LMFDB - Embedded newform 245.6.a.i.1.3

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:	$6$
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} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 $ x^6 - x^5 - 109x^4 + 41x^3 + 2208x^2 - 3204x + 560
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.203319$ 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)

$f(q)$	$=$	$q-0.796681 q^{2} +10.5748 q^{3} -31.3653 q^{4} -25.0000 q^{5} -8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} +O(q^{10})$	\(q-0.796681 q^{2} +10.5748 q^{3} -31.3653 q^{4} -25.0000 q^{5} -8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} +19.9170 q^{10} +525.291 q^{11} -331.683 q^{12} +819.361 q^{13} -264.371 q^{15} +963.472 q^{16} -921.367 q^{17} +104.503 q^{18} -696.175 q^{19} +784.132 q^{20} -418.489 q^{22} +2381.87 q^{23} +533.838 q^{24} +625.000 q^{25} -652.769 q^{26} -3956.82 q^{27} -6200.04 q^{29} +210.619 q^{30} -8011.35 q^{31} -2383.00 q^{32} +5554.86 q^{33} +734.036 q^{34} +4114.28 q^{36} -8137.67 q^{37} +554.630 q^{38} +8664.60 q^{39} -1262.05 q^{40} +1703.92 q^{41} -8132.54 q^{43} -16475.9 q^{44} +3279.33 q^{45} -1897.59 q^{46} -3326.02 q^{47} +10188.5 q^{48} -497.926 q^{50} -9743.30 q^{51} -25699.5 q^{52} -32684.7 q^{53} +3152.32 q^{54} -13132.3 q^{55} -7361.94 q^{57} +4939.45 q^{58} +32368.3 q^{59} +8292.07 q^{60} +46496.9 q^{61} +6382.49 q^{62} -28932.6 q^{64} -20484.0 q^{65} -4425.45 q^{66} -5352.68 q^{67} +28899.0 q^{68} +25187.9 q^{69} -44485.5 q^{71} -6621.87 q^{72} -70525.0 q^{73} +6483.12 q^{74} +6609.27 q^{75} +21835.8 q^{76} -6902.92 q^{78} +46387.5 q^{79} -24086.8 q^{80} -9967.59 q^{81} -1357.48 q^{82} +27244.4 q^{83} +23034.2 q^{85} +6479.04 q^{86} -65564.4 q^{87} +26517.7 q^{88} -64637.8 q^{89} -2612.58 q^{90} -74708.2 q^{92} -84718.6 q^{93} +2649.77 q^{94} +17404.4 q^{95} -25199.8 q^{96} +31410.9 q^{97} -68904.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 20 * q^3 + 31 * q^4 - 150 * q^5 + 96 * q^6 - 135 * q^8 + 378 * q^9	\( 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9} + 125 q^{10} - 924 q^{11} + 370 q^{12} - 150 q^{13} - 500 q^{15} + 435 q^{16} + 1540 q^{17} + 195 q^{18} + 92 q^{19} - 775 q^{20} - 6855 q^{22} - 3920 q^{23} - 7200 q^{24} + 3750 q^{25} + 2635 q^{26} + 2060 q^{27} + 1264 q^{29} - 2400 q^{30} - 7160 q^{31} + 9105 q^{32} + 4460 q^{33} + 2166 q^{34} - 26375 q^{36} - 14170 q^{37} - 46215 q^{38} - 15376 q^{39} + 3375 q^{40} + 4098 q^{41} - 24460 q^{43} - 27873 q^{44} - 9450 q^{45} + 6815 q^{46} + 42940 q^{47} + 11610 q^{48} - 3125 q^{50} - 42008 q^{51} - 36115 q^{52} - 2450 q^{53} + 19566 q^{54} + 23100 q^{55} - 97100 q^{57} - 36110 q^{58} - 64600 q^{59} - 9250 q^{60} + 73620 q^{61} + 111440 q^{62} - 157997 q^{64} + 3750 q^{65} - 139138 q^{66} - 142620 q^{67} + 124330 q^{68} + 17344 q^{69} - 154256 q^{71} - 117495 q^{72} - 5120 q^{73} + 2785 q^{74} + 12500 q^{75} + 7775 q^{76} - 214090 q^{78} - 222504 q^{79} - 10875 q^{80} - 43986 q^{81} + 31665 q^{82} + 179580 q^{83} - 38500 q^{85} - 207160 q^{86} - 209300 q^{87} - 45145 q^{88} + 41648 q^{89} - 4875 q^{90} - 292185 q^{92} - 198520 q^{93} - 333699 q^{94} - 2300 q^{95} + 61824 q^{96} - 73980 q^{97} - 190772 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 20 * q^3 + 31 * q^4 - 150 * q^5 + 96 * q^6 - 135 * q^8 + 378 * q^9 + 125 * q^10 - 924 * q^11 + 370 * q^12 - 150 * q^13 - 500 * q^15 + 435 * q^16 + 1540 * q^17 + 195 * q^18 + 92 * q^19 - 775 * q^20 - 6855 * q^22 - 3920 * q^23 - 7200 * q^24 + 3750 * q^25 + 2635 * q^26 + 2060 * q^27 + 1264 * q^29 - 2400 * q^30 - 7160 * q^31 + 9105 * q^32 + 4460 * q^33 + 2166 * q^34 - 26375 * q^36 - 14170 * q^37 - 46215 * q^38 - 15376 * q^39 + 3375 * q^40 + 4098 * q^41 - 24460 * q^43 - 27873 * q^44 - 9450 * q^45 + 6815 * q^46 + 42940 * q^47 + 11610 * q^48 - 3125 * q^50 - 42008 * q^51 - 36115 * q^52 - 2450 * q^53 + 19566 * q^54 + 23100 * q^55 - 97100 * q^57 - 36110 * q^58 - 64600 * q^59 - 9250 * q^60 + 73620 * q^61 + 111440 * q^62 - 157997 * q^64 + 3750 * q^65 - 139138 * q^66 - 142620 * q^67 + 124330 * q^68 + 17344 * q^69 - 154256 * q^71 - 117495 * q^72 - 5120 * q^73 + 2785 * q^74 + 12500 * q^75 + 7775 * q^76 - 214090 * q^78 - 222504 * q^79 - 10875 * q^80 - 43986 * q^81 + 31665 * q^82 + 179580 * q^83 - 38500 * q^85 - 207160 * q^86 - 209300 * q^87 - 45145 * q^88 + 41648 * q^89 - 4875 * q^90 - 292185 * q^92 - 198520 * q^93 - 333699 * q^94 - 2300 * q^95 + 61824 * q^96 - 73980 * q^97 - 190772 * 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 $

$2$	−0.796681	−0.140835	−0.0704173	−	0.997518i	$-0.522433\pi$
$2$	−0.796681	−0.140835	−0.0704173	+	0.997518i	$0.522433\pi$
$3$	10.5748	0.678375	0.339188	−	0.940719i	$-0.389848\pi$
$3$	10.5748	0.678375	0.339188	+	0.940719i	$0.389848\pi$
$4$	−31.3653	−0.980166
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−8.42477	−0.0955388
$7$	0	0
$7$	0	0
$8$	50.4819	0.278876
$9$	−131.173	−0.539807
$10$	19.9170	0.0629832
$11$	525.291	1.30894	0.654468	−	0.756090i	$-0.272893\pi$
$11$	525.291	1.30894	0.654468	+	0.756090i	$0.272893\pi$
$12$	−331.683	−0.664920
$13$	819.361	1.34467	0.672337	−	0.740245i	$-0.265291\pi$
$13$	819.361	1.34467	0.672337	+	0.740245i	$0.265291\pi$
$14$	0	0
$15$	−264.371	−0.303379
$16$	963.472	0.940890
$17$	−921.367	−0.773233	−0.386616	−	0.922241i	$-0.626356\pi$
$17$	−921.367	−0.773233	−0.386616	+	0.922241i	$0.626356\pi$
$18$	104.503	0.0760235
$19$	−696.175	−0.442420	−0.221210	−	0.975226i	$-0.571001\pi$
$19$	−696.175	−0.442420	−0.221210	+	0.975226i	$0.571001\pi$
$20$	784.132	0.438343
$21$	0	0
$22$	−418.489	−0.184344
$23$	2381.87	0.938856	0.469428	−	0.882971i	$-0.344460\pi$
$23$	2381.87	0.938856	0.469428	+	0.882971i	$0.344460\pi$
$24$	533.838	0.189183
$25$	625.000	0.200000
$26$	−652.769	−0.189377
$27$	−3956.82	−1.04457
$28$	0	0
$29$	−6200.04	−1.36899	−0.684494	−	0.729019i	$-0.739977\pi$
$29$	−6200.04	−1.36899	−0.684494	+	0.729019i	$0.739977\pi$
$30$	210.619	0.0427262
$31$	−8011.35	−1.49727	−0.748637	−	0.662980i	$-0.769291\pi$
$31$	−8011.35	−1.49727	−0.748637	+	0.662980i	$0.769291\pi$
