LMFDB - Embedded newform 925.2.m.b.899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(249,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("925.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.m (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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	925.899
Dual form			925.2.m.b.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{6} +(3.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{6} +(3.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(2.23205 + 3.86603i) q^{9} -4.73205 q^{11} +(2.36603 - 1.36603i) q^{12} +(-1.73205 + 3.00000i) q^{13} +3.46410i q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.86603 - 3.23205i) q^{17} +(-2.23205 + 3.86603i) q^{18} +(-1.09808 - 0.633975i) q^{19} +(4.73205 + 8.19615i) q^{21} +(-2.36603 - 4.09808i) q^{22} +0.732051 q^{23} +(7.09808 + 4.09808i) q^{24} -3.46410 q^{26} +4.00000i q^{27} +(3.00000 - 1.73205i) q^{28} -0.267949i q^{29} -8.19615i q^{31} +(2.50000 - 4.33013i) q^{32} +(-11.1962 - 6.46410i) q^{33} +(1.86603 - 3.23205i) q^{34} +4.46410 q^{36} +(6.06218 - 0.500000i) q^{37} -1.26795i q^{38} +(-8.19615 + 4.73205i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-4.73205 + 8.19615i) q^{42} -3.46410 q^{43} +(-2.36603 + 4.09808i) q^{44} +(0.366025 + 0.633975i) q^{46} +2.19615i q^{47} +2.73205i q^{48} +(2.50000 + 4.33013i) q^{49} -10.1962i q^{51} +(1.73205 + 3.00000i) q^{52} +(-2.19615 + 1.26795i) q^{53} +(-3.46410 + 2.00000i) q^{54} +(9.00000 + 5.19615i) q^{56} +(-1.73205 - 3.00000i) q^{57} +(0.232051 - 0.133975i) q^{58} +(11.6603 - 6.73205i) q^{59} +(3.69615 + 2.13397i) q^{61} +(7.09808 - 4.09808i) q^{62} +15.4641i q^{63} +7.00000 q^{64} -12.9282i q^{66} +(-6.29423 - 3.63397i) q^{67} -3.73205 q^{68} +(1.73205 + 1.00000i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(6.69615 + 11.5981i) q^{72} +(3.46410 + 5.00000i) q^{74} +(-1.09808 + 0.633975i) q^{76} +(-14.1962 - 8.19615i) q^{77} +(-8.19615 - 4.73205i) q^{78} +(-3.29423 - 1.90192i) q^{79} +(1.23205 - 2.13397i) q^{81} -3.00000 q^{82} +(-7.09808 + 4.09808i) q^{83} +9.46410 q^{84} +(-1.73205 - 3.00000i) q^{86} +(0.366025 - 0.633975i) q^{87} -14.1962 q^{88} +(-7.96410 + 4.59808i) q^{89} +(-10.3923 + 6.00000i) q^{91} +(0.366025 - 0.633975i) q^{92} +(11.1962 - 19.3923i) q^{93} +(-1.90192 + 1.09808i) q^{94} +(11.8301 - 6.83013i) q^{96} -4.26795 q^{97} +(-2.50000 + 4.33013i) q^{98} +(-10.5622 - 18.2942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 12 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 + 12 * q^7 + 12 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 12 q^{7} + 12 q^{8} + 2 q^{9} - 12 q^{11} + 6 q^{12} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 6 q^{19} + 12 q^{21} - 6 q^{22} - 4 q^{23} + 18 q^{24} + 12 q^{28} + 10 q^{32} - 24 q^{33} + 4 q^{34} + 4 q^{36} - 12 q^{39} - 6 q^{41} - 12 q^{42} - 6 q^{44} - 2 q^{46} + 10 q^{49} + 12 q^{53} + 36 q^{56} - 6 q^{58} + 12 q^{59} - 6 q^{61} + 18 q^{62} + 28 q^{64} + 6 q^{67} - 8 q^{68} - 12 q^{71} + 6 q^{72} + 6 q^{76} - 36 q^{77} - 12 q^{78} + 18 q^{79} - 2 q^{81} - 12 q^{82} - 18 q^{83} + 24 q^{84} - 2 q^{87} - 36 q^{88} - 18 q^{89} - 2 q^{92} + 24 q^{93} - 18 q^{94} + 30 q^{96} - 24 q^{97} - 10 q^{98} - 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 + 12 * q^7 + 12 * q^8 + 2 * q^9 - 12 * q^11 + 6 * q^12 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 6 * q^19 + 12 * q^21 - 6 * q^22 - 4 * q^23 + 18 * q^24 + 12 * q^28 + 10 * q^32 - 24 * q^33 + 4 * q^34 + 4 * q^36 - 12 * q^39 - 6 * q^41 - 12 * q^42 - 6 * q^44 - 2 * q^46 + 10 * q^49 + 12 * q^53 + 36 * q^56 - 6 * q^58 + 12 * q^59 - 6 * q^61 + 18 * q^62 + 28 * q^64 + 6 * q^67 - 8 * q^68 - 12 * q^71 + 6 * q^72 + 6 * q^76 - 36 * q^77 - 12 * q^78 + 18 * q^79 - 2 * q^81 - 12 * q^82 - 18 * q^83 + 24 * q^84 - 2 * q^87 - 36 * q^88 - 18 * q^89 - 2 * q^92 + 24 * q^93 - 18 * q^94 + 30 * q^96 - 24 * q^97 - 10 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.990418	−	0.138104i	$-0.0441007\pi$
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.375608	+	0.926779i	$0.377434\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.73205i			1.11536i
$7$	3.00000	+	1.73205i	1.13389	+	0.654654i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	3.00000	+	1.73205i	1.13389	+	0.654654i	0.188982	+	0.981981i	$0.439481\pi$
$8$	3.00000			1.06066
$9$	2.23205	+	3.86603i	0.744017	+	1.28868i
$10$		0			0
$11$	−4.73205			−1.42677			−0.713384	−	0.700774i	$-0.752838\pi$
$11$	−4.73205			−1.42677			−0.713384	+	0.700774i	$0.752838\pi$
$12$	2.36603	−	1.36603i	0.683013	−	0.394338i
$13$	−1.73205	+	3.00000i	−0.480384	+	0.832050i	−0.999747	−	0.0225039i	$-0.992836\pi$
$13$	−1.73205	+	3.00000i	−0.480384	+	0.832050i	0.519362	+	0.854554i	$0.326170\pi$
$14$			3.46410i			0.925820i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.86603	−	3.23205i	−0.452578	−	0.783887i	0.545968	−	0.837806i	$-0.316162\pi$
$17$	−1.86603	−	3.23205i	−0.452578	−	0.783887i	−0.998545	+	0.0539188i	$0.982829\pi$
$18$	−2.23205	+	3.86603i	−0.526099	+	0.911231i
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	0.368725	−	0.929538i	$-0.379794\pi$
$19$	−1.09808	−	0.633975i	−0.251916	−	0.145444i	−0.620641	+	0.784095i	$0.713128\pi$
$20$		0			0
$21$	4.73205	+	8.19615i	1.03262	+	1.78855i
$22$	−2.36603	−	4.09808i	−0.504438	−	0.873713i
$23$	0.732051			0.152643			0.0763216	−	0.997083i	$-0.475682\pi$
$23$	0.732051			0.152643			0.0763216	+	0.997083i	$0.475682\pi$
$24$	7.09808	+	4.09808i	1.44889	+	0.836516i
$25$		0			0
$26$	−3.46410			−0.679366
$27$			4.00000i			0.769800i
$28$	3.00000	−	1.73205i	0.566947	−	0.327327i
$29$		−	0.267949i		−	0.0497569i	−0.999690	−	0.0248785i	$-0.992080\pi$
$29$		−	0.267949i		−	0.0497569i	0.999690	−	0.0248785i	$-0.00791988\pi$
$30$		0			0
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	−11.1962	−	6.46410i	−1.94900	−	1.12526i
$34$	1.86603	−	3.23205i	0.320021	−	0.554292i
$35$		0			0
$36$	4.46410			0.744017
$37$	6.06218	−	0.500000i	0.996616	−	0.0821995i
$37$	6.06218	−	0.500000i	0.996616	−	0.0821995i
$38$		−	1.26795i		−	0.205689i
$39$	−8.19615	+	4.73205i	−1.31243	+	0.757735i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	−4.73205	+	8.19615i	−0.730171	+	1.26469i
$43$	−3.46410			−0.528271			−0.264135	−	0.964486i	$-0.585087\pi$
$43$	−3.46410			−0.528271			−0.264135	+	0.964486i	$0.585087\pi$
$44$	−2.36603	+	4.09808i	−0.356692	+	0.617808i
$45$		0			0
$46$	0.366025	+	0.633975i	0.0539675	+	0.0934745i
$47$			2.19615i			0.320342i	0.987089	+	0.160171i	$0.0512045\pi$
$47$			2.19615i			0.320342i	−0.987089	+	0.160171i	$0.948795\pi$
$48$			2.73205i			0.394338i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$		0			0
$51$		−	10.1962i		−	1.42775i
$52$	1.73205	+	3.00000i	0.240192	+	0.416025i
$53$	−2.19615	+	1.26795i	−0.301665	+	0.174166i	−0.643191	−	0.765706i	$-0.722390\pi$
$53$	−2.19615	+	1.26795i	−0.301665	+	0.174166i	0.341526	+	0.939872i	$0.389056\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$		0			0
$56$	9.00000	+	5.19615i	1.20268	+	0.694365i
$57$	−1.73205	−	3.00000i	−0.229416	−	0.397360i
$58$	0.232051	−	0.133975i	0.0304698	−	0.0175917i
$59$	11.6603	−	6.73205i	1.51804	−	0.876438i	0.518261	−	0.855223i	$-0.326580\pi$
$59$	11.6603	−	6.73205i	1.51804	−	0.876438i	0.999775	−	0.0212158i	$-0.00675370\pi$
$60$		0			0
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	0.717597	−	0.696459i	$-0.245242\pi$
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	−0.244353	+	0.969686i	$0.578576\pi$
$62$	7.09808	−	4.09808i	0.901457	−	0.520456i
$63$			15.4641i			1.94829i
$64$	7.00000			0.875000
$65$		0			0
$66$		−	12.9282i		−	1.59135i
$67$	−6.29423	−	3.63397i	−0.768962	−	0.443961i	0.0635419	−	0.997979i	$-0.479760\pi$
$67$	−6.29423	−	3.63397i	−0.768962	−	0.443961i	−0.832504	+	0.554019i	$0.813094\pi$
$68$	−3.73205			−0.452578
