LMFDB - Embedded newform 245.6.a.l.1.10

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			1.10
Root			$-9.33424$ 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)

$f(q)$	$=$	$q+10.3342 q^{2} -10.7786 q^{3} +74.7964 q^{4} -25.0000 q^{5} -111.389 q^{6} +442.268 q^{8} -126.821 q^{9} +O(q^{10})$	\(q+10.3342 q^{2} -10.7786 q^{3} +74.7964 q^{4} -25.0000 q^{5} -111.389 q^{6} +442.268 q^{8} -126.821 q^{9} -258.356 q^{10} -262.917 q^{11} -806.204 q^{12} -688.927 q^{13} +269.466 q^{15} +2177.02 q^{16} -1678.08 q^{17} -1310.60 q^{18} -925.109 q^{19} -1869.91 q^{20} -2717.05 q^{22} +4608.33 q^{23} -4767.06 q^{24} +625.000 q^{25} -7119.53 q^{26} +3986.17 q^{27} -3413.30 q^{29} +2784.73 q^{30} +5534.34 q^{31} +8345.25 q^{32} +2833.89 q^{33} -17341.7 q^{34} -9485.74 q^{36} -14971.8 q^{37} -9560.29 q^{38} +7425.70 q^{39} -11056.7 q^{40} -14959.7 q^{41} -19652.7 q^{43} -19665.3 q^{44} +3170.52 q^{45} +47623.6 q^{46} +11299.0 q^{47} -23465.3 q^{48} +6458.90 q^{50} +18087.4 q^{51} -51529.3 q^{52} -21380.7 q^{53} +41194.0 q^{54} +6572.93 q^{55} +9971.42 q^{57} -35273.8 q^{58} +3476.31 q^{59} +20155.1 q^{60} +22396.1 q^{61} +57193.2 q^{62} +16577.2 q^{64} +17223.2 q^{65} +29286.1 q^{66} +44935.8 q^{67} -125514. q^{68} -49671.6 q^{69} +10904.9 q^{71} -56088.8 q^{72} +9209.41 q^{73} -154722. q^{74} -6736.65 q^{75} -69194.8 q^{76} +76738.9 q^{78} -3355.92 q^{79} -54425.5 q^{80} -12148.1 q^{81} -154597. q^{82} -45537.7 q^{83} +41951.9 q^{85} -203096. q^{86} +36790.7 q^{87} -116280. q^{88} +52889.1 q^{89} +32764.9 q^{90} +344687. q^{92} -59652.7 q^{93} +116766. q^{94} +23127.7 q^{95} -89950.5 q^{96} +164527. q^{97} +33343.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.3342	1.82685	0.913426	−	0.407005i	$-0.133427\pi$
$2$	10.3342	1.82685	0.913426	+	0.407005i	$0.133427\pi$
$3$	−10.7786	−0.691451	−0.345725	−	0.938336i	$-0.612367\pi$
$3$	−10.7786	−0.691451	−0.345725	+	0.938336i	$0.612367\pi$
$4$	74.7964	2.33739
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−111.389	−1.26318
$7$	0	0
$7$	0	0
$8$	442.268	2.44321
$9$	−126.821	−0.521896
$10$	−258.356	−0.816993
$11$	−262.917	−0.655145	−0.327572	−	0.944826i	$-0.606231\pi$
$11$	−262.917	−0.655145	−0.327572	+	0.944826i	$0.606231\pi$
$12$	−806.204	−1.61619
$13$	−688.927	−1.13061	−0.565307	−	0.824880i	$-0.691242\pi$
$13$	−688.927	−1.13061	−0.565307	+	0.824880i	$0.691242\pi$
$14$	0	0
$15$	269.466	0.309226
$16$	2177.02	2.12600
$17$	−1678.08	−1.40828	−0.704141	−	0.710060i	$-0.748668\pi$
$17$	−1678.08	−1.40828	−0.704141	+	0.710060i	$0.748668\pi$
$18$	−1310.60	−0.953427
$19$	−925.109	−0.587907	−0.293954	−	0.955820i	$-0.594971\pi$
$19$	−925.109	−0.587907	−0.293954	+	0.955820i	$0.594971\pi$
$20$	−1869.91	−1.04531
$21$	0	0
$22$	−2717.05	−1.19685
$23$	4608.33	1.81645	0.908226	−	0.418480i	$-0.137437\pi$
$23$	4608.33	1.81645	0.908226	+	0.418480i	$0.137437\pi$
$24$	−4767.06	−1.68936
$25$	625.000	0.200000
$26$	−7119.53	−2.06547
$27$	3986.17	1.05232
$28$	0	0
$29$	−3413.30	−0.753666	−0.376833	−	0.926281i	$-0.622987\pi$
$29$	−3413.30	−0.753666	−0.376833	+	0.926281i	$0.622987\pi$
$30$	2784.73	0.564910
$31$	5534.34	1.03434	0.517168	−	0.855884i	$-0.326986\pi$
$31$	5534.34	1.03434	0.517168	+	0.855884i	$0.326986\pi$
$32$	8345.25	1.44067
$33$	2833.89	0.453000
$34$	−17341.7	−2.57272
$35$	0	0
$36$	−9485.74	−1.21987
$37$	−14971.8	−1.79791	−0.898956	−	0.438038i	$-0.855674\pi$
$37$	−14971.8	−1.79791	−0.898956	+	0.438038i	$0.855674\pi$
$38$	−9560.29	−1.07402
$39$	7425.70	0.781764
$40$	−11056.7	−1.09264
$41$	−14959.7	−1.38983	−0.694916	−	0.719091i	$-0.744558\pi$
$41$	−14959.7	−1.38983	−0.694916	+	0.719091i	$0.744558\pi$
$42$	0	0
$43$	−19652.7	−1.62088	−0.810442	−	0.585818i	$-0.800773\pi$
$43$	−19652.7	−1.62088	−0.810442	+	0.585818i	$0.800773\pi$
$44$	−19665.3	−1.53133
$45$	3170.52	0.233399
$46$	47623.6	3.31839
$47$	11299.0	0.746096	0.373048	−	0.927812i	$-0.378313\pi$
$47$	11299.0	0.746096	0.373048	+	0.927812i	$0.378313\pi$
$48$	−23465.3	−1.47002
$49$	0	0
$50$	6458.90	0.365370
$51$	18087.4	0.973758
$52$	−51529.3	−2.64269
$53$	−21380.7	−1.04552	−0.522759	−	0.852480i	$-0.675097\pi$
$53$	−21380.7	−1.04552	−0.522759	+	0.852480i	$0.675097\pi$
$54$	41194.0	1.92243
$55$	6572.93	0.292990
$56$	0	0
$57$	9971.42	0.406509
$58$	−35273.8	−1.37684
$59$	3476.31	0.130014	0.0650068	−	0.997885i	$-0.479293\pi$
$59$	3476.31	0.130014	0.0650068	+	0.997885i	$0.479293\pi$
$60$	20155.1	0.722782
$61$	22396.1	0.770633	0.385317	−	0.922784i	$-0.374092\pi$
$61$	22396.1	0.770633	0.385317	+	0.922784i	$0.374092\pi$
$62$	57193.2	1.88958
$63$	0	0
$64$	16577.2	0.505895
$65$	17223.2	0.505626
$66$	29286.1	0.827564
$67$	44935.8	1.22294	0.611470	−	0.791267i	$-0.290578\pi$
$67$	44935.8	1.22294	0.611470	+	0.791267i	$0.290578\pi$
$68$	−125514.	−3.29170
$69$	−49671.6	−1.25599
$70$	0	0
$71$	10904.9	0.256729	0.128365	−	0.991727i	$-0.459027\pi$
$71$	10904.9	0.256729	0.128365	+	0.991727i	$0.459027\pi$
$72$	−56088.8	−1.27510
$73$	9209.41	0.202267	0.101133	−	0.994873i	$-0.467753\pi$
$73$	9209.41	0.202267	0.101133	+	0.994873i	$0.467753\pi$
$74$	−154722.	−3.28452
$75$	−6736.65	−0.138290
$76$	−69194.8	−1.37417
$77$	0	0
$78$	76738.9	1.42817
$79$	−3355.92	−0.0604984	−0.0302492	−	0.999542i	$-0.509630\pi$
$79$	−3355.92	−0.0604984	−0.0302492	+	0.999542i	$0.509630\pi$
$80$	−54425.5	−0.950775
$81$	−12148.1	−0.205728
$82$	−154597.	−2.53902
