LMFDB - Embedded newform 121.8.a.g.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,8,Mod(1,121)] 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("121.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-24] 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:	$37.7985880836$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 995 x^{10} + 4070 x^{9} + 370502 x^{8} - 918126 x^{7} - 61207003 x^{6} + \cdots + 7839497781 $ x^12 - 6x^11 - 995x^10 + 4070x^9 + 370502x^8 - 918126x^7 - 61207003x^6 + 82133282x^5 + 3967374334x^4 - 3620593482x^3 - 45572873963x^2 + 73699513674*x + 7839497781
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 11^{5} $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-15.1049$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-18.7229 q^{2} -57.3611 q^{3} +222.547 q^{4} +489.146 q^{5} +1073.97 q^{6} -672.943 q^{7} -1770.20 q^{8} +1103.30 q^{9} -9158.23 q^{10} -12765.6 q^{12} -4763.55 q^{13} +12599.4 q^{14} -28057.9 q^{15} +4657.25 q^{16} +16146.9 q^{17} -20657.0 q^{18} -27308.6 q^{19} +108858. q^{20} +38600.8 q^{21} +32348.3 q^{23} +101541. q^{24} +161139. q^{25} +89187.6 q^{26} +62162.3 q^{27} -149762. q^{28} -31301.1 q^{29} +525326. q^{30} -80312.6 q^{31} +139388. q^{32} -302316. q^{34} -329167. q^{35} +245536. q^{36} +133096. q^{37} +511297. q^{38} +273243. q^{39} -865886. q^{40} -30865.3 q^{41} -722719. q^{42} -776273. q^{43} +539674. q^{45} -605655. q^{46} +619108. q^{47} -267145. q^{48} -370691. q^{49} -3.01698e6 q^{50} -926202. q^{51} -1.06012e6 q^{52} +1.68943e6 q^{53} -1.16386e6 q^{54} +1.19124e6 q^{56} +1.56645e6 q^{57} +586047. q^{58} -453835. q^{59} -6.24422e6 q^{60} +2.37350e6 q^{61} +1.50368e6 q^{62} -742457. q^{63} -3.20588e6 q^{64} -2.33007e6 q^{65} +201563. q^{67} +3.59344e6 q^{68} -1.85554e6 q^{69} +6.16297e6 q^{70} -2.73550e6 q^{71} -1.95306e6 q^{72} +1.81214e6 q^{73} -2.49194e6 q^{74} -9.24309e6 q^{75} -6.07746e6 q^{76} -5.11590e6 q^{78} +1.53520e6 q^{79} +2.27808e6 q^{80} -5.97862e6 q^{81} +577889. q^{82} -1.44936e6 q^{83} +8.59050e6 q^{84} +7.89817e6 q^{85} +1.45341e7 q^{86} +1.79547e6 q^{87} -8.72198e6 q^{89} -1.01043e7 q^{90} +3.20560e6 q^{91} +7.19904e6 q^{92} +4.60682e6 q^{93} -1.15915e7 q^{94} -1.33579e7 q^{95} -7.99547e6 q^{96} -7.16171e6 q^{97} +6.94041e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 12 q^{3} + 550 q^{4} + 144 q^{5} - 649 q^{6} - 2244 q^{7} - 3810 q^{8} + 9094 q^{9} - 2120 q^{10} + 5819 q^{12} - 8688 q^{13} + 23988 q^{14} - 29008 q^{15} - 32238 q^{16} - 26214 q^{17}+ \cdots + 25767018 q^{98}+O(q^{100}) $ 12 * q - 24 * q^2 - 12 * q^3 + 550 * q^4 + 144 * q^5 - 649 * q^6 - 2244 * q^7 - 3810 * q^8 + 9094 * q^9 - 2120 * q^10 + 5819 * q^12 - 8688 * q^13 + 23988 * q^14 - 29008 * q^15 - 32238 * q^16 - 26214 * q^17 - 76543 * q^18 - 52308 * q^19 - 16374 * q^20 - 69152 * q^21 - 13152 * q^23 - 73443 * q^24 + 155752 * q^25 + 167268 * q^26 + 302400 * q^27 - 382952 * q^28 - 159276 * q^29 - 7788 * q^30 - 432468 * q^31 + 130446 * q^32 + 756081 * q^34 - 258456 * q^35 + 1376129 * q^36 - 189896 * q^37 + 272025 * q^38 - 2263776 * q^39 - 1249506 * q^40 - 1767102 * q^41 - 3537912 * q^42 - 1438728 * q^43 + 1558636 * q^45 - 2758162 * q^46 + 1951644 * q^47 - 508717 * q^48 - 620888 * q^49 - 8781084 * q^50 - 5437672 * q^51 - 7729734 * q^52 - 5997012 * q^53 - 8805010 * q^54 + 5715540 * q^56 - 3344580 * q^57 + 8127100 * q^58 - 1100004 * q^59 - 4320206 * q^60 - 8453788 * q^61 - 6663978 * q^62 - 11044228 * q^63 - 16086302 * q^64 - 5558820 * q^65 + 8341264 * q^67 - 5706597 * q^68 + 3505424 * q^69 - 2370222 * q^70 - 1323204 * q^71 - 27395985 * q^72 - 28258 * q^73 - 19524798 * q^74 - 24181280 * q^75 - 9045603 * q^76 + 7766546 * q^78 - 9616244 * q^79 + 11429082 * q^80 + 1578028 * q^81 + 2776323 * q^82 - 18527868 * q^83 - 95370 * q^84 - 391164 * q^85 - 12467391 * q^86 - 18304620 * q^87 - 1238658 * q^89 + 13787116 * q^90 - 136352 * q^91 + 4026894 * q^92 + 3799596 * q^93 + 11859084 * q^94 - 26322264 * q^95 + 16012845 * q^96 + 3970134 * q^97 + 25767018 * q^98

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 $

$2$	−18.7229	−1.65489	−0.827443	−	0.561549i	$-0.810206\pi$
$2$	−18.7229	−1.65489	−0.827443	+	0.561549i	$0.810206\pi$
$3$	−57.3611	−1.22657	−0.613286	−	0.789861i	$-0.710153\pi$
$3$	−57.3611	−1.22657	−0.613286	+	0.789861i	$0.710153\pi$
$4$	222.547	1.73865
$5$	489.146	1.75002	0.875010	−	0.484104i	$-0.160854\pi$
$5$	489.146	1.75002	0.875010	+	0.484104i	$0.160854\pi$
$6$	1073.97	2.02984
$7$	−672.943	−0.741541	−0.370770	−	0.928725i	$-0.620906\pi$
$7$	−672.943	−0.741541	−0.370770	+	0.928725i	$0.620906\pi$
$8$	−1770.20	−1.22238
$9$	1103.30	0.504480
$10$	−9158.23	−2.89609
$11$	0	0
$11$	0	0
$12$	−12765.6	−2.13258
$13$	−4763.55	−0.601353	−0.300676	−	0.953726i	$-0.597212\pi$
$13$	−4763.55	−0.601353	−0.300676	+	0.953726i	$0.597212\pi$
$14$	12599.4	1.22717
$15$	−28057.9	−2.14653
$16$	4657.25	0.284256
$17$	16146.9	0.797107	0.398554	−	0.917145i	$-0.369512\pi$
$17$	16146.9	0.797107	0.398554	+	0.917145i	$0.369512\pi$
$18$	−20657.0	−0.834858
$19$	−27308.6	−0.913403	−0.456701	−	0.889620i	$-0.650969\pi$
$19$	−27308.6	−0.913403	−0.456701	+	0.889620i	$0.650969\pi$
$20$	108858.	3.04268
$21$	38600.8	0.909554
$22$	0	0
$23$	32348.3	0.554376	0.277188	−	0.960816i	$-0.410597\pi$
$23$	32348.3	0.554376	0.277188	+	0.960816i	$0.410597\pi$
$24$	101541.	1.49934
$25$	161139.	2.06257
$26$	89187.6	0.995171
$27$	62162.3	0.607791
$28$	−149762.	−1.28928
$29$	−31301.1	−0.238323	−0.119162	−	0.992875i	$-0.538021\pi$
$29$	−31301.1	−0.238323	−0.119162	+	0.992875i	$0.538021\pi$
$30$	525326.	3.55226
$31$	−80312.6	−0.484192	−0.242096	−	0.970252i	$-0.577835\pi$
$31$	−80312.6	−0.484192	−0.242096	+	0.970252i	$0.577835\pi$
$32$	139388.	0.751972
$33$	0	0
$34$	−302316.	−1.31912
$35$	−329167.	−1.29771
$36$	245536.	0.877115
$37$	133096.	0.431975	0.215988	−	0.976396i	$-0.430703\pi$
$37$	133096.	0.431975	0.215988	+	0.976396i	$0.430703\pi$
$38$	511297.	1.51158
$39$	273243.	0.737603
$40$	−865886.	−2.13920
$41$	−30865.3	−0.0699403	−0.0349701	−	0.999388i	$-0.511134\pi$
$41$	−30865.3	−0.0699403	−0.0349701	+	0.999388i	$0.511134\pi$
