LMFDB - Embedded newform 605.2.j.a.269.1

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			269.1
Root			$-1.26313 - 1.73855i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26313 + 0.410415i) q^{2} +(-0.190983 + 0.138757i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(2.52626 + 3.47709i) q^{7} +(1.74560 - 2.40261i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})$	\(q+(-1.26313 + 0.410415i) q^{2} +(-0.190983 + 0.138757i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(2.52626 + 3.47709i) q^{7} +(1.74560 - 2.40261i) q^{8} +(0.927051 + 2.85317i) q^{9} -2.96979i q^{10} +(6.61382 - 2.14896i) q^{13} +(-4.61803 - 3.35520i) q^{14} +(-1.07295 + 3.30220i) q^{16} +(-1.56131 - 0.507301i) q^{17} +(-2.34197 - 3.22344i) q^{18} +(-0.163119 - 0.502029i) q^{20} +(-4.04508 - 2.93893i) q^{25} +(-7.47214 + 5.42882i) q^{26} +(-0.964944 - 0.313529i) q^{28} +(2.76393 + 8.50651i) q^{31} +1.32813i q^{32} +2.18034 q^{34} +(-9.14008 + 2.96979i) q^{35} +(-0.572949 - 0.416272i) q^{36} +(3.90328 + 5.37240i) q^{40} -1.01460i q^{43} -6.70820 q^{45} +(-3.54508 + 10.9106i) q^{49} +(6.31564 + 2.05208i) q^{50} +(-0.964944 + 1.32813i) q^{52} +12.7639 q^{56} +(3.23607 - 2.35114i) q^{59} +(-6.98240 - 9.61045i) q^{62} +(-7.57877 + 10.4313i) q^{63} +(-2.69098 - 8.28199i) q^{64} +15.5500i q^{65} +(0.368576 - 0.119757i) q^{68} +(10.3262 - 7.50245i) q^{70} +(2.47214 - 7.60845i) q^{71} +(8.47332 + 2.75315i) q^{72} +(-7.21019 - 9.92398i) q^{73} +(-6.28115 - 4.56352i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-17.3152 - 5.62605i) q^{83} +(2.15768 - 2.96979i) q^{85} +(0.416408 + 1.28157i) q^{86} -13.4164 q^{89} +(8.47332 - 2.75315i) q^{90} +(24.1803 + 17.5680i) q^{91} -15.2365i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.26313	+	0.410415i	−0.893166	+	0.290207i	−0.719413	−	0.694582i	$-0.755589\pi$
$2$	−1.26313	+	0.410415i	−0.893166	+	0.290207i	−0.173753	+	0.984789i	$0.555589\pi$
$3$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$3$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$4$	−0.190983	+	0.138757i	−0.0954915	+	0.0693786i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$		0			0
$7$	2.52626	+	3.47709i	0.954835	+	1.31422i	0.949346	+	0.314232i	$0.101747\pi$
$7$	2.52626	+	3.47709i	0.954835	+	1.31422i	0.00548867	+	0.999985i	$0.498253\pi$
$8$	1.74560	−	2.40261i	0.617163	−	0.849451i
$9$	0.927051	+	2.85317i	0.309017	+	0.951057i
$10$		−	2.96979i		−	0.939130i
$11$		0			0
$11$		0			0
$12$		0			0
$13$	6.61382	−	2.14896i	1.83434	−	0.596015i	0.835422	−	0.549610i	$-0.185224\pi$
$13$	6.61382	−	2.14896i	1.83434	−	0.596015i	0.998923	−	0.0464049i	$-0.0147764\pi$
$14$	−4.61803	−	3.35520i	−1.23422	−	0.896714i
$15$		0			0
$16$	−1.07295	+	3.30220i	−0.268237	+	0.825549i
$17$	−1.56131	−	0.507301i	−0.378674	−	0.123039i	0.113495	−	0.993539i	$-0.463796\pi$
$17$	−1.56131	−	0.507301i	−0.378674	−	0.123039i	−0.492168	+	0.870500i	$0.663796\pi$
$18$	−2.34197	−	3.22344i	−0.552007	−	0.759772i
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	−0.163119	−	0.502029i	−0.0364745	−	0.112257i
$21$		0			0
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	−7.47214	+	5.42882i	−1.46541	+	1.06468i
$27$		0			0
$28$	−0.964944	−	0.313529i	−0.182357	−	0.0592515i
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$		0			0
$31$	2.76393	+	8.50651i	0.496417	+	1.52781i	0.814737	+	0.579831i	$0.196881\pi$
$31$	2.76393	+	8.50651i	0.496417	+	1.52781i	−0.318320	+	0.947983i	$0.603119\pi$
$32$			1.32813i			0.234783i
$33$		0			0
$34$	2.18034			0.373925
$35$	−9.14008	+	2.96979i	−1.54496	+	0.501986i
$36$	−0.572949	−	0.416272i	−0.0954915	−	0.0693786i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$		0			0
$40$	3.90328	+	5.37240i	0.617163	+	0.849451i
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$		0			0
$43$		−	1.01460i		−	0.154725i	−0.997003	−	0.0773627i	$-0.975350\pi$
$43$		−	1.01460i		−	0.154725i	0.997003	−	0.0773627i	$-0.0246499\pi$
$44$		0			0
$45$	−6.70820			−1.00000
$46$		0			0
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$		0			0
$49$	−3.54508	+	10.9106i	−0.506441	+	1.55866i
$50$	6.31564	+	2.05208i	0.893166	+	0.290207i
$51$		0			0
$52$	−0.964944	+	1.32813i	−0.133814	+	0.184179i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$		0			0
$55$		0			0
$56$	12.7639			1.70565
$57$		0			0
$58$		0			0
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	−0.356861	−	0.934158i	$-0.616153\pi$
$59$	3.23607	−	2.35114i	0.421300	−	0.306092i	0.778161	+	0.628065i	$0.216153\pi$
$60$		0			0
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	−6.98240	−	9.61045i	−0.886765	−	1.22053i
$63$	−7.57877	+	10.4313i	−0.954835	+	1.31422i
$64$	−2.69098	−	8.28199i	−0.336373	−	1.03525i
$65$			15.5500i			1.92874i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	0.368576	−	0.119757i	0.0446964	−	0.0145227i
$69$		0			0
$70$	10.3262	−	7.50245i	1.23422	−	0.896714i
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	−0.690369	−	0.723457i	$-0.742552\pi$
