LMFDB - Embedded newform 9251.2.a.ba.1.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.14689 q^{2} +2.50811 q^{3} +2.60915 q^{4} -0.390383 q^{5} +5.38465 q^{6} -3.27881 q^{7} +1.30779 q^{8} +3.29062 q^{9} +O(q^{10})$	\(q+2.14689 q^{2} +2.50811 q^{3} +2.60915 q^{4} -0.390383 q^{5} +5.38465 q^{6} -3.27881 q^{7} +1.30779 q^{8} +3.29062 q^{9} -0.838111 q^{10} +1.00000 q^{11} +6.54404 q^{12} -1.62624 q^{13} -7.03925 q^{14} -0.979123 q^{15} -2.41063 q^{16} -3.12464 q^{17} +7.06461 q^{18} -1.25340 q^{19} -1.01857 q^{20} -8.22362 q^{21} +2.14689 q^{22} -4.86405 q^{23} +3.28007 q^{24} -4.84760 q^{25} -3.49136 q^{26} +0.728904 q^{27} -8.55491 q^{28} -2.10207 q^{30} +4.55458 q^{31} -7.79093 q^{32} +2.50811 q^{33} -6.70827 q^{34} +1.27999 q^{35} +8.58573 q^{36} -7.71400 q^{37} -2.69092 q^{38} -4.07879 q^{39} -0.510537 q^{40} +6.47989 q^{41} -17.6552 q^{42} -5.78421 q^{43} +2.60915 q^{44} -1.28460 q^{45} -10.4426 q^{46} +2.07562 q^{47} -6.04612 q^{48} +3.75059 q^{49} -10.4073 q^{50} -7.83695 q^{51} -4.24311 q^{52} -5.55393 q^{53} +1.56488 q^{54} -0.390383 q^{55} -4.28798 q^{56} -3.14367 q^{57} +1.30679 q^{59} -2.55468 q^{60} -10.3202 q^{61} +9.77821 q^{62} -10.7893 q^{63} -11.9050 q^{64} +0.634856 q^{65} +5.38465 q^{66} +9.06163 q^{67} -8.15267 q^{68} -12.1996 q^{69} +2.74800 q^{70} -13.1939 q^{71} +4.30342 q^{72} +16.3268 q^{73} -16.5611 q^{74} -12.1583 q^{75} -3.27032 q^{76} -3.27881 q^{77} -8.75672 q^{78} +3.07383 q^{79} +0.941068 q^{80} -8.04368 q^{81} +13.9116 q^{82} +13.2132 q^{83} -21.4567 q^{84} +1.21981 q^{85} -12.4181 q^{86} +1.30779 q^{88} +5.59075 q^{89} -2.75790 q^{90} +5.33213 q^{91} -12.6911 q^{92} +11.4234 q^{93} +4.45612 q^{94} +0.489307 q^{95} -19.5405 q^{96} +1.48903 q^{97} +8.05212 q^{98} +3.29062 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) $ 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * 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 $

$2$	2.14689	1.51808	0.759042	−	0.651042i	$-0.225668\pi$
$2$	2.14689	1.51808	0.759042	+	0.651042i	$0.225668\pi$
$3$	2.50811	1.44806	0.724029	−	0.689769i	$-0.242288\pi$
$3$	2.50811	1.44806	0.724029	+	0.689769i	$0.242288\pi$
$4$	2.60915	1.30458
$5$	−0.390383	−0.174585	−0.0872923	−	0.996183i	$-0.527821\pi$
$5$	−0.390383	−0.174585	−0.0872923	+	0.996183i	$0.527821\pi$
$6$	5.38465	2.19827
$7$	−3.27881	−1.23927	−0.619637	−	0.784889i	$-0.712720\pi$
$7$	−3.27881	−1.23927	−0.619637	+	0.784889i	$0.712720\pi$
$8$	1.30779	0.462372
$9$	3.29062	1.09687
$10$	−0.838111	−0.265034
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	6.54404	1.88910
$13$	−1.62624	−0.451038	−0.225519	−	0.974239i	$-0.572408\pi$
$13$	−1.62624	−0.451038	−0.225519	+	0.974239i	$0.572408\pi$
$14$	−7.03925	−1.88132
$15$	−0.979123	−0.252809
$16$	−2.41063	−0.602657
$17$	−3.12464	−0.757837	−0.378918	−	0.925430i	$-0.623704\pi$
$17$	−3.12464	−0.757837	−0.378918	+	0.925430i	$0.623704\pi$
$18$	7.06461	1.66514
$19$	−1.25340	−0.287550	−0.143775	−	0.989610i	$-0.545924\pi$
$19$	−1.25340	−0.287550	−0.143775	+	0.989610i	$0.545924\pi$
$20$	−1.01857	−0.227759
$21$	−8.22362	−1.79454
$22$	2.14689	0.457719
$23$	−4.86405	−1.01423	−0.507113	−	0.861880i	$-0.669287\pi$
$23$	−4.86405	−1.01423	−0.507113	+	0.861880i	$0.669287\pi$
$24$	3.28007	0.669542
$25$	−4.84760	−0.969520
$26$	−3.49136	−0.684712
$27$	0.728904	0.140278
$28$	−8.55491	−1.61673
$29$	0	0
$29$	0	0
$30$	−2.10207	−0.383784
$31$	4.55458	0.818027	0.409014	−	0.912528i	$-0.365873\pi$
$31$	4.55458	0.818027	0.409014	+	0.912528i	$0.365873\pi$
$32$	−7.79093	−1.37726
$33$	2.50811	0.436606
$34$	−6.70827	−1.15046
$35$	1.27999	0.216358
$36$	8.58573	1.43095
$37$	−7.71400	−1.26817	−0.634087	−	0.773262i	$-0.718624\pi$
$37$	−7.71400	−1.26817	−0.634087	+	0.773262i	$0.718624\pi$
$38$	−2.69092	−0.436525
$39$	−4.07879	−0.653129
$40$	−0.510537	−0.0807230
$41$	6.47989	1.01199	0.505995	−	0.862537i	$-0.331126\pi$
$41$	6.47989	1.01199	0.505995	+	0.862537i	$0.331126\pi$
$42$	−17.6552	−2.72426
$43$	−5.78421	−0.882084	−0.441042	−	0.897486i	$-0.645391\pi$
$43$	−5.78421	−0.882084	−0.441042	+	0.897486i	$0.645391\pi$
$44$	2.60915	0.393345
$45$	−1.28460	−0.191497
$46$	−10.4426	−1.53968
$47$	2.07562	0.302760	0.151380	−	0.988476i	$-0.451628\pi$
$47$	2.07562	0.302760	0.151380	+	0.988476i	$0.451628\pi$
$48$	−6.04612	−0.872683
$49$	3.75059	0.535798
$50$	−10.4073	−1.47181
$51$	−7.83695	−1.09739
$52$	−4.24311	−0.588413
$53$	−5.55393	−0.762891	−0.381446	−	0.924391i	$-0.624574\pi$
$53$	−5.55393	−0.762891	−0.381446	+	0.924391i	$0.624574\pi$
$54$	1.56488	0.212953
$55$	−0.390383	−0.0526392
$56$	−4.28798	−0.573005
$57$	−3.14367	−0.416390
$58$	0	0
$59$	1.30679	0.170129	0.0850646	−	0.996375i	$-0.472890\pi$
$59$	1.30679	0.170129	0.0850646	+	0.996375i	$0.472890\pi$
$60$	−2.55468	−0.329808
$61$	−10.3202	−1.32137	−0.660684	−	0.750665i	$-0.729733\pi$
$61$	−10.3202	−1.32137	−0.660684	+	0.750665i	$0.729733\pi$
$62$	9.77821	1.24183
$63$	−10.7893	−1.35933
$64$	−11.9050	−1.48813
$65$	0.634856	0.0787442
$66$	5.38465	0.662804
$67$	9.06163	1.10705	0.553527	−	0.832831i	$-0.313282\pi$
$67$	9.06163	1.10705	0.553527	+	0.832831i	$0.313282\pi$
$68$	−8.15267	−0.988656
$69$	−12.1996	−1.46866
$70$	2.74800	0.328449
$71$	−13.1939	−1.56582	−0.782912	−	0.622133i	$-0.786266\pi$
$71$	−13.1939	−1.56582	−0.782912	+	0.622133i	$0.786266\pi$
$72$	4.30342	0.507163
$73$	16.3268	1.91091	0.955456	−	0.295133i	$-0.0953639\pi$
$73$	16.3268	1.91091	0.955456	+	0.295133i	$0.0953639\pi$
$74$	−16.5611	−1.92519
$75$	−12.1583	−1.40392
$76$	−3.27032	−0.375132
$77$	−3.27881	−0.373655
$78$	−8.75672	−0.991504
$79$	3.07383	0.345833	0.172917	−	0.984936i	$-0.444681\pi$
$79$	3.07383	0.345833	0.172917	+	0.984936i	$0.444681\pi$
$80$	0.941068	0.105215
$81$	−8.04368	−0.893743
$82$	13.9116	1.53628
