LMFDB - Embedded newform 2013.4.a.c.1.17

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			1.17
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.624353 q^{2} +3.00000 q^{3} -7.61018 q^{4} -20.5187 q^{5} -1.87306 q^{6} -20.9935 q^{7} +9.74626 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.624353 q^{2} +3.00000 q^{3} -7.61018 q^{4} -20.5187 q^{5} -1.87306 q^{6} -20.9935 q^{7} +9.74626 q^{8} +9.00000 q^{9} +12.8109 q^{10} -11.0000 q^{11} -22.8306 q^{12} -16.3826 q^{13} +13.1074 q^{14} -61.5561 q^{15} +54.7964 q^{16} -5.61986 q^{17} -5.61918 q^{18} -124.555 q^{19} +156.151 q^{20} -62.9805 q^{21} +6.86788 q^{22} +205.853 q^{23} +29.2388 q^{24} +296.017 q^{25} +10.2285 q^{26} +27.0000 q^{27} +159.764 q^{28} -64.8159 q^{29} +38.4327 q^{30} -95.2618 q^{31} -112.182 q^{32} -33.0000 q^{33} +3.50878 q^{34} +430.759 q^{35} -68.4917 q^{36} +211.902 q^{37} +77.7665 q^{38} -49.1479 q^{39} -199.981 q^{40} +372.241 q^{41} +39.3221 q^{42} +241.953 q^{43} +83.7120 q^{44} -184.668 q^{45} -128.525 q^{46} +445.535 q^{47} +164.389 q^{48} +97.7271 q^{49} -184.819 q^{50} -16.8596 q^{51} +124.675 q^{52} -670.404 q^{53} -16.8575 q^{54} +225.706 q^{55} -204.608 q^{56} -373.666 q^{57} +40.4680 q^{58} +580.104 q^{59} +468.453 q^{60} -61.0000 q^{61} +59.4770 q^{62} -188.942 q^{63} -368.329 q^{64} +336.151 q^{65} +20.6036 q^{66} -892.022 q^{67} +42.7682 q^{68} +617.560 q^{69} -268.946 q^{70} -168.219 q^{71} +87.7164 q^{72} -470.587 q^{73} -132.302 q^{74} +888.052 q^{75} +947.889 q^{76} +230.929 q^{77} +30.6856 q^{78} +1393.53 q^{79} -1124.35 q^{80} +81.0000 q^{81} -232.410 q^{82} -1099.25 q^{83} +479.293 q^{84} +115.312 q^{85} -151.064 q^{86} -194.448 q^{87} -107.209 q^{88} -645.606 q^{89} +115.298 q^{90} +343.929 q^{91} -1566.58 q^{92} -285.785 q^{93} -278.171 q^{94} +2555.71 q^{95} -336.547 q^{96} +1106.15 q^{97} -61.0162 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.624353	−0.220742	−0.110371	−	0.993890i	$-0.535204\pi$
$2$	−0.624353	−0.220742	−0.110371	+	0.993890i	$0.535204\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.61018	−0.951273
$5$	−20.5187	−1.83525	−0.917624	−	0.397449i	$-0.869896\pi$
$5$	−20.5187	−1.83525	−0.917624	+	0.397449i	$0.869896\pi$
$6$	−1.87306	−0.127446
$7$	−20.9935	−1.13354	−0.566771	−	0.823875i	$-0.691808\pi$
$7$	−20.9935	−1.13354	−0.566771	+	0.823875i	$0.691808\pi$
$8$	9.74626	0.430728
$9$	9.00000	0.333333
$10$	12.8109	0.405117
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−22.8306	−0.549218
$13$	−16.3826	−0.349517	−0.174759	−	0.984611i	$-0.555915\pi$
$13$	−16.3826	−0.349517	−0.174759	+	0.984611i	$0.555915\pi$
$14$	13.1074	0.250221
$15$	−61.5561	−1.05958
$16$	54.7964	0.856193
$17$	−5.61986	−0.0801775	−0.0400887	−	0.999196i	$-0.512764\pi$
$17$	−5.61986	−0.0801775	−0.0400887	+	0.999196i	$0.512764\pi$
$18$	−5.61918	−0.0735807
$19$	−124.555	−1.50395	−0.751973	−	0.659194i	$-0.770897\pi$
$19$	−124.555	−1.50395	−0.751973	+	0.659194i	$0.770897\pi$
$20$	156.151	1.74582
$21$	−62.9805	−0.654451
$22$	6.86788	0.0665562
$23$	205.853	1.86624	0.933118	−	0.359571i	$-0.117077\pi$
$23$	205.853	1.86624	0.933118	+	0.359571i	$0.117077\pi$
$24$	29.2388	0.248681
$25$	296.017	2.36814
$26$	10.2285	0.0771532
$27$	27.0000	0.192450
$28$	159.764	1.07831
$29$	−64.8159	−0.415035	−0.207518	−	0.978231i	$-0.566538\pi$
$29$	−64.8159	−0.415035	−0.207518	+	0.978231i	$0.566538\pi$
$30$	38.4327	0.233894
$31$	−95.2618	−0.551920	−0.275960	−	0.961169i	$-0.588996\pi$
$31$	−95.2618	−0.551920	−0.275960	+	0.961169i	$0.588996\pi$
$32$	−112.182	−0.619726
$33$	−33.0000	−0.174078
$34$	3.50878	0.0176985
$35$	430.759	2.08033
$36$	−68.4917	−0.317091
$37$	211.902	0.941525	0.470763	−	0.882260i	$-0.343979\pi$
$37$	211.902	0.941525	0.470763	+	0.882260i	$0.343979\pi$
$38$	77.7665	0.331984
$39$	−49.1479	−0.201794
$40$	−199.981	−0.790493
$41$	372.241	1.41791	0.708955	−	0.705254i	$-0.249167\pi$
$41$	372.241	1.41791	0.708955	+	0.705254i	$0.249167\pi$
$42$	39.3221	0.144465
$43$	241.953	0.858082	0.429041	−	0.903285i	$-0.358852\pi$
$43$	241.953	0.858082	0.429041	+	0.903285i	$0.358852\pi$
$44$	83.7120	0.286820
$45$	−184.668	−0.611750
$46$	−128.525	−0.411957
$47$	445.535	1.38272	0.691361	−	0.722510i	$-0.257012\pi$
$47$	445.535	1.38272	0.691361	+	0.722510i	$0.257012\pi$
$48$	164.389	0.494323
$49$	97.7271	0.284919
$50$	−184.819	−0.522748
$51$	−16.8596	−0.0462905
$52$	124.675	0.332486
$53$	−670.404	−1.73749	−0.868745	−	0.495259i	$-0.835073\pi$
$53$	−670.404	−1.73749	−0.868745	+	0.495259i	$0.835073\pi$
$54$	−16.8575	−0.0424818
$55$	225.706	0.553348
$56$	−204.608	−0.488249
$57$	−373.666	−0.868303
$58$	40.4680	0.0916157
$59$	580.104	1.28005	0.640026	−	0.768353i	$-0.278923\pi$
$59$	580.104	1.28005	0.640026	+	0.768353i	$0.278923\pi$
$60$	468.453	1.00795
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	59.4770	0.121832
$63$	−188.942	−0.377848
$64$	−368.329	−0.719394
$65$	336.151	0.641451
$66$	20.6036	0.0384263
$67$	−892.022	−1.62653	−0.813267	−	0.581891i	$-0.802313\pi$
$67$	−892.022	−1.62653	−0.813267	+	0.581891i	$0.802313\pi$
$68$	42.7682	0.0762706
$69$	617.560	1.07747
$70$	−268.946	−0.459217
$71$	−168.219	−0.281183	−0.140591	−	0.990068i	$-0.544900\pi$
$71$	−168.219	−0.281183	−0.140591	+	0.990068i	$0.544900\pi$
$72$	87.7164	0.143576
$73$	−470.587	−0.754494	−0.377247	−	0.926113i	$-0.623129\pi$
$73$	−470.587	−0.754494	−0.377247	+	0.926113i	$0.623129\pi$
$74$	−132.302	−0.207834
$75$	888.052	1.36725
$76$	947.889	1.43066
$77$	230.929	0.341776
$78$	30.6856	0.0445444
$79$	1393.53	1.98462	0.992308	−	0.123795i	$-0.0395066\pi$
