LMFDB - Embedded newform 966.4.a.r.1.6

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 411x^{4} + 1741x^{3} + 37570x^{2} - 116091x - 993528 $ x^6 - 2x^5 - 411x^4 + 1741x^3 + 37570x^2 - 116091*x - 993528
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$12.6646$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.6646 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.6646 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +31.3293 q^{10} -41.0616 q^{11} +12.0000 q^{12} -14.2437 q^{13} +14.0000 q^{14} +46.9939 q^{15} +16.0000 q^{16} +78.4383 q^{17} +18.0000 q^{18} +25.2024 q^{19} +62.6585 q^{20} +21.0000 q^{21} -82.1233 q^{22} +23.0000 q^{23} +24.0000 q^{24} +120.381 q^{25} -28.4874 q^{26} +27.0000 q^{27} +28.0000 q^{28} +170.311 q^{29} +93.9878 q^{30} -43.3112 q^{31} +32.0000 q^{32} -123.185 q^{33} +156.877 q^{34} +109.652 q^{35} +36.0000 q^{36} +41.2032 q^{37} +50.4049 q^{38} -42.7311 q^{39} +125.317 q^{40} -34.6183 q^{41} +42.0000 q^{42} +494.062 q^{43} -164.247 q^{44} +140.982 q^{45} +46.0000 q^{46} +346.986 q^{47} +48.0000 q^{48} +49.0000 q^{49} +240.761 q^{50} +235.315 q^{51} -56.9749 q^{52} -507.897 q^{53} +54.0000 q^{54} -643.215 q^{55} +56.0000 q^{56} +75.6073 q^{57} +340.622 q^{58} +466.829 q^{59} +187.976 q^{60} -58.6216 q^{61} -86.6223 q^{62} +63.0000 q^{63} +64.0000 q^{64} -223.123 q^{65} -246.370 q^{66} +880.363 q^{67} +313.753 q^{68} +69.0000 q^{69} +219.305 q^{70} -954.844 q^{71} +72.0000 q^{72} -1187.49 q^{73} +82.4064 q^{74} +361.142 q^{75} +100.810 q^{76} -287.431 q^{77} -85.4623 q^{78} -545.186 q^{79} +250.634 q^{80} +81.0000 q^{81} -69.2366 q^{82} -544.181 q^{83} +84.0000 q^{84} +1228.71 q^{85} +988.125 q^{86} +510.934 q^{87} -328.493 q^{88} -1160.71 q^{89} +281.963 q^{90} -99.7060 q^{91} +92.0000 q^{92} -129.934 q^{93} +693.973 q^{94} +394.787 q^{95} +96.0000 q^{96} -1543.79 q^{97} +98.0000 q^{98} -369.555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 79 q^{11} + 72 q^{12} + 52 q^{13} + 84 q^{14} + 60 q^{15} + 96 q^{16} + 140 q^{17} + 108 q^{18} + 93 q^{19} + 80 q^{20} + 126 q^{21} + 158 q^{22} + 138 q^{23} + 144 q^{24} + 142 q^{25} + 104 q^{26} + 162 q^{27} + 168 q^{28} + 143 q^{29} + 120 q^{30} + 130 q^{31} + 192 q^{32} + 237 q^{33} + 280 q^{34} + 140 q^{35} + 216 q^{36} + 151 q^{37} + 186 q^{38} + 156 q^{39} + 160 q^{40} + 412 q^{41} + 252 q^{42} + 250 q^{43} + 316 q^{44} + 180 q^{45} + 276 q^{46} + 666 q^{47} + 288 q^{48} + 294 q^{49} + 284 q^{50} + 420 q^{51} + 208 q^{52} - 96 q^{53} + 324 q^{54} + 51 q^{55} + 336 q^{56} + 279 q^{57} + 286 q^{58} + 514 q^{59} + 240 q^{60} + 422 q^{61} + 260 q^{62} + 378 q^{63} + 384 q^{64} + 277 q^{65} + 474 q^{66} + 669 q^{67} + 560 q^{68} + 414 q^{69} + 280 q^{70} - 357 q^{71} + 432 q^{72} + 430 q^{73} + 302 q^{74} + 426 q^{75} + 372 q^{76} + 553 q^{77} + 312 q^{78} + 750 q^{79} + 320 q^{80} + 486 q^{81} + 824 q^{82} + 222 q^{83} + 504 q^{84} + 601 q^{85} + 500 q^{86} + 429 q^{87} + 632 q^{88} + 763 q^{89} + 360 q^{90} + 364 q^{91} + 552 q^{92} + 390 q^{93} + 1332 q^{94} - 541 q^{95} + 576 q^{96} + 575 q^{97} + 588 q^{98} + 711 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 79 * q^11 + 72 * q^12 + 52 * q^13 + 84 * q^14 + 60 * q^15 + 96 * q^16 + 140 * q^17 + 108 * q^18 + 93 * q^19 + 80 * q^20 + 126 * q^21 + 158 * q^22 + 138 * q^23 + 144 * q^24 + 142 * q^25 + 104 * q^26 + 162 * q^27 + 168 * q^28 + 143 * q^29 + 120 * q^30 + 130 * q^31 + 192 * q^32 + 237 * q^33 + 280 * q^34 + 140 * q^35 + 216 * q^36 + 151 * q^37 + 186 * q^38 + 156 * q^39 + 160 * q^40 + 412 * q^41 + 252 * q^42 + 250 * q^43 + 316 * q^44 + 180 * q^45 + 276 * q^46 + 666 * q^47 + 288 * q^48 + 294 * q^49 + 284 * q^50 + 420 * q^51 + 208 * q^52 - 96 * q^53 + 324 * q^54 + 51 * q^55 + 336 * q^56 + 279 * q^57 + 286 * q^58 + 514 * q^59 + 240 * q^60 + 422 * q^61 + 260 * q^62 + 378 * q^63 + 384 * q^64 + 277 * q^65 + 474 * q^66 + 669 * q^67 + 560 * q^68 + 414 * q^69 + 280 * q^70 - 357 * q^71 + 432 * q^72 + 430 * q^73 + 302 * q^74 + 426 * q^75 + 372 * q^76 + 553 * q^77 + 312 * q^78 + 750 * q^79 + 320 * q^80 + 486 * q^81 + 824 * q^82 + 222 * q^83 + 504 * q^84 + 601 * q^85 + 500 * q^86 + 429 * q^87 + 632 * q^88 + 763 * q^89 + 360 * q^90 + 364 * q^91 + 552 * q^92 + 390 * q^93 + 1332 * q^94 - 541 * q^95 + 576 * q^96 + 575 * q^97 + 588 * q^98 + 711 * 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
$5$	15.6646	1.40109	0.700544	−	0.713610i	$-0.252941\pi$
$5$	15.6646	1.40109	0.700544	+	0.713610i	$0.252941\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	31.3293	0.990718
$11$	−41.0616	−1.12550	−0.562752	−	0.826626i	$-0.690257\pi$
$11$	−41.0616	−1.12550	−0.562752	+	0.826626i	$0.690257\pi$
$12$	12.0000	0.288675
$13$	−14.2437	−0.303884	−0.151942	−	0.988389i	$-0.548553\pi$
$13$	−14.2437	−0.303884	−0.151942	+	0.988389i	$0.548553\pi$
$14$	14.0000	0.267261
$15$	46.9939	0.808918
$16$	16.0000	0.250000
$17$	78.4383	1.11906	0.559532	−	0.828809i	$-0.310981\pi$
$17$	78.4383	1.11906	0.559532	+	0.828809i	$0.310981\pi$
$18$	18.0000	0.235702
$19$	25.2024	0.304307	0.152154	−	0.988357i	$-0.451379\pi$
$19$	25.2024	0.304307	0.152154	+	0.988357i	$0.451379\pi$
$20$	62.6585	0.700544
$21$	21.0000	0.218218
$22$	−82.1233	−0.795852
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	24.0000	0.204124
$25$	120.381	0.963046
$26$	−28.4874	−0.214879
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	170.311	1.09055	0.545276	−	0.838257i	$-0.316425\pi$
$29$	170.311	1.09055	0.545276	+	0.838257i	$0.316425\pi$
$30$	93.9878	0.571991
$31$	−43.3112	−0.250933	−0.125466	−	0.992098i	$-0.540043\pi$
$31$	−43.3112	−0.250933	−0.125466	+	0.992098i	$0.540043\pi$
$32$	32.0000	0.176777
$33$	−123.185	−0.649810
$34$	156.877	0.791297
$35$	109.652	0.529561
$36$	36.0000	0.166667
$37$	41.2032	0.183075	0.0915373	−	0.995802i	$-0.470822\pi$
$37$	41.2032	0.183075	0.0915373	+	0.995802i	$0.470822\pi$
$38$	50.4049	0.215178
$39$	−42.7311	−0.175448
$40$	125.317	0.495359
$41$	−34.6183	−0.131865	−0.0659325	−	0.997824i	$-0.521002\pi$
$41$	−34.6183	−0.131865	−0.0659325	+	0.997824i	$0.521002\pi$
