LMFDB - Embedded newform 538.6.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,6,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	538.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:	$86.2864950594$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} -18.1958 q^{3} +16.0000 q^{4} +98.2549 q^{5} -72.7833 q^{6} -6.69779 q^{7} +64.0000 q^{8} +88.0879 q^{9} +393.020 q^{10} +188.510 q^{11} -291.133 q^{12} +852.913 q^{13} -26.7911 q^{14} -1787.83 q^{15} +256.000 q^{16} +1882.50 q^{17} +352.352 q^{18} -2701.87 q^{19} +1572.08 q^{20} +121.872 q^{21} +754.040 q^{22} -152.822 q^{23} -1164.53 q^{24} +6529.03 q^{25} +3411.65 q^{26} +2818.75 q^{27} -107.165 q^{28} -555.148 q^{29} -7151.32 q^{30} +5531.42 q^{31} +1024.00 q^{32} -3430.10 q^{33} +7530.00 q^{34} -658.090 q^{35} +1409.41 q^{36} -10815.9 q^{37} -10807.5 q^{38} -15519.5 q^{39} +6288.31 q^{40} +13451.6 q^{41} +487.487 q^{42} +1969.54 q^{43} +3016.16 q^{44} +8655.07 q^{45} -611.287 q^{46} -14628.4 q^{47} -4658.13 q^{48} -16762.1 q^{49} +26116.1 q^{50} -34253.6 q^{51} +13646.6 q^{52} -19648.9 q^{53} +11275.0 q^{54} +18522.0 q^{55} -428.658 q^{56} +49162.7 q^{57} -2220.59 q^{58} +2743.24 q^{59} -28605.3 q^{60} +8168.00 q^{61} +22125.7 q^{62} -589.994 q^{63} +4096.00 q^{64} +83802.9 q^{65} -13720.4 q^{66} -43649.2 q^{67} +30120.0 q^{68} +2780.72 q^{69} -2632.36 q^{70} +25434.6 q^{71} +5637.63 q^{72} +29732.4 q^{73} -43263.4 q^{74} -118801. q^{75} -43229.9 q^{76} -1262.60 q^{77} -62077.8 q^{78} +60105.0 q^{79} +25153.3 q^{80} -72694.9 q^{81} +53806.3 q^{82} -14875.8 q^{83} +1949.95 q^{84} +184965. q^{85} +7878.15 q^{86} +10101.4 q^{87} +12064.6 q^{88} +101711. q^{89} +34620.3 q^{90} -5712.63 q^{91} -2445.15 q^{92} -100649. q^{93} -58513.6 q^{94} -265472. q^{95} -18632.5 q^{96} +167113. q^{97} -67048.6 q^{98} +16605.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 128 q^{2} + 32 q^{3} + 512 q^{4} + 214 q^{5} + 128 q^{6} + 428 q^{7} + 2048 q^{8} + 3196 q^{9} + 856 q^{10} + 1357 q^{11} + 512 q^{12} + 1747 q^{13} + 1712 q^{14} + 2728 q^{15} + 8192 q^{16} + 3766 q^{17}+ \cdots + 338392 q^{99}+O(q^{100}) $ 32 * q + 128 * q^2 + 32 * q^3 + 512 * q^4 + 214 * q^5 + 128 * q^6 + 428 * q^7 + 2048 * q^8 + 3196 * q^9 + 856 * q^10 + 1357 * q^11 + 512 * q^12 + 1747 * q^13 + 1712 * q^14 + 2728 * q^15 + 8192 * q^16 + 3766 * q^17 + 12784 * q^18 + 1417 * q^19 + 3424 * q^20 + 9693 * q^21 + 5428 * q^22 + 11030 * q^23 + 2048 * q^24 + 30524 * q^25 + 6988 * q^26 + 11924 * q^27 + 6848 * q^28 + 21206 * q^29 + 10912 * q^30 + 18142 * q^31 + 32768 * q^32 + 27879 * q^33 + 15064 * q^34 + 14971 * q^35 + 51136 * q^36 + 24725 * q^37 + 5668 * q^38 + 25201 * q^39 + 13696 * q^40 + 38470 * q^41 + 38772 * q^42 + 18145 * q^43 + 21712 * q^44 + 54227 * q^45 + 44120 * q^46 + 50173 * q^47 + 8192 * q^48 + 114490 * q^49 + 122096 * q^50 + 28981 * q^51 + 27952 * q^52 + 109649 * q^53 + 47696 * q^54 + 53077 * q^55 + 27392 * q^56 + 90298 * q^57 + 84824 * q^58 + 78978 * q^59 + 43648 * q^60 + 105671 * q^61 + 72568 * q^62 + 138923 * q^63 + 131072 * q^64 + 149825 * q^65 + 111516 * q^66 + 135561 * q^67 + 60256 * q^68 + 281851 * q^69 + 59884 * q^70 + 306266 * q^71 + 204544 * q^72 + 253098 * q^73 + 98900 * q^74 + 440869 * q^75 + 22672 * q^76 + 501432 * q^77 + 100804 * q^78 + 331657 * q^79 + 54784 * q^80 + 613516 * q^81 + 153880 * q^82 + 421327 * q^83 + 155088 * q^84 + 526007 * q^85 + 72580 * q^86 + 617560 * q^87 + 86848 * q^88 + 392845 * q^89 + 216908 * q^90 + 306534 * q^91 + 176480 * q^92 + 471703 * q^93 + 200692 * q^94 + 337292 * q^95 + 32768 * q^96 + 451994 * q^97 + 457960 * q^98 + 338392 * 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
$3$	−18.1958	−1.16726	−0.583631	−	0.812019i	$-0.698369\pi$
$3$	−18.1958	−1.16726	−0.583631	+	0.812019i	$0.698369\pi$
$4$	16.0000	0.500000
$5$	98.2549	1.75764	0.878819	−	0.477156i	$-0.158332\pi$
$5$	98.2549	1.75764	0.878819	+	0.477156i	$0.158332\pi$
$6$	−72.7833	−0.825379
$7$	−6.69779	−0.0516638	−0.0258319	−	0.999666i	$-0.508223\pi$
$7$	−6.69779	−0.0516638	−0.0258319	+	0.999666i	$0.508223\pi$
$8$	64.0000	0.353553
$9$	88.0879	0.362502
$10$	393.020	1.24284
$11$	188.510	0.469735	0.234867	−	0.972027i	$-0.424534\pi$
$11$	188.510	0.469735	0.234867	+	0.972027i	$0.424534\pi$
$12$	−291.133	−0.583631
$13$	852.913	1.39974	0.699869	−	0.714272i	$-0.253242\pi$
$13$	852.913	1.39974	0.699869	+	0.714272i	$0.253242\pi$
$14$	−26.7911	−0.0365318
$15$	−1787.83	−2.05162
$16$	256.000	0.250000
$17$	1882.50	1.57984	0.789919	−	0.613211i	$-0.210122\pi$
$17$	1882.50	1.57984	0.789919	+	0.613211i	$0.210122\pi$
$18$	352.352	0.256327
$19$	−2701.87	−1.71704	−0.858519	−	0.512782i	$-0.828615\pi$
$19$	−2701.87	−1.71704	−0.858519	+	0.512782i	$0.828615\pi$
$20$	1572.08	0.878819
$21$	121.872	0.0603052
$22$	754.040	0.332153
$23$	−152.822	−0.0602373	−0.0301187	−	0.999546i	$-0.509589\pi$
$23$	−152.822	−0.0602373	−0.0301187	+	0.999546i	$0.509589\pi$
$24$	−1164.53	−0.412690
$25$	6529.03	2.08929
$26$	3411.65	0.989764
$27$	2818.75	0.744128
$28$	−107.165	−0.0258319
$29$	−555.148	−0.122578	−0.0612892	−	0.998120i	$-0.519521\pi$
$29$	−555.148	−0.122578	−0.0612892	+	0.998120i	$0.519521\pi$
$30$	−7151.32	−1.45072
$31$	5531.42	1.03379	0.516895	−	0.856049i	$-0.327088\pi$
$31$	5531.42	1.03379	0.516895	+	0.856049i	$0.327088\pi$
$32$	1024.00	0.176777
$33$	−3430.10	−0.548304
$34$	7530.00	1.11711
$35$	−658.090	−0.0908062
$36$	1409.41	0.181251
$37$	−10815.9	−1.29884	−0.649421	−	0.760429i	$-0.724989\pi$
$37$	−10815.9	−1.29884	−0.649421	+	0.760429i	$0.724989\pi$
$38$	−10807.5	−1.21413
$39$	−15519.5	−1.63386
$40$	6288.31	0.621419
$41$	13451.6	1.24972	0.624861	−	0.780736i	$-0.285155\pi$
$41$	13451.6	1.24972	0.624861	+	0.780736i	$0.285155\pi$
$42$	487.487	0.0426422
$43$	1969.54	0.162440	0.0812200	−	0.996696i	$-0.474118\pi$
$43$	1969.54	0.162440	0.0812200	+	0.996696i	$0.474118\pi$
$44$	3016.16	0.234867
$45$	8655.07	0.637147
$46$	−611.287	−0.0425942
$47$	−14628.4	−0.965944	−0.482972	−	0.875636i	$-0.660443\pi$
$47$	−14628.4	−0.965944	−0.482972	+	0.875636i	$0.660443\pi$
$48$	−4658.13	−0.291816
$49$	−16762.1	−0.997331
$50$	26116.1	1.47735
