LMFDB - Embedded newform 169.10.a.h.1.4

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:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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	$-0.789698\pi$
$2$	−35.7320	−1.57915	−0.789573	+	0.613657i	$0.789698\pi$
$3$	−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	$-0.820651\pi$
$5$	−2363.03	−1.69084	−0.845422	+	0.534099i	$0.820651\pi$
$6$	5625.74	1.77214
$7$	−3406.89	−0.536311	−0.268155	−	0.963376i	$-0.586414\pi$
$7$	−3406.89	−0.536311	−0.268155	+	0.963376i	$0.586414\pi$
$8$	−9032.12	−0.779623
$9$	5105.19	0.259371
$10$	84435.6	2.67009
$11$	85358.9	1.75785	0.878925	−	0.476959i	$-0.158261\pi$
$11$	85358.9	1.75785	0.878925	+	0.476959i	$0.158261\pi$
$12$	−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	$-0.200307\pi$
$19$	918491.	1.61690	0.808451	+	0.588564i	$0.200307\pi$
$20$	−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	$-0.445456\pi$
$31$	1.75360e6	0.341037	0.170519	+	0.985354i	$0.445456\pi$
$32$	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	$-0.622593\pi$
$37$	−8.56572e6	−0.751374	−0.375687	+	0.926747i	$0.622593\pi$
$38$	−3.28195e7	−2.55332
$39$	0	0
$40$	2.13431e7	1.31822
$41$	1.45701e7	0.805258	0.402629	−	0.915363i	$-0.368097\pi$
$41$	1.45701e7	0.805258	0.402629	+	0.915363i	$0.368097\pi$
$42$	−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	$-0.514164\pi$
$47$	−2.97614e6	−0.0889638	−0.0444819	+	0.999010i	$0.514164\pi$
$48$	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	$-0.733797\pi$
$59$	−1.24760e8	−1.34042	−0.670212	+	0.742170i	$0.733797\pi$
$60$	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	$-0.265501\pi$
$67$	2.21634e8	1.34369	0.671847	+	0.740690i	$0.265501\pi$
$68$	−1.32923e8	−0.753892
$69$	1.60659e8	0.853266
$70$	−2.87663e8	−1.43200
$71$	−3.19651e7	−0.149284	−0.0746419	−	0.997210i	$-0.523781\pi$
$71$	−3.19651e7	−0.149284	−0.0746419	+	0.997210i	$0.523781\pi$
$72$	−4.61107e7	−0.202211
$73$	−8.39854e7	−0.346139	−0.173070	−	0.984910i	$-0.555369\pi$
$73$	−8.39854e7	−0.346139	−0.173070	+	0.984910i	$0.555369\pi$
$74$	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	$-0.398310\pi$
$83$	2.71578e8	0.628121	0.314061	+	0.949403i	$0.398310\pi$
$84$	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	$-0.420892\pi$
$89$	2.91190e8	0.491950	0.245975	+	0.969276i	$0.420892\pi$
$90$	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	$-0.774646\pi$
$97$	−1.32475e9	−1.51937	−0.759683	+	0.650293i	$0.774646\pi$
$98$	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	$-0.123184\pi$
$109$	2.72950e9	1.85209	0.926047	+	0.377407i	$0.123184\pi$
$110$	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	$-0.478096\pi$
$137$	5.67025e8	0.137518	0.0687590	+	0.997633i	$0.478096\pi$
$138$	−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	$-0.333355\pi$
$149$	6.01571e9	0.999881	0.499941	+	0.866060i	$0.333355\pi$
$150$	2.04257e10	3.29433
$151$	−1.04382e10	−1.63391	−0.816956	−	0.576700i	$-0.804340\pi$
$151$	−1.04382e10	−1.63391	−0.816956	+	0.576700i	$0.804340\pi$
$152$	−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	$-0.544603\pi$
$163$	−2.51750e9	−0.279335	−0.139667	+	0.990198i	$0.544603\pi$
$164$	1.11428e10	1.20281
$165$	3.17570e10	3.33551
$166$	−9.70403e9	−0.991895
$167$	5.52083e9	0.549263	0.274632	−	0.961550i	$-0.411444\pi$
$167$	5.52083e9	0.549263	0.274632	+	0.961550i	$0.411444\pi$
$168$	−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	$-0.559463\pi$
$193$	−7.15989e9	−0.371449	−0.185724	+	0.982602i	$0.559463\pi$
$194$	4.73361e10	2.39930
$195$	0	0
$196$	−2.19848e10	−1.06407
$197$	1.83537e10	0.868212	0.434106	−	0.900862i	$-0.357064\pi$
$197$	1.83537e10	0.868212	0.434106	+	0.900862i	$0.357064\pi$
$198$	−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	$-0.495362\pi$
