LMFDB - Embedded newform 605.2.j.a.124.1

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			124.1
Root			$-1.46782 - 0.476925i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.a.444.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46782 - 2.02029i) q^{2} +(-1.30902 + 4.02874i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(2.93565 + 0.953850i) q^{7} +(5.31064 - 1.72553i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})$	\(q+(-1.46782 - 2.02029i) q^{2} +(-1.30902 + 4.02874i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(2.93565 + 0.953850i) q^{7} +(5.31064 - 1.72553i) q^{8} +(-2.42705 + 1.76336i) q^{9} +5.58394i q^{10} +(1.12132 + 1.54336i) q^{13} +(-2.38197 - 7.33094i) q^{14} +(-4.42705 - 3.21644i) q^{16} +(4.74998 - 6.53779i) q^{17} +(7.12497 + 2.31504i) q^{18} +(7.66312 - 5.56758i) q^{20} +(1.54508 + 4.75528i) q^{25} +(1.47214 - 4.53077i) q^{26} +(-7.68563 + 10.5784i) q^{28} +(7.23607 - 5.25731i) q^{31} +2.49721i q^{32} -20.1803 q^{34} +(-4.05697 - 5.58394i) q^{35} +(-3.92705 - 12.0862i) q^{36} +(-11.8749 - 3.85840i) q^{40} -13.0756i q^{43} +6.70820 q^{45} +(2.04508 + 1.48584i) q^{49} +(7.33912 - 10.1014i) q^{50} +(-7.68563 + 2.49721i) q^{52} +17.2361 q^{56} +(-1.23607 + 3.80423i) q^{59} +(-21.2426 - 6.90212i) q^{62} +(-8.80695 + 2.86155i) q^{63} +(-3.80902 + 2.76741i) q^{64} -4.26575i q^{65} +(20.1212 + 27.6945i) q^{68} +(-5.32624 + 16.3925i) q^{70} +(-6.47214 - 4.70228i) q^{71} +(-9.84647 + 13.5525i) q^{72} +(11.3143 + 3.67624i) q^{73} +(3.78115 + 11.6372i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-0.428305 + 0.589512i) q^{83} +(-17.1856 + 5.58394i) q^{85} +(-26.4164 + 19.1926i) q^{86} +13.4164 q^{89} +(-9.84647 - 13.5525i) q^{90} +(1.81966 + 5.60034i) q^{91} -6.31261i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 10 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q - 6 * q^4 - 10 * q^5 - 6 * q^9	$ 8 q - 6 q^{4} - 10 q^{5} - 6 q^{9} - 28 q^{14} - 22 q^{16} + 30 q^{20} - 10 q^{25} - 24 q^{26} + 40 q^{31} - 72 q^{34} - 18 q^{36} - 6 q^{49} + 120 q^{56} + 8 q^{59} - 26 q^{64} + 20 q^{70} - 16 q^{71} - 10 q^{80} - 18 q^{81} - 104 q^{86} + 104 q^{91}+O(q^{100}) $ 8 * q - 6 * q^4 - 10 * q^5 - 6 * q^9 - 28 * q^14 - 22 * q^16 + 30 * q^20 - 10 * q^25 - 24 * q^26 + 40 * q^31 - 72 * q^34 - 18 * q^36 - 6 * q^49 + 120 * q^56 + 8 * q^59 - 26 * q^64 + 20 * q^70 - 16 * q^71 - 10 * q^80 - 18 * q^81 - 104 * q^86 + 104 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.46782	−	2.02029i	−1.03791	−	1.42856i	−0.898841	−	0.438276i	$-0.855589\pi$
$2$	−1.46782	−	2.02029i	−1.03791	−	1.42856i	−0.139068	−	0.990283i	$-0.544411\pi$
$3$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$3$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$4$	−1.30902	+	4.02874i	−0.654508	+	2.01437i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$		0			0
$7$	2.93565	+	0.953850i	1.10957	+	0.360521i	0.805779	−	0.592217i	$-0.201747\pi$
$7$	2.93565	+	0.953850i	1.10957	+	0.360521i	0.303792	+	0.952738i	$0.401747\pi$
$8$	5.31064	−	1.72553i	1.87759	−	0.610067i
$9$	−2.42705	+	1.76336i	−0.809017	+	0.587785i
$10$			5.58394i			1.76580i
$11$		0			0
$11$		0			0
$12$		0			0
$13$	1.12132	+	1.54336i	0.310998	+	0.428052i	0.935692	−	0.352818i	$-0.114776\pi$
$13$	1.12132	+	1.54336i	0.310998	+	0.428052i	−0.624694	+	0.780869i	$0.714776\pi$
$14$	−2.38197	−	7.33094i	−0.636607	−	1.95928i
$15$		0			0
$16$	−4.42705	−	3.21644i	−1.10676	−	0.804110i
$17$	4.74998	−	6.53779i	1.15204	−	1.58565i	0.414960	−	0.909840i	$-0.363796\pi$
$17$	4.74998	−	6.53779i	1.15204	−	1.58565i	0.737079	−	0.675806i	$-0.236204\pi$
$18$	7.12497	+	2.31504i	1.67937	+	0.545661i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	7.66312	−	5.56758i	1.71353	−	1.24495i
$21$		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
$26$	1.47214	−	4.53077i	0.288710	−	0.888557i
$27$		0			0
$28$	−7.68563	+	10.5784i	−1.45245	+	1.99912i
$29$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$29$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$30$		0			0
$31$	7.23607	−	5.25731i	1.29964	−	0.944241i	0.299684	−	0.954038i	$-0.403119\pi$
$31$	7.23607	−	5.25731i	1.29964	−	0.944241i	0.999952	+	0.00979752i	$0.00311870\pi$
$32$			2.49721i			0.441449i
$33$		0			0
$34$	−20.1803			−3.46090
$35$	−4.05697	−	5.58394i	−0.685753	−	0.943857i
$36$	−3.92705	−	12.0862i	−0.654508	−	2.01437i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$		0			0
$39$		0			0
$40$	−11.8749	−	3.85840i	−1.87759	−	0.610067i
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$		−	13.0756i		−	1.99401i	−0.0773627	−	0.997003i	$-0.524650\pi$
$43$		−	13.0756i		−	1.99401i	0.0773627	−	0.997003i	$-0.475350\pi$
$44$		0			0
$45$	6.70820			1.00000
$46$		0			0
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$		0			0
$49$	2.04508	+	1.48584i	0.292155	+	0.212263i
$50$	7.33912	−	10.1014i	1.03791	−	1.42856i
$51$		0			0
$52$	−7.68563	+	2.49721i	−1.06580	+	0.346301i
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$		0			0
$55$		0			0
$56$	17.2361			2.30327
$57$		0			0
$58$		0			0
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	−0.998713	−	0.0507240i	$-0.983847\pi$
$59$	−1.23607	+	3.80423i	−0.160922	+	0.495268i	0.837790	+	0.545992i	$0.183847\pi$
$60$		0			0
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	−21.2426	−	6.90212i	−2.69781	−	0.876571i
