LMFDB - Embedded newform 22.6.a.d.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [22,6,Mod(1,22)] 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("22.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8,29] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$3.52844403589$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{793}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 198 $ x^2 - x - 198
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-13.5801$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +28.5801 q^{3} +16.0000 q^{4} -76.9006 q^{5} +114.321 q^{6} -91.4808 q^{7} +64.0000 q^{8} +573.824 q^{9} -307.603 q^{10} -121.000 q^{11} +457.282 q^{12} -463.801 q^{13} -365.923 q^{14} -2197.83 q^{15} +256.000 q^{16} +1641.94 q^{17} +2295.29 q^{18} -1693.53 q^{19} -1230.41 q^{20} -2614.53 q^{21} -484.000 q^{22} +75.9391 q^{23} +1829.13 q^{24} +2788.71 q^{25} -1855.21 q^{26} +9454.98 q^{27} -1463.69 q^{28} -2942.33 q^{29} -8791.32 q^{30} +8443.63 q^{31} +1024.00 q^{32} -3458.20 q^{33} +6567.74 q^{34} +7034.93 q^{35} +9181.18 q^{36} -35.5610 q^{37} -6774.10 q^{38} -13255.5 q^{39} -4921.64 q^{40} +9222.25 q^{41} -10458.1 q^{42} -11516.7 q^{43} -1936.00 q^{44} -44127.4 q^{45} +303.756 q^{46} +6179.00 q^{47} +7316.51 q^{48} -8438.27 q^{49} +11154.8 q^{50} +46926.7 q^{51} -7420.82 q^{52} +25255.1 q^{53} +37819.9 q^{54} +9304.98 q^{55} -5854.77 q^{56} -48401.2 q^{57} -11769.3 q^{58} +40786.8 q^{59} -35165.3 q^{60} -7368.85 q^{61} +33774.5 q^{62} -52493.8 q^{63} +4096.00 q^{64} +35666.6 q^{65} -13832.8 q^{66} -11024.7 q^{67} +26271.0 q^{68} +2170.35 q^{69} +28139.7 q^{70} -46964.9 q^{71} +36724.7 q^{72} -60727.5 q^{73} -142.244 q^{74} +79701.6 q^{75} -27096.4 q^{76} +11069.2 q^{77} -53022.0 q^{78} +18386.1 q^{79} -19686.6 q^{80} +130785. q^{81} +36889.0 q^{82} -59321.9 q^{83} -41832.5 q^{84} -126266. q^{85} -46066.6 q^{86} -84092.1 q^{87} -7744.00 q^{88} +5070.71 q^{89} -176510. q^{90} +42428.9 q^{91} +1215.03 q^{92} +241320. q^{93} +24716.0 q^{94} +130233. q^{95} +29266.1 q^{96} -130795. q^{97} -33753.1 q^{98} -69432.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9} - 52 q^{10} - 242 q^{11} + 464 q^{12} - 646 q^{13} - 56 q^{14} - 2171 q^{15} + 512 q^{16} - 208 q^{17} + 1324 q^{18}+ \cdots - 40051 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9 - 52 * q^10 - 242 * q^11 + 464 * q^12 - 646 * q^13 - 56 * q^14 - 2171 * q^15 + 512 * q^16 - 208 * q^17 + 1324 * q^18 - 2148 * q^19 - 208 * q^20 - 2582 * q^21 - 968 * q^22 + 349 * q^23 + 1856 * q^24 + 3747 * q^25 - 2584 * q^26 + 9251 * q^27 - 224 * q^28 + 4422 * q^29 - 8684 * q^30 + 14381 * q^31 + 2048 * q^32 - 3509 * q^33 - 832 * q^34 + 11986 * q^35 + 5296 * q^36 - 4267 * q^37 - 8592 * q^38 - 13332 * q^39 - 832 * q^40 - 10110 * q^41 - 10328 * q^42 - 9798 * q^43 - 3872 * q^44 - 59644 * q^45 + 1396 * q^46 + 21144 * q^47 + 7424 * q^48 - 19242 * q^49 + 14988 * q^50 + 46150 * q^51 - 10336 * q^52 + 39584 * q^53 + 37004 * q^54 + 1573 * q^55 - 896 * q^56 - 48592 * q^57 + 17688 * q^58 + 90951 * q^59 - 34736 * q^60 - 29550 * q^61 + 57524 * q^62 - 71308 * q^63 + 8192 * q^64 + 24024 * q^65 - 14036 * q^66 - 64149 * q^67 - 3328 * q^68 + 2285 * q^69 + 47944 * q^70 + 23583 * q^71 + 21184 * q^72 - 39058 * q^73 - 17068 * q^74 + 80104 * q^75 - 34368 * q^76 + 1694 * q^77 - 53328 * q^78 - 54974 * q^79 - 3328 * q^80 + 189706 * q^81 - 40440 * q^82 + 29986 * q^83 - 41312 * q^84 - 244478 * q^85 - 39192 * q^86 - 81000 * q^87 - 15488 * q^88 - 18047 * q^89 - 238576 * q^90 + 28312 * q^91 + 5584 * q^92 + 243813 * q^93 + 84576 * q^94 + 101192 * q^95 + 29696 * q^96 - 30309 * q^97 - 76968 * q^98 - 40051 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	28.5801	1.83342	0.916708	−	0.399558i	$-0.130836\pi$
$3$	28.5801	1.83342	0.916708	+	0.399558i	$0.130836\pi$
$4$	16.0000	0.500000
$5$	−76.9006	−1.37564	−0.687820	−	0.725881i	$-0.741432\pi$
$5$	−76.9006	−1.37564	−0.687820	+	0.725881i	$0.741432\pi$
$6$	114.321	1.29642
$7$	−91.4808	−0.705642	−0.352821	−	0.935691i	$-0.614778\pi$
$7$	−91.4808	−0.705642	−0.352821	+	0.935691i	$0.614778\pi$
$8$	64.0000	0.353553
$9$	573.824	2.36141
$10$	−307.603	−0.972725
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	457.282	0.916708
$13$	−463.801	−0.761156	−0.380578	−	0.924749i	$-0.624275\pi$
$13$	−463.801	−0.761156	−0.380578	+	0.924749i	$0.624275\pi$
$14$	−365.923	−0.498965
$15$	−2197.83	−2.52212
$16$	256.000	0.250000
$17$	1641.94	1.37795	0.688976	−	0.724784i	$-0.258061\pi$
$17$	1641.94	1.37795	0.688976	+	0.724784i	$0.258061\pi$
$18$	2295.29	1.66977
$19$	−1693.53	−1.07624	−0.538118	−	0.842869i	$-0.680865\pi$
$19$	−1693.53	−1.07624	−0.538118	+	0.842869i	$0.680865\pi$
$20$	−1230.41	−0.687820
$21$	−2614.53	−1.29374
$22$	−484.000	−0.213201
$23$	75.9391	0.0299327	0.0149663	−	0.999888i	$-0.495236\pi$
$23$	75.9391	0.0299327	0.0149663	+	0.999888i	$0.495236\pi$
$24$	1829.13	0.648210
$25$	2788.71	0.892387
$26$	−1855.21	−0.538218
$27$	9454.98	2.49604
$28$	−1463.69	−0.352821
$29$	−2942.33	−0.649675	−0.324837	−	0.945770i	$-0.605310\pi$
$29$	−2942.33	−0.649675	−0.324837	+	0.945770i	$0.605310\pi$
$30$	−8791.32	−1.78341
$31$	8443.63	1.57807	0.789033	−	0.614351i	$-0.210582\pi$
$31$	8443.63	1.57807	0.789033	+	0.614351i	$0.210582\pi$
$32$	1024.00	0.176777
$33$	−3458.20	−0.552796
$34$	6567.74	0.974359
$35$	7034.93	0.970710
$36$	9181.18	1.18071
$37$	−35.5610	−0.00427041	−0.00213520	−	0.999998i	$-0.500680\pi$
$37$	−35.5610	−0.00427041	−0.00213520	+	0.999998i	$0.500680\pi$
$38$	−6774.10	−0.761014
$39$	−13255.5	−1.39552
$40$	−4921.64	−0.486362
$41$	9222.25	0.856796	0.428398	−	0.903590i	$-0.359078\pi$
$41$	9222.25	0.856796	0.428398	+	0.903590i	$0.359078\pi$
$42$	−10458.1	−0.914810
$43$	−11516.7	−0.949851	−0.474925	−	0.880026i	$-0.657525\pi$
$43$	−11516.7	−0.949851	−0.474925	+	0.880026i	$0.657525\pi$
$44$	−1936.00	−0.150756
$45$	−44127.4	−3.24846
$46$	303.756	0.0211656
$47$	6179.00	0.408013	0.204006	−	0.978970i	$-0.434604\pi$
$47$	6179.00	0.408013	0.204006	+	0.978970i	$0.434604\pi$
$48$	7316.51	0.458354
$49$	−8438.27	−0.502069
$50$	11154.8	0.631013
$51$	46926.7	2.52636
$52$	−7420.82	−0.380578
$53$	25255.1	1.23498	0.617489	−	0.786579i	$-0.288150\pi$
