LMFDB - Embedded newform 2013.4.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.801460 q^{2} +3.00000 q^{3} -7.35766 q^{4} +19.8509 q^{5} +2.40438 q^{6} +26.4285 q^{7} -12.3086 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.801460 q^{2} +3.00000 q^{3} -7.35766 q^{4} +19.8509 q^{5} +2.40438 q^{6} +26.4285 q^{7} -12.3086 q^{8} +9.00000 q^{9} +15.9097 q^{10} +11.0000 q^{11} -22.0730 q^{12} +36.4889 q^{13} +21.1814 q^{14} +59.5528 q^{15} +48.9965 q^{16} -19.2649 q^{17} +7.21314 q^{18} +44.2659 q^{19} -146.056 q^{20} +79.2856 q^{21} +8.81606 q^{22} -41.0371 q^{23} -36.9257 q^{24} +269.060 q^{25} +29.2444 q^{26} +27.0000 q^{27} -194.452 q^{28} +50.9651 q^{29} +47.7292 q^{30} -33.1046 q^{31} +137.737 q^{32} +33.0000 q^{33} -15.4401 q^{34} +524.631 q^{35} -66.2190 q^{36} -161.830 q^{37} +35.4773 q^{38} +109.467 q^{39} -244.336 q^{40} +118.606 q^{41} +63.5442 q^{42} +34.0387 q^{43} -80.9343 q^{44} +178.658 q^{45} -32.8896 q^{46} +482.547 q^{47} +146.989 q^{48} +355.467 q^{49} +215.641 q^{50} -57.7948 q^{51} -268.473 q^{52} +113.695 q^{53} +21.6394 q^{54} +218.360 q^{55} -325.297 q^{56} +132.798 q^{57} +40.8465 q^{58} -182.848 q^{59} -438.169 q^{60} -61.0000 q^{61} -26.5320 q^{62} +237.857 q^{63} -281.581 q^{64} +724.339 q^{65} +26.4482 q^{66} -769.255 q^{67} +141.745 q^{68} -123.111 q^{69} +420.471 q^{70} +442.669 q^{71} -110.777 q^{72} -690.184 q^{73} -129.700 q^{74} +807.179 q^{75} -325.693 q^{76} +290.714 q^{77} +87.7332 q^{78} +184.723 q^{79} +972.626 q^{80} +81.0000 q^{81} +95.0576 q^{82} -990.293 q^{83} -583.357 q^{84} -382.427 q^{85} +27.2806 q^{86} +152.895 q^{87} -135.394 q^{88} -468.444 q^{89} +143.188 q^{90} +964.348 q^{91} +301.937 q^{92} -99.3137 q^{93} +386.742 q^{94} +878.719 q^{95} +413.211 q^{96} +772.341 q^{97} +284.893 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.801460	0.283359	0.141679	−	0.989913i	$-0.454750\pi$
$2$	0.801460	0.283359	0.141679	+	0.989913i	$0.454750\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.35766	−0.919708
$5$	19.8509	1.77552	0.887761	−	0.460305i	$-0.152260\pi$
$5$	19.8509	1.77552	0.887761	+	0.460305i	$0.152260\pi$
$6$	2.40438	0.163597
$7$	26.4285	1.42701	0.713503	−	0.700652i	$-0.247107\pi$
$7$	26.4285	1.42701	0.713503	+	0.700652i	$0.247107\pi$
$8$	−12.3086	−0.543966
$9$	9.00000	0.333333
$10$	15.9097	0.503110
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−22.0730	−0.530994
$13$	36.4889	0.778477	0.389239	−	0.921137i	$-0.372738\pi$
$13$	36.4889	0.778477	0.389239	+	0.921137i	$0.372738\pi$
$14$	21.1814	0.404355
$15$	59.5528	1.02510
$16$	48.9965	0.765570
$17$	−19.2649	−0.274849	−0.137425	−	0.990512i	$-0.543882\pi$
$17$	−19.2649	−0.274849	−0.137425	+	0.990512i	$0.543882\pi$
$18$	7.21314	0.0944530
$19$	44.2659	0.534489	0.267244	−	0.963629i	$-0.413887\pi$
$19$	44.2659	0.534489	0.267244	+	0.963629i	$0.413887\pi$
$20$	−146.056	−1.63296
$21$	79.2856	0.823883
$22$	8.81606	0.0854359
$23$	−41.0371	−0.372036	−0.186018	−	0.982546i	$-0.559558\pi$
$23$	−41.0371	−0.372036	−0.186018	+	0.982546i	$0.559558\pi$
$24$	−36.9257	−0.314059
$25$	269.060	2.15248
$26$	29.2444	0.220588
$27$	27.0000	0.192450
$28$	−194.452	−1.31243
$29$	50.9651	0.326344	0.163172	−	0.986598i	$-0.447827\pi$
$29$	50.9651	0.326344	0.163172	+	0.986598i	$0.447827\pi$
$30$	47.7292	0.290471
$31$	−33.1046	−0.191799	−0.0958993	−	0.995391i	$-0.530573\pi$
$31$	−33.1046	−0.191799	−0.0958993	+	0.995391i	$0.530573\pi$
$32$	137.737	0.760897
$33$	33.0000	0.174078
$34$	−15.4401	−0.0778810
$35$	524.631	2.53368
$36$	−66.2190	−0.306569
$37$	−161.830	−0.719046	−0.359523	−	0.933136i	$-0.617061\pi$
$37$	−161.830	−0.719046	−0.359523	+	0.933136i	$0.617061\pi$
$38$	35.4773	0.151452
$39$	109.467	0.449454
$40$	−244.336	−0.965824
$41$	118.606	0.451782	0.225891	−	0.974153i	$-0.427471\pi$
$41$	118.606	0.451782	0.225891	+	0.974153i	$0.427471\pi$
$42$	63.5442	0.233454
$43$	34.0387	0.120717	0.0603587	−	0.998177i	$-0.480776\pi$
$43$	34.0387	0.120717	0.0603587	+	0.998177i	$0.480776\pi$
$44$	−80.9343	−0.277302
$45$	178.658	0.591841
$46$	−32.8896	−0.105420
$47$	482.547	1.49759	0.748795	−	0.662801i	$-0.230633\pi$
$47$	482.547	1.49759	0.748795	+	0.662801i	$0.230633\pi$
$48$	146.989	0.442002
$49$	355.467	1.03635
$50$	215.641	0.609924
$51$	−57.7948	−0.158684
$52$	−268.473	−0.715971
$53$	113.695	0.294665	0.147332	−	0.989087i	$-0.452931\pi$
$53$	113.695	0.294665	0.147332	+	0.989087i	$0.452931\pi$
$54$	21.6394	0.0545324
$55$	218.360	0.535340
$56$	−325.297	−0.776243
$57$	132.798	0.308587
$58$	40.8465	0.0924725
$59$	−182.848	−0.403472	−0.201736	−	0.979440i	$-0.564658\pi$
$59$	−182.848	−0.403472	−0.201736	+	0.979440i	$0.564658\pi$
$60$	−438.169	−0.942791
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−26.5320	−0.0543478
$63$	237.857	0.475669
$64$	−281.581	−0.549963
$65$	724.339	1.38220
$66$	26.4482	0.0493264
$67$	−769.255	−1.40268	−0.701340	−	0.712827i	$-0.747414\pi$
$67$	−769.255	−1.40268	−0.701340	+	0.712827i	$0.747414\pi$
$68$	141.745	0.252781
$69$	−123.111	−0.214795
$70$	420.471	0.717941
$71$	442.669	0.739932	0.369966	−	0.929045i	$-0.379369\pi$
$71$	442.669	0.739932	0.369966	+	0.929045i	$0.379369\pi$
$72$	−110.777	−0.181322
$73$	−690.184	−1.10657	−0.553287	−	0.832990i	$-0.686627\pi$
$73$	−690.184	−1.10657	−0.553287	+	0.832990i	$0.686627\pi$
$74$	−129.700	−0.203748
$75$	807.179	1.24273
$76$	−325.693	−0.491573
$77$	290.714	0.430259
$78$	87.7332	0.127357
$79$	184.723	0.263075	0.131538	−	0.991311i	$-0.458009\pi$
$79$	184.723	0.263075	0.131538	+	0.991311i	$0.458009\pi$
