LMFDB - Embedded newform 230.6.a.d.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,12,-34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.27980.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 47x - 106 $ x^3 - 47*x - 106
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.65230$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +2.35610 q^{3} +16.0000 q^{4} +25.0000 q^{5} +9.42439 q^{6} -9.44632 q^{7} +64.0000 q^{8} -237.449 q^{9} +100.000 q^{10} -248.872 q^{11} +37.6975 q^{12} -898.786 q^{13} -37.7853 q^{14} +58.9024 q^{15} +256.000 q^{16} -1177.51 q^{17} -949.795 q^{18} +116.462 q^{19} +400.000 q^{20} -22.2564 q^{21} -995.490 q^{22} -529.000 q^{23} +150.790 q^{24} +625.000 q^{25} -3595.14 q^{26} -1131.98 q^{27} -151.141 q^{28} +2766.81 q^{29} +235.610 q^{30} -661.945 q^{31} +1024.00 q^{32} -586.368 q^{33} -4710.03 q^{34} -236.158 q^{35} -3799.18 q^{36} -5965.93 q^{37} +465.848 q^{38} -2117.63 q^{39} +1600.00 q^{40} -7482.54 q^{41} -89.0258 q^{42} +8158.86 q^{43} -3981.96 q^{44} -5936.22 q^{45} -2116.00 q^{46} +14818.9 q^{47} +603.161 q^{48} -16717.8 q^{49} +2500.00 q^{50} -2774.32 q^{51} -14380.6 q^{52} -24766.8 q^{53} -4527.94 q^{54} -6221.81 q^{55} -604.565 q^{56} +274.396 q^{57} +11067.2 q^{58} -7935.48 q^{59} +942.439 q^{60} +5864.34 q^{61} -2647.78 q^{62} +2243.02 q^{63} +4096.00 q^{64} -22469.6 q^{65} -2345.47 q^{66} -5691.52 q^{67} -18840.1 q^{68} -1246.38 q^{69} -944.632 q^{70} -30857.3 q^{71} -15196.7 q^{72} +24861.4 q^{73} -23863.7 q^{74} +1472.56 q^{75} +1863.39 q^{76} +2350.93 q^{77} -8470.51 q^{78} -43677.4 q^{79} +6400.00 q^{80} +55033.0 q^{81} -29930.1 q^{82} -42211.7 q^{83} -356.103 q^{84} -29437.7 q^{85} +32635.4 q^{86} +6518.86 q^{87} -15927.8 q^{88} +92378.1 q^{89} -23744.9 q^{90} +8490.22 q^{91} -8464.00 q^{92} -1559.61 q^{93} +59275.5 q^{94} +2911.55 q^{95} +2412.64 q^{96} -4948.63 q^{97} -66871.1 q^{98} +59094.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12 q^{2} - 34 q^{3} + 48 q^{4} + 75 q^{5} - 136 q^{6} - 121 q^{7} + 192 q^{8} + 89 q^{9} + 300 q^{10} - 502 q^{11} - 544 q^{12} + 76 q^{13} - 484 q^{14} - 850 q^{15} + 768 q^{16} - 1167 q^{17} + 356 q^{18}+ \cdots + 344510 q^{99}+O(q^{100}) $ 3 * q + 12 * q^2 - 34 * q^3 + 48 * q^4 + 75 * q^5 - 136 * q^6 - 121 * q^7 + 192 * q^8 + 89 * q^9 + 300 * q^10 - 502 * q^11 - 544 * q^12 + 76 * q^13 - 484 * q^14 - 850 * q^15 + 768 * q^16 - 1167 * q^17 + 356 * q^18 - 1694 * q^19 + 1200 * q^20 + 3624 * q^21 - 2008 * q^22 - 1587 * q^23 - 2176 * q^24 + 1875 * q^25 + 304 * q^26 - 3742 * q^27 - 1936 * q^28 - 4999 * q^29 - 3400 * q^30 - 9691 * q^31 + 3072 * q^32 - 4972 * q^33 - 4668 * q^34 - 3025 * q^35 + 1424 * q^36 + 925 * q^37 - 6776 * q^38 - 14326 * q^39 + 4800 * q^40 - 1513 * q^41 + 14496 * q^42 - 30552 * q^43 - 8032 * q^44 + 2225 * q^45 - 6348 * q^46 - 2070 * q^47 - 8704 * q^48 - 26828 * q^49 + 7500 * q^50 + 1920 * q^51 + 1216 * q^52 - 34923 * q^53 - 14968 * q^54 - 12550 * q^55 - 7744 * q^56 + 7964 * q^57 - 19996 * q^58 - 36665 * q^59 - 13600 * q^60 - 44364 * q^61 - 38764 * q^62 - 74805 * q^63 + 12288 * q^64 + 1900 * q^65 - 19888 * q^66 - 85969 * q^67 - 18672 * q^68 + 17986 * q^69 - 12100 * q^70 - 105817 * q^71 + 5696 * q^72 - 71348 * q^73 + 3700 * q^74 - 21250 * q^75 - 27104 * q^76 - 79494 * q^77 - 57304 * q^78 + 12196 * q^79 + 19200 * q^80 + 111227 * q^81 - 6052 * q^82 - 66689 * q^83 + 57984 * q^84 - 29175 * q^85 - 122208 * q^86 + 129542 * q^87 - 32128 * q^88 + 149868 * q^89 + 8900 * q^90 + 12970 * q^91 - 25392 * q^92 + 164202 * q^93 - 8280 * q^94 - 42350 * q^95 - 34816 * q^96 + 215238 * q^97 - 107312 * q^98 + 344510 * 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
$3$	2.35610	0.151144	0.0755718	−	0.997140i	$-0.475922\pi$
$3$	2.35610	0.151144	0.0755718	+	0.997140i	$0.475922\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	9.42439	0.106875
$7$	−9.44632	−0.0728648	−0.0364324	−	0.999336i	$-0.511599\pi$
$7$	−9.44632	−0.0728648	−0.0364324	+	0.999336i	$0.511599\pi$
$8$	64.0000	0.353553
$9$	−237.449	−0.977156
$10$	100.000	0.316228
$11$	−248.872	−0.620148	−0.310074	−	0.950712i	$-0.600354\pi$
$11$	−248.872	−0.620148	−0.310074	+	0.950712i	$0.600354\pi$
$12$	37.6975	0.0755718
$13$	−898.786	−1.47502	−0.737510	−	0.675336i	$-0.763998\pi$
$13$	−898.786	−1.47502	−0.737510	+	0.675336i	$0.763998\pi$
$14$	−37.7853	−0.0515232
$15$	58.9024	0.0675935
$16$	256.000	0.250000
$17$	−1177.51	−0.988193	−0.494097	−	0.869407i	$-0.664501\pi$
$17$	−1177.51	−0.988193	−0.494097	+	0.869407i	$0.664501\pi$
$18$	−949.795	−0.690953
$19$	116.462	0.0740117	0.0370058	−	0.999315i	$-0.488218\pi$
$19$	116.462	0.0740117	0.0370058	+	0.999315i	$0.488218\pi$
$20$	400.000	0.223607
$21$	−22.2564	−0.0110130
$22$	−995.490	−0.438511
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	150.790	0.0534374
$25$	625.000	0.200000
$26$	−3595.14	−1.04300
$27$	−1131.98	−0.298835
$28$	−151.141	−0.0364324
$29$	2766.81	0.610919	0.305459	−	0.952205i	$-0.401190\pi$
$29$	2766.81	0.610919	0.305459	+	0.952205i	$0.401190\pi$
$30$	235.610	0.0477958
$31$	−661.945	−0.123714	−0.0618568	−	0.998085i	$-0.519702\pi$
$31$	−661.945	−0.123714	−0.0618568	+	0.998085i	$0.519702\pi$
$32$	1024.00	0.176777
$33$	−586.368	−0.0937314
$34$	−4710.03	−0.698758
$35$	−236.158	−0.0325861
$36$	−3799.18	−0.488578
$37$	−5965.93	−0.716430	−0.358215	−	0.933639i	$-0.616614\pi$
$37$	−5965.93	−0.716430	−0.358215	+	0.933639i	$0.616614\pi$
$38$	465.848	0.0523342
$39$	−2117.63	−0.222940
$40$	1600.00	0.158114
$41$	−7482.54	−0.695167	−0.347584	−	0.937649i	$-0.612998\pi$
$41$	−7482.54	−0.695167	−0.347584	+	0.937649i	$0.612998\pi$
$42$	−89.0258	−0.00778740
$43$	8158.86	0.672912	0.336456	−	0.941699i	$-0.390772\pi$
$43$	8158.86	0.672912	0.336456	+	0.941699i	$0.390772\pi$
$44$	−3981.96	−0.310074
$45$	−5936.22	−0.436997
$46$	−2116.00	−0.147442
$47$	14818.9	0.978522	0.489261	−	0.872137i	$-0.337267\pi$
$47$	14818.9	0.978522	0.489261	+	0.872137i	$0.337267\pi$
$48$	603.161	0.0377859
$49$	−16717.8	−0.994691
$50$	2500.00	0.141421
$51$	−2774.32	−0.149359
$52$	−14380.6	−0.737510
$53$	−24766.8	−1.21110	−0.605551	−	0.795807i	$-0.707047\pi$
