LMFDB - Embedded newform 169.10.a.g.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$169 = 13^{2}$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	169.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:	$87.0410563117$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	169.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+35.7320 q^{2} -157.443 q^{3} +764.774 q^{4} +2363.03 q^{5} -5625.74 q^{6} +3406.89 q^{7} +9032.12 q^{8} +5105.19 q^{9} +84435.6 q^{10} -85358.9 q^{11} -120408. q^{12} +121735. q^{14} -372041. q^{15} -68828.8 q^{16} -173806. q^{17} +182419. q^{18} -918491. q^{19} +1.80718e6 q^{20} -536389. q^{21} -3.05004e6 q^{22} -1.02043e6 q^{23} -1.42204e6 q^{24} +3.63077e6 q^{25} +2.29517e6 q^{27} +2.60550e6 q^{28} +4.16258e6 q^{29} -1.32938e7 q^{30} -1.75360e6 q^{31} -7.08384e6 q^{32} +1.34391e7 q^{33} -6.21045e6 q^{34} +8.05056e6 q^{35} +3.90432e6 q^{36} +8.56572e6 q^{37} -3.28195e7 q^{38} +2.13431e7 q^{40} -1.45701e7 q^{41} -1.91663e7 q^{42} -3.74371e7 q^{43} -6.52803e7 q^{44} +1.20637e7 q^{45} -3.64620e7 q^{46} +2.97614e6 q^{47} +1.08366e7 q^{48} -2.87467e7 q^{49} +1.29734e8 q^{50} +2.73645e7 q^{51} +1.44169e7 q^{53} +8.20109e7 q^{54} -2.01705e8 q^{55} +3.07714e7 q^{56} +1.44610e8 q^{57} +1.48737e8 q^{58} +1.24760e8 q^{59} -2.84527e8 q^{60} -3.77625e7 q^{61} -6.26594e7 q^{62} +1.73928e7 q^{63} -2.17879e8 q^{64} +4.80207e8 q^{66} -2.21634e8 q^{67} -1.32923e8 q^{68} +1.60659e8 q^{69} +2.87663e8 q^{70} +3.19651e7 q^{71} +4.61107e7 q^{72} +8.39854e7 q^{73} +3.06070e8 q^{74} -5.71638e8 q^{75} -7.02438e8 q^{76} -2.90808e8 q^{77} -1.56307e8 q^{79} -1.62644e8 q^{80} -4.61843e8 q^{81} -5.20618e8 q^{82} -2.71578e8 q^{83} -4.10217e8 q^{84} -4.10709e8 q^{85} -1.33770e9 q^{86} -6.55367e8 q^{87} -7.70972e8 q^{88} -2.91190e8 q^{89} +4.31060e8 q^{90} -7.80398e8 q^{92} +2.76091e8 q^{93} +1.06343e8 q^{94} -2.17042e9 q^{95} +1.11530e9 q^{96} +1.32475e9 q^{97} -1.02718e9 q^{98} -4.35774e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$27 q - 65 q^{2} + q^{3} + 7169 q^{4} - 3238 q^{5} - 8490 q^{6} - 17378 q^{7} - 54204 q^{8} + 191118 q^{9} + 11697 q^{10} - 164171 q^{11} - 181941 q^{12} - 77651 q^{14} - 614110 q^{15} + 3012565 q^{16}+ \cdots - 5866875443 q^{99}+O(q^{100})$ 27 * q - 65 * q^2 + q^3 + 7169 * q^4 - 3238 * q^5 - 8490 * q^6 - 17378 * q^7 - 54204 * q^8 + 191118 * q^9 + 11697 * q^10 - 164171 * q^11 - 181941 * q^12 - 77651 * q^14 - 614110 * q^15 + 3012565 * q^16 + 105667 * q^17 - 584849 * q^18 - 2140031 * q^19 - 3722382 * q^20 - 2953252 * q^21 + 3789362 * q^22 + 3586420 * q^23 - 6334338 * q^24 + 10278737 * q^25 - 4332980 * q^27 - 5293616 * q^28 - 4203616 * q^29 - 34788079 * q^30 - 18634294 * q^31 - 38778128 * q^32 - 15170356 * q^33 - 10546914 * q^34 + 16260796 * q^35 + 112071987 * q^36 - 7214770 * q^37 - 60128169 * q^38 - 46270051 * q^40 - 67544533 * q^41 - 31249012 * q^42 - 55585357 * q^43 - 246583161 * q^44 - 172236942 * q^45 - 168715272 * q^46 - 175569972 * q^47 - 48573948 * q^48 + 144680057 * q^49 - 3455750 * q^50 + 122191382 * q^51 + 105504478 * q^53 + 359394409 * q^54 - 2471426 * q^55 + 260765426 * q^56 + 307372146 * q^57 + 777873375 * q^58 - 267562255 * q^59 + 745460915 * q^60 - 371334848 * q^61 + 52175323 * q^62 - 431551952 * q^63 + 642079732 * q^64 + 973549503 * q^66 - 213848603 * q^67 - 278629116 * q^68 - 201174310 * q^69 + 122562066 * q^70 - 970709202 * q^71 - 773619646 * q^72 - 271733895 * q^73 - 1068711482 * q^74 + 1236853937 * q^75 - 2585634844 * q^76 - 244285066 * q^77 + 1052001020 * q^79 - 3293699123 * q^80 - 456846001 * q^81 - 3832425 * q^82 - 1491498691 * q^83 - 5153327787 * q^84 - 2713007958 * q^85 - 3421126005 * q^86 - 1622618562 * q^87 + 6574070508 * q^88 - 4616501291 * q^89 - 2822436128 * q^90 + 3684890562 * q^92 - 3324407374 * q^93 - 5582614303 * q^94 - 2892286998 * q^95 - 12902380548 * q^96 - 3944038157 * q^97 - 7822213576 * q^98 - 5866875443 * 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

)

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

$2$	35.7320	1.57915	0.789573	−	0.613657i	$-0.210302\pi$
$2$	35.7320	1.57915	0.789573	+	0.613657i	$0.210302\pi$
$3$	−157.443	−1.12222	−0.561108	−	0.827742i	$-0.689625\pi$
$3$	−157.443	−1.12222	−0.561108	+	0.827742i	$0.689625\pi$
$4$	764.774	1.49370
$5$	2363.03	1.69084	0.845422	−	0.534099i	$-0.179349\pi$
$5$	2363.03	1.69084	0.845422	+	0.534099i	$0.179349\pi$
$6$	−5625.74	−1.77214
$7$	3406.89	0.536311	0.268155	−	0.963376i	$-0.413586\pi$
$7$	3406.89	0.536311	0.268155	+	0.963376i	$0.413586\pi$
$8$	9032.12	0.779623
$9$	5105.19	0.259371
$10$	84435.6	2.67009
$11$	−85358.9	−1.75785	−0.878925	−	0.476959i	$-0.841739\pi$
$11$	−85358.9	−1.75785	−0.878925	+	0.476959i	$0.841739\pi$
$12$	−120408.	−1.67625
$13$	0	0
$13$	0	0
$14$	121735.	0.846913
$15$	−372041.	−1.89749
$16$	−68828.8	−0.262561
$17$	−173806.	−0.504714	−0.252357	−	0.967634i	$-0.581206\pi$
$17$	−173806.	−0.504714	−0.252357	+	0.967634i	$0.581206\pi$
$18$	182419.	0.409584
$19$	−918491.	−1.61690	−0.808451	−	0.588564i	$-0.799693\pi$
$19$	−918491.	−1.61690	−0.808451	+	0.588564i	$0.799693\pi$
$20$	1.80718e6	2.52561
$21$	−536389.	−0.601857
$22$	−3.05004e6	−2.77590
$23$	−1.02043e6	−0.760340	−0.380170	−	0.924917i	$-0.624135\pi$
$23$	−1.02043e6	−0.760340	−0.380170	+	0.924917i	$0.624135\pi$
$24$	−1.42204e6	−0.874907
$25$	3.63077e6	1.85895
$26$	0	0
$27$	2.29517e6	0.831147
$28$	2.60550e6	0.801087
$29$	4.16258e6	1.09288	0.546438	−	0.837499i	$-0.315983\pi$
$29$	4.16258e6	1.09288	0.546438	+	0.837499i	$0.315983\pi$
$30$	−1.32938e7	−2.99642
$31$	−1.75360e6	−0.341037	−0.170519	−	0.985354i	$-0.554544\pi$
$31$	−1.75360e6	−0.341037	−0.170519	+	0.985354i	$0.554544\pi$
$32$	−7.08384e6	−1.19425
$33$	1.34391e7	1.97269
$34$	−6.21045e6	−0.797017
$35$	8.05056e6	0.906818
$36$	3.90432e6	0.387422
$37$	8.56572e6	0.751374	0.375687	−	0.926747i	$-0.377407\pi$
