LMFDB - Embedded newform 961.6.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,6,Mod(1,961)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("961.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	961.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$154.128850840$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 199x^{6} + 256x^{5} + 12633x^{4} - 18583x^{3} - 260319x^{2} + 410640x + 275908 $ x^8 - x^7 - 199x^6 + 256x^5 + 12633x^4 - 18583x^3 - 260319x^2 + 410640x + 275908
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 5\cdot 13 $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-7.89102$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.89102 q^{2} -18.9313 q^{3} +47.0502 q^{4} -33.8630 q^{5} -168.319 q^{6} -134.850 q^{7} +133.811 q^{8} +115.395 q^{9} -301.077 q^{10} +191.415 q^{11} -890.722 q^{12} -766.219 q^{13} -1198.95 q^{14} +641.071 q^{15} -315.888 q^{16} -1357.39 q^{17} +1025.98 q^{18} -164.832 q^{19} -1593.26 q^{20} +2552.89 q^{21} +1701.88 q^{22} -3313.68 q^{23} -2533.22 q^{24} -1978.30 q^{25} -6812.46 q^{26} +2415.73 q^{27} -6344.71 q^{28} +6675.50 q^{29} +5699.78 q^{30} -7090.52 q^{32} -3623.74 q^{33} -12068.6 q^{34} +4566.42 q^{35} +5429.35 q^{36} -10334.6 q^{37} -1465.53 q^{38} +14505.5 q^{39} -4531.25 q^{40} +13434.9 q^{41} +22697.7 q^{42} -16907.4 q^{43} +9006.12 q^{44} -3907.62 q^{45} -29462.0 q^{46} -18714.2 q^{47} +5980.17 q^{48} +1377.48 q^{49} -17589.1 q^{50} +25697.2 q^{51} -36050.7 q^{52} -11410.8 q^{53} +21478.3 q^{54} -6481.90 q^{55} -18044.4 q^{56} +3120.50 q^{57} +59351.9 q^{58} +7475.61 q^{59} +30162.5 q^{60} +55634.9 q^{61} -15561.0 q^{63} -52933.5 q^{64} +25946.5 q^{65} -32218.8 q^{66} +26388.2 q^{67} -63865.5 q^{68} +62732.4 q^{69} +40600.1 q^{70} -14258.2 q^{71} +15441.1 q^{72} -6721.72 q^{73} -91885.2 q^{74} +37451.8 q^{75} -7755.39 q^{76} -25812.3 q^{77} +128969. q^{78} +29059.9 q^{79} +10696.9 q^{80} -73774.0 q^{81} +119450. q^{82} +37568.9 q^{83} +120114. q^{84} +45965.3 q^{85} -150324. q^{86} -126376. q^{87} +25613.5 q^{88} -91193.1 q^{89} -34742.7 q^{90} +103325. q^{91} -155909. q^{92} -166388. q^{94} +5581.72 q^{95} +134233. q^{96} +95596.4 q^{97} +12247.2 q^{98} +22088.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 7 q^{2} + 2 q^{3} + 149 q^{4} + 128 q^{5} - 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9} + 1581 q^{10} - 574 q^{11} + 46 q^{12} + 122 q^{13} - 309 q^{14} + 524 q^{15} + 833 q^{16} - 1932 q^{17} - 6845 q^{18}+ \cdots + 180150 q^{99}+O(q^{100}) $ 8 * q + 7 * q^2 + 2 * q^3 + 149 * q^4 + 128 * q^5 - 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9 + 1581 * q^10 - 574 * q^11 + 46 * q^12 + 122 * q^13 - 309 * q^14 + 524 * q^15 + 833 * q^16 - 1932 * q^17 - 6845 * q^18 - 1796 * q^19 - 37 * q^20 - 996 * q^21 + 9000 * q^22 + 4136 * q^23 + 17468 * q^24 + 3308 * q^25 - 1524 * q^26 + 2624 * q^27 - 21245 * q^28 - 5050 * q^29 + 30450 * q^30 + 21045 * q^32 + 27920 * q^33 + 24738 * q^34 + 25700 * q^35 + 21637 * q^36 - 23674 * q^37 - 4289 * q^38 + 38652 * q^39 + 36606 * q^40 + 44828 * q^41 + 9994 * q^42 - 21058 * q^43 - 13168 * q^44 - 1344 * q^45 - 6198 * q^46 + 5348 * q^47 + 69588 * q^48 + 19356 * q^49 + 33242 * q^50 + 22300 * q^51 + 60386 * q^52 - 4926 * q^53 + 24476 * q^54 + 56892 * q^55 - 87652 * q^56 - 22072 * q^57 + 25002 * q^58 + 16944 * q^59 + 138556 * q^60 + 73682 * q^61 - 138784 * q^63 - 1300 * q^64 - 63316 * q^65 - 128796 * q^66 - 134768 * q^67 + 9524 * q^68 + 3992 * q^69 - 142737 * q^70 + 123724 * q^71 + 93232 * q^72 - 70792 * q^73 - 307468 * q^74 + 302902 * q^75 - 65405 * q^76 - 107932 * q^77 + 36820 * q^78 + 26036 * q^79 + 576783 * q^80 + 82528 * q^81 + 142335 * q^82 - 21882 * q^83 - 299144 * q^84 + 130464 * q^85 - 480478 * q^86 - 440244 * q^87 + 71982 * q^88 - 164392 * q^89 + 397969 * q^90 + 60028 * q^91 - 31012 * q^92 - 170388 * q^94 - 7404 * q^95 + 331010 * q^96 - 131948 * q^97 + 288768 * q^98 + 180150 * 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 $

$2$	8.89102	1.57172	0.785862	−	0.618402i	$-0.212220\pi$
$2$	8.89102	1.57172	0.785862	+	0.618402i	$0.212220\pi$
$3$	−18.9313	−1.21444	−0.607222	−	0.794532i	$-0.707716\pi$
$3$	−18.9313	−1.21444	−0.607222	+	0.794532i	$0.707716\pi$
$4$	47.0502	1.47032
$5$	−33.8630	−0.605760	−0.302880	−	0.953029i	$-0.597948\pi$
$5$	−33.8630	−0.605760	−0.302880	+	0.953029i	$0.597948\pi$
$6$	−168.319	−1.90877
$7$	−134.850	−1.04017	−0.520086	−	0.854114i	$-0.674100\pi$
$7$	−134.850	−1.04017	−0.520086	+	0.854114i	$0.674100\pi$
$8$	133.811	0.739209
$9$	115.395	0.474876
$10$	−301.077	−0.952088
$11$	191.415	0.476974	0.238487	−	0.971146i	$-0.423349\pi$
$11$	191.415	0.476974	0.238487	+	0.971146i	$0.423349\pi$
$12$	−890.722	−1.78562
$13$	−766.219	−1.25746	−0.628730	−	0.777623i	$-0.716425\pi$
$13$	−766.219	−1.25746	−0.628730	+	0.777623i	$0.716425\pi$
$14$	−1198.95	−1.63486
$15$	641.071	0.735662
$16$	−315.888	−0.308484
$17$	−1357.39	−1.13915	−0.569577	−	0.821938i	$-0.692893\pi$
$17$	−1357.39	−1.13915	−0.569577	+	0.821938i	$0.692893\pi$
$18$	1025.98	0.746375
$19$	−164.832	−0.104751	−0.0523755	−	0.998627i	$-0.516679\pi$
$19$	−164.832	−0.104751	−0.0523755	+	0.998627i	$0.516679\pi$
$20$	−1593.26	−0.890659
$21$	2552.89	1.26323
$22$	1701.88	0.749672
$23$	−3313.68	−1.30615	−0.653073	−	0.757295i	$-0.726520\pi$
$23$	−3313.68	−1.30615	−0.653073	+	0.757295i	$0.726520\pi$
$24$	−2533.22	−0.897729
$25$	−1978.30	−0.633055
$26$	−6812.46	−1.97638
$27$	2415.73	0.637734
$28$	−6344.71	−1.52938
$29$	6675.50	1.47397	0.736985	−	0.675909i	$-0.236249\pi$
$29$	6675.50	1.47397	0.736985	+	0.675909i	$0.236249\pi$
$30$	5699.78	1.15626
$31$	0	0
$31$	0	0
$32$	−7090.52	−1.22406
$33$	−3623.74	−0.579259
$34$	−12068.6	−1.79044
$35$	4566.42	0.630095
$36$	5429.35	0.698219
$37$	−10334.6	−1.24105	−0.620526	−	0.784186i	$-0.713081\pi$
$37$	−10334.6	−1.24105	−0.620526	+	0.784186i	$0.713081\pi$
$38$	−1465.53	−0.164640
$39$	14505.5	1.52712
$40$	−4531.25	−0.447783
$41$	13434.9	1.24817	0.624085	−	0.781356i	$-0.285472\pi$
$41$	13434.9	1.24817	0.624085	+	0.781356i	$0.285472\pi$
$42$	22697.7	1.98545
$43$	−16907.4	−1.39446	−0.697228	−	0.716850i	$-0.745583\pi$