$69$	1.73205	+	1.00000i	0.208514	+	0.120386i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	6.69615	+	11.5981i	0.789149	+	1.36685i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	3.46410	+	5.00000i	0.402694	+	0.581238i
$75$		0			0
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	−14.1962	−	8.19615i	−1.61780	−	0.934038i
$78$	−8.19615	−	4.73205i	−0.928032	−	0.535799i
$79$	−3.29423	−	1.90192i	−0.370630	−	0.213983i	0.303104	−	0.952958i	$-0.401977\pi$
$79$	−3.29423	−	1.90192i	−0.370630	−	0.213983i	−0.673734	+	0.738974i	$0.735310\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	−3.00000			−0.331295
$83$	−7.09808	+	4.09808i	−0.779115	+	0.449822i	−0.836117	−	0.548552i	$-0.815179\pi$
$83$	−7.09808	+	4.09808i	−0.779115	+	0.449822i	0.0570015	+	0.998374i	$0.481846\pi$
$84$	9.46410			1.03262
$85$		0			0
$86$	−1.73205	−	3.00000i	−0.186772	−	0.323498i
$87$	0.366025	−	0.633975i	0.0392420	−	0.0679692i
$88$	−14.1962			−1.51331
$89$	−7.96410	+	4.59808i	−0.844193	+	0.487395i	−0.858687	−	0.512500i	$-0.828720\pi$
$89$	−7.96410	+	4.59808i	−0.844193	+	0.487395i	0.0144942	+	0.999895i	$0.495386\pi$
$90$		0			0
$91$	−10.3923	+	6.00000i	−1.08941	+	0.628971i
$92$	0.366025	−	0.633975i	0.0381608	−	0.0660964i
$93$	11.1962	−	19.3923i	1.16099	−	2.01089i
$94$	−1.90192	+	1.09808i	−0.196168	+	0.113258i
$95$		0			0
$96$	11.8301	−	6.83013i	1.20741	−	0.697097i
$97$	−4.26795			−0.433345			−0.216672	−	0.976244i	$-0.569520\pi$
$97$	−4.26795			−0.433345			−0.216672	+	0.976244i	$0.569520\pi$
$98$	−2.50000	+	4.33013i	−0.252538	+	0.437409i
$99$	−10.5622	−	18.2942i	−1.06154	−	1.83864i
$100$		0			0
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$	8.83013	−	5.09808i	0.874313	−	0.504785i
$103$	12.9282			1.27385			0.636927	−	0.770924i	$-0.280205\pi$
$103$	12.9282			1.27385			0.636927	+	0.770924i	$0.280205\pi$
$104$	−5.19615	+	9.00000i	−0.509525	+	0.882523i
$105$		0			0
$106$	−2.19615	−	1.26795i	−0.213309	−	0.123154i
$107$	−11.1962	−	6.46410i	−1.08237	−	0.624908i	−0.150837	−	0.988559i	$-0.548197\pi$
$107$	−11.1962	−	6.46410i	−1.08237	−	0.624908i	−0.931536	+	0.363650i	$0.881530\pi$
$108$	3.46410	+	2.00000i	0.333333	+	0.192450i
$109$	5.89230	−	3.40192i	0.564380	−	0.325845i	−0.190521	−	0.981683i	$-0.561018\pi$
$109$	5.89230	−	3.40192i	0.564380	−	0.325845i	0.754902	+	0.655838i	$0.227685\pi$
$110$		0			0
$111$	15.0263	+	7.09808i	1.42623	+	0.673720i
$112$			3.46410i			0.327327i
$113$	−2.26795	−	3.92820i	−0.213351	−	0.369534i	0.739410	−	0.673255i	$-0.235104\pi$
$113$	−2.26795	−	3.92820i	−0.213351	−	0.369534i	−0.952761	+	0.303721i	$0.901771\pi$
$114$	1.73205	−	3.00000i	0.162221	−	0.280976i
$115$		0			0
$116$	−0.232051	−	0.133975i	−0.0215454	−	0.0124392i
$117$	−15.4641			−1.42966
$118$	11.6603	+	6.73205i	1.07341	+	0.619736i
$119$		−	12.9282i		−	1.18513i
$120$		0			0
$121$	11.3923			1.03566
$122$			4.26795i			0.386402i
$123$	−7.09808	+	4.09808i	−0.640012	+	0.369511i
$124$	−7.09808	−	4.09808i	−0.637426	−	0.368018i
$125$		0			0
$126$	−13.3923	+	7.73205i	−1.19308	+	0.688826i
$127$	10.5622	−	6.09808i	0.937242	−	0.541117i	0.0481471	−	0.998840i	$-0.484668\pi$
$127$	10.5622	−	6.09808i	0.937242	−	0.541117i	0.889095	+	0.457723i	$0.151335\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−8.19615	−	4.73205i	−0.721631	−	0.416634i
$130$		0			0
$131$	−9.16987	+	5.29423i	−0.801176	+	0.462559i	−0.843882	−	0.536529i	$-0.819735\pi$
$131$	−9.16987	+	5.29423i	−0.801176	+	0.462559i	0.0427065	+	0.999088i	$0.486402\pi$
$132$	−11.1962	+	6.46410i	−0.974500	+	0.562628i
$133$	−2.19615	−	3.80385i	−0.190431	−	0.329835i
$134$		−	7.26795i		−	0.627855i
$135$		0			0
$136$	−5.59808	−	9.69615i	−0.480031	−	0.831438i
$137$			6.46410i			0.552265i	0.961120	+	0.276133i	$0.0890529\pi$
$137$			6.46410i			0.552265i	−0.961120	+	0.276133i	$0.910947\pi$
$138$			2.00000i			0.170251i
$139$	6.29423	+	10.9019i	0.533870	+	0.924689i	0.999217	+	0.0395611i	$0.0125960\pi$
$139$	6.29423	+	10.9019i	0.533870	+	0.924689i	−0.465348	+	0.885128i	$0.654071\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$	−6.00000			−0.503509
$143$	8.19615	−	14.1962i	0.685397	−	1.18714i
$144$	−2.23205	+	3.86603i	−0.186004	+	0.322169i
$145$		0			0
$146$		0			0
$147$			13.6603i			1.12668i
$148$	2.59808	−	5.50000i	0.213561	−	0.452097i
$149$	−5.53590			−0.453518			−0.226759	−	0.973951i	$-0.572813\pi$
$149$	−5.53590			−0.453518			−0.226759	+	0.973951i	$0.572813\pi$
$150$		0			0
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	0.301502	+	0.953466i	$0.402512\pi$
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	−0.976476	+	0.215625i	$0.930821\pi$
$152$	−3.29423	−	1.90192i	−0.267197	−	0.154266i
$153$	8.33013	−	14.4282i	0.673451	−	1.16645i
$154$		−	16.3923i		−	1.32093i
$155$		0			0
$156$			9.46410i			0.757735i
$157$	12.4019	−	7.16025i	0.989781	−	0.571450i	0.0845724	−	0.996417i	$-0.473048\pi$
$157$	12.4019	−	7.16025i	0.989781	−	0.571450i	0.905209	+	0.424967i	$0.139714\pi$
$158$		−	3.80385i		−	0.302618i
$159$	−6.92820			−0.549442
$160$		0			0
$161$	2.19615	+	1.26795i	0.173081	+	0.0999284i
$162$	2.46410			0.193598
$163$	11.1962	+	19.3923i	0.876950	+	1.51892i	0.854671	+	0.519171i	$0.173759\pi$
$163$	11.1962	+	19.3923i	0.876950	+	1.51892i	0.0222798	+	0.999752i	$0.492908\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−7.09808	−	4.09808i	−0.550918	−	0.318072i
$167$	5.46410	−	9.46410i	0.422825	−	0.732354i	−0.573390	−	0.819283i	$-0.694372\pi$
$167$	5.46410	−	9.46410i	0.422825	−	0.732354i	0.996215	+	0.0869286i	$0.0277052\pi$
$168$	14.1962	+	24.5885i	1.09526	+	1.89704i
$169$	0.500000	+	0.866025i	0.0384615	+	0.0666173i
$170$		0			0
$171$		−	5.66025i		−	0.432850i
$172$	−1.73205	+	3.00000i	−0.132068	+	0.228748i
$173$	8.59808	−	4.96410i	0.653700	−	0.377414i	−0.136173	−	0.990685i	$-0.543480\pi$
$173$	8.59808	−	4.96410i	0.653700	−	0.377414i	0.789872	+	0.613271i	$0.210147\pi$
$174$	0.732051			0.0554966
$175$		0			0
$176$	−2.36603	−	4.09808i	−0.178346	−	0.308904i
$177$	36.7846			2.76490
$178$	−7.96410	−	4.59808i	−0.596935	−	0.344640i
$179$		−	1.46410i		−	0.109432i	−0.998502	−	0.0547160i	$-0.982575\pi$
$179$		−	1.46410i		−	0.109432i	0.998502	−	0.0547160i	$-0.0174254\pi$
$180$		0			0
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	−0.989406	−	0.145174i	$-0.953626\pi$
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	0.620427	+	0.784264i	$0.286959\pi$
$182$	−10.3923	−	6.00000i	−0.770329	−	0.444750i
$183$	5.83013	+	10.0981i	0.430975	+	0.746471i
$184$	2.19615			0.161903
$185$		0			0
$186$	22.3923			1.64188
$187$	8.83013	+	15.2942i	0.645723	+	1.11842i
$188$	1.90192	+	1.09808i	0.138712	+	0.0800854i
$189$	−6.92820	+	12.0000i	−0.503953	+	0.872872i
$190$		0			0
$191$		−	6.19615i		−	0.448338i	−0.974550	−	0.224169i	$-0.928033\pi$
$191$		−	6.19615i		−	0.448338i	0.974550	−	0.224169i	$-0.0719667\pi$
$192$	16.5622	+	9.56218i	1.19527	+	0.690091i
$193$	14.6603			1.05527			0.527634	−	0.849472i	$-0.323079\pi$
$193$	14.6603			1.05527			0.527634	+	0.849472i	$0.323079\pi$
$194$	−2.13397	−	3.69615i	−0.153210	−	0.265368i
$195$		0			0
$196$	5.00000			0.357143
$197$	−24.1865	+	13.9641i	−1.72322	+	0.994901i	−0.811182	+	0.584794i	$0.801175\pi$
$197$	−24.1865	+	13.9641i	−1.72322	+	0.994901i	−0.912038	+	0.410107i	$0.865491\pi$
$198$	10.5622	−	18.2942i	0.750621	−	1.30011i
$199$			11.0718i			0.784859i	0.919782	+	0.392429i	$0.128365\pi$
$199$			11.0718i			0.784859i	−0.919782	+	0.392429i	$0.871635\pi$
$200$		0			0
$201$	−9.92820	−	17.1962i	−0.700281	−	1.21292i
$202$	−4.50000	−	7.79423i	−0.316619	−	0.548400i
$203$	0.464102	−	0.803848i	0.0325735	−	0.0564190i
$204$	−8.83013	−	5.09808i	−0.618233	−	0.356937i
$205$		0			0
$206$	6.46410	+	11.1962i	0.450375	+	0.780073i
$207$	1.63397	+	2.83013i	0.113569	+	0.196707i
$208$	−3.46410			−0.240192
$209$	5.19615	+	3.00000i	0.359425	+	0.207514i
