LMFDB - Embedded newform 7381.2.a.p.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, 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("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.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:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.63927 q^{2} -2.57212 q^{3} +0.687210 q^{4} -4.16256 q^{5} +4.21640 q^{6} -3.92225 q^{7} +2.15202 q^{8} +3.61581 q^{9} +O(q^{10})$	\(q-1.63927 q^{2} -2.57212 q^{3} +0.687210 q^{4} -4.16256 q^{5} +4.21640 q^{6} -3.92225 q^{7} +2.15202 q^{8} +3.61581 q^{9} +6.82356 q^{10} -1.76759 q^{12} +2.96848 q^{13} +6.42964 q^{14} +10.7066 q^{15} -4.90216 q^{16} -2.15715 q^{17} -5.92729 q^{18} -0.0888055 q^{19} -2.86055 q^{20} +10.0885 q^{21} -3.24642 q^{23} -5.53525 q^{24} +12.3269 q^{25} -4.86614 q^{26} -1.58393 q^{27} -2.69541 q^{28} +7.68864 q^{29} -17.5510 q^{30} +5.63330 q^{31} +3.73194 q^{32} +3.53616 q^{34} +16.3266 q^{35} +2.48482 q^{36} +6.87441 q^{37} +0.145576 q^{38} -7.63528 q^{39} -8.95790 q^{40} +8.48229 q^{41} -16.5378 q^{42} -3.71850 q^{43} -15.0510 q^{45} +5.32177 q^{46} +9.62556 q^{47} +12.6090 q^{48} +8.38406 q^{49} -20.2071 q^{50} +5.54846 q^{51} +2.03997 q^{52} +0.282945 q^{53} +2.59648 q^{54} -8.44076 q^{56} +0.228419 q^{57} -12.6038 q^{58} +12.0727 q^{59} +7.35769 q^{60} +1.00000 q^{61} -9.23450 q^{62} -14.1821 q^{63} +3.68667 q^{64} -12.3565 q^{65} -4.33834 q^{67} -1.48242 q^{68} +8.35019 q^{69} -26.7637 q^{70} +14.8109 q^{71} +7.78128 q^{72} -6.84395 q^{73} -11.2690 q^{74} -31.7063 q^{75} -0.0610281 q^{76} +12.5163 q^{78} +9.16050 q^{79} +20.4055 q^{80} -6.77337 q^{81} -13.9048 q^{82} +10.5300 q^{83} +6.93293 q^{84} +8.97927 q^{85} +6.09563 q^{86} -19.7761 q^{87} -1.30025 q^{89} +24.6727 q^{90} -11.6431 q^{91} -2.23098 q^{92} -14.4895 q^{93} -15.7789 q^{94} +0.369658 q^{95} -9.59900 q^{96} +9.52184 q^{97} -13.7438 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} + 21 q^{16} + 8 q^{17} + 16 q^{19} - 16 q^{20} + 12 q^{21} + 3 q^{23} + 62 q^{24} + 26 q^{25} - 4 q^{26} - 13 q^{27} - 42 q^{28} + 28 q^{29} + 12 q^{30} - q^{31} + 35 q^{32} + 8 q^{34} + 62 q^{35} + 17 q^{36} - 7 q^{37} + 20 q^{38} - 27 q^{40} + 28 q^{41} - 34 q^{42} + 22 q^{43} + 58 q^{46} - 2 q^{47} + 10 q^{48} + 25 q^{49} - 15 q^{50} + 38 q^{51} + 12 q^{52} - 4 q^{53} + 24 q^{54} - 48 q^{56} + 40 q^{57} + 8 q^{58} + 9 q^{59} + 18 q^{60} + 25 q^{61} + 4 q^{62} + 30 q^{63} + 41 q^{64} + 32 q^{65} - 15 q^{67} + 112 q^{68} - q^{69} + 14 q^{70} - 9 q^{71} - 59 q^{72} - 8 q^{73} + 54 q^{74} - 4 q^{75} + 32 q^{76} + 20 q^{78} + 30 q^{79} - 18 q^{80} + 17 q^{81} + 10 q^{83} - 39 q^{84} + 52 q^{85} - 6 q^{86} + 24 q^{87} - 5 q^{89} + 110 q^{90} - 38 q^{92} - q^{93} - 120 q^{94} + 50 q^{95} + 130 q^{96} + 5 q^{97} + 35 q^{98}+O(q^{100}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 10 * q^14 + q^15 + 21 * q^16 + 8 * q^17 + 16 * q^19 - 16 * q^20 + 12 * q^21 + 3 * q^23 + 62 * q^24 + 26 * q^25 - 4 * q^26 - 13 * q^27 - 42 * q^28 + 28 * q^29 + 12 * q^30 - q^31 + 35 * q^32 + 8 * q^34 + 62 * q^35 + 17 * q^36 - 7 * q^37 + 20 * q^38 - 27 * q^40 + 28 * q^41 - 34 * q^42 + 22 * q^43 + 58 * q^46 - 2 * q^47 + 10 * q^48 + 25 * q^49 - 15 * q^50 + 38 * q^51 + 12 * q^52 - 4 * q^53 + 24 * q^54 - 48 * q^56 + 40 * q^57 + 8 * q^58 + 9 * q^59 + 18 * q^60 + 25 * q^61 + 4 * q^62 + 30 * q^63 + 41 * q^64 + 32 * q^65 - 15 * q^67 + 112 * q^68 - q^69 + 14 * q^70 - 9 * q^71 - 59 * q^72 - 8 * q^73 + 54 * q^74 - 4 * q^75 + 32 * q^76 + 20 * q^78 + 30 * q^79 - 18 * q^80 + 17 * q^81 + 10 * q^83 - 39 * q^84 + 52 * q^85 - 6 * q^86 + 24 * q^87 - 5 * q^89 + 110 * q^90 - 38 * q^92 - q^93 - 120 * q^94 + 50 * q^95 + 130 * q^96 + 5 * q^97 + 35 * q^98

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 $

$2$	−1.63927	−1.15914	−0.579570	−	0.814923i	$-0.696779\pi$
$2$	−1.63927	−1.15914	−0.579570	+	0.814923i	$0.696779\pi$
$3$	−2.57212	−1.48501	−0.742507	−	0.669838i	$-0.766364\pi$
$3$	−2.57212	−1.48501	−0.742507	+	0.669838i	$0.766364\pi$
$4$	0.687210	0.343605
$5$	−4.16256	−1.86155	−0.930776	−	0.365589i	$-0.880868\pi$
$5$	−4.16256	−1.86155	−0.930776	+	0.365589i	$0.880868\pi$
$6$	4.21640	1.72134
$7$	−3.92225	−1.48247	−0.741236	−	0.671244i	$-0.765760\pi$
$7$	−3.92225	−1.48247	−0.741236	+	0.671244i	$0.765760\pi$
$8$	2.15202	0.760853
$9$	3.61581	1.20527
$10$	6.82356	2.15780
$11$	0	0
$11$	0	0
$12$	−1.76759	−0.510259
$13$	2.96848	0.823307	0.411654	−	0.911340i	$-0.364951\pi$
$13$	2.96848	0.823307	0.411654	+	0.911340i	$0.364951\pi$
$14$	6.42964	1.71839
$15$	10.7066	2.76443
$16$	−4.90216	−1.22554
$17$	−2.15715	−0.523186	−0.261593	−	0.965178i	$-0.584248\pi$
$17$	−2.15715	−0.523186	−0.261593	+	0.965178i	$0.584248\pi$
$18$	−5.92729	−1.39707
$19$	−0.0888055	−0.0203734	−0.0101867	−	0.999948i	$-0.503243\pi$
$19$	−0.0888055	−0.0203734	−0.0101867	+	0.999948i	$0.503243\pi$
$20$	−2.86055	−0.639639
$21$	10.0885	2.20149
$22$	0	0
$23$	−3.24642	−0.676926	−0.338463	−	0.940980i	$-0.609907\pi$
$23$	−3.24642	−0.676926	−0.338463	+	0.940980i	$0.609907\pi$
$24$	−5.53525	−1.12988
$25$	12.3269	2.46538
$26$	−4.86614	−0.954328
$27$	−1.58393	−0.304827
$28$	−2.69541	−0.509385
$29$	7.68864	1.42774	0.713872	−	0.700276i	$-0.246940\pi$
$29$	7.68864	1.42774	0.713872	+	0.700276i	$0.246940\pi$
$30$	−17.5510	−3.20436
$31$	5.63330	1.01177	0.505885	−	0.862601i	$-0.331166\pi$
$31$	5.63330	1.01177	0.505885	+	0.862601i	$0.331166\pi$
$32$	3.73194	0.659720
$33$	0	0
$34$	3.53616	0.606446
$35$	16.3266	2.75970
$36$	2.48482	0.414137
$37$	6.87441	1.13015	0.565073	−	0.825041i	$-0.308848\pi$
$37$	6.87441	1.13015	0.565073	+	0.825041i	$0.308848\pi$
$38$	0.145576	0.0236156
$39$	−7.63528	−1.22262
$40$	−8.95790	−1.41637
$41$	8.48229	1.32471	0.662355	−	0.749190i	$-0.269557\pi$
$41$	8.48229	1.32471	0.662355	+	0.749190i	$0.269557\pi$
$42$	−16.5378	−2.55184
