LMFDB - Embedded newform 605.6.a.e.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,6,Mod(1,605)] 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("605.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$97.0322109869$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 149x^{4} + 297x^{3} + 4052x^{2} - 6522x - 20692 $ x^6 - 3x^5 - 149x^4 + 297x^3 + 4052x^2 - 6522*x - 20692
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-5.32252$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-6.32252 q^{2} +28.4424 q^{3} +7.97424 q^{4} -25.0000 q^{5} -179.828 q^{6} -115.579 q^{7} +151.903 q^{8} +565.969 q^{9} +158.063 q^{10} +226.806 q^{12} -40.3015 q^{13} +730.751 q^{14} -711.060 q^{15} -1215.59 q^{16} +1793.42 q^{17} -3578.35 q^{18} +1813.85 q^{19} -199.356 q^{20} -3287.35 q^{21} +2472.87 q^{23} +4320.49 q^{24} +625.000 q^{25} +254.807 q^{26} +9186.02 q^{27} -921.656 q^{28} -2885.91 q^{29} +4495.69 q^{30} -8563.73 q^{31} +2824.67 q^{32} -11339.0 q^{34} +2889.48 q^{35} +4513.17 q^{36} -7357.47 q^{37} -11468.1 q^{38} -1146.27 q^{39} -3797.58 q^{40} +7373.27 q^{41} +20784.3 q^{42} -22795.2 q^{43} -14149.2 q^{45} -15634.8 q^{46} -1677.08 q^{47} -34574.2 q^{48} -3448.46 q^{49} -3951.57 q^{50} +51009.2 q^{51} -321.373 q^{52} +1548.56 q^{53} -58078.8 q^{54} -17556.9 q^{56} +51590.2 q^{57} +18246.2 q^{58} +44363.7 q^{59} -5670.16 q^{60} +19327.2 q^{61} +54144.4 q^{62} -65414.2 q^{63} +21039.8 q^{64} +1007.54 q^{65} +52145.9 q^{67} +14301.2 q^{68} +70334.3 q^{69} -18268.8 q^{70} +7613.84 q^{71} +85972.6 q^{72} +35728.1 q^{73} +46517.7 q^{74} +17776.5 q^{75} +14464.1 q^{76} +7247.31 q^{78} -66658.6 q^{79} +30389.7 q^{80} +123742. q^{81} -46617.6 q^{82} -8742.57 q^{83} -26214.1 q^{84} -44835.6 q^{85} +144123. q^{86} -82082.2 q^{87} -12117.7 q^{89} +89458.8 q^{90} +4658.01 q^{91} +19719.3 q^{92} -243573. q^{93} +10603.4 q^{94} -45346.2 q^{95} +80340.3 q^{96} +26058.0 q^{97} +21803.0 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 115 q^{4} - 150 q^{5} - 325 q^{6} + 66 q^{7} - 249 q^{8} + 832 q^{9} + 75 q^{10} + 1301 q^{12} + 972 q^{13} + 2017 q^{14} + 6675 q^{16} - 712 q^{17} - 5920 q^{18} - 610 q^{19} - 2875 q^{20}+ \cdots + 351884 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 115 * q^4 - 150 * q^5 - 325 * q^6 + 66 * q^7 - 249 * q^8 + 832 * q^9 + 75 * q^10 + 1301 * q^12 + 972 * q^13 + 2017 * q^14 + 6675 * q^16 - 712 * q^17 - 5920 * q^18 - 610 * q^19 - 2875 * q^20 - 2508 * q^21 + 7100 * q^23 - 13447 * q^24 + 3750 * q^25 - 7742 * q^26 - 2520 * q^27 + 33171 * q^28 - 10964 * q^29 + 8125 * q^30 + 8868 * q^31 - 10861 * q^32 - 42673 * q^34 - 1650 * q^35 - 30116 * q^36 - 15506 * q^37 + 26185 * q^38 - 7208 * q^39 + 6225 * q^40 - 160 * q^41 - 47111 * q^42 - 7032 * q^43 - 20800 * q^45 - 1650 * q^46 - 46320 * q^47 - 22215 * q^48 + 48512 * q^49 - 1875 * q^50 + 43378 * q^51 + 145838 * q^52 + 30518 * q^53 + 56881 * q^54 - 21297 * q^56 + 5640 * q^57 + 51477 * q^58 + 120532 * q^59 - 32525 * q^60 + 9228 * q^61 + 81355 * q^62 - 222460 * q^63 + 302839 * q^64 - 24300 * q^65 + 47432 * q^67 - 78111 * q^68 + 118960 * q^69 - 50425 * q^70 + 163948 * q^71 + 212580 * q^72 - 78528 * q^73 - 133501 * q^74 + 29355 * q^76 - 138086 * q^78 + 36712 * q^79 - 166875 * q^80 + 202166 * q^81 - 128902 * q^82 - 133792 * q^83 - 119033 * q^84 + 17800 * q^85 + 83996 * q^86 + 267082 * q^87 + 254946 * q^89 + 148000 * q^90 + 167844 * q^91 - 5134 * q^92 - 224250 * q^93 - 31414 * q^94 + 15250 * q^95 - 234415 * q^96 + 17404 * q^97 + 351884 * q^98

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 $

$2$	−6.32252	−1.11767	−0.558837	−	0.829278i	$-0.688752\pi$
$2$	−6.32252	−1.11767	−0.558837	+	0.829278i	$0.688752\pi$
$3$	28.4424	1.82458	0.912290	−	0.409545i	$-0.134313\pi$
$3$	28.4424	1.82458	0.912290	+	0.409545i	$0.134313\pi$
$4$	7.97424	0.249195
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−179.828	−2.03929
$7$	−115.579	−0.891527	−0.445763	−	0.895151i	$-0.647068\pi$
$7$	−115.579	−0.891527	−0.445763	+	0.895151i	$0.647068\pi$
$8$	151.903	0.839155
$9$	565.969	2.32909
$10$	158.063	0.499839
$11$	0	0
$11$	0	0
$12$	226.806	0.454676
$13$	−40.3015	−0.0661397	−0.0330699	−	0.999453i	$-0.510528\pi$
$13$	−40.3015	−0.0661397	−0.0330699	+	0.999453i	$0.510528\pi$
$14$	730.751	0.996436
$15$	−711.060	−0.815977
$16$	−1215.59	−1.18710
$17$	1793.42	1.50508	0.752542	−	0.658545i	$-0.228828\pi$
$17$	1793.42	1.50508	0.752542	+	0.658545i	$0.228828\pi$
$18$	−3578.35	−2.60316
$19$	1813.85	1.15270	0.576351	−	0.817202i	$-0.304476\pi$
$19$	1813.85	1.15270	0.576351	+	0.817202i	$0.304476\pi$
$20$	−199.356	−0.111443
$21$	−3287.35	−1.62666
$22$	0	0
$23$	2472.87	0.974724	0.487362	−	0.873200i	$-0.337959\pi$
$23$	2472.87	0.974724	0.487362	+	0.873200i	$0.337959\pi$
$24$	4320.49	1.53111
$25$	625.000	0.200000
$26$	254.807	0.0739226
$27$	9186.02	2.42503
$28$	−921.656	−0.222164
$29$	−2885.91	−0.637218	−0.318609	−	0.947886i	$-0.603216\pi$
$29$	−2885.91	−0.637218	−0.318609	+	0.947886i	$0.603216\pi$
$30$	4495.69	0.911996
$31$	−8563.73	−1.60051	−0.800256	−	0.599659i	$-0.795303\pi$
$31$	−8563.73	−1.60051	−0.800256	+	0.599659i	$0.795303\pi$
$32$	2824.67	0.487632
$33$	0	0
$34$	−11339.0	−1.68219
$35$	2889.48	0.398703
$36$	4513.17	0.580398
$37$	−7357.47	−0.883536	−0.441768	−	0.897129i	$-0.645649\pi$
$37$	−7357.47	−0.883536	−0.441768	+	0.897129i	$0.645649\pi$
$38$	−11468.1	−1.28835
$39$	−1146.27	−0.120677
$40$	−3797.58	−0.375282
$41$	7373.27	0.685016	0.342508	−	0.939515i	$-0.388724\pi$
$41$	7373.27	0.685016	0.342508	+	0.939515i	$0.388724\pi$
$42$	20784.3	1.81808
$43$	−22795.2	−1.88006	−0.940032	−	0.341087i	$-0.889205\pi$
$43$	−22795.2	−1.88006	−0.940032	+	0.341087i	$0.889205\pi$
$44$	0	0
$45$	−14149.2	−1.04160
$46$	−15634.8	−1.08942
$47$	−1677.08	−0.110741	−0.0553706	−	0.998466i	$-0.517634\pi$
$47$	−1677.08	−0.110741	−0.0553706	+	0.998466i	$0.517634\pi$
$48$	−34574.2	−2.16595
$49$	−3448.46	−0.205180
$50$	−3951.57	−0.223535
