LMFDB - Embedded newform 975.2.bb.k.724.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, 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("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			724.1
Root			$-0.385124 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.724
Dual form			975.2.bb.k.874.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.25312 - 1.30084i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.38437 + 4.12985i) q^{4} +(1.30084 + 2.25312i) q^{6} +(3.11915 - 1.80084i) q^{7} -7.20336i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.25312 - 1.30084i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.38437 + 4.12985i) q^{4} +(1.30084 + 2.25312i) q^{6} +(3.11915 - 1.80084i) q^{7} -7.20336i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.60168 - 4.50624i) q^{11} -4.76873i q^{12} +(1.97250 - 3.01815i) q^{13} -9.37041 q^{14} +(-4.60168 + 7.97034i) q^{16} +(-2.54247 + 1.46789i) q^{17} -2.60168i q^{18} +(3.38437 + 5.86190i) q^{19} -3.60168 q^{21} +(-11.7238 + 6.76873i) q^{22} +(4.79559 + 2.76873i) q^{23} +(-3.60168 + 6.23829i) q^{24} +(-8.37041 + 4.23435i) q^{26} -1.00000i q^{27} +(14.8744 + 8.58773i) q^{28} +(0.916472 - 1.58738i) q^{29} +4.10284 q^{31} +(8.25969 - 4.76873i) q^{32} +(-4.50624 + 2.60168i) q^{33} +7.63798 q^{34} +(-2.38437 + 4.12985i) q^{36} +(3.06354 + 1.76873i) q^{37} -17.6101i q^{38} +(-3.21731 + 1.62755i) q^{39} +(2.68521 - 4.65091i) q^{41} +(8.11502 + 4.68521i) q^{42} +(-2.74275 + 1.58353i) q^{43} +24.8134 q^{44} +(-7.20336 - 12.4766i) q^{46} +3.80504i q^{47} +(7.97034 - 4.60168i) q^{48} +(2.98605 - 5.17198i) q^{49} +2.93579 q^{51} +(17.1677 + 0.949743i) q^{52} +5.20336i q^{53} +(-1.30084 + 2.25312i) q^{54} +(-12.9721 - 22.4683i) q^{56} -6.76873i q^{57} +(-4.12985 + 2.38437i) q^{58} +(-3.68521 - 6.38297i) q^{59} +(1.71731 + 2.97447i) q^{61} +(-9.24420 - 5.33714i) q^{62} +(3.11915 + 1.80084i) q^{63} -6.40672 q^{64} +13.5375 q^{66} +(-3.03210 - 1.75058i) q^{67} +(-12.1244 - 7.00000i) q^{68} +(-2.76873 - 4.79559i) q^{69} +(4.85226 + 8.40436i) q^{71} +(6.23829 - 3.60168i) q^{72} +0.805037i q^{73} +(-4.60168 - 7.97034i) q^{74} +(-16.1391 + 27.9538i) q^{76} -18.7408i q^{77} +(9.36617 + 0.518152i) q^{78} +4.10284 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-12.1002 + 6.98605i) q^{82} +11.5375i q^{83} +(-8.58773 - 14.8744i) q^{84} +8.23966 q^{86} +(-1.58738 + 0.916472i) q^{87} +(-32.4601 - 18.7408i) q^{88} +(4.91647 - 8.51558i) q^{89} +(0.717312 - 12.9662i) q^{91} +26.4067i q^{92} +(-3.55317 - 2.05142i) q^{93} +(4.94974 - 8.57321i) q^{94} -9.53747 q^{96} +(-4.82703 + 2.78689i) q^{97} +(-13.4558 + 7.76873i) q^{98} +5.20336 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q + 12 * q^4 + 6 * q^9	$ 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) $ 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−2.25312	−	1.30084i	−1.59320	−	0.919832i	−0.992754	−	0.120165i	$-0.961658\pi$
$2$	−2.25312	−	1.30084i	−1.59320	−	0.919832i	−0.600443	−	0.799668i	$-0.705009\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	2.38437	+	4.12985i	1.19218	+	2.06492i
$5$		0			0
$5$		0			0
$6$	1.30084	+	2.25312i	0.531066	+	0.919832i
$7$	3.11915	−	1.80084i	1.17893	−	0.680653i	0.223160	−	0.974782i	$-0.428363\pi$
$7$	3.11915	−	1.80084i	1.17893	−	0.680653i	0.955766	+	0.294128i	$0.0950293\pi$
$8$		−	7.20336i		−	2.54677i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.60168	−	4.50624i	0.784436	−	1.35868i	−0.144900	−	0.989446i	$-0.546286\pi$
$11$	2.60168	−	4.50624i	0.784436	−	1.35868i	0.929336	−	0.369236i	$-0.120381\pi$
$12$		−	4.76873i		−	1.37662i
$13$	1.97250	−	3.01815i	0.547073	−	0.837085i
$13$	1.97250	−	3.01815i	0.547073	−	0.837085i
$14$	−9.37041			−2.50435
$15$		0			0
$16$	−4.60168	+	7.97034i	−1.15042	+	1.99259i
$17$	−2.54247	+	1.46789i	−0.616639	+	0.356017i	−0.775559	−	0.631275i	$-0.782532\pi$
$17$	−2.54247	+	1.46789i	−0.616639	+	0.356017i	0.158920	+	0.987291i	$0.449199\pi$
$18$		−	2.60168i		−	0.613222i
$19$	3.38437	+	5.86190i	0.776427	+	1.34481i	0.933989	+	0.357302i	$0.116303\pi$
$19$	3.38437	+	5.86190i	0.776427	+	1.34481i	−0.157562	+	0.987509i	$0.550363\pi$
$20$		0			0
$21$	−3.60168			−0.785951
$22$	−11.7238	+	6.76873i	−2.49952	+	1.44310i
$23$	4.79559	+	2.76873i	0.999949	+	0.577321i	0.908233	−	0.418464i	$-0.137431\pi$
$23$	4.79559	+	2.76873i	0.999949	+	0.577321i	0.0917160	+	0.995785i	$0.470765\pi$
$24$	−3.60168	+	6.23829i	−0.735190	+	1.27339i
$25$		0			0
$26$	−8.37041	+	4.23435i	−1.64157	+	0.830424i
$27$		−	1.00000i		−	0.192450i
$28$	14.8744	+	8.58773i	2.81099	+	1.62293i
$29$	0.916472	−	1.58738i	0.170185	−	0.294768i	−0.768300	−	0.640090i	$-0.778897\pi$
$29$	0.916472	−	1.58738i	0.170185	−	0.294768i	0.938484	+	0.345322i	$0.112230\pi$
$30$		0			0
$31$	4.10284			0.736893			0.368446	−	0.929649i	$-0.379890\pi$
$31$	4.10284			0.736893			0.368446	+	0.929649i	$0.379890\pi$
$32$	8.25969	−	4.76873i	1.46012	−	0.843001i
$33$	−4.50624	+	2.60168i	−0.784436	+	0.452894i
$34$	7.63798			1.30990
$35$		0			0
$36$	−2.38437	+	4.12985i	−0.397395	+	0.688308i
$37$	3.06354	+	1.76873i	0.503642	+	0.290778i	0.730217	−	0.683216i	$-0.239419\pi$
$37$	3.06354	+	1.76873i	0.503642	+	0.290778i	−0.226574	+	0.973994i	$0.572753\pi$
$38$		−	17.6101i		−	2.85673i
$39$	−3.21731	+	1.62755i	−0.515182	+	0.260616i
$40$		0			0
$41$	2.68521	−	4.65091i	0.419359	−	0.726351i	−0.576516	−	0.817086i	$-0.695588\pi$
$41$	2.68521	−	4.65091i	0.419359	−	0.726351i	0.995875	+	0.0907349i	$0.0289216\pi$
$42$	8.11502	+	4.68521i	1.25217	+	0.722943i
$43$	−2.74275	+	1.58353i	−0.418265	+	0.241486i	−0.694335	−	0.719652i	$-0.744301\pi$
$43$	−2.74275	+	1.58353i	−0.418265	+	0.241486i	0.276069	+	0.961138i	$0.410968\pi$
$44$	24.8134			3.74077
$45$		0			0
$46$	−7.20336	−	12.4766i	−1.06208	−	1.83957i
$47$			3.80504i			0.555022i	0.960722	+	0.277511i	$0.0895095\pi$
$47$			3.80504i			0.555022i	−0.960722	+	0.277511i	$0.910491\pi$
$48$	7.97034	−	4.60168i	1.15042	−	0.664195i
$49$	2.98605	−	5.17198i	0.426578	−	0.738855i
$50$		0			0
$51$	2.93579			0.411093
$52$	17.1677	+	0.949743i	2.38073	+	0.131706i
$53$			5.20336i			0.714736i	0.933964	+	0.357368i	$0.116326\pi$
$53$			5.20336i			0.714736i	−0.933964	+	0.357368i	$0.883674\pi$
$54$	−1.30084	+	2.25312i	−0.177022	+	0.306611i
$55$		0			0
$56$	−12.9721	−	22.4683i	−1.73347	−	3.00246i
$57$		−	6.76873i		−	0.896541i
$58$	−4.12985	+	2.38437i	−0.542275	+	0.313083i
$59$	−3.68521	−	6.38297i	−0.479773	−	0.830991i	0.519958	−	0.854192i	$-0.325948\pi$
$59$	−3.68521	−	6.38297i	−0.479773	−	0.830991i	−0.999731	+	0.0232007i	$0.992614\pi$
$60$		0			0
$61$	1.71731	+	2.97447i	0.219879	+	0.380842i	0.954771	−	0.297343i	$-0.0961003\pi$
$61$	1.71731	+	2.97447i	0.219879	+	0.380842i	−0.734892	+	0.678185i	$0.762767\pi$
$62$	−9.24420	−	5.33714i	−1.17401	−	0.677818i
$63$	3.11915	+	1.80084i	0.392975	+	0.226884i
$64$	−6.40672			−0.800840
$65$		0			0
$66$	13.5375			1.66635
$67$	−3.03210	−	1.75058i	−0.370430	−	0.213868i	0.303216	−	0.952922i	$-0.401939\pi$
$67$	−3.03210	−	1.75058i	−0.370430	−	0.213868i	−0.673646	+	0.739054i	$0.735273\pi$
$68$	−12.1244	−	7.00000i	−1.47029	−	0.848875i
$69$	−2.76873	−	4.79559i	−0.333316	−	0.577321i
$70$		0			0
$71$	4.85226	+	8.40436i	0.575858	+	0.997415i	0.995948	+	0.0899322i	$0.0286650\pi$
$71$	4.85226	+	8.40436i	0.575858	+	0.997415i	−0.420090	+	0.907482i	$0.638002\pi$
$72$	6.23829	−	3.60168i	0.735190	−	0.424462i
$73$			0.805037i			0.0942225i	0.998890	+	0.0471113i	$0.0150015\pi$
$73$			0.805037i			0.0942225i	−0.998890	+	0.0471113i	$0.984998\pi$
$74$	−4.60168	−	7.97034i	−0.534934	−	0.926533i
$75$		0			0
$76$	−16.1391	+	27.9538i	−1.85129	+	3.20652i
$77$		−	18.7408i		−	2.13572i
$78$	9.36617	+	0.518152i	1.06051	+	0.0586691i
$79$	4.10284			0.461606			0.230803	−	0.973000i	$-0.425865\pi$