$53$	25255.1	1.23498	0.617489	+	0.786579i	$0.288150\pi$
$54$	37819.9	1.76497
$55$	9304.98	0.414771
$56$	−5854.77	−0.249482
$57$	−48401.2	−1.97319
$58$	−11769.3	−0.459389
$59$	40786.8	1.52542	0.762711	−	0.646740i	$-0.223868\pi$
$59$	40786.8	1.52542	0.762711	+	0.646740i	$0.223868\pi$
$60$	−35165.3	−1.26106
$61$	−7368.85	−0.253557	−0.126778	−	0.991931i	$-0.540464\pi$
$61$	−7368.85	−0.253557	−0.126778	+	0.991931i	$0.540464\pi$
$62$	33774.5	1.11586
$63$	−52493.8	−1.66631
$64$	4096.00	0.125000
$65$	35666.6	1.04708
$66$	−13832.8	−0.390886
$67$	−11024.7	−0.300041	−0.150020	−	0.988683i	$-0.547934\pi$
$67$	−11024.7	−0.300041	−0.150020	+	0.988683i	$0.547934\pi$
$68$	26271.0	0.688976
$69$	2170.35	0.0548791
$70$	28139.7	0.686396
$71$	−46964.9	−1.10567	−0.552837	−	0.833289i	$-0.686455\pi$
$71$	−46964.9	−1.10567	−0.552837	+	0.833289i	$0.686455\pi$
$72$	36724.7	0.834886
$73$	−60727.5	−1.33376	−0.666880	−	0.745165i	$-0.732371\pi$
$73$	−60727.5	−1.33376	−0.666880	+	0.745165i	$0.732371\pi$
$74$	−142.244	−0.00301963
$75$	79701.6	1.63612
$76$	−27096.4	−0.538118
$77$	11069.2	0.212759
$78$	−53022.0	−0.986778
$79$	18386.1	0.331452	0.165726	−	0.986172i	$-0.447003\pi$
$79$	18386.1	0.331452	0.165726	+	0.986172i	$0.447003\pi$
$80$	−19686.6	−0.343910
$81$	130785.	2.21486
$82$	36889.0	0.605846
$83$	−59321.9	−0.945192	−0.472596	−	0.881279i	$-0.656683\pi$
$83$	−59321.9	−0.945192	−0.472596	+	0.881279i	$0.656683\pi$
$84$	−41832.5	−0.646868
$85$	−126266.	−1.89557
$86$	−46066.6	−0.671646
$87$	−84092.1	−1.19112
$88$	−7744.00	−0.106600
$89$	5070.71	0.0678568	0.0339284	−	0.999424i	$-0.489198\pi$
$89$	5070.71	0.0678568	0.0339284	+	0.999424i	$0.489198\pi$
$90$	−176510.	−2.29701
$91$	42428.9	0.537104
$92$	1215.03	0.0149663
$93$	241320.	2.89325
$94$	24716.0	0.288508
$95$	130233.	1.48051
$96$	29266.1	0.324105
$97$	−130795.	−1.41143	−0.705717	−	0.708494i	$-0.749375\pi$
$97$	−130795.	−1.41143	−0.705717	+	0.708494i	$0.749375\pi$
$98$	−33753.1	−0.355016
$99$	−69432.7	−0.711993
$100$	44619.3	0.446193
$101$	−27114.8	−0.264486	−0.132243	−	0.991217i	$-0.542218\pi$
$101$	−27114.8	−0.264486	−0.132243	+	0.991217i	$0.542218\pi$
$102$	187707.	1.78640
$103$	−12802.9	−0.118909	−0.0594546	−	0.998231i	$-0.518936\pi$
$103$	−12802.9	−0.118909	−0.0594546	+	0.998231i	$0.518936\pi$
$104$	−29683.3	−0.269109
$105$	201059.	1.77972
$106$	101020.	0.873261
$107$	−64131.5	−0.541516	−0.270758	−	0.962647i	$-0.587274\pi$
$107$	−64131.5	−0.541516	−0.270758	+	0.962647i	$0.587274\pi$
$108$	151280.	1.24802
$109$	−126630.	−1.02087	−0.510434	−	0.859917i	$-0.670515\pi$
$109$	−126630.	−1.02087	−0.510434	+	0.859917i	$0.670515\pi$
$110$	37219.9	0.293288
$111$	−1016.34	−0.00782943
$112$	−23419.1	−0.176411
$113$	131953.	0.972130	0.486065	−	0.873923i	$-0.338432\pi$
$113$	131953.	0.972130	0.486065	+	0.873923i	$0.338432\pi$
$114$	−193605.	−1.39526
$115$	−5839.77	−0.0411766
$116$	−47077.2	−0.324837
$117$	−266140.	−1.79740
$118$	163147.	1.07864
$119$	−150206.	−0.972341
$120$	−140661.	−0.891705
$121$	14641.0	0.0909091
$122$	−29475.4	−0.179292
$123$	263573.	1.57086
$124$	135098.	0.789033
$125$	25861.0	0.148037
$126$	−209975.	−1.17826
$127$	118876.	0.654013	0.327006	−	0.945022i	$-0.393960\pi$
$127$	118876.	0.654013	0.327006	+	0.945022i	$0.393960\pi$
$128$	16384.0	0.0883883
$129$	−329148.	−1.74147
$130$	142666.	0.740395
$131$	205935.	1.04846	0.524229	−	0.851577i	$-0.324353\pi$
$131$	205935.	1.04846	0.524229	+	0.851577i	$0.324353\pi$
$132$	−55331.1	−0.276398
$133$	154925.	0.759438
$134$	−44098.8	−0.212161
$135$	−727094.	−3.43365
$136$	105084.	0.487179
$137$	−196568.	−0.894769	−0.447385	−	0.894342i	$-0.647645\pi$
$137$	−196568.	−0.894769	−0.447385	+	0.894342i	$0.647645\pi$
$138$	8681.40	0.0388054
$139$	−29936.4	−0.131420	−0.0657102	−	0.997839i	$-0.520931\pi$
$139$	−29936.4	−0.131420	−0.0657102	+	0.997839i	$0.520931\pi$
$140$	112559.	0.485355
$141$	176597.	0.748057
$142$	−187859.	−0.781830
$143$	56120.0	0.229497
$144$	146899.	0.590354
$145$	226267.	0.893719
$146$	−242910.	−0.943111
$147$	−241167.	−0.920501
$148$	−568.975	−0.00213520
$149$	−362800.	−1.33876	−0.669379	−	0.742921i	$-0.733440\pi$
$149$	−362800.	−1.33876	−0.669379	+	0.742921i	$0.733440\pi$
$150$	318807.	1.15691
$151$	226244.	0.807485	0.403742	−	0.914873i	$-0.367709\pi$
$151$	226244.	0.807485	0.403742	+	0.914873i	$0.367709\pi$
$152$	−108386.	−0.380507
$153$	942182.	3.25391
$154$	44276.7	0.150443
$155$	−649321.	−2.17085
$156$	−212088.	−0.697758
$157$	392007.	1.26924	0.634621	−	0.772824i	$-0.281156\pi$
$157$	392007.	1.26924	0.634621	+	0.772824i	$0.281156\pi$
$158$	73544.2	0.234372
$159$	721794.	2.26423
$160$	−78746.3	−0.243181
$161$	−6946.97	−0.0211218
$162$	523142.	1.56615
$163$	−84380.4	−0.248755	−0.124378	−	0.992235i	$-0.539693\pi$
$163$	−84380.4	−0.248755	−0.124378	+	0.992235i	$0.539693\pi$
$164$	147556.	0.428398
$165$	265937.	0.760448
$166$	−237288.	−0.668352
$167$	543654.	1.50845	0.754226	−	0.656615i	$-0.228012\pi$
$167$	543654.	1.50845	0.754226	+	0.656615i	$0.228012\pi$
$168$	−167330.	−0.457405
$169$	−156181.	−0.420642
$170$	−505064.	−1.34037
$171$	−971785.	−2.54144
$172$	−184267.	−0.474925
$173$	356699.	0.906123	0.453061	−	0.891479i	$-0.350332\pi$
$173$	356699.	0.906123	0.453061	+	0.891479i	$0.350332\pi$
$174$	−336368.	−0.842252
$175$	−255113.	−0.629706
$176$	−30976.0	−0.0753778
$177$	1.16569e6	2.79673
$178$	20282.8	0.0479820
$179$	−521697.	−1.21699	−0.608493	−	0.793559i	$-0.708226\pi$
$179$	−521697.	−1.21699	−0.608493	+	0.793559i	$0.708226\pi$
$180$	−706039.	−1.62423
$181$	−698048.	−1.58376	−0.791879	−	0.610678i	$-0.790897\pi$
$181$	−698048.	−1.58376	−0.791879	+	0.610678i	$0.790897\pi$
$182$	169716.	0.379790
$183$	−210603.	−0.464875
$184$	4860.10	0.0105828
$185$	2734.66	0.00587454
$186$	965280.	2.04584
$187$	−198674.	−0.415468
$188$	98864.0	0.204006
$189$	−864949.	−1.76131
$190$	520933.	1.04688
$191$	612931.	1.21571	0.607853	−	0.794050i	$-0.292031\pi$
$191$	612931.	1.21571	0.607853	+	0.794050i	$0.292031\pi$
$192$	117064.	0.229177
$193$	−184465.	−0.356467	−0.178234	−	0.983988i	$-0.557038\pi$
$193$	−184465.	−0.356467	−0.178234	+	0.983988i	$0.557038\pi$
$194$	−523178.	−0.998034
