LMFDB - Embedded newform 966.4.a.m.1.5

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} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 $ x^5 - x^4 - 351x^3 - 663x^2 + 18451*x - 19243
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.11377$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -43.3153 q^{10} -7.67965 q^{11} -12.0000 q^{12} +63.7565 q^{13} +14.0000 q^{14} -64.9729 q^{15} +16.0000 q^{16} +9.23862 q^{17} -18.0000 q^{18} -145.686 q^{19} +86.6306 q^{20} +21.0000 q^{21} +15.3593 q^{22} -23.0000 q^{23} +24.0000 q^{24} +344.054 q^{25} -127.513 q^{26} -27.0000 q^{27} -28.0000 q^{28} +223.788 q^{29} +129.946 q^{30} +165.935 q^{31} -32.0000 q^{32} +23.0389 q^{33} -18.4772 q^{34} -151.604 q^{35} +36.0000 q^{36} +292.555 q^{37} +291.371 q^{38} -191.269 q^{39} -173.261 q^{40} -335.500 q^{41} -42.0000 q^{42} +121.574 q^{43} -30.7186 q^{44} +194.919 q^{45} +46.0000 q^{46} +140.326 q^{47} -48.0000 q^{48} +49.0000 q^{49} -688.107 q^{50} -27.7159 q^{51} +255.026 q^{52} -91.7378 q^{53} +54.0000 q^{54} -166.323 q^{55} +56.0000 q^{56} +437.057 q^{57} -447.576 q^{58} +10.3736 q^{59} -259.892 q^{60} +10.9004 q^{61} -331.869 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1380.81 q^{65} -46.0779 q^{66} -444.657 q^{67} +36.9545 q^{68} +69.0000 q^{69} +303.207 q^{70} -345.504 q^{71} -72.0000 q^{72} +283.982 q^{73} -585.110 q^{74} -1032.16 q^{75} -582.743 q^{76} +53.7575 q^{77} +382.539 q^{78} -308.066 q^{79} +346.522 q^{80} +81.0000 q^{81} +671.001 q^{82} -139.248 q^{83} +84.0000 q^{84} +200.087 q^{85} -243.148 q^{86} -671.364 q^{87} +61.4372 q^{88} +888.786 q^{89} -389.838 q^{90} -446.295 q^{91} -92.0000 q^{92} -497.804 q^{93} -280.651 q^{94} -3155.21 q^{95} +96.0000 q^{96} -778.098 q^{97} -98.0000 q^{98} -69.1168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * 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
$5$	21.6576	1.93712	0.968559	−	0.248783i	$-0.0800304\pi$
$5$	21.6576	1.93712	0.968559	+	0.248783i	$0.0800304\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−43.3153	−1.36975
$11$	−7.67965	−0.210500	−0.105250	−	0.994446i	$-0.533564\pi$
$11$	−7.67965	−0.210500	−0.105250	+	0.994446i	$0.533564\pi$
$12$	−12.0000	−0.288675
$13$	63.7565	1.36022	0.680110	−	0.733110i	$-0.261932\pi$
$13$	63.7565	1.36022	0.680110	+	0.733110i	$0.261932\pi$
$14$	14.0000	0.267261
$15$	−64.9729	−1.11840
$16$	16.0000	0.250000
$17$	9.23862	0.131806	0.0659028	−	0.997826i	$-0.479007\pi$
$17$	9.23862	0.131806	0.0659028	+	0.997826i	$0.479007\pi$
$18$	−18.0000	−0.235702
$19$	−145.686	−1.75908	−0.879542	−	0.475821i	$-0.842151\pi$
$19$	−145.686	−1.75908	−0.879542	+	0.475821i	$0.842151\pi$
$20$	86.6306	0.968559
$21$	21.0000	0.218218
$22$	15.3593	0.148846
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	344.054	2.75243
$26$	−127.513	−0.961821
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	223.788	1.43298	0.716489	−	0.697598i	$-0.245748\pi$
$29$	223.788	1.43298	0.716489	+	0.697598i	$0.245748\pi$
$30$	129.946	0.790825
$31$	165.935	0.961378	0.480689	−	0.876891i	$-0.340387\pi$
$31$	165.935	0.961378	0.480689	+	0.876891i	$0.340387\pi$
$32$	−32.0000	−0.176777
$33$	23.0389	0.121532
$34$	−18.4772	−0.0932006
$35$	−151.604	−0.732162
$36$	36.0000	0.166667
$37$	292.555	1.29988	0.649942	−	0.759984i	$-0.274793\pi$
$37$	292.555	1.29988	0.649942	+	0.759984i	$0.274793\pi$
$38$	291.371	1.24386
$39$	−191.269	−0.785323
$40$	−173.261	−0.684875
$41$	−335.500	−1.27796	−0.638980	−	0.769223i	$-0.720643\pi$
$41$	−335.500	−1.27796	−0.638980	+	0.769223i	$0.720643\pi$
$42$	−42.0000	−0.154303
$43$	121.574	0.431159	0.215580	−	0.976486i	$-0.430836\pi$
$43$	121.574	0.431159	0.215580	+	0.976486i	$0.430836\pi$
$44$	−30.7186	−0.105250
$45$	194.919	0.645706
$46$	46.0000	0.147442
$47$	140.326	0.435502	0.217751	−	0.976004i	$-0.430128\pi$
$47$	140.326	0.435502	0.217751	+	0.976004i	$0.430128\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−688.107	−1.94626
$51$	−27.7159	−0.0760980
$52$	255.026	0.680110
$53$	−91.7378	−0.237758	−0.118879	−	0.992909i	$-0.537930\pi$
$53$	−91.7378	−0.237758	−0.118879	+	0.992909i	$0.537930\pi$
$54$	54.0000	0.136083
$55$	−166.323	−0.407764
$56$	56.0000	0.133631
$57$	437.057	1.01561
$58$	−447.576	−1.01327
$59$	10.3736	0.0228902	0.0114451	−	0.999935i	$-0.496357\pi$
$59$	10.3736	0.0228902	0.0114451	+	0.999935i	$0.496357\pi$
$60$	−259.892	−0.559198
$61$	10.9004	0.0228795	0.0114398	−	0.999935i	$-0.496359\pi$
$61$	10.9004	0.0228795	0.0114398	+	0.999935i	$0.496359\pi$
$62$	−331.869	−0.679797
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	1380.81	2.63491
$66$	−46.0779	−0.0859363
$67$	−444.657	−0.810799	−0.405399	−	0.914140i	$-0.632868\pi$
$67$	−444.657	−0.810799	−0.405399	+	0.914140i	$0.632868\pi$
$68$	36.9545	0.0659028
$69$	69.0000	0.120386
$70$	303.207	0.517717
$71$	−345.504	−0.577519	−0.288759	−	0.957402i	$-0.593243\pi$
$71$	−345.504	−0.577519	−0.288759	+	0.957402i	$0.593243\pi$
$72$	−72.0000	−0.117851
$73$	283.982	0.455309	0.227655	−	0.973742i	$-0.426894\pi$
$73$	283.982	0.455309	0.227655	+	0.973742i	$0.426894\pi$
$74$	−585.110	−0.919157
$75$	−1032.16	−1.58912
$76$	−582.743	−0.879542
$77$	53.7575	0.0795616
$78$	382.539	0.555308
$79$	−308.066	−0.438736	−0.219368	−	0.975642i	$-0.570400\pi$
$79$	−308.066	−0.438736	−0.219368	+	0.975642i	$0.570400\pi$
$80$	346.522	0.484280
$81$	81.0000	0.111111
$82$	671.001	0.903654
$83$	−139.248	−0.184150	−0.0920750	−	0.995752i	$-0.529350\pi$
