LMFDB - Embedded newform 230.6.a.f.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 = [5,-20,1] 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:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 $ x^5 - x^4 - 774x^3 - 197x^2 + 66287*x + 154128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.48374$ 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)

$f(q)$	$=$	\(q-4.00000 q^{2} -2.48374 q^{3} +16.0000 q^{4} +25.0000 q^{5} +9.93494 q^{6} -252.275 q^{7} -64.0000 q^{8} -236.831 q^{9} -100.000 q^{10} -739.487 q^{11} -39.7398 q^{12} +876.961 q^{13} +1009.10 q^{14} -62.0934 q^{15} +256.000 q^{16} -1363.74 q^{17} +947.324 q^{18} +1725.29 q^{19} +400.000 q^{20} +626.584 q^{21} +2957.95 q^{22} -529.000 q^{23} +158.959 q^{24} +625.000 q^{25} -3507.84 q^{26} +1191.77 q^{27} -4036.39 q^{28} +3068.97 q^{29} +248.374 q^{30} -8425.04 q^{31} -1024.00 q^{32} +1836.69 q^{33} +5454.97 q^{34} -6306.87 q^{35} -3789.30 q^{36} -4041.30 q^{37} -6901.15 q^{38} -2178.14 q^{39} -1600.00 q^{40} -1633.86 q^{41} -2506.33 q^{42} +8735.57 q^{43} -11831.8 q^{44} -5920.78 q^{45} +2116.00 q^{46} +18989.0 q^{47} -635.836 q^{48} +46835.5 q^{49} -2500.00 q^{50} +3387.18 q^{51} +14031.4 q^{52} +18955.0 q^{53} -4767.09 q^{54} -18487.2 q^{55} +16145.6 q^{56} -4285.16 q^{57} -12275.9 q^{58} -49726.2 q^{59} -993.494 q^{60} +19031.8 q^{61} +33700.1 q^{62} +59746.5 q^{63} +4096.00 q^{64} +21924.0 q^{65} -7346.76 q^{66} -9397.24 q^{67} -21819.9 q^{68} +1313.90 q^{69} +25227.5 q^{70} -28928.8 q^{71} +15157.2 q^{72} +2535.03 q^{73} +16165.2 q^{74} -1552.33 q^{75} +27604.6 q^{76} +186554. q^{77} +8712.56 q^{78} -17637.4 q^{79} +6400.00 q^{80} +54589.9 q^{81} +6535.44 q^{82} +87609.8 q^{83} +10025.3 q^{84} -34093.6 q^{85} -34942.3 q^{86} -7622.51 q^{87} +47327.2 q^{88} +33219.0 q^{89} +23683.1 q^{90} -221235. q^{91} -8464.00 q^{92} +20925.6 q^{93} -75956.0 q^{94} +43132.2 q^{95} +2543.35 q^{96} +41331.2 q^{97} -187342. q^{98} +175133. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18}+ \cdots + 386925 q^{99}+O(q^{100}) $ 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * 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
$3$	−2.48374	−0.159332	−0.0796659	−	0.996822i	$-0.525385\pi$
$3$	−2.48374	−0.159332	−0.0796659	+	0.996822i	$0.525385\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	9.93494	0.112665
$7$	−252.275	−1.94594	−0.972968	−	0.230940i	$-0.925820\pi$
$7$	−252.275	−1.94594	−0.972968	+	0.230940i	$0.925820\pi$
$8$	−64.0000	−0.353553
$9$	−236.831	−0.974613
$10$	−100.000	−0.316228
$11$	−739.487	−1.84268	−0.921338	−	0.388763i	$-0.872902\pi$
$11$	−739.487	−1.84268	−0.921338	+	0.388763i	$0.872902\pi$
$12$	−39.7398	−0.0796659
$13$	876.961	1.43920	0.719601	−	0.694387i	$-0.244325\pi$
$13$	876.961	1.43920	0.719601	+	0.694387i	$0.244325\pi$
$14$	1009.10	1.37598
$15$	−62.0934	−0.0712553
$16$	256.000	0.250000
$17$	−1363.74	−1.14449	−0.572243	−	0.820084i	$-0.693926\pi$
$17$	−1363.74	−1.14449	−0.572243	+	0.820084i	$0.693926\pi$
$18$	947.324	0.689156
$19$	1725.29	1.09642	0.548211	−	0.836340i	$-0.315309\pi$
$19$	1725.29	1.09642	0.548211	+	0.836340i	$0.315309\pi$
$20$	400.000	0.223607
$21$	626.584	0.310049
$22$	2957.95	1.30297
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	158.959	0.0563323
$25$	625.000	0.200000
$26$	−3507.84	−1.01767
$27$	1191.77	0.314619
$28$	−4036.39	−0.972968
$29$	3068.97	0.677638	0.338819	−	0.940852i	$-0.389973\pi$
$29$	3068.97	0.677638	0.338819	+	0.940852i	$0.389973\pi$
$30$	248.374	0.0503851
$31$	−8425.04	−1.57459	−0.787295	−	0.616576i	$-0.788519\pi$
$31$	−8425.04	−1.57459	−0.787295	+	0.616576i	$0.788519\pi$
$32$	−1024.00	−0.176777
$33$	1836.69	0.293597
$34$	5454.97	0.809273
$35$	−6306.87	−0.870249
$36$	−3789.30	−0.487307
$37$	−4041.30	−0.485308	−0.242654	−	0.970113i	$-0.578018\pi$
$37$	−4041.30	−0.485308	−0.242654	+	0.970113i	$0.578018\pi$
$38$	−6901.15	−0.775287
$39$	−2178.14	−0.229311
$40$	−1600.00	−0.158114
$41$	−1633.86	−0.151794	−0.0758971	−	0.997116i	$-0.524182\pi$
$41$	−1633.86	−0.151794	−0.0758971	+	0.997116i	$0.524182\pi$
$42$	−2506.33	−0.219238
$43$	8735.57	0.720477	0.360238	−	0.932860i	$-0.382695\pi$
$43$	8735.57	0.720477	0.360238	+	0.932860i	$0.382695\pi$
$44$	−11831.8	−0.921338
$45$	−5920.78	−0.435860
$46$	2116.00	0.147442
$47$	18989.0	1.25388	0.626942	−	0.779066i	$-0.284306\pi$
$47$	18989.0	1.25388	0.626942	+	0.779066i	$0.284306\pi$
$48$	−635.836	−0.0398329
$49$	46835.5	2.78667
$50$	−2500.00	−0.141421
$51$	3387.18	0.182353
$52$	14031.4	0.719601
$53$	18955.0	0.926903	0.463452	−	0.886122i	$-0.346611\pi$
$53$	18955.0	0.926903	0.463452	+	0.886122i	$0.346611\pi$
$54$	−4767.09	−0.222469
$55$	−18487.2	−0.824069
$56$	16145.6	0.687992
$57$	−4285.16	−0.174695
$58$	−12275.9	−0.479162
$59$	−49726.2	−1.85975	−0.929876	−	0.367873i	$-0.880086\pi$
$59$	−49726.2	−1.85975	−0.929876	+	0.367873i	$0.880086\pi$
$60$	−993.494	−0.0356277
$61$	19031.8	0.654871	0.327436	−	0.944873i	$-0.393816\pi$
$61$	19031.8	0.654871	0.327436	+	0.944873i	$0.393816\pi$
$62$	33700.1	1.11340
$63$	59746.5	1.89654
$64$	4096.00	0.125000
$65$	21924.0	0.643631
$66$	−7346.76	−0.207604
$67$	−9397.24	−0.255749	−0.127874	−	0.991790i	$-0.540815\pi$
$67$	−9397.24	−0.255749	−0.127874	+	0.991790i	$0.540815\pi$
$68$	−21819.9	−0.572243
$69$	1313.90	0.0332230
$70$	25227.5	0.615359
$71$	−28928.8	−0.681058	−0.340529	−	0.940234i	$-0.610606\pi$
$71$	−28928.8	−0.681058	−0.340529	+	0.940234i	$0.610606\pi$
$72$	15157.2	0.344578
$73$	2535.03	0.0556770	0.0278385	−	0.999612i	$-0.491138\pi$
$73$	2535.03	0.0556770	0.0278385	+	0.999612i	$0.491138\pi$
$74$	16165.2	0.343164
$75$	−1552.33	−0.0318663
$76$	27604.6	0.548211
$77$	186554.	3.58573
$78$	8712.56	0.162147