$71$	2.47214	−	7.60845i	0.293389	−	0.902957i	0.983758	−	0.179500i	$-0.0574480\pi$
$72$	8.47332	+	2.75315i	0.998590	+	0.324462i
$73$	−7.21019	−	9.92398i	−0.843889	−	1.16151i	−0.985176	−	0.171545i	$-0.945124\pi$
$73$	−7.21019	−	9.92398i	−0.843889	−	1.16151i	0.141287	−	0.989969i	$-0.454876\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$	−6.28115	−	4.56352i	−0.702254	−	0.510218i
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$		0			0
$83$	−17.3152	−	5.62605i	−1.90059	−	0.617540i	−0.962654	−	0.270736i	$-0.912733\pi$
$83$	−17.3152	−	5.62605i	−1.90059	−	0.617540i	−0.937938	−	0.346804i	$-0.887267\pi$
$84$		0			0
$85$	2.15768	−	2.96979i	0.234033	−	0.322119i
$86$	0.416408	+	1.28157i	0.0449024	+	0.138195i
$87$		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	$0.751788\pi$
$90$	8.47332	−	2.75315i	0.893166	−	0.290207i
$91$	24.1803	+	17.5680i	2.53479	+	1.84163i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$		−	15.2365i		−	1.53912i
$99$		0			0
$100$	1.18034			0.118034
$101$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$101$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$102$		0			0
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$	6.38197	−	19.6417i	0.625803	−	1.92602i
$105$		0			0
$106$		0			0
$107$	4.45614	−	6.13335i	0.430792	−	0.592934i	−0.537343	−	0.843364i	$-0.680572\pi$
$107$	4.45614	−	6.13335i	0.430792	−	0.592934i	0.968135	+	0.250430i	$0.0805720\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	−14.1926	+	4.61145i	−1.34107	+	0.435741i
$113$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	12.2627	+	16.8782i	1.13369	+	1.56039i
$118$	−3.12262	+	4.29792i	−0.287461	+	0.395656i
$119$	−2.18034	−	6.71040i	−0.199871	−	0.615141i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$	−1.70820	−	1.24108i	−0.153401	−	0.111453i
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$	5.29180	−	16.2865i	0.471431	−	1.45091i
$127$	14.1926	+	4.61145i	1.25939	+	0.409200i	0.861276	−	0.508137i	$-0.169666\pi$
$127$	14.1926	+	4.61145i	1.25939	+	0.409200i	0.398112	+	0.917337i	$0.369666\pi$
$128$	5.23680	+	7.20783i	0.462872	+	0.637089i
$129$		0			0
$130$	−6.38197	−	19.6417i	−0.559735	−	1.72269i
$131$		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
$136$	−3.94427	+	2.86568i	−0.338219	+	0.245730i
$137$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$137$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$138$		0			0
$139$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$139$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$140$	1.33352	−	1.83543i	0.112703	−	0.155122i
$141$		0			0
$142$			10.6250i			0.891634i
$143$		0			0
$144$	−10.4164			−0.868034
$145$		0			0
$146$	13.1803	+	9.57608i	1.09081	+	0.792522i
$147$		0			0
$148$		0			0
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$		0			0
$151$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$151$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$152$		0			0
$153$		−	4.92498i		−	0.398161i
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$157$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$158$		0			0
$159$		0			0
$160$	−2.82444	−	0.917716i	−0.223292	−	0.0725518i
$161$		0			0
$162$	7.02590	−	9.67033i	0.552007	−	0.759772i
$163$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$163$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$164$		0			0
$165$		0			0
$166$	24.1803			1.87676
$167$	22.3677	−	7.26771i	1.73087	−	0.562393i	0.737292	−	0.675574i	$-0.236104\pi$
$167$	22.3677	−	7.26771i	1.73087	−	0.562393i	0.993574	+	0.113182i	$0.0361042\pi$
$168$		0			0
$169$	28.6074	−	20.7845i	2.20057	−	1.59881i
$170$	−1.50658	+	4.63677i	−0.115549	+	0.355624i
$171$		0			0
$172$	0.140783	+	0.193772i	0.0107346	+	0.0147750i
$173$	14.1926	−	19.5344i	1.07904	−	1.48517i	0.218472	−	0.975843i	$-0.429893\pi$
$173$	14.1926	−	19.5344i	1.07904	−	1.48517i	0.860570	−	0.509331i	$-0.170107\pi$
$174$		0			0
$175$		−	21.4896i		−	1.62446i
$176$		0			0
$177$		0			0
$178$	16.9466	−	5.50630i	1.27020	−	0.412714i
$179$	14.4721	+	10.5146i	1.08170	+	0.785900i	0.977978	−	0.208707i	$-0.0669254\pi$
$179$	14.4721	+	10.5146i	1.08170	+	0.785900i	0.103720	+	0.994607i	$0.466925\pi$
$180$	1.28115	−	0.930812i	0.0954915	−	0.0693786i
$181$	−1.38197	+	4.25325i	−0.102721	+	0.316142i	−0.989189	−	0.146648i	$-0.953152\pi$
$181$	−1.38197	+	4.25325i	−0.102721	+	0.316142i	0.886468	+	0.462790i	$0.153152\pi$
$182$	−37.7530	−	12.2667i	−2.79844	−	0.909269i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−21.7082	+	15.7719i	−1.57075	+	1.14122i	−0.644317	+	0.764758i	$0.722858\pi$
$191$	−21.7082	+	15.7719i	−1.57075	+	1.14122i	−0.926433	+	0.376459i	$0.877142\pi$
$192$		0			0
$193$	17.9116	+	5.81983i	1.28930	+	0.418920i	0.871848	−	0.489777i	$-0.162922\pi$
$193$	17.9116	+	5.81983i	1.28930	+	0.418920i	0.417456	+	0.908697i	$0.362922\pi$
$194$		0			0
$195$		0			0
$196$	−0.836881	−	2.57565i	−0.0597772	−	0.183975i
$197$		−	17.5792i		−	1.25247i	−0.779635	−	0.626234i	$-0.784595\pi$
