LMFDB - Embedded newform 245.6.a.m.1.4

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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 $ x^10 - 246x^8 - 192x^7 + 20336x^6 + 25380x^5 - 639206x^4 - 722920x^3 + 7583055x^2 + 5935300x - 22888100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 7^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.48290$ 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)

$f(q)$	$=$	$q-3.48290 q^{2} +0.931256 q^{3} -19.8694 q^{4} +25.0000 q^{5} -3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} +O(q^{10})$	\(q-3.48290 q^{2} +0.931256 q^{3} -19.8694 q^{4} +25.0000 q^{5} -3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} -87.0725 q^{10} +286.749 q^{11} -18.5035 q^{12} -129.957 q^{13} +23.2814 q^{15} +6.61475 q^{16} -445.334 q^{17} +843.324 q^{18} -828.537 q^{19} -496.735 q^{20} -998.719 q^{22} -550.366 q^{23} +168.237 q^{24} +625.000 q^{25} +452.628 q^{26} -451.783 q^{27} +4844.75 q^{29} -81.0868 q^{30} -5807.64 q^{31} -5804.03 q^{32} +267.037 q^{33} +1551.05 q^{34} +4811.04 q^{36} -14016.6 q^{37} +2885.71 q^{38} -121.023 q^{39} +4516.40 q^{40} +11869.9 q^{41} +15813.2 q^{43} -5697.54 q^{44} -6053.32 q^{45} +1916.87 q^{46} +10394.5 q^{47} +6.16002 q^{48} -2176.81 q^{50} -414.720 q^{51} +2582.17 q^{52} +7473.83 q^{53} +1573.51 q^{54} +7168.73 q^{55} -771.580 q^{57} -16873.8 q^{58} +22516.6 q^{59} -462.588 q^{60} +21943.7 q^{61} +20227.4 q^{62} +20003.2 q^{64} -3248.93 q^{65} -930.064 q^{66} -1266.67 q^{67} +8848.52 q^{68} -512.532 q^{69} +25833.3 q^{71} -43742.7 q^{72} +4003.05 q^{73} +48818.4 q^{74} +582.035 q^{75} +16462.5 q^{76} +421.512 q^{78} -64829.8 q^{79} +165.369 q^{80} +58417.5 q^{81} -41341.6 q^{82} +91596.2 q^{83} -11133.3 q^{85} -55075.8 q^{86} +4511.70 q^{87} +51803.0 q^{88} +120374. q^{89} +21083.1 q^{90} +10935.5 q^{92} -5408.40 q^{93} -36202.9 q^{94} -20713.4 q^{95} -5405.04 q^{96} +159506. q^{97} -69431.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19} + 4550 q^{20} + 3948 q^{22} + 3708 q^{23} + 2092 q^{24} + 6250 q^{25} + 6576 q^{26} + 11818 q^{27} - 8866 q^{29} + 3600 q^{30} + 13292 q^{31} + 2590 q^{32} + 9854 q^{33} + 44468 q^{34} - 10690 q^{36} + 16124 q^{37} + 2180 q^{38} - 24982 q^{39} + 6750 q^{40} + 34836 q^{41} - 28604 q^{43} - 31120 q^{44} + 17500 q^{45} - 39732 q^{46} + 18106 q^{47} + 101788 q^{48} + 6250 q^{50} + 31602 q^{51} - 22480 q^{52} + 36440 q^{53} + 80836 q^{54} + 19850 q^{55} + 126988 q^{57} - 100356 q^{58} + 18644 q^{59} + 64000 q^{60} + 68120 q^{61} + 181052 q^{62} - 59358 q^{64} + 11850 q^{65} + 157780 q^{66} + 92328 q^{67} + 288540 q^{68} + 170888 q^{69} + 5044 q^{71} - 61654 q^{72} + 170160 q^{73} - 216584 q^{74} + 36250 q^{75} + 505180 q^{76} - 158008 q^{78} + 26442 q^{79} + 59850 q^{80} - 56314 q^{81} + 353948 q^{82} + 353360 q^{83} + 20050 q^{85} - 52940 q^{86} - 3190 q^{87} - 114916 q^{88} + 90704 q^{89} + 92550 q^{90} + 183520 q^{92} + 188560 q^{93} - 121388 q^{94} + 182300 q^{95} + 442220 q^{96} + 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * 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 $

$2$	−3.48290	−0.615695	−0.307848	−	0.951436i	$-0.599609\pi$
$2$	−3.48290	−0.615695	−0.307848	+	0.951436i	$0.599609\pi$
$3$	0.931256	0.0597401	0.0298701	−	0.999554i	$-0.490491\pi$
$3$	0.931256	0.0597401	0.0298701	+	0.999554i	$0.490491\pi$
$4$	−19.8694	−0.620919
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−3.24347	−0.0367817
$7$	0	0
$7$	0	0
$8$	180.656	0.997993
$9$	−242.133	−0.996431
$10$	−87.0725	−0.275347
$11$	286.749	0.714530	0.357265	−	0.934003i	$-0.383709\pi$
$11$	286.749	0.714530	0.357265	+	0.934003i	$0.383709\pi$
$12$	−18.5035	−0.0370938
$13$	−129.957	−0.213276	−0.106638	−	0.994298i	$-0.534009\pi$
$13$	−129.957	−0.213276	−0.106638	+	0.994298i	$0.534009\pi$
$14$	0	0
$15$	23.2814	0.0267166
$16$	6.61475	0.00645971
$17$	−445.334	−0.373734	−0.186867	−	0.982385i	$-0.559833\pi$
$17$	−445.334	−0.373734	−0.186867	+	0.982385i	$0.559833\pi$
$18$	843.324	0.613498
$19$	−828.537	−0.526536	−0.263268	−	0.964723i	$-0.584800\pi$
$19$	−828.537	−0.526536	−0.263268	+	0.964723i	$0.584800\pi$
$20$	−496.735	−0.277683
$21$	0	0
$22$	−998.719	−0.439933
$23$	−550.366	−0.216936	−0.108468	−	0.994100i	$-0.534595\pi$
$23$	−550.366	−0.216936	−0.108468	+	0.994100i	$0.534595\pi$
$24$	168.237	0.0596202
$25$	625.000	0.200000
$26$	452.628	0.131313
$27$	−451.783	−0.119267
$28$	0	0
$29$	4844.75	1.06973	0.534867	−	0.844936i	$-0.320362\pi$
$29$	4844.75	1.06973	0.534867	+	0.844936i	$0.320362\pi$
$30$	−81.0868	−0.0164493
$31$	−5807.64	−1.08541	−0.542707	−	0.839922i	$-0.682600\pi$
$31$	−5807.64	−1.08541	−0.542707	+	0.839922i	$0.682600\pi$
$32$	−5804.03	−1.00197
$33$	267.037	0.0426861
$34$	1551.05	0.230107
$35$	0	0
$36$	4811.04	0.618703
$37$	−14016.6	−1.68321	−0.841605	−	0.540093i	$-0.818389\pi$
$37$	−14016.6	−1.68321	−0.841605	+	0.540093i	$0.818389\pi$
$38$	2885.71	0.324186
$39$	−121.023	−0.0127411
$40$	4516.40	0.446316
$41$	11869.9	1.10278	0.551388	−	0.834249i	$-0.314098\pi$
$41$	11869.9	1.10278	0.551388	+	0.834249i	$0.314098\pi$
$42$	0	0
$43$	15813.2	1.30421	0.652107	−	0.758127i	$-0.273885\pi$
$43$	15813.2	1.30421	0.652107	+	0.758127i	$0.273885\pi$
$44$	−5697.54	−0.443666
$45$	−6053.32	−0.445618
$46$	1916.87	0.133567
$47$	10394.5	0.686368	0.343184	−	0.939268i	$-0.388494\pi$
$47$	10394.5	0.686368	0.343184	+	0.939268i	$0.388494\pi$
$48$	6.16002	0.000385904 0
$49$	0	0
$50$	−2176.81	−0.123139
$51$	−414.720	−0.0223269
$52$	2582.17	0.132427
$53$	7473.83	0.365471	0.182736	−	0.983162i	$-0.441505\pi$
$53$	7473.83	0.365471	0.182736	+	0.983162i	$0.441505\pi$
$54$	1573.51	0.0734322
$55$	7168.73	0.319548
$56$	0	0
$57$	−771.580	−0.0314553
$58$	−16873.8	−0.658631