$53$	−24766.8	−1.21110	−0.605551	+	0.795807i	$0.707047\pi$
$54$	−4527.94	−0.211308
$55$	−6221.81	−0.277339
$56$	−604.565	−0.0257616
$57$	274.396	0.0111864
$58$	11067.2	0.431985
$59$	−7935.48	−0.296786	−0.148393	−	0.988928i	$-0.547410\pi$
$59$	−7935.48	−0.296786	−0.148393	+	0.988928i	$0.547410\pi$
$60$	942.439	0.0337968
$61$	5864.34	0.201788	0.100894	−	0.994897i	$-0.467830\pi$
$61$	5864.34	0.201788	0.100894	+	0.994897i	$0.467830\pi$
$62$	−2647.78	−0.0874787
$63$	2243.02	0.0712002
$64$	4096.00	0.125000
$65$	−22469.6	−0.659649
$66$	−2345.47	−0.0662781
$67$	−5691.52	−0.154896	−0.0774482	−	0.996996i	$-0.524677\pi$
$67$	−5691.52	−0.154896	−0.0774482	+	0.996996i	$0.524677\pi$
$68$	−18840.1	−0.494097
$69$	−1246.38	−0.0315156
$70$	−944.632	−0.0230419
$71$	−30857.3	−0.726460	−0.363230	−	0.931699i	$-0.618326\pi$
$71$	−30857.3	−0.726460	−0.363230	+	0.931699i	$0.618326\pi$
$72$	−15196.7	−0.345477
$73$	24861.4	0.546032	0.273016	−	0.962009i	$-0.411979\pi$
$73$	24861.4	0.546032	0.273016	+	0.962009i	$0.411979\pi$
$74$	−23863.7	−0.506592
$75$	1472.56	0.0302287
$76$	1863.39	0.0370058
$77$	2350.93	0.0451869
$78$	−8470.51	−0.157642
$79$	−43677.4	−0.787389	−0.393694	−	0.919241i	$-0.628803\pi$
$79$	−43677.4	−0.787389	−0.393694	+	0.919241i	$0.628803\pi$
$80$	6400.00	0.111803
$81$	55033.0	0.931989
$82$	−29930.1	−0.491557
$83$	−42211.7	−0.672570	−0.336285	−	0.941760i	$-0.609170\pi$
$83$	−42211.7	−0.672570	−0.336285	+	0.941760i	$0.609170\pi$
$84$	−356.103	−0.00550652
$85$	−29437.7	−0.441933
$86$	32635.4	0.475821
$87$	6518.86	0.0923365
$88$	−15927.8	−0.219255
$89$	92378.1	1.23621	0.618107	−	0.786094i	$-0.287900\pi$
$89$	92378.1	1.23621	0.618107	+	0.786094i	$0.287900\pi$
$90$	−23744.9	−0.309004
$91$	8490.22	0.107477
$92$	−8464.00	−0.104257
$93$	−1559.61	−0.0186985
$94$	59275.5	0.691920
$95$	2911.55	0.0330990
$96$	2412.64	0.0267187
$97$	−4948.63	−0.0534018	−0.0267009	−	0.999643i	$-0.508500\pi$
$97$	−4948.63	−0.0534018	−0.0267009	+	0.999643i	$0.508500\pi$
$98$	−66871.1	−0.703353
$99$	59094.5	0.605981
$100$	10000.0	0.100000
$101$	−10809.9	−0.105444	−0.0527218	−	0.998609i	$-0.516790\pi$
$101$	−10809.9	−0.105444	−0.0527218	+	0.998609i	$0.516790\pi$
$102$	−11097.3	−0.105613
$103$	−14880.3	−0.138204	−0.0691018	−	0.997610i	$-0.522013\pi$
$103$	−14880.3	−0.138204	−0.0691018	+	0.997610i	$0.522013\pi$
$104$	−57522.3	−0.521498
$105$	−556.411	−0.00492519
$106$	−99067.3	−0.856378
$107$	−35453.0	−0.299360	−0.149680	−	0.988734i	$-0.547824\pi$
$107$	−35453.0	−0.299360	−0.149680	+	0.988734i	$0.547824\pi$
$108$	−18111.7	−0.149417
$109$	98180.7	0.791516	0.395758	−	0.918355i	$-0.370482\pi$
$109$	98180.7	0.791516	0.395758	+	0.918355i	$0.370482\pi$
$110$	−24887.2	−0.196108
$111$	−14056.3	−0.108284
$112$	−2418.26	−0.0182162
$113$	−51475.0	−0.379228	−0.189614	−	0.981859i	$-0.560724\pi$
$113$	−51475.0	−0.379228	−0.189614	+	0.981859i	$0.560724\pi$
$114$	1097.58	0.00790998
$115$	−13225.0	−0.0932505
$116$	44268.9	0.305459
$117$	213416.	1.44132
$118$	−31741.9	−0.209859
$119$	11123.1	0.0720045
$120$	3769.75	0.0238979
$121$	−99113.5	−0.615417
$122$	23457.4	0.142685
$123$	−17629.6	−0.105070
$124$	−10591.1	−0.0618568
$125$	15625.0	0.0894427
$126$	8972.07	0.0503462
$127$	249474.	1.37251	0.686256	−	0.727360i	$-0.259253\pi$
$127$	249474.	1.37251	0.686256	+	0.727360i	$0.259253\pi$
$128$	16384.0	0.0883883
$129$	19223.1	0.101706
$130$	−89878.6	−0.466442
$131$	−9987.91	−0.0508507	−0.0254253	−	0.999677i	$-0.508094\pi$
$131$	−9987.91	−0.0508507	−0.0254253	+	0.999677i	$0.508094\pi$
$132$	−9381.88	−0.0468657
$133$	−1100.14	−0.00539284
$134$	−22766.1	−0.109528
$135$	−28299.6	−0.133643
$136$	−75360.6	−0.349379
$137$	9929.64	0.0451994	0.0225997	−	0.999745i	$-0.492806\pi$
$137$	9929.64	0.0451994	0.0225997	+	0.999745i	$0.492806\pi$
$138$	−4985.50	−0.0222849
$139$	131576.	0.577615	0.288808	−	0.957387i	$-0.406741\pi$
$139$	131576.	0.577615	0.288808	+	0.957387i	$0.406741\pi$
$140$	−3778.53	−0.0162931
$141$	34914.7	0.147897
$142$	−123429.	−0.513685
$143$	223683.	0.914730
$144$	−60786.9	−0.244289
$145$	69170.1	0.273211
$146$	99445.5	0.386103
$147$	−39388.7	−0.150341
$148$	−95454.8	−0.358215
$149$	−70147.9	−0.258851	−0.129425	−	0.991589i	$-0.541313\pi$
$149$	−70147.9	−0.258851	−0.129425	+	0.991589i	$0.541313\pi$
$150$	5890.24	0.0213749
$151$	−436974.	−1.55960	−0.779799	−	0.626030i	$-0.784679\pi$
$151$	−436974.	−1.55960	−0.779799	+	0.626030i	$0.784679\pi$
$152$	7453.57	0.0261671
$153$	279598.	0.965618
$154$	9403.72	0.0319520
$155$	−16548.6	−0.0553264
$156$	−33882.0	−0.111470
$157$	−278487.	−0.901688	−0.450844	−	0.892603i	$-0.648877\pi$
$157$	−278487.	−0.901688	−0.450844	+	0.892603i	$0.648877\pi$
$158$	−174710.	−0.556768
$159$	−58353.0	−0.183050
$160$	25600.0	0.0790569
$161$	4997.10	0.0151934
$162$	220132.	0.659015
$163$	409675.	1.20773	0.603865	−	0.797086i	$-0.293627\pi$
$163$	409675.	1.20773	0.603865	+	0.797086i	$0.293627\pi$
$164$	−119721.	−0.347584
$165$	−14659.2	−0.0419180
$166$	−168847.	−0.475579
$167$	−83087.3	−0.230538	−0.115269	−	0.993334i	$-0.536773\pi$
$167$	−83087.3	−0.230538	−0.115269	+	0.993334i	$0.536773\pi$
$168$	−1424.41	−0.00389370
$169$	436523.	1.17568
$170$	−117751.	−0.312494
$171$	−27653.8	−0.0723209
$172$	130542.	0.336456
$173$	280046.	0.711400	0.355700	−	0.934600i	$-0.384243\pi$
$173$	280046.	0.711400	0.355700	+	0.934600i	$0.384243\pi$
$174$	26075.4	0.0652918
$175$	−5903.95	−0.0145730
$176$	−63711.4	−0.155037
$177$	−18696.8	−0.0448573
$178$	369512.	0.874136
$179$	452794.	1.05625	0.528127	−	0.849166i	$-0.322895\pi$
$179$	452794.	1.05625	0.528127	+	0.849166i	$0.322895\pi$
$180$	−94979.5	−0.218499
$181$	467418.	1.06050	0.530248	−	0.847842i	$-0.322099\pi$
$181$	467418.	1.06050	0.530248	+	0.847842i	$0.322099\pi$
$182$	33960.9	0.0759977
$183$	13817.0	0.0304989
$184$	−33856.0	−0.0737210
$185$	−149148.	−0.320397
$186$	−6238.42	−0.0132219
$187$	293050.	0.612826
$188$	237102.	0.489261
$189$	10693.1	0.0217745
$190$	11646.2	0.0234045
$191$	312868.	0.620552	0.310276	−	0.950647i	$-0.399579\pi$
$191$	312868.	0.620552	0.310276	+	0.950647i	$0.399579\pi$
$192$	9650.57	0.0188930
