LMFDB - Embedded newform 2013.4.a.a.1.5

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:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-4.51714 q^{2} +3.00000 q^{3} +12.4046 q^{4} +19.2722 q^{5} -13.5514 q^{6} -8.39412 q^{7} -19.8961 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.51714 q^{2} +3.00000 q^{3} +12.4046 q^{4} +19.2722 q^{5} -13.5514 q^{6} -8.39412 q^{7} -19.8961 q^{8} +9.00000 q^{9} -87.0554 q^{10} +11.0000 q^{11} +37.2137 q^{12} -69.5315 q^{13} +37.9174 q^{14} +57.8167 q^{15} -9.36319 q^{16} +25.9653 q^{17} -40.6543 q^{18} -84.4322 q^{19} +239.064 q^{20} -25.1823 q^{21} -49.6886 q^{22} -153.535 q^{23} -59.6882 q^{24} +246.419 q^{25} +314.084 q^{26} +27.0000 q^{27} -104.125 q^{28} +105.617 q^{29} -261.166 q^{30} -175.634 q^{31} +201.463 q^{32} +33.0000 q^{33} -117.289 q^{34} -161.773 q^{35} +111.641 q^{36} +295.613 q^{37} +381.392 q^{38} -208.595 q^{39} -383.441 q^{40} +381.828 q^{41} +113.752 q^{42} -516.343 q^{43} +136.450 q^{44} +173.450 q^{45} +693.541 q^{46} +310.044 q^{47} -28.0896 q^{48} -272.539 q^{49} -1113.11 q^{50} +77.8958 q^{51} -862.509 q^{52} +535.291 q^{53} -121.963 q^{54} +211.994 q^{55} +167.010 q^{56} -253.297 q^{57} -477.088 q^{58} -319.431 q^{59} +717.191 q^{60} +61.0000 q^{61} +793.363 q^{62} -75.5470 q^{63} -835.133 q^{64} -1340.03 q^{65} -149.066 q^{66} +663.192 q^{67} +322.088 q^{68} -460.606 q^{69} +730.753 q^{70} +601.363 q^{71} -179.065 q^{72} -141.968 q^{73} -1335.33 q^{74} +739.256 q^{75} -1047.35 q^{76} -92.3353 q^{77} +942.252 q^{78} -1150.13 q^{79} -180.450 q^{80} +81.0000 q^{81} -1724.77 q^{82} -313.223 q^{83} -312.376 q^{84} +500.409 q^{85} +2332.39 q^{86} +316.852 q^{87} -218.857 q^{88} -1298.79 q^{89} -783.498 q^{90} +583.656 q^{91} -1904.54 q^{92} -526.902 q^{93} -1400.51 q^{94} -1627.20 q^{95} +604.390 q^{96} +751.217 q^{97} +1231.10 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * 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 $

$2$	−4.51714	−1.59705	−0.798525	−	0.601961i	$-0.794386\pi$
$2$	−4.51714	−1.59705	−0.798525	+	0.601961i	$0.794386\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.4046	1.55057
$5$	19.2722	1.72376	0.861880	−	0.507112i	$-0.169287\pi$
$5$	19.2722	1.72376	0.861880	+	0.507112i	$0.169287\pi$
$6$	−13.5514	−0.922058
$7$	−8.39412	−0.453240	−0.226620	−	0.973983i	$-0.572767\pi$
$7$	−8.39412	−0.453240	−0.226620	+	0.973983i	$0.572767\pi$
$8$	−19.8961	−0.879290
$9$	9.00000	0.333333
$10$	−87.0554	−2.75293
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	37.2137	0.895223
$13$	−69.5315	−1.48343	−0.741715	−	0.670716i	$-0.765987\pi$
$13$	−69.5315	−1.48343	−0.741715	+	0.670716i	$0.765987\pi$
$14$	37.9174	0.723847
$15$	57.8167	0.995213
$16$	−9.36319	−0.146300
$17$	25.9653	0.370441	0.185221	−	0.982697i	$-0.440700\pi$
$17$	25.9653	0.370441	0.185221	+	0.982697i	$0.440700\pi$
$18$	−40.6543	−0.532350
$19$	−84.4322	−1.01948	−0.509739	−	0.860329i	$-0.670258\pi$
$19$	−84.4322	−1.01948	−0.509739	+	0.860329i	$0.670258\pi$
$20$	239.064	2.67281
$21$	−25.1823	−0.261678
$22$	−49.6886	−0.481529
$23$	−153.535	−1.39193	−0.695964	−	0.718076i	$-0.745023\pi$
$23$	−153.535	−1.39193	−0.695964	+	0.718076i	$0.745023\pi$
$24$	−59.6882	−0.507659
$25$	246.419	1.97135
$26$	314.084	2.36911
$27$	27.0000	0.192450
$28$	−104.125	−0.702780
$29$	105.617	0.676298	0.338149	−	0.941093i	$-0.390199\pi$
$29$	105.617	0.676298	0.338149	+	0.941093i	$0.390199\pi$
$30$	−261.166	−1.58941
$31$	−175.634	−1.01757	−0.508787	−	0.860893i	$-0.669906\pi$
$31$	−175.634	−1.01757	−0.508787	+	0.860893i	$0.669906\pi$
$32$	201.463	1.11294
$33$	33.0000	0.174078
$34$	−117.289	−0.591614
$35$	−161.773	−0.781276
$36$	111.641	0.516857
$37$	295.613	1.31347	0.656737	−	0.754120i	$-0.271936\pi$
$37$	295.613	1.31347	0.656737	+	0.754120i	$0.271936\pi$
$38$	381.392	1.62816
$39$	−208.595	−0.856458
$40$	−383.441	−1.51569
$41$	381.828	1.45443	0.727213	−	0.686412i	$-0.240815\pi$
$41$	381.828	1.45443	0.727213	+	0.686412i	$0.240815\pi$
$42$	113.752	0.417913
$43$	−516.343	−1.83120	−0.915599	−	0.402092i	$-0.868283\pi$
$43$	−516.343	−1.83120	−0.915599	+	0.402092i	$0.868283\pi$
$44$	136.450	0.467515
$45$	173.450	0.574587
$46$	693.541	2.22298
$47$	310.044	0.962225	0.481113	−	0.876659i	$-0.340233\pi$
$47$	310.044	0.962225	0.481113	+	0.876659i	$0.340233\pi$
$48$	−28.0896	−0.0844663
$49$	−272.539	−0.794574
$50$	−1113.11	−3.14834
$51$	77.8958	0.213874
$52$	−862.509	−2.30016
$53$	535.291	1.38732	0.693659	−	0.720303i	$-0.255997\pi$
$53$	535.291	1.38732	0.693659	+	0.720303i	$0.255997\pi$
$54$	−121.963	−0.307353
$55$	211.994	0.519733
$56$	167.010	0.398529
$57$	−253.297	−0.588596
$58$	−477.088	−1.08008
$59$	−319.431	−0.704854	−0.352427	−	0.935839i	$-0.614644\pi$
$59$	−319.431	−0.704854	−0.352427	+	0.935839i	$0.614644\pi$
$60$	717.191	1.54315
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	793.363	1.62512
$63$	−75.5470	−0.151080
$64$	−835.133	−1.63112
$65$	−1340.03	−2.55708
$66$	−149.066	−0.278011
$67$	663.192	1.20928	0.604640	−	0.796499i	$-0.293317\pi$
$67$	663.192	1.20928	0.604640	+	0.796499i	$0.293317\pi$
$68$	322.088	0.574396
$69$	−460.606	−0.803630
$70$	730.753	1.24774
$71$	601.363	1.00519	0.502596	−	0.864521i	$-0.332378\pi$
$71$	601.363	1.00519	0.502596	+	0.864521i	$0.332378\pi$
$72$	−179.065	−0.293097
$73$	−141.968	−0.227618	−0.113809	−	0.993503i	$-0.536305\pi$
$73$	−141.968	−0.227618	−0.113809	+	0.993503i	$0.536305\pi$
$74$	−1335.33	−2.09768
$75$	739.256	1.13816
$76$	−1047.35	−1.58077
$77$	−92.3353	−0.136657
