LMFDB - Embedded newform 130.6.a.d.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,6,Mod(1,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	130.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8,-26,32,-50,-104,160] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$20.8498965757$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{235}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 235 $ x^2 - 235
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$15.3297$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} +2.32971 q^{3} +16.0000 q^{4} -25.0000 q^{5} +9.31884 q^{6} -11.9783 q^{7} +64.0000 q^{8} -237.572 q^{9} -100.000 q^{10} -592.946 q^{11} +37.2754 q^{12} +169.000 q^{13} -47.9130 q^{14} -58.2427 q^{15} +256.000 q^{16} -1152.07 q^{17} -950.290 q^{18} +1968.42 q^{19} -400.000 q^{20} -27.9059 q^{21} -2371.78 q^{22} -4924.36 q^{23} +149.101 q^{24} +625.000 q^{25} +676.000 q^{26} -1119.59 q^{27} -191.652 q^{28} -3173.80 q^{29} -232.971 q^{30} +811.533 q^{31} +1024.00 q^{32} -1381.39 q^{33} -4608.26 q^{34} +299.456 q^{35} -3801.16 q^{36} +3670.00 q^{37} +7873.70 q^{38} +393.721 q^{39} -1600.00 q^{40} -4409.33 q^{41} -111.623 q^{42} +358.098 q^{43} -9487.13 q^{44} +5939.31 q^{45} -19697.4 q^{46} -12522.3 q^{47} +596.406 q^{48} -16663.5 q^{49} +2500.00 q^{50} -2683.98 q^{51} +2704.00 q^{52} +6679.07 q^{53} -4478.38 q^{54} +14823.6 q^{55} -766.609 q^{56} +4585.86 q^{57} -12695.2 q^{58} +19291.8 q^{59} -931.884 q^{60} +37674.6 q^{61} +3246.13 q^{62} +2845.70 q^{63} +4096.00 q^{64} -4225.00 q^{65} -5525.56 q^{66} -32133.1 q^{67} -18433.0 q^{68} -11472.3 q^{69} +1197.83 q^{70} -8921.14 q^{71} -15204.6 q^{72} +30600.6 q^{73} +14680.0 q^{74} +1456.07 q^{75} +31494.8 q^{76} +7102.46 q^{77} +1574.88 q^{78} -11135.1 q^{79} -6400.00 q^{80} +55121.8 q^{81} -17637.3 q^{82} +24534.4 q^{83} -446.494 q^{84} +28801.6 q^{85} +1432.39 q^{86} -7394.04 q^{87} -37948.5 q^{88} -31623.3 q^{89} +23757.2 q^{90} -2024.33 q^{91} -78789.7 q^{92} +1890.64 q^{93} -50089.1 q^{94} -49210.6 q^{95} +2385.62 q^{96} +138544. q^{97} -66654.1 q^{98} +140868. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 26 q^{3} + 32 q^{4} - 50 q^{5} - 104 q^{6} + 160 q^{7} + 128 q^{8} + 322 q^{9} - 200 q^{10} - 726 q^{11} - 416 q^{12} + 338 q^{13} + 640 q^{14} + 650 q^{15} + 512 q^{16} - 2856 q^{17} + 1288 q^{18}+ \cdots + 66414 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 - 26 * q^3 + 32 * q^4 - 50 * q^5 - 104 * q^6 + 160 * q^7 + 128 * q^8 + 322 * q^9 - 200 * q^10 - 726 * q^11 - 416 * q^12 + 338 * q^13 + 640 * q^14 + 650 * q^15 + 512 * q^16 - 2856 * q^17 + 1288 * q^18 - 938 * q^19 - 800 * q^20 - 4900 * q^21 - 2904 * q^22 - 4422 * q^23 - 1664 * q^24 + 1250 * q^25 + 1352 * q^26 - 10088 * q^27 + 2560 * q^28 - 4692 * q^29 + 2600 * q^30 + 6130 * q^31 + 2048 * q^32 + 2388 * q^33 - 11424 * q^34 - 4000 * q^35 + 5152 * q^36 - 9584 * q^37 - 3752 * q^38 - 4394 * q^39 - 3200 * q^40 - 20040 * q^41 - 19600 * q^42 + 10006 * q^43 - 11616 * q^44 - 8050 * q^45 - 17688 * q^46 - 10512 * q^47 - 6656 * q^48 - 3894 * q^49 + 5000 * q^50 + 45588 * q^51 + 5408 * q^52 + 5448 * q^53 - 40352 * q^54 + 18150 * q^55 + 10240 * q^56 + 86924 * q^57 - 18768 * q^58 - 22398 * q^59 + 10400 * q^60 + 12988 * q^61 + 24520 * q^62 + 99080 * q^63 + 8192 * q^64 - 8450 * q^65 + 9552 * q^66 - 56540 * q^67 - 45696 * q^68 - 25704 * q^69 - 16000 * q^70 - 69810 * q^71 + 20608 * q^72 + 99832 * q^73 - 38336 * q^74 - 16250 * q^75 - 15008 * q^76 - 15780 * q^77 - 17576 * q^78 - 31652 * q^79 - 12800 * q^80 + 173218 * q^81 - 80160 * q^82 + 69120 * q^83 - 78400 * q^84 + 71400 * q^85 + 40024 * q^86 + 35616 * q^87 - 46464 * q^88 - 141612 * q^89 - 32200 * q^90 + 27040 * q^91 - 70752 * q^92 - 148780 * q^93 - 42048 * q^94 + 23450 * q^95 - 26624 * q^96 - 7676 * q^97 - 15576 * q^98 + 66414 * q^99

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	2.32971	0.149451	0.0747255	−	0.997204i	$-0.476192\pi$
$3$	2.32971	0.149451	0.0747255	+	0.997204i	$0.476192\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	9.31884	0.105678
$7$	−11.9783	−0.0923950	−0.0461975	−	0.998932i	$-0.514710\pi$
$7$	−11.9783	−0.0923950	−0.0461975	+	0.998932i	$0.514710\pi$
$8$	64.0000	0.353553
$9$	−237.572	−0.977664
$10$	−100.000	−0.316228
$11$	−592.946	−1.47752	−0.738760	−	0.673969i	$-0.764588\pi$
$11$	−592.946	−1.47752	−0.738760	+	0.673969i	$0.764588\pi$
$12$	37.2754	0.0747255
$13$	169.000	0.277350
$13$	169.000	0.277350
$14$	−47.9130	−0.0653331
$15$	−58.2427	−0.0668365
$16$	256.000	0.250000
$17$	−1152.07	−0.966840	−0.483420	−	0.875388i	$-0.660606\pi$
$17$	−1152.07	−0.966840	−0.483420	+	0.875388i	$0.660606\pi$
$18$	−950.290	−0.691313
$19$	1968.42	1.25093	0.625467	−	0.780250i	$-0.284908\pi$
$19$	1968.42	1.25093	0.625467	+	0.780250i	$0.284908\pi$
$20$	−400.000	−0.223607
$21$	−27.9059	−0.0138085
$22$	−2371.78	−1.04476
$23$	−4924.36	−1.94102	−0.970510	−	0.241060i	$-0.922505\pi$
$23$	−4924.36	−1.94102	−0.970510	+	0.241060i	$0.922505\pi$
$24$	149.101	0.0528389
$25$	625.000	0.200000
$26$	676.000	0.196116
$27$	−1119.59	−0.295564
$28$	−191.652	−0.0461975
$29$	−3173.80	−0.700786	−0.350393	−	0.936603i	$-0.613952\pi$
$29$	−3173.80	−0.700786	−0.350393	+	0.936603i	$0.613952\pi$
$30$	−232.971	−0.0472605
$31$	811.533	0.151671	0.0758354	−	0.997120i	$-0.475838\pi$
$31$	811.533	0.151671	0.0758354	+	0.997120i	$0.475838\pi$
$32$	1024.00	0.176777
$33$	−1381.39	−0.220817
$34$	−4608.26	−0.683659
$35$	299.456	0.0413203
$36$	−3801.16	−0.488832
$37$	3670.00	0.440719	0.220359	−	0.975419i	$-0.429277\pi$
$37$	3670.00	0.440719	0.220359	+	0.975419i	$0.429277\pi$
$38$	7873.70	0.884544
$39$	393.721	0.0414502
$40$	−1600.00	−0.158114
$41$	−4409.33	−0.409650	−0.204825	−	0.978799i	$-0.565662\pi$
$41$	−4409.33	−0.409650	−0.204825	+	0.978799i	$0.565662\pi$
$42$	−111.623	−0.00976410
$43$	358.098	0.0295346	0.0147673	−	0.999891i	$-0.495299\pi$
$43$	358.098	0.0295346	0.0147673	+	0.999891i	$0.495299\pi$
$44$	−9487.13	−0.738760
$45$	5939.31	0.437225
$46$	−19697.4	−1.37251
$47$	−12522.3	−0.826873	−0.413437	−	0.910533i	$-0.635672\pi$
$47$	−12522.3	−0.826873	−0.413437	+	0.910533i	$0.635672\pi$
$48$	596.406	0.0373627
