i
$573$			9.52718i			0.398004i
$574$	9.91856	−	2.69795i	0.413993	−	0.112610i
$575$		0			0
$576$	1.36042	−	2.35631i	0.0566840	−	0.0981796i
$577$	2.35289	−	1.35844i	0.0979523	−	0.0565528i	−0.450224	−	0.892916i	$-0.648656\pi$
$577$	2.35289	−	1.35844i	0.0979523	−	0.0565528i	0.548176	+	0.836363i	$0.315322\pi$
$578$	−7.22295	+	4.17017i	−0.300435	+	0.173456i
$579$	7.55299	−	13.0822i	0.313892	−	0.543676i
$580$		0			0
$581$	−12.9076	−	12.8102i	−0.535497	−	0.531458i
$582$			2.71792i			0.112661i
$583$	−29.2511	−	16.8881i	−1.21146	−	0.699435i
$584$	7.12437	+	12.3398i	0.294808	+	0.510623i
$585$		0			0
$586$	3.83846	−	6.64842i	0.158566	−	0.274644i
$587$			9.02317i			0.372426i	0.982509	+	0.186213i	$0.0596215\pi$
$587$			9.02317i			0.372426i	−0.982509	+	0.186213i	$0.940379\pi$
$588$	−6.06452	+	10.6901i	−0.250097	+	0.440854i
$589$	−16.9302			−0.697597
$590$		0			0
$591$	8.44451	+	14.6263i	0.347361	+	0.601647i
$592$	−7.91605	+	4.57033i	−0.325348	+	0.187840i
$593$	−9.06305	−	5.23255i	−0.372175	−	0.214875i	0.302233	−	0.953234i	$-0.402268\pi$
$593$	−9.06305	−	5.23255i	−0.372175	−	0.214875i	−0.674408	+	0.738359i	$0.735601\pi$
$594$	−2.63816			−0.108245
$595$		0			0
$596$	−34.0565			−1.39501
$597$	−21.8477	−	12.6138i	−0.894167	−	0.516248i
$598$	16.3768	−	9.45513i	0.669696	−	0.386649i
$599$	4.81915	+	8.34701i	0.196905	+	0.341050i	0.947523	−	0.319686i	$-0.103578\pi$
$599$	4.81915	+	8.34701i	0.196905	+	0.341050i	−0.750618	+	0.660736i	$0.770244\pi$
$600$		0			0
$601$	−7.19544			−0.293508			−0.146754	−	0.989173i	$-0.546883\pi$
$601$	−7.19544			−0.293508			−0.146754	+	0.989173i	$0.546883\pi$
$602$	0.486366	+	1.78804i	0.0198228	+	0.0728752i
$603$		−	3.75579i		−	0.152948i
$604$	−16.2649	+	28.1717i	−0.661811	+	1.14629i
$605$		0			0
$606$	−0.407647	−	0.706065i	−0.0165595	−	0.0286819i
$607$	34.0681	+	19.6692i	1.38278	+	0.798348i	0.992488	−	0.122343i	$-0.0390408\pi$
$607$	34.0681	+	19.6692i	1.38278	+	0.798348i	0.390292	+	0.920691i	$0.372374\pi$
$608$			13.8209i			0.560512i
$609$	2.70037	−	10.2327i	0.109425	−	0.414650i
$610$		0			0
$611$	22.5427	−	39.0451i	0.911980	−	1.57960i
$612$	−0.532479	+	0.307427i	−0.0215242	+	0.0124270i
$613$	16.9277	−	9.77320i	0.683703	−	0.394736i	−0.117546	−	0.993067i	$-0.537503\pi$
$613$	16.9277	−	9.77320i	0.683703	−	0.394736i	0.801249	+	0.598331i	$0.204169\pi$
$614$	0.838601	−	1.45250i	0.0338432	−	0.0586181i
$615$		0			0
$616$	6.68908	−	25.3474i	0.269511	−	1.02127i
$617$			35.9588i			1.44765i	0.689985	+	0.723824i	$0.257617\pi$
$617$			35.9588i			1.44765i	−0.689985	+	0.723824i	$0.742383\pi$
$618$	−4.34874	−	2.51075i	−0.174932	−	0.100997i
$619$	4.27972	+	7.41269i	0.172016	+	0.297941i	0.939125	−	0.343577i	$-0.111638\pi$
$619$	4.27972	+	7.41269i	0.172016	+	0.297941i	−0.767108	+	0.641518i	$0.778305\pi$
$620$		0			0
$621$	3.75579	−	6.50522i	0.150715	−	0.261046i
$622$			1.21819i			0.0488450i
$623$	−3.02094	−	11.1060i	−0.121031	−	0.444952i
$624$	13.2167			0.529091
$625$		0			0
$626$	−0.117496	−	0.203509i	−0.00469609	−	0.00813387i
$627$	−12.7947	+	7.38705i	−0.510973	+	0.295010i
$628$	7.29802	+	4.21352i	0.291223	+	0.168138i
$629$	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	$0.613381\pi$