$37$	8.56572e6	0.751374	0.375687	+	0.926747i	$0.377407\pi$
$38$	−3.28195e7	−2.55332
$39$	0	0
$40$	2.13431e7	1.31822
$41$	−1.45701e7	−0.805258	−0.402629	−	0.915363i	$-0.631903\pi$
$41$	−1.45701e7	−0.805258	−0.402629	+	0.915363i	$0.631903\pi$
$42$	−1.91663e7	−0.950420
$43$	−3.74371e7	−1.66992	−0.834958	−	0.550314i	$-0.814508\pi$
$43$	−3.74371e7	−1.66992	−0.834958	+	0.550314i	$0.814508\pi$
$44$	−6.52803e7	−2.62570
$45$	1.20637e7	0.438555
$46$	−3.64620e7	−1.20069
$47$	2.97614e6	0.0889638	0.0444819	−	0.999010i	$-0.485836\pi$
$47$	2.97614e6	0.0889638	0.0444819	+	0.999010i	$0.485836\pi$
$48$	1.08366e7	0.294650
$49$	−2.87467e7	−0.712371
$50$	1.29734e8	2.93556
$51$	2.73645e7	0.566399
$52$	0	0
$53$	1.44169e7	0.250974	0.125487	−	0.992095i	$-0.459951\pi$
$53$	1.44169e7	0.250974	0.125487	+	0.992095i	$0.459951\pi$
$54$	8.20109e7	1.31250
$55$	−2.01705e8	−2.97225
$56$	3.07714e7	0.418121
$57$	1.44610e8	1.81451
$58$	1.48737e8	1.72581
$59$	1.24760e8	1.34042	0.670212	−	0.742170i	$-0.266203\pi$
$59$	1.24760e8	1.34042	0.670212	+	0.742170i	$0.266203\pi$
$60$	−2.84527e8	−2.83428
$61$	−3.77625e7	−0.349201	−0.174601	−	0.984639i	$-0.555863\pi$
$61$	−3.77625e7	−0.349201	−0.174601	+	0.984639i	$0.555863\pi$
$62$	−6.26594e7	−0.538547
$63$	1.73928e7	0.139103
$64$	−2.17879e8	−1.62333
$65$	0	0
$66$	4.80207e8	3.11516
$67$	−2.21634e8	−1.34369	−0.671847	−	0.740690i	$-0.734499\pi$
$67$	−2.21634e8	−1.34369	−0.671847	+	0.740690i	$0.734499\pi$
$68$	−1.32923e8	−0.753892
$69$	1.60659e8	0.853266
$70$	2.87663e8	1.43200
$71$	3.19651e7	0.149284	0.0746419	−	0.997210i	$-0.476219\pi$
$71$	3.19651e7	0.149284	0.0746419	+	0.997210i	$0.476219\pi$
$72$	4.61107e7	0.202211
$73$	8.39854e7	0.346139	0.173070	−	0.984910i	$-0.444631\pi$
$73$	8.39854e7	0.346139	0.173070	+	0.984910i	$0.444631\pi$
$74$	3.06070e8	1.18653
$75$	−5.71638e8	−2.08615
$76$	−7.02438e8	−2.41516
$77$	−2.90808e8	−0.942755
$78$	0	0
$79$	−1.56307e8	−0.451498	−0.225749	−	0.974186i	$-0.572483\pi$
$79$	−1.56307e8	−0.451498	−0.225749	+	0.974186i	$0.572483\pi$
$80$	−1.62644e8	−0.443950
$81$	−4.61843e8	−1.19210
$82$	−5.20618e8	−1.27162
$83$	−2.71578e8	−0.628121	−0.314061	−	0.949403i	$-0.601690\pi$
$83$	−2.71578e8	−0.628121	−0.314061	+	0.949403i	$0.601690\pi$
$84$	−4.10217e8	−0.898994
$85$	−4.10709e8	−0.853393
$86$	−1.33770e9	−2.63704
$87$	−6.55367e8	−1.22644
$88$	−7.70972e8	−1.37046
$89$	−2.91190e8	−0.491950	−0.245975	−	0.969276i	$-0.579108\pi$
$89$	−2.91190e8	−0.491950	−0.245975	+	0.969276i	$0.579108\pi$
$90$	4.31060e8	0.692542
$91$	0	0
$92$	−7.80398e8	−1.13572
$93$	2.76091e8	0.382718
$94$	1.06343e8	0.140487
$95$	−2.17042e9	−2.73393
$96$	1.11530e9	1.34020
$97$	1.32475e9	1.51937	0.759683	−	0.650293i	$-0.225354\pi$
$97$	1.32475e9	1.51937	0.759683	+	0.650293i	$0.225354\pi$
$98$	−1.02718e9	−1.12494
$99$	−4.35774e8	−0.455935
$100$	2.77672e9	2.77672
$101$	1.28960e9	1.23313	0.616564	−	0.787305i	$-0.288524\pi$
$101$	1.28960e9	1.23313	0.616564	+	0.787305i	$0.288524\pi$
$102$	9.77789e8	0.894426
$103$	5.51028e8	0.482399	0.241199	−	0.970476i	$-0.422459\pi$
$103$	5.51028e8	0.482399	0.241199	+	0.970476i	$0.422459\pi$
$104$	0	0
$105$	−1.26750e9	−1.01765
$106$	5.15143e8	0.396325
$107$	−4.61092e8	−0.340064	−0.170032	−	0.985439i	$-0.554387\pi$
$107$	−4.61092e8	−0.340064	−0.170032	+	0.985439i	$0.554387\pi$
$108$	1.75529e9	1.24148
$109$	−2.72950e9	−1.85209	−0.926047	−	0.377407i	$-0.876816\pi$
$109$	−2.72950e9	−1.85209	−0.926047	+	0.377407i	$0.876816\pi$
$110$	−7.20733e9	−4.69362
$111$	−1.34861e9	−0.843204
$112$	−2.34492e8	−0.140814
$113$	−9.31113e8	−0.537217	−0.268608	−	0.963249i	$-0.586564\pi$
$113$	−9.31113e8	−0.537217	−0.268608	+	0.963249i	$0.586564\pi$
$114$	5.16719e9	2.86538
$115$	−2.41130e9	−1.28562
$116$	3.18343e9	1.63243
$117$	0	0
$118$	4.45793e9	2.11672
$119$	−5.92139e8	−0.270684
$120$	−3.36032e9	−1.47933
$121$	4.92820e9	2.09004
$122$	−1.34933e9	−0.551440
$123$	2.29395e9	0.903674
$124$	−1.34110e9	−0.509407
$125$	3.96431e9	1.45235
$126$	6.21479e8	0.219664
$127$	−1.60685e9	−0.548097	−0.274048	−	0.961716i	$-0.588363\pi$
$127$	−1.60685e9	−0.548097	−0.274048	+	0.961716i	$0.588363\pi$
$128$	−4.15833e9	−1.36922
$129$	5.89420e9	1.87401
$130$	0	0
$131$	1.85853e9	0.551376	0.275688	−	0.961247i	$-0.411094\pi$
$131$	1.85853e9	0.551376	0.275688	+	0.961247i	$0.411094\pi$
$132$	1.02779e10	2.94661
$133$	−3.12919e9	−0.867162
$134$	−7.91943e9	−2.12189
$135$	5.42354e9	1.40534
$136$	−1.56984e9	−0.393487
$137$	−5.67025e8	−0.137518	−0.0687590	−	0.997633i	$-0.521904\pi$
$137$	−5.67025e8	−0.137518	−0.0687590	+	0.997633i	$0.521904\pi$
$138$	5.74067e9	1.34743
$139$	−3.79337e9	−0.861903	−0.430951	−	0.902375i	$-0.641822\pi$
$139$	−3.79337e9	−0.861903	−0.430951	+	0.902375i	$0.641822\pi$
$140$	6.15686e9	1.35451
$141$	−4.68572e8	−0.0998367
$142$	1.14217e9	0.235741
$143$	0	0
$144$	−3.51384e8	−0.0681006
$145$	9.83627e9	1.84788
$146$	3.00097e9	0.546604
$147$	4.52596e9	0.799434
$148$	6.55084e9	1.12233
$149$	−6.01571e9	−0.999881	−0.499941	−	0.866060i	$-0.666645\pi$
$149$	−6.01571e9	−0.999881	−0.499941	+	0.866060i	$0.666645\pi$
$150$	−2.04257e10	−3.29433
$151$	1.04382e10	1.63391	0.816956	−	0.576700i	$-0.195660\pi$
$151$	1.04382e10	1.63391	0.816956	+	0.576700i	$0.195660\pi$
$152$	−8.29592e9	−1.26057
$153$	−8.87315e8	−0.130908
$154$	−1.03912e10	−1.48875
$155$	−4.14379e9	−0.576641
$156$	0	0
$157$	6.51978e9	0.856416	0.428208	−	0.903680i	$-0.359145\pi$
$157$	6.51978e9	0.856416	0.428208	+	0.903680i	$0.359145\pi$
$158$	−5.58515e9	−0.712980
$159$	−2.26983e9	−0.281648
$160$	−1.67393e10	−2.01928
$161$	−3.47649e9	−0.407779
$162$	−1.65026e10	−1.88250
$163$	2.51750e9	0.279335	0.139667	−	0.990198i	$-0.455397\pi$
$163$	2.51750e9	0.279335	0.139667	+	0.990198i	$0.455397\pi$
$164$	−1.11428e10	−1.20281
$165$	3.17570e10	3.33551
$166$	−9.70403e9	−0.991895
$167$	−5.52083e9	−0.549263	−0.274632	−	0.961550i	$-0.588556\pi$
$167$	−5.52083e9	−0.549263	−0.274632	+	0.961550i	$0.588556\pi$
