LMFDB - Embedded newform 169.10.a.g.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,10,Mod(1,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [27,-65] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			1.4
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)

$f(q)$	$=$	$q-40.6641 q^{2} -254.108 q^{3} +1141.57 q^{4} -1761.73 q^{5} +10333.1 q^{6} +1279.48 q^{7} -25601.0 q^{8} +44887.8 q^{9} +71639.4 q^{10} -52620.5 q^{11} -290082. q^{12} -52029.0 q^{14} +447670. q^{15} +456557. q^{16} -223297. q^{17} -1.82532e6 q^{18} -545238. q^{19} -2.01114e6 q^{20} -325126. q^{21} +2.13977e6 q^{22} -1.10556e6 q^{23} +6.50541e6 q^{24} +1.15058e6 q^{25} -6.40472e6 q^{27} +1.46062e6 q^{28} -1.27842e6 q^{29} -1.82041e7 q^{30} -7.41062e6 q^{31} -5.45779e6 q^{32} +1.33713e7 q^{33} +9.08018e6 q^{34} -2.25411e6 q^{35} +5.12426e7 q^{36} +4.37006e6 q^{37} +2.21716e7 q^{38} +4.51021e7 q^{40} -1.41271e7 q^{41} +1.32210e7 q^{42} +2.97937e7 q^{43} -6.00701e7 q^{44} -7.90803e7 q^{45} +4.49568e7 q^{46} +1.62162e7 q^{47} -1.16015e8 q^{48} -3.87165e7 q^{49} -4.67873e7 q^{50} +5.67415e7 q^{51} +8.73853e7 q^{53} +2.60443e8 q^{54} +9.27033e7 q^{55} -3.27560e7 q^{56} +1.38549e8 q^{57} +5.19860e7 q^{58} -1.01196e8 q^{59} +5.11047e8 q^{60} +2.03191e8 q^{61} +3.01346e8 q^{62} +5.74331e7 q^{63} -1.18209e7 q^{64} -5.43732e8 q^{66} +1.43897e8 q^{67} -2.54909e8 q^{68} +2.80932e8 q^{69} +9.16612e7 q^{70} -6.26152e7 q^{71} -1.14917e9 q^{72} +3.27462e8 q^{73} -1.77705e8 q^{74} -2.92371e8 q^{75} -6.22428e8 q^{76} -6.73270e7 q^{77} +2.96852e8 q^{79} -8.04331e8 q^{80} +7.43965e8 q^{81} +5.74466e8 q^{82} -6.46415e8 q^{83} -3.71155e8 q^{84} +3.93390e8 q^{85} -1.21154e9 q^{86} +3.24857e8 q^{87} +1.34714e9 q^{88} -5.31202e8 q^{89} +3.21573e9 q^{90} -1.26208e9 q^{92} +1.88310e9 q^{93} -6.59420e8 q^{94} +9.60564e8 q^{95} +1.38687e9 q^{96} -8.88218e8 q^{97} +1.57437e9 q^{98} -2.36202e9 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$27 q - 65 q^{2} + q^{3} + 7169 q^{4} - 3238 q^{5} - 8490 q^{6} - 17378 q^{7} - 54204 q^{8} + 191118 q^{9} + 11697 q^{10} - 164171 q^{11} - 181941 q^{12} - 77651 q^{14} - 614110 q^{15} + 3012565 q^{16}+ \cdots - 5866875443 q^{99}+O(q^{100})$ 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

)

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

$2$	−40.6641	−1.79712	−0.898559	−	0.438853i	$-0.855385\pi$
$2$	−40.6641	−1.79712	−0.898559	+	0.438853i	$0.855385\pi$
$3$	−254.108	−1.81122	−0.905612	−	0.424107i	$-0.860588\pi$
$3$	−254.108	−1.81122	−0.905612	+	0.424107i	$0.860588\pi$
$4$	1141.57	2.22963
$5$	−1761.73	−1.26059	−0.630297	−	0.776354i	$-0.717067\pi$
$5$	−1761.73	−1.26059	−0.630297	+	0.776354i	$0.717067\pi$
$6$	10333.1	3.25498
$7$	1279.48	0.201416	0.100708	−	0.994916i	$-0.467889\pi$
$7$	1279.48	0.201416	0.100708	+	0.994916i	$0.467889\pi$
$8$	−25601.0	−2.20979
$9$	44887.8	2.28053
$10$	71639.4	2.26544
$11$	−52620.5	−1.08365	−0.541824	−	0.840492i	$-0.682266\pi$
$11$	−52620.5	−1.08365	−0.541824	+	0.840492i	$0.682266\pi$
$12$	−290082.	−4.03836
$13$	0	0
$13$	0	0
$14$	−52029.0	−0.361967
$15$	447670.	2.28322
$16$	456557.	1.74163
$17$	−223297.	−0.648429	−0.324215	−	0.945984i	$-0.605100\pi$
$17$	−223297.	−0.648429	−0.324215	+	0.945984i	$0.605100\pi$
$18$	−1.82532e6	−4.09839
$19$	−545238.	−0.959831	−0.479916	−	0.877315i	$-0.659333\pi$
$19$	−545238.	−0.959831	−0.479916	+	0.877315i	$0.659333\pi$
$20$	−2.01114e6	−2.81066
$21$	−325126.	−0.364809
$22$	2.13977e6	1.94744
$23$	−1.10556e6	−0.823775	−0.411888	−	0.911235i	$-0.635130\pi$
$23$	−1.10556e6	−0.823775	−0.411888	+	0.911235i	$0.635130\pi$
$24$	6.50541e6	4.00243
$25$	1.15058e6	0.589097
$26$	0	0
$27$	−6.40472e6	−2.31934
$28$	1.46062e6	0.449082
$29$	−1.27842e6	−0.335648	−0.167824	−	0.985817i	$-0.553674\pi$
$29$	−1.27842e6	−0.335648	−0.167824	+	0.985817i	$0.553674\pi$
$30$	−1.82041e7	−4.10321
$31$	−7.41062e6	−1.44121	−0.720605	−	0.693346i	$-0.756136\pi$
$31$	−7.41062e6	−1.44121	−0.720605	+	0.693346i	$0.756136\pi$
$32$	−5.45779e6	−0.920114
$33$	1.33713e7	1.96273
$34$	9.08018e6	1.16530
$35$	−2.25411e6	−0.253903
$36$	5.12426e7	5.08475
$37$	4.37006e6	0.383336	0.191668	−	0.981460i	$-0.438610\pi$
$37$	4.37006e6	0.383336	0.191668	+	0.981460i	$0.438610\pi$
$38$	2.21716e7	1.72493
$39$	0	0
$40$	4.51021e7	2.78565
$41$	−1.41271e7	−0.780775	−0.390387	−	0.920651i	$-0.627659\pi$
$41$	−1.41271e7	−0.780775	−0.390387	+	0.920651i	$0.627659\pi$
$42$	1.32210e7	0.655604
$43$	2.97937e7	1.32898	0.664488	−	0.747299i	$-0.268650\pi$
$43$	2.97937e7	1.32898	0.664488	+	0.747299i	$0.268650\pi$
$44$	−6.00701e7	−2.41613
$45$	−7.90803e7	−2.87483
$46$	4.49568e7	1.48042
$47$	1.62162e7	0.484741	0.242371	−	0.970184i	$-0.422075\pi$
$47$	1.62162e7	0.484741	0.242371	+	0.970184i	$0.422075\pi$
$48$	−1.16015e8	−3.15448
$49$	−3.87165e7	−0.959432
$50$	−4.67873e7	−1.05868
$51$	5.67415e7	1.17445
$52$	0	0
$53$	8.73853e7	1.52124	0.760619	−	0.649199i	$-0.224896\pi$
$53$	8.73853e7	1.52124	0.760619	+	0.649199i	$0.224896\pi$
$54$	2.60443e8	4.16812
$55$	9.27033e7	1.36604
$56$	−3.27560e7	−0.445087
$57$	1.38549e8	1.73847
$58$	5.19860e7	0.603199
$59$	−1.01196e8	−1.08725	−0.543625	−	0.839329i	$-0.682948\pi$
$59$	−1.01196e8	−1.08725	−0.543625	+	0.839329i	$0.682948\pi$
$60$	5.11047e8	5.09074
$61$	2.03191e8	1.87897	0.939487	−	0.342585i	$-0.111303\pi$
$61$	2.03191e8	1.87897	0.939487	+	0.342585i	$0.111303\pi$
$62$	3.01346e8	2.59002
$63$	5.74331e7	0.459335
$64$	−1.18209e7	−0.0880729
$65$	0	0
$66$	−5.43732e8	−3.52725
$67$	1.43897e8	0.872398	0.436199	−	0.899850i	$-0.356324\pi$
$67$	1.43897e8	0.872398	0.436199	+	0.899850i	$0.356324\pi$
$68$	−2.54909e8	−1.44576