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$			2.53590i			0.174166i
$213$	−14.1962	+	8.19615i	−0.972704	+	0.561591i
$214$		−	12.9282i		−	0.883754i
$215$		0			0
$216$			12.0000i			0.816497i
$217$	14.1962	−	24.5885i	0.963698	−	1.66917i
$218$	5.89230	+	3.40192i	0.399077	+	0.230407i
$219$		0			0
$220$		0			0
$221$	12.9282			0.869645
$222$	1.36603	+	16.5622i	0.0916816	+	1.11158i
$223$			4.58846i			0.307266i	0.988128	+	0.153633i	$0.0490973\pi$
$223$			4.58846i			0.307266i	−0.988128	+	0.153633i	$0.950903\pi$
$224$	15.0000	−	8.66025i	1.00223	−	0.578638i
$225$		0			0
$226$	2.26795	−	3.92820i	0.150862	−	0.261300i
$227$	11.5622	−	20.0263i	0.767409	−	1.32919i	−0.171555	−	0.985175i	$-0.554879\pi$
$227$	11.5622	−	20.0263i	0.767409	−	1.32919i	0.938964	−	0.344016i	$-0.111788\pi$
$228$	−3.46410			−0.229416
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	3.50000	−	6.06218i	0.231287	−	0.400600i	0.958187	+	0.286143i	$0.0923732\pi$
$230$		0			0
$231$	−22.3923	−	38.7846i	−1.47331	−	2.55184i
$232$		−	0.803848i		−	0.0527752i
$233$		−	10.8564i		−	0.711227i	−0.934633	−	0.355613i	$-0.884272\pi$
$233$		−	10.8564i		−	0.711227i	0.934633	−	0.355613i	$-0.115728\pi$
$234$	−7.73205	−	13.3923i	−0.505460	−	0.875482i
$235$		0			0
$236$		−	13.4641i		−	0.876438i
$237$	−5.19615	−	9.00000i	−0.337526	−	0.584613i
$238$	11.1962	−	6.46410i	0.725739	−	0.419005i
$239$	−14.6603	+	8.46410i	−0.948293	+	0.547497i	−0.892550	−	0.450948i	$-0.851086\pi$
$239$	−14.6603	+	8.46410i	−0.948293	+	0.547497i	−0.0557428	+	0.998445i	$0.517753\pi$
$240$		0			0
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	0.00223270	−	0.999998i	$-0.499289\pi$
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	−0.864907	+	0.501932i	$0.832623\pi$
$242$	5.69615	+	9.86603i	0.366163	+	0.634212i
$243$	16.2224	−	9.36603i	1.04067	−	0.600831i
$244$	3.69615	−	2.13397i	0.236622	−	0.136614i
$245$		0			0
$246$	−7.09808	−	4.09808i	−0.452557	−	0.261284i
$247$	3.80385	−	2.19615i	0.242033	−	0.139738i
$248$		−	24.5885i		−	1.56137i
$249$	−22.3923			−1.41905
$250$		0			0
$251$			25.7128i			1.62298i	0.584367	+	0.811489i	$0.301343\pi$
$251$			25.7128i			1.62298i	−0.584367	+	0.811489i	$0.698657\pi$
$252$	13.3923	+	7.73205i	0.843636	+	0.487073i
$253$	−3.46410			−0.217786
$254$	10.5622	+	6.09808i	0.662730	+	0.382627i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−9.79423	−	16.9641i	−0.610947	−	1.05819i	−0.991081	−	0.133260i	$-0.957455\pi$
$257$	−9.79423	−	16.9641i	−0.610947	−	1.05819i	0.380134	−	0.924931i	$-0.375878\pi$
$258$		−	9.46410i		−	0.589209i
$259$	19.0526	+	9.00000i	1.18387	+	0.559233i
$260$		0			0
$261$	1.03590	−	0.598076i	0.0641205	−	0.0370200i
$262$	−9.16987	−	5.29423i	−0.566517	−	0.327079i
$263$	6.58846	+	3.80385i	0.406262	+	0.234555i	0.689182	−	0.724588i	$-0.257970\pi$
$263$	6.58846	+	3.80385i	0.406262	+	0.234555i	−0.282921	+	0.959143i	$0.591303\pi$
$264$	−33.5885	−	19.3923i	−2.06723	−	1.19351i
$265$		0			0
$266$	2.19615	−	3.80385i	0.134655	−	0.233229i
$267$	−25.1244			−1.53759
$268$	−6.29423	+	3.63397i	−0.384481	+	0.221980i
$269$	−14.5359			−0.886269			−0.443135	−	0.896455i	$-0.646134\pi$
$269$	−14.5359			−0.886269			−0.443135	+	0.896455i	$0.646134\pi$
$270$		0			0
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	0.986973	−	0.160886i	$-0.0514352\pi$
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	−0.632818	+	0.774301i	$0.718102\pi$
$272$	1.86603	−	3.23205i	0.113144	−	0.195972i
$273$	−32.7846			−1.98421
$274$	−5.59808	+	3.23205i	−0.338192	+	0.195255i
$275$		0			0
$276$	1.73205	−	1.00000i	0.104257	−	0.0601929i
$277$	−5.13397	+	8.89230i	−0.308471	+	0.534287i	−0.978028	−	0.208474i	$-0.933150\pi$
$277$	−5.13397	+	8.89230i	−0.308471	+	0.534287i	0.669557	+	0.742760i	$0.266484\pi$
$278$	−6.29423	+	10.9019i	−0.377503	+	0.653854i
$279$	31.6865	−	18.2942i	1.89702	−	1.09525i
$280$		0			0
$281$	28.7487	−	16.5981i	1.71500	−	0.990158i	0.787526	−	0.616282i	$-0.211362\pi$
$281$	28.7487	−	16.5981i	1.71500	−	0.990158i	0.927478	−	0.373877i	$-0.121972\pi$
$282$	−6.00000			−0.357295
$283$	−5.19615	+	9.00000i	−0.308879	+	0.534994i	−0.978117	−	0.208053i	$-0.933287\pi$
$283$	−5.19615	+	9.00000i	−0.308879	+	0.534994i	0.669238	+	0.743048i	$0.266621\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	16.3923			0.969297
$287$	−9.00000	+	5.19615i	−0.531253	+	0.306719i
$288$	22.3205			1.31525
$289$	1.53590	−	2.66025i	0.0903470	−	0.156486i
$290$		0			0
$291$	−10.0981	−	5.83013i	−0.591960	−	0.341768i
$292$		0			0
$293$	−24.9904	−	14.4282i	−1.45995	−	0.842905i	−0.460945	−	0.887429i	$-0.652490\pi$
$293$	−24.9904	−	14.4282i	−1.45995	−	0.842905i	−0.999008	+	0.0445239i	$0.985823\pi$
$294$	−11.8301	+	6.83013i	−0.689947	+	0.398341i
$295$		0			0
$296$	18.1865	−	1.50000i	1.05707	−	0.0871857i
$297$		−	18.9282i		−	1.09833i
$298$	−2.76795	−	4.79423i	−0.160343	−	0.277722i
$299$	−1.26795	+	2.19615i	−0.0733274	+	0.127007i
$300$		0			0
$301$	−10.3923	−	6.00000i	−0.599002	−	0.345834i
$302$	−16.5885			−0.954558
$303$	−21.2942	−	12.2942i	−1.22332	−	0.706285i
$304$		−	1.26795i		−	0.0727219i
$305$		0			0
$306$	16.6603			0.952403
$307$			14.3923i			0.821412i	0.911768	+	0.410706i	$0.134718\pi$
$307$			14.3923i			0.821412i	−0.911768	+	0.410706i	$0.865282\pi$
$308$	−14.1962	+	8.19615i	−0.808901	+	0.467019i
$309$	30.5885	+	17.6603i	1.74012	+	1.00466i
$310$		0			0
$311$	−26.3205	+	15.1962i	−1.49250	+	0.861695i	−0.999963	−	0.00859730i	$-0.997263\pi$
$311$	−26.3205	+	15.1962i	−1.49250	+	0.861695i	−0.492536	+	0.870292i	$0.663930\pi$
$312$	−24.5885	+	14.1962i	−1.39205	+	0.803699i
$313$	−7.79423	−	13.5000i	−0.440556	−	0.763065i	0.557175	−	0.830395i	$-0.311885\pi$
$313$	−7.79423	−	13.5000i	−0.440556	−	0.763065i	−0.997731	+	0.0673300i	$0.978552\pi$
$314$	12.4019	+	7.16025i	0.699881	+	0.404077i
$315$		0			0
$316$	−3.29423	+	1.90192i	−0.185315	+	0.106992i
$317$	13.7942	−	7.96410i	0.774761	−	0.447309i	−0.0598093	−	0.998210i	$-0.519049\pi$
$317$	13.7942	−	7.96410i	0.774761	−	0.447309i	0.834570	+	0.550901i	$0.185716\pi$
$318$	−3.46410	−	6.00000i	−0.194257	−	0.336463i
$319$			1.26795i			0.0709915i
$320$		0			0
$321$	−17.6603	−	30.5885i	−0.985699	−	1.70728i
$322$			2.53590i			0.141320i
$323$			4.73205i			0.263298i
$324$	−1.23205	−	2.13397i	−0.0684473	−	0.118554i
$325$		0			0
$326$	−11.1962	+	19.3923i	−0.620098	+	1.07404i
$327$	18.5885			1.02794
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	−3.80385	+	6.58846i	−0.209713	+	0.363233i
$330$		0			0
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.563384	−	0.826195i	$-0.309499\pi$
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.997198	−	0.0748075i	$-0.0238342\pi$
$332$			8.19615i			0.449822i
$333$	15.4641	+	22.3205i	0.847428	+	1.22316i
$334$	10.9282			0.597965
$335$		0			0
$336$	−4.73205	+	8.19615i	−0.258155	+	0.447137i
$337$	25.4545	+	14.6962i	1.38659	+	0.800550i	0.992930	−	0.118704i	$-0.0378739\pi$
$337$	25.4545	+	14.6962i	1.38659	+	0.800550i	0.393664	+	0.919254i	$0.371207\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		−	12.3923i		−	0.673058i
$340$		0			0
$341$			38.7846i			2.10030i
$342$	4.90192	−	2.83013i	0.265066	−	0.153036i
$343$		−	6.92820i		−	0.374088i
$344$	−10.3923			−0.560316
$345$		0			0
$346$	8.59808	+	4.96410i	0.462235	+	0.266872i
$347$	12.7321			0.683492			0.341746	−	0.939792i	$-0.388982\pi$
$347$	12.7321			0.683492			0.341746	+	0.939792i	$0.388982\pi$
$348$	−0.366025	−	0.633975i	−0.0196210	−	0.0339846i
$349$	4.03590	+	6.99038i	0.216037	+	0.374187i	0.953593	−	0.301099i	$-0.0973536\pi$
$349$	4.03590	+	6.99038i	0.216037	+	0.374187i	−0.737556	+	0.675286i	$0.764020\pi$
$350$		0			0
$351$	−12.0000	−	6.92820i	−0.640513	−	0.369800i
$352$	−11.8301	+	20.4904i	−0.630548	+	1.09214i
$353$	6.13397	+	10.6244i	0.326479	+	0.565477i	0.981810	−	0.189864i	$-0.0608046\pi$
$353$	6.13397	+	10.6244i	0.326479	+	0.565477i	−0.655332	+	0.755341i	$0.727471\pi$
