LMFDB - Embedded newform 2013.4.a.d.1.18

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:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-0.441122 q^{2} -3.00000 q^{3} -7.80541 q^{4} +14.6691 q^{5} +1.32336 q^{6} -18.4288 q^{7} +6.97211 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.441122 q^{2} -3.00000 q^{3} -7.80541 q^{4} +14.6691 q^{5} +1.32336 q^{6} -18.4288 q^{7} +6.97211 q^{8} +9.00000 q^{9} -6.47085 q^{10} +11.0000 q^{11} +23.4162 q^{12} -46.7528 q^{13} +8.12933 q^{14} -44.0072 q^{15} +59.3677 q^{16} +52.3426 q^{17} -3.97009 q^{18} -105.853 q^{19} -114.498 q^{20} +55.2863 q^{21} -4.85234 q^{22} +189.190 q^{23} -20.9163 q^{24} +90.1819 q^{25} +20.6237 q^{26} -27.0000 q^{27} +143.844 q^{28} -155.362 q^{29} +19.4125 q^{30} -31.6522 q^{31} -81.9652 q^{32} -33.0000 q^{33} -23.0894 q^{34} -270.333 q^{35} -70.2487 q^{36} +62.0633 q^{37} +46.6938 q^{38} +140.258 q^{39} +102.274 q^{40} -31.1751 q^{41} -24.3880 q^{42} +172.605 q^{43} -85.8595 q^{44} +132.022 q^{45} -83.4560 q^{46} +136.646 q^{47} -178.103 q^{48} -3.38007 q^{49} -39.7812 q^{50} -157.028 q^{51} +364.925 q^{52} +367.696 q^{53} +11.9103 q^{54} +161.360 q^{55} -128.487 q^{56} +317.558 q^{57} +68.5337 q^{58} -270.763 q^{59} +343.495 q^{60} -61.0000 q^{61} +13.9625 q^{62} -165.859 q^{63} -438.785 q^{64} -685.821 q^{65} +14.5570 q^{66} +339.885 q^{67} -408.555 q^{68} -567.571 q^{69} +119.250 q^{70} +603.402 q^{71} +62.7490 q^{72} +156.217 q^{73} -27.3775 q^{74} -270.546 q^{75} +826.223 q^{76} -202.717 q^{77} -61.8710 q^{78} -75.7174 q^{79} +870.870 q^{80} +81.0000 q^{81} +13.7520 q^{82} -778.415 q^{83} -431.533 q^{84} +767.817 q^{85} -76.1397 q^{86} +466.087 q^{87} +76.6932 q^{88} -1157.53 q^{89} -58.2376 q^{90} +861.598 q^{91} -1476.71 q^{92} +94.9567 q^{93} -60.2773 q^{94} -1552.76 q^{95} +245.896 q^{96} +334.910 q^{97} +1.49102 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * 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 $

$2$	−0.441122	−0.155960	−0.0779800	−	0.996955i	$-0.524847\pi$
$2$	−0.441122	−0.155960	−0.0779800	+	0.996955i	$0.524847\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.80541	−0.975676
$5$	14.6691	1.31204	0.656021	−	0.754743i	$-0.272238\pi$
$5$	14.6691	1.31204	0.656021	+	0.754743i	$0.272238\pi$
$6$	1.32336	0.0900436
$7$	−18.4288	−0.995061	−0.497530	−	0.867447i	$-0.665760\pi$
$7$	−18.4288	−0.995061	−0.497530	+	0.867447i	$0.665760\pi$
$8$	6.97211	0.308127
$9$	9.00000	0.333333
$10$	−6.47085	−0.204626
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	23.4162	0.563307
$13$	−46.7528	−0.997454	−0.498727	−	0.866759i	$-0.666199\pi$
$13$	−46.7528	−0.997454	−0.498727	+	0.866759i	$0.666199\pi$
$14$	8.12933	0.155190
$15$	−44.0072	−0.757508
$16$	59.3677	0.927621
$17$	52.3426	0.746761	0.373381	−	0.927678i	$-0.378199\pi$
$17$	52.3426	0.746761	0.373381	+	0.927678i	$0.378199\pi$
$18$	−3.97009	−0.0519867
$19$	−105.853	−1.27812	−0.639059	−	0.769158i	$-0.720676\pi$
$19$	−105.853	−1.27812	−0.639059	+	0.769158i	$0.720676\pi$
$20$	−114.498	−1.28013
$21$	55.2863	0.574498
$22$	−4.85234	−0.0470237
$23$	189.190	1.71517	0.857585	−	0.514342i	$-0.171964\pi$
$23$	189.190	1.71517	0.857585	+	0.514342i	$0.171964\pi$
$24$	−20.9163	−0.177897
$25$	90.1819	0.721455
$26$	20.6237	0.155563
$27$	−27.0000	−0.192450
$28$	143.844	0.970857
$29$	−155.362	−0.994831	−0.497415	−	0.867513i	$-0.665717\pi$
$29$	−155.362	−0.994831	−0.497415	+	0.867513i	$0.665717\pi$
$30$	19.4125	0.118141
$31$	−31.6522	−0.183384	−0.0916921	−	0.995787i	$-0.529228\pi$
$31$	−31.6522	−0.183384	−0.0916921	+	0.995787i	$0.529228\pi$
$32$	−81.9652	−0.452798
$33$	−33.0000	−0.174078
$34$	−23.0894	−0.116465
$35$	−270.333	−1.30556
$36$	−70.2487	−0.325225
$37$	62.0633	0.275761	0.137880	−	0.990449i	$-0.455971\pi$
$37$	62.0633	0.275761	0.137880	+	0.990449i	$0.455971\pi$
$38$	46.6938	0.199335
$39$	140.258	0.575880
$40$	102.274	0.404275
$41$	−31.1751	−0.118749	−0.0593747	−	0.998236i	$-0.518911\pi$
$41$	−31.1751	−0.118749	−0.0593747	+	0.998236i	$0.518911\pi$
$42$	−24.3880	−0.0895988
$43$	172.605	0.612139	0.306070	−	0.952009i	$-0.400986\pi$
$43$	172.605	0.612139	0.306070	+	0.952009i	$0.400986\pi$
$44$	−85.8595	−0.294178
$45$	132.022	0.437347
$46$	−83.4560	−0.267498
$47$	136.646	0.424081	0.212041	−	0.977261i	$-0.431989\pi$
$47$	136.646	0.424081	0.212041	+	0.977261i	$0.431989\pi$
$48$	−178.103	−0.535562
$49$	−3.38007	−0.00985443
$50$	−39.7812	−0.112518
$51$	−157.028	−0.431143
$52$	364.925	0.973192
$53$	367.696	0.952962	0.476481	−	0.879185i	$-0.341912\pi$
$53$	367.696	0.952962	0.476481	+	0.879185i	$0.341912\pi$
$54$	11.9103	0.0300145
$55$	161.360	0.395596
$56$	−128.487	−0.306605
$57$	317.558	0.737922
$58$	68.5337	0.155154
$59$	−270.763	−0.597464	−0.298732	−	0.954337i	$-0.596564\pi$
$59$	−270.763	−0.597464	−0.298732	+	0.954337i	$0.596564\pi$
$60$	343.495	0.739083
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	13.9625	0.0286006
$63$	−165.859	−0.331687
$64$	−438.785	−0.857003
$65$	−685.821	−1.30870
$66$	14.5570	0.0271492
$67$	339.885	0.619754	0.309877	−	0.950777i	$-0.399712\pi$
$67$	339.885	0.619754	0.309877	+	0.950777i	$0.399712\pi$
$68$	−408.555	−0.728597
$69$	−567.571	−0.990254
$70$	119.250	0.203615
$71$	603.402	1.00860	0.504300	−	0.863529i	$-0.331751\pi$
$71$	603.402	1.00860	0.504300	+	0.863529i	$0.331751\pi$
$72$	62.7490	0.102709
$73$	156.217	0.250464	0.125232	−	0.992128i	$-0.460033\pi$
$73$	156.217	0.250464	0.125232	+	0.992128i	$0.460033\pi$
$74$	−27.3775	−0.0430076
$75$	−270.546	−0.416532
$76$	826.223	1.24703
$77$	−202.717	−0.300022
$78$	−61.8710	−0.0898143
$79$	−75.7174	−0.107834	−0.0539169	−	0.998545i	$-0.517171\pi$
$79$	−75.7174	−0.107834	−0.0539169	+	0.998545i	$0.517171\pi$
$80$	870.870	1.21708
