LMFDB - Embedded newform 7942.2.a.bo.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 14x^{6} + 29x^{5} + 64x^{4} - 50x^{3} - 36x^{2} + 30x - 5 $ x^8 - 3x^7 - 14x^6 + 29x^5 + 64x^4 - 50x^3 - 36x^2 + 30*x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.29456$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.29456 q^{3} +1.00000 q^{4} +1.67652 q^{5} -3.29456 q^{6} -4.86985 q^{7} -1.00000 q^{8} +7.85409 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.29456 q^{3} +1.00000 q^{4} +1.67652 q^{5} -3.29456 q^{6} -4.86985 q^{7} -1.00000 q^{8} +7.85409 q^{9} -1.67652 q^{10} -1.00000 q^{11} +3.29456 q^{12} -3.50363 q^{13} +4.86985 q^{14} +5.52339 q^{15} +1.00000 q^{16} +3.62777 q^{17} -7.85409 q^{18} +1.67652 q^{20} -16.0440 q^{21} +1.00000 q^{22} +2.18509 q^{23} -3.29456 q^{24} -2.18928 q^{25} +3.50363 q^{26} +15.9921 q^{27} -4.86985 q^{28} +4.29197 q^{29} -5.52339 q^{30} +7.19082 q^{31} -1.00000 q^{32} -3.29456 q^{33} -3.62777 q^{34} -8.16440 q^{35} +7.85409 q^{36} +3.40235 q^{37} -11.5429 q^{39} -1.67652 q^{40} +1.63779 q^{41} +16.0440 q^{42} -6.70515 q^{43} -1.00000 q^{44} +13.1676 q^{45} -2.18509 q^{46} +1.19844 q^{47} +3.29456 q^{48} +16.7154 q^{49} +2.18928 q^{50} +11.9519 q^{51} -3.50363 q^{52} +11.9661 q^{53} -15.9921 q^{54} -1.67652 q^{55} +4.86985 q^{56} -4.29197 q^{58} -11.7352 q^{59} +5.52339 q^{60} +9.63915 q^{61} -7.19082 q^{62} -38.2482 q^{63} +1.00000 q^{64} -5.87392 q^{65} +3.29456 q^{66} -11.2143 q^{67} +3.62777 q^{68} +7.19891 q^{69} +8.16440 q^{70} -13.2301 q^{71} -7.85409 q^{72} +10.6778 q^{73} -3.40235 q^{74} -7.21269 q^{75} +4.86985 q^{77} +11.5429 q^{78} +9.01696 q^{79} +1.67652 q^{80} +29.1245 q^{81} -1.63779 q^{82} +10.7783 q^{83} -16.0440 q^{84} +6.08203 q^{85} +6.70515 q^{86} +14.1401 q^{87} +1.00000 q^{88} -2.91509 q^{89} -13.1676 q^{90} +17.0622 q^{91} +2.18509 q^{92} +23.6905 q^{93} -1.19844 q^{94} -3.29456 q^{96} +8.91344 q^{97} -16.7154 q^{98} -7.85409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * q^98 - 15 * 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
$3$	3.29456	1.90211	0.951056	−	0.309018i	$-0.100000\pi$
$3$	3.29456	1.90211	0.951056	+	0.309018i	$0.100000\pi$
$4$	1.00000	0.500000
$5$	1.67652	0.749763	0.374882	−	0.927073i	$-0.377683\pi$
$5$	1.67652	0.749763	0.374882	+	0.927073i	$0.377683\pi$
$6$	−3.29456	−1.34500
$7$	−4.86985	−1.84063	−0.920315	−	0.391179i	$-0.872067\pi$
$7$	−4.86985	−1.84063	−0.920315	+	0.391179i	$0.872067\pi$
$8$	−1.00000	−0.353553
$9$	7.85409	2.61803
$10$	−1.67652	−0.530163
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.29456	0.951056
$13$	−3.50363	−0.971733	−0.485867	−	0.874033i	$-0.661496\pi$
$13$	−3.50363	−0.971733	−0.485867	+	0.874033i	$0.661496\pi$
$14$	4.86985	1.30152
$15$	5.52339	1.42613
$16$	1.00000	0.250000
$17$	3.62777	0.879862	0.439931	−	0.898032i	$-0.355003\pi$
$17$	3.62777	0.879862	0.439931	+	0.898032i	$0.355003\pi$
$18$	−7.85409	−1.85123
$19$	0	0
$19$	0	0
$20$	1.67652	0.374882
$21$	−16.0440	−3.50108
$22$	1.00000	0.213201
$23$	2.18509	0.455624	0.227812	−	0.973705i	$-0.426843\pi$
$23$	2.18509	0.455624	0.227812	+	0.973705i	$0.426843\pi$
$24$	−3.29456	−0.672498
$25$	−2.18928	−0.437855
$26$	3.50363	0.687119
$27$	15.9921	3.07768
$28$	−4.86985	−0.920315
$29$	4.29197	0.796998	0.398499	−	0.917169i	$-0.369531\pi$
$29$	4.29197	0.796998	0.398499	+	0.917169i	$0.369531\pi$
$30$	−5.52339	−1.00843
$31$	7.19082	1.29151	0.645755	−	0.763545i	$-0.276543\pi$
$31$	7.19082	1.29151	0.645755	+	0.763545i	$0.276543\pi$
$32$	−1.00000	−0.176777
$33$	−3.29456	−0.573508
$34$	−3.62777	−0.622157
$35$	−8.16440	−1.38004
$36$	7.85409	1.30902
$37$	3.40235	0.559344	0.279672	−	0.960096i	$-0.409774\pi$
$37$	3.40235	0.559344	0.279672	+	0.960096i	$0.409774\pi$
$38$	0	0
$39$	−11.5429	−1.84835
$40$	−1.67652	−0.265081
$41$	1.63779	0.255780	0.127890	−	0.991788i	$-0.459179\pi$
$41$	1.63779	0.255780	0.127890	+	0.991788i	$0.459179\pi$
$42$	16.0440	2.47564
$43$	−6.70515	−1.02253	−0.511263	−	0.859424i	$-0.670822\pi$
$43$	−6.70515	−1.02253	−0.511263	+	0.859424i	$0.670822\pi$
$44$	−1.00000	−0.150756
$45$	13.1676	1.96290
$46$	−2.18509	−0.322174
$47$	1.19844	0.174810	0.0874052	−	0.996173i	$-0.472143\pi$
$47$	1.19844	0.174810	0.0874052	+	0.996173i	$0.472143\pi$
$48$	3.29456	0.475528
$49$	16.7154	2.38792
$50$	2.18928	0.309610
$51$	11.9519	1.67360
$52$	−3.50363	−0.485867
$53$	11.9661	1.64367	0.821833	−	0.569729i	$-0.192952\pi$
$53$	11.9661	1.64367	0.821833	+	0.569729i	$0.192952\pi$
$54$	−15.9921	−2.17625
$55$	−1.67652	−0.226062
$56$	4.86985	0.650761
$57$	0	0
$58$	−4.29197	−0.563563
$59$	−11.7352	−1.52779	−0.763895	−	0.645341i	$-0.776715\pi$
$59$	−11.7352	−1.52779	−0.763895	+	0.645341i	$0.776715\pi$
$60$	5.52339	0.713067
$61$	9.63915	1.23417	0.617083	−	0.786898i	$-0.288314\pi$
$61$	9.63915	1.23417	0.617083	+	0.786898i	$0.288314\pi$
$62$	−7.19082	−0.913235
$63$	−38.2482	−4.81883
$64$	1.00000	0.125000
$65$	−5.87392	−0.728570
$66$	3.29456	0.405532
$67$	−11.2143	−1.37004	−0.685022	−	0.728523i	$-0.740207\pi$
$67$	−11.2143	−1.37004	−0.685022	+	0.728523i	$0.740207\pi$
$68$	3.62777	0.439931
$69$	7.19891	0.866647
$70$	8.16440	0.975833
$71$	−13.2301	−1.57012	−0.785061	−	0.619419i	$-0.787368\pi$
$71$	−13.2301	−1.57012	−0.785061	+	0.619419i	$0.787368\pi$
$72$	−7.85409	−0.925614
$73$	10.6778	1.24974	0.624872	−	0.780727i	$-0.285151\pi$
$73$	10.6778	1.24974	0.624872	+	0.780727i	$0.285151\pi$
$74$	−3.40235	−0.395516