$79$	−17637.4	−0.317956	−0.158978	−	0.987282i	$-0.550820\pi$
$79$	−17637.4	−0.317956	−0.158978	+	0.987282i	$0.550820\pi$
$80$	6400.00	0.111803
$81$	54589.9	0.924485
$82$	6535.44	0.107335
$83$	87609.8	1.39591	0.697955	−	0.716142i	$-0.254094\pi$
$83$	87609.8	1.39591	0.697955	+	0.716142i	$0.254094\pi$
$84$	10025.3	0.155025
$85$	−34093.6	−0.511829
$86$	−34942.3	−0.509454
$87$	−7622.51	−0.107969
$88$	47327.2	0.651484
$89$	33219.0	0.444541	0.222270	−	0.974985i	$-0.428653\pi$
$89$	33219.0	0.444541	0.222270	+	0.974985i	$0.428653\pi$
$90$	23683.1	0.308200
$91$	−221235.	−2.80060
$92$	−8464.00	−0.104257
$93$	20925.6	0.250882
$94$	−75956.0	−0.886630
$95$	43132.2	0.490334
$96$	2543.35	0.0281661
$97$	41331.2	0.446014	0.223007	−	0.974817i	$-0.428413\pi$
$97$	41331.2	0.446014	0.223007	+	0.974817i	$0.428413\pi$
$98$	−187342.	−1.97047
$99$	175133.	1.79590
$100$	10000.0	0.100000
$101$	−51868.0	−0.505936	−0.252968	−	0.967475i	$-0.581407\pi$
$101$	−51868.0	−0.505936	−0.252968	+	0.967475i	$0.581407\pi$
$102$	−13548.7	−0.128943
$103$	54330.3	0.504602	0.252301	−	0.967649i	$-0.418813\pi$
$103$	54330.3	0.504602	0.252301	+	0.967649i	$0.418813\pi$
$104$	−56125.5	−0.508835
$105$	15664.6	0.138658
$106$	−75820.1	−0.655420
$107$	−106154.	−0.896353	−0.448176	−	0.893945i	$-0.647926\pi$
$107$	−106154.	−0.896353	−0.448176	+	0.893945i	$0.647926\pi$
$108$	19068.4	0.157309
$109$	−173904.	−1.40198	−0.700992	−	0.713169i	$-0.747259\pi$
$109$	−173904.	−1.40198	−0.700992	+	0.713169i	$0.747259\pi$
$110$	73948.7	0.582705
$111$	10037.5	0.0773249
$112$	−64582.3	−0.486484
$113$	262107.	1.93100	0.965501	−	0.260399i	$-0.0838541\pi$
$113$	262107.	1.93100	0.965501	+	0.260399i	$0.0838541\pi$
$114$	17140.6	0.123528
$115$	−13225.0	−0.0932505
$116$	49103.5	0.338819
$117$	−207692.	−1.40267
$118$	198905.	1.31504
$119$	344038.	2.22710
$120$	3973.98	0.0251926
$121$	385790.	2.39545
$122$	−76127.3	−0.463064
$123$	4058.08	0.0241856
$124$	−134801.	−0.787295
$125$	15625.0	0.0894427
$126$	−238986.	−1.34105
$127$	227525.	1.25176	0.625878	−	0.779921i	$-0.284741\pi$
$127$	227525.	1.25176	0.625878	+	0.779921i	$0.284741\pi$
$128$	−16384.0	−0.0883883
$129$	−21696.8	−0.114795
$130$	−87696.1	−0.455116
$131$	205957.	1.04857	0.524286	−	0.851542i	$-0.324332\pi$
$131$	205957.	1.04857	0.524286	+	0.851542i	$0.324332\pi$
$132$	29387.0	0.146798
$133$	−435246.	−2.13357
$134$	37589.0	0.180842
$135$	29794.3	0.140702
$136$	87279.6	0.404637
$137$	−320648.	−1.45958	−0.729788	−	0.683673i	$-0.760381\pi$
$137$	−320648.	−1.45958	−0.729788	+	0.683673i	$0.760381\pi$
$138$	−5255.58	−0.0234922
$139$	194736.	0.854887	0.427444	−	0.904042i	$-0.359414\pi$
$139$	194736.	0.854887	0.427444	+	0.904042i	$0.359414\pi$
$140$	−100910.	−0.435125
$141$	−47163.7	−0.199784
$142$	115715.	0.481581
$143$	−648501.	−2.65198
$144$	−60628.8	−0.243653
$145$	76724.2	0.303049
$146$	−10140.1	−0.0393696
$147$	−116327.	−0.444004
$148$	−64660.8	−0.242654
$149$	−393030.	−1.45031	−0.725155	−	0.688586i	$-0.758232\pi$
$149$	−393030.	−1.45031	−0.725155	+	0.688586i	$0.758232\pi$
$150$	6209.34	0.0225329
$151$	−5358.24	−0.0191240	−0.00956202	−	0.999954i	$-0.503044\pi$
$151$	−5358.24	−0.0191240	−0.00956202	+	0.999954i	$0.503044\pi$
$152$	−110418.	−0.387643
$153$	322977.	1.11543
$154$	−746215.	−2.53549
$155$	−210626.	−0.704178
$156$	−34850.2	−0.114655
$157$	290851.	0.941721	0.470860	−	0.882208i	$-0.343944\pi$
$157$	290851.	0.941721	0.470860	+	0.882208i	$0.343944\pi$
$158$	70549.7	0.224829
$159$	−47079.3	−0.147685
$160$	−25600.0	−0.0790569
$161$	133453.	0.405756
$162$	−218360.	−0.653709
$163$	−163365.	−0.481604	−0.240802	−	0.970574i	$-0.577410\pi$
$163$	−163365.	−0.481604	−0.240802	+	0.970574i	$0.577410\pi$
$164$	−26141.8	−0.0758971
$165$	45917.3	0.131300
$166$	−350439.	−0.987058
$167$	−264211.	−0.733094	−0.366547	−	0.930400i	$-0.619460\pi$
$167$	−264211.	−0.733094	−0.366547	+	0.930400i	$0.619460\pi$
$168$	−40101.4	−0.109619
$169$	397768.	1.07130
$170$	136374.	0.361918
$171$	−408602.	−1.06859
$172$	139769.	0.360238
$173$	341880.	0.868478	0.434239	−	0.900798i	$-0.357017\pi$
$173$	341880.	0.868478	0.434239	+	0.900798i	$0.357017\pi$
$174$	30490.0	0.0763457
$175$	−157672.	−0.389187
$176$	−189309.	−0.460669
$177$	123507.	0.296317
$178$	−132876.	−0.314338
$179$	311766.	0.727271	0.363636	−	0.931541i	$-0.381535\pi$
$179$	311766.	0.727271	0.363636	+	0.931541i	$0.381535\pi$
$180$	−94732.4	−0.217930
$181$	−263189.	−0.597132	−0.298566	−	0.954389i	$-0.596508\pi$
$181$	−263189.	−0.597132	−0.298566	+	0.954389i	$0.596508\pi$
$182$	884940.	1.98032
$183$	−47270.0	−0.104342
$184$	33856.0	0.0737210
$185$	−101033.	−0.217036
$186$	−83702.2	−0.177400
$187$	1.00847e6	2.10891
$188$	303824.	0.626942
$189$	−300654.	−0.612228
$190$	−172529.	−0.346719
$191$	−755404.	−1.49829	−0.749145	−	0.662406i	$-0.769535\pi$
$191$	−755404.	−1.49829	−0.749145	+	0.662406i	$0.769535\pi$
$192$	−10173.4	−0.0199165
$193$	−773822.	−1.49537	−0.747683	−	0.664056i	$-0.768834\pi$
$193$	−773822.	−1.49537	−0.747683	+	0.664056i	$0.768834\pi$
$194$	−165325.	−0.315379
$195$	−54453.5	−0.102551
$196$	749368.	1.39333
$197$	465100.	0.853848	0.426924	−	0.904288i	$-0.359597\pi$
$197$	465100.	0.853848	0.426924	+	0.904288i	$0.359597\pi$
$198$	−700534.	−1.26989
$199$	−601491.	−1.07671	−0.538353	−	0.842720i	$-0.680953\pi$
$199$	−601491.	−1.07671	−0.538353	+	0.842720i	$0.680953\pi$
$200$	−40000.0	−0.0707107
$201$	23340.3	0.0407489
$202$	207472.	0.357751
$203$	−774223.	−1.31864
$204$	54194.8	0.0911764
$205$	−40846.5	−0.0678844
$206$	−217321.	−0.356807
$207$	125284.	0.203221
$208$	224502.	0.359801
$209$	−1.27583e6	−2.02035
$210$	−62658.4	−0.0980462
$211$	−6024.40	−0.00931553	−0.00465777	−	0.999989i	$-0.501483\pi$