$79$	1393.53	1.98462	0.992308	+	0.123795i	$0.0395066\pi$
$80$	−1124.35	−1.57133
$81$	81.0000	0.111111
$82$	−232.410	−0.312992
$83$	−1099.25	−1.45372	−0.726858	−	0.686788i	$-0.759020\pi$
$83$	−1099.25	−1.45372	−0.726858	+	0.686788i	$0.759020\pi$
$84$	479.293	0.622562
$85$	115.312	0.147146
$86$	−151.064	−0.189415
$87$	−194.448	−0.239621
$88$	−107.209	−0.129869
$89$	−645.606	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$89$	−645.606	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$90$	115.298	0.135039
$91$	343.929	0.396193
$92$	−1566.58	−1.77530
$93$	−285.785	−0.318651
$94$	−278.171	−0.305225
$95$	2555.71	2.76011
$96$	−336.547	−0.357799
$97$	1106.15	1.15786	0.578930	−	0.815378i	$-0.303471\pi$
$97$	1106.15	1.15786	0.578930	+	0.815378i	$0.303471\pi$
$98$	−61.0162	−0.0628936
$99$	−99.0000	−0.100504
$100$	−2252.75	−2.25275
$101$	597.021	0.588176	0.294088	−	0.955778i	$-0.404984\pi$
$101$	597.021	0.588176	0.294088	+	0.955778i	$0.404984\pi$
$102$	10.5263	0.0102183
$103$	−546.017	−0.522337	−0.261168	−	0.965293i	$-0.584108\pi$
$103$	−546.017	−0.522337	−0.261168	+	0.965293i	$0.584108\pi$
$104$	−159.670	−0.150547
$105$	1292.28	1.20108
$106$	418.568	0.383537
$107$	1569.98	1.41846	0.709230	−	0.704977i	$-0.249043\pi$
$107$	1569.98	1.41846	0.709230	+	0.704977i	$0.249043\pi$
$108$	−205.475	−0.183073
$109$	866.556	0.761477	0.380738	−	0.924683i	$-0.375670\pi$
$109$	866.556	0.761477	0.380738	+	0.924683i	$0.375670\pi$
$110$	−140.920	−0.122147
$111$	635.705	0.543590
$112$	−1150.37	−0.970531
$113$	1073.99	0.894091	0.447045	−	0.894511i	$-0.352476\pi$
$113$	1073.99	0.894091	0.447045	+	0.894511i	$0.352476\pi$
$114$	233.300	0.191671
$115$	−4223.85	−3.42501
$116$	493.261	0.394812
$117$	−147.444	−0.116506
$118$	−362.190	−0.282561
$119$	117.981	0.0908846
$120$	−599.942	−0.456391
$121$	121.000	0.0909091
$122$	38.0855	0.0282631
$123$	1116.72	0.818630
$124$	724.959	0.525026
$125$	−3509.05	−2.51087
$126$	117.966	0.0834069
$127$	2399.90	1.67682	0.838412	−	0.545037i	$-0.183484\pi$
$127$	2399.90	1.67682	0.838412	+	0.545037i	$0.183484\pi$
$128$	1127.43	0.778526
$129$	725.860	0.495414
$130$	−209.877	−0.141595
$131$	−70.5831	−0.0470754	−0.0235377	−	0.999723i	$-0.507493\pi$
$131$	−70.5831	−0.0470754	−0.0235377	+	0.999723i	$0.507493\pi$
$132$	251.136	0.165595
$133$	2614.85	1.70479
$134$	556.936	0.359045
$135$	−554.005	−0.353194
$136$	−54.7727	−0.0345347
$137$	−998.984	−0.622985	−0.311492	−	0.950249i	$-0.600829\pi$
$137$	−998.984	−0.622985	−0.311492	+	0.950249i	$0.600829\pi$
$138$	−385.576	−0.237843
$139$	−903.257	−0.551174	−0.275587	−	0.961276i	$-0.588872\pi$
$139$	−903.257	−0.551174	−0.275587	+	0.961276i	$0.588872\pi$
$140$	−3278.16	−1.97896
$141$	1336.60	0.798315
$142$	105.028	0.0620688
$143$	180.209	0.105383
$144$	493.167	0.285398
$145$	1329.94	0.761693
$146$	293.812	0.166549
$147$	293.181	0.164498
$148$	−1612.61	−0.895648
$149$	−2158.47	−1.18677	−0.593386	−	0.804918i	$-0.702209\pi$
$149$	−2158.47	−1.18677	−0.593386	+	0.804918i	$0.702209\pi$
$150$	−554.458	−0.301809
$151$	−813.869	−0.438621	−0.219310	−	0.975655i	$-0.570381\pi$
$151$	−813.869	−0.438621	−0.219310	+	0.975655i	$0.570381\pi$
$152$	−1213.95	−0.647791
$153$	−50.5788	−0.0267258
$154$	−144.181	−0.0754443
$155$	1954.65	1.01291
$156$	374.025	0.191961
$157$	−1044.54	−0.530977	−0.265488	−	0.964114i	$-0.585533\pi$
$157$	−1044.54	−0.530977	−0.265488	+	0.964114i	$0.585533\pi$
$158$	−870.056	−0.438088
$159$	−2011.21	−1.00314
$160$	2301.84	1.13735
$161$	−4321.59	−2.11546
$162$	−50.5726	−0.0245269
$163$	−1319.81	−0.634206	−0.317103	−	0.948391i	$-0.602710\pi$
$163$	−1319.81	−0.634206	−0.317103	+	0.948391i	$0.602710\pi$
$164$	−2832.82	−1.34882
$165$	677.117	0.319476
$166$	686.320	0.320896
$167$	1023.46	0.474239	0.237120	−	0.971480i	$-0.423797\pi$
$167$	1023.46	0.474239	0.237120	+	0.971480i	$0.423797\pi$
$168$	−613.825	−0.281890
$169$	−1928.61	−0.877838
$170$	−71.9956	−0.0324812
$171$	−1121.00	−0.501315
$172$	−1841.31	−0.816270
$173$	−1591.59	−0.699459	−0.349730	−	0.936851i	$-0.613727\pi$
$173$	−1591.59	−0.699459	−0.349730	+	0.936851i	$0.613727\pi$
$174$	121.404	0.0528944
$175$	−6214.44	−2.68439
$176$	−602.760	−0.258152
$177$	1740.31	0.739039
$178$	403.086	0.169733
$179$	−3256.61	−1.35984	−0.679918	−	0.733288i	$-0.737985\pi$
$179$	−3256.61	−1.35984	−0.679918	+	0.733288i	$0.737985\pi$
$180$	1405.36	0.581941
$181$	−2018.04	−0.828730	−0.414365	−	0.910111i	$-0.635996\pi$
$181$	−2018.04	−0.828730	−0.414365	+	0.910111i	$0.635996\pi$
$182$	−214.733	−0.0874564
$183$	−183.000	−0.0739221
$184$	2006.30	0.803840
$185$	−4347.95	−1.72793
$186$	178.431	0.0703397
$187$	61.8185	0.0241744
$188$	−3390.60	−1.31535
$189$	−566.825	−0.218150
$190$	−1595.67	−0.609273
$191$	−1488.90	−0.564048	−0.282024	−	0.959407i	$-0.591006\pi$
$191$	−1488.90	−0.564048	−0.282024	+	0.959407i	$0.591006\pi$
$192$	−1104.99	−0.415342
$193$	1174.82	0.438163	0.219081	−	0.975707i	$-0.429694\pi$
$193$	1174.82	0.438163	0.219081	+	0.975707i	$0.429694\pi$
$194$	−690.627	−0.255588
$195$	1008.45	0.370342
$196$	−743.721	−0.271035
$197$	−1247.75	−0.451260	−0.225630	−	0.974213i	$-0.572444\pi$
$197$	−1247.75	−0.451260	−0.225630	+	0.974213i	$0.572444\pi$
$198$	61.8109	0.0221854
$199$	4704.23	1.67575	0.837874	−	0.545864i	$-0.183799\pi$
$199$	4704.23	1.67575	0.837874	+	0.545864i	$0.183799\pi$
$200$	2885.06	1.02002
$201$	−2676.06	−0.939080
$202$	−372.752	−0.129835
$203$	1360.71	0.470460
$204$	128.305	0.0440349
$205$	−7637.90	−2.60222
$206$	340.907	0.115302
$207$	1852.68	0.622079
