LMFDB - Embedded newform 245.6.a.h.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	$-0.610152\pi$
$3$	−10.5748	−0.678375	−0.339188	+	0.940719i	$0.610152\pi$
$4$	−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	$-0.734709\pi$
$13$	−819.361	−1.34467	−0.672337	+	0.740245i	$0.734709\pi$
$14$	0	0
$15$	−264.371	−0.303379
$16$	963.472	0.940890
$17$	921.367	0.773233	0.386616	−	0.922241i	$-0.373644\pi$
$17$	921.367	0.773233	0.386616	+	0.922241i	$0.373644\pi$
$18$	104.503	0.0760235
$19$	696.175	0.442420	0.221210	−	0.975226i	$-0.428999\pi$
$19$	696.175	0.442420	0.221210	+	0.975226i	$0.428999\pi$
$20$	−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	$-0.230709\pi$
$31$	8011.35	1.49727	0.748637	+	0.662980i	$0.230709\pi$
$32$	−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	$-0.525221\pi$
$41$	−1703.92	−0.158304	−0.0791518	+	0.996863i	$0.525221\pi$
$42$	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	$-0.464975\pi$
$47$	3326.02	0.219624	0.109812	+	0.993952i	$0.464975\pi$
$48$	−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	$-0.706941\pi$
$59$	−32368.3	−1.21057	−0.605285	+	0.796009i	$0.706941\pi$
$60$	8292.07	0.297361
$61$	−46496.9	−1.59993	−0.799963	−	0.600050i	$-0.795147\pi$
$61$	−46496.9	−1.59993	−0.799963	+	0.600050i	$0.795147\pi$
$62$	−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	$-0.218016\pi$
$73$	70525.0	1.54894	0.774472	+	0.632608i	$0.218016\pi$
$74$	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	$-0.569642\pi$
$83$	−27244.4	−0.434093	−0.217046	+	0.976161i	$0.569642\pi$
$84$	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	$-0.357633\pi$
$89$	64637.8	0.864991	0.432496	+	0.901636i	$0.357633\pi$
$90$	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	$-0.554209\pi$
$97$	−31410.9	−0.338962	−0.169481	+	0.985533i	$0.554209\pi$
$98$	0	0
$99$	−68904.0	−0.706572
$100$	−19603.3	−0.196033
$101$	62003.4	0.604800	0.302400	−	0.953181i	$-0.402212\pi$
$101$	62003.4	0.604800	0.302400	+	0.953181i	$0.402212\pi$
$102$	7762.30	0.0738737
$103$	−3845.49	−0.0357156	−0.0178578	−	0.999841i	$-0.505685\pi$
$103$	−3845.49	−0.0357156	−0.0178578	+	0.999841i	$0.505685\pi$
$104$	−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	$-0.479418\pi$
$131$	25383.3	0.129232	0.0646160	+	0.997910i	$0.479418\pi$
$132$	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	$-0.488796\pi$
$139$	16033.1	0.0703850	0.0351925	+	0.999381i	$0.488796\pi$
$140$	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	$-0.644808\pi$
$157$	−271417.	−0.878795	−0.439397	+	0.898293i	$0.644808\pi$
$158$	−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	$-0.567098\pi$
$167$	−150821.	−0.418476	−0.209238	+	0.977865i	$0.567098\pi$
$168$	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	$-0.538669\pi$
$173$	−95408.6	−0.242366	−0.121183	+	0.992630i	$0.538669\pi$
$174$	−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	$-0.335448\pi$
$181$	435672.	0.988469	0.494235	+	0.869329i	$0.335448\pi$
$182$	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	$-0.638544\pi$
$199$	−471086.	−0.843271	−0.421636	+	0.906765i	$0.638544\pi$
$200$	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	$-0.438482\pi$
$223$	285256.	0.384126	0.192063	+	0.981383i	$0.438482\pi$
$224$	0	0
$225$	−81983.1	−0.107961
$226$	95016.8	0.123745
$227$	−1.11635e6	−1.43792	−0.718960	−	0.695051i	$-0.755382\pi$
$227$	−1.11635e6	−1.43792	−0.718960	+	0.695051i	$0.755382\pi$
$228$	230909.	0.294174
$229$	1.19466e6	1.50542	0.752708	−	0.658355i	$-0.228747\pi$
$229$	1.19466e6	1.50542	0.752708	+	0.658355i	$0.228747\pi$
