LMFDB - Embedded newform 121.8.a.g.1.10

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			1.10
Root			$15.8590$ 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)

$f(q)$	$=$	\(q+12.2409 q^{2} -80.7053 q^{3} +21.8407 q^{4} +102.520 q^{5} -987.908 q^{6} +743.309 q^{7} -1299.49 q^{8} +4326.34 q^{9} +1254.94 q^{10} -1762.66 q^{12} +7217.04 q^{13} +9098.81 q^{14} -8273.88 q^{15} -18702.6 q^{16} +26971.2 q^{17} +52958.5 q^{18} -25741.5 q^{19} +2239.10 q^{20} -59989.0 q^{21} -103362. q^{23} +104876. q^{24} -67614.7 q^{25} +88343.4 q^{26} -172656. q^{27} +16234.4 q^{28} +106751. q^{29} -101280. q^{30} -51007.6 q^{31} -62602.6 q^{32} +330153. q^{34} +76203.8 q^{35} +94490.1 q^{36} -279405. q^{37} -315101. q^{38} -582453. q^{39} -133223. q^{40} -107006. q^{41} -734321. q^{42} -399488. q^{43} +443535. q^{45} -1.26525e6 q^{46} -35651.5 q^{47} +1.50940e6 q^{48} -271034. q^{49} -827668. q^{50} -2.17672e6 q^{51} +157625. q^{52} -1.01095e6 q^{53} -2.11347e6 q^{54} -965923. q^{56} +2.07748e6 q^{57} +1.30674e6 q^{58} -1.78457e6 q^{59} -180707. q^{60} +206316. q^{61} -624381. q^{62} +3.21581e6 q^{63} +1.62762e6 q^{64} +739889. q^{65} +1.61162e6 q^{67} +589069. q^{68} +8.34187e6 q^{69} +932807. q^{70} -2.15734e6 q^{71} -5.62203e6 q^{72} +1.60961e6 q^{73} -3.42018e6 q^{74} +5.45686e6 q^{75} -562212. q^{76} -7.12978e6 q^{78} -1.01586e6 q^{79} -1.91738e6 q^{80} +4.47253e6 q^{81} -1.30985e6 q^{82} +4.68474e6 q^{83} -1.31020e6 q^{84} +2.76508e6 q^{85} -4.89011e6 q^{86} -8.61538e6 q^{87} +5.83358e6 q^{89} +5.42928e6 q^{90} +5.36449e6 q^{91} -2.25750e6 q^{92} +4.11658e6 q^{93} -436408. q^{94} -2.63902e6 q^{95} +5.05236e6 q^{96} -1.48600e7 q^{97} -3.31771e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	12.2409	1.08196	0.540978	−	0.841037i	$-0.318054\pi$
$2$	12.2409	1.08196	0.540978	+	0.841037i	$0.318054\pi$
$3$	−80.7053	−1.72575	−0.862874	−	0.505419i	$-0.831338\pi$
$3$	−80.7053	−1.72575	−0.862874	+	0.505419i	$0.831338\pi$
$4$	21.8407	0.170630
$5$	102.520	0.366786	0.183393	−	0.983040i	$-0.441292\pi$
$5$	102.520	0.366786	0.183393	+	0.983040i	$0.441292\pi$
$6$	−987.908	−1.86718
$7$	743.309	0.819080	0.409540	−	0.912292i	$-0.365689\pi$
$7$	743.309	0.819080	0.409540	+	0.912292i	$0.365689\pi$
$8$	−1299.49	−0.897342
$9$	4326.34	1.97821
$10$	1254.94	0.396846
$11$	0	0
$11$	0	0
$12$	−1762.66	−0.294465
$13$	7217.04	0.911082	0.455541	−	0.890215i	$-0.349446\pi$
$13$	7217.04	0.911082	0.455541	+	0.890215i	$0.349446\pi$
$14$	9098.81	0.886209
$15$	−8273.88	−0.632979
$16$	−18702.6	−1.14152
$17$	26971.2	1.33146	0.665731	−	0.746192i	$-0.268120\pi$
$17$	26971.2	1.33146	0.665731	+	0.746192i	$0.268120\pi$
$18$	52958.5	2.14033
$19$	−25741.5	−0.860988	−0.430494	−	0.902593i	$-0.641661\pi$
$19$	−25741.5	−0.860988	−0.430494	+	0.902593i	$0.641661\pi$
$20$	2239.10	0.0625847
$21$	−59989.0	−1.41353
$22$	0	0
$23$	−103362.	−1.77139	−0.885695	−	0.464267i	$-0.846318\pi$
$23$	−103362.	−1.77139	−0.885695	+	0.464267i	$0.846318\pi$
$24$	104876.	1.54859
$25$	−67614.7	−0.865468
$26$	88343.4	0.985751
$27$	−172656.	−1.68814
$28$	16234.4	0.139760
$29$	106751.	0.812793	0.406396	−	0.913697i	$-0.366785\pi$
$29$	106751.	0.812793	0.406396	+	0.913697i	$0.366785\pi$
$30$	−101280.	−0.684856
$31$	−51007.6	−0.307517	−0.153758	−	0.988108i	$-0.549138\pi$
$31$	−51007.6	−0.307517	−0.153758	+	0.988108i	$0.549138\pi$
$32$	−62602.6	−0.337728
$33$	0	0
$34$	330153.	1.44058
$35$	76203.8	0.300427
$36$	94490.1	0.337542
$37$	−279405.	−0.906834	−0.453417	−	0.891299i	$-0.649795\pi$
$37$	−279405.	−0.906834	−0.453417	+	0.891299i	$0.649795\pi$
$38$	−315101.	−0.931552
$39$	−582453.	−1.57230
$40$	−133223.	−0.329132
$41$	−107006.	−0.242474	−0.121237	−	0.992624i	$-0.538686\pi$
$41$	−107006.	−0.242474	−0.121237	+	0.992624i	$0.538686\pi$
$42$	−734321.	−1.52937
$43$	−399488.	−0.766239	−0.383120	−	0.923699i	$-0.625150\pi$
$43$	−399488.	−0.766239	−0.383120	+	0.923699i	$0.625150\pi$
$44$	0	0
$45$	443535.	0.725578
$46$	−1.26525e6	−1.91657
$47$	−35651.5	−0.0500882	−0.0250441	−	0.999686i	$-0.507973\pi$
$47$	−35651.5	−0.0500882	−0.0250441	+	0.999686i	$0.507973\pi$
$48$	1.50940e6	1.96997
$49$	−271034.	−0.329108
$50$	−827668.	−0.936399
$51$	−2.17672e6	−2.29777
$52$	157625.	0.155458
$53$	−1.01095e6	−0.932748	−0.466374	−	0.884588i	$-0.654440\pi$
$53$	−1.01095e6	−0.932748	−0.466374	+	0.884588i	$0.654440\pi$
$54$	−2.11347e6	−1.82649
$55$	0	0
$56$	−965923.	−0.734995
$57$	2.07748e6	1.48585
$58$	1.30674e6	0.879406
$59$	−1.78457e6	−1.13123	−0.565615	−	0.824669i	$-0.691361\pi$
$59$	−1.78457e6	−1.13123	−0.565615	+	0.824669i	$0.691361\pi$
$60$	−180707.	−0.108005
$61$	206316.	0.116380	0.0581901	−	0.998306i	$-0.481467\pi$
$61$	206316.	0.116380	0.0581901	+	0.998306i	$0.481467\pi$
$62$	−624381.	−0.332720
$63$	3.21581e6	1.62031
$64$	1.62762e6	0.776108
$65$	739889.	0.334172
$66$	0	0
$67$	1.61162e6	0.654637	0.327319	−	0.944914i	$-0.393855\pi$
$67$	1.61162e6	0.654637	0.327319	+	0.944914i	$0.393855\pi$
$68$	589069.	0.227188
$69$	8.34187e6	3.05697
$70$	932807.	0.325049
$71$	−2.15734e6	−0.715344	−0.357672	−	0.933847i	$-0.616429\pi$
$71$	−2.15734e6	−0.715344	−0.357672	+	0.933847i	$0.616429\pi$
$72$	−5.62203e6	−1.77513
$73$	1.60961e6	0.484274	0.242137	−	0.970242i	$-0.422152\pi$
$73$	1.60961e6	0.484274	0.242137	+	0.970242i	$0.422152\pi$
$74$	−3.42018e6	−0.981155
$75$	5.45686e6	1.49358
$76$	−562212.	−0.146911
$77$	0	0
$78$	−7.12978e6	−1.70116
$79$	−1.01586e6	−0.231813	−0.115906	−	0.993260i	$-0.536977\pi$
$79$	−1.01586e6	−0.231813	−0.115906	+	0.993260i	$0.536977\pi$
$80$	−1.91738e6	−0.418691
$81$	4.47253e6	0.935095
$82$	−1.30985e6	−0.262346
$83$	4.68474e6	0.899317	0.449658	−	0.893201i	$-0.351546\pi$