$32$	−2383.00	−0.411386
$33$	5554.86	0.887950
$34$	734.036	0.108898
$35$	0	0
$36$	4114.28	0.529100
$37$	−8137.67	−0.977227	−0.488614	−	0.872500i	$-0.662497\pi$
$37$	−8137.67	−0.977227	−0.488614	+	0.872500i	$0.662497\pi$
$38$	554.630	0.0623081
$39$	8664.60	0.912194
$40$	−1262.05	−0.124717
$41$	1703.92	0.158304	0.0791518	−	0.996863i	$-0.474779\pi$
$41$	1703.92	0.158304	0.0791518	+	0.996863i	$0.474779\pi$
$42$	0	0
$43$	−8132.54	−0.670741	−0.335370	−	0.942086i	$-0.608861\pi$
$43$	−8132.54	−0.670741	−0.335370	+	0.942086i	$0.608861\pi$
$44$	−16475.9	−1.28297
$45$	3279.33	0.241409
$46$	−1897.59	−0.132224
$47$	−3326.02	−0.219624	−0.109812	−	0.993952i	$-0.535025\pi$
$47$	−3326.02	−0.219624	−0.109812	+	0.993952i	$0.535025\pi$
$48$	10188.5	0.638277
$49$	0	0
$50$	−497.926	−0.0281669
$51$	−9743.30	−0.524542
$52$	−25699.5	−1.31800
$53$	−32684.7	−1.59829	−0.799144	−	0.601139i	$-0.794714\pi$
$53$	−32684.7	−1.59829	−0.799144	+	0.601139i	$0.794714\pi$
$54$	3152.32	0.147111
$55$	−13132.3	−0.585374
$56$	0	0
$57$	−7361.94	−0.300127
$58$	4939.45	0.192801
$59$	32368.3	1.21057	0.605285	−	0.796009i	$-0.293059\pi$
$59$	32368.3	1.21057	0.605285	+	0.796009i	$0.293059\pi$
$60$	8292.07	0.297361
$61$	46496.9	1.59993	0.799963	−	0.600050i	$-0.204853\pi$
$61$	46496.9	1.59993	0.799963	+	0.600050i	$0.204853\pi$
$62$	6382.49	0.210868
$63$	0	0
$64$	−28932.6	−0.882953
$65$	−20484.0	−0.601356
$66$	−4425.45	−0.125054
$67$	−5352.68	−0.145675	−0.0728373	−	0.997344i	$-0.523205\pi$
$67$	−5352.68	−0.145675	−0.0728373	+	0.997344i	$0.523205\pi$
$68$	28899.0	0.757896
$69$	25187.9	0.636897
$70$	0	0
$71$	−44485.5	−1.04730	−0.523651	−	0.851933i	$-0.675431\pi$
$71$	−44485.5	−1.04730	−0.523651	+	0.851933i	$0.675431\pi$
$72$	−6621.87	−0.150539
$73$	−70525.0	−1.54894	−0.774472	−	0.632608i	$-0.781984\pi$
$73$	−70525.0	−1.54894	−0.774472	+	0.632608i	$0.781984\pi$
$74$	6483.12	0.137627
$75$	6609.27	0.135675
$76$	21835.8	0.433645
$77$	0	0
$78$	−6902.92	−0.128468
$79$	46387.5	0.836244	0.418122	−	0.908391i	$-0.362688\pi$
$79$	46387.5	0.836244	0.418122	+	0.908391i	$0.362688\pi$
$80$	−24086.8	−0.420779
$81$	−9967.59	−0.168802
$82$	−1357.48	−0.0222946
$83$	27244.4	0.434093	0.217046	−	0.976161i	$-0.430358\pi$
$83$	27244.4	0.434093	0.217046	+	0.976161i	$0.430358\pi$
$84$	0	0
$85$	23034.2	0.345800
$86$	6479.04	0.0944636
$87$	−65564.4	−0.928688
$88$	26517.7	0.365031
$89$	−64637.8	−0.864991	−0.432496	−	0.901636i	$-0.642367\pi$
$89$	−64637.8	−0.864991	−0.432496	+	0.901636i	$0.642367\pi$
$90$	−2612.58	−0.0339987
$91$	0	0
$92$	−74708.2	−0.920235
$93$	−84718.6	−1.01571
$94$	2649.77	0.0309307
$95$	17404.4	0.197856
$96$	−25199.8	−0.279074
$97$	31410.9	0.338962	0.169481	−	0.985533i	$-0.445791\pi$
$97$	31410.9	0.338962	0.169481	+	0.985533i	$0.445791\pi$
$98$	0	0
$99$	−68904.0	−0.706572
$100$	−19603.3	−0.196033
$101$	−62003.4	−0.604800	−0.302400	−	0.953181i	$-0.597788\pi$
$101$	−62003.4	−0.604800	−0.302400	+	0.953181i	$0.597788\pi$
$102$	7762.30	0.0738737
$103$	3845.49	0.0357156	0.0178578	−	0.999841i	$-0.494315\pi$
$103$	3845.49	0.0357156	0.0178578	+	0.999841i	$0.494315\pi$
$104$	41362.9	0.374997
$105$	0	0
$106$	26039.3	0.225094
$107$	−199544.	−1.68492	−0.842458	−	0.538761i	$-0.818892\pi$
$107$	−199544.	−1.68492	−0.842458	+	0.538761i	$0.818892\pi$
$108$	124107.	1.02385
$109$	−226791.	−1.82835	−0.914175	−	0.405320i	$-0.867160\pi$
$109$	−226791.	−1.82835	−0.914175	+	0.405320i	$0.867160\pi$
$110$	10462.2	0.0824409
$111$	−86054.4	−0.662927
$112$	0	0
$113$	−119266.	−0.878657	−0.439329	−	0.898326i	$-0.644784\pi$
$113$	−119266.	−0.878657	−0.439329	+	0.898326i	$0.644784\pi$
$114$	5865.12	0.0422683
$115$	−59546.8	−0.419869
$116$	194466.	1.34183
$117$	−107478.	−0.725864
$118$	−25787.2	−0.170490
$119$	0	0
$120$	−13345.9	−0.0846050
$121$	114880.	0.713313
$122$	−37043.2	−0.225325
$123$	18018.7	0.107389
$124$	251278.	1.46758
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	56826.0	0.312635	0.156318	−	0.987707i	$-0.450038\pi$
$127$	56826.0	0.312635	0.156318	+	0.987707i	$0.450038\pi$
$128$	99306.1	0.535736
$129$	−86000.2	−0.455014
$130$	16319.2	0.0846918
$131$	−25383.3	−0.129232	−0.0646160	−	0.997910i	$-0.520582\pi$
$131$	−25383.3	−0.129232	−0.0646160	+	0.997910i	$0.520582\pi$
$132$	−174230.	−0.870338
$133$	0	0
$134$	4264.38	0.0205160
$135$	98920.4	0.467145
$136$	−46512.4	−0.215636
$137$	−163627.	−0.744824	−0.372412	−	0.928067i	$-0.621469\pi$
$137$	−163627.	−0.744824	−0.372412	+	0.928067i	$0.621469\pi$
$138$	−20066.7	−0.0896972
$139$	−16033.1	−0.0703850	−0.0351925	−	0.999381i	$-0.511204\pi$
$139$	−16033.1	−0.0703850	−0.0351925	+	0.999381i	$0.511204\pi$
$140$	0	0
$141$	−35172.0	−0.148988
$142$	35440.7	0.147497
$143$	430403.	1.76009
$144$	−126381.	−0.507899
$145$	155001.	0.612230
$146$	56185.9	0.218145
$147$	0	0
$148$	255240.	0.957844
$149$	188193.	0.694446	0.347223	−	0.937783i	$-0.387125\pi$
$149$	188193.	0.694446	0.347223	+	0.937783i	$0.387125\pi$
$150$	−5265.48	−0.0191078
$151$	284507.	1.01543	0.507716	−	0.861524i	$-0.330490\pi$
$151$	284507.	1.01543	0.507716	+	0.861524i	$0.330490\pi$
$152$	−35144.3	−0.123380
$153$	120859.	0.417396
$154$	0	0
$155$	200284.	0.669601
$156$	−271768.	−0.894101
$157$	271417.	0.878795	0.439397	−	0.898293i	$-0.355192\pi$
$157$	271417.	0.878795	0.439397	+	0.898293i	$0.355192\pi$
$158$	−36956.0	−0.117772
$159$	−345635.	−1.08424
$160$	59575.0	0.183977
$161$	0	0
$162$	7940.99	0.0237732
$163$	−54628.4	−0.161046	−0.0805229	−	0.996753i	$-0.525659\pi$
$163$	−54628.4	−0.161046	−0.0805229	+	0.996753i	$0.525659\pi$
$164$	−53444.1	−0.155164
$165$	−138872.	−0.397103
$166$	−21705.1	−0.0611353
$167$	150821.	0.418476	0.209238	−	0.977865i	$-0.432902\pi$
$167$	150821.	0.418476	0.209238	+	0.977865i	$0.432902\pi$
$168$	0	0
$169$	300059.	0.808147
$170$	−18350.9	−0.0487007
$171$	91319.4	0.238821
$172$	255079.	0.657437
$173$	95408.6	0.242366	0.121183	−	0.992630i	$-0.461331\pi$
$173$	95408.6	0.242366	0.121183	+	0.992630i	$0.461331\pi$
$174$	52233.9	0.130791
$175$	0	0
$176$	506103.	1.23156
$177$	342289.	0.821221
$178$	51495.7	0.121821
$179$	418881.	0.977144	0.488572	−	0.872524i	$-0.337518\pi$