$208$	−897.709	−0.299254
$209$	1370.11	0.453457
$210$	−806.838	−0.265129
$211$	−1475.96	−0.481561	−0.240780	−	0.970580i	$-0.577403\pi$
$211$	−1475.96	−0.481561	−0.240780	+	0.970580i	$0.577403\pi$
$212$	5101.89	1.65283
$213$	−504.658	−0.162341
$214$	−980.219	−0.313114
$215$	−4964.57	−1.57479
$216$	263.149	0.0828937
$217$	1999.88	0.625625
$218$	−541.037	−0.168090
$219$	−1411.76	−0.435607
$220$	−1717.66	−0.526385
$221$	92.0682	0.0280234
$222$	−396.905	−0.119993
$223$	−1003.46	−0.301330	−0.150665	−	0.988585i	$-0.548141\pi$
$223$	−1003.46	−0.301330	−0.150665	+	0.988585i	$0.548141\pi$
$224$	2355.10	0.702486
$225$	2664.16	0.789379
$226$	−670.547	−0.197363
$227$	−2661.12	−0.778084	−0.389042	−	0.921220i	$-0.627194\pi$
$227$	−2661.12	−0.778084	−0.389042	+	0.921220i	$0.627194\pi$
$228$	2843.67	0.825993
$229$	194.256	0.0560558	0.0280279	−	0.999607i	$-0.491077\pi$
$229$	194.256	0.0560558	0.0280279	+	0.999607i	$0.491077\pi$
$230$	2637.17	0.756043
$231$	692.786	0.197324
$232$	−631.713	−0.178767
$233$	3340.77	0.939319	0.469659	−	0.882848i	$-0.344377\pi$
$233$	3340.77	0.939319	0.469659	+	0.882848i	$0.344377\pi$
$234$	92.0569	0.0257177
$235$	−9141.79	−2.53764
$236$	−4414.70	−1.21768
$237$	4180.60	1.14582
$238$	−73.6615	−0.0200620
$239$	−889.828	−0.240829	−0.120415	−	0.992724i	$-0.538422\pi$
$239$	−889.828	−0.240829	−0.120415	+	0.992724i	$0.538422\pi$
$240$	−3373.05	−0.907206
$241$	5842.92	1.56172	0.780862	−	0.624704i	$-0.214780\pi$
$241$	5842.92	1.56172	0.780862	+	0.624704i	$0.214780\pi$
$242$	−75.5467	−0.0200675
$243$	243.000	0.0641500
$244$	464.221	0.121798
$245$	−2005.23	−0.522897
$246$	−697.229	−0.180706
$247$	2040.55	0.525655
$248$	−928.446	−0.237727
$249$	−3297.75	−0.839303
$250$	2190.89	0.554256
$251$	5745.01	1.44471	0.722354	−	0.691523i	$-0.243060\pi$
$251$	5745.01	1.44471	0.722354	+	0.691523i	$0.243060\pi$
$252$	1437.88	0.359436
$253$	−2264.39	−0.562691
$254$	−1498.38	−0.370146
$255$	345.937	0.0849545
$256$	2242.72	0.547540
$257$	7098.90	1.72302	0.861512	−	0.507737i	$-0.169518\pi$
$257$	7098.90	1.72302	0.861512	+	0.507737i	$0.169518\pi$
$258$	−453.193	−0.109359
$259$	−4448.56	−1.06726
$260$	−2558.17	−0.610195
$261$	−583.344	−0.138345
$262$	44.0688	0.0103915
$263$	−4223.41	−0.990216	−0.495108	−	0.868831i	$-0.664872\pi$
$263$	−4223.41	−0.990216	−0.495108	+	0.868831i	$0.664872\pi$
$264$	−321.627	−0.0749801
$265$	13755.8	3.18873
$266$	−1632.59	−0.376318
$267$	−1936.82	−0.443937
$268$	6788.45	1.54728
$269$	−4397.99	−0.996841	−0.498421	−	0.866935i	$-0.666086\pi$
$269$	−4397.99	−0.996841	−0.498421	+	0.866935i	$0.666086\pi$
$270$	345.895	0.0779647
$271$	4481.79	1.00461	0.502306	−	0.864690i	$-0.332485\pi$
$271$	4481.79	1.00461	0.502306	+	0.864690i	$0.332485\pi$
$272$	−307.948	−0.0686474
$273$	1031.79	0.228742
$274$	623.718	0.137519
$275$	−3256.19	−0.714020
$276$	−4699.75	−1.02497
$277$	7421.08	1.60971	0.804855	−	0.593471i	$-0.202243\pi$
$277$	7421.08	1.60971	0.804855	+	0.593471i	$0.202243\pi$
$278$	563.951	0.121667
$279$	−857.356	−0.183973
$280$	4198.30	0.896058
$281$	−2147.11	−0.455821	−0.227910	−	0.973682i	$-0.573189\pi$
$281$	−2147.11	−0.455821	−0.227910	+	0.973682i	$0.573189\pi$
$282$	−834.513	−0.176222
$283$	−777.809	−0.163378	−0.0816890	−	0.996658i	$-0.526031\pi$
$283$	−777.809	−0.163378	−0.0816890	+	0.996658i	$0.526031\pi$
$284$	1280.18	0.267481
$285$	7667.14	1.59355
$286$	−112.514	−0.0232626
$287$	−7814.64	−1.60726
$288$	−1009.64	−0.206575
$289$	−4881.42	−0.993572
$290$	−830.352	−0.168138
$291$	3318.44	0.668490
$292$	3581.25	0.717729
$293$	9226.42	1.83964	0.919818	−	0.392345i	$-0.128336\pi$
$293$	9226.42	1.83964	0.919818	+	0.392345i	$0.128336\pi$
$294$	−183.049	−0.0363116
$295$	−11903.0	−2.34921
$296$	2065.25	0.405541
$297$	−297.000	−0.0580259
$298$	1347.65	0.261971
$299$	−3372.42	−0.652282
$300$	−6758.24	−1.30062
$301$	−5079.44	−0.972672
$302$	508.142	0.0968221
$303$	1791.06	0.339584
$304$	−6825.18	−1.28767
$305$	1251.64	0.234980
$306$	31.5790	0.00589951
$307$	−3997.79	−0.743211	−0.371606	−	0.928391i	$-0.621193\pi$
$307$	−3997.79	−0.743211	−0.371606	+	0.928391i	$0.621193\pi$
$308$	−1757.41	−0.325122
$309$	−1638.05	−0.301571
$310$	−1220.39	−0.223592
$311$	−3659.72	−0.667279	−0.333640	−	0.942701i	$-0.608277\pi$
$311$	−3659.72	−0.667279	−0.333640	+	0.942701i	$0.608277\pi$
$312$	−479.009	−0.0869183
$313$	−5920.31	−1.06912	−0.534562	−	0.845129i	$-0.679523\pi$
$313$	−5920.31	−1.06912	−0.534562	+	0.845129i	$0.679523\pi$
$314$	652.161	0.117209
$315$	3876.84	0.693444
$316$	−10605.0	−1.88791
$317$	−883.503	−0.156538	−0.0782689	−	0.996932i	$-0.524939\pi$
$317$	−883.503	−0.156538	−0.0782689	+	0.996932i	$0.524939\pi$
$318$	1255.71	0.221435
$319$	712.975	0.125138
$320$	7557.64	1.32027
$321$	4709.93	0.818948
$322$	2698.19	0.466971
$323$	699.984	0.120583
$324$	−616.425	−0.105697
$325$	−4849.54	−0.827706
$326$	824.028	0.139996
$327$	2599.67	0.439639
$328$	3627.96	0.610733
$329$	−9353.33	−1.56737
$330$	−422.760	−0.0705218
$331$	−3915.52	−0.650201	−0.325101	−	0.945679i	$-0.605398\pi$
$331$	−3915.52	−0.650201	−0.325101	+	0.945679i	$0.605398\pi$
$332$	8365.49	1.38288
$333$	1907.12	0.313842
$334$	−639.002	−0.104685
$335$	18303.1	2.98509
$336$	−3451.10	−0.560337
$337$	1179.21	0.190610	0.0953049	−	0.995448i	$-0.469617\pi$
$337$	1179.21	0.190610	0.0953049	+	0.995448i	$0.469617\pi$
$338$	1204.13	0.193776
$339$	3221.96	0.516204
$340$	−877.548	−0.139976
$341$	1047.88	0.166410
$342$	699.899	0.110661
$343$	5149.14	0.810575
$344$	2358.14	0.369600
$345$	−12671.5	−1.97743
$346$	993.715	0.154400