$49$	−16663.5	−0.991463
$50$	2500.00	0.141421
$51$	−2683.98	−0.144495
$52$	2704.00	0.138675
$53$	6679.07	0.326607	0.163304	−	0.986576i	$-0.447785\pi$
$53$	6679.07	0.326607	0.163304	+	0.986576i	$0.447785\pi$
$54$	−4478.38	−0.208995
$55$	14823.6	0.660767
$56$	−766.609	−0.0326666
$57$	4585.86	0.186953
$58$	−12695.2	−0.495530
$59$	19291.8	0.721510	0.360755	−	0.932661i	$-0.382519\pi$
$59$	19291.8	0.721510	0.360755	+	0.932661i	$0.382519\pi$
$60$	−931.884	−0.0334182
$61$	37674.6	1.29636	0.648178	−	0.761489i	$-0.275531\pi$
$61$	37674.6	1.29636	0.648178	+	0.761489i	$0.275531\pi$
$62$	3246.13	0.107247
$63$	2845.70	0.0903313
$64$	4096.00	0.125000
$65$	−4225.00	−0.124035
$66$	−5525.56	−0.156141
$67$	−32133.1	−0.874511	−0.437256	−	0.899337i	$-0.644050\pi$
$67$	−32133.1	−0.874511	−0.437256	+	0.899337i	$0.644050\pi$
$68$	−18433.0	−0.483420
$69$	−11472.3	−0.290087
$70$	1197.83	0.0292179
$71$	−8921.14	−0.210027	−0.105013	−	0.994471i	$-0.533489\pi$
$71$	−8921.14	−0.210027	−0.105013	+	0.994471i	$0.533489\pi$
$72$	−15204.6	−0.345657
$73$	30600.6	0.672082	0.336041	−	0.941847i	$-0.390912\pi$
$73$	30600.6	0.672082	0.336041	+	0.941847i	$0.390912\pi$
$74$	14680.0	0.311635
$75$	1456.07	0.0298902
$76$	31494.8	0.625467
$77$	7102.46	0.136515
$78$	1574.88	0.0293097
$79$	−11135.1	−0.200737	−0.100368	−	0.994950i	$-0.532002\pi$
$79$	−11135.1	−0.200737	−0.100368	+	0.994950i	$0.532002\pi$
$80$	−6400.00	−0.111803
$81$	55121.8	0.933492
$82$	−17637.3	−0.289666
$83$	24534.4	0.390913	0.195456	−	0.980712i	$-0.437381\pi$
$83$	24534.4	0.390913	0.195456	+	0.980712i	$0.437381\pi$
$84$	−446.494	−0.00690426
$85$	28801.6	0.432384
$86$	1432.39	0.0208841
$87$	−7394.04	−0.104733
$88$	−37948.5	−0.522382
$89$	−31623.3	−0.423186	−0.211593	−	0.977358i	$-0.567865\pi$
$89$	−31623.3	−0.423186	−0.211593	+	0.977358i	$0.567865\pi$
$90$	23757.2	0.309165
$91$	−2024.33	−0.0256258
$92$	−78789.7	−0.970510
$93$	1890.64	0.0226673
$94$	−50089.1	−0.584688
$95$	−49210.6	−0.559435
$96$	2385.62	0.0264194
$97$	138544.	1.49506	0.747531	−	0.664226i	$-0.231239\pi$
$97$	138544.	1.49506	0.747531	+	0.664226i	$0.231239\pi$
$98$	−66654.1	−0.701070
$99$	140868.	1.44452
$100$	10000.0	0.100000
$101$	111185.	1.08453	0.542265	−	0.840208i	$-0.317567\pi$
$101$	111185.	1.08453	0.542265	+	0.840208i	$0.317567\pi$
$102$	−10735.9	−0.102174
$103$	29905.5	0.277753	0.138876	−	0.990310i	$-0.455651\pi$
$103$	29905.5	0.277753	0.138876	+	0.990310i	$0.455651\pi$
$104$	10816.0	0.0980581
$105$	697.647	0.00617536
$106$	26716.3	0.230946
$107$	214435.	1.81066	0.905329	−	0.424710i	$-0.139624\pi$
$107$	214435.	1.81066	0.905329	+	0.424710i	$0.139624\pi$
$108$	−17913.5	−0.147782
$109$	−229893.	−1.85336	−0.926681	−	0.375849i	$-0.877351\pi$
$109$	−229893.	−1.85336	−0.926681	+	0.375849i	$0.877351\pi$
$110$	59294.6	0.467233
$111$	8550.03	0.0658659
$112$	−3066.43	−0.0230988
$113$	−187452.	−1.38100	−0.690501	−	0.723331i	$-0.742610\pi$
$113$	−187452.	−1.38100	−0.690501	+	0.723331i	$0.742610\pi$
$114$	18343.4	0.132196
$115$	123109.	0.868051
$116$	−50780.9	−0.350393
$117$	−40149.7	−0.271155
$118$	77167.2	0.510185
$119$	13799.7	0.0893312
$120$	−3727.54	−0.0236303
$121$	190534.	1.18306
$122$	150699.	0.916662
$123$	−10272.5	−0.0612225
$124$	12984.5	0.0758354
$125$	−15625.0	−0.0894427
$126$	11382.8	0.0638739
$127$	234608.	1.29072	0.645361	−	0.763878i	$-0.276707\pi$
$127$	234608.	1.29072	0.645361	+	0.763878i	$0.276707\pi$
$128$	16384.0	0.0883883
$129$	834.264	0.00441397
$130$	−16900.0	−0.0877058
$131$	165736.	0.843799	0.421899	−	0.906643i	$-0.361364\pi$
$131$	165736.	0.843799	0.421899	+	0.906643i	$0.361364\pi$
$132$	−22102.3	−0.110408
$133$	−23578.3	−0.115580
$134$	−128532.	−0.618373
$135$	27989.9	0.132180
$136$	−73732.2	−0.341830
$137$	−22506.0	−0.102446	−0.0512231	−	0.998687i	$-0.516312\pi$
$137$	−22506.0	−0.102446	−0.0512231	+	0.998687i	$0.516312\pi$
$138$	−45889.3	−0.205123
$139$	−121670.	−0.534128	−0.267064	−	0.963679i	$-0.586053\pi$
$139$	−121670.	−0.534128	−0.267064	+	0.963679i	$0.586053\pi$
$140$	4791.30	0.0206602
$141$	−29173.3	−0.123577
$142$	−35684.6	−0.148511
$143$	−100208.	−0.409790
$144$	−60818.5	−0.244416
$145$	79345.1	0.313401
$146$	122402.	0.475234
$147$	−38821.2	−0.148175
$148$	58720.0	0.220359
$149$	−395990.	−1.46123	−0.730614	−	0.682791i	$-0.760766\pi$
$149$	−395990.	−1.46123	−0.730614	+	0.682791i	$0.760766\pi$
$150$	5824.27	0.0211356
$151$	−426046.	−1.52060	−0.760299	−	0.649573i	$-0.774948\pi$
$151$	−426046.	−1.52060	−0.760299	+	0.649573i	$0.774948\pi$
$152$	125979.	0.442272
$153$	273699.	0.945245
$154$	28409.8	0.0965310
$155$	−20288.3	−0.0678292
$156$	6299.54	0.0207251
$157$	−383765.	−1.24256	−0.621279	−	0.783589i	$-0.713387\pi$
$157$	−383765.	−1.24256	−0.621279	+	0.783589i	$0.713387\pi$
$158$	−44540.4	−0.141942
$159$	15560.3	0.0488118
$160$	−25600.0	−0.0790569
$161$	58985.2	0.179341
$162$	220487.	0.660079
$163$	−389149.	−1.14722	−0.573611	−	0.819128i	$-0.694458\pi$
$163$	−389149.	−1.14722	−0.573611	+	0.819128i	$0.694458\pi$
$164$	−70549.2	−0.204825
$165$	34534.8	0.0987522
$166$	98137.5	0.276417
$167$	−260784.	−0.723586	−0.361793	−	0.932259i	$-0.617835\pi$
$167$	−260784.	−0.723586	−0.361793	+	0.932259i	$0.617835\pi$
$168$	−1785.98	−0.00488205
$169$	28561.0	0.0769231
$170$	115207.	0.305742
$171$	−467643.	−1.22299
$172$	5729.57	0.0147673
$173$	−76020.3	−0.193114	−0.0965572	−	0.995327i	$-0.530783\pi$
$173$	−76020.3	−0.193114	−0.0965572	+	0.995327i	$0.530783\pi$
$174$	−29576.2	−0.0740575
$175$	−7486.41	−0.0184790
$176$	−151794.	−0.369380
$177$	44944.3	0.107830
$178$	−126493.	−0.299238
$179$	−693005.	−1.61661	−0.808303	−	0.588767i	$-0.799613\pi$
$179$	−693005.	−1.61661	−0.808303	+	0.588767i	$0.799613\pi$
$180$	95029.0	0.218612
$181$	−491399.	−1.11491	−0.557453	−	0.830209i	$-0.688221\pi$
$181$	−491399.	−1.11491	−0.557453	+	0.830209i	$0.688221\pi$
$182$	−8097.30	−0.0181202
$183$	87771.0	0.193742
$184$	−315159.	−0.686254
$185$	−91750.0	−0.197096
$186$	7562.54	0.0160282
$187$	683112.	1.42853
$188$	−200357.	−0.413437
$189$	13410.8	0.0273086
$190$	−196842.	−0.395580
$191$	748139.	1.48388	0.741941	−	0.670466i	$-0.233906\pi$
$191$	748139.	1.48388	0.741941	+	0.670466i	$0.233906\pi$