$83$	−45537.7	−0.725565	−0.362782	−	0.931874i	$-0.618173\pi$
$83$	−45537.7	−0.725565	−0.362782	+	0.931874i	$0.618173\pi$
$84$	0	0
$85$	41951.9	0.629803
$86$	−203096.	−2.96112
$87$	36790.7	0.521123
$88$	−116280.	−1.60066
$89$	52889.1	0.707768	0.353884	−	0.935289i	$-0.384861\pi$
$89$	52889.1	0.707768	0.353884	+	0.935289i	$0.384861\pi$
$90$	32764.9	0.426386
$91$	0	0
$92$	344687.	4.24575
$93$	−59652.7	−0.715193
$94$	116766.	1.36301
$95$	23127.7	0.262920
$96$	−89950.5	−0.996152
$97$	164527.	1.77545	0.887725	−	0.460375i	$-0.152285\pi$
$97$	164527.	1.77545	0.887725	+	0.460375i	$0.152285\pi$
$98$	0	0
$99$	33343.4	0.341917
$100$	46747.8	0.467478
$101$	−24003.0	−0.234132	−0.117066	−	0.993124i	$-0.537349\pi$
$101$	−24003.0	−0.234132	−0.117066	+	0.993124i	$0.537349\pi$
$102$	186920.	1.77891
$103$	110339.	1.02479	0.512394	−	0.858750i	$-0.328759\pi$
$103$	110339.	1.02479	0.512394	+	0.858750i	$0.328759\pi$
$104$	−304690.	−2.76233
$105$	0	0
$106$	−220953.	−1.91001
$107$	90804.3	0.766738	0.383369	−	0.923595i	$-0.374764\pi$
$107$	90804.3	0.766738	0.383369	+	0.923595i	$0.374764\pi$
$108$	298151.	2.45967
$109$	141520.	1.14091	0.570454	−	0.821330i	$-0.306767\pi$
$109$	141520.	1.14091	0.570454	+	0.821330i	$0.306767\pi$
$110$	67926.2	0.535249
$111$	161375.	1.24317
$112$	0	0
$113$	−116848.	−0.860845	−0.430423	−	0.902627i	$-0.641636\pi$
$113$	−116848.	−0.860845	−0.430423	+	0.902627i	$0.641636\pi$
$114$	103047.	0.742631
$115$	−115208.	−0.812342
$116$	−255303.	−1.76161
$117$	87370.2	0.590063
$118$	35925.0	0.237516
$119$	0	0
$120$	119176.	0.755505
$121$	−91925.6	−0.570785
$122$	231447.	1.40783
$123$	161245.	0.961000
$124$	413949.	2.41765
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−147879.	−0.813574	−0.406787	−	0.913523i	$-0.633351\pi$
$127$	−147879.	−0.813574	−0.406787	+	0.913523i	$0.633351\pi$
$128$	−95735.8	−0.516475
$129$	211830.	1.12076
$130$	177988.	0.923704
$131$	73626.8	0.374850	0.187425	−	0.982279i	$-0.439986\pi$
$131$	73626.8	0.374850	0.187425	+	0.982279i	$0.439986\pi$
$132$	211965.	1.05884
$133$	0	0
$134$	464377.	2.23413
$135$	−99654.2	−0.470610
$136$	−742161.	−3.44073
$137$	338575.	1.54118	0.770589	−	0.637332i	$-0.219962\pi$
$137$	338575.	1.54118	0.770589	+	0.637332i	$0.219962\pi$
$138$	−513318.	−2.29450
$139$	−372518.	−1.63535	−0.817675	−	0.575680i	$-0.804737\pi$
$139$	−372518.	−1.63535	−0.817675	+	0.575680i	$0.804737\pi$
$140$	0	0
$141$	−121788.	−0.515889
$142$	112694.	0.469006
$143$	181131.	0.740716
$144$	−276091.	−1.10955
$145$	85332.4	0.337050
$146$	95172.2	0.369511
$147$	0	0
$148$	−1.11983e6	−4.20242
$149$	−155353.	−0.573263	−0.286632	−	0.958041i	$-0.592536\pi$
$149$	−155353.	−0.573263	−0.286632	+	0.958041i	$0.592536\pi$
$150$	−69618.2	−0.252636
$151$	220907.	0.788439	0.394219	−	0.919016i	$-0.371015\pi$
$151$	220907.	0.788439	0.394219	+	0.919016i	$0.371015\pi$
$152$	−409146.	−1.43638
$153$	212815.	0.734977
$154$	0	0
$155$	−138359.	−0.462569
$156$	555416.	1.82729
$157$	−543726.	−1.76048	−0.880240	−	0.474529i	$-0.842618\pi$
$157$	−543726.	−1.76048	−0.880240	+	0.474529i	$0.842618\pi$
$158$	−34680.9	−0.110522
$159$	230455.	0.722925
$160$	−208631.	−0.644287
$161$	0	0
$162$	−125541.	−0.375835
$163$	11753.3	0.0346490	0.0173245	−	0.999850i	$-0.494485\pi$
$163$	11753.3	0.0346490	0.0173245	+	0.999850i	$0.494485\pi$
$164$	−1.11893e6	−3.24858
$165$	−70847.3	−0.202588
$166$	−470598.	−1.32550
$167$	−38571.8	−0.107023	−0.0535117	−	0.998567i	$-0.517041\pi$
$167$	−38571.8	−0.107023	−0.0535117	+	0.998567i	$0.517041\pi$
$168$	0	0
$169$	103327.	0.278289
$170$	433541.	1.15056
$171$	117323.	0.306826
$172$	−1.46996e6	−3.78864
$173$	−26934.3	−0.0684213	−0.0342106	−	0.999415i	$-0.510892\pi$
$173$	−26934.3	−0.0684213	−0.0342106	+	0.999415i	$0.510892\pi$
$174$	380204.	0.952015
$175$	0	0
$176$	−572376.	−1.39284
$177$	−37469.9	−0.0898979
$178$	546568.	1.29299
$179$	261941.	0.611041	0.305521	−	0.952185i	$-0.401170\pi$
$179$	261941.	0.611041	0.305521	+	0.952185i	$0.401170\pi$
$180$	237144.	0.545544
$181$	−447956.	−1.01634	−0.508170	−	0.861257i	$-0.669678\pi$
$181$	−447956.	−1.01634	−0.508170	+	0.861257i	$0.669678\pi$
$182$	0	0
$183$	−241400.	−0.532855
$184$	2.03812e6	4.43798
$185$	374294.	0.804051
$186$	−616465.	−1.30655
$187$	441195.	0.922629
$188$	845124.	1.74392
$189$	0	0
$190$	239007.	0.480316
$191$	−159526.	−0.316409	−0.158204	−	0.987406i	$-0.550570\pi$
$191$	−159526.	−0.316409	−0.158204	+	0.987406i	$0.550570\pi$
$192$	−178679.	−0.349801
$193$	348995.	0.674413	0.337207	−	0.941431i	$-0.390518\pi$
$193$	348995.	0.674413	0.337207	+	0.941431i	$0.390518\pi$
$194$	1.70026e6	3.24348
$195$	−185642.	−0.349616
$196$	0	0
$197$	−459058.	−0.842755	−0.421378	−	0.906885i	$-0.638453\pi$
$197$	−459058.	−0.842755	−0.421378	+	0.906885i	$0.638453\pi$
$198$	344578.	0.624633
$199$	−1.02765e6	−1.83955	−0.919776	−	0.392444i	$-0.871630\pi$
$199$	−1.02765e6	−1.83955	−0.919776	+	0.392444i	$0.871630\pi$
$200$	276418.	0.488642
$201$	−484347.	−0.845603
$202$	−248052.	−0.427725
$203$	0	0
$204$	1.35287e6	2.27605
$205$	373992.	0.621552
$206$	1.14026e6	1.87214
$207$	−584432.	−0.947999
$208$	−1.49981e6	−2.40368
$209$	243227.	0.385164
$210$	0	0
$211$	−854033.	−1.32059	−0.660296	−	0.751006i	$-0.729569\pi$
$211$	−854033.	−1.32059	−0.660296	+	0.751006i	$0.729569\pi$
$212$	−1.59920e6	−2.44378
$213$	−117540.	−0.177515
$214$	938393.	1.40072
$215$	491319.	0.724882
$216$	1.76296e6	2.57103
$217$	0	0
