LMFDB - Embedded newform 6.22.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,22,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	6.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:	$16.7686406572$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1024.00 q^{2} +59049.0 q^{3} +1.04858e6 q^{4} +2.64446e7 q^{5} -6.04662e7 q^{6} +1.66116e8 q^{7} -1.07374e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$

\(q-1024.00 q^{2} +59049.0 q^{3} +1.04858e6 q^{4} +2.64446e7 q^{5} -6.04662e7 q^{6} +1.66116e8 q^{7} -1.07374e9 q^{8} +3.48678e9 q^{9} -2.70792e10 q^{10} -1.04879e11 q^{11} +6.19174e10 q^{12} +3.35591e11 q^{13} -1.70103e11 q^{14} +1.56152e12 q^{15} +1.09951e12 q^{16} +1.45961e13 q^{17} -3.57047e12 q^{18} +3.56953e12 q^{19} +2.77291e13 q^{20} +9.80898e12 q^{21} +1.07396e14 q^{22} +2.22369e14 q^{23} -6.34034e13 q^{24} +2.22477e14 q^{25} -3.43646e14 q^{26} +2.05891e14 q^{27} +1.74185e14 q^{28} +2.19411e15 q^{29} -1.59900e15 q^{30} -8.72363e15 q^{31} -1.12590e15 q^{32} -6.19299e15 q^{33} -1.49465e16 q^{34} +4.39286e15 q^{35} +3.65616e15 q^{36} +3.74709e16 q^{37} -3.65520e15 q^{38} +1.98163e16 q^{39} -2.83946e16 q^{40} +8.66167e16 q^{41} -1.00444e16 q^{42} +1.31417e17 q^{43} -1.09973e17 q^{44} +9.22064e16 q^{45} -2.27706e17 q^{46} +3.39041e17 q^{47} +6.49251e16 q^{48} -5.30951e17 q^{49} -2.27817e17 q^{50} +8.61888e17 q^{51} +3.51893e17 q^{52} -1.57149e18 q^{53} -2.10833e17 q^{54} -2.77347e18 q^{55} -1.78366e17 q^{56} +2.10777e17 q^{57} -2.24677e18 q^{58} +5.23298e18 q^{59} +1.63738e18 q^{60} -4.78838e18 q^{61} +8.93299e18 q^{62} +5.79210e17 q^{63} +1.15292e18 q^{64} +8.87456e18 q^{65} +6.34162e18 q^{66} -1.54803e19 q^{67} +1.53052e19 q^{68} +1.31307e19 q^{69} -4.49829e18 q^{70} -1.29309e19 q^{71} -3.74391e18 q^{72} -4.42572e19 q^{73} -3.83702e19 q^{74} +1.31370e19 q^{75} +3.74292e18 q^{76} -1.74220e19 q^{77} -2.02919e19 q^{78} -1.48886e19 q^{79} +2.90761e19 q^{80} +1.21577e19 q^{81} -8.86955e19 q^{82} +3.70851e19 q^{83} +1.02855e19 q^{84} +3.85988e20 q^{85} -1.34571e20 q^{86} +1.29560e20 q^{87} +1.12613e20 q^{88} -1.05572e20 q^{89} -9.44194e19 q^{90} +5.57470e19 q^{91} +2.33171e20 q^{92} -5.15121e20 q^{93} -3.47178e20 q^{94} +9.43946e19 q^{95} -6.64833e19 q^{96} +1.38109e21 q^{97} +5.43694e20 q^{98} -3.65690e20 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−1024.00	−0.707107
$2$	−1024.00	−0.707107
$3$	59049.0	0.577350
$3$	59049.0	0.577350
$4$	1.04858e6	0.500000
$5$	2.64446e7	1.21102	0.605510	−	0.795838i	$-0.292969\pi$
$5$	2.64446e7	1.21102	0.605510	+	0.795838i	$0.292969\pi$
$6$	−6.04662e7	−0.408248
$7$	1.66116e8	0.222270	0.111135	−	0.993805i	$-0.464551\pi$
$7$	1.66116e8	0.222270	0.111135	+	0.993805i	$0.464551\pi$
$8$	−1.07374e9	−0.353553
$9$	3.48678e9	0.333333
$10$	−2.70792e10	−0.856320
$11$	−1.04879e11	−1.21917	−0.609585	−	0.792721i	$-0.708664\pi$
$11$	−1.04879e11	−1.21917	−0.609585	+	0.792721i	$0.708664\pi$
$12$	6.19174e10	0.288675
$13$	3.35591e11	0.675158	0.337579	−	0.941297i	$-0.390392\pi$
$13$	3.35591e11	0.675158	0.337579	+	0.941297i	$0.390392\pi$
$14$	−1.70103e11	−0.157169
$15$	1.56152e12	0.699182
$16$	1.09951e12	0.250000
$17$	1.45961e13	1.75600	0.878000	−	0.478661i	$-0.158878\pi$
$17$	1.45961e13	1.75600	0.878000	+	0.478661i	$0.158878\pi$
$18$	−3.57047e12	−0.235702
$19$	3.56953e12	0.133567	0.0667834	−	0.997767i	$-0.478726\pi$
$19$	3.56953e12	0.133567	0.0667834	+	0.997767i	$0.478726\pi$
$20$	2.77291e13	0.605510
$21$	9.80898e12	0.128328
$22$	1.07396e14	0.862084
$23$	2.22369e14	1.11926	0.559632	−	0.828741i	$-0.310943\pi$
$23$	2.22369e14	1.11926	0.559632	+	0.828741i	$0.310943\pi$
$24$	−6.34034e13	−0.204124
$25$	2.22477e14	0.466568
$26$	−3.43646e14	−0.477409
$27$	2.05891e14	0.192450
$28$	1.74185e14	0.111135
$29$	2.19411e15	0.968455	0.484227	−	0.874942i	$-0.339101\pi$
$29$	2.19411e15	0.968455	0.484227	+	0.874942i	$0.339101\pi$
$30$	−1.59900e15	−0.494397
$31$	−8.72363e15	−1.91161	−0.955805	−	0.294001i	$-0.905013\pi$
$31$	−8.72363e15	−1.91161	−0.955805	+	0.294001i	$0.905013\pi$
$32$	−1.12590e15	−0.176777
$33$	−6.19299e15	−0.703888
$34$	−1.49465e16	−1.24168
$35$	4.39286e15	0.269174
$36$	3.65616e15	0.166667
$37$	3.74709e16	1.28108	0.640540	−	0.767925i	$-0.278711\pi$
$37$	3.74709e16	1.28108	0.640540	+	0.767925i	$0.278711\pi$
$38$	−3.65520e15	−0.0944459
$39$	1.98163e16	0.389803
$40$	−2.83946e16	−0.428160
$41$	8.66167e16	1.00779	0.503897	−	0.863764i	$-0.331899\pi$
$41$	8.66167e16	1.00779	0.503897	+	0.863764i	$0.331899\pi$
$42$	−1.00444e16	−0.0907415
$43$	1.31417e17	0.927326	0.463663	−	0.886012i	$-0.346535\pi$
$43$	1.31417e17	0.927326	0.463663	+	0.886012i	$0.346535\pi$
$44$	−1.09973e17	−0.609585
$45$	9.22064e16	0.403673
$46$	−2.27706e17	−0.791439
$47$	3.39041e17	0.940210	0.470105	−	0.882610i	$-0.344216\pi$
$47$	3.39041e17	0.940210	0.470105	+	0.882610i	$0.344216\pi$
$48$	6.49251e16	0.144338
$49$	−5.30951e17	−0.950596
$50$	−2.27817e17	−0.329914
$51$	8.61888e17	1.01383
$52$	3.51893e17	0.337579
$53$	−1.57149e18	−1.23429	−0.617144	−	0.786850i	$-0.711710\pi$
$53$	−1.57149e18	−1.23429	−0.617144	+	0.786850i	$0.711710\pi$
$54$	−2.10833e17	−0.136083
$55$	−2.77347e18	−1.47644
$56$	−1.78366e17	−0.0785845
$57$	2.10777e17	0.0771148
$58$	−2.24677e18	−0.684801
$59$	5.23298e18	1.33292	0.666459	−	0.745542i	$-0.267809\pi$
$59$	5.23298e18	1.33292	0.666459	+	0.745542i	$0.267809\pi$
$60$	1.63738e18	0.349591
$61$	−4.78838e18	−0.859460	−0.429730	−	0.902957i	$-0.641391\pi$
$61$	−4.78838e18	−0.859460	−0.429730	+	0.902957i	$0.641391\pi$
$62$	8.93299e18	1.35171
$63$	5.79210e17	0.0740901
$64$	1.15292e18	0.125000
$65$	8.87456e18	0.817630
$66$	6.34162e18	0.497724
$67$	−1.54803e19	−1.03752	−0.518758	−	0.854921i	$-0.673605\pi$
$67$	−1.54803e19	−1.03752	−0.518758	+	0.854921i	$0.673605\pi$
$68$	1.53052e19	0.878000
$69$	1.31307e19	0.646207
