LMFDB - Embedded newform 966.4.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 456x^{3} - 1295x^{2} + 36752x + 117404 $ x^5 - 456x^3 - 1295x^2 + 36752*x + 117404
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.23635$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.23635 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.23635 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.4727 q^{10} -33.6919 q^{11} -12.0000 q^{12} -12.8893 q^{13} -14.0000 q^{14} +15.7091 q^{15} +16.0000 q^{16} -88.6845 q^{17} +18.0000 q^{18} +155.110 q^{19} -20.9454 q^{20} +21.0000 q^{21} -67.3838 q^{22} +23.0000 q^{23} -24.0000 q^{24} -97.5806 q^{25} -25.7786 q^{26} -27.0000 q^{27} -28.0000 q^{28} +305.406 q^{29} +31.4181 q^{30} -203.108 q^{31} +32.0000 q^{32} +101.076 q^{33} -177.369 q^{34} +36.6545 q^{35} +36.0000 q^{36} -145.994 q^{37} +310.220 q^{38} +38.6680 q^{39} -41.8908 q^{40} +233.468 q^{41} +42.0000 q^{42} +97.1337 q^{43} -134.768 q^{44} -47.1272 q^{45} +46.0000 q^{46} +356.969 q^{47} -48.0000 q^{48} +49.0000 q^{49} -195.161 q^{50} +266.054 q^{51} -51.5573 q^{52} +626.834 q^{53} -54.0000 q^{54} +176.423 q^{55} -56.0000 q^{56} -465.330 q^{57} +610.811 q^{58} -838.063 q^{59} +62.8362 q^{60} +683.668 q^{61} -406.216 q^{62} -63.0000 q^{63} +64.0000 q^{64} +67.4930 q^{65} +202.151 q^{66} -455.072 q^{67} -354.738 q^{68} -69.0000 q^{69} +73.3089 q^{70} +656.306 q^{71} +72.0000 q^{72} -320.872 q^{73} -291.988 q^{74} +292.742 q^{75} +620.440 q^{76} +235.843 q^{77} +77.3359 q^{78} +946.173 q^{79} -83.7816 q^{80} +81.0000 q^{81} +466.935 q^{82} +112.700 q^{83} +84.0000 q^{84} +464.383 q^{85} +194.267 q^{86} -916.217 q^{87} -269.535 q^{88} -1038.97 q^{89} -94.2543 q^{90} +90.2252 q^{91} +92.0000 q^{92} +609.324 q^{93} +713.938 q^{94} -812.210 q^{95} -96.0000 q^{96} +192.499 q^{97} +98.0000 q^{98} -303.227 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−5.23635	−0.468354	−0.234177	−	0.972194i	$-0.575239\pi$
$5$	−5.23635	−0.468354	−0.234177	+	0.972194i	$0.575239\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−10.4727	−0.331176
$11$	−33.6919	−0.923499	−0.461750	−	0.887010i	$-0.652778\pi$
$11$	−33.6919	−0.923499	−0.461750	+	0.887010i	$0.652778\pi$
$12$	−12.0000	−0.288675
$13$	−12.8893	−0.274989	−0.137494	−	0.990503i	$-0.543905\pi$
$13$	−12.8893	−0.274989	−0.137494	+	0.990503i	$0.543905\pi$
$14$	−14.0000	−0.267261
$15$	15.7091	0.270404
$16$	16.0000	0.250000
$17$	−88.6845	−1.26524	−0.632622	−	0.774461i	$-0.718021\pi$
$17$	−88.6845	−1.26524	−0.632622	+	0.774461i	$0.718021\pi$
$18$	18.0000	0.235702
$19$	155.110	1.87288	0.936438	−	0.350833i	$-0.114101\pi$
$19$	155.110	1.87288	0.936438	+	0.350833i	$0.114101\pi$
$20$	−20.9454	−0.234177
$21$	21.0000	0.218218
$22$	−67.3838	−0.653012
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	−97.5806	−0.780645
$26$	−25.7786	−0.194446
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	305.406	1.95560	0.977800	−	0.209539i	$-0.0671962\pi$
$29$	305.406	1.95560	0.977800	+	0.209539i	$0.0671962\pi$
$30$	31.4181	0.191205
$31$	−203.108	−1.17675	−0.588376	−	0.808588i	$-0.700232\pi$
$31$	−203.108	−1.17675	−0.588376	+	0.808588i	$0.700232\pi$
$32$	32.0000	0.176777
$33$	101.076	0.533182
$34$	−177.369	−0.894663
$35$	36.6545	0.177021
$36$	36.0000	0.166667
$37$	−145.994	−0.648683	−0.324342	−	0.945940i	$-0.605143\pi$
$37$	−145.994	−0.648683	−0.324342	+	0.945940i	$0.605143\pi$
$38$	310.220	1.32432
$39$	38.6680	0.158765
$40$	−41.8908	−0.165588
$41$	233.468	0.889306	0.444653	−	0.895703i	$-0.353327\pi$
$41$	233.468	0.889306	0.444653	+	0.895703i	$0.353327\pi$
$42$	42.0000	0.154303
$43$	97.1337	0.344483	0.172241	−	0.985055i	$-0.444899\pi$
$43$	97.1337	0.344483	0.172241	+	0.985055i	$0.444899\pi$
$44$	−134.768	−0.461750
$45$	−47.1272	−0.156118
$46$	46.0000	0.147442
$47$	356.969	1.10786	0.553929	−	0.832564i	$-0.313128\pi$
$47$	356.969	1.10786	0.553929	+	0.832564i	$0.313128\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−195.161	−0.551999
$51$	266.054	0.730489
$52$	−51.5573	−0.137494
$53$	626.834	1.62457	0.812285	−	0.583260i	$-0.198223\pi$
$53$	626.834	1.62457	0.812285	+	0.583260i	$0.198223\pi$
$54$	−54.0000	−0.136083
$55$	176.423	0.432524
$56$	−56.0000	−0.133631
$57$	−465.330	−1.08131
$58$	610.811	1.38282
$59$	−838.063	−1.84926	−0.924631	−	0.380864i	$-0.875626\pi$
$59$	−838.063	−1.84926	−0.924631	+	0.380864i	$0.875626\pi$
$60$	62.8362	0.135202
$61$	683.668	1.43500	0.717498	−	0.696561i	$-0.245287\pi$
$61$	683.668	1.43500	0.717498	+	0.696561i	$0.245287\pi$
$62$	−406.216	−0.832089
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	67.4930	0.128792
$66$	202.151	0.377017
$67$	−455.072	−0.829789	−0.414895	−	0.909869i	$-0.636182\pi$
$67$	−455.072	−0.829789	−0.414895	+	0.909869i	$0.636182\pi$
$68$	−354.738	−0.632622
$69$	−69.0000	−0.120386
$70$	73.3089	0.125173
$71$	656.306	1.09703	0.548516	−	0.836140i	$-0.315193\pi$
$71$	656.306	1.09703	0.548516	+	0.836140i	$0.315193\pi$
$72$	72.0000	0.117851
$73$	−320.872	−0.514455	−0.257228	−	0.966351i	$-0.582809\pi$
$73$	−320.872	−0.514455	−0.257228	+	0.966351i	$0.582809\pi$
$74$	−291.988	−0.458688
$75$	292.742	0.450706
$76$	620.440	0.936438
$77$	235.843	0.349050
$78$	77.3359	0.112264
$79$	946.173	1.34750	0.673752	−	0.738958i	$-0.264682\pi$
$79$	946.173	1.34750	0.673752	+	0.738958i	$0.264682\pi$
$80$	−83.7816	−0.117088
$81$	81.0000	0.111111
$82$	466.935	0.628834
$83$	112.700	0.149041	0.0745205	−	0.997219i	$-0.476257\pi$
$83$	112.700	0.149041	0.0745205	+	0.997219i	$0.476257\pi$
$84$	84.0000	0.109109
$85$	464.383	0.592582
$86$	194.267	0.243586
$87$	−916.217	−1.12907
$88$	−269.535	−0.326506
$89$	−1038.97	−1.23742	−0.618710	−	0.785619i	$-0.712345\pi$
$89$	−1038.97	−1.23742	−0.618710	+	0.785619i	$0.712345\pi$
$90$	−94.2543	−0.110392
$91$	90.2252	0.103936