$218$	1.46250e6	2.08427
$219$	−99264.9	−0.139857
$220$	491632.	0.684831
$221$	1.15607e6	1.59222
$222$	1.66769e6	2.27108
$223$	−274209.	−0.369249	−0.184625	−	0.982809i	$-0.559107\pi$
$223$	−274209.	−0.369249	−0.184625	+	0.982809i	$0.559107\pi$
$224$	0	0
$225$	−79263.0	−0.104379
$226$	−1.20753e6	−1.57264
$227$	1.32207e6	1.70290	0.851450	−	0.524435i	$-0.175724\pi$
$227$	1.32207e6	1.70290	0.851450	+	0.524435i	$0.175724\pi$
$228$	745827.	0.950169
$229$	−163985.	−0.206640	−0.103320	−	0.994648i	$-0.532947\pi$
$229$	−163985.	−0.206640	−0.103320	+	0.994648i	$0.532947\pi$
$230$	−1.19059e6	−1.48403
$231$	0	0
$232$	−1.50959e6	−1.84137
$233$	−1.10695e6	−1.33579	−0.667895	−	0.744256i	$-0.732804\pi$
$233$	−1.10695e6	−1.33579	−0.667895	+	0.744256i	$0.732804\pi$
$234$	902904.	1.07796
$235$	−282475.	−0.333664
$236$	260016.	0.303892
$237$	36172.3	0.0418316
$238$	0	0
$239$	576115.	0.652401	0.326200	−	0.945301i	$-0.394232\pi$
$239$	576115.	0.652401	0.326200	+	0.945301i	$0.394232\pi$
$240$	586633.	0.657414
$241$	1.01805e6	1.12908	0.564541	−	0.825405i	$-0.309053\pi$
$241$	1.01805e6	1.12908	0.564541	+	0.825405i	$0.309053\pi$
$242$	−949980.	−1.04274
$243$	−837699.	−0.910065
$244$	1.67515e6	1.80127
$245$	0	0
$246$	1.66634e6	1.75561
$247$	637332.	0.664696
$248$	2.44767e6	2.52710
$249$	490835.	0.501692
$250$	−161472.	−0.163399
$251$	44770.6	0.0448548	0.0224274	−	0.999748i	$-0.492861\pi$
$251$	44770.6	0.0448548	0.0224274	+	0.999748i	$0.492861\pi$
$252$	0	0
$253$	−1.21161e6	−1.19004
$254$	−1.52822e6	−1.48628
$255$	−452185.	−0.435478
$256$	−1.51983e6	−1.44942
$257$	−300025.	−0.283351	−0.141676	−	0.989913i	$-0.545249\pi$
$257$	−300025.	−0.283351	−0.141676	+	0.989913i	$0.545249\pi$
$258$	2.18910e6	2.04747
$259$	0	0
$260$	1.28823e6	1.18184
$261$	432877.	0.393336
$262$	760877.	0.684796
$263$	−151046.	−0.134654	−0.0673271	−	0.997731i	$-0.521447\pi$
$263$	−151046.	−0.134654	−0.0673271	+	0.997731i	$0.521447\pi$
$264$	1.25334e6	1.10677
$265$	534517.	0.467570
$266$	0	0
$267$	−570073.	−0.489387
$268$	3.36104e6	2.85849
$269$	−1.18347e6	−0.997191	−0.498595	−	0.866835i	$-0.666151\pi$
$269$	−1.18347e6	−0.997191	−0.498595	+	0.866835i	$0.666151\pi$
$270$	−1.02985e6	−0.859735
$271$	1.43453e6	1.18655	0.593276	−	0.804999i	$-0.297834\pi$
$271$	1.43453e6	1.18655	0.593276	+	0.804999i	$0.297834\pi$
$272$	−3.65321e6	−2.99400
$273$	0	0
$274$	3.49891e6	2.81551
$275$	−164323.	−0.131029
$276$	−3.71526e6	−2.93573
$277$	−485316.	−0.380036	−0.190018	−	0.981781i	$-0.560855\pi$
$277$	−485316.	−0.380036	−0.190018	+	0.981781i	$0.560855\pi$
$278$	−3.84969e6	−2.98754
$279$	−701870.	−0.539816
$280$	0	0
$281$	110465.	0.0834564	0.0417282	−	0.999129i	$-0.486714\pi$
$281$	110465.	0.0834564	0.0417282	+	0.999129i	$0.486714\pi$
$282$	−1.25858e6	−0.942452
$283$	−324717.	−0.241012	−0.120506	−	0.992713i	$-0.538452\pi$
$283$	−324717.	−0.241012	−0.120506	+	0.992713i	$0.538452\pi$
$284$	815646.	0.600076
$285$	−249286.	−0.181796
$286$	1.87185e6	1.35318
$287$	0	0
$288$	−1.05835e6	−0.751880
$289$	1.39609e6	0.983259
$290$	881846.	0.615740
$291$	−1.77338e6	−1.22764
$292$	688831.	0.472776
$293$	−1.30456e6	−0.887758	−0.443879	−	0.896087i	$-0.646398\pi$
$293$	−1.30456e6	−0.887758	−0.443879	+	0.896087i	$0.646398\pi$
$294$	0	0
$295$	−86907.8	−0.0581438
$296$	−6.62154e6	−4.39268
$297$	−1.04803e6	−0.689419
$298$	−1.60545e6	−1.04727
$299$	−3.17480e6	−2.05371
$300$	−503878.	−0.323238
$301$	0	0
$302$	2.28291e6	1.44036
$303$	258720.	0.161891
$304$	−2.01398e6	−1.24989
$305$	−559903.	−0.344638
$306$	2.19928e6	1.34269
$307$	774592.	0.469058	0.234529	−	0.972109i	$-0.424645\pi$
$307$	774592.	0.469058	0.234529	+	0.972109i	$0.424645\pi$
$308$	0	0
$309$	−1.18930e6	−0.708590
$310$	−1.42983e6	−0.845046
$311$	−3.06756e6	−1.79842	−0.899211	−	0.437515i	$-0.855859\pi$
$311$	−3.06756e6	−1.79842	−0.899211	+	0.437515i	$0.855859\pi$
$312$	3.28415e6	1.91001
$313$	−949654.	−0.547904	−0.273952	−	0.961743i	$-0.588331\pi$
$313$	−949654.	−0.547904	−0.273952	+	0.961743i	$0.588331\pi$
$314$	−5.61899e6	−3.21614
$315$	0	0
$316$	−251011.	−0.141408
$317$	2.31477e6	1.29378	0.646889	−	0.762584i	$-0.276070\pi$
$317$	2.31477e6	1.29378	0.646889	+	0.762584i	$0.276070\pi$
$318$	2.38157e6	1.32068
$319$	897415.	0.493761
$320$	−414429.	−0.226243
$321$	−978747.	−0.530161
$322$	0	0
$323$	1.55240e6	0.827939
$324$	−908631.	−0.480867
$325$	−430579.	−0.226123
$326$	121461.	0.0632986
$327$	−1.52539e6	−0.788881
$328$	−6.61619e6	−3.39565
$329$	0	0
$330$	−732153.	−0.370098
$331$	−300877.	−0.150945	−0.0754726	−	0.997148i	$-0.524047\pi$
$331$	−300877.	−0.150945	−0.0754726	+	0.997148i	$0.524047\pi$
$332$	−3.40606e6	−1.69593
$333$	1.89873e6	0.938324
$334$	−398610.	−0.195516
$335$	−1.12339e6	−0.546916
$336$	0	0
$337$	−484462.	−0.232373	−0.116186	−	0.993227i	$-0.537067\pi$
$337$	−484462.	−0.232373	−0.116186	+	0.993227i	$0.537067\pi$
$338$	1.06780e6	0.508394
$339$	1.25946e6	0.595232
$340$	3.13786e6	1.47209
$341$	−1.45507e6	−0.677640
$342$	1.21244e6	0.560527
$343$	0	0
$344$	−8.69179e6	−3.96016
$345$	1.24179e6	0.561694
$346$	−278346.	−0.124996
$347$	3.02605e6	1.34912	0.674562	−	0.738218i	$-0.264332\pi$
$347$	3.02605e6	1.34912	0.674562	+	0.738218i	$0.264332\pi$
$348$	2.75182e6	1.21807
$349$	2.48201e6	1.09079	0.545393	−	0.838181i	$-0.316381\pi$
$349$	2.48201e6	1.09079	0.545393	+	0.838181i	$0.316381\pi$
$350$	0	0
$351$	−2.74618e6	−1.18976
$352$	−2.19411e6	−0.943847
