LMFDB - Embedded newform 669.2.a.g.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(1,669)] 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("669.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$5.34199189522$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	669.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -3.48119 q^{5} +1.48119 q^{6} -1.19394 q^{7} -2.67513 q^{8} +1.00000 q^{9} -5.15633 q^{10} -4.15633 q^{11} +0.193937 q^{12} -2.80606 q^{13} -1.76845 q^{14} -3.48119 q^{15} -4.35026 q^{16} +4.54420 q^{17} +1.48119 q^{18} -5.19394 q^{19} -0.675131 q^{20} -1.19394 q^{21} -6.15633 q^{22} +3.76845 q^{23} -2.67513 q^{24} +7.11871 q^{25} -4.15633 q^{26} +1.00000 q^{27} -0.231548 q^{28} +7.35026 q^{29} -5.15633 q^{30} -4.80606 q^{31} -1.09332 q^{32} -4.15633 q^{33} +6.73084 q^{34} +4.15633 q^{35} +0.193937 q^{36} -0.224254 q^{37} -7.69323 q^{38} -2.80606 q^{39} +9.31265 q^{40} +5.27504 q^{41} -1.76845 q^{42} -9.50659 q^{43} -0.806063 q^{44} -3.48119 q^{45} +5.58181 q^{46} +3.24965 q^{47} -4.35026 q^{48} -5.57452 q^{49} +10.5442 q^{50} +4.54420 q^{51} -0.544198 q^{52} -6.46898 q^{53} +1.48119 q^{54} +14.4690 q^{55} +3.19394 q^{56} -5.19394 q^{57} +10.8872 q^{58} -14.7005 q^{59} -0.675131 q^{60} -1.42548 q^{61} -7.11871 q^{62} -1.19394 q^{63} +7.08110 q^{64} +9.76845 q^{65} -6.15633 q^{66} -5.31265 q^{67} +0.881286 q^{68} +3.76845 q^{69} +6.15633 q^{70} +3.03761 q^{71} -2.67513 q^{72} -2.68735 q^{73} -0.332163 q^{74} +7.11871 q^{75} -1.00729 q^{76} +4.96239 q^{77} -4.15633 q^{78} +11.7308 q^{79} +15.1441 q^{80} +1.00000 q^{81} +7.81336 q^{82} -0.100615 q^{83} -0.231548 q^{84} -15.8192 q^{85} -14.0811 q^{86} +7.35026 q^{87} +11.1187 q^{88} -0.775746 q^{89} -5.15633 q^{90} +3.35026 q^{91} +0.730841 q^{92} -4.80606 q^{93} +4.81336 q^{94} +18.0811 q^{95} -1.09332 q^{96} -15.5369 q^{97} -8.25694 q^{98} -4.15633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} + q^{4} - 5 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + q^{12} - 8 q^{13} + 6 q^{14} - 5 q^{15} - 3 q^{16} + 4 q^{17} - q^{18} - 16 q^{19} + 3 q^{20} - 4 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 + q^4 - 5 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + q^12 - 8 * q^13 + 6 * q^14 - 5 * q^15 - 3 * q^16 + 4 * q^17 - q^18 - 16 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^22 - 3 * q^24 - 2 * q^26 + 3 * q^27 - 12 * q^28 + 12 * q^29 - 5 * q^30 - 14 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^35 + q^36 + q^37 + 10 * q^38 - 8 * q^39 + 7 * q^40 - 16 * q^41 + 6 * q^42 - 8 * q^43 - 2 * q^44 - 5 * q^45 + 18 * q^46 - 7 * q^47 - 3 * q^48 - 5 * q^49 + 22 * q^50 + 4 * q^51 + 8 * q^52 + 12 * q^53 - q^54 + 12 * q^55 + 10 * q^56 - 16 * q^57 - 24 * q^59 + 3 * q^60 - 16 * q^61 - 4 * q^63 - 11 * q^64 + 18 * q^65 - 8 * q^66 + 5 * q^67 + 24 * q^68 + 8 * q^70 + 20 * q^71 - 3 * q^72 - 29 * q^73 - 19 * q^74 - 16 * q^76 + 4 * q^77 - 2 * q^78 + 13 * q^79 + 9 * q^80 + 3 * q^81 + 36 * q^82 - 7 * q^83 - 12 * q^84 - 6 * q^85 - 10 * q^86 + 12 * q^87 + 12 * q^88 - 4 * q^89 - 5 * q^90 - 20 * q^92 - 14 * q^93 + 27 * q^94 + 22 * q^95 + 3 * q^96 - 24 * q^97 - 21 * q^98 - 2 * 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 $

$2$	1.48119	1.04736	0.523681	−	0.851914i	$-0.324558\pi$
$2$	1.48119	1.04736	0.523681	+	0.851914i	$0.324558\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.193937	0.0969683
$5$	−3.48119	−1.55684	−0.778419	−	0.627745i	$-0.783978\pi$
$5$	−3.48119	−1.55684	−0.778419	+	0.627745i	$0.783978\pi$
$6$	1.48119	0.604695
$7$	−1.19394	−0.451266	−0.225633	−	0.974212i	$-0.572445\pi$
$7$	−1.19394	−0.451266	−0.225633	+	0.974212i	$0.572445\pi$
$8$	−2.67513	−0.945802
$9$	1.00000	0.333333
$10$	−5.15633	−1.63057
$11$	−4.15633	−1.25318	−0.626590	−	0.779349i	$-0.715550\pi$
$11$	−4.15633	−1.25318	−0.626590	+	0.779349i	$0.715550\pi$
$12$	0.193937	0.0559847
$13$	−2.80606	−0.778262	−0.389131	−	0.921182i	$-0.627225\pi$
$13$	−2.80606	−0.778262	−0.389131	+	0.921182i	$0.627225\pi$
$14$	−1.76845	−0.472639
$15$	−3.48119	−0.898841
$16$	−4.35026	−1.08757
$17$	4.54420	1.10213	0.551065	−	0.834462i	$-0.314222\pi$
$17$	4.54420	1.10213	0.551065	+	0.834462i	$0.314222\pi$
$18$	1.48119	0.349121
$19$	−5.19394	−1.19157	−0.595785	−	0.803144i	$-0.703159\pi$
$19$	−5.19394	−1.19157	−0.595785	+	0.803144i	$0.703159\pi$
$20$	−0.675131	−0.150964
$21$	−1.19394	−0.260538
$22$	−6.15633	−1.31253
$23$	3.76845	0.785777	0.392888	−	0.919586i	$-0.371476\pi$
$23$	3.76845	0.785777	0.392888	+	0.919586i	$0.371476\pi$
$24$	−2.67513	−0.546059
$25$	7.11871	1.42374
$26$	−4.15633	−0.815122
$27$	1.00000	0.192450
$28$	−0.231548	−0.0437585
$29$	7.35026	1.36491	0.682455	−	0.730928i	$-0.260912\pi$
$29$	7.35026	1.36491	0.682455	+	0.730928i	$0.260912\pi$
$30$	−5.15633	−0.941412
$31$	−4.80606	−0.863194	−0.431597	−	0.902066i	$-0.642050\pi$
$31$	−4.80606	−0.863194	−0.431597	+	0.902066i	$0.642050\pi$
$32$	−1.09332	−0.193274
$33$	−4.15633	−0.723523
$34$	6.73084	1.15433
$35$	4.15633	0.702547
$36$	0.193937	0.0323228
$37$	−0.224254	−0.0368671	−0.0184335	−	0.999830i	$-0.505868\pi$
$37$	−0.224254	−0.0368671	−0.0184335	+	0.999830i	$0.505868\pi$
$38$	−7.69323	−1.24801
$39$	−2.80606	−0.449330
$40$	9.31265	1.47246
$41$	5.27504	0.823823	0.411911	−	0.911224i	$-0.364861\pi$
$41$	5.27504	0.823823	0.411911	+	0.911224i	$0.364861\pi$
$42$	−1.76845	−0.272878
$43$	−9.50659	−1.44974	−0.724870	−	0.688885i	$-0.758100\pi$
$43$	−9.50659	−1.44974	−0.724870	+	0.688885i	$0.758100\pi$
$44$	−0.806063	−0.121519
$45$	−3.48119	−0.518946
$46$	5.58181	0.822993
$47$	3.24965	0.474010	0.237005	−	0.971508i	$-0.423834\pi$
$47$	3.24965	0.474010	0.237005	+	0.971508i	$0.423834\pi$
$48$	−4.35026	−0.627906
$49$	−5.57452	−0.796359
$50$	10.5442	1.49117
$51$	4.54420	0.636315
$52$	−0.544198	−0.0754667
$53$	−6.46898	−0.888582	−0.444291	−	0.895882i	$-0.646544\pi$