$92$	92.0000	0.104257
$93$	609.324	0.679398
$94$	713.938	0.783374
$95$	−812.210	−0.877168
$96$	−96.0000	−0.102062
$97$	192.499	0.201498	0.100749	−	0.994912i	$-0.467876\pi$
$97$	192.499	0.201498	0.100749	+	0.994912i	$0.467876\pi$
$98$	98.0000	0.101015
$99$	−303.227	−0.307833
$100$	−390.322	−0.390322
$101$	1665.32	1.64065	0.820327	−	0.571895i	$-0.193792\pi$
$101$	1665.32	1.64065	0.820327	+	0.571895i	$0.193792\pi$
$102$	532.107	0.516534
$103$	588.034	0.562531	0.281265	−	0.959630i	$-0.409246\pi$
$103$	588.034	0.562531	0.281265	+	0.959630i	$0.409246\pi$
$104$	−103.115	−0.0972232
$105$	−109.963	−0.102203
$106$	1253.67	1.14874
$107$	1752.00	1.58291	0.791457	−	0.611225i	$-0.209323\pi$
$107$	1752.00	1.58291	0.791457	+	0.611225i	$0.209323\pi$
$108$	−108.000	−0.0962250
$109$	568.352	0.499434	0.249717	−	0.968319i	$-0.419662\pi$
$109$	568.352	0.499434	0.249717	+	0.968319i	$0.419662\pi$
$110$	352.845	0.305841
$111$	437.982	0.374518
$112$	−112.000	−0.0944911
$113$	1573.13	1.30963	0.654813	−	0.755791i	$-0.272747\pi$
$113$	1573.13	1.30963	0.654813	+	0.755791i	$0.272747\pi$
$114$	−930.659	−0.764599
$115$	−120.436	−0.0976585
$116$	1221.62	0.977800
$117$	−116.004	−0.0916629
$118$	−1676.13	−1.30763
$119$	620.792	0.478217
$120$	125.672	0.0956023
$121$	−195.856	−0.147149
$122$	1367.34	1.01469
$123$	−700.403	−0.513441
$124$	−812.433	−0.588376
$125$	1165.51	0.833971
$126$	−126.000	−0.0890871
$127$	−35.5371	−0.0248300	−0.0124150	−	0.999923i	$-0.503952\pi$
$127$	−35.5371	−0.0248300	−0.0124150	+	0.999923i	$0.503952\pi$
$128$	128.000	0.0883883
$129$	−291.401	−0.198887
$130$	134.986	0.0910697
$131$	−295.473	−0.197066	−0.0985328	−	0.995134i	$-0.531415\pi$
$131$	−295.473	−0.197066	−0.0985328	+	0.995134i	$0.531415\pi$
$132$	404.303	0.266591
$133$	−1085.77	−0.707881
$134$	−910.144	−0.586750
$135$	141.382	0.0901347
$136$	−709.476	−0.447331
$137$	1457.22	0.908752	0.454376	−	0.890810i	$-0.349862\pi$
$137$	1457.22	0.908752	0.454376	+	0.890810i	$0.349862\pi$
$138$	−138.000	−0.0851257
$139$	2827.12	1.72513	0.862567	−	0.505944i	$-0.168856\pi$
$139$	2827.12	1.72513	0.862567	+	0.505944i	$0.168856\pi$
$140$	146.618	0.0885105
$141$	−1070.91	−0.639622
$142$	1312.61	0.775718
$143$	434.266	0.253952
$144$	144.000	0.0833333
$145$	−1599.21	−0.915913
$146$	−641.744	−0.363775
$147$	−147.000	−0.0824786
$148$	−583.977	−0.324342
$149$	−1883.82	−1.03576	−0.517882	−	0.855452i	$-0.673279\pi$
$149$	−1883.82	−1.03576	−0.517882	+	0.855452i	$0.673279\pi$
$150$	585.484	0.318697
$151$	1954.51	1.05335	0.526674	−	0.850068i	$-0.323439\pi$
$151$	1954.51	1.05335	0.526674	+	0.850068i	$0.323439\pi$
$152$	1240.88	0.662162
$153$	−798.161	−0.421748
$154$	471.687	0.246816
$155$	1063.55	0.551136
$156$	154.672	0.0793824
$157$	−1377.49	−0.700230	−0.350115	−	0.936707i	$-0.613857\pi$
$157$	−1377.49	−0.700230	−0.350115	+	0.936707i	$0.613857\pi$
$158$	1892.35	0.952829
$159$	−1880.50	−0.937946
$160$	−167.563	−0.0827940
$161$	−161.000	−0.0788110
$162$	162.000	0.0785674
$163$	−1419.18	−0.681955	−0.340977	−	0.940071i	$-0.610758\pi$
$163$	−1419.18	−0.681955	−0.340977	+	0.940071i	$0.610758\pi$
$164$	933.871	0.444653
$165$	−529.268	−0.249718
$166$	225.400	0.105388
$167$	−3262.06	−1.51153	−0.755766	−	0.654842i	$-0.772735\pi$
$167$	−3262.06	−1.51153	−0.755766	+	0.654842i	$0.772735\pi$
$168$	168.000	0.0771517
$169$	−2030.87	−0.924381
$170$	928.767	0.419019
$171$	1395.99	0.624292
$172$	388.535	0.172241
$173$	−2366.43	−1.03998	−0.519989	−	0.854173i	$-0.674064\pi$
$173$	−2366.43	−1.03998	−0.519989	+	0.854173i	$0.674064\pi$
$174$	−1832.43	−0.798371
$175$	683.064	0.295056
$176$	−539.070	−0.230875
$177$	2514.19	1.06767
$178$	−2077.94	−0.874988
$179$	3024.61	1.26296	0.631480	−	0.775393i	$-0.282448\pi$
$179$	3024.61	1.26296	0.631480	+	0.775393i	$0.282448\pi$
$180$	−188.509	−0.0780589
$181$	866.532	0.355850	0.177925	−	0.984044i	$-0.443062\pi$
$181$	866.532	0.355850	0.177925	+	0.984044i	$0.443062\pi$
$182$	180.450	0.0734938
$183$	−2051.00	−0.828495
$184$	184.000	0.0737210
$185$	764.477	0.303813
$186$	1218.65	0.480407
$187$	2987.95	1.16845
$188$	1427.88	0.553929
$189$	189.000	0.0727393
$190$	−1624.42	−0.620252
$191$	3821.49	1.44771	0.723857	−	0.689950i	$-0.242367\pi$
$191$	3821.49	1.44771	0.723857	+	0.689950i	$0.242367\pi$
$192$	−192.000	−0.0721688
$193$	−208.378	−0.0777169	−0.0388585	−	0.999245i	$-0.512372\pi$
$193$	−208.378	−0.0777169	−0.0388585	+	0.999245i	$0.512372\pi$
$194$	384.997	0.142480
$195$	−202.479	−0.0743581
$196$	196.000	0.0714286
$197$	738.146	0.266958	0.133479	−	0.991052i	$-0.457385\pi$
$197$	738.146	0.266958	0.133479	+	0.991052i	$0.457385\pi$
$198$	−606.454	−0.217671
$199$	−2073.37	−0.738580	−0.369290	−	0.929314i	$-0.620399\pi$
$199$	−2073.37	−0.738580	−0.369290	+	0.929314i	$0.620399\pi$
$200$	−780.645	−0.276000
$201$	1365.22	0.479079
$202$	3330.65	1.16012
$203$	−2137.84	−0.739148
$204$	1064.21	0.365245
$205$	−1222.52	−0.416509
$206$	1176.07	0.397769
$207$	207.000	0.0695048
$208$	−206.229	−0.0687472
$209$	−5225.95	−1.72960
$210$	−219.927	−0.0722685
$211$	3719.24	1.21347	0.606736	−	0.794903i	$-0.292478\pi$
$211$	3719.24	1.21347	0.606736	+	0.794903i	$0.292478\pi$
$212$	2507.33	0.812285
$213$	−1968.92	−0.633371
$214$	3503.99	1.11929
$215$	−508.626	−0.161340
$216$	−216.000	−0.0680414
$217$	1421.76	0.444770
$218$	1136.70	0.353153
$219$	962.616	0.297021
$220$	705.691	0.216262
$221$	1143.08	0.347928
$222$	875.965	0.264824
$223$	−271.302	−0.0814695	−0.0407347	−	0.999170i	$-0.512970\pi$
$223$	−271.302	−0.0814695	−0.0407347	+	0.999170i	$0.512970\pi$
$224$	−224.000	−0.0668153
$225$	−878.226	−0.260215
$226$	3146.26	0.926045
$227$	−2655.32	−0.776386	−0.388193	−	0.921578i	$-0.626901\pi$
$227$	−2655.32	−0.776386	−0.388193	+	0.921578i	$0.626901\pi$
$228$	−1861.32	−0.540653
$229$	−555.766	−0.160376	−0.0801879	−	0.996780i	$-0.525552\pi$
