LMFDB - Embedded newform 1338.2.a.i.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(1,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.232773917.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 12x^{4} - x^{3} + 33x^{2} + 5x - 22 $ x^6 - 12x^4 - x^3 + 33x^2 + 5*x - 22
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.36937$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36937 q^{5} +1.00000 q^{6} +3.68274 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.36937 q^{10} -5.92506 q^{11} +1.00000 q^{12} +2.87295 q^{13} +3.68274 q^{14} +2.36937 q^{15} +1.00000 q^{16} +6.47611 q^{17} +1.00000 q^{18} -7.48297 q^{19} +2.36937 q^{20} +3.68274 q^{21} -5.92506 q^{22} -3.33505 q^{23} +1.00000 q^{24} +0.613915 q^{25} +2.87295 q^{26} +1.00000 q^{27} +3.68274 q^{28} +4.99778 q^{29} +2.36937 q^{30} -7.04303 q^{31} +1.00000 q^{32} -5.92506 q^{33} +6.47611 q^{34} +8.72577 q^{35} +1.00000 q^{36} -8.68737 q^{37} -7.48297 q^{38} +2.87295 q^{39} +2.36937 q^{40} +3.14107 q^{41} +3.68274 q^{42} -4.56477 q^{43} -5.92506 q^{44} +2.36937 q^{45} -3.33505 q^{46} -1.68441 q^{47} +1.00000 q^{48} +6.56254 q^{49} +0.613915 q^{50} +6.47611 q^{51} +2.87295 q^{52} +3.46926 q^{53} +1.00000 q^{54} -14.0387 q^{55} +3.68274 q^{56} -7.48297 q^{57} +4.99778 q^{58} -10.7886 q^{59} +2.36937 q^{60} +5.81331 q^{61} -7.04303 q^{62} +3.68274 q^{63} +1.00000 q^{64} +6.80709 q^{65} -5.92506 q^{66} +1.64434 q^{67} +6.47611 q^{68} -3.33505 q^{69} +8.72577 q^{70} +12.3833 q^{71} +1.00000 q^{72} +0.779919 q^{73} -8.68737 q^{74} +0.613915 q^{75} -7.48297 q^{76} -21.8204 q^{77} +2.87295 q^{78} -15.0857 q^{79} +2.36937 q^{80} +1.00000 q^{81} +3.14107 q^{82} +5.37448 q^{83} +3.68274 q^{84} +15.3443 q^{85} -4.56477 q^{86} +4.99778 q^{87} -5.92506 q^{88} -7.50543 q^{89} +2.36937 q^{90} +10.5803 q^{91} -3.33505 q^{92} -7.04303 q^{93} -1.68441 q^{94} -17.7299 q^{95} +1.00000 q^{96} +8.15885 q^{97} +6.56254 q^{98} -5.92506 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + q^{11} + 6 q^{12} + 6 q^{13} + 5 q^{14} + 6 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} - 4 q^{19} + 6 q^{20}+ \cdots + q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + q^11 + 6 * q^12 + 6 * q^13 + 5 * q^14 + 6 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 - 4 * q^19 + 6 * q^20 + 5 * q^21 + q^22 + 2 * q^23 + 6 * q^24 + 6 * q^26 + 6 * q^27 + 5 * q^28 + 6 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + q^33 + 10 * q^34 - 2 * q^35 + 6 * q^36 + q^37 - 4 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 5 * q^42 - 11 * q^43 + q^44 + 6 * q^45 + 2 * q^46 + 5 * q^47 + 6 * q^48 - q^49 + 10 * q^51 + 6 * q^52 + 4 * q^53 + 6 * q^54 - 15 * q^55 + 5 * q^56 - 4 * q^57 + 6 * q^58 + q^59 + 6 * q^60 - 8 * q^61 - 5 * q^62 + 5 * q^63 + 6 * q^64 + 5 * q^65 + q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 2 * q^70 + q^71 + 6 * q^72 - 10 * q^73 + q^74 - 4 * q^76 - 8 * q^77 + 6 * q^78 - 10 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 6 * q^83 + 5 * q^84 - 2 * q^85 - 11 * q^86 + 6 * q^87 + q^88 - 3 * q^89 + 6 * q^90 - 16 * q^91 + 2 * q^92 - 5 * q^93 + 5 * q^94 - 10 * q^95 + 6 * q^96 + 3 * q^97 - q^98 + q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.36937	1.05961	0.529807	−	0.848118i	$-0.322264\pi$
$5$	2.36937	1.05961	0.529807	+	0.848118i	$0.322264\pi$
$6$	1.00000	0.408248
$7$	3.68274	1.39194	0.695972	−	0.718069i	$-0.254974\pi$
$7$	3.68274	1.39194	0.695972	+	0.718069i	$0.254974\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.36937	0.749261
$11$	−5.92506	−1.78647	−0.893236	−	0.449588i	$-0.851571\pi$
$11$	−5.92506	−1.78647	−0.893236	+	0.449588i	$0.851571\pi$
$12$	1.00000	0.288675
$13$	2.87295	0.796814	0.398407	−	0.917209i	$-0.369563\pi$
$13$	2.87295	0.796814	0.398407	+	0.917209i	$0.369563\pi$
$14$	3.68274	0.984253
$15$	2.36937	0.611769
$16$	1.00000	0.250000
$17$	6.47611	1.57069	0.785344	−	0.619059i	$-0.212486\pi$
$17$	6.47611	1.57069	0.785344	+	0.619059i	$0.212486\pi$
$18$	1.00000	0.235702
$19$	−7.48297	−1.71671	−0.858356	−	0.513055i	$-0.828514\pi$
$19$	−7.48297	−1.71671	−0.858356	+	0.513055i	$0.828514\pi$
$20$	2.36937	0.529807
$21$	3.68274	0.803639
$22$	−5.92506	−1.26323
$23$	−3.33505	−0.695405	−0.347703	−	0.937605i	$-0.613038\pi$
$23$	−3.33505	−0.695405	−0.347703	+	0.937605i	$0.613038\pi$
$24$	1.00000	0.204124
$25$	0.613915	0.122783
$26$	2.87295	0.563432
$27$	1.00000	0.192450
$28$	3.68274	0.695972
$29$	4.99778	0.928064	0.464032	−	0.885818i	$-0.346402\pi$
$29$	4.99778	0.928064	0.464032	+	0.885818i	$0.346402\pi$
$30$	2.36937	0.432586
$31$	−7.04303	−1.26497	−0.632483	−	0.774575i	$-0.717964\pi$
$31$	−7.04303	−1.26497	−0.632483	+	0.774575i	$0.717964\pi$
$32$	1.00000	0.176777
$33$	−5.92506	−1.03142
$34$	6.47611	1.11064
$35$	8.72577	1.47492
$36$	1.00000	0.166667
$37$	−8.68737	−1.42819	−0.714097	−	0.700046i	$-0.753163\pi$
$37$	−8.68737	−1.42819	−0.714097	+	0.700046i	$0.753163\pi$
$38$	−7.48297	−1.21390
$39$	2.87295	0.460041
$40$	2.36937	0.374630
$41$	3.14107	0.490552	0.245276	−	0.969453i	$-0.421121\pi$
$41$	3.14107	0.490552	0.245276	+	0.969453i	$0.421121\pi$
$42$	3.68274	0.568258
$43$	−4.56477	−0.696120	−0.348060	−	0.937472i	$-0.613160\pi$
$43$	−4.56477	−0.696120	−0.348060	+	0.937472i	$0.613160\pi$
$44$	−5.92506	−0.893236
$45$	2.36937	0.353205
$46$	−3.33505	−0.491726
$47$	−1.68441	−0.245697	−0.122848	−	0.992425i	$-0.539203\pi$
$47$	−1.68441	−0.245697	−0.122848	+	0.992425i	$0.539203\pi$
$48$	1.00000	0.144338
$49$	6.56254	0.937506
$50$	0.613915	0.0868207
$51$	6.47611	0.906837
$52$	2.87295	0.398407
$53$	3.46926	0.476539	0.238270	−	0.971199i	$-0.423420\pi$
$53$	3.46926	0.476539	0.238270	+	0.971199i	$0.423420\pi$
$54$	1.00000	0.136083
$55$	−14.0387	−1.89297
$56$	3.68274	0.492126
$57$	−7.48297	−0.991144
$58$	4.99778	0.656240