$43$	−16907.4	−1.39446	−0.697228	+	0.716850i	$0.745583\pi$
$44$	9006.12	0.701303
$45$	−3907.62	−0.287661
$46$	−29462.0	−2.05290
$47$	−18714.2	−1.23574	−0.617869	−	0.786281i	$-0.712004\pi$
$47$	−18714.2	−1.23574	−0.617869	+	0.786281i	$0.712004\pi$
$48$	5980.17	0.374637
$49$	1377.48	0.0819589
$50$	−17589.1	−0.994988
$51$	25697.2	1.38344
$52$	−36050.7	−1.84887
$53$	−11410.8	−0.557990	−0.278995	−	0.960293i	$-0.590001\pi$
$53$	−11410.8	−0.557990	−0.278995	+	0.960293i	$0.590001\pi$
$54$	21478.3	1.00234
$55$	−6481.90	−0.288932
$56$	−18044.4	−0.768905
$57$	3120.50	0.127214
$58$	59351.9	2.31667
$59$	7475.61	0.279587	0.139793	−	0.990181i	$-0.455356\pi$
$59$	7475.61	0.279587	0.139793	+	0.990181i	$0.455356\pi$
$60$	30162.5	1.08166
$61$	55634.9	1.91436	0.957179	−	0.289498i	$-0.0934884\pi$
$61$	55634.9	1.91436	0.957179	+	0.289498i	$0.0934884\pi$
$62$	0	0
$63$	−15561.0	−0.493953
$64$	−52933.5	−1.61540
$65$	25946.5	0.761719
$66$	−32218.8	−0.910435
$67$	26388.2	0.718161	0.359081	−	0.933307i	$-0.383090\pi$
$67$	26388.2	0.718161	0.359081	+	0.933307i	$0.383090\pi$
$68$	−63865.5	−1.67492
$69$	62732.4	1.58624
$70$	40600.1	0.990335
$71$	−14258.2	−0.335674	−0.167837	−	0.985815i	$-0.553678\pi$
$71$	−14258.2	−0.335674	−0.167837	+	0.985815i	$0.553678\pi$
$72$	15441.1	0.351033
$73$	−6721.72	−0.147630	−0.0738148	−	0.997272i	$-0.523517\pi$
$73$	−6721.72	−0.147630	−0.0738148	+	0.997272i	$0.523517\pi$
$74$	−91885.2	−1.95059
$75$	37451.8	0.768810
$76$	−7755.39	−0.154017
$77$	−25812.3	−0.496135
$78$	128969.	2.40021
$79$	29059.9	0.523874	0.261937	−	0.965085i	$-0.415639\pi$
$79$	29059.9	0.523874	0.261937	+	0.965085i	$0.415639\pi$
$80$	10696.9	0.186867
$81$	−73774.0	−1.24937
$82$	119450.	1.96178
$83$	37568.9	0.598595	0.299298	−	0.954160i	$-0.403248\pi$
$83$	37568.9	0.598595	0.299298	+	0.954160i	$0.403248\pi$
$84$	120114.	1.85735
$85$	45965.3	0.690054
$86$	−150324.	−2.19170
$87$	−126376.	−1.79005
$88$	25613.5	0.352584
$89$	−91193.1	−1.22036	−0.610179	−	0.792264i	$-0.708902\pi$
$89$	−91193.1	−1.22036	−0.610179	+	0.792264i	$0.708902\pi$
$90$	−34742.7	−0.452124
$91$	103325.	1.30798
$92$	−155909.	−1.92045
$93$	0	0
$94$	−166388.	−1.94224
$95$	5581.72	0.0634540
$96$	134233.	1.48655
$97$	95596.4	1.03160	0.515801	−	0.856708i	$-0.327494\pi$
$97$	95596.4	1.03160	0.515801	+	0.856708i	$0.327494\pi$
$98$	12247.2	0.128817
$99$	22088.4	0.226504
$100$	−93079.2	−0.930792
$101$	−71056.1	−0.693103	−0.346551	−	0.938031i	$-0.612647\pi$
$101$	−71056.1	−0.693103	−0.346551	+	0.938031i	$0.612647\pi$
$102$	228474.	2.17439
$103$	−176351.	−1.63789	−0.818946	−	0.573870i	$-0.805441\pi$
$103$	−176351.	−1.63789	−0.818946	+	0.573870i	$0.805441\pi$
$104$	−102529.	−0.929527
$105$	−86448.4	−0.765215
$106$	−101454.	−0.877006
$107$	141241.	1.19262	0.596308	−	0.802756i	$-0.296634\pi$
$107$	141241.	1.19262	0.596308	+	0.802756i	$0.296634\pi$
$108$	113661.	0.937671
$109$	−70513.7	−0.568470	−0.284235	−	0.958755i	$-0.591740\pi$
$109$	−70513.7	−0.568470	−0.284235	+	0.958755i	$0.591740\pi$
$110$	−57630.6	−0.454121
$111$	195648.	1.50719
$112$	42597.4	0.320877
$113$	170060.	1.25287	0.626436	−	0.779473i	$-0.284513\pi$
$113$	170060.	1.25287	0.626436	+	0.779473i	$0.284513\pi$
$114$	27744.4	0.199946
$115$	112211.	0.791211
$116$	314083.	2.16720
$117$	−88417.8	−0.597138
$118$	66465.7	0.439433
$119$	183044.	1.18492
$120$	85782.5	0.543808
$121$	−124411.	−0.772496
$122$	494651.	3.00884
$123$	−254340.	−1.51583
$124$	0	0
$125$	172813.	0.989239
$126$	−138353.	−0.776358
$127$	198550.	1.09235	0.546175	−	0.837671i	$-0.316084\pi$
$127$	198550.	1.09235	0.546175	+	0.837671i	$0.316084\pi$
$128$	−243736.	−1.31491
$129$	320079.	1.69349
$130$	230691.	1.19721
$131$	−78021.3	−0.397223	−0.198612	−	0.980078i	$-0.563643\pi$
$131$	−78021.3	−0.397223	−0.198612	+	0.980078i	$0.563643\pi$
$132$	−170498.	−0.851694
$133$	22227.6	0.108959
$134$	234618.	1.12875
$135$	−81804.0	−0.386314
$136$	−181634.	−0.842074
$137$	−131437.	−0.598298	−0.299149	−	0.954206i	$-0.596703\pi$
$137$	−131437.	−0.598298	−0.299149	+	0.954206i	$0.596703\pi$
$138$	557755.	2.49313
$139$	42476.0	0.186469	0.0932345	−	0.995644i	$-0.470279\pi$
$139$	42476.0	0.186469	0.0932345	+	0.995644i	$0.470279\pi$
$140$	214851.	0.926439
$141$	354284.	1.50074
$142$	−126770.	−0.527587
$143$	−146666.	−0.599776
$144$	−36451.8	−0.146492
$145$	−226052.	−0.892872
$146$	−59762.9	−0.232033
$147$	−26077.6	−0.0995346
$148$	−486245.	−1.82474
$149$	292210.	1.07827	0.539137	−	0.842218i	$-0.318751\pi$
$149$	292210.	1.07827	0.539137	+	0.842218i	$0.318751\pi$
$150$	332984.	1.20836
$151$	425103.	1.51723	0.758615	−	0.651539i	$-0.225876\pi$
$151$	425103.	1.51723	0.758615	+	0.651539i	$0.225876\pi$
$152$	−22056.4	−0.0774330
$153$	−156636.	−0.540957
$154$	−229498.	−0.779788
$155$	0	0
$156$	682488.	2.24535
$157$	−239463.	−0.775336	−0.387668	−	0.921799i	$-0.626719\pi$
$157$	−239463.	−0.775336	−0.387668	+	0.921799i	$0.626719\pi$
$158$	258372.	0.823385
$159$	216022.	0.677648
$160$	240106.	0.741487
$161$	446850.	1.35862
$162$	−655926.	−1.96366
$163$	388547.	1.14544	0.572722	−	0.819749i	$-0.305887\pi$
$163$	388547.	1.14544	0.572722	+	0.819749i	$0.305887\pi$
$164$	632113.	1.83521
$165$	122711.	0.350892
$166$	334026.	0.940827
$167$	306915.	0.851583	0.425792	−	0.904821i	$-0.359996\pi$
$167$	306915.	0.851583	0.425792	+	0.904821i	$0.359996\pi$
$168$	341605.	0.933793
$169$	215798.	0.581208
$170$	408679.	1.08457
$171$	−19020.8	−0.0497438
$172$	−795494.	−2.05029
$173$	655244.	1.66451	0.832257	−	0.554389i	$-0.187048\pi$
$173$	655244.	1.66451	0.832257	+	0.554389i	$0.187048\pi$
$174$	−1.12361e6	−2.81347
$175$	266773.	0.658486
$176$	−60465.7	−0.147139
$177$	−141523.	−0.339543
$178$	−810799.	−1.91807
$179$	−50816.0	−0.118541	−0.0592705	−	0.998242i	$-0.518877\pi$
$179$	−50816.0	−0.118541	−0.0592705	+	0.998242i	$0.518877\pi$
$180$	−183854.	−0.422953
$181$	549255.	1.24617	0.623085	−	0.782154i	$-0.285879\pi$
$181$	549255.	1.24617	0.623085	+	0.782154i	$0.285879\pi$
$182$	918660.	2.05578
$183$	−1.05324e6	−2.32488
$184$	−443408.	−0.965515
$185$	349961.	0.751779
$186$	0	0
$187$	−259825.	−0.543347