$80$	972.626	1.35929
$81$	81.0000	0.111111
$82$	95.0576	0.128017
$83$	−990.293	−1.30962	−0.654812	−	0.755792i	$-0.727252\pi$
$83$	−990.293	−1.30962	−0.654812	+	0.755792i	$0.727252\pi$
$84$	−583.357	−0.757731
$85$	−382.427	−0.488001
$86$	27.2806	0.0342063
$87$	152.895	0.188415
$88$	−135.394	−0.164012
$89$	−468.444	−0.557921	−0.278961	−	0.960303i	$-0.589990\pi$
$89$	−468.444	−0.557921	−0.278961	+	0.960303i	$0.589990\pi$
$90$	143.188	0.167703
$91$	964.348	1.11089
$92$	301.937	0.342165
$93$	−99.3137	−0.110735
$94$	386.742	0.424356
$95$	878.719	0.948996
$96$	413.211	0.439304
$97$	772.341	0.808447	0.404223	−	0.914660i	$-0.367542\pi$
$97$	772.341	0.808447	0.404223	+	0.914660i	$0.367542\pi$
$98$	284.893	0.293658
$99$	99.0000	0.100504
$100$	−1979.65	−1.97965
$101$	−695.027	−0.684730	−0.342365	−	0.939567i	$-0.611228\pi$
$101$	−695.027	−0.684730	−0.342365	+	0.939567i	$0.611228\pi$
$102$	−46.3203	−0.0449646
$103$	390.495	0.373559	0.186780	−	0.982402i	$-0.440195\pi$
$103$	390.495	0.373559	0.186780	+	0.982402i	$0.440195\pi$
$104$	−449.126	−0.423465
$105$	1573.89	1.46282
$106$	91.1221	0.0834958
$107$	−364.262	−0.329108	−0.164554	−	0.986368i	$-0.552618\pi$
$107$	−364.262	−0.329108	−0.164554	+	0.986368i	$0.552618\pi$
$108$	−198.657	−0.176998
$109$	789.199	0.693500	0.346750	−	0.937958i	$-0.387285\pi$
$109$	789.199	0.693500	0.346750	+	0.937958i	$0.387285\pi$
$110$	175.007	0.151693
$111$	−485.490	−0.415141
$112$	1294.91	1.09247
$113$	−1014.51	−0.844578	−0.422289	−	0.906461i	$-0.638773\pi$
$113$	−1014.51	−0.844578	−0.422289	+	0.906461i	$0.638773\pi$
$114$	106.432	0.0874409
$115$	−814.626	−0.660558
$116$	−374.984	−0.300141
$117$	328.400	0.259492
$118$	−146.546	−0.114327
$119$	−509.144	−0.392212
$120$	−733.009	−0.557619
$121$	121.000	0.0909091
$122$	−48.8891	−0.0362804
$123$	355.817	0.260837
$124$	243.572	0.176399
$125$	2859.72	2.04625
$126$	190.633	0.134785
$127$	−119.900	−0.0837748	−0.0418874	−	0.999122i	$-0.513337\pi$
$127$	−119.900	−0.0837748	−0.0418874	+	0.999122i	$0.513337\pi$
$128$	−1327.57	−0.916734
$129$	102.116	0.0696962
$130$	580.529	0.391659
$131$	−731.075	−0.487590	−0.243795	−	0.969827i	$-0.578392\pi$
$131$	−731.075	−0.487590	−0.243795	+	0.969827i	$0.578392\pi$
$132$	−242.803	−0.160101
$133$	1169.88	0.762719
$134$	−616.527	−0.397462
$135$	535.975	0.341699
$136$	237.124	0.149509
$137$	464.631	0.289752	0.144876	−	0.989450i	$-0.453722\pi$
$137$	464.631	0.289752	0.144876	+	0.989450i	$0.453722\pi$
$138$	−98.6689	−0.0608641
$139$	−139.173	−0.0849246	−0.0424623	−	0.999098i	$-0.513520\pi$
$139$	−139.173	−0.0849246	−0.0424623	+	0.999098i	$0.513520\pi$
$140$	−3860.06	−2.33025
$141$	1447.64	0.864634
$142$	354.782	0.209666
$143$	401.378	0.234720
$144$	440.968	0.255190
$145$	1011.70	0.579431
$146$	−553.155	−0.313558
$147$	1066.40	0.598335
$148$	1190.69	0.661312
$149$	−388.889	−0.213819	−0.106910	−	0.994269i	$-0.534096\pi$
$149$	−388.889	−0.213819	−0.106910	+	0.994269i	$0.534096\pi$
$150$	646.922	0.352140
$151$	469.897	0.253243	0.126621	−	0.991951i	$-0.459587\pi$
$151$	469.897	0.253243	0.126621	+	0.991951i	$0.459587\pi$
$152$	−544.849	−0.290744
$153$	−173.385	−0.0916164
$154$	232.995	0.121918
$155$	−657.157	−0.340543
$156$	−805.419	−0.413366
$157$	1108.44	0.563457	0.281729	−	0.959494i	$-0.409092\pi$
$157$	1108.44	0.563457	0.281729	+	0.959494i	$0.409092\pi$
$158$	148.048	0.0745447
$159$	341.085	0.170125
$160$	2734.21	1.35099
$161$	−1084.55	−0.530898
$162$	64.9183	0.0314843
$163$	−687.060	−0.330151	−0.165076	−	0.986281i	$-0.552787\pi$
$163$	−687.060	−0.330151	−0.165076	+	0.986281i	$0.552787\pi$
$164$	−872.660	−0.415508
$165$	655.081	0.309079
$166$	−793.680	−0.371093
$167$	−2953.29	−1.36846	−0.684229	−	0.729267i	$-0.739861\pi$
$167$	−2953.29	−1.36846	−0.684229	+	0.729267i	$0.739861\pi$
$168$	−975.891	−0.448164
$169$	−865.560	−0.393974
$170$	−306.500	−0.138279
$171$	398.393	0.178163
$172$	−250.445	−0.111025
$173$	1367.95	0.601174	0.300587	−	0.953754i	$-0.402817\pi$
$173$	1367.95	0.601174	0.300587	+	0.953754i	$0.402817\pi$
$174$	122.539	0.0533890
$175$	7110.85	3.07160
$176$	538.961	0.230828
$177$	−548.545	−0.232945
$178$	−375.439	−0.158092
$179$	3597.35	1.50211	0.751057	−	0.660237i	$-0.229544\pi$
$179$	3597.35	1.50211	0.751057	+	0.660237i	$0.229544\pi$
$180$	−1314.51	−0.544320
$181$	281.808	0.115727	0.0578635	−	0.998325i	$-0.481571\pi$
$181$	281.808	0.115727	0.0578635	+	0.998325i	$0.481571\pi$
$182$	772.886	0.314781
$183$	−183.000	−0.0739221
$184$	505.108	0.202375
$185$	−3212.48	−1.27668
$186$	−79.5960	−0.0313777
$187$	−211.914	−0.0828702
$188$	−3550.42	−1.37735
$189$	713.570	0.274628
$190$	704.258	0.268907
$191$	−293.907	−0.111342	−0.0556711	−	0.998449i	$-0.517730\pi$
$191$	−293.907	−0.111342	−0.0556711	+	0.998449i	$0.517730\pi$
$192$	−844.743	−0.317521
$193$	−699.013	−0.260705	−0.130353	−	0.991468i	$-0.541611\pi$
$193$	−699.013	−0.260705	−0.130353	+	0.991468i	$0.541611\pi$
$194$	619.000	0.229081
$195$	2173.02	0.798015
$196$	−2615.41	−0.953137
$197$	−1332.17	−0.481792	−0.240896	−	0.970551i	$-0.577441\pi$
$197$	−1332.17	−0.481792	−0.240896	+	0.970551i	$0.577441\pi$
$198$	79.3445	0.0284786
$199$	−2830.26	−1.00820	−0.504100	−	0.863645i	$-0.668176\pi$
$199$	−2830.26	−1.00820	−0.504100	+	0.863645i	$0.668176\pi$
$200$	−3311.73	−1.17087
$201$	−2307.77	−0.809837
$202$	−557.036	−0.194024
$203$	1346.93	0.465695
$204$	425.235	0.145943
$205$	2354.43	0.802150
$206$	312.966	0.105851
$207$	−369.334	−0.124012
$208$	1787.83	0.595979
$209$	486.925	0.161154
$210$	1261.41	0.414503
