LMFDB - Embedded newform 2013.4.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-3.61193 q^{2} +3.00000 q^{3} +5.04607 q^{4} -17.1653 q^{5} -10.8358 q^{6} +13.1780 q^{7} +10.6694 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.61193 q^{2} +3.00000 q^{3} +5.04607 q^{4} -17.1653 q^{5} -10.8358 q^{6} +13.1780 q^{7} +10.6694 q^{8} +9.00000 q^{9} +61.9998 q^{10} -11.0000 q^{11} +15.1382 q^{12} +67.4605 q^{13} -47.5982 q^{14} -51.4958 q^{15} -78.9057 q^{16} -8.59148 q^{17} -32.5074 q^{18} +37.3491 q^{19} -86.6172 q^{20} +39.5341 q^{21} +39.7313 q^{22} -131.887 q^{23} +32.0082 q^{24} +169.646 q^{25} -243.663 q^{26} +27.0000 q^{27} +66.4972 q^{28} -179.912 q^{29} +185.999 q^{30} -18.8728 q^{31} +199.647 q^{32} -33.0000 q^{33} +31.0319 q^{34} -226.204 q^{35} +45.4146 q^{36} +293.053 q^{37} -134.903 q^{38} +202.382 q^{39} -183.143 q^{40} -112.513 q^{41} -142.794 q^{42} -345.273 q^{43} -55.5068 q^{44} -154.487 q^{45} +476.369 q^{46} +53.1694 q^{47} -236.717 q^{48} -169.340 q^{49} -612.752 q^{50} -25.7744 q^{51} +340.411 q^{52} -198.619 q^{53} -97.5222 q^{54} +188.818 q^{55} +140.602 q^{56} +112.047 q^{57} +649.832 q^{58} +160.706 q^{59} -259.851 q^{60} -61.0000 q^{61} +68.1675 q^{62} +118.602 q^{63} -89.8666 q^{64} -1157.98 q^{65} +119.194 q^{66} -479.221 q^{67} -43.3532 q^{68} -395.662 q^{69} +817.035 q^{70} +1014.62 q^{71} +96.0246 q^{72} +765.711 q^{73} -1058.49 q^{74} +508.939 q^{75} +188.466 q^{76} -144.958 q^{77} -730.989 q^{78} +208.056 q^{79} +1354.44 q^{80} +81.0000 q^{81} +406.391 q^{82} +1055.26 q^{83} +199.492 q^{84} +147.475 q^{85} +1247.10 q^{86} -539.737 q^{87} -117.363 q^{88} -320.189 q^{89} +557.998 q^{90} +888.997 q^{91} -665.513 q^{92} -56.6185 q^{93} -192.045 q^{94} -641.108 q^{95} +598.941 q^{96} +888.943 q^{97} +611.644 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * 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 $

$2$	−3.61193	−1.27701	−0.638506	−	0.769617i	$-0.720447\pi$
$2$	−3.61193	−1.27701	−0.638506	+	0.769617i	$0.720447\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	5.04607	0.630759
$5$	−17.1653	−1.53531	−0.767654	−	0.640864i	$-0.778576\pi$
$5$	−17.1653	−1.53531	−0.767654	+	0.640864i	$0.778576\pi$
$6$	−10.8358	−0.737283
$7$	13.1780	0.711546	0.355773	−	0.934572i	$-0.384218\pi$
$7$	13.1780	0.711546	0.355773	+	0.934572i	$0.384218\pi$
$8$	10.6694	0.471525
$9$	9.00000	0.333333
$10$	61.9998	1.96061
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	15.1382	0.364169
$13$	67.4605	1.43924	0.719622	−	0.694366i	$-0.244315\pi$
$13$	67.4605	1.43924	0.719622	+	0.694366i	$0.244315\pi$
$14$	−47.5982	−0.908653
$15$	−51.4958	−0.886411
$16$	−78.9057	−1.23290
$17$	−8.59148	−0.122573	−0.0612865	−	0.998120i	$-0.519520\pi$
$17$	−8.59148	−0.122573	−0.0612865	+	0.998120i	$0.519520\pi$
$18$	−32.5074	−0.425671
$19$	37.3491	0.450972	0.225486	−	0.974246i	$-0.427603\pi$
$19$	37.3491	0.450972	0.225486	+	0.974246i	$0.427603\pi$
$20$	−86.6172	−0.968409
$21$	39.5341	0.410812
$22$	39.7313	0.385034
$23$	−131.887	−1.19567	−0.597835	−	0.801619i	$-0.703972\pi$
$23$	−131.887	−1.19567	−0.597835	+	0.801619i	$0.703972\pi$
$24$	32.0082	0.272235
$25$	169.646	1.35717
$26$	−243.663	−1.83793
$27$	27.0000	0.192450
$28$	66.4972	0.448814
$29$	−179.912	−1.15203	−0.576015	−	0.817439i	$-0.695393\pi$
$29$	−179.912	−1.15203	−0.576015	+	0.817439i	$0.695393\pi$
$30$	185.999	1.13196
$31$	−18.8728	−0.109344	−0.0546720	−	0.998504i	$-0.517411\pi$
$31$	−18.8728	−0.109344	−0.0546720	+	0.998504i	$0.517411\pi$
$32$	199.647	1.10291
$33$	−33.0000	−0.174078
$34$	31.0319	0.156527
$35$	−226.204	−1.09244
$36$	45.4146	0.210253
$37$	293.053	1.30210	0.651049	−	0.759036i	$-0.274329\pi$
$37$	293.053	1.30210	0.651049	+	0.759036i	$0.274329\pi$
$38$	−134.903	−0.575897
$39$	202.382	0.830948
$40$	−183.143	−0.723937
$41$	−112.513	−0.428576	−0.214288	−	0.976770i	$-0.568743\pi$
$41$	−112.513	−0.428576	−0.214288	+	0.976770i	$0.568743\pi$
$42$	−142.794	−0.524611
$43$	−345.273	−1.22450	−0.612252	−	0.790663i	$-0.709736\pi$
$43$	−345.273	−1.22450	−0.612252	+	0.790663i	$0.709736\pi$
$44$	−55.5068	−0.190181
$45$	−154.487	−0.511769
$46$	476.369	1.52689
$47$	53.1694	0.165012	0.0825059	−	0.996591i	$-0.473708\pi$
$47$	53.1694	0.165012	0.0825059	+	0.996591i	$0.473708\pi$
$48$	−236.717	−0.711816
$49$	−169.340	−0.493702
$50$	−612.752	−1.73312
$51$	−25.7744	−0.0707675
$52$	340.411	0.907816
$53$	−198.619	−0.514762	−0.257381	−	0.966310i	$-0.582860\pi$
$53$	−198.619	−0.514762	−0.257381	+	0.966310i	$0.582860\pi$
$54$	−97.5222	−0.245761
$55$	188.818	0.462913
$56$	140.602	0.335512
$57$	112.047	0.260369
$58$	649.832	1.47116
$59$	160.706	0.354613	0.177306	−	0.984156i	$-0.443262\pi$
$59$	160.706	0.354613	0.177306	+	0.984156i	$0.443262\pi$
$60$	−259.851	−0.559111
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	68.1675	0.139633
$63$	118.602	0.237182
$64$	−89.8666	−0.175521
$65$	−1157.98	−2.20968
$66$	119.194	0.222299
$67$	−479.221	−0.873823	−0.436911	−	0.899505i	$-0.643928\pi$
$67$	−479.221	−0.873823	−0.436911	+	0.899505i	$0.643928\pi$
$68$	−43.3532	−0.0773140
$69$	−395.662	−0.690321
$70$	817.035	1.39506
$71$	1014.62	1.69596	0.847982	−	0.530026i	$-0.177818\pi$
$71$	1014.62	1.69596	0.847982	+	0.530026i	$0.177818\pi$
$72$	96.0246	0.157175
$73$	765.711	1.22767	0.613833	−	0.789436i	$-0.289627\pi$
$73$	765.711	1.22767	0.613833	+	0.789436i	$0.289627\pi$
$74$	−1058.49	−1.66279
$75$	508.939	0.783563
$76$	188.466	0.284455
$77$	−144.958	−0.214539
$78$	−730.989	−1.06113