$83$	13.2132	1.45034	0.725170	−	0.688570i	$-0.241761\pi$
$83$	13.2132	1.45034	0.725170	+	0.688570i	$0.241761\pi$
$84$	−21.4567	−2.34111
$85$	1.21981	0.132307
$86$	−12.4181	−1.33908
$87$	0	0
$88$	1.30779	0.139410
$89$	5.59075	0.592618	0.296309	−	0.955092i	$-0.404244\pi$
$89$	5.59075	0.592618	0.296309	+	0.955092i	$0.404244\pi$
$90$	−2.75790	−0.290708
$91$	5.33213	0.558959
$92$	−12.6911	−1.32313
$93$	11.4234	1.18455
$94$	4.45612	0.459614
$95$	0.489307	0.0502019
$96$	−19.5405	−1.99435
$97$	1.48903	0.151188	0.0755941	−	0.997139i	$-0.475915\pi$
$97$	1.48903	0.151188	0.0755941	+	0.997139i	$0.475915\pi$
$98$	8.05212	0.813386
$99$	3.29062	0.330720
$100$	−12.6481	−1.26481
$101$	10.3834	1.03319	0.516594	−	0.856230i	$-0.327199\pi$
$101$	10.3834	1.03319	0.516594	+	0.856230i	$0.327199\pi$
$102$	−16.8251	−1.66593
$103$	2.96985	0.292628	0.146314	−	0.989238i	$-0.453259\pi$
$103$	2.96985	0.292628	0.146314	+	0.989238i	$0.453259\pi$
$104$	−2.12677	−0.208547
$105$	3.21036	0.313299
$106$	−11.9237	−1.15813
$107$	18.5521	1.79350	0.896749	−	0.442541i	$-0.145923\pi$
$107$	18.5521	1.79350	0.896749	+	0.442541i	$0.145923\pi$
$108$	1.90182	0.183003
$109$	−3.52128	−0.337277	−0.168639	−	0.985678i	$-0.553937\pi$
$109$	−3.52128	−0.337277	−0.168639	+	0.985678i	$0.553937\pi$
$110$	−0.838111	−0.0799107
$111$	−19.3476	−1.83639
$112$	7.90399	0.746857
$113$	−9.12378	−0.858293	−0.429146	−	0.903235i	$-0.641186\pi$
$113$	−9.12378	−0.858293	−0.429146	+	0.903235i	$0.641186\pi$
$114$	−6.74913	−0.632114
$115$	1.89884	0.177068
$116$	0	0
$117$	−5.35133	−0.494731
$118$	2.80553	0.258270
$119$	10.2451	0.939167
$120$	−1.28048	−0.116892
$121$	1.00000	0.0909091
$122$	−22.1564	−2.00595
$123$	16.2523	1.46542
$124$	11.8836	1.06718
$125$	3.84433	0.343848
$126$	−23.1635	−2.06357
$127$	−8.16946	−0.724922	−0.362461	−	0.931999i	$-0.618063\pi$
$127$	−8.16946	−0.724922	−0.362461	+	0.931999i	$0.618063\pi$
$128$	−9.97701	−0.881851
$129$	−14.5074	−1.27731
$130$	1.36297	0.119540
$131$	−21.3048	−1.86141	−0.930705	−	0.365770i	$-0.880806\pi$
$131$	−21.3048	−1.86141	−0.930705	+	0.365770i	$0.880806\pi$
$132$	6.54404	0.569586
$133$	4.10967	0.356354
$134$	19.4543	1.68060
$135$	−0.284552	−0.0244903
$136$	−4.08636	−0.350403
$137$	6.36170	0.543517	0.271758	−	0.962366i	$-0.412395\pi$
$137$	6.36170	0.543517	0.271758	+	0.962366i	$0.412395\pi$
$138$	−26.1912	−2.22954
$139$	−8.01749	−0.680034	−0.340017	−	0.940419i	$-0.610433\pi$
$139$	−8.01749	−0.680034	−0.340017	+	0.940419i	$0.610433\pi$
$140$	3.33969	0.282255
$141$	5.20587	0.438414
$142$	−28.3258	−2.37705
$143$	−1.62624	−0.135993
$144$	−7.93246	−0.661038
$145$	0	0
$146$	35.0520	2.90092
$147$	9.40689	0.775867
$148$	−20.1270	−1.65443
$149$	−18.4155	−1.50866	−0.754329	−	0.656496i	$-0.772038\pi$
$149$	−18.4155	−1.50866	−0.754329	+	0.656496i	$0.772038\pi$
$150$	−26.1026	−2.13127
$151$	9.74040	0.792663	0.396331	−	0.918108i	$-0.370283\pi$
$151$	9.74040	0.792663	0.396331	+	0.918108i	$0.370283\pi$
$152$	−1.63918	−0.132955
$153$	−10.2820	−0.831251
$154$	−7.03925	−0.567239
$155$	−1.77803	−0.142815
$156$	−10.6422	−0.852056
$157$	18.4248	1.47046	0.735230	−	0.677818i	$-0.237074\pi$
$157$	18.4248	1.47046	0.735230	+	0.677818i	$0.237074\pi$
$158$	6.59919	0.525003
$159$	−13.9299	−1.10471
$160$	3.04145	0.240448
$161$	15.9483	1.25690
$162$	−17.2689	−1.35678
$163$	−23.2577	−1.82168	−0.910842	−	0.412755i	$-0.864566\pi$
$163$	−23.2577	−1.82168	−0.910842	+	0.412755i	$0.864566\pi$
$164$	16.9070	1.32022
$165$	−0.979123	−0.0762247
$166$	28.3674	2.20174
$167$	−16.1560	−1.25019	−0.625094	−	0.780549i	$-0.714939\pi$
$167$	−16.1560	−1.25019	−0.625094	+	0.780549i	$0.714939\pi$
$168$	−10.7547	−0.829745
$169$	−10.3553	−0.796565
$170$	2.61880	0.200852
$171$	−4.12447	−0.315406
$172$	−15.0919	−1.15075
$173$	7.81508	0.594169	0.297085	−	0.954851i	$-0.403986\pi$
$173$	7.81508	0.594169	0.297085	+	0.954851i	$0.403986\pi$
$174$	0	0
$175$	15.8944	1.20150
$176$	−2.41063	−0.181708
$177$	3.27757	0.246357
$178$	12.0027	0.899643
$179$	17.5186	1.30940	0.654701	−	0.755888i	$-0.272795\pi$
$179$	17.5186	1.30940	0.654701	+	0.755888i	$0.272795\pi$
$180$	−3.35172	−0.249822
$181$	5.04998	0.375362	0.187681	−	0.982230i	$-0.439903\pi$
$181$	5.04998	0.375362	0.187681	+	0.982230i	$0.439903\pi$
$182$	11.4475	0.848546
$183$	−25.8842	−1.91342
$184$	−6.36114	−0.468949
$185$	3.01141	0.221404
$186$	24.5248	1.79825
$187$	−3.12464	−0.228496
$188$	5.41560	0.394973
$189$	−2.38994	−0.173842
$190$	1.05049	0.0762106
$191$	−15.5853	−1.12771	−0.563856	−	0.825873i	$-0.690683\pi$
$191$	−15.5853	−1.12771	−0.563856	+	0.825873i	$0.690683\pi$
$192$	−29.8592	−2.15490
$193$	−0.702559	−0.0505713	−0.0252857	−	0.999680i	$-0.508050\pi$
$193$	−0.702559	−0.0505713	−0.0252857	+	0.999680i	$0.508050\pi$
$194$	3.19679	0.229516
$195$	1.59229	0.114026
$196$	9.78586	0.698990
$197$	−21.0688	−1.50109	−0.750545	−	0.660819i	$-0.770209\pi$
$197$	−21.0688	−1.50109	−0.750545	+	0.660819i	$0.770209\pi$
$198$	7.06461	0.502060
$199$	10.7033	0.758739	0.379369	−	0.925245i	$-0.376141\pi$
$199$	10.7033	0.758739	0.379369	+	0.925245i	$0.376141\pi$
$200$	−6.33962	−0.448279
$201$	22.7276	1.60308
$202$	22.2921	1.56847
$203$	0	0
$204$	−20.4478	−1.43163
$205$	−2.52964	−0.176678
$206$	6.37595	0.444233
$207$	−16.0057	−1.11248
$208$	3.92026	0.271821
$209$	−1.25340	−0.0866997
$210$	6.89230	0.475614
$211$	−10.2537	−0.705895	−0.352947	−	0.935643i	$-0.614820\pi$
$211$	−10.2537	−0.705895	−0.352947	+	0.935643i	$0.614820\pi$
$212$	−14.4911	−0.995250
$213$	−33.0917	−2.26740
$214$	39.8293	2.72268
$215$	2.25806	0.153998
$216$	0.953250	0.0648605
$217$	−14.9336	−1.01376
$218$	−7.55981	−0.512015
$219$	40.9495	2.76711
$220$	−1.01857	−0.0686719
$221$	5.08141	0.341813
$222$	−41.5372	−2.78779