$347$	7513.47	1.16238	0.581188	−	0.813770i	$-0.302588\pi$
$347$	7513.47	1.16238	0.581188	+	0.813770i	$0.302588\pi$
$348$	1479.78	0.227945
$349$	−7281.21	−1.11677	−0.558387	−	0.829580i	$-0.688580\pi$
$349$	−7281.21	−1.11677	−0.558387	+	0.829580i	$0.688580\pi$
$350$	3880.00	0.592557
$351$	−442.331	−0.0672647
$352$	1234.01	0.186854
$353$	−12053.4	−1.81738	−0.908692	−	0.417468i	$-0.862918\pi$
$353$	−12053.4	−1.81738	−0.908692	+	0.417468i	$0.862918\pi$
$354$	−1086.57	−0.163137
$355$	3451.64	0.516040
$356$	4913.18	0.731455
$357$	353.942	0.0524722
$358$	2033.28	0.300173
$359$	−8514.23	−1.25171	−0.625855	−	0.779940i	$-0.715250\pi$
$359$	−8514.23	−1.25171	−0.625855	+	0.779940i	$0.715250\pi$
$360$	−1799.83	−0.263498
$361$	8655.04	1.26185
$362$	1259.97	0.182936
$363$	363.000	0.0524864
$364$	−2617.36	−0.376888
$365$	9655.84	1.38468
$366$	114.257	0.0163177
$367$	8664.73	1.23241	0.616206	−	0.787585i	$-0.288669\pi$
$367$	8664.73	1.23241	0.616206	+	0.787585i	$0.288669\pi$
$368$	11280.0	1.59786
$369$	3350.17	0.472636
$370$	2714.66	0.381428
$371$	14074.1	1.96952
$372$	2174.88	0.303124
$373$	330.340	0.0458561	0.0229281	−	0.999737i	$-0.492701\pi$
$373$	330.340	0.0458561	0.0229281	+	0.999737i	$0.492701\pi$
$374$	−38.5966	−0.00533631
$375$	−10527.2	−1.44965
$376$	4342.30	0.595577
$377$	1061.86	0.145062
$378$	353.899	0.0481550
$379$	−7243.95	−0.981786	−0.490893	−	0.871220i	$-0.663329\pi$
$379$	−7243.95	−0.981786	−0.490893	+	0.871220i	$0.663329\pi$
$380$	−19449.5	−2.62562
$381$	7199.70	0.968115
$382$	929.600	0.124509
$383$	−5770.39	−0.769852	−0.384926	−	0.922947i	$-0.625773\pi$
$383$	−5770.39	−0.769852	−0.384926	+	0.922947i	$0.625773\pi$
$384$	3382.28	0.449482
$385$	−4738.35	−0.627244
$386$	−733.502	−0.0967209
$387$	2177.58	0.286027
$388$	−8417.99	−1.10144
$389$	−2599.55	−0.338824	−0.169412	−	0.985545i	$-0.554187\pi$
$389$	−2599.55	−0.338824	−0.169412	+	0.985545i	$0.554187\pi$
$390$	−629.630	−0.0817501
$391$	−1156.87	−0.149630
$392$	952.474	0.122722
$393$	−211.749	−0.0271790
$394$	779.034	0.0996121
$395$	−28593.5	−3.64226
$396$	753.408	0.0956065
$397$	14411.9	1.82195	0.910973	−	0.412466i	$-0.135333\pi$
$397$	14411.9	1.82195	0.910973	+	0.412466i	$0.135333\pi$
$398$	−2937.10	−0.369908
$399$	7844.56	0.984259
$400$	16220.7	2.02758
$401$	4672.07	0.581825	0.290913	−	0.956750i	$-0.406041\pi$
$401$	4672.07	0.581825	0.290913	+	0.956750i	$0.406041\pi$
$402$	1670.81	0.207294
$403$	1560.64	0.192906
$404$	−4543.44	−0.559516
$405$	−1662.02	−0.203917
$406$	−849.566	−0.103850
$407$	−2330.92	−0.283881
$408$	−164.318	−0.0199386
$409$	876.360	0.105949	0.0529746	−	0.998596i	$-0.483130\pi$
$409$	876.360	0.105949	0.0529746	+	0.998596i	$0.483130\pi$
$410$	4768.75	0.574419
$411$	−2996.95	−0.359680
$412$	4155.29	0.496885
$413$	−12178.4	−1.45099
$414$	−1156.73	−0.137319
$415$	22555.2	2.66793
$416$	1837.84	0.216605
$417$	−2709.77	−0.318221
$418$	−855.432	−0.100097
$419$	4798.73	0.559507	0.279753	−	0.960072i	$-0.409747\pi$
$419$	4798.73	0.559507	0.279753	+	0.960072i	$0.409747\pi$
$420$	−9834.48	−1.14256
$421$	10282.2	1.19032	0.595160	−	0.803608i	$-0.297089\pi$
$421$	10282.2	1.19032	0.595160	+	0.803608i	$0.297089\pi$
$422$	921.520	0.106301
$423$	4009.81	0.460907
$424$	−6533.93	−0.748386
$425$	−1663.58	−0.189871
$426$	315.085	0.0358355
$427$	1280.60	0.145135
$428$	−11947.8	−1.34934
$429$	540.627	0.0608432
$430$	3099.64	0.347623
$431$	6976.27	0.779664	0.389832	−	0.920886i	$-0.372533\pi$
$431$	6976.27	0.779664	0.389832	+	0.920886i	$0.372533\pi$
$432$	1479.50	0.164774
$433$	4229.99	0.469469	0.234735	−	0.972059i	$-0.424578\pi$
$433$	4229.99	0.469469	0.234735	+	0.972059i	$0.424578\pi$
$434$	−1248.63	−0.138102
$435$	3989.82	0.439764
$436$	−6594.65	−0.724372
$437$	−25640.2	−2.80672
$438$	881.437	0.0961568
$439$	−1335.85	−0.145231	−0.0726155	−	0.997360i	$-0.523135\pi$
$439$	−1335.85	−0.145231	−0.0726155	+	0.997360i	$0.523135\pi$
$440$	2199.79	0.238343
$441$	879.544	0.0949729
$442$	−57.4830	−0.00618595
$443$	−5780.85	−0.619992	−0.309996	−	0.950738i	$-0.600328\pi$
$443$	−5780.85	−0.619992	−0.309996	+	0.950738i	$0.600328\pi$
$444$	−4837.83	−0.517102
$445$	13247.0	1.41116
$446$	626.512	0.0665161
$447$	−6475.42	−0.685183
$448$	7732.53	0.815463
$449$	−5748.28	−0.604183	−0.302091	−	0.953279i	$-0.597685\pi$
$449$	−5748.28	−0.604183	−0.302091	+	0.953279i	$0.597685\pi$
$450$	−1663.37	−0.174249
$451$	−4094.65	−0.427516
$452$	−8173.24	−0.850524
$453$	−2441.61	−0.253238
$454$	1661.48	0.171756
$455$	−7056.98	−0.727112
$456$	−3641.85	−0.374003
$457$	−675.315	−0.0691245	−0.0345623	−	0.999403i	$-0.511004\pi$
$457$	−675.315	−0.0691245	−0.0345623	+	0.999403i	$0.511004\pi$
$458$	−121.284	−0.0123739
$459$	−151.736	−0.0154302
$460$	32144.3	3.25812
$461$	−6581.79	−0.664956	−0.332478	−	0.943111i	$-0.607885\pi$
$461$	−6581.79	−0.664956	−0.332478	+	0.943111i	$0.607885\pi$
$462$	−432.543	−0.0435578
$463$	−4413.09	−0.442967	−0.221483	−	0.975164i	$-0.571090\pi$
$463$	−4413.09	−0.442967	−0.221483	+	0.975164i	$0.571090\pi$
$464$	−3551.68	−0.355350
$465$	5863.94	0.584804
$466$	−2085.82	−0.207347
$467$	4138.62	0.410091	0.205045	−	0.978752i	$-0.434266\pi$
$467$	4138.62	0.410091	0.205045	+	0.978752i	$0.434266\pi$
$468$	1122.07	0.110829
$469$	18726.7	1.84375
$470$	5707.71	0.560164
$471$	−3133.62	−0.306560
$472$	5653.85	0.551355
$473$	−2661.48	−0.258721
$474$	−2610.17	−0.252930
$475$	−36870.5	−3.56155
$476$	−897.854	−0.0864560
$477$	−6033.63	−0.579164
$478$	555.567	0.0531612
$479$	−660.382	−0.0629930	−0.0314965	−	0.999504i	$-0.510027\pi$