$63$	−8.80695	+	2.86155i	−1.10957	+	0.360521i
$64$	−3.80902	+	2.76741i	−0.476127	+	0.345927i
$65$		−	4.26575i		−	0.529101i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	20.1212	+	27.6945i	2.44006	+	3.35845i
$69$		0			0
$70$	−5.32624	+	16.3925i	−0.636607	+	1.95928i
$71$	−6.47214	−	4.70228i	−0.768101	−	0.558058i	0.133283	−	0.991078i	$-0.457448\pi$
$71$	−6.47214	−	4.70228i	−0.768101	−	0.558058i	−0.901384	+	0.433020i	$0.857448\pi$
$72$	−9.84647	+	13.5525i	−1.16042	+	1.59718i
$73$	11.3143	+	3.67624i	1.32424	+	0.430271i	0.883948	−	0.467585i	$-0.154876\pi$
$73$	11.3143	+	3.67624i	1.32424	+	0.430271i	0.440289	+	0.897856i	$0.354876\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$	3.78115	+	11.6372i	0.422746	+	1.30108i
$81$	2.78115	−	8.55951i	0.309017	−	0.951057i
$82$		0			0
$83$	−0.428305	+	0.589512i	−0.0470126	+	0.0647073i	−0.831876	−	0.554961i	$-0.812733\pi$
$83$	−0.428305	+	0.589512i	−0.0470126	+	0.0647073i	0.784863	+	0.619669i	$0.212733\pi$
$84$		0			0
$85$	−17.1856	+	5.58394i	−1.86404	+	0.605663i
$86$	−26.4164	+	19.1926i	−2.84855	+	2.06960i
$87$		0			0
$88$		0			0
$89$	13.4164			1.42214			0.711068	−	0.703123i	$-0.248212\pi$
$89$	13.4164			1.42214			0.711068	+	0.703123i	$0.248212\pi$
$90$	−9.84647	−	13.5525i	−1.03791	−	1.42856i
$91$	1.81966	+	5.60034i	0.190752	+	0.587075i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$		−	6.31261i		−	0.637670i
$99$		0			0
$100$	−21.1803			−2.11803
$101$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$101$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	8.61803	+	6.26137i	0.845068	+	0.613978i
$105$		0			0
$106$		0			0
$107$	18.3069	−	5.94827i	1.76980	−	0.575041i	0.771657	−	0.636038i	$-0.219428\pi$
$107$	18.3069	−	5.94827i	1.76980	−	0.575041i	0.998138	+	0.0609970i	$0.0194280\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	−9.92826	−	13.6651i	−0.938133	−	1.29123i
$113$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$113$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.44299	−	1.76854i	−0.503205	−	0.163501i
$118$	9.49996	−	3.08672i	0.874542	−	0.284156i
$119$	20.1803	−	14.6619i	1.84993	−	1.34405i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	11.7082	+	36.0341i	1.05143	+	3.23596i
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	18.7082	+	13.5923i	1.66666	+	1.21090i
$127$	9.92826	−	13.6651i	0.880991	−	1.21258i	−0.0951544	−	0.995463i	$-0.530334\pi$
$127$	9.92826	−	13.6651i	0.880991	−	1.21258i	0.976145	−	0.217118i	$-0.0696655\pi$
$128$	15.9319	+	5.17659i	1.40820	+	0.457551i
$129$		0			0
$130$	−8.61803	+	6.26137i	−0.755852	+	0.549158i
$131$		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
$136$	13.9443	−	42.9161i	1.19571	−	3.68002i
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	27.8069	−	9.03500i	2.35011	−	0.763597i
$141$		0			0
$142$			19.9777i			1.67649i
$143$		0			0
$144$	16.4164			1.36803
$145$		0			0
$146$	−9.18034	−	28.2542i	−0.759770	−	2.33833i
$147$		0			0
$148$		0			0
$149$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$149$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$150$		0			0
$151$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$151$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$152$		0			0
$153$			24.2434i			1.95997i
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$		0			0
$159$		0			0
$160$	3.28216	−	4.51750i	0.259477	−	0.357140i
$161$		0			0
$162$	−21.3749	+	6.94513i	−1.67937	+	0.545661i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$		0			0
$166$	1.81966			0.141233
$167$	6.29960	+	8.67066i	0.487478	+	0.670956i	0.979920	−	0.199389i	$-0.0638958\pi$
$167$	6.29960	+	8.67066i	0.487478	+	0.670956i	−0.492442	+	0.870345i	$0.663896\pi$
$168$		0			0
$169$	2.89261	−	8.90254i	0.222508	−	0.684810i
$170$	36.5066	+	26.5236i	2.79993	+	2.03427i
$171$		0			0
$172$	52.6781	+	17.1161i	4.01667	+	1.30509i
$173$	9.92826	−	3.22589i	0.754832	−	0.245260i	0.0937729	−	0.995594i	$-0.470107\pi$
$173$	9.92826	−	3.22589i	0.754832	−	0.245260i	0.661059	+	0.750334i	$0.270107\pi$
$174$		0			0
$175$			15.4336i			1.16667i
$176$		0			0
$177$		0			0
$178$	−19.6929	−	27.1050i	−1.47605	−	2.03161i
$179$	5.52786	+	17.0130i	0.413172	+	1.27161i	0.913876	+	0.405994i	$0.133075\pi$
$179$	5.52786	+	17.0130i	0.413172	+	1.27161i	−0.500704	+	0.865619i	$0.666925\pi$
$180$	−8.78115	+	27.0256i	−0.654508	+	2.01437i
$181$	−3.61803	−	2.62866i	−0.268926	−	0.195386i	0.445147	−	0.895458i	$-0.353152\pi$
$181$	−3.61803	−	2.62866i	−0.268926	−	0.195386i	−0.714073	+	0.700071i	$0.753152\pi$
$182$	8.64335	−	11.8965i	0.640688	−	0.881831i
$183$		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	−0.0717497	+	0.997423i	$0.522858\pi$
$191$	−8.29180	+	25.5195i	−0.599973	+	1.84653i	−0.528224	+	0.849105i	$0.677142\pi$
$192$		0			0
$193$	−12.0073	+	16.5266i	−0.864305	+	1.18961i	0.116221	+	0.993223i	$0.462922\pi$
$193$	−12.0073	+	16.5266i	−0.864305	+	1.18961i	−0.980526	+	0.196390i	$0.937078\pi$
$194$		0			0
$195$		0			0
$196$	−8.66312	+	6.29412i	−0.618794	+	0.449580i
$197$		−	21.8854i		−	1.55927i	−0.626234	−	0.779635i	$-0.715405\pi$
$197$		−	21.8854i		−	1.55927i	0.626234	−	0.779635i	$-0.284595\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	16.4108	+	22.5875i	1.16042	+	1.59718i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		−	10.4392i		−	0.723828i