$168$	−4.84474e9	−0.469222
$169$	0	0
$170$	−1.46755e10	−1.34763
$171$	−4.68907e9	−0.419377
$172$	−2.86309e10	−2.49435
$173$	1.00712e10	0.854815	0.427408	−	0.904059i	$-0.359427\pi$
$173$	1.00712e10	0.854815	0.427408	+	0.904059i	$0.359427\pi$
$174$	−2.34176e10	−1.93673
$175$	1.23696e10	0.996977
$176$	5.87515e9	0.461543
$177$	−1.96426e10	−1.50425
$178$	−1.04048e10	−0.776861
$179$	−6.12641e9	−0.446033	−0.223017	−	0.974815i	$-0.571590\pi$
$179$	−6.12641e9	−0.446033	−0.223017	+	0.974815i	$0.571590\pi$
$180$	9.22600e9	0.655069
$181$	2.48881e8	0.0172361	0.00861804	−	0.999963i	$-0.497257\pi$
$181$	2.48881e8	0.0172361	0.00861804	+	0.999963i	$0.497257\pi$
$182$	0	0
$183$	5.94542e9	0.391880
$184$	−9.21665e9	−0.592779
$185$	2.02410e10	1.27046
$186$	9.86527e9	0.604367
$187$	1.48359e10	0.887213
$188$	2.27608e9	0.132885
$189$	7.81938e9	0.445753
$190$	−7.75533e10	−4.31727
$191$	4.45138e9	0.242016	0.121008	−	0.992652i	$-0.461387\pi$
$191$	4.45138e9	0.242016	0.121008	+	0.992652i	$0.461387\pi$
$192$	3.43035e10	1.82172
$193$	7.15989e9	0.371449	0.185724	−	0.982602i	$-0.440537\pi$
$193$	7.15989e9	0.371449	0.185724	+	0.982602i	$0.440537\pi$
$194$	4.73361e10	2.39930
$195$	0	0
$196$	−2.19848e10	−1.06407
$197$	−1.83537e10	−0.868212	−0.434106	−	0.900862i	$-0.642936\pi$
$197$	−1.83537e10	−0.868212	−0.434106	+	0.900862i	$0.642936\pi$
$198$	−1.55711e10	−0.719987
$199$	−3.64234e10	−1.64642	−0.823211	−	0.567735i	$-0.807820\pi$
$199$	−3.64234e10	−1.64642	−0.823211	+	0.567735i	$0.807820\pi$
$200$	3.27935e10	1.44928
$201$	3.48947e10	1.50792
$202$	4.60799e10	1.94729
$203$	1.41814e10	0.586122
$204$	2.09277e10	0.846030
$205$	−3.44295e10	−1.36156
$206$	1.96893e10	0.761778
$207$	−5.20949e9	−0.197210
$208$	0	0
$209$	7.84014e10	2.84227
$210$	−4.52904e10	−1.60701
$211$	−6.89867e8	−0.0239604	−0.0119802	−	0.999928i	$-0.503814\pi$
$211$	−6.89867e8	−0.0239604	−0.0119802	+	0.999928i	$0.503814\pi$
$212$	1.10256e10	0.374880
$213$	−5.03266e9	−0.167529
$214$	−1.64757e10	−0.537011
$215$	−8.84649e10	−2.82357
$216$	2.07302e10	0.647982
$217$	−5.97430e9	−0.182902
$218$	−9.75303e10	−2.92473
$219$	−1.32229e10	−0.388443
$220$	−1.54259e11	−4.43965
$221$	0	0
$222$	−4.81885e10	−1.33154
$223$	−1.07609e9	−0.0291393	−0.0145696	−	0.999894i	$-0.504638\pi$
$223$	−1.07609e9	−0.0291393	−0.0145696	+	0.999894i	$0.504638\pi$
$224$	−2.41338e10	−0.640487
$225$	1.85358e10	0.482157
$226$	−3.32705e10	−0.848343
$227$	3.29551e10	0.823770	0.411885	−	0.911236i	$-0.364871\pi$
$227$	3.29551e10	0.823770	0.411885	+	0.911236i	$0.364871\pi$
$228$	1.10594e11	2.71034
$229$	7.20168e9	0.173051	0.0865255	−	0.996250i	$-0.472424\pi$
$229$	7.20168e9	0.173051	0.0865255	+	0.996250i	$0.472424\pi$
$230$	−8.61606e10	−2.03017
$231$	4.57856e10	1.05797
$232$	3.75969e10	0.852032
$233$	−5.53301e10	−1.22987	−0.614935	−	0.788577i	$-0.710818\pi$
$233$	−5.53301e10	−1.22987	−0.614935	+	0.788577i	$0.710818\pi$
$234$	0	0
$235$	7.03270e9	0.150424
$236$	9.54134e10	2.00219
$237$	2.46093e10	0.506678
$238$	−2.11583e10	−0.427449
$239$	1.00013e10	0.198274	0.0991371	−	0.995074i	$-0.468392\pi$
$239$	1.00013e10	0.198274	0.0991371	+	0.995074i	$0.468392\pi$
$240$	2.56071e10	0.498208
$241$	3.13793e10	0.599193	0.299597	−	0.954066i	$-0.403148\pi$
$241$	3.13793e10	0.599193	0.299597	+	0.954066i	$0.403148\pi$
$242$	1.76094e11	3.30047
$243$	2.75380e10	0.506645
$244$	−2.88798e10	−0.521602
$245$	−6.79292e10	−1.20451
$246$	8.19675e10	1.42703
$247$	0	0
$248$	−1.58387e10	−0.265881
$249$	4.27580e10	0.704888
$250$	1.41653e11	2.29348
$251$	1.93052e10	0.307003	0.153501	−	0.988148i	$-0.450945\pi$
$251$	1.93052e10	0.307003	0.153501	+	0.988148i	$0.450945\pi$
$252$	1.33016e10	0.207778
$253$	8.71028e10	1.33656
$254$	−5.74157e10	−0.865524
$255$	6.46631e10	0.957692
$256$	−3.70312e10	−0.538874
$257$	1.58735e10	0.226973	0.113487	−	0.993540i	$-0.463798\pi$
$257$	1.58735e10	0.226973	0.113487	+	0.993540i	$0.463798\pi$
$258$	2.10611e11	2.95933
$259$	2.91824e10	0.402970
$260$	0	0
$261$	2.12507e10	0.283460
$262$	6.64088e10	0.870703
$263$	5.70447e10	0.735215	0.367608	−	0.929981i	$-0.380177\pi$
$263$	5.70447e10	0.735215	0.367608	+	0.929981i	$0.380177\pi$
$264$	1.21384e11	1.53795
$265$	3.40674e10	0.424359
$266$	−1.11812e11	−1.36937
$267$	4.58457e10	0.552075
$268$	−1.69500e11	−2.00707
$269$	−9.29049e10	−1.08182	−0.540908	−	0.841082i	$-0.681919\pi$
$269$	−9.29049e10	−1.08182	−0.540908	+	0.841082i	$0.681919\pi$
$270$	1.93794e11	2.21923
$271$	3.88666e10	0.437738	0.218869	−	0.975754i	$-0.429763\pi$
$271$	3.88666e10	0.437738	0.218869	+	0.975754i	$0.429763\pi$
$272$	1.19629e10	0.132518
$273$	0	0
$274$	−2.02609e10	−0.217161
$275$	−3.09918e11	−3.26776
$276$	1.22868e11	1.27452
$277$	−6.61138e10	−0.674735	−0.337367	−	0.941373i	$-0.609536\pi$
$277$	−6.61138e10	−0.674735	−0.337367	+	0.941373i	$0.609536\pi$
$278$	−1.35545e11	−1.36107
$279$	−8.95244e9	−0.0884550
$280$	7.27137e10	0.706977
$281$	1.76046e11	1.68441	0.842205	−	0.539158i	$-0.181257\pi$
$281$	1.76046e11	1.68441	0.842205	+	0.539158i	$0.181257\pi$
$282$	−1.67430e10	−0.157657
$283$	1.29727e11	1.20224	0.601122	−	0.799158i	$-0.294721\pi$
$283$	1.29727e11	1.20224	0.601122	+	0.799158i	$0.294721\pi$
$284$	2.44461e10	0.222985
$285$	3.41716e11	3.06806
$286$	0	0
$287$	−4.96387e10	−0.431868
$288$	−3.61643e10	−0.309752
$289$	−8.83792e10	−0.745263
$290$	3.51470e11	2.91808
$291$	−2.08573e11	−1.70506
$292$	6.42299e10	0.517028
$293$	1.66120e11	1.31679	0.658396	−	0.752672i	$-0.271235\pi$
$293$	1.66120e11	1.31679	0.658396	+	0.752672i	$0.271235\pi$
$294$	1.61722e11	1.26242
$295$	2.94812e11	2.26645
$296$	7.73666e10	0.585788
$297$	−1.95913e11	−1.46103
$298$	−2.14953e11	−1.57896
$299$	0	0
$300$	−4.37174e11	−3.11608
$301$	−1.27544e11	−0.895594
$302$	3.72977e11	2.58018
$303$	−2.03038e11	−1.38384
$304$	6.32186e10	0.424535
$305$	−8.92337e10	−0.590445
$306$	−3.17055e10	−0.206723
$307$	6.66942e10	0.428515	0.214257	−	0.976777i	$-0.431267\pi$