$79$	208.056	0.296306	0.148153	−	0.988964i	$-0.452667\pi$
$79$	208.056	0.296306	0.148153	+	0.988964i	$0.452667\pi$
$80$	1354.44	1.89288
$81$	81.0000	0.111111
$82$	406.391	0.547297
$83$	1055.26	1.39554	0.697769	−	0.716323i	$-0.254176\pi$
$83$	1055.26	1.39554	0.697769	+	0.716323i	$0.254176\pi$
$84$	199.492	0.259123
$85$	147.475	0.188187
$86$	1247.10	1.56370
$87$	−539.737	−0.665125
$88$	−117.363	−0.142170
$89$	−320.189	−0.381348	−0.190674	−	0.981653i	$-0.561067\pi$
$89$	−320.189	−0.381348	−0.190674	+	0.981653i	$0.561067\pi$
$90$	557.998	0.653536
$91$	888.997	1.02409
$92$	−665.513	−0.754180
$93$	−56.6185	−0.0631297
$94$	−192.045	−0.210722
$95$	−641.108	−0.692382
$96$	598.941	0.636763
$97$	888.943	0.930500	0.465250	−	0.885179i	$-0.345964\pi$
$97$	888.943	0.930500	0.465250	+	0.885179i	$0.345964\pi$
$98$	611.644	0.630463
$99$	−99.0000	−0.100504
$100$	856.048	0.856048
$101$	−1249.27	−1.23076	−0.615381	−	0.788230i	$-0.710998\pi$
$101$	−1249.27	−1.23076	−0.615381	+	0.788230i	$0.710998\pi$
$102$	93.0956	0.0903710
$103$	−465.335	−0.445154	−0.222577	−	0.974915i	$-0.571447\pi$
$103$	−465.335	−0.445154	−0.222577	+	0.974915i	$0.571447\pi$
$104$	719.763	0.678640
$105$	−678.613	−0.630722
$106$	717.399	0.657358
$107$	−680.367	−0.614706	−0.307353	−	0.951596i	$-0.599443\pi$
$107$	−680.367	−0.614706	−0.307353	+	0.951596i	$0.599443\pi$
$108$	136.244	0.121390
$109$	1768.76	1.55428	0.777139	−	0.629329i	$-0.216670\pi$
$109$	1768.76	1.55428	0.777139	+	0.629329i	$0.216670\pi$
$110$	−681.998	−0.591145
$111$	879.159	0.751766
$112$	−1039.82	−0.877267
$113$	2200.74	1.83211	0.916055	−	0.401052i	$-0.131355\pi$
$113$	2200.74	1.83211	0.916055	+	0.401052i	$0.131355\pi$
$114$	−404.708	−0.332494
$115$	2263.88	1.83572
$116$	−907.851	−0.726654
$117$	607.145	0.479748
$118$	−580.460	−0.452844
$119$	−113.219	−0.0872164
$120$	−549.429	−0.417965
$121$	121.000	0.0909091
$122$	220.328	0.163505
$123$	−337.540	−0.247439
$124$	−95.2337	−0.0689697
$125$	−766.368	−0.548368
$126$	−428.383	−0.302884
$127$	−2023.86	−1.41408	−0.707041	−	0.707173i	$-0.749970\pi$
$127$	−2023.86	−1.41408	−0.707041	+	0.707173i	$0.749970\pi$
$128$	−1272.59	−0.878763
$129$	−1035.82	−0.706967
$130$	4182.54	2.82179
$131$	−157.851	−0.105279	−0.0526395	−	0.998614i	$-0.516763\pi$
$131$	−157.851	−0.105279	−0.0526395	+	0.998614i	$0.516763\pi$
$132$	−166.520	−0.109801
$133$	492.188	0.320888
$134$	1730.91	1.11588
$135$	−463.462	−0.295470
$136$	−91.6659	−0.0577963
$137$	−438.486	−0.273448	−0.136724	−	0.990609i	$-0.543657\pi$
$137$	−438.486	−0.273448	−0.136724	+	0.990609i	$0.543657\pi$
$138$	1429.11	0.881548
$139$	−3199.58	−1.95241	−0.976204	−	0.216854i	$-0.930420\pi$
$139$	−3199.58	−1.95241	−0.976204	+	0.216854i	$0.930420\pi$
$140$	−1141.44	−0.689068
$141$	159.508	0.0952697
$142$	−3664.75	−2.16576
$143$	−742.066	−0.433949
$144$	−710.152	−0.410967
$145$	3088.24	1.76872
$146$	−2765.70	−1.56774
$147$	−508.019	−0.285039
$148$	1478.77	0.821310
$149$	−749.478	−0.412078	−0.206039	−	0.978544i	$-0.566057\pi$
$149$	−749.478	−0.412078	−0.206039	+	0.978544i	$0.566057\pi$
$150$	−1838.26	−1.00062
$151$	−2930.38	−1.57928	−0.789638	−	0.613573i	$-0.789732\pi$
$151$	−2930.38	−1.57928	−0.789638	+	0.613573i	$0.789732\pi$
$152$	398.493	0.212645
$153$	−77.3233	−0.0408577
$154$	523.580	0.273969
$155$	323.957	0.167877
$156$	1021.23	0.524128
$157$	−1438.75	−0.731368	−0.365684	−	0.930739i	$-0.619165\pi$
$157$	−1438.75	−0.731368	−0.365684	+	0.930739i	$0.619165\pi$
$158$	−751.486	−0.378386
$159$	−595.857	−0.297198
$160$	−3427.00	−1.69330
$161$	−1738.02	−0.850775
$162$	−292.567	−0.141890
$163$	2181.77	1.04840	0.524199	−	0.851596i	$-0.324365\pi$
$163$	2181.77	1.04840	0.524199	+	0.851596i	$0.324365\pi$
$164$	−567.750	−0.270328
$165$	566.454	0.267263
$166$	−3811.53	−1.78212
$167$	3730.27	1.72848	0.864241	−	0.503077i	$-0.167799\pi$
$167$	3730.27	1.72848	0.864241	+	0.503077i	$0.167799\pi$
$168$	421.805	0.193708
$169$	2353.92	1.07143
$170$	−532.670	−0.240317
$171$	336.142	0.150324
$172$	−1742.27	−0.772366
$173$	3047.07	1.33910	0.669550	−	0.742767i	$-0.266487\pi$
$173$	3047.07	1.33910	0.669550	+	0.742767i	$0.266487\pi$
$174$	1949.50	0.849373
$175$	2235.60	0.965690
$176$	867.963	0.371734
$177$	482.118	0.204736
$178$	1156.50	0.486986
$179$	−4489.21	−1.87452	−0.937261	−	0.348628i	$-0.886648\pi$
$179$	−4489.21	−1.87452	−0.937261	+	0.348628i	$0.886648\pi$
$180$	−779.554	−0.322803
$181$	1865.38	0.766037	0.383018	−	0.923741i	$-0.374885\pi$
$181$	1865.38	0.766037	0.383018	+	0.923741i	$0.374885\pi$
$182$	−3211.00	−1.30777
$183$	−183.000	−0.0739221
$184$	−1407.16	−0.563789
$185$	−5030.33	−1.99912
$186$	204.502	0.0806174
$187$	94.5063	0.0369571
$188$	268.297	0.104083
$189$	355.807	0.136937
$190$	2315.64	0.884180
$191$	−4360.39	−1.65187	−0.825935	−	0.563766i	$-0.809352\pi$
$191$	−4360.39	−1.65187	−0.825935	+	0.563766i	$0.809352\pi$
$192$	−269.600	−0.101337
$193$	3694.63	1.37796	0.688978	−	0.724782i	$-0.258060\pi$
$193$	3694.63	1.37796	0.688978	+	0.724782i	$0.258060\pi$
$194$	−3210.80	−1.18826
$195$	−3473.93	−1.27576
$196$	−854.500	−0.311407
$197$	−4589.24	−1.65975	−0.829873	−	0.557952i	$-0.811587\pi$
$197$	−4589.24	−1.65975	−0.829873	+	0.557952i	$0.811587\pi$
$198$	357.582	0.128345
$199$	1113.60	0.396687	0.198343	−	0.980133i	$-0.436444\pi$
$199$	1113.60	0.396687	0.198343	+	0.980133i	$0.436444\pi$
$200$	1810.03	0.639941
$201$	−1437.66	−0.504502
$202$	4512.28	1.57170
$203$	−2370.89	−0.819723
$204$	−130.060	−0.0446372
$205$	1931.32	0.657997
$206$	1680.76	0.568467
$207$	−1186.99	−0.398557
