LMFDB - Embedded newform 2299.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,2,Mod(1,2299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2299, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$18.3576074247$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.71457$ of defining polynomial
Character	$\chi$	$=$	2299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.65432 q^{2} +0.121872 q^{3} +5.04540 q^{4} -1.06025 q^{5} -0.323487 q^{6} +3.36889 q^{7} -8.08346 q^{8} -2.98515 q^{9} +2.81425 q^{10} +0.614893 q^{12} +2.15993 q^{13} -8.94209 q^{14} -0.129215 q^{15} +11.3653 q^{16} -3.67288 q^{17} +7.92353 q^{18} +1.00000 q^{19} -5.34940 q^{20} +0.410573 q^{21} +3.15468 q^{23} -0.985147 q^{24} -3.87587 q^{25} -5.73313 q^{26} -0.729422 q^{27} +16.9974 q^{28} -7.17849 q^{29} +0.342978 q^{30} +4.65295 q^{31} -14.0001 q^{32} +9.74900 q^{34} -3.57187 q^{35} -15.0613 q^{36} +2.27446 q^{37} -2.65432 q^{38} +0.263235 q^{39} +8.57050 q^{40} +11.3852 q^{41} -1.08979 q^{42} -9.38838 q^{43} +3.16501 q^{45} -8.37352 q^{46} -5.77094 q^{47} +1.38511 q^{48} +4.34940 q^{49} +10.2878 q^{50} -0.447622 q^{51} +10.8977 q^{52} -5.65820 q^{53} +1.93612 q^{54} -27.2322 q^{56} +0.121872 q^{57} +19.0540 q^{58} -13.7944 q^{59} -0.651942 q^{60} -6.98152 q^{61} -12.3504 q^{62} -10.0566 q^{63} +14.4301 q^{64} -2.29007 q^{65} -4.81332 q^{67} -18.5312 q^{68} +0.384467 q^{69} +9.48087 q^{70} +15.2629 q^{71} +24.1303 q^{72} +8.08806 q^{73} -6.03713 q^{74} -0.472360 q^{75} +5.04540 q^{76} -0.698709 q^{78} -13.4291 q^{79} -12.0500 q^{80} +8.86655 q^{81} -30.2199 q^{82} -9.96666 q^{83} +2.07150 q^{84} +3.89418 q^{85} +24.9197 q^{86} -0.874858 q^{87} -4.61626 q^{89} -8.40094 q^{90} +7.27655 q^{91} +15.9166 q^{92} +0.567064 q^{93} +15.3179 q^{94} -1.06025 q^{95} -1.70622 q^{96} -4.09907 q^{97} -11.5447 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21}+ \cdots + 10 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.65432	−1.87689	−0.938443	−	0.345435i	$-0.887732\pi$
$2$	−2.65432	−1.87689	−0.938443	+	0.345435i	$0.887732\pi$
$3$	0.121872	0.0703629	0.0351814	−	0.999381i	$-0.488799\pi$
$3$	0.121872	0.0703629	0.0351814	+	0.999381i	$0.488799\pi$
$4$	5.04540	2.52270
$5$	−1.06025	−0.474159	−0.237080	−	0.971490i	$-0.576190\pi$
$5$	−1.06025	−0.474159	−0.237080	+	0.971490i	$0.576190\pi$
$6$	−0.323487	−0.132063
$7$	3.36889	1.27332	0.636660	−	0.771145i	$-0.280316\pi$
$7$	3.36889	1.27332	0.636660	+	0.771145i	$0.280316\pi$
$8$	−8.08346	−2.85793
$9$	−2.98515	−0.995049
$10$	2.81425	0.889943
$11$	0	0
$11$	0	0
$12$	0.614893	0.177504
$13$	2.15993	0.599056	0.299528	−	0.954087i	$-0.403171\pi$
$13$	2.15993	0.599056	0.299528	+	0.954087i	$0.403171\pi$
$14$	−8.94209	−2.38987
$15$	−0.129215	−0.0333632
$16$	11.3653	2.84131
$17$	−3.67288	−0.890805	−0.445402	−	0.895330i	$-0.646939\pi$
$17$	−3.67288	−0.890805	−0.445402	+	0.895330i	$0.646939\pi$
$18$	7.92353	1.86759
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−5.34940	−1.19616
$21$	0.410573	0.0895944
$22$	0	0
$23$	3.15468	0.657797	0.328898	−	0.944365i	$-0.393323\pi$
$23$	3.15468	0.657797	0.328898	+	0.944365i	$0.393323\pi$
$24$	−0.985147	−0.201092
$25$	−3.87587	−0.775173
$26$	−5.73313	−1.12436
$27$	−0.729422	−0.140377
$28$	16.9974	3.21220
$29$	−7.17849	−1.33301	−0.666506	−	0.745499i	$-0.732211\pi$
$29$	−7.17849	−1.33301	−0.666506	+	0.745499i	$0.732211\pi$
$30$	0.342978	0.0626189
$31$	4.65295	0.835694	0.417847	−	0.908517i	$-0.362785\pi$
$31$	4.65295	0.835694	0.417847	+	0.908517i	$0.362785\pi$
$32$	−14.0001	−2.47489
$33$	0	0
$34$	9.74900	1.67194
$35$	−3.57187	−0.603756
$36$	−15.0613	−2.51021
$37$	2.27446	0.373918	0.186959	−	0.982368i	$-0.440137\pi$
$37$	2.27446	0.373918	0.186959	+	0.982368i	$0.440137\pi$
$38$	−2.65432	−0.430587
$39$	0.263235	0.0421513
$40$	8.57050	1.35512
$41$	11.3852	1.77807	0.889034	−	0.457841i	$-0.151377\pi$
$41$	11.3852	1.77807	0.889034	+	0.457841i	$0.151377\pi$
$42$	−1.08979	−0.168158
$43$	−9.38838	−1.43171	−0.715857	−	0.698247i	$-0.753964\pi$
$43$	−9.38838	−1.43171	−0.715857	+	0.698247i	$0.753964\pi$
$44$	0	0
$45$	3.16501	0.471812
$46$	−8.37352	−1.23461
$47$	−5.77094	−0.841778	−0.420889	−	0.907112i	$-0.638282\pi$
$47$	−5.77094	−0.841778	−0.420889	+	0.907112i	$0.638282\pi$
$48$	1.38511	0.199923
$49$	4.34940	0.621342
$50$	10.2878	1.45491
$51$	−0.447622	−0.0626796
$52$	10.8977	1.51124
$53$	−5.65820	−0.777213	−0.388607	−	0.921404i	$-0.627043\pi$
$53$	−5.65820	−0.777213	−0.388607	+	0.921404i	$0.627043\pi$
$54$	1.93612	0.263472
$55$	0	0
$56$	−27.2322	−3.63906
$57$	0.121872	0.0161423
$58$	19.0540	2.50191
$59$	−13.7944	−1.79588	−0.897939	−	0.440121i	$-0.854936\pi$
$59$	−13.7944	−1.79588	−0.897939	+	0.440121i	$0.854936\pi$
$60$	−0.651942	−0.0841653
$61$	−6.98152	−0.893892	−0.446946	−	0.894561i	$-0.647488\pi$
$61$	−6.98152	−0.893892	−0.446946	+	0.894561i	$0.647488\pi$
$62$	−12.3504	−1.56850
$63$	−10.0566	−1.26702
$64$	14.4301	1.80377
$65$	−2.29007	−0.284048
$66$	0	0
$67$	−4.81332	−0.588041	−0.294020	−	0.955799i	$-0.594993\pi$
$67$	−4.81332	−0.588041	−0.294020	+	0.955799i	$0.594993\pi$
$68$	−18.5312	−2.24723
$69$	0.384467	0.0462844
$70$	9.48087	1.13318
$71$	15.2629	1.81137	0.905685	−	0.423951i	$-0.139357\pi$
$71$	15.2629	1.81137	0.905685	+	0.423951i	$0.139357\pi$
$72$	24.1303	2.84378
$73$	8.08806	0.946636	0.473318	−	0.880892i	$-0.343056\pi$
$73$	8.08806	0.946636	0.473318	+	0.880892i	$0.343056\pi$