$70$	−4.49829e18	−0.190335
$71$	−1.29309e19	−0.471429	−0.235715	−	0.971822i	$-0.575743\pi$
$71$	−1.29309e19	−0.471429	−0.235715	+	0.971822i	$0.575743\pi$
$72$	−3.74391e18	−0.117851
$73$	−4.42572e19	−1.20530	−0.602648	−	0.798007i	$-0.705888\pi$
$73$	−4.42572e19	−1.20530	−0.602648	+	0.798007i	$0.705888\pi$
$74$	−3.83702e19	−0.905860
$75$	1.31370e19	0.269373
$76$	3.74292e18	0.0667834
$77$	−1.74220e19	−0.270985
$78$	−2.02919e19	−0.275632
$79$	−1.48886e19	−0.176917	−0.0884583	−	0.996080i	$-0.528194\pi$
$79$	−1.48886e19	−0.176917	−0.0884583	+	0.996080i	$0.528194\pi$
$80$	2.90761e19	0.302755
$81$	1.21577e19	0.111111
$82$	−8.86955e19	−0.712617
$83$	3.70851e19	0.262349	0.131174	−	0.991359i	$-0.458125\pi$
$83$	3.70851e19	0.262349	0.131174	+	0.991359i	$0.458125\pi$
$84$	1.02855e19	0.0641639
$85$	3.85988e20	2.12655
$86$	−1.34571e20	−0.655719
$87$	1.29560e20	0.559138
$88$	1.12613e20	0.431042
$89$	−1.05572e20	−0.358884	−0.179442	−	0.983769i	$-0.557429\pi$
$89$	−1.05572e20	−0.358884	−0.179442	+	0.983769i	$0.557429\pi$
$90$	−9.44194e19	−0.285440
$91$	5.57470e19	0.150068
$92$	2.33171e20	0.559632
$93$	−5.15121e20	−1.10367
$94$	−3.47178e20	−0.664829
$95$	9.43946e19	0.161752
$96$	−6.64833e19	−0.102062
$97$	1.38109e21	1.90160	0.950801	−	0.309803i	$-0.100263\pi$
$97$	1.38109e21	1.90160	0.950801	+	0.309803i	$0.100263\pi$
$98$	5.43694e20	0.672173
$99$	−3.65690e20	−0.406390
$100$	2.33284e20	0.233284
$101$	−1.49419e21	−1.34596	−0.672979	−	0.739662i	$-0.734986\pi$
$101$	−1.49419e21	−1.34596	−0.672979	+	0.739662i	$0.734986\pi$
$102$	−8.82573e20	−0.716884
$103$	−1.72821e21	−1.26708	−0.633542	−	0.773708i	$-0.718400\pi$
$103$	−1.72821e21	−1.26708	−0.633542	+	0.773708i	$0.718400\pi$
$104$	−3.60338e20	−0.238704
$105$	2.59394e20	0.155408
$106$	1.60921e21	0.872773
$107$	−3.21208e21	−1.57854	−0.789272	−	0.614044i	$-0.789542\pi$
$107$	−3.21208e21	−1.57854	−0.789272	+	0.614044i	$0.789542\pi$
$108$	2.15892e20	0.0962250
$109$	−5.26985e20	−0.213216	−0.106608	−	0.994301i	$-0.533999\pi$
$109$	−5.26985e20	−0.213216	−0.106608	+	0.994301i	$0.533999\pi$
$110$	2.84003e21	1.04400
$111$	2.21262e21	0.739631
$112$	1.82646e20	0.0555676
$113$	2.65376e20	0.0735425	0.0367713	−	0.999324i	$-0.488293\pi$
$113$	2.65376e20	0.0735425	0.0367713	+	0.999324i	$0.488293\pi$
$114$	−2.15836e20	−0.0545284
$115$	5.88045e21	1.35545
$116$	2.30069e21	0.484227
$117$	1.17013e21	0.225053
$118$	−5.35858e21	−0.942515
$119$	2.42465e21	0.390307
$120$	−1.67667e21	−0.247198
$121$	3.59930e21	0.486376
$122$	4.90331e21	0.607730
$123$	5.11463e21	0.581850
$124$	−9.14739e21	−0.955805
$125$	−6.72644e21	−0.645996
$126$	−5.93111e20	−0.0523896
$127$	−1.95043e22	−1.58559	−0.792797	−	0.609485i	$-0.791376\pi$
$127$	−1.95043e22	−1.58559	−0.792797	+	0.609485i	$0.791376\pi$
$128$	−1.18059e21	−0.0883883
$129$	7.76004e21	0.535392
$130$	−9.08755e21	−0.578152
$131$	−9.92728e21	−0.582749	−0.291375	−	0.956609i	$-0.594113\pi$
$131$	−9.92728e21	−0.582749	−0.291375	+	0.956609i	$0.594113\pi$
$132$	−6.49382e21	−0.351944
$133$	5.92956e20	0.0296879
$134$	1.58519e22	0.733635
$135$	5.44470e21	0.233061
$136$	−1.56725e22	−0.620840
$137$	4.13768e22	1.51772	0.758858	−	0.651256i	$-0.225758\pi$
$137$	4.13768e22	1.51772	0.758858	+	0.651256i	$0.225758\pi$
$138$	−1.34458e22	−0.456938
$139$	−1.86724e22	−0.588228	−0.294114	−	0.955770i	$-0.595025\pi$
$139$	−1.86724e22	−0.588228	−0.294114	+	0.955770i	$0.595025\pi$
$140$	4.60625e21	0.134587
$141$	2.00200e22	0.542831
$142$	1.32412e22	0.333351
$143$	−3.51964e22	−0.823133
$144$	3.83376e21	0.0833333
$145$	5.80222e22	1.17282
$146$	4.53194e22	0.852273
$147$	−3.13521e22	−0.548827
$148$	3.92911e22	0.640540
$149$	−4.48377e22	−0.681064	−0.340532	−	0.940233i	$-0.610607\pi$
$149$	−4.48377e22	−0.681064	−0.340532	+	0.940233i	$0.610607\pi$
$150$	−1.34523e22	−0.190476
$151$	5.27798e22	0.696963	0.348482	−	0.937316i	$-0.386697\pi$
$151$	5.27798e22	0.696963	0.348482	+	0.937316i	$0.386697\pi$
$152$	−3.83275e21	−0.0472230
$153$	5.08936e22	0.585333
$154$	1.78402e22	0.191616
$155$	−2.30692e23	−2.31500
$156$	2.07789e22	0.194901
$157$	4.76649e22	0.418074	0.209037	−	0.977908i	$-0.432967\pi$
$157$	4.76649e22	0.418074	0.209037	+	0.977908i	$0.432967\pi$
$158$	1.52459e22	0.125099
$159$	−9.27952e22	−0.712616
$160$	−2.97739e22	−0.214080
$161$	3.69391e22	0.248779
$162$	−1.24494e22	−0.0785674
$163$	4.68583e22	0.277215	0.138607	−	0.990347i	$-0.455737\pi$
$163$	4.68583e22	0.277215	0.138607	+	0.990347i	$0.455737\pi$
$164$	9.08242e22	0.503897
$165$	−1.63771e23	−0.852422
$166$	−3.79751e22	−0.185509
$167$	4.21072e22	0.193123	0.0965613	−	0.995327i	$-0.469216\pi$
$167$	4.21072e22	0.193123	0.0965613	+	0.995327i	$0.469216\pi$
$168$	−1.05323e22	−0.0453708
$169$	−1.34443e23	−0.544161
$170$	−3.95252e23	−1.50370
$171$	1.24462e22	0.0445222
$172$	1.37801e23	0.463663
$173$	4.51089e23	1.42816	0.714082	−	0.700062i	$-0.246844\pi$
$173$	4.51089e23	1.42816	0.714082	+	0.700062i	$0.246844\pi$
$174$	−1.32669e23	−0.395370
$175$	3.69570e22	0.103704
$176$	−1.15315e23	−0.304793
$177$	3.09003e23	0.769560
$178$	1.08106e23	0.253769
$179$	2.06595e23	0.457259	0.228629	−	0.973514i	$-0.426576\pi$
$179$	2.06595e23	0.457259	0.228629	+	0.973514i	$0.426576\pi$
$180$	9.66855e22	0.201837
$181$	7.17280e23	1.41274	0.706372	−	0.707841i	$-0.250331\pi$
$181$	7.17280e23	1.41274	0.706372	+	0.707841i	$0.250331\pi$
$182$	−5.70850e22	−0.106114
$183$	−2.82749e23	−0.496210
$184$	−2.38767e23	−0.395719
$185$	9.90901e23	1.55141
$186$	5.27484e23	0.780412
$187$	−1.53083e24	−2.14086
$188$	3.55510e23	0.470105
$189$	3.42018e22	0.0427760
$190$	−9.66601e22	−0.114376
$191$	−4.48187e23	−0.501890	−0.250945	−	0.968001i	$-0.580741\pi$
$191$	−4.48187e23	−0.501890	−0.250945	+	0.968001i	$0.580741\pi$
$192$	6.80789e22	0.0721688
$193$	−7.88064e23	−0.791061	−0.395530	−	0.918453i	$-0.629439\pi$
