LMFDB - Embedded newform 1058.2.a.j.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1058,2,Mod(1,1058)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1058.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1058, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1058 = 2 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1058.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-5,0,5,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.44817253385$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.91899$ of defining polynomial
Character	$\chi$	$=$	1058.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -0.609264 q^{3} +1.00000 q^{4} +0.372786 q^{5} +0.609264 q^{6} +2.05954 q^{7} -1.00000 q^{8} -2.62880 q^{9} -0.372786 q^{10} +2.46519 q^{11} -0.609264 q^{12} -3.73269 q^{13} -2.05954 q^{14} -0.227125 q^{15} +1.00000 q^{16} -6.30909 q^{17} +2.62880 q^{18} -3.28887 q^{19} +0.372786 q^{20} -1.25480 q^{21} -2.46519 q^{22} +0.609264 q^{24} -4.86103 q^{25} +3.73269 q^{26} +3.42943 q^{27} +2.05954 q^{28} +7.13278 q^{29} +0.227125 q^{30} +5.84511 q^{31} -1.00000 q^{32} -1.50195 q^{33} +6.30909 q^{34} +0.767766 q^{35} -2.62880 q^{36} -4.67961 q^{37} +3.28887 q^{38} +2.27420 q^{39} -0.372786 q^{40} -4.78084 q^{41} +1.25480 q^{42} -11.1379 q^{43} +2.46519 q^{44} -0.979978 q^{45} +2.44502 q^{47} -0.609264 q^{48} -2.75831 q^{49} +4.86103 q^{50} +3.84391 q^{51} -3.73269 q^{52} +6.04752 q^{53} -3.42943 q^{54} +0.918986 q^{55} -2.05954 q^{56} +2.00379 q^{57} -7.13278 q^{58} -11.8100 q^{59} -0.227125 q^{60} +1.68675 q^{61} -5.84511 q^{62} -5.41411 q^{63} +1.00000 q^{64} -1.39149 q^{65} +1.50195 q^{66} -14.0947 q^{67} -6.30909 q^{68} -0.767766 q^{70} +4.03869 q^{71} +2.62880 q^{72} +8.69002 q^{73} +4.67961 q^{74} +2.96165 q^{75} -3.28887 q^{76} +5.07714 q^{77} -2.27420 q^{78} -2.38398 q^{79} +0.372786 q^{80} +5.79696 q^{81} +4.78084 q^{82} +4.23705 q^{83} -1.25480 q^{84} -2.35194 q^{85} +11.1379 q^{86} -4.34575 q^{87} -2.46519 q^{88} -9.03115 q^{89} +0.979978 q^{90} -7.68762 q^{91} -3.56122 q^{93} -2.44502 q^{94} -1.22605 q^{95} +0.609264 q^{96} -11.3067 q^{97} +2.75831 q^{98} -6.48047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{4} - 2 q^{5} - 9 q^{7} - 5 q^{8} + 7 q^{9} + 2 q^{10} - q^{11} + q^{13} + 9 q^{14} - 11 q^{15} + 5 q^{16} + q^{17} - 7 q^{18} - 10 q^{19} - 2 q^{20} + q^{22} - 11 q^{25} - q^{26}+ \cdots - 8 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 + 5 * q^4 - 2 * q^5 - 9 * q^7 - 5 * q^8 + 7 * q^9 + 2 * q^10 - q^11 + q^13 + 9 * q^14 - 11 * q^15 + 5 * q^16 + q^17 - 7 * q^18 - 10 * q^19 - 2 * q^20 + q^22 - 11 * q^25 - q^26 - 9 * q^28 + 10 * q^29 + 11 * q^30 - 5 * q^32 - 11 * q^33 - q^34 - 3 * q^35 + 7 * q^36 - 20 * q^37 + 10 * q^38 - 22 * q^39 + 2 * q^40 - 3 * q^41 - 27 * q^43 - q^44 - 5 * q^45 - 11 * q^47 + 12 * q^49 + 11 * q^50 + q^52 + 2 * q^53 - 4 * q^55 + 9 * q^56 - 11 * q^57 - 10 * q^58 - 17 * q^59 - 11 * q^60 - 7 * q^61 - 39 * q^63 + 5 * q^64 + 15 * q^65 + 11 * q^66 - 28 * q^67 + q^68 + 3 * q^70 - 7 * q^72 + 8 * q^73 + 20 * q^74 + 22 * q^75 - 10 * q^76 + 26 * q^77 + 22 * q^78 - 16 * q^79 - 2 * q^80 + q^81 + 3 * q^82 - 18 * q^83 - 7 * q^85 + 27 * q^86 + 22 * q^87 + q^88 + 14 * q^89 + 5 * q^90 - 26 * q^91 - 44 * q^93 + 11 * q^94 + 26 * q^95 - 47 * q^97 - 12 * q^98 - 8 * q^99

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
$3$	−0.609264	−0.351759	−0.175880	−	0.984412i	$-0.556277\pi$
$3$	−0.609264	−0.351759	−0.175880	+	0.984412i	$0.556277\pi$
$4$	1.00000	0.500000
$5$	0.372786	0.166715	0.0833574	−	0.996520i	$-0.473436\pi$
$5$	0.372786	0.166715	0.0833574	+	0.996520i	$0.473436\pi$
$6$	0.609264	0.248731
$7$	2.05954	0.778432	0.389216	−	0.921147i	$-0.372746\pi$
$7$	2.05954	0.778432	0.389216	+	0.921147i	$0.372746\pi$
$8$	−1.00000	−0.353553
$9$	−2.62880	−0.876266
$10$	−0.372786	−0.117885
$11$	2.46519	0.743282	0.371641	−	0.928377i	$-0.378795\pi$
$11$	2.46519	0.743282	0.371641	+	0.928377i	$0.378795\pi$
$12$	−0.609264	−0.175880
$13$	−3.73269	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$13$	−3.73269	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$14$	−2.05954	−0.550435
$15$	−0.227125	−0.0586434
$16$	1.00000	0.250000
$17$	−6.30909	−1.53018	−0.765090	−	0.643924i	$-0.777305\pi$
$17$	−6.30909	−1.53018	−0.765090	+	0.643924i	$0.777305\pi$
$18$	2.62880	0.619613
$19$	−3.28887	−0.754520	−0.377260	−	0.926107i	$-0.623134\pi$
$19$	−3.28887	−0.754520	−0.377260	+	0.926107i	$0.623134\pi$
$20$	0.372786	0.0833574
$21$	−1.25480	−0.273820
$22$	−2.46519	−0.525579
$23$	0	0
$23$	0	0
$24$	0.609264	0.124366
$25$	−4.86103	−0.972206
$26$	3.73269	0.732041
$27$	3.42943	0.659993
$28$	2.05954	0.389216
$29$	7.13278	1.32452	0.662262	−	0.749272i	$-0.269597\pi$
$29$	7.13278	1.32452	0.662262	+	0.749272i	$0.269597\pi$
$30$	0.227125	0.0414672
$31$	5.84511	1.04981	0.524907	−	0.851160i	$-0.324100\pi$
$31$	5.84511	1.04981	0.524907	+	0.851160i	$0.324100\pi$
$32$	−1.00000	−0.176777
$33$	−1.50195	−0.261456
$34$	6.30909	1.08200
$35$	0.767766	0.129776
$36$	−2.62880	−0.438133
$37$	−4.67961	−0.769323	−0.384662	−	0.923058i	$-0.625682\pi$
$37$	−4.67961	−0.769323	−0.384662	+	0.923058i	$0.625682\pi$
$38$	3.28887	0.533526
$39$	2.27420	0.364163
$40$	−0.372786	−0.0589426
$41$	−4.78084	−0.746642	−0.373321	−	0.927702i	$-0.621781\pi$
$41$	−4.78084	−0.746642	−0.373321	+	0.927702i	$0.621781\pi$
$42$	1.25480	0.193620
$43$	−11.1379	−1.69851	−0.849256	−	0.527981i	$-0.822949\pi$
$43$	−11.1379	−1.69851	−0.849256	+	0.527981i	$0.822949\pi$
$44$	2.46519	0.371641
$45$	−0.979978	−0.146086
$46$	0	0
$47$	2.44502	0.356643	0.178322	−	0.983972i	$-0.442933\pi$
$47$	2.44502	0.356643	0.178322	+	0.983972i	$0.442933\pi$
$48$	−0.609264	−0.0879398
$49$	−2.75831	−0.394044
$50$	4.86103	0.687454
$51$	3.84391	0.538254
$52$	−3.73269	−0.517631
$53$	6.04752	0.830691	0.415345	−	0.909664i	$-0.363661\pi$