$59$	22516.6	0.842117	0.421058	−	0.907034i	$-0.361659\pi$
$59$	22516.6	0.842117	0.421058	+	0.907034i	$0.361659\pi$
$60$	−462.588	−0.0165888
$61$	21943.7	0.755065	0.377533	−	0.925996i	$-0.376773\pi$
$61$	21943.7	0.755065	0.377533	+	0.925996i	$0.376773\pi$
$62$	20227.4	0.668284
$63$	0	0
$64$	20003.2	0.610448
$65$	−3248.93	−0.0953799
$66$	−930.064	−0.0262817
$67$	−1266.67	−0.0344729	−0.0172364	−	0.999851i	$-0.505487\pi$
$67$	−1266.67	−0.0344729	−0.0172364	+	0.999851i	$0.505487\pi$
$68$	8848.52	0.232059
$69$	−512.532	−0.0129598
$70$	0	0
$71$	25833.3	0.608184	0.304092	−	0.952643i	$-0.401647\pi$
$71$	25833.3	0.608184	0.304092	+	0.952643i	$0.401647\pi$
$72$	−43742.7	−0.994431
$73$	4003.05	0.0879192	0.0439596	−	0.999033i	$-0.486003\pi$
$73$	4003.05	0.0879192	0.0439596	+	0.999033i	$0.486003\pi$
$74$	48818.4	1.03634
$75$	582.035	0.0119480
$76$	16462.5	0.326936
$77$	0	0
$78$	421.512	0.00784465
$79$	−64829.8	−1.16871	−0.584356	−	0.811498i	$-0.698653\pi$
$79$	−64829.8	−1.16871	−0.584356	+	0.811498i	$0.698653\pi$
$80$	165.369	0.00288887
$81$	58417.5	0.989306
$82$	−41341.6	−0.678974
$83$	91596.2	1.45943	0.729714	−	0.683753i	$-0.239653\pi$
$83$	91596.2	1.45943	0.729714	+	0.683753i	$0.239653\pi$
$84$	0	0
$85$	−11133.3	−0.167139
$86$	−55075.8	−0.802999
$87$	4511.70	0.0639061
$88$	51803.0	0.713096
$89$	120374.	1.61086	0.805432	−	0.592689i	$-0.201934\pi$
$89$	120374.	1.61086	0.805432	+	0.592689i	$0.201934\pi$
$90$	21083.1	0.274365
$91$	0	0
$92$	10935.5	0.134700
$93$	−5408.40	−0.0648427
$94$	−36202.9	−0.422594
$95$	−20713.4	−0.235474
$96$	−5405.04	−0.0598578
$97$	159506.	1.72127	0.860635	−	0.509222i	$-0.170067\pi$
$97$	159506.	1.72127	0.860635	+	0.509222i	$0.170067\pi$
$98$	0	0
$99$	−69431.4	−0.711980
$100$	−12418.4	−0.124184
$101$	179178.	1.74776	0.873878	−	0.486145i	$-0.161597\pi$
$101$	179178.	1.74776	0.873878	+	0.486145i	$0.161597\pi$
$102$	1444.43	0.0137466
$103$	24403.9	0.226656	0.113328	−	0.993558i	$-0.463849\pi$
$103$	24403.9	0.226656	0.113328	+	0.993558i	$0.463849\pi$
$104$	−23477.5	−0.212848
$105$	0	0
$106$	−26030.6	−0.225019
$107$	97747.7	0.825367	0.412683	−	0.910875i	$-0.364592\pi$
$107$	97747.7	0.825367	0.412683	+	0.910875i	$0.364592\pi$
$108$	8976.66	0.0740552
$109$	9407.25	0.0758397	0.0379198	−	0.999281i	$-0.487927\pi$
$109$	9407.25	0.0758397	0.0379198	+	0.999281i	$0.487927\pi$
$110$	−24968.0	−0.196744
$111$	−13053.0	−0.100555
$112$	0	0
$113$	53300.2	0.392674	0.196337	−	0.980536i	$-0.437095\pi$
$113$	53300.2	0.392674	0.196337	+	0.980536i	$0.437095\pi$
$114$	2687.34	0.0193669
$115$	−13759.2	−0.0970169
$116$	−96262.2	−0.664219
$117$	31466.9	0.212515
$118$	−78423.0	−0.518488
$119$	0	0
$120$	4205.93	0.0266630
$121$	−78825.8	−0.489446
$122$	−76427.6	−0.464890
$123$	11053.9	0.0658800
$124$	115394.	0.673954
$125$	15625.0	0.0894427
$126$	0	0
$127$	84941.2	0.467314	0.233657	−	0.972319i	$-0.424931\pi$
$127$	84941.2	0.467314	0.233657	+	0.972319i	$0.424931\pi$
$128$	116060.	0.626119
$129$	14726.2	0.0779139
$130$	11315.7	0.0587250
$131$	−163970.	−0.834809	−0.417404	−	0.908721i	$-0.637060\pi$
$131$	−163970.	−0.834809	−0.417404	+	0.908721i	$0.637060\pi$
$132$	−5305.87	−0.0265046
$133$	0	0
$134$	4411.70	0.0212248
$135$	−11294.6	−0.0533378
$136$	−80452.2	−0.372984
$137$	−55283.2	−0.251647	−0.125823	−	0.992053i	$-0.540157\pi$
$137$	−55283.2	−0.251647	−0.125823	+	0.992053i	$0.540157\pi$
$138$	1785.10	0.00797929
$139$	−264642.	−1.16178	−0.580888	−	0.813983i	$-0.697295\pi$
$139$	−264642.	−1.16178	−0.580888	+	0.813983i	$0.697295\pi$
$140$	0	0
$141$	9679.91	0.0410037
$142$	−89974.9	−0.374456
$143$	−37265.1	−0.152392
$144$	−1601.65	−0.00643666
$145$	121119.	0.478400
$146$	−13942.2	−0.0541315
$147$	0	0
$148$	278502.	1.04514
$149$	11418.0	0.0421332	0.0210666	−	0.999778i	$-0.493294\pi$
$149$	11418.0	0.0421332	0.0210666	+	0.999778i	$0.493294\pi$
$150$	−2027.17	−0.00735635
$151$	−178864.	−0.638380	−0.319190	−	0.947691i	$-0.603411\pi$
$151$	−178864.	−0.638380	−0.319190	+	0.947691i	$0.603411\pi$
$152$	−149680.	−0.525479
$153$	107830.	0.372401
$154$	0	0
$155$	−145191.	−0.485412
$156$	2404.66	0.00791121
$157$	23669.8	0.0766381	0.0383190	−	0.999266i	$-0.487800\pi$
$157$	23669.8	0.0766381	0.0383190	+	0.999266i	$0.487800\pi$
$158$	225796.	0.719570
$159$	6960.05	0.0218333
$160$	−145101.	−0.448094
$161$	0	0
$162$	−203462.	−0.609111
$163$	544589.	1.60546	0.802731	−	0.596341i	$-0.203379\pi$
$163$	544589.	1.60546	0.802731	+	0.596341i	$0.203379\pi$
$164$	−235848.	−0.684734
$165$	6675.93	0.0190898
$166$	−319020.	−0.898563
$167$	−456922.	−1.26780	−0.633901	−	0.773414i	$-0.718547\pi$
$167$	−456922.	−1.26780	−0.633901	+	0.773414i	$0.718547\pi$
$168$	0	0
$169$	−354404.	−0.954513
$170$	38776.3	0.102907
$171$	200616.	0.524657
$172$	−314199.	−0.809812
$173$	−479837.	−1.21893	−0.609465	−	0.792813i	$-0.708616\pi$
$173$	−479837.	−1.21893	−0.609465	+	0.792813i	$0.708616\pi$
$174$	−15713.8	−0.0393467
$175$	0	0
$176$	1896.77	0.00461566
$177$	20968.7	0.0503082
$178$	−419251.	−0.991801
$179$	−385543.	−0.899374	−0.449687	−	0.893186i	$-0.648465\pi$
$179$	−385543.	−0.899374	−0.449687	+	0.893186i	$0.648465\pi$
$180$	120276.	0.276692
$181$	−304138.	−0.690040	−0.345020	−	0.938595i	$-0.612128\pi$
$181$	−304138.	−0.690040	−0.345020	+	0.938595i	$0.612128\pi$
$182$	0	0
$183$	20435.2	0.0451077
$184$	−99426.9	−0.216501
$185$	−350415.	−0.752755
$186$	18836.9	0.0399234
$187$	−127699.	−0.267045
$188$	−206532.	−0.426179
$189$	0	0
$190$	72142.8	0.144980
$191$	524740.	1.04079	0.520393	−	0.853927i	$-0.325786\pi$
$191$	524740.	1.04079	0.520393	+	0.853927i	$0.325786\pi$
$192$	18628.1	0.0364683
$193$	−230225.	−0.444897	−0.222449	−	0.974944i	$-0.571405\pi$
$193$	−230225.	−0.444897	−0.222449	+	0.974944i	$0.571405\pi$
