LMFDB - Embedded newform 6069.2.a.q.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6069,2,Mod(1,6069)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6069.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 6069 = 3 \cdot 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6069.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,0,3,4,-2,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$48.4612089867$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
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			$2.19869$ of defining polynomial
Character	$\chi$	$=$	6069.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.83424 q^{2} +1.00000 q^{3} +1.36445 q^{4} +1.19869 q^{5} +1.83424 q^{6} +1.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} +2.19869 q^{10} -6.23163 q^{11} +1.36445 q^{12} -4.83424 q^{13} +1.83424 q^{14} +1.19869 q^{15} -4.86718 q^{16} +1.83424 q^{18} +3.30404 q^{19} +1.63555 q^{20} +1.00000 q^{21} -11.4303 q^{22} +1.19869 q^{23} -1.16576 q^{24} -3.56314 q^{25} -8.86718 q^{26} +1.00000 q^{27} +1.36445 q^{28} -5.06587 q^{29} +2.19869 q^{30} +3.39738 q^{31} -6.59607 q^{32} -6.23163 q^{33} +1.19869 q^{35} +1.36445 q^{36} -10.8277 q^{37} +6.06041 q^{38} -4.83424 q^{39} -1.39738 q^{40} +2.92759 q^{41} +1.83424 q^{42} +2.43032 q^{43} -8.50273 q^{44} +1.19869 q^{45} +2.19869 q^{46} -4.46980 q^{47} -4.86718 q^{48} +1.00000 q^{49} -6.53566 q^{50} -6.59607 q^{52} -4.59607 q^{53} +1.83424 q^{54} -7.46980 q^{55} -1.16576 q^{56} +3.30404 q^{57} -9.29204 q^{58} +6.50273 q^{59} +1.63555 q^{60} +9.96052 q^{61} +6.23163 q^{62} +1.00000 q^{63} -2.36445 q^{64} -5.79476 q^{65} -11.4303 q^{66} -2.12628 q^{67} +1.19869 q^{69} +2.19869 q^{70} -4.45779 q^{71} -1.16576 q^{72} -10.3370 q^{73} -19.8606 q^{74} -3.56314 q^{75} +4.50819 q^{76} -6.23163 q^{77} -8.86718 q^{78} -13.0000 q^{79} -5.83424 q^{80} +1.00000 q^{81} +5.36991 q^{82} -14.2316 q^{83} +1.36445 q^{84} +4.45779 q^{86} -5.06587 q^{87} +7.26456 q^{88} +7.33151 q^{89} +2.19869 q^{90} -4.83424 q^{91} +1.63555 q^{92} +3.39738 q^{93} -8.19869 q^{94} +3.96052 q^{95} -6.59607 q^{96} -17.7673 q^{97} +1.83424 q^{98} -6.23163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 4 q^{4} - 2 q^{5} + 3 q^{7} - 9 q^{8} + 3 q^{9} + q^{10} - 2 q^{11} + 4 q^{12} - 9 q^{13} - 2 q^{15} + 2 q^{16} - q^{19} + 5 q^{20} + 3 q^{21} - 12 q^{22} - 2 q^{23} - 9 q^{24} - 5 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 4 * q^4 - 2 * q^5 + 3 * q^7 - 9 * q^8 + 3 * q^9 + q^10 - 2 * q^11 + 4 * q^12 - 9 * q^13 - 2 * q^15 + 2 * q^16 - q^19 + 5 * q^20 + 3 * q^21 - 12 * q^22 - 2 * q^23 - 9 * q^24 - 5 * q^25 - 10 * q^26 + 3 * q^27 + 4 * q^28 + 7 * q^29 + q^30 - q^31 - 3 * q^32 - 2 * q^33 - 2 * q^35 + 4 * q^36 + q^37 + 29 * q^38 - 9 * q^39 + 7 * q^40 + 3 * q^41 - 15 * q^43 - 9 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + 2 * q^48 + 3 * q^49 + 8 * q^50 - 3 * q^52 + 3 * q^53 - 17 * q^55 - 9 * q^56 - q^57 - 22 * q^58 + 3 * q^59 + 5 * q^60 + 13 * q^61 + 2 * q^62 + 3 * q^63 - 7 * q^64 + 5 * q^65 - 12 * q^66 + 5 * q^67 - 2 * q^69 + q^70 - 13 * q^71 - 9 * q^72 - 9 * q^73 - 15 * q^74 - 5 * q^75 - 36 * q^76 - 2 * q^77 - 10 * q^78 - 39 * q^79 - 12 * q^80 + 3 * q^81 - 17 * q^82 - 26 * q^83 + 4 * q^84 + 13 * q^86 + 7 * q^87 - 6 * q^88 + 33 * q^89 + q^90 - 9 * q^91 + 5 * q^92 - q^93 - 19 * q^94 - 5 * q^95 - 3 * q^96 - 9 * q^97 - 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 $

$2$	1.83424	1.29701	0.648503	−	0.761212i	$-0.275395\pi$
$2$	1.83424	1.29701	0.648503	+	0.761212i	$0.275395\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.36445	0.682224
$5$	1.19869	0.536071	0.268036	−	0.963409i	$-0.413626\pi$
$5$	1.19869	0.536071	0.268036	+	0.963409i	$0.413626\pi$
$6$	1.83424	0.748827
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.16576	−0.412157
$9$	1.00000	0.333333
$10$	2.19869	0.695287
$11$	−6.23163	−1.87891	−0.939453	−	0.342678i	$-0.888666\pi$
$11$	−6.23163	−1.87891	−0.939453	+	0.342678i	$0.888666\pi$
$12$	1.36445	0.393882
$13$	−4.83424	−1.34078	−0.670389	−	0.742010i	$-0.733873\pi$
$13$	−4.83424	−1.34078	−0.670389	+	0.742010i	$0.733873\pi$
$14$	1.83424	0.490222
$15$	1.19869	0.309501
$16$	−4.86718	−1.21679
$17$	0	0
$17$	0	0
$18$	1.83424	0.432335
$19$	3.30404	0.757998	0.378999	−	0.925397i	$-0.376268\pi$
$19$	3.30404	0.757998	0.378999	+	0.925397i	$0.376268\pi$
$20$	1.63555	0.365721
$21$	1.00000	0.218218
$22$	−11.4303	−2.43695
$23$	1.19869	0.249944	0.124972	−	0.992160i	$-0.460116\pi$
$23$	1.19869	0.249944	0.124972	+	0.992160i	$0.460116\pi$
$24$	−1.16576	−0.237959
$25$	−3.56314	−0.712628
$26$	−8.86718	−1.73900
$27$	1.00000	0.192450
$28$	1.36445	0.257856
$29$	−5.06587	−0.940708	−0.470354	−	0.882478i	$-0.655874\pi$
$29$	−5.06587	−0.940708	−0.470354	+	0.882478i	$0.655874\pi$
$30$	2.19869	0.401424
$31$	3.39738	0.610188	0.305094	−	0.952322i	$-0.401312\pi$
$31$	3.39738	0.610188	0.305094	+	0.952322i	$0.401312\pi$
$32$	−6.59607	−1.16603
$33$	−6.23163	−1.08479
$34$	0	0
$35$	1.19869	0.202616
$36$	1.36445	0.227408
$37$	−10.8277	−1.78006	−0.890031	−	0.455899i	$-0.849318\pi$
$37$	−10.8277	−1.78006	−0.890031	+	0.455899i	$0.849318\pi$
$38$	6.06041	0.983128
$39$	−4.83424	−0.774098
$40$	−1.39738	−0.220946
$41$	2.92759	0.457212	0.228606	−	0.973519i	$-0.426583\pi$
$41$	2.92759	0.457212	0.228606	+	0.973519i	$0.426583\pi$
$42$	1.83424	0.283030
$43$	2.43032	0.370620	0.185310	−	0.982680i	$-0.440671\pi$
$43$	2.43032	0.370620	0.185310	+	0.982680i	$0.440671\pi$
$44$	−8.50273	−1.28183
$45$	1.19869	0.178690
$46$	2.19869	0.324179
$47$	−4.46980	−0.651987	−0.325993	−	0.945372i	$-0.605699\pi$
$47$	−4.46980	−0.651987	−0.325993	+	0.945372i	$0.605699\pi$
$48$	−4.86718	−0.702517
$49$	1.00000	0.142857
$50$	−6.53566	−0.924282
$51$	0	0