$211$	1331.75	0.434510	0.217255	−	0.976115i	$-0.430290\pi$
$211$	1331.75	0.434510	0.217255	+	0.976115i	$0.430290\pi$
$212$	−836.530	−0.271005
$213$	1328.01	0.427200
$214$	−291.941	−0.0932556
$215$	675.699	0.214336
$216$	−332.331	−0.104686
$217$	−874.905	−0.273698
$218$	632.511	0.196509
$219$	−2070.55	−0.638881
$220$	−1606.62	−0.492356
$221$	−702.957	−0.213964
$222$	−389.101	−0.117634
$223$	33.1604	0.00995779	0.00497889	−	0.999988i	$-0.498415\pi$
$223$	33.1604	0.00995779	0.00497889	+	0.999988i	$0.498415\pi$
$224$	3640.19	1.08581
$225$	2421.54	0.717492
$226$	−813.091	−0.239319
$227$	−464.552	−0.135830	−0.0679149	−	0.997691i	$-0.521635\pi$
$227$	−464.552	−0.135830	−0.0679149	+	0.997691i	$0.521635\pi$
$228$	−977.080	−0.283810
$229$	−6305.28	−1.81950	−0.909748	−	0.415161i	$-0.863725\pi$
$229$	−6305.28	−1.81950	−0.909748	+	0.415161i	$0.863725\pi$
$230$	−652.890	−0.187175
$231$	872.141	0.248410
$232$	−627.306	−0.177520
$233$	3629.58	1.02052	0.510261	−	0.860020i	$-0.329549\pi$
$233$	3629.58	1.02052	0.510261	+	0.860020i	$0.329549\pi$
$234$	263.200	0.0735295
$235$	9579.02	2.65900
$236$	1345.34	0.371076
$237$	554.169	0.151887
$238$	−408.059	−0.111137
$239$	2884.24	0.780612	0.390306	−	0.920685i	$-0.372369\pi$
$239$	2884.24	0.780612	0.390306	+	0.920685i	$0.372369\pi$
$240$	2917.88	0.784784
$241$	−3522.62	−0.941543	−0.470772	−	0.882255i	$-0.656024\pi$
$241$	−3522.62	−0.941543	−0.470772	+	0.882255i	$0.656024\pi$
$242$	96.9766	0.0257599
$243$	243.000	0.0641500
$244$	448.817	0.117757
$245$	7056.36	1.84006
$246$	285.173	0.0739104
$247$	1615.21	0.416087
$248$	407.469	0.104332
$249$	−2970.88	−0.756111
$250$	2291.95	0.579823
$251$	5839.21	1.46840	0.734199	−	0.678935i	$-0.237558\pi$
$251$	5839.21	1.46840	0.734199	+	0.678935i	$0.237558\pi$
$252$	−1750.07	−0.437476
$253$	−451.409	−0.112173
$254$	−96.0950	−0.0237383
$255$	−1147.28	−0.281747
$256$	1188.65	0.290198
$257$	5375.90	1.30482	0.652412	−	0.757865i	$-0.273757\pi$
$257$	5375.90	1.30482	0.652412	+	0.757865i	$0.273757\pi$
$258$	81.8419	0.0197490
$259$	−4276.93	−1.02608
$260$	−5329.44	−1.27122
$261$	458.686	0.108781
$262$	−585.927	−0.138163
$263$	2600.78	0.609776	0.304888	−	0.952388i	$-0.401381\pi$
$263$	2600.78	0.609776	0.304888	+	0.952388i	$0.401381\pi$
$264$	−406.182	−0.0946924
$265$	2256.95	0.523183
$266$	937.613	0.216123
$267$	−1405.33	−0.322116
$268$	5659.92	1.29005
$269$	3108.06	0.704468	0.352234	−	0.935912i	$-0.385422\pi$
$269$	3108.06	0.704468	0.352234	+	0.935912i	$0.385422\pi$
$270$	429.563	0.0968235
$271$	2982.33	0.668500	0.334250	−	0.942484i	$-0.391517\pi$
$271$	2982.33	0.668500	0.334250	+	0.942484i	$0.391517\pi$
$272$	−943.915	−0.210416
$273$	2893.04	0.641374
$274$	372.383	0.0821039
$275$	2959.66	0.648996
$276$	905.812	0.197549
$277$	5930.66	1.28642	0.643211	−	0.765689i	$-0.277602\pi$
$277$	5930.66	1.28642	0.643211	+	0.765689i	$0.277602\pi$
$278$	−111.542	−0.0240641
$279$	−297.941	−0.0639329
$280$	−6457.45	−1.37824
$281$	−4678.15	−0.993150	−0.496575	−	0.867994i	$-0.665409\pi$
$281$	−4678.15	−0.993150	−0.496575	+	0.867994i	$0.665409\pi$
$282$	1160.23	0.245002
$283$	1400.98	0.294274	0.147137	−	0.989116i	$-0.452994\pi$
$283$	1400.98	0.294274	0.147137	+	0.989116i	$0.452994\pi$
$284$	−3257.01	−0.680522
$285$	2636.16	0.547903
$286$	321.688	0.0665099
$287$	3134.57	0.644696
$288$	1239.63	0.253632
$289$	−4541.86	−0.924458
$290$	810.841	0.164187
$291$	2317.02	0.466757
$292$	5078.14	1.01773
$293$	76.0393	0.0151613	0.00758065	−	0.999971i	$-0.497587\pi$
$293$	76.0393	0.0151613	0.00758065	+	0.999971i	$0.497587\pi$
$294$	854.678	0.169544
$295$	−3629.71	−0.716373
$296$	1991.89	0.391137
$297$	297.000	0.0580259
$298$	−311.679	−0.0605875
$299$	−1497.40	−0.289622
$300$	−5938.95	−1.14295
$301$	899.592	0.172265
$302$	376.604	0.0717586
$303$	−2085.08	−0.395329
$304$	2168.87	0.409189
$305$	−1210.91	−0.227332
$306$	−138.961	−0.0259603
$307$	8225.65	1.52919	0.764597	−	0.644509i	$-0.222938\pi$
$307$	8225.65	1.52919	0.764597	+	0.644509i	$0.222938\pi$
$308$	−2138.97	−0.395712
$309$	1171.48	0.215675
$310$	−526.685	−0.0964958
$311$	−2416.09	−0.440527	−0.220263	−	0.975440i	$-0.570692\pi$
$311$	−2416.09	−0.440527	−0.220263	+	0.975440i	$0.570692\pi$
$312$	−1347.38	−0.244488
$313$	5123.54	0.925238	0.462619	−	0.886557i	$-0.346910\pi$
$313$	5123.54	0.925238	0.462619	+	0.886557i	$0.346910\pi$
$314$	888.367	0.159661
$315$	4721.68	0.844560
$316$	−1359.13	−0.241952
$317$	−1914.66	−0.339237	−0.169618	−	0.985510i	$-0.554253\pi$
$317$	−1914.66	−0.339237	−0.169618	+	0.985510i	$0.554253\pi$
$318$	273.366	0.0482063
$319$	560.616	0.0983965
$320$	−5589.65	−0.976471
$321$	−1092.79	−0.190010
$322$	−869.224	−0.150435
$323$	−852.780	−0.146904
$324$	−595.971	−0.102190
$325$	9817.69	1.67565
$326$	−550.651	−0.0935513
$327$	2367.60	0.400393
$328$	−1459.86	−0.245754
$329$	12753.0	2.13707
$330$	525.021	0.0875802
$331$	8904.69	1.47869	0.739344	−	0.673328i	$-0.235136\pi$
$331$	8904.69	1.47869	0.739344	+	0.673328i	$0.235136\pi$
$332$	7286.24	1.20447
$333$	−1456.47	−0.239682
$334$	−2366.94	−0.387765
$335$	−15270.4	−2.49049
$336$	3884.72	0.630740
$337$	6448.59	1.04236	0.521182	−	0.853445i	$-0.325491\pi$
$337$	6448.59	1.04236	0.521182	+	0.853445i	$0.325491\pi$
$338$	−693.712	−0.111636
$339$	−3043.54	−0.487617
$340$	2813.77	0.448818
$341$	−364.150	−0.0578295
$342$	319.296	0.0504840
$343$	329.489	0.0518681
$344$	−418.967	−0.0656662
$345$	−2443.88	−0.381374
$346$	1096.35	0.170348
$347$	−5448.32	−0.842885	−0.421442	−	0.906855i	$-0.638476\pi$
$347$	−5448.32	−0.842885	−0.421442	+	0.906855i	$0.638476\pi$
