LMFDB - Embedded newform 26.6.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,6,Mod(1,26)] 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("26.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	26.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8] 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:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{849}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 212 $ x^2 - x - 212
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			1.1
Root			$15.0688$ of defining polynomial
Character	$\chi$	$=$	26.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} -10.0688 q^{3} +16.0000 q^{4} +80.2064 q^{5} -40.2752 q^{6} +208.619 q^{7} +64.0000 q^{8} -141.619 q^{9} +320.826 q^{10} -459.651 q^{11} -161.101 q^{12} -169.000 q^{13} +834.477 q^{14} -807.582 q^{15} +256.000 q^{16} +1784.88 q^{17} -566.477 q^{18} -2122.13 q^{19} +1283.30 q^{20} -2100.55 q^{21} -1838.61 q^{22} -3095.43 q^{23} -644.403 q^{24} +3308.07 q^{25} -676.000 q^{26} +3872.65 q^{27} +3337.91 q^{28} -2896.16 q^{29} -3230.33 q^{30} -4108.01 q^{31} +1024.00 q^{32} +4628.14 q^{33} +7139.50 q^{34} +16732.6 q^{35} -2265.91 q^{36} +6323.82 q^{37} -8488.51 q^{38} +1701.63 q^{39} +5133.21 q^{40} -913.787 q^{41} -8402.18 q^{42} -5225.07 q^{43} -7354.42 q^{44} -11358.8 q^{45} -12381.7 q^{46} -6844.14 q^{47} -2577.61 q^{48} +26715.0 q^{49} +13232.3 q^{50} -17971.6 q^{51} -2704.00 q^{52} -13932.9 q^{53} +15490.6 q^{54} -36867.0 q^{55} +13351.6 q^{56} +21367.3 q^{57} -11584.7 q^{58} -18353.4 q^{59} -12921.3 q^{60} +42558.3 q^{61} -16432.0 q^{62} -29544.5 q^{63} +4096.00 q^{64} -13554.9 q^{65} +18512.6 q^{66} +32199.0 q^{67} +28558.0 q^{68} +31167.3 q^{69} +66930.4 q^{70} +28557.5 q^{71} -9063.63 q^{72} -21354.2 q^{73} +25295.3 q^{74} -33308.3 q^{75} -33954.1 q^{76} -95892.1 q^{77} +6806.51 q^{78} +41396.7 q^{79} +20532.8 q^{80} -4579.53 q^{81} -3655.15 q^{82} -35400.0 q^{83} -33608.7 q^{84} +143158. q^{85} -20900.3 q^{86} +29160.9 q^{87} -29417.7 q^{88} -11452.0 q^{89} -45435.1 q^{90} -35256.6 q^{91} -49526.9 q^{92} +41362.7 q^{93} -27376.5 q^{94} -170208. q^{95} -10310.5 q^{96} +135588. q^{97} +106860. q^{98} +65095.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} + 9 q^{3} + 32 q^{4} + 73 q^{5} + 36 q^{6} + 155 q^{7} + 128 q^{8} - 21 q^{9} + 292 q^{10} - 220 q^{11} + 144 q^{12} - 338 q^{13} + 620 q^{14} - 945 q^{15} + 512 q^{16} - 189 q^{17} - 84 q^{18}+ \cdots + 94002 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 + 9 * q^3 + 32 * q^4 + 73 * q^5 + 36 * q^6 + 155 * q^7 + 128 * q^8 - 21 * q^9 + 292 * q^10 - 220 * q^11 + 144 * q^12 - 338 * q^13 + 620 * q^14 - 945 * q^15 + 512 * q^16 - 189 * q^17 - 84 * q^18 - 2496 * q^19 + 1168 * q^20 - 3123 * q^21 - 880 * q^22 - 3044 * q^23 + 576 * q^24 + 235 * q^25 - 1352 * q^26 + 1539 * q^27 + 2480 * q^28 + 1900 * q^29 - 3780 * q^30 + 2798 * q^31 + 2048 * q^32 + 9198 * q^33 - 756 * q^34 + 17119 * q^35 - 336 * q^36 + 17805 * q^37 - 9984 * q^38 - 1521 * q^39 + 4672 * q^40 + 11634 * q^41 - 12492 * q^42 - 4069 * q^43 - 3520 * q^44 - 12228 * q^45 - 12176 * q^46 - 25489 * q^47 + 2304 * q^48 + 12783 * q^49 + 940 * q^50 - 55611 * q^51 - 5408 * q^52 - 4614 * q^53 + 6156 * q^54 - 38594 * q^55 + 9920 * q^56 + 14238 * q^57 + 7600 * q^58 - 23420 * q^59 - 15120 * q^60 + 96830 * q^61 + 11192 * q^62 - 36012 * q^63 + 8192 * q^64 - 12337 * q^65 + 36792 * q^66 + 72440 * q^67 - 3024 * q^68 + 32148 * q^69 + 68476 * q^70 - 36679 * q^71 - 1344 * q^72 + 47152 * q^73 + 71220 * q^74 - 91908 * q^75 - 39936 * q^76 - 108742 * q^77 - 6084 * q^78 + 52024 * q^79 + 18688 * q^80 - 78390 * q^81 + 46536 * q^82 - 37758 * q^83 - 49968 * q^84 + 157383 * q^85 - 16276 * q^86 + 120618 * q^87 - 14080 * q^88 - 105072 * q^89 - 48912 * q^90 - 26195 * q^91 - 48704 * q^92 + 173052 * q^93 - 101956 * q^94 - 167514 * q^95 + 9216 * q^96 + 104392 * q^97 + 51132 * q^98 + 94002 * 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
$3$	−10.0688	−0.645914	−0.322957	−	0.946414i	$-0.604677\pi$
$3$	−10.0688	−0.645914	−0.322957	+	0.946414i	$0.604677\pi$
$4$	16.0000	0.500000
$5$	80.2064	1.43478	0.717388	−	0.696674i	$-0.245338\pi$
$5$	80.2064	1.43478	0.717388	+	0.696674i	$0.245338\pi$
$6$	−40.2752	−0.456730
$7$	208.619	1.60920	0.804599	−	0.593819i	$-0.202381\pi$
$7$	208.619	1.60920	0.804599	+	0.593819i	$0.202381\pi$
$8$	64.0000	0.353553
$9$	−141.619	−0.582795
$10$	320.826	1.01454
$11$	−459.651	−1.14537	−0.572686	−	0.819775i	$-0.694099\pi$
$11$	−459.651	−1.14537	−0.572686	+	0.819775i	$0.694099\pi$
$12$	−161.101	−0.322957
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	834.477	1.13787
$15$	−807.582	−0.926742
$16$	256.000	0.250000
$17$	1784.88	1.49791	0.748955	−	0.662621i	$-0.230556\pi$
$17$	1784.88	1.49791	0.748955	+	0.662621i	$0.230556\pi$
$18$	−566.477	−0.412098
$19$	−2122.13	−1.34861	−0.674307	−	0.738451i	$-0.735558\pi$
$19$	−2122.13	−1.34861	−0.674307	+	0.738451i	$0.735558\pi$
$20$	1283.30	0.717388
$21$	−2100.55	−1.03940
$22$	−1838.61	−0.809901
$23$	−3095.43	−1.22012	−0.610059	−	0.792356i	$-0.708854\pi$
$23$	−3095.43	−1.22012	−0.610059	+	0.792356i	$0.708854\pi$
$24$	−644.403	−0.228365
$25$	3308.07	1.05858
$26$	−676.000	−0.196116
$27$	3872.65	1.02235
$28$	3337.91	0.804599
$29$	−2896.16	−0.639482	−0.319741	−	0.947505i	$-0.603596\pi$
$29$	−2896.16	−0.639482	−0.319741	+	0.947505i	$0.603596\pi$
$30$	−3230.33	−0.655305
$31$	−4108.01	−0.767763	−0.383881	−	0.923382i	$-0.625413\pi$
$31$	−4108.01	−0.767763	−0.383881	+	0.923382i	$0.625413\pi$
$32$	1024.00	0.176777
$33$	4628.14	0.739812
$34$	7139.50	1.05918
$35$	16732.6	2.30884
$36$	−2265.91	−0.291398
$37$	6323.82	0.759408	0.379704	−	0.925108i	$-0.376026\pi$
$37$	6323.82	0.759408	0.379704	+	0.925108i	$0.376026\pi$
$38$	−8488.51	−0.953614
$39$	1701.63	0.179144
$40$	5133.21	0.507270
$41$	−913.787	−0.0848956	−0.0424478	−	0.999099i	$-0.513516\pi$
$41$	−913.787	−0.0848956	−0.0424478	+	0.999099i	$0.513516\pi$
$42$	−8402.18	−0.734969
$43$	−5225.07	−0.430944	−0.215472	−	0.976510i	$-0.569129\pi$
$43$	−5225.07	−0.430944	−0.215472	+	0.976510i	$0.569129\pi$
$44$	−7354.42	−0.572686
$45$	−11358.8	−0.836180
$46$	−12381.7	−0.862753
$47$	−6844.14	−0.451933	−0.225966	−	0.974135i	$-0.572554\pi$