$83$	4.68474e6	0.899317	0.449658	+	0.893201i	$0.351546\pi$
$84$	−1.31020e6	−0.241190
$85$	2.76508e6	0.488361
$86$	−4.89011e6	−0.829038
$87$	−8.61538e6	−1.40268
$88$	0	0
$89$	5.83358e6	0.877142	0.438571	−	0.898697i	$-0.355485\pi$
$89$	5.83358e6	0.877142	0.438571	+	0.898697i	$0.355485\pi$
$90$	5.42928e6	0.785044
$91$	5.36449e6	0.746249
$92$	−2.25750e6	−0.302253
$93$	4.11658e6	0.530697
$94$	−436408.	−0.0541933
$95$	−2.63902e6	−0.315798
$96$	5.05236e6	0.582834
$97$	−1.48600e7	−1.65317	−0.826587	−	0.562809i	$-0.809721\pi$
$97$	−1.48600e7	−1.65317	−0.826587	+	0.562809i	$0.809721\pi$
$98$	−3.31771e6	−0.356080
$99$	0	0
$100$	−1.47675e6	−0.147675
$101$	−7.68858e6	−0.742542	−0.371271	−	0.928524i	$-0.621078\pi$
$101$	−7.68858e6	−0.742542	−0.371271	+	0.928524i	$0.621078\pi$
$102$	−2.66451e7	−2.48609
$103$	−1.21522e7	−1.09578	−0.547892	−	0.836549i	$-0.684569\pi$
$103$	−1.21522e7	−1.09578	−0.547892	+	0.836549i	$0.684569\pi$
$104$	−9.37848e6	−0.817552
$105$	−6.15005e6	−0.518461
$106$	−1.23750e7	−1.00919
$107$	−1.60633e7	−1.26763	−0.633814	−	0.773486i	$-0.718512\pi$
$107$	−1.60633e7	−1.26763	−0.633814	+	0.773486i	$0.718512\pi$
$108$	−3.77092e6	−0.288047
$109$	2.07604e7	1.53547	0.767737	−	0.640765i	$-0.221383\pi$
$109$	2.07604e7	1.53547	0.767737	+	0.640765i	$0.221383\pi$
$110$	0	0
$111$	2.25494e7	1.56497
$112$	−1.39018e7	−0.934993
$113$	−6.15574e6	−0.401334	−0.200667	−	0.979660i	$-0.564311\pi$
$113$	−6.15574e6	−0.401334	−0.200667	+	0.979660i	$0.564311\pi$
$114$	2.54303e7	1.60762
$115$	−1.05967e7	−0.649721
$116$	2.33152e6	0.138687
$117$	3.12234e7	1.80231
$118$	−2.18448e7	−1.22394
$119$	2.00479e7	1.09057
$120$	1.07518e7	0.567999
$121$	0	0
$122$	2.52551e6	0.125918
$123$	8.63594e6	0.418448
$124$	−1.11404e6	−0.0524716
$125$	−1.49412e7	−0.684227
$126$	3.93645e7	1.75311
$127$	−2.46971e6	−0.106987	−0.0534937	−	0.998568i	$-0.517036\pi$
$127$	−2.46971e6	−0.106987	−0.0534937	+	0.998568i	$0.517036\pi$
$128$	2.79367e7	1.17744
$129$	3.22408e7	1.32234
$130$	9.05694e6	0.361559
$131$	6.36488e6	0.247367	0.123683	−	0.992322i	$-0.460529\pi$
$131$	6.36488e6	0.247367	0.123683	+	0.992322i	$0.460529\pi$
$132$	0	0
$133$	−1.91339e7	−0.705218
$134$	1.97277e7	0.708289
$135$	−1.77006e7	−0.619185
$136$	−3.50488e7	−1.19478
$137$	1.07987e7	0.358797	0.179398	−	0.983776i	$-0.442585\pi$
$137$	1.07987e7	0.358797	0.179398	+	0.983776i	$0.442585\pi$
$138$	1.02112e8	3.30751
$139$	−2.08171e7	−0.657460	−0.328730	−	0.944424i	$-0.606621\pi$
$139$	−2.08171e7	−0.657460	−0.328730	+	0.944424i	$0.606621\pi$
$140$	1.66434e6	0.0512619
$141$	2.87727e6	0.0864397
$142$	−2.64079e7	−0.773971
$143$	0	0
$144$	−8.09137e7	−2.25815
$145$	1.09441e7	0.298121
$146$	1.97032e7	0.523964
$147$	2.18739e7	0.567957
$148$	−6.10239e6	−0.154733
$149$	−8.05587e6	−0.199508	−0.0997541	−	0.995012i	$-0.531806\pi$
$149$	−8.05587e6	−0.199508	−0.0997541	+	0.995012i	$0.531806\pi$
$150$	6.67971e7	1.61599
$151$	−1.84499e7	−0.436089	−0.218044	−	0.975939i	$-0.569968\pi$
$151$	−1.84499e7	−0.436089	−0.218044	+	0.975939i	$0.569968\pi$
$152$	3.34509e7	0.772601
$153$	1.16686e8	2.63391
$154$	0	0
$155$	−5.22928e6	−0.112793
$156$	−1.27212e7	−0.268281
$157$	−4.33040e7	−0.893057	−0.446528	−	0.894770i	$-0.647340\pi$
$157$	−4.33040e7	−0.893057	−0.446528	+	0.894770i	$0.647340\pi$
$158$	−1.24350e7	−0.250811
$159$	8.15890e7	1.60969
$160$	−6.41799e6	−0.123874
$161$	−7.68301e7	−1.45091
$162$	5.47480e7	1.01173
$163$	9.90156e7	1.79080	0.895400	−	0.445263i	$-0.146890\pi$
$163$	9.90156e7	1.79080	0.895400	+	0.445263i	$0.146890\pi$
$164$	−2.33708e6	−0.0413733
$165$	0	0
$166$	5.73457e7	0.973021
$167$	−7.12229e7	−1.18335	−0.591673	−	0.806178i	$-0.701532\pi$
$167$	−7.12229e7	−1.18335	−0.591673	+	0.806178i	$0.701532\pi$
$168$	7.79551e7	1.26842
$169$	−1.06628e7	−0.169930
$170$	3.38472e7	0.528386
$171$	−1.11367e8	−1.70321
$172$	−8.72509e6	−0.130744
$173$	−5.57603e7	−0.818774	−0.409387	−	0.912361i	$-0.634257\pi$
$173$	−5.57603e7	−0.818774	−0.409387	+	0.912361i	$0.634257\pi$
$174$	−1.05460e8	−1.51763
$175$	−5.02586e7	−0.708888
$176$	0	0
$177$	1.44024e8	1.95222
$178$	7.14085e7	0.949029
$179$	3.81416e7	0.497065	0.248533	−	0.968624i	$-0.420052\pi$
$179$	3.81416e7	0.497065	0.248533	+	0.968624i	$0.420052\pi$
$180$	9.68709e6	0.123805
$181$	−4.79963e7	−0.601634	−0.300817	−	0.953682i	$-0.597259\pi$
$181$	−4.79963e7	−0.601634	−0.300817	+	0.953682i	$0.597259\pi$
$182$	6.56665e7	0.807409
$183$	−1.66508e7	−0.200843
$184$	1.34318e8	1.58954
$185$	−2.86445e7	−0.332614
$186$	5.03908e7	0.574191
$187$	0	0
$188$	−778653.	−0.00854656
$189$	−1.28337e8	−1.38272
$190$	−3.23040e7	−0.341680
$191$	7.09173e7	0.736437	0.368218	−	0.929739i	$-0.379968\pi$
$191$	7.09173e7	0.736437	0.368218	+	0.929739i	$0.379968\pi$
$192$	−1.31357e8	−1.33937
$193$	−7.75279e7	−0.776260	−0.388130	−	0.921605i	$-0.626879\pi$
$193$	−7.75279e7	−0.776260	−0.388130	+	0.921605i	$0.626879\pi$
$194$	−1.81901e8	−1.78866
$195$	−5.97129e7	−0.576696
$196$	−5.91957e6	−0.0561557
$197$	−1.52795e8	−1.42389	−0.711947	−	0.702233i	$-0.752186\pi$
$197$	−1.52795e8	−1.42389	−0.711947	+	0.702233i	$0.752186\pi$
$198$	0	0
$199$	−1.32401e8	−1.19098	−0.595491	−	0.803362i	$-0.703043\pi$
$199$	−1.32401e8	−1.19098	−0.595491	+	0.803362i	$0.703043\pi$
$200$	8.78647e7	0.776621
$201$	−1.30066e8	−1.12974
$202$	−9.41154e7	−0.803399
$203$	7.93492e7	0.665742
$204$	−4.75409e7	−0.392069
$205$	−1.09702e7	−0.0889358
$206$	−1.48754e8	−1.18559
$207$	−4.47180e8	−3.50418
$208$	−1.34977e8	−1.04001
$209$	0	0
$210$	−7.52824e7	−0.560952
$211$	−1.15418e8	−0.845835	−0.422918	−	0.906168i	$-0.638994\pi$
$211$	−1.15418e8	−0.845835	−0.422918	+	0.906168i	$0.638994\pi$
$212$	−2.20798e7	−0.159155
$213$	1.74109e8	1.23450
$214$	−1.96630e8	−1.37152