$209$		0			0
$210$		0			0
$211$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$211$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$212$		0			0
$213$		0			0
$214$	−38.8885	−	28.2542i	−2.65837	−	1.93142i
$215$	−17.1856	+	23.6539i	−1.17205	+	1.61318i
$216$		0			0
$217$	26.2572	−	8.53149i	1.78246	−	0.579156i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.4164			1.03702
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$	−2.38197	+	7.33094i	−0.159152	+	0.489819i
$225$	−12.1353	−	8.81678i	−0.809017	−	0.587785i
$226$		0			0
$227$	−24.1782	−	7.85597i	−1.60476	−	0.521419i	−0.636484	−	0.771290i	$-0.719612\pi$
$227$	−24.1782	−	7.85597i	−1.60476	−	0.521419i	−0.968279	+	0.249870i	$0.919612\pi$
$228$		0			0
$229$	−4.85410	+	3.52671i	−0.320768	+	0.233052i	−0.736503	−	0.676434i	$-0.763524\pi$
$229$	−4.85410	+	3.52671i	−0.320768	+	0.233052i	0.415735	+	0.909486i	$0.363524\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.23525	−	12.7112i	−0.605021	−	0.832741i	0.391135	−	0.920333i	$-0.372083\pi$
$233$	−9.23525	−	12.7112i	−0.605021	−	0.832741i	−0.996156	+	0.0875928i	$0.972083\pi$
$234$	4.41641	+	13.5923i	0.288710	+	0.888557i
$235$		0			0
$236$	−13.7082	−	9.95959i	−0.892328	−	0.648314i
$237$		0			0
$238$	−59.2424	−	19.2490i	−3.84011	−	1.24773i
$239$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$239$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$240$		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
$245$	−1.74671	−	5.37582i	−0.111593	−	0.343449i
$246$		0			0
$247$		0			0
$248$	29.3565	−	40.4057i	1.86414	−	2.56577i
$249$		0			0
$250$	−26.5532	+	8.62766i	−1.67937	+	0.545661i
$251$	−22.6525	+	16.4580i	−1.42981	+	1.03882i	−0.439760	+	0.898115i	$0.644936\pi$
$251$	−22.6525	+	16.4580i	−1.42981	+	1.03882i	−0.990052	+	0.140704i	$0.955064\pi$
$252$		−	39.2267i		−	2.47105i
$253$		0			0
$254$	−42.1803			−2.64663
$255$		0			0
$256$	−10.0172	−	30.8298i	−0.626076	−	1.92686i
$257$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$257$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$		0			0
$260$	17.1856	+	5.58394i	1.06580	+	0.346301i
$261$		0			0
$262$		0			0
$263$			4.54408i			0.280200i	0.990137	+	0.140100i	$0.0447424\pi$
$263$			4.54408i			0.280200i	−0.990137	+	0.140100i	$0.955258\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.3262	+	8.22899i	0.690573	+	0.501731i	0.876848	−	0.480767i	$-0.159642\pi$
$269$	11.3262	+	8.22899i	0.690573	+	0.501731i	−0.186275	+	0.982498i	$0.559642\pi$
$270$		0			0
$271$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$271$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$272$	−42.0568	+	13.6651i	−2.55007	+	0.828567i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	17.8786	+	24.6078i	1.07422	+	1.47854i	0.865728	+	0.500514i	$0.166856\pi$
$277$	17.8786	+	24.6078i	1.07422	+	1.47854i	0.208493	+	0.978024i	$0.433144\pi$
$278$		0			0
$279$	−8.29180	+	25.5195i	−0.496417	+	1.52781i
$280$	−31.1803	−	22.6538i	−1.86338	−	1.35383i
$281$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$281$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$282$		0			0
$283$	−25.5642	+	8.30632i	−1.51964	+	0.493760i	−0.945672	−	0.325121i	$-0.894595\pi$
$283$	−25.5642	+	8.30632i	−1.51964	+	0.493760i	−0.573963	+	0.818881i	$0.694595\pi$
$284$	27.4164	−	19.9192i	1.62686	−	1.18199i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.40347	−	6.06086i	−0.259477	−	0.357140i
$289$	−14.9271	−	45.9407i	−0.878062	−	2.70240i
$290$		0			0
$291$		0			0
$292$	−29.6212	+	40.7701i	−1.73345	+	2.38589i
$293$	−32.5568	−	10.5784i	−1.90199	−	0.617994i	−0.954494	−	0.298231i	$-0.903603\pi$
$293$	−32.5568	−	10.5784i	−1.90199	−	0.617994i	−0.947497	−	0.319763i	$-0.896397\pi$
$294$		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
$301$	12.4721	−	38.3853i	0.718882	−	2.21249i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	48.9787	−	35.5851i	2.79993	−	2.03427i
$307$			33.0533i			1.88645i	0.332155	+	0.943225i	$0.392224\pi$
$307$			33.0533i			1.88645i	−0.332155	+	0.943225i	$0.607776\pi$
$308$		0			0
$309$		0			0
$310$	29.3565	+	40.4057i	1.66734	+	2.29489i
$311$	9.88854	+	30.4338i	0.560728	+	1.72574i	0.680316	+	0.732919i	$0.261843\pi$
$311$	9.88854	+	30.4338i	0.560728	+	1.72574i	−0.119588	+	0.992824i	$0.538157\pi$
$312$		0			0
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$		0			0
$315$	19.6929	+	6.39862i	1.10957	+	0.360521i
$316$		0			0
$317$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$317$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$	10.5279			0.588525
$321$		0			0
$322$		0			0
$323$		0			0
$324$	30.8435	+	22.4091i	1.71353	+	1.24495i
$325$	−5.60659	+	7.71681i	−0.310998	+	0.428052i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−35.7771			−1.96649			−0.983243	−	0.182298i	$-0.941646\pi$
$331$	−35.7771			−1.96649			−0.983243	+	0.182298i	$0.941646\pi$
$332$	−1.81433	−	2.49721i	−0.0995743	−	0.137052i
$333$		0			0
$334$	8.27051	−	25.4540i	0.452542	−	1.39278i
$335$		0			0
$336$		0			0
$337$	−15.7996	−	5.13359i	−0.860657	−	0.279644i	−0.154754	−	0.987953i	$-0.549459\pi$
$337$	−15.7996	−	5.13359i	−0.860657	−	0.279644i	−0.705903	+	0.708309i	$0.749459\pi$
$338$	−22.2315	+	7.22346i	−1.20924	+	0.392904i
$339$		0			0
$340$		−	76.5457i		−	4.15128i