$208$	−5323.02	−1.77445
$209$	−410.840	−0.135973
$210$	2451.11	0.805440
$211$	−4233.97	−1.38141	−0.690707	−	0.723135i	$-0.742700\pi$
$211$	−4233.97	−1.38141	−0.690707	+	0.723135i	$0.742700\pi$
$212$	−1002.25	−0.324691
$213$	3043.86	0.979165
$214$	2457.44	0.784987
$215$	5926.70	1.87999
$216$	288.074	0.0907451
$217$	−248.707	−0.0778033
$218$	−6388.64	−1.98483
$219$	2297.13	0.708794
$220$	952.789	0.291986
$221$	−579.586	−0.176413
$222$	−3175.46	−0.960014
$223$	−1863.02	−0.559448	−0.279724	−	0.960081i	$-0.590243\pi$
$223$	−1863.02	−0.559448	−0.279724	+	0.960081i	$0.590243\pi$
$224$	2630.96	0.784768
$225$	1526.82	0.452390
$226$	−7948.94	−2.33963
$227$	−1297.21	−0.379291	−0.189646	−	0.981853i	$-0.560734\pi$
$227$	−1297.21	−0.379291	−0.189646	+	0.981853i	$0.560734\pi$
$228$	565.399	0.164230
$229$	5165.41	1.49057	0.745284	−	0.666748i	$-0.232314\pi$
$229$	5165.41	1.49057	0.745284	+	0.666748i	$0.232314\pi$
$230$	−8176.99	−2.34424
$231$	−434.875	−0.123864
$232$	−1919.56	−0.543212
$233$	−1650.58	−0.464090	−0.232045	−	0.972705i	$-0.574542\pi$
$233$	−1650.58	−0.464090	−0.232045	+	0.972705i	$0.574542\pi$
$234$	−2192.97	−0.612644
$235$	−912.668	−0.253344
$236$	810.934	0.223675
$237$	624.169	0.171072
$238$	408.939	0.111376
$239$	−7024.37	−1.90113	−0.950563	−	0.310533i	$-0.899493\pi$
$239$	−7024.37	−1.90113	−0.950563	+	0.310533i	$0.899493\pi$
$240$	4063.31	1.09286
$241$	2552.06	0.682128	0.341064	−	0.940040i	$-0.389213\pi$
$241$	2552.06	0.682128	0.341064	+	0.940040i	$0.389213\pi$
$242$	−437.044	−0.116092
$243$	243.000	0.0641500
$244$	−307.810	−0.0807604
$245$	2906.76	0.757984
$246$	1219.17	0.315982
$247$	2519.59	0.649060
$248$	−201.362	−0.0515584
$249$	3165.78	0.805714
$250$	2768.07	0.700272
$251$	−1963.77	−0.493832	−0.246916	−	0.969037i	$-0.579417\pi$
$251$	−1963.77	−0.493832	−0.246916	+	0.969037i	$0.579417\pi$
$252$	598.475	0.149605
$253$	1450.76	0.360508
$254$	7310.04	1.80580
$255$	442.425	0.108650
$256$	5315.43	1.29771
$257$	5233.67	1.27030	0.635150	−	0.772389i	$-0.280938\pi$
$257$	5233.67	1.27030	0.635150	+	0.772389i	$0.280938\pi$
$258$	3741.31	0.902805
$259$	3861.86	0.926503
$260$	−5843.24	−1.39378
$261$	−1619.21	−0.384010
$262$	570.149	0.134443
$263$	6637.12	1.55613	0.778066	−	0.628183i	$-0.216201\pi$
$263$	6637.12	1.55613	0.778066	+	0.628183i	$0.216201\pi$
$264$	−352.090	−0.0820820
$265$	3409.35	0.790319
$266$	−1777.75	−0.409778
$267$	−960.568	−0.220172
$268$	−2418.18	−0.551171
$269$	3878.89	0.879183	0.439591	−	0.898198i	$-0.355123\pi$
$269$	3878.89	0.879183	0.439591	+	0.898198i	$0.355123\pi$
$270$	1674.00	0.377319
$271$	−4333.97	−0.971476	−0.485738	−	0.874105i	$-0.661449\pi$
$271$	−4333.97	−0.971476	−0.485738	+	0.874105i	$0.661449\pi$
$272$	677.917	0.151120
$273$	2666.99	0.591258
$274$	1583.78	0.349196
$275$	−1866.11	−0.409203
$276$	−1996.54	−0.435426
$277$	4070.21	0.882871	0.441435	−	0.897293i	$-0.354469\pi$
$277$	4070.21	0.882871	0.441435	+	0.897293i	$0.354469\pi$
$278$	11556.7	2.49325
$279$	−169.856	−0.0364480
$280$	−2413.46	−0.515115
$281$	−6135.63	−1.30257	−0.651283	−	0.758835i	$-0.725769\pi$
$281$	−6135.63	−1.30257	−0.651283	+	0.758835i	$0.725769\pi$
$282$	−576.134	−0.121660
$283$	−2167.69	−0.455322	−0.227661	−	0.973740i	$-0.573108\pi$
$283$	−2167.69	−0.455322	−0.227661	+	0.973740i	$0.573108\pi$
$284$	5119.85	1.06974
$285$	−1923.32	−0.399747
$286$	2680.29	0.554158
$287$	−1482.70	−0.304952
$288$	1796.82	0.367635
$289$	−4839.19	−0.984976
$290$	−11154.5	−2.25868
$291$	2666.83	0.537225
$292$	3863.83	0.774361
$293$	−513.504	−0.102386	−0.0511932	−	0.998689i	$-0.516302\pi$
$293$	−513.504	−0.102386	−0.0511932	+	0.998689i	$0.516302\pi$
$294$	1834.93	0.363998
$295$	−2758.56	−0.544440
$296$	3126.70	0.613972
$297$	−297.000	−0.0580259
$298$	2707.06	0.526228
$299$	−8897.19	−1.72086
$300$	2568.14	0.494239
$301$	−4550.02	−0.871291
$302$	10584.3	2.01675
$303$	−3747.81	−0.710581
$304$	−2947.06	−0.556005
$305$	1047.08	0.196576
$306$	279.287	0.0521757
$307$	8447.05	1.57035	0.785177	−	0.619271i	$-0.212572\pi$
$307$	8447.05	1.57035	0.785177	+	0.619271i	$0.212572\pi$
$308$	−731.470	−0.135323
$309$	−1396.01	−0.257010
$310$	−1170.11	−0.214380
$311$	−2569.70	−0.468536	−0.234268	−	0.972172i	$-0.575269\pi$
$311$	−2569.70	−0.468536	−0.234268	+	0.972172i	$0.575269\pi$
$312$	2159.29	0.391813
$313$	−3314.82	−0.598609	−0.299305	−	0.954158i	$-0.596755\pi$
$313$	−3314.82	−0.598609	−0.299305	+	0.954158i	$0.596755\pi$
$314$	5196.67	0.933966
$315$	−2035.84	−0.364148
$316$	1049.87	0.186898
$317$	−4767.64	−0.844723	−0.422362	−	0.906427i	$-0.638799\pi$
$317$	−4767.64	−0.844723	−0.422362	+	0.906427i	$0.638799\pi$
$318$	2152.20	0.379526
$319$	1979.04	0.347350
$320$	1542.58	0.269478
$321$	−2041.10	−0.354901
$322$	6277.60	1.08645
$323$	−320.884	−0.0552770
$324$	408.732	0.0700843
$325$	11444.4	1.95330
$326$	−7880.39	−1.33882
$327$	5306.27	0.897362
$328$	−1200.45	−0.202085
$329$	700.668	0.117414
$330$	−2045.99	−0.341298
$331$	−2755.56	−0.457580	−0.228790	−	0.973476i	$-0.573477\pi$
$331$	−2755.56	−0.457580	−0.228790	+	0.973476i	$0.573477\pi$
$332$	5324.91	0.880248
$333$	2637.48	0.434032
$334$	−13473.5	−2.20729
$335$	8225.95	1.34159
$336$	−3119.47	−0.506490
$337$	−7689.51	−1.24295	−0.621476	−	0.783434i	$-0.713466\pi$
$337$	−7689.51	−1.24295	−0.621476	+	0.783434i	$0.713466\pi$
$338$	−8502.21	−1.36822
$339$	6602.23	1.05777
$340$	744.170	0.118701
$341$	207.601	0.0329684
$342$	−1214.12	−0.191966
$343$	−6751.62	−1.06284
$344$	−3683.86	−0.577384
$345$	6791.65	1.05985