$81$	81.0000	0.111111
$82$	13.7520	0.0185202
$83$	−778.415	−1.02942	−0.514712	−	0.857363i	$-0.672101\pi$
$83$	−778.415	−1.02942	−0.514712	+	0.857363i	$0.672101\pi$
$84$	−431.533	−0.560525
$85$	767.817	0.979782
$86$	−76.1397	−0.0954693
$87$	466.087	0.574366
$88$	76.6932	0.0929036
$89$	−1157.53	−1.37863	−0.689315	−	0.724462i	$-0.742088\pi$
$89$	−1157.53	−1.37863	−0.689315	+	0.724462i	$0.742088\pi$
$90$	−58.2376	−0.0682087
$91$	861.598	0.992527
$92$	−1476.71	−1.67345
$93$	94.9567	0.105877
$94$	−60.2773	−0.0661397
$95$	−1552.76	−1.67694
$96$	245.896	0.261423
$97$	334.910	0.350567	0.175283	−	0.984518i	$-0.443916\pi$
$97$	334.910	0.350567	0.175283	+	0.984518i	$0.443916\pi$
$98$	1.49102	0.00153690
$99$	99.0000	0.100504
$100$	−703.907	−0.703907
$101$	595.226	0.586408	0.293204	−	0.956050i	$-0.405278\pi$
$101$	595.226	0.586408	0.293204	+	0.956050i	$0.405278\pi$
$102$	69.2683	0.0672410
$103$	1698.43	1.62477	0.812384	−	0.583122i	$-0.198169\pi$
$103$	1698.43	1.62477	0.812384	+	0.583122i	$0.198169\pi$
$104$	−325.966	−0.307342
$105$	811.000	0.753766
$106$	−162.199	−0.148624
$107$	24.9144	0.0225099	0.0112550	−	0.999937i	$-0.496417\pi$
$107$	24.9144	0.0225099	0.0112550	+	0.999937i	$0.496417\pi$
$108$	210.746	0.187769
$109$	593.723	0.521728	0.260864	−	0.965376i	$-0.415993\pi$
$109$	593.723	0.521728	0.260864	+	0.965376i	$0.415993\pi$
$110$	−71.1793	−0.0616971
$111$	−186.190	−0.159211
$112$	−1094.08	−0.923039
$113$	711.723	0.592506	0.296253	−	0.955109i	$-0.404263\pi$
$113$	711.723	0.592506	0.296253	+	0.955109i	$0.404263\pi$
$114$	−140.081	−0.115086
$115$	2775.25	2.25038
$116$	1212.67	0.970633
$117$	−420.775	−0.332485
$118$	119.439	0.0931804
$119$	−964.610	−0.743073
$120$	−306.823	−0.233408
$121$	121.000	0.0909091
$122$	26.9084	0.0199686
$123$	93.5252	0.0685600
$124$	247.059	0.178924
$125$	−510.750	−0.365463
$126$	73.1640	0.0517299
$127$	−1103.61	−0.771099	−0.385549	−	0.922687i	$-0.625988\pi$
$127$	−1103.61	−0.771099	−0.385549	+	0.922687i	$0.625988\pi$
$128$	849.280	0.586456
$129$	−517.815	−0.353419
$130$	302.530	0.204105
$131$	542.811	0.362028	0.181014	−	0.983481i	$-0.442062\pi$
$131$	542.811	0.362028	0.181014	+	0.983481i	$0.442062\pi$
$132$	257.579	0.169843
$133$	1950.73	1.27180
$134$	−149.930	−0.0966569
$135$	−396.065	−0.252503
$136$	364.938	0.230097
$137$	1474.77	0.919696	0.459848	−	0.887998i	$-0.347904\pi$
$137$	1474.77	0.919696	0.459848	+	0.887998i	$0.347904\pi$
$138$	250.368	0.154440
$139$	−2359.95	−1.44006	−0.720029	−	0.693944i	$-0.755872\pi$
$139$	−2359.95	−1.44006	−0.720029	+	0.693944i	$0.755872\pi$
$140$	2110.06	1.27381
$141$	−409.937	−0.244843
$142$	−266.173	−0.157301
$143$	−514.281	−0.300744
$144$	534.310	0.309207
$145$	−2279.02	−1.30526
$146$	−68.9108	−0.0390623
$147$	10.1402	0.00568946
$148$	−484.430	−0.269053
$149$	−1449.06	−0.796723	−0.398361	−	0.917229i	$-0.630421\pi$
$149$	−1449.06	−0.796723	−0.398361	+	0.917229i	$0.630421\pi$
$150$	119.343	0.0649624
$151$	672.595	0.362483	0.181242	−	0.983439i	$-0.441988\pi$
$151$	672.595	0.362483	0.181242	+	0.983439i	$0.441988\pi$
$152$	−738.015	−0.393822
$153$	471.083	0.248920
$154$	89.4226	0.0467914
$155$	−464.309	−0.240608
$156$	−1094.78	−0.561873
$157$	2241.78	1.13958	0.569789	−	0.821791i	$-0.307025\pi$
$157$	2241.78	1.13958	0.569789	+	0.821791i	$0.307025\pi$
$158$	33.4006	0.0168178
$159$	−1103.09	−0.550193
$160$	−1202.35	−0.594091
$161$	−3486.55	−1.70670
$162$	−35.7308	−0.0173289
$163$	−1115.44	−0.535999	−0.268000	−	0.963419i	$-0.586363\pi$
$163$	−1115.44	−0.535999	−0.268000	+	0.963419i	$0.586363\pi$
$164$	243.334	0.115861
$165$	−484.080	−0.228397
$166$	343.376	0.160549
$167$	−2830.02	−1.31134	−0.655670	−	0.755047i	$-0.727614\pi$
$167$	−2830.02	−1.31134	−0.655670	+	0.755047i	$0.727614\pi$
$168$	385.462	0.177018
$169$	−11.1734	−0.00508577
$170$	−338.701	−0.152807
$171$	−952.673	−0.426039
$172$	−1347.25	−0.597250
$173$	245.293	0.107799	0.0538996	−	0.998546i	$-0.482835\pi$
$173$	245.293	0.107799	0.0538996	+	0.998546i	$0.482835\pi$
$174$	−205.601	−0.0895781
$175$	−1661.94	−0.717891
$176$	653.045	0.279688
$177$	812.289	0.344946
$178$	510.612	0.215011
$179$	382.567	0.159745	0.0798726	−	0.996805i	$-0.474549\pi$
$179$	382.567	0.159745	0.0798726	+	0.996805i	$0.474549\pi$
$180$	−1030.48	−0.426710
$181$	550.859	0.226216	0.113108	−	0.993583i	$-0.463919\pi$
$181$	550.859	0.226216	0.113108	+	0.993583i	$0.463919\pi$
$182$	−380.069	−0.154795
$183$	183.000	0.0739221
$184$	1319.06	0.528490
$185$	910.412	0.361810
$186$	−41.8874	−0.0165126
$187$	575.768	0.225157
$188$	−1066.58	−0.413766
$189$	497.577	0.191499
$190$	684.955	0.261536
$191$	−4537.93	−1.71912	−0.859562	−	0.511031i	$-0.829264\pi$
$191$	−4537.93	−1.71912	−0.859562	+	0.511031i	$0.829264\pi$
$192$	1316.36	0.494791
$193$	4359.20	1.62581	0.812906	−	0.582394i	$-0.197884\pi$
$193$	4359.20	1.62581	0.812906	+	0.582394i	$0.197884\pi$
$194$	−147.736	−0.0546744
$195$	2057.46	0.755579
$196$	26.3828	0.00961473
$197$	−119.064	−0.0430606	−0.0215303	−	0.999768i	$-0.506854\pi$
$197$	−119.064	−0.0430606	−0.0215303	+	0.999768i	$0.506854\pi$
$198$	−43.6710	−0.0156746
$199$	−1120.31	−0.399079	−0.199540	−	0.979890i	$-0.563945\pi$
$199$	−1120.31	−0.399079	−0.199540	+	0.979890i	$0.563945\pi$
$200$	628.758	0.222299
$201$	−1019.65	−0.357815
$202$	−262.567	−0.0914562
$203$	2863.14	0.989917
$204$	1225.67	0.420656
$205$	−457.309	−0.155804
$206$	−749.213	−0.253399
$207$	1702.71	0.571724
$208$	−2775.61	−0.925259
$209$	−1164.38	−0.385367
$210$	−357.749	−0.117557
$211$	−3707.65	−1.20969	−0.604847	−	0.796342i	$-0.706766\pi$
$211$	−3707.65	−1.20969	−0.604847	+	0.796342i	$0.706766\pi$
$212$	−2870.02	−0.929783
$213$	−1810.20	−0.582315
$214$	−10.9903	−0.00351065
$215$	2531.95	0.803153
$216$	−188.247	−0.0592990