$69$	2.80932e8	1.49204
$70$	9.16612e7	0.456294
$71$	−6.26152e7	−0.292427	−0.146213	−	0.989253i	$-0.546709\pi$
$71$	−6.26152e7	−0.292427	−0.146213	+	0.989253i	$0.546709\pi$
$72$	−1.14917e9	−5.03951
$73$	3.27462e8	1.34961	0.674805	−	0.737996i	$-0.264228\pi$
$73$	3.27462e8	1.34961	0.674805	+	0.737996i	$0.264228\pi$
$74$	−1.77705e8	−0.688900
$75$	−2.92371e8	−1.06699
$76$	−6.22428e8	−2.14007
$77$	−6.73270e7	−0.218263
$78$	0	0
$79$	2.96852e8	0.857468	0.428734	−	0.903431i	$-0.358960\pi$
$79$	2.96852e8	0.857468	0.428734	+	0.903431i	$0.358960\pi$
$80$	−8.04331e8	−2.19548
$81$	7.43965e8	1.92030
$82$	5.74466e8	1.40314
$83$	−6.46415e8	−1.49507	−0.747533	−	0.664225i	$-0.768762\pi$
$83$	−6.46415e8	−1.49507	−0.747533	+	0.664225i	$0.768762\pi$
$84$	−3.71155e8	−0.813389
$85$	3.93390e8	0.817406
$86$	−1.21154e9	−2.38832
$87$	3.24857e8	0.607934
$88$	1.34714e9	2.39464
$89$	−5.31202e8	−0.897438	−0.448719	−	0.893673i	$-0.648120\pi$
$89$	−5.31202e8	−0.897438	−0.448719	+	0.893673i	$0.648120\pi$
$90$	3.21573e9	5.16640
$91$	0	0
$92$	−1.26208e9	−1.83672
$93$	1.88310e9	2.61035
$94$	−6.59420e8	−0.871137
$95$	9.60564e8	1.20996
$96$	1.38687e9	1.66653
$97$	−8.88218e8	−1.01870	−0.509351	−	0.860559i	$-0.670114\pi$
$97$	−8.88218e8	−1.01870	−0.509351	+	0.860559i	$0.670114\pi$
$98$	1.57437e9	1.72421
$99$	−2.36202e9	−2.47130
$100$	1.31347e9	1.31347
$101$	3.45113e8	0.330001	0.165000	−	0.986294i	$-0.447237\pi$
$101$	3.45113e8	0.330001	0.165000	+	0.986294i	$0.447237\pi$
$102$	−2.30734e9	−2.11063
$103$	−1.65802e9	−1.45151	−0.725757	−	0.687951i	$-0.758510\pi$
$103$	−1.65802e9	−1.45151	−0.725757	+	0.687951i	$0.758510\pi$
$104$	0	0
$105$	5.72786e8	0.459876
$106$	−3.55345e9	−2.73384
$107$	9.87711e8	0.728455	0.364228	−	0.931310i	$-0.381333\pi$
$107$	9.87711e8	0.728455	0.364228	+	0.931310i	$0.381333\pi$
$108$	−7.31145e9	−5.17126
$109$	1.10461e9	0.749529	0.374765	−	0.927120i	$-0.377723\pi$
$109$	1.10461e9	0.749529	0.374765	+	0.927120i	$0.377723\pi$
$110$	−3.76970e9	−2.45493
$111$	−1.11047e9	−0.694307
$112$	5.84156e8	0.350791
$113$	−353967.	−0.000204226 0	−0.000102113	−	1.00000i	$-0.500033\pi$
$113$	−353967.	−0.000204226 0	−0.000102113		1.00000i	$0.500033\pi$
$114$	−5.63398e9	−3.12423
$115$	1.94771e9	1.03845
$116$	−1.45941e9	−0.748371
$117$	0	0
$118$	4.11504e9	1.95391
$119$	−2.85704e8	−0.130604
$120$	−1.14608e10	−5.04544
$121$	4.10971e8	0.174292
$122$	−8.26259e9	−3.37674
$123$	3.58981e9	1.41416
$124$	−8.45975e9	−3.21337
$125$	1.41387e9	0.517982
$126$	−2.33547e9	−0.825479
$127$	3.21555e9	1.09683	0.548415	−	0.836207i	$-0.315232\pi$
$127$	3.21555e9	1.09683	0.548415	+	0.836207i	$0.315232\pi$
$128$	3.27508e9	1.07839
$129$	−7.57082e9	−2.40707
$130$	0	0
$131$	1.09467e9	0.324761	0.162380	−	0.986728i	$-0.448083\pi$
$131$	1.09467e9	0.324761	0.162380	+	0.986728i	$0.448083\pi$
$132$	1.52643e10	4.37616
$133$	−6.97622e8	−0.193325
$134$	−5.85144e9	−1.56780
$135$	1.12834e10	2.92374
$136$	5.71662e9	1.43289
$137$	1.47148e9	0.356872	0.178436	−	0.983952i	$-0.442896\pi$
$137$	1.47148e9	0.356872	0.178436	+	0.983952i	$0.442896\pi$
$138$	−1.14239e10	−2.68137
$139$	3.79795e9	0.862943	0.431472	−	0.902127i	$-0.357995\pi$
$139$	3.79795e9	0.862943	0.431472	+	0.902127i	$0.357995\pi$
$140$	−2.57322e9	−0.566110
$141$	−4.12068e9	−0.877975
$142$	2.54619e9	0.525526
$143$	0	0
$144$	2.04938e10	3.97184
$145$	2.25224e9	0.423116
$146$	−1.33160e10	−2.42541
$147$	9.83817e9	1.73775
$148$	4.98873e9	0.854698
$149$	1.56982e9	0.260922	0.130461	−	0.991453i	$-0.458354\pi$
$149$	1.56982e9	0.260922	0.130461	+	0.991453i	$0.458354\pi$
$150$	1.18890e10	1.91750
$151$	5.16487e9	0.808469	0.404235	−	0.914655i	$-0.367538\pi$
$151$	5.16487e9	0.808469	0.404235	+	0.914655i	$0.367538\pi$
$152$	1.39586e10	2.12103
$153$	−1.00233e10	−1.47877
$154$	2.73779e9	0.392245
$155$	1.30555e10	1.81678
$156$	0	0
$157$	6.83691e9	0.898073	0.449037	−	0.893513i	$-0.351767\pi$
$157$	6.83691e9	0.898073	0.449037	+	0.893513i	$0.351767\pi$
$158$	−1.20712e10	−1.54097
$159$	−2.22053e10	−2.75530
$160$	9.61517e9	1.15989
$161$	−1.41455e9	−0.165921
$162$	−3.02527e10	−3.45101
$163$	−6.22569e9	−0.690786	−0.345393	−	0.938458i	$-0.612254\pi$
$163$	−6.22569e9	−0.690786	−0.345393	+	0.938458i	$0.612254\pi$
$164$	−1.61271e10	−1.74084
$165$	−2.35566e10	−2.47420
$166$	2.62859e10	2.68681
$167$	1.18052e10	1.17449	0.587244	−	0.809410i	$-0.300213\pi$
$167$	1.18052e10	1.17449	0.587244	+	0.809410i	$0.300213\pi$
$168$	8.32355e9	0.806152
$169$	0	0
$170$	−1.59969e10	−1.46897
$171$	−2.44745e10	−2.18893
$172$	3.40117e10	2.96312
$173$	−2.25103e9	−0.191062	−0.0955310	−	0.995426i	$-0.530455\pi$
$173$	−2.25103e9	−0.191062	−0.0955310	+	0.995426i	$0.530455\pi$
$174$	−1.32100e10	−1.09253
$175$	1.47215e9	0.118653
$176$	−2.40243e10	−1.88731
$177$	2.57147e10	1.96925
$178$	2.16009e10	1.61280
$179$	−6.08458e9	−0.442988	−0.221494	−	0.975162i	$-0.571093\pi$
$179$	−6.08458e9	−0.442988	−0.221494	+	0.975162i	$0.571093\pi$
$180$	−9.02758e10	−6.40981
$181$	−9.34985e9	−0.647517	−0.323758	−	0.946140i	$-0.604947\pi$
$181$	−9.34985e9	−0.647517	−0.323758	+	0.946140i	$0.604947\pi$
$182$	0	0
$183$	−5.16325e10	−3.40324
$184$	2.83035e10	1.82037
$185$	−7.69888e9	−0.483231
$186$	−7.65745e10	−4.69111
$187$	1.17500e10	0.702669
$188$	1.85120e10	1.08079
$189$	−8.19473e9	−0.467150
$190$	−3.90605e10	−2.17444
$191$	−2.72447e10	−1.48126	−0.740631	−	0.671912i	$-0.765473\pi$
$191$	−2.72447e10	−1.48126	−0.740631	+	0.671912i	$0.765473\pi$
$192$	3.00379e9	0.159520
$193$	2.75300e10	1.42823	0.714115	−	0.700029i	$-0.246829\pi$
$193$	2.75300e10	1.42823	0.714115	+	0.700029i	$0.246829\pi$
$194$	3.61186e10	1.83073
