LMFDB - Embedded newform 245.6.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$1$
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} - 2x^{4} - 128x^{3} + 288x^{2} + 3551x - 6510 $ x^5 - 2x^4 - 128x^3 + 288x^2 + 3551x - 6510
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.03043$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.03043 q^{2} -10.0622 q^{3} +17.4270 q^{4} +25.0000 q^{5} +70.7416 q^{6} +102.455 q^{8} -141.752 q^{9} +O(q^{10})$	\(q-7.03043 q^{2} -10.0622 q^{3} +17.4270 q^{4} +25.0000 q^{5} +70.7416 q^{6} +102.455 q^{8} -141.752 q^{9} -175.761 q^{10} -125.462 q^{11} -175.353 q^{12} -40.4297 q^{13} -251.555 q^{15} -1277.96 q^{16} -1147.62 q^{17} +996.579 q^{18} +2098.06 q^{19} +435.674 q^{20} +882.054 q^{22} +1220.57 q^{23} -1030.92 q^{24} +625.000 q^{25} +284.238 q^{26} +3871.45 q^{27} +3033.31 q^{29} +1768.54 q^{30} -2115.77 q^{31} +5706.08 q^{32} +1262.43 q^{33} +8068.29 q^{34} -2470.31 q^{36} -1024.77 q^{37} -14750.3 q^{38} +406.811 q^{39} +2561.37 q^{40} +21343.3 q^{41} +6918.23 q^{43} -2186.43 q^{44} -3543.81 q^{45} -8581.16 q^{46} -2673.13 q^{47} +12859.1 q^{48} -4394.02 q^{50} +11547.6 q^{51} -704.566 q^{52} -22318.4 q^{53} -27218.0 q^{54} -3136.56 q^{55} -21111.1 q^{57} -21325.4 q^{58} -21193.2 q^{59} -4383.83 q^{60} -19623.8 q^{61} +14874.8 q^{62} +778.620 q^{64} -1010.74 q^{65} -8875.40 q^{66} +19335.0 q^{67} -19999.6 q^{68} -12281.7 q^{69} -3892.18 q^{71} -14523.2 q^{72} -53619.2 q^{73} +7204.58 q^{74} -6288.87 q^{75} +36562.8 q^{76} -2860.06 q^{78} +96435.3 q^{79} -31949.1 q^{80} -4509.49 q^{81} -150053. q^{82} -103120. q^{83} -28690.6 q^{85} -48638.1 q^{86} -30521.7 q^{87} -12854.2 q^{88} -78710.3 q^{89} +24914.5 q^{90} +21270.9 q^{92} +21289.3 q^{93} +18793.3 q^{94} +52451.6 q^{95} -57415.7 q^{96} -129260. q^{97} +17784.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} - 7 q^{3} + 101 q^{4} + 125 q^{5} - 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 - 7 * q^3 + 101 * q^4 + 125 * q^5 - 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} - 7 q^{3} + 101 q^{4} + 125 q^{5} - 304 q^{6} - 675 q^{8} + 284 q^{9} - 75 q^{10} + 1033 q^{11} + 1226 q^{12} - 1117 q^{13} - 175 q^{15} + 297 q^{16} - 3403 q^{17} + 887 q^{18} - 2846 q^{19} + 2525 q^{20} - 1858 q^{22} - 2756 q^{23} - 13290 q^{24} + 3125 q^{25} - 2544 q^{26} - 3661 q^{27} + 485 q^{29} - 7600 q^{30} - 10726 q^{31} - 17383 q^{32} - 12597 q^{33} + 16414 q^{34} + 38165 q^{36} - 2660 q^{37} + 14378 q^{38} - 13171 q^{39} - 16875 q^{40} + 8334 q^{41} - 17294 q^{43} + 42876 q^{44} + 7100 q^{45} + 45724 q^{46} - 59799 q^{47} + 94218 q^{48} - 1875 q^{50} - 12049 q^{51} - 87974 q^{52} - 9250 q^{53} - 106342 q^{54} + 25825 q^{55} - 121778 q^{57} + 35868 q^{58} - 52994 q^{59} + 30650 q^{60} - 81540 q^{61} + 74048 q^{62} + 39745 q^{64} - 27925 q^{65} - 311614 q^{66} - 726 q^{67} - 276216 q^{68} - 21388 q^{69} + 3760 q^{71} - 154815 q^{72} - 90634 q^{73} - 57342 q^{74} - 4375 q^{75} - 43902 q^{76} + 152598 q^{78} + 68243 q^{79} + 7425 q^{80} + 17645 q^{81} - 191552 q^{82} + 133292 q^{83} - 85075 q^{85} - 88352 q^{86} - 216813 q^{87} - 273040 q^{88} - 102852 q^{89} + 22175 q^{90} - 140852 q^{92} + 184862 q^{93} - 332618 q^{94} - 71150 q^{95} - 245574 q^{96} - 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 7 * q^3 + 101 * q^4 + 125 * q^5 - 304 * q^6 - 675 * q^8 + 284 * q^9 - 75 * q^10 + 1033 * q^11 + 1226 * q^12 - 1117 * q^13 - 175 * q^15 + 297 * q^16 - 3403 * q^17 + 887 * q^18 - 2846 * q^19 + 2525 * q^20 - 1858 * q^22 - 2756 * q^23 - 13290 * q^24 + 3125 * q^25 - 2544 * q^26 - 3661 * q^27 + 485 * q^29 - 7600 * q^30 - 10726 * q^31 - 17383 * q^32 - 12597 * q^33 + 16414 * q^34 + 38165 * q^36 - 2660 * q^37 + 14378 * q^38 - 13171 * q^39 - 16875 * q^40 + 8334 * q^41 - 17294 * q^43 + 42876 * q^44 + 7100 * q^45 + 45724 * q^46 - 59799 * q^47 + 94218 * q^48 - 1875 * q^50 - 12049 * q^51 - 87974 * q^52 - 9250 * q^53 - 106342 * q^54 + 25825 * q^55 - 121778 * q^57 + 35868 * q^58 - 52994 * q^59 + 30650 * q^60 - 81540 * q^61 + 74048 * q^62 + 39745 * q^64 - 27925 * q^65 - 311614 * q^66 - 726 * q^67 - 276216 * q^68 - 21388 * q^69 + 3760 * q^71 - 154815 * q^72 - 90634 * q^73 - 57342 * q^74 - 4375 * q^75 - 43902 * q^76 + 152598 * q^78 + 68243 * q^79 + 7425 * q^80 + 17645 * q^81 - 191552 * q^82 + 133292 * q^83 - 85075 * q^85 - 88352 * q^86 - 216813 * q^87 - 273040 * q^88 - 102852 * q^89 + 22175 * q^90 - 140852 * q^92 + 184862 * q^93 - 332618 * q^94 - 71150 * q^95 - 245574 * q^96 - 186175 * q^97 + 454710 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−7.03043	−1.24282	−0.621408	−	0.783487i	$-0.713439\pi$
$2$	−7.03043	−1.24282	−0.621408	+	0.783487i	$0.713439\pi$
$3$	−10.0622	−0.645490	−0.322745	−	0.946486i	$-0.604606\pi$
$3$	−10.0622	−0.645490	−0.322745	+	0.946486i	$0.604606\pi$
$4$	17.4270	0.544592
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	70.7416	0.802225
$7$	0	0
$7$	0	0
$8$	102.455	0.565988
$9$	−141.752	−0.583343
$10$	−175.761	−0.555804
$11$	−125.462	−0.312631	−0.156315	−	0.987707i	$-0.549962\pi$
$11$	−125.462	−0.312631	−0.156315	+	0.987707i	$0.549962\pi$
$12$	−175.353	−0.351529
$13$	−40.4297	−0.0663501	−0.0331751	−	0.999450i	$-0.510562\pi$
$13$	−40.4297	−0.0663501	−0.0331751	+	0.999450i	$0.510562\pi$
$14$	0	0
$15$	−251.555	−0.288672
$16$	−1277.96	−1.24801
$17$	−1147.62	−0.963114	−0.481557	−	0.876415i	$-0.659928\pi$
$17$	−1147.62	−0.963114	−0.481557	+	0.876415i	$0.659928\pi$
$18$	996.579	0.724988
$19$	2098.06	1.33332	0.666660	−	0.745362i	$-0.267723\pi$
$19$	2098.06	1.33332	0.666660	+	0.745362i	$0.267723\pi$
$20$	435.674	0.243549
$21$	0	0
$22$	882.054	0.388542
$23$	1220.57	0.481110	0.240555	−	0.970635i	$-0.422671\pi$
$23$	1220.57	0.481110	0.240555	+	0.970635i	$0.422671\pi$
$24$	−1030.92	−0.365340
$25$	625.000	0.200000
$26$	284.238	0.0824610
$27$	3871.45	1.02203
$28$	0	0
$29$	3033.31	0.669763	0.334882	−	0.942260i	$-0.391304\pi$
$29$	3033.31	0.669763	0.334882	+	0.942260i	$0.391304\pi$
$30$	1768.54	0.358766
$31$	−2115.77	−0.395425	−0.197712	−	0.980260i	$-0.563351\pi$