$348$	−1124.95	−0.173287
$349$	9251.93	1.41904	0.709519	−	0.704686i	$-0.248912\pi$
$349$	9251.93	1.41904	0.709519	+	0.704686i	$0.248912\pi$
$350$	5699.06	0.870365
$351$	985.200	0.149818
$352$	1515.11	0.229419
$353$	6630.58	0.999745	0.499872	−	0.866099i	$-0.333380\pi$
$353$	6630.58	0.999745	0.499872	+	0.866099i	$0.333380\pi$
$354$	−439.637	−0.0660069
$355$	8787.40	1.31377
$356$	3446.66	0.513125
$357$	−1527.43	−0.226443
$358$	2883.13	0.425637
$359$	4821.88	0.708883	0.354441	−	0.935078i	$-0.384671\pi$
$359$	4821.88	0.708883	0.354441	+	0.935078i	$0.384671\pi$
$360$	−2199.03	−0.321941
$361$	−4899.53	−0.714322
$362$	225.858	0.0327923
$363$	363.000	0.0524864
$364$	−7095.35	−1.02170
$365$	−13700.8	−1.96475
$366$	−146.667	−0.0209465
$367$	−3537.41	−0.503137	−0.251569	−	0.967839i	$-0.580946\pi$
$367$	−3537.41	−0.503137	−0.251569	+	0.967839i	$0.580946\pi$
$368$	−2010.68	−0.284820
$369$	1067.45	0.150594
$370$	−2574.67	−0.361759
$371$	3004.79	0.420488
$372$	730.717	0.101844
$373$	−6918.43	−0.960382	−0.480191	−	0.877164i	$-0.659433\pi$
$373$	−6918.43	−0.960382	−0.480191	+	0.877164i	$0.659433\pi$
$374$	−169.841	−0.0234820
$375$	8579.16	1.18140
$376$	−5939.46	−0.814639
$377$	1859.66	0.254051
$378$	571.898	0.0778181
$379$	−3573.12	−0.484272	−0.242136	−	0.970242i	$-0.577848\pi$
$379$	−3573.12	−0.484272	−0.242136	+	0.970242i	$0.577848\pi$
$380$	−6465.32	−0.872799
$381$	−359.700	−0.0483674
$382$	−235.555	−0.0315498
$383$	−6383.41	−0.851637	−0.425818	−	0.904809i	$-0.640014\pi$
$383$	−6383.41	−0.851637	−0.425818	+	0.904809i	$0.640014\pi$
$384$	−3982.72	−0.529277
$385$	5770.94	0.763934
$386$	−560.231	−0.0738731
$387$	306.348	0.0402391
$388$	−5682.62	−0.743535
$389$	260.847	0.0339986	0.0169993	−	0.999856i	$-0.494589\pi$
$389$	260.847	0.0339986	0.0169993	+	0.999856i	$0.494589\pi$
$390$	1741.59	0.226125
$391$	790.578	0.102254
$392$	−4375.29	−0.563738
$393$	−2193.23	−0.281510
$394$	−1067.68	−0.136520
$395$	3666.92	0.467096
$396$	−728.409	−0.0924341
$397$	13898.3	1.75702	0.878509	−	0.477725i	$-0.158539\pi$
$397$	13898.3	1.75702	0.878509	+	0.477725i	$0.158539\pi$
$398$	−2268.34	−0.285682
$399$	3509.65	0.440356
$400$	13183.0	1.64787
$401$	−11273.4	−1.40391	−0.701954	−	0.712222i	$-0.747689\pi$
$401$	−11273.4	−1.40391	−0.701954	+	0.712222i	$0.747689\pi$
$402$	−1849.58	−0.229475
$403$	−1207.95	−0.149311
$404$	5113.77	0.629752
$405$	1607.93	0.197280
$406$	1079.51	0.131959
$407$	−1780.13	−0.216801
$408$	711.371	0.0863189
$409$	12299.7	1.48699	0.743495	−	0.668741i	$-0.233167\pi$
$409$	12299.7	1.48699	0.743495	+	0.668741i	$0.233167\pi$
$410$	1886.98	0.227296
$411$	1393.89	0.167289
$412$	−2873.13	−0.343565
$413$	−4832.42	−0.575757
$414$	−296.007	−0.0351399
$415$	−19658.2	−2.32526
$416$	5025.88	0.592341
$417$	−417.520	−0.0490312
$418$	390.250	0.0456645
$419$	500.348	0.0583380	0.0291690	−	0.999574i	$-0.490714\pi$
$419$	500.348	0.0583380	0.0291690	+	0.999574i	$0.490714\pi$
$420$	−11580.2	−1.34537
$421$	−10524.4	−1.21836	−0.609180	−	0.793032i	$-0.708501\pi$
$421$	−10524.4	−1.21836	−0.609180	+	0.793032i	$0.708501\pi$
$422$	1067.35	0.123122
$423$	4342.93	0.499197
$424$	−1399.42	−0.160288
$425$	−5183.42	−0.591607
$426$	1064.35	0.121051
$427$	−1612.14	−0.182709
$428$	2680.12	0.302683
$429$	1204.13	0.135515
$430$	541.546	0.0607341
$431$	−14579.6	−1.62940	−0.814701	−	0.579881i	$-0.803099\pi$
$431$	−14579.6	−1.62940	−0.814701	+	0.579881i	$0.803099\pi$
$432$	1322.91	0.147334
$433$	−5310.67	−0.589409	−0.294705	−	0.955588i	$-0.595221\pi$
$433$	−5310.67	−0.589409	−0.294705	+	0.955588i	$0.595221\pi$
$434$	−701.202	−0.0775547
$435$	3035.11	0.334535
$436$	−5806.66	−0.637817
$437$	−1816.54	−0.198849
$438$	−1659.47	−0.181033
$439$	−11871.0	−1.29059	−0.645296	−	0.763932i	$-0.723266\pi$
$439$	−11871.0	−1.29059	−0.645296	+	0.763932i	$0.723266\pi$
$440$	−2687.70	−0.291207
$441$	3199.20	0.345449
$442$	−563.392	−0.0606285
$443$	−12410.9	−1.33106	−0.665529	−	0.746372i	$-0.731794\pi$
$443$	−12410.9	−1.33106	−0.665529	+	0.746372i	$0.731794\pi$
$444$	3572.07	0.381809
$445$	−9299.06	−0.990602
$446$	26.5768	0.00282163
$447$	−1166.67	−0.123449
$448$	−7441.77	−0.784801
$449$	−454.223	−0.0477419	−0.0238710	−	0.999715i	$-0.507599\pi$
$449$	−454.223	−0.0477419	−0.0238710	+	0.999715i	$0.507599\pi$
$450$	1940.76	0.203308
$451$	1304.66	0.136218
$452$	7464.44	0.776764
$453$	1409.69	0.146210
$454$	−372.319	−0.0384886
$455$	19143.2	1.97241
$456$	−1634.55	−0.167861
$457$	−10916.3	−1.11738	−0.558692	−	0.829375i	$-0.688697\pi$
$457$	−10916.3	−1.11738	−0.558692	+	0.829375i	$0.688697\pi$
$458$	−5053.43	−0.515570
$459$	−520.154	−0.0528948
$460$	5993.74	0.607521
$461$	10579.3	1.06882	0.534411	−	0.845225i	$-0.320533\pi$
$461$	10579.3	1.06882	0.534411	+	0.845225i	$0.320533\pi$
$462$	698.986	0.0703892
$463$	10201.0	1.02393	0.511966	−	0.859006i	$-0.328918\pi$
$463$	10201.0	1.02393	0.511966	+	0.859006i	$0.328918\pi$
$464$	2497.11	0.249839
$465$	−1971.47	−0.196612
$466$	2908.96	0.289174
$467$	6033.84	0.597886	0.298943	−	0.954271i	$-0.403366\pi$
$467$	6033.84	0.597886	0.298943	+	0.954271i	$0.403366\pi$
$468$	−2416.26	−0.238657
$469$	−20330.3	−2.00163
$470$	7677.20	0.753452
$471$	3325.31	0.325312
$472$	2250.60	0.219475
$473$	374.425	0.0363977
$474$	444.144	0.0430384
$475$	11910.2	1.15047
$476$	3746.11	0.360720
$477$	1023.26	0.0982215
$478$	2311.61	0.221193
$479$	−11109.6	−1.05973	−0.529867	−	0.848081i	$-0.677758\pi$
$479$	−11109.6	−1.05973	−0.529867	+	0.848081i	$0.677758\pi$
$480$	8202.63	0.779994
$481$	−5905.00	−0.559761