$195$	0	0
$196$	−4.41977e10	−2.13918
$197$	2.77018e10	1.31042	0.655208	−	0.755448i	$-0.272581\pi$
$197$	2.77018e10	1.31042	0.655208	+	0.755448i	$0.272581\pi$
$198$	9.60494e10	4.44121
$199$	2.44000e10	1.10294	0.551469	−	0.834196i	$-0.314068\pi$
$199$	2.44000e10	1.10294	0.551469	+	0.834196i	$0.314068\pi$
$200$	−2.94560e10	−1.30178
$201$	−3.65653e10	−1.58011
$202$	−1.40337e10	−0.593050
$203$	−1.63572e9	−0.0676047
$204$	6.47745e10	2.61859
$205$	2.48882e10	0.984240
$206$	6.74218e10	2.60854
$207$	−4.96263e10	−1.87865
$208$	0	0
$209$	2.86907e10	1.04012
$210$	−2.32918e10	−0.826451
$211$	−1.26026e10	−0.437711	−0.218855	−	0.975757i	$-0.570232\pi$
$211$	−1.26026e10	−0.437711	−0.218855	+	0.975757i	$0.570232\pi$
$212$	9.97566e10	3.39180
$213$	1.59110e10	0.529651
$214$	−4.01644e10	−1.30912
$215$	−5.24886e10	−1.67530
$216$	1.63967e11	5.12525
$217$	−9.48175e9	−0.290282
$218$	−4.49179e10	−1.34699
$219$	−8.32107e10	−2.44445
$220$	1.05827e11	3.04576
$221$	0	0
$222$	4.51561e10	1.24775
$223$	2.40428e10	0.651048	0.325524	−	0.945534i	$-0.394459\pi$
$223$	2.40428e10	0.651048	0.325524	+	0.945534i	$0.394459\pi$
$224$	−6.98314e9	−0.185325
$225$	5.16469e10	1.34346
$226$	1.43938e7	0.000367017 0
$227$	1.50190e10	0.375426	0.187713	−	0.982224i	$-0.439893\pi$
$227$	1.50190e10	0.375426	0.187713	+	0.982224i	$0.439893\pi$
$228$	1.58164e11	3.87615
$229$	−2.06015e9	−0.0495038	−0.0247519	−	0.999694i	$-0.507880\pi$
$229$	−2.06015e9	−0.0495038	−0.0247519	+	0.999694i	$0.507880\pi$
$230$	−7.92019e10	−1.86621
$231$	1.71083e10	0.395324
$232$	3.27289e10	0.741712
$233$	−2.46956e10	−0.548932	−0.274466	−	0.961597i	$-0.588501\pi$
$233$	−2.46956e10	−0.548932	−0.274466	+	0.961597i	$0.588501\pi$
$234$	0	0
$235$	−2.85687e10	−0.611062
$236$	−1.15522e11	−2.42416
$237$	−7.54324e10	−1.55307
$238$	1.16179e10	0.234710
$239$	2.81577e10	0.558222	0.279111	−	0.960259i	$-0.409960\pi$
$239$	2.81577e10	0.558222	0.279111	+	0.960259i	$0.409960\pi$
$240$	2.04387e11	3.97651
$241$	8.07535e10	1.54200	0.771000	−	0.636835i	$-0.219757\pi$
$241$	8.07535e10	1.54200	0.771000	+	0.636835i	$0.219757\pi$
$242$	−1.67118e10	−0.313223
$243$	−6.29830e10	−1.15876
$244$	2.31957e11	4.18942
$245$	6.82082e10	1.20945
$246$	−1.45976e11	−2.54141
$247$	0	0
$248$	1.89719e11	3.18477
$249$	1.64259e11	2.70790
$250$	−5.74938e10	−0.930875
$251$	1.04221e11	1.65738	0.828692	−	0.559705i	$-0.189086\pi$
$251$	1.04221e11	1.65738	0.828692	+	0.559705i	$0.189086\pi$
$252$	6.55639e10	1.02415
$253$	5.81754e10	0.892682
$254$	−1.30758e11	−1.97113
$255$	−9.99634e10	−1.48051
$256$	−1.27126e11	−1.84992
$257$	−1.04145e11	−1.48915	−0.744575	−	0.667539i	$-0.767348\pi$
$257$	−1.04145e11	−1.48915	−0.744575	+	0.667539i	$0.767348\pi$
$258$	3.07861e11	4.32579
$259$	5.59141e9	0.0772098
$260$	0	0
$261$	−5.73856e10	−0.765456
$262$	−4.45139e10	−0.583634
$263$	1.03028e11	1.32787	0.663936	−	0.747790i	$-0.268885\pi$
$263$	1.03028e11	1.32787	0.663936	+	0.747790i	$0.268885\pi$
$264$	−3.42318e11	−4.33722
$265$	−1.53950e11	−1.91766
$266$	2.83682e10	0.347428
$267$	1.34983e11	1.62546
$268$	1.64268e11	1.94513
$269$	1.14754e11	1.33624	0.668118	−	0.744055i	$-0.267100\pi$
$269$	1.14754e11	1.33624	0.668118	+	0.744055i	$0.267100\pi$
$270$	−4.58830e11	−5.25430
$271$	−1.23193e11	−1.38747	−0.693734	−	0.720232i	$-0.744036\pi$
$271$	−1.23193e11	−1.38747	−0.693734	+	0.720232i	$0.744036\pi$
$272$	−1.01948e11	−1.12932
$273$	0	0
$274$	−5.98365e10	−0.641341
$275$	−6.05441e10	−0.638373
$276$	3.20704e11	3.32670
$277$	−1.77863e10	−0.181521	−0.0907603	−	0.995873i	$-0.528930\pi$
$277$	−1.77863e10	−0.181521	−0.0907603	+	0.995873i	$0.528930\pi$
$278$	−1.54440e11	−1.55081
$279$	−3.32646e11	−3.28673
$280$	5.77073e10	0.561073
$281$	−5.40996e10	−0.517625	−0.258813	−	0.965928i	$-0.583331\pi$
$281$	−5.40996e10	−0.517625	−0.258813	+	0.965928i	$0.583331\pi$
$282$	1.67564e11	1.57783
$283$	−2.25498e10	−0.208980	−0.104490	−	0.994526i	$-0.533321\pi$
$283$	−2.25498e10	−0.208980	−0.104490	+	0.994526i	$0.533321\pi$
$284$	−7.14797e10	−0.652004
$285$	−2.44087e11	−2.19150
$286$	0	0
$287$	−1.80754e10	−0.157260
$288$	−2.44988e11	−2.09835
$289$	−6.87263e10	−0.579539
$290$	−9.15855e10	−0.760389
$291$	2.25703e11	1.84510
$292$	3.73822e11	3.00913
$293$	2.73911e10	0.217123	0.108561	−	0.994090i	$-0.465376\pi$
$293$	2.73911e10	0.217123	0.108561	+	0.994090i	$0.465376\pi$
$294$	−4.00061e11	−3.12293
$295$	1.78280e11	1.37058
$296$	−1.11878e11	−0.847093
$297$	3.37020e11	2.51334
$298$	−6.38353e10	−0.468908
$299$	0	0
$300$	−3.33763e11	−2.37899
$301$	3.81205e10	0.267676
$302$	−2.10025e11	−1.45291
$303$	−8.76958e10	−0.597705
$304$	−2.48932e11	−1.67167
$305$	−3.57969e11	−2.36862
$306$	4.07589e11	2.65752
$307$	−2.35180e11	−1.51104	−0.755522	−	0.655124i	$-0.772617\pi$
$307$	−2.35180e11	−1.51104	−0.755522	+	0.655124i	$0.772617\pi$
$308$	−7.68586e10	−0.486647
$309$	4.21315e11	2.62902
$310$	−5.30892e11	−3.26497
$311$	−3.92759e10	−0.238070	−0.119035	−	0.992890i	$-0.537980\pi$
$311$	−3.92759e10	−0.238070	−0.119035	+	0.992890i	$0.537980\pi$
$312$	0	0
$313$	−4.58563e10	−0.270054	−0.135027	−	0.990842i	$-0.543112\pi$
$313$	−4.58563e10	−0.270054	−0.135027	+	0.990842i	$0.543112\pi$
$314$	−2.78017e11	−1.61394
$315$	−1.01182e11	−0.579035
$316$	3.38878e11	1.91184
$317$	1.39591e9	0.00776409	0.00388205	−	0.999992i	$-0.498764\pi$
$317$	1.39591e9	0.00776409	0.00388205	+	0.999992i	$0.498764\pi$
$318$	9.02959e11	4.95160
$319$	6.72713e10	0.363724
$320$	2.08253e10	0.111024
$321$	−2.50985e11	−1.31940
$322$	5.75214e10	0.298180
$323$	1.21750e11	0.622383
$324$	8.49289e11	4.28157
$325$	0	0
$326$	2.53162e11	1.24142
$327$	−2.80689e11	−1.35757