$195$	1.01936e6	1.91973
$196$	−135012.	−0.251034
$197$	−1.03211e6	−1.89479	−0.947393	−	0.320074i	$-0.896292\pi$
$197$	−1.03211e6	−1.89479	−0.947393	+	0.320074i	$0.896292\pi$
$198$	−277731.	−0.503455
$199$	244463.	0.437603	0.218801	−	0.975769i	$-0.429785\pi$
$199$	244463.	0.437603	0.218801	+	0.975769i	$0.429785\pi$
$200$	178477.	0.315506
$201$	−315088.	−0.550099
$202$	−108459.	−0.187020
$203$	269166.	0.458438
$204$	750828.	1.26318
$205$	−709197.	−1.17864
$206$	−51211.6	−0.0840814
$207$	43575.7	0.0706835
$208$	−118733.	−0.190289
$209$	204917.	0.324498
$210$	804237.	1.25845
$211$	1.12590e6	1.74098	0.870488	−	0.492190i	$-0.163803\pi$
$211$	1.12590e6	1.74098	0.870488	+	0.492190i	$0.163803\pi$
$212$	404081.	0.617489
$213$	−1.34226e6	−2.02716
$214$	−256526.	−0.382910
$215$	885639.	1.30665
$216$	605119.	0.882483
$217$	−772430.	−1.11355
$218$	−506519.	−0.721863
$219$	−1.73560e6	−2.44534
$220$	148880.	0.207386
$221$	−761532.	−1.04884
$222$	−4065.35	−0.00553624
$223$	72016.8	0.0969776	0.0484888	−	0.998824i	$-0.484559\pi$
$223$	72016.8	0.0969776	0.0484888	+	0.998824i	$0.484559\pi$
$224$	−93676.3	−0.124741
$225$	1.60023e6	2.10729
$226$	527813.	0.687400
$227$	1.13240e6	1.45860	0.729298	−	0.684196i	$-0.239847\pi$
$227$	1.13240e6	1.45860	0.729298	+	0.684196i	$0.239847\pi$
$228$	−774419.	−0.986595
$229$	−34423.7	−0.0433779	−0.0216890	−	0.999765i	$-0.506904\pi$
$229$	−34423.7	−0.0433779	−0.0216890	+	0.999765i	$0.506904\pi$
$230$	−23359.1	−0.0291163
$231$	316358.	0.390076
$232$	−188309.	−0.229695
$233$	689707.	0.832290	0.416145	−	0.909298i	$-0.363381\pi$
$233$	689707.	0.832290	0.416145	+	0.909298i	$0.363381\pi$
$234$	−1.06456e6	−1.27096
$235$	−475169.	−0.561279
$236$	652589.	0.762711
$237$	525476.	0.607690
$238$	−600822.	−0.687549
$239$	289978.	0.328375	0.164188	−	0.986429i	$-0.447500\pi$
$239$	289978.	0.328375	0.164188	+	0.986429i	$0.447500\pi$
$240$	−562645.	−0.630530
$241$	1.40673e6	1.56016	0.780078	−	0.625682i	$-0.215179\pi$
$241$	1.40673e6	1.56016	0.780078	+	0.625682i	$0.215179\pi$
$242$	58564.0	0.0642824
$243$	1.44030e6	1.56473
$244$	−117902.	−0.126778
$245$	648908.	0.690666
$246$	1.05429e6	1.11077
$247$	785459.	0.819184
$248$	540392.	0.557930
$249$	−1.69543e6	−1.73293
$250$	103444.	0.104678
$251$	580131.	0.581222	0.290611	−	0.956841i	$-0.406141\pi$
$251$	580131.	0.581222	0.290611	+	0.956841i	$0.406141\pi$
$252$	−839901.	−0.833157
$253$	−9188.63	−0.00902505
$254$	475505.	0.462457
$255$	−3.60870e6	−3.47536
$256$	65536.0	0.0625000
$257$	−407104.	−0.384479	−0.192240	−	0.981348i	$-0.561575\pi$
$257$	−407104.	−0.384479	−0.192240	+	0.981348i	$0.561575\pi$
$258$	−1.31659e6	−1.23141
$259$	3253.14	0.00301338
$260$	570666.	0.523538
$261$	−1.68838e6	−1.53415
$262$	823739.	0.741372
$263$	−1.57675e6	−1.40564	−0.702819	−	0.711369i	$-0.748076\pi$
$263$	−1.57675e6	−1.40564	−0.702819	+	0.711369i	$0.748076\pi$
$264$	−221325.	−0.195443
$265$	−1.94213e6	−1.69889
$266$	619700.	0.537004
$267$	144921.	0.124410
$268$	−176395.	−0.150020
$269$	−752593.	−0.634132	−0.317066	−	0.948404i	$-0.602698\pi$
$269$	−752593.	−0.634132	−0.317066	+	0.948404i	$0.602698\pi$
$270$	−2.90838e6	−2.42796
$271$	−208553.	−0.172501	−0.0862507	−	0.996273i	$-0.527489\pi$
$271$	−208553.	−0.172501	−0.0862507	+	0.996273i	$0.527489\pi$
$272$	420336.	0.344488
$273$	1.21262e6	0.984735
$274$	−786272.	−0.632698
$275$	−337434.	−0.269065
$276$	34725.6	0.0274395
$277$	1.01926e6	0.798151	0.399075	−	0.916918i	$-0.369331\pi$
$277$	1.01926e6	0.798151	0.399075	+	0.916918i	$0.369331\pi$
$278$	−119746.	−0.0929282
$279$	4.84516e6	3.72647
$280$	450235.	0.343198
$281$	865597.	0.653958	0.326979	−	0.945032i	$-0.393969\pi$
$281$	865597.	0.653958	0.326979	+	0.945032i	$0.393969\pi$
$282$	706386.	0.528956
$283$	1.72508e6	1.28040	0.640198	−	0.768210i	$-0.278852\pi$
$283$	1.72508e6	1.28040	0.640198	+	0.768210i	$0.278852\pi$
$284$	−751438.	−0.552837
$285$	3.72208e6	2.71440
$286$	224480.	0.162279
$287$	−843658.	−0.604591
$288$	587595.	0.417443
$289$	1.27610e6	0.898750
$290$	905067.	0.631955
$291$	−3.73813e6	−2.58774
$292$	−971639.	−0.666880
$293$	1.25254e6	0.852361	0.426181	−	0.904638i	$-0.359859\pi$
$293$	1.25254e6	0.852361	0.426181	+	0.904638i	$0.359859\pi$
$294$	−964667.	−0.650892
$295$	−3.13653e6	−2.09843
$296$	−2275.90	−0.00150982
$297$	−1.14405e6	−0.752584
$298$	−1.45120e6	−0.946645
$299$	−35220.7	−0.0227834
$300$	1.27523e6	0.818058
$301$	1.05355e6	0.670255
$302$	904975.	0.570978
$303$	−774945.	−0.484914
$304$	−433543.	−0.269059
$305$	566669.	0.348803
$306$	3.76873e6	2.30086
$307$	2.69819e6	1.63390	0.816951	−	0.576707i	$-0.195663\pi$
$307$	2.69819e6	1.63390	0.816951	+	0.576707i	$0.195663\pi$
$308$	177107.	0.106380
$309$	−365908.	−0.218010
$310$	−2.59728e6	−1.53502
$311$	−1.74373e6	−1.02230	−0.511150	−	0.859491i	$-0.670780\pi$
$311$	−1.74373e6	−1.02230	−0.511150	+	0.859491i	$0.670780\pi$
$312$	−848352.	−0.493389
$313$	−1.15038e6	−0.663714	−0.331857	−	0.943330i	$-0.607675\pi$
$313$	−1.15038e6	−0.663714	−0.331857	+	0.943330i	$0.607675\pi$
$314$	1.56803e6	0.897489
$315$	4.03681e6	2.29225
$316$	294177.	0.165726
$317$	−1.16110e6	−0.648967	−0.324484	−	0.945891i	$-0.605190\pi$
$317$	−1.16110e6	−0.648967	−0.324484	+	0.945891i	$0.605190\pi$
$318$	2.88717e6	1.60105
$319$	356022.	0.195884
$320$	−314985.	−0.171955
$321$	−1.83289e6	−0.992825
$322$	−27787.9	−0.0149354
$323$	−2.78066e6	−1.48300
$324$	2.09257e6	1.10743
$325$	−1.29341e6	−0.679245
$326$	−337522.	−0.175897
$327$	−3.61910e6	−1.87168
$328$	590224.	0.302923
$329$	−565260.	−0.287911
$330$	1.06375e6	0.537718
$331$	−2.31915e6	−1.16348	−0.581740	−	0.813375i	$-0.697628\pi$
$331$	−2.31915e6	−1.16348	−0.581740	+	0.813375i	$0.697628\pi$
$332$	−949151.	−0.472596
$333$	−20405.7	−0.0100842
$334$	2.17462e6	1.06664
$335$	847807.	0.412748
$336$	−669320.	−0.323434
$337$	1.43786e6	0.689671	0.344835	−	0.938663i	$-0.387935\pi$
$337$	1.43786e6	0.689671	0.344835	+	0.938663i	$0.387935\pi$
$338$	−624725.	−0.297439
$339$	3.77124e6	1.78232
$340$	−2.02025e6	−0.947783
$341$	−1.02168e6	−0.475805
$342$	−3.88714e6	−1.79707
$343$	2.30946e6	1.05992
$344$	−737066.	−0.335823
$345$	−166901.	−0.0754939
$346$	1.42680e6	0.640726