$51$	−34253.6	−1.84409
$52$	13646.6	0.699869
$53$	−19648.9	−0.960834	−0.480417	−	0.877040i	$-0.659515\pi$
$53$	−19648.9	−0.960834	−0.480417	+	0.877040i	$0.659515\pi$
$54$	11275.0	0.526178
$55$	18522.0	0.825624
$56$	−428.658	−0.0182659
$57$	49162.7	2.00423
$58$	−2220.59	−0.0866760
$59$	2743.24	0.102597	0.0512985	−	0.998683i	$-0.483664\pi$
$59$	2743.24	0.102597	0.0512985	+	0.998683i	$0.483664\pi$
$60$	−28605.3	−1.02581
$61$	8168.00	0.281055	0.140527	−	0.990077i	$-0.455120\pi$
$61$	8168.00	0.281055	0.140527	+	0.990077i	$0.455120\pi$
$62$	22125.7	0.731000
$63$	−589.994	−0.0187282
$64$	4096.00	0.125000
$65$	83802.9	2.46023
$66$	−13720.4	−0.387709
$67$	−43649.2	−1.18792	−0.593962	−	0.804493i	$-0.702437\pi$
$67$	−43649.2	−1.18792	−0.593962	+	0.804493i	$0.702437\pi$
$68$	30120.0	0.789919
$69$	2780.72	0.0703128
$70$	−2632.36	−0.0642097
$71$	25434.6	0.598797	0.299399	−	0.954128i	$-0.403214\pi$
$71$	25434.6	0.598797	0.299399	+	0.954128i	$0.403214\pi$
$72$	5637.63	0.128164
$73$	29732.4	0.653014	0.326507	−	0.945195i	$-0.394128\pi$
$73$	29732.4	0.653014	0.326507	+	0.945195i	$0.394128\pi$
$74$	−43263.4	−0.918421
$75$	−118801.	−2.43875
$76$	−43229.9	−0.858519
$77$	−1262.60	−0.0242683
$78$	−62077.8	−1.15531
$79$	60105.0	1.08353	0.541767	−	0.840529i	$-0.317756\pi$
$79$	60105.0	1.08353	0.541767	+	0.840529i	$0.317756\pi$
$80$	25153.3	0.439409
$81$	−72694.9	−1.23109
$82$	53806.3	0.883688
$83$	−14875.8	−0.237020	−0.118510	−	0.992953i	$-0.537812\pi$
$83$	−14875.8	−0.237020	−0.118510	+	0.992953i	$0.537812\pi$
$84$	1949.95	0.0301526
$85$	184965.	2.77678
$86$	7878.15	0.114862
$87$	10101.4	0.143081
$88$	12064.6	0.166076
$89$	101711.	1.36111	0.680557	−	0.732695i	$-0.261738\pi$
$89$	101711.	1.36111	0.680557	+	0.732695i	$0.261738\pi$
$90$	34620.3	0.450531
$91$	−5712.63	−0.0723157
$92$	−2445.15	−0.0301187
$93$	−100649.	−1.20670
$94$	−58513.6	−0.683026
$95$	−265472.	−3.01793
$96$	−18632.5	−0.206345
$97$	167113.	1.80335	0.901677	−	0.432410i	$-0.142337\pi$
$97$	167113.	1.80335	0.901677	+	0.432410i	$0.142337\pi$
$98$	−67048.6	−0.705219
$99$	16605.5	0.170280
$100$	104464.	1.04464
$101$	148740.	1.45086	0.725430	−	0.688296i	$-0.241641\pi$
$101$	148740.	1.45086	0.725430	+	0.688296i	$0.241641\pi$
$102$	−137015.	−1.30397
$103$	39062.2	0.362797	0.181399	−	0.983410i	$-0.441938\pi$
$103$	39062.2	0.362797	0.181399	+	0.983410i	$0.441938\pi$
$104$	54586.5	0.494882
$105$	11974.5	0.105995
$106$	−78595.5	−0.679412
$107$	−176687.	−1.49192	−0.745961	−	0.665990i	$-0.768009\pi$
$107$	−176687.	−1.49192	−0.745961	+	0.665990i	$0.768009\pi$
$108$	45100.0	0.372064
$109$	−115518.	−0.931290	−0.465645	−	0.884972i	$-0.654178\pi$
$109$	−115518.	−0.931290	−0.465645	+	0.884972i	$0.654178\pi$
$110$	74088.2	0.583804
$111$	196803.	1.51609
$112$	−1714.63	−0.0129159
$113$	55408.6	0.408208	0.204104	−	0.978949i	$-0.434572\pi$
$113$	55408.6	0.408208	0.204104	+	0.978949i	$0.434572\pi$
$114$	196651.	1.41721
$115$	−15015.5	−0.105875
$116$	−8882.37	−0.0612892
$117$	75131.4	0.507407
$118$	10973.0	0.0725470
$119$	−12608.6	−0.0816204
$120$	−114421.	−0.725359
$121$	−125515.	−0.779349
$122$	32672.0	0.198736
$123$	−244763.	−1.45875
$124$	88502.7	0.516895
$125$	334463.	1.91458
$126$	−2359.98	−0.0132428
$127$	290356.	1.59743	0.798716	−	0.601709i	$-0.205513\pi$
$127$	290356.	1.59743	0.798716	+	0.601709i	$0.205513\pi$
$128$	16384.0	0.0883883
$129$	−35837.3	−0.189610
$130$	335212.	1.73965
$131$	−261528.	−1.33150	−0.665749	−	0.746176i	$-0.731888\pi$
$131$	−261528.	−1.33150	−0.665749	+	0.746176i	$0.731888\pi$
$132$	−54881.5	−0.274152
$133$	18096.5	0.0887086
$134$	−174597.	−0.839989
$135$	276956.	1.30791
$136$	120480.	0.558557
$137$	399036.	1.81640	0.908199	−	0.418539i	$-0.137458\pi$
$137$	399036.	1.81640	0.908199	+	0.418539i	$0.137458\pi$
$138$	11122.9	0.0497186
$139$	260034.	1.14155	0.570773	−	0.821108i	$-0.306644\pi$
$139$	260034.	1.14155	0.570773	+	0.821108i	$0.306644\pi$
$140$	−10529.4	−0.0454031
$141$	266176.	1.12751
$142$	101739.	0.423414
$143$	160783.	0.657506
$144$	22550.5	0.0906255
$145$	−54546.0	−0.215448
$146$	118930.	0.461751
$147$	305001.	1.16415
$148$	−173054.	−0.649421
$149$	443725.	1.63738	0.818688	−	0.574238i	$-0.194702\pi$
$149$	443725.	1.63738	0.818688	+	0.574238i	$0.194702\pi$
$150$	−475204.	−1.72446
$151$	−307787.	−1.09852	−0.549261	−	0.835651i	$-0.685091\pi$
$151$	−307787.	−1.09852	−0.549261	+	0.835651i	$0.685091\pi$
$152$	−172919.	−0.607064
$153$	165826.	0.572695
$154$	−5050.40	−0.0171603
$155$	543489.	1.81703
$156$	−248311.	−0.816931
$157$	287204.	0.929911	0.464956	−	0.885334i	$-0.346070\pi$
$157$	287204.	0.929911	0.464956	+	0.885334i	$0.346070\pi$
$158$	240420.	0.766174
$159$	357528.	1.12155
$160$	100613.	0.310709
$161$	1023.57	0.00311209
$162$	−290780.	−0.870515
$163$	320561.	0.945022	0.472511	−	0.881325i	$-0.343348\pi$
$163$	320561.	0.945022	0.472511	+	0.881325i	$0.343348\pi$
$164$	215225.	0.624861
$165$	−337024.	−0.963720
$166$	−59503.1	−0.167598
$167$	559212.	1.55162	0.775810	−	0.630966i	$-0.217341\pi$
$167$	559212.	1.55162	0.775810	+	0.630966i	$0.217341\pi$
$168$	7799.79	0.0213211
$169$	356168.	0.959265
$170$	739860.	1.96348
$171$	−238002.	−0.622429
$172$	31512.6	0.0812200
$173$	−9563.14	−0.0242932	−0.0121466	−	0.999926i	$-0.503866\pi$
$173$	−9563.14	−0.0242932	−0.0121466	+	0.999926i	$0.503866\pi$
$174$	40405.5	0.101174
$175$	−43730.0	−0.107941
$176$	48258.6	0.117434
$177$	−49915.6	−0.119758
$178$	406846.	0.962453
$179$	352738.	0.822849	0.411425	−	0.911444i	$-0.365031\pi$
$179$	352738.	0.822849	0.411425	+	0.911444i	$0.365031\pi$
$180$	138481.	0.318573
$181$	−344177.	−0.780882	−0.390441	−	0.920628i	$-0.627677\pi$
$181$	−344177.	−0.780882	−0.390441	+	0.920628i	$0.627677\pi$
$182$	−22850.5	−0.0511349
$183$	−148623.	−0.328065
$184$	−9780.59	−0.0212971
$185$	−1.06271e6	−2.28289
$186$	−402595.	−0.853269
$187$	354870.	0.742106
$188$	−234054.	−0.482972
$189$	−18879.4	−0.0384444
$190$	−1.06189e6	−2.13400
$191$	−693367.	−1.37524	−0.687622	−	0.726069i	$-0.741345\pi$
$191$	−693367.	−1.37524	−0.687622	+	0.726069i	$0.741345\pi$
$192$	−74530.1	−0.145908