$47$	−6844.14	−0.451933	−0.225966	+	0.974135i	$0.572554\pi$
$48$	−2577.61	−0.161478
$49$	26715.0	1.58952
$50$	13232.3	0.748530
$51$	−17971.6	−0.967521
$52$	−2704.00	−0.138675
$53$	−13932.9	−0.681321	−0.340661	−	0.940186i	$-0.610651\pi$
$53$	−13932.9	−0.681321	−0.340661	+	0.940186i	$0.610651\pi$
$54$	15490.6	0.722910
$55$	−36867.0	−1.64335
$56$	13351.6	0.568937
$57$	21367.3	0.871088
$58$	−11584.7	−0.452182
$59$	−18353.4	−0.686414	−0.343207	−	0.939260i	$-0.611513\pi$
$59$	−18353.4	−0.686414	−0.343207	+	0.939260i	$0.611513\pi$
$60$	−12921.3	−0.463371
$61$	42558.3	1.46440	0.732201	−	0.681089i	$-0.238493\pi$
$61$	42558.3	1.46440	0.732201	+	0.681089i	$0.238493\pi$
$62$	−16432.0	−0.542890
$63$	−29544.5	−0.937832
$64$	4096.00	0.125000
$65$	−13554.9	−0.397935
$66$	18512.6	0.523126
$67$	32199.0	0.876305	0.438153	−	0.898901i	$-0.355633\pi$
$67$	32199.0	0.876305	0.438153	+	0.898901i	$0.355633\pi$
$68$	28558.0	0.748955
$69$	31167.3	0.788091
$70$	66930.4	1.63259
$71$	28557.5	0.672317	0.336158	−	0.941805i	$-0.390872\pi$
$71$	28557.5	0.672317	0.336158	+	0.941805i	$0.390872\pi$
$72$	−9063.63	−0.206049
$73$	−21354.2	−0.469003	−0.234502	−	0.972116i	$-0.575346\pi$
$73$	−21354.2	−0.469003	−0.234502	+	0.972116i	$0.575346\pi$
$74$	25295.3	0.536983
$75$	−33308.3	−0.683753
$76$	−33954.1	−0.674307
$77$	−95892.1	−1.84313
$78$	6806.51	0.126674
$79$	41396.7	0.746273	0.373136	−	0.927777i	$-0.378282\pi$
$79$	41396.7	0.746273	0.373136	+	0.927777i	$0.378282\pi$
$80$	20532.8	0.358694
$81$	−4579.53	−0.0775547
$82$	−3655.15	−0.0600303
$83$	−35400.0	−0.564038	−0.282019	−	0.959409i	$-0.591004\pi$
$83$	−35400.0	−0.564038	−0.282019	+	0.959409i	$0.591004\pi$
$84$	−33608.7	−0.519701
$85$	143158.	2.14916
$86$	−20900.3	−0.304723
$87$	29160.9	0.413050
$88$	−29417.7	−0.404950
$89$	−11452.0	−0.153252	−0.0766259	−	0.997060i	$-0.524415\pi$
$89$	−11452.0	−0.153252	−0.0766259	+	0.997060i	$0.524415\pi$
$90$	−45435.1	−0.591269
$91$	−35256.6	−0.446311
$92$	−49526.9	−0.610059
$93$	41362.7	0.495909
$94$	−27376.5	−0.319565
$95$	−170208.	−1.93496
$96$	−10310.5	−0.114183
$97$	135588.	1.46316	0.731579	−	0.681756i	$-0.238784\pi$
$97$	135588.	1.46316	0.731579	+	0.681756i	$0.238784\pi$
$98$	106860.	1.12396
$99$	65095.5	0.667518
$100$	52929.1	0.529291
$101$	−193417.	−1.88665	−0.943327	−	0.331866i	$-0.892322\pi$
$101$	−193417.	−1.88665	−0.943327	+	0.331866i	$0.892322\pi$
$102$	−71886.2	−0.684141
$103$	119127.	1.10641	0.553207	−	0.833044i	$-0.313404\pi$
$103$	119127.	1.10641	0.553207	+	0.833044i	$0.313404\pi$
$104$	−10816.0	−0.0980581
$105$	−168477.	−1.49131
$106$	−55731.6	−0.481767
$107$	−56734.5	−0.479057	−0.239529	−	0.970889i	$-0.576993\pi$
$107$	−56734.5	−0.479057	−0.239529	+	0.970889i	$0.576993\pi$
$108$	61962.5	0.511175
$109$	120715.	0.973182	0.486591	−	0.873630i	$-0.338240\pi$
$109$	120715.	0.973182	0.486591	+	0.873630i	$0.338240\pi$
$110$	−147468.	−1.16203
$111$	−63673.3	−0.490512
$112$	53406.5	0.402299
$113$	266090.	1.96034	0.980172	−	0.198146i	$-0.0634922\pi$
$113$	266090.	1.96034	0.980172	+	0.198146i	$0.0634922\pi$
$114$	85469.2	0.615953
$115$	−248273.	−1.75059
$116$	−46338.6	−0.319741
$117$	23933.6	0.161638
$118$	−73413.5	−0.485368
$119$	372359.	2.41043
$120$	−51685.3	−0.327653
$121$	50228.3	0.311878
$122$	170233.	1.03549
$123$	9200.74	0.0548353
$124$	−65728.1	−0.383881
$125$	14683.2	0.0840516
$126$	−118178.	−0.663148
$127$	−48634.0	−0.267566	−0.133783	−	0.991011i	$-0.542712\pi$
$127$	−48634.0	−0.267566	−0.133783	+	0.991011i	$0.542712\pi$
$128$	16384.0	0.0883883
$129$	52610.2	0.278353
$130$	−54219.5	−0.281383
$131$	214673.	1.09295	0.546473	−	0.837477i	$-0.315970\pi$
$131$	214673.	1.09295	0.546473	+	0.837477i	$0.315970\pi$
$132$	74050.2	0.369906
$133$	−442717.	−2.17019
$134$	128796.	0.619642
$135$	310612.	1.46684
$136$	114232.	0.529591
$137$	−124409.	−0.566307	−0.283154	−	0.959075i	$-0.591381\pi$
$137$	−124409.	−0.566307	−0.283154	+	0.959075i	$0.591381\pi$
$138$	124669.	0.557264
$139$	−90271.7	−0.396292	−0.198146	−	0.980173i	$-0.563492\pi$
$139$	−90271.7	−0.396292	−0.198146	+	0.980173i	$0.563492\pi$
$140$	267722.	1.15442
$141$	68912.2	0.291910
$142$	114230.	0.475400
$143$	77681.1	0.317669
$144$	−36254.5	−0.145699
$145$	−232291.	−0.917513
$146$	−85416.7	−0.331635
$147$	−268988.	−1.02669
$148$	101181.	0.379704
$149$	−288945.	−1.06623	−0.533113	−	0.846044i	$-0.678978\pi$
$149$	−288945.	−1.06623	−0.533113	+	0.846044i	$0.678978\pi$
$150$	−133233.	−0.483486
$151$	180912.	0.645693	0.322846	−	0.946451i	$-0.395360\pi$
$151$	180912.	0.645693	0.322846	+	0.946451i	$0.395360\pi$
$152$	−135816.	−0.476807
$153$	−252773.	−0.872974
$154$	−383568.	−1.30329
$155$	−329489.	−1.10157
$156$	27226.0	0.0895722
$157$	−445322.	−1.44187	−0.720934	−	0.693004i	$-0.756287\pi$
$157$	−445322.	−1.44187	−0.720934	+	0.693004i	$0.756287\pi$
$158$	165587.	0.527694
$159$	140288.	0.440075
$160$	82131.4	0.253635
$161$	−645766.	−1.96341
$162$	−18318.1	−0.0548394
$163$	427486.	1.26024	0.630120	−	0.776498i	$-0.283006\pi$
$163$	427486.	1.26024	0.630120	+	0.776498i	$0.283006\pi$
$164$	−14620.6	−0.0424478
$165$	371206.	1.06146
$166$	−141600.	−0.398835
$167$	−33528.0	−0.0930287	−0.0465144	−	0.998918i	$-0.514811\pi$
$167$	−33528.0	−0.0930287	−0.0465144	+	0.998918i	$0.514811\pi$
$168$	−134435.	−0.367484
$169$	28561.0	0.0769231
$170$	572634.	1.51969
$171$	300534.	0.785966
$172$	−83601.1	−0.215472
$173$	436654.	1.10923	0.554615	−	0.832107i	$-0.312865\pi$
$173$	436654.	1.10923	0.554615	+	0.832107i	$0.312865\pi$
$174$	116644.	0.292071
$175$	690127.	1.70347
$176$	−117671.	−0.286343
$177$	184796.	0.443364
$178$	−45807.9	−0.108365
$179$	−70697.5	−0.164919	−0.0824597	−	0.996594i	$-0.526278\pi$
$179$	−70697.5	−0.164919	−0.0824597	+	0.996594i	$0.526278\pi$
$180$	−181740.	−0.418090
$181$	−22799.2	−0.0517278	−0.0258639	−	0.999665i	$-0.508234\pi$
$181$	−22799.2	−0.0517278	−0.0258639	+	0.999665i	$0.508234\pi$
$182$	−141027.	−0.315589
$183$	−428512.	−0.945877
$184$	−198108.	−0.431377
$185$	507211.	1.08958
$186$	165451.	0.350660
$187$	−820420.	−1.71566
$188$	−109506.	−0.225966
$189$	807910.	1.64516
$190$	−680833.	−1.36822
$191$	570738.	1.13202	0.566009	−	0.824399i	$-0.308487\pi$
$191$	570738.	1.13202	0.566009	+	0.824399i	$0.308487\pi$