$223$	−6.27399	−0.420138	−0.210069	−	0.977687i	$-0.567369\pi$
$223$	−6.27399	−0.420138	−0.210069	+	0.977687i	$0.567369\pi$
$224$	25.5450	1.70680
$225$	−15.9516	−1.06344
$226$	−19.5878	−1.30296
$227$	22.9158	1.52097	0.760486	−	0.649354i	$-0.224961\pi$
$227$	22.9158	1.52097	0.760486	+	0.649354i	$0.224961\pi$
$228$	−8.20233	−0.543212
$229$	23.4240	1.54790	0.773950	−	0.633246i	$-0.218278\pi$
$229$	23.4240	1.54790	0.773950	+	0.633246i	$0.218278\pi$
$230$	4.07662	0.268804
$231$	−8.22362	−0.541074
$232$	0	0
$233$	6.36213	0.416797	0.208398	−	0.978044i	$-0.433175\pi$
$233$	6.36213	0.416797	0.208398	+	0.978044i	$0.433175\pi$
$234$	−11.4887	−0.751043
$235$	−0.810285	−0.0528571
$236$	3.40961	0.221946
$237$	7.70951	0.500786
$238$	21.9951	1.42573
$239$	−10.7139	−0.693024	−0.346512	−	0.938045i	$-0.612634\pi$
$239$	−10.7139	−0.693024	−0.346512	+	0.938045i	$0.612634\pi$
$240$	2.36030	0.152357
$241$	13.6172	0.877161	0.438580	−	0.898692i	$-0.355481\pi$
$241$	13.6172	0.877161	0.438580	+	0.898692i	$0.355481\pi$
$242$	2.14689	0.138008
$243$	−22.3612	−1.43447
$244$	−26.9270	−1.72382
$245$	−1.46417	−0.0935421
$246$	34.8919	2.22463
$247$	2.03833	0.129696
$248$	5.95642	0.378233
$249$	33.1402	2.10018
$250$	8.25338	0.521989
$251$	−30.7328	−1.93984	−0.969919	−	0.243426i	$-0.921729\pi$
$251$	−30.7328	−1.93984	−0.969919	+	0.243426i	$0.921729\pi$
$252$	−28.1510	−1.77334
$253$	−4.86405	−0.305800
$254$	−17.5390	−1.10049
$255$	3.05941	0.191588
$256$	2.39052	0.149408
$257$	−6.04304	−0.376954	−0.188477	−	0.982078i	$-0.560355\pi$
$257$	−6.04304	−0.376954	−0.188477	+	0.982078i	$0.560355\pi$
$258$	−31.1459	−1.93906
$259$	25.2927	1.57161
$260$	1.65644	0.102728
$261$	0	0
$262$	−45.7392	−2.82578
$263$	6.54409	0.403526	0.201763	−	0.979434i	$-0.435333\pi$
$263$	6.54409	0.403526	0.201763	+	0.979434i	$0.435333\pi$
$264$	3.28007	0.201874
$265$	2.16816	0.133189
$266$	8.82303	0.540974
$267$	14.0222	0.858145
$268$	23.6432	1.44424
$269$	−3.61913	−0.220662	−0.110331	−	0.993895i	$-0.535191\pi$
$269$	−3.61913	−0.220662	−0.110331	+	0.993895i	$0.535191\pi$
$270$	−0.610902	−0.0371783
$271$	13.2943	0.807568	0.403784	−	0.914854i	$-0.367695\pi$
$271$	13.2943	0.807568	0.403784	+	0.914854i	$0.367695\pi$
$272$	7.53235	0.456716
$273$	13.3736	0.809405
$274$	13.6579	0.825103
$275$	−4.84760	−0.292321
$276$	−31.8306	−1.91598
$277$	10.3571	0.622299	0.311149	−	0.950361i	$-0.399286\pi$
$277$	10.3571	0.622299	0.311149	+	0.950361i	$0.399286\pi$
$278$	−17.2127	−1.03235
$279$	14.9874	0.897272
$280$	1.67395	0.100038
$281$	0.186983	0.0111545	0.00557724	−	0.999984i	$-0.498225\pi$
$281$	0.186983	0.0111545	0.00557724	+	0.999984i	$0.498225\pi$
$282$	11.1765	0.665548
$283$	10.0949	0.600079	0.300040	−	0.953927i	$-0.403000\pi$
$283$	10.0949	0.600079	0.300040	+	0.953927i	$0.403000\pi$
$284$	−34.4248	−2.04274
$285$	1.22724	0.0726952
$286$	−3.49136	−0.206449
$287$	−21.2463	−1.25413
$288$	−25.6370	−1.51067
$289$	−7.23661	−0.425683
$290$	0	0
$291$	3.73465	0.218929
$292$	42.5992	2.49293
$293$	−28.4218	−1.66042	−0.830211	−	0.557449i	$-0.811780\pi$
$293$	−28.4218	−1.66042	−0.830211	+	0.557449i	$0.811780\pi$
$294$	20.1956	1.17783
$295$	−0.510147	−0.0297019
$296$	−10.0883	−0.586368
$297$	0.728904	0.0422953
$298$	−39.5362	−2.29027
$299$	7.91011	0.457454
$300$	−31.7229	−1.83152
$301$	18.9653	1.09314
$302$	20.9116	1.20333
$303$	26.0428	1.49612
$304$	3.02149	0.173294
$305$	4.02883	0.230690
$306$	−22.0744	−1.26191
$307$	15.2632	0.871119	0.435560	−	0.900160i	$-0.356551\pi$
$307$	15.2632	0.871119	0.435560	+	0.900160i	$0.356551\pi$
$308$	−8.55491	−0.487461
$309$	7.44871	0.423742
$310$	−3.81724	−0.216805
$311$	7.94714	0.450641	0.225320	−	0.974285i	$-0.427657\pi$
$311$	7.94714	0.450641	0.225320	+	0.974285i	$0.427657\pi$
$312$	−5.33418	−0.301988
$313$	12.7653	0.721537	0.360768	−	0.932655i	$-0.382514\pi$
$313$	12.7653	0.721537	0.360768	+	0.932655i	$0.382514\pi$
$314$	39.5561	2.23228
$315$	4.21196	0.237317
$316$	8.02009	0.451166
$317$	13.8462	0.777683	0.388841	−	0.921305i	$-0.372875\pi$
$317$	13.8462	0.777683	0.388841	+	0.921305i	$0.372875\pi$
$318$	−29.9060	−1.67704
$319$	0	0
$320$	4.64753	0.259805
$321$	46.5307	2.59709
$322$	34.2393	1.90808
$323$	3.91644	0.217916
$324$	−20.9872	−1.16596
$325$	7.88336	0.437290
$326$	−49.9318	−2.76547
$327$	−8.83175	−0.488397
$328$	8.47431	0.467915
$329$	−6.80555	−0.375202
$330$	−2.10207	−0.115715
$331$	−18.0409	−0.991617	−0.495809	−	0.868432i	$-0.665128\pi$
$331$	−18.0409	−0.991617	−0.495809	+	0.868432i	$0.665128\pi$
$332$	34.4753	1.89208
$333$	−25.3838	−1.39103
$334$	−34.6852	−1.89789
$335$	−3.53750	−0.193274
$336$	19.8241	1.08149
$337$	−34.0769	−1.85629	−0.928143	−	0.372223i	$-0.878596\pi$
$337$	−34.0769	−1.85629	−0.928143	+	0.372223i	$0.878596\pi$
$338$	−22.2318	−1.20925
$339$	−22.8834	−1.24286
$340$	3.18266	0.172604
$341$	4.55458	0.246645
$342$	−8.85480	−0.478813
$343$	10.6542	0.575273
$344$	−7.56451	−0.407851
$345$	4.76251	0.256405
$346$	16.7781	0.901998
$347$	17.2613	0.926635	0.463317	−	0.886192i	$-0.346659\pi$
$347$	17.2613	0.926635	0.463317	+	0.886192i	$0.346659\pi$
$348$	0	0
$349$	−8.50234	−0.455120	−0.227560	−	0.973764i	$-0.573075\pi$
$349$	−8.50234	−0.455120	−0.227560	+	0.973764i	$0.573075\pi$
$350$	34.1235	1.82398
$351$	−1.18537	−0.0632705
$352$	−7.79093	−0.415258
$353$	20.9991	1.11767	0.558834	−	0.829280i	$-0.311249\pi$
$353$	20.9991	1.11767	0.558834	+	0.829280i	$0.311249\pi$
$354$	7.03658	0.373990
$355$	5.15066	0.273369
$356$	14.5871	0.773115
$357$	25.6959	1.35997
$358$	37.6106	1.98778
$359$	−2.09180	−0.110401	−0.0552006	−	0.998475i	$-0.517580\pi$
$359$	−2.09180	−0.110401	−0.0552006	+	0.998475i	$0.517580\pi$
$360$	−1.67998	−0.0885429
$361$	−17.4290	−0.917315
$362$	10.8418	0.569830
$363$	2.50811	0.131642
$364$	13.9123	0.729204
