LMFDB - Embedded newform 5054.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

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:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{29}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 7 $ x^2 - x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.19258$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.19258 q^{3} +1.00000 q^{4} +2.19258 q^{5} -3.19258 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.19258 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.19258 q^{3} +1.00000 q^{4} +2.19258 q^{5} -3.19258 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.19258 q^{9} +2.19258 q^{10} -1.19258 q^{11} -3.19258 q^{12} +6.38516 q^{13} -1.00000 q^{14} -7.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +7.19258 q^{18} +2.19258 q^{20} +3.19258 q^{21} -1.19258 q^{22} -8.38516 q^{23} -3.19258 q^{24} -0.192582 q^{25} +6.38516 q^{26} -13.3852 q^{27} -1.00000 q^{28} +0.192582 q^{29} -7.00000 q^{30} -10.0000 q^{31} +1.00000 q^{32} +3.80742 q^{33} -4.00000 q^{34} -2.19258 q^{35} +7.19258 q^{36} -4.19258 q^{37} -20.3852 q^{39} +2.19258 q^{40} -6.57775 q^{41} +3.19258 q^{42} +10.1926 q^{43} -1.19258 q^{44} +15.7703 q^{45} -8.38516 q^{46} -4.80742 q^{47} -3.19258 q^{48} +1.00000 q^{49} -0.192582 q^{50} +12.7703 q^{51} +6.38516 q^{52} +5.19258 q^{53} -13.3852 q^{54} -2.61484 q^{55} -1.00000 q^{56} +0.192582 q^{58} +4.57775 q^{59} -7.00000 q^{60} -0.807418 q^{61} -10.0000 q^{62} -7.19258 q^{63} +1.00000 q^{64} +14.0000 q^{65} +3.80742 q^{66} +2.00000 q^{67} -4.00000 q^{68} +26.7703 q^{69} -2.19258 q^{70} +1.19258 q^{71} +7.19258 q^{72} -4.38516 q^{73} -4.19258 q^{74} +0.614835 q^{75} +1.19258 q^{77} -20.3852 q^{78} -1.80742 q^{79} +2.19258 q^{80} +21.1555 q^{81} -6.57775 q^{82} +8.00000 q^{83} +3.19258 q^{84} -8.77033 q^{85} +10.1926 q^{86} -0.614835 q^{87} -1.19258 q^{88} -2.42225 q^{89} +15.7703 q^{90} -6.38516 q^{91} -8.38516 q^{92} +31.9258 q^{93} -4.80742 q^{94} -3.19258 q^{96} -8.80742 q^{97} +1.00000 q^{98} -8.57775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 9 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 9 q^{9} - q^{10} + 3 q^{11} - q^{12} + 2 q^{13} - 2 q^{14} - 14 q^{15} + 2 q^{16} - 8 q^{17} + 9 q^{18} - q^{20} + q^{21} + 3 q^{22} - 6 q^{23} - q^{24} + 5 q^{25} + 2 q^{26} - 16 q^{27} - 2 q^{28} - 5 q^{29} - 14 q^{30} - 20 q^{31} + 2 q^{32} + 13 q^{33} - 8 q^{34} + q^{35} + 9 q^{36} - 3 q^{37} - 30 q^{39} - q^{40} + 3 q^{41} + q^{42} + 15 q^{43} + 3 q^{44} + 10 q^{45} - 6 q^{46} - 15 q^{47} - q^{48} + 2 q^{49} + 5 q^{50} + 4 q^{51} + 2 q^{52} + 5 q^{53} - 16 q^{54} - 16 q^{55} - 2 q^{56} - 5 q^{58} - 7 q^{59} - 14 q^{60} - 7 q^{61} - 20 q^{62} - 9 q^{63} + 2 q^{64} + 28 q^{65} + 13 q^{66} + 4 q^{67} - 8 q^{68} + 32 q^{69} + q^{70} - 3 q^{71} + 9 q^{72} + 2 q^{73} - 3 q^{74} + 12 q^{75} - 3 q^{77} - 30 q^{78} - 9 q^{79} - q^{80} + 10 q^{81} + 3 q^{82} + 16 q^{83} + q^{84} + 4 q^{85} + 15 q^{86} - 12 q^{87} + 3 q^{88} - 21 q^{89} + 10 q^{90} - 2 q^{91} - 6 q^{92} + 10 q^{93} - 15 q^{94} - q^{96} - 23 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 9 * q^9 - q^10 + 3 * q^11 - q^12 + 2 * q^13 - 2 * q^14 - 14 * q^15 + 2 * q^16 - 8 * q^17 + 9 * q^18 - q^20 + q^21 + 3 * q^22 - 6 * q^23 - q^24 + 5 * q^25 + 2 * q^26 - 16 * q^27 - 2 * q^28 - 5 * q^29 - 14 * q^30 - 20 * q^31 + 2 * q^32 + 13 * q^33 - 8 * q^34 + q^35 + 9 * q^36 - 3 * q^37 - 30 * q^39 - q^40 + 3 * q^41 + q^42 + 15 * q^43 + 3 * q^44 + 10 * q^45 - 6 * q^46 - 15 * q^47 - q^48 + 2 * q^49 + 5 * q^50 + 4 * q^51 + 2 * q^52 + 5 * q^53 - 16 * q^54 - 16 * q^55 - 2 * q^56 - 5 * q^58 - 7 * q^59 - 14 * q^60 - 7 * q^61 - 20 * q^62 - 9 * q^63 + 2 * q^64 + 28 * q^65 + 13 * q^66 + 4 * q^67 - 8 * q^68 + 32 * q^69 + q^70 - 3 * q^71 + 9 * q^72 + 2 * q^73 - 3 * q^74 + 12 * q^75 - 3 * q^77 - 30 * q^78 - 9 * q^79 - q^80 + 10 * q^81 + 3 * q^82 + 16 * q^83 + q^84 + 4 * q^85 + 15 * q^86 - 12 * q^87 + 3 * q^88 - 21 * q^89 + 10 * q^90 - 2 * q^91 - 6 * q^92 + 10 * q^93 - 15 * q^94 - q^96 - 23 * q^97 + 2 * q^98 - q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.19258	−1.84324	−0.921619	−	0.388096i	$-0.873133\pi$
$3$	−3.19258	−1.84324	−0.921619	+	0.388096i	$0.873133\pi$
$4$	1.00000	0.500000
$5$	2.19258	0.980553	0.490276	−	0.871567i	$-0.336896\pi$
$5$	2.19258	0.980553	0.490276	+	0.871567i	$0.336896\pi$
$6$	−3.19258	−1.30337
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	7.19258	2.39753
$10$	2.19258	0.693355
$11$	−1.19258	−0.359577	−0.179789	−	0.983705i	$-0.557541\pi$
$11$	−1.19258	−0.359577	−0.179789	+	0.983705i	$0.557541\pi$
$12$	−3.19258	−0.921619
$13$	6.38516	1.77093	0.885463	−	0.464710i	$-0.153841\pi$
$13$	6.38516	1.77093	0.885463	+	0.464710i	$0.153841\pi$
$14$	−1.00000	−0.267261
$15$	−7.00000	−1.80739
$16$	1.00000	0.250000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	7.19258	1.69531
$19$	0	0
$19$	0	0
$20$	2.19258	0.490276
$21$	3.19258	0.696679
$22$	−1.19258	−0.254259
$23$	−8.38516	−1.74843	−0.874214	−	0.485541i	$-0.838623\pi$
$23$	−8.38516	−1.74843	−0.874214	+	0.485541i	$0.838623\pi$
$24$	−3.19258	−0.651683
$25$	−0.192582	−0.0385165
$26$	6.38516	1.25223
$27$	−13.3852	−2.57598
$28$	−1.00000	−0.188982
$29$	0.192582	0.0357617	0.0178808	−	0.999840i	$-0.494308\pi$
$29$	0.192582	0.0357617	0.0178808	+	0.999840i	$0.494308\pi$
$30$	−7.00000	−1.27802
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	1.00000	0.176777
$33$	3.80742	0.662786
$34$	−4.00000	−0.685994
$35$	−2.19258	−0.370614
$36$	7.19258	1.19876
$37$	−4.19258	−0.689256	−0.344628	−	0.938739i	$-0.611995\pi$
$37$	−4.19258	−0.689256	−0.344628	+	0.938739i	$0.611995\pi$
$38$	0	0
$39$	−20.3852	−3.26424
$40$	2.19258	0.346678
$41$	−6.57775	−1.02727	−0.513636	−	0.858008i	$-0.671702\pi$
$41$	−6.57775	−1.02727	−0.513636	+	0.858008i	$0.671702\pi$
$42$	3.19258	0.492626
