LMFDB - Embedded newform 62.6.a.c.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(1,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.1"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-16] 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:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 221x^{2} - 140x + 2412 $ x^4 - 2x^3 - 221x^2 - 140*x + 2412
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.02119$ of defining polynomial
Character	$\chi$	$=$	62.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} +23.5432 q^{3} +16.0000 q^{4} +4.68379 q^{5} -94.1729 q^{6} +223.045 q^{7} -64.0000 q^{8} +311.283 q^{9} -18.7352 q^{10} -697.575 q^{11} +376.692 q^{12} +608.528 q^{13} -892.181 q^{14} +110.272 q^{15} +256.000 q^{16} -1134.55 q^{17} -1245.13 q^{18} +2216.76 q^{19} +74.9407 q^{20} +5251.21 q^{21} +2790.30 q^{22} +4952.73 q^{23} -1506.77 q^{24} -3103.06 q^{25} -2434.11 q^{26} +1607.61 q^{27} +3568.73 q^{28} +4252.87 q^{29} -441.087 q^{30} +961.000 q^{31} -1024.00 q^{32} -16423.2 q^{33} +4538.22 q^{34} +1044.70 q^{35} +4980.53 q^{36} -11542.5 q^{37} -8867.06 q^{38} +14326.7 q^{39} -299.763 q^{40} -7267.04 q^{41} -21004.8 q^{42} -2660.85 q^{43} -11161.2 q^{44} +1457.99 q^{45} -19810.9 q^{46} -4011.52 q^{47} +6027.07 q^{48} +32942.2 q^{49} +12412.2 q^{50} -26711.1 q^{51} +9736.45 q^{52} -26632.7 q^{53} -6430.44 q^{54} -3267.30 q^{55} -14274.9 q^{56} +52189.8 q^{57} -17011.5 q^{58} +9837.40 q^{59} +1764.35 q^{60} -25660.4 q^{61} -3844.00 q^{62} +69430.3 q^{63} +4096.00 q^{64} +2850.22 q^{65} +65692.6 q^{66} -22067.8 q^{67} -18152.9 q^{68} +116603. q^{69} -4178.79 q^{70} -29062.7 q^{71} -19922.1 q^{72} -20167.7 q^{73} +46170.1 q^{74} -73056.1 q^{75} +35468.2 q^{76} -155591. q^{77} -57306.8 q^{78} -18775.8 q^{79} +1199.05 q^{80} -37793.5 q^{81} +29068.1 q^{82} -8063.50 q^{83} +84019.3 q^{84} -5314.02 q^{85} +10643.4 q^{86} +100126. q^{87} +44644.8 q^{88} +37717.2 q^{89} -5831.95 q^{90} +135729. q^{91} +79243.6 q^{92} +22625.0 q^{93} +16046.1 q^{94} +10382.9 q^{95} -24108.3 q^{96} +23398.0 q^{97} -131769. q^{98} -217143. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 10 q^{3} + 64 q^{4} + 2 q^{5} - 40 q^{6} + 146 q^{7} - 256 q^{8} - 36 q^{9} - 8 q^{10} - 270 q^{11} + 160 q^{12} + 1038 q^{13} - 584 q^{14} + 1864 q^{15} + 1024 q^{16} + 2020 q^{17} + 144 q^{18}+ \cdots - 324354 q^{99}+O(q^{100}) $ 4 * q - 16 * q^2 + 10 * q^3 + 64 * q^4 + 2 * q^5 - 40 * q^6 + 146 * q^7 - 256 * q^8 - 36 * q^9 - 8 * q^10 - 270 * q^11 + 160 * q^12 + 1038 * q^13 - 584 * q^14 + 1864 * q^15 + 1024 * q^16 + 2020 * q^17 + 144 * q^18 + 6214 * q^19 + 32 * q^20 + 7256 * q^21 + 1080 * q^22 + 8292 * q^23 - 640 * q^24 + 9974 * q^25 - 4152 * q^26 + 5032 * q^27 + 2336 * q^28 + 1894 * q^29 - 7456 * q^30 + 3844 * q^31 - 4096 * q^32 - 11280 * q^33 - 8080 * q^34 - 9146 * q^35 - 576 * q^36 - 5470 * q^37 - 24856 * q^38 - 1628 * q^39 - 128 * q^40 - 16878 * q^41 - 29024 * q^42 + 1530 * q^43 - 4320 * q^44 + 5642 * q^45 - 33168 * q^46 - 25460 * q^47 + 2560 * q^48 + 21630 * q^49 - 39896 * q^50 - 40372 * q^51 + 16608 * q^52 - 7790 * q^53 - 20128 * q^54 + 5760 * q^55 - 9344 * q^56 + 15036 * q^57 - 7576 * q^58 - 35802 * q^59 + 29824 * q^60 + 48366 * q^61 - 15376 * q^62 + 53634 * q^63 + 16384 * q^64 + 12096 * q^65 + 45120 * q^66 + 54696 * q^67 + 32320 * q^68 + 110760 * q^69 + 36584 * q^70 - 35342 * q^71 + 2304 * q^72 + 59336 * q^73 + 21880 * q^74 - 24510 * q^75 + 99424 * q^76 - 86976 * q^77 + 6512 * q^78 - 3652 * q^79 + 512 * q^80 - 73452 * q^81 + 67512 * q^82 - 80074 * q^83 + 116096 * q^84 + 81860 * q^85 - 6120 * q^86 + 112364 * q^87 + 17280 * q^88 - 12060 * q^89 - 22568 * q^90 - 74952 * q^91 + 132672 * q^92 + 9610 * q^93 + 101840 * q^94 - 286138 * q^95 - 10240 * q^96 + 232670 * q^97 - 86520 * q^98 - 324354 * 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
$3$	23.5432	1.51030	0.755149	−	0.655553i	$-0.227564\pi$
$3$	23.5432	1.51030	0.755149	+	0.655553i	$0.227564\pi$
$4$	16.0000	0.500000
$5$	4.68379	0.0837863	0.0418931	−	0.999122i	$-0.486661\pi$
$5$	4.68379	0.0837863	0.0418931	+	0.999122i	$0.486661\pi$
$6$	−94.1729	−1.06794
$7$	223.045	1.72047	0.860237	−	0.509895i	$-0.170316\pi$
$7$	223.045	1.72047	0.860237	+	0.509895i	$0.170316\pi$
$8$	−64.0000	−0.353553
$9$	311.283	1.28100
$10$	−18.7352	−0.0592458
$11$	−697.575	−1.73824	−0.869119	−	0.494604i	$-0.835313\pi$
$11$	−697.575	−1.73824	−0.869119	+	0.494604i	$0.835313\pi$
$12$	376.692	0.755149
$13$	608.528	0.998670	0.499335	−	0.866409i	$-0.333578\pi$
$13$	608.528	0.998670	0.499335	+	0.866409i	$0.333578\pi$
$14$	−892.181	−1.21656
$15$	110.272	0.126542
$16$	256.000	0.250000
$17$	−1134.55	−0.952145	−0.476072	−	0.879406i	$-0.657940\pi$
$17$	−1134.55	−0.952145	−0.476072	+	0.879406i	$0.657940\pi$
$18$	−1245.13	−0.905805
$19$	2216.76	1.40875	0.704377	−	0.709826i	$-0.251226\pi$
$19$	2216.76	1.40875	0.704377	+	0.709826i	$0.251226\pi$
$20$	74.9407	0.0418931
$21$	5251.21	2.59843
$22$	2790.30	1.22912
$23$	4952.73	1.95220	0.976101	−	0.217318i	$-0.0697310\pi$
$23$	4952.73	1.95220	0.976101	+	0.217318i	$0.0697310\pi$
$24$	−1506.77	−0.533971
$25$	−3103.06	−0.992980
$26$	−2434.11	−0.706166
$27$	1607.61	0.424396
$28$	3568.73	0.860237
$29$	4252.87	0.939047	0.469523	−	0.882920i	$-0.344426\pi$
$29$	4252.87	0.939047	0.469523	+	0.882920i	$0.344426\pi$
$30$	−441.087	−0.0894789
$31$	961.000	0.179605
$31$	961.000	0.179605
$32$	−1024.00	−0.176777
$33$	−16423.2	−2.62526
$34$	4538.22	0.673268
$35$	1044.70	0.144152
$36$	4980.53	0.640501
$37$	−11542.5	−1.38611	−0.693053	−	0.720887i	$-0.743735\pi$
$37$	−11542.5	−1.38611	−0.693053	+	0.720887i	$0.743735\pi$
$38$	−8867.06	−0.996140
$39$	14326.7	1.50829
$40$	−299.763	−0.0296229
$41$	−7267.04	−0.675146	−0.337573	−	0.941299i	$-0.609606\pi$
$41$	−7267.04	−0.675146	−0.337573	+	0.941299i	$0.609606\pi$
$42$	−21004.8	−1.83737
$43$	−2660.85	−0.219457	−0.109728	−	0.993962i	$-0.534998\pi$
$43$	−2660.85	−0.219457	−0.109728	+	0.993962i	$0.534998\pi$
$44$	−11161.2	−0.869119
$45$	1457.99	0.107330
$46$	−19810.9	−1.38041
$47$	−4011.52	−0.264889	−0.132445	−	0.991190i	$-0.542283\pi$
$47$	−4011.52	−0.264889	−0.132445	+	0.991190i	$0.542283\pi$