$42$	−722719.	−1.50521
$43$	−776273.	−1.48893	−0.744466	−	0.667660i	$-0.767296\pi$
$43$	−776273.	−1.48893	−0.744466	+	0.667660i	$0.767296\pi$
$44$	0	0
$45$	539674.	0.882851
$46$	−605655.	−0.917430
$47$	619108.	0.869809	0.434905	−	0.900477i	$-0.356782\pi$
$47$	619108.	0.869809	0.434905	+	0.900477i	$0.356782\pi$
$48$	−267145.	−0.348661
$49$	−370691.	−0.450117
$50$	−3.01698e6	−3.41333
$51$	−926202.	−0.977710
$52$	−1.06012e6	−1.04554
$53$	1.68943e6	1.55874	0.779371	−	0.626563i	$-0.215539\pi$
$53$	1.68943e6	1.55874	0.779371	+	0.626563i	$0.215539\pi$
$54$	−1.16386e6	−1.00582
$55$	0	0
$56$	1.19124e6	0.906448
$57$	1.56645e6	1.12035
$58$	586047.	0.394398
$59$	−453835.	−0.287684	−0.143842	−	0.989601i	$-0.545946\pi$
$59$	−453835.	−0.287684	−0.143842	+	0.989601i	$0.545946\pi$
$60$	−6.24422e6	−3.73206
$61$	2.37350e6	1.33886	0.669428	−	0.742877i	$-0.266539\pi$
$61$	2.37350e6	1.33886	0.669428	+	0.742877i	$0.266539\pi$
$62$	1.50368e6	0.801283
$63$	−742457.	−0.374093
$64$	−3.20588e6	−1.52868
$65$	−2.33007e6	−1.05238
$66$	0	0
$67$	201563.	0.0818745	0.0409373	−	0.999162i	$-0.486966\pi$
$67$	201563.	0.0818745	0.0409373	+	0.999162i	$0.486966\pi$
$68$	3.59344e6	1.38589
$69$	−1.85554e6	−0.679983
$70$	6.16297e6	2.14757
$71$	−2.73550e6	−0.907054	−0.453527	−	0.891243i	$-0.649834\pi$
$71$	−2.73550e6	−0.907054	−0.453527	+	0.891243i	$0.649834\pi$
$72$	−1.95306e6	−0.616669
$73$	1.81214e6	0.545208	0.272604	−	0.962126i	$-0.412115\pi$
$73$	1.81214e6	0.545208	0.272604	+	0.962126i	$0.412115\pi$
$74$	−2.49194e6	−0.714871
$75$	−9.24309e6	−2.52990
$76$	−6.07746e6	−1.58809
$77$	0	0
$78$	−5.11590e6	−1.22065
$79$	1.53520e6	0.350325	0.175163	−	0.984540i	$-0.443955\pi$
$79$	1.53520e6	0.350325	0.175163	+	0.984540i	$0.443955\pi$
$80$	2.27808e6	0.497454
$81$	−5.97862e6	−1.24998
$82$	577889.	0.115743
$83$	−1.44936e6	−0.278230	−0.139115	−	0.990276i	$-0.544426\pi$
$83$	−1.44936e6	−0.278230	−0.139115	+	0.990276i	$0.544426\pi$
$84$	8.59050e6	1.58140
$85$	7.89817e6	1.39495
$86$	1.45341e7	2.46401
$87$	1.79547e6	0.292321
$88$	0	0
$89$	−8.72198e6	−1.31144	−0.655722	−	0.755002i	$-0.727636\pi$
$89$	−8.72198e6	−1.31144	−0.655722	+	0.755002i	$0.727636\pi$
$90$	−1.01043e7	−1.46102
$91$	3.20560e6	0.445928
$92$	7.19904e6	0.963867
$93$	4.60682e6	0.593897
$94$	−1.15915e7	−1.43944
$95$	−1.33579e7	−1.59847
$96$	−7.99547e6	−0.922348
$97$	−7.16171e6	−0.796738	−0.398369	−	0.917225i	$-0.630424\pi$
$97$	−7.16171e6	−0.796738	−0.398369	+	0.917225i	$0.630424\pi$
$98$	6.94041e6	0.744893
$99$	0	0
$100$	3.58609e7	3.58609
$101$	−62134.3	−0.00600076	−0.00300038	−	0.999995i	$-0.500955\pi$
$101$	−62134.3	−0.00600076	−0.00300038	+	0.999995i	$0.500955\pi$
$102$	1.73412e7	1.61800
$103$	−5.16764e6	−0.465974	−0.232987	−	0.972480i	$-0.574850\pi$
$103$	−5.16764e6	−0.465974	−0.232987	+	0.972480i	$0.574850\pi$
$104$	8.43245e6	0.735084
$105$	1.88814e7	1.59174
$106$	−3.16310e7	−2.57954
$107$	8.34032e6	0.658172	0.329086	−	0.944300i	$-0.393259\pi$
$107$	8.34032e6	0.658172	0.329086	+	0.944300i	$0.393259\pi$
$108$	1.38341e7	1.05674
$109$	−3.19518e6	−0.236321	−0.118161	−	0.992994i	$-0.537700\pi$
$109$	−3.19518e6	−0.236321	−0.118161	+	0.992994i	$0.537700\pi$
$110$	0	0
$111$	−7.63454e6	−0.529849
$112$	−3.13407e6	−0.210788
$113$	−2.52368e7	−1.64535	−0.822676	−	0.568510i	$-0.807520\pi$
$113$	−2.52368e7	−1.64535	−0.822676	+	0.568510i	$0.807520\pi$
$114$	−2.93286e7	−1.85406
$115$	1.58231e7	0.970170
$116$	−6.96597e6	−0.414361
$117$	−5.25562e6	−0.303371
$118$	8.49712e6	0.476085
$119$	−1.08659e7	−0.591088
$120$	4.96682e7	2.62388
$121$	0	0
$122$	−4.44387e7	−2.21566
$123$	1.77047e6	0.0857868
$124$	−1.78733e7	−0.841841
$125$	4.06057e7	1.85953
$126$	1.39010e7	0.619081
$127$	1.86301e7	0.807052	0.403526	−	0.914968i	$-0.367785\pi$
$127$	1.86301e7	0.807052	0.403526	+	0.914968i	$0.367785\pi$
$128$	4.21818e7	1.77783
$129$	4.45279e7	1.82628
$130$	4.36257e7	1.74157
$131$	−3.61322e7	−1.40425	−0.702126	−	0.712053i	$-0.747765\pi$
$131$	−3.61322e7	−1.40425	−0.702126	+	0.712053i	$0.747765\pi$
$132$	0	0
$133$	1.83772e7	0.677326
$134$	−3.77384e6	−0.135493
$135$	3.04064e7	1.06365
$136$	−2.85832e7	−0.974371
$137$	2.14096e7	0.711354	0.355677	−	0.934609i	$-0.384250\pi$
$137$	2.14096e7	0.711354	0.355677	+	0.934609i	$0.384250\pi$
$138$	3.47411e7	1.12529
$139$	1.50505e7	0.475333	0.237667	−	0.971347i	$-0.423617\pi$
$139$	1.50505e7	0.475333	0.237667	+	0.971347i	$0.423617\pi$
$140$	−7.32553e7	−2.25627
$141$	−3.55127e7	−1.06688
$142$	5.12166e7	1.50107
$143$	0	0
$144$	5.13834e6	0.143402
$145$	−1.53108e7	−0.417071
$146$	−3.39286e7	−0.902258
$147$	2.12632e7	0.552101
$148$	2.96202e7	0.751055
$149$	−1.46038e7	−0.361670	−0.180835	−	0.983513i	$-0.557880\pi$
$149$	−1.46038e7	−0.361670	−0.180835	+	0.983513i	$0.557880\pi$
$150$	1.73057e8	4.18669
$151$	−7.45470e7	−1.76202	−0.881010	−	0.473098i	$-0.843136\pi$
$151$	−7.45470e7	−1.76202	−0.881010	+	0.473098i	$0.843136\pi$
$152$	4.83418e7	1.11653
$153$	1.78148e7	0.402125
$154$	0	0
$155$	−3.92845e7	−0.847346
$156$	6.08095e7	1.28243
$157$	−6.29287e7	−1.29778	−0.648888	−	0.760884i	$-0.724766\pi$
$157$	−6.29287e7	−1.29778	−0.648888	+	0.760884i	$0.724766\pi$
$158$	−2.87435e7	−0.579749
$159$	−9.69075e7	−1.91191
$160$	6.81812e7	1.31597
$161$	−2.17686e7	−0.411093
$162$	1.11937e8	2.06858
$163$	−7.45200e7	−1.34777	−0.673886	−	0.738836i	$-0.735376\pi$
$163$	−7.45200e7	−1.34777	−0.673886	+	0.738836i	$0.735376\pi$
$164$	−6.86900e6	−0.121602
$165$	0	0
$166$	2.71363e7	0.460438
$167$	−6.30554e7	−1.04765	−0.523823	−	0.851827i	$-0.675495\pi$
$167$	−6.30554e7	−1.04765	−0.523823	+	0.851827i	$0.675495\pi$
$168$	−6.83311e7	−1.11182
$169$	−4.00571e7	−0.638375
$170$	−1.47877e8	−2.30849
$171$	−3.01296e7	−0.460794
$172$	−1.72758e8	−2.58873
$173$	−1.15095e8	−1.69003	−0.845015	−	0.534743i	$-0.820408\pi$
$173$	−1.15095e8	−1.69003	−0.845015	+	0.534743i	$0.820408\pi$
$174$	−3.36163e7	−0.483758
$175$	−1.08437e8	−1.52948
$176$	0	0
$177$	2.60325e7	0.352866
$178$	1.63301e8	2.17029
$179$	−7.98657e7	−1.04082	−0.520409	−	0.853917i	$-0.674220\pi$
$179$	−7.98657e7	−1.04082	−0.520409	+	0.853917i	$0.674220\pi$
$180$	1.20103e8	1.53497