$75$	−7.21269	−0.832850
$76$	0	0
$77$	4.86985	0.554971
$78$	11.5429	1.30698
$79$	9.01696	1.01449	0.507244	−	0.861803i	$-0.330664\pi$
$79$	9.01696	1.01449	0.507244	+	0.861803i	$0.330664\pi$
$80$	1.67652	0.187441
$81$	29.1245	3.23606
$82$	−1.63779	−0.180864
$83$	10.7783	1.18307	0.591535	−	0.806280i	$-0.298522\pi$
$83$	10.7783	1.18307	0.591535	+	0.806280i	$0.298522\pi$
$84$	−16.0440	−1.75054
$85$	6.08203	0.659688
$86$	6.70515	0.723035
$87$	14.1401	1.51598
$88$	1.00000	0.106600
$89$	−2.91509	−0.308999	−0.154499	−	0.987993i	$-0.549376\pi$
$89$	−2.91509	−0.308999	−0.154499	+	0.987993i	$0.549376\pi$
$90$	−13.1676	−1.38798
$91$	17.0622	1.78860
$92$	2.18509	0.227812
$93$	23.6905	2.45660
$94$	−1.19844	−0.123610
$95$	0	0
$96$	−3.29456	−0.336249
$97$	8.91344	0.905022	0.452511	−	0.891759i	$-0.350528\pi$
$97$	8.91344	0.905022	0.452511	+	0.891759i	$0.350528\pi$
$98$	−16.7154	−1.68851
$99$	−7.85409	−0.789366
$100$	−2.18928	−0.218928
$101$	14.2011	1.41306	0.706530	−	0.707683i	$-0.250260\pi$
$101$	14.2011	1.41306	0.706530	+	0.707683i	$0.250260\pi$
$102$	−11.9519	−1.18341
$103$	14.1838	1.39757	0.698786	−	0.715330i	$-0.253724\pi$
$103$	14.1838	1.39757	0.698786	+	0.715330i	$0.253724\pi$
$104$	3.50363	0.343560
$105$	−26.8981	−2.62498
$106$	−11.9661	−1.16225
$107$	−8.67056	−0.838214	−0.419107	−	0.907937i	$-0.637657\pi$
$107$	−8.67056	−0.838214	−0.419107	+	0.907937i	$0.637657\pi$
$108$	15.9921	1.53884
$109$	11.7099	1.12160	0.560801	−	0.827951i	$-0.310493\pi$
$109$	11.7099	1.12160	0.560801	+	0.827951i	$0.310493\pi$
$110$	1.67652	0.159850
$111$	11.2092	1.06393
$112$	−4.86985	−0.460157
$113$	3.77211	0.354850	0.177425	−	0.984134i	$-0.443223\pi$
$113$	3.77211	0.354850	0.177425	+	0.984134i	$0.443223\pi$
$114$	0	0
$115$	3.66336	0.341610
$116$	4.29197	0.398499
$117$	−27.5179	−2.54403
$118$	11.7352	1.08031
$119$	−17.6667	−1.61950
$120$	−5.52339	−0.504214
$121$	1.00000	0.0909091
$122$	−9.63915	−0.872688
$123$	5.39580	0.486523
$124$	7.19082	0.645755
$125$	−12.0530	−1.07805
$126$	38.2482	3.40742
$127$	−1.76950	−0.157018	−0.0785088	−	0.996913i	$-0.525016\pi$
$127$	−1.76950	−0.157018	−0.0785088	+	0.996913i	$0.525016\pi$
$128$	−1.00000	−0.0883883
$129$	−22.0905	−1.94496
$130$	5.87392	0.515177
$131$	−10.2055	−0.891661	−0.445830	−	0.895117i	$-0.647092\pi$
$131$	−10.2055	−0.891661	−0.445830	+	0.895117i	$0.647092\pi$
$132$	−3.29456	−0.286754
$133$	0	0
$134$	11.2143	0.968767
$135$	26.8111	2.30753
$136$	−3.62777	−0.311078
$137$	−12.4319	−1.06213	−0.531064	−	0.847332i	$-0.678208\pi$
$137$	−12.4319	−1.06213	−0.531064	+	0.847332i	$0.678208\pi$
$138$	−7.19891	−0.612812
$139$	−14.6781	−1.24498	−0.622490	−	0.782628i	$-0.713879\pi$
$139$	−14.6781	−1.24498	−0.622490	+	0.782628i	$0.713879\pi$
$140$	−8.16440	−0.690018
$141$	3.94833	0.332509
$142$	13.2301	1.11024
$143$	3.50363	0.292989
$144$	7.85409	0.654508
$145$	7.19557	0.597560
$146$	−10.6778	−0.883703
$147$	55.0699	4.54209
$148$	3.40235	0.279672
$149$	−7.88026	−0.645576	−0.322788	−	0.946471i	$-0.604620\pi$
$149$	−7.88026	−0.645576	−0.322788	+	0.946471i	$0.604620\pi$
$150$	7.21269	0.588914
$151$	−9.88572	−0.804488	−0.402244	−	0.915532i	$-0.631770\pi$
$151$	−9.88572	−0.804488	−0.402244	+	0.915532i	$0.631770\pi$
$152$	0	0
$153$	28.4928	2.30351
$154$	−4.86985	−0.392423
$155$	12.0556	0.968326
$156$	−11.5429	−0.924173
$157$	1.66922	0.133218	0.0666090	−	0.997779i	$-0.478782\pi$
$157$	1.66922	0.133218	0.0666090	+	0.997779i	$0.478782\pi$
$158$	−9.01696	−0.717351
$159$	39.4229	3.12644
$160$	−1.67652	−0.132541
$161$	−10.6411	−0.838634
$162$	−29.1245	−2.28824
$163$	4.57250	0.358146	0.179073	−	0.983836i	$-0.442690\pi$
$163$	4.57250	0.358146	0.179073	+	0.983836i	$0.442690\pi$
$164$	1.63779	0.127890
$165$	−5.52339	−0.429995
$166$	−10.7783	−0.836556
$167$	11.7350	0.908083	0.454041	−	0.890981i	$-0.349982\pi$
$167$	11.7350	0.908083	0.454041	+	0.890981i	$0.349982\pi$
$168$	16.0440	1.23782
$169$	−0.724542	−0.0557340
$170$	−6.08203	−0.466470
$171$	0	0
$172$	−6.70515	−0.511263
$173$	8.09627	0.615548	0.307774	−	0.951460i	$-0.400416\pi$
$173$	8.09627	0.615548	0.307774	+	0.951460i	$0.400416\pi$
$174$	−14.1401	−1.07196
$175$	10.6614	0.805929
$176$	−1.00000	−0.0753778
$177$	−38.6622	−2.90603
$178$	2.91509	0.218495
$179$	−6.49701	−0.485610	−0.242805	−	0.970075i	$-0.578067\pi$
$179$	−6.49701	−0.485610	−0.242805	+	0.970075i	$0.578067\pi$
$180$	13.1676	0.981452
$181$	4.69340	0.348858	0.174429	−	0.984670i	$-0.444192\pi$
$181$	4.69340	0.348858	0.174429	+	0.984670i	$0.444192\pi$
$182$	−17.0622	−1.26473
$183$	31.7567	2.34752
$184$	−2.18509	−0.161087
$185$	5.70412	0.419375
$186$	−23.6905	−1.73708
$187$	−3.62777	−0.265288
$188$	1.19844	0.0874052
$189$	−77.8790	−5.66486
$190$	0	0
$191$	3.16605	0.229087	0.114544	−	0.993418i	$-0.463459\pi$
$191$	3.16605	0.229087	0.114544	+	0.993418i	$0.463459\pi$
$192$	3.29456	0.237764
$193$	12.4006	0.892612	0.446306	−	0.894880i	$-0.352739\pi$
$193$	12.4006	0.892612	0.446306	+	0.894880i	$0.352739\pi$
$194$	−8.91344	−0.639947
$195$	−19.3519	−1.38582
$196$	16.7154	1.19396
$197$	−1.51112	−0.107663	−0.0538313	−	0.998550i	$-0.517143\pi$
$197$	−1.51112	−0.107663	−0.0538313	+	0.998550i	$0.517143\pi$
$198$	7.85409	0.558166
$199$	13.7261	0.973016	0.486508	−	0.873676i	$-0.338270\pi$
$199$	13.7261	0.973016	0.486508	+	0.873676i	$0.338270\pi$
$200$	2.18928	0.154805
$201$	−36.9461	−2.60598
$202$	−14.2011	−0.999184
$203$	−20.9012	−1.46698
$204$	11.9519	0.836798