$211$	−6024.40	−0.00931553	−0.00465777	+	0.999989i	$0.501483\pi$
$212$	303280.	0.463452
$213$	71851.4	0.108514
$214$	424618.	0.633817
$215$	218389.	0.322207
$216$	−76273.5	−0.111234
$217$	2.12542e6	3.06405
$218$	695615.	0.991352
$219$	−6296.34	−0.00887111
$220$	−295795.	−0.412035
$221$	−1.19595e6	−1.64715
$222$	−40150.1	−0.0546770
$223$	1.29198e6	1.73978	0.869891	−	0.493244i	$-0.164189\pi$
$223$	1.29198e6	1.73978	0.869891	+	0.493244i	$0.164189\pi$
$224$	258329.	0.343996
$225$	−148019.	−0.194923
$226$	−1.04843e6	−1.36542
$227$	64294.3	0.0828148	0.0414074	−	0.999142i	$-0.486816\pi$
$227$	64294.3	0.0828148	0.0414074	+	0.999142i	$0.486816\pi$
$228$	−68562.5	−0.0873473
$229$	74653.2	0.0940718	0.0470359	−	0.998893i	$-0.485022\pi$
$229$	74653.2	0.0940718	0.0470359	+	0.998893i	$0.485022\pi$
$230$	52900.0	0.0659380
$231$	−463350.	−0.571320
$232$	−196414.	−0.239581
$233$	−163107.	−0.196826	−0.0984129	−	0.995146i	$-0.531377\pi$
$233$	−163107.	−0.196826	−0.0984129	+	0.995146i	$0.531377\pi$
$234$	830767.	0.991835
$235$	474725.	0.560754
$236$	−795619.	−0.929876
$237$	43806.7	0.0506605
$238$	−1.37615e6	−1.57479
$239$	−458112.	−0.518773	−0.259386	−	0.965774i	$-0.583520\pi$
$239$	−458112.	−0.518773	−0.259386	+	0.965774i	$0.583520\pi$
$240$	−15895.9	−0.0178138
$241$	1.74728e6	1.93785	0.968924	−	0.247360i	$-0.0795631\pi$
$241$	1.74728e6	1.93785	0.968924	+	0.247360i	$0.0795631\pi$
$242$	−1.54316e6	−1.69384
$243$	−425188.	−0.461918
$244$	304509.	0.327436
$245$	1.17089e6	1.24624
$246$	−16232.3	−0.0171018
$247$	1.51301e6	1.57797
$248$	539202.	0.556702
$249$	−217600.	−0.222413
$250$	−62500.0	−0.0632456
$251$	−509792.	−0.510751	−0.255375	−	0.966842i	$-0.582199\pi$
$251$	−509792.	−0.510751	−0.255375	+	0.966842i	$0.582199\pi$
$252$	955944.	0.948268
$253$	391189.	0.384224
$254$	−910100.	−0.885126
$255$	84679.4	0.0815507
$256$	65536.0	0.0625000
$257$	253793.	0.239688	0.119844	−	0.992793i	$-0.461761\pi$
$257$	253793.	0.239688	0.119844	+	0.992793i	$0.461761\pi$
$258$	86787.4	0.0811722
$259$	1.01952e6	0.944378
$260$	350784.	0.321816
$261$	−726827.	−0.660435
$262$	−823827.	−0.741452
$263$	−245617.	−0.218962	−0.109481	−	0.993989i	$-0.534919\pi$
$263$	−245617.	−0.218962	−0.109481	+	0.993989i	$0.534919\pi$
$264$	−117548.	−0.103802
$265$	473875.	0.414524
$266$	1.74099e6	1.50866
$267$	−82507.2	−0.0708294
$268$	−150356.	−0.127874
$269$	−1.30972e6	−1.10356	−0.551782	−	0.833989i	$-0.686052\pi$
$269$	−1.30972e6	−1.10356	−0.551782	+	0.833989i	$0.686052\pi$
$270$	−119177.	−0.0994911
$271$	335307.	0.277345	0.138672	−	0.990338i	$-0.455717\pi$
$271$	335307.	0.277345	0.138672	+	0.990338i	$0.455717\pi$
$272$	−349118.	−0.286121
$273$	549490.	0.446224
$274$	1.28259e6	1.03208
$275$	−462179.	−0.368535
$276$	21022.3	0.0166115
$277$	1.24277e6	0.973173	0.486586	−	0.873633i	$-0.338242\pi$
$277$	1.24277e6	0.973173	0.486586	+	0.873633i	$0.338242\pi$
$278$	−778943.	−0.604497
$279$	1.99531e6	1.53462
$280$	403639.	0.307680
$281$	−549120.	−0.414860	−0.207430	−	0.978250i	$-0.566510\pi$
$281$	−549120.	−0.414860	−0.207430	+	0.978250i	$0.566510\pi$
$282$	188655.	0.141268
$283$	−687675.	−0.510407	−0.255204	−	0.966887i	$-0.582143\pi$
$283$	−687675.	−0.510407	−0.255204	+	0.966887i	$0.582143\pi$
$284$	−462860.	−0.340529
$285$	−107129.	−0.0781258
$286$	2.59401e6	1.87524
$287$	412182.	0.295382
$288$	242515.	0.172289
$289$	439938.	0.309847
$290$	−306897.	−0.214288
$291$	−102656.	−0.0710641
$292$	40560.4	0.0278385
$293$	−1.30317e6	−0.886813	−0.443406	−	0.896321i	$-0.646230\pi$
$293$	−1.30317e6	−0.886813	−0.443406	+	0.896321i	$0.646230\pi$
$294$	465308.	0.313959
$295$	−1.24315e6	−0.831706
$296$	258643.	0.171582
$297$	−881301.	−0.579740
$298$	1.57212e6	1.02552
$299$	−463912.	−0.300095
$300$	−24837.4	−0.0159332
$301$	−2.20376e6	−1.40200
$302$	21433.0	0.0135227
$303$	128826.	0.0806117
$304$	441674.	0.274105
$305$	475796.	0.292867
$306$	−1.29191e6	−0.788729
$307$	2.67886e6	1.62220	0.811099	−	0.584909i	$-0.198870\pi$
$307$	2.67886e6	1.62220	0.811099	+	0.584909i	$0.198870\pi$
$308$	2.98486e6	1.79286
$309$	−134942.	−0.0803991
$310$	842504.	0.497929
$311$	2.66680e6	1.56347	0.781734	−	0.623612i	$-0.214335\pi$
$311$	2.66680e6	1.56347	0.781734	+	0.623612i	$0.214335\pi$
$312$	139401.	0.0810736
$313$	935722.	0.539866	0.269933	−	0.962879i	$-0.412998\pi$
$313$	935722.	0.539866	0.269933	+	0.962879i	$0.412998\pi$
$314$	−1.16341e6	−0.665897
$315$	1.49366e6	0.848156
$316$	−282199.	−0.158978
$317$	−1.45385e6	−0.812592	−0.406296	−	0.913742i	$-0.633180\pi$
$317$	−1.45385e6	−0.812592	−0.406296	+	0.913742i	$0.633180\pi$
$318$	188317.	0.104429
$319$	−2.26946e6	−1.24867
$320$	102400.	0.0559017
$321$	263660.	0.142817
$322$	−533813.	−0.286913
$323$	−2.35285e6	−1.25484
$324$	873438.	0.462242
$325$	548101.	0.287841
$326$	653461.	0.340546
$327$	431931.	0.223380
$328$	104567.	0.0536674
$329$	−4.79045e6	−2.43998
$330$	−183669.	−0.0928434
$331$	−13841.3	−0.00694395	−0.00347198	−	0.999994i	$-0.501105\pi$
$331$	−13841.3	−0.00694395	−0.00347198	+	0.999994i	$0.501105\pi$
$332$	1.40176e6	0.697955
$333$	957106.	0.472987
$334$	1.05684e6	0.518376
$335$	−234931.	−0.114374
$336$	160405.	0.0775123
$337$	−1.93165e6	−0.926520	−0.463260	−	0.886222i	$-0.653320\pi$
$337$	−1.93165e6	−0.926520	−0.463260	+	0.886222i	$0.653320\pi$
$338$	−1.59107e6	−0.757527
$339$	−651005.	−0.307670
$340$	−545497.	−0.255915
$341$	6.23020e6	2.90146
$342$	1.63441e6	0.755605
$343$	−7.57543e6	−3.47674
$344$	−559076.	−0.254727
$345$	32847.4	0.0148578
$346$	−1.36752e6	−0.614107
$347$	−2.44241e6	−1.08892	−0.544458	−	0.838788i	$-0.683265\pi$
$347$	−2.44241e6	−1.08892	−0.544458	+	0.838788i	$0.683265\pi$
$348$	−121960.	−0.0539846
$349$	956707.	0.420451	0.210226	−	0.977653i	$-0.432580\pi$