$341$		0			0
$342$		0			0
$343$	−8.11393	−	11.1679i	−0.438111	−	0.603008i
$344$	−22.5623	−	69.4396i	−1.21648	−	3.74393i
$345$		0			0
$346$	−21.0902	−	15.3229i	−1.13381	−	0.823764i
$347$	−6.82902	+	9.39934i	−0.366601	+	0.504583i	−0.951973	−	0.306182i	$-0.900948\pi$
$347$	−6.82902	+	9.39934i	−0.366601	+	0.504583i	0.585372	+	0.810765i	$0.300948\pi$
$348$		0			0
$349$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$349$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$350$	31.1803	−	22.6538i	1.66666	−	1.21090i
$351$		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
$356$	−17.5623	+	54.0512i	−0.930800	+	2.86471i
$357$		0			0
$358$	26.2572	−	36.1400i	1.38774	−	1.91006i
$359$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$359$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$360$	35.6248	−	11.5752i	1.87759	−	0.610067i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$			11.1679i			0.586970i
$363$		0			0
$364$	−24.9443			−1.30744
$365$	−15.6360	−	21.5211i	−0.818424	−	1.12646i
$366$		0			0
$367$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$367$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$			6.62379i			0.342967i	0.985187	+	0.171484i	$0.0548560\pi$
$373$			6.62379i			0.342967i	−0.985187	+	0.171484i	$0.945144\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	29.1246	+	21.1603i	1.49603	+	1.08693i	0.971929	+	0.235274i	$0.0755989\pi$
$379$	29.1246	+	21.1603i	1.49603	+	1.08693i	0.524102	+	0.851656i	$0.324401\pi$
$380$		0			0
$381$		0			0
$382$	63.7277	−	20.7064i	3.26059	−	1.05943i
$383$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$383$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$384$		0			0
$385$		0			0
$386$	51.0132			2.59650
$387$	23.0569	+	31.7351i	1.17205	+	1.61318i
$388$		0			0
$389$	−8.03444	+	24.7275i	−0.407362	+	1.25373i	0.511544	+	0.859257i	$0.329074\pi$
$389$	−8.03444	+	24.7275i	−0.407362	+	1.25373i	−0.918906	+	0.394475i	$0.870926\pi$
$390$		0			0
$391$		0			0
$392$	13.4246	+	4.36191i	0.678043	+	0.220310i
$393$		0			0
$394$	−44.2148	+	32.1239i	−2.22751	+	1.61838i
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−35.2278	−	48.4869i	−1.76581	−	2.43043i
$399$		0			0
$400$	8.45492	−	26.0216i	0.422746	−	1.30108i
$401$	−3.61803	−	2.62866i	−0.180676	−	0.131269i	0.493771	−	0.869592i	$-0.335618\pi$
$401$	−3.61803	−	2.62866i	−0.180676	−	0.131269i	−0.674447	+	0.738323i	$0.735618\pi$
$402$		0			0
$403$	16.2279	+	5.27275i	0.808368	+	0.262655i
$404$		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	$-0.700000\pi$
$409$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.25732	+	9.98885i	−0.357110	+	0.491519i
$414$		0			0
$415$	1.54962	−	0.503503i	0.0760680	−	0.0247160i
$416$	−3.85410	+	2.80017i	−0.188963	+	0.137290i
$417$		0			0
$418$		0			0
$419$	−35.7771			−1.74783			−0.873913	−	0.486083i	$-0.838425\pi$
$419$	−35.7771			−1.74783			−0.873913	+	0.486083i	$0.838425\pi$
$420$		0			0
$421$	−9.67376	−	29.7728i	−0.471470	−	1.45104i	−0.850659	−	0.525717i	$-0.823797\pi$
$421$	−9.67376	−	29.7728i	−0.471470	−	1.45104i	0.379189	−	0.925319i	$-0.376203\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	38.4281	+	12.4861i	1.86404	+	0.605663i
$426$		0			0
$427$		0			0
$428$			81.5402i			3.94139i
$429$		0			0
$430$	73.0132			3.52101
$431$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$431$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$432$		0			0
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$	−55.7771	−	40.5244i	−2.67739	−	1.94523i
$435$		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
$441$	−7.58359			−0.361123
$442$	−22.6286	−	31.1456i	−1.07633	−	1.48144i
$443$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$443$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$	−24.2705	−	17.6336i	−1.15053	−	0.835911i
$446$		0			0
$447$		0			0
$448$	−13.8216	+	4.49092i	−0.653011	+	0.212176i
$449$	−32.5623	+	23.6579i	−1.53671	+	1.11649i	−0.584353	+	0.811499i	$0.698652\pi$
$449$	−32.5623	+	23.6579i	−1.53671	+	1.11649i	−0.952357	+	0.304986i	$0.901348\pi$
$450$			37.4582i			1.76580i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	19.6180	+	60.3781i	0.920720	+	2.83368i
$455$	4.06888	−	12.5227i	0.190752	−	0.587075i
$456$		0			0
$457$	21.5073	−	29.6022i	1.00607	−	1.38473i	0.0845396	−	0.996420i	$-0.473058\pi$
$457$	21.5073	−	29.6022i	1.00607	−	1.38473i	0.921528	−	0.388313i	$-0.126942\pi$
$458$	14.2499	+	4.63009i	0.665856	+	0.216350i
$459$		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
$466$	−12.1246	+	37.3157i	−0.561662	+	1.72862i
$467$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$467$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$468$	14.2499	−	19.6134i	0.658704	−	0.906628i
$469$		0			0
$470$		0			0
$471$		0			0
$472$			22.3357i			1.02809i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	32.6525	+	100.494i	1.49662	+	4.60613i
$477$		0			0
$478$		0			0
$479$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$479$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$480$		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	$-0.600000\pi$
$487$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$488$		0			0
$489$		0			0
$490$	−8.29684	+	11.4196i	−0.374813	+	0.515886i
$491$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$491$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−48.9443			−2.19766