$48$	6027.07	0.377575
$49$	32942.2	1.96003
$50$	12412.2	0.702143
$51$	−26711.1	−1.43802
$52$	9736.45	0.499335
$53$	−26632.7	−1.30234	−0.651172	−	0.758931i	$-0.725722\pi$
$53$	−26632.7	−1.30234	−0.651172	+	0.758931i	$0.725722\pi$
$54$	−6430.44	−0.300094
$55$	−3267.30	−0.145640
$56$	−14274.9	−0.608279
$57$	52189.8	2.12764
$58$	−17011.5	−0.664006
$59$	9837.40	0.367917	0.183959	−	0.982934i	$-0.441109\pi$
$59$	9837.40	0.367917	0.183959	+	0.982934i	$0.441109\pi$
$60$	1764.35	0.0632711
$61$	−25660.4	−0.882955	−0.441477	−	0.897272i	$-0.645545\pi$
$61$	−25660.4	−0.882955	−0.441477	+	0.897272i	$0.645545\pi$
$62$	−3844.00	−0.127000
$63$	69430.3	2.20393
$64$	4096.00	0.125000
$65$	2850.22	0.0836749
$66$	65692.6	1.85634
$67$	−22067.8	−0.600581	−0.300291	−	0.953848i	$-0.597084\pi$
$67$	−22067.8	−0.600581	−0.300291	+	0.953848i	$0.597084\pi$
$68$	−18152.9	−0.476072
$69$	116603.	2.94841
$70$	−4178.79	−0.101931
$71$	−29062.7	−0.684212	−0.342106	−	0.939661i	$-0.611140\pi$
$71$	−29062.7	−0.684212	−0.342106	+	0.939661i	$0.611140\pi$
$72$	−19922.1	−0.452902
$73$	−20167.7	−0.442944	−0.221472	−	0.975167i	$-0.571086\pi$
$73$	−20167.7	−0.442944	−0.221472	+	0.975167i	$0.571086\pi$
$74$	46170.1	0.980124
$75$	−73056.1	−1.49970
$76$	35468.2	0.704377
$77$	−155591.	−2.99059
$78$	−57306.8	−1.06652
$79$	−18775.8	−0.338478	−0.169239	−	0.985575i	$-0.554131\pi$
$79$	−18775.8	−0.338478	−0.169239	+	0.985575i	$0.554131\pi$
$80$	1199.05	0.0209466
$81$	−37793.5	−0.640036
$82$	29068.1	0.477400
$83$	−8063.50	−0.128478	−0.0642390	−	0.997935i	$-0.520462\pi$
$83$	−8063.50	−0.128478	−0.0642390	+	0.997935i	$0.520462\pi$
$84$	84019.3	1.29921
$85$	−5314.02	−0.0797767
$86$	10643.4	0.155179
$87$	100126.	1.41824
$88$	44644.8	0.614560
$89$	37717.2	0.504736	0.252368	−	0.967631i	$-0.418791\pi$
$89$	37717.2	0.504736	0.252368	+	0.967631i	$0.418791\pi$
$90$	−5831.95	−0.0758940
$91$	135729.	1.71819
$92$	79243.6	0.976101
$93$	22625.0	0.271258
$94$	16046.1	0.187305
$95$	10382.9	0.118034
$96$	−24108.3	−0.266986
$97$	23398.0	0.252493	0.126247	−	0.991999i	$-0.459707\pi$
$97$	23398.0	0.252493	0.126247	+	0.991999i	$0.459707\pi$
$98$	−131769.	−1.38595
$99$	−217143.	−2.22668
$100$	−49649.0	−0.496490
$101$	−41048.5	−0.400400	−0.200200	−	0.979755i	$-0.564159\pi$
$101$	−41048.5	−0.400400	−0.200200	+	0.979755i	$0.564159\pi$
$102$	106844.	1.01684
$103$	50513.9	0.469156	0.234578	−	0.972097i	$-0.424629\pi$
$103$	50513.9	0.469156	0.234578	+	0.972097i	$0.424629\pi$
$104$	−38945.8	−0.353083
$105$	24595.6	0.217713
$106$	106531.	0.920896
$107$	15991.7	0.135032	0.0675159	−	0.997718i	$-0.478493\pi$
$107$	15991.7	0.135032	0.0675159	+	0.997718i	$0.478493\pi$
$108$	25721.8	0.212198
$109$	−33598.4	−0.270865	−0.135432	−	0.990787i	$-0.543242\pi$
$109$	−33598.4	−0.270865	−0.135432	+	0.990787i	$0.543242\pi$
$110$	13069.2	0.102983
$111$	−271748.	−2.09343
$112$	57099.6	0.430118
$113$	94717.0	0.697802	0.348901	−	0.937160i	$-0.386555\pi$
$113$	94717.0	0.697802	0.348901	+	0.937160i	$0.386555\pi$
$114$	−208759.	−1.50447
$115$	23197.5	0.163568
$116$	68045.9	0.469523
$117$	189425.	1.27930
$118$	−39349.6	−0.260157
$119$	−253057.	−1.63814
$120$	−7057.38	−0.0447395
$121$	325559.	2.02147
$122$	102642.	0.624343
$123$	−171089.	−1.01967
$124$	15376.0	0.0898027
$125$	−29171.0	−0.166984
$126$	−277721.	−1.55841
$127$	−199995.	−1.10030	−0.550148	−	0.835067i	$-0.685429\pi$
$127$	−199995.	−1.10030	−0.550148	+	0.835067i	$0.685429\pi$
$128$	−16384.0	−0.0883883
$129$	−62644.9	−0.331445
$130$	−11400.9	−0.0591671
$131$	24450.2	0.124482	0.0622408	−	0.998061i	$-0.480175\pi$
$131$	24450.2	0.124482	0.0622408	+	0.998061i	$0.480175\pi$
$132$	−262771.	−1.31263
$133$	494439.	2.42373
$134$	88271.2	0.424675
$135$	7529.72	0.0355586
$136$	72611.5	0.336634
$137$	−335345.	−1.52648	−0.763239	−	0.646117i	$-0.776392\pi$
$137$	−335345.	−1.52648	−0.763239	+	0.646117i	$0.776392\pi$
$138$	−466412.	−2.08484
$139$	−355730.	−1.56165	−0.780824	−	0.624751i	$-0.785201\pi$
$139$	−355730.	−1.56165	−0.780824	+	0.624751i	$0.785201\pi$
$140$	16715.2	0.0720760
$141$	−94444.1	−0.400062
$142$	116251.	0.483811
$143$	−424494.	−1.73593
$144$	79688.5	0.320250
$145$	19919.6	0.0786792
$146$	80670.8	0.313209
$147$	775566.	2.96023
$148$	−184680.	−0.693053
$149$	335641.	1.23854	0.619269	−	0.785179i	$-0.287429\pi$
$149$	335641.	1.23854	0.619269	+	0.785179i	$0.287429\pi$
$150$	292224.	1.06045
$151$	−24794.1	−0.0884923	−0.0442462	−	0.999021i	$-0.514089\pi$
$151$	−24794.1	−0.0884923	−0.0442462	+	0.999021i	$0.514089\pi$
$152$	−141873.	−0.498070
$153$	−353168.	−1.21970
$154$	622363.	2.11467
$155$	4501.13	0.0150485
$156$	229227.	0.754145
$157$	412132.	1.33440	0.667202	−	0.744877i	$-0.267492\pi$
$157$	412132.	1.33440	0.667202	+	0.744877i	$0.267492\pi$
$158$	75103.1	0.239340
$159$	−627019.	−1.96693
$160$	−4796.21	−0.0148115
$161$	1.10468e6	3.35871
$162$	151174.	0.452574
$163$	−342794.	−1.01056	−0.505282	−	0.862954i	$-0.668612\pi$
$163$	−342794.	−1.01056	−0.505282	+	0.862954i	$0.668612\pi$
$164$	−116273.	−0.337573
$165$	−76922.7	−0.219960
$166$	32254.0	0.0908476
$167$	369801.	1.02607	0.513035	−	0.858367i	$-0.328521\pi$
$167$	369801.	1.02607	0.513035	+	0.858367i	$0.328521\pi$
$168$	−336077.	−0.918683
$169$	−986.835	−0.00265783
$170$	21256.1	0.0564106
$171$	690042.	1.80462
$172$	−42573.5	−0.109728
$173$	−577230.	−1.46634	−0.733168	−	0.680047i	$-0.761959\pi$
$173$	−577230.	−1.46634	−0.733168	+	0.680047i	$0.761959\pi$
$174$	−400505.	−1.00285
$175$	−692123.	−1.70840
$176$	−178579.	−0.434559
$177$	231604.	0.555665
$178$	−150869.	−0.356902
$179$	569871.	1.32936	0.664682	−	0.747127i	$-0.268567\pi$
$179$	569871.	1.32936	0.664682	+	0.747127i	$0.268567\pi$
$180$	23327.8	0.0536652
$181$	645580.	1.46472	0.732358	−	0.680920i	$-0.238420\pi$
$181$	645580.	1.46472	0.732358	+	0.680920i	$0.238420\pi$
$182$	−542917.	−1.21494
$183$	−604128.	−1.33353
$184$	−316974.	−0.690207
$185$	−54062.8	−0.116137
$186$	−90500.2	−0.191808
$187$	791436.	1.65505
$188$	−64184.3	−0.132445
$189$	358570.	0.730163
$190$	−41531.5	−0.0834629
$191$	64481.5	0.127894	0.0639472	−	0.997953i	$-0.479631\pi$
$191$	64481.5	0.127894	0.0639472	+	0.997953i	$0.479631\pi$