$43$	−3.71850	−0.567066	−0.283533	−	0.958963i	$-0.591507\pi$
$43$	−3.71850	−0.567066	−0.283533	+	0.958963i	$0.591507\pi$
$44$	0	0
$45$	−15.0510	−2.24367
$46$	5.32177	0.784652
$47$	9.62556	1.40403	0.702016	−	0.712161i	$-0.252283\pi$
$47$	9.62556	1.40403	0.702016	+	0.712161i	$0.252283\pi$
$48$	12.6090	1.81995
$49$	8.38406	1.19772
$50$	−20.2071	−2.85772
$51$	5.54846	0.776939
$52$	2.03997	0.282893
$53$	0.282945	0.0388655	0.0194328	−	0.999811i	$-0.493814\pi$
$53$	0.282945	0.0388655	0.0194328	+	0.999811i	$0.493814\pi$
$54$	2.59648	0.353337
$55$	0	0
$56$	−8.44076	−1.12794
$57$	0.228419	0.0302548
$58$	−12.6038	−1.65495
$59$	12.0727	1.57174	0.785868	−	0.618395i	$-0.212217\pi$
$59$	12.0727	1.57174	0.785868	+	0.618395i	$0.212217\pi$
$60$	7.35769	0.949874
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−9.23450	−1.17278
$63$	−14.1821	−1.78678
$64$	3.68667	0.460833
$65$	−12.3565	−1.53263
$66$	0	0
$67$	−4.33834	−0.530013	−0.265007	−	0.964247i	$-0.585374\pi$
$67$	−4.33834	−0.530013	−0.265007	+	0.964247i	$0.585374\pi$
$68$	−1.48242	−0.179770
$69$	8.35019	1.00524
$70$	−26.7637	−3.19888
$71$	14.8109	1.75773	0.878867	−	0.477067i	$-0.158300\pi$
$71$	14.8109	1.75773	0.878867	+	0.477067i	$0.158300\pi$
$72$	7.78128	0.917033
$73$	−6.84395	−0.801024	−0.400512	−	0.916292i	$-0.631168\pi$
$73$	−6.84395	−0.801024	−0.400512	+	0.916292i	$0.631168\pi$
$74$	−11.2690	−1.31000
$75$	−31.7063	−3.66112
$76$	−0.0610281	−0.00700040
$77$	0	0
$78$	12.5163	1.41719
$79$	9.16050	1.03064	0.515318	−	0.856999i	$-0.327674\pi$
$79$	9.16050	1.03064	0.515318	+	0.856999i	$0.327674\pi$
$80$	20.4055	2.28141
$81$	−6.77337	−0.752596
$82$	−13.9048	−1.53553
$83$	10.5300	1.15581	0.577907	−	0.816103i	$-0.303870\pi$
$83$	10.5300	1.15581	0.577907	+	0.816103i	$0.303870\pi$
$84$	6.93293	0.756444
$85$	8.97927	0.973939
$86$	6.09563	0.657309
$87$	−19.7761	−2.12022
$88$	0	0
$89$	−1.30025	−0.137827	−0.0689133	−	0.997623i	$-0.521953\pi$
$89$	−1.30025	−0.137827	−0.0689133	+	0.997623i	$0.521953\pi$
$90$	24.6727	2.60073
$91$	−11.6431	−1.22053
$92$	−2.23098	−0.232595
$93$	−14.4895	−1.50249
$94$	−15.7789	−1.62747
$95$	0.369658	0.0379261
$96$	−9.59900	−0.979693
$97$	9.52184	0.966796	0.483398	−	0.875401i	$-0.339402\pi$
$97$	9.52184	0.966796	0.483398	+	0.875401i	$0.339402\pi$
$98$	−13.7438	−1.38833
$99$	0	0
$100$	8.47117	0.847117
$101$	−0.810983	−0.0806959	−0.0403479	−	0.999186i	$-0.512847\pi$
$101$	−0.810983	−0.0806959	−0.0403479	+	0.999186i	$0.512847\pi$
$102$	−9.09542	−0.900581
$103$	15.0810	1.48597	0.742987	−	0.669305i	$-0.233408\pi$
$103$	15.0810	1.48597	0.742987	+	0.669305i	$0.233408\pi$
$104$	6.38821	0.626416
$105$	−41.9940	−4.09819
$106$	−0.463824	−0.0450506
$107$	13.9636	1.34991	0.674956	−	0.737858i	$-0.264163\pi$
$107$	13.9636	1.34991	0.674956	+	0.737858i	$0.264163\pi$
$108$	−1.08849	−0.104740
$109$	12.0021	1.14960	0.574798	−	0.818295i	$-0.305081\pi$
$109$	12.0021	1.14960	0.574798	+	0.818295i	$0.305081\pi$
$110$	0	0
$111$	−17.6818	−1.67828
$112$	19.2275	1.81683
$113$	−15.7947	−1.48584	−0.742922	−	0.669378i	$-0.766561\pi$
$113$	−15.7947	−1.48584	−0.742922	+	0.669378i	$0.766561\pi$
$114$	−0.374440	−0.0350695
$115$	13.5134	1.26013
$116$	5.28371	0.490580
$117$	10.7334	0.992306
$118$	−19.7905	−1.82186
$119$	8.46089	0.775609
$120$	23.0408	2.10333
$121$	0	0
$122$	−1.63927	−0.148413
$123$	−21.8175	−1.96722
$124$	3.87126	0.347650
$125$	−30.4986	−2.72788
$126$	23.2483	2.07112
$127$	−9.98124	−0.885692	−0.442846	−	0.896598i	$-0.646031\pi$
$127$	−9.98124	−0.885692	−0.442846	+	0.896598i	$0.646031\pi$
$128$	−13.5073	−1.19389
$129$	9.56443	0.842101
$130$	20.2556	1.77653
$131$	−1.08839	−0.0950930	−0.0475465	−	0.998869i	$-0.515140\pi$
$131$	−1.08839	−0.0950930	−0.0475465	+	0.998869i	$0.515140\pi$
$132$	0	0
$133$	0.348318	0.0302030
$134$	7.11172	0.614359
$135$	6.59318	0.567451
$136$	−4.64223	−0.398068
$137$	−9.90621	−0.846344	−0.423172	−	0.906049i	$-0.639083\pi$
$137$	−9.90621	−0.846344	−0.423172	+	0.906049i	$0.639083\pi$
$138$	−13.6882	−1.16522
$139$	−11.9170	−1.01078	−0.505392	−	0.862890i	$-0.668652\pi$
$139$	−11.9170	−1.01078	−0.505392	+	0.862890i	$0.668652\pi$
$140$	11.2198	0.948247
$141$	−24.7581	−2.08501
$142$	−24.2791	−2.03746
$143$	0	0
$144$	−17.7253	−1.47711
$145$	−32.0044	−2.65782
$146$	11.2191	0.928499
$147$	−21.5648	−1.77864
$148$	4.72416	0.388324
$149$	−22.7767	−1.86594	−0.932970	−	0.359953i	$-0.882793\pi$
$149$	−22.7767	−1.86594	−0.932970	+	0.359953i	$0.882793\pi$
$150$	51.9752	4.24375
$151$	10.4899	0.853656	0.426828	−	0.904333i	$-0.359631\pi$
$151$	10.4899	0.853656	0.426828	+	0.904333i	$0.359631\pi$
$152$	−0.191111	−0.0155012
$153$	−7.79984	−0.630580
$154$	0	0
$155$	−23.4489	−1.88346
$156$	−5.24704	−0.420100
$157$	−14.4735	−1.15511	−0.577555	−	0.816352i	$-0.695993\pi$
$157$	−14.4735	−1.15511	−0.577555	+	0.816352i	$0.695993\pi$
$158$	−15.0165	−1.19465
$159$	−0.727769	−0.0577158
$160$	−15.5344	−1.22810
$161$	12.7333	1.00352
$162$	11.1034	0.872364
$163$	3.05132	0.238998	0.119499	−	0.992834i	$-0.461871\pi$
$163$	3.05132	0.238998	0.119499	+	0.992834i	$0.461871\pi$
$164$	5.82912	0.455178
$165$	0	0
$166$	−17.2615	−1.33975
$167$	18.1693	1.40598	0.702990	−	0.711200i	$-0.251848\pi$
$167$	18.1693	1.40598	0.702990	+	0.711200i	$0.251848\pi$
$168$	21.7107	1.67501
$169$	−4.18815	−0.322165
$170$	−14.7195	−1.12893
$171$	−0.321103	−0.0245554
$172$	−2.55539	−0.194847
$173$	3.83929	0.291895	0.145948	−	0.989292i	$-0.453377\pi$
$173$	3.83929	0.291895	0.145948	+	0.989292i	$0.453377\pi$
$174$	32.4184	2.45763
$175$	−48.3492	−3.65486
$176$	0	0
$177$	−31.0525	−2.33405
$178$	2.13147	0.159760
$179$	11.6590	0.871438	0.435719	−	0.900083i	$-0.356494\pi$
$179$	11.6590	0.871438	0.435719	+	0.900083i	$0.356494\pi$
$180$	−10.3432	−0.770937
$181$	−13.7386	−1.02119	−0.510593	−	0.859823i	$-0.670574\pi$