$223$	1.07609e9	0.0291393	0.0145696	+	0.999894i	$0.495362\pi$
$224$	−2.41338e10	−0.640487
$225$	1.85358e10	0.482157
$226$	3.32705e10	0.848343
$227$	−3.29551e10	−0.823770	−0.411885	−	0.911236i	$-0.635129\pi$
$227$	−3.29551e10	−0.823770	−0.411885	+	0.911236i	$0.635129\pi$
$228$	−1.10594e11	−2.71034
$229$	−7.20168e9	−0.173051	−0.0865255	−	0.996250i	$-0.527576\pi$
$229$	−7.20168e9	−0.173051	−0.0865255	+	0.996250i	$0.527576\pi$
$230$	−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	$-0.531608\pi$
$239$	−1.00013e10	−0.198274	−0.0991371	+	0.995074i	$0.531608\pi$
$240$	−2.56071e10	−0.498208
$241$	−3.13793e10	−0.599193	−0.299597	−	0.954066i	$-0.596852\pi$
$241$	−3.13793e10	−0.599193	−0.299597	+	0.954066i	$0.596852\pi$
$242$	−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	$-0.570237\pi$
$271$	−3.88666e10	−0.437738	−0.218869	+	0.975754i	$0.570237\pi$
$272$	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	$-0.818743\pi$
$281$	−1.76046e11	−1.68441	−0.842205	+	0.539158i	$0.818743\pi$
$282$	−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	$-0.728765\pi$
$293$	−1.66120e11	−1.31679	−0.658396	+	0.752672i	$0.728765\pi$
$294$	−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	$-0.568733\pi$
$307$	−6.66942e10	−0.428515	−0.214257	+	0.976777i	$0.568733\pi$
$308$	−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	$-0.239576\pi$
$317$	2.62451e11	1.45976	0.729880	+	0.683576i	$0.239576\pi$
$318$	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	$-0.833022\pi$
$331$	−3.78043e11	−1.73107	−0.865537	+	0.500846i	$0.833022\pi$
$332$	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	$-0.365378\pi$
$349$	2.27503e11	0.820866	0.410433	+	0.911891i	$0.365378\pi$
$350$	4.41991e11	1.57437
$351$	0	0
$352$	6.04669e11	2.09930
$353$	4.58333e11	1.57107	0.785533	−	0.618819i	$-0.212389\pi$
$353$	4.58333e11	1.57107	0.785533	+	0.618819i	$0.212389\pi$
$354$	−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	$-0.239047\pi$
$359$	4.60131e11	1.46203	0.731016	+	0.682360i	$0.239047\pi$
$360$	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	$-0.760904\pi$
$379$	−5.87179e11	−1.46182	−0.730910	+	0.682474i	$0.760904\pi$
$380$	−1.65988e12	−4.08367
$381$	2.52986e11	0.615083
$382$	−1.59057e11	−0.382179
$383$	4.78147e11	1.13545	0.567723	−	0.823220i	$-0.307824\pi$
$383$	4.78147e11	1.13545	0.567723	+	0.823220i	$0.307824\pi$
$384$	−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	$-0.485371\pi$
$397$	4.54781e10	0.0918850	0.0459425	+	0.998944i	$0.485371\pi$
$398$	1.30148e12	2.59994
$399$	4.92669e11	0.973144
$400$	−2.49901e11	−0.488088
$401$	−7.41103e11	−1.43129	−0.715647	−	0.698462i	$-0.753868\pi$
$401$	−7.41103e11	−1.43129	−0.715647	+	0.698462i	$0.753868\pi$
$402$	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	$-0.325703\pi$
$409$	5.89252e11	1.04123	0.520614	+	0.853792i	$0.325703\pi$
$410$	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	$-0.337233\pi$
$421$	6.30842e11	0.978704	0.489352	+	0.872086i	$0.337233\pi$
$422$	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	$-0.474197\pi$
$431$	1.16016e11	0.161946	0.0809730	+	0.996716i	$0.474197\pi$
$432$	−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	$-0.843514\pi$
$449$	−1.51844e12	−1.76314	−0.881572	+	0.472050i	$0.843514\pi$
$450$	−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	$-0.416141\pi$
$457$	4.85641e11	0.520825	0.260413	+	0.965497i	$0.416141\pi$
$458$	2.57330e11	0.273273
$459$	−3.98915e11	−0.419492
$460$	1.84410e12	1.92032
$461$	−1.60851e12	−1.65871	−0.829353	−	0.558725i	$-0.811291\pi$
$461$	−1.60851e12	−1.65871	−0.829353	+	0.558725i	$0.811291\pi$
$462$	−1.63601e12	−1.67070
$463$	−1.76369e12	−1.78364	−0.891819	−	0.452392i	$-0.850571\pi$
$463$	−1.76369e12	−1.78364	−0.891819	+	0.452392i	$0.850571\pi$