$192$	−41241.8	−0.0807392
$193$	747134.	1.44379	0.721897	−	0.692001i	$-0.243270\pi$
$193$	747134.	1.44379	0.721897	+	0.692001i	$0.243270\pi$
$194$	542351.	1.03461
$195$	136481.	0.257032
$196$	427440.	0.794758
$197$	−608996.	−1.11802	−0.559009	−	0.829162i	$-0.688818\pi$
$197$	−608996.	−1.11802	−0.559009	+	0.829162i	$0.688818\pi$
$198$	260382.	0.472006
$199$	−610090.	−1.09210	−0.546049	−	0.837753i	$-0.683869\pi$
$199$	−610090.	−1.09210	−0.546049	+	0.837753i	$0.683869\pi$
$200$	211716.	0.374265
$201$	−324205.	−0.566018
$202$	−773670.	−1.33407
$203$	−604195.	−1.02905
$204$	−287545.	−0.483760
$205$	−73291.5	−0.121806
$206$	476508.	0.782353
$207$	438372.	0.711078
$208$	−43264.0	−0.0693375
$209$	975439.	1.54467
$210$	−673909.	−1.05452
$211$	839125.	1.29754	0.648769	−	0.760985i	$-0.275284\pi$
$211$	839125.	1.29754	0.648769	+	0.760985i	$0.275284\pi$
$212$	−222926.	−0.340661
$213$	−287540.	−0.434259
$214$	−226938.	−0.338745
$215$	−419084.	−0.618308
$216$	247850.	0.361455
$217$	−857009.	−1.23548
$218$	482859.	0.688143
$219$	215011.	0.302936
$220$	−589872.	−0.821676
$221$	−301644.	−0.415445
$222$	−254693.	−0.346845
$223$	−255461.	−0.344003	−0.172002	−	0.985097i	$-0.555023\pi$
$223$	−255461.	−0.344003	−0.172002	+	0.985097i	$0.555023\pi$
$224$	213626.	0.284469
$225$	−468486.	−0.616936
$226$	1.06436e6	1.38617
$227$	−338589.	−0.436123	−0.218061	−	0.975935i	$-0.569973\pi$
$227$	−338589.	−0.436123	−0.218061	+	0.975935i	$0.569973\pi$
$228$	341877.	0.435544
$229$	91538.8	0.115350	0.0576749	−	0.998335i	$-0.481631\pi$
$229$	91538.8	0.115350	0.0576749	+	0.998335i	$0.481631\pi$
$230$	−993093.	−1.23786
$231$	965518.	1.19050
$232$	−185354.	−0.226091
$233$	−817902.	−0.986987	−0.493494	−	0.869749i	$-0.664280\pi$
$233$	−817902.	−0.986987	−0.493494	+	0.869749i	$0.664280\pi$
$234$	95734.6	0.114296
$235$	−548943.	−0.648422
$236$	−293654.	−0.343207
$237$	−416815.	−0.482028
$238$	1.48944e6	1.70443
$239$	−13071.7	−0.0148026	−0.00740128	−	0.999973i	$-0.502356\pi$
$239$	−13071.7	−0.0148026	−0.00740128	+	0.999973i	$0.502356\pi$
$240$	−206741.	−0.231685
$241$	−1.35299e6	−1.50056	−0.750280	−	0.661120i	$-0.770081\pi$
$241$	−1.35299e6	−1.50056	−0.750280	+	0.661120i	$0.770081\pi$
$242$	200913.	0.220531
$243$	−894945.	−0.972256
$244$	680933.	0.732201
$245$	2.14271e6	2.28060
$246$	36802.9	0.0387744
$247$	358640.	0.374038
$248$	−262912.	−0.271445
$249$	356436.	0.364320
$250$	58732.8	0.0594334
$251$	−946373.	−0.948153	−0.474076	−	0.880484i	$-0.657218\pi$
$251$	−946373.	−0.948153	−0.474076	+	0.880484i	$0.657218\pi$
$252$	−472712.	−0.468916
$253$	1.42282e6	1.39749
$254$	−194536.	−0.189198
$255$	−1.44143e6	−1.38818
$256$	65536.0	0.0625000
$257$	188354.	0.177886	0.0889429	−	0.996037i	$-0.471651\pi$
$257$	188354.	0.177886	0.0889429	+	0.996037i	$0.471651\pi$
$258$	210441.	0.196825
$259$	1.31927e6	1.22204
$260$	−216878.	−0.198968
$261$	410152.	0.372687
$262$	858692.	0.772830
$263$	−196644.	−0.175304	−0.0876521	−	0.996151i	$-0.527936\pi$
$263$	−196644.	−0.175304	−0.0876521	+	0.996151i	$0.527936\pi$
$264$	296201.	0.261563
$265$	−1.11751e6	−0.977543
$266$	−1.77087e6	−1.53455
$267$	115308.	0.0989875
$268$	515184.	0.438153
$269$	543163.	0.457667	0.228834	−	0.973466i	$-0.426509\pi$
$269$	543163.	0.457667	0.228834	+	0.973466i	$0.426509\pi$
$270$	1.24245e6	1.03721
$271$	1.83549e6	1.51820	0.759100	−	0.650974i	$-0.225639\pi$
$271$	1.83549e6	1.51820	0.759100	+	0.650974i	$0.225639\pi$
$272$	456928.	0.374477
$273$	354992.	0.288278
$274$	−497638.	−0.400440
$275$	−1.52056e6	−1.21247
$276$	498676.	0.394045
$277$	−518660.	−0.406147	−0.203073	−	0.979164i	$-0.565093\pi$
$277$	−518660.	−0.406147	−0.203073	+	0.979164i	$0.565093\pi$
$278$	−361087.	−0.280220
$279$	581773.	0.447448
$280$	1.07089e6	0.816297
$281$	229325.	0.173255	0.0866274	−	0.996241i	$-0.472391\pi$
$281$	229325.	0.173255	0.0866274	+	0.996241i	$0.472391\pi$
$282$	275649.	0.206411
$283$	−1.67201e6	−1.24101	−0.620503	−	0.784204i	$-0.713072\pi$
$283$	−1.67201e6	−1.24101	−0.620503	+	0.784204i	$0.713072\pi$
$284$	456920.	0.336158
$285$	1.71379e6	1.24982
$286$	310724.	0.224626
$287$	−190633.	−0.136614
$288$	−145018.	−0.103025
$289$	1.76592e6	1.24373
$290$	−929164.	−0.648780
$291$	−1.36521e6	−0.945074
$292$	−341667.	−0.234502
$293$	−699644.	−0.476111	−0.238055	−	0.971252i	$-0.576510\pi$
$293$	−699644.	−0.476111	−0.238055	+	0.971252i	$0.576510\pi$
$294$	−1.07595e6	−0.725979
$295$	−1.47206e6	−0.984850
$296$	404725.	0.268491
$297$	−1.78007e6	−1.17097
$298$	−1.15578e6	−0.753936
$299$	523128.	0.338400
$300$	−532932.	−0.341876
$301$	−1.09005e6	−0.693474
$302$	723649.	0.456574
$303$	1.94748e6	1.21862
$304$	−543265.	−0.337153
$305$	3.41345e6	2.10109
$306$	−1.01109e6	−0.617286
$307$	2.65074e6	1.60517	0.802586	−	0.596537i	$-0.203457\pi$
$307$	2.65074e6	1.60517	0.802586	+	0.596537i	$0.203457\pi$
$308$	−1.53427e6	−0.921565
$309$	−1.19947e6	−0.714648
$310$	−1.31795e6	−0.778926
$311$	582158.	0.341303	0.170652	−	0.985331i	$-0.445413\pi$
$311$	582158.	0.341303	0.170652	+	0.985331i	$0.445413\pi$
$312$	108904.	0.0633371
$313$	2.82898e6	1.63218	0.816091	−	0.577923i	$-0.196137\pi$
$313$	2.82898e6	1.63218	0.816091	+	0.577923i	$0.196137\pi$
$314$	−1.78129e6	−1.01955
$315$	−2.36966e6	−1.34558
$316$	662346.	0.373136
$317$	−1.48118e6	−0.827863	−0.413931	−	0.910308i	$-0.635845\pi$
$317$	−1.48118e6	−0.827863	−0.413931	+	0.910308i	$0.635845\pi$
$318$	561151.	0.311180
$319$	1.33123e6	0.732445
$320$	328525.	0.179347
$321$	571248.	0.309430
$322$	−2.58307e6	−1.38834
$323$	−3.78773e6	−2.02010
$324$	−73272.4	−0.0387773
$325$	−559063.	−0.293598
$326$	1.70995e6	0.891124
$327$	−1.21545e6	−0.628592
$328$	−58482.3	−0.0300151
$329$	−1.42782e6	−0.727249
$330$	1.48483e6	0.750569
$331$	−2.43838e6	−1.22330	−0.611648	−	0.791130i	$-0.709493\pi$
$331$	−2.43838e6	−1.22330	−0.611648	+	0.791130i	$0.709493\pi$
$332$	−566400.	−0.282019
$333$	−895575.	−0.442579
$334$	−134112.	−0.0657812
$335$	2.58257e6	1.25730
$336$	−537740.	−0.259851
$337$	−898353.	−0.430896	−0.215448	−	0.976515i	$-0.569121\pi$
$337$	−898353.	−0.430896	−0.215448	+	0.976515i	$0.569121\pi$
$338$	114244.	0.0543928
$339$	−2.67921e6	−1.26621
$340$	2.29054e6	1.07458
$341$	1.88825e6	0.879374