$193$	634549.	1.22623	0.613115	−	0.789994i	$-0.289916\pi$
$193$	634549.	1.22623	0.613115	+	0.789994i	$0.289916\pi$
$194$	−19794.5	−0.0377608
$195$	−52940.7	−0.0997018
$196$	−267484.	−0.497345
$197$	−526186.	−0.965993	−0.482997	−	0.875622i	$-0.660452\pi$
$197$	−526186.	−0.965993	−0.482997	+	0.875622i	$0.660452\pi$
$198$	236378.	0.428493
$199$	333249.	0.596536	0.298268	−	0.954482i	$-0.403591\pi$
$199$	333249.	0.596536	0.298268	+	0.954482i	$0.403591\pi$
$200$	40000.0	0.0707107
$201$	−13409.8	−0.0234116
$202$	−43239.8	−0.0745599
$203$	−26136.1	−0.0445145
$204$	−44389.2	−0.0746796
$205$	−187063.	−0.310888
$206$	−59521.3	−0.0977246
$207$	125610.	0.203751
$208$	−230089.	−0.368755
$209$	−28984.2	−0.0458982
$210$	−2225.64	−0.00348263
$211$	−500655.	−0.774164	−0.387082	−	0.922045i	$-0.626517\pi$
$211$	−500655.	−0.774164	−0.387082	+	0.922045i	$0.626517\pi$
$212$	−396269.	−0.605551
$213$	−72702.7	−0.109800
$214$	−141812.	−0.211680
$215$	203971.	0.300935
$216$	−72447.0	−0.105654
$217$	6252.94	0.00901436
$218$	392723.	0.559687
$219$	58575.8	0.0825293
$220$	−99549.0	−0.138669
$221$	1.05833e6	1.45760
$222$	−56225.2	−0.0765682
$223$	−766101.	−1.03163	−0.515815	−	0.856700i	$-0.672511\pi$
$223$	−766101.	−1.03163	−0.515815	+	0.856700i	$0.672511\pi$
$224$	−9673.03	−0.0128808
$225$	−148406.	−0.195431
$226$	−205900.	−0.268154
$227$	−78680.5	−0.101345	−0.0506725	−	0.998715i	$-0.516136\pi$
$227$	−78680.5	−0.101345	−0.0506725	+	0.998715i	$0.516136\pi$
$228$	4390.33	0.00559320
$229$	1.24781e6	1.57239	0.786197	−	0.617977i	$-0.212047\pi$
$229$	1.24781e6	1.57239	0.786197	+	0.617977i	$0.212047\pi$
$230$	−52900.0	−0.0659380
$231$	5539.02	0.00682972
$232$	177076.	0.215992
$233$	545547.	0.658328	0.329164	−	0.944273i	$-0.393233\pi$
$233$	545547.	0.658328	0.329164	+	0.944273i	$0.393233\pi$
$234$	853663.	1.01917
$235$	370472.	0.437608
$236$	−126968.	−0.148393
$237$	−102908.	−0.119009
$238$	44492.5	0.0509148
$239$	604172.	0.684173	0.342086	−	0.939668i	$-0.388866\pi$
$239$	604172.	0.684173	0.342086	+	0.939668i	$0.388866\pi$
$240$	15079.0	0.0168984
$241$	−720233.	−0.798786	−0.399393	−	0.916780i	$-0.630779\pi$
$241$	−720233.	−0.798786	−0.399393	+	0.916780i	$0.630779\pi$
$242$	−396454.	−0.435165
$243$	404735.	0.439699
$244$	93829.5	0.100894
$245$	−417944.	−0.444839
$246$	−70518.3	−0.0742958
$247$	−104674.	−0.109169
$248$	−42364.5	−0.0437394
$249$	−99454.8	−0.101655
$250$	62500.0	0.0632456
$251$	−667638.	−0.668893	−0.334447	−	0.942415i	$-0.608549\pi$
$251$	−667638.	−0.668893	−0.334447	+	0.942415i	$0.608549\pi$
$252$	35888.3	0.0356001
$253$	131654.	0.129310
$254$	997897.	0.970513
$255$	−69358.1	−0.0667954
$256$	65536.0	0.0625000
$257$	−671078.	−0.633783	−0.316891	−	0.948462i	$-0.602639\pi$
$257$	−671078.	−0.633783	−0.316891	+	0.948462i	$0.602639\pi$
$258$	76892.2	0.0719173
$259$	56356.0	0.0522025
$260$	−359514.	−0.329824
$261$	−656975.	−0.596963
$262$	−39951.7	−0.0359568
$263$	−962332.	−0.857898	−0.428949	−	0.903329i	$-0.641116\pi$
$263$	−962332.	−0.857898	−0.428949	+	0.903329i	$0.641116\pi$
$264$	−37527.5	−0.0331391
$265$	−619171.	−0.541621
$266$	−4400.55	−0.00381332
$267$	217652.	0.186846
$268$	−91064.3	−0.0774482
$269$	405581.	0.341741	0.170870	−	0.985294i	$-0.445342\pi$
$269$	405581.	0.341741	0.170870	+	0.985294i	$0.445342\pi$
$270$	−113198.	−0.0944998
$271$	−763574.	−0.631579	−0.315790	−	0.948829i	$-0.602269\pi$
$271$	−763574.	−0.631579	−0.315790	+	0.948829i	$0.602269\pi$
$272$	−301442.	−0.247048
$273$	20003.8	0.0162445
$274$	39718.6	0.0319608
$275$	−155545.	−0.124030
$276$	−19942.0	−0.0157578
$277$	−1.25365e6	−0.981697	−0.490848	−	0.871245i	$-0.663313\pi$
$277$	−1.25365e6	−0.981697	−0.490848	+	0.871245i	$0.663313\pi$
$278$	526303.	0.408436
$279$	157178.	0.120887
$280$	−15114.1	−0.0115209
$281$	864071.	0.652805	0.326403	−	0.945231i	$-0.394164\pi$
$281$	864071.	0.652805	0.326403	+	0.945231i	$0.394164\pi$
$282$	139659.	0.104579
$283$	−906004.	−0.672457	−0.336228	−	0.941781i	$-0.609151\pi$
$283$	−906004.	−0.672457	−0.336228	+	0.941781i	$0.609151\pi$
$284$	−493717.	−0.363230
$285$	6859.89	0.00500271
$286$	894732.	0.646812
$287$	70682.4	0.0506532
$288$	−243148.	−0.172738
$289$	−33330.4	−0.0234745
$290$	276681.	0.193190
$291$	−11659.5	−0.00807134
$292$	397782.	0.273016
$293$	−2.59187e6	−1.76378	−0.881888	−	0.471459i	$-0.843727\pi$
$293$	−2.59187e6	−1.76378	−0.881888	+	0.471459i	$0.843727\pi$
$294$	−157555.	−0.106307
$295$	−198387.	−0.132727
$296$	−381819.	−0.253296
$297$	281720.	0.185322
$298$	−280592.	−0.183035
$299$	475458.	0.307563
$300$	23561.0	0.0151144
$301$	−77071.2	−0.0490316
$302$	−1.74789e6	−1.10280
$303$	−25469.3	−0.0159371
$304$	29814.3	0.0185029
$305$	146609.	0.0902422
$306$	1.11839e6	0.682795
$307$	−2.38503e6	−1.44427	−0.722134	−	0.691753i	$-0.756839\pi$
$307$	−2.38503e6	−1.44427	−0.722134	+	0.691753i	$0.756839\pi$
$308$	37614.9	0.0225935
$309$	−35059.5	−0.0208886
$310$	−66194.5	−0.0391217
$311$	−1.75699e6	−1.03008	−0.515038	−	0.857167i	$-0.672222\pi$
$311$	−1.75699e6	−1.03008	−0.515038	+	0.857167i	$0.672222\pi$
$312$	−135528.	−0.0788212
$313$	840202.	0.484756	0.242378	−	0.970182i	$-0.422073\pi$
$313$	840202.	0.484756	0.242378	+	0.970182i	$0.422073\pi$
$314$	−1.11395e6	−0.637590
$315$	56075.4	0.0318417
$316$	−698839.	−0.393694
$317$	−3.07745e6	−1.72006	−0.860028	−	0.510247i	$-0.829554\pi$
$317$	−3.07745e6	−1.72006	−0.860028	+	0.510247i	$0.829554\pi$
$318$	−233412.	−0.129436
$319$	−688582.	−0.378860
$320$	102400.	0.0559017
$321$	−83530.8	−0.0452464
$322$	19988.4	0.0107433
$323$	−137135.	−0.0731378
$324$	880528.	0.465994
$325$	−561741.	−0.295004
$326$	1.63870e6	0.853994
$327$	231323.	0.119633
$328$	−478882.	−0.245779
$329$	−139984.	−0.0712998
$330$	−58636.8	−0.0296405
$331$	−1.77017e6	−0.888068	−0.444034	−	0.896010i	$-0.646453\pi$
$331$	−1.77017e6	−0.888068	−0.444034	+	0.896010i	$0.646453\pi$
$332$	−675387.	−0.336285
$333$	1.41660e6	0.700063
$334$	−332349.	−0.163015
$335$	−142288.	−0.0692717
$336$	−5697.65	−0.00275326
$337$	−185971.	−0.0892010	−0.0446005	−	0.999005i	$-0.514201\pi$
$337$	−185971.	−0.0892010	−0.0446005	+	0.999005i	$0.514201\pi$
$338$	1.74609e6	0.831334