$53$	−6.46898	−0.888582	−0.444291	+	0.895882i	$0.646544\pi$
$54$	1.48119	0.201565
$55$	14.4690	1.95100
$56$	3.19394	0.426808
$57$	−5.19394	−0.687954
$58$	10.8872	1.42955
$59$	−14.7005	−1.91385	−0.956923	−	0.290343i	$-0.906231\pi$
$59$	−14.7005	−1.91385	−0.956923	+	0.290343i	$0.906231\pi$
$60$	−0.675131	−0.0871590
$61$	−1.42548	−0.182515	−0.0912573	−	0.995827i	$-0.529089\pi$
$61$	−1.42548	−0.182515	−0.0912573	+	0.995827i	$0.529089\pi$
$62$	−7.11871	−0.904078
$63$	−1.19394	−0.150422
$64$	7.08110	0.885138
$65$	9.76845	1.21163
$66$	−6.15633	−0.757791
$67$	−5.31265	−0.649044	−0.324522	−	0.945878i	$-0.605203\pi$
$67$	−5.31265	−0.649044	−0.324522	+	0.945878i	$0.605203\pi$
$68$	0.881286	0.106872
$69$	3.76845	0.453668
$70$	6.15633	0.735822
$71$	3.03761	0.360498	0.180249	−	0.983621i	$-0.442310\pi$
$71$	3.03761	0.360498	0.180249	+	0.983621i	$0.442310\pi$
$72$	−2.67513	−0.315267
$73$	−2.68735	−0.314530	−0.157265	−	0.987556i	$-0.550268\pi$
$73$	−2.68735	−0.314530	−0.157265	+	0.987556i	$0.550268\pi$
$74$	−0.332163	−0.0386132
$75$	7.11871	0.821998
$76$	−1.00729	−0.115545
$77$	4.96239	0.565517
$78$	−4.15633	−0.470611
$79$	11.7308	1.31982	0.659911	−	0.751343i	$-0.270594\pi$
$79$	11.7308	1.31982	0.659911	+	0.751343i	$0.270594\pi$
$80$	15.1441	1.69316
$81$	1.00000	0.111111
$82$	7.81336	0.862841
$83$	−0.100615	−0.0110440	−0.00552199	−	0.999985i	$-0.501758\pi$
$83$	−0.100615	−0.0110440	−0.00552199	+	0.999985i	$0.501758\pi$
$84$	−0.231548	−0.0252640
$85$	−15.8192	−1.71584
$86$	−14.0811	−1.51840
$87$	7.35026	0.788031
$88$	11.1187	1.18526
$89$	−0.775746	−0.0822289	−0.0411145	−	0.999154i	$-0.513091\pi$
$89$	−0.775746	−0.0822289	−0.0411145	+	0.999154i	$0.513091\pi$
$90$	−5.15633	−0.543524
$91$	3.35026	0.351203
$92$	0.730841	0.0761954
$93$	−4.80606	−0.498366
$94$	4.81336	0.496460
$95$	18.0811	1.85508
$96$	−1.09332	−0.111587
$97$	−15.5369	−1.57753	−0.788767	−	0.614693i	$-0.789280\pi$
$97$	−15.5369	−1.57753	−0.788767	+	0.614693i	$0.789280\pi$
$98$	−8.25694	−0.834077
$99$	−4.15633	−0.417726
$100$	1.38058	0.138058
$101$	14.4690	1.43972	0.719858	−	0.694121i	$-0.244207\pi$
$101$	14.4690	1.43972	0.719858	+	0.694121i	$0.244207\pi$
$102$	6.73084	0.666453
$103$	4.22425	0.416228	0.208114	−	0.978105i	$-0.433267\pi$
$103$	4.22425	0.416228	0.208114	+	0.978105i	$0.433267\pi$
$104$	7.50659	0.736081
$105$	4.15633	0.405616
$106$	−9.58181	−0.930668
$107$	−4.18664	−0.404738	−0.202369	−	0.979309i	$-0.564864\pi$
$107$	−4.18664	−0.404738	−0.202369	+	0.979309i	$0.564864\pi$
$108$	0.193937	0.0186616
$109$	4.76845	0.456735	0.228367	−	0.973575i	$-0.426661\pi$
$109$	4.76845	0.456735	0.228367	+	0.973575i	$0.426661\pi$
$110$	21.4314	2.04340
$111$	−0.224254	−0.0212852
$112$	5.19394	0.490781
$113$	−8.39375	−0.789618	−0.394809	−	0.918763i	$-0.629189\pi$
$113$	−8.39375	−0.789618	−0.394809	+	0.918763i	$0.629189\pi$
$114$	−7.69323	−0.720537
$115$	−13.1187	−1.22333
$116$	1.42548	0.132353
$117$	−2.80606	−0.259421
$118$	−21.7743	−2.00449
$119$	−5.42548	−0.497353
$120$	9.31265	0.850125
$121$	6.27504	0.570458
$122$	−2.11142	−0.191159
$123$	5.27504	0.475634
$124$	−0.932071	−0.0837025
$125$	−7.37565	−0.659699
$126$	−1.76845	−0.157546
$127$	−2.77575	−0.246308	−0.123154	−	0.992388i	$-0.539301\pi$
$127$	−2.77575	−0.246308	−0.123154	+	0.992388i	$0.539301\pi$
$128$	12.6751	1.12033
$129$	−9.50659	−0.837008
$130$	14.4690	1.26901
$131$	−22.3380	−1.95168	−0.975842	−	0.218478i	$-0.929891\pi$
$131$	−22.3380	−1.95168	−0.975842	+	0.218478i	$0.929891\pi$
$132$	−0.806063	−0.0701588
$133$	6.20123	0.537715
$134$	−7.86907	−0.679784
$135$	−3.48119	−0.299614
$136$	−12.1563	−1.04240
$137$	−10.0254	−0.856527	−0.428264	−	0.903654i	$-0.640875\pi$
$137$	−10.0254	−0.856527	−0.428264	+	0.903654i	$0.640875\pi$
$138$	5.58181	0.475155
$139$	13.5574	1.14992	0.574961	−	0.818181i	$-0.305017\pi$
$139$	13.5574	1.14992	0.574961	+	0.818181i	$0.305017\pi$
$140$	0.806063	0.0681248
$141$	3.24965	0.273670
$142$	4.49929	0.377572
$143$	11.6629	0.975302
$144$	−4.35026	−0.362522
$145$	−25.5877	−2.12494
$146$	−3.98049	−0.329427
$147$	−5.57452	−0.459778
$148$	−0.0434910	−0.00357494
$149$	−2.15633	−0.176653	−0.0883265	−	0.996092i	$-0.528152\pi$
$149$	−2.15633	−0.176653	−0.0883265	+	0.996092i	$0.528152\pi$
$150$	10.5442	0.860930
$151$	−0.693229	−0.0564142	−0.0282071	−	0.999602i	$-0.508980\pi$
$151$	−0.693229	−0.0564142	−0.0282071	+	0.999602i	$0.508980\pi$
$152$	13.8945	1.12699
$153$	4.54420	0.367377
$154$	7.35026	0.592301
$155$	16.7308	1.34385
$156$	−0.544198	−0.0435707
$157$	−9.69323	−0.773604	−0.386802	−	0.922163i	$-0.626420\pi$
$157$	−9.69323	−0.773604	−0.386802	+	0.922163i	$0.626420\pi$
$158$	17.3757	1.38233
$159$	−6.46898	−0.513023
$160$	3.80606	0.300896
$161$	−4.49929	−0.354594
$162$	1.48119	0.116374
$163$	−4.38058	−0.343113	−0.171557	−	0.985174i	$-0.554880\pi$
$163$	−4.38058	−0.343113	−0.171557	+	0.985174i	$0.554880\pi$
$164$	1.02302	0.0798847
$165$	14.4690	1.12641
$166$	−0.149031	−0.0115670
$167$	−7.27504	−0.562959	−0.281480	−	0.959567i	$-0.590825\pi$
$167$	−7.27504	−0.562959	−0.281480	+	0.959567i	$0.590825\pi$
$168$	3.19394	0.246418
$169$	−5.12601	−0.394308
$170$	−23.4314	−1.79710
$171$	−5.19394	−0.397190
$172$	−1.84367	−0.140579
$173$	14.7259	1.11959	0.559795	−	0.828631i	$-0.310880\pi$
$173$	14.7259	1.11959	0.559795	+	0.828631i	$0.310880\pi$
$174$	10.8872	0.825354
$175$	−8.49929	−0.642486
$176$	18.0811	1.36291
$177$	−14.7005	−1.10496
$178$	−1.14903	−0.0861235
$179$	17.9805	1.34392	0.671962	−	0.740585i	$-0.265452\pi$
$179$	17.9805	1.34392	0.671962	+	0.740585i	$0.265452\pi$
$180$	−0.675131	−0.0503213
$181$	−16.0435	−1.19250	−0.596252	−	0.802798i	$-0.703344\pi$
$181$	−16.0435	−1.19250	−0.596252	+	0.802798i	$0.703344\pi$
$182$	4.96239	0.367837
$183$	−1.42548	−0.105375
$184$	−10.0811	−0.743189
$185$	0.780671	0.0573961
$186$	−7.11871	−0.521969
$187$	−18.8872	−1.38117
$188$	0.630225	0.0459639
$189$	−1.19394	−0.0868461