$192$	96433.0	0.188787
$193$	231863.	0.448061	0.224031	−	0.974582i	$-0.428078\pi$
$193$	231863.	0.448061	0.224031	+	0.974582i	$0.428078\pi$
$194$	−93592.1	−0.178540
$195$	67103.4	0.126374
$196$	527075.	0.980015
$197$	−419129.	−0.769454	−0.384727	−	0.923030i	$-0.625704\pi$
$197$	−419129.	−0.769454	−0.384727	+	0.923030i	$0.625704\pi$
$198$	868574.	1.57450
$199$	224958.	0.402688	0.201344	−	0.979521i	$-0.435469\pi$
$199$	224958.	0.402688	0.201344	+	0.979521i	$0.435469\pi$
$200$	198596.	0.351071
$201$	−519547.	−0.907057
$202$	164194.	0.283126
$203$	948583.	1.61560
$204$	−427377.	−0.719012
$205$	−34037.3	−0.0565680
$206$	−202056.	−0.331744
$207$	1.54170e6	2.50077
$208$	155783.	0.249668
$209$	−1.54636e6	−2.44875
$210$	−98382.3	−0.153946
$211$	−499777.	−0.772805	−0.386403	−	0.922330i	$-0.626283\pi$
$211$	−499777.	−0.772805	−0.386403	+	0.922330i	$0.626283\pi$
$212$	−426123.	−0.651172
$213$	−684230.	−1.03336
$214$	−63966.9	−0.0954818
$215$	−12462.9	−0.0183874
$216$	−102887.	−0.150047
$217$	214347.	0.309006
$218$	134394.	0.191530
$219$	−474813.	−0.668978
$220$	−52276.7	−0.0728202
$221$	−690408.	−0.950879
$222$	1.08699e6	1.48028
$223$	453035.	0.610056	0.305028	−	0.952343i	$-0.401334\pi$
$223$	453035.	0.610056	0.305028	+	0.952343i	$0.401334\pi$
$224$	−228398.	−0.304140
$225$	−965932.	−1.27201
$226$	−378868.	−0.493420
$227$	−109538.	−0.141091	−0.0705456	−	0.997509i	$-0.522474\pi$
$227$	−109538.	−0.141091	−0.0705456	+	0.997509i	$0.522474\pi$
$228$	835036.	1.06382
$229$	676432.	0.852384	0.426192	−	0.904633i	$-0.359855\pi$
$229$	676432.	0.852384	0.426192	+	0.904633i	$0.359855\pi$
$230$	−92790.2	−0.115660
$231$	−3.66311e6	−4.51669
$232$	−272184.	−0.332003
$233$	1.54715e6	1.86700	0.933499	−	0.358581i	$-0.116739\pi$
$233$	1.54715e6	1.86700	0.933499	+	0.358581i	$0.116739\pi$
$234$	−757698.	−0.904600
$235$	−18789.1	−0.0221941
$236$	157398.	0.183959
$237$	−442042.	−0.511203
$238$	1.01223e6	1.15834
$239$	−1.14833e6	−1.30039	−0.650194	−	0.759768i	$-0.725313\pi$
$239$	−1.14833e6	−1.30039	−0.650194	+	0.759768i	$0.725313\pi$
$240$	28229.5	0.0316356
$241$	253058.	0.280658	0.140329	−	0.990105i	$-0.455184\pi$
$241$	253058.	0.280658	0.140329	+	0.990105i	$0.455184\pi$
$242$	−1.30224e6	−1.42939
$243$	−1.28043e6	−1.39104
$244$	−410566.	−0.441477
$245$	154295.	0.164224
$246$	684358.	0.721017
$247$	1.34896e6	1.40688
$248$	−61504.0	−0.0635001
$249$	−189841.	−0.194040
$250$	116684.	0.118076
$251$	978120.	0.979959	0.489980	−	0.871734i	$-0.337004\pi$
$251$	978120.	0.979959	0.489980	+	0.871734i	$0.337004\pi$
$252$	1.11088e6	1.10196
$253$	−3.45490e6	−3.39339
$254$	799979.	0.778026
$255$	−125109.	−0.120487
$256$	65536.0	0.0625000
$257$	527626.	0.498303	0.249151	−	0.968465i	$-0.419848\pi$
$257$	527626.	0.498303	0.249151	+	0.968465i	$0.419848\pi$
$258$	250580.	0.234367
$259$	−2.57450e6	−2.38476
$260$	45603.5	0.0418374
$261$	1.32385e6	1.20292
$262$	−97801.0	−0.0880218
$263$	−129057.	−0.115051	−0.0575257	−	0.998344i	$-0.518321\pi$
$263$	−129057.	−0.115051	−0.0575257	+	0.998344i	$0.518321\pi$
$264$	1.05108e6	0.928168
$265$	−124742.	−0.109118
$266$	−1.97776e6	−1.71383
$267$	887985.	0.762302
$268$	−353085.	−0.300291
$269$	106600.	0.0898205	0.0449103	−	0.998991i	$-0.485700\pi$
$269$	106600.	0.0898205	0.0449103	+	0.998991i	$0.485700\pi$
$270$	−30118.9	−0.0251437
$271$	1.19192e6	0.985879	0.492939	−	0.870064i	$-0.335922\pi$
$271$	1.19192e6	0.985879	0.492939	+	0.870064i	$0.335922\pi$
$272$	−290446.	−0.238036
$273$	3.19551e6	2.59497
$274$	1.34138e6	1.07938
$275$	2.16462e6	1.72603
$276$	1.86565e6	1.47420
$277$	−916761.	−0.717888	−0.358944	−	0.933359i	$-0.616863\pi$
$277$	−916761.	−0.717888	−0.358944	+	0.933359i	$0.616863\pi$
$278$	1.42292e6	1.10425
$279$	299143.	0.230075
$280$	−66860.7	−0.0509655
$281$	−658158.	−0.497238	−0.248619	−	0.968601i	$-0.579977\pi$
$281$	−658158.	−0.497238	−0.248619	+	0.968601i	$0.579977\pi$
$282$	377776.	0.282886
$283$	712136.	0.528563	0.264282	−	0.964446i	$-0.414865\pi$
$283$	712136.	0.528563	0.264282	+	0.964446i	$0.414865\pi$
$284$	−465004.	−0.342106
$285$	244446.	0.178267
$286$	1.69797e6	1.22748
$287$	−1.62088e6	−1.16157
$288$	−318754.	−0.226451
$289$	−132643.	−0.0934201
$290$	−79678.3	−0.0556346
$291$	550865.	0.381340
$292$	−322683.	−0.221472
$293$	2.46729e6	1.67900	0.839500	−	0.543360i	$-0.182848\pi$
$293$	2.46729e6	1.67900	0.839500	+	0.543360i	$0.182848\pi$
$294$	−3.10226e6	−2.09320
$295$	46076.4	0.0308264
$296$	738721.	0.490062
$297$	−1.12143e6	−0.737701
$298$	−1.34256e6	−0.875779
$299$	3.01387e6	1.94961
$300$	−1.16890e6	−0.749848
$301$	−593489.	−0.377569
$302$	99176.3	0.0625735
$303$	−966415.	−0.604724
$304$	567492.	0.352189
$305$	−120188.	−0.0739795
$306$	1.41267e6	0.862458
$307$	1.00251e6	0.607076	0.303538	−	0.952819i	$-0.401832\pi$
$307$	1.00251e6	0.607076	0.303538	+	0.952819i	$0.401832\pi$
$308$	−2.48945e6	−1.49530
$309$	1.18926e6	0.708566
$310$	−18004.5	−0.0106409
$311$	1.58696e6	0.930392	0.465196	−	0.885208i	$-0.345984\pi$
$311$	1.58696e6	0.930392	0.465196	+	0.885208i	$0.345984\pi$
$312$	−916909.	−0.533261
$313$	3.07317e6	1.77307	0.886534	−	0.462664i	$-0.153106\pi$
$313$	3.07317e6	1.77307	0.886534	+	0.462664i	$0.153106\pi$
$314$	−1.64853e6	−0.943566
$315$	325197.	0.184659
$316$	−300412.	−0.169239
$317$	763883.	0.426951	0.213476	−	0.976948i	$-0.431522\pi$
$317$	763883.	0.426951	0.213476	+	0.976948i	$0.431522\pi$
$318$	2.50808e6	1.39083
$319$	−2.96669e6	−1.63229
$320$	19184.8	0.0104733
$321$	376497.	0.203938
$322$	−4.41873e6	−2.37497
$323$	−2.51504e6	−1.34134
$324$	−604696.	−0.320018
$325$	−1.88830e6	−0.991659
$326$	1.37117e6	0.714577
$327$	−791015.	−0.409087
$328$	465090.	0.238700
$329$	−894751.	−0.455735
$330$	307691.	0.155536
$331$	−1.96459e6	−0.985605	−0.492803	−	0.870141i	$-0.664028\pi$
$331$	−1.96459e6	−0.985605	−0.492803	+	0.870141i	$0.664028\pi$
$332$	−129016.	−0.0642390
$333$	−3.59299e6	−1.77560
$334$	−1.47921e6	−0.725542
$335$	−103361.	−0.0503205
$336$	1.34431e6	0.649607
$337$	973571.	0.466974	0.233487	−	0.972360i	$-0.424986\pi$
$337$	973571.	0.466974	0.233487	+	0.972360i	$0.424986\pi$
$338$	3947.34	0.00187937