$83$	−139.248	−0.184150	−0.0920750	+	0.995752i	$0.529350\pi$
$84$	84.0000	0.109109
$85$	200.087	0.255323
$86$	−243.148	−0.304876
$87$	−671.364	−0.827331
$88$	61.4372	0.0744230
$89$	888.786	1.05855	0.529276	−	0.848450i	$-0.322464\pi$
$89$	888.786	1.05855	0.529276	+	0.848450i	$0.322464\pi$
$90$	−389.838	−0.456583
$91$	−446.295	−0.514115
$92$	−92.0000	−0.104257
$93$	−497.804	−0.555052
$94$	−280.651	−0.307947
$95$	−3155.21	−3.40755
$96$	96.0000	0.102062
$97$	−778.098	−0.814473	−0.407237	−	0.913323i	$-0.633508\pi$
$97$	−778.098	−0.814473	−0.407237	+	0.913323i	$0.633508\pi$
$98$	−98.0000	−0.101015
$99$	−69.1168	−0.0701667
$100$	1376.21	1.37621
$101$	1405.96	1.38514	0.692568	−	0.721353i	$-0.256479\pi$
$101$	1405.96	1.38514	0.692568	+	0.721353i	$0.256479\pi$
$102$	55.4317	0.0538094
$103$	809.058	0.773969	0.386984	−	0.922086i	$-0.373517\pi$
$103$	809.058	0.773969	0.386984	+	0.922086i	$0.373517\pi$
$104$	−510.052	−0.480910
$105$	454.811	0.422714
$106$	183.476	0.168120
$107$	380.224	0.343529	0.171765	−	0.985138i	$-0.445053\pi$
$107$	380.224	0.343529	0.171765	+	0.985138i	$0.445053\pi$
$108$	−108.000	−0.0962250
$109$	−1836.52	−1.61382	−0.806912	−	0.590671i	$-0.798863\pi$
$109$	−1836.52	−1.61382	−0.806912	+	0.590671i	$0.798863\pi$
$110$	332.646	0.288332
$111$	−877.664	−0.750488
$112$	−112.000	−0.0944911
$113$	−1682.63	−1.40078	−0.700392	−	0.713759i	$-0.746991\pi$
$113$	−1682.63	−1.40078	−0.700392	+	0.713759i	$0.746991\pi$
$114$	−874.114	−0.718143
$115$	−498.126	−0.403917
$116$	895.152	0.716489
$117$	573.808	0.453407
$118$	−20.7471	−0.0161858
$119$	−64.6703	−0.0498178
$120$	519.784	0.395413
$121$	−1272.02	−0.955690
$122$	−21.8007	−0.0161783
$123$	1006.50	0.737831
$124$	663.738	0.480689
$125$	4744.19	3.39466
$126$	126.000	0.0890871
$127$	2608.82	1.82280	0.911400	−	0.411521i	$-0.135002\pi$
$127$	2608.82	1.82280	0.911400	+	0.411521i	$0.135002\pi$
$128$	−128.000	−0.0883883
$129$	−364.722	−0.248930
$130$	−2761.63	−1.86316
$131$	2139.80	1.42714	0.713569	−	0.700585i	$-0.247077\pi$
$131$	2139.80	1.42714	0.713569	+	0.700585i	$0.247077\pi$
$132$	92.1558	0.0607661
$133$	1019.80	0.664871
$134$	889.314	0.573321
$135$	−584.756	−0.372799
$136$	−73.9090	−0.0466003
$137$	−1087.17	−0.677983	−0.338991	−	0.940790i	$-0.610086\pi$
$137$	−1087.17	−0.677983	−0.338991	+	0.940790i	$0.610086\pi$
$138$	−138.000	−0.0851257
$139$	1485.73	0.906603	0.453301	−	0.891357i	$-0.350246\pi$
$139$	1485.73	0.906603	0.453301	+	0.891357i	$0.350246\pi$
$140$	−606.414	−0.366081
$141$	−420.977	−0.251437
$142$	691.009	0.408367
$143$	−489.627	−0.286326
$144$	144.000	0.0833333
$145$	4846.72	2.77585
$146$	−567.964	−0.321952
$147$	−147.000	−0.0824786
$148$	1170.22	0.649942
$149$	1551.38	0.852980	0.426490	−	0.904492i	$-0.359750\pi$
$149$	1551.38	0.852980	0.426490	+	0.904492i	$0.359750\pi$
$150$	2064.32	1.12367
$151$	2830.68	1.52555	0.762774	−	0.646665i	$-0.223837\pi$
$151$	2830.68	1.52555	0.762774	+	0.646665i	$0.223837\pi$
$152$	1165.49	0.621930
$153$	83.1476	0.0439352
$154$	−107.515	−0.0562585
$155$	3593.75	1.86230
$156$	−765.078	−0.392662
$157$	−2463.32	−1.25219	−0.626096	−	0.779746i	$-0.715348\pi$
$157$	−2463.32	−1.25219	−0.626096	+	0.779746i	$0.715348\pi$
$158$	616.132	0.310233
$159$	275.213	0.137269
$160$	−693.045	−0.342437
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	1464.76	0.703858	0.351929	−	0.936027i	$-0.385526\pi$
$163$	1464.76	0.703858	0.351929	+	0.936027i	$0.385526\pi$
$164$	−1342.00	−0.638980
$165$	498.969	0.235422
$166$	278.496	0.130214
$167$	2390.35	1.10761	0.553805	−	0.832646i	$-0.313175\pi$
$167$	2390.35	1.10761	0.553805	+	0.832646i	$0.313175\pi$
$168$	−168.000	−0.0771517
$169$	1867.89	0.850199
$170$	−400.173	−0.180541
$171$	−1311.17	−0.586361
$172$	486.296	0.215580
$173$	2785.56	1.22418	0.612088	−	0.790790i	$-0.290330\pi$
$173$	2785.56	1.22418	0.612088	+	0.790790i	$0.290330\pi$
$174$	1342.73	0.585011
$175$	−2408.38	−1.04032
$176$	−122.874	−0.0526250
$177$	−31.1207	−0.0132157
$178$	−1777.57	−0.748509
$179$	2809.84	1.17328	0.586641	−	0.809847i	$-0.300450\pi$
$179$	2809.84	1.17328	0.586641	+	0.809847i	$0.300450\pi$
$180$	779.675	0.322853
$181$	125.390	0.0514925	0.0257463	−	0.999669i	$-0.491804\pi$
$181$	125.390	0.0514925	0.0257463	+	0.999669i	$0.491804\pi$
$182$	892.591	0.363534
$183$	−32.7011	−0.0132095
$184$	184.000	0.0737210
$185$	6336.05	2.51803
$186$	995.607	0.392481
$187$	−70.9493	−0.0277451
$188$	561.303	0.217751
$189$	189.000	0.0727393
$190$	6310.42	2.40950
$191$	2966.84	1.12394	0.561972	−	0.827157i	$-0.310043\pi$
$191$	2966.84	1.12394	0.561972	+	0.827157i	$0.310043\pi$
$192$	−192.000	−0.0721688
$193$	2844.63	1.06094	0.530468	−	0.847705i	$-0.322016\pi$
$193$	2844.63	1.06094	0.530468	+	0.847705i	$0.322016\pi$
$194$	1556.20	0.575920
$195$	−4142.44	−1.52126
$196$	196.000	0.0714286
$197$	−2906.03	−1.05100	−0.525498	−	0.850795i	$-0.676121\pi$
$197$	−2906.03	−1.05100	−0.525498	+	0.850795i	$0.676121\pi$
$198$	138.234	0.0496153
$199$	−3752.84	−1.33684	−0.668422	−	0.743783i	$-0.733030\pi$
$199$	−3752.84	−1.33684	−0.668422	+	0.743783i	$0.733030\pi$
$200$	−2752.43	−0.973131
$201$	1333.97	0.468115
$202$	−2811.93	−0.979439
$203$	−1566.52	−0.541615
$204$	−110.863	−0.0380490
$205$	−7266.15	−2.47556
$206$	−1618.12	−0.547279
$207$	−207.000	−0.0695048
$208$	1020.10	0.340055
$209$	1118.81	0.370287
$210$	−909.621	−0.298904
$211$	−2467.89	−0.805195	−0.402598	−	0.915377i	$-0.631893\pi$
$211$	−2467.89	−0.805195	−0.402598	+	0.915377i	$0.631893\pi$