$79$	4.10284			0.461606			0.230803	+	0.973000i	$0.425865\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−12.1002	+	6.98605i	−1.33624	+	0.771480i
$83$			11.5375i			1.26640i	0.773988	+	0.633201i	$0.218259\pi$
$83$			11.5375i			1.26640i	−0.773988	+	0.633201i	$0.781741\pi$
$84$	−8.58773	−	14.8744i	−0.936998	−	1.62293i
$85$		0			0
$86$	8.23966			0.888506
$87$	−1.58738	+	0.916472i	−0.170185	+	0.0982562i
$88$	−32.4601	−	18.7408i	−3.46025	−	1.99778i
$89$	4.91647	−	8.51558i	0.521145	−	0.902650i	−0.478553	−	0.878059i	$-0.658838\pi$
$89$	4.91647	−	8.51558i	0.521145	−	0.902650i	0.999698	−	0.0245908i	$-0.00782827\pi$
$90$		0			0
$91$	0.717312	−	12.9662i	0.0751947	−	1.35923i
$92$			26.4067i			2.75309i
$93$	−3.55317	−	2.05142i	−0.368446	−	0.212723i
$94$	4.94974	−	8.57321i	0.510527	−	0.884259i
$95$		0			0
$96$	−9.53747			−0.973414
$97$	−4.82703	+	2.78689i	−0.490110	+	0.282965i	−0.724620	−	0.689148i	$-0.757985\pi$
$97$	−4.82703	+	2.78689i	−0.490110	+	0.282965i	0.234510	+	0.972114i	$0.424651\pi$
$98$	−13.4558	+	7.76873i	−1.35925	+	0.784761i
$99$	5.20336			0.522957
$100$		0			0
$101$	−1.20336	+	2.08428i	−0.119739	+	0.207393i	−0.919664	−	0.392706i	$-0.871539\pi$
$101$	−1.20336	+	2.08428i	−0.119739	+	0.207393i	0.799925	+	0.600099i	$0.204872\pi$
$102$	−6.61469	−	3.81899i	−0.654952	−	0.378136i
$103$		−	18.4430i		−	1.81724i	−0.417619	−	0.908622i	$-0.637135\pi$
$103$		−	18.4430i		−	1.81724i	0.417619	−	0.908622i	$-0.362865\pi$
$104$	−21.7408	−	14.2086i	−2.13186	−	1.39327i
$105$		0			0
$106$	6.76873	−	11.7238i	0.657438	−	1.13872i
$107$	−9.47067	−	5.46789i	−0.915564	−	0.528601i	−0.0333471	−	0.999444i	$-0.510617\pi$
$107$	−9.47067	−	5.46789i	−0.915564	−	0.528601i	−0.882217	+	0.470842i	$0.843950\pi$
$108$	4.12985	−	2.38437i	0.397395	−	0.229436i
$109$	−13.8692			−1.32843			−0.664217	−	0.747540i	$-0.731235\pi$
$109$	−13.8692			−1.32843			−0.664217	+	0.747540i	$0.731235\pi$
$110$		0			0
$111$	−1.76873	−	3.06354i	−0.167881	−	0.290778i
$112$			33.1475i			3.13215i
$113$	9.70239	−	5.60168i	0.912724	−	0.526962i	0.0314176	−	0.999506i	$-0.489998\pi$
$113$	9.70239	−	5.60168i	0.912724	−	0.526962i	0.881307	+	0.472545i	$0.156664\pi$
$114$	−8.80504	+	15.2508i	−0.824667	+	1.42837i
$115$		0			0
$116$	8.74083			0.811565
$117$	3.60005	+	0.199160i	0.332824	+	0.0184124i
$118$			19.1755i			1.76524i
$119$	−5.28689	+	9.15715i	−0.484648	+	0.839435i
$120$		0			0
$121$	−8.03747	−	13.9213i	−0.730679	−	1.26557i
$122$		−	8.93579i		−	0.809008i
$123$	−4.65091	+	2.68521i	−0.419359	+	0.242117i
$124$	9.78269	+	16.9441i	0.878511	+	1.52163i
$125$		0			0
$126$	−4.68521	−	8.11502i	−0.417391	−	0.722943i
$127$	2.76692	+	1.59748i	0.245524	+	0.141754i	0.617713	−	0.786403i	$-0.288059\pi$
$127$	2.76692	+	1.59748i	0.245524	+	0.141754i	−0.372189	+	0.928157i	$0.621393\pi$
$128$	−2.08428	−	1.20336i	−0.184226	−	0.106363i
$129$	3.16706			0.278844
$130$		0			0
$131$	−4.57377			−0.399612			−0.199806	−	0.979835i	$-0.564031\pi$
$131$	−4.57377			−0.399612			−0.199806	+	0.979835i	$0.564031\pi$
$132$	−21.4891	−	12.4067i	−1.87038	−	1.07987i
$133$	21.1127	+	12.1894i	1.83070	+	1.05696i
$134$	4.55445	+	7.88855i	0.393445	+	0.681467i
$135$		0			0
$136$	10.5738	+	18.3143i	0.906693	+	1.57044i
$137$	9.24420	−	5.33714i	0.789785	−	0.455983i	−0.0501015	−	0.998744i	$-0.515954\pi$
$137$	9.24420	−	5.33714i	0.789785	−	0.455983i	0.839887	+	0.542761i	$0.182621\pi$
$138$			14.4067i			1.22638i
$139$	−8.07377	−	13.9842i	−0.684808	−	1.18612i	−0.973497	−	0.228700i	$-0.926553\pi$
$139$	−8.07377	−	13.9842i	−0.684808	−	1.18612i	0.288689	−	0.957423i	$-0.406781\pi$
$140$		0			0
$141$	1.90252	−	3.29526i	0.160221	−	0.277511i
$142$		−	25.2481i		−	2.11877i
$143$	−8.46870	−	16.7408i	−0.708188	−	1.39994i
$144$	−9.20336			−0.766947
$145$		0			0
$146$	1.04722	−	1.81385i	0.0866689	−	0.150115i
$147$	−5.17198	+	2.98605i	−0.426578	+	0.246285i
$148$			16.8692i			1.38664i
$149$	−4.83294	−	8.37091i	−0.395930	−	0.685771i	0.597289	−	0.802026i	$-0.296244\pi$
$149$	−4.83294	−	8.37091i	−0.395930	−	0.685771i	−0.993219	+	0.116255i	$0.962911\pi$
$150$		0			0
$151$	−18.7129			−1.52284			−0.761418	−	0.648261i	$-0.775496\pi$
$151$	−18.7129			−1.52284			−0.761418	+	0.648261i	$0.775496\pi$
$152$	42.2253	−	24.3788i	3.42493	−	1.97738i
$153$	−2.54247	−	1.46789i	−0.205546	−	0.118672i
$154$	−24.3788	+	42.2253i	−1.96450	+	3.40261i
$155$		0			0
$156$	−14.3928	−	9.40633i	−1.15234	−	0.753109i
$157$		−	10.3704i		−	0.827649i	−0.910357	−	0.413825i	$-0.864193\pi$
$157$		−	10.3704i		−	0.827649i	0.910357	−	0.413825i	$-0.135807\pi$
$158$	−9.24420	−	5.33714i	−0.735429	−	0.424600i
$159$	2.60168	−	4.50624i	0.206327	−	0.357368i
$160$		0			0
$161$	19.9442			1.57182
$162$	2.25312	−	1.30084i	0.177022	−	0.102204i
$163$	9.93613	−	5.73663i	0.778258	−	0.449327i	−0.0575546	−	0.998342i	$-0.518330\pi$
$163$	9.93613	−	5.73663i	0.778258	−	0.449327i	0.835813	+	0.549015i	$0.184997\pi$
$164$	25.6101			1.99981
$165$		0			0
$166$	15.0084	−	25.9953i	1.16488	−	2.01763i
$167$	2.71131	+	1.56538i	0.209808	+	0.121132i	0.601222	−	0.799082i	$-0.294681\pi$
$167$	2.71131	+	1.56538i	0.209808	+	0.121132i	−0.391414	+	0.920215i	$0.628014\pi$
$168$			25.9442i			2.00164i
$169$	−5.21848	−	11.9066i	−0.401421	−	0.915893i
$170$		0			0
$171$	−3.38437	+	5.86190i	−0.258809	+	0.448270i
$172$	−13.0794	−	7.55142i	−0.997298	−	0.575791i
$173$	−7.15992	+	4.13378i	−0.544359	+	0.314286i	−0.746844	−	0.665000i	$-0.768432\pi$
$173$	−7.15992	+	4.13378i	−0.544359	+	0.314286i	0.202485	+	0.979285i	$0.435098\pi$
$174$	4.76873			0.361517
$175$		0			0
$176$	23.9442	+	41.4725i	1.80486	+	3.12611i
$177$			7.37041i			0.553994i
$178$	−22.1548	+	12.7911i	−1.66057	+	0.958732i
$179$	−9.22268	+	15.9741i	−0.689335	+	1.19396i	0.282718	+	0.959203i	$0.408764\pi$
$179$	−9.22268	+	15.9741i	−0.689335	+	1.19396i	−0.972053	+	0.234760i	$0.924569\pi$
$180$		0			0
$181$	21.1028			1.56856			0.784281	−	0.620406i	$-0.213032\pi$
$181$	21.1028			1.56856			0.784281	+	0.620406i	$0.213032\pi$
$182$	−18.4832	+	28.2813i	−1.37006	+	2.09635i
$183$		−	3.43462i		−	0.253895i
$184$	19.9442	−	34.5443i	1.47030	−	2.54664i
$185$		0			0
$186$	5.33714	+	9.24420i	0.391338	+	0.677818i
$187$			15.2760i			1.11709i
$188$	−15.7142	+	9.07261i	−1.14608	+	0.661688i
$189$	−1.80084	−	3.11915i	−0.130992	−	0.226884i
$190$		0			0
$191$	4.35110	+	7.53632i	0.314834	+	0.545309i	0.979402	−	0.201919i	$-0.0647177\pi$
$191$	4.35110	+	7.53632i	0.314834	+	0.545309i	−0.664568	+	0.747228i	$0.731384\pi$
$192$	5.54838	+	3.20336i	0.400420	+	0.231182i
$193$	16.6862	+	9.63378i	1.20110	+	0.693455i	0.960800	−	0.277244i	$-0.0894210\pi$
$193$	16.6862	+	9.63378i	1.20110	+	0.693455i	0.240300	+	0.970699i	$0.422754\pi$
$194$	14.5012			1.04112
$195$		0			0
$196$	28.4793			2.03424
$197$	13.1182	+	7.57377i	0.934630	+	0.539609i	0.888273	−	0.459316i	$-0.151905\pi$
$197$	13.1182	+	7.57377i	0.934630	+	0.539609i	0.0463571	+	0.998925i	$0.485239\pi$
$198$	−11.7238	−	6.76873i	−0.833174	−	0.481033i
$199$	−2.26873	−	3.92956i	−0.160826	−	0.278559i	0.774339	−	0.632771i	$-0.218083\pi$
$199$	−2.26873	−	3.92956i	−0.160826	−	0.278559i	−0.935165	+	0.354212i	$0.884749\pi$
$200$		0			0
$201$	1.75058	+	3.03210i	0.123477	+	0.213868i
$202$	5.42262	−	3.13075i	0.381534	−	0.220279i
$203$		−	6.60168i		−	0.463347i
$204$	7.00000	+	12.1244i	0.490098	+	0.848875i
$205$		0			0
$206$	−23.9914	+	41.5543i	−1.67156	+	2.89523i
$207$			5.53747i			0.384881i
$208$	14.9789	+	29.6101i	1.03860	+	2.05309i
$209$	35.2201			2.43623
$210$		0			0
$211$	11.0738	−	19.1803i	0.762350	−	1.32043i	−0.179286	−	0.983797i	$-0.557379\pi$
$211$	11.0738	−	19.1803i	0.762350	−	1.32043i	0.941636	−	0.336632i	$-0.109288\pi$
$212$	−21.4891	+	12.4067i	−1.47587	+	0.852097i
$213$		−	9.70452i		−	0.664943i