$78$	942.252	1.36781
$79$	−1150.13	−1.63797	−0.818987	−	0.573812i	$-0.805464\pi$
$79$	−1150.13	−1.63797	−0.818987	+	0.573812i	$0.805464\pi$
$80$	−180.450	−0.252186
$81$	81.0000	0.111111
$82$	−1724.77	−2.32279
$83$	−313.223	−0.414225	−0.207112	−	0.978317i	$-0.566407\pi$
$83$	−313.223	−0.414225	−0.207112	+	0.978317i	$0.566407\pi$
$84$	−312.376	−0.405750
$85$	500.409	0.638552
$86$	2332.39	2.92452
$87$	316.852	0.390461
$88$	−218.857	−0.265116
$89$	−1298.79	−1.54688	−0.773438	−	0.633872i	$-0.781465\pi$
$89$	−1298.79	−1.54688	−0.773438	+	0.633872i	$0.781465\pi$
$90$	−783.498	−0.917644
$91$	583.656	0.672349
$92$	−1904.54	−2.15828
$93$	−526.902	−0.587496
$94$	−1400.51	−1.53672
$95$	−1627.20	−1.75733
$96$	604.390	0.642555
$97$	751.217	0.786335	0.393168	−	0.919467i	$-0.371379\pi$
$97$	751.217	0.786335	0.393168	+	0.919467i	$0.371379\pi$
$98$	1231.10	1.26897
$99$	99.0000	0.100504
$100$	3056.72	3.05672
$101$	6.91174	0.00680935	0.00340467	−	0.999994i	$-0.498916\pi$
$101$	6.91174	0.00680935	0.00340467	+	0.999994i	$0.498916\pi$
$102$	−351.866	−0.341568
$103$	−1782.09	−1.70480	−0.852400	−	0.522890i	$-0.824854\pi$
$103$	−1782.09	−1.70480	−0.852400	+	0.522890i	$0.824854\pi$
$104$	1383.40	1.30437
$105$	−485.320	−0.451070
$106$	−2417.99	−2.21562
$107$	−1354.06	−1.22338	−0.611691	−	0.791097i	$-0.709510\pi$
$107$	−1354.06	−1.22338	−0.611691	+	0.791097i	$0.709510\pi$
$108$	334.923	0.298408
$109$	−421.277	−0.370193	−0.185096	−	0.982720i	$-0.559260\pi$
$109$	−421.277	−0.370193	−0.185096	+	0.982720i	$0.559260\pi$
$110$	−957.609	−0.830040
$111$	886.840	0.758334
$112$	78.5957	0.0663089
$113$	−1745.76	−1.45334	−0.726669	−	0.686987i	$-0.758933\pi$
$113$	−1745.76	−1.45334	−0.726669	+	0.686987i	$0.758933\pi$
$114$	1144.18	0.940017
$115$	−2958.97	−2.39935
$116$	1310.14	1.04865
$117$	−625.784	−0.494476
$118$	1442.92	1.12569
$119$	−217.956	−0.167899
$120$	−1150.32	−0.875081
$121$	121.000	0.0909091
$122$	−275.546	−0.204481
$123$	1145.48	0.839714
$124$	−2178.66	−1.57782
$125$	2340.00	1.67437
$126$	341.257	0.241282
$127$	−2053.68	−1.43492	−0.717461	−	0.696599i	$-0.754696\pi$
$127$	−2053.68	−1.43492	−0.717461	+	0.696599i	$0.754696\pi$
$128$	2160.71	1.49204
$129$	−1549.03	−1.05724
$130$	6053.09	4.08378
$131$	−1157.26	−0.771834	−0.385917	−	0.922534i	$-0.626115\pi$
$131$	−1157.26	−0.771834	−0.385917	+	0.922534i	$0.626115\pi$
$132$	409.351	0.269920
$133$	708.734	0.462068
$134$	−2995.73	−1.93128
$135$	520.350	0.331738
$136$	−516.607	−0.325726
$137$	394.157	0.245804	0.122902	−	0.992419i	$-0.460780\pi$
$137$	394.157	0.245804	0.122902	+	0.992419i	$0.460780\pi$
$138$	2080.62	1.28344
$139$	451.395	0.275445	0.137722	−	0.990471i	$-0.456022\pi$
$139$	451.395	0.275445	0.137722	+	0.990471i	$0.456022\pi$
$140$	−2006.73	−1.21142
$141$	930.132	0.555541
$142$	−2716.44	−1.60534
$143$	−764.847	−0.447271
$144$	−84.2687	−0.0487666
$145$	2035.48	1.16578
$146$	641.289	0.363517
$147$	−817.616	−0.458747
$148$	3666.96	2.03663
$149$	3309.08	1.81940	0.909698	−	0.415270i	$-0.136313\pi$
$149$	3309.08	1.81940	0.909698	+	0.415270i	$0.136313\pi$
$150$	−3339.32	−1.81770
$151$	−579.167	−0.312132	−0.156066	−	0.987747i	$-0.549881\pi$
$151$	−579.167	−0.312132	−0.156066	+	0.987747i	$0.549881\pi$
$152$	1679.87	0.896417
$153$	233.687	0.123480
$154$	417.092	0.218248
$155$	−3384.86	−1.75405
$156$	−2587.53	−1.32800
$157$	673.313	0.342269	0.171135	−	0.985248i	$-0.445257\pi$
$157$	673.313	0.342269	0.171135	+	0.985248i	$0.445257\pi$
$158$	5195.31	2.61593
$159$	1605.87	0.800969
$160$	3882.65	1.91844
$161$	1288.79	0.630877
$162$	−365.888	−0.177450
$163$	1158.56	0.556720	0.278360	−	0.960477i	$-0.410209\pi$
$163$	1158.56	0.556720	0.278360	+	0.960477i	$0.410209\pi$
$164$	4736.41	2.25519
$165$	635.983	0.300068
$166$	1414.87	0.661538
$167$	−3712.65	−1.72032	−0.860159	−	0.510026i	$-0.829636\pi$
$167$	−3712.65	−1.72032	−0.860159	+	0.510026i	$0.829636\pi$
$168$	501.030	0.230091
$169$	2637.64	1.20056
$170$	−2260.42	−1.01980
$171$	−759.890	−0.339826
$172$	−6405.01	−2.83940
$173$	−3737.97	−1.64273	−0.821365	−	0.570402i	$-0.806787\pi$
$173$	−3737.97	−1.64273	−0.821365	+	0.570402i	$0.806787\pi$
$174$	−1431.27	−0.623586
$175$	−2068.47	−0.893493
$176$	−102.995	−0.0441111
$177$	−958.293	−0.406948
$178$	5866.84	2.47044
$179$	−801.306	−0.334595	−0.167297	−	0.985906i	$-0.553504\pi$
$179$	−801.306	−0.334595	−0.167297	+	0.985906i	$0.553504\pi$
$180$	2151.57	0.890938
$181$	−162.904	−0.0668979	−0.0334490	−	0.999440i	$-0.510649\pi$
$181$	−162.904	−0.0668979	−0.0334490	+	0.999440i	$0.510649\pi$
$182$	−2636.46	−1.07378
$183$	183.000	0.0739221
$184$	3054.75	1.22391
$185$	5697.13	2.26411
$186$	2380.09	0.938262
$187$	285.618	0.111692
$188$	3845.96	1.49200
$189$	−226.641	−0.0872260
$190$	7350.28	2.80655
$191$	−1118.95	−0.423896	−0.211948	−	0.977281i	$-0.567981\pi$
$191$	−1118.95	−0.423896	−0.211948	+	0.977281i	$0.567981\pi$
$192$	−2505.40	−0.941727
$193$	−319.624	−0.119208	−0.0596038	−	0.998222i	$-0.518984\pi$
$193$	−319.624	−0.119208	−0.0596038	+	0.998222i	$0.518984\pi$
$194$	−3393.35	−1.25582
$195$	−4020.08	−1.47633
$196$	−3380.73	−1.23204
$197$	1095.95	0.396360	0.198180	−	0.980166i	$-0.436497\pi$
$197$	1095.95	0.396360	0.198180	+	0.980166i	$0.436497\pi$
$198$	−447.197	−0.160510
$199$	−3709.01	−1.32123	−0.660615	−	0.750725i	$-0.729704\pi$
$199$	−3709.01	−1.32123	−0.660615	+	0.750725i	$0.729704\pi$
$200$	−4902.76	−1.73339
$201$	1989.58	0.698179
$202$	−31.2213	−0.0108749
$203$	−886.564	−0.306525
$204$	966.264	0.331628
$205$	7358.67	2.50708