$347$	575629.	0.256637	0.128318	−	0.991733i	$-0.459042\pi$
$347$	575629.	0.256637	0.128318	+	0.991733i	$0.459042\pi$
$348$	−1.34547e6	−0.595562
$349$	−2.77702e6	−1.22044	−0.610219	−	0.792233i	$-0.708919\pi$
$349$	−2.77702e6	−1.22044	−0.610219	+	0.792233i	$0.708919\pi$
$350$	−1.02045e6	−0.445269
$351$	−4.38523e6	−1.89987
$352$	−123904.	−0.0533002
$353$	2.18172e6	0.931885	0.465942	−	0.884815i	$-0.345715\pi$
$353$	2.18172e6	0.931885	0.465942	+	0.884815i	$0.345715\pi$
$354$	4.66277e6	1.97759
$355$	3.61163e6	1.52101
$356$	81131.3	0.0339284
$357$	−4.29289e6	−1.78271
$358$	−2.08679e6	−0.860539
$359$	−2.14848e6	−0.879822	−0.439911	−	0.898041i	$-0.644990\pi$
$359$	−2.14848e6	−0.879822	−0.439911	+	0.898041i	$0.644990\pi$
$360$	−2.82415e6	−1.14850
$361$	391930.	0.158285
$362$	−2.79219e6	−1.11989
$363$	418442.	0.166674
$364$	678862.	0.268552
$365$	4.66998e6	1.83478
$366$	−842411.	−0.328716
$367$	15838.0	0.00613813	0.00306907	−	0.999995i	$-0.499023\pi$
$367$	15838.0	0.00613813	0.00306907	+	0.999995i	$0.499023\pi$
$368$	19440.4	0.00748317
$369$	5.29195e6	2.02325
$370$	10938.6	0.00415393
$371$	−2.31035e6	−0.871453
$372$	3.86112e6	1.44663
$373$	−394343.	−0.146758	−0.0733791	−	0.997304i	$-0.523378\pi$
$373$	−394343.	−0.146758	−0.0733791	+	0.997304i	$0.523378\pi$
$374$	−794697.	−0.293780
$375$	739112.	0.271414
$376$	395456.	0.144254
$377$	1.36465e6	0.494504
$378$	−3.45980e6	−1.24544
$379$	1.68501e6	0.602567	0.301283	−	0.953535i	$-0.402585\pi$
$379$	1.68501e6	0.602567	0.301283	+	0.953535i	$0.402585\pi$
$380$	2.08373e6	0.740257
$381$	3.39750e6	1.19908
$382$	2.45172e6	0.859633
$383$	3.94284e6	1.37345	0.686724	−	0.726918i	$-0.259048\pi$
$383$	3.94284e6	1.37345	0.686724	+	0.726918i	$0.259048\pi$
$384$	468257.	0.162053
$385$	−851226.	−0.292680
$386$	−737859.	−0.252061
$387$	−6.60853e6	−2.24299
$388$	−2.09271e6	−0.705717
$389$	−571118.	−0.191360	−0.0956801	−	0.995412i	$-0.530503\pi$
$389$	−571118.	−0.191360	−0.0956801	+	0.995412i	$0.530503\pi$
$390$	4.07743e6	1.35745
$391$	124687.	0.0412458
$392$	−540049.	−0.177508
$393$	5.88564e6	1.92226
$394$	−4.12844e6	−1.33982
$395$	−1.41390e6	−0.455959
$396$	−1.11092e6	−0.355997
$397$	6.17025e6	1.96484	0.982419	−	0.186689i	$-0.0597756\pi$
$397$	6.17025e6	1.96484	0.982419	+	0.186689i	$0.0597756\pi$
$398$	977851.	0.309432
$399$	4.42778e6	1.39237
$400$	713909.	0.223097
$401$	1.82838e6	0.567814	0.283907	−	0.958852i	$-0.408369\pi$
$401$	1.82838e6	0.567814	0.283907	+	0.958852i	$0.408369\pi$
$402$	−1.26035e6	−0.388979
$403$	−3.91617e6	−1.20115
$404$	−433837.	−0.132243
$405$	−1.00575e7	−3.04686
$406$	1.07667e6	0.324165
$407$	4302.88	0.00128758
$408$	3.00331e6	0.893202
$409$	−5.94235e6	−1.75651	−0.878254	−	0.478195i	$-0.841291\pi$
$409$	−5.94235e6	−1.75651	−0.878254	+	0.478195i	$0.841291\pi$
$410$	−2.83679e6	−0.833426
$411$	−5.61794e6	−1.64048
$412$	−204846.	−0.0594546
$413$	−3.73121e6	−1.07640
$414$	174303.	0.0499808
$415$	4.56189e6	1.30024
$416$	−474933.	−0.134555
$417$	−855586.	−0.240948
$418$	819666.	0.229454
$419$	−2.80473e6	−0.780468	−0.390234	−	0.920716i	$-0.627606\pi$
$419$	−2.80473e6	−0.780468	−0.390234	+	0.920716i	$0.627606\pi$
$420$	3.21695e6	0.889858
$421$	3.57571e6	0.983234	0.491617	−	0.870812i	$-0.336406\pi$
$421$	3.57571e6	0.983234	0.491617	+	0.870812i	$0.336406\pi$
$422$	4.50359e6	1.23106
$423$	3.54566e6	0.963487
$424$	1.61633e6	0.436631
$425$	4.57888e6	1.22967
$426$	−5.36905e6	−1.43342
$427$	674108.	0.178920
$428$	−1.02610e6	−0.270758
$429$	1.60392e6	0.420764
$430$	3.54255e6	0.923943
$431$	−2.82711e6	−0.733078	−0.366539	−	0.930403i	$-0.619457\pi$
$431$	−2.82711e6	−0.733078	−0.366539	+	0.930403i	$0.619457\pi$
$432$	2.42048e6	0.624010
$433$	−765652.	−0.196251	−0.0981254	−	0.995174i	$-0.531285\pi$
$433$	−765652.	−0.196251	−0.0981254	+	0.995174i	$0.531285\pi$
$434$	−3.08972e6	−0.787399
$435$	6.46673e6	1.63856
$436$	−2.02608e6	−0.510434
$437$	−128605.	−0.0322147
$438$	−6.94239e6	−1.72912
$439$	4.65788e6	1.15352	0.576762	−	0.816912i	$-0.304316\pi$
$439$	4.65788e6	1.15352	0.576762	+	0.816912i	$0.304316\pi$
$440$	595519.	0.146644
$441$	−4.84208e6	−1.18559
$442$	−3.04613e6	−0.741639
$443$	−4.99700e6	−1.20976	−0.604881	−	0.796316i	$-0.706779\pi$
$443$	−4.99700e6	−1.20976	−0.604881	+	0.796316i	$0.706779\pi$
$444$	−16261.4	−0.00391471
$445$	−389941.	−0.0933466
$446$	288067.	0.0685735
$447$	−1.03689e7	−2.45450
$448$	−374705.	−0.0882053
$449$	165769.	0.0388050	0.0194025	−	0.999812i	$-0.493824\pi$
$449$	165769.	0.0388050	0.0194025	+	0.999812i	$0.493824\pi$
$450$	6.40091e6	1.49008
$451$	−1.11589e6	−0.258334
$452$	2.11125e6	0.486065
$453$	6.46608e6	1.48046
$454$	4.52960e6	1.03138
$455$	−3.26281e6	−0.738862
$456$	−3.09768e6	−0.697628
$457$	−8.07259e6	−1.80810	−0.904050	−	0.427428i	$-0.859420\pi$
$457$	−8.07259e6	−1.80810	−0.904050	+	0.427428i	$0.859420\pi$
$458$	−137695.	−0.0306728
$459$	1.55245e7	3.43942
$460$	−93436.3	−0.0205883
$461$	−5.87512e6	−1.28755	−0.643776	−	0.765214i	$-0.722633\pi$
$461$	−5.87512e6	−1.28755	−0.643776	+	0.765214i	$0.722633\pi$
$462$	1.26543e6	0.275825
$463$	−1.02289e6	−0.221757	−0.110878	−	0.993834i	$-0.535366\pi$
$463$	−1.02289e6	−0.221757	−0.110878	+	0.993834i	$0.535366\pi$
$464$	−753236.	−0.162419
$465$	−1.85577e7	−3.98007
$466$	2.75883e6	0.588518
$467$	−6.17201e6	−1.30959	−0.654794	−	0.755807i	$-0.727245\pi$
$467$	−6.17201e6	−1.30959	−0.654794	+	0.755807i	$0.727245\pi$
$468$	−4.25824e6	−0.898702
$469$	1.00855e6	0.211721
$470$	−1.90068e6	−0.396884
$471$	1.12036e7	2.32705
$472$	2.61036e6	0.539318
$473$	1.39352e6	0.286391
$474$	2.10190e6	0.429702
$475$	−4.72275e6	−0.960419
$476$	−2.40329e6	−0.486170
$477$	1.44920e7	2.91629
$478$	1.15991e6	0.232196
$479$	−7.00244e6	−1.39447	−0.697237	−	0.716841i	$-0.745588\pi$
$479$	−7.00244e6	−1.39447	−0.697237	+	0.716841i	$0.745588\pi$
$480$	−2.25058e6	−0.445852
$481$	16493.2	0.00325044
$482$	5.62692e6	1.10320
$483$	−198545.	−0.0387250
$484$	234256.	0.0454545
$485$	1.00582e7	1.94163
$486$	5.76122e6	1.10643
$487$	365769.	0.0698852	0.0349426	−	0.999389i	$-0.488875\pi$
$487$	365769.	0.0698852	0.0349426	+	0.999389i	$0.488875\pi$
$488$	−471607.	−0.0896459
$489$	−2.41160e6	−0.456072
$490$	2.59563e6	0.488375
$491$	5.00170e6	0.936297	0.468149	−	0.883650i	$-0.344921\pi$