$190$	26.7816	1.94294
$191$	−2.78163	−0.201271	−0.100636	−	0.994923i	$-0.532088\pi$
$191$	−2.78163	−0.201271	−0.100636	+	0.994923i	$0.532088\pi$
$192$	7.08110	0.511035
$193$	20.6253	1.48464	0.742321	−	0.670045i	$-0.233725\pi$
$193$	20.6253	1.48464	0.742321	+	0.670045i	$0.233725\pi$
$194$	−23.0132	−1.65225
$195$	9.76845	0.699533
$196$	−1.08110	−0.0772216
$197$	3.24472	0.231177	0.115588	−	0.993297i	$-0.463125\pi$
$197$	3.24472	0.231177	0.115588	+	0.993297i	$0.463125\pi$
$198$	−6.15633	−0.437511
$199$	12.5139	0.887086	0.443543	−	0.896253i	$-0.353721\pi$
$199$	12.5139	0.887086	0.443543	+	0.896253i	$0.353721\pi$
$200$	−19.0435	−1.34658
$201$	−5.31265	−0.374725
$202$	21.4314	1.50791
$203$	−8.77575	−0.615937
$204$	0.881286	0.0617024
$205$	−18.3634	−1.28256
$206$	6.25694	0.435942
$207$	3.76845	0.261926
$208$	12.2071	0.846411
$209$	21.5877	1.49325
$210$	6.15633	0.424827
$211$	−21.7440	−1.49692	−0.748460	−	0.663180i	$-0.769206\pi$
$211$	−21.7440	−1.49692	−0.748460	+	0.663180i	$0.769206\pi$
$212$	−1.25457	−0.0861643
$213$	3.03761	0.208134
$214$	−6.20123	−0.423907
$215$	33.0943	2.25701
$216$	−2.67513	−0.182020
$217$	5.73813	0.389530
$218$	7.06300	0.478367
$219$	−2.68735	−0.181594
$220$	2.80606	0.189185
$221$	−12.7513	−0.857746
$222$	−0.332163	−0.0222933
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	1.30536	0.0872178
$225$	7.11871	0.474581
$226$	−12.4328	−0.827016
$227$	25.1949	1.67224	0.836122	−	0.548544i	$-0.184818\pi$
$227$	25.1949	1.67224	0.836122	+	0.548544i	$0.184818\pi$
$228$	−1.00729	−0.0667097
$229$	26.0059	1.71852	0.859258	−	0.511542i	$-0.170925\pi$
$229$	26.0059	1.71852	0.859258	+	0.511542i	$0.170925\pi$
$230$	−19.4314	−1.28127
$231$	4.96239	0.326501
$232$	−19.6629	−1.29093
$233$	4.41819	0.289445	0.144723	−	0.989472i	$-0.453771\pi$
$233$	4.41819	0.289445	0.144723	+	0.989472i	$0.453771\pi$
$234$	−4.15633	−0.271707
$235$	−11.3127	−0.737956
$236$	−2.85097	−0.185582
$237$	11.7308	0.762000
$238$	−8.03620	−0.520909
$239$	−2.16125	−0.139800	−0.0698998	−	0.997554i	$-0.522268\pi$
$239$	−2.16125	−0.139800	−0.0698998	+	0.997554i	$0.522268\pi$
$240$	15.1441	0.977548
$241$	−17.7513	−1.14346	−0.571731	−	0.820441i	$-0.693728\pi$
$241$	−17.7513	−1.14346	−0.571731	+	0.820441i	$0.693728\pi$
$242$	9.29455	0.597476
$243$	1.00000	0.0641500
$244$	−0.276454	−0.0176981
$245$	19.4060	1.23980
$246$	7.81336	0.498161
$247$	14.5745	0.927354
$248$	12.8568	0.816411
$249$	−0.100615	−0.00637624
$250$	−10.9248	−0.690944
$251$	−23.5926	−1.48915	−0.744576	−	0.667537i	$-0.767348\pi$
$251$	−23.5926	−1.48915	−0.744576	+	0.667537i	$0.767348\pi$
$252$	−0.231548	−0.0145862
$253$	−15.6629	−0.984719
$254$	−4.11142	−0.257973
$255$	−15.8192	−0.990639
$256$	4.61213	0.288258
$257$	22.5296	1.40536	0.702679	−	0.711507i	$-0.251987\pi$
$257$	22.5296	1.40536	0.702679	+	0.711507i	$0.251987\pi$
$258$	−14.0811	−0.876651
$259$	0.267745	0.0166368
$260$	1.89446	0.117489
$261$	7.35026	0.454970
$262$	−33.0870	−2.04412
$263$	19.2301	1.18578	0.592890	−	0.805283i	$-0.297987\pi$
$263$	19.2301	1.18578	0.592890	+	0.805283i	$0.297987\pi$
$264$	11.1187	0.684310
$265$	22.5198	1.38338
$266$	9.18523	0.563182
$267$	−0.775746	−0.0474749
$268$	−1.03032	−0.0629366
$269$	−28.3987	−1.73150	−0.865749	−	0.500479i	$-0.833157\pi$
$269$	−28.3987	−1.73150	−0.865749	+	0.500479i	$0.833157\pi$
$270$	−5.15633	−0.313804
$271$	−19.4763	−1.18310	−0.591550	−	0.806269i	$-0.701484\pi$
$271$	−19.4763	−1.18310	−0.591550	+	0.806269i	$0.701484\pi$
$272$	−19.7685	−1.19864
$273$	3.35026	0.202767
$274$	−14.8496	−0.897094
$275$	−29.5877	−1.78420
$276$	0.730841	0.0439914
$277$	−13.2750	−0.797620	−0.398810	−	0.917034i	$-0.630577\pi$
$277$	−13.2750	−0.797620	−0.398810	+	0.917034i	$0.630577\pi$
$278$	20.0811	1.20438
$279$	−4.80606	−0.287731
$280$	−11.1187	−0.664470
$281$	13.2447	0.790114	0.395057	−	0.918657i	$-0.370725\pi$
$281$	13.2447	0.790114	0.395057	+	0.918657i	$0.370725\pi$
$282$	4.81336	0.286631
$283$	−33.2203	−1.97474	−0.987370	−	0.158428i	$-0.949357\pi$
$283$	−33.2203	−1.97474	−0.987370	+	0.158428i	$0.949357\pi$
$284$	0.589104	0.0349569
$285$	18.0811	1.07103
$286$	17.2750	1.02149
$287$	−6.29806	−0.371763
$288$	−1.09332	−0.0644246
$289$	3.64974	0.214690
$290$	−37.9003	−2.22558
$291$	−15.5369	−0.910789
$292$	−0.521175	−0.0304995
$293$	−26.1925	−1.53018	−0.765092	−	0.643921i	$-0.777306\pi$
$293$	−26.1925	−1.53018	−0.765092	+	0.643921i	$0.777306\pi$
$294$	−8.25694	−0.481555
$295$	51.1754	2.97955
$296$	0.599908	0.0348689
$297$	−4.15633	−0.241174
$298$	−3.19394	−0.185020
$299$	−10.5745	−0.611540
$300$	1.38058	0.0797078
$301$	11.3503	0.654218
$302$	−1.02681	−0.0590861
$303$	14.4690	0.831221
$304$	22.5950	1.29591
$305$	4.96239	0.284146
$306$	6.73084	0.384777
$307$	14.6326	0.835126	0.417563	−	0.908648i	$-0.362884\pi$
$307$	14.6326	0.835126	0.417563	+	0.908648i	$0.362884\pi$
$308$	0.962389	0.0548372
$309$	4.22425	0.240309
$310$	24.7816	1.40750
$311$	−20.5296	−1.16413	−0.582064	−	0.813143i	$-0.697755\pi$
$311$	−20.5296	−1.16413	−0.582064	+	0.813143i	$0.697755\pi$
$312$	7.50659	0.424977
$313$	26.4749	1.49645	0.748224	−	0.663447i	$-0.230907\pi$
$313$	26.4749	1.49645	0.748224	+	0.663447i	$0.230907\pi$
$314$	−14.3576	−0.810244
$315$	4.15633	0.234182
$316$	2.27504	0.127981
$317$	−2.52373	−0.141747	−0.0708734	−	0.997485i	$-0.522579\pi$
$317$	−2.52373	−0.141747	−0.0708734	+	0.997485i	$0.522579\pi$
$318$	−9.58181	−0.537321
$319$	−30.5501	−1.71048
$320$	−24.6507	−1.37802
$321$	−4.18664	−0.233676
$322$	−6.66433	−0.371388
$323$	−23.6023	−1.31327
$324$	0.193937	0.0107743
$325$	−19.9756	−1.10804
$326$	−6.48849	−0.359364
$327$	4.76845	0.263696
$328$	−14.1114	−0.779173
$329$	−3.87987	−0.213904
$330$	21.4314	1.17976
$331$	30.4894	1.67585	0.837926	−	0.545784i	$-0.183768\pi$
$331$	30.4894	1.67585	0.837926	+	0.545784i	$0.183768\pi$
$332$	−0.0195130	−0.00107092
$333$	−0.224254	−0.0122890