$353$	−3.77106e6	−1.61075	−0.805373	−	0.592768i	$-0.798035\pi$
$353$	−3.77106e6	−1.61075	−0.805373	+	0.592768i	$0.798035\pi$
$354$	−387223.	−0.164230
$355$	−272622.	−0.114813
$356$	3.95591e6	1.65433
$357$	0	0
$358$	2.70696e6	1.11628
$359$	199028.	0.0815039	0.0407519	−	0.999169i	$-0.487025\pi$
$359$	199028.	0.0815039	0.0407519	+	0.999169i	$0.487025\pi$
$360$	1.40222e6	0.570243
$361$	−1.62027e6	−0.654365
$362$	−4.62929e6	−1.85670
$363$	990833.	0.394670
$364$	0	0
$365$	−230235.	−0.0904564
$366$	−2.49468e6	−0.973447
$367$	−2.68132e6	−1.03916	−0.519581	−	0.854421i	$-0.673912\pi$
$367$	−2.68132e6	−1.03916	−0.519581	+	0.854421i	$0.673912\pi$
$368$	1.00324e7	3.86177
$369$	1.89720e6	0.725348
$370$	3.86804e6	1.46888
$371$	0	0
$372$	−4.46181e6	−1.67168
$373$	−550183.	−0.204755	−0.102378	−	0.994746i	$-0.532645\pi$
$373$	−550183.	−0.204755	−0.102378	+	0.994746i	$0.532645\pi$
$374$	4.55942e6	1.68551
$375$	168416.	0.0618452
$376$	4.99718e6	1.82287
$377$	2.35151e6	0.852106
$378$	0	0
$379$	939596.	0.336003	0.168002	−	0.985787i	$-0.446269\pi$
$379$	939596.	0.336003	0.168002	+	0.985787i	$0.446269\pi$
$380$	1.72987e6	0.614546
$381$	1.59394e6	0.562546
$382$	−1.64858e6	−0.578032
$383$	4.48212e6	1.56130	0.780650	−	0.624969i	$-0.214888\pi$
$383$	4.48212e6	1.56130	0.780650	+	0.624969i	$0.214888\pi$
$384$	1.03190e6	0.357117
$385$	0	0
$386$	3.60660e6	1.23205
$387$	2.49238e6	0.845933
$388$	1.23060e7	4.14992
$389$	−5.21921e6	−1.74876	−0.874381	−	0.485241i	$-0.838732\pi$
$389$	−5.21921e6	−1.74876	−0.874381	+	0.485241i	$0.838732\pi$
$390$	−1.91847e6	−0.638696
$391$	−7.73314e6	−2.55808
$392$	0	0
$393$	−793598.	−0.259190
$394$	−4.74401e6	−1.53959
$395$	83898.0	0.0270557
$396$	2.49396e6	0.799194
$397$	−1.06864e6	−0.340294	−0.170147	−	0.985419i	$-0.554424\pi$
$397$	−1.06864e6	−0.340294	−0.170147	+	0.985419i	$0.554424\pi$
$398$	−1.06200e7	−3.36059
$399$	0	0
$400$	1.36064e6	0.425199
$401$	464941.	0.144390	0.0721950	−	0.997391i	$-0.477000\pi$
$401$	464941.	0.144390	0.0721950	+	0.997391i	$0.477000\pi$
$402$	−5.00536e6	−1.54479
$403$	−3.81276e6	−1.16944
$404$	−1.79534e6	−0.547258
$405$	303701.	0.0920045
$406$	0	0
$407$	3.93633e6	1.17789
$408$	7.99949e6	2.37910
$409$	−4.46546e6	−1.31995	−0.659976	−	0.751286i	$-0.729434\pi$
$409$	−4.46546e6	−1.31995	−0.659976	+	0.751286i	$0.729434\pi$
$410$	3.86492e6	1.13548
$411$	−3.64938e6	−1.06565
$412$	8.25293e6	2.39533
$413$	0	0
$414$	−6.03966e6	−1.73185
$415$	1.13844e6	0.324482
$416$	−5.74927e6	−1.62884
$417$	4.01525e6	1.13076
$418$	2.51356e6	0.703638
$419$	−6.25416e6	−1.74034	−0.870170	−	0.492751i	$-0.835991\pi$
$419$	−6.25416e6	−1.74034	−0.870170	+	0.492751i	$0.835991\pi$
$420$	0	0
$421$	5.01694e6	1.37954	0.689768	−	0.724030i	$-0.257712\pi$
$421$	5.01694e6	1.37954	0.689768	+	0.724030i	$0.257712\pi$
$422$	−8.82578e6	−2.41253
$423$	−1.43295e6	−0.389385
$424$	−9.45600e6	−2.55442
$425$	−1.04880e6	−0.281656
$426$	−1.21468e6	−0.324294
$427$	0	0
$428$	6.79183e6	1.79216
$429$	−1.95234e6	−0.512169
$430$	5.07740e6	1.32425
$431$	−4.52767e6	−1.17404	−0.587018	−	0.809574i	$-0.699698\pi$
$431$	−4.52767e6	−1.17404	−0.587018	+	0.809574i	$0.699698\pi$
$432$	8.67797e6	2.23722
$433$	1.88959e6	0.484338	0.242169	−	0.970234i	$-0.422141\pi$
$433$	1.88959e6	0.484338	0.242169	+	0.970234i	$0.422141\pi$
$434$	0	0
$435$	−919768.	−0.233053
$436$	1.05852e7	2.66674
$437$	−4.26321e6	−1.06791
$438$	−1.02583e6	−0.255499
$439$	−5.31281e6	−1.31572	−0.657859	−	0.753141i	$-0.728538\pi$
$439$	−5.31281e6	−1.31572	−0.657859	+	0.753141i	$0.728538\pi$
$440$	2.90700e6	0.715835
$441$	0	0
$442$	1.19471e7	2.90876
$443$	3.37858e6	0.817946	0.408973	−	0.912546i	$-0.365887\pi$
$443$	3.37858e6	0.817946	0.408973	+	0.912546i	$0.365887\pi$
$444$	1.20703e7	2.90577
$445$	−1.32223e6	−0.316524
$446$	−2.83374e6	−0.674564
$447$	1.67450e6	0.396383
$448$	0	0
$449$	−1.32305e6	−0.309714	−0.154857	−	0.987937i	$-0.549492\pi$
$449$	−1.32305e6	−0.309714	−0.154857	+	0.987937i	$0.549492\pi$
$450$	−819122.	−0.190685
$451$	3.93315e6	0.910541
$452$	−8.73981e6	−2.01213
$453$	−2.38108e6	−0.545166
$454$	1.36626e7	3.11095
$455$	0	0
$456$	4.41004e6	0.993187
$457$	−664.505	−0.000148836 0	−7.44179e−5	−	1.00000i	$-0.500024\pi$
$457$	−664.505	−0.000148836 0	−7.44179e−5		1.00000i	$0.500024\pi$
$458$	−1.69466e6	−0.377501
$459$	−6.68910e6	−1.48196
$460$	−8.61717e6	−1.89876
$461$	381694.	0.0836495	0.0418247	−	0.999125i	$-0.486683\pi$
$461$	381694.	0.0836495	0.0418247	+	0.999125i	$0.486683\pi$
$462$	0	0
$463$	−3.44698e6	−0.747284	−0.373642	−	0.927573i	$-0.621891\pi$
$463$	−3.44698e6	−0.747284	−0.373642	+	0.927573i	$0.621891\pi$
$464$	−7.43082e6	−1.60229
$465$	1.49132e6	0.319844
$466$	−1.14395e7	−2.44029
$467$	3.77979e6	0.802002	0.401001	−	0.916078i	$-0.368662\pi$
$467$	3.77979e6	0.802002	0.401001	+	0.916078i	$0.368662\pi$
$468$	6.53498e6	1.37921
$469$	0	0
$470$	−2.91916e6	−0.609555
$471$	5.86063e6	1.21728
$472$	1.53746e6	0.317651
$473$	5.16704e6	1.06191
$474$	373813.	0.0764202
$475$	−578193.	−0.117581
$476$	0	0
$477$	2.71151e6	0.545652
$478$	5.95371e6	1.19184
$479$	3.31921e6	0.660992	0.330496	−	0.943807i	$-0.392784\pi$
$479$	3.31921e6	0.660992	0.330496	+	0.943807i	$0.392784\pi$
$480$	2.24876e6	0.445493
$481$	1.03144e7	2.03275
$482$	1.05207e7	2.06267
$483$	0	0
$484$	−6.87570e6	−1.33415
$485$	−4.11318e6	−0.794005
$486$	−8.65698e6	−1.66255
$487$	−2.61900e6	−0.500394	−0.250197	−	0.968195i	$-0.580495\pi$