$339$	2.22994e6	1.05389
$340$	−85024.3	−0.0398883
$341$	−670369.	−0.312197
$342$	−2.76017e6	−1.27606
$343$	3.59888e6	1.65171
$344$	170294.	0.0775896
$345$	546145.	0.247036
$346$	2.30892e6	1.03686
$347$	−825632.	−0.368097	−0.184049	−	0.982917i	$-0.558920\pi$
$347$	−825632.	−0.368097	−0.184049	+	0.982917i	$0.558920\pi$
$348$	1.60202e6	0.709120
$349$	−1.13449e6	−0.498584	−0.249292	−	0.968428i	$-0.580198\pi$
$349$	−1.13449e6	−0.498584	−0.249292	+	0.968428i	$0.580198\pi$
$350$	2.76849e6	1.20802
$351$	978276.	0.423832
$352$	714316.	0.307280
$353$	332778.	0.142140	0.0710702	−	0.997471i	$-0.477359\pi$
$353$	332778.	0.142140	0.0710702	+	0.997471i	$0.477359\pi$
$354$	−926416.	−0.392914
$355$	−136124.	−0.0573275
$356$	603475.	0.252368
$357$	−5.95778e6	−2.47408
$358$	−2.27948e6	−0.940002
$359$	992000.	0.406233	0.203117	−	0.979155i	$-0.434893\pi$
$359$	992000.	0.406233	0.203117	+	0.979155i	$0.434893\pi$
$360$	−93311.2	−0.0379470
$361$	2.43794e6	0.984590
$362$	−2.58232e6	−1.03571
$363$	7.66472e6	3.05302
$364$	2.17167e6	0.859093
$365$	−94461.4	−0.0371127
$366$	2.41651e6	0.942945
$367$	4.81905e6	1.86765	0.933827	−	0.357724i	$-0.116447\pi$
$367$	4.81905e6	1.86765	0.933827	+	0.357724i	$0.116447\pi$
$368$	1.26790e6	0.488050
$369$	−2.26211e6	−0.864863
$370$	216251.	0.0821210
$371$	−5.94030e6	−2.24065
$372$	362001.	0.135629
$373$	684010.	0.254560	0.127280	−	0.991867i	$-0.459375\pi$
$373$	684010.	0.254560	0.127280	+	0.991867i	$0.459375\pi$
$374$	−3.16575e6	−1.17030
$375$	−686779.	−0.252196
$376$	256737.	0.0936525
$377$	2.58799e6	0.937798
$378$	−1.43428e6	−0.516303
$379$	−3.17152e6	−1.13415	−0.567073	−	0.823668i	$-0.691924\pi$
$379$	−3.17152e6	−1.13415	−0.567073	+	0.823668i	$0.691924\pi$
$380$	166126.	0.0590172
$381$	−4.70852e6	−1.66177
$382$	−257926.	−0.0904351
$383$	−3.27993e6	−1.14253	−0.571265	−	0.820766i	$-0.693547\pi$
$383$	−3.27993e6	−1.14253	−0.571265	+	0.820766i	$0.693547\pi$
$384$	−385732.	−0.133493
$385$	−728755.	−0.250570
$386$	−927450.	−0.316827
$387$	−828277.	−0.281124
$388$	374368.	0.126247
$389$	1.13995e6	0.381953	0.190977	−	0.981595i	$-0.438835\pi$
$389$	1.13995e6	0.381953	0.190977	+	0.981595i	$0.438835\pi$
$390$	−268413.	−0.0893599
$391$	−5.61914e6	−1.85878
$392$	−2.10830e6	−0.692975
$393$	575638.	0.188004
$394$	1.67652e6	0.544086
$395$	−87941.9	−0.0283598
$396$	−3.47429e6	−1.11334
$397$	5.52647e6	1.75983	0.879917	−	0.475128i	$-0.157598\pi$
$397$	5.52647e6	1.75983	0.879917	+	0.475128i	$0.157598\pi$
$398$	−899832.	−0.284744
$399$	1.16407e7	3.66055
$400$	−794384.	−0.248245
$401$	1.64448e6	0.510702	0.255351	−	0.966848i	$-0.417809\pi$
$401$	1.64448e6	0.510702	0.255351	+	0.966848i	$0.417809\pi$
$402$	2.07819e6	0.641386
$403$	584795.	0.179366
$404$	−656777.	−0.200200
$405$	−177017.	−0.0536263
$406$	−3.79433e6	−1.14241
$407$	8.05177e6	2.40938
$408$	1.70951e6	0.508418
$409$	−4.67117e6	−1.38076	−0.690378	−	0.723449i	$-0.742556\pi$
$409$	−4.67117e6	−1.38076	−0.690378	+	0.723449i	$0.742556\pi$
$410$	136149.	0.0399996
$411$	−7.89510e6	−2.30544
$412$	808222.	0.234578
$413$	2.19419e6	0.632992
$414$	−6.16680e6	−1.76831
$415$	−37767.8	−0.0107647
$416$	−623133.	−0.176542
$417$	−8.37503e6	−2.35855
$418$	6.18543e6	1.73153
$419$	−705742.	−0.196386	−0.0981931	−	0.995167i	$-0.531306\pi$
$419$	−705742.	−0.196386	−0.0981931	+	0.995167i	$0.531306\pi$
$420$	393529.	0.108856
$421$	−115874.	−0.0318625	−0.0159313	−	0.999873i	$-0.505071\pi$
$421$	−115874.	−0.0318625	−0.0159313	+	0.999873i	$0.505071\pi$
$422$	1.99911e6	0.546456
$423$	−1.24872e6	−0.339323
$424$	1.70449e6	0.460448
$425$	3.52059e6	0.945461
$426$	2.73692e6	0.730699
$427$	−5.72343e6	−1.51910
$428$	255868.	0.0675159
$429$	−9.99395e6	−2.62177
$430$	49851.4	0.0130019
$431$	−6.27049e6	−1.62595	−0.812977	−	0.582296i	$-0.802155\pi$
$431$	−6.27049e6	−1.62595	−0.812977	+	0.582296i	$0.802155\pi$
$432$	411548.	0.106099
$433$	−4.06089e6	−1.04088	−0.520441	−	0.853898i	$-0.674232\pi$
$433$	−4.06089e6	−1.04088	−0.520441	+	0.853898i	$0.674232\pi$
$434$	−857386.	−0.218500
$435$	468971.	0.118829
$436$	−537575.	−0.135432
$437$	1.09790e7	2.75017
$438$	1.89925e6	0.473039
$439$	5.40713e6	1.33908	0.669539	−	0.742777i	$-0.266492\pi$
$439$	5.40713e6	1.33908	0.669539	+	0.742777i	$0.266492\pi$
$440$	209107.	0.0514917
$441$	1.02544e7	2.51080
$442$	2.76163e6	0.672373
$443$	2.50805e6	0.607194	0.303597	−	0.952801i	$-0.401812\pi$
$443$	2.50805e6	0.607194	0.303597	+	0.952801i	$0.401812\pi$
$444$	−4.34797e6	−1.04672
$445$	176660.	0.0422900
$446$	−1.81214e6	−0.431375
$447$	7.90207e6	1.87056
$448$	913594.	0.215059
$449$	3.09796e6	0.725203	0.362601	−	0.931944i	$-0.381889\pi$
$449$	3.09796e6	0.725203	0.362601	+	0.931944i	$0.381889\pi$
$450$	3.86373e6	0.899446
$451$	5.06930e6	1.17356
$452$	1.51547e6	0.348901
$453$	−583733.	−0.133650
$454$	438152.	0.0997665
$455$	635728.	0.143960
$456$	−3.34015e6	−0.752234
$457$	−7.64379e6	−1.71206	−0.856028	−	0.516929i	$-0.827075\pi$
$457$	−7.64379e6	−1.71206	−0.856028	+	0.516929i	$0.827075\pi$
$458$	−2.70573e6	−0.602727
$459$	−1.82392e6	−0.404087
$460$	371161.	0.0817838
$461$	2.29806e6	0.503628	0.251814	−	0.967776i	$-0.418973\pi$
$461$	2.29806e6	0.503628	0.251814	+	0.967776i	$0.418973\pi$
$462$	1.46524e7	3.19378
$463$	−2.13584e6	−0.463037	−0.231518	−	0.972831i	$-0.574369\pi$
$463$	−2.13584e6	−0.463037	−0.231518	+	0.972831i	$0.574369\pi$
$464$	1.08873e6	0.234762
$465$	105971.	0.0227277
$466$	−6.18862e6	−1.32017
$467$	−508175.	−0.107825	−0.0539127	−	0.998546i	$-0.517169\pi$
$467$	−508175.	−0.107825	−0.0539127	+	0.998546i	$0.517169\pi$
$468$	3.03079e6	0.639649
$469$	−4.92212e6	−1.03328
$470$	75156.5	0.0156936
$471$	9.70292e6	2.01535
$472$	−629594.	−0.130078
$473$	1.85614e6	0.381468
$474$	1.76817e6	0.361475
$475$	−6.87876e6	−1.39887
$476$	−4.04891e6	−0.819070
$477$	−8.29032e6	−1.66830
$478$	4.59333e6	0.919514
$479$	715922.	0.142570	0.0712848	−	0.997456i	$-0.477290\pi$
$479$	715922.	0.142570	0.0712848	+	0.997456i	$0.477290\pi$
$480$	−112918.	−0.0223697
$481$	−7.02394e6	−1.38426
$482$	−1.01223e6	−0.198455
$483$	2.60078e7	5.07266
$484$	5.20895e6	1.01073
$485$	109592.	0.0211555
$486$	5.12172e6	0.983616