$632$	−3.79631	−	2.19180i	−0.151009	−	0.0871852i
$633$	17.6640	−	10.1983i	0.702082	−	0.405347i
$634$	−3.53321	−	6.11971i	−0.140322	−	0.243045i
$635$		0			0
$636$	−11.1087			−0.440488
$637$	−35.6593	+	0.269945i	−1.41287	+	0.0106956i
$638$			10.5526i			0.417783i
$639$	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	$0.937536\pi$
$642$	2.29469	+	1.32484i	0.0905641	+	0.0522872i
$643$			15.7544i			0.621294i	0.950525	+	0.310647i	$0.100546\pi$
$643$			15.7544i			0.621294i	−0.950525	+	0.310647i	$0.899454\pi$
$644$	24.7672	+	24.5804i	0.975963	+	0.968603i
$645$		0			0
$646$	0.239457	−	0.414751i	0.00942131	−	0.0163182i
$647$	39.3517	−	22.7197i	1.54707	−	0.893203i	0.548710	−	0.836013i	$-0.315119\pi$
$647$	39.3517	−	22.7197i	1.54707	−	0.893203i	0.998363	−	0.0571903i	$-0.0182142\pi$
$648$	−1.60735	+	0.928006i	−0.0631428	+	0.0364555i
$649$	34.3004	−	59.4100i	1.34641	−	2.33205i
$650$		0			0
$651$	15.6182	−	4.24832i	0.612127	−	0.166505i
$652$		−	1.45195i		−	0.0568627i
$653$	16.5943	+	9.58070i	0.649384	+	0.374922i	0.788220	−	0.615394i	$-0.211003\pi$
$653$	16.5943	+	9.58070i	0.649384	+	0.374922i	−0.138836	+	0.990315i	$0.544336\pi$
$654$	−0.0261859	−	0.0453554i	−0.00102395	−	0.00177354i
$655$		0			0
$656$	10.1983	−	17.6639i	0.398175	−	0.689660i
$657$			7.67707i			0.299511i
$658$	−11.1882	−	2.95251i	−0.436160	−	0.115101i
$659$	8.76258			0.341342			0.170671	−	0.985328i	$-0.445407\pi$
$659$	8.76258			0.341342			0.170671	+	0.985328i	$0.445407\pi$
$660$		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	$0.776853\pi$
$662$	8.38192	−	4.83930i	0.325773	−	0.188085i
$663$	−1.54496	−	0.891981i	−0.0600011	−	0.0346417i
$664$	12.7572			0.495074
$665$		0			0
$666$	1.74109			0.0674659
$667$	−26.0209	−	15.0232i	−1.00753	−	0.581699i
$668$	7.01717	−	4.05136i	0.271502	−	0.156752i
$669$	11.2869	+	19.5495i	0.436377	+	0.755827i
$670$		0			0
$671$	−26.6927			−1.03046
$672$	−3.46810	−	12.7499i	−0.133785	−	0.491838i
$673$			18.3460i			0.707185i	0.935400	+	0.353593i	$0.115040\pi$
$673$			18.3460i			0.707185i	−0.935400	+	0.353593i	$0.884960\pi$
$674$	−1.08281	+	1.87548i	−0.0417082	+	0.0722407i
$675$		0			0
$676$	11.3706	+	19.6945i	0.437333	+	0.757482i
$677$	1.55532	+	0.897966i	0.0597759	+	0.0345116i	0.529590	−	0.848254i	$-0.322346\pi$
$677$	1.55532	+	0.897966i	0.0597759	+	0.0345116i	−0.469814	+	0.882765i	$0.655679\pi$
$678$			2.31128i			0.0887642i
$679$	−10.3283	−	10.2504i	−0.396364	−	0.393375i
$680$		0			0
$681$	−7.08267	+	12.2675i	−0.271409	+	0.470093i
$682$	−13.9770	+	8.06965i	−0.535209	+	0.309003i
$683$	38.4454	−	22.1965i	1.47107	−	0.849324i	0.471599	−	0.881813i	$-0.343677\pi$
$683$	38.4454	−	22.1965i	1.47107	−	0.849324i	0.999472	+	0.0324893i	$0.0103435\pi$
$684$	−2.42953	+	4.20807i	−0.0928954	+	0.160900i
$685$		0			0
$686$	2.46900	+	8.81290i	0.0942667	+	0.336478i
$687$			17.8062i			0.679349i
$688$	3.18431	+	1.83846i	0.121401	+	0.0700908i
$689$	−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	$0.859771\pi$
$692$			22.2583i			0.846134i
$693$	9.94961	−	10.0252i	0.377954	−	0.380826i
$694$	−4.74263			−0.180028
$695$		0			0
$696$	3.71203	+	6.42942i	0.140704	+	0.243706i
$697$	−2.38424	+	1.37654i	−0.0903095	+	0.0521402i
$698$	8.51683	+	4.91719i	0.322367	+	0.186118i
