LMFDB - Embedded newform 245.6.a.l.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:	$1$
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	$-0.509509\pi$
$3$	−0.931256	−0.0597401	−0.0298701	+	0.999554i	$0.509509\pi$
$4$	−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	$-0.465991\pi$
$13$	129.957	0.213276	0.106638	+	0.994298i	$0.465991\pi$
$14$	0	0
$15$	23.2814	0.0267166
$16$	6.61475	0.00645971
$17$	445.334	0.373734	0.186867	−	0.982385i	$-0.440167\pi$
$17$	445.334	0.373734	0.186867	+	0.982385i	$0.440167\pi$
$18$	843.324	0.613498
$19$	828.537	0.526536	0.263268	−	0.964723i	$-0.415200\pi$
$19$	828.537	0.526536	0.263268	+	0.964723i	$0.415200\pi$
$20$	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	$-0.317400\pi$
$31$	5807.64	1.08541	0.542707	+	0.839922i	$0.317400\pi$
$32$	−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	$-0.685902\pi$
$41$	−11869.9	−1.10278	−0.551388	+	0.834249i	$0.685902\pi$
$42$	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	$-0.611506\pi$
$47$	−10394.5	−0.686368	−0.343184	+	0.939268i	$0.611506\pi$
$48$	−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	$-0.638341\pi$
$59$	−22516.6	−0.842117	−0.421058	+	0.907034i	$0.638341\pi$
$60$	−462.588	−0.0165888
$61$	−21943.7	−0.755065	−0.377533	−	0.925996i	$-0.623227\pi$
$61$	−21943.7	−0.755065	−0.377533	+	0.925996i	$0.623227\pi$
$62$	−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	$-0.513997\pi$
$73$	−4003.05	−0.0879192	−0.0439596	+	0.999033i	$0.513997\pi$
$74$	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	$-0.760347\pi$
$83$	−91596.2	−1.45943	−0.729714	+	0.683753i	$0.760347\pi$
$84$	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	$-0.798066\pi$
$89$	−120374.	−1.61086	−0.805432	+	0.592689i	$0.798066\pi$
$90$	−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	$-0.829933\pi$
$97$	−159506.	−1.72127	−0.860635	+	0.509222i	$0.829933\pi$
$98$	0	0
$99$	−69431.4	−0.711980
$100$	−12418.4	−0.124184
$101$	−179178.	−1.74776	−0.873878	−	0.486145i	$-0.838403\pi$
$101$	−179178.	−1.74776	−0.873878	+	0.486145i	$0.838403\pi$
$102$	1444.43	0.0137466
$103$	−24403.9	−0.226656	−0.113328	−	0.993558i	$-0.536151\pi$
$103$	−24403.9	−0.226656	−0.113328	+	0.993558i	$0.536151\pi$
$104$	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	$-0.362940\pi$
$131$	163970.	0.834809	0.417404	+	0.908721i	$0.362940\pi$
$132$	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	$-0.302705\pi$
$139$	264642.	1.16178	0.580888	+	0.813983i	$0.302705\pi$
$140$	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	$-0.512200\pi$
$157$	−23669.8	−0.0766381	−0.0383190	+	0.999266i	$0.512200\pi$
$158$	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	$-0.281453\pi$
$167$	456922.	1.26780	0.633901	+	0.773414i	$0.281453\pi$
$168$	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	$-0.291384\pi$
$173$	479837.	1.21893	0.609465	+	0.792813i	$0.291384\pi$
$174$	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	$-0.387872\pi$
$181$	304138.	0.690040	0.345020	+	0.938595i	$0.387872\pi$
$182$	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	$-0.518031\pi$
$199$	−63255.8	−0.113232	−0.0566158	+	0.998396i	$0.518031\pi$
$200$	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	$-0.943635\pi$
$223$	−1.46200e6	−1.96873	−0.984363	+	0.176152i	$0.943635\pi$
$224$	0	0
$225$	−151333.	−0.199286
$226$	−185639.	−0.241768
$227$	−1.33797e6	−1.72339	−0.861693	−	0.507430i	$-0.830596\pi$
$227$	−1.33797e6	−1.72339	−0.861693	+	0.507430i	$0.830596\pi$
$228$	15330.8	0.0195312