$365$	−6.37372	−0.333616
$366$	−55.5707	−2.90473
$367$	−36.7761	−1.91969	−0.959847	−	0.280523i	$-0.909492\pi$
$367$	−36.7761	−1.91969	−0.959847	+	0.280523i	$0.909492\pi$
$368$	11.7254	0.611230
$369$	21.3229	1.11002
$370$	6.46519	0.336109
$371$	18.2103	0.945431
$372$	29.8054	1.54534
$373$	−30.4759	−1.57798	−0.788991	−	0.614405i	$-0.789396\pi$
$373$	−30.4759	−1.57798	−0.788991	+	0.614405i	$0.789396\pi$
$374$	−6.70827	−0.346877
$375$	9.64202	0.497912
$376$	2.71446	0.139988
$377$	0	0
$378$	−5.13094	−0.263907
$379$	−21.5170	−1.10526	−0.552628	−	0.833428i	$-0.686375\pi$
$379$	−21.5170	−1.10526	−0.552628	+	0.833428i	$0.686375\pi$
$380$	1.27668	0.0654922
$381$	−20.4899	−1.04973
$382$	−33.4600	−1.71196
$383$	−14.2416	−0.727713	−0.363856	−	0.931455i	$-0.618540\pi$
$383$	−14.2416	−0.727713	−0.363856	+	0.931455i	$0.618540\pi$
$384$	−25.0234	−1.27697
$385$	1.27999	0.0652344
$386$	−1.50832	−0.0767715
$387$	−19.0336	−0.967534
$388$	3.88511	0.197237
$389$	−34.9432	−1.77169	−0.885845	−	0.463981i	$-0.846421\pi$
$389$	−34.9432	−1.77169	−0.885845	+	0.463981i	$0.846421\pi$
$390$	3.41847	0.173101
$391$	15.1984	0.768618
$392$	4.90497	0.247738
$393$	−53.4348	−2.69543
$394$	−45.2325	−2.27878
$395$	−1.19997	−0.0603771
$396$	8.58573	0.431449
$397$	30.3970	1.52558	0.762790	−	0.646646i	$-0.223829\pi$
$397$	30.3970	1.52558	0.762790	+	0.646646i	$0.223829\pi$
$398$	22.9789	1.15183
$399$	10.3075	0.516021
$400$	11.6858	0.584288
$401$	26.2320	1.30996	0.654982	−	0.755644i	$-0.272676\pi$
$401$	26.2320	1.30996	0.654982	+	0.755644i	$0.272676\pi$
$402$	48.7937	2.43361
$403$	−7.40684	−0.368961
$404$	27.0919	1.34787
$405$	3.14012	0.156034
$406$	0	0
$407$	−7.71400	−0.382369
$408$	−10.2490	−0.507403
$409$	−15.9524	−0.788794	−0.394397	−	0.918940i	$-0.629047\pi$
$409$	−15.9524	−0.788794	−0.394397	+	0.918940i	$0.629047\pi$
$410$	−5.43087	−0.268211
$411$	15.9558	0.787044
$412$	7.74878	0.381755
$413$	−4.28470	−0.210836
$414$	−34.3626	−1.68883
$415$	−5.15822	−0.253207
$416$	12.6699	0.621194
$417$	−20.1087	−0.984729
$418$	−2.69092	−0.131617
$419$	2.86736	0.140080	0.0700399	−	0.997544i	$-0.477687\pi$
$419$	2.86736	0.140080	0.0700399	+	0.997544i	$0.477687\pi$
$420$	8.37632	0.408722
$421$	5.64587	0.275163	0.137581	−	0.990490i	$-0.456067\pi$
$421$	5.64587	0.275163	0.137581	+	0.990490i	$0.456067\pi$
$422$	−22.0136	−1.07161
$423$	6.83006	0.332089
$424$	−7.26335	−0.352740
$425$	15.1470	0.734738
$426$	−71.0443	−3.44211
$427$	33.8380	1.63754
$428$	48.4052	2.33975
$429$	−4.07879	−0.196926
$430$	4.84781	0.233782
$431$	−1.44170	−0.0694444	−0.0347222	−	0.999397i	$-0.511055\pi$
$431$	−1.44170	−0.0694444	−0.0347222	+	0.999397i	$0.511055\pi$
$432$	−1.75712	−0.0845394
$433$	7.65508	0.367880	0.183940	−	0.982938i	$-0.441115\pi$
$433$	7.65508	0.367880	0.183940	+	0.982938i	$0.441115\pi$
$434$	−32.0609	−1.53897
$435$	0	0
$436$	−9.18755	−0.440004
$437$	6.09662	0.291641
$438$	87.9143	4.20071
$439$	−24.6839	−1.17810	−0.589050	−	0.808097i	$-0.700498\pi$
$439$	−24.6839	−1.17810	−0.589050	+	0.808097i	$0.700498\pi$
$440$	−0.510537	−0.0243389
$441$	12.3418	0.587703
$442$	10.9093	0.518900
$443$	−29.9473	−1.42284	−0.711421	−	0.702766i	$-0.751948\pi$
$443$	−29.9473	−1.42284	−0.711421	+	0.702766i	$0.751948\pi$
$444$	−50.4808	−2.39571
$445$	−2.18253	−0.103462
$446$	−13.4696	−0.637804
$447$	−46.1882	−2.18463
$448$	39.0344	1.84420
$449$	−25.4259	−1.19992	−0.599960	−	0.800030i	$-0.704817\pi$
$449$	−25.4259	−1.19992	−0.599960	+	0.800030i	$0.704817\pi$
$450$	−34.2464	−1.61439
$451$	6.47989	0.305126
$452$	−23.8053	−1.11971
$453$	24.4300	1.14782
$454$	49.1977	2.30896
$455$	−2.08157	−0.0975856
$456$	−4.11125	−0.192527
$457$	27.6582	1.29380	0.646898	−	0.762576i	$-0.276066\pi$
$457$	27.6582	1.29380	0.646898	+	0.762576i	$0.276066\pi$
$458$	50.2888	2.34984
$459$	−2.27756	−0.106308
$460$	4.95437	0.230999
$461$	−27.3717	−1.27483	−0.637413	−	0.770523i	$-0.719995\pi$
$461$	−27.3717	−1.27483	−0.637413	+	0.770523i	$0.719995\pi$
$462$	−17.6552	−0.821396
$463$	6.22403	0.289255	0.144628	−	0.989486i	$-0.453802\pi$
$463$	6.22403	0.289255	0.144628	+	0.989486i	$0.453802\pi$
$464$	0	0
$465$	−4.45950	−0.206804
$466$	13.6588	0.632732
$467$	−35.5992	−1.64733	−0.823667	−	0.567074i	$-0.808075\pi$
$467$	−35.5992	−1.64733	−0.823667	+	0.567074i	$0.808075\pi$
$468$	−13.9624	−0.645414
$469$	−29.7113	−1.37194
$470$	−1.73959	−0.0802415
$471$	46.2115	2.12931
$472$	1.70900	0.0786629
$473$	−5.78421	−0.265958
$474$	16.5515	0.760235
$475$	6.07600	0.278786
$476$	26.7310	1.22522
$477$	−18.2759	−0.836795
$478$	−23.0016	−1.05207
$479$	40.5281	1.85178	0.925888	−	0.377799i	$-0.123319\pi$
$479$	40.5281	1.85178	0.925888	+	0.377799i	$0.123319\pi$
$480$	7.62829	0.348182
$481$	12.5448	0.571994
$482$	29.2347	1.33160
$483$	40.0001	1.82007
$484$	2.60915	0.118598
$485$	−0.581292	−0.0263951
$486$	−48.0070	−2.17764
$487$	−1.23675	−0.0560423	−0.0280212	−	0.999607i	$-0.508921\pi$
$487$	−1.23675	−0.0560423	−0.0280212	+	0.999607i	$0.508921\pi$
$488$	−13.4966	−0.610963
$489$	−58.3329	−2.63790
$490$	−3.14341	−0.142005
$491$	34.1836	1.54269	0.771343	−	0.636420i	$-0.219585\pi$
$491$	34.1836	1.54269	0.771343	+	0.636420i	$0.219585\pi$
$492$	42.4047	1.91175
$493$	0	0
$494$	4.37609	0.196889
$495$	−1.28460	−0.0577385
$496$	−10.9794	−0.492990
$497$	43.2602	1.94048
$498$	71.1485	3.18824
$499$	−22.0524	−0.987201	−0.493601	−	0.869689i	$-0.664320\pi$
$499$	−22.0524	−0.987201	−0.493601	+	0.869689i	$0.664320\pi$
$500$	10.0305	0.448576
$501$	−40.5210	−1.81035
$502$	−65.9801	−2.94484
$503$	−14.3415	−0.639455	−0.319728	−	0.947509i	$-0.603591\pi$
$503$	−14.3415	−0.639455	−0.319728	+	0.947509i	$0.603591\pi$
$504$	−14.1101	−0.628514
$505$	−4.05351	−0.180379
$506$	−10.4426	−0.464231
$507$	−25.9724	−1.15347