$328$	3.61668e11	1.72535
$329$	2.07484e10	0.0976344
$330$	9.57910e11	4.44644
$331$	−2.54109e11	−1.16358	−0.581788	−	0.813341i	$-0.697647\pi$
$331$	−2.54109e11	−1.16358	−0.581788	+	0.813341i	$0.697647\pi$
$332$	−7.37929e11	−3.33345
$333$	1.96162e11	0.874211
$334$	−4.80048e11	−2.11069
$335$	−2.53508e11	−1.09974
$336$	−1.48439e11	−0.635360
$337$	4.04480e8	0.00170829	0.000854147	−	1.00000i	$-0.499728\pi$
$337$	4.04480e8	0.00170829	0.000854147		1.00000i	$0.499728\pi$
$338$	0	0
$339$	8.99458e7	0.000369898 0
$340$	4.49083e11	1.82251
$341$	3.89951e11	1.56176
$342$	9.95235e11	3.93376
$343$	−1.01169e11	−0.394660
$344$	−7.62749e11	−2.93676
$345$	−4.94928e11	−1.88086
$346$	9.15362e10	0.343361
$347$	−3.15844e11	−1.16947	−0.584735	−	0.811224i	$-0.698802\pi$
$347$	−3.15844e11	−1.16947	−0.584735	+	0.811224i	$0.698802\pi$
$348$	3.70848e11	1.35547
$349$	−7.87721e10	−0.284222	−0.142111	−	0.989851i	$-0.545389\pi$
$349$	−7.87721e10	−0.284222	−0.142111	+	0.989851i	$0.545389\pi$
$350$	−5.98635e10	−0.213234
$351$	0	0
$352$	2.87192e11	0.997079
$353$	−4.51207e11	−1.54664	−0.773320	−	0.634015i	$-0.781406\pi$
$353$	−4.51207e11	−1.54664	−0.773320	+	0.634015i	$0.781406\pi$
$354$	−1.04566e12	−3.53898
$355$	1.10311e11	0.368632
$356$	−6.06405e11	−2.00096
$357$	7.25997e10	0.236553
$358$	2.47424e11	0.796101
$359$	1.35064e11	0.429154	0.214577	−	0.976707i	$-0.431163\pi$
$359$	1.35064e11	0.429154	0.214577	+	0.976707i	$0.431163\pi$
$360$	2.02453e12	6.35277
$361$	−2.54032e10	−0.0787239
$362$	3.80204e11	1.16366
$363$	−1.04431e11	−0.315681
$364$	0	0
$365$	−5.76901e11	−1.70131
$366$	2.09959e12	6.11603
$367$	−4.09975e11	−1.17967	−0.589834	−	0.807525i	$-0.700807\pi$
$367$	−4.09975e11	−1.17967	−0.589834	+	0.807525i	$0.700807\pi$
$368$	−5.04753e11	−1.43471
$369$	−6.34134e11	−1.78058
$370$	3.13068e11	0.868423
$371$	1.11808e11	0.306401
$372$	2.14969e12	5.82013
$373$	−9.83115e10	−0.262975	−0.131488	−	0.991318i	$-0.541975\pi$
$373$	−9.83115e10	−0.262975	−0.131488	+	0.991318i	$0.541975\pi$
$374$	−4.77804e11	−1.26278
$375$	−3.59276e11	−0.938182
$376$	−4.15152e11	−1.07118
$377$	0	0
$378$	3.33231e11	0.839524
$379$	1.75017e11	0.435717	0.217858	−	0.975980i	$-0.430093\pi$
$379$	1.75017e11	0.435717	0.217858	+	0.975980i	$0.430093\pi$
$380$	1.09655e12	2.69776
$381$	−8.17097e11	−1.98660
$382$	1.10788e12	2.66200
$383$	2.36022e11	0.560477	0.280238	−	0.959930i	$-0.409586\pi$
$383$	2.36022e11	0.560477	0.280238	+	0.959930i	$0.409586\pi$
$384$	−8.32222e11	−1.95321
$385$	1.18612e11	0.275141
$386$	−1.11948e12	−2.56670
$387$	1.33737e12	3.03077
$388$	−1.01396e12	−2.27133
$389$	−3.45347e11	−0.764686	−0.382343	−	0.924021i	$-0.624883\pi$
$389$	−3.45347e11	−0.764686	−0.382343	+	0.924021i	$0.624883\pi$
$390$	0	0
$391$	2.46869e11	0.534160
$392$	9.91181e11	2.12015
$393$	−2.78165e11	−0.588215
$394$	−1.12647e12	−2.35497
$395$	−5.22974e11	−1.08092
$396$	−2.69641e12	−5.51008
$397$	1.39044e11	0.280929	0.140464	−	0.990086i	$-0.455140\pi$
$397$	1.39044e11	0.280929	0.140464	+	0.990086i	$0.455140\pi$
$398$	−9.92204e11	−1.98211
$399$	1.77271e11	0.350155
$400$	5.25305e11	1.02599
$401$	−3.50321e11	−0.676577	−0.338288	−	0.941042i	$-0.609848\pi$
$401$	−3.50321e11	−0.676577	−0.338288	+	0.941042i	$0.609848\pi$
$402$	1.48690e12	2.83964
$403$	0	0
$404$	3.93971e11	0.735780
$405$	−1.31067e12	−2.42072
$406$	6.65151e10	0.121494
$407$	−2.29955e11	−0.415401
$408$	−1.45264e12	−2.59529
$409$	2.65188e11	0.468597	0.234299	−	0.972165i	$-0.424721\pi$
$409$	2.65188e11	0.468597	0.234299	+	0.972165i	$0.424721\pi$
$410$	−1.01206e12	−1.76879
$411$	−3.73915e11	−0.646375
$412$	−1.89274e12	−3.23634
$413$	−1.29478e11	−0.218989
$414$	2.01801e12	3.37615
$415$	1.13881e12	1.88467
$416$	0	0
$417$	−9.65087e11	−1.56298
$418$	−1.16668e12	−1.86922
$419$	−1.32004e10	−0.0209230	−0.0104615	−	0.999945i	$-0.503330\pi$
$419$	−1.32004e10	−0.0209230	−0.0104615	+	0.999945i	$0.503330\pi$
$420$	6.53876e11	1.02535
$421$	9.69359e11	1.50389	0.751944	−	0.659227i	$-0.229117\pi$
$421$	9.69359e11	1.50389	0.751944	+	0.659227i	$0.229117\pi$
$422$	5.12472e11	0.786618
$423$	7.27911e11	1.10547
$424$	−2.23715e12	−3.36162
$425$	−2.56921e11	−0.381988
$426$	−6.47007e11	−0.951845
$427$	2.59979e11	0.378454
$428$	1.12754e12	1.62419
$429$	0	0
$430$	2.13440e12	3.01071
$431$	3.68494e11	0.514379	0.257189	−	0.966361i	$-0.417204\pi$
$431$	3.68494e11	0.514379	0.257189	+	0.966361i	$0.417204\pi$
$432$	−2.92412e12	−4.03941
$433$	−1.27102e11	−0.173763	−0.0868816	−	0.996219i	$-0.527690\pi$
$433$	−1.27102e11	−0.173763	−0.0868816	+	0.996219i	$0.527690\pi$
$434$	3.85567e11	0.521671
$435$	−5.72312e11	−0.766357
$436$	1.26099e12	1.67117
$437$	6.02796e11	0.790685
$438$	3.38369e12	4.39296
$439$	1.19411e12	1.53445	0.767225	−	0.641378i	$-0.221637\pi$
$439$	1.19411e12	1.53445	0.767225	+	0.641378i	$0.221637\pi$
$440$	−2.37330e12	−3.01866
$441$	−1.73790e12	−2.18802
$442$	0	0
$443$	1.38757e12	1.71174	0.855869	−	0.517193i	$-0.173023\pi$
$443$	1.38757e12	1.71174	0.855869	+	0.517193i	$0.173023\pi$
$444$	−1.26768e12	−1.54805
$445$	9.35836e11	1.13130
$446$	−9.77680e11	−1.17001
$447$	−3.98903e11	−0.472589
$448$	−1.51247e10	−0.0177392
$449$	1.48266e12	1.72161	0.860804	−	0.508936i	$-0.169961\pi$
$449$	1.48266e12	1.72161	0.860804	+	0.508936i	$0.169961\pi$
$450$	−2.10018e12	−2.41435
$451$	7.43375e11	0.846084
$452$	−4.04079e8	−0.000455348 0
$453$	−1.31243e12	−1.46432
$454$	−6.10734e11	−0.674684
$455$	0	0
$456$	−3.54699e12	−3.84166
$457$	4.40447e11	0.472357	0.236179	−	0.971710i	$-0.424105\pi$
$457$	4.40447e11	0.472357	0.236179	+	0.971710i	$0.424105\pi$
$458$	8.37740e10	0.0889641
$459$	1.43016e12	1.50393
$460$	2.22345e12	2.31535