$59$	−10.7886	−1.40456	−0.702280	−	0.711901i	$-0.747834\pi$
$59$	−10.7886	−1.40456	−0.702280	+	0.711901i	$0.747834\pi$
$60$	2.36937	0.305884
$61$	5.81331	0.744318	0.372159	−	0.928169i	$-0.378618\pi$
$61$	5.81331	0.744318	0.372159	+	0.928169i	$0.378618\pi$
$62$	−7.04303	−0.894466
$63$	3.68274	0.463981
$64$	1.00000	0.125000
$65$	6.80709	0.844316
$66$	−5.92506	−0.729324
$67$	1.64434	0.200888	0.100444	−	0.994943i	$-0.467974\pi$
$67$	1.64434	0.200888	0.100444	+	0.994943i	$0.467974\pi$
$68$	6.47611	0.785344
$69$	−3.33505	−0.401492
$70$	8.72577	1.04293
$71$	12.3833	1.46962	0.734811	−	0.678272i	$-0.237271\pi$
$71$	12.3833	1.46962	0.734811	+	0.678272i	$0.237271\pi$
$72$	1.00000	0.117851
$73$	0.779919	0.0912826	0.0456413	−	0.998958i	$-0.485467\pi$
$73$	0.779919	0.0912826	0.0456413	+	0.998958i	$0.485467\pi$
$74$	−8.68737	−1.00989
$75$	0.613915	0.0708888
$76$	−7.48297	−0.858356
$77$	−21.8204	−2.48667
$78$	2.87295	0.325298
$79$	−15.0857	−1.69728	−0.848640	−	0.528971i	$-0.822578\pi$
$79$	−15.0857	−1.69728	−0.848640	+	0.528971i	$0.822578\pi$
$80$	2.36937	0.264904
$81$	1.00000	0.111111
$82$	3.14107	0.346873
$83$	5.37448	0.589925	0.294963	−	0.955509i	$-0.404693\pi$
$83$	5.37448	0.589925	0.294963	+	0.955509i	$0.404693\pi$
$84$	3.68274	0.401819
$85$	15.3443	1.66432
$86$	−4.56477	−0.492231
$87$	4.99778	0.535818
$88$	−5.92506	−0.631613
$89$	−7.50543	−0.795574	−0.397787	−	0.917478i	$-0.630222\pi$
$89$	−7.50543	−0.795574	−0.397787	+	0.917478i	$0.630222\pi$
$90$	2.36937	0.249754
$91$	10.5803	1.10912
$92$	−3.33505	−0.347703
$93$	−7.04303	−0.730328
$94$	−1.68441	−0.173734
$95$	−17.7299	−1.81905
$96$	1.00000	0.102062
$97$	8.15885	0.828406	0.414203	−	0.910185i	$-0.364060\pi$
$97$	8.15885	0.828406	0.414203	+	0.910185i	$0.364060\pi$
$98$	6.56254	0.662917
$99$	−5.92506	−0.595491
$100$	0.613915	0.0613915
$101$	−11.8823	−1.18233	−0.591166	−	0.806550i	$-0.701332\pi$
$101$	−11.8823	−1.18233	−0.591166	+	0.806550i	$0.701332\pi$
$102$	6.47611	0.641231
$103$	6.60780	0.651085	0.325543	−	0.945527i	$-0.394453\pi$
$103$	6.60780	0.651085	0.325543	+	0.945527i	$0.394453\pi$
$104$	2.87295	0.281716
$105$	8.72577	0.851547
$106$	3.46926	0.336964
$107$	17.8368	1.72435	0.862176	−	0.506609i	$-0.169101\pi$
$107$	17.8368	1.72435	0.862176	+	0.506609i	$0.169101\pi$
$108$	1.00000	0.0962250
$109$	0.117660	0.0112698	0.00563488	−	0.999984i	$-0.498206\pi$
$109$	0.117660	0.0112698	0.00563488	+	0.999984i	$0.498206\pi$
$110$	−14.0387	−1.33853
$111$	−8.68737	−0.824569
$112$	3.68274	0.347986
$113$	−5.47444	−0.514992	−0.257496	−	0.966279i	$-0.582897\pi$
$113$	−5.47444	−0.514992	−0.257496	+	0.966279i	$0.582897\pi$
$114$	−7.48297	−0.700844
$115$	−7.90196	−0.736862
$116$	4.99778	0.464032
$117$	2.87295	0.265605
$118$	−10.7886	−0.993173
$119$	23.8498	2.18631
$120$	2.36937	0.216293
$121$	24.1063	2.19148
$122$	5.81331	0.526312
$123$	3.14107	0.283221
$124$	−7.04303	−0.632483
$125$	−10.3923	−0.929512
$126$	3.68274	0.328084
$127$	−1.05057	−0.0932226	−0.0466113	−	0.998913i	$-0.514842\pi$
$127$	−1.05057	−0.0932226	−0.0466113	+	0.998913i	$0.514842\pi$
$128$	1.00000	0.0883883
$129$	−4.56477	−0.401905
$130$	6.80709	0.597021
$131$	17.3438	1.51534	0.757669	−	0.652639i	$-0.226338\pi$
$131$	17.3438	1.51534	0.757669	+	0.652639i	$0.226338\pi$
$132$	−5.92506	−0.515710
$133$	−27.5578	−2.38956
$134$	1.64434	0.142049
$135$	2.36937	0.203923
$136$	6.47611	0.555322
$137$	20.0510	1.71307	0.856534	−	0.516090i	$-0.172613\pi$
$137$	20.0510	1.71307	0.856534	+	0.516090i	$0.172613\pi$
$138$	−3.33505	−0.283898
$139$	10.0545	0.852813	0.426407	−	0.904532i	$-0.359779\pi$
$139$	10.0545	0.852813	0.426407	+	0.904532i	$0.359779\pi$
$140$	8.72577	0.737462
$141$	−1.68441	−0.141853
$142$	12.3833	1.03918
$143$	−17.0224	−1.42349
$144$	1.00000	0.0833333
$145$	11.8416	0.983390
$146$	0.779919	0.0645465
$147$	6.56254	0.541270
$148$	−8.68737	−0.714097
$149$	17.0239	1.39465	0.697327	−	0.716753i	$-0.254372\pi$
$149$	17.0239	1.39465	0.697327	+	0.716753i	$0.254372\pi$
$150$	0.613915	0.0501260
$151$	19.9467	1.62324	0.811618	−	0.584188i	$-0.198587\pi$
$151$	19.9467	1.62324	0.811618	+	0.584188i	$0.198587\pi$
$152$	−7.48297	−0.606949
$153$	6.47611	0.523563
$154$	−21.8204	−1.75834
$155$	−16.6875	−1.34038
$156$	2.87295	0.230020
$157$	−23.3954	−1.86715	−0.933577	−	0.358378i	$-0.883330\pi$
$157$	−23.3954	−1.86715	−0.933577	+	0.358378i	$0.883330\pi$
$158$	−15.0857	−1.20016
$159$	3.46926	0.275130
$160$	2.36937	0.187315
$161$	−12.2821	−0.967965
$162$	1.00000	0.0785674
$163$	−15.2069	−1.19110	−0.595548	−	0.803320i	$-0.703065\pi$
$163$	−15.2069	−1.19110	−0.595548	+	0.803320i	$0.703065\pi$
$164$	3.14107	0.245276
$165$	−14.0387	−1.09291
$166$	5.37448	0.417140
$167$	8.85449	0.685181	0.342590	−	0.939485i	$-0.388696\pi$
$167$	8.85449	0.685181	0.342590	+	0.939485i	$0.388696\pi$
$168$	3.68274	0.284129
$169$	−4.74614	−0.365088
$170$	15.3443	1.17686
$171$	−7.48297	−0.572237
$172$	−4.56477	−0.348060
$173$	−8.20552	−0.623854	−0.311927	−	0.950106i	$-0.600974\pi$
$173$	−8.20552	−0.623854	−0.311927	+	0.950106i	$0.600974\pi$
$174$	4.99778	0.378881
$175$	2.26089	0.170907
$176$	−5.92506	−0.446618
$177$	−10.7886	−0.810923
$178$	−7.50543	−0.562556
$179$	−5.28915	−0.395330	−0.197665	−	0.980270i	$-0.563336\pi$
$179$	−5.28915	−0.395330	−0.197665	+	0.980270i	$0.563336\pi$
$180$	2.36937	0.176602
$181$	−9.19861	−0.683727	−0.341864	−	0.939750i	$-0.611058\pi$
$181$	−9.19861	−0.683727	−0.341864	+	0.939750i	$0.611058\pi$
$182$	10.5803	0.784266
$183$	5.81331	0.429732
$184$	−3.33505	−0.245863
$185$	−20.5836	−1.51334
$186$	−7.04303	−0.516420
$187$	−38.3714	−2.80599
$188$	−1.68441	−0.122848
$189$	3.68274	0.267880
$190$	−17.7299	−1.28626
$191$	6.41200	0.463956	0.231978	−	0.972721i	$-0.425480\pi$
$191$	6.41200	0.463956	0.231978	+	0.972721i	$0.425480\pi$
$192$	1.00000	0.0721688