$51$	51009.2	2.74614
$52$	−321.373	−0.0164817
$53$	1548.56	0.0757248	0.0378624	−	0.999283i	$-0.487945\pi$
$53$	1548.56	0.0757248	0.0378624	+	0.999283i	$0.487945\pi$
$54$	−58078.8	−2.71040
$55$	0	0
$56$	−17556.9	−0.748129
$57$	51590.2	2.10320
$58$	18246.2	0.712202
$59$	44363.7	1.65920	0.829599	−	0.558360i	$-0.188569\pi$
$59$	44363.7	1.65920	0.829599	+	0.558360i	$0.188569\pi$
$60$	−5670.16	−0.203337
$61$	19327.2	0.665036	0.332518	−	0.943097i	$-0.392102\pi$
$61$	19327.2	0.665036	0.332518	+	0.943097i	$0.392102\pi$
$62$	54144.4	1.78885
$63$	−65414.2	−2.07645
$64$	21039.8	0.642083
$65$	1007.54	0.0295786
$66$	0	0
$67$	52145.9	1.41917	0.709583	−	0.704622i	$-0.248883\pi$
$67$	52145.9	1.41917	0.709583	+	0.704622i	$0.248883\pi$
$68$	14301.2	0.375059
$69$	70334.3	1.77846
$70$	−18268.8	−0.445620
$71$	7613.84	0.179249	0.0896247	−	0.995976i	$-0.471433\pi$
$71$	7613.84	0.179249	0.0896247	+	0.995976i	$0.471433\pi$
$72$	85972.6	1.95447
$73$	35728.1	0.784699	0.392350	−	0.919816i	$-0.371662\pi$
$73$	35728.1	0.784699	0.392350	+	0.919816i	$0.371662\pi$
$74$	46517.7	0.987505
$75$	17776.5	0.364916
$76$	14464.1	0.287248
$77$	0	0
$78$	7247.31	0.134878
$79$	−66658.6	−1.20168	−0.600839	−	0.799370i	$-0.705167\pi$
$79$	−66658.6	−1.20168	−0.600839	+	0.799370i	$0.705167\pi$
$80$	30389.7	0.530886
$81$	123742.	2.09558
$82$	−46617.6	−0.765624
$83$	−8742.57	−0.139298	−0.0696489	−	0.997572i	$-0.522188\pi$
$83$	−8742.57	−0.139298	−0.0696489	+	0.997572i	$0.522188\pi$
$84$	−26214.1	−0.405356
$85$	−44835.6	−0.673094
$86$	144123.	2.10130
$87$	−82082.2	−1.16266
$88$	0	0
$89$	−12117.7	−0.162160	−0.0810801	−	0.996708i	$-0.525837\pi$
$89$	−12117.7	−0.162160	−0.0810801	+	0.996708i	$0.525837\pi$
$90$	89458.8	1.16417
$91$	4658.01	0.0589653
$92$	19719.3	0.242896
$93$	−243573.	−2.92026
$94$	10603.4	0.123773
$95$	−45346.2	−0.515504
$96$	80340.3	0.889724
$97$	26058.0	0.281197	0.140599	−	0.990067i	$-0.455097\pi$
$97$	26058.0	0.281197	0.140599	+	0.990067i	$0.455097\pi$
$98$	21803.0	0.229325
$99$	0	0
$100$	4983.90	0.0498390
$101$	28978.9	0.282669	0.141335	−	0.989962i	$-0.454861\pi$
$101$	28978.9	0.282669	0.141335	+	0.989962i	$0.454861\pi$
$102$	−322507.	−3.06929
$103$	153033.	1.42132	0.710659	−	0.703537i	$-0.248397\pi$
$103$	153033.	1.42132	0.710659	+	0.703537i	$0.248397\pi$
$104$	−6121.92	−0.0555015
$105$	82183.7	0.727465
$106$	−9790.79	−0.0846356
$107$	98744.4	0.833783	0.416892	−	0.908956i	$-0.363119\pi$
$107$	98744.4	0.833783	0.416892	+	0.908956i	$0.363119\pi$
$108$	73251.5	0.604306
$109$	181305.	1.46165	0.730824	−	0.682566i	$-0.239136\pi$
$109$	181305.	1.46165	0.730824	+	0.682566i	$0.239136\pi$
$110$	0	0
$111$	−209264.	−1.61208
$112$	140497.	1.05833
$113$	261899.	1.92947	0.964734	−	0.263228i	$-0.0847870\pi$
$113$	261899.	1.92947	0.964734	+	0.263228i	$0.0847870\pi$
$114$	−326180.	−2.35069
$115$	−61821.7	−0.435910
$116$	−23013.0	−0.158792
$117$	−22809.4	−0.154045
$118$	−280491.	−1.85444
$119$	−207282.	−1.34182
$120$	−108012.	−0.684731
$121$	0	0
$122$	−122197.	−0.743293
$123$	209713.	1.24987
$124$	−68289.3	−0.398840
$125$	−15625.0	−0.0894427
$126$	413583.	2.32079
$127$	176690.	0.972080	0.486040	−	0.873937i	$-0.338441\pi$
$127$	176690.	0.972080	0.486040	+	0.873937i	$0.338441\pi$
$128$	−223414.	−1.20527
$129$	−648350.	−3.43033
$130$	−6370.17	−0.0330592
$131$	−171005.	−0.870624	−0.435312	−	0.900280i	$-0.643362\pi$
$131$	−171005.	−0.870624	−0.435312	+	0.900280i	$0.643362\pi$
$132$	0	0
$133$	−209643.	−1.02766
$134$	−329694.	−1.58617
$135$	−229650.	−1.08451
$136$	272427.	1.26300
$137$	339628.	1.54597	0.772987	−	0.634422i	$-0.218762\pi$
$137$	339628.	1.54597	0.772987	+	0.634422i	$0.218762\pi$
$138$	−444690.	−1.98774
$139$	−262788.	−1.15364	−0.576818	−	0.816873i	$-0.695706\pi$
$139$	−262788.	−1.15364	−0.576818	+	0.816873i	$0.695706\pi$
$140$	23041.4	0.0993548
$141$	−47700.2	−0.202056
$142$	−48138.6	−0.200342
$143$	0	0
$144$	−687985.	−2.76486
$145$	72147.8	0.284973
$146$	−225892.	−0.877038
$147$	−98082.5	−0.374368
$148$	−58670.2	−0.220173
$149$	224470.	0.828311	0.414155	−	0.910206i	$-0.364077\pi$
$149$	224470.	0.828311	0.414155	+	0.910206i	$0.364077\pi$
$150$	−112392.	−0.407857
$151$	193407.	0.690286	0.345143	−	0.938550i	$-0.387830\pi$
$151$	193407.	0.690286	0.345143	+	0.938550i	$0.387830\pi$
$152$	275530.	0.967296
$153$	1.01502e6	3.50548
$154$	0	0
$155$	214093.	0.715771
$156$	−9140.63	−0.0300722
$157$	−333959.	−1.08129	−0.540647	−	0.841250i	$-0.681820\pi$
$157$	−333959.	−1.08129	−0.540647	+	0.841250i	$0.681820\pi$
$158$	421450.	1.34309
$159$	44044.7	0.138166
$160$	−70616.7	−0.218076
$161$	−285812.	−0.868992
$162$	−782359.	−2.34217
$163$	13290.3	0.0391802	0.0195901	−	0.999808i	$-0.493764\pi$
$163$	13290.3	0.0391802	0.0195901	+	0.999808i	$0.493764\pi$
$164$	58796.2	0.170703
$165$	0	0
$166$	55275.1	0.155689
$167$	143469.	0.398076	0.199038	−	0.979992i	$-0.436218\pi$
$167$	143469.	0.398076	0.199038	+	0.979992i	$0.436218\pi$
$168$	−499359.	−1.36502
$169$	−369669.	−0.995626
$170$	283474.	0.752299
$171$	1.02658e6	2.68475
$172$	−181774.	−0.468502
$173$	−206434.	−0.524405	−0.262203	−	0.965013i	$-0.584449\pi$
$173$	−206434.	−0.524405	−0.262203	+	0.965013i	$0.584449\pi$
$174$	518966.	1.29947
$175$	−72237.0	−0.178305
$176$	0	0
$177$	1.26181e6	3.02734
$178$	76614.2	0.181242
$179$	512076.	1.19454	0.597272	−	0.802039i	$-0.296251\pi$
$179$	512076.	1.19454	0.597272	+	0.802039i	$0.296251\pi$
$180$	−112829.	−0.259562
$181$	−579632.	−1.31509	−0.657546	−	0.753414i	$-0.728405\pi$
$181$	−579632.	−1.31509	−0.657546	+	0.753414i	$0.728405\pi$
$182$	−29450.3	−0.0659040
$183$	549712.	1.21341
$184$	375637.	0.817945
$185$	183937.	0.395129
$186$	1.53999e6	3.26390
$187$	0	0
$188$	−13373.5	−0.0275962
$189$	−1.06171e6	−2.16198
$190$	286702.	0.576165
$191$	203162.	0.402957	0.201479	−	0.979493i	$-0.435425\pi$
$191$	203162.	0.402957	0.201479	+	0.979493i	$0.435425\pi$
$192$	598422.	1.17153
$193$	404312.	0.781311	0.390655	−	0.920537i	$-0.372248\pi$