$31$	−2115.77	−0.395425	−0.197712	+	0.980260i	$0.563351\pi$
$32$	5706.08	0.985061
$33$	1262.43	0.201800
$34$	8068.29	1.19697
$35$	0	0
$36$	−2470.31	−0.317684
$37$	−1024.77	−0.123062	−0.0615308	−	0.998105i	$-0.519598\pi$
$37$	−1024.77	−0.123062	−0.0615308	+	0.998105i	$0.519598\pi$
$38$	−14750.3	−1.65707
$39$	406.811	0.0428284
$40$	2561.37	0.253118
$41$	21343.3	1.98290	0.991452	−	0.130469i	$-0.0416484\pi$
$41$	21343.3	1.98290	0.991452	+	0.130469i	$0.0416484\pi$
$42$	0	0
$43$	6918.23	0.570589	0.285295	−	0.958440i	$-0.407909\pi$
$43$	6918.23	0.570589	0.285295	+	0.958440i	$0.407909\pi$
$44$	−2186.43	−0.170256
$45$	−3543.81	−0.260879
$46$	−8581.16	−0.597932
$47$	−2673.13	−0.176513	−0.0882563	−	0.996098i	$-0.528129\pi$
$47$	−2673.13	−0.176513	−0.0882563	+	0.996098i	$0.528129\pi$
$48$	12859.1	0.805579
$49$	0	0
$50$	−4394.02	−0.248563
$51$	11547.6	0.621680
$52$	−704.566	−0.0361338
$53$	−22318.4	−1.09137	−0.545686	−	0.837990i	$-0.683731\pi$
$53$	−22318.4	−1.09137	−0.545686	+	0.837990i	$0.683731\pi$
$54$	−27218.0	−1.27020
$55$	−3136.56	−0.139813
$56$	0	0
$57$	−21111.1	−0.860645
$58$	−21325.4	−0.832393
$59$	−21193.2	−0.792622	−0.396311	−	0.918116i	$-0.629710\pi$
$59$	−21193.2	−0.792622	−0.396311	+	0.918116i	$0.629710\pi$
$60$	−4383.83	−0.157209
$61$	−19623.8	−0.675242	−0.337621	−	0.941282i	$-0.609622\pi$
$61$	−19623.8	−0.675242	−0.337621	+	0.941282i	$0.609622\pi$
$62$	14874.8	0.491440
$63$	0	0
$64$	778.620	0.0237616
$65$	−1010.74	−0.0296727
$66$	−8875.40	−0.250800
$67$	19335.0	0.526207	0.263103	−	0.964768i	$-0.415254\pi$
$67$	19335.0	0.526207	0.263103	+	0.964768i	$0.415254\pi$
$68$	−19999.6	−0.524504
$69$	−12281.7	−0.310552
$70$	0	0
$71$	−3892.18	−0.0916319	−0.0458159	−	0.998950i	$-0.514589\pi$
$71$	−3892.18	−0.0916319	−0.0458159	+	0.998950i	$0.514589\pi$
$72$	−14523.2	−0.330165
$73$	−53619.2	−1.17764	−0.588821	−	0.808263i	$-0.700408\pi$
$73$	−53619.2	−1.17764	−0.588821	+	0.808263i	$0.700408\pi$
$74$	7204.58	0.152943
$75$	−6288.87	−0.129098
$76$	36562.8	0.726116
$77$	0	0
$78$	−2860.06	−0.0532278
$79$	96435.3	1.73847	0.869237	−	0.494395i	$-0.164610\pi$
$79$	96435.3	1.73847	0.869237	+	0.494395i	$0.164610\pi$
$80$	−31949.1	−0.558128
$81$	−4509.49	−0.0763687
$82$	−150053.	−2.46439
$83$	−103120.	−1.64304	−0.821518	−	0.570182i	$-0.806873\pi$
$83$	−103120.	−1.64304	−0.821518	+	0.570182i	$0.806873\pi$
$84$	0	0
$85$	−28690.6	−0.430718
$86$	−48638.1	−0.709138
$87$	−30521.7	−0.432325
$88$	−12854.2	−0.176945
$89$	−78710.3	−1.05331	−0.526656	−	0.850079i	$-0.676554\pi$
$89$	−78710.3	−1.05331	−0.526656	+	0.850079i	$0.676554\pi$
$90$	24914.5	0.324224
$91$	0	0
$92$	21270.9	0.262009
$93$	21289.3	0.255243
$94$	18793.3	0.219373
$95$	52451.6	0.596279
$96$	−57415.7	−0.635847
$97$	−129260.	−1.39487	−0.697437	−	0.716646i	$-0.745676\pi$
$97$	−129260.	−1.39487	−0.697437	+	0.716646i	$0.745676\pi$
$98$	0	0
$99$	17784.6	0.182371
$100$	10891.8	0.108918
$101$	−41609.4	−0.405871	−0.202936	−	0.979192i	$-0.565048\pi$
$101$	−41609.4	−0.405871	−0.202936	+	0.979192i	$0.565048\pi$
$102$	−81184.7	−0.772634
$103$	−128313.	−1.19173	−0.595864	−	0.803085i	$-0.703190\pi$
$103$	−128313.	−1.19173	−0.595864	+	0.803085i	$0.703190\pi$
$104$	−4142.21	−0.0375534
$105$	0	0
$106$	156908.	1.35637
$107$	−152250.	−1.28557	−0.642787	−	0.766045i	$-0.722222\pi$
$107$	−152250.	−1.28557	−0.642787	+	0.766045i	$0.722222\pi$
$108$	67467.6	0.556591
$109$	156411.	1.26096	0.630482	−	0.776204i	$-0.282857\pi$
$109$	156411.	1.26096	0.630482	+	0.776204i	$0.282857\pi$
$110$	22051.3	0.173761
$111$	10311.4	0.0794350
$112$	0	0
$113$	67748.4	0.499117	0.249559	−	0.968360i	$-0.419714\pi$
$113$	67748.4	0.499117	0.249559	+	0.968360i	$0.419714\pi$
$114$	148420.	1.06962
$115$	30514.4	0.215159
$116$	52861.3	0.364748
$117$	5731.00	0.0387049
$118$	148997.	0.985083
$119$	0	0
$120$	−25773.0	−0.163385
$121$	−145310.	−0.902262
$122$	137964.	0.839201
$123$	−214760.	−1.27995
$124$	−36871.4	−0.215345
$125$	15625.0	0.0894427
$126$	0	0
$127$	−135384.	−0.744830	−0.372415	−	0.928066i	$-0.621470\pi$
$127$	−135384.	−0.744830	−0.372415	+	0.928066i	$0.621470\pi$
$128$	−188069.	−1.01459
$129$	−69612.5	−0.368310
$130$	7105.95	0.0368777
$131$	212815.	1.08349	0.541745	−	0.840543i	$-0.317764\pi$
$131$	212815.	1.08349	0.541745	+	0.840543i	$0.317764\pi$
$132$	22000.2	0.109899
$133$	0	0
$134$	−135933.	−0.653978
$135$	96786.3	0.457067
$136$	−117580.	−0.545111
$137$	126163.	0.574290	0.287145	−	0.957887i	$-0.407294\pi$
$137$	126163.	0.574290	0.287145	+	0.957887i	$0.407294\pi$
$138$	86345.3	0.385959
$139$	−174576.	−0.766387	−0.383194	−	0.923668i	$-0.625176\pi$
$139$	−174576.	−0.766387	−0.383194	+	0.923668i	$0.625176\pi$
$140$	0	0
$141$	26897.6	0.113937
$142$	27363.7	0.113882
$143$	5072.40	0.0207431
$144$	181154.	0.728018
$145$	75832.7	0.299527
$146$	376966.	1.46359
$147$	0	0
$148$	−17858.6	−0.0670184
$149$	515665.	1.90284	0.951420	−	0.307897i	$-0.0996254\pi$
$149$	515665.	1.90284	0.951420	+	0.307897i	$0.0996254\pi$
$150$	44213.5	0.160445
$151$	30723.7	0.109656	0.0548278	−	0.998496i	$-0.482539\pi$
$151$	30723.7	0.109656	0.0548278	+	0.998496i	$0.482539\pi$
$152$	214957.	0.754643
$153$	162678.	0.561825
$154$	0	0
$155$	−52894.2	−0.176839
$156$	7089.48	0.0233240
$157$	−118289.	−0.382995	−0.191498	−	0.981493i	$-0.561334\pi$
$157$	−118289.	−0.382995	−0.191498	+	0.981493i	$0.561334\pi$
$158$	−677982.	−2.16061
$159$	224572.	0.704470
$160$	142652.	0.440533
$161$	0	0
$162$	31703.7	0.0949122
$163$	−430122.	−1.26801	−0.634005	−	0.773329i	$-0.718590\pi$
$163$	−430122.	−1.26801	−0.634005	+	0.773329i	$0.718590\pi$
$164$	371949.	1.07987
$165$	31560.6	0.0902477
$166$	724977.	2.04199
$167$	−303276.	−0.841487	−0.420743	−	0.907180i	$-0.638231\pi$
$167$	−303276.	−0.841487	−0.420743	+	0.907180i	$0.638231\pi$
$168$	0	0
$169$	−369658.	−0.995598
$170$	201707.	0.535303
$171$	−297405.	−0.777783
$172$	120564.	0.310739
$173$	467177.	1.18677	0.593384	−	0.804919i	$-0.297791\pi$
$173$	467177.	1.18677	0.593384	+	0.804919i	$0.297791\pi$
$174$	214581.	0.537301
$175$	0	0
$176$	160336.	0.390167
$177$	213250.	0.511629
$178$	553368.	1.30907
