LMFDB - Embedded newform 245.6.a.m.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 $ x^10 - 246x^8 - 192x^7 + 20336x^6 + 25380x^5 - 639206x^4 - 722920x^3 + 7583055x^2 + 5935300x - 22888100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 7^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.66104$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.66104 q^{2} +29.0676 q^{3} -18.5968 q^{4} +25.0000 q^{5} +106.418 q^{6} -185.237 q^{8} +601.928 q^{9} +O(q^{10})$	\(q+3.66104 q^{2} +29.0676 q^{3} -18.5968 q^{4} +25.0000 q^{5} +106.418 q^{6} -185.237 q^{8} +601.928 q^{9} +91.5259 q^{10} +621.487 q^{11} -540.566 q^{12} +95.0340 q^{13} +726.691 q^{15} -83.0602 q^{16} -1374.26 q^{17} +2203.68 q^{18} +1644.17 q^{19} -464.920 q^{20} +2275.29 q^{22} +678.152 q^{23} -5384.40 q^{24} +625.000 q^{25} +347.923 q^{26} +10433.2 q^{27} -6104.68 q^{29} +2660.44 q^{30} +1453.40 q^{31} +5623.49 q^{32} +18065.2 q^{33} -5031.21 q^{34} -11193.9 q^{36} +10933.0 q^{37} +6019.36 q^{38} +2762.41 q^{39} -4630.92 q^{40} +16505.5 q^{41} +9828.10 q^{43} -11557.7 q^{44} +15048.2 q^{45} +2482.74 q^{46} -27158.7 q^{47} -2414.36 q^{48} +2288.15 q^{50} -39946.4 q^{51} -1767.33 q^{52} -10196.7 q^{53} +38196.3 q^{54} +15537.2 q^{55} +47792.1 q^{57} -22349.5 q^{58} +23231.7 q^{59} -13514.1 q^{60} -30454.9 q^{61} +5320.93 q^{62} +23245.7 q^{64} +2375.85 q^{65} +66137.2 q^{66} -14381.8 q^{67} +25556.8 q^{68} +19712.3 q^{69} -56459.2 q^{71} -111499. q^{72} +20585.2 q^{73} +40026.2 q^{74} +18167.3 q^{75} -30576.3 q^{76} +10113.3 q^{78} -75056.9 q^{79} -2076.51 q^{80} +157000. q^{81} +60427.4 q^{82} +44886.2 q^{83} -34356.5 q^{85} +35981.0 q^{86} -177449. q^{87} -115122. q^{88} -141947. q^{89} +55092.0 q^{90} -12611.5 q^{92} +42246.8 q^{93} -99428.9 q^{94} +41104.2 q^{95} +163462. q^{96} -33101.8 q^{97} +374090. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19} + 4550 q^{20} + 3948 q^{22} + 3708 q^{23} + 2092 q^{24} + 6250 q^{25} + 6576 q^{26} + 11818 q^{27} - 8866 q^{29} + 3600 q^{30} + 13292 q^{31} + 2590 q^{32} + 9854 q^{33} + 44468 q^{34} - 10690 q^{36} + 16124 q^{37} + 2180 q^{38} - 24982 q^{39} + 6750 q^{40} + 34836 q^{41} - 28604 q^{43} - 31120 q^{44} + 17500 q^{45} - 39732 q^{46} + 18106 q^{47} + 101788 q^{48} + 6250 q^{50} + 31602 q^{51} - 22480 q^{52} + 36440 q^{53} + 80836 q^{54} + 19850 q^{55} + 126988 q^{57} - 100356 q^{58} + 18644 q^{59} + 64000 q^{60} + 68120 q^{61} + 181052 q^{62} - 59358 q^{64} + 11850 q^{65} + 157780 q^{66} + 92328 q^{67} + 288540 q^{68} + 170888 q^{69} + 5044 q^{71} - 61654 q^{72} + 170160 q^{73} - 216584 q^{74} + 36250 q^{75} + 505180 q^{76} - 158008 q^{78} + 26442 q^{79} + 59850 q^{80} - 56314 q^{81} + 353948 q^{82} + 353360 q^{83} + 20050 q^{85} - 52940 q^{86} - 3190 q^{87} - 114916 q^{88} + 90704 q^{89} + 92550 q^{90} + 183520 q^{92} + 188560 q^{93} - 121388 q^{94} + 182300 q^{95} + 442220 q^{96} + 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.66104	0.647186	0.323593	−	0.946196i	$-0.395109\pi$
$2$	3.66104	0.647186	0.323593	+	0.946196i	$0.395109\pi$
$3$	29.0676	1.86469	0.932345	−	0.361570i	$-0.117759\pi$
$3$	29.0676	1.86469	0.932345	+	0.361570i	$0.117759\pi$
$4$	−18.5968	−0.581151
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	106.418	1.20680
$7$	0	0
$7$	0	0
$8$	−185.237	−1.02330
$9$	601.928	2.47707
$10$	91.5259	0.289430
$11$	621.487	1.54864	0.774320	−	0.632794i	$-0.218092\pi$
$11$	621.487	1.54864	0.774320	+	0.632794i	$0.218092\pi$
$12$	−540.566	−1.08367
$13$	95.0340	0.155963	0.0779813	−	0.996955i	$-0.475153\pi$
$13$	95.0340	0.155963	0.0779813	+	0.996955i	$0.475153\pi$
$14$	0	0
$15$	726.691	0.833915
$16$	−83.0602	−0.0811135
$17$	−1374.26	−1.15331	−0.576655	−	0.816988i	$-0.695642\pi$
$17$	−1374.26	−1.15331	−0.576655	+	0.816988i	$0.695642\pi$
$18$	2203.68	1.60312
$19$	1644.17	1.04487	0.522435	−	0.852679i	$-0.325024\pi$
$19$	1644.17	1.04487	0.522435	+	0.852679i	$0.325024\pi$
$20$	−464.920	−0.259898
$21$	0	0
$22$	2275.29	1.00226
$23$	678.152	0.267305	0.133653	−	0.991028i	$-0.457329\pi$
$23$	678.152	0.267305	0.133653	+	0.991028i	$0.457329\pi$
$24$	−5384.40	−1.90813
$25$	625.000	0.200000
$26$	347.923	0.100937
$27$	10433.2	2.75428
$28$	0	0
$29$	−6104.68	−1.34793	−0.673966	−	0.738762i	$-0.735411\pi$
$29$	−6104.68	−1.34793	−0.673966	+	0.738762i	$0.735411\pi$
$30$	2660.44	0.539698
$31$	1453.40	0.271631	0.135816	−	0.990734i	$-0.456635\pi$
$31$	1453.40	0.271631	0.135816	+	0.990734i	$0.456635\pi$
$32$	5623.49	0.970803
$33$	18065.2	2.88773
$34$	−5031.21	−0.746406
$35$	0	0
$36$	−11193.9	−1.43955
$37$	10933.0	1.31291	0.656456	−	0.754364i	$-0.272055\pi$
$37$	10933.0	1.31291	0.656456	+	0.754364i	$0.272055\pi$
$38$	6019.36	0.676225
$39$	2762.41	0.290822
$40$	−4630.92	−0.457633
$41$	16505.5	1.53345	0.766726	−	0.641974i	$-0.221884\pi$
$41$	16505.5	1.53345	0.766726	+	0.641974i	$0.221884\pi$
$42$	0	0
$43$	9828.10	0.810585	0.405292	−	0.914187i	$-0.367170\pi$
$43$	9828.10	0.810585	0.405292	+	0.914187i	$0.367170\pi$
$44$	−11557.7	−0.899993
$45$	15048.2	1.10778
$46$	2482.74	0.172996
$47$	−27158.7	−1.79335	−0.896673	−	0.442693i	$-0.854023\pi$
$47$	−27158.7	−1.79335	−0.896673	+	0.442693i	$0.854023\pi$
$48$	−2414.36	−0.151252
$49$	0	0
$50$	2288.15	0.129437
$51$	−39946.4	−2.15057
$52$	−1767.33	−0.0906378
$53$	−10196.7	−0.498621	−0.249311	−	0.968424i	$-0.580204\pi$
$53$	−10196.7	−0.498621	−0.249311	+	0.968424i	$0.580204\pi$
$54$	38196.3	1.78253
$55$	15537.2	0.692573
$56$	0	0
$57$	47792.1	1.94836
$58$	−22349.5	−0.872362