$217$	583.312	0.182478
$218$	−261.904	−0.0813686
$219$	−468.652	−0.144605
$220$	−1259.48	−0.385973
$221$	−2447.16	−0.744860
$222$	82.1324	0.0248305
$223$	−2390.31	−0.717789	−0.358894	−	0.933378i	$-0.616846\pi$
$223$	−2390.31	−0.717789	−0.358894	+	0.933378i	$0.616846\pi$
$224$	1510.52	0.450562
$225$	811.637	0.240485
$226$	−313.956	−0.0924073
$227$	602.014	0.176022	0.0880112	−	0.996119i	$-0.471949\pi$
$227$	602.014	0.176022	0.0880112	+	0.996119i	$0.471949\pi$
$228$	−2478.67	−0.719973
$229$	1715.84	0.495134	0.247567	−	0.968871i	$-0.420369\pi$
$229$	1715.84	0.495134	0.247567	+	0.968871i	$0.420369\pi$
$230$	−1224.22	−0.350969
$231$	608.150	0.173218
$232$	−1083.20	−0.306534
$233$	1898.62	0.533832	0.266916	−	0.963720i	$-0.413995\pi$
$233$	1898.62	0.533832	0.266916	+	0.963720i	$0.413995\pi$
$234$	185.613	0.0518543
$235$	2004.47	0.556412
$236$	2113.42	0.582931
$237$	227.152	0.0622579
$238$	425.510	0.115890
$239$	−3694.92	−1.00002	−0.500009	−	0.866020i	$-0.666670\pi$
$239$	−3694.92	−1.00002	−0.500009	+	0.866020i	$0.666670\pi$
$240$	−2612.61	−0.702680
$241$	−1716.75	−0.458860	−0.229430	−	0.973325i	$-0.573686\pi$
$241$	−1716.75	−0.458860	−0.229430	+	0.973325i	$0.573686\pi$
$242$	−53.3757	−0.0141782
$243$	−243.000	−0.0641500
$244$	476.130	0.124923
$245$	−49.5825	−0.0129294
$246$	−41.2560	−0.0106926
$247$	4948.90	1.27486
$248$	−220.683	−0.0565055
$249$	2335.25	0.594338
$250$	225.303	0.0569976
$251$	−5706.57	−1.43504	−0.717521	−	0.696537i	$-0.754723\pi$
$251$	−5706.57	−1.43504	−0.717521	+	0.696537i	$0.754723\pi$
$252$	1294.60	0.323619
$253$	2081.09	0.517143
$254$	486.826	0.120261
$255$	−2303.45	−0.565678
$256$	3135.65	0.765539
$257$	−1796.03	−0.435926	−0.217963	−	0.975957i	$-0.569941\pi$
$257$	−1796.03	−0.435926	−0.217963	+	0.975957i	$0.569941\pi$
$258$	228.419	0.0551192
$259$	−1143.75	−0.274399
$260$	5353.11	1.27687
$261$	−1398.26	−0.331610
$262$	−239.446	−0.0564619
$263$	−3588.61	−0.841381	−0.420690	−	0.907204i	$-0.638212\pi$
$263$	−3588.61	−0.841381	−0.420690	+	0.907204i	$0.638212\pi$
$264$	−230.080	−0.0536379
$265$	5393.77	1.25033
$266$	−860.510	−0.198351
$267$	3472.60	0.795953
$268$	−2652.94	−0.604680
$269$	−3453.44	−0.782750	−0.391375	−	0.920231i	$-0.628001\pi$
$269$	−3453.44	−0.782750	−0.391375	+	0.920231i	$0.628001\pi$
$270$	174.713	0.0393803
$271$	−1763.55	−0.395306	−0.197653	−	0.980272i	$-0.563332\pi$
$271$	−1763.55	−0.395306	−0.197653	+	0.980272i	$0.563332\pi$
$272$	3107.46	0.692711
$273$	−2584.79	−0.573036
$274$	−650.554	−0.143436
$275$	992.000	0.217527
$276$	4430.13	0.966168
$277$	−4084.94	−0.886066	−0.443033	−	0.896505i	$-0.646098\pi$
$277$	−4084.94	−0.886066	−0.443033	+	0.896505i	$0.646098\pi$
$278$	1041.02	0.224591
$279$	−284.870	−0.0611281
$280$	−1884.79	−0.402278
$281$	−2920.35	−0.619976	−0.309988	−	0.950740i	$-0.600325\pi$
$281$	−2920.35	−0.619976	−0.309988	+	0.950740i	$0.600325\pi$
$282$	180.832	0.0381858
$283$	−6146.25	−1.29101	−0.645507	−	0.763755i	$-0.723354\pi$
$283$	−6146.25	−1.29101	−0.645507	+	0.763755i	$0.723354\pi$
$284$	−4709.80	−0.984067
$285$	4658.28	0.968184
$286$	226.860	0.0469040
$287$	574.518	0.118163
$288$	−737.687	−0.150933
$289$	−2173.25	−0.442348
$290$	1005.33	0.203568
$291$	−1004.73	−0.202400
$292$	−1219.34	−0.244372
$293$	−5090.45	−1.01497	−0.507487	−	0.861659i	$-0.669425\pi$
$293$	−5090.45	−1.01497	−0.507487	+	0.861659i	$0.669425\pi$
$294$	−4.47306	−0.000887327 0
$295$	−3971.85	−0.783897
$296$	432.712	0.0849692
$297$	−297.000	−0.0580259
$298$	639.212	0.124257
$299$	−8845.19	−1.71080
$300$	2111.72	0.406401
$301$	−3180.90	−0.609116
$302$	−296.696	−0.0565329
$303$	−1785.68	−0.338563
$304$	−6284.23	−1.18561
$305$	−894.814	−0.167990
$306$	−207.805	−0.0388216
$307$	−5664.16	−1.05300	−0.526499	−	0.850175i	$-0.676496\pi$
$307$	−5664.16	−1.05300	−0.526499	+	0.850175i	$0.676496\pi$
$308$	1582.29	0.292724
$309$	−5095.29	−0.938061
$310$	204.817	0.0375252
$311$	−2079.73	−0.379198	−0.189599	−	0.981862i	$-0.560719\pi$
$311$	−2079.73	−0.379198	−0.189599	+	0.981862i	$0.560719\pi$
$312$	977.897	0.177444
$313$	−1451.86	−0.262185	−0.131092	−	0.991370i	$-0.541848\pi$
$313$	−1451.86	−0.262185	−0.131092	+	0.991370i	$0.541848\pi$
$314$	−988.899	−0.177729
$315$	−2433.00	−0.435187
$316$	591.005	0.105211
$317$	−4263.92	−0.755475	−0.377737	−	0.925913i	$-0.623298\pi$
$317$	−4263.92	−0.755475	−0.377737	+	0.925913i	$0.623298\pi$
$318$	486.596	0.0858081
$319$	−1708.99	−0.299953
$320$	−6436.58	−1.12442
$321$	−74.7431	−0.0129961
$322$	1537.99	0.266177
$323$	−5540.59	−0.954449
$324$	−632.238	−0.108408
$325$	−4216.26	−0.719618
$326$	492.044	0.0835945
$327$	−1781.17	−0.301220
$328$	−217.356	−0.0365899
$329$	−2518.21	−0.421986
$330$	213.538	0.0356208
$331$	934.026	0.155102	0.0775509	−	0.996988i	$-0.475290\pi$
$331$	934.026	0.155102	0.0775509	+	0.996988i	$0.475290\pi$
$332$	6075.85	1.00438
$333$	558.570	0.0919202
$334$	1248.38	0.204517
$335$	4985.80	0.813144
$336$	3282.23	0.532917
$337$	7069.23	1.14269	0.571343	−	0.820711i	$-0.306422\pi$
$337$	7069.23	1.14269	0.571343	+	0.820711i	$0.306422\pi$
$338$	4.92884	0.000793177 0
$339$	−2135.17	−0.342084
$340$	−5993.13	−0.955951
$341$	−348.175	−0.0552924
$342$	420.244	0.0664451
$343$	6383.36	1.00487
$344$	1203.42	0.188616
$345$	−8325.75	−1.29926
$346$	−108.204	−0.0168124
$347$	−10754.4	−1.66377	−0.831884	−	0.554950i	$-0.812737\pi$
$347$	−10754.4	−1.66377	−0.831884	+	0.554950i	$0.812737\pi$
$348$	−3638.00	−0.560395
$349$	−9219.06	−1.41400	−0.706998	−	0.707215i	$-0.749951\pi$
$349$	−9219.06	−1.41400	−0.706998	+	0.707215i	$0.749951\pi$
$350$	733.118	0.111962
$351$	1262.33	0.191960
$352$	−901.618	−0.136524
$353$	7163.97	1.08017	0.540085	−	0.841611i	$-0.318392\pi$
$353$	7163.97	1.08017	0.540085	+	0.841611i	$0.318392\pi$