$179$	416875.	0.972464	0.486232	−	0.873830i	$-0.338371\pi$
$179$	416875.	0.972464	0.486232	+	0.873830i	$0.338371\pi$
$180$	−61757.8	−0.142073
$181$	−598553.	−1.35802	−0.679010	−	0.734129i	$-0.737591\pi$
$181$	−598553.	−1.35802	−0.679010	+	0.734129i	$0.737591\pi$
$182$	0	0
$183$	197459.	0.435862
$184$	125054.	0.272303
$185$	−25619.3	−0.0550348
$186$	−149673.	−0.317220
$187$	143984.	0.301099
$188$	−46584.5	−0.0961274
$189$	0	0
$190$	−368757.	−0.741065
$191$	−717832.	−1.42377	−0.711884	−	0.702297i	$-0.752158\pi$
$191$	−717832.	−1.42377	−0.711884	+	0.702297i	$0.752158\pi$
$192$	−7834.62	−0.0153379
$193$	−740064.	−1.43013	−0.715066	−	0.699057i	$-0.753603\pi$
$193$	−740064.	−1.43013	−0.715066	+	0.699057i	$0.753603\pi$
$194$	908754.	1.73357
$195$	10170.3	0.0191534
$196$	0	0
$197$	901133.	1.65434	0.827168	−	0.561955i	$-0.189951\pi$
$197$	901133.	1.65434	0.827168	+	0.561955i	$0.189951\pi$
$198$	−125033.	−0.226653
$199$	−143392.	−0.256680	−0.128340	−	0.991730i	$-0.540965\pi$
$199$	−143392.	−0.256680	−0.128340	+	0.991730i	$0.540965\pi$
$200$	64034.2	0.113198
$201$	−194552.	−0.339661
$202$	292532.	0.504423
$203$	0	0
$204$	201240.	0.338562
$205$	533582.	0.886782
$206$	902095.	1.48110
$207$	−173019.	−0.280652
$208$	51667.7	0.0828057
$209$	−263228.	−0.416837
$210$	0	0
$211$	333358.	0.515472	0.257736	−	0.966215i	$-0.417024\pi$
$211$	333358.	0.515472	0.257736	+	0.966215i	$0.417024\pi$
$212$	−388941.	−0.594353
$213$	39163.8	0.0591475
$214$	1.07038e6	1.59773
$215$	172956.	0.255175
$216$	396649.	0.578458
$217$	0	0
$218$	−1.09964e6	−1.56715
$219$	539527.	0.760156
$220$	−54660.6	−0.0761409
$221$	46398.1	0.0639027
$222$	−72493.9	−0.0987231
$223$	−1.01463e6	−1.36630	−0.683149	−	0.730279i	$-0.739390\pi$
$223$	−1.01463e6	−1.36630	−0.683149	+	0.730279i	$0.739390\pi$
$224$	0	0
$225$	−88595.2	−0.116669
$226$	−476300.	−0.620311
$227$	1.44611e6	1.86267	0.931337	−	0.364158i	$-0.118643\pi$
$227$	1.44611e6	1.86267	0.931337	+	0.364158i	$0.118643\pi$
$228$	−367902.	−0.468701
$229$	−1.49205e6	−1.88016	−0.940078	−	0.340960i	$-0.889248\pi$
$229$	−1.49205e6	−1.88016	−0.940078	+	0.340960i	$0.889248\pi$
$230$	−214529.	−0.267403
$231$	0	0
$232$	310777.	0.379078
$233$	−659904.	−0.796326	−0.398163	−	0.917315i	$-0.630352\pi$
$233$	−659904.	−0.796326	−0.398163	+	0.917315i	$0.630352\pi$
$234$	−40291.4	−0.0481030
$235$	−66828.3	−0.0789388
$236$	−369332.	−0.431656
$237$	−970351.	−1.12217
$238$	0	0
$239$	−1.06584e6	−1.20697	−0.603486	−	0.797373i	$-0.706222\pi$
$239$	−1.06584e6	−1.20697	−0.603486	+	0.797373i	$0.706222\pi$
$240$	321478.	0.360266
$241$	347481.	0.385379	0.192689	−	0.981260i	$-0.438279\pi$
$241$	347481.	0.385379	0.192689	+	0.981260i	$0.438279\pi$
$242$	1.02159e6	1.12135
$243$	−895387.	−0.972737
$244$	−341984.	−0.367731
$245$	0	0
$246$	1.50986e6	1.59074
$247$	−84824.0	−0.0884660
$248$	−216770.	−0.223806
$249$	1.03761e6	1.06056
$250$	−109850.	−0.111161
$251$	−985578.	−0.987430	−0.493715	−	0.869624i	$-0.664361\pi$
$251$	−985578.	−0.987430	−0.493715	+	0.869624i	$0.664361\pi$
$252$	0	0
$253$	−153136.	−0.150410
$254$	951806.	0.925687
$255$	288691.	0.278024
$256$	1.29729e6	1.23719
$257$	410674.	0.387851	0.193925	−	0.981016i	$-0.437878\pi$
$257$	410674.	0.387851	0.193925	+	0.981016i	$0.437878\pi$
$258$	489406.	0.457741
$259$	0	0
$260$	−17614.2	−0.0161595
$261$	−429978.	−0.390701
$262$	−1.49618e6	−1.34658
$263$	−1.87300e6	−1.66974	−0.834869	−	0.550449i	$-0.814457\pi$
$263$	−1.87300e6	−1.66974	−0.834869	+	0.550449i	$0.814457\pi$
$264$	129342.	0.114216
$265$	−557959.	−0.488076
$266$	0	0
$267$	791999.	0.679902
$268$	336949.	0.286568
$269$	1.24593e6	1.04981	0.524907	−	0.851160i	$-0.324100\pi$
$269$	1.24593e6	1.04981	0.524907	+	0.851160i	$0.324100\pi$
$270$	−680449.	−0.568050
$271$	−1.63560e6	−1.35286	−0.676430	−	0.736507i	$-0.736474\pi$
$271$	−1.63560e6	−1.35286	−0.676430	+	0.736507i	$0.736474\pi$
$272$	1.46662e6	1.20198
$273$	0	0
$274$	−886981.	−0.713737
$275$	−78413.9	−0.0625261
$276$	−214032.	−0.169124
$277$	−1.03318e6	−0.809054	−0.404527	−	0.914526i	$-0.632564\pi$
$277$	−1.03318e6	−0.809054	−0.404527	+	0.914526i	$0.632564\pi$
$278$	1.22735e6	0.952479
$279$	299915.	0.230668
$280$	0	0
$281$	168917.	0.127617	0.0638084	−	0.997962i	$-0.479675\pi$
$281$	168917.	0.127617	0.0638084	+	0.997962i	$0.479675\pi$
$282$	−189101.	−0.141603
$283$	−1.97561e6	−1.46634	−0.733172	−	0.680043i	$-0.761961\pi$
$283$	−1.97561e6	−1.46634	−0.733172	+	0.680043i	$0.761961\pi$
$284$	−67828.8	−0.0499020
$285$	−527778.	−0.384892
$286$	−35661.1	−0.0257798
$287$	0	0
$288$	−808850.	−0.574628
$289$	−102815.	−0.0724121
$290$	−533136.	−0.372257
$291$	1.30064e6	0.900377
$292$	−934420.	−0.641335
$293$	−810147.	−0.551309	−0.275654	−	0.961257i	$-0.588895\pi$
$293$	−810147.	−0.551309	−0.275654	+	0.961257i	$0.588895\pi$
$294$	0	0
$295$	−529829.	−0.354471
$296$	−104993.	−0.0696514
$297$	−485721.	−0.319518
$298$	−3.62535e6	−2.36488
$299$	−49347.4	−0.0319217
$300$	−109596.	−0.0703058
$301$	0	0
$302$	−216001.	−0.136282
$303$	418682.	0.261986
$304$	−2.68125e6	−1.66400
$305$	−490596.	−0.301977
$306$	−1.14370e6	−0.698246
$307$	1.48839e6	0.901304	0.450652	−	0.892700i	$-0.351192\pi$
$307$	1.48839e6	0.901304	0.450652	+	0.892700i	$0.351192\pi$
$308$	0	0
$309$	1.29111e6	0.769248
$310$	371869.	0.219779
$311$	773532.	0.453500	0.226750	−	0.973953i	$-0.427190\pi$
$311$	773532.	0.453500	0.226750	+	0.973953i	$0.427190\pi$
$312$	41679.7	0.0242403
$313$	−1.37234e6	−0.791771	−0.395886	−	0.918300i	$-0.629562\pi$
$313$	−1.37234e6	−0.791771	−0.395886	+	0.918300i	$0.629562\pi$
$314$	831619.	0.475993
$315$	0	0
$316$	1.68057e6	0.946760
$317$	39821.8	0.0222573	0.0111286	−	0.999938i	$-0.496458\pi$
$317$	39821.8	0.0222573	0.0111286	+	0.999938i	$0.496458\pi$
$318$	−1.57884e6	−0.875526
$319$	−380565.	−0.209388
$320$	19465.5	0.0106265
$321$	1.53197e6	0.829826
$322$	0	0
$323$	−2.40779e6	−1.28414
$324$	−78586.7	−0.0415898
$325$	−25268.5	−0.0132700
$326$	3.02394e6	1.57590
$327$	−1.57384e6	−0.813939
$328$	2.18672e6	1.12230
$329$	0	0
$330$	−221885.	−0.112161
$331$	−1.77584e6	−0.890909	−0.445454	−	0.895305i	$-0.646958\pi$