$193$	−24.0509	−1.73122	−0.865612	−	0.500716i	$-0.833070\pi$
$193$	−24.0509	−1.73122	−0.865612	+	0.500716i	$0.833070\pi$
$194$	8.15885	0.585771
$195$	6.80709	0.487466
$196$	6.56254	0.468753
$197$	−24.3937	−1.73798	−0.868991	−	0.494829i	$-0.835231\pi$
$197$	−24.3937	−1.73798	−0.868991	+	0.494829i	$0.835231\pi$
$198$	−5.92506	−0.421076
$199$	−11.0011	−0.779845	−0.389923	−	0.920848i	$-0.627498\pi$
$199$	−11.0011	−0.779845	−0.389923	+	0.920848i	$0.627498\pi$
$200$	0.613915	0.0434104
$201$	1.64434	0.115983
$202$	−11.8823	−0.836035
$203$	18.4055	1.29181
$204$	6.47611	0.453419
$205$	7.44235	0.519796
$206$	6.60780	0.460387
$207$	−3.33505	−0.231802
$208$	2.87295	0.199203
$209$	44.3370	3.06686
$210$	8.72577	0.602135
$211$	1.26320	0.0869622	0.0434811	−	0.999054i	$-0.486155\pi$
$211$	1.26320	0.0869622	0.0434811	+	0.999054i	$0.486155\pi$
$212$	3.46926	0.238270
$213$	12.3833	0.848487
$214$	17.8368	1.21930
$215$	−10.8156	−0.737619
$216$	1.00000	0.0680414
$217$	−25.9376	−1.76076
$218$	0.117660	0.00796892
$219$	0.779919	0.0527020
$220$	−14.0387	−0.946486
$221$	18.6056	1.25155
$222$	−8.68737	−0.583058
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	3.68274	0.246063
$225$	0.613915	0.0409277
$226$	−5.47444	−0.364154
$227$	−26.0600	−1.72967	−0.864833	−	0.502060i	$-0.832576\pi$
$227$	−26.0600	−1.72967	−0.864833	+	0.502060i	$0.832576\pi$
$228$	−7.48297	−0.495572
$229$	−8.20934	−0.542489	−0.271244	−	0.962511i	$-0.587435\pi$
$229$	−8.20934	−0.542489	−0.271244	+	0.962511i	$0.587435\pi$
$230$	−7.90196	−0.521040
$231$	−21.8204	−1.43568
$232$	4.99778	0.328120
$233$	−9.30454	−0.609561	−0.304780	−	0.952423i	$-0.598583\pi$
$233$	−9.30454	−0.609561	−0.304780	+	0.952423i	$0.598583\pi$
$234$	2.87295	0.187811
$235$	−3.99100	−0.260344
$236$	−10.7886	−0.702280
$237$	−15.0857	−0.979925
$238$	23.8498	1.54595
$239$	12.5859	0.814114	0.407057	−	0.913403i	$-0.366555\pi$
$239$	12.5859	0.814114	0.407057	+	0.913403i	$0.366555\pi$
$240$	2.36937	0.152942
$241$	5.73022	0.369116	0.184558	−	0.982822i	$-0.440915\pi$
$241$	5.73022	0.369116	0.184558	+	0.982822i	$0.440915\pi$
$242$	24.1063	1.54961
$243$	1.00000	0.0641500
$244$	5.81331	0.372159
$245$	15.5491	0.993395
$246$	3.14107	0.200267
$247$	−21.4982	−1.36790
$248$	−7.04303	−0.447233
$249$	5.37448	0.340594
$250$	−10.3923	−0.657264
$251$	16.5457	1.04435	0.522177	−	0.852837i	$-0.325120\pi$
$251$	16.5457	1.04435	0.522177	+	0.852837i	$0.325120\pi$
$252$	3.68274	0.231991
$253$	19.7604	1.24232
$254$	−1.05057	−0.0659184
$255$	15.3443	0.960898
$256$	1.00000	0.0625000
$257$	19.7435	1.23157	0.615784	−	0.787915i	$-0.288839\pi$
$257$	19.7435	1.23157	0.615784	+	0.787915i	$0.288839\pi$
$258$	−4.56477	−0.284190
$259$	−31.9933	−1.98797
$260$	6.80709	0.422158
$261$	4.99778	0.309355
$262$	17.3438	1.07151
$263$	2.70806	0.166986	0.0834929	−	0.996508i	$-0.473392\pi$
$263$	2.70806	0.166986	0.0834929	+	0.996508i	$0.473392\pi$
$264$	−5.92506	−0.364662
$265$	8.21996	0.504948
$266$	−27.5578	−1.68968
$267$	−7.50543	−0.459325
$268$	1.64434	0.100444
$269$	−9.02584	−0.550315	−0.275158	−	0.961399i	$-0.588730\pi$
$269$	−9.02584	−0.550315	−0.275158	+	0.961399i	$0.588730\pi$
$270$	2.36937	0.144195
$271$	−10.5394	−0.640221	−0.320111	−	0.947380i	$-0.603720\pi$
$271$	−10.5394	−0.640221	−0.320111	+	0.947380i	$0.603720\pi$
$272$	6.47611	0.392672
$273$	10.5803	0.640351
$274$	20.0510	1.21132
$275$	−3.63748	−0.219349
$276$	−3.33505	−0.200746
$277$	9.31793	0.559860	0.279930	−	0.960020i	$-0.409689\pi$
$277$	9.31793	0.559860	0.279930	+	0.960020i	$0.409689\pi$
$278$	10.0545	0.603030
$279$	−7.04303	−0.421655
$280$	8.72577	0.521464
$281$	6.58372	0.392752	0.196376	−	0.980529i	$-0.437083\pi$
$281$	6.58372	0.392752	0.196376	+	0.980529i	$0.437083\pi$
$282$	−1.68441	−0.100305
$283$	28.3400	1.68464	0.842318	−	0.538981i	$-0.181191\pi$
$283$	28.3400	1.68464	0.842318	+	0.538981i	$0.181191\pi$
$284$	12.3833	0.734811
$285$	−17.7299	−1.05023
$286$	−17.0224	−1.00656
$287$	11.5677	0.682821
$288$	1.00000	0.0589256
$289$	24.9401	1.46706
$290$	11.8416	0.695362
$291$	8.15885	0.478280
$292$	0.779919	0.0456413
$293$	−17.3983	−1.01642	−0.508211	−	0.861233i	$-0.669693\pi$
$293$	−17.3983	−1.01642	−0.508211	+	0.861233i	$0.669693\pi$
$294$	6.56254	0.382735
$295$	−25.5622	−1.48829
$296$	−8.68737	−0.504943
$297$	−5.92506	−0.343807
$298$	17.0239	0.986170
$299$	−9.58143	−0.554109
$300$	0.613915	0.0354444
$301$	−16.8108	−0.968960
$302$	19.9467	1.14780
$303$	−11.8823	−0.682620
$304$	−7.48297	−0.429178
$305$	13.7739	0.788690
$306$	6.47611	0.370215
$307$	−18.7757	−1.07159	−0.535794	−	0.844349i	$-0.679988\pi$
$307$	−18.7757	−1.07159	−0.535794	+	0.844349i	$0.679988\pi$
$308$	−21.8204	−1.24333
$309$	6.60780	0.375904
$310$	−16.6875	−0.947789
$311$	−27.2344	−1.54432	−0.772161	−	0.635427i	$-0.780824\pi$
$311$	−27.2344	−1.54432	−0.772161	+	0.635427i	$0.780824\pi$
$312$	2.87295	0.162649
$313$	9.02461	0.510101	0.255051	−	0.966928i	$-0.417908\pi$
$313$	9.02461	0.510101	0.255051	+	0.966928i	$0.417908\pi$
$314$	−23.3954	−1.32028
$315$	8.72577	0.491641
$316$	−15.0857	−0.848640
$317$	−11.3753	−0.638901	−0.319450	−	0.947603i	$-0.603498\pi$
$317$	−11.3753	−0.638901	−0.319450	+	0.947603i	$0.603498\pi$
$318$	3.46926	0.194546
$319$	−29.6121	−1.65796
$320$	2.36937	0.132452
$321$	17.8368	0.995555
$322$	−12.2821	−0.684455
$323$	−48.4606	−2.69642
$324$	1.00000	0.0555556
$325$	1.76375	0.0978352
$326$	−15.2069	−0.842231
$327$	0.117660	0.00650660
$328$	3.14107	0.173436
$329$	−6.20325	−0.341996
$330$	−14.0387	−0.772803
$331$	−3.04513	−0.167375	−0.0836877	−	0.996492i	$-0.526670\pi$
$331$	−3.04513	−0.167375	−0.0836877	+	0.996492i	$0.526670\pi$
$332$	5.37448	0.294963
$333$	−8.68737	−0.476065
$334$	8.85449	0.484496
$335$	3.89605	0.212864
$336$	3.68274	0.200910
$337$	20.1514	1.09772	0.548858	−	0.835915i	$-0.315063\pi$