$181$	6.15645e7	0.771713	0.385856	−	0.922559i	$-0.373906\pi$
$181$	6.15645e7	0.771713	0.385856	+	0.922559i	$0.373906\pi$
$182$	−6.00181e7	−0.737960
$183$	−1.36146e8	−1.64220
$184$	−5.72631e7	−0.677660
$185$	6.51034e7	0.755966
$186$	−8.62531e7	−0.982832
$187$	0	0
$188$	1.37781e8	1.51229
$189$	−4.18317e7	−0.450702
$190$	2.50099e8	2.64529
$191$	−1.09159e8	−1.13356	−0.566779	−	0.823870i	$-0.691810\pi$
$191$	−1.09159e8	−1.13356	−0.566779	+	0.823870i	$0.691810\pi$
$192$	1.83893e8	1.87504
$193$	5.81065e7	0.581800	0.290900	−	0.956753i	$-0.406045\pi$
$193$	5.81065e7	0.581800	0.290900	+	0.956753i	$0.406045\pi$
$194$	1.34088e8	1.31851
$195$	1.33656e8	1.29082
$196$	−8.24963e7	−0.782597
$197$	1.92574e8	1.79459	0.897295	−	0.441432i	$-0.145529\pi$
$197$	1.92574e8	1.79459	0.897295	+	0.441432i	$0.145529\pi$
$198$	0	0
$199$	6.68567e7	0.601394	0.300697	−	0.953720i	$-0.402781\pi$
$199$	6.68567e7	0.601394	0.300697	+	0.953720i	$0.402781\pi$
$200$	−2.85248e8	−2.52126
$201$	−1.15619e7	−0.100425
$202$	1.16333e6	0.00993058
$203$	2.10638e7	0.176726
$204$	−2.06124e8	−1.69990
$205$	−1.50976e7	−0.122397
$206$	9.67533e7	0.771135
$207$	3.56899e7	0.279672
$208$	−2.21851e7	−0.170938
$209$	0	0
$210$	−3.53515e8	−2.63415
$211$	−1.24647e8	−0.913469	−0.456735	−	0.889603i	$-0.650981\pi$
$211$	−1.24647e8	−0.913469	−0.456735	+	0.889603i	$0.650981\pi$
$212$	3.75978e8	2.71011
$213$	1.56912e8	1.11257
$214$	−1.56155e8	−1.08920
$215$	−3.79711e8	−2.60566
$216$	−1.10040e8	−0.742954
$217$	5.40458e7	0.359048
$218$	5.98231e7	0.391085
$219$	−1.03947e8	−0.668737
$220$	0	0
$221$	−7.69164e7	−0.479343
$222$	1.42941e8	0.876841
$223$	5.58732e7	0.337393	0.168697	−	0.985668i	$-0.446044\pi$
$223$	5.58732e7	0.337393	0.168697	+	0.985668i	$0.446044\pi$
$224$	−9.38004e7	−0.557618
$225$	1.77784e8	1.04053
$226$	4.72505e8	2.72287
$227$	−2.51831e8	−1.42896	−0.714479	−	0.699657i	$-0.753336\pi$
$227$	−2.51831e8	−1.42896	−0.714479	+	0.699657i	$0.753336\pi$
$228$	3.48610e8	1.94791
$229$	4.07394e7	0.224177	0.112088	−	0.993698i	$-0.464246\pi$
$229$	4.07394e7	0.224177	0.112088	+	0.993698i	$0.464246\pi$
$230$	−2.96254e8	−1.60552
$231$	0	0
$232$	5.54092e7	0.291323
$233$	3.66087e8	1.89600	0.948000	−	0.318272i	$-0.103102\pi$
$233$	3.66087e8	1.89600	0.948000	+	0.318272i	$0.103102\pi$
$234$	9.84005e7	0.502044
$235$	3.02834e8	1.52218
$236$	−1.01000e8	−0.500183
$237$	−8.80611e7	−0.429699
$238$	2.03442e8	0.978183
$239$	8.76304e7	0.415205	0.207602	−	0.978213i	$-0.433434\pi$
$239$	8.76304e7	0.415205	0.207602	+	0.978213i	$0.433434\pi$
$240$	−1.30673e8	−0.610164
$241$	2.01334e8	0.926526	0.463263	−	0.886221i	$-0.346679\pi$
$241$	2.01334e8	0.926526	0.463263	+	0.886221i	$0.346679\pi$
$242$	0	0
$243$	2.06991e8	0.925400
$244$	5.28215e8	2.32780
$245$	−1.81322e8	−0.787714
$246$	−3.31484e7	−0.141968
$247$	1.30086e8	0.549277
$248$	1.42169e8	0.591868
$249$	8.31370e7	0.341269
$250$	−7.60257e8	−3.07730
$251$	−2.07957e8	−0.830071	−0.415036	−	0.909805i	$-0.636231\pi$
$251$	−2.07957e8	−0.830071	−0.415036	+	0.909805i	$0.636231\pi$
$252$	−1.65232e8	−0.650417
$253$	0	0
$254$	−3.48809e8	−1.33558
$255$	−4.53048e8	−1.71101
$256$	−3.79412e8	−1.41342
$257$	−4.89865e8	−1.80016	−0.900079	−	0.435726i	$-0.856492\pi$
$257$	−4.89865e8	−1.80016	−0.900079	+	0.435726i	$0.856492\pi$
$258$	−8.33692e8	−3.02229
$259$	−8.95660e7	−0.320327
$260$	−5.18551e8	−1.82972
$261$	−3.45345e7	−0.120229
$262$	6.76500e8	2.32388
$263$	2.20241e7	0.0746540	0.0373270	−	0.999303i	$-0.488116\pi$
$263$	2.20241e7	0.0746540	0.0373270	+	0.999303i	$0.488116\pi$
$264$	0	0
$265$	8.26377e8	2.72783
$266$	−3.44074e8	−1.12090
$267$	5.00302e8	1.60858
$268$	4.48573e7	0.142351
$269$	−5.31207e8	−1.66391	−0.831957	−	0.554840i	$-0.812780\pi$
$269$	−5.31207e8	−1.66391	−0.831957	+	0.554840i	$0.812780\pi$
$270$	−5.69297e8	−1.76021
$271$	4.53571e8	1.38437	0.692187	−	0.721719i	$-0.256648\pi$
$271$	4.53571e8	1.38437	0.692187	+	0.721719i	$0.256648\pi$
$272$	7.52000e7	0.226583
$273$	−1.83877e8	−0.546963
$274$	−4.00849e8	−1.17721
$275$	0	0
$276$	−4.12945e8	−1.18225
$277$	−2.71807e8	−0.768389	−0.384195	−	0.923252i	$-0.625521\pi$
$277$	−2.71807e8	−0.768389	−0.384195	+	0.923252i	$0.625521\pi$
$278$	−2.81789e8	−0.786623
$279$	−8.86088e7	−0.244265
$280$	5.82692e8	1.58630
$281$	3.03732e8	0.816616	0.408308	−	0.912844i	$-0.366119\pi$
$281$	3.03732e8	0.816616	0.408308	+	0.912844i	$0.366119\pi$
$282$	6.64902e8	1.76557
$283$	−6.12447e8	−1.60626	−0.803131	−	0.595803i	$-0.796834\pi$
$283$	−6.12447e8	−1.60626	−0.803131	+	0.595803i	$0.796834\pi$
$284$	−6.08779e8	−1.57705
$285$	7.66224e8	1.96064
$286$	0	0
$287$	2.07706e7	0.0518636
$288$	1.53787e8	0.379355
$289$	−1.49618e8	−0.364620
$290$	2.86663e8	0.690205
$291$	4.10804e8	0.977257
$292$	4.03287e8	0.947927
$293$	1.17102e8	0.271973	0.135987	−	0.990711i	$-0.456580\pi$
$293$	1.17102e8	0.271973	0.135987	+	0.990711i	$0.456580\pi$
$294$	−3.98110e8	−0.913665
$295$	−2.21992e8	−0.503454
$296$	−2.35607e8	−0.528040
$297$	0	0
$298$	2.73425e8	0.598523
$299$	−1.54093e8	−0.333376
$300$	−2.05702e9	−4.39861
$301$	5.22388e8	1.10410
$302$	1.39574e9	2.91594
$303$	3.56409e6	0.00736037
$304$	−1.27183e8	−0.259640
$305$	1.16099e9	2.34303
$306$	−3.33545e8	−0.665472
$307$	−4.22604e8	−0.833584	−0.416792	−	0.909002i	$-0.636846\pi$
$307$	−4.22604e8	−0.833584	−0.416792	+	0.909002i	$0.636846\pi$
$308$	0	0
$309$	2.96422e8	0.571552
$310$	7.35521e8	1.40226
$311$	5.95645e8	1.12286	0.561431	−	0.827524i	$-0.310251\pi$
$311$	5.95645e8	1.12286	0.561431	+	0.827524i	$0.310251\pi$
$312$	−4.83695e8	−0.901634
$313$	−4.25610e8	−0.784525	−0.392262	−	0.919853i	$-0.628307\pi$
$313$	−4.25610e8	−0.784525	−0.392262	+	0.919853i	$0.628307\pi$
$314$	1.17821e9	2.14767
$315$	−3.63170e8	−0.654670
$316$	3.41656e8	0.609093
$317$	2.20763e8	0.389241	0.194621	−	0.980879i	$-0.437652\pi$
$317$	2.20763e8	0.389241	0.194621	+	0.980879i	$0.437652\pi$
$318$	1.81439e9	3.16400
$319$	0	0
$320$	−1.56814e9	−2.67523
$321$	−4.78410e8	−0.807296
$322$	4.07571e8	0.680312
$323$	−4.40949e8	−0.728080
$324$	−1.33052e9	−2.17328
$325$	−7.67592e8	−1.24033
$326$	1.39523e9	2.23041
$327$	1.83279e8	0.289865
$328$	5.46378e7	0.0854939
$329$	−4.16624e8	−0.644999
$330$	0	0
