LMFDB - Embedded newform 49.6.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.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:	$7.85880717084$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{37}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 9 $ x^2 - x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.54138$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.08276 q^{2} +2.08276 q^{3} -6.16553 q^{4} +41.8276 q^{5} -10.5862 q^{6} +193.986 q^{8} -238.662 q^{9} +O(q^{10})$	\(q-5.08276 q^{2} +2.08276 q^{3} -6.16553 q^{4} +41.8276 q^{5} -10.5862 q^{6} +193.986 q^{8} -238.662 q^{9} -212.600 q^{10} +72.0965 q^{11} -12.8413 q^{12} -632.317 q^{13} +87.1170 q^{15} -788.689 q^{16} -1975.92 q^{17} +1213.06 q^{18} -1864.93 q^{19} -257.889 q^{20} -366.449 q^{22} +413.711 q^{23} +404.027 q^{24} -1375.45 q^{25} +3213.92 q^{26} -1003.19 q^{27} +731.934 q^{29} -442.795 q^{30} +6123.18 q^{31} -2198.84 q^{32} +150.160 q^{33} +10043.2 q^{34} +1471.48 q^{36} +10350.4 q^{37} +9478.97 q^{38} -1316.97 q^{39} +8113.99 q^{40} -3529.84 q^{41} -14515.2 q^{43} -444.513 q^{44} -9982.67 q^{45} -2102.79 q^{46} -21423.3 q^{47} -1642.65 q^{48} +6991.08 q^{50} -4115.38 q^{51} +3898.57 q^{52} +12579.5 q^{53} +5098.97 q^{54} +3015.62 q^{55} -3884.20 q^{57} -3720.25 q^{58} -36133.9 q^{59} -537.122 q^{60} +4024.80 q^{61} -31122.6 q^{62} +36414.2 q^{64} -26448.3 q^{65} -763.227 q^{66} +15565.9 q^{67} +12182.6 q^{68} +861.661 q^{69} +12180.8 q^{71} -46297.2 q^{72} +19589.1 q^{73} -52608.5 q^{74} -2864.74 q^{75} +11498.2 q^{76} +6693.83 q^{78} +36089.8 q^{79} -32989.0 q^{80} +55905.5 q^{81} +17941.3 q^{82} -24572.6 q^{83} -82648.2 q^{85} +73777.5 q^{86} +1524.44 q^{87} +13985.7 q^{88} -70243.3 q^{89} +50739.5 q^{90} -2550.74 q^{92} +12753.1 q^{93} +108890. q^{94} -78005.4 q^{95} -4579.66 q^{96} +105758. q^{97} -17206.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 8 q^{3} + 12 q^{4} - 38 q^{5} - 82 q^{6} + 96 q^{8} - 380 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 8 * q^3 + 12 * q^4 - 38 * q^5 - 82 * q^6 + 96 * q^8 - 380 * q^9	\( 2 q + 2 q^{2} - 8 q^{3} + 12 q^{4} - 38 q^{5} - 82 q^{6} + 96 q^{8} - 380 q^{9} - 778 q^{10} + 424 q^{11} - 196 q^{12} - 924 q^{13} + 892 q^{15} - 2064 q^{16} - 2346 q^{17} + 212 q^{18} - 360 q^{19} - 1708 q^{20} + 2126 q^{22} - 12 q^{23} + 1392 q^{24} + 1872 q^{25} + 1148 q^{26} + 2872 q^{27} - 7052 q^{29} + 5258 q^{30} + 3548 q^{31} - 8096 q^{32} - 3398 q^{33} + 7422 q^{34} - 1096 q^{36} + 11090 q^{37} + 20138 q^{38} + 1624 q^{39} + 15936 q^{40} + 3500 q^{41} - 12680 q^{43} + 5948 q^{44} + 1300 q^{45} - 5118 q^{46} - 22956 q^{47} + 11216 q^{48} + 29992 q^{50} - 384 q^{51} - 1400 q^{52} + 3042 q^{53} + 32546 q^{54} - 25076 q^{55} - 19058 q^{57} - 58852 q^{58} - 65808 q^{59} + 14084 q^{60} - 42486 q^{61} - 49362 q^{62} + 35456 q^{64} - 3164 q^{65} - 25894 q^{66} + 42312 q^{67} + 5460 q^{68} + 5154 q^{69} - 2208 q^{71} - 32448 q^{72} - 50506 q^{73} - 47370 q^{74} - 35608 q^{75} + 38836 q^{76} + 27524 q^{78} + 9004 q^{79} + 68816 q^{80} + 51178 q^{81} + 67732 q^{82} - 104328 q^{83} - 53106 q^{85} + 86776 q^{86} + 80008 q^{87} - 20496 q^{88} - 26666 q^{89} + 130652 q^{90} - 10284 q^{92} + 38718 q^{93} + 98034 q^{94} - 198140 q^{95} + 54880 q^{96} + 209132 q^{97} - 66944 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 8 * q^3 + 12 * q^4 - 38 * q^5 - 82 * q^6 + 96 * q^8 - 380 * q^9 - 778 * q^10 + 424 * q^11 - 196 * q^12 - 924 * q^13 + 892 * q^15 - 2064 * q^16 - 2346 * q^17 + 212 * q^18 - 360 * q^19 - 1708 * q^20 + 2126 * q^22 - 12 * q^23 + 1392 * q^24 + 1872 * q^25 + 1148 * q^26 + 2872 * q^27 - 7052 * q^29 + 5258 * q^30 + 3548 * q^31 - 8096 * q^32 - 3398 * q^33 + 7422 * q^34 - 1096 * q^36 + 11090 * q^37 + 20138 * q^38 + 1624 * q^39 + 15936 * q^40 + 3500 * q^41 - 12680 * q^43 + 5948 * q^44 + 1300 * q^45 - 5118 * q^46 - 22956 * q^47 + 11216 * q^48 + 29992 * q^50 - 384 * q^51 - 1400 * q^52 + 3042 * q^53 + 32546 * q^54 - 25076 * q^55 - 19058 * q^57 - 58852 * q^58 - 65808 * q^59 + 14084 * q^60 - 42486 * q^61 - 49362 * q^62 + 35456 * q^64 - 3164 * q^65 - 25894 * q^66 + 42312 * q^67 + 5460 * q^68 + 5154 * q^69 - 2208 * q^71 - 32448 * q^72 - 50506 * q^73 - 47370 * q^74 - 35608 * q^75 + 38836 * q^76 + 27524 * q^78 + 9004 * q^79 + 68816 * q^80 + 51178 * q^81 + 67732 * q^82 - 104328 * q^83 - 53106 * q^85 + 86776 * q^86 + 80008 * q^87 - 20496 * q^88 - 26666 * q^89 + 130652 * q^90 - 10284 * q^92 + 38718 * q^93 + 98034 * q^94 - 198140 * q^95 + 54880 * q^96 + 209132 * q^97 - 66944 * 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 $

$2$	−5.08276	−0.898514	−0.449257	−	0.893403i	$-0.648311\pi$
$2$	−5.08276	−0.898514	−0.449257	+	0.893403i	$0.648311\pi$
$3$	2.08276	0.133609	0.0668046	−	0.997766i	$-0.478720\pi$
$3$	2.08276	0.133609	0.0668046	+	0.997766i	$0.478720\pi$
$4$	−6.16553	−0.192673
$5$	41.8276	0.748235	0.374118	−	0.927381i	$-0.377946\pi$
$5$	41.8276	0.748235	0.374118	+	0.927381i	$0.377946\pi$
$6$	−10.5862	−0.120050
$7$	0	0
$7$	0	0
$8$	193.986	1.07163
$9$	−238.662	−0.982149
$10$	−212.600	−0.672300
$11$	72.0965	0.179652	0.0898260	−	0.995957i	$-0.471369\pi$
$11$	72.0965	0.179652	0.0898260	+	0.995957i	$0.471369\pi$
$12$	−12.8413	−0.0257429
$13$	−632.317	−1.03771	−0.518856	−	0.854862i	$-0.673642\pi$
$13$	−632.317	−1.03771	−0.518856	+	0.854862i	$0.673642\pi$
$14$	0	0
$15$	87.1170	0.0999712
$16$	−788.689	−0.770205
$17$	−1975.92	−1.65824	−0.829121	−	0.559069i	$-0.811159\pi$
$17$	−1975.92	−1.65824	−0.829121	+	0.559069i	$0.811159\pi$
$18$	1213.06	0.882474
$19$	−1864.93	−1.18516	−0.592581	−	0.805511i	$-0.701891\pi$
$19$	−1864.93	−1.18516	−0.592581	+	0.805511i	$0.701891\pi$
$20$	−257.889	−0.144164
$21$	0	0
$22$	−366.449	−0.161420
$23$	413.711	0.163071	0.0815356	−	0.996670i	$-0.474018\pi$
$23$	413.711	0.163071	0.0815356	+	0.996670i	$0.474018\pi$
$24$	404.027	0.143180
$25$	−1375.45	−0.440144
$26$	3213.92	0.932398
$27$	−1003.19	−0.264833
$28$	0	0
$29$	731.934	0.161613	0.0808066	−	0.996730i	$-0.474250\pi$
$29$	731.934	0.161613	0.0808066	+	0.996730i	$0.474250\pi$
$30$	−442.795	−0.0898255
$31$	6123.18	1.14439	0.572193	−	0.820119i	$-0.306093\pi$