$482$	−2823.24	−0.266795
$483$	−3253.65	−0.306514
$484$	−890.277	−0.0836098
$485$	15331.7	1.43541
$486$	194.755	0.0181775
$487$	10607.9	0.987043	0.493522	−	0.869733i	$-0.335709\pi$
$487$	10607.9	0.987043	0.493522	+	0.869733i	$0.335709\pi$
$488$	750.822	0.0696477
$489$	−2061.18	−0.190613
$490$	5655.39	0.521397
$491$	−12462.9	−1.14550	−0.572750	−	0.819730i	$-0.694124\pi$
$491$	−12462.9	−1.14550	−0.572750	+	0.819730i	$0.694124\pi$
$492$	−2617.98	−0.239894
$493$	−981.840	−0.0896954
$494$	1294.53	0.117902
$495$	1965.24	0.178447
$496$	−1622.01	−0.146835
$497$	11699.1	1.05589
$498$	−2381.04	−0.214251
$499$	8315.00	0.745953	0.372976	−	0.927841i	$-0.378337\pi$
$499$	8315.00	0.745953	0.372976	+	0.927841i	$0.378337\pi$
$500$	−21040.8	−1.88195
$501$	−8859.87	−0.790079
$502$	4679.89	0.416083
$503$	19945.0	1.76800	0.884001	−	0.467485i	$-0.154840\pi$
$503$	19945.0	1.76800	0.884001	+	0.467485i	$0.154840\pi$
$504$	−2927.67	−0.258748
$505$	−13796.9	−1.21575
$506$	−361.786	−0.0317853
$507$	−2596.68	−0.227461
$508$	882.183	0.0770483
$509$	7788.88	0.678263	0.339132	−	0.940739i	$-0.389867\pi$
$509$	7788.88	0.678263	0.339132	+	0.940739i	$0.389867\pi$
$510$	−919.500	−0.0798356
$511$	−18240.6	−1.57909
$512$	11573.2	0.998964
$513$	1195.18	0.102862
$514$	4308.57	0.369733
$515$	7751.69	0.663263
$516$	−751.335	−0.0641002
$517$	5308.02	0.451541
$518$	−3427.79	−0.290750
$519$	4103.84	0.347088
$520$	−8915.56	−0.751872
$521$	−5799.74	−0.487699	−0.243849	−	0.969813i	$-0.578410\pi$
$521$	−5799.74	−0.487699	−0.243849	+	0.969813i	$0.578410\pi$
$522$	367.618	0.0308242
$523$	11173.1	0.934160	0.467080	−	0.884215i	$-0.345306\pi$
$523$	11173.1	0.934160	0.467080	+	0.884215i	$0.345306\pi$
$524$	5379.00	0.448441
$525$	21332.6	1.77339
$526$	2084.42	0.172785
$527$	637.758	0.0527157
$528$	1616.88	0.133269
$529$	−10483.0	−0.861589
$530$	1808.86	0.148249
$531$	−1645.64	−0.134491
$532$	−8607.59	−0.701478
$533$	4327.79	0.351702
$534$	−1126.32	−0.0912744
$535$	−7230.94	−0.584338
$536$	9468.42	0.763010
$537$	10792.0	0.867246
$538$	2490.99	0.199617
$539$	3910.14	0.312471
$540$	−3943.52	−0.314264
$541$	−2536.00	−0.201537	−0.100768	−	0.994910i	$-0.532130\pi$
$541$	−2536.00	−0.201537	−0.100768	+	0.994910i	$0.532130\pi$
$542$	2390.22	0.189426
$543$	845.423	0.0668151
$544$	−2653.50	−0.209132
$545$	15666.3	1.23132
$546$	2318.66	0.181739
$547$	3004.69	0.234865	0.117433	−	0.993081i	$-0.462534\pi$
$547$	3004.69	0.234865	0.117433	+	0.993081i	$0.462534\pi$
$548$	−3418.60	−0.266488
$549$	−549.000	−0.0426790
$550$	2372.05	0.183899
$551$	2256.01	0.174427
$552$	1515.32	0.116841
$553$	4881.95	0.375410
$554$	4753.18	0.364519
$555$	−9637.44	−0.737093
$556$	1023.99	0.0781058
$557$	−18019.9	−1.37078	−0.685392	−	0.728174i	$-0.740369\pi$
$557$	−18019.9	−1.37078	−0.685392	+	0.728174i	$0.740369\pi$
$558$	−238.788	−0.0181159
$559$	1242.03	0.0939757
$560$	25705.1	1.93971
$561$	−635.743	−0.0478451
$562$	−3749.35	−0.281418
$563$	−474.620	−0.0355291	−0.0177645	−	0.999842i	$-0.505655\pi$
$563$	−474.620	−0.0355291	−0.0177645	+	0.999842i	$0.505655\pi$
$564$	−10651.3	−0.795211
$565$	−20139.0	−1.49957
$566$	1122.83	0.0833852
$567$	2140.71	0.158556
$568$	−5448.62	−0.402498
$569$	−10047.9	−0.740295	−0.370148	−	0.928973i	$-0.620693\pi$
$569$	−10047.9	−0.740295	−0.370148	+	0.928973i	$0.620693\pi$
$570$	2112.77	0.155253
$571$	−4146.27	−0.303881	−0.151940	−	0.988390i	$-0.548552\pi$
$571$	−4146.27	−0.303881	−0.151940	+	0.988390i	$0.548552\pi$
$572$	−2953.20	−0.215873
$573$	−881.722	−0.0642835
$574$	2512.23	0.182680
$575$	−11041.4	−0.800800
$576$	−2534.23	−0.183321
$577$	−25196.2	−1.81791	−0.908954	−	0.416896i	$-0.863118\pi$
$577$	−25196.2	−1.81791	−0.908954	+	0.416896i	$0.863118\pi$
$578$	−3640.12	−0.261953
$579$	−2097.04	−0.150518
$580$	−7443.78	−0.532907
$581$	−26172.0	−1.86884
$582$	1857.00	0.132260
$583$	1250.65	0.0888447
$584$	8495.17	0.601939
$585$	6519.05	0.460734
$586$	60.9424	0.00429609
$587$	−3077.54	−0.216395	−0.108197	−	0.994129i	$-0.534508\pi$
$587$	−3077.54	−0.216395	−0.108197	+	0.994129i	$0.534508\pi$
$588$	−7846.22	−0.550294
$589$	−1465.40	−0.102514
$590$	−2909.07	−0.202991
$591$	−3996.50	−0.278163
$592$	−7929.11	−0.550480
$593$	19593.7	1.35686	0.678430	−	0.734665i	$-0.262661\pi$
$593$	19593.7	1.35686	0.678430	+	0.734665i	$0.262661\pi$
$594$	238.034	0.0164421
$595$	−10107.0	−0.696380
$596$	2861.32	0.196651
$597$	−8490.78	−0.582084
$598$	−1200.11	−0.0820669
$599$	−11101.6	−0.757260	−0.378630	−	0.925548i	$-0.623605\pi$
$599$	−11101.6	−0.757260	−0.378630	+	0.925548i	$0.623605\pi$
$600$	−9935.20	−0.676005
$601$	−16710.9	−1.13420	−0.567099	−	0.823650i	$-0.691934\pi$
$601$	−16710.9	−1.13420	−0.567099	+	0.823650i	$0.691934\pi$
$602$	720.987	0.0488127
$603$	−6923.30	−0.467560
$604$	−3457.34	−0.232910
$605$	2401.96	0.161411
$606$	−1671.11	−0.112020
$607$	−7306.15	−0.488546	−0.244273	−	0.969706i	$-0.578549\pi$
$607$	−7306.15	−0.488546	−0.244273	+	0.969706i	$0.578549\pi$
$608$	6097.05	0.406691
$609$	4040.80	0.268869
$610$	−970.494	−0.0644166
$611$	17607.6	1.16584
$612$	1275.70	0.0842603
$613$	−18978.2	−1.25044	−0.625222	−	0.780447i	$-0.714992\pi$
$613$	−18978.2	−1.25044	−0.625222	+	0.780447i	$0.714992\pi$
$614$	6592.53	0.433311
$615$	7063.30	0.463121
$616$	−3578.27	−0.234046
$617$	10910.3	0.711884	0.355942	−	0.934508i	$-0.384160\pi$
$617$	10910.3	0.711884	0.355942	+	0.934508i	$0.384160\pi$
$618$	938.898	0.0611133
$619$	−30716.2	−1.99449	−0.997245	−	0.0741812i	$-0.976366\pi$
$619$	−30716.2	−1.99449	−0.997245	+	0.0741812i	$0.976366\pi$