$53$	6.04752	0.830691	0.415345	+	0.909664i	$0.363661\pi$
$54$	−3.42943	−0.466686
$55$	0.918986	0.123916
$56$	−2.05954	−0.275217
$57$	2.00379	0.265409
$58$	−7.13278	−0.936580
$59$	−11.8100	−1.53754	−0.768768	−	0.639528i	$-0.779130\pi$
$59$	−11.8100	−1.53754	−0.768768	+	0.639528i	$0.779130\pi$
$60$	−0.227125	−0.0293217
$61$	1.68675	0.215966	0.107983	−	0.994153i	$-0.465561\pi$
$61$	1.68675	0.215966	0.107983	+	0.994153i	$0.465561\pi$
$62$	−5.84511	−0.742330
$63$	−5.41411	−0.682113
$64$	1.00000	0.125000
$65$	−1.39149	−0.172594
$66$	1.50195	0.184877
$67$	−14.0947	−1.72194	−0.860969	−	0.508658i	$-0.830142\pi$
$67$	−14.0947	−1.72194	−0.860969	+	0.508658i	$0.830142\pi$
$68$	−6.30909	−0.765090
$69$	0	0
$70$	−0.767766	−0.0917656
$71$	4.03869	0.479304	0.239652	−	0.970859i	$-0.422967\pi$
$71$	4.03869	0.479304	0.239652	+	0.970859i	$0.422967\pi$
$72$	2.62880	0.309807
$73$	8.69002	1.01709	0.508545	−	0.861035i	$-0.330183\pi$
$73$	8.69002	1.01709	0.508545	+	0.861035i	$0.330183\pi$
$74$	4.67961	0.543994
$75$	2.96165	0.341982
$76$	−3.28887	−0.377260
$77$	5.07714	0.578594
$78$	−2.27420	−0.257502
$79$	−2.38398	−0.268218	−0.134109	−	0.990967i	$-0.542817\pi$
$79$	−2.38398	−0.268218	−0.134109	+	0.990967i	$0.542817\pi$
$80$	0.372786	0.0416787
$81$	5.79696	0.644107
$82$	4.78084	0.527956
$83$	4.23705	0.465076	0.232538	−	0.972587i	$-0.425297\pi$
$83$	4.23705	0.465076	0.232538	+	0.972587i	$0.425297\pi$
$84$	−1.25480	−0.136910
$85$	−2.35194	−0.255104
$86$	11.1379	1.20103
$87$	−4.34575	−0.465913
$88$	−2.46519	−0.262790
$89$	−9.03115	−0.957300	−0.478650	−	0.878006i	$-0.658874\pi$
$89$	−9.03115	−0.957300	−0.478650	+	0.878006i	$0.658874\pi$
$90$	0.979978	0.103299
$91$	−7.68762	−0.805881
$92$	0	0
$93$	−3.56122	−0.369281
$94$	−2.44502	−0.252185
$95$	−1.22605	−0.125790
$96$	0.609264	0.0621828
$97$	−11.3067	−1.14802	−0.574010	−	0.818848i	$-0.694613\pi$
$97$	−11.3067	−1.14802	−0.574010	+	0.818848i	$0.694613\pi$
$98$	2.75831	0.278631
$99$	−6.48047	−0.651312
$100$	−4.86103	−0.486103
$101$	−8.05177	−0.801181	−0.400590	−	0.916257i	$-0.631195\pi$
$101$	−8.05177	−0.801181	−0.400590	+	0.916257i	$0.631195\pi$
$102$	−3.84391	−0.380603
$103$	−14.7518	−1.45354	−0.726771	−	0.686879i	$-0.758980\pi$
$103$	−14.7518	−1.45354	−0.726771	+	0.686879i	$0.758980\pi$
$104$	3.73269	0.366020
$105$	−0.467772	−0.0456499
$106$	−6.04752	−0.587387
$107$	−6.68158	−0.645932	−0.322966	−	0.946411i	$-0.604680\pi$
$107$	−6.68158	−0.645932	−0.322966	+	0.946411i	$0.604680\pi$
$108$	3.42943	0.329997
$109$	−4.07970	−0.390764	−0.195382	−	0.980727i	$-0.562595\pi$
$109$	−4.07970	−0.390764	−0.195382	+	0.980727i	$0.562595\pi$
$110$	−0.918986	−0.0876219
$111$	2.85112	0.270616
$112$	2.05954	0.194608
$113$	5.58523	0.525414	0.262707	−	0.964876i	$-0.415385\pi$
$113$	5.58523	0.525414	0.262707	+	0.964876i	$0.415385\pi$
$114$	−2.00379	−0.187673
$115$	0	0
$116$	7.13278	0.662262
$117$	9.81249	0.907165
$118$	11.8100	1.08720
$119$	−12.9938	−1.19114
$120$	0.227125	0.0207336
$121$	−4.92286	−0.447532
$122$	−1.68675	−0.152711
$123$	2.91280	0.262638
$124$	5.84511	0.524907
$125$	−3.67605	−0.328796
$126$	5.41411	0.482327
$127$	−7.54884	−0.669851	−0.334926	−	0.942245i	$-0.608711\pi$
$127$	−7.54884	−0.669851	−0.334926	+	0.942245i	$0.608711\pi$
$128$	−1.00000	−0.0883883
$129$	6.78592	0.597467
$130$	1.39149	0.122042
$131$	−3.27067	−0.285760	−0.142880	−	0.989740i	$-0.545636\pi$
$131$	−3.27067	−0.285760	−0.142880	+	0.989740i	$0.545636\pi$
$132$	−1.50195	−0.130728
$133$	−6.77356	−0.587342
$134$	14.0947	1.21759
$135$	1.27844	0.110031
$136$	6.30909	0.541000
$137$	15.9297	1.36096	0.680482	−	0.732765i	$-0.261771\pi$
$137$	15.9297	1.36096	0.680482	+	0.732765i	$0.261771\pi$
$138$	0	0
$139$	−2.85447	−0.242113	−0.121056	−	0.992646i	$-0.538628\pi$
$139$	−2.85447	−0.242113	−0.121056	+	0.992646i	$0.538628\pi$
$140$	0.767766	0.0648881
$141$	−1.48967	−0.125453
$142$	−4.03869	−0.338919
$143$	−9.20178	−0.769491
$144$	−2.62880	−0.219066
$145$	2.65900	0.220818
$146$	−8.69002	−0.719191
$147$	1.68054	0.138608
$148$	−4.67961	−0.384662
$149$	−2.91873	−0.239112	−0.119556	−	0.992827i	$-0.538147\pi$
$149$	−2.91873	−0.239112	−0.119556	+	0.992827i	$0.538147\pi$
$150$	−2.96165	−0.241818
$151$	24.5622	1.99884	0.999421	−	0.0340202i	$-0.0108311\pi$
$151$	24.5622	1.99884	0.999421	+	0.0340202i	$0.0108311\pi$
$152$	3.28887	0.266763
$153$	16.5853	1.34084
$154$	−5.07714	−0.409128
$155$	2.17897	0.175019
$156$	2.27420	0.182081
$157$	−13.1045	−1.04585	−0.522927	−	0.852378i	$-0.675160\pi$
$157$	−13.1045	−1.04585	−0.522927	+	0.852378i	$0.675160\pi$
$158$	2.38398	0.189659
$159$	−3.68454	−0.292203
$160$	−0.372786	−0.0294713
$161$	0	0
$162$	−5.79696	−0.455452
$163$	4.61907	0.361793	0.180897	−	0.983502i	$-0.442100\pi$
$163$	4.61907	0.361793	0.180897	+	0.983502i	$0.442100\pi$
$164$	−4.78084	−0.373321
$165$	−0.559905	−0.0435886
$166$	−4.23705	−0.328859
$167$	−3.93949	−0.304847	−0.152424	−	0.988315i	$-0.548708\pi$
$167$	−3.93949	−0.304847	−0.152424	+	0.988315i	$0.548708\pi$
$168$	1.25480	0.0968102
$169$	0.932979	0.0717677
$170$	2.35194	0.180385
$171$	8.64578	0.661160
$172$	−11.1379	−0.849256
$173$	19.0007	1.44460	0.722298	−	0.691582i	$-0.243086\pi$
$173$	19.0007	1.44460	0.722298	+	0.691582i	$0.243086\pi$
$174$	4.34575	0.329450
$175$	−10.0115	−0.756796
$176$	2.46519	0.185820
$177$	7.19544	0.540842
$178$	9.03115	0.676914
$179$	2.39943	0.179342	0.0896708	−	0.995971i	$-0.471419\pi$
$179$	2.39943	0.179342	0.0896708	+	0.995971i	$0.471419\pi$
$180$	−0.979978	−0.0730432
$181$	26.0063	1.93304	0.966518	−	0.256600i	$-0.0826024\pi$
$181$	26.0063	1.93304	0.966518	+	0.256600i	$0.0826024\pi$
$182$	7.68762	0.569844
$183$	−1.02768	−0.0759681
$184$	0	0
$185$	−1.74449	−0.128258
$186$	3.56122	0.261121
$187$	−15.5531	−1.13735
$188$	2.44502	0.178322
$189$	7.06303	0.513760
$190$	1.22605	0.0889467
$191$	−10.4691	−0.757521	−0.378760	−	0.925495i	$-0.623650\pi$