$487$	−2.61900e6	−0.500394	−0.250197	+	0.968195i	$0.580495\pi$
$488$	9.90509e6	1.88282
$489$	−126685.	−0.0239581
$490$	0	0
$491$	−1.05614e7	−1.97706	−0.988528	−	0.151035i	$-0.951739\pi$
$491$	−1.05614e7	−1.97706	−0.988528	+	0.151035i	$0.951739\pi$
$492$	1.20606e7	2.24623
$493$	5.72778e6	1.06138
$494$	6.58634e6	1.21430
$495$	−833584.	−0.152910
$496$	1.20484e7	2.19900
$497$	0	0
$498$	5.07241e6	0.916517
$499$	−605466.	−0.108852	−0.0544262	−	0.998518i	$-0.517333\pi$
$499$	−605466.	−0.108852	−0.0544262	+	0.998518i	$0.517333\pi$
$500$	−1.16869e6	−0.209062
$501$	415752.	0.0740014
$502$	462670.	0.0819431
$503$	−511276.	−0.0901023	−0.0450511	−	0.998985i	$-0.514345\pi$
$503$	−511276.	−0.0901023	−0.0450511	+	0.998985i	$0.514345\pi$
$504$	0	0
$505$	600074.	0.104707
$506$	−1.25211e7	−2.17403
$507$	−1.11372e6	−0.192423
$508$	−1.10608e7	−1.90164
$509$	−6.53778e6	−1.11850	−0.559250	−	0.828999i	$-0.688911\pi$
$509$	−6.53778e6	−1.11850	−0.559250	+	0.828999i	$0.688911\pi$
$510$	−4.67299e6	−0.795553
$511$	0	0
$512$	−1.26427e7	−2.13140
$513$	−3.68764e6	−0.618664
$514$	−3.10053e6	−0.517641
$515$	−2.75846e6	−0.458299
$516$	1.58441e7	2.61966
$517$	−2.97070e6	−0.488801
$518$	0	0
$519$	290316.	0.0473099
$520$	7.61726e6	1.23535
$521$	4.28064e6	0.690899	0.345449	−	0.938437i	$-0.387727\pi$
$521$	4.28064e6	0.690899	0.345449	+	0.938437i	$0.387727\pi$
$522$	4.47345e6	0.718566
$523$	5.42616e6	0.867438	0.433719	−	0.901048i	$-0.357201\pi$
$523$	5.42616e6	0.867438	0.433719	+	0.901048i	$0.357201\pi$
$524$	5.50702e6	0.876171
$525$	0	0
$526$	−1.56095e6	−0.245993
$527$	−9.28706e6	−1.45664
$528$	6.16944e6	0.963077
$529$	1.48004e7	2.29950
$530$	5.52383e6	0.854182
$531$	−440868.	−0.0678536
$532$	0	0
$533$	1.03061e7	1.57136
$534$	−5.89127e6	−0.894037
$535$	−2.27011e6	−0.342896
$536$	1.98737e7	2.98790
$537$	−2.82337e6	−0.422505
$538$	−1.22303e7	−1.82172
$539$	0	0
$540$	−7.45378e6	−1.10000
$541$	−6.45696e6	−0.948495	−0.474248	−	0.880392i	$-0.657280\pi$
$541$	−6.45696e6	−0.948495	−0.474248	+	0.880392i	$0.657280\pi$
$542$	1.48248e7	2.16766
$543$	4.82836e6	0.702749
$544$	−1.40040e7	−2.02887
$545$	−3.53799e6	−0.510229
$546$	0	0
$547$	5.38834e6	0.769993	0.384996	−	0.922918i	$-0.374203\pi$
$547$	5.38834e6	0.769993	0.384996	+	0.922918i	$0.374203\pi$
$548$	2.53242e7	3.60233
$549$	−2.84029e6	−0.402191
$550$	−1.69815e6	−0.239370
$551$	3.15767e6	0.443086
$552$	−2.19682e7	−3.06864
$553$	0	0
$554$	−5.01537e6	−0.694270
$555$	−4.03438e6	−0.555962
$556$	−2.78631e7	−3.82245
$557$	1.09891e7	1.50080	0.750400	−	0.660984i	$-0.229861\pi$
$557$	1.09891e7	1.50080	0.750400	+	0.660984i	$0.229861\pi$
$558$	−7.25329e6	−0.986164
$559$	1.35393e7	1.83260
$560$	0	0
$561$	−4.75549e6	−0.637952
$562$	1.14157e6	0.152462
$563$	−2.71099e6	−0.360460	−0.180230	−	0.983625i	$-0.557684\pi$
$563$	−2.71099e6	−0.360460	−0.180230	+	0.983625i	$0.557684\pi$
$564$	−9.10929e6	−1.20583
$565$	2.92120e6	0.384982
$566$	−3.35571e6	−0.440294
$567$	0	0
$568$	4.82288e6	0.627243
$569$	9.28980e6	1.20289	0.601444	−	0.798915i	$-0.294592\pi$
$569$	9.28980e6	1.20289	0.601444	+	0.798915i	$0.294592\pi$
$570$	−2.57618e6	−0.332115
$571$	2.93605e6	0.376854	0.188427	−	0.982087i	$-0.439661\pi$
$571$	2.93605e6	0.376854	0.188427	+	0.982087i	$0.439661\pi$
$572$	1.35479e7	1.73134
$573$	1.71947e6	0.218781
$574$	0	0
$575$	2.88021e6	0.363290
$576$	−2.10233e6	−0.264024
$577$	5.47983e6	0.685217	0.342608	−	0.939478i	$-0.388690\pi$
$577$	5.47983e6	0.685217	0.342608	+	0.939478i	$0.388690\pi$
$578$	1.44275e7	1.79627
$579$	−3.76170e6	−0.466324
$580$	6.38256e6	0.787817
$581$	0	0
$582$	−1.83265e7	−2.24271
$583$	5.62135e6	0.684966
$584$	4.07303e6	0.494180
$585$	−2.18426e6	−0.263884
$586$	−1.34816e7	−1.62180
$587$	3.99203e6	0.478188	0.239094	−	0.970996i	$-0.423150\pi$
$587$	3.99203e6	0.478188	0.239094	+	0.970996i	$0.423150\pi$
$588$	0	0
$589$	−5.11987e6	−0.608094
$590$	−898125.	−0.106220
$591$	4.94802e6	0.582724
$592$	−3.25938e7	−3.82236
$593$	5.63897e6	0.658511	0.329256	−	0.944241i	$-0.393202\pi$
$593$	5.63897e6	0.658511	0.329256	+	0.944241i	$0.393202\pi$
$594$	−1.08306e7	−1.25947
$595$	0	0
$596$	−1.16199e7	−1.33994
$597$	1.10767e7	1.27196
$598$	−3.28091e7	−3.75182
$599$	2.96431e6	0.337565	0.168782	−	0.985653i	$-0.446017\pi$
$599$	2.96431e6	0.337565	0.168782	+	0.985653i	$0.446017\pi$
$600$	−2.97941e6	−0.337872
$601$	−9.79673e6	−1.10636	−0.553178	−	0.833063i	$-0.686585\pi$
$601$	−9.79673e6	−1.10636	−0.553178	+	0.833063i	$0.686585\pi$
$602$	0	0
$603$	−5.69879e6	−0.638248
$604$	1.65231e7	1.84289
$605$	2.29814e6	0.255263
$606$	2.67367e6	0.295751
$607$	−9.37747e6	−1.03303	−0.516516	−	0.856277i	$-0.672771\pi$
$607$	−9.37747e6	−1.03303	−0.516516	+	0.856277i	$0.672771\pi$
$608$	−7.72027e6	−0.846980
$609$	0	0
$610$	−5.78616e6	−0.629602
$611$	−7.78417e6	−0.843547
$612$	1.59178e7	1.71793
$613$	−772746.	−0.0830588	−0.0415294	−	0.999137i	$-0.513223\pi$
$613$	−772746.	−0.0830588	−0.0415294	+	0.999137i	$0.513223\pi$
$614$	8.00481e6	0.856900
$615$	−4.03112e6	−0.429772
$616$	0	0
$617$	5.62192e6	0.594528	0.297264	−	0.954795i	$-0.403926\pi$
$617$	5.62192e6	0.594528	0.297264	+	0.954795i	$0.403926\pi$
$618$	−1.22905e7	−1.29449
$619$	−7.31530e6	−0.767371	−0.383685	−	0.923464i	$-0.625345\pi$
$619$	−7.31530e6	−0.767371	−0.383685	+	0.923464i	$0.625345\pi$
$620$	−1.03487e7	−1.08120
$621$	1.83696e7	1.91148
$622$	−3.17009e7	−3.28545
$623$	0	0
$624$	1.61659e7	1.66203