$508$	−21.3154	−0.945717
$509$	−0.601537	−0.0266627	−0.0133313	−	0.999911i	$-0.504244\pi$
$509$	−0.601537	−0.0266627	−0.0133313	+	0.999911i	$0.504244\pi$
$510$	6.56823	0.290846
$511$	−53.5326	−2.36814
$512$	25.0862	1.10866
$513$	−0.913611	−0.0403369
$514$	−12.9738	−0.572248
$515$	−1.15938	−0.0510883
$516$	−37.8521	−1.66635
$517$	2.07562	0.0912854
$518$	54.3008	2.38584
$519$	19.6011	0.860392
$520$	0.830255	0.0364091
$521$	14.4105	0.631337	0.315669	−	0.948869i	$-0.397771\pi$
$521$	14.4105	0.631337	0.315669	+	0.948869i	$0.397771\pi$
$522$	0	0
$523$	0.924450	0.0404234	0.0202117	−	0.999796i	$-0.493566\pi$
$523$	0.924450	0.0404234	0.0202117	+	0.999796i	$0.493566\pi$
$524$	−55.5875	−2.42835
$525$	39.8648	1.73984
$526$	14.0495	0.612586
$527$	−14.2314	−0.619931
$528$	−6.04612	−0.263124
$529$	0.659024	0.0286532
$530$	4.65481	0.202192
$531$	4.30014	0.186610
$532$	10.7228	0.464890
$533$	−10.5379	−0.456445
$534$	30.1042	1.30274
$535$	−7.24241	−0.313117
$536$	11.8507	0.511871
$537$	43.9386	1.89609
$538$	−7.76989	−0.334984
$539$	3.75059	0.161549
$540$	−0.742439	−0.0319495
$541$	28.4528	1.22328	0.611642	−	0.791135i	$-0.290509\pi$
$541$	28.4528	1.22328	0.611642	+	0.791135i	$0.290509\pi$
$542$	28.5413	1.22596
$543$	12.6659	0.543546
$544$	24.3439	1.04374
$545$	1.37465	0.0588834
$546$	28.7116	1.22874
$547$	−35.9514	−1.53717	−0.768586	−	0.639746i	$-0.779039\pi$
$547$	−35.9514	−1.53717	−0.768586	+	0.639746i	$0.779039\pi$
$548$	16.5986	0.709059
$549$	−33.9599	−1.44937
$550$	−10.4073	−0.443768
$551$	0	0
$552$	−15.9544	−0.679066
$553$	−10.0785	−0.428582
$554$	22.2356	0.944701
$555$	7.55296	0.320605
$556$	−20.9188	−0.887157
$557$	6.13072	0.259767	0.129884	−	0.991529i	$-0.458540\pi$
$557$	6.13072	0.259767	0.129884	+	0.991529i	$0.458540\pi$
$558$	32.1764	1.36213
$559$	9.40651	0.397853
$560$	−3.08558	−0.130390
$561$	−7.83695	−0.330876
$562$	0.401433	0.0169334
$563$	7.39981	0.311865	0.155932	−	0.987768i	$-0.450162\pi$
$563$	7.39981	0.311865	0.155932	+	0.987768i	$0.450162\pi$
$564$	13.5829	0.571944
$565$	3.56177	0.149845
$566$	21.6727	0.910970
$567$	26.3737	1.10759
$568$	−17.2547	−0.723993
$569$	11.1549	0.467637	0.233818	−	0.972280i	$-0.424878\pi$
$569$	11.1549	0.467637	0.233818	+	0.972280i	$0.424878\pi$
$570$	2.63475	0.110357
$571$	−13.3039	−0.556750	−0.278375	−	0.960473i	$-0.589796\pi$
$571$	−13.3039	−0.556750	−0.278375	+	0.960473i	$0.589796\pi$
$572$	−4.24311	−0.177413
$573$	−39.0896	−1.63299
$574$	−45.6136	−1.90388
$575$	23.5790	0.983312
$576$	−39.1750	−1.63229
$577$	4.65374	0.193738	0.0968688	−	0.995297i	$-0.469117\pi$
$577$	4.65374	0.193738	0.0968688	+	0.995297i	$0.469117\pi$
$578$	−15.5362	−0.646222
$579$	−1.76210	−0.0732302
$580$	0	0
$581$	−43.3236	−1.79737
$582$	8.01791	0.332353
$583$	−5.55393	−0.230020
$584$	21.3520	0.883552
$585$	2.08907	0.0863724
$586$	−61.0187	−2.52066
$587$	−11.9845	−0.494655	−0.247328	−	0.968932i	$-0.579552\pi$
$587$	−11.9845	−0.494655	−0.247328	+	0.968932i	$0.579552\pi$
$588$	24.5440	1.01218
$589$	−5.70873	−0.235224
$590$	−1.09523	−0.0450900
$591$	−52.8429	−2.17367
$592$	18.5956	0.764274
$593$	17.1810	0.705538	0.352769	−	0.935710i	$-0.385240\pi$
$593$	17.1810	0.705538	0.352769	+	0.935710i	$0.385240\pi$
$594$	1.56488	0.0642078
$595$	−3.99951	−0.163964
$596$	−48.0489	−1.96816
$597$	26.8451	1.09870
$598$	16.9822	0.694453
$599$	−40.7333	−1.66432	−0.832158	−	0.554539i	$-0.812895\pi$
$599$	−40.7333	−1.66432	−0.832158	+	0.554539i	$0.812895\pi$
$600$	−15.9005	−0.649134
$601$	−3.18410	−0.129882	−0.0649411	−	0.997889i	$-0.520686\pi$
$601$	−3.18410	−0.129882	−0.0649411	+	0.997889i	$0.520686\pi$
$602$	40.7165	1.65948
$603$	29.8184	1.21430
$604$	25.4142	1.03409
$605$	−0.390383	−0.0158713
$606$	55.9111	2.27123
$607$	24.5755	0.997490	0.498745	−	0.866749i	$-0.333794\pi$
$607$	24.5755	0.997490	0.498745	+	0.866749i	$0.333794\pi$
$608$	9.76518	0.396030
$609$	0	0
$610$	8.64947	0.350207
$611$	−3.37545	−0.136556
$612$	−26.8273	−1.08443
$613$	23.4950	0.948956	0.474478	−	0.880267i	$-0.342637\pi$
$613$	23.4950	0.948956	0.474478	+	0.880267i	$0.342637\pi$
$614$	32.7686	1.32243
$615$	−6.34461	−0.255840
$616$	−4.28798	−0.172768
$617$	41.5857	1.67418	0.837088	−	0.547069i	$-0.184256\pi$
$617$	41.5857	1.67418	0.837088	+	0.547069i	$0.184256\pi$
$618$	15.9916	0.643276
$619$	34.4112	1.38310	0.691551	−	0.722327i	$-0.256928\pi$
$619$	34.4112	1.38310	0.691551	+	0.722327i	$0.256928\pi$
$620$	−4.63916	−0.186313
$621$	−3.54543	−0.142273
$622$	17.0617	0.684110
$623$	−18.3310	−0.734416
$624$	9.83244	0.393613
$625$	22.7372	0.909490
$626$	27.4057	1.09535
$627$	−3.14367	−0.125546
$628$	48.0731	1.91833
$629$	24.1035	0.961069
$630$	9.04264	0.360267
$631$	10.7504	0.427968	0.213984	−	0.976837i	$-0.431356\pi$
$631$	10.7504	0.427968	0.213984	+	0.976837i	$0.431356\pi$
$632$	4.01991	0.159904
$633$	−25.7174	−1.02218
$634$	29.7264	1.18059
$635$	3.18922	0.126560
$636$	−36.3452	−1.44118
$637$	−6.09935	−0.241665
$638$	0	0
$639$	−43.4160	−1.71751
$640$	3.89485	0.153958
$641$	−4.06789	−0.160672	−0.0803360	−	0.996768i	$-0.525599\pi$
$641$	−4.06789	−0.160672	−0.0803360	+	0.996768i	$0.525599\pi$
$642$	99.8964	3.94260
$643$	−41.7131	−1.64500	−0.822502	−	0.568762i	$-0.807423\pi$
$643$	−41.7131	−1.64500	−0.822502	+	0.568762i	$0.807423\pi$
$644$	41.6116	1.63973
$645$	5.66346	0.222998
$646$	8.40817	0.330815
$647$	6.21730	0.244427	0.122214	−	0.992504i	$-0.461001\pi$
$647$	6.21730	0.244427	0.122214	+	0.992504i	$0.461001\pi$
$648$	−10.5194	−0.413242
$649$	1.30679	0.0512959
$650$	16.9247	0.663843
$651$	−37.4551	−1.46798
$652$	−60.6829	−2.37653
$653$	−7.41752	−0.290270	−0.145135	−	0.989412i	$-0.546362\pi$
$653$	−7.41752	−0.290270	−0.145135	+	0.989412i	$0.546362\pi$
$654$	−18.9608	−0.741427
$655$	8.31704	0.324974