$214$	14.2257	+	24.6396i	0.972449	+	1.68433i
$215$		0			0
$216$	−7.20336			−0.490126
$217$	12.7974	−	7.38856i	0.868742	−	0.501568i
$218$	31.2491	+	18.0417i	2.11645	+	1.22194i
$219$	0.402519	−	0.697183i	0.0271997	−	0.0471113i
$220$		0			0
$221$	−0.584693	+	10.5690i	−0.0393307	+	0.710946i
$222$			9.20336i			0.617689i
$223$	−6.59052	−	3.80504i	−0.441334	−	0.254804i	0.262829	−	0.964842i	$-0.415344\pi$
$223$	−6.59052	−	3.80504i	−0.441334	−	0.254804i	−0.704163	+	0.710038i	$0.748678\pi$
$224$	17.1755	−	29.7488i	1.14758	−	1.98767i
$225$		0			0
$226$	−29.1475			−1.93887
$227$	20.2152	−	11.6713i	1.34173	−	0.774648i	0.354669	−	0.934992i	$-0.384594\pi$
$227$	20.2152	−	11.6713i	1.34173	−	0.774648i	0.987061	+	0.160344i	$0.0512603\pi$
$228$	27.9538	−	16.1391i	1.85129	−	1.06884i
$229$	−0.824549			−0.0544877			−0.0272439	−	0.999629i	$-0.508673\pi$
$229$	−0.824549			−0.0544877			−0.0272439	+	0.999629i	$0.508673\pi$
$230$		0			0
$231$	−9.37041	+	16.2300i	−0.616528	+	1.06786i
$232$	−11.4344	−	6.60168i	−0.750708	−	0.433421i
$233$			13.4044i			0.878150i	0.898450	+	0.439075i	$0.144694\pi$
$233$			13.4044i			0.878150i	−0.898450	+	0.439075i	$0.855306\pi$
$234$	−7.85226	−	5.13182i	−0.513318	−	0.335477i
$235$		0			0
$236$	17.5738	−	30.4387i	1.14396	−	1.98139i
$237$	−3.55317	−	2.05142i	−0.230803	−	0.133254i
$238$	23.8240	−	13.7548i	1.54428	−	0.891590i
$239$	−12.7966			−0.827746			−0.413873	−	0.910335i	$-0.635824\pi$
$239$	−12.7966			−0.827746			−0.413873	+	0.910335i	$0.635824\pi$
$240$		0			0
$241$	−6.38437	−	11.0580i	−0.411253	−	0.712312i	0.583774	−	0.811916i	$-0.301575\pi$
$241$	−6.38437	−	11.0580i	−0.411253	−	0.712312i	−0.995027	+	0.0996048i	$0.968242\pi$
$242$			41.8218i			2.68841i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−8.18940	+	14.1845i	−0.524273	+	0.908067i
$245$		0			0
$246$	13.9721			0.890828
$247$	24.3678	+	1.34806i	1.55048	+	0.0857753i
$248$		−	29.5543i		−	1.87670i
$249$	5.76873	−	9.99174i	0.365579	−	0.633201i
$250$		0			0
$251$	4.20336	+	7.28043i	0.265314	+	0.459537i	0.967646	−	0.252313i	$-0.0811912\pi$
$251$	4.20336	+	7.28043i	0.265314	+	0.459537i	−0.702332	+	0.711849i	$0.747858\pi$
$252$			17.1755i			1.08195i
$253$	24.9532	−	14.4067i	1.56879	−	0.905743i
$254$	−4.15613	−	7.19863i	−0.260779	−	0.451683i
$255$		0			0
$256$	9.53747	+	16.5194i	0.596092	+	1.03246i
$257$	−5.31666	−	3.06957i	−0.331644	−	0.191475i	0.324927	−	0.945739i	$-0.394660\pi$
$257$	−5.31666	−	3.06957i	−0.331644	−	0.191475i	−0.656571	+	0.754264i	$0.727994\pi$
$258$	−7.13576	−	4.11983i	−0.444253	−	0.256489i
$259$	12.7408			0.791676
$260$		0			0
$261$	1.83294			0.113456
$262$	10.3053	+	5.94974i	0.636661	+	0.367576i
$263$	−4.09639	−	2.36505i	−0.252594	−	0.145835i	0.368357	−	0.929684i	$-0.379920\pi$
$263$	−4.09639	−	2.36505i	−0.252594	−	0.145835i	−0.620951	+	0.783849i	$0.713254\pi$
$264$	18.7408	+	32.4601i	1.15342	+	1.99778i
$265$		0			0
$266$	−31.7129	−	54.9284i	−1.94444	−	3.36788i
$267$	−8.51558	+	4.91647i	−0.521145	+	0.300883i
$268$		−	16.6961i		−	1.01988i
$269$	−2.72151	−	4.71379i	−0.165933	−	0.287405i	0.771053	−	0.636771i	$-0.219730\pi$
$269$	−2.72151	−	4.71379i	−0.165933	−	0.287405i	−0.936986	+	0.349366i	$0.886397\pi$
$270$		0			0
$271$	−12.7397	+	22.0657i	−0.773879	+	1.34040i	0.161543	+	0.986866i	$0.448353\pi$
$271$	−12.7397	+	22.0657i	−0.773879	+	1.34040i	−0.935422	+	0.353533i	$0.884980\pi$
$272$		−	27.0191i		−	1.63827i
$273$	−7.10432	+	10.8704i	−0.429973	+	0.657907i
$274$	−27.7711			−1.67771
$275$		0			0
$276$	13.2034	−	22.8689i	0.794749	−	1.37655i
$277$	−19.7570	+	11.4067i	−1.18708	+	0.685363i	−0.957643	−	0.287959i	$-0.907023\pi$
$277$	−19.7570	+	11.4067i	−1.18708	+	0.685363i	−0.229441	+	0.973323i	$0.573690\pi$
$278$			42.0107i			2.51964i
$279$	2.05142	+	3.55317i	0.122815	+	0.212723i
$280$		0			0
$281$	−2.16706			−0.129276			−0.0646378	−	0.997909i	$-0.520589\pi$
$281$	−2.16706			−0.129276			−0.0646378	+	0.997909i	$0.520589\pi$
$282$	−8.57321	+	4.94974i	−0.510527	+	0.294753i
$283$	−25.7616	−	14.8734i	−1.53137	−	0.884135i	−0.999299	−	0.0374322i	$-0.988082\pi$
$283$	−25.7616	−	14.8734i	−1.53137	−	0.884135i	−0.532067	−	0.846702i	$-0.678584\pi$
$284$	−23.1391	+	40.0782i	−1.37306	+	2.37820i
$285$		0			0
$286$	−2.69613	+	48.7355i	−0.159425	+	2.88179i
$287$		−	19.3425i		−	1.14175i
$288$	8.25969	+	4.76873i	0.486707	+	0.281000i
$289$	−4.19057	+	7.25828i	−0.246504	+	0.426958i
$290$		0			0
$291$	5.57377			0.326740
$292$	−3.32468	+	1.91950i	−0.194562	+	0.112331i
$293$	−28.6530	+	16.5428i	−1.67393	+	0.966443i	−0.708522	+	0.705688i	$0.750638\pi$
$293$	−28.6530	+	16.5428i	−1.67393	+	0.966443i	−0.965405	+	0.260754i	$0.916029\pi$
$294$	15.5375			0.906164
$295$		0			0
$296$	12.7408	−	22.0678i	0.740546	−	1.28266i
$297$	−4.50624	−	2.60168i	−0.261479	−	0.150965i
$298$			25.1475i			1.45676i
$299$	17.8158	−	9.01248i	1.03031	−	0.521205i
$300$		0			0
$301$	−5.70336	+	9.87851i	−0.328736	+	0.569388i
$302$	42.1625	+	24.3425i	2.42618	+	1.40075i
$303$	2.08428	−	1.20336i	0.119739	−	0.0691311i
$304$	−62.2951			−3.57287
$305$		0			0
$306$	3.81899	+	6.61469i	0.218317	+	0.378136i
$307$		−	14.3704i		−	0.820163i	−0.912049	−	0.410081i	$-0.865500\pi$
$307$		−	14.3704i		−	0.820163i	0.912049	−	0.410081i	$-0.134500\pi$
$308$	77.3967	−	44.6850i	4.41009	−	2.54616i
$309$	−9.22151	+	15.9721i	−0.524593	+	0.908622i
$310$		0			0
$311$	−8.70685			−0.493720			−0.246860	−	0.969051i	$-0.579399\pi$
$311$	−8.70685			−0.493720			−0.246860	+	0.969051i	$0.579399\pi$
$312$	11.7238	+	23.1755i	0.663729	+	1.31205i
$313$			8.16472i			0.461497i	0.973013	+	0.230749i	$0.0741175\pi$
$313$			8.16472i			0.461497i	−0.973013	+	0.230749i	$0.925882\pi$
$314$	−13.4902	+	23.3658i	−0.761299	+	1.31861i
$315$		0			0
$316$	9.78269	+	16.9441i	0.550319	+	0.953181i
$317$			13.4090i			0.753127i	0.926391	+	0.376564i	$0.122894\pi$
$317$			13.4090i			0.753127i	−0.926391	+	0.376564i	$0.877106\pi$
$318$	−11.7238	+	6.76873i	−0.657438	+	0.379572i
$319$	−4.76873	−	8.25969i	−0.266998	−	0.462454i
$320$		0			0
$321$	5.46789	+	9.47067i	0.305188	+	0.528601i
$322$	−44.9366	−	25.9442i	−2.50422	−	1.44581i
$323$	−17.2093	−	9.93579i	−0.957551	−	0.552842i
$324$	−4.76873			−0.264930
$325$		0			0
$326$	−29.8497			−1.65322
$327$	12.0111	+	6.93462i	0.664217	+	0.383486i
$328$	−33.5022	−	19.3425i	−1.84985	−	1.06801i
$329$	6.85226	+	11.8685i	0.377777	+	0.654330i
$330$		0			0
$331$	−10.7397	−	18.6016i	−0.590305	−	1.02244i	−0.994191	−	0.107629i	$-0.965674\pi$
$331$	−10.7397	−	18.6016i	−0.590305	−	1.02244i	0.403886	−	0.914809i	$-0.367659\pi$
$332$	−47.6480	+	27.5096i	−2.61502	+	1.50978i
$333$			3.53747i			0.193852i
$334$	−4.07261	−	7.05396i	−0.222843	−	0.385976i
$335$		0			0
$336$	16.5738	−	28.7066i	0.904173	−	1.56607i
$337$		−	7.44535i		−	0.405574i	−0.979223	−	0.202787i	$-0.935000\pi$
$337$		−	7.44535i		−	0.405574i	0.979223	−	0.202787i	$-0.0649999\pi$
$338$	−3.73074	+	33.6154i	−0.202925	+	1.82844i
$339$	−11.2034			−0.608483
$340$		0			0
$341$	10.6743	−	18.4884i	0.578045	−	1.00120i
$342$	15.2508	−	8.80504i	0.824667	−	0.476122i
$343$			3.70219i			0.199900i
$344$	11.4067	+	19.7570i	0.615009	+	1.06523i
$345$		0			0
$346$	21.5096			1.15636
$347$	−21.6043	+	12.4733i	−1.15978	+	0.669600i	−0.951251	−	0.308417i	$-0.900201\pi$
$347$	−21.6043	+	12.4733i	−1.15978	+	0.669600i	−0.208529	+	0.978016i	$0.566868\pi$
$348$	−7.56978	−	4.37041i	−0.405783	−	0.234279i
$349$	1.05142	−	1.82112i	0.0562813	−	0.0974822i	−0.836512	−	0.547949i	$-0.815409\pi$
$349$	1.05142	−	1.82112i	0.0562813	−	0.0974822i	0.892793	+	0.450466i	$0.148742\pi$
$350$		0			0
$351$	−3.01815	−	1.97250i	−0.161097	−	0.105284i
$352$		−	49.6269i		−	2.64512i
$353$	16.0559	+	9.26990i	0.854571	+	0.493387i	0.862191	−	0.506584i	$-0.169092\pi$