$205$	2.74580	0.191775
$206$	−14.1838	−0.988233
$207$	17.1619	1.19284
$208$	−3.50363	−0.242933
$209$	0	0
$210$	26.8981	1.85614
$211$	5.35804	0.368863	0.184431	−	0.982845i	$-0.440956\pi$
$211$	5.35804	0.368863	0.184431	+	0.982845i	$0.440956\pi$
$212$	11.9661	0.821833
$213$	−43.5872	−2.98655
$214$	8.67056	0.592707
$215$	−11.2413	−0.766652
$216$	−15.9921	−1.08812
$217$	−35.0182	−2.37719
$218$	−11.7099	−0.793093
$219$	35.1787	2.37715
$220$	−1.67652	−0.113031
$221$	−12.7104	−0.854992
$222$	−11.2092	−0.752315
$223$	27.2577	1.82531	0.912655	−	0.408731i	$-0.134028\pi$
$223$	27.2577	1.82531	0.912655	+	0.408731i	$0.134028\pi$
$224$	4.86985	0.325380
$225$	−17.1948	−1.14632
$226$	−3.77211	−0.250917
$227$	22.3811	1.48549	0.742743	−	0.669576i	$-0.233524\pi$
$227$	22.3811	1.48549	0.742743	+	0.669576i	$0.233524\pi$
$228$	0	0
$229$	3.13168	0.206947	0.103474	−	0.994632i	$-0.467004\pi$
$229$	3.13168	0.206947	0.103474	+	0.994632i	$0.467004\pi$
$230$	−3.66336	−0.241555
$231$	16.0440	1.05562
$232$	−4.29197	−0.281781
$233$	0.318884	0.0208908	0.0104454	−	0.999945i	$-0.496675\pi$
$233$	0.318884	0.0208908	0.0104454	+	0.999945i	$0.496675\pi$
$234$	27.5179	1.79890
$235$	2.00921	0.131066
$236$	−11.7352	−0.763895
$237$	29.7069	1.92967
$238$	17.6667	1.14516
$239$	22.1707	1.43410	0.717052	−	0.697020i	$-0.245491\pi$
$239$	22.1707	1.43410	0.717052	+	0.697020i	$0.245491\pi$
$240$	5.52339	0.356533
$241$	12.2020	0.786001	0.393001	−	0.919538i	$-0.371437\pi$
$241$	12.2020	0.786001	0.393001	+	0.919538i	$0.371437\pi$
$242$	−1.00000	−0.0642824
$243$	47.9761	3.07767
$244$	9.63915	0.617083
$245$	28.0237	1.79037
$246$	−5.39580	−0.344024
$247$	0	0
$248$	−7.19082	−0.456617
$249$	35.5096	2.25033
$250$	12.0530	0.762297
$251$	−24.2058	−1.52786	−0.763929	−	0.645300i	$-0.776732\pi$
$251$	−24.2058	−1.52786	−0.763929	+	0.645300i	$0.776732\pi$
$252$	−38.2482	−2.40941
$253$	−2.18509	−0.137376
$254$	1.76950	0.111028
$255$	20.0376	1.25480
$256$	1.00000	0.0625000
$257$	18.7346	1.16863	0.584316	−	0.811526i	$-0.301363\pi$
$257$	18.7346	1.16863	0.584316	+	0.811526i	$0.301363\pi$
$258$	22.0905	1.37529
$259$	−16.5689	−1.02954
$260$	−5.87392	−0.364285
$261$	33.7095	2.08657
$262$	10.2055	0.630499
$263$	21.5801	1.33069	0.665344	−	0.746537i	$-0.268285\pi$
$263$	21.5801	1.33069	0.665344	+	0.746537i	$0.268285\pi$
$264$	3.29456	0.202766
$265$	20.0614	1.23236
$266$	0	0
$267$	−9.60392	−0.587750
$268$	−11.2143	−0.685022
$269$	−0.794184	−0.0484222	−0.0242111	−	0.999707i	$-0.507707\pi$
$269$	−0.794184	−0.0484222	−0.0242111	+	0.999707i	$0.507707\pi$
$270$	−26.8111	−1.63167
$271$	−29.1960	−1.77353	−0.886764	−	0.462222i	$-0.847052\pi$
$271$	−29.1960	−1.77353	−0.886764	+	0.462222i	$0.847052\pi$
$272$	3.62777	0.219966
$273$	56.2123	3.40212
$274$	12.4319	0.751038
$275$	2.18928	0.132018
$276$	7.19891	0.433324
$277$	−1.48899	−0.0894649	−0.0447325	−	0.998999i	$-0.514244\pi$
$277$	−1.48899	−0.0894649	−0.0447325	+	0.998999i	$0.514244\pi$
$278$	14.6781	0.880333
$279$	56.4774	3.38121
$280$	8.16440	0.487916
$281$	18.1085	1.08026	0.540132	−	0.841580i	$-0.318374\pi$
$281$	18.1085	1.08026	0.540132	+	0.841580i	$0.318374\pi$
$282$	−3.94833	−0.235119
$283$	−21.5718	−1.28231	−0.641154	−	0.767412i	$-0.721544\pi$
$283$	−21.5718	−1.28231	−0.641154	+	0.767412i	$0.721544\pi$
$284$	−13.2301	−0.785061
$285$	0	0
$286$	−3.50363	−0.207174
$287$	−7.97581	−0.470797
$288$	−7.85409	−0.462807
$289$	−3.83932	−0.225842
$290$	−7.19557	−0.422539
$291$	29.3658	1.72145
$292$	10.6778	0.624872
$293$	−3.86911	−0.226036	−0.113018	−	0.993593i	$-0.536052\pi$
$293$	−3.86911	−0.226036	−0.113018	+	0.993593i	$0.536052\pi$
$294$	−55.0699	−3.21174
$295$	−19.6743	−1.14548
$296$	−3.40235	−0.197758
$297$	−15.9921	−0.927955
$298$	7.88026	0.456491
$299$	−7.65577	−0.442745
$300$	−7.21269	−0.416425
$301$	32.6530	1.88209
$302$	9.88572	0.568859
$303$	46.7862	2.68780
$304$	0	0
$305$	16.1602	0.925333
$306$	−28.4928	−1.62883
$307$	19.2969	1.10133	0.550667	−	0.834725i	$-0.314373\pi$
$307$	19.2969	1.10133	0.550667	+	0.834725i	$0.314373\pi$
$308$	4.86985	0.277485
$309$	46.7294	2.65834
$310$	−12.0556	−0.684710
$311$	−22.6482	−1.28426	−0.642131	−	0.766595i	$-0.721949\pi$
$311$	−22.6482	−1.28426	−0.642131	+	0.766595i	$0.721949\pi$
$312$	11.5429	0.653489
$313$	−16.3913	−0.926493	−0.463246	−	0.886229i	$-0.653316\pi$
$313$	−16.3913	−0.926493	−0.463246	+	0.886229i	$0.653316\pi$
$314$	−1.66922	−0.0941994
$315$	−64.1240	−3.61298
$316$	9.01696	0.507244
$317$	11.8723	0.666817	0.333409	−	0.942782i	$-0.391801\pi$
$317$	11.8723	0.666817	0.333409	+	0.942782i	$0.391801\pi$
$318$	−39.4229	−2.21072
$319$	−4.29197	−0.240304
$320$	1.67652	0.0937204
$321$	−28.5656	−1.59438
$322$	10.6411	0.593004
$323$	0	0
$324$	29.1245	1.61803
$325$	7.67043	0.425479
$326$	−4.57250	−0.253247
$327$	38.5788	2.13341
$328$	−1.63779	−0.0904320
$329$	−5.83622	−0.321761
$330$	5.52339	0.304053
$331$	17.7376	0.974945	0.487472	−	0.873138i	$-0.337919\pi$
$331$	17.7376	0.974945	0.487472	+	0.873138i	$0.337919\pi$
$332$	10.7783	0.591535
$333$	26.7224	1.46438
$334$	−11.7350	−0.642112
$335$	−18.8010	−1.02721
$336$	−16.0440	−0.875271
$337$	−12.7153	−0.692645	−0.346323	−	0.938115i	$-0.612570\pi$
$337$	−12.7153	−0.692645	−0.346323	+	0.938115i	$0.612570\pi$
$338$	0.724542	0.0394099
$339$	12.4274	0.674964
$340$	6.08203	0.329844
$341$	−7.19082	−0.389405
$342$	0	0
$343$	−47.3126	−2.55464
$344$	6.70515	0.361517
$345$	12.0691	0.649780