$179$	418881.	0.977144	0.488572	+	0.872524i	$0.337518\pi$
$180$	−102857.	−0.236621
$181$	−435672.	−0.988469	−0.494235	−	0.869329i	$-0.664552\pi$
$181$	−435672.	−0.988469	−0.494235	+	0.869329i	$0.664552\pi$
$182$	0	0
$183$	491697.	1.08535
$184$	120242.	0.261824
$185$	203442.	0.437029
$186$	67493.7	0.143048
$187$	−483986.	−1.01211
$188$	104321.	0.215268
$189$	0	0
$190$	−13865.7	−0.0278650
$191$	546991.	1.08492	0.542459	−	0.840082i	$-0.317493\pi$
$191$	546991.	1.08492	0.542459	+	0.840082i	$0.317493\pi$
$192$	−305957.	−0.598974
$193$	−43180.5	−0.0834439	−0.0417219	−	0.999129i	$-0.513284\pi$
$193$	−43180.5	−0.0834439	−0.0417219	+	0.999129i	$0.513284\pi$
$194$	−25024.4	−0.0477375
$195$	−216615.	−0.407945
$196$	0	0
$197$	−46410.0	−0.0852012	−0.0426006	−	0.999092i	$-0.513564\pi$
$197$	−46410.0	−0.0852012	−0.0426006	+	0.999092i	$0.513564\pi$
$198$	54894.5	0.0995099
$199$	471086.	0.843271	0.421636	−	0.906765i	$-0.361456\pi$
$199$	471086.	0.843271	0.421636	+	0.906765i	$0.361456\pi$
$200$	31551.2	0.0557752
$201$	−56603.6	−0.0988221
$202$	49396.9	0.0851768
$203$	0	0
$204$	305601.	0.514138
$205$	−42598.1	−0.0707955
$206$	−3063.63	−0.00503000
$207$	−312438.	−0.506801
$208$	789431.	1.26519
$209$	−365695.	−0.579099
$210$	0	0
$211$	−844273.	−1.30550	−0.652750	−	0.757573i	$-0.726385\pi$
$211$	−844273.	−1.30550	−0.652750	+	0.757573i	$0.726385\pi$
$212$	1.02517e6	1.56659
$213$	−470426.	−0.710464
$214$	158973.	0.237295
$215$	203313.	0.299964
$216$	−199748.	−0.291305
$217$	0	0
$218$	180680.	0.257495
$219$	−745789.	−1.05077
$220$	411898.	0.573763
$221$	−754932.	−1.03975
$222$	68557.9	0.0933631
$223$	−285256.	−0.384126	−0.192063	−	0.981383i	$-0.561518\pi$
$223$	−285256.	−0.384126	−0.192063	+	0.981383i	$0.561518\pi$
$224$	0	0
$225$	−81983.1	−0.107961
$226$	95016.8	0.123745
$227$	1.11635e6	1.43792	0.718960	−	0.695051i	$-0.244618\pi$
$227$	1.11635e6	1.43792	0.718960	+	0.695051i	$0.244618\pi$
$228$	230909.	0.294174
$229$	−1.19466e6	−1.50542	−0.752708	−	0.658355i	$-0.771253\pi$
$229$	−1.19466e6	−1.50542	−0.752708	+	0.658355i	$0.771253\pi$
$230$	47439.9	0.0591322
$231$	0	0
$232$	−312990.	−0.381778
$233$	−844898.	−1.01956	−0.509782	−	0.860303i	$-0.670274\pi$
$233$	−844898.	−1.01956	−0.509782	+	0.860303i	$0.670274\pi$
$234$	85625.7	0.102227
$235$	83150.4	0.0982188
$236$	−1.01524e6	−1.18656
$237$	490540.	0.567287
$238$	0	0
$239$	−627392.	−0.710467	−0.355234	−	0.934778i	$-0.615599\pi$
$239$	−627392.	−0.710467	−0.355234	+	0.934778i	$0.615599\pi$
$240$	−254714.	−0.285446
$241$	−557012.	−0.617763	−0.308882	−	0.951100i	$-0.599955\pi$
$241$	−557012.	−0.617763	−0.308882	+	0.951100i	$0.599955\pi$
$242$	−91522.5	−0.100459
$243$	856101.	0.930056
$244$	−1.45839e6	−1.56819
$245$	0	0
$246$	−14355.2	−0.0151241
$247$	−570419.	−0.594910
$248$	−404428.	−0.417554
$249$	288105.	0.294478
$250$	12448.1	0.0125966
$251$	1.52712e6	1.52999	0.764997	−	0.644034i	$-0.222740\pi$
$251$	1.52712e6	1.52999	0.764997	+	0.644034i	$0.222740\pi$
$252$	0	0
$253$	1.25118e6	1.22890
$254$	−45272.2	−0.0440299
$255$	243582.	0.234582
$256$	846728.	0.807503
$257$	−230230.	−0.217435	−0.108717	−	0.994073i	$-0.534674\pi$
$257$	−230230.	−0.217435	−0.108717	+	0.994073i	$0.534674\pi$
$258$	68514.7	0.0640818
$259$	0	0
$260$	642487.	0.589429
$261$	813278.	0.738989
$262$	20222.4	0.0182004
$263$	−2.19071e6	−1.95297	−0.976485	−	0.215584i	$-0.930835\pi$
$263$	−2.19071e6	−1.95297	−0.976485	+	0.215584i	$0.930835\pi$
$264$	280420.	0.247628
$265$	817118.	0.714776
$266$	0	0
$267$	−683534.	−0.586789
$268$	167888.	0.142785
$269$	−1.35700e6	−1.14340	−0.571701	−	0.820462i	$-0.693716\pi$
$269$	−1.35700e6	−1.14340	−0.571701	+	0.820462i	$0.693716\pi$
$270$	−78808.0	−0.0657902
$271$	−1.27610e6	−1.05551	−0.527754	−	0.849397i	$-0.676966\pi$
$271$	−1.27610e6	−1.05551	−0.527754	+	0.849397i	$0.676966\pi$
$272$	−887711.	−0.727527
$273$	0	0
$274$	130359.	0.104897
$275$	328307.	0.261787
$276$	−790026.	−0.624265
$277$	1.09549e6	0.857843	0.428921	−	0.903342i	$-0.358894\pi$
$277$	1.09549e6	0.857843	0.428921	+	0.903342i	$0.358894\pi$
$278$	12773.3	0.00991265
$279$	1.05087e6	0.808239
$280$	0	0
$281$	−1.83715e6	−1.38797	−0.693984	−	0.719990i	$-0.744146\pi$
$281$	−1.83715e6	−1.38797	−0.693984	+	0.719990i	$0.744146\pi$
$282$	28020.9	0.0209826
$283$	2.07948e6	1.54344	0.771719	−	0.635964i	$-0.219397\pi$
$283$	2.07948e6	1.54344	0.771719	+	0.635964i	$0.219397\pi$
$284$	1.39530e6	1.02653
$285$	184048.	0.134221
$286$	−342894.	−0.247882
$287$	0	0
$288$	312586.	0.222069
$289$	−570940.	−0.402111
$290$	−123486.	−0.0862232
$291$	332164.	0.229943
$292$	2.21204e6	1.51822
$293$	955084.	0.649939	0.324969	−	0.945725i	$-0.394646\pi$
$293$	955084.	0.649939	0.324969	+	0.945725i	$0.394646\pi$
$294$	0	0
$295$	−809208.	−0.541384
$296$	−410805.	−0.272525
$297$	−2.07848e6	−1.36727
$298$	−149930.	−0.0978021
$299$	1.95161e6	1.26246
$300$	−207302.	−0.132984
$301$	0	0
$302$	−226662.	−0.143008
$303$	−655675.	−0.410282
$304$	−670745.	−0.416269
$305$	−1.16242e6	−0.715508
$306$	−96285.7	−0.0587839
$307$	1.30192e6	0.788382	0.394191	−	0.919029i	$-0.371025\pi$
$307$	1.30192e6	0.788382	0.394191	+	0.919029i	$0.371025\pi$
$308$	0	0
$309$	40665.4	0.0242286
$310$	−159562.	−0.0943031
$311$	−1.76771e6	−1.03636	−0.518180	−	0.855272i	$-0.673390\pi$
$311$	−1.76771e6	−1.03636	−0.518180	+	0.855272i	$0.673390\pi$
$312$	437406.	0.254389
$313$	2.93086e6	1.69096	0.845482	−	0.534004i	$-0.179313\pi$
$313$	2.93086e6	1.69096	0.845482	+	0.534004i	$0.179313\pi$
$314$	−216233.	−0.123765
$315$	0	0
$316$	−1.45496e6	−0.819658
$317$	7396.35	0.00413399	0.00206700	−	0.999998i	$-0.499342\pi$
$317$	7396.35	0.00413399	0.00206700	+	0.999998i	$0.499342\pi$
$318$	275361.	0.152699
$319$	−3.25683e6	−1.79192
$320$	723315.	0.394868
$321$	−2.11014e6	−1.14301
$322$	0	0
$323$	641433.	0.342094
$324$	312636.	0.165454
$325$	512101.	0.268935
$326$	43521.4	0.0226808
$327$	−2.39827e6	−1.24031
$328$	86017.4	0.0441471
$329$	0	0
$330$	110636.	0.0559259
$331$	−1.76372e6	−0.884830	−0.442415	−	0.896811i	$-0.645878\pi$
$331$	−1.76372e6	−0.884830	−0.442415	+	0.896811i	$0.645878\pi$