$620$	4835.14	0.313200
$621$	−1108.00	−0.0715984
$622$	−1936.40	−0.124827
$623$	−12380.3	−0.796157
$624$	5363.48	0.344088
$625$	23135.6	1.48068
$626$	4106.31	0.262174
$627$	1460.77	0.0930425
$628$	−8155.49	−0.518216
$629$	3117.65	0.197629
$630$	3784.24	0.239314
$631$	24076.8	1.51899	0.759494	−	0.650515i	$-0.225447\pi$
$631$	24076.8	1.51899	0.759494	+	0.650515i	$0.225447\pi$
$632$	−2273.67	−0.143104
$633$	3995.26	0.250865
$634$	−1534.52	−0.0961257
$635$	−2380.13	−0.148744
$636$	−2509.59	−0.156465
$637$	12970.6	0.806773
$638$	449.311	0.0278815
$639$	3984.02	0.246644
$640$	−26353.6	−1.62768
$641$	−2305.92	−0.142088	−0.0710440	−	0.997473i	$-0.522633\pi$
$641$	−2305.92	−0.142088	−0.0710440	+	0.997473i	$0.522633\pi$
$642$	−875.824	−0.0538411
$643$	−21227.6	−1.30192	−0.650961	−	0.759111i	$-0.725634\pi$
$643$	−21227.6	−1.30192	−0.650961	+	0.759111i	$0.725634\pi$
$644$	7979.76	0.488271
$645$	2027.10	0.123747
$646$	−683.469	−0.0416265
$647$	17641.4	1.07195	0.535976	−	0.844233i	$-0.319944\pi$
$647$	17641.4	1.07195	0.535976	+	0.844233i	$0.319944\pi$
$648$	−996.993	−0.0604407
$649$	−2011.33	−0.121651
$650$	7868.49	0.474811
$651$	−2624.72	−0.158020
$652$	5055.15	0.303643
$653$	−236.220	−0.0141562	−0.00707810	−	0.999975i	$-0.502253\pi$
$653$	−236.220	−0.0141562	−0.00707810	+	0.999975i	$0.502253\pi$
$654$	1897.53	0.113455
$655$	−14512.5	−0.865727
$656$	5811.26	0.345871
$657$	−6211.66	−0.368858
$658$	10221.0	0.605558
$659$	10048.3	0.593969	0.296985	−	0.954882i	$-0.404019\pi$
$659$	10048.3	0.593969	0.296985	+	0.954882i	$0.404019\pi$
$660$	−4819.86	−0.284262
$661$	−14890.7	−0.876218	−0.438109	−	0.898922i	$-0.644352\pi$
$661$	−14890.7	−0.876218	−0.438109	+	0.898922i	$0.644352\pi$
$662$	7136.75	0.419000
$663$	−2108.87	−0.123532
$664$	12189.1	0.712391
$665$	23223.2	1.35422
$666$	−1167.30	−0.0679160
$667$	−2091.46	−0.121412
$668$	21729.3	1.25858
$669$	99.4813	0.00574913
$670$	−12238.6	−0.705702
$671$	−671.000	−0.0386046
$672$	10920.6	0.626890
$673$	−1053.68	−0.0603511	−0.0301756	−	0.999545i	$-0.509607\pi$
$673$	−1053.68	−0.0603511	−0.0301756	+	0.999545i	$0.509607\pi$
$674$	5168.28	0.295363
$675$	7264.61	0.414244
$676$	6368.50	0.362340
$677$	17462.6	0.991345	0.495673	−	0.868509i	$-0.334922\pi$
$677$	17462.6	0.991345	0.495673	+	0.868509i	$0.334922\pi$
$678$	−2439.27	−0.138171
$679$	20411.8	1.15366
$680$	4707.13	0.265456
$681$	−1393.65	−0.0784214
$682$	−291.852	−0.0163865
$683$	−13326.3	−0.746583	−0.373291	−	0.927714i	$-0.621771\pi$
$683$	−13326.3	−0.746583	−0.373291	+	0.927714i	$0.621771\pi$
$684$	−2931.24	−0.163858
$685$	9223.35	0.514462
$686$	264.073	0.0146973
$687$	−18915.8	−1.05049
$688$	1667.78	0.0924176
$689$	4148.61	0.229390
$690$	−1958.67	−0.108066
$691$	−9943.90	−0.547444	−0.273722	−	0.961809i	$-0.588255\pi$
$691$	−9943.90	−0.547444	−0.273722	+	0.961809i	$0.588255\pi$
$692$	−10064.9	−0.552904
$693$	2616.42	0.143420
$694$	−4366.61	−0.238839
$695$	−2762.72	−0.150785
$696$	−1881.92	−0.102491
$697$	−2284.93	−0.124172
$698$	7415.05	0.402097
$699$	10888.7	0.589198
$700$	−52319.2	−2.82497
$701$	−1023.78	−0.0551609	−0.0275804	−	0.999620i	$-0.508780\pi$
$701$	−1023.78	−0.0551609	−0.0275804	+	0.999620i	$0.508780\pi$
$702$	789.599	0.0424523
$703$	−7163.55	−0.384322
$704$	−3097.39	−0.165820
$705$	28737.0	1.53518
$706$	5314.14	0.283287
$707$	−18368.5	−0.977115
$708$	4036.01	0.214241
$709$	5934.05	0.314327	0.157163	−	0.987573i	$-0.449765\pi$
$709$	5934.05	0.314327	0.157163	+	0.987573i	$0.449765\pi$
$710$	7042.75	0.372267
$711$	1662.51	0.0876918
$712$	5765.87	0.303490
$713$	1358.52	0.0713561
$714$	−1224.18	−0.0641648
$715$	7967.73	0.416750
$716$	−26468.1	−1.38151
$717$	8652.73	0.450687
$718$	3864.54	0.200868
$719$	14662.9	0.760549	0.380275	−	0.924874i	$-0.375829\pi$
$719$	14662.9	0.760549	0.380275	+	0.924874i	$0.375829\pi$
$720$	8753.64	0.453095
$721$	10320.2	0.533071
$722$	−3926.78	−0.202409
$723$	−10567.9	−0.543600
$724$	−2073.45	−0.106435
$725$	13712.7	0.702448
$726$	290.930	0.0148725
$727$	−24111.4	−1.23005	−0.615023	−	0.788509i	$-0.710853\pi$
$727$	−24111.4	−1.23005	−0.615023	+	0.788509i	$0.710853\pi$
$728$	−11869.7	−0.604288
$729$	729.000	0.0370370
$730$	−10980.6	−0.556729
$731$	−655.753	−0.0331791
$732$	1346.45	0.0679868
$733$	22743.4	1.14604	0.573020	−	0.819541i	$-0.305772\pi$
$733$	22743.4	1.14604	0.573020	+	0.819541i	$0.305772\pi$
$734$	−2835.09	−0.142568
$735$	21169.1	1.06236
$736$	−5652.34	−0.283081
$737$	−8461.81	−0.422924
$738$	855.519	0.0426722
$739$	17765.0	0.884296	0.442148	−	0.896942i	$-0.354217\pi$
$739$	17765.0	0.884296	0.442148	+	0.896942i	$0.354217\pi$
$740$	23636.3	1.17417
$741$	4845.64	0.240228
$742$	2408.22	0.119149
$743$	−7029.30	−0.347079	−0.173540	−	0.984827i	$-0.555520\pi$
$743$	−7029.30	−0.347079	−0.173540	+	0.984827i	$0.555520\pi$
$744$	1222.41	0.0602361
$745$	−7719.82	−0.379640
$746$	−5544.84	−0.272133
$747$	−8912.63	−0.436541
$748$	1559.19	0.0762163
$749$	−9626.90	−0.469639
$750$	6875.85	0.334761
$751$	9042.47	0.439367	0.219683	−	0.975571i	$-0.429498\pi$
$751$	9042.47	0.439367	0.219683	+	0.975571i	$0.429498\pi$
$752$	23643.1	1.14651
$753$	17517.6	0.847780
$754$	1490.44	0.0719877
$755$	9327.90	0.449638
$756$	−5250.21	−0.252577
$757$	17759.5	0.852683	0.426342	−	0.904562i	$-0.359802\pi$
$757$	17759.5	0.852683	0.426342	+	0.904562i	$0.359802\pi$
$758$	−2863.72	−0.137223
$759$	−1354.23	−0.0647632
$760$	−10815.8	−0.516222
$761$	37751.0	1.79826	0.899128	−	0.437685i	$-0.144202\pi$
$761$	37751.0	1.79826	0.899128	+	0.437685i	$0.144202\pi$
$762$	−288.285	−0.0137053