$74$	−6.03713	−0.701802
$75$	−0.472360	−0.0545434
$76$	5.04540	0.578747
$77$	0	0
$78$	−0.698709	−0.0791132
$79$	−13.4291	−1.51090	−0.755448	−	0.655209i	$-0.772581\pi$
$79$	−13.4291	−1.51090	−0.755448	+	0.655209i	$0.772581\pi$
$80$	−12.0500	−1.34724
$81$	8.86655	0.985172
$82$	−30.2199	−3.33723
$83$	−9.96666	−1.09398	−0.546992	−	0.837138i	$-0.684227\pi$
$83$	−9.96666	−1.09398	−0.546992	+	0.837138i	$0.684227\pi$
$84$	2.07150	0.226020
$85$	3.89418	0.422383
$86$	24.9197	2.68716
$87$	−0.874858	−0.0937946
$88$	0	0
$89$	−4.61626	−0.489323	−0.244661	−	0.969609i	$-0.578677\pi$
$89$	−4.61626	−0.489323	−0.244661	+	0.969609i	$0.578677\pi$
$90$	−8.40094	−0.885537
$91$	7.27655	0.762790
$92$	15.9166	1.65942
$93$	0.567064	0.0588018
$94$	15.3179	1.57992
$95$	−1.06025	−0.108780
$96$	−1.70622	−0.174140
$97$	−4.09907	−0.416197	−0.208099	−	0.978108i	$-0.566727\pi$
$97$	−4.09907	−0.416197	−0.208099	+	0.978108i	$0.566727\pi$
$98$	−11.5447	−1.16619
$99$	0	0
$100$	−19.5553	−1.95553
$101$	10.8730	1.08190	0.540950	−	0.841055i	$-0.318065\pi$
$101$	10.8730	1.08190	0.540950	+	0.841055i	$0.318065\pi$
$102$	1.18813	0.117642
$103$	8.85864	0.872867	0.436434	−	0.899736i	$-0.356241\pi$
$103$	8.85864	0.872867	0.436434	+	0.899736i	$0.356241\pi$
$104$	−17.4597	−1.71206
$105$	−0.435311	−0.0424820
$106$	15.0186	1.45874
$107$	18.1669	1.75626	0.878131	−	0.478421i	$-0.158791\pi$
$107$	18.1669	1.75626	0.878131	+	0.478421i	$0.158791\pi$
$108$	−3.68023	−0.354130
$109$	0.211303	0.0202392	0.0101196	−	0.999949i	$-0.496779\pi$
$109$	0.211303	0.0202392	0.0101196	+	0.999949i	$0.496779\pi$
$110$	0	0
$111$	0.277193	0.0263100
$112$	38.2883	3.61790
$113$	−0.198345	−0.0186587	−0.00932935	−	0.999956i	$-0.502970\pi$
$113$	−0.198345	−0.0186587	−0.00932935	+	0.999956i	$0.502970\pi$
$114$	−0.323487	−0.0302973
$115$	−3.34476	−0.311900
$116$	−36.2184	−3.36279
$117$	−6.44770	−0.596090
$118$	36.6147	3.37066
$119$	−12.3735	−1.13428
$120$	1.04450	0.0953498
$121$	0	0
$122$	18.5312	1.67773
$123$	1.38754	0.125110
$124$	23.4760	2.10821
$125$	9.41066	0.841715
$126$	26.6935	2.37804
$127$	3.60331	0.319742	0.159871	−	0.987138i	$-0.448892\pi$
$127$	3.60331	0.319742	0.159871	+	0.987138i	$0.448892\pi$
$128$	−10.3020	−0.910578
$129$	−1.14418	−0.100739
$130$	6.07857	0.533126
$131$	−16.8741	−1.47430	−0.737150	−	0.675729i	$-0.763829\pi$
$131$	−16.8741	−1.47430	−0.737150	+	0.675729i	$0.763829\pi$
$132$	0	0
$133$	3.36889	0.292119
$134$	12.7761	1.10369
$135$	0.773371	0.0665612
$136$	29.6896	2.54586
$137$	−6.10839	−0.521875	−0.260937	−	0.965356i	$-0.584032\pi$
$137$	−6.10839	−0.521875	−0.260937	+	0.965356i	$0.584032\pi$
$138$	−1.02050	−0.0868706
$139$	−11.3347	−0.961398	−0.480699	−	0.876886i	$-0.659617\pi$
$139$	−11.3347	−0.961398	−0.480699	+	0.876886i	$0.659617\pi$
$140$	−18.0215	−1.52310
$141$	−0.703316	−0.0592299
$142$	−40.5125	−3.39973
$143$	0	0
$144$	−33.9270	−2.82725
$145$	7.61101	0.632060
$146$	−21.4683	−1.77673
$147$	0.530070	0.0437194
$148$	11.4755	0.943284
$149$	−6.75698	−0.553554	−0.276777	−	0.960934i	$-0.589266\pi$
$149$	−6.75698	−0.553554	−0.276777	+	0.960934i	$0.589266\pi$
$150$	1.25379	0.102372
$151$	−6.46231	−0.525895	−0.262948	−	0.964810i	$-0.584695\pi$
$151$	−6.46231	−0.525895	−0.262948	+	0.964810i	$0.584695\pi$
$152$	−8.08346	−0.655655
$153$	10.9641	0.886395
$154$	0	0
$155$	−4.93330	−0.396252
$156$	1.32813	0.106335
$157$	0.248382	0.0198230	0.00991152	−	0.999951i	$-0.496845\pi$
$157$	0.248382	0.0198230	0.00991152	+	0.999951i	$0.496845\pi$
$158$	35.6452	2.83578
$159$	−0.689576	−0.0546869
$160$	14.8436	1.17349
$161$	10.6278	0.837585
$162$	−23.5346	−1.84905
$163$	−16.9710	−1.32927	−0.664637	−	0.747167i	$-0.731414\pi$
$163$	−16.9710	−1.32927	−0.664637	+	0.747167i	$0.731414\pi$
$164$	57.4428	4.48553
$165$	0	0
$166$	26.4547	2.05328
$167$	0.865538	0.0669773	0.0334887	−	0.999439i	$-0.489338\pi$
$167$	0.865538	0.0669773	0.0334887	+	0.999439i	$0.489338\pi$
$168$	−3.31885	−0.256055
$169$	−8.33471	−0.641132
$170$	−10.3364	−0.792765
$171$	−2.98515	−0.228280
$172$	−47.3681	−3.61178
$173$	4.14483	0.315125	0.157563	−	0.987509i	$-0.449636\pi$
$173$	4.14483	0.315125	0.157563	+	0.987509i	$0.449636\pi$
$174$	2.32215	0.176042
$175$	−13.0574	−0.987043
$176$	0	0
$177$	−1.68115	−0.126363
$178$	12.2530	0.918403
$179$	2.04584	0.152913	0.0764567	−	0.997073i	$-0.475639\pi$
$179$	2.04584	0.152913	0.0764567	+	0.997073i	$0.475639\pi$
$180$	15.9687	1.19024
$181$	5.27519	0.392101	0.196051	−	0.980594i	$-0.437188\pi$
$181$	5.27519	0.392101	0.196051	+	0.980594i	$0.437188\pi$
$182$	−19.3143	−1.43167
$183$	−0.850852	−0.0628968
$184$	−25.5007	−1.87994
$185$	−2.41150	−0.177297
$186$	−1.50517	−0.110364
$187$	0	0
$188$	−29.1167	−2.12355
$189$	−2.45734	−0.178745
$190$	2.81425	0.204167
$191$	−16.1899	−1.17146	−0.585729	−	0.810507i	$-0.699192\pi$
$191$	−16.1899	−1.17146	−0.585729	+	0.810507i	$0.699192\pi$
$192$	1.75863	0.126918
$193$	20.0620	1.44409	0.722045	−	0.691846i	$-0.243202\pi$
$193$	20.0620	1.44409	0.722045	+	0.691846i	$0.243202\pi$
$194$	10.8802	0.781155
$195$	−0.279095	−0.0199864
$196$	21.9444	1.56746
$197$	23.8398	1.69851	0.849257	−	0.527979i	$-0.177050\pi$
$197$	23.8398	1.69851	0.849257	+	0.527979i	$0.177050\pi$
$198$	0	0
$199$	−1.90194	−0.134825	−0.0674125	−	0.997725i	$-0.521474\pi$
$199$	−1.90194	−0.134825	−0.0674125	+	0.997725i	$0.521474\pi$
$200$	31.3304	2.21539
$201$	−0.586609	−0.0413762
$202$	−28.8603	−2.03060