$197$		−	17.5792i		−	1.25247i	0.779635	−	0.626234i	$-0.215405\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−14.1222	+	4.58858i	−0.998590	+	0.324462i
$201$		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		0.951057	−	0.309017i	$-0.100000\pi$
$211$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$212$		0			0
$213$		0			0
$214$	−3.11146	+	9.57608i	−0.212695	+	0.654607i
$215$	2.15768	+	0.701073i	0.147153	+	0.0478128i
$216$		0			0
$217$	−22.5955	+	31.1001i	−1.53388	+	2.11121i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−11.4164			−0.767951
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$	−4.61803	+	3.35520i	−0.308555	+	0.224179i
$225$	4.63525	−	14.2658i	0.309017	−	0.951057i
$226$		0			0
$227$	−9.50865	−	13.0875i	−0.631111	−	0.868650i	0.366991	−	0.930224i	$-0.380388\pi$
$227$	−9.50865	−	13.0875i	−0.631111	−	0.868650i	−0.998103	+	0.0615740i	$0.980388\pi$
$228$		0			0
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	0.993442	−	0.114341i	$-0.0364756\pi$
$229$	1.85410	+	5.70634i	0.122523	+	0.377086i	−0.870919	+	0.491426i	$0.836476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−24.8940	+	8.08854i	−1.63086	+	0.529898i	−0.974469	−	0.224524i	$-0.927917\pi$
$233$	−24.8940	+	8.08854i	−1.63086	+	0.529898i	−0.656390	+	0.754422i	$0.727917\pi$
$234$	−22.4164	−	16.2865i	−1.46541	−	1.06468i
$235$		0			0
$236$	−0.291796	+	0.898056i	−0.0189943	+	0.0584585i
$237$		0			0
$238$	5.50810	+	7.58124i	0.357037	+	0.491419i
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$		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
$245$	−20.7533	−	15.0781i	−1.32588	−	0.963307i
$246$		0			0
$247$		0			0
$248$	25.2626	+	8.20830i	1.60417	+	0.521228i
$249$		0			0
$250$	−8.72800	+	12.0131i	−0.552007	+	0.759772i
$251$	8.65248	+	26.6296i	0.546139	+	1.68084i	0.718265	+	0.695769i	$0.244936\pi$
$251$	8.65248	+	26.6296i	0.546139	+	1.68084i	−0.172126	+	0.985075i	$0.555064\pi$
$252$		−	3.04381i		−	0.191742i
$253$		0			0
$254$	−19.8197			−1.24360
$255$		0			0
$256$	4.51722	+	3.28195i	0.282326	+	0.205122i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$		0			0
$260$	−2.15768	−	2.96979i	−0.133814	−	0.184179i
$261$		0			0
$262$		0			0
$263$			32.1147i			1.98027i	0.140100	+	0.990137i	$0.455258\pi$
$263$			32.1147i			1.98027i	−0.140100	+	0.990137i	$0.544742\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.32624	+	13.3148i	−0.263775	+	0.811817i	0.728198	+	0.685367i	$0.240358\pi$
$269$	−4.32624	+	13.3148i	−0.263775	+	0.811817i	−0.991973	+	0.126450i	$0.959642\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$	3.35042	−	4.61145i	0.203149	−	0.279610i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−12.8591	+	4.17816i	−0.772627	+	0.251042i	−0.668689	−	0.743542i	$-0.733144\pi$
$277$	−12.8591	+	4.17816i	−0.772627	+	0.251042i	−0.103938	+	0.994584i	$0.533144\pi$
$278$		0			0
$279$	−21.7082	+	15.7719i	−1.29964	+	0.944241i
$280$	−8.81966	+	27.1441i	−0.527076	+	1.62217i
$281$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$281$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$282$		0			0
$283$	11.8941	−	16.3709i	0.707032	−	0.973147i	−0.292823	−	0.956167i	$-0.594595\pi$
$283$	11.8941	−	16.3709i	0.707032	−	0.973147i	0.999856	−	0.0169800i	$-0.00540517\pi$
$284$	0.583592	+	1.79611i	0.0346298	+	0.106580i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−3.78938	+	1.23125i	−0.223292	+	0.0725518i
$289$	−11.5729	−	8.40824i	−0.680762	−	0.494602i
$290$		0			0
$291$		0			0
$292$	2.75405	+	0.894844i	0.161168	+	0.0523668i
$293$	0.227792	+	0.313529i	0.0133078	+	0.0183166i	0.815619	−	0.578589i	$-0.196397\pi$
$293$	0.227792	+	0.313529i	0.0133078	+	0.0183166i	−0.802311	+	0.596906i	$0.796397\pi$
$294$		0			0
$295$	2.76393	+	8.50651i	0.160922	+	0.495268i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	3.52786	−	2.56314i	0.203343	−	0.147737i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	2.02129	+	6.22088i	0.115549	+	0.355624i
$307$			11.6397i			0.664310i	0.943225	+	0.332155i	$0.107776\pi$
$307$			11.6397i			0.664310i	−0.943225	+	0.332155i	$0.892224\pi$
$308$		0			0
$309$		0			0
$310$	25.2626	−	8.20830i	1.43482	−	0.466200i
$311$	−25.8885	−	18.8091i	−1.46800	−	1.06657i	−0.981186	−	0.193065i	$-0.938157\pi$
$311$	−25.8885	−	18.8091i	−1.46800	−	1.06657i	−0.486819	−	0.873503i	$-0.661843\pi$
$312$		0			0
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$	−16.9466	−	23.3250i	−0.954835	−	1.31422i
$316$		0			0
$317$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$317$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$		0			0
$320$	19.4721			1.08853
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.656541	−	2.02063i	0.0364745	−	0.112257i
$325$	−33.0691	−	10.7448i	−1.83434	−	0.596015i
$326$		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	$0.0583536\pi$
$332$	4.08757	−	1.32813i	0.224334	−	0.0728907i
$333$		0			0
$334$	−25.2705	+	18.3601i	−1.38274	+	1.00462i
$335$		0			0
$336$		0			0
$337$	−19.2451	−	26.4886i	−1.04835	−	1.44293i	−0.890233	−	0.455506i	$-0.849459\pi$
