LMFDB - Embedded newform 605.2.j.c.444.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.484000000.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121 $ x^8 - x^6 + 16x^4 - 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			444.1
Root			$1.26313 + 1.73855i$ of defining polynomial
Character	$\chi$	$=$	605.444
Dual form			605.2.j.c.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780656 + 1.07448i) q^{2} +(0.0729490 + 0.224514i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-4.08757 + 1.32813i) q^{7} +(-2.82444 - 0.917716i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})$	\(q+(-0.780656 + 1.07448i) q^{2} +(0.0729490 + 0.224514i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-4.08757 + 1.32813i) q^{7} +(-2.82444 - 0.917716i) q^{8} +(-2.42705 - 1.76336i) q^{9} +2.96979i q^{10} +(4.08757 - 5.62605i) q^{13} +(1.76393 - 5.42882i) q^{14} +(2.80902 - 2.04087i) q^{16} +(-0.964944 - 1.32813i) q^{17} +(3.78938 - 1.23125i) q^{18} +(0.427051 + 0.310271i) q^{20} +(1.54508 - 4.75528i) q^{25} +(2.85410 + 8.78402i) q^{26} +(-0.596368 - 0.820830i) q^{28} +(-7.23607 - 5.25731i) q^{31} -1.32813i q^{32} +2.18034 q^{34} +(-5.64888 + 7.77501i) q^{35} +(0.218847 - 0.673542i) q^{36} +(-6.31564 + 2.05208i) q^{40} +1.01460i q^{43} -6.70820 q^{45} +(9.28115 - 6.74315i) q^{49} +(3.90328 + 5.37240i) q^{50} +(1.56131 + 0.507301i) q^{52} +12.7639 q^{56} +(-1.23607 - 3.80423i) q^{59} +(11.2978 - 3.67086i) q^{62} +(12.2627 + 3.98439i) q^{63} +(7.04508 + 5.11855i) q^{64} -15.5500i q^{65} +(0.227792 - 0.313529i) q^{68} +(-3.94427 - 12.1392i) q^{70} +(-6.47214 + 4.70228i) q^{71} +(5.23680 + 7.20783i) q^{72} +(11.6663 - 3.79062i) q^{73} +(2.39919 - 7.38394i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-10.7014 - 14.7292i) q^{83} +(-3.49120 - 1.13436i) q^{85} +(-1.09017 - 0.792055i) q^{86} -13.4164 q^{89} +(5.23680 - 7.20783i) q^{90} +(-9.23607 + 28.4257i) q^{91} +15.2365i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9	$ 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9} + 32 q^{14} + 18 q^{16} - 10 q^{20} - 10 q^{25} - 4 q^{26} - 40 q^{31} - 72 q^{34} + 42 q^{36} + 34 q^{49} + 120 q^{56} + 8 q^{59} + 34 q^{64} + 40 q^{70} - 16 q^{71} - 30 q^{80} - 18 q^{81} + 36 q^{86} - 56 q^{91}+O(q^{100}) $ 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9 + 32 * q^14 + 18 * q^16 - 10 * q^20 - 10 * q^25 - 4 * q^26 - 40 * q^31 - 72 * q^34 + 42 * q^36 + 34 * q^49 + 120 * q^56 + 8 * q^59 + 34 * q^64 + 40 * q^70 - 16 * q^71 - 30 * q^80 - 18 * q^81 + 36 * q^86 - 56 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.780656	+	1.07448i	−0.552007	+	0.759772i	−0.990283	−	0.139068i	$-0.955589\pi$
$2$	−0.780656	+	1.07448i	−0.552007	+	0.759772i	0.438276	+	0.898841i	$0.355589\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	0.0729490	+	0.224514i	0.0364745	+	0.112257i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$5$	1.80902	−	1.31433i	0.809017	−	0.587785i
$6$		0			0
$7$	−4.08757	+	1.32813i	−1.54496	+	0.501986i	−0.952738	−	0.303792i	$-0.901747\pi$
$7$	−4.08757	+	1.32813i	−1.54496	+	0.501986i	−0.592217	+	0.805779i	$0.701747\pi$
$8$	−2.82444	−	0.917716i	−0.998590	−	0.324462i
$9$	−2.42705	−	1.76336i	−0.809017	−	0.587785i
$10$			2.96979i			0.939130i
$11$		0			0
$11$		0			0
$12$		0			0
$13$	4.08757	−	5.62605i	1.13369	−	1.56039i	0.352818	−	0.935692i	$-0.385224\pi$
$13$	4.08757	−	5.62605i	1.13369	−	1.56039i	0.780869	−	0.624694i	$-0.214776\pi$
$14$	1.76393	−	5.42882i	0.471431	−	1.45091i
$15$		0			0
$16$	2.80902	−	2.04087i	0.702254	−	0.510218i
$17$	−0.964944	−	1.32813i	−0.234033	−	0.322119i	0.675806	−	0.737079i	$-0.263796\pi$
$17$	−0.964944	−	1.32813i	−0.234033	−	0.322119i	−0.909840	+	0.414960i	$0.863796\pi$
$18$	3.78938	−	1.23125i	0.893166	−	0.290207i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	0.427051	+	0.310271i	0.0954915	+	0.0693786i
$21$		0			0
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	2.85410	+	8.78402i	0.559735	+	1.72269i
$27$		0			0
$28$	−0.596368	−	0.820830i	−0.112703	−	0.155122i
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$		0			0
$31$	−7.23607	−	5.25731i	−1.29964	−	0.944241i	−0.299684	−	0.954038i	$-0.596881\pi$
$31$	−7.23607	−	5.25731i	−1.29964	−	0.944241i	−0.999952	+	0.00979752i	$0.996881\pi$
$32$		−	1.32813i		−	0.234783i
$33$		0			0
$34$	2.18034			0.373925
$35$	−5.64888	+	7.77501i	−0.954835	+	1.31422i
$36$	0.218847	−	0.673542i	0.0364745	−	0.112257i
$37$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$37$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$38$		0			0
$39$		0			0
$40$	−6.31564	+	2.05208i	−0.998590	+	0.324462i
$41$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$41$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$42$		0			0
$43$			1.01460i			0.154725i	0.997003	+	0.0773627i	$0.0246499\pi$
$43$			1.01460i			0.154725i	−0.997003	+	0.0773627i	$0.975350\pi$
$44$		0			0
$45$	−6.70820			−1.00000
$46$		0			0
$47$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$47$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$48$		0			0
$49$	9.28115	−	6.74315i	1.32588	−	0.963307i
$50$	3.90328	+	5.37240i	0.552007	+	0.759772i
$51$		0			0
$52$	1.56131	+	0.507301i	0.216515	+	0.0703500i
$53$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$53$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$54$		0			0
$55$		0			0
$56$	12.7639			1.70565
$57$		0			0
$58$		0			0
$59$	−1.23607	−	3.80423i	−0.160922	−	0.495268i	0.837790	−	0.545992i	$-0.183847\pi$