$52$	−6.59607	−0.914711
$53$	−4.59607	−0.631319	−0.315660	−	0.948872i	$-0.602226\pi$
$53$	−4.59607	−0.631319	−0.315660	+	0.948872i	$0.602226\pi$
$54$	1.83424	0.249609
$55$	−7.46980	−1.00723
$56$	−1.16576	−0.155781
$57$	3.30404	0.437631
$58$	−9.29204	−1.22010
$59$	6.50273	0.846583	0.423292	−	0.905993i	$-0.360875\pi$
$59$	6.50273	0.846583	0.423292	+	0.905993i	$0.360875\pi$
$60$	1.63555	0.211149
$61$	9.96052	1.27531	0.637657	−	0.770320i	$-0.279904\pi$
$61$	9.96052	1.27531	0.637657	+	0.770320i	$0.279904\pi$
$62$	6.23163	0.791417
$63$	1.00000	0.125988
$64$	−2.36445	−0.295556
$65$	−5.79476	−0.718752
$66$	−11.4303	−1.40697
$67$	−2.12628	−0.259766	−0.129883	−	0.991529i	$-0.541460\pi$
$67$	−2.12628	−0.259766	−0.129883	+	0.991529i	$0.541460\pi$
$68$	0	0
$69$	1.19869	0.144305
$70$	2.19869	0.262794
$71$	−4.45779	−0.529043	−0.264521	−	0.964380i	$-0.585214\pi$
$71$	−4.45779	−0.529043	−0.264521	+	0.964380i	$0.585214\pi$
$72$	−1.16576	−0.137386
$73$	−10.3370	−1.20985	−0.604926	−	0.796282i	$-0.706797\pi$
$73$	−10.3370	−1.20985	−0.604926	+	0.796282i	$0.706797\pi$
$74$	−19.8606	−2.30875
$75$	−3.56314	−0.411436
$76$	4.50819	0.517125
$77$	−6.23163	−0.710160
$78$	−8.86718	−1.00401
$79$	−13.0000	−1.46261	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−13.0000	−1.46261	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−5.83424	−0.652288
$81$	1.00000	0.111111
$82$	5.36991	0.593007
$83$	−14.2316	−1.56212	−0.781062	−	0.624454i	$-0.785322\pi$
$83$	−14.2316	−1.56212	−0.781062	+	0.624454i	$0.785322\pi$
$84$	1.36445	0.148873
$85$	0	0
$86$	4.45779	0.480696
$87$	−5.06587	−0.543118
$88$	7.26456	0.774405
$89$	7.33151	0.777139	0.388569	−	0.921419i	$-0.372969\pi$
$89$	7.33151	0.777139	0.388569	+	0.921419i	$0.372969\pi$
$90$	2.19869	0.231762
$91$	−4.83424	−0.506766
$92$	1.63555	0.170518
$93$	3.39738	0.352292
$94$	−8.19869	−0.845630
$95$	3.96052	0.406341
$96$	−6.59607	−0.673209
$97$	−17.7673	−1.80399	−0.901997	−	0.431741i	$-0.857899\pi$
$97$	−17.7673	−1.80399	−0.901997	+	0.431741i	$0.857899\pi$
$98$	1.83424	0.185287
$99$	−6.23163	−0.626302
$100$	−4.86172	−0.486172
$101$	12.9605	1.28962	0.644810	−	0.764343i	$-0.276936\pi$
$101$	12.9605	1.28962	0.644810	+	0.764343i	$0.276936\pi$
$102$	0	0
$103$	18.6015	1.83286	0.916432	−	0.400191i	$-0.131056\pi$
$103$	18.6015	1.83286	0.916432	+	0.400191i	$0.131056\pi$
$104$	5.63555	0.552611
$105$	1.19869	0.116980
$106$	−8.43032	−0.818825
$107$	6.99346	0.676083	0.338041	−	0.941131i	$-0.390236\pi$
$107$	6.99346	0.676083	0.338041	+	0.941131i	$0.390236\pi$
$108$	1.36445	0.131294
$109$	−14.7224	−1.41015	−0.705073	−	0.709135i	$-0.749086\pi$
$109$	−14.7224	−1.41015	−0.705073	+	0.709135i	$0.749086\pi$
$110$	−13.7014	−1.30638
$111$	−10.8277	−1.02772
$112$	−4.86718	−0.459905
$113$	0.292035	0.0274724	0.0137362	−	0.999906i	$-0.495627\pi$
$113$	0.292035	0.0274724	0.0137362	+	0.999906i	$0.495627\pi$
$114$	6.06041	0.567609
$115$	1.43686	0.133988
$116$	−6.91211	−0.641774
$117$	−4.83424	−0.446926
$118$	11.9276	1.09802
$119$	0	0
$120$	−1.39738	−0.127563
$121$	27.8332	2.53029
$122$	18.2700	1.65409
$123$	2.92759	0.263972
$124$	4.63555	0.416285
$125$	−10.2646	−0.918090
$126$	1.83424	0.163407
$127$	3.46980	0.307895	0.153947	−	0.988079i	$-0.450801\pi$
$127$	3.46980	0.307895	0.153947	+	0.988079i	$0.450801\pi$
$128$	8.85517	0.782694
$129$	2.43032	0.213977
$130$	−10.6290	−0.932226
$131$	−16.6356	−1.45345	−0.726727	−	0.686926i	$-0.758960\pi$
$131$	−16.6356	−1.45345	−0.726727	+	0.686926i	$0.758960\pi$
$132$	−8.50273	−0.740068
$133$	3.30404	0.286496
$134$	−3.90011	−0.336918
$135$	1.19869	0.103167
$136$	0	0
$137$	4.72235	0.403458	0.201729	−	0.979441i	$-0.435344\pi$
$137$	4.72235	0.403458	0.201729	+	0.979441i	$0.435344\pi$
$138$	2.19869	0.187165
$139$	10.6949	0.907128	0.453564	−	0.891224i	$-0.350152\pi$
$139$	10.6949	0.907128	0.453564	+	0.891224i	$0.350152\pi$
$140$	1.63555	0.138229
$141$	−4.46980	−0.376425
$142$	−8.17668	−0.686171
$143$	30.1252	2.51920
$144$	−4.86718	−0.405598
$145$	−6.07241	−0.504286
$146$	−18.9605	−1.56918
$147$	1.00000	0.0824786
$148$	−14.7738	−1.21440
$149$	−13.3250	−1.09162	−0.545812	−	0.837908i	$-0.683779\pi$
$149$	−13.3250	−1.09162	−0.545812	+	0.837908i	$0.683779\pi$
$150$	−6.53566	−0.533635
$151$	−11.0449	−0.898824	−0.449412	−	0.893325i	$-0.648367\pi$
$151$	−11.0449	−0.898824	−0.449412	+	0.893325i	$0.648367\pi$
$152$	−3.85171	−0.312415
$153$	0	0
$154$	−11.4303	−0.921081
$155$	4.07241	0.327104
$156$	−6.59607	−0.528109
$157$	−2.92759	−0.233647	−0.116823	−	0.993153i	$-0.537271\pi$
$157$	−2.92759	−0.233647	−0.116823	+	0.993153i	$0.537271\pi$
$158$	−23.8452	−1.89702
$159$	−4.59607	−0.364492
$160$	−7.90666	−0.625076
$161$	1.19869	0.0944701
$162$	1.83424	0.144112
$163$	−21.3974	−1.67597	−0.837986	−	0.545691i	$-0.816267\pi$
$163$	−21.3974	−1.67597	−0.837986	+	0.545691i	$0.816267\pi$
$164$	3.99454	0.311921
$165$	−7.46980	−0.581523
$166$	−26.1043	−2.02608
$167$	11.7553	0.909651	0.454826	−	0.890580i	$-0.349702\pi$
$167$	11.7553	0.909651	0.454826	+	0.890580i	$0.349702\pi$
$168$	−1.16576	−0.0899401
$169$	10.3699	0.797685
$170$	0	0
$171$	3.30404	0.252666
$172$	3.31604	0.252846
$173$	−0.623549	−0.0474076	−0.0237038	−	0.999719i	$-0.507546\pi$
$173$	−0.623549	−0.0474076	−0.0237038	+	0.999719i	$0.507546\pi$
$174$	−9.29204	−0.704427
$175$	−3.56314	−0.269348
$176$	30.3304	2.28624
$177$	6.50273	0.488775
$178$	13.4478	1.00795
$179$	20.5566	1.53647	0.768236	−	0.640167i	$-0.221135\pi$
$179$	20.5566	1.53647	0.768236	+	0.640167i	$0.221135\pi$
$180$	1.63555	0.121907
$181$	−2.20524	−0.163914	−0.0819569	−	0.996636i	$-0.526117\pi$
$181$	−2.20524	−0.163914	−0.0819569	+	0.996636i	$0.526117\pi$
$182$	−8.86718	−0.657279
$183$	9.96052	0.736303
$184$	−1.39738	−0.103016
$185$	−12.9791	−0.954240