$206$	8049.95	2.72265
$207$	−1381.82	−0.463976
$208$	651.037	0.217026
$209$	−928.754	−0.307384
$210$	2192.26	0.720382
$211$	3270.16	1.06695	0.533477	−	0.845815i	$-0.320885\pi$
$211$	3270.16	1.06695	0.533477	+	0.845815i	$0.320885\pi$
$212$	6640.06	2.15114
$213$	1804.09	0.580348
$214$	6116.48	1.95380
$215$	−9951.07	−3.15655
$216$	−537.194	−0.169220
$217$	1474.29	0.461205
$218$	1902.97	0.591217
$219$	−425.904	−0.131415
$220$	2629.70	0.805883
$221$	−1805.41	−0.549524
$222$	−4005.98	−1.21110
$223$	1010.82	0.303540	0.151770	−	0.988416i	$-0.451503\pi$
$223$	1010.82	0.303540	0.151770	+	0.988416i	$0.451503\pi$
$224$	−1691.11	−0.504428
$225$	2217.77	0.657116
$226$	7885.85	2.32106
$227$	6087.22	1.77984	0.889919	−	0.456119i	$-0.150761\pi$
$227$	6087.22	1.77984	0.889919	+	0.456119i	$0.150761\pi$
$228$	−3142.04	−0.912660
$229$	588.885	0.169933	0.0849665	−	0.996384i	$-0.472922\pi$
$229$	588.885	0.169933	0.0849665	+	0.996384i	$0.472922\pi$
$230$	13366.1	3.83188
$231$	−277.006	−0.0788989
$232$	−2101.37	−0.594662
$233$	−6266.47	−1.76193	−0.880966	−	0.473179i	$-0.843106\pi$
$233$	−6266.47	−1.76193	−0.880966	+	0.473179i	$0.843106\pi$
$234$	2826.75	0.789704
$235$	5975.24	1.65865
$236$	−3962.41	−1.09293
$237$	−3450.40	−0.945685
$238$	984.536	0.268143
$239$	−3292.77	−0.891179	−0.445589	−	0.895237i	$-0.647006\pi$
$239$	−3292.77	−0.891179	−0.445589	+	0.895237i	$0.647006\pi$
$240$	−541.349	−0.145600
$241$	4009.02	1.07155	0.535776	−	0.844360i	$-0.320019\pi$
$241$	4009.02	1.07155	0.535776	+	0.844360i	$0.320019\pi$
$242$	−546.574	−0.145186
$243$	243.000	0.0641500
$244$	756.679	0.198530
$245$	−5252.43	−1.36965
$246$	−5174.31	−1.34107
$247$	5870.70	1.51232
$248$	3494.42	0.894743
$249$	−939.668	−0.239153
$250$	−10570.1	−2.67406
$251$	7724.02	1.94237	0.971187	−	0.238318i	$-0.0765962\pi$
$251$	7724.02	1.94237	0.971187	+	0.238318i	$0.0765962\pi$
$252$	−937.129	−0.234260
$253$	−1688.89	−0.419682
$254$	9276.78	2.29164
$255$	1501.23	0.368668
$256$	−3079.16	−0.751748
$257$	−1296.11	−0.314588	−0.157294	−	0.987552i	$-0.550277\pi$
$257$	−1296.11	−0.314588	−0.157294	+	0.987552i	$0.550277\pi$
$258$	6997.18	1.68847
$259$	−2481.41	−0.595318
$260$	−16622.5	−3.96493
$261$	950.556	0.225433
$262$	5227.50	1.23266
$263$	−7406.51	−1.73652	−0.868260	−	0.496109i	$-0.834762\pi$
$263$	−7406.51	−1.73652	−0.868260	+	0.496109i	$0.834762\pi$
$264$	−656.570	−0.153065
$265$	10316.3	2.39140
$266$	−3201.45	−0.737946
$267$	−3896.38	−0.893089
$268$	8226.61	1.87508
$269$	−983.404	−0.222897	−0.111448	−	0.993770i	$-0.535549\pi$
$269$	−983.404	−0.222897	−0.111448	+	0.993770i	$0.535549\pi$
$270$	−2350.49	−0.529802
$271$	−5315.16	−1.19141	−0.595707	−	0.803202i	$-0.703128\pi$
$271$	−5315.16	−1.19141	−0.595707	+	0.803202i	$0.703128\pi$
$272$	−243.118	−0.0541955
$273$	1750.97	0.388181
$274$	−1780.46	−0.392561
$275$	2710.60	0.594384
$276$	−5713.62	−1.24609
$277$	2045.14	0.443612	0.221806	−	0.975091i	$-0.428805\pi$
$277$	2045.14	0.443612	0.221806	+	0.975091i	$0.428805\pi$
$278$	−2039.01	−0.439899
$279$	−1580.71	−0.339191
$280$	3218.65	0.686969
$281$	−3003.19	−0.637563	−0.318781	−	0.947828i	$-0.603274\pi$
$281$	−3003.19	−0.637563	−0.318781	+	0.947828i	$0.603274\pi$
$282$	−4201.54	−0.887227
$283$	134.132	0.0281743	0.0140872	−	0.999901i	$-0.495516\pi$
$283$	134.132	0.0281743	0.0140872	+	0.999901i	$0.495516\pi$
$284$	7459.65	1.55862
$285$	−4881.59	−1.01460
$286$	3454.92	0.714314
$287$	−3205.11	−0.659204
$288$	1813.17	0.370980
$289$	−4238.80	−0.862773
$290$	−9194.55	−1.86180
$291$	2253.65	0.453991
$292$	−1761.05	−0.352938
$293$	−5488.74	−1.09439	−0.547194	−	0.837006i	$-0.684304\pi$
$293$	−5488.74	−1.09439	−0.547194	+	0.837006i	$0.684304\pi$
$294$	3693.29	0.732643
$295$	−6156.15	−1.21500
$296$	−5881.54	−1.15492
$297$	297.000	0.0580259
$298$	−14947.6	−2.90567
$299$	10675.6	2.06483
$300$	9170.15	1.76480
$301$	4334.24	0.829972
$302$	2616.18	0.498491
$303$	20.7352	0.00393138
$304$	790.555	0.149149
$305$	1175.61	0.220705
$306$	−1055.60	−0.197205
$307$	−8186.26	−1.52187	−0.760936	−	0.648827i	$-0.775260\pi$
$307$	−8186.26	−1.52187	−0.760936	+	0.648827i	$0.775260\pi$
$308$	−1145.38	−0.211896
$309$	−5346.27	−0.984267
$310$	15289.9	2.80131
$311$	2069.89	0.377404	0.188702	−	0.982034i	$-0.439572\pi$
$311$	2069.89	0.377404	0.188702	+	0.982034i	$0.439572\pi$
$312$	4150.21	0.753076
$313$	−4398.12	−0.794239	−0.397119	−	0.917767i	$-0.629990\pi$
$313$	−4398.12	−0.794239	−0.397119	+	0.917767i	$0.629990\pi$
$314$	−3041.45	−0.546621
$315$	−1455.96	−0.260425
$316$	−14266.9	−2.53980
$317$	−531.576	−0.0941838	−0.0470919	−	0.998891i	$-0.514995\pi$
$317$	−531.576	−0.0941838	−0.0470919	+	0.998891i	$0.514995\pi$
$318$	−7253.96	−1.27919
$319$	1161.79	0.203912
$320$	−16094.9	−2.81166
$321$	−4062.18	−0.706320
$322$	−5821.67	−1.00754
$323$	−2192.31	−0.377657
$324$	1004.77	0.172286
$325$	−17133.9	−2.92436
$326$	−5233.38	−0.889110
$327$	−1263.83	−0.213731
$328$	−7596.87	−1.27886
$329$	−2602.55	−0.436119
$330$	−2872.83	−0.479224
$331$	−3295.51	−0.547244	−0.273622	−	0.961837i	$-0.588222\pi$
$331$	−3295.51	−0.547244	−0.273622	+	0.961837i	$0.588222\pi$
$332$	−3885.39	−0.642285
$333$	2660.52	0.437825
$334$	16770.5	2.74744
$335$	12781.2	2.08451
$336$	235.787	0.0382835
$337$	2625.34	0.424367	0.212183	−	0.977230i	$-0.431943\pi$
$337$	2625.34	0.424367	0.212183	+	0.977230i	$0.431943\pi$
$338$	−11914.6	−1.91736
$339$	−5237.28	−0.839086
$340$	6207.35	0.990121
$341$	−1931.97	−0.306810
$342$	3432.53	0.542719
$343$	5166.90	0.813372
$344$	10273.2	1.61016