$215$	−4.09554e7	−0.281045
$216$	2.24365e8	1.51484
$217$	−3.79144e7	−0.251881
$218$	2.54127e8	1.66132
$219$	−1.29904e8	−0.835735
$220$	0	0
$221$	1.94652e8	1.21307
$222$	2.76026e8	1.69323
$223$	1.74686e8	1.05485	0.527425	−	0.849601i	$-0.323157\pi$
$223$	1.74686e8	1.05485	0.527425	+	0.849601i	$0.323157\pi$
$224$	−4.65331e7	−0.276626
$225$	−2.92524e8	−1.71208
$226$	−7.53521e7	−0.434226
$227$	1.24752e8	0.707874	0.353937	−	0.935269i	$-0.384843\pi$
$227$	1.24752e8	0.707874	0.353937	+	0.935269i	$0.384843\pi$
$228$	4.53735e7	0.253531
$229$	1.70263e8	0.936905	0.468452	−	0.883489i	$-0.344812\pi$
$229$	1.70263e8	0.936905	0.468452	+	0.883489i	$0.344812\pi$
$230$	−1.29713e8	−0.702969
$231$	0	0
$232$	−1.38722e8	−0.729353
$233$	2.52540e8	1.30793	0.653966	−	0.756524i	$-0.273104\pi$
$233$	2.52540e8	1.30793	0.653966	+	0.756524i	$0.273104\pi$
$234$	3.82203e8	1.95002
$235$	−3.65498e6	−0.0183716
$236$	−3.89762e7	−0.193022
$237$	8.19849e7	0.400050
$238$	2.45406e8	1.17995
$239$	4.54773e7	0.215477	0.107739	−	0.994179i	$-0.465639\pi$
$239$	4.54773e7	0.215477	0.107739	+	0.994179i	$0.465639\pi$
$240$	1.54743e8	0.722556
$241$	1.50043e8	0.690489	0.345244	−	0.938513i	$-0.387796\pi$
$241$	1.50043e8	0.690489	0.345244	+	0.938513i	$0.387796\pi$
$242$	0	0
$243$	1.66415e7	0.0743997
$244$	4.50608e6	0.0198580
$245$	−2.77863e7	−0.120712
$246$	1.05712e8	0.452743
$247$	−1.85778e8	−0.784431
$248$	6.62839e7	0.275948
$249$	−3.78083e8	−1.55199
$250$	−1.82894e8	−0.740304
$251$	−1.00589e8	−0.401505	−0.200753	−	0.979642i	$-0.564339\pi$
$251$	−1.00589e8	−0.401505	−0.200753	+	0.979642i	$0.564339\pi$
$252$	7.02354e7	0.276474
$253$	0	0
$254$	−3.02315e7	−0.115756
$255$	−2.23156e8	−0.842788
$256$	1.33636e8	0.497835
$257$	−1.20341e8	−0.442228	−0.221114	−	0.975248i	$-0.570969\pi$
$257$	−1.20341e8	−0.442228	−0.221114	+	0.975248i	$0.570969\pi$
$258$	3.94658e8	1.43071
$259$	−2.07684e8	−0.742770
$260$	1.61597e7	0.0570198
$261$	4.61842e8	1.60787
$262$	7.79122e7	0.267640
$263$	−1.77779e8	−0.602610	−0.301305	−	0.953528i	$-0.597422\pi$
$263$	−1.77779e8	−0.602610	−0.301305	+	0.953528i	$0.597422\pi$
$264$	0	0
$265$	−1.03642e8	−0.342119
$266$	−2.34217e8	−0.763015
$267$	−4.70800e8	−1.51373
$268$	3.51988e7	0.111701
$269$	3.08396e8	0.965998	0.482999	−	0.875621i	$-0.339548\pi$
$269$	3.08396e8	0.965998	0.482999	+	0.875621i	$0.339548\pi$
$270$	−2.16672e8	−0.669931
$271$	−5.79835e8	−1.76975	−0.884876	−	0.465827i	$-0.845757\pi$
$271$	−5.79835e8	−1.76975	−0.884876	+	0.465827i	$0.845757\pi$
$272$	−5.04431e8	−1.51988
$273$	−4.32943e8	−1.28784
$274$	1.32186e8	0.388203
$275$	0	0
$276$	1.82192e8	0.521612
$277$	8.86220e7	0.250532	0.125266	−	0.992123i	$-0.460022\pi$
$277$	8.86220e7	0.250532	0.125266	+	0.992123i	$0.460022\pi$
$278$	−2.54821e8	−0.711343
$279$	−2.20676e8	−0.608332
$280$	−9.90261e7	−0.269586
$281$	3.92522e8	1.05534	0.527670	−	0.849450i	$-0.323066\pi$
$281$	3.92522e8	1.05534	0.527670	+	0.849450i	$0.323066\pi$
$282$	3.52204e7	0.0935240
$283$	6.55946e8	1.72035	0.860173	−	0.510003i	$-0.170356\pi$
$283$	6.55946e8	1.72035	0.860173	+	0.510003i	$0.170356\pi$
$284$	−4.71178e7	−0.122059
$285$	2.12982e8	0.544988
$286$	0	0
$287$	−7.95385e7	−0.198605
$288$	−2.70840e8	−0.668096
$289$	3.17106e8	0.772792
$290$	1.33966e8	0.322554
$291$	1.19928e9	2.85296
$292$	3.51550e7	0.0826318
$293$	−5.45457e8	−1.26685	−0.633423	−	0.773806i	$-0.718351\pi$
$293$	−5.45457e8	−1.26685	−0.633423	+	0.773806i	$0.718351\pi$
$294$	2.67757e8	0.614505
$295$	−1.82953e8	−0.414919
$296$	3.63084e8	0.813740
$297$	0	0
$298$	−9.86115e7	−0.215859
$299$	−7.45969e8	−1.61388
$300$	1.19181e8	0.254850
$301$	−2.96943e8	−0.627611
$302$	−2.25844e8	−0.471829
$303$	6.20509e8	1.28144
$304$	4.81434e8	0.982831
$305$	2.11515e7	0.0426866
$306$	1.42835e9	2.84977
$307$	1.57160e8	0.309998	0.154999	−	0.987915i	$-0.450463\pi$
$307$	1.57160e8	0.309998	0.154999	+	0.987915i	$0.450463\pi$
$308$	0	0
$309$	9.80747e8	1.89105
$310$	−6.40113e7	−0.122037
$311$	1.71765e8	0.323797	0.161898	−	0.986807i	$-0.448238\pi$
$311$	1.71765e8	0.323797	0.161898	+	0.986807i	$0.448238\pi$
$312$	7.56892e8	1.41089
$313$	−1.93878e8	−0.357374	−0.178687	−	0.983906i	$-0.557185\pi$
$313$	−1.93878e8	−0.357374	−0.178687	+	0.983906i	$0.557185\pi$
$314$	−5.30081e8	−0.966249
$315$	3.29684e8	0.594306
$316$	−2.21870e7	−0.0395542
$317$	−4.95671e8	−0.873949	−0.436974	−	0.899474i	$-0.643950\pi$
$317$	−4.95671e8	−0.873949	−0.436974	+	0.899474i	$0.643950\pi$
$318$	9.98727e8	1.74161
$319$	0	0
$320$	1.66863e8	0.284665
$321$	1.29639e9	2.18761
$322$	−9.40473e8	−1.56982
$323$	−6.94280e8	−1.14637
$324$	9.76830e7	0.159555
$325$	−4.87978e8	−0.788513
$326$	1.21204e9	1.93757
$327$	−1.67547e9	−2.64984
$328$	1.39053e8	0.217582
$329$	−2.65001e7	−0.0410263
$330$	0	0
$331$	−1.01012e9	−1.53099	−0.765496	−	0.643440i	$-0.777507\pi$
$331$	−1.01012e9	−1.53099	−0.765496	+	0.643440i	$0.777507\pi$
$332$	1.02318e8	0.153451
$333$	−1.20880e9	−1.79391
$334$	−8.71835e8	−1.28033
$335$	1.65223e8	0.240111
$336$	1.12195e9	1.61356
$337$	9.04242e8	1.28700	0.643502	−	0.765444i	$-0.277481\pi$
$337$	9.04242e8	1.28700	0.643502	+	0.765444i	$0.277481\pi$
$338$	−1.30523e8	−0.183856
$339$	4.96801e8	0.692601
$340$	6.03911e7	0.0833291
$341$	0	0
$342$	−1.36323e9	−1.84280
$343$	−8.13609e8	−1.08865
$344$	5.19131e8	0.687579
$345$	8.55206e8	1.12125
$346$	−6.82559e8	−0.885878
$347$	1.52752e9	1.96261	0.981304	−	0.192465i	$-0.0616482\pi$
$347$	1.52752e9	1.96261	0.981304	+	0.192465i	$0.0616482\pi$
$348$	−1.88166e8	−0.239339
$349$	1.22963e9	1.54840	0.774202	−	0.632939i	$-0.218152\pi$
$349$	1.22963e9	1.54840	0.774202	+	0.632939i	$0.218152\pi$
$350$	−6.15213e8	−0.766986
$351$	−1.24606e9	−1.53803
$352$	0	0