$186$	6.23163	0.456925
$187$	0	0
$188$	−6.09880	−0.444801
$189$	1.00000	0.0727393
$190$	7.26456	0.527027
$191$	1.74090	0.125967	0.0629835	−	0.998015i	$-0.479938\pi$
$191$	1.74090	0.125967	0.0629835	+	0.998015i	$0.479938\pi$
$192$	−2.36445	−0.170639
$193$	−6.24363	−0.449426	−0.224713	−	0.974425i	$-0.572144\pi$
$193$	−6.24363	−0.449426	−0.224713	+	0.974425i	$0.572144\pi$
$194$	−32.5895	−2.33979
$195$	−5.79476	−0.414972
$196$	1.36445	0.0974606
$197$	24.0504	1.71352	0.856760	−	0.515716i	$-0.172474\pi$
$197$	24.0504	1.71352	0.856760	+	0.515716i	$0.172474\pi$
$198$	−11.4303	−0.812317
$199$	10.5566	0.748337	0.374169	−	0.927361i	$-0.377928\pi$
$199$	10.5566	0.748337	0.374169	+	0.927361i	$0.377928\pi$
$200$	4.15375	0.293715
$201$	−2.12628	−0.149976
$202$	23.7727	1.67264
$203$	−5.06587	−0.355554
$204$	0	0
$205$	3.50927	0.245098
$206$	34.1197	2.37723
$207$	1.19869	0.0833148
$208$	23.5291	1.63145
$209$	−20.5895	−1.42421
$210$	2.19869	0.151724
$211$	−8.07241	−0.555728	−0.277864	−	0.960620i	$-0.589626\pi$
$211$	−8.07241	−0.555728	−0.277864	+	0.960620i	$0.589626\pi$
$212$	−6.27110	−0.430701
$213$	−4.45779	−0.305443
$214$	12.8277	0.876883
$215$	2.91320	0.198679
$216$	−1.16576	−0.0793197
$217$	3.39738	0.230629
$218$	−27.0044	−1.82897
$219$	−10.3370	−0.698508
$220$	−10.1921	−0.687154
$221$	0	0
$222$	−19.8606	−1.33296
$223$	9.00546	0.603050	0.301525	−	0.953458i	$-0.402504\pi$
$223$	9.00546	0.603050	0.301525	+	0.953458i	$0.402504\pi$
$224$	−6.59607	−0.440719
$225$	−3.56314	−0.237543
$226$	0.535664	0.0356318
$227$	25.5016	1.69260	0.846302	−	0.532704i	$-0.178824\pi$
$227$	25.5016	1.69260	0.846302	+	0.532704i	$0.178824\pi$
$228$	4.50819	0.298562
$229$	3.75637	0.248228	0.124114	−	0.992268i	$-0.460391\pi$
$229$	3.75637	0.248228	0.124114	+	0.992268i	$0.460391\pi$
$230$	2.63555	0.173783
$231$	−6.23163	−0.410011
$232$	5.90557	0.387720
$233$	−29.9320	−1.96091	−0.980454	−	0.196748i	$-0.936962\pi$
$233$	−29.9320	−1.96091	−0.980454	+	0.196748i	$0.936962\pi$
$234$	−8.86718	−0.579666
$235$	−5.35790	−0.349511
$236$	8.87264	0.577559
$237$	−13.0000	−0.844441
$238$	0	0
$239$	−4.53020	−0.293035	−0.146517	−	0.989208i	$-0.546806\pi$
$239$	−4.53020	−0.293035	−0.146517	+	0.989208i	$0.546806\pi$
$240$	−5.83424	−0.376599
$241$	−15.0449	−0.969130	−0.484565	−	0.874755i	$-0.661022\pi$
$241$	−15.0449	−0.969130	−0.484565	+	0.874755i	$0.661022\pi$
$242$	51.0528	3.28180
$243$	1.00000	0.0641500
$244$	13.5906	0.870050
$245$	1.19869	0.0765816
$246$	5.36991	0.342373
$247$	−15.9725	−1.01631
$248$	−3.96052	−0.251493
$249$	−14.2316	−0.901893
$250$	−18.8277	−1.19077
$251$	15.2436	0.962169	0.481085	−	0.876674i	$-0.340243\pi$
$251$	15.2436	0.962169	0.481085	+	0.876674i	$0.340243\pi$
$252$	1.36445	0.0859521
$253$	−7.46980	−0.469622
$254$	6.36445	0.399341
$255$	0	0
$256$	20.9714	1.31072
$257$	−0.569683	−0.0355359	−0.0177679	−	0.999842i	$-0.505656\pi$
$257$	−0.569683	−0.0355359	−0.0177679	+	0.999842i	$0.505656\pi$
$258$	4.45779	0.277530
$259$	−10.8277	−0.672801
$260$	−7.90666	−0.490350
$261$	−5.06587	−0.313569
$262$	−30.5136	−1.88514
$263$	26.4512	1.63105	0.815527	−	0.578719i	$-0.196447\pi$
$263$	26.4512	1.63105	0.815527	+	0.578719i	$0.196447\pi$
$264$	7.26456	0.447103
$265$	−5.50927	−0.338432
$266$	6.06041	0.371588
$267$	7.33151	0.448681
$268$	−2.90120	−0.177219
$269$	−11.3315	−0.690895	−0.345447	−	0.938438i	$-0.612273\pi$
$269$	−11.3315	−0.690895	−0.345447	+	0.938438i	$0.612273\pi$
$270$	2.19869	0.133808
$271$	−13.6290	−0.827903	−0.413952	−	0.910299i	$-0.635852\pi$
$271$	−13.6290	−0.827903	−0.413952	+	0.910299i	$0.635852\pi$
$272$	0	0
$273$	−4.83424	−0.292582
$274$	8.66194	0.523287
$275$	22.2042	1.33896
$276$	1.63555	0.0984487
$277$	28.3514	1.70347	0.851734	−	0.523974i	$-0.175551\pi$
$277$	28.3514	1.70347	0.851734	+	0.523974i	$0.175551\pi$
$278$	19.6170	1.17655
$279$	3.39738	0.203396
$280$	−1.39738	−0.0835096
$281$	0.117350	0.00700051	0.00350026	−	0.999994i	$-0.498886\pi$
$281$	0.117350	0.00700051	0.00350026	+	0.999994i	$0.498886\pi$
$282$	−8.19869	−0.488225
$283$	9.39192	0.558292	0.279146	−	0.960249i	$-0.409949\pi$
$283$	9.39192	0.558292	0.279146	+	0.960249i	$0.409949\pi$
$284$	−6.08243	−0.360926
$285$	3.96052	0.234601
$286$	55.2569	3.26741
$287$	2.92759	0.172810
$288$	−6.59607	−0.388677
$289$	0	0
$290$	−11.1383	−0.654062
$291$	−17.7673	−1.04154
$292$	−14.1043	−0.825390
$293$	22.2700	1.30103	0.650514	−	0.759494i	$-0.274553\pi$
$293$	22.2700	1.30103	0.650514	+	0.759494i	$0.274553\pi$
$294$	1.83424	0.106975
$295$	7.79476	0.453829
$296$	12.6225	0.733666
$297$	−6.23163	−0.361596
$298$	−24.4412	−1.41584
$299$	−5.79476	−0.335120
$300$	−4.86172	−0.280691
$301$	2.43032	0.140081
$302$	−20.2591	−1.16578
$303$	12.9605	0.744563
$304$	−16.0813	−0.922328
$305$	11.9396	0.683659
$306$	0	0
$307$	−1.09989	−0.0627739	−0.0313870	−	0.999507i	$-0.509992\pi$
$307$	−1.09989	−0.0627739	−0.0313870	+	0.999507i	$0.509992\pi$
$308$	−8.50273	−0.484488
$309$	18.6015	1.05820
$310$	7.46980	0.424256
$311$	0.509273	0.0288782	0.0144391	−	0.999896i	$-0.495404\pi$
$311$	0.509273	0.0288782	0.0144391	+	0.999896i	$0.495404\pi$
$312$	5.63555	0.319050
$313$	12.7224	0.719110	0.359555	−	0.933124i	$-0.382929\pi$
$313$	12.7224	0.719110	0.359555	+	0.933124i	$0.382929\pi$
$314$	−5.36991	−0.303041
$315$	1.19869	0.0675386
$316$	−17.7378	−0.997831
$317$	−10.7014	−0.601052	−0.300526	−	0.953774i	$-0.597162\pi$
$317$	−10.7014	−0.601052	−0.300526	+	0.953774i	$0.597162\pi$
$318$	−8.43032	−0.472749
$319$	31.5686	1.76750
$320$	−2.83424	−0.158439
$321$	6.99346	0.390337
$322$	2.19869	0.122528
$323$	0	0
$324$	1.36445	0.0758027
$325$	17.2251	0.955476
$326$	−39.2480	−2.17375
$327$	−14.7224	−0.814148
$328$	−3.41285	−0.188443
$329$	−4.46980	−0.246428
$330$	−13.7014	−0.754238