$334$	−10.7757	−0.589623
$335$	18.4944	1.01046
$336$	5.19394	0.283352
$337$	−29.6932	−1.61749	−0.808747	−	0.588157i	$-0.799854\pi$
$337$	−29.6932	−1.61749	−0.808747	+	0.588157i	$0.799854\pi$
$338$	−7.59261	−0.412984
$339$	−8.39375	−0.455886
$340$	−3.06793	−0.166382
$341$	19.9756	1.08174
$342$	−7.69323	−0.416002
$343$	15.0132	0.810635
$344$	25.4314	1.37117
$345$	−13.1187	−0.706288
$346$	21.8119	1.17262
$347$	16.9076	0.907649	0.453825	−	0.891091i	$-0.350059\pi$
$347$	16.9076	0.907649	0.453825	+	0.891091i	$0.350059\pi$
$348$	1.42548	0.0764140
$349$	23.0870	1.23582	0.617909	−	0.786250i	$-0.287980\pi$
$349$	23.0870	1.23582	0.617909	+	0.786250i	$0.287980\pi$
$350$	−12.5891	−0.672916
$351$	−2.80606	−0.149777
$352$	4.54420	0.242207
$353$	−33.4069	−1.77807	−0.889036	−	0.457838i	$-0.848624\pi$
$353$	−33.4069	−1.77807	−0.889036	+	0.457838i	$0.848624\pi$
$354$	−21.7743	−1.15729
$355$	−10.5745	−0.561237
$356$	−0.150446	−0.00797360
$357$	−5.42548	−0.287147
$358$	26.6326	1.40758
$359$	4.99271	0.263505	0.131752	−	0.991283i	$-0.457940\pi$
$359$	4.99271	0.263505	0.131752	+	0.991283i	$0.457940\pi$
$360$	9.31265	0.490820
$361$	7.97698	0.419841
$362$	−23.7635	−1.24898
$363$	6.27504	0.329354
$364$	0.649738	0.0340555
$365$	9.35519	0.489673
$366$	−2.11142	−0.110366
$367$	−15.9003	−0.829991	−0.414995	−	0.909823i	$-0.636217\pi$
$367$	−15.9003	−0.829991	−0.414995	+	0.909823i	$0.636217\pi$
$368$	−16.3938	−0.854583
$369$	5.27504	0.274608
$370$	1.15633	0.0601145
$371$	7.72355	0.400987
$372$	−0.932071	−0.0483257
$373$	5.67276	0.293724	0.146862	−	0.989157i	$-0.453083\pi$
$373$	5.67276	0.293724	0.146862	+	0.989157i	$0.453083\pi$
$374$	−27.9756	−1.44658
$375$	−7.37565	−0.380877
$376$	−8.69323	−0.448319
$377$	−20.6253	−1.06226
$378$	−1.76845	−0.0909594
$379$	7.35614	0.377860	0.188930	−	0.981991i	$-0.439498\pi$
$379$	7.35614	0.377860	0.188930	+	0.981991i	$0.439498\pi$
$380$	3.50659	0.179884
$381$	−2.77575	−0.142206
$382$	−4.12013	−0.210804
$383$	−33.7948	−1.72683	−0.863417	−	0.504491i	$-0.831680\pi$
$383$	−33.7948	−1.72683	−0.863417	+	0.504491i	$0.831680\pi$
$384$	12.6751	0.646825
$385$	−17.2750	−0.880418
$386$	30.5501	1.55496
$387$	−9.50659	−0.483247
$388$	−3.01317	−0.152971
$389$	34.7718	1.76300	0.881500	−	0.472185i	$-0.156535\pi$
$389$	34.7718	1.76300	0.881500	+	0.472185i	$0.156535\pi$
$390$	14.4690	0.732665
$391$	17.1246	0.866028
$392$	14.9126	0.753198
$393$	−22.3380	−1.12681
$394$	4.80606	0.242126
$395$	−40.8373	−2.05475
$396$	−0.806063	−0.0405062
$397$	−22.7572	−1.14215	−0.571075	−	0.820898i	$-0.693474\pi$
$397$	−22.7572	−1.14215	−0.571075	+	0.820898i	$0.693474\pi$
$398$	18.5355	0.929100
$399$	6.20123	0.310450
$400$	−30.9683	−1.54841
$401$	38.0263	1.89895	0.949473	−	0.313850i	$-0.101619\pi$
$401$	38.0263	1.89895	0.949473	+	0.313850i	$0.101619\pi$
$402$	−7.86907	−0.392473
$403$	13.4861	0.671791
$404$	2.80606	0.139607
$405$	−3.48119	−0.172982
$406$	−12.9986	−0.645109
$407$	0.932071	0.0462011
$408$	−12.1563	−0.601828
$409$	−5.21440	−0.257836	−0.128918	−	0.991655i	$-0.541150\pi$
$409$	−5.21440	−0.257836	−0.128918	+	0.991655i	$0.541150\pi$
$410$	−27.1998	−1.34330
$411$	−10.0254	−0.494516
$412$	0.819237	0.0403609
$413$	17.5515	0.863652
$414$	5.58181	0.274331
$415$	0.350262	0.0171937
$416$	3.06793	0.150418
$417$	13.5574	0.663907
$418$	31.9756	1.56398
$419$	−25.8945	−1.26503	−0.632514	−	0.774549i	$-0.717977\pi$
$419$	−25.8945	−1.26503	−0.632514	+	0.774549i	$0.717977\pi$
$420$	0.806063	0.0393319
$421$	14.4690	0.705175	0.352587	−	0.935779i	$-0.385302\pi$
$421$	14.4690	0.705175	0.352587	+	0.935779i	$0.385302\pi$
$422$	−32.2071	−1.56782
$423$	3.24965	0.158003
$424$	17.3054	0.840422
$425$	32.3488	1.56915
$426$	4.49929	0.217991
$427$	1.70194	0.0823626
$428$	−0.811943	−0.0392467
$429$	11.6629	0.563091
$430$	49.0191	2.36391
$431$	−33.2955	−1.60379	−0.801894	−	0.597466i	$-0.796174\pi$
$431$	−33.2955	−1.60379	−0.801894	+	0.597466i	$0.796174\pi$
$432$	−4.35026	−0.209302
$433$	24.7948	1.19156	0.595781	−	0.803147i	$-0.296843\pi$
$433$	24.7948	1.19156	0.595781	+	0.803147i	$0.296843\pi$
$434$	8.49929	0.407979
$435$	−25.5877	−1.22684
$436$	0.924777	0.0442888
$437$	−19.5731	−0.936308
$438$	−3.98049	−0.190195
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	−38.7064	−1.84526
$441$	−5.57452	−0.265453
$442$	−18.8872	−0.898371
$443$	11.0835	0.526592	0.263296	−	0.964715i	$-0.415190\pi$
$443$	11.0835	0.526592	0.263296	+	0.964715i	$0.415190\pi$
$444$	−0.0434910	−0.00206399
$445$	2.70052	0.128017
$446$	1.48119	0.0701366
$447$	−2.15633	−0.101991
$448$	−8.45439	−0.399432
$449$	11.6180	0.548288	0.274144	−	0.961689i	$-0.411606\pi$
$449$	11.6180	0.548288	0.274144	+	0.961689i	$0.411606\pi$
$450$	10.5442	0.497058
$451$	−21.9248	−1.03240
$452$	−1.62786	−0.0765679
$453$	−0.693229	−0.0325708
$454$	37.3185	1.75145
$455$	−11.6629	−0.546766
$456$	13.8945	0.650668
$457$	−9.89446	−0.462843	−0.231422	−	0.972854i	$-0.574338\pi$
$457$	−9.89446	−0.462843	−0.231422	+	0.972854i	$0.574338\pi$
$458$	38.5198	1.79991
$459$	4.54420	0.212105
$460$	−2.54420	−0.118624
$461$	7.17935	0.334376	0.167188	−	0.985925i	$-0.446531\pi$
$461$	7.17935	0.334376	0.167188	+	0.985925i	$0.446531\pi$
$462$	7.35026	0.341965
$463$	20.2981	0.943331	0.471665	−	0.881778i	$-0.343653\pi$
$463$	20.2981	0.943331	0.471665	+	0.881778i	$0.343653\pi$
$464$	−31.9756	−1.48443
$465$	16.7308	0.775874
$466$	6.54420	0.303154
$467$	9.73813	0.450627	0.225314	−	0.974286i	$-0.427659\pi$
$467$	9.73813	0.450627	0.225314	+	0.974286i	$0.427659\pi$
$468$	−0.544198	−0.0251556
$469$	6.34297	0.292891
$470$	−16.7562	−0.772907
$471$	−9.69323	−0.446640
$472$	39.3258	1.81012
$473$	39.5125	1.81679
$474$	17.3757	0.798090
$475$	−36.9741	−1.69649
$476$	−1.05220	−0.0482275
$477$	−6.46898	−0.296194
$478$	−3.20123	−0.146421
$479$	−31.1939	−1.42529	−0.712644	−	0.701526i	$-0.752502\pi$