$353$	4.99236e7	0.0604080	0.0302040	−	0.999544i	$-0.490384\pi$
$353$	4.99236e7	0.0604080	0.0302040	+	0.999544i	$0.490384\pi$
$354$	1.76299e9	2.11222
$355$	−2.21170e8	−0.262378
$356$	1.27409e8	0.149667
$357$	−1.61797e9	−1.88206
$358$	4.66889e8	0.537803
$359$	8.36618e7	0.0954325	0.0477163	−	0.998861i	$-0.484806\pi$
$359$	8.36618e7	0.0954325	0.0477163	+	0.998861i	$0.484806\pi$
$360$	−5.76369e8	−0.651091
$361$	−2.31244e8	−0.258700
$362$	−5.87520e8	−0.650942
$363$	0	0
$364$	1.17164e8	0.127333
$365$	1.65017e8	0.177625
$366$	−2.03822e8	−0.217303
$367$	3.20115e7	0.0338045	0.0169022	−	0.999857i	$-0.494620\pi$
$367$	3.20115e7	0.0338045	0.0169022	+	0.999857i	$0.494620\pi$
$368$	1.93314e9	2.02207
$369$	−4.62944e8	−0.479663
$370$	−3.50636e8	−0.359873
$371$	−7.51449e8	−0.763996
$372$	8.99088e7	0.0905528
$373$	1.75838e9	1.75441	0.877205	−	0.480115i	$-0.159405\pi$
$373$	1.75838e9	1.75441	0.877205	+	0.480115i	$0.159405\pi$
$374$	0	0
$375$	1.20583e9	1.18080
$376$	4.63288e7	0.0449463
$377$	7.70428e8	0.740521
$378$	−1.57096e9	−1.49604
$379$	−7.21418e8	−0.680691	−0.340345	−	0.940301i	$-0.610544\pi$
$379$	−7.21418e8	−0.680691	−0.340345	+	0.940301i	$0.610544\pi$
$380$	−5.76378e7	−0.0538846
$381$	1.99318e8	0.184633
$382$	8.68095e8	0.796793
$383$	6.73803e8	0.612826	0.306413	−	0.951899i	$-0.400871\pi$
$383$	6.73803e8	0.612826	0.306413	+	0.951899i	$0.400871\pi$
$384$	−2.25464e9	−2.03197
$385$	0	0
$386$	−9.49014e8	−0.839880
$387$	−1.72832e9	−1.51578
$388$	−3.24553e8	−0.282081
$389$	1.97081e9	1.69754	0.848771	−	0.528761i	$-0.177343\pi$
$389$	1.97081e9	1.69754	0.848771	+	0.528761i	$0.177343\pi$
$390$	−7.30942e8	−0.623960
$391$	−2.78780e9	−2.35854
$392$	3.52206e8	0.295322
$393$	−5.13680e8	−0.426892
$394$	−1.87036e9	−1.54059
$395$	−1.04145e8	−0.0850255
$396$	0	0
$397$	1.79667e9	1.44112	0.720561	−	0.693391i	$-0.243884\pi$
$397$	1.79667e9	1.44112	0.720561	+	0.693391i	$0.243884\pi$
$398$	−1.62071e9	−1.28859
$399$	1.54421e9	1.21703
$400$	1.26457e9	0.987946
$401$	1.23711e9	0.958085	0.479042	−	0.877792i	$-0.340984\pi$
$401$	1.23711e9	0.958085	0.479042	+	0.877792i	$0.340984\pi$
$402$	−1.59213e9	−1.22233
$403$	−3.68124e8	−0.280173
$404$	−1.67924e8	−0.126700
$405$	4.58522e8	0.342979
$406$	9.71308e8	0.720304
$407$	0	0
$408$	2.82862e9	2.06188
$409$	3.89663e8	0.281616	0.140808	−	0.990037i	$-0.455030\pi$
$409$	3.89663e8	0.281616	0.140808	+	0.990037i	$0.455030\pi$
$410$	−1.34286e8	−0.0962246
$411$	−8.71510e8	−0.619193
$412$	−2.65412e8	−0.186974
$413$	−1.32649e9	−0.926569
$414$	−5.47390e9	−3.79137
$415$	4.80278e8	0.329856
$416$	−4.51805e8	−0.307698
$417$	1.68005e9	1.13461
$418$	0	0
$419$	−2.14825e9	−1.42671	−0.713355	−	0.700803i	$-0.752825\pi$
$419$	−2.14825e9	−1.42671	−0.713355	+	0.700803i	$0.752825\pi$
$420$	−1.34321e8	−0.0884651
$421$	−2.34814e8	−0.153369	−0.0766845	−	0.997055i	$-0.524433\pi$
$421$	−2.34814e8	−0.153369	−0.0766845	+	0.997055i	$0.524433\pi$
$422$	−1.41283e9	−0.915157
$423$	−1.54241e8	−0.0990849
$424$	1.31372e9	0.836994
$425$	−1.82365e9	−1.15234
$426$	2.13126e9	1.33568
$427$	1.53357e8	0.0953247
$428$	−3.50833e8	−0.216296
$429$	0	0
$430$	−5.01333e8	−0.304079
$431$	−2.49512e8	−0.150114	−0.0750570	−	0.997179i	$-0.523914\pi$
$431$	−2.49512e8	−0.150114	−0.0750570	+	0.997179i	$0.523914\pi$
$432$	3.22911e9	1.92704
$433$	6.95768e8	0.411867	0.205933	−	0.978566i	$-0.433977\pi$
$433$	6.95768e8	0.411867	0.205933	+	0.978566i	$0.433977\pi$
$434$	−4.64108e8	−0.272524
$435$	−8.83246e8	−0.514481
$436$	4.53420e8	0.261998
$437$	2.66070e9	1.52515
$438$	−1.59015e9	−0.904230
$439$	−3.16156e9	−1.78351	−0.891756	−	0.452516i	$-0.850527\pi$
$439$	−3.16156e9	−1.78351	−0.891756	+	0.452516i	$0.850527\pi$
$440$	0	0
$441$	−1.17259e9	−0.651043
$442$	2.38273e9	1.31249
$443$	−4.00643e8	−0.218950	−0.109475	−	0.993990i	$-0.534917\pi$
$443$	−4.00643e8	−0.218950	−0.109475	+	0.993990i	$0.534917\pi$
$444$	4.92495e8	0.267031
$445$	5.98056e8	0.321723
$446$	2.13832e9	1.14130
$447$	6.50151e8	0.344301
$448$	1.20982e9	0.635695
$449$	8.52259e6	0.00444334	0.00222167	−	0.999998i	$-0.499293\pi$
$449$	8.52259e6	0.00444334	0.00222167	+	0.999998i	$0.499293\pi$
$450$	−3.58077e9	−1.85239
$451$	0	0
$452$	−1.34445e8	−0.0684797
$453$	1.48900e9	0.752579
$454$	1.52708e9	0.765889
$455$	5.49966e8	0.273713
$456$	−2.69966e9	−1.33331
$457$	−1.56372e8	−0.0766392	−0.0383196	−	0.999266i	$-0.512200\pi$
$457$	−1.56372e8	−0.0766392	−0.0383196	+	0.999266i	$0.512200\pi$
$458$	2.08418e9	1.01369
$459$	−4.65673e9	−2.24769
$460$	−2.31438e8	−0.110862
$461$	−2.07419e9	−0.986041	−0.493021	−	0.870018i	$-0.664107\pi$
$461$	−2.07419e9	−0.986041	−0.493021	+	0.870018i	$0.664107\pi$
$462$	0	0
$463$	−1.63176e9	−0.764051	−0.382025	−	0.924152i	$-0.624773\pi$
$463$	−1.63176e9	−0.764051	−0.382025	+	0.924152i	$0.624773\pi$
$464$	−1.99652e9	−0.927815
$465$	4.22030e8	0.194652
$466$	3.09133e9	1.41513
$467$	3.42028e9	1.55401	0.777003	−	0.629497i	$-0.216739\pi$
$467$	3.42028e9	1.55401	0.777003	+	0.629497i	$0.216739\pi$
$468$	6.81939e8	0.307528
$469$	1.19793e9	0.536200
$470$	−4.47404e7	−0.0198773
$471$	3.49486e9	1.54119
$472$	2.31903e9	1.01510
$473$	0	0
$474$	1.00357e9	0.432837
$475$	1.74051e9	0.745158
$476$	4.37860e8	0.186085
$477$	−4.37371e9	−1.84517
$478$	5.56684e8	0.233137
$479$	−4.04368e9	−1.68113	−0.840567	−	0.541707i	$-0.817778\pi$
$479$	−4.04368e9	−1.68113	−0.840567	+	0.541707i	$0.817778\pi$
$480$	5.17966e8	0.213775
$481$	−2.01648e9	−0.826200
$482$	1.83667e9	0.747079
$483$	6.20059e9	2.50391
$484$	0	0
$485$	−1.52345e9	−0.606360
$486$	2.03708e8	0.0804973
$487$	7.86728e8	0.308655	0.154327	−	0.988020i	$-0.450679\pi$
$487$	7.86728e8	0.308655	0.154327	+	0.988020i	$0.450679\pi$
$488$	−2.68106e8	−0.104433
$489$	−7.99108e9	−3.09047