$191$	−10.4691	−0.757521	−0.378760	+	0.925495i	$0.623650\pi$
$192$	−0.609264	−0.0439699
$193$	0.771242	0.0555152	0.0277576	−	0.999615i	$-0.491163\pi$
$193$	0.771242	0.0555152	0.0277576	+	0.999615i	$0.491163\pi$
$194$	11.3067	0.811773
$195$	0.847787	0.0607113
$196$	−2.75831	−0.197022
$197$	5.20731	0.371005	0.185503	−	0.982644i	$-0.440609\pi$
$197$	5.20731	0.371005	0.185503	+	0.982644i	$0.440609\pi$
$198$	6.48047	0.460547
$199$	−23.3427	−1.65472	−0.827361	−	0.561670i	$-0.810159\pi$
$199$	−23.3427	−1.65472	−0.827361	+	0.561670i	$0.810159\pi$
$200$	4.86103	0.343727
$201$	8.58738	0.605707
$202$	8.05177	0.566520
$203$	14.6902	1.03105
$204$	3.84391	0.269127
$205$	−1.78223	−0.124476
$206$	14.7518	1.02781
$207$	0	0
$208$	−3.73269	−0.258816
$209$	−8.10769	−0.560821
$210$	0.467772	0.0322794
$211$	−8.69603	−0.598659	−0.299330	−	0.954150i	$-0.596763\pi$
$211$	−8.69603	−0.598659	−0.299330	+	0.954150i	$0.596763\pi$
$212$	6.04752	0.415345
$213$	−2.46063	−0.168600
$214$	6.68158	0.456743
$215$	−4.15204	−0.283167
$216$	−3.42943	−0.233343
$217$	12.0382	0.817208
$218$	4.07970	0.276312
$219$	−5.29452	−0.357771
$220$	0.918986	0.0619580
$221$	23.5499	1.58414
$222$	−2.85112	−0.191355
$223$	−3.84115	−0.257223	−0.128611	−	0.991695i	$-0.541052\pi$
$223$	−3.84115	−0.257223	−0.128611	+	0.991695i	$0.541052\pi$
$224$	−2.05954	−0.137609
$225$	12.7787	0.851911
$226$	−5.58523	−0.371524
$227$	2.03403	0.135003	0.0675016	−	0.997719i	$-0.478497\pi$
$227$	2.03403	0.135003	0.0675016	+	0.997719i	$0.478497\pi$
$228$	2.00379	0.132705
$229$	27.4406	1.81333	0.906664	−	0.421853i	$-0.138620\pi$
$229$	27.4406	1.81333	0.906664	+	0.421853i	$0.138620\pi$
$230$	0	0
$231$	−3.09332	−0.203526
$232$	−7.13278	−0.468290
$233$	7.04480	0.461520	0.230760	−	0.973011i	$-0.425879\pi$
$233$	7.04480	0.461520	0.230760	+	0.973011i	$0.425879\pi$
$234$	−9.81249	−0.641462
$235$	0.911470	0.0594577
$236$	−11.8100	−0.768768
$237$	1.45247	0.0943482
$238$	12.9938	0.842264
$239$	26.0807	1.68702	0.843510	−	0.537113i	$-0.180485\pi$
$239$	26.0807	1.68702	0.843510	+	0.537113i	$0.180485\pi$
$240$	−0.227125	−0.0146609
$241$	1.39021	0.0895515	0.0447757	−	0.998997i	$-0.485743\pi$
$241$	1.39021	0.0895515	0.0447757	+	0.998997i	$0.485743\pi$
$242$	4.92286	0.316453
$243$	−13.8202	−0.886564
$244$	1.68675	0.107983
$245$	−1.02826	−0.0656929
$246$	−2.91280	−0.185713
$247$	12.2764	0.781126
$248$	−5.84511	−0.371165
$249$	−2.58148	−0.163595
$250$	3.67605	0.232494
$251$	26.0912	1.64686	0.823431	−	0.567416i	$-0.192057\pi$
$251$	26.0912	1.64686	0.823431	+	0.567416i	$0.192057\pi$
$252$	−5.41411	−0.341057
$253$	0	0
$254$	7.54884	0.473656
$255$	1.43295	0.0897350
$256$	1.00000	0.0625000
$257$	−27.9953	−1.74630	−0.873149	−	0.487453i	$-0.837926\pi$
$257$	−27.9953	−1.74630	−0.873149	+	0.487453i	$0.837926\pi$
$258$	−6.78592	−0.422473
$259$	−9.63783	−0.598866
$260$	−1.39149	−0.0862968
$261$	−18.7506	−1.16063
$262$	3.27067	0.202063
$263$	9.43346	0.581692	0.290846	−	0.956770i	$-0.406063\pi$
$263$	9.43346	0.581692	0.290846	+	0.956770i	$0.406063\pi$
$264$	1.50195	0.0924387
$265$	2.25443	0.138488
$266$	6.77356	0.415314
$267$	5.50236	0.336739
$268$	−14.0947	−0.860969
$269$	17.3711	1.05914	0.529568	−	0.848268i	$-0.322354\pi$
$269$	17.3711	1.05914	0.529568	+	0.848268i	$0.322354\pi$
$270$	−1.27844	−0.0778034
$271$	17.9046	1.08763	0.543813	−	0.839206i	$-0.316980\pi$
$271$	17.9046	1.08763	0.543813	+	0.839206i	$0.316980\pi$
$272$	−6.30909	−0.382545
$273$	4.68379	0.283476
$274$	−15.9297	−0.962346
$275$	−11.9833	−0.722623
$276$	0	0
$277$	−15.2821	−0.918212	−0.459106	−	0.888382i	$-0.651830\pi$
$277$	−15.2821	−0.918212	−0.459106	+	0.888382i	$0.651830\pi$
$278$	2.85447	0.171200
$279$	−15.3656	−0.919915
$280$	−0.767766	−0.0458828
$281$	5.92708	0.353580	0.176790	−	0.984249i	$-0.443429\pi$
$281$	5.92708	0.353580	0.176790	+	0.984249i	$0.443429\pi$
$282$	1.48967	0.0887083
$283$	1.56356	0.0929440	0.0464720	−	0.998920i	$-0.485202\pi$
$283$	1.56356	0.0929440	0.0464720	+	0.998920i	$0.485202\pi$
$284$	4.03869	0.239652
$285$	0.746986	0.0442476
$286$	9.20178	0.544113
$287$	−9.84632	−0.581210
$288$	2.62880	0.154903
$289$	22.8046	1.34145
$290$	−2.65900	−0.156142
$291$	6.88876	0.403826
$292$	8.69002	0.508545
$293$	2.05817	0.120239	0.0601197	−	0.998191i	$-0.480852\pi$
$293$	2.05817	0.120239	0.0601197	+	0.998191i	$0.480852\pi$
$294$	−1.68054	−0.0980109
$295$	−4.40261	−0.256330
$296$	4.67961	0.271997
$297$	8.45417	0.490561
$298$	2.91873	0.169078
$299$	0	0
$300$	2.96165	0.170991
$301$	−22.9389	−1.32218
$302$	−24.5622	−1.41339
$303$	4.90566	0.281823
$304$	−3.28887	−0.188630
$305$	0.628797	0.0360048
$306$	−16.5853	−0.948120
$307$	10.8341	0.618333	0.309167	−	0.951008i	$-0.399950\pi$
$307$	10.8341	0.618333	0.309167	+	0.951008i	$0.399950\pi$
$308$	5.07714	0.289297
$309$	8.98778	0.511297
$310$	−2.17897	−0.123757
$311$	−22.8972	−1.29838	−0.649191	−	0.760625i	$-0.724893\pi$
$311$	−22.8972	−1.29838	−0.649191	+	0.760625i	$0.724893\pi$
$312$	−2.27420	−0.128751
$313$	−23.3481	−1.31971	−0.659856	−	0.751392i	$-0.729383\pi$
$313$	−23.3481	−1.31971	−0.659856	+	0.751392i	$0.729383\pi$
$314$	13.1045	0.739530
$315$	−2.01830	−0.113718
$316$	−2.38398	−0.134109
$317$	0.503430	0.0282754	0.0141377	−	0.999900i	$-0.495500\pi$
$317$	0.503430	0.0282754	0.0141377	+	0.999900i	$0.495500\pi$
$318$	3.68454	0.206619
$319$	17.5836	0.984494
$320$	0.372786	0.0208393
$321$	4.07085	0.227213
$322$	0	0
$323$	20.7498	1.15455
$324$	5.79696	0.322053
$325$	18.1447	1.00649
$326$	−4.61907	−0.255827
$327$	2.48562	0.137455
$328$	4.78084	0.263978
$329$	5.03562	0.277623
$330$	0.559905	0.0308218
$331$	20.2032	1.11047	0.555235	−	0.831694i	$-0.312628\pi$
$331$	20.2032	1.11047	0.555235	+	0.831694i	$0.312628\pi$
$332$	4.23705	0.232538
$333$	12.3017	0.674131
$334$	3.93949	0.215559
$335$	−5.25429	−0.287072
$336$	−1.25480	−0.0684551
$337$	4.10576	0.223655	0.111827	−	0.993728i	$-0.464330\pi$