$346$	−8.09627	−0.435258
$347$	1.10562	0.0593526	0.0296763	−	0.999560i	$-0.490552\pi$
$347$	1.10562	0.0593526	0.0296763	+	0.999560i	$0.490552\pi$
$348$	14.1401	0.757990
$349$	−1.31374	−0.0703228	−0.0351614	−	0.999382i	$-0.511195\pi$
$349$	−1.31374	−0.0703228	−0.0351614	+	0.999382i	$0.511195\pi$
$350$	−10.6614	−0.569878
$351$	−56.0304	−2.99068
$352$	1.00000	0.0533002
$353$	14.5567	0.774776	0.387388	−	0.921917i	$-0.373377\pi$
$353$	14.5567	0.774776	0.387388	+	0.921917i	$0.373377\pi$
$354$	38.6622	2.05487
$355$	−22.1805	−1.17722
$356$	−2.91509	−0.154499
$357$	−58.2038	−3.08047
$358$	6.49701	0.343378
$359$	27.2333	1.43732	0.718660	−	0.695362i	$-0.244756\pi$
$359$	27.2333	1.43732	0.718660	+	0.695362i	$0.244756\pi$
$360$	−13.1676	−0.693991
$361$	0	0
$362$	−4.69340	−0.246680
$363$	3.29456	0.172919
$364$	17.0622	0.894301
$365$	17.9016	0.937012
$366$	−31.7567	−1.65995
$367$	21.8221	1.13910	0.569552	−	0.821955i	$-0.307117\pi$
$367$	21.8221	1.13910	0.569552	+	0.821955i	$0.307117\pi$
$368$	2.18509	0.113906
$369$	12.8634	0.669641
$370$	−5.70412	−0.296543
$371$	−58.2729	−3.02538
$372$	23.6905	1.22830
$373$	5.69784	0.295023	0.147512	−	0.989060i	$-0.452874\pi$
$373$	5.69784	0.295023	0.147512	+	0.989060i	$0.452874\pi$
$374$	3.62777	0.187587
$375$	−39.7092	−2.05057
$376$	−1.19844	−0.0618048
$377$	−15.0375	−0.774470
$378$	77.8790	4.00566
$379$	1.17318	0.0602624	0.0301312	−	0.999546i	$-0.490407\pi$
$379$	1.17318	0.0602624	0.0301312	+	0.999546i	$0.490407\pi$
$380$	0	0
$381$	−5.82971	−0.298665
$382$	−3.16605	−0.161989
$383$	−29.8860	−1.52710	−0.763552	−	0.645746i	$-0.776546\pi$
$383$	−29.8860	−1.52710	−0.763552	+	0.645746i	$0.776546\pi$
$384$	−3.29456	−0.168125
$385$	8.16440	0.416096
$386$	−12.4006	−0.631172
$387$	−52.6629	−2.67700
$388$	8.91344	0.452511
$389$	−9.80583	−0.497175	−0.248588	−	0.968609i	$-0.579966\pi$
$389$	−9.80583	−0.497175	−0.248588	+	0.968609i	$0.579966\pi$
$390$	19.3519	0.979924
$391$	7.92701	0.400886
$392$	−16.7154	−0.844256
$393$	−33.6227	−1.69604
$394$	1.51112	0.0761290
$395$	15.1171	0.760625
$396$	−7.85409	−0.394683
$397$	6.56666	0.329571	0.164786	−	0.986329i	$-0.447307\pi$
$397$	6.56666	0.329571	0.164786	+	0.986329i	$0.447307\pi$
$398$	−13.7261	−0.688027
$399$	0	0
$400$	−2.18928	−0.109464
$401$	−6.23259	−0.311241	−0.155620	−	0.987817i	$-0.549738\pi$
$401$	−6.23259	−0.311241	−0.155620	+	0.987817i	$0.549738\pi$
$402$	36.9461	1.84270
$403$	−25.1940	−1.25500
$404$	14.2011	0.706530
$405$	48.8279	2.42628
$406$	20.9012	1.03731
$407$	−3.40235	−0.168648
$408$	−11.9519	−0.591706
$409$	0.0264468	0.00130771	0.000653854	−	1.00000i	$-0.499792\pi$
$409$	0.0264468	0.00130771	0.000653854		1.00000i	$0.499792\pi$
$410$	−2.74580	−0.135605
$411$	−40.9576	−2.02029
$412$	14.1838	0.698786
$413$	57.1485	2.81209
$414$	−17.1619	−0.843463
$415$	18.0700	0.887022
$416$	3.50363	0.171780
$417$	−48.3578	−2.36809
$418$	0	0
$419$	30.7629	1.50287	0.751433	−	0.659810i	$-0.229363\pi$
$419$	30.7629	1.50287	0.751433	+	0.659810i	$0.229363\pi$
$420$	−26.8981	−1.31249
$421$	−28.4947	−1.38875	−0.694373	−	0.719615i	$-0.744318\pi$
$421$	−28.4947	−1.38875	−0.694373	+	0.719615i	$0.744318\pi$
$422$	−5.35804	−0.260825
$423$	9.41266	0.457659
$424$	−11.9661	−0.581123
$425$	−7.94218	−0.385252
$426$	43.5872	2.11181
$427$	−46.9412	−2.27164
$428$	−8.67056	−0.419107
$429$	11.5429	0.557297
$430$	11.2413	0.542105
$431$	−3.05195	−0.147007	−0.0735036	−	0.997295i	$-0.523418\pi$
$431$	−3.05195	−0.147007	−0.0735036	+	0.997295i	$0.523418\pi$
$432$	15.9921	0.769419
$433$	7.96434	0.382742	0.191371	−	0.981518i	$-0.438707\pi$
$433$	7.96434	0.382742	0.191371	+	0.981518i	$0.438707\pi$
$434$	35.0182	1.68093
$435$	23.7062	1.13663
$436$	11.7099	0.560801
$437$	0	0
$438$	−35.1787	−1.68090
$439$	3.27637	0.156372	0.0781862	−	0.996939i	$-0.475087\pi$
$439$	3.27637	0.156372	0.0781862	+	0.996939i	$0.475087\pi$
$440$	1.67652	0.0799250
$441$	131.284	6.25164
$442$	12.7104	0.604570
$443$	17.8946	0.850200	0.425100	−	0.905146i	$-0.360239\pi$
$443$	17.8946	0.850200	0.425100	+	0.905146i	$0.360239\pi$
$444$	11.2092	0.531967
$445$	−4.88721	−0.231676
$446$	−27.2577	−1.29069
$447$	−25.9619	−1.22796
$448$	−4.86985	−0.230079
$449$	−27.9052	−1.31693	−0.658464	−	0.752612i	$-0.728794\pi$
$449$	−27.9052	−1.31693	−0.658464	+	0.752612i	$0.728794\pi$
$450$	17.1948	0.810570
$451$	−1.63779	−0.0771207
$452$	3.77211	0.177425
$453$	−32.5690	−1.53023
$454$	−22.3811	−1.05040
$455$	28.6051	1.34103
$456$	0	0
$457$	−41.6109	−1.94648	−0.973238	−	0.229797i	$-0.926194\pi$
$457$	−41.6109	−1.94648	−0.973238	+	0.229797i	$0.926194\pi$
$458$	−3.13168	−0.146334
$459$	58.0155	2.70793
$460$	3.66336	0.170805
$461$	5.41182	0.252053	0.126027	−	0.992027i	$-0.459777\pi$
$461$	5.41182	0.252053	0.126027	+	0.992027i	$0.459777\pi$
$462$	−16.0440	−0.746434
$463$	−19.8369	−0.921901	−0.460950	−	0.887426i	$-0.652491\pi$
$463$	−19.8369	−0.921901	−0.460950	+	0.887426i	$0.652491\pi$
$464$	4.29197	0.199250
$465$	39.7177	1.84186
$466$	−0.318884	−0.0147720
$467$	−11.1659	−0.516698	−0.258349	−	0.966052i	$-0.583178\pi$
$467$	−11.1659	−0.516698	−0.258349	+	0.966052i	$0.583178\pi$
$468$	−27.5179	−1.27201
$469$	54.6119	2.52174
$470$	−2.00921	−0.0926780
$471$	5.49933	0.253396
$472$	11.7352	0.540155
$473$	6.70515	0.308303
$474$	−29.7069	−1.36448
$475$	0	0
$476$	−17.6667	−0.809750
$477$	93.9826	4.30317
$478$	−22.1707	−1.01406
$479$	−23.4157	−1.06989	−0.534946	−	0.844886i	$-0.679668\pi$