$43$	10.1926	1.55435	0.777177	−	0.629282i	$-0.216651\pi$
$43$	10.1926	1.55435	0.777177	+	0.629282i	$0.216651\pi$
$44$	−1.19258	−0.179789
$45$	15.7703	2.35090
$46$	−8.38516	−1.23633
$47$	−4.80742	−0.701234	−0.350617	−	0.936519i	$-0.614028\pi$
$47$	−4.80742	−0.701234	−0.350617	+	0.936519i	$0.614028\pi$
$48$	−3.19258	−0.460810
$49$	1.00000	0.142857
$50$	−0.192582	−0.0272353
$51$	12.7703	1.78820
$52$	6.38516	0.885463
$53$	5.19258	0.713256	0.356628	−	0.934246i	$-0.383926\pi$
$53$	5.19258	0.713256	0.356628	+	0.934246i	$0.383926\pi$
$54$	−13.3852	−1.82149
$55$	−2.61484	−0.352584
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.192582	0.0252873
$59$	4.57775	0.595972	0.297986	−	0.954570i	$-0.403685\pi$
$59$	4.57775	0.595972	0.297986	+	0.954570i	$0.403685\pi$
$60$	−7.00000	−0.903696
$61$	−0.807418	−0.103379	−0.0516896	−	0.998663i	$-0.516461\pi$
$61$	−0.807418	−0.103379	−0.0516896	+	0.998663i	$0.516461\pi$
$62$	−10.0000	−1.27000
$63$	−7.19258	−0.906180
$64$	1.00000	0.125000
$65$	14.0000	1.73649
$66$	3.80742	0.468661
$67$	2.00000	0.244339	0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000	0.244339	0.122169	+	0.992509i	$0.461015\pi$
$68$	−4.00000	−0.485071
$69$	26.7703	3.22277
$70$	−2.19258	−0.262064
$71$	1.19258	0.141533	0.0707667	−	0.997493i	$-0.477455\pi$
$71$	1.19258	0.141533	0.0707667	+	0.997493i	$0.477455\pi$
$72$	7.19258	0.847654
$73$	−4.38516	−0.513245	−0.256622	−	0.966512i	$-0.582610\pi$
$73$	−4.38516	−0.513245	−0.256622	+	0.966512i	$0.582610\pi$
$74$	−4.19258	−0.487378
$75$	0.614835	0.0709951
$76$	0	0
$77$	1.19258	0.135907
$78$	−20.3852	−2.30817
$79$	−1.80742	−0.203350	−0.101675	−	0.994818i	$-0.532420\pi$
$79$	−1.80742	−0.203350	−0.101675	+	0.994818i	$0.532420\pi$
$80$	2.19258	0.245138
$81$	21.1555	2.35061
$82$	−6.57775	−0.726391
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	3.19258	0.348339
$85$	−8.77033	−0.951276
$86$	10.1926	1.09909
$87$	−0.614835	−0.0659173
$88$	−1.19258	−0.127130
$89$	−2.42225	−0.256758	−0.128379	−	0.991725i	$-0.540977\pi$
$89$	−2.42225	−0.256758	−0.128379	+	0.991725i	$0.540977\pi$
$90$	15.7703	1.66234
$91$	−6.38516	−0.669347
$92$	−8.38516	−0.874214
$93$	31.9258	3.31055
$94$	−4.80742	−0.495847
$95$	0	0
$96$	−3.19258	−0.325842
$97$	−8.80742	−0.894258	−0.447129	−	0.894470i	$-0.647553\pi$
$97$	−8.80742	−0.894258	−0.447129	+	0.894470i	$0.647553\pi$
$98$	1.00000	0.101015
$99$	−8.57775	−0.862096
$100$	−0.192582	−0.0192582
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	12.7703	1.26445
$103$	−4.38516	−0.432083	−0.216042	−	0.976384i	$-0.569315\pi$
$103$	−4.38516	−0.432083	−0.216042	+	0.976384i	$0.569315\pi$
$104$	6.38516	0.626117
$105$	7.00000	0.683130
$106$	5.19258	0.504348
$107$	−7.61484	−0.736154	−0.368077	−	0.929795i	$-0.619984\pi$
$107$	−7.61484	−0.736154	−0.368077	+	0.929795i	$0.619984\pi$
$108$	−13.3852	−1.28799
$109$	5.19258	0.497359	0.248680	−	0.968586i	$-0.420003\pi$
$109$	5.19258	0.497359	0.248680	+	0.968586i	$0.420003\pi$
$110$	−2.61484	−0.249315
$111$	13.3852	1.27046
$112$	−1.00000	−0.0944911
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	−18.3852	−1.71443
$116$	0.192582	0.0178808
$117$	45.9258	4.24584
$118$	4.57775	0.421416
$119$	4.00000	0.366679
$120$	−7.00000	−0.639010
$121$	−9.57775	−0.870704
$122$	−0.807418	−0.0731002
$123$	21.0000	1.89351
$124$	−10.0000	−0.898027
$125$	−11.3852	−1.01832
$126$	−7.19258	−0.640766
$127$	−15.5777	−1.38230	−0.691151	−	0.722711i	$-0.742896\pi$
$127$	−15.5777	−1.38230	−0.691151	+	0.722711i	$0.742896\pi$
$128$	1.00000	0.0883883
$129$	−32.5407	−2.86505
$130$	14.0000	1.22788
$131$	9.61484	0.840052	0.420026	−	0.907512i	$-0.362021\pi$
$131$	9.61484	0.840052	0.420026	+	0.907512i	$0.362021\pi$
$132$	3.80742	0.331393
$133$	0	0
$134$	2.00000	0.172774
$135$	−29.3481	−2.52588
$136$	−4.00000	−0.342997
$137$	4.57775	0.391103	0.195552	−	0.980693i	$-0.437350\pi$
$137$	4.57775	0.391103	0.195552	+	0.980693i	$0.437350\pi$
$138$	26.7703	2.27884
$139$	−12.7703	−1.08317	−0.541583	−	0.840648i	$-0.682175\pi$
$139$	−12.7703	−1.08317	−0.541583	+	0.840648i	$0.682175\pi$
$140$	−2.19258	−0.185307
$141$	15.3481	1.29254
$142$	1.19258	0.100079
$143$	−7.61484	−0.636785
$144$	7.19258	0.599382
$145$	0.422253	0.0350662
$146$	−4.38516	−0.362919
$147$	−3.19258	−0.263320
$148$	−4.19258	−0.344628
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0.614835	0.0502011
$151$	−21.5407	−1.75295	−0.876477	−	0.481444i	$-0.840113\pi$
$151$	−21.5407	−1.75295	−0.876477	+	0.481444i	$0.840113\pi$
$152$	0	0
$153$	−28.7703	−2.32594
$154$	1.19258	0.0961010
$155$	−21.9258	−1.76112
$156$	−20.3852	−1.63212
$157$	−21.5777	−1.72209	−0.861046	−	0.508527i	$-0.830190\pi$
$157$	−21.5777	−1.72209	−0.861046	+	0.508527i	$0.830190\pi$
$158$	−1.80742	−0.143790
$159$	−16.5777	−1.31470
$160$	2.19258	0.173339
$161$	8.38516	0.660844
$162$	21.1555	1.66213
$163$	19.5777	1.53345	0.766724	−	0.641977i	$-0.221886\pi$
$163$	19.5777	1.53345	0.766724	+	0.641977i	$0.221886\pi$
$164$	−6.57775	−0.513636
$165$	8.34808	0.649897
$166$	8.00000	0.620920
$167$	−6.77033	−0.523904	−0.261952	−	0.965081i	$-0.584366\pi$
$167$	−6.77033	−0.523904	−0.261952	+	0.965081i	$0.584366\pi$
$168$	3.19258	0.246313
$169$	27.7703	2.13618
$170$	−8.77033	−0.672654
$171$	0	0
$172$	10.1926	0.777177
$173$	21.1555	1.60842	0.804211	−	0.594344i	$-0.202588\pi$
$173$	21.1555	1.60842	0.804211	+	0.594344i	$0.202588\pi$
$174$	−0.614835	−0.0466105
$175$	0.192582	0.0145579
$176$	−1.19258	−0.0898943
$177$	−14.6148	−1.09852
$178$	−2.42225	−0.181556
$179$	4.38516	0.327763	0.163881	−	0.986480i	$-0.447599\pi$
$179$	4.38516	0.327763	0.163881	+	0.986480i	$0.447599\pi$
$180$	15.7703	1.17545
$181$	−20.3852	−1.51522	−0.757609	−	0.652709i	$-0.773632\pi$
$181$	−20.3852	−1.51522	−0.757609	+	0.652709i	$0.773632\pi$
$182$	−6.38516	−0.473300
$183$	2.57775	0.190553
$184$	−8.38516	−0.618163
$185$	−9.19258	−0.675852