$42$	42.0000	0.154303
$43$	494.062	1.75218	0.876091	−	0.482146i	$-0.160143\pi$
$43$	494.062	1.75218	0.876091	+	0.482146i	$0.160143\pi$
$44$	−164.247	−0.562752
$45$	140.982	0.467029
$46$	46.0000	0.147442
$47$	346.986	1.07688	0.538438	−	0.842665i	$-0.319015\pi$
$47$	346.986	1.07688	0.538438	+	0.842665i	$0.319015\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	240.761	0.680976
$51$	235.315	0.646091
$52$	−56.9749	−0.151942
$53$	−507.897	−1.31632	−0.658161	−	0.752877i	$-0.728665\pi$
$53$	−507.897	−1.31632	−0.658161	+	0.752877i	$0.728665\pi$
$54$	54.0000	0.136083
$55$	−643.215	−1.57693
$56$	56.0000	0.133631
$57$	75.6073	0.175692
$58$	340.622	0.771137
$59$	466.829	1.03010	0.515051	−	0.857160i	$-0.327773\pi$
$59$	466.829	1.03010	0.515051	+	0.857160i	$0.327773\pi$
$60$	187.976	0.404459
$61$	−58.6216	−0.123045	−0.0615223	−	0.998106i	$-0.519596\pi$
$61$	−58.6216	−0.123045	−0.0615223	+	0.998106i	$0.519596\pi$
$62$	−86.6223	−0.177436
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−223.123	−0.425768
$66$	−246.370	−0.459485
$67$	880.363	1.60528	0.802638	−	0.596466i	$-0.203429\pi$
$67$	880.363	1.60528	0.802638	+	0.596466i	$0.203429\pi$
$68$	313.753	0.559532
$69$	69.0000	0.120386
$70$	219.305	0.374456
$71$	−954.844	−1.59604	−0.798022	−	0.602629i	$-0.794120\pi$
$71$	−954.844	−1.59604	−0.798022	+	0.602629i	$0.794120\pi$
$72$	72.0000	0.117851
$73$	−1187.49	−1.90391	−0.951953	−	0.306243i	$-0.900928\pi$
$73$	−1187.49	−1.90391	−0.951953	+	0.306243i	$0.900928\pi$
$74$	82.4064	0.129453
$75$	361.142	0.556015
$76$	100.810	0.152154
$77$	−287.431	−0.425401
$78$	−85.4623	−0.124060
$79$	−545.186	−0.776433	−0.388217	−	0.921568i	$-0.626909\pi$
$79$	−545.186	−0.776433	−0.388217	+	0.921568i	$0.626909\pi$
$80$	250.634	0.350272
$81$	81.0000	0.111111
$82$	−69.2366	−0.0932427
$83$	−544.181	−0.719658	−0.359829	−	0.933018i	$-0.617165\pi$
$83$	−544.181	−0.719658	−0.359829	+	0.933018i	$0.617165\pi$
$84$	84.0000	0.109109
$85$	1228.71	1.56791
$86$	988.125	1.23898
$87$	510.934	0.629630
$88$	−328.493	−0.397926
$89$	−1160.71	−1.38242	−0.691208	−	0.722655i	$-0.742921\pi$
$89$	−1160.71	−1.38242	−0.691208	+	0.722655i	$0.742921\pi$
$90$	281.963	0.330239
$91$	−99.7060	−0.114857
$92$	92.0000	0.104257
$93$	−129.934	−0.144876
$94$	693.973	0.761466
$95$	394.787	0.426361
$96$	96.0000	0.102062
$97$	−1543.79	−1.61596	−0.807982	−	0.589207i	$-0.799440\pi$
$97$	−1543.79	−1.61596	−0.807982	+	0.589207i	$0.799440\pi$
$98$	98.0000	0.101015
$99$	−369.555	−0.375168
$100$	481.523	0.481523
$101$	1777.99	1.75165	0.875823	−	0.482632i	$-0.160319\pi$
$101$	1777.99	1.75165	0.875823	+	0.482632i	$0.160319\pi$
$102$	470.630	0.456856
$103$	−1059.64	−1.01368	−0.506841	−	0.862040i	$-0.669187\pi$
$103$	−1059.64	−1.01368	−0.506841	+	0.862040i	$0.669187\pi$
$104$	−113.950	−0.107439
$105$	328.957	0.305742
$106$	−1015.79	−0.930780
$107$	1676.99	1.51514	0.757572	−	0.652751i	$-0.226385\pi$
$107$	1676.99	1.51514	0.757572	+	0.652751i	$0.226385\pi$
$108$	108.000	0.0962250
$109$	−1238.47	−1.08829	−0.544145	−	0.838991i	$-0.683146\pi$
$109$	−1238.47	−1.08829	−0.544145	+	0.838991i	$0.683146\pi$
$110$	−1286.43	−1.11506
$111$	123.610	0.105698
$112$	112.000	0.0944911
$113$	708.275	0.589636	0.294818	−	0.955553i	$-0.404741\pi$
$113$	708.275	0.589636	0.294818	+	0.955553i	$0.404741\pi$
$114$	151.215	0.124233
$115$	360.287	0.292147
$116$	681.245	0.545276
$117$	−128.193	−0.101295
$118$	933.658	0.728392
$119$	549.068	0.422966
$120$	375.951	0.285996
$121$	355.057	0.266760
$122$	−117.243	−0.0870057
$123$	−103.855	−0.0761323
$124$	−173.245	−0.125466
$125$	−72.3597	−0.0517764
$126$	126.000	0.0890871
$127$	1836.70	1.28331	0.641657	−	0.766992i	$-0.278247\pi$
$127$	1836.70	1.28331	0.641657	+	0.766992i	$0.278247\pi$
$128$	128.000	0.0883883
$129$	1482.19	1.01162
$130$	−446.245	−0.301064
$131$	302.385	0.201676	0.100838	−	0.994903i	$-0.467848\pi$
$131$	302.385	0.201676	0.100838	+	0.994903i	$0.467848\pi$
$132$	−492.740	−0.324905
$133$	176.417	0.115017
$134$	1760.73	1.13510
$135$	422.945	0.269639
$136$	627.506	0.395649
$137$	1809.78	1.12861	0.564306	−	0.825566i	$-0.309144\pi$
$137$	1809.78	1.12861	0.564306	+	0.825566i	$0.309144\pi$
$138$	138.000	0.0851257
$139$	−841.134	−0.513267	−0.256633	−	0.966509i	$-0.582613\pi$
$139$	−841.134	−0.513267	−0.256633	+	0.966509i	$0.582613\pi$
$140$	438.610	0.264781
$141$	1040.96	0.621734
$142$	−1909.69	−1.12857
$143$	584.870	0.342023
$144$	144.000	0.0833333
$145$	2667.86	1.52796
$146$	−2374.98	−1.34627
$147$	147.000	0.0824786
$148$	164.813	0.0915373
$149$	−2554.77	−1.40466	−0.702331	−	0.711851i	$-0.747857\pi$
$149$	−2554.77	−1.40466	−0.702331	+	0.711851i	$0.747857\pi$
$150$	722.284	0.393162
$151$	−1476.88	−0.795939	−0.397970	−	0.917399i	$-0.630285\pi$
$151$	−1476.88	−0.795939	−0.397970	+	0.917399i	$0.630285\pi$
$152$	201.620	0.107589
$153$	705.944	0.373021
$154$	−574.863	−0.300804
$155$	−678.454	−0.351579
$156$	−170.925	−0.0877238
$157$	−833.186	−0.423538	−0.211769	−	0.977320i	$-0.567922\pi$
$157$	−833.186	−0.423538	−0.211769	+	0.977320i	$0.567922\pi$
$158$	−1090.37	−0.549021
$159$	−1523.69	−0.759979
$160$	501.268	0.247680
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	576.389	0.276971	0.138485	−	0.990364i	$-0.455777\pi$
$163$	576.389	0.276971	0.138485	+	0.990364i	$0.455777\pi$
$164$	−138.473	−0.0659325
$165$	−1929.65	−0.910441
$166$	−1088.36	−0.508875
$167$	1082.11	0.501416	0.250708	−	0.968063i	$-0.419337\pi$
$167$	1082.11	0.501416	0.250708	+	0.968063i	$0.419337\pi$
$168$	168.000	0.0771517
$169$	−1994.12	−0.907654
$170$	2457.41	1.10868
$171$	226.822	0.101436
$172$	1976.25	0.876091
$173$	−2388.32	−1.04960	−0.524799	−	0.851226i	$-0.675859\pi$
$173$	−2388.32	−1.04960	−0.524799	+	0.851226i	$0.675859\pi$
$174$	1021.87	0.445216
$175$	842.665	0.363997
$176$	−656.986	−0.281376
$177$	1400.49	0.594729
$178$	−2321.42	−0.977516
$179$	2248.85	0.939033	0.469516	−	0.882924i	$-0.344428\pi$
$179$	2248.85	0.939033	0.469516	+	0.882924i	$0.344428\pi$
$180$	563.927	0.233515
$181$	2942.59	1.20840	0.604202	−	0.796831i	$-0.293492\pi$