$487$	−4.06580e6	−0.776825	−0.388413	−	0.921486i	$-0.626976\pi$
$487$	−4.06580e6	−0.776825	−0.388413	+	0.921486i	$0.626976\pi$
$488$	1.64226e6	0.312172
$489$	−8.07047e6	−1.52625
$490$	−617178.	−0.116124
$491$	−2.14116e6	−0.400816	−0.200408	−	0.979713i	$-0.564227\pi$
$491$	−2.14116e6	−0.400816	−0.200408	+	0.979713i	$0.564227\pi$
$492$	−2.73743e6	−0.509836
$493$	−4.82511e6	−0.894108
$494$	−5.39585e6	−0.994815
$495$	−1.01706e6	−0.186566
$496$	246016.	0.0449013
$497$	−6.48230e6	−1.17717
$498$	759363.	0.137207
$499$	−8.35595e6	−1.50226	−0.751129	−	0.660155i	$-0.770491\pi$
$499$	−8.35595e6	−1.50226	−0.751129	+	0.660155i	$0.770491\pi$
$500$	−466735.	−0.0834922
$501$	8.70632e6	1.54967
$502$	−3.91248e6	−0.692936
$503$	4.45563e6	0.785215	0.392608	−	0.919706i	$-0.371573\pi$
$503$	4.45563e6	0.785215	0.392608	+	0.919706i	$0.371573\pi$
$504$	−4.44354e6	−0.779207
$505$	−192263.	−0.0335480
$506$	1.38196e7	2.39949
$507$	−23233.3	−0.00401412
$508$	−3.19992e6	−0.550148
$509$	−4.70860e6	−0.805559	−0.402779	−	0.915297i	$-0.631956\pi$
$509$	−4.70860e6	−0.805559	−0.402779	+	0.915297i	$0.631956\pi$
$510$	500437.	0.0851969
$511$	−4.49831e6	−0.762074
$512$	−262144.	−0.0441942
$513$	3.56369e6	0.597870
$514$	−2.11050e6	−0.352353
$515$	236597.	0.0393089
$516$	−1.00232e6	−0.165722
$517$	2.79833e6	0.460440
$518$	1.02980e7	1.68628
$519$	−1.35899e7	−2.21461
$520$	−182414.	−0.0295835
$521$	256990.	0.0414784	0.0207392	−	0.999785i	$-0.493398\pi$
$521$	256990.	0.0414784	0.0207392	+	0.999785i	$0.493398\pi$
$522$	−5.29539e6	−0.850593
$523$	−9.77502e6	−1.56266	−0.781328	−	0.624120i	$-0.785457\pi$
$523$	−9.77502e6	−1.56266	−0.781328	+	0.624120i	$0.785457\pi$
$524$	391204.	0.0622408
$525$	−1.62948e7	−2.58019
$526$	516227.	0.0813536
$527$	−1.09031e6	−0.171010
$528$	−4.20433e6	−0.656314
$529$	1.80931e7	2.81109
$530$	498968.	0.0771584
$531$	3.06222e6	0.471303
$532$	7.91102e6	1.21186
$533$	−4.42219e6	−0.674248
$534$	−3.55194e6	−0.539029
$535$	74901.9	0.0113138
$536$	1.41234e6	0.212338
$537$	1.34166e7	2.00774
$538$	−426399.	−0.0635127
$539$	−2.29797e7	−3.40700
$540$	120476.	0.0177793
$541$	−5.69126e6	−0.836017	−0.418009	−	0.908443i	$-0.637272\pi$
$541$	−5.69126e6	−0.836017	−0.418009	+	0.908443i	$0.637272\pi$
$542$	−4.76768e6	−0.697122
$543$	1.51990e7	2.21216
$544$	1.16178e6	0.168317
$545$	−157368.	−0.0226948
$546$	−1.27820e7	−1.83492
$547$	4.52243e6	0.646254	0.323127	−	0.946356i	$-0.395266\pi$
$547$	4.52243e6	0.646254	0.323127	+	0.946356i	$0.395266\pi$
$548$	−5.36552e6	−0.763239
$549$	−7.98765e6	−1.13107
$550$	−8.65847e6	−1.22049
$551$	9.42761e6	1.32289
$552$	−7.46260e6	−1.04242
$553$	−4.18785e6	−0.582342
$554$	3.66704e6	0.507623
$555$	−1.27281e6	−0.175401
$556$	−5.69168e6	−0.780824
$557$	844618.	0.115351	0.0576756	−	0.998335i	$-0.481631\pi$
$557$	844618.	0.115351	0.0576756	+	0.998335i	$0.481631\pi$
$558$	−1.19657e6	−0.162687
$559$	−1.61920e6	−0.219165
$560$	267443.	0.0360380
$561$	1.86330e7	2.49962
$562$	2.63263e6	0.351600
$563$	−1.37503e6	−0.182827	−0.0914135	−	0.995813i	$-0.529139\pi$
$563$	−1.37503e6	−0.182827	−0.0914135	+	0.995813i	$0.529139\pi$
$564$	−1.51111e6	−0.200031
$565$	443635.	0.0584662
$566$	−2.84855e6	−0.373751
$567$	−8.42967e6	−1.10117
$568$	1.86001e6	0.241905
$569$	1.34420e7	1.74054	0.870269	−	0.492576i	$-0.163945\pi$
$569$	1.34420e7	1.74054	0.870269	+	0.492576i	$0.163945\pi$
$570$	−977785.	−0.126054
$571$	1.12408e7	1.44281	0.721404	−	0.692514i	$-0.243497\pi$
$571$	1.12408e7	1.44281	0.721404	+	0.692514i	$0.243497\pi$
$572$	−6.79190e6	−0.867963
$573$	1.51810e6	0.193159
$574$	6.48351e6	0.821355
$575$	−1.53686e7	−1.93850
$576$	1.27502e6	0.160125
$577$	−2.66356e6	−0.333061	−0.166530	−	0.986036i	$-0.553256\pi$
$577$	−2.66356e6	−0.333061	−0.166530	+	0.986036i	$0.553256\pi$
$578$	530572.	0.0660580
$579$	5.45879e6	0.676706
$580$	318713.	0.0393396
$581$	−1.79853e6	−0.221043
$582$	−2.20346e6	−0.269648
$583$	1.85783e7	2.26378
$584$	1.29073e6	0.156605
$585$	887226.	0.107188
$586$	−9.86915e6	−1.18723
$587$	8.77559e6	1.05119	0.525595	−	0.850735i	$-0.323843\pi$
$587$	8.77559e6	1.05119	0.525595	+	0.850735i	$0.323843\pi$
$588$	1.24091e7	1.48011
$589$	2.13031e6	0.253020
$590$	−184305.	−0.0217976
$591$	−9.86766e6	−1.16211
$592$	−2.95488e6	−0.346526
$593$	4.55045e6	0.531395	0.265697	−	0.964057i	$-0.414398\pi$
$593$	4.55045e6	0.531395	0.265697	+	0.964057i	$0.414398\pi$
$594$	4.48572e6	0.521634
$595$	−1.18527e6	−0.137254
$596$	5.37026e6	0.619269
$597$	5.29624e6	0.608179
$598$	−1.20555e7	−1.37858
$599$	−5.37769e6	−0.612391	−0.306195	−	0.951969i	$-0.599056\pi$
$599$	−5.37769e6	−0.612391	−0.306195	+	0.951969i	$0.599056\pi$
$600$	4.67559e6	0.530223
$601$	9.92474e6	1.12081	0.560406	−	0.828218i	$-0.310645\pi$
$601$	9.92474e6	1.12081	0.560406	+	0.828218i	$0.310645\pi$
$602$	2.37396e6	0.266982
$603$	−6.86934e6	−0.769346
$604$	−396705.	−0.0442462
$605$	1.52485e6	0.169371
$606$	3.86566e6	0.427604
$607$	−1.19072e7	−1.31171	−0.655854	−	0.754888i	$-0.727691\pi$
$607$	−1.19072e7	−1.31171	−0.655854	+	0.754888i	$0.727691\pi$
$608$	−2.26997e6	−0.249035
$609$	2.23327e7	2.44005
$610$	480752.	0.0523114
$611$	−2.44112e6	−0.264537
$612$	−5.65069e6	−0.609850
$613$	−8.81440e6	−0.947418	−0.473709	−	0.880681i	$-0.657085\pi$
$613$	−8.81440e6	−0.947418	−0.473709	+	0.880681i	$0.657085\pi$
$614$	−4.01004e6	−0.429267
$615$	−801348.	−0.0854345
$616$	9.95781e6	1.05733
$617$	−185755.	−0.0196439	−0.00982197	−	0.999952i	$-0.503126\pi$
$617$	−185755.	−0.0196439	−0.00982197	+	0.999952i	$0.503126\pi$
$618$	−4.75704e6	−0.501032
$619$	7.57371e6	0.794478	0.397239	−	0.917715i	$-0.369968\pi$
$619$	7.57371e6	0.794478	0.397239	+	0.917715i	$0.369968\pi$
$620$	72018.0	0.00752423
$621$	7.96206e6	0.828507
$622$	−6.34786e6	−0.657887
$623$	8.41265e6	0.868385
$624$	3.66764e6	0.377073
$625$	9.56044e6	0.978989
$626$	−1.22927e7	−1.25375
$627$	−3.64063e7	−3.69834
$628$	6.59412e6	0.667202
$629$	1.30956e7	1.31977
$630$	−1.30079e6	−0.130574
$631$	−1.08066e7	−1.08048	−0.540239	−	0.841512i	$-0.681666\pi$
$631$	−1.08066e7	−1.08048	−0.540239	+	0.841512i	$0.681666\pi$
$632$	1.20165e6	0.119670
$633$	−1.17664e7	−1.16717
$634$	−3.05553e6	−0.301900
$635$	−936734.	−0.0921896