$194$	−555545.	−1.05978
$195$	−3025.59	−0.00569801
$196$	0	0
$197$	−444693.	−0.816385	−0.408192	−	0.912896i	$-0.633841\pi$
$197$	−444693.	−0.816385	−0.408192	+	0.912896i	$0.633841\pi$
$198$	241823.	0.438363
$199$	63255.8	0.113232	0.0566158	−	0.998396i	$-0.481969\pi$
$199$	63255.8	0.113232	0.0566158	+	0.998396i	$0.481969\pi$
$200$	112910.	0.199599
$201$	−1179.60	−0.00205942
$202$	−624059.	−1.07609
$203$	0	0
$204$	8240.24	0.0138632
$205$	296747.	0.493176
$206$	−84996.4	−0.139551
$207$	133262.	0.216162
$208$	−859.633	−0.00137770
$209$	−237582.	−0.376226
$210$	0	0
$211$	8586.36	0.0132771	0.00663855	−	0.999978i	$-0.497887\pi$
$211$	8586.36	0.0132771	0.00663855	+	0.999978i	$0.497887\pi$
$212$	−148501.	−0.226928
$213$	24057.5	0.0363330
$214$	−340445.	−0.508175
$215$	395330.	0.583262
$216$	−81617.3	−0.119028
$217$	0	0
$218$	−32764.5	−0.0466941
$219$	3727.87	0.00525231
$220$	−142439.	−0.198413
$221$	57874.3	0.0797085
$222$	45462.5	0.0619114
$223$	1.46200e6	1.96873	0.984363	−	0.176152i	$-0.0563651\pi$
$223$	1.46200e6	1.96873	0.984363	+	0.176152i	$0.0563651\pi$
$224$	0	0
$225$	−151333.	−0.199286
$226$	−185639.	−0.241768
$227$	1.33797e6	1.72339	0.861693	−	0.507430i	$-0.169404\pi$
$227$	1.33797e6	1.72339	0.861693	+	0.507430i	$0.169404\pi$
$228$	15330.8	0.0195312
$229$	1.17801e6	1.48443	0.742213	−	0.670164i	$-0.233776\pi$
$229$	1.17801e6	1.48443	0.742213	+	0.670164i	$0.233776\pi$
$230$	47921.8	0.0597328
$231$	0	0
$232$	875232.	1.06759
$233$	1.53081e6	1.84727	0.923637	−	0.383268i	$-0.125201\pi$
$233$	1.53081e6	1.84727	0.923637	+	0.383268i	$0.125201\pi$
$234$	−109596.	−0.130844
$235$	259861.	0.306953
$236$	−447391.	−0.522886
$237$	−60373.2	−0.0698190
$238$	0	0
$239$	−1.54480e6	−1.74936	−0.874678	−	0.484704i	$-0.838927\pi$
$239$	−1.54480e6	−1.74936	−0.874678	+	0.484704i	$0.838927\pi$
$240$	154.001	0.000172582 0
$241$	1.49692e6	1.66018	0.830090	−	0.557629i	$-0.188289\pi$
$241$	1.49692e6	1.66018	0.830090	+	0.557629i	$0.188289\pi$
$242$	274542.	0.301350
$243$	164185.	0.178368
$244$	−436008.	−0.468835
$245$	0	0
$246$	−38499.7	−0.0405620
$247$	107674.	0.112297
$248$	−1.04918e6	−1.08323
$249$	85299.6	0.0871864
$250$	−54420.3	−0.0550695
$251$	−218578.	−0.218989	−0.109494	−	0.993987i	$-0.534923\pi$
$251$	−218578.	−0.218989	−0.109494	+	0.993987i	$0.534923\pi$
$252$	0	0
$253$	−157817.	−0.155008
$254$	−295842.	−0.287723
$255$	−10368.0	−0.00998491
$256$	−1.04433e6	−0.995947
$257$	−440875.	−0.416373	−0.208186	−	0.978089i	$-0.566756\pi$
$257$	−440875.	−0.416373	−0.208186	+	0.978089i	$0.566756\pi$
$258$	−51289.7	−0.0479713
$259$	0	0
$260$	64554.3	0.0592232
$261$	−1.17307e6	−1.06592
$262$	571092.	0.513988
$263$	1.63847e6	1.46066	0.730330	−	0.683094i	$-0.239366\pi$
$263$	1.63847e6	1.46066	0.730330	+	0.683094i	$0.239366\pi$
$264$	48241.9	0.0426004
$265$	186846.	0.163444
$266$	0	0
$267$	112099.	0.0962332
$268$	25168.1	0.0214049
$269$	−164988.	−0.139018	−0.0695091	−	0.997581i	$-0.522143\pi$
$269$	−164988.	−0.139018	−0.0695091	+	0.997581i	$0.522143\pi$
$270$	39337.9	0.0328399
$271$	−792518.	−0.655520	−0.327760	−	0.944761i	$-0.606294\pi$
$271$	−792518.	−0.655520	−0.327760	+	0.944761i	$0.606294\pi$
$272$	−2945.77	−0.00241422
$273$	0	0
$274$	192546.	0.154938
$275$	179218.	0.142906
$276$	10183.7	0.00804699
$277$	493282.	0.386274	0.193137	−	0.981172i	$-0.438134\pi$
$277$	493282.	0.386274	0.193137	+	0.981172i	$0.438134\pi$
$278$	921723.	0.715300
$279$	1.40622e6	1.08154
$280$	0	0
$281$	−810468.	−0.612308	−0.306154	−	0.951982i	$-0.599042\pi$
$281$	−810468.	−0.612308	−0.306154	+	0.951982i	$0.599042\pi$
$282$	−33714.1	−0.0252458
$283$	−1.84043e6	−1.36601	−0.683005	−	0.730414i	$-0.739327\pi$
$283$	−1.84043e6	−1.36601	−0.683005	+	0.730414i	$0.739327\pi$
$284$	−513293.	−0.377633
$285$	−19289.5	−0.0140672
$286$	129791.	0.0938271
$287$	0	0
$288$	1.40535e6	0.998394
$289$	−1.22154e6	−0.860323
$290$	−421844.	−0.294549
$291$	148541.	0.102829
$292$	−79538.2	−0.0545907
$293$	635152.	0.432224	0.216112	−	0.976369i	$-0.430662\pi$
$293$	635152.	0.432224	0.216112	+	0.976369i	$0.430662\pi$
$294$	0	0
$295$	562914.	0.376606
$296$	−2.53218e6	−1.67983
$297$	−129548.	−0.0852199
$298$	−39767.7	−0.0259412
$299$	71524.0	0.0462673
$300$	−11564.7	−0.00741876
$301$	0	0
$302$	622964.	0.393048
$303$	166861.	0.104411
$304$	−5480.56	−0.00340127
$305$	548592.	0.337676
$306$	−375561.	−0.229285
$307$	2.04984e6	1.24130	0.620648	−	0.784090i	$-0.286870\pi$
$307$	2.04984e6	1.24130	0.620648	+	0.784090i	$0.286870\pi$
$308$	0	0
$309$	22726.3	0.0135404
$310$	505685.	0.298866
$311$	3.03081e6	1.77688	0.888439	−	0.458994i	$-0.151790\pi$
$311$	3.03081e6	1.77688	0.888439	+	0.458994i	$0.151790\pi$
$312$	−21863.6	−0.0127156
$313$	2.39794e6	1.38350	0.691748	−	0.722139i	$-0.256841\pi$
$313$	2.39794e6	1.38350	0.691748	+	0.722139i	$0.256841\pi$
$314$	−82439.4	−0.0471857
$315$	0	0
$316$	1.28813e6	0.725675
$317$	−1.40852e6	−0.787253	−0.393626	−	0.919271i	$-0.628780\pi$
$317$	−1.40852e6	−0.787253	−0.393626	+	0.919271i	$0.628780\pi$
$318$	−24241.2	−0.0134427
$319$	1.38923e6	0.764358
$320$	500079.	0.273001
$321$	91028.2	0.0493075
$322$	0	0
$323$	368975.	0.196785
$324$	−1.16072e6	−0.614279
$325$	−81223.2	−0.0426552
$326$	−1.89675e6	−0.988476
$327$	8760.56	0.00453067
$328$	2.14437e6	1.10056
$329$	0	0
$330$	−23251.6	−0.0117535
$331$	−3.30863e6	−1.65989	−0.829943	−	0.557849i	$-0.811627\pi$
$331$	−3.30863e6	−1.65989	−0.829943	+	0.557849i	$0.811627\pi$
$332$	−1.81996e6	−0.906186
$333$	3.39388e6	1.67720
$334$	1.59141e6	0.780579
$335$	−31666.8	−0.0154167
$336$	0	0
$337$	−703558.	−0.337462	−0.168731	−	0.985662i	$-0.553967\pi$
$337$	−703558.	−0.337462	−0.168731	+	0.985662i	$0.553967\pi$
$338$	1.23435e6	0.587690
$339$	49636.1	0.0234584