$337$	4.10576	0.223655	0.111827	+	0.993728i	$0.464330\pi$
$338$	−0.932979	−0.0507474
$339$	−3.40288	−0.184819
$340$	−2.35194	−0.127552
$341$	14.4093	0.780307
$342$	−8.64578	−0.467510
$343$	−20.0976	−1.08517
$344$	11.1379	0.600515
$345$	0	0
$346$	−19.0007	−1.02148
$347$	24.4155	1.31069	0.655347	−	0.755328i	$-0.272522\pi$
$347$	24.4155	1.31069	0.655347	+	0.755328i	$0.272522\pi$
$348$	−4.34575	−0.232957
$349$	17.2951	0.925785	0.462893	−	0.886414i	$-0.346812\pi$
$349$	17.2951	0.925785	0.462893	+	0.886414i	$0.346812\pi$
$350$	10.0115	0.535136
$351$	−12.8010	−0.683266
$352$	−2.46519	−0.131395
$353$	−9.57877	−0.509827	−0.254913	−	0.966964i	$-0.582047\pi$
$353$	−9.57877	−0.509827	−0.254913	+	0.966964i	$0.582047\pi$
$354$	−7.19544	−0.382433
$355$	1.50557	0.0799071
$356$	−9.03115	−0.478650
$357$	7.91667	0.418994
$358$	−2.39943	−0.126814
$359$	0.125276	0.00661183	0.00330591	−	0.999995i	$-0.498948\pi$
$359$	0.125276	0.00661183	0.00330591	+	0.999995i	$0.498948\pi$
$360$	0.979978	0.0516494
$361$	−8.18330	−0.430700
$362$	−26.0063	−1.36686
$363$	2.99932	0.157424
$364$	−7.68762	−0.402941
$365$	3.23952	0.169564
$366$	1.02768	0.0537176
$367$	−4.23470	−0.221050	−0.110525	−	0.993873i	$-0.535253\pi$
$367$	−4.23470	−0.221050	−0.110525	+	0.993873i	$0.535253\pi$
$368$	0	0
$369$	12.5679	0.654257
$370$	1.74449	0.0906918
$371$	12.4551	0.646636
$372$	−3.56122	−0.184641
$373$	−0.626453	−0.0324365	−0.0162183	−	0.999868i	$-0.505163\pi$
$373$	−0.626453	−0.0324365	−0.0162183	+	0.999868i	$0.505163\pi$
$374$	15.5531	0.804231
$375$	2.23969	0.115657
$376$	−2.44502	−0.126093
$377$	−26.6245	−1.37123
$378$	−7.06303	−0.363283
$379$	−10.5210	−0.540427	−0.270214	−	0.962800i	$-0.587094\pi$
$379$	−10.5210	−0.540427	−0.270214	+	0.962800i	$0.587094\pi$
$380$	−1.22605	−0.0628948
$381$	4.59924	0.235626
$382$	10.4691	0.535648
$383$	−15.3699	−0.785364	−0.392682	−	0.919674i	$-0.628453\pi$
$383$	−15.3699	−0.785364	−0.392682	+	0.919674i	$0.628453\pi$
$384$	0.609264	0.0310914
$385$	1.89269	0.0964602
$386$	−0.771242	−0.0392552
$387$	29.2792	1.48835
$388$	−11.3067	−0.574010
$389$	21.7347	1.10200	0.550998	−	0.834507i	$-0.314247\pi$
$389$	21.7347	1.10200	0.550998	+	0.834507i	$0.314247\pi$
$390$	−0.847787	−0.0429294
$391$	0	0
$392$	2.75831	0.139315
$393$	1.99270	0.100519
$394$	−5.20731	−0.262340
$395$	−0.888712	−0.0447160
$396$	−6.48047	−0.325656
$397$	10.1590	0.509866	0.254933	−	0.966959i	$-0.417947\pi$
$397$	10.1590	0.509866	0.254933	+	0.966959i	$0.417947\pi$
$398$	23.3427	1.17007
$399$	4.12689	0.206603
$400$	−4.86103	−0.243052
$401$	−31.8980	−1.59291	−0.796456	−	0.604696i	$-0.793294\pi$
$401$	−31.8980	−1.59291	−0.796456	+	0.604696i	$0.793294\pi$
$402$	−8.58738	−0.428300
$403$	−21.8180	−1.08683
$404$	−8.05177	−0.400590
$405$	2.16102	0.107382
$406$	−14.6902	−0.729064
$407$	−11.5361	−0.571824
$408$	−3.84391	−0.190302
$409$	−13.2147	−0.653424	−0.326712	−	0.945124i	$-0.605941\pi$
$409$	−13.2147	−0.653424	−0.326712	+	0.945124i	$0.605941\pi$
$410$	1.78223	0.0880180
$411$	−9.70538	−0.478731
$412$	−14.7518	−0.726771
$413$	−24.3232	−1.19687
$414$	0	0
$415$	1.57951	0.0775351
$416$	3.73269	0.183010
$417$	1.73913	0.0851654
$418$	8.10769	0.396560
$419$	4.20296	0.205328	0.102664	−	0.994716i	$-0.467263\pi$
$419$	4.20296	0.205328	0.102664	+	0.994716i	$0.467263\pi$
$420$	−0.467772	−0.0228250
$421$	7.03533	0.342881	0.171440	−	0.985194i	$-0.445158\pi$
$421$	7.03533	0.342881	0.171440	+	0.985194i	$0.445158\pi$
$422$	8.69603	0.423316
$423$	−6.42747	−0.312514
$424$	−6.04752	−0.293694
$425$	30.6687	1.48765
$426$	2.46063	0.119218
$427$	3.47393	0.168115
$428$	−6.68158	−0.322966
$429$	5.60632	0.270676
$430$	4.15204	0.200229
$431$	36.8195	1.77353	0.886766	−	0.462219i	$-0.152947\pi$
$431$	36.8195	1.77353	0.886766	+	0.462219i	$0.152947\pi$
$432$	3.42943	0.164998
$433$	−27.2275	−1.30847	−0.654235	−	0.756291i	$-0.727009\pi$
$433$	−27.2275	−1.30847	−0.654235	+	0.756291i	$0.727009\pi$
$434$	−12.0382	−0.577854
$435$	−1.62003	−0.0776746
$436$	−4.07970	−0.195382
$437$	0	0
$438$	5.29452	0.252982
$439$	−24.1877	−1.15441	−0.577207	−	0.816598i	$-0.695857\pi$
$439$	−24.1877	−1.15441	−0.577207	+	0.816598i	$0.695857\pi$
$440$	−0.918986	−0.0438109
$441$	7.25102	0.345287
$442$	−23.5499	−1.12015
$443$	15.4275	0.732982	0.366491	−	0.930422i	$-0.380559\pi$
$443$	15.4275	0.732982	0.366491	+	0.930422i	$0.380559\pi$
$444$	2.85112	0.135308
$445$	−3.36668	−0.159596
$446$	3.84115	0.181884
$447$	1.77828	0.0841097
$448$	2.05954	0.0973040
$449$	17.3241	0.817574	0.408787	−	0.912630i	$-0.365952\pi$
$449$	17.3241	0.817574	0.408787	+	0.912630i	$0.365952\pi$
$450$	−12.7787	−0.602392
$451$	−11.7857	−0.554965
$452$	5.58523	0.262707
$453$	−14.9649	−0.703111
$454$	−2.03403	−0.0954617
$455$	−2.86583	−0.134352
$456$	−2.00379	−0.0938363
$457$	−6.86896	−0.321317	−0.160658	−	0.987010i	$-0.551362\pi$
$457$	−6.86896	−0.321317	−0.160658	+	0.987010i	$0.551362\pi$
$458$	−27.4406	−1.28222
$459$	−21.6366	−1.00991
$460$	0	0
$461$	−0.341091	−0.0158862	−0.00794309	−	0.999968i	$-0.502528\pi$
$461$	−0.341091	−0.0158862	−0.00794309	+	0.999968i	$0.502528\pi$
$462$	3.09332	0.143914
$463$	16.3184	0.758378	0.379189	−	0.925319i	$-0.376203\pi$
$463$	16.3184	0.758378	0.379189	+	0.925319i	$0.376203\pi$
$464$	7.13278	0.331131
$465$	−1.32757	−0.0615647
$466$	−7.04480	−0.326344
$467$	−36.2344	−1.67673	−0.838365	−	0.545109i	$-0.816488\pi$
$467$	−36.2344	−1.67673	−0.838365	+	0.545109i	$0.816488\pi$
$468$	9.81249	0.453582
$469$	−29.0285	−1.34041
$470$	−0.911470	−0.0420430
$471$	7.98411	0.367888
$472$	11.8100	0.543601
$473$	−27.4570	−1.26247
$474$	−1.45247	−0.0667143
$475$	15.9873	0.733549
$476$	−12.9938	−0.595570
$477$	−15.8977	−0.727906
$478$	−26.0807	−1.19290
$479$	−12.7557	−0.582823	−0.291411	−	0.956598i	$-0.594125\pi$
$479$	−12.7557	−0.582823	−0.291411	+	0.956598i	$0.594125\pi$
$480$	0.227125	0.0103668
$481$	17.4675	0.796451