$461$	8.41995e11	0.868271	0.434135	−	0.900848i	$-0.357054\pi$
$461$	8.41995e11	0.868271	0.434135	+	0.900848i	$0.357054\pi$
$462$	−6.95695e11	−0.710444
$463$	−1.44593e11	−0.146229	−0.0731143	−	0.997324i	$-0.523294\pi$
$463$	−1.44593e11	−0.146229	−0.0731143	+	0.997324i	$0.523294\pi$
$464$	−5.83673e11	−0.584573
$465$	−3.31751e12	−3.29059
$466$	1.00423e12	0.986495
$467$	−4.63622e11	−0.451064	−0.225532	−	0.974236i	$-0.572412\pi$
$467$	−4.63622e11	−0.451064	−0.225532	+	0.974236i	$0.572412\pi$
$468$	0	0
$469$	1.84113e11	0.175714
$470$	1.16172e12	1.09815
$471$	−1.73731e12	−1.62661
$472$	2.59071e12	2.40260
$473$	−1.56776e12	−1.44014
$474$	3.06739e12	2.79104
$475$	−6.27340e11	−0.565433
$476$	−3.26152e11	−0.291198
$477$	3.92253e12	3.46924
$478$	−1.14501e12	−1.00319
$479$	−1.85861e11	−0.161316	−0.0806581	−	0.996742i	$-0.525702\pi$
$479$	−1.85861e11	−0.161316	−0.0806581	+	0.996742i	$0.525702\pi$
$480$	−2.44329e12	−2.10082
$481$	0	0
$482$	−3.28377e12	−2.77116
$483$	3.59448e11	0.300520
$484$	4.69152e11	0.388606
$485$	1.56480e12	1.28417
$486$	2.56115e12	2.08243
$487$	−7.95509e11	−0.640862	−0.320431	−	0.947272i	$-0.603828\pi$
$487$	−7.95509e11	−0.640862	−0.320431	+	0.947272i	$0.603828\pi$
$488$	−5.20189e12	−4.15214
$489$	1.58200e12	1.25117
$490$	−2.77363e12	−2.17353
$491$	−2.27710e12	−1.76814	−0.884069	−	0.467357i	$-0.845206\pi$
$491$	−2.27710e12	−1.76814	−0.884069	+	0.467357i	$0.845206\pi$
$492$	4.09802e12	3.15305
$493$	2.85468e11	0.217644
$494$	0	0
$495$	4.16124e12	3.11530
$496$	−3.38337e12	−2.51005
$497$	−8.01150e10	−0.0588993
$498$	−6.67946e12	−4.86641
$499$	−1.86405e12	−1.34587	−0.672937	−	0.739700i	$-0.734967\pi$
$499$	−1.86405e12	−1.34587	−0.672937	+	0.739700i	$0.734967\pi$
$500$	1.61404e12	1.15491
$501$	−2.99979e12	−2.12726
$502$	−4.23805e12	−2.97851
$503$	3.40170e11	0.236941	0.118470	−	0.992958i	$-0.462201\pi$
$503$	3.40170e11	0.236941	0.118470	+	0.992958i	$0.462201\pi$
$504$	−1.47034e12	−1.01504
$505$	−6.07997e11	−0.415997
$506$	−2.36565e12	−1.60425
$507$	0	0
$508$	3.67078e12	2.44552
$509$	2.95969e11	0.195441	0.0977205	−	0.995214i	$-0.468845\pi$
$509$	2.95969e11	0.195441	0.0977205	+	0.995214i	$0.468845\pi$
$510$	4.06492e12	2.66064
$511$	4.18982e11	0.271832
$512$	3.49262e12	2.24614
$513$	3.49210e12	2.22617
$514$	4.23496e12	2.67618
$515$	2.92098e12	1.82977
$516$	−8.64263e12	−5.36688
$517$	−8.53307e11	−0.525289
$518$	−2.27370e11	−0.138755
$519$	5.72005e11	0.346056
$520$	0	0
$521$	−2.47380e12	−1.47094	−0.735470	−	0.677557i	$-0.763039\pi$
$521$	−2.47380e12	−1.47094	−0.735470	+	0.677557i	$0.763039\pi$
$522$	2.33353e12	1.37562
$523$	−2.37854e12	−1.39012	−0.695061	−	0.718951i	$-0.744623\pi$
$523$	−2.37854e12	−1.39012	−0.695061	+	0.718951i	$0.744623\pi$
$524$	1.24965e12	0.724097
$525$	−3.74084e11	−0.214908
$526$	−4.18956e12	−2.38634
$527$	1.65477e12	0.934522
$528$	6.10475e12	3.41834
$529$	−5.78880e11	−0.321394
$530$	6.26023e12	3.44627
$531$	−4.54246e12	−2.47951
$532$	−7.96385e11	−0.431043
$533$	0	0
$534$	−5.48895e12	−2.92115
$535$	−1.74008e12	−0.918286
$536$	−3.68390e12	−1.92782
$537$	1.54614e12	0.802351
$538$	−4.66638e12	−2.40137
$539$	2.03728e12	1.03969
$540$	1.28808e13	6.51886
$541$	−1.08363e12	−0.543869	−0.271934	−	0.962316i	$-0.587663\pi$
$541$	−1.08363e12	−0.543869	−0.271934	+	0.962316i	$0.587663\pi$
$542$	5.00952e12	2.49344
$543$	2.37587e12	1.17280
$544$	1.21871e12	0.596629
$545$	−1.94602e12	−0.944852
$546$	0	0
$547$	3.68219e12	1.75858	0.879291	−	0.476284i	$-0.158017\pi$
$547$	3.68219e12	1.75858	0.879291	+	0.476284i	$0.158017\pi$
$548$	1.67980e12	0.795693
$549$	9.12080e12	4.28506
$550$	2.46197e12	1.14723
$551$	6.97045e11	0.322165
$552$	−7.19215e12	−3.29710
$553$	3.79817e11	0.172707
$554$	7.23263e11	0.326214
$555$	1.95634e12	0.875240
$556$	4.33563e12	1.92405
$557$	3.50754e12	1.54402	0.772012	−	0.635608i	$-0.219251\pi$
$557$	3.50754e12	1.54402	0.772012	+	0.635608i	$0.219251\pi$
$558$	1.35268e13	5.90663
$559$	0	0
$560$	−1.02913e12	−0.442204
$561$	−2.98577e12	−1.27269
$562$	2.19991e12	0.930234
$563$	−1.84360e12	−0.773354	−0.386677	−	0.922215i	$-0.626377\pi$
$563$	−1.84360e12	−0.773354	−0.386677	+	0.922215i	$0.626377\pi$
$564$	−4.70405e12	−1.95756
$565$	6.23596e8	0.000257446 0
$566$	9.16968e11	0.375561
$567$	9.51889e11	0.386779
$568$	1.60301e12	0.646203
$569$	4.36016e12	1.74380	0.871900	−	0.489684i	$-0.162888\pi$
$569$	4.36016e12	1.74380	0.871900	+	0.489684i	$0.162888\pi$
$570$	9.92558e12	3.93839
$571$	2.04857e12	0.806469	0.403234	−	0.915097i	$-0.367886\pi$
$571$	2.04857e12	0.806469	0.403234	+	0.915097i	$0.367886\pi$
$572$	0	0
$573$	6.92309e12	2.68290
$574$	7.35019e11	0.282615
$575$	−1.27204e12	−0.485283
$576$	−5.30616e11	−0.200853
$577$	−1.07704e12	−0.404522	−0.202261	−	0.979332i	$-0.564829\pi$
$577$	−1.07704e12	−0.404522	−0.202261	+	0.979332i	$0.564829\pi$
$578$	2.79470e12	1.04150
$579$	−6.99558e12	−2.58684
$580$	2.57110e12	0.943392
$581$	−8.27077e11	−0.301129
$582$	−9.17802e12	−3.31586
$583$	−4.59826e12	−1.64849
$584$	−8.38335e12	−2.98236
$585$	0	0
$586$	−1.11384e12	−0.390195
$587$	4.32734e11	0.150435	0.0752176	−	0.997167i	$-0.476035\pi$
$587$	4.32734e11	0.150435	0.0752176	+	0.997167i	$0.476035\pi$
$588$	1.12310e13	3.87453
$589$	4.04055e12	1.38332
$590$	−7.24961e12	−2.46309
$591$	−7.03923e12	−2.37346
$592$	1.99518e12	0.667628
$593$	1.08152e10	0.00359159	0.00179579	−	0.999998i	$-0.499428\pi$
$593$	1.08152e10	0.00359159	0.00179579	+	0.999998i	$0.499428\pi$
$594$	−1.37046e13	−4.51677
$595$	5.03335e11	0.164638
$596$	1.79206e12	0.581761
$597$	−6.20023e12	−1.99767
$598$	0	0
$599$	−5.31446e12	−1.68670	−0.843351	−	0.537363i	$-0.819420\pi$