$59$	23231.7	0.868861	0.434430	−	0.900705i	$-0.356950\pi$
$59$	23231.7	0.868861	0.434430	+	0.900705i	$0.356950\pi$
$60$	−13514.1	−0.484630
$61$	−30454.9	−1.04793	−0.523966	−	0.851739i	$-0.675548\pi$
$61$	−30454.9	−1.04793	−0.523966	+	0.851739i	$0.675548\pi$
$62$	5320.93	0.175796
$63$	0	0
$64$	23245.7	0.709403
$65$	2375.85	0.0697486
$66$	66137.2	1.86890
$67$	−14381.8	−0.391404	−0.195702	−	0.980663i	$-0.562699\pi$
$67$	−14381.8	−0.391404	−0.195702	+	0.980663i	$0.562699\pi$
$68$	25556.8	0.670247
$69$	19712.3	0.498441
$70$	0	0
$71$	−56459.2	−1.32920	−0.664598	−	0.747201i	$-0.731397\pi$
$71$	−56459.2	−1.32920	−0.664598	+	0.747201i	$0.731397\pi$
$72$	−111499.	−2.53478
$73$	20585.2	0.452113	0.226057	−	0.974114i	$-0.427417\pi$
$73$	20585.2	0.452113	0.226057	+	0.974114i	$0.427417\pi$
$74$	40026.2	0.849698
$75$	18167.3	0.372938
$76$	−30576.3	−0.607226
$77$	0	0
$78$	10113.3	0.188216
$79$	−75056.9	−1.35308	−0.676539	−	0.736406i	$-0.736521\pi$
$79$	−75056.9	−1.35308	−0.676539	+	0.736406i	$0.736521\pi$
$80$	−2076.51	−0.0362751
$81$	157000.	2.65880
$82$	60427.4	0.992429
$83$	44886.2	0.715184	0.357592	−	0.933878i	$-0.383598\pi$
$83$	44886.2	0.715184	0.357592	+	0.933878i	$0.383598\pi$
$84$	0	0
$85$	−34356.5	−0.515776
$86$	35981.0	0.524599
$87$	−177449.	−2.51348
$88$	−115122.	−1.58472
$89$	−141947.	−1.89956	−0.949779	−	0.312921i	$-0.898693\pi$
$89$	−141947.	−1.89956	−0.949779	+	0.312921i	$0.898693\pi$
$90$	55092.0	0.716939
$91$	0	0
$92$	−12611.5	−0.155345
$93$	42246.8	0.506508
$94$	−99428.9	−1.16063
$95$	41104.2	0.467280
$96$	163462.	1.81025
$97$	−33101.8	−0.357209	−0.178604	−	0.983921i	$-0.557158\pi$
$97$	−33101.8	−0.357209	−0.178604	+	0.983921i	$0.557158\pi$
$98$	0	0
$99$	374090.	3.83609
$100$	−11623.0	−0.116230
$101$	69549.6	0.678408	0.339204	−	0.940713i	$-0.389842\pi$
$101$	69549.6	0.678408	0.339204	+	0.940713i	$0.389842\pi$
$102$	−146245.	−1.39182
$103$	40713.2	0.378130	0.189065	−	0.981965i	$-0.439454\pi$
$103$	40713.2	0.378130	0.189065	+	0.981965i	$0.439454\pi$
$104$	−17603.8	−0.159596
$105$	0	0
$106$	−37330.5	−0.322700
$107$	−140988.	−1.19048	−0.595242	−	0.803546i	$-0.702944\pi$
$107$	−140988.	−1.19048	−0.595242	+	0.803546i	$0.702944\pi$
$108$	−194024.	−1.60065
$109$	−32830.6	−0.264675	−0.132337	−	0.991205i	$-0.542248\pi$
$109$	−32830.6	−0.264675	−0.132337	+	0.991205i	$0.542248\pi$
$110$	56882.2	0.448223
$111$	317797.	2.44818
$112$	0	0
$113$	130138.	0.958753	0.479377	−	0.877609i	$-0.340863\pi$
$113$	130138.	0.958753	0.479377	+	0.877609i	$0.340863\pi$
$114$	174968.	1.26095
$115$	16953.8	0.119542
$116$	113528.	0.783351
$117$	57203.6	0.386330
$118$	85051.9	0.562314
$119$	0	0
$120$	−134610.	−0.853344
$121$	225195.	1.39828
$122$	−111497.	−0.678206
$123$	479777.	2.85941
$124$	−27028.5	−0.157859
$125$	15625.0	0.0894427
$126$	0	0
$127$	165584.	0.910981	0.455490	−	0.890241i	$-0.349464\pi$
$127$	165584.	0.910981	0.455490	+	0.890241i	$0.349464\pi$
$128$	−94848.3	−0.511687
$129$	285680.	1.51149
$130$	8698.07	0.0451403
$131$	2862.81	0.0145752	0.00728759	−	0.999973i	$-0.497680\pi$
$131$	2862.81	0.0145752	0.00728759	+	0.999973i	$0.497680\pi$
$132$	−335955.	−1.67821
$133$	0	0
$134$	−52652.2	−0.253311
$135$	260830.	1.23175
$136$	254563.	1.18018
$137$	−336120.	−1.53001	−0.765003	−	0.644026i	$-0.777263\pi$
$137$	−336120.	−1.53001	−0.765003	+	0.644026i	$0.777263\pi$
$138$	72167.3	0.322584
$139$	2327.02	0.0102156	0.00510780	−	0.999987i	$-0.498374\pi$
$139$	2327.02	0.0102156	0.00510780	+	0.999987i	$0.498374\pi$
$140$	0	0
$141$	−789439.	−3.34404
$142$	−206699.	−0.860236
$143$	59062.4	0.241530
$144$	−49996.3	−0.200924
$145$	−152617.	−0.602813
$146$	75363.0	0.292601
$147$	0	0
$148$	−203319.	−0.763000
$149$	3732.12	0.0137718	0.00688590	−	0.999976i	$-0.497808\pi$
$149$	3732.12	0.0137718	0.00688590	+	0.999976i	$0.497808\pi$
$150$	66511.1	0.241360
$151$	−492339.	−1.75720	−0.878601	−	0.477557i	$-0.841522\pi$
$151$	−492339.	−1.75720	−0.878601	+	0.477557i	$0.841522\pi$
$152$	−304560.	−1.06921
$153$	−827204.	−2.85683
$154$	0	0
$155$	36334.9	0.121477
$156$	−51372.1	−0.169011
$157$	−101809.	−0.329638	−0.164819	−	0.986324i	$-0.552704\pi$
$157$	−101809.	−0.329638	−0.164819	+	0.986324i	$0.552704\pi$
$158$	−274786.	−0.875693
$159$	−296394.	−0.929774
$160$	140587.	0.434156
$161$	0	0
$162$	574782.	1.72074
$163$	−312836.	−0.922248	−0.461124	−	0.887336i	$-0.652554\pi$
$163$	−312836.	−0.922248	−0.461124	+	0.887336i	$0.652554\pi$
$164$	−306951.	−0.891167
$165$	451629.	1.29143
$166$	164330.	0.462857
$167$	118342.	0.328359	0.164180	−	0.986430i	$-0.447502\pi$
$167$	118342.	0.328359	0.164180	+	0.986430i	$0.447502\pi$
$168$	0	0
$169$	−362262.	−0.975676
$170$	−125780.	−0.333803
$171$	989670.	2.58821
$172$	−182771.	−0.471072
$173$	156863.	0.398480	0.199240	−	0.979951i	$-0.436153\pi$
$173$	156863.	0.398480	0.199240	+	0.979951i	$0.436153\pi$
$174$	−649646.	−1.62669
$175$	0	0
$176$	−51620.8	−0.125616
$177$	675290.	1.62016
$178$	−519675.	−1.22937
$179$	−275501.	−0.642675	−0.321337	−	0.946965i	$-0.604132\pi$
$179$	−275501.	−0.642675	−0.321337	+	0.946965i	$0.604132\pi$
$180$	−279849.	−0.643787
$181$	−219727.	−0.498524	−0.249262	−	0.968436i	$-0.580188\pi$
$181$	−219727.	−0.498524	−0.249262	+	0.968436i	$0.580188\pi$
$182$	0	0
$183$	−885253.	−1.95407
$184$	−125619.	−0.273533
$185$	273326.	0.587152
$186$	154667.	0.327805
$187$	−854084.	−1.78606
$188$	505065.	1.04220
$189$	0	0
$190$	150484.	0.302417
$191$	−238001.	−0.472057	−0.236029	−	0.971746i	$-0.575846\pi$
$191$	−238001.	−0.472057	−0.236029	+	0.971746i	$0.575846\pi$