$346$	−11005.8	−1.71005
$347$	8127.34	1.25734	0.628672	−	0.777670i	$-0.283599\pi$
$347$	8127.34	1.25734	0.628672	+	0.777670i	$0.283599\pi$
$348$	−2723.55	−0.419534
$349$	−5073.25	−0.778122	−0.389061	−	0.921212i	$-0.627200\pi$
$349$	−5073.25	−0.778122	−0.389061	+	0.921212i	$0.627200\pi$
$350$	−8074.86	−1.23320
$351$	1821.43	0.276983
$352$	−2196.12	−0.332538
$353$	10776.1	1.62481	0.812403	−	0.583097i	$-0.198159\pi$
$353$	10776.1	1.62481	0.812403	+	0.583097i	$0.198159\pi$
$354$	−1741.38	−0.261450
$355$	−17416.2	−2.60383
$356$	−1615.70	−0.240539
$357$	−339.656	−0.0503544
$358$	16214.7	2.39379
$359$	5387.61	0.792053	0.396027	−	0.918239i	$-0.370389\pi$
$359$	5387.61	0.792053	0.396027	+	0.918239i	$0.370389\pi$
$360$	−1648.29	−0.241312
$361$	−5464.04	−0.796624
$362$	−6737.63	−0.978238
$363$	363.000	0.0524864
$364$	4485.94	0.645954
$365$	−13143.6	−1.88485
$366$	660.984	0.0943994
$367$	3504.14	0.498405	0.249203	−	0.968451i	$-0.419831\pi$
$367$	3504.14	0.498405	0.249203	+	0.968451i	$0.419831\pi$
$368$	10406.7	1.47414
$369$	−1012.62	−0.142859
$370$	18169.2	2.55290
$371$	−2617.41	−0.366277
$372$	−285.701	−0.0398196
$373$	−9101.50	−1.26343	−0.631713	−	0.775202i	$-0.717648\pi$
$373$	−9101.50	−1.26343	−0.631713	+	0.775202i	$0.717648\pi$
$374$	−341.351	−0.0471947
$375$	−2299.10	−0.316600
$376$	567.286	0.0778073
$377$	−12137.0	−1.65805
$378$	−1285.15	−0.174870
$379$	3500.82	0.474472	0.237236	−	0.971452i	$-0.423759\pi$
$379$	3500.82	0.474472	0.237236	+	0.971452i	$0.423759\pi$
$380$	−3235.08	−0.436726
$381$	−6071.57	−0.816420
$382$	15749.5	2.10946
$383$	−11300.9	−1.50770	−0.753851	−	0.657046i	$-0.771806\pi$
$383$	−11300.9	−1.50770	−0.753851	+	0.657046i	$0.771806\pi$
$384$	−3817.76	−0.507354
$385$	2488.25	0.329384
$386$	−13344.8	−1.75967
$387$	−3107.46	−0.408168
$388$	4485.67	0.586921
$389$	−5266.22	−0.686396	−0.343198	−	0.939263i	$-0.611510\pi$
$389$	−5266.22	−0.686396	−0.343198	+	0.939263i	$0.611510\pi$
$390$	12547.6	1.62916
$391$	1133.11	0.146557
$392$	−1806.75	−0.232793
$393$	−473.554	−0.0607829
$394$	16576.0	2.11952
$395$	−3571.34	−0.454921
$396$	−499.561	−0.0633936
$397$	−13984.5	−1.76792	−0.883960	−	0.467563i	$-0.845132\pi$
$397$	−13984.5	−1.76792	−0.883960	+	0.467563i	$0.845132\pi$
$398$	−4022.23	−0.506574
$399$	1476.56	0.185265
$400$	−13386.1	−1.67326
$401$	−9219.92	−1.14818	−0.574091	−	0.818792i	$-0.694644\pi$
$401$	−9219.92	−1.14818	−0.574091	+	0.818792i	$0.694644\pi$
$402$	5192.74	0.644255
$403$	−1273.17	−0.157373
$404$	−6303.90	−0.776314
$405$	−1390.39	−0.170590
$406$	8563.50	1.04680
$407$	−3223.58	−0.392597
$408$	−274.998	−0.0333687
$409$	3412.52	0.412563	0.206281	−	0.978493i	$-0.433864\pi$
$409$	3412.52	0.412563	0.206281	+	0.978493i	$0.433864\pi$
$410$	−6975.81	−0.840270
$411$	−1315.46	−0.157875
$412$	−2348.12	−0.280785
$413$	2117.79	0.252323
$414$	4287.32	0.508962
$415$	−18113.8	−2.14258
$416$	13468.3	1.58735
$417$	−9598.74	−1.12722
$418$	1483.93	0.173640
$419$	9113.56	1.06259	0.531297	−	0.847186i	$-0.321705\pi$
$419$	9113.56	1.06259	0.531297	+	0.847186i	$0.321705\pi$
$420$	−3424.33	−0.397834
$421$	−3228.27	−0.373720	−0.186860	−	0.982387i	$-0.559831\pi$
$421$	−3228.27	−0.373720	−0.186860	+	0.982387i	$0.559831\pi$
$422$	15292.8	1.76408
$423$	478.525	0.0550040
$424$	−2119.14	−0.242723
$425$	−1457.51	−0.166353
$426$	−10994.2	−1.25040
$427$	−803.860	−0.0911042
$428$	−3433.18	−0.387731
$429$	−2226.20	−0.250540
$430$	−21406.9	−2.40077
$431$	10376.3	1.15965	0.579827	−	0.814740i	$-0.303120\pi$
$431$	10376.3	1.15965	0.579827	+	0.814740i	$0.303120\pi$
$432$	−2130.45	−0.237272
$433$	−6233.82	−0.691867	−0.345934	−	0.938259i	$-0.612438\pi$
$433$	−6233.82	−0.691867	−0.345934	+	0.938259i	$0.612438\pi$
$434$	898.312	0.0993557
$435$	9264.73	1.02117
$436$	8925.28	0.980374
$437$	−4925.88	−0.539214
$438$	−8297.09	−0.905138
$439$	−13567.6	−1.47504	−0.737522	−	0.675323i	$-0.764004\pi$
$439$	−13567.6	−1.47504	−0.737522	+	0.675323i	$0.764004\pi$
$440$	2014.57	0.218275
$441$	−1524.06	−0.164567
$442$	2093.43	0.225281
$443$	−13691.2	−1.46837	−0.734183	−	0.678951i	$-0.762435\pi$
$443$	−13691.2	−1.46837	−0.734183	+	0.678951i	$0.762435\pi$
$444$	4436.30	0.474183
$445$	5496.14	0.585487
$446$	6729.09	0.714421
$447$	−2248.43	−0.237913
$448$	−1184.26	−0.124891
$449$	−7574.51	−0.796132	−0.398066	−	0.917357i	$-0.630319\pi$
$449$	−7574.51	−0.796132	−0.398066	+	0.917357i	$0.630319\pi$
$450$	−5514.77	−0.577708
$451$	1237.65	0.129221
$452$	11105.1	1.15562
$453$	−8791.13	−0.911795
$454$	4685.45	0.484360
$455$	−15259.9	−1.57229
$456$	1195.48	0.122771
$457$	−5054.37	−0.517360	−0.258680	−	0.965963i	$-0.583287\pi$
$457$	−5054.37	−0.517360	−0.258680	+	0.965963i	$0.583287\pi$
$458$	−18657.1	−1.90347
$459$	−231.970	−0.0235892
$460$	11423.7	1.15790
$461$	−13592.3	−1.37323	−0.686614	−	0.727022i	$-0.740904\pi$
$461$	−13592.3	−1.37323	−0.686614	+	0.727022i	$0.740904\pi$
$462$	1570.74	0.158176
$463$	5057.12	0.507612	0.253806	−	0.967255i	$-0.418317\pi$
$463$	5057.12	0.507612	0.253806	+	0.967255i	$0.418317\pi$
$464$	14196.1	1.42034
$465$	971.872	0.0969236
$466$	5961.77	0.592648
$467$	−3539.43	−0.350718	−0.175359	−	0.984505i	$-0.556109\pi$
$467$	−3539.43	−0.350718	−0.175359	+	0.984505i	$0.556109\pi$
$468$	3063.70	0.302605
$469$	−6315.18	−0.621766
$470$	3296.50	0.323523
$471$	−4316.25	−0.422256
$472$	1714.64	0.167209
$473$	3798.00	0.369202
$474$	−2254.46	−0.218461
$475$	6336.15	0.612047
$476$	−571.310	−0.0550125
$477$	−1787.57	−0.171587
$478$	25371.6	2.42776