$307$	6.66942e10	0.428515	0.214257	+	0.976777i	$0.431267\pi$
$308$	−2.22403e11	−1.40819
$309$	−8.67553e10	−0.541356
$310$	−1.48066e11	−0.910599
$311$	7.80144e10	0.472882	0.236441	−	0.971646i	$-0.424019\pi$
$311$	7.80144e10	0.472882	0.236441	+	0.971646i	$0.424019\pi$
$312$	0	0
$313$	−9.04014e10	−0.532385	−0.266193	−	0.963920i	$-0.585766\pi$
$313$	−9.04014e10	−0.532385	−0.266193	+	0.963920i	$0.585766\pi$
$314$	2.32965e11	1.35240
$315$	4.10997e10	0.235202
$316$	−1.19539e11	−0.674402
$317$	−2.62451e11	−1.45976	−0.729880	−	0.683576i	$-0.760424\pi$
$317$	−2.62451e11	−1.45976	−0.729880	+	0.683576i	$0.760424\pi$
$318$	−8.11055e10	−0.444763
$319$	−3.55313e11	−1.92111
$320$	−5.14854e11	−2.74479
$321$	7.25956e10	0.381626
$322$	−1.24222e11	−0.643942
$323$	1.59640e11	0.816073
$324$	−3.53206e11	−1.78064
$325$	0	0
$326$	8.99551e10	0.441110
$327$	4.29739e11	2.07845
$328$	−1.31599e11	−0.627798
$329$	1.01394e10	0.0477123
$330$	1.13474e12	5.26725
$331$	3.78043e11	1.73107	0.865537	−	0.500846i	$-0.166978\pi$
$331$	3.78043e11	1.73107	0.865537	+	0.500846i	$0.166978\pi$
$332$	−2.07696e11	−0.938225
$333$	4.37296e10	0.194884
$334$	−1.97270e11	−0.867366
$335$	−5.23727e11	−2.27198
$336$	3.69190e10	0.158024
$337$	−1.39921e11	−0.590947	−0.295473	−	0.955351i	$-0.595477\pi$
$337$	−1.39921e11	−0.590947	−0.295473	+	0.955351i	$0.595477\pi$
$338$	0	0
$339$	1.46597e11	0.602874
$340$	−3.14100e11	−1.27471
$341$	1.49685e11	0.599492
$342$	−1.67550e11	−0.662256
$343$	−2.35417e11	−0.918363
$344$	−3.38137e11	−1.30190
$345$	3.79642e11	1.44274
$346$	3.59863e11	1.34988
$347$	1.54612e11	0.572479	0.286240	−	0.958158i	$-0.407595\pi$
$347$	1.54612e11	0.572479	0.286240	+	0.958158i	$0.407595\pi$
$348$	−5.01208e11	−1.83194
$349$	−2.27503e11	−0.820866	−0.410433	−	0.911891i	$-0.634622\pi$
$349$	−2.27503e11	−0.820866	−0.410433	+	0.911891i	$0.634622\pi$
$350$	4.41991e11	1.57437
$351$	0	0
$352$	6.04669e11	2.09930
$353$	−4.58333e11	−1.57107	−0.785533	−	0.618819i	$-0.787611\pi$
$353$	−4.58333e11	−1.57107	−0.785533	+	0.618819i	$0.787611\pi$
$354$	−7.01868e11	−2.37542
$355$	7.55343e10	0.252416
$356$	−2.22694e11	−0.734826
$357$	9.32280e10	0.303766
$358$	−2.18909e11	−0.704351
$359$	−4.60131e11	−1.46203	−0.731016	−	0.682360i	$-0.760953\pi$
$359$	−4.60131e11	−1.46203	−0.731016	+	0.682360i	$0.760953\pi$
$360$	1.08961e11	0.341908
$361$	5.20937e11	1.61437
$362$	8.89301e9	0.0272183
$363$	−7.75909e11	−2.34548
$364$	0	0
$365$	1.98460e11	0.585268
$366$	2.12442e11	0.618835
$367$	−3.17602e11	−0.913874	−0.456937	−	0.889499i	$-0.651054\pi$
$367$	−3.17602e11	−0.913874	−0.456937	+	0.889499i	$0.651054\pi$
$368$	7.02349e10	0.199636
$369$	−7.43831e10	−0.208860
$370$	7.23251e11	2.00623
$371$	4.91166e10	0.134600
$372$	2.11147e11	0.571665
$373$	−1.31409e11	−0.351507	−0.175754	−	0.984434i	$-0.556236\pi$
$373$	−1.31409e11	−0.351507	−0.175754	+	0.984434i	$0.556236\pi$
$374$	5.30117e11	1.40104
$375$	−6.24152e11	−1.62986
$376$	2.68809e10	0.0693583
$377$	0	0
$378$	2.79402e11	0.703909
$379$	5.87179e11	1.46182	0.730910	−	0.682474i	$-0.239096\pi$
$379$	5.87179e11	1.46182	0.730910	+	0.682474i	$0.239096\pi$
$380$	−1.65988e12	−4.08367
$381$	2.52986e11	0.615083
$382$	1.59057e11	0.382179
$383$	−4.78147e11	−1.13545	−0.567723	−	0.823220i	$-0.692176\pi$
$383$	−4.78147e11	−1.13545	−0.567723	+	0.823220i	$0.692176\pi$
$384$	6.54698e11	1.53656
$385$	−6.87188e11	−1.59405
$386$	2.55837e11	0.586571
$387$	−1.91124e11	−0.433127
$388$	1.01314e12	2.26948
$389$	4.44374e11	0.983955	0.491977	−	0.870608i	$-0.336274\pi$
$389$	4.44374e11	0.983955	0.491977	+	0.870608i	$0.336274\pi$
$390$	0	0
$391$	1.77357e11	0.383755
$392$	−2.59644e11	−0.555381
$393$	−2.92611e11	−0.618764
$394$	−6.55815e11	−1.37103
$395$	−3.69357e11	−0.763412
$396$	−3.33268e11	−0.681029
$397$	−4.54781e10	−0.0918850	−0.0459425	−	0.998944i	$-0.514629\pi$
$397$	−4.54781e10	−0.0918850	−0.0459425	+	0.998944i	$0.514629\pi$
$398$	−1.30148e12	−2.59994
$399$	4.92669e11	0.973144
$400$	−2.49901e11	−0.488088
$401$	7.41103e11	1.43129	0.715647	−	0.698462i	$-0.246132\pi$
$401$	7.41103e11	1.43129	0.715647	+	0.698462i	$0.246132\pi$
$402$	1.24686e12	2.38122
$403$	0	0
$404$	9.86252e11	1.84192
$405$	−1.09135e12	−2.01565
$406$	5.06730e11	0.925571
$407$	−7.31161e11	−1.32080
$408$	2.47160e11	0.441578
$409$	−5.89252e11	−1.04123	−0.520614	−	0.853792i	$-0.674297\pi$
$409$	−5.89252e11	−1.04123	−0.520614	+	0.853792i	$0.674297\pi$
$410$	−1.23023e12	−2.15011
$411$	8.92739e10	0.154325
$412$	4.21412e11	0.720559
$413$	4.25044e11	0.718884
$414$	−1.86145e11	−0.311423
$415$	−6.41746e11	−1.06205
$416$	0	0
$417$	5.97238e11	0.967242
$418$	2.80144e12	4.48836
$419$	1.19505e12	1.89419	0.947093	−	0.320961i	$-0.104006\pi$
$419$	1.19505e12	1.89419	0.947093	+	0.320961i	$0.104006\pi$
$420$	−9.69353e11	−1.52006
$421$	−6.30842e11	−0.978704	−0.489352	−	0.872086i	$-0.662767\pi$
$421$	−6.30842e11	−0.978704	−0.489352	+	0.872086i	$0.662767\pi$
$422$	−2.46503e10	−0.0378370
$423$	1.51938e10	0.0230746
$424$	1.30215e11	0.195666
$425$	−6.31051e11	−0.938240
$426$	−1.79827e11	−0.264552
$427$	−1.28652e11	−0.187281
$428$	−3.52632e11	−0.507954
$429$	0	0
$430$	−3.16103e12	−4.45882
$431$	−1.16016e11	−0.161946	−0.0809730	−	0.996716i	$-0.525803\pi$
$431$	−1.16016e11	−0.161946	−0.0809730	+	0.996716i	$0.525803\pi$
$432$	−1.57974e11	−0.218227
$433$	5.34527e11	0.730759	0.365380	−	0.930859i	$-0.380939\pi$
$433$	5.34527e11	0.730759	0.365380	+	0.930859i	$0.380939\pi$
$434$	−2.13474e11	−0.288829
$435$	−1.54865e12	−2.07373
$436$	−2.08745e12	−2.76647
$437$	9.37255e11	1.22939
$438$	−4.72480e11	−0.613409
$439$	6.73196e11	0.865070	0.432535	−	0.901617i	$-0.357619\pi$
$439$	6.73196e11	0.865070	0.432535	+	0.901617i	$0.357619\pi$
$440$	−1.82183e12	−2.31724
$441$	−1.46757e11	−0.184768
$442$	0	0
$443$	−6.93075e11	−0.854995	−0.427498	−	0.904017i	$-0.640605\pi$