$354$	18.3923	+	31.8564i	0.977540	+	1.69315i
$355$		0			0
$356$			9.19615i			0.487395i
$357$	17.6603	−	30.5885i	0.934680	−	1.61891i
$358$	1.26795	−	0.732051i	0.0670132	−	0.0386901i
$359$	−16.3923			−0.865153			−0.432576	−	0.901597i	$-0.642395\pi$
$359$	−16.3923			−0.865153			−0.432576	+	0.901597i	$0.642395\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$	−9.92820			−0.521815
$363$	26.9545	+	15.5622i	1.41474	+	0.816803i
$364$			12.0000i			0.628971i
$365$		0			0
$366$	−5.83013	+	10.0981i	−0.304746	+	0.527835i
$367$	−17.6603	−	10.1962i	−0.921858	−	0.532235i	−0.0376305	−	0.999292i	$-0.511981\pi$
$367$	−17.6603	−	10.1962i	−0.921858	−	0.532235i	−0.884227	+	0.467057i	$0.845314\pi$
$368$	0.366025	+	0.633975i	0.0190804	+	0.0330482i
$369$	−13.3923			−0.697176
$370$		0			0
$371$	−8.78461			−0.456074
$372$	−11.1962	−	19.3923i	−0.580493	−	1.00544i
$373$	−15.1865	−	8.76795i	−0.786329	−	0.453987i	0.0523397	−	0.998629i	$-0.483332\pi$
$373$	−15.1865	−	8.76795i	−0.786329	−	0.453987i	−0.838669	+	0.544642i	$0.816665\pi$
$374$	−8.83013	+	15.2942i	−0.456595	+	0.790846i
$375$		0			0
$376$			6.58846i			0.339774i
$377$	0.803848	+	0.464102i	0.0414003	+	0.0239024i
$378$	−13.8564			−0.712697
$379$	4.26795	+	7.39230i	0.219230	+	0.379717i	0.954573	−	0.297978i	$-0.0963122\pi$
$379$	4.26795	+	7.39230i	0.219230	+	0.379717i	−0.735343	+	0.677695i	$0.762979\pi$
$380$		0			0
$381$	33.3205			1.70706
$382$	5.36603	−	3.09808i	0.274550	−	0.158511i
$383$	7.92820	−	13.7321i	0.405112	−	0.701675i	−0.589222	−	0.807971i	$-0.700566\pi$
$383$	7.92820	−	13.7321i	0.405112	−	0.701675i	0.994335	+	0.106296i	$0.0338991\pi$
$384$		−	8.19615i		−	0.418258i
$385$		0			0
$386$	7.33013	+	12.6962i	0.373094	+	0.646217i
$387$	−7.73205	−	13.3923i	−0.393042	−	0.680769i
$388$	−2.13397	+	3.69615i	−0.108336	+	0.187644i
$389$	−27.0167	−	15.5981i	−1.36980	−	0.790854i	−0.378897	−	0.925439i	$-0.623697\pi$
$389$	−27.0167	−	15.5981i	−1.36980	−	0.790854i	−0.990902	+	0.134585i	$0.957030\pi$
$390$		0			0
$391$	−1.36603	−	2.36603i	−0.0690829	−	0.119655i
$392$	7.50000	+	12.9904i	0.378807	+	0.656113i
$393$	−28.9282			−1.45923
$394$	−24.1865	−	13.9641i	−1.21850	−	0.703501i
$395$		0			0
$396$	−21.1244			−1.06154
$397$			21.2487i			1.06644i	0.845976	+	0.533221i	$0.179019\pi$
$397$			21.2487i			1.06644i	−0.845976	+	0.533221i	$0.820981\pi$
$398$	−9.58846	+	5.53590i	−0.480626	+	0.277490i
$399$		−	12.0000i		−	0.600751i
$400$		0			0
$401$		−	5.60770i		−	0.280035i	−0.990149	−	0.140017i	$-0.955284\pi$
$401$		−	5.60770i		−	0.280035i	0.990149	−	0.140017i	$-0.0447159\pi$
$402$	9.92820	−	17.1962i	0.495174	−	0.857666i
$403$	24.5885	+	14.1962i	1.22484	+	0.707161i
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$		0			0
$406$	0.928203			0.0460660
$407$	−28.6865	+	2.36603i	−1.42194	+	0.117280i
$408$		−	30.5885i		−	1.51435i
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	−0.673830	−	0.738886i	$-0.735352\pi$
$409$	−7.50000	+	4.33013i	−0.370851	+	0.214111i	0.302979	+	0.952997i	$0.402019\pi$
$410$		0			0
$411$	−8.83013	+	15.2942i	−0.435558	+	0.754409i
$412$	6.46410	−	11.1962i	0.318463	−	0.551595i
$413$	46.6410			2.29505
$414$	−1.63397	+	2.83013i	−0.0803055	+	0.139093i
$415$		0			0
$416$	8.66025	+	15.0000i	0.424604	+	0.735436i
$417$			34.3923i			1.68420i
$418$			6.00000i			0.293470i
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	0.996239	−	0.0866469i	$-0.0276152\pi$
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	−0.573158	+	0.819445i	$0.694282\pi$
$420$		0			0
$421$			16.2679i			0.792851i	0.918067	+	0.396426i	$0.129750\pi$
$421$			16.2679i			0.792851i	−0.918067	+	0.396426i	$0.870250\pi$
$422$	−5.00000	−	8.66025i	−0.243396	−	0.421575i
$423$	−8.49038	+	4.90192i	−0.412816	+	0.238340i
$424$	−6.58846	+	3.80385i	−0.319964	+	0.184731i
$425$		0			0
$426$	−14.1962	−	8.19615i	−0.687806	−	0.397105i
$427$	7.39230	+	12.8038i	0.357739	+	0.619622i
$428$	−11.1962	+	6.46410i	−0.541186	+	0.312454i
$429$	38.7846	−	22.3923i	1.87254	−	1.08111i
$430$		0			0
$431$	−9.97372	−	5.75833i	−0.480417	−	0.277369i	0.240173	−	0.970730i	$-0.422796\pi$
$431$	−9.97372	−	5.75833i	−0.480417	−	0.277369i	−0.720590	+	0.693361i	$0.756129\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$			27.0000i			1.29754i	0.760986	+	0.648769i	$0.224716\pi$
$433$			27.0000i			1.29754i	−0.760986	+	0.648769i	$0.775284\pi$
$434$	28.3923			1.36287
$435$		0			0
$436$		−	6.80385i		−	0.325845i
$437$	−0.803848	−	0.464102i	−0.0384532	−	0.0222010i
$438$		0			0
$439$	−12.5885	−	7.26795i	−0.600814	−	0.346880i	0.168548	−	0.985694i	$-0.446092\pi$
$439$	−12.5885	−	7.26795i	−0.600814	−	0.346880i	−0.769362	+	0.638813i	$0.779426\pi$
$440$		0			0
$441$	−11.1603	+	19.3301i	−0.531441	+	0.920482i
$442$	6.46410	+	11.1962i	0.307466	+	0.532547i
$443$			33.4641i			1.58993i	0.606657	+	0.794964i	$0.292510\pi$
$443$			33.4641i			1.58993i	−0.606657	+	0.794964i	$0.707490\pi$
$444$	13.6603	−	9.46410i	0.648287	−	0.449146i
$445$		0			0
$446$	−3.97372	+	2.29423i	−0.188161	+	0.108635i
$447$	−13.0981	−	7.56218i	−0.619518	−	0.357679i
$448$	21.0000	+	12.1244i	0.992157	+	0.572822i
$449$	27.9282	+	16.1244i	1.31801	+	0.760955i	0.983409	−	0.181403i	$-0.0580639\pi$
$449$	27.9282	+	16.1244i	1.31801	+	0.760955i	0.334605	+	0.942359i	$0.391397\pi$
$450$		0			0
$451$	7.09808	−	12.2942i	0.334235	−	0.578913i
$452$	−4.53590			−0.213351
$453$	−39.2487	+	22.6603i	−1.84407	+	1.06467i
$454$	23.1244			1.08528
$455$		0			0
$456$	−5.19615	−	9.00000i	−0.243332	−	0.421464i
$457$	−18.0622	+	31.2846i	−0.844913	+	1.46343i	0.0407837	+	0.999168i	$0.487015\pi$
$457$	−18.0622	+	31.2846i	−0.844913	+	1.46343i	−0.885697	+	0.464264i	$0.846319\pi$
$458$	7.00000			0.327089
$459$	12.9282	−	7.46410i	0.603437	−	0.348394i
$460$		0			0
$461$	−14.3205	+	8.26795i	−0.666973	+	0.385077i	−0.794929	−	0.606703i	$-0.792492\pi$
$461$	−14.3205	+	8.26795i	−0.666973	+	0.385077i	0.127956	+	0.991780i	$0.459158\pi$
$462$	22.3923	−	38.7846i	1.04178	−	1.80442i
$463$	7.73205	−	13.3923i	0.359339	−	0.622393i	−0.628512	−	0.777800i	$-0.716336\pi$
$463$	7.73205	−	13.3923i	0.359339	−	0.622393i	0.987851	+	0.155407i	$0.0496689\pi$
$464$	0.232051	−	0.133975i	0.0107727	−	0.00621961i
$465$		0			0
$466$	9.40192	−	5.42820i	0.435536	−	0.251457i
$467$	−3.32051			−0.153655			−0.0768274	−	0.997044i	$-0.524479\pi$
$467$	−3.32051			−0.153655			−0.0768274	+	0.997044i	$0.524479\pi$
$468$	−7.73205	+	13.3923i	−0.357414	+	0.619060i
$469$	−12.5885	−	21.8038i	−0.581281	−	1.00681i
$470$		0			0
$471$	39.1244			1.80276
$472$	34.9808	−	20.1962i	1.61012	−	0.929603i
$473$	16.3923			0.753719
$474$	5.19615	−	9.00000i	0.238667	−	0.413384i
$475$		0			0
$476$	−11.1962	−	6.46410i	−0.513175	−	0.296282i
$477$	−9.80385	−	5.66025i	−0.448887	−	0.259165i
$478$	−14.6603	−	8.46410i	−0.670544	−	0.387139i
$479$	34.0526	−	19.6603i	1.55590	−	0.898300i	0.558259	−	0.829667i	$-0.311469\pi$
$479$	34.0526	−	19.6603i	1.55590	−	0.898300i	0.997642	−	0.0686333i	$-0.0218639\pi$
$480$		0			0
$481$	−9.00000	+	19.0526i	−0.410365	+	0.868722i
$482$		−	15.4641i		−	0.704371i
$483$	3.46410	+	6.00000i	0.157622	+	0.273009i
$484$	5.69615	−	9.86603i	0.258916	−	0.448456i
$485$		0			0
$486$	16.2224	+	9.36603i	0.735864	+	0.424852i
$487$	32.4449			1.47022			0.735109	−	0.677949i	$-0.237131\pi$
$487$	32.4449			1.47022			0.735109	+	0.677949i	$0.237131\pi$
$488$	11.0885	+	6.40192i	0.501951	+	0.289801i
$489$			61.1769i			2.76652i
$490$		0			0
$491$	31.2679			1.41110			0.705551	−	0.708659i	$-0.250699\pi$
$491$	31.2679			1.41110			0.705551	+	0.708659i	$0.250699\pi$
$492$			8.19615i			0.369511i
$493$	−0.866025	+	0.500000i	−0.0390038	+	0.0225189i
$494$	3.80385	+	2.19615i	0.171143	+	0.0988096i
$495$		0			0
$496$	7.09808	−	4.09808i	0.318713	−	0.184009i
$497$	−18.0000	+	10.3923i	−0.807410	+	0.466159i
$498$	−11.1962	−	19.3923i	−0.501712	−	0.868990i