$479$	−23.4157	−1.06989	−0.534946	+	0.844886i	$0.679668\pi$
$480$	−5.52339	−0.252107
$481$	−11.9206	−0.543533
$482$	−12.2020	−0.555787
$483$	−35.0576	−1.59518
$484$	1.00000	0.0454545
$485$	14.9436	0.678552
$486$	−47.9761	−2.17624
$487$	20.5501	0.931215	0.465607	−	0.884991i	$-0.345836\pi$
$487$	20.5501	0.931215	0.465607	+	0.884991i	$0.345836\pi$
$488$	−9.63915	−0.436344
$489$	15.0644	0.681234
$490$	−28.0237	−1.26598
$491$	−5.75038	−0.259511	−0.129756	−	0.991546i	$-0.541419\pi$
$491$	−5.75038	−0.259511	−0.129756	+	0.991546i	$0.541419\pi$
$492$	5.39580	0.243262
$493$	15.5702	0.701249
$494$	0	0
$495$	−13.1676	−0.591838
$496$	7.19082	0.322877
$497$	64.4285	2.89001
$498$	−35.5096	−1.59122
$499$	31.4420	1.40754	0.703769	−	0.710429i	$-0.251499\pi$
$499$	31.4420	1.40754	0.703769	+	0.710429i	$0.251499\pi$
$500$	−12.0530	−0.539025
$501$	38.6617	1.72728
$502$	24.2058	1.08036
$503$	−16.5777	−0.739162	−0.369581	−	0.929199i	$-0.620499\pi$
$503$	−16.5777	−0.739162	−0.369581	+	0.929199i	$0.620499\pi$
$504$	38.2482	1.70371
$505$	23.8084	1.05946
$506$	2.18509	0.0971393
$507$	−2.38704	−0.106012
$508$	−1.76950	−0.0785088
$509$	1.98921	0.0881701	0.0440850	−	0.999028i	$-0.485963\pi$
$509$	1.98921	0.0881701	0.0440850	+	0.999028i	$0.485963\pi$
$510$	−20.0376	−0.887278
$511$	−51.9994	−2.30032
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−18.7346	−0.826348
$515$	23.7795	1.04785
$516$	−22.0905	−0.972479
$517$	−1.19844	−0.0527073
$518$	16.5689	0.727998
$519$	26.6736	1.17084
$520$	5.87392	0.257588
$521$	−15.8010	−0.692254	−0.346127	−	0.938188i	$-0.612503\pi$
$521$	−15.8010	−0.692254	−0.346127	+	0.938188i	$0.612503\pi$
$522$	−33.7095	−1.47543
$523$	8.32744	0.364134	0.182067	−	0.983286i	$-0.441721\pi$
$523$	8.32744	0.364134	0.182067	+	0.983286i	$0.441721\pi$
$524$	−10.2055	−0.445830
$525$	35.1247	1.53297
$526$	−21.5801	−0.940939
$527$	26.0866	1.13635
$528$	−3.29456	−0.143377
$529$	−18.2254	−0.792407
$530$	−20.0614	−0.871410
$531$	−92.1692	−3.99980
$532$	0	0
$533$	−5.73823	−0.248550
$534$	9.60392	0.415602
$535$	−14.5364	−0.628462
$536$	11.2143	0.484383
$537$	−21.4048	−0.923684
$538$	0.794184	0.0342397
$539$	−16.7154	−0.719984
$540$	26.8111	1.15376
$541$	−46.0805	−1.98116	−0.990578	−	0.136951i	$-0.956270\pi$
$541$	−46.0805	−1.98116	−0.990578	+	0.136951i	$0.956270\pi$
$542$	29.1960	1.25407
$543$	15.4627	0.663567
$544$	−3.62777	−0.155539
$545$	19.6318	0.840936
$546$	−56.2123	−2.40566
$547$	28.1273	1.20264	0.601319	−	0.799009i	$-0.294642\pi$
$547$	28.1273	1.20264	0.601319	+	0.799009i	$0.294642\pi$
$548$	−12.4319	−0.531064
$549$	75.7068	3.23109
$550$	−2.18928	−0.0933511
$551$	0	0
$552$	−7.19891	−0.306406
$553$	−43.9112	−1.86729
$554$	1.48899	0.0632613
$555$	18.7925	0.797699
$556$	−14.6781	−0.622490
$557$	−28.9354	−1.22603	−0.613017	−	0.790070i	$-0.710044\pi$
$557$	−28.9354	−1.22603	−0.613017	+	0.790070i	$0.710044\pi$
$558$	−56.4774	−2.39088
$559$	23.4924	0.993622
$560$	−8.16440	−0.345009
$561$	−11.9519	−0.504608
$562$	−18.1085	−0.763862
$563$	11.1742	0.470938	0.235469	−	0.971882i	$-0.424337\pi$
$563$	11.1742	0.470938	0.235469	+	0.971882i	$0.424337\pi$
$564$	3.94833	0.166255
$565$	6.32402	0.266053
$566$	21.5718	0.906729
$567$	−141.832	−5.95638
$568$	13.2301	0.555122
$569$	−13.9637	−0.585387	−0.292693	−	0.956206i	$-0.594552\pi$
$569$	−13.9637	−0.585387	−0.292693	+	0.956206i	$0.594552\pi$
$570$	0	0
$571$	27.9573	1.16998	0.584989	−	0.811041i	$-0.301099\pi$
$571$	27.9573	1.16998	0.584989	+	0.811041i	$0.301099\pi$
$572$	3.50363	0.146494
$573$	10.4307	0.435750
$574$	7.97581	0.332904
$575$	−4.78377	−0.199497
$576$	7.85409	0.327254
$577$	−34.1588	−1.42205	−0.711024	−	0.703168i	$-0.751768\pi$
$577$	−34.1588	−1.42205	−0.711024	+	0.703168i	$0.751768\pi$
$578$	3.83932	0.159695
$579$	40.8543	1.69785
$580$	7.19557	0.298780
$581$	−52.4886	−2.17759
$582$	−29.3658	−1.21725
$583$	−11.9661	−0.495584
$584$	−10.6778	−0.441851
$585$	−46.1343	−1.90742
$586$	3.86911	0.159832
$587$	−32.7581	−1.35207	−0.676035	−	0.736869i	$-0.736303\pi$
$587$	−32.7581	−1.35207	−0.676035	+	0.736869i	$0.736303\pi$
$588$	55.0699	2.27104
$589$	0	0
$590$	19.6743	0.809977
$591$	−4.97846	−0.204786
$592$	3.40235	0.139836
$593$	−9.33156	−0.383201	−0.191601	−	0.981473i	$-0.561368\pi$
$593$	−9.33156	−0.383201	−0.191601	+	0.981473i	$0.561368\pi$
$594$	15.9921	0.656163
$595$	−29.6185	−1.21424
$596$	−7.88026	−0.322788
$597$	45.2213	1.85079
$598$	7.65577	0.313068
$599$	−15.5996	−0.637384	−0.318692	−	0.947858i	$-0.603244\pi$
$599$	−15.5996	−0.637384	−0.318692	+	0.947858i	$0.603244\pi$
$600$	7.21269	0.294457
$601$	−7.04863	−0.287520	−0.143760	−	0.989613i	$-0.545919\pi$
$601$	−7.04863	−0.287520	−0.143760	+	0.989613i	$0.545919\pi$
$602$	−32.6530	−1.33084
$603$	−88.0781	−3.58682
$604$	−9.88572	−0.402244
$605$	1.67652	0.0681603
$606$	−46.7862	−1.90056
$607$	−29.3230	−1.19018	−0.595091	−	0.803658i	$-0.702884\pi$
$607$	−29.3230	−1.19018	−0.595091	+	0.803658i	$0.702884\pi$
$608$	0	0
$609$	−68.8602	−2.79036
$610$	−16.1602	−0.654309
$611$	−4.19890	−0.169869
$612$	28.4928	1.15175
$613$	16.4015	0.662449	0.331225	−	0.943552i	$-0.392538\pi$
$613$	16.4015	0.662449	0.331225	+	0.943552i	$0.392538\pi$
$614$	−19.2969	−0.778761
$615$	9.04618	0.364777
$616$	−4.86985	−0.196212
$617$	−29.5426	−1.18934	−0.594670	−	0.803970i	$-0.702717\pi$
$617$	−29.5426	−1.18934	−0.594670	+	0.803970i	$0.702717\pi$
$618$	−46.7294	−1.87973
$619$	−31.3311	−1.25930	−0.629652	−	0.776877i	$-0.716803\pi$