$193$	−975351.	−1.88481	−0.942405	−	0.334473i	$-0.891442\pi$
$193$	−975351.	−1.88481	−0.942405	+	0.334473i	$0.891442\pi$
$194$	668452.	1.27516
$195$	−1.52486e6	−2.87174
$196$	−268194.	−0.498665
$197$	−510402.	−0.937015	−0.468507	−	0.883460i	$-0.655208\pi$
$197$	−510402.	−0.937015	−0.468507	+	0.883460i	$0.655208\pi$
$198$	66421.9	0.120406
$199$	713458.	1.27713	0.638566	−	0.769567i	$-0.279528\pi$
$199$	713458.	1.27713	0.638566	+	0.769567i	$0.279528\pi$
$200$	417858.	0.738675
$201$	794232.	1.38662
$202$	594962.	1.02591
$203$	3718.26	0.00633286
$204$	−548058.	−0.922043
$205$	1.32168e6	2.19656
$206$	156249.	0.256536
$207$	−13461.8	−0.0218361
$208$	218346.	0.349934
$209$	−509329.	−0.806553
$210$	47898.0	0.0749495
$211$	647710.	1.00155	0.500777	−	0.865576i	$-0.333048\pi$
$211$	647710.	1.00155	0.500777	+	0.865576i	$0.333048\pi$
$212$	−314382.	−0.480417
$213$	−462804.	−0.698954
$214$	−706750.	−1.05495
$215$	193517.	0.285511
$216$	180400.	0.263089
$217$	−37048.3	−0.0534095
$218$	−462073.	−0.658521
$219$	−541005.	−0.762239
$220$	296353.	0.412812
$221$	1.60561e6	2.21136
$222$	787214.	1.07204
$223$	−40632.0	−0.0547149	−0.0273575	−	0.999626i	$-0.508709\pi$
$223$	−40632.0	−0.0547149	−0.0273575	+	0.999626i	$0.508709\pi$
$224$	−6858.53	−0.00913295
$225$	575129.	0.757371
$226$	221635.	0.288647
$227$	−1.48719e6	−1.91558	−0.957791	−	0.287466i	$-0.907187\pi$
$227$	−1.48719e6	−1.91558	−0.957791	+	0.287466i	$0.907187\pi$
$228$	786603.	1.00212
$229$	−1.32028e6	−1.66371	−0.831853	−	0.554996i	$-0.812720\pi$
$229$	−1.32028e6	−1.66371	−0.831853	+	0.554996i	$0.812720\pi$
$230$	−60062.0	−0.0748652
$231$	22974.0	0.0283275
$232$	−35529.5	−0.0433380
$233$	−1.06045e6	−1.27968	−0.639841	−	0.768507i	$-0.721000\pi$
$233$	−1.06045e6	−1.27968	−0.639841	+	0.768507i	$0.721000\pi$
$234$	300526.	0.358791
$235$	−1.43731e6	−1.69778
$236$	43891.9	0.0512985
$237$	−1.09366e6	−1.26477
$238$	−50434.3	−0.0577144
$239$	696059.	0.788227	0.394114	−	0.919062i	$-0.371052\pi$
$239$	696059.	0.788227	0.394114	+	0.919062i	$0.371052\pi$
$240$	−457684.	−0.512906
$241$	542190.	0.601324	0.300662	−	0.953731i	$-0.402792\pi$
$241$	542190.	0.601324	0.300662	+	0.953731i	$0.402792\pi$
$242$	−502060.	−0.551083
$243$	637786.	0.692882
$244$	130688.	0.140527
$245$	−1.64696e6	−1.75295
$246$	−979050.	−1.03150
$247$	−2.30446e6	−2.40340
$248$	354011.	0.365500
$249$	270677.	0.276664
$250$	1.33785e6	1.35381
$251$	596895.	0.598017	0.299008	−	0.954250i	$-0.403344\pi$
$251$	596895.	0.598017	0.299008	+	0.954250i	$0.403344\pi$
$252$	−9439.91	−0.00936411
$253$	−28808.4	−0.0282956
$254$	1.16143e6	1.12955
$255$	−3.36559e6	−3.24124
$256$	65536.0	0.0625000
$257$	183594.	0.173391	0.0866953	−	0.996235i	$-0.472369\pi$
$257$	183594.	0.173391	0.0866953	+	0.996235i	$0.472369\pi$
$258$	−143349.	−0.134075
$259$	72442.3	0.0671031
$260$	1.34085e6	1.23012
$261$	−48901.8	−0.0444349
$262$	−1.04611e6	−0.941511
$263$	−1.80420e6	−1.60841	−0.804204	−	0.594354i	$-0.797408\pi$
$263$	−1.80420e6	−1.60841	−0.804204	+	0.594354i	$0.797408\pi$
$264$	−219526.	−0.193855
$265$	−1.93060e6	−1.68880
$266$	72386.1	0.0627265
$267$	−1.85072e6	−1.58878
$268$	−698386.	−0.593962
$269$	−72361.0	−0.0609711
$269$	−72361.0	−0.0609711
$270$	1.10783e6	0.924830
$271$	2.04446e6	1.69104	0.845522	−	0.533940i	$-0.179289\pi$
$271$	2.04446e6	1.69104	0.845522	+	0.533940i	$0.179289\pi$
$272$	481920.	0.394960
$273$	103946.	0.0844114
$274$	1.59615e6	1.28439
$275$	1.23079e6	0.981412
$276$	44491.5	0.0351564
$277$	1.76364e6	1.38105	0.690526	−	0.723307i	$-0.257379\pi$
$277$	1.76364e6	1.38105	0.690526	+	0.723307i	$0.257379\pi$
$278$	1.04014e6	0.807195
$279$	487251.	0.374751
$280$	−42117.8	−0.0321048
$281$	−1.53263e6	−1.15790	−0.578949	−	0.815364i	$-0.696537\pi$
$281$	−1.53263e6	−1.15790	−0.578949	+	0.815364i	$0.696537\pi$
$282$	1.06470e6	0.797270
$283$	−1.54923e6	−1.14987	−0.574937	−	0.818197i	$-0.694974\pi$
$283$	−1.54923e6	−1.14987	−0.574937	+	0.818197i	$0.694974\pi$
$284$	406954.	0.299399
$285$	4.83047e6	3.52272
$286$	643131.	0.464927
$287$	−90095.8	−0.0645654
$288$	90202.1	0.0640819
$289$	2.12395e6	1.49589
$290$	−218184.	−0.152345
$291$	−3.04076e6	−2.10499
$292$	475718.	0.326507
$293$	−489212.	−0.332911	−0.166456	−	0.986049i	$-0.553232\pi$
$293$	−489212.	−0.332911	−0.166456	+	0.986049i	$0.553232\pi$
$294$	1.22000e6	0.823176
$295$	269537.	0.180328
$296$	−692215.	−0.459210
$297$	531363.	0.349543
$298$	1.77490e6	1.15780
$299$	−130344.	−0.0843164
$300$	−1.90082e6	−1.21937
$301$	−13191.5	−0.00839226
$302$	−1.23115e6	−0.776772
$303$	−2.70645e6	−1.69354
$304$	−691678.	−0.429259
$305$	802546.	0.493992
$306$	663302.	0.404956
$307$	1.95849e6	1.18597	0.592986	−	0.805213i	$-0.297949\pi$
$307$	1.95849e6	1.18597	0.592986	+	0.805213i	$0.297949\pi$
$308$	−20201.6	−0.0121341
$309$	−710770.	−0.423480
$310$	2.17396e6	1.28483
$311$	−1.17428e6	−0.688447	−0.344224	−	0.938888i	$-0.611858\pi$
$311$	−1.17428e6	−0.688447	−0.344224	+	0.938888i	$0.611858\pi$
$312$	−993246.	−0.577657
$313$	1.49631e6	0.863299	0.431650	−	0.902041i	$-0.357932\pi$
$313$	1.49631e6	0.863299	0.431650	+	0.902041i	$0.357932\pi$
$314$	1.14882e6	0.657547
$315$	−57969.8	−0.0329174
$316$	961679.	0.541767
$317$	−1.34767e6	−0.753243	−0.376621	−	0.926367i	$-0.622914\pi$
$317$	−1.34767e6	−0.753243	−0.376621	+	0.926367i	$0.622914\pi$
$318$	1.43011e6	0.793052
$319$	−104651.	−0.0575793
$320$	402452.	0.219705
$321$	3.21497e6	1.74146
$322$	4094.27	0.00220058
$323$	−5.08626e6	−2.71264
$324$	−1.16312e6	−0.615547
$325$	5.56870e6	2.92446
$326$	1.28225e6	0.668232
$327$	2.10195e6	1.08706
$328$	860901.	0.441844
$329$	97977.8	0.0499043
$330$	−1.34810e6	−0.681453
$331$	459267.	0.230407	0.115203	−	0.993342i	$-0.463248\pi$
$331$	459267.	0.230407	0.115203	+	0.993342i	$0.463248\pi$
$332$	−238012.	−0.118510
$333$	−952747.	−0.470833
$334$	2.23685e6	1.09716
$335$	−4.28874e6	−2.08794
$336$	31199.2	0.0150763
$337$	−2.22881e6	−1.06905	−0.534524	−	0.845153i	$-0.679509\pi$
$337$	−2.22881e6	−1.06905	−0.534524	+	0.845153i	$0.679509\pi$
$338$	1.42467e6	0.678303
$339$	−1.00821e6	−0.476486
$340$	2.95944e6	1.38839
$341$	1.04273e6	0.485607
$342$	−952007.	−0.440124
$343$	224839.	0.103190