$192$	675698.	1.32282
$193$	440439.	0.851124	0.425562	−	0.904929i	$-0.360076\pi$
$193$	440439.	0.851124	0.425562	+	0.904929i	$0.360076\pi$
$194$	−121187.	−0.231181
$195$	69060.3	0.130060
$196$	0	0
$197$	−405416.	−0.744278	−0.372139	−	0.928177i	$-0.621375\pi$
$197$	−405416.	−0.744278	−0.372139	+	0.928177i	$0.621375\pi$
$198$	1.36956e6	2.48266
$199$	−325353.	−0.582401	−0.291201	−	0.956662i	$-0.594055\pi$
$199$	−325353.	−0.582401	−0.291201	+	0.956662i	$0.594055\pi$
$200$	−115773.	−0.204660
$201$	−418044.	−0.729847
$202$	254623.	0.439056
$203$	0	0
$204$	742877.	1.24980
$205$	412639.	0.685781
$206$	149052.	0.244721
$207$	408199.	0.662133
$208$	−7893.54	−0.0126507
$209$	1.02183e6	1.61813
$210$	0	0
$211$	−715875.	−1.10696	−0.553479	−	0.832863i	$-0.686700\pi$
$211$	−715875.	−1.10696	−0.553479	+	0.832863i	$0.686700\pi$
$212$	189626.	0.289774
$213$	−1.64114e6	−2.47854
$214$	−516163.	−0.770465
$215$	245702.	0.362505
$216$	−1.93261e6	−2.81845
$217$	0	0
$218$	−120194.	−0.171294
$219$	598362.	0.843051
$220$	−288942.	−0.402489
$221$	−130601.	−0.179873
$222$	1.16347e6	1.58442
$223$	122787.	0.165345	0.0826723	−	0.996577i	$-0.473655\pi$
$223$	122787.	0.165345	0.0826723	+	0.996577i	$0.473655\pi$
$224$	0	0
$225$	376205.	0.495414
$226$	476439.	0.620492
$227$	−759786.	−0.978648	−0.489324	−	0.872102i	$-0.662757\pi$
$227$	−759786.	−0.978648	−0.489324	+	0.872102i	$0.662757\pi$
$228$	−888781.	−1.13229
$229$	524219.	0.660577	0.330289	−	0.943880i	$-0.392854\pi$
$229$	524219.	0.660577	0.330289	+	0.943880i	$0.392854\pi$
$230$	62068.4	0.0773662
$231$	0	0
$232$	1.13081e6	1.37934
$233$	280167.	0.338086	0.169043	−	0.985609i	$-0.445932\pi$
$233$	280167.	0.338086	0.169043	+	0.985609i	$0.445932\pi$
$234$	209424.	0.250027
$235$	−678967.	−0.802009
$236$	−432035.	−0.504939
$237$	−2.18173e6	−2.52307
$238$	0	0
$239$	443643.	0.502387	0.251194	−	0.967937i	$-0.419177\pi$
$239$	443643.	0.502387	0.251194	+	0.967937i	$0.419177\pi$
$240$	−60359.1	−0.0676417
$241$	−1.15029e6	−1.27574	−0.637871	−	0.770143i	$-0.720185\pi$
$241$	−1.15029e6	−1.27574	−0.637871	+	0.770143i	$0.720185\pi$
$242$	824447.	0.904950
$243$	2.02835e6	2.20357
$244$	566365.	0.609006
$245$	0	0
$246$	1.75648e6	1.85057
$247$	156252.	0.162961
$248$	−269222.	−0.277960
$249$	1.30474e6	1.33360
$250$	57203.7	0.0578861
$251$	768062.	0.769506	0.384753	−	0.923020i	$-0.374287\pi$
$251$	768062.	0.769506	0.384753	+	0.923020i	$0.374287\pi$
$252$	0	0
$253$	421463.	0.413959
$254$	606209.	0.589574
$255$	−998661.	−0.961762
$256$	−1.09111e6	−1.04056
$257$	948417.	0.895708	0.447854	−	0.894107i	$-0.352188\pi$
$257$	948417.	0.895708	0.447854	+	0.894107i	$0.352188\pi$
$258$	1.04588e6	0.978214
$259$	0	0
$260$	−44183.2	−0.0405344
$261$	−3.67458e6	−3.33892
$262$	10480.8	0.00943285
$263$	311018.	0.277266	0.138633	−	0.990344i	$-0.455729\pi$
$263$	311018.	0.277266	0.138633	+	0.990344i	$0.455729\pi$
$264$	−3.34633e6	−2.95501
$265$	−254918.	−0.222990
$266$	0	0
$267$	−4.12608e6	−3.54209
$268$	267455.	0.227465
$269$	2.02391e6	1.70534	0.852669	−	0.522451i	$-0.174982\pi$
$269$	2.02391e6	1.70534	0.852669	+	0.522451i	$0.174982\pi$
$270$	954907.	0.797171
$271$	−436033.	−0.360658	−0.180329	−	0.983606i	$-0.557716\pi$
$271$	−436033.	−0.360658	−0.180329	+	0.983606i	$0.557716\pi$
$272$	114146.	0.0935490
$273$	0	0
$274$	−1.23055e6	−0.990199
$275$	388429.	0.309728
$276$	−366586.	−0.289669
$277$	302117.	0.236579	0.118289	−	0.992979i	$-0.462259\pi$
$277$	302117.	0.236579	0.118289	+	0.992979i	$0.462259\pi$
$278$	8519.31	0.00661139
$279$	874839.	0.672849
$280$	0	0
$281$	1.08889e6	0.822658	0.411329	−	0.911487i	$-0.365065\pi$
$281$	1.08889e6	0.822658	0.411329	+	0.911487i	$0.365065\pi$
$282$	−2.89016e6	−2.16421
$283$	972565.	0.721859	0.360930	−	0.932593i	$-0.382459\pi$
$283$	972565.	0.721859	0.360930	+	0.932593i	$0.382459\pi$
$284$	1.04996e6	0.772462
$285$	1.19480e6	0.871332
$286$	216229.	0.156315
$287$	0	0
$288$	3.38494e6	2.40475
$289$	468728.	0.330124
$290$	−558736.	−0.390132
$291$	−962191.	−0.666084
$292$	−382819.	−0.262746
$293$	2.10428e6	1.43197	0.715985	−	0.698116i	$-0.245978\pi$
$293$	2.10428e6	1.43197	0.715985	+	0.698116i	$0.245978\pi$
$294$	0	0
$295$	580792.	0.388566
$296$	−2.02520e6	−1.34350
$297$	6.48409e6	4.26538
$298$	13663.4	0.00891291
$299$	64447.5	0.0416896
$300$	−337854.	−0.216733
$301$	0	0
$302$	−1.80247e6	−1.13724
$303$	2.02164e6	1.26502
$304$	−136565.	−0.0847530
$305$	−761373.	−0.468649
$306$	−3.02842e6	−1.84890
$307$	2.82398e6	1.71007	0.855037	−	0.518567i	$-0.173534\pi$
$307$	2.82398e6	1.71007	0.855037	+	0.518567i	$0.173534\pi$
$308$	0	0
$309$	1.18344e6	0.705096
$310$	133023.	0.0786183
$311$	−991023.	−0.581009	−0.290504	−	0.956874i	$-0.593823\pi$
$311$	−991023.	−0.581009	−0.290504	+	0.956874i	$0.593823\pi$
$312$	−511701.	−0.297598
$313$	1.51083e6	0.871673	0.435836	−	0.900026i	$-0.356453\pi$
$313$	1.51083e6	0.871673	0.435836	+	0.900026i	$0.356453\pi$
$314$	−372726.	−0.213337
$315$	0	0
$316$	1.39582e6	0.786343
$317$	−2.96453e6	−1.65694	−0.828471	−	0.560032i	$-0.810789\pi$
$317$	−2.96453e6	−1.65694	−0.828471	+	0.560032i	$0.810789\pi$
$318$	−1.08511e6	−0.601736
$319$	−3.79398e6	−2.08746
$320$	581143.	0.317255
$321$	−4.09820e6	−2.21988
$322$	0	0
$323$	−2.25951e6	−1.20506
$324$	−2.91970e6	−1.54517
$325$	59396.2	0.0311925
$326$	−1.14530e6	−0.596866
$327$	−954308.	−0.493536
$328$	−3.05743e6	−1.56918
$329$	0	0
$330$	1.65343e6	0.835797
$331$	−795951.	−0.399315	−0.199658	−	0.979866i	$-0.563983\pi$
$331$	−795951.	−0.399315	−0.199658	+	0.979866i	$0.563983\pi$
$332$	−834741.	−0.415630