$331$	−1.77584e6	−0.890909	−0.445454	+	0.895305i	$0.646958\pi$
$332$	−1.79707e6	−0.894785
$333$	145264.	0.0717871
$334$	2.13216e6	1.04581
$335$	483374.	0.235327
$336$	0	0
$337$	22161.8	0.0106299	0.00531496	−	0.999986i	$-0.498308\pi$
$337$	22161.8	0.0106299	0.00531496	+	0.999986i	$0.498308\pi$
$338$	2.59886e6	1.23735
$339$	−681697.	−0.322175
$340$	−499990.	−0.234565
$341$	265449.	0.123622
$342$	2.09089e6	0.966641
$343$	0	0
$344$	708805.	0.322947
$345$	−307041.	−0.138883
$346$	−3.28445e6	−1.47494
$347$	1.80155e6	0.803196	0.401598	−	0.915816i	$-0.368455\pi$
$347$	1.80155e6	0.803196	0.401598	+	0.915816i	$0.368455\pi$
$348$	−531901.	−0.235441
$349$	2.95997e6	1.30084	0.650420	−	0.759574i	$-0.274593\pi$
$349$	2.95997e6	1.30084	0.650420	+	0.759574i	$0.274593\pi$
$350$	0	0
$351$	−156522.	−0.0678120
$352$	−715898.	−0.307960
$353$	3.76084e6	1.60638	0.803189	−	0.595725i	$-0.203135\pi$
$353$	3.76084e6	1.60638	0.803189	+	0.595725i	$0.203135\pi$
$354$	−1.49924e6	−0.635861
$355$	−97304.4	−0.0409790
$356$	−1.37168e6	−0.573625
$357$	0	0
$358$	−2.93081e6	−1.20859
$359$	−1.14557e6	−0.469121	−0.234560	−	0.972102i	$-0.575365\pi$
$359$	−1.14557e6	−0.469121	−0.234560	+	0.972102i	$0.575365\pi$
$360$	−363080.	−0.147654
$361$	1.92577e6	0.777743
$362$	4.20808e6	1.68777
$363$	1.46214e6	0.582401
$364$	0	0
$365$	−1.34048e6	−0.526658
$366$	−1.38822e6	−0.541696
$367$	−734425.	−0.284631	−0.142315	−	0.989821i	$-0.545455\pi$
$367$	−734425.	−0.284631	−0.142315	+	0.989821i	$0.545455\pi$
$368$	−1.55985e6	−0.600431
$369$	−3.02546e6	−1.15671
$370$	180115.	0.0683982
$371$	0	0
$372$	371007.	0.139003
$373$	5.20799e6	1.93820	0.969099	−	0.246672i	$-0.0793369\pi$
$373$	5.20799e6	1.93820	0.969099	+	0.246672i	$0.0793369\pi$
$374$	−1.01227e6	−0.374210
$375$	−157222.	−0.0577344
$376$	−273875.	−0.0999040
$377$	−122636.	−0.0444389
$378$	0	0
$379$	3.09957e6	1.10842	0.554209	−	0.832378i	$-0.313021\pi$
$379$	3.09957e6	1.10842	0.554209	+	0.832378i	$0.313021\pi$
$380$	914071.	0.324729
$381$	1.36226e6	0.480780
$382$	5.04667e6	1.76948
$383$	−649169.	−0.226131	−0.113066	−	0.993588i	$-0.536067\pi$
$383$	−649169.	−0.226131	−0.113066	+	0.993588i	$0.536067\pi$
$384$	1.89238e6	0.654909
$385$	0	0
$386$	5.20297e6	1.77739
$387$	−980674.	−0.332849
$388$	−2.25261e6	−0.759638
$389$	−1.65155e6	−0.553373	−0.276687	−	0.960960i	$-0.589236\pi$
$389$	−1.65155e6	−0.553373	−0.276687	+	0.960960i	$0.589236\pi$
$390$	−71501.4	−0.0238042
$391$	−1.40076e6	−0.463364
$392$	0	0
$393$	−2.14139e6	−0.699382
$394$	−6.33536e6	−2.05604
$395$	2.41088e6	0.777470
$396$	309931.	0.0993177
$397$	1.28117e6	0.407971	0.203986	−	0.978974i	$-0.434610\pi$
$397$	1.28117e6	0.407971	0.203986	+	0.978974i	$0.434610\pi$
$398$	1.00811e6	0.319006
$399$	0	0
$400$	−798727.	−0.249602
$401$	1.64612e6	0.511210	0.255605	−	0.966781i	$-0.417725\pi$
$401$	1.64612e6	0.511210	0.255605	+	0.966781i	$0.417725\pi$
$402$	1.36778e6	0.422136
$403$	85539.8	0.0262365
$404$	−725125.	−0.221034
$405$	−112737.	−0.0341531
$406$	0	0
$407$	128570.	0.0384728
$408$	1.18311e6	0.351864
$409$	1.48179e6	0.438003	0.219002	−	0.975725i	$-0.429720\pi$
$409$	1.48179e6	0.438003	0.219002	+	0.975725i	$0.429720\pi$
$410$	−3.75131e6	−1.10211
$411$	−1.26948e6	−0.370698
$412$	−2.23610e6	−0.649006
$413$	0	0
$414$	1.21640e6	0.348799
$415$	−2.57800e6	−0.734788
$416$	−230695.	−0.0653589
$417$	1.75662e6	0.494695
$418$	1.85060e6	0.518051
$419$	−4.52631e6	−1.25953	−0.629766	−	0.776785i	$-0.716849\pi$
$419$	−4.52631e6	−1.25953	−0.629766	+	0.776785i	$0.716849\pi$
$420$	0	0
$421$	2.05257e6	0.564408	0.282204	−	0.959354i	$-0.408935\pi$
$421$	2.05257e6	0.564408	0.282204	+	0.959354i	$0.408935\pi$
$422$	−2.34365e6	−0.640637
$423$	378922.	0.102967
$424$	−2.28662e6	−0.617703
$425$	−717265.	−0.192623
$426$	−275339.	−0.0735094
$427$	0	0
$428$	−2.65325e6	−0.700114
$429$	−51039.5	−0.0133895
$430$	−1.21595e6	−0.317136
$431$	5.71263e6	1.48130	0.740650	−	0.671891i	$-0.234518\pi$
$431$	5.71263e6	1.48130	0.740650	+	0.671891i	$0.234518\pi$
$432$	−4.94758e6	−1.27551
$433$	−3.25420e6	−0.834112	−0.417056	−	0.908881i	$-0.636938\pi$
$433$	−3.25420e6	−0.834112	−0.417056	+	0.908881i	$0.636938\pi$
$434$	0	0
$435$	−763043.	−0.193342
$436$	2.72578e6	0.686711
$437$	2.56084e6	0.641474
$438$	−3.79311e6	−0.944735
$439$	−142095.	−0.0351897	−0.0175949	−	0.999845i	$-0.505601\pi$
$439$	−142095.	−0.0351897	−0.0175949	+	0.999845i	$0.505601\pi$
$440$	−321355.	−0.0791323
$441$	0	0
$442$	−326199.	−0.0794193
$443$	2.21139e6	0.535374	0.267687	−	0.963506i	$-0.413741\pi$
$443$	2.21139e6	0.535374	0.267687	+	0.963506i	$0.413741\pi$
$444$	179697.	0.0432597
$445$	−1.96776e6	−0.471055
$446$	7.13329e6	1.69806
$447$	−5.18872e6	−1.22826
$448$	0	0
$449$	7.61612e6	1.78286	0.891431	−	0.453156i	$-0.149702\pi$
$449$	7.61612e6	1.78286	0.891431	+	0.453156i	$0.149702\pi$
$450$	622862.	0.144998
$451$	−2.67778e6	−0.619917
$452$	1.18065e6	0.271816
$453$	−309147.	−0.0707816
$454$	−1.01668e7	−2.31496
$455$	0	0
$456$	−2.16293e6	−0.487115
$457$	2.70104e6	0.604979	0.302490	−	0.953153i	$-0.402182\pi$
$457$	2.70104e6	0.604979	0.302490	+	0.953153i	$0.402182\pi$
$458$	1.04897e7	2.33669
$459$	−4.44297e6	−0.984333
$460$	531772.	0.117174
$461$	−3.46295e6	−0.758917	−0.379459	−	0.925209i	$-0.623890\pi$
$461$	−3.46295e6	−0.758917	−0.379459	+	0.925209i	$0.623890\pi$
$462$	0	0
$463$	−4.83059e6	−1.04724	−0.523621	−	0.851951i	$-0.675419\pi$
$463$	−4.83059e6	−1.04724	−0.523621	+	0.851951i	$0.675419\pi$
$464$	−3.87646e6	−0.835872
$465$	532231.	0.114148
$466$	4.63941e6	0.989687
$467$	−1.45949e6	−0.309677	−0.154838	−	0.987940i	$-0.549486\pi$
$467$	−1.45949e6	−0.309677	−0.154838	+	0.987940i	$0.549486\pi$
$468$	99873.8	0.0210784
$469$	0	0
$470$	469832.	0.0981065
$471$	1.19024e6	0.247220
$472$	−2.17134e6	−0.448614
$473$	−867976.	−0.178384
$474$	6.82198e6	1.39465
$475$	1.31129e6	0.266664
$476$	0	0
$477$	3.16368e6	0.636644
$478$	7.49332e6	1.50005
$479$	9.06198e6	1.80461	0.902307	−	0.431093i	$-0.141872\pi$
$479$	9.06198e6	1.80461	0.902307	+	0.431093i	$0.141872\pi$
$480$	−1.43539e6	−0.284359
$481$	41431.2	0.00816515