$181$	2942.59	1.20840	0.604202	+	0.796831i	$0.293492\pi$
$182$	−199.412	−0.0812165
$183$	−175.865	−0.0710398
$184$	184.000	0.0737210
$185$	645.433	0.256504
$186$	−259.867	−0.102443
$187$	−3220.80	−1.25951
$188$	1387.95	0.538438
$189$	189.000	0.0727393
$190$	789.574	0.301483
$191$	2976.98	1.12778	0.563892	−	0.825848i	$-0.309303\pi$
$191$	2976.98	1.12778	0.563892	+	0.825848i	$0.309303\pi$
$192$	192.000	0.0721688
$193$	1442.27	0.537911	0.268955	−	0.963153i	$-0.413322\pi$
$193$	1442.27	0.537911	0.268955	+	0.963153i	$0.413322\pi$
$194$	−3087.59	−1.14266
$195$	−669.368	−0.245817
$196$	196.000	0.0714286
$197$	−4061.37	−1.46884	−0.734418	−	0.678698i	$-0.762545\pi$
$197$	−4061.37	−1.46884	−0.734418	+	0.678698i	$0.762545\pi$
$198$	−739.109	−0.265284
$199$	2311.84	0.823526	0.411763	−	0.911291i	$-0.364913\pi$
$199$	2311.84	0.823526	0.411763	+	0.911291i	$0.364913\pi$
$200$	963.046	0.340488
$201$	2641.09	0.926807
$202$	3555.97	1.23860
$203$	1192.18	0.412190
$204$	941.259	0.323046
$205$	−542.283	−0.184754
$206$	−2119.27	−0.716781
$207$	207.000	0.0695048
$208$	−227.899	−0.0759711
$209$	−1034.85	−0.342499
$210$	657.915	0.216192
$211$	−3431.33	−1.11954	−0.559769	−	0.828649i	$-0.689110\pi$
$211$	−3431.33	−1.11954	−0.559769	+	0.828649i	$0.689110\pi$
$212$	−2031.59	−0.658161
$213$	−2864.53	−0.921476
$214$	3353.98	1.07137
$215$	7739.31	2.45496
$216$	216.000	0.0680414
$217$	−303.178	−0.0948437
$218$	−2476.93	−0.769537
$219$	−3562.47	−1.09922
$220$	−2572.86	−0.788465
$221$	−1117.25	−0.340066
$222$	247.219	0.0747399
$223$	2032.48	0.610335	0.305167	−	0.952299i	$-0.401288\pi$
$223$	2032.48	0.610335	0.305167	+	0.952299i	$0.401288\pi$
$224$	224.000	0.0668153
$225$	1083.43	0.321015
$226$	1416.55	0.416936
$227$	1319.50	0.385807	0.192904	−	0.981218i	$-0.438210\pi$
$227$	1319.50	0.385807	0.192904	+	0.981218i	$0.438210\pi$
$228$	302.429	0.0878459
$229$	5358.47	1.54628	0.773138	−	0.634237i	$-0.218686\pi$
$229$	5358.47	1.54628	0.773138	+	0.634237i	$0.218686\pi$
$230$	720.573	0.206579
$231$	−862.294	−0.245605
$232$	1362.49	0.385568
$233$	−3621.29	−1.01819	−0.509096	−	0.860710i	$-0.670020\pi$
$233$	−3621.29	−1.01819	−0.509096	+	0.860710i	$0.670020\pi$
$234$	−256.387	−0.0716262
$235$	5435.41	1.50880
$236$	1867.32	0.515051
$237$	−1635.56	−0.448274
$238$	1098.14	0.299082
$239$	−2373.71	−0.642439	−0.321219	−	0.947005i	$-0.604093\pi$
$239$	−2373.71	−0.642439	−0.321219	+	0.947005i	$0.604093\pi$
$240$	751.902	0.202230
$241$	−672.233	−0.179678	−0.0898389	−	0.995956i	$-0.528635\pi$
$241$	−672.233	−0.179678	−0.0898389	+	0.995956i	$0.528635\pi$
$242$	710.115	0.188628
$243$	243.000	0.0641500
$244$	−234.486	−0.0615223
$245$	767.567	0.200155
$246$	−207.710	−0.0538337
$247$	−358.976	−0.0924742
$248$	−346.489	−0.0887181
$249$	−1632.54	−0.415495
$250$	−144.719	−0.0366114
$251$	−6176.25	−1.55315	−0.776577	−	0.630022i	$-0.783046\pi$
$251$	−6176.25	−1.55315	−0.776577	+	0.630022i	$0.783046\pi$
$252$	252.000	0.0629941
$253$	−944.417	−0.234684
$254$	3673.40	0.907439
$255$	3686.12	0.905230
$256$	256.000	0.0625000
$257$	−2384.75	−0.578821	−0.289410	−	0.957205i	$-0.593459\pi$
$257$	−2384.75	−0.578821	−0.289410	+	0.957205i	$0.593459\pi$
$258$	2964.37	0.715325
$259$	288.422	0.0691957
$260$	−892.490	−0.212884
$261$	1532.80	0.363517
$262$	604.771	0.142606
$263$	−5527.75	−1.29603	−0.648015	−	0.761628i	$-0.724400\pi$
$263$	−5527.75	−1.29603	−0.648015	+	0.761628i	$0.724400\pi$
$264$	−985.479	−0.229743
$265$	−7956.03	−1.84428
$266$	352.834	0.0813295
$267$	−3482.13	−0.798139
$268$	3521.45	0.802638
$269$	−2778.55	−0.629782	−0.314891	−	0.949128i	$-0.601968\pi$
$269$	−2778.55	−0.629782	−0.314891	+	0.949128i	$0.601968\pi$
$270$	845.890	0.190664
$271$	−3363.43	−0.753925	−0.376962	−	0.926229i	$-0.623031\pi$
$271$	−3363.43	−0.753925	−0.376962	+	0.926229i	$0.623031\pi$
$272$	1255.01	0.279766
$273$	−299.118	−0.0663130
$274$	3619.56	0.798049
$275$	−4943.03	−1.08391
$276$	276.000	0.0601929
$277$	4972.04	1.07849	0.539243	−	0.842150i	$-0.318710\pi$
$277$	4972.04	1.07849	0.539243	+	0.842150i	$0.318710\pi$
$278$	−1682.27	−0.362934
$279$	−389.801	−0.0836443
$280$	877.219	0.187228
$281$	−8372.63	−1.77747	−0.888735	−	0.458422i	$-0.848415\pi$
$281$	−8372.63	−1.77747	−0.888735	+	0.458422i	$0.848415\pi$
$282$	2081.92	0.439633
$283$	−945.767	−0.198657	−0.0993287	−	0.995055i	$-0.531670\pi$
$283$	−945.767	−0.198657	−0.0993287	+	0.995055i	$0.531670\pi$
$284$	−3819.37	−0.798022
$285$	1184.36	0.246160
$286$	1169.74	0.241847
$287$	−242.328	−0.0498403
$288$	288.000	0.0589256
$289$	1239.56	0.252302
$290$	5335.73	1.08043
$291$	−4631.38	−0.932978
$292$	−4749.96	−0.951953
$293$	−7149.99	−1.42562	−0.712810	−	0.701357i	$-0.752578\pi$
$293$	−7149.99	−1.42562	−0.712810	+	0.701357i	$0.752578\pi$
$294$	294.000	0.0583212
$295$	7312.71	1.44326
$296$	329.626	0.0647267
$297$	−1108.66	−0.216603
$298$	−5109.53	−0.993246
$299$	−327.605	−0.0633642
$300$	1444.57	0.278007
$301$	3458.44	0.662262
$302$	−2953.76	−0.562814
$303$	5333.96	1.01131
$304$	403.239	0.0760768
$305$	−918.285	−0.172396
$306$	1411.89	0.263766
$307$	162.739	0.0302541	0.0151271	−	0.999886i	$-0.495185\pi$
$307$	162.739	0.0302541	0.0151271	+	0.999886i	$0.495185\pi$
$308$	−1149.73	−0.212700
$309$	−3178.91	−0.585249
$310$	−1356.91	−0.248604
$311$	2925.90	0.533481	0.266740	−	0.963768i	$-0.414053\pi$
$311$	2925.90	0.533481	0.266740	+	0.963768i	$0.414053\pi$
$312$	−341.849	−0.0620301
$313$	−3563.52	−0.643521	−0.321760	−	0.946821i	$-0.604275\pi$
$313$	−3563.52	−0.643521	−0.321760	+	0.946821i	$0.604275\pi$
$314$	−1666.37	−0.299487
$315$	986.872	0.176520
$316$	−2180.74	−0.388217
$317$	3735.00	0.661761	0.330881	−	0.943673i	$-0.392654\pi$
$317$	3735.00	0.661761	0.330881	+	0.943673i	$0.392654\pi$
$318$	−3047.38	−0.537386
$319$	−6993.26	−1.22742
$320$	1002.54	0.175136
$321$	5030.96	0.874769
$322$	322.000	0.0557278
$323$	1976.84	0.340539
$324$	324.000	0.0555556
$325$	−1714.67	−0.292654
$326$	1152.78	0.195848
$327$	−3715.40	−0.628325
$328$	−276.946	−0.0466213
$329$	2428.90	0.407021
$330$	−3859.29	−0.643779
$331$	−10583.2	−1.75742	−0.878712	−	0.477352i	$-0.841597\pi$