$482$	−1.39021	−0.0633224
$483$	0	0
$484$	−4.92286	−0.223766
$485$	−4.21497	−0.191392
$486$	13.8202	0.626895
$487$	33.5403	1.51985	0.759927	−	0.650008i	$-0.225235\pi$
$487$	33.5403	1.51985	0.759927	+	0.650008i	$0.225235\pi$
$488$	−1.68675	−0.0763557
$489$	−2.81423	−0.127264
$490$	1.02826	0.0464519
$491$	−36.8776	−1.66426	−0.832132	−	0.554577i	$-0.812880\pi$
$491$	−36.8776	−1.66426	−0.832132	+	0.554577i	$0.812880\pi$
$492$	2.91280	0.131319
$493$	−45.0014	−2.02676
$494$	−12.2764	−0.552339
$495$	−2.41583	−0.108583
$496$	5.84511	0.262453
$497$	8.31783	0.373106
$498$	2.58148	0.115679
$499$	1.81660	0.0813223	0.0406611	−	0.999173i	$-0.487054\pi$
$499$	1.81660	0.0813223	0.0406611	+	0.999173i	$0.487054\pi$
$500$	−3.67605	−0.164398
$501$	2.40019	0.107233
$502$	−26.0912	−1.16451
$503$	−43.2260	−1.92735	−0.963676	−	0.267076i	$-0.913943\pi$
$503$	−43.2260	−1.92735	−0.963676	+	0.267076i	$0.913943\pi$
$504$	5.41411	0.241163
$505$	−3.00158	−0.133569
$506$	0	0
$507$	−0.568431	−0.0252449
$508$	−7.54884	−0.334926
$509$	23.6091	1.04646	0.523228	−	0.852193i	$-0.324728\pi$
$509$	23.6091	1.04646	0.523228	+	0.852193i	$0.324728\pi$
$510$	−1.43295	−0.0634522
$511$	17.8974	0.791736
$512$	−1.00000	−0.0441942
$513$	−11.2790	−0.497978
$514$	27.9953	1.23482
$515$	−5.49928	−0.242327
$516$	6.78592	0.298733
$517$	6.02744	0.265087
$518$	9.63783	0.423462
$519$	−11.5765	−0.508150
$520$	1.39149	0.0610210
$521$	13.2531	0.580627	0.290314	−	0.956932i	$-0.406240\pi$
$521$	13.2531	0.580627	0.290314	+	0.956932i	$0.406240\pi$
$522$	18.7506	0.820693
$523$	−16.5018	−0.721572	−0.360786	−	0.932649i	$-0.617491\pi$
$523$	−16.5018	−0.721572	−0.360786	+	0.932649i	$0.617491\pi$
$524$	−3.27067	−0.142880
$525$	6.09964	0.266210
$526$	−9.43346	−0.411318
$527$	−36.8774	−1.60640
$528$	−1.50195	−0.0653640
$529$	0	0
$530$	−2.25443	−0.0979261
$531$	31.0462	1.34729
$532$	−6.77356	−0.293671
$533$	17.8454	0.772970
$534$	−5.50236	−0.238110
$535$	−2.49080	−0.107686
$536$	14.0947	0.608797
$537$	−1.46189	−0.0630850
$538$	−17.3711	−0.748922
$539$	−6.79974	−0.292885
$540$	1.27844	0.0550153
$541$	−17.5752	−0.755615	−0.377808	−	0.925884i	$-0.623322\pi$
$541$	−17.5752	−0.755615	−0.377808	+	0.925884i	$0.623322\pi$
$542$	−17.9046	−0.769068
$543$	−15.8447	−0.679963
$544$	6.30909	0.270500
$545$	−1.52085	−0.0651462
$546$	−4.68379	−0.200448
$547$	−16.7827	−0.717576	−0.358788	−	0.933419i	$-0.616810\pi$
$547$	−16.7827	−0.717576	−0.358788	+	0.933419i	$0.616810\pi$
$548$	15.9297	0.680482
$549$	−4.43413	−0.189244
$550$	11.9833	0.510972
$551$	−23.4588	−0.999379
$552$	0	0
$553$	−4.90989	−0.208790
$554$	15.2821	0.649274
$555$	1.06286	0.0451157
$556$	−2.85447	−0.121056
$557$	−7.07870	−0.299934	−0.149967	−	0.988691i	$-0.547917\pi$
$557$	−7.07870	−0.299934	−0.149967	+	0.988691i	$0.547917\pi$
$558$	15.3656	0.650478
$559$	41.5743	1.75841
$560$	0.767766	0.0324440
$561$	9.47594	0.400075
$562$	−5.92708	−0.250019
$563$	21.1902	0.893061	0.446530	−	0.894769i	$-0.352660\pi$
$563$	21.1902	0.893061	0.446530	+	0.894769i	$0.352660\pi$
$564$	−1.48967	−0.0627263
$565$	2.08209	0.0875944
$566$	−1.56356	−0.0657213
$567$	11.9391	0.501393
$568$	−4.03869	−0.169460
$569$	−13.2182	−0.554134	−0.277067	−	0.960851i	$-0.589362\pi$
$569$	−13.2182	−0.554134	−0.277067	+	0.960851i	$0.589362\pi$
$570$	−0.746986	−0.0312878
$571$	22.5366	0.943126	0.471563	−	0.881832i	$-0.343690\pi$
$571$	22.5366	0.943126	0.471563	+	0.881832i	$0.343690\pi$
$572$	−9.20178	−0.384746
$573$	6.37848	0.266465
$574$	9.84632	0.410978
$575$	0	0
$576$	−2.62880	−0.109533
$577$	−14.7870	−0.615592	−0.307796	−	0.951452i	$-0.599591\pi$
$577$	−14.7870	−0.615592	−0.307796	+	0.951452i	$0.599591\pi$
$578$	−22.8046	−0.948548
$579$	−0.469890	−0.0195280
$580$	2.65900	0.110409
$581$	8.72636	0.362030
$582$	−6.88876	−0.285548
$583$	14.9083	0.617437
$584$	−8.69002	−0.359596
$585$	3.65795	0.151238
$586$	−2.05817	−0.0850221
$587$	15.2561	0.629689	0.314844	−	0.949143i	$-0.398048\pi$
$587$	15.2561	0.629689	0.314844	+	0.949143i	$0.398048\pi$
$588$	1.68054	0.0693042
$589$	−19.2238	−0.792105
$590$	4.40261	0.181253
$591$	−3.17263	−0.130504
$592$	−4.67961	−0.192331
$593$	−3.71324	−0.152484	−0.0762422	−	0.997089i	$-0.524292\pi$
$593$	−3.71324	−0.152484	−0.0762422	+	0.997089i	$0.524292\pi$
$594$	−8.45417	−0.346879
$595$	−4.84391	−0.198581
$596$	−2.91873	−0.119556
$597$	14.2219	0.582063
$598$	0	0
$599$	−8.17752	−0.334124	−0.167062	−	0.985946i	$-0.553428\pi$
$599$	−8.17752	−0.334124	−0.167062	+	0.985946i	$0.553428\pi$
$600$	−2.96165	−0.120909
$601$	34.4600	1.40565	0.702825	−	0.711362i	$-0.251921\pi$
$601$	34.4600	1.40565	0.702825	+	0.711362i	$0.251921\pi$
$602$	22.9389	0.934920
$603$	37.0520	1.50887
$604$	24.5622	0.999421
$605$	−1.83517	−0.0746103
$606$	−4.90566	−0.199279
$607$	19.0695	0.774009	0.387005	−	0.922078i	$-0.373510\pi$
$607$	19.0695	0.774009	0.387005	+	0.922078i	$0.373510\pi$
$608$	3.28887	0.133381
$609$	−8.95023	−0.362682
$610$	−0.628797	−0.0254592
$611$	−9.12652	−0.369219
$612$	16.5853	0.670422
$613$	11.8822	0.479916	0.239958	−	0.970783i	$-0.422866\pi$
$613$	11.8822	0.479916	0.239958	+	0.970783i	$0.422866\pi$
$614$	−10.8341	−0.437228
$615$	1.08585	0.0437856
$616$	−5.07714	−0.204564
$617$	−10.7162	−0.431418	−0.215709	−	0.976458i	$-0.569206\pi$
$617$	−10.7162	−0.431418	−0.215709	+	0.976458i	$0.569206\pi$
$618$	−8.98778	−0.361541
$619$	−5.74573	−0.230940	−0.115470	−	0.993311i	$-0.536837\pi$
$619$	−5.74573	−0.230940	−0.115470	+	0.993311i	$0.536837\pi$
$620$	2.17897	0.0875097
$621$	0	0
$622$	22.8972	0.918095
$623$	−18.6000	−0.745193
$624$	2.27420	0.0910407
$625$	22.9348	0.917391
$626$	23.3481	0.933177
$627$	4.93973	0.197274
$628$	−13.1045	−0.522927
$629$	29.5241	1.17720
$630$	2.01830	0.0804110
$631$	−13.7296	−0.546568	−0.273284	−	0.961933i	$-0.588110\pi$
$631$	−13.7296	−0.546568	−0.273284	+	0.961933i	$0.588110\pi$
$632$	2.38398	0.0948295
$633$	5.29818	0.210584