$499$	−10.9019	−	6.29423i	−0.488037	−	0.281768i	0.235723	−	0.971820i	$-0.424254\pi$
$499$	−10.9019	−	6.29423i	−0.488037	−	0.281768i	−0.723760	+	0.690052i	$0.757588\pi$
$500$		0			0
$501$	25.8564	−	14.9282i	1.15518	−	0.666943i
$502$	−22.2679	+	12.8564i	−0.993867	+	0.573810i
$503$	−4.49038	−	7.77757i	−0.200216	−	0.346785i	0.748382	−	0.663268i	$-0.230831\pi$
$503$	−4.49038	−	7.77757i	−0.200216	−	0.346785i	−0.948598	+	0.316484i	$0.897498\pi$
$504$			46.3923i			2.06648i
$505$		0			0
$506$	−1.73205	−	3.00000i	−0.0769991	−	0.133366i
$507$			2.73205i			0.121335i
$508$		−	12.1962i		−	0.541117i
$509$	−2.89230	−	5.00962i	−0.128199	−	0.222047i	0.794780	−	0.606898i	$-0.207586\pi$
$509$	−2.89230	−	5.00962i	−0.128199	−	0.222047i	−0.922979	+	0.384850i	$0.874253\pi$
$510$		0			0
$511$		0			0
$512$	11.0000			0.486136
$513$	2.53590	−	4.39230i	0.111963	−	0.193925i
$514$	9.79423	−	16.9641i	0.432005	−	0.748254i
$515$		0			0
$516$	−8.19615	+	4.73205i	−0.360815	+	0.208317i
$517$		−	10.3923i		−	0.457053i
$518$	1.73205	+	21.0000i	0.0761019	+	0.922687i
$519$	27.1244			1.19063
$520$		0			0
$521$	−3.46410	+	6.00000i	−0.151765	+	0.262865i	−0.931876	−	0.362776i	$-0.881829\pi$
$521$	−3.46410	+	6.00000i	−0.151765	+	0.262865i	0.780111	+	0.625641i	$0.215162\pi$
$522$	1.03590	+	0.598076i	0.0453400	+	0.0261771i
$523$	−8.02628	+	13.9019i	−0.350965	+	0.607889i	−0.986419	−	0.164250i	$-0.947480\pi$
$523$	−8.02628	+	13.9019i	−0.350965	+	0.607889i	0.635454	+	0.772139i	$0.280813\pi$
$524$			10.5885i			0.462559i
$525$		0			0
$526$			7.60770i			0.331711i
$527$	−26.4904	+	15.2942i	−1.15394	+	0.666227i
$528$		−	12.9282i		−	0.562628i
$529$	−22.4641			−0.976700
$530$		0			0
$531$	52.0526	+	30.0526i	2.25889	+	1.30417i
$532$	−4.39230			−0.190431
$533$	−5.19615	−	9.00000i	−0.225070	−	0.389833i
$534$	−12.5622	−	21.7583i	−0.543619	−	0.941575i
$535$		0			0
$536$	−18.8827	−	10.9019i	−0.815608	−	0.470891i
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$	−7.26795	−	12.5885i	−0.313344	−	0.542727i
$539$	−11.8301	−	20.4904i	−0.509560	−	0.882583i
$540$		0			0
$541$		−	4.26795i		−	0.183493i	−0.995782	−	0.0917467i	$-0.970755\pi$
$541$		−	4.26795i		−	0.183493i	0.995782	−	0.0917467i	$-0.0292450\pi$
$542$	−5.83013	+	10.0981i	−0.250425	+	0.433750i
$543$	−23.4904	+	13.5622i	−1.00807	+	0.582009i
$544$	−18.6603			−0.800052
$545$		0			0
$546$	−16.3923	−	28.3923i	−0.701526	−	1.21508i
$547$	3.80385			0.162641			0.0813204	−	0.996688i	$-0.474086\pi$
$547$	3.80385			0.162641			0.0813204	+	0.996688i	$0.474086\pi$
$548$	5.59808	+	3.23205i	0.239138	+	0.138066i
$549$			19.0526i			0.813143i
$550$		0			0
$551$	−0.169873	+	0.294229i	−0.00723683	+	0.0125346i
$552$	5.19615	+	3.00000i	0.221163	+	0.127688i
$553$	−6.58846	−	11.4115i	−0.280170	−	0.485268i
$554$	−10.2679			−0.436243
$555$		0			0
$556$	12.5885			0.533870
$557$	8.86603	+	15.3564i	0.375666	+	0.650672i	0.990426	−	0.138042i	$-0.0440808\pi$
$557$	8.86603	+	15.3564i	0.375666	+	0.650672i	−0.614761	+	0.788714i	$0.710747\pi$
$558$	31.6865	+	18.2942i	1.34140	+	0.774456i
$559$	6.00000	−	10.3923i	0.253773	−	0.439548i
$560$		0			0
$561$			48.2487i			2.03706i
$562$	28.7487	+	16.5981i	1.21269	+	0.700148i
$563$	−34.5885			−1.45773			−0.728865	−	0.684658i	$-0.759952\pi$
$563$	−34.5885			−1.45773			−0.728865	+	0.684658i	$0.759952\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	−10.3923			−0.436821
$567$	7.39230	−	4.26795i	0.310448	−	0.179237i
$568$	−9.00000	+	15.5885i	−0.377632	+	0.654077i
$569$			36.5167i			1.53086i	0.643520	+	0.765429i	$0.277473\pi$
$569$			36.5167i			1.53086i	−0.643520	+	0.765429i	$0.722527\pi$
$570$		0			0
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	0.980754	+	0.195247i	$0.0625507\pi$
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	−0.321289	+	0.946981i	$0.604116\pi$
$572$	−8.19615	−	14.1962i	−0.342698	−	0.593571i
$573$	8.46410	−	14.6603i	0.353593	−	0.612441i
$574$	−9.00000	−	5.19615i	−0.375653	−	0.216883i
$575$		0			0
$576$	15.6244	+	27.0622i	0.651015	+	1.12759i
$577$	−6.46410	−	11.1962i	−0.269104	−	0.466102i	0.699527	−	0.714607i	$-0.253394\pi$
$577$	−6.46410	−	11.1962i	−0.269104	−	0.466102i	−0.968631	+	0.248505i	$0.920061\pi$
$578$	3.07180			0.127770
$579$	34.6865	+	20.0263i	1.44152	+	0.832264i
$580$		0			0
$581$	−28.3923			−1.17791
$582$		−	11.6603i		−	0.483333i
$583$	10.3923	−	6.00000i	0.430405	−	0.248495i
$584$		0			0
$585$		0			0
$586$		−	28.8564i		−	1.19205i
$587$	−8.16987	+	14.1506i	−0.337207	+	0.584059i	−0.983906	−	0.178686i	$-0.942815\pi$
$587$	−8.16987	+	14.1506i	−0.337207	+	0.584059i	0.646699	+	0.762745i	$0.276149\pi$
$588$	11.8301	+	6.83013i	0.487866	+	0.281670i
$589$	−5.19615	+	9.00000i	−0.214104	+	0.370839i
$590$		0			0
$591$	−76.3013			−3.13861
$592$	3.46410	+	5.00000i	0.142374	+	0.205499i
$593$			17.7846i			0.730326i	0.930944	+	0.365163i	$0.118987\pi$
$593$			17.7846i			0.730326i	−0.930944	+	0.365163i	$0.881013\pi$
$594$	16.3923	−	9.46410i	0.672584	−	0.388317i
$595$		0			0
$596$	−2.76795	+	4.79423i	−0.113380	+	0.196379i
$597$	−15.1244	+	26.1962i	−0.618999	+	1.07214i
$598$	−2.53590			−0.103701
$599$	3.97372	−	6.88269i	0.162362	−	0.281219i	−0.773353	−	0.633975i	$-0.781422\pi$
$599$	3.97372	−	6.88269i	0.162362	−	0.281219i	0.935715	+	0.352756i	$0.114755\pi$
$600$		0			0
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	−0.985375	−	0.170402i	$-0.945494\pi$
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	0.345115	−	0.938560i	$-0.387840\pi$
$602$		−	12.0000i		−	0.489083i
$603$		−	32.4449i		−	1.32126i
$604$	8.29423	+	14.3660i	0.337487	+	0.584545i
$605$		0			0
$606$		−	24.5885i		−	0.998838i
$607$	−2.83013	−	4.90192i	−0.114871	−	0.198963i	0.802857	−	0.596172i	$-0.203312\pi$
$607$	−2.83013	−	4.90192i	−0.114871	−	0.198963i	−0.917728	+	0.397209i	$0.869979\pi$
$608$	−5.49038	+	3.16987i	−0.222664	+	0.128555i
$609$	2.19615	−	1.26795i	0.0889926	−	0.0513799i
$610$		0			0
$611$	−6.58846	−	3.80385i	−0.266540	−	0.153887i
$612$	−8.33013	−	14.4282i	−0.336725	−	0.583226i
$613$	2.93782	−	1.69615i	0.118658	−	0.0685070i	−0.439497	−	0.898244i	$-0.644843\pi$
$613$	2.93782	−	1.69615i	0.118658	−	0.0685070i	0.558154	+	0.829737i	$0.311510\pi$
$614$	−12.4641	+	7.19615i	−0.503010	+	0.290413i
$615$		0			0
$616$	−42.5885	−	24.5885i	−1.71594	−	0.990697i
$617$	21.8038	−	12.5885i	0.877790	−	0.506792i	0.00786080	−	0.999969i	$-0.497498\pi$
$617$	21.8038	−	12.5885i	0.877790	−	0.506792i	0.869929	+	0.493177i	$0.164164\pi$
$618$			35.3205i			1.42080i
$619$	−6.78461			−0.272696			−0.136348	−	0.990661i	$-0.543537\pi$
$619$	−6.78461			−0.272696			−0.136348	+	0.990661i	$0.543537\pi$
$620$		0			0
$621$			2.92820i			0.117505i
$622$	−26.3205	−	15.1962i	−1.05536	−	0.609310i
$623$	−31.8564			−1.27630
$624$	−8.19615	−	4.73205i	−0.328109	−	0.189434i
$625$		0			0
$626$	7.79423	−	13.5000i	0.311520	−	0.539569i
$627$	8.19615	+	14.1962i	0.327323	+	0.566940i
$628$		−	14.3205i		−	0.571450i
$629$	−12.9282	−	18.6603i	−0.515481	−	0.744033i
$630$		0			0
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	−0.129626	−	0.991563i	$-0.541378\pi$
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	0.793906	+	0.608041i	$0.208044\pi$
$632$	−9.88269	−	5.70577i	−0.393112	−	0.226963i
$633$	−23.6603	−	13.6603i	−0.940411	−	0.542946i
$634$	13.7942	+	7.96410i	0.547839	+	0.316295i
$635$		0			0
$636$	−3.46410	+	6.00000i	−0.137361	+	0.237915i
$637$	−17.3205			−0.686264
$638$	−1.09808	+	0.633975i	−0.0434733	+	0.0250993i
$639$	−26.7846			−1.05958
$640$		0			0
$641$	8.89230	+	15.4019i	0.351225	+	0.608339i	0.986464	−	0.163976i	$-0.0524319\pi$
$641$	8.89230	+	15.4019i	0.351225	+	0.608339i	−0.635239	+	0.772315i	$0.719099\pi$
$642$	17.6603	−	30.5885i	0.696995	−	1.20723i
$643$	−5.66025			−0.223219			−0.111609	−	0.993752i	$-0.535601\pi$
$643$	−5.66025			−0.223219			−0.111609	+	0.993752i	$0.535601\pi$