$625$	390625.	0.0400000
$626$	−9.81395e6	−1.00094
$627$	−2.62166e6	−0.266322
$628$	−4.06688e7	−4.11493
$629$	2.51238e7	2.53197
$630$	0	0
$631$	1.13464e6	0.113444	0.0567222	−	0.998390i	$-0.481935\pi$
$631$	1.13464e6	0.113444	0.0567222	+	0.998390i	$0.481935\pi$
$632$	−1.48422e6	−0.147810
$633$	9.20532e6	0.913124
$634$	2.39214e7	2.36354
$635$	3.69697e6	0.363841
$636$	1.72372e7	1.68976
$637$	0	0
$638$	9.27409e6	0.902028
$639$	−1.38297e6	−0.133986
$640$	2.39340e6	0.230975
$641$	−1.53233e7	−1.47301	−0.736506	−	0.676431i	$-0.763526\pi$
$641$	−1.53233e7	−1.47301	−0.736506	+	0.676431i	$0.763526\pi$
$642$	−1.01146e7	−0.968526
$643$	3.65136e6	0.348279	0.174139	−	0.984721i	$-0.444286\pi$
$643$	3.65136e6	0.348279	0.174139	+	0.984721i	$0.444286\pi$
$644$	0	0
$645$	−5.29575e6	−0.501220
$646$	1.60429e7	1.51252
$647$	−3.97508e6	−0.373324	−0.186662	−	0.982424i	$-0.559767\pi$
$647$	−3.97508e6	−0.373324	−0.186662	+	0.982424i	$0.559767\pi$
$648$	−5.37270e6	−0.502638
$649$	−913982.	−0.0851777
$650$	−4.44971e6	−0.413093
$651$	0	0
$652$	879105.	0.0809882
$653$	−6.29637e6	−0.577840	−0.288920	−	0.957353i	$-0.593296\pi$
$653$	−6.29637e6	−0.577840	−0.288920	+	0.957353i	$0.593296\pi$
$654$	−1.57637e7	−1.44117
$655$	−1.84067e6	−0.167638
$656$	−3.25675e7	−2.95478
$657$	−1.16794e6	−0.105562
$658$	0	0
$659$	1.26507e7	1.13476	0.567378	−	0.823457i	$-0.307958\pi$
$659$	1.26507e7	1.13476	0.567378	+	0.823457i	$0.307958\pi$
$660$	−5.29912e6	−0.473526
$661$	7.73188e6	0.688306	0.344153	−	0.938914i	$-0.388166\pi$
$661$	7.73188e6	0.688306	0.344153	+	0.938914i	$0.388166\pi$
$662$	−3.10934e6	−0.275755
$663$	−1.24609e7	−1.10094
$664$	−2.01399e7	−1.77271
$665$	0	0
$666$	1.96219e7	1.71418
$667$	−1.57296e7	−1.36900
$668$	−2.88503e6	−0.250155
$669$	2.95560e6	0.255318
$670$	−1.16094e7	−0.999134
$671$	−5.88832e6	−0.504876
$672$	0	0
$673$	−1.97858e7	−1.68390	−0.841948	−	0.539558i	$-0.818591\pi$
$673$	−1.97858e7	−1.68390	−0.841948	+	0.539558i	$0.818591\pi$
$674$	−5.00655e6	−0.424511
$675$	2.49135e6	0.210463
$676$	7.72849e6	0.650471
$677$	9.72065e6	0.815124	0.407562	−	0.913178i	$-0.366379\pi$
$677$	9.72065e6	0.815124	0.407562	+	0.913178i	$0.366379\pi$
$678$	1.30156e7	1.08740
$679$	0	0
$680$	1.85540e7	1.53874
$681$	−1.42501e7	−1.17747
$682$	−1.50371e7	−1.23795
$683$	3.48276e6	0.285675	0.142837	−	0.989746i	$-0.454377\pi$
$683$	3.48276e6	0.285675	0.142837	+	0.989746i	$0.454377\pi$
$684$	8.77534e6	0.717173
$685$	−8.46437e6	−0.689236
$686$	0	0
$687$	1.76753e6	0.142881
$688$	−4.27844e7	−3.44600
$689$	1.47297e7	1.18208
$690$	1.28329e7	1.02613
$691$	−5.55426e6	−0.442518	−0.221259	−	0.975215i	$-0.571017\pi$
$691$	−5.55426e6	−0.442518	−0.221259	+	0.975215i	$0.571017\pi$
$692$	−2.01459e6	−0.159927
$693$	0	0
$694$	3.12719e7	2.46465
$695$	9.31296e6	0.731351
$696$	1.62714e7	1.27321
$697$	2.51035e7	1.95728
$698$	2.56496e7	1.99270
$699$	1.19314e7	0.923632
$700$	0	0
$701$	−6.82510e6	−0.524583	−0.262291	−	0.964989i	$-0.584478\pi$
$701$	−6.82510e6	−0.524583	−0.262291	+	0.964989i	$0.584478\pi$
$702$	−2.83796e7	−2.17352
$703$	1.38505e7	1.05701
$704$	−4.35842e6	−0.331434
$705$	3.04469e6	0.230712
$706$	−3.89711e7	−2.94259
$707$	0	0
$708$	−2.80262e6	−0.210126
$709$	−7.64382e6	−0.571077	−0.285539	−	0.958367i	$-0.592172\pi$
$709$	−7.64382e6	−0.571077	−0.285539	+	0.958367i	$0.592172\pi$
$710$	−2.81734e6	−0.209746
$711$	425600.	0.0315739
$712$	2.33912e7	1.72923
$713$	2.55041e7	1.87882
$714$	0	0
$715$	−4.52827e6	−0.331258
$716$	1.95922e7	1.42824
$717$	−6.20974e6	−0.451103
$718$	2.05680e6	0.148896
$719$	1.15186e7	0.830954	0.415477	−	0.909604i	$-0.363615\pi$
$719$	1.15186e7	0.830954	0.415477	+	0.909604i	$0.363615\pi$
$720$	6.90228e6	0.496206
$721$	0	0
$722$	−1.67443e7	−1.19543
$723$	−1.09732e7	−0.780705
$724$	−3.35055e7	−2.37558
$725$	−2.13331e6	−0.150733
$726$	1.02395e7	0.721004
$727$	2.26458e7	1.58910	0.794550	−	0.607199i	$-0.207707\pi$
$727$	2.26458e7	1.58910	0.794550	+	0.607199i	$0.207707\pi$
$728$	0	0
$729$	1.19812e7	0.834993
$730$	−2.37930e6	−0.165251
$731$	3.29788e7	2.28266
$732$	−1.80558e7	−1.24549
$733$	1.46343e7	1.00603	0.503015	−	0.864278i	$-0.332224\pi$
$733$	1.46343e7	1.00603	0.503015	+	0.864278i	$0.332224\pi$
$734$	−2.77094e7	−1.89839
$735$	0	0
$736$	3.84577e7	2.61691
$737$	−1.18144e7	−0.801203
$738$	1.96061e7	1.32510
$739$	−1.76251e7	−1.18719	−0.593596	−	0.804763i	$-0.702292\pi$
$739$	−1.76251e7	−1.18719	−0.593596	+	0.804763i	$0.702292\pi$
$740$	2.79959e7	1.87938
$741$	−6.86958e6	−0.459605
$742$	0	0
$743$	2.03747e7	1.35400	0.677002	−	0.735981i	$-0.263279\pi$
$743$	2.03747e7	1.35400	0.677002	+	0.735981i	$0.263279\pi$
$744$	−2.63825e7	−1.74737
$745$	3.88383e6	0.256371
$746$	−5.68572e6	−0.374057
$747$	5.77513e6	0.378669
$748$	3.29998e7	2.15654
$749$	0	0
$750$	1.74045e6	0.112982
$751$	1.21784e7	0.787935	0.393967	−	0.919124i	$-0.371102\pi$
$751$	1.21784e7	0.787935	0.393967	+	0.919124i	$0.371102\pi$
$752$	2.45981e7	1.58620
$753$	−482567.	−0.0310149
$754$	2.43011e7	1.55667
$755$	−5.52269e6	−0.352601
$756$	0	0
$757$	9.83013e6	0.623476	0.311738	−	0.950168i	$-0.399089\pi$
$757$	9.83013e6	0.623476	0.311738	+	0.950168i	$0.399089\pi$
$758$	9.71001e6	0.613828
$759$	1.30595e7	0.822853
$760$	1.02287e7	0.642369
$761$	−1.49014e7	−0.932749	−0.466375	−	0.884587i	$-0.654440\pi$
$761$	−1.49014e7	−0.932749	−0.466375	+	0.884587i	$0.654440\pi$
$762$	1.64721e7	1.02769
$763$	0	0
$764$	−1.19320e7	−0.739570