$490$	−3.40131e8	−0.130605
$491$	2.88772e9	1.10096	0.550478	−	0.834850i	$-0.314446\pi$
$491$	2.88772e9	1.10096	0.550478	+	0.834850i	$0.314446\pi$
$492$	1.88615e8	0.0713999
$493$	2.87921e9	1.08220
$494$	−2.27410e9	−0.848720
$495$	0	0
$496$	9.53974e8	0.351035
$497$	−1.60357e9	−0.585924
$498$	−4.62810e9	−1.67919
$499$	2.89822e9	1.04419	0.522096	−	0.852887i	$-0.325150\pi$
$499$	2.89822e9	1.04419	0.522096	+	0.852887i	$0.325150\pi$
$500$	−3.26325e8	−0.116750
$501$	5.74806e9	2.04216
$502$	−1.23130e9	−0.434411
$503$	−1.45439e9	−0.509557	−0.254779	−	0.966999i	$-0.582003\pi$
$503$	−1.45439e9	−0.509557	−0.254779	+	0.966999i	$0.582003\pi$
$504$	−4.17891e9	−1.45397
$505$	−7.88230e8	−0.272354
$506$	0	0
$507$	8.60546e8	0.293256
$508$	−5.39400e7	−0.0182553
$509$	2.38027e9	0.800045	0.400022	−	0.916505i	$-0.369002\pi$
$509$	2.38027e9	0.800045	0.400022	+	0.916505i	$0.369002\pi$
$510$	−2.73164e9	−0.911860
$511$	1.19644e9	0.396659
$512$	−1.94006e9	−0.638808
$513$	4.44443e9	1.45347
$514$	−1.47308e9	−0.478472
$515$	−1.24584e9	−0.401918
$516$	7.04160e8	0.225630
$517$	0	0
$518$	−2.54225e9	−0.803645
$519$	4.50015e9	1.41300
$520$	−9.61478e8	−0.299866
$521$	−2.30350e9	−0.713604	−0.356802	−	0.934180i	$-0.616133\pi$
$521$	−2.30350e9	−0.713604	−0.356802	+	0.934180i	$0.616133\pi$
$522$	5.65338e9	1.73965
$523$	5.87580e9	1.79602	0.898010	−	0.439975i	$-0.145013\pi$
$523$	5.87580e9	1.79602	0.898010	+	0.439975i	$0.145013\pi$
$524$	1.39013e8	0.0422082
$525$	4.05614e9	1.22336
$526$	−2.17619e9	−0.651998
$527$	−1.37574e9	−0.409447
$528$	0	0
$529$	7.27892e9	2.13783
$530$	−1.26868e9	−0.370157
$531$	−7.72065e9	−2.23781
$532$	−4.17898e8	−0.120331
$533$	−7.72266e8	−0.220913
$534$	−5.76304e9	−1.63779
$535$	−1.64681e9	−0.464948
$536$	−2.09428e9	−0.587434
$537$	−3.07823e9	−0.857810
$538$	3.77506e9	1.04517
$539$	0	0
$540$	−3.86593e8	−0.105652
$541$	2.71352e9	0.736789	0.368395	−	0.929670i	$-0.379908\pi$
$541$	2.71352e9	0.736789	0.368395	+	0.929670i	$0.379908\pi$
$542$	−7.09773e9	−1.91479
$543$	3.87355e9	1.03827
$544$	−1.68847e9	−0.449672
$545$	2.12835e9	0.563190
$546$	−5.29963e9	−1.39339
$547$	4.34522e9	1.13516	0.567579	−	0.823319i	$-0.307880\pi$
$547$	4.34522e9	1.13516	0.567579	+	0.823319i	$0.307880\pi$
$548$	2.35850e8	0.0612216
$549$	8.92594e8	0.230224
$550$	0	0
$551$	−2.74794e9	−0.699805
$552$	−1.08402e10	−2.74315
$553$	−7.55095e8	−0.189873
$554$	1.08482e9	0.271064
$555$	2.31176e9	0.574007
$556$	−4.54660e8	−0.112182
$557$	−1.90803e9	−0.467834	−0.233917	−	0.972257i	$-0.575154\pi$
$557$	−1.90803e9	−0.467834	−0.233917	+	0.972257i	$0.575154\pi$
$558$	−2.70128e9	−0.658189
$559$	−2.88312e9	−0.698107
$560$	−1.42521e9	−0.342942
$561$	0	0
$562$	4.80484e9	1.14183
$563$	−4.35460e9	−1.02842	−0.514208	−	0.857665i	$-0.671914\pi$
$563$	−4.35460e9	−1.02842	−0.514208	+	0.857665i	$0.671914\pi$
$564$	6.28414e7	0.0147492
$565$	−6.31085e8	−0.147203
$566$	8.02940e9	1.86134
$567$	3.32447e9	0.765918
$568$	2.80344e9	0.641908
$569$	−6.60949e9	−1.50409	−0.752047	−	0.659109i	$-0.770934\pi$
$569$	−6.60949e9	−1.50409	−0.752047	+	0.659109i	$0.770934\pi$
$570$	2.60710e9	0.589653
$571$	5.10068e8	0.114657	0.0573287	−	0.998355i	$-0.481742\pi$
$571$	5.10068e8	0.114657	0.0573287	+	0.998355i	$0.481742\pi$
$572$	0	0
$573$	−5.72340e9	−1.27090
$574$	−9.73626e8	−0.214882
$575$	6.98881e9	1.53308
$576$	7.04162e9	1.53530
$577$	1.98648e9	0.430495	0.215247	−	0.976560i	$-0.430944\pi$
$577$	1.98648e9	0.430495	0.215247	+	0.976560i	$0.430944\pi$
$578$	3.88168e9	0.836127
$579$	6.25691e9	1.33963
$580$	2.39026e8	0.0508684
$581$	3.48221e9	0.736612
$582$	1.46803e10	3.08678
$583$	0	0
$584$	−2.09168e9	−0.434560
$585$	3.20101e9	0.661061
$586$	−6.67691e9	−1.37067
$587$	−8.55093e9	−1.74494	−0.872469	−	0.488670i	$-0.837482\pi$
$587$	−8.55093e9	−1.74494	−0.872469	+	0.488670i	$0.837482\pi$
$588$	4.77740e8	0.0969106
$589$	1.31301e9	0.264768
$590$	−2.23952e9	−0.448924
$591$	1.23314e10	2.45728
$592$	5.22559e9	1.03517
$593$	−3.11643e9	−0.613714	−0.306857	−	0.951756i	$-0.599277\pi$
$593$	−3.11643e9	−0.613714	−0.306857	+	0.951756i	$0.599277\pi$
$594$	0	0
$595$	2.05531e9	0.400007
$596$	−1.75946e8	−0.0340421
$597$	1.06855e10	2.05534
$598$	−9.13137e9	−1.74615
$599$	−8.13585e9	−1.54671	−0.773356	−	0.633973i	$-0.781423\pi$
$599$	−8.13585e9	−1.54671	−0.773356	+	0.633973i	$0.781423\pi$
$600$	−7.09114e9	−1.34025
$601$	−2.60416e9	−0.489335	−0.244668	−	0.969607i	$-0.578679\pi$
$601$	−2.60416e9	−0.489335	−0.244668	+	0.969607i	$0.578679\pi$
$602$	−3.63487e9	−0.679048
$603$	6.97241e9	1.29501
$604$	−4.02958e8	−0.0744099
$605$	0	0
$606$	7.59561e9	1.38646
$607$	4.53948e9	0.823845	0.411923	−	0.911219i	$-0.364857\pi$
$607$	4.53948e9	0.823845	0.411923	+	0.911219i	$0.364857\pi$
$608$	1.61149e9	0.290780
$609$	−6.40389e9	−1.14890
$610$	2.58914e8	0.0461850
$611$	−2.57299e8	−0.0456345
$612$	2.54851e9	0.449424
$613$	−5.05155e9	−0.885754	−0.442877	−	0.896582i	$-0.646042\pi$
$613$	−5.05155e9	−0.885754	−0.442877	+	0.896582i	$0.646042\pi$
$614$	1.92379e9	0.335404
$615$	8.85354e8	0.153481
$616$	0	0
$617$	−7.95634e9	−1.36369	−0.681844	−	0.731497i	$-0.738822\pi$
$617$	−7.95634e9	−1.36369	−0.681844	+	0.731497i	$0.738822\pi$
$618$	1.20053e10	2.04603
$619$	1.34302e9	0.227597	0.113798	−	0.993504i	$-0.463698\pi$
$619$	1.34302e9	0.227597	0.113798	+	0.993504i	$0.463698\pi$
$620$	−1.14211e8	−0.0192458
$621$	1.78461e10	2.99035
$622$	2.10256e9	0.350334
$623$	4.33615e9	0.718450
$624$	1.08934e10	1.79480
$625$	3.75063e9	0.614504
$626$	−2.37324e9	−0.386663
$627$	0	0
$628$	−9.45787e8	−0.152382
$629$	−7.53588e9	−1.20742
$630$	4.03564e9	0.643014
$631$	1.15421e10	1.82887	0.914435	−	0.404734i	$-0.132636\pi$
$631$	1.15421e10	1.82887	0.914435	+	0.404734i	$0.132636\pi$