$229$	−555.766	−0.160376	−0.0801879	+	0.996780i	$0.525552\pi$
$230$	−240.872	−0.0690550
$231$	−707.530	−0.201524
$232$	2443.25	0.691409
$233$	−3491.26	−0.981632	−0.490816	−	0.871263i	$-0.663301\pi$
$233$	−3491.26	−0.981632	−0.490816	+	0.871263i	$0.663301\pi$
$234$	−232.008	−0.0648155
$235$	−1869.22	−0.518869
$236$	−3352.25	−0.924631
$237$	−2838.52	−0.777981
$238$	1241.58	0.338151
$239$	6109.95	1.65364	0.826820	−	0.562466i	$-0.190147\pi$
$239$	6109.95	1.65364	0.826820	+	0.562466i	$0.190147\pi$
$240$	251.345	0.0676010
$241$	−587.851	−0.157124	−0.0785618	−	0.996909i	$-0.525033\pi$
$241$	−587.851	−0.157124	−0.0785618	+	0.996909i	$0.525033\pi$
$242$	−391.712	−0.104050
$243$	−243.000	−0.0641500
$244$	2734.67	0.717498
$245$	−256.581	−0.0669077
$246$	−1400.81	−0.363058
$247$	−1999.26	−0.515020
$248$	−1624.87	−0.416044
$249$	−338.099	−0.0860489
$250$	2331.02	0.589707
$251$	3064.65	0.770673	0.385336	−	0.922776i	$-0.374085\pi$
$251$	3064.65	0.770673	0.385336	+	0.922776i	$0.374085\pi$
$252$	−252.000	−0.0629941
$253$	−774.914	−0.192563
$254$	−71.0741	−0.0175574
$255$	−1393.15	−0.342127
$256$	256.000	0.0625000
$257$	−7002.61	−1.69965	−0.849826	−	0.527063i	$-0.823293\pi$
$257$	−7002.61	−1.69965	−0.849826	+	0.527063i	$0.823293\pi$
$258$	−582.802	−0.140634
$259$	1021.96	0.245179
$260$	269.972	0.0643960
$261$	2748.65	0.651867
$262$	−590.946	−0.139346
$263$	−543.061	−0.127325	−0.0636627	−	0.997971i	$-0.520278\pi$
$263$	−543.061	−0.127325	−0.0636627	+	0.997971i	$0.520278\pi$
$264$	808.606	0.188508
$265$	−3282.32	−0.760873
$266$	−2171.54	−0.500547
$267$	3116.91	0.714425
$268$	−1820.29	−0.414895
$269$	554.837	0.125758	0.0628792	−	0.998021i	$-0.479972\pi$
$269$	554.837	0.125758	0.0628792	+	0.998021i	$0.479972\pi$
$270$	282.763	0.0637348
$271$	−4581.80	−1.02703	−0.513514	−	0.858081i	$-0.671656\pi$
$271$	−4581.80	−1.02703	−0.513514	+	0.858081i	$0.671656\pi$
$272$	−1418.95	−0.316311
$273$	−270.676	−0.0600075
$274$	2914.45	0.642585
$275$	3287.68	0.720925
$276$	−276.000	−0.0601929
$277$	−7957.44	−1.72605	−0.863025	−	0.505161i	$-0.831433\pi$
$277$	−7957.44	−1.72605	−0.863025	+	0.505161i	$0.831433\pi$
$278$	5654.25	1.21985
$279$	−1827.97	−0.392251
$280$	293.236	0.0625864
$281$	2202.07	0.467489	0.233745	−	0.972298i	$-0.424902\pi$
$281$	2202.07	0.467489	0.233745	+	0.972298i	$0.424902\pi$
$282$	−2141.81	−0.452281
$283$	6380.59	1.34024	0.670118	−	0.742255i	$-0.266244\pi$
$283$	6380.59	1.34024	0.670118	+	0.742255i	$0.266244\pi$
$284$	2625.23	0.548516
$285$	2436.63	0.506433
$286$	868.531	0.179571
$287$	−1634.27	−0.336126
$288$	288.000	0.0589256
$289$	2951.94	0.600843
$290$	−3198.42	−0.647648
$291$	−577.496	−0.116335
$292$	−1283.49	−0.257228
$293$	3325.24	0.663013	0.331507	−	0.943453i	$-0.392443\pi$
$293$	3325.24	0.663013	0.331507	+	0.943453i	$0.392443\pi$
$294$	−294.000	−0.0583212
$295$	4388.39	0.866108
$296$	−1167.95	−0.229344
$297$	909.681	0.177727
$298$	−3767.64	−0.732395
$299$	−296.454	−0.0573391
$300$	1170.97	0.225353
$301$	−679.936	−0.130202
$302$	3909.01	0.744829
$303$	−4995.97	−0.947232
$304$	2481.76	0.468219
$305$	−3579.93	−0.672085
$306$	−1596.32	−0.298221
$307$	−6170.84	−1.14719	−0.573597	−	0.819138i	$-0.694452\pi$
$307$	−6170.84	−1.14719	−0.573597	+	0.819138i	$0.694452\pi$
$308$	943.373	0.174525
$309$	−1764.10	−0.324777
$310$	2127.09	0.389712
$311$	8668.19	1.58048	0.790238	−	0.612800i	$-0.209957\pi$
$311$	8668.19	1.58048	0.790238	+	0.612800i	$0.209957\pi$
$312$	309.344	0.0561319
$313$	382.592	0.0690907	0.0345454	−	0.999403i	$-0.489002\pi$
$313$	382.592	0.0690907	0.0345454	+	0.999403i	$0.489002\pi$
$314$	−2754.99	−0.495137
$315$	329.890	0.0590070
$316$	3784.69	0.673752
$317$	8745.84	1.54957	0.774787	−	0.632222i	$-0.217857\pi$
$317$	8745.84	1.54957	0.774787	+	0.632222i	$0.217857\pi$
$318$	−3761.00	−0.663228
$319$	−10289.7	−1.80600
$320$	−335.127	−0.0585442
$321$	−5255.99	−0.913896
$322$	−322.000	−0.0557278
$323$	−13755.8	−2.36965
$324$	324.000	0.0555556
$325$	1257.75	0.214669
$326$	−2838.36	−0.482215
$327$	−1705.06	−0.288348
$328$	1867.74	0.314417
$329$	−2498.78	−0.418731
$330$	−1058.54	−0.176577
$331$	−5310.72	−0.881883	−0.440942	−	0.897536i	$-0.645355\pi$
$331$	−5310.72	−0.881883	−0.440942	+	0.897536i	$0.645355\pi$
$332$	450.799	0.0745205
$333$	−1313.95	−0.216228
$334$	−6524.12	−1.06881
$335$	2382.92	0.388635
$336$	336.000	0.0545545
$337$	−4373.01	−0.706864	−0.353432	−	0.935460i	$-0.614985\pi$
$337$	−4373.01	−0.706864	−0.353432	+	0.935460i	$0.614985\pi$
$338$	−4061.73	−0.653636
$339$	−4719.39	−0.756113
$340$	1857.53	0.296291
$341$	6843.10	1.08673
$342$	2791.98	0.441441
$343$	−343.000	−0.0539949
$344$	777.070	0.121793
$345$	361.308	0.0563831
$346$	−4732.86	−0.735376
$347$	−5888.85	−0.911037	−0.455518	−	0.890226i	$-0.650546\pi$
$347$	−5888.85	−0.911037	−0.455518	+	0.890226i	$0.650546\pi$
$348$	−3664.87	−0.564533
$349$	−9548.84	−1.46458	−0.732289	−	0.680994i	$-0.761548\pi$
$349$	−9548.84	−1.46458	−0.732289	+	0.680994i	$0.761548\pi$
$350$	1366.13	0.208636
$351$	348.012	0.0529216
$352$	−1078.14	−0.163253
$353$	−7501.82	−1.13111	−0.565555	−	0.824711i	$-0.691338\pi$
$353$	−7501.82	−1.13111	−0.565555	+	0.824711i	$0.691338\pi$
$354$	5028.38	0.754958
$355$	−3436.65	−0.513799
$356$	−4155.87	−0.618710
$357$	−1862.37	−0.276099
$358$	6049.21	0.893047
$359$	−12536.2	−1.84300	−0.921499	−	0.388381i	$-0.873035\pi$
$359$	−12536.2	−1.84300	−0.921499	+	0.388381i	$0.873035\pi$
$360$	−377.017	−0.0551960
$361$	17200.1	2.50767
$362$	1733.06	0.251624
$363$	587.567	0.0849567
$364$	360.901	0.0519680
$365$	1680.20	0.240947
$366$	−4102.01	−0.585834
$367$	−9247.40	−1.31529	−0.657643	−	0.753329i	$-0.728447\pi$
$367$	−9247.40	−1.31529	−0.657643	+	0.753329i	$0.728447\pi$
$368$	368.000	0.0521286
$369$	2101.21	0.296435
$370$	1528.95	0.214828