$337$	20.1514	1.09772	0.548858	+	0.835915i	$0.315063\pi$
$338$	−4.74614	−0.258156
$339$	−5.47444	−0.297331
$340$	15.3443	0.832162
$341$	41.7304	2.25983
$342$	−7.48297	−0.404633
$343$	−1.61103	−0.0869877
$344$	−4.56477	−0.246116
$345$	−7.90196	−0.425427
$346$	−8.20552	−0.441131
$347$	12.8590	0.690306	0.345153	−	0.938546i	$-0.387827\pi$
$347$	12.8590	0.690306	0.345153	+	0.938546i	$0.387827\pi$
$348$	4.99778	0.267909
$349$	18.7442	1.00335	0.501677	−	0.865055i	$-0.332717\pi$
$349$	18.7442	1.00335	0.501677	+	0.865055i	$0.332717\pi$
$350$	2.26089	0.120850
$351$	2.87295	0.153347
$352$	−5.92506	−0.315807
$353$	−31.0339	−1.65177	−0.825885	−	0.563839i	$-0.809324\pi$
$353$	−31.0339	−1.65177	−0.825885	+	0.563839i	$0.809324\pi$
$354$	−10.7886	−0.573409
$355$	29.3405	1.55723
$356$	−7.50543	−0.397787
$357$	23.8498	1.26227
$358$	−5.28915	−0.279540
$359$	8.50064	0.448647	0.224323	−	0.974515i	$-0.427983\pi$
$359$	8.50064	0.448647	0.224323	+	0.974515i	$0.427983\pi$
$360$	2.36937	0.124877
$361$	36.9948	1.94710
$362$	−9.19861	−0.483468
$363$	24.1063	1.26525
$364$	10.5803	0.554560
$365$	1.84792	0.0967244
$366$	5.81331	0.303867
$367$	−0.248358	−0.0129642	−0.00648208	−	0.999979i	$-0.502063\pi$
$367$	−0.248358	−0.0129642	−0.00648208	+	0.999979i	$0.502063\pi$
$368$	−3.33505	−0.173851
$369$	3.14107	0.163517
$370$	−20.5836	−1.07009
$371$	12.7764	0.663316
$372$	−7.04303	−0.365164
$373$	2.17789	0.112767	0.0563833	−	0.998409i	$-0.482043\pi$
$373$	2.17789	0.112767	0.0563833	+	0.998409i	$0.482043\pi$
$374$	−38.3714	−1.98414
$375$	−10.3923	−0.536654
$376$	−1.68441	−0.0868669
$377$	14.3584	0.739494
$378$	3.68274	0.189419
$379$	11.7774	0.604966	0.302483	−	0.953155i	$-0.402185\pi$
$379$	11.7774	0.604966	0.302483	+	0.953155i	$0.402185\pi$
$380$	−17.7299	−0.909526
$381$	−1.05057	−0.0538221
$382$	6.41200	0.328067
$383$	5.81808	0.297290	0.148645	−	0.988891i	$-0.452509\pi$
$383$	5.81808	0.297290	0.148645	+	0.988891i	$0.452509\pi$
$384$	1.00000	0.0510310
$385$	−51.7007	−2.63491
$386$	−24.0509	−1.22416
$387$	−4.56477	−0.232040
$388$	8.15885	0.414203
$389$	8.66072	0.439116	0.219558	−	0.975599i	$-0.429539\pi$
$389$	8.66072	0.439116	0.219558	+	0.975599i	$0.429539\pi$
$390$	6.80709	0.344690
$391$	−21.5981	−1.09227
$392$	6.56254	0.331459
$393$	17.3438	0.874881
$394$	−24.3937	−1.22894
$395$	−35.7437	−1.79846
$396$	−5.92506	−0.297745
$397$	−11.4324	−0.573776	−0.286888	−	0.957964i	$-0.592621\pi$
$397$	−11.4324	−0.573776	−0.286888	+	0.957964i	$0.592621\pi$
$398$	−11.0011	−0.551434
$399$	−27.5578	−1.37962
$400$	0.613915	0.0306958
$401$	−0.885941	−0.0442418	−0.0221209	−	0.999755i	$-0.507042\pi$
$401$	−0.885941	−0.0442418	−0.0221209	+	0.999755i	$0.507042\pi$
$402$	1.64434	0.0820122
$403$	−20.2343	−1.00794
$404$	−11.8823	−0.591166
$405$	2.36937	0.117735
$406$	18.4055	0.913449
$407$	51.4732	2.55143
$408$	6.47611	0.320615
$409$	8.45734	0.418189	0.209094	−	0.977895i	$-0.432948\pi$
$409$	8.45734	0.418189	0.209094	+	0.977895i	$0.432948\pi$
$410$	7.44235	0.367552
$411$	20.0510	0.989041
$412$	6.60780	0.325543
$413$	−39.7317	−1.95507
$414$	−3.33505	−0.163909
$415$	12.7341	0.625093
$416$	2.87295	0.140858
$417$	10.0545	0.492372
$418$	44.3370	2.16860
$419$	11.5955	0.566480	0.283240	−	0.959049i	$-0.408591\pi$
$419$	11.5955	0.566480	0.283240	+	0.959049i	$0.408591\pi$
$420$	8.72577	0.425774
$421$	−30.1802	−1.47089	−0.735446	−	0.677583i	$-0.763027\pi$
$421$	−30.1802	−1.47089	−0.735446	+	0.677583i	$0.763027\pi$
$422$	1.26320	0.0614916
$423$	−1.68441	−0.0818989
$424$	3.46926	0.168482
$425$	3.97579	0.192854
$426$	12.3833	0.599971
$427$	21.4089	1.03605
$428$	17.8368	0.862176
$429$	−17.0224	−0.821850
$430$	−10.8156	−0.521576
$431$	22.9847	1.10713	0.553567	−	0.832805i	$-0.313266\pi$
$431$	22.9847	1.10713	0.553567	+	0.832805i	$0.313266\pi$
$432$	1.00000	0.0481125
$433$	−20.9595	−1.00725	−0.503625	−	0.863922i	$-0.668001\pi$
$433$	−20.9595	−1.00725	−0.503625	+	0.863922i	$0.668001\pi$
$434$	−25.9376	−1.24505
$435$	11.8416	0.567761
$436$	0.117660	0.00563488
$437$	24.9561	1.19381
$438$	0.779919	0.0372660
$439$	8.90504	0.425014	0.212507	−	0.977159i	$-0.431837\pi$
$439$	8.90504	0.425014	0.212507	+	0.977159i	$0.431837\pi$
$440$	−14.0387	−0.669267
$441$	6.56254	0.312502
$442$	18.6056	0.884977
$443$	−24.7773	−1.17721	−0.588603	−	0.808422i	$-0.700322\pi$
$443$	−24.7773	−1.17721	−0.588603	+	0.808422i	$0.700322\pi$
$444$	−8.68737	−0.412284
$445$	−17.7832	−0.843002
$446$	1.00000	0.0473514
$447$	17.0239	0.805204
$448$	3.68274	0.173993
$449$	33.3970	1.57610	0.788051	−	0.615610i	$-0.211090\pi$
$449$	33.3970	1.57610	0.788051	+	0.615610i	$0.211090\pi$
$450$	0.613915	0.0289402
$451$	−18.6110	−0.876358
$452$	−5.47444	−0.257496
$453$	19.9467	0.937176
$454$	−26.0600	−1.22306
$455$	25.0687	1.17524
$456$	−7.48297	−0.350422
$457$	−20.0787	−0.939241	−0.469620	−	0.882869i	$-0.655609\pi$
$457$	−20.0787	−0.939241	−0.469620	+	0.882869i	$0.655609\pi$
$458$	−8.20934	−0.383597
$459$	6.47611	0.302279
$460$	−7.90196	−0.368431
$461$	−7.41441	−0.345324	−0.172662	−	0.984981i	$-0.555237\pi$
$461$	−7.41441	−0.345324	−0.172662	+	0.984981i	$0.555237\pi$
$462$	−21.8204	−1.01518
$463$	17.9516	0.834283	0.417141	−	0.908842i	$-0.363032\pi$
$463$	17.9516	0.834283	0.417141	+	0.908842i	$0.363032\pi$
$464$	4.99778	0.232016
$465$	−16.6875	−0.773866
$466$	−9.30454	−0.431024
$467$	−11.1950	−0.518041	−0.259020	−	0.965872i	$-0.583400\pi$
$467$	−11.1950	−0.518041	−0.259020	+	0.965872i	$0.583400\pi$
$468$	2.87295	0.132802
$469$	6.05567	0.279625
$470$	−3.99100	−0.184091
$471$	−23.3954	−1.07800
$472$	−10.7886	−0.496587
$473$	27.0465	1.24360
$474$	−15.0857	−0.692911
$475$	−4.59391	−0.210783
$476$	23.8498	1.09315
$477$	3.46926	0.158846
$478$	12.5859	0.575666
$479$	26.1072	1.19287	0.596434	−	0.802662i	$-0.296584\pi$
$479$	26.1072	1.19287	0.596434	+	0.802662i	$0.296584\pi$