$765$	−5.32038e6	−0.328692
$766$	4.63193e7	2.85226
$767$	−2.39492e6	−0.146995
$768$	1.63817e7	1.00220
$769$	−3.08958e7	−1.88401	−0.942004	−	0.335600i	$-0.891061\pi$
$769$	−3.08958e7	−1.88401	−0.942004	+	0.335600i	$0.891061\pi$
$770$	0	0
$771$	3.23387e6	0.195923
$772$	2.61036e7	1.57637
$773$	−3.80951e6	−0.229308	−0.114654	−	0.993405i	$-0.536576\pi$
$773$	−3.80951e6	−0.229308	−0.114654	+	0.993405i	$0.536576\pi$
$774$	2.57568e7	1.54540
$775$	3.45896e6	0.206867
$776$	7.27652e7	4.33780
$777$	0	0
$778$	−5.39365e7	−3.19473
$779$	1.38393e7	0.817092
$780$	−1.38854e7	−0.817187
$781$	−2.86708e6	−0.168195
$782$	−7.99160e7	−4.67323
$783$	−1.36060e7	−0.793095
$784$	0	0
$785$	1.35932e7	0.787311
$786$	−8.20123e6	−0.473503
$787$	−3.11509e7	−1.79281	−0.896405	−	0.443237i	$-0.853830\pi$
$787$	−3.11509e7	−1.79281	−0.896405	+	0.443237i	$0.853830\pi$
$788$	−3.43359e7	−1.96985
$789$	1.62807e6	0.0931068
$790$	867021.	0.0494268
$791$	0	0
$792$	1.47467e7	0.835377
$793$	−1.54293e7	−0.871289
$794$	−1.10436e7	−0.621667
$795$	−5.76137e6	−0.323302
$796$	−7.68644e7	−4.29975
$797$	1.85777e7	1.03597	0.517983	−	0.855391i	$-0.326683\pi$
$797$	1.85777e7	1.03597	0.517983	+	0.855391i	$0.326683\pi$
$798$	0	0
$799$	−1.89606e7	−1.05071
$800$	5.21578e6	0.288134
$801$	−6.70743e6	−0.369381
$802$	4.80481e6	0.263779
$803$	−2.42131e6	−0.132514
$804$	−3.62274e7	−1.97650
$805$	0	0
$806$	−3.94019e7	−2.13639
$807$	1.27563e7	0.689508
$808$	−1.06158e7	−0.572035
$809$	−7.53243e6	−0.404635	−0.202318	−	0.979320i	$-0.564847\pi$
$809$	−7.53243e6	−0.404635	−0.202318	+	0.979320i	$0.564847\pi$
$810$	3.13852e6	0.168079
$811$	−9.91517e6	−0.529356	−0.264678	−	0.964337i	$-0.585266\pi$
$811$	−9.91517e6	−0.529356	−0.264678	+	0.964337i	$0.585266\pi$
$812$	0	0
$813$	−1.54623e7	−0.820442
$814$	4.06790e7	2.15184
$815$	−293833.	−0.0154955
$816$	3.93767e7	2.07021
$817$	1.81809e7	0.952930
$818$	−4.61472e7	−2.41136
$819$	0	0
$820$	2.79732e7	1.45281
$821$	−1.33726e7	−0.692402	−0.346201	−	0.938160i	$-0.612528\pi$
$821$	−1.33726e7	−0.692402	−0.346201	+	0.938160i	$0.612528\pi$
$822$	−3.77135e7	−1.94678
$823$	225760.	0.0116184	0.00580921	−	0.999983i	$-0.498151\pi$
$823$	225760.	0.0116184	0.00580921	+	0.999983i	$0.498151\pi$
$824$	4.87993e7	2.50377
$825$	1.77118e6	0.0906000
$826$	0	0
$827$	3.75070e7	1.90699	0.953495	−	0.301409i	$-0.0974570\pi$
$827$	3.75070e7	1.90699	0.953495	+	0.301409i	$0.0974570\pi$
$828$	−4.37134e7	−2.21584
$829$	−2.38271e6	−0.120416	−0.0602082	−	0.998186i	$-0.519176\pi$
$829$	−2.38271e6	−0.120416	−0.0602082	+	0.998186i	$0.519176\pi$
$830$	1.17649e7	0.592781
$831$	5.23105e6	0.262776
$832$	−1.14204e7	−0.571972
$833$	0	0
$834$	4.14945e7	2.06574
$835$	964296.	0.0478624
$836$	1.81925e7	0.900278
$837$	2.20608e7	1.08845
$838$	−6.46320e7	−3.17934
$839$	1.72260e7	0.844848	0.422424	−	0.906398i	$-0.361179\pi$
$839$	1.72260e7	0.844848	0.422424	+	0.906398i	$0.361179\pi$
$840$	0	0
$841$	−8.86055e6	−0.431987
$842$	5.18462e7	2.52021
$843$	−1.19066e6	−0.0577059
$844$	−6.38786e7	−3.08674
$845$	−2.58317e6	−0.124455
$846$	−1.48084e7	−0.711348
$847$	0	0
$848$	−4.65462e7	−2.22277
$849$	3.50001e6	0.166648
$850$	−1.08385e7	−0.514545
$851$	−6.89948e7	−3.26582
$852$	−8.79156e6	−0.414923
$853$	−7.69238e6	−0.361983	−0.180992	−	0.983485i	$-0.557931\pi$
$853$	−7.69238e6	−0.361983	−0.180992	+	0.983485i	$0.557931\pi$
$854$	0	0
$855$	−2.93307e6	−0.137217
$856$	4.01599e7	1.87330
$857$	3.27783e7	1.52452	0.762262	−	0.647269i	$-0.224089\pi$
$857$	3.27783e7	1.52452	0.762262	+	0.647269i	$0.224089\pi$
$858$	−2.01760e7	−0.935656
$859$	−1.42531e7	−0.659062	−0.329531	−	0.944145i	$-0.606891\pi$
$859$	−1.42531e7	−0.659062	−0.329531	+	0.944145i	$0.606891\pi$
$860$	3.67489e7	1.69433
$861$	0	0
$862$	−4.67900e7	−2.14479
$863$	−5.53788e6	−0.253114	−0.126557	−	0.991959i	$-0.540393\pi$
$863$	−5.53788e6	−0.253114	−0.126557	+	0.991959i	$0.540393\pi$
$864$	3.32656e7	1.51604
$865$	673359.	0.0305989
$866$	1.95275e7	0.884814
$867$	−1.50479e7	−0.679875
$868$	0	0
$869$	882329.	0.0396352
$870$	−9.50510e6	−0.425754
$871$	−3.09575e7	−1.38267
$872$	6.25896e7	2.78748
$873$	−2.08655e7	−0.926600
$874$	−4.40570e7	−1.95090
$875$	0	0
$876$	−7.42466e6	−0.326901
$877$	1.95012e7	0.856173	0.428086	−	0.903738i	$-0.359188\pi$
$877$	1.95012e7	0.856173	0.428086	+	0.903738i	$0.359188\pi$
$878$	−5.49038e7	−2.40362
$879$	1.40614e7	0.613841
$880$	1.43094e7	0.622895
$881$	−609895.	−0.0264737	−0.0132369	−	0.999912i	$-0.504214\pi$
$881$	−609895.	−0.0264737	−0.0132369	+	0.999912i	$0.504214\pi$
$882$	0	0
$883$	2.55781e7	1.10399	0.551996	−	0.833847i	$-0.313866\pi$
$883$	2.55781e7	1.10399	0.551996	+	0.833847i	$0.313866\pi$
$884$	8.64701e7	3.72165
$885$	936748.	0.0402036
$886$	3.49150e7	1.49427
$887$	−3.29071e7	−1.40436	−0.702182	−	0.711997i	$-0.747791\pi$
$887$	−3.29071e7	−1.40436	−0.702182	+	0.711997i	$0.747791\pi$
$888$	7.13712e7	3.03732
$889$	0	0
$890$	−1.36642e7	−0.578242
$891$	3.19393e6	0.134782
$892$	−2.05099e7	−0.863079
$893$	−1.04528e7	−0.438635
$894$	1.73046e7	0.724133
$895$	−6.54852e6	−0.273266
$896$	0	0
$897$	3.42201e7	1.42004
$898$	−1.36727e7	−0.565802
$899$	−1.88904e7	−0.779545
$900$	−5.92859e6	−0.243975
$901$	3.58784e7	1.47239
$902$	4.06461e7	1.66342
$903$	0	0
$904$	−5.16782e7	−2.10323
$905$	1.11989e7	0.454521
$906$	−2.46067e7	−0.995938
$907$	2.76339e7	1.11538	0.557692	−	0.830048i	$-0.311687\pi$
$907$	2.76339e7	1.11538	0.557692	+	0.830048i	$0.311687\pi$