$339$	−121280.	−0.0573179
$340$	−471003.	−0.220967
$341$	164740.	0.0767207
$342$	−110615.	−0.0511386
$343$	316686.	0.145343
$344$	522167.	0.237910
$345$	−31159.4	−0.0140942
$346$	1.12018e6	0.503035
$347$	−2.14626e6	−0.956882	−0.478441	−	0.878120i	$-0.658798\pi$
$347$	−2.14626e6	−0.956882	−0.478441	+	0.878120i	$0.658798\pi$
$348$	104302.	0.0461683
$349$	−1.83833e6	−0.807903	−0.403951	−	0.914780i	$-0.632364\pi$
$349$	−1.83833e6	−0.807903	−0.403951	+	0.914780i	$0.632364\pi$
$350$	−23615.8	−0.0103046
$351$	1.01741e6	0.440787
$352$	−254845.	−0.109628
$353$	1.45416e6	0.621119	0.310559	−	0.950554i	$-0.399484\pi$
$353$	1.45416e6	0.621119	0.310559	+	0.950554i	$0.399484\pi$
$354$	−74787.0	−0.0317189
$355$	−771432.	−0.324883
$356$	1.47805e6	0.618107
$357$	26207.2	0.0108830
$358$	1.81118e6	0.746884
$359$	−158990.	−0.0651079	−0.0325540	−	0.999470i	$-0.510364\pi$
$359$	−158990.	−0.0651079	−0.0325540	+	0.999470i	$0.510364\pi$
$360$	−379918.	−0.154502
$361$	−2.46254e6	−0.994522
$362$	1.86967e6	0.749884
$363$	−233521.	−0.0930163
$364$	135844.	0.0537385
$365$	621535.	0.244193
$366$	55267.8	0.0215660
$367$	−4.39291e6	−1.70250	−0.851251	−	0.524759i	$-0.824155\pi$
$367$	−4.39291e6	−1.70250	−0.851251	+	0.524759i	$0.824155\pi$
$368$	−135424.	−0.0521286
$369$	1.77672e6	0.679286
$370$	−596593.	−0.226555
$371$	233955.	0.0882467
$372$	−24953.7	−0.00934926
$373$	853721.	0.317720	0.158860	−	0.987301i	$-0.449218\pi$
$373$	853721.	0.317720	0.158860	+	0.987301i	$0.449218\pi$
$374$	1.17220e6	0.433333
$375$	36814.0	0.0135187
$376$	948408.	0.345960
$377$	−2.48677e6	−0.901117
$378$	42772.3	0.0153969
$379$	4.83295e6	1.72828	0.864141	−	0.503250i	$-0.167862\pi$
$379$	4.83295e6	1.72828	0.864141	+	0.503250i	$0.167862\pi$
$380$	46584.8	0.0165495
$381$	587786.	0.207447
$382$	1.25147e6	0.438796
$383$	−1.95110e6	−0.679646	−0.339823	−	0.940489i	$-0.610367\pi$
$383$	−1.95110e6	−0.679646	−0.339823	+	0.940489i	$0.610367\pi$
$384$	38602.3	0.0133593
$385$	58773.2	0.0202082
$386$	2.53820e6	0.867075
$387$	−1.93731e6	−0.657540
$388$	−79178.1	−0.0267009
$389$	2.32918e6	0.780422	0.390211	−	0.920725i	$-0.372402\pi$
$389$	2.32918e6	0.780422	0.390211	+	0.920725i	$0.372402\pi$
$390$	−211763.	−0.0704998
$391$	622902.	0.206052
$392$	−1.06994e6	−0.351676
$393$	−23532.5	−0.00768576
$394$	−2.10475e6	−0.683060
$395$	−1.09194e6	−0.352131
$396$	945512.	0.302990
$397$	−2.30502e6	−0.734004	−0.367002	−	0.930220i	$-0.619616\pi$
$397$	−2.30502e6	−0.734004	−0.367002	+	0.930220i	$0.619616\pi$
$398$	1.33300e6	0.421814
$399$	−2592.03	−0.000815094 0
$400$	160000.	0.0500000
$401$	904601.	0.280929	0.140464	−	0.990086i	$-0.455140\pi$
$401$	904601.	0.280929	0.140464	+	0.990086i	$0.455140\pi$
$402$	−53639.1	−0.0165545
$403$	594946.	0.182480
$404$	−172959.	−0.0527218
$405$	1.37582e6	0.416798
$406$	−104545.	−0.0314765
$407$	1.48475e6	0.444292
$408$	−177557.	−0.0528064
$409$	4.80236e6	1.41954	0.709768	−	0.704436i	$-0.248800\pi$
$409$	4.80236e6	1.41954	0.709768	+	0.704436i	$0.248800\pi$
$410$	−748254.	−0.219831
$411$	23395.2	0.00683160
$412$	−238085.	−0.0691018
$413$	74961.1	0.0216252
$414$	502442.	0.144074
$415$	−1.05529e6	−0.300782
$416$	−920357.	−0.260749
$417$	310005.	0.0873029
$418$	−115937.	−0.0324549
$419$	−1.55511e6	−0.432739	−0.216370	−	0.976312i	$-0.569422\pi$
$419$	−1.55511e6	−0.432739	−0.216370	+	0.976312i	$0.569422\pi$
$420$	−8902.58	−0.00246259
$421$	2.15341e6	0.592137	0.296069	−	0.955167i	$-0.404324\pi$
$421$	2.15341e6	0.592137	0.296069	+	0.955167i	$0.404324\pi$
$422$	−2.00262e6	−0.547416
$423$	−3.51873e6	−0.956168
$424$	−1.58508e6	−0.428189
$425$	−735943.	−0.197639
$426$	−290811.	−0.0776402
$427$	−55396.5	−0.0147032
$428$	−567249.	−0.149680
$429$	527019.	0.138256
$430$	815886.	0.212793
$431$	2.75892e6	0.715394	0.357697	−	0.933838i	$-0.383562\pi$
$431$	2.75892e6	0.715394	0.357697	+	0.933838i	$0.383562\pi$
$432$	−289788.	−0.0747086
$433$	7.76317e6	1.98985	0.994923	−	0.100643i	$-0.0320901\pi$
$433$	7.76317e6	1.98985	0.994923	+	0.100643i	$0.0320901\pi$
$434$	25011.8	0.00637412
$435$	162972.	0.0412942
$436$	1.57089e6	0.395758
$437$	−61608.4	−0.0154325
$438$	234303.	0.0583570
$439$	5.38240e6	1.33295	0.666476	−	0.745527i	$-0.267802\pi$
$439$	5.38240e6	1.33295	0.666476	+	0.745527i	$0.267802\pi$
$440$	−398196.	−0.0980540
$441$	3.96961e6	0.971968
$442$	4.23331e6	1.03068
$443$	−3.25646e6	−0.788382	−0.394191	−	0.919029i	$-0.628975\pi$
$443$	−3.25646e6	−0.788382	−0.394191	+	0.919029i	$0.628975\pi$
$444$	−224901.	−0.0541419
$445$	2.30945e6	0.552852
$446$	−3.06440e6	−0.729472
$447$	−165275.	−0.0391236
$448$	−38692.1	−0.00910810
$449$	4.19928e6	0.983013	0.491506	−	0.870874i	$-0.336446\pi$
$449$	4.19928e6	0.983013	0.491506	+	0.870874i	$0.336446\pi$
$450$	−593622.	−0.138191
$451$	1.86220e6	0.431106
$452$	−823600.	−0.189614
$453$	−1.02955e6	−0.235723
$454$	−314722.	−0.0716618
$455$	212255.	0.0480652
$456$	17561.3	0.00395499
$457$	2.83004e6	0.633872	0.316936	−	0.948447i	$-0.397346\pi$
$457$	2.83004e6	0.633872	0.316936	+	0.948447i	$0.397346\pi$
$458$	4.99126e6	1.11185
$459$	1.33292e6	0.295306
$460$	−211600.	−0.0466252
$461$	4.05115e6	0.887821	0.443911	−	0.896071i	$-0.353591\pi$
$461$	4.05115e6	0.887821	0.443911	+	0.896071i	$0.353591\pi$
$462$	22156.1	0.00482934
$463$	−4.15579e6	−0.900951	−0.450476	−	0.892789i	$-0.648746\pi$
$463$	−4.15579e6	−0.900951	−0.450476	+	0.892789i	$0.648746\pi$
$464$	708302.	0.152730
$465$	−38990.1	−0.00836223
$466$	2.18219e6	0.465508
$467$	−4.22033e6	−0.895477	−0.447738	−	0.894165i	$-0.647770\pi$
$467$	−4.22033e6	−0.895477	−0.447738	+	0.894165i	$0.647770\pi$
$468$	3.41465e6	0.720662
$469$	53763.9	0.0112865
$470$	1.48189e6	0.309436
$471$	−656143.	−0.136284
$472$	−507871.	−0.104930
$473$	−2.03052e6	−0.417305
$474$	−411633.	−0.0841519
$475$	72788.7	0.0148023
$476$	177970.	0.0360022
$477$	5.88085e6	1.18343
$478$	2.41669e6	0.483783
$479$	6.35763e6	1.26607	0.633033	−	0.774125i	$-0.281810\pi$
$479$	6.35763e6	1.26607	0.633033	+	0.774125i	$0.281810\pi$
$480$	60316.1	0.0119490
$481$	5.36209e6	1.05675
$482$	−2.88093e6	−0.564827
$483$	11773.7	0.00229638
$484$	−1.58582e6	−0.307708
$485$	−123716.	−0.0238820