$331$	−1.98049e8	−0.300176	−0.150088	−	0.988673i	$-0.547956\pi$
$331$	−1.98049e8	−0.300176	−0.150088	+	0.988673i	$0.547956\pi$
$332$	−3.22551e8	−0.483744
$333$	1.46845e8	0.217923
$334$	1.18058e9	1.73374
$335$	9.85936e7	0.143282
$336$	1.79774e8	0.258546
$337$	−1.28156e9	−1.82404	−0.912022	−	0.410141i	$-0.865480\pi$
$337$	−1.28156e9	−1.82404	−0.912022	+	0.410141i	$0.865480\pi$
$338$	7.49985e8	1.05644
$339$	1.44761e9	2.01814
$340$	1.75772e9	2.42534
$341$	0	0
$342$	5.64113e8	0.762562
$343$	8.03651e8	1.07532
$344$	1.37416e9	1.82005
$345$	−9.07628e8	−1.18998
$346$	2.15491e9	2.79681
$347$	5.46679e7	0.0702391	0.0351196	−	0.999383i	$-0.488819\pi$
$347$	5.46679e7	0.0702391	0.0351196	+	0.999383i	$0.488819\pi$
$348$	3.99576e8	0.508244
$349$	−1.01482e9	−1.27791	−0.638954	−	0.769245i	$-0.720633\pi$
$349$	−1.01482e9	−1.27791	−0.638954	+	0.769245i	$0.720633\pi$
$350$	2.03026e9	2.53112
$351$	−2.96114e8	−0.365497
$352$	0	0
$353$	1.24216e9	1.50302	0.751511	−	0.659720i	$-0.229325\pi$
$353$	1.24216e9	1.50302	0.751511	+	0.659720i	$0.229325\pi$
$354$	−4.87404e8	−0.583953
$355$	−1.33806e9	−1.58736
$356$	−1.94105e9	−2.28014
$357$	6.23281e8	0.725012
$358$	1.49532e9	1.72244
$359$	−6.97951e7	−0.0796149	−0.0398075	−	0.999207i	$-0.512674\pi$
$359$	−6.97951e7	−0.0796149	−0.0398075	+	0.999207i	$0.512674\pi$
$360$	−9.55331e8	−1.07918
$361$	−1.48110e8	−0.165695
$362$	−1.15267e9	−1.27710
$363$	0	0
$364$	7.13398e8	0.775313
$365$	8.86402e8	0.954126
$366$	2.54906e9	2.71766
$367$	2.06451e8	0.218015	0.109007	−	0.994041i	$-0.465233\pi$
$367$	2.06451e8	0.218015	0.109007	+	0.994041i	$0.465233\pi$
$368$	1.50654e8	0.157585
$369$	−3.40537e7	−0.0352835
$370$	−1.21892e9	−1.25104
$371$	−1.13689e9	−1.15587
$372$	1.02524e9	1.03258
$373$	4.06112e8	0.405195	0.202598	−	0.979262i	$-0.435062\pi$
$373$	4.06112e8	0.405195	0.202598	+	0.979262i	$0.435062\pi$
$374$	0	0
$375$	−2.32919e9	−2.28084
$376$	−1.09595e9	−1.06324
$377$	1.49104e8	0.143316
$378$	7.83211e8	0.745860
$379$	1.29105e9	1.21816	0.609082	−	0.793107i	$-0.291538\pi$
$379$	1.29105e9	1.21816	0.609082	+	0.793107i	$0.291538\pi$
$380$	−2.97277e9	−2.77919
$381$	−1.06864e9	−0.989908
$382$	2.04378e9	1.87591
$383$	−5.30203e8	−0.482221	−0.241111	−	0.970498i	$-0.577512\pi$
$383$	−5.30203e8	−0.482221	−0.241111	+	0.970498i	$0.577512\pi$
$384$	−2.41959e9	−2.18064
$385$	0	0
$386$	−1.08792e9	−0.962814
$387$	−8.56461e8	−0.751137
$388$	−1.59382e9	−1.38525
$389$	9.49094e8	0.817496	0.408748	−	0.912647i	$-0.365966\pi$
$389$	9.49094e8	0.817496	0.408748	+	0.912647i	$0.365966\pi$
$390$	−2.50242e9	−2.13616
$391$	5.22324e8	0.441897
$392$	6.56197e8	0.550216
$393$	2.07258e9	1.72242
$394$	−3.60554e9	−2.96984
$395$	7.50939e8	0.613077
$396$	0	0
$397$	−6.46600e8	−0.518644	−0.259322	−	0.965791i	$-0.583499\pi$
$397$	−6.46600e8	−0.518644	−0.259322	+	0.965791i	$0.583499\pi$
$398$	−1.25175e9	−0.995240
$399$	−1.05413e9	−0.830789
$400$	7.50463e8	0.586299
$401$	−1.68521e9	−1.30511	−0.652556	−	0.757740i	$-0.726303\pi$
$401$	−1.68521e9	−1.30511	−0.652556	+	0.757740i	$0.726303\pi$
$402$	2.16472e8	0.166192
$403$	3.82573e8	0.291170
$404$	−1.38278e7	−0.0104332
$405$	−2.92441e9	−2.18749
$406$	−3.94376e8	−0.292462
$407$	0	0
$408$	1.63956e9	1.19514
$409$	5.94779e8	0.429857	0.214929	−	0.976630i	$-0.431048\pi$
$409$	5.94779e8	0.429857	0.214929	+	0.976630i	$0.431048\pi$
$410$	2.82672e8	0.202553
$411$	−1.22808e9	−0.872527
$412$	−1.15004e9	−0.810167
$413$	3.05405e8	0.213330
$414$	−6.68218e8	−0.462825
$415$	−7.08949e8	−0.486907
$416$	−6.63984e8	−0.452200
$417$	−8.63312e8	−0.583031
$418$	0	0
$419$	6.15212e8	0.408579	0.204289	−	0.978911i	$-0.434512\pi$
$419$	6.15212e8	0.408579	0.204289	+	0.978911i	$0.434512\pi$
$420$	4.20200e9	2.76748
$421$	−3.39261e8	−0.221588	−0.110794	−	0.993843i	$-0.535339\pi$
$421$	−3.39261e8	−0.221588	−0.110794	+	0.993843i	$0.535339\pi$
$422$	2.33376e9	1.51169
$423$	6.83061e8	0.438802
$424$	−2.99063e9	−1.90538
$425$	2.60188e9	1.64409
$426$	−2.93784e9	−1.84117
$427$	−1.59723e9	−0.992817
$428$	1.85612e9	1.14433
$429$	0	0
$430$	7.10929e9	4.31208
$431$	−3.13409e9	−1.88556	−0.942780	−	0.333415i	$-0.891799\pi$
$431$	−3.13409e9	−1.88556	−0.942780	+	0.333415i	$0.891799\pi$
$432$	2.89506e8	0.172768
$433$	2.57578e9	1.52476	0.762379	−	0.647131i	$-0.224031\pi$
$433$	2.57578e9	1.52476	0.762379	+	0.647131i	$0.224031\pi$
$434$	−1.01189e9	−0.594184
$435$	8.78244e8	0.511568
$436$	−7.11079e8	−0.410880
$437$	−8.83389e8	−0.506369
$438$	1.94618e9	1.10668
$439$	−9.98381e8	−0.563210	−0.281605	−	0.959530i	$-0.590867\pi$
$439$	−9.98381e8	−0.563210	−0.281605	+	0.959530i	$0.590867\pi$
$440$	0	0
$441$	−4.08983e8	−0.227075
$442$	1.44010e9	0.793258
$443$	−1.83226e9	−1.00132	−0.500662	−	0.865643i	$-0.666910\pi$
$443$	−1.83226e9	−1.00132	−0.500662	+	0.865643i	$0.666910\pi$
$444$	−1.69905e9	−0.921223
$445$	−4.26632e9	−2.29506
$446$	−1.04611e9	−0.558348
$447$	8.37688e8	0.443615
$448$	2.15738e9	1.13358
$449$	4.49375e8	0.234286	0.117143	−	0.993115i	$-0.462626\pi$
$449$	4.49375e8	0.234286	0.117143	+	0.993115i	$0.462626\pi$
$450$	−3.32863e9	−1.72196
$451$	0	0
$452$	−5.61637e9	−2.86069
$453$	4.27610e9	2.16125
$454$	4.71501e9	2.36476
$455$	1.56801e9	0.780383
$456$	−2.77294e9	−1.36950
$457$	−1.05361e9	−0.516384	−0.258192	−	0.966094i	$-0.583127\pi$
$457$	−1.05361e9	−0.516384	−0.258192	+	0.966094i	$0.583127\pi$
$458$	−7.62760e8	−0.370987
$459$	1.00373e9	0.484474
$460$	3.52138e9	1.68679
$461$	−3.11354e9	−1.48014	−0.740068	−	0.672532i	$-0.765207\pi$
$461$	−3.11354e9	−1.48014	−0.740068	+	0.672532i	$0.765207\pi$
$462$	0	0
$463$	−2.78973e9	−1.30626	−0.653128	−	0.757248i	$-0.726543\pi$
$463$	−2.78973e9	−1.30626	−0.653128	+	0.757248i	$0.726543\pi$
$464$	−1.45777e8	−0.0677449
$465$	2.25341e9	1.03933
$466$	−6.85421e9	−3.13766
$467$	2.34779e9	1.06672	0.533359	−	0.845889i	$-0.320930\pi$
$467$	2.34779e9	1.06672	0.533359	+	0.845889i	$0.320930\pi$
$468$	−1.16962e9	−0.527456
$469$	−1.35640e8	−0.0607133
$470$	−5.66994e9	−2.51904
$471$	3.60966e9	1.59182
$472$	8.03380e8	0.351661
$473$	0	0
$474$	1.64876e9	0.711104
$475$	−4.40047e9	−1.88396
$476$	−2.41818e9	−1.02770
$477$	1.86394e9	0.786355
$478$	−1.64070e9	−0.687117