$193$	−7.88064e23	−0.791061	−0.395530	+	0.918453i	$0.629439\pi$
$194$	−1.41424e24	−1.34464
$195$	5.24034e23	0.472059
$196$	−5.56743e23	−0.475298
$197$	−5.38083e23	−0.435466	−0.217733	−	0.976008i	$-0.569866\pi$
$197$	−5.38083e23	−0.435466	−0.217733	+	0.976008i	$0.569866\pi$
$198$	3.74466e23	0.287361
$199$	−1.82843e24	−1.33083	−0.665414	−	0.746475i	$-0.731745\pi$
$199$	−1.82843e24	−1.33083	−0.665414	+	0.746475i	$0.731745\pi$
$200$	−2.38883e23	−0.164957
$201$	−9.14098e23	−0.599010
$202$	1.53005e24	0.951736
$203$	3.64476e23	0.215259
$204$	9.03755e23	0.506914
$205$	2.29054e24	1.22046
$206$	1.76969e24	0.895964
$207$	7.75354e23	0.373088
$208$	3.68987e23	0.168790
$209$	−3.74368e23	−0.162841
$210$	−2.65619e23	−0.109890
$211$	−2.17230e24	−0.854974	−0.427487	−	0.904021i	$-0.640601\pi$
$211$	−2.17230e24	−0.854974	−0.427487	+	0.904021i	$0.640601\pi$
$212$	−1.64783e24	−0.617144
$213$	−7.63557e23	−0.272180
$214$	3.28917e24	1.11620
$215$	3.47526e24	1.12301
$216$	−2.21074e23	−0.0680414
$217$	−1.44913e24	−0.424894
$218$	5.39632e23	0.150766
$219$	−2.61334e24	−0.695878
$220$	−2.90820e24	−0.738219
$221$	4.89834e24	1.18558
$222$	−2.26572e24	−0.522998
$223$	8.40788e24	1.85134	0.925668	−	0.378336i	$-0.123504\pi$
$223$	8.40788e24	1.85134	0.925668	+	0.378336i	$0.123504\pi$
$224$	−1.87030e23	−0.0392922
$225$	7.75730e23	0.155523
$226$	−2.71745e23	−0.0520024
$227$	−6.09701e24	−1.11390	−0.556949	−	0.830547i	$-0.688028\pi$
$227$	−6.09701e24	−1.11390	−0.556949	+	0.830547i	$0.688028\pi$
$228$	2.21016e23	0.0385574
$229$	−6.53459e23	−0.108879	−0.0544397	−	0.998517i	$-0.517337\pi$
$229$	−6.53459e23	−0.108879	−0.0544397	+	0.998517i	$0.517337\pi$
$230$	−6.02159e24	−0.958448
$231$	−1.02875e24	−0.156454
$232$	−2.35591e24	−0.342400
$233$	−1.09090e25	−1.51547	−0.757735	−	0.652562i	$-0.773694\pi$
$233$	−1.09090e25	−1.51547	−0.757735	+	0.652562i	$0.773694\pi$
$234$	−1.19822e24	−0.159136
$235$	8.96579e24	1.13861
$236$	5.48718e24	0.666459
$237$	−8.79156e23	−0.102143
$238$	−2.48284e24	−0.275989
$239$	5.96515e21	0.000634517 0	0.000317258	−	1.00000i	$-0.499899\pi$
$239$	5.96515e21	0.000634517 0	0.000317258		1.00000i	$0.499899\pi$
$240$	1.71691e24	0.174796
$241$	8.17929e24	0.797144	0.398572	−	0.917137i	$-0.369506\pi$
$241$	8.17929e24	0.797144	0.398572	+	0.917137i	$0.369506\pi$
$242$	−3.68569e24	−0.343920
$243$	7.17898e23	0.0641500
$244$	−5.02099e24	−0.429730
$245$	−1.40408e25	−1.15119
$246$	−5.23738e24	−0.411430
$247$	1.19790e24	0.0901787
$248$	9.36692e24	0.675856
$249$	2.18984e24	0.151467
$250$	6.88787e24	0.456788
$251$	1.37352e25	0.873499	0.436749	−	0.899583i	$-0.356130\pi$
$251$	1.37352e25	0.873499	0.436749	+	0.899583i	$0.356130\pi$
$252$	6.07346e23	0.0370451
$253$	−2.33218e25	−1.36457
$254$	1.99724e25	1.12118
$255$	2.27922e25	1.22776
$256$	1.20893e24	0.0625000
$257$	4.53006e24	0.224805	0.112403	−	0.993663i	$-0.464145\pi$
$257$	4.53006e24	0.224805	0.112403	+	0.993663i	$0.464145\pi$
$258$	−7.94628e24	−0.378579
$259$	6.22451e24	0.284746
$260$	9.30565e24	0.408815
$261$	7.65039e24	0.322818
$262$	1.01655e25	0.412066
$263$	−5.23061e24	−0.203712	−0.101856	−	0.994799i	$-0.532478\pi$
$263$	−5.23061e24	−0.203712	−0.101856	+	0.994799i	$0.532478\pi$
$264$	6.64967e24	0.248862
$265$	−4.15575e25	−1.49475
$266$	−6.07186e23	−0.0209925
$267$	−6.23392e24	−0.207202
$268$	−1.62323e25	−0.518758
$269$	−1.15814e25	−0.355927	−0.177964	−	0.984037i	$-0.556951\pi$
$269$	−1.15814e25	−0.355927	−0.177964	+	0.984037i	$0.556951\pi$
$270$	−5.57537e24	−0.164799
$271$	1.66790e25	0.474234	0.237117	−	0.971481i	$-0.423798\pi$
$271$	1.66790e25	0.474234	0.237117	+	0.971481i	$0.423798\pi$
$272$	1.60486e25	0.439000
$273$	3.29181e24	0.0866416
$274$	−4.23698e25	−1.07319
$275$	−2.33331e25	−0.568826
$276$	1.37685e25	0.323104
$277$	−4.99177e25	−1.12776	−0.563880	−	0.825857i	$-0.690692\pi$
$277$	−4.99177e25	−1.12776	−0.563880	+	0.825857i	$0.690692\pi$
$278$	1.91206e25	0.415940
$279$	−3.04174e25	−0.637203
$280$	−4.71680e24	−0.0951673
$281$	2.39858e25	0.466162	0.233081	−	0.972457i	$-0.425119\pi$
$281$	2.39858e25	0.466162	0.233081	+	0.972457i	$0.425119\pi$
$282$	−2.05005e25	−0.383839
$283$	−2.68871e25	−0.485050	−0.242525	−	0.970145i	$-0.577976\pi$
$283$	−2.68871e25	−0.485050	−0.242525	+	0.970145i	$0.577976\pi$
$284$	−1.35590e25	−0.235715
$285$	5.57391e24	0.0933875
$286$	3.60411e25	0.582043
$287$	1.43884e25	0.224003
$288$	−3.92577e24	−0.0589256
$289$	1.43956e26	2.08354
$290$	−5.94148e25	−0.829307
$291$	8.15521e25	1.09789
$292$	−4.64070e25	−0.602648
$293$	1.29122e25	0.161767	0.0808835	−	0.996724i	$-0.474226\pi$
$293$	1.29122e25	0.161767	0.0808835	+	0.996724i	$0.474226\pi$
$294$	3.21046e25	0.388079
$295$	1.38384e26	1.61419
$296$	−4.02341e25	−0.452930
$297$	−2.15936e25	−0.234629
$298$	4.59138e25	0.481585
$299$	7.46252e25	0.755680
$300$	1.37752e25	0.134687
$301$	2.18304e25	0.206117
$302$	−5.40465e25	−0.492827
$303$	−8.82304e25	−0.777089
$304$	3.92474e24	0.0333917
$305$	−1.26627e26	−1.04082
$306$	−5.21151e25	−0.413893
$307$	−1.45907e26	−1.11976	−0.559878	−	0.828575i	$-0.689152\pi$
$307$	−1.45907e26	−1.11976	−0.559878	+	0.828575i	$0.689152\pi$
$308$	−1.82683e25	−0.135493
$309$	−1.02049e26	−0.731552
$310$	2.36229e26	1.63695
$311$	−1.00016e25	−0.0670015	−0.0335008	−	0.999439i	$-0.510666\pi$
$311$	−1.00016e25	−0.0670015	−0.0335008	+	0.999439i	$0.510666\pi$
$312$	−2.12776e25	−0.137816
$313$	2.08348e25	0.130489	0.0652445	−	0.997869i	$-0.479217\pi$
$313$	2.08348e25	0.130489	0.0652445	+	0.997869i	$0.479217\pi$
$314$	−4.88089e25	−0.295623
$315$	1.53170e25	0.0897246
$316$	−1.56118e25	−0.0884583
$317$	1.30949e26	0.717762	0.358881	−	0.933383i	$-0.383158\pi$
$317$	1.30949e26	0.717762	0.358881	+	0.933383i	$0.383158\pi$
$318$	9.50223e25	0.503896
$319$	−2.30116e26	−1.18071
$320$	3.04885e25	0.151377
$321$	−1.89670e26	−0.911373
$322$	−3.78256e25	−0.175913
$323$	5.21014e25	0.234543