$340$	221213.	0.103780
$341$	−1.66534e6	−0.775561
$342$	−698725.	−0.323029
$343$	0	0
$344$	2.85675e6	1.30160
$345$	−12813.3	−0.00579580
$346$	1.67122e6	0.750489
$347$	−1.72432e6	−0.768765	−0.384382	−	0.923174i	$-0.625586\pi$
$347$	−1.72432e6	−0.768765	−0.384382	+	0.923174i	$0.625586\pi$
$348$	−89644.8	−0.0396805
$349$	−47194.2	−0.0207408	−0.0103704	−	0.999946i	$-0.503301\pi$
$349$	−47194.2	−0.0207408	−0.0103704	+	0.999946i	$0.503301\pi$
$350$	0	0
$351$	58712.4	0.0254368
$352$	−1.66430e6	−0.715938
$353$	−3.16931e6	−1.35372	−0.676858	−	0.736114i	$-0.736659\pi$
$353$	−3.16931e6	−1.35372	−0.676858	+	0.736114i	$0.736659\pi$
$354$	−73031.9	−0.0309745
$355$	645834.	0.271988
$356$	−2.39177e6	−1.00022
$357$	0	0
$358$	1.34281e6	0.553741
$359$	1.19418e6	0.489030	0.244515	−	0.969646i	$-0.421371\pi$
$359$	1.19418e6	0.489030	0.244515	+	0.969646i	$0.421371\pi$
$360$	−1.09357e6	−0.444723
$361$	−1.78963e6	−0.722760
$362$	1.05928e6	0.424854
$363$	−73407.0	−0.0292396
$364$	0	0
$365$	100076.	0.0393187
$366$	−71173.7	−0.0277726
$367$	3.35489e6	1.30021	0.650104	−	0.759845i	$-0.274725\pi$
$367$	3.35489e6	1.30021	0.650104	+	0.759845i	$0.274725\pi$
$368$	−3640.53	−0.00140135
$369$	−2.87409e6	−1.09884
$370$	1.22046e6	0.463468
$371$	0	0
$372$	107462.	0.0402621
$373$	3.29223e6	1.22523	0.612616	−	0.790381i	$-0.290117\pi$
$373$	3.29223e6	1.22523	0.612616	+	0.790381i	$0.290117\pi$
$374$	444763.	0.164418
$375$	14550.9	0.00534332
$376$	1.87782e6	0.684991
$377$	−629609.	−0.228149
$378$	0	0
$379$	2.69330e6	0.963135	0.481568	−	0.876409i	$-0.340068\pi$
$379$	2.69330e6	0.963135	0.481568	+	0.876409i	$0.340068\pi$
$380$	411563.	0.146210
$381$	79102.0	0.0279174
$382$	−1.82762e6	−0.640807
$383$	4.31533e6	1.50320	0.751601	−	0.659618i	$-0.229282\pi$
$383$	4.31533e6	1.50320	0.751601	+	0.659618i	$0.229282\pi$
$384$	108082.	0.0374045
$385$	0	0
$386$	801851.	0.273921
$387$	−3.82890e6	−1.29956
$388$	−3.16930e6	−1.06877
$389$	114668.	0.0384208	0.0192104	−	0.999815i	$-0.493885\pi$
$389$	114668.	0.0384208	0.0192104	+	0.999815i	$0.493885\pi$
$390$	10537.8	0.00350824
$391$	245097.	0.0810766
$392$	0	0
$393$	−152698.	−0.0498716
$394$	1.54882e6	0.502644
$395$	−1.62075e6	−0.522664
$396$	1.37956e6	0.442082
$397$	−1.03907e6	−0.330879	−0.165439	−	0.986220i	$-0.552904\pi$
$397$	−1.03907e6	−0.330879	−0.165439	+	0.986220i	$0.552904\pi$
$398$	−220313.	−0.0697161
$399$	0	0
$400$	4134.22	0.00129194
$401$	−1.14709e6	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$401$	−1.14709e6	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$402$	4108.42	0.00126797
$403$	754744.	0.231492
$404$	−3.56016e6	−1.08522
$405$	1.46044e6	0.442431
$406$	0	0
$407$	−4.01925e6	−1.20271
$408$	−74921.6	−0.0222821
$409$	6.29539e6	1.86086	0.930431	−	0.366466i	$-0.119432\pi$
$409$	6.29539e6	1.86086	0.930431	+	0.366466i	$0.119432\pi$
$410$	−1.03354e6	−0.303646
$411$	−51482.8	−0.0150334
$412$	−484891.	−0.140735
$413$	0	0
$414$	−464137.	−0.133090
$415$	2.28991e6	0.652676
$416$	754275.	0.213696
$417$	−246450.	−0.0694047
$418$	827476.	0.231640
$419$	692588.	0.192726	0.0963629	−	0.995346i	$-0.469279\pi$
$419$	692588.	0.192726	0.0963629	+	0.995346i	$0.469279\pi$
$420$	0	0
$421$	−4.69540e6	−1.29112	−0.645561	−	0.763708i	$-0.723377\pi$
$421$	−4.69540e6	−1.29112	−0.645561	+	0.763708i	$0.723377\pi$
$422$	−29905.4	−0.00817465
$423$	−2.51684e6	−0.683919
$424$	1.35019e6	0.364738
$425$	−278333.	−0.0747469
$426$	−83789.7	−0.0223700
$427$	0	0
$428$	−1.94219e6	−0.512486
$429$	−34703.4	−0.00910392
$430$	−1.37690e6	−0.359112
$431$	1.34143e6	0.347837	0.173919	−	0.984760i	$-0.444357\pi$
$431$	1.34143e6	0.347837	0.173919	+	0.984760i	$0.444357\pi$
$432$	−2988.43	−0.000770431 0
$433$	2.19513e6	0.562653	0.281326	−	0.959612i	$-0.409226\pi$
$433$	2.19513e6	0.562653	0.281326	+	0.959612i	$0.409226\pi$
$434$	0	0
$435$	112793.	0.0285797
$436$	−186916.	−0.0470903
$437$	455999.	0.114225
$438$	−12983.8	−0.00323382
$439$	19857.4	0.00491768	0.00245884	−	0.999997i	$-0.499217\pi$
$439$	19857.4	0.00491768	0.00245884	+	0.999997i	$0.499217\pi$
$440$	1.29507e6	0.318906
$441$	0	0
$442$	−201570.	−0.0490762
$443$	3.79513e6	0.918793	0.459397	−	0.888231i	$-0.348066\pi$
$443$	3.79513e6	0.918793	0.459397	+	0.888231i	$0.348066\pi$
$444$	259356.	0.0624366
$445$	3.00936e6	0.720400
$446$	−5.09200e6	−1.21214
$447$	10633.1	0.00251704
$448$	0	0
$449$	−2.19547e6	−0.513939	−0.256970	−	0.966419i	$-0.582724\pi$
$449$	−2.19547e6	−0.513939	−0.256970	+	0.966419i	$0.582724\pi$
$450$	527078.	0.122700
$451$	3.40368e6	0.787967
$452$	−1.05904e6	−0.243819
$453$	−166568.	−0.0381369
$454$	−4.66002e6	−1.06108
$455$	0	0
$456$	−139391.	−0.0313922
$457$	3.07567e6	0.688888	0.344444	−	0.938807i	$-0.388067\pi$
$457$	3.07567e6	0.688888	0.344444	+	0.938807i	$0.388067\pi$
$458$	−4.10287e6	−0.913954
$459$	201194.	0.0445742
$460$	273386.	0.0602396
$461$	−6.56759e6	−1.43931	−0.719654	−	0.694333i	$-0.755699\pi$
$461$	−6.56759e6	−1.43931	−0.719654	+	0.694333i	$0.755699\pi$
$462$	0	0
$463$	−4.76926e6	−1.03395	−0.516974	−	0.856001i	$-0.672942\pi$
$463$	−4.76926e6	−1.03395	−0.516974	+	0.856001i	$0.672942\pi$
$464$	32046.8	0.00691018
$465$	−135210.	−0.0289986
$466$	−5.33166e6	−1.13736
$467$	−8.45034e6	−1.79301	−0.896503	−	0.443037i	$-0.853901\pi$
$467$	−8.45034e6	−1.79301	−0.896503	+	0.443037i	$0.853901\pi$
$468$	−625228.	−0.131954
$469$	0	0
$470$	−905071.	−0.188990
$471$	22042.6	0.00457837
$472$	4.06775e6	0.840426
$473$	4.53443e6	0.931901
$474$	210274.	0.0429872
$475$	−517835.	−0.105307
$476$	0	0
$477$	−1.80966e6	−0.364167
$478$	5.38039e6	1.07707
$479$	−2.27675e6	−0.453395	−0.226698	−	0.973965i	$-0.572793\pi$
$479$	−2.27675e6	−0.453395	−0.226698	+	0.973965i	$0.572793\pi$
$480$	−135126.	−0.0267692