$186$	31.9258	2.34091
$187$	4.77033	0.348841
$188$	−4.80742	−0.350617
$189$	13.3852	0.973627
$190$	0	0
$191$	−8.38516	−0.606729	−0.303365	−	0.952875i	$-0.598110\pi$
$191$	−8.38516	−0.606729	−0.303365	+	0.952875i	$0.598110\pi$
$192$	−3.19258	−0.230405
$193$	13.1555	0.946953	0.473477	−	0.880806i	$-0.342999\pi$
$193$	13.1555	0.946953	0.473477	+	0.880806i	$0.342999\pi$
$194$	−8.80742	−0.632336
$195$	−44.6962	−3.20076
$196$	1.00000	0.0714286
$197$	5.22967	0.372599	0.186299	−	0.982493i	$-0.440351\pi$
$197$	5.22967	0.372599	0.186299	+	0.982493i	$0.440351\pi$
$198$	−8.57775	−0.609594
$199$	−16.5777	−1.17517	−0.587583	−	0.809164i	$-0.699920\pi$
$199$	−16.5777	−1.17517	−0.587583	+	0.809164i	$0.699920\pi$
$200$	−0.192582	−0.0136176
$201$	−6.38516	−0.450375
$202$	−10.0000	−0.703598
$203$	−0.192582	−0.0135166
$204$	12.7703	0.894102
$205$	−14.4223	−1.00729
$206$	−4.38516	−0.305529
$207$	−60.3110	−4.19190
$208$	6.38516	0.442732
$209$	0	0
$210$	7.00000	0.483046
$211$	7.22967	0.497711	0.248856	−	0.968541i	$-0.419946\pi$
$211$	7.22967	0.497711	0.248856	+	0.968541i	$0.419946\pi$
$212$	5.19258	0.356628
$213$	−3.80742	−0.260880
$214$	−7.61484	−0.520539
$215$	22.3481	1.52413
$216$	−13.3852	−0.910745
$217$	10.0000	0.678844
$218$	5.19258	0.351686
$219$	14.0000	0.946032
$220$	−2.61484	−0.176292
$221$	−25.5407	−1.71805
$222$	13.3852	0.898353
$223$	−2.38516	−0.159722	−0.0798612	−	0.996806i	$-0.525448\pi$
$223$	−2.38516	−0.159722	−0.0798612	+	0.996806i	$0.525448\pi$
$224$	−1.00000	−0.0668153
$225$	−1.38516	−0.0923443
$226$	8.00000	0.532152
$227$	8.00000	0.530979	0.265489	−	0.964114i	$-0.414466\pi$
$227$	8.00000	0.530979	0.265489	+	0.964114i	$0.414466\pi$
$228$	0	0
$229$	−5.80742	−0.383765	−0.191882	−	0.981418i	$-0.561459\pi$
$229$	−5.80742	−0.383765	−0.191882	+	0.981418i	$0.561459\pi$
$230$	−18.3852	−1.21228
$231$	−3.80742	−0.250510
$232$	0.192582	0.0126437
$233$	17.1926	1.12632	0.563162	−	0.826347i	$-0.309585\pi$
$233$	17.1926	1.12632	0.563162	+	0.826347i	$0.309585\pi$
$234$	45.9258	3.00227
$235$	−10.5407	−0.687597
$236$	4.57775	0.297986
$237$	5.77033	0.374823
$238$	4.00000	0.259281
$239$	−9.61484	−0.621932	−0.310966	−	0.950421i	$-0.600653\pi$
$239$	−9.61484	−0.621932	−0.310966	+	0.950421i	$0.600653\pi$
$240$	−7.00000	−0.451848
$241$	−10.1926	−0.656562	−0.328281	−	0.944580i	$-0.606469\pi$
$241$	−10.1926	−0.656562	−0.328281	+	0.944580i	$0.606469\pi$
$242$	−9.57775	−0.615681
$243$	−27.3852	−1.75676
$244$	−0.807418	−0.0516896
$245$	2.19258	0.140079
$246$	21.0000	1.33891
$247$	0	0
$248$	−10.0000	−0.635001
$249$	−25.5407	−1.61857
$250$	−11.3852	−0.720061
$251$	19.1555	1.20908	0.604542	−	0.796573i	$-0.293356\pi$
$251$	19.1555	1.20908	0.604542	+	0.796573i	$0.293356\pi$
$252$	−7.19258	−0.453090
$253$	10.0000	0.628695
$254$	−15.5777	−0.977435
$255$	28.0000	1.75343
$256$	1.00000	0.0625000
$257$	18.1926	1.13482	0.567411	−	0.823435i	$-0.307945\pi$
$257$	18.1926	1.13482	0.567411	+	0.823435i	$0.307945\pi$
$258$	−32.5407	−2.02589
$259$	4.19258	0.260514
$260$	14.0000	0.868243
$261$	1.38516	0.0857395
$262$	9.61484	0.594007
$263$	23.1555	1.42783	0.713914	−	0.700233i	$-0.246921\pi$
$263$	23.1555	1.42783	0.713914	+	0.700233i	$0.246921\pi$
$264$	3.80742	0.234330
$265$	11.3852	0.699385
$266$	0	0
$267$	7.73324	0.473267
$268$	2.00000	0.122169
$269$	−11.5407	−0.703646	−0.351823	−	0.936066i	$-0.614438\pi$
$269$	−11.5407	−0.703646	−0.351823	+	0.936066i	$0.614438\pi$
$270$	−29.3481	−1.78607
$271$	24.5777	1.49299	0.746496	−	0.665390i	$-0.231735\pi$
$271$	24.5777	1.49299	0.746496	+	0.665390i	$0.231735\pi$
$272$	−4.00000	−0.242536
$273$	20.3852	1.23377
$274$	4.57775	0.276552
$275$	0.229670	0.0138496
$276$	26.7703	1.61138
$277$	−15.6148	−0.938205	−0.469102	−	0.883144i	$-0.655422\pi$
$277$	−15.6148	−0.938205	−0.469102	+	0.883144i	$0.655422\pi$
$278$	−12.7703	−0.765913
$279$	−71.9258	−4.30609
$280$	−2.19258	−0.131032
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	15.3481	0.913965
$283$	−25.5407	−1.51823	−0.759117	−	0.650954i	$-0.774369\pi$
$283$	−25.5407	−1.51823	−0.759117	+	0.650954i	$0.774369\pi$
$284$	1.19258	0.0707667
$285$	0	0
$286$	−7.61484	−0.450275
$287$	6.57775	0.388272
$288$	7.19258	0.423827
$289$	−1.00000	−0.0588235
$290$	0.422253	0.0247955
$291$	28.1184	1.64833
$292$	−4.38516	−0.256622
$293$	−18.3852	−1.07407	−0.537036	−	0.843559i	$-0.680456\pi$
$293$	−18.3852	−1.07407	−0.537036	+	0.843559i	$0.680456\pi$
$294$	−3.19258	−0.186195
$295$	10.0371	0.584382
$296$	−4.19258	−0.243689
$297$	15.9629	0.926262
$298$	0	0
$299$	−53.5407	−3.09634
$300$	0.614835	0.0354975
$301$	−10.1926	−0.587491
$302$	−21.5407	−1.23953
$303$	31.9258	1.83409
$304$	0	0
$305$	−1.77033	−0.101369
$306$	−28.7703	−1.64469
$307$	−12.5777	−0.717850	−0.358925	−	0.933366i	$-0.616857\pi$
$307$	−12.5777	−0.717850	−0.358925	+	0.933366i	$0.616857\pi$
$308$	1.19258	0.0679537
$309$	14.0000	0.796432
$310$	−21.9258	−1.24530
$311$	−31.1184	−1.76456	−0.882281	−	0.470722i	$-0.843993\pi$
$311$	−31.1184	−1.76456	−0.882281	+	0.470722i	$0.843993\pi$
$312$	−20.3852	−1.15408
$313$	−3.22967	−0.182552	−0.0912759	−	0.995826i	$-0.529095\pi$
$313$	−3.22967	−0.182552	−0.0912759	+	0.995826i	$0.529095\pi$
$314$	−21.5777	−1.21770
$315$	−15.7703	−0.888557
$316$	−1.80742	−0.101675
$317$	−21.1926	−1.19029	−0.595147	−	0.803617i	$-0.702906\pi$
$317$	−21.1926	−1.19029	−0.595147	+	0.803617i	$0.702906\pi$
$318$	−16.5777	−0.929634
$319$	−0.229670	−0.0128591
$320$	2.19258	0.122569
$321$	24.3110	1.35691
$322$	8.38516	0.467287
$323$	0	0
$324$	21.1555	1.17531
$325$	−1.22967	−0.0682098
$326$	19.5777	1.08431
$327$	−16.5777	−0.916752
$328$	−6.57775	−0.363195
$329$	4.80742	0.265042
$330$	8.34808	0.459547
$331$	2.77033	0.152271	0.0761355	−	0.997097i	$-0.475742\pi$
$331$	2.77033	0.152271	0.0761355	+	0.997097i	$0.475742\pi$
$332$	8.00000	0.439057
$333$	−30.1555	−1.65251