$486$	1.61894e6	0.310914
$487$	−5.24048e6	−1.00126	−0.500632	−	0.865660i	$-0.666899\pi$
$487$	−5.24048e6	−1.00126	−0.500632	+	0.865660i	$0.666899\pi$
$488$	375318.	0.0713427
$489$	965233.	0.182541
$490$	−1.67178e6	−0.314549
$491$	1.05280e6	0.197080	0.0985402	−	0.995133i	$-0.468583\pi$
$491$	1.05280e6	0.197080	0.0985402	+	0.995133i	$0.468583\pi$
$492$	−282073.	−0.0525351
$493$	−3.25794e6	−0.603706
$494$	−418698.	−0.0771939
$495$	1.47736e6	0.271003
$496$	−169458.	−0.0309284
$497$	291488.	0.0529334
$498$	−397819.	−0.0718807
$499$	−9.41686e6	−1.69299	−0.846496	−	0.532395i	$-0.821292\pi$
$499$	−9.41686e6	−1.69299	−0.846496	+	0.532395i	$0.821292\pi$
$500$	250000.	0.0447214
$501$	−195762.	−0.0348444
$502$	−2.67055e6	−0.472979
$503$	2.05520e6	0.362188	0.181094	−	0.983466i	$-0.442036\pi$
$503$	2.05520e6	0.362188	0.181094	+	0.983466i	$0.442036\pi$
$504$	143553.	0.0251731
$505$	−270249.	−0.0471558
$506$	526614.	0.0914358
$507$	1.02849e6	0.177697
$508$	3.99159e6	0.686256
$509$	−1.07533e6	−0.183970	−0.0919848	−	0.995760i	$-0.529321\pi$
$509$	−1.07533e6	−0.183970	−0.0919848	+	0.995760i	$0.529321\pi$
$510$	−277432.	−0.0472315
$511$	−234849.	−0.0397865
$512$	262144.	0.0441942
$513$	−131833.	−0.0221172
$514$	−2.68431e6	−0.448152
$515$	−372008.	−0.0618065
$516$	307569.	0.0508532
$517$	−3.68801e6	−0.606828
$518$	225424.	0.0369127
$519$	659815.	0.107524
$520$	−1.43806e6	−0.233221
$521$	313555.	0.0506080	0.0253040	−	0.999680i	$-0.491945\pi$
$521$	313555.	0.0506080	0.0253040	+	0.999680i	$0.491945\pi$
$522$	−2.62790e6	−0.422116
$523$	−5.21202e6	−0.833205	−0.416603	−	0.909089i	$-0.636779\pi$
$523$	−5.21202e6	−0.833205	−0.416603	+	0.909089i	$0.636779\pi$
$524$	−159807.	−0.0254253
$525$	−13910.3	−0.00220261
$526$	−3.84933e6	−0.606626
$527$	779445.	0.122253
$528$	−150110.	−0.0234329
$529$	279841.	0.0434783
$530$	−2.47668e6	−0.382984
$531$	1.88427e6	0.290006
$532$	−17602.2	−0.00269642
$533$	6.72520e6	1.02539
$534$	870607.	0.132120
$535$	−886326.	−0.133878
$536$	−364257.	−0.0547641
$537$	1.06683e6	0.159646
$538$	1.62232e6	0.241647
$539$	4.16059e6	0.616855
$540$	−452794.	−0.0668214
$541$	−1.03751e6	−0.152405	−0.0762024	−	0.997092i	$-0.524280\pi$
$541$	−1.03751e6	−0.152405	−0.0762024	+	0.997092i	$0.524280\pi$
$542$	−3.05430e6	−0.446594
$543$	1.10128e6	0.160287
$544$	−1.20577e6	−0.174690
$545$	2.45452e6	0.353977
$546$	80015.1	0.0114866
$547$	−1.37643e7	−1.96692	−0.983461	−	0.181119i	$-0.942028\pi$
$547$	−1.37643e7	−1.96692	−0.983461	+	0.181119i	$0.942028\pi$
$548$	158874.	0.0225997
$549$	−1.39248e6	−0.197178
$550$	−622181.	−0.0877021
$551$	322228.	0.0452151
$552$	−79768.0	−0.0111425
$553$	412591.	0.0573729
$554$	−5.01460e6	−0.694164
$555$	−351407.	−0.0484260
$556$	2.10521e6	0.288808
$557$	6.55713e6	0.895522	0.447761	−	0.894153i	$-0.352222\pi$
$557$	6.55713e6	0.895522	0.447761	+	0.894153i	$0.352222\pi$
$558$	628712.	0.0854803
$559$	−7.33307e6	−0.992558
$560$	−60456.5	−0.00814653
$561$	690453.	0.0926247
$562$	3.45628e6	0.461603
$563$	1.03758e6	0.137960	0.0689799	−	0.997618i	$-0.478026\pi$
$563$	1.03758e6	0.137960	0.0689799	+	0.997618i	$0.478026\pi$
$564$	558635.	0.0739487
$565$	−1.28687e6	−0.169596
$566$	−3.62402e6	−0.475499
$567$	−519859.	−0.0679091
$568$	−1.97487e6	−0.256842
$569$	2.73424e6	0.354043	0.177022	−	0.984207i	$-0.443354\pi$
$569$	2.73424e6	0.354043	0.177022	+	0.984207i	$0.443354\pi$
$570$	27439.6	0.00353745
$571$	304642.	0.0391021	0.0195510	−	0.999809i	$-0.493776\pi$
$571$	304642.	0.0391021	0.0195510	+	0.999809i	$0.493776\pi$
$572$	3.57893e6	0.457365
$573$	737148.	0.0937925
$574$	282730.	0.0358172
$575$	−330625.	−0.0417029
$576$	−972590.	−0.122144
$577$	−4.26839e6	−0.533734	−0.266867	−	0.963733i	$-0.585988\pi$
$577$	−4.26839e6	−0.533734	−0.266867	+	0.963733i	$0.585988\pi$
$578$	−133321.	−0.0165989
$579$	1.49506e6	0.185337
$580$	1.10672e6	0.136606
$581$	398745.	0.0490066
$582$	−46637.8	−0.00570730
$583$	6.16378e6	0.751062
$584$	1.59113e6	0.193051
$585$	5.33539e6	0.644580
$586$	−1.03675e7	−1.24718
$587$	8.95255e6	1.07239	0.536193	−	0.844095i	$-0.319862\pi$
$587$	8.95255e6	1.07239	0.536193	+	0.844095i	$0.319862\pi$
$588$	−630219.	−0.0751706
$589$	−77091.4	−0.00915625
$590$	−793548.	−0.0938519
$591$	−1.23975e6	−0.146004
$592$	−1.52728e6	−0.179107
$593$	891844.	0.104148	0.0520742	−	0.998643i	$-0.483417\pi$
$593$	891844.	0.104148	0.0520742	+	0.998643i	$0.483417\pi$
$594$	1.12688e6	0.131042
$595$	278078.	0.0322014
$596$	−1.12237e6	−0.129425
$597$	785167.	0.0901626
$598$	1.90183e6	0.217480
$599$	8.36368e6	0.952424	0.476212	−	0.879331i	$-0.342010\pi$
$599$	8.36368e6	0.952424	0.476212	+	0.879331i	$0.342010\pi$
$600$	94243.9	0.0106875
$601$	−8.54102e6	−0.964547	−0.482273	−	0.876021i	$-0.660189\pi$
$601$	−8.54102e6	−0.964547	−0.482273	+	0.876021i	$0.660189\pi$
$602$	−308285.	−0.0346706
$603$	1.35144e6	0.151358
$604$	−6.99158e6	−0.779799
$605$	−2.47784e6	−0.275223
$606$	−101877.	−0.0112693
$607$	−1.68584e7	−1.85714	−0.928568	−	0.371162i	$-0.878959\pi$
$607$	−1.68584e7	−1.85714	−0.928568	+	0.371162i	$0.878959\pi$
$608$	119257.	0.0130835
$609$	−61579.2	−0.00672808
$610$	586434.	0.0638109
$611$	−1.33190e7	−1.44334
$612$	4.47357e6	0.482809
$613$	−1.14220e7	−1.22769	−0.613847	−	0.789425i	$-0.710379\pi$
$613$	−1.14220e7	−1.22769	−0.613847	+	0.789425i	$0.710379\pi$
$614$	−9.54012e6	−1.02125
$615$	−440739.	−0.0469888
$616$	150459.	0.0159760
$617$	−4.05632e6	−0.428962	−0.214481	−	0.976728i	$-0.568806\pi$
$617$	−4.05632e6	−0.428962	−0.214481	+	0.976728i	$0.568806\pi$
$618$	−140238.	−0.0147705
$619$	−9.02063e6	−0.946259	−0.473130	−	0.880993i	$-0.656876\pi$
$619$	−9.02063e6	−0.946259	−0.473130	+	0.880993i	$0.656876\pi$
$620$	−264778.	−0.0276632
$621$	598819.	0.0623113
$622$	−7.02797e6	−0.728374
$623$	−872633.	−0.0900765
$624$	−542112.	−0.0557350
$625$	390625.	0.0400000
$626$	3.36081e6	0.342774
$627$	−68289.5	−0.00693722
$628$	−4.45580e6	−0.450844
$629$	7.02493e6	0.707971
$630$	224302.	0.0225155
$631$	−1.61649e7	−1.61622	−0.808110	−	0.589032i	$-0.799509\pi$
$631$	−1.61649e7	−1.61622	−0.808110	+	0.589032i	$0.799509\pi$
$632$	−2.79535e6	−0.278384
$633$	−1.17959e6	−0.117010