$331$	−3.99892	−0.219800	−0.109900	−	0.993943i	$-0.535053\pi$
$331$	−3.99892	−0.219800	−0.109900	+	0.993943i	$0.535053\pi$
$332$	−19.4183	−1.06572
$333$	−10.8277	−0.593354
$334$	21.5621	1.17982
$335$	−2.54875	−0.139253
$336$	−4.86718	−0.265526
$337$	22.1712	1.20774	0.603872	−	0.797082i	$-0.293624\pi$
$337$	22.1712	1.20774	0.603872	+	0.797082i	$0.293624\pi$
$338$	19.0209	1.03460
$339$	0.292035	0.0158612
$340$	0	0
$341$	−21.1712	−1.14649
$342$	6.06041	0.327709
$343$	1.00000	0.0539949
$344$	−2.83316	−0.152754
$345$	1.43686	0.0773580
$346$	−1.14374	−0.0614879
$347$	3.21962	0.172838	0.0864192	−	0.996259i	$-0.472458\pi$
$347$	3.21962	0.172838	0.0864192	+	0.996259i	$0.472458\pi$
$348$	−6.91211	−0.370528
$349$	−27.8212	−1.48923	−0.744616	−	0.667493i	$-0.767367\pi$
$349$	−27.8212	−1.48923	−0.744616	+	0.667493i	$0.767367\pi$
$350$	−6.53566	−0.349346
$351$	−4.83424	−0.258033
$352$	41.1043	2.19086
$353$	31.1557	1.65825	0.829126	−	0.559061i	$-0.188838\pi$
$353$	31.1557	1.65825	0.829126	+	0.559061i	$0.188838\pi$
$354$	11.9276	0.633944
$355$	−5.34352	−0.283604
$356$	10.0035	0.530183
$357$	0	0
$358$	37.7058	1.99281
$359$	−25.5895	−1.35056	−0.675282	−	0.737560i	$-0.735978\pi$
$359$	−25.5895	−1.35056	−0.675282	+	0.737560i	$0.735978\pi$
$360$	−1.39738	−0.0736485
$361$	−8.08333	−0.425438
$362$	−4.04494	−0.212597
$363$	27.8332	1.46086
$364$	−6.59607	−0.345728
$365$	−12.3908	−0.648566
$366$	18.2700	0.954989
$367$	2.46980	0.128922	0.0644611	−	0.997920i	$-0.479467\pi$
$367$	2.46980	0.128922	0.0644611	+	0.997920i	$0.479467\pi$
$368$	−5.83424	−0.304131
$369$	2.92759	0.152404
$370$	−23.8068	−1.23765
$371$	−4.59607	−0.238616
$372$	4.63555	0.240342
$373$	12.5147	0.647988	0.323994	−	0.946059i	$-0.394974\pi$
$373$	12.5147	0.647988	0.323994	+	0.946059i	$0.394974\pi$
$374$	0	0
$375$	−10.2646	−0.530060
$376$	5.21069	0.268721
$377$	24.4896	1.26128
$378$	1.83424	0.0943433
$379$	−28.3040	−1.45388	−0.726940	−	0.686701i	$-0.759058\pi$
$379$	−28.3040	−1.45388	−0.726940	+	0.686701i	$0.759058\pi$
$380$	5.40393	0.277216
$381$	3.46980	0.177763
$382$	3.19323	0.163380
$383$	12.7278	0.650361	0.325180	−	0.945652i	$-0.394575\pi$
$383$	12.7278	0.650361	0.325180	+	0.945652i	$0.394575\pi$
$384$	8.85517	0.451889
$385$	−7.46980	−0.380696
$386$	−11.4523	−0.582908
$387$	2.43032	0.123540
$388$	−24.2425	−1.23073
$389$	12.5117	0.634366	0.317183	−	0.948364i	$-0.397263\pi$
$389$	12.5117	0.634366	0.317183	+	0.948364i	$0.397263\pi$
$390$	−10.6290	−0.538221
$391$	0	0
$392$	−1.16576	−0.0588796
$393$	−16.6356	−0.839153
$394$	44.1143	2.22245
$395$	−15.5830	−0.784065
$396$	−8.50273	−0.427278
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	19.3634	0.970598
$399$	3.30404	0.165409
$400$	17.3424	0.867122
$401$	−3.83424	−0.191473	−0.0957365	−	0.995407i	$-0.530521\pi$
$401$	−3.83424	−0.191473	−0.0957365	+	0.995407i	$0.530521\pi$
$402$	−3.90011	−0.194520
$403$	−16.4238	−0.818126
$404$	17.6840	0.879810
$405$	1.19869	0.0595634
$406$	−9.29204	−0.461156
$407$	67.4742	3.34457
$408$	0	0
$409$	5.78584	0.286091	0.143046	−	0.989716i	$-0.454310\pi$
$409$	5.78584	0.286091	0.143046	+	0.989716i	$0.454310\pi$
$410$	6.43686	0.317894
$411$	4.72235	0.232936
$412$	25.3808	1.25042
$413$	6.50273	0.319978
$414$	2.19869	0.108060
$415$	−17.0593	−0.837409
$416$	31.8870	1.56339
$417$	10.6949	0.523730
$418$	−37.7662	−1.84721
$419$	−13.0449	−0.637287	−0.318643	−	0.947875i	$-0.603227\pi$
$419$	−13.0449	−0.637287	−0.318643	+	0.947875i	$0.603227\pi$
$420$	1.63555	0.0798068
$421$	26.5741	1.29514	0.647570	−	0.762006i	$-0.275785\pi$
$421$	26.5741	1.29514	0.647570	+	0.762006i	$0.275785\pi$
$422$	−14.8068	−0.720782
$423$	−4.46980	−0.217329
$424$	5.35790	0.260203
$425$	0	0
$426$	−8.17668	−0.396161
$427$	9.96052	0.482023
$428$	9.54221	0.461240
$429$	30.1252	1.45446
$430$	5.34352	0.257687
$431$	−5.09880	−0.245601	−0.122800	−	0.992431i	$-0.539187\pi$
$431$	−5.09880	−0.245601	−0.122800	+	0.992431i	$0.539187\pi$
$432$	−4.86718	−0.234172
$433$	−27.1503	−1.30476	−0.652380	−	0.757892i	$-0.726229\pi$
$433$	−27.1503	−1.30476	−0.652380	+	0.757892i	$0.726229\pi$
$434$	6.23163	0.299128
$435$	−6.07241	−0.291150
$436$	−20.0879	−0.962035
$437$	3.96052	0.189457
$438$	−18.9605	−0.905969
$439$	27.1557	1.29607	0.648036	−	0.761609i	$-0.275590\pi$
$439$	27.1557	1.29607	0.648036	+	0.761609i	$0.275590\pi$
$440$	8.70796	0.415136
$441$	1.00000	0.0476190
$442$	0	0
$443$	−8.92650	−0.424111	−0.212055	−	0.977258i	$-0.568016\pi$
$443$	−8.92650	−0.424111	−0.212055	+	0.977258i	$0.568016\pi$
$444$	−14.7738	−0.701135
$445$	8.78822	0.416602
$446$	16.5182	0.782160
$447$	−13.3250	−0.630249
$448$	−2.36445	−0.111710
$449$	−39.5675	−1.86731	−0.933653	−	0.358178i	$-0.883398\pi$
$449$	−39.5675	−1.86731	−0.933653	+	0.358178i	$0.883398\pi$
$450$	−6.53566	−0.308094
$451$	−18.2436	−0.859059
$452$	0.398467	0.0187423
$453$	−11.0449	−0.518936
$454$	46.7762	2.19532
$455$	−5.79476	−0.271663
$456$	−3.85171	−0.180373
$457$	−6.62901	−0.310092	−0.155046	−	0.987907i	$-0.549553\pi$
$457$	−6.62901	−0.310092	−0.155046	+	0.987907i	$0.549553\pi$
$458$	6.89010	0.321953
$459$	0	0
$460$	1.96052	0.0914098
$461$	−19.2425	−0.896215	−0.448107	−	0.893980i	$-0.647902\pi$
$461$	−19.2425	−0.896215	−0.448107	+	0.893980i	$0.647902\pi$
$462$	−11.4303	−0.531786
$463$	−39.2755	−1.82529	−0.912643	−	0.408757i	$-0.865962\pi$
$463$	−39.2755	−1.82529	−0.912643	+	0.408757i	$0.865962\pi$
$464$	24.6565	1.14465
$465$	4.07241	0.188854
$466$	−54.9025	−2.54331
$467$	−7.53566	−0.348709	−0.174354	−	0.984683i	$-0.555784\pi$
$467$	−7.53566	−0.348709	−0.174354	+	0.984683i	$0.555784\pi$
$468$	−6.59607	−0.304904
$469$	−2.12628	−0.0981824
$470$	−9.82770	−0.453318
$471$	−2.92759	−0.134896
$472$	−7.58060	−0.348925
$473$	−15.1448	−0.696360