$699$	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	$0.558616\pi$
$702$	−2.18020	−	1.25874i	−0.0822864	−	0.0475081i
$703$	8.44407	−	4.87519i	0.318474	−	0.183871i
$704$	−7.26263	−	12.5792i	−0.273721	−	0.474098i
$705$		0			0
$706$	−13.5387			−0.509536
$707$	4.22051	+	1.11378i	0.158729	+	0.0418879i
$708$		−	22.5621i		−	0.847937i
$709$	9.07685	−	15.7216i	0.340888	−	0.590435i	−0.643710	−	0.765270i	$-0.722606\pi$
$709$	9.07685	−	15.7216i	0.340888	−	0.590435i	0.984598	+	0.174834i	$0.0559389\pi$
$710$		0			0
$711$	−1.18092	−	2.04541i	−0.0442879	−	0.0767090i
$712$	6.99229	+	4.03700i	0.262047	+	0.151293i
$713$		−	45.9531i		−	1.72096i
$714$	−0.116827	+	0.442699i	−0.00437213	+	0.0165676i
$715$		0			0
$716$	11.4535	−	19.8380i	0.428036	−	0.741380i
$717$	6.52541	−	3.76745i	0.243696	−	0.140698i
$718$	10.9348	−	6.31319i	0.408082	−	0.235606i
$719$	−17.5904	+	30.4675i	−0.656011	+	1.13624i	0.325628	+	0.945498i	$0.394424\pi$
$719$	−17.5904	+	30.4675i	−0.656011	+	1.13624i	−0.981639	+	0.190747i	$0.938909\pi$
$720$		0			0
$721$	25.9419	−	7.05647i	0.966128	−	0.262797i
$722$			5.60454i			0.208579i
$723$	−24.7017	−	14.2616i	−0.918667	−	0.530393i
$724$	−13.2206	−	22.8987i	−0.491338	−	0.851023i
$725$		0			0
$726$	−4.32400	+	7.48939i	−0.160479	+	0.277957i
$727$		−	4.79075i		−	0.177679i	−0.996046	−	0.0888396i	$-0.971684\pi$
$727$		−	4.79075i		−	0.177679i	0.996046	−	0.0888396i	$-0.0283158\pi$
$728$	17.6219	−	17.7558i	0.653109	−	0.658072i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−0.248152	−	0.429812i	−0.00917825	−	0.0158972i
$732$	−7.60281	+	4.38948i	−0.281008	+	0.162240i
$733$	−10.4999	−	6.06214i	−0.387824	−	0.223910i	0.293393	−	0.955992i	$-0.405216\pi$
$733$	−10.4999	−	6.06214i	−0.387824	−	0.223910i	−0.681217	+	0.732082i	$0.738549\pi$
$734$	−11.0060			−0.406237
$735$		0			0
$736$	−37.5136			−1.38277
$737$	−17.3642	−	10.0252i	−0.639618	−	0.369283i
$738$	−3.36458	+	1.94254i	−0.123852	+	0.0715058i
$739$	−16.4581	−	28.5063i	−0.605422	−	1.04862i	−0.991985	−	0.126359i	$-0.959671\pi$
$739$	−16.4581	−	28.5063i	−0.605422	−	1.04862i	0.386562	−	0.922263i	$-0.373662\pi$
$740$		0			0
$741$	−14.0983			−0.517913
$742$	−5.82711	+	5.87138i	−0.213920	+	0.215545i
$743$			38.8112i			1.42385i	0.702258	+	0.711923i	$0.252175\pi$
$743$			38.8112i			1.42385i	−0.702258	+	0.711923i	$0.747825\pi$
$744$	−5.67720	+	9.83320i	−0.208136	+	0.360503i
$745$		0			0
$746$	−1.30827	−	2.26598i	−0.0478990	−	0.0829635i
$747$	5.95256	+	3.43671i	0.217793	+	0.125743i
$748$			3.28242i			0.120017i
$749$	−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	$-0.0181729\pi$
$752$	−19.8845	+	11.4803i	−0.725115	+	0.418645i
$753$	−19.7888	+	11.4251i	−0.721143	+	0.416352i
$754$	−5.03496	+	8.72081i	−0.183362	+	0.317593i
$755$		0			0
$756$	1.18532	−	4.49162i	0.0431098	−	0.163359i
$757$			7.17713i			0.260857i	0.991458	+	0.130429i	$0.0416354\pi$
$757$			7.17713i			0.260857i	−0.991458	+	0.130429i	$0.958365\pi$
$758$	−1.32757	−	0.766471i	−0.0482194	−	0.0278395i
$759$	−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	$0.122629\pi$
$762$		−	8.66723i		−	0.313980i
$763$	0.271112	+	0.0715455i	0.00981491	+	0.00259012i
$764$	16.7278			0.605189
$765$		0			0