$192$	9542.49	0.0186814
$193$	−588558.	−1.13736	−0.568678	−	0.822561i	$-0.692545\pi$
$193$	−588558.	−1.13736	−0.568678	+	0.822561i	$0.692545\pi$
$194$	554177.	1.05717
$195$	−9843.02	−0.0185371
$196$	−266616.	−0.495732
$197$	150202.	0.275747	0.137873	−	0.990450i	$-0.455973\pi$
$197$	150202.	0.275747	0.137873	+	0.990450i	$0.455973\pi$
$198$	563470.	1.02143
$199$	−742264.	−1.32870	−0.664348	−	0.747423i	$-0.731291\pi$
$199$	−742264.	−1.32870	−0.664348	+	0.747423i	$0.731291\pi$
$200$	40000.0	0.0707107
$201$	−74860.8	−0.130697
$202$	444739.	0.766878
$203$	38016.6	0.0647491
$204$	−42943.6	−0.0722476
$205$	110233.	0.183201
$206$	119622.	0.196401
$207$	1.16989e6	1.89767
$208$	43264.0	0.0693375
$209$	−1.16717e6	−1.84828
$210$	2790.59	0.00436664
$211$	−144836.	−0.223960	−0.111980	−	0.993710i	$-0.535719\pi$
$211$	−144836.	−0.223960	−0.111980	+	0.993710i	$0.535719\pi$
$212$	106865.	0.163304
$213$	−20783.7	−0.0313887
$214$	857741.	1.28033
$215$	−8952.45	−0.0132083
$216$	−71654.0	−0.104498
$217$	−9720.75	−0.0140136
$218$	−919574.	−1.31052
$219$	71290.4	0.100443
$220$	237178.	0.330383
$221$	−194699.	−0.268153
$222$	34200.1	0.0465742
$223$	−79928.8	−0.107632	−0.0538159	−	0.998551i	$-0.517138\pi$
$223$	−79928.8	−0.107632	−0.0538159	+	0.998551i	$0.517138\pi$
$224$	−12265.7	−0.0163333
$225$	−148483.	−0.195533
$226$	−749809.	−0.976516
$227$	1.03559e6	1.33390	0.666949	−	0.745103i	$-0.267600\pi$
$227$	1.03559e6	1.33390	0.666949	+	0.745103i	$0.267600\pi$
$228$	73373.7	0.0934767
$229$	−1.12731e6	−1.42054	−0.710272	−	0.703927i	$-0.751428\pi$
$229$	−1.12731e6	−1.42054	−0.710272	+	0.703927i	$0.751428\pi$
$230$	492436.	0.613805
$231$	16546.7	0.0204024
$232$	−203123.	−0.247765
$233$	−790483.	−0.953900	−0.476950	−	0.878930i	$-0.658258\pi$
$233$	−790483.	−0.953900	−0.476950	+	0.878930i	$0.658258\pi$
$234$	−160599.	−0.191736
$235$	313057.	0.369789
$236$	308669.	0.360755
$237$	−25941.6	−0.0300003
$238$	55198.9	0.0631667
$239$	1.42285e6	1.61126	0.805629	−	0.592421i	$-0.201828\pi$
$239$	1.42285e6	1.61126	0.805629	+	0.592421i	$0.201828\pi$
$240$	−14910.1	−0.0167091
$241$	−470644.	−0.521976	−0.260988	−	0.965342i	$-0.584048\pi$
$241$	−470644.	−0.521976	−0.260988	+	0.965342i	$0.584048\pi$
$242$	762134.	0.836552
$243$	400479.	0.435075
$244$	602794.	0.648178
$245$	416588.	0.443396
$246$	−41089.8	−0.0432909
$247$	332664.	0.346947
$248$	51938.1	0.0536237
$249$	57158.0	0.0584223
$250$	−62500.0	−0.0632456
$251$	−715187.	−0.716531	−0.358266	−	0.933620i	$-0.616632\pi$
$251$	−715187.	−0.716531	−0.358266	+	0.933620i	$0.616632\pi$
$252$	45531.3	0.0451657
$253$	2.91988e6	2.86790
$254$	938430.	0.912678
$255$	67099.4	0.0646202
$256$	65536.0	0.0625000
$257$	558699.	0.527649	0.263824	−	0.964571i	$-0.415016\pi$
$257$	558699.	0.527649	0.263824	+	0.964571i	$0.415016\pi$
$258$	3337.06	0.00312115
$259$	−43960.2	−0.0407202
$260$	−67600.0	−0.0620174
$261$	754008.	0.685133
$262$	662945.	0.596656
$263$	324539.	0.289319	0.144660	−	0.989481i	$-0.453791\pi$
$263$	324539.	0.289319	0.144660	+	0.989481i	$0.453791\pi$
$264$	−88409.0	−0.0780705
$265$	−166977.	−0.146063
$266$	−94313.2	−0.0817275
$267$	−73673.0	−0.0632456
$268$	−514129.	−0.437256
$269$	−570285.	−0.480520	−0.240260	−	0.970709i	$-0.577233\pi$
$269$	−570285.	−0.480520	−0.240260	+	0.970709i	$0.577233\pi$
$270$	111959.	0.0934655
$271$	1.61579e6	1.33647	0.668237	−	0.743949i	$-0.267049\pi$
$271$	1.61579e6	1.33647	0.668237	+	0.743949i	$0.267049\pi$
$272$	−294929.	−0.241710
$273$	−4716.09	−0.00382980
$274$	−90023.8	−0.0724404
$275$	−370591.	−0.295504
$276$	−183557.	−0.145044
$277$	1.45584e6	1.14002	0.570011	−	0.821637i	$-0.306939\pi$
$277$	1.45584e6	1.14002	0.570011	+	0.821637i	$0.306939\pi$
$278$	−486678.	−0.377685
$279$	−192798.	−0.148283
$280$	19165.2	0.0146089
$281$	−2.51152e6	−1.89745	−0.948726	−	0.316098i	$-0.897627\pi$
$281$	−2.51152e6	−1.89745	−0.948726	+	0.316098i	$0.897627\pi$
$282$	−116693.	−0.0873821
$283$	1.71185e6	1.27057	0.635286	−	0.772277i	$-0.280882\pi$
$283$	1.71185e6	1.27057	0.635286	+	0.772277i	$0.280882\pi$
$284$	−142738.	−0.105013
$285$	−114646.	−0.0836081
$286$	−400831.	−0.289765
$287$	52816.0	0.0378496
$288$	−243274.	−0.172828
$289$	−92602.7	−0.0652197
$290$	317380.	0.221608
$291$	322768.	0.223439
$292$	489609.	0.336041
$293$	136642.	0.0929854	0.0464927	−	0.998919i	$-0.485196\pi$
$293$	136642.	0.0929854	0.0464927	+	0.998919i	$0.485196\pi$
$294$	−155285.	−0.104776
$295$	−482295.	−0.322669
$296$	234880.	0.155818
$297$	663859.	0.436701
$298$	−1.58396e6	−1.03324
$299$	−832217.	−0.538342
$300$	23297.1	0.0149451
$301$	−4289.39	−0.00272885
$302$	−1.70418e6	−1.07522
$303$	259028.	0.162084
$304$	503917.	0.312734
$305$	−941866.	−0.579748
$306$	1.09480e6	0.668389
$307$	773128.	0.468172	0.234086	−	0.972216i	$-0.424790\pi$
$307$	773128.	0.468172	0.234086	+	0.972216i	$0.424790\pi$
$308$	113639.	0.0682577
$309$	69671.2	0.0415104
$310$	−81153.3	−0.0479625
$311$	−1.00187e6	−0.587368	−0.293684	−	0.955903i	$-0.594881\pi$
$311$	−1.00187e6	−0.587368	−0.293684	+	0.955903i	$0.594881\pi$
$312$	25198.1	0.0146549
$313$	−2.47191e6	−1.42617	−0.713085	−	0.701077i	$-0.752703\pi$
$313$	−2.47191e6	−1.42617	−0.713085	+	0.701077i	$0.752703\pi$
$314$	−1.53506e6	−0.878621
$315$	−71142.6	−0.0403974
$316$	−178162.	−0.100368
$317$	−930057.	−0.519830	−0.259915	−	0.965632i	$-0.583695\pi$
$317$	−930057.	−0.519830	−0.259915	+	0.965632i	$0.583695\pi$
$318$	62241.1	0.0345151
$319$	1.88189e6	1.03542
$320$	−102400.	−0.0559017
$321$	499572.	0.270605
$322$	235941.	0.126813
$323$	−2.26775e6	−1.20945
$324$	881948.	0.466746
$325$	105625.	0.0554700
$326$	−1.55660e6	−0.811208
$327$	−535585.	−0.276987
$328$	−282197.	−0.144833
$329$	149995.	0.0763990
$330$	138139.	0.0698284
$331$	3.12514e6	1.56783	0.783916	−	0.620866i	$-0.213219\pi$
$331$	3.12514e6	1.56783	0.783916	+	0.620866i	$0.213219\pi$
$332$	392550.	0.195456
$333$	−871891.	−0.430875
$334$	−1.04314e6	−0.511652
$335$	803327.	0.391093
$336$	−7143.90	−0.00345213
$337$	1.69627e6	0.813617	0.406809	−	0.913513i	$-0.366642\pi$
$337$	1.69627e6	0.813617	0.406809	+	0.913513i	$0.366642\pi$
$338$	114244.	0.0543928
$339$	−436709.	−0.206392
$340$	460826.	0.216192