$344$	126050.	0.0574312
$345$	273219.	0.123584
$346$	−38252.6	−0.0171779
$347$	−3.50477e6	−1.56256	−0.781279	−	0.624182i	$-0.785432\pi$
$347$	−3.50477e6	−1.56256	−0.781279	+	0.624182i	$0.785432\pi$
$348$	161622.	0.0715406
$349$	−3.43667e6	−1.51034	−0.755169	−	0.655530i	$-0.772445\pi$
$349$	−3.43667e6	−1.51034	−0.755169	+	0.655530i	$0.772445\pi$
$350$	−174920.	−0.0763255
$351$	2.40415e6	1.04158
$352$	193034.	0.0830382
$353$	112627.	0.0481069	0.0240534	−	0.999711i	$-0.492343\pi$
$353$	112627.	0.0481069	0.0240534	+	0.999711i	$0.492343\pi$
$354$	−199662.	−0.0846814
$355$	2.49908e6	1.05247
$356$	1.62738e6	0.680557
$357$	229424.	0.0952725
$358$	1.41095e6	0.581842
$359$	242975.	0.0995007	0.0497503	−	0.998762i	$-0.484157\pi$
$359$	242975.	0.0995007	0.0497503	+	0.998762i	$0.484157\pi$
$360$	553925.	0.225265
$361$	4.82398e6	1.94822
$362$	−1.37671e6	−0.552167
$363$	2.28385e6	0.909705
$364$	−91402.1	−0.0361579
$365$	2.92135e6	1.14776
$366$	−594494.	−0.231977
$367$	2.44928e6	0.949233	0.474616	−	0.880193i	$-0.342587\pi$
$367$	2.44928e6	0.949233	0.474616	+	0.880193i	$0.342587\pi$
$368$	−39122.4	−0.0150593
$369$	1.18492e6	0.453027
$370$	−4.25084e6	−1.61425
$371$	131604.	0.0496403
$372$	−1.61038e6	−0.603352
$373$	395676.	0.147254	0.0736271	−	0.997286i	$-0.476543\pi$
$373$	395676.	0.147254	0.0736271	+	0.997286i	$0.476543\pi$
$374$	1.41948e6	0.524748
$375$	−6.08582e6	−2.23481
$376$	−936217.	−0.341513
$377$	−473493.	−0.171578
$378$	−75517.6	−0.0271843
$379$	−3.35732e6	−1.20059	−0.600294	−	0.799779i	$-0.704950\pi$
$379$	−3.35732e6	−1.20059	−0.600294	+	0.799779i	$0.704950\pi$
$380$	−4.24755e6	−1.50896
$381$	−5.28327e6	−1.86462
$382$	−2.77347e6	−0.972444
$383$	591636.	0.206090	0.103045	−	0.994677i	$-0.467141\pi$
$383$	591636.	0.206090	0.103045	+	0.994677i	$0.467141\pi$
$384$	−298120.	−0.103172
$385$	−124057.	−0.0426548
$386$	−3.90140e6	−1.33276
$387$	173492.	0.0588848
$388$	2.67381e6	0.901677
$389$	−1.30912e6	−0.438637	−0.219318	−	0.975653i	$-0.570383\pi$
$389$	−1.30912e6	−0.438637	−0.219318	+	0.975653i	$0.570383\pi$
$390$	−6.09945e6	−2.03062
$391$	−287687.	−0.0951653
$392$	−1.07278e6	−0.352610
$393$	4.75872e6	1.55421
$394$	−2.04161e6	−0.662569
$395$	5.90561e6	1.90446
$396$	265687.	0.0851399
$397$	−855682.	−0.272481	−0.136240	−	0.990676i	$-0.543502\pi$
$397$	−855682.	−0.272481	−0.136240	+	0.990676i	$0.543502\pi$
$398$	2.85383e6	0.903069
$399$	−329281.	−0.103546
$400$	1.67143e6	0.522322
$401$	−4.84841e6	−1.50570	−0.752850	−	0.658192i	$-0.771322\pi$
$401$	−4.84841e6	−1.50570	−0.752850	+	0.658192i	$0.771322\pi$
$402$	3.17693e6	0.980488
$403$	4.71782e6	1.44703
$404$	2.37985e6	0.725430
$405$	−7.14263e6	−2.16382
$406$	14873.0	0.00447801
$407$	−2.03890e6	−0.610112
$408$	−2.19223e6	−0.651983
$409$	1.15066e6	0.340125	0.170063	−	0.985433i	$-0.445603\pi$
$409$	1.15066e6	0.340125	0.170063	+	0.985433i	$0.445603\pi$
$410$	5.28674e6	1.55320
$411$	−7.26079e6	−2.12021
$412$	624996.	0.181399
$413$	−18373.7	−0.00530055
$414$	−53847.0	−0.0154405
$415$	−1.46162e6	−0.416595
$416$	873383.	0.247441
$417$	−4.73153e6	−1.33248
$418$	−2.03732e6	−0.570319
$419$	−1.30593e6	−0.363401	−0.181700	−	0.983354i	$-0.558160\pi$
$419$	−1.30593e6	−0.363401	−0.181700	+	0.983354i	$0.558160\pi$
$420$	191592.	0.0529973
$421$	705974.	0.194126	0.0970629	−	0.995278i	$-0.469055\pi$
$421$	705974.	0.194126	0.0970629	+	0.995278i	$0.469055\pi$
$422$	2.59084e6	0.708205
$423$	−1.28859e6	−0.350157
$424$	−1.25753e6	−0.339706
$425$	1.22909e7	3.30074
$426$	−1.85122e6	−0.494235
$427$	−54707.5	−0.0145204
$428$	−2.82700e6	−0.745961
$429$	−2.92557e6	−0.767482
$430$	774067.	0.201886
$431$	2.42803e6	0.629596	0.314798	−	0.949159i	$-0.398063\pi$
$431$	2.42803e6	0.629596	0.314798	+	0.949159i	$0.398063\pi$
$432$	721601.	0.186032
$433$	−1.09578e6	−0.280868	−0.140434	−	0.990090i	$-0.544850\pi$
$433$	−1.09578e6	−0.280868	−0.140434	+	0.990090i	$0.544850\pi$
$434$	−148193.	−0.0377662
$435$	992510.	0.251485
$436$	−1.84829e6	−0.465645
$437$	412904.	0.103430
$438$	−2.16402e6	−0.538985
$439$	−1.39084e6	−0.344441	−0.172221	−	0.985058i	$-0.555094\pi$
$439$	−1.39084e6	−0.344441	−0.172221	+	0.985058i	$0.555094\pi$
$440$	1.18541e6	0.291902
$441$	−1.47654e6	−0.361534
$442$	6.42244e6	1.56367
$443$	−4.64211e6	−1.12384	−0.561922	−	0.827190i	$-0.689938\pi$
$443$	−4.64211e6	−1.12384	−0.561922	+	0.827190i	$0.689938\pi$
$444$	3.14885e6	0.758045
$445$	9.99364e6	2.39235
$446$	−162528.	−0.0386893
$447$	−8.07395e6	−1.91125
$448$	−27434.1	−0.00645797
$449$	−6.03036e6	−1.41165	−0.705825	−	0.708386i	$-0.749424\pi$
$449$	−6.03036e6	−1.41165	−0.705825	+	0.708386i	$0.749424\pi$
$450$	2.30051e6	0.535542
$451$	2.53576e6	0.587039
$452$	886538.	0.204104
$453$	5.60045e6	1.28226
$454$	−5.94874e6	−1.35452
$455$	−561294.	−0.127105
$456$	3.14641e6	0.708604
$457$	−1.79510e6	−0.402067	−0.201033	−	0.979584i	$-0.564430\pi$
$457$	−1.79510e6	−0.402067	−0.201033	+	0.979584i	$0.564430\pi$
$458$	−5.28111e6	−1.17642
$459$	5.30630e6	1.17560
$460$	−240248.	−0.0529377
$461$	7.32753e6	1.60585	0.802926	−	0.596079i	$-0.203275\pi$
$461$	7.32753e6	1.60585	0.802926	+	0.596079i	$0.203275\pi$
$462$	91896.2	0.0200305
$463$	−1.83154e6	−0.397067	−0.198534	−	0.980094i	$-0.563618\pi$
$463$	−1.83154e6	−0.397067	−0.198534	+	0.980094i	$0.563618\pi$
$464$	−142118.	−0.0306446
$465$	−9.88923e6	−2.12095
$466$	−4.24182e6	−0.904872
$467$	−4.25111e6	−0.902008	−0.451004	−	0.892522i	$-0.648934\pi$
$467$	−4.25111e6	−0.902008	−0.451004	+	0.892522i	$0.648934\pi$
$468$	1.20210e6	0.253704
$469$	292353.	0.0613727
$470$	−5.74925e6	−1.20051
$471$	−5.22592e6	−1.08545
$472$	175568.	0.0362735
$473$	371277.	0.0763037
$474$	−4.37464e6	−0.894326
$475$	−1.76406e7	−3.58739
$476$	−201737.	−0.0408102
$477$	−1.73083e6	−0.348304
$478$	2.78424e6	0.557361
$479$	−1.77463e6	−0.353402	−0.176701	−	0.984265i	$-0.556543\pi$
$479$	−1.77463e6	−0.353402	−0.176701	+	0.984265i	$0.556543\pi$
$480$	−1.83074e6	−0.362679
$481$	−9.22499e6	−1.81804
$482$	2.16876e6	0.425201
$483$	−18624.7	−0.00363262
$484$	−2.00824e6	−0.389675
$485$	1.64197e7	3.16964
$486$	2.55115e6	0.489942
$487$	−2.50288e6	−0.478210	−0.239105	−	0.970994i	$-0.576854\pi$