$349$	956707.	0.420451	0.210226	+	0.977653i	$0.432580\pi$
$350$	630687.	0.275197
$351$	1.04514e6	0.452800
$352$	757235.	0.325742
$353$	3.71100e6	1.58509	0.792545	−	0.609813i	$-0.208756\pi$
$353$	3.71100e6	1.58509	0.792545	+	0.609813i	$0.208756\pi$
$354$	−494027.	−0.209528
$355$	−723219.	−0.304578
$356$	531504.	0.222270
$357$	−854499.	−0.354847
$358$	−1.24706e6	−0.514258
$359$	−1.33403e6	−0.546298	−0.273149	−	0.961972i	$-0.588065\pi$
$359$	−1.33403e6	−0.546298	−0.273149	+	0.961972i	$0.588065\pi$
$360$	378930.	0.154100
$361$	500518.	0.202140
$362$	1.05275e6	0.422236
$363$	−958200.	−0.381671
$364$	−3.53976e6	−1.40030
$365$	63375.7	0.0248995
$366$	189080.	0.0737808
$367$	2.92197e6	1.13243	0.566214	−	0.824258i	$-0.308408\pi$
$367$	2.92197e6	1.13243	0.566214	+	0.824258i	$0.308408\pi$
$368$	−135424.	−0.0521286
$369$	386949.	0.147941
$370$	404130.	0.153468
$371$	−4.78187e6	−1.80369
$372$	334809.	0.125441
$373$	−3.06510e6	−1.14070	−0.570352	−	0.821401i	$-0.693193\pi$
$373$	−3.06510e6	−1.14070	−0.570352	+	0.821401i	$0.693193\pi$
$374$	−4.03388e6	−1.49123
$375$	−38808.4	−0.0142511
$376$	−1.21530e6	−0.443315
$377$	2.69137e6	0.975258
$378$	1.20262e6	0.432910
$379$	296537.	0.106043	0.0530214	−	0.998593i	$-0.483115\pi$
$379$	296537.	0.106043	0.0530214	+	0.998593i	$0.483115\pi$
$380$	690115.	0.245167
$381$	−565112.	−0.199445
$382$	3.02162e6	1.05945
$383$	2.25387e6	0.785113	0.392556	−	0.919728i	$-0.371591\pi$
$383$	2.25387e6	0.785113	0.392556	+	0.919728i	$0.371591\pi$
$384$	40693.5	0.0140831
$385$	4.66385e6	1.60359
$386$	3.09529e6	1.05738
$387$	−2.06885e6	−0.702186
$388$	661299.	0.223007
$389$	−956682.	−0.320548	−0.160274	−	0.987073i	$-0.551238\pi$
$389$	−956682.	−0.320548	−0.160274	+	0.987073i	$0.551238\pi$
$390$	217814.	0.0725144
$391$	721420.	0.238642
$392$	−2.99747e6	−0.985236
$393$	−511542.	−0.167071
$394$	−1.86040e6	−0.603762
$395$	−440935.	−0.142194
$396$	2.80214e6	0.897948
$397$	2.14436e6	0.682843	0.341421	−	0.939910i	$-0.389092\pi$
$397$	2.14436e6	0.682843	0.341421	+	0.939910i	$0.389092\pi$
$398$	2.40597e6	0.761345
$399$	1.08104e6	0.339945
$400$	160000.	0.0500000
$401$	702874.	0.218281	0.109141	−	0.994026i	$-0.465190\pi$
$401$	702874.	0.218281	0.109141	+	0.994026i	$0.465190\pi$
$402$	−93361.0	−0.0288138
$403$	−7.38843e6	−2.26615
$404$	−829888.	−0.252968
$405$	1.36475e6	0.413442
$406$	3.09689e6	0.932419
$407$	2.98849e6	0.894264
$408$	−216779.	−0.0644715
$409$	2.71607e6	0.802848	0.401424	−	0.915892i	$-0.368515\pi$
$409$	2.71607e6	0.802848	0.401424	+	0.915892i	$0.368515\pi$
$410$	163386.	0.0480015
$411$	796404.	0.232557
$412$	869284.	0.252301
$413$	1.25447e7	3.61896
$414$	−501135.	−0.143699
$415$	2.19025e6	0.624270
$416$	−898008.	−0.254418
$417$	−483672.	−0.136211
$418$	5.10331e6	1.42860
$419$	−3.78764e6	−1.05398	−0.526992	−	0.849870i	$-0.676680\pi$
$419$	−3.78764e6	−1.05398	−0.526992	+	0.849870i	$0.676680\pi$
$420$	250633.	0.0693291
$421$	−1.72773e6	−0.475085	−0.237542	−	0.971377i	$-0.576342\pi$
$421$	−1.72773e6	−0.475085	−0.237542	+	0.971377i	$0.576342\pi$
$422$	24097.6	0.00658707
$423$	−4.49719e6	−1.22205
$424$	−1.21312e6	−0.327710
$425$	−852339.	−0.228897
$426$	−287406.	−0.0767311
$427$	−4.80125e6	−1.27434
$428$	−1.69847e6	−0.448176
$429$	1.61071e6	0.422545
$430$	−873557.	−0.227835
$431$	−5.04905e6	−1.30923	−0.654615	−	0.755962i	$-0.727169\pi$
$431$	−5.04905e6	−1.30923	−0.654615	+	0.755962i	$0.727169\pi$
$432$	305094.	0.0786546
$433$	37457.0	0.00960093	0.00480047	−	0.999988i	$-0.498472\pi$
$433$	37457.0	0.00960093	0.00480047	+	0.999988i	$0.498472\pi$
$434$	−8.50169e6	−2.16661
$435$	−190563.	−0.0482853
$436$	−2.78246e6	−0.700992
$437$	−912677.	−0.228620
$438$	25185.4	0.00627282
$439$	−99673.6	−0.0246842	−0.0123421	−	0.999924i	$-0.503929\pi$
$439$	−99673.6	−0.0246842	−0.0123421	+	0.999924i	$0.503929\pi$
$440$	1.18318e6	0.291353
$441$	−1.10921e7	−2.71592
$442$	4.78380e6	1.16471
$443$	−4.60309e6	−1.11440	−0.557199	−	0.830379i	$-0.688124\pi$
$443$	−4.60309e6	−1.11440	−0.557199	+	0.830379i	$0.688124\pi$
$444$	160600.	0.0386624
$445$	830475.	0.198805
$446$	−5.16793e6	−1.23021
$447$	976184.	0.231080
$448$	−1.03332e6	−0.243242
$449$	3.74524e6	0.876725	0.438363	−	0.898798i	$-0.355559\pi$
$449$	3.74524e6	0.876725	0.438363	+	0.898798i	$0.355559\pi$
$450$	592078.	0.137831
$451$	1.20822e6	0.279707
$452$	4.19371e6	0.965501
$453$	13308.5	0.00304707
$454$	−257177.	−0.0585589
$455$	−5.53088e6	−1.25246
$456$	274250.	0.0617639
$457$	499745.	0.111933	0.0559665	−	0.998433i	$-0.482176\pi$
$457$	499745.	0.111933	0.0559665	+	0.998433i	$0.482176\pi$
$458$	−298613.	−0.0665188
$459$	−1.62527e6	−0.360076
$460$	−211600.	−0.0466252
$461$	1.73935e6	0.381183	0.190592	−	0.981669i	$-0.438959\pi$
$461$	1.73935e6	0.381183	0.190592	+	0.981669i	$0.438959\pi$
$462$	1.85340e6	0.403984
$463$	866807.	0.187919	0.0939594	−	0.995576i	$-0.470048\pi$
$463$	866807.	0.187919	0.0939594	+	0.995576i	$0.470048\pi$
$464$	785656.	0.169409
$465$	523139.	0.112198
$466$	652427.	0.139177
$467$	−1.52340e6	−0.323238	−0.161619	−	0.986853i	$-0.551672\pi$
$467$	−1.52340e6	−0.323238	−0.161619	+	0.986853i	$0.551672\pi$
$468$	−3.32307e6	−0.701333
$469$	2.37069e6	0.497671
$470$	−1.89890e6	−0.396513
$471$	−722398.	−0.150046
$472$	3.18247e6	0.657522
$473$	−6.45984e6	−1.32760
$474$	−175227.	−0.0358224
$475$	1.07830e6	0.219284
$476$	5.50461e6	1.11355
$477$	−4.48914e6	−0.903373
$478$	1.83245e6	0.366828
$479$	9.23081e6	1.83824	0.919118	−	0.393983i	$-0.128903\pi$
$479$	9.23081e6	1.83824	0.919118	+	0.393983i	$0.128903\pi$
$480$	63583.6	0.0125963
$481$	−3.54407e6	−0.698456
$482$	−6.98911e6	−1.37026
$483$	−331463.	−0.0646498
$484$	6.17264e6	1.19773
$485$	1.03328e6	0.199463
$486$	1.70075e6	0.326626