$353$	16.0559	+	9.26990i	0.854571	+	0.493387i	−0.00761929	+	0.999971i	$0.502425\pi$
$354$	9.58773	−	16.6064i	0.509582	−	0.882622i
$355$		0			0
$356$	46.8907			2.48520
$357$	9.15715	−	5.28689i	0.484648	−	0.279812i
$358$	41.5596	−	23.9944i	2.19649	−	1.26815i
$359$	4.75801			0.251118			0.125559	−	0.992086i	$-0.459928\pi$
$359$	4.75801			0.251118			0.125559	+	0.992086i	$0.459928\pi$
$360$		0			0
$361$	−13.4079	+	23.2231i	−0.705678	+	1.22227i
$362$	−47.5472	−	27.4514i	−2.49903	−	1.44281i
$363$			16.0749i			0.843715i
$364$	55.2588	−	27.9538i	2.89635	−	1.46518i
$365$		0			0
$366$	−4.46789	+	7.73862i	−0.233541	+	0.404504i
$367$	8.86983	+	5.12100i	0.463001	+	0.267314i	0.713305	−	0.700853i	$-0.247197\pi$
$367$	8.86983	+	5.12100i	0.463001	+	0.267314i	−0.250304	+	0.968167i	$0.580531\pi$
$368$	−44.1355	+	25.4817i	−2.30072	+	1.32832i
$369$	5.37041			0.279573
$370$		0			0
$371$	9.37041	+	16.2300i	0.486488	+	0.842621i
$372$		−	19.5654i		−	1.01442i
$373$	20.2132	−	11.6701i	1.04660	−	0.604254i	0.124904	−	0.992169i	$-0.460138\pi$
$373$	20.2132	−	11.6701i	1.04660	−	0.604254i	0.921695	+	0.387915i	$0.126804\pi$
$374$	19.8716	−	34.4186i	1.02753	−	1.77974i
$375$		0			0
$376$	27.4090			1.41351
$377$	−2.98320	−	5.89716i	−0.153643	−	0.303719i
$378$			9.37041i			0.481962i
$379$	−17.8286	+	30.8800i	−0.915791	+	1.58620i	−0.110052	+	0.993926i	$0.535102\pi$
$379$	−17.8286	+	30.8800i	−0.915791	+	1.58620i	−0.805739	+	0.592271i	$0.798231\pi$
$380$		0			0
$381$	−1.59748	−	2.76692i	−0.0818414	−	0.141754i
$382$		−	22.6403i		−	1.15838i
$383$	26.5164	−	15.3092i	1.35492	−	0.782265i	0.365989	−	0.930619i	$-0.380731\pi$
$383$	26.5164	−	15.3092i	1.35492	−	0.782265i	0.988934	+	0.148354i	$0.0473974\pi$
$384$	1.20336	+	2.08428i	0.0614086	+	0.106363i
$385$		0			0
$386$	−25.0640	−	43.4121i	−1.27572	−	2.20962i
$387$	−2.74275	−	1.58353i	−0.139422	−	0.0804952i
$388$	−23.0188	−	13.2899i	−1.16860	−	0.674693i
$389$	−25.0191			−1.26852			−0.634260	−	0.773120i	$-0.718695\pi$
$389$	−25.0191			−1.26852			−0.634260	+	0.773120i	$0.718695\pi$
$390$		0			0
$391$	−16.2568			−0.822144
$392$	−37.2557	−	21.5096i	−1.88169	−	1.08640i
$393$	3.96100	+	2.28689i	0.199806	+	0.115358i
$394$	−19.7045	−	34.1292i	−0.992700	−	1.71941i
$395$		0			0
$396$	12.4067	+	21.4891i	0.623461	+	1.07987i
$397$	9.38161	−	5.41647i	0.470849	−	0.271845i	−0.245746	−	0.969334i	$-0.579033\pi$
$397$	9.38161	−	5.41647i	0.470849	−	0.271845i	0.716595	+	0.697489i	$0.245700\pi$
$398$			11.8050i			0.591733i
$399$	−12.1894	−	21.1127i	−0.610233	−	1.05696i
$400$		0			0
$401$	12.2397	−	21.1997i	0.611220	−	1.05866i	−0.379816	−	0.925062i	$-0.624013\pi$
$401$	12.2397	−	21.1997i	0.611220	−	1.05866i	0.991035	−	0.133601i	$-0.0426541\pi$
$402$		−	9.10891i		−	0.454311i
$403$	8.09287	−	12.3830i	0.403134	−	0.616842i
$404$	−11.4770			−0.571002
$405$		0			0
$406$	−8.58773	+	14.8744i	−0.426202	+	0.738203i
$407$	15.9407	−	9.20336i	0.790150	−	0.456194i
$408$		−	21.1475i		−	1.04696i
$409$	13.3553	+	23.1320i	0.660377	+	1.14381i	0.980517	+	0.196436i	$0.0629368\pi$
$409$	13.3553	+	23.1320i	0.660377	+	1.14381i	−0.320140	+	0.947370i	$0.603730\pi$
$410$		0			0
$411$	−10.6743			−0.526524
$412$	76.1668	−	43.9749i	3.75247	−	2.16649i
$413$	−22.9894	−	13.2729i	−1.13123	−	0.653118i
$414$	7.20336	−	12.4766i	0.354026	−	0.613191i
$415$		0			0
$416$	1.89949	−	34.3353i	0.0931300	−	1.68343i
$417$			16.1475i			0.790749i
$418$	−79.3552	−	45.8158i	−3.88139	−	2.24092i
$419$	7.51815	−	13.0218i	0.367286	−	0.636158i	−0.621854	−	0.783133i	$-0.713620\pi$
$419$	7.51815	−	13.0218i	0.367286	−	0.636158i	0.989140	+	0.146975i	$0.0469538\pi$
$420$		0			0
$421$	−5.90182			−0.287637			−0.143818	−	0.989604i	$-0.545938\pi$
$421$	−5.90182			−0.287637			−0.143818	+	0.989604i	$0.545938\pi$
$422$	−49.9011	+	28.8104i	−2.42915	+	1.40247i
$423$	−3.29526	+	1.90252i	−0.160221	+	0.0925036i
$424$	37.4817			1.82027
$425$		0			0
$426$	−12.6240	+	21.8655i	−0.611636	+	1.05938i
$427$	10.7131	+	6.18521i	0.518443	+	0.299323i
$428$		−	52.1499i		−	2.52076i
$429$	−1.03630	+	18.7323i	−0.0500332	+	0.904406i
$430$		0			0
$431$	−19.6743	+	34.0769i	−0.947677	+	1.64142i	−0.197376	+	0.980328i	$0.563242\pi$
$431$	−19.6743	+	34.0769i	−0.947677	+	1.64142i	−0.750301	+	0.661097i	$0.770091\pi$
$432$	7.97034	+	4.60168i	0.383473	+	0.221398i
$433$	−10.7518	+	6.20756i	−0.516699	+	0.298316i	−0.735583	−	0.677435i	$-0.763092\pi$
$433$	−10.7518	+	6.20756i	−0.516699	+	0.298316i	0.218884	+	0.975751i	$0.429758\pi$
$434$	−38.4454			−1.84544
$435$		0			0
$436$	−33.0694	−	57.2778i	−1.58374	−	2.74311i
$437$			37.4817i			1.79299i
$438$	−1.81385	+	1.04722i	−0.0866689	+	0.0500383i
$439$	15.9207	−	27.5754i	0.759852	−	1.31610i	−0.183074	−	0.983099i	$-0.558605\pi$
$439$	15.9207	−	27.5754i	0.759852	−	1.31610i	0.942926	−	0.333003i	$-0.108062\pi$
$440$		0			0
$441$	5.97209			0.284385
$442$	15.0659	−	23.0526i	0.716613	−	1.09650i
$443$			1.06421i			0.0505622i	0.999680	+	0.0252811i	$0.00804808\pi$
$443$			1.06421i			0.0505622i	−0.999680	+	0.0252811i	$0.991952\pi$
$444$	8.43462	−	14.6092i	0.400290	−	0.693322i
$445$		0			0
$446$	9.89949	+	17.1464i	0.468754	+	0.811906i
$447$			9.66589i			0.457181i
$448$	−19.9835	+	11.5375i	−0.944131	+	0.545094i
$449$	7.70219	+	13.3406i	0.363489	+	0.629581i	0.988532	−	0.151009i	$-0.0482521\pi$
$449$	7.70219	+	13.3406i	0.363489	+	0.629581i	−0.625044	+	0.780590i	$0.714919\pi$
$450$		0			0
$451$	−13.9721	−	24.2004i	−0.657920	−	1.13955i
$452$	46.2681	+	26.7129i	2.17627	+	1.25647i
$453$	16.2059	+	9.35646i	0.761418	+	0.439605i
$454$	−60.7297			−2.85019
$455$		0			0
$456$	−48.7576			−2.28328
$457$	8.29113	+	4.78689i	0.387843	+	0.223921i	0.681225	−	0.732074i	$-0.261448\pi$
$457$	8.29113	+	4.78689i	0.387843	+	0.223921i	−0.293382	+	0.955995i	$0.594781\pi$
$458$	1.85781	+	1.07261i	0.0868097	+	0.0501196i
$459$	1.46789	+	2.54247i	0.0685155	+	0.118672i
$460$		0			0
$461$	−8.18637	−	14.1792i	−0.381277	−	0.660392i	0.609968	−	0.792426i	$-0.291182\pi$
$461$	−8.18637	−	14.1792i	−0.381277	−	0.660392i	−0.991245	+	0.132034i	$0.957849\pi$
$462$	42.2253	−	24.3788i	1.96450	−	1.13420i
$463$			24.6487i			1.14552i	0.819722	+	0.572761i	$0.194128\pi$
$463$			24.6487i			1.14552i	−0.819722	+	0.572761i	$0.805872\pi$
$464$	8.43462	+	14.6092i	0.391568	+	0.678215i
$465$		0			0
$466$	17.4370	−	30.2017i	0.807751	−	1.39907i
$467$		−	20.3402i		−	0.941231i	−0.882338	−	0.470616i	$-0.844032\pi$
$467$		−	20.3402i		−	0.941231i	0.882338	−	0.470616i	$-0.155968\pi$
$468$	7.76133	+	15.3425i	0.358768	+	0.709208i
$469$	−12.6101			−0.582279
$470$		0			0
$471$	−5.18521	+	8.98104i	−0.238922	+	0.413825i
$472$	−45.9788	+	26.5459i	−2.11635	+	1.22187i
$473$			16.4793i			0.757720i
$474$	5.33714	+	9.24420i	0.245143	+	0.424600i
$475$		0			0
$476$	−50.4235			−2.31116
$477$	−4.50624	+	2.60168i	−0.206327	+	0.119123i
$478$	28.8324	+	16.6464i	1.31876	+	0.761388i
$479$	−0.0811965	+	0.140637i	−0.00370996	+	0.00642585i	−0.867874	−	0.496784i	$-0.834514\pi$
$479$	−0.0811965	+	0.140637i	−0.00370996	+	0.00642585i	0.864164	+	0.503209i	$0.167848\pi$
$480$		0			0
$481$	11.3811	−	5.75739i	0.518935	−	0.262514i
$482$			33.2201i			1.51314i
$483$	−17.2722	−	9.97209i	−0.785911	−	0.453746i
$484$	38.3286	−	66.3870i	1.74221	−	3.01759i
$485$		0			0
$486$	−2.60168			−0.118015
$487$	2.21966	−	1.28152i	0.100582	−	0.0580713i	−0.448865	−	0.893600i	$-0.648172\pi$
$487$	2.21966	−	1.28152i	0.100582	−	0.0580713i	0.549447	+	0.835528i	$0.314838\pi$
$488$	21.4262	−	12.3704i	0.969918	−	0.559982i
$489$	−11.4733			−0.518839
$490$		0			0
$491$	−14.2203	+	24.6304i	−0.641755	+	1.11155i	0.343286	+	0.939231i	$0.388460\pi$
$491$	−14.2203	+	24.6304i	−0.641755	+	1.11155i	−0.985041	+	0.172321i	$0.944873\pi$
$492$	−22.1790	−	12.8050i	−0.999905	−	0.577296i
$493$			5.38114i			0.242354i
