LMFDB - Embedded newform 1859.4.a.j.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 108 x^{16} + 212 x^{15} + 4721 x^{14} - 8963 x^{13} - 107626 x^{12} + 194656 x^{11} + \cdots + 9847296 $ x^18 - 2x^17 - 108x^16 + 212x^15 + 4721x^14 - 8963x^13 - 107626x^12 + 194656x^11 + 1375700x^10 - 2336289x^9 - 9875440x^8 + 15599166x^7 + 37652624x^6 - 55787484x^5 - 64147728x^4 + 92949968x^3 + 22620800x^2 - 43697856*x + 9847296
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.40428$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.40428 q^{2} +7.21858 q^{3} -2.21943 q^{4} +9.84845 q^{5} +17.3555 q^{6} +8.26104 q^{7} -24.5704 q^{8} +25.1078 q^{9} +23.6784 q^{10} -11.0000 q^{11} -16.0212 q^{12} +19.8618 q^{14} +71.0918 q^{15} -41.3186 q^{16} -113.178 q^{17} +60.3663 q^{18} -121.759 q^{19} -21.8580 q^{20} +59.6329 q^{21} -26.4471 q^{22} -69.3004 q^{23} -177.363 q^{24} -28.0079 q^{25} -13.6587 q^{27} -18.3348 q^{28} -209.888 q^{29} +170.925 q^{30} +18.1919 q^{31} +97.2215 q^{32} -79.4043 q^{33} -272.112 q^{34} +81.3584 q^{35} -55.7252 q^{36} -228.240 q^{37} -292.742 q^{38} -241.980 q^{40} -460.524 q^{41} +143.374 q^{42} +386.056 q^{43} +24.4138 q^{44} +247.273 q^{45} -166.618 q^{46} +322.380 q^{47} -298.262 q^{48} -274.755 q^{49} -67.3390 q^{50} -816.984 q^{51} +249.880 q^{53} -32.8393 q^{54} -108.333 q^{55} -202.977 q^{56} -878.923 q^{57} -504.629 q^{58} -56.7513 q^{59} -157.784 q^{60} +775.933 q^{61} +43.7384 q^{62} +207.417 q^{63} +564.297 q^{64} -190.910 q^{66} -387.156 q^{67} +251.191 q^{68} -500.250 q^{69} +195.609 q^{70} +116.894 q^{71} -616.909 q^{72} +1016.35 q^{73} -548.754 q^{74} -202.177 q^{75} +270.235 q^{76} -90.8714 q^{77} -429.294 q^{79} -406.925 q^{80} -776.508 q^{81} -1107.23 q^{82} +950.500 q^{83} -132.351 q^{84} -1114.63 q^{85} +928.187 q^{86} -1515.09 q^{87} +270.274 q^{88} +671.495 q^{89} +594.515 q^{90} +153.808 q^{92} +131.320 q^{93} +775.093 q^{94} -1199.13 q^{95} +701.801 q^{96} +968.442 q^{97} -660.589 q^{98} -276.186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 76 q^{4} - 20 q^{5} - 49 q^{6} - 28 q^{7} + 12 q^{8} + 180 q^{9} + 56 q^{10} - 198 q^{11} + 54 q^{12} + 4 q^{14} - 60 q^{15} + 364 q^{16} - 138 q^{17} - 298 q^{18} - 24 q^{19} - 160 q^{20}+ \cdots - 1980 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + 76 * q^4 - 20 * q^5 - 49 * q^6 - 28 * q^7 + 12 * q^8 + 180 * q^9 + 56 * q^10 - 198 * q^11 + 54 * q^12 + 4 * q^14 - 60 * q^15 + 364 * q^16 - 138 * q^17 - 298 * q^18 - 24 * q^19 - 160 * q^20 - 352 * q^21 + 22 * q^22 + 236 * q^23 - 124 * q^24 + 586 * q^25 - 6 * q^27 - 691 * q^28 - 286 * q^29 - 356 * q^30 - 642 * q^31 + 379 * q^32 - 2068 * q^34 + 34 * q^35 + 215 * q^36 - 530 * q^37 + 25 * q^38 - 108 * q^40 - 608 * q^41 + 563 * q^42 - 460 * q^43 - 836 * q^44 - 452 * q^45 + 580 * q^46 - 986 * q^47 + 837 * q^48 + 1082 * q^49 + 2578 * q^50 + 170 * q^51 + 1216 * q^53 - 1539 * q^54 + 220 * q^55 + 1137 * q^56 - 1282 * q^57 - 90 * q^58 - 1366 * q^59 - 5104 * q^60 - 922 * q^61 - 1398 * q^62 + 3236 * q^63 + 1296 * q^64 + 539 * q^66 - 1118 * q^67 - 2274 * q^68 + 1644 * q^69 - 416 * q^70 - 1118 * q^71 - 3295 * q^72 - 2444 * q^73 - 2018 * q^74 - 410 * q^75 + 1326 * q^76 + 308 * q^77 + 180 * q^79 - 5446 * q^80 + 426 * q^81 - 974 * q^82 + 696 * q^83 - 1061 * q^84 - 4580 * q^85 - 4652 * q^86 - 1240 * q^87 - 132 * q^88 + 3664 * q^89 + 248 * q^90 + 227 * q^92 - 3696 * q^93 - 244 * q^94 - 476 * q^95 + 5426 * q^96 - 2660 * q^97 - 6003 * q^98 - 1980 * 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 $

$2$	2.40428	0.850042	0.425021	−	0.905184i	$-0.360267\pi$
$2$	2.40428	0.850042	0.425021	+	0.905184i	$0.360267\pi$
$3$	7.21858	1.38922	0.694608	−	0.719389i	$-0.255578\pi$
$3$	7.21858	1.38922	0.694608	+	0.719389i	$0.255578\pi$
$4$	−2.21943	−0.277429
$5$	9.84845	0.880873	0.440436	−	0.897784i	$-0.354824\pi$
$5$	9.84845	0.880873	0.440436	+	0.897784i	$0.354824\pi$
$6$	17.3555	1.18089
$7$	8.26104	0.446054	0.223027	−	0.974812i	$-0.428406\pi$
$7$	8.26104	0.446054	0.223027	+	0.974812i	$0.428406\pi$
$8$	−24.5704	−1.08587
$9$	25.1078	0.929920
$10$	23.6784	0.748778
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−16.0212	−0.385409
$13$	0	0
$13$	0	0
$14$	19.8618	0.379164
$15$	71.0918	1.22372
$16$	−41.3186	−0.645604
$17$	−113.178	−1.61469	−0.807344	−	0.590082i	$-0.799096\pi$
$17$	−113.178	−1.61469	−0.807344	+	0.590082i	$0.799096\pi$
$18$	60.3663	0.790471
$19$	−121.759	−1.47017	−0.735087	−	0.677972i	$-0.762859\pi$
$19$	−121.759	−1.47017	−0.735087	+	0.677972i	$0.762859\pi$
$20$	−21.8580	−0.244380
$21$	59.6329	0.619665
$22$	−26.4471	−0.256297
$23$	−69.3004	−0.628266	−0.314133	−	0.949379i	$-0.601714\pi$
$23$	−69.3004	−0.628266	−0.314133	+	0.949379i	$0.601714\pi$
$24$	−177.363	−1.50850
$25$	−28.0079	−0.224064
$26$	0	0
$27$	−13.6587	−0.0973561
$28$	−18.3348	−0.123748
$29$	−209.888	−1.34397	−0.671985	−	0.740564i	$-0.734558\pi$
$29$	−209.888	−1.34397	−0.671985	+	0.740564i	$0.734558\pi$
$30$	170.925	1.04021
$31$	18.1919	0.105399	0.0526994	−	0.998610i	$-0.483217\pi$
$31$	18.1919	0.105399	0.0526994	+	0.998610i	$0.483217\pi$
$32$	97.2215	0.537078
$33$	−79.4043	−0.418864
$34$	−272.112	−1.37255
$35$	81.3584	0.392917
$36$	−55.7252	−0.257987
$37$	−228.240	−1.01412	−0.507060	−	0.861911i	$-0.669268\pi$
$37$	−228.240	−1.01412	−0.507060	+	0.861911i	$0.669268\pi$
$38$	−292.742	−1.24971
$39$	0	0
$40$	−241.980	−0.956511
$41$	−460.524	−1.75419	−0.877095	−	0.480317i	$-0.840522\pi$
$41$	−460.524	−1.75419	−0.877095	+	0.480317i	$0.840522\pi$
$42$	143.374	0.526741
$43$	386.056	1.36914	0.684570	−	0.728947i	$-0.259990\pi$
$43$	386.056	1.36914	0.684570	+	0.728947i	$0.259990\pi$
$44$	24.4138	0.0836481
$45$	247.273	0.819141
$46$	−166.618	−0.534053
$47$	322.380	1.00051	0.500255	−	0.865878i	$-0.333239\pi$