$599$	−5.31446e12	−1.68670	−0.843351	+	0.537363i	$0.819420\pi$
$600$	7.48499e12	2.35782
$601$	−6.13776e12	−1.91900	−0.959500	−	0.281708i	$-0.909099\pi$
$601$	−6.13776e12	−1.91900	−0.959500	+	0.281708i	$0.909099\pi$
$602$	−1.55014e12	−0.481046
$603$	6.45920e12	1.98953
$604$	5.89607e12	1.80259
$605$	−7.24021e11	−0.219711
$606$	3.56607e12	1.07415
$607$	−1.27115e12	−0.380055	−0.190028	−	0.981779i	$-0.560858\pi$
$607$	−1.27115e12	−0.380055	−0.190028	+	0.981779i	$0.560858\pi$
$608$	2.97579e12	0.883154
$609$	4.15649e11	0.122447
$610$	1.45565e13	4.25669
$611$	0	0
$612$	−1.14423e13	−3.29710
$613$	−5.01818e12	−1.43540	−0.717701	−	0.696351i	$-0.754806\pi$
$613$	−5.01818e12	−1.43540	−0.717701	+	0.696351i	$0.754806\pi$
$614$	9.56337e12	2.71552
$615$	−6.32428e12	−1.78268
$616$	1.72364e12	0.482317
$617$	6.53801e12	1.81620	0.908098	−	0.418758i	$-0.137535\pi$
$617$	6.53801e12	1.81620	0.908098	+	0.418758i	$0.137535\pi$
$618$	−1.71324e13	−4.72465
$619$	3.42618e12	0.937999	0.468999	−	0.883198i	$-0.344615\pi$
$619$	3.42618e12	0.937999	0.468999	+	0.883198i	$0.344615\pi$
$620$	1.49038e13	4.05075
$621$	7.08083e12	1.91061
$622$	1.59712e12	0.427839
$623$	−6.79663e11	−0.180758
$624$	0	0
$625$	−4.73809e12	−1.24206
$626$	1.86471e12	0.485318
$627$	−7.29053e12	−1.88389
$628$	7.80483e12	2.00237
$629$	−9.75821e11	−0.248566
$630$	4.11447e12	1.04059
$631$	5.02001e11	0.126059	0.0630293	−	0.998012i	$-0.479924\pi$
$631$	5.02001e11	0.126059	0.0630293	+	0.998012i	$0.479924\pi$
$632$	−7.59970e12	−1.89483
$633$	3.20241e12	0.792793
$634$	−5.67635e10	−0.0139530
$635$	−5.66495e12	−1.38266
$636$	−2.53489e13	−6.14331
$637$	0	0
$638$	−2.73553e12	−0.653655
$639$	−2.81066e12	−0.666890
$640$	−5.76981e12	−1.35941
$641$	2.54269e10	0.00594883	0.00297441	−	0.999996i	$-0.499053\pi$
$641$	2.54269e10	0.00594883	0.00297441	+	0.999996i	$0.499053\pi$
$642$	1.02061e13	2.37111
$643$	8.59506e12	1.98290	0.991448	−	0.130506i	$-0.0416602\pi$
$643$	8.59506e12	1.98290	0.991448	+	0.130506i	$0.0416602\pi$
$644$	−1.61481e12	−0.369943
$645$	1.33378e13	3.03434
$646$	−4.95086e12	−1.11850
$647$	−1.50426e12	−0.337484	−0.168742	−	0.985660i	$-0.553971\pi$
$647$	−1.50426e12	−0.337484	−0.168742	+	0.985660i	$0.553971\pi$
$648$	−1.90462e13	−4.24347
$649$	5.32498e12	1.17819
$650$	0	0
$651$	2.40939e12	0.525766
$652$	−7.10707e12	−1.54020
$653$	9.45747e11	0.203548	0.101774	−	0.994808i	$-0.467548\pi$
$653$	9.45747e11	0.203548	0.101774	+	0.994808i	$0.467548\pi$
$654$	1.14140e13	2.43971
$655$	−1.92852e12	−0.409392
$656$	−6.44982e12	−1.35982
$657$	1.46990e13	3.07783
$658$	−8.43715e11	−0.175461
$659$	−2.35144e12	−0.485679	−0.242840	−	0.970066i	$-0.578079\pi$
$659$	−2.35144e12	−0.485679	−0.242840	+	0.970066i	$0.578079\pi$
$660$	−2.68916e13	−5.51656
$661$	4.90465e12	0.999313	0.499657	−	0.866224i	$-0.333459\pi$
$661$	4.90465e12	0.999313	0.499657	+	0.866224i	$0.333459\pi$
$662$	1.03331e13	2.09108
$663$	0	0
$664$	1.65489e13	3.30379
$665$	1.22902e12	0.243704
$666$	−7.97676e12	−1.57106
$667$	1.41338e12	0.276498
$668$	1.34765e13	2.61868
$669$	−6.10946e12	−1.17919
$670$	1.03087e13	1.97636
$671$	−1.06920e13	−2.03614
$672$	1.77447e12	0.335666
$673$	−9.17082e12	−1.72322	−0.861609	−	0.507572i	$-0.830543\pi$
$673$	−9.17082e12	−1.72322	−0.861609	+	0.507572i	$0.830543\pi$
$674$	−1.64478e10	−0.00307001
$675$	−7.36914e12	−1.36631
$676$	0	0
$677$	−1.90752e12	−0.348996	−0.174498	−	0.984657i	$-0.555830\pi$
$677$	−1.90752e12	−0.348996	−0.174498	+	0.984657i	$0.555830\pi$
$678$	−3.65757e9	−0.000664751 0
$679$	−1.13646e12	−0.205182
$680$	−1.00712e13	−1.80630
$681$	−3.81644e12	−0.679980
$682$	−1.58570e13	−2.80667
$683$	−4.52924e12	−0.796402	−0.398201	−	0.917298i	$-0.630365\pi$
$683$	−4.52924e12	−0.796402	−0.398201	+	0.917298i	$0.630365\pi$
$684$	−2.79394e13	−4.88050
$685$	−2.59236e12	−0.449871
$686$	4.11394e12	0.709250
$687$	5.23499e11	0.0896625
$688$	1.36025e13	2.31458
$689$	0	0
$690$	2.01258e13	3.38012
$691$	−2.30053e12	−0.383864	−0.191932	−	0.981408i	$-0.561475\pi$
$691$	−2.30053e12	−0.383864	−0.191932	+	0.981408i	$0.561475\pi$
$692$	−2.56971e12	−0.425998
$693$	−3.02216e12	−0.497757
$694$	1.28435e13	2.10168
$695$	−6.69097e12	−1.08782
$696$	−8.31667e12	−1.34341
$697$	3.15454e12	0.506277
$698$	3.20320e12	0.510781
$699$	6.27535e12	0.994239
$700$	1.68056e12	0.264553
$701$	3.06626e11	0.0479599	0.0239799	−	0.999712i	$-0.492366\pi$
$701$	3.06626e11	0.0479599	0.0239799	+	0.999712i	$0.492366\pi$
$702$	0	0
$703$	−2.38272e12	−0.367938
$704$	6.22024e11	0.0954399
$705$	7.25953e12	1.10677
$706$	1.83479e13	2.77950
$707$	4.41565e11	0.0664673
$708$	2.93551e13	4.39071
$709$	6.04990e12	0.899167	0.449584	−	0.893238i	$-0.351572\pi$
$709$	6.04990e12	0.899167	0.449584	+	0.893238i	$0.351572\pi$
$710$	−4.48571e12	−0.662474
$711$	1.33250e13	1.95548
$712$	1.35993e13	1.98315
$713$	8.19292e12	1.18723
$714$	−2.95220e12	−0.425113
$715$	0	0
$716$	−6.94598e12	−0.987700
$717$	−7.15510e12	−1.01107
$718$	−5.49225e12	−0.771241
$719$	−9.16534e12	−1.27899	−0.639497	−	0.768793i	$-0.720857\pi$
$719$	−9.16534e12	−1.27899	−0.639497	+	0.768793i	$0.720857\pi$
$720$	−3.61046e13	−5.00687
$721$	−2.12140e12	−0.292357
$722$	1.03300e12	0.141476
$723$	−2.05201e13	−2.79291
$724$	−1.06735e13	−1.44372
$725$	−1.47093e12	−0.197729
$726$	4.24659e12	0.567317
$727$	8.62172e12	1.14469	0.572347	−	0.820012i	$-0.306033\pi$
$727$	8.62172e12	1.14469	0.572347	+	0.820012i	$0.306033\pi$
$728$	0	0
$729$	1.36101e12	0.178479
$730$	2.34592e13	3.05746
$731$	−6.65285e12	−0.861746
$732$	−5.89421e13	−7.58798
$733$	−9.24331e12	−1.18266	−0.591330	−	0.806430i	$-0.701397\pi$