$31$	6123.18	1.14439	0.572193	+	0.820119i	$0.306093\pi$
$32$	−2198.84	−0.379593
$33$	150.160	0.0240032
$34$	10043.2	1.48995
$35$	0	0
$36$	1471.48	0.189233
$37$	10350.4	1.24295	0.621473	−	0.783436i	$-0.286535\pi$
$37$	10350.4	1.24295	0.621473	+	0.783436i	$0.286535\pi$
$38$	9478.97	1.06488
$39$	−1316.97	−0.138648
$40$	8113.99	0.801834
$41$	−3529.84	−0.327941	−0.163970	−	0.986465i	$-0.552430\pi$
$41$	−3529.84	−0.327941	−0.163970	+	0.986465i	$0.552430\pi$
$42$	0	0
$43$	−14515.2	−1.19716	−0.598581	−	0.801062i	$-0.704269\pi$
$43$	−14515.2	−1.19716	−0.598581	+	0.801062i	$0.704269\pi$
$44$	−444.513	−0.0346140
$45$	−9982.67	−0.734878
$46$	−2102.79	−0.146522
$47$	−21423.3	−1.41463	−0.707314	−	0.706900i	$-0.750093\pi$
$47$	−21423.3	−1.41463	−0.707314	+	0.706900i	$0.750093\pi$
$48$	−1642.65	−0.102906
$49$	0	0
$50$	6991.08	0.395475
$51$	−4115.38	−0.221557
$52$	3898.57	0.199939
$53$	12579.5	0.615138	0.307569	−	0.951526i	$-0.400485\pi$
$53$	12579.5	0.615138	0.307569	+	0.951526i	$0.400485\pi$
$54$	5098.97	0.237957
$55$	3015.62	0.134422
$56$	0	0
$57$	−3884.20	−0.158349
$58$	−3720.25	−0.145212
$59$	−36133.9	−1.35140	−0.675702	−	0.737175i	$-0.736159\pi$
$59$	−36133.9	−1.35140	−0.675702	+	0.737175i	$0.736159\pi$
$60$	−537.122	−0.0192617
$61$	4024.80	0.138490	0.0692451	−	0.997600i	$-0.477941\pi$
$61$	4024.80	0.138490	0.0692451	+	0.997600i	$0.477941\pi$
$62$	−31122.6	−1.02825
$63$	0	0
$64$	36414.2	1.11127
$65$	−26448.3	−0.776453
$66$	−763.227	−0.0215672
$67$	15565.9	0.423632	0.211816	−	0.977310i	$-0.432062\pi$
$67$	15565.9	0.423632	0.211816	+	0.977310i	$0.432062\pi$
$68$	12182.6	0.319498
$69$	861.661	0.0217878
$70$	0	0
$71$	12180.8	0.286766	0.143383	−	0.989667i	$-0.454202\pi$
$71$	12180.8	0.286766	0.143383	+	0.989667i	$0.454202\pi$
$72$	−46297.2	−1.05250
$73$	19589.1	0.430237	0.215119	−	0.976588i	$-0.430986\pi$
$73$	19589.1	0.430237	0.215119	+	0.976588i	$0.430986\pi$
$74$	−52608.5	−1.11680
$75$	−2864.74	−0.0588073
$76$	11498.2	0.228348
$77$	0	0
$78$	6693.83	0.124577
$79$	36089.8	0.650604	0.325302	−	0.945610i	$-0.394534\pi$
$79$	36089.8	0.650604	0.325302	+	0.945610i	$0.394534\pi$
$80$	−32989.0	−0.576294
$81$	55905.5	0.946764
$82$	17941.3	0.294659
$83$	−24572.6	−0.391522	−0.195761	−	0.980652i	$-0.562718\pi$
$83$	−24572.6	−0.391522	−0.195761	+	0.980652i	$0.562718\pi$
$84$	0	0
$85$	−82648.2	−1.24076
$86$	73777.5	1.07567
$87$	1524.44	0.0215930
$88$	13985.7	0.192521
$89$	−70243.3	−0.940005	−0.470002	−	0.882665i	$-0.655747\pi$
$89$	−70243.3	−0.940005	−0.470002	+	0.882665i	$0.655747\pi$
$90$	50739.5	0.660298
$91$	0	0
$92$	−2550.74	−0.0314193
$93$	12753.1	0.152901
$94$	108890.	1.27106
$95$	−78005.4	−0.886779
$96$	−4579.66	−0.0507172
$97$	105758.	1.14126	0.570630	−	0.821207i	$-0.306699\pi$
$97$	105758.	1.14126	0.570630	+	0.821207i	$0.306699\pi$
$98$	0	0
$99$	−17206.7	−0.176445
$100$	8480.37	0.0848037
$101$	36461.8	0.355660	0.177830	−	0.984061i	$-0.443092\pi$
$101$	36461.8	0.355660	0.177830	+	0.984061i	$0.443092\pi$
$102$	20917.5	0.199072
$103$	64520.1	0.599242	0.299621	−	0.954058i	$-0.403140\pi$
$103$	64520.1	0.599242	0.299621	+	0.954058i	$0.403140\pi$
$104$	−122661.	−1.11205
$105$	0	0
$106$	−63938.4	−0.552710
$107$	66045.6	0.557679	0.278840	−	0.960338i	$-0.410050\pi$
$107$	66045.6	0.557679	0.278840	+	0.960338i	$0.410050\pi$
$108$	6185.18	0.0510262
$109$	−37938.0	−0.305850	−0.152925	−	0.988238i	$-0.548869\pi$
$109$	−37938.0	−0.305850	−0.152925	+	0.988238i	$0.548869\pi$
$110$	−15327.7	−0.120780
$111$	21557.4	0.166069
$112$	0	0
$113$	123802.	0.912080	0.456040	−	0.889959i	$-0.349267\pi$
$113$	123802.	0.912080	0.456040	+	0.889959i	$0.349267\pi$
$114$	19742.4	0.142278
$115$	17304.5	0.122016
$116$	−4512.76	−0.0311384
$117$	150910.	1.01919
$118$	183660.	1.21426
$119$	0	0
$120$	16899.5	0.107132
$121$	−155853.	−0.967725
$122$	−20457.1	−0.124435
$123$	−7351.81	−0.0438159
$124$	−37752.6	−0.220492
$125$	−188243.	−1.07757
$126$	0	0
$127$	128724.	0.708189	0.354095	−	0.935210i	$-0.384789\pi$
$127$	128724.	0.708189	0.354095	+	0.935210i	$0.384789\pi$
$128$	−114722.	−0.618902
$129$	−30231.8	−0.159952
$130$	134431.	0.697653
$131$	−147902.	−0.753003	−0.376501	−	0.926416i	$-0.622873\pi$
$131$	−147902.	−0.753003	−0.376501	+	0.926416i	$0.622873\pi$
$132$	−925.814	−0.00462476
$133$	0	0
$134$	−79118.0	−0.380639
$135$	−41961.0	−0.198158
$136$	−383302.	−1.77703
$137$	−91157.4	−0.414945	−0.207472	−	0.978241i	$-0.566524\pi$
$137$	−91157.4	−0.414945	−0.207472	+	0.978241i	$0.566524\pi$
$138$	−4379.62	−0.0195767
$139$	−334657.	−1.46914	−0.734570	−	0.678533i	$-0.762616\pi$
$139$	−334657.	−1.46914	−0.734570	+	0.678533i	$0.762616\pi$
$140$	0	0
$141$	−44619.7	−0.189007
$142$	−61911.9	−0.257664
$143$	−45587.8	−0.186427
$144$	188230.	0.756455
$145$	30615.1	0.120925
$146$	−99566.9	−0.386574
$147$	0	0
$148$	−63815.5	−0.239482
$149$	138271.	0.510231	0.255115	−	0.966911i	$-0.417887\pi$
$149$	138271.	0.510231	0.255115	+	0.966911i	$0.417887\pi$
$150$	14560.8	0.0528392
$151$	111169.	0.396773	0.198386	−	0.980124i	$-0.436430\pi$
$151$	111169.	0.396773	0.198386	+	0.980124i	$0.436430\pi$
$152$	−361770.	−1.27006
$153$	471578.	1.62864
$154$	0	0
$155$	256118.	0.856270
$156$	8119.79	0.0267137
$157$	−38148.5	−0.123517	−0.0617587	−	0.998091i	$-0.519671\pi$
$157$	−38148.5	−0.123517	−0.0617587	+	0.998091i	$0.519671\pi$
$158$	−183436.	−0.584577
$159$	26200.0	0.0821881
$160$	−91972.3	−0.284025
$161$	0	0
$162$	−284154.	−0.850681
$163$	−212905.	−0.627648	−0.313824	−	0.949481i	$-0.601610\pi$
$163$	−212905.	−0.627648	−0.313824	+	0.949481i	$0.601610\pi$
$164$	21763.3	0.0631852
$165$	6280.83	0.0179600
$166$	124897.	0.351788
$167$	−120396.	−0.334057	−0.167028	−	0.985952i	$-0.553417\pi$
$167$	−120396.	−0.334057	−0.167028	+	0.985952i	$0.553417\pi$
$168$	0	0
$169$	28532.2	0.0768456
$170$	420081.	1.11484
$171$	445087.	1.16400
$172$	89494.0	0.230660
$173$	712914.	1.81101	0.905507	−	0.424331i	$-0.139491\pi$
$173$	712914.	1.81101	0.905507	+	0.424331i	$0.139491\pi$
$174$	−7748.39	−0.0194016
$175$	0	0
$176$	−56861.7	−0.138369
$177$	−75258.4	−0.180560
$178$	357030.	0.844607
$179$	−749738.	−1.74895	−0.874474	−	0.485072i	$-0.838793\pi$
$179$	−749738.	−1.74895	−0.874474	+	0.485072i	$0.838793\pi$