$47$	322.380	1.00051	0.500255	+	0.865878i	$0.333239\pi$
$48$	−298.262	−0.896883
$49$	−274.755	−0.801036
$50$	−67.3390	−0.190463
$51$	−816.984	−2.24315
$52$	0	0
$53$	249.880	0.647617	0.323809	−	0.946123i	$-0.395037\pi$
$53$	249.880	0.647617	0.323809	+	0.946123i	$0.395037\pi$
$54$	−32.8393	−0.0827568
$55$	−108.333	−0.265593
$56$	−202.977	−0.484356
$57$	−878.923	−2.04239
$58$	−504.629	−1.14243
$59$	−56.7513	−0.125227	−0.0626135	−	0.998038i	$-0.519944\pi$
$59$	−56.7513	−0.125227	−0.0626135	+	0.998038i	$0.519944\pi$
$60$	−157.784	−0.339496
$61$	775.933	1.62866	0.814328	−	0.580405i	$-0.197106\pi$
$61$	775.933	1.62866	0.814328	+	0.580405i	$0.197106\pi$
$62$	43.7384	0.0895933
$63$	207.417	0.414795
$64$	564.297	1.10214
$65$	0	0
$66$	−190.910	−0.356052
$67$	−387.156	−0.705949	−0.352975	−	0.935633i	$-0.614830\pi$
$67$	−387.156	−0.705949	−0.352975	+	0.935633i	$0.614830\pi$
$68$	251.191	0.447962
$69$	−500.250	−0.872797
$70$	195.609	0.333996
$71$	116.894	0.195391	0.0976957	−	0.995216i	$-0.468853\pi$
$71$	116.894	0.195391	0.0976957	+	0.995216i	$0.468853\pi$
$72$	−616.909	−1.00977
$73$	1016.35	1.62952	0.814759	−	0.579800i	$-0.196869\pi$
$73$	1016.35	1.62952	0.814759	+	0.579800i	$0.196869\pi$
$74$	−548.754	−0.862045
$75$	−202.177	−0.311273
$76$	270.235	0.407870
$77$	−90.8714	−0.134490
$78$	0	0
$79$	−429.294	−0.611384	−0.305692	−	0.952131i	$-0.598888\pi$
$79$	−429.294	−0.611384	−0.305692	+	0.952131i	$0.598888\pi$
$80$	−406.925	−0.568695
$81$	−776.508	−1.06517
$82$	−1107.23	−1.49113
$83$	950.500	1.25700	0.628500	−	0.777810i	$-0.283669\pi$
$83$	950.500	1.25700	0.628500	+	0.777810i	$0.283669\pi$
$84$	−132.351	−0.171913
$85$	−1114.63	−1.42233
$86$	928.187	1.16383
$87$	−1515.09	−1.86706
$88$	270.274	0.327402
$89$	671.495	0.799757	0.399878	−	0.916568i	$-0.369052\pi$
$89$	671.495	0.799757	0.399878	+	0.916568i	$0.369052\pi$
$90$	594.515	0.696304
$91$	0	0
$92$	153.808	0.174300
$93$	131.320	0.146422
$94$	775.093	0.850476
$95$	−1199.13	−1.29504
$96$	701.801	0.746117
$97$	968.442	1.01371	0.506857	−	0.862030i	$-0.330807\pi$
$97$	968.442	1.01371	0.506857	+	0.862030i	$0.330807\pi$
$98$	−660.589	−0.680914
$99$	−276.186	−0.280381
$100$	62.1618	0.0621618
$101$	498.778	0.491388	0.245694	−	0.969347i	$-0.420984\pi$
$101$	498.778	0.491388	0.245694	+	0.969347i	$0.420984\pi$
$102$	−1964.26	−1.90677
$103$	774.677	0.741079	0.370540	−	0.928817i	$-0.379173\pi$
$103$	774.677	0.741079	0.370540	+	0.928817i	$0.379173\pi$
$104$	0	0
$105$	587.292	0.545846
$106$	600.782	0.550501
$107$	−1370.11	−1.23788	−0.618940	−	0.785438i	$-0.712438\pi$
$107$	−1370.11	−1.23788	−0.618940	+	0.785438i	$0.712438\pi$
$108$	30.3146	0.0270094
$109$	−845.710	−0.743159	−0.371579	−	0.928401i	$-0.621184\pi$
$109$	−845.710	−0.743159	−0.371579	+	0.928401i	$0.621184\pi$
$110$	−260.463	−0.225765
$111$	−1647.57	−1.40883
$112$	−341.335	−0.287974
$113$	1313.27	1.09330	0.546648	−	0.837362i	$-0.315904\pi$
$113$	1313.27	1.09330	0.546648	+	0.837362i	$0.315904\pi$
$114$	−2113.18	−1.73612
$115$	−682.502	−0.553423
$116$	465.832	0.372857
$117$	0	0
$118$	−136.446	−0.106448
$119$	−934.967	−0.720238
$120$	−1746.75	−1.32880
$121$	121.000	0.0909091
$122$	1865.56	1.38442
$123$	−3324.33	−2.43695
$124$	−40.3757	−0.0292407
$125$	−1506.89	−1.07824
$126$	498.688	0.352593
$127$	43.6232	0.0304798	0.0152399	−	0.999884i	$-0.495149\pi$
$127$	43.6232	0.0304798	0.0152399	+	0.999884i	$0.495149\pi$
$128$	578.956	0.399789
$129$	2786.78	1.90203
$130$	0	0
$131$	728.367	0.485784	0.242892	−	0.970053i	$-0.421904\pi$
$131$	728.367	0.485784	0.242892	+	0.970053i	$0.421904\pi$
$132$	176.233	0.116205
$133$	−1005.85	−0.655777
$134$	−930.831	−0.600086
$135$	−134.517	−0.0857583
$136$	2780.83	1.75334
$137$	34.8683	0.0217445	0.0108723	−	0.999941i	$-0.496539\pi$
$137$	34.8683	0.0217445	0.0108723	+	0.999941i	$0.496539\pi$
$138$	−1202.74	−0.741914
$139$	−298.899	−0.182391	−0.0911954	−	0.995833i	$-0.529069\pi$
$139$	−298.899	−0.182391	−0.0911954	+	0.995833i	$0.529069\pi$
$140$	−180.570	−0.109007
$141$	2327.13	1.38992
$142$	281.046	0.166091
$143$	0	0
$144$	−1037.42	−0.600360
$145$	−2067.07	−1.18387
$146$	2443.59	1.38516
$147$	−1983.34	−1.11281
$148$	506.564	0.281347
$149$	58.7860	0.0323217	0.0161609	−	0.999869i	$-0.494856\pi$
$149$	58.7860	0.0323217	0.0161609	+	0.999869i	$0.494856\pi$
$150$	−486.091	−0.264595
$151$	−2550.58	−1.37459	−0.687296	−	0.726378i	$-0.741202\pi$
$151$	−2550.58	−1.37459	−0.687296	+	0.726378i	$0.741202\pi$
$152$	2991.65	1.59642
$153$	−2841.65	−1.50153
$154$	−218.480	−0.114322
$155$	179.162	0.0928429
$156$	0	0
$157$	−373.767	−0.189999	−0.0949995	−	0.995477i	$-0.530285\pi$
$157$	−373.767	−0.189999	−0.0949995	+	0.995477i	$0.530285\pi$
$158$	−1032.14	−0.519701
$159$	1803.78	0.899680
$160$	957.482	0.473097
$161$	−572.493	−0.280241
$162$	−1866.94	−0.905438
$163$	−3013.03	−1.44784	−0.723922	−	0.689882i	$-0.757662\pi$
$163$	−3013.03	−1.44784	−0.723922	+	0.689882i	$0.757662\pi$
$164$	1022.10	0.486664
$165$	−782.010	−0.368966
$166$	2285.27	1.06850
$167$	−2373.33	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$167$	−2373.33	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$168$	−1465.20	−0.672875
$169$	0	0
$170$	−2679.88	−1.20904
$171$	−3057.09	−1.36714
$172$	−856.826	−0.379839
$173$	913.000	0.401237	0.200619	−	0.979669i	$-0.435705\pi$
$173$	913.000	0.401237	0.200619	+	0.979669i	$0.435705\pi$
$174$	−3642.70	−1.58708
$175$	−231.375	−0.0999444
$176$	454.505	0.194657
$177$	−409.664	−0.173967
$178$	1614.46	0.679826
$179$	1911.51	0.798173	0.399086	−	0.916913i	$-0.369327\pi$
$179$	1911.51	0.798173	0.399086	+	0.916913i	$0.369327\pi$
$180$	−548.807	−0.227254
$181$	3241.61	1.33120	0.665600	−	0.746308i	$-0.268176\pi$
$181$	3241.61	1.33120	0.665600	+	0.746308i	$0.268176\pi$