$479$	−5525.84	−0.527102	−0.263551	−	0.964645i	$-0.584894\pi$
$479$	−5525.84	−0.527102	−0.263551	+	0.964645i	$0.584894\pi$
$480$	−10281.0	−0.977627
$481$	19769.5	1.87404
$482$	−9217.88	−0.871085
$483$	−5214.05	−0.491195
$484$	610.575	0.0573417
$485$	−15258.9	−1.42860
$486$	−877.700	−0.0819203
$487$	−489.052	−0.0455053	−0.0227526	−	0.999741i	$-0.507243\pi$
$487$	−489.052	−0.0455053	−0.0227526	+	0.999741i	$0.507243\pi$
$488$	−650.833	−0.0603726
$489$	6545.30	0.605293
$490$	−10499.0	−0.967955
$491$	−3772.79	−0.346769	−0.173384	−	0.984854i	$-0.555470\pi$
$491$	−3772.79	−0.346769	−0.173384	+	0.984854i	$0.555470\pi$
$492$	−1703.25	−0.156074
$493$	1545.71	0.141208
$494$	−9100.60	−0.828857
$495$	1699.36	0.154304
$496$	1489.18	0.134810
$497$	13370.7	1.20676
$498$	−11434.6	−1.02891
$499$	2004.39	0.179817	0.0899087	−	0.995950i	$-0.471342\pi$
$499$	2004.39	0.179817	0.0899087	+	0.995950i	$0.471342\pi$
$500$	−3867.14	−0.345888
$501$	11190.8	0.997940
$502$	7093.00	0.630630
$503$	−7171.51	−0.635710	−0.317855	−	0.948139i	$-0.602962\pi$
$503$	−7171.51	−0.635710	−0.317855	+	0.948139i	$0.602962\pi$
$504$	1265.41	0.111837
$505$	21444.0	1.88960
$506$	−5240.05	−0.460373
$507$	7061.77	0.618588
$508$	−10212.5	−0.891944
$509$	−10195.9	−0.887865	−0.443933	−	0.896060i	$-0.646417\pi$
$509$	−10195.9	−0.887865	−0.443933	+	0.896060i	$0.646417\pi$
$510$	−1598.01	−0.138747
$511$	10090.6	0.873542
$512$	−9018.29	−0.778430
$513$	1008.43	0.0867897
$514$	−18903.7	−1.62219
$515$	7987.61	0.683448
$516$	−5226.82	−0.445926
$517$	−584.864	−0.0497530
$518$	−13948.8	−1.18316
$519$	9141.20	0.773130
$520$	−12354.9	−1.04192
$521$	−9397.86	−0.790265	−0.395132	−	0.918624i	$-0.629301\pi$
$521$	−9397.86	−0.790265	−0.395132	+	0.918624i	$0.629301\pi$
$522$	5848.49	0.490386
$523$	8164.01	0.682576	0.341288	−	0.939959i	$-0.389137\pi$
$523$	8164.01	0.682576	0.341288	+	0.939959i	$0.389137\pi$
$524$	−796.530	−0.0664057
$525$	6706.81	0.557542
$526$	−23972.9	−1.98720
$527$	162.146	0.0134026
$528$	2603.89	0.214621
$529$	5227.28	0.429628
$530$	−12314.3	−1.00925
$531$	1446.35	0.118204
$532$	2483.61	0.202403
$533$	−7590.21	−0.616826
$534$	3469.51	0.281162
$535$	11678.7	0.943763
$536$	−5113.00	−0.412030
$537$	−13467.6	−1.08226
$538$	−14010.3	−1.12273
$539$	1862.74	0.148857
$540$	−2338.66	−0.186370
$541$	1514.45	0.120353	0.0601767	−	0.998188i	$-0.480834\pi$
$541$	1514.45	0.120353	0.0601767	+	0.998188i	$0.480834\pi$
$542$	15654.0	1.24059
$543$	5596.14	0.442272
$544$	−1715.26	−0.135186
$545$	−30361.2	−2.38629
$546$	−9632.99	−0.755044
$547$	19538.1	1.52722	0.763610	−	0.645678i	$-0.223425\pi$
$547$	19538.1	1.52722	0.763610	+	0.645678i	$0.223425\pi$
$548$	−2212.63	−0.172480
$549$	−549.000	−0.0426790
$550$	6740.27	0.522556
$551$	−6719.57	−0.519534
$552$	−4221.48	−0.325504
$553$	2741.77	0.210835
$554$	−14701.3	−1.12744
$555$	−15091.0	−1.15419
$556$	−16145.3	−1.23150
$557$	9553.21	0.726719	0.363359	−	0.931649i	$-0.381630\pi$
$557$	9553.21	0.726719	0.363359	+	0.931649i	$0.381630\pi$
$558$	613.507	0.0465445
$559$	−23292.3	−1.76236
$560$	17848.8	1.34688
$561$	283.519	0.0213372
$562$	22161.5	1.66339
$563$	−4634.25	−0.346910	−0.173455	−	0.984842i	$-0.555493\pi$
$563$	−4634.25	−0.346910	−0.173455	+	0.984842i	$0.555493\pi$
$564$	804.890	0.0600922
$565$	−37776.3	−2.81285
$566$	7829.57	0.581451
$567$	1067.42	0.0790607
$568$	10825.4	0.799690
$569$	−19883.8	−1.46498	−0.732488	−	0.680780i	$-0.761641\pi$
$569$	−19883.8	−1.46498	−0.732488	+	0.680780i	$0.761641\pi$
$570$	6946.92	0.510481
$571$	−21765.9	−1.59523	−0.797614	−	0.603168i	$-0.793905\pi$
$571$	−21765.9	−1.59523	−0.797614	+	0.603168i	$0.793905\pi$
$572$	−3744.52	−0.273717
$573$	−13081.2	−0.953707
$574$	5355.43	0.389427
$575$	−22374.2	−1.62273
$576$	−808.799	−0.0585069
$577$	6042.71	0.435981	0.217991	−	0.975951i	$-0.430050\pi$
$577$	6042.71	0.435981	0.217991	+	0.975951i	$0.430050\pi$
$578$	17478.8	1.25783
$579$	11083.9	0.795563
$580$	15583.5	1.11564
$581$	13906.2	0.992990
$582$	−9632.41	−0.686042
$583$	2184.81	0.155207
$584$	8169.67	0.578876
$585$	−10421.8	−0.736561
$586$	1854.74	0.130749
$587$	−23504.8	−1.65272	−0.826359	−	0.563144i	$-0.809592\pi$
$587$	−23504.8	−1.65272	−0.826359	+	0.563144i	$0.809592\pi$
$588$	−2563.50	−0.179791
$589$	−704.884	−0.0493111
$590$	9963.75	0.695256
$591$	−13767.7	−0.958255
$592$	−23123.6	−1.60536
$593$	14492.8	1.00362	0.501811	−	0.864977i	$-0.332667\pi$
$593$	14492.8	1.00362	0.501811	+	0.864977i	$0.332667\pi$
$594$	1072.74	0.0740997
$595$	1943.43	0.133904
$596$	−3781.92	−0.259922
$597$	3340.79	0.229027
$598$	32136.1	2.19756
$599$	9019.02	0.615204	0.307602	−	0.951515i	$-0.400474\pi$
$599$	9019.02	0.615204	0.307602	+	0.951515i	$0.400474\pi$
$600$	5430.08	0.369470
$601$	6139.59	0.416704	0.208352	−	0.978054i	$-0.433190\pi$
$601$	6139.59	0.416704	0.208352	+	0.978054i	$0.433190\pi$
$602$	16434.4	1.11265
$603$	−4312.99	−0.291274
$604$	−14786.9	−0.996142
$605$	−2077.00	−0.139573
$606$	13536.8	0.907420
$607$	8847.36	0.591603	0.295802	−	0.955249i	$-0.404413\pi$
$607$	8847.36	0.591603	0.295802	+	0.955249i	$0.404413\pi$
$608$	7456.65	0.497380
$609$	−7112.67	−0.473268
$610$	−3781.99	−0.251030
$611$	3586.84	0.237493
$612$	−390.179	−0.0257713
$613$	−1477.71	−0.0973638	−0.0486819	−	0.998814i	$-0.515502\pi$
$613$	−1477.71	−0.0973638	−0.0486819	+	0.998814i	$0.515502\pi$
$614$	−30510.2	−2.00536
$615$	5793.96	0.379895
$616$	−1546.62	−0.101161
$617$	18725.5	1.22181	0.610907	−	0.791702i	$-0.290805\pi$
$617$	18725.5	1.22181	0.610907	+	0.791702i	$0.290805\pi$
$618$	5042.28	0.328204