$188$	−880505.	−1.81693
$189$	−325761.	−0.663353
$190$	49627.2	0.0997322
$191$	−554457.	−1.09973	−0.549863	−	0.835255i	$-0.685320\pi$
$191$	−554457.	−1.09973	−0.549863	+	0.835255i	$0.685320\pi$
$192$	1.00210e6	1.96182
$193$	47999.3	0.0927559	0.0463780	−	0.998924i	$-0.485232\pi$
$193$	47999.3	0.0927559	0.0463780	+	0.998924i	$0.485232\pi$
$194$	849949.	1.62139
$195$	−491201.	−0.925066
$196$	64810.8	0.120506
$197$	−1.00912e6	−1.85258	−0.926292	−	0.376807i	$-0.877022\pi$
$197$	−1.00912e6	−1.85258	−0.926292	+	0.376807i	$0.877022\pi$
$198$	196388.	0.356001
$199$	−504306.	−0.902738	−0.451369	−	0.892337i	$-0.649064\pi$
$199$	−504306.	−0.902738	−0.451369	+	0.892337i	$0.649064\pi$
$200$	−264718.	−0.467960
$201$	−499563.	−0.872167
$202$	−631761.	−1.08937
$203$	−900190.	−1.53318
$204$	1.20906e6	2.03410
$205$	−454945.	−0.756092
$206$	−1.56794e6	−2.57432
$207$	−382382.	−0.620258
$208$	242039.	0.387907
$209$	−31551.4	−0.0499636
$210$	−768614.	−1.20271
$211$	403332.	0.623673	0.311836	−	0.950136i	$-0.399056\pi$
$211$	403332.	0.623673	0.311836	+	0.950136i	$0.399056\pi$
$212$	−536880.	−0.820422
$213$	269926.	0.407658
$214$	1.25577e6	1.87446
$215$	572534.	0.844705
$216$	323252.	0.471419
$217$	0	0
$218$	−626939.	−0.893478
$219$	127251.	0.179288
$220$	−304974.	−0.424822
$221$	1.04006e6	1.43244
$222$	1.73951e6	2.36889
$223$	−381052.	−0.513124	−0.256562	−	0.966528i	$-0.582590\pi$
$223$	−381052.	−0.513124	−0.256562	+	0.966528i	$0.582590\pi$
$224$	956156.	1.27323
$225$	−228285.	−0.300623
$226$	1.51201e6	1.96917
$227$	−1.00818e6	−1.29860	−0.649298	−	0.760534i	$-0.724937\pi$
$227$	−1.00818e6	−1.29860	−0.649298	+	0.760534i	$0.724937\pi$
$228$	146820.	0.187046
$229$	840771.	1.05947	0.529735	−	0.848163i	$-0.322291\pi$
$229$	840771.	1.05947	0.529735	+	0.848163i	$0.322291\pi$
$230$	997673.	1.24357
$231$	488661.	0.602529
$232$	893256.	1.08957
$233$	−1.18940e6	−1.43528	−0.717640	−	0.696415i	$-0.754778\pi$
$233$	−1.18940e6	−1.43528	−0.717640	+	0.696415i	$0.754778\pi$
$234$	−786124.	−0.938537
$235$	633719.	0.748560
$236$	351729.	0.411081
$237$	−550143.	−0.636216
$238$	1.62745e6	1.86236
$239$	−1.06364e6	−1.20448	−0.602240	−	0.798315i	$-0.705725\pi$
$239$	−1.06364e6	−1.20448	−0.602240	+	0.798315i	$0.705725\pi$
$240$	−202507.	−0.226940
$241$	−1.10322e6	−1.22354	−0.611772	−	0.791034i	$-0.709543\pi$
$241$	−1.10322e6	−1.22354	−0.611772	+	0.791034i	$0.709543\pi$
$242$	−1.10614e6	−1.21415
$243$	809616.	0.879556
$244$	2.61763e6	2.81471
$245$	−46645.7	−0.0496474
$246$	−2.26134e6	−2.38247
$247$	126298.	0.131720
$248$	0	0
$249$	−711229.	−0.726961
$250$	1.53648e6	1.55481
$251$	103694.	0.103889	0.0519445	−	0.998650i	$-0.483458\pi$
$251$	103694.	0.103889	0.0519445	+	0.998650i	$0.483458\pi$
$252$	−732147.	−0.726268
$253$	−634290.	−0.622998
$254$	1.76531e6	1.71687
$255$	−870185.	−0.838033
$256$	−473189.	−0.451268
$257$	423080.	0.399567	0.199783	−	0.979840i	$-0.435976\pi$
$257$	423080.	0.399567	0.199783	+	0.979840i	$0.435976\pi$
$258$	2.84582e6	2.66170
$259$	1.39362e6	1.29091
$260$	1.22079e6	1.11997
$261$	770318.	0.699953
$262$	−693688.	−0.624326
$263$	−1.79143e6	−1.59702	−0.798511	−	0.601980i	$-0.794379\pi$
$263$	−1.79143e6	−1.59702	−0.798511	+	0.601980i	$0.794379\pi$
$264$	−484897.	−0.428194
$265$	386404.	0.338008
$266$	197626.	0.171254
$267$	1.72641e6	1.48206
$268$	1.24157e6	1.05593
$269$	67703.6	0.0570468	0.0285234	−	0.999593i	$-0.490919\pi$
$269$	67703.6	0.0570468	0.0285234	+	0.999593i	$0.490919\pi$
$270$	−727320.	−0.607178
$271$	936407.	0.774536	0.387268	−	0.921967i	$-0.373419\pi$
$271$	936407.	0.774536	0.387268	+	0.921967i	$0.373419\pi$
$272$	428783.	0.351411
$273$	−1.95607e6	−1.58846
$274$	−1.16861e6	−0.940360
$275$	−378676.	−0.301951
$276$	2.95157e6	2.33228
$277$	−713290.	−0.558556	−0.279278	−	0.960210i	$-0.590095\pi$
$277$	−713290.	−0.558556	−0.279278	+	0.960210i	$0.590095\pi$
$278$	377655.	0.293078
$279$	0	0
$280$	611038.	0.465772
$281$	908575.	0.686428	0.343214	−	0.939257i	$-0.388484\pi$
$281$	908575.	0.686428	0.343214	+	0.939257i	$0.388484\pi$
$282$	3.14995e6	2.35874
$283$	−1.96084e6	−1.45538	−0.727691	−	0.685905i	$-0.759406\pi$
$283$	−1.96084e6	−1.45538	−0.727691	+	0.685905i	$0.759406\pi$
$284$	−670849.	−0.493547
$285$	−105669.	−0.0770614
$286$	−1.30401e6	−0.942683
$287$	−1.81169e6	−1.29831
$288$	−818210.	−0.581278
$289$	422653.	0.297673
$290$	−2.00984e6	−1.40335
$291$	−1.80977e6	−1.25282
$292$	−316258.	−0.217062
$293$	816856.	0.555874	0.277937	−	0.960599i	$-0.410349\pi$
$293$	816856.	0.555874	0.277937	+	0.960599i	$0.410349\pi$
$294$	−231856.	−0.156441
$295$	−253147.	−0.169362
$296$	−1.38289e6	−0.917397
$297$	462408.	0.304183
$298$	2.59804e6	1.69475
$299$	2.53901e6	1.64243
$300$	1.76211e6	1.13040
$301$	2.27995e6	1.45047
$302$	3.77960e6	2.38467
$303$	1.34519e6	0.841735
$304$	52068.5	0.0323141
$305$	−1.88397e6	−1.15964
$306$	−1.39265e6	−0.850236
$307$	842.455	0.000510153 0	0.000255077	−	1.00000i	$-0.499919\pi$
$307$	842.455	0.000510153 0	0.000255077		1.00000i	$0.499919\pi$
$308$	−1.21447e6	−0.729477
$309$	3.33856e6	1.98913
$310$	0	0
$311$	−275493.	−0.161514	−0.0807568	−	0.996734i	$-0.525734\pi$
$311$	−275493.	−0.161514	−0.0807568	+	0.996734i	$0.525734\pi$
$312$	1.94100e6	1.12886
$313$	919046.	0.530245	0.265122	−	0.964215i	$-0.414588\pi$
$313$	919046.	0.530245	0.265122	+	0.964215i	$0.414588\pi$
$314$	−2.12907e6	−1.21861
$315$	526942.	0.299217
$316$	1.36727e6	0.770261
$317$	−297343.	−0.166192	−0.0830960	−	0.996542i	$-0.526481\pi$
$317$	−297343.	−0.166192	−0.0830960	+	0.996542i	$0.526481\pi$
$318$	1.92065e6	1.06508
$319$	1.27779e6	0.703045
$320$	1.79249e6	0.978546
$321$	−2.67387e6	−1.44837
$322$	3.97295e6	2.13537
$323$	223742.	0.119328
$324$	−3.47108e6	−1.83697
$325$	1.51581e6	0.796042
$326$	3.45457e6	1.80032
$327$	1.33492e6	0.690375
$328$	1.79774e6	0.922660
$329$	2.52361e6	1.28538
$330$	1.09102e6	0.551505
$331$	808752.	0.405738	0.202869	−	0.979206i	$-0.434974\pi$
$331$	808752.	0.405738	0.202869	+	0.979206i	$0.434974\pi$
$332$	1.76762e6	0.880125
$333$	−1.19256e6	−0.589346
$334$	2.72879e6	1.33845
$335$	−893582.	−0.435033
$336$	−806425.	−0.389687