$342$	1.20214e6	0.555762
$343$	2.06699e6	0.948646
$344$	−334404.	−0.152362
$345$	2.49982e6	1.13073
$346$	1.74662e6	0.784345
$347$	1.30924e6	0.583706	0.291853	−	0.956463i	$-0.405728\pi$
$347$	1.30924e6	0.583706	0.291853	+	0.956463i	$0.405728\pi$
$348$	466574.	0.206525
$349$	784972.	0.344977	0.172489	−	0.985011i	$-0.444819\pi$
$349$	784972.	0.344977	0.172489	+	0.985011i	$0.444819\pi$
$350$	2.76051e6	1.20453
$351$	−654479.	−0.283549
$352$	−470683.	−0.202475
$353$	3.22479e6	1.37741	0.688707	−	0.725040i	$-0.258179\pi$
$353$	3.22479e6	1.37741	0.688707	+	0.725040i	$0.258179\pi$
$354$	739186.	0.313506
$355$	2.29049e6	0.964624
$356$	−183232.	−0.0766259
$357$	−3.74921e6	−1.55693
$358$	−282790.	−0.116616
$359$	4.41400e6	1.80758	0.903788	−	0.427980i	$-0.140775\pi$
$359$	4.41400e6	1.80758	0.903788	+	0.427980i	$0.140775\pi$
$360$	−726961.	−0.295634
$361$	2.02733e6	0.818759
$362$	−91196.9	−0.0365771
$363$	−505739.	−0.201446
$364$	−564106.	−0.223155
$365$	−1.71274e6	−0.672915
$366$	−1.71405e6	−0.668836
$367$	703866.	0.272788	0.136394	−	0.990655i	$-0.456449\pi$
$367$	703866.	0.272788	0.136394	+	0.990655i	$0.456449\pi$
$368$	−792430.	−0.305029
$369$	129410.	0.0494767
$370$	2.02884e6	0.770450
$371$	−2.90667e6	−1.09638
$372$	661803.	0.247954
$373$	−4.24526e6	−1.57991	−0.789955	−	0.613165i	$-0.789896\pi$
$373$	−4.24526e6	−1.57991	−0.789955	+	0.613165i	$0.789896\pi$
$374$	−3.28168e6	−1.21316
$375$	−147842.	−0.0542901
$376$	−438025.	−0.159782
$377$	489452.	0.177360
$378$	3.23164e6	1.16331
$379$	1.39414e6	0.498548	0.249274	−	0.968433i	$-0.419808\pi$
$379$	1.39414e6	0.498548	0.249274	+	0.968433i	$0.419808\pi$
$380$	−2.72333e6	−0.967479
$381$	489686.	0.172824
$382$	2.28295e6	0.800458
$383$	2.23700e6	0.779235	0.389618	−	0.920977i	$-0.372607\pi$
$383$	2.23700e6	0.779235	0.389618	+	0.920977i	$0.372607\pi$
$384$	−164967.	−0.0570913
$385$	−7.69116e6	−2.64448
$386$	2.98854e6	1.02092
$387$	739970.	0.251152
$388$	2.16941e6	0.731579
$389$	66104.3	0.0221491	0.0110745	−	0.999939i	$-0.496475\pi$
$389$	66104.3	0.0221491	0.0110745	+	0.999939i	$0.496475\pi$
$390$	545926.	0.181749
$391$	−5.52496e6	−1.82763
$392$	1.70976e6	0.561978
$393$	−2.16150e6	−0.705950
$394$	−2.43598e6	−0.790558
$395$	3.32028e6	1.07073
$396$	1.04153e6	0.333759
$397$	1.92689e6	0.613593	0.306797	−	0.951775i	$-0.400743\pi$
$397$	1.92689e6	0.613593	0.306797	+	0.951775i	$0.400743\pi$
$398$	−2.44036e6	−0.772230
$399$	4.45763e6	1.40175
$400$	846865.	0.264645
$401$	−5.75402e6	−1.78694	−0.893471	−	0.449121i	$-0.851737\pi$
$401$	−5.75402e6	−1.78694	−0.893471	+	0.449121i	$0.851737\pi$
$402$	−1.29682e6	−0.400235
$403$	694253.	0.212939
$404$	−3.09468e6	−0.943327
$405$	−367307.	−0.111274
$406$	−2.41678e6	−0.727650
$407$	−2.90675e6	−0.869805
$408$	−1.15018e6	−0.342070
$409$	−2.90555e6	−0.858855	−0.429427	−	0.903101i	$-0.641285\pi$
$409$	−2.90555e6	−0.858855	−0.429427	+	0.903101i	$0.641285\pi$
$410$	−293166.	−0.0861300
$411$	1.25265e6	0.365786
$412$	1.90603e6	0.553207
$413$	−3.82887e6	−1.10457
$414$	1.75349e6	0.502808
$415$	−2.83931e6	−0.809268
$416$	−173056.	−0.0490290
$417$	908928.	0.255970
$418$	3.90176e6	1.09224
$419$	−5.95953e6	−1.65835	−0.829176	−	0.558988i	$-0.811190\pi$
$419$	−5.95953e6	−1.65835	−0.829176	+	0.558988i	$0.811190\pi$
$420$	−2.69564e6	−0.745655
$421$	5.60113e6	1.54017	0.770087	−	0.637938i	$-0.220213\pi$
$421$	5.60113e6	1.54017	0.770087	+	0.637938i	$0.220213\pi$
$422$	3.35650e6	0.917499
$423$	969261.	0.263384
$424$	−891706.	−0.240883
$425$	5.90449e6	1.58566
$426$	−1.15016e6	−0.307067
$427$	8.87849e6	2.35651
$428$	−907751.	−0.239529
$429$	−782155.	−0.205187
$430$	−1.67634e6	−0.437210
$431$	2.69481e6	0.698772	0.349386	−	0.936979i	$-0.386390\pi$
$431$	2.69481e6	0.698772	0.349386	+	0.936979i	$0.386390\pi$
$432$	991400.	0.255587
$433$	−3.32140e6	−0.851337	−0.425668	−	0.904879i	$-0.639961\pi$
$433$	−3.32140e6	−0.851337	−0.425668	+	0.904879i	$0.639961\pi$
$434$	−3.42804e6	−0.873617
$435$	2.33889e6	0.592634
$436$	1.93143e6	0.486591
$437$	6.56890e6	1.64547
$438$	860044.	0.214208
$439$	−4.04883e6	−1.00269	−0.501347	−	0.865246i	$-0.667162\pi$
$439$	−4.04883e6	−1.00269	−0.501347	+	0.865246i	$0.667162\pi$
$440$	−2.35949e6	−0.581013
$441$	−3.78335e6	−0.926362
$442$	−1.20658e6	−0.293764
$443$	4.16599e6	1.00858	0.504289	−	0.863535i	$-0.331755\pi$
$443$	4.16599e6	1.00858	0.504289	+	0.863535i	$0.331755\pi$
$444$	−1.01877e6	−0.245256
$445$	−918522.	−0.219882
$446$	−1.02184e6	−0.243247
$447$	2.90933e6	0.688690
$448$	854504.	0.201150
$449$	2.12545e6	0.497549	0.248774	−	0.968561i	$-0.419972\pi$
$449$	2.12545e6	0.497549	0.248774	+	0.968561i	$0.419972\pi$
$450$	−1.87394e6	−0.436240
$451$	420023.	0.0972371
$452$	4.25744e6	0.980172
$453$	−1.82157e6	−0.417062
$454$	−1.35436e6	−0.308385
$455$	−2.82781e6	−0.640356
$456$	1.36751e6	0.307976
$457$	2.43540e6	0.545482	0.272741	−	0.962088i	$-0.412070\pi$
$457$	2.43540e6	0.545482	0.272741	+	0.962088i	$0.412070\pi$
$458$	366155.	0.0815646
$459$	6.91221e6	1.53139
$460$	−3.97237e6	−0.875297
$461$	−7.40738e6	−1.62335	−0.811675	−	0.584109i	$-0.801444\pi$
$461$	−7.40738e6	−1.62335	−0.811675	+	0.584109i	$0.801444\pi$
$462$	3.86207e6	0.841813
$463$	−8.34671e6	−1.80952	−0.904759	−	0.425924i	$-0.859949\pi$
$463$	−8.34671e6	−1.80952	−0.904759	+	0.425924i	$0.859949\pi$
$464$	−741418.	−0.159870
$465$	3.31755e6	0.711518
$466$	−3.27161e6	−0.697906
$467$	−373460.	−0.0792414	−0.0396207	−	0.999215i	$-0.512615\pi$
$467$	−373460.	−0.0792414	−0.0396207	+	0.999215i	$0.512615\pi$
$468$	382938.	0.0808191
$469$	6.71733e6	1.41015
$470$	−2.19577e6	−0.458504
$471$	4.48386e6	0.931322
$472$	−1.17462e6	−0.242684
$473$	2.40171e6	0.493591
$474$	−1.66726e6	−0.340845
$475$	−7.02014e6	−1.42762
$476$	5.95775e6	1.20522
$477$	1.97317e6	0.397071
$478$	−52286.7	−0.0104670
$479$	−2.94442e6	−0.586356	−0.293178	−	0.956058i	$-0.594713\pi$
$479$	−2.94442e6	−0.586356	−0.293178	+	0.956058i	$0.594713\pi$
$480$	−826964.	−0.163826
$481$	−1.06873e6	−0.210622
$482$	−5.41198e6	−1.06106
$483$	6.50209e6	1.26819
$484$	803652.	0.155939
$485$	1.08750e7	2.09930
$486$	−3.57978e6	−0.687489
$487$	3.58165e6	0.684323	0.342162	−	0.939641i	$-0.388841\pi$
$487$	3.58165e6	0.684323	0.342162	+	0.939641i	$0.388841\pi$
$488$	2.72373e6	0.517744