$193$	404312.	0.781311	0.390655	+	0.920537i	$0.372248\pi$
$194$	−164752.	−0.314287
$195$	28656.7	0.0539685
$196$	−27498.9	−0.0511299
$197$	293541.	0.538894	0.269447	−	0.963015i	$-0.413159\pi$
$197$	293541.	0.538894	0.269447	+	0.963015i	$0.413159\pi$
$198$	0	0
$199$	−546251.	−0.977821	−0.488911	−	0.872334i	$-0.662606\pi$
$199$	−546251.	−0.977821	−0.488911	+	0.872334i	$0.662606\pi$
$200$	94939.6	0.167831
$201$	1.48315e6	2.58938
$202$	−183220.	−0.315932
$203$	333551.	0.568097
$204$	406760.	0.684325
$205$	−184332.	−0.306348
$206$	−967552.	−1.58857
$207$	1.39957e6	2.27022
$208$	48989.9	0.0785142
$209$	0	0
$210$	−519608.	−0.813069
$211$	872573.	1.34926	0.674630	−	0.738156i	$-0.264303\pi$
$211$	872573.	1.34926	0.674630	+	0.738156i	$0.264303\pi$
$212$	12348.6	0.0188702
$213$	216556.	0.327055
$214$	−624313.	−0.931898
$215$	569880.	0.840790
$216$	1.39539e6	2.03498
$217$	989789.	1.42690
$218$	−1.14630e6	−1.63365
$219$	1.01619e6	1.43175
$220$	0	0
$221$	−72277.6	−0.0995458
$222$	1.32308e6	1.80178
$223$	−541596.	−0.729312	−0.364656	−	0.931142i	$-0.618813\pi$
$223$	−541596.	−0.729312	−0.364656	+	0.931142i	$0.618813\pi$
$224$	−326473.	−0.434737
$225$	353731.	0.465818
$226$	−1.65586e6	−2.15652
$227$	171255.	0.220586	0.110293	−	0.993899i	$-0.464821\pi$
$227$	171255.	0.220586	0.110293	+	0.993899i	$0.464821\pi$
$228$	411393.	0.524106
$229$	1.39952e6	1.76356	0.881778	−	0.471664i	$-0.156346\pi$
$229$	1.39952e6	1.76356	0.881778	+	0.471664i	$0.156346\pi$
$230$	390869.	0.487205
$231$	0	0
$232$	−438380.	−0.534725
$233$	−62933.3	−0.0759435	−0.0379717	−	0.999279i	$-0.512090\pi$
$233$	−62933.3	−0.0759435	−0.0379717	+	0.999279i	$0.512090\pi$
$234$	144213.	0.172173
$235$	41927.0	0.0495250
$236$	353767.	0.413464
$237$	−1.89593e6	−2.19256
$238$	1.31055e6	1.49972
$239$	1.21874e6	1.38011	0.690057	−	0.723755i	$-0.257585\pi$
$239$	1.21874e6	1.38011	0.690057	+	0.723755i	$0.257585\pi$
$240$	864355.	0.968644
$241$	−366694.	−0.406687	−0.203344	−	0.979107i	$-0.565181\pi$
$241$	−366694.	−0.406687	−0.203344	+	0.979107i	$0.565181\pi$
$242$	0	0
$243$	1.28731e6	1.39851
$244$	154120.	0.165724
$245$	86211.6	0.0917594
$246$	−1.32592e6	−1.39694
$247$	−73100.7	−0.0762394
$248$	−1.30086e6	−1.34308
$249$	−248660.	−0.254160
$250$	98789.4	0.0999678
$251$	555490.	0.556534	0.278267	−	0.960504i	$-0.410240\pi$
$251$	555490.	0.556534	0.278267	+	0.960504i	$0.410240\pi$
$252$	−521629.	−0.517440
$253$	0	0
$254$	−1.11712e6	−1.08647
$255$	−1.27523e6	−1.22811
$256$	739264.	0.705018
$257$	−917109.	−0.866141	−0.433070	−	0.901360i	$-0.642570\pi$
$257$	−917109.	−0.866141	−0.433070	+	0.901360i	$0.642570\pi$
$258$	4.09921e6	3.83399
$259$	850370.	0.787696
$260$	8034.34	0.00737083
$261$	−1.63334e6	−1.48414
$262$	1.08118e6	0.973074
$263$	1.17971e6	1.05169	0.525844	−	0.850581i	$-0.323750\pi$
$263$	1.17971e6	1.05169	0.525844	+	0.850581i	$0.323750\pi$
$264$	0	0
$265$	−38714.0	−0.0338652
$266$	1.32547e6	1.14859
$267$	−344656.	−0.295874
$268$	415824.	0.353649
$269$	−1.16493e6	−0.981567	−0.490784	−	0.871282i	$-0.663289\pi$
$269$	−1.16493e6	−0.981567	−0.490784	+	0.871282i	$0.663289\pi$
$270$	1.45197e6	1.21213
$271$	−89750.0	−0.0742354	−0.0371177	−	0.999311i	$-0.511818\pi$
$271$	−89750.0	−0.0742354	−0.0371177	+	0.999311i	$0.511818\pi$
$272$	−2.18006e6	−1.78668
$273$	132485.	0.107587
$274$	−2.14730e6	−1.72789
$275$	0	0
$276$	560863.	0.443184
$277$	902270.	0.706541	0.353270	−	0.935521i	$-0.385070\pi$
$277$	902270.	0.706541	0.353270	+	0.935521i	$0.385070\pi$
$278$	1.66148e6	1.28939
$279$	−4.84681e6	−3.72774
$280$	438921.	0.334574
$281$	−1.10175e6	−0.832369	−0.416185	−	0.909280i	$-0.636633\pi$
$281$	−1.10175e6	−0.832369	−0.416185	+	0.909280i	$0.636633\pi$
$282$	301585.	0.225833
$283$	1.44900e6	1.07548	0.537740	−	0.843111i	$-0.319278\pi$
$283$	1.44900e6	1.07548	0.537740	+	0.843111i	$0.319278\pi$
$284$	60714.6	0.0446681
$285$	−1.28975e6	−0.940578
$286$	0	0
$287$	−852196.	−0.610710
$288$	1.59867e6	1.13574
$289$	1.79651e6	1.26528
$290$	−456156.	−0.318507
$291$	741151.	0.513067
$292$	284905.	0.195543
$293$	−447709.	−0.304668	−0.152334	−	0.988329i	$-0.548679\pi$
$293$	−447709.	−0.304668	−0.152334	+	0.988329i	$0.548679\pi$
$294$	620129.	0.418421
$295$	−1.10909e6	−0.742016
$296$	−1.11762e6	−0.741424
$297$	0	0
$298$	−1.41922e6	−0.925781
$299$	−99660.2	−0.0644680
$300$	141754.	0.0909352
$301$	2.63465e6	1.67613
$302$	−1.22282e6	−0.771515
$303$	824229.	0.515752
$304$	−2.20489e6	−1.36837
$305$	−483181.	−0.297413
$306$	−6.41750e6	−3.91798
$307$	1.24231e6	0.752290	0.376145	−	0.926561i	$-0.377249\pi$
$307$	1.24231e6	0.752290	0.376145	+	0.926561i	$0.377249\pi$
$308$	0	0
$309$	4.35262e6	2.59331
$310$	−1.35361e6	−0.799998
$311$	2.44658e6	1.43436	0.717181	−	0.696887i	$-0.245432\pi$
$311$	2.44658e6	1.43436	0.717181	+	0.696887i	$0.245432\pi$
$312$	−174122.	−0.101267
$313$	−2.28648e6	−1.31919	−0.659594	−	0.751622i	$-0.729272\pi$
$313$	−2.28648e6	−1.31919	−0.659594	+	0.751622i	$0.729272\pi$
$314$	2.11146e6	1.20853
$315$	1.63536e6	0.928615
$316$	−531552.	−0.299452
$317$	−1.71237e6	−0.957083	−0.478542	−	0.878065i	$-0.658834\pi$
$317$	−1.71237e6	−0.957083	−0.478542	+	0.878065i	$0.658834\pi$
$318$	−278474.	−0.154424
$319$	0	0
$320$	−525995.	−0.287148
$321$	2.80853e6	1.52130
$322$	1.80705e6	0.971250
$323$	3.25300e6	1.73491
$324$	986746.	0.522207
$325$	−25188.4	−0.0132279
$326$	−84028.4	−0.0437907
$327$	5.15674e6	2.66689
$328$	1.12002e6	0.574834
$329$	193836.	0.0987288
$330$	0	0
$331$	3.48374e6	1.74773	0.873867	−	0.486166i	$-0.161605\pi$
$331$	3.48374e6	1.74773	0.873867	+	0.486166i	$0.161605\pi$
$332$	−69715.4	−0.0347123
$333$	−4.16410e6	−2.05784
$334$	−907083.	−0.444919
$335$	−1.30365e6	−0.634671
$336$	3.99606e6	1.93100
$337$	−979949.	−0.470034	−0.235017	−	0.971991i	$-0.575515\pi$
$337$	−979949.	−0.470034	−0.235017	+	0.971991i	$0.575515\pi$
$338$	2.33724e6	1.11278
$339$	7.44903e6	3.52047
$340$	−357530.	−0.167732
$341$	0	0