$494$	−53.1499	−	34.7359i	−2.39133	−	1.56284i
$495$		0			0
$496$	−18.8800	+	32.7011i	−0.847736	+	1.46832i
$497$	30.2698	+	17.4763i	1.35779	+	0.783919i
$498$	−25.9953	+	15.0084i	−1.16488	+	0.672542i
$499$	27.8605			1.24721			0.623603	−	0.781741i	$-0.285668\pi$
$499$	27.8605			1.24721			0.623603	+	0.781741i	$0.285668\pi$
$500$		0			0
$501$	−1.56538	−	2.71131i	−0.0699358	−	0.121132i
$502$		−	21.8716i		−	0.976176i
$503$	−27.2156	+	15.7129i	−1.21348	+	0.700604i	−0.963516	−	0.267650i	$-0.913753\pi$
$503$	−27.2156	+	15.7129i	−1.21348	+	0.700604i	−0.249966	+	0.968255i	$0.580420\pi$
$504$	12.9721	−	22.4683i	0.577823	−	1.00082i
$505$		0			0
$506$	−74.9633			−3.33253
$507$	−1.43397	+	12.9207i	−0.0636850	+	0.573827i
$508$			15.2359i			0.675985i
$509$	8.11124	−	14.0491i	0.359524	−	0.622715i	−0.628357	−	0.777925i	$-0.716272\pi$
$509$	8.11124	−	14.0491i	0.359524	−	0.622715i	0.987881	+	0.155211i	$0.0496056\pi$
$510$		0			0
$511$	1.44974	+	2.51103i	0.0641329	+	0.111081i
$512$		−	44.8134i		−	1.98049i
$513$	5.86190	−	3.38437i	0.258809	−	0.149423i
$514$	7.98605	+	13.8322i	0.352249	+	0.610114i
$515$		0			0
$516$	7.55142	+	13.0794i	0.332433	+	0.575791i
$517$	17.1464	+	9.89949i	0.754098	+	0.435379i
$518$	−28.7066	−	16.5738i	−1.26130	−	0.728210i
$519$	8.26757			0.362906
$520$		0			0
$521$	−20.0386			−0.877909			−0.438954	−	0.898509i	$-0.644651\pi$
$521$	−20.0386			−0.877909			−0.438954	+	0.898509i	$0.644651\pi$
$522$	−4.12985	−	2.38437i	−0.180758	−	0.104361i
$523$	−11.4828	−	6.62959i	−0.502107	−	0.289892i	0.227476	−	0.973784i	$-0.426953\pi$
$523$	−11.4828	−	6.62959i	−0.502107	−	0.289892i	−0.729583	+	0.683892i	$0.760286\pi$
$524$	−10.9056	−	18.8890i	−0.476411	−	0.825168i
$525$		0			0
$526$	6.15310	+	10.6575i	0.268288	+	0.464688i
$527$	−10.4314	+	6.02254i	−0.454397	+	0.262346i
$528$		−	47.8884i		−	2.08407i
$529$	3.83178	+	6.63684i	0.166599	+	0.288558i
$530$		0			0
$531$	3.68521	−	6.38297i	0.159924	−	0.276997i
$532$			116.256i			5.04034i
$533$	−8.74059	−	17.2783i	−0.378597	−	0.748406i
$534$	25.5822			1.10705
$535$		0			0
$536$	−12.6101	+	21.8413i	−0.544672	+	0.943400i
$537$	15.9741	−	9.22268i	0.689335	−	0.397988i
$538$			14.1610i			0.610524i
$539$	−15.5375	−	26.9117i	−0.669246	−	1.15917i
$540$		0			0
$541$	35.6850			1.53422			0.767109	−	0.641516i	$-0.221694\pi$
$541$	35.6850			1.53422			0.767109	+	0.641516i	$0.221694\pi$
$542$	57.4080	−	33.1445i	2.46588	−	1.42368i
$543$	−18.2756	−	10.5514i	−0.784281	−	0.452805i
$544$	−14.0000	+	24.2487i	−0.600245	+	1.03965i
$545$		0			0
$546$	30.1475	−	15.2508i	1.29020	−	0.652673i
$547$		−	0.627256i		−	0.0268195i	−0.999910	−	0.0134098i	$-0.995731\pi$
$547$		−	0.627256i		−	0.0268195i	0.999910	−	0.0134098i	$-0.00426859\pi$
$548$	44.0831	+	25.4514i	1.88314	+	1.08723i
$549$	−1.71731	+	2.97447i	−0.0732931	+	0.126947i
$550$		0			0
$551$	12.4067			0.528544
$552$	−34.5443	+	19.9442i	−1.47030	+	0.848881i
$553$	12.7974	−	7.38856i	0.544200	−	0.314194i
$554$	59.3532			2.52168
$555$		0			0
$556$	38.5017	−	66.6869i	1.63283	−	2.82815i
$557$	−7.97438	−	4.60401i	−0.337885	−	0.195078i	0.321451	−	0.946926i	$-0.395829\pi$
$557$	−7.97438	−	4.60401i	−0.337885	−	0.195078i	−0.659337	+	0.751848i	$0.729163\pi$
$558$		−	10.6743i		−	0.451879i
$559$	−0.630752	+	11.4015i	−0.0266780	+	0.482234i
$560$		0			0
$561$	7.63798	−	13.2294i	0.322476	−	0.558545i
$562$	4.88264	+	2.81899i	0.205962	+	0.118912i
$563$	−2.31075	+	1.33411i	−0.0973864	+	0.0562260i	−0.547902	−	0.836542i	$-0.684573\pi$
$563$	−2.31075	+	1.33411i	−0.0973864	+	0.0562260i	0.450516	+	0.892768i	$0.351240\pi$
$564$	18.1452			0.764051
$565$		0			0
$566$	38.6959	+	67.0233i	1.62651	+	2.81720i
$567$			3.60168i			0.151256i
$568$	60.5396	−	34.9526i	2.54019	−	1.46658i
$569$	−13.0919	+	22.6759i	−0.548842	+	0.950622i	0.449512	+	0.893274i	$0.351598\pi$
$569$	−13.0919	+	22.6759i	−0.548842	+	0.950622i	−0.998354	+	0.0573480i	$0.981736\pi$
$570$		0			0
$571$	−19.2481			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$571$	−19.2481			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$572$	48.9445	−	74.8907i	2.04647	−	3.13134i
$573$		−	8.70219i		−	0.363539i
$574$	−25.1615	+	43.5810i	−1.05022	+	1.81904i
$575$		0			0
$576$	−3.20336	−	5.54838i	−0.133473	−	0.231182i
$577$			23.8716i			0.993787i	0.867812	+	0.496893i	$0.165526\pi$
$577$			23.8716i			0.993787i	−0.867812	+	0.496893i	$0.834474\pi$
$578$	18.8837	−	10.9025i	0.785459	−	0.453485i
$579$	−9.63378	−	16.6862i	−0.400366	−	0.693455i
$580$		0			0
$581$	20.7771	+	35.9870i	0.861981	+	1.49299i
$582$	−12.5584	−	7.25058i	−0.520562	−	0.300546i
$583$	23.4476	+	13.5375i	0.971100	+	0.560665i
$584$	5.79897			0.239963
$585$		0			0
$586$	86.0783			3.55586
$587$	−25.0068	−	14.4377i	−1.03214	−	0.595906i	−0.114542	−	0.993418i	$-0.536540\pi$
$587$	−25.0068	−	14.4377i	−1.03214	−	0.595906i	−0.917597	+	0.397513i	$0.869874\pi$
$588$	−24.6638	−	14.2397i	−1.01712	−	0.587234i
$589$	13.8855	+	24.0504i	0.572143	+	0.990981i
$590$		0			0
$591$	−7.57377	−	13.1182i	−0.311543	−	0.539609i
$592$	−28.1948	+	16.2783i	−1.15880	+	0.669034i
$593$			8.74083i			0.358943i	0.983763	+	0.179471i	$0.0574387\pi$
$593$			8.74083i			0.358943i	−0.983763	+	0.179471i	$0.942561\pi$
$594$	6.76873	+	11.7238i	0.277725	+	0.481033i
$595$		0			0
$596$	23.0470	−	39.9186i	0.944043	−	1.63513i
$597$			4.53747i			0.185706i
$598$	−51.8649	−	2.86925i	−2.12091	−	0.117332i
$599$	−21.5929			−0.882262			−0.441131	−	0.897443i	$-0.645423\pi$
$599$	−21.5929			−0.882262			−0.441131	+	0.897443i	$0.645423\pi$
$600$		0			0
$601$	−15.1252	+	26.1976i	−0.616970	+	1.06862i	0.373066	+	0.927805i	$0.378306\pi$
$601$	−15.1252	+	26.1976i	−0.616970	+	1.06862i	−0.990036	+	0.140818i	$0.955027\pi$
$602$	25.7007	−	14.8383i	1.04748	−	0.604764i
$603$		−	3.50117i		−	0.142578i
$604$	−44.6185	−	77.2815i	−1.81550	−	3.14454i
$605$		0			0
$606$	−6.26150			−0.254356
$607$	−19.4918	+	11.2536i	−0.791149	+	0.456770i	−0.840367	−	0.542018i	$-0.817660\pi$
$607$	−19.4918	+	11.2536i	−0.791149	+	0.456770i	0.0492178	+	0.998788i	$0.484327\pi$
$608$	55.9076	+	32.2783i	2.26735	+	1.30906i
$609$	−3.30084	+	5.71722i	−0.133757	+	0.231674i
$610$		0			0
$611$	11.4842	+	7.50544i	0.464600	+	0.303638i
$612$		−	14.0000i		−	0.565916i
$613$	16.2615	+	9.38856i	0.656795	+	0.379201i	0.791055	−	0.611746i	$-0.209532\pi$
$613$	16.2615	+	9.38856i	0.656795	+	0.379201i	−0.134260	+	0.990946i	$0.542866\pi$
$614$	−18.6936	+	32.3783i	−0.754412	+	1.30668i
$615$		0			0
$616$	−134.997			−5.43918
$617$	−3.12642	+	1.80504i	−0.125865	+	0.0726681i	−0.561610	−	0.827402i	$-0.689818\pi$
$617$	−3.12642	+	1.80504i	−0.125865	+	0.0726681i	0.435746	+	0.900070i	$0.356485\pi$
$618$	41.5543	−	23.9914i	1.67156	−	0.965076i
$619$	−2.87158			−0.115419			−0.0577093	−	0.998333i	$-0.518380\pi$
$619$	−2.87158			−0.115419			−0.0577093	+	0.998333i	$0.518380\pi$
$620$		0			0
$621$	2.76873	−	4.79559i	0.111105	−	0.192440i
$622$	19.6176	+	11.3262i	0.786594	+	0.454140i
$623$		−	35.4151i		−	1.41888i
$624$	1.83294	−	33.1325i	0.0733765	−	1.32636i
$625$		0			0
$626$	10.6210	−	18.3961i	0.424500	−	0.735256i
$627$	−30.5015	−	17.6101i	−1.21811	−	0.703279i
$628$	42.8282	−	24.7269i	1.70903	−	0.986710i
$629$	−10.3853			−0.414088
$630$		0			0
$631$	−8.49444	−	14.7128i	−0.338158	−	0.585708i	0.645928	−	0.763398i	$-0.276471\pi$
$631$	−8.49444	−	14.7128i	−0.338158	−	0.585708i	−0.984086	+	0.177691i	$0.943137\pi$
$632$		−	29.5543i		−	1.17561i
$633$	−19.1803	+	11.0738i	−0.762350	+	0.440143i
$634$	17.4430	−	30.2122i	0.692751	−	1.19988i
$635$		0			0
$636$	24.8134			0.983917
$637$	−9.71985	−	19.2141i	−0.385115	−	0.761290i
$638$			24.8134i			0.982373i
$639$	−4.85226	+	8.40436i	−0.191953	+	0.332472i
$640$		0			0
$641$	8.30620	+	14.3868i	0.328075	+	0.568243i	0.982130	−	0.188204i	$-0.0602667\pi$