$619$	−28835.7	−1.87238	−0.936190	−	0.351494i	$-0.885674\pi$
$619$	−28835.7	−1.87238	−0.936190	+	0.351494i	$0.885674\pi$
$620$	1634.71	0.105890
$621$	−3560.96	−0.230107
$622$	9281.61	0.598326
$623$	−4219.46	−0.271347
$624$	−15969.1	−1.02448
$625$	−8050.90	−0.515257
$626$	11972.9	0.764431
$627$	−1232.52	−0.0785042
$628$	−7260.04	−0.461317
$629$	−2517.76	−0.159602
$630$	7353.32	0.465021
$631$	12269.0	0.774041	0.387021	−	0.922071i	$-0.373504\pi$
$631$	12269.0	0.774041	0.387021	+	0.922071i	$0.373504\pi$
$632$	2219.84	0.139716
$633$	−12701.9	−0.797559
$634$	17220.4	1.07872
$635$	34740.1	2.17105
$636$	−3006.74	−0.187460
$637$	−11423.7	−0.710557
$638$	−7148.15	−0.443570
$639$	9131.59	0.565321
$640$	21844.3	1.34917
$641$	−2028.57	−0.124998	−0.0624988	−	0.998045i	$-0.519907\pi$
$641$	−2028.57	−0.124998	−0.0624988	+	0.998045i	$0.519907\pi$
$642$	7372.32	0.453212
$643$	−17955.3	−1.10122	−0.550611	−	0.834762i	$-0.685605\pi$
$643$	−17955.3	−1.10122	−0.550611	+	0.834762i	$0.685605\pi$
$644$	−8770.15	−0.536634
$645$	17780.1	1.08541
$646$	1159.01	0.0705894
$647$	−13784.1	−0.837571	−0.418785	−	0.908085i	$-0.637544\pi$
$647$	−13784.1	−0.837571	−0.418785	+	0.908085i	$0.637544\pi$
$648$	864.221	0.0523917
$649$	−1767.77	−0.106920
$650$	−41336.6	−2.49439
$651$	−746.120	−0.0449198
$652$	11009.3	0.661287
$653$	−416.238	−0.0249444	−0.0124722	−	0.999922i	$-0.503970\pi$
$653$	−416.238	−0.0249444	−0.0124722	+	0.999922i	$0.503970\pi$
$654$	−19165.9	−1.14594
$655$	2709.56	0.161636
$656$	8877.95	0.528393
$657$	6891.40	0.409222
$658$	−2530.77	−0.149939
$659$	−22427.5	−1.32572	−0.662861	−	0.748743i	$-0.730658\pi$
$659$	−22427.5	−1.32572	−0.662861	+	0.748743i	$0.730658\pi$
$660$	2858.37	0.168578
$661$	7927.34	0.466471	0.233236	−	0.972420i	$-0.425069\pi$
$661$	7927.34	0.466471	0.233236	+	0.972420i	$0.425069\pi$
$662$	9952.89	0.584335
$663$	−1738.76	−0.101852
$664$	11259.0	0.658032
$665$	−8448.53	−0.492662
$666$	−9526.39	−0.554265
$667$	23728.2	1.37745
$668$	18823.2	1.09026
$669$	−5589.05	−0.322997
$670$	−29711.6	−1.71322
$671$	671.000	0.0386046
$672$	7892.87	0.453086
$673$	−12381.5	−0.709172	−0.354586	−	0.935023i	$-0.615378\pi$
$673$	−12381.5	−0.709172	−0.354586	+	0.935023i	$0.615378\pi$
$674$	27774.0	1.58726
$675$	4580.45	0.261188
$676$	11878.1	0.675811
$677$	−1508.71	−0.0856490	−0.0428245	−	0.999083i	$-0.513636\pi$
$677$	−1508.71	−0.0856490	−0.0428245	+	0.999083i	$0.513636\pi$
$678$	−23846.8	−1.35078
$679$	11714.5	0.662094
$680$	1573.47	0.0887351
$681$	−3891.64	−0.218984
$682$	−749.842	−0.0421011
$683$	−1226.78	−0.0687282	−0.0343641	−	0.999409i	$-0.510941\pi$
$683$	−1226.78	−0.0687282	−0.0343641	+	0.999409i	$0.510941\pi$
$684$	1696.20	0.0948183
$685$	7526.72	0.419827
$686$	24386.4	1.35726
$687$	15496.2	0.860579
$688$	27244.0	1.50969
$689$	−13398.9	−0.740869
$690$	−24531.0	−1.35345
$691$	−6078.13	−0.334621	−0.167310	−	0.985904i	$-0.553508\pi$
$691$	−6078.13	−0.334621	−0.167310	+	0.985904i	$0.553508\pi$
$692$	15375.7	0.844649
$693$	−1304.62	−0.0715131
$694$	−29355.4	−1.60564
$695$	54921.6	2.99755
$696$	−5758.67	−0.313623
$697$	966.656	0.0525319
$698$	18324.2	0.993671
$699$	−4951.73	−0.267942
$700$	11281.0	0.609118
$701$	15180.9	0.817937	0.408969	−	0.912548i	$-0.365889\pi$
$701$	15180.9	0.817937	0.408969	+	0.912548i	$0.365889\pi$
$702$	−6578.90	−0.353710
$703$	10945.3	0.587210
$704$	988.532	0.0529215
$705$	−2738.00	−0.146268
$706$	−38922.7	−2.07490
$707$	−16462.9	−0.875744
$708$	2432.80	0.129139
$709$	3929.41	0.208141	0.104071	−	0.994570i	$-0.466813\pi$
$709$	3929.41	0.208141	0.104071	+	0.994570i	$0.466813\pi$
$710$	62906.3	3.32512
$711$	1872.51	0.0987686
$712$	−3416.23	−0.179815
$713$	2489.09	0.130739
$714$	1226.82	0.0643031
$715$	12737.8	0.666245
$716$	−22652.9	−1.18237
$717$	−21073.1	−1.09762
$718$	−19459.7	−1.01146
$719$	−31402.4	−1.62880	−0.814402	−	0.580301i	$-0.802935\pi$
$719$	−31402.4	−1.62880	−0.814402	+	0.580301i	$0.802935\pi$
$720$	12189.9	0.630962
$721$	−6132.20	−0.316748
$722$	19735.8	1.01730
$723$	7656.19	0.393827
$724$	9412.84	0.483185
$725$	−30521.5	−1.56350
$726$	−1311.13	−0.0670257
$727$	−3399.41	−0.173421	−0.0867106	−	0.996234i	$-0.527636\pi$
$727$	−3399.41	−0.173421	−0.0867106	+	0.996234i	$0.527636\pi$
$728$	9485.06	0.482884
$729$	729.000	0.0370370
$730$	47473.9	2.40697
$731$	2966.41	0.150091
$732$	−923.431	−0.0466270
$733$	−25206.2	−1.27014	−0.635070	−	0.772454i	$-0.719029\pi$
$733$	−25206.2	−1.27014	−0.635070	+	0.772454i	$0.719029\pi$
$734$	−12656.7	−0.636469
$735$	8720.28	0.437622
$736$	−26330.9	−1.31871
$737$	5271.43	0.263467
$738$	3657.52	0.182432
$739$	16162.2	0.804513	0.402256	−	0.915527i	$-0.368226\pi$
$739$	16162.2	0.804513	0.402256	+	0.915527i	$0.368226\pi$
$740$	−25383.4	−1.26096
$741$	7558.78	0.374735
$742$	9453.90	0.467741
$743$	−34324.3	−1.69480	−0.847400	−	0.530955i	$-0.821833\pi$
$743$	−34324.3	−1.69480	−0.847400	+	0.530955i	$0.821833\pi$
$744$	−604.086	−0.0297673
$745$	12865.0	0.632667
$746$	32874.0	1.61341
$747$	9497.33	0.465179
$748$	476.885	0.0233110
$749$	−8965.89	−0.437392
$750$	8304.21	0.404302
$751$	−14521.7	−0.705599	−0.352800	−	0.935699i	$-0.614770\pi$
$751$	−14521.7	−0.705599	−0.352800	+	0.935699i	$0.614770\pi$
$752$	−4195.37	−0.203444
$753$	−5891.30	−0.285114
$754$	43838.0	2.11735
$755$	50300.7	2.42467
$756$	1795.43	0.0863743
$757$	−16129.8	−0.774437	−0.387219	−	0.921988i	$-0.626564\pi$
$757$	−16129.8	−0.774437	−0.387219	+	0.921988i	$0.626564\pi$
$758$	−12644.7	−0.605907
$759$	4352.28	0.208140