$474$	−23.8452	−1.09524
$475$	−11.7727	−0.540171
$476$	0	0
$477$	−4.59607	−0.210440
$478$	−8.30950	−0.380068
$479$	−25.5501	−1.16741	−0.583706	−	0.811965i	$-0.698398\pi$
$479$	−25.5501	−1.16741	−0.583706	+	0.811965i	$0.698398\pi$
$480$	−7.90666	−0.360888
$481$	52.3437	2.38667
$482$	−27.5961	−1.25697
$483$	1.19869	0.0545423
$484$	37.9769	1.72622
$485$	−21.2975	−0.967069
$486$	1.83424	0.0832030
$487$	−4.18669	−0.189717	−0.0948585	−	0.995491i	$-0.530240\pi$
$487$	−4.18669	−0.189717	−0.0948585	+	0.995491i	$0.530240\pi$
$488$	−11.6115	−0.525630
$489$	−21.3974	−0.967623
$490$	2.19869	0.0993267
$491$	−10.9276	−0.493155	−0.246578	−	0.969123i	$-0.579306\pi$
$491$	−10.9276	−0.493155	−0.246578	+	0.969123i	$0.579306\pi$
$492$	3.99454	0.180088
$493$	0	0
$494$	−29.2975	−1.31816
$495$	−7.46980	−0.335742
$496$	−16.5357	−0.742473
$497$	−4.45779	−0.199959
$498$	−26.1043	−1.16976
$499$	16.6609	0.745842	0.372921	−	0.927863i	$-0.378356\pi$
$499$	16.6609	0.745842	0.372921	+	0.927863i	$0.378356\pi$
$500$	−14.0055	−0.626343
$501$	11.7553	0.525187
$502$	27.9605	1.24794
$503$	−36.7793	−1.63991	−0.819954	−	0.572430i	$-0.806001\pi$
$503$	−36.7793	−1.63991	−0.819954	+	0.572430i	$0.806001\pi$
$504$	−1.16576	−0.0519269
$505$	15.5357	0.691328
$506$	−13.7014	−0.609102
$507$	10.3699	0.460544
$508$	4.73436	0.210053
$509$	−32.0373	−1.42003	−0.710014	−	0.704187i	$-0.751312\pi$
$509$	−32.0373	−1.42003	−0.710014	+	0.704187i	$0.751312\pi$
$510$	0	0
$511$	−10.3370	−0.457281
$512$	20.7564	0.917311
$513$	3.30404	0.145877
$514$	−1.04494	−0.0460902
$515$	22.2975	0.982545
$516$	3.31604	0.145981
$517$	27.8541	1.22502
$518$	−19.8606	−0.872626
$519$	−0.623549	−0.0273708
$520$	6.75529	0.296239
$521$	27.1581	1.18982	0.594910	−	0.803793i	$-0.297188\pi$
$521$	27.1581	1.18982	0.594910	+	0.803793i	$0.297188\pi$
$522$	−9.29204	−0.406701
$523$	−29.3293	−1.28248	−0.641241	−	0.767339i	$-0.721580\pi$
$523$	−29.3293	−1.28248	−0.641241	+	0.767339i	$0.721580\pi$
$524$	−22.6983	−0.991582
$525$	−3.56314	−0.155508
$526$	48.5180	2.11549
$527$	0	0
$528$	30.3304	1.31996
$529$	−21.5631	−0.937528
$530$	−10.1053	−0.438948
$531$	6.50273	0.282194
$532$	4.50819	0.195455
$533$	−14.1527	−0.613020
$534$	13.4478	0.581942
$535$	8.38299	0.362428
$536$	2.47872	0.107065
$537$	20.5566	0.887083
$538$	−20.7848	−0.896094
$539$	−6.23163	−0.268415
$540$	1.63555	0.0703829
$541$	13.3304	0.573120	0.286560	−	0.958062i	$-0.407488\pi$
$541$	13.3304	0.573120	0.286560	+	0.958062i	$0.407488\pi$
$542$	−24.9989	−1.07380
$543$	−2.20524	−0.0946357
$544$	0	0
$545$	−17.6476	−0.755938
$546$	−8.86718	−0.379480
$547$	−25.5884	−1.09408	−0.547041	−	0.837106i	$-0.684246\pi$
$547$	−25.5884	−1.09408	−0.547041	+	0.837106i	$0.684246\pi$
$548$	6.44340	0.275249
$549$	9.96052	0.425105
$550$	40.7278	1.73664
$551$	−16.7378	−0.713055
$552$	−1.39738	−0.0594765
$553$	−13.0000	−0.552816
$554$	52.0033	2.20941
$555$	−12.9791	−0.550931
$556$	14.5926	0.618864
$557$	20.1143	0.852269	0.426135	−	0.904660i	$-0.359875\pi$
$557$	20.1143	0.852269	0.426135	+	0.904660i	$0.359875\pi$
$558$	6.23163	0.263806
$559$	−11.7487	−0.496919
$560$	−5.83424	−0.246542
$561$	0	0
$562$	0.215248	0.00907970
$563$	−36.7093	−1.54711	−0.773556	−	0.633729i	$-0.781524\pi$
$563$	−36.7093	−1.54711	−0.773556	+	0.633729i	$0.781524\pi$
$564$	−6.09880	−0.256806
$565$	0.350060	0.0147271
$566$	17.2271	0.724108
$567$	1.00000	0.0419961
$568$	5.19670	0.218049
$569$	−12.8857	−0.540198	−0.270099	−	0.962833i	$-0.587056\pi$
$569$	−12.8857	−0.540198	−0.270099	+	0.962833i	$0.587056\pi$
$570$	7.26456	0.304279
$571$	27.2899	1.14205	0.571023	−	0.820934i	$-0.306547\pi$
$571$	27.2899	1.14205	0.571023	+	0.820934i	$0.306547\pi$
$572$	41.1043	1.71866
$573$	1.74090	0.0727271
$574$	5.36991	0.224136
$575$	−4.27110	−0.178117
$576$	−2.36445	−0.0985187
$577$	40.7806	1.69772	0.848859	−	0.528619i	$-0.177290\pi$
$577$	40.7806	1.69772	0.848859	+	0.528619i	$0.177290\pi$
$578$	0	0
$579$	−6.24363	−0.259476
$580$	−8.28549	−0.344036
$581$	−14.2316	−0.590427
$582$	−32.5895	−1.35088
$583$	28.6410	1.18619
$584$	12.0504	0.498649
$585$	−5.79476	−0.239584
$586$	40.8486	1.68744
$587$	−15.1801	−0.626552	−0.313276	−	0.949662i	$-0.601426\pi$
$587$	−15.1801	−0.626552	−0.313276	+	0.949662i	$0.601426\pi$
$588$	1.36445	0.0562689
$589$	11.2251	0.462521
$590$	14.2975	0.588619
$591$	24.0504	0.989301
$592$	52.7003	2.16597
$593$	−26.5226	−1.08915	−0.544576	−	0.838712i	$-0.683309\pi$
$593$	−26.5226	−1.08915	−0.544576	+	0.838712i	$0.683309\pi$
$594$	−11.4303	−0.468992
$595$	0	0
$596$	−18.1812	−0.744732
$597$	10.5566	0.432053
$598$	−10.6290	−0.434652
$599$	−26.0659	−1.06502	−0.532511	−	0.846423i	$-0.678752\pi$
$599$	−26.0659	−1.06502	−0.532511	+	0.846423i	$0.678752\pi$
$600$	4.15375	0.169576
$601$	−6.58299	−0.268526	−0.134263	−	0.990946i	$-0.542867\pi$
$601$	−6.58299	−0.268526	−0.134263	+	0.990946i	$0.542867\pi$
$602$	4.45779	0.181686
$603$	−2.12628	−0.0865888
$604$	−15.0702	−0.613200
$605$	33.3634	1.35641
$606$	23.7727	0.965702
$607$	1.61462	0.0655354	0.0327677	−	0.999463i	$-0.489568\pi$
$607$	1.61462	0.0655354	0.0327677	+	0.999463i	$0.489568\pi$
$608$	−21.7937	−0.883850
$609$	−5.06587	−0.205279
$610$	21.9001	0.886710
$611$	21.6081	0.874169
$612$	0	0
$613$	−36.9804	−1.49362	−0.746812	−	0.665036i	$-0.768416\pi$
$613$	−36.9804	−1.49362	−0.746812	+	0.665036i	$0.768416\pi$
$614$	−2.01746	−0.0814181
$615$	3.50927	0.141508
$616$	7.26456	0.292697
$617$	−16.5621	−0.666763	−0.333382	−	0.942792i	$-0.608190\pi$
$617$	−16.5621	−0.666763	−0.333382	+	0.942792i	$0.608190\pi$
$618$	34.1197	1.37250
$619$	−28.6081	−1.14986	−0.574928	−	0.818204i	$-0.694970\pi$
$619$	−28.6081	−1.14986	−0.574928	+	0.818204i	$0.694970\pi$
$620$	5.55660	0.223158
$621$	1.19869	0.0481018
$622$	0.934131	0.0374552