$634$	−0.503430	−0.0199938
$635$	−2.81410	−0.111674
$636$	−3.68454	−0.146102
$637$	10.2959	0.407938
$638$	−17.5836	−0.696143
$639$	−10.6169	−0.419998
$640$	−0.372786	−0.0147356
$641$	36.2879	1.43328	0.716642	−	0.697441i	$-0.245678\pi$
$641$	36.2879	1.43328	0.716642	+	0.697441i	$0.245678\pi$
$642$	−4.07085	−0.160664
$643$	−14.8477	−0.585535	−0.292768	−	0.956184i	$-0.594576\pi$
$643$	−14.8477	−0.585535	−0.292768	+	0.956184i	$0.594576\pi$
$644$	0	0
$645$	2.52969	0.0996066
$646$	−20.7498	−0.816390
$647$	1.91936	0.0754578	0.0377289	−	0.999288i	$-0.487988\pi$
$647$	1.91936	0.0754578	0.0377289	+	0.999288i	$0.487988\pi$
$648$	−5.79696	−0.227726
$649$	−29.1139	−1.14282
$650$	−18.1447	−0.711695
$651$	−7.33447	−0.287460
$652$	4.61907	0.180897
$653$	−23.8874	−0.934785	−0.467392	−	0.884050i	$-0.654806\pi$
$653$	−23.8874	−0.934785	−0.467392	+	0.884050i	$0.654806\pi$
$654$	−2.48562	−0.0971953
$655$	−1.21926	−0.0476404
$656$	−4.78084	−0.186660
$657$	−22.8443	−0.891241
$658$	−5.03562	−0.196309
$659$	−1.74417	−0.0679431	−0.0339716	−	0.999423i	$-0.510816\pi$
$659$	−1.74417	−0.0679431	−0.0339716	+	0.999423i	$0.510816\pi$
$660$	−0.559905	−0.0217943
$661$	30.7040	1.19425	0.597124	−	0.802149i	$-0.296310\pi$
$661$	30.7040	1.19425	0.597124	+	0.802149i	$0.296310\pi$
$662$	−20.2032	−0.785221
$663$	−14.3481	−0.557234
$664$	−4.23705	−0.164429
$665$	−2.52509	−0.0979186
$666$	−12.3017	−0.476683
$667$	0	0
$668$	−3.93949	−0.152424
$669$	2.34028	0.0904804
$670$	5.25429	0.202991
$671$	4.15816	0.160524
$672$	1.25480	0.0484051
$673$	11.7825	0.454181	0.227091	−	0.973874i	$-0.427079\pi$
$673$	11.7825	0.454181	0.227091	+	0.973874i	$0.427079\pi$
$674$	−4.10576	−0.158148
$675$	−16.6705	−0.641650
$676$	0.932979	0.0358838
$677$	28.5452	1.09708	0.548541	−	0.836124i	$-0.315183\pi$
$677$	28.5452	1.09708	0.548541	+	0.836124i	$0.315183\pi$
$678$	3.40288	0.130687
$679$	−23.2865	−0.893655
$680$	2.35194	0.0901927
$681$	−1.23926	−0.0474886
$682$	−14.4093	−0.551760
$683$	15.0197	0.574712	0.287356	−	0.957824i	$-0.407224\pi$
$683$	15.0197	0.574712	0.287356	+	0.957824i	$0.407224\pi$
$684$	8.64578	0.330580
$685$	5.93835	0.226893
$686$	20.0976	0.767330
$687$	−16.7186	−0.637855
$688$	−11.1379	−0.424628
$689$	−22.5735	−0.859983
$690$	0	0
$691$	20.7588	0.789701	0.394851	−	0.918745i	$-0.370796\pi$
$691$	20.7588	0.789701	0.394851	+	0.918745i	$0.370796\pi$
$692$	19.0007	0.722298
$693$	−13.3468	−0.507002
$694$	−24.4155	−0.926801
$695$	−1.06410	−0.0403638
$696$	4.34575	0.164725
$697$	30.1628	1.14250
$698$	−17.2951	−0.654629
$699$	−4.29215	−0.162344
$700$	−10.0115	−0.378398
$701$	23.8262	0.899902	0.449951	−	0.893053i	$-0.351441\pi$
$701$	23.8262	0.899902	0.449951	+	0.893053i	$0.351441\pi$
$702$	12.8010	0.483142
$703$	15.3906	0.580469
$704$	2.46519	0.0929102
$705$	−0.555326	−0.0209148
$706$	9.57877	0.360502
$707$	−16.5829	−0.623665
$708$	7.19544	0.270421
$709$	−18.2057	−0.683731	−0.341865	−	0.939749i	$-0.611059\pi$
$709$	−18.2057	−0.683731	−0.341865	+	0.939749i	$0.611059\pi$
$710$	−1.50557	−0.0565029
$711$	6.26699	0.235031
$712$	9.03115	0.338457
$713$	0	0
$714$	−7.91667	−0.296274
$715$	−3.43029	−0.128286
$716$	2.39943	0.0896708
$717$	−15.8900	−0.593425
$718$	−0.125276	−0.00467527
$719$	−12.5234	−0.467043	−0.233521	−	0.972352i	$-0.575025\pi$
$719$	−12.5234	−0.467043	−0.233521	+	0.972352i	$0.575025\pi$
$720$	−0.979978	−0.0365216
$721$	−30.3820	−1.13148
$722$	8.18330	0.304551
$723$	−0.847007	−0.0315005
$724$	26.0063	0.966518
$725$	−34.6727	−1.28771
$726$	−2.99932	−0.111315
$727$	−12.3982	−0.459823	−0.229911	−	0.973212i	$-0.573844\pi$
$727$	−12.3982	−0.459823	−0.229911	+	0.973212i	$0.573844\pi$
$728$	7.68762	0.284922
$729$	−8.97076	−0.332250
$730$	−3.23952	−0.119900
$731$	70.2700	2.59903
$732$	−1.02768	−0.0379841
$733$	−16.4066	−0.605992	−0.302996	−	0.952992i	$-0.597987\pi$
$733$	−16.4066	−0.605992	−0.302996	+	0.952992i	$0.597987\pi$
$734$	4.23470	0.156306
$735$	0.626480	0.0231081
$736$	0	0
$737$	−34.7460	−1.27988
$738$	−12.5679	−0.462629
$739$	−42.2265	−1.55333	−0.776663	−	0.629916i	$-0.783089\pi$
$739$	−42.2265	−1.55333	−0.776663	+	0.629916i	$0.783089\pi$
$740$	−1.74449	−0.0641288
$741$	−7.47954	−0.274768
$742$	−12.4551	−0.457241
$743$	−14.4754	−0.531052	−0.265526	−	0.964104i	$-0.585546\pi$
$743$	−14.4754	−0.531052	−0.265526	+	0.964104i	$0.585546\pi$
$744$	3.56122	0.130561
$745$	−1.08806	−0.0398635
$746$	0.626453	0.0229361
$747$	−11.1383	−0.407530
$748$	−15.5531	−0.568677
$749$	−13.7610	−0.502814
$750$	−2.23969	−0.0817818
$751$	−29.1984	−1.06547	−0.532733	−	0.846283i	$-0.678835\pi$
$751$	−29.1984	−1.06547	−0.532733	+	0.846283i	$0.678835\pi$
$752$	2.44502	0.0891609
$753$	−15.8964	−0.579299
$754$	26.6245	0.969606
$755$	9.15643	0.333237
$756$	7.06303	0.256880
$757$	−16.3495	−0.594233	−0.297116	−	0.954841i	$-0.596025\pi$
$757$	−16.3495	−0.594233	−0.297116	+	0.954841i	$0.596025\pi$
$758$	10.5210	0.382140
$759$	0	0
$760$	1.22605	0.0444733
$761$	−5.10898	−0.185201	−0.0926003	−	0.995703i	$-0.529518\pi$
$761$	−5.10898	−0.185201	−0.0926003	+	0.995703i	$0.529518\pi$
$762$	−4.59924	−0.166613
$763$	−8.40229	−0.304183
$764$	−10.4691	−0.378760
$765$	6.18277	0.223538
$766$	15.3699	0.555336
$767$	44.0832	1.59175
$768$	−0.609264	−0.0219849
$769$	28.6372	1.03269	0.516343	−	0.856382i	$-0.327293\pi$
$769$	28.6372	1.03269	0.516343	+	0.856382i	$0.327293\pi$
$770$	−1.89269	−0.0682077
$771$	17.0565	0.614276
$772$	0.771242	0.0277576
$773$	24.9280	0.896599	0.448299	−	0.893884i	$-0.352030\pi$
$773$	24.9280	0.896599	0.448299	+	0.893884i	$0.352030\pi$
$774$	−29.2792	−1.05242
$775$	−28.4133	−1.02064
$776$	11.3067	0.405886
$777$	5.87199	0.210656
$778$	−21.7347	−0.779228
$779$	15.7236	0.563356
$780$	0.847787	0.0303557
$781$	9.95612	0.356258
$782$	0	0
$783$	24.4613	0.874177
$784$	−2.75831	−0.0985109
$785$	−4.88517	−0.174359
$786$	−1.99270	−0.0710773