$331$	−10583.2	−1.75742	−0.878712	+	0.477352i	$0.841597\pi$
$332$	−2176.72	−0.359829
$333$	370.829	0.0610249
$334$	2164.23	0.354555
$335$	13790.6	2.24913
$336$	336.000	0.0545545
$337$	4282.53	0.692237	0.346119	−	0.938191i	$-0.387499\pi$
$337$	4282.53	0.692237	0.346119	+	0.938191i	$0.387499\pi$
$338$	−3988.23	−0.641809
$339$	2124.82	0.340426
$340$	4914.83	0.783953
$341$	1778.43	0.282426
$342$	453.644	0.0717259
$343$	343.000	0.0539949
$344$	3952.50	0.619490
$345$	1080.86	0.168671
$346$	−4776.64	−0.742178
$347$	10703.3	1.65586	0.827931	−	0.560829i	$-0.189518\pi$
$347$	10703.3	1.65586	0.827931	+	0.560829i	$0.189518\pi$
$348$	2043.73	0.314815
$349$	−5781.60	−0.886767	−0.443384	−	0.896332i	$-0.646222\pi$
$349$	−5781.60	−0.886767	−0.443384	+	0.896332i	$0.646222\pi$
$350$	1685.33	0.257385
$351$	−384.580	−0.0584826
$352$	−1313.97	−0.198963
$353$	−2252.26	−0.339591	−0.169796	−	0.985479i	$-0.554311\pi$
$353$	−2252.26	−0.339591	−0.169796	+	0.985479i	$0.554311\pi$
$354$	2800.98	0.420537
$355$	−14957.3	−2.23620
$356$	−4642.84	−0.691208
$357$	1647.20	0.244200
$358$	4497.70	0.663997
$359$	−7819.05	−1.14951	−0.574754	−	0.818326i	$-0.694902\pi$
$359$	−7819.05	−1.14951	−0.574754	+	0.818326i	$0.694902\pi$
$360$	1127.85	0.165120
$361$	−6223.84	−0.907397
$362$	5885.18	0.854470
$363$	1065.17	0.154014
$364$	−398.824	−0.0574287
$365$	−18601.6	−2.66754
$366$	−351.729	−0.0502328
$367$	5845.51	0.831426	0.415713	−	0.909496i	$-0.363532\pi$
$367$	5845.51	0.831426	0.415713	+	0.909496i	$0.363532\pi$
$368$	368.000	0.0521286
$369$	−311.565	−0.0439550
$370$	1290.87	0.181375
$371$	−3555.28	−0.497523
$372$	−519.734	−0.0724380
$373$	11575.4	1.60684	0.803422	−	0.595410i	$-0.203010\pi$
$373$	11575.4	1.60684	0.803422	+	0.595410i	$0.203010\pi$
$374$	−6441.61	−0.890608
$375$	−217.079	−0.0298931
$376$	2775.89	0.380733
$377$	−2425.86	−0.331402
$378$	378.000	0.0514344
$379$	4411.89	0.597951	0.298976	−	0.954261i	$-0.403355\pi$
$379$	4411.89	0.597951	0.298976	+	0.954261i	$0.403355\pi$
$380$	1579.15	0.213181
$381$	5510.10	0.740921
$382$	5953.96	0.797464
$383$	−4878.61	−0.650875	−0.325438	−	0.945564i	$-0.605512\pi$
$383$	−4878.61	−0.650875	−0.325438	+	0.945564i	$0.605512\pi$
$384$	384.000	0.0510310
$385$	−4502.51	−0.596023
$386$	2884.54	0.380360
$387$	4446.56	0.584061
$388$	−6175.18	−0.807982
$389$	−5414.58	−0.705733	−0.352866	−	0.935674i	$-0.614793\pi$
$389$	−5414.58	−0.705733	−0.352866	+	0.935674i	$0.614793\pi$
$390$	−1338.74	−0.173819
$391$	1804.08	0.233341
$392$	392.000	0.0505076
$393$	907.156	0.116438
$394$	−8122.74	−1.03862
$395$	−8540.14	−1.08785
$396$	−1478.22	−0.187584
$397$	8484.39	1.07259	0.536296	−	0.844030i	$-0.319823\pi$
$397$	8484.39	1.07259	0.536296	+	0.844030i	$0.319823\pi$
$398$	4623.67	0.582321
$399$	529.251	0.0664053
$400$	1926.09	0.240761
$401$	14924.6	1.85860	0.929298	−	0.369332i	$-0.120413\pi$
$401$	14924.6	1.85860	0.929298	+	0.369332i	$0.120413\pi$
$402$	5282.18	0.655351
$403$	616.912	0.0762545
$404$	7111.95	0.875823
$405$	1268.84	0.155676
$406$	2384.36	0.291462
$407$	−1691.87	−0.206051
$408$	1882.52	0.228428
$409$	9025.61	1.09117	0.545584	−	0.838056i	$-0.316308\pi$
$409$	9025.61	1.09117	0.545584	+	0.838056i	$0.316308\pi$
$410$	−1084.57	−0.130641
$411$	5429.34	0.651605
$412$	−4238.55	−0.506841
$413$	3267.80	0.389342
$414$	414.000	0.0491473
$415$	−8524.39	−1.00830
$416$	−455.799	−0.0537197
$417$	−2523.40	−0.296335
$418$	−2069.71	−0.242183
$419$	−10699.8	−1.24754	−0.623770	−	0.781608i	$-0.714400\pi$
$419$	−10699.8	−1.24754	−0.623770	+	0.781608i	$0.714400\pi$
$420$	1315.83	0.152871
$421$	−2196.34	−0.254259	−0.127130	−	0.991886i	$-0.540576\pi$
$421$	−2196.34	−0.254259	−0.127130	+	0.991886i	$0.540576\pi$
$422$	−6862.66	−0.791633
$423$	3122.88	0.358959
$424$	−4063.18	−0.465390
$425$	9442.45	1.07771
$426$	−5729.06	−0.651582
$427$	−410.351	−0.0465065
$428$	6707.95	0.757572
$429$	1754.61	0.197467
$430$	15478.6	1.73592
$431$	−12038.1	−1.34537	−0.672685	−	0.739929i	$-0.734859\pi$
$431$	−12038.1	−1.34537	−0.672685	+	0.739929i	$0.734859\pi$
$432$	432.000	0.0481125
$433$	4919.60	0.546007	0.273003	−	0.962013i	$-0.411983\pi$
$433$	4919.60	0.546007	0.273003	+	0.962013i	$0.411983\pi$
$434$	−606.356	−0.0670646
$435$	8003.59	0.882167
$436$	−4953.87	−0.544145
$437$	579.656	0.0634525
$438$	−7124.94	−0.777267
$439$	1758.49	0.191180	0.0955902	−	0.995421i	$-0.469526\pi$
$439$	1758.49	0.191180	0.0955902	+	0.995421i	$0.469526\pi$
$440$	−5145.72	−0.557529
$441$	441.000	0.0476190
$442$	−2234.50	−0.240463
$443$	−7385.45	−0.792084	−0.396042	−	0.918232i	$-0.629617\pi$
$443$	−7385.45	−0.792084	−0.396042	+	0.918232i	$0.629617\pi$
$444$	494.438	0.0528491
$445$	−18182.1	−1.93689
$446$	4064.95	0.431572
$447$	−7664.30	−0.810982
$448$	448.000	0.0472456
$449$	−3349.26	−0.352029	−0.176015	−	0.984388i	$-0.556321\pi$
$449$	−3349.26	−0.352029	−0.176015	+	0.984388i	$0.556321\pi$
$450$	2166.85	0.226992
$451$	1421.48	0.148415
$452$	2833.10	0.294818
$453$	−4430.64	−0.459536
$454$	2639.00	0.272807
$455$	−1561.86	−0.160925
$456$	604.859	0.0621165
$457$	−9045.61	−0.925899	−0.462949	−	0.886385i	$-0.653209\pi$
$457$	−9045.61	−0.925899	−0.462949	+	0.886385i	$0.653209\pi$
$458$	10716.9	1.09338
$459$	2117.83	0.215364
$460$	1441.15	0.146073
$461$	−1333.76	−0.134749	−0.0673745	−	0.997728i	$-0.521462\pi$
$461$	−1333.76	−0.134749	−0.0673745	+	0.997728i	$0.521462\pi$
$462$	−1724.59	−0.173669
$463$	4055.12	0.407035	0.203518	−	0.979071i	$-0.434763\pi$
$463$	4055.12	0.407035	0.203518	+	0.979071i	$0.434763\pi$
$464$	2724.98	0.272638
$465$	−2035.36	−0.202984
$466$	−7242.59	−0.719971
$467$	7723.31	0.765294	0.382647	−	0.923895i	$-0.375013\pi$
$467$	7723.31	0.765294	0.382647	+	0.923895i	$0.375013\pi$
$468$	−512.774	−0.0506474
$469$	6162.54	0.606737
$470$	10870.8	1.06688
$471$	−2499.56	−0.244530
$472$	3734.63	0.364196
$473$	−20287.0	−1.97209
$474$	−3271.12	−0.316978
$475$	3033.89	0.293062
$476$	2196.27	0.211483
$477$	−4571.08	−0.438774
$478$	−4747.43	−0.454273
$479$	1606.26	0.153219	0.0766095	−	0.997061i	$-0.475591\pi$
$479$	1606.26	0.153219	0.0766095	+	0.997061i	$0.475591\pi$