$479$	1.77484e9	0.737877	0.368938	−	0.929454i	$-0.379721\pi$
$479$	1.77484e9	0.737877	0.368938	+	0.929454i	$0.379721\pi$
$480$	−3.91095e9	−1.61413
$481$	−6.34010e8	−0.259770
$482$	−3.76956e9	−1.53330
$483$	1.24867e9	0.504235
$484$	0	0
$485$	−3.50312e9	−1.39431
$486$	−3.87548e9	−1.53143
$487$	−9.53725e8	−0.374173	−0.187086	−	0.982343i	$-0.559904\pi$
$487$	−9.53725e8	−0.374173	−0.187086	+	0.982343i	$0.559904\pi$
$488$	−4.20156e9	−1.63660
$489$	4.27455e9	1.65314
$490$	3.39487e9	1.30358
$491$	1.27036e9	0.484329	0.242165	−	0.970235i	$-0.422143\pi$
$491$	1.27036e9	0.484329	0.242165	+	0.970235i	$0.422143\pi$
$492$	3.94013e8	0.149153
$493$	−5.05414e8	−0.189969
$494$	−2.43559e9	−0.908992
$495$	0	0
$496$	−3.74036e8	−0.137635
$497$	1.84084e9	0.672617
$498$	−1.55657e9	−0.564761
$499$	2.57626e8	0.0928191	0.0464096	−	0.998922i	$-0.485222\pi$
$499$	2.57626e8	0.0928191	0.0464096	+	0.998922i	$0.485222\pi$
$500$	9.03669e9	3.23307
$501$	3.61693e9	1.28501
$502$	3.89356e9	1.37367
$503$	3.99146e8	0.139844	0.0699219	−	0.997552i	$-0.477725\pi$
$503$	3.99146e8	0.139844	0.0699219	+	0.997552i	$0.477725\pi$
$504$	1.31430e9	0.457285
$505$	−3.03927e7	−0.0105015
$506$	0	0
$507$	2.29772e9	0.783013
$508$	4.14607e9	1.40318
$509$	4.78305e9	1.60766	0.803828	−	0.594862i	$-0.202793\pi$
$509$	4.78305e9	1.60766	0.803828	+	0.594862i	$0.202793\pi$
$510$	8.48237e9	2.83153
$511$	−1.21947e9	−0.404294
$512$	1.70443e9	0.561223
$513$	−1.69757e9	−0.555158
$514$	9.17171e9	2.97906
$515$	−2.52773e9	−0.815465
$516$	9.90957e9	3.17527
$517$	0	0
$518$	1.67694e9	0.530106
$519$	6.60197e9	2.07294
$520$	4.12470e9	1.28641
$521$	−2.37654e9	−0.736228	−0.368114	−	0.929781i	$-0.619996\pi$
$521$	−2.37654e9	−0.736228	−0.368114	+	0.929781i	$0.619996\pi$
$522$	6.46585e8	0.198966
$523$	−1.30396e9	−0.398572	−0.199286	−	0.979941i	$-0.563862\pi$
$523$	−1.30396e9	−0.398572	−0.199286	+	0.979941i	$0.563862\pi$
$524$	−8.04112e9	−2.44150
$525$	6.22007e9	1.87602
$526$	−4.12355e8	−0.123544
$527$	−1.29680e9	−0.385953
$528$	0	0
$529$	−2.35841e9	−0.692667
$530$	−1.54722e10	−4.51425
$531$	−5.00716e8	−0.145131
$532$	4.08979e9	1.17763
$533$	1.47029e8	0.0420588
$534$	−9.36712e9	−2.66202
$535$	4.07963e9	1.15181
$536$	−3.56807e8	−0.100082
$537$	4.58119e9	1.27664
$538$	9.94574e9	2.75359
$539$	0	0
$540$	6.76687e9	1.84931
$541$	−1.36653e8	−0.0371047	−0.0185524	−	0.999828i	$-0.505906\pi$
$541$	−1.36653e8	−0.0371047	−0.0185524	+	0.999828i	$0.505906\pi$
$542$	−8.49218e9	−2.29098
$543$	−3.53141e9	−0.946562
$544$	2.25068e9	0.599402
$545$	−1.56291e9	−0.413567
$546$	3.44271e9	0.905161
$547$	−1.29370e9	−0.337970	−0.168985	−	0.985619i	$-0.554049\pi$
$547$	−1.29370e9	−0.337970	−0.168985	+	0.985619i	$0.554049\pi$
$548$	4.76464e9	1.23680
$549$	2.61867e9	0.675427
$550$	0	0
$551$	8.54790e8	0.217685
$552$	3.28467e9	0.831200
$553$	−1.03311e9	−0.259781
$554$	5.08902e9	1.27160
$555$	−3.73440e9	−0.927247
$556$	3.34944e9	0.826439
$557$	−1.89723e9	−0.465185	−0.232593	−	0.972574i	$-0.574721\pi$
$557$	−1.89723e9	−0.465185	−0.232593	+	0.972574i	$0.574721\pi$
$558$	1.65901e9	0.404232
$559$	3.69782e9	0.895374
$560$	−1.53302e9	−0.368883
$561$	0	0
$562$	−5.68674e9	−1.35141
$563$	1.48135e9	0.349847	0.174923	−	0.984582i	$-0.444032\pi$
$563$	1.48135e9	0.349847	0.174923	+	0.984582i	$0.444032\pi$
$564$	−7.90327e9	−1.85494
$565$	−1.23445e10	−2.87940
$566$	1.14668e10	2.65818
$567$	4.02327e9	0.926911
$568$	4.84239e9	1.10877
$569$	−5.66792e9	−1.28982	−0.644912	−	0.764257i	$-0.723106\pi$
$569$	−5.66792e9	−1.28982	−0.644912	+	0.764257i	$0.723106\pi$
$570$	−1.43459e10	−3.24465
$571$	6.65726e9	1.49647	0.748237	−	0.663432i	$-0.230901\pi$
$571$	6.65726e9	1.49647	0.748237	+	0.663432i	$0.230901\pi$
$572$	0	0
$573$	6.26149e9	1.39039
$574$	−3.88886e8	−0.0858284
$575$	5.21256e9	1.14344
$576$	−3.53705e9	−0.771192
$577$	−3.20943e9	−0.695525	−0.347763	−	0.937583i	$-0.613058\pi$
$577$	−3.20943e9	−0.695525	−0.347763	+	0.937583i	$0.613058\pi$
$578$	2.80128e9	0.603405
$579$	−3.33305e9	−0.713620
$580$	−3.40738e9	−0.725140
$581$	9.75337e8	0.206319
$582$	−7.69144e9	−1.61725
$583$	0	0
$584$	−3.20786e9	−0.666454
$585$	−2.57077e9	−0.530905
$586$	−2.19248e9	−0.450085
$587$	3.68593e9	0.752165	0.376083	−	0.926586i	$-0.377271\pi$
$587$	3.68593e9	0.752165	0.376083	+	0.926586i	$0.377271\pi$
$588$	4.73208e9	0.959912
$589$	2.19323e9	0.442262
$590$	4.15633e9	0.833159
$591$	−1.10462e10	−2.20119
$592$	6.19862e8	0.122792
$593$	−6.79361e9	−1.33786	−0.668928	−	0.743327i	$-0.733247\pi$
$593$	−6.79361e9	−1.33786	−0.668928	+	0.743327i	$0.733247\pi$
$594$	0	0
$595$	−5.31502e9	−1.03442
$596$	−3.25003e9	−0.628818
$597$	−3.83498e9	−0.737654
$598$	2.88507e9	0.551699
$599$	−4.56318e9	−0.867509	−0.433755	−	0.901031i	$-0.642812\pi$
$599$	−4.56318e9	−0.867509	−0.433755	+	0.901031i	$0.642812\pi$
$600$	1.63621e10	3.09250
$601$	−1.86582e9	−0.350597	−0.175298	−	0.984515i	$-0.556089\pi$
$601$	−1.86582e9	−0.350597	−0.175298	+	0.984515i	$0.556089\pi$
$602$	−9.78061e9	−1.82717
$603$	2.22384e8	0.0413041
$604$	−1.65902e10	−3.06354
$605$	0	0
$606$	−6.67302e7	−0.0121806
$607$	8.04937e9	1.46084	0.730418	−	0.683001i	$-0.239325\pi$
$607$	8.04937e9	1.46084	0.730418	+	0.683001i	$0.239325\pi$
$608$	−3.80651e9	−0.686853
$609$	−1.20825e9	−0.216768
$610$	−2.17370e10	−3.87744
$611$	−2.94915e9	−0.523062
$612$	3.96464e9	0.699155
$613$	1.49074e9	0.261391	0.130695	−	0.991423i	$-0.458279\pi$
$613$	1.49074e9	0.261391	0.130695	+	0.991423i	$0.458279\pi$
$614$	7.91238e9	1.37949
$615$	8.66018e8	0.150129
$616$	0	0
$617$	5.19586e9	0.890552	0.445276	−	0.895393i	$-0.353106\pi$
$617$	5.19586e9	0.890552	0.445276	+	0.895393i	$0.353106\pi$
$618$	−5.54988e9	−0.945853
$619$	−8.61278e8	−0.145957	−0.0729787	−	0.997333i	$-0.523251\pi$
$619$	−8.61278e8	−0.145957	−0.0729787	+	0.997333i	$0.523251\pi$
$620$	−8.74267e9	−1.47324
$621$	2.01085e9	0.336945
$622$	−1.11522e10	−1.85821
$623$	5.86939e9	0.972490
$624$	1.27256e9	0.209668
$625$	7.27316e9	1.19164
$626$	7.96866e9	1.29830
$627$	0	0
$628$	−1.40046e10	−2.25638
$629$	2.14908e9	0.344331
$630$	6.79959e9	1.08341
$631$	3.83217e9	0.607214	0.303607	−	0.952797i	$-0.401809\pi$