$337$	−3.71052e6	−1.77975	−0.889876	−	0.456203i	$-0.849209\pi$
$337$	−3.71052e6	−1.77975	−0.889876	+	0.456203i	$0.849209\pi$
$338$	1.91867e6	0.913498
$339$	−3.21947e6	−1.52154
$340$	2.16268e6	1.01460
$341$	0	0
$342$	−169114.	−0.0781836
$343$	2.08067e6	0.954921
$344$	−2.26239e6	−1.03079
$345$	−2.12431e6	−0.960882
$346$	5.82578e6	2.61616
$347$	−1.52902e6	−0.681694	−0.340847	−	0.940119i	$-0.610714\pi$
$347$	−1.52902e6	−0.681694	−0.340847	+	0.940119i	$0.610714\pi$
$348$	−5.94601e6	−2.63195
$349$	3.11316e6	1.36816	0.684082	−	0.729405i	$-0.260203\pi$
$349$	3.11316e6	1.36816	0.684082	+	0.729405i	$0.260203\pi$
$350$	2.37188e6	1.03496
$351$	−1.85098e6	−0.801925
$352$	−1.35723e6	−0.583846
$353$	−1.90044e6	−0.811741	−0.405871	−	0.913931i	$-0.633032\pi$
$353$	−1.90044e6	−0.811741	−0.405871	+	0.913931i	$0.633032\pi$
$354$	−1.25828e6	−0.533667
$355$	482824.	0.203338
$356$	−4.29065e6	−1.79431
$357$	−3.46526e6	−1.43902
$358$	−451806.	−0.186314
$359$	6638.27	0.00271844	0.00135922	−	0.999999i	$-0.499567\pi$
$359$	6638.27	0.00271844	0.00135922	+	0.999999i	$0.499567\pi$
$360$	−522883.	−0.212642
$361$	−2.44893e6	−0.989027
$362$	4.88343e6	1.95864
$363$	2.35527e6	0.938153
$364$	4.86143e6	1.92314
$365$	227618.	0.0894281
$366$	−9.36440e6	−3.65407
$367$	154555.	0.0598989	0.0299494	−	0.999551i	$-0.490465\pi$
$367$	154555.	0.0598989	0.0299494	+	0.999551i	$0.490465\pi$
$368$	1.04675e6	0.402925
$369$	1.55032e6	0.592727
$370$	3.11151e6	1.18159
$371$	1.53874e6	0.580406
$372$	0	0
$373$	2.82330e6	1.05072	0.525358	−	0.850881i	$-0.323931\pi$
$373$	2.82330e6	1.05072	0.525358	+	0.850881i	$0.323931\pi$
$374$	−2.31011e6	−0.853992
$375$	−3.27158e6	−1.20138
$376$	−2.50417e6	−0.913469
$377$	−5.11489e6	−1.85346
$378$	−2.89635e6	−1.04261
$379$	−2.30151e6	−0.823028	−0.411514	−	0.911403i	$-0.635000\pi$
$379$	−2.30151e6	−0.823028	−0.411514	+	0.911403i	$0.635000\pi$
$380$	262621.	0.0932975
$381$	−3.75882e6	−1.32660
$382$	−4.92969e6	−1.72847
$383$	416401.	0.145049	0.0725245	−	0.997367i	$-0.476894\pi$
$383$	416401.	0.145049	0.0725245	+	0.997367i	$0.476894\pi$
$384$	4.61425e6	1.59688
$385$	874083.	0.300539
$386$	426763.	0.145787
$387$	−1.95102e6	−0.662194
$388$	4.49783e6	1.51678
$389$	−3.82595e6	−1.28193	−0.640967	−	0.767568i	$-0.721467\pi$
$389$	−3.82595e6	−1.28193	−0.640967	+	0.767568i	$0.721467\pi$
$390$	−4.36728e6	−1.45395
$391$	4.49797e6	1.48790
$392$	184323.	0.0605848
$393$	1.47705e6	0.482406
$394$	−8.97211e6	−2.91175
$395$	−984056.	−0.317342
$396$	1.03926e6	0.333032
$397$	3.10740e6	0.989513	0.494756	−	0.869032i	$-0.335257\pi$
$397$	3.10740e6	0.989513	0.494756	+	0.869032i	$0.335257\pi$
$398$	−4.48380e6	−1.41886
$399$	−420798.	−0.132325
$400$	624920.	0.195287
$401$	−339771.	−0.105518	−0.0527588	−	0.998607i	$-0.516801\pi$
$401$	−339771.	−0.105518	−0.0527588	+	0.998607i	$0.516801\pi$
$402$	−4.44162e6	−1.37081
$403$	0	0
$404$	−3.34320e6	−1.01908
$405$	2.49821e6	0.756818
$406$	−8.00360e6	−2.40974
$407$	−1.97820e6	−0.591950
$408$	3.43857e6	1.02265
$409$	−1.56215e6	−0.461759	−0.230880	−	0.972982i	$-0.574160\pi$
$409$	−1.56215e6	−0.461759	−0.230880	+	0.972982i	$0.574160\pi$
$410$	−4.04493e6	−1.18837
$411$	2.48829e6	0.726600
$412$	−8.29735e6	−2.40822
$413$	−1.00808e6	−0.290818
$414$	−3.39977e6	−0.974874
$415$	−1.27220e6	−0.362605
$416$	5.43289e6	1.53921
$417$	−804127.	−0.226456
$418$	−280524.	−0.0785290
$419$	−430682.	−0.119846	−0.0599228	−	0.998203i	$-0.519085\pi$
$419$	−430682.	−0.119846	−0.0599228	+	0.998203i	$0.519085\pi$
$420$	−4.06741e6	−1.12511
$421$	−3.15827e6	−0.868448	−0.434224	−	0.900805i	$-0.642977\pi$
$421$	−3.15827e6	−0.868448	−0.434224	+	0.900805i	$0.642977\pi$
$422$	3.58603e6	0.980241
$423$	−2.15952e6	−0.586822
$424$	−1.52689e6	−0.412471
$425$	2.68532e6	0.721147
$426$	2.39992e6	0.640725
$427$	−7.50236e6	−1.99126
$428$	6.64540e6	1.75352
$429$	2.77658e6	0.728395
$430$	5.09041e6	1.32764
$431$	2.85837e6	0.741182	0.370591	−	0.928796i	$-0.379155\pi$
$431$	2.85837e6	0.741182	0.370591	+	0.928796i	$0.379155\pi$
$432$	−763100.	−0.196731
$433$	4.33104e6	1.11013	0.555063	−	0.831808i	$-0.312694\pi$
$433$	4.33104e6	1.11013	0.555063	+	0.831808i	$0.312694\pi$
$434$	0	0
$435$	4.27947e6	1.08434
$436$	−3.31768e6	−0.835831
$437$	546203.	0.136820
$438$	1.13139e6	0.281791
$439$	−7.01460e6	−1.73717	−0.868584	−	0.495542i	$-0.834969\pi$
$439$	−7.01460e6	−1.73717	−0.868584	+	0.495542i	$0.834969\pi$
$440$	−867350.	−0.213581
$441$	158955.	0.0389203
$442$	9.24718e6	2.25140
$443$	−5.04828e6	−1.22218	−0.611088	−	0.791563i	$-0.709268\pi$
$443$	−5.04828e6	−1.22218	−0.611088	+	0.791563i	$0.709268\pi$
$444$	9.20526e6	2.21605
$445$	3.08807e6	0.739244
$446$	−3.38794e6	−0.806490
$447$	−5.53191e6	−1.30950
$448$	7.13808e6	1.68030
$449$	108991.	0.0255138	0.0127569	−	0.999919i	$-0.495939\pi$
$449$	108991.	0.0255138	0.0127569	+	0.999919i	$0.495939\pi$
$450$	−2.02969e6	−0.472496
$451$	2.57164e6	0.595345
$452$	8.00136e6	1.84212
$453$	−8.04776e6	−1.84259
$454$	−8.96375e6	−2.04103
$455$	−3.49888e6	−0.792320
$456$	417557.	0.0940381
$457$	813040.	0.182105	0.0910524	−	0.995846i	$-0.470977\pi$
$457$	813040.	0.182105	0.0910524	+	0.995846i	$0.470977\pi$
$458$	7.47531e6	1.66520
$459$	−3.27909e6	−0.726477
$460$	5.27956e6	1.16333
$461$	8.69658e6	1.90588	0.952941	−	0.303155i	$-0.0980400\pi$
$461$	8.69658e6	1.90588	0.952941	+	0.303155i	$0.0980400\pi$
$462$	4.34470e6	0.947010
$463$	−6.93409e6	−1.50327	−0.751635	−	0.659579i	$-0.770735\pi$
$463$	−6.93409e6	−1.50327	−0.751635	+	0.659579i	$0.770735\pi$
$464$	−2.10871e6	−0.454696
$465$	0	0
$466$	−1.05749e7	−2.25586
$467$	−6.34554e6	−1.34641	−0.673204	−	0.739457i	$-0.735082\pi$
$467$	−6.34554e6	−1.34641	−0.673204	+	0.739457i	$0.735082\pi$
$468$	−4.16007e6	−0.877983
$469$	−3.55844e6	−0.747012
$470$	5.63440e6	1.17653
$471$	4.53336e6	0.941603
$472$	1.00032e6	0.206673
$473$	−3.23633e6	−0.665119
$474$	−4.89133e6	−0.999956
$475$	326087.	0.0663132
$476$	8.61225e6	1.74220
$477$	−1.31675e6	−0.264976
$478$	−9.45683e6	−1.89311
$479$	5.97957e6	1.19078	0.595390	−	0.803437i	$-0.296998\pi$
$479$	5.97957e6	1.19078	0.595390	+	0.803437i	$0.296998\pi$
$480$	−4.54553e6	−0.900495
$481$	7.91857e6	1.56057