$632$	1.32009e9	0.208015
$633$	9.31486e9	1.45970
$634$	−6.06748e9	−0.945575
$635$	−2.53194e8	−0.0392414
$636$	1.78196e9	0.274661
$637$	−1.95607e9	−0.299844
$638$	0	0
$639$	−9.33339e9	−1.41510
$640$	2.86406e9	0.431869
$641$	−8.93131e6	−0.00133941	−0.000669703	−	1.00000i	$-0.500213\pi$
$641$	−8.93131e6	−0.00133941	−0.000669703		1.00000i	$0.500213\pi$
$642$	1.58691e10	2.36690
$643$	−3.62320e9	−0.537470	−0.268735	−	0.963214i	$-0.586606\pi$
$643$	−3.62320e9	−0.537470	−0.268735	+	0.963214i	$0.586606\pi$
$644$	−1.67802e9	−0.247569
$645$	3.30532e9	0.485014
$646$	−8.49864e9	−1.24033
$647$	−6.09089e9	−0.884129	−0.442064	−	0.896983i	$-0.645754\pi$
$647$	−6.09089e9	−0.884129	−0.442064	+	0.896983i	$0.645754\pi$
$648$	−5.81201e9	−0.839100
$649$	0	0
$650$	−5.97331e9	−0.853137
$651$	3.05989e9	0.434683
$652$	2.16257e9	0.305564
$653$	−6.44425e9	−0.905683	−0.452842	−	0.891591i	$-0.649590\pi$
$653$	−6.44425e9	−0.905683	−0.452842	+	0.891591i	$0.649590\pi$
$654$	−2.05094e10	−2.86701
$655$	6.52526e8	0.0907305
$656$	2.00129e9	0.276787
$657$	6.96373e9	0.957995
$658$	−3.24386e8	−0.0443886
$659$	−4.17157e9	−0.567807	−0.283904	−	0.958853i	$-0.591630\pi$
$659$	−4.17157e9	−0.567807	−0.283904	+	0.958853i	$0.591630\pi$
$660$	0	0
$661$	−1.61108e9	−0.216976	−0.108488	−	0.994098i	$-0.534601\pi$
$661$	−1.61108e9	−0.216976	−0.108488	+	0.994098i	$0.534601\pi$
$662$	−1.23648e10	−1.65647
$663$	−1.57095e10	−2.09346
$664$	−6.08778e9	−0.806995
$665$	−1.96160e9	−0.258664
$666$	−1.47968e10	−1.94093
$667$	−1.10340e10	−1.43977
$668$	−1.55555e9	−0.201915
$669$	−1.40981e10	−1.82041
$670$	2.02248e9	0.259790
$671$	0	0
$672$	3.75546e9	0.477387
$673$	8.35749e9	1.05687	0.528437	−	0.848973i	$-0.322778\pi$
$673$	8.35749e9	1.05687	0.528437	+	0.848973i	$0.322778\pi$
$674$	1.10688e10	1.39248
$675$	1.16741e10	1.46103
$676$	−2.32883e8	−0.0289951
$677$	1.22902e9	0.152230	0.0761149	−	0.997099i	$-0.475748\pi$
$677$	1.22902e9	0.152230	0.0761149	+	0.997099i	$0.475748\pi$
$678$	6.08131e9	0.749365
$679$	−1.10456e10	−1.35408
$680$	−3.59319e9	−0.438227
$681$	−1.00681e10	−1.22161
$682$	0	0
$683$	1.27446e10	1.53057	0.765286	−	0.643690i	$-0.222597\pi$
$683$	1.27446e10	1.53057	0.765286	+	0.643690i	$0.222597\pi$
$684$	−2.43232e9	−0.290619
$685$	1.10708e9	0.131602
$686$	−9.95935e9	−1.17787
$687$	−1.37411e10	−1.61686
$688$	7.47146e9	0.874674
$689$	−7.29607e9	−0.849810
$690$	1.04685e10	1.21315
$691$	−3.13354e9	−0.361295	−0.180648	−	0.983548i	$-0.557819\pi$
$691$	−3.13354e9	−0.361295	−0.180648	+	0.983548i	$0.557819\pi$
$692$	−1.21784e9	−0.139707
$693$	0	0
$694$	1.86983e10	2.12346
$695$	−2.13417e9	−0.241147
$696$	1.11956e10	1.25868
$697$	−2.88608e9	−0.322844
$698$	1.50518e10	1.67531
$699$	−2.03813e10	−2.25716
$700$	−1.09768e9	−0.120958
$701$	5.79438e9	0.635321	0.317661	−	0.948204i	$-0.397103\pi$
$701$	5.79438e9	0.635321	0.317661	+	0.948204i	$0.397103\pi$
$702$	−1.52530e10	−1.66408
$703$	7.19231e9	0.780773
$704$	0	0
$705$	2.94976e8	0.0317048
$706$	6.11111e8	0.0653588
$707$	−5.71499e9	−0.608202
$708$	3.14558e9	0.333108
$709$	−2.60858e9	−0.274879	−0.137440	−	0.990510i	$-0.543887\pi$
$709$	−2.60858e9	−0.274879	−0.137440	+	0.990510i	$0.543887\pi$
$710$	−2.70733e9	−0.283881
$711$	−4.39493e9	−0.458573
$712$	−7.58068e9	−0.787096
$713$	5.27226e9	0.544732
$714$	−1.98055e10	−2.03630
$715$	0	0
$716$	8.33038e8	0.0848143
$717$	−3.67025e9	−0.371860
$718$	1.02410e9	0.103254
$719$	−3.96297e9	−0.397621	−0.198811	−	0.980038i	$-0.563708\pi$
$719$	−3.96297e9	−0.397621	−0.198811	+	0.980038i	$0.563708\pi$
$720$	−8.29525e9	−0.828258
$721$	−9.03285e9	−0.897535
$722$	−2.83065e9	−0.279902
$723$	−1.21093e10	−1.19161
$724$	−1.04827e9	−0.102657
$725$	−7.21795e9	−0.703446
$726$	0	0
$727$	2.85430e9	0.275505	0.137752	−	0.990467i	$-0.456012\pi$
$727$	2.85430e9	0.275505	0.137752	+	0.990467i	$0.456012\pi$
$728$	−6.97111e9	−0.669641
$729$	−1.11245e10	−1.06349
$730$	2.01996e9	0.192182
$731$	−1.07747e10	−1.02022
$732$	−3.63665e8	−0.0342699
$733$	1.63458e9	0.153300	0.0766501	−	0.997058i	$-0.475578\pi$
$733$	1.63458e9	0.153300	0.0766501	+	0.997058i	$0.475578\pi$
$734$	3.91850e8	0.0365750
$735$	2.24250e9	0.208318
$736$	6.47074e9	0.598248
$737$	0	0
$738$	−5.66687e9	−0.518974
$739$	4.41487e9	0.402404	0.201202	−	0.979550i	$-0.435515\pi$
$739$	4.41487e9	0.402404	0.201202	+	0.979550i	$0.435515\pi$
$740$	−6.25615e8	−0.0567539
$741$	1.49932e10	1.35373
$742$	−9.19844e9	−0.826610
$743$	−1.54974e10	−1.38611	−0.693054	−	0.720886i	$-0.743735\pi$
$743$	−1.54974e10	−1.38611	−0.693054	+	0.720886i	$0.743735\pi$
$744$	−5.34946e9	−0.476216
$745$	−8.25885e8	−0.0731767
$746$	2.15242e10	1.89820
$747$	2.02678e10	1.77903
$748$	0	0
$749$	−1.19400e10	−1.03829
$750$	1.47605e10	1.27758
$751$	−5.88301e9	−0.506827	−0.253414	−	0.967358i	$-0.581553\pi$
$751$	−5.88301e9	−0.506827	−0.253414	+	0.967358i	$0.581553\pi$
$752$	6.66776e8	0.0571765
$753$	8.11804e9	0.692897
$754$	9.43076e9	0.801211
$755$	−1.89148e9	−0.159951
$756$	−2.80296e9	−0.235934
$757$	−1.84363e10	−1.54468	−0.772339	−	0.635211i	$-0.780913\pi$
$757$	−1.84363e10	−1.54468	−0.772339	+	0.635211i	$0.780913\pi$
$758$	−8.83084e9	−0.736478
$759$	0	0
$760$	3.42937e9	0.283379
$761$	−1.67116e9	−0.137459	−0.0687293	−	0.997635i	$-0.521894\pi$
$761$	−1.67116e9	−0.137459	−0.0687293	+	0.997635i	$0.521894\pi$
$762$	2.43984e9	0.199765
$763$	1.54314e10	1.25768
$764$	1.54888e9	0.125658
$765$	1.19627e10	0.966079
$766$	8.24799e9	0.663052
$767$	−1.28793e10	−1.03064
$768$	−1.07852e10	−0.859137
$769$	−2.39264e10	−1.89730	−0.948649	−	0.316329i	$-0.897550\pi$
$769$	−2.39264e10	−1.89730	−0.948649	+	0.316329i	$0.897550\pi$
$770$	0	0
$771$	9.71213e9	0.763175
$772$	−1.69326e9	−0.132453