$212$	−366.951	−0.118879
$213$	1036.51	0.333431
$214$	−760.447	−0.242912
$215$	2633.00	0.835207
$216$	216.000	0.0680414
$217$	−1161.54	−0.363367
$218$	3673.04	1.14115
$219$	−851.946	−0.262873
$220$	−665.292	−0.203882
$221$	589.022	0.179285
$222$	1755.33	0.530675
$223$	−5855.47	−1.75835	−0.879173	−	0.476504i	$-0.841904\pi$
$223$	−5855.47	−1.75835	−0.879173	+	0.476504i	$0.841904\pi$
$224$	224.000	0.0668153
$225$	3096.48	0.917476
$226$	3365.26	0.990503
$227$	3318.38	0.970258	0.485129	−	0.874443i	$-0.338773\pi$
$227$	3318.38	0.970258	0.485129	+	0.874443i	$0.338773\pi$
$228$	1748.23	0.507804
$229$	−4276.81	−1.23415	−0.617073	−	0.786906i	$-0.711682\pi$
$229$	−4276.81	−1.23415	−0.617073	+	0.786906i	$0.711682\pi$
$230$	996.252	0.285613
$231$	−161.273	−0.0459349
$232$	−1790.30	−0.506635
$233$	4982.08	1.40080	0.700401	−	0.713750i	$-0.253005\pi$
$233$	4982.08	1.40080	0.700401	+	0.713750i	$0.253005\pi$
$234$	−1147.62	−0.320607
$235$	3039.13	0.843620
$236$	41.4943	0.0114451
$237$	924.198	0.253304
$238$	129.341	0.0352265
$239$	5664.37	1.53305	0.766523	−	0.642217i	$-0.221985\pi$
$239$	5664.37	1.53305	0.766523	+	0.642217i	$0.221985\pi$
$240$	−1039.57	−0.279599
$241$	3584.05	0.957962	0.478981	−	0.877825i	$-0.341006\pi$
$241$	3584.05	0.957962	0.478981	+	0.877825i	$0.341006\pi$
$242$	2544.05	0.675775
$243$	−243.000	−0.0641500
$244$	43.6015	0.0114398
$245$	1061.22	0.276731
$246$	−2013.00	−0.521725
$247$	−9288.41	−2.39274
$248$	−1327.48	−0.339899
$249$	417.744	0.106319
$250$	−9488.37	−2.40039
$251$	−4147.76	−1.04305	−0.521523	−	0.853237i	$-0.674636\pi$
$251$	−4147.76	−1.04305	−0.521523	+	0.853237i	$0.674636\pi$
$252$	−252.000	−0.0629941
$253$	176.632	0.0438923
$254$	−5217.65	−1.28891
$255$	−600.260	−0.147411
$256$	256.000	0.0625000
$257$	5416.54	1.31469	0.657343	−	0.753591i	$-0.271680\pi$
$257$	5416.54	1.31469	0.657343	+	0.753591i	$0.271680\pi$
$258$	729.443	0.176020
$259$	−2047.88	−0.491310
$260$	5523.26	1.31745
$261$	2014.09	0.477660
$262$	−4279.60	−1.00914
$263$	−5233.81	−1.22711	−0.613556	−	0.789651i	$-0.710261\pi$
$263$	−5233.81	−1.22711	−0.613556	+	0.789651i	$0.710261\pi$
$264$	−184.312	−0.0429681
$265$	−1986.82	−0.460565
$266$	−2039.60	−0.470135
$267$	−2666.36	−0.611155
$268$	−1778.63	−0.405399
$269$	2204.45	0.499656	0.249828	−	0.968290i	$-0.419626\pi$
$269$	2204.45	0.499656	0.249828	+	0.968290i	$0.419626\pi$
$270$	1169.51	0.263608
$271$	8283.32	1.85674	0.928369	−	0.371659i	$-0.121211\pi$
$271$	8283.32	1.85674	0.928369	+	0.371659i	$0.121211\pi$
$272$	147.818	0.0329514
$273$	1338.89	0.296824
$274$	2174.35	0.479406
$275$	−2642.21	−0.579387
$276$	276.000	0.0601929
$277$	340.659	0.0738925	0.0369463	−	0.999317i	$-0.488237\pi$
$277$	340.659	0.0738925	0.0369463	+	0.999317i	$0.488237\pi$
$278$	−2971.46	−0.641065
$279$	1493.41	0.320459
$280$	1212.83	0.258858
$281$	1603.50	0.340415	0.170207	−	0.985408i	$-0.445556\pi$
$281$	1603.50	0.340415	0.170207	+	0.985408i	$0.445556\pi$
$282$	841.954	0.177793
$283$	7515.82	1.57869	0.789345	−	0.613950i	$-0.210421\pi$
$283$	7515.82	1.57869	0.789345	+	0.613950i	$0.210421\pi$
$284$	−1382.02	−0.288759
$285$	9465.63	1.96735
$286$	979.254	0.202463
$287$	2348.50	0.483023
$288$	−288.000	−0.0589256
$289$	−4827.65	−0.982627
$290$	−9693.44	−1.96282
$291$	2334.29	0.470236
$292$	1135.93	0.227655
$293$	−1807.73	−0.360439	−0.180220	−	0.983626i	$-0.557681\pi$
$293$	−1807.73	−0.360439	−0.180220	+	0.983626i	$0.557681\pi$
$294$	294.000	0.0583212
$295$	224.667	0.0443411
$296$	−2340.44	−0.459578
$297$	207.350	0.0405108
$298$	−3102.76	−0.603148
$299$	−1466.40	−0.283626
$300$	−4128.64	−0.794558
$301$	−851.017	−0.162963
$302$	−5661.37	−1.07873
$303$	−4217.89	−0.799709
$304$	−2330.97	−0.439771
$305$	236.076	0.0443203
$306$	−166.295	−0.0310669
$307$	−9486.62	−1.76362	−0.881808	−	0.471609i	$-0.843674\pi$
$307$	−9486.62	−1.76362	−0.881808	+	0.471609i	$0.843674\pi$
$308$	215.030	0.0397808
$309$	−2427.17	−0.446851
$310$	−7187.50	−1.31685
$311$	2011.36	0.366732	0.183366	−	0.983045i	$-0.441301\pi$
$311$	2011.36	0.366732	0.183366	+	0.983045i	$0.441301\pi$
$312$	1530.16	0.277654
$313$	−8481.05	−1.53156	−0.765778	−	0.643105i	$-0.777646\pi$
$313$	−8481.05	−1.53156	−0.765778	+	0.643105i	$0.777646\pi$
$314$	4926.63	0.885433
$315$	−1364.43	−0.244054
$316$	−1232.26	−0.219368
$317$	−1379.68	−0.244450	−0.122225	−	0.992502i	$-0.539003\pi$
$317$	−1379.68	−0.244450	−0.122225	+	0.992502i	$0.539003\pi$
$318$	−550.427	−0.0970642
$319$	−1718.61	−0.301642
$320$	1386.09	0.242140
$321$	−1140.67	−0.198337
$322$	−322.000	−0.0557278
$323$	−1345.93	−0.231857
$324$	324.000	0.0555556
$325$	21935.6	3.74391
$326$	−2929.52	−0.497703
$327$	5509.56	0.931742
$328$	2684.00	0.451827
$329$	−982.280	−0.164604
$330$	−997.939	−0.166469
$331$	−447.040	−0.0742343	−0.0371171	−	0.999311i	$-0.511817\pi$
$331$	−447.040	−0.0742343	−0.0371171	+	0.999311i	$0.511817\pi$
$332$	−556.992	−0.0920750
$333$	2632.99	0.433295
$334$	−4780.70	−0.783199
$335$	−9630.23	−1.57061
$336$	336.000	0.0545545
$337$	−7611.82	−1.23039	−0.615196	−	0.788374i	$-0.710923\pi$
$337$	−7611.82	−1.23039	−0.615196	+	0.788374i	$0.710923\pi$
$338$	−3735.77	−0.601181
$339$	5047.89	0.808743
$340$	800.347	0.127661
$341$	−1274.32	−0.202370
$342$	2622.34	0.414620
$343$	−343.000	−0.0539949
$344$	−972.591	−0.152438
$345$	1494.38	0.233202
$346$	−5571.13	−0.865623
$347$	−1936.99	−0.299663	−0.149832	−	0.988712i	$-0.547873\pi$
$347$	−1936.99	−0.299663	−0.149832	+	0.988712i	$0.547873\pi$
$348$	−2685.46	−0.413665