$342$	−6.49059e6	−3.00067
$343$	2.34111e6	1.07445
$344$	−3.46267e6	−1.57766
$345$	−1.75836e6	−0.795352
$346$	1.30519e6	0.586114
$347$	−2.96242e6	−1.32076	−0.660378	−	0.750933i	$-0.729604\pi$
$347$	−2.96242e6	−1.32076	−0.660378	+	0.750933i	$0.729604\pi$
$348$	−654544.	−0.289728
$349$	−3.50510e6	−1.54041	−0.770207	−	0.637794i	$-0.779847\pi$
$349$	−3.50510e6	−1.54041	−0.770207	+	0.637794i	$0.779847\pi$
$350$	456720.	0.199287
$351$	−370210.	−0.160391
$352$	0	0
$353$	1.36459e6	0.582860	0.291430	−	0.956592i	$-0.405869\pi$
$353$	1.36459e6	0.582860	0.291430	+	0.956592i	$0.405869\pi$
$354$	−7.97782e6	−3.38358
$355$	−190346.	−0.0801628
$356$	−96629.3	−0.0404095
$357$	−5.89560e6	−2.44826
$358$	−3.23761e6	−1.33511
$359$	−264000.	−0.108110	−0.0540552	−	0.998538i	$-0.517215\pi$
$359$	−264000.	−0.108110	−0.0540552	+	0.998538i	$0.517215\pi$
$360$	−2.14932e6	−0.874065
$361$	813948.	0.328722
$362$	3.66474e6	1.46984
$363$	0	0
$364$	37144.1	0.0146939
$365$	−893204.	−0.350928
$366$	−3.47557e6	−1.35620
$367$	4.56469e6	1.76907	0.884537	−	0.466470i	$-0.154474\pi$
$367$	4.56469e6	1.76907	0.884537	+	0.466470i	$0.154474\pi$
$368$	−3.00599e6	−1.15709
$369$	4.17304e6	1.59546
$370$	−1.16294e6	−0.441626
$371$	−178981.	−0.0675107
$372$	−1.94231e6	−0.727715
$373$	693510.	0.258096	0.129048	−	0.991638i	$-0.458808\pi$
$373$	693510.	0.258096	0.129048	+	0.991638i	$0.458808\pi$
$374$	0	0
$375$	−444412.	−0.163195
$376$	−254754.	−0.0929291
$377$	116306.	0.0421454
$378$	6.71269e6	2.41639
$379$	−10054.6	−0.00359558	−0.00179779	−	0.999998i	$-0.500572\pi$
$379$	−10054.6	−0.00359558	−0.00179779	+	0.999998i	$0.500572\pi$
$380$	−361602.	−0.128461
$381$	5.02548e6	1.77364
$382$	−1.28450e6	−0.450375
$383$	−1.93772e6	−0.674986	−0.337493	−	0.941328i	$-0.609579\pi$
$383$	−1.93772e6	−0.674986	−0.337493	+	0.941328i	$0.609579\pi$
$384$	−6.35442e6	−2.19911
$385$	0	0
$386$	−2.55627e6	−0.873250
$387$	−1.29014e7	−4.37884
$388$	207793.	0.0700730
$389$	2.53186e6	0.848333	0.424166	−	0.905584i	$-0.360567\pi$
$389$	2.53186e6	0.848333	0.424166	+	0.905584i	$0.360567\pi$
$390$	−181183.	−0.0603192
$391$	4.43490e6	1.46704
$392$	−523833.	−0.172178
$393$	−4.86379e6	−1.58852
$394$	−1.85592e6	−0.602307
$395$	1.66646e6	0.537407
$396$	0	0
$397$	−652266.	−0.207706	−0.103853	−	0.994593i	$-0.533117\pi$
$397$	−652266.	−0.207706	−0.103853	+	0.994593i	$0.533117\pi$
$398$	3.45368e6	1.09289
$399$	−5.96275e6	−1.87506
$400$	−759742.	−0.237419
$401$	1.23788e6	0.384431	0.192216	−	0.981353i	$-0.438433\pi$
$401$	1.23788e6	0.384431	0.192216	+	0.981353i	$0.438433\pi$
$402$	−9.37727e6	−2.89409
$403$	345131.	0.105857
$404$	231085.	0.0704397
$405$	−3.09354e6	−0.937170
$406$	−2.10888e6	−0.634947
$407$	0	0
$408$	7.74847e6	2.30444
$409$	4.93612e6	1.45907	0.729537	−	0.683941i	$-0.239736\pi$
$409$	4.93612e6	1.45907	0.729537	+	0.683941i	$0.239736\pi$
$410$	1.16544e6	0.342398
$411$	9.65983e6	2.82075
$412$	1.22032e6	0.354185
$413$	−5.12752e6	−1.47922
$414$	−8.84880e6	−2.53737
$415$	218564.	0.0622958
$416$	−113838.	−0.0322518
$417$	−7.47432e6	−2.10490
$418$	0	0
$419$	−5.51510e6	−1.53468	−0.767341	−	0.641239i	$-0.778421\pi$
$419$	−5.51510e6	−1.53468	−0.767341	+	0.641239i	$0.778421\pi$
$420$	655352.	0.181281
$421$	−1.51550e6	−0.416727	−0.208364	−	0.978051i	$-0.566814\pi$
$421$	−1.51550e6	−0.416727	−0.208364	+	0.978051i	$0.566814\pi$
$422$	−5.51686e6	−1.50803
$423$	−949177.	−0.257927
$424$	235231.	0.0635449
$425$	1.12089e6	0.301017
$426$	−1.36918e6	−0.365541
$427$	−2.23382e6	−0.592897
$428$	787412.	0.207775
$429$	0	0
$430$	−3.60308e6	−0.939729
$431$	−5.55099e6	−1.43939	−0.719693	−	0.694293i	$-0.755717\pi$
$431$	−5.55099e6	−1.43939	−0.719693	+	0.694293i	$0.755717\pi$
$432$	−1.11664e7	−2.87875
$433$	−3.52967e6	−0.904722	−0.452361	−	0.891835i	$-0.649418\pi$
$433$	−3.52967e6	−0.904722	−0.452361	+	0.891835i	$0.649418\pi$
$434$	−6.25796e6	−1.59481
$435$	2.05206e6	0.519955
$436$	1.44577e6	0.364235
$437$	4.48541e6	1.12357
$438$	−6.42490e6	−1.60023
$439$	−2.84748e6	−0.705179	−0.352589	−	0.935778i	$-0.614699\pi$
$439$	−2.84748e6	−0.705179	−0.352589	+	0.935778i	$0.614699\pi$
$440$	0	0
$441$	−1.95172e6	−0.477884
$442$	456976.	0.111260
$443$	−735978.	−0.178179	−0.0890893	−	0.996024i	$-0.528396\pi$
$443$	−735978.	−0.178179	−0.0890893	+	0.996024i	$0.528396\pi$
$444$	−1.66872e6	−0.401723
$445$	302942.	0.0725202
$446$	3.42425e6	0.815133
$447$	6.38447e6	1.51132
$448$	−2.43176e6	−0.572434
$449$	2.63635e6	0.617145	0.308572	−	0.951201i	$-0.400149\pi$
$449$	2.63635e6	0.617145	0.308572	+	0.951201i	$0.400149\pi$
$450$	−2.23647e6	−0.520633
$451$	0	0
$452$	2.08844e6	0.480814
$453$	5.50095e6	1.25948
$454$	−1.08276e6	−0.246543
$455$	−116450.	−0.0263701
$456$	7.83672e6	1.76491
$457$	−3.52607e6	−0.789769	−0.394885	−	0.918731i	$-0.629215\pi$
$457$	−3.52607e6	−0.789769	−0.394885	+	0.918731i	$0.629215\pi$
$458$	−8.84847e6	−1.97108
$459$	1.64744e7	3.64988
$460$	−492981.	−0.108627
$461$	3.10340e6	0.680120	0.340060	−	0.940404i	$-0.389553\pi$
$461$	3.10340e6	0.680120	0.340060	+	0.940404i	$0.389553\pi$
$462$	0	0
$463$	4.73279e6	1.02604	0.513021	−	0.858376i	$-0.328526\pi$
$463$	4.73279e6	1.02604	0.513021	+	0.858376i	$0.328526\pi$
$464$	3.50808e6	0.756440
$465$	6.08933e6	1.30598
$466$	397897.	0.0848801
$467$	−1.08142e6	−0.229458	−0.114729	−	0.993397i	$-0.536600\pi$
$467$	−1.08142e6	−0.229458	−0.114729	+	0.993397i	$0.536600\pi$
$468$	−181888.	−0.0383874
$469$	−6.02698e6	−1.26522
$470$	−265085.	−0.0553528
$471$	−9.49858e6	−1.97291
$472$	6.73900e6	1.39232
$473$	0	0
$474$	1.19870e7	2.45057
$475$	1.13366e6	0.230540
$476$	−1.65292e6	−0.334375
$477$	876437.	0.176370
$478$	−7.70549e6	−1.54252
$479$	71998.1	0.0143378	0.00716890	−	0.999974i	$-0.497718\pi$
$479$	71998.1	0.0143378	0.00716890	+	0.999974i	$0.497718\pi$
$480$	−2.00851e6	−0.397896
$481$	296517.	0.0584368
$482$	2.31843e6	0.454544
$483$	−8.12918e6	−1.58555
$484$	0	0
$485$	−651449.	−0.125755
$486$	−8.13902e6	−1.56308