$333$	6.58089e6	3.25218
$334$	433256.	0.212510
$335$	−359544.	−0.175041
$336$	0	0
$337$	488585.	0.234350	0.117175	−	0.993111i	$-0.462616\pi$
$337$	488585.	0.234350	0.117175	+	0.993111i	$0.462616\pi$
$338$	−1.32625e6	−0.631443
$339$	3.78280e6	1.78778
$340$	638921.	0.299743
$341$	903266.	0.420659
$342$	3.62322e6	1.67506
$343$	0	0
$344$	−1.82053e6	−0.829470
$345$	492807.	0.222910
$346$	574282.	0.257890
$347$	746574.	0.332851	0.166425	−	0.986054i	$-0.446778\pi$
$347$	746574.	0.332851	0.166425	+	0.986054i	$0.446778\pi$
$348$	3.29998e6	1.46071
$349$	1.62813e6	0.715526	0.357763	−	0.933812i	$-0.383540\pi$
$349$	1.62813e6	0.715526	0.357763	+	0.933812i	$0.383540\pi$
$350$	0	0
$351$	991507.	0.429564
$352$	3.49493e6	1.50342
$353$	−3.09297e6	−1.32111	−0.660554	−	0.750779i	$-0.729679\pi$
$353$	−3.09297e6	−1.32111	−0.660554	+	0.750779i	$0.729679\pi$
$354$	2.47226e6	1.04854
$355$	−1.41148e6	−0.594434
$356$	2.63977e6	1.10393
$357$	0	0
$358$	−1.00862e6	−0.415930
$359$	−1.03320e6	−0.423107	−0.211554	−	0.977366i	$-0.567852\pi$
$359$	−1.03320e6	−0.423107	−0.211554	+	0.977366i	$0.567852\pi$
$360$	−2.78748e6	−1.13359
$361$	227188.	0.0917523
$362$	−804427.	−0.322638
$363$	6.54589e6	2.60737
$364$	0	0
$365$	514629.	0.202191
$366$	−3.24094e6	−1.26464
$367$	3.28554e6	1.27333	0.636666	−	0.771140i	$-0.280313\pi$
$367$	3.28554e6	1.27333	0.636666	+	0.771140i	$0.280313\pi$
$368$	−56327.4	−0.0216820
$369$	9.93515e6	3.79847
$370$	1.00065e6	0.379997
$371$	0	0
$372$	−785656.	−0.294357
$373$	4.23488e6	1.57605	0.788024	−	0.615645i	$-0.211104\pi$
$373$	4.23488e6	1.57605	0.788024	+	0.615645i	$0.211104\pi$
$374$	−3.12683e6	−1.15591
$375$	454182.	0.166783
$376$	5.03079e6	1.83513
$377$	−580152.	−0.210227
$378$	0	0
$379$	−4.51729e6	−1.61540	−0.807700	−	0.589594i	$-0.799288\pi$
$379$	−4.51729e6	−1.61540	−0.807700	+	0.589594i	$0.799288\pi$
$380$	−764407.	−0.271560
$381$	4.81314e6	1.69870
$382$	−871329.	−0.305509
$383$	−2.55952e6	−0.891581	−0.445791	−	0.895137i	$-0.647077\pi$
$383$	−2.55952e6	−0.891581	−0.445791	+	0.895137i	$0.647077\pi$
$384$	−2.75702e6	−0.954138
$385$	0	0
$386$	1.61246e6	0.550835
$387$	5.91581e6	2.00787
$388$	615588.	0.207592
$389$	5.02248e6	1.68285	0.841423	−	0.540378i	$-0.181719\pi$
$389$	5.02248e6	1.68285	0.841423	+	0.540378i	$0.181719\pi$
$390$	252832.	0.0841727
$391$	−931956.	−0.308286
$392$	0	0
$393$	83215.1	0.0271782
$394$	−1.48424e6	−0.481686
$395$	−1.87642e6	−0.605115
$396$	−6.95689e6	−2.22934
$397$	−2.92949e6	−0.932857	−0.466428	−	0.884559i	$-0.654459\pi$
$397$	−2.92949e6	−0.932857	−0.466428	+	0.884559i	$0.654459\pi$
$398$	−1.19113e6	−0.376922
$399$	0	0
$400$	−51912.6	−0.0162227
$401$	751063.	0.233247	0.116623	−	0.993176i	$-0.462793\pi$
$401$	751063.	0.233247	0.116623	+	0.993176i	$0.462793\pi$
$402$	−1.53047e6	−0.472347
$403$	138122.	0.0423643
$404$	−1.29340e6	−0.394257
$405$	3.92499e6	1.18905
$406$	0	0
$407$	6.79473e6	2.03323
$408$	7.39955e6	2.20067
$409$	−1.20530e6	−0.356276	−0.178138	−	0.984006i	$-0.557007\pi$
$409$	−1.20530e6	−0.356276	−0.178138	+	0.984006i	$0.557007\pi$
$410$	1.51069e6	0.443828
$411$	−9.77023e6	−2.85299
$412$	−757135.	−0.219751
$413$	0	0
$414$	1.49443e6	0.428523
$415$	1.12216e6	0.319840
$416$	534423.	0.151409
$417$	67641.1	0.0190489
$418$	3.74095e6	1.04723
$419$	−2.09714e6	−0.583568	−0.291784	−	0.956484i	$-0.594249\pi$
$419$	−2.09714e6	−0.583568	−0.291784	+	0.956484i	$0.594249\pi$
$420$	0	0
$421$	2.38522e6	0.655879	0.327939	−	0.944699i	$-0.393646\pi$
$421$	2.38522e6	0.655879	0.327939	+	0.944699i	$0.393646\pi$
$422$	−2.62084e6	−0.716408
$423$	−1.63476e7	−4.44224
$424$	1.88881e6	0.510238
$425$	−858911.	−0.230662
$426$	−6.00826e6	−1.60407
$427$	0	0
$428$	2.62193e6	0.691851
$429$	1.71680e6	0.450378
$430$	899526.	0.234608
$431$	−727174.	−0.188558	−0.0942790	−	0.995546i	$-0.530055\pi$
$431$	−727174.	−0.188558	−0.0942790	+	0.995546i	$0.530055\pi$
$432$	−866583.	−0.223409
$433$	1.62099e6	0.415489	0.207745	−	0.978183i	$-0.433388\pi$
$433$	1.62099e6	0.415489	0.207745	+	0.978183i	$0.433388\pi$
$434$	0	0
$435$	−4.43622e6	−1.12406
$436$	610545.	0.153816
$437$	1.11500e6	0.279299
$438$	2.19063e6	0.545611
$439$	2.46004e6	0.609230	0.304615	−	0.952476i	$-0.401472\pi$
$439$	2.46004e6	0.609230	0.304615	+	0.952476i	$0.401472\pi$
$440$	−2.87806e6	−0.708708
$441$	0	0
$442$	−478136.	−0.116411
$443$	−5.61046e6	−1.35828	−0.679140	−	0.734009i	$-0.737647\pi$
$443$	−5.61046e6	−1.35828	−0.679140	+	0.734009i	$0.737647\pi$
$444$	−5.91002e6	−1.42276
$445$	−3.54869e6	−0.849508
$446$	449527.	0.107009
$447$	108484.	0.0256801
$448$	0	0
$449$	2.65808e6	0.622233	0.311116	−	0.950372i	$-0.399297\pi$
$449$	2.65808e6	0.622233	0.311116	+	0.950372i	$0.399297\pi$
$450$	1.37730e6	0.320625
$451$	1.02580e7	2.37477
$452$	−2.42015e6	−0.557180
$453$	−1.43111e7	−3.27664
$454$	−2.78160e6	−0.633367
$455$	0	0
$456$	−8.85285e6	−1.99375
$457$	−3.67032e6	−0.822079	−0.411039	−	0.911618i	$-0.634834\pi$
$457$	−3.67032e6	−0.822079	−0.411039	+	0.911618i	$0.634834\pi$
$458$	1.91918e6	0.427516
$459$	−1.43379e7	−3.17654
$460$	−315287.	−0.0694722
$461$	−895928.	−0.196345	−0.0981727	−	0.995169i	$-0.531300\pi$
$461$	−895928.	−0.196345	−0.0981727	+	0.995169i	$0.531300\pi$
$462$	0	0
$463$	2.00402e6	0.434461	0.217230	−	0.976120i	$-0.430298\pi$
$463$	2.00402e6	0.434461	0.217230	+	0.976120i	$0.430298\pi$
$464$	507056.	0.109335
$465$	1.05617e6	0.226517
$466$	1.02570e6	0.218804
$467$	1.76483e6	0.374464	0.187232	−	0.982316i	$-0.440048\pi$
$467$	1.76483e6	0.374464	0.187232	+	0.982316i	$0.440048\pi$