$334$	−6.77033	−0.370456
$335$	4.38516	0.239587
$336$	3.19258	0.174170
$337$	−5.61484	−0.305860	−0.152930	−	0.988237i	$-0.548871\pi$
$337$	−5.61484	−0.305860	−0.152930	+	0.988237i	$0.548871\pi$
$338$	27.7703	1.51051
$339$	−25.5407	−1.38718
$340$	−8.77033	−0.475638
$341$	11.9258	0.645820
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	10.1926	0.549547
$345$	58.6962	3.16009
$346$	21.1555	1.13733
$347$	30.3110	1.62718	0.813590	−	0.581440i	$-0.197510\pi$
$347$	30.3110	1.62718	0.813590	+	0.581440i	$0.197510\pi$
$348$	−0.614835	−0.0329586
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0.192582	0.0102940
$351$	−85.4665	−4.56186
$352$	−1.19258	−0.0635649
$353$	−34.3110	−1.82619	−0.913095	−	0.407747i	$-0.866314\pi$
$353$	−34.3110	−1.82619	−0.913095	+	0.407747i	$0.866314\pi$
$354$	−14.6148	−0.776770
$355$	2.61484	0.138781
$356$	−2.42225	−0.128379
$357$	−12.7703	−0.675878
$358$	4.38516	0.231763
$359$	−13.1555	−0.694320	−0.347160	−	0.937806i	$-0.612854\pi$
$359$	−13.1555	−0.694320	−0.347160	+	0.937806i	$0.612854\pi$
$360$	15.7703	0.831169
$361$	0	0
$362$	−20.3852	−1.07142
$363$	30.5777	1.60492
$364$	−6.38516	−0.334674
$365$	−9.61484	−0.503263
$366$	2.57775	0.134741
$367$	−13.5777	−0.708753	−0.354376	−	0.935103i	$-0.615307\pi$
$367$	−13.5777	−0.708753	−0.354376	+	0.935103i	$0.615307\pi$
$368$	−8.38516	−0.437107
$369$	−47.3110	−2.46291
$370$	−9.19258	−0.477900
$371$	−5.19258	−0.269585
$372$	31.9258	1.65528
$373$	0.192582	0.00997154	0.00498577	−	0.999988i	$-0.498413\pi$
$373$	0.192582	0.00997154	0.00498577	+	0.999988i	$0.498413\pi$
$374$	4.77033	0.246668
$375$	36.3481	1.87701
$376$	−4.80742	−0.247924
$377$	1.22967	0.0633312
$378$	13.3852	0.688459
$379$	−27.1555	−1.39488	−0.697442	−	0.716641i	$-0.745679\pi$
$379$	−27.1555	−1.39488	−0.697442	+	0.716641i	$0.745679\pi$
$380$	0	0
$381$	49.7332	2.54791
$382$	−8.38516	−0.429022
$383$	9.15549	0.467824	0.233912	−	0.972258i	$-0.424847\pi$
$383$	9.15549	0.467824	0.233912	+	0.972258i	$0.424847\pi$
$384$	−3.19258	−0.162921
$385$	2.61484	0.133264
$386$	13.1555	0.669597
$387$	73.3110	3.72661
$388$	−8.80742	−0.447129
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	−44.6962	−2.26328
$391$	33.5407	1.69622
$392$	1.00000	0.0505076
$393$	−30.6962	−1.54842
$394$	5.22967	0.263467
$395$	−3.96291	−0.199396
$396$	−8.57775	−0.431048
$397$	−21.5777	−1.08296	−0.541478	−	0.840715i	$-0.682135\pi$
$397$	−21.5777	−1.08296	−0.541478	+	0.840715i	$0.682135\pi$
$398$	−16.5777	−0.830967
$399$	0	0
$400$	−0.192582	−0.00962912
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	−6.38516	−0.318463
$403$	−63.8516	−3.18068
$404$	−10.0000	−0.497519
$405$	46.3852	2.30490
$406$	−0.192582	−0.00955770
$407$	5.00000	0.247841
$408$	12.7703	0.632226
$409$	10.4223	0.515347	0.257674	−	0.966232i	$-0.417044\pi$
$409$	10.4223	0.515347	0.257674	+	0.966232i	$0.417044\pi$
$410$	−14.4223	−0.712264
$411$	−14.6148	−0.720897
$412$	−4.38516	−0.216042
$413$	−4.57775	−0.225256
$414$	−60.3110	−2.96412
$415$	17.5407	0.861037
$416$	6.38516	0.313058
$417$	40.7703	1.99653
$418$	0	0
$419$	−6.77033	−0.330752	−0.165376	−	0.986231i	$-0.552884\pi$
$419$	−6.77033	−0.330752	−0.165376	+	0.986231i	$0.552884\pi$
$420$	7.00000	0.341565
$421$	−36.3110	−1.76969	−0.884845	−	0.465886i	$-0.845736\pi$
$421$	−36.3110	−1.76969	−0.884845	+	0.465886i	$0.845736\pi$
$422$	7.22967	0.351935
$423$	−34.5777	−1.68123
$424$	5.19258	0.252174
$425$	0.770330	0.0373665
$426$	−3.80742	−0.184470
$427$	0.807418	0.0390737
$428$	−7.61484	−0.368077
$429$	24.3110	1.17375
$430$	22.3481	1.07772
$431$	7.57775	0.365007	0.182504	−	0.983205i	$-0.441580\pi$
$431$	7.57775	0.365007	0.182504	+	0.983205i	$0.441580\pi$
$432$	−13.3852	−0.643994
$433$	−0.651923	−0.0313294	−0.0156647	−	0.999877i	$-0.504986\pi$
$433$	−0.651923	−0.0313294	−0.0156647	+	0.999877i	$0.504986\pi$
$434$	10.0000	0.480015
$435$	−1.34808	−0.0646353
$436$	5.19258	0.248680
$437$	0	0
$438$	14.0000	0.668946
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	−2.61484	−0.124657
$441$	7.19258	0.342504
$442$	−25.5407	−1.21485
$443$	2.57775	0.122472	0.0612362	−	0.998123i	$-0.480496\pi$
$443$	2.57775	0.122472	0.0612362	+	0.998123i	$0.480496\pi$
$444$	13.3852	0.635232
$445$	−5.31099	−0.251765
$446$	−2.38516	−0.112941
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	31.1555	1.47032	0.735159	−	0.677894i	$-0.237107\pi$
$449$	31.1555	1.47032	0.735159	+	0.677894i	$0.237107\pi$
$450$	−1.38516	−0.0652973
$451$	7.84451	0.369383
$452$	8.00000	0.376288
$453$	68.7703	3.23111
$454$	8.00000	0.375459
$455$	−14.0000	−0.656330
$456$	0	0
$457$	−21.1184	−0.987877	−0.493939	−	0.869497i	$-0.664443\pi$
$457$	−21.1184	−0.987877	−0.493939	+	0.869497i	$0.664443\pi$
$458$	−5.80742	−0.271363
$459$	53.5407	2.49906
$460$	−18.3852	−0.857213
$461$	−34.3481	−1.59975	−0.799875	−	0.600167i	$-0.795101\pi$
$461$	−34.3481	−1.59975	−0.799875	+	0.600167i	$0.795101\pi$
$462$	−3.80742	−0.177137
$463$	−13.6148	−0.632735	−0.316368	−	0.948637i	$-0.602463\pi$
$463$	−13.6148	−0.632735	−0.316368	+	0.948637i	$0.602463\pi$
$464$	0.192582	0.00894041
$465$	70.0000	3.24617
$466$	17.1926	0.796431
$467$	36.3852	1.68370	0.841852	−	0.539708i	$-0.181465\pi$
$467$	36.3852	1.68370	0.841852	+	0.539708i	$0.181465\pi$
$468$	45.9258	2.12292
$469$	−2.00000	−0.0923514
$470$	−10.5407	−0.486204
$471$	68.8887	3.17423
$472$	4.57775	0.210708
$473$	−12.1555	−0.558910
$474$	5.77033	0.265040
$475$	0	0
$476$	4.00000	0.183340
$477$	37.3481	1.71005
$478$	−9.61484	−0.439772
$479$	19.8074	0.905024	0.452512	−	0.891758i	$-0.350528\pi$
$479$	19.8074	0.905024	0.452512	+	0.891758i	$0.350528\pi$
$480$	−7.00000	−0.319505
$481$	−26.7703	−1.22062
$482$	−10.1926	−0.464259
$483$	−26.7703	−1.21809
$484$	−9.57775	−0.435352
$485$	−19.3110	−0.876867
$486$	−27.3852	−1.24222
$487$	−3.34808	−0.151716	−0.0758579	−	0.997119i	$-0.524170\pi$