$203$	−24.1835	−1.69735
$204$	−2.25843	−0.158122
$205$	−12.0712	−0.843087
$206$	−23.5136	−1.63827
$207$	−9.41719	−0.654540
$208$	24.5481	1.70211
$209$	0	0
$210$	1.15545	0.0797339
$211$	−12.3048	−0.847100	−0.423550	−	0.905873i	$-0.639216\pi$
$211$	−12.3048	−0.847100	−0.423550	+	0.905873i	$0.639216\pi$
$212$	−28.5479	−1.96068
$213$	1.86012	0.127453
$214$	−48.2207	−3.29630
$215$	9.95405	0.678860
$216$	5.89625	0.401189
$217$	15.6753	1.06411
$218$	−0.560865	−0.0379866
$219$	0.985709	0.0666080
$220$	0	0
$221$	−7.93316	−0.533642
$222$	−0.735757	−0.0493808
$223$	22.8473	1.52997	0.764985	−	0.644048i	$-0.222746\pi$
$223$	22.8473	1.52997	0.764985	+	0.644048i	$0.222746\pi$
$224$	−47.1647	−3.15132
$225$	11.5700	0.771335
$226$	0.526470	0.0350202
$227$	−4.00654	−0.265923	−0.132962	−	0.991121i	$-0.542449\pi$
$227$	−4.00654	−0.265923	−0.132962	+	0.991121i	$0.542449\pi$
$228$	0.614893	0.0407223
$229$	−24.6024	−1.62577	−0.812887	−	0.582422i	$-0.802105\pi$
$229$	−24.6024	−1.62577	−0.812887	+	0.582422i	$0.802105\pi$
$230$	8.87805	0.585401
$231$	0	0
$232$	58.0270	3.80966
$233$	−16.2994	−1.06781	−0.533903	−	0.845545i	$-0.679275\pi$
$233$	−16.2994	−1.06781	−0.533903	+	0.845545i	$0.679275\pi$
$234$	17.1143	1.11879
$235$	6.11865	0.399137
$236$	−69.5982	−4.53046
$237$	−1.63664	−0.106311
$238$	32.8433	2.12891
$239$	15.4182	0.997324	0.498662	−	0.866797i	$-0.333825\pi$
$239$	15.4182	0.997324	0.498662	+	0.866797i	$0.333825\pi$
$240$	−1.46856	−0.0947953
$241$	−24.1441	−1.55526	−0.777629	−	0.628723i	$-0.783578\pi$
$241$	−24.1441	−1.55526	−0.777629	+	0.628723i	$0.783578\pi$
$242$	0	0
$243$	3.26885	0.209697
$244$	−35.2245	−2.25502
$245$	−4.61146	−0.294615
$246$	−3.68296	−0.234817
$247$	2.15993	0.137433
$248$	−37.6119	−2.38836
$249$	−1.21466	−0.0769758
$250$	−24.9789	−1.57980
$251$	−19.9099	−1.25670	−0.628350	−	0.777931i	$-0.716269\pi$
$251$	−19.9099	−1.25670	−0.628350	+	0.777931i	$0.716269\pi$
$252$	−50.7397	−3.19630
$253$	0	0
$254$	−9.56433	−0.600119
$255$	0.474592	0.0297201
$256$	−1.51547	−0.0947166
$257$	−22.3126	−1.39182	−0.695911	−	0.718128i	$-0.744999\pi$
$257$	−22.3126	−1.39182	−0.695911	+	0.718128i	$0.744999\pi$
$258$	3.03702	0.189076
$259$	7.66239	0.476118
$260$	−11.5543	−0.716568
$261$	21.4289	1.32641
$262$	44.7893	2.76709
$263$	−13.7963	−0.850716	−0.425358	−	0.905025i	$-0.639852\pi$
$263$	−13.7963	−0.850716	−0.425358	+	0.905025i	$0.639852\pi$
$264$	0	0
$265$	5.99912	0.368523
$266$	−8.94209	−0.548275
$267$	−0.562593	−0.0344301
$268$	−24.2851	−1.48345
$269$	−11.2028	−0.683048	−0.341524	−	0.939873i	$-0.610943\pi$
$269$	−11.2028	−0.683048	−0.341524	+	0.939873i	$0.610943\pi$
$270$	−2.05277	−0.124928
$271$	−17.1234	−1.04017	−0.520085	−	0.854115i	$-0.674100\pi$
$271$	−17.1234	−1.04017	−0.520085	+	0.854115i	$0.674100\pi$
$272$	−41.7433	−2.53106
$273$	0.886808	0.0536721
$274$	16.2136	0.979499
$275$	0	0
$276$	1.93979	0.116762
$277$	13.7127	0.823919	0.411960	−	0.911202i	$-0.364844\pi$
$277$	13.7127	0.823919	0.411960	+	0.911202i	$0.364844\pi$
$278$	30.0859	1.80443
$279$	−13.8897	−0.831557
$280$	28.8730	1.72549
$281$	−25.8599	−1.54267	−0.771337	−	0.636427i	$-0.780412\pi$
$281$	−25.8599	−1.54267	−0.771337	+	0.636427i	$0.780412\pi$
$282$	1.86682	0.111168
$283$	−28.8711	−1.71621	−0.858103	−	0.513477i	$-0.828357\pi$
$283$	−28.8711	−1.71621	−0.858103	+	0.513477i	$0.828357\pi$
$284$	77.0073	4.56954
$285$	−0.129215	−0.00765404
$286$	0	0
$287$	38.3554	2.26405
$288$	41.7923	2.46264
$289$	−3.50993	−0.206467
$290$	−20.2020	−1.18630
$291$	−0.499562	−0.0292848
$292$	40.8075	2.38808
$293$	−6.37971	−0.372707	−0.186353	−	0.982483i	$-0.559667\pi$
$293$	−6.37971	−0.372707	−0.186353	+	0.982483i	$0.559667\pi$
$294$	−1.40697	−0.0820563
$295$	14.6255	0.851532
$296$	−18.3855	−1.06863
$297$	0	0
$298$	17.9352	1.03896
$299$	6.81389	0.394057
$300$	−2.38324	−0.137597
$301$	−31.6284	−1.82303
$302$	17.1530	0.987045
$303$	1.32511	0.0761256
$304$	11.3653	0.651842
$305$	7.40217	0.423847
$306$	−29.1022	−1.66366
$307$	−10.4299	−0.595264	−0.297632	−	0.954681i	$-0.596197\pi$
$307$	−10.4299	−0.595264	−0.297632	+	0.954681i	$0.596197\pi$
$308$	0	0
$309$	1.07962	0.0614174
$310$	13.0945	0.743720
$311$	−8.26224	−0.468508	−0.234254	−	0.972175i	$-0.575265\pi$
$311$	−8.26224	−0.468508	−0.234254	+	0.972175i	$0.575265\pi$
$312$	−2.12785	−0.120466
$313$	−24.1167	−1.36315	−0.681577	−	0.731746i	$-0.738706\pi$
$313$	−24.1167	−1.36315	−0.681577	+	0.731746i	$0.738706\pi$
$314$	−0.659285	−0.0372056
$315$	10.6626	0.600767
$316$	−67.7554	−3.81154
$317$	−11.7330	−0.658989	−0.329495	−	0.944157i	$-0.606878\pi$
$317$	−11.7330	−0.658989	−0.329495	+	0.944157i	$0.606878\pi$
$318$	1.83035	0.102641
$319$	0	0
$320$	−15.2996	−0.855273
$321$	2.21404	0.123576
$322$	−28.2095	−1.57205
$323$	−3.67288	−0.204365
$324$	44.7353	2.48529
$325$	−8.37159	−0.464372
$326$	45.0465	2.49489
$327$	0.0257519	0.00142409
$328$	−92.0317	−5.08160
$329$	−19.4416	−1.07185
$330$	0	0
$331$	−6.95223	−0.382129	−0.191065	−	0.981577i	$-0.561194\pi$
$331$	−6.95223	−0.382129	−0.191065	+	0.981577i	$0.561194\pi$
$332$	−50.2858	−2.75979
$333$	−6.78959	−0.372067
$334$	−2.29741	−0.125709
$335$	5.10333	0.278825
$336$	4.66627	0.254566
$337$	−29.4416	−1.60379	−0.801893	−	0.597468i	$-0.796174\pi$
$337$	−29.4416	−1.60379	−0.801893	+	0.597468i	$0.796174\pi$
$338$	22.1230	1.20333
$339$	−0.0241727	−0.00131288
$340$	19.6477	1.06555
$341$	0	0
$342$	7.92353	0.428455