$497$	−14.5146	−	19.9777i	−0.651071	−	0.896122i
$498$		0			0
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	−0.974904	−	0.222626i	$-0.928537\pi$
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	0.919570	+	0.392926i	$0.128537\pi$
$500$	38.3156	+	27.8379i	1.71353	+	1.24495i
$501$		0			0
$502$	66.4997	+	21.6071i	2.96803	+	0.964371i
$503$	35.0642	−	11.3930i	1.56343	−	0.507991i	0.605712	−	0.795684i	$-0.292888\pi$
$503$	35.0642	−	11.3930i	1.56343	−	0.507991i	0.957723	+	0.287693i	$0.0928883\pi$
$504$	−41.8328	+	30.3933i	−1.86338	+	1.35383i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	42.0568	+	57.8862i	1.86597	+	2.56829i
$509$	−10.5066	−	32.3359i	−0.465696	−	1.43326i	−0.858105	−	0.513474i	$-0.828358\pi$
$509$	−10.5066	−	32.3359i	−0.465696	−	1.43326i	0.392409	−	0.919791i	$-0.371642\pi$
$510$		0			0
$511$	29.7082	+	21.5843i	1.31421	+	0.954832i
$512$	−27.8887	+	38.3855i	−1.23252	+	1.69641i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−7.36068	−	22.6538i	−0.322787	−	0.993437i
$521$	6.90983	−	21.2663i	0.302725	−	0.931692i	−0.677791	−	0.735254i	$-0.737063\pi$
$521$	6.90983	−	21.2663i	0.302725	−	0.931692i	0.980516	−	0.196438i	$-0.0629374\pi$
$522$		0			0
$523$	26.6855	−	36.7295i	1.16688	−	1.60607i	0.485235	−	0.874384i	$-0.338734\pi$
$523$	26.6855	−	36.7295i	1.16688	−	1.60607i	0.681643	−	0.731685i	$-0.261266\pi$
$524$		0			0
$525$		0			0
$526$	9.18034	−	6.66991i	0.400282	−	0.290822i
$527$		−	72.2800i		−	3.14857i
$528$		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
$535$	−40.9355	−	13.3007i	−1.76980	−	0.575041i
$536$		0			0
$537$		0			0
$538$		−	34.9610i		−	1.50727i
$539$		0			0
$540$		0			0
$541$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$541$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$542$		0			0
$543$		0			0
$544$	16.3262	+	11.8617i	0.699982	+	0.508566i
$545$		0			0
$546$		0			0
$547$	7.95034	−	2.58322i	0.339932	−	0.110451i	−0.134076	−	0.990971i	$-0.542807\pi$
$547$	7.95034	−	2.58322i	0.339932	−	0.110451i	0.474008	+	0.880520i	$0.342807\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	23.4721	−	72.2398i	0.997235	−	3.06918i
$555$		0			0
$556$		0			0
$557$	21.6709	+	7.04129i	0.918224	+	0.298349i	0.729738	−	0.683727i	$-0.239642\pi$
$557$	21.6709	+	7.04129i	0.918224	+	0.298349i	0.188486	+	0.982076i	$0.439642\pi$
$558$	63.7277	−	20.7064i	2.69781	−	0.876571i
$559$	20.1803	−	14.6619i	0.853537	−	0.620131i
$560$			37.7694i			1.59605i
$561$		0			0
$562$		0			0
$563$	−10.4577	−	14.3938i	−0.440739	−	0.606625i	0.529637	−	0.848224i	$-0.322328\pi$
$563$	−10.4577	−	14.3938i	−0.440739	−	0.606625i	−0.970376	+	0.241599i	$0.922328\pi$
$564$		0			0
$565$		0			0
$566$	54.3050	+	39.4549i	2.28261	+	1.65841i
$567$	16.3290	−	22.4749i	0.685753	−	0.943857i
$568$	−42.4851	−	13.8042i	−1.78264	−	0.579213i
$569$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$569$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$570$		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
$576$	4.36475	−	13.4333i	0.181864	−	0.559721i
$577$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$577$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$578$	−70.9032	+	97.5899i	−2.94918	+	4.05920i
$579$		0			0
$580$		0			0
$581$	−1.81966	+	1.32206i	−0.0754922	+	0.0548483i
$582$		0			0
$583$		0			0
$584$	66.4296			2.74887
$585$	7.52203	+	10.3532i	0.310998	+	0.428052i
$586$	26.4164	+	81.3013i	1.09125	+	3.35853i
$587$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$587$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$588$		0			0
$589$		0			0
$590$	−21.2426	−	6.90212i	−0.874542	−	0.284156i
$591$		0			0
$592$		0			0
$593$		−	32.7749i		−	1.34591i	−0.739686	−	0.672953i	$-0.765026\pi$
$593$		−	32.7749i		−	1.34591i	0.739686	−	0.672953i	$-0.234974\pi$
$594$		0			0
$595$	−55.7771			−2.28664
$596$		0			0
$597$		0			0
$598$		0			0
$599$	36.1803	+	26.2866i	1.47829	+	1.07404i	0.978103	+	0.208121i	$0.0667349\pi$
$599$	36.1803	+	26.2866i	1.47829	+	1.07404i	0.500186	+	0.865918i	$0.333265\pi$
$600$		0			0
$601$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$601$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$602$	−95.8562	+	31.1456i	−3.90681	+	1.26940i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−14.4135	−	19.8385i	−0.585027	−	0.805221i	0.409208	−	0.912441i	$-0.365805\pi$
$607$	−14.4135	−	19.8385i	−0.585027	−	0.805221i	−0.994235	+	0.107220i	$0.965805\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−97.6705	−	31.7351i	−3.94810	−	1.28281i
$613$	−44.2994	+	14.3938i	−1.78924	+	0.581359i	−0.999486	−	0.0320680i	$-0.989791\pi$
$613$	−44.2994	+	14.3938i	−1.78924	+	0.581359i	−0.789752	+	0.613426i	$0.789791\pi$
$614$	66.7771	−	48.5164i	2.69490	−	1.95796i
$615$		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	0.998565	+	0.0535478i	$0.0170530\pi$
$619$	5.52786	+	17.0130i	0.222184	+	0.683811i	−0.776382	+	0.630263i	$0.782947\pi$
$620$	26.1803	−	80.5748i	1.05143	−	3.23596i
$621$		0			0
$622$	46.9704	−	64.6492i	1.88334	−	2.59220i
$623$	39.3859	+	12.7972i	1.57796	+	0.512711i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−15.9787	−	49.1774i	−0.636607	−	1.95928i
$631$	−14.8328	+	45.6507i	−0.590485	+	1.81733i	−0.0144581	+	0.999895i	$0.504602\pi$