$631$	3.83217e9	0.607214	0.303607	+	0.952797i	$0.401809\pi$
$632$	−2.71762e9	−0.428232
$633$	7.14990e9	1.12044
$634$	−4.13332e9	−0.644150
$635$	9.11282e9	1.41236
$636$	−2.15665e10	−3.32414
$637$	1.76581e9	0.270679
$638$	0	0
$639$	−3.01808e9	−0.457591
$640$	2.06330e10	3.11124
$641$	3.33136e9	0.499595	0.249798	−	0.968298i	$-0.419636\pi$
$641$	3.33136e9	0.499595	0.249798	+	0.968298i	$0.419636\pi$
$642$	8.95723e9	1.33598
$643$	2.64858e9	0.392893	0.196447	−	0.980515i	$-0.437060\pi$
$643$	2.64858e9	0.392893	0.196447	+	0.980515i	$0.437060\pi$
$644$	−4.84454e9	−0.714746
$645$	2.17806e10	3.19603
$646$	8.25584e9	1.20489
$647$	9.56794e9	1.38884	0.694422	−	0.719568i	$-0.255660\pi$
$647$	9.56794e9	1.38884	0.694422	+	0.719568i	$0.255660\pi$
$648$	1.05834e10	1.52796
$649$	0	0
$650$	1.43716e10	2.05261
$651$	−3.10013e9	−0.440399
$652$	−1.65842e10	−2.34330
$653$	3.91287e9	0.549920	0.274960	−	0.961456i	$-0.411335\pi$
$653$	3.91287e9	0.549920	0.274960	+	0.961456i	$0.411335\pi$
$654$	−3.43152e9	−0.479694
$655$	−1.76739e10	−2.45747
$656$	−1.43748e8	−0.0198810
$657$	1.99933e9	0.275047
$658$	7.80042e9	1.06740
$659$	−8.65766e8	−0.117842	−0.0589212	−	0.998263i	$-0.518766\pi$
$659$	−8.65766e8	−0.117842	−0.0589212	+	0.998263i	$0.518766\pi$
$660$	0	0
$661$	6.69631e9	0.901842	0.450921	−	0.892564i	$-0.351096\pi$
$661$	6.69631e9	0.901842	0.450921	+	0.892564i	$0.351096\pi$
$662$	3.70806e9	0.496757
$663$	4.41201e9	0.587949
$664$	2.56566e9	0.340103
$665$	8.98910e9	1.18533
$666$	−2.74936e9	−0.360638
$667$	−1.01254e9	−0.132121
$668$	−1.40328e10	−1.82149
$669$	−3.20495e9	−0.413837
$670$	−1.84596e9	−0.237116
$671$	0	0
$672$	5.38050e9	0.683959
$673$	−9.12204e9	−1.15356	−0.576779	−	0.816900i	$-0.695691\pi$
$673$	−9.12204e9	−1.15356	−0.576779	+	0.816900i	$0.695691\pi$
$674$	2.39946e10	3.01859
$675$	1.00167e10	1.25361
$676$	−8.91460e9	−1.10991
$677$	8.51516e9	1.05471	0.527354	−	0.849646i	$-0.323184\pi$
$677$	8.51516e9	1.05471	0.527354	+	0.849646i	$0.323184\pi$
$678$	−2.71034e10	−3.33980
$679$	4.81942e9	0.590814
$680$	−1.39813e10	−1.70517
$681$	1.44453e10	1.75272
$682$	0	0
$683$	3.73512e9	0.448571	0.224286	−	0.974523i	$-0.427995\pi$
$683$	3.73512e9	0.448571	0.224286	+	0.974523i	$0.427995\pi$
$684$	−6.70526e9	−0.801160
$685$	1.04724e10	1.24488
$686$	−1.50467e10	−1.77953
$687$	−2.33686e9	−0.274969
$688$	−3.61530e9	−0.423238
$689$	−8.04768e9	−0.937354
$690$	1.69934e10	1.96929
$691$	−1.37945e10	−1.59050	−0.795248	−	0.606284i	$-0.792659\pi$
$691$	−1.37945e10	−1.59050	−0.795248	+	0.606284i	$0.792659\pi$
$692$	−2.56140e10	−2.93837
$693$	0	0
$694$	−1.02354e9	−0.116238
$695$	7.36187e9	0.831843
$696$	−3.17834e9	−0.357328
$697$	−4.98378e8	−0.0557499
$698$	1.90004e10	2.11479
$699$	−2.09991e10	−2.32558
$700$	−2.41324e10	−2.65924
$701$	4.45882e9	0.488886	0.244443	−	0.969664i	$-0.421395\pi$
$701$	4.45882e9	0.488886	0.244443	+	0.969664i	$0.421395\pi$
$702$	5.54411e9	0.604856
$703$	−3.63467e9	−0.394568
$704$	0	0
$705$	−1.73709e10	−1.86707
$706$	−2.32568e10	−2.48733
$707$	4.18128e7	0.00444981
$708$	5.79346e9	0.613510
$709$	6.12515e8	0.0645438	0.0322719	−	0.999479i	$-0.489726\pi$
$709$	6.12515e8	0.0645438	0.0322719	+	0.999479i	$0.489726\pi$
$710$	2.50524e10	2.62691
$711$	1.69379e9	0.176732
$712$	1.54397e10	1.60309
$713$	−2.59798e9	−0.268424
$714$	−1.16696e10	−1.19981
$715$	0	0
$716$	−1.77739e10	−1.80962
$717$	−5.02658e9	−0.509279
$718$	1.30677e9	0.131754
$719$	7.67812e9	0.770378	0.385189	−	0.922838i	$-0.374136\pi$
$719$	7.67812e9	0.770378	0.385189	+	0.922838i	$0.374136\pi$
$720$	2.51340e9	0.250956
$721$	3.47753e9	0.345539
$722$	2.77306e9	0.274207
$723$	−1.15487e10	−1.13645
$724$	1.37010e10	1.34174
$725$	−5.04381e9	−0.491559
$726$	0	0
$727$	1.08717e10	1.04937	0.524683	−	0.851298i	$-0.324184\pi$
$727$	1.08717e10	1.04937	0.524683	+	0.851298i	$0.324184\pi$
$728$	−5.67456e9	−0.545095
$729$	1.20199e9	0.114909
$730$	−1.65960e10	−1.57897
$731$	−1.25344e10	−1.18684
$732$	−3.02990e10	−2.85522
$733$	8.63676e9	0.810003	0.405002	−	0.914316i	$-0.367271\pi$
$733$	8.63676e9	0.810003	0.405002	+	0.914316i	$0.367271\pi$
$734$	−3.86536e9	−0.360790
$735$	1.04008e10	0.966189
$736$	4.50898e9	0.416875
$737$	0	0
$738$	6.37584e8	0.0583902
$739$	−1.70305e10	−1.55229	−0.776144	−	0.630555i	$-0.782827\pi$
$739$	−1.70305e10	−1.55229	−0.776144	+	0.630555i	$0.782827\pi$
$740$	1.44886e10	1.31436
$741$	−7.46189e9	−0.673729
$742$	2.12859e10	1.91284
$743$	1.82193e9	0.162956	0.0814782	−	0.996675i	$-0.474036\pi$
$743$	1.82193e9	0.162956	0.0814782	+	0.996675i	$0.474036\pi$
$744$	−8.15500e9	−0.725970
$745$	−7.14336e9	−0.632930
$746$	−7.60359e9	−0.670552
$747$	−1.59908e9	−0.140361
$748$	0	0
$749$	−5.61256e9	−0.488061
$750$	4.36092e10	3.77454
$751$	1.07122e9	0.0922862	0.0461431	−	0.998935i	$-0.485307\pi$
$751$	1.07122e9	0.0922862	0.0461431	+	0.998935i	$0.485307\pi$
$752$	2.88334e9	0.247249
$753$	1.19286e10	1.01814
$754$	−2.79167e9	−0.237172
$755$	−3.64643e10	−3.08357
$756$	−9.30953e9	−0.783613
$757$	1.33200e9	0.111602	0.0558008	−	0.998442i	$-0.482229\pi$
$757$	1.33200e9	0.111602	0.0558008	+	0.998442i	$0.482229\pi$
$758$	−2.41722e10	−2.01592
$759$	0	0
$760$	2.36462e10	1.95395
$761$	−9.54306e8	−0.0784949	−0.0392474	−	0.999230i	$-0.512496\pi$
$761$	−9.54306e8	−0.0784949	−0.0392474	+	0.999230i	$0.512496\pi$
$762$	2.00081e10	1.63819
$763$	2.15017e9	0.175242
$764$	−2.42931e10	−1.97086
$765$	8.71404e9	0.703727
$766$	9.92694e9	0.798022
$767$	2.16187e9	0.173000
$768$	2.17635e10	1.73366
$769$	1.03220e10	0.818509	0.409254	−	0.912420i	$-0.365789\pi$
$769$	1.03220e10	0.818509	0.409254	+	0.912420i	$0.365789\pi$
$770$	0	0
$771$	2.80992e10	2.20803
$772$	1.29314e10	1.01155
$773$	−1.82539e10	−1.42144	−0.710720	−	0.703475i	$-0.751631\pi$
$773$	−1.82539e10	−1.42144	−0.710720	+	0.703475i	$0.751631\pi$
$774$	1.60354e10	1.24305
$775$	−1.29414e10	−0.998681
$776$	1.26777e10	0.973920
$777$	5.13761e9	0.392905
$778$	−1.77698e10	−1.35286
$779$	8.42890e8	0.0638837
$780$	2.97447e10	2.24429
$781$	0	0
$782$	−9.77943e9	−0.731290
$783$	−1.94575e9	−0.144851
$784$	−1.72640e9	−0.127949
$785$	−3.07813e10	−2.27114
$786$	−3.88048e10	−2.85040
$787$	−1.50165e10	−1.09814	−0.549068	−	0.835778i	$-0.685017\pi$