$343$	−8.92959	−0.482152
$344$	75.8905	4.09174
$345$	−0.407632	−0.0219462
$346$	−11.0017	−0.591454
$347$	17.2180	0.924311	0.462155	−	0.886799i	$-0.347076\pi$
$347$	17.2180	0.924311	0.462155	+	0.886799i	$0.347076\pi$
$348$	−4.41401	−0.236616
$349$	−4.32405	−0.231461	−0.115731	−	0.993281i	$-0.536921\pi$
$349$	−4.32405	−0.231461	−0.115731	+	0.993281i	$0.536921\pi$
$350$	34.6583	1.85257
$351$	−1.57550	−0.0840939
$352$	0	0
$353$	23.4421	1.24770	0.623848	−	0.781545i	$-0.285568\pi$
$353$	23.4421	1.24770	0.623848	+	0.781545i	$0.285568\pi$
$354$	4.46231	0.237169
$355$	−16.1825	−0.858878
$356$	−23.2909	−1.23441
$357$	−1.50799	−0.0798111
$358$	−5.43031	−0.287001
$359$	−8.20544	−0.433066	−0.216533	−	0.976275i	$-0.569475\pi$
$359$	−8.20544	−0.433066	−0.216533	+	0.976275i	$0.569475\pi$
$360$	−25.5842	−1.34841
$361$	1.00000	0.0526316
$362$	−14.0020	−0.735930
$363$	0	0
$364$	36.7131	1.92429
$365$	−8.57539	−0.448856
$366$	2.25843	0.118050
$367$	33.1494	1.73039	0.865193	−	0.501439i	$-0.167196\pi$
$367$	33.1494	1.73039	0.865193	+	0.501439i	$0.167196\pi$
$368$	35.8538	1.86901
$369$	−33.9865	−1.76926
$370$	6.40088	0.332766
$371$	−19.0618	−0.989640
$372$	2.86107	0.148339
$373$	16.5840	0.858685	0.429343	−	0.903142i	$-0.358745\pi$
$373$	16.5840	0.858685	0.429343	+	0.903142i	$0.358745\pi$
$374$	0	0
$375$	1.14690	0.0592254
$376$	46.6492	2.40575
$377$	−15.5050	−0.798550
$378$	6.52256	0.335484
$379$	5.79467	0.297652	0.148826	−	0.988863i	$-0.452451\pi$
$379$	5.79467	0.297652	0.148826	+	0.988863i	$0.452451\pi$
$380$	−5.34940	−0.274418
$381$	0.439143	0.0224980
$382$	42.9730	2.19869
$383$	5.89016	0.300973	0.150487	−	0.988612i	$-0.451916\pi$
$383$	5.89016	0.300973	0.150487	+	0.988612i	$0.451916\pi$
$384$	−1.25553	−0.0640709
$385$	0	0
$386$	−53.2508	−2.71039
$387$	28.0257	1.42463
$388$	−20.6814	−1.04994
$389$	13.8055	0.699964	0.349982	−	0.936756i	$-0.386188\pi$
$389$	13.8055	0.699964	0.349982	+	0.936756i	$0.386188\pi$
$390$	0.740808	0.0375122
$391$	−11.5868	−0.585968
$392$	−35.1581	−1.77575
$393$	−2.05649	−0.103736
$394$	−63.2784	−3.18792
$395$	14.2383	0.716405
$396$	0	0
$397$	6.48471	0.325458	0.162729	−	0.986671i	$-0.447970\pi$
$397$	6.48471	0.325458	0.162729	+	0.986671i	$0.447970\pi$
$398$	5.04835	0.253051
$399$	0.410573	0.0205544
$400$	−44.0502	−2.20251
$401$	3.70806	0.185172	0.0925858	−	0.995705i	$-0.470487\pi$
$401$	3.70806	0.185172	0.0925858	+	0.995705i	$0.470487\pi$
$402$	1.55705	0.0776584
$403$	10.0500	0.500628
$404$	54.8584	2.72931
$405$	−9.40077	−0.467128
$406$	64.1908	3.18573
$407$	0	0
$408$	3.61833	0.179134
$409$	−31.0569	−1.53567	−0.767833	−	0.640650i	$-0.778665\pi$
$409$	−31.0569	−1.53567	−0.767833	+	0.640650i	$0.778665\pi$
$410$	32.0407	1.58238
$411$	−0.744442	−0.0367206
$412$	44.6954	2.20198
$413$	−46.4717	−2.28673
$414$	24.9962	1.22850
$415$	10.5672	0.518722
$416$	−30.2392	−1.48260
$417$	−1.38138	−0.0676467
$418$	0	0
$419$	−11.2871	−0.551410	−0.275705	−	0.961242i	$-0.588911\pi$
$419$	−11.2871	−0.551410	−0.275705	+	0.961242i	$0.588911\pi$
$420$	−2.19632	−0.107169
$421$	34.5194	1.68237	0.841186	−	0.540746i	$-0.181858\pi$
$421$	34.5194	1.68237	0.841186	+	0.540746i	$0.181858\pi$
$422$	32.6609	1.58991
$423$	17.2271	0.837611
$424$	45.7378	2.22122
$425$	14.2356	0.690528
$426$	−4.93734	−0.239215
$427$	−23.5199	−1.13821
$428$	91.6593	4.43052
$429$	0	0
$430$	−26.4212	−1.27414
$431$	−18.1654	−0.874996	−0.437498	−	0.899219i	$-0.644135\pi$
$431$	−18.1654	−0.874996	−0.437498	+	0.899219i	$0.644135\pi$
$432$	−8.29007	−0.398856
$433$	10.7804	0.518075	0.259037	−	0.965867i	$-0.416595\pi$
$433$	10.7804	0.518075	0.259037	+	0.965867i	$0.416595\pi$
$434$	−41.6071	−1.99720
$435$	0.927570	0.0444736
$436$	1.06611	0.0510573
$437$	3.15468	0.150909
$438$	−2.61638	−0.125016
$439$	1.38742	0.0662180	0.0331090	−	0.999452i	$-0.489459\pi$
$439$	1.38742	0.0662180	0.0331090	+	0.999452i	$0.489459\pi$
$440$	0	0
$441$	−12.9836	−0.618266
$442$	21.0571	1.00159
$443$	−7.26792	−0.345310	−0.172655	−	0.984982i	$-0.555234\pi$
$443$	−7.26792	−0.345310	−0.172655	+	0.984982i	$0.555234\pi$
$444$	1.39855	0.0663722
$445$	4.89440	0.232017
$446$	−60.6441	−2.87158
$447$	−0.823487	−0.0389496
$448$	48.6135	2.29677
$449$	21.4298	1.01134	0.505668	−	0.862728i	$-0.331246\pi$
$449$	21.4298	1.01134	0.505668	+	0.862728i	$0.331246\pi$
$450$	−30.7105	−1.44771
$451$	0	0
$452$	−1.00073	−0.0470703
$453$	−0.787575	−0.0370035
$454$	10.6346	0.499108
$455$	−7.71498	−0.361684
$456$	−0.985147	−0.0461337
$457$	17.6312	0.824754	0.412377	−	0.911013i	$-0.364699\pi$
$457$	17.6312	0.824754	0.412377	+	0.911013i	$0.364699\pi$
$458$	65.3026	3.05139
$459$	2.67908	0.125049
$460$	−16.8756	−0.786831
$461$	−34.2073	−1.59320	−0.796598	−	0.604510i	$-0.793369\pi$
$461$	−34.2073	−1.59320	−0.796598	+	0.604510i	$0.793369\pi$
$462$	0	0
$463$	−11.0009	−0.511253	−0.255626	−	0.966776i	$-0.582282\pi$
$463$	−11.0009	−0.511253	−0.255626	+	0.966776i	$0.582282\pi$
$464$	−81.5854	−3.78751
$465$	−0.601231	−0.0278814
$466$	43.2637	2.00415
$467$	4.38453	0.202892	0.101446	−	0.994841i	$-0.467653\pi$
$467$	4.38453	0.202892	0.101446	+	0.994841i	$0.467653\pi$
$468$	−32.5312	−1.50376
$469$	−16.2155	−0.748764
$470$	−16.2408	−0.749134
$471$	0.0302708	0.00139481
$472$	111.506	5.13250
$473$	0	0
$474$	4.34415	0.199534
$475$	−3.87587	−0.177837
$476$	−62.4294	−2.86145
$477$	16.8905	0.773365
$478$	−40.9249	−1.87186
$479$	14.3683	0.656505	0.328253	−	0.944590i	$-0.393540\pi$