$324$	1.27482e25	0.0555556
$325$	7.46614e25	0.315007
$326$	−4.79829e25	−0.196021
$327$	−3.11179e25	−0.123100
$328$	−9.30040e25	−0.356309
$329$	5.63201e25	0.208981
$330$	1.67701e26	0.602754
$331$	5.53748e24	0.0192805	0.00964026	−	0.999954i	$-0.496931\pi$
$331$	5.53748e24	0.0192805	0.00964026	+	0.999954i	$0.496931\pi$
$332$	3.88865e25	0.131174
$333$	1.30653e26	0.427026
$334$	−4.31177e25	−0.136558
$335$	−4.09370e26	−1.25645
$336$	1.07851e25	0.0320820
$337$	−2.35227e26	−0.678223	−0.339112	−	0.940746i	$-0.610126\pi$
$337$	−2.35227e26	−0.678223	−0.339112	+	0.940746i	$0.610126\pi$
$338$	1.37670e26	0.384780
$339$	1.56702e25	0.0424598
$340$	4.04738e26	1.06328
$341$	9.14923e26	2.33058
$342$	−1.27449e25	−0.0314820
$343$	−1.80983e26	−0.433560
$344$	−1.41108e26	−0.327859
$345$	3.47235e26	0.782570
$346$	−4.61915e26	−1.00986
$347$	−1.60491e26	−0.340401	−0.170200	−	0.985409i	$-0.554441\pi$
$347$	−1.60491e26	−0.340401	−0.170200	+	0.985409i	$0.554441\pi$
$348$	1.35853e26	0.279569
$349$	3.71912e26	0.742631	0.371315	−	0.928507i	$-0.378907\pi$
$349$	3.71912e26	0.742631	0.371315	+	0.928507i	$0.378907\pi$
$350$	−3.78439e25	−0.0733300
$351$	6.90953e25	0.129934
$352$	1.18083e26	0.215521
$353$	7.03252e26	1.24588	0.622941	−	0.782269i	$-0.285938\pi$
$353$	7.03252e26	1.24588	0.622941	+	0.782269i	$0.285938\pi$
$354$	−3.16419e26	−0.544161
$355$	−3.41952e26	−0.570910
$356$	−1.10700e26	−0.179442
$357$	1.43173e26	0.225344
$358$	−2.11553e26	−0.323331
$359$	−5.01731e26	−0.744696	−0.372348	−	0.928093i	$-0.621447\pi$
$359$	−5.01731e26	−0.744696	−0.372348	+	0.928093i	$0.621447\pi$
$360$	−9.90059e25	−0.142720
$361$	−7.01468e26	−0.982160
$362$	−7.34494e26	−0.998961
$363$	2.12535e26	0.280809
$364$	5.84550e25	0.0750338
$365$	−1.17036e27	−1.45964
$366$	2.89535e26	0.350873
$367$	5.69112e26	0.670200	0.335100	−	0.942183i	$-0.391230\pi$
$367$	5.69112e26	0.670200	0.335100	+	0.942183i	$0.391230\pi$
$368$	2.44498e26	0.279816
$369$	3.02014e26	0.335931
$370$	−1.01468e27	−1.09701
$371$	−2.61050e26	−0.274346
$372$	−5.40144e26	−0.551834
$373$	2.59366e26	0.257615	0.128807	−	0.991670i	$-0.458885\pi$
$373$	2.59366e26	0.257615	0.128807	+	0.991670i	$0.458885\pi$
$374$	1.56757e27	1.51382
$375$	−3.97189e26	−0.372966
$376$	−3.64043e26	−0.332414
$377$	7.36324e26	0.653860
$378$	−3.50226e25	−0.0302472
$379$	1.10384e27	0.927241	0.463621	−	0.886034i	$-0.346550\pi$
$379$	1.10384e27	0.927241	0.463621	+	0.886034i	$0.346550\pi$
$380$	9.89799e25	0.0808759
$381$	−1.15171e27	−0.915444
$382$	4.58943e26	0.354890
$383$	−6.37501e26	−0.479616	−0.239808	−	0.970820i	$-0.577084\pi$
$383$	−6.37501e26	−0.479616	−0.239808	+	0.970820i	$0.577084\pi$
$384$	−6.97128e25	−0.0510310
$385$	−4.60718e26	−0.328169
$386$	8.06978e26	0.559364
$387$	4.58222e26	0.309109
$388$	1.44818e27	0.950801
$389$	3.61461e25	0.0230989	0.0115494	−	0.999933i	$-0.496324\pi$
$389$	3.61461e25	0.0230989	0.0115494	+	0.999933i	$0.496324\pi$
$390$	−5.36611e26	−0.333796
$391$	3.24573e27	1.96543
$392$	5.70105e26	0.336086
$393$	−5.86196e26	−0.336450
$394$	5.50997e26	0.307921
$395$	−3.93722e26	−0.214250
$396$	−3.83453e26	−0.203195
$397$	6.60817e26	0.341021	0.170511	−	0.985356i	$-0.445458\pi$
$397$	6.60817e26	0.341021	0.170511	+	0.985356i	$0.445458\pi$
$398$	1.87232e27	0.941037
$399$	3.50134e25	0.0171403
$400$	2.44616e26	0.116642
$401$	−3.16192e27	−1.46871	−0.734354	−	0.678767i	$-0.762515\pi$
$401$	−3.16192e27	−1.46871	−0.734354	+	0.678767i	$0.762515\pi$
$402$	9.36036e26	0.423564
$403$	−2.92757e27	−1.29064
$404$	−1.56677e27	−0.672979
$405$	3.21504e26	0.134558
$406$	−3.73224e26	−0.152211
$407$	−3.92990e27	−1.56185
$408$	−9.25445e26	−0.358442
$409$	1.26849e27	0.478843	0.239422	−	0.970916i	$-0.423042\pi$
$409$	1.26849e27	0.478843	0.239422	+	0.970916i	$0.423042\pi$
$410$	−2.34551e27	−0.862993
$411$	2.44326e27	0.876254
$412$	−1.81216e27	−0.633542
$413$	8.69282e26	0.296268
$414$	−7.93962e26	−0.263813
$415$	9.80698e26	0.317710
$416$	−3.77842e26	−0.119352
$417$	−1.10259e27	−0.339614
$418$	3.83353e26	0.115146
$419$	4.00666e27	1.17364	0.586821	−	0.809717i	$-0.300379\pi$
$419$	4.00666e27	1.17364	0.586821	+	0.809717i	$0.300379\pi$
$420$	2.71994e26	0.0777038
$421$	−5.33195e27	−1.48568	−0.742838	−	0.669471i	$-0.766521\pi$
$421$	−5.33195e27	−1.48568	−0.742838	+	0.669471i	$0.766521\pi$
$422$	2.22443e27	0.604558
$423$	1.18216e27	0.313403
$424$	1.68738e27	0.436387
$425$	3.24731e27	0.819294
$426$	7.81882e26	0.192460
$427$	−7.95427e26	−0.191033
$428$	−3.36811e27	−0.789272
$429$	−2.07831e27	−0.475236
$430$	−3.55867e27	−0.794088
$431$	2.82207e27	0.614548	0.307274	−	0.951621i	$-0.400583\pi$
$431$	2.82207e27	0.614548	0.307274	+	0.951621i	$0.400583\pi$
$432$	2.26380e26	0.0481125
$433$	−1.58069e26	−0.0327886	−0.0163943	−	0.999866i	$-0.505219\pi$
$433$	−1.58069e26	−0.0327886	−0.0163943	+	0.999866i	$0.505219\pi$
$434$	1.48391e27	0.300446
$435$	3.42616e27	0.677127
$436$	−5.52584e26	−0.106608
$437$	7.93754e26	0.149496
$438$	2.67606e27	0.492060
$439$	8.74620e27	1.57015	0.785077	−	0.619398i	$-0.212623\pi$
$439$	8.74620e27	1.57015	0.785077	+	0.619398i	$0.212623\pi$
$440$	2.97799e27	0.522000
$441$	−1.85131e27	−0.316865
$442$	−5.01590e27	−0.838330
$443$	1.81520e27	0.296269	0.148135	−	0.988967i	$-0.452673\pi$
$443$	1.81520e27	0.296269	0.148135	+	0.988967i	$0.452673\pi$
$444$	2.32010e27	0.369816
$445$	−2.79180e27	−0.434615
$446$	−8.60967e27	−1.30909
$447$	−2.64762e27	−0.393212
$448$	1.91519e26	0.0277838
$449$	1.06970e28	1.51592	0.757958	−	0.652304i	$-0.226197\pi$
$449$	1.06970e28	1.51592	0.757958	+	0.652304i	$0.226197\pi$
$450$	−7.94347e26	−0.109971
$451$	−9.08426e27	−1.22867
$452$	2.78267e26	0.0367713
$453$	3.11659e27	0.402392
$454$	6.24334e27	0.787644
$455$	1.47421e27	0.181735
$456$	−2.26320e26	−0.0272642
$457$	−1.59372e28	−1.87626	−0.938129	−	0.346285i	$-0.887443\pi$