$464$	−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	$-0.485130\pi$
$479$	1.07610e11	0.0933991	0.0466996	+	0.998909i	$0.485130\pi$
$480$	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	$-0.165110\pi$
$487$	2.15606e12	1.73692	0.868460	+	0.495760i	$0.165110\pi$
$488$	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	$-0.434192\pi$
$499$	5.68605e11	0.410543	0.205271	+	0.978705i	$0.434192\pi$
$500$	−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	$-0.474369\pi$
$509$	2.43617e11	0.160871	0.0804354	+	0.996760i	$0.474369\pi$
$510$	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	$-0.543639\pi$
$541$	−5.44604e11	−0.273333	−0.136667	+	0.990617i	$0.543639\pi$
$542$	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	$-0.270932\pi$
$557$	2.99460e12	1.31823	0.659113	+	0.752044i	$0.270932\pi$
$558$	−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	$-0.528529\pi$
$577$	−4.76628e11	−0.179015	−0.0895073	+	0.995986i	$0.528529\pi$
$578$	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	$-0.507787\pi$
$587$	−1.40719e11	−0.0489194	−0.0244597	+	0.999701i	$0.507787\pi$
$588$	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	$-0.196912\pi$
$593$	4.90641e12	1.62936	0.814681	+	0.579909i	$0.196912\pi$
$594$	−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	$-0.872254\pi$
$613$	−6.43646e12	−1.84109	−0.920544	+	0.390639i	$0.872254\pi$
$614$	2.38312e12	0.676687
$615$	5.42067e12	1.52797
$616$	2.62662e12	0.734994
$617$	−6.09818e10	−0.0169401	−0.00847007	−	0.999964i	$-0.502696\pi$
$617$	−6.09818e10	−0.0169401	−0.00847007	+	0.999964i	$0.502696\pi$
$618$	3.09994e12	0.854880
$619$	3.71099e12	1.01597	0.507986	−	0.861365i	$-0.330390\pi$
$619$	3.71099e12	1.01597	0.507986	+	0.861365i	$0.330390\pi$
$620$	−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	$-0.431828\pi$
$631$	1.69274e12	0.425068	0.212534	+	0.977154i	$0.431828\pi$
$632$	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	$-0.266605\pi$
$643$	5.80209e12	1.33855	0.669275	+	0.743015i	$0.266605\pi$
$644$	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	$-0.689061\pi$
$661$	−5.49347e12	−1.11928	−0.559642	+	0.828735i	$0.689061\pi$
$662$	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	$-0.356061\pi$
$683$	4.96989e12	0.873884	0.436942	+	0.899490i	$0.356061\pi$
$684$	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	$-0.525820\pi$
$691$	−9.71204e11	−0.162054	−0.0810269	+	0.996712i	$0.525820\pi$
$692$	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	$-0.204865\pi$
$709$	1.07645e13	1.59988	0.799940	+	0.600080i	$0.204865\pi$
$710$	−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	$-0.251442\pi$
$733$	1.10029e13	1.40779	0.703896	+	0.710303i	$0.251442\pi$
$734$	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	$-0.168894\pi$
$739$	1.39859e13	1.72501	0.862505	+	0.506048i	$0.168894\pi$
$740$	1.54798e13	1.89768
$741$	0	0
$742$	1.75503e12	0.212553
$743$	4.61053e12	0.555011	0.277505	−	0.960724i	$-0.410492\pi$
$743$	4.61053e12	0.555011	0.277505	+	0.960724i	$0.410492\pi$
$744$	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	$-0.349498\pi$
$761$	8.42654e12	0.910790	0.455395	+	0.890289i	$0.349498\pi$
$762$	−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	$-0.258595\pi$
$769$	1.33393e13	1.37552	0.687758	+	0.725940i	$0.258595\pi$
$770$	−2.45546e13	−2.51724
$771$	−2.49917e12	−0.254713
$772$	−5.47570e12	−0.554833
$773$	−1.25115e13	−1.26038	−0.630190	−	0.776441i	$-0.717023\pi$
$773$	−1.25115e13	−1.26038	−0.630190	+	0.776441i	$0.717023\pi$
$774$	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	$-0.570042\pi$
$787$	−4.69799e12	−0.436542	−0.218271	+	0.975888i	$0.570042\pi$
$788$	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	$-0.576749\pi$
$811$	−5.88340e12	−0.477567	−0.238784	+	0.971073i	$0.576749\pi$