$644$	2.19615	−	1.26795i	0.0865405	−	0.0499642i
$645$		0			0
$646$	−4.09808	+	2.36603i	−0.161237	+	0.0930900i
$647$	21.7321	−	37.6410i	0.854375	−	1.47982i	−0.0228485	−	0.999739i	$-0.507274\pi$
$647$	21.7321	−	37.6410i	0.854375	−	1.47982i	0.877224	−	0.480082i	$-0.159393\pi$
$648$	3.69615	−	6.40192i	0.145199	−	0.251491i
$649$	−55.1769	+	31.8564i	−2.16588	+	1.25047i
$650$		0			0
$651$	67.1769	−	38.7846i	2.63287	−	1.52009i
$652$	22.3923			0.876950
$653$	1.40192	−	2.42820i	0.0548615	−	0.0950229i	−0.837290	−	0.546758i	$-0.815862\pi$
$653$	1.40192	−	2.42820i	0.0548615	−	0.0950229i	0.892152	+	0.451736i	$0.149195\pi$
$654$	9.29423	+	16.0981i	0.363433	+	0.629485i
$655$		0			0
$656$	−3.00000			−0.117130
$657$		0			0
$658$	−7.60770			−0.296579
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	−0.759018	−	0.651070i	$-0.774320\pi$
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	0.943352	+	0.331793i	$0.107654\pi$
$660$		0			0
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	0.268605	−	0.963250i	$-0.413437\pi$
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	−0.699896	+	0.714244i	$0.746771\pi$
$662$	28.3923	+	16.3923i	1.10350	+	0.637105i
$663$	30.5885	+	17.6603i	1.18796	+	0.685867i
$664$	−21.2942	+	12.2942i	−0.826376	+	0.477109i
$665$		0			0
$666$	−11.5981	+	24.5526i	−0.449416	+	0.951392i
$667$		−	0.196152i		−	0.00759505i
$668$	−5.46410	−	9.46410i	−0.211412	−	0.366177i
$669$	−6.26795	+	10.8564i	−0.242333	+	0.419733i
$670$		0			0
$671$	−17.4904	−	10.0981i	−0.675209	−	0.389832i
$672$	47.3205			1.82543
$673$	−13.6077	−	7.85641i	−0.524538	−	0.302842i	0.214251	−	0.976779i	$-0.431269\pi$
$673$	−13.6077	−	7.85641i	−0.524538	−	0.302842i	−0.738789	+	0.673936i	$0.764602\pi$
$674$			29.3923i			1.13215i
$675$		0			0
$676$	1.00000			0.0384615
$677$			44.3205i			1.70338i	0.524050	+	0.851688i	$0.324421\pi$
$677$			44.3205i			1.70338i	−0.524050	+	0.851688i	$0.675579\pi$
$678$	10.7321	−	6.19615i	0.412162	−	0.237962i
$679$	−12.8038	−	7.39230i	−0.491367	−	0.283691i
$680$		0			0
$681$	54.7128	−	31.5885i	2.09660	−	1.21047i
$682$	−33.5885	+	19.3923i	−1.28617	+	0.742570i
$683$	15.5359	+	26.9090i	0.594465	+	1.02964i	0.993622	+	0.112761i	$0.0359693\pi$
$683$	15.5359	+	26.9090i	0.594465	+	1.02964i	−0.399158	+	0.916882i	$0.630697\pi$
$684$	−4.90192	−	2.83013i	−0.187430	−	0.108213i
$685$		0			0
$686$	6.00000	−	3.46410i	0.229081	−	0.132260i
$687$	16.5622	−	9.56218i	0.631886	−	0.364820i
$688$	−1.73205	−	3.00000i	−0.0660338	−	0.114374i
$689$		−	8.78461i		−	0.334667i
$690$		0			0
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	0.672002	−	0.740550i	$-0.265435\pi$
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	−0.977336	+	0.211696i	$0.932101\pi$
$692$		−	9.92820i		−	0.377414i
$693$		−	73.1769i		−	2.77976i
$694$	6.36603	+	11.0263i	0.241651	+	0.418552i
$695$		0			0
$696$	1.09808	−	1.90192i	0.0416225	−	0.0720922i
$697$	11.1962			0.424085
$698$	−4.03590	+	6.99038i	−0.152761	+	0.264590i
$699$	14.8301	−	25.6865i	0.560927	−	0.971554i
$700$		0			0
$701$	−5.07180	+	2.92820i	−0.191559	+	0.110597i	−0.592712	−	0.805414i	$-0.701943\pi$
$701$	−5.07180	+	2.92820i	−0.191559	+	0.110597i	0.401153	+	0.916011i	$0.368610\pi$
$702$		−	13.8564i		−	0.522976i
$703$	−6.97372	−	3.29423i	−0.263019	−	0.124244i
$704$	−33.1244			−1.24842
$705$		0			0
$706$	−6.13397	+	10.6244i	−0.230855	+	0.399853i
$707$	−27.0000	−	15.5885i	−1.01544	−	0.586264i
$708$	18.3923	−	31.8564i	0.691225	−	1.19724i
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		0			0
$711$		−	16.9808i		−	0.636828i
$712$	−23.8923	+	13.7942i	−0.895402	+	0.516961i
$713$		−	6.00000i		−	0.224702i
$714$	35.3205			1.32184
$715$		0			0
$716$	−1.26795	−	0.732051i	−0.0473855	−	0.0273580i
$717$	−46.2487			−1.72719
$718$	−8.19615	−	14.1962i	−0.305878	−	0.529796i
$719$	13.2224	+	22.9019i	0.493114	+	0.854098i	0.999969	−	0.00793367i	$-0.00252539\pi$
$719$	13.2224	+	22.9019i	0.493114	+	0.854098i	−0.506855	+	0.862031i	$0.669192\pi$
$720$		0			0
$721$	38.7846	+	22.3923i	1.44441	+	0.833933i
$722$	8.69615	−	15.0622i	0.323637	−	0.560556i
$723$	−21.1244	−	36.5885i	−0.785623	−	1.36074i
$724$	4.96410	+	8.59808i	0.184489	+	0.319545i
$725$		0			0
$726$			31.1244i			1.15513i
$727$	−0.928203	+	1.60770i	−0.0344252	+	0.0596261i	−0.882725	−	0.469891i	$-0.844293\pi$
$727$	−0.928203	+	1.60770i	−0.0344252	+	0.0596261i	0.848300	+	0.529517i	$0.177627\pi$
$728$	−31.1769	+	18.0000i	−1.15549	+	0.667124i
$729$	43.7846			1.62165
$730$		0			0
$731$	6.46410	+	11.1962i	0.239083	+	0.414105i
$732$	11.6603			0.430975
$733$	−24.9282	−	14.3923i	−0.920744	−	0.531592i	−0.0368718	−	0.999320i	$-0.511739\pi$
$733$	−24.9282	−	14.3923i	−0.920744	−	0.531592i	−0.883872	+	0.467728i	$0.845073\pi$
$734$		−	20.3923i		−	0.752694i
$735$		0			0
$736$	1.83013	−	3.16987i	0.0674594	−	0.116843i
$737$	29.7846	+	17.1962i	1.09713	+	0.633428i
$738$	−6.69615	−	11.5981i	−0.246489	−	0.426931i
$739$	23.8038			0.875639			0.437819	−	0.899063i	$-0.355751\pi$
$739$	23.8038			0.875639			0.437819	+	0.899063i	$0.355751\pi$
$740$		0			0
$741$	12.0000			0.440831
$742$	−4.39230	−	7.60770i	−0.161247	−	0.279287i
$743$	37.4711	+	21.6340i	1.37468	+	0.793674i	0.991513	−	0.130004i	$-0.0414992\pi$
$743$	37.4711	+	21.6340i	1.37468	+	0.793674i	0.383170	+	0.923678i	$0.374833\pi$
$744$	33.5885	−	58.1769i	1.23141	−	2.13287i
$745$		0			0
$746$		−	17.5359i		−	0.642035i
$747$	−31.6865	−	18.2942i	−1.15935	−	0.669351i
$748$	17.6603			0.645723
$749$	−22.3923	−	38.7846i	−0.818197	−	1.41716i
$750$		0			0
$751$	−9.21539			−0.336274			−0.168137	−	0.985764i	$-0.553775\pi$
$751$	−9.21539			−0.336274			−0.168137	+	0.985764i	$0.553775\pi$
$752$	−1.90192	+	1.09808i	−0.0693560	+	0.0400427i
$753$	−35.1244	+	60.8372i	−1.28000	+	2.21703i
$754$			0.928203i			0.0338032i
$755$		0			0
$756$	6.92820	+	12.0000i	0.251976	+	0.436436i
$757$	−21.1865	−	36.6962i	−0.770038	−	1.33374i	−0.937542	−	0.347873i	$-0.886904\pi$
$757$	−21.1865	−	36.6962i	−0.770038	−	1.33374i	0.167504	−	0.985871i	$-0.446429\pi$
$758$	−4.26795	+	7.39230i	−0.155019	+	0.268501i
$759$	−8.19615	−	4.73205i	−0.297501	−	0.171763i
$760$		0			0
$761$	1.83975	+	3.18653i	0.0666907	+	0.115512i	0.897443	−	0.441131i	$-0.145423\pi$
$761$	1.83975	+	3.18653i	0.0666907	+	0.115512i	−0.830752	+	0.556643i	$0.812089\pi$
$762$	16.6603	+	28.8564i	0.603537	+	1.04536i
$763$	23.5692			0.853263
$764$	−5.36603	−	3.09808i	−0.194136	−	0.112084i
$765$		0			0
$766$	15.8564			0.572915
$767$			46.6410i			1.68411i
$768$	40.2224	−	23.2224i	1.45140	−	0.837967i
$769$		−	20.5359i		−	0.740543i	−0.928923	−	0.370272i	$-0.879265\pi$
$769$		−	20.5359i		−	0.740543i	0.928923	−	0.370272i	$-0.120735\pi$
$770$		0			0
$771$		−	53.5167i		−	1.92736i
$772$	7.33013	−	12.6962i	0.263817	−	0.456945i
$773$	41.5981	+	24.0167i	1.49618	+	0.863819i	0.999990	−	0.00439560i	$-0.00139917\pi$
$773$	41.5981	+	24.0167i	1.49618	+	0.863819i	0.496188	+	0.868215i	$0.334733\pi$
$774$	7.73205	−	13.3923i	0.277923	−	0.481376i
$775$		0			0
$776$	−12.8038			−0.459631
$777$	32.7846	+	47.3205i	1.17614	+	1.69761i
$778$		−	31.1962i		−	1.11844i
$779$	3.29423	−	1.90192i	0.118028	−	0.0681435i
$780$		0			0
$781$	14.1962	−	24.5885i	0.507978	−	0.879844i
$782$	1.36603	−	2.36603i	0.0488490	−	0.0846089i
$783$	1.07180			0.0383029
$784$	−2.50000	+	4.33013i	−0.0892857	+	0.154647i
$785$		0			0
$786$	−14.4641	−	25.0526i	−0.515917	−	0.893595i
$787$		−	0.392305i		−	0.0139842i	−0.999976	−	0.00699208i	$-0.997774\pi$
$787$		−	0.392305i		−	0.0139842i	0.999976	−	0.00699208i	$-0.00222567\pi$
$788$			27.9282i			0.994901i
$789$	10.3923	+	18.0000i	0.369976	+	0.640817i
$790$		0			0
$791$		−	15.7128i		−	0.558683i
$792$	−31.6865	−	54.8827i	−1.12593	−	1.95017i
$793$	−12.8038	+	7.39230i	−0.454678	+	0.262508i
$794$	−18.4019	+	10.6244i	−0.653060	+	0.377044i
$795$		0			0
$796$	9.58846	+	5.53590i	0.339854	+	0.196215i