$487$	−2.26049e6	−0.431898	−0.215949	−	0.976405i	$-0.569284\pi$
$487$	−2.26049e6	−0.431898	−0.215949	+	0.976405i	$0.569284\pi$
$488$	2.93587e6	0.558068
$489$	378009.	0.0714875
$490$	−545074.	−0.102557
$491$	−680974.	−0.127476	−0.0637378	−	0.997967i	$-0.520302\pi$
$491$	−680974.	−0.127476	−0.0637378	+	0.997967i	$0.520302\pi$
$492$	1.67231e6	0.311460
$493$	−5.17566e6	−0.959066
$494$	462181.	0.0852108
$495$	0	0
$496$	1.04100e7	1.89996
$497$	−880001.	−0.159806
$498$	1.57215e6	0.284068
$499$	−5.86965e6	−1.05526	−0.527632	−	0.849473i	$-0.676920\pi$
$499$	−5.86965e6	−1.05526	−0.527632	+	0.849473i	$0.676920\pi$
$500$	−124598.	−0.0222887
$501$	4.08059e6	0.726321
$502$	−3.51209e6	−0.622024
$503$	−9.74322e6	−1.71705	−0.858524	−	0.512773i	$-0.828618\pi$
$503$	−9.74322e6	−1.71705	−0.858524	+	0.512773i	$0.828618\pi$
$504$	−9.93664e6	−1.74246
$505$	−724472.	−0.126413
$506$	0	0
$507$	−1.05143e7	−1.81660
$508$	1.40897e6	0.242237
$509$	7.64806e6	1.30845	0.654225	−	0.756300i	$-0.272995\pi$
$509$	7.64806e6	1.30845	0.654225	+	0.756300i	$0.272995\pi$
$510$	8.06267e6	1.37263
$511$	−4.12943e6	−0.699581
$512$	2.47523e6	0.417292
$513$	1.66620e7	2.79534
$514$	5.79844e6	0.968063
$515$	−3.82582e6	−0.635633
$516$	−5.17010e6	−0.854820
$517$	0	0
$518$	−5.37648e6	−0.880387
$519$	−5.87149e6	−0.956819
$520$	153048.	0.0248210
$521$	−1.81174e6	−0.292416	−0.146208	−	0.989254i	$-0.546707\pi$
$521$	−1.81174e6	−0.292416	−0.146208	+	0.989254i	$0.546707\pi$
$522$	1.03268e7	1.65878
$523$	5.43513e6	0.868872	0.434436	−	0.900703i	$-0.356948\pi$
$523$	5.43513e6	0.868872	0.434436	+	0.900703i	$0.356948\pi$
$524$	−1.36364e6	−0.216955
$525$	−2.05459e6	−0.325332
$526$	−7.45875e6	−1.17544
$527$	−1.53584e7	−2.40890
$528$	0	0
$529$	−321260.	−0.0499134
$530$	244770.	0.0378502
$531$	2.51085e7	3.86442
$532$	−1.67174e6	−0.256089
$533$	−297154.	−0.0453067
$534$	2.17909e6	0.330691
$535$	−2.46861e6	−0.372879
$536$	7.92114e6	1.19090
$537$	1.45647e7	2.17954
$538$	7.36531e6	1.09707
$539$	0	0
$540$	−1.83129e6	−0.270254
$541$	6.05948e6	0.890108	0.445054	−	0.895504i	$-0.353185\pi$
$541$	6.05948e6	0.890108	0.445054	+	0.895504i	$0.353185\pi$
$542$	567446.	0.0829710
$543$	−1.64861e7	−2.39949
$544$	5.06582e6	0.733927
$545$	−4.53262e6	−0.653669
$546$	−837638.	−0.120247
$547$	−7.68998e6	−1.09890	−0.549449	−	0.835528i	$-0.685162\pi$
$547$	−7.68998e6	−1.09890	−0.549449	+	0.835528i	$0.685162\pi$
$548$	2.70827e6	0.385249
$549$	1.09386e7	1.54893
$550$	0	0
$551$	−5.23461e6	−0.734523
$552$	1.06840e7	1.49241
$553$	7.70434e6	1.07133
$554$	−5.70462e6	−0.789682
$555$	5.23160e6	0.720945
$556$	−2.09554e6	−0.287480
$557$	5.42049e6	0.740287	0.370144	−	0.928975i	$-0.379308\pi$
$557$	5.42049e6	0.740287	0.370144	+	0.928975i	$0.379308\pi$
$558$	3.06440e7	4.16640
$559$	918680.	0.124347
$560$	−3.51241e6	−0.473299
$561$	0	0
$562$	6.96581e6	0.930317
$563$	−1.00596e7	−1.33755	−0.668777	−	0.743463i	$-0.733182\pi$
$563$	−1.00596e7	−1.33755	−0.668777	+	0.743463i	$0.733182\pi$
$564$	−380373.	−0.0503514
$565$	−6.54747e6	−0.862884
$566$	−9.16133e6	−1.20204
$567$	−1.43020e7	−1.86826
$568$	1.15657e6	0.150418
$569$	−8.25019e6	−1.06828	−0.534138	−	0.845397i	$-0.679364\pi$
$569$	−8.25019e6	−1.06828	−0.534138	+	0.845397i	$0.679364\pi$
$570$	8.15450e6	1.05126
$571$	−4.66309e6	−0.598526	−0.299263	−	0.954171i	$-0.596741\pi$
$571$	−4.66309e6	−0.598526	−0.299263	+	0.954171i	$0.596741\pi$
$572$	0	0
$573$	5.77841e6	0.735228
$574$	5.38803e6	0.682574
$575$	1.54554e6	0.194945
$576$	1.19079e7	1.49547
$577$	−2.64513e6	−0.330755	−0.165378	−	0.986230i	$-0.552884\pi$
$577$	−2.64513e6	−0.330755	−0.165378	+	0.986230i	$0.552884\pi$
$578$	−1.13585e7	−1.41416
$579$	1.14996e7	1.42556
$580$	575324.	0.0710138
$581$	1.01046e6	0.124188
$582$	−4.68594e6	−0.573442
$583$	0	0
$584$	5.42722e6	0.658485
$585$	570235.	0.0688912
$586$	2.83065e6	0.340519
$587$	−9.66682e6	−1.15795	−0.578973	−	0.815346i	$-0.696546\pi$
$587$	−9.66682e6	−1.15795	−0.578973	+	0.815346i	$0.696546\pi$
$588$	−782134.	−0.0932906
$589$	−1.55333e7	−1.84491
$590$	7.01226e6	0.829332
$591$	8.34900e6	0.983254
$592$	8.94365e6	1.04884
$593$	−5.91513e6	−0.690760	−0.345380	−	0.938463i	$-0.612250\pi$
$593$	−5.91513e6	−0.690760	−0.345380	+	0.938463i	$0.612250\pi$
$594$	0	0
$595$	5.18206e6	0.600081
$596$	1.78998e6	0.206411
$597$	−1.55367e7	−1.78411
$598$	630104.	0.0720542
$599$	−3.97320e6	−0.452453	−0.226227	−	0.974075i	$-0.572639\pi$
$599$	−3.97320e6	−0.452453	−0.226227	+	0.974075i	$0.572639\pi$
$600$	2.70031e6	0.306221
$601$	9.46810e6	1.06924	0.534622	−	0.845091i	$-0.320454\pi$
$601$	9.46810e6	1.06924	0.534622	+	0.845091i	$0.320454\pi$
$602$	−1.66576e7	−1.87336
$603$	2.95130e7	3.30537
$604$	1.54227e6	0.172016
$605$	0	0
$606$	−5.21120e6	−0.576443
$607$	1.06710e7	1.17553	0.587764	−	0.809033i	$-0.300008\pi$
$607$	1.06710e7	1.17553	0.587764	+	0.809033i	$0.300008\pi$
$608$	5.12352e6	0.562094
$609$	9.48699e6	1.03654
$610$	3.05492e6	0.332411
$611$	67588.8	0.00732440
$612$	8.09403e6	0.873547
$613$	9.84284e6	1.05796	0.528980	−	0.848634i	$-0.322575\pi$
$613$	9.84284e6	1.05796	0.528980	+	0.848634i	$0.322575\pi$
$614$	−7.85455e6	−0.840815
$615$	−5.24284e6	−0.558957
$616$	0	0
$617$	1.26350e7	1.33618	0.668088	−	0.744082i	$-0.267113\pi$
$617$	1.26350e7	1.33618	0.668088	+	0.744082i	$0.267113\pi$
$618$	−2.75195e7	−2.89847
$619$	3.82798e6	0.401553	0.200777	−	0.979637i	$-0.435653\pi$
$619$	3.82798e6	0.401553	0.200777	+	0.979637i	$0.435653\pi$
$620$	1.70723e6	0.178366
$621$	2.27158e7	2.36374
$622$	−1.54686e7	−1.60315
$623$	1.40055e6	0.144570
$624$	1.39339e6	0.143256
$625$	390625.	0.0400000
$626$	1.44563e7	1.47442
$627$	0	0
$628$	−2.66307e6	−0.269453
$629$	−1.31951e7	−1.32979
$630$	−1.03396e7	−1.03789
$631$	−7.61882e6	−0.761753	−0.380877	−	0.924626i	$-0.624378\pi$
$631$	−7.61882e6	−0.761753	−0.380877	+	0.924626i	$0.624378\pi$
$632$	−1.01257e7	−1.00840
$633$	2.48181e7	2.46183
$634$	1.08265e7	1.06971
$635$	−4.41724e6	−0.434727
$636$	351223.	0.0344303
$637$	138978.	0.0135706