$479$	−660.382	−0.0629930	−0.0314965	+	0.999504i	$0.510027\pi$
$480$	6905.51	0.656650
$481$	−3471.51	−0.329080
$482$	−3648.04	−0.344738
$483$	−12964.8	−1.22136
$484$	−920.832	−0.0864794
$485$	−22696.7	−2.12496
$486$	−151.718	−0.0141606
$487$	−464.893	−0.0432573	−0.0216287	−	0.999766i	$-0.506885\pi$
$487$	−464.893	−0.0432573	−0.0216287	+	0.999766i	$0.506885\pi$
$488$	−594.522	−0.0551491
$489$	−3959.43	−0.366159
$490$	1251.97	0.115425
$491$	−18907.7	−1.73787	−0.868934	−	0.494928i	$-0.835195\pi$
$491$	−18907.7	−1.73787	−0.868934	+	0.494928i	$0.835195\pi$
$492$	−8498.47	−0.778741
$493$	364.257	0.0332765
$494$	−1274.02	−0.116034
$495$	2031.35	0.184449
$496$	−5220.00	−0.472550
$497$	3531.51	0.318732
$498$	2058.96	0.185269
$499$	−13640.3	−1.22370	−0.611849	−	0.790974i	$-0.709574\pi$
$499$	−13640.3	−1.22370	−0.611849	+	0.790974i	$0.709574\pi$
$500$	26704.5	2.38853
$501$	3070.39	0.273802
$502$	−3586.91	−0.318908
$503$	10026.6	0.888794	0.444397	−	0.895830i	$-0.353418\pi$
$503$	10026.6	0.888794	0.444397	+	0.895830i	$0.353418\pi$
$504$	−1841.47	−0.162750
$505$	−12250.1	−1.07945
$506$	1413.78	0.124210
$507$	−5785.83	−0.506820
$508$	−18263.7	−1.59512
$509$	6440.51	0.560846	0.280423	−	0.959877i	$-0.409525\pi$
$509$	6440.51	0.560846	0.280423	+	0.959877i	$0.409525\pi$
$510$	−215.987	−0.0187530
$511$	9879.27	0.855251
$512$	−10419.7	−0.899391
$513$	−3363.00	−0.289434
$514$	−4432.22	−0.380344
$515$	11203.6	0.958618
$516$	−5523.92	−0.471274
$517$	−4900.88	−0.416906
$518$	2777.47	0.235589
$519$	−4774.77	−0.403833
$520$	3276.21	0.276291
$521$	−5009.67	−0.421262	−0.210631	−	0.977566i	$-0.567552\pi$
$521$	−5009.67	−0.421262	−0.210631	+	0.977566i	$0.567552\pi$
$522$	364.212	0.0305386
$523$	−2430.08	−0.203174	−0.101587	−	0.994827i	$-0.532392\pi$
$523$	−2430.08	−0.203174	−0.101587	+	0.994827i	$0.532392\pi$
$524$	537.150	0.0447815
$525$	−18643.3	−1.54983
$526$	2636.90	0.218582
$527$	535.358	0.0442515
$528$	−1808.28	−0.149044
$529$	30208.7	2.48284
$530$	−8588.48	−0.703886
$531$	5220.94	0.426684
$532$	−19899.5	−1.62172
$533$	−6098.29	−0.495584
$534$	1209.26	0.0979957
$535$	−32213.9	−2.60323
$536$	−8693.88	−0.700594
$537$	−9769.84	−0.785102
$538$	2745.90	0.220045
$539$	−1075.00	−0.0859062
$540$	4216.08	0.335984
$541$	23816.6	1.89271	0.946353	−	0.323136i	$-0.104737\pi$
$541$	23816.6	1.89271	0.946353	+	0.323136i	$0.104737\pi$
$542$	−2798.22	−0.221760
$543$	−6054.13	−0.478467
$544$	630.450	0.0496881
$545$	−17780.6	−1.39750
$546$	−644.199	−0.0504930
$547$	16083.4	1.25718	0.628590	−	0.777737i	$-0.283633\pi$
$547$	16083.4	1.25718	0.628590	+	0.777737i	$0.283633\pi$
$548$	7602.45	0.592629
$549$	−549.000	−0.0426790
$550$	2033.01	0.157614
$551$	8073.17	0.624190
$552$	6018.91	0.464097
$553$	−29255.1	−2.24965
$554$	−4633.38	−0.355331
$555$	−13043.9	−0.997623
$556$	6873.95	0.524317
$557$	−7378.18	−0.561263	−0.280632	−	0.959816i	$-0.590544\pi$
$557$	−7378.18	−0.561263	−0.280632	+	0.959816i	$0.590544\pi$
$558$	535.293	0.0406107
$559$	−3963.83	−0.299915
$560$	23604.1	1.78117
$561$	185.455	0.0139571
$562$	1340.55	0.100619
$563$	1219.95	0.0913226	0.0456613	−	0.998957i	$-0.485461\pi$
$563$	1219.95	0.0913226	0.0456613	+	0.998957i	$0.485461\pi$
$564$	−10171.8	−0.759415
$565$	−22036.8	−1.64088
$566$	485.627	0.0360644
$567$	−1700.47	−0.125949
$568$	−1639.51	−0.121113
$569$	8328.77	0.613638	0.306819	−	0.951768i	$-0.400735\pi$
$569$	8328.77	0.613638	0.306819	+	0.951768i	$0.400735\pi$
$570$	−4787.00	−0.351764
$571$	14719.7	1.07881	0.539403	−	0.842048i	$-0.318650\pi$
$571$	14719.7	1.07881	0.539403	+	0.842048i	$0.318650\pi$
$572$	−1371.42	−0.100248
$573$	−4466.70	−0.325653
$574$	4879.09	0.354790
$575$	60936.2	4.41950
$576$	−3314.97	−0.239798
$577$	−9458.92	−0.682461	−0.341231	−	0.939980i	$-0.610844\pi$
$577$	−9458.92	−0.682461	−0.341231	+	0.939980i	$0.610844\pi$
$578$	3047.73	0.219323
$579$	3524.46	0.252973
$580$	−10121.1	−0.724578
$581$	23077.1	1.64785
$582$	−2071.88	−0.147564
$583$	7374.44	0.523873
$584$	−4586.47	−0.324982
$585$	3025.35	0.213817
$586$	−5760.55	−0.406085
$587$	7975.70	0.560805	0.280402	−	0.959883i	$-0.409532\pi$
$587$	7975.70	0.560805	0.280402	+	0.959883i	$0.409532\pi$
$588$	−2231.16	−0.156482
$589$	11865.4	0.830057
$590$	7431.66	0.518571
$591$	−3743.24	−0.260535
$592$	11611.4	0.806128
$593$	−9687.09	−0.670828	−0.335414	−	0.942071i	$-0.608876\pi$
$593$	−9687.09	−0.670828	−0.335414	+	0.942071i	$0.608876\pi$
$594$	185.433	0.0128088
$595$	−2420.81	−0.166796
$596$	16426.4	1.12894
$597$	14112.7	0.967493
$598$	2105.58	0.143986
$599$	28289.1	1.92965	0.964827	−	0.262884i	$-0.0846737\pi$
$599$	28289.1	1.92965	0.964827	+	0.262884i	$0.0846737\pi$
$600$	8655.19	0.588911
$601$	−22142.4	−1.50284	−0.751420	−	0.659824i	$-0.770631\pi$
$601$	−22142.4	−1.50284	−0.751420	+	0.659824i	$0.770631\pi$
$602$	3171.37	0.214710
$603$	−8028.19	−0.542178
$604$	6193.69	0.417248
$605$	−2482.76	−0.166841
$606$	−1118.25	−0.0749604
$607$	27683.8	1.85115	0.925577	−	0.378560i	$-0.123581\pi$
$607$	27683.8	1.85115	0.925577	+	0.378560i	$0.123581\pi$
$608$	13972.9	0.932034
$609$	4082.14	0.271620
$610$	−781.466	−0.0518699
$611$	−7299.03	−0.483285
$612$	384.914	0.0254235
$613$	3935.32	0.259292	0.129646	−	0.991560i	$-0.458616\pi$
$613$	3935.32	0.259292	0.129646	+	0.991560i	$0.458616\pi$
$614$	2496.03	0.164058
$615$	−22913.7	−1.50239
$616$	2250.69	0.147212
$617$	120.759	0.00787935	0.00393967	−	0.999992i	$-0.498746\pi$
$617$	120.759	0.00787935	0.00393967	+	0.999992i	$0.498746\pi$
$618$	1022.72	0.0665695
$619$	−8008.15	−0.519991	−0.259996	−	0.965610i	$-0.583721\pi$