$489$	−4.30428e6	−0.814007
$490$	8.57085e6	1.61263
$491$	−5.10341e6	−0.955338	−0.477669	−	0.878540i	$-0.658518\pi$
$491$	−5.10341e6	−0.955338	−0.477669	+	0.878540i	$0.658518\pi$
$492$	147212.	0.0274176
$493$	−5.16929e6	−0.957886
$494$	1.43456e6	0.264485
$495$	5.22107e6	0.957738
$496$	−1.05165e6	−0.191941
$497$	5.95764e6	1.08189
$498$	1.42574e6	0.257613
$499$	4.21965e6	0.758621	0.379310	−	0.925269i	$-0.376161\pi$
$499$	4.21965e6	0.758621	0.379310	+	0.925269i	$0.376161\pi$
$500$	234931.	0.0420258
$501$	337587.	0.0600885
$502$	−3.78549e6	−0.670445
$503$	−6.56926e6	−1.15770	−0.578850	−	0.815434i	$-0.696498\pi$
$503$	−6.56926e6	−1.15770	−0.578850	+	0.815434i	$0.696498\pi$
$504$	−1.89085e6	−0.331574
$505$	−1.55133e7	−2.70692
$506$	5.69127e6	0.988174
$507$	−287575.	−0.0496857
$508$	−778144.	−0.133783
$509$	−5.61314e6	−0.960310	−0.480155	−	0.877184i	$-0.659420\pi$
$509$	−5.61314e6	−0.960310	−0.480155	+	0.877184i	$0.659420\pi$
$510$	−5.76574e6	−0.981588
$511$	−4.45489e6	−0.754719
$512$	262144.	0.0441942
$513$	−8.21827e6	−1.37875
$514$	753414.	0.125784
$515$	9.55476e6	1.58746
$516$	841763.	0.139176
$517$	3.14592e6	0.517631
$518$	5.27708e6	0.864111
$519$	−4.39658e6	−0.716468
$520$	−867512.	−0.140691
$521$	1.19847e6	0.193434	0.0967172	−	0.995312i	$-0.469166\pi$
$521$	1.19847e6	0.193434	0.0967172	+	0.995312i	$0.469166\pi$
$522$	1.64061e6	0.263529
$523$	−6.09023e6	−0.973597	−0.486798	−	0.873514i	$-0.661835\pi$
$523$	−6.09023e6	−0.973597	−0.486798	+	0.873514i	$0.661835\pi$
$524$	3.43477e6	0.546473
$525$	−6.94875e6	−1.10029
$526$	−786577.	−0.123959
$527$	−7.33228e6	−1.15004
$528$	1.18480e6	0.184953
$529$	3.14535e6	0.488686
$530$	−4.47003e6	−0.691228
$531$	2.59919e6	0.400039
$532$	−7.08347e6	−1.08509
$533$	154430.	0.0235458
$534$	461231.	0.0699947
$535$	−4.55047e6	−0.687340
$536$	2.06074e6	0.309821
$537$	711839.	0.106524
$538$	2.17265e6	0.323619
$539$	−1.22796e7	−1.82059
$540$	4.96979e6	0.733421
$541$	−858076.	−0.126047	−0.0630235	−	0.998012i	$-0.520074\pi$
$541$	−858076.	−0.126047	−0.0630235	+	0.998012i	$0.520074\pi$
$542$	7.34196e6	1.07353
$543$	229561.	0.0334117
$544$	1.82771e6	0.264796
$545$	9.68209e6	1.39630
$546$	1.41997e6	0.203844
$547$	3.72893e6	0.532863	0.266432	−	0.963854i	$-0.414155\pi$
$547$	3.72893e6	0.532863	0.266432	+	0.963854i	$0.414155\pi$
$548$	−1.99055e6	−0.283154
$549$	−6.02708e6	−0.853446
$550$	−6.08223e6	−0.857346
$551$	6.14603e6	0.862414
$552$	1.99471e6	0.278632
$553$	8.63614e6	1.20090
$554$	−2.07464e6	−0.287189
$555$	−5.10701e6	−0.703775
$556$	−1.44435e6	−0.198146
$557$	3.40690e6	0.465287	0.232644	−	0.972562i	$-0.425262\pi$
$557$	3.40690e6	0.465287	0.232644	+	0.972562i	$0.425262\pi$
$558$	2.32709e6	0.316394
$559$	883036.	0.119522
$560$	4.28355e6	0.577209
$561$	8.26065e6	1.10817
$562$	917299.	0.122510
$563$	−6.71361e6	−0.892658	−0.446329	−	0.894869i	$-0.647269\pi$
$563$	−6.71361e6	−0.892658	−0.446329	+	0.894869i	$0.647269\pi$
$564$	1.10260e6	0.145955
$565$	2.13421e7	2.81266
$566$	−6.68806e6	−0.877524
$567$	−955377.	−0.124801
$568$	1.82768e6	0.237700
$569$	2.13854e6	0.276909	0.138454	−	0.990369i	$-0.455787\pi$
$569$	2.13854e6	0.276909	0.138454	+	0.990369i	$0.455787\pi$
$570$	6.85517e6	0.883754
$571$	1.66594e6	0.213830	0.106915	−	0.994268i	$-0.465903\pi$
$571$	1.66594e6	0.213830	0.106915	+	0.994268i	$0.465903\pi$
$572$	1.24290e6	0.158835
$573$	−5.74665e6	−0.731187
$574$	−762534.	−0.0966005
$575$	−1.02399e7	−1.29159
$576$	−580072.	−0.0728494
$577$	−9.29528e6	−1.16231	−0.581156	−	0.813792i	$-0.697399\pi$
$577$	−9.29528e6	−1.16231	−0.581156	+	0.813792i	$0.697399\pi$
$578$	7.06369e6	0.879452
$579$	−7.52274e6	−0.932567
$580$	−3.71665e6	−0.458756
$581$	−7.38512e6	−0.907648
$582$	−5.46083e6	−0.668269
$583$	6.40428e6	0.780367
$584$	−1.36667e6	−0.165818
$585$	1.91963e6	0.231915
$586$	−2.79858e6	−0.336661
$587$	7.04955e6	0.844435	0.422217	−	0.906495i	$-0.361252\pi$
$587$	7.04955e6	0.844435	0.422217	+	0.906495i	$0.361252\pi$
$588$	−4.30381e6	−0.513345
$589$	8.71772e6	1.03542
$590$	−5.88823e6	−0.696394
$591$	6.13186e6	0.722143
$592$	1.61890e6	0.189852
$593$	1.12914e7	1.31859	0.659295	−	0.751884i	$-0.270855\pi$
$593$	1.12914e7	1.31859	0.659295	+	0.751884i	$0.270855\pi$
$594$	−7.12028e6	−0.828002
$595$	2.98656e7	3.45843
$596$	−4.62312e6	−0.533113
$597$	6.14288e6	0.705401
$598$	2.09251e6	0.239285
$599$	−1.43629e7	−1.63559	−0.817794	−	0.575511i	$-0.804803\pi$
$599$	−1.43629e7	−1.63559	−0.817794	+	0.575511i	$0.804803\pi$
$600$	−2.13173e6	−0.241743
$601$	1.73182e7	1.95576	0.977881	−	0.209164i	$-0.0670742\pi$
$601$	1.73182e7	1.95576	0.977881	+	0.209164i	$0.0670742\pi$
$602$	−4.36020e6	−0.490360
$603$	−4.56000e6	−0.510707
$604$	2.89460e6	0.322846
$605$	4.02863e6	0.447475
$606$	7.78993e6	0.861691
$607$	−8.14344e6	−0.897090	−0.448545	−	0.893760i	$-0.648058\pi$
$607$	−8.14344e6	−0.897090	−0.448545	+	0.893760i	$0.648058\pi$
$608$	−2.17306e6	−0.238403
$609$	6.08352e6	0.664679
$610$	1.36538e7	1.48569
$611$	1.15666e6	0.125344
$612$	−4.04436e6	−0.436487
$613$	−1.67984e7	−1.80558	−0.902789	−	0.430085i	$-0.858484\pi$
$613$	−1.67984e7	−1.80558	−0.902789	+	0.430085i	$0.858484\pi$
$614$	1.06030e7	1.13503
$615$	737958.	0.0786763
$616$	−6.13709e6	−0.651645
$617$	−1.22398e7	−1.29438	−0.647190	−	0.762329i	$-0.724056\pi$
$617$	−1.22398e7	−1.29438	−0.647190	+	0.762329i	$0.724056\pi$
$618$	−4.79787e6	−0.505332
$619$	−7.24433e6	−0.759927	−0.379964	−	0.925001i	$-0.624063\pi$
$619$	−7.24433e6	−0.759927	−0.379964	+	0.925001i	$0.624063\pi$
$620$	−5.27182e6	−0.550784
$621$	−1.19875e7	−1.24739
$622$	2.32863e6	0.241338
$623$	−2.38910e6	−0.246612
$624$	435617.	0.0447861
$625$	−9.16002e6	−0.937987
$626$	1.13159e7	1.15413
$627$	−9.82150e6	−0.997721
$628$	−7.12516e6	−0.720934
$629$	1.12872e7	1.13753
$630$	−9.47863e6	−0.951468
$631$	−3.25271e6	−0.325216	−0.162608	−	0.986691i	$-0.551991\pi$
$631$	−3.25271e6	−0.325216	−0.162608	+	0.986691i	$0.551991\pi$
$632$	2.64939e6	0.263847
$633$	−8.44898e6	−0.838099
$634$	−5.92470e6	−0.585388
$635$	−3.90076e6	−0.383897
$636$	2.24460e6	0.220037
$637$	−4.51483e6	−0.440852
$638$	5.32490e6	0.517917
$639$	−4.04429e6	−0.391823
$640$	1.31410e6	0.126817
$641$	−5.41673e6	−0.520706	−0.260353	−	0.965514i	$-0.583839\pi$