$341$	−481195.	−0.224096
$342$	−1.87057e6	−0.864788
$343$	400919.	0.184001
$344$	22918.3	0.0104420
$345$	286808.	0.129731
$346$	−304081.	−0.136552
$347$	−1.14325e6	−0.509704	−0.254852	−	0.966980i	$-0.582027\pi$
$347$	−1.14325e6	−0.509704	−0.254852	+	0.966980i	$0.582027\pi$
$348$	−118305.	−0.0523665
$349$	−3.76980e6	−1.65674	−0.828371	−	0.560180i	$-0.810732\pi$
$349$	−3.76980e6	−1.65674	−0.828371	+	0.560180i	$0.810732\pi$
$350$	−29945.6	−0.0130666
$351$	−189211.	−0.0819747
$352$	−607176.	−0.261191
$353$	−1.39455e6	−0.595657	−0.297829	−	0.954619i	$-0.596262\pi$
$353$	−1.39455e6	−0.595657	−0.297829	+	0.954619i	$0.596262\pi$
$354$	179777.	0.0762476
$355$	223029.	0.0939268
$356$	−505972.	−0.211593
$357$	32149.4	0.0133506
$358$	−2.77202e6	−1.14311
$359$	−1.66623e6	−0.682338	−0.341169	−	0.940002i	$-0.610823\pi$
$359$	−1.66623e6	−0.682338	−0.341169	+	0.940002i	$0.610823\pi$
$360$	380116.	0.154582
$361$	1.39859e6	0.564837
$362$	−1.96560e6	−0.788357
$363$	443888.	0.176810
$364$	−32389.2	−0.0128129
$365$	−765014.	−0.300564
$366$	351084.	0.136996
$367$	265755.	0.102995	0.0514975	−	0.998673i	$-0.483601\pi$
$367$	265755.	0.102995	0.0514975	+	0.998673i	$0.483601\pi$
$368$	−1.26064e6	−0.485255
$369$	1.04753e6	0.400500
$370$	−367000.	−0.139368
$371$	−80003.6	−0.0301769
$372$	30250.2	0.0113337
$373$	3.43512e6	1.27841	0.639205	−	0.769037i	$-0.279264\pi$
$373$	3.43512e6	1.27841	0.639205	+	0.769037i	$0.279264\pi$
$374$	2.73245e6	1.01012
$375$	−36401.7	−0.0133673
$376$	−801426.	−0.292344
$377$	−536373.	−0.194363
$378$	53643.2	0.0193101
$379$	−1.48045e6	−0.529416	−0.264708	−	0.964329i	$-0.585276\pi$
$379$	−1.48045e6	−0.529416	−0.264708	+	0.964329i	$0.585276\pi$
$380$	−787370.	−0.279717
$381$	546567.	0.192900
$382$	2.99256e6	1.04926
$383$	4.28932e6	1.49414	0.747070	−	0.664745i	$-0.231460\pi$
$383$	4.28932e6	1.49414	0.747070	+	0.664745i	$0.231460\pi$
$384$	38170.0	0.0132097
$385$	−177561.	−0.0610516
$386$	−2.35423e6	−0.804232
$387$	−85074.2	−0.0288749
$388$	2.21671e6	0.747531
$389$	2.22336e6	0.744964	0.372482	−	0.928039i	$-0.378507\pi$
$389$	2.22336e6	0.744964	0.372482	+	0.928039i	$0.378507\pi$
$390$	−39372.1	−0.0131077
$391$	5.67318e6	1.87666
$392$	−1.06647e6	−0.350535
$393$	386117.	0.126107
$394$	600809.	0.194983
$395$	278378.	0.0897722
$396$	2.25388e6	0.722259
$397$	−5.42270e6	−1.72679	−0.863395	−	0.504528i	$-0.831667\pi$
$397$	−5.42270e6	−1.72679	−0.863395	+	0.504528i	$0.831667\pi$
$398$	−2.96906e6	−0.939530
$399$	−54930.6	−0.0172736
$400$	160000.	0.0500000
$401$	−2.06419e6	−0.641044	−0.320522	−	0.947241i	$-0.603858\pi$
$401$	−2.06419e6	−0.641044	−0.320522	+	0.947241i	$0.603858\pi$
$402$	−299443.	−0.0924164
$403$	137149.	0.0420659
$404$	1.77895e6	0.542265
$405$	−1.37804e6	−0.417470
$406$	152067.	0.0457845
$407$	−2.17611e6	−0.651171
$408$	−171775.	−0.0510868
$409$	−430276.	−0.127186	−0.0635930	−	0.997976i	$-0.520256\pi$
$409$	−430276.	−0.127186	−0.0635930	+	0.997976i	$0.520256\pi$
$410$	440933.	0.129543
$411$	−52432.3	−0.0153107
$412$	478489.	0.138876
$413$	−231082.	−0.0666640
$414$	4.67957e6	1.34185
$415$	−613359.	−0.174821
$416$	173056.	0.0490290
$417$	−283455.	−0.0798259
$418$	−4.66867e6	−1.30693
$419$	−3.98854e6	−1.10989	−0.554944	−	0.831888i	$-0.687260\pi$
$419$	−3.98854e6	−1.10989	−0.554944	+	0.831888i	$0.687260\pi$
$420$	11162.3	0.00308768
$421$	−1.46324e6	−0.402357	−0.201178	−	0.979555i	$-0.564477\pi$
$421$	−1.46324e6	−0.402357	−0.201178	+	0.979555i	$0.564477\pi$
$422$	−579343.	−0.158363
$423$	2.97495e6	0.808404
$424$	427460.	0.115473
$425$	−720041.	−0.193368
$426$	−83134.7	−0.0221952
$427$	−451276.	−0.119777
$428$	3.43096e6	0.905329
$429$	−233455.	−0.0612435
$430$	−35809.8	−0.00933965
$431$	−1.18853e6	−0.308188	−0.154094	−	0.988056i	$-0.549246\pi$
$431$	−1.18853e6	−0.308188	−0.154094	+	0.988056i	$0.549246\pi$
$432$	−286616.	−0.0738910
$433$	1.82965e6	0.468974	0.234487	−	0.972119i	$-0.424659\pi$
$433$	1.82965e6	0.468974	0.234487	+	0.972119i	$0.424659\pi$
$434$	−38883.0	−0.00990913
$435$	184851.	0.0468381
$436$	−3.67829e6	−0.926681
$437$	−9.69322e6	−2.42809
$438$	285162.	0.0710241
$439$	4.15757e6	1.02962	0.514812	−	0.857303i	$-0.327862\pi$
$439$	4.15757e6	1.02962	0.514812	+	0.857303i	$0.327862\pi$
$440$	948713.	0.233616
$441$	3.95879e6	0.969318
$442$	−778796.	−0.189613
$443$	7.16327e6	1.73421	0.867106	−	0.498124i	$-0.165977\pi$
$443$	7.16327e6	1.73421	0.867106	+	0.498124i	$0.165977\pi$
$444$	136801.	0.0329329
$445$	790582.	0.189255
$446$	−319715.	−0.0761072
$447$	−922541.	−0.218382
$448$	−49062.9	−0.0115494
$449$	663475.	0.155313	0.0776566	−	0.996980i	$-0.475256\pi$
$449$	663475.	0.155313	0.0776566	+	0.996980i	$0.475256\pi$
$450$	−593931.	−0.138263
$451$	2.61449e6	0.605265
$452$	−2.99923e6	−0.690501
$453$	−992564.	−0.227255
$454$	4.14235e6	0.943208
$455$	50608.1	0.0114602
$456$	293495.	0.0660980
$457$	−4.10927e6	−0.920396	−0.460198	−	0.887816i	$-0.652222\pi$
$457$	−4.10927e6	−0.920396	−0.460198	+	0.887816i	$0.652222\pi$
$458$	−4.50924e6	−1.00448
$459$	1.28985e6	0.285763
$460$	1.96974e6	0.434025
$461$	4.89027e6	1.07172	0.535859	−	0.844307i	$-0.319988\pi$
$461$	4.89027e6	1.07172	0.535859	+	0.844307i	$0.319988\pi$
$462$	66186.6	0.0144266
$463$	6.29740e6	1.36524	0.682619	−	0.730774i	$-0.260841\pi$
$463$	6.29740e6	1.36524	0.682619	+	0.730774i	$0.260841\pi$
$464$	−812494.	−0.175196
$465$	−47265.9	−0.0101371
$466$	−3.16193e6	−0.674509
$467$	−3.70606e6	−0.786358	−0.393179	−	0.919462i	$-0.628625\pi$
$467$	−3.70606e6	−0.786358	−0.393179	+	0.919462i	$0.628625\pi$
$468$	−642396.	−0.135578
$469$	384898.	0.0808005
$470$	1.25223e6	0.261480
$471$	−894062.	−0.185701
$472$	1.23467e6	0.255092
$473$	−212333.	−0.0436379
$474$	−103766.	−0.0212134
$475$	1.23026e6	0.250187
$476$	220796.	0.0446656
$477$	−1.58676e6	−0.319312
$478$	5.69141e6	1.13933
$479$	−1.60841e6	−0.320300	−0.160150	−	0.987093i	$-0.551198\pi$
$479$	−1.60841e6	−0.320300	−0.160150	+	0.987093i	$0.551198\pi$
$480$	−59640.6	−0.0118151
$481$	620230.	0.122233
$482$	−1.88258e6	−0.369093
$483$	137418.	0.0268026
$484$	3.04854e6	0.591532
$485$	−3.46361e6	−0.668612
$486$	1.60192e6	0.307645
$487$	7.96047e6	1.52095	0.760477	−	0.649365i	$-0.224965\pi$