$180$	61548.4	0.141591
$181$	623718.	1.41511	0.707557	−	0.706656i	$-0.249797\pi$
$181$	623718.	1.41511	0.707557	+	0.706656i	$0.249797\pi$
$182$	0	0
$183$	8382.69	0.0185036
$184$	80254.2	0.174752
$185$	432932.	0.930016
$186$	−64821.1	−0.137383
$187$	−142457.	−0.297907
$188$	132086.	0.272560
$189$	0	0
$190$	396483.	0.796784
$191$	417726.	0.828530	0.414265	−	0.910156i	$-0.364039\pi$
$191$	417726.	0.828530	0.414265	+	0.910156i	$0.364039\pi$
$192$	75842.2	0.148477
$193$	770700.	1.48933	0.744667	−	0.667436i	$-0.232608\pi$
$193$	770700.	1.48933	0.744667	+	0.667436i	$0.232608\pi$
$194$	−537544.	−1.02544
$195$	−55085.6	−0.103741
$196$	0	0
$197$	−479193.	−0.879721	−0.439861	−	0.898066i	$-0.644972\pi$
$197$	−479193.	−0.879721	−0.439861	+	0.898066i	$0.644972\pi$
$198$	87457.5	0.158538
$199$	−428686.	−0.767373	−0.383687	−	0.923463i	$-0.625346\pi$
$199$	−428686.	−0.767373	−0.383687	+	0.923463i	$0.625346\pi$
$200$	−266818.	−0.471673
$201$	32420.2	0.0566011
$202$	−185327.	−0.319565
$203$	0	0
$204$	25373.5	0.0426879
$205$	−147645.	−0.245377
$206$	−327940.	−0.538427
$207$	−98737.0	−0.160160
$208$	498702.	0.799250
$209$	−134455.	−0.212917
$210$	0	0
$211$	−588544.	−0.910066	−0.455033	−	0.890475i	$-0.650373\pi$
$211$	−588544.	−0.910066	−0.455033	+	0.890475i	$0.650373\pi$
$212$	−77559.0	−0.118520
$213$	25369.6	0.0383147
$214$	−335694.	−0.501083
$215$	−607138.	−0.895759
$216$	−194605.	−0.283804
$217$	0	0
$218$	192830.	0.274811
$219$	40799.5	0.0574837
$220$	−18592.9	−0.0258994
$221$	1.24941e6	1.72078
$222$	−109571.	−0.149215
$223$	−363249.	−0.489151	−0.244575	−	0.969630i	$-0.578649\pi$
$223$	−363249.	−0.489151	−0.244575	+	0.969630i	$0.578649\pi$
$224$	0	0
$225$	328268.	0.432287
$226$	−629258.	−0.819517
$227$	−843041.	−1.08589	−0.542943	−	0.839770i	$-0.682690\pi$
$227$	−843041.	−1.08589	−0.542943	+	0.839770i	$0.682690\pi$
$228$	23948.1	0.0305094
$229$	−568666.	−0.716587	−0.358293	−	0.933609i	$-0.616641\pi$
$229$	−568666.	−0.716587	−0.358293	+	0.933609i	$0.616641\pi$
$230$	−87954.8	−0.109633
$231$	0	0
$232$	141985.	0.173190
$233$	−1.05651e6	−1.27492	−0.637461	−	0.770482i	$-0.720015\pi$
$233$	−1.05651e6	−1.27492	−0.637461	+	0.770482i	$0.720015\pi$
$234$	−767041.	−0.915754
$235$	−896086.	−1.05847
$236$	222785.	0.260379
$237$	75166.5	0.0869267
$238$	0	0
$239$	853715.	0.966759	0.483379	−	0.875411i	$-0.339409\pi$
$239$	853715.	0.966759	0.483379	+	0.875411i	$0.339409\pi$
$240$	−68708.3	−0.0769983
$241$	−388888.	−0.431302	−0.215651	−	0.976470i	$-0.569187\pi$
$241$	−388888.	−0.431302	−0.215651	+	0.976470i	$0.569187\pi$
$242$	792164.	0.869515
$243$	360212.	0.391330
$244$	−24815.0	−0.0266833
$245$	0	0
$246$	37367.5	0.0393692
$247$	1.17922e6	1.22986
$248$	1.18781e6	1.22636
$249$	−51178.9	−0.0523109
$250$	956795.	0.968209
$251$	−839328.	−0.840906	−0.420453	−	0.907314i	$-0.638129\pi$
$251$	−839328.	−0.840906	−0.420453	+	0.907314i	$0.638129\pi$
$252$	0	0
$253$	29827.1	0.0292961
$254$	−654272.	−0.636318
$255$	−172137.	−0.165776
$256$	−582151.	−0.555182
$257$	291986.	0.275759	0.137879	−	0.990449i	$-0.455971\pi$
$257$	291986.	0.275759	0.137879	+	0.990449i	$0.455971\pi$
$258$	153661.	0.143719
$259$	0	0
$260$	163068.	0.149601
$261$	−174685.	−0.158728
$262$	751752.	0.676584
$263$	−288495.	−0.257187	−0.128594	−	0.991697i	$-0.541046\pi$
$263$	−288495.	−0.257187	−0.128594	+	0.991697i	$0.541046\pi$
$264$	29128.9	0.0257226
$265$	526169.	0.460268
$266$	0	0
$267$	−146300.	−0.125593
$268$	−95972.2	−0.0816222
$269$	−259370.	−0.218544	−0.109272	−	0.994012i	$-0.534852\pi$
$269$	−259370.	−0.218544	−0.109272	+	0.994012i	$0.534852\pi$
$270$	213278.	0.178047
$271$	−2.19551e6	−1.81599	−0.907994	−	0.418984i	$-0.862386\pi$
$271$	−2.19551e6	−1.81599	−0.907994	+	0.418984i	$0.862386\pi$
$272$	1.55839e6	1.27719
$273$	0	0
$274$	463331.	0.372834
$275$	−99165.1	−0.0790728
$276$	−5312.59	−0.00419792
$277$	126991.	0.0994426	0.0497213	−	0.998763i	$-0.484167\pi$
$277$	126991.	0.0994426	0.0497213	+	0.998763i	$0.484167\pi$
$278$	1.70098e6	1.32004
$279$	−1.46137e6	−1.12396
$280$	0	0
$281$	−2.22759e6	−1.68294	−0.841472	−	0.540301i	$-0.818310\pi$
$281$	−2.22759e6	−1.68294	−0.841472	+	0.540301i	$0.818310\pi$
$282$	226791.	0.169826
$283$	1.18895e6	0.882463	0.441231	−	0.897393i	$-0.354542\pi$
$283$	1.18895e6	0.882463	0.441231	+	0.897393i	$0.354542\pi$
$284$	−75100.7	−0.0552520
$285$	−162467.	−0.118482
$286$	231712.	0.167507
$287$	0	0
$288$	524780.	0.372817
$289$	2.48442e6	1.74977
$290$	−155609.	−0.108653
$291$	220269.	0.152483
$292$	−120777.	−0.0828949
$293$	1.83223e6	1.24684	0.623421	−	0.781886i	$-0.285742\pi$
$293$	1.83223e6	1.24684	0.623421	+	0.781886i	$0.285742\pi$
$294$	0	0
$295$	−1.51140e6	−1.01117
$296$	2.00783e6	1.33198
$297$	−72326.3	−0.0475779
$298$	−702800.	−0.458449
$299$	−261596.	−0.169221
$300$	17662.6	0.0113306
$301$	0	0
$302$	−565047.	−0.356506
$303$	75941.3	0.0475194
$304$	1.47085e6	0.912817
$305$	168348.	0.103623
$306$	−2.39692e6	−1.46336
$307$	−717638.	−0.434569	−0.217285	−	0.976108i	$-0.569720\pi$
$307$	−717638.	−0.434569	−0.217285	+	0.976108i	$0.569720\pi$
$308$	0	0
$309$	134380.	0.0800642
$310$	−1.30179e6	−0.769370
$311$	−856892.	−0.502372	−0.251186	−	0.967939i	$-0.580821\pi$
$311$	−856892.	−0.502372	−0.251186	+	0.967939i	$0.580821\pi$
$312$	−255474.	−0.148580
$313$	1.61699e6	0.932924	0.466462	−	0.884541i	$-0.345528\pi$
$313$	1.61699e6	0.932924	0.466462	+	0.884541i	$0.345528\pi$
$314$	193900.	0.110982
$315$	0	0
$316$	−222512.	−0.125354
$317$	−2.26559e6	−1.26629	−0.633145	−	0.774033i	$-0.718236\pi$
$317$	−2.26559e6	−1.26629	−0.633145	+	0.774033i	$0.718236\pi$
$318$	−133169.	−0.0738472
$319$	52769.8	0.0290341
$320$	1.52312e6	0.831495
$321$	137557.	0.0745111
$322$	0	0
$323$	3.68495e6	1.96528
$324$	−344687.	−0.182416
$325$	869721.	0.456743
$326$	1.08214e6	0.563950
$327$	−79015.9	−0.0408644
$328$	−684740.	−0.351432
$329$	0	0
$330$	−31924.0	−0.0161373
$331$	709650.	0.356020	0.178010	−	0.984029i	$-0.443034\pi$
$331$	709650.	0.356020	0.178010	+	0.984029i	$0.443034\pi$
$332$	151503.	0.0754355
$333$	−2.47024e6	−1.22076
$334$	611943.	0.300155
$335$	651086.	0.316976
$336$	0	0
$337$	603572.	0.289504	0.144752	−	0.989468i	$-0.453762\pi$