$480$	2.36937	0.108146
$481$	−24.9584	−1.13801
$482$	5.73022	0.261004
$483$	−12.2821	−0.558855
$484$	24.1063	1.09574
$485$	19.3313	0.877791
$486$	1.00000	0.0453609
$487$	6.41842	0.290846	0.145423	−	0.989370i	$-0.453546\pi$
$487$	6.41842	0.290846	0.145423	+	0.989370i	$0.453546\pi$
$488$	5.81331	0.263156
$489$	−15.2069	−0.687679
$490$	15.5491	0.702437
$491$	11.4128	0.515053	0.257526	−	0.966271i	$-0.417093\pi$
$491$	11.4128	0.515053	0.257526	+	0.966271i	$0.417093\pi$
$492$	3.14107	0.141610
$493$	32.3662	1.45770
$494$	−21.4982	−0.967251
$495$	−14.0387	−0.630991
$496$	−7.04303	−0.316241
$497$	45.6043	2.04563
$498$	5.37448	0.240836
$499$	−42.5880	−1.90650	−0.953251	−	0.302180i	$-0.902286\pi$
$499$	−42.5880	−1.90650	−0.953251	+	0.302180i	$0.902286\pi$
$500$	−10.3923	−0.464756
$501$	8.85449	0.395589
$502$	16.5457	0.738469
$503$	34.6176	1.54352	0.771762	−	0.635911i	$-0.219376\pi$
$503$	34.6176	1.54352	0.771762	+	0.635911i	$0.219376\pi$
$504$	3.68274	0.164042
$505$	−28.1536	−1.25282
$506$	19.7604	0.878455
$507$	−4.74614	−0.210784
$508$	−1.05057	−0.0466113
$509$	−5.93303	−0.262977	−0.131489	−	0.991318i	$-0.541976\pi$
$509$	−5.93303	−0.262977	−0.131489	+	0.991318i	$0.541976\pi$
$510$	15.3443	0.679458
$511$	2.87224	0.127060
$512$	1.00000	0.0441942
$513$	−7.48297	−0.330381
$514$	19.7435	0.870851
$515$	15.6563	0.689900
$516$	−4.56477	−0.200953
$517$	9.98024	0.438931
$518$	−31.9933	−1.40570
$519$	−8.20552	−0.360182
$520$	6.80709	0.298511
$521$	−1.56240	−0.0684498	−0.0342249	−	0.999414i	$-0.510896\pi$
$521$	−1.56240	−0.0684498	−0.0342249	+	0.999414i	$0.510896\pi$
$522$	4.99778	0.218747
$523$	25.2389	1.10362	0.551809	−	0.833970i	$-0.313938\pi$
$523$	25.2389	1.10362	0.551809	+	0.833970i	$0.313938\pi$
$524$	17.3438	0.757669
$525$	2.26089	0.0986733
$526$	2.70806	0.118077
$527$	−45.6115	−1.98687
$528$	−5.92506	−0.257855
$529$	−11.8775	−0.516411
$530$	8.21996	0.357052
$531$	−10.7886	−0.468186
$532$	−27.5578	−1.19478
$533$	9.02414	0.390879
$534$	−7.50543	−0.324792
$535$	42.2621	1.82715
$536$	1.64434	0.0710247
$537$	−5.28915	−0.228244
$538$	−9.02584	−0.389132
$539$	−38.8835	−1.67483
$540$	2.36937	0.101961
$541$	40.4155	1.73760	0.868798	−	0.495166i	$-0.164893\pi$
$541$	40.4155	1.73760	0.868798	+	0.495166i	$0.164893\pi$
$542$	−10.5394	−0.452705
$543$	−9.19861	−0.394750
$544$	6.47611	0.277661
$545$	0.278779	0.0119416
$546$	10.5803	0.452796
$547$	23.8714	1.02067	0.510333	−	0.859977i	$-0.329522\pi$
$547$	23.8714	1.02067	0.510333	+	0.859977i	$0.329522\pi$
$548$	20.0510	0.856534
$549$	5.81331	0.248106
$550$	−3.63748	−0.155103
$551$	−37.3982	−1.59322
$552$	−3.33505	−0.141949
$553$	−55.5568	−2.36252
$554$	9.31793	0.395881
$555$	−20.5836	−0.873725
$556$	10.0545	0.426407
$557$	25.8236	1.09418	0.547091	−	0.837073i	$-0.315735\pi$
$557$	25.8236	1.09418	0.547091	+	0.837073i	$0.315735\pi$
$558$	−7.04303	−0.298155
$559$	−13.1144	−0.554678
$560$	8.72577	0.368731
$561$	−38.3714	−1.62004
$562$	6.58372	0.277717
$563$	−0.735710	−0.0310065	−0.0155032	−	0.999880i	$-0.504935\pi$
$563$	−0.735710	−0.0310065	−0.0155032	+	0.999880i	$0.504935\pi$
$564$	−1.68441	−0.0709266
$565$	−12.9710	−0.545693
$566$	28.3400	1.19122
$567$	3.68274	0.154660
$568$	12.3833	0.519590
$569$	0.00122694	5.14361e−5 0	2.57181e−5	−	1.00000i	$-0.499992\pi$
$569$	0.00122694	5.14361e−5 0	2.57181e−5		1.00000i	$0.499992\pi$
$570$	−17.7299	−0.742625
$571$	−24.8196	−1.03867	−0.519334	−	0.854571i	$-0.673820\pi$
$571$	−24.8196	−1.03867	−0.519334	+	0.854571i	$0.673820\pi$
$572$	−17.0224	−0.711743
$573$	6.41200	0.267865
$574$	11.5677	0.482827
$575$	−2.04744	−0.0853840
$576$	1.00000	0.0416667
$577$	−9.07498	−0.377797	−0.188898	−	0.981997i	$-0.560492\pi$
$577$	−9.07498	−0.377797	−0.188898	+	0.981997i	$0.560492\pi$
$578$	24.9401	1.03737
$579$	−24.0509	−0.999523
$580$	11.8416	0.491695
$581$	19.7928	0.821143
$582$	8.15885	0.338195
$583$	−20.5556	−0.851325
$584$	0.779919	0.0322733
$585$	6.80709	0.281439
$586$	−17.3983	−0.718718
$587$	16.2962	0.672614	0.336307	−	0.941752i	$-0.390822\pi$
$587$	16.2962	0.672614	0.336307	+	0.941752i	$0.390822\pi$
$588$	6.56254	0.270635
$589$	52.7028	2.17158
$590$	−25.5622	−1.05238
$591$	−24.3937	−1.00342
$592$	−8.68737	−0.357049
$593$	−32.2541	−1.32452	−0.662259	−	0.749275i	$-0.730402\pi$
$593$	−32.2541	−1.32452	−0.662259	+	0.749275i	$0.730402\pi$
$594$	−5.92506	−0.243108
$595$	56.5091	2.31665
$596$	17.0239	0.697327
$597$	−11.0011	−0.450244
$598$	−9.58143	−0.391814
$599$	−9.74849	−0.398313	−0.199156	−	0.979968i	$-0.563820\pi$
$599$	−9.74849	−0.398313	−0.199156	+	0.979968i	$0.563820\pi$
$600$	0.613915	0.0250630
$601$	37.6795	1.53698	0.768489	−	0.639863i	$-0.221009\pi$
$601$	37.6795	1.53698	0.768489	+	0.639863i	$0.221009\pi$
$602$	−16.8108	−0.685158
$603$	1.64434	0.0669627
$604$	19.9467	0.811618
$605$	57.1168	2.32213
$606$	−11.8823	−0.482685
$607$	−27.5216	−1.11707	−0.558533	−	0.829482i	$-0.688636\pi$
$607$	−27.5216	−1.11707	−0.558533	+	0.829482i	$0.688636\pi$
$608$	−7.48297	−0.303475
$609$	18.4055	0.745828
$610$	13.7739	0.557688
$611$	−4.83924	−0.195775
$612$	6.47611	0.261781
$613$	11.3228	0.457325	0.228663	−	0.973506i	$-0.426565\pi$
$613$	11.3228	0.457325	0.228663	+	0.973506i	$0.426565\pi$
$614$	−18.7757	−0.757728
$615$	7.44235	0.300105
$616$	−21.8204	−0.879170
$617$	−9.65337	−0.388630	−0.194315	−	0.980939i	$-0.562248\pi$
$617$	−9.65337	−0.388630	−0.194315	+	0.980939i	$0.562248\pi$
$618$	6.60780	0.265805
$619$	35.6694	1.43367	0.716836	−	0.697241i	$-0.245589\pi$
$619$	35.6694	1.43367	0.716836	+	0.697241i	$0.245589\pi$
$620$	−16.6875	−0.670188
$621$	−3.33505	−0.133831
$622$	−27.2344	−1.09200
$623$	−27.6405	−1.10739
$624$	2.87295	0.115010
$625$	−27.6927	−1.10771
$626$	9.02461	0.360696
$627$	44.3370	1.77065
$628$	−23.3954	−0.933577
$629$	−56.2604	−2.24325
$630$	8.72577	0.347643