$337$	−19.2451	−	26.4886i	−1.04835	−	1.44293i	−0.158114	−	0.987421i	$-0.550541\pi$
$338$	−27.6045	+	37.9944i	−1.50149	+	2.06662i
$339$		0			0
$340$			0.866573i			0.0469965i
$341$		0			0
$342$		0			0
$343$	−18.2802	+	5.93958i	−0.987036	+	0.320707i
$344$	−2.43769	−	1.77109i	−0.131432	−	0.0954907i
$345$		0			0
$346$	−9.90983	+	30.4993i	−0.532756	+	1.63965i
$347$	33.6655	+	10.9386i	1.80726	+	0.587214i	0.999996	−	0.00297954i	$-0.000948417\pi$
$347$	33.6655	+	10.9386i	1.80726	+	0.587214i	0.807262	+	0.590193i	$0.200948\pi$
$348$		0			0
$349$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$349$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$350$	8.81966	+	27.1441i	0.471431	+	1.45091i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$	14.4721	+	10.5146i	0.768101	+	0.558058i
$356$	2.56231	−	1.86162i	0.135802	−	0.0986659i
$357$		0			0
$358$	−22.5955	−	7.34173i	−1.19421	−	0.388022i
$359$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$359$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$360$	−11.7098	+	16.1172i	−0.617163	+	0.849451i
$361$	−5.87132	−	18.0701i	−0.309017	−	0.951057i
$362$		−	5.93958i		−	0.312178i
$363$		0			0
$364$	−7.05573			−0.369821
$365$	26.0867	−	8.47609i	1.36544	−	0.443659i
$366$		0			0
$367$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$367$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		−	38.0542i		−	1.97037i	−0.171484	−	0.985187i	$-0.554856\pi$
$373$		−	38.0542i		−	1.97037i	0.171484	−	0.985187i	$-0.445144\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−11.1246	+	34.2380i	−0.571433	+	1.75869i	0.0765833	+	0.997063i	$0.475599\pi$
$379$	−11.1246	+	34.2380i	−0.571433	+	1.75869i	−0.648016	+	0.761627i	$0.724401\pi$
$380$		0			0
$381$		0			0
$382$	20.9472	−	28.8313i	1.07175	−	1.47514i
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$		0			0
$385$		0			0
$386$	−25.0132			−1.27314
$387$	2.89483	−	0.940588i	0.147153	−	0.0478128i
$388$		0			0
$389$	21.0344	−	15.2824i	1.06649	−	0.774849i	0.0912107	−	0.995832i	$-0.470926\pi$
$389$	21.0344	−	15.2824i	1.06649	−	0.774849i	0.975278	+	0.220982i	$0.0709263\pi$
$390$		0			0
$391$		0			0
$392$	20.0258	+	27.5631i	1.01145	+	1.39215i
$393$		0			0
$394$	7.21478	+	22.2048i	0.363475	+	1.11866i
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−30.3151	+	9.84996i	−1.51956	+	0.493734i
$399$		0			0
$400$	14.0451	−	10.2044i	0.702254	−	0.510218i
$401$	−1.38197	+	4.25325i	−0.0690121	+	0.212397i	−0.979615	−	0.200886i	$-0.935618\pi$
$401$	−1.38197	+	4.25325i	−0.0690121	+	0.212397i	0.910603	+	0.413283i	$0.135618\pi$
$402$		0			0
$403$	36.5603	+	50.3210i	1.82120	+	2.50667i
$404$		0			0
$405$	−6.21885	−	19.1396i	−0.309017	−	0.951057i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.3503	+	5.31252i	0.804544	+	0.261412i
$414$		0			0
$415$	23.9290	−	32.9355i	1.17463	−	1.61674i
$416$	2.85410	+	8.78402i	0.139934	+	0.430672i
$417$		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
$421$	−25.3262	−	18.4006i	−1.23433	−	0.896790i	−0.237119	−	0.971481i	$-0.576203\pi$
$421$	−25.3262	−	18.4006i	−1.23433	−	0.896790i	−0.997207	+	0.0746909i	$0.976203\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.82472	+	6.64066i	0.234033	+	0.322119i
$426$		0			0
$427$		0			0
$428$			1.78969i			0.0865079i
$429$		0			0
$430$	−3.01316			−0.145307
$431$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$431$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$432$		0			0
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$	15.7771	−	48.5569i	0.757324	−	2.33080i
$435$		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
$442$	14.4204	−	4.68547i	0.685908	−	0.222865i
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$		0			0
$445$	9.27051	−	28.5317i	0.439464	−	1.35253i
$446$		0			0
$447$		0			0
$448$	21.9991	−	30.2792i	1.03936	−	1.43056i
$449$	−12.4377	−	38.2793i	−0.586971	−	1.80651i	−0.591207	−	0.806520i	$-0.701348\pi$
$449$	−12.4377	−	38.2793i	−0.586971	−	1.80651i	0.00423548	−	0.999991i	$-0.498652\pi$
$450$			19.9220i			0.939130i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	17.3820	+	12.6287i	0.815776	+	0.592696i
$455$	−54.0689	+	39.2833i	−2.53479	+	1.84163i
$456$		0			0
$457$	−21.0342	−	6.83443i	−0.983939	−	0.319701i	−0.227509	−	0.973776i	$-0.573058\pi$
$457$	−21.0342	−	6.83443i	−0.983939	−	0.319701i	−0.756430	+	0.654075i	$0.773058\pi$
$458$	−4.68393	−	6.44688i	−0.218866	−	0.301243i
$459$		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
$466$	28.1246	−	20.4337i	1.30285	−	0.946574i
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−4.68393	−	1.52190i	−0.216515	−	0.0703500i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		−	11.8792i		−	0.546783i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	1.34752	+	0.979034i	0.0617637	+	0.0448739i
$477$		0			0
$478$		0			0
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$		0			0
$489$		0			0
$490$	32.4024	+	10.5282i	1.46379	+	0.475614i