$641$	8.30620	+	14.3868i	0.328075	+	0.568243i	−0.654055	+	0.756447i	$0.726933\pi$
$642$		−	28.4514i		−	1.12289i
$643$	−39.2657	+	22.6701i	−1.54849	+	0.894021i	−0.550232	+	0.835012i	$0.685461\pi$
$643$	−39.2657	+	22.6701i	−1.54849	+	0.894021i	−0.998257	+	0.0590094i	$0.981206\pi$
$644$	47.5543	+	82.3664i	1.87390	+	3.24569i
$645$		0			0
$646$	25.8497	+	44.7731i	1.01704	+	1.76157i
$647$	−4.21689	−	2.43462i	−0.165783	−	0.0957149i	0.414813	−	0.909907i	$-0.363847\pi$
$647$	−4.21689	−	2.43462i	−0.165783	−	0.0957149i	−0.580596	+	0.814192i	$0.697180\pi$
$648$	6.23829	+	3.60168i	0.245063	+	0.141487i
$649$	−38.3509			−1.50540
$650$		0			0
$651$	−14.7771			−0.579161
$652$	47.3828	+	27.3565i	1.85565	+	1.07136i
$653$	16.6882	+	9.63495i	0.653061	+	0.377045i	0.789628	−	0.613586i	$-0.210274\pi$
$653$	16.6882	+	9.63495i	0.653061	+	0.377045i	−0.136567	+	0.990631i	$0.543607\pi$
$654$	−18.0417	−	31.2491i	−0.705485	−	1.22194i
$655$		0			0
$656$	24.7129	+	42.8040i	0.964877	+	1.67122i
$657$	−0.697183	+	0.402519i	−0.0271997	+	0.0157038i
$658$		−	35.6548i		−	1.38997i
$659$	0.167055	+	0.289348i	0.00650755	+	0.0112714i	0.869261	−	0.494354i	$-0.164595\pi$
$659$	0.167055	+	0.289348i	0.00650755	+	0.0112714i	−0.862753	+	0.505625i	$0.831262\pi$
$660$		0			0
$661$	6.83411	−	11.8370i	0.265816	−	0.460407i	−0.701961	−	0.712215i	$-0.747692\pi$
$661$	6.83411	−	11.8370i	0.265816	−	0.460407i	0.967777	+	0.251808i	$0.0810253\pi$
$662$			55.8823i			2.17193i
$663$	5.79085	−	8.86066i	0.224898	−	0.344119i
$664$	83.1085			3.22524
$665$		0			0
$666$	4.60168	−	7.97034i	0.178311	−	0.308844i
$667$	8.79005	−	5.07494i	0.340352	−	0.196502i
$668$			14.9297i			0.577648i
$669$	3.80504	+	6.59052i	0.147111	+	0.254804i
$670$		0			0
$671$	17.8716			0.689925
$672$	−29.7488	+	17.1755i	−1.14758	+	0.662557i
$673$	−18.9486	−	10.9400i	−0.730415	−	0.421706i	0.0881587	−	0.996106i	$-0.471902\pi$
$673$	−18.9486	−	10.9400i	−0.730415	−	0.421706i	−0.818574	+	0.574401i	$0.805235\pi$
$674$	−9.68521	+	16.7753i	−0.373060	+	0.646159i
$675$		0			0
$676$	36.7297	−	49.9412i	1.41268	−	1.92082i
$677$		−	17.0749i		−	0.656243i	−0.944636	−	0.328122i	$-0.893584\pi$
$677$		−	17.0749i		−	0.656243i	0.944636	−	0.328122i	$-0.106416\pi$
$678$	25.2425	+	14.5738i	0.969433	+	0.559702i
$679$	−10.0375	+	17.3854i	−0.385203	+	0.667191i
$680$		0			0
$681$	−23.3425			−0.894487
$682$	−48.1009	+	27.7711i	−1.84188	+	1.06341i
$683$	23.1489	−	13.3651i	0.885770	−	0.511399i	0.0132133	−	0.999913i	$-0.495794\pi$
$683$	23.1489	−	13.3651i	0.885770	−	0.511399i	0.872556	+	0.488513i	$0.162461\pi$
$684$	−32.2783			−1.23419
$685$		0			0
$686$	4.81596	−	8.34149i	0.183874	−	0.318479i
$687$	0.714081	+	0.412275i	0.0272439	+	0.0157293i
$688$		−	29.1475i		−	1.11124i
$689$	15.7045	+	10.2636i	0.598295	+	0.391013i
$690$		0			0
$691$	−24.3576	+	42.1886i	−0.926608	+	1.60493i	−0.137653	+	0.990481i	$0.543956\pi$
$691$	−24.3576	+	42.1886i	−0.926608	+	1.60493i	−0.788955	+	0.614451i	$0.789378\pi$
$692$	−34.1438	−	19.7129i	−1.29795	−	0.749373i
$693$	16.2300	−	9.37041i	0.616528	−	0.355953i
$694$	64.9028			2.46368
$695$		0			0
$696$	6.60168	+	11.4344i	0.250236	+	0.433421i
$697$			15.7664i			0.597195i
$698$	−4.73796	+	2.73546i	−0.179334	+	0.103539i
$699$	6.70219	−	11.6085i	0.253500	−	0.439075i
$700$		0			0
$701$	22.9419			0.866502			0.433251	−	0.901273i	$-0.357366\pi$
$701$	22.9419			0.866502			0.433251	+	0.901273i	$0.357366\pi$
$702$	4.23435	+	8.37041i	0.159815	+	0.315921i
$703$			23.9442i			0.903072i
$704$	−16.6682	+	28.8702i	−0.628207	+	1.08809i
$705$		0			0
$706$	−24.1173	−	41.7724i	−0.907667	−	1.57212i
$707$			8.66822i			0.326002i
$708$	−30.4387	+	17.5738i	−1.14396	+	0.660463i
$709$	−3.57261	−	6.18794i	−0.134172	−	0.232393i	0.791109	−	0.611675i	$-0.209504\pi$
$709$	−3.57261	−	6.18794i	−0.134172	−	0.232393i	−0.925281	+	0.379283i	$0.876171\pi$
$710$		0			0
$711$	2.05142	+	3.55317i	0.0769343	+	0.133254i
$712$	−61.3408	−	35.4151i	−2.29884	−	1.32724i
$713$	19.6756	+	11.3597i	0.736855	+	0.425424i
$714$	−27.5096			−1.02952
$715$		0			0
$716$	−87.9610			−3.28726
$717$	11.0822	+	6.39832i	0.413873	+	0.238950i
$718$	−10.7204	−	6.18940i	−0.400080	−	0.230987i
$719$	20.9891	+	36.3542i	0.782761	+	1.35578i	0.930328	+	0.366729i	$0.119522\pi$
$719$	20.9891	+	36.3542i	0.782761	+	1.35578i	−0.147567	+	0.989052i	$0.547144\pi$
$720$		0			0
$721$	−33.2129	−	57.5265i	−1.23691	−	2.14240i
$722$	60.4191	−	34.8830i	2.24857	−	1.29821i
$723$			12.7687i			0.474874i
$724$	50.3169	+	87.1515i	1.87001	+	3.23896i
$725$		0			0
$726$	20.9109	−	36.2188i	0.776077	−	1.34420i
$727$		−	11.4965i		−	0.426382i	−0.977011	−	0.213191i	$-0.931614\pi$
$727$		−	11.4965i		−	0.426382i	0.977011	−	0.213191i	$-0.0683856\pi$
$728$	−93.4003	−	5.16706i	−3.46164	−	0.191504i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.64890	−	8.05214i	0.171946	−	0.297819i
$732$	14.1845	−	8.18940i	0.524273	−	0.302689i
$733$		−	46.1136i		−	1.70324i	−0.524157	−	0.851622i	$-0.675619\pi$
$733$		−	46.1136i		−	1.70324i	0.524157	−	0.851622i	$-0.324381\pi$
$734$	−13.3232	−	23.0764i	−0.491768	−	0.851767i
$735$		0			0
$736$	52.8134			1.94673
$737$	−15.7771	+	9.10891i	−0.581157	+	0.335531i
$738$	−12.1002	−	6.98605i	−0.445414	−	0.257160i
$739$	−5.80504	+	10.0546i	−0.213542	+	0.369865i	−0.952820	−	0.303534i	$-0.901833\pi$
$739$	−5.80504	+	10.0546i	−0.213542	+	0.369865i	0.739279	+	0.673400i	$0.235167\pi$
$740$		0			0
$741$	−20.4291	−	13.3513i	−0.750480	−	0.490474i
$742$		−	48.7576i		−	1.78995i
$743$	11.6178	+	6.70756i	0.426217	+	0.246076i	0.697734	−	0.716357i	$-0.254192\pi$
$743$	11.6178	+	6.70756i	0.426217	+	0.246076i	−0.271517	+	0.962434i	$0.587525\pi$
$744$	−14.7771	+	25.5947i	−0.541756	+	0.938349i
$745$		0			0
$746$	−60.7236			−2.22325
$747$	−9.99174	+	5.76873i	−0.365579	+	0.211067i
$748$	−63.0874	+	36.4235i	−2.30670	+	1.33178i
$749$	−39.3872			−1.43918
$750$		0			0
$751$	−22.0866	+	38.2550i	−0.805950	+	1.39595i	0.109698	+	0.993965i	$0.465012\pi$
$751$	−22.0866	+	38.2550i	−0.805950	+	1.39595i	−0.915648	+	0.401981i	$0.868322\pi$
$752$	−30.3274	−	17.5096i	−1.10593	−	0.638508i
$753$		−	8.40672i		−	0.306358i
$754$	−0.949743	+	17.1677i	−0.0345876	+	0.625210i
$755$		0			0
$756$	8.58773	−	14.8744i	0.312333	−	0.540976i
$757$	−6.90403	−	3.98605i	−0.250931	−	0.144875i	0.369259	−	0.929326i	$-0.379611\pi$
$757$	−6.90403	−	3.98605i	−0.250931	−	0.144875i	−0.620191	+	0.784451i	$0.712945\pi$
$758$	80.3397	−	46.3842i	2.91807	−	1.68475i
$759$	−28.8134			−1.04586
$760$		0			0
$761$	−6.83294	−	11.8350i	−0.247694	−	0.429019i	0.715192	−	0.698928i	$-0.246339\pi$
$761$	−6.83294	−	11.8350i	−0.247694	−	0.429019i	−0.962886	+	0.269910i	$0.913006\pi$
$762$			8.31227i			0.301122i
$763$	−43.2602	+	24.9763i	−1.56612	+	0.904202i
$764$	−20.7492	+	35.9387i	−0.750681	+	1.30022i
$765$		0			0
$766$	−79.6594			−2.87821
$767$	−26.5338	−	1.46789i	−0.958081	−	0.0530026i
$768$		−	19.0749i		−	0.688308i
$769$	8.24522	−	14.2811i	0.297330	−	0.514991i	−0.678194	−	0.734883i	$-0.737237\pi$
$769$	8.24522	−	14.2811i	0.297330	−	0.514991i	0.975524	+	0.219892i	$0.0705704\pi$
$770$		0			0
$771$	3.06957	+	5.31666i	0.110548	+	0.191475i
$772$			91.8819i			3.30690i
$773$	39.5809	−	22.8521i	1.42363	−	0.821932i	0.427021	−	0.904242i	$-0.359563\pi$
$773$	39.5809	−	22.8521i	1.42363	−	0.821932i	0.996607	+	0.0823101i	$0.0262298\pi$
$774$	4.11983	+	7.13576i	0.148084	+	0.256489i
$775$		0			0
$776$	20.0749	+	34.7708i	0.720648	+	1.24820i
$777$	−11.0339	−	6.37041i	−0.395838	−	0.228537i
$778$	56.3711	+	32.5459i	2.02100	+	1.16683i
$779$	36.3509			1.30241
$780$		0			0
$781$	50.4961			1.80689
$782$	36.6286	+	21.1475i	1.30984	+	0.756235i
$783$	−1.58738	−	0.916472i	−0.0567282	−	0.0327521i
$784$	27.4817	+	47.5996i	0.981488	+	1.69999i
$785$		0			0
$786$	−5.94974	−	10.3053i	−0.212220	−	0.367576i