$349$	−4777.25	−0.732724	−0.366362	−	0.930472i	$-0.619397\pi$
$349$	−4777.25	−0.732724	−0.366362	+	0.930472i	$0.619397\pi$
$350$	4816.75	0.735618
$351$	−1721.42	−0.261774
$352$	245.749	0.0372115
$353$	−9788.48	−1.47589	−0.737943	−	0.674863i	$-0.764203\pi$
$353$	−9788.48	−1.47589	−0.737943	+	0.674863i	$0.764203\pi$
$354$	62.2414	0.00934490
$355$	−7482.81	−1.11872
$356$	3555.14	0.529276
$357$	194.011	0.0287623
$358$	−5619.68	−0.829635
$359$	7786.60	1.14474	0.572369	−	0.819996i	$-0.306024\pi$
$359$	7786.60	1.14474	0.572369	+	0.819996i	$0.306024\pi$
$360$	−1559.35	−0.228292
$361$	14365.3	2.09438
$362$	−250.779	−0.0364107
$363$	3816.07	0.551768
$364$	−1785.18	−0.257057
$365$	6150.38	0.881988
$366$	65.4022	0.00934052
$367$	1369.04	0.194723	0.0973614	−	0.995249i	$-0.468960\pi$
$367$	1369.04	0.194723	0.0973614	+	0.995249i	$0.468960\pi$
$368$	−368.000	−0.0521286
$369$	−3019.50	−0.425987
$370$	−12672.1	−1.78052
$371$	642.165	0.0898640
$372$	−1991.21	−0.277526
$373$	11348.7	1.57537	0.787687	−	0.616076i	$-0.211278\pi$
$373$	11348.7	1.57537	0.787687	+	0.616076i	$0.211278\pi$
$374$	141.899	0.0196187
$375$	−14232.6	−1.95991
$376$	−1122.61	−0.153973
$377$	14267.9	1.94917
$378$	−378.000	−0.0514344
$379$	1931.79	0.261819	0.130910	−	0.991394i	$-0.458210\pi$
$379$	1931.79	0.261819	0.130910	+	0.991394i	$0.458210\pi$
$380$	−12620.8	−1.70378
$381$	−7826.47	−1.05239
$382$	−5933.68	−0.794748
$383$	2075.41	0.276890	0.138445	−	0.990370i	$-0.455790\pi$
$383$	2075.41	0.276890	0.138445	+	0.990370i	$0.455790\pi$
$384$	384.000	0.0510310
$385$	1164.26	0.154120
$386$	−5689.25	−0.750195
$387$	1094.17	0.143720
$388$	−3112.39	−0.407237
$389$	−7434.25	−0.968975	−0.484488	−	0.874798i	$-0.660994\pi$
$389$	−7434.25	−0.968975	−0.484488	+	0.874798i	$0.660994\pi$
$390$	8284.89	1.07570
$391$	−212.488	−0.0274834
$392$	−392.000	−0.0505076
$393$	−6419.40	−0.823959
$394$	5812.06	0.743166
$395$	−6671.99	−0.849884
$396$	−276.467	−0.0350833
$397$	−2829.73	−0.357733	−0.178866	−	0.983873i	$-0.557243\pi$
$397$	−2829.73	−0.357733	−0.178866	+	0.983873i	$0.557243\pi$
$398$	7505.68	0.945291
$399$	−3059.40	−0.383864
$400$	5504.86	0.688107
$401$	5719.37	0.712248	0.356124	−	0.934439i	$-0.384098\pi$
$401$	5719.37	0.712248	0.356124	+	0.934439i	$0.384098\pi$
$402$	−2667.94	−0.331007
$403$	10579.4	1.30769
$404$	5623.86	0.692568
$405$	1754.27	0.215235
$406$	3133.03	0.382980
$407$	−2246.72	−0.273626
$408$	221.727	0.0269047
$409$	−2913.31	−0.352209	−0.176105	−	0.984371i	$-0.556350\pi$
$409$	−2913.31	−0.352209	−0.176105	+	0.984371i	$0.556350\pi$
$410$	14532.3	1.75049
$411$	3261.52	0.391433
$412$	3236.23	0.386984
$413$	−72.6150	−0.00865169
$414$	414.000	0.0491473
$415$	−3015.78	−0.356720
$416$	−2040.21	−0.240455
$417$	−4457.18	−0.523427
$418$	−2237.63	−0.261833
$419$	11518.7	1.34301	0.671507	−	0.740998i	$-0.265647\pi$
$419$	11518.7	1.34301	0.671507	+	0.740998i	$0.265647\pi$
$420$	1819.24	0.211357
$421$	−10074.9	−1.16632	−0.583162	−	0.812356i	$-0.698185\pi$
$421$	−10074.9	−1.16632	−0.583162	+	0.812356i	$0.698185\pi$
$422$	4935.77	0.569359
$423$	1262.93	0.145167
$424$	733.902	0.0840600
$425$	3178.58	0.362785
$426$	−2073.03	−0.235771
$427$	−76.3026	−0.00864764
$428$	1520.89	0.171765
$429$	1468.88	0.165311
$430$	−5266.01	−0.590580
$431$	−4889.20	−0.546414	−0.273207	−	0.961955i	$-0.588084\pi$
$431$	−4889.20	−0.546414	−0.273207	+	0.961955i	$0.588084\pi$
$432$	−432.000	−0.0481125
$433$	−12480.8	−1.38520	−0.692600	−	0.721322i	$-0.743535\pi$
$433$	−12480.8	−1.38520	−0.692600	+	0.721322i	$0.743535\pi$
$434$	2323.08	0.256939
$435$	−14540.2	−1.60264
$436$	−7346.09	−0.806912
$437$	3350.77	0.366794
$438$	1703.89	0.185879
$439$	10614.2	1.15396	0.576978	−	0.816759i	$-0.304232\pi$
$439$	10614.2	1.15396	0.576978	+	0.816759i	$0.304232\pi$
$440$	1330.58	0.144166
$441$	441.000	0.0476190
$442$	−1178.04	−0.126773
$443$	8956.50	0.960578	0.480289	−	0.877110i	$-0.340532\pi$
$443$	8956.50	0.960578	0.480289	+	0.877110i	$0.340532\pi$
$444$	−3510.66	−0.375244
$445$	19249.0	2.05054
$446$	11710.9	1.24334
$447$	−4654.14	−0.492468
$448$	−448.000	−0.0472456
$449$	1848.59	0.194300	0.0971498	−	0.995270i	$-0.469027\pi$
$449$	1848.59	0.194300	0.0971498	+	0.995270i	$0.469027\pi$
$450$	−6192.97	−0.648754
$451$	2576.52	0.269011
$452$	−6730.52	−0.700392
$453$	−8492.05	−0.880775
$454$	−6636.76	−0.686076
$455$	−9665.70	−0.995902
$456$	−3496.46	−0.359071
$457$	13880.5	1.42079	0.710395	−	0.703803i	$-0.248516\pi$
$457$	13880.5	1.42079	0.710395	+	0.703803i	$0.248516\pi$
$458$	8553.62	0.872673
$459$	−249.443	−0.0253660
$460$	−1992.50	−0.201959
$461$	6171.03	0.623457	0.311729	−	0.950171i	$-0.399092\pi$
$461$	6171.03	0.623457	0.311729	+	0.950171i	$0.399092\pi$
$462$	322.545	0.0324809
$463$	11742.8	1.17869	0.589346	−	0.807880i	$-0.299385\pi$
$463$	11742.8	1.17869	0.589346	+	0.807880i	$0.299385\pi$
$464$	3580.61	0.358245
$465$	−10781.3	−1.07520
$466$	−9964.15	−0.990516
$467$	−2037.06	−0.201850	−0.100925	−	0.994894i	$-0.532180\pi$
$467$	−2037.06	−0.201850	−0.100925	+	0.994894i	$0.532180\pi$
$468$	2295.23	0.226703
$469$	3112.60	0.306453
$470$	−6078.25	−0.596529
$471$	7389.95	0.722953
$472$	−82.9885	−0.00809292
$473$	−933.645	−0.0907591
$474$	−1848.40	−0.179113
$475$	−50123.7	−4.84175
$476$	−258.681	−0.0249089
$477$	−825.640	−0.0792526
$478$	−11328.7	−1.08403
$479$	18344.6	1.74986	0.874931	−	0.484247i	$-0.160907\pi$
$479$	18344.6	1.74986	0.874931	+	0.484247i	$0.160907\pi$
$480$	2079.13	0.197706