$457$	−1.59372e28	−1.87626	−0.938129	+	0.346285i	$0.887443\pi$
$458$	6.69142e26	0.0769894
$459$	3.00522e27	0.337942
$460$	6.16610e27	0.677725
$461$	5.33663e27	0.573334	0.286667	−	0.958030i	$-0.407453\pi$
$461$	5.33663e27	0.573334	0.286667	+	0.958030i	$0.407453\pi$
$462$	1.05344e27	0.110629
$463$	3.38648e27	0.347655	0.173828	−	0.984776i	$-0.444386\pi$
$463$	3.38648e27	0.347655	0.173828	+	0.984776i	$0.444386\pi$
$464$	2.41245e27	0.242114
$465$	−1.36222e28	−1.33656
$466$	1.11708e28	1.07160
$467$	−1.57577e28	−1.47797	−0.738986	−	0.673721i	$-0.764695\pi$
$467$	−1.57577e28	−1.47797	−0.738986	+	0.673721i	$0.764695\pi$
$468$	1.22698e27	0.112526
$469$	−2.57153e27	−0.230609
$470$	−9.18097e27	−0.805121
$471$	2.81457e27	0.241375
$472$	−5.61887e27	−0.471258
$473$	−1.37828e28	−1.13057
$474$	9.00255e26	0.0722259
$475$	7.94139e26	0.0623180
$476$	2.54243e27	0.195153
$477$	−5.47946e27	−0.411429
$478$	−6.10831e24	−0.000448671 0
$479$	−2.12973e28	−1.53039	−0.765193	−	0.643801i	$-0.777356\pi$
$479$	−2.12973e28	−1.53039	−0.765193	+	0.643801i	$0.777356\pi$
$480$	−1.75812e27	−0.123599
$481$	1.25749e28	0.864931
$482$	−8.37559e27	−0.563666
$483$	2.18121e27	0.143633
$484$	3.77414e27	0.243188
$485$	3.65224e28	2.30288
$486$	−7.35128e26	−0.0453609
$487$	1.68508e28	1.01757	0.508786	−	0.860893i	$-0.330094\pi$
$487$	1.68508e28	1.01757	0.508786	+	0.860893i	$0.330094\pi$
$488$	5.14149e27	0.303865
$489$	2.76694e27	0.160050
$490$	1.43777e28	0.814014
$491$	−1.57697e28	−0.873910	−0.436955	−	0.899483i	$-0.643943\pi$
$491$	−1.57697e28	−0.873910	−0.436955	+	0.899483i	$0.643943\pi$
$492$	5.36308e27	0.290925
$493$	3.20255e28	1.70061
$494$	−1.22665e27	−0.0637659
$495$	−9.67050e27	−0.492146
$496$	−9.59173e27	−0.477903
$497$	−2.14803e27	−0.104785
$498$	−2.24239e27	−0.107103
$499$	2.57185e28	1.20279	0.601395	−	0.798952i	$-0.294612\pi$
$499$	2.57185e28	1.20279	0.601395	+	0.798952i	$0.294612\pi$
$500$	−7.05318e27	−0.322998
$501$	2.48639e27	0.111499
$502$	−1.40649e28	−0.617657
$503$	2.83510e28	1.21928	0.609642	−	0.792677i	$-0.291313\pi$
$503$	2.83510e28	1.21928	0.609642	+	0.792677i	$0.291313\pi$
$504$	−6.21922e26	−0.0261948
$505$	−3.95132e28	−1.62998
$506$	2.38815e28	0.964899
$507$	−7.93872e27	−0.314172
$508$	−2.04518e28	−0.792797
$509$	2.41622e28	0.917485	0.458743	−	0.888569i	$-0.348300\pi$
$509$	2.41622e28	0.917485	0.458743	+	0.888569i	$0.348300\pi$
$510$	−2.33392e28	−0.868160
$511$	−7.35182e27	−0.267902
$512$	−1.23794e27	−0.0441942
$513$	7.34935e26	0.0257049
$514$	−4.63879e27	−0.158961
$515$	−4.57017e28	−1.53446
$516$	8.13699e27	0.267696
$517$	−3.55582e28	−1.14628
$518$	−6.37390e27	−0.201346
$519$	2.66363e28	0.824551
$520$	−9.52899e27	−0.289076
$521$	4.35634e28	1.29517	0.647584	−	0.761994i	$-0.275780\pi$
$521$	4.35634e28	1.29517	0.647584	+	0.761994i	$0.275780\pi$
$522$	−7.83400e27	−0.228267
$523$	1.92361e28	0.549351	0.274676	−	0.961537i	$-0.411430\pi$
$523$	1.92361e28	0.549351	0.274676	+	0.961537i	$0.411430\pi$
$524$	−1.04095e28	−0.291375
$525$	2.18227e27	0.0598737
$526$	5.35615e27	0.144046
$527$	−1.27331e29	−3.35679
$528$	−6.80926e27	−0.175972
$529$	9.97650e27	0.252751
$530$	4.25549e28	1.05695
$531$	1.82463e28	0.444306
$532$	6.21759e26	0.0148440
$533$	2.90678e28	0.680420
$534$	6.38354e27	0.146514
$535$	−8.49420e28	−1.91165
$536$	1.66219e28	0.366817
$537$	1.21992e28	0.263998
$538$	1.18593e28	0.251678
$539$	5.56855e28	1.15894
$540$	5.70918e27	0.116530
$541$	7.52925e28	1.50723	0.753617	−	0.657314i	$-0.228307\pi$
$541$	7.52925e28	1.50723	0.753617	+	0.657314i	$0.228307\pi$
$542$	−1.70793e28	−0.335334
$543$	4.23546e28	0.815648
$544$	−1.64338e28	−0.310420
$545$	−1.39359e28	−0.258209
$546$	−3.37081e27	−0.0612649
$547$	−6.21957e28	−1.10890	−0.554451	−	0.832216i	$-0.687072\pi$
$547$	−6.21957e28	−1.10890	−0.554451	+	0.832216i	$0.687072\pi$
$548$	4.33867e28	0.758858
$549$	−1.66961e28	−0.286487
$550$	2.38931e28	0.402221
$551$	7.83194e27	0.129353
$552$	−1.40990e28	−0.228469
$553$	−2.47323e27	−0.0393233
$554$	5.11157e28	0.797447
$555$	5.85117e28	0.895708
$556$	−1.95795e28	−0.294114
$557$	5.50617e27	0.0811652	0.0405826	−	0.999176i	$-0.487079\pi$
$557$	5.50617e27	0.0811652	0.0405826	+	0.999176i	$0.487079\pi$
$558$	3.11474e28	0.450571
$559$	4.41024e28	0.626092
$560$	4.83000e27	0.0672935
$561$	−9.03937e28	−1.23603
$562$	−2.45614e28	−0.329627
$563$	−1.21599e29	−1.60174	−0.800868	−	0.598840i	$-0.795628\pi$
$563$	−1.21599e29	−1.60174	−0.800868	+	0.598840i	$0.795628\pi$
$564$	2.09925e28	0.271415
$565$	7.01776e27	0.0890614
$566$	2.75324e28	0.342982
$567$	2.01958e27	0.0246967
$568$	1.38845e28	0.166675
$569$	−3.49889e28	−0.412337	−0.206168	−	0.978517i	$-0.566099\pi$
$569$	−3.49889e28	−0.412337	−0.206168	+	0.978517i	$0.566099\pi$
$570$	−5.70768e27	−0.0660349
$571$	9.42449e28	1.07048	0.535240	−	0.844700i	$-0.320221\pi$
$571$	9.42449e28	1.07048	0.535240	+	0.844700i	$0.320221\pi$
$572$	−3.69061e28	−0.411566
$573$	−2.64650e28	−0.289766
$574$	−1.47337e28	−0.158394
$575$	4.94721e28	0.522213
$576$	4.01999e27	0.0416667
$577$	−1.55441e29	−1.58205	−0.791025	−	0.611784i	$-0.790452\pi$
$577$	−1.55441e29	−1.58205	−0.791025	+	0.611784i	$0.790452\pi$
$578$	−1.47410e29	−1.47328
$579$	−4.65344e28	−0.456719
$580$	6.08407e28	0.586409
$581$	6.16042e27	0.0583124
$582$	−8.35094e28	−0.776326
$583$	1.64816e29	1.50481
$584$	4.75208e28	0.426137
$585$	3.09437e28	0.272543
$586$	−1.32221e28	−0.114387
$587$	1.17789e29	1.00093	0.500465	−	0.865757i	$-0.333162\pi$
$587$	1.17789e29	1.00093	0.500465	+	0.865757i	$0.333162\pi$
$588$	−3.28751e28	−0.274413
$589$	−3.11392e28	−0.255327
$590$	−1.41705e29	−1.14140
$591$	−3.17733e28	−0.251416
$592$	4.11997e28	0.320270
$593$	1.16653e29	0.890884	0.445442	−	0.895311i	$-0.353047\pi$
$593$	1.16653e29	0.890884	0.445442	+	0.895311i	$0.353047\pi$
$594$	2.21119e28	0.165908
$595$	6.41188e28	0.472669