$480$	1503.80	0.142998
$481$	−586.886	−0.0556335
$482$	−1344.47	−0.127051
$483$	483.000	0.0455016
$484$	1420.23	0.133380
$485$	−24183.0	−2.26411
$486$	486.000	0.0453609
$487$	−425.512	−0.0395930	−0.0197965	−	0.999804i	$-0.506302\pi$
$487$	−425.512	−0.0395930	−0.0197965	+	0.999804i	$0.506302\pi$
$488$	−468.972	−0.0435028
$489$	1729.17	0.159909
$490$	1535.13	0.141531
$491$	1161.29	0.106738	0.0533690	−	0.998575i	$-0.483004\pi$
$491$	1161.29	0.106738	0.0533690	+	0.998575i	$0.483004\pi$
$492$	−415.419	−0.0380662
$493$	13358.9	1.22040
$494$	−717.953	−0.0653891
$495$	−5788.94	−0.525643
$496$	−692.979	−0.0627332
$497$	−6683.90	−0.603248
$498$	−3265.08	−0.293799
$499$	−6226.43	−0.558584	−0.279292	−	0.960206i	$-0.590100\pi$
$499$	−6226.43	−0.558584	−0.279292	+	0.960206i	$0.590100\pi$
$500$	−289.439	−0.0258882
$501$	3246.34	0.289493
$502$	−12352.5	−1.09825
$503$	5054.24	0.448026	0.224013	−	0.974586i	$-0.428084\pi$
$503$	5054.24	0.448026	0.224013	+	0.974586i	$0.428084\pi$
$504$	504.000	0.0445435
$505$	27851.5	2.45421
$506$	−1888.83	−0.165947
$507$	−5982.35	−0.524034
$508$	7346.80	0.641657
$509$	−4458.15	−0.388220	−0.194110	−	0.980980i	$-0.562182\pi$
$509$	−4458.15	−0.388220	−0.194110	+	0.980980i	$0.562182\pi$
$510$	7372.24	0.640095
$511$	−8312.43	−0.719609
$512$	512.000	0.0441942
$513$	680.466	0.0585640
$514$	−4769.51	−0.409288
$515$	−16598.8	−1.42026
$516$	5928.75	0.505811
$517$	−14247.8	−1.21203
$518$	576.845	0.0489288
$519$	−7164.95	−0.605986
$520$	−1784.98	−0.150532
$521$	4257.67	0.358027	0.179013	−	0.983847i	$-0.442709\pi$
$521$	4257.67	0.358027	0.179013	+	0.983847i	$0.442709\pi$
$522$	3065.60	0.257046
$523$	−1216.85	−0.101739	−0.0508694	−	0.998705i	$-0.516199\pi$
$523$	−1216.85	−0.101739	−0.0508694	+	0.998705i	$0.516199\pi$
$524$	1209.54	0.100838
$525$	2527.99	0.210154
$526$	−11055.5	−0.916431
$527$	−3397.25	−0.280810
$528$	−1970.96	−0.162453
$529$	529.000	0.0434783
$530$	−15912.1	−1.30410
$531$	4201.46	0.343367
$532$	705.669	0.0575087
$533$	493.093	0.0400717
$534$	−6964.27	−0.564369
$535$	26269.4	2.12285
$536$	7042.91	0.567551
$537$	6746.55	0.542151
$538$	−5557.11	−0.445323
$539$	−2012.02	−0.160786
$540$	1691.78	0.134820
$541$	−17106.2	−1.35943	−0.679715	−	0.733476i	$-0.737897\pi$
$541$	−17106.2	−1.35943	−0.679715	+	0.733476i	$0.737897\pi$
$542$	−6726.85	−0.533105
$543$	8827.77	0.697672
$544$	2510.02	0.197824
$545$	−19400.1	−1.52479
$546$	−598.236	−0.0468904
$547$	5856.10	0.457749	0.228875	−	0.973456i	$-0.426495\pi$
$547$	5856.10	0.457749	0.228875	+	0.973456i	$0.426495\pi$
$548$	7239.12	0.564306
$549$	−527.594	−0.0410149
$550$	−9886.05	−0.766441
$551$	4292.26	0.331863
$552$	552.000	0.0425628
$553$	−3816.30	−0.293464
$554$	9944.08	0.762605
$555$	1936.30	0.148092
$556$	−3364.54	−0.256633
$557$	−20383.9	−1.55062	−0.775308	−	0.631584i	$-0.782405\pi$
$557$	−20383.9	−1.55062	−0.775308	+	0.631584i	$0.782405\pi$
$558$	−779.601	−0.0591454
$559$	−7037.28	−0.532460
$560$	1754.44	0.132390
$561$	−9662.41	−0.727179
$562$	−16745.3	−1.25686
$563$	−13396.6	−1.00284	−0.501419	−	0.865205i	$-0.667188\pi$
$563$	−13396.6	−1.00284	−0.501419	+	0.865205i	$0.667188\pi$
$564$	4163.84	0.310867
$565$	11094.9	0.826131
$566$	−1891.53	−0.140472
$567$	567.000	0.0419961
$568$	−7638.75	−0.564287
$569$	14019.7	1.03293	0.516465	−	0.856309i	$-0.327248\pi$
$569$	14019.7	1.03293	0.516465	+	0.856309i	$0.327248\pi$
$570$	2368.72	0.174061
$571$	−4704.66	−0.344805	−0.172403	−	0.985027i	$-0.555153\pi$
$571$	−4704.66	−0.344805	−0.172403	+	0.985027i	$0.555153\pi$
$572$	2339.48	0.171012
$573$	8930.94	0.651127
$574$	−484.656	−0.0352424
$575$	2768.76	0.200809
$576$	576.000	0.0416667
$577$	22638.1	1.63334	0.816668	−	0.577107i	$-0.195819\pi$
$577$	22638.1	1.63334	0.816668	+	0.577107i	$0.195819\pi$
$578$	2479.12	0.178405
$579$	4326.81	0.310563
$580$	10671.5	0.763979
$581$	−3809.26	−0.272005
$582$	−9262.77	−0.659715
$583$	20855.1	1.48153
$584$	−9499.92	−0.673133
$585$	−2008.10	−0.141923
$586$	−14300.0	−1.00807
$587$	4850.29	0.341044	0.170522	−	0.985354i	$-0.445455\pi$
$587$	4850.29	0.341044	0.170522	+	0.985354i	$0.445455\pi$
$588$	588.000	0.0412393
$589$	−1091.55	−0.0763607
$590$	14625.4	1.02054
$591$	−12184.1	−0.848032
$592$	659.251	0.0457687
$593$	−11984.4	−0.829915	−0.414958	−	0.909841i	$-0.636204\pi$
$593$	−11984.4	−0.829915	−0.414958	+	0.909841i	$0.636204\pi$
$594$	−2217.33	−0.153162
$595$	8600.95	0.592612
$596$	−10219.1	−0.702331
$597$	6935.51	0.475463
$598$	−655.211	−0.0448053
$599$	−13344.5	−0.910256	−0.455128	−	0.890426i	$-0.650407\pi$
$599$	−13344.5	−0.910256	−0.455128	+	0.890426i	$0.650407\pi$
$600$	2889.14	0.196581
$601$	17124.7	1.16228	0.581139	−	0.813804i	$-0.302607\pi$
$601$	17124.7	1.16228	0.581139	+	0.813804i	$0.302607\pi$
$602$	6916.87	0.468290
$603$	7923.27	0.535092
$604$	−5907.52	−0.397970
$605$	5561.84	0.373754
$606$	10667.9	0.715107
$607$	12470.8	0.833893	0.416946	−	0.908931i	$-0.363100\pi$
$607$	12470.8	0.833893	0.416946	+	0.908931i	$0.363100\pi$
$608$	806.478	0.0537944
$609$	3576.54	0.237978
$610$	−1836.57	−0.121903
$611$	−4942.37	−0.327246
$612$	2823.78	0.186511
$613$	8662.64	0.570768	0.285384	−	0.958413i	$-0.407879\pi$
$613$	8662.64	0.570768	0.285384	+	0.958413i	$0.407879\pi$
$614$	325.478	0.0213929
$615$	−1626.85	−0.106668
$616$	−2299.45	−0.150402
$617$	−20138.9	−1.31404	−0.657020	−	0.753873i	$-0.728183\pi$
$617$	−20138.9	−1.31404	−0.657020	+	0.753873i	$0.728183\pi$
$618$	−6357.82	−0.413834
$619$	−11612.2	−0.754013	−0.377006	−	0.926211i	$-0.623046\pi$
$619$	−11612.2	−0.754013	−0.377006	+	0.926211i	$0.623046\pi$
$620$	−2713.81	−0.175789
$621$	621.000	0.0401286
$622$	5851.80	0.377228
$623$	−8124.98	−0.522505
$624$	−683.698	−0.0438619
$625$	−16181.1	−1.03559
$626$	−7127.04	−0.455038
$627$	−3104.56	−0.197742
$628$	−3332.74	−0.211769
$629$	3231.91	0.204872
$630$	1973.74	0.124819
$631$	31294.9	1.97437	0.987187	−	0.159567i	$-0.0510099\pi$
$631$	31294.9	1.97437	0.987187	+	0.159567i	$0.0510099\pi$
$632$	−4361.49	−0.274511
$633$	−10294.0	−0.646365
$634$	7469.99	0.467936
$635$	28771.2	1.79803