$229$	−1.17801e6	−1.48443	−0.742213	−	0.670164i	$-0.766224\pi$
$229$	−1.17801e6	−1.48443	−0.742213	+	0.670164i	$0.766224\pi$
$230$	−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	$-0.811711\pi$
$241$	−1.49692e6	−1.66018	−0.830090	+	0.557629i	$0.811711\pi$
$242$	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	$-0.465077\pi$
$251$	218578.	0.218989	0.109494	+	0.993987i	$0.465077\pi$
$252$	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	$-0.433244\pi$
$257$	440875.	0.416373	0.208186	+	0.978089i	$0.433244\pi$
$258$	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	$-0.477857\pi$
$269$	164988.	0.139018	0.0695091	+	0.997581i	$0.477857\pi$
$270$	39337.9	0.0328399
$271$	792518.	0.655520	0.327760	−	0.944761i	$-0.393706\pi$
$271$	792518.	0.655520	0.327760	+	0.944761i	$0.393706\pi$
$272$	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	$-0.260673\pi$
$283$	1.84043e6	1.36601	0.683005	+	0.730414i	$0.260673\pi$
$284$	−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	$-0.569338\pi$
$293$	−635152.	−0.432224	−0.216112	+	0.976369i	$0.569338\pi$
$294$	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	$-0.713130\pi$
$307$	−2.04984e6	−1.24130	−0.620648	+	0.784090i	$0.713130\pi$
$308$	0	0
$309$	22726.3	0.0135404
$310$	505685.	0.298866
$311$	−3.03081e6	−1.77688	−0.888439	−	0.458994i	$-0.848210\pi$
$311$	−3.03081e6	−1.77688	−0.888439	+	0.458994i	$0.848210\pi$
$312$	−21863.6	−0.0127156
$313$	−2.39794e6	−1.38350	−0.691748	−	0.722139i	$-0.743159\pi$
$313$	−2.39794e6	−1.38350	−0.691748	+	0.722139i	$0.743159\pi$
$314$	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	$-0.496699\pi$
$349$	47194.2	0.0207408	0.0103704	+	0.999946i	$0.496699\pi$
$350$	0	0
$351$	58712.4	0.0254368
$352$	−1.66430e6	−0.715938
$353$	3.16931e6	1.35372	0.676858	−	0.736114i	$-0.263341\pi$
$353$	3.16931e6	1.35372	0.676858	+	0.736114i	$0.263341\pi$
$354$	−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	$-0.725275\pi$
$367$	−3.35489e6	−1.30021	−0.650104	+	0.759845i	$0.725275\pi$
$368$	−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	$-0.770718\pi$
$383$	−4.31533e6	−1.50320	−0.751601	+	0.659618i	$0.770718\pi$
$384$	−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	$-0.447096\pi$
$397$	1.03907e6	0.330879	0.165439	+	0.986220i	$0.447096\pi$
$398$	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	$-0.880568\pi$
$409$	−6.29539e6	−1.86086	−0.930431	+	0.366466i	$0.880568\pi$
$410$	−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	$-0.530721\pi$
$419$	−692588.	−0.192726	−0.0963629	+	0.995346i	$0.530721\pi$
$420$	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	$-0.590774\pi$
$433$	−2.19513e6	−0.562653	−0.281326	+	0.959612i	$0.590774\pi$
$434$	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	$-0.500783\pi$
$439$	−19857.4	−0.00491768	−0.00245884	+	0.999997i	$0.500783\pi$
$440$	−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	$-0.244301\pi$
$461$	6.56759e6	1.43931	0.719654	+	0.694333i	$0.244301\pi$
$462$	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	$-0.146099\pi$
$467$	8.45034e6	1.79301	0.896503	+	0.443037i	$0.146099\pi$
$468$	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	$-0.427207\pi$
$479$	2.27675e6	0.453395	0.226698	+	0.973965i	$0.427207\pi$
$480$	−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	$-0.289929\pi$
$503$	6.95776e6	1.22617	0.613083	+	0.790018i	$0.289929\pi$
$504$	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	$-0.315974\pi$
$509$	6.38828e6	1.09292	0.546462	+	0.837484i	$0.315974\pi$