$491$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$491$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−31.0557			−1.39444
$497$	32.7005	−	10.6250i	1.46682	−	0.476599i
$498$		0			0
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	−0.512992	−	0.858394i	$-0.671463\pi$
$499$	3.23607	−	2.35114i	0.144866	−	0.105252i	0.657858	+	0.753142i	$0.271463\pi$
$500$	−0.815595	+	2.51014i	−0.0364745	+	0.112257i
$501$		0			0
$502$	−21.8584	−	30.0855i	−0.975586	−	1.34278i
$503$	−15.0167	+	20.6688i	−0.669564	+	0.921575i	−0.999750	−	0.0223402i	$-0.992888\pi$
$503$	−15.0167	+	20.6688i	−0.669564	+	0.921575i	0.330187	+	0.943916i	$0.392888\pi$
$504$	11.8328	+	36.4177i	0.527076	+	1.62217i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−3.35042	+	1.08862i	−0.148651	+	0.0482995i
$509$	27.5066	+	19.9847i	1.21921	+	0.885806i	0.996034	−	0.0889725i	$-0.0283583\pi$
$509$	27.5066	+	19.9847i	1.21921	+	0.885806i	0.223174	+	0.974779i	$0.428358\pi$
$510$		0			0
$511$	16.2918	−	50.1410i	0.720707	−	2.21811i
$512$	−23.9994	−	7.79789i	−1.06063	−	0.344621i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	37.3607	+	27.1441i	1.63837	+	1.19035i
$521$	18.0902	−	13.1433i	0.792545	−	0.575817i	−0.116173	−	0.993229i	$-0.537063\pi$
$521$	18.0902	−	13.1433i	0.792545	−	0.575817i	0.908718	+	0.417412i	$0.137063\pi$
$522$		0			0
$523$	−5.28030	−	1.71567i	−0.230892	−	0.0750212i	0.191286	−	0.981534i	$-0.438734\pi$
$523$	−5.28030	−	1.71567i	−0.230892	−	0.0750212i	−0.422178	+	0.906513i	$0.638734\pi$
$524$		0			0
$525$		0			0
$526$	−13.1803	−	40.5649i	−0.574690	−	1.76871i
$527$		−	14.6835i		−	0.639621i
$528$		0			0
$529$	23.0000			1.00000
$530$		0			0
$531$	9.70820	+	7.05342i	0.421300	+	0.306092i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	9.96424	+	13.7146i	0.430792	+	0.592934i
$536$		0			0
$537$		0			0
$538$		−	18.5938i		−	0.801637i
$539$		0			0
$540$		0			0
$541$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$541$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$542$		0			0
$543$		0			0
$544$	0.673762	−	2.07363i	0.0288873	−	0.0889060i
$545$		0			0
$546$		0			0
$547$	−27.0517	+	37.2334i	−1.15665	+	1.59199i	−0.433741	+	0.901038i	$0.642807\pi$
$547$	−27.0517	+	37.2334i	−1.15665	+	1.59199i	−0.722904	+	0.690948i	$0.757193\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	14.5279	−	10.5551i	0.617230	−	0.448444i
$555$		0			0
$556$		0			0
$557$	24.2976	+	33.4428i	1.02952	+	1.41702i	0.905305	+	0.424762i	$0.139642\pi$
$557$	24.2976	+	33.4428i	1.02952	+	1.41702i	0.124217	+	0.992255i	$0.460358\pi$
$558$	20.9472	−	28.8313i	0.886765	−	1.22053i
$559$	−2.18034	−	6.71040i	−0.0922186	−	0.283820i
$560$		−	33.3688i		−	1.41009i
$561$		0			0
$562$		0			0
$563$	41.8406	−	13.5948i	1.76337	−	0.572954i	0.765831	−	0.643042i	$-0.222328\pi$
$563$	41.8406	−	13.5948i	1.76337	−	0.572954i	0.997541	+	0.0700880i	$0.0223280\pi$
$564$		0			0
$565$		0			0
$566$	−8.30495	+	25.5600i	−0.349083	+	1.07437i
$567$	−36.7881	−	11.9532i	−1.54496	−	0.501986i
$568$	−13.9648	−	19.2209i	−0.585950	−	0.806491i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		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
$576$	21.1353	−	15.3557i	0.880636	−	0.639819i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	18.0690	+	5.87097i	0.751570	+	0.244200i
$579$		0			0
$580$		0			0
$581$	−24.1803	−	74.4194i	−1.00317	−	3.08744i
$582$		0			0
$583$		0			0
$584$	−36.4296			−1.50747
$585$	−44.3669	+	14.4157i	−1.83434	+	0.596015i
$586$	−0.416408	−	0.302538i	−0.0172017	−	0.0124977i
$587$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$587$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$588$		0			0
$589$		0			0
$590$	−6.98240	−	9.61045i	−0.287461	−	0.395656i
$591$		0			0
$592$		0			0
$593$			36.0250i			1.47937i	0.672953	+	0.739686i	$0.265026\pi$
$593$			36.0250i			1.47937i	−0.672953	+	0.739686i	$0.734974\pi$
$594$		0			0
$595$	15.7771			0.646798
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.8197	−	42.5325i	0.564656	−	1.73783i	−0.104315	−	0.994544i	$-0.533265\pi$
$599$	13.8197	−	42.5325i	0.564656	−	1.73783i	0.668971	−	0.743288i	$-0.266735\pi$
$600$		0			0
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$	−3.40419	+	4.68547i	−0.138744	+	0.190965i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−40.6479	+	13.2073i	−1.64985	+	0.536068i	−0.978707	−	0.205263i	$-0.934195\pi$
$607$	−40.6479	+	13.2073i	−1.64985	+	0.536068i	−0.671140	+	0.741331i	$0.734195\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.683377	+	0.940588i	0.0276239	+	0.0380210i
$613$	−9.87723	+	13.5948i	−0.398938	+	0.549090i	−0.960477	−	0.278360i	$-0.910209\pi$
$613$	−9.87723	+	13.5948i	−0.398938	+	0.549090i	0.561539	+	0.827450i	$0.310209\pi$
$614$	−4.77709	−	14.7024i	−0.192788	−	0.593339i
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	14.4721	+	10.5146i	0.581684	+	0.422618i	0.839331	−	0.543621i	$-0.182947\pi$
$619$	14.4721	+	10.5146i	0.581684	+	0.422618i	−0.257647	+	0.966239i	$0.582947\pi$
$620$	3.81966	−	2.77515i	0.153401	−	0.111453i
$621$		0			0