$619$	−31.3311	−1.25930	−0.629652	+	0.776877i	$0.716803\pi$
$620$	12.0556	0.484163
$621$	34.9442	1.40226
$622$	22.6482	0.908110
$623$	14.1960	0.568752
$624$	−11.5429	−0.462087
$625$	−9.26069	−0.370427
$626$	16.3913	0.655129
$627$	0	0
$628$	1.66922	0.0666090
$629$	12.3429	0.492145
$630$	64.1240	2.55476
$631$	−21.3338	−0.849284	−0.424642	−	0.905361i	$-0.639600\pi$
$631$	−21.3338	−0.849284	−0.424642	+	0.905361i	$0.639600\pi$
$632$	−9.01696	−0.358675
$633$	17.6524	0.701618
$634$	−11.8723	−0.471511
$635$	−2.96660	−0.117726
$636$	39.4229	1.56322
$637$	−58.5647	−2.32042
$638$	4.29197	0.169921
$639$	−103.910	−4.11063
$640$	−1.67652	−0.0662703
$641$	−12.0612	−0.476391	−0.238195	−	0.971217i	$-0.576556\pi$
$641$	−12.0612	−0.476391	−0.238195	+	0.971217i	$0.576556\pi$
$642$	28.5656	1.12740
$643$	−34.2982	−1.35259	−0.676295	−	0.736631i	$-0.736416\pi$
$643$	−34.2982	−1.35259	−0.676295	+	0.736631i	$0.736416\pi$
$644$	−10.6411	−0.419317
$645$	−37.0352	−1.45826
$646$	0	0
$647$	25.6399	1.00801	0.504005	−	0.863701i	$-0.331859\pi$
$647$	25.6399	1.00801	0.504005	+	0.863701i	$0.331859\pi$
$648$	−29.1245	−1.14412
$649$	11.7352	0.460646
$650$	−7.67043	−0.300859
$651$	−115.369	−4.52168
$652$	4.57250	0.179073
$653$	−9.38082	−0.367100	−0.183550	−	0.983010i	$-0.558759\pi$
$653$	−9.38082	−0.367100	−0.183550	+	0.983010i	$0.558759\pi$
$654$	−38.5788	−1.50855
$655$	−17.1098	−0.668534
$656$	1.63779	0.0639451
$657$	83.8646	3.27187
$658$	5.83622	0.227520
$659$	−22.6418	−0.882001	−0.441001	−	0.897507i	$-0.645376\pi$
$659$	−22.6418	−0.882001	−0.441001	+	0.897507i	$0.645376\pi$
$660$	−5.52339	−0.214998
$661$	−27.4592	−1.06804	−0.534019	−	0.845472i	$-0.679319\pi$
$661$	−27.4592	−1.06804	−0.534019	+	0.845472i	$0.679319\pi$
$662$	−17.7376	−0.689390
$663$	−41.8750	−1.62629
$664$	−10.7783	−0.418278
$665$	0	0
$666$	−26.7224	−1.03547
$667$	9.37835	0.363131
$668$	11.7350	0.454041
$669$	89.8020	3.47194
$670$	18.8010	0.726346
$671$	−9.63915	−0.372115
$672$	16.0440	0.618910
$673$	15.0792	0.581259	0.290630	−	0.956836i	$-0.406135\pi$
$673$	15.0792	0.581259	0.290630	+	0.956836i	$0.406135\pi$
$674$	12.7153	0.489774
$675$	−35.0111	−1.34758
$676$	−0.724542	−0.0278670
$677$	−8.63437	−0.331846	−0.165923	−	0.986139i	$-0.553060\pi$
$677$	−8.63437	−0.331846	−0.165923	+	0.986139i	$0.553060\pi$
$678$	−12.4274	−0.477272
$679$	−43.4071	−1.66581
$680$	−6.08203	−0.233235
$681$	73.7358	2.82556
$682$	7.19082	0.275351
$683$	26.4516	1.01214	0.506071	−	0.862492i	$-0.331097\pi$
$683$	26.4516	1.01214	0.506071	+	0.862492i	$0.331097\pi$
$684$	0	0
$685$	−20.8423	−0.796345
$686$	47.3126	1.80640
$687$	10.3175	0.393637
$688$	−6.70515	−0.255631
$689$	−41.9247	−1.59720
$690$	−12.0691	−0.459464
$691$	−35.0454	−1.33319	−0.666594	−	0.745421i	$-0.732249\pi$
$691$	−35.0454	−1.33319	−0.666594	+	0.745421i	$0.732249\pi$
$692$	8.09627	0.307774
$693$	38.2482	1.45293
$694$	−1.10562	−0.0419686
$695$	−24.6081	−0.933440
$696$	−14.1401	−0.535980
$697$	5.94153	0.225052
$698$	1.31374	0.0497258
$699$	1.05058	0.0397366
$700$	10.6614	0.402965
$701$	4.89080	0.184723	0.0923614	−	0.995726i	$-0.470558\pi$
$701$	4.89080	0.184723	0.0923614	+	0.995726i	$0.470558\pi$
$702$	56.0304	2.11473
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	6.61946	0.249303
$706$	−14.5567	−0.547849
$707$	−69.1571	−2.60092
$708$	−38.6622	−1.45301
$709$	9.84878	0.369879	0.184939	−	0.982750i	$-0.440791\pi$
$709$	9.84878	0.369879	0.184939	+	0.982750i	$0.440791\pi$
$710$	22.1805	0.832420
$711$	70.8200	2.65596
$712$	2.91509	0.109248
$713$	15.7126	0.588442
$714$	58.2038	2.17822
$715$	5.87392	0.219672
$716$	−6.49701	−0.242805
$717$	73.0426	2.72783
$718$	−27.2333	−1.01634
$719$	−21.5329	−0.803043	−0.401521	−	0.915850i	$-0.631518\pi$
$719$	−21.5329	−0.803043	−0.401521	+	0.915850i	$0.631518\pi$
$720$	13.1676	0.490726
$721$	−69.0730	−2.57241
$722$	0	0
$723$	40.2002	1.49506
$724$	4.69340	0.174429
$725$	−9.39630	−0.348970
$726$	−3.29456	−0.122272
$727$	−31.1088	−1.15376	−0.576881	−	0.816828i	$-0.695730\pi$
$727$	−31.1088	−1.15376	−0.576881	+	0.816828i	$0.695730\pi$
$728$	−17.0622	−0.632366
$729$	70.6863	2.61801
$730$	−17.9016	−0.662568
$731$	−24.3247	−0.899682
$732$	31.7567	1.17376
$733$	24.4809	0.904223	0.452112	−	0.891961i	$-0.350671\pi$
$733$	24.4809	0.904223	0.452112	+	0.891961i	$0.350671\pi$
$734$	−21.8221	−0.805469
$735$	92.3258	3.40549
$736$	−2.18509	−0.0805436
$737$	11.2143	0.413084
$738$	−12.8634	−0.473508
$739$	19.5185	0.718001	0.359000	−	0.933337i	$-0.383118\pi$
$739$	19.5185	0.718001	0.359000	+	0.933337i	$0.383118\pi$
$740$	5.70412	0.209688
$741$	0	0
$742$	58.2729	2.13927
$743$	−46.0099	−1.68794	−0.843969	−	0.536392i	$-0.819787\pi$
$743$	−46.0099	−1.68794	−0.843969	+	0.536392i	$0.819787\pi$
$744$	−23.6905	−0.868538
$745$	−13.2114	−0.484029
$746$	−5.69784	−0.208613
$747$	84.6536	3.09731
$748$	−3.62777	−0.132644
$749$	42.2243	1.54284
$750$	39.7092	1.44997
$751$	38.4214	1.40202	0.701008	−	0.713154i	$-0.252734\pi$
$751$	38.4214	1.40202	0.701008	+	0.713154i	$0.252734\pi$
$752$	1.19844	0.0437026
$753$	−79.7474	−2.90616
$754$	15.0375	0.547633
$755$	−16.5736	−0.603175
$756$	−77.8790	−2.83243
$757$	30.1222	1.09481	0.547406	−	0.836867i	$-0.315615\pi$
$757$	30.1222	1.09481	0.547406	+	0.836867i	$0.315615\pi$
$758$	−1.17318	−0.0426120
$759$	−7.19891	−0.261304
$760$	0	0
$761$	11.6134	0.420987	0.210493	−	0.977595i	$-0.432493\pi$