$345$	−8876.91	−1.38527
$346$	16884.9	2.62352
$347$	−2769.46	−0.428451	−0.214226	−	0.976784i	$-0.568723\pi$
$347$	−2769.46	−0.428451	−0.214226	+	0.976784i	$0.568723\pi$
$348$	3930.41	0.605437
$349$	1774.10	0.272107	0.136053	−	0.990701i	$-0.456558\pi$
$349$	1774.10	0.272107	0.136053	+	0.990701i	$0.456558\pi$
$350$	9343.55	1.42695
$351$	−1877.35	−0.285486
$352$	2216.10	0.335564
$353$	1016.08	0.153202	0.0766009	−	0.997062i	$-0.475593\pi$
$353$	1016.08	0.153202	0.0766009	+	0.997062i	$0.475593\pi$
$354$	4328.75	0.649916
$355$	11589.6	1.73271
$356$	−16111.0	−2.39854
$357$	−653.867	−0.0969364
$358$	3619.61	0.534365
$359$	−1815.38	−0.266886	−0.133443	−	0.991056i	$-0.542603\pi$
$359$	−1815.38	−0.266886	−0.133443	+	0.991056i	$0.542603\pi$
$360$	−3450.97	−0.505229
$361$	269.798	0.0393349
$362$	735.859	0.106839
$363$	363.000	0.0524864
$364$	7240.00	1.04253
$365$	−2736.04	−0.392358
$366$	−826.637	−0.118057
$367$	−4610.16	−0.655717	−0.327859	−	0.944727i	$-0.606327\pi$
$367$	−4610.16	−0.655717	−0.327859	+	0.944727i	$0.606327\pi$
$368$	1437.58	0.203639
$369$	3436.45	0.484809
$370$	−25734.7	−3.61590
$371$	−4493.30	−0.628788
$372$	−6535.99	−0.910955
$373$	−9817.78	−1.36286	−0.681428	−	0.731885i	$-0.738641\pi$
$373$	−9817.78	−1.36286	−0.681428	+	0.731885i	$0.738641\pi$
$374$	−1290.18	−0.178378
$375$	7020.01	0.966699
$376$	−6168.66	−0.846075
$377$	−7343.74	−1.00324
$378$	1023.77	0.139304
$379$	−4083.30	−0.553417	−0.276708	−	0.960954i	$-0.589244\pi$
$379$	−4083.30	−0.553417	−0.276708	+	0.960954i	$0.589244\pi$
$380$	−20184.7	−2.72487
$381$	−6161.05	−0.828452
$382$	5054.44	0.676984
$383$	−1116.53	−0.148961	−0.0744806	−	0.997222i	$-0.523730\pi$
$383$	−1116.53	−0.148961	−0.0744806	+	0.997222i	$0.523730\pi$
$384$	6482.13	0.861431
$385$	−1779.51	−0.235564
$386$	1443.79	0.190380
$387$	−4647.08	−0.610399
$388$	9318.52	1.21927
$389$	−667.105	−0.0869501	−0.0434750	−	0.999055i	$-0.513843\pi$
$389$	−667.105	−0.0869501	−0.0434750	+	0.999055i	$0.513843\pi$
$390$	18159.3	2.35777
$391$	−3986.59	−0.515628
$392$	5422.45	0.698661
$393$	−3471.78	−0.445618
$394$	−4950.55	−0.633008
$395$	−22165.6	−2.82347
$396$	1228.05	0.155838
$397$	−3033.86	−0.383539	−0.191770	−	0.981440i	$-0.561423\pi$
$397$	−3033.86	−0.383539	−0.191770	+	0.981440i	$0.561423\pi$
$398$	16754.1	2.11007
$399$	2126.20	0.266775
$400$	−2307.26	−0.288408
$401$	2151.19	0.267893	0.133947	−	0.990989i	$-0.457235\pi$
$401$	2151.19	0.267893	0.133947	+	0.990989i	$0.457235\pi$
$402$	−8987.20	−1.11503
$403$	12212.1	1.50950
$404$	85.7372	0.0105584
$405$	1561.05	0.191529
$406$	4004.74	0.489536
$407$	3251.75	0.396027
$408$	−1549.82	−0.188058
$409$	−7933.94	−0.959189	−0.479594	−	0.877490i	$-0.659216\pi$
$409$	−7933.94	−0.959189	−0.479594	+	0.877490i	$0.659216\pi$
$410$	−33240.2	−4.00394
$411$	1182.47	0.141915
$412$	−22106.0	−2.64341
$413$	2681.34	0.319468
$414$	6241.87	0.740994
$415$	−6036.50	−0.714024
$416$	−14008.1	−1.65097
$417$	1354.18	0.159028
$418$	4195.31	0.490908
$419$	10452.1	1.21866	0.609331	−	0.792916i	$-0.291438\pi$
$419$	10452.1	1.21866	0.609331	+	0.792916i	$0.291438\pi$
$420$	−6020.18	−0.699416
$421$	9459.08	1.09503	0.547515	−	0.836796i	$-0.315574\pi$
$421$	9459.08	1.09503	0.547515	+	0.836796i	$0.315574\pi$
$422$	−14771.8	−1.70398
$423$	2790.40	0.320742
$424$	−10650.2	−1.21986
$425$	6398.33	0.730269
$426$	−8149.32	−0.926845
$427$	−512.041	−0.0580314
$428$	−16796.5	−1.89694
$429$	−2294.54	−0.258232
$430$	44950.4	5.04117
$431$	17812.1	1.99067	0.995334	−	0.0964886i	$-0.0307611\pi$
$431$	17812.1	1.99067	0.995334	+	0.0964886i	$0.0307611\pi$
$432$	−252.806	−0.0281554
$433$	−8531.00	−0.946822	−0.473411	−	0.880842i	$-0.656977\pi$
$433$	−8531.00	−0.946822	−0.473411	+	0.880842i	$0.656977\pi$
$434$	−6659.58	−0.736567
$435$	6106.44	0.673061
$436$	−5225.76	−0.574010
$437$	12963.3	1.41904
$438$	1923.87	0.209877
$439$	6520.64	0.708914	0.354457	−	0.935072i	$-0.384666\pi$
$439$	6520.64	0.708914	0.354457	+	0.935072i	$0.384666\pi$
$440$	−4217.86	−0.456996
$441$	−2452.85	−0.264858
$442$	8155.27	0.877617
$443$	6492.89	0.696358	0.348179	−	0.937428i	$-0.386800\pi$
$443$	6492.89	0.696358	0.348179	+	0.937428i	$0.386800\pi$
$444$	11000.9	1.17585
$445$	−25030.7	−2.66644
$446$	−4566.02	−0.484770
$447$	9927.23	1.05043
$448$	7010.21	0.739288
$449$	−16799.8	−1.76577	−0.882887	−	0.469586i	$-0.844403\pi$
$449$	−16799.8	−1.76577	−0.882887	+	0.469586i	$0.844403\pi$
$450$	−10018.0	−1.04945
$451$	4200.11	0.438526
$452$	−21655.4	−2.25351
$453$	−1737.50	−0.180210
$454$	−27496.8	−2.84249
$455$	11248.3	1.15897
$456$	5039.61	0.517547
$457$	−16736.7	−1.71315	−0.856576	−	0.516021i	$-0.827413\pi$
$457$	−16736.7	−1.71315	−0.856576	+	0.516021i	$0.827413\pi$
$458$	−2660.08	−0.271392
$459$	701.062	0.0712915
$460$	−36704.7	−3.72036
$461$	11237.2	1.13529	0.567644	−	0.823274i	$-0.307855\pi$
$461$	11237.2	1.13529	0.567644	+	0.823274i	$0.307855\pi$
$462$	1251.27	0.126006
$463$	−10398.8	−1.04378	−0.521892	−	0.853012i	$-0.674774\pi$
$463$	−10398.8	−1.04378	−0.521892	+	0.853012i	$0.674774\pi$
$464$	−988.915	−0.0989423
$465$	−10154.6	−1.01270
$466$	28306.5	2.81390
$467$	−13573.6	−1.34499	−0.672496	−	0.740101i	$-0.734778\pi$
$467$	−13573.6	−1.34499	−0.672496	+	0.740101i	$0.734778\pi$
$468$	−7762.58	−0.766721
$469$	−5566.91	−0.548094
$470$	−26991.0	−2.64894
$471$	2019.94	0.197609
$472$	6355.42	0.619771
$473$	−5679.77	−0.552127
$474$	15585.9	1.51031
$475$	−20805.7	−2.00975
$476$	−2703.64	−0.260339
$477$	4817.62	0.462440
$478$	14873.9	1.42326