$487$	7.96047e6	1.52095	0.760477	+	0.649365i	$0.224965\pi$
$488$	2.41118e6	0.458331
$489$	−906605.	−0.171453
$490$	1.66635e6	0.313528
$491$	4.21788e6	0.789570	0.394785	−	0.918774i	$-0.370819\pi$
$491$	4.21788e6	0.789570	0.394785	+	0.918774i	$0.370819\pi$
$492$	−164359.	−0.0306113
$493$	3.65643e6	0.677548
$494$	1.33065e6	0.245328
$495$	−3.52169e6	−0.646008
$496$	207752.	0.0379177
$497$	106860.	0.0194054
$498$	228632.	0.0413108
$499$	−8.07469e6	−1.45169	−0.725846	−	0.687857i	$-0.758552\pi$
$499$	−8.07469e6	−1.45169	−0.725846	+	0.687857i	$0.758552\pi$
$500$	−250000.	−0.0447214
$501$	−607551.	−0.108141
$502$	−2.86075e6	−0.506664
$503$	−4.93452e6	−0.869610	−0.434805	−	0.900525i	$-0.643183\pi$
$503$	−4.93452e6	−0.869610	−0.434805	+	0.900525i	$0.643183\pi$
$504$	182125.	0.0319369
$505$	−2.77962e6	−0.485016
$506$	1.16795e7	2.02791
$507$	66538.8	0.0114962
$508$	3.75372e6	0.645361
$509$	−6.00126e6	−1.02671	−0.513356	−	0.858176i	$-0.671598\pi$
$509$	−6.00126e6	−1.02671	−0.513356	+	0.858176i	$0.671598\pi$
$510$	268398.	0.0456934
$511$	−366541.	−0.0620970
$512$	262144.	0.0441942
$513$	−2.20384e6	−0.369731
$514$	2.23480e6	0.373104
$515$	−747638.	−0.124215
$516$	13348.2	0.00220699
$517$	7.42503e6	1.22172
$518$	−175841.	−0.0287936
$519$	−177105.	−0.0288611
$520$	−270400.	−0.0438529
$521$	−1.00674e7	−1.62489	−0.812447	−	0.583035i	$-0.801865\pi$
$521$	−1.00674e7	−1.62489	−0.812447	+	0.583035i	$0.801865\pi$
$522$	3.01603e6	0.484462
$523$	−2.91846e6	−0.466552	−0.233276	−	0.972411i	$-0.574945\pi$
$523$	−2.91846e6	−0.466552	−0.233276	+	0.972411i	$0.574945\pi$
$524$	2.65178e6	0.421899
$525$	−17441.2	−0.00276170
$526$	1.29816e6	0.204580
$527$	−934939.	−0.146641
$528$	−353636.	−0.0552042
$529$	1.78130e7	2.76756
$530$	−667907.	−0.103282
$531$	−4.58320e6	−0.705395
$532$	−377253.	−0.0577901
$533$	−745176.	−0.113616
$534$	−294692.	−0.0447214
$535$	−5.36088e6	−0.809751
$536$	−2.05652e6	−0.309186
$537$	−1.61450e6	−0.241603
$538$	−2.28114e6	−0.339779
$539$	9.88056e6	1.46491
$540$	447838.	0.0660901
$541$	1.10243e7	1.61941	0.809704	−	0.586839i	$-0.199628\pi$
$541$	1.10243e7	1.61941	0.809704	+	0.586839i	$0.199628\pi$
$542$	6.46314e6	0.945030
$543$	−1.14482e6	−0.166624
$544$	−1.17971e6	−0.170915
$545$	5.74733e6	0.828849
$546$	−18864.4	−0.00270807
$547$	−860978.	−0.123034	−0.0615168	−	0.998106i	$-0.519594\pi$
$547$	−860978.	−0.123034	−0.0615168	+	0.998106i	$0.519594\pi$
$548$	−360095.	−0.0512231
$549$	−8.95045e6	−1.26740
$550$	−1.48236e6	−0.208953
$551$	−6.24739e6	−0.876637
$552$	−734229.	−0.102561
$553$	133379.	0.0185471
$554$	5.82335e6	0.806117
$555$	−213751.	−0.0294561
$556$	−1.94671e6	−0.267064
$557$	6.49940e6	0.887637	0.443818	−	0.896117i	$-0.353624\pi$
$557$	6.49940e6	0.887637	0.443818	+	0.896117i	$0.353624\pi$
$558$	−771191.	−0.104852
$559$	60518.6	0.00819142
$560$	76660.9	0.0103301
$561$	1.59145e6	0.213494
$562$	−1.00461e7	−1.34170
$563$	−5.46465e6	−0.726594	−0.363297	−	0.931673i	$-0.618349\pi$
$563$	−5.46465e6	−0.726594	−0.363297	+	0.931673i	$0.618349\pi$
$564$	−466773.	−0.0617885
$565$	4.68630e6	0.617603
$566$	6.84739e6	0.898430
$567$	−660263.	−0.0862500
$568$	−570953.	−0.0742557
$569$	8.30646e6	1.07556	0.537781	−	0.843085i	$-0.319263\pi$
$569$	8.30646e6	1.07556	0.537781	+	0.843085i	$0.319263\pi$
$570$	−458586.	−0.0591198
$571$	−2.57189e6	−0.330112	−0.165056	−	0.986284i	$-0.552780\pi$
$571$	−2.57189e6	−0.330112	−0.165056	+	0.986284i	$0.552780\pi$
$572$	−1.60333e6	−0.204895
$573$	1.74295e6	0.221767
$574$	211264.	0.0267637
$575$	−3.07772e6	−0.388204
$576$	−973097.	−0.122208
$577$	−1.38747e7	−1.73494	−0.867470	−	0.497490i	$-0.834255\pi$
$577$	−1.38747e7	−1.73494	−0.867470	+	0.497490i	$0.834255\pi$
$578$	−370411.	−0.0461173
$579$	−1.37117e6	−0.169979
$580$	1.26952e6	0.156700
$581$	−293879.	−0.0361184
$582$	1.29107e6	0.157995
$583$	−3.96032e6	−0.482569
$584$	1.95844e6	0.237617
$585$	1.00374e6	0.121264
$586$	546568.	0.0657506
$587$	−1.36095e7	−1.63022	−0.815112	−	0.579304i	$-0.803324\pi$
$587$	−1.36095e7	−1.63022	−0.815112	+	0.579304i	$0.803324\pi$
$588$	−621139.	−0.0740876
$589$	1.59744e6	0.189730
$590$	−1.92918e6	−0.228162
$591$	349928.	0.0412106
$592$	939520.	0.110180
$593$	4.97677e6	0.581180	0.290590	−	0.956848i	$-0.406148\pi$
$593$	4.97677e6	0.581180	0.290590	+	0.956848i	$0.406148\pi$
$594$	2.65543e6	0.308794
$595$	−344993.	−0.0399501
$596$	−6.33583e6	−0.730614
$597$	−1.72926e6	−0.198575
$598$	−3.32887e6	−0.380665
$599$	529408.	0.0602870	0.0301435	−	0.999546i	$-0.490404\pi$
$599$	529408.	0.0602870	0.0301435	+	0.999546i	$0.490404\pi$
$600$	93188.4	0.0105678
$601$	−3.47716e6	−0.392680	−0.196340	−	0.980536i	$-0.562906\pi$
$601$	−3.47716e6	−0.392680	−0.196340	+	0.980536i	$0.562906\pi$
$602$	−17157.6	−0.00192959
$603$	7.63394e6	0.854979
$604$	−6.81674e6	−0.760299
$605$	−4.76334e6	−0.529082
$606$	1.03611e6	0.114611
$607$	3.14423e6	0.346372	0.173186	−	0.984889i	$-0.444594\pi$
$607$	3.14423e6	0.346372	0.173186	+	0.984889i	$0.444594\pi$
$608$	2.01567e6	0.221136
$609$	88567.8	0.00967681
$610$	−3.76746e6	−0.409944
$611$	−2.11627e6	−0.229333
$612$	4.37918e6	0.472623
$613$	2.57275e6	0.276532	0.138266	−	0.990395i	$-0.455847\pi$
$613$	2.57275e6	0.276532	0.138266	+	0.990395i	$0.455847\pi$
$614$	3.09251e6	0.331048
$615$	256811.	0.0273795
$616$	454557.	0.0482655
$617$	−5.35535e6	−0.566337	−0.283169	−	0.959070i	$-0.591386\pi$
$617$	−5.35535e6	−0.566337	−0.283169	+	0.959070i	$0.591386\pi$
$618$	278685.	0.0293523
$619$	−2.64595e6	−0.277559	−0.138779	−	0.990323i	$-0.544318\pi$
$619$	−2.64595e6	−0.277559	−0.138779	+	0.990323i	$0.544318\pi$
$620$	−324613.	−0.0339146
$621$	5.51328e6	0.573695
$622$	−4.00748e6	−0.415332
$623$	378792.	0.0391003
$624$	100793.	0.0103626
$625$	390625.	0.0400000
$626$	−9.88763e6	−1.00846
$627$	−2.71916e6	−0.276227
$628$	−6.14025e6	−0.621279
$629$	−4.22808e6	−0.426105
$630$	−284570.	−0.0285653
$631$	−1.08305e7	−1.08287	−0.541433	−	0.840744i	$-0.682118\pi$
$631$	−1.08305e7	−1.08287	−0.541433	+	0.840744i	$0.682118\pi$
$632$	−712647.	−0.0709711
$633$	−337425.	−0.0334710
$634$	−3.72023e6	−0.367575
$635$	−5.86519e6	−0.577228
$636$	248965.	0.0244059
$637$	−2.81614e6	−0.274982