$761$	11.6134	0.420987	0.210493	+	0.977595i	$0.432493\pi$
$762$	5.82971	0.211188
$763$	−57.0253	−2.06445
$764$	3.16605	0.114544
$765$	47.7688	1.72708
$766$	29.8860	1.07983
$767$	41.1158	1.48460
$768$	3.29456	0.118882
$769$	−30.6287	−1.10450	−0.552249	−	0.833679i	$-0.686230\pi$
$769$	−30.6287	−1.10450	−0.552249	+	0.833679i	$0.686230\pi$
$770$	−8.16440	−0.294225
$771$	61.7222	2.22287
$772$	12.4006	0.446306
$773$	−16.4407	−0.591332	−0.295666	−	0.955291i	$-0.595542\pi$
$773$	−16.4407	−0.591332	−0.295666	+	0.955291i	$0.595542\pi$
$774$	52.6629	1.89293
$775$	−15.7427	−0.565494
$776$	−8.91344	−0.319974
$777$	−54.5873	−1.95831
$778$	9.80583	0.351556
$779$	0	0
$780$	−19.3519	−0.692911
$781$	13.2301	0.473409
$782$	−7.92701	−0.283469
$783$	68.6375	2.45290
$784$	16.7154	0.596979
$785$	2.79848	0.0998820
$786$	33.6227	1.19928
$787$	15.5531	0.554409	0.277205	−	0.960811i	$-0.410592\pi$
$787$	15.5531	0.554409	0.277205	+	0.960811i	$0.410592\pi$
$788$	−1.51112	−0.0538313
$789$	71.0970	2.53112
$790$	−15.1171	−0.537843
$791$	−18.3696	−0.653147
$792$	7.85409	0.279083
$793$	−33.7721	−1.19928
$794$	−6.56666	−0.233042
$795$	66.0933	2.34409
$796$	13.7261	0.486508
$797$	23.3805	0.828178	0.414089	−	0.910236i	$-0.364100\pi$
$797$	23.3805	0.828178	0.414089	+	0.910236i	$0.364100\pi$
$798$	0	0
$799$	4.34766	0.153809
$800$	2.18928	0.0774026
$801$	−22.8954	−0.808969
$802$	6.23259	0.220080
$803$	−10.6778	−0.376812
$804$	−36.9461	−1.30299
$805$	−17.8400	−0.628777
$806$	25.1940	0.887421
$807$	−2.61648	−0.0921045
$808$	−14.2011	−0.499592
$809$	4.27045	0.150141	0.0750704	−	0.997178i	$-0.476082\pi$
$809$	4.27045	0.150141	0.0750704	+	0.997178i	$0.476082\pi$
$810$	−48.8279	−1.71564
$811$	−22.4398	−0.787969	−0.393984	−	0.919117i	$-0.628904\pi$
$811$	−22.4398	−0.787969	−0.393984	+	0.919117i	$0.628904\pi$
$812$	−20.9012	−0.733489
$813$	−96.1877	−3.37345
$814$	3.40235	0.119252
$815$	7.66589	0.268525
$816$	11.9519	0.418399
$817$	0	0
$818$	−0.0264468	−0.000924689 0
$819$	134.008	4.68261
$820$	2.74580	0.0958874
$821$	1.11922	0.0390610	0.0195305	−	0.999809i	$-0.493783\pi$
$821$	1.11922	0.0390610	0.0195305	+	0.999809i	$0.493783\pi$
$822$	40.9576	1.42856
$823$	18.2155	0.634951	0.317476	−	0.948266i	$-0.397165\pi$
$823$	18.2155	0.634951	0.317476	+	0.948266i	$0.397165\pi$
$824$	−14.1838	−0.494117
$825$	7.21269	0.251114
$826$	−57.1485	−1.98845
$827$	−51.4953	−1.79067	−0.895334	−	0.445395i	$-0.853063\pi$
$827$	−51.4953	−1.79067	−0.895334	+	0.445395i	$0.853063\pi$
$828$	17.1619	0.596418
$829$	31.0585	1.07871	0.539354	−	0.842079i	$-0.318668\pi$
$829$	31.0585	1.07871	0.539354	+	0.842079i	$0.318668\pi$
$830$	−18.0700	−0.627219
$831$	−4.90557	−0.170172
$832$	−3.50363	−0.121467
$833$	60.6396	2.10104
$834$	48.3578	1.67449
$835$	19.6740	0.680847
$836$	0	0
$837$	114.996	3.97485
$838$	−30.7629	−1.06269
$839$	−2.09105	−0.0721910	−0.0360955	−	0.999348i	$-0.511492\pi$
$839$	−2.09105	−0.0721910	−0.0360955	+	0.999348i	$0.511492\pi$
$840$	26.8981	0.928072
$841$	−10.5790	−0.364794
$842$	28.4947	0.981992
$843$	59.6596	2.05478
$844$	5.35804	0.184431
$845$	−1.21471	−0.0417873
$846$	−9.41266	−0.323614
$847$	−4.86985	−0.167330
$848$	11.9661	0.410916
$849$	−71.0694	−2.43909
$850$	7.94218	0.272415
$851$	7.43446	0.254850
$852$	−43.5872	−1.49327
$853$	−27.4695	−0.940539	−0.470270	−	0.882523i	$-0.655843\pi$
$853$	−27.4695	−0.940539	−0.470270	+	0.882523i	$0.655843\pi$
$854$	46.9412	1.60629
$855$	0	0
$856$	8.67056	0.296353
$857$	12.9079	0.440924	0.220462	−	0.975396i	$-0.429243\pi$
$857$	12.9079	0.440924	0.220462	+	0.975396i	$0.429243\pi$
$858$	−11.5429	−0.394069
$859$	−33.3916	−1.13931	−0.569654	−	0.821885i	$-0.692923\pi$
$859$	−33.3916	−1.13931	−0.569654	+	0.821885i	$0.692923\pi$
$860$	−11.2413	−0.383326
$861$	−26.2767	−0.895509
$862$	3.05195	0.103950
$863$	48.4259	1.64844	0.824219	−	0.566272i	$-0.191615\pi$
$863$	48.4259	1.64844	0.824219	+	0.566272i	$0.191615\pi$
$864$	−15.9921	−0.544062
$865$	13.5736	0.461515
$866$	−7.96434	−0.270639
$867$	−12.6488	−0.429577
$868$	−35.0182	−1.18859
$869$	−9.01696	−0.305879
$870$	−23.7062	−0.803716
$871$	39.2908	1.33132
$872$	−11.7099	−0.396546
$873$	70.0070	2.36938
$874$	0	0
$875$	58.6961	1.98429
$876$	35.1787	1.18858
$877$	−12.9083	−0.435881	−0.217941	−	0.975962i	$-0.569934\pi$
$877$	−12.9083	−0.435881	−0.217941	+	0.975962i	$0.569934\pi$
$878$	−3.27637	−0.110572
$879$	−12.7470	−0.429946
$880$	−1.67652	−0.0565155
$881$	−9.43781	−0.317968	−0.158984	−	0.987281i	$-0.550822\pi$
$881$	−9.43781	−0.317968	−0.158984	+	0.987281i	$0.550822\pi$
$882$	−131.284	−4.42058
$883$	−4.95507	−0.166751	−0.0833757	−	0.996518i	$-0.526570\pi$
$883$	−4.95507	−0.166751	−0.0833757	+	0.996518i	$0.526570\pi$
$884$	−12.7104	−0.427496
$885$	−64.8180	−2.17883
$886$	−17.8946	−0.601182
$887$	−48.5378	−1.62974	−0.814871	−	0.579643i	$-0.803192\pi$
$887$	−48.5378	−1.62974	−0.814871	+	0.579643i	$0.803192\pi$
$888$	−11.2092	−0.376158
$889$	8.61719	0.289011
$890$	4.88721	0.163820
$891$	−29.1245	−0.975708
$892$	27.2577	0.912655
$893$	0	0
$894$	25.9619	0.868297
$895$	−10.8924	−0.364092
$896$	4.86985	0.162690
$897$	−25.2224	−0.842150
$898$	27.9052	0.931209
$899$	30.8628	1.02933
$900$	−17.1948	−0.573159
$901$	43.4101	1.44620
$902$	1.63779	0.0545326
$903$	107.577	3.57995
$904$	−3.77211	−0.125458
$905$	7.86859	0.261561
$906$	32.5690	1.08203
$907$	38.2388	1.26970	0.634850	−	0.772636i	$-0.281062\pi$
$907$	38.2388	1.26970	0.634850	+	0.772636i	$0.281062\pi$