$636$	−1.00323e7	−0.983463
$637$	2.00463e7	1.95742
$638$	1.18668e7	1.15420
$639$	−9.04674e6	−0.876476
$640$	−76739.3	−0.00740573
$641$	1.04529e7	1.00483	0.502415	−	0.864627i	$-0.332445\pi$
$641$	1.04529e7	1.00483	0.502415	+	0.864627i	$0.332445\pi$
$642$	−1.50599e6	−0.144206
$643$	−4.02341e6	−0.383766	−0.191883	−	0.981418i	$-0.561459\pi$
$643$	−4.02341e6	−0.383766	−0.191883	+	0.981418i	$0.561459\pi$
$644$	1.76749e7	1.67936
$645$	−293416.	−0.0277705
$646$	1.00602e7	0.948470
$647$	6.26614e6	0.588490	0.294245	−	0.955730i	$-0.404932\pi$
$647$	6.26614e6	0.588490	0.294245	+	0.955730i	$0.404932\pi$
$648$	2.41878e6	0.226287
$649$	−6.86232e6	−0.639528
$650$	7.55320e6	0.701209
$651$	5.04641e6	0.466692
$652$	−5.48470e6	−0.505282
$653$	−4.84802e6	−0.444919	−0.222460	−	0.974942i	$-0.571409\pi$
$653$	−4.84802e6	−0.444919	−0.222460	+	0.974942i	$0.571409\pi$
$654$	3.16406e6	0.289268
$655$	114520.	0.0104298
$656$	−1.86036e6	−0.168786
$657$	−6.27787e6	−0.567413
$658$	3.57900e6	0.322253
$659$	−1.92462e7	−1.72636	−0.863178	−	0.504899i	$-0.831530\pi$
$659$	−1.92462e7	−1.72636	−0.863178	+	0.504899i	$0.831530\pi$
$660$	−1.23076e6	−0.109980
$661$	1.94105e7	1.72796	0.863980	−	0.503527i	$-0.167964\pi$
$661$	1.94105e7	1.72796	0.863980	+	0.503527i	$0.167964\pi$
$662$	7.85838e6	0.696928
$663$	−1.62544e7	−1.43611
$664$	516064.	0.0454238
$665$	2.31585e6	0.203075
$666$	1.43720e7	1.25554
$667$	2.10633e7	1.83321
$668$	5.91682e6	0.513035
$669$	1.06659e7	0.921367
$670$	413444.	0.0355819
$671$	1.79000e7	1.53478
$672$	−5.37723e6	−0.459342
$673$	1.79680e7	1.52919	0.764597	−	0.644509i	$-0.222938\pi$
$673$	1.79680e7	1.52919	0.764597	+	0.644509i	$0.222938\pi$
$674$	−3.89428e6	−0.330200
$675$	−4.98852e6	−0.421417
$676$	−15789.4	−0.00132892
$677$	−1.13996e7	−0.955912	−0.477956	−	0.878384i	$-0.658622\pi$
$677$	−1.13996e7	−0.955912	−0.477956	+	0.878384i	$0.658622\pi$
$678$	−8.91978e6	−0.745212
$679$	5.21882e6	0.434408
$680$	340097.	0.0282053
$681$	−2.57888e6	−0.213090
$682$	2.68148e6	0.220756
$683$	−1.06569e7	−0.874138	−0.437069	−	0.899428i	$-0.643984\pi$
$683$	−1.06569e7	−0.874138	−0.437069	+	0.899428i	$0.643984\pi$
$684$	1.10407e7	0.902309
$685$	−1.57069e6	−0.127898
$686$	−1.43955e7	−1.16793
$687$	1.59254e7	1.28735
$688$	−681177.	−0.0548641
$689$	−1.62067e7	−1.30061
$690$	−2.18458e6	−0.174681
$691$	7.42580e6	0.591627	0.295814	−	0.955246i	$-0.404409\pi$
$691$	7.42580e6	0.591627	0.295814	+	0.955246i	$0.404409\pi$
$692$	−9.23568e6	−0.733168
$693$	−4.84328e7	−3.83095
$694$	3.30253e6	0.260284
$695$	−1.66617e6	−0.130845
$696$	−6.40808e6	−0.501424
$697$	8.24485e6	0.642837
$698$	4.53797e6	0.352552
$699$	3.64250e7	2.81972
$700$	−1.10740e7	−0.854198
$701$	−1.05567e7	−0.811398	−0.405699	−	0.914007i	$-0.632972\pi$
$701$	−1.05567e7	−0.811398	−0.405699	+	0.914007i	$0.632972\pi$
$702$	−3.91310e6	−0.299694
$703$	−2.55870e7	−1.95268
$704$	−2.85727e6	−0.217280
$705$	−442357.	−0.0335197
$706$	−1.33111e6	−0.100508
$707$	−9.15569e6	−0.688878
$708$	3.70567e6	0.277833
$709$	−1.80867e6	−0.135127	−0.0675637	−	0.997715i	$-0.521523\pi$
$709$	−1.80867e6	−0.135127	−0.0675637	+	0.997715i	$0.521523\pi$
$710$	544495.	0.0405367
$711$	−5.84459e6	−0.433591
$712$	−2.41390e6	−0.178451
$713$	4.75957e6	0.350626
$714$	2.38311e7	1.74944
$715$	−1.98824e6	−0.145447
$716$	9.11793e6	0.664682
$717$	−2.70355e7	−1.96398
$718$	−3.96800e6	−0.287250
$719$	−73457.0	−0.00529921	−0.00264960	−	0.999996i	$-0.500843\pi$
$719$	−73457.0	−0.00529921	−0.00264960	+	0.999996i	$0.500843\pi$
$720$	373245.	0.0268326
$721$	1.12669e7	0.807171
$722$	−9.75177e6	−0.696210
$723$	5.95781e6	0.423878
$724$	1.03293e7	0.732358
$725$	−1.31969e7	−0.932454
$726$	−3.06589e7	−2.15881
$727$	1.10069e7	0.772379	0.386190	−	0.922419i	$-0.373791\pi$
$727$	1.10069e7	0.772379	0.386190	+	0.922419i	$0.373791\pi$
$728$	−8.68667e6	−0.607470
$729$	−2.09616e7	−1.46085
$730$	377846.	0.0262426
$731$	3.01887e6	0.208954
$732$	−9.66605e6	−0.666763
$733$	−2.69655e7	−1.85374	−0.926868	−	0.375388i	$-0.877509\pi$
$733$	−2.69655e7	−1.85374	−0.926868	+	0.375388i	$0.877509\pi$
$734$	−1.92762e7	−1.32063
$735$	3.63259e6	0.248027
$736$	−5.07159e6	−0.345104
$737$	1.53939e7	1.04395
$738$	9.04843e6	0.611551
$739$	−800226.	−0.0539016	−0.0269508	−	0.999637i	$-0.508580\pi$
$739$	−800226.	−0.0539016	−0.0269508	+	0.999637i	$0.508580\pi$
$740$	−865005.	−0.0580683
$741$	3.17589e7	2.12481
$742$	2.37612e7	1.58438
$743$	−1.66717e7	−1.10792	−0.553960	−	0.832544i	$-0.686884\pi$
$743$	−1.66717e7	−1.10792	−0.553960	+	0.832544i	$0.686884\pi$
$744$	−1.44800e6	−0.0959041
$745$	1.57207e6	0.103772
$746$	−2.73604e6	−0.180001
$747$	−2.51003e6	−0.164580
$748$	1.26630e7	0.827527
$749$	3.56688e6	0.232318
$750$	2.74711e6	0.178330
$751$	1.51782e7	0.982021	0.491011	−	0.871154i	$-0.336628\pi$
$751$	1.51782e7	0.982021	0.491011	+	0.871154i	$0.336628\pi$
$752$	−1.02695e6	−0.0662223
$753$	2.30281e7	1.48003
$754$	−1.03520e7	−0.663123
$755$	−116130.	−0.00741444
$756$	5.73712e6	0.365081
$757$	−8.97321e6	−0.569126	−0.284563	−	0.958657i	$-0.591848\pi$
$757$	−8.97321e6	−0.569126	−0.284563	+	0.958657i	$0.591848\pi$
$758$	1.26861e7	0.801962
$759$	−8.13394e7	−5.12503
$760$	−664503.	−0.0417314
$761$	−2.22534e7	−1.39295	−0.696475	−	0.717581i	$-0.745249\pi$
$761$	−2.22534e7	−1.39295	−0.696475	+	0.717581i	$0.745249\pi$
$762$	1.88341e7	1.17505
$763$	−7.49397e6	−0.466016
$764$	1.03170e6	0.0639472
$765$	−1.65417e6	−0.102194
$766$	1.31197e7	0.807891
$767$	5.98633e6	0.367428
$768$	1.54293e6	0.0943937
$769$	1.79652e7	1.09551	0.547755	−	0.836639i	$-0.315483\pi$
$769$	1.79652e7	1.09551	0.547755	+	0.836639i	$0.315483\pi$
$770$	2.91502e6	0.177180
$771$	1.24220e7	0.752586
$772$	3.70980e6	0.224031
$773$	2.10629e7	1.26785	0.633927	−	0.773393i	$-0.281442\pi$
$773$	2.10629e7	1.26785	0.633927	+	0.773393i	$0.281442\pi$
$774$	3.31311e6	0.198785
$775$	−2.98204e6	−0.178344
$776$	−1.49747e6	−0.0892699
$777$	−6.06121e7	−3.60170
$778$	−4.55978e6	−0.270082
$779$	−1.61093e7	−0.951115
$780$	1.07365e6	0.0631870
$781$	2.02734e7	1.18932
$782$	2.24765e7	1.31436
$783$	6.83696e6	0.398528
$784$	8.43321e6	0.490007
$785$	1.93034e6	0.111805
$786$	−2.30255e6	−0.132939