$773$	1.42938e10	1.11306	0.556530	−	0.830827i	$-0.312132\pi$
$773$	1.42938e10	1.11306	0.556530	+	0.830827i	$0.312132\pi$
$774$	−2.11563e10	−1.64001
$775$	3.44886e9	0.266146
$776$	1.93105e10	1.48346
$777$	1.67612e10	1.28183
$778$	2.41245e10	1.83667
$779$	2.75450e9	0.208767
$780$	−1.30417e9	−0.0984018
$781$	0	0
$782$	−3.41253e10	−2.55184
$783$	−1.84312e10	−1.37211
$784$	5.06904e9	0.375681
$785$	−4.43951e9	−0.327560
$786$	−6.28792e9	−0.461879
$787$	−2.22118e9	−0.162432	−0.0812160	−	0.996697i	$-0.525880\pi$
$787$	−2.22118e9	−0.162432	−0.0812160	+	0.996697i	$0.525880\pi$
$788$	−3.33715e9	−0.242959
$789$	1.43477e10	1.03995
$790$	−1.27484e9	−0.0919939
$791$	−4.57562e9	−0.328725
$792$	0	0
$793$	1.48899e9	0.106032
$794$	2.19929e10	1.55923
$795$	8.36448e9	0.590410
$796$	−2.89172e9	−0.203218
$797$	1.26391e10	0.884322	0.442161	−	0.896936i	$-0.354212\pi$
$797$	1.26391e10	0.884322	0.442161	+	0.896936i	$0.354212\pi$
$798$	1.89026e10	1.31677
$799$	−9.61564e8	−0.0666906
$800$	4.23285e9	0.292293
$801$	2.52380e10	1.73517
$802$	1.51434e10	1.03661
$803$	0	0
$804$	−2.84073e9	−0.192768
$805$	−7.87660e9	−0.532173
$806$	−4.50618e9	−0.303135
$807$	−2.48892e10	−1.66707
$808$	9.99123e9	0.666315
$809$	9.13438e9	0.606540	0.303270	−	0.952905i	$-0.401922\pi$
$809$	9.13438e9	0.606540	0.303270	+	0.952905i	$0.401922\pi$
$810$	5.61275e9	0.371089
$811$	6.59262e9	0.433995	0.216998	−	0.976172i	$-0.430374\pi$
$811$	6.59262e9	0.433995	0.216998	+	0.976172i	$0.430374\pi$
$812$	1.73304e9	0.113596
$813$	4.67958e10	3.05415
$814$	0	0
$815$	1.01510e10	0.656840
$816$	4.07102e10	2.62294
$817$	1.02834e10	0.659723
$818$	4.76984e9	0.304697
$819$	2.32086e10	1.47624
$820$	−2.39597e8	−0.0151751
$821$	9.94261e9	0.627046	0.313523	−	0.949581i	$-0.398491\pi$
$821$	9.94261e9	0.627046	0.313523	+	0.949581i	$0.398491\pi$
$822$	−1.06681e10	−0.669940
$823$	2.56421e10	1.60345	0.801723	−	0.597696i	$-0.203917\pi$
$823$	2.56421e10	1.60345	0.801723	+	0.597696i	$0.203917\pi$
$824$	1.57917e10	0.983293
$825$	0	0
$826$	−1.62374e10	−1.00251
$827$	7.64437e9	0.469972	0.234986	−	0.971999i	$-0.424496\pi$
$827$	7.64437e9	0.469972	0.234986	+	0.971999i	$0.424496\pi$
$828$	−9.76671e9	−0.597918
$829$	9.28353e9	0.565943	0.282971	−	0.959128i	$-0.408680\pi$
$829$	9.28353e9	0.565943	0.282971	+	0.959128i	$0.408680\pi$
$830$	5.87906e9	0.356890
$831$	−7.15226e9	−0.432354
$832$	1.17466e10	0.707098
$833$	−7.31012e9	−0.438194
$834$	2.05654e10	1.22760
$835$	−7.30175e9	−0.434034
$836$	0	0
$837$	8.80676e9	0.519131
$838$	−2.62966e10	−1.54364
$839$	4.23770e7	0.00247721	0.00123861	−	0.999999i	$-0.499606\pi$
$839$	4.23770e7	0.00247721	0.00123861	+	0.999999i	$0.499606\pi$
$840$	7.99193e9	0.465237
$841$	−5.85406e9	−0.339368
$842$	−2.87435e9	−0.165939
$843$	−3.16786e10	−1.82125
$844$	−2.52081e9	−0.144325
$845$	−1.09315e9	−0.0623277
$846$	−1.88805e9	−0.107206
$847$	0	0
$848$	1.89074e10	1.06475
$849$	−5.29383e10	−2.96888
$850$	−2.23232e10	−1.24678
$851$	2.88799e10	1.60636
$852$	3.80265e9	0.210643
$853$	−2.40741e10	−1.32809	−0.664046	−	0.747692i	$-0.731162\pi$
$853$	−2.40741e10	−1.32809	−0.664046	+	0.747692i	$0.731162\pi$
$854$	1.87723e9	0.103137
$855$	−1.14173e10	−0.624714
$856$	2.08741e10	1.13750
$857$	−1.40911e9	−0.0764734	−0.0382367	−	0.999269i	$-0.512174\pi$
$857$	−1.40911e9	−0.0764734	−0.0382367	+	0.999269i	$0.512174\pi$
$858$	0	0
$859$	−1.31310e10	−0.706840	−0.353420	−	0.935465i	$-0.614981\pi$
$859$	−1.31310e10	−0.706840	−0.353420	+	0.935465i	$0.614981\pi$
$860$	−8.94493e8	−0.0479548
$861$	6.41917e9	0.342743
$862$	−3.05426e9	−0.162417
$863$	6.00993e9	0.318296	0.159148	−	0.987255i	$-0.449125\pi$
$863$	6.00993e9	0.318296	0.159148	+	0.987255i	$0.449125\pi$
$864$	1.08087e10	0.570132
$865$	−5.71653e9	−0.300314
$866$	8.51686e9	0.445622
$867$	−2.55922e10	−1.33364
$868$	−8.28076e8	−0.0429785
$869$	0	0
$870$	−1.08118e10	−0.556646
$871$	1.16311e10	0.596428
$872$	−2.69779e10	−1.37785
$873$	−6.42895e10	−3.27032
$874$	3.25695e10	1.65014
$875$	−1.11059e10	−0.560437
$876$	−2.83719e9	−0.142602
$877$	3.53346e10	1.76889	0.884447	−	0.466641i	$-0.154536\pi$
$877$	3.53346e10	1.76889	0.884447	+	0.466641i	$0.154536\pi$
$878$	−3.87005e10	−1.92968
$879$	4.40213e10	2.18626
$880$	0	0
$881$	2.47432e10	1.21910	0.609551	−	0.792747i	$-0.291350\pi$
$881$	2.47432e10	1.21910	0.609551	+	0.792747i	$0.291350\pi$
$882$	−1.43536e10	−0.704400
$883$	−1.26434e10	−0.618020	−0.309010	−	0.951059i	$-0.599998\pi$
$883$	−1.26434e10	−0.618020	−0.309010	+	0.951059i	$0.599998\pi$
$884$	4.25133e9	0.206987
$885$	1.47653e10	0.716046
$886$	−4.90424e9	−0.236894
$887$	2.02638e10	0.974966	0.487483	−	0.873133i	$-0.337915\pi$
$887$	2.02638e10	0.974966	0.487483	+	0.873133i	$0.337915\pi$
$888$	−2.93028e10	−1.40431
$889$	−1.83576e9	−0.0876312
$890$	7.32077e9	0.348090
$891$	0	0
$892$	3.81526e9	0.179989
$893$	9.17725e8	0.0431254
$894$	7.95846e9	0.372519
$895$	3.91027e9	0.182316
$896$	2.07656e10	0.964421
$897$	6.02037e10	2.78515
$898$	1.04324e8	0.00480750
$899$	−5.44512e9	−0.249947
$900$	−6.38892e9	−0.292132
$901$	−2.72665e10	−1.24192
$902$	0	0
$903$	2.39649e10	1.08310
$904$	7.99933e9	0.360134
$905$	−4.92056e9	−0.220671
$906$	1.82268e10	0.814258
$907$	−4.16194e10	−1.85213	−0.926063	−	0.377368i	$-0.876829\pi$
$907$	−4.16194e10	−1.85213	−0.926063	+	0.377368i	$0.876829\pi$
$908$	2.72466e9	0.120785
$909$	−3.32634e10	−1.46890
$910$	6.73210e9	0.296146
$911$	−1.93086e10	−0.846127	−0.423064	−	0.906100i	$-0.639045\pi$
$911$	−1.93086e10	−0.846127	−0.423064	+	0.906100i	$0.639045\pi$
$912$	−3.88542e10	−1.69612
$913$	0	0
$914$	−1.91413e9	−0.0829203
$915$	−1.70704e9	−0.0736663
$916$	3.71865e9	0.159864
$917$	4.73108e9	0.202613
$918$	−5.70028e10	−2.43191