$481$	1.82156e6	0.358988
$482$	−5.21361e6	−1.02217
$483$	0	0
$484$	1.56622e6	0.303907
$485$	3.98766e6	0.769775
$486$	−571840.	−0.109821
$487$	−7.60452e6	−1.45294	−0.726472	−	0.687196i	$-0.758842\pi$
$487$	−7.60452e6	−1.45294	−0.726472	+	0.687196i	$0.758842\pi$
$488$	3.96425e6	0.753550
$489$	507152.	0.0959105
$490$	0	0
$491$	−1.30855e6	−0.244954	−0.122477	−	0.992471i	$-0.539084\pi$
$491$	−1.30855e6	−0.244954	−0.122477	+	0.992471i	$0.539084\pi$
$492$	−219635.	−0.0409061
$493$	−2.15753e6	−0.399797
$494$	−375019.	−0.0691410
$495$	−1.73579e6	−0.318407
$496$	−38416.0	−0.00701146
$497$	0	0
$498$	−297090.	−0.0536802
$499$	7.45146e6	1.33965	0.669823	−	0.742521i	$-0.266370\pi$
$499$	7.45146e6	1.33965	0.669823	+	0.742521i	$0.266370\pi$
$500$	−310460.	−0.0555367
$501$	−425512.	−0.0757386
$502$	761284.	0.134830
$503$	−6.95776e6	−1.22617	−0.613083	−	0.790018i	$-0.710071\pi$
$503$	−6.95776e6	−1.22617	−0.613083	+	0.790018i	$0.710071\pi$
$504$	0	0
$505$	4.47945e6	0.781621
$506$	549661.	0.0954375
$507$	−330041.	−0.0570228
$508$	−1.68773e6	−0.290164
$509$	−6.38828e6	−1.09292	−0.546462	−	0.837484i	$-0.684026\pi$
$509$	−6.38828e6	−1.09292	−0.546462	+	0.837484i	$0.684026\pi$
$510$	36110.7	0.00614767
$511$	0	0
$512$	−76631.9	−0.0129192
$513$	374319.	0.0627984
$514$	1.53552e6	0.256359
$515$	610098.	0.101363
$516$	−292600.	−0.0483783
$517$	2.98060e6	0.490431
$518$	0	0
$519$	−446851.	−0.0728190
$520$	−586938.	−0.0951884
$521$	4.04171e6	0.652335	0.326168	−	0.945312i	$-0.394243\pi$
$521$	4.04171e6	0.652335	0.326168	+	0.945312i	$0.394243\pi$
$522$	4.08569e6	0.656280
$523$	9.56520e6	1.52911	0.764557	−	0.644556i	$-0.222958\pi$
$523$	9.56520e6	1.52911	0.764557	+	0.644556i	$0.222958\pi$
$524$	3.25799e6	0.518349
$525$	0	0
$526$	−5.70663e6	−0.899322
$527$	2.58634e6	0.405656
$528$	1766.38	0.000275740 0
$529$	−6.13344e6	−0.952939
$530$	−650765.	−0.100632
$531$	−5.45200e6	−0.839111
$532$	0	0
$533$	−1.54258e6	−0.235195
$534$	−390431.	−0.0592503
$535$	2.44369e6	0.369115
$536$	−228832.	−0.0344037
$537$	−359040.	−0.0537287
$538$	574637.	0.0855929
$539$	0	0
$540$	224417.	0.0331185
$541$	−5.23399e6	−0.768847	−0.384423	−	0.923157i	$-0.625600\pi$
$541$	−5.23399e6	−0.768847	−0.384423	+	0.923157i	$0.625600\pi$
$542$	2.76026e6	0.403601
$543$	−283230.	−0.0412231
$544$	2.58473e6	0.374471
$545$	235181.	0.0339165
$546$	0	0
$547$	6.70068e6	0.957527	0.478763	−	0.877944i	$-0.341085\pi$
$547$	6.70068e6	0.957527	0.478763	+	0.877944i	$0.341085\pi$
$548$	1.09844e6	0.156252
$549$	−5.31328e6	−0.752371
$550$	−624199.	−0.0879866
$551$	−4.01405e6	−0.563253
$552$	−92592.0	−0.0129338
$553$	0	0
$554$	−1.71805e6	−0.237827
$555$	−326326.	−0.0449697
$556$	5.25829e6	0.721369
$557$	6.48410e6	0.885547	0.442773	−	0.896634i	$-0.353995\pi$
$557$	6.48410e6	0.885547	0.442773	+	0.896634i	$0.353995\pi$
$558$	−4.89772e6	−0.665899
$559$	−2.05504e6	−0.278157
$560$	0	0
$561$	−118921.	−0.0159533
$562$	2.82278e6	0.376995
$563$	−8.78466e6	−1.16803	−0.584015	−	0.811743i	$-0.698519\pi$
$563$	−8.78466e6	−1.16803	−0.584015	+	0.811743i	$0.698519\pi$
$564$	−192334.	−0.0254600
$565$	1.33250e6	0.175609
$566$	6.41004e6	0.841046
$567$	0	0
$568$	4.66695e6	0.606963
$569$	−5.15843e6	−0.667939	−0.333970	−	0.942584i	$-0.608388\pi$
$569$	−5.15843e6	−0.667939	−0.333970	+	0.942584i	$0.608388\pi$
$570$	67183.4	0.00866114
$571$	−1.41270e7	−1.81326	−0.906630	−	0.421927i	$-0.861354\pi$
$571$	−1.41270e7	−1.81326	−0.906630	+	0.421927i	$0.861354\pi$
$572$	740436.	0.0946232
$573$	488668.	0.0621766
$574$	0	0
$575$	−343979.	−0.0433873
$576$	−4.84342e6	−0.608270
$577$	−1.01722e7	−1.27197	−0.635983	−	0.771703i	$-0.719405\pi$
$577$	−1.01722e7	−1.27197	−0.635983	+	0.771703i	$0.719405\pi$
$578$	4.25448e6	0.529697
$579$	−214399.	−0.0265782
$580$	−2.40656e6	−0.297048
$581$	0	0
$582$	−517355.	−0.0633113
$583$	2.14312e6	0.261140
$584$	723175.	0.0877427
$585$	786672.	0.0950395
$586$	−2.21217e6	−0.266118
$587$	−1.60193e6	−0.191888	−0.0959441	−	0.995387i	$-0.530587\pi$
$587$	−1.60193e6	−0.191888	−0.0959441	+	0.995387i	$0.530587\pi$
$588$	0	0
$589$	4.81184e6	0.571509
$590$	−1.96057e6	−0.231875
$591$	−414123.	−0.0487709
$592$	−92716.2	−0.0108731
$593$	−4.04363e6	−0.472209	−0.236105	−	0.971728i	$-0.575871\pi$
$593$	−4.04363e6	−0.472209	−0.236105	+	0.971728i	$0.575871\pi$
$594$	451204.	0.0524695
$595$	0	0
$596$	−226869.	−0.0261613
$597$	58907.3	0.00676447
$598$	−249111.	−0.0284866
$599$	−527518.	−0.0600718	−0.0300359	−	0.999549i	$-0.509562\pi$
$599$	−527518.	−0.0600718	−0.0300359	+	0.999549i	$0.509562\pi$
$600$	105148.	0.0119240
$601$	−2.93892e6	−0.331896	−0.165948	−	0.986134i	$-0.553068\pi$
$601$	−2.93892e6	−0.331896	−0.165948	+	0.986134i	$0.553068\pi$
$602$	0	0
$603$	306703.	0.0343499
$604$	3.55391e6	0.396382
$605$	−1.97065e6	−0.218887
$606$	−581159.	−0.0642855
$607$	1.27495e7	1.40450	0.702249	−	0.711931i	$-0.252179\pi$
$607$	1.27495e7	1.40450	0.702249	+	0.711931i	$0.252179\pi$
$608$	4.80885e6	0.527573
$609$	0	0
$610$	−1.91069e6	−0.207905
$611$	−1.35083e6	−0.146386
$612$	−2.14252e6	−0.231231
$613$	−1.02219e7	−1.09871	−0.549353	−	0.835591i	$-0.685126\pi$
$613$	−1.02219e7	−1.09871	−0.549353	+	0.835591i	$0.685126\pi$
$614$	−7.13940e6	−0.764260
$615$	276348.	0.0294624
$616$	0	0
$617$	7.79117e6	0.823929	0.411965	−	0.911200i	$-0.364843\pi$
$617$	7.79117e6	0.823929	0.411965	+	0.911200i	$0.364843\pi$
$618$	−79153.4	−0.00833678
$619$	−756319.	−0.0793375	−0.0396688	−	0.999213i	$-0.512630\pi$
$619$	−756319.	−0.0793375	−0.0396688	+	0.999213i	$0.512630\pi$
$620$	2.88486e6	0.301401
$621$	248646.	0.0258734
$622$	−1.05560e7	−1.09402
$623$	0	0
$624$	−800.539	−8.23040e−5 0
$625$	390625.	0.0400000
$626$	−8.35179e6	−0.851812
$627$	−221250.	−0.0224758
$628$	−470304.	−0.0475861