$482$	−9.80875e6	−1.92307
$483$	−8.45946e6	−1.64997
$484$	−5.85357e6	−1.13581
$485$	−3.23718e6	−0.624903
$486$	7.19831e6	1.38242
$487$	−4.60436e6	−0.879724	−0.439862	−	0.898065i	$-0.644973\pi$
$487$	−4.60436e6	−0.879724	−0.439862	+	0.898065i	$0.644973\pi$
$488$	7.44458e6	1.41511
$489$	−7.35570e6	−1.39108
$490$	−414728.	−0.0780321
$491$	−1.79128e6	−0.335321	−0.167660	−	0.985845i	$-0.553621\pi$
$491$	−1.79128e6	−0.335321	−0.167660	+	0.985845i	$0.553621\pi$
$492$	−1.19667e7	−2.22876
$493$	−9.06126e6	−1.67908
$494$	1.12291e6	0.207028
$495$	−747978.	−0.137207
$496$	0	0
$497$	1.92271e6	0.349159
$498$	−6.32355e6	−1.14258
$499$	6.85216e6	1.23190	0.615951	−	0.787785i	$-0.288772\pi$
$499$	6.85216e6	1.23190	0.615951	+	0.787785i	$0.288772\pi$
$500$	8.13088e6	1.45450
$501$	−5.81031e6	−1.03420
$502$	921945.	0.163285
$503$	−2.80195e6	−0.493787	−0.246894	−	0.969043i	$-0.579410\pi$
$503$	−2.80195e6	−0.493787	−0.246894	+	0.969043i	$0.579410\pi$
$504$	−2.08223e6	−0.365135
$505$	2.40617e6	0.419854
$506$	−5.63948e6	−0.979181
$507$	−4.08535e6	−0.705845
$508$	9.34183e6	1.60610
$509$	−2.09295e6	−0.358066	−0.179033	−	0.983843i	$-0.557297\pi$
$509$	−2.09295e6	−0.358066	−0.179033	+	0.983843i	$0.557297\pi$
$510$	−7.73682e6	−1.31716
$511$	906423.	0.153560
$512$	3.59243e6	0.605638
$513$	−398191.	−0.0668033
$514$	3.76161e6	0.628009
$515$	5.97178e6	0.992170
$516$	1.50597e7	2.48997
$517$	−3.58218e6	−0.589415
$518$	1.23907e7	2.02895
$519$	−1.24046e7	−2.02146
$520$	3.47193e6	0.563070
$521$	8.12070e6	1.31069	0.655344	−	0.755331i	$-0.272524\pi$
$521$	8.12070e6	1.31069	0.655344	+	0.755331i	$0.272524\pi$
$522$	6.84891e6	1.10013
$523$	7.70062e6	1.23104	0.615519	−	0.788122i	$-0.288947\pi$
$523$	7.70062e6	1.23104	0.615519	+	0.788122i	$0.288947\pi$
$524$	−3.67091e6	−0.584044
$525$	−5.05037e6	−0.799695
$526$	−1.59277e7	−2.51008
$527$	0	0
$528$	1.14470e6	0.178692
$529$	4.54416e6	0.706016
$530$	3.43552e6	0.531255
$531$	862647.	0.132769
$532$	1.04581e6	0.160205
$533$	−1.02941e7	−1.56953
$534$	1.53495e7	2.32938
$535$	−4.78283e6	−0.722438
$536$	3.53103e6	0.530872
$537$	962015.	0.143961
$538$	601954.	0.0896618
$539$	263671.	0.0390923
$540$	−3.84889e6	−0.568004
$541$	5.20442e6	0.764504	0.382252	−	0.924058i	$-0.375149\pi$
$541$	5.20442e6	0.764504	0.382252	+	0.924058i	$0.375149\pi$
$542$	8.32561e6	1.21736
$543$	−1.03981e7	−1.51341
$544$	9.62461e6	1.39439
$545$	2.38781e6	0.344356
$546$	−1.73914e7	−2.49663
$547$	−8.48906e6	−1.21309	−0.606543	−	0.795051i	$-0.707444\pi$
$547$	−8.48906e6	−1.21309	−0.606543	+	0.795051i	$0.707444\pi$
$548$	−6.18415e6	−0.879688
$549$	6.41999e6	0.909083
$550$	−3.36682e6	−0.474584
$551$	−1.10034e6	−0.154400
$552$	8.39430e6	1.17256
$553$	−3.91873e6	−0.544919
$554$	−6.34187e6	−0.877895
$555$	−6.62523e6	−0.912995
$556$	1.99850e6	0.274169
$557$	4.24828e6	0.580197	0.290098	−	0.956997i	$-0.406312\pi$
$557$	4.24828e6	0.580197	0.290098	+	0.956997i	$0.406312\pi$
$558$	0	0
$559$	1.29547e7	1.75347
$560$	−1.44248e6	−0.194374
$561$	4.91884e6	0.659865
$562$	8.07816e6	1.07888
$563$	7.61230e6	1.01215	0.506075	−	0.862489i	$-0.331096\pi$
$563$	7.61230e6	1.01215	0.506075	+	0.862489i	$0.331096\pi$
$564$	1.66691e7	2.20656
$565$	−5.75875e6	−0.758940
$566$	−1.74339e7	−2.28746
$567$	9.94841e6	1.29956
$568$	−1.90790e6	−0.248133
$569$	−1.33947e7	−1.73441	−0.867204	−	0.497953i	$-0.834085\pi$
$569$	−1.33947e7	−1.73441	−0.867204	+	0.497953i	$0.834085\pi$
$570$	−939508.	−0.121119
$571$	8.74767e6	1.12280	0.561400	−	0.827545i	$-0.310263\pi$
$571$	8.74767e6	1.12280	0.561400	+	0.827545i	$0.310263\pi$
$572$	−6.90066e6	−0.881862
$573$	1.04966e7	1.33556
$574$	−1.61078e7	−2.04059
$575$	6.55545e6	0.826862
$576$	−6.10826e6	−0.767116
$577$	1.01902e7	1.27421	0.637106	−	0.770776i	$-0.280131\pi$
$577$	1.01902e7	1.27421	0.637106	+	0.770776i	$0.280131\pi$
$578$	3.75782e6	0.467860
$579$	−908690.	−0.112647
$580$	−1.06358e7	−1.31280
$581$	−5.06616e6	−0.622642
$582$	−1.60907e7	−1.96909
$583$	−2.18420e6	−0.266147
$584$	−899441.	−0.109129
$585$	2.99409e6	0.361722
$586$	7.26268e6	0.873681
$587$	1.15490e7	1.38340	0.691702	−	0.722183i	$-0.256861\pi$
$587$	1.15490e7	1.38340	0.691702	+	0.722183i	$0.256861\pi$
$588$	−1.22695e6	−0.146347
$589$	0	0
$590$	−2.25073e6	−0.266191
$591$	1.91040e7	2.24986
$592$	3.26458e6	0.382845
$593$	5.09360e6	0.594824	0.297412	−	0.954749i	$-0.403877\pi$
$593$	5.09360e6	0.594824	0.297412	+	0.954749i	$0.403877\pi$
$594$	4.11128e6	0.478091
$595$	−6.19842e6	−0.717775
$596$	1.37485e7	1.58540
$597$	9.54719e6	1.09633
$598$	2.25744e7	2.58144
$599$	−1.18765e7	−1.35245	−0.676227	−	0.736694i	$-0.736386\pi$
$599$	−1.18765e7	−1.35245	−0.676227	+	0.736694i	$0.736386\pi$
$600$	5.01147e6	0.568312
$601$	−1.19316e7	−1.34745	−0.673726	−	0.738981i	$-0.735307\pi$
$601$	−1.19316e7	−1.34745	−0.673726	+	0.738981i	$0.735307\pi$
$602$	2.02711e7	2.27975
$603$	3.04506e6	0.341038
$604$	2.00012e7	2.23081
$605$	4.21294e6	0.467947
$606$	1.19601e7	1.32298
$607$	−5.04218e6	−0.555452	−0.277726	−	0.960660i	$-0.589581\pi$
$607$	−5.04218e6	−0.555452	−0.277726	+	0.960660i	$0.589581\pi$
$608$	1.16875e6	0.128222
$609$	1.70418e7	1.86197
$610$	−1.67504e7	−1.82264
$611$	1.43392e7	1.55389
$612$	−7.36975e6	−0.795379
$613$	4.40032e6	0.472969	0.236485	−	0.971635i	$-0.424005\pi$
$613$	4.40032e6	0.472969	0.236485	+	0.971635i	$0.424005\pi$
$614$	7490.28	0.000801821 0
$615$	8.61272e6	0.918232
$616$	−3.45398e6	−0.366748
$617$	−1.19518e7	−1.26393	−0.631964	−	0.774998i	$-0.717751\pi$
$617$	−1.19518e7	−1.26393	−0.631964	+	0.774998i	$0.717751\pi$
$618$	2.96832e7	3.12636
$619$	−1.26938e7	−1.33158	−0.665789	−	0.746140i	$-0.731905\pi$
$619$	−1.26938e7	−1.33158	−0.665789	+	0.746140i	$0.731905\pi$
$620$	0	0
$621$	−8.00498e6	−0.832973
$622$	−2.44941e6	−0.253855
$623$	1.22974e7	1.26938
$624$	−4.58212e6	−0.471091
$625$	330210.	0.0338135
$626$	8.17125e6	0.833399
$627$	597310.	0.0606780
$628$	−1.12668e7	−1.13999
$629$	1.40281e7	1.41375
$630$	4.68505e6	0.470287
$631$	1.48083e7	1.48058	0.740290	−	0.672287i	$-0.234688\pi$
$631$	1.48083e7	1.48058	0.740290	+	0.672287i	$0.234688\pi$
$632$	3.88854e6	0.387252
$633$	−7.63561e6	−0.757416