$479$	−31.1939	−1.42529	−0.712644	+	0.701526i	$0.752502\pi$
$480$	3.80606	0.173722
$481$	0.629270	0.0286923
$482$	−26.2931	−1.19762
$483$	−4.49929	−0.204725
$484$	1.21696	0.0553163
$485$	54.0870	2.45596
$486$	1.48119	0.0671883
$487$	−21.1187	−0.956980	−0.478490	−	0.878093i	$-0.658816\pi$
$487$	−21.1187	−0.956980	−0.478490	+	0.878093i	$0.658816\pi$
$488$	3.81336	0.172623
$489$	−4.38058	−0.198097
$490$	28.7440	1.29852
$491$	−30.8423	−1.39189	−0.695946	−	0.718094i	$-0.745015\pi$
$491$	−30.8423	−1.39189	−0.695946	+	0.718094i	$0.745015\pi$
$492$	1.02302	0.0461214
$493$	33.4010	1.50431
$494$	21.5877	0.971276
$495$	14.4690	0.650332
$496$	20.9076	0.938780
$497$	−3.62672	−0.162680
$498$	−0.149031	−0.00667824
$499$	16.5745	0.741977	0.370989	−	0.928637i	$-0.379019\pi$
$499$	16.5745	0.741977	0.370989	+	0.928637i	$0.379019\pi$
$500$	−1.43041	−0.0639698
$501$	−7.27504	−0.325025
$502$	−34.9452	−1.55968
$503$	−26.8021	−1.19505	−0.597523	−	0.801852i	$-0.703848\pi$
$503$	−26.8021	−1.19505	−0.597523	+	0.801852i	$0.703848\pi$
$504$	3.19394	0.142269
$505$	−50.3693	−2.24141
$506$	−23.1998	−1.03136
$507$	−5.12601	−0.227654
$508$	−0.538319	−0.0238840
$509$	−0.207110	−0.00918001	−0.00459000	−	0.999989i	$-0.501461\pi$
$509$	−0.207110	−0.00918001	−0.00459000	+	0.999989i	$0.501461\pi$
$510$	−23.4314	−1.03756
$511$	3.20853	0.141937
$512$	−18.5188	−0.818423
$513$	−5.19394	−0.229318
$514$	33.3707	1.47192
$515$	−14.7054	−0.647999
$516$	−1.84367	−0.0811633
$517$	−13.5066	−0.594019
$518$	0.396582	0.0174248
$519$	14.7259	0.646396
$520$	−26.1319	−1.14596
$521$	−22.1270	−0.969400	−0.484700	−	0.874681i	$-0.661071\pi$
$521$	−22.1270	−0.969400	−0.484700	+	0.874681i	$0.661071\pi$
$522$	10.8872	0.476518
$523$	−35.1147	−1.53546	−0.767730	−	0.640773i	$-0.778614\pi$
$523$	−35.1147	−1.53546	−0.767730	+	0.640773i	$0.778614\pi$
$524$	−4.33216	−0.189251
$525$	−8.49929	−0.370940
$526$	28.4836	1.24194
$527$	−21.8397	−0.951353
$528$	18.0811	0.786879
$529$	−8.79877	−0.382555
$530$	33.3561	1.44890
$531$	−14.7005	−0.637948
$532$	1.20265	0.0521413
$533$	−14.8021	−0.641150
$534$	−1.14903	−0.0497234
$535$	14.5745	0.630111
$536$	14.2120	0.613866
$537$	17.9805	0.775915
$538$	−42.0640	−1.81351
$539$	23.1695	0.997981
$540$	−0.675131	−0.0290530
$541$	−16.2619	−0.699152	−0.349576	−	0.936908i	$-0.613674\pi$
$541$	−16.2619	−0.699152	−0.349576	+	0.936908i	$0.613674\pi$
$542$	−28.8481	−1.23913
$543$	−16.0435	−0.688492
$544$	−4.96827	−0.213013
$545$	−16.5999	−0.711062
$546$	4.96239	0.212371
$547$	2.80606	0.119979	0.0599893	−	0.998199i	$-0.480893\pi$
$547$	2.80606	0.119979	0.0599893	+	0.998199i	$0.480893\pi$
$548$	−1.94429	−0.0830560
$549$	−1.42548	−0.0608382
$550$	−43.8251	−1.86871
$551$	−38.1768	−1.62639
$552$	−10.0811	−0.429080
$553$	−14.0059	−0.595591
$554$	−19.6629	−0.835397
$555$	0.780671	0.0331376
$556$	2.62927	0.111506
$557$	2.75035	0.116536	0.0582681	−	0.998301i	$-0.481442\pi$
$557$	2.75035	0.116536	0.0582681	+	0.998301i	$0.481442\pi$
$558$	−7.11871	−0.301359
$559$	26.6761	1.12828
$560$	−18.0811	−0.764066
$561$	−18.8872	−0.797417
$562$	19.6180	0.827536
$563$	−6.16617	−0.259873	−0.129937	−	0.991522i	$-0.541477\pi$
$563$	−6.16617	−0.259873	−0.129937	+	0.991522i	$0.541477\pi$
$564$	0.630225	0.0265373
$565$	29.2203	1.22931
$566$	−49.2057	−2.06827
$567$	−1.19394	−0.0501406
$568$	−8.12601	−0.340960
$569$	23.9053	1.00216	0.501080	−	0.865401i	$-0.332936\pi$
$569$	23.9053	1.00216	0.501080	+	0.865401i	$0.332936\pi$
$570$	26.7816	1.12176
$571$	30.5183	1.27715	0.638577	−	0.769558i	$-0.279524\pi$
$571$	30.5183	1.27715	0.638577	+	0.769558i	$0.279524\pi$
$572$	2.26187	0.0945733
$573$	−2.78163	−0.116204
$574$	−9.32865	−0.389370
$575$	26.8265	1.11874
$576$	7.08110	0.295046
$577$	24.4069	1.01607	0.508037	−	0.861335i	$-0.330371\pi$
$577$	24.4069	1.01607	0.508037	+	0.861335i	$0.330371\pi$
$578$	5.40597	0.224859
$579$	20.6253	0.857158
$580$	−4.96239	−0.206052
$581$	0.120128	0.00498377
$582$	−23.0132	−0.953927
$583$	26.8872	1.11355
$584$	7.18901	0.297483
$585$	9.76845	0.403876
$586$	−38.7962	−1.60266
$587$	37.9307	1.56557	0.782783	−	0.622295i	$-0.213800\pi$
$587$	37.9307	1.56557	0.782783	+	0.622295i	$0.213800\pi$
$588$	−1.08110	−0.0445839
$589$	24.9624	1.02856
$590$	75.8007	3.12066
$591$	3.24472	0.133470
$592$	0.975562	0.0400954
$593$	8.54324	0.350829	0.175414	−	0.984495i	$-0.443873\pi$
$593$	8.54324	0.350829	0.175414	+	0.984495i	$0.443873\pi$
$594$	−6.15633	−0.252597
$595$	18.8872	0.774298
$596$	−0.418190	−0.0171297
$597$	12.5139	0.512159
$598$	−15.6629	−0.640504
$599$	9.43136	0.385355	0.192678	−	0.981262i	$-0.438283\pi$
$599$	9.43136	0.385355	0.192678	+	0.981262i	$0.438283\pi$
$600$	−19.0435	−0.777447
$601$	13.7381	0.560390	0.280195	−	0.959943i	$-0.409601\pi$
$601$	13.7381	0.560390	0.280195	+	0.959943i	$0.409601\pi$
$602$	16.8119	0.685204
$603$	−5.31265	−0.216348
$604$	−0.134443	−0.00547039
$605$	−21.8446	−0.888110
$606$	21.4314	0.870590
$607$	−8.70308	−0.353247	−0.176624	−	0.984278i	$-0.556518\pi$
$607$	−8.70308	−0.353247	−0.176624	+	0.984278i	$0.556518\pi$
$608$	5.67864	0.230299
$609$	−8.77575	−0.355611
$610$	7.35026	0.297603
$611$	−9.11871	−0.368904
$612$	0.881286	0.0356239
$613$	13.6180	0.550026	0.275013	−	0.961440i	$-0.411318\pi$
$613$	13.6180	0.550026	0.275013	+	0.961440i	$0.411318\pi$
$614$	21.6737	0.874680
$615$	−18.3634	−0.740485
$616$	−13.2750	−0.534867
$617$	14.8510	0.597878	0.298939	−	0.954272i	$-0.403367\pi$
$617$	14.8510	0.597878	0.298939	+	0.954272i	$0.403367\pi$
$618$	6.25694	0.251691
$619$	−15.5296	−0.624188	−0.312094	−	0.950051i	$-0.601030\pi$
$619$	−15.5296	−0.624188	−0.312094	+	0.950051i	$0.601030\pi$
$620$	3.24472	0.130311
$621$	3.76845	0.151223
$622$	−30.4083	−1.21926
$623$	0.926192	0.0371071
$624$	12.2071	0.488676
$625$	−9.91748	−0.396699
$626$	39.2144	1.56732
$627$	21.5877	0.862129
$628$	−1.87987	−0.0750150
$629$	−1.01905	−0.0406323
$630$	6.15633	0.245274