$487$	−2.50288e6	−0.478210	−0.239105	+	0.970994i	$0.576854\pi$
$488$	522752.	0.0993679
$489$	−5.83288e6	−1.10309
$490$	−6.58785e6	−1.23952
$491$	6.26595e6	1.17296	0.586480	−	0.809963i	$-0.300513\pi$
$491$	6.26595e6	1.17296	0.586480	+	0.809963i	$0.300513\pi$
$492$	−3.91620e6	−0.729377
$493$	−1.04507e6	−0.193654
$494$	−9.21783e6	−1.69946
$495$	1.63157e6	0.299290
$496$	1.41604e6	0.258447
$497$	−170356.	−0.0309361
$498$	1.08271e6	0.195631
$499$	3.40011e6	0.611282	0.305641	−	0.952147i	$-0.401129\pi$
$499$	3.40011e6	0.611282	0.305641	+	0.952147i	$0.401129\pi$
$500$	5.35140e6	0.957288
$501$	−1.01753e7	−1.81115
$502$	2.38758e6	0.422862
$503$	−1.46365e6	−0.257939	−0.128970	−	0.991649i	$-0.541167\pi$
$503$	−1.46365e6	−0.257939	−0.128970	+	0.991649i	$0.541167\pi$
$504$	−37759.6	−0.00662142
$505$	1.46145e7	2.55009
$506$	−115234.	−0.0200080
$507$	−6.48078e6	−1.11971
$508$	4.64570e6	0.798716
$509$	1.75009e6	0.299410	0.149705	−	0.988731i	$-0.452168\pi$
$509$	1.75009e6	0.299410	0.149705	+	0.988731i	$0.452168\pi$
$510$	−1.34624e7	−2.29190
$511$	−199141.	−0.0337372
$512$	262144.	0.0441942
$513$	−7.61589e6	−1.27770
$514$	734376.	0.122606
$515$	3.83806e6	0.637666
$516$	−573397.	−0.0948050
$517$	−2.75760e6	−0.453738
$518$	289769.	0.0474491
$519$	174009.	0.0283566
$520$	5.36339e6	0.869823
$521$	5.22622e6	0.843515	0.421758	−	0.906709i	$-0.361413\pi$
$521$	5.22622e6	0.843515	0.421758	+	0.906709i	$0.361413\pi$
$522$	−195607.	−0.0314202
$523$	7.95580e6	1.27183	0.635916	−	0.771758i	$-0.280622\pi$
$523$	7.95580e6	1.27183	0.635916	+	0.771758i	$0.280622\pi$
$524$	−4.18445e6	−0.665749
$525$	795704.	0.125995
$526$	−7.21681e6	−1.13732
$527$	1.04129e7	1.63322
$528$	−878105.	−0.137076
$529$	−6.41299e6	−0.996371
$530$	−7.72240e6	−1.19416
$531$	241647.	0.0371916
$532$	289544.	0.0443543
$533$	1.14730e7	1.74928
$534$	−7.40289e6	−1.12344
$535$	−1.73604e7	−2.62226
$536$	−2.79355e6	−0.419995
$537$	−6.41836e6	−0.960481
$538$	−289444.	−0.0431131
$539$	−3.15983e6	−0.468481
$540$	4.43130e6	0.653953
$541$	4.56097e6	0.669983	0.334992	−	0.942221i	$-0.391266\pi$
$541$	4.56097e6	0.669983	0.334992	+	0.942221i	$0.391266\pi$
$542$	8.17783e6	1.19575
$543$	6.26258e6	0.911494
$544$	1.92768e6	0.279279
$545$	−1.13502e7	−1.63687
$546$	415784.	0.0596879
$547$	1.03097e7	1.47326	0.736628	−	0.676298i	$-0.236417\pi$
$547$	1.03097e7	1.47326	0.736628	+	0.676298i	$0.236417\pi$
$548$	6.38458e6	0.908199
$549$	719502.	0.101883
$550$	4.92315e6	0.693963
$551$	1.49994e6	0.210472
$552$	177966.	0.0248593
$553$	−402570.	−0.0559795
$554$	7.05455e6	0.976551
$555$	1.93369e7	2.66474
$556$	4.16055e6	0.570773
$557$	5.28602e6	0.721923	0.360962	−	0.932581i	$-0.382449\pi$
$557$	5.28602e6	0.721923	0.360962	+	0.932581i	$0.382449\pi$
$558$	1.94901e6	0.264989
$559$	1.67984e6	0.227373
$560$	−168471.	−0.0227015
$561$	−6.45716e6	−0.866232
$562$	−6.13050e6	−0.818758
$563$	4.39048e6	0.583769	0.291885	−	0.956454i	$-0.405718\pi$
$563$	4.39048e6	0.583769	0.291885	+	0.956454i	$0.405718\pi$
$564$	4.25881e6	0.563755
$565$	5.44417e6	0.717481
$566$	−6.19693e6	−0.813084
$567$	486895.	0.0636030
$568$	1.62782e6	0.211707
$569$	−7.77570e6	−1.00684	−0.503418	−	0.864043i	$-0.667924\pi$
$569$	−7.77570e6	−1.00684	−0.503418	+	0.864043i	$0.667924\pi$
$570$	1.93219e7	2.49094
$571$	899436.	0.115446	0.0577232	−	0.998333i	$-0.481616\pi$
$571$	899436.	0.115446	0.0577232	+	0.998333i	$0.481616\pi$
$572$	2.57252e6	0.328753
$573$	1.26164e7	1.60527
$574$	−360383.	−0.0456546
$575$	−997778.	−0.125853
$576$	360808.	0.0453127
$577$	7.40039e6	0.925369	0.462685	−	0.886523i	$-0.346886\pi$
$577$	7.40039e6	0.925369	0.462685	+	0.886523i	$0.346886\pi$
$578$	8.49581e6	1.05775
$579$	1.77473e7	2.20007
$580$	−872736.	−0.107724
$581$	99634.7	0.0122453
$582$	−1.21630e7	−1.48845
$583$	−3.70401e6	−0.451337
$584$	1.90287e6	0.230875
$585$	7.38203e6	0.891838
$586$	−1.95685e6	−0.235404
$587$	−4.52261e6	−0.541744	−0.270872	−	0.962615i	$-0.587312\pi$
$587$	−4.52261e6	−0.541744	−0.270872	+	0.962615i	$0.587312\pi$
$588$	4.88001e6	0.582073
$589$	−1.49452e7	−1.77506
$590$	1.07815e6	0.127511
$591$	9.28718e6	1.09374
$592$	−2.76886e6	−0.324711
$593$	−5.04734e6	−0.589421	−0.294710	−	0.955587i	$-0.595223\pi$
$593$	−5.04734e6	−0.589421	−0.294710	+	0.955587i	$0.595223\pi$
$594$	2.12545e6	0.247164
$595$	−1.23886e6	−0.143459
$596$	7.09960e6	0.818688
$597$	−1.29820e7	−1.49075
$598$	−521375.	−0.0596207
$599$	−675662.	−0.0769418	−0.0384709	−	0.999260i	$-0.512249\pi$
$599$	−675662.	−0.0769418	−0.0384709	+	0.999260i	$0.512249\pi$
$600$	−7.60327e6	−0.862228
$601$	8.86478e6	1.00111	0.500555	−	0.865705i	$-0.333129\pi$
$601$	8.86478e6	1.00111	0.500555	+	0.865705i	$0.333129\pi$
$602$	−52766.1	−0.00593423
$603$	−3.84496e6	−0.430625
$604$	−4.92460e6	−0.549261
$605$	−1.23325e7	−1.36981
$606$	−1.08258e7	−1.19751
$607$	−9.16793e6	−1.00995	−0.504974	−	0.863134i	$-0.668498\pi$
$607$	−9.16793e6	−1.00995	−0.504974	+	0.863134i	$0.668498\pi$
$608$	−2.76671e6	−0.303532
$609$	−67656.8	−0.00739211
$610$	3.21018e6	0.349305
$611$	−1.24768e7	−1.35207
$612$	2.65321e6	0.286347
$613$	−3.32092e6	−0.356949	−0.178475	−	0.983944i	$-0.557116\pi$
$613$	−3.32092e6	−0.356949	−0.178475	+	0.983944i	$0.557116\pi$
$614$	7.83394e6	0.838609
$615$	−2.40491e7	−2.56396
$616$	−80806.4	−0.00858013
$617$	−8.84235e6	−0.935093	−0.467547	−	0.883968i	$-0.654862\pi$
$617$	−8.84235e6	−0.935093	−0.467547	+	0.883968i	$0.654862\pi$
$618$	−2.84308e6	−0.299445
$619$	−1.30506e7	−1.36900	−0.684498	−	0.729015i	$-0.739979\pi$
$619$	−1.30506e7	−1.36900	−0.684498	+	0.729015i	$0.739979\pi$
$620$	8.69583e6	0.908514
$621$	−430767.	−0.0448243
$622$	−4.69712e6	−0.486806
$623$	−681241.	−0.0703203
$624$	−3.97298e6	−0.408465
$625$	1.24594e7	1.27584
$626$	5.98525e6	0.610445
$627$	9.26766e6	0.941459
$628$	4.59527e6	0.464956
$629$	−2.03609e7	−2.05196
$630$	−231879.	−0.0232761
$631$	−1.85585e7	−1.85554	−0.927768	−	0.373158i	$-0.878275\pi$
$631$	−1.85585e7	−1.85554	−0.927768	+	0.373158i	$0.878275\pi$
$632$	3.84672e6	0.383087
$633$	−1.17856e7	−1.16908
$634$	−5.39068e6	−0.532623
$635$	2.85290e7	2.80771
$636$	5.72044e6	0.560773