$487$	−1.22749e6	−0.234529	−0.117264	−	0.993101i	$-0.537413\pi$
$487$	−1.22749e6	−0.234529	−0.117264	+	0.993101i	$0.537413\pi$
$488$	−1.21804e6	−0.231532
$489$	405756.	0.0767348
$490$	−4.68355e6	−0.881222
$491$	−2.99377e6	−0.560421	−0.280210	−	0.959939i	$-0.590404\pi$
$491$	−2.99377e6	−0.560421	−0.280210	+	0.959939i	$0.590404\pi$
$492$	64929.2	0.0120928
$493$	−4.18529e6	−0.775546
$494$	−6.05204e6	−1.11580
$495$	4.37834e6	0.803149
$496$	−2.15681e6	−0.393648
$497$	7.29799e6	1.32529
$498$	870398.	0.157270
$499$	−123550.	−0.0222121	−0.0111061	−	0.999938i	$-0.503535\pi$
$499$	−123550.	−0.0222121	−0.0111061	+	0.999938i	$0.503535\pi$
$500$	250000.	0.0447214
$501$	656230.	0.116805
$502$	2.03917e6	0.361155
$503$	2.10833e6	0.371551	0.185775	−	0.982592i	$-0.440520\pi$
$503$	2.10833e6	0.371551	0.185775	+	0.982592i	$0.440520\pi$
$504$	−3.82377e6	−0.670527
$505$	−1.29670e6	−0.226262
$506$	−1.56475e6	−0.271688
$507$	−987950.	−0.170693
$508$	3.64040e6	0.625878
$509$	1.57302e6	0.269116	0.134558	−	0.990906i	$-0.457038\pi$
$509$	1.57302e6	0.269116	0.134558	+	0.990906i	$0.457038\pi$
$510$	−338718.	−0.0576650
$511$	−639523.	−0.108344
$512$	−262144.	−0.0441942
$513$	2.05615e6	0.344954
$514$	−1.01517e6	−0.169485
$515$	1.35826e6	0.225665
$516$	−347150.	−0.0573974
$517$	−1.40421e7	−2.31050
$518$	−4.07807e6	−0.667776
$519$	−849140.	−0.138376
$520$	−1.40314e6	−0.227558
$521$	−1.90859e6	−0.308049	−0.154024	−	0.988067i	$-0.549223\pi$
$521$	−1.90859e6	−0.308049	−0.154024	+	0.988067i	$0.549223\pi$
$522$	2.90731e6	0.466998
$523$	7.33852e6	1.17315	0.586576	−	0.809894i	$-0.300475\pi$
$523$	7.33852e6	1.17315	0.586576	+	0.809894i	$0.300475\pi$
$524$	3.29531e6	0.524286
$525$	391615.	0.0620099
$526$	982467.	0.154829
$527$	1.14896e7	1.80210
$528$	470193.	0.0733992
$529$	279841.	0.0434783
$530$	−1.89550e6	−0.293113
$531$	1.17767e7	1.81254
$532$	−6.96394e6	−1.06678
$533$	−1.43283e6	−0.218463
$534$	330029.	0.0500840
$535$	−2.65386e6	−0.400861
$536$	601423.	0.0904208
$537$	−774345.	−0.115877
$538$	5.23887e6	0.780337
$539$	−3.46343e7	−5.13492
$540$	476709.	0.0703508
$541$	1.09412e7	1.60721	0.803606	−	0.595162i	$-0.202912\pi$
$541$	1.09412e7	1.60721	0.803606	+	0.595162i	$0.202912\pi$
$542$	−1.34123e6	−0.196112
$543$	653691.	0.0951421
$544$	1.39647e6	0.202318
$545$	−4.34760e6	−0.626986
$546$	−2.19796e6	−0.315528
$547$	7.37797e6	1.05431	0.527155	−	0.849769i	$-0.323259\pi$
$547$	7.37797e6	1.05431	0.527155	+	0.849769i	$0.323259\pi$
$548$	−5.13036e6	−0.729788
$549$	−4.50733e6	−0.638246
$550$	1.84872e6	0.260594
$551$	5.29485e6	0.742976
$552$	−84089.4	−0.0117461
$553$	4.44947e6	0.618722
$554$	−4.97106e6	−0.688137
$555$	250938.	0.0345807
$556$	3.11577e6	0.427444
$557$	7.81229e6	1.06694	0.533471	−	0.845819i	$-0.320887\pi$
$557$	7.81229e6	1.06694	0.533471	+	0.845819i	$0.320887\pi$
$558$	−7.98124e6	−1.08514
$559$	7.66076e6	1.03691
$560$	−1.61456e6	−0.217562
$561$	−2.50477e6	−0.336017
$562$	2.19648e6	0.293350
$563$	−9.88567e6	−1.31442	−0.657212	−	0.753706i	$-0.728264\pi$
$563$	−9.88567e6	−1.31442	−0.657212	+	0.753706i	$0.728264\pi$
$564$	−754619.	−0.0998918
$565$	6.55268e6	0.863570
$566$	2.75070e6	0.360913
$567$	−1.37716e7	−1.79899
$568$	1.85144e6	0.240790
$569$	3.37792e6	0.437390	0.218695	−	0.975793i	$-0.429820\pi$
$569$	3.37792e6	0.437390	0.218695	+	0.975793i	$0.429820\pi$
$570$	428516.	0.0552433
$571$	1.44970e7	1.86075	0.930375	−	0.366610i	$-0.119482\pi$
$571$	1.44970e7	1.86075	0.930375	+	0.366610i	$0.119482\pi$
$572$	−1.03760e7	−1.32599
$573$	1.87622e6	0.238725
$574$	−1.64873e6	−0.208866
$575$	−330625.	−0.0417029
$576$	−970060.	−0.121827
$577$	−2.74177e6	−0.342840	−0.171420	−	0.985198i	$-0.554836\pi$
$577$	−2.74177e6	−0.342840	−0.171420	+	0.985198i	$0.554836\pi$
$578$	−1.75975e6	−0.219095
$579$	1.92197e6	0.238259
$580$	1.22759e6	0.151524
$581$	−2.21017e7	−2.71635
$582$	410623.	0.0502499
$583$	−1.40170e7	−1.70798
$584$	−162242.	−0.0196848
$585$	−5.19229e6	−0.627291
$586$	5.21268e6	0.627071
$587$	2.70287e6	0.323765	0.161882	−	0.986810i	$-0.448243\pi$
$587$	2.70287e6	0.323765	0.161882	+	0.986810i	$0.448243\pi$
$588$	−1.86123e6	−0.222002
$589$	−1.45356e7	−1.72641
$590$	4.97262e6	0.588105
$591$	−1.15518e6	−0.136045
$592$	−1.03457e6	−0.121327
$593$	5.21163e6	0.608607	0.304303	−	0.952575i	$-0.401576\pi$
$593$	5.21163e6	0.608607	0.304303	+	0.952575i	$0.401576\pi$
$594$	3.52520e6	0.409938
$595$	8.60095e6	0.995987
$596$	−6.28849e6	−0.725155
$597$	1.49395e6	0.171553
$598$	1.85565e6	0.212199
$599$	1.51225e7	1.72210	0.861049	−	0.508523i	$-0.169808\pi$
$599$	1.51225e7	1.72210	0.861049	+	0.508523i	$0.169808\pi$
$600$	99349.4	0.0112665
$601$	1.54889e7	1.74918	0.874592	−	0.484860i	$-0.161129\pi$
$601$	1.54889e7	1.74918	0.874592	+	0.484860i	$0.161129\pi$
$602$	8.81505e6	0.991365
$603$	2.22556e6	0.249256
$604$	−85731.8	−0.00956202
$605$	9.64475e6	1.07128
$606$	−515305.	−0.0570011
$607$	−1.32452e7	−1.45910	−0.729551	−	0.683926i	$-0.760271\pi$
$607$	−1.32452e7	−1.45910	−0.729551	+	0.683926i	$0.760271\pi$
$608$	−1.76669e6	−0.193822
$609$	1.92297e6	0.210101
$610$	−1.90318e6	−0.207088
$611$	1.66526e7	1.80459
$612$	5.16763e6	0.557715
$613$	9.10746e6	0.978918	0.489459	−	0.872026i	$-0.337194\pi$
$613$	9.10746e6	0.978918	0.489459	+	0.872026i	$0.337194\pi$
$614$	−1.07154e7	−1.14707
$615$	101452.	0.0108161
$616$	−1.19394e7	−1.26775
$617$	−2.14311e6	−0.226637	−0.113319	−	0.993559i	$-0.536148\pi$
$617$	−2.14311e6	−0.226637	−0.113319	+	0.993559i	$0.536148\pi$
$618$	539768.	0.0568507
$619$	1.74838e7	1.83404	0.917021	−	0.398839i	$-0.130587\pi$
$619$	1.74838e7	1.83404	0.917021	+	0.398839i	$0.130587\pi$
$620$	−3.37001e6	−0.352089
$621$	−630448.	−0.0656025
$622$	−1.06672e7	−1.10554
$623$	−8.38031e6	−0.865048