$479$	14.3683	0.656505	0.328253	+	0.944590i	$0.393540\pi$
$480$	1.80902	0.0825702
$481$	4.91266	0.223998
$482$	64.0861	2.91904
$483$	1.29523	0.0589349
$484$	0	0
$485$	4.34604	0.197344
$486$	−8.67657	−0.393577
$487$	1.01712	0.0460899	0.0230449	−	0.999734i	$-0.492664\pi$
$487$	1.01712	0.0460899	0.0230449	+	0.999734i	$0.492664\pi$
$488$	56.4348	2.55468
$489$	−2.06829	−0.0935314
$490$	12.2403	0.552959
$491$	2.41045	0.108782	0.0543910	−	0.998520i	$-0.482678\pi$
$491$	2.41045	0.108782	0.0543910	+	0.998520i	$0.482678\pi$
$492$	7.00067	0.315615
$493$	26.3658	1.18745
$494$	−5.73313	−0.257946
$495$	0	0
$496$	52.8820	2.37447
$497$	51.4189	2.30645
$498$	3.22409	0.144475
$499$	4.07426	0.182389	0.0911945	−	0.995833i	$-0.470931\pi$
$499$	4.07426	0.182389	0.0911945	+	0.995833i	$0.470931\pi$
$500$	47.4805	2.12339
$501$	0.105485	0.00471272
$502$	52.8471	2.35868
$503$	19.9553	0.889762	0.444881	−	0.895590i	$-0.353246\pi$
$503$	19.9553	0.889762	0.444881	+	0.895590i	$0.353246\pi$
$504$	81.2923	3.62104
$505$	−11.5281	−0.512993
$506$	0	0
$507$	−1.01577	−0.0451118
$508$	18.1801	0.806613
$509$	−8.79239	−0.389716	−0.194858	−	0.980831i	$-0.562425\pi$
$509$	−8.79239	−0.389716	−0.194858	+	0.980831i	$0.562425\pi$
$510$	−1.25972	−0.0557812
$511$	27.2478	1.20537
$512$	24.6266	1.08835
$513$	−0.729422	−0.0322048
$514$	59.2247	2.61229
$515$	−9.39239	−0.413878
$516$	−5.77285	−0.254135
$517$	0	0
$518$	−20.3384	−0.893618
$519$	0.505138	0.0221731
$520$	18.5117	0.811790
$521$	27.3483	1.19815	0.599075	−	0.800693i	$-0.295535\pi$
$521$	27.3483	1.19815	0.599075	+	0.800693i	$0.295535\pi$
$522$	−56.8790	−2.48953
$523$	41.7043	1.82360	0.911800	−	0.410634i	$-0.134693\pi$
$523$	41.7043	1.82360	0.911800	+	0.410634i	$0.134693\pi$
$524$	−85.1368	−3.71922
$525$	−1.59133	−0.0694512
$526$	36.6197	1.59670
$527$	−17.0897	−0.744441
$528$	0	0
$529$	−13.0480	−0.567304
$530$	−15.9236	−0.691675
$531$	41.1783	1.78699
$532$	16.9974	0.736930
$533$	24.5912	1.06516
$534$	1.49330	0.0646214
$535$	−19.2615	−0.832748
$536$	38.9083	1.68058
$537$	0.249331	0.0107594
$538$	29.7358	1.28200
$539$	0	0
$540$	3.90197	0.167914
$541$	20.7584	0.892472	0.446236	−	0.894915i	$-0.352764\pi$
$541$	20.7584	0.892472	0.446236	+	0.894915i	$0.352764\pi$
$542$	45.4508	1.95228
$543$	0.642898	0.0275894
$544$	51.4207	2.20464
$545$	−0.224035	−0.00959659
$546$	−2.35387	−0.100736
$547$	−5.39396	−0.230629	−0.115315	−	0.993329i	$-0.536788\pi$
$547$	−5.39396	−0.230629	−0.115315	+	0.993329i	$0.536788\pi$
$548$	−30.8193	−1.31653
$549$	20.8409	0.889466
$550$	0	0
$551$	−7.17849	−0.305814
$552$	−3.10783	−0.132278
$553$	−45.2412	−1.92385
$554$	−36.3980	−1.54640
$555$	−0.293894	−0.0124751
$556$	−57.1881	−2.42532
$557$	38.0076	1.61043	0.805217	−	0.592981i	$-0.202049\pi$
$557$	38.0076	1.61043	0.805217	+	0.592981i	$0.202049\pi$
$558$	36.8678	1.56074
$559$	−20.2782	−0.857677
$560$	−40.5952	−1.71546
$561$	0	0
$562$	68.6404	2.89542
$563$	26.4313	1.11395	0.556973	−	0.830530i	$-0.311963\pi$
$563$	26.4313	1.11395	0.556973	+	0.830530i	$0.311963\pi$
$564$	−3.54851	−0.149419
$565$	0.210295	0.00884719
$566$	76.6330	3.22112
$567$	29.8704	1.25444
$568$	−123.377	−5.17677
$569$	−40.6105	−1.70248	−0.851239	−	0.524778i	$-0.824148\pi$
$569$	−40.6105	−1.70248	−0.851239	+	0.524778i	$0.824148\pi$
$570$	0.342978	0.0143658
$571$	−8.44299	−0.353328	−0.176664	−	0.984271i	$-0.556531\pi$
$571$	−8.44299	−0.353328	−0.176664	+	0.984271i	$0.556531\pi$
$572$	0	0
$573$	−1.97309	−0.0824271
$574$	−101.807	−4.24936
$575$	−12.2271	−0.509906
$576$	−43.0761	−1.79484
$577$	20.9771	0.873288	0.436644	−	0.899634i	$-0.356167\pi$
$577$	20.9771	0.873288	0.436644	+	0.899634i	$0.356167\pi$
$578$	9.31648	0.387514
$579$	2.44499	0.101610
$580$	38.4006	1.59450
$581$	−33.5766	−1.39299
$582$	1.32600	0.0549643
$583$	0	0
$584$	−65.3795	−2.70542
$585$	6.83619	0.282642
$586$	16.9338	0.699528
$587$	−21.1452	−0.872756	−0.436378	−	0.899764i	$-0.643739\pi$
$587$	−21.1452	−0.872756	−0.436378	+	0.899764i	$0.643739\pi$
$588$	2.67441	0.110291
$589$	4.65295	0.191721
$590$	−38.8208	−1.59823
$591$	2.90540	0.119512
$592$	25.8498	1.06242
$593$	−27.7731	−1.14051	−0.570253	−	0.821469i	$-0.693155\pi$
$593$	−27.7731	−1.14051	−0.570253	+	0.821469i	$0.693155\pi$
$594$	0	0
$595$	13.1191	0.537829
$596$	−34.0917	−1.39645
$597$	−0.231793	−0.00948667
$598$	−18.0862	−0.739600
$599$	23.0129	0.940281	0.470140	−	0.882592i	$-0.344203\pi$
$599$	23.0129	0.940281	0.470140	+	0.882592i	$0.344203\pi$
$600$	3.81830	0.155881
$601$	−23.3322	−0.951738	−0.475869	−	0.879516i	$-0.657866\pi$
$601$	−23.3322	−0.951738	−0.475869	+	0.879516i	$0.657866\pi$
$602$	83.9517	3.42162
$603$	14.3685	0.585129
$604$	−32.6049	−1.32668
$605$	0	0
$606$	−3.51726	−0.142879
$607$	3.22857	0.131044	0.0655218	−	0.997851i	$-0.479129\pi$
$607$	3.22857	0.131044	0.0655218	+	0.997851i	$0.479129\pi$
$608$	−14.0001	−0.567778
$609$	−2.94730	−0.119430
$610$	−19.6477	−0.795512
$611$	−12.4648	−0.504273
$612$	55.3182	2.23611
$613$	17.2202	0.695519	0.347759	−	0.937584i	$-0.386943\pi$
$613$	17.2202	0.695519	0.347759	+	0.937584i	$0.386943\pi$
$614$	27.6842	1.11724
$615$	−1.47114	−0.0593220
$616$	0	0
$617$	−27.4776	−1.10621	−0.553103	−	0.833113i	$-0.686557\pi$
$617$	−27.4776	−1.10621	−0.553103	+	0.833113i	$0.686557\pi$
$618$	−2.86565	−0.115274
$619$	−9.53870	−0.383393	−0.191696	−	0.981454i	$-0.561399\pi$
$619$	−9.53870	−0.383393	−0.191696	+	0.981454i	$0.561399\pi$