$337$	603572.	0.289504	0.144752	+	0.989468i	$0.453762\pi$
$338$	−145023.	−0.0690468
$339$	257851.	0.121862
$340$	509570.	0.239060
$341$	441459.	0.205591
$342$	−2.26227e6	−1.04587
$343$	0	0
$344$	−2.81576e6	−1.28292
$345$	36041.2	0.0163024
$346$	−3.62357e6	−1.62722
$347$	1.75731e6	0.783474	0.391737	−	0.920077i	$-0.371874\pi$
$347$	1.75731e6	0.783474	0.391737	+	0.920077i	$0.371874\pi$
$348$	−9399.00	−0.00416038
$349$	391875.	0.172220	0.0861102	−	0.996286i	$-0.472556\pi$
$349$	391875.	0.172220	0.0861102	+	0.996286i	$0.472556\pi$
$350$	0	0
$351$	634333.	0.274821
$352$	−158529.	−0.0681948
$353$	492407.	0.210323	0.105162	−	0.994455i	$-0.466464\pi$
$353$	492407.	0.210323	0.105162	+	0.994455i	$0.466464\pi$
$354$	382521.	0.162236
$355$	509492.	0.214569
$356$	433087.	0.181113
$357$	0	0
$358$	3.81074e6	1.57145
$359$	−3.77032e6	−1.54398	−0.771991	−	0.635634i	$-0.780739\pi$
$359$	−3.77032e6	−1.54398	−0.771991	+	0.635634i	$0.780739\pi$
$360$	−1.93650e6	−0.787520
$361$	1.00185e6	0.404607
$362$	−3.17021e6	−1.27150
$363$	−324605.	−0.129297
$364$	0	0
$365$	819367.	0.321919
$366$	−42607.2	−0.0166257
$367$	−2.19768e6	−0.851726	−0.425863	−	0.904788i	$-0.640030\pi$
$367$	−2.19768e6	−0.851726	−0.425863	+	0.904788i	$0.640030\pi$
$368$	−326289.	−0.125598
$369$	842439.	0.322086
$370$	−2.20049e6	−0.835632
$371$	0	0
$372$	−78629.7	−0.0294598
$373$	−1.65636e6	−0.616427	−0.308213	−	0.951317i	$-0.599731\pi$
$373$	−1.65636e6	−0.616427	−0.308213	+	0.951317i	$0.599731\pi$
$374$	724076.	0.267673
$375$	−392066.	−0.143973
$376$	−4.15583e6	−1.51596
$377$	−462814.	−0.167708
$378$	0	0
$379$	−2.82050e6	−1.00862	−0.504310	−	0.863523i	$-0.668253\pi$
$379$	−2.82050e6	−1.00862	−0.504310	+	0.863523i	$0.668253\pi$
$380$	480944.	0.170858
$381$	268101.	0.0946206
$382$	−2.12320e6	−0.744446
$383$	3.24845e6	1.13156	0.565781	−	0.824555i	$-0.308575\pi$
$383$	3.24845e6	1.13156	0.565781	+	0.824555i	$0.308575\pi$
$384$	−238939.	−0.0826911
$385$	0	0
$386$	−3.91729e6	−1.33819
$387$	3.46424e6	1.17579
$388$	−652055.	−0.219890
$389$	4.65348e6	1.55921	0.779604	−	0.626273i	$-0.215420\pi$
$389$	4.65348e6	1.55921	0.779604	+	0.626273i	$0.215420\pi$
$390$	279987.	0.0932130
$391$	−817461.	−0.270411
$392$	0	0
$393$	−308045.	−0.100608
$394$	2.43563e6	0.790442
$395$	1.50955e6	0.486805
$396$	106088.	0.0339961
$397$	−1.16361e6	−0.370536	−0.185268	−	0.982688i	$-0.559315\pi$
$397$	−1.16361e6	−0.370536	−0.185268	+	0.982688i	$0.559315\pi$
$398$	2.17891e6	0.689495
$399$	0	0
$400$	1.08480e6	0.339001
$401$	322380.	0.100117	0.0500584	−	0.998746i	$-0.484059\pi$
$401$	322380.	0.100117	0.0500584	+	0.998746i	$0.484059\pi$
$402$	−164784.	−0.0508569
$403$	−3.87179e6	−1.18754
$404$	−224806.	−0.0685259
$405$	2.33839e6	0.708403
$406$	0	0
$407$	746226.	0.223298
$408$	−798328.	−0.237427
$409$	1.38690e6	0.409956	0.204978	−	0.978767i	$-0.434288\pi$
$409$	1.38690e6	0.409956	0.204978	+	0.978767i	$0.434288\pi$
$410$	750443.	0.220474
$411$	−189859.	−0.0554405
$412$	−397800.	−0.115457
$413$	0	0
$414$	501857.	0.143906
$415$	−1.02781e6	−0.292950
$416$	1.39036e6	0.393909
$417$	−697011.	−0.196291
$418$	683400.	0.191309
$419$	4.90871e6	1.36594	0.682971	−	0.730446i	$-0.260688\pi$
$419$	4.90871e6	1.36594	0.682971	+	0.730446i	$0.260688\pi$
$420$	0	0
$421$	2.43924e6	0.670733	0.335367	−	0.942088i	$-0.391140\pi$
$421$	2.43924e6	0.670733	0.335367	+	0.942088i	$0.391140\pi$
$422$	2.99143e6	0.817707
$423$	5.11293e6	1.38937
$424$	2.44024e6	0.659202
$425$	2.71779e6	0.729865
$426$	−128948.	−0.0344263
$427$	0	0
$428$	−407206.	−0.107450
$429$	−94948.7	−0.0249084
$430$	3.08594e6	0.804852
$431$	−5.22752e6	−1.35551	−0.677755	−	0.735288i	$-0.737047\pi$
$431$	−5.22752e6	−1.35551	−0.677755	+	0.735288i	$0.737047\pi$
$432$	791204.	0.203976
$433$	−2.63022e6	−0.674174	−0.337087	−	0.941473i	$-0.609442\pi$
$433$	−2.63022e6	−0.674174	−0.337087	+	0.941473i	$0.609442\pi$
$434$	0	0
$435$	63763.9	0.0161567
$436$	233908.	0.0589289
$437$	−771539.	−0.193266
$438$	−207374.	−0.0516499
$439$	2.55412e6	0.632527	0.316264	−	0.948671i	$-0.397572\pi$
$439$	2.55412e6	0.632527	0.316264	+	0.948671i	$0.397572\pi$
$440$	584990.	0.144051
$441$	0	0
$442$	−6.35046e6	−1.54614
$443$	3.83900e6	0.929414	0.464707	−	0.885465i	$-0.346160\pi$
$443$	3.83900e6	0.929414	0.464707	+	0.885465i	$0.346160\pi$
$444$	−132913.	−0.0319970
$445$	−2.93811e6	−0.703345
$446$	1.84631e6	0.439509
$447$	287986.	0.0681715
$448$	0	0
$449$	1.49369e6	0.349658	0.174829	−	0.984599i	$-0.444063\pi$
$449$	1.49369e6	0.349658	0.174829	+	0.984599i	$0.444063\pi$
$450$	−1.66851e6	−0.388416
$451$	−254489.	−0.0589152
$452$	−763307.	−0.175733
$453$	231539.	0.0530126
$454$	4.28498e6	0.975684
$455$	0	0
$456$	−753481.	−0.169692
$457$	−2.16221e6	−0.484293	−0.242146	−	0.970240i	$-0.577851\pi$
$457$	−2.16221e6	−0.484293	−0.242146	+	0.970240i	$0.577851\pi$
$458$	2.89040e6	0.643863
$459$	1.98222e6	0.439158
$460$	−106692.	−0.0235091
$461$	−6.11949e6	−1.34111	−0.670553	−	0.741862i	$-0.733943\pi$
$461$	−6.11949e6	−1.34111	−0.670553	+	0.741862i	$0.733943\pi$
$462$	0	0
$463$	3.93615e6	0.853335	0.426667	−	0.904409i	$-0.359687\pi$
$463$	3.93615e6	0.853335	0.426667	+	0.904409i	$0.359687\pi$
$464$	−577268.	−0.124475
$465$	533433.	0.114406
$466$	5.36999e6	1.14554
$467$	−5.47044e6	−1.16073	−0.580363	−	0.814358i	$-0.697089\pi$
$467$	−5.47044e6	−1.16073	−0.580363	+	0.814358i	$0.697089\pi$
$468$	−930441.	−0.196369
$469$	0	0
$470$	4.55459e6	0.951054
$471$	−79454.3	−0.0165031
$472$	−7.00949e6	−1.44821
$473$	−1.04650e6	−0.215073
$474$	−382053.	−0.0781049
$475$	2.56511e6	0.521641
$476$	0	0
$477$	−3.00224e6	−0.604157
$478$	−4.33923e6	−0.868646
$479$	−6.66289e6	−1.32686	−0.663428	−	0.748240i	$-0.730899\pi$
$479$	−6.66289e6	−1.32686	−0.663428	+	0.748240i	$0.730899\pi$
$480$	−191556.	−0.0379484
$481$	−6.54473e6	−1.28982
$482$	1.97663e6	0.387531
$483$	0	0
$484$	960916.	0.186454
$485$	4.42362e6	0.853931
$486$	−1.83087e6	−0.351615
$487$	9.53693e6	1.82216	0.911079	−	0.412232i	$-0.135251\pi$
$487$	9.53693e6	1.82216	0.911079	+	0.412232i	$0.135251\pi$
$488$	780755.	0.148411
$489$	−443430.	−0.0838595
$490$	0	0
$491$	−8.19294e6	−1.53369	−0.766843	−	0.641835i	$-0.778173\pi$