$760$	−6840.23	−0.326476
$761$	26449.6	1.25992	0.629959	−	0.776629i	$-0.283072\pi$
$761$	26449.6	1.25992	0.629959	+	0.776629i	$0.283072\pi$
$762$	21930.1	1.04258
$763$	23308.7	1.10594
$764$	−22002.9	−1.04193
$765$	1327.28	0.0627291
$766$	40818.1	1.92535
$767$	10841.3	0.510374
$768$	15946.3	0.749234
$769$	6747.61	0.316418	0.158209	−	0.987406i	$-0.449428\pi$
$769$	6747.61	0.316418	0.158209	+	0.987406i	$0.449428\pi$
$770$	−8987.39	−0.420627
$771$	15701.0	0.733408
$772$	18643.4	0.869158
$773$	31052.8	1.44488	0.722440	−	0.691433i	$-0.243020\pi$
$773$	31052.8	1.44488	0.722440	+	0.691433i	$0.243020\pi$
$774$	11223.9	0.521235
$775$	−3201.71	−0.148398
$776$	9484.49	0.438754
$777$	11585.6	0.534917
$778$	19021.2	0.876536
$779$	−4202.27	−0.193276
$780$	−17529.7	−0.804698
$781$	−11160.8	−0.511352
$782$	−4092.71	−0.187155
$783$	−4857.63	−0.221708
$784$	13361.9	0.608686
$785$	24696.5	1.12288
$786$	1710.45	0.0776204
$787$	36978.0	1.67487	0.837434	−	0.546538i	$-0.184055\pi$
$787$	36978.0	1.67487	0.837434	+	0.546538i	$0.184055\pi$
$788$	−23157.6	−1.04690
$789$	19911.4	0.898433
$790$	12899.5	0.580939
$791$	29001.4	1.30363
$792$	−1056.27	−0.0473901
$793$	−4115.09	−0.184276
$794$	50511.2	2.25765
$795$	10228.0	0.456291
$796$	5619.28	0.250214
$797$	31331.5	1.39250	0.696248	−	0.717801i	$-0.254851\pi$
$797$	31331.5	1.39250	0.696248	+	0.717801i	$0.254851\pi$
$798$	−5333.25	−0.236585
$799$	−456.804	−0.0202260
$800$	33869.4	1.49683
$801$	−2881.71	−0.127116
$802$	33301.8	1.46624
$803$	−8422.82	−0.370155
$804$	−7254.54	−0.318219
$805$	29833.5	1.30620
$806$	4598.61	0.200967
$807$	11636.7	0.507597
$808$	−13329.0	−0.580335
$809$	5698.48	0.247649	0.123824	−	0.992304i	$-0.460484\pi$
$809$	5698.48	0.247649	0.123824	+	0.992304i	$0.460484\pi$
$810$	5021.99	0.217845
$811$	−17697.0	−0.766245	−0.383122	−	0.923698i	$-0.625151\pi$
$811$	−17697.0	−0.766245	−0.383122	+	0.923698i	$0.625151\pi$
$812$	−11963.7	−0.517048
$813$	−13001.9	−0.560882
$814$	11643.4	0.501351
$815$	−37450.6	−1.60962
$816$	2033.75	0.0872494
$817$	−12895.6	−0.552217
$818$	−12325.8	−0.526848
$819$	8000.97	0.341363
$820$	9745.58	0.415037
$821$	−17988.7	−0.764688	−0.382344	−	0.924020i	$-0.624883\pi$
$821$	−17988.7	−0.764688	−0.382344	+	0.924020i	$0.624883\pi$
$822$	4751.35	0.201609
$823$	17706.2	0.749938	0.374969	−	0.927037i	$-0.377653\pi$
$823$	17706.2	0.749938	0.374969	+	0.927037i	$0.377653\pi$
$824$	−4964.85	−0.209901
$825$	−5598.33	−0.236253
$826$	−7649.31	−0.322220
$827$	6569.90	0.276249	0.138124	−	0.990415i	$-0.455893\pi$
$827$	6569.90	0.276249	0.138124	+	0.990415i	$0.455893\pi$
$828$	−5989.62	−0.251393
$829$	11474.2	0.480717	0.240358	−	0.970684i	$-0.422735\pi$
$829$	11474.2	0.480717	0.240358	+	0.970684i	$0.422735\pi$
$830$	65425.8	2.73610
$831$	12210.6	0.509726
$832$	−6062.45	−0.252617
$833$	1454.88	0.0605145
$834$	34670.0	1.43948
$835$	−64031.0	−2.65375
$836$	−2073.13	−0.0857664
$837$	−509.567	−0.0210432
$838$	−32917.6	−1.35694
$839$	19922.7	0.819794	0.409897	−	0.912132i	$-0.365565\pi$
$839$	19922.7	0.819794	0.409897	+	0.912132i	$0.365565\pi$
$840$	−7240.39	−0.297402
$841$	7979.47	0.327175
$842$	11660.3	0.477245
$843$	−18406.9	−0.752037
$844$	−21364.9	−0.871339
$845$	−40405.7	−1.64497
$846$	−1728.40	−0.0702407
$847$	1594.54	0.0646860
$848$	15672.2	0.634652
$849$	−6503.08	−0.262880
$850$	5264.45	0.212434
$851$	−38650.0	−1.55688
$852$	15359.6	0.617617
$853$	8834.19	0.354604	0.177302	−	0.984157i	$-0.443263\pi$
$853$	8834.19	0.354604	0.177302	+	0.984157i	$0.443263\pi$
$854$	2903.49	0.116341
$855$	−5769.97	−0.230794
$856$	−7259.10	−0.289849
$857$	−15359.4	−0.612216	−0.306108	−	0.951997i	$-0.599027\pi$
$857$	−15359.4	−0.612216	−0.306108	+	0.951997i	$0.599027\pi$
$858$	8040.88	0.319943
$859$	17910.8	0.711420	0.355710	−	0.934596i	$-0.384239\pi$
$859$	17910.8	0.711420	0.355710	+	0.934596i	$0.384239\pi$
$860$	29906.6	1.18582
$861$	−4448.11	−0.176064
$862$	−37478.7	−1.48089
$863$	−12016.6	−0.473988	−0.236994	−	0.971511i	$-0.576162\pi$
$863$	−12016.6	−0.473988	−0.236994	+	0.971511i	$0.576162\pi$
$864$	5390.47	0.212254
$865$	−52303.7	−2.05593
$866$	22516.2	0.883522
$867$	−14517.6	−0.568676
$868$	−1254.99	−0.0490751
$869$	−2288.62	−0.0893396
$870$	−33463.6	−1.30405
$871$	−32328.5	−1.25764
$872$	18871.6	0.732881
$873$	8000.49	0.310167
$874$	17792.0	0.688583
$875$	−10099.2	−0.390189
$876$	11591.5	0.447078
$877$	39765.1	1.53110	0.765548	−	0.643379i	$-0.222468\pi$
$877$	39765.1	1.53110	0.765548	+	0.643379i	$0.222468\pi$
$878$	49005.2	1.88365
$879$	−1540.51	−0.0591129
$880$	−14898.8	−0.570726
$881$	−15603.6	−0.596708	−0.298354	−	0.954455i	$-0.596438\pi$
$881$	−15603.6	−0.596708	−0.298354	+	0.954455i	$0.596438\pi$
$882$	5504.79	0.210154
$883$	20076.9	0.765167	0.382584	−	0.923921i	$-0.375034\pi$
$883$	20076.9	0.765167	0.382584	+	0.923921i	$0.375034\pi$
$884$	−2924.63	−0.111274
$885$	−8275.69	−0.314332
$886$	49451.6	1.87512
$887$	46509.7	1.76059	0.880295	−	0.474427i	$-0.157345\pi$
$887$	46509.7	1.76059	0.880295	+	0.474427i	$0.157345\pi$
$888$	9380.10	0.354477
$889$	−26670.4	−1.00618
$890$	−19851.7	−0.747674
$891$	−891.000	−0.0335013
$892$	−9400.91	−0.352876
$893$	1985.83	0.0744158
$894$	8121.19	0.303818
$895$	77058.5	2.87797
$896$	−16770.2	−0.625281
$897$	−26691.6	−0.993540
$898$	27358.6	1.01667
$899$	3395.46	0.125968
$900$	7704.43	0.285349
$901$	1706.43	0.0630960
$902$	−4470.30	−0.165016
$903$	−13650.0	−0.503040
$904$	23480.6	0.863886
$905$	−32019.8	−1.17610
$906$	31753.0	1.16437
$907$	−8882.18	−0.325169	−0.162584	−	0.986695i	$-0.551983\pi$