$332$	−854529.	−0.425483
$333$	1.06744e6	0.527514
$334$	−120156.	−0.0589359
$335$	133817.	0.0651477
$336$	0	0
$337$	−1.03364e6	−0.495785	−0.247893	−	0.968788i	$-0.579738\pi$
$337$	−1.03364e6	−0.495785	−0.247893	+	0.968788i	$0.579738\pi$
$338$	−239052.	−0.113815
$339$	−1.26121e6	−0.596060
$340$	−722474.	−0.338942
$341$	−4.20829e6	−1.95984
$342$	−72752.5	−0.0336343
$343$	0	0
$344$	−410546.	−0.187054
$345$	−629698.	−0.284829
$346$	−76010.2	−0.0341336
$347$	1.79841e6	0.801797	0.400899	−	0.916122i	$-0.368698\pi$
$347$	1.79841e6	0.801797	0.400899	+	0.916122i	$0.368698\pi$
$348$	2.05645e6	0.910268
$349$	2.06164e6	0.906046	0.453023	−	0.891499i	$-0.350346\pi$
$349$	2.06164e6	0.906046	0.453023	+	0.891499i	$0.350346\pi$
$350$	0	0
$351$	−3.24206e6	−1.40460
$352$	−1.25177e6	−0.538478
$353$	4.14450e6	1.77025	0.885127	−	0.465350i	$-0.154071\pi$
$353$	4.14450e6	1.77025	0.885127	+	0.465350i	$0.154071\pi$
$354$	−272696.	−0.115656
$355$	1.11214e6	0.468368
$356$	2.02738e6	0.847835
$357$	0	0
$358$	−333715.	−0.137616
$359$	2.32541e6	0.952277	0.476138	−	0.879370i	$-0.342036\pi$
$359$	2.32541e6	0.952277	0.476138	+	0.879370i	$0.342036\pi$
$360$	165547.	0.0673231
$361$	−1.99144e6	−0.804265
$362$	347092.	0.139211
$363$	1.21483e6	0.483894
$364$	0	0
$365$	1.76312e6	0.692709
$366$	−391726.	−0.152855
$367$	−3.07807e6	−1.19293	−0.596463	−	0.802640i	$-0.703428\pi$
$367$	−3.07807e6	−1.19293	−0.596463	+	0.802640i	$0.703428\pi$
$368$	2.29487e6	0.883361
$369$	−223509.	−0.0854533
$370$	−162078.	−0.0615489
$371$	0	0
$372$	2.65722e6	0.995568
$373$	−4.15254e6	−1.54540	−0.772702	−	0.634769i	$-0.781095\pi$
$373$	−4.15254e6	−1.54540	−0.772702	+	0.634769i	$0.781095\pi$
$374$	385582.	0.142540
$375$	−165232.	−0.0606757
$376$	−167904.	−0.0612478
$377$	−5.08007e6	−1.84084
$378$	0	0
$379$	−2.22011e6	−0.793919	−0.396959	−	0.917836i	$-0.629935\pi$
$379$	−2.22011e6	−0.793919	−0.396959	+	0.917836i	$0.629935\pi$
$380$	−545894.	−0.193932
$381$	600925.	0.212084
$382$	−435778.	−0.152794
$383$	1.48326e6	0.516678	0.258339	−	0.966054i	$-0.416825\pi$
$383$	1.48326e6	0.516678	0.258339	+	0.966054i	$0.416825\pi$
$384$	1.05014e6	0.363430
$385$	0	0
$386$	34401.1	0.0117518
$387$	1.06677e6	0.362070
$388$	−985211.	−0.332238
$389$	2.39821e6	0.803549	0.401775	−	0.915739i	$-0.368394\pi$
$389$	2.39821e6	0.803549	0.401775	+	0.915739i	$0.368394\pi$
$390$	172573.	0.0574528
$391$	−2.19458e6	−0.725955
$392$	0	0
$393$	−268424.	−0.0876679
$394$	36973.9	0.0119993
$395$	−1.15969e6	−0.373980
$396$	2.16120e6	0.692558
$397$	−2.32112e6	−0.739130	−0.369565	−	0.929205i	$-0.620493\pi$
$397$	−2.32112e6	−0.739130	−0.369565	+	0.929205i	$0.620493\pi$
$398$	−375305.	−0.118762
$399$	0	0
$400$	602170.	0.188178
$401$	1.34986e6	0.419207	0.209604	−	0.977786i	$-0.432783\pi$
$401$	1.34986e6	0.419207	0.209604	+	0.977786i	$0.432783\pi$
$402$	45095.0	0.0139176
$403$	−6.56419e6	−2.01335
$404$	1.94475e6	0.592804
$405$	249190.	0.0754906
$406$	0	0
$407$	−4.27464e6	−1.27913
$408$	−491861.	−0.146282
$409$	1.14659e6	0.338923	0.169461	−	0.985537i	$-0.445797\pi$
$409$	1.14659e6	0.338923	0.169461	+	0.985537i	$0.445797\pi$
$410$	33937.1	0.00997046
$411$	−1.73033e6	−0.505270
$412$	−120615.	−0.0350072
$413$	0	0
$414$	248913.	0.0713751
$415$	−681111.	−0.194132
$416$	−1.95254e6	−0.553180
$417$	−169547.	−0.0477475
$418$	291342.	0.0815572
$419$	−296047.	−0.0823807	−0.0411904	−	0.999151i	$-0.513115\pi$
$419$	−296047.	−0.0823807	−0.0411904	+	0.999151i	$0.513115\pi$
$420$	0	0
$421$	−3.55304e6	−0.977000	−0.488500	−	0.872564i	$-0.662456\pi$
$421$	−3.55304e6	−0.977000	−0.488500	+	0.872564i	$0.662456\pi$
$422$	672617.	0.183860
$423$	436284.	0.118554
$424$	−1.64999e6	−0.445724
$425$	−575854.	−0.154647
$426$	374780.	0.100058
$427$	0	0
$428$	6.25875e6	1.65150
$429$	4.55144e6	1.19400
$430$	−161976.	−0.0422454
$431$	3.08326e6	0.799497	0.399748	−	0.916625i	$-0.369098\pi$
$431$	3.08326e6	0.799497	0.399748	+	0.916625i	$0.369098\pi$
$432$	−3.81228e6	−0.982823
$433$	−657454.	−0.168518	−0.0842589	−	0.996444i	$-0.526852\pi$
$433$	−657454.	−0.168518	−0.0842589	+	0.996444i	$0.526852\pi$
$434$	0	0
$435$	1.63911e6	0.415322
$436$	7.11336e6	1.79209
$437$	−1.65820e6	−0.415369
$438$	594156.	0.147984
$439$	−2.67883e6	−0.663413	−0.331707	−	0.943383i	$-0.607624\pi$
$439$	−2.67883e6	−0.663413	−0.331707	+	0.943383i	$0.607624\pi$
$440$	−662943.	−0.163247
$441$	0	0
$442$	601440.	0.146432
$443$	4.38546e6	1.06171	0.530854	−	0.847463i	$-0.321871\pi$
$443$	4.38546e6	1.06171	0.530854	+	0.847463i	$0.321871\pi$
$444$	2.69912e6	0.649778
$445$	1.61595e6	0.386836
$446$	227258.	0.0540982
$447$	1.99011e6	0.471095
$448$	0	0
$449$	2.51676e6	0.589150	0.294575	−	0.955628i	$-0.404822\pi$
$449$	2.51676e6	0.589150	0.294575	+	0.955628i	$0.404822\pi$
$450$	65314.4	0.0152047
$451$	895056.	0.207209
$452$	3.74081e6	0.861230
$453$	3.00862e6	0.688845
$454$	−889373.	−0.202509
$455$	0	0
$456$	−371645.	−0.0836982
$457$	−3.41528e6	−0.764955	−0.382477	−	0.923965i	$-0.624929\pi$
$457$	−3.41528e6	−0.764955	−0.382477	+	0.923965i	$0.624929\pi$
$458$	951765.	0.212015
$459$	3.64568e6	0.807694
$460$	1.86770e6	0.411541
$461$	5.20706e6	1.14114	0.570571	−	0.821248i	$-0.306722\pi$
$461$	5.20706e6	1.14114	0.570571	+	0.821248i	$0.306722\pi$
$462$	0	0
$463$	8.10341e6	1.75677	0.878386	−	0.477953i	$-0.158621\pi$
$463$	8.10341e6	1.75677	0.878386	+	0.477953i	$0.158621\pi$
$464$	−5.97356e6	−1.28807
$465$	2.11797e6	0.454241
$466$	673115.	0.143590
$467$	181131.	0.0384327	0.0192164	−	0.999815i	$-0.493883\pi$
$467$	181131.	0.0384327	0.0192164	+	0.999815i	$0.493883\pi$
$468$	3.37108e6	0.711467
$469$	0	0
$470$	−66244.4	−0.0138326
$471$	2.87018e6	0.596153
$472$	1.63402e6	0.337599
$473$	−4.27195e6	−0.877957
$474$	−390804.	−0.0798937
$475$	−435110.	−0.0884840
$476$	0	0
$477$	4.28735e6	0.862767
$478$	499831.	0.100058
$479$	7.85592e6	1.56444	0.782219	−	0.623004i	$-0.214088\pi$
$479$	7.85592e6	1.56444	0.782219	+	0.623004i	$0.214088\pi$
$480$	629996.	0.124806
$481$	−6.66768e6	−1.31405
$482$	443761.	0.0870025
$483$	0	0
$484$	−3.60324e6	−0.699164
$485$	−785271.	−0.151588