$491$	−8.19294e6	−1.53369	−0.766843	+	0.641835i	$0.778173\pi$
$492$	45327.8	0.00844213
$493$	−1.44625e6	−0.267994
$494$	−5.99372e6	−1.10504
$495$	−719715.	−0.132022
$496$	−4.82928e6	−0.881411
$497$	0	0
$498$	260130.	0.0470021
$499$	−4.31437e6	−0.775650	−0.387825	−	0.921733i	$-0.626774\pi$
$499$	−4.31437e6	−0.775650	−0.387825	+	0.921733i	$0.626774\pi$
$500$	1.16062e6	0.207618
$501$	−250756.	−0.0446331
$502$	4.26610e6	0.755566
$503$	−1.04015e7	−1.83306	−0.916529	−	0.399968i	$-0.869021\pi$
$503$	−1.04015e7	−1.83306	−0.916529	+	0.399968i	$0.869021\pi$
$504$	0	0
$505$	1.52511e6	0.266117
$506$	−151604.	−0.0263229
$507$	59425.9	0.0102673
$508$	−793649.	−0.136449
$509$	−3.09396e6	−0.529322	−0.264661	−	0.964342i	$-0.585260\pi$
$509$	−3.09396e6	−0.529322	−0.264661	+	0.964342i	$0.585260\pi$
$510$	874930.	0.148952
$511$	0	0
$512$	6.63004e6	1.11774
$513$	1.87087e6	0.313870
$514$	−1.48410e6	−0.247773
$515$	2.69872e6	0.448374
$516$	186395.	0.0308184
$517$	−1.54455e6	−0.254141
$518$	0	0
$519$	1.48483e6	0.241968
$520$	−5.13061e6	−0.832072
$521$	−7.60175e6	−1.22693	−0.613464	−	0.789723i	$-0.710224\pi$
$521$	−7.60175e6	−1.22693	−0.613464	+	0.789723i	$0.710224\pi$
$522$	887882.	0.142619
$523$	4.75669e6	0.760415	0.380208	−	0.924901i	$-0.375853\pi$
$523$	4.75669e6	0.760415	0.380208	+	0.924901i	$0.375853\pi$
$524$	911895.	0.145083
$525$	0	0
$526$	1.46635e6	0.231086
$527$	−1.20989e7	−1.89767
$528$	−118429.	−0.0184874
$529$	−6.26519e6	−0.973408
$530$	−2.67439e6	−0.413557
$531$	8.62380e6	1.32728
$532$	0	0
$533$	2.23198e6	0.340308
$534$	743609.	0.112847
$535$	2.76253e6	0.417275
$536$	3.01958e6	0.453978
$537$	−1.56153e6	−0.233676
$538$	1.31832e6	0.196365
$539$	0	0
$540$	258711.	0.0381796
$541$	1.10052e7	1.61661	0.808305	−	0.588764i	$-0.200385\pi$
$541$	1.10052e7	1.61661	0.808305	+	0.588764i	$0.200385\pi$
$542$	1.11593e7	1.63169
$543$	1.29906e6	0.189072
$544$	4.34474e6	0.629458
$545$	−1.58686e6	−0.228848
$546$	0	0
$547$	−4.46311e6	−0.637778	−0.318889	−	0.947792i	$-0.603310\pi$
$547$	−4.46311e6	−0.637778	−0.318889	+	0.947792i	$0.603310\pi$
$548$	562033.	0.0799485
$549$	−960566.	−0.136018
$550$	504032.	0.0710480
$551$	−1.36500e6	−0.191538
$552$	167150.	0.0233485
$553$	0	0
$554$	−645463.	−0.0893505
$555$	901694.	0.124259
$556$	2.06334e6	0.283063
$557$	−6.45222e6	−0.881194	−0.440597	−	0.897705i	$-0.645233\pi$
$557$	−6.45222e6	−0.881194	−0.440597	+	0.897705i	$0.645233\pi$
$558$	7.42780e6	1.00989
$559$	9.17823e6	1.24231
$560$	0	0
$561$	−296704.	−0.0398031
$562$	1.13223e7	1.51215
$563$	1.74748e6	0.232349	0.116175	−	0.993229i	$-0.462937\pi$
$563$	1.74748e6	0.232349	0.116175	+	0.993229i	$0.462937\pi$
$564$	275104.	0.0364165
$565$	5.17836e6	0.682450
$566$	−6.04313e6	−0.792905
$567$	0	0
$568$	2.36290e6	0.307308
$569$	512789.	0.0663985	0.0331992	−	0.999449i	$-0.489430\pi$
$569$	512789.	0.0663985	0.0331992	+	0.999449i	$0.489430\pi$
$570$	825780.	0.106458
$571$	5.22364e6	0.670475	0.335238	−	0.942134i	$-0.391183\pi$
$571$	5.22364e6	0.670475	0.335238	+	0.942134i	$0.391183\pi$
$572$	281073.	0.0359194
$573$	870024.	0.110699
$574$	0	0
$575$	−569038.	−0.0717748
$576$	−8.69070e6	−1.09144
$577$	6.63973e6	0.830254	0.415127	−	0.909763i	$-0.363737\pi$
$577$	6.63973e6	0.830254	0.415127	+	0.909763i	$0.363737\pi$
$578$	−1.26277e7	−1.57219
$579$	1.60519e6	0.198989
$580$	−188758.	−0.0232989
$581$	0	0
$582$	−1.11958e6	−0.137008
$583$	906935.	0.110511
$584$	3.80002e6	0.461056
$585$	6.31221e6	0.762592
$586$	−9.31280e6	−1.12030
$587$	774096.	0.0927256	0.0463628	−	0.998925i	$-0.485237\pi$
$587$	774096.	0.0927256	0.0463628	+	0.998925i	$0.485237\pi$
$588$	0	0
$589$	−1.14193e7	−1.35628
$590$	7.68207e6	0.908549
$591$	−998046.	−0.117539
$592$	−8.16324e6	−0.957322
$593$	−1.43756e7	−1.67876	−0.839379	−	0.543546i	$-0.817081\pi$
$593$	−1.43756e7	−1.67876	−0.839379	+	0.543546i	$0.817081\pi$
$594$	367617.	0.0427494
$595$	0	0
$596$	−852515.	−0.0983075
$597$	−892851.	−0.102528
$598$	1.32963e6	0.152047
$599$	1.20835e7	1.37602	0.688010	−	0.725701i	$-0.258484\pi$
$599$	1.20835e7	1.37602	0.688010	+	0.725701i	$0.258484\pi$
$600$	−555719.	−0.0630199
$601$	5.75607e6	0.650040	0.325020	−	0.945707i	$-0.394629\pi$
$601$	5.75607e6	0.650040	0.325020	+	0.945707i	$0.394629\pi$
$602$	0	0
$603$	−3.71500e6	−0.416069
$604$	−685416.	−0.0764473
$605$	−6.51897e6	−0.724086
$606$	−385991.	−0.0426969
$607$	4.20121e6	0.462810	0.231405	−	0.972858i	$-0.425668\pi$
$607$	4.20121e6	0.462810	0.231405	+	0.972858i	$0.425668\pi$
$608$	4.10067e6	0.449879
$609$	0	0
$610$	−855671.	−0.0931070
$611$	1.35463e7	1.46798
$612$	−2.90753e6	−0.313795
$613$	−2.64543e6	−0.284344	−0.142172	−	0.989842i	$-0.545409\pi$
$613$	−2.64543e6	−0.284344	−0.142172	+	0.989842i	$0.545409\pi$
$614$	3.64758e6	0.390467
$615$	−307509.	−0.0327846
$616$	0	0
$617$	6.43533e6	0.680546	0.340273	−	0.940327i	$-0.389480\pi$
$617$	6.43533e6	0.680546	0.340273	+	0.940327i	$0.389480\pi$
$618$	−683022.	−0.0719388
$619$	1.41177e7	1.48094	0.740469	−	0.672090i	$-0.234603\pi$
$619$	1.41177e7	1.48094	0.740469	+	0.672090i	$0.234603\pi$
$620$	−1.57910e6	−0.164980
$621$	−415029.	−0.0431867
$622$	4.35538e6	0.451388
$623$	0	0
$624$	1.03868e6	0.106787
$625$	−3.57548e6	−0.366129
$626$	−8.21877e6	−0.838246
$627$	−280037.	−0.0284476
$628$	235206.	0.0237984
$629$	−2.04516e7	−2.06111
$630$	0	0
$631$	−4.70856e6	−0.470777	−0.235388	−	0.971901i	$-0.575636\pi$
$631$	−4.70856e6	−0.470777	−0.235388	+	0.971901i	$0.575636\pi$
$632$	7.00092e6	0.697208
$633$	−1.22580e6	−0.121593
$634$	1.15155e7	1.13778
$635$	5.38421e6	0.529892
$636$	−161537.	−0.0158354
$637$	0	0
$638$	−268217.	−0.0260876
$639$	−2.90708e6	−0.281647
$640$	−4.79855e6	−0.463085
$641$	−1.04174e7	−1.00141	−0.500707	−	0.865617i	$-0.666927\pi$
$641$	−1.04174e7	−1.00141	−0.500707	+	0.865617i	$0.666927\pi$
$642$	−699171.	−0.0669493
$643$	1.27284e7	1.21407	0.607037	−	0.794674i	$-0.292358\pi$
$643$	1.27284e7	1.21407	0.607037	+	0.794674i	$0.292358\pi$
$644$	0	0
$645$	−1.26452e6	−0.119682
$646$	−1.87297e7	−1.76584
$647$	−1.61348e7	−1.51531	−0.757657	−	0.652653i	$-0.773656\pi$
$647$	−1.61348e7	−1.51531	−0.757657	+	0.652653i	$0.773656\pi$
$648$	1.08449e7	1.01458
$649$	−2.60513e6	−0.242783