$623$	7.33151	0.293731
$624$	23.5291	0.941919
$625$	5.51166	0.220466
$626$	23.3359	0.932690
$627$	−20.5895	−0.822267
$628$	−3.99454	−0.159400
$629$	0	0
$630$	2.19869	0.0875980
$631$	18.0593	0.718930	0.359465	−	0.933158i	$-0.382959\pi$
$631$	18.0593	0.718930	0.359465	+	0.933158i	$0.382959\pi$
$632$	15.1548	0.602827
$633$	−8.07241	−0.320850
$634$	−19.6290	−0.779568
$635$	4.15921	0.165053
$636$	−6.27110	−0.248665
$637$	−4.83424	−0.191540
$638$	57.9045	2.29246
$639$	−4.45779	−0.176348
$640$	10.6146	0.419580
$641$	−10.0185	−0.395709	−0.197854	−	0.980231i	$-0.563397\pi$
$641$	−10.0185	−0.395709	−0.197854	+	0.980231i	$0.563397\pi$
$642$	12.8277	0.506269
$643$	−3.86410	−0.152385	−0.0761927	−	0.997093i	$-0.524276\pi$
$643$	−3.86410	−0.152385	−0.0761927	+	0.997093i	$0.524276\pi$
$644$	1.63555	0.0644498
$645$	2.91320	0.114707
$646$	0	0
$647$	20.9660	0.824258	0.412129	−	0.911126i	$-0.364785\pi$
$647$	20.9660	0.824258	0.412129	+	0.911126i	$0.364785\pi$
$648$	−1.16576	−0.0457953
$649$	−40.5226	−1.59065
$650$	31.5950	1.23926
$651$	3.39738	0.133154
$652$	−29.1956	−1.14339
$653$	−8.27349	−0.323767	−0.161883	−	0.986810i	$-0.551757\pi$
$653$	−8.27349	−0.323767	−0.161883	+	0.986810i	$0.551757\pi$
$654$	−27.0044	−1.05595
$655$	−19.9409	−0.779155
$656$	−14.2491	−0.556333
$657$	−10.3370	−0.403284
$658$	−8.19869	−0.319618
$659$	12.8737	0.501489	0.250744	−	0.968053i	$-0.419325\pi$
$659$	12.8737	0.501489	0.250744	+	0.968053i	$0.419325\pi$
$660$	−10.1921	−0.396729
$661$	3.70034	0.143926	0.0719632	−	0.997407i	$-0.477074\pi$
$661$	3.70034	0.143926	0.0719632	+	0.997407i	$0.477074\pi$
$662$	−7.33498	−0.285082
$663$	0	0
$664$	16.5906	0.643841
$665$	3.96052	0.153582
$666$	−19.8606	−0.769584
$667$	−6.07241	−0.235125
$668$	16.0395	0.620586
$669$	9.00546	0.348171
$670$	−4.67503	−0.180612
$671$	−62.0702	−2.39620
$672$	−6.59607	−0.254449
$673$	50.7991	1.95816	0.979081	−	0.203469i	$-0.0652215\pi$
$673$	50.7991	1.95816	0.979081	+	0.203469i	$0.0652215\pi$
$674$	40.6674	1.56645
$675$	−3.56314	−0.137145
$676$	14.1492	0.544200
$677$	33.4292	1.28479	0.642395	−	0.766374i	$-0.277941\pi$
$677$	33.4292	1.28479	0.642395	+	0.766374i	$0.277941\pi$
$678$	0.535664	0.0205721
$679$	−17.7673	−0.681846
$680$	0	0
$681$	25.5016	0.977225
$682$	−38.8332	−1.48700
$683$	20.2899	0.776370	0.388185	−	0.921581i	$-0.373102\pi$
$683$	20.2899	0.776370	0.388185	+	0.921581i	$0.373102\pi$
$684$	4.50819	0.172375
$685$	5.66064	0.216282
$686$	1.83424	0.0700317
$687$	3.75637	0.143315
$688$	−11.8288	−0.450968
$689$	22.2185	0.846459
$690$	2.63555	0.100334
$691$	−13.2142	−0.502690	−0.251345	−	0.967898i	$-0.580873\pi$
$691$	−13.2142	−0.502690	−0.251345	+	0.967898i	$0.580873\pi$
$692$	−0.850800	−0.0323426
$693$	−6.23163	−0.236720
$694$	5.90557	0.224172
$695$	12.8199	0.486285
$696$	5.90557	0.223850
$697$	0	0
$698$	−51.0308	−1.93154
$699$	−29.9320	−1.13213
$700$	−4.86172	−0.183756
$701$	20.5961	0.777903	0.388951	−	0.921258i	$-0.372837\pi$
$701$	20.5961	0.777903	0.388951	+	0.921258i	$0.372837\pi$
$702$	−8.86718	−0.334670
$703$	−35.7751	−1.34928
$704$	14.7344	0.555322
$705$	−5.35790	−0.201790
$706$	57.1472	2.15076
$707$	12.9605	0.487431
$708$	8.87264	0.333454
$709$	1.41484	0.0531356	0.0265678	−	0.999647i	$-0.491542\pi$
$709$	1.41484	0.0531356	0.0265678	+	0.999647i	$0.491542\pi$
$710$	−9.80131	−0.367837
$711$	−13.0000	−0.487538
$712$	−8.54676	−0.320303
$713$	4.07241	0.152513
$714$	0	0
$715$	36.1108	1.35047
$716$	28.0484	1.04822
$717$	−4.53020	−0.169184
$718$	−46.9374	−1.75169
$719$	3.93066	0.146589	0.0732945	−	0.997310i	$-0.476649\pi$
$719$	3.93066	0.146589	0.0732945	+	0.997310i	$0.476649\pi$
$720$	−5.83424	−0.217429
$721$	18.6015	0.692757
$722$	−14.8268	−0.551796
$723$	−15.0449	−0.559527
$724$	−3.00893	−0.111826
$725$	18.0504	0.670375
$726$	51.0528	1.89475
$727$	2.61462	0.0969709	0.0484855	−	0.998824i	$-0.484561\pi$
$727$	2.61462	0.0969709	0.0484855	+	0.998824i	$0.484561\pi$
$728$	5.63555	0.208867
$729$	1.00000	0.0370370
$730$	−22.7278	−0.841194
$731$	0	0
$732$	13.5906	0.502324
$733$	−28.3843	−1.04840	−0.524199	−	0.851596i	$-0.675635\pi$
$733$	−28.3843	−1.04840	−0.524199	+	0.851596i	$0.675635\pi$
$734$	4.53020	0.167213
$735$	1.19869	0.0442144
$736$	−7.90666	−0.291443
$737$	13.2502	0.488076
$738$	5.36991	0.197669
$739$	5.13521	0.188902	0.0944508	−	0.995530i	$-0.469890\pi$
$739$	5.13521	0.188902	0.0944508	+	0.995530i	$0.469890\pi$
$740$	−17.7093	−0.651006
$741$	−15.9725	−0.586765
$742$	−8.43032	−0.309487
$743$	40.4028	1.48224	0.741118	−	0.671375i	$-0.234296\pi$
$743$	40.4028	1.48224	0.741118	+	0.671375i	$0.234296\pi$
$744$	−3.96052	−0.145200
$745$	−15.9725	−0.585188
$746$	22.9551	0.840445
$747$	−14.2316	−0.520708
$748$	0	0
$749$	6.99346	0.255535
$750$	−18.8277	−0.687490
$751$	−29.7278	−1.08478	−0.542392	−	0.840126i	$-0.682481\pi$
$751$	−29.7278	−1.08478	−0.542392	+	0.840126i	$0.682481\pi$
$752$	21.7553	0.793334
$753$	15.2436	0.555509
$754$	44.9200	1.63589
$755$	−13.2395	−0.481834
$756$	1.36445	0.0496245
$757$	30.0748	1.09309	0.546544	−	0.837431i	$-0.315943\pi$
$757$	30.0748	1.09309	0.546544	+	0.837431i	$0.315943\pi$
$758$	−51.9165	−1.88569
$759$	−7.46980	−0.271136
$760$	−4.61701	−0.167476
$761$	53.6993	1.94660	0.973298	−	0.229544i	$-0.0737236\pi$
$761$	53.6993	1.94660	0.973298	+	0.229544i	$0.0737236\pi$
$762$	6.36445	0.230560
$763$	−14.7224	−0.532985
$764$	2.37537	0.0859377
$765$	0	0
$766$	23.3459	0.843522
$767$	−31.4358	−1.13508
$768$	20.9714	0.756742
$769$	16.8212	0.606586	0.303293	−	0.952897i	$-0.401914\pi$
$769$	16.8212	0.606586	0.303293	+	0.952897i	$0.401914\pi$
$770$	−13.7014	−0.493765
$771$	−0.569683	−0.0205166
$772$	−8.51911	−0.306609
$773$	−45.0397	−1.61997	−0.809983	−	0.586454i	$-0.800524\pi$