$656$	−15.6206	−0.609882
$657$	53.7254	2.09603
$658$	−14.6108	−0.569588
$659$	19.8383	0.772790	0.386395	−	0.922333i	$-0.373720\pi$
$659$	19.8383	0.772790	0.386395	+	0.922333i	$0.373720\pi$
$660$	−2.55468	−0.0994409
$661$	−12.8411	−0.499463	−0.249731	−	0.968315i	$-0.580342\pi$
$661$	−12.8411	−0.499463	−0.249731	+	0.968315i	$0.580342\pi$
$662$	−38.7319	−1.50536
$663$	12.7447	0.494965
$664$	17.2801	0.670596
$665$	−1.60434	−0.0622138
$666$	−54.4964	−2.11169
$667$	0	0
$668$	−42.1534	−1.63097
$669$	−15.7359	−0.608384
$670$	−7.59464	−0.293407
$671$	−10.3202	−0.398407
$672$	64.0696	2.47154
$673$	−35.7907	−1.37963	−0.689815	−	0.723986i	$-0.742308\pi$
$673$	−35.7907	−1.37963	−0.689815	+	0.723986i	$0.742308\pi$
$674$	−73.1595	−2.81800
$675$	−3.53344	−0.136002
$676$	−27.0187	−1.03918
$677$	−37.4946	−1.44103	−0.720517	−	0.693437i	$-0.756095\pi$
$677$	−37.4946	−1.44103	−0.720517	+	0.693437i	$0.756095\pi$
$678$	−49.1283	−1.88676
$679$	−4.88225	−0.187363
$680$	1.59525	0.0611749
$681$	57.4753	2.20246
$682$	9.77821	0.374427
$683$	21.6760	0.829408	0.414704	−	0.909956i	$-0.363885\pi$
$683$	21.6760	0.829408	0.414704	+	0.909956i	$0.363885\pi$
$684$	−10.7614	−0.411472
$685$	−2.48350	−0.0948896
$686$	22.8734	0.873312
$687$	58.7500	2.24145
$688$	13.9436	0.531594
$689$	9.03202	0.344093
$690$	10.2246	0.389244
$691$	−44.5346	−1.69418	−0.847088	−	0.531453i	$-0.821646\pi$
$691$	−44.5346	−1.69418	−0.847088	+	0.531453i	$0.821646\pi$
$692$	20.3907	0.775139
$693$	−10.7893	−0.409852
$694$	37.0582	1.40671
$695$	3.12989	0.118723
$696$	0	0
$697$	−20.2473	−0.766923
$698$	−18.2536	−0.690910
$699$	15.9569	0.603546
$700$	41.4708	1.56745
$701$	−0.536351	−0.0202577	−0.0101288	−	0.999949i	$-0.503224\pi$
$701$	−0.536351	−0.0202577	−0.0101288	+	0.999949i	$0.503224\pi$
$702$	−2.54487	−0.0960499
$703$	9.66876	0.364664
$704$	−11.9050	−0.448688
$705$	−2.03228	−0.0765402
$706$	45.0828	1.69671
$707$	−34.0453	−1.28040
$708$	8.55167	0.321391
$709$	15.1946	0.570644	0.285322	−	0.958432i	$-0.407899\pi$
$709$	15.1946	0.570644	0.285322	+	0.958432i	$0.407899\pi$
$710$	11.0579	0.414996
$711$	10.1148	0.379335
$712$	7.31150	0.274010
$713$	−22.1537	−0.829664
$714$	55.1663	2.06455
$715$	0.634856	0.0237423
$716$	45.7087	1.70821
$717$	−26.8716	−1.00354
$718$	−4.49088	−0.167598
$719$	−30.7384	−1.14635	−0.573174	−	0.819433i	$-0.694288\pi$
$719$	−30.7384	−1.14635	−0.573174	+	0.819433i	$0.694288\pi$
$720$	3.09670	0.115407
$721$	−9.73756	−0.362646
$722$	−37.4182	−1.39256
$723$	34.1534	1.27018
$724$	13.1762	0.489688
$725$	0	0
$726$	5.38465	0.199843
$727$	28.9363	1.07319	0.536594	−	0.843840i	$-0.319711\pi$
$727$	28.9363	1.07319	0.536594	+	0.843840i	$0.319711\pi$
$728$	6.97328	0.258447
$729$	−31.9532	−1.18345
$730$	−13.6837	−0.506456
$731$	18.0736	0.668476
$732$	−67.5359	−2.49620
$733$	2.45142	0.0905453	0.0452726	−	0.998975i	$-0.485584\pi$
$733$	2.45142	0.0905453	0.0452726	+	0.998975i	$0.485584\pi$
$734$	−78.9543	−2.91426
$735$	−3.67229	−0.135454
$736$	37.8955	1.39685
$737$	9.06163	0.333789
$738$	45.7779	1.68511
$739$	19.6027	0.721096	0.360548	−	0.932741i	$-0.382590\pi$
$739$	19.6027	0.721096	0.360548	+	0.932741i	$0.382590\pi$
$740$	7.85724	0.288838
$741$	5.11237	0.187807
$742$	39.0956	1.43524
$743$	6.55524	0.240488	0.120244	−	0.992744i	$-0.461632\pi$
$743$	6.55524	0.240488	0.120244	+	0.992744i	$0.461632\pi$
$744$	14.9394	0.547703
$745$	7.18911	0.263388
$746$	−65.4285	−2.39551
$747$	43.4797	1.59084
$748$	−8.15267	−0.298091
$749$	−60.8287	−2.22263
$750$	20.7004	0.755871
$751$	29.2921	1.06888	0.534442	−	0.845205i	$-0.320522\pi$
$751$	29.2921	1.06888	0.534442	+	0.845205i	$0.320522\pi$
$752$	−5.00354	−0.182460
$753$	−77.0813	−2.80900
$754$	0	0
$755$	−3.80249	−0.138387
$756$	−6.23571	−0.226791
$757$	48.7456	1.77169	0.885845	−	0.463982i	$-0.153580\pi$
$757$	48.7456	1.77169	0.885845	+	0.463982i	$0.153580\pi$
$758$	−46.1948	−1.67787
$759$	−12.1996	−0.442817
$760$	0.639909	0.0232119
$761$	40.5770	1.47092	0.735458	−	0.677570i	$-0.236967\pi$
$761$	40.5770	1.47092	0.735458	+	0.677570i	$0.236967\pi$
$762$	−43.9897	−1.59358
$763$	11.5456	0.417979
$764$	−40.6644	−1.47119
$765$	4.01392	0.145124
$766$	−30.5752	−1.10473
$767$	−2.12515	−0.0767346
$768$	5.99570	0.216351
$769$	27.9347	1.00735	0.503676	−	0.863893i	$-0.331981\pi$
$769$	27.9347	1.00735	0.503676	+	0.863893i	$0.331981\pi$
$770$	2.74800	0.0990312
$771$	−15.1566	−0.545852
$772$	−1.83308	−0.0659741
$773$	13.3897	0.481593	0.240796	−	0.970576i	$-0.422591\pi$
$773$	13.3897	0.481593	0.240796	+	0.970576i	$0.422591\pi$
$774$	−40.8632	−1.46880
$775$	−22.0788	−0.793094
$776$	1.94733	0.0699052
$777$	63.4370	2.27579
$778$	−75.0193	−2.68957
$779$	−8.12192	−0.290998
$780$	4.15452	0.148756
$781$	−13.1939	−0.472113
$782$	32.6294	1.16683
$783$	0	0
$784$	−9.04128	−0.322903
$785$	−7.19273	−0.256720
$786$	−114.719	−4.09189
$787$	−17.6598	−0.629504	−0.314752	−	0.949174i	$-0.601921\pi$
$787$	−17.6598	−0.629504	−0.314752	+	0.949174i	$0.601921\pi$
$788$	−54.9717	−1.95829
$789$	16.4133	0.584329
$790$	−2.57621	−0.0916574
$791$	29.9151	1.06366
$792$	4.30342	0.152916
$793$	16.7831	0.595986
$794$	65.2591	2.31596
$795$	5.43799	0.192866
$796$	27.9266	0.989833
$797$	−4.94138	−0.175033	−0.0875164	−	0.996163i	$-0.527893\pi$
$797$	−4.94138	−0.175033	−0.0875164	+	0.996163i	$0.527893\pi$
$798$	22.1291	0.783363
$799$	−6.48555	−0.229442
$800$	37.7673	1.33528
$801$	18.3970	0.650027
$802$	56.3174	1.98863
$803$	16.3268	0.576162
$804$	59.2997	2.09134
$805$	−6.22595	−0.219436
$806$	−15.9017	−0.560114
$807$	−9.07718	−0.319532
$808$	13.5793	0.477718
$809$	38.3860	1.34958	0.674790	−	0.738010i	$-0.264234\pi$
$809$	38.3860	1.34958	0.674790	+	0.738010i	$0.264234\pi$
$810$	6.74150	0.236872
$811$	11.8714	0.416861	0.208430	−	0.978037i	$-0.433165\pi$