$230$	−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	$-0.400045\pi$
$241$	557012.	0.617763	0.308882	+	0.951100i	$0.400045\pi$
$242$	−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	$-0.777260\pi$
$251$	−1.52712e6	−1.52999	−0.764997	+	0.644034i	$0.777260\pi$
$252$	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	$-0.465326\pi$
$257$	230230.	0.217435	0.108717	+	0.994073i	$0.465326\pi$
$258$	−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	$-0.306284\pi$
$269$	1.35700e6	1.14340	0.571701	+	0.820462i	$0.306284\pi$
$270$	−78808.0	−0.0657902
$271$	1.27610e6	1.05551	0.527754	−	0.849397i	$-0.323034\pi$
$271$	1.27610e6	1.05551	0.527754	+	0.849397i	$0.323034\pi$
$272$	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	$-0.780603\pi$
$283$	−2.07948e6	−1.54344	−0.771719	+	0.635964i	$0.780603\pi$
$284$	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	$-0.605354\pi$
$293$	−955084.	−0.649939	−0.324969	+	0.945725i	$0.605354\pi$
$294$	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	$-0.628975\pi$
$307$	−1.30192e6	−0.788382	−0.394191	+	0.919029i	$0.628975\pi$
$308$	0	0
$309$	40665.4	0.0242286
$310$	−159562.	−0.0943031
$311$	1.76771e6	1.03636	0.518180	−	0.855272i	$-0.326610\pi$
$311$	1.76771e6	1.03636	0.518180	+	0.855272i	$0.326610\pi$
$312$	437406.	0.254389
$313$	−2.93086e6	−1.69096	−0.845482	−	0.534004i	$-0.820687\pi$
$313$	−2.93086e6	−1.69096	−0.845482	+	0.534004i	$0.820687\pi$
$314$	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	$-0.649654\pi$
$349$	−2.06164e6	−0.906046	−0.453023	+	0.891499i	$0.649654\pi$
$350$	0	0
$351$	−3.24206e6	−1.40460
$352$	−1.25177e6	−0.538478
$353$	−4.14450e6	−1.77025	−0.885127	−	0.465350i	$-0.845929\pi$
$353$	−4.14450e6	−1.77025	−0.885127	+	0.465350i	$0.845929\pi$
$354$	−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	$-0.296572\pi$
$367$	3.07807e6	1.19293	0.596463	+	0.802640i	$0.296572\pi$
$368$	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	$-0.583175\pi$
$383$	−1.48326e6	−0.516678	−0.258339	+	0.966054i	$0.583175\pi$
$384$	−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	$-0.379507\pi$
$397$	2.32112e6	0.739130	0.369565	+	0.929205i	$0.379507\pi$
$398$	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	$-0.554203\pi$
$409$	−1.14659e6	−0.338923	−0.169461	+	0.985537i	$0.554203\pi$
$410$	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	$-0.486885\pi$
$419$	296047.	0.0823807	0.0411904	+	0.999151i	$0.486885\pi$
$420$	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	$-0.473148\pi$
$433$	657454.	0.168518	0.0842589	+	0.996444i	$0.473148\pi$
$434$	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	$-0.392376\pi$
$439$	2.67883e6	0.663413	0.331707	+	0.943383i	$0.392376\pi$
$440$	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	$-0.693278\pi$
$461$	−5.20706e6	−1.14114	−0.570571	+	0.821248i	$0.693278\pi$
$462$	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	$-0.506117\pi$
$467$	−181131.	−0.0384327	−0.0192164	+	0.999815i	$0.506117\pi$
$468$	−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	$-0.785912\pi$
$479$	−7.85592e6	−1.56444	−0.782219	+	0.623004i	$0.785912\pi$
$480$	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	$-0.348116\pi$
$503$	5.21201e6	0.918513	0.459256	+	0.888304i	$0.348116\pi$
$504$	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	$-0.232579\pi$
$509$	8.70606e6	1.48946	0.744728	+	0.667369i	$0.232579\pi$
$510$	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	$-0.272276\pi$
$521$	8.12797e6	1.31186	0.655931	+	0.754821i	$0.272276\pi$
$522$	−647923.	−0.104075