$491$	5.00170e6	0.936297	0.468149	+	0.883650i	$0.344921\pi$
$492$	4.21717e6	0.785431
$493$	−4.83111e6	−0.895220
$494$	3.14184e6	0.579250
$495$	5.33942e6	0.979447
$496$	2.16157e6	0.394516
$497$	4.29638e6	0.780211
$498$	−6.78171e6	−1.22537
$499$	−1.63517e6	−0.293976	−0.146988	−	0.989138i	$-0.546958\pi$
$499$	−1.63517e6	−0.293976	−0.146988	+	0.989138i	$0.546958\pi$
$500$	413777.	0.0740186
$501$	1.55377e7	2.76562
$502$	2.32053e6	0.410986
$503$	5.20393e6	0.917088	0.458544	−	0.888672i	$-0.348371\pi$
$503$	5.20393e6	0.917088	0.458544	+	0.888672i	$0.348371\pi$
$504$	−3.35961e6	−0.589131
$505$	2.08515e6	0.363838
$506$	−36754.5	−0.00638167
$507$	−4.46368e6	−0.771212
$508$	1.90202e6	0.327006
$509$	−8.62390e6	−1.47540	−0.737699	−	0.675130i	$-0.764088\pi$
$509$	−8.62390e6	−1.47540	−0.737699	+	0.675130i	$0.764088\pi$
$510$	−1.44348e7	−2.45745
$511$	5.55539e6	0.941158
$512$	262144.	0.0441942
$513$	−1.60123e7	−2.68633
$514$	−1.62842e6	−0.271868
$515$	984551.	0.163576
$516$	−5.26636e6	−0.870736
$517$	−747659.	−0.123020
$518$	13012.6	0.00213078
$519$	1.01945e7	1.66130
$520$	2.28266e6	0.370198
$521$	140764.	0.0227194	0.0113597	−	0.999935i	$-0.496384\pi$
$521$	140764.	0.0227194	0.0113597	+	0.999935i	$0.496384\pi$
$522$	−6.75351e6	−1.08481
$523$	−9.29900e6	−1.48656	−0.743279	−	0.668981i	$-0.766731\pi$
$523$	−9.29900e6	−1.48656	−0.743279	+	0.668981i	$0.766731\pi$
$524$	3.29496e6	0.524229
$525$	−7.29117e6	−1.15451
$526$	−6.30700e6	−0.993936
$527$	1.38639e7	2.17450
$528$	−885298.	−0.138199
$529$	−6.43058e6	−0.999104
$530$	−7.76853e6	−1.20129
$531$	2.34044e7	3.60215
$532$	2.47880e6	0.379719
$533$	−4.27729e6	−0.652155
$534$	579686.	0.0879710
$535$	4.93175e6	0.744932
$536$	−705581.	−0.106080
$537$	−1.49102e7	−2.23124
$538$	−3.01037e6	−0.448399
$539$	1.02103e6	0.151379
$540$	−1.16335e7	−1.71683
$541$	−4.98590e6	−0.732403	−0.366202	−	0.930536i	$-0.619342\pi$
$541$	−4.98590e6	−0.732403	−0.366202	+	0.930536i	$0.619342\pi$
$542$	−834211.	−0.121977
$543$	−1.99503e7	−2.90369
$544$	1.68134e6	0.243590
$545$	9.73792e6	1.40435
$546$	4.85049e6	0.696313
$547$	−3.57048e6	−0.510221	−0.255111	−	0.966912i	$-0.582112\pi$
$547$	−3.57048e6	−0.510221	−0.255111	+	0.966912i	$0.582112\pi$
$548$	−3.14509e6	−0.447385
$549$	−4.22842e6	−0.598753
$550$	−1.34973e6	−0.190257
$551$	4.98291e6	0.699204
$552$	138902.	0.0194027
$553$	−1.68197e6	−0.233887
$554$	4.07703e6	0.564378
$555$	78156.9	0.0107705
$556$	−478983.	−0.0657102
$557$	1.24799e7	1.70441	0.852206	−	0.523207i	$-0.175264\pi$
$557$	1.24799e7	1.70441	0.852206	+	0.523207i	$0.175264\pi$
$558$	1.93806e7	2.63501
$559$	5.34144e6	0.722984
$560$	1.80094e6	0.242678
$561$	−5.67814e6	−0.761726
$562$	3.46239e6	0.462418
$563$	−5.12581e6	−0.681540	−0.340770	−	0.940147i	$-0.610688\pi$
$563$	−5.12581e6	−0.681540	−0.340770	+	0.940147i	$0.610688\pi$
$564$	2.82555e6	0.374028
$565$	−1.01473e7	−1.33730
$566$	6.90033e6	0.905376
$567$	−1.19644e7	−1.56290
$568$	−3.00575e6	−0.390915
$569$	−1.09610e6	−0.141929	−0.0709645	−	0.997479i	$-0.522608\pi$
$569$	−1.09610e6	−0.141929	−0.0709645	+	0.997479i	$0.522608\pi$
$570$	1.48883e7	1.91937
$571$	−1.08787e7	−1.39632	−0.698162	−	0.715940i	$-0.745998\pi$
$571$	−1.08787e7	−1.39632	−0.698162	+	0.715940i	$0.745998\pi$
$572$	897919.	0.114749
$573$	1.75176e7	2.22889
$574$	−3.37463e6	−0.427511
$575$	211772.	0.0267115
$576$	2.35038e6	0.295177
$577$	1.37408e7	1.71820	0.859101	−	0.511807i	$-0.171024\pi$
$577$	1.37408e7	1.71820	0.859101	+	0.511807i	$0.171024\pi$
$578$	5.10439e6	0.635512
$579$	−5.27202e6	−0.653553
$580$	3.62027e6	0.446859
$581$	5.42681e6	0.666967
$582$	−1.49525e7	−1.82981
$583$	−3.05587e6	−0.372360
$584$	−3.88656e6	−0.471556
$585$	2.04663e7	2.47258
$586$	5.01017e6	0.602711
$587$	7.50167e6	0.898593	0.449296	−	0.893383i	$-0.351675\pi$
$587$	7.50167e6	0.898593	0.449296	+	0.893383i	$0.351675\pi$
$588$	−3.85867e6	−0.460250
$589$	−1.42995e7	−1.69837
$590$	−1.25461e7	−1.48381
$591$	−2.94978e7	−3.47393
$592$	−9103.60	−0.00106760
$593$	1.23281e7	1.43966	0.719829	−	0.694151i	$-0.244220\pi$
$593$	1.23281e7	1.43966	0.719829	+	0.694151i	$0.244220\pi$
$594$	−4.57621e6	−0.532157
$595$	1.15509e7	1.33759
$596$	−5.80481e6	−0.669379
$597$	6.98677e6	0.802308
$598$	−140883.	−0.0161103
$599$	3.71959e6	0.423573	0.211786	−	0.977316i	$-0.432072\pi$
$599$	3.71959e6	0.423573	0.211786	+	0.977316i	$0.432072\pi$
$600$	5.10090e6	0.578454
$601$	−8.89207e6	−1.00419	−0.502096	−	0.864812i	$-0.667437\pi$
$601$	−8.89207e6	−1.00419	−0.502096	+	0.864812i	$0.667437\pi$
$602$	4.21421e6	0.473942
$603$	−6.32624e6	−0.708520
$604$	3.61990e6	0.403742
$605$	−1.12590e6	−0.125058
$606$	−3.09978e6	−0.342886
$607$	1.18740e7	1.30805	0.654027	−	0.756471i	$-0.273078\pi$
$607$	1.18740e7	1.30805	0.654027	+	0.756471i	$0.273078\pi$
$608$	−1.73417e6	−0.190254
$609$	7.69281e6	0.840508
$610$	2.26668e6	0.246641
$611$	−2.86583e6	−0.310561
$612$	1.50749e7	1.62696
$613$	9.08062e6	0.976033	0.488016	−	0.872834i	$-0.337721\pi$
$613$	9.08062e6	0.976033	0.488016	+	0.872834i	$0.337721\pi$
$614$	1.07927e7	1.15534
$615$	−2.02689e7	−2.16094
$616$	708427.	0.0752217
$617$	−9.98190e6	−1.05560	−0.527801	−	0.849368i	$-0.676983\pi$
$617$	−9.98190e6	−1.05560	−0.527801	+	0.849368i	$0.676983\pi$
$618$	−1.46363e6	−0.154156
$619$	−3.86586e6	−0.405527	−0.202763	−	0.979228i	$-0.564992\pi$
$619$	−3.86586e6	−0.405527	−0.202763	+	0.979228i	$0.564992\pi$
$620$	−1.03891e7	−1.08543
$621$	718003.	0.0747132
$622$	−6.97492e6	−0.722876
$623$	−463872.	−0.0478827
$624$	−3.39341e6	−0.348879
$625$	−1.07034e7	−1.09603
$626$	−4.60152e6	−0.469316
$627$	5.85654e6	0.594939
$628$	6.27211e6	0.634621
$629$	−58388.8	−0.00588441
$630$	1.61472e7	1.62087
$631$	1.45626e7	1.45601	0.728007	−	0.685570i	$-0.240447\pi$
$631$	1.45626e7	1.45601	0.728007	+	0.685570i	$0.240447\pi$
$632$	1.17671e6	0.117186
$633$	3.21783e7	3.19193
$634$	−4.64441e6	−0.458889
$635$	−9.14167e6	−0.899686
$636$	1.15487e7	1.13211
$637$	3.91368e6	0.382153
$638$	1.42409e6	0.138511
$639$	−2.69496e7	−2.61096
$640$	−1.25994e6	−0.121591
$641$	−1.34201e7	−1.29006	−0.645032	−	0.764155i	$-0.723156\pi$
$641$	−1.34201e7	−1.29006	−0.645032	+	0.764155i	$0.723156\pi$
$642$	−7.33154e6	−0.702033