$620$	−24.8905	−0.999625
$621$	−2.30109	−0.0923397
$622$	21.9306	0.879337
$623$	−15.5517	−0.623064
$624$	2.99173	0.119765
$625$	9.40166	0.376066
$626$	64.0133	2.55848
$627$	0	0
$628$	1.25319	0.0500076
$629$	−8.35381	−0.333088
$630$	−28.3018	−1.12757
$631$	1.16647	0.0464363	0.0232182	−	0.999730i	$-0.492609\pi$
$631$	1.16647	0.0464363	0.0232182	+	0.999730i	$0.492609\pi$
$632$	108.554	4.31804
$633$	−1.49962	−0.0596044
$634$	31.1430	1.23685
$635$	−3.82042	−0.151609
$636$	−3.47919	−0.137959
$637$	9.39438	0.372219
$638$	0	0
$639$	−45.5619	−1.80240
$640$	10.9227	0.431759
$641$	10.0249	0.395960	0.197980	−	0.980206i	$-0.436562\pi$
$641$	10.0249	0.395960	0.197980	+	0.980206i	$0.436562\pi$
$642$	−5.87676	−0.231937
$643$	−40.7197	−1.60583	−0.802915	−	0.596094i	$-0.796719\pi$
$643$	−40.7197	−1.60583	−0.802915	+	0.596094i	$0.796719\pi$
$644$	53.6213	2.11298
$645$	1.21312	0.0477666
$646$	9.74900	0.383569
$647$	−16.6460	−0.654423	−0.327211	−	0.944951i	$-0.606109\pi$
$647$	−16.6460	−0.654423	−0.327211	+	0.944951i	$0.606109\pi$
$648$	−71.6723	−2.81555
$649$	0	0
$650$	22.2209	0.871574
$651$	1.91038	0.0748735
$652$	−85.6256	−3.35336
$653$	−34.7416	−1.35954	−0.679771	−	0.733424i	$-0.737921\pi$
$653$	−34.7416	−1.35954	−0.679771	+	0.733424i	$0.737921\pi$
$654$	−0.0683538	−0.00267285
$655$	17.8908	0.699053
$656$	129.396	5.05205
$657$	−24.1441	−0.941949
$658$	51.6043	2.01175
$659$	22.9537	0.894148	0.447074	−	0.894497i	$-0.352466\pi$
$659$	22.9537	0.894148	0.447074	+	0.894497i	$0.352466\pi$
$660$	0	0
$661$	−22.7141	−0.883476	−0.441738	−	0.897144i	$-0.645638\pi$
$661$	−22.7141	−0.883476	−0.441738	+	0.897144i	$0.645638\pi$
$662$	18.4534	0.717213
$663$	−0.966831	−0.0375486
$664$	80.5651	3.12653
$665$	−3.57187	−0.138511
$666$	18.0217	0.698328
$667$	−22.6459	−0.876851
$668$	4.36698	0.168964
$669$	2.78445	0.107653
$670$	−13.5459	−0.523322
$671$	0	0
$672$	−5.74806	−0.221736
$673$	−20.9448	−0.807364	−0.403682	−	0.914899i	$-0.632270\pi$
$673$	−20.9448	−0.807364	−0.403682	+	0.914899i	$0.632270\pi$
$674$	78.1473	3.01012
$675$	2.82714	0.108817
$676$	−42.0519	−1.61738
$677$	−11.4153	−0.438726	−0.219363	−	0.975643i	$-0.570398\pi$
$677$	−11.4153	−0.438726	−0.219363	+	0.975643i	$0.570398\pi$
$678$	0.0641619	0.00246412
$679$	−13.8093	−0.529952
$680$	−31.4784	−1.20714
$681$	−0.488285	−0.0187111
$682$	0	0
$683$	−34.9550	−1.33752	−0.668759	−	0.743479i	$-0.733174\pi$
$683$	−34.9550	−1.33752	−0.668759	+	0.743479i	$0.733174\pi$
$684$	−15.0613	−0.575882
$685$	6.47643	0.247452
$686$	23.7020	0.904945
$687$	−2.99835	−0.114394
$688$	−106.701	−4.06795
$689$	−12.2213	−0.465594
$690$	1.08199	0.0411905
$691$	−15.8717	−0.603789	−0.301894	−	0.953341i	$-0.597619\pi$
$691$	−15.8717	−0.603789	−0.301894	+	0.953341i	$0.597619\pi$
$692$	20.9123	0.794967
$693$	0	0
$694$	−45.7020	−1.73483
$695$	12.0177	0.455855
$696$	7.07187	0.268059
$697$	−41.8165	−1.58391
$698$	11.4774	0.434426
$699$	−1.98644	−0.0751339
$700$	−65.8795	−2.49001
$701$	18.5830	0.701869	0.350935	−	0.936400i	$-0.385864\pi$
$701$	18.5830	0.701869	0.350935	+	0.936400i	$0.385864\pi$
$702$	4.18188	0.157835
$703$	2.27446	0.0857828
$704$	0	0
$705$	0.745693	0.0280844
$706$	−62.2228	−2.34178
$707$	36.6298	1.37760
$708$	−8.48208	−0.318776
$709$	23.8063	0.894064	0.447032	−	0.894518i	$-0.352481\pi$
$709$	23.8063	0.894064	0.447032	+	0.894518i	$0.352481\pi$
$710$	42.9535	1.61202
$711$	40.0880	1.50342
$712$	37.3153	1.39845
$713$	14.6786	0.549717
$714$	4.00267	0.149796
$715$	0	0
$716$	10.3221	0.385755
$717$	1.87905	0.0701745
$718$	21.7798	0.812816
$719$	37.0144	1.38040	0.690202	−	0.723616i	$-0.257522\pi$
$719$	37.0144	1.38040	0.690202	+	0.723616i	$0.257522\pi$
$720$	35.9711	1.34057
$721$	29.8437	1.11144
$722$	−2.65432	−0.0987835
$723$	−2.94249	−0.109432
$724$	26.6154	0.989154
$725$	27.8229	1.03332
$726$	0	0
$727$	−22.0744	−0.818694	−0.409347	−	0.912379i	$-0.634243\pi$
$727$	−22.0744	−0.818694	−0.409347	+	0.912379i	$0.634243\pi$
$728$	−58.8197	−2.18000
$729$	−26.2013	−0.970417
$730$	22.7618	0.842452
$731$	34.4824	1.27538
$732$	−4.29289	−0.158670
$733$	18.7090	0.691031	0.345515	−	0.938413i	$-0.387704\pi$
$733$	18.7090	0.691031	0.345515	+	0.938413i	$0.387704\pi$
$734$	−87.9891	−3.24774
$735$	−0.562008	−0.0207300
$736$	−44.1658	−1.62797
$737$	0	0
$738$	90.2109	3.32071
$739$	5.91630	0.217635	0.108817	−	0.994062i	$-0.465294\pi$
$739$	5.91630	0.217635	0.108817	+	0.994062i	$0.465294\pi$
$740$	−12.1670	−0.447267
$741$	0.263235	0.00967017
$742$	50.5961	1.85744
$743$	−14.0422	−0.515159	−0.257579	−	0.966257i	$-0.582925\pi$
$743$	−14.0422	−0.515159	−0.257579	+	0.966257i	$0.582925\pi$
$744$	−4.58384	−0.168052
$745$	7.16411	0.262473
$746$	−44.0191	−1.61165
$747$	29.7520	1.08857
$748$	0	0
$749$	61.2023	2.23628
$750$	−3.04423	−0.111159
$751$	4.91166	0.179229	0.0896145	−	0.995977i	$-0.471437\pi$
$751$	4.91166	0.179229	0.0896145	+	0.995977i	$0.471437\pi$
$752$	−65.5882	−2.39176
$753$	−2.42646	−0.0884250
$754$	41.1553	1.49879
$755$	6.85168	0.249358
$756$	−12.3983	−0.450920
$757$	49.2829	1.79122	0.895609	−	0.444843i	$-0.146741\pi$
$757$	49.2829	1.79122	0.895609	+	0.444843i	$0.146741\pi$
$758$	−15.3809	−0.558659
$759$	0	0
$760$	8.57050	0.310885
$761$	7.25922	0.263146	0.131573	−	0.991306i	$-0.457997\pi$
$761$	7.25922	0.263146	0.131573	+	0.991306i	$0.457997\pi$
$762$	−1.16562	−0.0422261
$763$	0.711856	0.0257709
$764$	−81.6843	−2.95524
$765$	−11.6247	−0.420292