$811$	11.8714	0.416861	0.208430	+	0.978037i	$0.433165\pi$
$812$	0	0
$813$	33.3435	1.16941
$814$	−16.5611	−0.580468
$815$	9.07941	0.318038
$816$	18.8920	0.661351
$817$	7.24995	0.253644
$818$	−34.2480	−1.19745
$819$	17.5460	0.613107
$820$	−6.60021	−0.230489
$821$	−43.2135	−1.50816	−0.754080	−	0.656782i	$-0.771917\pi$
$821$	−43.2135	−1.50816	−0.754080	+	0.656782i	$0.771917\pi$
$822$	34.2555	1.19480
$823$	29.2697	1.02028	0.510139	−	0.860092i	$-0.329594\pi$
$823$	29.2697	1.02028	0.510139	+	0.860092i	$0.329594\pi$
$824$	3.88392	0.135303
$825$	−12.1583	−0.423298
$826$	−9.19880	−0.320067
$827$	7.45412	0.259205	0.129603	−	0.991566i	$-0.458630\pi$
$827$	7.45412	0.259205	0.129603	+	0.991566i	$0.458630\pi$
$828$	−41.7614	−1.45131
$829$	−27.5682	−0.957485	−0.478742	−	0.877955i	$-0.658907\pi$
$829$	−27.5682	−0.957485	−0.478742	+	0.877955i	$0.658907\pi$
$830$	−11.0741	−0.384389
$831$	25.9768	0.901125
$832$	19.3605	0.671203
$833$	−11.7192	−0.406048
$834$	−43.1713	−1.49490
$835$	6.30702	0.218264
$836$	−3.27032	−0.113106
$837$	3.31986	0.114751
$838$	6.15592	0.212653
$839$	16.0143	0.552876	0.276438	−	0.961032i	$-0.410846\pi$
$839$	16.0143	0.552876	0.276438	+	0.961032i	$0.410846\pi$
$840$	4.19846	0.144861
$841$	0	0
$842$	12.1211	0.417720
$843$	0.468975	0.0161523
$844$	−26.7535	−0.920893
$845$	4.04255	0.139068
$846$	14.6634	0.504138
$847$	−3.27881	−0.112661
$848$	13.3885	0.459762
$849$	25.3191	0.868950
$850$	32.5190	1.11539
$851$	37.5213	1.28621
$852$	−86.3412	−2.95800
$853$	35.5745	1.21805	0.609023	−	0.793152i	$-0.291562\pi$
$853$	35.5745	1.21805	0.609023	+	0.793152i	$0.291562\pi$
$854$	72.6466	2.48591
$855$	1.61012	0.0550651
$856$	24.2621	0.829263
$857$	−16.8297	−0.574892	−0.287446	−	0.957797i	$-0.592806\pi$
$857$	−16.8297	−0.574892	−0.287446	+	0.957797i	$0.592806\pi$
$858$	−8.75672	−0.298950
$859$	50.7174	1.73046	0.865228	−	0.501378i	$-0.167173\pi$
$859$	50.7174	1.73046	0.865228	+	0.501378i	$0.167173\pi$
$860$	5.89162	0.200902
$861$	−53.2881	−1.81606
$862$	−3.09518	−0.105422
$863$	−16.3671	−0.557142	−0.278571	−	0.960416i	$-0.589861\pi$
$863$	−16.3671	−0.557142	−0.278571	+	0.960416i	$0.589861\pi$
$864$	−5.67885	−0.193198
$865$	−3.05087	−0.103733
$866$	16.4346	0.558472
$867$	−18.1502	−0.616414
$868$	−38.9641	−1.32253
$869$	3.07383	0.104273
$870$	0	0
$871$	−14.7364	−0.499323
$872$	−4.60508	−0.155948
$873$	4.89983	0.165834
$874$	13.0888	0.442735
$875$	−12.6048	−0.426121
$876$	106.844	3.60991
$877$	−24.1532	−0.815596	−0.407798	−	0.913072i	$-0.633703\pi$
$877$	−24.1532	−0.815596	−0.407798	+	0.913072i	$0.633703\pi$
$878$	−52.9937	−1.78845
$879$	−71.2851	−2.40439
$880$	0.941068	0.0317234
$881$	−37.3861	−1.25957	−0.629785	−	0.776770i	$-0.716857\pi$
$881$	−37.3861	−1.25957	−0.629785	+	0.776770i	$0.716857\pi$
$882$	26.4964	0.892182
$883$	−8.31012	−0.279658	−0.139829	−	0.990176i	$-0.544655\pi$
$883$	−8.31012	−0.279658	−0.139829	+	0.990176i	$0.544655\pi$
$884$	13.2582	0.445921
$885$	−1.27951	−0.0430101
$886$	−64.2938	−2.15999
$887$	−3.37275	−0.113246	−0.0566229	−	0.998396i	$-0.518033\pi$
$887$	−3.37275	−0.113246	−0.0566229	+	0.998396i	$0.518033\pi$
$888$	−25.3025	−0.849095
$889$	26.7861	0.898377
$890$	−4.68566	−0.157064
$891$	−8.04368	−0.269474
$892$	−16.3698	−0.548102
$893$	−2.60158	−0.0870587
$894$	−99.1611	−3.31644
$895$	−6.83896	−0.228601
$896$	32.7127	1.09285
$897$	19.8394	0.662420
$898$	−54.5866	−1.82158
$899$	0	0
$900$	−41.6202	−1.38734
$901$	17.3541	0.578147
$902$	13.9116	0.463207
$903$	47.5671	1.58294
$904$	−11.9319	−0.396851
$905$	−1.97142	−0.0655324
$906$	52.4486	1.74249
$907$	−43.1250	−1.43194	−0.715972	−	0.698129i	$-0.754016\pi$
$907$	−43.1250	−1.43194	−0.715972	+	0.698129i	$0.754016\pi$
$908$	59.7907	1.98422
$909$	34.1679	1.13328
$910$	−4.46891	−0.148143
$911$	16.2483	0.538331	0.269165	−	0.963094i	$-0.413252\pi$
$911$	16.2483	0.538331	0.269165	+	0.963094i	$0.413252\pi$
$912$	7.57823	0.250940
$913$	13.2132	0.437294
$914$	59.3792	1.96409
$915$	10.1048	0.334053
$916$	61.1168	2.01935
$917$	69.8544	2.30680
$918$	−4.88969	−0.161384
$919$	43.7700	1.44384	0.721920	−	0.691977i	$-0.243260\pi$
$919$	43.7700	1.44384	0.721920	+	0.691977i	$0.243260\pi$
$920$	2.48328	0.0818713
$921$	38.2819	1.26143
$922$	−58.7641	−1.93529
$923$	21.4564	0.706245
$924$	−21.4567	−0.705873
$925$	37.3944	1.22952
$926$	13.3623	0.439114
$927$	9.77264	0.320975
$928$	0	0
$929$	9.14855	0.300154	0.150077	−	0.988674i	$-0.452048\pi$
$929$	9.14855	0.300154	0.150077	+	0.988674i	$0.452048\pi$
$930$	−9.57407	−0.313946
$931$	−4.70100	−0.154069
$932$	16.5998	0.543743
$933$	19.9323	0.652554
$934$	−76.4277	−2.50079
$935$	1.21981	0.0398919
$936$	−6.99840	−0.228750
$937$	50.9508	1.66449	0.832246	−	0.554407i	$-0.187055\pi$
$937$	50.9508	1.66449	0.832246	+	0.554407i	$0.187055\pi$
$938$	−63.7871	−2.08272
$939$	32.0168	1.04483
$940$	−2.11416	−0.0689562
$941$	7.31734	0.238538	0.119269	−	0.992862i	$-0.461945\pi$
$941$	7.31734	0.238538	0.119269	+	0.992862i	$0.461945\pi$
$942$	99.2111	3.23247
$943$	−31.5185	−1.02639
$944$	−3.15018	−0.102530
$945$	0.932991	0.0303502
$946$	−12.4181	−0.403747
$947$	−53.0244	−1.72306	−0.861530	−	0.507707i	$-0.830493\pi$
$947$	−53.0244	−1.72306	−0.861530	+	0.507707i	$0.830493\pi$
$948$	20.1153	0.653314
$949$	−26.5513	−0.861893
$950$	13.0445	0.423220
$951$	34.7279	1.12613
$952$	13.3984	0.434245
$953$	−35.0666	−1.13592	−0.567959	−	0.823057i	$-0.692267\pi$
$953$	−35.0666	−1.13592	−0.567959	+	0.823057i	$0.692267\pi$
$954$	−39.2364	−1.27032
$955$	6.08423	0.196881
$956$	−27.9542	−0.904103
$957$	0	0
$958$	87.0095	2.81115
$959$	−20.8588	−0.673566
$960$	11.6565	0.376212
$961$	−10.2558	−0.330831
$962$	26.9324	0.868335
$963$	61.0478	1.96724
$964$	35.5293	1.14432
$965$	0.274267	0.00882897