$631$	−30.2494	−1.20421	−0.602105	−	0.798417i	$-0.705671\pi$
$631$	−30.2494	−1.20421	−0.602105	+	0.798417i	$0.705671\pi$
$632$	−15.0857	−0.600079
$633$	1.26320	0.0502077
$634$	−11.3753	−0.451771
$635$	−2.48918	−0.0987801
$636$	3.46926	0.137565
$637$	18.8539	0.747018
$638$	−29.6121	−1.17236
$639$	12.3833	0.489874
$640$	2.36937	0.0936576
$641$	35.1379	1.38786	0.693932	−	0.720041i	$-0.255877\pi$
$641$	35.1379	1.38786	0.693932	+	0.720041i	$0.255877\pi$
$642$	17.8368	0.703964
$643$	1.47593	0.0582049	0.0291024	−	0.999576i	$-0.490735\pi$
$643$	1.47593	0.0582049	0.0291024	+	0.999576i	$0.490735\pi$
$644$	−12.2821	−0.483982
$645$	−10.8156	−0.425865
$646$	−48.4606	−1.90666
$647$	29.2534	1.15007	0.575035	−	0.818129i	$-0.304988\pi$
$647$	29.2534	1.15007	0.575035	+	0.818129i	$0.304988\pi$
$648$	1.00000	0.0392837
$649$	63.9232	2.50921
$650$	1.76375	0.0691800
$651$	−25.9376	−1.01658
$652$	−15.2069	−0.595548
$653$	43.9250	1.71892	0.859459	−	0.511205i	$-0.170801\pi$
$653$	43.9250	1.71892	0.859459	+	0.511205i	$0.170801\pi$
$654$	0.117660	0.00460086
$655$	41.0940	1.60567
$656$	3.14107	0.122638
$657$	0.779919	0.0304275
$658$	−6.20325	−0.241828
$659$	28.3329	1.10369	0.551846	−	0.833946i	$-0.313924\pi$
$659$	28.3329	1.10369	0.551846	+	0.833946i	$0.313924\pi$
$660$	−14.0387	−0.546454
$661$	−11.8666	−0.461557	−0.230779	−	0.973006i	$-0.574127\pi$
$661$	−11.8666	−0.461557	−0.230779	+	0.973006i	$0.574127\pi$
$662$	−3.04513	−0.118352
$663$	18.6056	0.722581
$664$	5.37448	0.208570
$665$	−65.2946	−2.53202
$666$	−8.68737	−0.336629
$667$	−16.6678	−0.645381
$668$	8.85449	0.342590
$669$	1.00000	0.0386622
$670$	3.89605	0.150518
$671$	−34.4442	−1.32970
$672$	3.68274	0.142065
$673$	−22.4795	−0.866521	−0.433261	−	0.901269i	$-0.642637\pi$
$673$	−22.4795	−0.866521	−0.433261	+	0.901269i	$0.642637\pi$
$674$	20.1514	0.776203
$675$	0.613915	0.0236296
$676$	−4.74614	−0.182544
$677$	31.3067	1.20322	0.601608	−	0.798792i	$-0.294527\pi$
$677$	31.3067	1.20322	0.601608	+	0.798792i	$0.294527\pi$
$678$	−5.47444	−0.210245
$679$	30.0469	1.15309
$680$	15.3443	0.588428
$681$	−26.0600	−0.998623
$682$	41.7304	1.59794
$683$	−5.35227	−0.204799	−0.102399	−	0.994743i	$-0.532652\pi$
$683$	−5.35227	−0.204799	−0.102399	+	0.994743i	$0.532652\pi$
$684$	−7.48297	−0.286119
$685$	47.5081	1.81519
$686$	−1.61103	−0.0615096
$687$	−8.20934	−0.313206
$688$	−4.56477	−0.174030
$689$	9.96702	0.379713
$690$	−7.90196	−0.300823
$691$	22.3421	0.849932	0.424966	−	0.905209i	$-0.360286\pi$
$691$	22.3421	0.849932	0.424966	+	0.905209i	$0.360286\pi$
$692$	−8.20552	−0.311927
$693$	−21.8204	−0.828890
$694$	12.8590	0.488120
$695$	23.8229	0.903653
$696$	4.99778	0.189440
$697$	20.3419	0.770505
$698$	18.7442	0.709478
$699$	−9.30454	−0.351930
$700$	2.26089	0.0854535
$701$	−6.44431	−0.243398	−0.121699	−	0.992567i	$-0.538834\pi$
$701$	−6.44431	−0.243398	−0.121699	+	0.992567i	$0.538834\pi$
$702$	2.87295	0.108433
$703$	65.0073	2.45180
$704$	−5.92506	−0.223309
$705$	−3.99100	−0.150310
$706$	−31.0339	−1.16798
$707$	−43.7593	−1.64574
$708$	−10.7886	−0.405461
$709$	−8.26315	−0.310329	−0.155165	−	0.987889i	$-0.549591\pi$
$709$	−8.26315	−0.310329	−0.155165	+	0.987889i	$0.549591\pi$
$710$	29.3405	1.10113
$711$	−15.0857	−0.565760
$712$	−7.50543	−0.281278
$713$	23.4888	0.879664
$714$	23.8498	0.892557
$715$	−40.3324	−1.50835
$716$	−5.28915	−0.197665
$717$	12.5859	0.470029
$718$	8.50064	0.317241
$719$	−9.84786	−0.367263	−0.183632	−	0.982995i	$-0.558785\pi$
$719$	−9.84786	−0.367263	−0.183632	+	0.982995i	$0.558785\pi$
$720$	2.36937	0.0883012
$721$	24.3348	0.906274
$722$	36.9948	1.37681
$723$	5.73022	0.213109
$724$	−9.19861	−0.341864
$725$	3.06821	0.113951
$726$	24.1063	0.894670
$727$	47.7211	1.76988	0.884938	−	0.465709i	$-0.154201\pi$
$727$	47.7211	1.76988	0.884938	+	0.465709i	$0.154201\pi$
$728$	10.5803	0.392133
$729$	1.00000	0.0370370
$730$	1.84792	0.0683945
$731$	−29.5619	−1.09339
$732$	5.81331	0.214866
$733$	25.7113	0.949668	0.474834	−	0.880075i	$-0.342508\pi$
$733$	25.7113	0.949668	0.474834	+	0.880075i	$0.342508\pi$
$734$	−0.248358	−0.00916705
$735$	15.5491	0.573537
$736$	−3.33505	−0.122931
$737$	−9.74281	−0.358881
$738$	3.14107	0.115624
$739$	−4.84445	−0.178206	−0.0891030	−	0.996022i	$-0.528400\pi$
$739$	−4.84445	−0.178206	−0.0891030	+	0.996022i	$0.528400\pi$
$740$	−20.5836	−0.756668
$741$	−21.4982	−0.789757
$742$	12.7764	0.469035
$743$	5.97474	0.219192	0.109596	−	0.993976i	$-0.465044\pi$
$743$	5.97474	0.219192	0.109596	+	0.993976i	$0.465044\pi$
$744$	−7.04303	−0.258210
$745$	40.3360	1.47780
$746$	2.17789	0.0797381
$747$	5.37448	0.196642
$748$	−38.3714	−1.40300
$749$	65.6883	2.40020
$750$	−10.3923	−0.379472
$751$	−47.6975	−1.74051	−0.870253	−	0.492605i	$-0.836045\pi$
$751$	−47.6975	−1.74051	−0.870253	+	0.492605i	$0.836045\pi$
$752$	−1.68441	−0.0614242
$753$	16.5457	0.602958
$754$	14.3584	0.522901
$755$	47.2610	1.72001
$756$	3.68274	0.133940
$757$	51.2494	1.86269	0.931346	−	0.364136i	$-0.118636\pi$
$757$	51.2494	1.86269	0.931346	+	0.364136i	$0.118636\pi$
$758$	11.7774	0.427775
$759$	19.7604	0.717255
$760$	−17.7299	−0.643132
$761$	−24.5511	−0.889977	−0.444989	−	0.895536i	$-0.646792\pi$
$761$	−24.5511	−0.889977	−0.444989	+	0.895536i	$0.646792\pi$
$762$	−1.05057	−0.0380580
$763$	0.433310	0.0156869
$764$	6.41200	0.231978
$765$	15.3443	0.554775
$766$	5.81808	0.210216
$767$	−30.9952	−1.11917
$768$	1.00000	0.0360844
$769$	−44.5326	−1.60589	−0.802943	−	0.596055i	$-0.796734\pi$
$769$	−44.5326	−1.60589	−0.802943	+	0.596055i	$0.796734\pi$
$770$	−51.7007	−1.86316
$771$	19.7435	0.711047
$772$	−24.0509	−0.865612
$773$	26.7048	0.960505	0.480253	−	0.877130i	$-0.340545\pi$
$773$	26.7048	0.960505	0.480253	+	0.877130i	$0.340545\pi$
$774$	−4.56477	−0.164077
$775$	−4.32382	−0.155316
$776$	8.15885	0.292886
$777$	−31.9933	−1.14775
$778$	8.66072	0.310502