$622$	40.4201	+	13.1333i	1.62070	+	0.526597i
$623$	−33.8933	−	46.6501i	−1.35791	−	1.86900i
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	30.9787	+	22.5074i	1.23422	+	0.896714i
$631$	38.8328	−	28.2137i	1.54591	−	1.12317i	0.599421	−	0.800434i	$-0.295398\pi$
$631$	38.8328	−	28.2137i	1.54591	−	1.12317i	0.946489	−	0.322735i	$-0.104602\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−19.6137	+	26.9959i	−0.778345	+	1.07130i
$636$		0			0
$637$			79.7793i			3.16097i
$638$		0			0
$639$	24.0000			0.949425
$640$	−18.9469	+	6.15623i	−0.748943	+	0.243346i
$641$	−25.3262	−	18.4006i	−1.00033	−	0.726780i	−0.0381681	−	0.999271i	$-0.512152\pi$
$641$	−25.3262	−	18.4006i	−1.00033	−	0.726780i	−0.962158	+	0.272492i	$0.912152\pi$
$642$		0			0
$643$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$643$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$			26.7281i			1.04998i
$649$		0			0
$650$	46.1803			1.81134
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	21.6306	−	29.7719i	0.843889	−	1.16151i
$658$		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	$0.804257\pi$
$662$	−45.1910	+	14.6835i	−1.75640	+	0.570689i
$663$		0			0
$664$	−43.7426	+	31.7809i	−1.69754	+	1.23334i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−3.26341	+	4.49169i	−0.126265	+	0.173789i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	18.6487	−	6.05934i	0.718856	−	0.233570i	0.0733287	−	0.997308i	$-0.476638\pi$
$673$	18.6487	−	6.05934i	0.718856	−	0.233570i	0.645527	+	0.763737i	$0.276638\pi$
$674$	35.1803	+	25.5600i	1.35510	+	0.984535i
$675$		0			0
$676$	−2.57953	+	7.93897i	−0.0992126	+	0.305345i
$677$	49.4194	+	16.0573i	1.89934	+	0.617133i	0.966347	+	0.257240i	$0.0828132\pi$
$677$	49.4194	+	16.0573i	1.89934	+	0.617133i	0.932994	+	0.359893i	$0.117187\pi$
$678$		0			0
$679$		0			0
$680$	−3.36881	−	10.3681i	−0.129188	−	0.397600i
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	20.6525	−	15.0049i	0.788515	−	0.572890i
$687$		0			0
$688$	3.35042	+	1.08862i	0.127733	+	0.0415031i
$689$		0			0
$690$		0			0
$691$	8.65248	+	26.6296i	0.329156	+	1.01304i	0.969530	+	0.244974i	$0.0787794\pi$
$691$	8.65248	+	26.6296i	0.329156	+	1.01304i	−0.640374	+	0.768063i	$0.721221\pi$
$692$			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
$700$	2.98184	+	4.10415i	0.112703	+	0.155122i
$701$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$701$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.38197	+	4.25325i	−0.0519008	+	0.159734i	−0.973647	−	0.228058i	$-0.926762\pi$
$709$	−1.38197	+	4.25325i	−0.0519008	+	0.159734i	0.921747	+	0.387793i	$0.126762\pi$
$710$	−22.5955	−	7.34173i	−0.847995	−	0.275530i
$711$		0			0
$712$	−23.4197	+	32.2344i	−0.877689	+	1.20804i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−4.22291			−0.157818
$717$		0			0
$718$		0			0
$719$	−21.7082	+	15.7719i	−0.809579	+	0.588194i	−0.913709	−	0.406370i	$-0.866794\pi$
$719$	−21.7082	+	15.7719i	−0.809579	+	0.588194i	0.104129	+	0.994564i	$0.466794\pi$
$720$	7.19756	−	22.1518i	0.268237	−	0.825549i
$721$		0			0
$722$	14.8325	+	20.4151i	0.552007	+	0.759772i
$723$		0			0
$724$	−0.326238	−	1.00406i	−0.0121245	−	0.0373155i
$725$		0			0
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	84.4184	−	27.4292i	3.12875	−	1.01659i
$729$	−21.8435	−	15.8702i	−0.809017	−	0.587785i
$730$	−29.4721	+	21.4128i	−1.09081	+	0.792522i
$731$	−0.514708	+	1.58411i	−0.0190372	+	0.0585904i
$732$		0			0
$733$	−26.6831	−	36.7261i	−0.985562	−	1.35651i	−0.933778	−	0.357852i	$-0.883509\pi$
$733$	−26.6831	−	36.7261i	−0.985562	−	1.35651i	−0.0517836	−	0.998658i	$-0.516491\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$739$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−48.8230	−	15.8636i	−1.79114	−	0.581978i	−0.791566	−	0.611083i	$-0.790734\pi$
$743$	−48.8230	−	15.8636i	−1.79114	−	0.581978i	−0.999576	+	0.0291059i	$0.990734\pi$
$744$		0			0
$745$		0			0
$746$	15.6180	+	48.0674i	0.571817	+	1.75987i
$747$		−	54.6189i		−	1.99840i
$748$		0			0
$749$	32.5836			1.19058
$750$		0			0
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	0.00485778	−	0.999988i	$-0.498454\pi$
$751$	−25.8885	−	18.8091i	−0.944686	−	0.686355i	−0.949544	+	0.313633i	$0.898454\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$757$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$758$		−	47.8127i		−	1.73664i
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$		0			0
$764$	1.95743	−	6.02434i	0.0708172	−	0.217953i
$765$	10.4736	+	3.40308i	0.378674	+	0.123039i
$766$		0			0
$767$	16.3503	−	22.5042i	0.590374	−	0.812580i
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	−4.22835	+	1.37387i	−0.152182	+	0.0494468i
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	−3.27051	+	2.37616i	−0.117556	+	0.0854095i
$775$	13.8197	−	42.5325i	0.496417	−	1.52781i
$776$		0			0
$777$		0			0
$778$	−20.2971	+	27.9365i	−0.727685	+	1.00157i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−32.2254	−	23.4131i	−1.15091	−	0.836184i
$785$		0			0
$786$		0			0