$634$	−2.64368e6	−0.261208
$635$	−6.72351e6	−0.661701
$636$	1.01638e7	0.996358
$637$	−1.05545e6	−0.103060
$638$	1.13609e7	1.10499
$639$	−1.64532e6	−0.159404
$640$	8.25364e6	0.796518
$641$	−1.32101e6	−0.126987	−0.0634937	−	0.997982i	$-0.520224\pi$
$641$	−1.32101e6	−0.126987	−0.0634937	+	0.997982i	$0.520224\pi$
$642$	−2.37734e7	−2.27643
$643$	5.16446e6	0.492603	0.246302	−	0.969193i	$-0.420785\pi$
$643$	5.16446e6	0.492603	0.246302	+	0.969193i	$0.420785\pi$
$644$	2.10244e7	1.99760
$645$	−1.08388e7	−1.02585
$646$	1.98929e6	0.187550
$647$	4.00756e6	0.376374	0.188187	−	0.982133i	$-0.439739\pi$
$647$	4.00756e6	0.376374	0.188187	+	0.982133i	$0.439739\pi$
$648$	−9.87178e6	−0.923545
$649$	1.43095e6	0.133356
$650$	1.34771e7	1.25116
$651$	0	0
$652$	1.82812e7	1.68417
$653$	−1.96976e7	−1.80772	−0.903858	−	0.427832i	$-0.859277\pi$
$653$	−1.96976e7	−1.80772	−0.903858	+	0.427832i	$0.859277\pi$
$654$	1.18688e7	1.08508
$655$	2.64203e6	0.240622
$656$	−4.24391e6	−0.385041
$657$	−775653.	−0.0701058
$658$	2.24374e7	2.02026
$659$	−1.19800e7	−1.07460	−0.537298	−	0.843393i	$-0.680555\pi$
$659$	−1.19800e7	−1.07460	−0.537298	+	0.843393i	$0.680555\pi$
$660$	5.77357e6	0.515922
$661$	−7.62846e6	−0.679099	−0.339550	−	0.940588i	$-0.610275\pi$
$661$	−7.62846e6	−0.679099	−0.339550	+	0.940588i	$0.610275\pi$
$662$	7.19062e6	0.637708
$663$	−1.96897e7	−1.73962
$664$	5.02714e6	0.442487
$665$	−752694.	−0.0660031
$666$	−1.06031e7	−0.926289
$667$	−2.21205e7	−1.92522
$668$	1.44404e7	1.25210
$669$	7.21382e6	0.623161
$670$	−7.94486e6	−0.683753
$671$	1.06494e7	0.913099
$672$	−1.81013e7	−1.54627
$673$	−3.71037e6	−0.315776	−0.157888	−	0.987457i	$-0.550469\pi$
$673$	−3.71037e6	−0.315776	−0.157888	+	0.987457i	$0.550469\pi$
$674$	−3.29902e7	−2.79728
$675$	−4.77904e6	−0.403721
$676$	1.01533e7	0.854560
$677$	−6.66373e6	−0.558786	−0.279393	−	0.960177i	$-0.590133\pi$
$677$	−6.66373e6	−0.558786	−0.279393	+	0.960177i	$0.590133\pi$
$678$	−2.86243e7	−2.39145
$679$	−1.28912e7	−1.07304
$680$	6.15068e6	0.510094
$681$	1.90862e7	1.57707
$682$	0	0
$683$	5.32022e6	0.436393	0.218196	−	0.975905i	$-0.429983\pi$
$683$	5.32022e6	0.436393	0.218196	+	0.975905i	$0.429983\pi$
$684$	−894933.	−0.0731392
$685$	4.45087e6	0.362425
$686$	1.84993e7	1.50087
$687$	−1.59169e7	−1.28667
$688$	5.34083e6	0.430167
$689$	8.74317e6	0.701651
$690$	−1.88873e7	−1.51024
$691$	2.44212e6	0.194568	0.0972842	−	0.995257i	$-0.468984\pi$
$691$	2.44212e6	0.194568	0.0972842	+	0.995257i	$0.468984\pi$
$692$	3.08293e7	2.44737
$693$	−2.97861e6	−0.235603
$694$	−1.35945e7	−1.07144
$695$	−1.43836e6	−0.112955
$696$	−1.69105e7	−1.32323
$697$	−1.82364e7	−1.42186
$698$	2.76792e7	2.15038
$699$	2.25168e7	1.74307
$700$	1.25517e7	0.968184
$701$	−9.95456e6	−0.765116	−0.382558	−	0.923932i	$-0.624957\pi$
$701$	−9.95456e6	−0.765116	−0.382558	+	0.923932i	$0.624957\pi$
$702$	−1.64571e7	−1.26041
$703$	1.70348e6	0.130002
$704$	−1.01323e7	−0.770506
$705$	−1.19971e7	−0.909085
$706$	−1.68968e7	−1.27583
$707$	9.58190e6	0.720947
$708$	−6.65869e6	−0.499235
$709$	4.30998e6	0.322003	0.161002	−	0.986954i	$-0.448528\pi$
$709$	4.30998e6	0.322003	0.161002	+	0.986954i	$0.448528\pi$
$710$	4.29280e6	0.319591
$711$	3.35337e6	0.248775
$712$	−1.22027e7	−0.902100
$713$	0	0
$714$	−3.08097e7	−2.26174
$715$	4.96655e6	0.363320
$716$	−2.39090e6	−0.174293
$717$	2.01361e7	1.46277
$718$	59021.0	0.00427263
$719$	8.19873e6	0.591459	0.295729	−	0.955272i	$-0.404437\pi$
$719$	8.19873e6	0.591459	0.295729	+	0.955272i	$0.404437\pi$
$720$	1.23437e6	0.0887389
$721$	2.37809e7	1.70369
$722$	−2.17735e7	−1.55448
$723$	2.08854e7	1.48593
$724$	2.58425e7	1.83227
$725$	−1.32061e7	−0.933104
$726$	2.09407e7	1.47452
$727$	−698821.	−0.0490377	−0.0245188	−	0.999699i	$-0.507805\pi$
$727$	−698821.	−0.0490377	−0.0245188	+	0.999699i	$0.507805\pi$
$728$	1.38260e7	0.966868
$729$	2.59998e6	0.181197
$730$	2.02375e6	0.140556
$731$	2.29499e7	1.58850
$732$	−4.95552e7	−3.41831
$733$	−4.55058e6	−0.312829	−0.156414	−	0.987692i	$-0.549994\pi$
$733$	−4.55058e6	−0.312829	−0.156414	+	0.987692i	$0.549994\pi$
$734$	1.37415e6	0.0941445
$735$	883065.	0.0602941
$736$	2.34957e7	1.59880
$737$	5.05110e6	0.342544
$738$	1.37839e7	0.931603
$739$	−2.71324e6	−0.182758	−0.0913791	−	0.995816i	$-0.529127\pi$
$739$	−2.71324e6	−0.182758	−0.0913791	+	0.995816i	$0.529127\pi$
$740$	1.64657e7	1.10535
$741$	−2.39098e6	−0.159967
$742$	1.36810e7	0.912238
$743$	7.49985e6	0.498403	0.249201	−	0.968452i	$-0.419832\pi$
$743$	7.49985e6	0.498403	0.249201	+	0.968452i	$0.419832\pi$
$744$	0	0
$745$	−9.89510e6	−0.653175
$746$	2.51020e7	1.65144
$747$	4.33526e6	0.284259
$748$	−1.22248e7	−0.798893
$749$	−1.90463e7	−1.24053
$750$	−2.90877e7	−1.88823
$751$	1.28965e7	0.834398	0.417199	−	0.908815i	$-0.363012\pi$
$751$	1.28965e7	0.834398	0.417199	+	0.908815i	$0.363012\pi$
$752$	5.91158e6	0.381205
$753$	−1.96306e6	−0.126167
$754$	−4.54766e7	−2.91313
$755$	−1.43953e7	−0.919078
$756$	−1.53271e7	−0.975340
$757$	−3.93920e6	−0.249844	−0.124922	−	0.992167i	$-0.539868\pi$
$757$	−3.93920e6	−0.249844	−0.124922	+	0.992167i	$0.539868\pi$
$758$	−2.04628e7	−1.29357
$759$	1.20079e7	0.756596
$760$	746897.	0.0469058
$761$	6.39591e6	0.400351	0.200175	−	0.979760i	$-0.435849\pi$
$761$	6.39591e6	0.400351	0.200175	+	0.979760i	$0.435849\pi$
$762$	−3.34197e7	−2.08505
$763$	9.50877e6	0.591307
$764$	−2.60873e7	−1.61695
$765$	5.30417e6	0.327690
$766$	3.70223e6	0.227977
$767$	−5.72795e6	−0.351569
$768$	8.95809e6	0.548040
$769$	−2.87887e7	−1.75552	−0.877760	−	0.479101i	$-0.840963\pi$
$769$	−2.87887e7	−1.75552	−0.877760	+	0.479101i	$0.840963\pi$
$770$	7.77148e6	0.472364
$771$	−8.00946e6	−0.485252
$772$	2.25838e6	0.136381
$773$	1.67733e6	0.100965	0.0504824	−	0.998725i	$-0.483924\pi$
$773$	1.67733e6	0.100965	0.0504824	+	0.998725i	$0.483924\pi$
$774$	−1.73466e7	−1.04079
$775$	0	0
$776$	1.27919e7	0.762570
$777$	−2.63831e7	−1.56774
$778$	−3.40166e7	−2.01485
$779$	−2.21450e6	−0.130747
$780$	−2.31111e7	−1.36014
$781$	−2.72923e6	−0.160108
$782$	3.99915e7	2.33857
$783$	1.61262e7	0.940000
$784$	−435130.	−0.0252830
$785$	8.10895e6	0.469668
$786$	1.31324e7	0.758209