$787$	−1.50165e10	−1.09814	−0.549068	+	0.835778i	$0.685017\pi$
$788$	4.28568e10	3.12016
$789$	−1.26333e9	−0.0915685
$790$	−1.40598e10	−1.01457
$791$	1.69829e10	1.22010
$792$	0	0
$793$	−1.13063e10	−0.805125
$794$	1.21062e10	0.858297
$795$	−4.74019e10	−3.34588
$796$	1.48788e10	1.04562
$797$	1.51683e10	1.06129	0.530643	−	0.847595i	$-0.321950\pi$
$797$	1.51683e10	1.06129	0.530643	+	0.847595i	$0.321950\pi$
$798$	1.97365e10	1.37486
$799$	9.99665e9	0.693331
$800$	2.24608e10	1.55100
$801$	−9.62294e9	−0.661598
$802$	3.15520e10	2.15981
$803$	0	0
$804$	−2.57306e9	−0.174604
$805$	−1.06480e10	−0.719421
$806$	−7.16288e9	−0.481854
$807$	3.04706e10	2.04091
$808$	1.09990e8	0.00733524
$809$	5.30195e9	0.352059	0.176030	−	0.984385i	$-0.443675\pi$
$809$	5.30195e9	0.352059	0.176030	+	0.984385i	$0.443675\pi$
$810$	5.47535e10	3.62005
$811$	−1.11494e9	−0.0733973	−0.0366987	−	0.999326i	$-0.511684\pi$
$811$	−1.11494e9	−0.0733973	−0.0366987	+	0.999326i	$0.511684\pi$
$812$	4.68770e9	0.307266
$813$	−2.60174e10	−1.69803
$814$	0	0
$815$	−3.64511e10	−2.35863
$816$	−4.31356e9	−0.277920
$817$	2.11990e10	1.36000
$818$	−1.11360e10	−0.711365
$819$	3.53673e9	0.224962
$820$	−3.35994e9	−0.212806
$821$	−5.99567e9	−0.378126	−0.189063	−	0.981965i	$-0.560545\pi$
$821$	−5.99567e9	−0.378126	−0.189063	+	0.981965i	$0.560545\pi$
$822$	2.29932e10	1.44393
$823$	−2.38626e10	−1.49217	−0.746084	−	0.665852i	$-0.768068\pi$
$823$	−2.38626e10	−1.49217	−0.746084	+	0.665852i	$0.768068\pi$
$824$	9.14776e9	0.569600
$825$	0	0
$826$	−5.71807e9	−0.353037
$827$	2.13343e10	1.31162	0.655812	−	0.754924i	$-0.272326\pi$
$827$	2.13343e10	1.31162	0.655812	+	0.754924i	$0.272326\pi$
$828$	7.94269e9	0.486252
$829$	−6.80738e8	−0.0414991	−0.0207496	−	0.999785i	$-0.506605\pi$
$829$	−6.80738e8	−0.0414991	−0.0207496	+	0.999785i	$0.506605\pi$
$830$	1.32736e10	0.805777
$831$	1.55911e10	0.942485
$832$	1.52714e10	0.919279
$833$	−5.98549e9	−0.358792
$834$	1.61637e10	0.964850
$835$	−3.08433e10	−1.83340
$836$	0	0
$837$	−4.99242e9	−0.294287
$838$	−1.15186e10	−0.676152
$839$	−2.51837e10	−1.47215	−0.736076	−	0.676899i	$-0.763323\pi$
$839$	−2.51837e10	−1.47215	−0.736076	+	0.676899i	$0.763323\pi$
$840$	−3.34239e10	−1.94571
$841$	−1.62701e10	−0.943202
$842$	6.35196e9	0.366704
$843$	−1.74224e10	−1.00164
$844$	−2.77399e10	−1.58820
$845$	−1.95937e10	−1.11717
$846$	−1.27889e10	−0.726167
$847$	0	0
$848$	7.86810e9	0.443082
$849$	3.51307e10	1.97020
$850$	−4.87148e10	−2.72079
$851$	4.30544e9	0.239477
$852$	3.49202e10	1.93437
$853$	1.39530e10	0.769742	0.384871	−	0.922970i	$-0.374246\pi$
$853$	1.39530e10	0.769742	0.384871	+	0.922970i	$0.374246\pi$
$854$	2.99047e10	1.64300
$855$	−1.47378e10	−0.806399
$856$	−1.47640e10	−0.804539
$857$	−1.94808e10	−1.05724	−0.528620	−	0.848859i	$-0.677290\pi$
$857$	−1.94808e10	−1.05724	−0.528620	+	0.848859i	$0.677290\pi$
$858$	0	0
$859$	2.31458e10	1.24594	0.622970	−	0.782246i	$-0.285926\pi$
$859$	2.31458e10	1.24594	0.622970	+	0.782246i	$0.285926\pi$
$860$	−8.45036e10	−4.53034
$861$	−1.19143e9	−0.0636145
$862$	5.86792e10	3.12039
$863$	1.31699e10	0.697502	0.348751	−	0.937216i	$-0.386606\pi$
$863$	1.31699e10	0.697502	0.348751	+	0.937216i	$0.386606\pi$
$864$	8.66471e9	0.457042
$865$	−5.62981e10	−2.95759
$866$	−4.82261e10	−2.52330
$867$	8.58224e9	0.447233
$868$	1.20277e10	0.624259
$869$	0	0
$870$	−1.64433e10	−0.846586
$871$	−9.60155e8	−0.0492355
$872$	5.65611e9	0.288875
$873$	−7.90151e9	−0.401939
$874$	1.65396e10	0.837983
$875$	−2.73253e10	−1.37891
$876$	−2.31330e10	−1.16270
$877$	3.03967e10	1.52170	0.760848	−	0.648931i	$-0.224784\pi$
$877$	3.03967e10	1.52170	0.760848	+	0.648931i	$0.224784\pi$
$878$	1.86926e10	0.932049
$879$	−6.71708e9	−0.333595
$880$	0	0
$881$	3.43349e10	1.69169	0.845844	−	0.533431i	$-0.179098\pi$
$881$	3.43349e10	1.69169	0.845844	+	0.533431i	$0.179098\pi$
$882$	7.65735e9	0.375784
$883$	1.89740e10	0.927461	0.463730	−	0.885976i	$-0.346511\pi$
$883$	1.89740e10	0.927461	0.463730	+	0.885976i	$0.346511\pi$
$884$	−1.71175e10	−0.833410
$885$	1.27337e10	0.617522
$886$	3.43053e10	1.65708
$887$	1.65544e10	0.796491	0.398246	−	0.917279i	$-0.369619\pi$
$887$	1.65544e10	0.796491	0.398246	+	0.917279i	$0.369619\pi$
$888$	1.35147e10	0.647679
$889$	−1.25370e10	−0.598462
$890$	7.98779e10	3.79806
$891$	0	0
$892$	1.24344e10	0.586609
$893$	−1.69070e10	−0.794486
$894$	−1.56840e10	−0.734132
$895$	−3.90660e10	−1.82145
$896$	−2.83859e10	−1.31833
$897$	8.83895e9	0.408909
$898$	−8.41361e9	−0.387717
$899$	2.51387e9	0.115394
$900$	3.95653e10	1.80911
$901$	2.72790e10	1.24248
$902$	0	0
$903$	−2.99647e10	−1.35426
$904$	4.46741e10	2.01125
$905$	3.01140e10	1.35051
$906$	−8.00610e10	−3.57662
$907$	1.55152e10	0.690450	0.345225	−	0.938520i	$-0.387803\pi$
$907$	1.55152e10	0.690450	0.345225	+	0.938520i	$0.387803\pi$
$908$	−5.60444e10	−2.48446
$909$	−6.85527e7	−0.00302727
$910$	−2.93576e10	−1.29145
$911$	2.85074e10	1.24923	0.624617	−	0.780931i	$-0.285255\pi$
$911$	2.85074e10	1.24923	0.624617	+	0.780931i	$0.285255\pi$
$912$	7.29537e9	0.318468
$913$	0	0
$914$	1.97266e10	0.854558
$915$	−6.65954e10	−2.87389
$916$	9.06644e9	0.389765
$917$	2.43149e10	1.04131
$918$	−1.87927e10	−0.801751
$919$	4.03491e10	1.71487	0.857433	−	0.514596i	$-0.172058\pi$
$919$	4.03491e10	1.71487	0.857433	+	0.514596i	$0.172058\pi$
$920$	−2.80100e10	−1.18592
$921$	2.42410e10	1.02245
$922$	5.82946e10	2.44946
$923$	1.30307e10	0.545459
$924$	0	0
$925$	2.14469e10	0.890981
$926$	5.22318e10	2.16170
$927$	−5.70145e9	−0.235075
$928$	−4.36301e9	−0.179212
$929$	−1.38631e10	−0.567292	−0.283646	−	0.958929i	$-0.591544\pi$
$929$	−1.38631e10	−0.567292	−0.283646	+	0.958929i	$0.591544\pi$
$930$	−4.21903e10	−1.71998
$931$	1.01231e10	0.411138
$932$	8.14716e10	3.29648
$933$	−3.41669e10	−1.37727
$934$	−4.39574e10	−1.76530
$935$	0	0
$936$	9.30351e9	0.370835
$937$	1.24992e10	0.496355	0.248178	−	0.968715i	$-0.420168\pi$
$937$	1.24992e10	0.496355	0.248178	+	0.968715i	$0.420168\pi$
$938$	2.53958e9	0.100474
$939$	2.44135e10	0.962276
$940$	6.73949e10	2.64655
$941$	−4.52891e10	−1.77186	−0.885932	−	0.463815i	$-0.846480\pi$
$941$	−4.52891e10	−1.77186	−0.885932	+	0.463815i	$0.846480\pi$