$487$	−3.34808	−0.151716	−0.0758579	+	0.997119i	$0.524170\pi$
$488$	−0.807418	−0.0365501
$489$	−62.5036	−2.82651
$490$	2.19258	0.0990508
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	21.0000	0.946753
$493$	−0.770330	−0.0346939
$494$	0	0
$495$	−18.8074	−0.845331
$496$	−10.0000	−0.449013
$497$	−1.19258	−0.0534946
$498$	−25.5407	−1.14450
$499$	11.3481	0.508010	0.254005	−	0.967203i	$-0.418252\pi$
$499$	11.3481	0.508010	0.254005	+	0.967203i	$0.418252\pi$
$500$	−11.3852	−0.509160
$501$	21.6148	0.965680
$502$	19.1555	0.854952
$503$	−24.9629	−1.11304	−0.556521	−	0.830834i	$-0.687864\pi$
$503$	−24.9629	−1.11304	−0.556521	+	0.830834i	$0.687864\pi$
$504$	−7.19258	−0.320383
$505$	−21.9258	−0.975686
$506$	10.0000	0.444554
$507$	−88.6591	−3.93749
$508$	−15.5777	−0.691151
$509$	25.1555	1.11500	0.557499	−	0.830178i	$-0.311761\pi$
$509$	25.1555	1.11500	0.557499	+	0.830178i	$0.311761\pi$
$510$	28.0000	1.23986
$511$	4.38516	0.193988
$512$	1.00000	0.0441942
$513$	0	0
$514$	18.1926	0.802440
$515$	−9.61484	−0.423680
$516$	−32.5407	−1.43252
$517$	5.73324	0.252148
$518$	4.19258	0.184211
$519$	−67.5407	−2.96471
$520$	14.0000	0.613941
$521$	−14.7703	−0.647100	−0.323550	−	0.946211i	$-0.604876\pi$
$521$	−14.7703	−0.647100	−0.323550	+	0.946211i	$0.604876\pi$
$522$	1.38516	0.0606270
$523$	41.5407	1.81645	0.908223	−	0.418486i	$-0.137439\pi$
$523$	41.5407	1.81645	0.908223	+	0.418486i	$0.137439\pi$
$524$	9.61484	0.420026
$525$	−0.614835	−0.0268336
$526$	23.1555	1.00963
$527$	40.0000	1.74243
$528$	3.80742	0.165697
$529$	47.3110	2.05700
$530$	11.3852	0.494540
$531$	32.9258	1.42886
$532$	0	0
$533$	−42.0000	−1.81922
$534$	7.73324	0.334650
$535$	−16.6962	−0.721838
$536$	2.00000	0.0863868
$537$	−14.0000	−0.604145
$538$	−11.5407	−0.497553
$539$	−1.19258	−0.0513682
$540$	−29.3481	−1.26294
$541$	37.9258	1.63056	0.815279	−	0.579068i	$-0.196583\pi$
$541$	37.9258	1.63056	0.815279	+	0.579068i	$0.196583\pi$
$542$	24.5777	1.05570
$543$	65.0813	2.79291
$544$	−4.00000	−0.171499
$545$	11.3852	0.487687
$546$	20.3852	0.872405
$547$	25.1555	1.07557	0.537786	−	0.843082i	$-0.319261\pi$
$547$	25.1555	1.07557	0.537786	+	0.843082i	$0.319261\pi$
$548$	4.57775	0.195552
$549$	−5.80742	−0.247855
$550$	0.229670	0.00979318
$551$	0	0
$552$	26.7703	1.13942
$553$	1.80742	0.0768592
$554$	−15.6148	−0.663411
$555$	29.3481	1.24576
$556$	−12.7703	−0.541583
$557$	−11.9258	−0.505313	−0.252657	−	0.967556i	$-0.581304\pi$
$557$	−11.9258	−0.505313	−0.252657	+	0.967556i	$0.581304\pi$
$558$	−71.9258	−3.04486
$559$	65.0813	2.75265
$560$	−2.19258	−0.0926535
$561$	−15.2297	−0.642997
$562$	0	0
$563$	−1.57775	−0.0664941	−0.0332471	−	0.999447i	$-0.510585\pi$
$563$	−1.57775	−0.0664941	−0.0332471	+	0.999447i	$0.510585\pi$
$564$	15.3481	0.646271
$565$	17.5407	0.737941
$566$	−25.5407	−1.07355
$567$	−21.1555	−0.888447
$568$	1.19258	0.0500396
$569$	−8.38516	−0.351524	−0.175762	−	0.984433i	$-0.556239\pi$
$569$	−8.38516	−0.351524	−0.175762	+	0.984433i	$0.556239\pi$
$570$	0	0
$571$	13.9629	0.584330	0.292165	−	0.956368i	$-0.405624\pi$
$571$	13.9629	0.584330	0.292165	+	0.956368i	$0.405624\pi$
$572$	−7.61484	−0.318392
$573$	26.7703	1.11835
$574$	6.57775	0.274550
$575$	1.61484	0.0673433
$576$	7.19258	0.299691
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	−1.00000	−0.0415945
$579$	−42.0000	−1.74546
$580$	0.422253	0.0175331
$581$	−8.00000	−0.331896
$582$	28.1184	1.16555
$583$	−6.19258	−0.256471
$584$	−4.38516	−0.181459
$585$	100.696	4.16327
$586$	−18.3852	−0.759484
$587$	−25.1555	−1.03828	−0.519139	−	0.854690i	$-0.673747\pi$
$587$	−25.1555	−1.03828	−0.519139	+	0.854690i	$0.673747\pi$
$588$	−3.19258	−0.131660
$589$	0	0
$590$	10.0371	0.413220
$591$	−16.6962	−0.686788
$592$	−4.19258	−0.172314
$593$	35.6148	1.46253	0.731263	−	0.682096i	$-0.238931\pi$
$593$	35.6148	1.46253	0.731263	+	0.682096i	$0.238931\pi$
$594$	15.9629	0.654966
$595$	8.77033	0.359548
$596$	0	0
$597$	52.9258	2.16611
$598$	−53.5407	−2.18944
$599$	−31.5777	−1.29023	−0.645116	−	0.764085i	$-0.723191\pi$
$599$	−31.5777	−1.29023	−0.645116	+	0.764085i	$0.723191\pi$
$600$	0.614835	0.0251005
$601$	14.0000	0.571072	0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000	0.571072	0.285536	+	0.958368i	$0.407828\pi$
$602$	−10.1926	−0.415419
$603$	14.3852	0.585809
$604$	−21.5407	−0.876477
$605$	−21.0000	−0.853771
$606$	31.9258	1.29690
$607$	−19.1555	−0.777498	−0.388749	−	0.921344i	$-0.627093\pi$
$607$	−19.1555	−0.777498	−0.388749	+	0.921344i	$0.627093\pi$
$608$	0	0
$609$	0.614835	0.0249144
$610$	−1.77033	−0.0716786
$611$	−30.6962	−1.24183
$612$	−28.7703	−1.16297
$613$	24.7703	1.00046	0.500232	−	0.865891i	$-0.333248\pi$
$613$	24.7703	1.00046	0.500232	+	0.865891i	$0.333248\pi$
$614$	−12.5777	−0.507597
$615$	46.0442	1.85668
$616$	1.19258	0.0480505
$617$	41.7332	1.68012	0.840059	−	0.542496i	$-0.182521\pi$
$617$	41.7332	1.68012	0.840059	+	0.542496i	$0.182521\pi$
$618$	14.0000	0.563163
$619$	27.6148	1.10993	0.554967	−	0.831872i	$-0.312731\pi$
$619$	27.6148	1.10993	0.554967	+	0.831872i	$0.312731\pi$
$620$	−21.9258	−0.880562
$621$	112.237	4.50391
$622$	−31.1184	−1.24773
$623$	2.42225	0.0970455
$624$	−20.3852	−0.816060
$625$	−24.0000	−0.960000
$626$	−3.22967	−0.129084
$627$	0	0
$628$	−21.5777	−0.861046
$629$	16.7703	0.668677
$630$	−15.7703	−0.628305
$631$	−5.54066	−0.220570	−0.110285	−	0.993900i	$-0.535176\pi$
$631$	−5.54066	−0.220570	−0.110285	+	0.993900i	$0.535176\pi$
$632$	−1.80742	−0.0718952
$633$	−23.0813	−0.917400
$634$	−21.1926	−0.841665
$635$	−34.1555	−1.35542
$636$	−16.5777	−0.657350
$637$	6.38516	0.252989
$638$	−0.229670	−0.00909274
$639$	8.57775	0.339330
$640$	2.19258	0.0866694
$641$	−15.6148	−0.616749	−0.308374	−	0.951265i	$-0.599785\pi$
$641$	−15.6148	−0.616749	−0.308374	+	0.951265i	$0.599785\pi$
$642$	24.3110	0.959478
$643$	2.45934	0.0969869	0.0484935	−	0.998823i	$-0.484558\pi$