$637$	−1.42967e7	−1.39600
$638$	−418604.	−0.0407147
$639$	2.24049e6	0.217065
$640$	1.60981e6	0.155355
$641$	−4.61135e6	−0.443285	−0.221643	−	0.975128i	$-0.571142\pi$
$641$	−4.61135e6	−0.443285	−0.221643	+	0.975128i	$0.571142\pi$
$642$	1.28599e7	1.23140
$643$	3.32909e6	0.317539	0.158770	−	0.987316i	$-0.449247\pi$
$643$	3.32909e6	0.317539	0.158770	+	0.987316i	$0.449247\pi$
$644$	16377.1	0.00155604
$645$	−3.52119e6	−0.333266
$646$	−2.03451e7	−1.91813
$647$	1.13166e7	1.06281	0.531405	−	0.847118i	$-0.321664\pi$
$647$	1.13166e7	1.06281	0.531405	+	0.847118i	$0.321664\pi$
$648$	−4.65247e6	−0.435258
$649$	517129.	0.0481934
$650$	2.22748e7	2.06790
$651$	674124.	0.0623429
$652$	5.12898e6	0.472511
$653$	−9.62890e6	−0.883678	−0.441839	−	0.897094i	$-0.645674\pi$
$653$	−9.62890e6	−0.883678	−0.441839	+	0.897094i	$0.645674\pi$
$654$	8.40781e6	0.768667
$655$	−2.56964e7	−2.34029
$656$	3.44361e6	0.312431
$657$	2.61907e6	0.236719
$658$	391911.	0.0352877
$659$	7.26685e6	0.651828	0.325914	−	0.945399i	$-0.394328\pi$
$659$	7.26685e6	0.651828	0.325914	+	0.945399i	$0.394328\pi$
$660$	−5.39238e6	−0.481860
$661$	1.73222e7	1.54205	0.771027	−	0.636803i	$-0.219743\pi$
$661$	1.73222e7	1.54205	0.771027	+	0.636803i	$0.219743\pi$
$662$	1.83707e6	0.162922
$663$	−2.92154e7	−2.58124
$664$	−952050.	−0.0837991
$665$	1.77807e6	0.155918
$666$	−3.81099e6	−0.332929
$667$	84838.7	0.00738379
$668$	8.94740e6	0.775810
$669$	739332.	0.0638667
$670$	−1.71550e7	−1.47640
$671$	1.53975e6	0.132021
$672$	124797.	0.0106606
$673$	7.30322e6	0.621551	0.310775	−	0.950483i	$-0.399411\pi$
$673$	7.30322e6	0.621551	0.310775	+	0.950483i	$0.399411\pi$
$674$	−8.91522e6	−0.755932
$675$	1.84037e7	1.55470
$676$	5.69869e6	0.479632
$677$	3.01057e6	0.252451	0.126225	−	0.992002i	$-0.459714\pi$
$677$	3.01057e6	0.252451	0.126225	+	0.992002i	$0.459714\pi$
$678$	−4.03282e6	−0.336926
$679$	−1.11929e6	−0.0931681
$680$	1.18378e7	0.981741
$681$	2.70606e7	2.23599
$682$	4.17091e6	0.343376
$683$	−1.38406e7	−1.13528	−0.567638	−	0.823278i	$-0.692143\pi$
$683$	−1.38406e7	−1.13528	−0.567638	+	0.823278i	$0.692143\pi$
$684$	−3.80803e6	−0.311215
$685$	3.92073e7	3.19257
$686$	899356.	0.0729661
$687$	2.40235e7	1.94198
$688$	504201.	0.0406100
$689$	−1.67588e7	−1.34491
$690$	1.09288e6	0.0873873
$691$	1.97940e7	1.57703	0.788513	−	0.615018i	$-0.210851\pi$
$691$	1.97940e7	1.57703	0.788513	+	0.615018i	$0.210851\pi$
$692$	−153010.	−0.0121466
$693$	−111220.	−0.00879730
$694$	−1.40191e7	−1.10490
$695$	2.55496e7	2.00642
$696$	646488.	0.0505868
$697$	2.53226e7	1.97436
$698$	−1.37467e7	−1.06797
$699$	1.92958e7	1.49372
$700$	−699681.	−0.0539703
$701$	−1.99103e6	−0.153033	−0.0765163	−	0.997068i	$-0.524380\pi$
$701$	−1.99103e6	−0.153033	−0.0765163	+	0.997068i	$0.524380\pi$
$702$	9.61661e6	0.736511
$703$	2.92230e7	2.23016
$704$	772137.	0.0587169
$705$	2.61531e7	1.98175
$706$	450510.	0.0340167
$707$	−996232.	−0.0749569
$708$	−798649.	−0.0598788
$709$	1.91599e6	0.143146	0.0715729	−	0.997435i	$-0.477198\pi$
$709$	1.91599e6	0.143146	0.0715729	+	0.997435i	$0.477198\pi$
$710$	9.99632e6	0.744208
$711$	5.29452e6	0.392783
$712$	6.50953e6	0.481227
$713$	−845321.	−0.0622727
$714$	917694.	0.0673678
$715$	1.57977e7	1.15566
$716$	5.64381e6	0.411425
$717$	−1.26654e7	−0.920068
$718$	971901.	0.0703576
$719$	−1.49892e7	−1.08133	−0.540664	−	0.841239i	$-0.681827\pi$
$719$	−1.49892e7	−1.08133	−0.540664	+	0.841239i	$0.681827\pi$
$720$	2.21570e6	0.159287
$721$	−261631.	−0.0187435
$722$	1.92959e7	1.37760
$723$	−9.86559e6	−0.701904
$724$	−5.50683e6	−0.390441
$725$	−3.62458e6	−0.256102
$726$	9.13539e6	0.643259
$727$	4.60476e6	0.323125	0.161563	−	0.986862i	$-0.448347\pi$
$727$	4.60476e6	0.323125	0.161563	+	0.986862i	$0.448347\pi$
$728$	−365608.	−0.0255675
$729$	6.05981e6	0.422319
$730$	1.16854e7	0.811591
$731$	3.70765e6	0.256629
$732$	−2.37797e6	−0.164032
$733$	−1.20784e7	−0.830326	−0.415163	−	0.909747i	$-0.636275\pi$
$733$	−1.20784e7	−0.830326	−0.415163	+	0.909747i	$0.636275\pi$
$734$	9.79711e6	0.671209
$735$	2.99678e7	2.04615
$736$	−156490.	−0.0106486
$737$	−8.22831e6	−0.558010
$738$	4.73969e6	0.320338
$739$	−2.62178e7	−1.76598	−0.882990	−	0.469392i	$-0.844473\pi$
$739$	−2.62178e7	−1.76598	−0.882990	+	0.469392i	$0.844473\pi$
$740$	−1.70034e7	−1.14145
$741$	4.19315e7	2.80540
$742$	526416.	0.0351010
$743$	1.03711e7	0.689212	0.344606	−	0.938747i	$-0.388013\pi$
$743$	1.03711e7	0.689212	0.344606	+	0.938747i	$0.388013\pi$
$744$	−6.44152e6	−0.426634
$745$	4.35982e7	2.87791
$746$	1.58270e6	0.104124
$747$	−1.31038e6	−0.0859201
$748$	5.67793e6	0.371053
$749$	1.18341e6	0.0770783
$750$	−2.43433e7	−1.58025
$751$	4.82274e6	0.312028	0.156014	−	0.987755i	$-0.450135\pi$
$751$	4.82274e6	0.312028	0.156014	+	0.987755i	$0.450135\pi$
$752$	−3.74487e6	−0.241486
$753$	−1.08610e7	−0.698043
$754$	−1.89397e6	−0.121324
$755$	−3.02416e7	−1.93080
$756$	−302070.	−0.0192222
$757$	3.06239e6	0.194232	0.0971161	−	0.995273i	$-0.469038\pi$
$757$	3.06239e6	0.194232	0.0971161	+	0.995273i	$0.469038\pi$
$758$	−1.34293e7	−0.848944
$759$	524193.	0.0330284
$760$	−1.69902e7	−1.06700
$761$	−5.74996e6	−0.359918	−0.179959	−	0.983674i	$-0.557596\pi$
$761$	−5.74996e6	−0.359918	−0.179959	+	0.983674i	$0.557596\pi$
$762$	−2.11331e7	−1.31849
$763$	773717.	0.0481139
$764$	−1.10939e7	−0.687622
$765$	1.62932e7	1.00659
$766$	2.36654e6	0.145728
$767$	2.33975e6	0.143609
$768$	−1.19248e6	−0.0729539
$769$	2.45008e7	1.49405	0.747023	−	0.664799i	$-0.231483\pi$
$769$	2.45008e7	1.49405	0.747023	+	0.664799i	$0.231483\pi$
$770$	−496227.	−0.0301615
$771$	−3.34064e6	−0.202392
$772$	−1.56056e7	−0.942405
$773$	−2.23920e7	−1.34786	−0.673929	−	0.738796i	$-0.735395\pi$
$773$	−2.23920e7	−1.34786	−0.673929	+	0.738796i	$0.735395\pi$
$774$	693970.	0.0416378
$775$	3.61148e7	2.15989
$776$	1.06952e7	0.637582
$777$	−1.31815e6	−0.0783270
$778$	−5.23648e6	−0.310163
$779$	−3.63444e7	−2.14582
$780$	−2.43978e7	−1.43587
$781$	4.79469e6	0.281276
$782$	−1.15075e6	−0.0672920
$783$	−1.56482e6	−0.0912140
$784$	−4.29111e6	−0.249333
$785$	2.82192e7	1.63445
$786$	1.90349e7	1.09899
$787$	−2.40101e7	−1.38184	−0.690920	−	0.722931i	$-0.742794\pi$