$638$	7.52757e6	0.732155
$639$	2.11942e6	0.205336
$640$	−409600.	−0.0395285
$641$	6.96410e6	0.669453	0.334726	−	0.942315i	$-0.391356\pi$
$641$	6.96410e6	0.669453	0.334726	+	0.942315i	$0.391356\pi$
$642$	1.99829e6	0.191346
$643$	7.71015e6	0.735420	0.367710	−	0.929941i	$-0.380142\pi$
$643$	7.71015e6	0.735420	0.367710	+	0.929941i	$0.380142\pi$
$644$	943764.	0.0896703
$645$	−20856.6	−0.00197399
$646$	−9.07101e6	−0.855213
$647$	7.99108e6	0.750489	0.375245	−	0.926926i	$-0.377559\pi$
$647$	7.99108e6	0.750489	0.375245	+	0.926926i	$0.377559\pi$
$648$	3.52779e6	0.330039
$649$	−1.14390e7	−1.06605
$650$	422500.	0.0392232
$651$	−22646.5	−0.00209435
$652$	−6.22639e6	−0.573611
$653$	−1.59994e7	−1.46832	−0.734160	−	0.678976i	$-0.762424\pi$
$653$	−1.59994e7	−1.46832	−0.734160	+	0.678976i	$0.762424\pi$
$654$	−2.14234e6	−0.195859
$655$	−4.14340e6	−0.377358
$656$	−1.12879e6	−0.102412
$657$	−7.26985e6	−0.657071
$658$	599981.	0.0540222
$659$	1.04554e7	0.937834	0.468917	−	0.883242i	$-0.344644\pi$
$659$	1.04554e7	0.937834	0.468917	+	0.883242i	$0.344644\pi$
$660$	552556.	0.0493761
$661$	−1.08083e7	−0.962175	−0.481087	−	0.876673i	$-0.659758\pi$
$661$	−1.08083e7	−0.962175	−0.481087	+	0.876673i	$0.659758\pi$
$662$	1.25006e7	1.10863
$663$	−453592.	−0.0400758
$664$	1.57020e6	0.138208
$665$	589457.	0.0516890
$666$	−3.48756e6	−0.304675
$667$	1.56290e7	1.36024
$668$	−4.17255e6	−0.361793
$669$	−186211.	−0.0160857
$670$	3.21331e6	0.276545
$671$	−2.23390e7	−1.91539
$672$	−28575.6	−0.00244103
$673$	4.48913e6	0.382054	0.191027	−	0.981585i	$-0.438818\pi$
$673$	4.48913e6	0.382054	0.191027	+	0.981585i	$0.438818\pi$
$674$	6.78508e6	0.575314
$675$	−699746.	−0.0591128
$676$	456976.	0.0384615
$677$	2.18426e7	1.83161	0.915805	−	0.401622i	$-0.131553\pi$
$677$	2.18426e7	1.83161	0.915805	+	0.401622i	$0.131553\pi$
$678$	−1.74684e6	−0.145941
$679$	−1.65952e6	−0.138136
$680$	1.84330e6	0.152871
$681$	2.41262e6	0.199352
$682$	−1.92478e6	−0.158460
$683$	−1.89182e7	−1.55177	−0.775887	−	0.630872i	$-0.782697\pi$
$683$	−1.89182e7	−1.55177	−0.775887	+	0.630872i	$0.782697\pi$
$684$	−7.48229e6	−0.611497
$685$	562649.	0.0458154
$686$	1.60367e6	0.130109
$687$	−2.62631e6	−0.212302
$688$	91673.1	0.00738364
$689$	1.12876e6	0.0905846
$690$	1.14723e6	0.0917337
$691$	1.16916e7	0.931492	0.465746	−	0.884918i	$-0.345786\pi$
$691$	1.16916e7	0.931492	0.465746	+	0.884918i	$0.345786\pi$
$692$	−1.21633e6	−0.0965572
$693$	−1.68735e6	−0.133466
$694$	−4.57300e6	−0.360415
$695$	3.04174e6	0.238869
$696$	−473219.	−0.0370287
$697$	5.07983e6	0.396066
$698$	−1.50792e7	−1.17149
$699$	−1.84160e6	−0.142561
$700$	−119783.	−0.00923950
$701$	1.91539e7	1.47218	0.736090	−	0.676883i	$-0.236670\pi$
$701$	1.91539e7	1.47218	0.736090	+	0.676883i	$0.236670\pi$
$702$	−756846.	−0.0579648
$703$	7.22412e6	0.551311
$704$	−2.42871e6	−0.184690
$705$	729332.	0.0552653
$706$	−5.57819e6	−0.421193
$707$	−1.33180e6	−0.100205
$708$	719108.	0.0539152
$709$	−1.09998e6	−0.0821805	−0.0410902	−	0.999155i	$-0.513083\pi$
$709$	−1.09998e6	−0.0821805	−0.0410902	+	0.999155i	$0.513083\pi$
$710$	892114.	0.0664163
$711$	2.64540e6	0.196253
$712$	−2.02389e6	−0.149619
$713$	−3.99628e6	−0.294396
$714$	128598.	0.00944033
$715$	2.50520e6	0.183264
$716$	−1.10881e7	−0.808303
$717$	3.31483e6	0.240804
$718$	−6.66493e6	−0.482486
$719$	2.18007e7	1.57271	0.786354	−	0.617776i	$-0.211966\pi$
$719$	2.18007e7	1.57271	0.786354	+	0.617776i	$0.211966\pi$
$720$	1.52046e6	0.109306
$721$	−358216.	−0.0256630
$722$	5.59437e6	0.399400
$723$	−1.09646e6	−0.0780098
$724$	−7.86239e6	−0.557453
$725$	−1.98363e6	−0.140157
$726$	1.77555e6	0.125024
$727$	2.51245e7	1.76304	0.881519	−	0.472149i	$-0.156522\pi$
$727$	2.51245e7	1.76304	0.881519	+	0.472149i	$0.156522\pi$
$728$	−129557.	−0.00906008
$729$	−1.24616e7	−0.868470
$730$	−3.06006e6	−0.212531
$731$	−412552.	−0.0285552
$732$	1.40434e6	0.0968708
$733$	2.16392e7	1.48759	0.743793	−	0.668410i	$-0.233025\pi$
$733$	2.16392e7	1.48759	0.743793	+	0.668410i	$0.233025\pi$
$734$	1.06302e6	0.0728284
$735$	970529.	0.0662659
$736$	−5.04254e6	−0.343127
$737$	1.90532e7	1.29211
$738$	4.19014e6	0.283196
$739$	−1.98134e7	−1.33459	−0.667294	−	0.744794i	$-0.732548\pi$
$739$	−1.98134e7	−1.33459	−0.667294	+	0.744794i	$0.732548\pi$
$740$	−1.46800e6	−0.0985478
$741$	775010.	0.0518515
$742$	−320014.	−0.0213383
$743$	−6.05253e6	−0.402221	−0.201111	−	0.979569i	$-0.564455\pi$
$743$	−6.05253e6	−0.402221	−0.201111	+	0.979569i	$0.564455\pi$
$744$	121001.	0.00801411
$745$	9.89974e6	0.653481
$746$	1.37405e7	0.903972
$747$	−5.82869e6	−0.382181
$748$	1.09298e7	0.714263
$749$	−2.56856e6	−0.167296
$750$	−145607.	−0.00945211
$751$	−8.24253e6	−0.533287	−0.266643	−	0.963795i	$-0.585915\pi$
$751$	−8.24253e6	−0.533287	−0.266643	+	0.963795i	$0.585915\pi$
$752$	−3.20570e6	−0.206718
$753$	−1.66618e6	−0.107086
$754$	−2.14549e6	−0.137435
$755$	1.06512e7	0.680032
$756$	214573.	0.0136543
$757$	−1.86071e7	−1.18015	−0.590076	−	0.807348i	$-0.700902\pi$
$757$	−1.86071e7	−1.18015	−0.590076	+	0.807348i	$0.700902\pi$
$758$	−5.92182e6	−0.374354
$759$	6.80247e6	0.428610
$760$	−3.14948e6	−0.197790
$761$	1.52852e7	0.956774	0.478387	−	0.878149i	$-0.341222\pi$
$761$	1.52852e7	0.956774	0.478387	+	0.878149i	$0.341222\pi$
$762$	2.18627e6	0.136401
$763$	2.75372e6	0.171241
$764$	1.19702e7	0.741941
$765$	−6.84247e6	−0.422727
$766$	1.71573e7	1.05652
$767$	3.26031e6	0.200111
$768$	152680.	0.00934068
$769$	−1.30293e7	−0.794520	−0.397260	−	0.917706i	$-0.630039\pi$
$769$	−1.30293e7	−0.794520	−0.397260	+	0.917706i	$0.630039\pi$
$770$	−710246.	−0.0431700
$771$	1.30161e6	0.0788576
$772$	−9.41693e6	−0.568678
$773$	2.78648e7	1.67729	0.838644	−	0.544680i	$-0.183349\pi$
$773$	2.78648e7	1.67729	0.838644	+	0.544680i	$0.183349\pi$
$774$	−340297.	−0.0204176
$775$	507208.	0.0303341
$776$	8.86684e6	0.528585
$777$	−102415.	−0.00608568
$778$	8.89343e6	0.526769
$779$	−8.67942e6	−0.512445
$780$	−157488.	−0.00926855
$781$	5.28975e6	0.310319
$782$	2.26927e7	1.32700
$783$	3.55337e6	0.207127
$784$	−4.26586e6	−0.247866
$785$	9.59413e6	0.555689
$786$	1.54447e6	0.0891708
$787$	1.13972e7	0.655935	0.327968	−	0.944689i	$-0.393636\pi$
$787$	1.13972e7	0.655935	0.327968	+	0.944689i	$0.393636\pi$