$787$	−5.13189	−0.182932	−0.0914660	−	0.995808i	$-0.529155\pi$
$787$	−5.13189	−0.182932	−0.0914660	+	0.995808i	$0.529155\pi$
$788$	5.20731	0.185503
$789$	−5.74747	−0.204615
$790$	0.888712	0.0316190
$791$	11.5030	0.408999
$792$	6.48047	0.230274
$793$	−6.29612	−0.223582
$794$	−10.1590	−0.360530
$795$	−1.37354	−0.0487146
$796$	−23.3427	−0.827361
$797$	−9.52437	−0.337371	−0.168685	−	0.985670i	$-0.553952\pi$
$797$	−9.52437	−0.337371	−0.168685	+	0.985670i	$0.553952\pi$
$798$	−4.12689	−0.146090
$799$	−15.4259	−0.545729
$800$	4.86103	0.171863
$801$	23.7411	0.838849
$802$	31.8980	1.12636
$803$	21.4225	0.755985
$804$	8.58738	0.302854
$805$	0	0
$806$	21.8180	0.768506
$807$	−10.5836	−0.372560
$808$	8.05177	0.283260
$809$	−10.6104	−0.373042	−0.186521	−	0.982451i	$-0.559721\pi$
$809$	−10.6104	−0.373042	−0.186521	+	0.982451i	$0.559721\pi$
$810$	−2.16102	−0.0759307
$811$	−30.8198	−1.08223	−0.541116	−	0.840948i	$-0.681998\pi$
$811$	−30.8198	−1.08223	−0.541116	+	0.840948i	$0.681998\pi$
$812$	14.6902	0.515526
$813$	−10.9086	−0.382582
$814$	11.5361	0.404340
$815$	1.72192	0.0603163
$816$	3.84391	0.134564
$817$	36.6311	1.28156
$818$	13.2147	0.462041
$819$	20.2092	0.706166
$820$	−1.78223	−0.0622381
$821$	42.0134	1.46628	0.733139	−	0.680079i	$-0.238054\pi$
$821$	42.0134	1.46628	0.733139	+	0.680079i	$0.238054\pi$
$822$	9.70538	0.338514
$823$	−28.0616	−0.978165	−0.489082	−	0.872238i	$-0.662668\pi$
$823$	−28.0616	−0.978165	−0.489082	+	0.872238i	$0.662668\pi$
$824$	14.7518	0.513905
$825$	7.30103	0.254189
$826$	24.3232	0.846313
$827$	36.3429	1.26377	0.631883	−	0.775064i	$-0.282282\pi$
$827$	36.3429	1.26377	0.631883	+	0.775064i	$0.282282\pi$
$828$	0	0
$829$	30.0375	1.04325	0.521623	−	0.853176i	$-0.325327\pi$
$829$	30.0375	1.04325	0.521623	+	0.853176i	$0.325327\pi$
$830$	−1.57951	−0.0548256
$831$	9.31083	0.322989
$832$	−3.73269	−0.129408
$833$	17.4024	0.602958
$834$	−1.73913	−0.0602210
$835$	−1.46859	−0.0508225
$836$	−8.10769	−0.280410
$837$	20.0454	0.692870
$838$	−4.20296	−0.145189
$839$	−33.4245	−1.15394	−0.576971	−	0.816765i	$-0.695765\pi$
$839$	−33.4245	−1.15394	−0.576971	+	0.816765i	$0.695765\pi$
$840$	0.467772	0.0161397
$841$	21.8766	0.754364
$842$	−7.03533	−0.242453
$843$	−3.61116	−0.124375
$844$	−8.69603	−0.299330
$845$	0.347801	0.0119647
$846$	6.42747	0.220981
$847$	−10.1388	−0.348374
$848$	6.04752	0.207673
$849$	−0.952622	−0.0326939
$850$	−30.6687	−1.05193
$851$	0	0
$852$	−2.46063	−0.0842998
$853$	5.87395	0.201120	0.100560	−	0.994931i	$-0.467937\pi$
$853$	5.87395	0.201120	0.100560	+	0.994931i	$0.467937\pi$
$854$	−3.47393	−0.118875
$855$	3.22302	0.110225
$856$	6.68158	0.228372
$857$	14.8919	0.508699	0.254349	−	0.967112i	$-0.418139\pi$
$857$	14.8919	0.508699	0.254349	+	0.967112i	$0.418139\pi$
$858$	−5.60632	−0.191396
$859$	−7.91064	−0.269908	−0.134954	−	0.990852i	$-0.543089\pi$
$859$	−7.91064	−0.269908	−0.134954	+	0.990852i	$0.543089\pi$
$860$	−4.15204	−0.141584
$861$	5.99901	0.204446
$862$	−36.8195	−1.25408
$863$	−4.03424	−0.137327	−0.0686636	−	0.997640i	$-0.521874\pi$
$863$	−4.03424	−0.137327	−0.0686636	+	0.997640i	$0.521874\pi$
$864$	−3.42943	−0.116671
$865$	7.08319	0.240836
$866$	27.2275	0.925228
$867$	−13.8941	−0.471867
$868$	12.0382	0.408604
$869$	−5.87695	−0.199362
$870$	1.62003	0.0549243
$871$	52.6110	1.78266
$872$	4.07970	0.138156
$873$	29.7230	1.00597
$874$	0	0
$875$	−7.57096	−0.255945
$876$	−5.29452	−0.178885
$877$	−51.8651	−1.75136	−0.875680	−	0.482892i	$-0.839586\pi$
$877$	−51.8651	−1.75136	−0.875680	+	0.482892i	$0.839586\pi$
$878$	24.1877	0.816294
$879$	−1.25397	−0.0422953
$880$	0.918986	0.0309790
$881$	−32.4415	−1.09298	−0.546491	−	0.837465i	$-0.684037\pi$
$881$	−32.4415	−1.09298	−0.546491	+	0.837465i	$0.684037\pi$
$882$	−7.25102	−0.244155
$883$	−6.65684	−0.224021	−0.112010	−	0.993707i	$-0.535729\pi$
$883$	−6.65684	−0.224021	−0.112010	+	0.993707i	$0.535729\pi$
$884$	23.5499	0.792068
$885$	2.68236	0.0901664
$886$	−15.4275	−0.518297
$887$	42.6040	1.43050	0.715252	−	0.698867i	$-0.246312\pi$
$887$	42.6040	1.43050	0.715252	+	0.698867i	$0.246312\pi$
$888$	−2.85112	−0.0956773
$889$	−15.5471	−0.521434
$890$	3.36668	0.112852
$891$	14.2906	0.478753
$892$	−3.84115	−0.128611
$893$	−8.04138	−0.269094
$894$	−1.77828	−0.0594745
$895$	0.894472	0.0298989
$896$	−2.05954	−0.0688043
$897$	0	0
$898$	−17.3241	−0.578112
$899$	41.6919	1.39050
$900$	12.7787	0.425955
$901$	−38.1544	−1.27111
$902$	11.7857	0.392420
$903$	13.9759	0.465087
$904$	−5.58523	−0.185762
$905$	9.69479	0.322266
$906$	14.9649	0.497174
$907$	34.2518	1.13731	0.568656	−	0.822576i	$-0.307464\pi$
$907$	34.2518	1.13731	0.568656	+	0.822576i	$0.307464\pi$
$908$	2.03403	0.0675016
$909$	21.1665	0.702047
$910$	2.86583	0.0950014
$911$	−35.2535	−1.16800	−0.584001	−	0.811753i	$-0.698514\pi$
$911$	−35.2535	−1.16800	−0.584001	+	0.811753i	$0.698514\pi$
$912$	2.00379	0.0663523
$913$	10.4451	0.345683
$914$	6.86896	0.227205
$915$	−0.383104	−0.0126650
$916$	27.4406	0.906664
$917$	−6.73607	−0.222444
$918$	21.6366	0.714113
$919$	34.5723	1.14043	0.570217	−	0.821494i	$-0.306859\pi$
$919$	34.5723	1.14043	0.570217	+	0.821494i	$0.306859\pi$
$920$	0	0
$921$	−6.60081	−0.217504
$922$	0.341091	0.0112332
$923$	−15.0752	−0.496206
$924$	−3.09332	−0.101763
$925$	22.7477	0.747941
$926$	−16.3184	−0.536254
$927$	38.7796	1.27369
$928$	−7.13278	−0.234145
$929$	30.8336	1.01162	0.505809	−	0.862646i	$-0.331194\pi$
$929$	30.8336	1.01162	0.505809	+	0.862646i	$0.331194\pi$
$930$	1.32757	0.0435328
$931$	9.07172	0.297314
$932$	7.04480	0.230760
$933$	13.9505	0.456718
$934$	36.2344	1.18563
$935$	−5.79797	−0.189614
$936$	−9.81249	−0.320731
$937$	−4.56731	−0.149207	−0.0746037	−	0.997213i	$-0.523769\pi$
$937$	−4.56731	−0.149207	−0.0746037	+	0.997213i	$0.523769\pi$
$938$	29.0285	0.947814
$939$	14.2252	0.464220
$940$	0.911470	0.0297289
$941$	11.5271	0.375773	0.187886	−	0.982191i	$-0.439836\pi$
$941$	11.5271	0.375773	0.187886	+	0.982191i	$0.439836\pi$