$787$	−29.3501	−	9.53643i	−1.04622	−	0.339937i	−0.265035	−	0.964239i	$-0.585384\pi$
$787$	−29.3501	−	9.53643i	−1.04622	−	0.339937i	−0.781183	+	0.624302i	$0.785384\pi$
$788$	2.43925	+	3.35733i	0.0868946	+	0.119600i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−4.58359	+	3.33017i	−0.162461	+	0.118035i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	3.90328	−	5.37240i	0.138002	−	0.189943i
$801$	−12.4377	−	38.2793i	−0.439464	−	1.35253i
$802$		−	5.93958i		−	0.209734i
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−66.8328	−	48.5569i	−2.35409	−	1.71034i
$807$		0			0
$808$		0			0
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	15.7104	+	21.6235i	0.552007	+	0.759772i
$811$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$811$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−27.7082	+	85.2771i	−0.968203	+	2.97982i
$820$		0			0
$821$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$821$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$823$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$824$		0			0
$825$		0			0
$826$	−22.8328			−0.794455
$827$	−21.1750	+	6.88017i	−0.736326	+	0.239247i	−0.653087	−	0.757283i	$-0.726527\pi$
$827$	−21.1750	+	6.88017i	−0.736326	+	0.239247i	−0.0832391	+	0.996530i	$0.526527\pi$
$828$		0			0
$829$	18.0902	−	13.1433i	0.628298	−	0.456485i	−0.227512	−	0.973775i	$-0.573059\pi$
$829$	18.0902	−	13.1433i	0.628298	−	0.456485i	0.855810	+	0.517290i	$0.173059\pi$
$830$	−16.7082	+	51.4226i	−0.579950	+	1.78490i
$831$		0			0
$832$	−35.5954	−	48.9928i	−1.23405	−	1.69852i
$833$	11.0700	−	15.2365i	0.383552	−	0.527913i
$834$		0			0
$835$			52.5897i			1.81994i
$836$		0			0
$837$		0			0
$838$	−45.1910	+	14.6835i	−1.56110	+	0.507232i
$839$	45.3050	+	32.9160i	1.56410	+	1.13639i	0.932544	+	0.361056i	$0.117584\pi$
$839$	45.3050	+	32.9160i	1.56410	+	1.13639i	0.631556	+	0.775330i	$0.282416\pi$
$840$		0			0
$841$	−8.96149	+	27.5806i	−0.309017	+	0.951057i
$842$	39.5422	+	12.8480i	1.36271	+	0.442772i
$843$		0			0
$844$		0			0
$845$	24.4336	+	75.1990i	0.840542	+	2.58692i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−8.81966	−	6.40786i	−0.302512	−	0.219788i
$851$		0			0
$852$		0			0
$853$	−52.5420	−	17.0719i	−1.79900	−	0.584532i	−0.799142	−	0.601142i	$-0.794712\pi$
$853$	−52.5420	−	17.0719i	−1.79900	−	0.584532i	−0.999862	+	0.0166106i	$0.994712\pi$
$854$		0			0
$855$		0			0
$856$	−6.95743	−	21.4128i	−0.237800	−	0.731873i
$857$		−	25.4000i		−	0.867647i	−0.900998	−	0.433824i	$-0.857164\pi$
$857$		−	25.4000i		−	0.867647i	0.900998	−	0.433824i	$-0.142836\pi$
$858$		0			0
$859$	35.7771			1.22070			0.610349	−	0.792132i	$-0.291029\pi$
$859$	35.7771			1.22070			0.610349	+	0.792132i	$0.291029\pi$
$860$	−0.509359	+	0.165501i	−0.0173690	+	0.00564353i
$861$		0			0
$862$		0			0
$863$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$863$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$864$		0			0
$865$	31.7356	+	43.6803i	1.07904	+	1.48517i
$866$		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
$875$	45.7004	+	14.8490i	1.54496	+	0.501986i
$876$		0			0
$877$	26.2275	−	36.0991i	0.885640	−	1.21898i	−0.0891871	−	0.996015i	$-0.528427\pi$
$877$	26.2275	−	36.0991i	0.885640	−	1.21898i	0.974827	−	0.222964i	$-0.0715731\pi$
$878$		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	$0.489274\pi$
$882$	43.4723	−	14.1250i	1.46379	−	0.475614i
$883$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$883$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$884$	2.18034	−	1.58411i	0.0733328	−	0.0532794i
$885$		0			0
$886$		0			0
$887$	34.0341	+	46.8439i	1.14275	+	1.57286i	0.761202	+	0.648514i	$0.224609\pi$
$887$	34.0341	+	46.8439i	1.14275	+	1.57286i	0.381549	+	0.924348i	$0.375391\pi$
$888$		0			0
$889$	19.8197	+	60.9986i	0.664730	+	2.04583i
$890$			39.8439i			1.33557i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−32.3607	+	23.5114i	−1.08170	+	0.785900i
$896$	−11.8328	+	36.4177i	−0.395307	+	1.21663i
$897$		0			0
$898$	31.4208	+	43.2470i	1.04853	+	1.44317i
$899$		0			0
$900$	1.09424	+	3.36771i	0.0364745	+	0.112257i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.09017	−	5.87785i	−0.268926	−	0.195386i
$906$		0			0
$907$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$907$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$908$	3.63198	+	1.18010i	0.120532	+	0.0391631i
$909$		0			0
$910$	52.1734	−	71.8106i	1.72953	−	2.38050i
$911$	2.76393	+	8.50651i	0.0915732	+	0.281833i	0.986345	−	0.164690i	$-0.0526622\pi$
$911$	2.76393	+	8.50651i	0.0915732	+	0.281833i	−0.894772	+	0.446523i	$0.852662\pi$
$912$		0			0
$913$		0			0
$914$	29.3738			0.971600
$915$		0			0
$916$	−1.14590	−	0.832544i	−0.0378615	−	0.0275080i
$917$		0			0
$918$		0			0
$919$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$919$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$920$		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
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	−0.996605	−	0.0823350i	$-0.973762\pi$