$443$	−6.93075e11	−0.854995	−0.427498	+	0.904017i	$0.640605\pi$
$444$	−1.03138e12	−1.25949
$445$	−6.88089e11	−0.831811
$446$	−3.84510e10	−0.0460151
$447$	9.47129e11	1.12208
$448$	−7.42290e11	−0.870607
$449$	1.51844e12	1.76314	0.881572	−	0.472050i	$-0.156486\pi$
$449$	1.51844e12	1.76314	0.881572	+	0.472050i	$0.156486\pi$
$450$	6.62319e11	0.761397
$451$	1.24369e12	1.41552
$452$	−7.12091e11	−0.802440
$453$	−1.64342e12	−1.83360
$454$	1.17755e12	1.30085
$455$	0	0
$456$	1.30613e12	1.41464
$457$	−4.85641e11	−0.520825	−0.260413	−	0.965497i	$-0.583859\pi$
$457$	−4.85641e11	−0.520825	−0.260413	+	0.965497i	$0.583859\pi$
$458$	2.57330e11	0.273273
$459$	−3.98915e11	−0.419492
$460$	−1.84410e12	−1.92032
$461$	1.60851e12	1.65871	0.829353	−	0.558725i	$-0.188709\pi$
$461$	1.60851e12	1.65871	0.829353	+	0.558725i	$0.188709\pi$
$462$	1.63601e12	1.67070
$463$	1.76369e12	1.78364	0.891819	−	0.452392i	$-0.149429\pi$
$463$	1.76369e12	1.78364	0.891819	+	0.452392i	$0.149429\pi$
$464$	−2.86505e11	−0.286947
$465$	6.52410e11	0.647116
$466$	−1.97705e12	−1.94214
$467$	−7.75997e11	−0.754978	−0.377489	−	0.926014i	$-0.623212\pi$
$467$	−7.75997e11	−0.754978	−0.377489	+	0.926014i	$0.623212\pi$
$468$	0	0
$469$	−7.55083e11	−0.720638
$470$	2.51292e11	0.237541
$471$	−1.02649e12	−0.961084
$472$	1.12685e12	1.04503
$473$	3.19559e12	2.93546
$474$	8.79340e11	0.800119
$475$	−3.33482e12	−3.00574
$476$	−4.52853e11	−0.404320
$477$	7.36008e10	0.0650954
$478$	3.57366e11	0.313104
$479$	−1.07610e11	−0.0933991	−0.0466996	−	0.998909i	$-0.514870\pi$
$479$	−1.07610e11	−0.0933991	−0.0466996	+	0.998909i	$0.514870\pi$
$480$	2.63548e12	2.26607
$481$	0	0
$482$	1.12125e12	0.946213
$483$	5.47348e11	0.457616
$484$	3.76896e12	3.12189
$485$	3.13043e12	2.56901
$486$	9.83986e11	0.800066
$487$	−2.15606e12	−1.73692	−0.868460	−	0.495760i	$-0.834890\pi$
$487$	−2.15606e12	−1.73692	−0.868460	+	0.495760i	$0.834890\pi$
$488$	−3.41075e11	−0.272246
$489$	−3.96361e11	−0.313474
$490$	−2.42725e12	−1.90209
$491$	5.77446e11	0.448378	0.224189	−	0.974546i	$-0.428027\pi$
$491$	5.77446e11	0.448378	0.224189	+	0.974546i	$0.428027\pi$
$492$	1.75436e12	1.34982
$493$	−7.23482e11	−0.551591
$494$	0	0
$495$	−1.02974e12	−0.770914
$496$	1.20698e11	0.0895431
$497$	1.08901e11	0.0800626
$498$	1.52783e12	1.11312
$499$	−5.68605e11	−0.410543	−0.205271	−	0.978705i	$-0.565808\pi$
$499$	−5.68605e11	−0.410543	−0.205271	+	0.978705i	$0.565808\pi$
$500$	3.03180e12	2.16938
$501$	8.69214e11	0.616392
$502$	6.89812e11	0.484802
$503$	−1.59855e12	−1.11345	−0.556724	−	0.830697i	$-0.687942\pi$
$503$	−1.59855e12	−1.11345	−0.556724	+	0.830697i	$0.687942\pi$
$504$	1.57094e11	0.108448
$505$	3.04736e12	2.08503
$506$	3.11236e12	2.11063
$507$	0	0
$508$	−1.22887e12	−0.818692
$509$	−2.43617e11	−0.160871	−0.0804354	−	0.996760i	$-0.525631\pi$
$509$	−2.43617e11	−0.160871	−0.0804354	+	0.996760i	$0.525631\pi$
$510$	2.31054e12	1.51234
$511$	2.86129e11	0.185638
$512$	8.05867e11	0.518261
$513$	−2.10809e12	−1.34388
$514$	5.67193e11	0.358423
$515$	1.30209e12	0.815661
$516$	4.50773e12	2.79920
$517$	−2.54040e11	−0.156385
$518$	1.04275e12	0.636348
$519$	−1.58563e12	−0.959288
$520$	0	0
$521$	7.24903e11	0.431033	0.215516	−	0.976500i	$-0.430857\pi$
$521$	7.24903e11	0.431033	0.215516	+	0.976500i	$0.430857\pi$
$522$	7.59331e11	0.447624
$523$	−2.96967e12	−1.73561	−0.867803	−	0.496908i	$-0.834469\pi$
$523$	−2.96967e12	−1.73561	−0.867803	+	0.496908i	$0.834469\pi$
$524$	1.42135e12	0.823590
$525$	−1.94750e12	−1.11882
$526$	2.03832e12	1.16101
$527$	3.04786e11	0.172126
$528$	−9.25000e11	−0.517951
$529$	−7.59876e11	−0.421883
$530$	1.21730e12	0.670124
$531$	6.36924e11	0.347666
$532$	−2.39313e12	−1.29528
$533$	0	0
$534$	1.63816e12	0.871806
$535$	−1.08957e12	−0.574996
$536$	−2.00183e12	−1.04757
$537$	9.64558e11	0.500546
$538$	−3.31967e12	−1.70834
$539$	2.45379e12	1.25224
$540$	4.14779e12	2.09915
$541$	5.44604e11	0.273333	0.136667	−	0.990617i	$-0.456361\pi$
$541$	5.44604e11	0.273333	0.136667	+	0.990617i	$0.456361\pi$
$542$	1.38878e12	0.691252
$543$	−3.91845e10	−0.0193426
$544$	1.23122e12	0.602753
$545$	−6.44987e12	−3.13160
$546$	0	0
$547$	−2.44853e12	−1.16940	−0.584699	−	0.811250i	$-0.698788\pi$
$547$	−2.44853e12	−1.16940	−0.584699	+	0.811250i	$0.698788\pi$
$548$	−4.33646e11	−0.205410
$549$	−1.92785e11	−0.0905726
$550$	−1.10740e13	−5.16027
$551$	−3.82329e12	−1.76707
$552$	1.45109e12	0.665226
$553$	−5.32519e11	−0.242143
$554$	−2.36238e12	−1.06550
$555$	−3.18680e12	−1.42573
$556$	−2.90107e12	−1.28742
$557$	−2.99460e12	−1.31823	−0.659113	−	0.752044i	$-0.729068\pi$
$557$	−2.99460e12	−1.31823	−0.659113	+	0.752044i	$0.729068\pi$
$558$	−3.19888e11	−0.139683
$559$	0	0
$560$	−5.54111e11	−0.238095
$561$	−2.33581e12	−0.995645
$562$	6.29047e12	2.65993
$563$	9.35795e8	0.000392548 0	0.000196274	−	1.00000i	$-0.499938\pi$
$563$	9.35795e8	0.000392548 0	0.000196274		1.00000i	$0.499938\pi$
$564$	−3.58352e11	−0.149126
$565$	−2.20024e12	−0.908349
$566$	4.63541e12	1.89852
$567$	−1.57345e12	−0.639335
$568$	2.88712e11	0.116385
$569$	5.21435e11	0.208543	0.104271	−	0.994549i	$-0.466749\pi$
$569$	5.21435e11	0.208543	0.104271	+	0.994549i	$0.466749\pi$
$570$	1.22102e13	4.84491
$571$	−2.60236e12	−1.02448	−0.512241	−	0.858842i	$-0.671185\pi$
$571$	−2.60236e12	−1.02448	−0.512241	+	0.858842i	$0.671185\pi$
$572$	0	0
$573$	−7.00838e11	−0.271595
$574$	−1.77369e12	−0.681983
$575$	−3.70494e12	−1.41344
$576$	−1.11231e12	−0.421043
$577$	4.76628e11	0.179015	0.0895073	−	0.995986i	$-0.471471\pi$
$577$	4.76628e11	0.179015	0.0895073	+	0.995986i	$0.471471\pi$
$578$	−3.15796e12	−1.17688
$579$	−1.12727e12	−0.416846
$580$	7.52253e12	2.76018
$581$	−9.25237e11	−0.336868
$582$	−7.45272e12	−2.69253
$583$	−1.23061e12	−0.441176
$584$	7.58567e11	0.269858
$585$	0	0
$586$	5.93579e12	2.07941
$587$	1.40719e11	0.0489194	0.0244597	−	0.999701i	$-0.492213\pi$
$587$	1.40719e11	0.0489194	0.0244597	+	0.999701i	$0.492213\pi$