$779$	−23.5045	−0.842137
$780$	6.80709	0.243733
$781$	−73.3715	−2.62544
$782$	−21.5981	−0.772348
$783$	4.99778	0.178606
$784$	6.56254	0.234377
$785$	−55.4323	−1.97846
$786$	17.3438	0.618634
$787$	39.3842	1.40389	0.701947	−	0.712229i	$-0.252314\pi$
$787$	39.3842	1.40389	0.701947	+	0.712229i	$0.252314\pi$
$788$	−24.3937	−0.868991
$789$	2.70806	0.0964093
$790$	−35.7437	−1.27170
$791$	−20.1609	−0.716839
$792$	−5.92506	−0.210538
$793$	16.7014	0.593083
$794$	−11.4324	−0.405721
$795$	8.21996	0.291532
$796$	−11.0011	−0.389923
$797$	29.6090	1.04880	0.524402	−	0.851471i	$-0.324289\pi$
$797$	29.6090	1.04880	0.524402	+	0.851471i	$0.324289\pi$
$798$	−27.5578	−0.975536
$799$	−10.9084	−0.385913
$800$	0.613915	0.0217052
$801$	−7.50543	−0.265191
$802$	−0.885941	−0.0312837
$803$	−4.62107	−0.163074
$804$	1.64434	0.0579914
$805$	−29.1008	−1.02567
$806$	−20.2343	−0.712723
$807$	−9.02584	−0.317725
$808$	−11.8823	−0.418018
$809$	−40.4725	−1.42294	−0.711469	−	0.702717i	$-0.751970\pi$
$809$	−40.4725	−1.42294	−0.711469	+	0.702717i	$0.751970\pi$
$810$	2.36937	0.0832512
$811$	10.7485	0.377430	0.188715	−	0.982032i	$-0.439568\pi$
$811$	10.7485	0.377430	0.188715	+	0.982032i	$0.439568\pi$
$812$	18.4055	0.645906
$813$	−10.5394	−0.369632
$814$	51.4732	1.80413
$815$	−36.0307	−1.26210
$816$	6.47611	0.226709
$817$	34.1580	1.19504
$818$	8.45734	0.295704
$819$	10.5803	0.369707
$820$	7.44235	0.259898
$821$	−15.5359	−0.542207	−0.271104	−	0.962550i	$-0.587389\pi$
$821$	−15.5359	−0.542207	−0.271104	+	0.962550i	$0.587389\pi$
$822$	20.0510	0.699357
$823$	43.6204	1.52051	0.760257	−	0.649623i	$-0.225073\pi$
$823$	43.6204	1.52051	0.760257	+	0.649623i	$0.225073\pi$
$824$	6.60780	0.230193
$825$	−3.63748	−0.126641
$826$	−39.7317	−1.38244
$827$	−32.9828	−1.14693	−0.573463	−	0.819232i	$-0.694400\pi$
$827$	−32.9828	−1.14693	−0.573463	+	0.819232i	$0.694400\pi$
$828$	−3.33505	−0.115901
$829$	−0.0750551	−0.00260677	−0.00130339	−	0.999999i	$-0.500415\pi$
$829$	−0.0750551	−0.00260677	−0.00130339	+	0.999999i	$0.500415\pi$
$830$	12.7341	0.442008
$831$	9.31793	0.323235
$832$	2.87295	0.0996017
$833$	42.4998	1.47253
$834$	10.0545	0.348159
$835$	20.9796	0.726028
$836$	44.3370	1.53343
$837$	−7.04303	−0.243443
$838$	11.5955	0.400562
$839$	42.8905	1.48074	0.740372	−	0.672197i	$-0.234649\pi$
$839$	42.8905	1.48074	0.740372	+	0.672197i	$0.234649\pi$
$840$	8.72577	0.301067
$841$	−4.02221	−0.138697
$842$	−30.1802	−1.04008
$843$	6.58372	0.226755
$844$	1.26320	0.0434811
$845$	−11.2454	−0.386852
$846$	−1.68441	−0.0579113
$847$	88.7772	3.05042
$848$	3.46926	0.119135
$849$	28.3400	0.972625
$850$	3.97579	0.136368
$851$	28.9728	0.993174
$852$	12.3833	0.424243
$853$	−10.6592	−0.364964	−0.182482	−	0.983209i	$-0.558413\pi$
$853$	−10.6592	−0.364964	−0.182482	+	0.983209i	$0.558413\pi$
$854$	21.4089	0.732597
$855$	−17.7299	−0.606351
$856$	17.8368	0.609650
$857$	−13.7715	−0.470424	−0.235212	−	0.971944i	$-0.575578\pi$
$857$	−13.7715	−0.470424	−0.235212	+	0.971944i	$0.575578\pi$
$858$	−17.0224	−0.581136
$859$	37.7719	1.28876	0.644381	−	0.764705i	$-0.277115\pi$
$859$	37.7719	1.28876	0.644381	+	0.764705i	$0.277115\pi$
$860$	−10.8156	−0.368810
$861$	11.5677	0.394227
$862$	22.9847	0.782861
$863$	13.1695	0.448294	0.224147	−	0.974555i	$-0.428040\pi$
$863$	13.1695	0.448294	0.224147	+	0.974555i	$0.428040\pi$
$864$	1.00000	0.0340207
$865$	−19.4419	−0.661045
$866$	−20.9595	−0.712234
$867$	24.9401	0.847009
$868$	−25.9376	−0.880380
$869$	89.3839	3.03214
$870$	11.8416	0.401467
$871$	4.72411	0.160070
$872$	0.117660	0.00398446
$873$	8.15885	0.276135
$874$	24.9561	0.844151
$875$	−38.2719	−1.29383
$876$	0.779919	0.0263510
$877$	−43.1577	−1.45733	−0.728667	−	0.684869i	$-0.759860\pi$
$877$	−43.1577	−1.45733	−0.728667	+	0.684869i	$0.759860\pi$
$878$	8.90504	0.300531
$879$	−17.3983	−0.586831
$880$	−14.0387	−0.473243
$881$	43.6302	1.46994	0.734970	−	0.678100i	$-0.237196\pi$
$881$	43.6302	1.46994	0.734970	+	0.678100i	$0.237196\pi$
$882$	6.56254	0.220972
$883$	−46.2461	−1.55631	−0.778153	−	0.628075i	$-0.783843\pi$
$883$	−46.2461	−1.55631	−0.778153	+	0.628075i	$0.783843\pi$
$884$	18.6056	0.625773
$885$	−25.5622	−0.859266
$886$	−24.7773	−0.832410
$887$	−34.2104	−1.14867	−0.574337	−	0.818619i	$-0.694740\pi$
$887$	−34.2104	−1.14867	−0.574337	+	0.818619i	$0.694740\pi$
$888$	−8.68737	−0.291529
$889$	−3.86896	−0.129761
$890$	−17.7832	−0.596093
$891$	−5.92506	−0.198497
$892$	1.00000	0.0334825
$893$	12.6044	0.421790
$894$	17.0239	0.569365
$895$	−12.5320	−0.418897
$896$	3.68274	0.123032
$897$	−9.58143	−0.319915
$898$	33.3970	1.11447
$899$	−35.1995	−1.17397
$900$	0.613915	0.0204638
$901$	22.4673	0.748495
$902$	−18.6110	−0.619679
$903$	−16.8108	−0.559429
$904$	−5.47444	−0.182077
$905$	−21.7949	−0.724488
$906$	19.9467	0.662684
$907$	−27.2409	−0.904520	−0.452260	−	0.891886i	$-0.649382\pi$
$907$	−27.2409	−0.904520	−0.452260	+	0.891886i	$0.649382\pi$
$908$	−26.0600	−0.864833
$909$	−11.8823	−0.394111
$910$	25.0687	0.831020
$911$	12.7823	0.423496	0.211748	−	0.977324i	$-0.432084\pi$
$911$	12.7823	0.423496	0.211748	+	0.977324i	$0.432084\pi$
$912$	−7.48297	−0.247786
$913$	−31.8441	−1.05389
$914$	−20.0787	−0.664143
$915$	13.7739	0.455351
$916$	−8.20934	−0.271244
$917$	63.8728	2.10927
$918$	6.47611	0.213744
$919$	34.5982	1.14129	0.570645	−	0.821197i	$-0.306693\pi$
$919$	34.5982	1.14129	0.570645	+	0.821197i	$0.306693\pi$
$920$	−7.90196	−0.260520
$921$	−18.7757	−0.618682
$922$	−7.41441	−0.244181
$923$	35.5765	1.17102
$924$	−21.8204	−0.717839
$925$	−5.33331	−0.175358
$926$	17.9516	0.589927
$927$	6.60780	0.217028
$928$	4.99778	0.164060
$929$	13.8858	0.455578	0.227789	−	0.973710i	$-0.426850\pi$
$929$	13.8858	0.455578	0.227789	+	0.973710i	$0.426850\pi$
$930$	−16.6875	−0.547206
$931$	−49.1073	−1.60943
$932$	−9.30454	−0.304780
$933$	−27.2344	−0.891615