$733$	−9.24331e12	−1.18266	−0.591330	+	0.806430i	$0.701397\pi$
$734$	1.66713e13	2.12000
$735$	−1.73322e13	−2.19059
$736$	6.03393e12	0.757967
$737$	−7.57192e12	−0.945371
$738$	2.57865e13	3.19992
$739$	−1.15675e13	−1.42673	−0.713363	−	0.700794i	$-0.752829\pi$
$739$	−1.15675e13	−1.42673	−0.713363	+	0.700794i	$0.752829\pi$
$740$	−8.78882e12	−1.07743
$741$	0	0
$742$	−4.54657e12	−0.550638
$743$	−2.33434e9	−0.000281006 0	−0.000140503	−	1.00000i	$-0.500045\pi$
$743$	−2.33434e9	−0.000281006 0	−0.000140503		1.00000i	$0.500045\pi$
$744$	−4.82091e13	−5.76834
$745$	−2.76560e12	−0.328917
$746$	3.99775e12	0.472597
$747$	−2.90161e13	−3.40955
$748$	1.34135e13	1.56669
$749$	1.26376e12	0.146722
$750$	1.46096e13	1.68602
$751$	−5.08938e12	−0.583828	−0.291914	−	0.956445i	$-0.594292\pi$
$751$	−5.08938e12	−0.583828	−0.291914	+	0.956445i	$0.594292\pi$
$752$	7.40364e12	0.844238
$753$	−2.64833e13	−3.00189
$754$	0	0
$755$	−9.09913e12	−1.01915
$756$	−9.35487e12	−1.04157
$757$	1.36230e13	1.50779	0.753895	−	0.656995i	$-0.228173\pi$
$757$	1.36230e13	1.50779	0.753895	+	0.656995i	$0.228173\pi$
$758$	−7.11692e12	−0.783034
$759$	−1.47828e13	−1.61685
$760$	−2.45914e13	−2.67376
$761$	1.35809e13	1.46791	0.733953	−	0.679200i	$-0.237673\pi$
$761$	1.35809e13	1.46791	0.733953	+	0.679200i	$0.237673\pi$
$762$	3.32265e13	3.57016
$763$	1.41332e12	0.150967
$764$	−3.11018e13	−3.30267
$765$	1.76584e13	1.86412
$766$	−9.59762e12	−1.00724
$767$	0	0
$768$	3.23036e13	3.35063
$769$	4.88931e12	0.504172	0.252086	−	0.967705i	$-0.418883\pi$
$769$	4.88931e12	0.504172	0.252086	+	0.967705i	$0.418883\pi$
$770$	−4.82326e12	−0.494462
$771$	2.64640e13	2.69718
$772$	3.14274e13	3.18443
$773$	−8.52939e12	−0.859231	−0.429616	−	0.903012i	$-0.641351\pi$
$773$	−8.52939e12	−0.859231	−0.429616	+	0.903012i	$0.641351\pi$
$774$	−5.43831e13	−5.44666
$775$	−8.52651e12	−0.849011
$776$	2.27393e13	2.25112
$777$	−1.42082e12	−0.139844
$778$	1.40432e13	1.37423
$779$	7.70263e12	0.749412
$780$	0	0
$781$	3.29484e12	0.316888
$782$	−1.00387e13	−0.959948
$783$	8.18795e12	0.778480
$784$	−1.76763e13	−1.67097
$785$	−1.20448e13	−1.13211
$786$	1.13113e13	1.05709
$787$	3.66557e12	0.340608	0.170304	−	0.985392i	$-0.445525\pi$
$787$	3.66557e12	0.340608	0.170304	+	0.985392i	$0.445525\pi$
$788$	3.16235e13	2.92175
$789$	−2.61803e13	−2.40507
$790$	2.12663e13	1.94254
$791$	−4.52895e8	−4.11342e−5 0
$792$	6.04699e13	5.46105
$793$	0	0
$794$	−5.65412e12	−0.504862
$795$	3.91198e13	3.47332
$796$	2.78543e13	2.45914
$797$	1.56877e13	1.37720	0.688599	−	0.725142i	$-0.258226\pi$
$797$	1.56877e13	1.37720	0.688599	+	0.725142i	$0.258226\pi$
$798$	−7.20858e12	−0.629269
$799$	−3.62104e12	−0.314321
$800$	−6.27962e12	−0.542036
$801$	−2.38445e13	−2.04664
$802$	1.42455e13	1.21589
$803$	−1.72312e13	−1.46250
$804$	−4.17419e13	−3.52306
$805$	2.49206e12	0.209159
$806$	0	0
$807$	−2.91599e13	−2.42022
$808$	−8.83522e12	−0.729233
$809$	−4.86826e12	−0.399581	−0.199791	−	0.979839i	$-0.564026\pi$
$809$	−4.86826e12	−0.399581	−0.199791	+	0.979839i	$0.564026\pi$
$810$	5.32971e13	4.35032
$811$	−2.59157e12	−0.210363	−0.105182	−	0.994453i	$-0.533542\pi$
$811$	−2.59157e12	−0.210363	−0.105182	+	0.994453i	$0.533542\pi$
$812$	−1.86729e12	−0.150734
$813$	3.13042e13	2.51302
$814$	9.35091e12	0.746524
$815$	1.09680e13	0.870800
$816$	2.59057e13	2.04546
$817$	−1.62447e13	−1.27559
$818$	−1.07837e13	−0.842124
$819$	0	0
$820$	2.84116e13	2.19449
$821$	8.93176e12	0.686109	0.343054	−	0.939316i	$-0.388538\pi$
$821$	8.93176e12	0.686109	0.343054	+	0.939316i	$0.388538\pi$
$822$	1.52049e13	1.16161
$823$	−1.15285e13	−0.875942	−0.437971	−	0.898989i	$-0.644303\pi$
$823$	−1.15285e13	−0.875942	−0.437971	+	0.898989i	$0.644303\pi$
$824$	4.24468e13	3.20755
$825$	1.53847e13	1.15624
$826$	5.26512e12	0.393549
$827$	1.39337e13	1.03584	0.517919	−	0.855430i	$-0.326707\pi$
$827$	1.39337e13	1.03584	0.517919	+	0.855430i	$0.326707\pi$
$828$	−5.66520e13	−4.18869
$829$	2.18269e13	1.60508	0.802539	−	0.596600i	$-0.203482\pi$
$829$	2.18269e13	1.60508	0.802539	+	0.596600i	$0.203482\pi$
$830$	−4.63088e13	−3.38697
$831$	4.51963e12	0.328774
$832$	0	0
$833$	8.64529e12	0.622124
$834$	3.92444e13	2.80887
$835$	−2.07976e13	−1.48055
$836$	3.27525e13	2.31908
$837$	4.74630e13	3.34265
$838$	5.36783e11	0.0376011
$839$	−1.38767e13	−0.966845	−0.483422	−	0.875387i	$-0.660606\pi$
$839$	−1.38767e13	−0.966845	−0.483422	+	0.875387i	$0.660606\pi$
$840$	−1.46639e13	−1.01623
$841$	−1.28728e13	−0.887341
$842$	−3.94181e13	−2.70266
$843$	1.37471e13	0.937536
$844$	−1.43867e13	−0.975934
$845$	0	0
$846$	−2.95999e13	−1.98666
$847$	5.25829e11	0.0351050
$848$	3.98964e13	2.64943
$849$	5.73008e12	0.378509
$850$	1.04475e13	0.686477
$851$	−4.83138e12	−0.315783
$852$	1.81636e13	1.18093
$853$	1.45244e13	0.939349	0.469674	−	0.882840i	$-0.344371\pi$
$853$	1.45244e13	0.939349	0.469674	+	0.882840i	$0.344371\pi$
$854$	−1.05718e13	−0.680127
$855$	4.31176e13	2.75935
$856$	−2.52864e13	−1.60974
$857$	9.74869e12	0.617352	0.308676	−	0.951167i	$-0.400114\pi$
$857$	9.74869e12	0.617352	0.308676	+	0.951167i	$0.400114\pi$
$858$	0	0
$859$	1.48176e13	0.928560	0.464280	−	0.885689i	$-0.346313\pi$
$859$	1.48176e13	0.928560	0.464280	+	0.885689i	$0.346313\pi$
$860$	−5.99195e13	−3.73530
$861$	4.59309e12	0.284833
$862$	−1.49845e13	−0.924399
$863$	−2.12803e13	−1.30596	−0.652978	−	0.757377i	$-0.726481\pi$
$863$	−2.12803e13	−1.30596	−0.652978	+	0.757377i	$0.726481\pi$
$864$	3.49556e13	2.13405
$865$	3.96572e12	0.240851
$866$	5.16851e12	0.312273
$867$	1.74639e13	1.04968
$868$	−1.08241e13	−0.647222
$869$	−1.56205e13	−0.929193
$870$	2.32726e13	1.37723
$871$	0	0
$872$	−2.82790e13	−1.65630