$371$	−4387.84	−0.614030
$372$	2437.30	0.339699
$373$	4951.09	0.687286	0.343643	−	0.939100i	$-0.388339\pi$
$373$	4951.09	0.687286	0.343643	+	0.939100i	$0.388339\pi$
$374$	5975.90	0.826220
$375$	−3496.53	−0.481494
$376$	2855.75	0.391687
$377$	−3936.47	−0.537768
$378$	378.000	0.0514344
$379$	−6959.04	−0.943171	−0.471586	−	0.881820i	$-0.656318\pi$
$379$	−6959.04	−0.943171	−0.471586	+	0.881820i	$0.656318\pi$
$380$	−3248.84	−0.438584
$381$	106.611	0.0143356
$382$	7642.98	1.02369
$383$	11204.2	1.49479	0.747396	−	0.664378i	$-0.231304\pi$
$383$	11204.2	1.49479	0.747396	+	0.664378i	$0.231304\pi$
$384$	−384.000	−0.0510310
$385$	−1234.96	−0.163479
$386$	−416.756	−0.0549541
$387$	874.204	0.114828
$388$	769.995	0.100749
$389$	5008.94	0.652862	0.326431	−	0.945221i	$-0.394154\pi$
$389$	5008.94	0.652862	0.326431	+	0.945221i	$0.394154\pi$
$390$	−404.958	−0.0525791
$391$	−2039.74	−0.263822
$392$	392.000	0.0505076
$393$	886.419	0.113776
$394$	1476.29	0.188768
$395$	−4954.49	−0.631108
$396$	−1212.91	−0.153917
$397$	−4897.01	−0.619078	−0.309539	−	0.950887i	$-0.600175\pi$
$397$	−4897.01	−0.619078	−0.309539	+	0.950887i	$0.600175\pi$
$398$	−4146.74	−0.522255
$399$	3257.31	0.408695
$400$	−1561.29	−0.195161
$401$	11267.9	1.40322	0.701610	−	0.712561i	$-0.252465\pi$
$401$	11267.9	1.40322	0.701610	+	0.712561i	$0.252465\pi$
$402$	2730.43	0.338760
$403$	2617.93	0.323593
$404$	6661.30	0.820327
$405$	−424.145	−0.0520393
$406$	−4275.68	−0.522656
$407$	4918.82	0.599059
$408$	2128.43	0.258267
$409$	−2788.28	−0.337094	−0.168547	−	0.985694i	$-0.553907\pi$
$409$	−2788.28	−0.337094	−0.168547	+	0.985694i	$0.553907\pi$
$410$	−2445.04	−0.294517
$411$	−4371.67	−0.524668
$412$	2352.13	0.281265
$413$	5866.44	0.698955
$414$	414.000	0.0491473
$415$	−590.136	−0.0698039
$416$	−412.458	−0.0486116
$417$	−8481.37	−0.996006
$418$	−10451.9	−1.22301
$419$	6108.20	0.712184	0.356092	−	0.934451i	$-0.384109\pi$
$419$	6108.20	0.712184	0.356092	+	0.934451i	$0.384109\pi$
$420$	−439.854	−0.0511016
$421$	−3960.58	−0.458496	−0.229248	−	0.973368i	$-0.573627\pi$
$421$	−3960.58	−0.458496	−0.229248	+	0.973368i	$0.573627\pi$
$422$	7438.47	0.858055
$423$	3212.72	0.369286
$424$	5014.67	0.574372
$425$	8653.89	0.987707
$426$	−3937.84	−0.447861
$427$	−4785.68	−0.542377
$428$	7007.98	0.791457
$429$	−1302.80	−0.146619
$430$	−1017.25	−0.114084
$431$	−12634.0	−1.41197	−0.705984	−	0.708228i	$-0.749495\pi$
$431$	−12634.0	−1.41197	−0.705984	+	0.708228i	$0.749495\pi$
$432$	−432.000	−0.0481125
$433$	9410.43	1.04443	0.522213	−	0.852815i	$-0.325107\pi$
$433$	9410.43	1.04443	0.522213	+	0.852815i	$0.325107\pi$
$434$	2843.51	0.314500
$435$	4797.64	0.528802
$436$	2273.41	0.249717
$437$	3567.53	0.390522
$438$	1925.23	0.210025
$439$	4307.66	0.468322	0.234161	−	0.972198i	$-0.424766\pi$
$439$	4307.66	0.468322	0.234161	+	0.972198i	$0.424766\pi$
$440$	1411.38	0.152920
$441$	441.000	0.0476190
$442$	2286.17	0.246022
$443$	14365.9	1.54073	0.770366	−	0.637602i	$-0.220073\pi$
$443$	14365.9	1.54073	0.770366	+	0.637602i	$0.220073\pi$
$444$	1751.93	0.187259
$445$	5440.40	0.579550
$446$	−542.603	−0.0576076
$447$	5651.47	0.597998
$448$	−448.000	−0.0472456
$449$	−6659.06	−0.699911	−0.349956	−	0.936766i	$-0.613803\pi$
$449$	−6659.06	−0.699911	−0.349956	+	0.936766i	$0.613803\pi$
$450$	−1756.45	−0.184000
$451$	−7865.97	−0.821273
$452$	6292.52	0.654813
$453$	−5863.52	−0.608150
$454$	−5310.63	−0.548988
$455$	−472.451	−0.0486788
$456$	−3722.64	−0.382299
$457$	7271.81	0.744335	0.372167	−	0.928166i	$-0.378615\pi$
$457$	7271.81	0.744335	0.372167	+	0.928166i	$0.378615\pi$
$458$	−1111.53	−0.113403
$459$	2394.48	0.243496
$460$	−481.744	−0.0488292
$461$	−18707.0	−1.88996	−0.944980	−	0.327128i	$-0.893919\pi$
$461$	−18707.0	−1.88996	−0.944980	+	0.327128i	$0.893919\pi$
$462$	−1415.06	−0.142499
$463$	8585.25	0.861751	0.430875	−	0.902411i	$-0.358205\pi$
$463$	8585.25	0.861751	0.430875	+	0.902411i	$0.358205\pi$
$464$	4886.49	0.488900
$465$	−3190.64	−0.318198
$466$	−6982.52	−0.694118
$467$	−4364.06	−0.432430	−0.216215	−	0.976346i	$-0.569371\pi$
$467$	−4364.06	−0.432430	−0.216215	+	0.976346i	$0.569371\pi$
$468$	−464.016	−0.0458315
$469$	3185.50	0.313631
$470$	−3738.43	−0.366896
$471$	4132.48	0.404278
$472$	−6704.50	−0.653813
$473$	−3272.62	−0.318129
$474$	−5677.04	−0.550116
$475$	−15135.7	−1.46205
$476$	2483.17	0.239109
$477$	5641.50	0.541523
$478$	12219.9	1.16930
$479$	3024.53	0.288506	0.144253	−	0.989541i	$-0.453922\pi$
$479$	3024.53	0.288506	0.144253	+	0.989541i	$0.453922\pi$
$480$	502.690	0.0478011
$481$	1881.77	0.178381
$482$	−1175.70	−0.111103
$483$	483.000	0.0455016
$484$	−783.423	−0.0735747
$485$	−1007.99	−0.0943722
$486$	−486.000	−0.0453609
$487$	17121.2	1.59309	0.796546	−	0.604577i	$-0.206658\pi$
$487$	17121.2	1.59309	0.796546	+	0.604577i	$0.206658\pi$
$488$	5469.34	0.507347
$489$	4257.54	0.393727
$490$	−513.162	−0.0473109
$491$	−2250.95	−0.206892	−0.103446	−	0.994635i	$-0.532987\pi$
$491$	−2250.95	−0.206892	−0.103446	+	0.994635i	$0.532987\pi$
$492$	−2801.61	−0.256720
$493$	−27084.8	−2.47431
$494$	−3998.52	−0.364174
$495$	1587.80	0.144175
$496$	−3249.73	−0.294188
$497$	−4594.14	−0.414639
$498$	−676.199	−0.0608458
$499$	11265.9	1.01068	0.505340	−	0.862920i	$-0.331367\pi$
$499$	11265.9	1.01068	0.505340	+	0.862920i	$0.331367\pi$
$500$	4662.04	0.416986
$501$	9786.18	0.872683
$502$	6129.29	0.544948
$503$	14385.0	1.27514	0.637570	−	0.770393i	$-0.279940\pi$
$503$	14385.0	1.27514	0.637570	+	0.770393i	$0.279940\pi$
$504$	−504.000	−0.0445435
$505$	−8720.22	−0.768406
$506$	−1549.83	−0.136163
$507$	6092.60	0.533692
$508$	−142.148	−0.0124150
$509$	−17019.8	−1.48210	−0.741052	−	0.671447i	$-0.765673\pi$
$509$	−17019.8	−1.48210	−0.741052	+	0.671447i	$0.765673\pi$
$510$	−2786.30	−0.241920
$511$	2246.10	0.194446
$512$	512.000	0.0441942