$619$	−8008.15	−0.519991	−0.259996	+	0.965610i	$0.583721\pi$
$620$	−14875.2	−0.963554
$621$	5558.04	0.359157
$622$	2284.96	0.147297
$623$	13553.5	0.871606
$624$	−2693.13	−0.172775
$625$	34999.1	2.23994
$626$	3696.36	0.236001
$627$	4110.33	0.261803
$628$	7949.14	0.505104
$629$	−1190.86	−0.0754891
$630$	−2420.51	−0.153072
$631$	−9451.25	−0.596273	−0.298137	−	0.954523i	$-0.596365\pi$
$631$	−9451.25	−0.596273	−0.298137	+	0.954523i	$0.596365\pi$
$632$	13581.7	0.854830
$633$	−4427.88	−0.278029
$634$	551.618	0.0345545
$635$	−49242.8	−3.07739
$636$	15305.7	0.954261
$637$	−1601.03	−0.0995841
$638$	−445.148	−0.0276232
$639$	−1513.97	−0.0937275
$640$	−23133.3	−1.42879
$641$	−23522.7	−1.44944	−0.724718	−	0.689045i	$-0.758030\pi$
$641$	−23522.7	−1.44944	−0.724718	+	0.689045i	$0.758030\pi$
$642$	−2940.66	−0.180776
$643$	−11382.3	−0.698095	−0.349048	−	0.937105i	$-0.613495\pi$
$643$	−11382.3	−0.698095	−0.349048	+	0.937105i	$0.613495\pi$
$644$	32888.1	2.01238
$645$	−14893.7	−0.909207
$646$	−437.037	−0.0266176
$647$	−636.397	−0.0386698	−0.0193349	−	0.999813i	$-0.506155\pi$
$647$	−636.397	−0.0386698	−0.0193349	+	0.999813i	$0.506155\pi$
$648$	789.447	0.0478587
$649$	−6381.14	−0.385950
$650$	3027.83	0.182709
$651$	5999.63	0.361205
$652$	10044.0	0.603303
$653$	−32372.2	−1.94000	−0.970001	−	0.243100i	$-0.921836\pi$
$653$	−32372.2	−1.94000	−0.970001	+	0.243100i	$0.921836\pi$
$654$	−1623.11	−0.0970468
$655$	1448.27	0.0863950
$656$	20397.5	1.21400
$657$	−4235.28	−0.251498
$658$	5839.78	0.345985
$659$	−12217.6	−0.722199	−0.361099	−	0.932527i	$-0.617598\pi$
$659$	−12217.6	−0.722199	−0.361099	+	0.932527i	$0.617598\pi$
$660$	−5152.99	−0.303909
$661$	1506.93	0.0886729	0.0443365	−	0.999017i	$-0.485883\pi$
$661$	1506.93	0.0886729	0.0443365	+	0.999017i	$0.485883\pi$
$662$	2444.67	0.143527
$663$	276.205	0.0161793
$664$	−10713.6	−0.626156
$665$	−53653.4	−3.12871
$666$	−1190.71	−0.0692781
$667$	−13342.6	−0.774553
$668$	−7788.74	−0.451131
$669$	−3010.37	−0.173973
$670$	−11427.6	−0.658936
$671$	671.000	0.0386046
$672$	7065.30	0.405580
$673$	−10134.9	−0.580492	−0.290246	−	0.956952i	$-0.593737\pi$
$673$	−10134.9	−0.580492	−0.290246	+	0.956952i	$0.593737\pi$
$674$	−736.241	−0.0420756
$675$	7992.47	0.455748
$676$	14677.1	0.835063
$677$	−6948.10	−0.394442	−0.197221	−	0.980359i	$-0.563192\pi$
$677$	−6948.10	−0.394442	−0.197221	+	0.980359i	$0.563192\pi$
$678$	−2011.64	−0.113948
$679$	−23221.9	−1.31248
$680$	1123.86	0.0633797
$681$	−7983.37	−0.449227
$682$	−654.247	−0.0367337
$683$	17788.9	0.996593	0.498296	−	0.867007i	$-0.333959\pi$
$683$	17788.9	0.996593	0.498296	+	0.867007i	$0.333959\pi$
$684$	8531.00	0.476888
$685$	20497.8	1.14333
$686$	−3214.88	−0.178928
$687$	582.767	0.0323638
$688$	13258.2	0.734684
$689$	10983.0	0.607283
$690$	7911.51	0.436502
$691$	−18353.0	−1.01039	−0.505195	−	0.863005i	$-0.668579\pi$
$691$	−18353.0	−1.01039	−0.505195	+	0.863005i	$0.668579\pi$
$692$	12112.3	0.665377
$693$	2078.36	0.113925
$694$	−4691.06	−0.256585
$695$	18533.7	1.01154
$696$	−1895.14	−0.103211
$697$	−2091.94	−0.113684
$698$	4546.05	0.246519
$699$	10022.3	0.542316
$700$	47293.0	2.55358
$701$	−2012.67	−0.108442	−0.0542208	−	0.998529i	$-0.517267\pi$
$701$	−2012.67	−0.108442	−0.0542208	+	0.998529i	$0.517267\pi$
$702$	276.171	0.0148481
$703$	−26393.5	−1.41600
$704$	4051.62	0.216905
$705$	−27425.4	−1.46511
$706$	7525.56	0.401173
$707$	−12533.6	−0.666722
$708$	−13244.1	−0.703027
$709$	19435.4	1.02950	0.514748	−	0.857341i	$-0.327885\pi$
$709$	19435.4	1.02950	0.514748	+	0.857341i	$0.327885\pi$
$710$	−2155.04	−0.113912
$711$	12541.8	0.661539
$712$	−6292.24	−0.331196
$713$	−19610.0	−1.03001
$714$	−220.985	−0.0115828
$715$	−3697.66	−0.193405
$716$	24783.4	1.29358
$717$	−2669.48	−0.139043
$718$	5315.88	0.276305
$719$	9115.91	0.472832	0.236416	−	0.971652i	$-0.424027\pi$
$719$	9115.91	0.472832	0.236416	+	0.971652i	$0.424027\pi$
$720$	−10119.2	−0.523776
$721$	11462.8	0.592091
$722$	−5403.80	−0.278544
$723$	17528.7	0.901661
$724$	15357.7	0.788348
$725$	−19186.6	−0.982861
$726$	−226.640	−0.0115860
$727$	−8117.98	−0.414139	−0.207070	−	0.978326i	$-0.566393\pi$
$727$	−8117.98	−0.414139	−0.207070	+	0.978326i	$0.566393\pi$
$728$	3352.02	0.170651
$729$	729.000	0.0370370
$730$	−6028.65	−0.305658
$731$	−1359.74	−0.0687988
$732$	1392.66	0.0703201
$733$	6679.33	0.336571	0.168286	−	0.985738i	$-0.446177\pi$
$733$	6679.33	0.336571	0.168286	+	0.985738i	$0.446177\pi$
$734$	−5409.85	−0.272045
$735$	−6015.70	−0.301895
$736$	−23093.1	−1.15655
$737$	9812.24	0.490418
$738$	−2091.69	−0.104331
$739$	9206.35	0.458269	0.229135	−	0.973395i	$-0.426410\pi$
$739$	9206.35	0.458269	0.229135	+	0.973395i	$0.426410\pi$
$740$	33088.7	1.64374
$741$	6121.64	0.303487
$742$	−8787.22	−0.434756
$743$	−27022.8	−1.33428	−0.667139	−	0.744933i	$-0.732481\pi$
$743$	−27022.8	−1.33428	−0.667139	+	0.744933i	$0.732481\pi$
$744$	−2785.34	−0.137252
$745$	44289.1	2.17802
$746$	−206.249	−0.0101224
$747$	−9893.25	−0.484572
$748$	−470.450	−0.0229965
$749$	−32959.3	−1.60789
$750$	6572.66	0.320000
$751$	31870.1	1.54854	0.774271	−	0.632854i	$-0.218117\pi$
$751$	31870.1	1.54854	0.774271	+	0.632854i	$0.218117\pi$
$752$	24413.7	1.18388
$753$	17235.0	0.834103
$754$	−662.973	−0.0320213
$755$	16699.5	0.804978
$756$	4313.64	0.207521
$757$	−3710.23	−0.178138	−0.0890690	−	0.996025i	$-0.528389\pi$
$757$	−3710.23	−0.178138	−0.0890690	+	0.996025i	$0.528389\pi$
$758$	4522.78	0.216721
$759$	−6793.17	−0.324870
$760$	24908.7	1.18886
$761$	−2777.30	−0.132296	−0.0661478	−	0.997810i	$-0.521071\pi$