$942$	−7.98411	−0.260136
$943$	0	0
$944$	−11.8100	−0.384384
$945$	2.63300	0.0856514
$946$	27.4570	0.892703
$947$	−60.0335	−1.95083	−0.975413	−	0.220386i	$-0.929268\pi$
$947$	−60.0335	−1.95083	−0.975413	+	0.220386i	$0.929268\pi$
$948$	1.45247	0.0471741
$949$	−32.4372	−1.05296
$950$	−15.9873	−0.518697
$951$	−0.306722	−0.00994614
$952$	12.9938	0.421132
$953$	−9.45086	−0.306143	−0.153072	−	0.988215i	$-0.548917\pi$
$953$	−9.45086	−0.306143	−0.153072	+	0.988215i	$0.548917\pi$
$954$	15.8977	0.514707
$955$	−3.90275	−0.126290
$956$	26.0807	0.843510
$957$	−10.7131	−0.346305
$958$	12.7557	0.412118
$959$	32.8077	1.05942
$960$	−0.227125	−0.00733043
$961$	3.16535	0.102108
$962$	−17.4675	−0.563176
$963$	17.5645	0.566008
$964$	1.39021	0.0447757
$965$	0.287508	0.00925520
$966$	0	0
$967$	−39.0760	−1.25660	−0.628300	−	0.777971i	$-0.716249\pi$
$967$	−39.0760	−1.25660	−0.628300	+	0.777971i	$0.716249\pi$
$968$	4.92286	0.158227
$969$	−12.6421	−0.406123
$970$	4.21497	0.135335
$971$	−41.4820	−1.33122	−0.665610	−	0.746299i	$-0.731829\pi$
$971$	−41.4820	−1.33122	−0.665610	+	0.746299i	$0.731829\pi$
$972$	−13.8202	−0.443282
$973$	−5.87888	−0.188468
$974$	−33.5403	−1.07470
$975$	−11.0549	−0.354041
$976$	1.68675	0.0539916
$977$	−20.7125	−0.662651	−0.331326	−	0.943516i	$-0.607496\pi$
$977$	−20.7125	−0.662651	−0.331326	+	0.943516i	$0.607496\pi$
$978$	2.81423	0.0899893
$979$	−22.2635	−0.711544
$980$	−1.02826	−0.0328465
$981$	10.7247	0.342413
$982$	36.8776	1.17681
$983$	−24.8727	−0.793315	−0.396658	−	0.917967i	$-0.629830\pi$
$983$	−24.8727	−0.793315	−0.396658	+	0.917967i	$0.629830\pi$
$984$	−2.91280	−0.0928566
$985$	1.94121	0.0618521
$986$	45.0014	1.43314
$987$	−3.06802	−0.0976563
$988$	12.2764	0.390563
$989$	0	0
$990$	2.41583	0.0767800
$991$	−9.20609	−0.292441	−0.146221	−	0.989252i	$-0.546711\pi$
$991$	−9.20609	−0.292441	−0.146221	+	0.989252i	$0.546711\pi$
$992$	−5.84511	−0.185583
$993$	−12.3091	−0.390618
$994$	−8.31783	−0.263826
$995$	−8.70183	−0.275867
$996$	−2.58148	−0.0817974
$997$	42.7206	1.35298	0.676488	−	0.736454i	$-0.263501\pi$
$997$	42.7206	1.35298	0.676488	+	0.736454i	$0.263501\pi$
$998$	−1.81660	−0.0575035
$999$	−16.0484	−0.507748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1058.2.a.j.1.3		5
3.2	odd	2		9522.2.a.bz.1.3		5
4.3	odd	2		8464.2.a.bu.1.3		5
23.4	even	11		46.2.c.b.39.1	yes	10
23.6	even	11		46.2.c.b.13.1	✓	10
23.22	odd	2		1058.2.a.k.1.3		5
69.29	odd	22		414.2.i.c.289.1		10
69.50	odd	22		414.2.i.c.361.1		10
69.68	even	2		9522.2.a.bw.1.3		5
92.27	odd	22		368.2.m.a.177.1		10
92.75	odd	22		368.2.m.a.289.1		10
92.91	even	2		8464.2.a.bv.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.13.1	✓	10	23.6	even	11
46.2.c.b.39.1	yes	10	23.4	even	11
368.2.m.a.177.1		10	92.27	odd	22
368.2.m.a.289.1		10	92.75	odd	22
414.2.i.c.289.1		10	69.29	odd	22
414.2.i.c.361.1		10	69.50	odd	22
1058.2.a.j.1.3		5	1.1	even	1	trivial
1058.2.a.k.1.3		5	23.22	odd	2
8464.2.a.bu.1.3		5	4.3	odd	2
8464.2.a.bv.1.3		5	92.91	even	2
9522.2.a.bw.1.3		5	69.68	even	2
9522.2.a.bz.1.3		5	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1058.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.609264 q^{3} +1.00000 q^{4} +0.372786 q^{5} +0.609264 q^{6} +2.05954 q^{7} -1.00000 q^{8} -2.62880 q^{9} -0.372786 q^{10} +2.46519 q^{11} -0.609264 q^{12} -3.73269 q^{13} -2.05954 q^{14} -0.227125 q^{15} +1.00000 q^{16} -6.30909 q^{17} +2.62880 q^{18} -3.28887 q^{19} +0.372786 q^{20} -1.25480 q^{21} -2.46519 q^{22} +0.609264 q^{24} -4.86103 q^{25} +3.73269 q^{26} +3.42943 q^{27} +2.05954 q^{28} +7.13278 q^{29} +0.227125 q^{30} +5.84511 q^{31} -1.00000 q^{32} -1.50195 q^{33} +6.30909 q^{34} +0.767766 q^{35} -2.62880 q^{36} -4.67961 q^{37} +3.28887 q^{38} +2.27420 q^{39} -0.372786 q^{40} -4.78084 q^{41} +1.25480 q^{42} -11.1379 q^{43} +2.46519 q^{44} -0.979978 q^{45} +2.44502 q^{47} -0.609264 q^{48} -2.75831 q^{49} +4.86103 q^{50} +3.84391 q^{51} -3.73269 q^{52} +6.04752 q^{53} -3.42943 q^{54} +0.918986 q^{55} -2.05954 q^{56} +2.00379 q^{57} -7.13278 q^{58} -11.8100 q^{59} -0.227125 q^{60} +1.68675 q^{61} -5.84511 q^{62} -5.41411 q^{63} +1.00000 q^{64} -1.39149 q^{65} +1.50195 q^{66} -14.0947 q^{67} -6.30909 q^{68} -0.767766 q^{70} +4.03869 q^{71} +2.62880 q^{72} +8.69002 q^{73} +4.67961 q^{74} +2.96165 q^{75} -3.28887 q^{76} +5.07714 q^{77} -2.27420 q^{78} -2.38398 q^{79} +0.372786 q^{80} +5.79696 q^{81} +4.78084 q^{82} +4.23705 q^{83} -1.25480 q^{84} -2.35194 q^{85} +11.1379 q^{86} -4.34575 q^{87} -2.46519 q^{88} -9.03115 q^{89} +0.979978 q^{90} -7.68762 q^{91} -3.56122 q^{93} -2.44502 q^{94} -1.22605 q^{95} +0.609264 q^{96} -11.3067 q^{97} +2.75831 q^{98} -6.48047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{4} - 2 q^{5} - 9 q^{7} - 5 q^{8} + 7 q^{9} + 2 q^{10} - q^{11} + q^{13} + 9 q^{14} - 11 q^{15} + 5 q^{16} + q^{17} - 7 q^{18} - 10 q^{19} - 2 q^{20} + q^{22} - 11 q^{25} - q^{26}+ \cdots - 8 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^4 - 2 * q^5 - 9 * q^7 - 5 * q^8 + 7 * q^9 + 2 * q^10 - q^11 + q^13 + 9 * q^14 - 11 * q^15 + 5 * q^16 + q^17 - 7 * q^18 - 10 * q^19 - 2 * q^20 + q^22 - 11 * q^25 - q^26 - 9 * q^28 + 10 * q^29 + 11 * q^30 - 5 * q^32 - 11 * q^33 - q^34 - 3 * q^35 + 7 * q^36 - 20 * q^37 + 10 * q^38 - 22 * q^39 + 2 * q^40 - 3 * q^41 - 27 * q^43 - q^44 - 5 * q^45 - 11 * q^47 + 12 * q^49 + 11 * q^50 + q^52 + 2 * q^53 - 4 * q^55 + 9 * q^56 - 11 * q^57 - 10 * q^58 - 17 * q^59 - 11 * q^60 - 7 * q^61 - 39 * q^63 + 5 * q^64 + 15 * q^65 + 11 * q^66 - 28 * q^67 + q^68 + 3 * q^70 - 7 * q^72 + 8 * q^73 + 20 * q^74 + 22 * q^75 - 10 * q^76 + 26 * q^77 + 22 * q^78 - 16 * q^79 - 2 * q^80 + q^81 + 3 * q^82 - 18 * q^83 - 7 * q^85 + 27 * q^86 + 22 * q^87 + q^88 + 14 * q^89 + 5 * q^90 - 26 * q^91 - 44 * q^93 + 11 * q^94 + 26 * q^95 - 47 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more