$907$	−8882.18	−0.325169	−0.162584	+	0.986695i	$0.551983\pi$
$908$	−6545.84	−0.239241
$909$	−11243.4	−0.410254
$910$	55117.6	2.00784
$911$	12657.9	0.460346	0.230173	−	0.973150i	$-0.426071\pi$
$911$	12657.9	0.460346	0.230173	+	0.973150i	$0.426071\pi$
$912$	−8841.18	−0.321010
$913$	−11607.8	−0.420771
$914$	18256.1	0.660675
$915$	3141.24	0.113493
$916$	26065.0	0.940188
$917$	−2080.17	−0.0749109
$918$	837.860	0.0301237
$919$	14900.5	0.534846	0.267423	−	0.963579i	$-0.413828\pi$
$919$	14900.5	0.534846	0.267423	+	0.963579i	$0.413828\pi$
$920$	24154.3	0.865590
$921$	25341.2	0.906645
$922$	49094.6	1.75363
$923$	68446.9	2.44091
$924$	−2194.41	−0.0781285
$925$	49715.4	1.76717
$926$	−18266.0	−0.648227
$927$	−4188.02	−0.148385
$928$	−35919.0	−1.27058
$929$	−616.808	−0.0217834	−0.0108917	−	0.999941i	$-0.503467\pi$
$929$	−616.808	−0.0217834	−0.0108917	+	0.999941i	$0.503467\pi$
$930$	−3510.34	−0.123773
$931$	−6324.69	−0.222646
$932$	−8328.93	−0.292729
$933$	−7709.11	−0.270509
$934$	12784.2	0.447871
$935$	−1622.23	−0.0567406
$936$	6477.87	0.226213
$937$	−30382.3	−1.05928	−0.529640	−	0.848222i	$-0.677673\pi$
$937$	−30382.3	−1.05928	−0.529640	+	0.848222i	$0.677673\pi$
$938$	22810.0	0.794002
$939$	−9944.46	−0.345607
$940$	−4605.39	−0.159799
$941$	5889.56	0.204032	0.102016	−	0.994783i	$-0.467471\pi$
$941$	5889.56	0.204032	0.102016	+	0.994783i	$0.467471\pi$
$942$	15590.0	0.539225
$943$	14839.1	0.512436
$944$	−12680.6	−0.437203
$945$	−6107.52	−0.210241
$946$	−13718.1	−0.471475
$947$	−9504.47	−0.326139	−0.163070	−	0.986615i	$-0.552140\pi$
$947$	−9504.47	−0.326139	−0.163070	+	0.986615i	$0.552140\pi$
$948$	3149.60	0.107905
$949$	51655.2	1.76691
$950$	−22885.7	−0.781591
$951$	−14302.9	−0.487701
$952$	−1207.98	−0.0411247
$953$	8649.86	0.294015	0.147008	−	0.989135i	$-0.453036\pi$
$953$	8649.86	0.294015	0.147008	+	0.989135i	$0.453036\pi$
$954$	6456.59	0.219119
$955$	74847.3	2.53613
$956$	−35445.5	−1.19915
$957$	5937.11	0.200543
$958$	19959.0	0.673115
$959$	−5778.38	−0.194571
$960$	4627.75	0.155583
$961$	−29434.8	−0.988044
$962$	−71406.2	−2.39317
$963$	−6123.30	−0.204902
$964$	12877.9	0.430258
$965$	−63419.4	−2.11559
$966$	18832.8	0.627262
$967$	−53596.6	−1.78237	−0.891185	−	0.453640i	$-0.850125\pi$
$967$	−53596.6	−1.78237	−0.891185	+	0.453640i	$0.850125\pi$
$968$	1291.00	0.0428659
$969$	−962.653	−0.0319142
$970$	55114.3	1.82434
$971$	42442.9	1.40274	0.701369	−	0.712798i	$-0.252572\pi$
$971$	42442.9	1.40274	0.701369	+	0.712798i	$0.252572\pi$
$972$	1226.20	0.0404632
$973$	−42164.1	−1.38923
$974$	1766.42	0.0581108
$975$	34333.3	1.12774
$976$	4813.25	0.157857
$977$	−43203.2	−1.41473	−0.707367	−	0.706847i	$-0.750117\pi$
$977$	−43203.2	−1.41473	−0.707367	+	0.706847i	$0.750117\pi$
$978$	−23641.2	−0.772967
$979$	3522.08	0.114981
$980$	14667.7	0.478105
$981$	15918.8	0.518092
$982$	13627.1	0.442828
$983$	−21992.7	−0.713590	−0.356795	−	0.934183i	$-0.616130\pi$
$983$	−21992.7	−0.713590	−0.356795	+	0.934183i	$0.616130\pi$
$984$	−3601.35	−0.116674
$985$	78775.6	2.54822
$986$	−5583.02	−0.180324
$987$	2102.00	0.0677888
$988$	12714.0	0.409400
$989$	45537.1	1.46410
$990$	−6137.98	−0.197048
$991$	30648.5	0.982423	0.491211	−	0.871040i	$-0.336554\pi$
$991$	30648.5	0.982423	0.491211	+	0.871040i	$0.336554\pi$
$992$	−3767.91	−0.120596
$993$	−8266.67	−0.264184
$994$	−48294.1	−1.54104
$995$	−19115.2	−0.609037
$996$	15974.7	0.508212
$997$	21055.6	0.668844	0.334422	−	0.942423i	$-0.391459\pi$
$997$	21055.6	0.668844	0.334422	+	0.942423i	$0.391459\pi$
$998$	−7239.73	−0.229629
$999$	7912.43	0.250589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.9	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-3.61193 q^{2} +3.00000 q^{3} +5.04607 q^{4} -17.1653 q^{5} -10.8358 q^{6} +13.1780 q^{7} +10.6694 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.61193 q^{2} +3.00000 q^{3} +5.04607 q^{4} -17.1653 q^{5} -10.8358 q^{6} +13.1780 q^{7} +10.6694 q^{8} +9.00000 q^{9} +61.9998 q^{10} -11.0000 q^{11} +15.1382 q^{12} +67.4605 q^{13} -47.5982 q^{14} -51.4958 q^{15} -78.9057 q^{16} -8.59148 q^{17} -32.5074 q^{18} +37.3491 q^{19} -86.6172 q^{20} +39.5341 q^{21} +39.7313 q^{22} -131.887 q^{23} +32.0082 q^{24} +169.646 q^{25} -243.663 q^{26} +27.0000 q^{27} +66.4972 q^{28} -179.912 q^{29} +185.999 q^{30} -18.8728 q^{31} +199.647 q^{32} -33.0000 q^{33} +31.0319 q^{34} -226.204 q^{35} +45.4146 q^{36} +293.053 q^{37} -134.903 q^{38} +202.382 q^{39} -183.143 q^{40} -112.513 q^{41} -142.794 q^{42} -345.273 q^{43} -55.5068 q^{44} -154.487 q^{45} +476.369 q^{46} +53.1694 q^{47} -236.717 q^{48} -169.340 q^{49} -612.752 q^{50} -25.7744 q^{51} +340.411 q^{52} -198.619 q^{53} -97.5222 q^{54} +188.818 q^{55} +140.602 q^{56} +112.047 q^{57} +649.832 q^{58} +160.706 q^{59} -259.851 q^{60} -61.0000 q^{61} +68.1675 q^{62} +118.602 q^{63} -89.8666 q^{64} -1157.98 q^{65} +119.194 q^{66} -479.221 q^{67} -43.3532 q^{68} -395.662 q^{69} +817.035 q^{70} +1014.62 q^{71} +96.0246 q^{72} +765.711 q^{73} -1058.49 q^{74} +508.939 q^{75} +188.466 q^{76} -144.958 q^{77} -730.989 q^{78} +208.056 q^{79} +1354.44 q^{80} +81.0000 q^{81} +406.391 q^{82} +1055.26 q^{83} +199.492 q^{84} +147.475 q^{85} +1247.10 q^{86} -539.737 q^{87} -117.363 q^{88} -320.189 q^{89} +557.998 q^{90} +888.997 q^{91} -665.513 q^{92} -56.6185 q^{93} -192.045 q^{94} -641.108 q^{95} +598.941 q^{96} +888.943 q^{97} +611.644 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

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