$182$	0	0
$183$	5601.13	2.26255
$184$	1702.74	0.682214
$185$	−2247.81	−0.893311
$186$	315.729	0.124464
$187$	1244.96	0.486846
$188$	−715.502	−0.277571
$189$	−112.835	−0.0434261
$190$	−2883.05	−1.10083
$191$	1252.48	0.474483	0.237242	−	0.971451i	$-0.423757\pi$
$191$	1252.48	0.474483	0.237242	+	0.971451i	$0.423757\pi$
$192$	4073.42	1.53111
$193$	−617.618	−0.230348	−0.115174	−	0.993345i	$-0.536743\pi$
$193$	−617.618	−0.230348	−0.115174	+	0.993345i	$0.536743\pi$
$194$	2328.41	0.861700
$195$	0	0
$196$	609.801	0.222231
$197$	2712.30	0.980930	0.490465	−	0.871461i	$-0.336827\pi$
$197$	2712.30	0.980930	0.490465	+	0.871461i	$0.336827\pi$
$198$	−664.029	−0.238336
$199$	2309.96	0.822856	0.411428	−	0.911442i	$-0.365030\pi$
$199$	2309.96	0.822856	0.411428	+	0.911442i	$0.365030\pi$
$200$	688.166	0.243303
$201$	−2794.71	−0.980716
$202$	1199.20	0.417701
$203$	−1733.89	−0.599483
$204$	1813.24	0.622315
$205$	−4535.45	−1.54522
$206$	1862.54	0.629948
$207$	−1739.98	−0.584238
$208$	0	0
$209$	1339.34	0.443274
$210$	1412.01	0.463992
$211$	−4349.05	−1.41896	−0.709481	−	0.704724i	$-0.751071\pi$
$211$	−4349.05	−1.41896	−0.709481	+	0.704724i	$0.751071\pi$
$212$	−554.593	−0.179668
$213$	843.810	0.271441
$214$	−3294.12	−1.05225
$215$	3802.06	1.20604
$216$	335.599	0.105716
$217$	150.284	0.0470135
$218$	−2033.32	−0.631716
$219$	7336.60	2.26375
$220$	240.438	0.0736833
$221$	0	0
$222$	−3961.22	−1.19757
$223$	−1591.00	−0.477762	−0.238881	−	0.971049i	$-0.576781\pi$
$223$	−1591.00	−0.477762	−0.238881	+	0.971049i	$0.576781\pi$
$224$	803.150	0.239566
$225$	−703.219	−0.208361
$226$	3157.48	0.929347
$227$	−4976.41	−1.45505	−0.727524	−	0.686083i	$-0.759329\pi$
$227$	−4976.41	−1.45505	−0.727524	+	0.686083i	$0.759329\pi$
$228$	1950.71	0.566619
$229$	−2216.11	−0.639495	−0.319748	−	0.947503i	$-0.603598\pi$
$229$	−2216.11	−0.639495	−0.319748	+	0.947503i	$0.603598\pi$
$230$	−1640.93	−0.470432
$231$	−655.962	−0.186836
$232$	5157.02	1.45937
$233$	−64.8342	−0.0182293	−0.00911465	−	0.999958i	$-0.502901\pi$
$233$	−64.8342	−0.0182293	−0.00911465	+	0.999958i	$0.502901\pi$
$234$	0	0
$235$	3174.95	0.881322
$236$	125.956	0.0347416
$237$	−3098.89	−0.849344
$238$	−2247.92	−0.612232
$239$	−3858.71	−1.04435	−0.522174	−	0.852839i	$-0.674879\pi$
$239$	−3858.71	−1.04435	−0.522174	+	0.852839i	$0.674879\pi$
$240$	−2937.42	−0.790039
$241$	−6737.07	−1.80072	−0.900359	−	0.435148i	$-0.856696\pi$
$241$	−6737.07	−1.80072	−0.900359	+	0.435148i	$0.856696\pi$
$242$	290.918	0.0772765
$243$	−5236.50	−1.38239
$244$	−1722.13	−0.451837
$245$	−2705.91	−0.705610
$246$	−7992.62	−2.07151
$247$	0	0
$248$	−446.982	−0.114449
$249$	6861.26	1.74624
$250$	−3622.99	−0.916552
$251$	2556.90	0.642989	0.321495	−	0.946911i	$-0.395815\pi$
$251$	2556.90	0.642989	0.321495	+	0.946911i	$0.395815\pi$
$252$	−460.348	−0.115076
$253$	762.304	0.189429
$254$	104.882	0.0259091
$255$	−8046.03	−1.97593
$256$	−3122.40	−0.762305
$257$	−5227.70	−1.26885	−0.634426	−	0.772983i	$-0.718764\pi$
$257$	−5227.70	−1.26885	−0.634426	+	0.772983i	$0.718764\pi$
$258$	6700.19	1.61680
$259$	−1885.50	−0.452353
$260$	0	0
$261$	−5269.82	−1.24979
$262$	1751.20	0.412937
$263$	6104.51	1.43125	0.715627	−	0.698482i	$-0.246141\pi$
$263$	6104.51	1.43125	0.715627	+	0.698482i	$0.246141\pi$
$264$	1951.00	0.454831
$265$	2460.93	0.570468
$266$	−2418.35	−0.557438
$267$	4847.24	1.11103
$268$	859.267	0.195851
$269$	6147.70	1.39343	0.696713	−	0.717350i	$-0.254645\pi$
$269$	6147.70	1.39343	0.696713	+	0.717350i	$0.254645\pi$
$270$	−323.416	−0.0728982
$271$	3285.68	0.736498	0.368249	−	0.929727i	$-0.379957\pi$
$271$	3285.68	0.736498	0.368249	+	0.929727i	$0.379957\pi$
$272$	4676.36	1.04245
$273$	0	0
$274$	83.8332	0.0184838
$275$	308.087	0.0675577
$276$	1110.27	0.242140
$277$	−750.813	−0.162859	−0.0814296	−	0.996679i	$-0.525949\pi$
$277$	−750.813	−0.162859	−0.0814296	+	0.996679i	$0.525949\pi$
$278$	−718.638	−0.155040
$279$	456.759	0.0980124
$280$	−1999.01	−0.426656
$281$	−7388.62	−1.56857	−0.784285	−	0.620400i	$-0.786970\pi$
$281$	−7388.62	−1.56857	−0.784285	+	0.620400i	$0.786970\pi$
$282$	5595.07	1.18149
$283$	−2895.26	−0.608145	−0.304073	−	0.952649i	$-0.598347\pi$
$283$	−2895.26	−0.608145	−0.304073	+	0.952649i	$0.598347\pi$
$284$	−259.439	−0.0542073
$285$	−8656.03	−1.79908
$286$	0	0
$287$	−3804.41	−0.782463
$288$	2441.02	0.499440
$289$	7896.25	1.60721
$290$	−4969.81	−1.00634
$291$	6990.77	1.40827
$292$	−2255.72	−0.452076
$293$	−2565.06	−0.511441	−0.255720	−	0.966751i	$-0.582313\pi$
$293$	−2565.06	−0.511441	−0.255720	+	0.966751i	$0.582313\pi$
$294$	−4768.51	−0.945936
$295$	−558.913	−0.110309
$296$	5607.95	1.10120
$297$	150.246	0.0293540
$298$	141.338	0.0274748
$299$	0	0
$300$	448.720	0.0863561
$301$	3189.22	0.610710
$302$	−6132.31	−1.16846
$303$	3600.46	0.682644
$304$	5030.90	0.949150
$305$	7641.74	1.43464
$306$	−6832.13	−1.27636
$307$	−5707.87	−1.06113	−0.530563	−	0.847646i	$-0.678019\pi$
$307$	−5707.87	−1.06113	−0.530563	+	0.847646i	$0.678019\pi$
$308$	201.683	0.0373116
$309$	5592.06	1.02952
$310$	430.756	0.0789203
$311$	1750.47	0.319165	0.159582	−	0.987185i	$-0.448985\pi$
$311$	1750.47	0.319165	0.159582	+	0.987185i	$0.448985\pi$
$312$	0	0
$313$	−6425.08	−1.16028	−0.580139	−	0.814518i	$-0.697002\pi$
$313$	−6425.08	−1.16028	−0.580139	+	0.814518i	$0.697002\pi$
$314$	−898.641	−0.161507
$315$	2042.73	0.365381
$316$	952.789	0.169616
$317$	9721.92	1.72252	0.861258	−	0.508168i	$-0.169677\pi$
$317$	9721.92	1.72252	0.861258	+	0.508168i	$0.169677\pi$
$318$	4336.79	0.764765
$319$	2308.76	0.405222
$320$	5557.45	0.970847
$321$	−9890.22	−1.71968
$322$	−1376.43	−0.238216
$323$	13780.4	2.37387
$324$	1723.41	0.295509
$325$	0	0
$326$	−7244.16	−1.23073
$327$	−6104.82	−1.03241
$328$	11315.3	1.90482
$329$	2663.20	0.446282