$468$	−1.06380e6	−0.224516
$469$	0	0
$470$	−2.48572e6	−0.519049
$471$	−2.95935e6	−0.614673
$472$	−4.30336e6	−0.889104
$473$	6.10804e6	1.25530
$474$	−7.98739e6	−1.63290
$475$	1.02760e6	0.208974
$476$	0	0
$477$	−6.13769e6	−1.23512
$478$	1.62419e6	0.325138
$479$	8.07115e6	1.60730	0.803649	−	0.595103i	$-0.202889\pi$
$479$	8.07115e6	1.60730	0.803649	+	0.595103i	$0.202889\pi$
$480$	4.08654e6	0.809567
$481$	1.03901e6	0.204765
$482$	−4.21123e6	−0.825642
$483$	0	0
$484$	−4.18791e6	−0.812614
$485$	−827545.	−0.159749
$486$	7.42586e6	1.42612
$487$	−7.05195e6	−1.34737	−0.673685	−	0.739018i	$-0.735290\pi$
$487$	−7.05195e6	−1.34737	−0.673685	+	0.739018i	$0.735290\pi$
$488$	5.64137e6	1.07235
$489$	−9.09340e6	−1.71971
$490$	0	0
$491$	−4.56641e6	−0.854812	−0.427406	−	0.904060i	$-0.640573\pi$
$491$	−4.56641e6	−0.854812	−0.427406	+	0.904060i	$0.640573\pi$
$492$	−8.92233e6	−1.66175
$493$	8.38941e6	1.55458
$494$	572043.	0.105466
$495$	9.35226e6	1.71555
$496$	−120719.	−0.0220329
$497$	0	0
$498$	4.77669e6	0.863085
$499$	7.03262e6	1.26435	0.632173	−	0.774827i	$-0.282163\pi$
$499$	7.03262e6	1.26435	0.632173	+	0.774827i	$0.282163\pi$
$500$	−290575.	−0.0519797
$501$	3.43994e6	0.612289
$502$	2.81190e6	0.498014
$503$	−1.26376e6	−0.222713	−0.111356	−	0.993781i	$-0.535520\pi$
$503$	−1.26376e6	−0.222713	−0.111356	+	0.993781i	$0.535520\pi$
$504$	0	0
$505$	1.73874e6	0.303393
$506$	1.54299e6	0.267909
$507$	−1.05301e7	−1.81933
$508$	−3.07934e6	−0.529417
$509$	−4.59782e6	−0.786606	−0.393303	−	0.919409i	$-0.628668\pi$
$509$	−4.59782e6	−0.786606	−0.393303	+	0.919409i	$0.628668\pi$
$510$	−3.65613e6	−0.622439
$511$	0	0
$512$	−959434.	−0.161748
$513$	1.71539e7	2.87786
$514$	3.47219e6	0.579690
$515$	1.01783e6	0.169105
$516$	−5.31273e6	−0.878403
$517$	−1.68788e7	−2.77725
$518$	0	0
$519$	4.55965e6	0.743041
$520$	−440095.	−0.0713736
$521$	6.91137e6	1.11550	0.557750	−	0.830009i	$-0.311665\pi$
$521$	6.91137e6	1.11550	0.557750	+	0.830009i	$0.311665\pi$
$522$	−1.34528e7	−2.16090
$523$	4.81606e6	0.769906	0.384953	−	0.922936i	$-0.374218\pi$
$523$	4.81606e6	0.769906	0.384953	+	0.922936i	$0.374218\pi$
$524$	−53239.1	−0.00847038
$525$	0	0
$526$	1.13865e6	0.179443
$527$	−1.99734e6	−0.313275
$528$	−1.50050e6	−0.234234
$529$	−5.97645e6	−0.928548
$530$	−933263.	−0.144316
$531$	1.39838e7	2.15223
$532$	0	0
$533$	1.56859e6	0.239161
$534$	−1.51057e7	−2.29239
$535$	−3.52471e6	−0.532401
$536$	2.66403e6	0.400523
$537$	−8.00817e6	−1.19839
$538$	7.40961e6	1.10367
$539$	0	0
$540$	−4.85060e6	−0.715832
$541$	3.94054e6	0.578846	0.289423	−	0.957201i	$-0.406537\pi$
$541$	3.94054e6	0.578846	0.289423	+	0.957201i	$0.406537\pi$
$542$	−1.59633e6	−0.233413
$543$	−6.38693e6	−0.929593
$544$	−7.72813e6	−1.11964
$545$	−820765.	−0.118366
$546$	0	0
$547$	1.25402e7	1.79199	0.895994	−	0.444066i	$-0.146464\pi$
$547$	1.25402e7	1.79199	0.895994	+	0.444066i	$0.146464\pi$
$548$	6.25077e6	0.889164
$549$	−1.83317e7	−2.59580
$550$	1.42205e6	0.200452
$551$	−1.00371e7	−1.40841
$552$	−3.65144e6	−0.510054
$553$	0	0
$554$	1.10606e6	0.153110
$555$	7.94493e6	1.09486
$556$	−43275.2	−0.00593680
$557$	7.53274e6	1.02876	0.514381	−	0.857562i	$-0.328022\pi$
$557$	7.53274e6	1.02876	0.514381	+	0.857562i	$0.328022\pi$
$558$	3.20282e6	0.435458
$559$	934003.	0.126421
$560$	0	0
$561$	−2.48262e7	−3.33045
$562$	3.98648e6	0.532413
$563$	2.42490e6	0.322421	0.161210	−	0.986920i	$-0.448460\pi$
$563$	2.42490e6	0.322421	0.161210	+	0.986920i	$0.448460\pi$
$564$	1.46811e7	1.94339
$565$	3.25344e6	0.428768
$566$	3.56059e6	0.467177
$567$	0	0
$568$	1.04583e7	1.36016
$569$	5.75085e6	0.744649	0.372324	−	0.928103i	$-0.378561\pi$
$569$	5.75085e6	0.744649	0.372324	+	0.928103i	$0.378561\pi$
$570$	4.37421e6	0.563914
$571$	4.11600e6	0.528306	0.264153	−	0.964481i	$-0.414908\pi$
$571$	4.11600e6	0.528306	0.264153	+	0.964481i	$0.414908\pi$
$572$	−1.09837e6	−0.140365
$573$	−6.91812e6	−0.880241
$574$	0	0
$575$	423845.	0.0534610
$576$	1.39923e7	1.75724
$577$	2.78687e6	0.348479	0.174239	−	0.984703i	$-0.444253\pi$
$577$	2.78687e6	0.348479	0.174239	+	0.984703i	$0.444253\pi$
$578$	1.71603e6	0.213651
$579$	1.28025e7	1.58708
$580$	2.83819e6	0.350325
$581$	0	0
$582$	−3.52262e6	−0.431080
$583$	−6.33713e6	−0.772184
$584$	−3.81313e6	−0.462647
$585$	1.43009e6	0.172772
$586$	7.70383e6	0.926750
$587$	6.43829e6	0.771214	0.385607	−	0.922663i	$-0.373992\pi$
$587$	6.43829e6	0.771214	0.385607	+	0.922663i	$0.373992\pi$
$588$	0	0
$589$	2.38963e6	0.283819
$590$	2.12630e6	0.251475
$591$	−1.17845e7	−1.38785
$592$	−908099.	−0.106495
$593$	1.99134e6	0.232546	0.116273	−	0.993217i	$-0.462905\pi$
$593$	1.99134e6	0.232546	0.116273	+	0.993217i	$0.462905\pi$
$594$	2.37385e7	2.76050
$595$	0	0
$596$	−69405.6	−0.00800349
$597$	−9.45725e6	−1.08600
$598$	235944.	0.0269809
$599$	−5.97734e6	−0.680677	−0.340339	−	0.940303i	$-0.610542\pi$
$599$	−5.97734e6	−0.680677	−0.340339	+	0.940303i	$0.610542\pi$
$600$	−3.36525e6	−0.381627
$601$	3.89968e6	0.440395	0.220198	−	0.975455i	$-0.429330\pi$
$601$	3.89968e6	0.440395	0.220198	+	0.975455i	$0.429330\pi$
$602$	0	0
$603$	−8.65679e6	−0.969535
$604$	9.15593e6	1.02120
$605$	5.62988e6	0.625332
$606$	7.40131e6	0.818704
$607$	9.06961e6	0.999118	0.499559	−	0.866280i	$-0.333495\pi$
$607$	9.06961e6	0.999118	0.499559	+	0.866280i	$0.333495\pi$
$608$	9.24596e6	1.01436
$609$	0	0
$610$	−2.78741e6	−0.303303
$611$	−2.58100e6	−0.279695
$612$	1.53834e7	1.66025
$613$	9.79829e6	1.05317	0.526586	−	0.850122i	$-0.323472\pi$
$613$	9.79829e6	1.05317	0.526586	+	0.850122i	$0.323472\pi$
$614$	1.03387e7	1.10674