$643$	1.50895e7	1.43929	0.719644	−	0.694344i	$-0.244305\pi$
$643$	1.50895e7	1.43929	0.719644	+	0.694344i	$0.244305\pi$
$644$	−111151.	−0.0105609
$645$	2.53117e7	2.39564
$646$	−1.11226e7	−1.04864
$647$	1.42974e7	1.34275	0.671377	−	0.741116i	$-0.265703\pi$
$647$	1.42974e7	1.34275	0.671377	+	0.741116i	$0.265703\pi$
$648$	8.37027e6	0.783073
$649$	−4.93520e6	−0.459932
$650$	−5.17363e6	−0.480299
$651$	−2.20761e7	−2.04160
$652$	−1.35009e6	−0.124378
$653$	−1.31607e6	−0.120780	−0.0603900	−	0.998175i	$-0.519234\pi$
$653$	−1.31607e6	−0.120780	−0.0603900	+	0.998175i	$0.519234\pi$
$654$	−1.44764e7	−1.32348
$655$	−1.58365e7	−1.44230
$656$	2.36090e6	0.214199
$657$	−3.48469e7	−3.14956
$658$	−2.26104e6	−0.203584
$659$	3.75917e6	0.337193	0.168596	−	0.985685i	$-0.446077\pi$
$659$	3.75917e6	0.337193	0.168596	+	0.985685i	$0.446077\pi$
$660$	4.25500e6	0.380224
$661$	−8.95170e6	−0.796896	−0.398448	−	0.917191i	$-0.630451\pi$
$661$	−8.95170e6	−0.796896	−0.398448	+	0.917191i	$0.630451\pi$
$662$	−9.27660e6	−0.822705
$663$	−2.17647e7	−1.92295
$664$	−3.79660e6	−0.334176
$665$	−1.19138e7	−1.04471
$666$	−81622.9	−0.00713060
$667$	−223438.	−0.0194465
$668$	8.69847e6	0.754226
$669$	2.05825e6	0.177800
$670$	3.39123e6	0.291857
$671$	891631.	0.0764503
$672$	−2.67728e6	−0.228702
$673$	−519050.	−0.0441745	−0.0220873	−	0.999756i	$-0.507031\pi$
$673$	−519050.	−0.0441745	−0.0220873	+	0.999756i	$0.507031\pi$
$674$	5.75144e6	0.487671
$675$	2.63672e7	2.22743
$676$	−2.49890e6	−0.210321
$677$	−4.12272e6	−0.345711	−0.172855	−	0.984947i	$-0.555299\pi$
$677$	−4.12272e6	−0.345711	−0.172855	+	0.984947i	$0.555299\pi$
$678$	1.50850e7	1.26029
$679$	1.19652e7	0.995967
$680$	−8.08102e6	−0.670184
$681$	3.23641e7	2.67421
$682$	−4.08672e6	−0.336445
$683$	8.35625e6	0.685425	0.342712	−	0.939440i	$-0.388654\pi$
$683$	8.35625e6	0.685425	0.342712	+	0.939440i	$0.388654\pi$
$684$	−1.55486e7	−1.27072
$685$	1.51162e7	1.23088
$686$	9.23783e6	0.749479
$687$	−983834.	−0.0795298
$688$	−2.94826e6	−0.237463
$689$	−1.17133e7	−0.940011
$690$	−667605.	−0.0533822
$691$	9.40353e6	0.749197	0.374598	−	0.927187i	$-0.377781\pi$
$691$	9.40353e6	0.749197	0.374598	+	0.927187i	$0.377781\pi$
$692$	5.70719e6	0.453061
$693$	6.35175e6	0.502413
$694$	2.30252e6	0.181470
$695$	2.30213e6	0.180787
$696$	−5.38189e6	−0.421126
$697$	1.51423e7	1.18062
$698$	−1.11081e7	−0.862980
$699$	1.97119e7	1.52593
$700$	−4.08181e6	−0.314853
$701$	−1.76888e7	−1.35957	−0.679787	−	0.733410i	$-0.737928\pi$
$701$	−1.76888e7	−1.35957	−0.679787	+	0.733410i	$0.737928\pi$
$702$	−1.75409e7	−1.34341
$703$	60223.4	0.00459597
$704$	−495616.	−0.0376889
$705$	−1.35804e7	−1.02906
$706$	8.72688e6	0.658942
$707$	2.48049e6	0.186633
$708$	1.86511e7	1.39837
$709$	−1.11343e7	−0.831853	−0.415926	−	0.909398i	$-0.636543\pi$
$709$	−1.11343e7	−0.831853	−0.415926	+	0.909398i	$0.636543\pi$
$710$	1.44465e7	1.07552
$711$	1.05504e7	0.782696
$712$	324525.	0.0239910
$713$	641202.	0.0472358
$714$	−1.71716e7	−1.26056
$715$	−4.31566e6	−0.315706
$716$	−8.34715e6	−0.608493
$717$	8.28761e6	0.602048
$718$	−8.59391e6	−0.622128
$719$	−9.55010e6	−0.688947	−0.344474	−	0.938796i	$-0.611943\pi$
$719$	−9.55010e6	−0.688947	−0.344474	+	0.938796i	$0.611943\pi$
$720$	−1.12966e7	−0.812114
$721$	1.17122e6	0.0839073
$722$	1.56772e6	0.111925
$723$	4.02045e7	2.86042
$724$	−1.11688e7	−0.791879
$725$	−8.20529e6	−0.579761
$726$	1.67377e6	0.117856
$727$	−1.89994e7	−1.33322	−0.666612	−	0.745405i	$-0.732256\pi$
$727$	−1.89994e7	−1.33322	−0.666612	+	0.745405i	$0.732256\pi$
$728$	2.71545e6	0.189895
$729$	9.38322e6	0.653933
$730$	1.86799e7	1.29738
$731$	−1.89096e7	−1.30885
$732$	−3.36964e6	−0.232438
$733$	−2.68111e7	−1.84312	−0.921561	−	0.388233i	$-0.873086\pi$
$733$	−2.68111e7	−1.84312	−0.921561	+	0.388233i	$0.873086\pi$
$734$	63352.2	0.00434032
$735$	1.85459e7	1.26628
$736$	77761.6	0.00529140
$737$	1.33399e6	0.0904657
$738$	2.11678e7	1.43065
$739$	−6.41899e6	−0.432370	−0.216185	−	0.976352i	$-0.569361\pi$
$739$	−6.41899e6	−0.432370	−0.216185	+	0.976352i	$0.569361\pi$
$740$	43754.6	0.00293727
$741$	2.24485e7	1.50190
$742$	−9.24142e6	−0.616210
$743$	4.66177e6	0.309798	0.154899	−	0.987930i	$-0.450495\pi$
$743$	4.66177e6	0.309798	0.154899	+	0.987930i	$0.450495\pi$
$744$	1.54445e7	1.02292
$745$	2.78996e7	1.84165
$746$	−1.57737e6	−0.103774
$747$	−3.40403e7	−2.23199
$748$	−3.17879e6	−0.207734
$749$	5.86679e6	0.382117
$750$	2.95645e6	0.191919
$751$	2.39792e7	1.55144	0.775721	−	0.631076i	$-0.217386\pi$
$751$	2.39792e7	1.55144	0.775721	+	0.631076i	$0.217386\pi$
$752$	1.58182e6	0.102003
$753$	1.65802e7	1.06562
$754$	5.45862e6	0.349667
$755$	−1.73983e7	−1.11081
$756$	−1.38392e7	−0.880656
$757$	4.65197e6	0.295051	0.147526	−	0.989058i	$-0.452869\pi$
$757$	4.65197e6	0.295051	0.147526	+	0.989058i	$0.452869\pi$
$758$	6.74005e6	0.426079
$759$	−262612.	−0.0165467
$760$	8.33492e6	0.523441
$761$	−1.91952e7	−1.20152	−0.600760	−	0.799429i	$-0.705135\pi$
$761$	−1.91952e7	−1.20152	−0.600760	+	0.799429i	$0.705135\pi$
$762$	1.35900e7	0.847876
$763$	1.15842e7	0.720368
$764$	9.80690e6	0.607853
$765$	−7.24544e7	−4.47622
$766$	1.57714e7	0.971175
$767$	−1.89170e7	−1.16108
$768$	1.87303e6	0.114589
$769$	1.47548e7	0.899743	0.449871	−	0.893093i	$-0.351470\pi$
$769$	1.47548e7	0.899743	0.449871	+	0.893093i	$0.351470\pi$
$770$	−3.40491e6	−0.206956
$771$	−1.16351e7	−0.704910
$772$	−2.95143e6	−0.178234
$773$	1.48823e7	0.895820	0.447910	−	0.894079i	$-0.352169\pi$
$773$	1.48823e7	0.895820	0.447910	+	0.894079i	$0.352169\pi$
$774$	−2.64341e7	−1.58603
$775$	2.35468e7	1.40824
$776$	−8.37085e6	−0.499017
$777$	92975.2	0.00552478
$778$	−2.28447e6	−0.135312
$779$	−1.56181e7	−0.922115
$780$	1.63097e7	0.959864
$781$	5.68275e6	0.333373
$782$	498749.	0.0291652
$783$	−2.78197e7	−1.62161
$784$	−2.16020e6	−0.125517
$785$	−3.01456e7	−1.74602
$786$	2.35426e7	1.35924
$787$	1.56041e7	0.898054	0.449027	−	0.893518i	$-0.351771\pi$
$787$	1.56041e7	0.898054	0.449027	+	0.893518i	$0.351771\pi$
$788$	−1.65137e7	−0.947393
$789$	−4.50637e7	−2.57712
$790$	−5.65560e6	−0.322412
$791$	−1.20712e7	−0.685976
$792$	−4.44369e6	−0.251728
$793$	3.41768e6	0.192996
$794$	2.46810e7	1.38935
$795$	−5.55064e7	−3.11476