$766$	5.34021	+	9.24952i	0.192950	+	0.334199i
$767$	56.6923	−	32.7313i	2.04704	−	1.18186i
$768$	0.137429	+	0.0793447i	0.00495904	+	0.00286310i
$769$	−50.2712			−1.81283			−0.906413	−	0.422393i	$-0.861190\pi$
$769$	−50.2712			−1.81283			−0.906413	+	0.422393i	$0.861190\pi$
$770$		0			0
$771$	−25.1381			−0.905326
$772$	−22.9696	−	13.2615i	−0.826693	−	0.477291i
$773$	23.4701	−	13.5505i	0.844162	−	0.487377i	−0.0145147	−	0.999895i	$-0.504620\pi$
$773$	23.4701	−	13.5505i	0.844162	−	0.487377i	0.858677	+	0.512517i	$0.171287\pi$
$774$	−0.350186	−	0.606540i	−0.0125872	−	0.0218016i
$775$		0			0
$776$	10.2079			0.366444
$777$	−6.56638	+	6.61628i	−0.235568	+	0.237358i
$778$		−	6.35588i		−	0.227869i
$779$	−10.8785	+	18.8421i	−0.389763	+	0.675090i
$780$		0			0
$781$	−41.3423	−	71.6070i	−1.47935	−	2.56230i
$782$	1.12575	+	0.649950i	0.0402566	+	0.0232422i
$783$			4.00000i			0.142948i
$784$	15.7960	+	8.96106i	0.564141	+	0.320038i
$785$		0			0
$786$	2.22951	−	3.86162i	0.0795238	−	0.137739i
$787$	−29.7480	+	17.1750i	−1.06040	+	0.612224i	−0.925543	−	0.378641i	$-0.876391\pi$
$787$	−29.7480	+	17.1750i	−1.06040	+	0.612224i	−0.134859	+	0.990865i	$0.543058\pi$
$788$	25.6808	−	14.8268i	0.914840	−	0.528183i
$789$	6.77910	−	11.7417i	0.241342	−	0.418017i
$790$		0			0
$791$	−8.78304	−	8.71681i	−0.312289	−	0.309934i
$792$			9.90838i			0.352079i
$793$	−22.0591	−	12.7358i	−0.783341	−	0.452262i
$794$	−1.72841	−	2.99369i	−0.0613388	−	0.106242i
$795$		0			0
$796$	−22.1472	+	38.3600i	−0.784986	+	1.35964i
$797$			16.5581i			0.586517i	0.956033	+	0.293258i	$0.0947396\pi$
$797$			16.5581i			0.586517i	−0.956033	+	0.293258i	$0.905260\pi$
$798$	0.949713	+	3.49146i	0.0336195	+	0.123596i
$799$	3.09919			0.109641
$800$		0			0
$801$	2.17509	+	3.76737i	0.0768531	+	0.133114i
$802$	1.35297	−	0.781140i	0.0477752	−	0.0275830i
$803$	35.4934	+	20.4921i	1.25254	+	0.723152i
$804$	−6.59439			−0.232566
$805$		0			0
$806$	−15.4010			−0.542478
$807$	−7.81783	−	4.51363i	−0.275201	−	0.158887i
$808$	−2.65184	+	1.53104i	−0.0932912	+	0.0538617i
$809$	−4.27903	−	7.41150i	−0.150443	−	0.260574i	0.780948	−	0.624597i	$-0.214737\pi$
$809$	−4.27903	−	7.41150i	−0.150443	−	0.260574i	−0.931390	+	0.364022i	$0.881403\pi$
$810$		0			0
$811$	21.4277			0.752429			0.376215	−	0.926533i	$-0.377226\pi$
$811$	21.4277			0.752429			0.376215	+	0.926533i	$0.377226\pi$
$812$	−17.9665	−	4.74129i	−0.630500	−	0.166387i
$813$			4.77639i			0.167515i
$814$	4.64743	−	8.04959i	0.162893	−	0.282138i
$815$		0			0
$816$	0.454260	+	0.786802i	0.0159023	+	0.0275436i
$817$	−3.39672	−	1.96110i	−0.118836	−	0.0686100i
$818$			1.23300i			0.0431107i
$819$	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	$0.0816745\pi$
$822$	−0.357147	+	0.206199i	−0.0124569	+	0.00719201i
$823$	21.3946	−	12.3522i	0.745768	−	0.430569i	−0.0783949	−	0.996922i	$-0.524980\pi$
$823$	21.3946	−	12.3522i	0.745768	−	0.430569i	0.824163	+	0.566353i	$0.191646\pi$
$824$	−9.42984	+	16.3330i	−0.328504	+	0.568986i
$825$		0			0
$826$	−11.9250	−	11.8351i	−0.414924	−	0.411794i
$827$			28.8578i			1.00348i	0.865017	+	0.501742i	$0.167307\pi$
$827$			28.8578i			1.00348i	−0.865017	+	0.501742i	$0.832693\pi$
$828$	−11.4218	−	6.59439i	−0.396936	−	0.229171i