$797$	4.00000	+	6.92820i	0.141687	+	0.245410i	0.928132	−	0.372251i	$-0.121414\pi$
$797$	4.00000	+	6.92820i	0.141687	+	0.245410i	−0.786445	+	0.617661i	$0.788081\pi$
$798$	10.3923	−	6.00000i	0.367884	−	0.212398i
$799$	7.09808	−	4.09808i	0.251112	−	0.144980i
$800$		0			0
$801$	−35.5526	−	20.5263i	−1.25619	−	0.725260i
$802$	4.85641	−	2.80385i	0.171486	−	0.0990073i
$803$		0			0
$804$	−19.8564			−0.700281
$805$		0			0
$806$			28.3923i			1.00008i
$807$	−34.3923	−	19.8564i	−1.21067	−	0.698979i
$808$	−27.0000			−0.949857
$809$	−29.3205	−	16.9282i	−1.03085	−	0.595164i	−0.113625	−	0.993524i	$-0.536246\pi$
$809$	−29.3205	−	16.9282i	−1.03085	−	0.595164i	−0.917229	+	0.398360i	$0.869580\pi$
$810$		0			0
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	−0.980570	−	0.196167i	$-0.937150\pi$
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	0.660171	+	0.751115i	$0.270484\pi$
$812$	−0.464102	−	0.803848i	−0.0162868	−	0.0282095i
$813$			31.8564i			1.11725i
$814$	−16.3923	−	23.6603i	−0.574550	−	0.829291i
$815$		0			0
$816$	8.83013	−	5.09808i	0.309116	−	0.178468i
$817$	3.80385	+	2.19615i	0.133080	+	0.0768336i
$818$	−7.50000	−	4.33013i	−0.262231	−	0.151399i
$819$	−46.3923	−	26.7846i	−1.62108	−	0.935930i
$820$		0			0
$821$	−24.5885	+	42.5885i	−0.858143	+	1.48635i	0.0155551	+	0.999879i	$0.495048\pi$
$821$	−24.5885	+	42.5885i	−0.858143	+	1.48635i	−0.873698	+	0.486468i	$0.838285\pi$
$822$	−17.6603			−0.615972
$823$	−2.61474	+	1.50962i	−0.0911440	+	0.0526220i	−0.544879	−	0.838515i	$-0.683425\pi$
$823$	−2.61474	+	1.50962i	−0.0911440	+	0.0526220i	0.453735	+	0.891137i	$0.350091\pi$
$824$	38.7846			1.35113
$825$		0			0
$826$	23.3205	+	40.3923i	0.811424	+	1.40543i
$827$	−11.4641	+	19.8564i	−0.398646	+	0.690475i	−0.993559	−	0.113315i	$-0.963853\pi$
$827$	−11.4641	+	19.8564i	−0.398646	+	0.690475i	0.594913	+	0.803790i	$0.297186\pi$
$828$	3.26795			0.113569
$829$	38.5692	−	22.2679i	1.33956	−	0.773398i	0.352822	−	0.935691i	$-0.385222\pi$
$829$	38.5692	−	22.2679i	1.33956	−	0.773398i	0.986743	+	0.162293i	$0.0518889\pi$
$830$		0			0
$831$	−24.2942	+	14.0263i	−0.842757	+	0.486566i
$832$	−12.1244	+	21.0000i	−0.420336	+	0.728044i
$833$	9.33013	−	16.1603i	0.323270	−	0.559920i
$834$	−29.7846	+	17.1962i	−1.03136	+	0.595454i
$835$		0			0
$836$	5.19615	−	3.00000i	0.179713	−	0.103757i
$837$	32.7846			1.13320
$838$	−8.66025	+	15.0000i	−0.299164	+	0.518166i
$839$	−14.8301	−	25.6865i	−0.511993	−	0.886798i	−0.999903	−	0.0139040i	$-0.995574\pi$
$839$	−14.8301	−	25.6865i	−0.511993	−	0.886798i	0.487910	−	0.872894i	$-0.337759\pi$
$840$		0			0
$841$	28.9282			0.997524
$842$	−14.0885	+	8.13397i	−0.485520	+	0.280315i
$843$	90.6936			3.12365
$844$	−5.00000	+	8.66025i	−0.172107	+	0.298098i
$845$		0			0
$846$	−8.49038	−	4.90192i	−0.291905	−	0.168532i
$847$	34.1769	+	19.7321i	1.17433	+	0.678001i
$848$	−2.19615	−	1.26795i	−0.0754162	−	0.0435416i
$849$	−24.5885	+	14.1962i	−0.843874	+	0.487211i
$850$		0			0
$851$	4.43782	−	0.366025i	0.152127	−	0.0125472i
$852$			16.3923i			0.561591i
$853$	21.0622	+	36.4808i	0.721155	+	1.24908i	0.960537	+	0.278152i	$0.0897219\pi$
$853$	21.0622	+	36.4808i	0.721155	+	1.24908i	−0.239382	+	0.970926i	$0.576945\pi$
$854$	−7.39230	+	12.8038i	−0.252959	+	0.438139i
$855$		0			0
$856$	−33.5885	−	19.3923i	−1.14803	−	0.662815i
$857$	23.7321			0.810671			0.405336	−	0.914168i	$-0.367155\pi$
$857$	23.7321			0.810671			0.405336	+	0.914168i	$0.367155\pi$
$858$	38.7846	+	22.3923i	1.32408	+	0.764461i
$859$			8.53590i			0.291241i	0.989341	+	0.145621i	$0.0465179\pi$
$859$			8.53590i			0.291241i	−0.989341	+	0.145621i	$0.953482\pi$
$860$		0			0
$861$	−28.3923			−0.967607
$862$		−	11.5167i		−	0.392259i
$863$	33.3731	−	19.2679i	1.13603	−	0.655889i	0.190587	−	0.981670i	$-0.438961\pi$
$863$	33.3731	−	19.2679i	1.13603	−	0.655889i	0.945445	+	0.325782i	$0.105627\pi$
$864$	17.3205	+	10.0000i	0.589256	+	0.340207i
$865$		0			0
$866$	−23.3827	+	13.5000i	−0.794576	+	0.458749i
$867$	7.26795	−	4.19615i	0.246832	−	0.142509i
$868$	−14.1962	−	24.5885i	−0.481849	−	0.834587i
$869$	15.5885	+	9.00000i	0.528802	+	0.305304i
$870$		0			0
$871$	21.8038	−	12.5885i	0.738795	−	0.426544i
$872$	17.6769	−	10.2058i	0.598616	−	0.345611i
$873$	−9.52628	−	16.5000i	−0.322416	−	0.558440i
$874$		−	0.928203i		−	0.0313969i
$875$		0			0
$876$		0			0
$877$		−	5.78461i		−	0.195332i	−0.995219	−	0.0976662i	$-0.968862\pi$
$877$		−	5.78461i		−	0.195332i	0.995219	−	0.0976662i	$-0.0311378\pi$
$878$		−	14.5359i		−	0.490563i
$879$	−39.4186	−	68.2750i	−1.32956	−	2.30286i
$880$		0			0
$881$	−16.1603	+	27.9904i	−0.544453	+	0.943020i	0.454188	+	0.890906i	$0.349929\pi$
$881$	−16.1603	+	27.9904i	−0.544453	+	0.943020i	−0.998641	+	0.0521142i	$0.983404\pi$
$882$	−22.3205			−0.751571
$883$	17.8301	−	30.8827i	0.600032	−	1.03929i	−0.392784	−	0.919631i	$-0.628488\pi$
$883$	17.8301	−	30.8827i	0.600032	−	1.03929i	0.992816	−	0.119654i	$-0.0381787\pi$
$884$	6.46410	−	11.1962i	0.217411	−	0.376567i
$885$		0			0
$886$	−28.9808	+	16.7321i	−0.973628	+	0.562124i
$887$		−	28.9808i		−	0.973079i	−0.873659	−	0.486539i	$-0.838259\pi$
$887$		−	28.9808i		−	0.973079i	0.873659	−	0.486539i	$-0.161741\pi$
$888$	45.0788	+	21.2942i	1.51275	+	0.714588i
$889$	42.2487			1.41698
$890$		0			0
$891$	−5.83013	+	10.0981i	−0.195317	+	0.338298i
$892$	3.97372	+	2.29423i	0.133050	+	0.0768165i
$893$	1.39230	−	2.41154i	0.0465917	−	0.0806992i
$894$		−	15.1244i		−	0.505834i
$895$		0			0
$896$		−	10.3923i		−	0.347183i
$897$	−6.00000	+	3.46410i	−0.200334	+	0.115663i
$898$			32.2487i			1.07615i
$899$	−2.19615			−0.0732458
$900$		0			0
$901$	8.19615	+	4.73205i	0.273053	+	0.157647i
$902$	14.1962			0.472680
$903$	−16.3923	−	28.3923i	−0.545502	−	0.944837i
$904$	−6.80385	−	11.7846i	−0.226293	−	0.391950i
$905$		0			0
$906$	−39.2487	−	22.6603i	−1.30395	−	0.752837i
$907$	0.633975	−	1.09808i	0.0210508	−	0.0364610i	−0.855308	−	0.518120i	$-0.826632\pi$
$907$	0.633975	−	1.09808i	0.0210508	−	0.0364610i	0.876359	+	0.481659i	$0.159965\pi$
$908$	−11.5622	−	20.0263i	−0.383704	−	0.664595i
$909$	−20.0885	−	34.7942i	−0.666292	−	1.15405i
$910$		0			0
$911$		−	53.5167i		−	1.77309i	−0.462646	−	0.886543i	$-0.653100\pi$
$911$		−	53.5167i		−	1.77309i	0.462646	−	0.886543i	$-0.346900\pi$
$912$	1.73205	−	3.00000i	0.0573539	−	0.0993399i
$913$	33.5885	−	19.3923i	1.11162	−	0.641792i
$914$	−36.1244			−1.19489
$915$		0			0
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$	−36.6795			−1.21126
$918$	12.9282	+	7.46410i	0.426694	+	0.246352i
$919$		−	4.05256i		−	0.133682i	−0.997764	−	0.0668408i	$-0.978708\pi$
$919$		−	4.05256i		−	0.133682i	0.997764	−	0.0668408i	$-0.0212920\pi$
$920$		0			0
$921$	−19.6603	+	34.0526i	−0.647827	+	1.12207i
$922$	−14.3205	−	8.26795i	−0.471621	−	0.272290i
$923$	−10.3923	−	18.0000i	−0.342067	−	0.592477i
$924$	−44.7846			−1.47331
$925$		0			0
$926$	15.4641			0.508182
$927$	28.8564	+	49.9808i	0.947769	+	1.64158i
$928$	−1.16025	−	0.669873i	−0.0380872	−	0.0219897i
$929$	−15.2321	+	26.3827i	−0.499747	+	0.865588i	−1.00000		0.000291680i	$-0.999907\pi$
$929$	−15.2321	+	26.3827i	−0.499747	+	0.865588i	0.500253	+	0.865880i	$0.333240\pi$
$930$		0			0
$931$		−	6.33975i		−	0.207777i
$932$	−9.40192	−	5.42820i	−0.307970	−	0.177807i
$933$	−83.0333			−2.71839
$934$	−1.66025	−	2.87564i	−0.0543252	−	0.0940940i
$935$		0			0
$936$	−46.3923			−1.51638
$937$	10.9186	−	6.30385i	0.356695	−	0.205938i	−0.310935	−	0.950431i	$-0.600642\pi$
$937$	10.9186	−	6.30385i	0.356695	−	0.205938i	0.667630	+	0.744493i	$0.267309\pi$
$938$	12.5885	−	21.8038i	0.411028	−	0.711921i
$939$		−	42.5885i		−	1.38982i
$940$		0			0
$941$	2.08846	+	3.61731i	0.0680818	+	0.117921i	0.898057	−	0.439879i	$-0.144979\pi$
$941$	2.08846	+	3.61731i	0.0680818	+	0.117921i	−0.829975	+	0.557800i	$0.811645\pi$
$942$	19.5622	+	33.8827i	0.637370	+	1.10396i
$943$	−1.09808	+	1.90192i	−0.0357583	+	0.0619352i