$787$	1.64671e7	0.947719	0.473859	−	0.880601i	$-0.342860\pi$
$787$	1.64671e7	0.947719	0.473859	+	0.880601i	$0.342860\pi$
$788$	−4.74793e7	−2.72389
$789$	3.39142e7	1.93950
$790$	−8.74926e6	−0.498774
$791$	−2.29326e7	−1.30320
$792$	2.95567e6	0.167434
$793$	−4.26285e7	−2.40723
$794$	2.76280e7	1.55524
$795$	−7.31514e6	−0.410492
$796$	−2.37277e7	−1.32731
$797$	2.06976e7	1.15418	0.577092	−	0.816679i	$-0.304187\pi$
$797$	2.06976e7	1.15418	0.577092	+	0.816679i	$0.304187\pi$
$798$	−3.74132e6	−0.207978
$799$	2.54025e7	1.40770
$800$	1.40272e7	0.774898
$801$	−1.05232e7	−0.579519
$802$	−3.02091e6	−0.165845
$803$	−1.28664e6	−0.0704155
$804$	−2.35045e7	−1.28236
$805$	−1.51317e7	−0.822996
$806$	0	0
$807$	−1.28172e6	−0.0692802
$808$	−9.50810e6	−0.512348
$809$	−1.76250e7	−0.946797	−0.473399	−	0.880848i	$-0.656973\pi$
$809$	−1.76250e7	−0.946797	−0.473399	+	0.880848i	$0.656973\pi$
$810$	2.22116e7	1.18951
$811$	3.58516e7	1.91406	0.957031	−	0.289987i	$-0.0936509\pi$
$811$	3.58516e7	1.91406	0.957031	+	0.289987i	$0.0936509\pi$
$812$	−4.23541e7	−2.25427
$813$	−1.77274e7	−0.940631
$814$	−1.75882e7	−0.930382
$815$	−1.31574e7	−0.693864
$816$	−8.11743e6	−0.426769
$817$	2.78688e6	0.146071
$818$	−1.38891e7	−0.725758
$819$	1.19231e7	0.621127
$820$	−2.14053e7	−1.11170
$821$	−1.26101e7	−0.652922	−0.326461	−	0.945211i	$-0.605856\pi$
$821$	−1.26101e7	−0.652922	−0.326461	+	0.945211i	$0.605856\pi$
$822$	2.21234e7	1.14202
$823$	412984.	0.0212537	0.0106268	−	0.999944i	$-0.496617\pi$
$823$	412984.	0.0212537	0.0106268	+	0.999944i	$0.496617\pi$
$824$	−2.35978e7	−1.21075
$825$	7.16884e6	0.366703
$826$	−8.96290e6	−0.457086
$827$	1.39510e7	0.709318	0.354659	−	0.934996i	$-0.384597\pi$
$827$	1.39510e7	0.709318	0.354659	+	0.934996i	$0.384597\pi$
$828$	−1.79912e7	−0.911975
$829$	−1.37175e7	−0.693247	−0.346623	−	0.938004i	$-0.612672\pi$
$829$	−1.37175e7	−0.693247	−0.346623	+	0.938004i	$0.612672\pi$
$830$	−1.13111e7	−0.569915
$831$	1.35035e7	0.678335
$832$	4.05587e7	2.03131
$833$	−1.86978e6	−0.0933639
$834$	−7.14950e6	−0.355927
$835$	−1.03931e7	−0.515855
$836$	−1.48450e6	−0.0734623
$837$	0	0
$838$	−3.82920e6	−0.188364
$839$	−1.98766e7	−0.974849	−0.487424	−	0.873165i	$-0.662063\pi$
$839$	−1.98766e7	−0.974849	−0.487424	+	0.873165i	$0.662063\pi$
$840$	−1.15678e7	−0.565654
$841$	2.40511e7	1.17259
$842$	−2.80802e7	−1.36496
$843$	−1.72005e7	−0.833629
$844$	1.89768e7	0.916997
$845$	−7.30758e6	−0.352072
$846$	−1.92003e7	−0.922323
$847$	1.67768e7	0.803529
$848$	3.60453e6	0.172131
$849$	3.71214e7	1.76748
$850$	2.38752e7	1.13344
$851$	3.42456e7	1.62099
$852$	1.27001e7	0.599386
$853$	−3.14168e7	−1.47839	−0.739196	−	0.673490i	$-0.764794\pi$
$853$	−3.14168e7	−1.47839	−0.739196	+	0.673490i	$0.764794\pi$
$854$	−6.67036e7	−3.12971
$855$	644102.	0.0301328
$856$	1.88996e7	0.881592
$857$	−1.20160e7	−0.558865	−0.279432	−	0.960165i	$-0.590146\pi$
$857$	−1.20160e7	−0.558865	−0.279432	+	0.960165i	$0.590146\pi$
$858$	2.46866e7	1.14484
$859$	−3.96288e6	−0.183243	−0.0916216	−	0.995794i	$-0.529205\pi$
$859$	−3.96288e6	−0.183243	−0.0916216	+	0.995794i	$0.529205\pi$
$860$	2.69378e7	1.24198
$861$	3.42977e7	1.57673
$862$	2.54138e7	1.16493
$863$	1.59005e7	0.726750	0.363375	−	0.931643i	$-0.381624\pi$
$863$	1.59005e7	0.726750	0.363375	+	0.931643i	$0.381624\pi$
$864$	−1.71288e7	−0.780625
$865$	−2.21885e7	−1.00830
$866$	3.85073e7	1.74481
$867$	−8.00138e6	−0.361507
$868$	0	0
$869$	5.56251e6	0.249874
$870$	3.80488e7	1.70429
$871$	−2.02191e7	−0.903060
$872$	−9.43553e6	−0.420218
$873$	1.10313e7	0.489883
$874$	4.85630e6	0.215044
$875$	−2.33038e7	−1.02898
$876$	5.98718e6	0.263610
$877$	−3.99748e7	−1.75504	−0.877520	−	0.479540i	$-0.840803\pi$
$877$	−3.99748e7	−1.75504	−0.877520	+	0.479540i	$0.840803\pi$
$878$	−6.23669e7	−2.73035
$879$	−1.54642e7	−0.675079
$880$	2.04755e6	0.0891309
$881$	−3.99093e7	−1.73235	−0.866173	−	0.499745i	$-0.833427\pi$
$881$	−3.99093e7	−1.73235	−0.866173	+	0.499745i	$0.833427\pi$
$882$	1.41327e6	0.0611721
$883$	1.13118e7	0.488235	0.244118	−	0.969746i	$-0.421502\pi$
$883$	1.13118e7	0.488235	0.244118	+	0.969746i	$0.421502\pi$
$884$	4.89349e7	2.10614
$885$	4.79240e6	0.205681
$886$	−4.48843e7	−1.92092
$887$	3.72644e7	1.59032	0.795161	−	0.606398i	$-0.207386\pi$
$887$	3.72644e7	1.59032	0.795161	+	0.606398i	$0.207386\pi$
$888$	2.61799e7	1.11413
$889$	−2.67745e7	−1.13623
$890$	2.74561e7	1.16189
$891$	−1.41215e7	−0.595917
$892$	−1.79286e7	−0.754455
$893$	3.08470e6	0.129445
$894$	−4.91843e7	−2.05818
$895$	1.72078e6	0.0718073
$896$	3.28678e7	1.36773
$897$	−4.80668e7	−1.99464
$898$	969041.	0.0401006
$899$	0	0
$900$	−1.07409e7	−0.442011
$901$	1.54889e7	0.635637
$902$	2.28645e7	0.935719
$903$	−4.31626e7	−1.76152
$904$	2.27560e7	0.926135
$905$	−1.85994e7	−0.754880
$906$	−7.15528e7	−2.89605
$907$	1.92037e7	0.775114	0.387557	−	0.921846i	$-0.373319\pi$
$907$	1.92037e7	0.775114	0.387557	+	0.921846i	$0.373319\pi$
$908$	−4.74351e7	−1.90935
$909$	−8.19951e6	−0.329138
$910$	−3.11086e7	−1.24531
$911$	1.78298e7	0.711788	0.355894	−	0.934526i	$-0.384176\pi$
$911$	1.78298e7	0.711788	0.355894	+	0.934526i	$0.384176\pi$
$912$	−985726.	−0.0392436
$913$	7.19126e6	0.285514
$914$	7.22875e6	0.286219
$915$	3.56660e7	1.40832
$916$	3.95584e7	1.55776
$917$	1.05212e7	0.413181
$918$	−2.91545e7	−1.14182
$919$	5.10041e7	1.99212	0.996061	−	0.0886662i	$-0.0282604\pi$
$919$	5.10041e7	1.99212	0.996061	+	0.0886662i	$0.0282604\pi$
$920$	1.50151e7	0.584870
$921$	−15948.8	−0.000619553 0
$922$	7.73214e7	2.99552
$923$	1.09249e7	0.422097
$924$	2.29916e7	0.885909
$925$	2.04449e7	0.785654
$926$	−6.16511e7	−2.36273
$927$	−2.03500e7	−0.777796
$928$	−4.73327e7	−1.80423
$929$	1.75776e7	0.668223	0.334111	−	0.942534i	$-0.391564\pi$
$929$	1.75776e7	0.668223	0.334111	+	0.942534i	$0.391564\pi$
$930$	0	0
$931$	−227054.	−0.00858529
$932$	−5.59612e7	−2.11032
$933$	5.21544e6	0.196149
$934$	−5.64183e7	−2.11618
$935$	8.79847e6	0.329138
$936$	−1.18313e7	−0.441410
$937$	−2.52501e7	−0.939537	−0.469768	−	0.882790i	$-0.655663\pi$
$937$	−2.52501e7	−0.939537	−0.469768	+	0.882790i	$0.655663\pi$
$938$	−3.16381e7	−1.17410
$939$	−1.73988e7	−0.643953
$940$	2.98166e7	1.10062