$59$	−1.23607	−	3.80423i	−0.160922	−	0.495268i	−0.998713	+	0.0507240i	$0.983847\pi$
$60$		0			0
$61$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$61$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$62$	11.2978	−	3.67086i	1.43482	−	0.466200i
$63$	12.2627	+	3.98439i	1.54496	+	0.501986i
$64$	7.04508	+	5.11855i	0.880636	+	0.639819i
$65$		−	15.5500i		−	1.92874i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	0.227792	−	0.313529i	0.0276239	−	0.0380210i
$69$		0			0
$70$	−3.94427	−	12.1392i	−0.471431	−	1.45091i
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	−0.901384	−	0.433020i	$-0.857448\pi$
$71$	−6.47214	+	4.70228i	−0.768101	+	0.558058i	0.133283	+	0.991078i	$0.457448\pi$
$72$	5.23680	+	7.20783i	0.617163	+	0.849451i
$73$	11.6663	−	3.79062i	1.36544	−	0.443659i	0.467585	−	0.883948i	$-0.345124\pi$
$73$	11.6663	−	3.79062i	1.36544	−	0.443659i	0.897856	+	0.440289i	$0.145124\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$	2.39919	−	7.38394i	0.268237	−	0.825549i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$		0			0
$83$	−10.7014	−	14.7292i	−1.17463	−	1.61674i	−0.619669	−	0.784863i	$-0.712733\pi$
$83$	−10.7014	−	14.7292i	−1.17463	−	1.61674i	−0.554961	−	0.831876i	$-0.687267\pi$
$84$		0			0
$85$	−3.49120	−	1.13436i	−0.378674	−	0.123039i
$86$	−1.09017	−	0.792055i	−0.117556	−	0.0854095i
$87$		0			0
$88$		0			0
$89$	−13.4164			−1.42214			−0.711068	−	0.703123i	$-0.751788\pi$
$89$	−13.4164			−1.42214			−0.711068	+	0.703123i	$0.751788\pi$
$90$	5.23680	−	7.20783i	0.552007	−	0.759772i
$91$	−9.23607	+	28.4257i	−0.968203	+	2.97982i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$			15.2365i			1.53912i
$99$		0			0
$100$	1.18034			0.118034
$101$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$101$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$102$		0			0
$103$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$103$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$104$	−16.7082	+	12.1392i	−1.63837	+	1.19035i
$105$		0			0
$106$		0			0
$107$	−7.21019	−	2.34273i	−0.697035	−	0.226481i	−0.0609970	−	0.998138i	$-0.519428\pi$
$107$	−7.21019	−	2.34273i	−0.697035	−	0.226481i	−0.636038	+	0.771657i	$0.719428\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	−8.77150	+	12.0729i	−0.828829	+	1.14079i
$113$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$113$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−19.8415	+	6.44688i	−1.83434	+	0.596015i
$118$	5.05251	+	1.64166i	0.465121	+	0.151127i
$119$	5.70820	+	4.14725i	0.523270	+	0.380178i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	0.652476	−	2.00811i	0.0585941	−	0.180334i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−13.8541	+	10.0656i	−1.23422	+	0.896714i
$127$	8.77150	+	12.0729i	0.778345	+	1.07130i	0.995463	+	0.0951544i	$0.0303345\pi$
$127$	8.77150	+	12.0729i	0.778345	+	1.07130i	−0.217118	+	0.976145i	$0.569666\pi$
$128$	−8.47332	+	2.75315i	−0.748943	+	0.243346i
$129$		0			0
$130$	16.7082	+	12.1392i	1.46541	+	1.06468i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.50658	+	4.63677i	0.129188	+	0.397600i
$137$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$137$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$138$		0			0
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$	−2.15768	−	0.701073i	−0.182357	−	0.0592515i
$141$		0			0
$142$		−	10.6250i		−	0.891634i
$143$		0			0
$144$	−10.4164			−0.868034
$145$		0			0
$146$	−5.03444	+	15.4944i	−0.416653	+	1.28233i
$147$		0			0
$148$		0			0
$149$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$149$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$150$		0			0
$151$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$151$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$152$		0			0
$153$			4.92498i			0.398161i
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$157$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$158$		0			0
$159$		0			0
$160$	−1.74560	−	2.40261i	−0.138002	−	0.189943i
$161$		0			0
$162$	−11.3681	−	3.69374i	−0.893166	−	0.290207i
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		0			0
$165$		0			0
$166$	24.1803			1.87676
$167$	13.8240	−	19.0271i	1.06973	−	1.47236i	0.199389	−	0.979920i	$-0.436104\pi$
$167$	13.8240	−	19.0271i	1.06973	−	1.47236i	0.870345	−	0.492442i	$-0.163896\pi$
$168$		0			0
$169$	−10.9271	−	33.6300i	−0.840542	−	2.58692i
$170$	3.94427	−	2.86568i	0.302512	−	0.219788i
$171$		0			0
$172$	−0.227792	+	0.0740142i	−0.0173690	+	0.00564353i
$173$	−22.9641	−	7.46149i	−1.74593	−	0.567286i	−0.750334	−	0.661059i	$-0.770107\pi$
$173$	−22.9641	−	7.46149i	−1.74593	−	0.567286i	−0.995594	+	0.0937729i	$0.970107\pi$
$174$		0			0
$175$			21.4896i			1.62446i
$176$		0			0
$177$		0			0
$178$	10.4736	−	14.4157i	0.785029	−	1.08050i
$179$	−5.52786	+	17.0130i	−0.413172	+	1.27161i	0.500704	+	0.865619i	$0.333075\pi$
$179$	−5.52786	+	17.0130i	−0.413172	+	1.27161i	−0.913876	+	0.405994i	$0.866925\pi$
$180$	−0.489357	−	1.50609i	−0.0364745	−	0.112257i
$181$	3.61803	−	2.62866i	0.268926	−	0.195386i	−0.445147	−	0.895458i	$-0.646848\pi$
$181$	3.61803	−	2.62866i	0.268926	−	0.195386i	0.714073	+	0.700071i	$0.246848\pi$
$182$	−23.3327	−	32.1147i	−1.72953	−	2.38050i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.29180	+	25.5195i	0.599973	+	1.84653i	0.528224	+	0.849105i	$0.322858\pi$
$191$	8.29180	+	25.5195i	0.599973	+	1.84653i	0.0717497	+	0.997423i	$0.477142\pi$
$192$		0			0
$193$	11.0700	+	15.2365i	0.796834	+	1.09675i	0.993223	+	0.116221i	$0.0370782\pi$