$486$	−682039.	−0.130984
$487$	−6.18272e6	−1.18129	−0.590646	−	0.806931i	$-0.701127\pi$
$487$	−6.18272e6	−1.18129	−0.590646	+	0.806931i	$0.701127\pi$
$488$	2.34726e6	0.446181
$489$	−577686.	−0.109250
$490$	0	0
$491$	1.00901e7	1.88882	0.944409	−	0.328773i	$-0.106635\pi$
$491$	1.00901e7	1.88882	0.944409	+	0.328773i	$0.106635\pi$
$492$	−565162.	−0.105259
$493$	5.71251e6	1.05855
$494$	454442.	0.0837840
$495$	1.72260e6	0.315989
$496$	−7.71871e6	−1.40877
$497$	0	0
$498$	−229528.	−0.0414727
$499$	−1.91389e6	−0.344085	−0.172042	−	0.985090i	$-0.555037\pi$
$499$	−1.91389e6	−0.344085	−0.172042	+	0.985090i	$0.555037\pi$
$500$	490083.	0.0876687
$501$	1.59490e6	0.283884
$502$	−1.21663e6	−0.215476
$503$	−5.21201e6	−0.918513	−0.459256	−	0.888304i	$-0.651884\pi$
$503$	−5.21201e6	−0.918513	−0.459256	+	0.888304i	$0.651884\pi$
$504$	0	0
$505$	1.55008e6	0.270475
$506$	−996789.	−0.173072
$507$	3.17307e6	0.548227
$508$	−1.78237e6	−0.306434
$509$	−8.70606e6	−1.48946	−0.744728	−	0.667369i	$-0.767421\pi$
$509$	−8.70606e6	−1.48946	−0.744728	+	0.667369i	$0.767421\pi$
$510$	−194058.	−0.0330373
$511$	0	0
$512$	−3.85237e6	−0.649461
$513$	2.75464e6	0.462137
$514$	183420.	0.0306224
$515$	−96137.2	−0.0159725
$516$	2.69742e6	0.445989
$517$	−1.74713e6	−0.287474
$518$	0	0
$519$	1.00893e6	0.164415
$520$	−1.03407e6	−0.167704
$521$	−8.12797e6	−1.31186	−0.655931	−	0.754821i	$-0.727724\pi$
$521$	−8.12797e6	−1.31186	−0.655931	+	0.754821i	$0.727724\pi$
$522$	−647923.	−0.104075
$523$	5.14016e6	0.821717	0.410858	−	0.911699i	$-0.365229\pi$
$523$	5.14016e6	0.821717	0.410858	+	0.911699i	$0.365229\pi$
$524$	796156.	0.126669
$525$	0	0
$526$	1.74530e6	0.275046
$527$	7.38139e6	1.15774
$528$	5.35195e6	0.835463
$529$	−763020.	−0.118549
$530$	−650983.	−0.100665
$531$	−4.24585e6	−0.653474
$532$	0	0
$533$	1.39613e6	0.212867
$534$	544559.	0.0826402
$535$	4.98859e6	0.753518
$536$	−270213.	−0.0406252
$537$	4.42960e6	0.662870
$538$	1.08110e6	0.161031
$539$	0	0
$540$	−3.10267e6	−0.457879
$541$	−6.23593e6	−0.916026	−0.458013	−	0.888945i	$-0.651439\pi$
$541$	−6.23593e6	−0.916026	−0.458013	+	0.888945i	$0.651439\pi$
$542$	1.01664e6	0.148652
$543$	−4.60716e6	−0.670553
$544$	2.19562e6	0.318097
$545$	5.66977e6	0.817663
$546$	0	0
$547$	−577784.	−0.0825652	−0.0412826	−	0.999148i	$-0.513144\pi$
$547$	−577784.	−0.0825652	−0.0412826	+	0.999148i	$0.513144\pi$
$548$	5.13221e6	0.730051
$549$	−6.09914e6	−0.863650
$550$	−261556.	−0.0368687
$551$	4.31632e6	0.605667
$552$	1.27153e6	0.177615
$553$	0	0
$554$	−872754.	−0.120814
$555$	2.15136e6	0.296470
$556$	502883.	0.0689890
$557$	5.85361e6	0.799440	0.399720	−	0.916637i	$-0.369107\pi$
$557$	5.85361e6	0.799440	0.399720	+	0.916637i	$0.369107\pi$
$558$	−837211.	−0.113828
$559$	−6.66348e6	−0.901928
$560$	0	0
$561$	−5.11807e6	−0.686592
$562$	1.46363e6	0.195474
$563$	−3.80115e6	−0.505411	−0.252705	−	0.967543i	$-0.581320\pi$
$563$	−3.80115e6	−0.505411	−0.252705	+	0.967543i	$0.581320\pi$
$564$	1.10318e6	0.146032
$565$	2.98164e6	0.392948
$566$	−1.65668e6	−0.217370
$567$	0	0
$568$	−2.24571e6	−0.292068
$569$	4.37485e6	0.566478	0.283239	−	0.959049i	$-0.408591\pi$
$569$	4.37485e6	0.566478	0.283239	+	0.959049i	$0.408591\pi$
$570$	−146628.	−0.0189029
$571$	6.41777e6	0.823747	0.411873	−	0.911241i	$-0.364875\pi$
$571$	6.41777e6	0.823747	0.411873	+	0.911241i	$0.364875\pi$
$572$	−1.34997e7	−1.72518
$573$	5.78434e6	0.735982
$574$	0	0
$575$	1.48867e6	0.187771
$576$	3.79518e6	0.476624
$577$	2.22468e6	0.278181	0.139091	−	0.990280i	$-0.455582\pi$
$577$	2.22468e6	0.278181	0.139091	+	0.990280i	$0.455582\pi$
$578$	454857.	0.0566311
$579$	−456626.	−0.0566063
$580$	−4.86165e6	−0.600087
$581$	0	0
$582$	−264629.	−0.0323840
$583$	−1.71690e7	−2.09206
$584$	−3.56024e6	−0.431963
$585$	2.68695e6	0.324616
$586$	−760897.	−0.0915339
$587$	6.76746e6	0.810645	0.405322	−	0.914174i	$-0.367159\pi$
$587$	6.76746e6	0.810645	0.405322	+	0.914174i	$0.367159\pi$
$588$	0	0
$589$	5.57730e6	0.662424
$590$	644681.	0.0762456
$591$	−490777.	−0.0577984
$592$	−7.84041e6	−0.919463
$593$	1.92770e6	0.225114	0.112557	−	0.993645i	$-0.464096\pi$
$593$	1.92770e6	0.225114	0.112557	+	0.993645i	$0.464096\pi$
$594$	1.65589e6	0.192559
$595$	0	0
$596$	−5.90274e6	−0.680672
$597$	4.98165e6	0.572055
$598$	−1.55481e6	−0.177797
$599$	−596664.	−0.0679458	−0.0339729	−	0.999423i	$-0.510816\pi$
$599$	−596664.	−0.0679458	−0.0339729	+	0.999423i	$0.510816\pi$
$600$	333649.	0.0378365
$601$	−1.06121e7	−1.19843	−0.599217	−	0.800586i	$-0.704521\pi$
$601$	−1.06121e7	−1.19843	−0.599217	+	0.800586i	$0.704521\pi$
$602$	0	0
$603$	702127.	0.0786361
$604$	−8.92366e6	−0.995292
$605$	−2.87199e6	−0.319003
$606$	522364.	0.0577819
$607$	892459.	0.0983143	0.0491572	−	0.998791i	$-0.484346\pi$
$607$	892459.	0.0983143	0.0491572	+	0.998791i	$0.484346\pi$
$608$	1.65899e6	0.182005
$609$	0	0
$610$	926081.	0.100768
$611$	−2.72521e6	−0.295323
$612$	−3.79076e6	−0.409118
$613$	1.53898e7	1.65417	0.827086	−	0.562075i	$-0.189997\pi$
$613$	1.53898e7	1.65417	0.827086	+	0.562075i	$0.189997\pi$
$614$	−1.03721e6	−0.111032
$615$	−450468.	−0.0480259
$616$	0	0
$617$	−9.30293e6	−0.983800	−0.491900	−	0.870652i	$-0.663697\pi$
$617$	−9.30293e6	−0.983800	−0.491900	+	0.870652i	$0.663697\pi$
$618$	−32397.3	−0.00341223
$619$	−9.06339e6	−0.950745	−0.475372	−	0.879785i	$-0.657687\pi$
$619$	−9.06339e6	−0.950745	−0.475372	+	0.879785i	$0.657687\pi$
$620$	−6.28196e6	−0.656320
$621$	−9.42463e6	−0.980699
$622$	1.40830e6	0.145955
$623$	0	0
$624$	8.34810e6	0.858274
$625$	390625.	0.0400000
$626$	−2.33496e6	−0.238146
$627$	−3.86716e6	−0.392847
$628$	−8.51307e6	−0.861364
$629$	7.49778e6	0.755624
$630$	0	0
$631$	−2.75198e6	−0.275152	−0.137576	−	0.990491i	$-0.543931\pi$
$631$	−2.75198e6	−0.275152	−0.137576	+	0.990491i	$0.543931\pi$
$632$	2.34173e6	0.233208
$633$	−8.92804e6	−0.885619
$634$	−5892.54	−0.000582209 0
$635$	−1.42065e6	−0.139815
$636$	1.08410e7	1.06273
$637$	0	0
$638$	2.59465e6	0.252364
$639$	5.83529e6	0.565341
$640$	−2.48265e6	−0.239589
$641$	6.77830e6	0.651592	0.325796	−	0.945440i	$-0.394368\pi$
$641$	6.77830e6	0.651592	0.325796	+	0.945440i	$0.394368\pi$