$481$	18652.3	1.76813
$482$	−7168.10	−0.677382
$483$	−483.000	−0.0455016
$484$	−5088.09	−0.477845
$485$	−16851.8	−1.57773
$486$	486.000	0.0453609
$487$	−5695.34	−0.529940	−0.264970	−	0.964257i	$-0.585362\pi$
$487$	−5695.34	−0.529940	−0.264970	+	0.964257i	$0.585362\pi$
$488$	−87.2030	−0.00808913
$489$	−4394.28	−0.406373
$490$	−2122.45	−0.195679
$491$	4.86414	0.000447078 0	0.000223539	−	1.00000i	$-0.499929\pi$
$491$	4.86414	0.000447078 0	0.000223539		1.00000i	$0.499929\pi$
$492$	4026.00	0.368915
$493$	2067.49	0.188875
$494$	18576.8	1.69192
$495$	−1496.91	−0.135921
$496$	2654.95	0.240345
$497$	2418.53	0.218282
$498$	−835.488	−0.0751789
$499$	−20659.3	−1.85338	−0.926689	−	0.375830i	$-0.877358\pi$
$499$	−20659.3	−1.85338	−0.926689	+	0.375830i	$0.877358\pi$
$500$	18976.7	1.69733
$501$	−7171.05	−0.639479
$502$	8295.53	0.737545
$503$	−17141.4	−1.51948	−0.759741	−	0.650226i	$-0.774674\pi$
$503$	−17141.4	−1.51948	−0.759741	+	0.650226i	$0.774674\pi$
$504$	504.000	0.0445435
$505$	30449.9	2.68317
$506$	−353.264	−0.0310365
$507$	−5603.66	−0.490863
$508$	10435.3	0.911400
$509$	−11323.8	−0.986084	−0.493042	−	0.870005i	$-0.664115\pi$
$509$	−11323.8	−0.986084	−0.493042	+	0.870005i	$0.664115\pi$
$510$	1200.52	0.104235
$511$	−1987.87	−0.172091
$512$	−512.000	−0.0441942
$513$	3933.51	0.338536
$514$	−10833.1	−0.929624
$515$	17522.3	1.49927
$516$	−1458.89	−0.124465
$517$	−1077.65	−0.0916733
$518$	4095.77	0.347409
$519$	−8356.69	−0.706779
$520$	−11046.5	−0.931581
$521$	9820.14	0.825774	0.412887	−	0.910782i	$-0.364520\pi$
$521$	9820.14	0.825774	0.412887	+	0.910782i	$0.364520\pi$
$522$	−4028.18	−0.337756
$523$	3490.61	0.291842	0.145921	−	0.989296i	$-0.453385\pi$
$523$	3490.61	0.291842	0.145921	+	0.989296i	$0.453385\pi$
$524$	8559.20	0.713569
$525$	7225.13	0.600629
$526$	10467.6	0.867699
$527$	1533.01	0.126715
$528$	368.623	0.0303831
$529$	529.000	0.0434783
$530$	3973.65	0.325669
$531$	93.3621	0.00763008
$532$	4079.20	0.332436
$533$	−21390.3	−1.73831
$534$	5332.71	0.432152
$535$	8234.75	0.665457
$536$	3557.26	0.286661
$537$	−8429.52	−0.677394
$538$	−4408.89	−0.353310
$539$	−376.303	−0.0300714
$540$	−2339.03	−0.186399
$541$	2812.06	0.223475	0.111737	−	0.993738i	$-0.464358\pi$
$541$	2812.06	0.223475	0.111737	+	0.993738i	$0.464358\pi$
$542$	−16566.6	−1.31291
$543$	−376.169	−0.0297292
$544$	−295.636	−0.0233001
$545$	−39774.7	−3.12617
$546$	−2677.77	−0.209887
$547$	21225.6	1.65912	0.829560	−	0.558417i	$-0.188591\pi$
$547$	21225.6	1.65912	0.829560	+	0.558417i	$0.188591\pi$
$548$	−4348.70	−0.338991
$549$	98.1034	0.00762650
$550$	5284.42	0.409688
$551$	−32602.7	−2.52073
$552$	−552.000	−0.0425628
$553$	2156.46	0.165827
$554$	−681.318	−0.0522499
$555$	−19008.1	−1.45379
$556$	5942.91	0.453301
$557$	−9319.31	−0.708926	−0.354463	−	0.935070i	$-0.615336\pi$
$557$	−9319.31	−0.708926	−0.354463	+	0.935070i	$0.615336\pi$
$558$	−2986.82	−0.226599
$559$	7751.12	0.586471
$560$	−2425.66	−0.183041
$561$	212.848	0.0160186
$562$	−3206.99	−0.240709
$563$	−11813.9	−0.884362	−0.442181	−	0.896926i	$-0.645795\pi$
$563$	−11813.9	−0.884362	−0.442181	+	0.896926i	$0.645795\pi$
$564$	−1683.91	−0.125719
$565$	−36441.8	−2.71348
$566$	−15031.6	−1.11630
$567$	−567.000	−0.0419961
$568$	2764.04	0.204184
$569$	331.923	0.0244551	0.0122275	−	0.999925i	$-0.496108\pi$
$569$	331.923	0.0244551	0.0122275	+	0.999925i	$0.496108\pi$
$570$	−18931.3	−1.39113
$571$	9252.25	0.678099	0.339050	−	0.940768i	$-0.389895\pi$
$571$	9252.25	0.678099	0.339050	+	0.940768i	$0.389895\pi$
$572$	−1958.51	−0.143163
$573$	−8900.52	−0.648909
$574$	−4697.01	−0.341549
$575$	−7913.23	−0.573921
$576$	576.000	0.0416667
$577$	−4323.91	−0.311970	−0.155985	−	0.987759i	$-0.549855\pi$
$577$	−4323.91	−0.311970	−0.155985	+	0.987759i	$0.549855\pi$
$578$	9655.30	0.694822
$579$	−8533.88	−0.612532
$580$	19386.9	1.38793
$581$	974.735	0.0696021
$582$	−4668.59	−0.332507
$583$	704.514	0.0500480
$584$	−2271.86	−0.160976
$585$	12427.3	0.878303
$586$	3615.46	0.254869
$587$	−18758.3	−1.31898	−0.659489	−	0.751714i	$-0.729227\pi$
$587$	−18758.3	−1.31898	−0.659489	+	0.751714i	$0.729227\pi$
$588$	−588.000	−0.0412393
$589$	−24174.3	−1.69114
$590$	−449.334	−0.0313539
$591$	8718.10	0.606793
$592$	4680.88	0.324971
$593$	−13282.8	−0.919832	−0.459916	−	0.887962i	$-0.652121\pi$
$593$	−13282.8	−0.919832	−0.459916	+	0.887962i	$0.652121\pi$
$594$	−414.701	−0.0286454
$595$	−1400.61	−0.0965030
$596$	6205.52	0.426490
$597$	11258.5	0.771827
$598$	2932.80	0.200554
$599$	−13385.4	−0.913044	−0.456522	−	0.889712i	$-0.650905\pi$
$599$	−13385.4	−0.913044	−0.456522	+	0.889712i	$0.650905\pi$
$600$	8257.29	0.561837
$601$	4439.00	0.301282	0.150641	−	0.988589i	$-0.451866\pi$
$601$	4439.00	0.301282	0.150641	+	0.988589i	$0.451866\pi$
$602$	1702.03	0.115232
$603$	−4001.92	−0.270266
$604$	11322.7	0.762774
$605$	−27549.0	−1.85128
$606$	8435.79	0.565479
$607$	4029.43	0.269439	0.134720	−	0.990884i	$-0.456987\pi$
$607$	4029.43	0.269439	0.134720	+	0.990884i	$0.456987\pi$
$608$	4661.94	0.310965
$609$	4699.55	0.312702
$610$	−472.153	−0.0313392
$611$	8946.67	0.592379
$612$	332.590	0.0219676
$613$	−13906.1	−0.916253	−0.458127	−	0.888887i	$-0.651479\pi$
$613$	−13906.1	−0.916253	−0.458127	+	0.888887i	$0.651479\pi$
$614$	18973.2	1.24706
$615$	21798.4	1.42927
$616$	−430.060	−0.0281293
$617$	−4546.72	−0.296668	−0.148334	−	0.988937i	$-0.547391\pi$
$617$	−4546.72	−0.296668	−0.148334	+	0.988937i	$0.547391\pi$
$618$	4854.35	0.315972