$354$	−358.318	−0.0537977
$355$	8851.34	1.32333
$356$	9035.01	1.34510
$357$	2893.83	0.429013
$358$	−168.758	−0.0249139
$359$	4746.28	0.697768	0.348884	−	0.937166i	$-0.386561\pi$
$359$	4746.28	0.697768	0.348884	+	0.937166i	$0.386561\pi$
$360$	920.469	0.134758
$361$	4345.76	0.633584
$362$	−242.996	−0.0352806
$363$	−363.000	−0.0524864
$364$	−6725.12	−0.968385
$365$	2291.56	0.328619
$366$	−80.7252	−0.0115289
$367$	−10135.0	−1.44154	−0.720769	−	0.693175i	$-0.756211\pi$
$367$	−10135.0	−1.44154	−0.720769	+	0.693175i	$0.756211\pi$
$368$	11231.8	1.59103
$369$	−280.576	−0.0395831
$370$	−401.602	−0.0564278
$371$	−6776.20	−0.948255
$372$	−741.176	−0.103302
$373$	−12949.6	−1.79760	−0.898802	−	0.438355i	$-0.855561\pi$
$373$	−12949.6	−1.79760	−0.898802	+	0.438355i	$0.855561\pi$
$374$	−253.984	−0.0351155
$375$	1532.25	0.211000
$376$	952.708	0.130671
$377$	7263.63	0.992298
$378$	−219.492	−0.0298663
$379$	1622.20	0.219859	0.109930	−	0.993939i	$-0.464937\pi$
$379$	1622.20	0.219859	0.109930	+	0.993939i	$0.464937\pi$
$380$	12119.9	1.63616
$381$	3310.83	0.445194
$382$	2001.78	0.268115
$383$	−10935.0	−1.45888	−0.729440	−	0.684044i	$-0.760219\pi$
$383$	−10935.0	−1.45888	−0.729440	+	0.684044i	$0.760219\pi$
$384$	−2547.84	−0.338591
$385$	−2973.67	−0.393642
$386$	−1922.94	−0.253562
$387$	1553.44	0.204046
$388$	−2614.11	−0.342040
$389$	4473.73	0.583102	0.291551	−	0.956555i	$-0.405829\pi$
$389$	4473.73	0.583102	0.291551	+	0.956555i	$0.405829\pi$
$390$	−907.591	−0.117840
$391$	9902.71	1.28082
$392$	−23.5662	−0.00303641
$393$	−1628.43	−0.209017
$394$	52.5215	0.00671573
$395$	−1110.70	−0.141482
$396$	−772.736	−0.0980592
$397$	−10954.7	−1.38489	−0.692447	−	0.721469i	$-0.743467\pi$
$397$	−10954.7	−1.38489	−0.692447	+	0.721469i	$0.743467\pi$
$398$	494.193	0.0622404
$399$	−5852.20	−0.734277
$400$	5353.89	0.669237
$401$	13351.4	1.66268	0.831342	−	0.555762i	$-0.187573\pi$
$401$	13351.4	1.66268	0.831342	+	0.555762i	$0.187573\pi$
$402$	449.791	0.0558049
$403$	1479.83	0.182917
$404$	−4645.98	−0.572144
$405$	1188.20	0.145782
$406$	−1262.99	−0.154387
$407$	682.696	0.0831450
$408$	−1094.81	−0.132847
$409$	5789.51	0.699933	0.349967	−	0.936762i	$-0.386193\pi$
$409$	5789.51	0.699933	0.349967	+	0.936762i	$0.386193\pi$
$410$	201.729	0.0242992
$411$	−4424.32	−0.530987
$412$	−13256.9	−1.58525
$413$	4989.83	0.594512
$414$	−751.104	−0.0891660
$415$	−11418.6	−1.35065
$416$	3832.11	0.451645
$417$	7079.84	0.831418
$418$	513.632	0.0601018
$419$	−4253.48	−0.495934	−0.247967	−	0.968768i	$-0.579762\pi$
$419$	−4253.48	−0.495934	−0.247967	+	0.968768i	$0.579762\pi$
$420$	−6330.19	−0.735432
$421$	2071.18	0.239770	0.119885	−	0.992788i	$-0.461747\pi$
$421$	2071.18	0.239770	0.119885	+	0.992788i	$0.461747\pi$
$422$	1635.53	0.188664
$423$	1229.81	0.141360
$424$	2563.62	0.293633
$425$	4720.35	0.538755
$426$	798.520	0.0908179
$427$	1124.16	0.127404
$428$	−194.467	−0.0219624
$429$	1542.84	0.173634
$430$	−1116.90	−0.125260
$431$	−3522.85	−0.393712	−0.196856	−	0.980432i	$-0.563073\pi$
$431$	−3522.85	−0.393712	−0.196856	+	0.980432i	$0.563073\pi$
$432$	−1602.93	−0.178521
$433$	−10378.0	−1.15182	−0.575909	−	0.817514i	$-0.695352\pi$
$433$	−10378.0	−1.15182	−0.575909	+	0.817514i	$0.695352\pi$
$434$	−257.312	−0.0284593
$435$	6837.07	0.753592
$436$	−4634.25	−0.509037
$437$	−20026.3	−2.19219
$438$	206.732	0.0225526
$439$	−8422.81	−0.915714	−0.457857	−	0.889026i	$-0.651383\pi$
$439$	−8422.81	−0.915714	−0.457857	+	0.889026i	$0.651383\pi$
$440$	1125.02	0.121894
$441$	−30.4206	−0.00328481
$442$	1079.50	0.116168
$443$	−10629.9	−1.14005	−0.570026	−	0.821627i	$-0.693067\pi$
$443$	−10629.9	−1.14005	−0.570026	+	0.821627i	$0.693067\pi$
$444$	1453.29	0.155338
$445$	−16979.9	−1.80882
$446$	1054.42	0.111946
$447$	4347.18	0.459988
$448$	8086.28	0.852770
$449$	6887.21	0.723892	0.361946	−	0.932199i	$-0.382113\pi$
$449$	6887.21	0.723892	0.361946	+	0.932199i	$0.382113\pi$
$450$	−358.030	−0.0375060
$451$	−342.926	−0.0358043
$452$	−5555.29	−0.578095
$453$	−2017.78	−0.209280
$454$	−265.561	−0.0274525
$455$	12638.8	1.30224
$456$	2214.05	0.227373
$457$	13868.7	1.41959	0.709793	−	0.704410i	$-0.248788\pi$
$457$	13868.7	1.41959	0.709793	+	0.704410i	$0.248788\pi$
$458$	−756.893	−0.0772211
$459$	−1413.25	−0.143714
$460$	−21662.0	−2.19564
$461$	9223.51	0.931848	0.465924	−	0.884825i	$-0.345722\pi$
$461$	9223.51	0.931848	0.465924	+	0.884825i	$0.345722\pi$
$462$	−268.268	−0.0270151
$463$	162.321	0.0162931	0.00814655	−	0.999967i	$-0.497407\pi$
$463$	162.321	0.0162931	0.00814655	+	0.999967i	$0.497407\pi$
$464$	−9223.52	−0.922826
$465$	1392.93	0.138915
$466$	−837.523	−0.0832564
$467$	−1222.94	−0.121180	−0.0605899	−	0.998163i	$-0.519298\pi$
$467$	−1222.94	−0.121180	−0.0605899	+	0.998163i	$0.519298\pi$
$468$	3284.33	0.324397
$469$	−6263.66	−0.616693
$470$	−884.213	−0.0867781
$471$	−6725.35	−0.657936
$472$	−1887.79	−0.184094
$473$	1898.65	0.184567
$474$	−100.202	−0.00970974
$475$	−9545.98	−0.922104
$476$	7529.18	0.724999
$477$	3309.27	0.317654
$478$	1629.91	0.155963
$479$	−2630.96	−0.250963	−0.125482	−	0.992096i	$-0.540048\pi$
$479$	−2630.96	−0.250963	−0.125482	+	0.992096i	$0.540048\pi$
$480$	3607.06	0.342998
$481$	−2901.64	−0.275059
$482$	757.293	0.0715638
$483$	10459.6	0.985363
$484$	−944.455	−0.0886979
$485$	4912.82	0.459958
$486$	107.193	0.0100048
$487$	1004.90	0.0935040	0.0467520	−	0.998907i	$-0.485113\pi$
$487$	1004.90	0.0935040	0.0467520	+	0.998907i	$0.485113\pi$
$488$	−425.299	−0.0394516
$489$	3346.32	0.309459
$490$	21.8719	0.00201647
$491$	4605.80	0.423333	0.211667	−	0.977342i	$-0.432111\pi$
$491$	4605.80	0.423333	0.211667	+	0.977342i	$0.432111\pi$
$492$	−730.003	−0.0668924
$493$	−8132.07	−0.742901
$494$	−2183.07	−0.198828
$495$	1452.24	0.131865