$634$	−1.23098e7	−1.21626
$635$	6.23686e6	0.613806
$636$	−933649.	−0.0915252
$637$	1.50257e7	1.46719
$638$	−2.75433e6	−0.267894
$639$	7.32703e6	0.709865
$640$	409600.	0.0395285
$641$	−1.60205e7	−1.54003	−0.770017	−	0.638023i	$-0.779752\pi$
$641$	−1.60205e7	−1.54003	−0.770017	+	0.638023i	$0.779752\pi$
$642$	−334123.	−0.0319940
$643$	−8.32578e6	−0.794140	−0.397070	−	0.917788i	$-0.629973\pi$
$643$	−8.32578e6	−0.794140	−0.397070	+	0.917788i	$0.629973\pi$
$644$	79953.7	0.00759668
$645$	480576.	0.0454845
$646$	−548540.	−0.0517162
$647$	6.02871e6	0.566192	0.283096	−	0.959092i	$-0.408639\pi$
$647$	6.02871e6	0.566192	0.283096	+	0.959092i	$0.408639\pi$
$648$	3.52211e6	0.329508
$649$	1.97492e6	0.184051
$650$	−2.24696e6	−0.208599
$651$	14732.5	0.00136246
$652$	6.55479e6	0.603865
$653$	8.22531e6	0.754865	0.377433	−	0.926037i	$-0.376807\pi$
$653$	8.22531e6	0.754865	0.377433	+	0.926037i	$0.376807\pi$
$654$	925293.	0.0845931
$655$	−249698.	−0.0227411
$656$	−1.91553e6	−0.173792
$657$	−5.90331e6	−0.533558
$658$	−559936.	−0.0504166
$659$	1.68658e7	1.51284	0.756420	−	0.654086i	$-0.226946\pi$
$659$	1.68658e7	1.51284	0.756420	+	0.654086i	$0.226946\pi$
$660$	−234547.	−0.0209590
$661$	−992213.	−0.0883286	−0.0441643	−	0.999024i	$-0.514063\pi$
$661$	−992213.	−0.0883286	−0.0441643	+	0.999024i	$0.514063\pi$
$662$	−7.08070e6	−0.627959
$663$	2.49352e6	0.220308
$664$	−2.70155e6	−0.237789
$665$	−27503.4	−0.00241175
$666$	5.66641e6	0.495019
$667$	−1.46364e6	−0.127385
$668$	−1.32940e6	−0.115269
$669$	−1.80501e6	−0.155924
$670$	−569152.	−0.0489825
$671$	−1.45947e6	−0.125138
$672$	−22790.6	−0.00194685
$673$	−8.36599e6	−0.711999	−0.356000	−	0.934486i	$-0.615860\pi$
$673$	−8.36599e6	−0.711999	−0.356000	+	0.934486i	$0.615860\pi$
$674$	−743883.	−0.0630746
$675$	−707490.	−0.0597669
$676$	6.98437e6	0.587842
$677$	1.59336e7	1.33611	0.668054	−	0.744113i	$-0.267128\pi$
$677$	1.59336e7	1.33611	0.668054	+	0.744113i	$0.267128\pi$
$678$	−485120.	−0.0405299
$679$	46746.4	0.00389111
$680$	−1.88401e6	−0.156247
$681$	−185379.	−0.0153177
$682$	658959.	0.0542497
$683$	4.02204e6	0.329909	0.164955	−	0.986301i	$-0.447252\pi$
$683$	4.02204e6	0.329909	0.164955	+	0.986301i	$0.447252\pi$
$684$	−442460.	−0.0361605
$685$	248241.	0.0202138
$686$	1.26674e6	0.102773
$687$	2.93997e6	0.237657
$688$	2.08867e6	0.168228
$689$	2.22601e7	1.78640
$690$	−124638.	−0.00996612
$691$	8.51156e6	0.678132	0.339066	−	0.940763i	$-0.389889\pi$
$691$	8.51156e6	0.678132	0.339066	+	0.940763i	$0.389889\pi$
$692$	4.48073e6	0.355700
$693$	−558225.	−0.0441547
$694$	−8.58503e6	−0.676617
$695$	3.28939e6	0.258317
$696$	417207.	0.0326459
$697$	8.81075e6	0.686959
$698$	−7.35331e6	−0.571274
$699$	1.28536e6	0.0995020
$700$	−94463.2	−0.00728648
$701$	1.13383e7	0.871472	0.435736	−	0.900074i	$-0.356488\pi$
$701$	1.13383e7	0.871472	0.435736	+	0.900074i	$0.356488\pi$
$702$	4.06964e6	0.311683
$703$	−694804.	−0.0530241
$704$	−1.01938e6	−0.0775185
$705$	872868.	0.0661417
$706$	5.81663e6	0.439197
$707$	102114.	0.00768312
$708$	−299148.	−0.0224286
$709$	6.85924e6	0.512460	0.256230	−	0.966616i	$-0.417520\pi$
$709$	6.85924e6	0.512460	0.256230	+	0.966616i	$0.417520\pi$
$710$	−3.08573e6	−0.229727
$711$	1.03712e7	0.769401
$712$	5.91220e6	0.437068
$713$	350169.	0.0257961
$714$	104829.	0.00769546
$715$	5.59208e6	0.409080
$716$	7.24471e6	0.528127
$717$	1.42349e6	0.103408
$718$	−635960.	−0.0460383
$719$	−1.86207e7	−1.34330	−0.671652	−	0.740867i	$-0.734415\pi$
$719$	−1.86207e7	−1.34330	−0.671652	+	0.740867i	$0.734415\pi$
$720$	−1.51967e6	−0.109249
$721$	140564.	0.0100702
$722$	−9.85014e6	−0.703233
$723$	−1.69694e6	−0.120732
$724$	7.47869e6	0.530248
$725$	1.72925e6	0.122184
$726$	−934084.	−0.0657725
$727$	9.72770e6	0.682612	0.341306	−	0.939952i	$-0.389131\pi$
$727$	9.72770e6	0.682612	0.341306	+	0.939952i	$0.389131\pi$
$728$	543374.	0.0379988
$729$	−1.24194e7	−0.865531
$730$	2.48614e6	0.172671
$731$	−9.60713e6	−0.664967
$732$	221071.	0.0152495
$733$	−2.08414e7	−1.43274	−0.716370	−	0.697720i	$-0.754198\pi$
$733$	−2.08414e7	−1.43274	−0.716370	+	0.697720i	$0.754198\pi$
$734$	−1.75717e7	−1.20385
$735$	−984717.	−0.0672346
$736$	−541696.	−0.0368605
$737$	1.41646e6	0.0960586
$738$	7.10688e6	0.480328
$739$	−2.75701e7	−1.85707	−0.928533	−	0.371250i	$-0.878929\pi$
$739$	−2.75701e7	−1.85707	−0.928533	+	0.371250i	$0.878929\pi$
$740$	−2.38637e6	−0.160199
$741$	−246623.	−0.0165002
$742$	935822.	0.0623998
$743$	−2.42438e6	−0.161112	−0.0805560	−	0.996750i	$-0.525670\pi$
$743$	−2.42438e6	−0.161112	−0.0805560	+	0.996750i	$0.525670\pi$
$744$	−99814.7	−0.00661093
$745$	−1.75370e6	−0.115762
$746$	3.41488e6	0.224662
$747$	1.00231e7	0.657205
$748$	4.68879e6	0.306413
$749$	334901.	0.0218128
$750$	147256.	0.00955917
$751$	−1.70442e7	−1.10275	−0.551375	−	0.834258i	$-0.685897\pi$
$751$	−1.70442e7	−1.10275	−0.551375	+	0.834258i	$0.685897\pi$
$752$	3.79363e6	0.244631
$753$	−1.57302e6	−0.101099
$754$	−9.94706e6	−0.637186
$755$	−1.09243e7	−0.697474
$756$	171089.	0.0108873
$757$	4.90700e6	0.311226	0.155613	−	0.987818i	$-0.450265\pi$
$757$	4.90700e6	0.311226	0.155613	+	0.987818i	$0.450265\pi$
$758$	1.93318e7	1.22208
$759$	310188.	0.0195444
$760$	186339.	0.0117023
$761$	−9.97216e6	−0.624206	−0.312103	−	0.950048i	$-0.601033\pi$
$761$	−9.97216e6	−0.624206	−0.312103	+	0.950048i	$0.601033\pi$
$762$	2.35114e6	0.146687
$763$	−927447.	−0.0576737
$764$	5.00589e6	0.310276
$765$	6.98995e6	0.431838
$766$	−7.80441e6	−0.480583
$767$	7.13229e6	0.437765
$768$	154409.	0.00944648
$769$	7.81599e6	0.476615	0.238308	−	0.971190i	$-0.423407\pi$
$769$	7.81599e6	0.476615	0.238308	+	0.971190i	$0.423407\pi$
$770$	235093.	0.0142894
$771$	−1.58113e6	−0.0957923
$772$	1.01528e7	0.613115
$773$	−2.20716e7	−1.32857	−0.664287	−	0.747478i	$-0.731265\pi$
$773$	−2.20716e7	−1.32857	−0.664287	+	0.747478i	$0.731265\pi$
$774$	−7.74924e6	−0.464951
$775$	−413715.	−0.0247427
$776$	−316713.	−0.0188804
$777$	132780.	0.00789007
$778$	9.31673e6	0.551842
$779$	−871431.	−0.0514505
$780$	−847051.	−0.0498509
$781$	7.67953e6	0.450513
$782$	2.49161e6	0.145701
$783$	−3.13198e6	−0.182564
$784$	−4.27975e6	−0.248673