$619$	−5364.47	−0.348330	−0.174165	−	0.984717i	$-0.555723\pi$
$619$	−5364.47	−0.348330	−0.174165	+	0.984717i	$0.555723\pi$
$620$	14375.0	0.931152
$621$	621.000	0.0401286
$622$	−4022.72	−0.259319
$623$	−6221.50	−0.400095
$624$	−3060.31	−0.196331
$625$	59741.2	3.82344
$626$	16962.1	1.08297
$627$	−3356.44	−0.213785
$628$	−9853.26	−0.626096
$629$	2702.80	0.171332
$630$	2728.86	0.172572
$631$	−16148.1	−1.01877	−0.509386	−	0.860538i	$-0.670127\pi$
$631$	−16148.1	−1.01877	−0.509386	+	0.860538i	$0.670127\pi$
$632$	2464.53	0.155117
$633$	7403.66	0.464880
$634$	2759.36	0.172852
$635$	56501.0	3.53098
$636$	1100.85	0.0686347
$637$	3124.07	0.194317
$638$	3437.23	0.213293
$639$	−3109.54	−0.192506
$640$	−2772.18	−0.171219
$641$	14977.6	0.922902	0.461451	−	0.887166i	$-0.347329\pi$
$641$	14977.6	0.922902	0.461451	+	0.887166i	$0.347329\pi$
$642$	2281.34	0.140245
$643$	−20284.5	−1.24408	−0.622038	−	0.782987i	$-0.713695\pi$
$643$	−20284.5	−1.24408	−0.622038	+	0.782987i	$0.713695\pi$
$644$	644.000	0.0394055
$645$	−7899.01	−0.482207
$646$	2691.87	0.163948
$647$	9511.42	0.577948	0.288974	−	0.957337i	$-0.406686\pi$
$647$	9511.42	0.577948	0.288974	+	0.957337i	$0.406686\pi$
$648$	−648.000	−0.0392837
$649$	−79.6653	−0.00481840
$650$	−43871.3	−2.64734
$651$	3484.63	0.209790
$652$	5859.04	0.351929
$653$	−19219.0	−1.15176	−0.575878	−	0.817535i	$-0.695340\pi$
$653$	−19219.0	−1.15176	−0.575878	+	0.817535i	$0.695340\pi$
$654$	−11019.1	−0.658841
$655$	46343.0	2.76454
$656$	−5368.01	−0.319490
$657$	2555.84	0.151770
$658$	1964.56	0.116393
$659$	−4176.90	−0.246902	−0.123451	−	0.992351i	$-0.539396\pi$
$659$	−4176.90	−0.246902	−0.123451	+	0.992351i	$0.539396\pi$
$660$	1995.88	0.117711
$661$	22086.9	1.29967	0.649833	−	0.760077i	$-0.274839\pi$
$661$	22086.9	1.29967	0.649833	+	0.760077i	$0.274839\pi$
$662$	894.080	0.0524916
$663$	−1767.07	−0.103510
$664$	1113.98	0.0651068
$665$	22086.5	1.28793
$666$	−5265.99	−0.306386
$667$	−5147.12	−0.298797
$668$	9561.41	0.553805
$669$	17566.4	1.01518
$670$	19260.5	1.11059
$671$	−83.7110	−0.00481614
$672$	−672.000	−0.0385758
$673$	23118.0	1.32412	0.662059	−	0.749451i	$-0.269683\pi$
$673$	23118.0	1.32412	0.662059	+	0.749451i	$0.269683\pi$
$674$	15223.6	0.870018
$675$	−9289.45	−0.529705
$676$	7471.55	0.425099
$677$	−9447.78	−0.536348	−0.268174	−	0.963370i	$-0.586420\pi$
$677$	−9447.78	−0.536348	−0.268174	+	0.963370i	$0.586420\pi$
$678$	−10095.8	−0.571867
$679$	5446.69	0.307842
$680$	−1600.69	−0.0902703
$681$	−9955.13	−0.560179
$682$	2548.64	0.143097
$683$	14305.1	0.801420	0.400710	−	0.916205i	$-0.368763\pi$
$683$	14305.1	0.801420	0.400710	+	0.916205i	$0.368763\pi$
$684$	−5244.69	−0.293181
$685$	−23545.6	−1.31333
$686$	686.000	0.0381802
$687$	12830.4	0.712535
$688$	1945.18	0.107790
$689$	−5848.88	−0.323403
$690$	−2988.76	−0.164898
$691$	−17572.7	−0.967433	−0.483717	−	0.875225i	$-0.660713\pi$
$691$	−17572.7	−0.967433	−0.483717	+	0.875225i	$0.660713\pi$
$692$	11142.3	0.612088
$693$	483.818	0.0265205
$694$	3873.98	0.211894
$695$	32177.4	1.75620
$696$	5370.91	0.292506
$697$	−3099.56	−0.168442
$698$	9554.51	0.518114
$699$	−14946.2	−0.808753
$700$	−9633.50	−0.520160
$701$	9881.83	0.532427	0.266214	−	0.963914i	$-0.414227\pi$
$701$	9881.83	0.532427	0.266214	+	0.963914i	$0.414227\pi$
$702$	3442.85	0.185103
$703$	−42621.0	−2.28660
$704$	−491.497	−0.0263125
$705$	−9117.38	−0.487064
$706$	19577.0	1.04361
$707$	−9841.75	−0.523532
$708$	−124.483	−0.00660784
$709$	−16184.5	−0.857293	−0.428646	−	0.903472i	$-0.641009\pi$
$709$	−16184.5	−0.857293	−0.428646	+	0.903472i	$0.641009\pi$
$710$	14965.6	0.791056
$711$	−2772.59	−0.146245
$712$	−7110.29	−0.374255
$713$	−3816.49	−0.200461
$714$	−388.022	−0.0203380
$715$	−10604.2	−0.554648
$716$	11239.4	0.586641
$717$	−16993.1	−0.885104
$718$	−15573.2	−0.809452
$719$	25430.9	1.31907	0.659536	−	0.751673i	$-0.270753\pi$
$719$	25430.9	1.31907	0.659536	+	0.751673i	$0.270753\pi$
$720$	3118.70	0.161427
$721$	−5663.40	−0.292533
$722$	−28730.6	−1.48095
$723$	−10752.1	−0.553080
$724$	501.559	0.0257463
$725$	76995.1	3.94417
$726$	−7632.14	−0.390159
$727$	7539.07	0.384606	0.192303	−	0.981336i	$-0.438404\pi$
$727$	7539.07	0.384606	0.192303	+	0.981336i	$0.438404\pi$
$728$	3570.36	0.181767
$729$	729.000	0.0370370
$730$	−12300.8	−0.623660
$731$	1123.18	0.0568292
$732$	−130.804	−0.00660474
$733$	−24919.5	−1.25569	−0.627847	−	0.778337i	$-0.716064\pi$
$733$	−24919.5	−1.25569	−0.627847	+	0.778337i	$0.716064\pi$
$734$	−2738.08	−0.137690
$735$	−3183.67	−0.159771
$736$	736.000	0.0368605
$737$	3414.81	0.170673
$738$	6039.01	0.301218
$739$	2288.29	0.113905	0.0569527	−	0.998377i	$-0.481862\pi$
$739$	2288.29	0.113905	0.0569527	+	0.998377i	$0.481862\pi$
$740$	25344.2	1.25901
$741$	27865.2	1.38145
$742$	−1284.33	−0.0635434
$743$	−28920.9	−1.42800	−0.714002	−	0.700144i	$-0.753119\pi$
$743$	−28920.9	−1.42800	−0.714002	+	0.700144i	$0.753119\pi$
$744$	3982.43	0.196240
$745$	33599.2	1.65232
$746$	−22697.4	−1.11396
$747$	−1253.23	−0.0613833
$748$	−283.797	−0.0138725
$749$	−2661.57	−0.129842
$750$	28465.1	1.38587
$751$	−23510.9	−1.14238	−0.571188	−	0.820819i	$-0.693517\pi$
$751$	−23510.9	−1.14238	−0.571188	+	0.820819i	$0.693517\pi$
$752$	2245.21	0.108876
$753$	12443.3	0.602203
$754$	−28535.9	−1.37827
$755$	61305.9	2.95517
$756$	756.000	0.0363696
$757$	−15189.4	−0.729284	−0.364642	−	0.931148i	$-0.618809\pi$
$757$	−15189.4	−0.729284	−0.364642	+	0.931148i	$0.618809\pi$
$758$	−3863.58	−0.185134
$759$	−529.896	−0.0253412
$760$	25241.7	1.20475