$787$	2.58789e7	1.48939	0.744697	−	0.667403i	$-0.232594\pi$
$787$	2.58789e7	1.48939	0.744697	+	0.667403i	$0.232594\pi$
$788$	−6.70607e6	−0.384727
$789$	−3.03841e6	−0.173762
$790$	351768.	0.0200534
$791$	2.11262e7	1.20055
$792$	1.38972e7	0.787252
$793$	−1.56151e7	−0.881781
$794$	−2.21059e7	−1.24439
$795$	−2.93683e6	−0.164801
$796$	3.59933e6	0.201344
$797$	6.65997e6	0.371387	0.185693	−	0.982608i	$-0.440547\pi$
$797$	6.65997e6	0.371387	0.185693	+	0.982608i	$0.440547\pi$
$798$	−4.65627e7	−2.58840
$799$	4.55129e6	0.252213
$800$	3.17754e6	0.175536
$801$	1.17407e7	0.646568
$802$	−6.57792e6	−0.361121
$803$	1.40685e7	0.769942
$804$	−8.31275e6	−0.453529
$805$	5.17410e6	0.281414
$806$	−2.33918e6	−0.126831
$807$	2.50970e6	0.135656
$808$	2.62711e6	0.141563
$809$	2.24564e7	1.20633	0.603167	−	0.797615i	$-0.293905\pi$
$809$	2.24564e7	1.20633	0.603167	+	0.797615i	$0.293905\pi$
$810$	708068.	0.0379195
$811$	2.11849e7	1.13103	0.565515	−	0.824738i	$-0.308677\pi$
$811$	2.11849e7	1.13103	0.565515	+	0.824738i	$0.308677\pi$
$812$	1.51773e7	0.807802
$813$	2.80616e7	1.48897
$814$	−3.22071e7	−1.70369
$815$	−1.60558e6	−0.0846714
$816$	−6.83803e6	−0.359506
$817$	−5.89847e6	−0.309161
$818$	1.86847e7	0.976342
$819$	4.22503e7	2.20100
$820$	−544597.	−0.0282840
$821$	−3.09018e7	−1.60002	−0.800010	−	0.599986i	$-0.795173\pi$
$821$	−3.09018e7	−1.60002	−0.800010	+	0.599986i	$0.795173\pi$
$822$	3.15804e7	1.63019
$823$	−2.47393e6	−0.127317	−0.0636586	−	0.997972i	$-0.520277\pi$
$823$	−2.47393e6	−0.127317	−0.0636586	+	0.997972i	$0.520277\pi$
$824$	−3.23289e6	−0.165872
$825$	5.09621e7	2.60683
$826$	−8.77674e6	−0.447593
$827$	−2.90215e7	−1.47556	−0.737780	−	0.675042i	$-0.764126\pi$
$827$	−2.90215e7	−1.47556	−0.737780	+	0.675042i	$0.764126\pi$
$828$	2.46672e7	1.25039
$829$	−9.17185e6	−0.463522	−0.231761	−	0.972773i	$-0.574449\pi$
$829$	−9.17185e6	−0.463522	−0.231761	+	0.972773i	$0.574449\pi$
$830$	151071.	0.00761178
$831$	−2.15835e7	−1.08423
$832$	2.49253e6	0.124834
$833$	−3.73747e7	−1.86623
$834$	3.35001e7	1.66775
$835$	1.73207e6	0.0859706
$836$	−2.47417e7	−1.22437
$837$	1.54491e6	0.0762238
$838$	2.82297e6	0.138866
$839$	9.92376e6	0.486711	0.243356	−	0.969937i	$-0.421752\pi$
$839$	9.92376e6	0.486711	0.243356	+	0.969937i	$0.421752\pi$
$840$	−1.57412e6	−0.0769730
$841$	−2.42424e6	−0.118191
$842$	463495.	0.0225302
$843$	−1.54952e7	−0.750978
$844$	−7.99643e6	−0.386403
$845$	−4622.13	−0.000222690 0
$846$	4.99488e6	0.239938
$847$	7.26145e7	3.47788
$848$	−6.81797e6	−0.325586
$849$	1.67660e7	0.798289
$850$	−1.40824e7	−0.668542
$851$	−5.71669e7	−2.70596
$852$	−1.09477e7	−0.516682
$853$	−3.64850e7	−1.71689	−0.858444	−	0.512908i	$-0.828568\pi$
$853$	−3.64850e7	−1.71689	−0.858444	+	0.512908i	$0.828568\pi$
$854$	2.28937e7	1.07417
$855$	3.23201e6	0.151202
$856$	−1.02347e6	−0.0477409
$857$	−2.73328e7	−1.27125	−0.635627	−	0.771996i	$-0.719258\pi$
$857$	−2.73328e7	−1.27125	−0.635627	+	0.771996i	$0.719258\pi$
$858$	3.99758e7	1.85387
$859$	−3.98534e7	−1.84282	−0.921409	−	0.388595i	$-0.872961\pi$
$859$	−3.98534e7	−1.84282	−0.921409	+	0.388595i	$0.872961\pi$
$860$	−199406.	−0.00919372
$861$	−3.81607e7	−1.75432
$862$	2.50820e7	1.14972
$863$	2.53256e7	1.15753	0.578765	−	0.815494i	$-0.303535\pi$
$863$	2.53256e7	1.15753	0.578765	+	0.815494i	$0.303535\pi$
$864$	−1.64619e6	−0.0750234
$865$	−2.70363e6	−0.122859
$866$	1.62435e7	0.736014
$867$	−3.12285e6	−0.141092
$868$	3.42954e6	0.154503
$869$	1.30975e7	0.588355
$870$	−1.87588e6	−0.0840249
$871$	−1.34289e7	−0.599783
$872$	2.15030e6	0.0957652
$873$	7.28342e6	0.323444
$874$	−4.39161e7	−1.94467
$875$	−6.50645e6	−0.287292
$876$	−7.59700e6	−0.334489
$877$	2.29767e7	1.00876	0.504381	−	0.863481i	$-0.331721\pi$
$877$	2.29767e7	1.00876	0.504381	+	0.863481i	$0.331721\pi$
$878$	−2.16285e7	−0.946871
$879$	5.80879e7	2.53579
$880$	−836428.	−0.0364101
$881$	−1.47864e7	−0.641834	−0.320917	−	0.947107i	$-0.603991\pi$
$881$	−1.47864e7	−0.641834	−0.320917	+	0.947107i	$0.603991\pi$
$882$	−4.10175e7	−1.77540
$883$	2.49004e7	1.07474	0.537371	−	0.843346i	$-0.319418\pi$
$883$	2.49004e7	1.07474	0.537371	+	0.843346i	$0.319418\pi$
$884$	−1.10465e7	−0.475439
$885$	1.08479e6	0.0465571
$886$	−1.00322e7	−0.429351
$887$	−2.55626e6	−0.109093	−0.0545464	−	0.998511i	$-0.517371\pi$
$887$	−2.55626e6	−0.109093	−0.0545464	+	0.998511i	$0.517371\pi$
$888$	1.73919e7	0.740140
$889$	−4.46079e7	−1.89303
$890$	−706639.	−0.0299035
$891$	2.63638e7	1.11254
$892$	7.24856e6	0.305028
$893$	−8.89259e6	−0.373164
$894$	−3.16083e7	−1.32269
$895$	2.66916e6	0.111382
$896$	−3.65437e6	−0.152070
$897$	7.09562e7	2.94449
$898$	−1.23918e7	−0.512796
$899$	4.08701e6	0.168658
$900$	−1.54549e7	−0.636004
$901$	3.02162e7	1.24002
$902$	−2.02772e7	−0.829835
$903$	−1.39727e7	−0.570242
$904$	−6.06189e6	−0.246710
$905$	3.02376e6	0.122723
$906$	2.33493e6	0.0945047
$907$	−1.48169e7	−0.598054	−0.299027	−	0.954245i	$-0.596662\pi$
$907$	−1.48169e7	−0.598054	−0.299027	+	0.954245i	$0.596662\pi$
$908$	−1.75261e6	−0.0705456
$909$	−1.27777e7	−0.512913
$910$	−2.54291e6	−0.101795
$911$	2.09632e7	0.836876	0.418438	−	0.908245i	$-0.362578\pi$
$911$	2.09632e7	0.836876	0.418438	+	0.908245i	$0.362578\pi$
$912$	1.33606e7	0.531910
$913$	5.62489e6	0.223325
$914$	3.05752e7	1.21061
$915$	−2.82961e6	−0.111731
$916$	1.08229e7	0.426192
$917$	5.45351e6	0.214167
$918$	7.29569e6	0.285733
$919$	6.13865e6	0.239764	0.119882	−	0.992788i	$-0.461748\pi$
$919$	6.13865e6	0.239764	0.119882	+	0.992788i	$0.461748\pi$
$920$	−1.48464e6	−0.0578299
$921$	2.36023e7	0.916866
$922$	−9.19225e6	−0.356119
$923$	−1.76855e7	−0.683302
$924$	−5.86097e7	−2.25834
$925$	3.58171e7	1.37637
$926$	8.54334e6	0.327416
$927$	1.57241e7	0.600990
$928$	−4.35494e6	−0.166002
$929$	4.90552e7	1.86486	0.932428	−	0.361355i	$-0.117686\pi$
$929$	4.90552e7	1.86486	0.932428	+	0.361355i	$0.117686\pi$
$930$	−423884.	−0.0160709
$931$	7.30251e7	2.76120
$932$	2.47545e7	0.933499
$933$	3.73622e7	1.40517
$934$	2.03270e6	0.0762441
$935$	3.70693e6	0.138671
$936$	−1.21232e7	−0.452300
$937$	−2.98959e7	−1.11240	−0.556201	−	0.831048i	$-0.687742\pi$
$937$	−2.98959e7	−1.11240	−0.556201	+	0.831048i	$0.687742\pi$
$938$	1.96885e7	0.730642