$785$	−6.96218e6	−0.403247
$786$	−94130.0	−0.00543465
$787$	2.88969e7	1.66308	0.831542	−	0.555462i	$-0.187459\pi$
$787$	2.88969e7	1.66308	0.831542	+	0.555462i	$0.187459\pi$
$788$	−8.41898e6	−0.482997
$789$	−2.26735e6	−0.129666
$790$	−4.36774e6	−0.248994
$791$	486249.	0.0276323
$792$	3.78205e6	0.214247
$793$	−5.27079e6	−0.297641
$794$	−9.22008e6	−0.519019
$795$	−1.45883e6	−0.0818626
$796$	5.33199e6	0.298268
$797$	3.54790e7	1.97845	0.989226	−	0.146394i	$-0.0467669\pi$
$797$	3.54790e7	1.97845	0.989226	+	0.146394i	$0.0467669\pi$
$798$	−10368.1	−0.000576359 0
$799$	−1.74494e7	−0.966969
$800$	640000.	0.0353553
$801$	−2.19351e7	−1.20797
$802$	3.61840e6	0.198647
$803$	−6.18731e6	−0.338621
$804$	−214556.	−0.0117058
$805$	124928.	0.00679467
$806$	2.37979e6	0.129033
$807$	955588.	0.0516520
$808$	−691837.	−0.0372799
$809$	1.54874e7	0.831970	0.415985	−	0.909371i	$-0.363437\pi$
$809$	1.54874e7	0.831970	0.415985	+	0.909371i	$0.363437\pi$
$810$	5.50330e6	0.294721
$811$	−1.51749e7	−0.810167	−0.405083	−	0.914280i	$-0.632757\pi$
$811$	−1.51749e7	−0.810167	−0.405083	+	0.914280i	$0.632757\pi$
$812$	−418178.	−0.0222572
$813$	−1.79905e6	−0.0954592
$814$	5.93902e6	0.314162
$815$	1.02419e7	0.540113
$816$	−710227.	−0.0373398
$817$	950197.	0.0498033
$818$	1.92094e7	1.00376
$819$	−2.01599e6	−0.105022
$820$	−2.99301e6	−0.155444
$821$	3.55262e7	1.83946	0.919730	−	0.392552i	$-0.128408\pi$
$821$	3.55262e7	1.83946	0.919730	+	0.392552i	$0.128408\pi$
$822$	93580.8	0.00483067
$823$	−3.14372e7	−1.61787	−0.808935	−	0.587898i	$-0.799956\pi$
$823$	−3.14372e7	−1.61787	−0.808935	+	0.587898i	$0.799956\pi$
$824$	−952340.	−0.0488623
$825$	−366480.	−0.0187463
$826$	299844.	0.0152913
$827$	1.46845e7	0.746615	0.373307	−	0.927708i	$-0.378224\pi$
$827$	1.46845e7	0.746615	0.373307	+	0.927708i	$0.378224\pi$
$828$	2.00977e6	0.101876
$829$	2.18365e7	1.10356	0.551781	−	0.833989i	$-0.313949\pi$
$829$	2.18365e7	1.10356	0.551781	+	0.833989i	$0.313949\pi$
$830$	−4.22117e6	−0.212685
$831$	−2.95372e6	−0.148377
$832$	−3.68143e6	−0.184377
$833$	1.96853e7	0.982946
$834$	1.24002e6	0.0617324
$835$	−2.07718e6	−0.103100
$836$	−463747.	−0.0229491
$837$	749311.	0.0369699
$838$	−6.22044e6	−0.305993
$839$	8.00659e6	0.392684	0.196342	−	0.980536i	$-0.437094\pi$
$839$	8.00659e6	0.392684	0.196342	+	0.980536i	$0.437094\pi$
$840$	−35610.3	−0.00174132
$841$	−1.28559e7	−0.626778
$842$	8.61365e6	0.418704
$843$	2.03583e6	0.0986673
$844$	−8.01049e6	−0.387082
$845$	1.09131e7	0.525782
$846$	−1.40749e7	−0.676113
$847$	936258.	0.0448422
$848$	−6.34031e6	−0.302775
$849$	−2.13463e6	−0.101638
$850$	−2.94377e6	−0.139752
$851$	3.15597e6	0.149386
$852$	−1.16324e6	−0.0548999
$853$	−2.73958e7	−1.28917	−0.644587	−	0.764531i	$-0.722971\pi$
$853$	−2.73958e7	−1.28917	−0.644587	+	0.764531i	$0.722971\pi$
$854$	−221586.	−0.0103967
$855$	−691344.	−0.0323429
$856$	−2.26900e6	−0.105840
$857$	−1.73328e7	−0.806153	−0.403076	−	0.915166i	$-0.632059\pi$
$857$	−1.73328e7	−0.806153	−0.403076	+	0.915166i	$0.632059\pi$
$858$	2.10808e6	0.0977615
$859$	1.52183e6	0.0703693	0.0351847	−	0.999381i	$-0.488798\pi$
$859$	1.52183e6	0.0703693	0.0351847	+	0.999381i	$0.488798\pi$
$860$	3.26354e6	0.150468
$861$	166535.	0.00765591
$862$	1.10357e7	0.505860
$863$	−1.94346e7	−0.888276	−0.444138	−	0.895958i	$-0.646490\pi$
$863$	−1.94346e7	−0.888276	−0.444138	+	0.895958i	$0.646490\pi$
$864$	−1.15915e6	−0.0528270
$865$	7.00114e6	0.318148
$866$	3.10527e7	1.40703
$867$	−78529.6	−0.00354802
$868$	100047.	0.00450718
$869$	1.08701e7	0.488297
$870$	651886.	0.0291994
$871$	5.11546e6	0.228475
$872$	6.28357e6	0.279843
$873$	1.17505e6	0.0521819
$874$	−246434.	−0.0109124
$875$	−147599.	−0.00651722
$876$	937213.	0.0412646
$877$	−2.54795e7	−1.11865	−0.559323	−	0.828950i	$-0.688939\pi$
$877$	−2.54795e7	−1.11865	−0.559323	+	0.828950i	$0.688939\pi$
$878$	2.15296e7	0.942539
$879$	−6.10669e6	−0.266584
$880$	−1.59278e6	−0.0693346
$881$	−6.59781e6	−0.286391	−0.143196	−	0.989694i	$-0.545738\pi$
$881$	−6.59781e6	−0.286391	−0.143196	+	0.989694i	$0.545738\pi$
$882$	1.58785e7	0.687285
$883$	−2.37423e7	−1.02476	−0.512378	−	0.858760i	$-0.671235\pi$
$883$	−2.37423e7	−1.02476	−0.512378	+	0.858760i	$0.671235\pi$
$884$	1.69332e7	0.728802
$885$	−467419.	−0.0200608
$886$	−1.30258e7	−0.557470
$887$	2.96051e7	1.26345	0.631724	−	0.775194i	$-0.282348\pi$
$887$	2.96051e7	1.26345	0.631724	+	0.775194i	$0.282348\pi$
$888$	−899603.	−0.0382841
$889$	−2.35661e6	−0.100008
$890$	9.23781e6	0.390925
$891$	−1.36962e7	−0.577971
$892$	−1.22576e7	−0.515815
$893$	1.72584e6	0.0724221
$894$	−661101.	−0.0276646
$895$	1.13199e7	0.472371
$896$	−154769.	−0.00644040
$897$	1.12022e6	0.0464862
$898$	1.67971e7	0.695095
$899$	−1.83147e6	−0.0755790
$900$	−2.37449e6	−0.0977156
$901$	2.91632e7	1.19680
$902$	7.44879e6	0.304838
$903$	−181587.	−0.00741081
$904$	−3.29440e6	−0.134077
$905$	1.16855e7	0.474268
$906$	−4.11821e6	−0.166682
$907$	−1.29526e7	−0.522803	−0.261402	−	0.965230i	$-0.584185\pi$
$907$	−1.29526e7	−0.522803	−0.261402	+	0.965230i	$0.584185\pi$
$908$	−1.25889e6	−0.0506725
$909$	2.56681e6	0.103035
$910$	849022.	0.0339872
$911$	−2.62067e7	−1.04620	−0.523102	−	0.852270i	$-0.675225\pi$
$911$	−2.62067e7	−1.04620	−0.523102	+	0.852270i	$0.675225\pi$
$912$	70245.3	0.00279660
$913$	1.05053e7	0.417093
$914$	1.13201e7	0.448215
$915$	345424.	0.0136395
$916$	1.99650e7	0.786197
$917$	94349.0	0.00370522
$918$	5.33168e6	0.208813
$919$	2.24232e7	0.875807	0.437904	−	0.899022i	$-0.355721\pi$
$919$	2.24232e7	0.875807	0.437904	+	0.899022i	$0.355721\pi$
$920$	−846400.	−0.0329690
$921$	−5.61936e6	−0.218292
$922$	1.62046e7	0.627784
$923$	2.77341e7	1.07154
$924$	88624.3	0.00341486
$925$	−3.72870e6	−0.143286
$926$	−1.66232e7	−0.637069
$927$	3.53331e6	0.135046
$928$	2.83321e6	0.107996
$929$	5.75572e6	0.218807	0.109403	−	0.993997i	$-0.465106\pi$
$929$	5.75572e6	0.218807	0.109403	+	0.993997i	$0.465106\pi$
$930$	−155961.	−0.00591299
$931$	−1.94698e6	−0.0736187
$932$	8.72874e6	0.329164
$933$	−4.13965e6	−0.155689
$934$	−1.68813e7	−0.633198
$935$	7.32624e6	0.274064
$936$	1.36586e7	0.509585
$937$	−1.96217e6	−0.0730109	−0.0365055	−	0.999333i	$-0.511623\pi$