$636$	−6094.77	−0.379990
$637$	−697.942	−0.0434120
$638$	−13986.5	−0.867918
$639$	−8593.59	−0.532014
$640$	2005.07	0.123840
$641$	−14757.6	−0.909344	−0.454672	−	0.890659i	$-0.650244\pi$
$641$	−14757.6	−0.909344	−0.454672	+	0.890659i	$0.650244\pi$
$642$	10061.9	0.618555
$643$	−23006.9	−1.41105	−0.705525	−	0.708685i	$-0.749289\pi$
$643$	−23006.9	−1.41105	−0.705525	+	0.708685i	$0.749289\pi$
$644$	644.000	0.0394055
$645$	23217.9	1.41737
$646$	3953.67	0.240797
$647$	17894.4	1.08733	0.543663	−	0.839304i	$-0.317037\pi$
$647$	17894.4	1.08733	0.543663	+	0.839304i	$0.317037\pi$
$648$	648.000	0.0392837
$649$	−19168.8	−1.15938
$650$	−3429.34	−0.206938
$651$	−909.535	−0.0547580
$652$	2305.56	0.138485
$653$	−13436.6	−0.805230	−0.402615	−	0.915369i	$-0.631899\pi$
$653$	−13436.6	−0.805230	−0.402615	+	0.915369i	$0.631899\pi$
$654$	−7430.80	−0.444293
$655$	4736.76	0.282565
$656$	−553.892	−0.0329663
$657$	−10687.4	−0.634636
$658$	4857.81	0.287807
$659$	6471.98	0.382568	0.191284	−	0.981535i	$-0.438735\pi$
$659$	6471.98	0.382568	0.191284	+	0.981535i	$0.438735\pi$
$660$	−7718.58	−0.455220
$661$	13545.5	0.797062	0.398531	−	0.917155i	$-0.369520\pi$
$661$	13545.5	0.797062	0.398531	+	0.917155i	$0.369520\pi$
$662$	−21166.5	−1.24269
$663$	−3351.76	−0.196337
$664$	−4353.44	−0.254437
$665$	2763.51	0.161149
$666$	741.657	0.0431511
$667$	3917.16	0.227396
$668$	4328.45	0.250708
$669$	6097.43	0.352377
$670$	27581.1	1.59038
$671$	2407.10	0.138487
$672$	672.000	0.0385758
$673$	9490.33	0.543574	0.271787	−	0.962357i	$-0.412385\pi$
$673$	9490.33	0.543574	0.271787	+	0.962357i	$0.412385\pi$
$674$	8565.05	0.489486
$675$	3250.28	0.185338
$676$	−7976.47	−0.453827
$677$	−1200.29	−0.0681401	−0.0340700	−	0.999419i	$-0.510847\pi$
$677$	−1200.29	−0.0681401	−0.0340700	+	0.999419i	$0.510847\pi$
$678$	4249.65	0.240718
$679$	−10806.6	−0.610777
$680$	9829.65	0.554338
$681$	3958.50	0.222746
$682$	3556.85	0.199705
$683$	−12270.6	−0.687440	−0.343720	−	0.939072i	$-0.611687\pi$
$683$	−12270.6	−0.687440	−0.343720	+	0.939072i	$0.611687\pi$
$684$	907.288	0.0507179
$685$	28349.5	1.58128
$686$	686.000	0.0381802
$687$	16075.4	0.892743
$688$	7905.00	0.438045
$689$	7234.35	0.400010
$690$	2161.72	0.119268
$691$	14926.5	0.821750	0.410875	−	0.911692i	$-0.365223\pi$
$691$	14926.5	0.821750	0.410875	+	0.911692i	$0.365223\pi$
$692$	−9553.27	−0.524799
$693$	−2586.88	−0.141800
$694$	21406.6	1.17087
$695$	−13176.1	−0.719132
$696$	4087.47	0.222608
$697$	−2715.40	−0.147565
$698$	−11563.2	−0.627039
$699$	−10863.9	−0.587854
$700$	3370.66	0.181999
$701$	2973.45	0.160208	0.0801038	−	0.996787i	$-0.474475\pi$
$701$	2973.45	0.160208	0.0801038	+	0.996787i	$0.474475\pi$
$702$	−769.161	−0.0413534
$703$	1038.42	0.0557110
$704$	−2627.94	−0.140688
$705$	16306.2	0.871104
$706$	−4504.52	−0.240127
$707$	12445.9	0.662060
$708$	5601.95	0.297365
$709$	−1065.16	−0.0564216	−0.0282108	−	0.999602i	$-0.508981\pi$
$709$	−1065.16	−0.0564216	−0.0282108	+	0.999602i	$0.508981\pi$
$710$	−29914.5	−1.58123
$711$	−4906.68	−0.258811
$712$	−9285.69	−0.488758
$713$	−996.157	−0.0523231
$714$	3294.41	0.172675
$715$	9161.77	0.479204
$716$	8995.40	0.469516
$717$	−7121.14	−0.370912
$718$	−15638.1	−0.812825
$719$	−21596.5	−1.12019	−0.560093	−	0.828430i	$-0.689234\pi$
$719$	−21596.5	−1.12019	−0.560093	+	0.828430i	$0.689234\pi$
$720$	2255.71	0.116757
$721$	−7417.46	−0.383135
$722$	−12447.7	−0.641627
$723$	−2016.70	−0.103737
$724$	11770.4	0.604202
$725$	20502.2	1.05025
$726$	2130.34	0.108904
$727$	25240.0	1.28762	0.643810	−	0.765185i	$-0.277353\pi$
$727$	25240.0	1.28762	0.643810	+	0.765185i	$0.277353\pi$
$728$	−797.648	−0.0406082
$729$	729.000	0.0370370
$730$	−37203.2	−1.88624
$731$	38753.4	1.96080
$732$	−703.459	−0.0355199
$733$	15674.9	0.789859	0.394930	−	0.918711i	$-0.370769\pi$
$733$	15674.9	0.789859	0.394930	+	0.918711i	$0.370769\pi$
$734$	11691.0	0.587907
$735$	2302.70	0.115560
$736$	736.000	0.0368605
$737$	−36149.2	−1.80675
$738$	−623.129	−0.0310809
$739$	−15214.4	−0.757336	−0.378668	−	0.925533i	$-0.623618\pi$
$739$	−15214.4	−0.757336	−0.378668	+	0.925533i	$0.623618\pi$
$740$	2581.73	0.128252
$741$	−1076.93	−0.0533900
$742$	−7110.56	−0.351802
$743$	−5724.82	−0.282669	−0.141335	−	0.989962i	$-0.545139\pi$
$743$	−5724.82	−0.282669	−0.141335	+	0.989962i	$0.545139\pi$
$744$	−1039.47	−0.0512214
$745$	−40019.5	−1.96805
$746$	23150.9	1.13621
$747$	−4897.63	−0.239886
$748$	−12883.2	−0.629755
$749$	11738.9	0.572671
$750$	−434.158	−0.0211376
$751$	−12154.2	−0.590565	−0.295282	−	0.955410i	$-0.595414\pi$
$751$	−12154.2	−0.590565	−0.295282	+	0.955410i	$0.595414\pi$
$752$	5551.78	0.269219
$753$	−18528.8	−0.896714
$754$	−4851.73	−0.234336
$755$	−23134.8	−1.11518
$756$	756.000	0.0363696
$757$	23567.7	1.13155	0.565775	−	0.824559i	$-0.308577\pi$
$757$	23567.7	1.13155	0.565775	+	0.824559i	$0.308577\pi$
$758$	8823.78	0.422815
$759$	−2833.25	−0.135495
$760$	3158.30	0.150741
$761$	−3502.26	−0.166829	−0.0834145	−	0.996515i	$-0.526583\pi$
$761$	−3502.26	−0.166829	−0.0834145	+	0.996515i	$0.526583\pi$
$762$	11020.2	0.523910
$763$	−8669.27	−0.411335
$764$	11907.9	0.563892
$765$	11058.4	0.522635
$766$	−9757.21	−0.460238
$767$	−6649.38	−0.313032
$768$	768.000	0.0360844
$769$	11792.9	0.553008	0.276504	−	0.961013i	$-0.410824\pi$
$769$	11792.9	0.553008	0.276504	+	0.961013i	$0.410824\pi$
$770$	−9005.01	−0.421452
$771$	−7154.26	−0.334182
$772$	5769.07	0.268955
$773$	39556.2	1.84054	0.920269	−	0.391286i	$-0.127970\pi$
$773$	39556.2	1.84054	0.920269	+	0.391286i	$0.127970\pi$
$774$	8893.12	0.412993
$775$	−5213.83	−0.241660
$776$	−12350.4	−0.571330
$777$	865.267	0.0399502
$778$	−10829.2	−0.499028
$779$	−872.465	−0.0401275
$780$	−2677.47	−0.122909
$781$	39207.4	1.79635
$782$	3608.16	0.164997
$783$	4598.40	0.209877
$784$	784.000	0.0357143
$785$	−13051.5	−0.593414
$786$	1814.31	0.0823338
$787$	35601.9	1.61254	0.806270	−	0.591547i	$-0.201483\pi$
$787$	35601.9	1.61254	0.806270	+	0.591547i	$0.201483\pi$
$788$	−16245.5	−0.734418
$789$	−16583.3	−0.748263
$790$	−17080.3	−0.769227
$791$	4957.92	0.222861
$792$	−2956.44	−0.132642