$624$	−557604.	−0.0573277
$625$	390625.	0.0400000
$626$	−3.74289e6	−0.381743
$627$	3.16882e6	0.321906
$628$	4.65362e6	0.470860
$629$	5.51130e6	0.555427
$630$	−5.97465e6	−0.599737
$631$	4.20504e6	0.420433	0.210216	−	0.977655i	$-0.432583\pi$
$631$	4.20504e6	0.420433	0.210216	+	0.977655i	$0.432583\pi$
$632$	1.12879e6	0.112414
$633$	14963.0	0.00148426
$634$	5.81541e6	0.574589
$635$	5.68813e6	0.559803
$636$	−753268.	−0.0738426
$637$	4.10729e7	4.01058
$638$	9.07785e6	0.882940
$639$	6.85123e6	0.663768
$640$	−409600.	−0.0395285
$641$	7.83415e6	0.753090	0.376545	−	0.926398i	$-0.377112\pi$
$641$	7.83415e6	0.753090	0.376545	+	0.926398i	$0.377112\pi$
$642$	−1.05464e6	−0.100987
$643$	−1.18578e7	−1.13103	−0.565517	−	0.824737i	$-0.691323\pi$
$643$	−1.18578e7	−1.13103	−0.565517	+	0.824737i	$0.691323\pi$
$644$	2.13525e6	0.202878
$645$	−542421.	−0.0513378
$646$	9.41139e6	0.887304
$647$	5.26318e6	0.494297	0.247148	−	0.968978i	$-0.420506\pi$
$647$	5.26318e6	0.494297	0.247148	+	0.968978i	$0.420506\pi$
$648$	−3.49375e6	−0.326855
$649$	3.67719e7	3.42692
$650$	−2.19240e6	−0.203534
$651$	−5.27899e6	−0.488201
$652$	−2.61384e6	−0.240802
$653$	1.64840e7	1.51279	0.756397	−	0.654113i	$-0.226958\pi$
$653$	1.64840e7	1.51279	0.756397	+	0.654113i	$0.226958\pi$
$654$	−1.72772e6	−0.157954
$655$	5.14892e6	0.468935
$656$	−418268.	−0.0379486
$657$	−600373.	−0.0542635
$658$	1.91618e7	1.72533
$659$	−1.73924e7	−1.56008	−0.780038	−	0.625732i	$-0.784800\pi$
$659$	−1.73924e7	−1.56008	−0.780038	+	0.625732i	$0.784800\pi$
$660$	734676.	0.0656502
$661$	1.03745e7	0.923553	0.461776	−	0.886996i	$-0.347212\pi$
$661$	1.03745e7	0.923553	0.461776	+	0.886996i	$0.347212\pi$
$662$	55365.2	0.00491012
$663$	2.97042e6	0.262443
$664$	−5.60703e6	−0.493529
$665$	−1.08812e7	−0.954160
$666$	−3.82842e6	−0.334453
$667$	−1.62348e6	−0.141297
$668$	−4.22737e6	−0.366547
$669$	−3.20895e6	−0.277202
$670$	939724.	0.0808748
$671$	−1.40738e7	−1.20672
$672$	−641622.	−0.0548095
$673$	−2.69576e6	−0.229426	−0.114713	−	0.993399i	$-0.536595\pi$
$673$	−2.69576e6	−0.229426	−0.114713	+	0.993399i	$0.536595\pi$
$674$	7.72662e6	0.655148
$675$	744858.	0.0629237
$676$	6.36429e6	0.535652
$677$	−229429.	−0.0192387	−0.00961937	−	0.999954i	$-0.503062\pi$
$677$	−229429.	−0.0192387	−0.00961937	+	0.999954i	$0.503062\pi$
$678$	2.60402e6	0.217555
$679$	−1.04268e7	−0.867914
$680$	2.18199e6	0.180959
$681$	−159690.	−0.0131950
$682$	−2.49208e7	−2.05164
$683$	1.09516e7	0.898313	0.449157	−	0.893453i	$-0.351725\pi$
$683$	1.09516e7	0.898313	0.449157	+	0.893453i	$0.351725\pi$
$684$	−6.53763e6	−0.534293
$685$	−8.01619e6	−0.652742
$686$	3.03017e7	2.45843
$687$	−185419.	−0.0149886
$688$	2.23631e6	0.180119
$689$	1.66228e7	1.33400
$690$	−131390.	−0.0105060
$691$	−2.33754e7	−1.86236	−0.931181	−	0.364558i	$-0.881220\pi$
$691$	−2.33754e7	−1.86236	−0.931181	+	0.364558i	$0.881220\pi$
$692$	5.47008e6	0.434239
$693$	−4.41817e7	−3.49470
$694$	9.76963e6	0.769980
$695$	4.86839e6	0.382317
$696$	487841.	0.0381729
$697$	2.22817e6	0.173726
$698$	−3.82683e6	−0.297304
$699$	405114.	0.0313606
$700$	−2.52275e6	−0.194594
$701$	−285635.	−0.0219542	−0.0109771	−	0.999940i	$-0.503494\pi$
$701$	−285635.	−0.0219542	−0.0109771	+	0.999940i	$0.503494\pi$
$702$	−4.18056e6	−0.320178
$703$	−6.97241e6	−0.532102
$704$	−3.02894e6	−0.230334
$705$	−1.17909e6	−0.0893459
$706$	−1.48440e7	−1.12083
$707$	1.30850e7	0.984520
$708$	1.97611e6	0.148159
$709$	7.04217e6	0.526127	0.263064	−	0.964778i	$-0.415267\pi$
$709$	7.04217e6	0.526127	0.263064	+	0.964778i	$0.415267\pi$
$710$	2.89288e6	0.215369
$711$	4.17709e6	0.309884
$712$	−2.12602e6	−0.157169
$713$	4.45684e6	0.328325
$714$	3.41800e6	0.250915
$715$	−1.62125e7	−1.18600
$716$	4.98826e6	0.363636
$717$	1.13783e6	0.0826569
$718$	5.33612e6	0.386291
$719$	1.60147e7	1.15531	0.577653	−	0.816283i	$-0.303969\pi$
$719$	1.60147e7	1.15531	0.577653	+	0.816283i	$0.303969\pi$
$720$	−1.51572e6	−0.108965
$721$	−1.37061e7	−0.981923
$722$	−2.00207e6	−0.142934
$723$	−4.33978e6	−0.308761
$724$	−4.21102e6	−0.298566
$725$	1.91811e6	0.135528
$726$	3.83280e6	0.269882
$727$	1.09411e7	0.767758	0.383879	−	0.923383i	$-0.374588\pi$
$727$	1.09411e7	0.767758	0.383879	+	0.923383i	$0.374588\pi$
$728$	1.41590e7	0.990160
$729$	−1.22093e7	−0.850886
$730$	−253503.	−0.0176066
$731$	−1.19131e7	−0.824575
$732$	−756321.	−0.0521709
$733$	1.33642e7	0.918718	0.459359	−	0.888251i	$-0.348079\pi$
$733$	1.33642e7	0.918718	0.459359	+	0.888251i	$0.348079\pi$
$734$	−1.16879e7	−0.800748
$735$	−2.90818e6	−0.198565
$736$	541696.	0.0368605
$737$	6.94914e6	0.471262
$738$	−1.54780e6	−0.104610
$739$	9.50621e6	0.640319	0.320159	−	0.947364i	$-0.396264\pi$
$739$	9.50621e6	0.640319	0.320159	+	0.947364i	$0.396264\pi$
$740$	−1.61652e6	−0.108518
$741$	−3.75792e6	−0.251421
$742$	1.91275e7	1.27540
$743$	−9.84795e6	−0.654446	−0.327223	−	0.944947i	$-0.606113\pi$
$743$	−9.84795e6	−0.654446	−0.327223	+	0.944947i	$0.606113\pi$
$744$	−1.33924e6	−0.0887002
$745$	−9.82576e6	−0.648598
$746$	1.22604e7	0.806599
$747$	−2.07487e7	−1.36047
$748$	1.61355e7	1.05446
$749$	2.67801e7	1.74425
$750$	155233.	0.0100770
$751$	−1.90181e7	−1.23046	−0.615230	−	0.788348i	$-0.710937\pi$
$751$	−1.90181e7	−1.23046	−0.615230	+	0.788348i	$0.710937\pi$
$752$	4.86119e6	0.313471
$753$	1.26619e6	0.0813788
$754$	−1.07655e7	−0.689612
$755$	−133956.	−0.00855253
$756$	−4.81047e6	−0.306114
$757$	−1.70495e7	−1.08136	−0.540681	−	0.841227i	$-0.681834\pi$
$757$	−1.70495e7	−1.08136	−0.540681	+	0.841227i	$0.681834\pi$
$758$	−1.18615e6	−0.0749836
$759$	−971609.	−0.0612191
$760$	−2.76046e6	−0.173359
$761$	−2.75852e6	−0.172669	−0.0863346	−	0.996266i	$-0.527515\pi$
$761$	−2.75852e6	−0.172669	−0.0863346	+	0.996266i	$0.527515\pi$
$762$	2.26045e6	0.141029