$812$	−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	$-0.316707\pi$
$821$	1.41774e13	1.08906	0.544532	+	0.838740i	$0.316707\pi$
$822$	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	$-0.489467\pi$
$827$	8.90088e11	0.0661696	0.0330848	+	0.999453i	$0.489467\pi$
$828$	−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	$-0.0918424\pi$
$839$	2.75185e13	1.91733	0.958663	+	0.284545i	$0.0918424\pi$
$840$	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	$-0.618449\pi$
$853$	−1.12438e13	−0.727181	−0.363591	+	0.931559i	$0.618449\pi$
$854$	−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	$-0.545488\pi$
$863$	−4.64134e12	−0.284836	−0.142418	+	0.989807i	$0.545488\pi$
$864$	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	$-0.156467\pi$
$877$	3.08887e13	1.76320	0.881599	+	0.471999i	$0.156467\pi$
$878$	−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	$-0.587160\pi$
$929$	−1.22780e13	−0.540827	−0.270414	+	0.962744i	$0.587160\pi$
$930$	−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	$-0.329426\pi$
$941$	2.45616e13	1.02118	0.510592	+	0.859823i	$0.329426\pi$
$942$	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	$-0.787643\pi$
$947$	−3.88870e13	−1.57119	−0.785596	+	0.618740i	$0.787643\pi$
$948$	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	$-0.580377\pi$
$967$	−1.35865e13	−0.499677	−0.249838	+	0.968288i	$0.580377\pi$
$968$	−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	$-0.705898\pi$
$977$	−3.43271e13	−1.20535	−0.602673	+	0.797988i	$0.705898\pi$
$978$	−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	$-0.351433\pi$
$983$	2.63457e13	0.899952	0.449976	+	0.893041i	$0.351433\pi$
$984$	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

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q-35.7320 q^{2} -157.443 q^{3} +764.774 q^{4} -2363.03 q^{5} +5625.74 q^{6} -3406.89 q^{7} -9032.12 q^{8} +5105.19 q^{9} +84435.6 q^{10} +85358.9 q^{11} -120408. q^{12} +121735. q^{14} +372041. q^{15} -68828.8 q^{16} -173806. q^{17} -182419. q^{18} +918491. q^{19} -1.80718e6 q^{20} +536389. q^{21} -3.05004e6 q^{22} -1.02043e6 q^{23} +1.42204e6 q^{24} +3.63077e6 q^{25} +2.29517e6 q^{27} -2.60550e6 q^{28} +4.16258e6 q^{29} -1.32938e7 q^{30} +1.75360e6 q^{31} +7.08384e6 q^{32} -1.34391e7 q^{33} +6.21045e6 q^{34} +8.05056e6 q^{35} +3.90432e6 q^{36} -8.56572e6 q^{37} -3.28195e7 q^{38} +2.13431e7 q^{40} +1.45701e7 q^{41} -1.91663e7 q^{42} -3.74371e7 q^{43} +6.52803e7 q^{44} -1.20637e7 q^{45} +3.64620e7 q^{46} -2.97614e6 q^{47} +1.08366e7 q^{48} -2.87467e7 q^{49} -1.29734e8 q^{50} +2.73645e7 q^{51} +1.44169e7 q^{53} -8.20109e7 q^{54} -2.01705e8 q^{55} +3.07714e7 q^{56} -1.44610e8 q^{57} -1.48737e8 q^{58} -1.24760e8 q^{59} +2.84527e8 q^{60} -3.77625e7 q^{61} -6.26594e7 q^{62} -1.73928e7 q^{63} -2.17879e8 q^{64} +4.80207e8 q^{66} +2.21634e8 q^{67} -1.32923e8 q^{68} +1.60659e8 q^{69} -2.87663e8 q^{70} -3.19651e7 q^{71} -4.61107e7 q^{72} -8.39854e7 q^{73} +3.06070e8 q^{74} -5.71638e8 q^{75} +7.02438e8 q^{76} -2.90808e8 q^{77} -1.56307e8 q^{79} +1.62644e8 q^{80} -4.61843e8 q^{81} -5.20618e8 q^{82} +2.71578e8 q^{83} +4.10217e8 q^{84} +4.10709e8 q^{85} +1.33770e9 q^{86} -6.55367e8 q^{87} -7.70972e8 q^{88} +2.91190e8 q^{89} +4.31060e8 q^{90} -7.80398e8 q^{92} -2.76091e8 q^{93} +1.06343e8 q^{94} -2.17042e9 q^{95} -1.11530e9 q^{96} -1.32475e9 q^{97} +1.02718e9 q^{98} +4.35774e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 65 q^{2} + q^{3} + 7169 q^{4} + 3238 q^{5} + 8490 q^{6} + 17378 q^{7} + 54204 q^{8} + 191118 q^{9} + 11697 q^{10} + 164171 q^{11} - 181941 q^{12} - 77651 q^{14} + 614110 q^{15} + 3012565 q^{16}+ \cdots + 5866875443 q^{99}+O(q^{100}) \) 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

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