$181$	−13.7386	−1.02119	−0.510593	+	0.859823i	$0.670574\pi$
$182$	19.0862	1.41476
$183$	−2.57212	−0.190137
$184$	−6.98636	−0.515041
$185$	−28.6151	−2.10383
$186$	23.7523	1.74160
$187$	0	0
$188$	6.61479	0.482433
$189$	6.21256	0.451897
$190$	−0.605970	−0.0439617
$191$	5.67171	0.410391	0.205195	−	0.978721i	$-0.434217\pi$
$191$	5.67171	0.410391	0.205195	+	0.978721i	$0.434217\pi$
$192$	−9.48255	−0.684344
$193$	21.3207	1.53470	0.767349	−	0.641229i	$-0.221575\pi$
$193$	21.3207	1.53470	0.767349	+	0.641229i	$0.221575\pi$
$194$	−15.6089	−1.12065
$195$	31.7823	2.27598
$196$	5.76162	0.411544
$197$	21.7714	1.55114	0.775572	−	0.631259i	$-0.217461\pi$
$197$	21.7714	1.55114	0.775572	+	0.631259i	$0.217461\pi$
$198$	0	0
$199$	9.35242	0.662976	0.331488	−	0.943460i	$-0.392449\pi$
$199$	9.35242	0.662976	0.331488	+	0.943460i	$0.392449\pi$
$200$	26.5277	1.87579
$201$	11.1587	0.787077
$202$	1.32942	0.0935378
$203$	−30.1568	−2.11659
$204$	3.81296	0.266960
$205$	−35.3080	−2.46602
$206$	−24.7218	−1.72245
$207$	−11.7384	−0.815878
$208$	−14.5520	−1.00900
$209$	0	0
$210$	68.8396	4.75038
$211$	17.3305	1.19308	0.596541	−	0.802582i	$-0.296541\pi$
$211$	17.3305	1.19308	0.596541	+	0.802582i	$0.296541\pi$
$212$	0.194443	0.0133544
$213$	−38.0955	−2.61026
$214$	−22.8901	−1.56474
$215$	15.4785	1.05562
$216$	−3.40864	−0.231928
$217$	−22.0952	−1.49992
$218$	−19.6748	−1.33254
$219$	17.6035	1.18953
$220$	0	0
$221$	−6.40345	−0.430743
$222$	28.9853	1.94536
$223$	−2.48044	−0.166103	−0.0830514	−	0.996545i	$-0.526467\pi$
$223$	−2.48044	−0.166103	−0.0830514	+	0.996545i	$0.526467\pi$
$224$	−14.6376	−0.978016
$225$	44.5716	2.97144
$226$	25.8919	1.72230
$227$	6.55938	0.435361	0.217681	−	0.976020i	$-0.430151\pi$
$227$	6.55938	0.435361	0.217681	+	0.976020i	$0.430151\pi$
$228$	0.156972	0.0103957
$229$	2.06090	0.136188	0.0680940	−	0.997679i	$-0.478308\pi$
$229$	2.06090	0.136188	0.0680940	+	0.997679i	$0.478308\pi$
$230$	−22.1522	−1.46067
$231$	0	0
$232$	16.5461	1.08630
$233$	−8.03418	−0.526337	−0.263168	−	0.964750i	$-0.584767\pi$
$233$	−8.03418	−0.526337	−0.263168	+	0.964750i	$0.584767\pi$
$234$	−17.5950	−1.15022
$235$	−40.0670	−2.61368
$236$	8.29650	0.540056
$237$	−23.5619	−1.53051
$238$	−13.8697	−0.899039
$239$	22.5071	1.45586	0.727932	−	0.685649i	$-0.240482\pi$
$239$	22.5071	1.45586	0.727932	+	0.685649i	$0.240482\pi$
$240$	−52.4855	−3.38793
$241$	7.31279	0.471058	0.235529	−	0.971867i	$-0.424318\pi$
$241$	7.31279	0.471058	0.235529	+	0.971867i	$0.424318\pi$
$242$	0	0
$243$	22.1737	1.42244
$244$	0.687210	0.0439941
$245$	−34.8992	−2.22963
$246$	35.7648	2.28028
$247$	−0.263617	−0.0167736
$248$	12.1230	0.769809
$249$	−27.0843	−1.71640
$250$	49.9955	3.16199
$251$	16.4298	1.03704	0.518519	−	0.855066i	$-0.326484\pi$
$251$	16.4298	1.03704	0.518519	+	0.855066i	$0.326484\pi$
$252$	−9.74609	−0.613946
$253$	0	0
$254$	16.3620	1.02664
$255$	−23.0958	−1.44631
$256$	14.7688	0.923052
$257$	−2.01748	−0.125847	−0.0629236	−	0.998018i	$-0.520042\pi$
$257$	−2.01748	−0.125847	−0.0629236	+	0.998018i	$0.520042\pi$
$258$	−15.6787	−0.976113
$259$	−26.9632	−1.67541
$260$	−8.49149	−0.526620
$261$	27.8006	1.72081
$262$	1.78417	0.110226
$263$	25.8589	1.59453	0.797264	−	0.603631i	$-0.206280\pi$
$263$	25.8589	1.59453	0.797264	+	0.603631i	$0.206280\pi$
$264$	0	0
$265$	−1.17778	−0.0723502
$266$	−0.570987	−0.0350095
$267$	3.34441	0.204675
$268$	−2.98136	−0.182115
$269$	−0.557511	−0.0339920	−0.0169960	−	0.999856i	$-0.505410\pi$
$269$	−0.557511	−0.0339920	−0.0169960	+	0.999856i	$0.505410\pi$
$270$	−10.8080	−0.657755
$271$	−18.2251	−1.10710	−0.553549	−	0.832817i	$-0.686727\pi$
$271$	−18.2251	−1.10710	−0.553549	+	0.832817i	$0.686727\pi$
$272$	10.5747	0.641186
$273$	29.9475	1.81250
$274$	16.2390	0.981032
$275$	0	0
$276$	5.73834	0.345407
$277$	−0.812240	−0.0488028	−0.0244014	−	0.999702i	$-0.507768\pi$
$277$	−0.812240	−0.0488028	−0.0244014	+	0.999702i	$0.507768\pi$
$278$	19.5351	1.17164
$279$	20.3689	1.21945
$280$	35.1352	2.09973
$281$	20.3351	1.21309	0.606546	−	0.795048i	$-0.292554\pi$
$281$	20.3351	1.21309	0.606546	+	0.795048i	$0.292554\pi$
$282$	40.5853	2.41682
$283$	6.01442	0.357520	0.178760	−	0.983893i	$-0.442791\pi$
$283$	6.01442	0.357520	0.178760	+	0.983893i	$0.442791\pi$
$284$	10.1782	0.603967
$285$	−0.950805	−0.0563209
$286$	0	0
$287$	−33.2697	−1.96385
$288$	13.4940	0.795139
$289$	−12.3467	−0.726276
$290$	52.4639	3.08079
$291$	−24.4913	−1.43571
$292$	−4.70324	−0.275236
$293$	27.1340	1.58519	0.792594	−	0.609750i	$-0.208730\pi$
$293$	27.1340	1.58519	0.792594	+	0.609750i	$0.208730\pi$
$294$	35.3506	2.06169
$295$	−50.2534	−2.92587
$296$	14.7938	0.859875
$297$	0	0
$298$	37.3372	2.16289
$299$	−9.63693	−0.557318
$300$	−21.7889	−1.25798
$301$	14.5849	0.840659
$302$	−17.1958	−0.989507
$303$	2.08595	0.119835
$304$	0.435339	0.0249684
$305$	−4.16256	−0.238347
$306$	12.7861	0.730930
$307$	−26.9512	−1.53819	−0.769094	−	0.639136i	$-0.779292\pi$
$307$	−26.9512	−1.53819	−0.769094	+	0.639136i	$0.779292\pi$
$308$	0	0
$309$	−38.7901	−2.20669
$310$	38.4392	2.18320
$311$	16.7548	0.950078	0.475039	−	0.879965i	$-0.342434\pi$
$311$	16.7548	0.950078	0.475039	+	0.879965i	$0.342434\pi$
$312$	−16.4313	−0.930237
$313$	−6.32885	−0.357728	−0.178864	−	0.983874i	$-0.557242\pi$
$313$	−6.32885	−0.357728	−0.178864	+	0.983874i	$0.557242\pi$
$314$	23.7260	1.33893
$315$	59.0338	3.32618
$316$	6.29519	0.354132
$317$	12.7636	0.716873	0.358436	−	0.933554i	$-0.383310\pi$
$317$	12.7636	0.716873	0.358436	+	0.933554i	$0.383310\pi$
$318$	1.19301	0.0669007
$319$	0	0
$320$	−15.3460	−0.857865
$321$	−35.9161	−2.00464
$322$	−20.8733	−1.16322
$323$	0.191567	0.0106591
$324$	−4.65473	−0.258596
$325$	36.5921	2.02976
$326$	−5.00194	−0.277032
$327$	−30.8709	−1.70717
$328$	18.2540	1.00791
$329$	−37.7539	−2.08144
$330$	0	0
$331$	30.2419	1.66225	0.831124	−	0.556087i	$-0.187698\pi$