$966$	85.8760	2.76301
$967$	−2.82686	−0.0909056	−0.0454528	−	0.998966i	$-0.514473\pi$
$967$	−2.82686	−0.0909056	−0.0454528	+	0.998966i	$0.514473\pi$
$968$	1.30779	0.0420338
$969$	9.82286	0.315556
$970$	−1.24797	−0.0400700
$971$	−22.8606	−0.733632	−0.366816	−	0.930294i	$-0.619552\pi$
$971$	−22.8606	−0.733632	−0.366816	+	0.930294i	$0.619552\pi$
$972$	−58.3437	−1.87137
$973$	26.2878	0.842748
$974$	−2.65516	−0.0850769
$975$	19.7723	0.633221
$976$	24.8782	0.796331
$977$	41.1605	1.31684	0.658420	−	0.752651i	$-0.271225\pi$
$977$	41.1605	1.31684	0.658420	+	0.752651i	$0.271225\pi$
$978$	−125.235	−4.00456
$979$	5.59075	0.178681
$980$	−3.82023	−0.122033
$981$	−11.5872	−0.369950
$982$	73.3886	2.34192
$983$	−30.3320	−0.967439	−0.483720	−	0.875223i	$-0.660715\pi$
$983$	−30.3320	−0.967439	−0.483720	+	0.875223i	$0.660715\pi$
$984$	21.2545	0.677569
$985$	8.22490	0.262067
$986$	0	0
$987$	−17.0691	−0.543314
$988$	5.31832	0.169198
$989$	28.1347	0.894632
$990$	−2.75790	−0.0876519
$991$	−23.7536	−0.754559	−0.377279	−	0.926100i	$-0.623140\pi$
$991$	−23.7536	−0.754559	−0.377279	+	0.926100i	$0.623140\pi$
$992$	−35.4845	−1.12663
$993$	−45.2486	−1.43592
$994$	92.8749	2.94581
$995$	−4.17840	−0.132464
$996$	86.4679	2.73984
$997$	−21.8372	−0.691590	−0.345795	−	0.938310i	$-0.612391\pi$
$997$	−21.8372	−0.691590	−0.345795	+	0.938310i	$0.612391\pi$
$998$	−47.3442	−1.49865
$999$	−5.62277	−0.177897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.ba.1.37	✓	40
29.28	even	2		9251.2.a.bb.1.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.ba.1.37	✓	40	1.1	even	1	trivial
9251.2.a.bb.1.4	yes	40	29.28	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+2.14689 q^{2} +2.50811 q^{3} +2.60915 q^{4} -0.390383 q^{5} +5.38465 q^{6} -3.27881 q^{7} +1.30779 q^{8} +3.29062 q^{9} +O(q^{10})\)	\(q+2.14689 q^{2} +2.50811 q^{3} +2.60915 q^{4} -0.390383 q^{5} +5.38465 q^{6} -3.27881 q^{7} +1.30779 q^{8} +3.29062 q^{9} -0.838111 q^{10} +1.00000 q^{11} +6.54404 q^{12} -1.62624 q^{13} -7.03925 q^{14} -0.979123 q^{15} -2.41063 q^{16} -3.12464 q^{17} +7.06461 q^{18} -1.25340 q^{19} -1.01857 q^{20} -8.22362 q^{21} +2.14689 q^{22} -4.86405 q^{23} +3.28007 q^{24} -4.84760 q^{25} -3.49136 q^{26} +0.728904 q^{27} -8.55491 q^{28} -2.10207 q^{30} +4.55458 q^{31} -7.79093 q^{32} +2.50811 q^{33} -6.70827 q^{34} +1.27999 q^{35} +8.58573 q^{36} -7.71400 q^{37} -2.69092 q^{38} -4.07879 q^{39} -0.510537 q^{40} +6.47989 q^{41} -17.6552 q^{42} -5.78421 q^{43} +2.60915 q^{44} -1.28460 q^{45} -10.4426 q^{46} +2.07562 q^{47} -6.04612 q^{48} +3.75059 q^{49} -10.4073 q^{50} -7.83695 q^{51} -4.24311 q^{52} -5.55393 q^{53} +1.56488 q^{54} -0.390383 q^{55} -4.28798 q^{56} -3.14367 q^{57} +1.30679 q^{59} -2.55468 q^{60} -10.3202 q^{61} +9.77821 q^{62} -10.7893 q^{63} -11.9050 q^{64} +0.634856 q^{65} +5.38465 q^{66} +9.06163 q^{67} -8.15267 q^{68} -12.1996 q^{69} +2.74800 q^{70} -13.1939 q^{71} +4.30342 q^{72} +16.3268 q^{73} -16.5611 q^{74} -12.1583 q^{75} -3.27032 q^{76} -3.27881 q^{77} -8.75672 q^{78} +3.07383 q^{79} +0.941068 q^{80} -8.04368 q^{81} +13.9116 q^{82} +13.2132 q^{83} -21.4567 q^{84} +1.21981 q^{85} -12.4181 q^{86} +1.30779 q^{88} +5.59075 q^{89} -2.75790 q^{90} +5.33213 q^{91} -12.6911 q^{92} +11.4234 q^{93} +4.45612 q^{94} +0.489307 q^{95} -19.5405 q^{96} +1.48903 q^{97} +8.05212 q^{98} +3.29062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9}+O(q^{10}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9	\( 40 q - 5 q^{3} + 28 q^{4} - 12 q^{5} - 8 q^{6} - 15 q^{7} - 3 q^{8} + 25 q^{9} - 25 q^{10} + 40 q^{11} - 17 q^{12} - 35 q^{13} + 3 q^{14} + 15 q^{15} - 6 q^{17} + 24 q^{18} + 2 q^{19} - 6 q^{20} - 5 q^{21} + 8 q^{23} - 18 q^{24} + 20 q^{25} - 20 q^{26} + q^{27} - 50 q^{28} - 5 q^{30} - 12 q^{31} - 6 q^{32} - 5 q^{33} - 26 q^{34} - 28 q^{35} - 22 q^{36} - 17 q^{37} - 12 q^{38} - 30 q^{39} + 30 q^{40} + 9 q^{41} - 34 q^{42} + 6 q^{43} + 28 q^{44} - 89 q^{45} - 7 q^{46} - 8 q^{47} + 33 q^{48} + q^{49} + 17 q^{50} - 52 q^{51} - 65 q^{52} - 51 q^{53} + 5 q^{54} - 12 q^{55} - 4 q^{56} - 49 q^{57} - 56 q^{59} + 15 q^{60} - 39 q^{61} + 53 q^{63} - 13 q^{64} - 13 q^{65} - 8 q^{66} - 68 q^{67} - 107 q^{68} - 31 q^{69} + 51 q^{70} - 47 q^{71} + 71 q^{72} + 19 q^{73} - 54 q^{74} - 22 q^{75} + 54 q^{76} - 15 q^{77} + 28 q^{78} + 10 q^{79} + 10 q^{80} - 4 q^{81} + 34 q^{82} - 40 q^{83} + 11 q^{84} + 26 q^{85} - 46 q^{86} - 3 q^{88} + 29 q^{89} - 100 q^{90} - 50 q^{91} + 76 q^{92} - 73 q^{93} - 116 q^{94} + 5 q^{95} + 13 q^{96} - 22 q^{97} + 102 q^{98} + 25 q^{99}+O(q^{100}) \) 40 * q - 5 * q^3 + 28 * q^4 - 12 * q^5 - 8 * q^6 - 15 * q^7 - 3 * q^8 + 25 * q^9 - 25 * q^10 + 40 * q^11 - 17 * q^12 - 35 * q^13 + 3 * q^14 + 15 * q^15 - 6 * q^17 + 24 * q^18 + 2 * q^19 - 6 * q^20 - 5 * q^21 + 8 * q^23 - 18 * q^24 + 20 * q^25 - 20 * q^26 + q^27 - 50 * q^28 - 5 * q^30 - 12 * q^31 - 6 * q^32 - 5 * q^33 - 26 * q^34 - 28 * q^35 - 22 * q^36 - 17 * q^37 - 12 * q^38 - 30 * q^39 + 30 * q^40 + 9 * q^41 - 34 * q^42 + 6 * q^43 + 28 * q^44 - 89 * q^45 - 7 * q^46 - 8 * q^47 + 33 * q^48 + q^49 + 17 * q^50 - 52 * q^51 - 65 * q^52 - 51 * q^53 + 5 * q^54 - 12 * q^55 - 4 * q^56 - 49 * q^57 - 56 * q^59 + 15 * q^60 - 39 * q^61 + 53 * q^63 - 13 * q^64 - 13 * q^65 - 8 * q^66 - 68 * q^67 - 107 * q^68 - 31 * q^69 + 51 * q^70 - 47 * q^71 + 71 * q^72 + 19 * q^73 - 54 * q^74 - 22 * q^75 + 54 * q^76 - 15 * q^77 + 28 * q^78 + 10 * q^79 + 10 * q^80 - 4 * q^81 + 34 * q^82 - 40 * q^83 + 11 * q^84 + 26 * q^85 - 46 * q^86 - 3 * q^88 + 29 * q^89 - 100 * q^90 - 50 * q^91 + 76 * q^92 - 73 * q^93 - 116 * q^94 + 5 * q^95 + 13 * q^96 - 22 * q^97 + 102 * q^98 + 25 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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