$643$	2.45934	0.0969869	0.0484935	+	0.998823i	$0.484558\pi$
$644$	8.38516	0.330422
$645$	−71.3481	−2.80933
$646$	0	0
$647$	25.7332	1.01168	0.505839	−	0.862628i	$-0.331183\pi$
$647$	25.7332	1.01168	0.505839	+	0.862628i	$0.331183\pi$
$648$	21.1555	0.831066
$649$	−5.45934	−0.214298
$650$	−1.22967	−0.0482316
$651$	−31.9258	−1.25127
$652$	19.5777	0.766724
$653$	23.1555	0.906145	0.453072	−	0.891474i	$-0.350328\pi$
$653$	23.1555	0.906145	0.453072	+	0.891474i	$0.350328\pi$
$654$	−16.5777	−0.648241
$655$	21.0813	0.823715
$656$	−6.57775	−0.256818
$657$	−31.5407	−1.23052
$658$	4.80742	0.187413
$659$	15.2297	0.593264	0.296632	−	0.954992i	$-0.404137\pi$
$659$	15.2297	0.593264	0.296632	+	0.954992i	$0.404137\pi$
$660$	8.34808	0.324948
$661$	14.7703	0.574499	0.287250	−	0.957856i	$-0.407259\pi$
$661$	14.7703	0.574499	0.287250	+	0.957856i	$0.407259\pi$
$662$	2.77033	0.107672
$663$	81.5407	3.16678
$664$	8.00000	0.310460
$665$	0	0
$666$	−30.1555	−1.16850
$667$	−1.61484	−0.0625267
$668$	−6.77033	−0.261952
$669$	7.61484	0.294407
$670$	4.38516	0.169414
$671$	0.962912	0.0371728
$672$	3.19258	0.123157
$673$	11.1555	0.430013	0.215006	−	0.976613i	$-0.431023\pi$
$673$	11.1555	0.430013	0.215006	+	0.976613i	$0.431023\pi$
$674$	−5.61484	−0.216275
$675$	2.57775	0.0992175
$676$	27.7703	1.06809
$677$	−37.0813	−1.42515	−0.712575	−	0.701596i	$-0.752471\pi$
$677$	−37.0813	−1.42515	−0.712575	+	0.701596i	$0.752471\pi$
$678$	−25.5407	−0.980883
$679$	8.80742	0.337998
$680$	−8.77033	−0.336327
$681$	−25.5407	−0.978720
$682$	11.9258	0.456663
$683$	23.5407	0.900758	0.450379	−	0.892837i	$-0.351289\pi$
$683$	23.5407	0.900758	0.450379	+	0.892837i	$0.351289\pi$
$684$	0	0
$685$	10.0371	0.383497
$686$	−1.00000	−0.0381802
$687$	18.5407	0.707370
$688$	10.1926	0.388589
$689$	33.1555	1.26312
$690$	58.6962	2.23452
$691$	−37.1555	−1.41346	−0.706731	−	0.707483i	$-0.749831\pi$
$691$	−37.1555	−1.41346	−0.706731	+	0.707483i	$0.749831\pi$
$692$	21.1555	0.804211
$693$	8.57775	0.325842
$694$	30.3110	1.15059
$695$	−28.0000	−1.06210
$696$	−0.614835	−0.0233053
$697$	26.3110	0.996600
$698$	−10.0000	−0.378506
$699$	−54.8887	−2.07608
$700$	0.192582	0.00727893
$701$	−11.6148	−0.438686	−0.219343	−	0.975648i	$-0.570391\pi$
$701$	−11.6148	−0.438686	−0.219343	+	0.975648i	$0.570391\pi$
$702$	−85.4665	−3.22572
$703$	0	0
$704$	−1.19258	−0.0449471
$705$	33.6519	1.26740
$706$	−34.3110	−1.29131
$707$	10.0000	0.376089
$708$	−14.6148	−0.549259
$709$	31.1555	1.17007	0.585035	−	0.811008i	$-0.301081\pi$
$709$	31.1555	1.17007	0.585035	+	0.811008i	$0.301081\pi$
$710$	2.61484	0.0981330
$711$	−13.0000	−0.487538
$712$	−2.42225	−0.0907778
$713$	83.8516	3.14027
$714$	−12.7703	−0.477918
$715$	−16.6962	−0.624401
$716$	4.38516	0.163881
$717$	30.6962	1.14637
$718$	−13.1555	−0.490959
$719$	−41.5407	−1.54921	−0.774603	−	0.632448i	$-0.782050\pi$
$719$	−41.5407	−1.54921	−0.774603	+	0.632448i	$0.782050\pi$
$720$	15.7703	0.587725
$721$	4.38516	0.163312
$722$	0	0
$723$	32.5407	1.21020
$724$	−20.3852	−0.757609
$725$	−0.0370880	−0.00137741
$726$	30.5777	1.13485
$727$	43.9629	1.63049	0.815247	−	0.579113i	$-0.196601\pi$
$727$	43.9629	1.63049	0.815247	+	0.579113i	$0.196601\pi$
$728$	−6.38516	−0.236650
$729$	23.9629	0.887515
$730$	−9.61484	−0.355861
$731$	−40.7703	−1.50795
$732$	2.57775	0.0952763
$733$	23.7332	0.876607	0.438304	−	0.898827i	$-0.355579\pi$
$733$	23.7332	0.876607	0.438304	+	0.898827i	$0.355579\pi$
$734$	−13.5777	−0.501164
$735$	−7.00000	−0.258199
$736$	−8.38516	−0.309081
$737$	−2.38516	−0.0878587
$738$	−47.3110	−1.74154
$739$	−50.5777	−1.86053	−0.930266	−	0.366885i	$-0.880424\pi$
$739$	−50.5777	−1.86053	−0.930266	+	0.366885i	$0.880424\pi$
$740$	−9.19258	−0.337926
$741$	0	0
$742$	−5.19258	−0.190626
$743$	−39.7332	−1.45767	−0.728836	−	0.684689i	$-0.759938\pi$
$743$	−39.7332	−1.45767	−0.728836	+	0.684689i	$0.759938\pi$
$744$	31.9258	1.17046
$745$	0	0
$746$	0.192582	0.00705094
$747$	57.5407	2.10530
$748$	4.77033	0.174421
$749$	7.61484	0.278240
$750$	36.3481	1.32724
$751$	−0.651923	−0.0237890	−0.0118945	−	0.999929i	$-0.503786\pi$
$751$	−0.651923	−0.0237890	−0.0118945	+	0.999929i	$0.503786\pi$
$752$	−4.80742	−0.175308
$753$	−61.1555	−2.22863
$754$	1.22967	0.0447820
$755$	−47.2297	−1.71886
$756$	13.3852	0.486814
$757$	7.22967	0.262767	0.131383	−	0.991332i	$-0.458058\pi$
$757$	7.22967	0.262767	0.131383	+	0.991332i	$0.458058\pi$
$758$	−27.1555	−0.986332
$759$	−31.9258	−1.15883
$760$	0	0
$761$	−33.2297	−1.20457	−0.602287	−	0.798279i	$-0.705744\pi$
$761$	−33.2297	−1.20457	−0.602287	+	0.798279i	$0.705744\pi$
$762$	49.7332	1.80165
$763$	−5.19258	−0.187984
$764$	−8.38516	−0.303365
$765$	−63.0813	−2.28071
$766$	9.15549	0.330801
$767$	29.2297	1.05542
$768$	−3.19258	−0.115202
$769$	−11.6148	−0.418842	−0.209421	−	0.977826i	$-0.567158\pi$
$769$	−11.6148	−0.418842	−0.209421	+	0.977826i	$0.567158\pi$
$770$	2.61484	0.0942321
$771$	−58.0813	−2.09175
$772$	13.1555	0.473477
$773$	−29.1555	−1.04865	−0.524325	−	0.851518i	$-0.675682\pi$
$773$	−29.1555	−1.04865	−0.524325	+	0.851518i	$0.675682\pi$
$774$	73.3110	2.63511
$775$	1.92582	0.0691776
$776$	−8.80742	−0.316168
$777$	−13.3852	−0.480190
$778$	−10.0000	−0.358517
$779$	0	0
$780$	−44.6962	−1.60038
$781$	−1.42225	−0.0508922
$782$	33.5407	1.19941
$783$	−2.57775	−0.0921212
$784$	1.00000	0.0357143
$785$	−47.3110	−1.68860
$786$	−30.6962	−1.09490
$787$	1.73324	0.0617834	0.0308917	−	0.999523i	$-0.490165\pi$
$787$	1.73324	0.0617834	0.0308917	+	0.999523i	$0.490165\pi$
$788$	5.22967	0.186299
$789$	−73.9258	−2.63183
$790$	−3.96291	−0.140994
$791$	−8.00000	−0.284447
$792$	−8.57775	−0.304797
$793$	−5.15549	−0.183077
$794$	−21.5777	−0.765766
$795$	−36.3481	−1.28913
$796$	−16.5777	−0.587583
$797$	−9.15549	−0.324304	−0.162152	−	0.986766i	$-0.551844\pi$
$797$	−9.15549	−0.324304	−0.162152	+	0.986766i	$0.551844\pi$
$798$	0	0
$799$	19.2297	0.680297
$800$	−0.192582	−0.00680882