$331$	30.2419	1.66225	0.831124	+	0.556087i	$0.187698\pi$
$332$	7.23630	0.397144
$333$	24.8565	1.36213
$334$	−29.7844	−1.62973
$335$	18.0586	0.986648
$336$	−49.4555	−2.69802
$337$	13.3536	0.727416	0.363708	−	0.931513i	$-0.381511\pi$
$337$	13.3536	0.727416	0.363708	+	0.931513i	$0.381511\pi$
$338$	6.86551	0.373435
$339$	40.6260	2.20650
$340$	6.17065	0.334650
$341$	0	0
$342$	0.526376	0.0284631
$343$	−5.42865	−0.293120
$344$	−8.00228	−0.431454
$345$	−34.7582	−1.87132
$346$	−6.29363	−0.338348
$347$	17.0732	0.916535	0.458267	−	0.888814i	$-0.348470\pi$
$347$	17.0732	0.916535	0.458267	+	0.888814i	$0.348470\pi$
$348$	−13.5903	−0.728519
$349$	28.4060	1.52054	0.760269	−	0.649608i	$-0.225067\pi$
$349$	28.4060	1.52054	0.760269	+	0.649608i	$0.225067\pi$
$350$	79.2574	4.23649
$351$	−4.70185	−0.250966
$352$	0	0
$353$	−12.1114	−0.644627	−0.322313	−	0.946633i	$-0.604460\pi$
$353$	−12.1114	−0.644627	−0.322313	+	0.946633i	$0.604460\pi$
$354$	50.9035	2.70549
$355$	−61.6514	−3.27212
$356$	−0.893548	−0.0473580
$357$	−21.7624	−1.15179
$358$	−19.1123	−1.01012
$359$	25.1974	1.32987	0.664933	−	0.746903i	$-0.268460\pi$
$359$	25.1974	1.32987	0.664933	+	0.746903i	$0.268460\pi$
$360$	−32.3900	−1.70710
$361$	−18.9921	−0.999585
$362$	22.5214	1.18370
$363$	0	0
$364$	−8.00127	−0.419380
$365$	28.4884	1.49115
$366$	4.21640	0.220395
$367$	3.89374	0.203252	0.101626	−	0.994823i	$-0.467596\pi$
$367$	3.89374	0.203252	0.101626	+	0.994823i	$0.467596\pi$
$368$	15.9145	0.829600
$369$	30.6703	1.59663
$370$	46.9079	2.43863
$371$	−1.10978	−0.0576170
$372$	−9.95735	−0.516265
$373$	13.7339	0.711115	0.355558	−	0.934654i	$-0.384291\pi$
$373$	13.7339	0.711115	0.355558	+	0.934654i	$0.384291\pi$
$374$	0	0
$375$	78.4461	4.05094
$376$	20.7144	1.06826
$377$	22.8235	1.17547
$378$	−10.1841	−0.523812
$379$	15.1100	0.776147	0.388074	−	0.921628i	$-0.373141\pi$
$379$	15.1100	0.776147	0.388074	+	0.921628i	$0.373141\pi$
$380$	0.254033	0.0130316
$381$	25.6730	1.31527
$382$	−9.29747	−0.475700
$383$	−11.8049	−0.603201	−0.301601	−	0.953434i	$-0.597521\pi$
$383$	−11.8049	−0.603201	−0.301601	+	0.953434i	$0.597521\pi$
$384$	34.7425	1.77294
$385$	0	0
$386$	−34.9504	−1.77893
$387$	−13.4454	−0.683466
$388$	6.54351	0.332196
$389$	26.3989	1.33848	0.669238	−	0.743048i	$-0.266621\pi$
$389$	26.3989	1.33848	0.669238	+	0.743048i	$0.266621\pi$
$390$	−52.0998	−2.63818
$391$	7.00303	0.354158
$392$	18.0427	0.911292
$393$	2.79947	0.141214
$394$	−35.6892	−1.79799
$395$	−38.1311	−1.91858
$396$	0	0
$397$	−27.6799	−1.38922	−0.694608	−	0.719388i	$-0.744422\pi$
$397$	−27.6799	−1.38922	−0.694608	+	0.719388i	$0.744422\pi$
$398$	−15.3312	−0.768481
$399$	−0.895915	−0.0448519
$400$	−60.4284	−3.02142
$401$	−26.6775	−1.33221	−0.666105	−	0.745858i	$-0.732040\pi$
$401$	−26.6775	−1.33221	−0.666105	+	0.745858i	$0.732040\pi$
$402$	−18.2922	−0.912333
$403$	16.7223	0.832998
$404$	−0.557316	−0.0277275
$405$	28.1945	1.40100
$406$	49.4351	2.45342
$407$	0	0
$408$	11.9404	0.591137
$409$	−5.91784	−0.292618	−0.146309	−	0.989239i	$-0.546739\pi$
$409$	−5.91784	−0.292618	−0.146309	+	0.989239i	$0.546739\pi$
$410$	57.8794	2.85846
$411$	25.4800	1.25683
$412$	10.3638	0.510589
$413$	−47.3523	−2.33005
$414$	19.2425	0.945716
$415$	−43.8316	−2.15161
$416$	11.0782	0.543152
$417$	30.6519	1.50103
$418$	0	0
$419$	−3.80591	−0.185931	−0.0929655	−	0.995669i	$-0.529635\pi$
$419$	−3.80591	−0.185931	−0.0929655	+	0.995669i	$0.529635\pi$
$420$	−28.8587	−1.40816
$421$	−3.55015	−0.173024	−0.0865118	−	0.996251i	$-0.527572\pi$
$421$	−3.55015	−0.173024	−0.0865118	+	0.996251i	$0.527572\pi$
$422$	−28.4094	−1.38295
$423$	34.8042	1.69224
$424$	0.608903	0.0295709
$425$	−26.5910	−1.28985
$426$	62.4489	3.02566
$427$	−3.92225	−0.189811
$428$	9.59593	0.463837
$429$	0	0
$430$	−25.3734	−1.22361
$431$	−30.9517	−1.49089	−0.745446	−	0.666566i	$-0.767763\pi$
$431$	−30.9517	−1.49089	−0.745446	+	0.666566i	$0.767763\pi$
$432$	7.76466	0.373578
$433$	39.4907	1.89780	0.948902	−	0.315571i	$-0.102196\pi$
$433$	39.4907	1.89780	0.948902	+	0.315571i	$0.102196\pi$
$434$	36.2201	1.73862
$435$	82.3192	3.94690
$436$	8.24799	0.395007
$437$	0.288300	0.0137913
$438$	−28.8569	−1.37883
$439$	−19.4565	−0.928606	−0.464303	−	0.885676i	$-0.653695\pi$
$439$	−19.4565	−0.928606	−0.464303	+	0.885676i	$0.653695\pi$
$440$	0	0
$441$	30.3151	1.44358
$442$	10.4970	0.499291
$443$	9.58573	0.455432	0.227716	−	0.973728i	$-0.426874\pi$
$443$	9.58573	0.455432	0.227716	+	0.973728i	$0.426874\pi$
$444$	−12.1511	−0.576667
$445$	5.41238	0.256572
$446$	4.06612	0.192536
$447$	58.5845	2.77095
$448$	−14.4600	−0.683172
$449$	32.2659	1.52272	0.761361	−	0.648328i	$-0.224531\pi$
$449$	32.2659	1.52272	0.761361	+	0.648328i	$0.224531\pi$
$450$	−73.0650	−3.44432
$451$	0	0
$452$	−10.8543	−0.510544
$453$	−26.9813	−1.26769
$454$	−10.7526	−0.504644
$455$	48.4651	2.27208
$456$	0.491561	0.0230194
$457$	−23.7930	−1.11299	−0.556496	−	0.830850i	$-0.687855\pi$
$457$	−23.7930	−1.11299	−0.556496	+	0.830850i	$0.687855\pi$
$458$	−3.37837	−0.157861
$459$	3.41677	0.159481
$460$	9.28657	0.432988
$461$	15.6826	0.730411	0.365205	−	0.930927i	$-0.380999\pi$
$461$	15.6826	0.730411	0.365205	+	0.930927i	$0.380999\pi$
$462$	0	0
$463$	8.22261	0.382137	0.191068	−	0.981577i	$-0.438805\pi$
$463$	8.22261	0.382137	0.191068	+	0.981577i	$0.438805\pi$
$464$	−37.6909	−1.74976
$465$	60.3135	2.79697
$466$	13.1702	0.610098
$467$	−18.1019	−0.837657	−0.418828	−	0.908065i	$-0.637559\pi$
$467$	−18.1019	−0.837657	−0.418828	+	0.908065i	$0.637559\pi$
$468$	7.37613	0.340962
$469$	17.0161	0.785730
$470$	65.6806	3.02962
$471$	37.2276	1.71536
$472$	25.9807	1.19586
$473$	0	0
$474$	38.6243	1.77408
$475$	−1.09470	−0.0502281
$476$	5.81442	0.266503
$477$	1.02307	0.0468434
$478$	−36.8953	−1.68755
$479$	−37.6606	−1.72076	−0.860379	−	0.509655i	$-0.829773\pi$