$510$	−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	$-0.605757\pi$
$521$	−4.04171e6	−0.652335	−0.326168	+	0.945312i	$0.605757\pi$
$522$	4.08569e6	0.656280
$523$	−9.56520e6	−1.52911	−0.764557	−	0.644556i	$-0.777042\pi$
$523$	−9.56520e6	−1.52911	−0.764557	+	0.644556i	$0.777042\pi$
$524$	−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	$-0.301481\pi$
$563$	8.78466e6	1.16803	0.584015	+	0.811743i	$0.301481\pi$
$564$	−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	$-0.280595\pi$
$577$	1.01722e7	1.27197	0.635983	+	0.771703i	$0.280595\pi$
$578$	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	$-0.469413\pi$
$587$	1.60193e6	0.191888	0.0959441	+	0.995387i	$0.469413\pi$
$588$	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	$-0.424129\pi$
$593$	4.04363e6	0.472209	0.236105	+	0.971728i	$0.424129\pi$
$594$	−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	$-0.446932\pi$
$601$	2.93892e6	0.331896	0.165948	+	0.986134i	$0.446932\pi$
$602$	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	$-0.747821\pi$
$607$	−1.27495e7	−1.40450	−0.702249	+	0.711931i	$0.747821\pi$
$608$	−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	$-0.487370\pi$
$619$	756319.	0.0793375	0.0396688	+	0.999213i	$0.487370\pi$
$620$	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	$-0.674799\pi$
$643$	−1.09445e7	−1.04392	−0.521959	+	0.852970i	$0.674799\pi$
$644$	0	0
$645$	368154.	0.0348442
$646$	−1.28510e6	−0.121159
$647$	−9.00960e6	−0.846145	−0.423072	−	0.906096i	$-0.639048\pi$
$647$	−9.00960e6	−0.846145	−0.423072	+	0.906096i	$0.639048\pi$
$648$	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	$-0.571812\pi$
$661$	−5.02560e6	−0.447388	−0.223694	+	0.974659i	$0.571812\pi$
$662$	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	$-0.474631\pi$
$677$	1.89889e6	0.159231	0.0796156	+	0.996826i	$0.474631\pi$
$678$	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	$-0.762726\pi$
$691$	−1.84458e7	−1.46961	−0.734804	+	0.678279i	$0.762726\pi$
$692$	−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	$-0.814244\pi$
$719$	−2.31355e7	−1.66900	−0.834501	+	0.551007i	$0.814244\pi$
$720$	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	$-0.626142\pi$
$727$	−1.10014e7	−0.771990	−0.385995	+	0.922501i	$0.626142\pi$
$728$	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	$-0.264894\pi$
$733$	1.95872e7	1.34652	0.673259	+	0.739407i	$0.264894\pi$
$734$	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	$-0.528410\pi$
$761$	−2.84798e6	−0.178269	−0.0891344	+	0.996020i	$0.528410\pi$
$762$	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	$-0.290791\pi$
$769$	2.00376e7	1.22188	0.610941	+	0.791676i	$0.290791\pi$
$770$	0	0
$771$	−410567.	−0.0248742
$772$	4.57444e6	0.276245
$773$	−8.53037e6	−0.513475	−0.256737	−	0.966481i	$-0.582648\pi$
$773$	−8.53037e6	−0.513475	−0.256737	+	0.966481i	$0.582648\pi$
$774$	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	$-0.490173\pi$
$787$	1.07271e6	0.0617373	0.0308686	+	0.999523i	$0.490173\pi$
$788$	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	$-0.688103\pi$
$797$	−1.99822e7	−1.11429	−0.557143	+	0.830416i	$0.688103\pi$
$798$	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	$-0.361164\pi$
$811$	1.58262e7	0.844938	0.422469	+	0.906377i	$0.361164\pi$
$812$	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	$-0.252629\pi$
$829$	2.77513e7	1.40248	0.701241	+	0.712924i	$0.252629\pi$
$830$	−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	$-0.465289\pi$
$839$	4.43800e6	0.217662	0.108831	+	0.994060i	$0.465289\pi$