$596$	−4.70158e28	−0.340532
$597$	−1.07967e29	−0.768353
$598$	−7.64162e28	−0.534346
$599$	−5.27398e28	−0.362374	−0.181187	−	0.983449i	$-0.557994\pi$
$599$	−5.27398e28	−0.362374	−0.181187	+	0.983449i	$0.557994\pi$
$600$	−1.41058e28	−0.0952378
$601$	−5.00756e28	−0.332234	−0.166117	−	0.986106i	$-0.553123\pi$
$601$	−5.00756e28	−0.332234	−0.166117	+	0.986106i	$0.553123\pi$
$602$	−2.23544e28	−0.145747
$603$	−5.39766e28	−0.345839
$604$	5.53436e28	0.348482
$605$	9.51820e28	0.589011
$606$	9.03480e28	0.549485
$607$	−6.44426e28	−0.385205	−0.192603	−	0.981277i	$-0.561693\pi$
$607$	−6.44426e28	−0.385205	−0.192603	+	0.981277i	$0.561693\pi$
$608$	−4.01893e27	−0.0236115
$609$	2.15220e28	0.124280
$610$	1.29666e29	0.735973
$611$	1.13779e29	0.634791
$612$	5.33658e28	0.292667
$613$	1.46854e29	0.791680	0.395840	−	0.918319i	$-0.370453\pi$
$613$	1.46854e29	0.791680	0.395840	+	0.918319i	$0.370453\pi$
$614$	1.49409e29	0.791788
$615$	1.35254e29	0.704631
$616$	1.87068e28	0.0958078
$617$	−2.87513e29	−1.44765	−0.723823	−	0.689985i	$-0.757617\pi$
$617$	−2.87513e29	−1.44765	−0.723823	+	0.689985i	$0.757617\pi$
$618$	1.04498e29	0.517285
$619$	3.83570e29	1.86678	0.933388	−	0.358869i	$-0.116837\pi$
$619$	3.83570e29	1.86678	0.933388	+	0.358869i	$0.116837\pi$
$620$	−2.41899e29	−1.15750
$621$	4.57839e28	0.215402
$622$	1.02416e28	0.0473772
$623$	−1.75372e28	−0.0797692
$624$	2.17883e28	0.0974507
$625$	−2.83963e29	−1.24888
$626$	−2.13349e28	−0.0922697
$627$	−2.21060e28	−0.0940160
$628$	4.99803e28	0.209037
$629$	5.46931e29	2.24957
$630$	−1.56846e28	−0.0634449
$631$	−4.12646e29	−1.64161	−0.820803	−	0.571211i	$-0.806474\pi$
$631$	−4.12646e29	−1.64161	−0.820803	+	0.571211i	$0.806474\pi$
$632$	1.59865e28	0.0625495
$633$	−1.28272e29	−0.493620
$634$	−1.34092e29	−0.507535
$635$	−5.15784e29	−1.92019
$636$	−9.73028e28	−0.356308
$637$	−1.78183e29	−0.641803
$638$	2.35638e29	0.834889
$639$	−4.50873e28	−0.157143
$640$	−3.12202e28	−0.107040
$641$	−4.45897e29	−1.50392	−0.751960	−	0.659208i	$-0.770891\pi$
$641$	−4.45897e29	−1.50392	−0.751960	+	0.659208i	$0.770891\pi$
$642$	1.94222e29	0.644438
$643$	−1.19395e29	−0.389736	−0.194868	−	0.980829i	$-0.562428\pi$
$643$	−1.19395e29	−0.389736	−0.194868	+	0.980829i	$0.562428\pi$
$644$	3.87334e28	0.124390
$645$	2.05211e29	0.648370
$646$	−5.33518e28	−0.165847
$647$	5.06908e29	1.55037	0.775183	−	0.631737i	$-0.217658\pi$
$647$	5.06908e29	1.55037	0.775183	+	0.631737i	$0.217658\pi$
$648$	−1.30542e28	−0.0392837
$649$	−5.48829e29	−1.62505
$650$	−7.64532e28	−0.222744
$651$	−8.55698e28	−0.245313
$652$	4.91345e28	0.138607
$653$	2.19335e29	0.608862	0.304431	−	0.952534i	$-0.401534\pi$
$653$	2.19335e29	0.608862	0.304431	+	0.952534i	$0.401534\pi$
$654$	3.18648e28	0.0870451
$655$	−2.62523e29	−0.705721
$656$	9.52361e28	0.251948
$657$	−1.54315e29	−0.401765
$658$	−5.76718e28	−0.147772
$659$	2.49016e29	0.627957	0.313979	−	0.949430i	$-0.398338\pi$
$659$	2.49016e29	0.627957	0.313979	+	0.949430i	$0.398338\pi$
$660$	−1.71726e29	−0.426211
$661$	3.02171e29	0.738137	0.369069	−	0.929402i	$-0.379677\pi$
$661$	3.02171e29	0.738137	0.369069	+	0.929402i	$0.379677\pi$
$662$	−5.67038e27	−0.0136334
$663$	2.89242e29	0.684494
$664$	−3.98198e28	−0.0927543
$665$	1.56804e28	0.0359527
$666$	−1.33789e29	−0.301953
$667$	4.87903e29	1.08396
$668$	4.41526e28	0.0965613
$669$	4.96477e29	1.06887
$670$	4.19195e29	0.888446
$671$	5.02200e29	1.04783
$672$	−1.10439e28	−0.0226854
$673$	1.15417e29	0.233406	0.116703	−	0.993167i	$-0.462767\pi$
$673$	1.15417e29	0.233406	0.116703	+	0.993167i	$0.462767\pi$
$674$	2.40872e29	0.479576
$675$	4.58061e28	0.0897911
$676$	−1.40974e29	−0.272081
$677$	−2.04966e29	−0.389494	−0.194747	−	0.980853i	$-0.562389\pi$
$677$	−2.04966e29	−0.389494	−0.194747	+	0.980853i	$0.562389\pi$
$678$	−1.60463e28	−0.0300236
$679$	2.29421e29	0.422670
$680$	−4.14452e29	−0.751849
$681$	−3.60022e29	−0.643109
$682$	−9.36881e29	−1.64797
$683$	−7.56950e29	−1.31114	−0.655571	−	0.755134i	$-0.727572\pi$
$683$	−7.56950e29	−1.31114	−0.655571	+	0.755134i	$0.727572\pi$
$684$	1.30508e28	0.0222611
$685$	1.09419e30	1.83798
$686$	1.85326e29	0.306573
$687$	−3.85861e28	−0.0628616
$688$	1.44494e29	0.231832
$689$	−5.27380e29	−0.833339
$690$	−3.55569e29	−0.553360
$691$	−4.98998e29	−0.764855	−0.382427	−	0.923986i	$-0.624912\pi$
$691$	−4.98998e29	−0.764855	−0.382427	+	0.923986i	$0.624912\pi$
$692$	4.73001e29	0.714082
$693$	−6.07468e28	−0.0903285
$694$	1.64342e29	0.240700
$695$	−4.93784e29	−0.712356
$696$	−1.39114e29	−0.197685
$697$	1.26427e30	1.76968
$698$	−3.80838e29	−0.525119
$699$	−6.44165e29	−0.874957
$700$	3.87522e28	0.0518522
$701$	4.27981e29	0.564137	0.282069	−	0.959394i	$-0.408979\pi$
$701$	4.27981e29	0.564137	0.282069	+	0.959394i	$0.408979\pi$
$702$	−7.07536e28	−0.0918774
$703$	1.33753e29	0.171110
$704$	−1.20917e29	−0.152396
$705$	5.29421e29	0.657378
$706$	−7.20130e29	−0.880971
$707$	−2.48209e29	−0.299167
$708$	3.24013e29	0.384780
$709$	3.31006e29	0.387303	0.193651	−	0.981070i	$-0.437967\pi$
$709$	3.31006e29	0.387303	0.193651	+	0.981070i	$0.437967\pi$
$710$	3.50159e29	0.403694
$711$	−5.19133e28	−0.0589722
$712$	1.13357e29	0.126885
$713$	−1.93987e30	−2.13960
$714$	−1.46609e29	−0.159342
$715$	−9.30753e29	−0.996830
$716$	2.16630e29	0.228629
$717$	3.52236e26	0.000366338 0
$718$	5.13772e29	0.526580
$719$	−1.36160e30	−1.37530	−0.687648	−	0.726044i	$-0.741357\pi$
$719$	−1.36160e30	−1.37530	−0.687648	+	0.726044i	$0.741357\pi$
$720$	1.01382e29	0.100918
$721$	−2.87083e29	−0.281636
$722$	7.18303e29	0.694492
$723$	4.82979e29	0.460231
$724$	7.52122e29	0.706372
$725$	4.88139e29	0.451850
$726$	−2.17636e29	−0.198562
$727$	−5.58942e29	−0.502638	−0.251319	−	0.967904i	$-0.580864\pi$
$727$	−5.58942e29	−0.502638	−0.251319	+	0.967904i	$0.580864\pi$
$728$	−5.98579e28	−0.0530569
$729$	4.23912e28	0.0370370
$730$	1.19845e30	1.03212