$766$	−15.6344	−0.564892
$767$	−29.7949	−1.07583
$768$	−0.184693	−0.00666453
$769$	21.5123	0.775755	0.387877	−	0.921711i	$-0.373208\pi$
$769$	21.5123	0.775755	0.387877	+	0.921711i	$0.373208\pi$
$770$	0	0
$771$	−2.71928	−0.0979325
$772$	101.221	3.64301
$773$	4.54038	0.163306	0.0816530	−	0.996661i	$-0.473980\pi$
$773$	4.54038	0.163306	0.0816530	+	0.996661i	$0.473980\pi$
$774$	−74.3891	−2.67386
$775$	−18.0342	−0.647808
$776$	33.1346	1.18946
$777$	0.933831	0.0335010
$778$	−36.6440	−1.31375
$779$	11.3852	0.407917
$780$	−1.40815	−0.0504198
$781$	0	0
$782$	30.7550	1.09980
$783$	5.23615	0.187125
$784$	49.4320	1.76543
$785$	−0.263348	−0.00939928
$786$	5.45856	0.194701
$787$	7.25028	0.258444	0.129222	−	0.991616i	$-0.458752\pi$
$787$	7.25028	0.258444	0.129222	+	0.991616i	$0.458752\pi$
$788$	120.281	4.28484
$789$	−1.68138	−0.0598588
$790$	−37.7929	−1.34461
$791$	−0.668201	−0.0237585
$792$	0	0
$793$	−15.0796	−0.535491
$794$	−17.2125	−0.610848
$795$	0.731124	0.0259303
$796$	−9.59605	−0.340123
$797$	18.8674	0.668319	0.334159	−	0.942517i	$-0.391548\pi$
$797$	18.8674	0.668319	0.334159	+	0.942517i	$0.391548\pi$
$798$	−1.08979	−0.0385782
$799$	21.1960	0.749860
$800$	54.2624	1.91847
$801$	13.7802	0.486900
$802$	−9.84236	−0.347546
$803$	0	0
$804$	−2.95968	−0.104380
$805$	−11.2681	−0.397149
$806$	−26.6760	−0.939622
$807$	−1.36531	−0.0480612
$808$	−87.8911	−3.09200
$809$	19.4948	0.685399	0.342700	−	0.939445i	$-0.388659\pi$
$809$	19.4948	0.685399	0.342700	+	0.939445i	$0.388659\pi$
$810$	24.9526	0.876746
$811$	−4.28635	−0.150514	−0.0752570	−	0.997164i	$-0.523978\pi$
$811$	−4.28635	−0.150514	−0.0752570	+	0.997164i	$0.523978\pi$
$812$	−122.016	−4.28191
$813$	−2.08686	−0.0731893
$814$	0	0
$815$	17.9936	0.630287
$816$	−5.08734	−0.178092
$817$	−9.38838	−0.328458
$818$	82.4350	2.88227
$819$	−21.7216	−0.759014
$820$	−60.9039	−2.12686
$821$	−5.37419	−0.187561	−0.0937803	−	0.995593i	$-0.529895\pi$
$821$	−5.37419	−0.187561	−0.0937803	+	0.995593i	$0.529895\pi$
$822$	1.97598	0.0689204
$823$	26.3196	0.917445	0.458723	−	0.888580i	$-0.348307\pi$
$823$	26.3196	0.917445	0.458723	+	0.888580i	$0.348307\pi$
$824$	−71.6084	−2.49460
$825$	0	0
$826$	123.351	4.29192
$827$	8.11186	0.282077	0.141039	−	0.990004i	$-0.454956\pi$
$827$	8.11186	0.282077	0.141039	+	0.990004i	$0.454956\pi$
$828$	−47.5135	−1.65121
$829$	−21.5948	−0.750017	−0.375009	−	0.927021i	$-0.622360\pi$
$829$	−21.5948	−0.750017	−0.375009	+	0.927021i	$0.622360\pi$
$830$	−28.0486	−0.973582
$831$	1.67120	0.0579733
$832$	31.1681	1.08056
$833$	−15.9748	−0.553495
$834$	3.66663	0.126965
$835$	−0.917688	−0.0317579
$836$	0	0
$837$	−3.39396	−0.117313
$838$	29.9595	1.03493
$839$	−4.35109	−0.150216	−0.0751082	−	0.997175i	$-0.523930\pi$
$839$	−4.35109	−0.150216	−0.0751082	+	0.997175i	$0.523930\pi$
$840$	3.51882	0.121411
$841$	22.5308	0.776923
$842$	−91.6254	−3.15762
$843$	−3.15160	−0.108547
$844$	−62.0828	−2.13698
$845$	8.83689	0.303998
$846$	−45.7262	−1.57210
$847$	0	0
$848$	−64.3069	−2.20831
$849$	−3.51858	−0.120757
$850$	−37.7858	−1.29604
$851$	7.17519	0.245962
$852$	9.38504	0.321526
$853$	−19.5022	−0.667744	−0.333872	−	0.942618i	$-0.608355\pi$
$853$	−19.5022	−0.667744	−0.333872	+	0.942618i	$0.608355\pi$
$854$	62.4294	2.13629
$855$	3.16501	0.108241
$856$	−146.851	−5.01928
$857$	−13.3462	−0.455898	−0.227949	−	0.973673i	$-0.573202\pi$
$857$	−13.3462	−0.455898	−0.227949	+	0.973673i	$0.573202\pi$
$858$	0	0
$859$	21.6016	0.737036	0.368518	−	0.929621i	$-0.379865\pi$
$859$	21.6016	0.737036	0.368518	+	0.929621i	$0.379865\pi$
$860$	50.2221	1.71256
$861$	4.67445	0.159305
$862$	48.2167	1.64227
$863$	−2.72425	−0.0927345	−0.0463673	−	0.998924i	$-0.514764\pi$
$863$	−2.72425	−0.0927345	−0.0463673	+	0.998924i	$0.514764\pi$
$864$	10.2120	0.347418
$865$	−4.39456	−0.149420
$866$	−28.6147	−0.972367
$867$	−0.427763	−0.0145276
$868$	79.0879	2.68442
$869$	0	0
$870$	−2.46206	−0.0834718
$871$	−10.3964	−0.352269
$872$	−1.70806	−0.0578422
$873$	12.2363	0.414137
$874$	−8.37352	−0.283239
$875$	31.7034	1.07177
$876$	4.97329	0.168032
$877$	−1.29130	−0.0436041	−0.0218021	−	0.999762i	$-0.506940\pi$
$877$	−1.29130	−0.0436041	−0.0218021	+	0.999762i	$0.506940\pi$
$878$	−3.68266	−0.124284
$879$	−0.777508	−0.0262247
$880$	0	0
$881$	24.9873	0.841844	0.420922	−	0.907097i	$-0.361707\pi$
$881$	24.9873	0.841844	0.420922	+	0.907097i	$0.361707\pi$
$882$	34.4626	1.16041
$883$	15.5046	0.521772	0.260886	−	0.965370i	$-0.415985\pi$
$883$	15.5046	0.521772	0.260886	+	0.965370i	$0.415985\pi$
$884$	−40.0260	−1.34622
$885$	1.78244	0.0599162
$886$	19.2914	0.648107
$887$	9.98029	0.335105	0.167553	−	0.985863i	$-0.446414\pi$
$887$	9.98029	0.335105	0.167553	+	0.985863i	$0.446414\pi$
$888$	−2.24068	−0.0751921
$889$	12.1391	0.407134
$890$	−12.9913	−0.435469
$891$	0	0
$892$	115.274	3.85966
$893$	−5.77094	−0.193117
$894$	2.18580	0.0731040
$895$	−2.16911	−0.0725053
$896$	−34.7063	−1.15946
$897$	0.830422	0.0277270
$898$	−56.8815	−1.89816
$899$	−33.4012	−1.11399
$900$	58.3754	1.94585
$901$	20.7819	0.692345
$902$	0	0
$903$	−3.85461	−0.128274
$904$	1.60331	0.0533253
$905$	−5.59303	−0.185919
$906$	2.09047	0.0694513
$907$	11.8887	0.394758	0.197379	−	0.980327i	$-0.436757\pi$
$907$	11.8887	0.394758	0.197379	+	0.980327i	$0.436757\pi$
$908$	−20.2146	−0.670845
$909$	−32.4574	−1.07654
$910$	20.4780	0.678839
$911$	−23.7166	−0.785767	−0.392883	−	0.919588i	$-0.628522\pi$