$788$	2.40324e6	0.137873
$789$	756082.	0.0432391
$790$	1.11351e6	0.0634785
$791$	2.24535e6	0.127598
$792$	9.01552e6	0.510714
$793$	6.36701e6	0.359545
$794$	−2.16908e7	−1.22103
$795$	−389007.	−0.0218293
$796$	−1.18762e7	−0.664348
$797$	1.92491e7	1.07341	0.536705	−	0.843770i	$-0.319669\pi$
$797$	1.92491e7	1.07341	0.536705	+	0.843770i	$0.319669\pi$
$798$	−219722.	−0.0122143
$799$	1.44265e7	0.799454
$800$	640000.	0.0353553
$801$	7.51282e6	0.413734
$802$	−8.25674e6	−0.453286
$803$	−1.81445e7	−0.993014
$804$	−1.19777e6	−0.0653483
$805$	−1.47463e6	−0.0802036
$806$	548596.	0.0297451
$807$	−1.32860e6	−0.0718141
$808$	7.11582e6	0.383439
$809$	2.71092e7	1.45628	0.728141	−	0.685427i	$-0.240385\pi$
$809$	2.71092e7	1.45628	0.728141	+	0.685427i	$0.240385\pi$
$810$	−5.51218e6	−0.295196
$811$	−2.72397e7	−1.45429	−0.727144	−	0.686485i	$-0.759153\pi$
$811$	−2.72397e7	−1.45429	−0.727144	+	0.686485i	$0.759153\pi$
$812$	608266.	0.0323745
$813$	3.76431e6	0.199737
$814$	−8.70444e6	−0.460447
$815$	9.72873e6	0.513053
$816$	−687098.	−0.0361238
$817$	704889.	0.0369458
$818$	−1.72111e6	−0.0899340
$819$	480924.	0.0250534
$820$	1.76373e6	0.0916004
$821$	1.42192e7	0.736236	0.368118	−	0.929779i	$-0.380002\pi$
$821$	1.42192e7	0.736236	0.368118	+	0.929779i	$0.380002\pi$
$822$	−209729.	−0.0108263
$823$	−1.08542e7	−0.558598	−0.279299	−	0.960204i	$-0.590102\pi$
$823$	−1.08542e7	−0.558598	−0.279299	+	0.960204i	$0.590102\pi$
$824$	1.91395e6	0.0982005
$825$	−863370.	−0.0441633
$826$	−924328.	−0.0471385
$827$	5.97981e6	0.304035	0.152017	−	0.988378i	$-0.451423\pi$
$827$	5.97981e6	0.304035	0.152017	+	0.988378i	$0.451423\pi$
$828$	1.87183e7	0.948833
$829$	1.77871e7	0.898916	0.449458	−	0.893301i	$-0.351617\pi$
$829$	1.77871e7	0.898916	0.449458	+	0.893301i	$0.351617\pi$
$830$	−2.45344e6	−0.123617
$831$	3.39168e6	0.170377
$832$	692224.	0.0346688
$833$	1.91975e7	0.958587
$834$	−1.13382e6	−0.0564454
$835$	6.51960e6	0.323597
$836$	−1.86747e7	−0.924140
$837$	−908587.	−0.0448284
$838$	−1.59542e7	−0.784810
$839$	−1.34398e7	−0.659153	−0.329577	−	0.944129i	$-0.606906\pi$
$839$	−1.34398e7	−0.659153	−0.329577	+	0.944129i	$0.606906\pi$
$840$	44649.4	0.00218332
$841$	−1.04381e7	−0.508900
$842$	−5.85298e6	−0.284509
$843$	−5.85111e6	−0.283576
$844$	−2.31737e6	−0.111980
$845$	−714025.	−0.0344010
$846$	1.18998e7	0.571628
$847$	−2.28226e6	−0.109309
$848$	1.70984e6	0.0816518
$849$	3.98811e6	0.189888
$850$	−2.88016e6	−0.136732
$851$	−1.80724e7	−0.855444
$852$	−332539.	−0.0156943
$853$	−1.33850e7	−0.629864	−0.314932	−	0.949114i	$-0.601982\pi$
$853$	−1.33850e7	−0.629864	−0.314932	+	0.949114i	$0.601982\pi$
$854$	−1.80511e6	−0.0846950
$855$	1.16911e7	0.546940
$856$	1.37239e7	0.640165
$857$	−2.99139e7	−1.39130	−0.695651	−	0.718380i	$-0.744884\pi$
$857$	−2.99139e7	−1.39130	−0.695651	+	0.718380i	$0.744884\pi$
$858$	−933820.	−0.0433057
$859$	−9.44220e6	−0.436607	−0.218303	−	0.975881i	$-0.570052\pi$
$859$	−9.44220e6	−0.436607	−0.218303	+	0.975881i	$0.570052\pi$
$860$	−143239.	−0.00660413
$861$	123046.	0.00565666
$862$	−4.75410e6	−0.217922
$863$	−3.39118e7	−1.54997	−0.774986	−	0.631978i	$-0.782243\pi$
$863$	−3.39118e7	−1.54997	−0.774986	+	0.631978i	$0.782243\pi$
$864$	−1.14646e6	−0.0522488
$865$	1.90051e6	0.0863634
$866$	7.31860e6	0.331614
$867$	−215737.	−0.00974715
$868$	−155532.	−0.00700681
$869$	6.60251e6	0.296592
$870$	739404.	0.0331195
$871$	−5.43049e6	−0.242546
$872$	−1.47132e7	−0.655262
$873$	−3.29143e7	−1.46167
$874$	−3.87729e7	−1.71692
$875$	187160.	0.00826406
$876$	1.14065e6	0.0502217
$877$	3.72390e7	1.63493	0.817465	−	0.575978i	$-0.195379\pi$
$877$	3.72390e7	1.63493	0.817465	+	0.575978i	$0.195379\pi$
$878$	1.66303e7	0.728053
$879$	318336.	0.0138968
$880$	3.79485e6	0.165192
$881$	2.35281e7	1.02128	0.510642	−	0.859794i	$-0.329408\pi$
$881$	2.35281e7	1.02128	0.510642	+	0.859794i	$0.329408\pi$
$882$	1.58352e7	0.685412
$883$	−1.21345e7	−0.523744	−0.261872	−	0.965103i	$-0.584340\pi$
$883$	−1.21345e7	−0.523744	−0.261872	+	0.965103i	$0.584340\pi$
$884$	−3.11518e6	−0.134077
$885$	−1.12361e6	−0.0482232
$886$	2.86531e7	1.22627
$887$	3.12454e7	1.33345	0.666725	−	0.745304i	$-0.267696\pi$
$887$	3.12454e7	1.33345	0.666725	+	0.745304i	$0.267696\pi$
$888$	547202.	0.0232871
$889$	−2.81019e6	−0.119256
$890$	3.16233e6	0.133823
$891$	−3.26842e7	−1.37925
$892$	−1.27886e6	−0.0538159
$893$	−2.46492e7	−1.03436
$894$	−3.69016e6	−0.154419
$895$	1.73251e7	0.722968
$896$	−196252.	−0.00816664
$897$	−1.93882e6	−0.0804557
$898$	2.65390e6	0.109823
$899$	−2.57565e6	−0.106289
$900$	−2.37572e6	−0.0977664
$901$	−7.69472e6	−0.315777
$902$	1.04580e7	0.427987
$903$	−9993.03	−0.000407829 0
$904$	−1.19969e7	−0.488258
$905$	1.22850e7	0.498601
$906$	−3.97026e6	−0.160693
$907$	−3.90936e7	−1.57793	−0.788964	−	0.614440i	$-0.789382\pi$
$907$	−3.90936e7	−1.57793	−0.788964	+	0.614440i	$0.789382\pi$
$908$	1.65694e7	0.666949
$909$	−2.64144e7	−1.06031
$910$	202433.	0.00810358
$911$	1.13740e7	0.454064	0.227032	−	0.973887i	$-0.427098\pi$
$911$	1.13740e7	0.454064	0.227032	+	0.973887i	$0.427098\pi$
$912$	1.17398e6	0.0467383
$913$	−1.45475e7	−0.577581
$914$	−1.64371e7	−0.650818
$915$	−2.19427e6	−0.0866439
$916$	−1.80370e7	−0.710272
$917$	−1.98523e6	−0.0779628
$918$	5.15938e6	0.202065
$919$	−4.78920e7	−1.87057	−0.935285	−	0.353897i	$-0.884856\pi$
$919$	−4.78920e7	−1.87057	−0.935285	+	0.353897i	$0.884856\pi$
$920$	7.87897e6	0.306902
$921$	1.80116e6	0.0699687
$922$	1.95611e7	0.757820
$923$	−1.50767e6	−0.0582509
$924$	264747.	0.0102012
$925$	2.29375e6	0.0881438
$926$	2.51896e7	0.965370
$927$	−7.10473e6	−0.271549
$928$	−3.24998e6	−0.123883
$929$	−2.62821e7	−0.999128	−0.499564	−	0.866277i	$-0.666506\pi$
$929$	−2.62821e7	−0.999128	−0.499564	+	0.866277i	$0.666506\pi$
$930$	−189064.	−0.00716804
$931$	−3.28009e7	−1.24026
$932$	−1.26477e7	−0.476950
$933$	−2.33406e6	−0.0877826
$934$	−1.48242e7	−0.556039
$935$	−1.70778e7	−0.638856
$936$	−2.56958e6	−0.0958679
$937$	−1.77518e7	−0.660533	−0.330266	−	0.943888i	$-0.607139\pi$
$937$	−1.77518e7	−0.660533	−0.330266	+	0.943888i	$0.607139\pi$
$938$	1.53959e6	0.0571346
$939$	−5.75883e6	−0.213143
$940$	5.00891e6	0.184894