$650$	−4.42058e6	−0.410390
$651$	0	0
$652$	1.31267e6	0.120931
$653$	−1.50295e7	−1.37931	−0.689654	−	0.724139i	$-0.742237\pi$
$653$	−1.50295e7	−1.37931	−0.689654	+	0.724139i	$0.742237\pi$
$654$	401619.	0.0367172
$655$	−6.18640e6	−0.563423
$656$	2.78395e6	0.252581
$657$	−4.67518e6	−0.422557
$658$	0	0
$659$	1.67927e7	1.50628	0.753140	−	0.657860i	$-0.228538\pi$
$659$	1.67927e7	1.50628	0.753140	+	0.657860i	$0.228538\pi$
$660$	−38724.6	−0.00346041
$661$	1.08540e7	0.966246	0.483123	−	0.875552i	$-0.339502\pi$
$661$	1.08540e7	0.966246	0.483123	+	0.875552i	$0.339502\pi$
$662$	−3.60698e6	−0.319889
$663$	2.60223e6	0.229912
$664$	−4.76675e6	−0.419567
$665$	0	0
$666$	1.25557e7	1.09687
$667$	302809.	0.0263544
$668$	742303.	0.0643636
$669$	−756562.	−0.0653551
$670$	−3.30932e6	−0.284807
$671$	290174.	0.0248801
$672$	0	0
$673$	1.23697e7	1.05274	0.526371	−	0.850255i	$-0.323552\pi$
$673$	1.23697e7	1.05274	0.526371	+	0.850255i	$0.323552\pi$
$674$	−3.06781e6	−0.260123
$675$	1.37983e6	0.116565
$676$	−175916.	−0.0148060
$677$	−1.00501e6	−0.0842746	−0.0421373	−	0.999112i	$-0.513417\pi$
$677$	−1.00501e6	−0.0842746	−0.0421373	+	0.999112i	$0.513417\pi$
$678$	−1.31060e6	−0.109495
$679$	0	0
$680$	−1.60326e7	−1.32963
$681$	−1.75586e6	−0.145084
$682$	−2.24383e6	−0.184727
$683$	1.87019e6	0.153403	0.0767014	−	0.997054i	$-0.475561\pi$
$683$	1.87019e6	0.153403	0.0767014	+	0.997054i	$0.475561\pi$
$684$	−2.74419e6	−0.224272
$685$	−3.81290e6	−0.310476
$686$	0	0
$687$	−1.18440e6	−0.0957426
$688$	1.14480e7	0.922060
$689$	−7.95421e6	−0.638336
$690$	−183189.	−0.0146479
$691$	1.93867e7	1.54457	0.772286	−	0.635275i	$-0.219113\pi$
$691$	1.93867e7	1.54457	0.772286	+	0.635275i	$0.219113\pi$
$692$	−4.39549e6	−0.348933
$693$	0	0
$694$	−8.93199e6	−0.703963
$695$	−1.39979e7	−1.09926
$696$	295721.	0.0231398
$697$	6.97469e6	0.543805
$698$	−1.99181e6	−0.154742
$699$	−2.20046e6	−0.170342
$700$	0	0
$701$	1.17488e7	0.903024	0.451512	−	0.892265i	$-0.350885\pi$
$701$	1.17488e7	0.903024	0.451512	+	0.892265i	$0.350885\pi$
$702$	−3.22416e6	−0.246930
$703$	−1.93027e7	−1.47309
$704$	2.62534e6	0.199643
$705$	−1.86634e6	−0.141422
$706$	−2.50279e6	−0.188978
$707$	0	0
$708$	464008.	0.0347890
$709$	1.67948e7	1.25475	0.627377	−	0.778716i	$-0.284129\pi$
$709$	1.67948e7	1.25475	0.627377	+	0.778716i	$0.284129\pi$
$710$	−2.58963e6	−0.192793
$711$	−8.61326e6	−0.638990
$712$	−1.36262e7	−1.00734
$713$	2.53322e6	0.186616
$714$	0	0
$715$	−1.90683e6	−0.139491
$716$	4.62253e6	0.336974
$717$	1.77809e6	0.129168
$718$	1.91636e7	1.38729
$719$	−1.65130e7	−1.19126	−0.595628	−	0.803261i	$-0.703097\pi$
$719$	−1.65130e7	−1.19126	−0.595628	+	0.803261i	$0.703097\pi$
$720$	7.87323e6	0.566007
$721$	0	0
$722$	−5.09215e6	−0.363545
$723$	−809961.	−0.0576260
$724$	−3.84555e6	−0.272654
$725$	−1.00674e6	−0.0711331
$726$	1.64989e6	0.116175
$727$	−1.25756e6	−0.0882453	−0.0441227	−	0.999026i	$-0.514049\pi$
$727$	−1.25756e6	−0.0882453	−0.0441227	+	0.999026i	$0.514049\pi$
$728$	0	0
$729$	−1.28348e7	−0.894479
$730$	−4.16465e6	−0.289248
$731$	2.86810e7	1.98518
$732$	−51683.7	−0.00356513
$733$	−1.98332e6	−0.136343	−0.0681716	−	0.997674i	$-0.521717\pi$
$733$	−1.98332e6	−0.136343	−0.0681716	+	0.997674i	$0.521717\pi$
$734$	1.11703e7	0.765288
$735$	0	0
$736$	−909684.	−0.0619007
$737$	1.12225e6	0.0761063
$738$	−4.28191e6	−0.289399
$739$	−2.38807e7	−1.60856	−0.804278	−	0.594253i	$-0.797448\pi$
$739$	−2.38807e7	−1.60856	−0.804278	+	0.594253i	$0.797448\pi$
$740$	−2.66925e6	−0.179189
$741$	2.45604e6	0.164320
$742$	0	0
$743$	−1.90819e7	−1.26809	−0.634043	−	0.773298i	$-0.718606\pi$
$743$	−1.90819e7	−1.26809	−0.634043	+	0.773298i	$0.718606\pi$
$744$	2.47393e6	0.163853
$745$	5.78356e6	0.381773
$746$	8.41886e6	0.553868
$747$	5.86455e6	0.384532
$748$	878323.	0.0573985
$749$	0	0
$750$	1.99278e6	0.129362
$751$	−3.75805e6	−0.243144	−0.121572	−	0.992583i	$-0.538794\pi$
$751$	−3.75805e6	−0.243144	−0.121572	+	0.992583i	$0.538794\pi$
$752$	1.68963e7	1.08955
$753$	−1.74812e6	−0.112353
$754$	2.35238e6	0.150688
$755$	4.64994e6	0.296880
$756$	0	0
$757$	1.69904e7	1.07761	0.538807	−	0.842429i	$-0.318875\pi$
$757$	1.69904e7	1.07761	0.538807	+	0.842429i	$0.318875\pi$
$758$	1.43359e7	0.906259
$759$	62122.7	0.00391423
$760$	−1.51320e7	−0.950302
$761$	2.23998e7	1.40211	0.701056	−	0.713106i	$-0.252712\pi$
$761$	2.23998e7	1.40211	0.701056	+	0.713106i	$0.252712\pi$
$762$	−1.36269e6	−0.0850180
$763$	0	0
$764$	−2.57550e6	−0.159635
$765$	1.97250e7	1.21861
$766$	−1.65111e7	−1.01672
$767$	2.28481e7	1.40237
$768$	−1.21248e6	−0.0741775
$769$	−1.87866e7	−1.14560	−0.572799	−	0.819696i	$-0.694142\pi$
$769$	−1.87866e7	−1.14560	−0.572799	+	0.819696i	$0.694142\pi$
$770$	0	0
$771$	608138.	0.0368439
$772$	−4.75177e6	−0.286954
$773$	9.30837e6	0.560306	0.280153	−	0.959955i	$-0.409615\pi$
$773$	9.30837e6	0.560306	0.280153	+	0.959955i	$0.409615\pi$
$774$	−1.76079e7	−1.05646
$775$	−8.42212e6	−0.503694
$776$	2.05156e7	1.22301
$777$	0	0
$778$	−2.36525e7	−1.40097
$779$	6.58288e6	0.388662
$780$	339632.	0.0199881
$781$	878189.	0.0515182
$782$	4.15496e6	0.242969
$783$	−734267.	−0.0428006
$784$	0	0
$785$	−1.59566e6	−0.0924201
$786$	1.56572e6	0.0903979
$787$	1.73427e7	0.998111	0.499056	−	0.866570i	$-0.333680\pi$
$787$	1.73427e7	0.998111	0.499056	+	0.866570i	$0.333680\pi$
$788$	2.95448e6	0.169498
$789$	−600867.	−0.0343626
$790$	−7.67268e6	−0.437401
$791$	0	0
$792$	−3.33786e6	−0.189084
$793$	−2.54495e6	−0.143713
$794$	5.91434e6	0.332932
$795$	1.09589e6	0.0614960
$796$	2.64307e6	0.147852
$797$	3.10445e7	1.73117	0.865584	−	0.500764i	$-0.166948\pi$
$797$	3.10445e7	1.73117	0.865584	+	0.500764i	$0.166948\pi$
$798$	0	0
$799$	4.23309e7	2.34580
$800$	3.02439e6	0.167076
$801$	1.67644e7	0.923224
$802$	−1.63858e6	−0.0899563
$803$	1.41231e6	0.0772930
$804$	−199887.	−0.0109055
$805$	0	0
$806$	1.96794e7	1.06702
$807$	−540206.	−0.0291995
$808$	7.07309e6	0.381137
$809$	−2.47038e7	−1.32707	−0.663533	−	0.748147i	$-0.730944\pi$
$809$	−2.47038e7	−1.32707	−0.663533	+	0.748147i	$0.730944\pi$
$810$	−1.18855e7	−0.636510
$811$	8.42005e6	0.449534	0.224767	−	0.974413i	$-0.427838\pi$
$811$	8.42005e6	0.449534	0.224767	+	0.974413i	$0.427838\pi$
$812$	0	0