$615$	1.19944e7	1.27877
$616$	0	0
$617$	1.41952e7	1.50117	0.750583	−	0.660776i	$-0.229773\pi$
$617$	1.41952e7	1.50117	0.750583	+	0.660776i	$0.229773\pi$
$618$	4.33260e6	0.456328
$619$	1.14553e7	1.20166	0.600829	−	0.799377i	$-0.294837\pi$
$619$	1.14553e7	1.20166	0.600829	+	0.799377i	$0.294837\pi$
$620$	−675713.	−0.0705965
$621$	7.07529e6	0.736233
$622$	−3.62817e6	−0.376021
$623$	0	0
$624$	−229447.	−0.0235896
$625$	390625.	0.0400000
$626$	5.53119e6	0.564134
$627$	2.97022e7	3.01730
$628$	1.89332e6	0.191569
$629$	−1.50248e7	−1.51420
$630$	0	0
$631$	−4.33292e6	−0.433219	−0.216610	−	0.976258i	$-0.569500\pi$
$631$	−4.33292e6	−0.433219	−0.216610	+	0.976258i	$0.569500\pi$
$632$	1.39033e7	1.38460
$633$	−2.08088e7	−2.06413
$634$	−1.08532e7	−1.07235
$635$	4.13960e6	0.407403
$636$	5.51199e6	0.540339
$637$	0	0
$638$	−1.38899e7	−1.35097
$639$	−3.39844e7	−3.29251
$640$	−2.37121e6	−0.228833
$641$	1.33619e7	1.28446	0.642232	−	0.766511i	$-0.278009\pi$
$641$	1.33619e7	1.28446	0.642232	+	0.766511i	$0.278009\pi$
$642$	−1.50037e7	−1.43668
$643$	−9.77420e6	−0.932296	−0.466148	−	0.884707i	$-0.654359\pi$
$643$	−9.77420e6	−0.932296	−0.466148	+	0.884707i	$0.654359\pi$
$644$	0	0
$645$	7.14199e6	0.675959
$646$	−8.27215e6	−0.779897
$647$	−1.37640e7	−1.29266	−0.646328	−	0.763059i	$-0.723696\pi$
$647$	−1.37640e7	−1.29266	−0.646328	+	0.763059i	$0.723696\pi$
$648$	−2.90821e7	−2.72075
$649$	1.44382e7	1.34555
$650$	217452.	0.0201874
$651$	0	0
$652$	5.81775e6	0.535965
$653$	−1.91377e7	−1.75634	−0.878168	−	0.478353i	$-0.841234\pi$
$653$	−1.91377e7	−1.75634	−0.878168	+	0.478353i	$0.841234\pi$
$654$	−3.49376e6	−0.319410
$655$	71570.2	0.00651822
$656$	−1.37095e6	−0.124384
$657$	1.23908e7	1.11992
$658$	0	0
$659$	−2.15820e7	−1.93588	−0.967940	−	0.251183i	$-0.919181\pi$
$659$	−2.15820e7	−1.93588	−0.967940	+	0.251183i	$0.919181\pi$
$660$	−8.39886e6	−0.750517
$661$	−1.17634e7	−1.04720	−0.523600	−	0.851964i	$-0.675411\pi$
$661$	−1.17634e7	−1.04720	−0.523600	+	0.851964i	$0.675411\pi$
$662$	−2.91400e6	−0.258431
$663$	−3.79627e6	−0.335408
$664$	−8.31458e6	−0.731847
$665$	0	0
$666$	2.40929e7	2.10476
$667$	−4.13990e6	−0.360309
$668$	−2.20079e6	−0.190826
$669$	3.56913e6	0.308317
$670$	−1.31630e6	−0.113284
$671$	−1.89273e7	−1.62287
$672$	0	0
$673$	9.79570e6	0.833677	0.416838	−	0.908981i	$-0.363138\pi$
$673$	9.79570e6	0.833677	0.416838	+	0.908981i	$0.363138\pi$
$674$	1.78873e6	0.151668
$675$	6.52074e6	0.550856
$676$	6.73691e6	0.567014
$677$	−1.60043e7	−1.34204	−0.671018	−	0.741441i	$-0.734143\pi$
$677$	−1.60043e7	−1.34204	−0.671018	+	0.741441i	$0.734143\pi$
$678$	1.38489e7	1.15702
$679$	0	0
$680$	6.36408e6	0.527792
$681$	−2.20852e7	−1.82488
$682$	3.30689e6	0.272244
$683$	6.53589e6	0.536109	0.268054	−	0.963404i	$-0.413619\pi$
$683$	6.53589e6	0.536109	0.268054	+	0.963404i	$0.413619\pi$
$684$	−1.84047e7	−1.50414
$685$	−8.40301e6	−0.684240
$686$	0	0
$687$	1.52378e7	1.23177
$688$	−816324.	−0.0657493
$689$	−969034.	−0.0777662
$690$	1.80418e6	0.144264
$691$	8.94591e6	0.712737	0.356369	−	0.934345i	$-0.384015\pi$
$691$	8.94591e6	0.712737	0.356369	+	0.934345i	$0.384015\pi$
$692$	−2.91716e6	−0.231577
$693$	0	0
$694$	2.73324e6	0.215416
$695$	58175.6	0.00456855
$696$	3.28700e7	2.57203
$697$	−2.26829e7	−1.76855
$698$	5.96064e6	0.463078
$699$	8.14379e6	0.630425
$700$	0	0
$701$	1.14357e7	0.878954	0.439477	−	0.898254i	$-0.355164\pi$
$701$	1.14357e7	0.878954	0.439477	+	0.898254i	$0.355164\pi$
$702$	3.62994e6	0.278008
$703$	1.79757e7	1.37182
$704$	1.44469e7	1.09861
$705$	−1.97360e7	−1.49550
$706$	−1.13235e7	−0.855002
$707$	0	0
$708$	−1.25582e7	−0.941555
$709$	1.65049e7	1.23309	0.616547	−	0.787318i	$-0.288531\pi$
$709$	1.65049e7	1.23309	0.616547	+	0.787318i	$0.288531\pi$
$710$	−5.16748e6	−0.384709
$711$	−4.51789e7	−3.35167
$712$	2.62939e7	1.94381
$713$	985623.	0.0726084
$714$	0	0
$715$	1.47656e6	0.108015
$716$	5.12345e6	0.373491
$717$	1.28956e7	0.936796
$718$	−3.78260e6	−0.273829
$719$	−1.48415e7	−1.07067	−0.535336	−	0.844639i	$-0.679815\pi$
$719$	−1.48415e7	−1.07067	−0.535336	+	0.844639i	$0.679815\pi$
$720$	−1.24991e6	−0.0898558
$721$	0	0
$722$	831742.	0.0593808
$723$	−3.34361e7	−2.37886
$724$	4.08621e6	0.289717
$725$	−3.81543e6	−0.269586
$726$	2.39647e7	1.68745
$727$	2.05802e7	1.44415	0.722076	−	0.691814i	$-0.243188\pi$
$727$	2.05802e7	1.44415	0.722076	+	0.691814i	$0.243188\pi$
$728$	0	0
$729$	2.08084e7	1.45017
$730$	1.88408e6	0.130855
$731$	−1.35063e7	−0.934855
$732$	1.64629e7	1.13561
$733$	4.75353e6	0.326780	0.163390	−	0.986562i	$-0.447757\pi$
$733$	4.75353e6	0.326780	0.163390	+	0.986562i	$0.447757\pi$
$734$	1.20285e7	0.824082
$735$	0	0
$736$	3.81358e6	0.259501
$737$	−8.93808e6	−0.606144
$738$	3.63729e7	2.45831
$739$	−1.24076e7	−0.835752	−0.417876	−	0.908504i	$-0.637225\pi$
$739$	−1.24076e7	−0.835752	−0.417876	+	0.908504i	$0.637225\pi$
$740$	−5.08298e6	−0.341224
$741$	4.54187e6	0.303871
$742$	0	0
$743$	−1.07061e7	−0.711475	−0.355738	−	0.934586i	$-0.615770\pi$
$743$	−1.07061e7	−0.711475	−0.355738	+	0.934586i	$0.615770\pi$
$744$	−7.82566e6	−0.518309
$745$	93303.1	0.00615893
$746$	1.55041e7	1.02000
$747$	2.70183e7	1.77156
$748$	1.58832e7	1.03797
$749$	0	0
$750$	1.66278e6	0.107940
$751$	7.73368e6	0.500364	0.250182	−	0.968199i	$-0.419509\pi$
$751$	7.73368e6	0.500364	0.250182	+	0.968199i	$0.419509\pi$
$752$	2.25581e6	0.145465
$753$	2.23258e7	1.43489
$754$	−2.12396e6	−0.136056
$755$	−1.23085e7	−0.785844
$756$	0	0
$757$	−2.35779e7	−1.49543	−0.747713	−	0.664022i	$-0.768848\pi$
$757$	−2.35779e7	−1.49543	−0.747713	+	0.664022i	$0.768848\pi$