$773$	−45.0397	−1.61997	−0.809983	+	0.586454i	$0.800524\pi$
$774$	4.45779	0.160232
$775$	−12.1053	−0.434837
$776$	20.7123	0.743530
$777$	−10.8277	−0.388442
$778$	22.9494	0.822777
$779$	9.67286	0.346566
$780$	−7.90666	−0.283104
$781$	27.7793	0.994021
$782$	0	0
$783$	−5.06587	−0.181039
$784$	−4.86718	−0.173828
$785$	−3.50927	−0.125251
$786$	−30.5136	−1.08839
$787$	−21.6674	−0.772359	−0.386180	−	0.922424i	$-0.626206\pi$
$787$	−21.6674	−0.772359	−0.386180	+	0.922424i	$0.626206\pi$
$788$	32.8155	1.16900
$789$	26.4512	0.941689
$790$	−28.5830	−1.01694
$791$	0.292035	0.0103836
$792$	7.26456	0.258135
$793$	−48.1516	−1.70991
$794$	−33.0164	−1.17171
$795$	−5.50927	−0.195394
$796$	14.4039	0.510534
$797$	20.4543	0.724529	0.362265	−	0.932075i	$-0.382004\pi$
$797$	20.4543	0.724529	0.362265	+	0.932075i	$0.382004\pi$
$798$	6.06041	0.214536
$799$	0	0
$800$	23.5027	0.830947
$801$	7.33151	0.259046
$802$	−7.03293	−0.248342
$803$	64.4161	2.27320
$804$	−2.90120	−0.102317
$805$	1.43686	0.0506427
$806$	−30.1252	−1.06111
$807$	−11.3315	−0.398888
$808$	−15.1088	−0.531526
$809$	14.2327	0.500395	0.250198	−	0.968195i	$-0.419504\pi$
$809$	14.2327	0.500395	0.250198	+	0.968195i	$0.419504\pi$
$810$	2.19869	0.0772541
$811$	1.55222	0.0545059	0.0272529	−	0.999629i	$-0.491324\pi$
$811$	1.55222	0.0545059	0.0272529	+	0.999629i	$0.491324\pi$
$812$	−6.91211	−0.242568
$813$	−13.6290	−0.477990
$814$	123.764	4.33793
$815$	−25.6489	−0.898440
$816$	0	0
$817$	8.02986	0.280929
$818$	10.6126	0.371062
$819$	−4.83424	−0.168922
$820$	4.78822	0.167212
$821$	30.1647	1.05275	0.526377	−	0.850251i	$-0.323550\pi$
$821$	30.1647	1.05275	0.526377	+	0.850251i	$0.323550\pi$
$822$	8.66194	0.302120
$823$	35.0253	1.22091	0.610453	−	0.792053i	$-0.290988\pi$
$823$	35.0253	1.22091	0.610453	+	0.792053i	$0.290988\pi$
$824$	−21.6849	−0.755428
$825$	22.2042	0.773049
$826$	11.9276	0.415014
$827$	−7.01439	−0.243914	−0.121957	−	0.992535i	$-0.538917\pi$
$827$	−7.01439	−0.243914	−0.121957	+	0.992535i	$0.538917\pi$
$828$	1.63555	0.0568394
$829$	−17.2776	−0.600078	−0.300039	−	0.953927i	$-0.597000\pi$
$829$	−17.2776	−0.600078	−0.300039	+	0.953927i	$0.597000\pi$
$830$	−31.2910	−1.08612
$831$	28.3514	0.983498
$832$	11.4303	0.396275
$833$	0	0
$834$	19.6170	0.679281
$835$	14.0910	0.487638
$836$	−28.0933	−0.971629
$837$	3.39738	0.117431
$838$	−23.9276	−0.826565
$839$	−22.2052	−0.766610	−0.383305	−	0.923622i	$-0.625214\pi$
$839$	−22.2052	−0.766610	−0.383305	+	0.923622i	$0.625214\pi$
$840$	−1.39738	−0.0482143
$841$	−3.33697	−0.115068
$842$	48.7433	1.67980
$843$	0.117350	0.00404175
$844$	−11.0144	−0.379131
$845$	12.4303	0.427616
$846$	−8.19869	−0.281877
$847$	27.8332	0.956359
$848$	22.3699	0.768186
$849$	9.39192	0.322330
$850$	0	0
$851$	−12.9791	−0.444917
$852$	−6.08243	−0.208380
$853$	−36.7302	−1.25762	−0.628809	−	0.777560i	$-0.716457\pi$
$853$	−36.7302	−1.25762	−0.628809	+	0.777560i	$0.716457\pi$
$854$	18.2700	0.625187
$855$	3.96052	0.135447
$856$	−8.15267	−0.278652
$857$	44.6015	1.52356	0.761780	−	0.647836i	$-0.224326\pi$
$857$	44.6015	1.52356	0.761780	+	0.647836i	$0.224326\pi$
$858$	55.2569	1.88644
$859$	−15.3830	−0.524861	−0.262431	−	0.964951i	$-0.584524\pi$
$859$	−15.3830	−0.524861	−0.262431	+	0.964951i	$0.584524\pi$
$860$	3.97491	0.135543
$861$	2.92759	0.0997719
$862$	−9.35245	−0.318546
$863$	37.7828	1.28614	0.643070	−	0.765807i	$-0.277660\pi$
$863$	37.7828	1.28614	0.643070	+	0.765807i	$0.277660\pi$
$864$	−6.59607	−0.224403
$865$	−0.747443	−0.0254138
$866$	−49.8002	−1.69228
$867$	0	0
$868$	4.63555	0.157341
$869$	81.0111	2.74811
$870$	−11.1383	−0.377623
$871$	10.2789	0.348289
$872$	17.1627	0.581202
$873$	−17.7673	−0.601332
$874$	7.26456	0.245727
$875$	−10.2646	−0.347005
$876$	−14.1043	−0.476539
$877$	−52.6783	−1.77882	−0.889410	−	0.457110i	$-0.848885\pi$
$877$	−52.6783	−1.77882	−0.889410	+	0.457110i	$0.848885\pi$
$878$	49.8102	1.68101
$879$	22.2700	0.751149
$880$	36.3568	1.22559
$881$	−35.1723	−1.18498	−0.592492	−	0.805576i	$-0.701856\pi$
$881$	−35.1723	−1.18498	−0.592492	+	0.805576i	$0.701856\pi$
$882$	1.83424	0.0617622
$883$	30.1677	1.01523	0.507613	−	0.861585i	$-0.330528\pi$
$883$	30.1677	1.01523	0.507613	+	0.861585i	$0.330528\pi$
$884$	0	0
$885$	7.79476	0.262018
$886$	−16.3734	−0.550074
$887$	42.5710	1.42939	0.714697	−	0.699434i	$-0.246565\pi$
$887$	42.5710	1.42939	0.714697	+	0.699434i	$0.246565\pi$
$888$	12.6225	0.423582
$889$	3.46980	0.116373
$890$	16.1197	0.540335
$891$	−6.23163	−0.208767
$892$	12.2875	0.411415
$893$	−14.7684	−0.494205
$894$	−24.4412	−0.817437
$895$	24.6410	0.823658
$896$	8.85517	0.295831
$897$	−5.79476	−0.193482
$898$	−72.5764	−2.42191
$899$	−17.2107	−0.574009
$900$	−4.86172	−0.162057
$901$	0	0
$902$	−33.4633	−1.11420
$903$	2.43032	0.0808759
$904$	−0.340442	−0.0113229
$905$	−2.64340	−0.0878695
$906$	−20.2591	−0.673064
$907$	−34.0953	−1.13212	−0.566058	−	0.824365i	$-0.691532\pi$
$907$	−34.0953	−1.13212	−0.566058	+	0.824365i	$0.691532\pi$
$908$	34.7957	1.15473
$909$	12.9605	0.429873
$910$	−10.6290	−0.352348
$911$	−1.07480	−0.0356096	−0.0178048	−	0.999841i	$-0.505668\pi$
$911$	−1.07480	−0.0356096	−0.0178048	+	0.999841i	$0.505668\pi$
$912$	−16.0813	−0.532506
$913$	88.6862	2.93508
$914$	−12.1592	−0.402191
$915$	11.9396	0.394711
$916$	5.12537	0.169347
$917$	−16.6356	−0.549354
$918$	0	0
$919$	−18.0923	−0.596809	−0.298404	−	0.954440i	$-0.596454\pi$
$919$	−18.0923	−0.596809	−0.298404	+	0.954440i	$0.596454\pi$
$920$	−1.67503	−0.0552241
$921$	−1.09989	−0.0362425
$922$	−35.2955	−1.16240
$923$	21.5501	0.709329
$924$	−8.50273	−0.279719
$925$	38.5806	1.26852
$926$	−72.0408	−2.36741
$927$	18.6015	0.610954
$928$	33.4148	1.09690
$929$	−1.66541	−0.0546404	−0.0273202	−	0.999627i	$-0.508697\pi$
$929$	−1.66541	−0.0546404	−0.0273202	+	0.999627i	$0.508697\pi$