$944$	11.6603	+	6.73205i	0.379509	+	0.219110i
$945$		0			0
$946$	8.19615	+	14.1962i	0.266480	+	0.461557i
$947$	13.8038	+	23.9090i	0.448565	+	0.776937i	0.998293	−	0.0584067i	$-0.0186020\pi$
$947$	13.8038	+	23.9090i	0.448565	+	0.776937i	−0.549728	+	0.835344i	$0.685269\pi$
$948$	−10.3923			−0.337526
$949$		0			0
$950$		0			0
$951$	43.5167			1.41112
$952$		−	38.7846i		−	1.25702i
$953$	−3.58846	+	2.07180i	−0.116242	+	0.0671121i	−0.556993	−	0.830517i	$-0.688045\pi$
$953$	−3.58846	+	2.07180i	−0.116242	+	0.0671121i	0.440752	+	0.897629i	$0.354712\pi$
$954$		−	11.3205i		−	0.366515i
$955$		0			0
$956$			16.9282i			0.547497i
$957$	−1.73205	+	3.00000i	−0.0559893	+	0.0969762i
$958$	34.0526	+	19.6603i	1.10019	+	0.635194i
$959$	−11.1962	+	19.3923i	−0.361543	+	0.626210i
$960$		0			0
$961$	−36.1769			−1.16700
$962$	−21.0000	+	1.73205i	−0.677067	+	0.0558436i
$963$		−	57.7128i		−	1.85977i
$964$	−13.3923	+	7.73205i	−0.431337	+	0.249033i
$965$		0			0
$966$	−3.46410	+	6.00000i	−0.111456	+	0.193047i
$967$	16.3923	−	28.3923i	0.527141	−	0.913035i	−0.472359	−	0.881406i	$-0.656597\pi$
$967$	16.3923	−	28.3923i	0.527141	−	0.913035i	0.999500	−	0.0316286i	$-0.0100694\pi$
$968$	34.1769			1.09849
$969$	−6.46410	+	11.1962i	−0.207657	+	0.359672i
$970$		0			0
$971$	4.09808	+	7.09808i	0.131514	+	0.227788i	0.924260	−	0.381763i	$-0.124683\pi$
$971$	4.09808	+	7.09808i	0.131514	+	0.227788i	−0.792747	+	0.609551i	$0.791350\pi$
$972$		−	18.7321i		−	0.600831i
$973$			43.6077i			1.39800i
$974$	16.2224	+	28.0981i	0.519800	+	0.900320i
$975$		0			0
$976$			4.26795i			0.136614i
$977$	8.12436	+	14.0718i	0.259921	+	0.450197i	0.966221	−	0.257717i	$-0.0829701\pi$
$977$	8.12436	+	14.0718i	0.259921	+	0.450197i	−0.706299	+	0.707913i	$0.749637\pi$
$978$	−52.9808	+	30.5885i	−1.69414	+	0.978111i
$979$	37.6865	−	21.7583i	1.20447	−	0.695399i
$980$		0			0
$981$	26.3038	+	15.1865i	0.839817	+	0.484869i
$982$	15.6340	+	27.0788i	0.498900	+	0.864120i
$983$	49.4711	−	28.5622i	1.57788	−	0.910992i	0.582730	−	0.812666i	$-0.301984\pi$
$983$	49.4711	−	28.5622i	1.57788	−	0.910992i	0.995154	−	0.0983263i	$-0.0313489\pi$
$984$	−21.2942	+	12.2942i	−0.678835	+	0.391926i
$985$		0			0
$986$	−0.866025	−	0.500000i	−0.0275799	−	0.0159232i
$987$	−18.0000	+	10.3923i	−0.572946	+	0.330791i
$988$		−	4.39230i		−	0.139738i
$989$	−2.53590			−0.0806369
$990$		0			0
$991$		−	46.3923i		−	1.47370i	−0.676056	−	0.736850i	$-0.736312\pi$
$991$		−	46.3923i		−	1.47370i	0.676056	−	0.736850i	$-0.263688\pi$
$992$	−35.4904	−	20.4904i	−1.12682	−	0.650570i
$993$	89.5692			2.84239
$994$	−18.0000	−	10.3923i	−0.570925	−	0.329624i
$995$		0			0
$996$	−11.1962	+	19.3923i	−0.354764	+	0.614469i
$997$	−10.2679	−	17.7846i	−0.325189	−	0.563244i	0.656361	−	0.754447i	$-0.272095\pi$
$997$	−10.2679	−	17.7846i	−0.325189	−	0.563244i	−0.981551	+	0.191202i	$0.938761\pi$
$998$		−	12.5885i		−	0.398481i
$999$	2.00000	+	24.2487i	0.0632772	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.m.b.899.2		4
5.2	odd	4		37.2.e.a.11.1	✓	4
5.3	odd	4		925.2.n.a.751.2		4
5.4	even	2		925.2.m.a.899.1		4
15.2	even	4		333.2.s.b.307.2		4
20.7	even	4		592.2.w.c.529.1		4
37.27	even	6		925.2.m.a.249.1		4
185.27	odd	12		37.2.e.a.27.1	yes	4
185.64	even	6	inner	925.2.m.b.249.2		4
185.82	even	12		1369.2.a.g.1.2		2
185.122	odd	12		1369.2.b.d.1368.3		4
185.137	odd	12		1369.2.b.d.1368.1		4
185.138	odd	12		925.2.n.a.101.2		4
185.177	even	12		1369.2.a.h.1.2		2
555.212	even	12		333.2.s.b.64.2		4
740.27	even	12		592.2.w.c.545.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.e.a.11.1	✓	4	5.2	odd	4
37.2.e.a.27.1	yes	4	185.27	odd	12
333.2.s.b.64.2		4	555.212	even	12
333.2.s.b.307.2		4	15.2	even	4
592.2.w.c.529.1		4	20.7	even	4
592.2.w.c.545.1		4	740.27	even	12
925.2.m.a.249.1		4	37.27	even	6
925.2.m.a.899.1		4	5.4	even	2
925.2.m.b.249.2		4	185.64	even	6	inner
925.2.m.b.899.2		4	1.1	even	1	trivial
925.2.n.a.101.2		4	185.138	odd	12
925.2.n.a.751.2		4	5.3	odd	4
1369.2.a.g.1.2		2	185.82	even	12
1369.2.a.h.1.2		2	185.177	even	12
1369.2.b.d.1368.1		4	185.137	odd	12
1369.2.b.d.1368.3		4	185.122	odd	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{6} +(3.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.36603 + 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +2.73205i q^{6} +(3.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(2.23205 + 3.86603i) q^{9} -4.73205 q^{11} +(2.36603 - 1.36603i) q^{12} +(-1.73205 + 3.00000i) q^{13} +3.46410i q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.86603 - 3.23205i) q^{17} +(-2.23205 + 3.86603i) q^{18} +(-1.09808 - 0.633975i) q^{19} +(4.73205 + 8.19615i) q^{21} +(-2.36603 - 4.09808i) q^{22} +0.732051 q^{23} +(7.09808 + 4.09808i) q^{24} -3.46410 q^{26} +4.00000i q^{27} +(3.00000 - 1.73205i) q^{28} -0.267949i q^{29} -8.19615i q^{31} +(2.50000 - 4.33013i) q^{32} +(-11.1962 - 6.46410i) q^{33} +(1.86603 - 3.23205i) q^{34} +4.46410 q^{36} +(6.06218 - 0.500000i) q^{37} -1.26795i q^{38} +(-8.19615 + 4.73205i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-4.73205 + 8.19615i) q^{42} -3.46410 q^{43} +(-2.36603 + 4.09808i) q^{44} +(0.366025 + 0.633975i) q^{46} +2.19615i q^{47} +2.73205i q^{48} +(2.50000 + 4.33013i) q^{49} -10.1962i q^{51} +(1.73205 + 3.00000i) q^{52} +(-2.19615 + 1.26795i) q^{53} +(-3.46410 + 2.00000i) q^{54} +(9.00000 + 5.19615i) q^{56} +(-1.73205 - 3.00000i) q^{57} +(0.232051 - 0.133975i) q^{58} +(11.6603 - 6.73205i) q^{59} +(3.69615 + 2.13397i) q^{61} +(7.09808 - 4.09808i) q^{62} +15.4641i q^{63} +7.00000 q^{64} -12.9282i q^{66} +(-6.29423 - 3.63397i) q^{67} -3.73205 q^{68} +(1.73205 + 1.00000i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(6.69615 + 11.5981i) q^{72} +(3.46410 + 5.00000i) q^{74} +(-1.09808 + 0.633975i) q^{76} +(-14.1962 - 8.19615i) q^{77} +(-8.19615 - 4.73205i) q^{78} +(-3.29423 - 1.90192i) q^{79} +(1.23205 - 2.13397i) q^{81} -3.00000 q^{82} +(-7.09808 + 4.09808i) q^{83} +9.46410 q^{84} +(-1.73205 - 3.00000i) q^{86} +(0.366025 - 0.633975i) q^{87} -14.1962 q^{88} +(-7.96410 + 4.59808i) q^{89} +(-10.3923 + 6.00000i) q^{91} +(0.366025 - 0.633975i) q^{92} +(11.1962 - 19.3923i) q^{93} +(-1.90192 + 1.09808i) q^{94} +(11.8301 - 6.83013i) q^{96} -4.26795 q^{97} +(-2.50000 + 4.33013i) q^{98} +(-10.5622 - 18.2942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 12 q^{7} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 + 12 * q^7 + 12 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} + 6 q^{3} + 2 q^{4} + 12 q^{7} + 12 q^{8} + 2 q^{9} - 12 q^{11} + 6 q^{12} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 6 q^{19} + 12 q^{21} - 6 q^{22} - 4 q^{23} + 18 q^{24} + 12 q^{28} + 10 q^{32} - 24 q^{33} + 4 q^{34} + 4 q^{36} - 12 q^{39} - 6 q^{41} - 12 q^{42} - 6 q^{44} - 2 q^{46} + 10 q^{49} + 12 q^{53} + 36 q^{56} - 6 q^{58} + 12 q^{59} - 6 q^{61} + 18 q^{62} + 28 q^{64} + 6 q^{67} - 8 q^{68} - 12 q^{71} + 6 q^{72} + 6 q^{76} - 36 q^{77} - 12 q^{78} + 18 q^{79} - 2 q^{81} - 12 q^{82} - 18 q^{83} + 24 q^{84} - 2 q^{87} - 36 q^{88} - 18 q^{89} - 2 q^{92} + 24 q^{93} - 18 q^{94} + 30 q^{96} - 24 q^{97} - 10 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 + 12 * q^7 + 12 * q^8 + 2 * q^9 - 12 * q^11 + 6 * q^12 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 6 * q^19 + 12 * q^21 - 6 * q^22 - 4 * q^23 + 18 * q^24 + 12 * q^28 + 10 * q^32 - 24 * q^33 + 4 * q^34 + 4 * q^36 - 12 * q^39 - 6 * q^41 - 12 * q^42 - 6 * q^44 - 2 * q^46 + 10 * q^49 + 12 * q^53 + 36 * q^56 - 6 * q^58 + 12 * q^59 - 6 * q^61 + 18 * q^62 + 28 * q^64 + 6 * q^67 - 8 * q^68 - 12 * q^71 + 6 * q^72 + 6 * q^76 - 36 * q^77 - 12 * q^78 + 18 * q^79 - 2 * q^81 - 12 * q^82 - 18 * q^83 + 24 * q^84 - 2 * q^87 - 36 * q^88 - 18 * q^89 - 2 * q^92 + 24 * q^93 - 18 * q^94 + 30 * q^96 - 24 * q^97 - 10 * q^98 - 18 * q^99

Introduction

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