$758$	−1.65380e7	−1.04546
$759$	1.22509e7	0.771906
$760$	−7.61401e6	−0.478167
$761$	−2.34036e7	−1.46495	−0.732473	−	0.680796i	$-0.761634\pi$
$761$	−2.34036e7	−1.46495	−0.732473	+	0.680796i	$0.761634\pi$
$762$	1.76211e7	1.09937
$763$	0	0
$764$	4.42606e6	0.274336
$765$	−2.06801e7	−1.27761
$766$	−9.37048e6	−0.577019
$767$	2.20780e6	0.135510
$768$	−3.17159e7	−1.94032
$769$	1.98228e7	1.20879	0.604394	−	0.796686i	$-0.293415\pi$
$769$	1.98228e7	1.20879	0.604394	+	0.796686i	$0.293415\pi$
$770$	0	0
$771$	2.75683e7	1.67022
$772$	−8.19077e6	−0.494631
$773$	−1.71966e7	−1.03513	−0.517563	−	0.855645i	$-0.673161\pi$
$773$	−1.71966e7	−1.03513	−0.517563	+	0.855645i	$0.673161\pi$
$774$	2.16580e7	1.29947
$775$	908372.	0.0543262
$776$	6.13167e6	0.365531
$777$	0	0
$778$	1.83875e7	1.08911
$779$	2.71379e7	1.60226
$780$	−1.28430e6	−0.0755842
$781$	−3.50887e7	−2.05844
$782$	−3.41192e6	−0.199518
$783$	−6.36913e7	−3.71258
$784$	0	0
$785$	−2.54523e6	−0.147419
$786$	304653.	0.0175893
$787$	1.06439e6	0.0612584	0.0306292	−	0.999531i	$-0.490249\pi$
$787$	1.06439e6	0.0612584	0.0306292	+	0.999531i	$0.490249\pi$
$788$	7.53944e6	0.432537
$789$	9.04057e6	0.517015
$790$	−6.86965e6	−0.391622
$791$	0	0
$792$	−6.92953e7	−3.92546
$793$	−2.89425e6	−0.163438
$794$	−1.07249e7	−0.603732
$795$	−7.40986e6	−0.415807
$796$	6.05053e6	0.338463
$797$	−2.11685e7	−1.18044	−0.590221	−	0.807241i	$-0.700960\pi$
$797$	−2.11685e7	−1.18044	−0.590221	+	0.807241i	$0.700960\pi$
$798$	0	0
$799$	3.73230e7	2.06828
$800$	3.51468e6	0.194161
$801$	−8.54422e7	−4.70534
$802$	2.74967e6	0.150954
$803$	1.27934e7	0.700161
$804$	7.77429e6	0.424151
$805$	0	0
$806$	505669.	0.0274176
$807$	5.88303e7	3.17993
$808$	−1.28831e7	−0.694214
$809$	−1.58351e7	−0.850647	−0.425324	−	0.905041i	$-0.639840\pi$
$809$	−1.58351e7	−0.850647	−0.425324	+	0.905041i	$0.639840\pi$
$810$	1.43695e7	0.769539
$811$	3.52439e7	1.88162	0.940810	−	0.338933i	$-0.110066\pi$
$811$	3.52439e7	1.88162	0.940810	+	0.338933i	$0.110066\pi$
$812$	0	0
$813$	−1.26744e7	−0.672516
$814$	2.48758e7	1.31588
$815$	−7.82090e6	−0.412442
$816$	3.31796e6	0.174440
$817$	1.61590e7	0.846955
$818$	−4.41264e6	−0.230576
$819$	0	0
$820$	−7.67377e6	−0.398542
$821$	−3.12880e7	−1.62002	−0.810010	−	0.586416i	$-0.800538\pi$
$821$	−3.12880e7	−1.62002	−0.810010	+	0.586416i	$0.800538\pi$
$822$	−3.57692e7	−1.84641
$823$	4.19410e6	0.215844	0.107922	−	0.994159i	$-0.465580\pi$
$823$	4.19410e6	0.215844	0.107922	+	0.994159i	$0.465580\pi$
$824$	−7.54157e6	−0.386940
$825$	1.12907e7	0.577547
$826$	0	0
$827$	−1.28940e7	−0.655576	−0.327788	−	0.944751i	$-0.606303\pi$
$827$	−1.28940e7	−0.655576	−0.327788	+	0.944751i	$0.606303\pi$
$828$	−7.59119e6	−0.384799
$829$	1.08986e7	0.550788	0.275394	−	0.961331i	$-0.411192\pi$
$829$	1.08986e7	0.550788	0.275394	+	0.961331i	$0.411192\pi$
$830$	4.10825e6	0.206996
$831$	8.78183e6	0.441146
$832$	2.20913e6	0.110640
$833$	0	0
$834$	247636.	0.0123282
$835$	2.95856e6	0.146847
$836$	−1.90028e7	−0.940375
$837$	1.51635e7	0.748148
$838$	−7.67769e6	−0.377677
$839$	−2.38675e7	−1.17058	−0.585291	−	0.810823i	$-0.699020\pi$
$839$	−2.38675e7	−1.17058	−0.585291	+	0.810823i	$0.699020\pi$
$840$	0	0
$841$	1.67560e7	0.816920
$842$	8.73238e6	0.424475
$843$	3.16516e7	1.53400
$844$	1.33130e7	0.643309
$845$	−9.05654e6	−0.436335
$846$	−5.98491e7	−2.87496
$847$	0	0
$848$	846941.	0.0404449
$849$	2.82702e7	1.34604
$850$	−3.14450e6	−0.149281
$851$	7.41425e6	0.350948
$852$	3.05199e7	1.44040
$853$	2.34306e7	1.10258	0.551292	−	0.834313i	$-0.314135\pi$
$853$	2.34306e7	1.10258	0.551292	+	0.834313i	$0.314135\pi$
$854$	0	0
$855$	2.47418e7	1.15748
$856$	2.61162e7	1.21822
$857$	1.75346e7	0.815539	0.407769	−	0.913085i	$-0.366307\pi$
$857$	1.75346e7	0.815539	0.407769	+	0.913085i	$0.366307\pi$
$858$	6.28528e6	0.291478
$859$	−3.20848e7	−1.48360	−0.741799	−	0.670623i	$-0.766027\pi$
$859$	−3.20848e7	−1.48360	−0.741799	+	0.670623i	$0.766027\pi$
$860$	−4.56928e6	−0.210670
$861$	0	0
$862$	−2.66221e6	−0.122032
$863$	3.43751e7	1.57115	0.785574	−	0.618768i	$-0.212368\pi$
$863$	3.43751e7	1.57115	0.785574	+	0.618768i	$0.212368\pi$
$864$	5.86709e7	2.67386
$865$	3.92158e6	0.178205
$866$	5.93449e6	0.268899
$867$	1.36248e7	0.615578
$868$	0	0
$869$	−4.66469e7	−2.09543
$870$	−1.62411e7	−0.727476
$871$	−1.36676e6	−0.0610444
$872$	6.08143e6	0.270841
$873$	−1.99249e7	−0.884831
$874$	4.08204e6	0.180758
$875$	0	0
$876$	−1.11276e7	−0.489940
$877$	−2.21293e7	−0.971556	−0.485778	−	0.874082i	$-0.661464\pi$
$877$	−2.21293e7	−0.971556	−0.485778	+	0.874082i	$0.661464\pi$
$878$	9.00630e6	0.394285
$879$	6.11664e7	2.67018
$880$	−1.29052e6	−0.0561770
$881$	3.24354e7	1.40792	0.703962	−	0.710238i	$-0.251413\pi$
$881$	3.24354e7	1.40792	0.703962	+	0.710238i	$0.251413\pi$
$882$	0	0
$883$	−8.39828e6	−0.362484	−0.181242	−	0.983439i	$-0.558012\pi$
$883$	−8.39828e6	−0.362484	−0.181242	+	0.983439i	$0.558012\pi$
$884$	2.42877e6	0.104533
$885$	1.68822e7	0.724556
$886$	−2.05401e7	−0.879059
$887$	−1.80485e7	−0.770249	−0.385124	−	0.922865i	$-0.625841\pi$
$887$	−1.80485e7	−0.770249	−0.385124	+	0.922865i	$0.625841\pi$
$888$	−5.88677e7	−2.50521
$889$	0	0
$890$	−1.29919e7	−0.549790
$891$	9.75733e7	4.11753
$892$	−2.28345e6	−0.0960901
$893$	−4.46534e7	−1.87381
$894$	397164.	0.0166198
$895$	−6.88753e6	−0.287413
$896$	0	0
$897$	1.87334e6	0.0777382
$898$	9.73134e6	0.402700
$899$	−8.87251e6	−0.366140
$900$	−6.99622e6	−0.287910
$901$	1.40129e7	0.575065
$902$	3.75548e7	1.53691
$903$	0	0
$904$	−2.41063e7	−0.981091
$905$	−5.49316e6	−0.222947