$513$	−4187.97	−0.360435
$514$	−14005.2	−1.20184
$515$	−3079.15	−0.263463
$516$	−1165.60	−0.0994436
$517$	−12027.0	−1.02311
$518$	2043.92	0.173368
$519$	7099.29	0.600432
$520$	539.944	0.0455348
$521$	−1024.96	−0.0861885	−0.0430942	−	0.999071i	$-0.513722\pi$
$521$	−1024.96	−0.0861885	−0.0430942	+	0.999071i	$0.513722\pi$
$522$	5497.30	0.460940
$523$	11279.2	0.943031	0.471516	−	0.881858i	$-0.343707\pi$
$523$	11279.2	0.943031	0.471516	+	0.881858i	$0.343707\pi$
$524$	−1181.89	−0.0985328
$525$	−2049.19	−0.170351
$526$	−1086.12	−0.0900326
$527$	18012.5	1.48888
$528$	1617.21	0.133296
$529$	529.000	0.0434783
$530$	−6564.64	−0.538019
$531$	−7542.56	−0.616421
$532$	−4343.08	−0.353940
$533$	−3009.24	−0.244549
$534$	6233.81	0.505175
$535$	−9174.06	−0.741363
$536$	−3640.58	−0.293375
$537$	−9073.82	−0.729170
$538$	1109.67	0.0889246
$539$	−1650.90	−0.131928
$540$	565.526	0.0450673
$541$	−15055.9	−1.19649	−0.598246	−	0.801312i	$-0.704135\pi$
$541$	−15055.9	−1.19649	−0.598246	+	0.801312i	$0.704135\pi$
$542$	−9163.59	−0.726218
$543$	−2599.60	−0.205450
$544$	−2837.90	−0.223666
$545$	−2976.09	−0.233912
$546$	−541.351	−0.0424317
$547$	−20440.9	−1.59778	−0.798892	−	0.601475i	$-0.794580\pi$
$547$	−20440.9	−1.59778	−0.798892	+	0.601475i	$0.794580\pi$
$548$	5828.90	0.454376
$549$	6153.01	0.478332
$550$	6575.35	0.509771
$551$	47371.5	3.66260
$552$	−552.000	−0.0425628
$553$	−6623.21	−0.509308
$554$	−15914.9	−1.22050
$555$	−2293.43	−0.175407
$556$	11308.5	0.862567
$557$	11513.3	0.875824	0.437912	−	0.899018i	$-0.355718\pi$
$557$	11513.3	0.875824	0.437912	+	0.899018i	$0.355718\pi$
$558$	−3655.95	−0.277363
$559$	−1251.99	−0.0947289
$560$	586.471	0.0442553
$561$	−8963.85	−0.674606
$562$	4404.14	0.330565
$563$	12537.1	0.938497	0.469249	−	0.883066i	$-0.344525\pi$
$563$	12537.1	0.938497	0.469249	+	0.883066i	$0.344525\pi$
$564$	−4283.63	−0.319811
$565$	−8237.47	−0.613368
$566$	12761.2	0.947690
$567$	−567.000	−0.0419961
$568$	5250.45	0.387859
$569$	13049.0	0.961409	0.480704	−	0.876883i	$-0.340381\pi$
$569$	13049.0	0.961409	0.480704	+	0.876883i	$0.340381\pi$
$570$	4873.26	0.358102
$571$	−9955.63	−0.729650	−0.364825	−	0.931076i	$-0.618871\pi$
$571$	−9955.63	−0.729650	−0.364825	+	0.931076i	$0.618871\pi$
$572$	1737.06	0.126976
$573$	−11464.5	−0.835838
$574$	−3268.55	−0.237677
$575$	−2244.35	−0.162776
$576$	576.000	0.0416667
$577$	−8500.60	−0.613318	−0.306659	−	0.951819i	$-0.599211\pi$
$577$	−8500.60	−0.613318	−0.306659	+	0.951819i	$0.599211\pi$
$578$	5903.89	0.424860
$579$	625.133	0.0448699
$580$	−6396.85	−0.457956
$581$	−788.898	−0.0563322
$582$	−1154.99	−0.0822611
$583$	−21119.2	−1.50029
$584$	−2566.98	−0.181887
$585$	607.437	0.0429307
$586$	6650.49	0.468821
$587$	22019.4	1.54828	0.774139	−	0.633016i	$-0.218183\pi$
$587$	22019.4	1.54828	0.774139	+	0.633016i	$0.218183\pi$
$588$	−588.000	−0.0412393
$589$	−31504.1	−2.20391
$590$	8776.78	0.612431
$591$	−2214.44	−0.154128
$592$	−2335.91	−0.162171
$593$	−9389.33	−0.650209	−0.325104	−	0.945678i	$-0.605399\pi$
$593$	−9389.33	−0.650209	−0.325104	+	0.945678i	$0.605399\pi$
$594$	1819.36	0.125672
$595$	−3250.68	−0.223975
$596$	−7535.29	−0.517882
$597$	6220.11	0.426419
$598$	−592.909	−0.0405449
$599$	1547.64	0.105567	0.0527837	−	0.998606i	$-0.483191\pi$
$599$	1547.64	0.105567	0.0527837	+	0.998606i	$0.483191\pi$
$600$	2341.93	0.159348
$601$	8693.27	0.590027	0.295013	−	0.955493i	$-0.404676\pi$
$601$	8693.27	0.590027	0.295013	+	0.955493i	$0.404676\pi$
$602$	−1359.87	−0.0920669
$603$	−4095.65	−0.276596
$604$	7818.02	0.526674
$605$	1025.57	0.0689179
$606$	−9991.95	−0.669794
$607$	1284.83	0.0859136	0.0429568	−	0.999077i	$-0.486322\pi$
$607$	1284.83	0.0859136	0.0429568	+	0.999077i	$0.486322\pi$
$608$	4963.52	0.331081
$609$	6413.52	0.426747
$610$	−7159.85	−0.475236
$611$	−4601.09	−0.304648
$612$	−3192.64	−0.210874
$613$	−20992.3	−1.38315	−0.691576	−	0.722304i	$-0.743083\pi$
$613$	−20992.3	−1.38315	−0.691576	+	0.722304i	$0.743083\pi$
$614$	−12341.7	−0.811188
$615$	3667.56	0.240472
$616$	1886.75	0.123408
$617$	21147.6	1.37986	0.689928	−	0.723878i	$-0.257642\pi$
$617$	21147.6	1.37986	0.689928	+	0.723878i	$0.257642\pi$
$618$	−3528.20	−0.229652
$619$	−14118.8	−0.916770	−0.458385	−	0.888754i	$-0.651572\pi$
$619$	−14118.8	−0.916770	−0.458385	+	0.888754i	$0.651572\pi$
$620$	4254.18	0.275568
$621$	−621.000	−0.0401286
$622$	17336.4	1.11756
$623$	7272.78	0.467701
$624$	618.687	0.0396912
$625$	6094.55	0.390051
$626$	765.185	0.0488545
$627$	15677.8	0.998585
$628$	−5509.98	−0.350115
$629$	12947.4	0.820743
$630$	659.780	0.0417243
$631$	−20949.1	−1.32166	−0.660831	−	0.750535i	$-0.729796\pi$
$631$	−20949.1	−1.32166	−0.660831	+	0.750535i	$0.729796\pi$
$632$	7569.38	0.476414
$633$	−11157.7	−0.700599
$634$	17491.7	1.09571
$635$	186.085	0.0116292
$636$	−7522.00	−0.468973
$637$	−631.577	−0.0392841
$638$	−20579.4	−1.27703
$639$	5906.76	0.365677
$640$	−670.253	−0.0413970
$641$	2783.58	0.171521	0.0857605	−	0.996316i	$-0.472668\pi$
$641$	2783.58	0.171521	0.0857605	+	0.996316i	$0.472668\pi$
$642$	−10512.0	−0.646222
$643$	23315.5	1.42998	0.714989	−	0.699136i	$-0.246432\pi$
$643$	23315.5	1.42998	0.714989	+	0.699136i	$0.246432\pi$
$644$	−644.000	−0.0394055
$645$	1525.88	0.0931495
$646$	−27511.7	−1.67559
$647$	14753.3	0.896466	0.448233	−	0.893917i	$-0.352054\pi$
$647$	14753.3	0.896466	0.448233	+	0.893917i	$0.352054\pi$
$648$	648.000	0.0392837
$649$	28235.9	1.70779
$650$	2515.50	0.151794
$651$	−4265.27	−0.256788
$652$	−5676.72	−0.340977
$653$	−9203.94	−0.551574	−0.275787	−	0.961219i	$-0.588938\pi$
$653$	−9203.94	−0.551574	−0.275787	+	0.961219i	$0.588938\pi$
$654$	−3410.11	−0.203893
$655$	1547.20	0.0922963
$656$	3735.48	0.222326
$657$	−2887.85	−0.171485
$658$	−4997.57	−0.296087
$659$	6950.80	0.410872	0.205436	−	0.978671i	$-0.434139\pi$