$330$	−1880.17	−0.313636
$331$	−4560.44	−0.757294	−0.378647	−	0.925541i	$-0.623611\pi$
$331$	−4560.44	−0.757294	−0.378647	+	0.925541i	$0.623611\pi$
$332$	−2109.57	−0.348728
$333$	−5730.62	−0.943051
$334$	−5706.14	−0.934809
$335$	−3812.89	−0.621851
$336$	−2463.95	−0.400058
$337$	−3870.54	−0.625643	−0.312822	−	0.949812i	$-0.601274\pi$
$337$	−3870.54	−0.625643	−0.312822	+	0.949812i	$0.601274\pi$
$338$	0	0
$339$	9479.97	1.51882
$340$	2473.84	0.394597
$341$	−200.111	−0.0317789
$342$	−7350.11	−1.16213
$343$	−5103.30	−0.803359
$344$	−9485.55	−1.48670
$345$	−4926.69	−0.768823
$346$	2195.11	0.341068
$347$	−2536.47	−0.392406	−0.196203	−	0.980563i	$-0.562861\pi$
$347$	−2536.47	−0.392406	−0.196203	+	0.980563i	$0.562861\pi$
$348$	3362.64	0.517979
$349$	450.127	0.0690394	0.0345197	−	0.999404i	$-0.489010\pi$
$349$	450.127	0.0690394	0.0345197	+	0.999404i	$0.489010\pi$
$350$	−556.290	−0.0849569
$351$	0	0
$352$	−1069.44	−0.161935
$353$	−7860.81	−1.18524	−0.592619	−	0.805483i	$-0.701906\pi$
$353$	−7860.81	−1.18524	−0.592619	+	0.805483i	$0.701906\pi$
$354$	−984.946	−0.147879
$355$	1151.23	0.172115
$356$	−1490.34	−0.221876
$357$	−6749.13	−1.00057
$358$	4595.81	0.678480
$359$	−7509.91	−1.10406	−0.552030	−	0.833824i	$-0.686147\pi$
$359$	−7509.91	−1.10406	−0.552030	+	0.833824i	$0.686147\pi$
$360$	−6075.60	−0.889479
$361$	7966.13	1.16141
$362$	7793.75	1.13158
$363$	873.448	0.126292
$364$	0	0
$365$	10009.5	1.43540
$366$	13466.7	1.92326
$367$	2168.03	0.308366	0.154183	−	0.988042i	$-0.450726\pi$
$367$	2168.03	0.308366	0.154183	+	0.988042i	$0.450726\pi$
$368$	2863.40	0.405611
$369$	−11562.8	−1.63126
$370$	−5404.38	−0.759352
$371$	2064.27	0.288872
$372$	−291.455	−0.0406217
$373$	−2525.90	−0.350633	−0.175317	−	0.984512i	$-0.556095\pi$
$373$	−2525.90	−0.350633	−0.175317	+	0.984512i	$0.556095\pi$
$374$	2993.23	0.413840
$375$	−10877.6	−1.49791
$376$	−7921.01	−1.08642
$377$	0	0
$378$	−271.287	−0.0369140
$379$	−12858.2	−1.74270	−0.871349	−	0.490663i	$-0.836755\pi$
$379$	−12858.2	−1.74270	−0.871349	+	0.490663i	$0.836755\pi$
$380$	2661.40	0.359281
$381$	314.897	0.0423430
$382$	3011.32	0.403331
$383$	−6495.09	−0.866536	−0.433268	−	0.901265i	$-0.642640\pi$
$383$	−6495.09	−0.866536	−0.433268	+	0.901265i	$0.642640\pi$
$384$	4179.24	0.555393
$385$	−894.943	−0.118469
$386$	−1484.93	−0.195805
$387$	9693.03	1.27319
$388$	−2149.39	−0.281234
$389$	10018.2	1.30577	0.652886	−	0.757456i	$-0.273558\pi$
$389$	10018.2	1.30577	0.652886	+	0.757456i	$0.273558\pi$
$390$	0	0
$391$	7843.27	1.01445
$392$	6750.84	0.869819
$393$	5257.77	0.674859
$394$	6521.12	0.833831
$395$	−4227.88	−0.538551
$396$	612.977	0.0777860
$397$	5201.52	0.657574	0.328787	−	0.944404i	$-0.393360\pi$
$397$	5201.52	0.657574	0.328787	+	0.944404i	$0.393360\pi$
$398$	5553.78	0.699462
$399$	−7260.82	−0.911016
$400$	1157.25	0.144656
$401$	−3116.36	−0.388088	−0.194044	−	0.980993i	$-0.562161\pi$
$401$	−3116.36	−0.388088	−0.194044	+	0.980993i	$0.562161\pi$
$402$	−6719.28	−0.833649
$403$	0	0
$404$	−1107.00	−0.136326
$405$	−7647.40	−0.938278
$406$	−4168.76	−0.509586
$407$	2510.64	0.305769
$408$	20073.6	2.43576
$409$	7577.28	0.916070	0.458035	−	0.888934i	$-0.348553\pi$
$409$	7577.28	0.916070	0.458035	+	0.888934i	$0.348553\pi$
$410$	−10904.5	−1.31350
$411$	251.700	0.0302078
$412$	−1719.34	−0.205597
$413$	−468.825	−0.0558580
$414$	−4183.41	−0.496626
$415$	9360.96	1.10726
$416$	0	0
$417$	−2157.63	−0.253380
$418$	3220.16	0.376802
$419$	1434.43	0.167247	0.0836234	−	0.996497i	$-0.473351\pi$
$419$	1434.43	0.167247	0.0836234	+	0.996497i	$0.473351\pi$
$420$	−1303.46	−0.151434
$421$	−84.9736	−0.00983696	−0.00491848	−	0.999988i	$-0.501566\pi$
$421$	−84.9736	−0.00983696	−0.00491848	+	0.999988i	$0.501566\pi$
$422$	−10456.3	−1.20618
$423$	8094.27	0.930395
$424$	−6139.66	−0.703227
$425$	3169.88	0.361793
$426$	2028.76	0.230736
$427$	6410.01	0.726468
$428$	3040.86	0.343424
$429$	0	0
$430$	9141.21	1.02518
$431$	10844.3	1.21195	0.605974	−	0.795484i	$-0.292783\pi$
$431$	10844.3	1.21195	0.605974	+	0.795484i	$0.292783\pi$
$432$	564.358	0.0628535
$433$	−4075.42	−0.452315	−0.226157	−	0.974091i	$-0.572616\pi$
$433$	−4075.42	−0.452315	−0.226157	+	0.974091i	$0.572616\pi$
$434$	361.325	0.0399635
$435$	−14921.3	−1.64465
$436$	1877.00	0.206174
$437$	8437.91	0.923661
$438$	17639.3	1.92428
$439$	15183.4	1.65071	0.825356	−	0.564613i	$-0.190975\pi$
$439$	15183.4	1.65071	0.825356	+	0.564613i	$0.190975\pi$
$440$	2661.78	0.288399
$441$	−6898.51	−0.744899
$442$	0	0
$443$	−2203.06	−0.236276	−0.118138	−	0.992997i	$-0.537693\pi$
$443$	−2203.06	−0.236276	−0.118138	+	0.992997i	$0.537693\pi$
$444$	3656.67	0.390851
$445$	6613.19	0.704484
$446$	−3825.20	−0.406118
$447$	424.351	0.0449018
$448$	4661.68	0.491615
$449$	−2387.96	−0.250990	−0.125495	−	0.992094i	$-0.540052\pi$
$449$	−2387.96	−0.250990	−0.125495	+	0.992094i	$0.540052\pi$
$450$	−1690.74	−0.177116
$451$	5065.77	0.528908
$452$	−2914.73	−0.303312
$453$	−18411.6	−1.90960
$454$	−11964.7	−1.23685
$455$	0	0
$456$	21595.5	2.21777
$457$	−13211.2	−1.35228	−0.676141	−	0.736772i	$-0.736349\pi$
$457$	−13211.2	−1.35228	−0.676141	+	0.736772i	$0.736349\pi$
$458$	−5328.14	−0.543598
$459$	1545.86	0.157200
$460$	1514.77	0.153536
$461$	15369.8	1.55280	0.776400	−	0.630240i	$-0.217044\pi$
$461$	15369.8	1.55280	0.776400	+	0.630240i	$0.217044\pi$
$462$	−1577.12	−0.158818
$463$	15981.6	1.60416	0.802081	−	0.597215i	$-0.203726\pi$
$463$	15981.6	1.60416	0.802081	+	0.597215i	$0.203726\pi$
$464$	8672.27	0.867672
$465$	1293.30	0.128979
$466$	−155.880	−0.0154957
$467$	−6285.94	−0.622867	−0.311433	−	0.950268i	$-0.600809\pi$
$467$	−6285.94	−0.622867	−0.311433	+	0.950268i	$0.600809\pi$
$468$	0	0
$469$	−3198.31	−0.314892
$470$	7633.46	0.749161
$471$	−2698.06	−0.263950
$472$	1394.40	0.135980