$906$	−5.23935e7	−2.12059
$907$	−2.21468e7	−0.893908	−0.446954	−	0.894557i	$-0.647491\pi$
$907$	−2.21468e7	−0.893908	−0.446954	+	0.894557i	$0.647491\pi$
$908$	1.41296e7	0.568742
$909$	4.18638e7	1.68046
$910$	0	0
$911$	5.37314e6	0.214502	0.107251	−	0.994232i	$-0.465795\pi$
$911$	5.37314e6	0.214502	0.107251	+	0.994232i	$0.465795\pi$
$912$	−3.96962e6	−0.158038
$913$	2.78962e7	1.10756
$914$	−1.34372e7	−0.532038
$915$	−2.21313e7	−0.873886
$916$	−9.74880e6	−0.383895
$917$	0	0
$918$	−5.24915e7	−2.05581
$919$	−2.42685e7	−0.947881	−0.473940	−	0.880557i	$-0.657169\pi$
$919$	−2.42685e7	−0.947881	−0.473940	+	0.880557i	$0.657169\pi$
$920$	−3.14047e6	−0.122328
$921$	8.20863e7	3.18876
$922$	−3.28002e6	−0.127072
$923$	−5.36554e6	−0.207305
$924$	0	0
$925$	6.83314e6	0.262583
$926$	7.33680e6	0.281177
$927$	2.45064e7	0.936656
$928$	−3.43296e7	−1.30858
$929$	−1.92015e7	−0.729955	−0.364977	−	0.931016i	$-0.618923\pi$
$929$	−1.92015e7	−0.729955	−0.364977	+	0.931016i	$0.618923\pi$
$930$	3.86667e6	0.146599
$931$	0	0
$932$	−5.21021e6	−0.196479
$933$	−2.88067e7	−1.08340
$934$	6.46110e6	0.242348
$935$	−2.13521e7	−0.798751
$936$	−1.05962e7	−0.395331
$937$	−3.45954e6	−0.128727	−0.0643635	−	0.997927i	$-0.520502\pi$
$937$	−3.45954e6	−0.128727	−0.0643635	+	0.997927i	$0.520502\pi$
$938$	0	0
$939$	4.39161e7	1.62540
$940$	1.26266e7	0.466088
$941$	1.25363e7	0.461525	0.230763	−	0.973010i	$-0.425878\pi$
$941$	1.25363e7	0.461525	0.230763	+	0.973010i	$0.425878\pi$
$942$	−1.08343e7	−0.397807
$943$	1.11933e7	0.409900
$944$	−1.92963e6	−0.0704763
$945$	0	0
$946$	2.23617e7	0.812415
$947$	2.57172e7	0.931856	0.465928	−	0.884823i	$-0.345721\pi$
$947$	2.57172e7	0.931856	0.465928	+	0.884823i	$0.345721\pi$
$948$	4.05732e7	1.46629
$949$	1.95629e6	0.0705128
$950$	3.76210e6	0.135245
$951$	−8.61718e7	−3.08968
$952$	0	0
$953$	−501528.	−0.0178881	−0.00894403	−	0.999960i	$-0.502847\pi$
$953$	−501528.	−0.0178881	−0.00894403	+	0.999960i	$0.502847\pi$
$954$	−2.24703e7	−0.799352
$955$	−5.95002e6	−0.211111
$956$	−8.25034e6	−0.291963
$957$	−1.10282e8	−3.89247
$958$	2.95488e7	1.04022
$959$	0	0
$960$	1.68925e7	0.591582
$961$	−2.65168e7	−0.926217
$962$	3.80385e6	0.132521
$963$	−8.48648e7	−2.94891
$964$	2.13916e7	0.741398
$965$	1.10110e7	0.380634
$966$	0	0
$967$	1.98935e7	0.684139	0.342070	−	0.939675i	$-0.388872\pi$
$967$	1.98935e7	0.684139	0.342070	+	0.939675i	$0.388872\pi$
$968$	−4.17144e7	−1.43086
$969$	−6.56786e7	−2.24706
$970$	−3.02967e6	−0.103387
$971$	1.09326e7	0.372113	0.186057	−	0.982539i	$-0.440429\pi$
$971$	1.09326e7	0.372113	0.186057	+	0.982539i	$0.440429\pi$
$972$	−3.77208e7	−1.28061
$973$	0	0
$974$	−2.58175e7	−0.871999
$975$	1.72651e6	0.0581644
$976$	2.52959e6	0.0850014
$977$	1.92730e7	0.645969	0.322985	−	0.946404i	$-0.395314\pi$
$977$	1.92730e7	0.645969	0.322985	+	0.946404i	$0.395314\pi$
$978$	−3.32913e7	−1.11297
$979$	−8.82185e7	−2.94173
$980$	0	0
$981$	−1.97617e7	−0.655618
$982$	−1.67178e7	−0.553222
$983$	2.54855e7	0.841220	0.420610	−	0.907241i	$-0.361816\pi$
$983$	2.54855e7	0.841220	0.420610	+	0.907241i	$0.361816\pi$
$984$	−8.88724e7	−2.92603
$985$	−1.01354e7	−0.332851
$986$	3.07139e7	1.00610
$987$	0	0
$988$	−2.90579e6	−0.0947046
$989$	6.66494e6	0.216673
$990$	3.42390e7	1.11028
$991$	1.45114e7	0.469380	0.234690	−	0.972070i	$-0.424592\pi$
$991$	1.45114e7	0.469380	0.234690	+	0.972070i	$0.424592\pi$
$992$	8.17315e6	0.263700
$993$	−2.31364e7	−0.744600
$994$	0	0
$995$	−8.13383e6	−0.260458
$996$	−2.42640e7	−0.775021
$997$	1.46470e7	0.466671	0.233336	−	0.972396i	$-0.425036\pi$
$997$	1.46470e7	0.466671	0.233336	+	0.972396i	$0.425036\pi$
$998$	2.57467e7	0.818267
$999$	1.14066e8	3.61613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.m.1.6	yes	10
7.6	odd	2		245.6.a.l.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.6	✓	10	7.6	odd	2
245.6.a.m.1.6	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+3.66104 q^{2} +29.0676 q^{3} -18.5968 q^{4} +25.0000 q^{5} +106.418 q^{6} -185.237 q^{8} +601.928 q^{9} +O(q^{10})\)	\(q+3.66104 q^{2} +29.0676 q^{3} -18.5968 q^{4} +25.0000 q^{5} +106.418 q^{6} -185.237 q^{8} +601.928 q^{9} +91.5259 q^{10} +621.487 q^{11} -540.566 q^{12} +95.0340 q^{13} +726.691 q^{15} -83.0602 q^{16} -1374.26 q^{17} +2203.68 q^{18} +1644.17 q^{19} -464.920 q^{20} +2275.29 q^{22} +678.152 q^{23} -5384.40 q^{24} +625.000 q^{25} +347.923 q^{26} +10433.2 q^{27} -6104.68 q^{29} +2660.44 q^{30} +1453.40 q^{31} +5623.49 q^{32} +18065.2 q^{33} -5031.21 q^{34} -11193.9 q^{36} +10933.0 q^{37} +6019.36 q^{38} +2762.41 q^{39} -4630.92 q^{40} +16505.5 q^{41} +9828.10 q^{43} -11557.7 q^{44} +15048.2 q^{45} +2482.74 q^{46} -27158.7 q^{47} -2414.36 q^{48} +2288.15 q^{50} -39946.4 q^{51} -1767.33 q^{52} -10196.7 q^{53} +38196.3 q^{54} +15537.2 q^{55} +47792.1 q^{57} -22349.5 q^{58} +23231.7 q^{59} -13514.1 q^{60} -30454.9 q^{61} +5320.93 q^{62} +23245.7 q^{64} +2375.85 q^{65} +66137.2 q^{66} -14381.8 q^{67} +25556.8 q^{68} +19712.3 q^{69} -56459.2 q^{71} -111499. q^{72} +20585.2 q^{73} +40026.2 q^{74} +18167.3 q^{75} -30576.3 q^{76} +10113.3 q^{78} -75056.9 q^{79} -2076.51 q^{80} +157000. q^{81} +60427.4 q^{82} +44886.2 q^{83} -34356.5 q^{85} +35981.0 q^{86} -177449. q^{87} -115122. q^{88} -141947. q^{89} +55092.0 q^{90} -12611.5 q^{92} +42246.8 q^{93} -99428.9 q^{94} +41104.2 q^{95} +163462. q^{96} -33101.8 q^{97} +374090. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 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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