$761$	15513.6	0.738984	0.369492	−	0.929234i	$-0.379532\pi$
$761$	15513.6	0.738984	0.369492	+	0.929234i	$0.379532\pi$
$762$	15652.9	0.744155
$763$	12855.7	0.609968
$764$	11867.4	0.561972
$765$	1800.78	0.0851077
$766$	−4150.83	−0.195791
$767$	661.382	0.0311358
$768$	−768.000	−0.0360844
$769$	3335.24	0.156400	0.0782002	−	0.996938i	$-0.475083\pi$
$769$	3335.24	0.156400	0.0782002	+	0.996938i	$0.475083\pi$
$770$	−2328.52	−0.108979
$771$	−16249.6	−0.759035
$772$	11378.5	0.530468
$773$	15879.9	0.738887	0.369444	−	0.929253i	$-0.379548\pi$
$773$	15879.9	0.738887	0.369444	+	0.929253i	$0.379548\pi$
$774$	−2188.33	−0.101625
$775$	57090.4	2.64613
$776$	6224.79	0.287960
$777$	6143.65	0.283658
$778$	14868.5	0.685169
$779$	48877.6	2.24804
$780$	−16569.8	−0.760632
$781$	2653.35	0.121568
$782$	424.976	0.0194337
$783$	−6042.28	−0.275777
$784$	784.000	0.0357143
$785$	−53349.6	−2.42564
$786$	12838.8	0.582627
$787$	−31903.3	−1.44502	−0.722509	−	0.691362i	$-0.757011\pi$
$787$	−31903.3	−1.44502	−0.722509	+	0.691362i	$0.757011\pi$
$788$	−11624.1	−0.525498
$789$	15701.4	0.708473
$790$	13344.0	0.600959
$791$	11778.4	0.529446
$792$	552.935	0.0248077
$793$	694.969	0.0311212
$794$	5659.45	0.252955
$795$	5960.47	0.265907
$796$	−15011.4	−0.668422
$797$	−42935.1	−1.90821	−0.954103	−	0.299479i	$-0.903187\pi$
$797$	−42935.1	−1.90821	−0.954103	+	0.299479i	$0.903187\pi$
$798$	6118.80	0.271433
$799$	1296.42	0.0574016
$800$	−11009.7	−0.486565
$801$	7999.07	0.352851
$802$	−11438.7	−0.503636
$803$	−2180.88	−0.0958427
$804$	5335.89	0.234057
$805$	3486.88	0.152666
$806$	−21158.8	−0.924674
$807$	−6613.34	−0.288476
$808$	−11247.7	−0.489719
$809$	21015.4	0.913301	0.456650	−	0.889646i	$-0.349049\pi$
$809$	21015.4	0.913301	0.456650	+	0.889646i	$0.349049\pi$
$810$	−3508.54	−0.152194
$811$	−5737.75	−0.248434	−0.124217	−	0.992255i	$-0.539642\pi$
$811$	−5737.75	−0.248434	−0.124217	+	0.992255i	$0.539642\pi$
$812$	−6266.06	−0.270808
$813$	−24850.0	−1.07199
$814$	4493.44	0.193483
$815$	31723.3	1.36346
$816$	−443.454	−0.0190245
$817$	−17711.6	−0.758445
$818$	5826.61	0.249050
$819$	−4016.66	−0.171372
$820$	−29064.6	−1.23778
$821$	−46055.2	−1.95778	−0.978891	−	0.204384i	$-0.934481\pi$
$821$	−46055.2	−1.95778	−0.978891	+	0.204384i	$0.934481\pi$
$822$	−6523.05	−0.276785
$823$	−39701.6	−1.68154	−0.840771	−	0.541391i	$-0.817898\pi$
$823$	−39701.6	−1.68154	−0.840771	+	0.541391i	$0.817898\pi$
$824$	−6472.46	−0.273639
$825$	7926.63	0.334509
$826$	145.230	0.00611767
$827$	−20446.2	−0.859714	−0.429857	−	0.902897i	$-0.641436\pi$
$827$	−20446.2	−0.859714	−0.429857	+	0.902897i	$0.641436\pi$
$828$	−828.000	−0.0347524
$829$	18481.2	0.774282	0.387141	−	0.922020i	$-0.373463\pi$
$829$	18481.2	0.774282	0.387141	+	0.922020i	$0.373463\pi$
$830$	6031.56	0.252239
$831$	−1021.98	−0.0426619
$832$	4080.41	0.170028
$833$	452.692	0.0188294
$834$	8914.37	0.370119
$835$	51769.4	2.14557
$836$	4475.26	0.185144
$837$	−4480.23	−0.185017
$838$	−23037.3	−0.949654
$839$	8223.46	0.338385	0.169193	−	0.985583i	$-0.445884\pi$
$839$	8223.46	0.338385	0.169193	+	0.985583i	$0.445884\pi$
$840$	−3638.48	−0.149452
$841$	25692.1	1.05343
$842$	20149.9	0.824716
$843$	−4810.49	−0.196538
$844$	−9871.54	−0.402598
$845$	40454.0	1.64694
$846$	−2525.86	−0.102649
$847$	8904.16	0.361217
$848$	−1467.80	−0.0594394
$849$	−22547.5	−0.911457
$850$	−6357.16	−0.256528
$851$	−6728.76	−0.271045
$852$	4146.05	0.166715
$853$	−14330.6	−0.575231	−0.287615	−	0.957746i	$-0.592862\pi$
$853$	−14330.6	−0.575231	−0.287615	+	0.957746i	$0.592862\pi$
$854$	152.605	0.00611480
$855$	−28396.9	−1.13585
$856$	−3041.79	−0.121456
$857$	−10483.2	−0.417853	−0.208927	−	0.977931i	$-0.566997\pi$
$857$	−10483.2	−0.417853	−0.208927	+	0.977931i	$0.566997\pi$
$858$	−2937.76	−0.116892
$859$	6682.74	0.265439	0.132720	−	0.991154i	$-0.457629\pi$
$859$	6682.74	0.265439	0.132720	+	0.991154i	$0.457629\pi$
$860$	10532.0	0.417603
$861$	−7045.51	−0.278874
$862$	9778.40	0.386373
$863$	−8687.33	−0.342665	−0.171333	−	0.985213i	$-0.554807\pi$
$863$	−8687.33	−0.342665	−0.171333	+	0.985213i	$0.554807\pi$
$864$	864.000	0.0340207
$865$	60328.8	2.37137
$866$	24961.7	0.979484
$867$	14482.9	0.567320
$868$	−4646.17	−0.181683
$869$	2365.84	0.0923540
$870$	29080.3	1.13324
$871$	−28349.8	−1.10287
$872$	14692.2	0.570573
$873$	−7002.88	−0.271491
$874$	−6701.54	−0.259363
$875$	−33209.3	−1.28306
$876$	−3407.78	−0.131436
$877$	−18871.9	−0.726635	−0.363317	−	0.931665i	$-0.618356\pi$
$877$	−18871.9	−0.726635	−0.363317	+	0.931665i	$0.618356\pi$
$878$	−21228.4	−0.815971
$879$	5423.19	0.208100
$880$	−2661.17	−0.101941
$881$	21401.1	0.818411	0.409206	−	0.912442i	$-0.365806\pi$
$881$	21401.1	0.818411	0.409206	+	0.912442i	$0.365806\pi$
$882$	−882.000	−0.0336718
$883$	7080.34	0.269844	0.134922	−	0.990856i	$-0.456922\pi$
$883$	7080.34	0.269844	0.134922	+	0.990856i	$0.456922\pi$
$884$	2356.09	0.0896423
$885$	−674.001	−0.0256003
$886$	−17913.0	−0.679231
$887$	−32048.7	−1.21318	−0.606590	−	0.795015i	$-0.707463\pi$
$887$	−32048.7	−1.21318	−0.606590	+	0.795015i	$0.707463\pi$
$888$	7021.31	0.265338
$889$	−18261.8	−0.688954
$890$	−38498.0	−1.44995
$891$	−622.051	−0.0233889
$892$	−23421.9	−0.879173
$893$	−20443.5	−0.766085
$894$	9308.28	0.348228
$895$	60854.5	2.27278
$896$	896.000	0.0334077
$897$	4399.20	0.163751
$898$	−3697.19	−0.137391
$899$	37134.2	1.37763
$900$	12385.9	0.458738
$901$	−847.531	−0.0313378
$902$	−5153.05	−0.190219
$903$	2553.05	0.0940867
$904$	13461.0	0.495252