$731$	1.91818e30	1.62838
$732$	−2.96484e29	−0.248105
$733$	1.20616e30	0.994975	0.497488	−	0.867471i	$-0.334256\pi$
$733$	1.20616e30	0.994975	0.497488	+	0.867471i	$0.334256\pi$
$734$	−5.82771e29	−0.473903
$735$	−8.29093e29	−0.664640
$736$	−2.50366e29	−0.197860
$737$	1.62356e30	1.26491
$738$	−3.09262e29	−0.237539
$739$	−1.99646e30	−1.51180	−0.755901	−	0.654686i	$-0.772801\pi$
$739$	−1.99646e30	−1.51180	−0.755901	+	0.654686i	$0.772801\pi$
$740$	1.03903e30	0.775706
$741$	7.07350e28	0.0520647
$742$	2.67315e29	0.193992
$743$	1.25058e30	0.894803	0.447402	−	0.894333i	$-0.352350\pi$
$743$	1.25058e30	0.894803	0.447402	+	0.894333i	$0.352350\pi$
$744$	5.53107e29	0.390206
$745$	−1.18571e30	−0.824782
$746$	−2.65591e29	−0.182161
$747$	1.29308e29	0.0874496
$748$	−1.60519e30	−1.07043
$749$	−5.33577e29	−0.350864
$750$	4.06722e29	0.263727
$751$	1.17402e30	0.750685	0.375343	−	0.926886i	$-0.377525\pi$
$751$	1.17402e30	0.750685	0.375343	+	0.926886i	$0.377525\pi$
$752$	3.72780e29	0.235053
$753$	8.11053e29	0.504315
$754$	−7.53996e29	−0.462349
$755$	1.39574e30	0.844036
$756$	3.58632e28	0.0213880
$757$	5.86936e29	0.345210	0.172605	−	0.984991i	$-0.444782\pi$
$757$	5.86936e29	0.345210	0.172605	+	0.984991i	$0.444782\pi$
$758$	−1.13033e30	−0.655658
$759$	−1.37713e30	−0.787837
$760$	−1.01355e29	−0.0571879
$761$	−1.13068e30	−0.629217	−0.314609	−	0.949221i	$-0.601873\pi$
$761$	−1.13068e30	−0.629217	−0.314609	+	0.949221i	$0.601873\pi$
$762$	1.17935e30	0.647316
$763$	−8.75405e28	−0.0473916
$764$	−4.69958e29	−0.250945
$765$	1.34586e30	0.708850
$766$	6.52801e29	0.339140
$767$	1.75614e30	0.899930
$768$	7.13859e28	0.0360844
$769$	−3.28732e30	−1.63914	−0.819569	−	0.572981i	$-0.805787\pi$
$769$	−3.28732e30	−1.63914	−0.819569	+	0.572981i	$0.805787\pi$
$770$	4.71775e29	0.232050
$771$	2.67496e29	0.129791
$772$	−8.26345e29	−0.395530
$773$	−2.96976e30	−1.40229	−0.701144	−	0.713020i	$-0.747327\pi$
$773$	−2.96976e30	−1.40229	−0.701144	+	0.713020i	$0.747327\pi$
$774$	−4.69220e29	−0.218573
$775$	−1.94081e30	−0.891897
$776$	−1.48294e30	−0.672318
$777$	3.67551e29	0.164398
$778$	−3.70136e28	−0.0163334
$779$	3.09181e29	0.134608
$780$	5.49489e29	0.236029
$781$	1.35618e30	0.574752
$782$	−3.32363e30	−1.38977
$783$	4.51748e29	0.186379
$784$	−5.83787e29	−0.237649
$785$	1.26048e30	0.506295
$786$	6.00265e29	0.237906
$787$	7.59025e29	0.296839	0.148420	−	0.988924i	$-0.452581\pi$
$787$	7.59025e29	0.296839	0.148420	+	0.988924i	$0.452581\pi$
$788$	−5.64221e29	−0.217733
$789$	−3.08862e29	−0.117613
$790$	4.03171e29	0.151497
$791$	4.40832e28	0.0163463
$792$	3.92656e29	0.143681
$793$	−1.60694e30	−0.580272
$794$	−6.76677e29	−0.241138
$795$	−2.45393e30	−0.862992
$796$	−1.91725e30	−0.665414
$797$	4.13590e30	1.41664	0.708318	−	0.705894i	$-0.249454\pi$
$797$	4.13590e30	1.41664	0.708318	+	0.705894i	$0.249454\pi$
$798$	−3.58538e28	−0.0121200
$799$	4.94869e30	1.65101
$800$	−2.50487e29	−0.0824784
$801$	−3.68107e29	−0.119628
$802$	3.23781e30	1.03853
$803$	4.64164e30	1.46946
$804$	−9.58501e29	−0.299505
$805$	9.76837e29	0.301277
$806$	2.99784e30	0.912620
$807$	−6.83868e29	−0.205495
$808$	1.60437e30	0.475868
$809$	−6.22694e30	−1.82312	−0.911560	−	0.411166i	$-0.865122\pi$
$809$	−6.22694e30	−1.82312	−0.911560	+	0.411166i	$0.865122\pi$
$810$	−3.29220e29	−0.0951467
$811$	1.69279e30	0.482930	0.241465	−	0.970409i	$-0.422372\pi$
$811$	1.69279e30	0.482930	0.241465	+	0.970409i	$0.422372\pi$
$812$	3.82181e29	0.107629
$813$	9.84878e29	0.273799
$814$	4.02422e30	1.10440
$815$	1.23915e30	0.335713
$816$	9.47656e29	0.253457
$817$	4.69097e29	0.123860
$818$	−1.29894e30	−0.338593
$819$	1.94378e29	0.0500226
$820$	2.40181e30	0.610228
$821$	−8.06422e29	−0.202283	−0.101141	−	0.994872i	$-0.532249\pi$
$821$	−8.06422e29	−0.202283	−0.101141	+	0.994872i	$0.532249\pi$
$822$	−2.50189e30	−0.619605
$823$	−2.36474e30	−0.578210	−0.289105	−	0.957297i	$-0.593358\pi$
$823$	−2.36474e30	−0.578210	−0.289105	+	0.957297i	$0.593358\pi$
$824$	1.85565e30	0.447982
$825$	−1.37780e30	−0.328412
$826$	−8.90145e29	−0.209493
$827$	−1.05624e30	−0.245445	−0.122722	−	0.992441i	$-0.539162\pi$
$827$	−1.05624e30	−0.245445	−0.122722	+	0.992441i	$0.539162\pi$
$828$	8.13017e29	0.186544
$829$	−3.64602e30	−0.826032	−0.413016	−	0.910724i	$-0.635525\pi$
$829$	−3.64602e30	−0.826032	−0.413016	+	0.910724i	$0.635525\pi$
$830$	−1.00423e30	−0.224655
$831$	−2.94759e30	−0.651113
$832$	3.86910e29	0.0843948
$833$	−7.74984e30	−1.66925
$834$	1.12905e30	0.240143
$835$	1.11351e30	0.233875
$836$	−3.92553e29	−0.0814203
$837$	−1.79612e30	−0.367890
$838$	−4.10282e30	−0.829890
$839$	−6.80400e29	−0.135914	−0.0679569	−	0.997688i	$-0.521648\pi$
$839$	−6.80400e29	−0.135914	−0.0679569	+	0.997688i	$0.521648\pi$
$840$	−2.78522e29	−0.0549449
$841$	−3.18725e29	−0.0620953
$842$	5.45992e30	1.05053
$843$	1.41634e30	0.269139
$844$	−2.27782e30	−0.427487
$845$	−3.55528e30	−0.658990
$846$	−1.21054e30	−0.221610
$847$	5.97902e29	0.108107
$848$	−1.72788e30	−0.308572
$849$	−1.58766e30	−0.280044
$850$	−3.32524e30	−0.579328
$851$	8.33237e30	1.43387
$852$	−8.00648e29	−0.136090
$853$	9.57477e30	1.60755	0.803773	−	0.594936i	$-0.202823\pi$
$853$	9.57477e30	1.60755	0.803773	+	0.594936i	$0.202823\pi$
$854$	8.14517e29	0.135080
$855$	3.29134e29	0.0539173
$856$	3.44894e30	0.558100
$857$	−4.04955e30	−0.647304	−0.323652	−	0.946176i	$-0.604911\pi$
$857$	−4.04955e30	−0.647304	−0.323652	+	0.946176i	$0.604911\pi$
$858$	2.12819e30	0.336043
$859$	−9.44318e30	−1.47296	−0.736479	−	0.676461i	$-0.763513\pi$
$859$	−9.44318e30	−1.47296	−0.736479	+	0.676461i	$0.763513\pi$
$860$	3.64408e30	0.561505
$861$	8.49622e29	0.129328
$862$	−2.88980e30	−0.434551
$863$	−5.03037e30	−0.747285	−0.373642	−	0.927573i	$-0.621891\pi$
$863$	−5.03037e30	−0.747285	−0.373642	+	0.927573i	$0.621891\pi$
$864$	−2.31813e29	−0.0340207
$865$	1.19288e31	1.72953