$482$	−2.44294e6	−0.478955
$483$	0	0
$484$	−2.53231e6	−0.491365
$485$	−3.23150e6	−0.623807
$486$	6.29496e6	1.20893
$487$	−844401.	−0.161334	−0.0806670	−	0.996741i	$-0.525705\pi$
$487$	−844401.	−0.161334	−0.0806670	+	0.996741i	$0.525705\pi$
$488$	−2.01056e6	−0.382179
$489$	4.32797e6	0.818487
$490$	0	0
$491$	−7.11894e6	−1.33264	−0.666319	−	0.745667i	$-0.732131\pi$
$491$	−7.11894e6	−1.33264	−0.666319	+	0.745667i	$0.732131\pi$
$492$	−3.74262e6	−0.697048
$493$	−3.48110e6	−0.645058
$494$	596349.	0.109947
$495$	444614.	0.0815587
$496$	2.70387e6	0.493494
$497$	0	0
$498$	−7.29486e6	−1.31809
$499$	−2.04294e6	−0.367286	−0.183643	−	0.982993i	$-0.558789\pi$
$499$	−2.04294e6	−0.367286	−0.183643	+	0.982993i	$0.558789\pi$
$500$	272296.	0.0487098
$501$	3.05162e6	0.543171
$502$	6.92903e6	1.22719
$503$	−2.98681e6	−0.526365	−0.263183	−	0.964746i	$-0.584772\pi$
$503$	−2.98681e6	−0.526365	−0.263183	+	0.964746i	$0.584772\pi$
$504$	0	0
$505$	−1.04024e6	−0.181511
$506$	1.07661e6	0.186932
$507$	3.71957e6	0.642648
$508$	−2.35933e6	−0.405629
$509$	1.06479e6	0.182167	0.0910837	−	0.995843i	$-0.470967\pi$
$509$	1.06479e6	0.182167	0.0910837	+	0.995843i	$0.470967\pi$
$510$	−2.02962e6	−0.345533
$511$	0	0
$512$	−3.10230e6	−0.523008
$513$	8.12255e6	1.36270
$514$	−2.88722e6	−0.482027
$515$	−3.20782e6	−0.532957
$516$	−1.21313e6	−0.200579
$517$	335377.	0.0551832
$518$	0	0
$519$	−4.70082e6	−0.766047
$520$	−103555.	−0.0167944
$521$	3.84799e6	0.621069	0.310534	−	0.950562i	$-0.399492\pi$
$521$	3.84799e6	0.621069	0.310534	+	0.950562i	$0.399492\pi$
$522$	3.02293e6	0.485570
$523$	7.15310e6	1.14351	0.571755	−	0.820424i	$-0.306263\pi$
$523$	7.15310e6	1.14351	0.571755	+	0.820424i	$0.306263\pi$
$524$	3.70873e6	0.590061
$525$	0	0
$526$	1.31680e7	2.07518
$527$	2.42811e6	0.380839
$528$	−1.61333e6	−0.251849
$529$	−4.94654e6	−0.768533
$530$	3.92269e6	0.606589
$531$	3.00418e6	0.462370
$532$	0	0
$533$	−862902.	−0.131566
$534$	−5.56809e6	−0.844993
$535$	−3.80625e6	−0.574926
$536$	1.98096e6	0.297827
$537$	−4.19468e6	−0.627716
$538$	−8.75941e6	−1.30473
$539$	0	0
$540$	1.68669e6	0.248915
$541$	−9.43037e6	−1.38527	−0.692637	−	0.721287i	$-0.743551\pi$
$541$	−9.43037e6	−1.38527	−0.692637	+	0.721287i	$0.743551\pi$
$542$	1.14989e7	1.68136
$543$	6.02275e6	0.876588
$544$	−6.54844e6	−0.948726
$545$	3.91029e6	0.563920
$546$	0	0
$547$	1.03119e7	1.47357	0.736786	−	0.676125i	$-0.236342\pi$
$547$	1.03119e7	1.47357	0.736786	+	0.676125i	$0.236342\pi$
$548$	2.19864e6	0.312754
$549$	2.78172e6	0.393897
$550$	551284.	0.0777085
$551$	6.36407e6	0.893009
$552$	−1.25831e6	−0.175769
$553$	0	0
$554$	7.26371e6	1.00551
$555$	257786.	0.0355244
$556$	−3.04233e6	−0.417369
$557$	−8.23462e6	−1.12462	−0.562310	−	0.826927i	$-0.690087\pi$
$557$	−8.23462e6	−1.12462	−0.562310	+	0.826927i	$0.690087\pi$
$558$	−2.10853e6	−0.286678
$559$	−279702.	−0.0378587
$560$	0	0
$561$	−1.44879e6	−0.194356
$562$	−1.18756e6	−0.158604
$563$	−7.73906e6	−1.02900	−0.514502	−	0.857489i	$-0.672023\pi$
$563$	−7.73906e6	−1.02900	−0.514502	+	0.857489i	$0.672023\pi$
$564$	468743.	0.0620493
$565$	1.69371e6	0.223212
$566$	1.38894e7	1.82240
$567$	0	0
$568$	−398772.	−0.0518625
$569$	−4.56109e6	−0.590593	−0.295296	−	0.955406i	$-0.595418\pi$
$569$	−4.56109e6	−0.590593	−0.295296	+	0.955406i	$0.595418\pi$
$570$	3.71051e6	0.478350
$571$	5.42727e6	0.696613	0.348306	−	0.937381i	$-0.386757\pi$
$571$	5.42727e6	0.696613	0.348306	+	0.937381i	$0.386757\pi$
$572$	88396.5	0.0112965
$573$	7.22296e6	0.919028
$574$	0	0
$575$	762859.	0.0962220
$576$	−110371.	−0.0138612
$577$	−6.08675e6	−0.761108	−0.380554	−	0.924759i	$-0.624267\pi$
$577$	−6.08675e6	−0.761108	−0.380554	+	0.924759i	$0.624267\pi$
$578$	722833.	0.0899950
$579$	7.44667e6	0.923136
$580$	1.32153e6	0.163120
$581$	0	0
$582$	−9.14406e6	−1.11900
$583$	2.80011e6	0.341196
$584$	−5.49355e6	−0.666531
$585$	143275.	0.0173093
$586$	5.69568e6	0.685176
$587$	6.55374e6	0.785044	0.392522	−	0.919743i	$-0.371603\pi$
$587$	6.55374e6	0.785044	0.392522	+	0.919743i	$0.371603\pi$
$588$	0	0
$589$	−4.43901e6	−0.527228
$590$	3.72493e6	0.440543
$591$	−9.06738e6	−1.06786
$592$	1.30962e6	0.153582
$593$	7.47250e6	0.872628	0.436314	−	0.899794i	$-0.356284\pi$
$593$	7.47250e6	0.872628	0.436314	+	0.899794i	$0.356284\pi$
$594$	3.41483e6	0.397103
$595$	0	0
$596$	8.98647e6	1.03627
$597$	1.44284e6	0.165684
$598$	346934.	0.0396728
$599$	1.91882e6	0.218508	0.109254	−	0.994014i	$-0.465154\pi$
$599$	1.91882e6	0.218508	0.109254	+	0.994014i	$0.465154\pi$
$600$	−644325.	−0.0730679
$601$	1.03299e6	0.116657	0.0583284	−	0.998297i	$-0.481423\pi$
$601$	1.03299e6	0.116657	0.0583284	+	0.998297i	$0.481423\pi$
$602$	0	0
$603$	−2.74077e6	−0.306959
$604$	535420.	0.0597176
$605$	−3.63276e6	−0.403504
$606$	−2.94351e6	−0.325600
$607$	6.87524e6	0.757384	0.378692	−	0.925523i	$-0.376374\pi$
$607$	6.87524e6	0.757384	0.378692	+	0.925523i	$0.376374\pi$
$608$	1.19717e7	1.31340
$609$	0	0
$610$	3.44910e6	0.375302
$611$	108074.	0.0117116
$612$	2.83499e6	0.305966
$613$	797372.	0.0857057	0.0428529	−	0.999081i	$-0.486355\pi$
$613$	797372.	0.0857057	0.0428529	+	0.999081i	$0.486355\pi$
$614$	−1.04640e7	−1.12015
$615$	−5.36901e6	−0.572409
$616$	0	0
$617$	9.58474e6	1.01360	0.506801	−	0.862063i	$-0.330828\pi$
$617$	9.58474e6	1.01360	0.506801	+	0.862063i	$0.330828\pi$
$618$	−9.07705e6	−0.956035
$619$	−1.16266e7	−1.21962	−0.609811	−	0.792547i	$-0.708755\pi$
$619$	−1.16266e7	−1.21962	−0.609811	+	0.792547i	$0.708755\pi$
$620$	−921785.	−0.0963053
$621$	4.72539e6	0.491710
$622$	−5.43827e6	−0.563617
$623$	0	0
$624$	−519890.	−0.0534503
$625$	390625.	0.0400000
$626$	9.64812e6	0.984026
$627$	2.64865e6	0.269064
$628$	−2.06141e6	−0.208576
$629$	1.17605e6	0.118522
$630$	0	0
$631$	−8.01257e6	−0.801122	−0.400561	−	0.916270i	$-0.631185\pi$
$631$	−8.01257e6	−0.801122	−0.400561	+	0.916270i	$0.631185\pi$
$632$	9.88026e6	0.983956
$633$	−3.35431e6	−0.332732
$634$	−279964.	−0.0276617
$635$	−3.38459e6	−0.333098
$636$	3.91360e6	0.383649
$637$	0	0
$638$	2.67554e6	0.260231
$639$	551725.	0.0534528
$640$	−4.70172e6	−0.453739
$641$	3.60860e6	0.346891	0.173446	−	0.984843i	$-0.444510\pi$