$829$	−0.434740	−	0.752992i	−0.0150991	−	0.0261525i	0.858377	−	0.513019i	$-0.171473\pi$
$829$	−0.434740	−	0.752992i	−0.0150991	−	0.0261525i	−0.873476	+	0.486867i	$0.838140\pi$
$830$		0			0
$831$	0.935357	−	1.62009i	0.0324472	−	0.0562002i
$832$		−	13.8608i		−	0.480537i
$833$	−1.24169	−	2.11355i	−0.0430219	−	0.0732302i
$834$	7.07420			0.244960
$835$		0			0
$836$	12.9701	+	22.4649i	0.448581	+	0.776966i
$837$	−5.29802	+	3.05882i	−0.183127	+	0.105728i
$838$	13.9837	+	8.07350i	0.483059	+	0.278895i
$839$	−21.7235			−0.749980			−0.374990	−	0.927029i	$-0.622354\pi$
$839$	−21.7235			−0.749980			−0.374990	+	0.927029i	$0.622354\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−11.5026	−	6.64104i	−0.396406	−	0.228865i
$843$	0.842425	−	0.486374i	0.0290147	−	0.0167516i
$844$	−17.9062	−	31.0144i	−0.616355	−	1.06756i
$845$		0			0
$846$	4.37349			0.150364
$847$	−12.1526	−	44.6771i	−0.417569	−	1.53512i
$848$			16.4144i			0.563673i
$849$	12.0899	−	20.9402i	0.414923	−	0.718667i
$850$		0			0
$851$	13.2326	+	22.9195i	0.453606	+	0.785669i
$852$	−23.5509	−	13.5971i	−0.806840	−	0.465829i
$853$		−	0.670546i		−	0.0229591i	−0.999934	−	0.0114795i	$-0.996346\pi$
$853$		−	0.670546i		−	0.0229591i	0.999934	−	0.0114795i	$-0.00365413\pi$
$854$	−1.66806	+	6.32090i	−0.0570800	+	0.216297i
$855$		0			0
$856$	4.97582	−	8.61837i	0.170070	−	0.294570i
$857$	21.2076	−	12.2442i	0.724437	−	0.418254i	−0.0919463	−	0.995764i	$-0.529309\pi$
$857$	21.2076	−	12.2442i	0.724437	−	0.418254i	0.816384	+	0.577510i	$0.195975\pi$
$858$	−11.6391	+	6.71982i	−0.397352	+	0.229411i
$859$	4.79970	−	8.31332i	0.163764	−	0.283647i	−0.772452	−	0.635073i	$-0.780970\pi$
$859$	4.79970	−	8.31332i	0.163764	−	0.283647i	0.936215	+	0.351426i	$0.114303\pi$
$860$		0			0
$861$	5.30743	−	20.1118i	0.180877	−	0.685407i
$862$		−	7.01165i		−	0.238818i
$863$	−25.5511	−	14.7519i	−0.869770	−	0.502162i	−0.00249807	−	0.999997i	$-0.500795\pi$
$863$	−25.5511	−	14.7519i	−0.869770	−	0.502162i	−0.867272	+	0.497835i	$0.834128\pi$
$864$	2.49705	+	4.32502i	0.0849515	+	0.147140i
$865$		0			0
$866$	7.40561	−	12.8269i	0.251653	−	0.435875i
$867$			16.8774i			0.573186i
$868$	−7.45917	−	27.4224i	−0.253181	−	0.930777i
$869$	−12.6088			−0.427723
$870$		0			0
$871$	−9.56662	−	16.5699i	−0.324152	−	0.561448i
$872$	−0.170345	+	0.0983489i	−0.00576862	+	0.00333052i
$873$	4.76308	+	2.74997i	0.161206	+	0.0930722i
$874$	10.2728			0.347484
$875$		0			0
$876$	13.4793			0.455425
$877$	4.59656	+	2.65383i	0.155215	+	0.0896134i	0.575596	−	0.817734i	$-0.304770\pi$
$877$	4.59656	+	2.65383i	0.155215	+	0.0896134i	−0.420381	+	0.907348i	$0.638104\pi$
$878$	−0.887545	+	0.512424i	−0.0299532	+	0.0172935i
$879$	−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	$0.188242\pi$
$882$	−1.75223	−	2.98259i	−0.0590008	−	0.100429i
$883$			6.02862i			0.202879i	0.994842	+	0.101440i	$0.0323449\pi$
$883$			6.02862i			0.202879i	−0.994842	+	0.101440i	$0.967655\pi$
$884$	−1.56613	+	2.71262i	−0.0526748	+	0.0912354i
$885$		0			0
$886$	7.92593	+	13.7281i	0.266277	+	0.461205i
$887$	−6.91509	−	3.99243i	−0.232186	−	0.134053i	0.379394	−	0.925235i	$-0.376132\pi$
$887$	−6.91509	−	3.99243i	−0.232186	−	0.134053i	−0.611580	+	0.791183i	$0.709466\pi$