$523$	−5.14016e6	−0.821717	−0.410858	−	0.911699i	$-0.634771\pi$
$523$	−5.14016e6	−0.821717	−0.410858	+	0.911699i	$0.634771\pi$
$524$	−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	$-0.418680\pi$
$563$	3.80115e6	0.505411	0.252705	+	0.967543i	$0.418680\pi$
$564$	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	$-0.544418\pi$
$577$	−2.22468e6	−0.278181	−0.139091	+	0.990280i	$0.544418\pi$
$578$	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	$-0.632841\pi$
$587$	−6.76746e6	−0.810645	−0.405322	+	0.914174i	$0.632841\pi$
$588$	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	$-0.535904\pi$
$593$	−1.92770e6	−0.225114	−0.112557	+	0.993645i	$0.535904\pi$
$594$	−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	$-0.295479\pi$
$601$	1.06121e7	1.19843	0.599217	+	0.800586i	$0.295479\pi$
$602$	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	$-0.515654\pi$
$607$	−892459.	−0.0983143	−0.0491572	+	0.998791i	$0.515654\pi$
$608$	−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	$-0.342313\pi$
$619$	9.06339e6	0.950745	0.475372	+	0.879785i	$0.342313\pi$
$620$	−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	$-0.333231\pi$
$643$	1.04898e7	1.00056	0.500278	+	0.865865i	$0.333231\pi$
$644$	0	0
$645$	2.15000e6	0.203489
$646$	−511018.	−0.0481786
$647$	−1.17836e7	−1.10667	−0.553334	−	0.832960i	$-0.686645\pi$
$647$	−1.17836e7	−1.10667	−0.553334	+	0.832960i	$0.686645\pi$
$648$	−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	$-0.638098\pi$
$661$	−9.44412e6	−0.840733	−0.420366	+	0.907355i	$0.638098\pi$
$662$	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	$-0.900909\pi$
$677$	−2.27043e7	−1.90387	−0.951935	+	0.306301i	$0.900909\pi$
$678$	−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	$-0.837679\pi$
$691$	−2.19091e7	−1.74554	−0.872770	+	0.488131i	$0.837679\pi$
$692$	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	$-0.564136\pi$
$719$	−5.54834e6	−0.400259	−0.200129	+	0.979769i	$0.564136\pi$
$720$	−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	$-0.203044\pi$
$727$	2.28969e7	1.60672	0.803359	+	0.595494i	$0.203044\pi$
$728$	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	$-0.569603\pi$
$733$	−6.31101e6	−0.433849	−0.216924	+	0.976188i	$0.569603\pi$
$734$	−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	$-0.579366\pi$
$761$	−7.88440e6	−0.493523	−0.246761	+	0.969076i	$0.579366\pi$
$762$	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	$-0.585956\pi$
$769$	−8.74943e6	−0.533537	−0.266768	+	0.963761i	$0.585956\pi$
$770$	0	0
$771$	−2.43464e6	−0.147503
$772$	1.35437e6	0.0817888
$773$	1.28494e7	0.773453	0.386727	−	0.922194i	$-0.373606\pi$
$773$	1.28494e7	0.773453	0.386727	+	0.922194i	$0.373606\pi$
$774$	−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	$-0.294806\pi$
$787$	2.08821e7	1.20181	0.600907	+	0.799319i	$0.294806\pi$
$788$	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	$-0.860263\pi$
$797$	−3.24646e7	−1.81036	−0.905179	+	0.425030i	$0.860263\pi$
$798$	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	$-0.341219\pi$
$811$	1.79212e7	0.956786	0.478393	+	0.878146i	$0.341219\pi$
$812$	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	$-0.568266\pi$
$829$	−8.42239e6	−0.425646	−0.212823	+	0.977091i	$0.568266\pi$
$830$	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	$-0.239157\pi$
$839$	2.98003e7	1.46156	0.730780	+	0.682614i	$0.239157\pi$
$840$	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	$-0.501480\pi$
$853$	−197592.	−0.00929815	−0.00464907	+	0.999989i	$0.501480\pi$
$854$	0	0
$855$	−2.28299e6	−0.106804