$919$	1.26514e10	0.537692	0.268846	−	0.963183i	$-0.413358\pi$
$919$	1.26514e10	0.537692	0.268846	+	0.963183i	$0.413358\pi$
$920$	1.37703e10	0.583022
$921$	−1.26837e10	−0.534979
$922$	−2.53900e10	−1.06685
$923$	−1.55696e10	−0.651737
$924$	0	0
$925$	1.88919e10	0.784836
$926$	−1.99743e10	−0.826670
$927$	−5.25745e10	−2.16769
$928$	−6.68290e9	−0.274503
$929$	−1.14676e10	−0.469264	−0.234632	−	0.972084i	$-0.575388\pi$
$929$	−1.14676e10	−0.469264	−0.234632	+	0.972084i	$0.575388\pi$
$930$	5.16605e9	0.210605
$931$	6.97684e9	0.283358
$932$	5.51565e9	0.223173
$933$	−1.38623e10	−0.558792
$934$	4.18674e10	1.68137
$935$	0	0
$936$	−4.05745e10	−1.61729
$937$	3.94549e10	1.56680	0.783399	−	0.621519i	$-0.213484\pi$
$937$	3.94549e10	1.56680	0.783399	+	0.621519i	$0.213484\pi$
$938$	1.46638e10	0.580146
$939$	1.56469e10	0.616737
$940$	−7.98272e7	−0.00313475
$941$	−1.15292e9	−0.0451063	−0.0225531	−	0.999746i	$-0.507179\pi$
$941$	−1.15292e9	−0.0451063	−0.0225531	+	0.999746i	$0.507179\pi$
$942$	4.27804e10	1.66750
$943$	1.10604e10	0.429515
$944$	3.33761e10	1.29132
$945$	−1.31570e10	−0.507162
$946$	0	0
$947$	−2.63741e9	−0.100914	−0.0504572	−	0.998726i	$-0.516068\pi$
$947$	−2.63741e9	−0.100914	−0.0504572	+	0.998726i	$0.516068\pi$
$948$	1.79060e9	0.0682606
$949$	1.16166e10	0.441214
$950$	2.13055e10	0.806228
$951$	4.00032e10	1.50822
$952$	−2.60521e10	−0.978618
$953$	−3.92027e10	−1.46721	−0.733603	−	0.679579i	$-0.762163\pi$
$953$	−3.92027e10	−1.46721	−0.733603	+	0.679579i	$0.762163\pi$
$954$	−5.35384e10	−1.99639
$955$	7.27042e9	0.270114
$956$	9.93253e8	0.0367669
$957$	0	0
$958$	−4.94985e10	−1.81891
$959$	8.02676e9	0.293883
$960$	−1.34667e10	−0.491261
$961$	−2.49108e10	−0.905433
$962$	−2.46836e10	−0.893913
$963$	−6.94953e10	−2.50763
$964$	3.27704e9	0.117818
$965$	−7.94813e9	−0.284721
$966$	7.59011e10	2.70912
$967$	3.73048e10	1.32670	0.663349	−	0.748310i	$-0.269134\pi$
$967$	3.73048e10	1.32670	0.663349	+	0.748310i	$0.269134\pi$
$968$	0	0
$969$	5.60321e10	1.97835
$970$	−1.86484e10	−0.656055
$971$	−1.48847e10	−0.521761	−0.260881	−	0.965371i	$-0.584013\pi$
$971$	−1.48847e10	−0.521761	−0.260881	+	0.965371i	$0.584013\pi$
$972$	3.63462e8	0.0126948
$973$	−1.54736e10	−0.538512
$974$	9.63029e9	0.333951
$975$	3.93824e10	1.36077
$976$	−3.85865e9	−0.132850
$977$	−2.91736e10	−1.00083	−0.500413	−	0.865787i	$-0.666819\pi$
$977$	−2.91736e10	−1.00083	−0.500413	+	0.865787i	$0.666819\pi$
$978$	−9.78184e10	−3.34375
$979$	0	0
$980$	−6.06872e8	−0.0205971
$981$	8.98164e10	3.03749
$982$	3.53484e10	1.19119
$983$	2.17500e10	0.730333	0.365167	−	0.930942i	$-0.381012\pi$
$983$	2.17500e10	0.730333	0.365167	+	0.930942i	$0.381012\pi$
$984$	−1.12223e10	−0.375491
$985$	−1.56645e10	−0.522264
$986$	3.52442e10	1.17090
$987$	2.13870e9	0.0708010
$988$	−4.05751e9	−0.133848
$989$	4.12920e10	1.35731
$990$	0	0
$991$	−5.54420e10	−1.80959	−0.904797	−	0.425844i	$-0.859977\pi$
$991$	−5.54420e10	−1.80959	−0.904797	+	0.425844i	$0.859977\pi$
$992$	3.19321e9	0.103857
$993$	8.15216e10	2.64211
$994$	−1.96292e10	−0.633944
$995$	−1.35737e10	−0.436835
$996$	−8.25759e9	−0.264817
$997$	5.68754e10	1.81757	0.908786	−	0.417263i	$-0.137010\pi$
$997$	5.68754e10	1.81757	0.908786	+	0.417263i	$0.137010\pi$
$998$	3.54770e10	1.12977
$999$	4.82409e10	1.53086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.g.1.10		12
11.7	odd	10		11.8.c.a.5.2	✓	24
11.8	odd	10		11.8.c.a.9.2	yes	24
11.10	odd	2		121.8.a.i.1.3		12
33.8	even	10		99.8.f.a.64.5		24
33.29	even	10		99.8.f.a.82.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.8.c.a.5.2	✓	24	11.7	odd	10
11.8.c.a.9.2	yes	24	11.8	odd	10
99.8.f.a.64.5		24	33.8	even	10
99.8.f.a.82.5		24	33.29	even	10
121.8.a.g.1.10		12	1.1	even	1	trivial
121.8.a.i.1.3		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)

\(f(q)\)	\(=\)	\(q+12.2409 q^{2} -80.7053 q^{3} +21.8407 q^{4} +102.520 q^{5} -987.908 q^{6} +743.309 q^{7} -1299.49 q^{8} +4326.34 q^{9} +1254.94 q^{10} -1762.66 q^{12} +7217.04 q^{13} +9098.81 q^{14} -8273.88 q^{15} -18702.6 q^{16} +26971.2 q^{17} +52958.5 q^{18} -25741.5 q^{19} +2239.10 q^{20} -59989.0 q^{21} -103362. q^{23} +104876. q^{24} -67614.7 q^{25} +88343.4 q^{26} -172656. q^{27} +16234.4 q^{28} +106751. q^{29} -101280. q^{30} -51007.6 q^{31} -62602.6 q^{32} +330153. q^{34} +76203.8 q^{35} +94490.1 q^{36} -279405. q^{37} -315101. q^{38} -582453. q^{39} -133223. q^{40} -107006. q^{41} -734321. q^{42} -399488. q^{43} +443535. q^{45} -1.26525e6 q^{46} -35651.5 q^{47} +1.50940e6 q^{48} -271034. q^{49} -827668. q^{50} -2.17672e6 q^{51} +157625. q^{52} -1.01095e6 q^{53} -2.11347e6 q^{54} -965923. q^{56} +2.07748e6 q^{57} +1.30674e6 q^{58} -1.78457e6 q^{59} -180707. q^{60} +206316. q^{61} -624381. q^{62} +3.21581e6 q^{63} +1.62762e6 q^{64} +739889. q^{65} +1.61162e6 q^{67} +589069. q^{68} +8.34187e6 q^{69} +932807. q^{70} -2.15734e6 q^{71} -5.62203e6 q^{72} +1.60961e6 q^{73} -3.42018e6 q^{74} +5.45686e6 q^{75} -562212. q^{76} -7.12978e6 q^{78} -1.01586e6 q^{79} -1.91738e6 q^{80} +4.47253e6 q^{81} -1.30985e6 q^{82} +4.68474e6 q^{83} -1.31020e6 q^{84} +2.76508e6 q^{85} -4.89011e6 q^{86} -8.61538e6 q^{87} +5.83358e6 q^{89} +5.42928e6 q^{90} +5.36449e6 q^{91} -2.25750e6 q^{92} +4.11658e6 q^{93} -436408. q^{94} -2.63902e6 q^{95} +5.05236e6 q^{96} -1.48600e7 q^{97} -3.31771e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 12 q^{3} + 550 q^{4} + 144 q^{5} - 649 q^{6} - 2244 q^{7} - 3810 q^{8} + 9094 q^{9} - 2120 q^{10} + 5819 q^{12} - 8688 q^{13} + 23988 q^{14} - 29008 q^{15} - 32238 q^{16} - 26214 q^{17}+ \cdots + 25767018 q^{98}+O(q^{100}) \) 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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