$905$	2715.65	0.0997471
$906$	16984.1	0.622802
$907$	49551.0	1.81402	0.907009	−	0.421111i	$-0.138360\pi$
$907$	49551.0	1.81402	0.907009	+	0.421111i	$0.138360\pi$
$908$	13273.5	0.485129
$909$	12653.7	0.461712
$910$	19331.4	0.704209
$911$	9888.98	0.359645	0.179822	−	0.983699i	$-0.442448\pi$
$911$	9888.98	0.359645	0.179822	+	0.983699i	$0.442448\pi$
$912$	6992.91	0.253902
$913$	1069.38	0.0387636
$914$	−27760.9	−1.00465
$915$	−708.229	−0.0255883
$916$	−17107.2	−0.617073
$917$	−14978.6	−0.539408
$918$	498.885	0.0179365
$919$	4847.06	0.173982	0.0869912	−	0.996209i	$-0.472275\pi$
$919$	4847.06	0.173982	0.0869912	+	0.996209i	$0.472275\pi$
$920$	3985.01	0.142806
$921$	28459.9	1.01822
$922$	−12342.1	−0.440851
$923$	−22028.1	−0.785553
$924$	−645.090	−0.0229674
$925$	100655.	3.57784
$926$	−23485.6	−0.833462
$927$	7281.52	0.257990
$928$	−7161.22	−0.253317
$929$	−6673.96	−0.235700	−0.117850	−	0.993031i	$-0.537600\pi$
$929$	−6673.96	−0.235700	−0.117850	+	0.993031i	$0.537600\pi$
$930$	21562.5	0.760282
$931$	−7138.60	−0.251298
$932$	19928.3	0.700401
$933$	−6034.08	−0.211733
$934$	4074.12	0.142729
$935$	−1536.60	−0.0537455
$936$	−4590.47	−0.160303
$937$	−44446.7	−1.54964	−0.774819	−	0.632183i	$-0.782159\pi$
$937$	−44446.7	−1.54964	−0.774819	+	0.632183i	$0.782159\pi$
$938$	−6225.20	−0.216695
$939$	25443.1	0.884245
$940$	12156.5	0.421810
$941$	−39330.0	−1.36251	−0.681254	−	0.732047i	$-0.738565\pi$
$941$	−39330.0	−1.36251	−0.681254	+	0.732047i	$0.738565\pi$
$942$	−14779.9	−0.511205
$943$	7716.51	0.266473
$944$	165.977	0.00572256
$945$	4093.30	0.140905
$946$	1867.29	0.0641763
$947$	−5808.03	−0.199299	−0.0996493	−	0.995023i	$-0.531772\pi$
$947$	−5808.03	−0.199299	−0.0996493	+	0.995023i	$0.531772\pi$
$948$	3696.79	0.126652
$949$	18105.7	0.619321
$950$	100247.	3.42364
$951$	4139.04	0.141133
$952$	517.363	0.0176133
$953$	39453.8	1.34106	0.670532	−	0.741880i	$-0.266066\pi$
$953$	39453.8	1.34106	0.670532	+	0.741880i	$0.266066\pi$
$954$	1651.28	0.0560400
$955$	64254.8	2.17721
$956$	22657.5	0.766523
$957$	5155.84	0.174153
$958$	−36689.1	−1.23734
$959$	7610.22	0.256253
$960$	−4158.27	−0.139800
$961$	−2256.73	−0.0757520
$962$	−37304.5	−1.25026
$963$	3422.01	0.114510
$964$	14336.2	0.478981
$965$	61607.9	2.05516
$966$	966.000	0.0321745
$967$	−16211.7	−0.539123	−0.269562	−	0.962983i	$-0.586879\pi$
$967$	−16211.7	−0.539123	−0.269562	+	0.962983i	$0.586879\pi$
$968$	10176.2	0.337887
$969$	4037.80	0.133863
$970$	33703.6	1.11562
$971$	40259.6	1.33058	0.665289	−	0.746586i	$-0.268308\pi$
$971$	40259.6	1.33058	0.665289	+	0.746586i	$0.268308\pi$
$972$	−972.000	−0.0320750
$973$	−10400.1	−0.342664
$974$	11390.7	0.374724
$975$	−65806.9	−2.16155
$976$	174.406	0.00571988
$977$	−28422.5	−0.930723	−0.465361	−	0.885121i	$-0.654076\pi$
$977$	−28422.5	−0.930723	−0.465361	+	0.885121i	$0.654076\pi$
$978$	8788.56	0.287349
$979$	−6825.56	−0.222825
$980$	4244.90	0.138366
$981$	−16528.7	−0.537941
$982$	−9.72827	−0.000316132 0
$983$	−16412.9	−0.532543	−0.266271	−	0.963898i	$-0.585792\pi$
$983$	−16412.9	−0.532543	−0.266271	+	0.963898i	$0.585792\pi$
$984$	−8052.01	−0.260862
$985$	−62937.8	−2.03590
$986$	−4134.98	−0.133554
$987$	2946.84	0.0950344
$988$	−37153.6	−1.19637
$989$	−2796.20	−0.0899029
$990$	2993.82	0.0961108
$991$	−34696.2	−1.11217	−0.556085	−	0.831126i	$-0.687697\pi$
$991$	−34696.2	−1.11217	−0.556085	+	0.831126i	$0.687697\pi$
$992$	−5309.91	−0.169949
$993$	1341.12	0.0428592
$994$	−4837.06	−0.154348
$995$	−81277.7	−2.58962
$996$	1670.98	0.0531595
$997$	9210.31	0.292571	0.146286	−	0.989242i	$-0.453268\pi$
$997$	9210.31	0.292571	0.146286	+	0.989242i	$0.453268\pi$
$998$	41318.5	1.31054
$999$	−7898.98	−0.250163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.m.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.m.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.6576 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -43.3153 q^{10} -7.67965 q^{11} -12.0000 q^{12} +63.7565 q^{13} +14.0000 q^{14} -64.9729 q^{15} +16.0000 q^{16} +9.23862 q^{17} -18.0000 q^{18} -145.686 q^{19} +86.6306 q^{20} +21.0000 q^{21} +15.3593 q^{22} -23.0000 q^{23} +24.0000 q^{24} +344.054 q^{25} -127.513 q^{26} -27.0000 q^{27} -28.0000 q^{28} +223.788 q^{29} +129.946 q^{30} +165.935 q^{31} -32.0000 q^{32} +23.0389 q^{33} -18.4772 q^{34} -151.604 q^{35} +36.0000 q^{36} +292.555 q^{37} +291.371 q^{38} -191.269 q^{39} -173.261 q^{40} -335.500 q^{41} -42.0000 q^{42} +121.574 q^{43} -30.7186 q^{44} +194.919 q^{45} +46.0000 q^{46} +140.326 q^{47} -48.0000 q^{48} +49.0000 q^{49} -688.107 q^{50} -27.7159 q^{51} +255.026 q^{52} -91.7378 q^{53} +54.0000 q^{54} -166.323 q^{55} +56.0000 q^{56} +437.057 q^{57} -447.576 q^{58} +10.3736 q^{59} -259.892 q^{60} +10.9004 q^{61} -331.869 q^{62} -63.0000 q^{63} +64.0000 q^{64} +1380.81 q^{65} -46.0779 q^{66} -444.657 q^{67} +36.9545 q^{68} +69.0000 q^{69} +303.207 q^{70} -345.504 q^{71} -72.0000 q^{72} +283.982 q^{73} -585.110 q^{74} -1032.16 q^{75} -582.743 q^{76} +53.7575 q^{77} +382.539 q^{78} -308.066 q^{79} +346.522 q^{80} +81.0000 q^{81} +671.001 q^{82} -139.248 q^{83} +84.0000 q^{84} +200.087 q^{85} -243.148 q^{86} -671.364 q^{87} +61.4372 q^{88} +888.786 q^{89} -389.838 q^{90} -446.295 q^{91} -92.0000 q^{92} -497.804 q^{93} -280.651 q^{94} -3155.21 q^{95} +96.0000 q^{96} -778.098 q^{97} -98.0000 q^{98} -69.1168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

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