$793$	834.989	0.0373913
$794$	16968.8	0.758437
$795$	−23868.1	−1.06480
$796$	9247.34	0.411763
$797$	15044.7	0.668644	0.334322	−	0.942459i	$-0.391493\pi$
$797$	15044.7	0.668644	0.334322	+	0.942459i	$0.391493\pi$
$798$	1058.50	0.0469556
$799$	27217.0	1.20509
$800$	3852.18	0.170244
$801$	−10446.4	−0.460806
$802$	29849.1	1.31423
$803$	48760.3	2.14285
$804$	10564.4	0.463403
$805$	2522.01	0.110421
$806$	1233.82	0.0539201
$807$	−8335.66	−0.363605
$808$	14223.9	0.619300
$809$	14290.7	0.621054	0.310527	−	0.950565i	$-0.399495\pi$
$809$	14290.7	0.621054	0.310527	+	0.950565i	$0.399495\pi$
$810$	2537.67	0.110080
$811$	38093.6	1.64938	0.824691	−	0.565584i	$-0.191349\pi$
$811$	38093.6	1.64938	0.824691	+	0.565584i	$0.191349\pi$
$812$	4768.71	0.206095
$813$	−10090.3	−0.435279
$814$	−3383.74	−0.145700
$815$	9028.92	0.388060
$816$	3765.04	0.161523
$817$	12451.6	0.533202
$818$	18051.2	0.771572
$819$	−897.354	−0.0382858
$820$	−2169.13	−0.0923772
$821$	−25271.4	−1.07427	−0.537136	−	0.843496i	$-0.680494\pi$
$821$	−25271.4	−1.07427	−0.537136	+	0.843496i	$0.680494\pi$
$822$	10858.7	0.460754
$823$	2865.28	0.121358	0.0606788	−	0.998157i	$-0.480673\pi$
$823$	2865.28	0.121358	0.0606788	+	0.998157i	$0.480673\pi$
$824$	−8477.10	−0.358390
$825$	−14829.1	−0.625797
$826$	6535.61	0.275306
$827$	29292.8	1.23169	0.615846	−	0.787866i	$-0.288814\pi$
$827$	29292.8	1.23169	0.615846	+	0.787866i	$0.288814\pi$
$828$	828.000	0.0347524
$829$	−8064.04	−0.337848	−0.168924	−	0.985629i	$-0.554029\pi$
$829$	−8064.04	−0.337848	−0.168924	+	0.985629i	$0.554029\pi$
$830$	−17048.8	−0.712978
$831$	14916.1	0.622665
$832$	−911.598	−0.0379855
$833$	3843.47	0.159866
$834$	−5046.81	−0.209540
$835$	16950.9	0.702527
$836$	−4139.41	−0.171250
$837$	−1169.40	−0.0482920
$838$	−21399.6	−0.882144
$839$	25900.2	1.06576	0.532881	−	0.846190i	$-0.321109\pi$
$839$	25900.2	1.06576	0.532881	+	0.846190i	$0.321109\pi$
$840$	2631.66	0.108096
$841$	4616.92	0.189303
$842$	−4392.68	−0.179788
$843$	−25117.9	−1.02622
$844$	−13725.3	−0.559769
$845$	−31237.1	−1.27170
$846$	6245.75	0.253822
$847$	2485.40	0.100826
$848$	−8126.36	−0.329081
$849$	−2837.30	−0.114695
$850$	18884.9	0.762055
$851$	947.673	0.0381737
$852$	−11458.1	−0.460738
$853$	6335.92	0.254323	0.127162	−	0.991882i	$-0.459413\pi$
$853$	6335.92	0.254323	0.127162	+	0.991882i	$0.459413\pi$
$854$	−820.702	−0.0328851
$855$	3553.08	0.142120
$856$	13415.9	0.535685
$857$	−28071.1	−1.11889	−0.559446	−	0.828867i	$-0.688986\pi$
$857$	−28071.1	−1.11889	−0.559446	+	0.828867i	$0.688986\pi$
$858$	3509.22	0.139630
$859$	−24241.4	−0.962869	−0.481434	−	0.876482i	$-0.659884\pi$
$859$	−24241.4	−0.962869	−0.481434	+	0.876482i	$0.659884\pi$
$860$	30957.2	1.22748
$861$	−726.984	−0.0287753
$862$	−24076.2	−0.951320
$863$	−33031.3	−1.30290	−0.651448	−	0.758693i	$-0.725838\pi$
$863$	−33031.3	−1.30290	−0.651448	+	0.758693i	$0.725838\pi$
$864$	864.000	0.0340207
$865$	−37412.1	−1.47058
$866$	9839.20	0.386085
$867$	3718.68	0.145667
$868$	−1212.71	−0.0474218
$869$	22386.2	0.873879
$870$	16007.2	0.623786
$871$	−12539.6	−0.487818
$872$	−9907.73	−0.384769
$873$	−13894.2	−0.538655
$874$	1159.31	0.0448677
$875$	−506.518	−0.0195696
$876$	−14249.9	−0.549610
$877$	−31569.6	−1.21554	−0.607771	−	0.794112i	$-0.707936\pi$
$877$	−31569.6	−1.21554	−0.607771	+	0.794112i	$0.707936\pi$
$878$	3516.98	0.135185
$879$	−21450.0	−0.823082
$880$	−10291.4	−0.394232
$881$	14117.9	0.539892	0.269946	−	0.962875i	$-0.412994\pi$
$881$	14117.9	0.539892	0.269946	+	0.962875i	$0.412994\pi$
$882$	882.000	0.0336718
$883$	18516.7	0.705705	0.352852	−	0.935679i	$-0.385212\pi$
$883$	18516.7	0.705705	0.352852	+	0.935679i	$0.385212\pi$
$884$	−4469.01	−0.170033
$885$	21938.1	0.833268
$886$	−14770.9	−0.560088
$887$	19958.0	0.755494	0.377747	−	0.925909i	$-0.376699\pi$
$887$	19958.0	0.755494	0.377747	+	0.925909i	$0.376699\pi$
$888$	988.877	0.0373700
$889$	12856.9	0.485047
$890$	−36364.2	−1.36959
$891$	−3325.99	−0.125056
$892$	8129.90	0.305167
$893$	8744.90	0.327701
$894$	−15328.6	−0.573451
$895$	35227.4	1.31567
$896$	896.000	0.0334077
$897$	−982.816	−0.0365834
$898$	−6698.51	−0.248922
$899$	−7376.38	−0.273655
$900$	4333.71	0.160508
$901$	−39838.6	−1.47305
$902$	2842.97	0.104945
$903$	10375.3	0.382357
$904$	5666.20	0.208468
$905$	46094.6	1.69308
$906$	−8861.28	−0.324941
$907$	5992.05	0.219363	0.109682	−	0.993967i	$-0.465017\pi$
$907$	5992.05	0.219363	0.109682	+	0.993967i	$0.465017\pi$
$908$	5277.99	0.192904
$909$	16001.9	0.583882
$910$	−3123.72	−0.113791
$911$	46442.8	1.68904	0.844522	−	0.535520i	$-0.179884\pi$
$911$	46442.8	1.68904	0.844522	+	0.535520i	$0.179884\pi$
$912$	1209.72	0.0439230
$913$	22344.9	0.809978
$914$	−18091.2	−0.654709
$915$	−2754.86	−0.0995330
$916$	21433.9	0.773138
$917$	2116.70	0.0762263
$918$	4235.67	0.152285
$919$	28341.6	1.01731	0.508653	−	0.860972i	$-0.330144\pi$
$919$	28341.6	1.01731	0.508653	+	0.860972i	$0.330144\pi$
$920$	2882.29	0.103290
$921$	488.217	0.0174672
$922$	−2667.51	−0.0952819
$923$	13600.5	0.485012
$924$	−3449.18	−0.122803
$925$	4960.07	0.176309
$926$	8110.23	0.287817
$927$	−9536.73	−0.337894
$928$	5449.96	0.192784
$929$	21328.8	0.753256	0.376628	−	0.926365i	$-0.377083\pi$
$929$	21328.8	0.753256	0.376628	+	0.926365i	$0.377083\pi$
$930$	−4070.72	−0.143531
$931$	1234.92	0.0434725
$932$	−14485.2	−0.509096
$933$	8777.70	0.308005
$934$	15446.6	0.541144
$935$	−50452.7	−1.76468
$936$	−1025.55	−0.0358131
$937$	21171.3	0.738141	0.369070	−	0.929401i	$-0.379676\pi$
$937$	21171.3	0.738141	0.369070	+	0.929401i	$0.379676\pi$
$938$	12325.1	0.429028
$939$	−10690.6	−0.371537
$940$	21741.7	0.754398
$941$	36049.9	1.24888	0.624439	−	0.781074i	$-0.285328\pi$
$941$	36049.9	1.24888	0.624439	+	0.781074i	$0.285328\pi$
$942$	−4999.11	−0.172909
$943$	−796.220	−0.0274958
$944$	7469.27	0.257525
$945$	2960.62	0.101914
$946$	−40574.0	−1.39448
$947$	−53347.8	−1.83059	−0.915296	−	0.402783i	$-0.868043\pi$
$947$	−53347.8	−1.83059	−0.915296	+	0.402783i	$0.868043\pi$
$948$	−6542.23	−0.224137
$949$	16914.3	0.578567
$950$	6067.78	0.207226
$951$	11205.0	0.382068
$952$	4392.54	0.149541