$642$	1.68111e6	0.160975
$643$	−1.04898e7	−1.00056	−0.500278	−	0.865865i	$-0.666769\pi$
$643$	−1.04898e7	−1.00056	−0.500278	+	0.865865i	$0.666769\pi$
$644$	0	0
$645$	2.15000e6	0.203489
$646$	−511018.	−0.0481786
$647$	1.17836e7	1.10667	0.553334	−	0.832960i	$-0.313355\pi$
$647$	1.17836e7	1.10667	0.553334	+	0.832960i	$0.313355\pi$
$648$	−503183.	−0.0470748
$649$	1.70028e7	1.58456
$650$	−407981.	−0.0378753
$651$	0	0
$652$	1.71344e6	0.157852
$653$	−606256.	−0.0556382	−0.0278191	−	0.999613i	$-0.508856\pi$
$653$	−606256.	−0.0556382	−0.0278191	+	0.999613i	$0.508856\pi$
$654$	1.91066e6	0.174678
$655$	634583.	0.0577943
$656$	1.64168e6	0.148946
$657$	9.25097e6	0.836130
$658$	0	0
$659$	−1.68400e7	−1.51053	−0.755263	−	0.655422i	$-0.772491\pi$
$659$	−1.68400e7	−1.51053	−0.755263	+	0.655422i	$0.772491\pi$
$660$	4.35575e6	0.389227
$661$	9.44412e6	0.840733	0.420366	−	0.907355i	$-0.361902\pi$
$661$	9.44412e6	0.840733	0.420366	+	0.907355i	$0.361902\pi$
$662$	1.40512e6	0.124615
$663$	−7.98328e6	−0.705338
$664$	1.37535e6	0.121058
$665$	0	0
$666$	−850411.	−0.0742922
$667$	−1.47677e7	−1.28528
$668$	−4.73054e6	−0.410175
$669$	−3.01654e6	−0.260581
$670$	−106609.	−0.00917505
$671$	2.44244e7	2.09420
$672$	0	0
$673$	−2.02543e7	−1.72377	−0.861884	−	0.507106i	$-0.830715\pi$
$673$	−2.02543e7	−1.72377	−0.861884	+	0.507106i	$0.830715\pi$
$674$	823479.	0.0698237
$675$	−2.47301e6	−0.208913
$676$	−9.41145e6	−0.792118
$677$	2.27043e7	1.90387	0.951935	−	0.306301i	$-0.0990915\pi$
$677$	2.27043e7	1.90387	0.951935	+	0.306301i	$0.0990915\pi$
$678$	1.00479e6	0.0839459
$679$	0	0
$680$	1.16281e6	0.0964354
$681$	1.18052e7	0.975450
$682$	3.35267e6	0.276013
$683$	−1.20828e6	−0.0991097	−0.0495548	−	0.998771i	$-0.515780\pi$
$683$	−1.20828e6	−0.0991097	−0.0495548	+	0.998771i	$0.515780\pi$
$684$	−2.86426e6	−0.234084
$685$	4.09068e6	0.333095
$686$	0	0
$687$	−1.26333e7	−1.02124
$688$	−7.83547e6	−0.631094
$689$	−2.67806e7	−2.14918
$690$	501668.	0.0401138
$691$	2.19091e7	1.74554	0.872770	−	0.488131i	$-0.162321\pi$
$691$	2.19091e7	1.74554	0.872770	+	0.488131i	$0.162321\pi$
$692$	−2.99252e6	−0.237559
$693$	0	0
$694$	−1.43276e6	−0.112921
$695$	400827.	0.0314771
$696$	−3.30982e6	−0.258989
$697$	−1.56994e6	−0.122406
$698$	−1.64247e6	−0.127603
$699$	−8.93465e6	−0.691648
$700$	0	0
$701$	1.03716e7	0.797169	0.398584	−	0.917132i	$-0.369502\pi$
$701$	1.03716e7	0.797169	0.398584	+	0.917132i	$0.369502\pi$
$702$	2.58289e6	0.197817
$703$	5.66524e6	0.432345
$704$	−1.51980e7	−1.15573
$705$	879301.	0.0666292
$706$	−3.30185e6	−0.249313
$707$	0	0
$708$	−1.07360e7	−0.804933
$709$	−9.28321e6	−0.693558	−0.346779	−	0.937947i	$-0.612725\pi$
$709$	−9.28321e6	−0.693558	−0.346779	+	0.937947i	$0.612725\pi$
$710$	−886018.	−0.0659624
$711$	−6.08479e6	−0.451410
$712$	−3.26304e6	−0.241225
$713$	−1.90820e7	−1.40573
$714$	0	0
$715$	−1.07601e7	−0.787137
$716$	−1.31383e7	−0.957763
$717$	−6.63456e6	−0.481964
$718$	−1.85261e6	−0.134114
$719$	5.54834e6	0.400259	0.200129	−	0.979769i	$-0.435864\pi$
$719$	5.54834e6	0.400259	0.200129	+	0.979769i	$0.435864\pi$
$720$	3.15954e6	0.227139
$721$	0	0
$722$	1.58654e6	0.113268
$723$	−5.89031e6	−0.419075
$724$	1.36650e7	0.968863
$725$	−3.87502e6	−0.273798
$726$	−967835.	−0.0681490
$727$	−2.28969e7	−1.60672	−0.803359	−	0.595494i	$-0.796956\pi$
$727$	−2.28969e7	−1.60672	−0.803359	+	0.595494i	$0.796956\pi$
$728$	0	0
$729$	1.14752e7	0.799729
$730$	−1.40465e6	−0.0975574
$731$	7.49305e6	0.518639
$732$	−1.54222e7	−1.06382
$733$	6.31101e6	0.433849	0.216924	−	0.976188i	$-0.430397\pi$
$733$	6.31101e6	0.433849	0.216924	+	0.976188i	$0.430397\pi$
$734$	2.45224e6	0.168005
$735$	0	0
$736$	−5.67601e6	−0.386232
$737$	−2.81171e6	−0.190679
$738$	178065.	0.0120348
$739$	2.89294e6	0.194863	0.0974313	−	0.995242i	$-0.468937\pi$
$739$	2.89294e6	0.194863	0.0974313	+	0.995242i	$0.468937\pi$
$740$	−6.38101e6	−0.428361
$741$	−6.03208e6	−0.403573
$742$	0	0
$743$	1.39332e7	0.925932	0.462966	−	0.886376i	$-0.346785\pi$
$743$	1.39332e7	0.925932	0.462966	+	0.886376i	$0.346785\pi$
$744$	−4.27676e6	−0.283258
$745$	−4.70483e6	−0.310566
$746$	3.30825e6	0.217647
$747$	−3.57373e6	−0.234326
$748$	1.51804e7	0.992038
$749$	0	0
$750$	131637.	0.00854525
$751$	−2.46666e7	−1.59591	−0.797957	−	0.602714i	$-0.794086\pi$
$751$	−2.46666e7	−1.59591	−0.797957	+	0.602714i	$0.794086\pi$
$752$	−3.20452e6	−0.206642
$753$	1.61491e7	1.03791
$754$	4.04720e6	0.259254
$755$	−7.11268e6	−0.454115
$756$	0	0
$757$	2.45027e7	1.55408	0.777040	−	0.629451i	$-0.216720\pi$
$757$	2.45027e7	1.55408	0.777040	+	0.629451i	$0.216720\pi$
$758$	1.76872e6	0.111811
$759$	1.32310e7	0.833657
$760$	878607.	0.0551773
$761$	7.88440e6	0.493523	0.246761	−	0.969076i	$-0.420634\pi$
$761$	7.88440e6	0.493523	0.246761	+	0.969076i	$0.420634\pi$
$762$	−478746.	−0.0298688
$763$	0	0
$764$	−1.71565e7	−1.06340
$765$	−3.02146e6	−0.186665
$766$	−1.18168e6	−0.0727662
$767$	2.65213e7	1.62782
$768$	8.95400e6	0.547790
$769$	8.74943e6	0.533537	0.266768	−	0.963761i	$-0.414044\pi$
$769$	8.74943e6	0.533537	0.266768	+	0.963761i	$0.414044\pi$
$770$	0	0
$771$	−2.43464e6	−0.147503
$772$	1.35437e6	0.0817888
$773$	−1.28494e7	−0.773453	−0.386727	−	0.922194i	$-0.626394\pi$
$773$	−1.28494e7	−0.773453	−0.386727	+	0.922194i	$0.626394\pi$
$774$	−849875.	−0.0509921
$775$	−5.00709e6	−0.299455
$776$	1.58568e6	0.0945282
$777$	0	0
$778$	−1.91061e6	−0.113168
$779$	−1.18623e6	−0.0700366
$780$	6.79419e6	0.399854
$781$	−2.33678e7	−1.37085
$782$	1.74838e6	0.102240
$783$	2.45324e7	1.43000
$784$	0	0
$785$	−6.78542e6	−0.393009
$786$	213849.	0.0123467
$787$	−2.08821e7	−1.20181	−0.600907	−	0.799319i	$-0.705194\pi$
$787$	−2.08821e7	−1.20181	−0.600907	+	0.799319i	$0.705194\pi$
$788$	1.45566e6	0.0835113
$789$	−2.31664e7	−1.32485
$790$	923901.	0.0526693
$791$	0	0
$792$	−3.47841e6	−0.197046
$793$	3.80978e7	2.15138
$794$	1.84919e6	0.104095
$795$	8.64088e6	0.484887
$796$	−1.47757e7	−0.826546
$797$	3.24646e7	1.81036	0.905179	−	0.425030i	$-0.139737\pi$
$797$	3.24646e7	1.81036	0.905179	+	0.425030i	$0.139737\pi$
$798$	0	0
$799$	3.06448e6	0.169820
$800$	−1.48938e6	−0.0822772