$496$	−1879.12	−0.170111
$497$	−11120.0	−1.00362
$498$	−1030.13	−0.0926930
$499$	10410.2	0.933916	0.466958	−	0.884279i	$-0.345350\pi$
$499$	10410.2	0.933916	0.466958	+	0.884279i	$0.345350\pi$
$500$	3986.61	0.356574
$501$	8490.07	0.757103
$502$	2517.29	0.223809
$503$	−14450.2	−1.28092	−0.640459	−	0.767993i	$-0.721256\pi$
$503$	−14450.2	−1.28092	−0.640459	+	0.767993i	$0.721256\pi$
$504$	−1156.39	−0.102202
$505$	8731.42	0.769392
$506$	−918.015	−0.0806537
$507$	33.5203	0.00293627
$508$	8614.13	0.752343
$509$	2612.27	0.227479	0.113739	−	0.993511i	$-0.463717\pi$
$509$	2612.27	0.227479	0.113739	+	0.993511i	$0.463717\pi$
$510$	1016.10	0.0882231
$511$	−2878.89	−0.249227
$512$	−8177.44	−0.705850
$513$	2858.02	0.245974
$514$	792.266	0.0679871
$515$	24914.4	2.13177
$516$	4041.76	0.344823
$517$	1503.10	0.127865
$518$	504.533	0.0427952
$519$	−735.878	−0.0622379
$520$	−4781.62	−0.403246
$521$	8943.43	0.752052	0.376026	−	0.926609i	$-0.377290\pi$
$521$	8943.43	0.752052	0.376026	+	0.926609i	$0.377290\pi$
$522$	616.804	0.0517179
$523$	−6909.11	−0.577656	−0.288828	−	0.957381i	$-0.593266\pi$
$523$	−6909.11	−0.577656	−0.288828	+	0.957381i	$0.593266\pi$
$524$	−4236.87	−0.353222
$525$	4985.82	0.414475
$526$	1583.01	0.131222
$527$	−1656.76	−0.136944
$528$	−1959.14	−0.161478
$529$	23626.0	1.94181
$530$	−2379.31	−0.195001
$531$	−2436.87	−0.199155
$532$	−15226.3	−1.24087
$533$	1457.52	0.118447
$534$	−1531.84	−0.124137
$535$	365.471	0.0295340
$536$	2369.71	0.190963
$537$	−1147.70	−0.0922289
$538$	1523.39	0.122078
$539$	−37.1807	−0.00297122
$540$	3091.45	0.246361
$541$	5676.22	0.451090	0.225545	−	0.974233i	$-0.427584\pi$
$541$	5676.22	0.451090	0.225545	+	0.974233i	$0.427584\pi$
$542$	777.940	0.0616520
$543$	−1652.58	−0.130606
$544$	−4290.27	−0.338132
$545$	8709.36	0.684529
$546$	1140.21	0.0893707
$547$	−13221.7	−1.03349	−0.516745	−	0.856139i	$-0.672856\pi$
$547$	−13221.7	−1.03349	−0.516745	+	0.856139i	$0.672856\pi$
$548$	−11511.2	−0.897326
$549$	−549.000	−0.0426790
$550$	−437.593	−0.0339255
$551$	16445.5	1.27151
$552$	−3957.17	−0.305124
$553$	1395.38	0.107301
$554$	1801.96	0.138191
$555$	−2731.23	−0.208891
$556$	18420.4	1.40503
$557$	10129.9	0.770587	0.385293	−	0.922794i	$-0.374100\pi$
$557$	10129.9	0.770587	0.385293	+	0.922794i	$0.374100\pi$
$558$	125.662	0.00953353
$559$	−8069.77	−0.610581
$560$	−16049.1	−1.21107
$561$	−1727.31	−0.129994
$562$	1288.23	0.0966915
$563$	6638.51	0.496944	0.248472	−	0.968639i	$-0.420072\pi$
$563$	6638.51	0.496944	0.248472	+	0.968639i	$0.420072\pi$
$564$	3199.73	0.238888
$565$	10440.3	0.777394
$566$	2711.24	0.201346
$567$	−1492.73	−0.110562
$568$	4206.98	0.310776
$569$	−413.983	−0.0305010	−0.0152505	−	0.999884i	$-0.504855\pi$
$569$	−413.983	−0.0305010	−0.0152505	+	0.999884i	$0.504855\pi$
$570$	−2054.87	−0.150998
$571$	−8506.03	−0.623409	−0.311704	−	0.950179i	$-0.600900\pi$
$571$	−8506.03	−0.623409	−0.311704	+	0.950179i	$0.600900\pi$
$572$	4014.18	0.293429
$573$	13613.8	0.992537
$574$	−253.432	−0.0184287
$575$	17061.5	1.23742
$576$	−3949.07	−0.285668
$577$	−21387.5	−1.54311	−0.771554	−	0.636164i	$-0.780520\pi$
$577$	−21387.5	−1.54311	−0.771554	+	0.636164i	$0.780520\pi$
$578$	958.669	0.0689885
$579$	−13077.6	−0.938664
$580$	17788.7	1.27351
$581$	14345.2	1.02434
$582$	443.208	0.0315663
$583$	4044.66	0.287329
$584$	1089.16	0.0771745
$585$	−6172.39	−0.436234
$586$	2245.51	0.158295
$587$	10663.9	0.749821	0.374910	−	0.927061i	$-0.377674\pi$
$587$	10663.9	0.749821	0.374910	+	0.927061i	$0.377674\pi$
$588$	−79.1485	−0.00555107
$589$	3350.47	0.234387
$590$	1752.07	0.122257
$591$	357.191	0.0248610
$592$	3684.56	0.255801
$593$	23176.1	1.60494	0.802469	−	0.596693i	$-0.203519\pi$
$593$	23176.1	1.60494	0.802469	+	0.596693i	$0.203519\pi$
$594$	131.013	0.00904972
$595$	−14149.9	−0.974943
$596$	11310.5	0.777343
$597$	3360.93	0.230408
$598$	3901.80	0.266817
$599$	25077.5	1.71058	0.855290	−	0.518150i	$-0.173379\pi$
$599$	25077.5	1.71058	0.855290	+	0.518150i	$0.173379\pi$
$600$	−1886.27	−0.128345
$601$	−1582.28	−0.107392	−0.0536960	−	0.998557i	$-0.517100\pi$
$601$	−1582.28	−0.107392	−0.0536960	+	0.998557i	$0.517100\pi$
$602$	1403.16	0.0949977
$603$	3058.96	0.206585
$604$	−5249.88	−0.353667
$605$	1774.96	0.119277
$606$	787.701	0.0528023
$607$	12966.5	0.867042	0.433521	−	0.901144i	$-0.357271\pi$
$607$	12966.5	0.867042	0.433521	+	0.901144i	$0.357271\pi$
$608$	8676.23	0.578729
$609$	−8589.42	−0.571529
$610$	394.722	0.0261997
$611$	−6388.57	−0.423001
$612$	−3677.00	−0.242866
$613$	−13316.9	−0.877430	−0.438715	−	0.898626i	$-0.644566\pi$
$613$	−13316.9	−0.877430	−0.438715	+	0.898626i	$0.644566\pi$
$614$	2498.58	0.164226
$615$	1371.93	0.0899536
$616$	−1413.36	−0.0924448
$617$	1145.96	0.0747725	0.0373862	−	0.999301i	$-0.488097\pi$
$617$	1145.96	0.0747725	0.0373862	+	0.999301i	$0.488097\pi$
$618$	2247.64	0.146300
$619$	5105.68	0.331526	0.165763	−	0.986166i	$-0.446991\pi$
$619$	5105.68	0.331526	0.165763	+	0.986166i	$0.446991\pi$
$620$	3624.12	0.234755
$621$	−5108.14	−0.330085
$622$	917.412	0.0591397
$623$	21331.9	1.37182
$624$	8326.83	0.534199
$625$	−18765.0	−1.20096
$626$	640.445	0.0408903
$627$	3493.13	0.222492
$628$	−17498.0	−1.11186
$629$	3248.55	0.205927
$630$	1073.25	0.0678718
$631$	16173.1	1.02035	0.510176	−	0.860070i	$-0.329580\pi$
$631$	16173.1	1.02035	0.510176	+	0.860070i	$0.329580\pi$
$632$	−527.909	−0.0332264
$633$	11123.0	0.698417
$634$	1880.91	0.117824
$635$	−16188.9	−1.01171
$636$	8610.07	0.536810
$637$	158.028	0.00982933
$638$	753.871	0.0467806
$639$	5430.61	0.336200
$640$	12458.1	0.769456
$641$	5164.68	0.318241	0.159121	−	0.987259i	$-0.449134\pi$
$641$	5164.68	0.318241	0.159121	+	0.987259i	$0.449134\pi$
$642$	32.9708	0.00202687
$643$	17146.2	1.05160	0.525802	−	0.850607i	$-0.323765\pi$