$473$	−4246.62	−0.412811
$474$	−7450.60	−0.721977
$475$	3410.21	0.329413
$476$	2075.10	0.199815
$477$	6273.96	0.602232
$478$	−9277.41	−0.887739
$479$	−2421.85	−0.231017	−0.115509	−	0.993306i	$-0.536850\pi$
$479$	−2421.85	−0.231017	−0.115509	+	0.993306i	$0.536850\pi$
$480$	6911.65	0.657234
$481$	0	0
$482$	−16197.8	−1.53069
$483$	−4132.58	−0.389315
$484$	−268.552	−0.0252208
$485$	9537.65	0.892954
$486$	−12590.0	−1.17509
$487$	−2565.70	−0.238733	−0.119367	−	0.992850i	$-0.538086\pi$
$487$	−2565.70	−0.238733	−0.119367	+	0.992850i	$0.538086\pi$
$488$	−19065.0	−1.76850
$489$	−21749.8	−2.01137
$490$	−6505.78	−0.599798
$491$	−12252.8	−1.12619	−0.563097	−	0.826391i	$-0.690390\pi$
$491$	−12252.8	−1.12619	−0.563097	+	0.826391i	$0.690390\pi$
$492$	7378.13	0.676081
$493$	23754.6	2.17009
$494$	0	0
$495$	−2720.01	−0.246980
$496$	−751.665	−0.0680458
$497$	965.667	0.0871551
$498$	16496.4	1.48438
$499$	−13403.0	−1.20241	−0.601203	−	0.799096i	$-0.705312\pi$
$499$	−13403.0	−1.20241	−0.601203	+	0.799096i	$0.705312\pi$
$500$	3344.45	0.299136
$501$	−17132.0	−1.52775
$502$	6147.51	0.546567
$503$	12682.2	1.12420	0.562098	−	0.827070i	$-0.309994\pi$
$503$	12682.2	1.12420	0.562098	+	0.827070i	$0.309994\pi$
$504$	−5096.31	−0.450412
$505$	4912.19	0.432851
$506$	1832.79	0.161023
$507$	0	0
$508$	−96.8188	−0.00845599
$509$	−12218.3	−1.06399	−0.531993	−	0.846749i	$-0.678557\pi$
$509$	−12218.3	−1.06399	−0.531993	+	0.846749i	$0.678557\pi$
$510$	−19344.9	−1.67962
$511$	8396.11	0.726853
$512$	−12138.8	−1.04778
$513$	1663.06	0.143131
$514$	−12568.9	−1.07858
$515$	7629.37	0.652796
$516$	−6185.06	−0.527679
$517$	−3546.18	−0.301665
$518$	−4533.27	−0.384519
$519$	6590.56	0.557405
$520$	0	0
$521$	−2805.00	−0.235872	−0.117936	−	0.993021i	$-0.537628\pi$
$521$	−2805.00	−0.235872	−0.117936	+	0.993021i	$0.537628\pi$
$522$	−12670.1	−1.06237
$523$	749.381	0.0626542	0.0313271	−	0.999509i	$-0.490027\pi$
$523$	749.381	0.0626542	0.0313271	+	0.999509i	$0.490027\pi$
$524$	−1616.56	−0.134771
$525$	−1670.20	−0.138844
$526$	14676.9	1.21663
$527$	−2058.92	−0.170186
$528$	3280.88	0.270420
$529$	−7364.46	−0.605281
$530$	5916.78	0.484922
$531$	−1424.90	−0.116451
$532$	2232.42	0.181932
$533$	0	0
$534$	11654.1	0.944425
$535$	−13493.4	−1.09042
$536$	9512.57	0.766568
$537$	13798.4	1.10883
$538$	14780.8	1.18447
$539$	3022.31	0.241521
$540$	298.552	0.0237919
$541$	−8234.62	−0.654407	−0.327203	−	0.944954i	$-0.606106\pi$
$541$	−8234.62	−0.654407	−0.327203	+	0.944954i	$0.606106\pi$
$542$	7899.70	0.626054
$543$	23399.8	1.84932
$544$	−11003.3	−0.867213
$545$	−8328.94	−0.654628
$546$	0	0
$547$	−9637.00	−0.753288	−0.376644	−	0.926358i	$-0.622922\pi$
$547$	−9637.00	−0.753288	−0.376644	+	0.926358i	$0.622922\pi$
$548$	−77.3879	−0.00603257
$549$	19482.0	1.51452
$550$	740.729	0.0574269
$551$	25555.6	1.97587
$552$	12291.3	0.947743
$553$	−3546.41	−0.272710
$554$	−1805.16	−0.138437
$555$	−16226.0	−1.24100
$556$	663.388	0.0506005
$557$	11704.8	0.890388	0.445194	−	0.895434i	$-0.353135\pi$
$557$	11704.8	0.890388	0.445194	+	0.895434i	$0.353135\pi$
$558$	1098.18	0.0833147
$559$	0	0
$560$	−3361.62	−0.253668
$561$	8986.82	0.676335
$562$	−17764.3	−1.33335
$563$	−14175.9	−1.06118	−0.530590	−	0.847628i	$-0.678030\pi$
$563$	−14175.9	−1.06118	−0.530590	+	0.847628i	$0.678030\pi$
$564$	−5164.91	−0.385606
$565$	12933.7	0.963055
$566$	−6961.01	−0.516949
$567$	−6414.76	−0.475123
$568$	−2872.14	−0.212169
$569$	−19427.1	−1.43133	−0.715665	−	0.698443i	$-0.753876\pi$
$569$	−19427.1	−1.43133	−0.715665	+	0.698443i	$0.753876\pi$
$570$	−20811.5	−1.52930
$571$	−18855.7	−1.38194	−0.690968	−	0.722886i	$-0.742815\pi$
$571$	−18855.7	−1.38194	−0.690968	+	0.722886i	$0.742815\pi$
$572$	0	0
$573$	9041.13	0.659160
$574$	−9146.86	−0.665126
$575$	1940.96	0.140772
$576$	14168.3	1.02490
$577$	2869.39	0.207026	0.103513	−	0.994628i	$-0.466992\pi$
$577$	2869.39	0.207026	0.103513	+	0.994628i	$0.466992\pi$
$578$	18984.8	1.36620
$579$	−4458.32	−0.320003
$580$	4587.72	0.328439
$581$	7852.11	0.560689
$582$	16807.8	1.19709
$583$	−2748.68	−0.195264
$584$	−24972.1	−1.76944
$585$	0	0
$586$	−6167.11	−0.434746
$587$	15021.8	1.05625	0.528123	−	0.849168i	$-0.322896\pi$
$587$	15021.8	1.05625	0.528123	+	0.849168i	$0.322896\pi$
$588$	4401.90	0.308727
$589$	−2215.02	−0.154955
$590$	−1343.78	−0.0937672
$591$	19578.9	1.36272
$592$	9430.58	0.654720
$593$	8072.54	0.559021	0.279511	−	0.960143i	$-0.409828\pi$
$593$	8072.54	0.559021	0.279511	+	0.960143i	$0.409828\pi$
$594$	361.232	0.0249521
$595$	−9207.98	−0.634438
$596$	−130.472	−0.00896699
$597$	16674.6	1.14313
$598$	0	0
$599$	−5732.54	−0.391027	−0.195514	−	0.980701i	$-0.562637\pi$
$599$	−5732.54	−0.391027	−0.195514	+	0.980701i	$0.562637\pi$
$600$	4967.58	0.338001
$601$	2207.06	0.149796	0.0748982	−	0.997191i	$-0.476137\pi$
$601$	2207.06	0.149796	0.0748982	+	0.997191i	$0.476137\pi$
$602$	7667.79	0.519129
$603$	−9720.65	−0.656476
$604$	5660.85	0.381352
$605$	1191.66	0.0800793
$606$	8656.53	0.580276
$607$	12291.7	0.821919	0.410959	−	0.911654i	$-0.365194\pi$
$607$	12291.7	0.821919	0.410959	+	0.911654i	$0.365194\pi$
$608$	−11837.5	−0.789599
$609$	−12516.2	−0.832812
$610$	18372.9	1.21950
$611$	0	0
$612$	6306.86	0.416568
$613$	−22390.4	−1.47527	−0.737634	−	0.675201i	$-0.764057\pi$
$613$	−22390.4	−1.47527	−0.737634	+	0.675201i	$0.764057\pi$
$614$	−13723.3	−0.902001
$615$	−32739.5	−2.14664
$616$	2232.75	0.146039
$617$	−28056.9	−1.83068	−0.915340	−	0.402683i	$-0.868078\pi$
$617$	−28056.9	−1.83068	−0.915340	+	0.402683i	$0.868078\pi$
$618$	13444.9	0.875134
$619$	17407.7	1.13033	0.565166	−	0.824977i	$-0.308812\pi$
$619$	17407.7	1.13033	0.565166	+	0.824977i	$0.308812\pi$
$620$	−397.639	−0.0257573
$621$	946.552	0.0611656
$622$	4208.63	0.271303
$623$	5547.25	0.356735
$624$	0	0