$941$	8.38617e6	0.308738	0.154369	−	0.988013i	$-0.450666\pi$
$941$	8.38617e6	0.308738	0.154369	+	0.988013i	$0.450666\pi$
$942$	4.03062e7	1.47994
$943$	−4.45189e7	−1.63029
$944$	−2.36145e6	−0.0862481
$945$	1.10313e7	0.401833
$946$	−2.87742e7	−1.04538
$947$	3.78162e7	1.37026	0.685129	−	0.728422i	$-0.259746\pi$
$947$	3.78162e7	1.37026	0.685129	+	0.728422i	$0.259746\pi$
$948$	−2.58843e7	−0.935439
$949$	5.15031e6	0.185638
$950$	2.89925e6	0.104226
$951$	5.62910e6	0.201831
$952$	2.44933e7	0.875902
$953$	−3.78762e7	−1.35093	−0.675467	−	0.737390i	$-0.736058\pi$
$953$	−3.78762e7	−1.35093	−0.675467	+	0.737390i	$0.736058\pi$
$954$	−1.17072e7	−0.416470
$955$	1.87756e7	0.666170
$956$	−5.00444e7	−1.77097
$957$	−2.41903e7	−0.853810
$958$	5.31645e7	1.87158
$959$	1.77243e7	0.622333
$960$	−3.39342e7	−1.18839
$961$	0	0
$962$	7.04042e7	2.45279
$963$	1.62985e7	0.566345
$964$	−5.19067e7	−1.79900
$965$	−1.62540e6	−0.0561878
$966$	−7.52132e7	−2.59329
$967$	2.07069e7	0.712113	0.356056	−	0.934465i	$-0.384121\pi$
$967$	2.07069e7	0.712113	0.356056	+	0.934465i	$0.384121\pi$
$968$	−1.66476e7	−0.571036
$969$	−4.23573e6	−0.144917
$970$	−2.87818e7	−0.982176
$971$	1.71800e7	0.584757	0.292379	−	0.956303i	$-0.405553\pi$
$971$	1.71800e7	0.584757	0.292379	+	0.956303i	$0.405553\pi$
$972$	3.80926e7	1.29323
$973$	−5.72788e6	−0.193960
$974$	−4.09374e7	−1.38268
$975$	−2.86963e7	−0.966749
$976$	−1.75744e7	−0.590549
$977$	2.05109e7	0.687462	0.343731	−	0.939068i	$-0.388309\pi$
$977$	2.05109e7	0.687462	0.343731	+	0.939068i	$0.388309\pi$
$978$	−6.53996e7	−2.18639
$979$	−1.74558e7	−0.582079
$980$	−2.19469e6	−0.0729975
$981$	−8.13693e6	−0.269953
$982$	−1.59263e7	−0.527032
$983$	1.21189e7	0.400019	0.200010	−	0.979794i	$-0.435903\pi$
$983$	1.21189e7	0.400019	0.200010	+	0.979794i	$0.435903\pi$
$984$	−3.40335e7	−1.12052
$985$	3.41719e7	1.12222
$986$	−8.05638e7	−2.63905
$987$	−4.77752e7	−1.56102
$988$	5.94233e6	0.193671
$989$	5.60256e7	1.82136
$990$	−6.65028e6	−0.215651
$991$	−3.37573e7	−1.09190	−0.545951	−	0.837817i	$-0.683831\pi$
$991$	−3.37573e7	−1.09190	−0.545951	+	0.837817i	$0.683831\pi$
$992$	0	0
$993$	−1.53107e7	−0.492746
$994$	1.70949e7	0.548782
$995$	1.70773e7	0.546843
$996$	−3.34634e7	−1.06886
$997$	1.84529e7	0.587932	0.293966	−	0.955816i	$-0.405025\pi$
$997$	1.84529e7	0.587932	0.293966	+	0.955816i	$0.405025\pi$
$998$	6.09226e7	1.93621
$999$	−2.49657e7	−0.791461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.6.a.c.1.7		8
31.30	odd	2		31.6.a.b.1.7	✓	8
93.92	even	2		279.6.a.f.1.2		8
124.123	even	2		496.6.a.h.1.3		8
155.154	odd	2		775.6.a.b.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.a.b.1.7	✓	8	31.30	odd	2
279.6.a.f.1.2		8	93.92	even	2
496.6.a.h.1.3		8	124.123	even	2
775.6.a.b.1.2		8	155.154	odd	2
961.6.a.c.1.7		8	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q+8.89102 q^{2} -18.9313 q^{3} +47.0502 q^{4} -33.8630 q^{5} -168.319 q^{6} -134.850 q^{7} +133.811 q^{8} +115.395 q^{9} -301.077 q^{10} +191.415 q^{11} -890.722 q^{12} -766.219 q^{13} -1198.95 q^{14} +641.071 q^{15} -315.888 q^{16} -1357.39 q^{17} +1025.98 q^{18} -164.832 q^{19} -1593.26 q^{20} +2552.89 q^{21} +1701.88 q^{22} -3313.68 q^{23} -2533.22 q^{24} -1978.30 q^{25} -6812.46 q^{26} +2415.73 q^{27} -6344.71 q^{28} +6675.50 q^{29} +5699.78 q^{30} -7090.52 q^{32} -3623.74 q^{33} -12068.6 q^{34} +4566.42 q^{35} +5429.35 q^{36} -10334.6 q^{37} -1465.53 q^{38} +14505.5 q^{39} -4531.25 q^{40} +13434.9 q^{41} +22697.7 q^{42} -16907.4 q^{43} +9006.12 q^{44} -3907.62 q^{45} -29462.0 q^{46} -18714.2 q^{47} +5980.17 q^{48} +1377.48 q^{49} -17589.1 q^{50} +25697.2 q^{51} -36050.7 q^{52} -11410.8 q^{53} +21478.3 q^{54} -6481.90 q^{55} -18044.4 q^{56} +3120.50 q^{57} +59351.9 q^{58} +7475.61 q^{59} +30162.5 q^{60} +55634.9 q^{61} -15561.0 q^{63} -52933.5 q^{64} +25946.5 q^{65} -32218.8 q^{66} +26388.2 q^{67} -63865.5 q^{68} +62732.4 q^{69} +40600.1 q^{70} -14258.2 q^{71} +15441.1 q^{72} -6721.72 q^{73} -91885.2 q^{74} +37451.8 q^{75} -7755.39 q^{76} -25812.3 q^{77} +128969. q^{78} +29059.9 q^{79} +10696.9 q^{80} -73774.0 q^{81} +119450. q^{82} +37568.9 q^{83} +120114. q^{84} +45965.3 q^{85} -150324. q^{86} -126376. q^{87} +25613.5 q^{88} -91193.1 q^{89} -34742.7 q^{90} +103325. q^{91} -155909. q^{92} -166388. q^{94} +5581.72 q^{95} +134233. q^{96} +95596.4 q^{97} +12247.2 q^{98} +22088.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 7 q^{2} + 2 q^{3} + 149 q^{4} + 128 q^{5} - 72 q^{6} + 88 q^{7} + 924 q^{8} + 1512 q^{9} + 1581 q^{10} - 574 q^{11} + 46 q^{12} + 122 q^{13} - 309 q^{14} + 524 q^{15} + 833 q^{16} - 1932 q^{17} - 6845 q^{18}+ \cdots + 180150 q^{99}+O(q^{100}) \) 8 * q + 7 * q^2 + 2 * q^3 + 149 * q^4 + 128 * q^5 - 72 * q^6 + 88 * q^7 + 924 * q^8 + 1512 * q^9 + 1581 * q^10 - 574 * q^11 + 46 * q^12 + 122 * q^13 - 309 * q^14 + 524 * q^15 + 833 * q^16 - 1932 * q^17 - 6845 * q^18 - 1796 * q^19 - 37 * q^20 - 996 * q^21 + 9000 * q^22 + 4136 * q^23 + 17468 * q^24 + 3308 * q^25 - 1524 * q^26 + 2624 * q^27 - 21245 * q^28 - 5050 * q^29 + 30450 * q^30 + 21045 * q^32 + 27920 * q^33 + 24738 * q^34 + 25700 * q^35 + 21637 * q^36 - 23674 * q^37 - 4289 * q^38 + 38652 * q^39 + 36606 * q^40 + 44828 * q^41 + 9994 * q^42 - 21058 * q^43 - 13168 * q^44 - 1344 * q^45 - 6198 * q^46 + 5348 * q^47 + 69588 * q^48 + 19356 * q^49 + 33242 * q^50 + 22300 * q^51 + 60386 * q^52 - 4926 * q^53 + 24476 * q^54 + 56892 * q^55 - 87652 * q^56 - 22072 * q^57 + 25002 * q^58 + 16944 * q^59 + 138556 * q^60 + 73682 * q^61 - 138784 * q^63 - 1300 * q^64 - 63316 * q^65 - 128796 * q^66 - 134768 * q^67 + 9524 * q^68 + 3992 * q^69 - 142737 * q^70 + 123724 * q^71 + 93232 * q^72 - 70792 * q^73 - 307468 * q^74 + 302902 * q^75 - 65405 * q^76 - 107932 * q^77 + 36820 * q^78 + 26036 * q^79 + 576783 * q^80 + 82528 * q^81 + 142335 * q^82 - 21882 * q^83 - 299144 * q^84 + 130464 * q^85 - 480478 * q^86 - 440244 * q^87 + 71982 * q^88 - 164392 * q^89 + 397969 * q^90 + 60028 * q^91 - 31012 * q^92 - 170388 * q^94 - 7404 * q^95 + 331010 * q^96 - 131948 * q^97 + 288768 * q^98 + 180150 * q^99

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