$479$	−37.6606	−1.72076	−0.860379	+	0.509655i	$0.829773\pi$
$480$	39.9564	1.82375
$481$	20.4065	0.930457
$482$	−11.9877	−0.546023
$483$	−32.7516	−1.49025
$484$	0	0
$485$	−39.6352	−1.79974
$486$	−36.3487	−1.64881
$487$	18.6295	0.844181	0.422091	−	0.906554i	$-0.361296\pi$
$487$	18.6295	0.844181	0.422091	+	0.906554i	$0.361296\pi$
$488$	2.15202	0.0974173
$489$	−7.84837	−0.354915
$490$	57.2092	2.58445
$491$	−3.69149	−0.166595	−0.0832973	−	0.996525i	$-0.526545\pi$
$491$	−3.69149	−0.166595	−0.0832973	+	0.996525i	$0.526545\pi$
$492$	−14.9932	−0.675945
$493$	−16.5856	−0.746976
$494$	0.432140	0.0194429
$495$	0	0
$496$	−27.6153	−1.23997
$497$	−58.0922	−2.60579
$498$	44.3986	1.98955
$499$	−35.6356	−1.59527	−0.797634	−	0.603141i	$-0.793915\pi$
$499$	−35.6356	−1.59527	−0.797634	+	0.603141i	$0.793915\pi$
$500$	−20.9590	−0.937314
$501$	−46.7336	−2.08790
$502$	−26.9328	−1.20207
$503$	−37.0297	−1.65107	−0.825537	−	0.564349i	$-0.809127\pi$
$503$	−37.0297	−1.65107	−0.825537	+	0.564349i	$0.809127\pi$
$504$	−30.5201	−1.35948
$505$	3.37577	0.150220
$506$	0	0
$507$	10.7724	0.478420
$508$	−6.85921	−0.304328
$509$	−26.6420	−1.18089	−0.590444	−	0.807079i	$-0.701047\pi$
$509$	−26.6420	−1.18089	−0.590444	+	0.807079i	$0.701047\pi$
$510$	37.8602	1.67648
$511$	26.8437	1.18750
$512$	2.80452	0.123943
$513$	0.140661	0.00621035
$514$	3.30720	0.145875
$515$	−62.7755	−2.76622
$516$	6.57278	0.289350
$517$	0	0
$518$	44.1999	1.94203
$519$	−9.87511	−0.433469
$520$	−26.5913	−1.16611
$521$	30.8996	1.35374	0.676869	−	0.736104i	$-0.263336\pi$
$521$	30.8996	1.35374	0.676869	+	0.736104i	$0.263336\pi$
$522$	−45.5727	−1.99466
$523$	−10.1036	−0.441800	−0.220900	−	0.975296i	$-0.570899\pi$
$523$	−10.1036	−0.441800	−0.220900	+	0.975296i	$0.570899\pi$
$524$	−0.747952	−0.0326745
$525$	124.360	5.42751
$526$	−42.3897	−1.84828
$527$	−12.1519	−0.529344
$528$	0	0
$529$	−12.4607	−0.541771
$530$	1.93069	0.0838640
$531$	43.6526	1.89436
$532$	0.239368	0.0103779
$533$	25.1795	1.09064
$534$	−5.48240	−0.237246
$535$	−58.1243	−2.51293
$536$	−9.33620	−0.403262
$537$	−29.9885	−1.29410
$538$	0.913912	0.0394015
$539$	0	0
$540$	4.53091	0.194979
$541$	36.3802	1.56411	0.782053	−	0.623212i	$-0.214172\pi$
$541$	36.3802	1.56411	0.782053	+	0.623212i	$0.214172\pi$
$542$	29.8759	1.28328
$543$	35.3375	1.51648
$544$	−8.05036	−0.345156
$545$	−49.9596	−2.14003
$546$	−49.0921	−2.10095
$547$	4.81346	0.205809	0.102904	−	0.994691i	$-0.467186\pi$
$547$	4.81346	0.205809	0.102904	+	0.994691i	$0.467186\pi$
$548$	−6.80765	−0.290808
$549$	3.61581	0.154319
$550$	0	0
$551$	−0.682793	−0.0290880
$552$	17.9698	0.764844
$553$	−35.9298	−1.52789
$554$	1.33148	0.0565692
$555$	73.6015	3.12421
$556$	−8.18946	−0.347311
$557$	−4.61025	−0.195342	−0.0976712	−	0.995219i	$-0.531139\pi$
$557$	−4.61025	−0.195342	−0.0976712	+	0.995219i	$0.531139\pi$
$558$	−33.3902	−1.41352
$559$	−11.0383	−0.466869
$560$	−80.0357	−3.38212
$561$	0	0
$562$	−33.3348	−1.40614
$563$	3.52439	0.148535	0.0742677	−	0.997238i	$-0.476338\pi$
$563$	3.52439	0.148535	0.0742677	+	0.997238i	$0.476338\pi$
$564$	−17.0140	−0.716420
$565$	65.7465	2.76598
$566$	−9.85926	−0.414416
$567$	26.5669	1.11570
$568$	31.8734	1.33738
$569$	20.8347	0.873435	0.436717	−	0.899599i	$-0.356141\pi$
$569$	20.8347	0.873435	0.436717	+	0.899599i	$0.356141\pi$
$570$	1.55863	0.0652837
$571$	19.5639	0.818723	0.409362	−	0.912372i	$-0.365751\pi$
$571$	19.5639	0.818723	0.409362	+	0.912372i	$0.365751\pi$
$572$	0	0
$573$	−14.5883	−0.609436
$574$	54.5380	2.27637
$575$	−40.0183	−1.66888
$576$	13.3303	0.555428
$577$	−18.5888	−0.773861	−0.386930	−	0.922109i	$-0.626465\pi$
$577$	−18.5888	−0.773861	−0.386930	+	0.922109i	$0.626465\pi$
$578$	20.2396	0.841856
$579$	−54.8394	−2.27905
$580$	−21.9938	−0.913241
$581$	−41.3012	−1.71346
$582$	40.1479	1.66418
$583$	0	0
$584$	−14.7283	−0.609462
$585$	−44.6785	−1.84723
$586$	−44.4801	−1.83745
$587$	−2.04973	−0.0846016	−0.0423008	−	0.999105i	$-0.513469\pi$
$587$	−2.04973	−0.0846016	−0.0423008	+	0.999105i	$0.513469\pi$
$588$	−14.8196	−0.611149
$589$	−0.500268	−0.0206132
$590$	82.3790	3.39149
$591$	−55.9985	−2.30347
$592$	−33.6995	−1.38504
$593$	30.9033	1.26905	0.634524	−	0.772903i	$-0.281196\pi$
$593$	30.9033	1.26905	0.634524	+	0.772903i	$0.281196\pi$
$594$	0	0
$595$	−35.2190	−1.44384
$596$	−15.6524	−0.641147
$597$	−24.0556	−0.984528
$598$	15.7975	0.646010
$599$	15.5744	0.636351	0.318175	−	0.948032i	$-0.396930\pi$
$599$	15.5744	0.636351	0.318175	+	0.948032i	$0.396930\pi$
$600$	−68.2324	−2.78558
$601$	40.5666	1.65475	0.827374	−	0.561652i	$-0.189834\pi$
$601$	40.5666	1.65475	0.827374	+	0.561652i	$0.189834\pi$
$602$	−23.9086	−0.974442
$603$	−15.6866	−0.638808
$604$	7.20877	0.293321
$605$	0	0
$606$	−3.41943	−0.138905
$607$	31.8817	1.29404	0.647019	−	0.762474i	$-0.276015\pi$
$607$	31.8817	1.29404	0.647019	+	0.762474i	$0.276015\pi$
$608$	−0.331417	−0.0134407
$609$	77.5669	3.14317
$610$	6.82356	0.276278
$611$	28.5732	1.15595
$612$	−5.36013	−0.216671
$613$	−39.1278	−1.58036	−0.790178	−	0.612877i	$-0.790012\pi$
$613$	−39.1278	−1.58036	−0.790178	+	0.612877i	$0.790012\pi$
$614$	44.1804	1.78298
$615$	90.8165	3.66207
$616$	0	0
$617$	15.6482	0.629973	0.314986	−	0.949096i	$-0.398000\pi$
$617$	15.6482	0.629973	0.314986	+	0.949096i	$0.398000\pi$
$618$	63.5876	2.55787
$619$	28.5378	1.14703	0.573515	−	0.819195i	$-0.305580\pi$
$619$	28.5378	1.14703	0.573515	+	0.819195i	$0.305580\pi$
$620$	−16.1144	−0.647168
$621$	5.14209	0.206345
$622$	−27.4657	−1.10127
$623$	5.09992	0.204324
$624$	37.4294	1.49837
$625$	65.3178	2.61271
$626$	10.3747	0.414657
$627$	0	0
$628$	−9.94633	−0.396902
$629$	−14.8291	−0.591276
$630$	−96.7725	−3.85551
$631$	7.91764	0.315196	0.157598	−	0.987503i	$-0.449625\pi$
$631$	7.91764	0.315196	0.157598	+	0.987503i	$0.449625\pi$
$632$	19.7136	0.784163
$633$	−44.5762	−1.77175
$634$	−20.9229	−0.830956