$631$	−14.8328	+	45.6507i	−0.590485	+	1.81733i	−0.576027	+	0.817431i	$0.695398\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−35.9208	+	11.6714i	−1.42547	+	0.463164i
$636$		0			0
$637$			4.82241i			0.191071i
$638$		0			0
$639$	24.0000			0.949425
$640$	−22.0174	−	30.3043i	−0.870313	−	1.19788i
$641$	−9.67376	−	29.7728i	−0.382091	−	1.17595i	−0.938569	−	0.345092i	$-0.887848\pi$
$641$	−9.67376	−	29.7728i	−0.382091	−	1.17595i	0.556478	−	0.830862i	$-0.312152\pi$
$642$		0			0
$643$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$643$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$		−	50.2554i		−	1.97422i
$649$		0			0
$650$	23.8197			0.934284
$651$		0			0
$652$		0			0
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−33.9429	+	11.0287i	−1.32424	+	0.430271i
$658$		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	$0.804257\pi$
$662$	52.5145	+	72.2800i	2.04103	+	2.80924i
$663$		0			0
$664$	−1.25735	+	3.86974i	−0.0487948	+	0.150175i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−43.1781	+	14.0294i	−1.67061	+	0.542815i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	28.2352	+	38.8624i	1.08839	+	1.49803i	0.849941	+	0.526879i	$0.176638\pi$
$673$	28.2352	+	38.8624i	1.08839	+	1.49803i	0.238445	+	0.971156i	$0.423362\pi$
$674$	12.8197	+	39.4549i	0.493795	+	1.51974i
$675$		0			0
$676$	32.0795	+	23.3071i	1.23383	+	0.896428i
$677$	−1.65073	+	2.27204i	−0.0634428	+	0.0873215i	−0.839559	−	0.543268i	$-0.817187\pi$
$677$	−1.65073	+	2.27204i	−0.0634428	+	0.0873215i	0.776117	+	0.630589i	$0.217187\pi$
$678$		0			0
$679$		0			0
$680$	−81.6312	+	59.3085i	−3.13041	+	2.27438i
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−10.6525	+	32.7849i	−0.406713	+	1.25174i
$687$		0			0
$688$	−42.0568	+	57.8862i	−1.60340	+	2.20689i
$689$		0			0
$690$		0			0
$691$	−22.6525	+	16.4580i	−0.861741	+	0.626091i	−0.928358	−	0.371687i	$-0.878779\pi$
$691$	−22.6525	+	16.4580i	−0.861741	+	0.626091i	0.0666172	+	0.997779i	$0.478779\pi$
$692$			44.2211i			1.68104i
$693$		0			0
$694$	29.0132			1.10132
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−62.1780	−	20.2029i	−2.35011	−	0.763597i
$701$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$701$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$702$		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	$-0.326762\pi$
$709$	−3.61803	−	2.62866i	−0.135878	−	0.0987212i	−0.653648	+	0.756799i	$0.726762\pi$
$710$	26.2572	−	36.1400i	0.985417	−	1.35631i
$711$		0			0
$712$	71.2497	−	23.1504i	2.67020	−	0.867599i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−75.7771			−2.83192
$717$		0			0
$718$		0			0
$719$	−8.29180	+	25.5195i	−0.309232	+	0.951718i	0.668832	+	0.743413i	$0.266794\pi$
$719$	−8.29180	+	25.5195i	−0.309232	+	0.951718i	−0.978064	+	0.208304i	$0.933206\pi$
$720$	−29.6976	−	21.5765i	−1.10676	−	0.804110i
$721$		0			0
$722$	−45.1248	−	14.6619i	−1.67937	−	0.545661i
$723$		0			0
$724$	15.3262	−	11.1352i	0.569595	−	0.413835i
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	19.3271	+	26.6015i	0.716311	+	0.985917i
$729$	8.34346	+	25.6785i	0.309017	+	0.951057i
$730$	−20.5279	+	63.1783i	−0.759770	+	2.33833i
$731$	−85.4853	−	62.1087i	−3.16179	−	2.29717i
$732$		0			0
$733$	28.0716	+	9.12101i	1.03685	+	0.336892i	0.777494	−	0.628890i	$-0.216491\pi$
$733$	28.0716	+	9.12101i	1.03685	+	0.336892i	0.259353	+	0.965783i	$0.416491\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$739$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.7849	+	14.8441i	−0.395659	+	0.544577i	−0.959648	−	0.281205i	$-0.909266\pi$
$743$	−10.7849	+	14.8441i	−0.395659	+	0.544577i	0.563989	+	0.825782i	$0.309266\pi$
$744$		0			0
$745$		0			0
$746$	13.3820	−	9.72257i	0.489949	−	0.355968i
$747$		−	2.18603i		−	0.0799827i
$748$		0			0
$749$	59.4164			2.17103
$750$		0			0
$751$	9.88854	+	30.4338i	0.360838	+	1.11055i	0.952546	+	0.304393i	$0.0984537\pi$
$751$	9.88854	+	30.4338i	0.360838	+	1.11055i	−0.591708	+	0.806152i	$0.701546\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$757$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$758$		−	89.8996i		−	3.26530i
$759$		0			0
$760$		0			0
$761$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$761$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$762$		0			0
$763$		0			0
$764$	−91.9574	−	66.8110i	−3.32690	−	2.41714i
$765$	31.8638	−	43.8568i	1.15204	−	1.58565i
$766$		0			0
$767$	−7.25732	+	2.35805i	−0.262047	+	0.0851441i
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−50.8637	−	70.0079i	−1.83063	−	2.51964i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	30.2705	−	93.1630i	1.08805	−	3.34868i
$775$	36.1803	+	26.2866i	1.29964	+	0.944241i
$776$		0			0
$777$		0			0
$778$	61.7497	−	20.0637i	2.21384	−	0.719319i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−4.27458	−	13.1558i	−0.152663	−	0.469850i
$785$		0			0
$786$		0			0
$787$	−27.5422	+	37.9085i	−0.981772	+	1.35129i	−0.0459025	+	0.998946i	$0.514616\pi$
$787$	−27.5422	+	37.9085i	−0.981772	+	1.35129i	−0.935869	+	0.352347i	$0.885384\pi$
$788$	88.1706	+	28.6484i	3.14095	+	1.02056i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−31.4164	+	96.6898i	−1.11353	+	3.42708i
$797$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$797$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$798$		0			0
$799$		0			0