$939$	7.23522e7	2.67786
$940$	−300626.	−0.0110970
$941$	−2.23165e7	−0.821584	−0.410792	−	0.911729i	$-0.634748\pi$
$941$	−2.23165e7	−0.821584	−0.410792	+	0.911729i	$0.634748\pi$
$942$	−3.88117e7	−1.42507
$943$	−3.59916e7	−1.31802
$944$	2.51837e6	0.0919793
$945$	1.67947e6	0.0611776
$946$	−7.42456e6	−0.269738
$947$	−1.32192e6	−0.0478994	−0.0239497	−	0.999713i	$-0.507624\pi$
$947$	−1.32192e6	−0.0478994	−0.0239497	+	0.999713i	$0.507624\pi$
$948$	−7.07268e6	−0.255601
$949$	−1.22726e7	−0.442355
$950$	2.75150e7	0.989147
$951$	1.79843e7	0.644824
$952$	1.61957e7	0.579170
$953$	2.49351e7	0.889364	0.444682	−	0.895689i	$-0.353317\pi$
$953$	2.49351e7	0.889364	0.444682	+	0.895689i	$0.353317\pi$
$954$	3.31613e7	1.17967
$955$	302018.	0.0107158
$956$	−1.83733e7	−0.650194
$957$	−6.98456e7	−2.46524
$958$	−2.86369e6	−0.100812
$959$	−7.47971e7	−2.62626
$960$	451673.	0.0158178
$961$	923521.	0.0322581
$962$	2.80958e7	0.978821
$963$	4.97796e6	0.172976
$964$	4.04893e6	0.140329
$965$	1.08600e6	0.0375414
$966$	−1.04031e8	−3.58691
$967$	−1.56638e7	−0.538681	−0.269341	−	0.963045i	$-0.586806\pi$
$967$	−1.56638e7	−0.538681	−0.269341	+	0.963045i	$0.586806\pi$
$968$	−2.08358e7	−0.714697
$969$	−5.92121e7	−2.02582
$970$	−438366.	−0.0149592
$971$	2.11281e7	0.719139	0.359570	−	0.933118i	$-0.382923\pi$
$971$	2.11281e7	0.719139	0.359570	+	0.933118i	$0.382923\pi$
$972$	−2.04869e7	−0.695521
$973$	−7.93439e7	−2.68677
$974$	1.62632e7	0.549298
$975$	−4.44567e7	−1.49770
$976$	−6.56906e6	−0.220739
$977$	3.71989e7	1.24679	0.623396	−	0.781907i	$-0.285753\pi$
$977$	3.71989e7	1.24679	0.623396	+	0.781907i	$0.285753\pi$
$978$	3.22819e7	1.07922
$979$	−2.63106e7	−0.877351
$980$	2.46871e6	0.0821118
$981$	−1.04586e7	−0.346978
$982$	8.56463e6	0.283420
$983$	−3.33723e7	−1.10155	−0.550773	−	0.834655i	$-0.685667\pi$
$983$	−3.33723e7	−1.10155	−0.550773	+	0.834655i	$0.685667\pi$
$984$	1.09497e7	0.360508
$985$	−1.96312e6	−0.0644697
$986$	1.93005e7	0.632230
$987$	−2.10653e7	−0.688296
$988$	2.15834e7	0.703441
$989$	−1.31784e7	−0.428423
$990$	4.06822e6	0.131922
$991$	3.39824e6	0.109918	0.0549592	−	0.998489i	$-0.482497\pi$
$991$	3.39824e6	0.109918	0.0549592	+	0.998489i	$0.482497\pi$
$992$	−984064.	−0.0317500
$993$	−4.62529e7	−1.48856
$994$	2.59292e7	0.832384
$995$	1.05366e6	0.0337397
$996$	−3.03745e6	−0.0970200
$997$	−8.75443e6	−0.278927	−0.139463	−	0.990227i	$-0.544538\pi$
$997$	−8.75443e6	−0.278927	−0.139463	+	0.990227i	$0.544538\pi$
$998$	3.34238e7	1.06226
$999$	−1.85559e7	−0.588258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.a.c.1.4	✓	4
3.2	odd	2		558.6.a.k.1.2		4
4.3	odd	2		496.6.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.a.c.1.4	✓	4	1.1	even	1	trivial
496.6.a.d.1.1		4	4.3	odd	2
558.6.a.k.1.2		4	3.2	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +23.5432 q^{3} +16.0000 q^{4} +4.68379 q^{5} -94.1729 q^{6} +223.045 q^{7} -64.0000 q^{8} +311.283 q^{9} -18.7352 q^{10} -697.575 q^{11} +376.692 q^{12} +608.528 q^{13} -892.181 q^{14} +110.272 q^{15} +256.000 q^{16} -1134.55 q^{17} -1245.13 q^{18} +2216.76 q^{19} +74.9407 q^{20} +5251.21 q^{21} +2790.30 q^{22} +4952.73 q^{23} -1506.77 q^{24} -3103.06 q^{25} -2434.11 q^{26} +1607.61 q^{27} +3568.73 q^{28} +4252.87 q^{29} -441.087 q^{30} +961.000 q^{31} -1024.00 q^{32} -16423.2 q^{33} +4538.22 q^{34} +1044.70 q^{35} +4980.53 q^{36} -11542.5 q^{37} -8867.06 q^{38} +14326.7 q^{39} -299.763 q^{40} -7267.04 q^{41} -21004.8 q^{42} -2660.85 q^{43} -11161.2 q^{44} +1457.99 q^{45} -19810.9 q^{46} -4011.52 q^{47} +6027.07 q^{48} +32942.2 q^{49} +12412.2 q^{50} -26711.1 q^{51} +9736.45 q^{52} -26632.7 q^{53} -6430.44 q^{54} -3267.30 q^{55} -14274.9 q^{56} +52189.8 q^{57} -17011.5 q^{58} +9837.40 q^{59} +1764.35 q^{60} -25660.4 q^{61} -3844.00 q^{62} +69430.3 q^{63} +4096.00 q^{64} +2850.22 q^{65} +65692.6 q^{66} -22067.8 q^{67} -18152.9 q^{68} +116603. q^{69} -4178.79 q^{70} -29062.7 q^{71} -19922.1 q^{72} -20167.7 q^{73} +46170.1 q^{74} -73056.1 q^{75} +35468.2 q^{76} -155591. q^{77} -57306.8 q^{78} -18775.8 q^{79} +1199.05 q^{80} -37793.5 q^{81} +29068.1 q^{82} -8063.50 q^{83} +84019.3 q^{84} -5314.02 q^{85} +10643.4 q^{86} +100126. q^{87} +44644.8 q^{88} +37717.2 q^{89} -5831.95 q^{90} +135729. q^{91} +79243.6 q^{92} +22625.0 q^{93} +16046.1 q^{94} +10382.9 q^{95} -24108.3 q^{96} +23398.0 q^{97} -131769. q^{98} -217143. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 10 q^{3} + 64 q^{4} + 2 q^{5} - 40 q^{6} + 146 q^{7} - 256 q^{8} - 36 q^{9} - 8 q^{10} - 270 q^{11} + 160 q^{12} + 1038 q^{13} - 584 q^{14} + 1864 q^{15} + 1024 q^{16} + 2020 q^{17} + 144 q^{18}+ \cdots - 324354 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 10 * q^3 + 64 * q^4 + 2 * q^5 - 40 * q^6 + 146 * q^7 - 256 * q^8 - 36 * q^9 - 8 * q^10 - 270 * q^11 + 160 * q^12 + 1038 * q^13 - 584 * q^14 + 1864 * q^15 + 1024 * q^16 + 2020 * q^17 + 144 * q^18 + 6214 * q^19 + 32 * q^20 + 7256 * q^21 + 1080 * q^22 + 8292 * q^23 - 640 * q^24 + 9974 * q^25 - 4152 * q^26 + 5032 * q^27 + 2336 * q^28 + 1894 * q^29 - 7456 * q^30 + 3844 * q^31 - 4096 * q^32 - 11280 * q^33 - 8080 * q^34 - 9146 * q^35 - 576 * q^36 - 5470 * q^37 - 24856 * q^38 - 1628 * q^39 - 128 * q^40 - 16878 * q^41 - 29024 * q^42 + 1530 * q^43 - 4320 * q^44 + 5642 * q^45 - 33168 * q^46 - 25460 * q^47 + 2560 * q^48 + 21630 * q^49 - 39896 * q^50 - 40372 * q^51 + 16608 * q^52 - 7790 * q^53 - 20128 * q^54 + 5760 * q^55 - 9344 * q^56 + 15036 * q^57 - 7576 * q^58 - 35802 * q^59 + 29824 * q^60 + 48366 * q^61 - 15376 * q^62 + 53634 * q^63 + 16384 * q^64 + 12096 * q^65 + 45120 * q^66 + 54696 * q^67 + 32320 * q^68 + 110760 * q^69 + 36584 * q^70 - 35342 * q^71 + 2304 * q^72 + 59336 * q^73 + 21880 * q^74 - 24510 * q^75 + 99424 * q^76 - 86976 * q^77 + 6512 * q^78 - 3652 * q^79 + 512 * q^80 - 73452 * q^81 + 67512 * q^82 - 80074 * q^83 + 116096 * q^84 + 81860 * q^85 - 6120 * q^86 + 112364 * q^87 + 17280 * q^88 - 12060 * q^89 - 22568 * q^90 - 74952 * q^91 + 132672 * q^92 + 9610 * q^93 + 101840 * q^94 - 286138 * q^95 - 10240 * q^96 + 232670 * q^97 - 86520 * q^98 - 324354 * q^99

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