$813$	−4.57273e6	−0.242633
$814$	−3.79289e6	−0.200636
$815$	−8.90529e6	−0.469628
$816$	3.24576e6	0.170644
$817$	2.70698e7	1.41883
$818$	−7.04930e6	−0.368352
$819$	0	0
$820$	910307.	0.0472774
$821$	−2.58827e7	−1.34014	−0.670071	−	0.742297i	$-0.733736\pi$
$821$	−2.58827e7	−1.34014	−0.670071	+	0.742297i	$0.733736\pi$
$822$	965009.	0.0498141
$823$	1.72004e7	0.885195	0.442597	−	0.896720i	$-0.354057\pi$
$823$	1.72004e7	0.885195	0.442597	+	0.896720i	$0.354057\pi$
$824$	1.25160e7	0.642167
$825$	−206537.	−0.0105649
$826$	0	0
$827$	−2.40337e7	−1.22196	−0.610979	−	0.791647i	$-0.709224\pi$
$827$	−2.40337e7	−1.22196	−0.610979	+	0.791647i	$0.709224\pi$
$828$	608766.	0.0308585
$829$	−3.24736e7	−1.64113	−0.820567	−	0.571550i	$-0.806342\pi$
$829$	−3.24736e7	−1.64113	−0.820567	+	0.571550i	$0.806342\pi$
$830$	5.22413e6	0.263220
$831$	264491.	0.0132865
$832$	−2.30254e7	−1.15318
$833$	0	0
$834$	3.54274e6	0.176370
$835$	−5.03587e6	−0.249953
$836$	828983.	0.0410232
$837$	−6.14269e6	−0.303072
$838$	−2.49498e7	−1.22732
$839$	−1.24404e7	−0.610139	−0.305069	−	0.952330i	$-0.598680\pi$
$839$	−1.24404e7	−0.610139	−0.305069	+	0.952330i	$0.598680\pi$
$840$	0	0
$841$	−1.99754e7	−0.973881
$842$	−1.23981e7	−0.602663
$843$	−4.63954e6	−0.224857
$844$	3.62868e6	0.175345
$845$	1.19344e6	0.0574986
$846$	−2.59878e7	−1.24837
$847$	0	0
$848$	−9.92129e6	−0.473782
$849$	2.47629e6	0.117905
$850$	−1.38139e7	−0.655794
$851$	4.28206e6	0.202689
$852$	−156417.	−0.00738219
$853$	−999355.	−0.0470270	−0.0235135	−	0.999724i	$-0.507485\pi$
$853$	−999355.	−0.0470270	−0.0235135	+	0.999724i	$0.507485\pi$
$854$	0	0
$855$	1.86169e7	0.870949
$856$	1.28119e7	0.597628
$857$	−2.64465e7	−1.23003	−0.615016	−	0.788514i	$-0.710851\pi$
$857$	−2.64465e7	−1.23003	−0.615016	+	0.788514i	$0.710851\pi$
$858$	482601.	0.0223805
$859$	−2.86716e7	−1.32577	−0.662887	−	0.748719i	$-0.730669\pi$
$859$	−2.86716e7	−1.32577	−0.662887	+	0.748719i	$0.730669\pi$
$860$	3.74332e6	0.172588
$861$	0	0
$862$	2.65703e7	1.21794
$863$	4.08173e6	0.186560	0.0932798	−	0.995640i	$-0.470265\pi$
$863$	4.08173e6	0.186560	0.0932798	+	0.995640i	$0.470265\pi$
$864$	2.20585e6	0.100529
$865$	2.98195e7	1.35506
$866$	1.33688e7	0.605755
$867$	5.17446e6	0.233785
$868$	0	0
$869$	2.60195e6	0.116882
$870$	−324097.	−0.0145170
$871$	−9.84261e6	−0.439608
$872$	−7.35946e6	−0.327759
$873$	−2.52405e7	−1.12089
$874$	3.92155e6	0.173652
$875$	0	0
$876$	−251550.	−0.0110755
$877$	−2.82405e7	−1.23986	−0.619931	−	0.784657i	$-0.712839\pi$
$877$	−2.82405e7	−1.23986	−0.619931	+	0.784657i	$0.712839\pi$
$878$	−1.29820e7	−0.568335
$879$	3.81610e6	0.166590
$880$	−2.37839e6	−0.103532
$881$	1.61480e7	0.700936	0.350468	−	0.936575i	$-0.386022\pi$
$881$	1.61480e7	0.700936	0.350468	+	0.936575i	$0.386022\pi$
$882$	0	0
$883$	−3.86021e7	−1.66613	−0.833065	−	0.553174i	$-0.813416\pi$
$883$	−3.86021e7	−1.66613	−0.833065	+	0.553174i	$0.813416\pi$
$884$	−7.70328e6	−0.331547
$885$	−3.14788e6	−0.135102
$886$	−1.95127e7	−0.835091
$887$	7.29088e6	0.311151	0.155575	−	0.987824i	$-0.450277\pi$
$887$	7.29088e6	0.311151	0.155575	+	0.987824i	$0.450277\pi$
$888$	4.18184e6	0.177965
$889$	0	0
$890$	1.49337e7	0.631965
$891$	4.03059e6	0.170088
$892$	2.23962e6	0.0942460
$893$	3.99529e7	1.67656
$894$	−1.46377e6	−0.0612531
$895$	−3.13598e7	−1.30862
$896$	0	0
$897$	−544843.	−0.0226095
$898$	−7.59205e6	−0.314173
$899$	4.48176e6	0.184948
$900$	−2.02394e6	−0.0832898
$901$	−2.48561e7	−1.02005
$902$	1.29351e6	0.0529361
$903$	0	0
$904$	2.40160e7	0.977415
$905$	2.60886e7	1.05884
$906$	−1.17686e6	−0.0476325
$907$	−3.73335e7	−1.50689	−0.753443	−	0.657514i	$-0.771608\pi$
$907$	−3.73335e7	−1.50689	−0.753443	+	0.657514i	$0.771608\pi$
$908$	5.19779e6	0.209221
$909$	−8.70205e6	−0.349311
$910$	0	0
$911$	−2475.17	−9.88120e−5 0	−4.94060e−5	−	1.00000i	$-0.500016\pi$
$911$	−2475.17	−9.88120e−5 0	−4.94060e−5		1.00000i	$0.500016\pi$
$912$	3.06342e6	0.121961
$913$	−1.77160e6	−0.0703377
$914$	1.09900e7	0.435144
$915$	350628.	0.0138450
$916$	3.50613e6	0.138067
$917$	0	0
$918$	−1.00752e7	−0.394590
$919$	−4.48238e6	−0.175073	−0.0875366	−	0.996161i	$-0.527899\pi$
$919$	−4.48238e6	−0.175073	−0.0875366	+	0.996161i	$0.527899\pi$
$920$	3.35684e6	0.130756
$921$	−1.49467e6	−0.0580625
$922$	3.11039e7	1.20500
$923$	−7.70210e6	−0.297581
$924$	0	0
$925$	−1.42364e7	−0.547075
$926$	−2.00065e7	−0.766733
$927$	−1.53985e7	−0.588544
$928$	−1.60941e6	−0.0613473
$929$	2.12859e7	0.809193	0.404596	−	0.914495i	$-0.367412\pi$
$929$	2.12859e7	0.809193	0.404596	+	0.914495i	$0.367412\pi$
$930$	−2.71131e6	−0.102795
$931$	0	0
$932$	6.51394e6	0.245643
$933$	−1.78470e6	−0.0671215
$934$	2.78049e7	1.04293
$935$	−5.95865e6	−0.222904
$936$	2.92745e7	1.09219
$937$	6.79757e6	0.252932	0.126466	−	0.991971i	$-0.459636\pi$
$937$	6.79757e6	0.252932	0.126466	+	0.991971i	$0.459636\pi$
$938$	0	0
$939$	3.36781e6	0.124647
$940$	5.52484e6	0.203939
$941$	4.90883e7	1.80719	0.903595	−	0.428388i	$-0.140918\pi$
$941$	4.90883e7	1.80719	0.903595	+	0.428388i	$0.140918\pi$
$942$	403847.	0.0148283
$943$	−1.46033e6	−0.0534776
$944$	2.84985e7	1.04086
$945$	0	0
$946$	5.31910e6	0.193246
$947$	2.45484e7	0.889505	0.444753	−	0.895653i	$-0.353292\pi$
$947$	2.45484e7	0.889505	0.444753	+	0.895653i	$0.353292\pi$
$948$	−463441.	−0.0167484
$949$	−1.23865e7	−0.446462
$950$	−1.30378e7	−0.468702
$951$	−4.71869e6	−0.169188
$952$	0	0
$953$	−513120.	−0.0183015	−0.00915075	−	0.999958i	$-0.502913\pi$
$953$	−513120.	−0.0183015	−0.00915075	+	0.999958i	$0.502913\pi$
$954$	1.52597e7	0.542843
$955$	1.74725e7	0.619935
$956$	−5.26360e6	−0.186268
$957$	109907.	0.00387923
$958$	3.38659e7	1.19220
$959$	0	0
$960$	3.17230e6	0.111095
$961$	8.86412e6	0.309619
$962$	3.32653e7	1.15892
$963$	−1.57626e7	−0.547724
$964$	2.39770e6	0.0831002
$965$	3.22366e7	1.11437
$966$	0	0
$967$	3.34818e7	1.15144	0.575722	−	0.817645i	$-0.304721\pi$
$967$	3.34818e7	1.15144	0.575722	+	0.817645i	$0.304721\pi$
$968$	−3.02334e7	−1.03705
$969$	7.67488e6	0.262580
$970$	−2.24842e7	−0.767269
$971$	4.76036e6	0.162029	0.0810143	−	0.996713i	$-0.474184\pi$
$971$	4.76036e6	0.162029	0.0810143	+	0.996713i	$0.474184\pi$
$972$	−2.22090e6	−0.0753986
$973$	0	0
$974$	−4.84739e7	−1.63723