$629$	6.24206e6	0.629074
$630$	0	0
$631$	1.66955e7	1.66927	0.834634	−	0.550805i	$-0.185679\pi$
$631$	1.66955e7	1.66927	0.834634	+	0.550805i	$0.185679\pi$
$632$	−1.17119e7	−1.16637
$633$	7996.11	0.000793175 0
$634$	4.90572e6	0.484708
$635$	2.12353e6	0.208989
$636$	−138292.	−0.0135567
$637$	0	0
$638$	−4.83854e6	−0.470612
$639$	−6.25510e6	−0.606013
$640$	2.90150e6	0.280009
$641$	1.61871e7	1.55605	0.778027	−	0.628231i	$-0.216221\pi$
$641$	1.61871e7	1.55605	0.778027	+	0.628231i	$0.216221\pi$
$642$	−317042.	−0.0303584
$643$	1.09445e7	1.04392	0.521959	−	0.852970i	$-0.325201\pi$
$643$	1.09445e7	1.04392	0.521959	+	0.852970i	$0.325201\pi$
$644$	0	0
$645$	368154.	0.0348442
$646$	−1.28510e6	−0.121159
$647$	9.00960e6	0.846145	0.423072	−	0.906096i	$-0.360952\pi$
$647$	9.00960e6	0.846145	0.423072	+	0.906096i	$0.360952\pi$
$648$	1.05535e7	0.987320
$649$	6.45661e6	0.601718
$650$	282892.	0.0262626
$651$	0	0
$652$	−1.08207e7	−0.996862
$653$	−1.91627e7	−1.75863	−0.879313	−	0.476244i	$-0.841998\pi$
$653$	−1.91627e7	−1.75863	−0.879313	+	0.476244i	$0.841998\pi$
$654$	−30512.2	−0.00278951
$655$	−4.09926e6	−0.373338
$656$	78516.3	0.00712361
$657$	−969269.	−0.0876054
$658$	0	0
$659$	889509.	0.0797879	0.0398939	−	0.999204i	$-0.487298\pi$
$659$	889509.	0.0797879	0.0398939	+	0.999204i	$0.487298\pi$
$660$	−132647.	−0.0118532
$661$	5.02560e6	0.447388	0.223694	−	0.974659i	$-0.428188\pi$
$661$	5.02560e6	0.447388	0.223694	+	0.974659i	$0.428188\pi$
$662$	1.15236e7	1.02198
$663$	53895.8	0.00476180
$664$	1.65474e7	1.45650
$665$	0	0
$666$	−1.18205e7	−1.03265
$667$	−2.66638e6	−0.232064
$668$	9.07878e6	0.787202
$669$	1.36150e6	0.117612
$670$	110292.	0.00949202
$671$	6.29233e6	0.539517
$672$	0	0
$673$	1.33555e7	1.13664	0.568320	−	0.822807i	$-0.307593\pi$
$673$	1.33555e7	1.13664	0.568320	+	0.822807i	$0.307593\pi$
$674$	2.45042e6	0.207774
$675$	−282364.	−0.0238534
$676$	7.04180e6	0.592676
$677$	−1.89889e6	−0.159231	−0.0796156	−	0.996826i	$-0.525369\pi$
$677$	−1.89889e6	−0.159231	−0.0796156	+	0.996826i	$0.525369\pi$
$678$	−172878.	−0.0144432
$679$	0	0
$680$	−2.01130e6	−0.166804
$681$	1.24600e6	0.102955
$682$	5.80020e6	0.477509
$683$	−8.04785e6	−0.660128	−0.330064	−	0.943959i	$-0.607070\pi$
$683$	−8.04785e6	−0.660128	−0.330064	+	0.943959i	$0.607070\pi$
$684$	−3.98612e6	−0.325769
$685$	−1.38208e6	−0.112540
$686$	0	0
$687$	1.09703e6	0.0886798
$688$	104600.	0.00842485
$689$	−971277.	−0.0779462
$690$	44627.4	0.00356845
$691$	1.84458e7	1.46961	0.734804	−	0.678279i	$-0.237274\pi$
$691$	1.84458e7	1.46961	0.734804	+	0.678279i	$0.237274\pi$
$692$	9.53408e6	0.756857
$693$	0	0
$694$	6.00562e6	0.473325
$695$	−6.61606e6	−0.519562
$696$	815065.	0.0637778
$697$	−5.28606e6	−0.412145
$698$	164372.	0.0127700
$699$	1.42558e6	0.110356
$700$	0	0
$701$	1.16054e7	0.891997	0.445998	−	0.895034i	$-0.352849\pi$
$701$	1.16054e7	0.891997	0.445998	+	0.895034i	$0.352849\pi$
$702$	−204489.	−0.0156613
$703$	1.16133e7	0.886270
$704$	5.73590e6	0.436184
$705$	241998.	0.0183374
$706$	1.10384e7	0.833476
$707$	0	0
$708$	−416636.	−0.0312373
$709$	−1.53671e7	−1.14809	−0.574044	−	0.818824i	$-0.694626\pi$
$709$	−1.53671e7	−1.14809	−0.574044	+	0.818824i	$0.694626\pi$
$710$	−2.24937e6	−0.167462
$711$	1.56974e7	1.16454
$712$	2.17463e7	1.60763
$713$	3.19633e6	0.235466
$714$	0	0
$715$	−931628.	−0.0681518
$716$	7.66052e6	0.558439
$717$	−1.43861e6	−0.104507
$718$	−4.15923e6	−0.301093
$719$	2.31355e7	1.66900	0.834501	−	0.551007i	$-0.185756\pi$
$719$	2.31355e7	1.66900	0.834501	+	0.551007i	$0.185756\pi$
$720$	−40041.2	−0.00287856
$721$	0	0
$722$	6.23309e6	0.445000
$723$	1.39401e6	0.0991794
$724$	6.04304e6	0.428459
$725$	3.02797e6	0.213947
$726$	255669.	0.0180027
$727$	1.10014e7	0.771990	0.385995	−	0.922501i	$-0.373858\pi$
$727$	1.10014e7	0.771990	0.385995	+	0.922501i	$0.373858\pi$
$728$	0	0
$729$	−1.40426e7	−0.978650
$730$	−348555.	−0.0242083
$731$	−7.04215e6	−0.487430
$732$	−406035.	−0.0280082
$733$	−1.95872e7	−1.34652	−0.673259	−	0.739407i	$-0.735106\pi$
$733$	−1.95872e7	−1.34652	−0.673259	+	0.739407i	$0.735106\pi$
$734$	−1.16847e7	−0.800532
$735$	0	0
$736$	3.19434e6	0.217364
$737$	−363218.	−0.0246319
$738$	1.00102e7	0.676551
$739$	−2.38000e7	−1.60312	−0.801561	−	0.597913i	$-0.795997\pi$
$739$	−2.38000e7	−1.60312	−0.801561	+	0.597913i	$0.795997\pi$
$740$	6.96254e6	0.467400
$741$	100272.	0.00670866
$742$	0	0
$743$	−2.25545e6	−0.149886	−0.0749429	−	0.997188i	$-0.523877\pi$
$743$	−2.25545e6	−0.149886	−0.0749429	+	0.997188i	$0.523877\pi$
$744$	−977059.	−0.0647126
$745$	285450.	0.0188425
$746$	−1.14665e7	−0.754370
$747$	−2.21785e7	−1.45422
$748$	2.53731e6	0.165813
$749$	0	0
$750$	−50679.3	−0.00328986
$751$	2.19573e7	1.42063	0.710313	−	0.703886i	$-0.248554\pi$
$751$	2.19573e7	1.42063	0.710313	+	0.703886i	$0.248554\pi$
$752$	68756.7	0.00443374
$753$	−203552.	−0.0130824
$754$	2.19287e6	0.140470
$755$	−4.47159e6	−0.285492
$756$	0	0
$757$	4.28556e6	0.271812	0.135906	−	0.990722i	$-0.456606\pi$
$757$	4.28556e6	0.271812	0.135906	+	0.990722i	$0.456606\pi$
$758$	−9.38050e6	−0.592998
$759$	−146968.	−0.00926017
$760$	−3.74200e6	−0.235001
$761$	2.84798e6	0.178269	0.0891344	−	0.996020i	$-0.471590\pi$
$761$	2.84798e6	0.178269	0.0891344	+	0.996020i	$0.471590\pi$
$762$	−275504.	−0.0171886
$763$	0	0
$764$	−1.04263e7	−0.646243
$765$	2.69575e6	0.166543
$766$	−1.50299e7	−0.925515
$767$	−2.92619e6	−0.179603
$768$	−972536.	−0.0594980
$769$	−2.00376e7	−1.22188	−0.610941	−	0.791676i	$-0.709209\pi$
$769$	−2.00376e7	−1.22188	−0.610941	+	0.791676i	$0.709209\pi$
$770$	0	0
$771$	−410567.	−0.0248742
$772$	4.57444e6	0.276245
$773$	8.53037e6	0.513475	0.256737	−	0.966481i	$-0.417352\pi$
$773$	8.53037e6	0.513475	0.256737	+	0.966481i	$0.417352\pi$
$774$	1.33357e7	0.800133