$801$	8.47874e6	0.466928
$802$	−1.07541e6	−0.0590389
$803$	−3.70461e7	−2.02747
$804$	1.77539e6	0.0968620
$805$	0	0
$806$	5.22956e6	0.283549
$807$	−1.43500e7	−0.775657
$808$	−3.13005e6	−0.168664
$809$	9.80878e6	0.526919	0.263459	−	0.964670i	$-0.415136\pi$
$809$	9.80878e6	0.526919	0.263459	+	0.964670i	$0.415136\pi$
$810$	−198525.	−0.0106317
$811$	−1.79212e7	−0.956786	−0.478393	−	0.878146i	$-0.658781\pi$
$811$	−1.79212e7	−0.956786	−0.478393	+	0.878146i	$0.658781\pi$
$812$	0	0
$813$	−1.34945e7	−0.716031
$814$	3.40553e6	0.180145
$815$	1.36571e6	0.0720219
$816$	−9.38739e6	−0.493537
$817$	5.66167e6	0.296749
$818$	−913468.	−0.0477320
$819$	0	0
$820$	1.33610e6	0.0693913
$821$	1.97786e7	1.02409	0.512045	−	0.858958i	$-0.328888\pi$
$821$	1.97786e7	1.02409	0.512045	+	0.858958i	$0.328888\pi$
$822$	1.37852e6	0.0711596
$823$	−1.35027e7	−0.694897	−0.347448	−	0.937699i	$-0.612952\pi$
$823$	−1.35027e7	−0.694897	−0.347448	+	0.937699i	$0.612952\pi$
$824$	194128.	0.00996023
$825$	3.47179e6	0.177590
$826$	0	0
$827$	2.08982e7	1.06254	0.531270	−	0.847203i	$-0.321715\pi$
$827$	2.08982e7	1.06254	0.531270	+	0.847203i	$0.321715\pi$
$828$	9.79970e6	0.496749
$829$	8.42239e6	0.425646	0.212823	−	0.977091i	$-0.431734\pi$
$829$	8.42239e6	0.425646	0.212823	+	0.977091i	$0.431734\pi$
$830$	542628.	0.0273405
$831$	1.15846e7	0.581939
$832$	−2.37062e7	−1.18728
$833$	0	0
$834$	135075.	0.00672450
$835$	−3.77052e6	−0.187148
$836$	1.14701e7	0.567613
$837$	3.16994e7	1.56400
$838$	235855.	0.0116021
$839$	−2.98003e7	−1.46156	−0.730780	−	0.682614i	$-0.760843\pi$
$839$	−2.98003e7	−1.46156	−0.730780	+	0.682614i	$0.760843\pi$
$840$	0	0
$841$	1.79293e7	0.874127
$842$	2.83064e6	0.137595
$843$	−1.94276e7	−0.941564
$844$	2.64809e7	1.27961
$845$	−7.50148e6	−0.361414
$846$	−347579.	−0.0166966
$847$	0	0
$848$	−3.14908e7	−1.50381
$849$	2.19902e7	1.04703
$850$	458772.	0.0217796
$851$	−1.93829e7	−0.917476
$852$	1.47551e7	0.696373
$853$	197592.	0.00929815	0.00464907	−	0.999989i	$-0.498520\pi$
$853$	197592.	0.00929815	0.00464907	+	0.999989i	$0.498520\pi$
$854$	0	0
$855$	−2.28299e6	−0.106804
$856$	−1.00734e7	−0.469883
$857$	−1.33012e6	−0.0618640	−0.0309320	−	0.999521i	$-0.509848\pi$
$857$	−1.33012e6	−0.0618640	−0.0309320	+	0.999521i	$0.509848\pi$
$858$	−3.62604e6	−0.168157
$859$	3.37491e6	0.156056	0.0780278	−	0.996951i	$-0.475138\pi$
$859$	3.37491e6	0.156056	0.0780278	+	0.996951i	$0.475138\pi$
$860$	−6.37699e6	−0.294015
$861$	0	0
$862$	−2.45637e6	−0.112597
$863$	2.75301e7	1.25829	0.629145	−	0.777288i	$-0.283405\pi$
$863$	2.75301e7	1.25829	0.629145	+	0.777288i	$0.283405\pi$
$864$	9.42910e6	0.429720
$865$	−2.38521e6	−0.108390
$866$	523781.	0.0237331
$867$	−6.03759e6	−0.272782
$868$	0	0
$869$	2.43669e7	1.09459
$870$	−1.30585e6	−0.0584917
$871$	−4.38577e6	−0.195885
$872$	−1.14488e7	−0.509883
$873$	−4.12026e6	−0.182974
$874$	1.32106e6	0.0584983
$875$	0	0
$876$	2.33919e7	1.02992
$877$	1.84523e7	0.810126	0.405063	−	0.914289i	$-0.367250\pi$
$877$	1.84523e7	0.810126	0.405063	+	0.914289i	$0.367250\pi$
$878$	2.13417e6	0.0934316
$879$	1.00998e7	0.440902
$880$	−1.26526e7	−0.550772
$881$	1.78607e7	0.775279	0.387640	−	0.921811i	$-0.373290\pi$
$881$	1.78607e7	0.775279	0.387640	+	0.921811i	$0.373290\pi$
$882$	0	0
$883$	3.95919e6	0.170885	0.0854426	−	0.996343i	$-0.472770\pi$
$883$	3.95919e6	0.170885	0.0854426	+	0.996343i	$0.472770\pi$
$884$	2.36787e7	1.01912
$885$	−8.55724e6	−0.367261
$886$	−3.49381e6	−0.149525
$887$	1.72210e7	0.734937	0.367469	−	0.930036i	$-0.380225\pi$
$887$	1.72210e7	0.734937	0.367469	+	0.930036i	$0.380225\pi$
$888$	−4.34419e6	−0.184874
$889$	0	0
$890$	−1.28739e6	−0.0544799
$891$	−5.23589e6	−0.220951
$892$	8.94715e6	0.376507
$893$	2.31549e6	0.0971660
$894$	−1.58549e6	−0.0663466
$895$	−1.04720e7	−0.436992
$896$	0	0
$897$	2.06380e7	0.856419
$898$	−2.00505e6	−0.0829727
$899$	4.96707e7	2.04975
$900$	2.57143e6	0.105820
$901$	3.01146e7	1.23585
$902$	−713074.	−0.0291822
$903$	0	0
$904$	−6.02077e6	−0.245036
$905$	1.08918e7	0.442057
$906$	−2.39691e6	−0.0970132
$907$	−71932.5	−0.00290340	−0.00145170	−	0.999999i	$-0.500462\pi$
$907$	−71932.5	−0.00290340	−0.00145170	+	0.999999i	$0.500462\pi$
$908$	−3.50146e7	−1.40940
$909$	8.13317e6	0.326475
$910$	0	0
$911$	−8.34294e6	−0.333060	−0.166530	−	0.986036i	$-0.553256\pi$
$911$	−8.34294e6	−0.333060	−0.166530	+	0.986036i	$0.553256\pi$
$912$	−7.09302e6	−0.282386
$913$	1.43113e7	0.568199
$914$	2.72089e6	0.107732
$915$	−1.22924e7	−0.485383
$916$	3.74709e7	1.47556
$917$	0	0
$918$	−2.90444e6	−0.113751
$919$	−8.76022e6	−0.342158	−0.171079	−	0.985257i	$-0.554725\pi$
$919$	−8.76022e6	−0.342158	−0.171079	+	0.985257i	$0.554725\pi$
$920$	−3.00604e6	−0.117091
$921$	1.37675e7	0.534819
$922$	−4.14836e6	−0.160712
$923$	−3.64496e7	−1.40828
$924$	0	0
$925$	−5.08604e6	−0.195445
$926$	−6.45583e6	−0.247414
$927$	−504424.	−0.0192795
$928$	1.47747e7	0.563182
$929$	−6.93249e6	−0.263542	−0.131771	−	0.991280i	$-0.542066\pi$
$929$	−6.93249e6	−0.263542	−0.131771	+	0.991280i	$0.542066\pi$
$930$	−1.68734e6	−0.0639729
$931$	0	0
$932$	2.65005e7	0.999342
$933$	−1.86933e7	−0.703041
$934$	−144304.	−0.00541266
$935$	1.20996e7	0.452630
$936$	−5.42570e6	−0.202426
$937$	−9.11630e6	−0.339211	−0.169605	−	0.985512i	$-0.554249\pi$
$937$	−9.11630e6	−0.339211	−0.169605	+	0.985512i	$0.554249\pi$
$938$	0	0
$939$	3.09933e7	1.14711
$940$	−2.60804e6	−0.0962707
$941$	4.28190e7	1.57639	0.788193	−	0.615428i	$-0.211017\pi$
$941$	4.28190e7	1.57639	0.788193	+	0.615428i	$0.211017\pi$
$942$	−2.28662e6	−0.0839590
$943$	4.05853e6	0.148624
$944$	3.11860e7	1.13901
$945$	0	0
$946$	3.40338e6	0.123647
$947$	−3.96419e7	−1.43641	−0.718206	−	0.695830i	$-0.755037\pi$
$947$	−3.96419e7	−1.43641	−0.718206	+	0.695830i	$0.755037\pi$
$948$	−1.53859e7	−0.556036
$949$	−5.77854e7	−2.08282
$950$	346644.	0.0124616
$951$	78215.2	0.00280440
$952$	0	0
$953$	9.94045e6	0.354547	0.177274	−	0.984162i	$-0.443272\pi$
$953$	9.94045e6	0.354547	0.177274	+	0.984162i	$0.443272\pi$
$954$	−3.41565e6	−0.121507
$955$	−1.36748e7	−0.485190
$956$	1.96783e7	0.696376
$957$	−3.44404e7	−1.21559