$641$	3.60860e6	0.346891	0.173446	+	0.984843i	$0.444510\pi$
$642$	−1.07704e7	−1.03132
$643$	−1.17297e7	−1.11882	−0.559408	−	0.828892i	$-0.688972\pi$
$643$	−1.17297e7	−1.11882	−0.559408	+	0.828892i	$0.688972\pi$
$644$	0	0
$645$	−1.74031e6	−0.164713
$646$	1.69278e7	1.59595
$647$	−2.07753e7	−1.95113	−0.975567	−	0.219703i	$-0.929491\pi$
$647$	−2.07753e7	−1.95113	−0.975567	+	0.219703i	$0.929491\pi$
$648$	−462019.	−0.0432238
$649$	2.65894e6	0.247798
$650$	177649.	0.0164922
$651$	0	0
$652$	−7.49571e6	−0.690548
$653$	−1.41775e7	−1.30112	−0.650561	−	0.759454i	$-0.725466\pi$
$653$	−1.41775e7	−1.30112	−0.650561	+	0.759454i	$0.725466\pi$
$654$	1.10648e7	1.01158
$655$	5.32039e6	0.484552
$656$	−2.72760e7	−2.47469
$657$	7.60065e6	0.686969
$658$	0	0
$659$	−5.01614e6	−0.449942	−0.224971	−	0.974365i	$-0.572229\pi$
$659$	−5.01614e6	−0.449942	−0.224971	+	0.974365i	$0.572229\pi$
$660$	550006.	0.0491482
$661$	−8.71507e6	−0.775831	−0.387915	−	0.921695i	$-0.626805\pi$
$661$	−8.71507e6	−0.775831	−0.387915	+	0.921695i	$0.626805\pi$
$662$	1.24849e7	1.10724
$663$	−466866.	−0.0412486
$664$	−1.05651e7	−0.929939
$665$	0	0
$666$	−1.02127e6	−0.0892181
$667$	3.70237e6	0.322230
$668$	−5.28518e6	−0.458267
$669$	1.02094e7	0.881932
$670$	−3.39833e6	−0.292468
$671$	2.46205e6	0.211101
$672$	0	0
$673$	6.64481e6	0.565516	0.282758	−	0.959191i	$-0.408751\pi$
$673$	6.64481e6	0.565516	0.282758	+	0.959191i	$0.408751\pi$
$674$	−155807.	−0.0132110
$675$	2.41966e6	0.204406
$676$	−6.44202e6	−0.542195
$677$	−1.49518e7	−1.25378	−0.626892	−	0.779106i	$-0.715673\pi$
$677$	−1.49518e7	−1.25378	−0.626892	+	0.779106i	$0.715673\pi$
$678$	4.79263e6	0.400405
$679$	0	0
$680$	−2.93949e6	−0.243781
$681$	−1.45510e7	−1.20234
$682$	−1.86622e6	−0.153639
$683$	−1.84572e7	−1.51396	−0.756979	−	0.653439i	$-0.773325\pi$
$683$	−1.84572e7	−1.51396	−0.756979	+	0.653439i	$0.773325\pi$
$684$	−5.18287e6	−0.423574
$685$	3.15408e6	0.256830
$686$	0	0
$687$	1.50133e7	1.21362
$688$	−8.84124e6	−0.712102
$689$	902324.	0.0724127
$690$	2.15863e6	0.172606
$691$	6.72077e6	0.535456	0.267728	−	0.963494i	$-0.413727\pi$
$691$	6.72077e6	0.535456	0.267728	+	0.963494i	$0.413727\pi$
$692$	8.14147e6	0.646305
$693$	0	0
$694$	−1.26656e7	−0.998226
$695$	−4.36441e6	−0.342739
$696$	−3.12710e6	−0.244691
$697$	−2.44941e7	−1.90976
$698$	−2.08099e7	−1.61671
$699$	6.64008e6	0.514021
$700$	0	0
$701$	−2.05787e7	−1.58170	−0.790849	−	0.612011i	$-0.790361\pi$
$701$	−2.05787e7	−1.58170	−0.790849	+	0.612011i	$0.790361\pi$
$702$	1.10041e6	0.0842778
$703$	−2.15003e6	−0.164081
$704$	−97687.4	−0.00742860
$705$	672439.	0.0509542
$706$	−2.64403e7	−1.99643
$707$	0	0
$708$	3.71629e6	0.278629
$709$	2.00499e7	1.49795	0.748975	−	0.662598i	$-0.230546\pi$
$709$	2.00499e7	1.49795	0.748975	+	0.662598i	$0.230546\pi$
$710$	684092.	0.0509294
$711$	−1.36699e7	−1.01413
$712$	−8.06425e6	−0.596162
$713$	−2.58245e6	−0.190243
$714$	0	0
$715$	126810.	0.00927659
$716$	7.26487e6	0.529597
$717$	1.07247e7	0.779089
$718$	8.05384e6	0.583031
$719$	−1.39329e7	−1.00512	−0.502561	−	0.864542i	$-0.667609\pi$
$719$	−1.39329e7	−1.00512	−0.502561	+	0.864542i	$0.667609\pi$
$720$	4.52886e6	0.325580
$721$	0	0
$722$	−1.35390e7	−0.966592
$723$	−3.49642e6	−0.248758
$724$	−1.04310e7	−0.739567
$725$	1.89582e6	0.133953
$726$	−1.02795e7	−0.723818
$727$	−1.54512e7	−1.08424	−0.542122	−	0.840300i	$-0.682379\pi$
$727$	−1.54512e7	−1.08424	−0.542122	+	0.840300i	$0.682379\pi$
$728$	0	0
$729$	1.01054e7	0.704260
$730$	9.42416e6	0.654539
$731$	−7.93953e6	−0.549542
$732$	3.44111e6	0.237367
$733$	−1.14965e7	−0.790325	−0.395162	−	0.918611i	$-0.629312\pi$
$733$	−1.14965e7	−0.790325	−0.395162	+	0.918611i	$0.629312\pi$
$734$	5.16332e6	0.353744
$735$	0	0
$736$	6.96470e6	0.473923
$737$	−2.42581e6	−0.164508
$738$	2.12703e7	1.43758
$739$	8.96456e6	0.603834	0.301917	−	0.953334i	$-0.402373\pi$
$739$	8.96456e6	0.603834	0.301917	+	0.953334i	$0.402373\pi$
$740$	−446466.	−0.0299715
$741$	853515.	0.0571039
$742$	0	0
$743$	1.98660e7	1.32019	0.660097	−	0.751180i	$-0.270515\pi$
$743$	1.98660e7	1.32019	0.660097	+	0.751180i	$0.270515\pi$
$744$	2.18119e6	0.144464
$745$	1.28916e7	0.850976
$746$	−3.66144e7	−2.40882
$747$	1.46175e7	0.958454
$748$	2.50920e6	0.163976
$749$	0	0
$750$	1.10534e6	0.0717532
$751$	−2.13450e7	−1.38101	−0.690503	−	0.723329i	$-0.742611\pi$
$751$	−2.13450e7	−1.38101	−0.690503	+	0.723329i	$0.742611\pi$
$752$	3.41617e6	0.220290
$753$	9.91707e6	0.637376
$754$	862181.	0.0552294
$755$	768092.	0.0490395
$756$	0	0
$757$	−5.74878e6	−0.364616	−0.182308	−	0.983241i	$-0.558357\pi$
$757$	−5.74878e6	−0.364616	−0.182308	+	0.983241i	$0.558357\pi$
$758$	−2.17913e7	−1.37756
$759$	1.54088e6	0.0970880
$760$	5.37391e6	0.337487
$761$	−1.59649e7	−0.999321	−0.499661	−	0.866221i	$-0.666542\pi$
$761$	−1.59649e7	−0.999321	−0.499661	+	0.866221i	$0.666542\pi$
$762$	−9.57726e6	−0.597522
$763$	0	0
$764$	−1.25096e7	−0.775373
$765$	4.06696e6	0.251256
$766$	4.56394e6	0.281040
$767$	856833.	0.0525906
$768$	−1.30536e7	−0.798594
$769$	1.19091e6	0.0726211	0.0363106	−	0.999341i	$-0.488439\pi$
$769$	1.19091e6	0.0726211	0.0363106	+	0.999341i	$0.488439\pi$
$770$	0	0
$771$	−4.13228e6	−0.250354
$772$	−1.28971e7	−0.778839
$773$	2.54609e6	0.153259	0.0766293	−	0.997060i	$-0.475584\pi$
$773$	2.54609e6	0.153259	0.0766293	+	0.997060i	$0.475584\pi$
$774$	6.89456e6	0.413670
$775$	−1.32235e6	−0.0790849
$776$	−1.32433e7	−0.789482
$777$	0	0
$778$	1.16111e7	0.687741
$779$	4.47796e7	2.64385
$780$	177237.	0.0104308
$781$	488321.	0.0286469
$782$	9.84795e6	0.575876
$783$	1.17433e7	0.684519
$784$	0	0
$785$	−2.95721e6	−0.171281
$786$	1.50549e7	0.869203
$787$	−2.22304e7	−1.27941	−0.639705	−	0.768621i	$-0.720943\pi$
$787$	−2.22304e7	−1.27941	−0.639705	+	0.768621i	$0.720943\pi$
$788$	1.57040e7	0.900938
$789$	1.88465e7	1.07780
$790$	−1.69495e7	−0.966252
$791$	0	0
$792$	1.82211e6	0.103220
$793$	793385.	0.0448024
$794$	−9.00716e6	−0.507033
$795$	5.61429e6	0.315048
$796$	−2.49889e6	−0.139786
$797$	2.43182e7	1.35608	0.678041	−	0.735024i	$-0.262829\pi$
$797$	2.43182e7	1.35608	0.678041	+	0.735024i	$0.262829\pi$