$873$	−3.98701e13	−2.32318
$874$	−2.45122e13	−1.42095
$875$	1.80902e12	0.104330
$876$	−9.49910e13	−5.45022
$877$	4.28604e12	0.244657	0.122329	−	0.992490i	$-0.460964\pi$
$877$	4.28604e12	0.244657	0.122329	+	0.992490i	$0.460964\pi$
$878$	−4.85573e13	−2.75759
$879$	−6.96029e12	−0.393258
$880$	4.23243e13	2.37913
$881$	−1.05775e13	−0.591548	−0.295774	−	0.955258i	$-0.595578\pi$
$881$	−1.05775e13	−0.591548	−0.295774	+	0.955258i	$0.595578\pi$
$882$	7.06701e13	3.93212
$883$	−2.42773e13	−1.34393	−0.671965	−	0.740582i	$-0.734550\pi$
$883$	−2.42773e13	−1.34393	−0.671965	+	0.740582i	$0.734550\pi$
$884$	0	0
$885$	−4.53024e13	−2.48243
$886$	−5.64242e13	−3.07619
$887$	−1.80906e13	−0.981288	−0.490644	−	0.871360i	$-0.663239\pi$
$887$	−1.80906e13	−0.981288	−0.490644	+	0.871360i	$0.663239\pi$
$888$	2.84290e13	1.53428
$889$	4.11424e12	0.220918
$890$	−3.80550e13	−2.03309
$891$	−3.91478e13	−2.08093
$892$	2.74466e13	1.45160
$893$	−8.84172e12	−0.465270
$894$	1.62211e13	0.849298
$895$	1.07194e13	0.558428
$896$	4.19040e12	0.217205
$897$	0	0
$898$	−6.02913e13	−3.09393
$899$	9.47391e12	0.483739
$900$	5.89587e13	2.99541
$901$	−1.95129e13	−0.986415
$902$	−3.02287e13	−1.52051
$903$	−9.68672e12	−0.484822
$904$	9.06191e9	0.000451296 0
$905$	1.64719e13	0.816256
$906$	5.33690e13	2.63155
$907$	−2.42475e13	−1.18969	−0.594845	−	0.803840i	$-0.702787\pi$
$907$	−2.42475e13	−1.18969	−0.594845	+	0.803840i	$0.702787\pi$
$908$	1.71452e13	0.837061
$909$	1.54913e13	0.752578
$910$	0	0
$911$	2.38182e13	1.14572	0.572858	−	0.819655i	$-0.305835\pi$
$911$	2.38182e13	1.14572	0.572858	+	0.819655i	$0.305835\pi$
$912$	6.32556e13	3.02776
$913$	3.40147e13	1.62012
$914$	−1.79104e13	−0.848881
$915$	9.09626e13	4.29011
$916$	−2.35180e12	−0.110375
$917$	1.40061e12	0.0654119
$918$	−5.81560e13	−2.70273
$919$	−1.33470e13	−0.617252	−0.308626	−	0.951183i	$-0.599869\pi$
$919$	−1.33470e13	−0.617252	−0.308626	+	0.951183i	$0.599869\pi$
$920$	−4.98633e13	−2.29475
$921$	5.97610e13	2.73684
$922$	−3.42390e13	−1.56038
$923$	0	0
$924$	1.95304e13	0.881427
$925$	5.02810e12	0.225822
$926$	5.87975e12	0.262790
$927$	−7.44246e13	−3.31023
$928$	6.97737e12	0.308834
$929$	−1.86929e13	−0.823392	−0.411696	−	0.911321i	$-0.635064\pi$
$929$	−1.86929e13	−0.823392	−0.411696	+	0.911321i	$0.635064\pi$
$930$	1.34904e14	5.91359
$931$	2.11097e13	0.920893
$932$	−2.81918e13	−1.22392
$933$	9.98031e12	0.431198
$934$	1.88528e13	0.810614
$935$	−2.07004e13	−0.885780
$936$	0	0
$937$	−1.15777e13	−0.490674	−0.245337	−	0.969438i	$-0.578899\pi$
$937$	−1.15777e13	−0.490674	−0.245337	+	0.969438i	$0.578899\pi$
$938$	−7.48681e12	−0.315779
$939$	1.16525e13	0.489128
$940$	−3.26132e13	−1.36244
$941$	−4.63482e11	−0.0192699	−0.00963495	−	0.999954i	$-0.503067\pi$
$941$	−4.63482e11	−0.0192699	−0.00963495	+	0.999954i	$0.503067\pi$
$942$	7.06463e13	2.92321
$943$	1.56184e13	0.643183
$944$	−4.62017e13	−1.89358
$945$	1.44369e13	0.588886
$946$	6.37516e13	2.58810
$947$	2.71824e12	0.109828	0.0549140	−	0.998491i	$-0.482512\pi$
$947$	2.71824e12	0.109828	0.0549140	+	0.998491i	$0.482512\pi$
$948$	−8.61114e13	−3.46277
$949$	0	0
$950$	2.55102e13	1.01615
$951$	−3.54712e11	−0.0140625
$952$	7.31431e12	0.288607
$953$	3.65718e13	1.43624	0.718122	−	0.695917i	$-0.245002\pi$
$953$	3.65718e13	1.43624	0.718122	+	0.695917i	$0.245002\pi$
$954$	−1.59506e14	−6.23462
$955$	4.79979e13	1.86727
$956$	3.21441e13	1.24463
$957$	−1.70942e13	−0.658786
$958$	7.55787e12	0.289904
$959$	1.88273e12	0.0718795
$960$	−5.29188e12	−0.201090
$961$	2.84777e13	1.07708
$962$	0	0
$963$	4.43361e13	1.66127
$964$	9.21859e13	3.43809
$965$	−4.85005e13	−1.80042
$966$	−1.46166e13	−0.540070
$967$	−1.32609e13	−0.487701	−0.243851	−	0.969813i	$-0.578411\pi$
$967$	−1.32609e13	−0.487701	−0.243851	+	0.969813i	$0.578411\pi$
$968$	−1.05212e13	−0.385149
$969$	−3.09376e13	−1.12728
$970$	−6.36314e13	−2.30780
$971$	−4.03802e13	−1.45775	−0.728874	−	0.684648i	$-0.759956\pi$
$971$	−4.03802e13	−1.45775	−0.728874	+	0.684648i	$0.759956\pi$
$972$	−7.18996e13	−2.58362
$973$	4.85940e12	0.173810
$974$	3.23487e13	1.15171
$975$	0	0
$976$	9.27683e13	3.27247
$977$	−2.14482e13	−0.753121	−0.376560	−	0.926392i	$-0.622893\pi$
$977$	−2.14482e13	−0.753121	−0.376560	+	0.926392i	$0.622893\pi$
$978$	−6.43305e13	−2.24850
$979$	2.79521e13	0.972506
$980$	7.78645e13	2.69664
$981$	4.95833e13	1.70933
$982$	9.25964e13	3.17755
$983$	−4.78240e13	−1.63364	−0.816818	−	0.576895i	$-0.804264\pi$
$983$	−4.78240e13	−1.63364	−0.816818	+	0.576895i	$0.804264\pi$
$984$	−9.19025e13	−3.12500
$985$	−4.88031e13	−1.65190
$986$	−1.16083e13	−0.391132
$987$	−5.27233e12	−0.176838
$988$	0	0
$989$	−3.29389e13	−1.09478
$990$	−1.69213e14	−5.59856
$991$	−3.83569e13	−1.26332	−0.631659	−	0.775246i	$-0.717626\pi$
$991$	−3.83569e13	−1.26332	−0.631659	+	0.775246i	$0.717626\pi$
$992$	4.04456e13	1.32608
$993$	6.45711e13	2.10750
$994$	3.25781e12	0.105849
$995$	−4.29863e13	−1.39036
$996$	1.87514e14	6.03762
$997$	6.36236e12	0.203934	0.101967	−	0.994788i	$-0.467486\pi$
$997$	6.36236e12	0.203934	0.101967	+	0.994788i	$0.467486\pi$
$998$	7.57998e13	2.41869
$999$	−2.79890e13	−0.889084

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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.1.4	✓	27
13.12	even	2		169.10.a.h.1.24	yes	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.10.a.g.1.4	✓	27	1.1	even	1	trivial
169.10.a.h.1.24	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 $\F_{q}$
Belyi maps

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Groups

Database

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.1.4

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