$942$	−6.75834e10	−2.63428
$943$	−9.98442e8	−0.0387732
$944$	−2.11363e9	−0.0817761
$945$	−2.04618e10	−0.788737
$946$	0	0
$947$	−1.72309e10	−0.659299	−0.329649	−	0.944103i	$-0.606931\pi$
$947$	−1.72309e10	−0.659299	−0.329649	+	0.944103i	$0.606931\pi$
$948$	−1.95978e10	−0.747097
$949$	−8.63224e9	−0.327862
$950$	8.23897e10	3.11774
$951$	−1.26632e10	−0.477433
$952$	1.92349e10	0.722536
$953$	−4.08556e9	−0.152907	−0.0764533	−	0.997073i	$-0.524360\pi$
$953$	−4.08556e9	−0.152907	−0.0764533	+	0.997073i	$0.524360\pi$
$954$	−3.48985e10	−1.30133
$955$	−5.33947e10	−1.98375
$956$	1.95019e10	0.721896
$957$	0	0
$958$	−3.32301e10	−1.22110
$959$	−1.44074e10	−0.527498
$960$	8.99505e10	3.28136
$961$	−2.10625e10	−0.765558
$962$	1.18705e10	0.429889
$963$	9.20186e9	0.332035
$964$	4.48064e10	1.61091
$965$	2.84225e10	1.01816
$966$	−2.33787e10	−0.834452
$967$	5.15510e10	1.83334	0.916672	−	0.399640i	$-0.130865\pi$
$967$	5.15510e10	1.83334	0.916672	+	0.399640i	$0.130865\pi$
$968$	0	0
$969$	2.52933e10	0.893043
$970$	6.55886e10	2.30742
$971$	9.63165e8	0.0337624	0.0168812	−	0.999858i	$-0.494626\pi$
$971$	9.63165e8	0.0337624	0.0168812	+	0.999858i	$0.494626\pi$
$972$	4.60653e10	1.60895
$973$	−1.01281e10	−0.352479
$974$	1.78565e10	0.619213
$975$	4.40299e10	1.52136
$976$	1.10540e10	0.380578
$977$	−1.13374e8	−0.00388939	−0.00194469	−	0.999998i	$-0.500619\pi$
$977$	−1.13374e8	−0.00388939	−0.00194469	+	0.999998i	$0.500619\pi$
$978$	−8.00320e10	−2.73576
$979$	0	0
$980$	−4.03527e10	−1.36956
$981$	−3.52524e9	−0.119219
$982$	−2.37848e10	−0.801510
$983$	3.10590e10	1.04292	0.521460	−	0.853276i	$-0.325388\pi$
$983$	3.10590e10	1.04292	0.521460	+	0.853276i	$0.325388\pi$
$984$	−3.13409e9	−0.104864
$985$	9.41966e10	3.14057
$986$	9.46283e9	0.314378
$987$	2.38980e10	0.791138
$988$	2.89503e10	0.955002
$989$	−2.51111e10	−0.825429
$990$	0	0
$991$	−1.47570e10	−0.481659	−0.240830	−	0.970567i	$-0.577420\pi$
$991$	−1.47570e10	−0.481659	−0.240830	+	0.970567i	$0.577420\pi$
$992$	−1.11946e10	−0.364099
$993$	1.13603e10	0.368187
$994$	−3.44658e10	−1.11311
$995$	3.27027e10	1.05245
$996$	1.85019e10	0.593347
$997$	−3.99639e9	−0.127713	−0.0638565	−	0.997959i	$-0.520340\pi$
$997$	−3.99639e9	−0.127713	−0.0638565	+	0.997959i	$0.520340\pi$
$998$	−4.82350e9	−0.153605
$999$	8.27356e9	0.262551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.g.1.1		12
11.7	odd	10		11.8.c.a.5.6	✓	24
11.8	odd	10		11.8.c.a.9.6	yes	24
11.10	odd	2		121.8.a.i.1.12		12
33.8	even	10		99.8.f.a.64.1		24
33.29	even	10		99.8.f.a.82.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.c.a.5.6	✓	24	11.7	odd	10
11.8.c.a.9.6	yes	24	11.8	odd	10
99.8.f.a.64.1		24	33.8	even	10
99.8.f.a.82.1		24	33.29	even	10
121.8.a.g.1.1		12	1.1	even	1	trivial
121.8.a.i.1.12		12	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q-18.7229 q^{2} -57.3611 q^{3} +222.547 q^{4} +489.146 q^{5} +1073.97 q^{6} -672.943 q^{7} -1770.20 q^{8} +1103.30 q^{9} -9158.23 q^{10} -12765.6 q^{12} -4763.55 q^{13} +12599.4 q^{14} -28057.9 q^{15} +4657.25 q^{16} +16146.9 q^{17} -20657.0 q^{18} -27308.6 q^{19} +108858. q^{20} +38600.8 q^{21} +32348.3 q^{23} +101541. q^{24} +161139. q^{25} +89187.6 q^{26} +62162.3 q^{27} -149762. q^{28} -31301.1 q^{29} +525326. q^{30} -80312.6 q^{31} +139388. q^{32} -302316. q^{34} -329167. q^{35} +245536. q^{36} +133096. q^{37} +511297. q^{38} +273243. q^{39} -865886. q^{40} -30865.3 q^{41} -722719. q^{42} -776273. q^{43} +539674. q^{45} -605655. q^{46} +619108. q^{47} -267145. q^{48} -370691. q^{49} -3.01698e6 q^{50} -926202. q^{51} -1.06012e6 q^{52} +1.68943e6 q^{53} -1.16386e6 q^{54} +1.19124e6 q^{56} +1.56645e6 q^{57} +586047. q^{58} -453835. q^{59} -6.24422e6 q^{60} +2.37350e6 q^{61} +1.50368e6 q^{62} -742457. q^{63} -3.20588e6 q^{64} -2.33007e6 q^{65} +201563. q^{67} +3.59344e6 q^{68} -1.85554e6 q^{69} +6.16297e6 q^{70} -2.73550e6 q^{71} -1.95306e6 q^{72} +1.81214e6 q^{73} -2.49194e6 q^{74} -9.24309e6 q^{75} -6.07746e6 q^{76} -5.11590e6 q^{78} +1.53520e6 q^{79} +2.27808e6 q^{80} -5.97862e6 q^{81} +577889. q^{82} -1.44936e6 q^{83} +8.59050e6 q^{84} +7.89817e6 q^{85} +1.45341e7 q^{86} +1.79547e6 q^{87} -8.72198e6 q^{89} -1.01043e7 q^{90} +3.20560e6 q^{91} +7.19904e6 q^{92} +4.60682e6 q^{93} -1.15915e7 q^{94} -1.33579e7 q^{95} -7.99547e6 q^{96} -7.16171e6 q^{97} +6.94041e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 12 q^{3} + 550 q^{4} + 144 q^{5} - 649 q^{6} - 2244 q^{7} - 3810 q^{8} + 9094 q^{9} - 2120 q^{10} + 5819 q^{12} - 8688 q^{13} + 23988 q^{14} - 29008 q^{15} - 32238 q^{16} - 26214 q^{17}+ \cdots + 25767018 q^{98}+O(q^{100}) \) 12 * q - 24 * q^2 - 12 * q^3 + 550 * q^4 + 144 * q^5 - 649 * q^6 - 2244 * q^7 - 3810 * q^8 + 9094 * q^9 - 2120 * q^10 + 5819 * q^12 - 8688 * q^13 + 23988 * q^14 - 29008 * q^15 - 32238 * q^16 - 26214 * q^17 - 76543 * q^18 - 52308 * q^19 - 16374 * q^20 - 69152 * q^21 - 13152 * q^23 - 73443 * q^24 + 155752 * q^25 + 167268 * q^26 + 302400 * q^27 - 382952 * q^28 - 159276 * q^29 - 7788 * q^30 - 432468 * q^31 + 130446 * q^32 + 756081 * q^34 - 258456 * q^35 + 1376129 * q^36 - 189896 * q^37 + 272025 * q^38 - 2263776 * q^39 - 1249506 * q^40 - 1767102 * q^41 - 3537912 * q^42 - 1438728 * q^43 + 1558636 * q^45 - 2758162 * q^46 + 1951644 * q^47 - 508717 * q^48 - 620888 * q^49 - 8781084 * q^50 - 5437672 * q^51 - 7729734 * q^52 - 5997012 * q^53 - 8805010 * q^54 + 5715540 * q^56 - 3344580 * q^57 + 8127100 * q^58 - 1100004 * q^59 - 4320206 * q^60 - 8453788 * q^61 - 6663978 * q^62 - 11044228 * q^63 - 16086302 * q^64 - 5558820 * q^65 + 8341264 * q^67 - 5706597 * q^68 + 3505424 * q^69 - 2370222 * q^70 - 1323204 * q^71 - 27395985 * q^72 - 28258 * q^73 - 19524798 * q^74 - 24181280 * q^75 - 9045603 * q^76 + 7766546 * q^78 - 9616244 * q^79 + 11429082 * q^80 + 1578028 * q^81 + 2776323 * q^82 - 18527868 * q^83 - 95370 * q^84 - 391164 * q^85 - 12467391 * q^86 - 18304620 * q^87 - 1238658 * q^89 + 13787116 * q^90 - 136352 * q^91 + 4026894 * q^92 + 3799596 * q^93 + 11859084 * q^94 - 26322264 * q^95 + 16012845 * q^96 + 3970134 * q^97 + 25767018 * q^98

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