$761$	−2777.30	−0.132296	−0.0661478	+	0.997810i	$0.521071\pi$
$762$	−4495.15	−0.213704
$763$	−18192.0	−0.863167
$764$	11330.8	0.536563
$765$	1037.81	0.0490485
$766$	3602.76	0.169939
$767$	−9503.63	−0.447401
$768$	6728.17	0.316122
$769$	−17027.8	−0.798491	−0.399245	−	0.916844i	$-0.630728\pi$
$769$	−17027.8	−0.798491	−0.399245	+	0.916844i	$0.630728\pi$
$770$	2958.41	0.138459
$771$	21296.7	0.994789
$772$	−8940.59	−0.416812
$773$	−10882.7	−0.506371	−0.253186	−	0.967418i	$-0.581478\pi$
$773$	−10882.7	−0.506371	−0.253186	+	0.967418i	$0.581478\pi$
$774$	−1359.58	−0.0631383
$775$	−28199.1	−1.30702
$776$	10780.8	0.498722
$777$	−13345.7	−0.616182
$778$	1623.04	0.0747926
$779$	−46364.6	−2.13246
$780$	−7674.50	−0.352296
$781$	1850.41	0.0847797
$782$	722.294	0.0330296
$783$	−1750.03	−0.0798736
$784$	5355.09	0.243945
$785$	21432.6	0.974474
$786$	132.206	0.00599954
$787$	17478.3	0.791655	0.395827	−	0.918325i	$-0.370458\pi$
$787$	17478.3	0.791655	0.395827	+	0.918325i	$0.370458\pi$
$788$	9495.57	0.429271
$789$	−12670.2	−0.571702
$790$	17852.4	0.804001
$791$	−22546.8	−1.01349
$792$	−964.880	−0.0432898
$793$	999.341	0.0447511
$794$	−8998.11	−0.402180
$795$	41267.4	1.84101
$796$	−35800.0	−1.59409
$797$	−41481.0	−1.84358	−0.921789	−	0.387692i	$-0.873272\pi$
$797$	−41481.0	−1.84358	−0.921789	+	0.387692i	$0.873272\pi$
$798$	−4897.77	−0.217267
$799$	−2503.84	−0.110863
$800$	−33207.9	−1.46760
$801$	−5810.45	−0.256307
$802$	−2917.02	−0.128433
$803$	5176.46	0.227488
$804$	20365.3	0.893321
$805$	88673.3	3.88239
$806$	−974.390	−0.0425824
$807$	−13194.0	−0.575527
$808$	5818.72	0.253344
$809$	33191.2	1.44245	0.721224	−	0.692702i	$-0.243580\pi$
$809$	33191.2	1.44245	0.721224	+	0.692702i	$0.243580\pi$
$810$	1037.68	0.0450130
$811$	−22807.2	−0.987508	−0.493754	−	0.869602i	$-0.664376\pi$
$811$	−22807.2	−0.987508	−0.493754	+	0.869602i	$0.664376\pi$
$812$	−10355.3	−0.447536
$813$	13445.4	0.580013
$814$	1455.32	0.0626644
$815$	27080.8	1.16393
$816$	−923.844	−0.0396336
$817$	−30136.6	−1.29051
$818$	−547.158	−0.0233874
$819$	3095.36	0.132064
$820$	58125.8	2.47542
$821$	25800.7	1.09677	0.548386	−	0.836226i	$-0.315243\pi$
$821$	25800.7	1.09677	0.548386	+	0.836226i	$0.315243\pi$
$822$	1871.15	0.0793966
$823$	30603.0	1.29618	0.648088	−	0.761565i	$-0.275569\pi$
$823$	30603.0	1.29618	0.648088	+	0.761565i	$0.275569\pi$
$824$	−5321.63	−0.224985
$825$	−9768.57	−0.412240
$826$	7603.63	0.320295
$827$	21096.5	0.887059	0.443530	−	0.896260i	$-0.353726\pi$
$827$	21096.5	0.887059	0.443530	+	0.896260i	$0.353726\pi$
$828$	−14099.2	−0.591767
$829$	−16164.3	−0.677212	−0.338606	−	0.940928i	$-0.609955\pi$
$829$	−16164.3	−0.677212	−0.338606	+	0.940928i	$0.609955\pi$
$830$	−14082.4	−0.588924
$831$	22263.3	0.929367
$832$	6034.21	0.251441
$833$	−549.213	−0.0228441
$834$	1691.85	0.0702447
$835$	−21000.1	−0.870347
$836$	−10426.8	−0.431361
$837$	−2572.07	−0.106217
$838$	−2996.10	−0.123507
$839$	−556.247	−0.0228889	−0.0114444	−	0.999935i	$-0.503643\pi$
$839$	−556.247	−0.0228889	−0.0114444	+	0.999935i	$0.503643\pi$
$840$	12594.9	0.517339
$841$	−20187.9	−0.827746
$842$	−6419.73	−0.262754
$843$	−6441.32	−0.263168
$844$	11232.3	0.458096
$845$	39572.6	1.61105
$846$	−2503.54	−0.101742
$847$	−2540.21	−0.103049
$848$	−36735.7	−1.48763
$849$	−2333.43	−0.0943263
$850$	1038.66	0.0419126
$851$	43620.7	1.75711
$852$	3840.54	0.154430
$853$	−10103.3	−0.405546	−0.202773	−	0.979226i	$-0.564995\pi$
$853$	−10103.3	−0.405546	−0.202773	+	0.979226i	$0.564995\pi$
$854$	−799.549	−0.0320375
$855$	23001.4	0.920038
$856$	15301.4	0.610971
$857$	−13163.0	−0.524668	−0.262334	−	0.964977i	$-0.584492\pi$
$857$	−13163.0	−0.524668	−0.262334	+	0.964977i	$0.584492\pi$
$858$	−337.542	−0.0134306
$859$	−14771.9	−0.586740	−0.293370	−	0.955999i	$-0.594777\pi$
$859$	−14771.9	−0.586740	−0.293370	+	0.955999i	$0.594777\pi$
$860$	37781.3	1.49806
$861$	−23443.9	−0.927952
$862$	−4355.65	−0.172105
$863$	−11832.6	−0.466729	−0.233364	−	0.972389i	$-0.574973\pi$
$863$	−11832.6	−0.466729	−0.233364	+	0.972389i	$0.574973\pi$
$864$	−3028.92	−0.119266
$865$	32657.4	1.28368
$866$	−2641.01	−0.103632
$867$	−14644.3	−0.573639
$868$	−15219.4	−0.595140
$869$	−15328.9	−0.598384
$870$	−2491.05	−0.0970743
$871$	14613.7	0.568502
$872$	8445.68	0.327990
$873$	9955.33	0.385953
$874$	16008.5	0.619561
$875$	73667.3	2.84618
$876$	10743.8	0.414381
$877$	44499.0	1.71337	0.856685	−	0.515840i	$-0.172520\pi$
$877$	44499.0	1.71337	0.856685	+	0.515840i	$0.172520\pi$
$878$	834.039	0.0320586
$879$	27679.3	1.06211
$880$	12367.9	0.473773
$881$	−37060.6	−1.41726	−0.708629	−	0.705581i	$-0.750686\pi$
$881$	−37060.6	−1.41726	−0.708629	+	0.705581i	$0.750686\pi$
$882$	−549.146	−0.0209645
$883$	−25802.0	−0.983359	−0.491680	−	0.870776i	$-0.663617\pi$
$883$	−25802.0	−0.983359	−0.491680	+	0.870776i	$0.663617\pi$
$884$	−700.656	−0.0266579
$885$	−35708.9	−1.35632
$886$	3609.29	0.136858
$887$	−23156.5	−0.876572	−0.438286	−	0.898836i	$-0.644414\pi$
$887$	−23156.5	−0.876572	−0.438286	+	0.898836i	$0.644414\pi$
$888$	6195.75	0.234139
$889$	−50382.3	−1.90075
$890$	−8270.80	−0.311503
$891$	−891.000	−0.0335013
$892$	7636.50	0.286647
$893$	−55493.7	−2.07954
$894$	4042.95	0.151249
$895$	66821.5	2.49564
$896$	−23668.6	−0.882493
$897$	−10117.3	−0.376595
$898$	3588.95	0.133369
$899$	6174.48	0.229066
$900$	−20274.7	−0.750915
$901$	3767.58	0.139308
$902$	2556.51	0.0943707
$903$	−15238.3	−0.561573
$904$	10467.4	0.385110
$905$	41407.7	1.52093
$906$	1524.42	0.0559002
$907$	43792.4	1.60320	0.801601	−	0.597859i	$-0.203982\pi$
$907$	43792.4	1.60320	0.801601	+	0.597859i	$0.203982\pi$