$888$		−	6.53918i		−	0.219440i
$889$	32.9361	+	32.6877i	1.10464	+	1.09631i
$890$		0			0
$891$	−2.66927	+	4.62330i	−0.0894238	+	0.154887i
$892$	34.3248	−	19.8175i	1.14928	−	0.663537i
$893$	21.2109	−	12.2461i	0.709795	−	0.409801i
$894$	4.79266	−	8.30113i	0.160290	−	0.277631i
$895$		0			0
$896$	−28.9325	+	7.86992i	−0.966565	+	0.262916i
$897$		−	38.2665i		−	1.27768i
$898$	1.90917	+	1.10226i	0.0637099	+	0.0367829i
$899$	12.2353	+	21.1921i	0.408069	+	0.706796i
$900$		0			0
$901$	1.10779	−	1.91875i	0.0369059	−	0.0639229i
$902$			20.7406i			0.690587i
$903$	3.62560	+	0.956782i	0.120652	+	0.0318397i
$904$	8.68069			0.288716
$905$		0			0
$906$	−4.57782	−	7.92902i	−0.152088	−	0.263424i
$907$	2.19198	−	1.26554i	0.0727836	−	0.0420216i	−0.463167	−	0.886271i	$-0.653287\pi$
$907$	2.19198	−	1.26554i	0.0727836	−	0.0420216i	0.535950	+	0.844250i	$0.319953\pi$
$908$	21.5393	+	12.4357i	0.714806	+	0.412693i
$909$	−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	$0.492562\pi$
$912$	6.21793	+	3.58992i	0.205896	+	0.118874i
$913$	31.7779	−	18.3470i	1.05170	−	0.607197i
$914$	0.560942	+	0.971580i	0.0185543	+	0.0321370i
$915$		0			0
$916$	31.2640			1.03299
$917$	6.26604	+	23.0361i	0.206923	+	0.760718i
$918$		−	0.173053i		−	0.00571159i
$919$	23.3418	−	40.4292i	0.769975	−	1.33364i	−0.167601	−	0.985855i	$-0.553602\pi$
$919$	23.3418	−	40.4292i	0.769975	−	1.33364i	0.937576	−	0.347780i	$-0.113065\pi$
$920$		0			0
$921$	−1.69698	−	2.93925i	−0.0559173	−	0.0968516i
$922$	1.85351	+	1.07012i	0.0610420	+	0.0352426i
$923$		−	78.9023i		−	2.59710i
$924$	−17.6022	−	17.4694i	−0.579070	−	0.574703i
$925$		0			0
$926$	−10.3247	+	17.8829i	−0.339290	+	0.587667i
$927$	−8.80003	+	5.08070i	−0.289031	+	0.166872i
$928$	17.3001	−	9.98821i	0.567903	−	0.327879i
$929$	−8.91923	+	15.4486i	−0.292631	+	0.506851i	−0.974431	−	0.224687i	$-0.927864\pi$
$929$	−8.91923	+	15.4486i	−0.292631	+	0.506851i	0.681800	+	0.731538i	$0.261197\pi$
$930$		0			0
$931$	−16.8496	−	9.55878i	−0.552223	−	0.313277i
$932$		−	23.9662i		−	0.785040i
$933$	2.13485	+	1.23255i	0.0698917	+	0.0403520i
$934$	−9.48252	−	16.4242i	−0.310278	−	0.537416i
$935$		0			0
$936$	−4.72757	+	8.18839i	−0.154525	+	0.267646i
$937$		−	0.343849i		−	0.0112330i	−0.999984	−	0.00561652i	$-0.998212\pi$
$937$		−	0.343849i		−	0.0112330i	0.999984	−	0.00561652i	$-0.00178780\pi$
$938$	−3.45911	+	3.48540i	−0.112944	+	0.113802i
$939$	−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	$0.562335\pi$
$942$	−2.05405	+	1.18591i	−0.0669246	+	0.0386389i
$943$	−51.1426	−	29.5272i	−1.66543	−	0.961537i
$944$	−33.3383			−1.08507
$945$		0			0
$946$	−3.73896			−0.121564
$947$	23.9558	+	13.8309i	0.778459	+	0.449444i	0.835884	−	0.548906i	$-0.184956\pi$
$947$	23.9558	+	13.8309i	0.778459	+	0.449444i	−0.0574248	+	0.998350i	$0.518289\pi$
$948$	−3.59132	+	2.07345i	−0.116641	+	0.0673425i
$949$	19.5547	+	33.8698i	0.634774	+	1.09946i
$950$		0			0
$951$	−14.2995			−0.463693
$952$	1.66268	+	0.438777i	0.0538879	+	0.0142208i
$953$		−	4.24907i		−	0.137641i	−0.997629	−	0.0688204i	$-0.978076\pi$
$953$		−	4.24907i		−	0.137641i	0.997629	−	0.0688204i	$-0.0219236\pi$
$954$	1.56329	−	2.70769i	0.0506133	−	0.0876648i
$955$		0			0
$956$	−6.61485	−	11.4573i	−0.213940	−	0.370554i