$643$	17146.2	1.05160	0.525802	+	0.850607i	$0.323765\pi$
$644$	27213.9	1.66519
$645$	−7595.86	−0.463701
$646$	2444.08	0.148856
$647$	−28557.4	−1.73525	−0.867626	−	0.497217i	$-0.834355\pi$
$647$	−28557.4	−1.73525	−0.867626	+	0.497217i	$0.834355\pi$
$648$	564.741	0.0342363
$649$	−2978.39	−0.180142
$650$	1859.88	0.112232
$651$	−1749.94	−0.105354
$652$	8706.46	0.522962
$653$	1641.69	0.0983835	0.0491917	−	0.998789i	$-0.484335\pi$
$653$	1641.69	0.0983835	0.0491917	+	0.998789i	$0.484335\pi$
$654$	785.711	0.0469782
$655$	7962.54	0.474996
$656$	−1850.79	−0.110154
$657$	1405.96	0.0834879
$658$	1110.84	0.0658130
$659$	−12827.9	−0.758276	−0.379138	−	0.925340i	$-0.623779\pi$
$659$	−12827.9	−0.758276	−0.379138	+	0.925340i	$0.623779\pi$
$660$	3778.44	0.222842
$661$	−4562.74	−0.268487	−0.134243	−	0.990948i	$-0.542860\pi$
$661$	−4562.74	−0.268487	−0.134243	+	0.990948i	$0.542860\pi$
$662$	−412.019	−0.0241897
$663$	7341.49	0.430045
$664$	−5427.20	−0.317193
$665$	28615.5	1.66866
$666$	−246.397	−0.0143359
$667$	−29393.1	−1.70630
$668$	22089.5	1.27944
$669$	7170.92	0.414415
$670$	−2199.34	−0.126818
$671$	−671.000	−0.0386046
$672$	−4531.56	−0.260132
$673$	27540.7	1.57744	0.788720	−	0.614752i	$-0.210744\pi$
$673$	27540.7	1.57744	0.788720	+	0.614752i	$0.210744\pi$
$674$	−3118.39	−0.178213
$675$	−2434.91	−0.138844
$676$	87.2133	0.00496207
$677$	−2140.68	−0.121526	−0.0607630	−	0.998152i	$-0.519353\pi$
$677$	−2140.68	−0.121526	−0.0607630	+	0.998152i	$0.519353\pi$
$678$	941.868	0.0533514
$679$	−6171.98	−0.348835
$680$	5353.31	0.301897
$681$	−1806.04	−0.101627
$682$	153.587	0.00862340
$683$	−1596.41	−0.0894362	−0.0447181	−	0.999000i	$-0.514239\pi$
$683$	−1596.41	−0.0894362	−0.0447181	+	0.999000i	$0.514239\pi$
$684$	7436.00	0.415676
$685$	21633.6	1.20668
$686$	−2815.84	−0.156719
$687$	−5147.51	−0.285866
$688$	10247.2	0.567833
$689$	−17190.8	−0.950536
$690$	3672.67	0.202632
$691$	−25240.9	−1.38959	−0.694796	−	0.719207i	$-0.744505\pi$
$691$	−25240.9	−1.38959	−0.694796	+	0.719207i	$0.744505\pi$
$692$	−1914.61	−0.105177
$693$	−1824.45	−0.100007
$694$	4744.01	0.259481
$695$	−34618.2	−1.88942
$696$	3249.61	0.176977
$697$	−1631.78	−0.0886775
$698$	4066.72	0.220527
$699$	−5695.87	−0.308208
$700$	12972.1	0.700430
$701$	20781.5	1.11969	0.559846	−	0.828596i	$-0.310860\pi$
$701$	20781.5	1.11969	0.559846	+	0.828596i	$0.310860\pi$
$702$	−556.839	−0.0299381
$703$	−6569.56	−0.352455
$704$	−4826.64	−0.258396
$705$	−6013.40	−0.321245
$706$	−3160.18	−0.168463
$707$	−10969.3	−0.583511
$708$	−6340.25	−0.336555
$709$	7145.20	0.378482	0.189241	−	0.981931i	$-0.439397\pi$
$709$	7145.20	0.378482	0.189241	+	0.981931i	$0.439397\pi$
$710$	−3904.52	−0.206386
$711$	−681.456	−0.0359446
$712$	−8070.43	−0.424793
$713$	−5988.30	−0.314535
$714$	−1276.53	−0.0669089
$715$	−7544.03	−0.394588
$716$	−2986.09	−0.155860
$717$	11084.7	0.577360
$718$	−2093.68	−0.108824
$719$	−29010.9	−1.50476	−0.752381	−	0.658729i	$-0.771095\pi$
$719$	−29010.9	−1.50476	−0.752381	+	0.658729i	$0.771095\pi$
$720$	7837.83	0.405693
$721$	−31300.0	−1.61674
$722$	−1917.01	−0.0988138
$723$	5150.24	0.264923
$724$	−4299.68	−0.220713
$725$	−14010.9	−0.717725
$726$	160.127	0.00818578
$727$	2196.47	0.112053	0.0560266	−	0.998429i	$-0.482157\pi$
$727$	2196.47	0.112053	0.0560266	+	0.998429i	$0.482157\pi$
$728$	6007.15	0.305824
$729$	729.000	0.0370370
$730$	−1010.86	−0.0512514
$731$	9034.59	0.457122
$732$	−1428.39	−0.0721241
$733$	−17336.7	−0.873596	−0.436798	−	0.899560i	$-0.643888\pi$
$733$	−17336.7	−0.873596	−0.436798	+	0.899560i	$0.643888\pi$
$734$	4470.78	0.224822
$735$	148.747	0.00746481
$736$	−15507.0	−0.776626
$737$	3738.73	0.186863
$738$	123.768	0.00617339
$739$	−2793.38	−0.139048	−0.0695238	−	0.997580i	$-0.522148\pi$
$739$	−2793.38	−0.139048	−0.0695238	+	0.997580i	$0.522148\pi$
$740$	−7106.14	−0.353009
$741$	−14846.7	−0.736043
$742$	2989.13	0.147890
$743$	−16114.9	−0.795690	−0.397845	−	0.917453i	$-0.630242\pi$
$743$	−16114.9	−0.795690	−0.397845	+	0.917453i	$0.630242\pi$
$744$	662.048	0.0326235
$745$	−21256.4	−1.04533
$746$	5712.36	0.280354
$747$	−7005.74	−0.343141
$748$	−4494.11	−0.219680
$749$	−459.141	−0.0223987
$750$	−675.908	−0.0329076
$751$	−17105.7	−0.831152	−0.415576	−	0.909558i	$-0.636420\pi$
$751$	−17105.7	−0.831152	−0.415576	+	0.909558i	$0.636420\pi$
$752$	8112.34	0.393387
$753$	17119.7	0.828522
$754$	−3204.15	−0.154759
$755$	9866.35	0.475594
$756$	−3883.79	−0.186842
$757$	−20059.7	−0.963120	−0.481560	−	0.876413i	$-0.659930\pi$
$757$	−20059.7	−0.963120	−0.481560	+	0.876413i	$0.659930\pi$
$758$	−715.586	−0.0342893
$759$	−6243.28	−0.298573
$760$	−10826.0	−0.516711
$761$	38367.3	1.82761	0.913806	−	0.406151i	$-0.133129\pi$
$761$	38367.3	1.82761	0.913806	+	0.406151i	$0.133129\pi$
$762$	−1460.48	−0.0694325
$763$	−10941.6	−0.519151
$764$	35420.4	1.67731
$765$	6910.36	0.326594
$766$	4823.65	0.227527
$767$	12658.9	0.595942
$768$	−9406.94	−0.441984
$769$	17967.7	0.842563	0.421282	−	0.906930i	$-0.361580\pi$
$769$	17967.7	0.842563	0.421282	+	0.906930i	$0.361580\pi$
$770$	1311.75	0.0613923
$771$	5388.08	0.251682
$772$	−34025.3	−1.58627
$773$	1365.70	0.0635455	0.0317727	−	0.999495i	$-0.489885\pi$
$773$	1365.70	0.0635455	0.0317727	+	0.999495i	$0.489885\pi$
$774$	−685.258	−0.0318231
$775$	−2854.46	−0.132303
$776$	2335.03	0.108019
$777$	3431.25	0.158424
$778$	−1973.46	−0.0909407
$779$	3299.96	0.151776
$780$	−16059.3	−0.737201
$781$	6637.42	0.304104
$782$	−4368.30	−0.199757
$783$	4194.79	0.191455
$784$	−200.667	−0.00914117
$785$	32884.9	1.49518
$786$	718.337	0.0325983
$787$	−18459.5	−0.836101	−0.418050	−	0.908424i	$-0.637286\pi$
$787$	−18459.5	−0.836101	−0.418050	+	0.908424i	$0.637286\pi$
$788$	929.341	0.0420132
$789$	10765.8	0.485771