$958$	−6.25866e6	−0.220327
$959$	0	0
$960$	7.64893e6	0.267869
$961$	3.55525e7	1.24183
$962$	5.31202e6	0.185064
$963$	2.61747e7	0.909529
$964$	1.74709e7	0.605510
$965$	1.07951e6	0.0373172
$966$	0	0
$967$	1.52078e7	0.522998	0.261499	−	0.965204i	$-0.415783\pi$
$967$	1.52078e7	0.522998	0.261499	+	0.965204i	$0.415783\pi$
$968$	5.79935e6	0.198926
$969$	6.78304e6	0.232068
$970$	625611.	0.0213489
$971$	1.24027e7	0.422152	0.211076	−	0.977470i	$-0.432303\pi$
$971$	1.24027e7	0.422152	0.211076	+	0.977470i	$0.432303\pi$
$972$	−2.68518e7	−0.911609
$973$	0	0
$974$	4.92566e6	0.166367
$975$	5.41537e6	0.182439
$976$	4.47985e7	1.50535
$977$	−2.90562e7	−0.973873	−0.486937	−	0.873437i	$-0.661886\pi$
$977$	−2.90562e7	−0.973873	−0.486937	+	0.873437i	$0.661886\pi$
$978$	460232.	0.0153861
$979$	−3.39537e7	−1.13222
$980$	0	0
$981$	2.97488e7	0.986956
$982$	−8.03856e6	−0.266011
$983$	−2.51710e7	−0.830839	−0.415419	−	0.909630i	$-0.636365\pi$
$983$	−2.51710e7	−0.830839	−0.415419	+	0.909630i	$0.636365\pi$
$984$	909619.	0.0299483
$985$	1.16025e6	0.0381031
$986$	−4.55105e6	−0.149080
$987$	0	0
$988$	1.78914e7	0.583111
$989$	−1.93707e7	−0.629729
$990$	−1.37236e6	−0.0445022
$991$	−3.11489e7	−1.00753	−0.503766	−	0.863840i	$-0.668053\pi$
$991$	−3.11489e7	−1.00753	−0.503766	+	0.863840i	$0.668053\pi$
$992$	1.90911e7	0.615958
$993$	−1.86510e7	−0.600247
$994$	0	0
$995$	−1.17771e7	−0.377122
$996$	−9.03650e6	−0.288637
$997$	5.15079e7	1.64110	0.820552	−	0.571572i	$-0.193666\pi$
$997$	5.15079e7	1.64110	0.820552	+	0.571572i	$0.193666\pi$
$998$	1.52476e6	0.0484591
$999$	3.21992e7	1.02078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.i.1.3		6
7.2	even	3		35.6.e.a.11.4	✓	12
7.4	even	3		35.6.e.a.16.4	yes	12
7.6	odd	2		245.6.a.h.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.e.a.11.4	✓	12	7.2	even	3
35.6.e.a.16.4	yes	12	7.4	even	3
245.6.a.h.1.3		6	7.6	odd	2
245.6.a.i.1.3		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.796681 q^{2} +10.5748 q^{3} -31.3653 q^{4} -25.0000 q^{5} -8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} +O(q^{10})\)	\(q-0.796681 q^{2} +10.5748 q^{3} -31.3653 q^{4} -25.0000 q^{5} -8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} +19.9170 q^{10} +525.291 q^{11} -331.683 q^{12} +819.361 q^{13} -264.371 q^{15} +963.472 q^{16} -921.367 q^{17} +104.503 q^{18} -696.175 q^{19} +784.132 q^{20} -418.489 q^{22} +2381.87 q^{23} +533.838 q^{24} +625.000 q^{25} -652.769 q^{26} -3956.82 q^{27} -6200.04 q^{29} +210.619 q^{30} -8011.35 q^{31} -2383.00 q^{32} +5554.86 q^{33} +734.036 q^{34} +4114.28 q^{36} -8137.67 q^{37} +554.630 q^{38} +8664.60 q^{39} -1262.05 q^{40} +1703.92 q^{41} -8132.54 q^{43} -16475.9 q^{44} +3279.33 q^{45} -1897.59 q^{46} -3326.02 q^{47} +10188.5 q^{48} -497.926 q^{50} -9743.30 q^{51} -25699.5 q^{52} -32684.7 q^{53} +3152.32 q^{54} -13132.3 q^{55} -7361.94 q^{57} +4939.45 q^{58} +32368.3 q^{59} +8292.07 q^{60} +46496.9 q^{61} +6382.49 q^{62} -28932.6 q^{64} -20484.0 q^{65} -4425.45 q^{66} -5352.68 q^{67} +28899.0 q^{68} +25187.9 q^{69} -44485.5 q^{71} -6621.87 q^{72} -70525.0 q^{73} +6483.12 q^{74} +6609.27 q^{75} +21835.8 q^{76} -6902.92 q^{78} +46387.5 q^{79} -24086.8 q^{80} -9967.59 q^{81} -1357.48 q^{82} +27244.4 q^{83} +23034.2 q^{85} +6479.04 q^{86} -65564.4 q^{87} +26517.7 q^{88} -64637.8 q^{89} -2612.58 q^{90} -74708.2 q^{92} -84718.6 q^{93} +2649.77 q^{94} +17404.4 q^{95} -25199.8 q^{96} +31410.9 q^{97} -68904.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 20 * q^3 + 31 * q^4 - 150 * q^5 + 96 * q^6 - 135 * q^8 + 378 * q^9	\( 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9} + 125 q^{10} - 924 q^{11} + 370 q^{12} - 150 q^{13} - 500 q^{15} + 435 q^{16} + 1540 q^{17} + 195 q^{18} + 92 q^{19} - 775 q^{20} - 6855 q^{22} - 3920 q^{23} - 7200 q^{24} + 3750 q^{25} + 2635 q^{26} + 2060 q^{27} + 1264 q^{29} - 2400 q^{30} - 7160 q^{31} + 9105 q^{32} + 4460 q^{33} + 2166 q^{34} - 26375 q^{36} - 14170 q^{37} - 46215 q^{38} - 15376 q^{39} + 3375 q^{40} + 4098 q^{41} - 24460 q^{43} - 27873 q^{44} - 9450 q^{45} + 6815 q^{46} + 42940 q^{47} + 11610 q^{48} - 3125 q^{50} - 42008 q^{51} - 36115 q^{52} - 2450 q^{53} + 19566 q^{54} + 23100 q^{55} - 97100 q^{57} - 36110 q^{58} - 64600 q^{59} - 9250 q^{60} + 73620 q^{61} + 111440 q^{62} - 157997 q^{64} + 3750 q^{65} - 139138 q^{66} - 142620 q^{67} + 124330 q^{68} + 17344 q^{69} - 154256 q^{71} - 117495 q^{72} - 5120 q^{73} + 2785 q^{74} + 12500 q^{75} + 7775 q^{76} - 214090 q^{78} - 222504 q^{79} - 10875 q^{80} - 43986 q^{81} + 31665 q^{82} + 179580 q^{83} - 38500 q^{85} - 207160 q^{86} - 209300 q^{87} - 45145 q^{88} + 41648 q^{89} - 4875 q^{90} - 292185 q^{92} - 198520 q^{93} - 333699 q^{94} - 2300 q^{95} + 61824 q^{96} - 73980 q^{97} - 190772 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 20 * q^3 + 31 * q^4 - 150 * q^5 + 96 * q^6 - 135 * q^8 + 378 * q^9 + 125 * q^10 - 924 * q^11 + 370 * q^12 - 150 * q^13 - 500 * q^15 + 435 * q^16 + 1540 * q^17 + 195 * q^18 + 92 * q^19 - 775 * q^20 - 6855 * q^22 - 3920 * q^23 - 7200 * q^24 + 3750 * q^25 + 2635 * q^26 + 2060 * q^27 + 1264 * q^29 - 2400 * q^30 - 7160 * q^31 + 9105 * q^32 + 4460 * q^33 + 2166 * q^34 - 26375 * q^36 - 14170 * q^37 - 46215 * q^38 - 15376 * q^39 + 3375 * q^40 + 4098 * q^41 - 24460 * q^43 - 27873 * q^44 - 9450 * q^45 + 6815 * q^46 + 42940 * q^47 + 11610 * q^48 - 3125 * q^50 - 42008 * q^51 - 36115 * q^52 - 2450 * q^53 + 19566 * q^54 + 23100 * q^55 - 97100 * q^57 - 36110 * q^58 - 64600 * q^59 - 9250 * q^60 + 73620 * q^61 + 111440 * q^62 - 157997 * q^64 + 3750 * q^65 - 139138 * q^66 - 142620 * q^67 + 124330 * q^68 + 17344 * q^69 - 154256 * q^71 - 117495 * q^72 - 5120 * q^73 + 2785 * q^74 + 12500 * q^75 + 7775 * q^76 - 214090 * q^78 - 222504 * q^79 - 10875 * q^80 - 43986 * q^81 + 31665 * q^82 + 179580 * q^83 - 38500 * q^85 - 207160 * q^86 - 209300 * q^87 - 45145 * q^88 + 41648 * q^89 - 4875 * q^90 - 292185 * q^92 - 198520 * q^93 - 333699 * q^94 - 2300 * q^95 + 61824 * q^96 - 73980 * q^97 - 190772 * q^99

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