$659$	6950.80	0.410872	0.205436	+	0.978671i	$0.434139\pi$
$660$	−2117.07	−0.124859
$661$	1595.26	0.0938708	0.0469354	−	0.998898i	$-0.485055\pi$
$661$	1595.26	0.0938708	0.0469354	+	0.998898i	$0.485055\pi$
$662$	−10621.4	−0.623586
$663$	−3429.25	−0.200876
$664$	901.598	0.0526940
$665$	5685.47	0.331538
$666$	−2627.89	−0.152896
$667$	7024.33	0.407771
$668$	−13048.2	−0.755766
$669$	813.905	0.0470364
$670$	4765.83	0.274806
$671$	−23034.1	−1.32522
$672$	672.000	0.0385758
$673$	5914.52	0.338764	0.169382	−	0.985551i	$-0.445823\pi$
$673$	5914.52	0.338764	0.169382	+	0.985551i	$0.445823\pi$
$674$	−8746.02	−0.499828
$675$	2634.68	0.150235
$676$	−8123.46	−0.462191
$677$	−257.909	−0.0146414	−0.00732072	−	0.999973i	$-0.502330\pi$
$677$	−257.909	−0.0146414	−0.00732072	+	0.999973i	$0.502330\pi$
$678$	−9438.79	−0.534653
$679$	−1347.49	−0.0761590
$680$	3715.07	0.209509
$681$	7965.95	0.448247
$682$	13686.2	0.768433
$683$	24462.1	1.37045	0.685224	−	0.728333i	$-0.259704\pi$
$683$	24462.1	1.37045	0.685224	+	0.728333i	$0.259704\pi$
$684$	5583.96	0.312146
$685$	−7630.54	−0.425617
$686$	−686.000	−0.0381802
$687$	1667.30	0.0925930
$688$	1554.14	0.0861207
$689$	−8079.46	−0.446739
$690$	722.617	0.0398689
$691$	24609.6	1.35484	0.677419	−	0.735598i	$-0.263099\pi$
$691$	24609.6	1.35484	0.677419	+	0.735598i	$0.263099\pi$
$692$	−9465.71	−0.519989
$693$	2122.59	0.116350
$694$	−11777.7	−0.644200
$695$	−14803.8	−0.807972
$696$	−7329.74	−0.399185
$697$	−20705.0	−1.12519
$698$	−19097.7	−1.03561
$699$	10473.8	0.566745
$700$	2732.26	0.147528
$701$	3204.35	0.172649	0.0863243	−	0.996267i	$-0.472488\pi$
$701$	3204.35	0.172649	0.0863243	+	0.996267i	$0.472488\pi$
$702$	696.023	0.0374212
$703$	−22645.1	−1.21490
$704$	−2156.28	−0.115437
$705$	5607.65	0.299569
$706$	−15003.6	−0.799815
$707$	−11657.3	−0.620109
$708$	10056.8	0.533836
$709$	−11656.4	−0.617442	−0.308721	−	0.951153i	$-0.599901\pi$
$709$	−11656.4	−0.617442	−0.308721	+	0.951153i	$0.599901\pi$
$710$	−6873.30	−0.363310
$711$	8515.55	0.449168
$712$	−8311.75	−0.437494
$713$	−4671.49	−0.245370
$714$	−3724.75	−0.195231
$715$	−2273.97	−0.118939
$716$	12098.4	0.631480
$717$	−18329.9	−0.954730
$718$	−25072.4	−1.30320
$719$	15953.8	0.827503	0.413752	−	0.910390i	$-0.364218\pi$
$719$	15953.8	0.827503	0.413752	+	0.910390i	$0.364218\pi$
$720$	−754.035	−0.0390295
$721$	−4116.24	−0.212617
$722$	34400.2	1.77319
$723$	1763.55	0.0907153
$724$	3466.13	0.177925
$725$	−29801.7	−1.52663
$726$	1175.13	0.0600735
$727$	19679.0	1.00393	0.501963	−	0.864889i	$-0.332611\pi$
$727$	19679.0	1.00393	0.501963	+	0.864889i	$0.332611\pi$
$728$	721.802	0.0367469
$729$	729.000	0.0370370
$730$	3360.40	0.170375
$731$	−8614.26	−0.435855
$732$	−8204.02	−0.414247
$733$	−10809.4	−0.544687	−0.272343	−	0.962200i	$-0.587799\pi$
$733$	−10809.4	−0.544687	−0.272343	+	0.962200i	$0.587799\pi$
$734$	−18494.8	−0.930048
$735$	769.744	0.0386292
$736$	736.000	0.0368605
$737$	15332.2	0.766310
$738$	4202.42	0.209611
$739$	19172.0	0.954333	0.477166	−	0.878813i	$-0.341664\pi$
$739$	19172.0	0.954333	0.477166	+	0.878813i	$0.341664\pi$
$740$	3057.91	0.151907
$741$	5997.78	0.297347
$742$	−8775.67	−0.434185
$743$	22222.5	1.09726	0.548629	−	0.836066i	$-0.315150\pi$
$743$	22222.5	1.09726	0.548629	+	0.836066i	$0.315150\pi$
$744$	4874.60	0.240203
$745$	9864.36	0.485103
$746$	9902.18	0.485985
$747$	1014.30	0.0496804
$748$	11951.8	0.584226
$749$	−12264.0	−0.598285
$750$	−6993.06	−0.340467
$751$	−5724.98	−0.278173	−0.139086	−	0.990280i	$-0.544417\pi$
$751$	−5724.98	−0.278173	−0.139086	+	0.990280i	$0.544417\pi$
$752$	5711.51	0.276964
$753$	−9193.94	−0.444948
$754$	−7872.95	−0.380260
$755$	−10234.5	−0.493339
$756$	756.000	0.0363696
$757$	21424.4	1.02864	0.514322	−	0.857597i	$-0.328044\pi$
$757$	21424.4	1.02864	0.514322	+	0.857597i	$0.328044\pi$
$758$	−13918.1	−0.666923
$759$	2324.74	0.111176
$760$	−6497.68	−0.310126
$761$	1436.74	0.0684385	0.0342193	−	0.999414i	$-0.489106\pi$
$761$	1436.74	0.0684385	0.0342193	+	0.999414i	$0.489106\pi$
$762$	213.222	0.0101368
$763$	−3978.47	−0.188768
$764$	15286.0	0.723857
$765$	4179.45	0.197527
$766$	22408.3	1.05698
$767$	10802.1	0.508526
$768$	−768.000	−0.0360844
$769$	12372.0	0.580163	0.290082	−	0.957002i	$-0.406318\pi$
$769$	12372.0	0.580163	0.290082	+	0.957002i	$0.406318\pi$
$770$	−2469.92	−0.115597
$771$	21007.8	0.981295
$772$	−833.511	−0.0388585
$773$	−31371.5	−1.45971	−0.729853	−	0.683604i	$-0.760412\pi$
$773$	−31371.5	−1.45971	−0.729853	+	0.683604i	$0.760412\pi$
$774$	1748.41	0.0811953
$775$	19819.4	0.918625
$776$	1539.99	0.0712402
$777$	−3065.88	−0.141554
$778$	10017.9	0.461643
$779$	36213.2	1.66556
$780$	−809.916	−0.0371790
$781$	−22112.2	−1.01311
$782$	−4079.49	−0.186550
$783$	−8245.95	−0.376356
$784$	784.000	0.0357143
$785$	7213.05	0.327955
$786$	1772.84	0.0804517
$787$	−23069.4	−1.04490	−0.522450	−	0.852670i	$-0.674982\pi$
$787$	−23069.4	−1.04490	−0.522450	+	0.852670i	$0.674982\pi$
$788$	2952.58	0.133479
$789$	1629.18	0.0735113
$790$	−9908.99	−0.446261
$791$	−11011.9	−0.494992
$792$	−2425.82	−0.108835
$793$	−8812.02	−0.394608
$794$	−9794.02	−0.437754
$795$	9846.97	0.439290
$796$	−8293.48	−0.369290
$797$	−3071.10	−0.136492	−0.0682459	−	0.997669i	$-0.521740\pi$
$797$	−3071.10	−0.136492	−0.0682459	+	0.997669i	$0.521740\pi$
$798$	6514.62	0.288991
$799$	−31657.6	−1.40171
$800$	−3122.58	−0.138000
$801$	−9350.72	−0.412474
$802$	22535.8	0.992227
$803$	10810.8	0.475099
$804$	5460.86	0.239540
$805$	843.053	0.0369114
$806$	5235.85	0.228815
$807$	−1664.51	−0.0726067
$808$	13322.6	0.580058
$809$	38358.2	1.66700	0.833500	−	0.552519i	$-0.186333\pi$
$809$	38358.2	1.66700	0.833500	+	0.552519i	$0.186333\pi$
$810$	−848.289	−0.0367973
$811$	−23024.4	−0.996912	−0.498456	−	0.866915i	$-0.666099\pi$
$811$	−23024.4	−0.996912	−0.498456	+	0.866915i	$0.666099\pi$