$796$	3.91140e6	0.218801
$797$	2.19852e7	1.22599	0.612993	−	0.790088i	$-0.289965\pi$
$797$	2.19852e7	1.22599	0.612993	+	0.790088i	$0.289965\pi$
$798$	1.77111e7	0.984552
$799$	1.01455e7	0.562221
$800$	2.85564e6	0.157753
$801$	2.90969e6	0.160238
$802$	7.31353e6	0.401505
$803$	7.34802e6	0.402144
$804$	−5.04140e6	−0.275050
$805$	534226.	0.0290560
$806$	−1.56647e7	−0.849344
$807$	−2.15092e7	−1.16263
$808$	−1.73535e6	−0.0935101
$809$	2.91738e7	1.56719	0.783596	−	0.621271i	$-0.213383\pi$
$809$	2.91738e7	1.56719	0.783596	+	0.621271i	$0.213383\pi$
$810$	−4.02299e7	−2.15445
$811$	2.59750e7	1.38677	0.693383	−	0.720569i	$-0.256119\pi$
$811$	2.59750e7	1.38677	0.693383	+	0.720569i	$0.256119\pi$
$812$	4.30666e6	0.229219
$813$	−5.96046e6	−0.316267
$814$	17211.5	0.000910453 0
$815$	6.48891e6	0.342198
$816$	1.20132e7	0.631590
$817$	1.95038e7	1.02226
$818$	−2.37694e7	−1.24204
$819$	2.43467e7	1.26832
$820$	−1.13472e7	−0.589321
$821$	3.42686e7	1.77435	0.887174	−	0.461436i	$-0.152666\pi$
$821$	3.42686e7	1.77435	0.887174	+	0.461436i	$0.152666\pi$
$822$	−2.24717e7	−1.16000
$823$	−2.37132e7	−1.22037	−0.610184	−	0.792259i	$-0.708905\pi$
$823$	−2.37132e7	−1.22037	−0.610184	+	0.792259i	$0.708905\pi$
$824$	−819385.	−0.0420407
$825$	−9.64390e6	−0.493308
$826$	−1.49248e7	−0.761131
$827$	1.83274e7	0.931833	0.465916	−	0.884829i	$-0.345725\pi$
$827$	1.83274e7	0.931833	0.465916	+	0.884829i	$0.345725\pi$
$828$	697211.	0.0353418
$829$	−2.66383e7	−1.34623	−0.673115	−	0.739538i	$-0.735044\pi$
$829$	−2.66383e7	−1.34623	−0.673115	+	0.739538i	$0.735044\pi$
$830$	1.82476e7	0.919411
$831$	2.91305e7	1.46334
$832$	−1.89973e6	−0.0951445
$833$	−1.38551e7	−0.691826
$834$	−3.42235e6	−0.170376
$835$	−4.18074e7	−2.07509
$836$	3.27867e6	0.162249
$837$	7.98344e7	3.93891
$838$	−1.12189e7	−0.551874
$839$	1.46709e7	0.719537	0.359768	−	0.933042i	$-0.382856\pi$
$839$	1.46709e7	0.719537	0.359768	+	0.933042i	$0.382856\pi$
$840$	1.28678e7	0.629225
$841$	−1.18539e7	−0.577923
$842$	1.43028e7	0.695251
$843$	2.47389e7	1.19898
$844$	1.80144e7	0.870488
$845$	1.20104e7	0.578652
$846$	1.41826e7	0.681288
$847$	−1.33937e6	−0.0641493
$848$	6.46530e6	0.308745
$849$	4.93031e7	2.34750
$850$	1.83155e7	0.869505
$851$	−2700.47	−0.000127825 0
$852$	−2.14762e7	−1.01358
$853$	−1.74709e7	−0.822133	−0.411066	−	0.911605i	$-0.634844\pi$
$853$	−1.74709e7	−0.822133	−0.411066	+	0.911605i	$0.634844\pi$
$854$	2.69643e6	0.126516
$855$	7.47309e7	3.49611
$856$	−4.10441e6	−0.191455
$857$	−2.49580e7	−1.16080	−0.580402	−	0.814330i	$-0.697104\pi$
$857$	−2.49580e7	−1.16080	−0.580402	+	0.814330i	$0.697104\pi$
$858$	6.41566e6	0.297525
$859$	−1.42612e7	−0.659439	−0.329719	−	0.944079i	$-0.606954\pi$
$859$	−1.42612e7	−0.659439	−0.329719	+	0.944079i	$0.606954\pi$
$860$	1.41702e7	0.653327
$861$	−2.41119e7	−1.10847
$862$	−1.13085e7	−0.518364
$863$	494514.	0.0226022	0.0113011	−	0.999936i	$-0.496403\pi$
$863$	494514.	0.0226022	0.0113011	+	0.999936i	$0.496403\pi$
$864$	9.68190e6	0.441242
$865$	−2.74304e7	−1.24650
$866$	−3.06261e6	−0.138770
$867$	3.64710e7	1.64778
$868$	−1.23589e7	−0.556775
$869$	−2.22471e6	−0.0999366
$870$	2.58669e7	1.15864
$871$	5.11327e6	0.228378
$872$	−8.10431e6	−0.360932
$873$	−7.50530e7	−3.33298
$874$	−514419.	−0.0227792
$875$	−2.36579e6	−0.104461
$876$	−2.77696e7	−1.22267
$877$	−8.07539e6	−0.354539	−0.177270	−	0.984162i	$-0.556726\pi$
$877$	−8.07539e6	−0.354539	−0.177270	+	0.984162i	$0.556726\pi$
$878$	1.86315e7	0.815665
$879$	3.57979e7	1.56273
$880$	2.38207e6	0.103693
$881$	−5.24166e6	−0.227525	−0.113763	−	0.993508i	$-0.536290\pi$
$881$	−5.24166e6	−0.227525	−0.113763	+	0.993508i	$0.536290\pi$
$882$	−1.93683e7	−0.838340
$883$	−4.02805e7	−1.73857	−0.869287	−	0.494308i	$-0.835422\pi$
$883$	−4.02805e7	−1.73857	−0.869287	+	0.494308i	$0.835422\pi$
$884$	−1.21845e7	−0.524418
$885$	−8.96425e7	−3.84730
$886$	−1.99880e7	−0.855431
$887$	1.38423e7	0.590745	0.295373	−	0.955382i	$-0.404556\pi$
$887$	1.38423e7	0.590745	0.295373	+	0.955382i	$0.404556\pi$
$888$	−65045.5	−0.00276812
$889$	−1.08749e7	−0.461499
$890$	−1.55976e6	−0.0660060
$891$	−1.58250e7	−0.667807
$892$	1.15227e6	0.0484888
$893$	−1.04643e7	−0.439118
$894$	−4.14755e7	−1.73559
$895$	4.01188e7	1.67413
$896$	−1.49882e6	−0.0623706
$897$	−1.00661e6	−0.0417715
$898$	663076.	0.0274393
$899$	−2.48439e7	−1.02523
$900$	2.56036e7	1.05365
$901$	4.14672e7	1.70174
$902$	−4.46357e6	−0.182669
$903$	3.01107e7	1.22886
$904$	8.44501e6	0.343700
$905$	5.36803e7	2.17868
$906$	2.58643e7	1.04684
$907$	−5.53908e6	−0.223573	−0.111786	−	0.993732i	$-0.535657\pi$
$907$	−5.53908e6	−0.223573	−0.111786	+	0.993732i	$0.535657\pi$
$908$	1.81184e7	0.729298
$909$	−1.55591e7	−0.624562
$910$	−1.30512e7	−0.522454
$911$	−1.76513e7	−0.704660	−0.352330	−	0.935876i	$-0.614611\pi$
$911$	−1.76513e7	−0.704660	−0.352330	+	0.935876i	$0.614611\pi$
$912$	−1.23907e7	−0.493297
$913$	7.17795e6	0.284986
$914$	−3.22903e7	−1.27852
$915$	1.61955e7	0.639501
$916$	−550779.	−0.0216890
$917$	−1.88391e7	−0.739837
$918$	6.20979e7	2.43204
$919$	−2.80718e7	−1.09643	−0.548215	−	0.836338i	$-0.684692\pi$
$919$	−2.80718e7	−1.09643	−0.548215	+	0.836338i	$0.684692\pi$
$920$	−373745.	−0.0145581
$921$	7.71145e7	2.99562
$922$	−2.35005e7	−0.910436
$923$	2.17824e7	0.841591
$924$	5.06173e6	0.195038
$925$	−99169.1	−0.00381085
$926$	−4.09156e6	−0.156806
$927$	−7.34660e6	−0.280794
$928$	−3.01294e6	−0.114847
$929$	−3.51046e6	−0.133452	−0.0667259	−	0.997771i	$-0.521255\pi$
$929$	−3.51046e6	−0.133452	−0.0667259	+	0.997771i	$0.521255\pi$
$930$	−7.42307e7	−2.81434
$931$	1.42904e7	0.540345
$932$	1.10353e7	0.416145
$933$	−4.98361e7	−1.87430
$934$	−2.46881e7	−0.926019
$935$	1.52782e7	0.571535
$936$	−1.70330e7	−0.635478
$937$	−3.60265e7	−1.34052	−0.670260	−	0.742126i	$-0.733818\pi$
$937$	−3.60265e7	−1.34052	−0.670260	+	0.742126i	$0.733818\pi$
$938$	4.03420e6	0.149710
$939$	−3.28780e7	−1.21686
$940$	−7.60270e6	−0.280639
$941$	2.51917e7	0.927435	0.463717	−	0.885983i	$-0.346515\pi$
$941$	2.51917e7	0.927435	0.463717	+	0.885983i	$0.346515\pi$
$942$	4.48144e7	1.64547
$943$	700329.	0.0256462
$944$	1.04414e7	0.381355
$945$	6.65151e7	2.42293
$946$	5.57406e6	0.202509
$947$	2.44815e6	0.0887082	0.0443541	−	0.999016i	$-0.485877\pi$