$934$	−11.1950	−0.366310
$935$	−90.9160	−2.97327
$936$	2.87295	0.0939054
$937$	−4.32232	−0.141204	−0.0706020	−	0.997505i	$-0.522492\pi$
$937$	−4.32232	−0.141204	−0.0706020	+	0.997505i	$0.522492\pi$
$938$	6.05567	0.197725
$939$	9.02461	0.294507
$940$	−3.99100	−0.130172
$941$	25.0093	0.815281	0.407641	−	0.913142i	$-0.366352\pi$
$941$	25.0093	0.815281	0.407641	+	0.913142i	$0.366352\pi$
$942$	−23.3954	−0.762262
$943$	−10.4756	−0.341133
$944$	−10.7886	−0.351140
$945$	8.72577	0.283849
$946$	27.0465	0.879358
$947$	4.70052	0.152746	0.0763732	−	0.997079i	$-0.475666\pi$
$947$	4.70052	0.152746	0.0763732	+	0.997079i	$0.475666\pi$
$948$	−15.0857	−0.489962
$949$	2.24067	0.0727352
$950$	−4.59391	−0.149046
$951$	−11.3753	−0.368870
$952$	23.8498	0.772977
$953$	−21.3837	−0.692684	−0.346342	−	0.938108i	$-0.612576\pi$
$953$	−21.3837	−0.692684	−0.346342	+	0.938108i	$0.612576\pi$
$954$	3.46926	0.112321
$955$	15.1924	0.491615
$956$	12.5859	0.407057
$957$	−29.6121	−0.957224
$958$	26.1072	0.843486
$959$	73.8424	2.38449
$960$	2.36937	0.0764711
$961$	18.6043	0.600137
$962$	−24.9584	−0.804691
$963$	17.8368	0.574784
$964$	5.73022	0.184558
$965$	−56.9856	−1.83443
$966$	−12.2821	−0.395170
$967$	0.971055	0.0312270	0.0156135	−	0.999878i	$-0.495030\pi$
$967$	0.971055	0.0312270	0.0156135	+	0.999878i	$0.495030\pi$
$968$	24.1063	0.774807
$969$	−48.4606	−1.55678
$970$	19.3313	0.620692
$971$	−59.2611	−1.90178	−0.950890	−	0.309530i	$-0.899828\pi$
$971$	−59.2611	−1.90178	−0.950890	+	0.309530i	$0.899828\pi$
$972$	1.00000	0.0320750
$973$	37.0281	1.18707
$974$	6.41842	0.205659
$975$	1.76375	0.0564852
$976$	5.81331	0.186080
$977$	39.0005	1.24774	0.623868	−	0.781529i	$-0.285560\pi$
$977$	39.0005	1.24774	0.623868	+	0.781529i	$0.285560\pi$
$978$	−15.2069	−0.486263
$979$	44.4701	1.42127
$980$	15.5491	0.496698
$981$	0.117660	0.00375658
$982$	11.4128	0.364197
$983$	−47.7568	−1.52321	−0.761603	−	0.648044i	$-0.775587\pi$
$983$	−47.7568	−1.52321	−0.761603	+	0.648044i	$0.775587\pi$
$984$	3.14107	0.100134
$985$	−57.7978	−1.84159
$986$	32.3662	1.03075
$987$	−6.20325	−0.197451
$988$	−21.4982	−0.683950
$989$	15.2237	0.484086
$990$	−14.0387	−0.446178
$991$	−8.00178	−0.254185	−0.127092	−	0.991891i	$-0.540564\pi$
$991$	−8.00178	−0.254185	−0.127092	+	0.991891i	$0.540564\pi$
$992$	−7.04303	−0.223616
$993$	−3.04513	−0.0966342
$994$	45.6043	1.44648
$995$	−26.0656	−0.826335
$996$	5.37448	0.170297
$997$	19.3403	0.612514	0.306257	−	0.951949i	$-0.400923\pi$
$997$	19.3403	0.612514	0.306257	+	0.951949i	$0.400923\pi$
$998$	−42.5880	−1.34810
$999$	−8.68737	−0.274856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.i.1.5	✓	6
3.2	odd	2		4014.2.a.s.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.i.1.5	✓	6	1.1	even	1	trivial
4014.2.a.s.1.2		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.36937 q^{5} +1.00000 q^{6} +3.68274 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.36937 q^{10} -5.92506 q^{11} +1.00000 q^{12} +2.87295 q^{13} +3.68274 q^{14} +2.36937 q^{15} +1.00000 q^{16} +6.47611 q^{17} +1.00000 q^{18} -7.48297 q^{19} +2.36937 q^{20} +3.68274 q^{21} -5.92506 q^{22} -3.33505 q^{23} +1.00000 q^{24} +0.613915 q^{25} +2.87295 q^{26} +1.00000 q^{27} +3.68274 q^{28} +4.99778 q^{29} +2.36937 q^{30} -7.04303 q^{31} +1.00000 q^{32} -5.92506 q^{33} +6.47611 q^{34} +8.72577 q^{35} +1.00000 q^{36} -8.68737 q^{37} -7.48297 q^{38} +2.87295 q^{39} +2.36937 q^{40} +3.14107 q^{41} +3.68274 q^{42} -4.56477 q^{43} -5.92506 q^{44} +2.36937 q^{45} -3.33505 q^{46} -1.68441 q^{47} +1.00000 q^{48} +6.56254 q^{49} +0.613915 q^{50} +6.47611 q^{51} +2.87295 q^{52} +3.46926 q^{53} +1.00000 q^{54} -14.0387 q^{55} +3.68274 q^{56} -7.48297 q^{57} +4.99778 q^{58} -10.7886 q^{59} +2.36937 q^{60} +5.81331 q^{61} -7.04303 q^{62} +3.68274 q^{63} +1.00000 q^{64} +6.80709 q^{65} -5.92506 q^{66} +1.64434 q^{67} +6.47611 q^{68} -3.33505 q^{69} +8.72577 q^{70} +12.3833 q^{71} +1.00000 q^{72} +0.779919 q^{73} -8.68737 q^{74} +0.613915 q^{75} -7.48297 q^{76} -21.8204 q^{77} +2.87295 q^{78} -15.0857 q^{79} +2.36937 q^{80} +1.00000 q^{81} +3.14107 q^{82} +5.37448 q^{83} +3.68274 q^{84} +15.3443 q^{85} -4.56477 q^{86} +4.99778 q^{87} -5.92506 q^{88} -7.50543 q^{89} +2.36937 q^{90} +10.5803 q^{91} -3.33505 q^{92} -7.04303 q^{93} -1.68441 q^{94} -17.7299 q^{95} +1.00000 q^{96} +8.15885 q^{97} +6.56254 q^{98} -5.92506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 6 q^{5} + 6 q^{6} + 5 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{10} + q^{11} + 6 q^{12} + 6 q^{13} + 5 q^{14} + 6 q^{15} + 6 q^{16} + 10 q^{17} + 6 q^{18} - 4 q^{19} + 6 q^{20}+ \cdots + q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 6 * q^5 + 6 * q^6 + 5 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^10 + q^11 + 6 * q^12 + 6 * q^13 + 5 * q^14 + 6 * q^15 + 6 * q^16 + 10 * q^17 + 6 * q^18 - 4 * q^19 + 6 * q^20 + 5 * q^21 + q^22 + 2 * q^23 + 6 * q^24 + 6 * q^26 + 6 * q^27 + 5 * q^28 + 6 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + q^33 + 10 * q^34 - 2 * q^35 + 6 * q^36 + q^37 - 4 * q^38 + 6 * q^39 + 6 * q^40 + 12 * q^41 + 5 * q^42 - 11 * q^43 + q^44 + 6 * q^45 + 2 * q^46 + 5 * q^47 + 6 * q^48 - q^49 + 10 * q^51 + 6 * q^52 + 4 * q^53 + 6 * q^54 - 15 * q^55 + 5 * q^56 - 4 * q^57 + 6 * q^58 + q^59 + 6 * q^60 - 8 * q^61 - 5 * q^62 + 5 * q^63 + 6 * q^64 + 5 * q^65 + q^66 - 6 * q^67 + 10 * q^68 + 2 * q^69 - 2 * q^70 + q^71 + 6 * q^72 - 10 * q^73 + q^74 - 4 * q^76 - 8 * q^77 + 6 * q^78 - 10 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 6 * q^83 + 5 * q^84 - 2 * q^85 - 11 * q^86 + 6 * q^87 + q^88 - 3 * q^89 + 6 * q^90 - 16 * q^91 + 2 * q^92 - 5 * q^93 + 5 * q^94 - 10 * q^95 + 6 * q^96 + 3 * q^97 - q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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