$798$	0	0
$799$	3.06775e6	0.170002
$800$	3.56630e6	0.197012
$801$	1.11574e7	0.614441
$802$	−1.15729e7	−0.635340
$803$	6.72719e6	0.368167
$804$	−3.39045e6	−0.184977
$805$	0	0
$806$	−601381.	−0.0326071
$807$	−1.25368e7	−0.677644
$808$	−4.26308e6	−0.229718
$809$	2.42290e7	1.30156	0.650781	−	0.759266i	$-0.274442\pi$
$809$	2.42290e7	1.30156	0.650781	+	0.759266i	$0.274442\pi$
$810$	792592.	0.0424460
$811$	−1.46062e7	−0.779804	−0.389902	−	0.920856i	$-0.627491\pi$
$811$	−1.46062e7	−0.779804	−0.389902	+	0.920856i	$0.627491\pi$
$812$	0	0
$813$	1.64577e7	0.873257
$814$	−903903.	−0.0478146
$815$	−1.07530e7	−0.567071
$816$	−1.47574e7	−0.775864
$817$	1.45149e7	0.760778
$818$	−1.04176e7	−0.544357
$819$	0	0
$820$	9.29872e6	0.482935
$821$	7.55673e6	0.391270	0.195635	−	0.980677i	$-0.437323\pi$
$821$	7.55673e6	0.391270	0.195635	+	0.980677i	$0.437323\pi$
$822$	8.92497e6	0.460710
$823$	5.29403e6	0.272450	0.136225	−	0.990678i	$-0.456503\pi$
$823$	5.29403e6	0.272450	0.136225	+	0.990678i	$0.456503\pi$
$824$	−1.31463e7	−0.674504
$825$	789016.	0.0403600
$826$	0	0
$827$	3.01205e6	0.153143	0.0765716	−	0.997064i	$-0.475603\pi$
$827$	3.01205e6	0.153143	0.0765716	+	0.997064i	$0.475603\pi$
$828$	−3.01520e6	−0.152841
$829$	−257336.	−0.0130051	−0.00650257	−	0.999979i	$-0.502070\pi$
$829$	−257336.	−0.0130051	−0.00650257	+	0.999979i	$0.502070\pi$
$830$	1.81244e7	0.913207
$831$	1.03961e7	0.522236
$832$	−31479.3	−0.00157659
$833$	0	0
$834$	−1.23498e7	−0.614815
$835$	−7.58191e6	−0.376324
$836$	−4.58726e6	−0.227006
$837$	−8.19109e6	−0.404137
$838$	3.18219e7	1.56537
$839$	8.35253e6	0.409650	0.204825	−	0.978799i	$-0.434337\pi$
$839$	8.35253e6	0.409650	0.204825	+	0.978799i	$0.434337\pi$
$840$	0	0
$841$	−1.13102e7	−0.551417
$842$	−1.44305e7	−0.701455
$843$	−1.69968e6	−0.0823753
$844$	5.80942e6	0.280722
$845$	−9.24146e6	−0.445245
$846$	−2.66399e6	−0.127969
$847$	0	0
$848$	2.85221e7	1.36204
$849$	1.98790e7	0.946511
$850$	5.04268e6	0.239395
$851$	−1.25081e6	−0.0592062
$852$	682506.	0.0322113
$853$	1.94172e7	0.913722	0.456861	−	0.889538i	$-0.348974\pi$
$853$	1.94172e7	0.913722	0.456861	+	0.889538i	$0.348974\pi$
$854$	0	0
$855$	−7.43513e6	−0.347835
$856$	−1.55987e7	−0.727620
$857$	6.44273e6	0.299652	0.149826	−	0.988712i	$-0.452129\pi$
$857$	6.44273e6	0.299652	0.149826	+	0.988712i	$0.452129\pi$
$858$	358829.	0.0166406
$859$	2.05557e7	0.950492	0.475246	−	0.879853i	$-0.342359\pi$
$859$	2.05557e7	0.950492	0.475246	+	0.879853i	$0.342359\pi$
$860$	3.01409e6	0.138967
$861$	0	0
$862$	−4.01622e7	−1.84098
$863$	−1.91353e7	−0.874598	−0.437299	−	0.899316i	$-0.644065\pi$
$863$	−1.91353e7	−0.874598	−0.437299	+	0.899316i	$0.644065\pi$
$864$	2.20908e7	1.00676
$865$	1.16794e7	0.530739
$866$	2.28784e7	1.03665
$867$	1.03454e6	0.0467413
$868$	0	0
$869$	−1.20990e7	−0.543500
$870$	5.36452e6	0.240288
$871$	−781706.	−0.0349139
$872$	1.60251e7	0.713690
$873$	1.83229e7	0.813689
$874$	−1.80038e7	−0.797234
$875$	0	0
$876$	9.40231e6	0.413975
$877$	2.05496e6	0.0902203	0.0451102	−	0.998982i	$-0.485636\pi$
$877$	2.05496e6	0.0902203	0.0451102	+	0.998982i	$0.485636\pi$
$878$	998986.	0.0437344
$879$	8.15186e6	0.355864
$880$	4.00841e6	0.174488
$881$	3.39035e7	1.47165	0.735825	−	0.677171i	$-0.236794\pi$
$881$	3.39035e7	1.47165	0.735825	+	0.677171i	$0.236794\pi$
$882$	0	0
$883$	1.48069e7	0.639091	0.319546	−	0.947571i	$-0.396470\pi$
$883$	1.48069e7	0.639091	0.319546	+	0.947571i	$0.396470\pi$
$884$	808577.	0.0348009
$885$	5.33125e6	0.228808
$886$	−1.55471e7	−0.665371
$887$	1.15472e7	0.492795	0.246397	−	0.969169i	$-0.420753\pi$
$887$	1.15472e7	0.492795	0.246397	+	0.969169i	$0.420753\pi$
$888$	1.05646e6	0.0449593
$889$	0	0
$890$	1.38342e7	0.585435
$891$	565771.	0.0238752
$892$	−1.76819e7	−0.744076
$893$	−5.60840e6	−0.235348
$894$	3.64789e7	1.52651
$895$	1.04219e7	0.434899
$896$	0	0
$897$	496543.	0.0206052
$898$	−5.35446e7	−2.21577
$899$	−6.41777e6	−0.264841
$900$	−1.54394e6	−0.0635368
$901$	2.56131e7	1.05111
$902$	1.88259e7	0.770442
$903$	0	0
$904$	6.94114e6	0.282495
$905$	−1.49638e7	−0.607325
$906$	2.17344e6	0.0879685
$907$	−3.85998e7	−1.55800	−0.778999	−	0.627025i	$-0.784272\pi$
$907$	−3.85998e7	−1.55800	−0.778999	+	0.627025i	$0.784272\pi$
$908$	2.52013e7	1.01440
$909$	5.89823e6	0.236762
$910$	0	0
$911$	−3.94460e7	−1.57473	−0.787367	−	0.616484i	$-0.788556\pi$
$911$	−3.94460e7	−1.57473	−0.787367	+	0.616484i	$0.788556\pi$
$912$	2.69792e7	1.07409
$913$	1.29377e7	0.513664
$914$	−1.89895e7	−0.751878
$915$	4.93647e6	0.194923
$916$	−2.60018e7	−1.02392
$917$	0	0
$918$	3.12360e7	1.22334
$919$	4.00878e7	1.56575	0.782877	−	0.622176i	$-0.213751\pi$
$919$	4.00878e7	1.56575	0.782877	+	0.622176i	$0.213751\pi$
$920$	3.12634e6	0.121777
$921$	−1.49765e7	−0.581783
$922$	2.43461e7	0.943195
$923$	157359.	0.00607979
$924$	0	0
$925$	−640482.	−0.0246123
$926$	3.39611e7	1.30153
$927$	1.81886e7	0.695186
$928$	1.73083e7	0.659758
$929$	−8.91452e6	−0.338890	−0.169445	−	0.985540i	$-0.554198\pi$
$929$	−8.91452e6	−0.338890	−0.169445	+	0.985540i	$0.554198\pi$
$930$	−3.74182e6	−0.141865
$931$	0	0
$932$	−1.15001e7	−0.433673
$933$	−7.78343e6	−0.292730
$934$	1.02608e7	0.384872
$935$	3.59959e6	0.134655
$936$	587168.	0.0219065
$937$	2.29072e7	0.852358	0.426179	−	0.904639i	$-0.359859\pi$
$937$	2.29072e7	0.852358	0.426179	+	0.904639i	$0.359859\pi$
$938$	0	0
$939$	1.38087e7	0.511080
$940$	−1.16461e6	−0.0429895
$941$	4.36837e7	1.60822	0.804109	−	0.594482i	$-0.202643\pi$
$941$	4.36837e7	1.60822	0.804109	+	0.594482i	$0.202643\pi$
$942$	−8.36791e6	−0.307249
$943$	2.60511e7	0.953996
$944$	2.70841e7	0.989201
$945$	0	0
$946$	6.10225e6	0.221698
$947$	608423.	0.0220460	0.0110230	−	0.999939i	$-0.496491\pi$
$947$	608423.	0.0220460	0.0110230	+	0.999939i	$0.496491\pi$
$948$	−1.69103e7	−0.611124
$949$	2.16781e6	0.0781367
$950$	−9.21893e6	−0.331414
$951$	−400694.	−0.0143669
$952$	0	0
$953$	5.71200e6	0.203730	0.101865	−	0.994798i	$-0.467519\pi$
$953$	5.71200e6	0.203730	0.101865	+	0.994798i	$0.467519\pi$
$954$	−2.22420e7	−0.791231
$955$	−1.79458e7	−0.636728
$956$	−1.85744e7	−0.657308
$957$	3.82932e6	0.135158