$635$	41.5475	1.64876
$636$	−0.500131	−0.0198315
$637$	24.8879	0.986094
$638$	0	0
$639$	53.5535	2.11854
$640$	56.2250	2.22249
$641$	25.7127	1.01559	0.507796	−	0.861477i	$-0.330460\pi$
$641$	25.7127	1.01559	0.507796	+	0.861477i	$0.330460\pi$
$642$	58.8762	2.32366
$643$	22.1335	0.872860	0.436430	−	0.899738i	$-0.356243\pi$
$643$	22.1335	0.872860	0.436430	+	0.899738i	$0.356243\pi$
$644$	8.75045	0.344816
$645$	−39.8125	−1.56762
$646$	−0.314030	−0.0123554
$647$	−24.9829	−0.982181	−0.491090	−	0.871109i	$-0.663402\pi$
$647$	−24.9829	−0.982181	−0.491090	+	0.871109i	$0.663402\pi$
$648$	−14.5764	−0.572615
$649$	0	0
$650$	−59.9844	−2.35278
$651$	56.8316	2.22740
$652$	2.09690	0.0821209
$653$	−18.3071	−0.716412	−0.358206	−	0.933643i	$-0.616611\pi$
$653$	−18.3071	−0.716412	−0.358206	+	0.933643i	$0.616611\pi$
$654$	50.6058	1.97885
$655$	4.53048	0.177021
$656$	−41.5816	−1.62349
$657$	−24.7464	−0.965449
$658$	61.8889	2.41268
$659$	49.7807	1.93918	0.969591	−	0.244732i	$-0.0787000\pi$
$659$	49.7807	1.93918	0.969591	+	0.244732i	$0.0787000\pi$
$660$	0	0
$661$	−21.9582	−0.854076	−0.427038	−	0.904234i	$-0.640443\pi$
$661$	−21.9582	−0.854076	−0.427038	+	0.904234i	$0.640443\pi$
$662$	−49.5748	−1.92678
$663$	16.4705	0.639660
$664$	22.6607	0.879405
$665$	−1.44989	−0.0562244
$666$	−40.7466	−1.57890
$667$	−24.9606	−0.966477
$668$	12.4861	0.483102
$669$	6.38000	0.246665
$670$	−29.6030	−1.14366
$671$	0	0
$672$	37.6497	1.45237
$673$	2.46060	0.0948491	0.0474246	−	0.998875i	$-0.484899\pi$
$673$	2.46060	0.0948491	0.0474246	+	0.998875i	$0.484899\pi$
$674$	−21.8901	−0.843177
$675$	−19.5249	−0.751513
$676$	−2.87814	−0.110698
$677$	−22.1116	−0.849817	−0.424908	−	0.905236i	$-0.639694\pi$
$677$	−22.1116	−0.849817	−0.424908	+	0.905236i	$0.639694\pi$
$678$	−66.5970	−2.55764
$679$	−37.3470	−1.43325
$680$	19.3236	0.741024
$681$	−16.8715	−0.646518
$682$	0	0
$683$	32.5085	1.24390	0.621952	−	0.783055i	$-0.286340\pi$
$683$	32.5085	1.24390	0.621952	+	0.783055i	$0.286340\pi$
$684$	−0.220666	−0.00843736
$685$	41.2352	1.57551
$686$	8.89903	0.339767
$687$	−5.30088	−0.202241
$688$	18.2287	0.694962
$689$	0.839916	0.0319982
$690$	56.9781	2.16912
$691$	21.8737	0.832116	0.416058	−	0.909338i	$-0.363411\pi$
$691$	21.8737	0.832116	0.416058	+	0.909338i	$0.363411\pi$
$692$	2.63840	0.100297
$693$	0	0
$694$	−27.9875	−1.06239
$695$	49.6051	1.88163
$696$	−42.5585	−1.61318
$697$	−18.2976	−0.693070
$698$	−46.5651	−1.76252
$699$	20.6649	0.781618
$700$	−33.2261	−1.25583
$701$	34.4110	1.29969	0.649843	−	0.760068i	$-0.274835\pi$
$701$	34.4110	1.29969	0.649843	+	0.760068i	$0.274835\pi$
$702$	7.70760	0.290905
$703$	−0.610485	−0.0230249
$704$	0	0
$705$	103.057	3.88135
$706$	19.8539	0.747212
$707$	3.18088	0.119629
$708$	−21.3396	−0.801992
$709$	30.6498	1.15108	0.575538	−	0.817775i	$-0.304793\pi$
$709$	30.6498	1.15108	0.575538	+	0.817775i	$0.304793\pi$
$710$	101.063	3.79284
$711$	33.1226	1.24219
$712$	−2.79817	−0.104866
$713$	−18.2881	−0.684893
$714$	35.6745	1.33509
$715$	0	0
$716$	8.01222	0.299431
$717$	−57.8910	−2.16198
$718$	−41.3053	−1.54150
$719$	0.609809	0.0227421	0.0113710	−	0.999935i	$-0.496380\pi$
$719$	0.609809	0.0227421	0.0113710	+	0.999935i	$0.496380\pi$
$720$	73.7825	2.74971
$721$	−59.1515	−2.20292
$722$	31.1332	1.15866
$723$	−18.8094	−0.699529
$724$	−9.44134	−0.350885
$725$	94.7770	3.51993
$726$	0	0
$727$	−41.9477	−1.55576	−0.777878	−	0.628416i	$-0.783704\pi$
$727$	−41.9477	−1.55576	−0.777878	+	0.628416i	$0.783704\pi$
$728$	−25.0562	−0.928644
$729$	−36.7133	−1.35975
$730$	−46.7001	−1.72845
$731$	8.02137	0.296681
$732$	−1.76759	−0.0653319
$733$	−35.7524	−1.32054	−0.660272	−	0.751026i	$-0.729559\pi$
$733$	−35.7524	−1.32054	−0.660272	+	0.751026i	$0.729559\pi$
$734$	−6.38290	−0.235597
$735$	89.7649	3.31103
$736$	−12.1154	−0.446581
$737$	0	0
$738$	−50.2770	−1.85072
$739$	−7.94248	−0.292169	−0.146084	−	0.989272i	$-0.546667\pi$
$739$	−7.94248	−0.292169	−0.146084	+	0.989272i	$0.546667\pi$
$740$	−19.6646	−0.722885
$741$	0.678055	0.0249090
$742$	1.81923	0.0667862
$743$	14.7967	0.542839	0.271419	−	0.962461i	$-0.412507\pi$
$743$	14.7967	0.542839	0.271419	+	0.962461i	$0.412507\pi$
$744$	−31.1817	−1.14318
$745$	94.8094	3.47355
$746$	−22.5136	−0.824282
$747$	38.0743	1.39307
$748$	0	0
$749$	−54.7688	−2.00121
$750$	−128.595	−4.69561
$751$	−42.2662	−1.54232	−0.771158	−	0.636643i	$-0.780322\pi$
$751$	−42.2662	−1.54232	−0.771158	+	0.636643i	$0.780322\pi$
$752$	−47.1861	−1.72070
$753$	−42.2593	−1.54002
$754$	−37.4140	−1.36254
$755$	−43.6648	−1.58913
$756$	4.26933	0.155274
$757$	−8.84099	−0.321331	−0.160666	−	0.987009i	$-0.551364\pi$
$757$	−8.84099	−0.321331	−0.160666	+	0.987009i	$0.551364\pi$
$758$	−24.7693	−0.899663
$759$	0	0
$760$	0.795511	0.0288562
$761$	25.8087	0.935563	0.467781	−	0.883844i	$-0.345053\pi$
$761$	25.8087	0.935563	0.467781	+	0.883844i	$0.345053\pi$
$762$	−42.0849	−1.52458
$763$	−47.0754	−1.70424
$764$	3.89766	0.141012
$765$	32.4673	1.17386
$766$	19.3514	0.699195
$767$	35.8376	1.29402
$768$	−37.9872	−1.37075
$769$	−37.4725	−1.35129	−0.675647	−	0.737225i	$-0.736136\pi$
$769$	−37.4725	−1.35129	−0.675647	+	0.737225i	$0.736136\pi$
$770$	0	0
$771$	5.18921	0.186885
$772$	14.6518	0.527330
$773$	2.28508	0.0821885	0.0410942	−	0.999155i	$-0.486916\pi$
$773$	2.28508	0.0821885	0.0410942	+	0.999155i	$0.486916\pi$
$774$	22.0406	0.792233
$775$	69.4411	2.49440
$776$	20.4912	0.735590
$777$	69.3525	2.48801
$778$	−43.2749	−1.55148
$779$	−0.753274	−0.0269888
$780$	21.8411	0.782038
$781$	0	0
$782$	−11.4799	−0.410519
$783$	−12.1782	−0.435214
$784$	−41.1000	−1.46786
$785$	60.2467	2.15030
$786$	−4.58909	−0.163687
$787$	−5.95381	−0.212230	−0.106115	−	0.994354i	$-0.533841\pi$
$787$	−5.95381	−0.212230	−0.106115	+	0.994354i	$0.533841\pi$
$788$	14.9615	0.532981
$789$	−66.5122	−2.36790
$790$	62.5072	2.22391
$791$	61.9510	2.20272