$908$	20251.6	0.740170
$909$	5373.19	0.196059
$910$	4406.04	0.160504
$911$	−50458.9	−1.83510	−0.917552	−	0.397617i	$-0.869837\pi$
$911$	−50458.9	−1.83510	−0.917552	+	0.397617i	$0.869837\pi$
$912$	−20475.5	−0.743435
$913$	12091.8	0.438312
$914$	421.635	0.0152587
$915$	3754.92	0.135665
$916$	−1478.32	−0.0533243
$917$	1481.79	0.0533619
$918$	94.7370	0.00340609
$919$	37245.6	1.33691	0.668455	−	0.743752i	$-0.266956\pi$
$919$	37245.6	1.33691	0.668455	+	0.743752i	$0.266956\pi$
$920$	−41166.7	−1.47525
$921$	−11993.4	−0.429093
$922$	4109.36	0.146784
$923$	2755.88	0.0982782
$924$	−5272.23	−0.187709
$925$	62726.6	2.22966
$926$	2755.32	0.0977814
$927$	−4914.16	−0.174112
$928$	7271.21	0.257208
$929$	−6001.43	−0.211949	−0.105974	−	0.994369i	$-0.533796\pi$
$929$	−6001.43	−0.211949	−0.105974	+	0.994369i	$0.533796\pi$
$930$	−3661.17	−0.129091
$931$	−12172.4	−0.428502
$932$	−25423.9	−0.893548
$933$	−10979.2	−0.385254
$934$	−2583.96	−0.0905243
$935$	−1268.44	−0.0443661
$936$	−1437.03	−0.0501823
$937$	47393.4	1.65237	0.826187	−	0.563397i	$-0.190506\pi$
$937$	47393.4	1.65237	0.826187	+	0.563397i	$0.190506\pi$
$938$	−11692.0	−0.406992
$939$	−17760.9	−0.617259
$940$	69570.7	2.41399
$941$	−19982.2	−0.692243	−0.346121	−	0.938190i	$-0.612501\pi$
$941$	−19982.2	−0.692243	−0.346121	+	0.938190i	$0.612501\pi$
$942$	1956.48	0.0676706
$943$	76627.1	2.64615
$944$	31787.6	1.09597
$945$	11630.5	0.400360
$946$	1661.71	0.0571107
$947$	8443.01	0.289716	0.144858	−	0.989452i	$-0.453728\pi$
$947$	8443.01	0.289716	0.144858	+	0.989452i	$0.453728\pi$
$948$	−31815.1	−1.08999
$949$	7709.46	0.263709
$950$	23020.2	0.786184
$951$	−2650.51	−0.0903771
$952$	1149.87	0.0391465
$953$	28996.3	0.985606	0.492803	−	0.870141i	$-0.335972\pi$
$953$	28996.3	0.985606	0.492803	+	0.870141i	$0.335972\pi$
$954$	3767.12	0.127846
$955$	30550.3	1.03517
$956$	6771.76	0.229094
$957$	2138.93	0.0722483
$958$	412.312	0.0139052
$959$	20972.2	0.706180
$960$	22672.9	0.762256
$961$	−20716.2	−0.695384
$962$	2167.45	0.0726417
$963$	14129.8	0.472820
$964$	−44465.7	−1.48562
$965$	−24105.8	−0.804137
$966$	8094.58	0.269606
$967$	34945.2	1.16211	0.581055	−	0.813864i	$-0.302640\pi$
$967$	34945.2	1.16211	0.581055	+	0.813864i	$0.302640\pi$
$968$	1179.30	0.0391571
$969$	2099.95	0.0696183
$970$	14170.8	0.469068
$971$	−59007.4	−1.95019	−0.975096	−	0.221781i	$-0.928813\pi$
$971$	−59007.4	−1.95019	−0.975096	+	0.221781i	$0.928813\pi$
$972$	−1849.27	−0.0610242
$973$	18962.5	0.624780
$974$	290.257	0.00954871
$975$	−14548.6	−0.477876
$976$	−3342.58	−0.109624
$977$	24770.4	0.811130	0.405565	−	0.914066i	$-0.367075\pi$
$977$	24770.4	0.811130	0.405565	+	0.914066i	$0.367075\pi$
$978$	2472.08	0.0808267
$979$	7101.66	0.231839
$980$	15260.2	0.497417
$981$	7799.00	0.253826
$982$	11805.1	0.383621
$983$	−41748.4	−1.35460	−0.677298	−	0.735709i	$-0.736849\pi$
$983$	−41748.4	−1.35460	−0.677298	+	0.735709i	$0.736849\pi$
$984$	10883.9	0.352607
$985$	25602.1	0.828174
$986$	−227.425	−0.00734552
$987$	−28060.0	−0.904924
$988$	−15528.9	−0.500041
$989$	49806.9	1.60138
$990$	−1268.28	−0.0407158
$991$	37643.3	1.20664	0.603319	−	0.797500i	$-0.293845\pi$
$991$	37643.3	1.20664	0.603319	+	0.797500i	$0.293845\pi$
$992$	10686.7	0.342039
$993$	−11746.6	−0.375394
$994$	−2204.91	−0.0703577
$995$	−96524.6	−3.07541
$996$	25096.5	0.798406
$997$	−41274.4	−1.31111	−0.655554	−	0.755149i	$-0.727565\pi$
$997$	−41274.4	−1.31111	−0.655554	+	0.755149i	$0.727565\pi$
$998$	8516.39	0.270122
$999$	5721.35	0.181197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.17	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.17	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-0.624353 q^{2} +3.00000 q^{3} -7.61018 q^{4} -20.5187 q^{5} -1.87306 q^{6} -20.9935 q^{7} +9.74626 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.624353 q^{2} +3.00000 q^{3} -7.61018 q^{4} -20.5187 q^{5} -1.87306 q^{6} -20.9935 q^{7} +9.74626 q^{8} +9.00000 q^{9} +12.8109 q^{10} -11.0000 q^{11} -22.8306 q^{12} -16.3826 q^{13} +13.1074 q^{14} -61.5561 q^{15} +54.7964 q^{16} -5.61986 q^{17} -5.61918 q^{18} -124.555 q^{19} +156.151 q^{20} -62.9805 q^{21} +6.86788 q^{22} +205.853 q^{23} +29.2388 q^{24} +296.017 q^{25} +10.2285 q^{26} +27.0000 q^{27} +159.764 q^{28} -64.8159 q^{29} +38.4327 q^{30} -95.2618 q^{31} -112.182 q^{32} -33.0000 q^{33} +3.50878 q^{34} +430.759 q^{35} -68.4917 q^{36} +211.902 q^{37} +77.7665 q^{38} -49.1479 q^{39} -199.981 q^{40} +372.241 q^{41} +39.3221 q^{42} +241.953 q^{43} +83.7120 q^{44} -184.668 q^{45} -128.525 q^{46} +445.535 q^{47} +164.389 q^{48} +97.7271 q^{49} -184.819 q^{50} -16.8596 q^{51} +124.675 q^{52} -670.404 q^{53} -16.8575 q^{54} +225.706 q^{55} -204.608 q^{56} -373.666 q^{57} +40.4680 q^{58} +580.104 q^{59} +468.453 q^{60} -61.0000 q^{61} +59.4770 q^{62} -188.942 q^{63} -368.329 q^{64} +336.151 q^{65} +20.6036 q^{66} -892.022 q^{67} +42.7682 q^{68} +617.560 q^{69} -268.946 q^{70} -168.219 q^{71} +87.7164 q^{72} -470.587 q^{73} -132.302 q^{74} +888.052 q^{75} +947.889 q^{76} +230.929 q^{77} +30.6856 q^{78} +1393.53 q^{79} -1124.35 q^{80} +81.0000 q^{81} -232.410 q^{82} -1099.25 q^{83} +479.293 q^{84} +115.312 q^{85} -151.064 q^{86} -194.448 q^{87} -107.209 q^{88} -645.606 q^{89} +115.298 q^{90} +343.929 q^{91} -1566.58 q^{92} -285.785 q^{93} -278.171 q^{94} +2555.71 q^{95} -336.547 q^{96} +1106.15 q^{97} -61.0162 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 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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