$641$	−5.41673e6	−0.520706	−0.260353	+	0.965514i	$0.583839\pi$
$642$	2.28499e6	0.218800
$643$	−3.74463e6	−0.357175	−0.178588	−	0.983924i	$-0.557153\pi$
$643$	−3.74463e6	−0.357175	−0.178588	+	0.983924i	$0.557153\pi$
$644$	−1.03323e7	−0.981704
$645$	4.21967e6	0.399374
$646$	−1.51509e7	−1.42843
$647$	8.09188e6	0.759957	0.379978	−	0.924995i	$-0.375931\pi$
$647$	8.09188e6	0.759957	0.379978	+	0.924995i	$0.375931\pi$
$648$	−293090.	−0.0274197
$649$	8.43615e6	0.786199
$650$	−2.23625e6	−0.207605
$651$	8.62906e6	0.798015
$652$	6.83978e6	0.630120
$653$	1.58199e7	1.45185	0.725923	−	0.687777i	$-0.241413\pi$
$653$	1.58199e7	1.45185	0.725923	+	0.687777i	$0.241413\pi$
$654$	−4.86181e6	−0.444481
$655$	1.72181e7	1.56813
$656$	−233929.	−0.0212239
$657$	3.02416e6	0.273333
$658$	−5.71127e6	−0.514243
$659$	7.21640e6	0.647302	0.323651	−	0.946177i	$-0.395090\pi$
$659$	7.21640e6	0.647302	0.323651	+	0.946177i	$0.395090\pi$
$660$	5.93930e6	0.530732
$661$	−8.74671e6	−0.778647	−0.389324	−	0.921101i	$-0.627291\pi$
$661$	−8.74671e6	−0.778647	−0.389324	+	0.921101i	$0.627291\pi$
$662$	−9.75353e6	−0.865001
$663$	3.03719e6	0.268342
$664$	−2.26560e6	−0.199418
$665$	−3.55087e7	−3.11373
$666$	−3.58230e6	−0.312951
$667$	8.96487e6	0.780243
$668$	−536449.	−0.0465144
$669$	2.57219e6	0.222196
$670$	1.03303e7	0.889047
$671$	−1.95620e7	−1.67728
$672$	−2.15096e6	−0.183742
$673$	−1.54748e7	−1.31701	−0.658504	−	0.752578i	$-0.728810\pi$
$673$	−1.54748e7	−1.31701	−0.658504	+	0.752578i	$0.728810\pi$
$674$	−3.59341e6	−0.304689
$675$	1.28110e7	1.08224
$676$	456976.	0.0384615
$677$	1.05103e7	0.881340	0.440670	−	0.897669i	$-0.354741\pi$
$677$	1.05103e7	0.881340	0.440670	+	0.897669i	$0.354741\pi$
$678$	−1.07168e7	−0.895349
$679$	2.82862e7	2.35451
$680$	9.16214e6	0.759844
$681$	3.40919e6	0.281698
$682$	7.55300e6	0.621811
$683$	4.19198e6	0.343849	0.171924	−	0.985110i	$-0.445001\pi$
$683$	4.19198e6	0.343849	0.171924	+	0.985110i	$0.445001\pi$
$684$	4.80855e6	0.392983
$685$	−9.97843e6	−0.812524
$686$	8.26798e6	0.670794
$687$	−921686.	−0.0745060
$688$	−1.33762e6	−0.107736
$689$	2.35466e6	0.188965
$690$	9.99926e6	0.799549
$691$	−3.77069e6	−0.300418	−0.150209	−	0.988654i	$-0.547995\pi$
$691$	−3.77069e6	−0.300418	−0.150209	+	0.988654i	$0.547995\pi$
$692$	6.98646e6	0.554615
$693$	1.35802e7	1.07417
$694$	5.23694e6	0.412743
$695$	−7.24037e6	−0.568590
$696$	1.86630e6	0.146035
$697$	−1.63100e6	−0.127166
$698$	3.13989e6	0.243936
$699$	8.23530e6	0.637509
$700$	1.10420e7	0.851733
$701$	5.92759e6	0.455599	0.227800	−	0.973708i	$-0.426847\pi$
$701$	5.92759e6	0.455599	0.227800	+	0.973708i	$0.426847\pi$
$702$	−2.61791e6	−0.200499
$703$	−1.34200e7	−1.02415
$704$	−1.88273e6	−0.143172
$705$	5.52720e6	0.418825
$706$	1.28992e7	0.973979
$707$	−4.03506e7	−3.03600
$708$	2.95674e6	0.221682
$709$	−760563.	−0.0568224	−0.0284112	−	0.999596i	$-0.509045\pi$
$709$	−760563.	−0.0568224	−0.0284112	+	0.999596i	$0.509045\pi$
$710$	9.16197e6	0.682092
$711$	−5.86256e6	−0.434924
$712$	−732927.	−0.0541827
$713$	1.27161e7	0.936760
$714$	−1.49969e7	−1.10092
$715$	6.23052e6	0.455784
$716$	−1.13116e6	−0.0824597
$717$	131616.	0.00956118
$718$	1.76560e7	1.27815
$719$	−1.55797e7	−1.12392	−0.561961	−	0.827164i	$-0.689953\pi$
$719$	−1.55797e7	−1.12392	−0.561961	+	0.827164i	$0.689953\pi$
$720$	−2.90784e6	−0.209045
$721$	2.48522e7	1.78044
$722$	8.10932e6	0.578950
$723$	1.36230e7	0.969233
$724$	−364788.	−0.0258639
$725$	−9.58071e6	−0.676944
$726$	−2.02295e6	−0.142444
$727$	−1.08887e7	−0.764081	−0.382040	−	0.924146i	$-0.624778\pi$
$727$	−1.08887e7	−0.764081	−0.382040	+	0.924146i	$0.624778\pi$
$728$	−2.25643e6	−0.157795
$729$	1.01238e7	0.705548
$730$	−6.85097e6	−0.475822
$731$	−9.32610e6	−0.645515
$732$	−6.85618e6	−0.472939
$733$	2.96685e6	0.203956	0.101978	−	0.994787i	$-0.467483\pi$
$733$	2.96685e6	0.203956	0.101978	+	0.994787i	$0.467483\pi$
$734$	2.81546e6	0.192890
$735$	−2.15745e7	−1.47307
$736$	−3.16972e6	−0.215688
$737$	−1.48003e7	−1.00370
$738$	517639.	0.0349853
$739$	1.10237e7	0.742537	0.371268	−	0.928526i	$-0.378923\pi$
$739$	1.10237e7	0.742537	0.371268	+	0.928526i	$0.378923\pi$
$740$	8.11538e6	0.544790
$741$	−3.61107e6	−0.241596
$742$	−1.16267e7	−0.775258
$743$	8.28375e6	0.550497	0.275248	−	0.961373i	$-0.411240\pi$
$743$	8.28375e6	0.550497	0.275248	+	0.961373i	$0.411240\pi$
$744$	2.64721e6	0.175330
$745$	−2.31752e7	−1.52980
$746$	−1.69810e7	−1.11717
$747$	5.01332e6	0.328719
$748$	−1.31267e7	−0.857832
$749$	−1.18359e7	−0.770898
$750$	−591369.	−0.0383889
$751$	9.93945e6	0.643077	0.321538	−	0.946897i	$-0.395800\pi$
$751$	9.93945e6	0.643077	0.321538	+	0.946897i	$0.395800\pi$
$752$	−1.75210e6	−0.112983
$753$	9.52885e6	0.612425
$754$	1.95781e6	0.125413
$755$	1.45103e7	0.926424
$756$	1.29266e7	0.822581
$757$	1.74890e6	0.110924	0.0554620	−	0.998461i	$-0.482337\pi$
$757$	1.74890e6	0.110924	0.0554620	+	0.998461i	$0.482337\pi$
$758$	5.57655e6	0.352527
$759$	−1.43261e7	−0.902657
$760$	−1.08933e7	−0.684111
$761$	9.13174e6	0.571600	0.285800	−	0.958289i	$-0.407741\pi$
$761$	9.13174e6	0.571600	0.285800	+	0.958289i	$0.407741\pi$
$762$	1.95874e6	0.122205
$763$	2.51834e7	1.56604
$764$	9.13181e6	0.566009
$765$	−2.02740e7	−1.25252
$766$	8.94799e6	0.551003
$767$	3.10172e6	0.190377
$768$	−659869.	−0.0403696
$769$	2.08814e7	1.27334	0.636669	−	0.771137i	$-0.280312\pi$
$769$	2.08814e7	1.27334	0.636669	+	0.771137i	$0.280312\pi$
$770$	−3.07646e7	−1.86993
$771$	−1.89649e6	−0.114899
$772$	1.19541e7	0.721897
$773$	1.36863e6	0.0823831	0.0411916	−	0.999151i	$-0.486885\pi$
$773$	1.36863e6	0.0823831	0.0411916	+	0.999151i	$0.486885\pi$
$774$	2.95988e6	0.177591
$775$	−1.35896e7	−0.812739
$776$	8.67762e6	0.517305
$777$	−1.32835e7	−0.789331
$778$	264417.	0.0156618
$779$	1.93917e6	0.114491
$780$	2.18370e6	0.128516
$781$	−1.31265e7	−0.770053
$782$	−2.20998e7	−1.29233
$783$	−1.12158e7	−0.653774
$784$	6.83903e6	0.397379
$785$	−3.57177e7	−2.06876
$786$	−8.64600e6	−0.499182
$787$	6.30683e6	0.362973	0.181486	−	0.983393i	$-0.441909\pi$
$787$	6.30683e6	0.362973	0.181486	+	0.983393i	$0.441909\pi$
$788$	−9.74393e6	−0.559009
$789$	1.97997e6	0.113231
$790$	1.32811e7	0.757123
$791$	5.55115e7	3.15458
$792$	4.16611e6	0.236003
$793$	−7.19236e6	−0.406152
$794$	7.70756e6	0.433876