$763$	4.38715e7	2.72817
$764$	−1.20865e7	−0.749145
$765$	8.07442e6	0.498836
$766$	−9.01548e6	−0.555158
$767$	−4.36079e7	−2.67656
$768$	−162774.	−0.00995823
$769$	1.87467e7	1.14316	0.571581	−	0.820546i	$-0.306330\pi$
$769$	1.87467e7	1.14316	0.571581	+	0.820546i	$0.306330\pi$
$770$	−1.86554e7	−1.13391
$771$	−630354.	−0.0381899
$772$	−1.23811e7	−0.747683
$773$	1.37482e7	0.827553	0.413776	−	0.910379i	$-0.364210\pi$
$773$	1.37482e7	0.827553	0.413776	+	0.910379i	$0.364210\pi$
$774$	8.27542e6	0.496521
$775$	−5.26565e6	−0.314918
$776$	−2.64519e6	−0.157690
$777$	−2.53221e6	−0.150469
$778$	3.82673e6	0.226662
$779$	−2.81888e6	−0.166430
$780$	−871256.	−0.0512754
$781$	2.13924e7	1.25497
$782$	−2.88568e6	−0.168745
$783$	3.65752e6	0.213197
$784$	1.19899e7	0.696667
$785$	7.27129e6	0.421150
$786$	2.04617e6	0.118137
$787$	6.89984e6	0.397102	0.198551	−	0.980091i	$-0.436376\pi$
$787$	6.89984e6	0.397102	0.198551	+	0.980091i	$0.436376\pi$
$788$	7.44160e6	0.426924
$789$	610047.	0.0348876
$790$	1.76374e6	0.100547
$791$	−6.61230e7	−3.75761
$792$	−1.12085e7	−0.634945
$793$	1.66902e7	0.942493
$794$	−8.57742e6	−0.482843
$795$	−1.17698e6	−0.0660468
$796$	−9.62386e6	−0.538353
$797$	1.13532e7	0.633098	0.316549	−	0.948576i	$-0.397476\pi$
$797$	1.13532e7	0.633098	0.316549	+	0.948576i	$0.397476\pi$
$798$	−4.32415e6	−0.240377
$799$	−2.58961e7	−1.43505
$800$	−640000.	−0.0353553
$801$	−7.86729e6	−0.433255
$802$	−2.81150e6	−0.154348
$803$	−1.87462e6	−0.102595
$804$	373444.	0.0203744
$805$	3.33633e6	0.181459
$806$	2.95537e7	1.60241
$807$	3.25299e6	0.175833
$808$	3.31955e6	0.178875
$809$	2.58652e7	1.38946	0.694728	−	0.719273i	$-0.255525\pi$
$809$	2.58652e7	1.38946	0.694728	+	0.719273i	$0.255525\pi$
$810$	−5.45899e6	−0.292348
$811$	3.88499e6	0.207414	0.103707	−	0.994608i	$-0.466930\pi$
$811$	3.88499e6	0.207414	0.103707	+	0.994608i	$0.466930\pi$
$812$	−1.23876e7	−0.659320
$813$	−832815.	−0.0441898
$814$	−1.19540e7	−0.632340
$815$	−4.08413e6	−0.215380
$816$	867117.	0.0455882
$817$	1.50714e7	0.789946
$818$	−1.08643e7	−0.567699
$819$	5.23953e7	2.72950
$820$	−653544.	−0.0339422
$821$	−1.98988e7	−1.03031	−0.515157	−	0.857096i	$-0.672266\pi$
$821$	−1.98988e7	−1.03031	−0.515157	+	0.857096i	$0.672266\pi$
$822$	−3.18562e6	−0.164442
$823$	3.02715e7	1.55788	0.778941	−	0.627097i	$-0.215757\pi$
$823$	3.02715e7	1.55788	0.778941	+	0.627097i	$0.215757\pi$
$824$	−3.47714e6	−0.178404
$825$	1.14793e6	0.0587193
$826$	−5.01786e7	−2.55899
$827$	1.36026e7	0.691605	0.345803	−	0.938307i	$-0.387607\pi$
$827$	1.36026e7	0.691605	0.345803	+	0.938307i	$0.387607\pi$
$828$	2.00454e6	0.101610
$829$	2.08242e6	0.105240	0.0526202	−	0.998615i	$-0.483243\pi$
$829$	2.08242e6	0.105240	0.0526202	+	0.998615i	$0.483243\pi$
$830$	−8.76098e6	−0.441426
$831$	−3.08670e6	−0.155057
$832$	3.59203e6	0.179900
$833$	−6.38716e7	−3.18930
$834$	1.93469e6	0.0963155
$835$	−6.60527e6	−0.327850
$836$	−2.04132e7	−1.01017
$837$	−1.00407e7	−0.495395
$838$	1.51506e7	0.745279
$839$	1.26418e7	0.620016	0.310008	−	0.950734i	$-0.399668\pi$
$839$	1.26418e7	0.620016	0.310008	+	0.950734i	$0.399668\pi$
$840$	−1.00253e6	−0.0490231
$841$	−1.10926e7	−0.540807
$842$	6.91093e6	0.335936
$843$	1.36387e6	0.0661003
$844$	−96390.4	−0.00465777
$845$	9.94420e6	0.479102
$846$	1.79887e7	0.864122
$847$	−9.73250e7	−4.66140
$848$	4.85248e6	0.231726
$849$	1.70800e6	0.0813241
$850$	3.40936e6	0.161855
$851$	2.13785e6	0.101194
$852$	1.14962e6	0.0542571
$853$	−2.77167e7	−1.30427	−0.652137	−	0.758101i	$-0.726127\pi$
$853$	−2.77167e7	−1.30427	−0.652137	+	0.758101i	$0.726127\pi$
$854$	1.92050e7	0.901093
$855$	−1.02150e7	−0.477887
$856$	6.79389e6	0.316909
$857$	−1.68037e7	−0.781541	−0.390770	−	0.920488i	$-0.627791\pi$
$857$	−1.68037e7	−0.781541	−0.390770	+	0.920488i	$0.627791\pi$
$858$	−6.44282e6	−0.298784
$859$	6.32943e6	0.292672	0.146336	−	0.989235i	$-0.453252\pi$
$859$	6.32943e6	0.292672	0.146336	+	0.989235i	$0.453252\pi$
$860$	3.49423e6	0.161104
$861$	−1.02375e6	−0.0470637
$862$	2.01962e7	0.925766
$863$	−3.58594e7	−1.63899	−0.819494	−	0.573088i	$-0.805745\pi$
$863$	−3.58594e7	−1.63899	−0.819494	+	0.573088i	$0.805745\pi$
$864$	−1.22038e6	−0.0556172
$865$	8.54701e6	0.388395
$866$	−149828.	−0.00678888
$867$	−1.09269e6	−0.0493684
$868$	3.40068e7	1.53203
$869$	1.30426e7	0.585890
$870$	762251.	0.0341429
$871$	−8.24101e6	−0.368074
$872$	1.11298e7	0.495676
$873$	−9.78850e6	−0.434691
$874$	3.65071e6	0.161658
$875$	−3.94179e6	−0.174050
$876$	−100741.	−0.00443555
$877$	757238.	0.0332455	0.0166228	−	0.999862i	$-0.494709\pi$
$877$	757238.	0.0332455	0.0166228	+	0.999862i	$0.494709\pi$
$878$	398694.	0.0174544
$879$	3.23673e6	0.141297
$880$	−4.73272e6	−0.206017
$881$	3.19130e6	0.138525	0.0692625	−	0.997598i	$-0.477935\pi$
$881$	3.19130e6	0.138525	0.0692625	+	0.997598i	$0.477935\pi$
$882$	4.43684e7	1.92045
$883$	1.92363e7	0.830271	0.415136	−	0.909760i	$-0.363734\pi$
$883$	1.92363e7	0.830271	0.415136	+	0.909760i	$0.363734\pi$
$884$	−1.91352e7	−0.823573
$885$	3.08767e6	0.132517
$886$	1.84124e7	0.787999
$887$	−2.68483e7	−1.14580	−0.572898	−	0.819627i	$-0.694181\pi$
$887$	−2.68483e7	−1.14580	−0.572898	+	0.819627i	$0.694181\pi$
$888$	−642402.	−0.0273385
$889$	−5.73988e7	−2.43584
$890$	−3.32190e6	−0.140576
$891$	−4.03685e7	−1.70353
$892$	2.06717e7	0.869891
$893$	3.27615e7	1.37479
$894$	−3.90474e6	−0.163398
$895$	7.79415e6	0.325246
$896$	4.13327e6	0.171998
$897$	1.15224e6	0.0478146
$898$	−1.49809e7	−0.619938
$899$	−2.58562e7	−1.06700
$900$	−2.36831e6	−0.0974613
$901$	−2.58498e7	−1.06083
$902$	−4.83287e6	−0.197783
$903$	5.47356e6	0.223383
$904$	−1.67749e7	−0.682712
$905$	−6.57971e6	−0.267046
$906$	−53233.8	−0.00215460
$907$	7.62585e6	0.307801	0.153901	−	0.988086i	$-0.450816\pi$