$625$	−11339.6	−0.725732
$626$	−15447.7	−0.986284
$627$	9668.15	0.615804
$628$	829.551	0.0527113
$629$	25831.8	1.63749
$630$	4911.31	0.310589
$631$	−23766.3	−1.49940	−0.749699	−	0.661779i	$-0.769802\pi$
$631$	−23766.3	−1.49940	−0.749699	+	0.661779i	$0.769802\pi$
$632$	10547.9	0.663882
$633$	−31394.0	−1.97124
$634$	23374.2	1.46421
$635$	429.621	0.0268488
$636$	−4003.37	−0.249598
$637$	0	0
$638$	5550.92	0.344456
$639$	2934.96	0.181698
$640$	5701.82	0.352163
$641$	−6864.68	−0.422993	−0.211497	−	0.977379i	$-0.567834\pi$
$641$	−6864.68	−0.422993	−0.211497	+	0.977379i	$0.567834\pi$
$642$	−23778.9	−1.46180
$643$	−25251.4	−1.54871	−0.774354	−	0.632752i	$-0.781925\pi$
$643$	−25251.4	−1.54871	−0.774354	+	0.632752i	$0.781925\pi$
$644$	1270.61	0.0777470
$645$	27445.4	1.67545
$646$	33131.9	2.01789
$647$	−28831.7	−1.75192	−0.875960	−	0.482384i	$-0.839771\pi$
$647$	−28831.7	−1.75192	−0.875960	+	0.482384i	$0.839771\pi$
$648$	19079.1	1.15663
$649$	624.264	0.0377574
$650$	0	0
$651$	1084.84	0.0653120
$652$	6687.22	0.401674
$653$	21931.3	1.31430	0.657150	−	0.753760i	$-0.271762\pi$
$653$	21931.3	1.31430	0.657150	+	0.753760i	$0.271762\pi$
$654$	−14677.7	−0.877590
$655$	7173.29	0.427914
$656$	19028.2	1.13251
$657$	25518.4	1.51532
$658$	6403.07	0.379358
$659$	−9007.44	−0.532443	−0.266222	−	0.963912i	$-0.585775\pi$
$659$	−9007.44	−0.532443	−0.266222	+	0.963912i	$0.585775\pi$
$660$	1735.62	0.102362
$661$	−15820.6	−0.930937	−0.465469	−	0.885064i	$-0.654114\pi$
$661$	−15820.6	−0.930937	−0.465469	+	0.885064i	$0.654114\pi$
$662$	−10964.6	−0.643731
$663$	0	0
$664$	−23354.2	−1.36494
$665$	−9906.08	−0.577656
$666$	−13778.0	−0.801633
$667$	14545.3	0.844372
$668$	5267.44	0.305095
$669$	−11484.7	−0.663715
$670$	−9167.25	−0.528600
$671$	−8535.26	−0.491058
$672$	5797.60	0.332809
$673$	−4378.50	−0.250786	−0.125393	−	0.992107i	$-0.540019\pi$
$673$	−4378.50	−0.250786	−0.125393	+	0.992107i	$0.540019\pi$
$674$	−9305.86	−0.531823
$675$	382.552	0.0218140
$676$	0	0
$677$	−20157.2	−1.14432	−0.572159	−	0.820142i	$-0.693894\pi$
$677$	−20157.2	−1.14432	−0.572159	+	0.820142i	$0.693894\pi$
$678$	22792.5	1.29106
$679$	8000.33	0.452172
$680$	27386.8	1.54447
$681$	−35922.6	−2.02137
$682$	−481.123	−0.0270134
$683$	−5932.96	−0.332384	−0.166192	−	0.986093i	$-0.553147\pi$
$683$	−5932.96	−0.332384	−0.166192	+	0.986093i	$0.553147\pi$
$684$	6785.02	0.379286
$685$	343.399	0.0191542
$686$	−12269.8	−0.682889
$687$	−15997.1	−0.888397
$688$	−15951.3	−0.883921
$689$	0	0
$690$	−11845.1	−0.653532
$691$	−1087.33	−0.0598613	−0.0299307	−	0.999552i	$-0.509529\pi$
$691$	−1087.33	−0.0598613	−0.0299307	+	0.999552i	$0.509529\pi$
$692$	−2026.34	−0.111315
$693$	−2281.58	−0.125065
$694$	−6098.39	−0.333562
$695$	−2943.70	−0.160663
$696$	37226.3	2.02739
$697$	52121.2	2.83247
$698$	1082.23	0.0586864
$699$	−468.010	−0.0253244
$700$	513.521	0.0277275
$701$	−22965.0	−1.23734	−0.618671	−	0.785650i	$-0.712329\pi$
$701$	−22965.0	−1.23734	−0.618671	+	0.785650i	$0.712329\pi$
$702$	0	0
$703$	27790.2	1.49093
$704$	−6207.27	−0.332308
$705$	22918.6	1.22435
$706$	−18899.6	−1.00750
$707$	4120.42	0.219186
$708$	909.222	0.0482636
$709$	17234.7	0.912923	0.456461	−	0.889743i	$-0.349117\pi$
$709$	17234.7	0.912923	0.456461	+	0.889743i	$0.349117\pi$
$710$	2767.87	0.146305
$711$	−10778.6	−0.568538
$712$	−16498.9	−0.868430
$713$	−1260.71	−0.0662185
$714$	−16226.8	−0.850522
$715$	0	0
$716$	−4242.47	−0.221437
$717$	−27854.4	−1.45082
$718$	−18055.9	−0.938497
$719$	−8404.20	−0.435916	−0.217958	−	0.975958i	$-0.569940\pi$
$719$	−8404.20	−0.435916	−0.217958	+	0.975958i	$0.569940\pi$
$720$	−10217.0	−0.528840
$721$	6399.63	0.330561
$722$	19152.8	0.987250
$723$	−48632.1	−2.50159
$724$	−7194.55	−0.369314
$725$	5878.52	0.301135
$726$	2100.01	0.107354
$727$	31053.6	1.58420	0.792101	−	0.610390i	$-0.208987\pi$
$727$	31053.6	1.58420	0.792101	+	0.610390i	$0.208987\pi$
$728$	0	0
$729$	−16834.3	−0.855273
$730$	24065.6	1.22015
$731$	−43693.0	−2.21073
$732$	−12431.3	−0.627699
$733$	4116.72	0.207441	0.103721	−	0.994606i	$-0.466925\pi$
$733$	4116.72	0.207441	0.103721	+	0.994606i	$0.466925\pi$
$734$	5212.55	0.262124
$735$	−19532.9	−0.980245
$736$	−6737.49	−0.337428
$737$	4258.71	0.212852
$738$	−27800.1	−1.38664
$739$	32205.9	1.60313	0.801565	−	0.597908i	$-0.204001\pi$
$739$	32205.9	1.60313	0.801565	+	0.597908i	$0.204001\pi$
$740$	4988.88	0.247831
$741$	0	0
$742$	4963.09	0.245553
$743$	−7624.80	−0.376483	−0.188241	−	0.982123i	$-0.560279\pi$
$743$	−7624.80	−0.376483	−0.188241	+	0.982123i	$0.560279\pi$
$744$	−3226.57	−0.158995
$745$	578.951	0.0284713
$746$	−6072.98	−0.298053
$747$	23865.0	1.16891
$748$	−2763.10	−0.135065
$749$	−11318.5	−0.552162
$750$	−26152.8	−1.27329
$751$	16416.1	0.797644	0.398822	−	0.917028i	$-0.369419\pi$
$751$	16416.1	0.797644	0.398822	+	0.917028i	$0.369419\pi$
$752$	−13320.3	−0.645933
$753$	18457.2	0.893250
$754$	0	0
$755$	−25119.3	−1.21084
$756$	250.430	0.0120477
$757$	18466.2	0.886610	0.443305	−	0.896371i	$-0.353806\pi$
$757$	18466.2	0.886610	0.443305	+	0.896371i	$0.353806\pi$
$758$	−30914.8	−1.48137
$759$	5502.75	0.263158
$760$	29463.2	1.40624
$761$	35699.7	1.70054	0.850270	−	0.526346i	$-0.176438\pi$
$761$	35699.7	1.70054	0.850270	+	0.526346i	$0.176438\pi$
$762$	757.102	0.0359933
$763$	−6986.44	−0.331489
$764$	−2779.80	−0.131636
$765$	−27985.9	−1.32266
$766$	−15616.0	−0.736592
$767$	0	0
$768$	−22539.3	−1.05901
$769$	17150.4	0.804237	0.402119	−	0.915588i	$-0.368274\pi$
$769$	17150.4	0.804237	0.402119	+	0.915588i	$0.368274\pi$
$770$	−2151.69	−0.100703
$771$	−37736.6	−1.76271
$772$	1370.76	0.0639052
$773$	−12687.9	−0.590365	−0.295182	−	0.955441i	$-0.595380\pi$
$773$	−12687.9	−0.590365	−0.295182	+	0.955441i	$0.595380\pi$
$774$	23304.8	1.08226
$775$	−509.518	−0.0236160
$776$	−23795.0	−1.10076