$795$	1.12520e7	0.631409
$796$	−9.76144e6	−0.546049
$797$	2.78632e7	1.55376	0.776882	−	0.629646i	$-0.216800\pi$
$797$	2.78632e7	1.55376	0.776882	+	0.629646i	$0.216800\pi$
$798$	1.78305e7	0.991189
$799$	−1.22159e7	−0.676955
$800$	3.38746e6	0.187133
$801$	1.62182e6	0.0893144
$802$	−2.30161e7	−1.26356
$803$	9.81548e6	0.537183
$804$	−5.18729e6	−0.283009
$805$	−5.17946e7	−2.81705
$806$	2.77701e6	0.150571
$807$	−5.46900e6	−0.295614
$808$	−1.23787e7	−0.667033
$809$	−2.43317e7	−1.30708	−0.653540	−	0.756892i	$-0.726717\pi$
$809$	−2.43317e7	−1.30708	−0.653540	+	0.756892i	$0.726717\pi$
$810$	−1.46923e6	−0.0786823
$811$	2.91892e7	1.55837	0.779184	−	0.626795i	$-0.215634\pi$
$811$	2.91892e7	1.55837	0.779184	+	0.626795i	$0.215634\pi$
$812$	−9.66713e6	−0.514526
$813$	−1.84812e7	−0.980626
$814$	−1.16270e7	−0.615045
$815$	3.42871e7	1.80816
$816$	−4.60072e6	−0.241880
$817$	1.10883e7	0.581177
$818$	−1.16222e7	−0.607302
$819$	4.99302e6	0.260108
$820$	−1.17266e6	−0.0609031
$821$	1.37611e7	0.712517	0.356258	−	0.934387i	$-0.384052\pi$
$821$	1.37611e7	0.712517	0.356258	+	0.934387i	$0.384052\pi$
$822$	5.01062e6	0.258649
$823$	−3.73431e7	−1.92181	−0.960906	−	0.276875i	$-0.910701\pi$
$823$	−3.73431e7	−1.92181	−0.960906	+	0.276875i	$0.910701\pi$
$824$	7.62413e6	0.391176
$825$	1.53102e7	0.783151
$826$	−1.53155e7	−0.781052
$827$	2.48774e7	1.26486	0.632429	−	0.774618i	$-0.282058\pi$
$827$	2.48774e7	1.26486	0.632429	+	0.774618i	$0.282058\pi$
$828$	7.01396e6	0.355539
$829$	−1.97379e7	−0.997505	−0.498753	−	0.866744i	$-0.666208\pi$
$829$	−1.97379e7	−0.997505	−0.498753	+	0.866744i	$0.666208\pi$
$830$	−1.13572e7	−0.572239
$831$	5.22228e6	0.262336
$832$	−692224.	−0.0346688
$833$	4.76829e7	2.38095
$834$	3.63571e6	0.180998
$835$	−2.68916e6	−0.133475
$836$	1.56070e7	0.772333
$837$	−1.59089e7	−0.784922
$838$	−2.38381e7	−1.17263
$839$	−6.01528e6	−0.295020	−0.147510	−	0.989061i	$-0.547126\pi$
$839$	−6.01528e6	−0.295020	−0.147510	+	0.989061i	$0.547126\pi$
$840$	−1.07825e7	−0.527258
$841$	−1.21234e7	−0.591063
$842$	2.24045e7	1.08907
$843$	−2.30903e6	−0.111908
$844$	1.34260e7	0.648769
$845$	2.29078e6	0.110367
$846$	3.87704e6	0.186241
$847$	1.04786e7	0.501873
$848$	−3.56682e6	−0.170330
$849$	1.68352e7	0.801583
$850$	2.36180e7	1.12123
$851$	−1.95750e7	−0.926567
$852$	−4.60063e6	−0.217129
$853$	3.37673e7	1.58900	0.794499	−	0.607266i	$-0.207734\pi$
$853$	3.37673e7	1.58900	0.794499	+	0.607266i	$0.207734\pi$
$854$	3.55140e7	1.66630
$855$	2.41048e7	1.12768
$856$	−3.63101e6	−0.169372
$857$	5.91162e6	0.274951	0.137475	−	0.990505i	$-0.456101\pi$
$857$	5.91162e6	0.274951	0.137475	+	0.990505i	$0.456101\pi$
$858$	−3.12862e6	−0.145089
$859$	−3.32002e7	−1.53517	−0.767587	−	0.640945i	$-0.778543\pi$
$859$	−3.32002e7	−1.53517	−0.767587	+	0.640945i	$0.778543\pi$
$860$	−6.70534e6	−0.309154
$861$	1.91945e6	0.0882407
$862$	1.07792e7	0.494106
$863$	4.15289e7	1.89812	0.949060	−	0.315095i	$-0.102036\pi$
$863$	4.15289e7	1.89812	0.949060	+	0.315095i	$0.102036\pi$
$864$	3.96560e6	0.180728
$865$	3.50224e7	1.59150
$866$	−1.32856e7	−0.601986
$867$	−1.77807e7	−0.803345
$868$	−1.37121e7	−0.617741
$869$	−1.90280e7	−0.854760
$870$	9.35556e6	0.419056
$871$	−5.44163e6	−0.243043
$872$	7.72574e6	0.344072
$873$	−1.92018e7	−0.852722
$874$	2.62756e7	1.16352
$875$	3.06320e6	0.135256
$876$	3.44018e6	0.151468
$877$	−2.43232e7	−1.06788	−0.533939	−	0.845523i	$-0.679289\pi$
$877$	−2.43232e7	−1.06788	−0.533939	+	0.845523i	$0.679289\pi$
$878$	−1.61953e7	−0.709012
$879$	7.04458e6	0.307527
$880$	−9.43795e6	−0.410838
$881$	−1.80739e7	−0.784535	−0.392267	−	0.919851i	$-0.628309\pi$
$881$	−1.80739e7	−0.784535	−0.392267	+	0.919851i	$0.628309\pi$
$882$	−1.51334e7	−0.655037
$883$	5.97320e6	0.257813	0.128907	−	0.991657i	$-0.458853\pi$
$883$	5.97320e6	0.257813	0.128907	+	0.991657i	$0.458853\pi$
$884$	−4.82630e6	−0.207723
$885$	1.48219e7	0.636128
$886$	1.66640e7	0.713172
$887$	−2.64744e7	−1.12984	−0.564921	−	0.825145i	$-0.691093\pi$
$887$	−2.64744e7	−1.12984	−0.564921	+	0.825145i	$0.691093\pi$
$888$	−4.07509e6	−0.173422
$889$	−1.01460e7	−0.430566
$890$	−3.67409e6	−0.155480
$891$	2.10498e6	0.0888290
$892$	−4.08738e6	−0.172002
$893$	1.45241e7	0.609483
$894$	1.16373e7	0.486978
$895$	−5.67039e6	−0.236622
$896$	3.41802e6	0.142234
$897$	−5.26727e6	−0.218577
$898$	8.50182e6	0.351820
$899$	1.18975e7	0.490970
$900$	−7.49578e6	−0.308468
$901$	−2.48685e7	−1.02056
$902$	1.68009e6	0.0687570
$903$	1.09755e7	0.447924
$904$	1.70298e7	0.693087
$905$	−1.82864e6	−0.0742177
$906$	−7.28628e6	−0.294907
$907$	−4.33417e7	−1.74940	−0.874698	−	0.484668i	$-0.838940\pi$
$907$	−4.33417e7	−1.74940	−0.874698	+	0.484668i	$0.838940\pi$
$908$	−5.41743e6	−0.218061
$909$	2.73916e7	1.09953
$910$	−1.13112e7	−0.452800
$911$	−1.85162e7	−0.739192	−0.369596	−	0.929193i	$-0.620504\pi$
$911$	−1.85162e7	−0.739192	−0.369596	+	0.929193i	$0.620504\pi$
$912$	5.47003e6	0.217772
$913$	1.62717e7	0.646033
$914$	9.74161e6	0.385714
$915$	−3.43694e7	−1.35712
$916$	1.46462e6	0.0576749
$917$	4.47849e7	1.75877
$918$	2.76488e7	1.08285
$919$	2.01153e7	0.785666	0.392833	−	0.919610i	$-0.371495\pi$
$919$	2.01153e7	0.785666	0.392833	+	0.919610i	$0.371495\pi$
$920$	−1.58895e7	−0.618929
$921$	−2.66898e7	−1.03680
$922$	−2.96295e7	−1.14788
$923$	−4.82621e6	−0.186467
$924$	1.54483e7	0.595252
$925$	2.09196e7	0.803896
$926$	−3.33868e7	−1.27952
$927$	−1.68707e7	−0.644812
$928$	−2.96567e6	−0.113045
$929$	2.02700e7	0.770575	0.385287	−	0.922797i	$-0.374102\pi$
$929$	2.02700e7	0.770575	0.385287	+	0.922797i	$0.374102\pi$
$930$	1.32702e7	0.503119
$931$	−5.66926e7	−2.14364
$932$	−1.30864e7	−0.493494
$933$	−5.86164e6	−0.220452
$934$	−1.49384e6	−0.0560321
$935$	−6.58030e7	−2.46159
$936$	1.53175e6	0.0571478
$937$	−4.72641e7	−1.75866	−0.879330	−	0.476212i	$-0.842009\pi$
$937$	−4.72641e7	−1.75866	−0.879330	+	0.476212i	$0.842009\pi$
$938$	2.68693e7	0.997125
$939$	−2.84844e7	−1.05425
$940$	−8.78310e6	−0.324211
$941$	−3.75847e7	−1.38368	−0.691841	−	0.722050i	$-0.743200\pi$
$941$	−3.75847e7	−1.38368	−0.691841	+	0.722050i	$0.743200\pi$
$942$	1.79355e7	0.658544
$943$	2.82856e6	0.103583
$944$	−4.69846e6	−0.171603
$945$	6.47996e7	2.36044
$946$	9.60684e6	0.349022
$947$	−3.39987e7	−1.23193	−0.615966	−	0.787772i	$-0.711234\pi$