$775$	−3.62977e6	−0.217083
$776$	2.88158e7	1.71781
$777$	0	0
$778$	−399376.	−0.0236555
$779$	−9.83464e6	−0.580651
$780$	60116.6	0.00353800
$781$	7.40769e6	0.434566
$782$	−853647.	−0.0499185
$783$	−2.18877e6	−0.127584
$784$	0	0
$785$	591744.	0.0342736
$786$	531833.	0.0307057
$787$	−1.07271e6	−0.0617373	−0.0308686	−	0.999523i	$-0.509827\pi$
$787$	−1.07271e6	−0.0617373	−0.0308686	+	0.999523i	$0.509827\pi$
$788$	8.83579e6	0.506909
$789$	1.52584e6	0.0872601
$790$	5.64490e6	0.321802
$791$	0	0
$792$	−1.25432e7	−0.710551
$793$	−2.85174e6	−0.161037
$794$	3.61898e6	0.203720
$795$	174001.	0.00976415
$796$	−1.25685e6	−0.0703076
$797$	1.99822e7	1.11429	0.557143	−	0.830416i	$-0.311897\pi$
$797$	1.99822e7	1.11429	0.557143	+	0.830416i	$0.311897\pi$
$798$	0	0
$799$	−4.62900e6	−0.256520
$800$	−3.62752e6	−0.200394
$801$	−2.91466e7	−1.60511
$802$	3.99520e6	0.219332
$803$	1.14787e6	0.0628210
$804$	23437.9	0.00127873
$805$	0	0
$806$	−2.62870e6	−0.142529
$807$	−153646.	−0.00830497
$808$	3.23696e7	1.74425
$809$	1.42313e7	0.764495	0.382247	−	0.924060i	$-0.375150\pi$
$809$	1.42313e7	0.764495	0.382247	+	0.924060i	$0.375150\pi$
$810$	−5.08656e6	−0.272403
$811$	−1.58262e7	−0.844938	−0.422469	−	0.906377i	$-0.638836\pi$
$811$	−1.58262e7	−0.844938	−0.422469	+	0.906377i	$0.638836\pi$
$812$	0	0
$813$	−738038.	−0.0391609
$814$	1.39986e7	0.740500
$815$	1.36147e7	0.717985
$816$	−2743.27	−0.000144226 0
$817$	−1.31018e7	−0.686715
$818$	−2.19262e7	−1.14572
$819$	0	0
$820$	−5.89619e6	−0.306223
$821$	1.55237e6	0.0803781	0.0401890	−	0.999192i	$-0.487204\pi$
$821$	1.55237e6	0.0803781	0.0401890	+	0.999192i	$0.487204\pi$
$822$	179310.	0.00925601
$823$	−1.64384e7	−0.845979	−0.422990	−	0.906135i	$-0.639019\pi$
$823$	−1.64384e7	−0.845979	−0.422990	+	0.906135i	$0.639019\pi$
$824$	4.40871e6	0.226201
$825$	166898.	0.00853723
$826$	0	0
$827$	1.55536e7	0.790799	0.395399	−	0.918509i	$-0.370606\pi$
$827$	1.55536e7	0.790799	0.395399	+	0.918509i	$0.370606\pi$
$828$	−2.64783e6	−0.134219
$829$	−2.77513e7	−1.40248	−0.701241	−	0.712924i	$-0.747371\pi$
$829$	−2.77513e7	−1.40248	−0.701241	+	0.712924i	$0.747371\pi$
$830$	−7.97551e6	−0.401849
$831$	459372.	0.0230761
$832$	−2.59956e6	−0.130194
$833$	0	0
$834$	858361.	0.0427321
$835$	−1.14231e7	−0.566978
$836$	4.72062e6	0.233606
$837$	2.62379e6	0.129454
$838$	−2.41221e6	−0.118660
$839$	−4.43800e6	−0.217662	−0.108831	−	0.994060i	$-0.534711\pi$
$839$	−4.43800e6	−0.217662	−0.108831	+	0.994060i	$0.534711\pi$
$840$	0	0
$841$	2.96041e6	0.144332
$842$	1.63536e7	0.794938
$843$	−754753.	−0.0365794
$844$	−170606.	−0.00824400
$845$	−8.86010e6	−0.426871
$846$	8.76590e6	0.421086
$847$	0	0
$848$	49437.5	0.00236084
$849$	−1.71391e6	−0.0816056
$850$	969407.	0.0460213
$851$	7.71426e6	0.365149
$852$	−478008.	−0.0225598
$853$	−3.31474e7	−1.55983	−0.779915	−	0.625886i	$-0.784738\pi$
$853$	−3.31474e7	−1.55983	−0.779915	+	0.625886i	$0.784738\pi$
$854$	0	0
$855$	5.01540e6	0.234634
$856$	1.76587e7	0.823710
$857$	−2.80933e7	−1.30662	−0.653312	−	0.757089i	$-0.726621\pi$
$857$	−2.80933e7	−1.30662	−0.653312	+	0.757089i	$0.726621\pi$
$858$	120868.	0.00560524
$859$	3.09400e7	1.43066	0.715331	−	0.698786i	$-0.246276\pi$
$859$	3.09400e7	1.43066	0.715331	+	0.698786i	$0.246276\pi$
$860$	−7.85498e6	−0.362159
$861$	0	0
$862$	−4.67208e6	−0.214162
$863$	−2.38628e7	−1.09067	−0.545335	−	0.838218i	$-0.683598\pi$
$863$	−2.38628e7	−1.09067	−0.545335	+	0.838218i	$0.683598\pi$
$864$	2.62216e6	0.119502
$865$	−1.19959e7	−0.545122
$866$	−7.64542e6	−0.346423
$867$	−1.13756e6	−0.0513958
$868$	0	0
$869$	−1.85899e7	−0.835080
$870$	−392845.	−0.0175964
$871$	164613.	0.00735224
$872$	1.69948e6	0.0756874
$873$	−3.86217e7	−1.71513
$874$	−1.58820e6	−0.0703276
$875$	0	0
$876$	−74070.5	−0.00326126
$877$	3.23570e7	1.42059	0.710296	−	0.703903i	$-0.248561\pi$
$877$	3.23570e7	1.42059	0.710296	+	0.703903i	$0.248561\pi$
$878$	−69161.2	−0.00302780
$879$	591489.	0.0258211
$880$	47419.3	0.00206419
$881$	−1.24007e7	−0.538278	−0.269139	−	0.963101i	$-0.586739\pi$
$881$	−1.24007e7	−0.538278	−0.269139	+	0.963101i	$0.586739\pi$
$882$	0	0
$883$	2.90605e7	1.25430	0.627150	−	0.778899i	$-0.284221\pi$
$883$	2.90605e7	1.25430	0.627150	+	0.778899i	$0.284221\pi$
$884$	−1.14993e6	−0.0494926
$885$	524218.	0.0224985
$886$	−1.32181e7	−0.565697
$887$	−1.15504e7	−0.492933	−0.246466	−	0.969151i	$-0.579269\pi$
$887$	−1.15504e7	−0.492933	−0.246466	+	0.969151i	$0.579269\pi$
$888$	−2.35811e6	−0.100353
$889$	0	0
$890$	−1.04813e7	−0.443547
$891$	1.67512e7	0.706889
$892$	−2.90491e7	−1.22242
$893$	−8.61219e6	−0.361397
$894$	−37033.9	−0.00154973
$895$	−9.63858e6	−0.402212
$896$	0	0
$897$	66607.2	0.00276401
$898$	7.64660e6	0.316430
$899$	−2.81365e7	−1.16110
$900$	3.00690e6	0.123741
$901$	−3.32835e6	−0.136589
$902$	−1.18547e7	−0.485147
$903$	0	0
$904$	9.62899e6	0.391886
$905$	−7.60345e6	−0.308595
$906$	580139.	0.0234807
$907$	−2.41287e7	−0.973901	−0.486951	−	0.873430i	$-0.661891\pi$
$907$	−2.41287e7	−0.973901	−0.486951	+	0.873430i	$0.661891\pi$
$908$	−2.65847e7	−1.07008
$909$	−4.33848e7	−1.74152
$910$	0	0
$911$	2.25808e7	0.901452	0.450726	−	0.892662i	$-0.351165\pi$
$911$	2.25808e7	0.901452	0.450726	+	0.892662i	$0.351165\pi$
$912$	−5103.81	−0.000203192 0
$913$	2.62652e7	1.04281
$914$	−1.07122e7	−0.424145
$915$	510879.	0.0201728
$916$	−2.34063e7	−0.921709
$917$	0	0
$918$	−700739.	−0.0274441
$919$	2.95150e7	1.15280	0.576400	−	0.817168i	$-0.304457\pi$
$919$	2.95150e7	1.15280	0.576400	+	0.817168i	$0.304457\pi$
$920$	−2.48567e6	−0.0968221
$921$	1.90893e6	0.0741551
$922$	2.28742e7	0.886175
$923$	−3.35723e6	−0.129711
$924$	0	0
$925$	−8.76038e6	−0.336642
$926$	1.66109e7	0.636597
$927$	−5.90899e6	−0.225847
$928$	−2.81190e7	−1.07184