$631$	2.38646	0.0950034	0.0475017	−	0.998871i	$-0.484874\pi$
$631$	2.38646	0.0950034	0.0475017	+	0.998871i	$0.484874\pi$
$632$	−31.3815	−1.24829
$633$	−21.7440	−0.864247
$634$	−3.73813	−0.148460
$635$	9.66291	0.383461
$636$	−1.25457	−0.0497470
$637$	15.6424	0.619776
$638$	−45.2506	−1.79149
$639$	3.03761	0.120166
$640$	−44.1246	−1.74418
$641$	6.05571	0.239186	0.119593	−	0.992823i	$-0.461841\pi$
$641$	6.05571	0.239186	0.119593	+	0.992823i	$0.461841\pi$
$642$	−6.20123	−0.244743
$643$	36.0625	1.42217	0.711084	−	0.703107i	$-0.248205\pi$
$643$	36.0625	1.42217	0.711084	+	0.703107i	$0.248205\pi$
$644$	−0.872577	−0.0343844
$645$	33.0943	1.30309
$646$	−34.9596	−1.37547
$647$	−0.432779	−0.0170143	−0.00850714	−	0.999964i	$-0.502708\pi$
$647$	−0.432779	−0.0170143	−0.00850714	+	0.999964i	$0.502708\pi$
$648$	−2.67513	−0.105089
$649$	61.1002	2.39839
$650$	−29.5877	−1.16052
$651$	5.73813	0.224895
$652$	−0.849554	−0.0332711
$653$	47.5936	1.86248	0.931240	−	0.364406i	$-0.118728\pi$
$653$	47.5936	1.86248	0.931240	+	0.364406i	$0.118728\pi$
$654$	7.06300	0.276185
$655$	77.7631	3.03845
$656$	−22.9478	−0.895961
$657$	−2.68735	−0.104843
$658$	−5.74684	−0.224035
$659$	33.9403	1.32213	0.661064	−	0.750330i	$-0.270105\pi$
$659$	33.9403	1.32213	0.661064	+	0.750330i	$0.270105\pi$
$660$	2.80606	0.109226
$661$	0.0956908	0.00372194	0.00186097	−	0.999998i	$-0.499408\pi$
$661$	0.0956908	0.00372194	0.00186097	+	0.999998i	$0.499408\pi$
$662$	45.1608	1.75522
$663$	−12.7513	−0.495220
$664$	0.269159	0.0104454
$665$	−21.5877	−0.837135
$666$	−0.332163	−0.0128711
$667$	27.6991	1.07251
$668$	−1.41090	−0.0545892
$669$	1.00000	0.0386622
$670$	27.3938	1.05831
$671$	5.92478	0.228723
$672$	1.30536	0.0503552
$673$	−0.700523	−0.0270032	−0.0135016	−	0.999909i	$-0.504298\pi$
$673$	−0.700523	−0.0270032	−0.0135016	+	0.999909i	$0.504298\pi$
$674$	−43.9814	−1.69410
$675$	7.11871	0.273999
$676$	−0.994120	−0.0382354
$677$	43.1998	1.66030	0.830152	−	0.557537i	$-0.188254\pi$
$677$	43.1998	1.66030	0.830152	+	0.557537i	$0.188254\pi$
$678$	−12.4328	−0.477478
$679$	18.5501	0.711887
$680$	42.3185	1.62284
$681$	25.1949	0.965470
$682$	29.5877	1.13297
$683$	−0.981902	−0.0375714	−0.0187857	−	0.999824i	$-0.505980\pi$
$683$	−0.981902	−0.0375714	−0.0187857	+	0.999824i	$0.505980\pi$
$684$	−1.00729	−0.0385149
$685$	34.9003	1.33347
$686$	22.2374	0.849029
$687$	26.0059	0.992186
$688$	41.3561	1.57669
$689$	18.1524	0.691550
$690$	−19.4314	−0.739739
$691$	−28.9003	−1.09942	−0.549710	−	0.835355i	$-0.685262\pi$
$691$	−28.9003	−1.09942	−0.549710	+	0.835355i	$0.685262\pi$
$692$	2.85589	0.108565
$693$	4.96239	0.188506
$694$	25.0435	0.950638
$695$	−47.1958	−1.79024
$696$	−19.6629	−0.745321
$697$	23.9708	0.907960
$698$	34.1963	1.29435
$699$	4.41819	0.167111
$700$	−1.64832	−0.0623008
$701$	38.5052	1.45432	0.727160	−	0.686468i	$-0.240840\pi$
$701$	38.5052	1.45432	0.727160	+	0.686468i	$0.240840\pi$
$702$	−4.15633	−0.156870
$703$	1.16476	0.0439297
$704$	−29.4314	−1.10924
$705$	−11.3127	−0.426059
$706$	−49.4821	−1.86229
$707$	−17.2750	−0.649695
$708$	−2.85097	−0.107146
$709$	−40.7875	−1.53181	−0.765903	−	0.642956i	$-0.777708\pi$
$709$	−40.7875	−1.53181	−0.765903	+	0.642956i	$0.777708\pi$
$710$	−15.6629	−0.587819
$711$	11.7308	0.439941
$712$	2.07522	0.0777723
$713$	−18.1114	−0.678278
$714$	−8.03620	−0.300747
$715$	−40.6009	−1.51839
$716$	3.48707	0.130318
$717$	−2.16125	−0.0807134
$718$	7.39517	0.275985
$719$	48.9937	1.82716	0.913578	−	0.406664i	$-0.133308\pi$
$719$	48.9937	1.82716	0.913578	+	0.406664i	$0.133308\pi$
$720$	15.1441	0.564388
$721$	−5.04349	−0.187829
$722$	11.8155	0.439726
$723$	−17.7513	−0.660178
$724$	−3.11142	−0.115635
$725$	52.3244	1.94328
$726$	9.29455	0.344953
$727$	17.8594	0.662369	0.331184	−	0.943566i	$-0.392552\pi$
$727$	17.8594	0.662369	0.331184	+	0.943566i	$0.392552\pi$
$728$	−8.96239	−0.332168
$729$	1.00000	0.0370370
$730$	13.8568	0.512865
$731$	−43.1998	−1.59780
$732$	−0.276454	−0.0102180
$733$	10.1260	0.374013	0.187006	−	0.982359i	$-0.440122\pi$
$733$	10.1260	0.374013	0.187006	+	0.982359i	$0.440122\pi$
$734$	−23.5515	−0.869301
$735$	19.4060	0.715800
$736$	−4.12013	−0.151870
$737$	22.0811	0.813368
$738$	7.81336	0.287614
$739$	−7.26187	−0.267132	−0.133566	−	0.991040i	$-0.542643\pi$
$739$	−7.26187	−0.267132	−0.133566	+	0.991040i	$0.542643\pi$
$740$	0.151401	0.00556560
$741$	14.5745	0.535408
$742$	11.4401	0.419978
$743$	−47.3914	−1.73862	−0.869311	−	0.494266i	$-0.835437\pi$
$743$	−47.3914	−1.73862	−0.869311	+	0.494266i	$0.835437\pi$
$744$	12.8568	0.471355
$745$	7.50659	0.275020
$746$	8.40246	0.307636
$747$	−0.100615	−0.00368132
$748$	−3.66291	−0.133929
$749$	4.99859	0.182644
$750$	−10.9248	−0.398916
$751$	−8.42407	−0.307399	−0.153699	−	0.988118i	$-0.549119\pi$
$751$	−8.42407	−0.307399	−0.153699	+	0.988118i	$0.549119\pi$
$752$	−14.1368	−0.515516
$753$	−23.5926	−0.859763
$754$	−30.5501	−1.11257
$755$	2.41327	0.0878277
$756$	−0.231548	−0.00842132
$757$	−25.1187	−0.912955	−0.456478	−	0.889735i	$-0.650889\pi$
$757$	−25.1187	−0.912955	−0.456478	+	0.889735i	$0.650889\pi$
$758$	10.8959	0.395756
$759$	−15.6629	−0.568528
$760$	−48.3693	−1.75454
$761$	−16.6751	−0.604473	−0.302237	−	0.953233i	$-0.597733\pi$
$761$	−16.6751	−0.604473	−0.302237	+	0.953233i	$0.597733\pi$
$762$	−4.11142	−0.148941
$763$	−5.69323	−0.206109
$764$	−0.539459	−0.0195169
$765$	−15.8192	−0.571946
$766$	−50.0567	−1.80862
$767$	41.2506	1.48947
$768$	4.61213	0.166426
$769$	−29.6385	−1.06879	−0.534395	−	0.845235i	$-0.679461\pi$
$769$	−29.6385	−1.06879	−0.534395	+	0.845235i	$0.679461\pi$
$770$	−25.5877	−0.922116
$771$	22.5296	0.811384
$772$	4.00000	0.143963
$773$	20.3938	0.733512	0.366756	−	0.930317i	$-0.380468\pi$
$773$	20.3938	0.733512	0.366756	+	0.930317i	$0.380468\pi$
$774$	−14.0811	−0.506135
$775$	−34.2130	−1.22897
$776$	41.5633	1.49203
$777$	0.267745	0.00960529
$778$	51.5038	1.84650