$479$	14537.2	1.38668	0.693342	−	0.720609i	$-0.256138\pi$
$479$	14537.2	1.38668	0.693342	+	0.720609i	$0.256138\pi$
$480$	11647.9	1.10761
$481$	−20554.5	−1.94845
$482$	−18109.3	−1.71132
$483$	3866.38	0.364237
$484$	1500.95	0.140961
$485$	14477.6	1.35545
$486$	−1097.67	−0.102451
$487$	3309.66	0.307957	0.153979	−	0.988074i	$-0.450791\pi$
$487$	3309.66	0.307957	0.153979	+	0.988074i	$0.450791\pi$
$488$	−1213.66	−0.112582
$489$	3475.68	0.321422
$490$	23726.0	2.18741
$491$	−1891.54	−0.173857	−0.0869287	−	0.996215i	$-0.527705\pi$
$491$	−1891.54	−0.173857	−0.0869287	+	0.996215i	$0.527705\pi$
$492$	14209.2	1.30204
$493$	2742.38	0.250529
$494$	−26518.8	−2.41526
$495$	1907.95	0.173244
$496$	1644.49	0.148871
$497$	−5047.91	−0.455593
$498$	4244.62	0.381939
$499$	4522.53	0.405724	0.202862	−	0.979207i	$-0.434976\pi$
$499$	4522.53	0.405724	0.202862	+	0.979207i	$0.434976\pi$
$500$	29026.8	2.59623
$501$	−11137.9	−0.993226
$502$	−34890.5	−3.10207
$503$	−4982.91	−0.441704	−0.220852	−	0.975307i	$-0.570884\pi$
$503$	−4982.91	−0.441704	−0.220852	+	0.975307i	$0.570884\pi$
$504$	1503.09	0.132843
$505$	133.205	0.0117377
$506$	7628.96	0.670254
$507$	7912.91	0.693145
$508$	−25475.1	−2.22495
$509$	16101.1	1.40210	0.701051	−	0.713112i	$-0.252715\pi$
$509$	16101.1	1.40210	0.701051	+	0.713112i	$0.252715\pi$
$510$	−6781.25	−0.588782
$511$	1191.70	0.103165
$512$	−3376.67	−0.291463
$513$	−2279.67	−0.196199
$514$	5854.71	0.502413
$515$	−34344.8	−2.93867
$516$	−19215.0	−1.63933
$517$	3410.49	0.290122
$518$	11208.9	0.950754
$519$	−11213.9	−0.948431
$520$	26661.3	2.24841
$521$	−3940.09	−0.331322	−0.165661	−	0.986183i	$-0.552976\pi$
$521$	−3940.09	−0.331322	−0.165661	+	0.986183i	$0.552976\pi$
$522$	−4293.80	−0.360027
$523$	14767.6	1.23469	0.617346	−	0.786692i	$-0.288208\pi$
$523$	14767.6	1.23469	0.617346	+	0.786692i	$0.288208\pi$
$524$	−14355.3	−1.19678
$525$	−6205.40	−0.515859
$526$	33456.3	2.77331
$527$	−4560.38	−0.376951
$528$	−308.985	−0.0254675
$529$	11406.1	0.937465
$530$	−46600.0	−3.81919
$531$	−2874.88	−0.234951
$532$	8791.54	0.716469
$533$	−26549.1	−2.15754
$534$	17600.5	1.42631
$535$	−26095.7	−2.10882
$536$	−13194.9	−1.06331
$537$	−2403.92	−0.193178
$538$	4442.17	0.355977
$539$	−2997.93	−0.239573
$540$	6454.72	0.514383
$541$	2676.50	0.212702	0.106351	−	0.994329i	$-0.466083\pi$
$541$	2676.50	0.212702	0.106351	+	0.994329i	$0.466083\pi$
$542$	24009.3	1.90275
$543$	−488.711	−0.0386235
$544$	5231.05	0.412279
$545$	−8118.94	−0.638123
$546$	−7909.37	−0.619945
$547$	12487.7	0.976118	0.488059	−	0.872811i	$-0.337705\pi$
$547$	12487.7	0.976118	0.488059	+	0.872811i	$0.337705\pi$
$548$	4889.35	0.381136
$549$	549.000	0.0426790
$550$	−12244.2	−0.949261
$551$	−8917.50	−0.689471
$552$	9164.26	0.706624
$553$	9654.34	0.742395
$554$	−9238.18	−0.708470
$555$	17091.4	1.30719
$556$	5599.36	0.427096
$557$	5196.47	0.395299	0.197650	−	0.980273i	$-0.436669\pi$
$557$	5196.47	0.395299	0.197650	+	0.980273i	$0.436669\pi$
$558$	7140.27	0.541706
$559$	35902.1	2.71645
$560$	1514.71	0.114301
$561$	856.854	0.0644856
$562$	13565.8	1.01822
$563$	19849.7	1.48591	0.742953	−	0.669343i	$-0.233424\pi$
$563$	19849.7	1.48591	0.742953	+	0.669343i	$0.233424\pi$
$564$	11537.9	0.861406
$565$	−33644.7	−2.50521
$566$	−605.894	−0.0449958
$567$	−679.923	−0.0503600
$568$	−11964.8	−0.883856
$569$	3488.97	0.257056	0.128528	−	0.991706i	$-0.458975\pi$
$569$	3488.97	0.257056	0.128528	+	0.991706i	$0.458975\pi$
$570$	22050.8	1.62036
$571$	−20490.5	−1.50175	−0.750877	−	0.660442i	$-0.770369\pi$
$571$	−20490.5	−1.50175	−0.750877	+	0.660442i	$0.770369\pi$
$572$	−9487.60	−0.693525
$573$	−3356.84	−0.244737
$574$	14477.9	1.05278
$575$	−37834.0	−2.74398
$576$	−7516.20	−0.543707
$577$	1947.35	0.140501	0.0702507	−	0.997529i	$-0.477620\pi$
$577$	1947.35	0.140501	0.0702507	+	0.997529i	$0.477620\pi$
$578$	19147.3	1.37789
$579$	−958.873	−0.0688245
$580$	25249.3	1.80762
$581$	2629.23	0.187743
$582$	−10180.1	−0.725046
$583$	5888.20	0.418292
$584$	2824.60	0.200142
$585$	−12060.2	−0.852359
$586$	24793.4	1.74779
$587$	12748.0	0.896366	0.448183	−	0.893942i	$-0.352071\pi$
$587$	12748.0	0.896366	0.448183	+	0.893942i	$0.352071\pi$
$588$	−10142.2	−0.711321
$589$	14829.2	1.03739
$590$	27808.2	1.94042
$591$	3287.84	0.228839
$592$	−2767.88	−0.192161
$593$	13896.4	0.962325	0.481162	−	0.876631i	$-0.340215\pi$
$593$	13896.4	0.962325	0.481162	+	0.876631i	$0.340215\pi$
$594$	−1341.59	−0.0926703
$595$	−4200.49	−0.289417
$596$	41047.7	2.82110
$597$	−11127.0	−0.762812
$598$	−48223.0	−3.29763
$599$	−21993.2	−1.50020	−0.750100	−	0.661324i	$-0.769995\pi$
$599$	−21993.2	−1.50020	−0.750100	+	0.661324i	$0.769995\pi$
$600$	−14708.3	−1.00077
$601$	−6768.87	−0.459414	−0.229707	−	0.973260i	$-0.573777\pi$
$601$	−6768.87	−0.459414	−0.229707	+	0.973260i	$0.573777\pi$
$602$	−19578.4	−1.32551
$603$	5968.73	0.403094
$604$	−7184.32	−0.483983
$605$	2331.94	0.156705
$606$	−93.6640	−0.00627861
$607$	−28622.1	−1.91390	−0.956948	−	0.290258i	$-0.906259\pi$
$607$	−28622.1	−1.91390	−0.956948	+	0.290258i	$0.906259\pi$
$608$	−17010.0	−1.13462
$609$	−2659.69	−0.176972
$610$	−5310.38	−0.352477
$611$	−21557.8	−1.42739
$612$	2898.79	0.191465
$613$	8657.94	0.570458	0.285229	−	0.958459i	$-0.407930\pi$
$613$	8657.94	0.570458	0.285229	+	0.958459i	$0.407930\pi$
$614$	36978.5	2.43051
$615$	22076.0	1.44746
$616$	1837.11	0.120161
$617$	15491.5	1.01080	0.505400	−	0.862885i	$-0.331345\pi$
$617$	15491.5	1.01080	0.505400	+	0.862885i	$0.331345\pi$
$618$	24149.8	1.57192
$619$	2660.88	0.172778	0.0863892	−	0.996261i	$-0.472467\pi$