$193$	11.0700	+	15.2365i	0.796834	+	1.09675i	−0.196390	+	0.980526i	$0.562922\pi$
$194$		0			0
$195$		0			0
$196$	2.19098	+	1.59184i	0.156499	+	0.113703i
$197$			17.5792i			1.25247i	0.779635	+	0.626234i	$0.215405\pi$
$197$			17.5792i			1.25247i	−0.779635	+	0.626234i	$0.784595\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−8.72800	+	12.0131i	−0.617163	+	0.849451i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		−	24.1459i		−	1.67422i
$209$		0			0
$210$		0			0
$211$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$211$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$212$		0			0
$213$		0			0
$214$	8.14590	−	5.91834i	0.556842	−	0.404569i
$215$	1.33352	+	1.83543i	0.0909453	+	0.125175i
$216$		0			0
$217$	36.5603	+	11.8792i	2.48188	+	0.806410i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.4164			−0.767951
$222$		0			0
$223$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$223$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$224$	1.76393	+	5.42882i	0.117858	+	0.362729i
$225$	−12.1353	+	8.81678i	−0.809017	+	0.587785i
$226$		0			0
$227$	15.3853	−	4.99899i	1.02116	−	0.331795i	0.249870	−	0.968279i	$-0.419612\pi$
$227$	15.3853	−	4.99899i	1.02116	−	0.331795i	0.771290	+	0.636484i	$0.219612\pi$
$228$		0			0
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	0.415735	−	0.909486i	$-0.363524\pi$
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	−0.736503	+	0.676434i	$0.763524\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.3853	+	21.1761i	−1.00793	+	1.38729i	−0.0875928	+	0.996156i	$0.527917\pi$
$233$	−15.3853	+	21.1761i	−1.00793	+	1.38729i	−0.920333	+	0.391135i	$0.872083\pi$
$234$	8.56231	−	26.3521i	0.559735	−	1.72269i
$235$		0			0
$236$	0.763932	−	0.555029i	0.0497277	−	0.0361293i
$237$		0			0
$238$	−8.91229	+	2.89578i	−0.577698	+	0.187705i
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.92705	−	24.3970i	0.506441	−	1.55866i
$246$		0			0
$247$		0			0
$248$	15.6131	+	21.4896i	0.991434	+	1.36459i
$249$		0			0
$250$	14.1222	+	4.58858i	0.893166	+	0.290207i
$251$	−22.6525	−	16.4580i	−1.42981	−	1.03882i	−0.990052	−	0.140704i	$-0.955064\pi$
$251$	−22.6525	−	16.4580i	−1.42981	−	1.03882i	−0.439760	−	0.898115i	$-0.644936\pi$
$252$			3.04381i			0.191742i
$253$		0			0
$254$	−19.8197			−1.24360
$255$		0			0
$256$	−1.72542	+	5.31031i	−0.107839	+	0.331894i
$257$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$257$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$258$		0			0
$259$		0			0
$260$	3.49120	−	1.13436i	0.216515	−	0.0703500i
$261$		0			0
$262$		0			0
$263$		−	32.1147i		−	1.98027i	−0.140100	−	0.990137i	$-0.544742\pi$
$263$		−	32.1147i		−	1.98027i	0.140100	−	0.990137i	$-0.455258\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.3262	−	8.22899i	0.690573	−	0.501731i	−0.186275	−	0.982498i	$-0.559642\pi$
$269$	11.3262	−	8.22899i	0.690573	−	0.501731i	0.876848	+	0.480767i	$0.159642\pi$
$270$		0			0
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$	−5.42109	−	1.76142i	−0.328702	−	0.106802i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−7.94734	+	10.9386i	−0.477509	+	0.657235i	−0.978024	−	0.208493i	$-0.933144\pi$
$277$	−7.94734	+	10.9386i	−0.477509	+	0.657235i	0.500514	+	0.865728i	$0.333144\pi$
$278$		0			0
$279$	8.29180	+	25.5195i	0.496417	+	1.52781i
$280$	23.0902	−	16.7760i	1.37990	−	1.00256i
$281$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$281$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$282$		0			0
$283$	−19.2451	−	6.25311i	−1.14400	−	0.371709i	−0.325121	−	0.945672i	$-0.605405\pi$
$283$	−19.2451	−	6.25311i	−1.14400	−	0.371709i	−0.818881	+	0.573963i	$0.805405\pi$
$284$	−1.52786	−	1.11006i	−0.0906621	−	0.0658698i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.34197	+	3.22344i	−0.138002	+	0.189943i
$289$	4.42047	−	13.6048i	0.260028	−	0.800283i
$290$		0			0
$291$		0			0
$292$	1.70210	+	2.34273i	0.0996076	+	0.137098i
$293$	−0.368576	+	0.119757i	−0.0215324	+	0.00699631i	−0.319763	−	0.947497i	$-0.603603\pi$
$293$	−0.368576	+	0.119757i	−0.0215324	+	0.00699631i	0.298231	+	0.954494i	$0.403603\pi$
$294$		0			0
$295$	−7.23607	−	5.25731i	−0.421300	−	0.306092i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−1.34752	−	4.14725i	−0.0776700	−	0.239044i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−5.29180	−	3.84471i	−0.302512	−	0.219788i
$307$		−	11.6397i		−	0.664310i	−0.943225	−	0.332155i	$-0.892224\pi$
$307$		−	11.6397i		−	0.664310i	0.943225	−	0.332155i	$-0.107776\pi$
$308$		0			0
$309$		0			0
$310$	15.6131	−	21.4896i	0.886765	−	1.22053i
$311$	9.88854	−	30.4338i	0.560728	−	1.72574i	−0.119588	−	0.992824i	$-0.538157\pi$
$311$	9.88854	−	30.4338i	0.560728	−	1.72574i	0.680316	−	0.732919i	$-0.261843\pi$
$312$		0			0
$313$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$313$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$314$		0			0
$315$	27.4202	−	8.90937i	1.54496	−	0.501986i
$316$		0			0
$317$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$317$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$318$		0			0
$319$		0			0
$320$	19.4721			1.08853
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.71885	+	1.24882i	−0.0954915	+	0.0693786i
$325$	−20.4378	−	28.1303i	−1.13369	−	1.56039i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	35.7771			1.96649			0.983243	−	0.182298i	$-0.0583536\pi$
$331$	35.7771			1.96649			0.983243	+	0.182298i	$0.0583536\pi$
$332$	2.52626	−	3.47709i	0.138646	−	0.190830i
$333$		0			0
$334$	9.65248	+	29.7073i	0.528160	+	1.62551i
$335$		0			0
$336$		0			0