$787$	−2.40101e7	−1.38184	−0.690920	+	0.722931i	$0.742794\pi$
$788$	−8.16643e6	−0.468507
$789$	3.28290e7	1.87743
$790$	2.36224e7	1.34666
$791$	−371115.	−0.0210896
$792$	1.06275e6	0.0602030
$793$	6.96659e6	0.393403
$794$	−3.42273e6	−0.192673
$795$	3.51288e7	1.97127
$796$	1.14153e7	0.638566
$797$	1.79372e7	1.00025	0.500126	−	0.865953i	$-0.333287\pi$
$797$	1.79372e7	1.00025	0.500126	+	0.865953i	$0.333287\pi$
$798$	−1.31712e6	−0.0732183
$799$	−2.75380e7	−1.52604
$800$	6.68573e6	0.369338
$801$	8.95955e6	0.493406
$802$	−1.93936e7	−1.06469
$803$	5.60486e6	0.306744
$804$	1.27077e7	0.693310
$805$	100571.	0.00546992
$806$	1.88713e7	1.02321
$807$	1.31667e6	0.0711693
$808$	9.51939e6	0.512957
$809$	5.51022e6	0.296004	0.148002	−	0.988987i	$-0.452716\pi$
$809$	5.51022e6	0.296004	0.148002	+	0.988987i	$0.452716\pi$
$810$	−2.85705e7	−1.53005
$811$	−2.32833e7	−1.24306	−0.621532	−	0.783389i	$-0.713489\pi$
$811$	−2.32833e7	−1.24306	−0.621532	+	0.783389i	$0.713489\pi$
$812$	59492.2	0.00316643
$813$	−3.72006e7	−1.97389
$814$	−8.15559e6	−0.431414
$815$	3.14967e7	1.66101
$816$	−8.76893e6	−0.461022
$817$	−5.32142e6	−0.278916
$818$	4.60264e6	0.240505
$819$	−503214.	−0.0262146
$820$	2.11469e7	1.09828
$821$	481660.	0.0249392	0.0124696	−	0.999922i	$-0.496031\pi$
$821$	481660.	0.0249392	0.0124696	+	0.999922i	$0.496031\pi$
$822$	−2.90432e7	−1.49922
$823$	−2.57350e7	−1.32442	−0.662208	−	0.749320i	$-0.730381\pi$
$823$	−2.57350e7	−1.32442	−0.662208	+	0.749320i	$0.730381\pi$
$824$	2.49998e6	0.128268
$825$	−2.23952e7	−1.14557
$826$	−73494.7	−0.00374805
$827$	5.72236e6	0.290945	0.145473	−	0.989362i	$-0.453530\pi$
$827$	5.72236e6	0.290945	0.145473	+	0.989362i	$0.453530\pi$
$828$	−215388.	−0.0109181
$829$	−2.46281e7	−1.24464	−0.622320	−	0.782763i	$-0.713810\pi$
$829$	−2.46281e7	−1.24464	−0.622320	+	0.782763i	$0.713810\pi$
$830$	−5.84647e6	−0.294577
$831$	−3.20909e7	−1.61205
$832$	3.49353e6	0.174967
$833$	−3.15547e7	−1.57562
$834$	−1.89261e7	−0.942208
$835$	5.49454e7	2.72719
$836$	−8.14926e6	−0.403276
$837$	1.55917e7	0.769272
$838$	−5.22373e6	−0.256963
$839$	−2.81029e7	−1.37831	−0.689154	−	0.724615i	$-0.742017\pi$
$839$	−2.81029e7	−1.37831	−0.689154	+	0.724615i	$0.742017\pi$
$840$	766368.	0.0374748
$841$	−2.02030e7	−0.984975
$842$	2.82389e6	0.137268
$843$	2.78874e7	1.35157
$844$	1.03634e7	0.500777
$845$	3.49953e7	1.68604
$846$	−5.15434e6	−0.247598
$847$	840672.	0.0402641
$848$	−5.03011e6	−0.240208
$849$	2.81896e7	1.34221
$850$	4.91636e7	2.33398
$851$	1.65290e6	0.0782388
$852$	−7.40487e6	−0.349477
$853$	−3.43018e7	−1.61415	−0.807077	−	0.590446i	$-0.798952\pi$
$853$	−3.43018e7	−1.61415	−0.807077	+	0.590446i	$0.798952\pi$
$854$	−218830.	−0.0102674
$855$	−2.33848e7	−1.09400
$856$	−1.13080e7	−0.527474
$857$	8.82299e6	0.410359	0.205179	−	0.978724i	$-0.434222\pi$
$857$	8.82299e6	0.410359	0.205179	+	0.978724i	$0.434222\pi$
$858$	−1.17023e7	−0.542691
$859$	1.13725e7	0.525865	0.262932	−	0.964814i	$-0.415310\pi$
$859$	1.13725e7	0.525865	0.262932	+	0.964814i	$0.415310\pi$
$860$	3.09627e6	0.142755
$861$	1.63937e6	0.0753648
$862$	9.71214e6	0.445191
$863$	−1.38566e7	−0.633329	−0.316665	−	0.948538i	$-0.602563\pi$
$863$	−1.38566e7	−0.633329	−0.316665	+	0.948538i	$0.602563\pi$
$864$	2.88640e6	0.131544
$865$	−939625.	−0.0426987
$866$	−4.38310e6	−0.198603
$867$	−3.86470e7	−1.74610
$868$	−592772.	−0.0267047
$869$	1.13304e7	0.508974
$870$	3.97004e6	0.177827
$871$	−3.72290e7	−1.66278
$872$	−7.39317e6	−0.329261
$873$	1.47206e7	0.653719
$874$	1.65162e6	0.0731359
$875$	−2.24016e6	−0.0989142
$876$	−8.65609e6	−0.381120
$877$	−5.33458e6	−0.234208	−0.117104	−	0.993120i	$-0.537361\pi$
$877$	−5.33458e6	−0.234208	−0.117104	+	0.993120i	$0.537361\pi$
$878$	−5.56335e6	−0.243557
$879$	8.90162e6	0.388595
$880$	4.74164e6	0.206406
$881$	2.23045e7	0.968171	0.484085	−	0.875021i	$-0.339152\pi$
$881$	2.23045e7	0.968171	0.484085	+	0.875021i	$0.339152\pi$
$882$	−5.90617e6	−0.255643
$883$	1.38980e7	0.599861	0.299931	−	0.953961i	$-0.403036\pi$
$883$	1.38980e7	0.599861	0.299931	+	0.953961i	$0.403036\pi$
$884$	2.56898e7	1.10568
$885$	−4.90445e6	−0.210490
$886$	−1.85684e7	−0.794678
$887$	1.80202e7	0.769045	0.384522	−	0.923116i	$-0.374366\pi$
$887$	1.80202e7	0.769045	0.384522	+	0.923116i	$0.374366\pi$
$888$	1.25954e7	0.536019
$889$	−1.94475e6	−0.0825293
$890$	3.99746e7	1.69164
$891$	−1.37037e7	−0.578288
$892$	−650112.	−0.0273575
$893$	3.95240e7	1.65856
$894$	−3.22958e7	−1.35146
$895$	3.46583e7	1.44627
$896$	−109737.	−0.00456648
$897$	2.37171e6	0.0984194
$898$	−2.41214e7	−0.998188
$899$	−3.07076e6	−0.126720
$900$	9.20206e6	0.378686
$901$	−3.69890e7	−1.51796
$902$	1.01430e7	0.415099
$903$	240031.	0.00979597
$904$	3.54615e6	0.144323
$905$	−3.38171e7	−1.37251
$906$	2.24018e7	0.906697
$907$	−1.88306e7	−0.760056	−0.380028	−	0.924975i	$-0.624086\pi$
$907$	−1.88306e7	−0.760056	−0.380028	+	0.924975i	$0.624086\pi$
$908$	−2.37950e7	−0.957791
$909$	1.31022e7	0.525940
$910$	−2.24518e6	−0.0898767
$911$	−2.20487e7	−0.880212	−0.440106	−	0.897946i	$-0.645059\pi$
$911$	−2.20487e7	−0.880212	−0.440106	+	0.897946i	$0.645059\pi$
$912$	1.25856e7	0.501058
$913$	−2.80423e6	−0.111336
$914$	−7.18040e6	−0.284304
$915$	−1.46030e7	−0.576619
$916$	−2.11245e7	−0.831853
$917$	1.75166e6	0.0687902
$918$	2.12252e7	0.831276
$919$	−1.98891e7	−0.776829	−0.388415	−	0.921485i	$-0.626977\pi$
$919$	−1.98891e7	−0.776829	−0.388415	+	0.921485i	$0.626977\pi$
$920$	−960991.	−0.0374326
$921$	−3.56363e7	−1.38434
$922$	2.93101e7	1.13551
$923$	2.16936e7	0.838159
$924$	367585.	0.0141637
$925$	−7.06170e7	−2.71366
$926$	−7.32616e6	−0.280769
$927$	3.44091e6	0.131515
$928$	−568472.	−0.0216690
$929$	−1.40360e7	−0.533586	−0.266793	−	0.963754i	$-0.585964\pi$
$929$	−1.40360e7	−0.533586	−0.266793	+	0.963754i	$0.585964\pi$
$930$	−3.95569e7	−1.49974
$931$	4.52891e7	1.71245
$932$	−1.69673e7	−0.639841
$933$	2.13670e7	0.803599
$934$	−1.70044e7	−0.637816
$935$	3.48678e7	1.30435
$936$	4.80841e6	0.179396
$937$	−1.50995e7	−0.561842	−0.280921	−	0.959731i	$-0.590640\pi$
$937$	−1.50995e7	−0.561842	−0.280921	+	0.959731i	$0.590640\pi$
$938$	1.16941e6	0.0433970