$777$	−13610.6	−0.628415
$778$	24086.7	1.10996
$779$	56072.7	2.57897
$780$	0	0
$781$	−1285.84	−0.0589127
$782$	18857.4	0.862328
$783$	2866.79	0.130844
$784$	11352.5	0.517152
$785$	−3681.03	−0.167365
$786$	12641.2	0.573658
$787$	8986.98	0.407053	0.203527	−	0.979069i	$-0.434760\pi$
$787$	8986.98	0.407053	0.203527	+	0.979069i	$0.434760\pi$
$788$	−6019.76	−0.272139
$789$	44065.8	1.98832
$790$	−10165.0	−0.457791
$791$	10849.0	0.487669
$792$	6786.00	0.304457
$793$	0	0
$794$	12505.9	0.558965
$795$	17764.4	0.792503
$796$	−5126.80	−0.228285
$797$	13773.0	0.612127	0.306064	−	0.952011i	$-0.400988\pi$
$797$	13773.0	0.612127	0.306064	+	0.952011i	$0.400988\pi$
$798$	−17457.0	−0.774402
$799$	−36486.3	−1.61551
$800$	−2722.97	−0.120340
$801$	16859.8	0.743710
$802$	−7492.60	−0.329891
$803$	−11179.9	−0.491318
$804$	6202.68	0.272079
$805$	−5638.17	−0.246856
$806$	0	0
$807$	44377.6	1.93577
$808$	−12255.2	−0.533583
$809$	−32953.4	−1.43211	−0.716057	−	0.698041i	$-0.754055\pi$
$809$	−32953.4	−1.43211	−0.716057	+	0.698041i	$0.754055\pi$
$810$	−18386.5	−0.797575
$811$	−2030.80	−0.0879299	−0.0439649	−	0.999033i	$-0.513999\pi$
$811$	−2030.80	−0.0879299	−0.0439649	+	0.999033i	$0.513999\pi$
$812$	3848.25	0.166314
$813$	23717.9	1.02315
$814$	6036.29	0.259916
$815$	−29673.7	−1.27537
$816$	33756.6	1.44818
$817$	−47005.6	−2.01287
$818$	18217.9	0.778698
$819$	0	0
$820$	10066.1	0.428689
$821$	29724.1	1.26355	0.631777	−	0.775150i	$-0.282326\pi$
$821$	29724.1	1.26355	0.631777	+	0.775150i	$0.282326\pi$
$822$	605.156	0.0256779
$823$	−8511.11	−0.360485	−0.180242	−	0.983622i	$-0.557688\pi$
$823$	−8511.11	−0.360485	−0.180242	+	0.983622i	$0.557688\pi$
$824$	−19034.1	−0.804714
$825$	2223.95	0.0938522
$826$	−1127.19	−0.0474816
$827$	−8120.27	−0.341438	−0.170719	−	0.985320i	$-0.554609\pi$
$827$	−8120.27	−0.341438	−0.170719	+	0.985320i	$0.554609\pi$
$828$	3861.78	0.162085
$829$	1460.74	0.0611986	0.0305993	−	0.999532i	$-0.490258\pi$
$829$	1460.74	0.0611986	0.0305993	+	0.999532i	$0.490258\pi$
$830$	22506.4	0.941214
$831$	−5419.80	−0.226246
$832$	0	0
$833$	31096.2	1.29342
$834$	−5187.54	−0.215384
$835$	−23373.6	−0.968715
$836$	−2972.59	−0.122977
$837$	−248.477	−0.0102612
$838$	3448.77	0.142167
$839$	−8636.35	−0.355376	−0.177688	−	0.984087i	$-0.556862\pi$
$839$	−8636.35	−0.355376	−0.177688	+	0.984087i	$0.556862\pi$
$840$	−14430.0	−0.592717
$841$	19663.8	0.806257
$842$	−204.300	−0.00836182
$843$	−53335.3	−2.17908
$844$	9652.43	0.393662
$845$	0	0
$846$	19460.9	0.790874
$847$	999.585	0.0405504
$848$	−10324.7	−0.418104
$849$	−20899.6	−0.844845
$850$	7621.28	0.307539
$851$	15817.1	0.637138
$852$	−1872.78	−0.0753056
$853$	13608.2	0.546232	0.273116	−	0.961981i	$-0.411946\pi$
$853$	13608.2	0.546232	0.273116	+	0.961981i	$0.411946\pi$
$854$	15411.5	0.617528
$855$	−30107.6	−1.20428
$856$	33664.1	1.34418
$857$	−42926.8	−1.71103	−0.855514	−	0.517780i	$-0.826759\pi$
$857$	−42926.8	−1.71103	−0.855514	+	0.517780i	$0.826759\pi$
$858$	0	0
$859$	46779.1	1.85807	0.929035	−	0.369993i	$-0.120640\pi$
$859$	46779.1	1.85807	0.929035	+	0.369993i	$0.120640\pi$
$860$	−8438.41	−0.334590
$861$	−27462.4	−1.08701
$862$	26072.7	1.03021
$863$	−14603.1	−0.576008	−0.288004	−	0.957629i	$-0.592992\pi$
$863$	−14603.1	−0.576008	−0.288004	+	0.957629i	$0.592992\pi$
$864$	−1327.92	−0.0522878
$865$	8991.63	0.353439
$866$	−9798.46	−0.384486
$867$	56999.6	2.23277
$868$	−333.545	−0.0130429
$869$	4722.23	0.184339
$870$	−35875.0	−1.39802
$871$	0	0
$872$	20779.4	0.806973
$873$	24315.5	0.942674
$874$	20287.1	0.785150
$875$	−12448.5	−0.480955
$876$	−16283.1	−0.628031
$877$	11327.6	0.436152	0.218076	−	0.975932i	$-0.430022\pi$
$877$	11327.6	0.436152	0.218076	+	0.975932i	$0.430022\pi$
$878$	36505.1	1.40317
$879$	−18516.1	−0.710502
$880$	4476.17	0.171468
$881$	49324.6	1.88625	0.943126	−	0.332435i	$-0.107870\pi$
$881$	49324.6	1.88625	0.943126	+	0.332435i	$0.107870\pi$
$882$	−16586.0	−0.633195
$883$	−471.552	−0.0179717	−0.00898584	−	0.999960i	$-0.502860\pi$
$883$	−471.552	−0.0179717	−0.00898584	+	0.999960i	$0.502860\pi$
$884$	0	0
$885$	−4034.55	−0.153243
$886$	−5296.77	−0.200845
$887$	6113.72	0.231430	0.115715	−	0.993282i	$-0.463084\pi$
$887$	6113.72	0.231430	0.115715	+	0.993282i	$0.463084\pi$
$888$	40481.4	1.52981
$889$	360.373	0.0135956
$890$	15900.0	0.598840
$891$	8541.59	0.321160
$892$	3531.11	0.132545
$893$	−39252.5	−1.47093
$894$	1020.26	0.0381684
$895$	18825.4	0.703089
$896$	4782.78	0.178327
$897$	0	0
$898$	−5741.32	−0.213352
$899$	−3818.25	−0.141653
$900$	1560.75	0.0578055
$901$	−28280.9	−1.04570
$902$	12179.5	0.449594
$903$	23021.6	0.848408
$904$	−32267.7	−1.18718
$905$	31924.9	1.17262
$906$	−44266.6	−1.62324
$907$	40444.5	1.48064	0.740319	−	0.672256i	$-0.234674\pi$
$907$	40444.5	1.48064	0.740319	+	0.672256i	$0.234674\pi$
$908$	11044.8	0.403673
$909$	12523.2	0.456952
$910$	0	0
$911$	−11594.1	−0.421657	−0.210829	−	0.977523i	$-0.567616\pi$
$911$	−11594.1	−0.421657	−0.210829	+	0.977523i	$0.567616\pi$
$912$	36315.9	1.31857
$913$	−10455.5	−0.378999
$914$	−31763.4	−1.14950
$915$	55162.5	1.99302
$916$	4918.50	0.177415
$917$	6017.07	0.216686
$918$	3716.69	0.133626
$919$	29311.0	1.05210	0.526050	−	0.850454i	$-0.323673\pi$
$919$	29311.0	1.05210	0.526050	+	0.850454i	$0.323673\pi$
$920$	16769.3	0.600944
$921$	−41202.7	−1.47413
$922$	36953.2	1.31995
$923$	0	0
$924$	1455.86	0.0518338
$925$	6392.54	0.227228
$926$	38424.2	1.36360
$927$	19450.5	0.689145
$928$	−20405.6	−0.721817
$929$	49127.2	1.73500	0.867498	−	0.497441i	$-0.165727\pi$
$929$	49127.2	1.73500	0.867498	+	0.497441i	$0.165727\pi$
$930$	3109.45	0.109637
$931$	33453.8	1.17766
$932$	143.895	0.00505734
$933$	12635.9	0.443389
$934$	−15113.2	−0.529463
$935$	12260.9	0.428850
$936$	0	0
$937$	39342.0	1.37166	0.685831	−	0.727761i	$-0.259439\pi$