$937$	−1.96217e6	−0.0730109	−0.0365055	+	0.999333i	$0.511623\pi$
$938$	215056.	0.00798075
$939$	1.97960e6	0.0732678
$940$	5.92755e6	0.218804
$941$	2.26215e7	0.832813	0.416406	−	0.909179i	$-0.363289\pi$
$941$	2.26215e7	0.832813	0.416406	+	0.909179i	$0.363289\pi$
$942$	−2.62457e6	−0.0963676
$943$	3.95826e6	0.144952
$944$	−2.03148e6	−0.0741964
$945$	267327.	0.00973786
$946$	−8.12206e6	−0.295079
$947$	9.29545e6	0.336818	0.168409	−	0.985717i	$-0.446137\pi$
$947$	9.29545e6	0.336818	0.168409	+	0.985717i	$0.446137\pi$
$948$	−1.64653e6	−0.0595044
$949$	−2.23451e7	−0.805408
$950$	291155.	0.0104668
$951$	−7.25076e6	−0.259975
$952$	711880.	0.0254574
$953$	−1.09761e7	−0.391484	−0.195742	−	0.980655i	$-0.562712\pi$
$953$	−1.09761e7	−0.391484	−0.195742	+	0.980655i	$0.562712\pi$
$954$	2.35234e7	0.836815
$955$	7.82171e6	0.277519
$956$	9.66675e6	0.342086
$957$	−1.62237e6	−0.0572623
$958$	2.54305e7	0.895244
$959$	−93798.6	−0.00329344
$960$	241264.	0.00844919
$961$	−2.81910e7	−0.984695
$962$	2.14484e7	0.747234
$963$	8.41828e6	0.292522
$964$	−1.15237e7	−0.399393
$965$	1.58637e7	0.548386
$966$	47094.6	0.00162379
$967$	1.31788e7	0.453219	0.226610	−	0.973986i	$-0.427236\pi$
$967$	1.31788e7	0.453219	0.226610	+	0.973986i	$0.427236\pi$
$968$	−6.34326e6	−0.217583
$969$	−323103.	−0.0110543
$970$	−494863.	−0.0168871
$971$	3.36061e7	1.14385	0.571927	−	0.820305i	$-0.306196\pi$
$971$	3.36061e7	1.14385	0.571927	+	0.820305i	$0.306196\pi$
$972$	6.47576e6	0.219849
$973$	−1.24291e6	−0.0420878
$974$	−2.09619e7	−0.708000
$975$	−1.32352e6	−0.0445880
$976$	1.50127e6	0.0504469
$977$	−5.56285e7	−1.86449	−0.932246	−	0.361824i	$-0.882154\pi$
$977$	−5.56285e7	−1.86449	−0.932246	+	0.361824i	$0.882154\pi$
$978$	3.86093e6	0.129076
$979$	−2.29904e7	−0.766636
$980$	−6.68711e6	−0.222420
$981$	−2.33129e7	−0.773435
$982$	4.21121e6	0.139357
$983$	−1.76368e7	−0.582150	−0.291075	−	0.956700i	$-0.594013\pi$
$983$	−1.76368e7	−0.582150	−0.291075	+	0.956700i	$0.594013\pi$
$984$	−1.12829e6	−0.0371479
$985$	−1.31547e7	−0.432005
$986$	−1.30317e7	−0.426884
$987$	−329816.	−0.0107765
$988$	−1.67479e6	−0.0545843
$989$	−4.31604e6	−0.140312
$990$	5.90945e6	0.191628
$991$	1.13075e7	0.365749	0.182875	−	0.983136i	$-0.441460\pi$
$991$	1.13075e7	0.365749	0.182875	+	0.983136i	$0.441460\pi$
$992$	−677831.	−0.0218697
$993$	−4.17070e6	−0.134226
$994$	1.16595e6	0.0374295
$995$	8.33123e6	0.266779
$996$	−1.59128e6	−0.0508273
$997$	2.57849e6	0.0821538	0.0410769	−	0.999156i	$-0.486921\pi$
$997$	2.57849e6	0.0821538	0.0410769	+	0.999156i	$0.486921\pi$
$998$	−3.76674e7	−1.19713
$999$	6.75333e6	0.214094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.d.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.d.1.3	✓	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +2.35610 q^{3} +16.0000 q^{4} +25.0000 q^{5} +9.42439 q^{6} -9.44632 q^{7} +64.0000 q^{8} -237.449 q^{9} +100.000 q^{10} -248.872 q^{11} +37.6975 q^{12} -898.786 q^{13} -37.7853 q^{14} +58.9024 q^{15} +256.000 q^{16} -1177.51 q^{17} -949.795 q^{18} +116.462 q^{19} +400.000 q^{20} -22.2564 q^{21} -995.490 q^{22} -529.000 q^{23} +150.790 q^{24} +625.000 q^{25} -3595.14 q^{26} -1131.98 q^{27} -151.141 q^{28} +2766.81 q^{29} +235.610 q^{30} -661.945 q^{31} +1024.00 q^{32} -586.368 q^{33} -4710.03 q^{34} -236.158 q^{35} -3799.18 q^{36} -5965.93 q^{37} +465.848 q^{38} -2117.63 q^{39} +1600.00 q^{40} -7482.54 q^{41} -89.0258 q^{42} +8158.86 q^{43} -3981.96 q^{44} -5936.22 q^{45} -2116.00 q^{46} +14818.9 q^{47} +603.161 q^{48} -16717.8 q^{49} +2500.00 q^{50} -2774.32 q^{51} -14380.6 q^{52} -24766.8 q^{53} -4527.94 q^{54} -6221.81 q^{55} -604.565 q^{56} +274.396 q^{57} +11067.2 q^{58} -7935.48 q^{59} +942.439 q^{60} +5864.34 q^{61} -2647.78 q^{62} +2243.02 q^{63} +4096.00 q^{64} -22469.6 q^{65} -2345.47 q^{66} -5691.52 q^{67} -18840.1 q^{68} -1246.38 q^{69} -944.632 q^{70} -30857.3 q^{71} -15196.7 q^{72} +24861.4 q^{73} -23863.7 q^{74} +1472.56 q^{75} +1863.39 q^{76} +2350.93 q^{77} -8470.51 q^{78} -43677.4 q^{79} +6400.00 q^{80} +55033.0 q^{81} -29930.1 q^{82} -42211.7 q^{83} -356.103 q^{84} -29437.7 q^{85} +32635.4 q^{86} +6518.86 q^{87} -15927.8 q^{88} +92378.1 q^{89} -23744.9 q^{90} +8490.22 q^{91} -8464.00 q^{92} -1559.61 q^{93} +59275.5 q^{94} +2911.55 q^{95} +2412.64 q^{96} -4948.63 q^{97} -66871.1 q^{98} +59094.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12 q^{2} - 34 q^{3} + 48 q^{4} + 75 q^{5} - 136 q^{6} - 121 q^{7} + 192 q^{8} + 89 q^{9} + 300 q^{10} - 502 q^{11} - 544 q^{12} + 76 q^{13} - 484 q^{14} - 850 q^{15} + 768 q^{16} - 1167 q^{17} + 356 q^{18}+ \cdots + 344510 q^{99}+O(q^{100}) \) 3 * q + 12 * q^2 - 34 * q^3 + 48 * q^4 + 75 * q^5 - 136 * q^6 - 121 * q^7 + 192 * q^8 + 89 * q^9 + 300 * q^10 - 502 * q^11 - 544 * q^12 + 76 * q^13 - 484 * q^14 - 850 * q^15 + 768 * q^16 - 1167 * q^17 + 356 * q^18 - 1694 * q^19 + 1200 * q^20 + 3624 * q^21 - 2008 * q^22 - 1587 * q^23 - 2176 * q^24 + 1875 * q^25 + 304 * q^26 - 3742 * q^27 - 1936 * q^28 - 4999 * q^29 - 3400 * q^30 - 9691 * q^31 + 3072 * q^32 - 4972 * q^33 - 4668 * q^34 - 3025 * q^35 + 1424 * q^36 + 925 * q^37 - 6776 * q^38 - 14326 * q^39 + 4800 * q^40 - 1513 * q^41 + 14496 * q^42 - 30552 * q^43 - 8032 * q^44 + 2225 * q^45 - 6348 * q^46 - 2070 * q^47 - 8704 * q^48 - 26828 * q^49 + 7500 * q^50 + 1920 * q^51 + 1216 * q^52 - 34923 * q^53 - 14968 * q^54 - 12550 * q^55 - 7744 * q^56 + 7964 * q^57 - 19996 * q^58 - 36665 * q^59 - 13600 * q^60 - 44364 * q^61 - 38764 * q^62 - 74805 * q^63 + 12288 * q^64 + 1900 * q^65 - 19888 * q^66 - 85969 * q^67 - 18672 * q^68 + 17986 * q^69 - 12100 * q^70 - 105817 * q^71 + 5696 * q^72 - 71348 * q^73 + 3700 * q^74 - 21250 * q^75 - 27104 * q^76 - 79494 * q^77 - 57304 * q^78 + 12196 * q^79 + 19200 * q^80 + 111227 * q^81 - 6052 * q^82 - 66689 * q^83 + 57984 * q^84 - 29175 * q^85 - 122208 * q^86 + 129542 * q^87 - 32128 * q^88 + 149868 * q^89 + 8900 * q^90 + 12970 * q^91 - 25392 * q^92 + 164202 * q^93 - 8280 * q^94 - 42350 * q^95 - 34816 * q^96 + 215238 * q^97 - 107312 * q^98 + 344510 * q^99

Introduction

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