$337$	31.1392	−	10.1177i	1.69626	−	0.551149i	0.708309	−	0.705903i	$-0.249459\pi$
$337$	31.1392	−	10.1177i	1.69626	−	0.551149i	0.987953	+	0.154754i	$0.0494585\pi$
$338$	44.6651	+	14.5126i	2.42946	+	0.789379i
$339$		0			0
$340$		−	0.866573i		−	0.0469965i
$341$		0			0
$342$		0			0
$343$	−11.2978	+	15.5500i	−0.610022	+	0.839623i
$344$	0.931116	−	2.86568i	0.0502024	−	0.154507i
$345$		0			0
$346$	25.9443	−	18.8496i	1.39477	−	1.01336i
$347$	20.8064	+	28.6376i	1.11695	+	1.53735i	0.810765	+	0.585372i	$0.199052\pi$
$347$	20.8064	+	28.6376i	1.11695	+	1.53735i	0.306182	+	0.951973i	$0.400948\pi$
$348$		0			0
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$	−23.0902	−	16.7760i	−1.23422	−	0.896714i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$	−5.52786	+	17.0130i	−0.293389	+	0.902957i
$356$	−0.978714	−	3.01217i	−0.0518717	−	0.159645i
$357$		0			0
$358$	−13.9648	−	19.2209i	−0.738062	−	1.01586i
$359$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$359$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$360$	18.9469	+	6.15623i	0.998590	+	0.324462i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$			5.93958i			0.312178i
$363$		0			0
$364$	−7.05573			−0.369821
$365$	16.1225	−	22.1907i	0.843889	−	1.16151i
$366$		0			0
$367$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$367$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$			38.0542i			1.97037i	0.171484	+	0.985187i	$0.445144\pi$
$373$			38.0542i			1.97037i	−0.171484	+	0.985187i	$0.554856\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	29.1246	−	21.1603i	1.49603	−	1.08693i	0.524102	−	0.851656i	$-0.324401\pi$
$379$	29.1246	−	21.1603i	1.49603	−	1.08693i	0.971929	−	0.235274i	$-0.0755989\pi$
$380$		0			0
$381$		0			0
$382$	−33.8933	−	11.0126i	−1.73413	−	0.563453i
$383$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$383$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$384$		0			0
$385$		0			0
$386$	−25.0132			−1.27314
$387$	1.78910	−	2.46249i	0.0909453	−	0.125175i
$388$		0			0
$389$	−8.03444	−	24.7275i	−0.407362	−	1.25373i	−0.918906	−	0.394475i	$-0.870926\pi$
$389$	−8.03444	−	24.7275i	−0.407362	−	1.25373i	0.511544	−	0.859257i	$-0.329074\pi$
$390$		0			0
$391$		0			0
$392$	−32.4024	+	10.5282i	−1.63657	+	0.531752i
$393$		0			0
$394$	−18.8885	−	13.7233i	−0.951591	−	0.691371i
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−18.7357	+	25.7875i	−0.939138	+	1.29261i
$399$		0			0
$400$	−5.36475	−	16.5110i	−0.268237	−	0.825549i
$401$	3.61803	−	2.62866i	0.180676	−	0.131269i	−0.493771	−	0.869592i	$-0.664382\pi$
$401$	3.61803	−	2.62866i	0.180676	−	0.131269i	0.674447	+	0.738323i	$0.264382\pi$
$402$		0			0
$403$	−59.1558	+	19.2209i	−2.94676	+	0.957461i
$404$		0			0
$405$	16.2812	+	11.8290i	0.809017	+	0.587785i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$409$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.1050	+	13.9084i	0.497236	+	0.684386i
$414$		0			0
$415$	−38.7180	−	12.5802i	−1.90059	−	0.617540i
$416$	−7.47214	−	5.42882i	−0.366352	−	0.266170i
$417$		0			0
$418$		0			0
$419$	35.7771			1.74783			0.873913	−	0.486083i	$-0.161575\pi$
$419$	35.7771			1.74783			0.873913	+	0.486083i	$0.161575\pi$
$420$		0			0
$421$	9.67376	−	29.7728i	0.471470	−	1.45104i	−0.379189	−	0.925319i	$-0.623797\pi$
$421$	9.67376	−	29.7728i	0.471470	−	1.45104i	0.850659	−	0.525717i	$-0.176203\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.80656	+	2.53650i	−0.378674	+	0.123039i
$426$		0			0
$427$		0			0
$428$		−	1.78969i		−	0.0865079i
$429$		0			0
$430$	−3.01316			−0.145307
$431$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$431$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$432$		0			0
$433$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$433$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$434$	−41.3050	+	30.0098i	−1.98270	+	1.44052i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−34.4164			−1.63888
$442$	8.91229	−	12.2667i	0.423914	−	0.583468i
$443$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$443$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$444$		0			0
$445$	−24.2705	+	17.6336i	−1.15053	+	0.835911i
$446$		0			0
$447$		0			0
$448$	−35.5954	−	11.5656i	−1.68172	−	0.546425i
$449$	32.5623	+	23.6579i	1.53671	+	1.11649i	0.952357	+	0.304986i	$0.0986518\pi$
$449$	32.5623	+	23.6579i	1.53671	+	1.11649i	0.584353	+	0.811499i	$0.301348\pi$
$450$		−	19.9220i		−	0.939130i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−6.63932	+	20.4337i	−0.311599	+	0.959002i
$455$	20.6525	+	63.5618i	0.968203	+	2.97982i
$456$		0			0
$457$	−12.9999	−	17.8928i	−0.608107	−	0.836988i	0.388313	−	0.921528i	$-0.373058\pi$
$457$	−12.9999	−	17.8928i	−0.608107	−	0.836988i	−0.996420	+	0.0845396i	$0.973058\pi$
$458$	7.57877	−	2.46249i	0.354132	−	0.115065i
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	−10.7426	−	33.0625i	−0.497643	−	1.53159i
$467$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$467$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$468$	−2.89483	−	3.98439i	−0.133814	−	0.184179i
$469$		0			0
$470$		0			0
$471$		0			0
$472$			11.8792i			0.546783i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.514708	+	1.58411i	−0.0235916	+	0.0726075i
$477$		0			0
$478$		0			0
$479$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$479$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$487$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$488$		0			0
$489$		0			0
$490$	20.0258	+	27.5631i	0.904671	+	1.24517i