$953$	38206.3	1.29866	0.649330	−	0.760507i	$-0.275049\pi$
$953$	38206.3	1.29866	0.649330	+	0.760507i	$0.275049\pi$
$954$	−9142.15	−0.310260
$955$	46633.3	1.58012
$956$	−9494.86	−0.321219
$957$	−20979.8	−0.708652
$958$	3212.52	0.108342
$959$	12668.5	0.426575
$960$	3007.61	0.101115
$961$	−27915.1	−0.937033
$962$	−1173.77	−0.0393388
$963$	15092.9	0.505048
$964$	−2688.93	−0.0898389
$965$	22592.6	0.753660
$966$	966.000	0.0321745
$967$	−34937.5	−1.16185	−0.580927	−	0.813956i	$-0.697310\pi$
$967$	−34937.5	−1.16185	−0.580927	+	0.813956i	$0.697310\pi$
$968$	2840.46	0.0943138
$969$	5930.51	0.196610
$970$	−48365.9	−1.60097
$971$	−9345.45	−0.308867	−0.154434	−	0.988003i	$-0.549355\pi$
$971$	−9345.45	−0.308867	−0.154434	+	0.988003i	$0.549355\pi$
$972$	972.000	0.0320750
$973$	−5887.94	−0.193997
$974$	−851.024	−0.0279965
$975$	−5144.00	−0.168964
$976$	−937.945	−0.0307612
$977$	−58593.9	−1.91871	−0.959357	−	0.282195i	$-0.908938\pi$
$977$	−58593.9	−1.91871	−0.959357	+	0.282195i	$0.908938\pi$
$978$	3458.33	0.113073
$979$	47660.7	1.55592
$980$	3070.27	0.100078
$981$	−11146.2	−0.362763
$982$	2322.58	0.0754752
$983$	11642.3	0.377755	0.188877	−	0.982001i	$-0.439515\pi$
$983$	11642.3	0.377755	0.188877	+	0.982001i	$0.439515\pi$
$984$	−830.839	−0.0269168
$985$	−63619.8	−2.05797
$986$	26717.8	0.862950
$987$	7286.71	0.234994
$988$	−1435.91	−0.0462371
$989$	11363.4	0.365355
$990$	−11577.9	−0.371686
$991$	−5953.15	−0.190825	−0.0954127	−	0.995438i	$-0.530417\pi$
$991$	−5953.15	−0.190825	−0.0954127	+	0.995438i	$0.530417\pi$
$992$	−1385.96	−0.0443591
$993$	−31749.7	−1.01465
$994$	−13367.8	−0.426561
$995$	36214.0	1.15383
$996$	−6530.17	−0.207747
$997$	22143.4	0.703399	0.351700	−	0.936113i	$-0.385604\pi$
$997$	22143.4	0.703399	0.351700	+	0.936113i	$0.385604\pi$
$998$	−12452.9	−0.394978
$999$	1112.49	0.0352327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.r.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.r.1.6	✓	6	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.6646 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.6646 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +31.3293 q^{10} -41.0616 q^{11} +12.0000 q^{12} -14.2437 q^{13} +14.0000 q^{14} +46.9939 q^{15} +16.0000 q^{16} +78.4383 q^{17} +18.0000 q^{18} +25.2024 q^{19} +62.6585 q^{20} +21.0000 q^{21} -82.1233 q^{22} +23.0000 q^{23} +24.0000 q^{24} +120.381 q^{25} -28.4874 q^{26} +27.0000 q^{27} +28.0000 q^{28} +170.311 q^{29} +93.9878 q^{30} -43.3112 q^{31} +32.0000 q^{32} -123.185 q^{33} +156.877 q^{34} +109.652 q^{35} +36.0000 q^{36} +41.2032 q^{37} +50.4049 q^{38} -42.7311 q^{39} +125.317 q^{40} -34.6183 q^{41} +42.0000 q^{42} +494.062 q^{43} -164.247 q^{44} +140.982 q^{45} +46.0000 q^{46} +346.986 q^{47} +48.0000 q^{48} +49.0000 q^{49} +240.761 q^{50} +235.315 q^{51} -56.9749 q^{52} -507.897 q^{53} +54.0000 q^{54} -643.215 q^{55} +56.0000 q^{56} +75.6073 q^{57} +340.622 q^{58} +466.829 q^{59} +187.976 q^{60} -58.6216 q^{61} -86.6223 q^{62} +63.0000 q^{63} +64.0000 q^{64} -223.123 q^{65} -246.370 q^{66} +880.363 q^{67} +313.753 q^{68} +69.0000 q^{69} +219.305 q^{70} -954.844 q^{71} +72.0000 q^{72} -1187.49 q^{73} +82.4064 q^{74} +361.142 q^{75} +100.810 q^{76} -287.431 q^{77} -85.4623 q^{78} -545.186 q^{79} +250.634 q^{80} +81.0000 q^{81} -69.2366 q^{82} -544.181 q^{83} +84.0000 q^{84} +1228.71 q^{85} +988.125 q^{86} +510.934 q^{87} -328.493 q^{88} -1160.71 q^{89} +281.963 q^{90} -99.7060 q^{91} +92.0000 q^{92} -129.934 q^{93} +693.973 q^{94} +394.787 q^{95} +96.0000 q^{96} -1543.79 q^{97} +98.0000 q^{98} -369.555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 79 q^{11} + 72 q^{12} + 52 q^{13} + 84 q^{14} + 60 q^{15} + 96 q^{16} + 140 q^{17} + 108 q^{18} + 93 q^{19} + 80 q^{20} + 126 q^{21} + 158 q^{22} + 138 q^{23} + 144 q^{24} + 142 q^{25} + 104 q^{26} + 162 q^{27} + 168 q^{28} + 143 q^{29} + 120 q^{30} + 130 q^{31} + 192 q^{32} + 237 q^{33} + 280 q^{34} + 140 q^{35} + 216 q^{36} + 151 q^{37} + 186 q^{38} + 156 q^{39} + 160 q^{40} + 412 q^{41} + 252 q^{42} + 250 q^{43} + 316 q^{44} + 180 q^{45} + 276 q^{46} + 666 q^{47} + 288 q^{48} + 294 q^{49} + 284 q^{50} + 420 q^{51} + 208 q^{52} - 96 q^{53} + 324 q^{54} + 51 q^{55} + 336 q^{56} + 279 q^{57} + 286 q^{58} + 514 q^{59} + 240 q^{60} + 422 q^{61} + 260 q^{62} + 378 q^{63} + 384 q^{64} + 277 q^{65} + 474 q^{66} + 669 q^{67} + 560 q^{68} + 414 q^{69} + 280 q^{70} - 357 q^{71} + 432 q^{72} + 430 q^{73} + 302 q^{74} + 426 q^{75} + 372 q^{76} + 553 q^{77} + 312 q^{78} + 750 q^{79} + 320 q^{80} + 486 q^{81} + 824 q^{82} + 222 q^{83} + 504 q^{84} + 601 q^{85} + 500 q^{86} + 429 q^{87} + 632 q^{88} + 763 q^{89} + 360 q^{90} + 364 q^{91} + 552 q^{92} + 390 q^{93} + 1332 q^{94} - 541 q^{95} + 576 q^{96} + 575 q^{97} + 588 q^{98} + 711 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 79 * q^11 + 72 * q^12 + 52 * q^13 + 84 * q^14 + 60 * q^15 + 96 * q^16 + 140 * q^17 + 108 * q^18 + 93 * q^19 + 80 * q^20 + 126 * q^21 + 158 * q^22 + 138 * q^23 + 144 * q^24 + 142 * q^25 + 104 * q^26 + 162 * q^27 + 168 * q^28 + 143 * q^29 + 120 * q^30 + 130 * q^31 + 192 * q^32 + 237 * q^33 + 280 * q^34 + 140 * q^35 + 216 * q^36 + 151 * q^37 + 186 * q^38 + 156 * q^39 + 160 * q^40 + 412 * q^41 + 252 * q^42 + 250 * q^43 + 316 * q^44 + 180 * q^45 + 276 * q^46 + 666 * q^47 + 288 * q^48 + 294 * q^49 + 284 * q^50 + 420 * q^51 + 208 * q^52 - 96 * q^53 + 324 * q^54 + 51 * q^55 + 336 * q^56 + 279 * q^57 + 286 * q^58 + 514 * q^59 + 240 * q^60 + 422 * q^61 + 260 * q^62 + 378 * q^63 + 384 * q^64 + 277 * q^65 + 474 * q^66 + 669 * q^67 + 560 * q^68 + 414 * q^69 + 280 * q^70 - 357 * q^71 + 432 * q^72 + 430 * q^73 + 302 * q^74 + 426 * q^75 + 372 * q^76 + 553 * q^77 + 312 * q^78 + 750 * q^79 + 320 * q^80 + 486 * q^81 + 824 * q^82 + 222 * q^83 + 504 * q^84 + 601 * q^85 + 500 * q^86 + 429 * q^87 + 632 * q^88 + 763 * q^89 + 360 * q^90 + 364 * q^91 + 552 * q^92 + 390 * q^93 + 1332 * q^94 - 541 * q^95 + 576 * q^96 + 575 * q^97 + 588 * q^98 + 711 * q^99

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