$812$	−8551.36	−0.369574
$813$	13745.4	0.592954
$814$	9837.64	0.423598
$815$	7431.32	0.319396
$816$	4256.86	0.182622
$817$	15066.4	0.645173
$818$	−5576.55	−0.238361
$819$	812.027	0.0346453
$820$	−4890.08	−0.208255
$821$	−1831.49	−0.0778557	−0.0389279	−	0.999242i	$-0.512394\pi$
$821$	−1831.49	−0.0778557	−0.0389279	+	0.999242i	$0.512394\pi$
$822$	−8743.34	−0.370997
$823$	33459.6	1.41717	0.708584	−	0.705626i	$-0.249334\pi$
$823$	33459.6	1.41717	0.708584	+	0.705626i	$0.249334\pi$
$824$	4704.27	0.198885
$825$	−9863.03	−0.416226
$826$	11732.9	0.494236
$827$	−40404.5	−1.69892	−0.849458	−	0.527656i	$-0.823071\pi$
$827$	−40404.5	−1.69892	−0.849458	+	0.527656i	$0.823071\pi$
$828$	828.000	0.0347524
$829$	26671.0	1.11740	0.558699	−	0.829370i	$-0.311301\pi$
$829$	26671.0	1.11740	0.558699	+	0.829370i	$0.311301\pi$
$830$	−1180.27	−0.0493588
$831$	23872.3	0.996536
$832$	−824.917	−0.0343736
$833$	−4345.54	−0.180749
$834$	−16962.7	−0.704283
$835$	17081.3	0.707931
$836$	−20903.8	−0.864800
$837$	5483.92	0.226466
$838$	12216.4	0.503590
$839$	20011.1	0.823431	0.411716	−	0.911312i	$-0.364930\pi$
$839$	20011.1	0.823431	0.411716	+	0.911312i	$0.364930\pi$
$840$	−879.707	−0.0361343
$841$	68883.7	2.82437
$842$	−7921.16	−0.324206
$843$	−6606.21	−0.269905
$844$	14876.9	0.606736
$845$	10634.3	0.432937
$846$	6425.44	0.261125
$847$	1370.99	0.0556172
$848$	10029.3	0.406143
$849$	−19141.8	−0.773786
$850$	17307.8	0.698414
$851$	−3357.86	−0.135260
$852$	−7875.68	−0.316686
$853$	11081.1	0.444795	0.222397	−	0.974956i	$-0.428612\pi$
$853$	11081.1	0.444795	0.222397	+	0.974956i	$0.428612\pi$
$854$	−9571.35	−0.383519
$855$	−7309.89	−0.292389
$856$	14016.0	0.559645
$857$	−14389.2	−0.573542	−0.286771	−	0.957999i	$-0.592582\pi$
$857$	−14389.2	−0.573542	−0.286771	+	0.957999i	$0.592582\pi$
$858$	−2605.59	−0.103675
$859$	32504.2	1.29107	0.645535	−	0.763730i	$-0.276634\pi$
$859$	32504.2	1.29107	0.645535	+	0.763730i	$0.276634\pi$
$860$	−2034.51	−0.0806698
$861$	4902.82	0.194062
$862$	−25268.0	−0.998412
$863$	−12259.4	−0.483564	−0.241782	−	0.970331i	$-0.577732\pi$
$863$	−12259.4	−0.483564	−0.241782	+	0.970331i	$0.577732\pi$
$864$	−864.000	−0.0340207
$865$	12391.5	0.487077
$866$	18820.9	0.738521
$867$	−8855.83	−0.346897
$868$	5687.03	0.222385
$869$	−31878.4	−1.24442
$870$	9595.27	0.373920
$871$	5865.57	0.228183
$872$	4546.82	0.176577
$873$	1732.49	0.0671659
$874$	7135.05	0.276141
$875$	−8158.57	−0.315212
$876$	3850.46	0.148510
$877$	12891.0	0.496350	0.248175	−	0.968715i	$-0.420169\pi$
$877$	12891.0	0.496350	0.248175	+	0.968715i	$0.420169\pi$
$878$	8615.31	0.331153
$879$	−9975.73	−0.382791
$880$	2822.76	0.108131
$881$	−20914.4	−0.799800	−0.399900	−	0.916559i	$-0.630955\pi$
$881$	−20914.4	−0.799800	−0.399900	+	0.916559i	$0.630955\pi$
$882$	882.000	0.0336718
$883$	−46394.4	−1.76817	−0.884086	−	0.467324i	$-0.845218\pi$
$883$	−46394.4	−1.76817	−0.884086	+	0.467324i	$0.845218\pi$
$884$	4572.33	0.173964
$885$	−13165.2	−0.500048
$886$	28731.8	1.08946
$887$	40841.6	1.54603	0.773014	−	0.634389i	$-0.218748\pi$
$887$	40841.6	1.54603	0.773014	+	0.634389i	$0.218748\pi$
$888$	3503.86	0.132412
$889$	248.759	0.00938484
$890$	10880.8	0.409804
$891$	−2729.04	−0.102611
$892$	−1085.21	−0.0407347
$893$	55369.4	2.07488
$894$	11302.9	0.422849
$895$	−15837.9	−0.591511
$896$	−896.000	−0.0334077
$897$	889.363	0.0331048
$898$	−13318.1	−0.494912
$899$	−62030.4	−2.30126
$900$	−3512.90	−0.130107
$901$	−55590.4	−2.05548
$902$	−15731.9	−0.580728
$903$	2039.81	0.0751723
$904$	12585.0	0.463023
$905$	−4537.47	−0.166663
$906$	−11727.0	−0.430027
$907$	46261.3	1.69359	0.846793	−	0.531923i	$-0.178530\pi$
$907$	46261.3	1.69359	0.846793	+	0.531923i	$0.178530\pi$
$908$	−10621.3	−0.388193
$909$	14987.9	0.546884
$910$	−944.902	−0.0344211
$911$	23092.6	0.839838	0.419919	−	0.907562i	$-0.362059\pi$
$911$	23092.6	0.839838	0.419919	+	0.907562i	$0.362059\pi$
$912$	−7445.27	−0.270326
$913$	−3797.07	−0.137639
$914$	14543.6	0.526324
$915$	10739.8	0.388029
$916$	−2223.06	−0.0801879
$917$	2068.31	0.0744838
$918$	4788.96	0.172178
$919$	39879.2	1.43144	0.715721	−	0.698387i	$-0.246098\pi$
$919$	39879.2	1.43144	0.715721	+	0.698387i	$0.246098\pi$
$920$	−963.489	−0.0345275
$921$	18512.5	0.662332
$922$	−37414.0	−1.33640
$923$	−8459.34	−0.301671
$924$	−2830.12	−0.100762
$925$	14246.2	0.506391
$926$	17170.5	0.609350
$927$	5292.30	0.187510
$928$	9772.98	0.345705
$929$	26630.8	0.940505	0.470252	−	0.882532i	$-0.344163\pi$
$929$	26630.8	0.940505	0.470252	+	0.882532i	$0.344163\pi$
$930$	−6381.27	−0.225000
$931$	7600.38	0.267554
$932$	−13965.0	−0.490816
$933$	−26004.6	−0.912488
$934$	−8728.12	−0.305774
$935$	−15646.0	−0.547249
$936$	−928.031	−0.0324077
$937$	−19835.9	−0.691582	−0.345791	−	0.938312i	$-0.612389\pi$
$937$	−19835.9	−0.691582	−0.345791	+	0.938312i	$0.612389\pi$
$938$	6371.01	0.221771
$939$	−1147.78	−0.0398896
$940$	−7476.86	−0.259435
$941$	15901.4	0.550874	0.275437	−	0.961319i	$-0.411178\pi$
$941$	15901.4	0.550874	0.275437	+	0.961319i	$0.411178\pi$
$942$	8264.97	0.285868
$943$	5369.76	0.185433
$944$	−13409.0	−0.462315
$945$	−989.671	−0.0340677
$946$	−6545.24	−0.224951
$947$	57637.2	1.97778	0.988891	−	0.148645i	$-0.0474911\pi$
$947$	57637.2	1.97778	0.988891	+	0.148645i	$0.0474911\pi$
$948$	−11354.1	−0.388991
$949$	4135.82	0.141469
$950$	−30271.4	−1.03383
$951$	−26237.5	−0.894647
$952$	4966.33	0.169075
$953$	8153.29	0.277136	0.138568	−	0.990353i	$-0.455750\pi$
$953$	8153.29	0.277136	0.138568	+	0.990353i	$0.455750\pi$
$954$	11283.0	0.382915
$955$	−20010.7	−0.678042
$956$	24439.8	0.826820
$957$	30869.1	1.04269
$958$	6049.06	0.204005
$959$	−10200.6	−0.343476
$960$	1005.38	0.0338005
$961$	11461.9	0.384744
$962$	3763.53	0.126134
$963$	15768.0	0.527638
$964$	−2351.40	−0.0785618
$965$	1091.14	0.0363990