$908$	9.88860e7	3.98034
$909$	3.04407e6	0.122193
$910$	0	0
$911$	−2.20633e7	−0.880796	−0.440398	−	0.897803i	$-0.645163\pi$
$911$	−2.20633e7	−0.880796	−0.440398	+	0.897803i	$0.645163\pi$
$912$	2.17080e7	0.864236
$913$	1.19727e7	0.475350
$914$	−6867.15	−0.000271901 0
$915$	6.03499e6	0.238300
$916$	−1.22655e7	−0.482998
$917$	0	0
$918$	−6.91267e7	−2.70732
$919$	5.70536e6	0.222841	0.111420	−	0.993773i	$-0.464460\pi$
$919$	5.70536e6	0.222841	0.111420	+	0.993773i	$0.464460\pi$
$920$	−5.09530e7	−1.98472
$921$	−8.34905e6	−0.324331
$922$	3.94452e6	0.152815
$923$	−7.51266e6	−0.290262
$924$	0	0
$925$	−9.35735e6	−0.359583
$926$	−3.56219e7	−1.36518
$927$	−1.39932e7	−0.534833
$928$	−2.84848e7	−1.08578
$929$	2.49645e7	0.949038	0.474519	−	0.880245i	$-0.342622\pi$
$929$	2.49645e7	0.949038	0.474519	+	0.880245i	$0.342622\pi$
$930$	1.54116e7	0.584307
$931$	0	0
$932$	−8.27959e7	−3.12226
$933$	3.30641e7	1.24352
$934$	3.90612e7	1.46514
$935$	−1.10299e7	−0.412612
$936$	3.86411e7	1.44165
$937$	3.62569e7	1.34909	0.674546	−	0.738233i	$-0.264339\pi$
$937$	3.62569e7	1.34909	0.674546	+	0.738233i	$0.264339\pi$
$938$	0	0
$939$	1.02360e7	0.378849
$940$	−2.11281e7	−0.779903
$941$	2.08967e7	0.769314	0.384657	−	0.923060i	$-0.374320\pi$
$941$	2.08967e7	0.769314	0.384657	+	0.923060i	$0.374320\pi$
$942$	6.05652e7	2.22380
$943$	−6.89391e7	−2.52456
$944$	7.56800e6	0.276408
$945$	0	0
$946$	5.33975e7	1.93996
$947$	5.27033e7	1.90969	0.954845	−	0.297104i	$-0.0960209\pi$
$947$	5.27033e7	1.90969	0.954845	+	0.297104i	$0.0960209\pi$
$948$	2.70556e6	0.0977768
$949$	−6.34461e6	−0.228686
$950$	−5.97518e6	−0.214804
$951$	−2.49501e7	−0.894584
$952$	0	0
$953$	−1.95159e7	−0.696077	−0.348039	−	0.937480i	$-0.613152\pi$
$953$	−1.95159e7	−0.696077	−0.348039	+	0.937480i	$0.613152\pi$
$954$	2.80214e7	0.996826
$955$	3.98815e6	0.141502
$956$	4.30913e7	1.52491
$957$	−9.67292e6	−0.341411
$958$	3.43015e7	1.20753
$959$	0	0
$960$	4.46698e6	0.156436
$961$	1.99980e6	0.0698519
$962$	1.06592e8	3.71353
$963$	−1.15159e7	−0.400157
$964$	7.61463e7	2.63910
$965$	−8.72488e6	−0.301607
$966$	0	0
$967$	4.66033e7	1.60269	0.801347	−	0.598200i	$-0.204117\pi$
$967$	4.66033e7	1.60269	0.801347	+	0.598200i	$0.204117\pi$
$968$	−4.06558e7	−1.39455
$969$	−1.67328e7	−0.572479
$970$	−4.25066e7	−1.45053
$971$	−9.65070e6	−0.328481	−0.164241	−	0.986420i	$-0.552517\pi$
$971$	−9.65070e6	−0.328481	−0.164241	+	0.986420i	$0.552517\pi$
$972$	−6.26569e7	−2.12718
$973$	0	0
$974$	−2.70653e7	−0.914146
$975$	4.64106e6	0.156353
$976$	4.87568e7	1.63836
$977$	−1.00843e7	−0.337994	−0.168997	−	0.985617i	$-0.554053\pi$
$977$	−1.00843e7	−0.337994	−0.168997	+	0.985617i	$0.554053\pi$
$978$	−1.30919e6	−0.0437679
$979$	−1.39054e7	−0.463691
$980$	0	0
$981$	−1.79476e7	−0.595435
$982$	−1.09144e8	−3.61179
$983$	−1.49185e7	−0.492427	−0.246213	−	0.969216i	$-0.579186\pi$
$983$	−1.49185e7	−0.492427	−0.246213	+	0.969216i	$0.579186\pi$
$984$	7.13136e7	2.34793
$985$	1.14764e7	0.376892
$986$	5.91922e7	1.93898
$987$	0	0
$988$	4.76702e7	1.55365
$989$	−9.05663e7	−2.94426
$990$	−8.61445e6	−0.279344
$991$	−1.33955e7	−0.433285	−0.216642	−	0.976251i	$-0.569511\pi$
$991$	−1.33955e7	−0.433285	−0.216642	+	0.976251i	$0.569511\pi$
$992$	4.61855e7	1.49014
$993$	3.24305e6	0.104371
$994$	0	0
$995$	2.56912e7	0.822672
$996$	3.67127e7	1.17265
$997$	−3.28464e7	−1.04653	−0.523263	−	0.852171i	$-0.675285\pi$
$997$	−3.28464e7	−1.04653	−0.523263	+	0.852171i	$0.675285\pi$
$998$	−6.25703e6	−0.198857
$999$	−5.96800e7	−1.89197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.l.1.10	✓	10
7.6	odd	2		245.6.a.m.1.10	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.10	✓	10	1.1	even	1	trivial
245.6.a.m.1.10	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)

\(f(q)\)	\(=\)	\(q+10.3342 q^{2} -10.7786 q^{3} +74.7964 q^{4} -25.0000 q^{5} -111.389 q^{6} +442.268 q^{8} -126.821 q^{9} +O(q^{10})\)	\(q+10.3342 q^{2} -10.7786 q^{3} +74.7964 q^{4} -25.0000 q^{5} -111.389 q^{6} +442.268 q^{8} -126.821 q^{9} -258.356 q^{10} -262.917 q^{11} -806.204 q^{12} -688.927 q^{13} +269.466 q^{15} +2177.02 q^{16} -1678.08 q^{17} -1310.60 q^{18} -925.109 q^{19} -1869.91 q^{20} -2717.05 q^{22} +4608.33 q^{23} -4767.06 q^{24} +625.000 q^{25} -7119.53 q^{26} +3986.17 q^{27} -3413.30 q^{29} +2784.73 q^{30} +5534.34 q^{31} +8345.25 q^{32} +2833.89 q^{33} -17341.7 q^{34} -9485.74 q^{36} -14971.8 q^{37} -9560.29 q^{38} +7425.70 q^{39} -11056.7 q^{40} -14959.7 q^{41} -19652.7 q^{43} -19665.3 q^{44} +3170.52 q^{45} +47623.6 q^{46} +11299.0 q^{47} -23465.3 q^{48} +6458.90 q^{50} +18087.4 q^{51} -51529.3 q^{52} -21380.7 q^{53} +41194.0 q^{54} +6572.93 q^{55} +9971.42 q^{57} -35273.8 q^{58} +3476.31 q^{59} +20155.1 q^{60} +22396.1 q^{61} +57193.2 q^{62} +16577.2 q^{64} +17223.2 q^{65} +29286.1 q^{66} +44935.8 q^{67} -125514. q^{68} -49671.6 q^{69} +10904.9 q^{71} -56088.8 q^{72} +9209.41 q^{73} -154722. q^{74} -6736.65 q^{75} -69194.8 q^{76} +76738.9 q^{78} -3355.92 q^{79} -54425.5 q^{80} -12148.1 q^{81} -154597. q^{82} -45537.7 q^{83} +41951.9 q^{85} -203096. q^{86} +36790.7 q^{87} -116280. q^{88} +52889.1 q^{89} +32764.9 q^{90} +344687. q^{92} -59652.7 q^{93} +116766. q^{94} +23127.7 q^{95} -89950.5 q^{96} +164527. q^{97} +33343.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 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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