$491$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$491$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−31.0557			−1.39444
$497$	20.2100	−	27.8167i	0.906544	−	1.24775i
$498$		0			0
$499$	−1.23607	−	3.80423i	−0.0553340	−	0.170301i	0.919570	−	0.392926i	$-0.128537\pi$
$499$	−1.23607	−	3.80423i	−0.0553340	−	0.170301i	−0.974904	+	0.222626i	$0.928537\pi$
$500$	2.13525	−	1.55135i	0.0954915	−	0.0693786i
$501$		0			0
$502$	35.3676	−	11.4916i	1.57853	−	0.512896i
$503$	24.2976	+	7.89477i	1.08338	+	0.352010i	0.795684	−	0.605712i	$-0.207112\pi$
$503$	24.2976	+	7.89477i	1.08338	+	0.352010i	0.287693	+	0.957723i	$0.407112\pi$
$504$	−30.9787	−	22.5074i	−1.37990	−	1.00256i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−2.07067	+	2.85003i	−0.0918712	+	0.126450i
$509$	−10.5066	+	32.3359i	−0.465696	+	1.43326i	0.392409	+	0.919791i	$0.371642\pi$
$509$	−10.5066	+	32.3359i	−0.465696	+	1.43326i	−0.858105	+	0.513474i	$0.828358\pi$
$510$		0			0
$511$	−42.6525	+	30.9888i	−1.88683	+	1.37087i
$512$	−14.8325	−	20.4151i	−0.655508	−	0.902230i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−14.2705	+	43.9201i	−0.625803	+	1.92602i
$521$	−6.90983	−	21.2663i	−0.302725	−	0.931692i	−0.980516	−	0.196438i	$-0.937063\pi$
$521$	−6.90983	−	21.2663i	−0.302725	−	0.931692i	0.677791	−	0.735254i	$-0.262937\pi$
$522$		0			0
$523$	−3.26341	−	4.49169i	−0.142699	−	0.196408i	0.731685	−	0.681643i	$-0.238734\pi$
$523$	−3.26341	−	4.49169i	−0.142699	−	0.196408i	−0.874384	+	0.485235i	$0.838734\pi$
$524$		0			0
$525$		0			0
$526$	34.5066	+	25.0705i	1.50456	+	1.09313i
$527$			14.6835i			0.639621i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	−3.70820	+	11.4127i	−0.160922	+	0.495268i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−16.1225	+	5.23851i	−0.697035	+	0.226481i
$536$		0			0
$537$		0			0
$538$			18.5938i			0.801637i
$539$		0			0
$540$		0			0
$541$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$541$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$542$		0			0
$543$		0			0
$544$	−1.76393	+	1.28157i	−0.0756280	+	0.0549469i
$545$		0			0
$546$		0			0
$547$	43.7705	+	14.2219i	1.87149	+	0.608084i	0.990971	+	0.134076i	$0.0428067\pi$
$547$	43.7705	+	14.2219i	1.87149	+	0.608084i	0.880520	+	0.474008i	$0.157193\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−5.54915	−	17.0785i	−0.235761	−	0.725597i
$555$		0			0
$556$		0			0
$557$	−39.3144	+	12.7740i	−1.66580	+	0.541252i	−0.982076	−	0.188486i	$-0.939642\pi$
$557$	−39.3144	+	12.7740i	−1.66580	+	0.541252i	−0.683727	+	0.729738i	$0.739642\pi$
$558$	−33.8933	−	11.0126i	−1.43482	−	0.466200i
$559$	5.70820	+	4.14725i	0.241431	+	0.175410i
$560$			33.3688i			1.41009i
$561$		0			0
$562$		0			0
$563$	25.8589	−	35.5918i	1.08982	−	1.50001i	0.241599	−	0.970376i	$-0.422328\pi$
$563$	25.8589	−	35.5918i	1.08982	−	1.50001i	0.848224	−	0.529637i	$-0.177672\pi$
$564$		0			0
$565$		0			0
$566$	21.7426	−	15.7970i	0.913912	−	0.663996i
$567$	−22.7363	−	31.2938i	−0.954835	−	1.31422i
$568$	22.5955	−	7.34173i	0.948087	−	0.308052i
$569$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$569$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−8.07295	−	24.8460i	−0.336373	−	1.03525i
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	11.1672	+	15.3704i	0.464496	+	0.639324i
$579$		0			0
$580$		0			0
$581$	63.3050	+	45.9937i	2.62633	+	1.90814i
$582$		0			0
$583$		0			0
$584$	−36.4296			−1.50747
$585$	−27.4202	+	37.7407i	−1.13369	+	1.56039i
$586$	0.159054	−	0.489517i	0.00657045	−	0.0202218i
$587$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$587$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$588$		0			0
$589$		0			0
$590$	11.2978	−	3.67086i	0.465121	−	0.151127i
$591$		0			0
$592$		0			0
$593$		−	36.0250i		−	1.47937i	−0.672953	−	0.739686i	$-0.734974\pi$
$593$		−	36.0250i		−	1.47937i	0.672953	−	0.739686i	$-0.265026\pi$
$594$		0			0
$595$	15.7771			0.646798
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−36.1803	+	26.2866i	−1.47829	+	1.07404i	−0.500186	+	0.865918i	$0.666735\pi$
$599$	−36.1803	+	26.2866i	−1.47829	+	1.07404i	−0.978103	+	0.208121i	$0.933265\pi$
$600$		0			0
$601$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$601$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$602$	5.50810	+	1.78969i	0.224493	+	0.0729423i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−25.1218	+	34.5771i	−1.01966	+	1.40344i	−0.107220	+	0.994235i	$0.534195\pi$
$607$	−25.1218	+	34.5771i	−1.01966	+	1.40344i	−0.912441	+	0.409208i	$0.865805\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.10573	+	0.359272i	−0.0446964	+	0.0145227i
$613$	15.9817	+	5.19277i	0.645494	+	0.209734i	0.613426	−	0.789752i	$-0.289791\pi$
$613$	15.9817	+	5.19277i	0.645494	+	0.209734i	0.0320680	+	0.999486i	$0.489791\pi$
$614$	12.5066	+	9.08656i	0.504724	+	0.366704i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−5.52786	+	17.0130i	−0.222184	+	0.683811i	0.776382	+	0.630263i	$0.217053\pi$
$619$	−5.52786	+	17.0130i	−0.222184	+	0.683811i	−0.998565	+	0.0535478i	$0.982947\pi$
$620$	−1.45898	−	4.49028i	−0.0585941	−	0.180334i
$621$		0			0
$622$	24.9810	+	34.3834i	1.00165	+	1.37865i
$623$	54.8405	−	17.8187i	2.19714	−	0.713893i
$624$		0			0
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−11.8328	+	36.4177i	−0.471431	+	1.45091i
$631$	−14.8328	−	45.6507i	−0.590485	−	1.81733i	−0.576027	−	0.817431i	$-0.695398\pi$
$631$	−14.8328	−	45.6507i	−0.590485	−	1.81733i	−0.0144581	−	0.999895i	$-0.504602\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	31.7356	+	10.3115i	1.25939	+	0.409200i