$856$	−1.00734e7	−0.469883
$857$	1.33012e6	0.0618640	0.0309320	−	0.999521i	$-0.490152\pi$
$857$	1.33012e6	0.0618640	0.0309320	+	0.999521i	$0.490152\pi$
$858$	−3.62604e6	−0.168157
$859$	−3.37491e6	−0.156056	−0.0780278	−	0.996951i	$-0.524862\pi$
$859$	−3.37491e6	−0.156056	−0.0780278	+	0.996951i	$0.524862\pi$
$860$	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	$-0.626710\pi$
$881$	−1.78607e7	−0.775279	−0.387640	+	0.921811i	$0.626710\pi$
$882$	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	$-0.619775\pi$
$887$	−1.72210e7	−0.734937	−0.367469	+	0.930036i	$0.619775\pi$
$888$	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	$-0.457934\pi$
$929$	6.93249e6	0.263542	0.131771	+	0.991280i	$0.457934\pi$
$930$	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	$-0.445751\pi$
$937$	9.11630e6	0.339211	0.169605	+	0.985512i	$0.445751\pi$
$938$	0	0
$939$	3.09933e7	1.14711
$940$	−2.60804e6	−0.0962707
$941$	−4.28190e7	−1.57639	−0.788193	−	0.615428i	$-0.788983\pi$
$941$	−4.28190e7	−1.57639	−0.788193	+	0.615428i	$0.788983\pi$
$942$	−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	$-0.567697\pi$
$971$	−1.24027e7	−0.422152	−0.211076	+	0.977470i	$0.567697\pi$
$972$	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	$-0.363635\pi$
$983$	2.51710e7	0.830839	0.415419	+	0.909630i	$0.363635\pi$
$984$	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	$-0.806334\pi$
$997$	−5.15079e7	−1.64110	−0.820552	+	0.571572i	$0.806334\pi$
$998$	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.h.1.3		6
7.3	odd	6		35.6.e.a.16.4	yes	12
7.5	odd	6		35.6.e.a.11.4	✓	12
7.6	odd	2		245.6.a.i.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.e.a.11.4	✓	12	7.5	odd	6
35.6.e.a.16.4	yes	12	7.3	odd	6
245.6.a.h.1.3		6	1.1	even	1	trivial
245.6.a.i.1.3		6	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)

\(f(q)\)	\(=\)	\(q-0.796681 q^{2} -10.5748 q^{3} -31.3653 q^{4} +25.0000 q^{5} +8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} +O(q^{10})\)	\(q-0.796681 q^{2} -10.5748 q^{3} -31.3653 q^{4} +25.0000 q^{5} +8.42477 q^{6} +50.4819 q^{8} -131.173 q^{9} -19.9170 q^{10} +525.291 q^{11} +331.683 q^{12} -819.361 q^{13} -264.371 q^{15} +963.472 q^{16} +921.367 q^{17} +104.503 q^{18} +696.175 q^{19} -784.132 q^{20} -418.489 q^{22} +2381.87 q^{23} -533.838 q^{24} +625.000 q^{25} +652.769 q^{26} +3956.82 q^{27} -6200.04 q^{29} +210.619 q^{30} +8011.35 q^{31} -2383.00 q^{32} -5554.86 q^{33} -734.036 q^{34} +4114.28 q^{36} -8137.67 q^{37} -554.630 q^{38} +8664.60 q^{39} +1262.05 q^{40} -1703.92 q^{41} -8132.54 q^{43} -16475.9 q^{44} -3279.33 q^{45} -1897.59 q^{46} +3326.02 q^{47} -10188.5 q^{48} -497.926 q^{50} -9743.30 q^{51} +25699.5 q^{52} -32684.7 q^{53} -3152.32 q^{54} +13132.3 q^{55} -7361.94 q^{57} +4939.45 q^{58} -32368.3 q^{59} +8292.07 q^{60} -46496.9 q^{61} -6382.49 q^{62} -28932.6 q^{64} -20484.0 q^{65} +4425.45 q^{66} -5352.68 q^{67} -28899.0 q^{68} -25187.9 q^{69} -44485.5 q^{71} -6621.87 q^{72} +70525.0 q^{73} +6483.12 q^{74} -6609.27 q^{75} -21835.8 q^{76} -6902.92 q^{78} +46387.5 q^{79} +24086.8 q^{80} -9967.59 q^{81} +1357.48 q^{82} -27244.4 q^{83} +23034.2 q^{85} +6479.04 q^{86} +65564.4 q^{87} +26517.7 q^{88} +64637.8 q^{89} +2612.58 q^{90} -74708.2 q^{92} -84718.6 q^{93} -2649.77 q^{94} +17404.4 q^{95} +25199.8 q^{96} -31410.9 q^{97} -68904.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} - 20 q^{3} + 31 q^{4} + 150 q^{5} - 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) \) 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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