$619$	2660.88	0.172778	0.0863892	+	0.996261i	$0.472467\pi$
$620$	−41987.7	−2.71978
$621$	−4145.46	−0.267877
$622$	−9349.98	−0.602733
$623$	10902.2	0.701105
$624$	1953.11	0.125300
$625$	14294.8	0.914866
$626$	19866.9	1.26844
$627$	−2786.26	−0.177468
$628$	8352.16	0.530713
$629$	7675.68	0.486565
$630$	6576.77	0.415913
$631$	9264.76	0.584507	0.292254	−	0.956341i	$-0.405595\pi$
$631$	9264.76	0.584507	0.292254	+	0.956341i	$0.405595\pi$
$632$	22883.1	1.44025
$633$	9810.49	0.616006
$634$	2401.20	0.150416
$635$	−39579.1	−2.47346
$636$	19920.2	1.24196
$637$	18950.0	1.17869
$638$	−5247.97	−0.325657
$639$	5412.27	0.335064
$640$	41641.7	2.57192
$641$	−17477.1	−1.07692	−0.538458	−	0.842652i	$-0.680993\pi$
$641$	−17477.1	−1.07692	−0.538458	+	0.842652i	$0.680993\pi$
$642$	18349.4	1.12803
$643$	−24878.8	−1.52585	−0.762927	−	0.646485i	$-0.776238\pi$
$643$	−24878.8	−1.52585	−0.762927	+	0.646485i	$0.776238\pi$
$644$	15986.9	0.978220
$645$	−29853.2	−1.82243
$646$	9902.96	0.603137
$647$	15066.3	0.915485	0.457742	−	0.889085i	$-0.348658\pi$
$647$	15066.3	0.915485	0.457742	+	0.889085i	$0.348658\pi$
$648$	−1611.58	−0.0976989
$649$	−3513.74	−0.212521
$650$	77396.1	4.67035
$651$	4422.87	0.266277
$652$	14371.4	0.863234
$653$	−8289.42	−0.496769	−0.248384	−	0.968662i	$-0.579900\pi$
$653$	−8289.42	−0.496769	−0.248384	+	0.968662i	$0.579900\pi$
$654$	5708.90	0.341339
$655$	−22303.0	−1.33046
$656$	−3575.13	−0.212782
$657$	−1277.71	−0.0758726
$658$	11756.1	0.696504
$659$	16852.4	0.996168	0.498084	−	0.867129i	$-0.334037\pi$
$659$	16852.4	0.996168	0.498084	+	0.867129i	$0.334037\pi$
$660$	7889.10	0.465277
$661$	−26747.0	−1.57388	−0.786941	−	0.617028i	$-0.788336\pi$
$661$	−26747.0	−1.57388	−0.786941	+	0.617028i	$0.788336\pi$
$662$	14886.3	0.873976
$663$	−5416.22	−0.317268
$664$	6231.90	0.364224
$665$	13658.9	0.796494
$666$	−12017.9	−0.699228
$667$	−16216.0	−0.941358
$668$	−46053.8	−2.66748
$669$	3032.46	0.175249
$670$	−57734.4	−3.32907
$671$	671.000	0.0386046
$672$	−5073.32	−0.291232
$673$	23164.7	1.32680	0.663399	−	0.748266i	$-0.269113\pi$
$673$	23164.7	1.32680	0.663399	+	0.748266i	$0.269113\pi$
$674$	−11859.0	−0.677735
$675$	6653.30	0.379386
$676$	32718.7	1.86156
$677$	20960.2	1.18991	0.594954	−	0.803760i	$-0.297170\pi$
$677$	20960.2	1.18991	0.594954	+	0.803760i	$0.297170\pi$
$678$	23657.5	1.34006
$679$	−6305.80	−0.356398
$680$	−9956.16	−0.561473
$681$	18261.7	1.02759
$682$	8727.00	0.489991
$683$	−30833.7	−1.72741	−0.863703	−	0.504002i	$-0.831861\pi$
$683$	−30833.7	−1.72741	−0.863703	+	0.504002i	$0.831861\pi$
$684$	−9426.11	−0.526924
$685$	7596.28	0.423707
$686$	−23339.6	−1.29900
$687$	1766.66	0.0981108
$688$	4834.62	0.267904
$689$	−37219.6	−2.05799
$690$	40098.3	2.21234
$691$	−32809.4	−1.80627	−0.903133	−	0.429362i	$-0.858739\pi$
$691$	−32809.4	−1.80627	−0.903133	+	0.429362i	$0.858739\pi$
$692$	−46367.9	−2.54717
$693$	−831.017	−0.0455523
$694$	12510.1	0.684258
$695$	8699.38	0.474800
$696$	−6304.11	−0.343328
$697$	9914.27	0.538780
$698$	−8013.86	−0.434569
$699$	−18799.4	−1.01725
$700$	−25658.4	−1.38542
$701$	−7972.66	−0.429562	−0.214781	−	0.976662i	$-0.568904\pi$
$701$	−7972.66	−0.429562	−0.214781	+	0.976662i	$0.568904\pi$
$702$	8480.26	0.455936
$703$	−24959.3	−1.33906
$704$	−9186.47	−0.491801
$705$	17925.7	0.957619
$706$	−4589.76	−0.244671
$707$	−58.0180	−0.00308627
$708$	−11887.2	−0.631001
$709$	−15128.6	−0.801362	−0.400681	−	0.916218i	$-0.631226\pi$
$709$	−15128.6	−0.801362	−0.400681	+	0.916218i	$0.631226\pi$
$710$	−52351.9	−2.76723
$711$	−10351.2	−0.545991
$712$	25840.9	1.36015
$713$	26966.0	1.41639
$714$	2953.61	0.154812
$715$	−14740.3	−0.770987
$716$	−9939.86	−0.518813
$717$	−9878.32	−0.514522
$718$	8200.32	0.426230
$719$	−4217.37	−0.218750	−0.109375	−	0.994001i	$-0.534885\pi$
$719$	−4217.37	−0.218750	−0.109375	+	0.994001i	$0.534885\pi$
$720$	−1624.05	−0.0840620
$721$	14959.1	0.772683
$722$	−1218.72	−0.0628198
$723$	12027.1	0.618660
$724$	−2020.75	−0.103730
$725$	26026.1	1.33322
$726$	−1639.72	−0.0838234
$727$	30206.4	1.54098	0.770491	−	0.637451i	$-0.220011\pi$
$727$	30206.4	1.54098	0.770491	+	0.637451i	$0.220011\pi$
$728$	−11612.5	−0.591190
$729$	729.000	0.0370370
$730$	12359.1	0.626616
$731$	−13407.0	−0.678352
$732$	2270.04	0.114622
$733$	18185.9	0.916385	0.458193	−	0.888853i	$-0.348497\pi$
$733$	18185.9	0.916385	0.458193	+	0.888853i	$0.348497\pi$
$734$	20824.7	1.04721
$735$	−15757.3	−0.790770
$736$	−30931.8	−1.54913
$737$	7295.11	0.364612
$738$	−15522.9	−0.774264
$739$	28275.3	1.40748	0.703738	−	0.710460i	$-0.251513\pi$
$739$	28275.3	1.40748	0.703738	+	0.710460i	$0.251513\pi$
$740$	70670.4	3.51067
$741$	17612.1	0.873140
$742$	20296.9	1.00421
$743$	24674.6	1.21833	0.609167	−	0.793042i	$-0.291504\pi$
$743$	24674.6	1.21833	0.609167	+	0.793042i	$0.291504\pi$
$744$	10483.3	0.516580
$745$	63773.2	3.13620
$746$	44348.3	2.17655
$747$	−2819.01	−0.138075
$748$	3542.97	0.173187
$749$	11366.1	0.554485
$750$	−31710.4	−1.54387
$751$	37428.7	1.81863	0.909317	−	0.416105i	$-0.136605\pi$
$751$	37428.7	1.81863	0.909317	+	0.416105i	$0.136605\pi$
$752$	−2903.00	−0.140773
$753$	23172.1	1.12143
$754$	33172.7	1.60223
$755$	−11161.8	−0.538041
$756$	−2811.39	−0.135250
$757$	4409.01	0.211689	0.105844	−	0.994383i	$-0.466245\pi$
$757$	4409.01	0.211689	0.105844	+	0.994383i	$0.466245\pi$
$758$	18444.8	0.883834
$759$	−5066.67	−0.242304
$760$	32374.8	1.54521
$761$	30252.5	1.44107	0.720534	−	0.693419i	$-0.243897\pi$
$761$	30252.5	1.44107	0.720534	+	0.693419i	$0.243897\pi$