$937$	39342.0	1.37166	0.685831	+	0.727761i	$0.259439\pi$
$938$	−7689.63	−0.267671
$939$	−46379.9	−1.61188
$940$	−7046.59	−0.244505
$941$	13059.3	0.452413	0.226207	−	0.974079i	$-0.427368\pi$
$941$	13059.3	0.452413	0.226207	+	0.974079i	$0.427368\pi$
$942$	−6486.90	−0.224368
$943$	31914.5	1.10210
$944$	2344.89	0.0808470
$945$	−1111.25	−0.0382529
$946$	−10210.1	−0.350907
$947$	7521.97	0.258111	0.129055	−	0.991637i	$-0.458805\pi$
$947$	7521.97	0.258111	0.129055	+	0.991637i	$0.458805\pi$
$948$	6877.78	0.235633
$949$	0	0
$950$	8199.09	0.280014
$951$	70178.4	2.39295
$952$	22972.5	0.782083
$953$	50289.9	1.70939	0.854696	−	0.519129i	$-0.173744\pi$
$953$	50289.9	1.70939	0.854696	+	0.519129i	$0.173744\pi$
$954$	15084.4	0.511922
$955$	12335.0	0.417959
$956$	8564.15	0.289733
$957$	16666.0	0.562941
$958$	−5822.82	−0.196374
$959$	288.048	0.00969924
$960$	40116.9	1.34872
$961$	−29460.1	−0.988891
$962$	0	0
$963$	−34400.4	−1.15113
$964$	14952.5	0.499572
$965$	−6082.58	−0.202907
$966$	−9935.89	−0.330934
$967$	41353.9	1.37524	0.687618	−	0.726073i	$-0.258657\pi$
$967$	41353.9	1.37524	0.687618	+	0.726073i	$0.258657\pi$
$968$	−2973.02	−0.0987153
$969$	99474.7	3.29782
$970$	22931.2	0.759048
$971$	22813.7	0.753992	0.376996	−	0.926215i	$-0.376957\pi$
$971$	22813.7	0.753992	0.376996	+	0.926215i	$0.376957\pi$
$972$	11622.1	0.383516
$973$	−2469.22	−0.0813561
$974$	−6168.66	−0.202933
$975$	0	0
$976$	−32060.5	−1.05147
$977$	40607.9	1.32975	0.664873	−	0.746956i	$-0.268486\pi$
$977$	40607.9	1.32975	0.664873	+	0.746956i	$0.268486\pi$
$978$	−52292.6	−1.70975
$979$	−7386.45	−0.241136
$980$	6005.60	0.195757
$981$	−21234.0	−0.691078
$982$	−29459.2	−0.957311
$983$	3870.30	0.125578	0.0627891	−	0.998027i	$-0.480000\pi$
$983$	3870.30	0.125578	0.0627891	+	0.998027i	$0.480000\pi$
$984$	81680.0	2.64620
$985$	26711.9	0.864074
$986$	57112.8	1.84467
$987$	19224.5	0.619982
$988$	0	0
$989$	−26753.8	−0.860184
$990$	−6539.66	−0.209944
$991$	16961.5	0.543692	0.271846	−	0.962341i	$-0.412366\pi$
$991$	16961.5	0.543692	0.271846	+	0.962341i	$0.412366\pi$
$992$	1768.64	0.0566074
$993$	−32919.9	−1.05204
$994$	2321.74	0.0740855
$995$	22749.5	0.724832
$996$	−15228.1	−0.484459
$997$	−19436.4	−0.617409	−0.308704	−	0.951158i	$-0.599895\pi$
$997$	−19436.4	−0.617409	−0.308704	+	0.951158i	$0.599895\pi$
$998$	−32224.6	−1.02210
$999$	3117.46	0.0987309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.j.1.14		18
13.5	odd	4		143.4.b.a.12.10	✓	36
13.8	odd	4		143.4.b.a.12.27	yes	36
13.12	even	2		1859.4.a.k.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.10	✓	36	13.5	odd	4
143.4.b.a.12.27	yes	36	13.8	odd	4
1859.4.a.j.1.14		18	1.1	even	1	trivial
1859.4.a.k.1.5		18	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.40428 q^{2} +7.21858 q^{3} -2.21943 q^{4} +9.84845 q^{5} +17.3555 q^{6} +8.26104 q^{7} -24.5704 q^{8} +25.1078 q^{9} +23.6784 q^{10} -11.0000 q^{11} -16.0212 q^{12} +19.8618 q^{14} +71.0918 q^{15} -41.3186 q^{16} -113.178 q^{17} +60.3663 q^{18} -121.759 q^{19} -21.8580 q^{20} +59.6329 q^{21} -26.4471 q^{22} -69.3004 q^{23} -177.363 q^{24} -28.0079 q^{25} -13.6587 q^{27} -18.3348 q^{28} -209.888 q^{29} +170.925 q^{30} +18.1919 q^{31} +97.2215 q^{32} -79.4043 q^{33} -272.112 q^{34} +81.3584 q^{35} -55.7252 q^{36} -228.240 q^{37} -292.742 q^{38} -241.980 q^{40} -460.524 q^{41} +143.374 q^{42} +386.056 q^{43} +24.4138 q^{44} +247.273 q^{45} -166.618 q^{46} +322.380 q^{47} -298.262 q^{48} -274.755 q^{49} -67.3390 q^{50} -816.984 q^{51} +249.880 q^{53} -32.8393 q^{54} -108.333 q^{55} -202.977 q^{56} -878.923 q^{57} -504.629 q^{58} -56.7513 q^{59} -157.784 q^{60} +775.933 q^{61} +43.7384 q^{62} +207.417 q^{63} +564.297 q^{64} -190.910 q^{66} -387.156 q^{67} +251.191 q^{68} -500.250 q^{69} +195.609 q^{70} +116.894 q^{71} -616.909 q^{72} +1016.35 q^{73} -548.754 q^{74} -202.177 q^{75} +270.235 q^{76} -90.8714 q^{77} -429.294 q^{79} -406.925 q^{80} -776.508 q^{81} -1107.23 q^{82} +950.500 q^{83} -132.351 q^{84} -1114.63 q^{85} +928.187 q^{86} -1515.09 q^{87} +270.274 q^{88} +671.495 q^{89} +594.515 q^{90} +153.808 q^{92} +131.320 q^{93} +775.093 q^{94} -1199.13 q^{95} +701.801 q^{96} +968.442 q^{97} -660.589 q^{98} -276.186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 76 q^{4} - 20 q^{5} - 49 q^{6} - 28 q^{7} + 12 q^{8} + 180 q^{9} + 56 q^{10} - 198 q^{11} + 54 q^{12} + 4 q^{14} - 60 q^{15} + 364 q^{16} - 138 q^{17} - 298 q^{18} - 24 q^{19} - 160 q^{20}+ \cdots - 1980 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 76 * q^4 - 20 * q^5 - 49 * q^6 - 28 * q^7 + 12 * q^8 + 180 * q^9 + 56 * q^10 - 198 * q^11 + 54 * q^12 + 4 * q^14 - 60 * q^15 + 364 * q^16 - 138 * q^17 - 298 * q^18 - 24 * q^19 - 160 * q^20 - 352 * q^21 + 22 * q^22 + 236 * q^23 - 124 * q^24 + 586 * q^25 - 6 * q^27 - 691 * q^28 - 286 * q^29 - 356 * q^30 - 642 * q^31 + 379 * q^32 - 2068 * q^34 + 34 * q^35 + 215 * q^36 - 530 * q^37 + 25 * q^38 - 108 * q^40 - 608 * q^41 + 563 * q^42 - 460 * q^43 - 836 * q^44 - 452 * q^45 + 580 * q^46 - 986 * q^47 + 837 * q^48 + 1082 * q^49 + 2578 * q^50 + 170 * q^51 + 1216 * q^53 - 1539 * q^54 + 220 * q^55 + 1137 * q^56 - 1282 * q^57 - 90 * q^58 - 1366 * q^59 - 5104 * q^60 - 922 * q^61 - 1398 * q^62 + 3236 * q^63 + 1296 * q^64 + 539 * q^66 - 1118 * q^67 - 2274 * q^68 + 1644 * q^69 - 416 * q^70 - 1118 * q^71 - 3295 * q^72 - 2444 * q^73 - 2018 * q^74 - 410 * q^75 + 1326 * q^76 + 308 * q^77 + 180 * q^79 - 5446 * q^80 + 426 * q^81 - 974 * q^82 + 696 * q^83 - 1061 * q^84 - 4580 * q^85 - 4652 * q^86 - 1240 * q^87 - 132 * q^88 + 3664 * q^89 + 248 * q^90 + 227 * q^92 - 3696 * q^93 - 244 * q^94 - 476 * q^95 + 5426 * q^96 - 2660 * q^97 - 6003 * q^98 - 1980 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more