$763$	20857.4	0.989629
$764$	2162.47	0.102402
$765$	−3441.85	−0.162667
$766$	−5116.04	−0.241319
$767$	−6671.94	−0.314094
$768$	3565.96	0.167546
$769$	−4945.60	−0.231915	−0.115958	−	0.993254i	$-0.536994\pi$
$769$	−4945.60	−0.231915	−0.115958	+	0.993254i	$0.536994\pi$
$770$	4625.18	0.216467
$771$	16127.7	0.753340
$772$	5143.10	0.239772
$773$	−25125.2	−1.16907	−0.584536	−	0.811368i	$-0.698723\pi$
$773$	−25125.2	−1.16907	−0.584536	+	0.811368i	$0.698723\pi$
$774$	245.526	0.0114021
$775$	−8907.11	−0.412842
$776$	−9506.40	−0.439768
$777$	−12830.8	−0.592410
$778$	209.058	0.00963381
$779$	5250.18	0.241473
$780$	−15988.3	−0.733941
$781$	4869.36	0.223098
$782$	633.617	0.0289745
$783$	1376.06	0.0628050
$784$	17416.6	0.793397
$785$	22003.5	1.00043
$786$	−1757.78	−0.0797685
$787$	−23868.0	−1.08107	−0.540536	−	0.841321i	$-0.681778\pi$
$787$	−23868.0	−1.08107	−0.540536	+	0.841321i	$0.681778\pi$
$788$	9801.64	0.443108
$789$	7802.34	0.352054
$790$	2938.89	0.132356
$791$	−26812.1	−1.20522
$792$	−1218.55	−0.0546707
$793$	−2225.82	−0.0996738
$794$	11138.9	0.497867
$795$	6770.86	0.302060
$796$	20824.1	0.927249
$797$	−30643.0	−1.36189	−0.680947	−	0.732333i	$-0.738431\pi$
$797$	−30643.0	−1.36189	−0.680947	+	0.732333i	$0.738431\pi$
$798$	2812.84	0.124779
$799$	−9296.25	−0.411612
$800$	37059.5	1.63781
$801$	−4216.00	−0.185974
$802$	−9035.19	−0.397810
$803$	−7592.03	−0.333645
$804$	16979.8	0.744814
$805$	−21529.4	−0.942621
$806$	−968.123	−0.0423085
$807$	9324.19	0.406725
$808$	8554.78	0.372470
$809$	−18107.3	−0.786919	−0.393460	−	0.919342i	$-0.628722\pi$
$809$	−18107.3	−0.786919	−0.393460	+	0.919342i	$0.628722\pi$
$810$	1288.69	0.0559011
$811$	−12737.3	−0.551502	−0.275751	−	0.961229i	$-0.588926\pi$
$811$	−12737.3	−0.551502	−0.275751	+	0.961229i	$0.588926\pi$
$812$	−9910.27	−0.428303
$813$	8946.99	0.385959
$814$	−1426.70	−0.0614324
$815$	−13638.8	−0.586191
$816$	−2831.74	−0.121484
$817$	1506.75	0.0645221
$818$	9857.69	0.421352
$819$	8679.13	0.370297
$820$	−17323.1	−0.737743
$821$	20358.1	0.865412	0.432706	−	0.901535i	$-0.357559\pi$
$821$	20358.1	0.865412	0.432706	+	0.901535i	$0.357559\pi$
$822$	1117.15	0.0474027
$823$	−23950.2	−1.01440	−0.507200	−	0.861828i	$-0.669320\pi$
$823$	−23950.2	−1.01440	−0.507200	+	0.861828i	$0.669320\pi$
$824$	−4806.43	−0.203204
$825$	8878.97	0.374698
$826$	−3872.99	−0.163146
$827$	9775.89	0.411053	0.205527	−	0.978652i	$-0.434109\pi$
$827$	9775.89	0.411053	0.205527	+	0.978652i	$0.434109\pi$
$828$	2717.44	0.114055
$829$	31919.5	1.33729	0.668643	−	0.743584i	$-0.266876\pi$
$829$	31919.5	1.33729	0.668643	+	0.743584i	$0.266876\pi$
$830$	−15755.3	−0.658884
$831$	17792.0	0.742716
$832$	−10274.6	−0.428134
$833$	−6848.06	−0.284839
$834$	−334.625	−0.0138934
$835$	−58625.6	−2.42973
$836$	−3582.63	−0.148215
$837$	−893.824	−0.0369117
$838$	401.009	0.0165306
$839$	−20843.8	−0.857695	−0.428848	−	0.903377i	$-0.641080\pi$
$839$	−20843.8	−0.857695	−0.428848	+	0.903377i	$0.641080\pi$
$840$	−19372.3	−0.795725
$841$	−21791.6	−0.893500
$842$	−8434.92	−0.345233
$843$	−14034.5	−0.573396
$844$	−9798.59	−0.399622
$845$	−17182.2	−0.699509
$846$	3480.68	0.141452
$847$	3197.85	0.129728
$848$	5570.66	0.225586
$849$	4202.94	0.169899
$850$	−4154.30	−0.167637
$851$	6641.04	0.267511
$852$	−9771.04	−0.392899
$853$	−33838.3	−1.35827	−0.679133	−	0.734016i	$-0.737644\pi$
$853$	−33838.3	−1.35827	−0.679133	+	0.734016i	$0.737644\pi$
$854$	−1292.07	−0.0517723
$855$	7908.47	0.316332
$856$	4483.53	0.179023
$857$	3771.43	0.150326	0.0751632	−	0.997171i	$-0.476052\pi$
$857$	3771.43	0.150326	0.0751632	+	0.997171i	$0.476052\pi$
$858$	965.065	0.0383995
$859$	−19001.0	−0.754722	−0.377361	−	0.926066i	$-0.623168\pi$
$859$	−19001.0	−0.754722	−0.377361	+	0.926066i	$0.623168\pi$
$860$	−4971.57	−0.197127
$861$	9403.71	0.372216
$862$	−11684.9	−0.461706
$863$	13668.8	0.539157	0.269579	−	0.962978i	$-0.413116\pi$
$863$	13668.8	0.539157	0.269579	+	0.962978i	$0.413116\pi$
$864$	3718.90	0.146435
$865$	27155.0	1.06740
$866$	−4256.29	−0.167014
$867$	−13625.6	−0.533736
$868$	6437.26	0.251722
$869$	2031.95	0.0793202
$870$	2432.52	0.0947934
$871$	−28069.3	−1.09195
$872$	−9713.89	−0.377241
$873$	6951.07	0.269482
$874$	−1455.89	−0.0563457
$875$	75578.2	2.92001
$876$	15234.4	0.587584
$877$	−29561.4	−1.13822	−0.569109	−	0.822262i	$-0.692712\pi$
$877$	−29561.4	−1.13822	−0.569109	+	0.822262i	$0.692712\pi$
$878$	−9514.10	−0.365701
$879$	228.118	0.00875338
$880$	10698.9	0.409840
$881$	−2340.12	−0.0894901	−0.0447450	−	0.998998i	$-0.514248\pi$
$881$	−2340.12	−0.0894901	−0.0447450	+	0.998998i	$0.514248\pi$
$882$	2564.03	0.0978861
$883$	−33961.2	−1.29432	−0.647160	−	0.762354i	$-0.724043\pi$
$883$	−33961.2	−1.29432	−0.647160	+	0.762354i	$0.724043\pi$
$884$	5172.12	0.196784
$885$	−10889.1	−0.413598
$886$	−9946.82	−0.377167
$887$	5419.74	0.205160	0.102580	−	0.994725i	$-0.467290\pi$
$887$	5419.74	0.205160	0.102580	+	0.994725i	$0.467290\pi$
$888$	5975.68	0.225823
$889$	−3168.78	−0.119547
$890$	−7452.82	−0.280696
$891$	891.000	0.0335013
$892$	−243.983	−0.00915825
$893$	21360.4	0.800445
$894$	−935.037	−0.0349802
$895$	71410.7	2.66704
$896$	−35085.8	−1.30819
$897$	−4492.20	−0.167213
$898$	−364.042	−0.0135281
$899$	−1687.18	−0.0625924
$900$	−17816.9	−0.659883
$901$	−2190.33	−0.0809883
$902$	1045.63	0.0385984
$903$	2698.78	0.0994570
$904$	12487.2	0.459422
$905$	5594.15	0.205476
$906$	1129.81	0.0414299
$907$	−3773.71	−0.138152	−0.0690761	−	0.997611i	$-0.522005\pi$
$907$	−3773.71	−0.138152	−0.0690761	+	0.997611i	$0.522005\pi$
$908$	3418.01	0.124924