$779$	−27.3982	−0.981643
$780$	1.89446	0.0678326
$781$	−12.6253	−0.451769
$782$	25.3649	0.907045
$783$	7.35026	0.262677
$784$	24.2506	0.866093
$785$	33.7440	1.20438
$786$	−33.0870	−1.18017
$787$	−41.5647	−1.48162	−0.740810	−	0.671714i	$-0.765558\pi$
$787$	−41.5647	−1.48162	−0.740810	+	0.671714i	$0.765558\pi$
$788$	0.629270	0.0224168
$789$	19.2301	0.684611
$790$	−60.4880	−2.15207
$791$	10.0216	0.356327
$792$	11.1187	0.395086
$793$	4.00000	0.142044
$794$	−33.7078	−1.19625
$795$	22.5198	0.798694
$796$	2.42690	0.0860192
$797$	24.1173	0.854279	0.427139	−	0.904186i	$-0.359521\pi$
$797$	24.1173	0.854279	0.427139	+	0.904186i	$0.359521\pi$
$798$	9.18523	0.325154
$799$	14.7670	0.522420
$800$	−7.78304	−0.275172
$801$	−0.775746	−0.0274096
$802$	56.3244	1.98888
$803$	11.1695	0.394163
$804$	−1.03032	−0.0363365
$805$	15.6629	0.552045
$806$	19.9756	0.703609
$807$	−28.3987	−0.999681
$808$	−38.7064	−1.36169
$809$	25.1587	0.884533	0.442266	−	0.896884i	$-0.354175\pi$
$809$	25.1587	0.884533	0.442266	+	0.896884i	$0.354175\pi$
$810$	−5.15633	−0.181175
$811$	−7.03761	−0.247124	−0.123562	−	0.992337i	$-0.539432\pi$
$811$	−7.03761	−0.247124	−0.123562	+	0.992337i	$0.539432\pi$
$812$	−1.70194	−0.0597263
$813$	−19.4763	−0.683063
$814$	1.38058	0.0483893
$815$	15.2496	0.534172
$816$	−19.7685	−0.692034
$817$	49.3766	1.72747
$818$	−7.72355	−0.270047
$819$	3.35026	0.117068
$820$	−3.56134	−0.124367
$821$	−6.55879	−0.228903	−0.114452	−	0.993429i	$-0.536511\pi$
$821$	−6.55879	−0.228903	−0.114452	+	0.993429i	$0.536511\pi$
$822$	−14.8496	−0.517938
$823$	−46.0092	−1.60378	−0.801890	−	0.597472i	$-0.796172\pi$
$823$	−46.0092	−1.60378	−0.801890	+	0.597472i	$0.796172\pi$
$824$	−11.3004	−0.393669
$825$	−29.5877	−1.03011
$826$	25.9972	0.904557
$827$	−6.20711	−0.215842	−0.107921	−	0.994159i	$-0.534419\pi$
$827$	−6.20711	−0.215842	−0.107921	+	0.994159i	$0.534419\pi$
$828$	0.730841	0.0253985
$829$	−15.4518	−0.536664	−0.268332	−	0.963326i	$-0.586472\pi$
$829$	−15.4518	−0.536664	−0.268332	+	0.963326i	$0.586472\pi$
$830$	0.518806	0.0180080
$831$	−13.2750	−0.460506
$832$	−19.8700	−0.688869
$833$	−25.3317	−0.877692
$834$	20.0811	0.695352
$835$	25.3258	0.876436
$836$	4.18664	0.144798
$837$	−4.80606	−0.166122
$838$	−38.3547	−1.32494
$839$	−28.2374	−0.974864	−0.487432	−	0.873161i	$-0.662066\pi$
$839$	−28.2374	−0.974864	−0.487432	+	0.873161i	$0.662066\pi$
$840$	−11.1187	−0.383632
$841$	25.0263	0.862978
$842$	21.4314	0.738574
$843$	13.2447	0.456172
$844$	−4.21696	−0.145154
$845$	17.8446	0.613874
$846$	4.81336	0.165487
$847$	−7.49200	−0.257428
$848$	28.1417	0.966391
$849$	−33.2203	−1.14012
$850$	47.9149	1.64347
$851$	−0.845089	−0.0289693
$852$	0.589104	0.0201824
$853$	38.6516	1.32341	0.661704	−	0.749766i	$-0.269834\pi$
$853$	38.6516	1.32341	0.661704	+	0.749766i	$0.269834\pi$
$854$	2.52090	0.0862635
$855$	18.0811	0.618361
$856$	11.1998	0.382802
$857$	−20.3693	−0.695803	−0.347901	−	0.937531i	$-0.613106\pi$
$857$	−20.3693	−0.695803	−0.347901	+	0.937531i	$0.613106\pi$
$858$	17.2750	0.589760
$859$	−16.0825	−0.548728	−0.274364	−	0.961626i	$-0.588467\pi$
$859$	−16.0825	−0.548728	−0.274364	+	0.961626i	$0.588467\pi$
$860$	6.41819	0.218858
$861$	−6.29806	−0.214637
$862$	−49.3171	−1.67975
$863$	17.8397	0.607271	0.303635	−	0.952788i	$-0.401800\pi$
$863$	17.8397	0.607271	0.303635	+	0.952788i	$0.401800\pi$
$864$	−1.09332	−0.0371955
$865$	−51.2638	−1.74302
$866$	36.7259	1.24800
$867$	3.64974	0.123952
$868$	1.11283	0.0377721
$869$	−48.7572	−1.65397
$870$	−37.9003	−1.28494
$871$	14.9076	0.505126
$872$	−12.7562	−0.431981
$873$	−15.5369	−0.525845
$874$	−28.9916	−0.980654
$875$	8.80606	0.297699
$876$	−0.521175	−0.0176089
$877$	21.1841	0.715336	0.357668	−	0.933849i	$-0.383572\pi$
$877$	21.1841	0.715336	0.357668	+	0.933849i	$0.383572\pi$
$878$	−1.48119	−0.0499879
$879$	−26.1925	−0.883452
$880$	−62.9438	−2.12184
$881$	−47.9716	−1.61620	−0.808102	−	0.589043i	$-0.799505\pi$
$881$	−47.9716	−1.61620	−0.808102	+	0.589043i	$0.799505\pi$
$882$	−8.25694	−0.278026
$883$	28.8799	0.971885	0.485943	−	0.873991i	$-0.338476\pi$
$883$	28.8799	0.971885	0.485943	+	0.873991i	$0.338476\pi$
$884$	−2.47295	−0.0831741
$885$	51.1754	1.72024
$886$	16.4168	0.551532
$887$	−44.7972	−1.50414	−0.752071	−	0.659082i	$-0.770945\pi$
$887$	−44.7972	−1.50414	−0.752071	+	0.659082i	$0.770945\pi$
$888$	0.599908	0.0201316
$889$	3.31406	0.111150
$890$	4.00000	0.134080
$891$	−4.15633	−0.139242
$892$	0.193937	0.00649348
$893$	−16.8785	−0.564816
$894$	−3.19394	−0.106821
$895$	−62.5936	−2.09227
$896$	−15.1333	−0.505568
$897$	−10.5745	−0.353073
$898$	17.2085	0.574256
$899$	−35.3258	−1.17818
$900$	1.38058	0.0460193
$901$	−29.3963	−0.979333
$902$	−32.4749	−1.08129
$903$	11.3503	0.377713
$904$	22.4544	0.746822
$905$	55.8505	1.85653
$906$	−1.02681	−0.0341134
$907$	4.06651	0.135026	0.0675132	−	0.997718i	$-0.478494\pi$
$907$	4.06651	0.135026	0.0675132	+	0.997718i	$0.478494\pi$
$908$	4.88621	0.162155
$909$	14.4690	0.479906
$910$	−17.2750	−0.572662
$911$	−55.7489	−1.84704	−0.923522	−	0.383545i	$-0.874703\pi$
$911$	−55.7489	−1.84704	−0.923522	+	0.383545i	$0.874703\pi$
$912$	22.5950	0.748195
$913$	0.418190	0.0138401
$914$	−14.6556	−0.484765
$915$	4.96239	0.164052
$916$	5.04349	0.166642
$917$	26.6702	0.880728
$918$	6.73084	0.222151
$919$	36.2882	1.19704	0.598519	−	0.801109i	$-0.295756\pi$
$919$	36.2882	1.19704	0.598519	+	0.801109i	$0.295756\pi$
$920$	35.0943	1.15702
$921$	14.6326	0.482160
$922$	10.6340	0.350212
$923$	−8.52373	−0.280562
$924$	0.962389	0.0316603
$925$	−1.59640	−0.0524892
$926$	30.0654	0.988009
$927$	4.22425	0.138743
$928$	−8.03620	−0.263801
$929$	−6.46898	−0.212240	−0.106120	−	0.994353i	$-0.533843\pi$
$929$	−6.46898	−0.212240	−0.106120	+	0.994353i	$0.533843\pi$
$930$	24.7816	0.812622
$931$	28.9537	0.948919
$932$	0.856849	0.0280670
$933$	−20.5296	−0.672109
$934$	14.4241	0.471970
$935$	65.7499	2.15025