$638$	0	0
$639$	4.30920e6	0.417488
$640$	5.58534e6	0.539014
$641$	9.96098e6	0.957540	0.478770	−	0.877940i	$-0.341083\pi$
$641$	9.96098e6	0.957540	0.478770	+	0.877940i	$0.341083\pi$
$642$	−1.77570e7	−1.70032
$643$	−3.19476e6	−0.304727	−0.152364	−	0.988325i	$-0.548688\pi$
$643$	−3.19476e6	−0.304727	−0.152364	+	0.988325i	$0.548688\pi$
$644$	−2.27913e6	−0.216549
$645$	1.62088e7	1.53409
$646$	−2.05671e7	−1.93907
$647$	−6.36474e6	−0.597751	−0.298875	−	0.954292i	$-0.596611\pi$
$647$	−6.36474e6	−0.597751	−0.298875	+	0.954292i	$0.596611\pi$
$648$	1.87968e7	1.75851
$649$	0	0
$650$	159254.	0.0147845
$651$	2.81520e7	2.60349
$652$	105980.	0.00976352
$653$	−5.79812e6	−0.532113	−0.266057	−	0.963957i	$-0.585721\pi$
$653$	−5.79812e6	−0.532113	−0.266057	+	0.963957i	$0.585721\pi$
$654$	−3.26036e7	−2.98072
$655$	4.27513e6	0.389355
$656$	−8.96285e6	−0.813180
$657$	2.02210e7	1.82764
$658$	−1.22553e6	−0.110347
$659$	1.88680e7	1.69244	0.846220	−	0.532834i	$-0.178873\pi$
$659$	1.88680e7	1.69244	0.846220	+	0.532834i	$0.178873\pi$
$660$	0	0
$661$	−3.12520e6	−0.278211	−0.139105	−	0.990278i	$-0.544423\pi$
$661$	−3.12520e6	−0.278211	−0.139105	+	0.990278i	$0.544423\pi$
$662$	−2.20260e7	−1.95340
$663$	−2.05575e6	−0.181629
$664$	−1.32803e6	−0.116892
$665$	5.24108e6	0.459586
$666$	2.63276e7	2.29999
$667$	−7.13649e6	−0.621112
$668$	1.14405e6	0.0991985
$669$	−1.54043e7	−1.33069
$670$	8.24234e6	0.709355
$671$	0	0
$672$	−9.28566e6	−0.793212
$673$	−6.27963e6	−0.534437	−0.267218	−	0.963636i	$-0.586104\pi$
$673$	−6.27963e6	−0.534437	−0.267218	+	0.963636i	$0.586104\pi$
$674$	6.19575e6	0.525344
$675$	5.74126e6	0.485007
$676$	−2.94783e6	−0.248105
$677$	−9.20532e6	−0.771911	−0.385956	−	0.922517i	$-0.626128\pi$
$677$	−9.20532e6	−0.771911	−0.385956	+	0.922517i	$0.626128\pi$
$678$	−4.70966e7	−3.93473
$679$	−3.01176e6	−0.250695
$680$	−6.81067e6	−0.564830
$681$	4.87090e6	0.402477
$682$	0	0
$683$	−7.43020e6	−0.609465	−0.304732	−	0.952438i	$-0.598567\pi$
$683$	−7.43020e6	−0.609465	−0.304732	+	0.952438i	$0.598567\pi$
$684$	8.18622e6	0.669026
$685$	−8.49070e6	−0.691380
$686$	−1.48017e7	−1.20089
$687$	3.98056e7	3.21775
$688$	2.77096e7	2.23182
$689$	−62409.2	−0.00500842
$690$	1.11172e7	0.888944
$691$	1.58376e7	1.26181	0.630905	−	0.775860i	$-0.282684\pi$
$691$	1.58376e7	1.26181	0.630905	+	0.775860i	$0.282684\pi$
$692$	−1.64616e6	−0.130679
$693$	0	0
$694$	1.87299e7	1.47617
$695$	6.56970e6	0.515922
$696$	−1.24686e7	−0.975648
$697$	1.32234e7	1.03101
$698$	2.21611e7	1.72168
$699$	−1.78997e6	−0.138565
$700$	−576035.	−0.0444328
$701$	−1.88996e7	−1.45264	−0.726319	−	0.687358i	$-0.758770\pi$
$701$	−1.88996e7	−1.45264	−0.726319	+	0.687358i	$0.758770\pi$
$702$	2.34066e6	0.179265
$703$	−1.33453e7	−1.01845
$704$	0	0
$705$	1.19251e6	0.0903623
$706$	−8.62762e6	−0.651447
$707$	−3.34936e6	−0.252007
$708$	1.00620e7	0.754398
$709$	1.14546e7	0.855782	0.427891	−	0.903830i	$-0.359257\pi$
$709$	1.14546e7	0.855782	0.427891	+	0.903830i	$0.359257\pi$
$710$	1.20347e6	0.0895958
$711$	−3.77267e7	−2.79882
$712$	−1.84071e6	−0.136078
$713$	−2.11770e7	−1.56006
$714$	3.72751e7	2.73636
$715$	0	0
$716$	4.08342e6	0.297674
$717$	3.46638e7	2.51813
$718$	1.66915e6	0.120832
$719$	1.34891e7	0.973111	0.486555	−	0.873650i	$-0.338253\pi$
$719$	1.34891e7	0.973111	0.486555	+	0.873650i	$0.338253\pi$
$720$	1.71996e7	1.23648
$721$	−1.76874e7	−1.26714
$722$	−5.14620e6	−0.367404
$723$	−1.04296e7	−0.742033
$724$	−4.62213e6	−0.327714
$725$	−1.80370e6	−0.127444
$726$	0	0
$727$	−1.25723e6	−0.0882220	−0.0441110	−	0.999027i	$-0.514046\pi$
$727$	−1.25723e6	−0.0882220	−0.0441110	+	0.999027i	$0.514046\pi$
$728$	707567.	0.0494811
$729$	6.54484e6	0.456121
$730$	5.64730e6	0.392223
$731$	−4.08815e7	−2.82965
$732$	4.38354e6	0.302376
$733$	1.21453e7	0.834928	0.417464	−	0.908694i	$-0.362919\pi$
$733$	1.21453e7	0.834928	0.417464	+	0.908694i	$0.362919\pi$
$734$	−2.88603e7	−1.97725
$735$	2.45206e6	0.167422
$736$	6.98503e6	0.475307
$737$	0	0
$738$	−2.63842e7	−1.78321
$739$	9.29090e6	0.625816	0.312908	−	0.949783i	$-0.398697\pi$
$739$	9.29090e6	0.625816	0.312908	+	0.949783i	$0.398697\pi$
$740$	1.46676e6	0.0984642
$741$	−2.07916e6	−0.139105
$742$	1.13161e6	0.0754549
$743$	−9.94361e6	−0.660803	−0.330402	−	0.943840i	$-0.607184\pi$
$743$	−9.94361e6	−0.660803	−0.330402	+	0.943840i	$0.607184\pi$
$744$	−3.69995e7	−2.45055
$745$	−5.61176e6	−0.370432
$746$	−4.38473e6	−0.288467
$747$	−4.94803e6	−0.324437
$748$	0	0
$749$	−1.14128e7	−0.743340
$750$	2.80980e6	0.182399
$751$	−778264.	−0.0503532	−0.0251766	−	0.999683i	$-0.508015\pi$
$751$	−778264.	−0.0503532	−0.0251766	+	0.999683i	$0.508015\pi$
$752$	2.03864e6	0.131461
$753$	1.57995e7	1.01544
$754$	−735350.	−0.0471049
$755$	−4.83517e6	−0.308705
$756$	−8.46634e6	−0.538755
$757$	9.35901e6	0.593595	0.296798	−	0.954940i	$-0.404081\pi$
$757$	9.35901e6	0.593595	0.296798	+	0.954940i	$0.404081\pi$
$758$	63570.7	0.00401869
$759$	0	0
$760$	−6.88824e6	−0.432588
$761$	−3.06947e6	−0.192133	−0.0960665	−	0.995375i	$-0.530626\pi$
$761$	−3.06947e6	−0.192133	−0.0960665	+	0.995375i	$0.530626\pi$
$762$	−3.17737e7	−1.98235
$763$	−2.09550e7	−1.30310
$764$	1.62006e6	0.100415
$765$	−2.53756e7	−1.56770
$766$	1.22513e7	0.754414
$767$	−1.78792e6	−0.109739
$768$	2.10264e7	1.28636
$769$	8.33061e6	0.507997	0.253998	−	0.967205i	$-0.418254\pi$
$769$	8.33061e6	0.507997	0.253998	+	0.967205i	$0.418254\pi$
$770$	0	0
$771$	−2.60848e7	−1.58034
$772$	3.22408e6	0.194699
$773$	−5.21228e6	−0.313746	−0.156873	−	0.987619i	$-0.550141\pi$
$773$	−5.21228e6	−0.313746	−0.156873	+	0.987619i	$0.550141\pi$
$774$	8.15693e7	4.89412
$775$	−5.35233e6	−0.320102
$776$	3.95829e6	0.235968
$777$	2.41865e7	1.43721
$778$	−1.60078e7	−0.948160
$779$	1.33740e7	0.789619
$780$	228516.	0.0134487
$781$	0	0
$782$	−2.80397e7	−1.63967
$783$	−2.65100e7	−1.54528
$784$	4.19191e6	0.243569
$785$	8.34897e6	0.483569
$786$	3.07514e7	1.77545
$787$	1.22408e7	0.704489	0.352245	−	0.935908i	$-0.385418\pi$