$588$	3.46134e12	1.19411
$589$	1.61066e12	0.551424
$590$	1.05342e13	3.57905
$591$	2.88966e12	0.974322
$592$	−5.89568e11	−0.197281
$593$	−4.90641e12	−1.62936	−0.814681	−	0.579909i	$-0.803088\pi$
$593$	−4.90641e12	−1.62936	−0.814681	+	0.579909i	$0.803088\pi$
$594$	−7.00037e12	−2.30718
$595$	−1.39924e12	−0.457684
$596$	−4.60066e12	−1.49352
$597$	5.73459e12	1.84764
$598$	0	0
$599$	3.29390e12	1.04542	0.522708	−	0.852512i	$-0.324922\pi$
$599$	3.29390e12	1.04542	0.522708	+	0.852512i	$0.324922\pi$
$600$	−5.16310e12	−1.62641
$601$	5.66204e12	1.77026	0.885132	−	0.465341i	$-0.154068\pi$
$601$	5.66204e12	1.77026	0.885132	+	0.465341i	$0.154068\pi$
$602$	−4.55740e12	−1.41427
$603$	−1.13148e12	−0.348514
$604$	7.98285e12	2.44057
$605$	1.16455e13	3.53393
$606$	−7.25494e12	−2.18528
$607$	6.16493e12	1.84323	0.921614	−	0.388108i	$-0.126871\pi$
$607$	6.16493e12	1.84323	0.921614	+	0.388108i	$0.126871\pi$
$608$	6.50644e12	1.93098
$609$	−2.23276e12	−0.657756
$610$	−3.18850e12	−0.932399
$611$	0	0
$612$	−6.78596e11	−0.195537
$613$	6.43646e12	1.84109	0.920544	−	0.390639i	$-0.127746\pi$
$613$	6.43646e12	1.84109	0.920544	+	0.390639i	$0.127746\pi$
$614$	2.38312e12	0.676687
$615$	5.42067e12	1.52797
$616$	−2.62662e12	−0.734994
$617$	6.09818e10	0.0169401	0.00847007	−	0.999964i	$-0.497304\pi$
$617$	6.09818e10	0.0169401	0.00847007	+	0.999964i	$0.497304\pi$
$618$	−3.09994e12	−0.854880
$619$	−3.71099e12	−1.01597	−0.507986	−	0.861365i	$-0.669610\pi$
$619$	−3.71099e12	−1.01597	−0.507986	+	0.861365i	$0.669610\pi$
$620$	−3.16906e12	−0.861328
$621$	−2.34206e12	−0.631954
$622$	2.78761e12	0.746750
$623$	−9.92051e11	−0.263838
$624$	0	0
$625$	2.27643e12	0.596752
$626$	−3.23022e12	−0.840713
$627$	−1.23437e13	−3.18964
$628$	4.98616e12	1.27923
$629$	−1.48878e12	−0.379229
$630$	1.46857e12	0.371418
$631$	−1.69274e12	−0.425068	−0.212534	−	0.977154i	$-0.568172\pi$
$631$	−1.69274e12	−0.425068	−0.212534	+	0.977154i	$0.568172\pi$
$632$	−1.41178e12	−0.351998
$633$	1.08614e11	0.0268888
$634$	−9.37789e12	−2.30517
$635$	−3.79702e12	−0.926746
$636$	−1.73591e12	−0.420697
$637$	0	0
$638$	−1.26960e13	−3.03372
$639$	1.63188e11	0.0387198
$640$	−9.82624e12	−2.31514
$641$	3.87167e12	0.905810	0.452905	−	0.891559i	$-0.350388\pi$
$641$	3.87167e12	0.905810	0.452905	+	0.891559i	$0.350388\pi$
$642$	2.59399e12	0.602643
$643$	−5.80209e12	−1.33855	−0.669275	−	0.743015i	$-0.733395\pi$
$643$	−5.80209e12	−1.33855	−0.669275	+	0.743015i	$0.733395\pi$
$644$	−2.65873e12	−0.609099
$645$	1.39281e13	3.16865
$646$	5.70424e12	1.28870
$647$	−2.47347e11	−0.0554928	−0.0277464	−	0.999615i	$-0.508833\pi$
$647$	−2.47347e11	−0.0554928	−0.0277464	+	0.999615i	$0.508833\pi$
$648$	−4.17142e12	−0.929387
$649$	−1.06494e13	−2.35626
$650$	0	0
$651$	9.40610e11	0.205256
$652$	1.92532e12	0.417242
$653$	7.76569e12	1.67136	0.835681	−	0.549215i	$-0.185073\pi$
$653$	7.76569e12	1.67136	0.835681	+	0.549215i	$0.185073\pi$
$654$	1.53554e13	3.28218
$655$	4.39175e12	0.932291
$656$	1.00284e12	0.211429
$657$	4.28762e11	0.0897784
$658$	3.62300e11	0.0753446
$659$	4.18896e12	0.865211	0.432605	−	0.901583i	$-0.357594\pi$
$659$	4.18896e12	0.865211	0.432605	+	0.901583i	$0.357594\pi$
$660$	2.42870e13	4.98225
$661$	5.49347e12	1.11928	0.559642	−	0.828735i	$-0.310939\pi$
$661$	5.49347e12	1.11928	0.559642	+	0.828735i	$0.310939\pi$
$662$	1.35082e13	2.73362
$663$	0	0
$664$	−2.45293e12	−0.489698
$665$	−7.39437e12	−1.46624
$666$	1.56255e12	0.307750
$667$	−4.24762e12	−0.830958
$668$	−4.22219e12	−0.820434
$669$	1.69423e11	0.0327006
$670$	−1.87138e13	−3.58778
$671$	3.22336e12	0.613844
$672$	3.79969e12	0.718765
$673$	−5.85305e12	−1.09980	−0.549901	−	0.835230i	$-0.685335\pi$
$673$	−5.85305e12	−1.09980	−0.549901	+	0.835230i	$0.685335\pi$
$674$	−4.99966e12	−0.933191
$675$	8.33322e12	1.54506
$676$	0	0
$677$	−7.83348e12	−1.43320	−0.716598	−	0.697486i	$-0.754302\pi$
$677$	−7.83348e12	−1.43320	−0.716598	+	0.697486i	$0.754302\pi$
$678$	5.23820e12	0.952025
$679$	4.51329e12	0.814853
$680$	−3.70958e12	−0.665325
$681$	−5.18853e12	−0.924448
$682$	5.34854e12	0.946686
$683$	−4.96989e12	−0.873884	−0.436942	−	0.899490i	$-0.643939\pi$
$683$	−4.96989e12	−0.873884	−0.436942	+	0.899490i	$0.643939\pi$
$684$	−3.58608e12	−0.626423
$685$	−1.33989e12	−0.232521
$686$	−8.41192e12	−1.45023
$687$	−1.13385e12	−0.194201
$688$	2.57675e12	0.438455
$689$	0	0
$690$	1.35654e13	2.27830
$691$	9.71204e11	0.162054	0.0810269	−	0.996712i	$-0.474180\pi$
$691$	9.71204e11	0.162054	0.0810269	+	0.996712i	$0.474180\pi$
$692$	7.70217e12	1.27684
$693$	−1.48463e12	−0.244523
$694$	5.52458e12	0.904028
$695$	−8.96383e12	−1.45734
$696$	−5.91935e12	−0.956165
$697$	2.53238e12	0.406425
$698$	−8.12912e12	−1.29627
$699$	8.71131e12	1.38018
$700$	9.45996e12	1.48918
$701$	6.96434e11	0.108930	0.0544651	−	0.998516i	$-0.482655\pi$
$701$	6.96434e11	0.108930	0.0544651	+	0.998516i	$0.482655\pi$
$702$	0	0
$703$	−7.86753e12	−1.21490
$704$	1.85979e13	2.85356
$705$	−1.10725e12	−0.168808
$706$	−1.63771e13	−2.48094
$707$	4.39352e12	0.661340
$708$	−1.50221e13	−2.24689
$709$	−1.07645e13	−1.59988	−0.799940	−	0.600080i	$-0.795135\pi$
$709$	−1.07645e13	−1.59988	−0.799940	+	0.600080i	$0.795135\pi$
$710$	2.69899e12	0.398601
$711$	−7.97975e11	−0.117105
$712$	−2.63006e12	−0.383536
$713$	1.78942e12	0.259304
$714$	3.33122e12	0.479691
$715$	0	0
$716$	−4.68532e12	−0.666240
$717$	−1.57463e12	−0.222507
$718$	−1.64414e13	−2.30876
$719$	−1.00049e13	−1.39616	−0.698078	−	0.716021i	$-0.745961\pi$
$719$	−1.00049e13	−1.39616	−0.698078	+	0.716021i	$0.745961\pi$
$720$	−8.30330e11	−0.115147
$721$	1.87729e12	0.258716
$722$	1.86141e13	2.54932
$723$	−4.94044e12	−0.672425
$724$	1.90338e11	0.0257455
$725$	1.51133e13	2.03161
$726$	−2.77248e13	−3.70385
$727$	3.07406e12	0.408138	0.204069	−	0.978957i	$-0.434583\pi$
$727$	3.07406e12	0.408138	0.204069	+	0.978957i	$0.434583\pi$
$728$	0	0
$729$	4.75480e12	0.623532
$730$	7.09136e12	0.924223