$966$	966.000	0.0321745
$967$	−40176.4	−1.33608	−0.668039	−	0.744127i	$-0.732866\pi$
$967$	−40176.4	−1.33608	−0.668039	+	0.744127i	$0.732866\pi$
$968$	−1566.85	−0.0520252
$969$	41267.5	1.36812
$970$	−2015.98	−0.0667312
$971$	28826.8	0.952725	0.476363	−	0.879249i	$-0.341955\pi$
$971$	28826.8	0.952725	0.476363	+	0.879249i	$0.341955\pi$
$972$	−972.000	−0.0320750
$973$	−19789.9	−0.652039
$974$	34242.4	1.12649
$975$	−3773.24	−0.123939
$976$	10938.7	0.358749
$977$	23194.2	0.759516	0.379758	−	0.925086i	$-0.376007\pi$
$977$	23194.2	0.759516	0.379758	+	0.925086i	$0.376007\pi$
$978$	8515.07	0.278407
$979$	35004.8	1.14276
$980$	−1026.32	−0.0334538
$981$	5115.17	0.166478
$982$	−4501.91	−0.146295
$983$	59263.5	1.92290	0.961450	−	0.274978i	$-0.0886707\pi$
$983$	59263.5	1.92290	0.961450	+	0.274978i	$0.0886707\pi$
$984$	−5603.23	−0.181529
$985$	−3865.19	−0.125031
$986$	−54169.5	−1.74960
$987$	7496.35	0.241754
$988$	−7997.04	−0.257510
$989$	2234.08	0.0718296
$990$	3175.61	0.101947
$991$	29918.3	0.959017	0.479508	−	0.877537i	$-0.340815\pi$
$991$	29918.3	0.959017	0.479508	+	0.877537i	$0.340815\pi$
$992$	−6499.46	−0.208022
$993$	15932.1	0.509156
$994$	−9188.29	−0.293194
$995$	10856.9	0.345916
$996$	−1352.40	−0.0430244
$997$	4456.70	0.141570	0.0707848	−	0.997492i	$-0.477450\pi$
$997$	4456.70	0.141570	0.0707848	+	0.997492i	$0.477450\pi$
$998$	22531.7	0.714659
$999$	3941.84	0.124839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.p.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.p.1.3	✓	5	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.23635 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -5.23635 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -10.4727 q^{10} -33.6919 q^{11} -12.0000 q^{12} -12.8893 q^{13} -14.0000 q^{14} +15.7091 q^{15} +16.0000 q^{16} -88.6845 q^{17} +18.0000 q^{18} +155.110 q^{19} -20.9454 q^{20} +21.0000 q^{21} -67.3838 q^{22} +23.0000 q^{23} -24.0000 q^{24} -97.5806 q^{25} -25.7786 q^{26} -27.0000 q^{27} -28.0000 q^{28} +305.406 q^{29} +31.4181 q^{30} -203.108 q^{31} +32.0000 q^{32} +101.076 q^{33} -177.369 q^{34} +36.6545 q^{35} +36.0000 q^{36} -145.994 q^{37} +310.220 q^{38} +38.6680 q^{39} -41.8908 q^{40} +233.468 q^{41} +42.0000 q^{42} +97.1337 q^{43} -134.768 q^{44} -47.1272 q^{45} +46.0000 q^{46} +356.969 q^{47} -48.0000 q^{48} +49.0000 q^{49} -195.161 q^{50} +266.054 q^{51} -51.5573 q^{52} +626.834 q^{53} -54.0000 q^{54} +176.423 q^{55} -56.0000 q^{56} -465.330 q^{57} +610.811 q^{58} -838.063 q^{59} +62.8362 q^{60} +683.668 q^{61} -406.216 q^{62} -63.0000 q^{63} +64.0000 q^{64} +67.4930 q^{65} +202.151 q^{66} -455.072 q^{67} -354.738 q^{68} -69.0000 q^{69} +73.3089 q^{70} +656.306 q^{71} +72.0000 q^{72} -320.872 q^{73} -291.988 q^{74} +292.742 q^{75} +620.440 q^{76} +235.843 q^{77} +77.3359 q^{78} +946.173 q^{79} -83.7816 q^{80} +81.0000 q^{81} +466.935 q^{82} +112.700 q^{83} +84.0000 q^{84} +464.383 q^{85} +194.267 q^{86} -916.217 q^{87} -269.535 q^{88} -1038.97 q^{89} -94.2543 q^{90} +90.2252 q^{91} +92.0000 q^{92} +609.324 q^{93} +713.938 q^{94} -812.210 q^{95} -96.0000 q^{96} +192.499 q^{97} +98.0000 q^{98} -303.227 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} - 15 q^{3} + 20 q^{4} - 10 q^{5} - 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 9 q^{11} - 60 q^{12} - 102 q^{13} - 70 q^{14} + 30 q^{15} + 80 q^{16} - 30 q^{17} + 90 q^{18} - 27 q^{19} - 40 q^{20} + 105 q^{21} + 18 q^{22} + 115 q^{23} - 120 q^{24} + 307 q^{25} - 204 q^{26} - 135 q^{27} - 140 q^{28} + 135 q^{29} + 60 q^{30} + 160 q^{31} + 160 q^{32} - 27 q^{33} - 60 q^{34} + 70 q^{35} + 180 q^{36} + 153 q^{37} - 54 q^{38} + 306 q^{39} - 80 q^{40} + 76 q^{41} + 210 q^{42} + 980 q^{43} + 36 q^{44} - 90 q^{45} + 230 q^{46} - 8 q^{47} - 240 q^{48} + 245 q^{49} + 614 q^{50} + 90 q^{51} - 408 q^{52} + 676 q^{53} - 270 q^{54} + 1403 q^{55} - 280 q^{56} + 81 q^{57} + 270 q^{58} - 208 q^{59} + 120 q^{60} + 204 q^{61} + 320 q^{62} - 315 q^{63} + 320 q^{64} + 971 q^{65} - 54 q^{66} + 767 q^{67} - 120 q^{68} - 345 q^{69} + 140 q^{70} + 1353 q^{71} + 360 q^{72} + 92 q^{73} + 306 q^{74} - 921 q^{75} - 108 q^{76} - 63 q^{77} + 612 q^{78} + 2958 q^{79} - 160 q^{80} + 405 q^{81} + 152 q^{82} + 1370 q^{83} + 420 q^{84} + 1725 q^{85} + 1960 q^{86} - 405 q^{87} + 72 q^{88} + 1207 q^{89} - 180 q^{90} + 714 q^{91} + 460 q^{92} - 480 q^{93} - 16 q^{94} + 2995 q^{95} - 480 q^{96} + 1633 q^{97} + 490 q^{98} + 81 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 - 15 * q^3 + 20 * q^4 - 10 * q^5 - 30 * q^6 - 35 * q^7 + 40 * q^8 + 45 * q^9 - 20 * q^10 + 9 * q^11 - 60 * q^12 - 102 * q^13 - 70 * q^14 + 30 * q^15 + 80 * q^16 - 30 * q^17 + 90 * q^18 - 27 * q^19 - 40 * q^20 + 105 * q^21 + 18 * q^22 + 115 * q^23 - 120 * q^24 + 307 * q^25 - 204 * q^26 - 135 * q^27 - 140 * q^28 + 135 * q^29 + 60 * q^30 + 160 * q^31 + 160 * q^32 - 27 * q^33 - 60 * q^34 + 70 * q^35 + 180 * q^36 + 153 * q^37 - 54 * q^38 + 306 * q^39 - 80 * q^40 + 76 * q^41 + 210 * q^42 + 980 * q^43 + 36 * q^44 - 90 * q^45 + 230 * q^46 - 8 * q^47 - 240 * q^48 + 245 * q^49 + 614 * q^50 + 90 * q^51 - 408 * q^52 + 676 * q^53 - 270 * q^54 + 1403 * q^55 - 280 * q^56 + 81 * q^57 + 270 * q^58 - 208 * q^59 + 120 * q^60 + 204 * q^61 + 320 * q^62 - 315 * q^63 + 320 * q^64 + 971 * q^65 - 54 * q^66 + 767 * q^67 - 120 * q^68 - 345 * q^69 + 140 * q^70 + 1353 * q^71 + 360 * q^72 + 92 * q^73 + 306 * q^74 - 921 * q^75 - 108 * q^76 - 63 * q^77 + 612 * q^78 + 2958 * q^79 - 160 * q^80 + 405 * q^81 + 152 * q^82 + 1370 * q^83 + 420 * q^84 + 1725 * q^85 + 1960 * q^86 - 405 * q^87 + 72 * q^88 + 1207 * q^89 - 180 * q^90 + 714 * q^91 + 460 * q^92 - 480 * q^93 - 16 * q^94 + 2995 * q^95 - 480 * q^96 + 1633 * q^97 + 490 * q^98 + 81 * q^99

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