$939$	−2.72266e7	−1.00770
$940$	−2.29970e7	−0.848890
$941$	−1.21940e6	−0.0448922	−0.0224461	−	0.999748i	$-0.507145\pi$
$941$	−1.21940e6	−0.0448922	−0.0224461	+	0.999748i	$0.507145\pi$
$942$	−2.09037e7	−0.767530
$943$	−2.05569e6	−0.0752800
$944$	702271.	0.0256492
$945$	−1.85499e6	−0.0675714
$946$	1.48511e6	0.0539549
$947$	−4.48712e6	−0.162590	−0.0812949	−	0.996690i	$-0.525906\pi$
$947$	−4.48712e6	−0.162590	−0.0812949	+	0.996690i	$0.525906\pi$
$948$	−1.74985e7	−0.632384
$949$	2.53592e7	0.914049
$950$	−7.05622e7	−2.53667
$951$	2.45219e7	0.879232
$952$	−806949.	−0.0288572
$953$	2.29668e7	0.819160	0.409580	−	0.912274i	$-0.365675\pi$
$953$	2.29668e7	0.819160	0.409580	+	0.912274i	$0.365675\pi$
$954$	−6.92332e6	−0.246288
$955$	−6.81267e7	−2.41718
$956$	1.11370e7	0.394114
$957$	1.90421e6	0.0672102
$958$	−7.09852e6	−0.249893
$959$	−2.67266e6	−0.0938420
$960$	−7.32295e6	−0.256453
$961$	1.96744e6	0.0687216
$962$	−3.69000e7	−1.28555
$963$	−1.55640e7	−0.540824
$964$	8.67504e6	0.300662
$965$	−9.58330e7	−3.31281
$966$	−74498.6	−0.00256865
$967$	3.54355e7	1.21863	0.609315	−	0.792928i	$-0.291444\pi$
$967$	3.54355e7	1.21863	0.609315	+	0.792928i	$0.291444\pi$
$968$	−8.03296e6	−0.275542
$969$	9.25488e7	3.16637
$970$	6.56787e7	2.24128
$971$	−5.58806e6	−0.190201	−0.0951005	−	0.995468i	$-0.530317\pi$
$971$	−5.58806e6	−0.190201	−0.0951005	+	0.995468i	$0.530317\pi$
$972$	1.02046e7	0.346441
$973$	−1.74165e6	−0.0589766
$974$	−1.00115e7	−0.338145
$975$	−1.01327e8	−3.41361
$976$	2.09101e6	0.0702637
$977$	3.84626e7	1.28915	0.644573	−	0.764543i	$-0.277035\pi$
$977$	3.84626e7	1.28915	0.644573	+	0.764543i	$0.277035\pi$
$978$	−2.33315e7	−0.780002
$979$	1.91736e7	0.639363
$980$	−2.63514e7	−0.876473
$981$	−1.01758e7	−0.337594
$982$	2.50638e7	0.829408
$983$	−9.56450e6	−0.315703	−0.157851	−	0.987463i	$-0.550457\pi$
$983$	−9.56450e6	−0.315703	−0.157851	+	0.987463i	$0.550457\pi$
$984$	−1.56648e7	−0.515748
$985$	−5.01495e7	−1.64693
$986$	−4.18027e6	−0.136934
$987$	−1.78279e6	−0.0582514
$988$	−3.68713e7	−1.20170
$989$	−300988.	−0.00978495
$990$	6.52627e6	0.211630
$991$	−5.20621e7	−1.68398	−0.841992	−	0.539490i	$-0.818617\pi$
$991$	−5.20621e7	−1.68398	−0.841992	+	0.539490i	$0.818617\pi$
$992$	5.66417e6	0.182750
$993$	−8.35674e6	−0.268945
$994$	−681423.	−0.0218751
$995$	7.01008e7	2.24473
$996$	4.33083e6	0.138332
$997$	−3.05250e7	−0.972563	−0.486281	−	0.873802i	$-0.661647\pi$
$997$	−3.05250e7	−0.972563	−0.486281	+	0.873802i	$0.661647\pi$
$998$	1.36004e7	0.432241
$999$	−3.04872e7	−0.966505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.6.a.d.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.6.a.d.1.6	✓	32	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -18.1958 q^{3} +16.0000 q^{4} +98.2549 q^{5} -72.7833 q^{6} -6.69779 q^{7} +64.0000 q^{8} +88.0879 q^{9} +393.020 q^{10} +188.510 q^{11} -291.133 q^{12} +852.913 q^{13} -26.7911 q^{14} -1787.83 q^{15} +256.000 q^{16} +1882.50 q^{17} +352.352 q^{18} -2701.87 q^{19} +1572.08 q^{20} +121.872 q^{21} +754.040 q^{22} -152.822 q^{23} -1164.53 q^{24} +6529.03 q^{25} +3411.65 q^{26} +2818.75 q^{27} -107.165 q^{28} -555.148 q^{29} -7151.32 q^{30} +5531.42 q^{31} +1024.00 q^{32} -3430.10 q^{33} +7530.00 q^{34} -658.090 q^{35} +1409.41 q^{36} -10815.9 q^{37} -10807.5 q^{38} -15519.5 q^{39} +6288.31 q^{40} +13451.6 q^{41} +487.487 q^{42} +1969.54 q^{43} +3016.16 q^{44} +8655.07 q^{45} -611.287 q^{46} -14628.4 q^{47} -4658.13 q^{48} -16762.1 q^{49} +26116.1 q^{50} -34253.6 q^{51} +13646.6 q^{52} -19648.9 q^{53} +11275.0 q^{54} +18522.0 q^{55} -428.658 q^{56} +49162.7 q^{57} -2220.59 q^{58} +2743.24 q^{59} -28605.3 q^{60} +8168.00 q^{61} +22125.7 q^{62} -589.994 q^{63} +4096.00 q^{64} +83802.9 q^{65} -13720.4 q^{66} -43649.2 q^{67} +30120.0 q^{68} +2780.72 q^{69} -2632.36 q^{70} +25434.6 q^{71} +5637.63 q^{72} +29732.4 q^{73} -43263.4 q^{74} -118801. q^{75} -43229.9 q^{76} -1262.60 q^{77} -62077.8 q^{78} +60105.0 q^{79} +25153.3 q^{80} -72694.9 q^{81} +53806.3 q^{82} -14875.8 q^{83} +1949.95 q^{84} +184965. q^{85} +7878.15 q^{86} +10101.4 q^{87} +12064.6 q^{88} +101711. q^{89} +34620.3 q^{90} -5712.63 q^{91} -2445.15 q^{92} -100649. q^{93} -58513.6 q^{94} -265472. q^{95} -18632.5 q^{96} +167113. q^{97} -67048.6 q^{98} +16605.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 128 q^{2} + 32 q^{3} + 512 q^{4} + 214 q^{5} + 128 q^{6} + 428 q^{7} + 2048 q^{8} + 3196 q^{9} + 856 q^{10} + 1357 q^{11} + 512 q^{12} + 1747 q^{13} + 1712 q^{14} + 2728 q^{15} + 8192 q^{16} + 3766 q^{17}+ \cdots + 338392 q^{99}+O(q^{100}) \) 32 * q + 128 * q^2 + 32 * q^3 + 512 * q^4 + 214 * q^5 + 128 * q^6 + 428 * q^7 + 2048 * q^8 + 3196 * q^9 + 856 * q^10 + 1357 * q^11 + 512 * q^12 + 1747 * q^13 + 1712 * q^14 + 2728 * q^15 + 8192 * q^16 + 3766 * q^17 + 12784 * q^18 + 1417 * q^19 + 3424 * q^20 + 9693 * q^21 + 5428 * q^22 + 11030 * q^23 + 2048 * q^24 + 30524 * q^25 + 6988 * q^26 + 11924 * q^27 + 6848 * q^28 + 21206 * q^29 + 10912 * q^30 + 18142 * q^31 + 32768 * q^32 + 27879 * q^33 + 15064 * q^34 + 14971 * q^35 + 51136 * q^36 + 24725 * q^37 + 5668 * q^38 + 25201 * q^39 + 13696 * q^40 + 38470 * q^41 + 38772 * q^42 + 18145 * q^43 + 21712 * q^44 + 54227 * q^45 + 44120 * q^46 + 50173 * q^47 + 8192 * q^48 + 114490 * q^49 + 122096 * q^50 + 28981 * q^51 + 27952 * q^52 + 109649 * q^53 + 47696 * q^54 + 53077 * q^55 + 27392 * q^56 + 90298 * q^57 + 84824 * q^58 + 78978 * q^59 + 43648 * q^60 + 105671 * q^61 + 72568 * q^62 + 138923 * q^63 + 131072 * q^64 + 149825 * q^65 + 111516 * q^66 + 135561 * q^67 + 60256 * q^68 + 281851 * q^69 + 59884 * q^70 + 306266 * q^71 + 204544 * q^72 + 253098 * q^73 + 98900 * q^74 + 440869 * q^75 + 22672 * q^76 + 501432 * q^77 + 100804 * q^78 + 331657 * q^79 + 54784 * q^80 + 613516 * q^81 + 153880 * q^82 + 421327 * q^83 + 155088 * q^84 + 526007 * q^85 + 72580 * q^86 + 617560 * q^87 + 86848 * q^88 + 392845 * q^89 + 216908 * q^90 + 306534 * q^91 + 176480 * q^92 + 471703 * q^93 + 200692 * q^94 + 337292 * q^95 + 32768 * q^96 + 451994 * q^97 + 457960 * q^98 + 338392 * q^99

Introduction

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