$907$	7.62585e6	0.307801	0.153901	+	0.988086i	$0.450816\pi$
$908$	1.02871e6	0.0414074
$909$	1.22839e7	0.493092
$910$	2.21235e7	0.885626
$911$	−3.05793e6	−0.122076	−0.0610381	−	0.998135i	$-0.519441\pi$
$911$	−3.05793e6	−0.122076	−0.0610381	+	0.998135i	$0.519441\pi$
$912$	−1.09700e6	−0.0436737
$913$	−6.47863e7	−2.57221
$914$	−1.99898e6	−0.0791485
$915$	−1.18175e6	−0.0466631
$916$	1.19445e6	0.0470359
$917$	−5.19577e7	−2.04045
$918$	6.50109e6	0.254612
$919$	−1.40082e7	−0.547134	−0.273567	−	0.961853i	$-0.588204\pi$
$919$	−1.40082e7	−0.547134	−0.273567	+	0.961853i	$0.588204\pi$
$920$	846400.	0.0329690
$921$	−6.65358e6	−0.258468
$922$	−6.95739e6	−0.269537
$923$	−2.53694e7	−0.980180
$924$	−7.41361e6	−0.285660
$925$	−2.52581e6	−0.0970615
$926$	−3.46723e6	−0.132879
$927$	−1.28671e7	−0.491792
$928$	−3.14262e6	−0.119791
$929$	1.68894e7	0.642061	0.321030	−	0.947069i	$-0.395971\pi$
$929$	1.68894e7	0.642061	0.321030	+	0.947069i	$0.395971\pi$
$930$	−2.09256e6	−0.0793359
$931$	8.08047e7	3.05536
$932$	−2.60971e6	−0.0984129
$933$	−6.62362e6	−0.249110
$934$	6.09362e6	0.228564
$935$	2.52118e7	0.943135
$936$	1.32923e7	0.495917
$937$	−7.56415e6	−0.281457	−0.140728	−	0.990048i	$-0.544944\pi$
$937$	−7.56415e6	−0.281457	−0.140728	+	0.990048i	$0.544944\pi$
$938$	−9.48274e6	−0.351906
$939$	−2.32409e6	−0.0860178
$940$	7.59560e6	0.280377
$941$	−3.45946e7	−1.27360	−0.636802	−	0.771027i	$-0.719743\pi$
$941$	−3.45946e7	−1.27360	−0.636802	+	0.771027i	$0.719743\pi$
$942$	2.88959e6	0.106099
$943$	864312.	0.0316513
$944$	−1.27299e7	−0.464938
$945$	−7.51636e6	−0.273797
$946$	2.58394e7	0.938758
$947$	2.11440e7	0.766149	0.383074	−	0.923717i	$-0.374865\pi$
$947$	2.11440e7	0.766149	0.383074	+	0.923717i	$0.374865\pi$
$948$	700907.	0.0253303
$949$	2.22312e6	0.0801304
$950$	−4.31322e6	−0.155057
$951$	3.61099e6	0.129472
$952$	−2.20184e7	−0.787397
$953$	−4.32490e6	−0.154257	−0.0771283	−	0.997021i	$-0.524575\pi$
$953$	−4.32490e6	−0.154257	−0.0771283	+	0.997021i	$0.524575\pi$
$954$	1.79565e7	0.638781
$955$	−1.88851e7	−0.670056
$956$	−7.32979e6	−0.259386
$957$	5.63675e6	0.198952
$958$	−3.69232e7	−1.29983
$959$	8.08913e7	2.84024
$960$	−254335.	−0.00890691
$961$	4.23521e7	1.47933
$962$	1.41763e7	0.493883
$963$	2.51407e7	0.873597
$964$	2.79565e7	0.968924
$965$	−1.93455e7	−0.668748
$966$	1.32585e6	0.0457143
$967$	−1.38356e7	−0.475807	−0.237904	−	0.971289i	$-0.576460\pi$
$967$	−1.38356e7	−0.475807	−0.237904	+	0.971289i	$0.576460\pi$
$968$	−2.46906e7	−0.846920
$969$	5.84385e6	0.199936
$970$	−4.13312e6	−0.141042
$971$	3.62720e7	1.23459	0.617296	−	0.786731i	$-0.288228\pi$
$971$	3.62720e7	1.23459	0.617296	+	0.786731i	$0.288228\pi$
$972$	−6.80301e6	−0.230959
$973$	−4.91269e7	−1.66356
$974$	4.90997e6	0.165837
$975$	−1.36134e6	−0.0458621
$976$	4.87215e6	0.163718
$977$	−1.26207e7	−0.423006	−0.211503	−	0.977377i	$-0.567836\pi$
$977$	−1.26207e7	−0.423006	−0.211503	+	0.977377i	$0.567836\pi$
$978$	−1.62302e6	−0.0542597
$979$	−2.45650e7	−0.819144
$980$	1.87342e7	0.623118
$981$	4.11858e7	1.36639
$982$	1.19751e7	0.396277
$983$	3.30183e7	1.08986	0.544930	−	0.838481i	$-0.316556\pi$
$983$	3.30183e7	1.08986	0.544930	+	0.838481i	$0.316556\pi$
$984$	−259717.	−0.00855091
$985$	1.16275e7	0.381852
$986$	1.67411e7	0.548394
$987$	1.18982e7	0.388766
$988$	2.42082e7	0.788986
$989$	−4.62112e6	−0.150230
$990$	−1.75133e7	−0.567912
$991$	5.10495e7	1.65123	0.825614	−	0.564235i	$-0.190829\pi$
$991$	5.10495e7	1.65123	0.825614	+	0.564235i	$0.190829\pi$
$992$	8.62724e6	0.278351
$993$	34378.1	0.00110639
$994$	−2.91920e7	−0.937125
$995$	−1.50373e7	−0.481517
$996$	−3.48159e6	−0.111206
$997$	−8.22079e6	−0.261924	−0.130962	−	0.991387i	$-0.541807\pi$
$997$	−8.22079e6	−0.261924	−0.130962	+	0.991387i	$0.541807\pi$
$998$	494198.	0.0157063
$999$	−4.81632e6	−0.152687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.f.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.f.1.3	✓	5	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -2.48374 q^{3} +16.0000 q^{4} +25.0000 q^{5} +9.93494 q^{6} -252.275 q^{7} -64.0000 q^{8} -236.831 q^{9} -100.000 q^{10} -739.487 q^{11} -39.7398 q^{12} +876.961 q^{13} +1009.10 q^{14} -62.0934 q^{15} +256.000 q^{16} -1363.74 q^{17} +947.324 q^{18} +1725.29 q^{19} +400.000 q^{20} +626.584 q^{21} +2957.95 q^{22} -529.000 q^{23} +158.959 q^{24} +625.000 q^{25} -3507.84 q^{26} +1191.77 q^{27} -4036.39 q^{28} +3068.97 q^{29} +248.374 q^{30} -8425.04 q^{31} -1024.00 q^{32} +1836.69 q^{33} +5454.97 q^{34} -6306.87 q^{35} -3789.30 q^{36} -4041.30 q^{37} -6901.15 q^{38} -2178.14 q^{39} -1600.00 q^{40} -1633.86 q^{41} -2506.33 q^{42} +8735.57 q^{43} -11831.8 q^{44} -5920.78 q^{45} +2116.00 q^{46} +18989.0 q^{47} -635.836 q^{48} +46835.5 q^{49} -2500.00 q^{50} +3387.18 q^{51} +14031.4 q^{52} +18955.0 q^{53} -4767.09 q^{54} -18487.2 q^{55} +16145.6 q^{56} -4285.16 q^{57} -12275.9 q^{58} -49726.2 q^{59} -993.494 q^{60} +19031.8 q^{61} +33700.1 q^{62} +59746.5 q^{63} +4096.00 q^{64} +21924.0 q^{65} -7346.76 q^{66} -9397.24 q^{67} -21819.9 q^{68} +1313.90 q^{69} +25227.5 q^{70} -28928.8 q^{71} +15157.2 q^{72} +2535.03 q^{73} +16165.2 q^{74} -1552.33 q^{75} +27604.6 q^{76} +186554. q^{77} +8712.56 q^{78} -17637.4 q^{79} +6400.00 q^{80} +54589.9 q^{81} +6535.44 q^{82} +87609.8 q^{83} +10025.3 q^{84} -34093.6 q^{85} -34942.3 q^{86} -7622.51 q^{87} +47327.2 q^{88} +33219.0 q^{89} +23683.1 q^{90} -221235. q^{91} -8464.00 q^{92} +20925.6 q^{93} -75956.0 q^{94} +43132.2 q^{95} +2543.35 q^{96} +41331.2 q^{97} -187342. q^{98} +175133. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18}+ \cdots + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

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