$911$	−23.7166	−0.785767	−0.392883	+	0.919588i	$0.628522\pi$
$912$	1.38511	0.0458655
$913$	0	0
$914$	−46.7989	−1.54797
$915$	0.902117	0.0298231
$916$	−124.129	−4.10134
$917$	−56.8471	−1.87726
$918$	−7.11113	−0.234702
$919$	−18.1426	−0.598470	−0.299235	−	0.954179i	$-0.596731\pi$
$919$	−18.1426	−0.598470	−0.299235	+	0.954179i	$0.596731\pi$
$920$	27.0372	0.891390
$921$	−1.27111	−0.0418845
$922$	90.7972	2.99024
$923$	32.9667	1.08511
$924$	0	0
$925$	−8.81549	−0.289852
$926$	29.1997	0.959563
$927$	−26.4443	−0.868546
$928$	100.500	3.29906
$929$	−50.5019	−1.65691	−0.828457	−	0.560053i	$-0.810781\pi$
$929$	−50.5019	−1.65691	−0.828457	+	0.560053i	$0.810781\pi$
$930$	1.59586	0.0523303
$931$	4.34940	0.142546
$932$	−82.2368	−2.69376
$933$	−1.00694	−0.0329656
$934$	−11.6379	−0.380805
$935$	0	0
$936$	52.1197	1.70359
$937$	39.6587	1.29559	0.647797	−	0.761813i	$-0.275691\pi$
$937$	39.6587	1.29559	0.647797	+	0.761813i	$0.275691\pi$
$938$	43.0412	1.40534
$939$	−2.93915	−0.0959154
$940$	30.8711	1.00690
$941$	34.8809	1.13709	0.568543	−	0.822653i	$-0.307507\pi$
$941$	34.8809	1.13709	0.568543	+	0.822653i	$0.307507\pi$
$942$	−0.0803484	−0.00261789
$943$	35.9166	1.16961
$944$	−156.777	−5.10265
$945$	2.60540	0.0847537
$946$	0	0
$947$	−30.3067	−0.984835	−0.492417	−	0.870359i	$-0.663887\pi$
$947$	−30.3067	−0.984835	−0.492417	+	0.870359i	$0.663887\pi$
$948$	−8.25748	−0.268191
$949$	17.4696	0.567088
$950$	10.2878	0.333780
$951$	−1.42992	−0.0463684
$952$	100.021	3.24169
$953$	6.65804	0.215675	0.107838	−	0.994169i	$-0.465607\pi$
$953$	6.65804	0.215675	0.107838	+	0.994169i	$0.465607\pi$
$954$	−44.8329	−1.45152
$955$	17.1653	0.555457
$956$	77.7912	2.51595
$957$	0	0
$958$	−38.1381	−1.23219
$959$	−20.5785	−0.664513
$960$	−1.86459	−0.0601795
$961$	−9.35006	−0.301615
$962$	−13.0398	−0.420419
$963$	−54.2309	−1.74757
$964$	−121.817	−3.92345
$965$	−21.2707	−0.684729
$966$	−3.43794	−0.110614
$967$	20.0020	0.643221	0.321611	−	0.946872i	$-0.395776\pi$
$967$	20.0020	0.643221	0.321611	+	0.946872i	$0.395776\pi$
$968$	0	0
$969$	−0.447622	−0.0143797
$970$	−11.5358	−0.370392
$971$	−0.491941	−0.0157871	−0.00789357	−	0.999969i	$-0.502513\pi$
$971$	−0.491941	−0.0157871	−0.00789357	+	0.999969i	$0.502513\pi$
$972$	16.4927	0.529002
$973$	−38.1853	−1.22417
$974$	−2.69975	−0.0865055
$975$	−1.02026	−0.0326746
$976$	−79.3467	−2.53983
$977$	23.6515	0.756679	0.378339	−	0.925667i	$-0.376495\pi$
$977$	23.6515	0.756679	0.378339	+	0.925667i	$0.376495\pi$
$978$	5.48991	0.175548
$979$	0	0
$980$	−23.2666	−0.743225
$981$	−0.630771	−0.0201390
$982$	−6.39809	−0.204171
$983$	39.5609	1.26180	0.630899	−	0.775865i	$-0.282686\pi$
$983$	39.5609	1.26180	0.630899	+	0.775865i	$0.282686\pi$
$984$	−11.2161	−0.357556
$985$	−25.2762	−0.805366
$986$	−69.9831	−2.22872
$987$	−2.36939	−0.0754186
$988$	10.8977	0.346702
$989$	−29.6173	−0.941777
$990$	0	0
$991$	−13.6096	−0.432322	−0.216161	−	0.976358i	$-0.569354\pi$
$991$	−13.6096	−0.432322	−0.216161	+	0.976358i	$0.569354\pi$
$992$	−65.1417	−2.06825
$993$	−0.847283	−0.0268877
$994$	−136.482	−4.32895
$995$	2.01654	0.0639285
$996$	−6.12843	−0.194187
$997$	−41.1821	−1.30425	−0.652125	−	0.758111i	$-0.726122\pi$
$997$	−41.1821	−1.30425	−0.652125	+	0.758111i	$0.726122\pi$
$998$	−10.8144	−0.342323
$999$	−1.65904	−0.0524897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.n.1.1		5
11.10	odd	2		209.2.a.c.1.5	✓	5
33.32	even	2		1881.2.a.k.1.1		5
44.43	even	2		3344.2.a.t.1.3		5
55.54	odd	2		5225.2.a.h.1.1		5
209.208	even	2		3971.2.a.h.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.c.1.5	✓	5	11.10	odd	2
1881.2.a.k.1.1		5	33.32	even	2
2299.2.a.n.1.1		5	1.1	even	1	trivial
3344.2.a.t.1.3		5	44.43	even	2
3971.2.a.h.1.1		5	209.208	even	2
5225.2.a.h.1.1		5	55.54	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65432 q^{2} +0.121872 q^{3} +5.04540 q^{4} -1.06025 q^{5} -0.323487 q^{6} +3.36889 q^{7} -8.08346 q^{8} -2.98515 q^{9} +2.81425 q^{10} +0.614893 q^{12} +2.15993 q^{13} -8.94209 q^{14} -0.129215 q^{15} +11.3653 q^{16} -3.67288 q^{17} +7.92353 q^{18} +1.00000 q^{19} -5.34940 q^{20} +0.410573 q^{21} +3.15468 q^{23} -0.985147 q^{24} -3.87587 q^{25} -5.73313 q^{26} -0.729422 q^{27} +16.9974 q^{28} -7.17849 q^{29} +0.342978 q^{30} +4.65295 q^{31} -14.0001 q^{32} +9.74900 q^{34} -3.57187 q^{35} -15.0613 q^{36} +2.27446 q^{37} -2.65432 q^{38} +0.263235 q^{39} +8.57050 q^{40} +11.3852 q^{41} -1.08979 q^{42} -9.38838 q^{43} +3.16501 q^{45} -8.37352 q^{46} -5.77094 q^{47} +1.38511 q^{48} +4.34940 q^{49} +10.2878 q^{50} -0.447622 q^{51} +10.8977 q^{52} -5.65820 q^{53} +1.93612 q^{54} -27.2322 q^{56} +0.121872 q^{57} +19.0540 q^{58} -13.7944 q^{59} -0.651942 q^{60} -6.98152 q^{61} -12.3504 q^{62} -10.0566 q^{63} +14.4301 q^{64} -2.29007 q^{65} -4.81332 q^{67} -18.5312 q^{68} +0.384467 q^{69} +9.48087 q^{70} +15.2629 q^{71} +24.1303 q^{72} +8.08806 q^{73} -6.03713 q^{74} -0.472360 q^{75} +5.04540 q^{76} -0.698709 q^{78} -13.4291 q^{79} -12.0500 q^{80} +8.86655 q^{81} -30.2199 q^{82} -9.96666 q^{83} +2.07150 q^{84} +3.89418 q^{85} +24.9197 q^{86} -0.874858 q^{87} -4.61626 q^{89} -8.40094 q^{90} +7.27655 q^{91} +15.9166 q^{92} +0.567064 q^{93} +15.3179 q^{94} -1.06025 q^{95} -1.70622 q^{96} -4.09907 q^{97} -11.5447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21}+ \cdots + 10 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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