$800$	−11.8749	+	3.85840i	−0.419843	+	0.136415i
$801$	−32.5623	+	23.6579i	−1.15053	+	0.835911i
$802$			11.1679i			0.394351i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−13.1672	−	40.5244i	−0.463794	−	1.42741i
$807$		0			0
$808$		0			0
$809$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$809$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$810$	47.7957	+	15.5298i	1.67937	+	0.545661i
$811$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$811$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−14.2918	−	10.3836i	−0.499396	−	0.362832i
$820$		0			0
$821$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$821$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$		0			0
$826$	30.8328			1.07281
$827$	−31.1708	−	42.9030i	−1.08392	−	1.49188i	−0.855136	−	0.518404i	$-0.826527\pi$
$827$	−31.1708	−	42.9030i	−1.08392	−	1.49188i	−0.228779	−	0.973478i	$-0.573473\pi$
$828$		0			0
$829$	6.90983	−	21.2663i	0.239988	−	0.738608i	−0.756432	−	0.654072i	$-0.773059\pi$
$829$	6.90983	−	21.2663i	0.239988	−	0.738608i	0.996420	−	0.0845359i	$-0.0269408\pi$
$830$	−3.29180	−	2.39163i	−0.114260	−	0.0830147i
$831$		0			0
$832$	−8.54224	−	2.77554i	−0.296149	−	0.0962246i
$833$	19.4282	−	6.31261i	0.673148	−	0.218719i
$834$		0			0
$835$		−	23.9651i		−	0.829347i
$836$		0			0
$837$		0			0
$838$	52.5145	+	72.2800i	1.81408	+	2.49687i
$839$	−17.3050	−	53.2592i	−0.597433	−	1.83871i	−0.542221	−	0.840236i	$-0.682416\pi$
$839$	−17.3050	−	53.2592i	−0.597433	−	1.83871i	−0.0552123	−	0.998475i	$-0.517584\pi$
$840$		0			0
$841$	23.4615	+	17.0458i	0.809017	+	0.587785i
$842$	−45.9502	+	63.2450i	−1.58355	+	2.17957i
$843$		0			0
$844$		0			0
$845$	−16.9336	+	12.3030i	−0.582535	+	0.423236i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−31.1803	−	95.9632i	−1.06948	−	3.29151i
$851$		0			0
$852$		0			0
$853$	11.1507	−	15.3476i	0.381792	−	0.525492i	−0.574266	−	0.818669i	$-0.694712\pi$
$853$	11.1507	−	15.3476i	0.381792	−	0.525492i	0.956058	+	0.293177i	$0.0947124\pi$
$854$		0			0
$855$		0			0
$856$	86.9574	−	63.1783i	2.97214	−	2.15939i
$857$			52.7526i			1.80200i	0.433824	+	0.900998i	$0.357164\pi$
$857$			52.7526i			1.80200i	−0.433824	+	0.900998i	$0.642836\pi$
$858$		0			0
$859$	−35.7771			−1.22070			−0.610349	−	0.792132i	$-0.708971\pi$
$859$	−35.7771			−1.22070			−0.610349	+	0.792132i	$0.708971\pi$
$860$	−72.7993	−	100.200i	−2.48244	−	3.41678i
$861$		0			0
$862$		0			0
$863$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$863$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$864$		0			0
$865$	−22.2003	−	7.21331i	−0.754832	−	0.245260i
$866$		0			0
$867$		0			0
$868$			116.951i			3.96959i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.2848	−	27.9197i	0.685753	−	0.943857i
$876$		0			0
$877$	37.0421	−	12.0357i	1.25082	−	0.406417i	0.392608	−	0.919706i	$-0.371573\pi$
$877$	37.0421	−	12.0357i	1.25082	−	0.406417i	0.858216	+	0.513289i	$0.171573\pi$
$878$		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	$0.489274\pi$
$882$	11.1314	+	15.3210i	0.374813	+	0.515886i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$	−20.1803	+	62.1087i	−0.678738	+	2.08894i
$885$		0			0
$886$		0			0
$887$	13.2922	+	4.31890i	0.446309	+	0.145015i	0.523545	−	0.851998i	$-0.324609\pi$
$887$	13.2922	+	4.31890i	0.446309	+	0.145015i	−0.0772356	+	0.997013i	$0.524609\pi$
$888$		0			0
$889$	42.1803	−	30.6458i	1.41468	−	1.02783i
$890$			74.9164i			2.51120i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	12.3607	−	38.0423i	0.413172	−	1.27161i
$896$	41.8328	+	30.3933i	1.39754	+	1.01537i
$897$		0			0
$898$	95.5915	+	31.0596i	3.18993	+	1.03647i
$899$		0			0
$900$	51.4058	−	37.3485i	1.71353	−	1.24495i
$901$		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	$-0.800000\pi$
$907$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$908$	63.2994	−	87.1241i	2.10066	−	2.89131i
$909$		0			0
$910$	−31.2719	+	10.1609i	−1.03665	+	0.336829i
$911$	7.23607	−	5.25731i	0.239742	−	0.174182i	−0.461427	−	0.887178i	$-0.652662\pi$
$911$	7.23607	−	5.25731i	0.239742	−	0.174182i	0.701168	+	0.712996i	$0.252662\pi$
$912$		0			0
$913$		0			0
$914$	−91.3738			−3.02238
$915$		0			0
$916$	−7.85410	−	24.1724i	−0.259507	−	0.798680i
$917$		0			0
$918$		0			0
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	15.2616i		−	0.502342i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.3262	+	8.22899i	0.371602	+	0.269985i	0.757875	−	0.652400i	$-0.226238\pi$
$929$	11.3262	+	8.22899i	0.371602	+	0.269985i	−0.386273	+	0.922384i	$0.626238\pi$
$930$		0			0
$931$		0			0
$932$	63.2994	−	20.5672i	2.07344	−	0.673701i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−31.9574			−1.04456
$937$	−5.27939	−	7.26646i	−0.172470	−	0.237385i	0.714028	−	0.700117i	$-0.246869\pi$
$937$	−5.27939	−	7.26646i	−0.172470	−	0.237385i	−0.886498	+	0.462732i	$0.846869\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$		0			0
$944$	17.7082	−	12.8658i	0.576353	−	0.418745i
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	7.01316	+	21.5843i	0.227657	+	0.700655i
$950$		0			0
$951$		0			0
$952$	81.8710	−	112.686i	2.65345	−	3.65217i
$953$	−49.3141	−	16.0231i	−1.59744	−	0.519040i	−0.630968	−	0.775809i	$-0.717342\pi$
$953$	−49.3141	−	16.0231i	−1.59744	−	0.519040i	−0.966473	+	0.256768i	$0.917342\pi$