$787$	−42.2809	+	24.4109i	−1.50715	+	0.870155i	−0.507187	+	0.861836i	$0.669315\pi$
$787$	−42.2809	+	24.4109i	−1.50715	+	0.870155i	−0.999965	+	0.00831938i	$0.997352\pi$
$788$			72.2346i			2.57325i
$789$	2.36505	+	4.09639i	0.0841980	+	0.145835i
$790$		0			0
$791$	20.1755	−	34.9449i	0.717356	−	1.24250i
$792$		−	37.4817i		−	1.33185i
$793$	12.3648	+	0.684041i	0.439087	+	0.0242910i
$794$	−28.1838			−1.00021
$795$		0			0
$796$	10.8190	−	18.7390i	0.383469	−	0.664188i
$797$	11.9072	−	6.87461i	0.421774	−	0.243511i	−0.274062	−	0.961712i	$-0.588367\pi$
$797$	11.9072	−	6.87461i	0.421774	−	0.243511i	0.695836	+	0.718201i	$0.255034\pi$
$798$			63.4258i			2.24525i
$799$	−5.58539	−	9.67419i	−0.197597	−	0.342248i
$800$		0			0
$801$	9.83294			0.347430
$802$	−55.1549	+	31.8437i	−1.94759	+	1.12444i
$803$	3.62769	+	2.09445i	0.128018	+	0.0739115i
$804$	−8.34806	+	14.4593i	−0.294414	+	0.509939i
$805$		0			0
$806$	−34.3425	+	17.3729i	−1.20966	+	0.611934i
$807$			5.44302i			0.191603i
$808$	15.0138	+	8.66822i	0.528184	+	0.304947i
$809$	10.1671	−	17.6099i	0.357455	−	0.619130i	−0.630080	−	0.776530i	$-0.716978\pi$
$809$	10.1671	−	17.6099i	0.357455	−	0.619130i	0.987535	+	0.157400i	$0.0503113\pi$
$810$		0			0
$811$	22.4817			0.789438			0.394719	−	0.918802i	$-0.370842\pi$
$811$	22.4817			0.789438			0.394719	+	0.918802i	$0.370842\pi$
$812$	27.2639	−	15.7408i	0.956776	−	0.552395i
$813$	22.0657	−	12.7397i	0.773879	−	0.446799i
$814$	−47.8884			−1.67849
$815$		0			0
$816$	−13.5096	+	23.3992i	−0.472929	+	0.819137i
$817$	−18.5649	−	10.7185i	−0.649505	−	0.374992i
$818$		−	69.4924i		−	2.42974i
$819$	11.5877	−	5.86190i	0.404908	−	0.204831i
$820$		0			0
$821$	16.3039	−	28.2391i	0.569009	−	0.985553i	−0.427655	−	0.903942i	$-0.640660\pi$
$821$	16.3039	−	28.2391i	0.569009	−	0.985553i	0.996664	−	0.0816107i	$-0.0260064\pi$
$822$	24.0504	+	13.8855i	0.838856	+	0.484314i
$823$	−28.9960	+	16.7408i	−1.01074	+	0.583549i	−0.911407	−	0.411506i	$-0.865003\pi$
$823$	−28.9960	+	16.7408i	−1.01074	+	0.583549i	−0.0993287	+	0.995055i	$0.531670\pi$
$824$	−132.852			−4.62811
$825$		0			0
$826$	34.5319	+	59.8110i	1.20152	+	2.08109i
$827$		−	51.0298i		−	1.77448i	−0.461306	−	0.887241i	$-0.652619\pi$
$827$		−	51.0298i		−	1.77448i	0.461306	−	0.887241i	$-0.347381\pi$
$828$	−22.8689	+	13.2034i	−0.794749	+	0.458848i
$829$	10.5973	−	18.3550i	0.368059	−	0.637497i	−0.621203	−	0.783650i	$-0.713356\pi$
$829$	10.5973	−	18.3550i	0.368059	−	0.637497i	0.989262	+	0.146153i	$0.0466891\pi$
$830$		0			0
$831$	22.8134			0.791389
$832$	−12.6373	+	19.3364i	−0.438118	+	0.670370i
$833$			17.5328i			0.607476i
$834$	21.0054	−	36.3824i	0.727356	−	1.25982i
$835$		0			0
$836$	83.9778	+	145.454i	2.90443	+	5.03062i
$837$		−	4.10284i		−	0.141815i
$838$	−33.8786	+	19.5598i	−1.17032	+	0.675683i
$839$	26.9419	+	46.6647i	0.930136	+	1.61104i	0.783086	+	0.621914i	$0.213645\pi$
$839$	26.9419	+	46.6647i	0.930136	+	1.61104i	0.147051	+	0.989129i	$0.453022\pi$
$840$		0			0
$841$	12.8202	+	22.2052i	0.442074	+	0.765695i
$842$	13.2975	+	7.67732i	0.458262	+	0.264578i
$843$	1.87672	+	1.08353i	0.0646378	+	0.0373187i
$844$	105.616			3.63544
$845$		0			0
$846$	9.89949			0.340351
$847$	−50.1401	−	28.9484i	−1.72283	−	0.994678i
$848$	−41.4725	−	23.9442i	−1.42417	−	0.822247i
$849$	14.8734	+	25.7616i	0.510455	+	0.884135i
$850$		0			0
$851$	9.79431	+	16.9642i	0.335745	+	0.581527i
$852$	40.0782	−	23.1391i	1.37306	−	0.792734i
$853$			4.06421i			0.139156i	0.997577	+	0.0695780i	$0.0221653\pi$
$853$			4.06421i			0.139156i	−0.997577	+	0.0695780i	$0.977835\pi$
$854$	−16.0919	−	27.8720i	−0.550654	−	0.953761i
$855$		0			0
$856$	−39.3872	+	68.2206i	−1.34623	+	2.33173i
$857$		−	39.2141i		−	1.33953i	−0.742574	−	0.669764i	$-0.766395\pi$
$857$		−	39.2141i		−	1.33953i	0.742574	−	0.669764i	$-0.233605\pi$
$858$	26.7027	−	40.8581i	0.911614	−	1.39487i
$859$	5.64031			0.192445			0.0962225	−	0.995360i	$-0.469324\pi$
$859$	5.64031			0.192445			0.0962225	+	0.995360i	$0.469324\pi$
$860$		0			0
$861$	−9.67125	+	16.7511i	−0.329595	+	0.570876i
$862$	88.6571	−	51.1862i	3.01967	−	1.74341i
$863$			9.66589i			0.329031i	0.986375	+	0.164515i	$0.0526060\pi$
$863$			9.66589i			0.329031i	−0.986375	+	0.164515i	$0.947394\pi$
$864$	−4.76873	−	8.25969i	−0.162236	−	0.281000i
$865$		0			0
$866$	32.3001			1.09760
$867$	7.25828	−	4.19057i	0.246504	−	0.142319i
$868$	61.0273	+	35.2341i	2.07140	+	1.19592i
$869$	10.6743	−	18.4884i	0.362100	−	0.627176i
$870$		0			0
$871$	−11.2643	+	5.69831i	−0.381678	+	0.193080i
$872$			99.9052i			3.38322i
$873$	−4.82703	−	2.78689i	−0.163370	−	0.0943218i
$874$	48.7576	−	84.4507i	1.64925	−	2.85659i
$875$		0			0
$876$	3.83901			0.129708
$877$	13.7452	−	7.93579i	0.464142	−	0.267973i	−0.249642	−	0.968338i	$-0.580313\pi$
$877$	13.7452	−	7.93579i	0.464142	−	0.267973i	0.713784	+	0.700366i	$0.246980\pi$
$878$	−71.7424	+	41.4205i	−2.42119	+	1.39787i
$879$	33.0857			1.11595
$880$		0			0
$881$	14.6017	−	25.2909i	0.491943	−	0.852070i	−0.508014	−	0.861349i	$-0.669620\pi$
$881$	14.6017	−	25.2909i	0.491943	−	0.852070i	0.999957	+	0.00927849i	$0.00295348\pi$
$882$	−13.4558	−	7.76873i	−0.453082	−	0.261587i
$883$		−	30.4598i		−	1.02505i	−0.858671	−	0.512527i	$-0.828709\pi$
$883$		−	30.4598i		−	1.02505i	0.858671	−	0.512527i	$-0.171291\pi$
$884$	−45.0424	+	22.7856i	−1.51494	+	0.766364i
$885$		0			0
$886$	1.38437	−	2.39779i	0.0465087	−	0.0805555i
$887$	−10.0453	−	5.79967i	−0.337289	−	0.194734i	0.321783	−	0.946813i	$-0.395718\pi$
$887$	−10.0453	−	5.79967i	−0.337289	−	0.194734i	−0.659073	+	0.752079i	$0.729051\pi$
$888$	−22.0678	+	12.7408i	−0.740546	+	0.427554i
$889$	11.5072			0.385940
$890$		0			0
$891$	2.60168	+	4.50624i	0.0871595	+	0.150965i
$892$		−	36.2904i		−	1.21509i
$893$	−22.3047	+	12.8776i	−0.746399	+	0.430934i
$894$	12.5738	−	21.7784i	0.420530	−	0.728379i
$895$		0			0
$896$	−8.66822			−0.289585
$897$	−19.9351	−	1.10284i	−0.665615	−	0.0368229i
$898$		−	40.0773i		−	1.33740i
$899$	3.76014	−	6.51276i	0.125408	−	0.217213i
$900$		0			0
$901$	−7.63798	−	13.2294i	−0.254458	−	0.440734i
$902$			72.7018i			2.42071i
$903$	9.87851	−	5.70336i	0.328736	−	0.189796i
$904$	−40.3509	−	69.8898i	−1.34205	−	2.32450i
$905$		0			0
$906$	−24.3425	−	42.1625i	−0.808726	−	1.40075i
$907$	−37.1686	−	21.4593i	−1.23416	−	0.712545i	−0.266268	−	0.963899i	$-0.585791\pi$
$907$	−37.1686	−	21.4593i	−1.23416	−	0.712545i	−0.967895	+	0.251354i	$0.919124\pi$
$908$	96.4009	+	55.6571i	3.19918	+	1.84705i
$909$	−2.40672			−0.0798257
$910$		0			0
$911$	42.0726			1.39393			0.696964	−	0.717106i	$-0.254534\pi$
$911$	42.0726			1.39393			0.696964	+	0.717106i	$0.254534\pi$
$912$	53.9491	+	31.1475i	1.78643	+	1.03140i
$913$	51.9906	+	30.0168i	1.72064	+	0.993411i
$914$	−12.4539	−	21.5709i	−0.411940	−	0.713501i
$915$		0			0
$916$	−1.96603	−	3.40526i	−0.0649594	−	0.112513i
$917$	−14.2663	+	8.23663i	−0.471113	+	0.271997i
$918$		−	7.63798i		−	0.252091i
$919$	19.5575	+	33.8746i	0.645142	+	1.11742i	0.984269	+	0.176678i	$0.0565351\pi$
$919$	19.5575	+	33.8746i	0.645142	+	1.11742i	−0.339127	+	0.940741i	$0.610132\pi$
$920$		0			0
$921$	−7.18521	+	12.4451i	−0.236761	+	0.410081i
$922$			42.5966i			1.40285i
$923$	34.9367	+	1.93276i	1.14996	+	0.0636175i
$924$	−89.3700			−2.94006
$925$		0			0
$926$	32.0640	−	55.5365i	1.05369	−	1.82504i
$927$	15.9721	−	9.22151i	0.524593	−	0.302874i
$928$		−	17.4817i		−	0.573863i
$929$	5.23127	+	9.06082i	0.171632	+	0.297276i	0.938991	−	0.343943i	$-0.111763\pi$
$929$	5.23127	+	9.06082i	0.171632	+	0.297276i	−0.767358	+	0.641218i	$0.778429\pi$
$930$		0			0
$931$	40.4235			1.32483
$932$	−55.3580	+	31.9610i	−1.81331	+	1.04692i
$933$	7.54036	+	4.35343i	0.246860	+	0.142525i
$934$	−26.4593	+	45.8289i	−0.865775	+	1.49957i
$935$		0			0