$762$	27830.4	1.32308
$763$	3536.25	0.167786
$764$	−13880.1	−0.657281
$765$	4503.68	0.212851
$766$	5043.54	0.237899
$767$	22210.5	1.04560
$768$	−9237.48	−0.434022
$769$	29740.4	1.39463	0.697313	−	0.716767i	$-0.254379\pi$
$769$	29740.4	1.39463	0.697313	+	0.716767i	$0.254379\pi$
$770$	8038.28	0.376207
$771$	−3888.33	−0.181627
$772$	−3964.80	−0.184840
$773$	−13431.6	−0.624969	−0.312484	−	0.949923i	$-0.601161\pi$
$773$	−13431.6	−0.624969	−0.312484	+	0.949923i	$0.601161\pi$
$774$	20991.5	0.974839
$775$	−43279.5	−2.00599
$776$	−14946.3	−0.691417
$777$	−7444.24	−0.343707
$778$	3013.41	0.138864
$779$	−32238.6	−1.48276
$780$	−49867.4	−2.28915
$781$	6614.99	0.303077
$782$	18008.0	0.823484
$783$	2851.67	0.130154
$784$	2551.83	0.116246
$785$	12976.2	0.589990
$786$	15682.5	0.711675
$787$	32897.9	1.49007	0.745034	−	0.667026i	$-0.232433\pi$
$787$	32897.9	1.49007	0.745034	+	0.667026i	$0.232433\pi$
$788$	13594.8	0.614585
$789$	−22219.5	−1.00258
$790$	100125.	4.50923
$791$	14654.1	0.658711
$792$	−1969.71	−0.0883720
$793$	−4241.42	−0.189934
$794$	13704.4	0.612532
$795$	30948.8	1.38068
$796$	−46008.7	−2.04866
$797$	−15777.1	−0.701195	−0.350598	−	0.936526i	$-0.614021\pi$
$797$	−15777.1	−0.701195	−0.350598	+	0.936526i	$0.614021\pi$
$798$	−9604.35	−0.426053
$799$	8050.38	0.356448
$800$	49644.3	2.19399
$801$	−11689.1	−0.515625
$802$	−9717.21	−0.427839
$803$	−1561.65	−0.0686293
$804$	24679.8	1.08258
$805$	24837.9	1.08748
$806$	−55163.8	−2.41075
$807$	−2950.21	−0.128689
$808$	−137.517	−0.00598739
$809$	−15163.7	−0.658998	−0.329499	−	0.944156i	$-0.606880\pi$
$809$	−15163.7	−0.658998	−0.329499	+	0.944156i	$0.606880\pi$
$810$	−7051.48	−0.305881
$811$	16575.0	0.717668	0.358834	−	0.933401i	$-0.383174\pi$
$811$	16575.0	0.717668	0.358834	+	0.933401i	$0.383174\pi$
$812$	−10997.4	−0.475289
$813$	−15945.5	−0.687863
$814$	−14688.6	−0.632476
$815$	22328.0	0.959651
$816$	−729.354	−0.0312898
$817$	43596.0	1.86687
$818$	35838.7	1.53187
$819$	5252.90	0.224116
$820$	91281.2	3.88741
$821$	17282.5	0.734669	0.367334	−	0.930089i	$-0.380270\pi$
$821$	17282.5	0.734669	0.367334	+	0.930089i	$0.380270\pi$
$822$	−5341.39	−0.226645
$823$	6879.88	0.291394	0.145697	−	0.989329i	$-0.453458\pi$
$823$	6879.88	0.291394	0.145697	+	0.989329i	$0.453458\pi$
$824$	35456.6	1.49901
$825$	8131.81	0.343168
$826$	−12112.0	−0.510206
$827$	3387.29	0.142428	0.0712138	−	0.997461i	$-0.477313\pi$
$827$	3387.29	0.142428	0.0712138	+	0.997461i	$0.477313\pi$
$828$	−17140.9	−0.719428
$829$	−5807.55	−0.243311	−0.121655	−	0.992572i	$-0.538820\pi$
$829$	−5807.55	−0.243311	−0.121655	+	0.992572i	$0.538820\pi$
$830$	27267.7	1.14033
$831$	6135.41	0.256119
$832$	58068.1	2.41965
$833$	−7076.55	−0.294343
$834$	−6117.04	−0.253976
$835$	−71550.9	−2.96542
$836$	−11520.8	−0.476621
$837$	−4742.12	−0.195832
$838$	−47213.7	−1.94627
$839$	39100.7	1.60894	0.804472	−	0.593990i	$-0.202448\pi$
$839$	39100.7	1.60894	0.804472	+	0.593990i	$0.202448\pi$
$840$	9655.96	0.396622
$841$	−13234.0	−0.542621
$842$	−42728.0	−1.74882
$843$	−9009.56	−0.368097
$844$	40565.0	1.65439
$845$	50833.1	2.06948
$846$	−12604.6	−0.512241
$847$	−1015.69	−0.0412036
$848$	−5012.03	−0.202965
$849$	402.397	0.0162664
$850$	−28902.1	−1.16628
$851$	−45387.1	−1.82826
$852$	22378.9	0.899871
$853$	−17877.9	−0.717619	−0.358810	−	0.933411i	$-0.616817\pi$
$853$	−17877.9	−0.717619	−0.358810	+	0.933411i	$0.616817\pi$
$854$	2312.96	0.0926791
$855$	−14644.8	−0.585778
$856$	26940.5	1.07571
$857$	−27673.3	−1.10304	−0.551519	−	0.834162i	$-0.685952\pi$
$857$	−27673.3	−1.10304	−0.551519	+	0.834162i	$0.685952\pi$
$858$	10364.8	0.412409
$859$	−10217.1	−0.405824	−0.202912	−	0.979197i	$-0.565041\pi$
$859$	−10217.1	−0.405824	−0.202912	+	0.979197i	$0.565041\pi$
$860$	−123439.	−4.89445
$861$	−9615.32	−0.380592
$862$	−80459.7	−3.17920
$863$	−15449.3	−0.609385	−0.304692	−	0.952451i	$-0.598554\pi$
$863$	−15449.3	−0.609385	−0.304692	+	0.952451i	$0.598554\pi$
$864$	5439.51	0.214185
$865$	−72038.9	−2.83167
$866$	38535.7	1.51212
$867$	−12716.4	−0.498122
$868$	18288.0	0.715131
$869$	−12651.4	−0.493868
$870$	−27583.7	−1.07491
$871$	−46112.8	−1.79388
$872$	8381.76	0.325507
$873$	6760.95	0.262112
$874$	−58557.2	−2.26628
$875$	−19642.3	−0.758891
$876$	−5283.15	−0.203769
$877$	−34847.7	−1.34176	−0.670881	−	0.741565i	$-0.734084\pi$
$877$	−34847.7	−1.34176	−0.670881	+	0.741565i	$0.734084\pi$
$878$	−29454.7	−1.13217
$879$	−16466.2	−0.631845
$880$	−1984.94	−0.0760369
$881$	−7640.94	−0.292202	−0.146101	−	0.989270i	$-0.546672\pi$
$881$	−7640.94	−0.292202	−0.146101	+	0.989270i	$0.546672\pi$
$882$	11079.9	0.422992
$883$	41214.3	1.57075	0.785376	−	0.619020i	$-0.212470\pi$
$883$	41214.3	1.57075	0.785376	+	0.619020i	$0.212470\pi$
$884$	−22395.3	−0.852076
$885$	−18468.4	−0.701480
$886$	−29329.3	−1.11212
$887$	19473.4	0.737152	0.368576	−	0.929598i	$-0.379845\pi$
$887$	19473.4	0.737152	0.368576	+	0.929598i	$0.379845\pi$
$888$	−17644.6	−0.666796
$889$	17238.9	0.650363
$890$	113067.	4.25844
$891$	891.000	0.0335013
$892$	12538.8	0.470661
$893$	−26177.7	−0.980967
$894$	−44842.7	−1.67759
$895$	−15442.9	−0.576761
$896$	−18137.2	−0.676253
$897$	32026.7	1.19213
$898$	75887.1	2.82003
$899$	−18550.0	−0.688183
$900$	27510.4	1.01891
$901$	13899.0	0.513920
$902$	−18972.5	−0.700349
$903$	13002.7	0.479184
$904$	34733.8	1.27791
$905$	−3139.51	−0.115316
$906$	7848.54	0.287804
$907$	−11870.1	−0.434554	−0.217277	−	0.976110i	$-0.569717\pi$
$907$	−11870.1	−0.434554	−0.217277	+	0.976110i	$0.569717\pi$
$908$	75509.4	2.75977