$790$	489.955	0.0220656
$791$	−13116.2	−0.589580
$792$	690.239	0.0309679
$793$	2851.92	0.127711
$794$	4832.38	0.215988
$795$	−16181.3	−0.721876
$796$	8744.49	0.389372
$797$	−34090.7	−1.51513	−0.757563	−	0.652762i	$-0.773610\pi$
$797$	−34090.7	−1.51513	−0.757563	+	0.652762i	$0.773610\pi$
$798$	2581.53	0.114518
$799$	7152.38	0.316687
$800$	−7391.78	−0.326674
$801$	−10417.8	−0.459543
$802$	−5889.58	−0.259312
$803$	1718.39	0.0755176
$804$	7958.82	0.349112
$805$	−51144.4	−2.23926
$806$	−652.786	−0.0285278
$807$	10360.3	0.451921
$808$	4149.98	0.180688
$809$	−13966.9	−0.606983	−0.303491	−	0.952834i	$-0.598152\pi$
$809$	−13966.9	−0.606983	−0.303491	+	0.952834i	$0.598152\pi$
$810$	−524.139	−0.0227362
$811$	7306.81	0.316371	0.158185	−	0.987409i	$-0.449436\pi$
$811$	7306.81	0.316371	0.158185	+	0.987409i	$0.449436\pi$
$812$	−22348.0	−0.965838
$813$	5290.65	0.228230
$814$	−301.152	−0.0129673
$815$	−16362.5	−0.703254
$816$	−9322.38	−0.399937
$817$	−18270.7	−0.782386
$818$	−2553.88	−0.109162
$819$	7754.38	0.330842
$820$	3569.49	0.152015
$821$	−36254.1	−1.54114	−0.770570	−	0.637356i	$-0.780028\pi$
$821$	−36254.1	−1.54114	−0.770570	+	0.637356i	$0.780028\pi$
$822$	1951.66	0.0828127
$823$	8429.98	0.357048	0.178524	−	0.983936i	$-0.442868\pi$
$823$	8429.98	0.357048	0.178524	+	0.983936i	$0.442868\pi$
$824$	11841.6	0.500634
$825$	−2976.00	−0.125589
$826$	−2201.12	−0.0927202
$827$	41886.6	1.76123	0.880617	−	0.473829i	$-0.157129\pi$
$827$	41886.6	1.76123	0.880617	+	0.473829i	$0.157129\pi$
$828$	−13290.4	−0.557817
$829$	−16666.4	−0.698247	−0.349124	−	0.937077i	$-0.613521\pi$
$829$	−16666.4	−0.698247	−0.349124	+	0.937077i	$0.613521\pi$
$830$	5037.01	0.210647
$831$	12254.8	0.511571
$832$	20514.5	0.854821
$833$	−176.921	−0.00735890
$834$	−3123.07	−0.129668
$835$	−41513.9	−1.72053
$836$	9088.45	0.375993
$837$	854.610	0.0352923
$838$	1876.30	0.0773458
$839$	11084.3	0.456106	0.228053	−	0.973649i	$-0.426764\pi$
$839$	11084.3	0.456106	0.228053	+	0.973649i	$0.426764\pi$
$840$	5654.38	0.232255
$841$	−251.500	−0.0103120
$842$	−913.644	−0.0373946
$843$	8761.04	0.357943
$844$	28939.8	1.18027
$845$	−163.904	−0.00667275
$846$	−542.496	−0.0220466
$847$	−2229.88	−0.0904601
$848$	21829.3	0.883988
$849$	18438.8	0.745367
$850$	−2082.25	−0.0840242
$851$	11741.8	0.472977
$852$	14129.4	0.568151
$853$	32841.7	1.31826	0.659132	−	0.752027i	$-0.270924\pi$
$853$	32841.7	1.31826	0.659132	+	0.752027i	$0.270924\pi$
$854$	−495.889	−0.0198700
$855$	−13974.8	−0.558981
$856$	173.706	0.00693591
$857$	−31194.0	−1.24337	−0.621684	−	0.783268i	$-0.713551\pi$
$857$	−31194.0	−1.24337	−0.621684	+	0.783268i	$0.713551\pi$
$858$	−680.581	−0.0270800
$859$	−48108.7	−1.91088	−0.955441	−	0.295183i	$-0.904620\pi$
$859$	−48108.7	−1.91088	−0.955441	+	0.295183i	$0.904620\pi$
$860$	−19762.9	−0.783617
$861$	−1723.56	−0.0682214
$862$	1554.00	0.0614033
$863$	−43731.2	−1.72494	−0.862472	−	0.506105i	$-0.831085\pi$
$863$	−43731.2	−1.72494	−0.862472	+	0.506105i	$0.831085\pi$
$864$	2213.06	0.0871411
$865$	3598.22	0.141437
$866$	4577.98	0.179638
$867$	6519.76	0.255390
$868$	−4552.99	−0.178040
$869$	−832.891	−0.0325131
$870$	−3015.98	−0.117530
$871$	−15890.6	−0.618176
$872$	4139.50	0.160758
$873$	3014.19	0.116856
$874$	8834.02	0.341894
$875$	9412.50	0.363658
$876$	3658.02	0.141088
$877$	14365.7	0.553129	0.276564	−	0.960995i	$-0.410804\pi$
$877$	14365.7	0.553129	0.276564	+	0.960995i	$0.410804\pi$
$878$	3715.48	0.142815
$879$	15271.4	0.585996
$880$	9579.57	0.366963
$881$	30216.5	1.15553	0.577764	−	0.816204i	$-0.303926\pi$
$881$	30216.5	1.15553	0.577764	+	0.816204i	$0.303926\pi$
$882$	13.4192	0.000512299 0
$883$	32387.3	1.23434	0.617168	−	0.786831i	$-0.288280\pi$
$883$	32387.3	1.23434	0.617168	+	0.786831i	$0.288280\pi$
$884$	19101.1	0.726742
$885$	11915.5	0.452583
$886$	4689.09	0.177802
$887$	43689.8	1.65384	0.826921	−	0.562318i	$-0.190090\pi$
$887$	43689.8	1.65384	0.826921	+	0.562318i	$0.190090\pi$
$888$	−1298.14	−0.0490570
$889$	20338.2	0.767290
$890$	7490.21	0.282104
$891$	891.000	0.0335013
$892$	18657.3	0.700329
$893$	−14464.3	−0.542025
$894$	−1917.64	−0.0717397
$895$	5611.90	0.209592
$896$	−15651.2	−0.583560
$897$	26535.6	0.987733
$898$	−3038.10	−0.112898
$899$	4917.57	0.182436
$900$	−6335.16	−0.234636
$901$	19246.2	0.711635
$902$	151.272	0.00558404
$903$	9542.69	0.351673
$904$	4962.21	0.182567
$905$	8080.59	0.296804
$906$	890.088	0.0326393
$907$	28031.8	1.02622	0.513110	−	0.858323i	$-0.328493\pi$
$907$	28031.8	1.02622	0.513110	+	0.858323i	$0.328493\pi$
$908$	−4698.97	−0.171741
$909$	5357.03	0.195469
$910$	−5575.26	−0.203097
$911$	−3678.23	−0.133771	−0.0668854	−	0.997761i	$-0.521306\pi$
$911$	−3678.23	−0.133771	−0.0668854	+	0.997761i	$0.521306\pi$
$912$	18852.7	0.684512
$913$	−8562.57	−0.310383
$914$	−6117.79	−0.221399
$915$	2684.44	0.0969890
$916$	−13392.8	−0.483091
$917$	−10003.4	−0.360240
$918$	623.415	0.0224137
$919$	32406.9	1.16323	0.581614	−	0.813465i	$-0.302421\pi$
$919$	32406.9	1.16323	0.581614	+	0.813465i	$0.302421\pi$
$920$	19349.3	0.693401
$921$	16992.5	0.607949
$922$	−4068.69	−0.145331
$923$	−28210.7	−1.00603
$924$	−4746.86	−0.169005
$925$	5596.98	0.198949
$926$	−71.6034	−0.00254107
$927$	15285.9	0.541590
$928$	12734.3	0.450458
$929$	−2852.57	−0.100742	−0.0503712	−	0.998731i	$-0.516040\pi$
$929$	−2852.57	−0.100742	−0.0503712	+	0.998731i	$0.516040\pi$
$930$	−614.450	−0.0216652
$931$	357.789	0.0125951
$932$	−14819.5	−0.520847
$933$	6239.18	0.218930
$934$	539.465	0.0188992
$935$	8445.99	0.295415
$936$	−2933.69	−0.102447
$937$	−12027.4	−0.419338	−0.209669	−	0.977772i	$-0.567239\pi$
$937$	−12027.4	−0.419338	−0.209669	+	0.977772i	$0.567239\pi$
$938$	2763.04	0.0961794
$939$	4355.57	0.151372
$940$	−15645.7	−0.542878