$787$	1.22408e7	0.704489	0.352245	+	0.935908i	$0.385418\pi$
$788$	2.34077e6	0.134290
$789$	3.35538e7	1.91889
$790$	−1.05363e7	−0.600646
$791$	−3.02700e7	−1.72017
$792$	0	0
$793$	−778915.	−0.0439853
$794$	4.12396e6	0.232147
$795$	−1.10112e6	−0.0617897
$796$	−4.35594e6	−0.243668
$797$	−1.91244e7	−1.06646	−0.533228	−	0.845972i	$-0.679021\pi$
$797$	−1.91244e7	−1.06646	−0.533228	+	0.845972i	$0.679021\pi$
$798$	3.76996e7	2.09570
$799$	−3.00772e6	−0.166675
$800$	1.76542e6	0.0975264
$801$	−6.85823e6	−0.377686
$802$	−7.82654e6	−0.429669
$803$	0	0
$804$	1.18270e7	0.645261
$805$	7.14530e6	0.388625
$806$	−2.18210e6	−0.118314
$807$	−3.31335e7	−1.79095
$808$	4.40199e6	0.237203
$809$	1.96698e6	0.105664	0.0528321	−	0.998603i	$-0.483175\pi$
$809$	1.96698e6	0.105664	0.0528321	+	0.998603i	$0.483175\pi$
$810$	1.95590e7	1.04745
$811$	−1.53296e7	−0.818425	−0.409212	−	0.912439i	$-0.634197\pi$
$811$	−1.53296e7	−0.818425	−0.409212	+	0.912439i	$0.634197\pi$
$812$	2.65982e6	0.141567
$813$	−2.55270e6	−0.135448
$814$	0	0
$815$	−332259.	−0.0175219
$816$	−6.20062e7	−3.25994
$817$	−4.13471e7	−2.16715
$818$	−3.12087e7	−1.63077
$819$	2.63629e6	0.137336
$820$	−1.46991e6	−0.0763405
$821$	6.69458e6	0.346629	0.173315	−	0.984867i	$-0.444552\pi$
$821$	6.69458e6	0.346629	0.173315	+	0.984867i	$0.444552\pi$
$822$	−6.10744e7	−3.15268
$823$	−2.15046e7	−1.10671	−0.553353	−	0.832947i	$-0.686652\pi$
$823$	−2.15046e7	−1.10671	−0.553353	+	0.832947i	$0.686652\pi$
$824$	2.32462e7	1.19271
$825$	0	0
$826$	3.24189e7	1.65328
$827$	9.77934e6	0.497217	0.248608	−	0.968604i	$-0.420027\pi$
$827$	9.77934e6	0.497217	0.248608	+	0.968604i	$0.420027\pi$
$828$	1.11605e7	0.565728
$829$	2.35297e7	1.18913	0.594566	−	0.804047i	$-0.297324\pi$
$829$	2.35297e7	1.18913	0.594566	+	0.804047i	$0.297324\pi$
$830$	−1.38188e6	−0.0696264
$831$	2.56627e7	1.28914
$832$	−847934.	−0.0424672
$833$	−6.18456e6	−0.308813
$834$	4.72565e7	2.35259
$835$	−3.58672e6	−0.178025
$836$	0	0
$837$	−7.86666e7	−3.88130
$838$	3.48693e7	1.71527
$839$	2.93448e7	1.43921	0.719607	−	0.694381i	$-0.244322\pi$
$839$	2.93448e7	1.43921	0.719607	+	0.694381i	$0.244322\pi$
$840$	1.24840e7	0.610456
$841$	−1.21827e7	−0.593953
$842$	9.58180e6	0.465765
$843$	−3.13363e7	−1.51872
$844$	6.95811e6	0.336229
$845$	9.24172e6	0.445257
$846$	6.00119e6	0.288278
$847$	0	0
$848$	−1.88241e6	−0.0898927
$849$	4.12130e7	1.96230
$850$	−7.08684e6	−0.336438
$851$	−1.81941e7	−0.861203
$852$	1.72687e6	0.0815004
$853$	−1.18462e7	−0.557451	−0.278725	−	0.960371i	$-0.589912\pi$
$853$	−1.18462e7	−0.557451	−0.278725	+	0.960371i	$0.589912\pi$
$854$	1.41234e7	0.662665
$855$	−2.56646e7	−1.20066
$856$	1.49996e7	0.699673
$857$	2.32639e7	1.08201	0.541004	−	0.841020i	$-0.318044\pi$
$857$	2.32639e7	1.08201	0.541004	+	0.841020i	$0.318044\pi$
$858$	0	0
$859$	2.67804e7	1.23832	0.619161	−	0.785264i	$-0.287473\pi$
$859$	2.67804e7	1.23832	0.619161	+	0.785264i	$0.287473\pi$
$860$	4.54436e6	0.209521
$861$	−2.42385e7	−1.11429
$862$	3.50962e7	1.60876
$863$	−3.35578e7	−1.53379	−0.766895	−	0.641772i	$-0.778199\pi$
$863$	−3.35578e7	−1.53379	−0.766895	+	0.641772i	$0.778199\pi$
$864$	2.59474e7	1.18252
$865$	5.16086e6	0.234521
$866$	2.23164e7	1.01118
$867$	5.10970e7	2.30860
$868$	7.89281e6	0.355576
$869$	0	0
$870$	−1.29742e7	−0.581141
$871$	−2.10156e6	−0.0938633
$872$	2.75408e7	1.22655
$873$	1.47480e7	0.654934
$874$	−2.83591e7	−1.25578
$875$	1.80592e6	0.0797406
$876$	8.10337e6	0.356784
$877$	5.75227e6	0.252546	0.126273	−	0.991996i	$-0.459698\pi$
$877$	5.75227e6	0.252546	0.126273	+	0.991996i	$0.459698\pi$
$878$	1.80032e7	0.788160
$879$	−1.27339e7	−0.555891
$880$	0	0
$881$	−1.27804e7	−0.554758	−0.277379	−	0.960761i	$-0.589466\pi$
$881$	−1.27804e7	−0.554758	−0.277379	+	0.960761i	$0.589466\pi$
$882$	1.23398e7	0.534118
$883$	−3.73344e7	−1.61142	−0.805708	−	0.592313i	$-0.798215\pi$
$883$	−3.73344e7	−1.61142	−0.805708	+	0.592313i	$0.798215\pi$
$884$	−576359.	−0.0248063
$885$	−3.15453e7	−1.35387
$886$	4.65324e6	0.199146
$887$	2.00040e7	0.853703	0.426852	−	0.904322i	$-0.359623\pi$
$887$	2.00040e7	0.853703	0.426852	+	0.904322i	$0.359623\pi$
$888$	−3.17879e7	−1.35279
$889$	−2.04216e7	−0.866635
$890$	−1.91536e6	−0.0810540
$891$	0	0
$892$	−4.31882e6	−0.181741
$893$	−3.04197e6	−0.127652
$894$	−4.03659e7	−1.68916
$895$	−1.28019e7	−0.534216
$896$	2.58220e7	1.07453
$897$	−2.83457e6	−0.117627
$898$	−1.66684e7	−0.689767
$899$	2.47142e7	1.01988
$900$	2.82073e6	0.116080
$901$	2.77722e6	0.113972
$902$	0	0
$903$	7.49358e7	3.05823
$904$	3.97833e7	1.61912
$905$	1.44908e7	0.588127
$906$	−3.47798e7	−1.40769
$907$	2.63834e7	1.06491	0.532455	−	0.846459i	$-0.321270\pi$
$907$	2.63834e7	1.06491	0.532455	+	0.846459i	$0.321270\pi$
$908$	1.36563e6	0.0549690
$909$	1.64012e7	0.658362
$910$	736258.	0.0294732
$911$	2.04638e7	0.816939	0.408470	−	0.912772i	$-0.366063\pi$
$911$	2.04638e7	0.816939	0.408470	+	0.912772i	$0.366063\pi$
$912$	−6.27124e7	−2.49670
$913$	0	0
$914$	2.22936e7	0.882704
$915$	−1.37428e7	−0.542654
$916$	1.11601e7	0.439470
$917$	1.97646e7	0.776185
$918$	−1.04160e8	−4.07937
$919$	3.88171e6	0.151612	0.0758060	−	0.997123i	$-0.475847\pi$
$919$	3.88171e6	0.151612	0.0758060	+	0.997123i	$0.475847\pi$
$920$	−9.39093e6	−0.365796
$921$	3.53344e7	1.37261
$922$	−1.96213e7	−0.760152
$923$	−306849.	−0.0118555
$924$	0	0
$925$	−4.59842e6	−0.176707
$926$	−2.99232e7	−1.14678
$927$	8.66118e7	3.31038
$928$	−8.15174e6	−0.310728
$929$	1.01671e7	0.386506	0.193253	−	0.981149i	$-0.438096\pi$
$929$	1.01671e7	0.386506	0.193253	+	0.981149i	$0.438096\pi$
$930$	−3.84999e7	−1.45966
$931$	−6.25499e6	−0.236512
$932$	−501845.	−0.0189247
$933$	6.95866e7	2.61711
$934$	6.83732e6	0.256460
$935$	0	0
$936$	−3.46482e6	−0.129268
$937$	−4.60409e7	−1.71315	−0.856574	−	0.516024i	$-0.827412\pi$
$937$	−4.60409e7	−1.71315	−0.856574	+	0.516024i	$0.827412\pi$
$938$	3.81057e7	1.41411
$939$	−6.50330e7	−2.40697
$940$	334336.	0.0123414
$941$	9.00399e6	0.331483	0.165741	−	0.986169i	$-0.446998\pi$