$929$	−1.08043e7	−0.410730	−0.205365	−	0.978686i	$-0.565838\pi$
$929$	−1.08043e7	−0.410730	−0.205365	+	0.978686i	$0.565838\pi$
$930$	470923.	0.0178543
$931$	0	0
$932$	−3.04163e7	−1.14701
$933$	2.82246e6	0.106151
$934$	2.94317e7	1.10395
$935$	−3.19248e6	−0.119426
$936$	5.68468e6	0.212088
$937$	1.64021e7	0.610310	0.305155	−	0.952303i	$-0.401292\pi$
$937$	1.64021e7	0.610310	0.305155	+	0.952303i	$0.401292\pi$
$938$	0	0
$939$	2.23310e6	0.0826502
$940$	−5.16330e6	−0.190593
$941$	−2.84644e7	−1.04792	−0.523959	−	0.851743i	$-0.675546\pi$
$941$	−2.84644e7	−1.04792	−0.523959	+	0.851743i	$0.675546\pi$
$942$	−76772.2	−0.00281888
$943$	−6.53279e6	−0.239232
$944$	148941.	0.00543983
$945$	0	0
$946$	−1.57930e7	−0.573767
$947$	2.49384e7	0.903635	0.451817	−	0.892110i	$-0.350776\pi$
$947$	2.49384e7	0.903635	0.451817	+	0.892110i	$0.350776\pi$
$948$	1.19958e6	0.0433519
$949$	−520225.	−0.0187510
$950$	1.80357e6	0.0648371
$951$	−1.31169e6	−0.0470306
$952$	0	0
$953$	−5.27090e7	−1.87998	−0.939989	−	0.341206i	$-0.889165\pi$
$953$	−5.27090e7	−1.87998	−0.939989	+	0.341206i	$0.889165\pi$
$954$	6.30286e6	0.224216
$955$	1.31185e7	0.465453
$956$	3.06943e7	1.08621
$957$	1.29373e6	0.0456628
$958$	7.92970e6	0.279153
$959$	0	0
$960$	465702.	0.0163091
$961$	5.09949e6	0.178122
$962$	−6.34430e6	−0.221027
$963$	−2.36679e7	−0.822421
$964$	−2.97429e7	−1.03084
$965$	−5.75563e6	−0.198964
$966$	0	0
$967$	1.40449e7	0.483005	0.241502	−	0.970400i	$-0.422360\pi$
$967$	1.40449e7	0.483005	0.241502	+	0.970400i	$0.422360\pi$
$968$	−1.42404e7	−0.488464
$969$	343611.	0.0117559
$970$	−1.38886e7	−0.473947
$971$	4.71595e6	0.160517	0.0802585	−	0.996774i	$-0.474425\pi$
$971$	4.71595e6	0.160517	0.0802585	+	0.996774i	$0.474425\pi$
$972$	−3.26226e6	−0.110752
$973$	0	0
$974$	2.64858e7	0.894572
$975$	−75639.6	−0.00254823
$976$	145152.	0.00487751
$977$	1.95987e7	0.656887	0.328444	−	0.944524i	$-0.393476\pi$
$977$	1.95987e7	0.656887	0.328444	+	0.944524i	$0.393476\pi$
$978$	−1.76636e6	−0.0590517
$979$	3.45172e7	1.15101
$980$	0	0
$981$	−2.27780e6	−0.0755690
$982$	4.55753e6	0.150817
$983$	3.69458e7	1.21950	0.609750	−	0.792594i	$-0.291270\pi$
$983$	3.69458e7	1.21950	0.609750	+	0.792594i	$0.291270\pi$
$984$	1.99696e6	0.0657477
$985$	−1.11173e7	−0.365098
$986$	7.51445e6	0.246153
$987$	0	0
$988$	−2.13942e6	−0.0697276
$989$	−8.70306e6	−0.282931
$990$	6.04557e6	0.196042
$991$	−1.05594e7	−0.341550	−0.170775	−	0.985310i	$-0.554627\pi$
$991$	−1.05594e7	−0.341550	−0.170775	+	0.985310i	$0.554627\pi$
$992$	3.37077e7	1.08755
$993$	−3.08118e6	−0.0991618
$994$	0	0
$995$	1.58139e6	0.0506387
$996$	−1.69485e6	−0.0541357
$997$	−1.47695e7	−0.470574	−0.235287	−	0.971926i	$-0.575603\pi$
$997$	−1.47695e7	−0.470574	−0.235287	+	0.971926i	$0.575603\pi$
$998$	−2.59527e7	−0.824814
$999$	6.33246e6	0.200752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.m.1.4	yes	10
7.6	odd	2		245.6.a.l.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.4	✓	10	7.6	odd	2
245.6.a.m.1.4	yes	10	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)

\(f(q)\)	\(=\)	\(q-3.48290 q^{2} +0.931256 q^{3} -19.8694 q^{4} +25.0000 q^{5} -3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} +O(q^{10})\)	\(q-3.48290 q^{2} +0.931256 q^{3} -19.8694 q^{4} +25.0000 q^{5} -3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} -87.0725 q^{10} +286.749 q^{11} -18.5035 q^{12} -129.957 q^{13} +23.2814 q^{15} +6.61475 q^{16} -445.334 q^{17} +843.324 q^{18} -828.537 q^{19} -496.735 q^{20} -998.719 q^{22} -550.366 q^{23} +168.237 q^{24} +625.000 q^{25} +452.628 q^{26} -451.783 q^{27} +4844.75 q^{29} -81.0868 q^{30} -5807.64 q^{31} -5804.03 q^{32} +267.037 q^{33} +1551.05 q^{34} +4811.04 q^{36} -14016.6 q^{37} +2885.71 q^{38} -121.023 q^{39} +4516.40 q^{40} +11869.9 q^{41} +15813.2 q^{43} -5697.54 q^{44} -6053.32 q^{45} +1916.87 q^{46} +10394.5 q^{47} +6.16002 q^{48} -2176.81 q^{50} -414.720 q^{51} +2582.17 q^{52} +7473.83 q^{53} +1573.51 q^{54} +7168.73 q^{55} -771.580 q^{57} -16873.8 q^{58} +22516.6 q^{59} -462.588 q^{60} +21943.7 q^{61} +20227.4 q^{62} +20003.2 q^{64} -3248.93 q^{65} -930.064 q^{66} -1266.67 q^{67} +8848.52 q^{68} -512.532 q^{69} +25833.3 q^{71} -43742.7 q^{72} +4003.05 q^{73} +48818.4 q^{74} +582.035 q^{75} +16462.5 q^{76} +421.512 q^{78} -64829.8 q^{79} +165.369 q^{80} +58417.5 q^{81} -41341.6 q^{82} +91596.2 q^{83} -11133.3 q^{85} -55075.8 q^{86} +4511.70 q^{87} +51803.0 q^{88} +120374. q^{89} +21083.1 q^{90} +10935.5 q^{92} -5408.40 q^{93} -36202.9 q^{94} -20713.4 q^{95} -5405.04 q^{96} +159506. q^{97} -69431.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19} + 4550 q^{20} + 3948 q^{22} + 3708 q^{23} + 2092 q^{24} + 6250 q^{25} + 6576 q^{26} + 11818 q^{27} - 8866 q^{29} + 3600 q^{30} + 13292 q^{31} + 2590 q^{32} + 9854 q^{33} + 44468 q^{34} - 10690 q^{36} + 16124 q^{37} + 2180 q^{38} - 24982 q^{39} + 6750 q^{40} + 34836 q^{41} - 28604 q^{43} - 31120 q^{44} + 17500 q^{45} - 39732 q^{46} + 18106 q^{47} + 101788 q^{48} + 6250 q^{50} + 31602 q^{51} - 22480 q^{52} + 36440 q^{53} + 80836 q^{54} + 19850 q^{55} + 126988 q^{57} - 100356 q^{58} + 18644 q^{59} + 64000 q^{60} + 68120 q^{61} + 181052 q^{62} - 59358 q^{64} + 11850 q^{65} + 157780 q^{66} + 92328 q^{67} + 288540 q^{68} + 170888 q^{69} + 5044 q^{71} - 61654 q^{72} + 170160 q^{73} - 216584 q^{74} + 36250 q^{75} + 505180 q^{76} - 158008 q^{78} + 26442 q^{79} + 59850 q^{80} - 56314 q^{81} + 353948 q^{82} + 353360 q^{83} + 20050 q^{85} - 52940 q^{86} - 3190 q^{87} - 114916 q^{88} + 90704 q^{89} + 92550 q^{90} + 183520 q^{92} + 188560 q^{93} - 121388 q^{94} + 182300 q^{95} + 442220 q^{96} + 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * q^99

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