$866$	1.61863e29	0.0231851
$867$	8.50043e30	1.20293
$868$	−1.51953e30	−0.212447
$869$	1.56150e30	0.215692
$870$	−3.50838e30	−0.478801
$871$	−5.19506e30	−0.700487
$872$	5.65846e29	0.0753832
$873$	4.81557e30	0.633867
$874$	−8.12804e29	−0.105710
$875$	−1.11737e30	−0.143586
$876$	−2.74029e30	−0.347939
$877$	1.56535e30	0.196388	0.0981942	−	0.995167i	$-0.468693\pi$
$877$	1.56535e30	0.196388	0.0981942	+	0.995167i	$0.468693\pi$
$878$	−8.95611e30	−1.11027
$879$	7.62452e29	0.0933963
$880$	−3.04946e30	−0.369110
$881$	4.04777e30	0.484138	0.242069	−	0.970259i	$-0.422174\pi$
$881$	4.04777e30	0.484138	0.242069	+	0.970259i	$0.422174\pi$
$882$	1.89574e30	0.224058
$883$	6.12581e29	0.0715445	0.0357723	−	0.999360i	$-0.488611\pi$
$883$	6.12581e29	0.0715445	0.0357723	+	0.999360i	$0.488611\pi$
$884$	5.13628e30	0.592789
$885$	8.17143e30	0.931953
$886$	−1.85877e30	−0.209494
$887$	9.40602e30	1.04763	0.523815	−	0.851832i	$-0.324508\pi$
$887$	9.40602e30	1.04763	0.523815	+	0.851832i	$0.324508\pi$
$888$	−2.37578e30	−0.261499
$889$	−3.23998e30	−0.352431
$890$	2.85881e30	0.307319
$891$	−1.27508e30	−0.135463
$892$	8.81630e30	0.925668
$893$	1.21022e30	0.125581
$894$	2.71117e30	0.278043
$895$	5.46330e30	0.553749
$896$	−1.96115e29	−0.0196461
$897$	4.40654e30	0.436292
$898$	−1.09537e31	−1.07191
$899$	−1.91406e31	−1.85131
$900$	8.13411e29	0.0777614
$901$	−2.29378e31	−2.16741
$902$	9.30228e30	0.868802
$903$	1.28907e30	0.119002
$904$	−2.84946e29	−0.0260012
$905$	1.89681e31	1.71086
$906$	−3.19139e30	−0.284534
$907$	−2.95076e30	−0.260051	−0.130025	−	0.991511i	$-0.541506\pi$
$907$	−2.95076e30	−0.260051	−0.130025	+	0.991511i	$0.541506\pi$
$908$	−6.39318e30	−0.556949
$909$	−5.20992e30	−0.448653
$910$	−1.50959e30	−0.128506
$911$	5.31915e30	0.447610	0.223805	−	0.974634i	$-0.428152\pi$
$911$	5.31915e30	0.447610	0.223805	+	0.974634i	$0.428152\pi$
$912$	2.31752e29	0.0192787
$913$	−3.88944e30	−0.319848
$914$	1.63197e31	1.32672
$915$	−7.47718e30	−0.600920
$916$	−6.85202e29	−0.0544397
$917$	−1.64908e30	−0.129528
$918$	−3.07734e30	−0.238961
$919$	3.46199e30	0.265774	0.132887	−	0.991131i	$-0.457575\pi$
$919$	3.46199e30	0.265774	0.132887	+	0.991131i	$0.457575\pi$
$920$	−6.31409e30	−0.479224
$921$	−8.61567e30	−0.646492
$922$	−5.46471e30	−0.405408
$923$	−4.33950e30	−0.318289
$924$	−1.07873e30	−0.0782268
$925$	8.33641e30	0.597711
$926$	−3.46776e30	−0.245829
$927$	−6.02590e30	−0.422362
$928$	−2.47035e30	−0.171200
$929$	−8.04165e30	−0.551036	−0.275518	−	0.961296i	$-0.588849\pi$
$929$	−8.04165e30	−0.551036	−0.275518	+	0.961296i	$0.588849\pi$
$930$	1.39491e31	0.945094
$931$	−1.89525e30	−0.126968
$932$	−1.14389e31	−0.757735
$933$	−5.90584e29	−0.0386834
$934$	1.61359e31	1.04508
$935$	−4.04820e31	−2.59263
$936$	−1.25642e30	−0.0795682
$937$	5.36884e30	0.336213	0.168106	−	0.985769i	$-0.446235\pi$
$937$	5.36884e30	0.336213	0.168106	+	0.985769i	$0.446235\pi$
$938$	2.63324e30	0.163065
$939$	1.23028e30	0.0753379
$940$	9.40131e30	0.569306
$941$	3.46189e30	0.207311	0.103655	−	0.994613i	$-0.466946\pi$
$941$	3.46189e30	0.207311	0.103655	+	0.994613i	$0.466946\pi$
$942$	−2.88212e30	−0.170678
$943$	1.92609e31	1.12799
$944$	5.75373e30	0.333229
$945$	9.04451e29	0.0518025
$946$	1.41136e31	0.799433
$947$	1.53479e31	0.859753	0.429877	−	0.902888i	$-0.358557\pi$
$947$	1.53479e31	0.859753	0.429877	+	0.902888i	$0.358557\pi$
$948$	−9.21862e29	−0.0510714
$949$	−1.48523e31	−0.813766
$950$	−8.13198e29	−0.0440655
$951$	7.73242e30	0.414400
$952$	−2.60345e30	−0.137994
$953$	3.39202e31	1.77821	0.889105	−	0.457703i	$-0.151328\pi$
$953$	3.39202e31	1.77821	0.889105	+	0.457703i	$0.151328\pi$
$954$	5.61097e30	0.290924
$955$	−1.18521e31	−0.607799
$956$	6.25491e27	0.000317258 0
$957$	−1.35881e31	−0.681684
$958$	2.18084e31	1.08215
$959$	6.87334e30	0.337343
$960$	1.80031e30	0.0873978
$961$	5.52762e31	2.65425
$962$	−1.28767e31	−0.611599
$963$	−1.11998e31	−0.526181
$964$	8.57661e30	0.398572
$965$	−2.08400e31	−0.957990
$966$	−2.23356e30	−0.101564
$967$	−5.24173e30	−0.235775	−0.117887	−	0.993027i	$-0.537612\pi$
$967$	−5.24173e30	−0.235775	−0.117887	+	0.993027i	$0.537612\pi$
$968$	−3.86472e30	−0.171960
$969$	3.07653e30	0.135414
$970$	−3.73989e31	−1.62838
$971$	−1.66001e31	−0.715004	−0.357502	−	0.933912i	$-0.616371\pi$
$971$	−1.66001e31	−0.715004	−0.357502	+	0.933912i	$0.616371\pi$
$972$	7.52771e29	0.0320750
$973$	−3.10179e30	−0.130746
$974$	−1.72552e31	−0.719533
$975$	4.40868e30	0.181870
$976$	−5.26488e30	−0.214865
$977$	4.02046e31	1.62324	0.811621	−	0.584185i	$-0.198586\pi$
$977$	4.02046e31	1.62324	0.811621	+	0.584185i	$0.198586\pi$
$978$	−2.83334e30	−0.113173
$979$	1.10723e31	0.437540
$980$	−1.47228e31	−0.575595
$981$	−1.83748e30	−0.0710720
$982$	1.61481e31	0.617948
$983$	1.31702e31	0.498633	0.249317	−	0.968422i	$-0.419794\pi$
$983$	1.31702e31	0.498633	0.249317	+	0.968422i	$0.419794\pi$
$984$	−5.49179e30	−0.205715
$985$	−1.42294e31	−0.527357
$986$	−3.27942e31	−1.20251
$987$	3.32565e30	0.120655
$988$	1.25609e30	0.0450893
$989$	2.92231e31	1.03792
$990$	9.90259e30	0.348000
$991$	−4.21282e31	−1.46487	−0.732436	−	0.680836i	$-0.761616\pi$
$991$	−4.21282e31	−1.46487	−0.732436	+	0.680836i	$0.761616\pi$
$992$	9.82193e30	0.337928
$993$	3.26983e29	0.0111316
$994$	2.19958e30	0.0740940
$995$	−4.83521e31	−1.61166
$996$	2.29621e30	0.0757336
$997$	−5.77509e31	−1.88477	−0.942387	−	0.334524i	$-0.891424\pi$
$997$	−5.77509e31	−1.88477	−0.942387	+	0.334524i	$0.891424\pi$
$998$	−2.63357e31	−0.850501
$999$	7.71492e30	0.246544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.22.a.a.1.1	✓	1
3.2	odd	2		18.22.a.d.1.1		1
4.3	odd	2		48.22.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.22.a.a.1.1	✓	1	1.1	even	1	trivial
18.22.a.d.1.1		1	3.2	odd	2
48.22.a.c.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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