$954$		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
$963$	−33.9429	+	46.7184i	−1.09379	+	1.50548i
$964$		0			0
$965$	43.4428	−	14.1154i	1.39847	−	0.454392i
$966$		0			0
$967$			61.5625i			1.97972i	0.142063	+	0.989858i	$0.454626\pi$
$967$			61.5625i			1.97972i	−0.142063	+	0.989858i	$0.545374\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.52786	+	17.0130i	0.177398	+	0.545974i	0.999735	−	0.0230267i	$-0.00733028\pi$
$971$	5.52786	+	17.0130i	0.177398	+	0.545974i	−0.822337	+	0.569000i	$0.807330\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	23.9443			0.764872
$981$		0			0
$982$		0			0
$983$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$983$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$	−28.7646	+	39.5911i	−0.916516	+	1.26148i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	62.6099			1.98887			0.994435	−	0.105356i	$-0.0335982\pi$
$991$	62.6099			1.98887			0.994435	+	0.105356i	$0.0335982\pi$
$992$	13.1286	+	18.0700i	0.416834	+	0.573723i
$993$		0			0
$994$	−19.0557	+	58.6475i	−0.604411	+	1.86019i
$995$	−43.4164	−	31.5439i	−1.37639	−	1.00001i
$996$		0			0
$997$	55.1854	+	17.9308i	1.74774	+	0.567875i	0.995817	−	0.0913754i	$-0.0291263\pi$
$997$	55.1854	+	17.9308i	1.74774	+	0.567875i	0.751923	+	0.659250i	$0.229126\pi$
$998$	9.49996	−	3.08672i	0.300716	−	0.0977085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.a.124.1		8
5.4	even	2	inner	605.2.j.a.124.2		8
11.2	odd	10		605.2.b.b.364.1	✓	4
11.3	even	5		605.2.j.c.269.1		8
11.4	even	5	inner	605.2.j.a.444.2		8
11.5	even	5		605.2.j.c.9.2		8
11.6	odd	10		605.2.j.c.9.1		8
11.7	odd	10	inner	605.2.j.a.444.1		8
11.8	odd	10		605.2.j.c.269.2		8
11.9	even	5		605.2.b.b.364.4	yes	4
11.10	odd	2	inner	605.2.j.a.124.2		8
55.2	even	20		3025.2.a.bb.1.4		4
55.4	even	10	inner	605.2.j.a.444.1		8
55.9	even	10		605.2.b.b.364.1	✓	4
55.13	even	20		3025.2.a.bb.1.1		4
55.14	even	10		605.2.j.c.269.2		8
55.19	odd	10		605.2.j.c.269.1		8
55.24	odd	10		605.2.b.b.364.4	yes	4
55.29	odd	10	inner	605.2.j.a.444.2		8
55.39	odd	10		605.2.j.c.9.2		8
55.42	odd	20		3025.2.a.bb.1.1		4
55.49	even	10		605.2.j.c.9.1		8
55.53	odd	20		3025.2.a.bb.1.4		4
55.54	odd	2	CM	605.2.j.a.124.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.b.364.1	✓	4	11.2	odd	10
605.2.b.b.364.1	✓	4	55.9	even	10
605.2.b.b.364.4	yes	4	11.9	even	5
605.2.b.b.364.4	yes	4	55.24	odd	10
605.2.j.a.124.1		8	1.1	even	1	trivial
605.2.j.a.124.1		8	55.54	odd	2	CM
605.2.j.a.124.2		8	5.4	even	2	inner
605.2.j.a.124.2		8	11.10	odd	2	inner
605.2.j.a.444.1		8	11.7	odd	10	inner
605.2.j.a.444.1		8	55.4	even	10	inner
605.2.j.a.444.2		8	11.4	even	5	inner
605.2.j.a.444.2		8	55.29	odd	10	inner
605.2.j.c.9.1		8	11.6	odd	10
605.2.j.c.9.1		8	55.49	even	10
605.2.j.c.9.2		8	11.5	even	5
605.2.j.c.9.2		8	55.39	odd	10
605.2.j.c.269.1		8	11.3	even	5
605.2.j.c.269.1		8	55.19	odd	10
605.2.j.c.269.2		8	11.8	odd	10
605.2.j.c.269.2		8	55.14	even	10
3025.2.a.bb.1.1		4	55.13	even	20
3025.2.a.bb.1.1		4	55.42	odd	20
3025.2.a.bb.1.4		4	55.2	even	20
3025.2.a.bb.1.4		4	55.53	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.46782 - 2.02029i) q^{2} +(-1.30902 + 4.02874i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(2.93565 + 0.953850i) q^{7} +(5.31064 - 1.72553i) q^{8} +(-2.42705 + 1.76336i) q^{9} +O(q^{10})\)	\(q+(-1.46782 - 2.02029i) q^{2} +(-1.30902 + 4.02874i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(2.93565 + 0.953850i) q^{7} +(5.31064 - 1.72553i) q^{8} +(-2.42705 + 1.76336i) q^{9} +5.58394i q^{10} +(1.12132 + 1.54336i) q^{13} +(-2.38197 - 7.33094i) q^{14} +(-4.42705 - 3.21644i) q^{16} +(4.74998 - 6.53779i) q^{17} +(7.12497 + 2.31504i) q^{18} +(7.66312 - 5.56758i) q^{20} +(1.54508 + 4.75528i) q^{25} +(1.47214 - 4.53077i) q^{26} +(-7.68563 + 10.5784i) q^{28} +(7.23607 - 5.25731i) q^{31} +2.49721i q^{32} -20.1803 q^{34} +(-4.05697 - 5.58394i) q^{35} +(-3.92705 - 12.0862i) q^{36} +(-11.8749 - 3.85840i) q^{40} -13.0756i q^{43} +6.70820 q^{45} +(2.04508 + 1.48584i) q^{49} +(7.33912 - 10.1014i) q^{50} +(-7.68563 + 2.49721i) q^{52} +17.2361 q^{56} +(-1.23607 + 3.80423i) q^{59} +(-21.2426 - 6.90212i) q^{62} +(-8.80695 + 2.86155i) q^{63} +(-3.80902 + 2.76741i) q^{64} -4.26575i q^{65} +(20.1212 + 27.6945i) q^{68} +(-5.32624 + 16.3925i) q^{70} +(-6.47214 - 4.70228i) q^{71} +(-9.84647 + 13.5525i) q^{72} +(11.3143 + 3.67624i) q^{73} +(3.78115 + 11.6372i) q^{80} +(2.78115 - 8.55951i) q^{81} +(-0.428305 + 0.589512i) q^{83} +(-17.1856 + 5.58394i) q^{85} +(-26.4164 + 19.1926i) q^{86} +13.4164 q^{89} +(-9.84647 - 13.5525i) q^{90} +(1.81966 + 5.60034i) q^{91} -6.31261i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 10 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q - 6 * q^4 - 10 * q^5 - 6 * q^9	\( 8 q - 6 q^{4} - 10 q^{5} - 6 q^{9} - 28 q^{14} - 22 q^{16} + 30 q^{20} - 10 q^{25} - 24 q^{26} + 40 q^{31} - 72 q^{34} - 18 q^{36} - 6 q^{49} + 120 q^{56} + 8 q^{59} - 26 q^{64} + 20 q^{70} - 16 q^{71} - 10 q^{80} - 18 q^{81} - 104 q^{86} + 104 q^{91}+O(q^{100}) \) 8 * q - 6 * q^4 - 10 * q^5 - 6 * q^9 - 28 * q^14 - 22 * q^16 + 30 * q^20 - 10 * q^25 - 24 * q^26 + 40 * q^31 - 72 * q^34 - 18 * q^36 - 6 * q^49 + 120 * q^56 + 8 * q^59 - 26 * q^64 + 20 * q^70 - 16 * q^71 - 10 * q^80 - 18 * q^81 - 104 * q^86 + 104 * q^91

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