$957$	18.4932	+	10.6771i	0.597801	+	0.345141i
$958$			18.7977i			0.607325i
$959$	0.563379	−	2.13485i	0.0181924	−	0.0689378i
$960$		0			0
$961$	−3.21271	+	5.56458i	−0.103636	+	0.179503i
$962$	7.68137	−	4.43484i	0.247657	−	0.142985i
$963$	4.64349	−	2.68092i	0.149634	−	0.0863914i
$964$	−25.0403	+	43.3711i	−0.806495	+	1.39689i
$965$		0			0
$966$	−9.47676	+	2.57777i	−0.304910	+	0.0829385i
$967$			59.6146i			1.91708i	0.284965	+	0.958538i	$0.408018\pi$
$967$			59.6146i			1.91708i	−0.284965	+	0.958538i	$0.591982\pi$
$968$	28.1286	+	16.2400i	0.904087	+	0.521975i
$969$	−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	$0.161808\pi$
$972$			1.75579i			0.0563171i
$973$	−26.6798	+	26.8825i	−0.855314	+	0.861814i
$974$	11.1598			0.357583
$975$		0			0
$976$	6.48598	+	11.2341i	0.207611	+	0.359593i
$977$	−19.9624	+	11.5253i	−0.638653	+	0.368726i	−0.784095	−	0.620640i	$-0.786873\pi$
$977$	−19.9624	+	11.5253i	−0.638653	+	0.368726i	0.145443	+	0.989367i	$0.453539\pi$
$978$	0.353906	+	0.204328i	0.0113167	+	0.00653368i
$979$	23.2236			0.742230
$980$		0			0
$981$	−0.105979			−0.00338364
$982$	−0.0574108	−	0.0331461i	−0.00183205	−	0.00105774i
$983$	−27.5698	+	15.9174i	−0.879339	+	0.507687i	−0.870441	−	0.492274i	$-0.836166\pi$
$983$	−27.5698	+	15.9174i	−0.879339	+	0.507687i	−0.00889883	+	0.999960i	$0.502833\pi$
$984$	7.29577	+	12.6367i	0.232581	+	0.402842i
$985$		0			0
$986$	−0.692210			−0.0220445
$987$	−16.4943	+	16.6196i	−0.525018	+	0.529008i
$988$			24.7536i			0.787518i
$989$	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	$0.792237\pi$
$992$	26.4589	+	15.2760i	0.840071	+	0.485015i
$993$		−	19.5855i		−	0.621525i
$994$	−19.5403	+	5.31516i	−0.619781	+	0.168587i
$995$		0			0
$996$	6.03415	−	10.4515i	0.191199	−	0.331167i
$997$	24.4625	−	14.1235i	0.774737	−	0.447294i	−0.0598251	−	0.998209i	$-0.519054\pi$
$997$	24.4625	−	14.1235i	0.774737	−	0.447294i	0.834562	+	0.550914i	$0.185721\pi$
$998$	−6.65717	+	3.84352i	−0.210729	+	0.121665i
$999$	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.r.h.499.5		16
5.2	odd	4		525.2.i.j.226.2	yes	8
5.3	odd	4		525.2.i.i.226.3	yes	8
5.4	even	2	inner	525.2.r.h.499.4		16
7.4	even	3	inner	525.2.r.h.424.4		16
35.2	odd	12		3675.2.a.br.1.3		4
35.4	even	6	inner	525.2.r.h.424.5		16
35.12	even	12		3675.2.a.bq.1.3		4
35.18	odd	12		525.2.i.i.151.3	✓	8
35.23	odd	12		3675.2.a.bw.1.2		4
35.32	odd	12		525.2.i.j.151.2	yes	8
35.33	even	12		3675.2.a.bx.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.i.i.151.3	✓	8	35.18	odd	12
525.2.i.i.226.3	yes	8	5.3	odd	4
525.2.i.j.151.2	yes	8	35.32	odd	12
525.2.i.j.226.2	yes	8	5.2	odd	4
525.2.r.h.424.4		16	7.4	even	3	inner
525.2.r.h.424.5		16	35.4	even	6	inner
525.2.r.h.499.4		16	5.4	even	2	inner
525.2.r.h.499.5		16	1.1	even	1	trivial
3675.2.a.bq.1.3		4	35.12	even	12
3675.2.a.br.1.3		4	35.2	odd	12
3675.2.a.bw.1.2		4	35.23	odd	12
3675.2.a.bx.1.2		4	35.33	even	12