$908$	22.3811	0.742743
$909$	111.537	3.69943
$910$	−28.6051	−0.948249
$911$	−23.5110	−0.778954	−0.389477	−	0.921036i	$-0.627344\pi$
$911$	−23.5110	−0.778954	−0.389477	+	0.921036i	$0.627344\pi$
$912$	0	0
$913$	−10.7783	−0.356709
$914$	41.6109	1.37637
$915$	53.2408	1.76009
$916$	3.13168	0.103474
$917$	49.6994	1.64122
$918$	−58.0155	−1.91480
$919$	1.98635	0.0655235	0.0327618	−	0.999463i	$-0.489570\pi$
$919$	1.98635	0.0655235	0.0327618	+	0.999463i	$0.489570\pi$
$920$	−3.66336	−0.120777
$921$	63.5748	2.09486
$922$	−5.41182	−0.178229
$923$	46.3534	1.52574
$924$	16.0440	0.527808
$925$	−7.44870	−0.244912
$926$	19.8369	0.651882
$927$	111.401	3.65889
$928$	−4.29197	−0.140891
$929$	−33.0225	−1.08343	−0.541716	−	0.840561i	$-0.682225\pi$
$929$	−33.0225	−1.08343	−0.541716	+	0.840561i	$0.682225\pi$
$930$	−39.7177	−1.30239
$931$	0	0
$932$	0.318884	0.0104454
$933$	−74.6157	−2.44281
$934$	11.1659	0.365360
$935$	−6.08203	−0.198904
$936$	27.5179	0.899450
$937$	−56.0210	−1.83013	−0.915063	−	0.403312i	$-0.867859\pi$
$937$	−56.0210	−1.83013	−0.915063	+	0.403312i	$0.867859\pi$
$938$	−54.6119	−1.78314
$939$	−54.0022	−1.76229
$940$	2.00921	0.0655332
$941$	−21.4166	−0.698161	−0.349081	−	0.937093i	$-0.613506\pi$
$941$	−21.4166	−0.698161	−0.349081	+	0.937093i	$0.613506\pi$
$942$	−5.49933	−0.179178
$943$	3.57873	0.116540
$944$	−11.7352	−0.381947
$945$	−130.566	−4.24731
$946$	−6.70515	−0.218003
$947$	45.2787	1.47136	0.735680	−	0.677329i	$-0.236863\pi$
$947$	45.2787	1.47136	0.735680	+	0.677329i	$0.236863\pi$
$948$	29.7069	0.964834
$949$	−37.4112	−1.21442
$950$	0	0
$951$	39.1141	1.26836
$952$	17.6667	0.572580
$953$	25.4398	0.824076	0.412038	−	0.911167i	$-0.364817\pi$
$953$	25.4398	0.824076	0.412038	+	0.911167i	$0.364817\pi$
$954$	−93.9826	−3.04280
$955$	5.30795	0.171761
$956$	22.1707	0.717052
$957$	−14.1401	−0.457085
$958$	23.4157	0.756529
$959$	60.5414	1.95498
$960$	5.52339	0.178267
$961$	20.7079	0.667996
$962$	11.9206	0.384336
$963$	−68.0994	−2.19447
$964$	12.2020	0.393001
$965$	20.7898	0.669248
$966$	35.0576	1.12796
$967$	−20.6262	−0.663295	−0.331647	−	0.943403i	$-0.607604\pi$
$967$	−20.6262	−0.663295	−0.331647	+	0.943403i	$0.607604\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−14.9436	−0.479809
$971$	−11.4513	−0.367490	−0.183745	−	0.982974i	$-0.558822\pi$
$971$	−11.4513	−0.367490	−0.183745	+	0.982974i	$0.558822\pi$
$972$	47.9761	1.53883
$973$	71.4801	2.29155
$974$	−20.5501	−0.658468
$975$	25.2706	0.809308
$976$	9.63915	0.308542
$977$	23.5947	0.754861	0.377430	−	0.926038i	$-0.376808\pi$
$977$	23.5947	0.754861	0.377430	+	0.926038i	$0.376808\pi$
$978$	−15.0644	−0.481705
$979$	2.91509	0.0931667
$980$	28.0237	0.895186
$981$	91.9704	2.93639
$982$	5.75038	0.183502
$983$	−10.1406	−0.323436	−0.161718	−	0.986837i	$-0.551703\pi$
$983$	−10.1406	−0.323436	−0.161718	+	0.986837i	$0.551703\pi$
$984$	−5.39580	−0.172012
$985$	−2.53342	−0.0807215
$986$	−15.5702	−0.495858
$987$	−19.2278	−0.612026
$988$	0	0
$989$	−14.6514	−0.465887
$990$	13.1676	0.418492
$991$	−15.8886	−0.504719	−0.252360	−	0.967634i	$-0.581207\pi$
$991$	−15.8886	−0.504719	−0.252360	+	0.967634i	$0.581207\pi$
$992$	−7.19082	−0.228309
$993$	58.4374	1.85445
$994$	−64.4285	−2.04355
$995$	23.0121	0.729532
$996$	35.5096	1.12517
$997$	18.1882	0.576025	0.288013	−	0.957627i	$-0.407006\pi$
$997$	18.1882	0.576025	0.288013	+	0.957627i	$0.407006\pi$
$998$	−31.4420	−0.995279
$999$	54.4107	1.72148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bo.1.8	✓	8
19.18	odd	2		7942.2.a.bp.1.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bo.1.8	✓	8	1.1	even	1	trivial
7942.2.a.bp.1.1	yes	8	19.18	odd	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.29456 q^{3} +1.00000 q^{4} +1.67652 q^{5} -3.29456 q^{6} -4.86985 q^{7} -1.00000 q^{8} +7.85409 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.29456 q^{3} +1.00000 q^{4} +1.67652 q^{5} -3.29456 q^{6} -4.86985 q^{7} -1.00000 q^{8} +7.85409 q^{9} -1.67652 q^{10} -1.00000 q^{11} +3.29456 q^{12} -3.50363 q^{13} +4.86985 q^{14} +5.52339 q^{15} +1.00000 q^{16} +3.62777 q^{17} -7.85409 q^{18} +1.67652 q^{20} -16.0440 q^{21} +1.00000 q^{22} +2.18509 q^{23} -3.29456 q^{24} -2.18928 q^{25} +3.50363 q^{26} +15.9921 q^{27} -4.86985 q^{28} +4.29197 q^{29} -5.52339 q^{30} +7.19082 q^{31} -1.00000 q^{32} -3.29456 q^{33} -3.62777 q^{34} -8.16440 q^{35} +7.85409 q^{36} +3.40235 q^{37} -11.5429 q^{39} -1.67652 q^{40} +1.63779 q^{41} +16.0440 q^{42} -6.70515 q^{43} -1.00000 q^{44} +13.1676 q^{45} -2.18509 q^{46} +1.19844 q^{47} +3.29456 q^{48} +16.7154 q^{49} +2.18928 q^{50} +11.9519 q^{51} -3.50363 q^{52} +11.9661 q^{53} -15.9921 q^{54} -1.67652 q^{55} +4.86985 q^{56} -4.29197 q^{58} -11.7352 q^{59} +5.52339 q^{60} +9.63915 q^{61} -7.19082 q^{62} -38.2482 q^{63} +1.00000 q^{64} -5.87392 q^{65} +3.29456 q^{66} -11.2143 q^{67} +3.62777 q^{68} +7.19891 q^{69} +8.16440 q^{70} -13.2301 q^{71} -7.85409 q^{72} +10.6778 q^{73} -3.40235 q^{74} -7.21269 q^{75} +4.86985 q^{77} +11.5429 q^{78} +9.01696 q^{79} +1.67652 q^{80} +29.1245 q^{81} -1.63779 q^{82} +10.7783 q^{83} -16.0440 q^{84} +6.08203 q^{85} +6.70515 q^{86} +14.1401 q^{87} +1.00000 q^{88} -2.91509 q^{89} -13.1676 q^{90} +17.0622 q^{91} +2.18509 q^{92} +23.6905 q^{93} -1.19844 q^{94} -3.29456 q^{96} +8.91344 q^{97} -16.7154 q^{98} -7.85409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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