$801$	−17.4223	−0.615585
$802$	0	0
$803$	5.22967	0.184551
$804$	−6.38516	−0.225187
$805$	18.3852	0.647992
$806$	−63.8516	−2.24908
$807$	36.8445	1.29699
$808$	−10.0000	−0.351799
$809$	−28.1926	−0.991198	−0.495599	−	0.868551i	$-0.665052\pi$
$809$	−28.1926	−0.991198	−0.495599	+	0.868551i	$0.665052\pi$
$810$	46.3852	1.62981
$811$	8.73324	0.306666	0.153333	−	0.988175i	$-0.450999\pi$
$811$	8.73324	0.306666	0.153333	+	0.988175i	$0.450999\pi$
$812$	−0.192582	−0.00675832
$813$	−78.4665	−2.75194
$814$	5.00000	0.175250
$815$	42.9258	1.50363
$816$	12.7703	0.447051
$817$	0	0
$818$	10.4223	0.364406
$819$	−45.9258	−1.60478
$820$	−14.4223	−0.503647
$821$	31.5407	1.10078	0.550388	−	0.834909i	$-0.314480\pi$
$821$	31.5407	1.10078	0.550388	+	0.834909i	$0.314480\pi$
$822$	−14.6148	−0.509751
$823$	−30.7703	−1.07259	−0.536293	−	0.844032i	$-0.680176\pi$
$823$	−30.7703	−1.07259	−0.536293	+	0.844032i	$0.680176\pi$
$824$	−4.38516	−0.152764
$825$	−0.733242	−0.0255282
$826$	−4.57775	−0.159280
$827$	29.1555	1.01384	0.506918	−	0.861994i	$-0.330785\pi$
$827$	29.1555	1.01384	0.506918	+	0.861994i	$0.330785\pi$
$828$	−60.3110	−2.09595
$829$	−40.7703	−1.41601	−0.708006	−	0.706206i	$-0.750405\pi$
$829$	−40.7703	−1.41601	−0.708006	+	0.706206i	$0.750405\pi$
$830$	17.5407	0.608845
$831$	49.8516	1.72933
$832$	6.38516	0.221366
$833$	−4.00000	−0.138592
$834$	40.7703	1.41176
$835$	−14.8445	−0.513715
$836$	0	0
$837$	133.852	4.62659
$838$	−6.77033	−0.233877
$839$	25.2297	0.871025	0.435512	−	0.900183i	$-0.356567\pi$
$839$	25.2297	0.871025	0.435512	+	0.900183i	$0.356567\pi$
$840$	7.00000	0.241523
$841$	−28.9629	−0.998721
$842$	−36.3110	−1.25136
$843$	0	0
$844$	7.22967	0.248856
$845$	60.8887	2.09464
$846$	−34.5777	−1.18881
$847$	9.57775	0.329095
$848$	5.19258	0.178314
$849$	81.5407	2.79847
$850$	0.770330	0.0264221
$851$	35.1555	1.20511
$852$	−3.80742	−0.130440
$853$	20.1184	0.688841	0.344421	−	0.938815i	$-0.388075\pi$
$853$	20.1184	0.688841	0.344421	+	0.938815i	$0.388075\pi$
$854$	0.807418	0.0276293
$855$	0	0
$856$	−7.61484	−0.260270
$857$	43.5407	1.48732	0.743660	−	0.668558i	$-0.233088\pi$
$857$	43.5407	1.48732	0.743660	+	0.668558i	$0.233088\pi$
$858$	24.3110	0.829963
$859$	−23.6148	−0.805728	−0.402864	−	0.915260i	$-0.631985\pi$
$859$	−23.6148	−0.805728	−0.402864	+	0.915260i	$0.631985\pi$
$860$	22.3481	0.762063
$861$	−21.0000	−0.715678
$862$	7.57775	0.258099
$863$	−34.9629	−1.19015	−0.595076	−	0.803670i	$-0.702878\pi$
$863$	−34.9629	−1.19015	−0.595076	+	0.803670i	$0.702878\pi$
$864$	−13.3852	−0.455373
$865$	46.3852	1.57714
$866$	−0.651923	−0.0221533
$867$	3.19258	0.108426
$868$	10.0000	0.339422
$869$	2.15549	0.0731201
$870$	−1.34808	−0.0457041
$871$	12.7703	0.432706
$872$	5.19258	0.175843
$873$	−63.3481	−2.14401
$874$	0	0
$875$	11.3852	0.384889
$876$	14.0000	0.473016
$877$	10.7332	0.362436	0.181218	−	0.983443i	$-0.441996\pi$
$877$	10.7332	0.362436	0.181218	+	0.983443i	$0.441996\pi$
$878$	14.0000	0.472477
$879$	58.6962	1.97977
$880$	−2.61484	−0.0881461
$881$	−22.3852	−0.754175	−0.377088	−	0.926178i	$-0.623074\pi$
$881$	−22.3852	−0.754175	−0.377088	+	0.926178i	$0.623074\pi$
$882$	7.19258	0.242187
$883$	16.3481	0.550157	0.275078	−	0.961422i	$-0.411296\pi$
$883$	16.3481	0.550157	0.275078	+	0.961422i	$0.411296\pi$
$884$	−25.5407	−0.859025
$885$	−32.0442	−1.07716
$886$	2.57775	0.0866011
$887$	14.0000	0.470074	0.235037	−	0.971986i	$-0.424479\pi$
$887$	14.0000	0.470074	0.235037	+	0.971986i	$0.424479\pi$
$888$	13.3852	0.449177
$889$	15.5777	0.522461
$890$	−5.31099	−0.178025
$891$	−25.2297	−0.845226
$892$	−2.38516	−0.0798612
$893$	0	0
$894$	0	0
$895$	9.61484	0.321388
$896$	−1.00000	−0.0334077
$897$	170.933	5.70729
$898$	31.1555	1.03967
$899$	−1.92582	−0.0642298
$900$	−1.38516	−0.0461722
$901$	−20.7703	−0.691960
$902$	7.84451	0.261193
$903$	32.5407	1.08289
$904$	8.00000	0.266076
$905$	−44.6962	−1.48575
$906$	68.7703	2.28474
$907$	23.9258	0.794444	0.397222	−	0.917723i	$-0.369974\pi$
$907$	23.9258	0.794444	0.397222	+	0.917723i	$0.369974\pi$
$908$	8.00000	0.265489
$909$	−71.9258	−2.38563
$910$	−14.0000	−0.464095
$911$	−11.7332	−0.388740	−0.194370	−	0.980928i	$-0.562266\pi$
$911$	−11.7332	−0.388740	−0.194370	+	0.980928i	$0.562266\pi$
$912$	0	0
$913$	−9.54066	−0.315750
$914$	−21.1184	−0.698535
$915$	5.65192	0.186847
$916$	−5.80742	−0.191882
$917$	−9.61484	−0.317510
$918$	53.5407	1.76711
$919$	−4.38516	−0.144653	−0.0723266	−	0.997381i	$-0.523042\pi$
$919$	−4.38516	−0.144653	−0.0723266	+	0.997381i	$0.523042\pi$
$920$	−18.3852	−0.606141
$921$	40.1555	1.32317
$922$	−34.3481	−1.13119
$923$	7.61484	0.250645
$924$	−3.80742	−0.125255
$925$	0.807418	0.0265477
$926$	−13.6148	−0.447411
$927$	−31.5407	−1.03593
$928$	0.192582	0.00632183
$929$	−6.38516	−0.209490	−0.104745	−	0.994499i	$-0.533403\pi$
$929$	−6.38516	−0.209490	−0.104745	+	0.994499i	$0.533403\pi$
$930$	70.0000	2.29539
$931$	0	0
$932$	17.1926	0.563162
$933$	99.3481	3.25251
$934$	36.3852	1.19056
$935$	10.4593	0.342057
$936$	45.9258	1.50113
$937$	35.0813	1.14606	0.573028	−	0.819536i	$-0.305768\pi$
$937$	35.0813	1.14606	0.573028	+	0.819536i	$0.305768\pi$
$938$	−2.00000	−0.0653023
$939$	10.3110	0.336486
$940$	−10.5407	−0.343798
$941$	−18.3852	−0.599339	−0.299670	−	0.954043i	$-0.596876\pi$
$941$	−18.3852	−0.599339	−0.299670	+	0.954043i	$0.596876\pi$
$942$	68.8887	2.24452
$943$	55.1555	1.79611
$944$	4.57775	0.148993
$945$	29.3481	0.954693
$946$	−12.1555	−0.395209
$947$	−56.3481	−1.83107	−0.915533	−	0.402242i	$-0.868231\pi$
$947$	−56.3481	−1.83107	−0.915533	+	0.402242i	$0.868231\pi$
$948$	5.77033	0.187412
$949$	−28.0000	−0.908918
$950$	0	0
$951$	67.6591	2.19400
$952$	4.00000	0.129641
$953$	−19.5407	−0.632984	−0.316492	−	0.948595i	$-0.602505\pi$
$953$	−19.5407	−0.632984	−0.316492	+	0.948595i	$0.602505\pi$
$954$	37.3481	1.20919
$955$	−18.3852	−0.594930
$956$	−9.61484	−0.310966