$731$	6.50681e12	0.842830
$732$	4.54691e12	0.585351
$733$	−1.10029e13	−1.40779	−0.703896	−	0.710303i	$-0.748558\pi$
$733$	−1.10029e13	−1.40779	−0.703896	+	0.710303i	$0.748558\pi$
$734$	−1.13486e13	−1.44314
$735$	1.06950e13	1.35172
$736$	7.22856e12	0.908033
$737$	1.89185e13	2.36201
$738$	−2.65785e12	−0.329820
$739$	−1.39859e13	−1.72501	−0.862505	−	0.506048i	$-0.831106\pi$
$739$	−1.39859e13	−1.72501	−0.862505	+	0.506048i	$0.831106\pi$
$740$	1.54798e13	1.89768
$741$	0	0
$742$	1.75503e12	0.212553
$743$	−4.61053e12	−0.555011	−0.277505	−	0.960724i	$-0.589508\pi$
$743$	−4.61053e12	−0.555011	−0.277505	+	0.960724i	$0.589508\pi$
$744$	2.49369e12	0.298376
$745$	−1.42153e13	−1.69064
$746$	−4.69549e12	−0.555081
$747$	−1.38646e12	−0.162916
$748$	1.13461e13	1.32523
$749$	−1.57089e12	−0.182380
$750$	−2.23022e13	−2.57378
$751$	7.70888e12	0.884324	0.442162	−	0.896935i	$-0.354212\pi$
$751$	7.70888e12	0.884324	0.442162	+	0.896935i	$0.354212\pi$
$752$	−2.04844e11	−0.0233584
$753$	−3.03946e12	−0.344523
$754$	0	0
$755$	2.46657e13	2.76269
$756$	5.98006e12	0.665821
$757$	1.68076e12	0.186027	0.0930133	−	0.995665i	$-0.470350\pi$
$757$	1.68076e12	0.186027	0.0930133	+	0.995665i	$0.470350\pi$
$758$	2.09811e13	2.30843
$759$	−1.37137e13	−1.49991
$760$	−1.96035e13	−2.13143
$761$	−8.42654e12	−0.910790	−0.455395	−	0.890289i	$-0.650502\pi$
$761$	−8.42654e12	−0.910790	−0.455395	+	0.890289i	$0.650502\pi$
$762$	9.03969e12	0.971306
$763$	−9.29909e12	−0.993299
$764$	3.40430e12	0.361500
$765$	−2.09675e12	−0.221345
$766$	−1.70851e13	−1.79303
$767$	0	0
$768$	5.83029e12	0.604734
$769$	−1.33393e13	−1.37552	−0.687758	−	0.725940i	$-0.741405\pi$
$769$	−1.33393e13	−1.37552	−0.687758	+	0.725940i	$0.741405\pi$
$770$	−2.45546e13	−2.51724
$771$	−2.49917e12	−0.254713
$772$	5.47570e12	0.554833
$773$	1.25115e13	1.26038	0.630190	−	0.776441i	$-0.282977\pi$
$773$	1.25115e13	1.26038	0.630190	+	0.776441i	$0.282977\pi$
$774$	−6.82922e12	−0.683970
$775$	−6.36690e12	−0.633972
$776$	1.19653e13	1.18453
$777$	−4.59456e12	−0.452220
$778$	1.58784e13	1.55381
$779$	1.33825e13	1.30202
$780$	0	0
$781$	−2.72850e12	−0.262419
$782$	6.33733e12	0.606004
$783$	9.55381e12	0.908341
$784$	1.97860e12	0.187041
$785$	1.54064e13	1.44807
$786$	−1.04556e13	−0.977118
$787$	4.69799e12	0.436542	0.218271	−	0.975888i	$-0.429958\pi$
$787$	4.69799e12	0.436542	0.218271	+	0.975888i	$0.429958\pi$
$788$	−1.40364e13	−1.29685
$789$	−8.98127e12	−0.825071
$790$	−1.31978e13	−1.20554
$791$	−3.17220e12	−0.288115
$792$	−3.93596e12	−0.355457
$793$	0	0
$794$	−1.62502e12	−0.145100
$795$	−5.36367e12	−0.476222
$796$	−2.78557e13	−2.45926
$797$	2.87905e11	0.0252747	0.0126374	−	0.999920i	$-0.495977\pi$
$797$	2.87905e11	0.0252747	0.0126374	+	0.999920i	$0.495977\pi$
$798$	1.76040e13	1.53674
$799$	−5.17273e11	−0.0449013
$800$	−2.57198e13	−2.22005
$801$	−1.48658e12	−0.127597
$802$	2.64811e13	2.26022
$803$	−7.16891e12	−0.608461
$804$	2.66866e13	2.25237
$805$	−8.21504e12	−0.689490
$806$	0	0
$807$	1.46272e13	1.21403
$808$	1.16478e13	0.961376
$809$	−8.27639e12	−0.679317	−0.339658	−	0.940549i	$-0.610311\pi$
$809$	−8.27639e12	−0.679317	−0.339658	+	0.940549i	$0.610311\pi$
$810$	−3.89960e13	−3.18300
$811$	5.88340e12	0.477567	0.238784	−	0.971073i	$-0.423251\pi$
$811$	5.88340e12	0.477567	0.238784	+	0.971073i	$0.423251\pi$
$812$	1.08456e13	0.875490
$813$	−6.11926e12	−0.491237
$814$	−2.61258e13	−2.08574
$815$	5.94891e12	0.472311
$816$	−1.88347e12	−0.148714
$817$	3.43856e13	2.70009
$818$	−2.10551e13	−1.64425
$819$	0	0
$820$	−2.63308e13	−2.03377
$821$	−1.41774e13	−1.08906	−0.544532	−	0.838740i	$-0.683293\pi$
$821$	−1.41774e13	−1.08906	−0.544532	+	0.838740i	$0.683293\pi$
$822$	3.18993e12	0.243701
$823$	8.59469e12	0.653026	0.326513	−	0.945193i	$-0.394126\pi$
$823$	8.59469e12	0.653026	0.326513	+	0.945193i	$0.394126\pi$
$824$	4.97695e12	0.376089
$825$	4.87944e13	3.66714
$826$	1.51877e13	1.13522
$827$	−8.90088e11	−0.0661696	−0.0330848	−	0.999453i	$-0.510533\pi$
$827$	−8.90088e11	−0.0661696	−0.0330848	+	0.999453i	$0.510533\pi$
$828$	−3.98408e12	−0.294572
$829$	4.44031e12	0.326526	0.163263	−	0.986583i	$-0.447798\pi$
$829$	4.44031e12	0.326526	0.163263	+	0.986583i	$0.447798\pi$
$830$	−2.29309e13	−1.67714
$831$	1.04091e13	0.757199
$832$	0	0
$833$	4.99637e12	0.359544
$834$	2.13405e13	1.52742
$835$	−1.30459e13	−0.928718
$836$	5.99594e13	4.24550
$837$	−4.02480e12	−0.283452
$838$	4.27014e13	2.99119
$839$	−2.75185e13	−1.91733	−0.958663	−	0.284545i	$-0.908158\pi$
$839$	−2.75185e13	−1.91733	−0.958663	+	0.284545i	$0.908158\pi$
$840$	−1.14482e13	−0.793381
$841$	2.81989e12	0.194379
$842$	−2.25412e13	−1.54552
$843$	−2.77171e13	−1.89027
$844$	−5.27592e11	−0.0357896
$845$	0	0
$846$	5.42904e11	0.0364381
$847$	1.67898e13	1.12091
$848$	−9.92296e11	−0.0658961
$849$	−2.04246e13	−1.34918
$850$	−2.25487e13	−1.48162
$851$	−8.74071e12	−0.571299
$852$	−3.84885e12	−0.250238
$853$	1.12438e13	0.727181	0.363591	−	0.931559i	$-0.381551\pi$
$853$	1.12438e13	0.727181	0.363591	+	0.931559i	$0.381551\pi$
$854$	−4.59701e12	−0.295743
$855$	−1.10804e13	−0.709100
$856$	−4.16464e12	−0.265122
$857$	1.20421e13	0.762584	0.381292	−	0.924455i	$-0.375479\pi$
$857$	1.20421e13	0.762584	0.381292	+	0.924455i	$0.375479\pi$
$858$	0	0
$859$	9.60758e12	0.602067	0.301033	−	0.953614i	$-0.402668\pi$
$859$	9.60758e12	0.602067	0.301033	+	0.953614i	$0.402668\pi$
$860$	−6.76557e13	−4.21756
$861$	7.81524e12	0.484650
$862$	−4.14548e12	−0.255736
$863$	4.64134e12	0.284836	0.142418	−	0.989807i	$-0.454512\pi$
$863$	4.64134e12	0.284836	0.142418	+	0.989807i	$0.454512\pi$
$864$	−1.62586e13	−0.992593
$865$	2.37984e13	1.44536
$866$	1.90997e13	1.15397
$867$	1.39147e13	0.836347
$868$	−4.56899e12	−0.273201
$869$	1.33422e13	0.793665
$870$	−5.53363e13	−3.27471
$871$	0	0
$872$	−2.46531e13	−1.44394
$873$	6.76312e12	0.394079
$874$	3.34900e13	1.94139
$875$	1.35060e13	0.778914
$876$	−1.01125e13	−0.580218