$930$	7.46980	0.244944
$931$	3.30404	0.108285
$932$	−40.8406	−1.33778
$933$	0.509273	0.0166729
$934$	−13.8222	−0.452278
$935$	0	0
$936$	5.63555	0.184204
$937$	28.0846	0.917485	0.458742	−	0.888569i	$-0.348300\pi$
$937$	28.0846	0.917485	0.458742	+	0.888569i	$0.348300\pi$
$938$	−3.90011	−0.127343
$939$	12.7224	0.415178
$940$	−7.31058	−0.238445
$941$	−7.50381	−0.244617	−0.122309	−	0.992492i	$-0.539030\pi$
$941$	−7.50381	−0.244617	−0.122309	+	0.992492i	$0.539030\pi$
$942$	−5.36991	−0.174961
$943$	3.50927	0.114278
$944$	−31.6499	−1.03012
$945$	1.19869	0.0389934
$946$	−27.7793	−0.903183
$947$	5.45125	0.177142	0.0885709	−	0.996070i	$-0.471770\pi$
$947$	5.45125	0.177142	0.0885709	+	0.996070i	$0.471770\pi$
$948$	−17.7378	−0.576098
$949$	49.9714	1.62214
$950$	−21.5941	−0.700605
$951$	−10.7014	−0.347017
$952$	0	0
$953$	20.4831	0.663513	0.331756	−	0.943365i	$-0.392359\pi$
$953$	20.4831	0.663513	0.331756	+	0.943365i	$0.392359\pi$
$954$	−8.43032	−0.272942
$955$	2.08680	0.0675273
$956$	−6.18123	−0.199915
$957$	31.5686	1.02047
$958$	−46.8650	−1.51414
$959$	4.72235	0.152493
$960$	−2.83424	−0.0914748
$961$	−19.4578	−0.627671
$962$	96.0111	3.09552
$963$	6.99346	0.225361
$964$	−20.5280	−0.661164
$965$	−7.48418	−0.240924
$966$	2.19869	0.0707417
$967$	−53.2284	−1.71171	−0.855855	−	0.517217i	$-0.826968\pi$
$967$	−53.2284	−1.71171	−0.855855	+	0.517217i	$0.826968\pi$
$968$	−32.4467	−1.04288
$969$	0	0
$970$	−39.0648	−1.25429
$971$	−13.2042	−0.423741	−0.211871	−	0.977298i	$-0.567956\pi$
$971$	−13.2042	−0.423741	−0.211871	+	0.977298i	$0.567956\pi$
$972$	1.36445	0.0437647
$973$	10.6949	0.342862
$974$	−7.67940	−0.246064
$975$	17.2251	0.551644
$976$	−48.4796	−1.55180
$977$	49.0593	1.56955	0.784773	−	0.619783i	$-0.212779\pi$
$977$	49.0593	1.56955	0.784773	+	0.619783i	$0.212779\pi$
$978$	−39.2480	−1.25501
$979$	−45.6872	−1.46017
$980$	1.63555	0.0522458
$981$	−14.7224	−0.470049
$982$	−20.0439	−0.639625
$983$	−56.8595	−1.81354	−0.906769	−	0.421628i	$-0.861459\pi$
$983$	−56.8595	−1.81354	−0.906769	+	0.421628i	$0.861459\pi$
$984$	−3.41285	−0.108798
$985$	28.8290	0.918568
$986$	0	0
$987$	−4.46980	−0.142275
$988$	−21.7937	−0.693349
$989$	2.91320	0.0926344
$990$	−13.7014	−0.435460
$991$	−51.2755	−1.62882	−0.814410	−	0.580290i	$-0.802939\pi$
$991$	−51.2755	−1.62882	−0.814410	+	0.580290i	$0.802939\pi$
$992$	−22.4094	−0.711499
$993$	−3.99892	−0.126902
$994$	−8.17668	−0.259348
$995$	12.6541	0.401162
$996$	−19.4183	−0.615293
$997$	43.2085	1.36843	0.684214	−	0.729281i	$-0.260145\pi$
$997$	43.2085	1.36843	0.684214	+	0.729281i	$0.260145\pi$
$998$	30.5601	0.967362
$999$	−10.8277	−0.342573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6069.2.a.q.1.3	yes	3
17.16	even	2		6069.2.a.o.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6069.2.a.o.1.3	✓	3	17.16	even	2
6069.2.a.q.1.3	yes	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6069.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83424 q^{2} +1.00000 q^{3} +1.36445 q^{4} +1.19869 q^{5} +1.83424 q^{6} +1.00000 q^{7} -1.16576 q^{8} +1.00000 q^{9} +2.19869 q^{10} -6.23163 q^{11} +1.36445 q^{12} -4.83424 q^{13} +1.83424 q^{14} +1.19869 q^{15} -4.86718 q^{16} +1.83424 q^{18} +3.30404 q^{19} +1.63555 q^{20} +1.00000 q^{21} -11.4303 q^{22} +1.19869 q^{23} -1.16576 q^{24} -3.56314 q^{25} -8.86718 q^{26} +1.00000 q^{27} +1.36445 q^{28} -5.06587 q^{29} +2.19869 q^{30} +3.39738 q^{31} -6.59607 q^{32} -6.23163 q^{33} +1.19869 q^{35} +1.36445 q^{36} -10.8277 q^{37} +6.06041 q^{38} -4.83424 q^{39} -1.39738 q^{40} +2.92759 q^{41} +1.83424 q^{42} +2.43032 q^{43} -8.50273 q^{44} +1.19869 q^{45} +2.19869 q^{46} -4.46980 q^{47} -4.86718 q^{48} +1.00000 q^{49} -6.53566 q^{50} -6.59607 q^{52} -4.59607 q^{53} +1.83424 q^{54} -7.46980 q^{55} -1.16576 q^{56} +3.30404 q^{57} -9.29204 q^{58} +6.50273 q^{59} +1.63555 q^{60} +9.96052 q^{61} +6.23163 q^{62} +1.00000 q^{63} -2.36445 q^{64} -5.79476 q^{65} -11.4303 q^{66} -2.12628 q^{67} +1.19869 q^{69} +2.19869 q^{70} -4.45779 q^{71} -1.16576 q^{72} -10.3370 q^{73} -19.8606 q^{74} -3.56314 q^{75} +4.50819 q^{76} -6.23163 q^{77} -8.86718 q^{78} -13.0000 q^{79} -5.83424 q^{80} +1.00000 q^{81} +5.36991 q^{82} -14.2316 q^{83} +1.36445 q^{84} +4.45779 q^{86} -5.06587 q^{87} +7.26456 q^{88} +7.33151 q^{89} +2.19869 q^{90} -4.83424 q^{91} +1.63555 q^{92} +3.39738 q^{93} -8.19869 q^{94} +3.96052 q^{95} -6.59607 q^{96} -17.7673 q^{97} +1.83424 q^{98} -6.23163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 4 q^{4} - 2 q^{5} + 3 q^{7} - 9 q^{8} + 3 q^{9} + q^{10} - 2 q^{11} + 4 q^{12} - 9 q^{13} - 2 q^{15} + 2 q^{16} - q^{19} + 5 q^{20} + 3 q^{21} - 12 q^{22} - 2 q^{23} - 9 q^{24} - 5 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 4 * q^4 - 2 * q^5 + 3 * q^7 - 9 * q^8 + 3 * q^9 + q^10 - 2 * q^11 + 4 * q^12 - 9 * q^13 - 2 * q^15 + 2 * q^16 - q^19 + 5 * q^20 + 3 * q^21 - 12 * q^22 - 2 * q^23 - 9 * q^24 - 5 * q^25 - 10 * q^26 + 3 * q^27 + 4 * q^28 + 7 * q^29 + q^30 - q^31 - 3 * q^32 - 2 * q^33 - 2 * q^35 + 4 * q^36 + q^37 + 29 * q^38 - 9 * q^39 + 7 * q^40 + 3 * q^41 - 15 * q^43 - 9 * q^44 - 2 * q^45 + q^46 - 8 * q^47 + 2 * q^48 + 3 * q^49 + 8 * q^50 - 3 * q^52 + 3 * q^53 - 17 * q^55 - 9 * q^56 - q^57 - 22 * q^58 + 3 * q^59 + 5 * q^60 + 13 * q^61 + 2 * q^62 + 3 * q^63 - 7 * q^64 + 5 * q^65 - 12 * q^66 + 5 * q^67 - 2 * q^69 + q^70 - 13 * q^71 - 9 * q^72 - 9 * q^73 - 15 * q^74 - 5 * q^75 - 36 * q^76 - 2 * q^77 - 10 * q^78 - 39 * q^79 - 12 * q^80 + 3 * q^81 - 17 * q^82 - 26 * q^83 + 4 * q^84 + 13 * q^86 + 7 * q^87 - 6 * q^88 + 33 * q^89 + q^90 - 9 * q^91 + 5 * q^92 - q^93 - 19 * q^94 - 5 * q^95 - 3 * q^96 - 9 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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