$941$	−17764.1	−0.615401	−0.307700	−	0.951483i	$-0.599559\pi$
$941$	−17764.1	−0.615401	−0.307700	+	0.951483i	$0.599559\pi$
$942$	2966.70	0.102612
$943$	−5898.02	−0.203676
$944$	−16074.6	−0.554220
$945$	7299.00	0.251255
$946$	−837.537	−0.0287851
$947$	26969.7	0.925448	0.462724	−	0.886502i	$-0.346872\pi$
$947$	26969.7	0.925448	0.462724	+	0.886502i	$0.346872\pi$
$948$	−1773.02	−0.0607435
$949$	−7303.60	−0.249826
$950$	4210.94	0.143811
$951$	12791.8	0.436174
$952$	−6725.36	−0.228960
$953$	−16986.1	−0.577371	−0.288686	−	0.957424i	$-0.593218\pi$
$953$	−16986.1	−0.577371	−0.288686	+	0.957424i	$0.593218\pi$
$954$	−1459.79	−0.0495413
$955$	−66567.2	−2.25556
$956$	28840.3	0.975694
$957$	5126.96	0.173178
$958$	1160.57	0.0391402
$959$	−27178.3	−0.915153
$960$	19309.7	0.649186
$961$	−28789.1	−0.966370
$962$	1279.97	0.0428981
$963$	224.229	0.00750331
$964$	13399.9	0.447699
$965$	63945.4	2.13314
$966$	−4613.97	−0.153677
$967$	21932.1	0.729357	0.364679	−	0.931133i	$-0.381179\pi$
$967$	21932.1	0.729357	0.364679	+	0.931133i	$0.381179\pi$
$968$	843.625	0.0280115
$969$	16621.8	0.551051
$970$	−2167.15	−0.0717351
$971$	−14856.3	−0.491002	−0.245501	−	0.969396i	$-0.578952\pi$
$971$	−14856.3	−0.491002	−0.245501	+	0.969396i	$0.578952\pi$
$972$	1896.72	0.0625897
$973$	43490.9	1.43294
$974$	−443.284	−0.0145829
$975$	12648.8	0.415472
$976$	−3621.43	−0.118770
$977$	−11011.2	−0.360573	−0.180287	−	0.983614i	$-0.557703\pi$
$977$	−11011.2	−0.360573	−0.180287	+	0.983614i	$0.557703\pi$
$978$	−1476.13	−0.0482633
$979$	−12732.8	−0.415673
$980$	387.012	0.0126149
$981$	5343.50	0.173909
$982$	−2031.72	−0.0660231
$983$	−27944.8	−0.906714	−0.453357	−	0.891329i	$-0.649774\pi$
$983$	−27944.8	−0.906714	−0.453357	+	0.891329i	$0.649774\pi$
$984$	652.068	0.0211252
$985$	−1746.55	−0.0564973
$986$	3587.23	0.115863
$987$	7554.64	0.243634
$988$	−38628.2	−1.24385
$989$	32655.2	1.04992
$990$	−640.614	−0.0205657
$991$	−31724.8	−1.01692	−0.508461	−	0.861085i	$-0.669786\pi$
$991$	−31724.8	−1.01692	−0.508461	+	0.861085i	$0.669786\pi$
$992$	2594.38	0.0830360
$993$	−2802.08	−0.0895481
$994$	4905.25	0.156524
$995$	−16433.9	−0.523609
$996$	−18227.6	−0.579882
$997$	52317.1	1.66188	0.830942	−	0.556360i	$-0.187802\pi$
$997$	52317.1	1.66188	0.830942	+	0.556360i	$0.187802\pi$
$998$	−4592.16	−0.145654
$999$	−1675.71	−0.0530702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.d.1.18	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.d.1.18	✓	37	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)

\(f(q)\)	\(=\)	\(q-0.441122 q^{2} -3.00000 q^{3} -7.80541 q^{4} +14.6691 q^{5} +1.32336 q^{6} -18.4288 q^{7} +6.97211 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.441122 q^{2} -3.00000 q^{3} -7.80541 q^{4} +14.6691 q^{5} +1.32336 q^{6} -18.4288 q^{7} +6.97211 q^{8} +9.00000 q^{9} -6.47085 q^{10} +11.0000 q^{11} +23.4162 q^{12} -46.7528 q^{13} +8.12933 q^{14} -44.0072 q^{15} +59.3677 q^{16} +52.3426 q^{17} -3.97009 q^{18} -105.853 q^{19} -114.498 q^{20} +55.2863 q^{21} -4.85234 q^{22} +189.190 q^{23} -20.9163 q^{24} +90.1819 q^{25} +20.6237 q^{26} -27.0000 q^{27} +143.844 q^{28} -155.362 q^{29} +19.4125 q^{30} -31.6522 q^{31} -81.9652 q^{32} -33.0000 q^{33} -23.0894 q^{34} -270.333 q^{35} -70.2487 q^{36} +62.0633 q^{37} +46.6938 q^{38} +140.258 q^{39} +102.274 q^{40} -31.1751 q^{41} -24.3880 q^{42} +172.605 q^{43} -85.8595 q^{44} +132.022 q^{45} -83.4560 q^{46} +136.646 q^{47} -178.103 q^{48} -3.38007 q^{49} -39.7812 q^{50} -157.028 q^{51} +364.925 q^{52} +367.696 q^{53} +11.9103 q^{54} +161.360 q^{55} -128.487 q^{56} +317.558 q^{57} +68.5337 q^{58} -270.763 q^{59} +343.495 q^{60} -61.0000 q^{61} +13.9625 q^{62} -165.859 q^{63} -438.785 q^{64} -685.821 q^{65} +14.5570 q^{66} +339.885 q^{67} -408.555 q^{68} -567.571 q^{69} +119.250 q^{70} +603.402 q^{71} +62.7490 q^{72} +156.217 q^{73} -27.3775 q^{74} -270.546 q^{75} +826.223 q^{76} -202.717 q^{77} -61.8710 q^{78} -75.7174 q^{79} +870.870 q^{80} +81.0000 q^{81} +13.7520 q^{82} -778.415 q^{83} -431.533 q^{84} +767.817 q^{85} -76.1397 q^{86} +466.087 q^{87} +76.6932 q^{88} -1157.53 q^{89} -58.2376 q^{90} +861.598 q^{91} -1476.71 q^{92} +94.9567 q^{93} -60.2773 q^{94} -1552.76 q^{95} +245.896 q^{96} +334.910 q^{97} +1.49102 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9	\( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 37 * q - 4 * q^2 - 111 * q^3 + 158 * q^4 - 15 * q^5 + 12 * q^6 - 77 * q^7 - 69 * q^8 + 333 * q^9 - 45 * q^10 + 407 * q^11 - 474 * q^12 - 169 * q^13 + 102 * q^14 + 45 * q^15 + 598 * q^16 - 338 * q^17 - 36 * q^18 - 235 * q^19 - 550 * q^20 + 231 * q^21 - 44 * q^22 - 53 * q^23 + 207 * q^24 + 750 * q^25 - 75 * q^26 - 999 * q^27 - 1378 * q^28 - 30 * q^29 + 135 * q^30 - 506 * q^31 - 841 * q^32 - 1221 * q^33 - 316 * q^34 - 822 * q^35 + 1422 * q^36 - 830 * q^37 - 371 * q^38 + 507 * q^39 - 613 * q^40 + 16 * q^41 - 306 * q^42 - 1137 * q^43 + 1738 * q^44 - 135 * q^45 - 659 * q^46 - 489 * q^47 - 1794 * q^48 + 2214 * q^49 + 1066 * q^50 + 1014 * q^51 - 2342 * q^52 + 731 * q^53 + 108 * q^54 - 165 * q^55 + 3051 * q^56 + 705 * q^57 - 611 * q^58 - 425 * q^59 + 1650 * q^60 - 2257 * q^61 + 453 * q^62 - 693 * q^63 + 4919 * q^64 + 1346 * q^65 + 132 * q^66 - 1907 * q^67 - 3236 * q^68 + 159 * q^69 - 1050 * q^70 - 561 * q^71 - 621 * q^72 - 2397 * q^73 - 1840 * q^74 - 2250 * q^75 - 3868 * q^76 - 847 * q^77 + 225 * q^78 + 393 * q^79 - 4031 * q^80 + 2997 * q^81 - 1946 * q^82 - 4191 * q^83 + 4134 * q^84 - 2667 * q^85 + 2405 * q^86 + 90 * q^87 - 759 * q^88 + 1437 * q^89 - 405 * q^90 - 5192 * q^91 - 737 * q^92 + 1518 * q^93 - 1960 * q^94 + 1356 * q^95 + 2523 * q^96 - 2368 * q^97 - 3014 * q^98 + 3663 * q^99

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