$941$	9.00399e6	0.331483	0.165741	+	0.986169i	$0.446998\pi$
$942$	6.00550e7	2.20507
$943$	1.82331e7	0.667701
$944$	−5.39280e7	−1.96963
$945$	2.65428e7	0.966868
$946$	0	0
$947$	−4.22133e7	−1.52959	−0.764793	−	0.644276i	$-0.777159\pi$
$947$	−4.22133e7	−1.52959	−0.764793	+	0.644276i	$0.777159\pi$
$948$	−1.51186e7	−0.546375
$949$	−1.43990e6	−0.0518998
$950$	−7.16756e6	−0.257669
$951$	−4.87039e7	−1.74628
$952$	−3.14869e7	−1.12600
$953$	−4.70636e7	−1.67862	−0.839312	−	0.543651i	$-0.817042\pi$
$953$	−4.70636e7	−1.67862	−0.839312	+	0.543651i	$0.817042\pi$
$954$	−5.54129e6	−0.197124
$955$	−5.07905e6	−0.180208
$956$	9.71850e6	0.343918
$957$	0	0
$958$	−455210.	−0.0160250
$959$	−3.92539e7	−1.37828
$960$	−1.49605e7	−0.523925
$961$	4.47084e7	1.56164
$962$	−1.87473e6	−0.0653133
$963$	5.58863e7	1.94196
$964$	−2.92410e6	−0.101344
$965$	−1.01078e7	−0.349413
$966$	5.13969e7	1.77212
$967$	−1.72935e7	−0.594727	−0.297364	−	0.954764i	$-0.596107\pi$
$967$	−1.72935e7	−0.594727	−0.297364	+	0.954764i	$0.596107\pi$
$968$	0	0
$969$	9.25230e7	3.16549
$970$	4.11880e6	0.140553
$971$	3.36009e7	1.14367	0.571837	−	0.820367i	$-0.306231\pi$
$971$	3.36009e7	1.14367	0.571837	+	0.820367i	$0.306231\pi$
$972$	1.02653e7	0.348502
$973$	3.03728e7	1.02850
$974$	1.42920e7	0.482721
$975$	−716418.	−0.0241354
$976$	−2.34939e7	−0.789462
$977$	−1.61553e7	−0.541475	−0.270738	−	0.962653i	$-0.587268\pi$
$977$	−1.61553e7	−0.541475	−0.270738	+	0.962653i	$0.587268\pi$
$978$	−2.38997e6	−0.0798997
$979$	0	0
$980$	687472.	0.0228660
$981$	1.02613e8	3.40431
$982$	4.30547e6	0.142476
$983$	−3.19593e7	−1.05490	−0.527452	−	0.849585i	$-0.676853\pi$
$983$	−3.19593e7	−1.05490	−0.527452	+	0.849585i	$0.676853\pi$
$984$	3.18562e7	1.04883
$985$	−7.33852e6	−0.241001
$986$	3.27232e7	1.07192
$987$	5.51315e6	0.180139
$988$	−582923.	−0.0189985
$989$	−5.63696e7	−1.83254
$990$	0	0
$991$	9.01234e6	0.291510	0.145755	−	0.989321i	$-0.453439\pi$
$991$	9.01234e6	0.291510	0.145755	+	0.989321i	$0.453439\pi$
$992$	−2.41897e7	−0.780461
$993$	9.90857e7	3.18888
$994$	5.56382e6	0.178611
$995$	1.36563e7	0.437295
$996$	−1.98287e6	−0.0633354
$997$	1.41378e7	0.450447	0.225224	−	0.974307i	$-0.427689\pi$
$997$	1.41378e7	0.450447	0.225224	+	0.974307i	$0.427689\pi$
$998$	3.71110e7	1.17944
$999$	−6.75858e7	−2.14260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.e.1.2		6
11.10	odd	2		55.6.a.d.1.5	✓	6
33.32	even	2		495.6.a.l.1.2		6
44.43	even	2		880.6.a.u.1.1		6
55.32	even	4		275.6.b.f.199.10		12
55.43	even	4		275.6.b.f.199.3		12
55.54	odd	2		275.6.a.f.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.a.d.1.5	✓	6	11.10	odd	2
275.6.a.f.1.2		6	55.54	odd	2
275.6.b.f.199.3		12	55.43	even	4
275.6.b.f.199.10		12	55.32	even	4
495.6.a.l.1.2		6	33.32	even	2
605.6.a.e.1.2		6	1.1	even	1	trivial
880.6.a.u.1.1		6	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q-6.32252 q^{2} +28.4424 q^{3} +7.97424 q^{4} -25.0000 q^{5} -179.828 q^{6} -115.579 q^{7} +151.903 q^{8} +565.969 q^{9} +158.063 q^{10} +226.806 q^{12} -40.3015 q^{13} +730.751 q^{14} -711.060 q^{15} -1215.59 q^{16} +1793.42 q^{17} -3578.35 q^{18} +1813.85 q^{19} -199.356 q^{20} -3287.35 q^{21} +2472.87 q^{23} +4320.49 q^{24} +625.000 q^{25} +254.807 q^{26} +9186.02 q^{27} -921.656 q^{28} -2885.91 q^{29} +4495.69 q^{30} -8563.73 q^{31} +2824.67 q^{32} -11339.0 q^{34} +2889.48 q^{35} +4513.17 q^{36} -7357.47 q^{37} -11468.1 q^{38} -1146.27 q^{39} -3797.58 q^{40} +7373.27 q^{41} +20784.3 q^{42} -22795.2 q^{43} -14149.2 q^{45} -15634.8 q^{46} -1677.08 q^{47} -34574.2 q^{48} -3448.46 q^{49} -3951.57 q^{50} +51009.2 q^{51} -321.373 q^{52} +1548.56 q^{53} -58078.8 q^{54} -17556.9 q^{56} +51590.2 q^{57} +18246.2 q^{58} +44363.7 q^{59} -5670.16 q^{60} +19327.2 q^{61} +54144.4 q^{62} -65414.2 q^{63} +21039.8 q^{64} +1007.54 q^{65} +52145.9 q^{67} +14301.2 q^{68} +70334.3 q^{69} -18268.8 q^{70} +7613.84 q^{71} +85972.6 q^{72} +35728.1 q^{73} +46517.7 q^{74} +17776.5 q^{75} +14464.1 q^{76} +7247.31 q^{78} -66658.6 q^{79} +30389.7 q^{80} +123742. q^{81} -46617.6 q^{82} -8742.57 q^{83} -26214.1 q^{84} -44835.6 q^{85} +144123. q^{86} -82082.2 q^{87} -12117.7 q^{89} +89458.8 q^{90} +4658.01 q^{91} +19719.3 q^{92} -243573. q^{93} +10603.4 q^{94} -45346.2 q^{95} +80340.3 q^{96} +26058.0 q^{97} +21803.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 115 q^{4} - 150 q^{5} - 325 q^{6} + 66 q^{7} - 249 q^{8} + 832 q^{9} + 75 q^{10} + 1301 q^{12} + 972 q^{13} + 2017 q^{14} + 6675 q^{16} - 712 q^{17} - 5920 q^{18} - 610 q^{19} - 2875 q^{20}+ \cdots + 351884 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 115 * q^4 - 150 * q^5 - 325 * q^6 + 66 * q^7 - 249 * q^8 + 832 * q^9 + 75 * q^10 + 1301 * q^12 + 972 * q^13 + 2017 * q^14 + 6675 * q^16 - 712 * q^17 - 5920 * q^18 - 610 * q^19 - 2875 * q^20 - 2508 * q^21 + 7100 * q^23 - 13447 * q^24 + 3750 * q^25 - 7742 * q^26 - 2520 * q^27 + 33171 * q^28 - 10964 * q^29 + 8125 * q^30 + 8868 * q^31 - 10861 * q^32 - 42673 * q^34 - 1650 * q^35 - 30116 * q^36 - 15506 * q^37 + 26185 * q^38 - 7208 * q^39 + 6225 * q^40 - 160 * q^41 - 47111 * q^42 - 7032 * q^43 - 20800 * q^45 - 1650 * q^46 - 46320 * q^47 - 22215 * q^48 + 48512 * q^49 - 1875 * q^50 + 43378 * q^51 + 145838 * q^52 + 30518 * q^53 + 56881 * q^54 - 21297 * q^56 + 5640 * q^57 + 51477 * q^58 + 120532 * q^59 - 32525 * q^60 + 9228 * q^61 + 81355 * q^62 - 222460 * q^63 + 302839 * q^64 - 24300 * q^65 + 47432 * q^67 - 78111 * q^68 + 118960 * q^69 - 50425 * q^70 + 163948 * q^71 + 212580 * q^72 - 78528 * q^73 - 133501 * q^74 + 29355 * q^76 - 138086 * q^78 + 36712 * q^79 - 166875 * q^80 + 202166 * q^81 - 128902 * q^82 - 133792 * q^83 - 119033 * q^84 + 17800 * q^85 + 83996 * q^86 + 267082 * q^87 + 254946 * q^89 + 148000 * q^90 + 167844 * q^91 - 5134 * q^92 - 224250 * q^93 - 31414 * q^94 + 15250 * q^95 - 234415 * q^96 + 17404 * q^97 + 351884 * q^98

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