$936$	1.43462	−	25.9324i	0.0468922	−	0.847628i
$937$			39.6269i			1.29455i	0.762255	+	0.647277i	$0.224092\pi$
$937$			39.6269i			1.29455i	−0.762255	+	0.647277i	$0.775908\pi$
$938$	28.4120	+	16.4037i	0.927685	+	0.535599i
$939$	4.08236	−	7.07086i	0.133223	−	0.230749i
$940$		0			0
$941$	15.3146			0.499242			0.249621	−	0.968344i	$-0.419694\pi$
$941$	15.3146			0.499242			0.249621	+	0.968344i	$0.419694\pi$
$942$	23.3658	−	13.4902i	0.761299	−	0.439536i
$943$	25.7543	−	14.8692i	0.838675	−	0.484209i
$944$	67.8326			2.20776
$945$		0			0
$946$	21.4370	−	37.1299i	0.696976	−	1.20720i
$947$	28.8271	+	16.6433i	0.936756	+	0.540836i	0.888942	−	0.458020i	$-0.151441\pi$
$947$	28.8271	+	16.6433i	0.936756	+	0.540836i	0.0478138	+	0.998856i	$0.484775\pi$
$948$		−	19.5654i		−	0.635454i
$949$	2.42972	+	1.58794i	0.0788722	+	0.0515466i
$950$		0			0
$951$	6.70452	−	11.6126i	0.217409	−	0.376564i
$952$	65.9623	+	38.0833i	2.13785	+	1.23429i
$953$	−20.2728	+	11.7045i	−0.656701	+	0.379147i	−0.791019	−	0.611792i	$-0.790449\pi$
$953$	−20.2728	+	11.7045i	−0.656701	+	0.379147i	0.134318	+	0.990938i	$0.457116\pi$
$954$	13.5375			0.438292
$955$		0			0
$956$	−30.5119	−	52.8481i	−0.986825	−	1.70923i
$957$			9.53747i			0.308303i
$958$	0.365891	−	0.211247i	0.0118214	−	0.00682509i
$959$	19.2227	−	33.2947i	0.620733	−	1.07514i
$960$		0			0
$961$	−14.1667			−0.456989
$962$	−33.1325	−	1.83294i	−1.06824	−	0.0590965i
$963$		−	10.9358i		−	0.352401i
$964$	30.4454	−	52.7329i	0.980579	−	1.69841i
$965$		0			0
$966$	25.9442	+	44.9366i	0.834740	+	1.44581i
$967$			27.8669i			0.896140i	0.893999	+	0.448070i	$0.147888\pi$
$967$			27.8669i			0.896140i	−0.893999	+	0.448070i	$0.852112\pi$
$968$	−100.280	+	57.8968i	−3.22313	+	1.86087i
$969$	9.93579	+	17.2093i	0.319184	+	0.552842i
$970$		0			0
$971$	2.25917	+	3.91300i	0.0725003	+	0.125574i	0.899997	−	0.435897i	$-0.143569\pi$
$971$	2.25917	+	3.91300i	0.0725003	+	0.125574i	−0.827496	+	0.561471i	$0.810236\pi$
$972$	4.12985	+	2.38437i	0.132465	+	0.0764786i
$973$	−50.3665	−	29.0791i	−1.61468	−	0.932234i
$974$	−6.66822			−0.213664
$975$		0			0
$976$	−31.6101			−1.01181
$977$	36.7922	+	21.2420i	1.17709	+	0.679592i	0.955339	−	0.295512i	$-0.0954904\pi$
$977$	36.7922	+	21.2420i	1.17709	+	0.679592i	0.221748	+	0.975104i	$0.428824\pi$
$978$	25.8506	+	14.9249i	0.826612	+	0.477245i
$979$	−25.5822	−	44.3096i	−0.817610	−	1.41614i
$980$		0			0
$981$	−6.93462	−	12.0111i	−0.221406	−	0.383486i
$982$	64.0803	−	36.9968i	2.04488	−	1.18061i
$983$		−	9.87158i		−	0.314854i	−0.987531	−	0.157427i	$-0.949680\pi$
$983$		−	9.87158i		−	0.314854i	0.987531	−	0.157427i	$-0.0503200\pi$
$984$	19.3425	+	33.5022i	0.616617	+	1.06801i
$985$		0			0
$986$	7.00000	−	12.1244i	0.222925	−	0.386118i
$987$		−	13.7045i		−	0.436220i
$988$	52.5344	+	103.849i	1.67134	+	3.30389i
$989$	−17.5375			−0.557659
$990$		0			0
$991$	−10.5598	+	18.2901i	−0.335444	+	0.581005i	−0.983570	−	0.180527i	$-0.942220\pi$
$991$	−10.5598	+	18.2901i	−0.335444	+	0.581005i	0.648126	+	0.761533i	$0.275553\pi$
$992$	33.8882	−	19.5654i	1.07595	−	0.621201i
$993$			21.4793i			0.681626i
$994$	−45.4677	−	78.7524i	−1.44215	−	2.49787i
$995$		0			0
$996$	55.0191			1.74335
$997$	14.7946	−	8.54167i	0.468550	−	0.270517i	−0.247083	−	0.968994i	$-0.579472\pi$
$997$	14.7946	−	8.54167i	0.468550	−	0.270517i	0.715632	+	0.698477i	$0.246139\pi$
$998$	−62.7730	−	36.2420i	−1.98704	−	1.14722i
$999$	1.76873	−	3.06354i	0.0559603	−	0.0969260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.k.724.1		12
5.2	odd	4		975.2.i.l.451.3		6
5.3	odd	4		195.2.i.d.61.1	yes	6
5.4	even	2	inner	975.2.bb.k.724.6		12
13.3	even	3	inner	975.2.bb.k.874.6		12
15.8	even	4		585.2.j.f.451.3		6
65.3	odd	12		195.2.i.d.16.1	✓	6
65.29	even	6	inner	975.2.bb.k.874.1		12
65.42	odd	12		975.2.i.l.601.3		6
65.43	odd	12		2535.2.a.ba.1.1		3
65.48	odd	12		2535.2.a.bb.1.3		3
195.68	even	12		585.2.j.f.406.3		6
195.113	even	12		7605.2.a.bv.1.1		3
195.173	even	12		7605.2.a.bw.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.1	✓	6	65.3	odd	12
195.2.i.d.61.1	yes	6	5.3	odd	4
585.2.j.f.406.3		6	195.68	even	12
585.2.j.f.451.3		6	15.8	even	4
975.2.i.l.451.3		6	5.2	odd	4
975.2.i.l.601.3		6	65.42	odd	12
975.2.bb.k.724.1		12	1.1	even	1	trivial
975.2.bb.k.724.6		12	5.4	even	2	inner
975.2.bb.k.874.1		12	65.29	even	6	inner
975.2.bb.k.874.6		12	13.3	even	3	inner
2535.2.a.ba.1.1		3	65.43	odd	12
2535.2.a.bb.1.3		3	65.48	odd	12
7605.2.a.bv.1.1		3	195.113	even	12
7605.2.a.bw.1.3		3	195.173	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.25312 - 1.30084i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.38437 + 4.12985i) q^{4} +(1.30084 + 2.25312i) q^{6} +(3.11915 - 1.80084i) q^{7} -7.20336i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.25312 - 1.30084i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(2.38437 + 4.12985i) q^{4} +(1.30084 + 2.25312i) q^{6} +(3.11915 - 1.80084i) q^{7} -7.20336i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.60168 - 4.50624i) q^{11} -4.76873i q^{12} +(1.97250 - 3.01815i) q^{13} -9.37041 q^{14} +(-4.60168 + 7.97034i) q^{16} +(-2.54247 + 1.46789i) q^{17} -2.60168i q^{18} +(3.38437 + 5.86190i) q^{19} -3.60168 q^{21} +(-11.7238 + 6.76873i) q^{22} +(4.79559 + 2.76873i) q^{23} +(-3.60168 + 6.23829i) q^{24} +(-8.37041 + 4.23435i) q^{26} -1.00000i q^{27} +(14.8744 + 8.58773i) q^{28} +(0.916472 - 1.58738i) q^{29} +4.10284 q^{31} +(8.25969 - 4.76873i) q^{32} +(-4.50624 + 2.60168i) q^{33} +7.63798 q^{34} +(-2.38437 + 4.12985i) q^{36} +(3.06354 + 1.76873i) q^{37} -17.6101i q^{38} +(-3.21731 + 1.62755i) q^{39} +(2.68521 - 4.65091i) q^{41} +(8.11502 + 4.68521i) q^{42} +(-2.74275 + 1.58353i) q^{43} +24.8134 q^{44} +(-7.20336 - 12.4766i) q^{46} +3.80504i q^{47} +(7.97034 - 4.60168i) q^{48} +(2.98605 - 5.17198i) q^{49} +2.93579 q^{51} +(17.1677 + 0.949743i) q^{52} +5.20336i q^{53} +(-1.30084 + 2.25312i) q^{54} +(-12.9721 - 22.4683i) q^{56} -6.76873i q^{57} +(-4.12985 + 2.38437i) q^{58} +(-3.68521 - 6.38297i) q^{59} +(1.71731 + 2.97447i) q^{61} +(-9.24420 - 5.33714i) q^{62} +(3.11915 + 1.80084i) q^{63} -6.40672 q^{64} +13.5375 q^{66} +(-3.03210 - 1.75058i) q^{67} +(-12.1244 - 7.00000i) q^{68} +(-2.76873 - 4.79559i) q^{69} +(4.85226 + 8.40436i) q^{71} +(6.23829 - 3.60168i) q^{72} +0.805037i q^{73} +(-4.60168 - 7.97034i) q^{74} +(-16.1391 + 27.9538i) q^{76} -18.7408i q^{77} +(9.36617 + 0.518152i) q^{78} +4.10284 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-12.1002 + 6.98605i) q^{82} +11.5375i q^{83} +(-8.58773 - 14.8744i) q^{84} +8.23966 q^{86} +(-1.58738 + 0.916472i) q^{87} +(-32.4601 - 18.7408i) q^{88} +(4.91647 - 8.51558i) q^{89} +(0.717312 - 12.9662i) q^{91} +26.4067i q^{92} +(-3.55317 - 2.05142i) q^{93} +(4.94974 - 8.57321i) q^{94} -9.53747 q^{96} +(-4.82703 + 2.78689i) q^{97} +(-13.4558 + 7.76873i) q^{98} +5.20336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q + 12 * q^4 + 6 * q^9	\( 12 q + 12 q^{4} + 6 q^{9} - 48 q^{14} - 24 q^{16} + 24 q^{19} - 12 q^{21} - 12 q^{24} - 36 q^{26} + 12 q^{29} + 12 q^{31} - 12 q^{36} - 24 q^{39} + 48 q^{44} - 24 q^{46} - 12 q^{49} - 60 q^{56} - 12 q^{59} + 6 q^{61} + 48 q^{64} + 96 q^{66} + 24 q^{71} - 24 q^{74} - 96 q^{76} + 12 q^{79} - 6 q^{81} - 24 q^{84} - 24 q^{86} + 60 q^{89} - 6 q^{91} + 72 q^{94} - 48 q^{96}+O(q^{100}) \) 12 * q + 12 * q^4 + 6 * q^9 - 48 * q^14 - 24 * q^16 + 24 * q^19 - 12 * q^21 - 12 * q^24 - 36 * q^26 + 12 * q^29 + 12 * q^31 - 12 * q^36 - 24 * q^39 + 48 * q^44 - 24 * q^46 - 12 * q^49 - 60 * q^56 - 12 * q^59 + 6 * q^61 + 48 * q^64 + 96 * q^66 + 24 * q^71 - 24 * q^74 - 96 * q^76 + 12 * q^79 - 6 * q^81 - 24 * q^84 - 24 * q^86 + 60 * q^89 - 6 * q^91 + 72 * q^94 - 48 * q^96

Introduction

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