$929$	−4.32624	+	13.3148i	−0.141939	+	0.436844i	0.854665	+	0.519179i	$0.173762\pi$
$930$		0			0
$931$		0			0
$932$	3.63198	−	4.99899i	0.118970	−	0.163748i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	61.9574			2.02514
$937$	57.5945	−	18.7136i	1.88153	−	0.611346i	0.895429	−	0.445205i	$-0.146869\pi$
$937$	57.5945	−	18.7136i	1.88153	−	0.611346i	0.986102	−	0.166142i	$-0.0531309\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$941$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$942$		0			0
$943$		0			0
$944$	4.29180	+	13.2088i	0.139686	+	0.429909i
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	−69.0132	−	50.1410i	−2.24026	−	1.62765i
$950$		0			0
$951$		0			0
$952$	−19.9285	−	6.47515i	−0.645886	−	0.209861i
$953$	19.7007	+	27.1157i	0.638168	+	0.878363i	0.998516	−	0.0544552i	$-0.0173422\pi$
$953$	19.7007	+	27.1157i	0.638168	+	0.878363i	−0.360348	+	0.932818i	$0.617342\pi$
$954$		0			0
$955$	−18.5410	−	57.0634i	−0.599973	−	1.84653i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−39.6418	+	28.8015i	−1.27877	+	0.929080i
$962$		0			0
$963$	21.6306	+	7.02820i	0.697035	+	0.226481i
$964$		0			0
$965$	−24.7532	+	34.0698i	−0.796834	+	1.09675i
$966$		0			0
$967$		−	8.83536i		−	0.284126i	−0.989858	−	0.142063i	$-0.954626\pi$
$967$		−	8.83536i		−	0.284126i	0.989858	−	0.142063i	$-0.0453736\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.4721	+	10.5146i	0.464433	+	0.337430i	0.795268	−	0.606258i	$-0.207330\pi$
$971$	14.4721	+	10.5146i	0.464433	+	0.337430i	−0.330835	+	0.943689i	$0.607330\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$977$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$978$		0			0
$979$		0			0
$980$	6.05573			0.193443
$981$		0			0
$982$		0			0
$983$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$983$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$	37.3845	+	12.1470i	1.19117	+	0.387034i
$986$		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	$0.966402\pi$
$992$	−11.2978	+	3.67086i	−0.358704	+	0.116550i
$993$		0			0
$994$	−36.9443	+	26.8416i	−1.17180	+	0.851363i
$995$	−16.5836	+	51.0390i	−0.525735	+	1.61805i
$996$		0			0
$997$	−14.6482	−	20.1615i	−0.463912	−	0.638520i	0.511402	−	0.859342i	$-0.329126\pi$
$997$	−14.6482	−	20.1615i	−0.463912	−	0.638520i	−0.975314	+	0.220821i	$0.929126\pi$
$998$	−3.12262	+	4.29792i	−0.0988449	+	0.136048i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.b.364.2	✓	4	11.8	odd	10
605.2.b.b.364.2	✓	4	55.14	even	10
605.2.b.b.364.3	yes	4	11.3	even	5
605.2.b.b.364.3	yes	4	55.19	odd	10
605.2.j.a.9.1		8	11.2	odd	10	inner
605.2.j.a.9.1		8	55.9	even	10	inner
605.2.j.a.9.2		8	11.9	even	5	inner
605.2.j.a.9.2		8	55.24	odd	10	inner
605.2.j.a.269.1		8	1.1	even	1	trivial
605.2.j.a.269.1		8	55.54	odd	2	CM
605.2.j.a.269.2		8	5.4	even	2	inner
605.2.j.a.269.2		8	11.10	odd	2	inner
605.2.j.c.124.1		8	11.4	even	5
605.2.j.c.124.1		8	55.29	odd	10
605.2.j.c.124.2		8	11.7	odd	10
605.2.j.c.124.2		8	55.4	even	10
605.2.j.c.444.1		8	11.6	odd	10
605.2.j.c.444.1		8	55.49	even	10
605.2.j.c.444.2		8	11.5	even	5
605.2.j.c.444.2		8	55.39	odd	10
3025.2.a.bb.1.2		4	55.8	even	20
3025.2.a.bb.1.2		4	55.47	odd	20
3025.2.a.bb.1.3		4	55.3	odd	20
3025.2.a.bb.1.3		4	55.52	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)

\(f(q)\)	\(=\)	\(q+(-1.26313 + 0.410415i) q^{2} +(-0.190983 + 0.138757i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(2.52626 + 3.47709i) q^{7} +(1.74560 - 2.40261i) q^{8} +(0.927051 + 2.85317i) q^{9} +O(q^{10})\)	\(q+(-1.26313 + 0.410415i) q^{2} +(-0.190983 + 0.138757i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(2.52626 + 3.47709i) q^{7} +(1.74560 - 2.40261i) q^{8} +(0.927051 + 2.85317i) q^{9} -2.96979i q^{10} +(6.61382 - 2.14896i) q^{13} +(-4.61803 - 3.35520i) q^{14} +(-1.07295 + 3.30220i) q^{16} +(-1.56131 - 0.507301i) q^{17} +(-2.34197 - 3.22344i) q^{18} +(-0.163119 - 0.502029i) q^{20} +(-4.04508 - 2.93893i) q^{25} +(-7.47214 + 5.42882i) q^{26} +(-0.964944 - 0.313529i) q^{28} +(2.76393 + 8.50651i) q^{31} +1.32813i q^{32} +2.18034 q^{34} +(-9.14008 + 2.96979i) q^{35} +(-0.572949 - 0.416272i) q^{36} +(3.90328 + 5.37240i) q^{40} -1.01460i q^{43} -6.70820 q^{45} +(-3.54508 + 10.9106i) q^{49} +(6.31564 + 2.05208i) q^{50} +(-0.964944 + 1.32813i) q^{52} +12.7639 q^{56} +(3.23607 - 2.35114i) q^{59} +(-6.98240 - 9.61045i) q^{62} +(-7.57877 + 10.4313i) q^{63} +(-2.69098 - 8.28199i) q^{64} +15.5500i q^{65} +(0.368576 - 0.119757i) q^{68} +(10.3262 - 7.50245i) q^{70} +(2.47214 - 7.60845i) q^{71} +(8.47332 + 2.75315i) q^{72} +(-7.21019 - 9.92398i) q^{73} +(-6.28115 - 4.56352i) q^{80} +(-7.28115 + 5.29007i) q^{81} +(-17.3152 - 5.62605i) q^{83} +(2.15768 - 2.96979i) q^{85} +(0.416408 + 1.28157i) q^{86} -13.4164 q^{89} +(8.47332 - 2.75315i) q^{90} +(24.1803 + 17.5680i) q^{91} -15.2365i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 10 q^{5} - 6 q^{9}+O(q^{10}) \) 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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