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.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.427967 + 0.247087i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.877896 - 1.52056i) q^{4} +0.494173 q^{6} +(-1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.427967 + 0.247087i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.877896 - 1.52056i) q^{4} +0.494173 q^{6} +(-1.86373 + 1.87790i) q^{7} -1.85601i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.66927 - 4.62330i) q^{11} +(-1.52056 - 0.877896i) q^{12} -5.09433i q^{13} +(-1.26162 + 0.343173i) q^{14} +(-1.29720 + 2.24681i) q^{16} +(0.303270 - 0.175093i) q^{17} +(0.427967 - 0.247087i) q^{18} +(1.38372 - 2.39668i) q^{19} +(-0.675093 + 2.55817i) q^{21} -2.63816i q^{22} +(6.50522 + 3.75579i) q^{23} +(-0.928006 - 1.60735i) q^{24} +(1.25874 - 2.18020i) q^{26} -1.00000i q^{27} +(4.49162 + 1.18532i) q^{28} -4.00000 q^{29} +(-3.05882 - 5.29802i) q^{31} +(-4.32502 + 2.49705i) q^{32} +(-4.62330 - 2.66927i) q^{33} +0.173053 q^{34} -1.75579 q^{36} +(3.05121 + 1.76162i) q^{37} +(1.18437 - 0.683799i) q^{38} +(-2.54716 - 4.41182i) q^{39} -7.86177 q^{41} +(-0.921008 + 0.928006i) q^{42} -1.41726i q^{43} +(-4.68668 + 8.11757i) q^{44} +(1.85601 + 3.21471i) q^{46} +(7.66443 + 4.42506i) q^{47} +2.59439i q^{48} +(-0.0529894 - 6.99980i) q^{49} +(0.175093 - 0.303270i) q^{51} +(-7.74623 + 4.47229i) q^{52} +(5.47924 - 3.16344i) q^{53} +(0.247087 - 0.427967i) q^{54} +(3.48540 + 3.45911i) q^{56} -2.76745i q^{57} +(-1.71187 - 0.988347i) q^{58} +(6.42506 + 11.1285i) q^{59} +(2.50000 - 4.33013i) q^{61} -3.02317i q^{62} +(0.694439 + 2.55299i) q^{63} +2.72083 q^{64} +(-1.31908 - 2.28471i) q^{66} +(3.25261 - 1.87790i) q^{67} +(-0.532479 - 0.307427i) q^{68} +7.51159 q^{69} +15.4883 q^{71} +(-1.60735 - 0.928006i) q^{72} +(-6.64853 + 3.83853i) q^{73} +(0.870545 + 1.50783i) q^{74} -4.85906 q^{76} +(13.6569 + 3.60401i) q^{77} -2.51748i q^{78} +(1.18092 - 2.04541i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.36458 - 1.94254i) q^{82} +6.87342i q^{83} +(4.48252 - 1.21929i) q^{84} +(0.350186 - 0.606540i) q^{86} +(-3.46410 + 2.00000i) q^{87} +(-8.58091 + 4.95419i) q^{88} +(-2.17509 + 3.76737i) q^{89} +(9.56662 + 9.49447i) q^{91} -13.1888i q^{92} +(-5.29802 - 3.05882i) q^{93} +(2.18675 + 3.78756i) q^{94} +(-2.49705 + 4.32502i) q^{96} +5.49993i q^{97} +(1.70688 - 3.00877i) q^{98} -5.33853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9	\( 16 q + 14 q^{4} - 4 q^{6} + 8 q^{9} - 16 q^{11} + 24 q^{14} - 34 q^{16} + 6 q^{19} + 4 q^{21} - 6 q^{24} + 38 q^{26} - 64 q^{29} - 18 q^{31} - 56 q^{34} + 28 q^{36} + 14 q^{39} + 16 q^{41} + 52 q^{44} + 12 q^{46} + 42 q^{49} - 12 q^{51} - 2 q^{54} - 42 q^{56} + 20 q^{59} + 40 q^{61} - 84 q^{64} - 24 q^{66} + 8 q^{69} + 88 q^{71} - 42 q^{74} - 92 q^{76} + 16 q^{79} - 8 q^{81} + 36 q^{84} - 24 q^{86} - 20 q^{89} + 42 q^{91} + 44 q^{94} + 34 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q + 14 * q^4 - 4 * q^6 + 8 * q^9 - 16 * q^11 + 24 * q^14 - 34 * q^16 + 6 * q^19 + 4 * q^21 - 6 * q^24 + 38 * q^26 - 64 * q^29 - 18 * q^31 - 56 * q^34 + 28 * q^36 + 14 * q^39 + 16 * q^41 + 52 * q^44 + 12 * q^46 + 42 * q^49 - 12 * q^51 - 2 * q^54 - 42 * q^56 + 20 * q^59 + 40 * q^61 - 84 * q^64 - 24 * q^66 + 8 * q^69 + 88 * q^71 - 42 * q^74 - 92 * q^76 + 16 * q^79 - 8 * q^81 + 36 * q^84 - 24 * q^86 - 20 * q^89 + 42 * q^91 + 44 * q^94 + 34 * q^96 - 32 * q^99

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