$636$		0			0
$637$		−	79.7793i		−	3.16097i
$638$		0			0
$639$	24.0000			0.949425
$640$	−11.7098	+	16.1172i	−0.462872	+	0.637089i
$641$	9.67376	−	29.7728i	0.382091	−	1.17595i	−0.556478	−	0.830862i	$-0.687848\pi$
$641$	9.67376	−	29.7728i	0.382091	−	1.17595i	0.938569	−	0.345092i	$-0.112152\pi$
$642$		0			0
$643$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$643$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$		−	26.7281i		−	1.04998i
$649$		0			0
$650$	46.1803			1.81134
$651$		0			0
$652$		0			0
$653$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$653$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−34.9990	−	11.3719i	−1.36544	−	0.443659i
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−42.0000			−1.63361			−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000			−1.63361			−0.816805	+	0.576913i	$0.804257\pi$
$662$	−27.9296	+	38.4418i	−1.08551	+	1.49408i
$663$		0			0
$664$	16.7082	+	51.4226i	0.648404	+	1.99558i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	5.28030	+	1.71567i	0.204301	+	0.0663814i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	11.5255	−	15.8636i	0.444277	−	0.611495i	−0.526879	−	0.849941i	$-0.676638\pi$
$673$	11.5255	−	15.8636i	0.444277	−	0.611495i	0.971156	+	0.238445i	$0.0766378\pi$
$674$	−13.4377	+	41.3570i	−0.517601	+	1.59301i
$675$		0			0
$676$	6.75329	−	4.90655i	0.259742	−	0.188714i
$677$	30.5429	+	42.0386i	1.17386	+	1.61568i	0.630589	+	0.776117i	$0.282813\pi$
$677$	30.5429	+	42.0386i	1.17386	+	1.61568i	0.543268	+	0.839559i	$0.317187\pi$
$678$		0			0
$679$		0			0
$680$	8.81966	+	6.40786i	0.338219	+	0.245730i
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−7.88854	−	24.2784i	−0.301186	−	0.926955i
$687$		0			0
$688$	2.07067	+	2.85003i	0.0789436	+	0.108657i
$689$		0			0
$690$		0			0
$691$	−22.6525	−	16.4580i	−0.861741	−	0.626091i	0.0666172	−	0.997779i	$-0.478779\pi$
$691$	−22.6525	−	16.4580i	−0.861741	−	0.626091i	−0.928358	+	0.371687i	$0.878779\pi$
$692$		−	5.70007i		−	0.216684i
$693$		0			0
$694$	−47.0132			−1.78459
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−4.82472	+	1.56765i	−0.182357	+	0.0592515i
$701$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$701$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.61803	−	2.62866i	0.135878	−	0.0987212i	−0.517770	−	0.855520i	$-0.673238\pi$
$709$	3.61803	−	2.62866i	0.135878	−	0.0987212i	0.653648	+	0.756799i	$0.273238\pi$
$710$	−13.9648	−	19.2209i	−0.524089	−	0.721347i
$711$		0			0
$712$	37.8938	+	12.3125i	1.42013	+	0.461429i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−4.22291			−0.157818
$717$		0			0
$718$		0			0
$719$	8.29180	+	25.5195i	0.309232	+	0.951718i	0.978064	+	0.208304i	$0.0667944\pi$
$719$	8.29180	+	25.5195i	0.309232	+	0.951718i	−0.668832	+	0.743413i	$0.733206\pi$
$720$	−18.8435	+	13.6906i	−0.702254	+	0.510218i
$721$		0			0
$722$	−23.9994	+	7.79789i	−0.893166	+	0.290207i
$723$		0			0
$724$	0.854102	+	0.620541i	0.0317424	+	0.0230622i
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	52.1734	−	71.8106i	1.93368	−	2.66148i
$729$	8.34346	−	25.6785i	0.309017	−	0.951057i
$730$	11.2574	+	34.6466i	0.416653	+	1.28233i
$731$	1.34752	−	0.979034i	0.0498400	−	0.0362109i
$732$		0			0
$733$	43.1741	−	14.0281i	1.59467	−	0.518141i	0.628890	−	0.777494i	$-0.283509\pi$
$733$	43.1741	−	14.0281i	1.59467	−	0.518141i	0.965783	+	0.259353i	$0.0835094\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$739$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.1743	−	41.5313i	−1.10699	−	1.52364i	−0.825782	−	0.563989i	$-0.809266\pi$
$743$	−30.1743	−	41.5313i	−1.10699	−	1.52364i	−0.281205	−	0.959648i	$-0.590734\pi$
$744$		0			0
$745$		0			0
$746$	−40.8885	−	29.7073i	−1.49704	−	1.08766i
$747$			54.6189i			1.99840i
$748$		0			0
$749$	32.5836			1.19058
$750$		0			0
$751$	9.88854	−	30.4338i	0.360838	−	1.11055i	−0.591708	−	0.806152i	$-0.701546\pi$
$751$	9.88854	−	30.4338i	0.360838	−	1.11055i	0.952546	−	0.304393i	$-0.0984537\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$757$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$758$			47.8127i			1.73664i
$759$		0			0
$760$		0			0
$761$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$761$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$762$		0			0
$763$		0			0
$764$	−5.12461	+	3.72325i	−0.185402	+	0.134702i
$765$	6.47304	+	8.90937i	0.234033	+	0.322119i
$766$		0			0
$767$	−26.4553	−	8.59584i	−0.955245	−	0.310378i
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−2.61326	+	3.59685i	−0.0940534	+	0.129453i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	1.24922	+	3.84471i	0.0449024	+	0.138195i
$775$	−36.1803	+	26.2866i	−1.29964	+	0.944241i
$776$		0			0
$777$		0			0
$778$	32.8413	+	10.6708i	1.17742	+	0.382566i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	12.3090	−	37.8833i	0.439608	−	1.35297i
$785$		0			0
$786$		0			0
$787$	−18.1394	−	24.9667i	−0.646599	−	0.889967i	0.352347	−	0.935869i	$-0.385384\pi$
$787$	−18.1394	−	24.9667i	−0.646599	−	0.889967i	−0.998946	+	0.0459025i	$0.985384\pi$
$788$	−3.94678	+	1.28239i	−0.140598	+	0.0456832i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.75078	+	5.38834i	0.0620546	+	0.190984i
$797$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$797$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$798$		0			0
$799$		0			0
$800$	−6.31564	−	2.05208i	−0.223292	−	0.0725518i
$801$	32.5623	+	23.6579i	1.15053	+	0.835911i
$802$			5.93958i			0.209734i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	25.5279	−	78.5667i	0.899181	−	2.76739i