$941$	−2.90357e7	−1.06895	−0.534477	−	0.845183i	$-0.679491\pi$
$941$	−2.90357e7	−1.06895	−0.534477	+	0.845183i	$0.679491\pi$
$942$	−3.57625e6	−0.131311
$943$	2.17131e7	0.795138
$944$	4.93870e6	0.180378
$945$	−335270.	−0.0122128
$946$	−849330.	−0.0308567
$947$	−2.19909e7	−0.796833	−0.398416	−	0.917205i	$-0.630440\pi$
$947$	−2.19909e7	−0.796833	−0.398416	+	0.917205i	$0.630440\pi$
$948$	−415065.	−0.0150001
$949$	5.17150e6	0.186402
$950$	4.92106e6	0.176909
$951$	−2.16676e6	−0.0776891
$952$	883183.	0.0315834
$953$	−9.09071e6	−0.324239	−0.162120	−	0.986771i	$-0.551833\pi$
$953$	−9.09071e6	−0.324239	−0.162120	+	0.986771i	$0.551833\pi$
$954$	−6.34705e6	−0.225788
$955$	−1.87035e7	−0.663612
$956$	2.27656e7	0.805629
$957$	4.38427e6	0.154745
$958$	−6.43363e6	−0.226487
$959$	269582.	0.00946552
$960$	−238562.	−0.00835456
$961$	−2.79706e7	−0.976996
$962$	2.48092e6	0.0864321
$963$	−5.09439e7	−1.77022
$964$	−7.53031e6	−0.260988
$965$	1.47140e7	0.508641
$966$	549674.	0.0189523
$967$	2.73591e7	0.940884	0.470442	−	0.882431i	$-0.344094\pi$
$967$	2.73591e7	0.940884	0.470442	+	0.882431i	$0.344094\pi$
$968$	1.21941e7	0.418276
$969$	−5.28321e6	−0.180754
$970$	−1.38544e7	−0.472780
$971$	3.24924e7	1.10595	0.552973	−	0.833199i	$-0.313493\pi$
$971$	3.24924e7	1.10595	0.552973	+	0.833199i	$0.313493\pi$
$972$	6.40767e6	0.217538
$973$	1.45739e6	0.0493507
$974$	3.18419e7	1.07548
$975$	246076.	0.00829005
$976$	9.64471e6	0.324089
$977$	2.66119e7	0.891948	0.445974	−	0.895046i	$-0.352857\pi$
$977$	2.66119e7	0.891948	0.445974	+	0.895046i	$0.352857\pi$
$978$	−3.62642e6	−0.121236
$979$	1.87509e7	0.625266
$980$	6.66541e6	0.221698
$981$	5.46163e7	1.81197
$982$	1.68715e7	0.558310
$983$	2.55262e7	0.842562	0.421281	−	0.906930i	$-0.361581\pi$
$983$	2.55262e7	0.842562	0.421281	+	0.906930i	$0.361581\pi$
$984$	−657437.	−0.0216454
$985$	−3.75506e6	−0.123318
$986$	1.46257e7	0.479099
$987$	349445.	0.0114179
$988$	5.32262e6	0.173473
$989$	−1.76340e6	−0.0573272
$990$	−1.40868e7	−0.456797
$991$	3.83361e7	1.24001	0.620003	−	0.784599i	$-0.287131\pi$
$991$	3.83361e7	1.24001	0.620003	+	0.784599i	$0.287131\pi$
$992$	831009.	0.0268119
$993$	7.28067e6	0.234314
$994$	427439.	0.0137217
$995$	1.85566e7	0.594211
$996$	914527.	0.0292111
$997$	−4.30414e7	−1.37135	−0.685676	−	0.727907i	$-0.740493\pi$
$997$	−4.30414e7	−1.37135	−0.685676	+	0.727907i	$0.740493\pi$
$998$	−3.22988e7	−1.02650
$999$	−4.10891e6	−0.130261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.6.a.d.1.2	✓	2
4.3	odd	2		1040.6.a.i.1.1		2
5.2	odd	4		650.6.b.b.599.3		4
5.3	odd	4		650.6.b.b.599.2		4
5.4	even	2		650.6.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.d.1.2	✓	2	1.1	even	1	trivial
650.6.a.d.1.1		2	5.4	even	2
650.6.b.b.599.2		4	5.3	odd	4
650.6.b.b.599.3		4	5.2	odd	4
1040.6.a.i.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +2.32971 q^{3} +16.0000 q^{4} -25.0000 q^{5} +9.31884 q^{6} -11.9783 q^{7} +64.0000 q^{8} -237.572 q^{9} -100.000 q^{10} -592.946 q^{11} +37.2754 q^{12} +169.000 q^{13} -47.9130 q^{14} -58.2427 q^{15} +256.000 q^{16} -1152.07 q^{17} -950.290 q^{18} +1968.42 q^{19} -400.000 q^{20} -27.9059 q^{21} -2371.78 q^{22} -4924.36 q^{23} +149.101 q^{24} +625.000 q^{25} +676.000 q^{26} -1119.59 q^{27} -191.652 q^{28} -3173.80 q^{29} -232.971 q^{30} +811.533 q^{31} +1024.00 q^{32} -1381.39 q^{33} -4608.26 q^{34} +299.456 q^{35} -3801.16 q^{36} +3670.00 q^{37} +7873.70 q^{38} +393.721 q^{39} -1600.00 q^{40} -4409.33 q^{41} -111.623 q^{42} +358.098 q^{43} -9487.13 q^{44} +5939.31 q^{45} -19697.4 q^{46} -12522.3 q^{47} +596.406 q^{48} -16663.5 q^{49} +2500.00 q^{50} -2683.98 q^{51} +2704.00 q^{52} +6679.07 q^{53} -4478.38 q^{54} +14823.6 q^{55} -766.609 q^{56} +4585.86 q^{57} -12695.2 q^{58} +19291.8 q^{59} -931.884 q^{60} +37674.6 q^{61} +3246.13 q^{62} +2845.70 q^{63} +4096.00 q^{64} -4225.00 q^{65} -5525.56 q^{66} -32133.1 q^{67} -18433.0 q^{68} -11472.3 q^{69} +1197.83 q^{70} -8921.14 q^{71} -15204.6 q^{72} +30600.6 q^{73} +14680.0 q^{74} +1456.07 q^{75} +31494.8 q^{76} +7102.46 q^{77} +1574.88 q^{78} -11135.1 q^{79} -6400.00 q^{80} +55121.8 q^{81} -17637.3 q^{82} +24534.4 q^{83} -446.494 q^{84} +28801.6 q^{85} +1432.39 q^{86} -7394.04 q^{87} -37948.5 q^{88} -31623.3 q^{89} +23757.2 q^{90} -2024.33 q^{91} -78789.7 q^{92} +1890.64 q^{93} -50089.1 q^{94} -49210.6 q^{95} +2385.62 q^{96} +138544. q^{97} -66654.1 q^{98} +140868. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 26 q^{3} + 32 q^{4} - 50 q^{5} - 104 q^{6} + 160 q^{7} + 128 q^{8} + 322 q^{9} - 200 q^{10} - 726 q^{11} - 416 q^{12} + 338 q^{13} + 640 q^{14} + 650 q^{15} + 512 q^{16} - 2856 q^{17} + 1288 q^{18}+ \cdots + 66414 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 26 * q^3 + 32 * q^4 - 50 * q^5 - 104 * q^6 + 160 * q^7 + 128 * q^8 + 322 * q^9 - 200 * q^10 - 726 * q^11 - 416 * q^12 + 338 * q^13 + 640 * q^14 + 650 * q^15 + 512 * q^16 - 2856 * q^17 + 1288 * q^18 - 938 * q^19 - 800 * q^20 - 4900 * q^21 - 2904 * q^22 - 4422 * q^23 - 1664 * q^24 + 1250 * q^25 + 1352 * q^26 - 10088 * q^27 + 2560 * q^28 - 4692 * q^29 + 2600 * q^30 + 6130 * q^31 + 2048 * q^32 + 2388 * q^33 - 11424 * q^34 - 4000 * q^35 + 5152 * q^36 - 9584 * q^37 - 3752 * q^38 - 4394 * q^39 - 3200 * q^40 - 20040 * q^41 - 19600 * q^42 + 10006 * q^43 - 11616 * q^44 - 8050 * q^45 - 17688 * q^46 - 10512 * q^47 - 6656 * q^48 - 3894 * q^49 + 5000 * q^50 + 45588 * q^51 + 5408 * q^52 + 5448 * q^53 - 40352 * q^54 + 18150 * q^55 + 10240 * q^56 + 86924 * q^57 - 18768 * q^58 - 22398 * q^59 + 10400 * q^60 + 12988 * q^61 + 24520 * q^62 + 99080 * q^63 + 8192 * q^64 - 8450 * q^65 + 9552 * q^66 - 56540 * q^67 - 45696 * q^68 - 25704 * q^69 - 16000 * q^70 - 69810 * q^71 + 20608 * q^72 + 99832 * q^73 - 38336 * q^74 - 16250 * q^75 - 15008 * q^76 - 15780 * q^77 - 17576 * q^78 - 31652 * q^79 - 12800 * q^80 + 173218 * q^81 - 80160 * q^82 + 69120 * q^83 - 78400 * q^84 + 71400 * q^85 + 40024 * q^86 + 35616 * q^87 - 46464 * q^88 - 141612 * q^89 - 32200 * q^90 + 27040 * q^91 - 70752 * q^92 - 148780 * q^93 - 42048 * q^94 + 23450 * q^95 - 26624 * q^96 - 7676 * q^97 - 15576 * q^98 + 66414 * q^99

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