$840$	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	$-0.215262\pi$
$853$	3.31474e7	1.55983	0.779915	+	0.625886i	$0.215262\pi$
$854$	0	0
$855$	5.01540e6	0.234634
$856$	1.76587e7	0.823710
$857$	2.80933e7	1.30662	0.653312	−	0.757089i	$-0.273379\pi$
$857$	2.80933e7	1.30662	0.653312	+	0.757089i	$0.273379\pi$
$858$	120868.	0.00560524
$859$	−3.09400e7	−1.43066	−0.715331	−	0.698786i	$-0.753724\pi$
$859$	−3.09400e7	−1.43066	−0.715331	+	0.698786i	$0.753724\pi$
$860$	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	$-0.413261\pi$
$881$	1.24007e7	0.538278	0.269139	+	0.963101i	$0.413261\pi$
$882$	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	$-0.420731\pi$
$887$	1.15504e7	0.492933	0.246466	+	0.969151i	$0.420731\pi$
$888$	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	$-0.434162\pi$
$929$	1.08043e7	0.410730	0.205365	+	0.978686i	$0.434162\pi$
$930$	−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	$-0.598708\pi$
$937$	−1.64021e7	−0.610310	−0.305155	+	0.952303i	$0.598708\pi$
$938$	0	0
$939$	2.23310e6	0.0826502
$940$	−5.16330e6	−0.190593
$941$	2.84644e7	1.04792	0.523959	−	0.851743i	$-0.324454\pi$
$941$	2.84644e7	1.04792	0.523959	+	0.851743i	$0.324454\pi$
$942$	−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	$-0.525575\pi$
$971$	−4.71595e6	−0.160517	−0.0802585	+	0.996774i	$0.525575\pi$
$972$	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	$-0.708730\pi$
$983$	−3.69458e7	−1.21950	−0.609750	+	0.792594i	$0.708730\pi$
$984$	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	$-0.424397\pi$
$997$	1.47695e7	0.470574	0.235287	+	0.971926i	$0.424397\pi$
$998$	−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.l.1.4	✓	10
7.6	odd	2		245.6.a.m.1.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.4	✓	10	1.1	even	1	trivial
245.6.a.m.1.4	yes	10	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)

\(f(q)\)	\(=\)	\(q-3.48290 q^{2} -0.931256 q^{3} -19.8694 q^{4} -25.0000 q^{5} +3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} +O(q^{10})\)	\(q-3.48290 q^{2} -0.931256 q^{3} -19.8694 q^{4} -25.0000 q^{5} +3.24347 q^{6} +180.656 q^{8} -242.133 q^{9} +87.0725 q^{10} +286.749 q^{11} +18.5035 q^{12} +129.957 q^{13} +23.2814 q^{15} +6.61475 q^{16} +445.334 q^{17} +843.324 q^{18} +828.537 q^{19} +496.735 q^{20} -998.719 q^{22} -550.366 q^{23} -168.237 q^{24} +625.000 q^{25} -452.628 q^{26} +451.783 q^{27} +4844.75 q^{29} -81.0868 q^{30} +5807.64 q^{31} -5804.03 q^{32} -267.037 q^{33} -1551.05 q^{34} +4811.04 q^{36} -14016.6 q^{37} -2885.71 q^{38} -121.023 q^{39} -4516.40 q^{40} -11869.9 q^{41} +15813.2 q^{43} -5697.54 q^{44} +6053.32 q^{45} +1916.87 q^{46} -10394.5 q^{47} -6.16002 q^{48} -2176.81 q^{50} -414.720 q^{51} -2582.17 q^{52} +7473.83 q^{53} -1573.51 q^{54} -7168.73 q^{55} -771.580 q^{57} -16873.8 q^{58} -22516.6 q^{59} -462.588 q^{60} -21943.7 q^{61} -20227.4 q^{62} +20003.2 q^{64} -3248.93 q^{65} +930.064 q^{66} -1266.67 q^{67} -8848.52 q^{68} +512.532 q^{69} +25833.3 q^{71} -43742.7 q^{72} -4003.05 q^{73} +48818.4 q^{74} -582.035 q^{75} -16462.5 q^{76} +421.512 q^{78} -64829.8 q^{79} -165.369 q^{80} +58417.5 q^{81} +41341.6 q^{82} -91596.2 q^{83} -11133.3 q^{85} -55075.8 q^{86} -4511.70 q^{87} +51803.0 q^{88} -120374. q^{89} -21083.1 q^{90} +10935.5 q^{92} -5408.40 q^{93} +36202.9 q^{94} -20713.4 q^{95} +5405.04 q^{96} -159506. q^{97} -69431.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 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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