$947$	2.44815e6	0.0887082	0.0443541	+	0.999016i	$0.485877\pi$
$948$	8.40761e6	0.303845
$949$	2.81655e7	1.01520
$950$	−1.88910e7	−0.679119
$951$	−3.31845e7	−1.18983
$952$	−9.61316e6	−0.343774
$953$	−4.51778e7	−1.61136	−0.805681	−	0.592349i	$-0.798200\pi$
$953$	−4.51778e7	−1.61136	−0.805681	+	0.592349i	$0.798200\pi$
$954$	5.79679e7	2.06213
$955$	−4.71348e7	−1.67237
$956$	4.63965e6	0.164188
$957$	1.01751e7	0.359137
$958$	−2.80098e7	−0.986042
$959$	1.79822e7	0.631387
$960$	−9.00231e6	−0.315265
$961$	4.26658e7	1.49029
$962$	65972.9	0.00229841
$963$	−3.68001e7	−1.27874
$964$	2.25077e7	0.780078
$965$	1.41855e7	0.490371
$966$	−794181.	−0.0273827
$967$	−1.09821e7	−0.377676	−0.188838	−	0.982008i	$-0.560472\pi$
$967$	−1.09821e7	−0.377676	−0.188838	+	0.982008i	$0.560472\pi$
$968$	937024.	0.0321412
$969$	−7.94716e7	−2.71896
$970$	4.02328e7	1.37294
$971$	8.62580e6	0.293597	0.146798	−	0.989166i	$-0.453103\pi$
$971$	8.62580e6	0.293597	0.146798	+	0.989166i	$0.453103\pi$
$972$	2.30449e7	0.782364
$973$	2.73861e6	0.0927358
$974$	1.46308e6	0.0494163
$975$	−3.69657e7	−1.24534
$976$	−1.88643e6	−0.0633892
$977$	1.06350e7	0.356451	0.178226	−	0.983990i	$-0.442964\pi$
$977$	1.06350e7	0.356451	0.178226	+	0.983990i	$0.442964\pi$
$978$	−9.64641e6	−0.322492
$979$	−613556.	−0.0204596
$980$	1.03825e7	0.345333
$981$	−7.26632e7	−2.41069
$982$	2.00068e7	0.662062
$983$	2.66620e7	0.880053	0.440026	−	0.897985i	$-0.354969\pi$
$983$	2.66620e7	0.880053	0.440026	+	0.897985i	$0.354969\pi$
$984$	1.68687e7	0.555384
$985$	7.93698e7	2.60654
$986$	−1.93244e7	−0.633016
$987$	−1.61552e7	−0.527861
$988$	1.25673e7	0.409592
$989$	−874565.	−0.0284316
$990$	2.13577e7	0.692573
$991$	2.56353e7	0.829190	0.414595	−	0.910006i	$-0.363923\pi$
$991$	2.56353e7	0.829190	0.414595	+	0.910006i	$0.363923\pi$
$992$	8.64628e6	0.278965
$993$	−6.62816e7	−2.13314
$994$	1.71855e7	0.551692
$995$	−1.87993e7	−0.601984
$996$	−2.71268e7	−0.866465
$997$	−588022.	−0.0187351	−0.00936754	−	0.999956i	$-0.502982\pi$
$997$	−588022.	−0.0187351	−0.00936754	+	0.999956i	$0.502982\pi$
$998$	−6.54069e6	−0.207873
$999$	−336228.	−0.0106591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.a.d.1.2	✓	2
3.2	odd	2		198.6.a.k.1.2		2
4.3	odd	2		176.6.a.f.1.1		2
5.2	odd	4		550.6.b.j.199.3		4
5.3	odd	4		550.6.b.j.199.2		4
5.4	even	2		550.6.a.h.1.1		2
7.6	odd	2		1078.6.a.h.1.1		2
8.3	odd	2		704.6.a.p.1.2		2
8.5	even	2		704.6.a.k.1.1		2
11.10	odd	2		242.6.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.a.d.1.2	✓	2	1.1	even	1	trivial
176.6.a.f.1.1		2	4.3	odd	2
198.6.a.k.1.2		2	3.2	odd	2
242.6.a.g.1.2		2	11.10	odd	2
550.6.a.h.1.1		2	5.4	even	2
550.6.b.j.199.2		4	5.3	odd	4
550.6.b.j.199.3		4	5.2	odd	4
704.6.a.k.1.1		2	8.5	even	2
704.6.a.p.1.2		2	8.3	odd	2
1078.6.a.h.1.1		2	7.6	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +28.5801 q^{3} +16.0000 q^{4} -76.9006 q^{5} +114.321 q^{6} -91.4808 q^{7} +64.0000 q^{8} +573.824 q^{9} -307.603 q^{10} -121.000 q^{11} +457.282 q^{12} -463.801 q^{13} -365.923 q^{14} -2197.83 q^{15} +256.000 q^{16} +1641.94 q^{17} +2295.29 q^{18} -1693.53 q^{19} -1230.41 q^{20} -2614.53 q^{21} -484.000 q^{22} +75.9391 q^{23} +1829.13 q^{24} +2788.71 q^{25} -1855.21 q^{26} +9454.98 q^{27} -1463.69 q^{28} -2942.33 q^{29} -8791.32 q^{30} +8443.63 q^{31} +1024.00 q^{32} -3458.20 q^{33} +6567.74 q^{34} +7034.93 q^{35} +9181.18 q^{36} -35.5610 q^{37} -6774.10 q^{38} -13255.5 q^{39} -4921.64 q^{40} +9222.25 q^{41} -10458.1 q^{42} -11516.7 q^{43} -1936.00 q^{44} -44127.4 q^{45} +303.756 q^{46} +6179.00 q^{47} +7316.51 q^{48} -8438.27 q^{49} +11154.8 q^{50} +46926.7 q^{51} -7420.82 q^{52} +25255.1 q^{53} +37819.9 q^{54} +9304.98 q^{55} -5854.77 q^{56} -48401.2 q^{57} -11769.3 q^{58} +40786.8 q^{59} -35165.3 q^{60} -7368.85 q^{61} +33774.5 q^{62} -52493.8 q^{63} +4096.00 q^{64} +35666.6 q^{65} -13832.8 q^{66} -11024.7 q^{67} +26271.0 q^{68} +2170.35 q^{69} +28139.7 q^{70} -46964.9 q^{71} +36724.7 q^{72} -60727.5 q^{73} -142.244 q^{74} +79701.6 q^{75} -27096.4 q^{76} +11069.2 q^{77} -53022.0 q^{78} +18386.1 q^{79} -19686.6 q^{80} +130785. q^{81} +36889.0 q^{82} -59321.9 q^{83} -41832.5 q^{84} -126266. q^{85} -46066.6 q^{86} -84092.1 q^{87} -7744.00 q^{88} +5070.71 q^{89} -176510. q^{90} +42428.9 q^{91} +1215.03 q^{92} +241320. q^{93} +24716.0 q^{94} +130233. q^{95} +29266.1 q^{96} -130795. q^{97} -33753.1 q^{98} -69432.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 29 q^{3} + 32 q^{4} - 13 q^{5} + 116 q^{6} - 14 q^{7} + 128 q^{8} + 331 q^{9} - 52 q^{10} - 242 q^{11} + 464 q^{12} - 646 q^{13} - 56 q^{14} - 2171 q^{15} + 512 q^{16} - 208 q^{17} + 1324 q^{18}+ \cdots - 40051 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 29 * q^3 + 32 * q^4 - 13 * q^5 + 116 * q^6 - 14 * q^7 + 128 * q^8 + 331 * q^9 - 52 * q^10 - 242 * q^11 + 464 * q^12 - 646 * q^13 - 56 * q^14 - 2171 * q^15 + 512 * q^16 - 208 * q^17 + 1324 * q^18 - 2148 * q^19 - 208 * q^20 - 2582 * q^21 - 968 * q^22 + 349 * q^23 + 1856 * q^24 + 3747 * q^25 - 2584 * q^26 + 9251 * q^27 - 224 * q^28 + 4422 * q^29 - 8684 * q^30 + 14381 * q^31 + 2048 * q^32 - 3509 * q^33 - 832 * q^34 + 11986 * q^35 + 5296 * q^36 - 4267 * q^37 - 8592 * q^38 - 13332 * q^39 - 832 * q^40 - 10110 * q^41 - 10328 * q^42 - 9798 * q^43 - 3872 * q^44 - 59644 * q^45 + 1396 * q^46 + 21144 * q^47 + 7424 * q^48 - 19242 * q^49 + 14988 * q^50 + 46150 * q^51 - 10336 * q^52 + 39584 * q^53 + 37004 * q^54 + 1573 * q^55 - 896 * q^56 - 48592 * q^57 + 17688 * q^58 + 90951 * q^59 - 34736 * q^60 - 29550 * q^61 + 57524 * q^62 - 71308 * q^63 + 8192 * q^64 + 24024 * q^65 - 14036 * q^66 - 64149 * q^67 - 3328 * q^68 + 2285 * q^69 + 47944 * q^70 + 23583 * q^71 + 21184 * q^72 - 39058 * q^73 - 17068 * q^74 + 80104 * q^75 - 34368 * q^76 + 1694 * q^77 - 53328 * q^78 - 54974 * q^79 - 3328 * q^80 + 189706 * q^81 - 40440 * q^82 + 29986 * q^83 - 41312 * q^84 - 244478 * q^85 - 39192 * q^86 - 81000 * q^87 - 15488 * q^88 - 18047 * q^89 - 238576 * q^90 + 28312 * q^91 + 5584 * q^92 + 243813 * q^93 + 84576 * q^94 + 101192 * q^95 + 29696 * q^96 - 30309 * q^97 - 76968 * q^98 - 40051 * q^99

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