$947$	−3.39987e7	−1.23193	−0.615966	+	0.787772i	$0.711234\pi$
$948$	−6.66904e6	−0.241014
$949$	3.60886e6	0.130078
$950$	−2.80806e7	−1.00948
$951$	1.49137e7	0.534728
$952$	2.38310e7	0.852216
$953$	−1.65163e7	−0.589089	−0.294545	−	0.955638i	$-0.595168\pi$
$953$	−1.65163e7	−0.589089	−0.294545	+	0.955638i	$0.595168\pi$
$954$	7.89267e6	0.280771
$955$	4.57769e7	1.62419
$956$	−209147.	−0.00740128
$957$	−1.34038e7	−0.473096
$958$	−1.17777e7	−0.414616
$959$	−2.59542e7	−0.911300
$960$	−3.30786e6	−0.115843
$961$	−1.17534e7	−0.410541
$962$	−4.27490e6	−0.148932
$963$	8.03469e6	0.279192
$964$	−2.16479e7	−0.750280
$965$	5.99249e7	2.07152
$966$	2.60084e7	0.896748
$967$	5.26159e7	1.80947	0.904733	−	0.425979i	$-0.140070\pi$
$967$	5.26159e7	1.80947	0.904733	+	0.425979i	$0.140070\pi$
$968$	3.21461e6	0.110266
$969$	3.81379e7	1.30481
$970$	4.35000e7	1.48443
$971$	2.54616e7	0.866639	0.433319	−	0.901240i	$-0.357342\pi$
$971$	2.54616e7	0.866639	0.433319	+	0.901240i	$0.357342\pi$
$972$	−1.43191e7	−0.486128
$973$	−1.88324e7	−0.637711
$974$	1.43266e7	0.483890
$975$	5.62910e6	0.189639
$976$	1.08949e7	0.366100
$977$	8.64073e6	0.289610	0.144805	−	0.989460i	$-0.453744\pi$
$977$	8.64073e6	0.289610	0.144805	+	0.989460i	$0.453744\pi$
$978$	−1.72171e7	−0.575590
$979$	5.26392e6	0.175530
$980$	3.42834e7	1.14030
$981$	−1.70955e7	−0.567165
$982$	−2.04137e7	−0.675526
$983$	2.50492e7	0.826818	0.413409	−	0.910545i	$-0.364338\pi$
$983$	2.50492e7	0.826818	0.413409	+	0.910545i	$0.364338\pi$
$984$	588847.	0.0193872
$985$	−4.88454e7	−1.60410
$986$	−2.06772e7	−0.677328
$987$	1.43764e7	0.469740
$988$	5.73823e6	0.187019
$989$	1.61738e7	0.525802
$990$	2.08843e7	0.677223
$991$	5.11941e6	0.165591	0.0827953	−	0.996567i	$-0.473615\pi$
$991$	5.11941e6	0.165591	0.0827953	+	0.996567i	$0.473615\pi$
$992$	−4.20660e6	−0.135723
$993$	2.45516e7	0.790144
$994$	2.38306e7	0.765012
$995$	−4.89331e7	−1.56692
$996$	5.70297e6	0.182160
$997$	4.73546e7	1.50878	0.754388	−	0.656429i	$-0.227934\pi$
$997$	4.73546e7	1.50878	0.754388	+	0.656429i	$0.227934\pi$
$998$	1.68786e7	0.536426
$999$	2.44900e7	0.776381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.a.c.1.1	✓	2
3.2	odd	2		234.6.a.h.1.1		2
4.3	odd	2		208.6.a.g.1.2		2
5.2	odd	4		650.6.b.h.599.4		4
5.3	odd	4		650.6.b.h.599.1		4
5.4	even	2		650.6.a.b.1.2		2
8.3	odd	2		832.6.a.m.1.1		2
8.5	even	2		832.6.a.k.1.2		2
13.5	odd	4		338.6.b.b.337.1		4
13.8	odd	4		338.6.b.b.337.3		4
13.12	even	2		338.6.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.a.c.1.1	✓	2	1.1	even	1	trivial
208.6.a.g.1.2		2	4.3	odd	2
234.6.a.h.1.1		2	3.2	odd	2
338.6.a.f.1.1		2	13.12	even	2
338.6.b.b.337.1		4	13.5	odd	4
338.6.b.b.337.3		4	13.8	odd	4
650.6.a.b.1.2		2	5.4	even	2
650.6.b.h.599.1		4	5.3	odd	4
650.6.b.h.599.4		4	5.2	odd	4
832.6.a.k.1.2		2	8.5	even	2
832.6.a.m.1.1		2	8.3	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -10.0688 q^{3} +16.0000 q^{4} +80.2064 q^{5} -40.2752 q^{6} +208.619 q^{7} +64.0000 q^{8} -141.619 q^{9} +320.826 q^{10} -459.651 q^{11} -161.101 q^{12} -169.000 q^{13} +834.477 q^{14} -807.582 q^{15} +256.000 q^{16} +1784.88 q^{17} -566.477 q^{18} -2122.13 q^{19} +1283.30 q^{20} -2100.55 q^{21} -1838.61 q^{22} -3095.43 q^{23} -644.403 q^{24} +3308.07 q^{25} -676.000 q^{26} +3872.65 q^{27} +3337.91 q^{28} -2896.16 q^{29} -3230.33 q^{30} -4108.01 q^{31} +1024.00 q^{32} +4628.14 q^{33} +7139.50 q^{34} +16732.6 q^{35} -2265.91 q^{36} +6323.82 q^{37} -8488.51 q^{38} +1701.63 q^{39} +5133.21 q^{40} -913.787 q^{41} -8402.18 q^{42} -5225.07 q^{43} -7354.42 q^{44} -11358.8 q^{45} -12381.7 q^{46} -6844.14 q^{47} -2577.61 q^{48} +26715.0 q^{49} +13232.3 q^{50} -17971.6 q^{51} -2704.00 q^{52} -13932.9 q^{53} +15490.6 q^{54} -36867.0 q^{55} +13351.6 q^{56} +21367.3 q^{57} -11584.7 q^{58} -18353.4 q^{59} -12921.3 q^{60} +42558.3 q^{61} -16432.0 q^{62} -29544.5 q^{63} +4096.00 q^{64} -13554.9 q^{65} +18512.6 q^{66} +32199.0 q^{67} +28558.0 q^{68} +31167.3 q^{69} +66930.4 q^{70} +28557.5 q^{71} -9063.63 q^{72} -21354.2 q^{73} +25295.3 q^{74} -33308.3 q^{75} -33954.1 q^{76} -95892.1 q^{77} +6806.51 q^{78} +41396.7 q^{79} +20532.8 q^{80} -4579.53 q^{81} -3655.15 q^{82} -35400.0 q^{83} -33608.7 q^{84} +143158. q^{85} -20900.3 q^{86} +29160.9 q^{87} -29417.7 q^{88} -11452.0 q^{89} -45435.1 q^{90} -35256.6 q^{91} -49526.9 q^{92} +41362.7 q^{93} -27376.5 q^{94} -170208. q^{95} -10310.5 q^{96} +135588. q^{97} +106860. q^{98} +65095.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} + 9 q^{3} + 32 q^{4} + 73 q^{5} + 36 q^{6} + 155 q^{7} + 128 q^{8} - 21 q^{9} + 292 q^{10} - 220 q^{11} + 144 q^{12} - 338 q^{13} + 620 q^{14} - 945 q^{15} + 512 q^{16} - 189 q^{17} - 84 q^{18}+ \cdots + 94002 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 + 9 * q^3 + 32 * q^4 + 73 * q^5 + 36 * q^6 + 155 * q^7 + 128 * q^8 - 21 * q^9 + 292 * q^10 - 220 * q^11 + 144 * q^12 - 338 * q^13 + 620 * q^14 - 945 * q^15 + 512 * q^16 - 189 * q^17 - 84 * q^18 - 2496 * q^19 + 1168 * q^20 - 3123 * q^21 - 880 * q^22 - 3044 * q^23 + 576 * q^24 + 235 * q^25 - 1352 * q^26 + 1539 * q^27 + 2480 * q^28 + 1900 * q^29 - 3780 * q^30 + 2798 * q^31 + 2048 * q^32 + 9198 * q^33 - 756 * q^34 + 17119 * q^35 - 336 * q^36 + 17805 * q^37 - 9984 * q^38 - 1521 * q^39 + 4672 * q^40 + 11634 * q^41 - 12492 * q^42 - 4069 * q^43 - 3520 * q^44 - 12228 * q^45 - 12176 * q^46 - 25489 * q^47 + 2304 * q^48 + 12783 * q^49 + 940 * q^50 - 55611 * q^51 - 5408 * q^52 - 4614 * q^53 + 6156 * q^54 - 38594 * q^55 + 9920 * q^56 + 14238 * q^57 + 7600 * q^58 - 23420 * q^59 - 15120 * q^60 + 96830 * q^61 + 11192 * q^62 - 36012 * q^63 + 8192 * q^64 - 12337 * q^65 + 36792 * q^66 + 72440 * q^67 - 3024 * q^68 + 32148 * q^69 + 68476 * q^70 - 36679 * q^71 - 1344 * q^72 + 47152 * q^73 + 71220 * q^74 - 91908 * q^75 - 39936 * q^76 - 108742 * q^77 - 6084 * q^78 + 52024 * q^79 + 18688 * q^80 - 78390 * q^81 + 46536 * q^82 - 37758 * q^83 - 49968 * q^84 + 157383 * q^85 - 16276 * q^86 + 120618 * q^87 - 14080 * q^88 - 105072 * q^89 - 48912 * q^90 - 26195 * q^91 - 48704 * q^92 + 173052 * q^93 - 101956 * q^94 - 167514 * q^95 + 9216 * q^96 + 104392 * q^97 + 51132 * q^98 + 94002 * q^99

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