$958$	−6.37097e7	−2.24280
$959$	0	0
$960$	−195866.	−0.00685930
$961$	−2.41527e7	−0.843639
$962$	−291279.	−0.0101478
$963$	2.15818e7	0.749931
$964$	6.05553e6	0.209874
$965$	−1.85016e7	−0.639575
$966$	0	0
$967$	−4.04624e6	−0.139151	−0.0695754	−	0.997577i	$-0.522164\pi$
$967$	−4.04624e6	−0.139151	−0.0695754	+	0.997577i	$0.522164\pi$
$968$	−1.48877e7	−0.510670
$969$	2.42276e7	0.828899
$970$	2.27188e7	0.775277
$971$	−4.70302e7	−1.60077	−0.800385	−	0.599486i	$-0.795372\pi$
$971$	−4.70302e7	−1.60077	−0.800385	+	0.599486i	$0.795372\pi$
$972$	−1.56039e7	−0.529745
$973$	0	0
$974$	5.93650e6	0.200509
$975$	254257.	0.00856567
$976$	2.50785e7	0.842709
$977$	6.12115e6	0.205162	0.102581	−	0.994725i	$-0.467290\pi$
$977$	6.12115e6	0.205162	0.102581	+	0.994725i	$0.467290\pi$
$978$	−3.04275e7	−1.01723
$979$	9.87518e6	0.329297
$980$	0	0
$981$	−2.21717e7	−0.735574
$982$	5.00492e7	1.65622
$983$	2.92671e6	0.0966040	0.0483020	−	0.998833i	$-0.484619\pi$
$983$	2.92671e6	0.0966040	0.0483020	+	0.998833i	$0.484619\pi$
$984$	−2.20032e7	−0.724434
$985$	2.25283e7	0.739841
$986$	2.44736e7	0.801689
$987$	0	0
$988$	−1.47822e6	−0.0481779
$989$	8.44421e6	0.274516
$990$	−3.12583e6	−0.101362
$991$	4.25857e6	0.137746	0.0688731	−	0.997625i	$-0.478060\pi$
$991$	4.25857e6	0.137746	0.0688731	+	0.997625i	$0.478060\pi$
$992$	−1.20727e7	−0.389517
$993$	1.78688e7	0.575073
$994$	0	0
$995$	−3.58480e6	−0.114791
$996$	1.80824e7	0.577575
$997$	5.29692e7	1.68766	0.843832	−	0.536608i	$-0.180295\pi$
$997$	5.29692e7	1.68766	0.843832	+	0.536608i	$0.180295\pi$
$998$	1.43628e7	0.456469
$999$	−3.96735e6	−0.125773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.f.1.2	✓	5
7.6	odd	2		245.6.a.g.1.2	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.f.1.2	✓	5	1.1	even	1	trivial
245.6.a.g.1.2	yes	5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-7.03043 q^{2} -10.0622 q^{3} +17.4270 q^{4} +25.0000 q^{5} +70.7416 q^{6} +102.455 q^{8} -141.752 q^{9} +O(q^{10})\)	\(q-7.03043 q^{2} -10.0622 q^{3} +17.4270 q^{4} +25.0000 q^{5} +70.7416 q^{6} +102.455 q^{8} -141.752 q^{9} -175.761 q^{10} -125.462 q^{11} -175.353 q^{12} -40.4297 q^{13} -251.555 q^{15} -1277.96 q^{16} -1147.62 q^{17} +996.579 q^{18} +2098.06 q^{19} +435.674 q^{20} +882.054 q^{22} +1220.57 q^{23} -1030.92 q^{24} +625.000 q^{25} +284.238 q^{26} +3871.45 q^{27} +3033.31 q^{29} +1768.54 q^{30} -2115.77 q^{31} +5706.08 q^{32} +1262.43 q^{33} +8068.29 q^{34} -2470.31 q^{36} -1024.77 q^{37} -14750.3 q^{38} +406.811 q^{39} +2561.37 q^{40} +21343.3 q^{41} +6918.23 q^{43} -2186.43 q^{44} -3543.81 q^{45} -8581.16 q^{46} -2673.13 q^{47} +12859.1 q^{48} -4394.02 q^{50} +11547.6 q^{51} -704.566 q^{52} -22318.4 q^{53} -27218.0 q^{54} -3136.56 q^{55} -21111.1 q^{57} -21325.4 q^{58} -21193.2 q^{59} -4383.83 q^{60} -19623.8 q^{61} +14874.8 q^{62} +778.620 q^{64} -1010.74 q^{65} -8875.40 q^{66} +19335.0 q^{67} -19999.6 q^{68} -12281.7 q^{69} -3892.18 q^{71} -14523.2 q^{72} -53619.2 q^{73} +7204.58 q^{74} -6288.87 q^{75} +36562.8 q^{76} -2860.06 q^{78} +96435.3 q^{79} -31949.1 q^{80} -4509.49 q^{81} -150053. q^{82} -103120. q^{83} -28690.6 q^{85} -48638.1 q^{86} -30521.7 q^{87} -12854.2 q^{88} -78710.3 q^{89} +24914.5 q^{90} +21270.9 q^{92} +21289.3 q^{93} +18793.3 q^{94} +52451.6 q^{95} -57415.7 q^{96} -129260. q^{97} +17784.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} - 7 q^{3} + 101 q^{4} + 125 q^{5} - 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 - 7 * q^3 + 101 * q^4 + 125 * q^5 - 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} - 7 q^{3} + 101 q^{4} + 125 q^{5} - 304 q^{6} - 675 q^{8} + 284 q^{9} - 75 q^{10} + 1033 q^{11} + 1226 q^{12} - 1117 q^{13} - 175 q^{15} + 297 q^{16} - 3403 q^{17} + 887 q^{18} - 2846 q^{19} + 2525 q^{20} - 1858 q^{22} - 2756 q^{23} - 13290 q^{24} + 3125 q^{25} - 2544 q^{26} - 3661 q^{27} + 485 q^{29} - 7600 q^{30} - 10726 q^{31} - 17383 q^{32} - 12597 q^{33} + 16414 q^{34} + 38165 q^{36} - 2660 q^{37} + 14378 q^{38} - 13171 q^{39} - 16875 q^{40} + 8334 q^{41} - 17294 q^{43} + 42876 q^{44} + 7100 q^{45} + 45724 q^{46} - 59799 q^{47} + 94218 q^{48} - 1875 q^{50} - 12049 q^{51} - 87974 q^{52} - 9250 q^{53} - 106342 q^{54} + 25825 q^{55} - 121778 q^{57} + 35868 q^{58} - 52994 q^{59} + 30650 q^{60} - 81540 q^{61} + 74048 q^{62} + 39745 q^{64} - 27925 q^{65} - 311614 q^{66} - 726 q^{67} - 276216 q^{68} - 21388 q^{69} + 3760 q^{71} - 154815 q^{72} - 90634 q^{73} - 57342 q^{74} - 4375 q^{75} - 43902 q^{76} + 152598 q^{78} + 68243 q^{79} + 7425 q^{80} + 17645 q^{81} - 191552 q^{82} + 133292 q^{83} - 85075 q^{85} - 88352 q^{86} - 216813 q^{87} - 273040 q^{88} - 102852 q^{89} + 22175 q^{90} - 140852 q^{92} + 184862 q^{93} - 332618 q^{94} - 71150 q^{95} - 245574 q^{96} - 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 7 * q^3 + 101 * q^4 + 125 * q^5 - 304 * q^6 - 675 * q^8 + 284 * q^9 - 75 * q^10 + 1033 * q^11 + 1226 * q^12 - 1117 * q^13 - 175 * q^15 + 297 * q^16 - 3403 * q^17 + 887 * q^18 - 2846 * q^19 + 2525 * q^20 - 1858 * q^22 - 2756 * q^23 - 13290 * q^24 + 3125 * q^25 - 2544 * q^26 - 3661 * q^27 + 485 * q^29 - 7600 * q^30 - 10726 * q^31 - 17383 * q^32 - 12597 * q^33 + 16414 * q^34 + 38165 * q^36 - 2660 * q^37 + 14378 * q^38 - 13171 * q^39 - 16875 * q^40 + 8334 * q^41 - 17294 * q^43 + 42876 * q^44 + 7100 * q^45 + 45724 * q^46 - 59799 * q^47 + 94218 * q^48 - 1875 * q^50 - 12049 * q^51 - 87974 * q^52 - 9250 * q^53 - 106342 * q^54 + 25825 * q^55 - 121778 * q^57 + 35868 * q^58 - 52994 * q^59 + 30650 * q^60 - 81540 * q^61 + 74048 * q^62 + 39745 * q^64 - 27925 * q^65 - 311614 * q^66 - 726 * q^67 - 276216 * q^68 - 21388 * q^69 + 3760 * q^71 - 154815 * q^72 - 90634 * q^73 - 57342 * q^74 - 4375 * q^75 - 43902 * q^76 + 152598 * q^78 + 68243 * q^79 + 7425 * q^80 + 17645 * q^81 - 191552 * q^82 + 133292 * q^83 - 85075 * q^85 - 88352 * q^86 - 216813 * q^87 - 273040 * q^88 - 102852 * q^89 + 22175 * q^90 - 140852 * q^92 + 184862 * q^93 - 332618 * q^94 - 71150 * q^95 - 245574 * q^96 - 186175 * q^97 + 454710 * q^99

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