$909$	62.2057	0.00226978
$910$	−50810.4	−1.85093
$911$	43225.9	1.57205	0.786025	−	0.618195i	$-0.212136\pi$
$911$	43225.9	1.57205	0.786025	+	0.618195i	$0.212136\pi$
$912$	2371.66	0.0861115
$913$	−3445.45	−0.124894
$914$	75602.1	2.73599
$915$	3526.82	0.127424
$916$	7304.87	0.263493
$917$	9714.17	0.349826
$918$	−3166.80	−0.113856
$919$	6932.86	0.248851	0.124425	−	0.992229i	$-0.460291\pi$
$919$	6932.86	0.248851	0.124425	+	0.992229i	$0.460291\pi$
$920$	58871.9	2.10973
$921$	−24558.8	−0.878653
$922$	−50760.0	−1.81311
$923$	−41813.7	−1.49113
$924$	−3436.14	−0.122338
$925$	72844.6	2.58931
$926$	46972.7	1.66698
$927$	−16038.8	−0.568267
$928$	21278.0	0.752678
$929$	−49083.0	−1.73344	−0.866718	−	0.498798i	$-0.833775\pi$
$929$	−49083.0	−1.73344	−0.866718	+	0.498798i	$0.833775\pi$
$930$	45869.6	1.61734
$931$	23011.1	0.810050
$932$	−77732.9	−2.73200
$933$	6209.66	0.217894
$934$	61313.8	2.14802
$935$	5504.49	0.192531
$936$	12450.6	0.434788
$937$	−17016.3	−0.593273	−0.296637	−	0.954990i	$-0.595865\pi$
$937$	−17016.3	−0.593273	−0.296637	+	0.954990i	$0.595865\pi$
$938$	25146.5	0.875334
$939$	−13194.4	−0.458554
$940$	74120.3	2.57185
$941$	−1042.89	−0.0361290	−0.0180645	−	0.999837i	$-0.505750\pi$
$941$	−1042.89	−0.0361290	−0.0180645	+	0.999837i	$0.505750\pi$
$942$	−9124.36	−0.315592
$943$	−58624.1	−2.02446
$944$	2990.89	0.103120
$945$	−4367.88	−0.150357
$946$	25656.3	0.881775
$947$	−35353.2	−1.21312	−0.606560	−	0.795038i	$-0.707451\pi$
$947$	−35353.2	−1.21312	−0.606560	+	0.795038i	$0.707451\pi$
$948$	−42800.7	−1.46635
$949$	9871.25	0.337655
$950$	93982.1	3.20967
$951$	−1594.73	−0.0543771
$952$	4336.46	0.147632
$953$	26948.2	0.915991	0.457995	−	0.888955i	$-0.348568\pi$
$953$	26948.2	0.915991	0.457995	+	0.888955i	$0.348568\pi$
$954$	−21761.9	−0.738540
$955$	−21564.6	−0.730695
$956$	−40845.4	−1.38184
$957$	3485.37	0.117728
$958$	−65666.6	−2.21460
$959$	−3308.60	−0.111408
$960$	−48284.6	−1.62331
$961$	1056.28	0.0354562
$962$	92847.4	3.11177
$963$	−12186.5	−0.407794
$964$	49730.2	1.66152
$965$	−6159.87	−0.205485
$966$	−17465.0	−0.581705
$967$	17311.0	0.575681	0.287841	−	0.957678i	$-0.407063\pi$
$967$	17311.0	0.575681	0.287841	+	0.957678i	$0.407063\pi$
$968$	−2407.42	−0.0799355
$969$	−6576.92	−0.218040
$970$	−65397.4	−2.16473
$971$	28473.5	0.941050	0.470525	−	0.882387i	$-0.344065\pi$
$971$	28473.5	0.941050	0.470525	+	0.882387i	$0.344065\pi$
$972$	3014.31	0.0994692
$973$	−3789.06	−0.124842
$974$	−14950.2	−0.491823
$975$	−51401.6	−1.68838
$976$	−571.155	−0.0187318
$977$	−42180.4	−1.38124	−0.690619	−	0.723218i	$-0.742662\pi$
$977$	−42180.4	−1.38124	−0.690619	+	0.723218i	$0.742662\pi$
$978$	−15700.1	−0.513328
$979$	−14286.7	−0.466401
$980$	−65154.1	−2.12375
$981$	−3791.49	−0.123398
$982$	8544.35	0.277659
$983$	−29205.4	−0.947616	−0.473808	−	0.880628i	$-0.657121\pi$
$983$	−29205.4	−0.947616	−0.473808	+	0.880628i	$0.657121\pi$
$984$	−22790.6	−0.738352
$985$	21121.3	0.683230
$986$	−12387.7	−0.400107
$987$	−7807.64	−0.251793
$988$	72823.5	2.34497
$989$	79276.9	2.54890
$990$	−8618.48	−0.276680
$991$	28373.7	0.909507	0.454753	−	0.890617i	$-0.349727\pi$
$991$	28373.7	0.909507	0.454753	+	0.890617i	$0.349727\pi$
$992$	−35383.8	−1.13250
$993$	−9886.53	−0.315951
$994$	22802.1	0.727605
$995$	−71480.8	−2.27748
$996$	−11656.2	−0.370824
$997$	−57127.2	−1.81468	−0.907341	−	0.420396i	$-0.861891\pi$
$997$	−57127.2	−1.81468	−0.907341	+	0.420396i	$0.861891\pi$
$998$	−20428.9	−0.647962
$999$	7981.56	0.252778

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.a.1.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.a.1.5	✓	36	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)

\(f(q)\)	\(=\)	\(q-4.51714 q^{2} +3.00000 q^{3} +12.4046 q^{4} +19.2722 q^{5} -13.5514 q^{6} -8.39412 q^{7} -19.8961 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.51714 q^{2} +3.00000 q^{3} +12.4046 q^{4} +19.2722 q^{5} -13.5514 q^{6} -8.39412 q^{7} -19.8961 q^{8} +9.00000 q^{9} -87.0554 q^{10} +11.0000 q^{11} +37.2137 q^{12} -69.5315 q^{13} +37.9174 q^{14} +57.8167 q^{15} -9.36319 q^{16} +25.9653 q^{17} -40.6543 q^{18} -84.4322 q^{19} +239.064 q^{20} -25.1823 q^{21} -49.6886 q^{22} -153.535 q^{23} -59.6882 q^{24} +246.419 q^{25} +314.084 q^{26} +27.0000 q^{27} -104.125 q^{28} +105.617 q^{29} -261.166 q^{30} -175.634 q^{31} +201.463 q^{32} +33.0000 q^{33} -117.289 q^{34} -161.773 q^{35} +111.641 q^{36} +295.613 q^{37} +381.392 q^{38} -208.595 q^{39} -383.441 q^{40} +381.828 q^{41} +113.752 q^{42} -516.343 q^{43} +136.450 q^{44} +173.450 q^{45} +693.541 q^{46} +310.044 q^{47} -28.0896 q^{48} -272.539 q^{49} -1113.11 q^{50} +77.8958 q^{51} -862.509 q^{52} +535.291 q^{53} -121.963 q^{54} +211.994 q^{55} +167.010 q^{56} -253.297 q^{57} -477.088 q^{58} -319.431 q^{59} +717.191 q^{60} +61.0000 q^{61} +793.363 q^{62} -75.5470 q^{63} -835.133 q^{64} -1340.03 q^{65} -149.066 q^{66} +663.192 q^{67} +322.088 q^{68} -460.606 q^{69} +730.753 q^{70} +601.363 q^{71} -179.065 q^{72} -141.968 q^{73} -1335.33 q^{74} +739.256 q^{75} -1047.35 q^{76} -92.3353 q^{77} +942.252 q^{78} -1150.13 q^{79} -180.450 q^{80} +81.0000 q^{81} -1724.77 q^{82} -313.223 q^{83} -312.376 q^{84} +500.409 q^{85} +2332.39 q^{86} +316.852 q^{87} -218.857 q^{88} -1298.79 q^{89} -783.498 q^{90} +583.656 q^{91} -1904.54 q^{92} -526.902 q^{93} -1400.51 q^{94} -1627.20 q^{95} +604.390 q^{96} +751.217 q^{97} +1231.10 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * q^99

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