$792$	0	0
$793$	2.96848	0.105414
$794$	45.3749	1.61030
$795$	3.02938	0.107441
$796$	6.42708	0.227802
$797$	−28.8393	−1.02154	−0.510770	−	0.859717i	$-0.670640\pi$
$797$	−28.8393	−1.02154	−0.510770	+	0.859717i	$0.670640\pi$
$798$	1.46865	0.0519896
$799$	−20.7638	−0.734570
$800$	46.0032	1.62646
$801$	−4.70147	−0.166118
$802$	43.7316	1.54422
$803$	0	0
$804$	7.66841	0.270444
$805$	−53.0031	−1.86811
$806$	−27.4124	−0.965561
$807$	1.43399	0.0504787
$808$	−1.74525	−0.0613977
$809$	−23.5794	−0.829006	−0.414503	−	0.910048i	$-0.636045\pi$
$809$	−23.5794	−0.829006	−0.414503	+	0.910048i	$0.636045\pi$
$810$	−46.2185	−1.62395
$811$	6.26733	0.220076	0.110038	−	0.993927i	$-0.464903\pi$
$811$	6.26733	0.220076	0.110038	+	0.993927i	$0.464903\pi$
$812$	−20.7240	−0.727272
$813$	46.8772	1.64406
$814$	0	0
$815$	−12.7013	−0.444907
$816$	−27.1994	−0.952171
$817$	0.330223	0.0115530
$818$	9.70094	0.339186
$819$	−42.0992	−1.47107
$820$	−24.2640	−0.847337
$821$	12.9750	0.452829	0.226415	−	0.974031i	$-0.427300\pi$
$821$	12.9750	0.452829	0.226415	+	0.974031i	$0.427300\pi$
$822$	−41.7686	−1.45685
$823$	−13.9673	−0.486870	−0.243435	−	0.969917i	$-0.578274\pi$
$823$	−13.9673	−0.486870	−0.243435	+	0.969917i	$0.578274\pi$
$824$	32.4546	1.13061
$825$	0	0
$826$	77.6232	2.70086
$827$	−16.8755	−0.586818	−0.293409	−	0.955987i	$-0.594790\pi$
$827$	−16.8755	−0.586818	−0.293409	+	0.955987i	$0.594790\pi$
$828$	−8.06677	−0.280340
$829$	−39.4407	−1.36983	−0.684915	−	0.728623i	$-0.740161\pi$
$829$	−39.4407	−1.36983	−0.684915	+	0.728623i	$0.740161\pi$
$830$	71.8519	2.49401
$831$	2.08918	0.0724728
$832$	10.9438	0.379407
$833$	−18.0857	−0.626632
$834$	−50.2467	−1.73990
$835$	−75.6306	−2.61731
$836$	0	0
$837$	−8.92273	−0.308415
$838$	6.23893	0.215520
$839$	−25.1931	−0.869761	−0.434881	−	0.900488i	$-0.643209\pi$
$839$	−25.1931	−0.869761	−0.434881	+	0.900488i	$0.643209\pi$
$840$	−90.3719	−3.11813
$841$	30.1151	1.03845
$842$	5.81966	0.200559
$843$	−52.3044	−1.80146
$844$	11.9097	0.409950
$845$	17.4334	0.599728
$846$	−57.0535	−1.96154
$847$	0	0
$848$	−1.38704	−0.0476313
$849$	−15.4698	−0.530922
$850$	43.5898	1.49512
$851$	−22.3172	−0.765025
$852$	−26.1796	−0.896899
$853$	3.01316	0.103169	0.0515843	−	0.998669i	$-0.483573\pi$
$853$	3.01316	0.103169	0.0515843	+	0.998669i	$0.483573\pi$
$854$	6.42964	0.220018
$855$	1.33661	0.0457112
$856$	30.0499	1.02709
$857$	33.5516	1.14610	0.573050	−	0.819520i	$-0.305760\pi$
$857$	33.5516	1.14610	0.573050	+	0.819520i	$0.305760\pi$
$858$	0	0
$859$	26.1335	0.891665	0.445832	−	0.895117i	$-0.352908\pi$
$859$	26.1335	0.891665	0.445832	+	0.895117i	$0.352908\pi$
$860$	10.6370	0.362718
$861$	85.5736	2.91634
$862$	50.7382	1.72815
$863$	9.58969	0.326437	0.163218	−	0.986590i	$-0.447812\pi$
$863$	9.58969	0.326437	0.163218	+	0.986590i	$0.447812\pi$
$864$	−5.91111	−0.201100
$865$	−15.9813	−0.543379
$866$	−64.7360	−2.19982
$867$	31.7572	1.07853
$868$	−15.1841	−0.515381
$869$	0	0
$870$	−134.943	−4.57501
$871$	−12.8783	−0.436364
$872$	25.8288	0.874674
$873$	34.4291	1.16525
$874$	−0.472602	−0.0159860
$875$	119.623	4.04401
$876$	12.0973	0.408730
$877$	39.9971	1.35061	0.675303	−	0.737540i	$-0.264013\pi$
$877$	39.9971	1.35061	0.675303	+	0.737540i	$0.264013\pi$
$878$	31.8944	1.07638
$879$	−69.7920	−2.35403
$880$	0	0
$881$	41.5622	1.40026	0.700132	−	0.714013i	$-0.253124\pi$
$881$	41.5622	1.40026	0.700132	+	0.714013i	$0.253124\pi$
$882$	−49.6948	−1.67331
$883$	−12.6901	−0.427058	−0.213529	−	0.976937i	$-0.568496\pi$
$883$	−12.6901	−0.427058	−0.213529	+	0.976937i	$0.568496\pi$
$884$	−4.40052	−0.148006
$885$	129.258	4.34496
$886$	−15.7136	−0.527909
$887$	−8.07111	−0.271001	−0.135501	−	0.990777i	$-0.543264\pi$
$887$	−8.07111	−0.271001	−0.135501	+	0.990777i	$0.543264\pi$
$888$	−38.0516	−1.27693
$889$	39.1489	1.31301
$890$	−8.87236	−0.297402
$891$	0	0
$892$	−1.70459	−0.0570738
$893$	−0.854803	−0.0286049
$894$	−96.0358	−3.21192
$895$	−48.5315	−1.62223
$896$	52.9791	1.76991
$897$	24.7873	0.827625
$898$	−52.8926	−1.76505
$899$	43.3124	1.44455
$900$	30.6301	1.02100
$901$	−0.610356	−0.0203339
$902$	0	0
$903$	−37.5141	−1.24839
$904$	−33.9906	−1.13051
$905$	57.1879	1.90099
$906$	44.2297	1.46943
$907$	−9.21459	−0.305965	−0.152983	−	0.988229i	$-0.548888\pi$
$907$	−9.21459	−0.305965	−0.152983	+	0.988229i	$0.548888\pi$
$908$	4.50767	0.149592
$909$	−2.93236	−0.0972602
$910$	−79.4475	−2.63366
$911$	15.6759	0.519366	0.259683	−	0.965694i	$-0.416382\pi$
$911$	15.6759	0.519366	0.259683	+	0.965694i	$0.416382\pi$
$912$	−1.11974	−0.0370785
$913$	0	0
$914$	39.0033	1.29011
$915$	10.7066	0.353949
$916$	1.41627	0.0467949
$917$	4.26894	0.140973
$918$	−5.60101	−0.184861
$919$	−1.72441	−0.0568830	−0.0284415	−	0.999595i	$-0.509054\pi$
$919$	−1.72441	−0.0568830	−0.0284415	+	0.999595i	$0.509054\pi$
$920$	29.0811	0.958777
$921$	69.3218	2.28423
$922$	−25.7080	−0.846648
$923$	43.9659	1.44716
$924$	0	0
$925$	84.7401	2.78624
$926$	−13.4791	−0.442950
$927$	54.5300	1.79100
$928$	28.6935	0.941911
$929$	−52.6262	−1.72661	−0.863305	−	0.504683i	$-0.831609\pi$
$929$	−52.6262	−1.72661	−0.863305	+	0.504683i	$0.831609\pi$
$930$	−98.8702	−3.24208
$931$	−0.744551	−0.0244017
$932$	−5.52118	−0.180852
$933$	−43.0954	−1.41088
$934$	29.6740	0.970961
$935$	0	0
$936$	23.0985	0.754999
$937$	−30.6303	−1.00065	−0.500324	−	0.865838i	$-0.666786\pi$
$937$	−30.6303	−1.00065	−0.500324	+	0.865838i	$0.666786\pi$
$938$	−27.8940	−0.910771
$939$	16.2786	0.531231
$940$	−27.5344	−0.898074
$941$	1.47261	0.0480058	0.0240029	−	0.999712i	$-0.492359\pi$
$941$	1.47261	0.0480058	0.0240029	+	0.999712i	$0.492359\pi$
$942$	−61.0261	−1.98834
$943$	−27.5371	−0.896731
$944$	−59.1825	−1.92623
$945$	−25.8601	−0.841230
$946$	0	0
$947$	33.1638	1.07768	0.538839	−	0.842409i	$-0.318863\pi$
$947$	33.1638	1.07768	0.538839	+	0.842409i	$0.318863\pi$