$807$		0			0
$808$		0			0
$809$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$809$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$810$	−25.4200	+	8.25944i	−0.893166	+	0.290207i
$811$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$811$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	72.5410	−	52.7041i	2.53479	−	1.84163i
$820$		0			0
$821$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$821$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$822$		0			0
$823$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$823$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$824$		0			0
$825$		0			0
$826$	−22.8328			−0.794455
$827$	−13.0869	+	18.0125i	−0.455075	+	0.626357i	−0.973478	−	0.228779i	$-0.926527\pi$
$827$	−13.0869	+	18.0125i	−0.455075	+	0.626357i	0.518404	+	0.855136i	$0.326527\pi$
$828$		0			0
$829$	−6.90983	−	21.2663i	−0.239988	−	0.738608i	−0.996420	−	0.0845359i	$-0.973059\pi$
$829$	−6.90983	−	21.2663i	−0.239988	−	0.738608i	0.756432	−	0.654072i	$-0.226941\pi$
$830$	43.7426	−	31.7809i	1.51833	−	1.10313i
$831$		0			0
$832$	57.5945	−	18.7136i	1.99673	−	0.648777i
$833$	−17.9116	−	5.81983i	−0.620599	−	0.201645i
$834$		0			0
$835$		−	52.5897i		−	1.81994i
$836$		0			0
$837$		0			0
$838$	−27.9296	+	38.4418i	−0.964812	+	1.32795i
$839$	−17.3050	+	53.2592i	−0.597433	+	1.83871i	−0.0552123	+	0.998475i	$0.517584\pi$
$839$	−17.3050	+	53.2592i	−0.597433	+	1.83871i	−0.542221	+	0.840236i	$0.682416\pi$
$840$		0			0
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$	24.4384	+	33.6366i	0.842203	+	1.15919i
$843$		0			0
$844$		0			0
$845$	−63.9681	−	46.4755i	−2.20057	−	1.59881i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	3.36881	−	10.3681i	0.115549	−	0.355624i
$851$		0			0
$852$		0			0
$853$	−32.4727	−	44.6949i	−1.11185	−	1.53032i	−0.818669	−	0.574266i	$-0.805288\pi$
$853$	−32.4727	−	44.6949i	−1.11185	−	1.53032i	−0.293177	−	0.956058i	$-0.594712\pi$
$854$		0			0
$855$		0			0
$856$	18.2148	+	13.2338i	0.622568	+	0.452322i
$857$			25.4000i			0.867647i	0.900998	+	0.433824i	$0.142836\pi$
$857$			25.4000i			0.867647i	−0.900998	+	0.433824i	$0.857164\pi$
$858$		0			0
$859$	35.7771			1.22070			0.610349	−	0.792132i	$-0.291029\pi$
$859$	35.7771			1.22070			0.610349	+	0.792132i	$0.291029\pi$
$860$	−0.314801	+	0.433287i	−0.0107346	+	0.0147750i
$861$		0			0
$862$		0			0
$863$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$863$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$864$		0			0
$865$	−51.3493	+	16.6844i	−1.74593	+	0.567286i
$866$		0			0
$867$		0			0
$868$			9.07487i			0.308021i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.2444	+	38.8751i	0.954835	+	1.31422i
$876$		0			0
$877$	−42.4370	−	13.7886i	−1.43300	−	0.465608i	−0.513289	−	0.858216i	$-0.671573\pi$
$877$	−42.4370	−	13.7886i	−1.43300	−	0.465608i	−0.919706	+	0.392608i	$0.871573\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	26.8674	−	36.9798i	0.904671	−	1.24517i
$883$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$883$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$884$	−0.832816	−	2.56314i	−0.0280106	−	0.0862078i
$885$		0			0
$886$		0			0
$887$	−55.0683	+	17.8928i	−1.84901	+	0.600780i	−0.851998	+	0.523545i	$0.824609\pi$
$887$	−55.0683	+	17.8928i	−1.84901	+	0.600780i	−0.997013	+	0.0772356i	$0.975391\pi$
$888$		0			0
$889$	−51.8885	−	37.6992i	−1.74029	−	1.26439i
$890$		−	39.8439i		−	1.33557i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	12.3607	+	38.0423i	0.413172	+	1.27161i
$896$	30.9787	−	22.5074i	1.03493	−	0.751918i
$897$		0			0
$898$	−50.8399	+	16.5189i	−1.69655	+	0.551242i
$899$		0			0
$900$	−2.86475	−	2.08136i	−0.0954915	−	0.0693786i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.09017	−	9.51057i	0.102721	−	0.316142i
$906$		0			0
$907$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$907$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$908$	2.24469	+	3.08955i	0.0744926	+	0.102530i
$909$		0			0
$910$	−84.4184	−	27.4292i	−2.79844	−	0.909269i
$911$	−7.23607	−	5.25731i	−0.239742	−	0.174182i	0.461427	−	0.887178i	$-0.347338\pi$
$911$	−7.23607	−	5.25731i	−0.239742	−	0.174182i	−0.701168	+	0.712996i	$0.747338\pi$
$912$		0			0
$913$		0			0
$914$	29.3738			0.971600
$915$		0			0
$916$	0.437694	−	1.34708i	0.0144618	−	0.0445089i
$917$		0			0
$918$		0			0
$919$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$919$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			55.6335i			1.83120i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.3262	−	8.22899i	0.371602	−	0.269985i	−0.386273	−	0.922384i	$-0.626238\pi$
$929$	11.3262	−	8.22899i	0.371602	−	0.269985i	0.757875	+	0.652400i	$0.226238\pi$
$930$		0			0
$931$		0			0
$932$	−5.87667	−	1.90945i	−0.192497	−	0.0625460i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	61.9574			2.02514
$937$	35.5954	−	48.9928i	1.16285	−	1.60053i	0.462732	−	0.886498i	$-0.346869\pi$
$937$	35.5954	−	48.9928i	1.16285	−	1.60053i	0.700117	−	0.714028i	$-0.253131\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$941$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$942$		0			0
$943$		0			0
$944$	−11.2361	−	8.16348i	−0.365703	−	0.265699i
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	26.3607	−	81.1298i	0.855704	−	2.63359i
$950$		0			0
$951$		0			0
$952$	−12.3165	−	16.9522i	−0.399179	−	0.549423i
$953$	−31.8764	+	10.3573i	−1.03258	+	0.335505i	−0.775809	−	0.630968i	$-0.782658\pi$
$953$	−31.8764	+	10.3573i	−1.03258	+	0.335505i	−0.256768	+	0.966473i	$0.582658\pi$