$936$	7.50659	0.245360
$937$	−16.7163	−0.546096	−0.273048	−	0.962000i	$-0.588032\pi$
$937$	−16.7163	−0.546096	−0.273048	+	0.962000i	$0.588032\pi$
$938$	9.39517	0.306763
$939$	26.4749	0.863974
$940$	−2.19394	−0.0715583
$941$	1.59166	0.0518866	0.0259433	−	0.999663i	$-0.491741\pi$
$941$	1.59166	0.0518866	0.0259433	+	0.999663i	$0.491741\pi$
$942$	−14.3576	−0.467794
$943$	19.8787	0.647341
$944$	63.9511	2.08143
$945$	4.15633	0.135205
$946$	58.5256	1.90283
$947$	36.8061	1.19604	0.598018	−	0.801483i	$-0.295955\pi$
$947$	36.8061	1.19604	0.598018	+	0.801483i	$0.295955\pi$
$948$	2.27504	0.0738898
$949$	7.54087	0.244787
$950$	−54.7659	−1.77684
$951$	−2.52373	−0.0818376
$952$	14.5139	0.470398
$953$	−3.69815	−0.119795	−0.0598975	−	0.998205i	$-0.519077\pi$
$953$	−3.69815	−0.119795	−0.0598975	+	0.998205i	$0.519077\pi$
$954$	−9.58181	−0.310223
$955$	9.68338	0.313347
$956$	−0.419145	−0.0135561
$957$	−30.5501	−0.987544
$958$	−46.2043	−1.49279
$959$	11.9697	0.386521
$960$	−24.6507	−0.795598
$961$	−7.90175	−0.254895
$962$	0.932071	0.0300512
$963$	−4.18664	−0.134913
$964$	−3.44263	−0.110880
$965$	−71.8007	−2.31135
$966$	−6.66433	−0.214421
$967$	25.4010	0.816843	0.408421	−	0.912794i	$-0.366079\pi$
$967$	25.4010	0.816843	0.408421	+	0.912794i	$0.366079\pi$
$968$	−16.7866	−0.539540
$969$	−23.6023	−0.758214
$970$	80.1133	2.57228
$971$	−22.1622	−0.711219	−0.355609	−	0.934635i	$-0.615727\pi$
$971$	−22.1622	−0.711219	−0.355609	+	0.934635i	$0.615727\pi$
$972$	0.193937	0.00622052
$973$	−16.1866	−0.518920
$974$	−31.2809	−1.00231
$975$	−19.9756	−0.639730
$976$	6.20123	0.198497
$977$	−10.5550	−0.337684	−0.168842	−	0.985643i	$-0.554003\pi$
$977$	−10.5550	−0.337684	−0.168842	+	0.985643i	$0.554003\pi$
$978$	−6.48849	−0.207479
$979$	3.22425	0.103048
$980$	3.76353	0.120221
$981$	4.76845	0.152245
$982$	−45.6834	−1.45782
$983$	53.1900	1.69650	0.848248	−	0.529599i	$-0.177658\pi$
$983$	53.1900	1.69650	0.848248	+	0.529599i	$0.177658\pi$
$984$	−14.1114	−0.449856
$985$	−11.2955	−0.359905
$986$	49.4734	1.57556
$987$	−3.87987	−0.123498
$988$	2.82653	0.0899239
$989$	−35.8251	−1.13917
$990$	21.4314	0.681133
$991$	−61.0348	−1.93883	−0.969417	−	0.245420i	$-0.921074\pi$
$991$	−61.0348	−1.93883	−0.969417	+	0.245420i	$0.921074\pi$
$992$	5.25457	0.166833
$993$	30.4894	0.967553
$994$	−5.37187	−0.170385
$995$	−43.5633	−1.38105
$996$	−0.0195130	−0.000618293 0
$997$	−9.24331	−0.292738	−0.146369	−	0.989230i	$-0.546759\pi$
$997$	−9.24331	−0.292738	−0.146369	+	0.989230i	$0.546759\pi$
$998$	24.5501	0.777119
$999$	−0.224254	−0.00709507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.a.g.1.3	✓	3
3.2	odd	2		2007.2.a.f.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.a.g.1.3	✓	3	1.1	even	1	trivial
2007.2.a.f.1.1		3	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:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.a (trivial)

\(f(q)\)	\(=\)	\(q+1.48119 q^{2} +1.00000 q^{3} +0.193937 q^{4} -3.48119 q^{5} +1.48119 q^{6} -1.19394 q^{7} -2.67513 q^{8} +1.00000 q^{9} -5.15633 q^{10} -4.15633 q^{11} +0.193937 q^{12} -2.80606 q^{13} -1.76845 q^{14} -3.48119 q^{15} -4.35026 q^{16} +4.54420 q^{17} +1.48119 q^{18} -5.19394 q^{19} -0.675131 q^{20} -1.19394 q^{21} -6.15633 q^{22} +3.76845 q^{23} -2.67513 q^{24} +7.11871 q^{25} -4.15633 q^{26} +1.00000 q^{27} -0.231548 q^{28} +7.35026 q^{29} -5.15633 q^{30} -4.80606 q^{31} -1.09332 q^{32} -4.15633 q^{33} +6.73084 q^{34} +4.15633 q^{35} +0.193937 q^{36} -0.224254 q^{37} -7.69323 q^{38} -2.80606 q^{39} +9.31265 q^{40} +5.27504 q^{41} -1.76845 q^{42} -9.50659 q^{43} -0.806063 q^{44} -3.48119 q^{45} +5.58181 q^{46} +3.24965 q^{47} -4.35026 q^{48} -5.57452 q^{49} +10.5442 q^{50} +4.54420 q^{51} -0.544198 q^{52} -6.46898 q^{53} +1.48119 q^{54} +14.4690 q^{55} +3.19394 q^{56} -5.19394 q^{57} +10.8872 q^{58} -14.7005 q^{59} -0.675131 q^{60} -1.42548 q^{61} -7.11871 q^{62} -1.19394 q^{63} +7.08110 q^{64} +9.76845 q^{65} -6.15633 q^{66} -5.31265 q^{67} +0.881286 q^{68} +3.76845 q^{69} +6.15633 q^{70} +3.03761 q^{71} -2.67513 q^{72} -2.68735 q^{73} -0.332163 q^{74} +7.11871 q^{75} -1.00729 q^{76} +4.96239 q^{77} -4.15633 q^{78} +11.7308 q^{79} +15.1441 q^{80} +1.00000 q^{81} +7.81336 q^{82} -0.100615 q^{83} -0.231548 q^{84} -15.8192 q^{85} -14.0811 q^{86} +7.35026 q^{87} +11.1187 q^{88} -0.775746 q^{89} -5.15633 q^{90} +3.35026 q^{91} +0.730841 q^{92} -4.80606 q^{93} +4.81336 q^{94} +18.0811 q^{95} -1.09332 q^{96} -15.5369 q^{97} -8.25694 q^{98} -4.15633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} + q^{4} - 5 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + q^{12} - 8 q^{13} + 6 q^{14} - 5 q^{15} - 3 q^{16} + 4 q^{17} - q^{18} - 16 q^{19} + 3 q^{20} - 4 q^{21}+ \cdots - 2 q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 + q^4 - 5 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + q^12 - 8 * q^13 + 6 * q^14 - 5 * q^15 - 3 * q^16 + 4 * q^17 - q^18 - 16 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^22 - 3 * q^24 - 2 * q^26 + 3 * q^27 - 12 * q^28 + 12 * q^29 - 5 * q^30 - 14 * q^31 + 3 * q^32 - 2 * q^33 - 2 * q^34 + 2 * q^35 + q^36 + q^37 + 10 * q^38 - 8 * q^39 + 7 * q^40 - 16 * q^41 + 6 * q^42 - 8 * q^43 - 2 * q^44 - 5 * q^45 + 18 * q^46 - 7 * q^47 - 3 * q^48 - 5 * q^49 + 22 * q^50 + 4 * q^51 + 8 * q^52 + 12 * q^53 - q^54 + 12 * q^55 + 10 * q^56 - 16 * q^57 - 24 * q^59 + 3 * q^60 - 16 * q^61 - 4 * q^63 - 11 * q^64 + 18 * q^65 - 8 * q^66 + 5 * q^67 + 24 * q^68 + 8 * q^70 + 20 * q^71 - 3 * q^72 - 29 * q^73 - 19 * q^74 - 16 * q^76 + 4 * q^77 - 2 * q^78 + 13 * q^79 + 9 * q^80 + 3 * q^81 + 36 * q^82 - 7 * q^83 - 12 * q^84 - 6 * q^85 - 10 * q^86 + 12 * q^87 + 12 * q^88 - 4 * q^89 - 5 * q^90 - 20 * q^92 - 14 * q^93 + 27 * q^94 + 22 * q^95 + 3 * q^96 - 24 * q^97 - 21 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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