$948$	−16.1920	−0.525891
$949$	−20.3161	−0.659489
$950$	1.79450	0.0582214
$951$	−32.8294	−1.06457
$952$	18.2080	0.590125
$953$	−31.6613	−1.02561	−0.512805	−	0.858505i	$-0.671394\pi$
$953$	−31.6613	−1.02561	−0.512805	+	0.858505i	$0.671394\pi$
$954$	−1.67710	−0.0542980
$955$	−23.6088	−0.763964
$956$	15.4671	0.500243
$957$	0	0
$958$	61.7360	1.99460
$959$	38.8546	1.25468
$960$	39.4717	1.27394
$961$	0.734039	0.0236787
$962$	−33.4518	−1.07853
$963$	50.4897	1.62701
$964$	5.02543	0.161858
$965$	−88.7487	−2.85692
$966$	53.6887	1.72741
$967$	−3.59796	−0.115703	−0.0578513	−	0.998325i	$-0.518425\pi$
$967$	−3.59796	−0.115703	−0.0578513	+	0.998325i	$0.518425\pi$
$968$	0	0
$969$	−0.492733	−0.0158289
$970$	64.9729	2.08615
$971$	7.73997	0.248387	0.124194	−	0.992258i	$-0.460366\pi$
$971$	7.73997	0.248387	0.124194	+	0.992258i	$0.460366\pi$
$972$	15.2380	0.488759
$973$	46.7414	1.49846
$974$	−30.5387	−0.978524
$975$	−94.1193	−3.01423
$976$	−4.90216	−0.156914
$977$	−8.79094	−0.281247	−0.140624	−	0.990063i	$-0.544911\pi$
$977$	−8.79094	−0.281247	−0.140624	+	0.990063i	$0.544911\pi$
$978$	12.8656	0.411397
$979$	0	0
$980$	−23.9831	−0.766111
$981$	43.3974	1.38557
$982$	6.05135	0.193106
$983$	16.1063	0.513710	0.256855	−	0.966450i	$-0.417314\pi$
$983$	16.1063	0.513710	0.256855	+	0.966450i	$0.417314\pi$
$984$	−46.9516	−1.49676
$985$	−90.6245	−2.88754
$986$	27.1882	0.865850
$987$	97.1075	3.09097
$988$	−0.181160	−0.00576348
$989$	12.0718	0.383862
$990$	0	0
$991$	−1.26273	−0.0401119	−0.0200560	−	0.999799i	$-0.506384\pi$
$991$	−1.26273	−0.0401119	−0.0200560	+	0.999799i	$0.506384\pi$
$992$	21.0231	0.667485
$993$	−77.7859	−2.46846
$994$	95.2289	3.02048
$995$	−38.9300	−1.23416
$996$	−18.6126	−0.589764
$997$	−31.7854	−1.00665	−0.503326	−	0.864097i	$-0.667891\pi$
$997$	−31.7854	−1.00665	−0.503326	+	0.864097i	$0.667891\pi$
$998$	58.4164	1.84914
$999$	−10.8886	−0.344498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.p.1.6	yes	25
11.10	odd	2		7381.2.a.m.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.m.1.20	✓	25	11.10	odd	2
7381.2.a.p.1.6	yes	25	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.63927 q^{2} -2.57212 q^{3} +0.687210 q^{4} -4.16256 q^{5} +4.21640 q^{6} -3.92225 q^{7} +2.15202 q^{8} +3.61581 q^{9} +O(q^{10})\)	\(q-1.63927 q^{2} -2.57212 q^{3} +0.687210 q^{4} -4.16256 q^{5} +4.21640 q^{6} -3.92225 q^{7} +2.15202 q^{8} +3.61581 q^{9} +6.82356 q^{10} -1.76759 q^{12} +2.96848 q^{13} +6.42964 q^{14} +10.7066 q^{15} -4.90216 q^{16} -2.15715 q^{17} -5.92729 q^{18} -0.0888055 q^{19} -2.86055 q^{20} +10.0885 q^{21} -3.24642 q^{23} -5.53525 q^{24} +12.3269 q^{25} -4.86614 q^{26} -1.58393 q^{27} -2.69541 q^{28} +7.68864 q^{29} -17.5510 q^{30} +5.63330 q^{31} +3.73194 q^{32} +3.53616 q^{34} +16.3266 q^{35} +2.48482 q^{36} +6.87441 q^{37} +0.145576 q^{38} -7.63528 q^{39} -8.95790 q^{40} +8.48229 q^{41} -16.5378 q^{42} -3.71850 q^{43} -15.0510 q^{45} +5.32177 q^{46} +9.62556 q^{47} +12.6090 q^{48} +8.38406 q^{49} -20.2071 q^{50} +5.54846 q^{51} +2.03997 q^{52} +0.282945 q^{53} +2.59648 q^{54} -8.44076 q^{56} +0.228419 q^{57} -12.6038 q^{58} +12.0727 q^{59} +7.35769 q^{60} +1.00000 q^{61} -9.23450 q^{62} -14.1821 q^{63} +3.68667 q^{64} -12.3565 q^{65} -4.33834 q^{67} -1.48242 q^{68} +8.35019 q^{69} -26.7637 q^{70} +14.8109 q^{71} +7.78128 q^{72} -6.84395 q^{73} -11.2690 q^{74} -31.7063 q^{75} -0.0610281 q^{76} +12.5163 q^{78} +9.16050 q^{79} +20.4055 q^{80} -6.77337 q^{81} -13.9048 q^{82} +10.5300 q^{83} +6.93293 q^{84} +8.97927 q^{85} +6.09563 q^{86} -19.7761 q^{87} -1.30025 q^{89} +24.6727 q^{90} -11.6431 q^{91} -2.23098 q^{92} -14.4895 q^{93} -15.7789 q^{94} +0.369658 q^{95} -9.59900 q^{96} +9.52184 q^{97} -13.7438 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 6 q^{6} + 4 q^{7} + 15 q^{8} + 24 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 10 q^{14} + q^{15} + 21 q^{16} + 8 q^{17} + 16 q^{19} - 16 q^{20} + 12 q^{21} + 3 q^{23} + 62 q^{24} + 26 q^{25} - 4 q^{26} - 13 q^{27} - 42 q^{28} + 28 q^{29} + 12 q^{30} - q^{31} + 35 q^{32} + 8 q^{34} + 62 q^{35} + 17 q^{36} - 7 q^{37} + 20 q^{38} - 27 q^{40} + 28 q^{41} - 34 q^{42} + 22 q^{43} + 58 q^{46} - 2 q^{47} + 10 q^{48} + 25 q^{49} - 15 q^{50} + 38 q^{51} + 12 q^{52} - 4 q^{53} + 24 q^{54} - 48 q^{56} + 40 q^{57} + 8 q^{58} + 9 q^{59} + 18 q^{60} + 25 q^{61} + 4 q^{62} + 30 q^{63} + 41 q^{64} + 32 q^{65} - 15 q^{67} + 112 q^{68} - q^{69} + 14 q^{70} - 9 q^{71} - 59 q^{72} - 8 q^{73} + 54 q^{74} - 4 q^{75} + 32 q^{76} + 20 q^{78} + 30 q^{79} - 18 q^{80} + 17 q^{81} + 10 q^{83} - 39 q^{84} + 52 q^{85} - 6 q^{86} + 24 q^{87} - 5 q^{89} + 110 q^{90} - 38 q^{92} - q^{93} - 120 q^{94} + 50 q^{95} + 130 q^{96} + 5 q^{97} + 35 q^{98}+O(q^{100}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 6 * q^6 + 4 * q^7 + 15 * q^8 + 24 * q^9 + 6 * q^10 + 2 * q^12 + 4 * q^13 - 10 * q^14 + q^15 + 21 * q^16 + 8 * q^17 + 16 * q^19 - 16 * q^20 + 12 * q^21 + 3 * q^23 + 62 * q^24 + 26 * q^25 - 4 * q^26 - 13 * q^27 - 42 * q^28 + 28 * q^29 + 12 * q^30 - q^31 + 35 * q^32 + 8 * q^34 + 62 * q^35 + 17 * q^36 - 7 * q^37 + 20 * q^38 - 27 * q^40 + 28 * q^41 - 34 * q^42 + 22 * q^43 + 58 * q^46 - 2 * q^47 + 10 * q^48 + 25 * q^49 - 15 * q^50 + 38 * q^51 + 12 * q^52 - 4 * q^53 + 24 * q^54 - 48 * q^56 + 40 * q^57 + 8 * q^58 + 9 * q^59 + 18 * q^60 + 25 * q^61 + 4 * q^62 + 30 * q^63 + 41 * q^64 + 32 * q^65 - 15 * q^67 + 112 * q^68 - q^69 + 14 * q^70 - 9 * q^71 - 59 * q^72 - 8 * q^73 + 54 * q^74 - 4 * q^75 + 32 * q^76 + 20 * q^78 + 30 * q^79 - 18 * q^80 + 17 * q^81 + 10 * q^83 - 39 * q^84 + 52 * q^85 - 6 * q^86 + 24 * q^87 - 5 * q^89 + 110 * q^90 - 38 * q^92 - q^93 - 120 * q^94 + 50 * q^95 + 130 * q^96 + 5 * q^97 + 35 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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