$957$	0.733242	0.0237023
$958$	19.8074	0.639949
$959$	−4.57775	−0.147823
$960$	−7.00000	−0.225924
$961$	69.0000	2.22581
$962$	−26.7703	−0.863110
$963$	−54.7703	−1.76495
$964$	−10.1926	−0.328281
$965$	28.8445	0.928537
$966$	−26.7703	−0.861321
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	−9.57775	−0.307840
$969$	0	0
$970$	−19.3110	−0.620038
$971$	−7.19258	−0.230821	−0.115410	−	0.993318i	$-0.536818\pi$
$971$	−7.19258	−0.230821	−0.115410	+	0.993318i	$0.536818\pi$
$972$	−27.3852	−0.878380
$973$	12.7703	0.409398
$974$	−3.34808	−0.107279
$975$	3.92582	0.125727
$976$	−0.807418	−0.0258448
$977$	33.9258	1.08538	0.542692	−	0.839932i	$-0.317405\pi$
$977$	33.9258	1.08538	0.542692	+	0.839932i	$0.317405\pi$
$978$	−62.5036	−1.99864
$979$	2.88874	0.0923244
$980$	2.19258	0.0700395
$981$	37.3481	1.19243
$982$	20.0000	0.638226
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	21.0000	0.669456
$985$	11.4665	0.365353
$986$	−0.770330	−0.0245323
$987$	−15.3481	−0.488535
$988$	0	0
$989$	−85.4665	−2.71768
$990$	−18.8074	−0.597739
$991$	−10.8074	−0.343309	−0.171654	−	0.985157i	$-0.554911\pi$
$991$	−10.8074	−0.343309	−0.171654	+	0.985157i	$0.554911\pi$
$992$	−10.0000	−0.317500
$993$	−8.84451	−0.280672
$994$	−1.19258	−0.0378264
$995$	−36.3481	−1.15231
$996$	−25.5407	−0.809287
$997$	−22.1926	−0.702846	−0.351423	−	0.936217i	$-0.614302\pi$
$997$	−22.1926	−0.702846	−0.351423	+	0.936217i	$0.614302\pi$
$998$	11.3481	0.359217
$999$	56.1184	1.77551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.n.1.1		2
19.18	odd	2		266.2.a.a.1.2	✓	2
57.56	even	2		2394.2.a.y.1.1		2
76.75	even	2		2128.2.a.g.1.1		2
95.94	odd	2		6650.2.a.bu.1.1		2
133.132	even	2		1862.2.a.h.1.1		2
152.37	odd	2		8512.2.a.p.1.1		2
152.75	even	2		8512.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.a.a.1.2	✓	2	19.18	odd	2
1862.2.a.h.1.1		2	133.132	even	2
2128.2.a.g.1.1		2	76.75	even	2
2394.2.a.y.1.1		2	57.56	even	2
5054.2.a.n.1.1		2	1.1	even	1	trivial
6650.2.a.bu.1.1		2	95.94	odd	2
8512.2.a.p.1.1		2	152.37	odd	2
8512.2.a.w.1.2		2	152.75	even	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.19258 q^{3} +1.00000 q^{4} +2.19258 q^{5} -3.19258 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.19258 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.19258 q^{3} +1.00000 q^{4} +2.19258 q^{5} -3.19258 q^{6} -1.00000 q^{7} +1.00000 q^{8} +7.19258 q^{9} +2.19258 q^{10} -1.19258 q^{11} -3.19258 q^{12} +6.38516 q^{13} -1.00000 q^{14} -7.00000 q^{15} +1.00000 q^{16} -4.00000 q^{17} +7.19258 q^{18} +2.19258 q^{20} +3.19258 q^{21} -1.19258 q^{22} -8.38516 q^{23} -3.19258 q^{24} -0.192582 q^{25} +6.38516 q^{26} -13.3852 q^{27} -1.00000 q^{28} +0.192582 q^{29} -7.00000 q^{30} -10.0000 q^{31} +1.00000 q^{32} +3.80742 q^{33} -4.00000 q^{34} -2.19258 q^{35} +7.19258 q^{36} -4.19258 q^{37} -20.3852 q^{39} +2.19258 q^{40} -6.57775 q^{41} +3.19258 q^{42} +10.1926 q^{43} -1.19258 q^{44} +15.7703 q^{45} -8.38516 q^{46} -4.80742 q^{47} -3.19258 q^{48} +1.00000 q^{49} -0.192582 q^{50} +12.7703 q^{51} +6.38516 q^{52} +5.19258 q^{53} -13.3852 q^{54} -2.61484 q^{55} -1.00000 q^{56} +0.192582 q^{58} +4.57775 q^{59} -7.00000 q^{60} -0.807418 q^{61} -10.0000 q^{62} -7.19258 q^{63} +1.00000 q^{64} +14.0000 q^{65} +3.80742 q^{66} +2.00000 q^{67} -4.00000 q^{68} +26.7703 q^{69} -2.19258 q^{70} +1.19258 q^{71} +7.19258 q^{72} -4.38516 q^{73} -4.19258 q^{74} +0.614835 q^{75} +1.19258 q^{77} -20.3852 q^{78} -1.80742 q^{79} +2.19258 q^{80} +21.1555 q^{81} -6.57775 q^{82} +8.00000 q^{83} +3.19258 q^{84} -8.77033 q^{85} +10.1926 q^{86} -0.614835 q^{87} -1.19258 q^{88} -2.42225 q^{89} +15.7703 q^{90} -6.38516 q^{91} -8.38516 q^{92} +31.9258 q^{93} -4.80742 q^{94} -3.19258 q^{96} -8.80742 q^{97} +1.00000 q^{98} -8.57775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 9 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 9 q^{9} - q^{10} + 3 q^{11} - q^{12} + 2 q^{13} - 2 q^{14} - 14 q^{15} + 2 q^{16} - 8 q^{17} + 9 q^{18} - q^{20} + q^{21} + 3 q^{22} - 6 q^{23} - q^{24} + 5 q^{25} + 2 q^{26} - 16 q^{27} - 2 q^{28} - 5 q^{29} - 14 q^{30} - 20 q^{31} + 2 q^{32} + 13 q^{33} - 8 q^{34} + q^{35} + 9 q^{36} - 3 q^{37} - 30 q^{39} - q^{40} + 3 q^{41} + q^{42} + 15 q^{43} + 3 q^{44} + 10 q^{45} - 6 q^{46} - 15 q^{47} - q^{48} + 2 q^{49} + 5 q^{50} + 4 q^{51} + 2 q^{52} + 5 q^{53} - 16 q^{54} - 16 q^{55} - 2 q^{56} - 5 q^{58} - 7 q^{59} - 14 q^{60} - 7 q^{61} - 20 q^{62} - 9 q^{63} + 2 q^{64} + 28 q^{65} + 13 q^{66} + 4 q^{67} - 8 q^{68} + 32 q^{69} + q^{70} - 3 q^{71} + 9 q^{72} + 2 q^{73} - 3 q^{74} + 12 q^{75} - 3 q^{77} - 30 q^{78} - 9 q^{79} - q^{80} + 10 q^{81} + 3 q^{82} + 16 q^{83} + q^{84} + 4 q^{85} + 15 q^{86} - 12 q^{87} + 3 q^{88} - 21 q^{89} + 10 q^{90} - 2 q^{91} - 6 q^{92} + 10 q^{93} - 15 q^{94} - q^{96} - 23 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 9 * q^9 - q^10 + 3 * q^11 - q^12 + 2 * q^13 - 2 * q^14 - 14 * q^15 + 2 * q^16 - 8 * q^17 + 9 * q^18 - q^20 + q^21 + 3 * q^22 - 6 * q^23 - q^24 + 5 * q^25 + 2 * q^26 - 16 * q^27 - 2 * q^28 - 5 * q^29 - 14 * q^30 - 20 * q^31 + 2 * q^32 + 13 * q^33 - 8 * q^34 + q^35 + 9 * q^36 - 3 * q^37 - 30 * q^39 - q^40 + 3 * q^41 + q^42 + 15 * q^43 + 3 * q^44 + 10 * q^45 - 6 * q^46 - 15 * q^47 - q^48 + 2 * q^49 + 5 * q^50 + 4 * q^51 + 2 * q^52 + 5 * q^53 - 16 * q^54 - 16 * q^55 - 2 * q^56 - 5 * q^58 - 7 * q^59 - 14 * q^60 - 7 * q^61 - 20 * q^62 - 9 * q^63 + 2 * q^64 + 28 * q^65 + 13 * q^66 + 4 * q^67 - 8 * q^68 + 32 * q^69 + q^70 - 3 * q^71 + 9 * q^72 + 2 * q^73 - 3 * q^74 + 12 * q^75 - 3 * q^77 - 30 * q^78 - 9 * q^79 - q^80 + 10 * q^81 + 3 * q^82 + 16 * q^83 + q^84 + 4 * q^85 + 15 * q^86 - 12 * q^87 + 3 * q^88 - 21 * q^89 + 10 * q^90 - 2 * q^91 - 6 * q^92 + 10 * q^93 - 15 * q^94 - q^96 - 23 * q^97 + 2 * q^98 - q^99

Introduction

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