$975$	1.81142e6	0.0610250
$976$	−3.17431e6	−0.106666
$977$	2.87338e7	0.963067	0.481534	−	0.876428i	$-0.340080\pi$
$977$	2.87338e7	0.963067	0.481534	+	0.876428i	$0.340080\pi$
$978$	2.25385e6	0.0753490
$979$	−5.06430e6	−0.168874
$980$	0	0
$981$	9.05437e6	0.300390
$982$	4.16428e7	1.37804
$983$	−4.97072e7	−1.64072	−0.820362	−	0.571845i	$-0.806228\pi$
$983$	−4.97072e7	−1.64072	−0.820362	+	0.571845i	$0.806228\pi$
$984$	−1.42615e6	−0.0469546
$985$	−2.00435e7	−0.658239
$986$	7.35092e6	0.240796
$987$	0	0
$988$	−7.27054e6	−0.236960
$989$	−6.00511e6	−0.195223
$990$	3.65814e6	0.118624
$991$	−2.91066e6	−0.0941471	−0.0470736	−	0.998891i	$-0.514990\pi$
$991$	−2.91066e6	−0.0941471	−0.0470736	+	0.998891i	$0.514990\pi$
$992$	−1.34639e7	−0.434401
$993$	1.47803e6	0.0475676
$994$	0	0
$995$	−1.79309e7	−0.574176
$996$	315545.	0.0100789
$997$	1.43353e7	0.456740	0.228370	−	0.973574i	$-0.426660\pi$
$997$	1.43353e7	0.456740	0.228370	+	0.973574i	$0.426660\pi$
$998$	2.19289e7	0.696933
$999$	−1.03834e7	−0.329174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.a.d.1.1		2
3.2	odd	2		441.6.a.n.1.2		2
4.3	odd	2		784.6.a.ba.1.1		2
7.2	even	3		7.6.c.a.4.2	yes	4
7.3	odd	6		49.6.c.f.30.2		4
7.4	even	3		7.6.c.a.2.2	✓	4
7.5	odd	6		49.6.c.f.18.2		4
7.6	odd	2		49.6.a.e.1.1		2
21.2	odd	6		63.6.e.d.46.1		4
21.11	odd	6		63.6.e.d.37.1		4
21.20	even	2		441.6.a.m.1.2		2
28.11	odd	6		112.6.i.c.65.2		4
28.23	odd	6		112.6.i.c.81.2		4
28.27	even	2		784.6.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.6.c.a.2.2	✓	4	7.4	even	3
7.6.c.a.4.2	yes	4	7.2	even	3
49.6.a.d.1.1		2	1.1	even	1	trivial
49.6.a.e.1.1		2	7.6	odd	2
49.6.c.f.18.2		4	7.5	odd	6
49.6.c.f.30.2		4	7.3	odd	6
63.6.e.d.37.1		4	21.11	odd	6
63.6.e.d.46.1		4	21.2	odd	6
112.6.i.c.65.2		4	28.11	odd	6
112.6.i.c.81.2		4	28.23	odd	6
441.6.a.m.1.2		2	21.20	even	2
441.6.a.n.1.2		2	3.2	odd	2
784.6.a.t.1.2		2	28.27	even	2
784.6.a.ba.1.1		2	4.3	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-5.08276 q^{2} +2.08276 q^{3} -6.16553 q^{4} +41.8276 q^{5} -10.5862 q^{6} +193.986 q^{8} -238.662 q^{9} +O(q^{10})\)	\(q-5.08276 q^{2} +2.08276 q^{3} -6.16553 q^{4} +41.8276 q^{5} -10.5862 q^{6} +193.986 q^{8} -238.662 q^{9} -212.600 q^{10} +72.0965 q^{11} -12.8413 q^{12} -632.317 q^{13} +87.1170 q^{15} -788.689 q^{16} -1975.92 q^{17} +1213.06 q^{18} -1864.93 q^{19} -257.889 q^{20} -366.449 q^{22} +413.711 q^{23} +404.027 q^{24} -1375.45 q^{25} +3213.92 q^{26} -1003.19 q^{27} +731.934 q^{29} -442.795 q^{30} +6123.18 q^{31} -2198.84 q^{32} +150.160 q^{33} +10043.2 q^{34} +1471.48 q^{36} +10350.4 q^{37} +9478.97 q^{38} -1316.97 q^{39} +8113.99 q^{40} -3529.84 q^{41} -14515.2 q^{43} -444.513 q^{44} -9982.67 q^{45} -2102.79 q^{46} -21423.3 q^{47} -1642.65 q^{48} +6991.08 q^{50} -4115.38 q^{51} +3898.57 q^{52} +12579.5 q^{53} +5098.97 q^{54} +3015.62 q^{55} -3884.20 q^{57} -3720.25 q^{58} -36133.9 q^{59} -537.122 q^{60} +4024.80 q^{61} -31122.6 q^{62} +36414.2 q^{64} -26448.3 q^{65} -763.227 q^{66} +15565.9 q^{67} +12182.6 q^{68} +861.661 q^{69} +12180.8 q^{71} -46297.2 q^{72} +19589.1 q^{73} -52608.5 q^{74} -2864.74 q^{75} +11498.2 q^{76} +6693.83 q^{78} +36089.8 q^{79} -32989.0 q^{80} +55905.5 q^{81} +17941.3 q^{82} -24572.6 q^{83} -82648.2 q^{85} +73777.5 q^{86} +1524.44 q^{87} +13985.7 q^{88} -70243.3 q^{89} +50739.5 q^{90} -2550.74 q^{92} +12753.1 q^{93} +108890. q^{94} -78005.4 q^{95} -4579.66 q^{96} +105758. q^{97} -17206.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 8 q^{3} + 12 q^{4} - 38 q^{5} - 82 q^{6} + 96 q^{8} - 380 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 8 * q^3 + 12 * q^4 - 38 * q^5 - 82 * q^6 + 96 * q^8 - 380 * q^9	\( 2 q + 2 q^{2} - 8 q^{3} + 12 q^{4} - 38 q^{5} - 82 q^{6} + 96 q^{8} - 380 q^{9} - 778 q^{10} + 424 q^{11} - 196 q^{12} - 924 q^{13} + 892 q^{15} - 2064 q^{16} - 2346 q^{17} + 212 q^{18} - 360 q^{19} - 1708 q^{20} + 2126 q^{22} - 12 q^{23} + 1392 q^{24} + 1872 q^{25} + 1148 q^{26} + 2872 q^{27} - 7052 q^{29} + 5258 q^{30} + 3548 q^{31} - 8096 q^{32} - 3398 q^{33} + 7422 q^{34} - 1096 q^{36} + 11090 q^{37} + 20138 q^{38} + 1624 q^{39} + 15936 q^{40} + 3500 q^{41} - 12680 q^{43} + 5948 q^{44} + 1300 q^{45} - 5118 q^{46} - 22956 q^{47} + 11216 q^{48} + 29992 q^{50} - 384 q^{51} - 1400 q^{52} + 3042 q^{53} + 32546 q^{54} - 25076 q^{55} - 19058 q^{57} - 58852 q^{58} - 65808 q^{59} + 14084 q^{60} - 42486 q^{61} - 49362 q^{62} + 35456 q^{64} - 3164 q^{65} - 25894 q^{66} + 42312 q^{67} + 5460 q^{68} + 5154 q^{69} - 2208 q^{71} - 32448 q^{72} - 50506 q^{73} - 47370 q^{74} - 35608 q^{75} + 38836 q^{76} + 27524 q^{78} + 9004 q^{79} + 68816 q^{80} + 51178 q^{81} + 67732 q^{82} - 104328 q^{83} - 53106 q^{85} + 86776 q^{86} + 80008 q^{87} - 20496 q^{88} - 26666 q^{89} + 130652 q^{90} - 10284 q^{92} + 38718 q^{93} + 98034 q^{94} - 198140 q^{95} + 54880 q^{96} + 209132 q^{97} - 66944 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 8 * q^3 + 12 * q^4 - 38 * q^5 - 82 * q^6 + 96 * q^8 - 380 * q^9 - 778 * q^10 + 424 * q^11 - 196 * q^12 - 924 * q^13 + 892 * q^15 - 2064 * q^16 - 2346 * q^17 + 212 * q^18 - 360 * q^19 - 1708 * q^20 + 2126 * q^22 - 12 * q^23 + 1392 * q^24 + 1872 * q^25 + 1148 * q^26 + 2872 * q^27 - 7052 * q^29 + 5258 * q^30 + 3548 * q^31 - 8096 * q^32 - 3398 * q^33 + 7422 * q^34 - 1096 * q^36 + 11090 * q^37 + 20138 * q^38 + 1624 * q^39 + 15936 * q^40 + 3500 * q^41 - 12680 * q^43 + 5948 * q^44 + 1300 * q^45 - 5118 * q^46 - 22956 * q^47 + 11216 * q^48 + 29992 * q^50 - 384 * q^51 - 1400 * q^52 + 3042 * q^53 + 32546 * q^54 - 25076 * q^55 - 19058 * q^57 - 58852 * q^58 - 65808 * q^59 + 14084 * q^60 - 42486 * q^61 - 49362 * q^62 + 35456 * q^64 - 3164 * q^65 - 25894 * q^66 + 42312 * q^67 + 5460 * q^68 + 5154 * q^69 - 2208 * q^71 - 32448 * q^72 - 50506 * q^73 - 47370 * q^74 - 35608 * q^75 + 38836 * q^76 + 27524 * q^78 + 9004 * q^79 + 68816 * q^80 + 51178 * q^81 + 67732 * q^82 - 104328 * q^83 - 53106 * q^85 + 86776 * q^86 + 80008 * q^87 - 20496 * q^88 - 26666 * q^89 + 130652 * q^90 - 10284 * q^92 + 38718 * q^93 + 98034 * q^94 - 198140 * q^95 + 54880 * q^96 + 209132 * q^97 - 66944 * q^99

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