$954$		0			0
$955$	48.5410	+	35.2671i	1.57075	+	1.14122i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1418	+	46.6018i	0.488446	+	1.50328i
$962$		0			0
$963$	13.3684	+	18.4001i	0.430792	+	0.592934i
$964$		0			0
$965$	40.0515	+	13.0135i	1.28930	+	0.418920i
$966$		0			0
$967$			8.83536i			0.284126i	0.989858	+	0.142063i	$0.0453736\pi$
$967$			8.83536i			0.284126i	−0.989858	+	0.142063i	$0.954626\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−5.52786	+	17.0130i	−0.177398	+	0.545974i	−0.999735	−	0.0230267i	$-0.992670\pi$
$971$	−5.52786	+	17.0130i	−0.177398	+	0.545974i	0.822337	+	0.569000i	$0.192670\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$977$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$978$		0			0
$979$		0			0
$980$	6.05573			0.193443
$981$		0			0
$982$		0			0
$983$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$983$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$984$		0			0
$985$	23.1049	+	31.8011i	0.736182	+	1.01327i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−62.6099			−1.98887			−0.994435	−	0.105356i	$-0.966402\pi$
$991$	−62.6099			−1.98887			−0.994435	+	0.105356i	$0.966402\pi$
$992$	−6.98240	+	9.61045i	−0.221691	+	0.305132i
$993$		0			0
$994$	14.1115	+	43.4306i	0.447588	+	1.37753i
$995$	43.4164	−	31.5439i	1.37639	−	1.00001i
$996$		0			0
$997$	23.7012	−	7.70100i	0.750626	−	0.243893i	0.0913754	−	0.995817i	$-0.470874\pi$
$997$	23.7012	−	7.70100i	0.750626	−	0.243893i	0.659250	+	0.751923i	$0.270874\pi$
$998$	5.05251	+	1.64166i	0.159934	+	0.0519658i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.c.444.1		8
5.4	even	2	inner	605.2.j.c.444.2		8
11.2	odd	10		605.2.j.a.269.1		8
11.3	even	5	inner	605.2.j.c.124.2		8
11.4	even	5		605.2.j.a.9.1		8
11.5	even	5		605.2.b.b.364.2	✓	4
11.6	odd	10		605.2.b.b.364.3	yes	4
11.7	odd	10		605.2.j.a.9.2		8
11.8	odd	10	inner	605.2.j.c.124.1		8
11.9	even	5		605.2.j.a.269.2		8
11.10	odd	2	inner	605.2.j.c.444.2		8
55.4	even	10		605.2.j.a.9.2		8
55.9	even	10		605.2.j.a.269.1		8
55.14	even	10	inner	605.2.j.c.124.1		8
55.17	even	20		3025.2.a.bb.1.2		4
55.19	odd	10	inner	605.2.j.c.124.2		8
55.24	odd	10		605.2.j.a.269.2		8
55.27	odd	20		3025.2.a.bb.1.3		4
55.28	even	20		3025.2.a.bb.1.3		4
55.29	odd	10		605.2.j.a.9.1		8
55.38	odd	20		3025.2.a.bb.1.2		4
55.39	odd	10		605.2.b.b.364.2	✓	4
55.49	even	10		605.2.b.b.364.3	yes	4
55.54	odd	2	CM	605.2.j.c.444.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.b.364.2	✓	4	11.5	even	5
605.2.b.b.364.2	✓	4	55.39	odd	10
605.2.b.b.364.3	yes	4	11.6	odd	10
605.2.b.b.364.3	yes	4	55.49	even	10
605.2.j.a.9.1		8	11.4	even	5
605.2.j.a.9.1		8	55.29	odd	10
605.2.j.a.9.2		8	11.7	odd	10
605.2.j.a.9.2		8	55.4	even	10
605.2.j.a.269.1		8	11.2	odd	10
605.2.j.a.269.1		8	55.9	even	10
605.2.j.a.269.2		8	11.9	even	5
605.2.j.a.269.2		8	55.24	odd	10
605.2.j.c.124.1		8	11.8	odd	10	inner
605.2.j.c.124.1		8	55.14	even	10	inner
605.2.j.c.124.2		8	11.3	even	5	inner
605.2.j.c.124.2		8	55.19	odd	10	inner
605.2.j.c.444.1		8	1.1	even	1	trivial
605.2.j.c.444.1		8	55.54	odd	2	CM
605.2.j.c.444.2		8	5.4	even	2	inner
605.2.j.c.444.2		8	11.10	odd	2	inner
3025.2.a.bb.1.2		4	55.17	even	20
3025.2.a.bb.1.2		4	55.38	odd	20
3025.2.a.bb.1.3		4	55.27	odd	20
3025.2.a.bb.1.3		4	55.28	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.780656 + 1.07448i) q^{2} +(0.0729490 + 0.224514i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-4.08757 + 1.32813i) q^{7} +(-2.82444 - 0.917716i) q^{8} +(-2.42705 - 1.76336i) q^{9} +O(q^{10})\)	\(q+(-0.780656 + 1.07448i) q^{2} +(0.0729490 + 0.224514i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-4.08757 + 1.32813i) q^{7} +(-2.82444 - 0.917716i) q^{8} +(-2.42705 - 1.76336i) q^{9} +2.96979i q^{10} +(4.08757 - 5.62605i) q^{13} +(1.76393 - 5.42882i) q^{14} +(2.80902 - 2.04087i) q^{16} +(-0.964944 - 1.32813i) q^{17} +(3.78938 - 1.23125i) q^{18} +(0.427051 + 0.310271i) q^{20} +(1.54508 - 4.75528i) q^{25} +(2.85410 + 8.78402i) q^{26} +(-0.596368 - 0.820830i) q^{28} +(-7.23607 - 5.25731i) q^{31} -1.32813i q^{32} +2.18034 q^{34} +(-5.64888 + 7.77501i) q^{35} +(0.218847 - 0.673542i) q^{36} +(-6.31564 + 2.05208i) q^{40} +1.01460i q^{43} -6.70820 q^{45} +(9.28115 - 6.74315i) q^{49} +(3.90328 + 5.37240i) q^{50} +(1.56131 + 0.507301i) q^{52} +12.7639 q^{56} +(-1.23607 - 3.80423i) q^{59} +(11.2978 - 3.67086i) q^{62} +(12.2627 + 3.98439i) q^{63} +(7.04508 + 5.11855i) q^{64} -15.5500i q^{65} +(0.227792 - 0.313529i) q^{68} +(-3.94427 - 12.1392i) q^{70} +(-6.47214 + 4.70228i) q^{71} +(5.23680 + 7.20783i) q^{72} +(11.6663 - 3.79062i) q^{73} +(2.39919 - 7.38394i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-10.7014 - 14.7292i) q^{83} +(-3.49120 - 1.13436i) q^{85} +(-1.09017 - 0.792055i) q^{86} -13.4164 q^{89} +(5.23680 - 7.20783i) q^{90} +(-9.23607 + 28.4257i) q^{91} +15.2365i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9	\( 8 q + 14 q^{4} + 10 q^{5} - 6 q^{9} + 32 q^{14} + 18 q^{16} - 10 q^{20} - 10 q^{25} - 4 q^{26} - 40 q^{31} - 72 q^{34} + 42 q^{36} + 34 q^{49} + 120 q^{56} + 8 q^{59} + 34 q^{64} + 40 q^{70} - 16 q^{71} - 30 q^{80} - 18 q^{81} + 36 q^{86} - 56 q^{91}+O(q^{100}) \) 8 * q + 14 * q^4 + 10 * q^5 - 6 * q^9 + 32 * q^14 + 18 * q^16 - 10 * q^20 - 10 * q^25 - 4 * q^26 - 40 * q^31 - 72 * q^34 + 42 * q^36 + 34 * q^49 + 120 * q^56 + 8 * q^59 + 34 * q^64 + 40 * q^70 - 16 * q^71 - 30 * q^80 - 18 * q^81 + 36 * q^86 - 56 * q^91

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