$909$	−6255.24	−0.228243
$910$	15342.5	0.558901
$911$	40530.5	1.47402	0.737011	−	0.675880i	$-0.236236\pi$
$911$	40530.5	1.47402	0.737011	+	0.675880i	$0.236236\pi$
$912$	6506.62	0.236245
$913$	−10893.2	−0.394866
$914$	−8749.01	−0.316621
$915$	−3632.72	−0.131250
$916$	46392.1	1.67340
$917$	−19321.2	−0.695794
$918$	−416.882	−0.0149882
$919$	2943.22	0.105645	0.0528226	−	0.998604i	$-0.483178\pi$
$919$	2943.22	0.105645	0.0528226	+	0.998604i	$0.483178\pi$
$920$	10026.9	0.359322
$921$	24676.9	0.882880
$922$	8478.88	0.302860
$923$	16152.5	0.576020
$924$	−6416.92	−0.228465
$925$	−43542.0	−1.54773
$926$	8175.68	0.290140
$927$	3514.45	0.124520
$928$	7019.78	0.248314
$929$	−26989.3	−0.953165	−0.476583	−	0.879130i	$-0.658125\pi$
$929$	−26989.3	−0.953165	−0.476583	+	0.879130i	$0.658125\pi$
$930$	−1580.05	−0.0557119
$931$	15735.1	0.553916
$932$	−26705.2	−0.938581
$933$	−7248.26	−0.254338
$934$	4835.88	0.169416
$935$	−4206.70	−0.147138
$936$	−4042.13	−0.141155
$937$	−9314.44	−0.324749	−0.162374	−	0.986729i	$-0.551915\pi$
$937$	−9314.44	−0.324749	−0.162374	+	0.986729i	$0.551915\pi$
$938$	−16293.9	−0.567180
$939$	15370.6	0.534186
$940$	−70479.2	−2.44551
$941$	35657.3	1.23528	0.617638	−	0.786462i	$-0.288090\pi$
$941$	35657.3	1.23528	0.617638	+	0.786462i	$0.288090\pi$
$942$	2665.10	0.0921801
$943$	−4867.23	−0.168079
$944$	−8958.93	−0.308886
$945$	14165.0	0.487607
$946$	300.087	0.0103136
$947$	7379.85	0.253234	0.126617	−	0.991952i	$-0.459588\pi$
$947$	7379.85	0.253234	0.126617	+	0.991952i	$0.459588\pi$
$948$	−4077.39	−0.139691
$949$	−25184.1	−0.861443
$950$	9545.52	0.325997
$951$	−5743.98	−0.195858
$952$	6266.83	0.213350
$953$	−44510.7	−1.51295	−0.756477	−	0.654021i	$-0.773081\pi$
$953$	−44510.7	−1.51295	−0.756477	+	0.654021i	$0.773081\pi$
$954$	820.099	0.0278319
$955$	−5834.33	−0.197691
$956$	−21221.3	−0.717935
$957$	1681.85	0.0568092
$958$	−8903.93	−0.300285
$959$	12279.5	0.413479
$960$	−16768.9	−0.563766
$961$	−28695.1	−0.963213
$962$	−4732.62	−0.158613
$963$	−3278.36	−0.109703
$964$	25918.2	0.865944
$965$	−13876.1	−0.462888
$966$	−2607.67	−0.0868535
$967$	−6904.96	−0.229626	−0.114813	−	0.993387i	$-0.536627\pi$
$967$	−6904.96	−0.229626	−0.114813	+	0.993387i	$0.536627\pi$
$968$	−1489.33	−0.0494515
$969$	−2558.34	−0.0848150
$970$	12287.7	0.406738
$971$	−51770.9	−1.71103	−0.855513	−	0.517782i	$-0.826758\pi$
$971$	−51770.9	−1.71103	−0.855513	+	0.517782i	$0.826758\pi$
$972$	−1787.91	−0.0589993
$973$	−3678.14	−0.121188
$974$	8501.81	0.279688
$975$	29453.1	0.967439
$976$	−2988.79	−0.0980212
$977$	18085.1	0.592214	0.296107	−	0.955155i	$-0.404311\pi$
$977$	18085.1	0.592214	0.296107	+	0.955155i	$0.404311\pi$
$978$	−1651.95	−0.0540119
$979$	−5152.89	−0.168220
$980$	−51918.3	−1.69232
$981$	7102.79	0.231167
$982$	−9988.48	−0.324588
$983$	−32847.9	−1.06580	−0.532902	−	0.846177i	$-0.678899\pi$
$983$	−32847.9	−1.06580	−0.532902	+	0.846177i	$0.678899\pi$
$984$	−4379.59	−0.141886
$985$	−26444.8	−0.855432
$986$	−786.905	−0.0254160
$987$	38259.0	1.23384
$988$	−11884.2	−0.382679
$989$	−1396.85	−0.0449113
$990$	1575.06	0.0505644
$991$	−27333.7	−0.876168	−0.438084	−	0.898934i	$-0.644343\pi$
$991$	−27333.7	−0.876168	−0.438084	+	0.898934i	$0.644343\pi$
$992$	−4559.73	−0.145939
$993$	26714.1	0.853721
$994$	9376.36	0.299195
$995$	−56183.3	−1.79008
$996$	21858.7	0.695402
$997$	−9098.74	−0.289027	−0.144513	−	0.989503i	$-0.546162\pi$
$997$	−9098.74	−0.289027	−0.144513	+	0.989503i	$0.546162\pi$
$998$	6664.14	0.211372
$999$	−4369.41	−0.138380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.f.1.19	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.f.1.19	✓	38	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+0.801460 q^{2} +3.00000 q^{3} -7.35766 q^{4} +19.8509 q^{5} +2.40438 q^{6} +26.4285 q^{7} -12.3086 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.801460 q^{2} +3.00000 q^{3} -7.35766 q^{4} +19.8509 q^{5} +2.40438 q^{6} +26.4285 q^{7} -12.3086 q^{8} +9.00000 q^{9} +15.9097 q^{10} +11.0000 q^{11} -22.0730 q^{12} +36.4889 q^{13} +21.1814 q^{14} +59.5528 q^{15} +48.9965 q^{16} -19.2649 q^{17} +7.21314 q^{18} +44.2659 q^{19} -146.056 q^{20} +79.2856 q^{21} +8.81606 q^{22} -41.0371 q^{23} -36.9257 q^{24} +269.060 q^{25} +29.2444 q^{26} +27.0000 q^{27} -194.452 q^{28} +50.9651 q^{29} +47.7292 q^{30} -33.1046 q^{31} +137.737 q^{32} +33.0000 q^{33} -15.4401 q^{34} +524.631 q^{35} -66.2190 q^{36} -161.830 q^{37} +35.4773 q^{38} +109.467 q^{39} -244.336 q^{40} +118.606 q^{41} +63.5442 q^{42} +34.0387 q^{43} -80.9343 q^{44} +178.658 q^{45} -32.8896 q^{46} +482.547 q^{47} +146.989 q^{48} +355.467 q^{49} +215.641 q^{50} -57.7948 q^{51} -268.473 q^{52} +113.695 q^{53} +21.6394 q^{54} +218.360 q^{55} -325.297 q^{56} +132.798 q^{57} +40.8465 q^{58} -182.848 q^{59} -438.169 q^{60} -61.0000 q^{61} -26.5320 q^{62} +237.857 q^{63} -281.581 q^{64} +724.339 q^{65} +26.4482 q^{66} -769.255 q^{67} +141.745 q^{68} -123.111 q^{69} +420.471 q^{70} +442.669 q^{71} -110.777 q^{72} -690.184 q^{73} -129.700 q^{74} +807.179 q^{75} -325.693 q^{76} +290.714 q^{77} +87.7332 q^{78} +184.723 q^{79} +972.626 q^{80} +81.0000 q^{81} +95.0576 q^{82} -990.293 q^{83} -583.357 q^{84} -382.427 q^{85} +27.2806 q^{86} +152.895 q^{87} -135.394 q^{88} -468.444 q^{89} +143.188 q^{90} +964.348 q^{91} +301.937 q^{92} -99.3137 q^{93} +386.742 q^{94} +878.719 q^{95} +413.211 q^{96} +772.341 q^{97} +284.893 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * q^99

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