$877$	−3.08887e13	−1.76320	−0.881599	−	0.471999i	$-0.843533\pi$
$877$	−3.08887e13	−1.76320	−0.881599	+	0.471999i	$0.843533\pi$
$878$	2.40546e13	1.36607
$879$	−2.61543e13	−1.47773
$880$	1.38831e13	0.780397
$881$	−3.27975e13	−1.83421	−0.917105	−	0.398645i	$-0.869480\pi$
$881$	−3.27975e13	−1.83421	−0.917105	+	0.398645i	$0.869480\pi$
$882$	−5.24393e12	−0.291775
$883$	−2.21183e12	−0.122441	−0.0612206	−	0.998124i	$-0.519499\pi$
$883$	−2.21183e12	−0.122441	−0.0612206	+	0.998124i	$0.519499\pi$
$884$	0	0
$885$	−4.64159e13	−2.54344
$886$	−2.47649e13	−1.35016
$887$	−1.15100e13	−0.624336	−0.312168	−	0.950027i	$-0.601055\pi$
$887$	−1.15100e13	−0.624336	−0.312168	+	0.950027i	$0.601055\pi$
$888$	−1.21808e13	−0.657382
$889$	−5.47434e12	−0.293950
$890$	−2.45868e13	−1.31355
$891$	3.94224e13	2.09553
$892$	−8.22970e11	−0.0435253
$893$	−2.73356e12	−0.143846
$894$	3.38428e13	1.77193
$895$	−1.44769e13	−0.754172
$896$	−1.41670e13	−0.734329
$897$	0	0
$898$	5.42567e13	2.78426
$899$	−7.29947e12	−0.372712
$900$	1.41757e13	0.720198
$901$	−2.50574e12	−0.126670
$902$	4.44394e13	2.23532
$903$	2.00809e13	1.00505
$904$	−8.40993e12	−0.418827
$905$	5.88113e11	0.0291435
$906$	−5.87225e13	−2.89553
$907$	1.01540e13	0.498201	0.249100	−	0.968478i	$-0.419865\pi$
$907$	1.01540e13	0.498201	0.249100	+	0.968478i	$0.419865\pi$
$908$	2.52032e13	1.23046
$909$	6.58365e12	0.319837
$910$	0	0
$911$	1.68956e13	0.812719	0.406360	−	0.913713i	$-0.366798\pi$
$911$	1.68956e13	0.812719	0.406360	+	0.913713i	$0.366798\pi$
$912$	−9.95330e12	−0.476421
$913$	2.31816e13	1.10414
$914$	−1.73529e13	−0.822459
$915$	1.40492e13	0.662607
$916$	5.50766e12	0.258486
$917$	6.33179e12	0.295709
$918$	−1.42540e13	−0.662439
$919$	−3.90729e11	−0.0180699	−0.00903496	−	0.999959i	$-0.502876\pi$
$919$	−3.90729e11	−0.0180699	−0.00903496	+	0.999959i	$0.502876\pi$
$920$	−2.17792e13	−1.00230
$921$	−1.05005e13	−0.480886
$922$	5.74752e13	2.61934
$923$	0	0
$924$	3.50157e13	1.58030
$925$	3.11001e13	1.39677
$926$	6.30200e13	2.81662
$927$	2.81310e12	0.125120
$928$	−2.94870e13	−1.30516
$929$	1.22780e13	0.540827	0.270414	−	0.962744i	$-0.412840\pi$
$929$	1.22780e13	0.540827	0.270414	+	0.962744i	$0.412840\pi$
$930$	2.33119e13	1.02189
$931$	2.64036e13	1.15183
$932$	−4.23150e13	−1.83706
$933$	−1.22828e13	−0.530676
$934$	−2.77279e13	−1.19222
$935$	3.50577e13	1.50014
$936$	0	0
$937$	−3.14738e13	−1.33389	−0.666946	−	0.745106i	$-0.732399\pi$
$937$	−3.14738e13	−1.33389	−0.666946	+	0.745106i	$0.732399\pi$
$938$	−2.69806e13	−1.13799
$939$	1.42330e13	0.597451
$940$	5.37843e12	0.224688
$941$	−2.45616e13	−1.02118	−0.510592	−	0.859823i	$-0.670574\pi$
$941$	−2.45616e13	−1.02118	−0.510592	+	0.859823i	$0.670574\pi$
$942$	−3.66786e13	−1.51769
$943$	1.48678e13	0.612270
$944$	−8.58709e12	−0.351943
$945$	1.84774e13	0.753699
$946$	1.14185e14	4.63552
$947$	3.88870e13	1.57119	0.785596	−	0.618740i	$-0.212357\pi$
$947$	3.88870e13	1.57119	0.785596	+	0.618740i	$0.212357\pi$
$948$	1.88206e13	0.756825
$949$	0	0
$950$	−1.19160e14	−4.74650
$951$	4.13210e13	1.63817
$952$	−5.34827e12	−0.211032
$953$	−2.34348e13	−0.920329	−0.460165	−	0.887834i	$-0.652210\pi$
$953$	−2.34348e13	−0.920329	−0.460165	+	0.887834i	$0.652210\pi$
$954$	2.62990e12	0.102795
$955$	1.05187e13	0.409212
$956$	7.64874e12	0.296162
$957$	5.59414e13	2.15591
$958$	−3.84512e12	−0.147491
$959$	−1.93179e12	−0.0737524
$960$	8.10600e13	3.08025
$961$	−2.33645e13	−0.883694
$962$	0	0
$963$	−2.35396e12	−0.0882026
$964$	2.39981e13	0.895015
$965$	1.69190e13	0.628061
$966$	1.95578e13	0.722642
$967$	1.35865e13	0.499677	0.249838	−	0.968288i	$-0.419623\pi$
$967$	1.35865e13	0.499677	0.249838	+	0.968288i	$0.419623\pi$
$968$	4.45121e13	1.62944
$969$	−2.51341e13	−0.915811
$970$	1.11856e14	4.05684
$971$	−7.53765e12	−0.272113	−0.136057	−	0.990701i	$-0.543443\pi$
$971$	−7.53765e12	−0.272113	−0.136057	+	0.990701i	$0.543443\pi$
$972$	2.10603e13	0.756775
$973$	−1.29236e13	−0.462248
$974$	−7.70401e13	−2.74285
$975$	0	0
$976$	2.59914e12	0.0916867
$977$	3.43271e13	1.20535	0.602673	−	0.797988i	$-0.294102\pi$
$977$	3.43271e13	1.20535	0.602673	+	0.797988i	$0.294102\pi$
$978$	−1.41628e13	−0.495021
$979$	2.48556e13	0.864775
$980$	−5.19505e13	−1.79917
$981$	−1.39346e13	−0.480379
$982$	2.06333e13	0.708054
$983$	−2.63457e13	−0.899952	−0.449976	−	0.893041i	$-0.648567\pi$
$983$	−2.63457e13	−0.899952	−0.449976	+	0.893041i	$0.648567\pi$
$984$	2.07193e13	0.704525
$985$	−4.33703e13	−1.46801
$986$	−2.58515e13	−0.871042
$987$	−1.59637e12	−0.0535435
$988$	0	0
$989$	3.82019e13	1.26970
$990$	−3.67948e13	−1.21739
$991$	−1.18374e13	−0.389876	−0.194938	−	0.980816i	$-0.562451\pi$
$991$	−1.18374e13	−0.389876	−0.194938	+	0.980816i	$0.562451\pi$
$992$	1.24222e13	0.407282
$993$	−5.95201e13	−1.94264
$994$	3.89126e12	0.126430
$995$	−8.60694e13	−2.78384
$996$	3.27002e13	1.05289
$997$	−3.89835e13	−1.24955	−0.624774	−	0.780806i	$-0.714809\pi$
$997$	−3.89835e13	−1.24955	−0.624774	+	0.780806i	$0.714809\pi$
$998$	−2.03174e13	−0.648306
$999$	1.96598e13	0.624502

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p

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a_n

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a_n

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a_n

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.g.1.24	✓	27
13.12	even	2		169.10.a.h.1.4	yes	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.10.a.g.1.24	✓	27	1.1	even	1	trivial
169.10.a.h.1.4	yes	27	13.12	even	2

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Classical	Maass
Hilbert	Bianchi

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

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Groups

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	169.10.a.g.1.24

Level	$169$
Weight	$10$
Character	169.1
Self dual	yes
Analytic conductor	$87.041$
Analytic rank	$1$
Dimension	$27$
CM	no
Inner twists	$1$