LMFDB - Embedded newform 966.4.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 $ x^5 - 570x^3 - 189x^2 + 63838*x + 254320
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.94452$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +2.94452 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +2.94452 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +5.88904 q^{10} +33.3030 q^{11} +12.0000 q^{12} +71.9263 q^{13} -14.0000 q^{14} +8.83356 q^{15} +16.0000 q^{16} +53.4542 q^{17} +18.0000 q^{18} -75.3776 q^{19} +11.7781 q^{20} -21.0000 q^{21} +66.6060 q^{22} -23.0000 q^{23} +24.0000 q^{24} -116.330 q^{25} +143.853 q^{26} +27.0000 q^{27} -28.0000 q^{28} +76.0785 q^{29} +17.6671 q^{30} +150.370 q^{31} +32.0000 q^{32} +99.9090 q^{33} +106.908 q^{34} -20.6116 q^{35} +36.0000 q^{36} -54.5216 q^{37} -150.755 q^{38} +215.779 q^{39} +23.5562 q^{40} -222.763 q^{41} -42.0000 q^{42} -289.007 q^{43} +133.212 q^{44} +26.5007 q^{45} -46.0000 q^{46} -36.1212 q^{47} +48.0000 q^{48} +49.0000 q^{49} -232.660 q^{50} +160.363 q^{51} +287.705 q^{52} +200.898 q^{53} +54.0000 q^{54} +98.0614 q^{55} -56.0000 q^{56} -226.133 q^{57} +152.157 q^{58} +904.079 q^{59} +35.3343 q^{60} +630.351 q^{61} +300.740 q^{62} -63.0000 q^{63} +64.0000 q^{64} +211.789 q^{65} +199.818 q^{66} +898.686 q^{67} +213.817 q^{68} -69.0000 q^{69} -41.2233 q^{70} +516.037 q^{71} +72.0000 q^{72} -662.453 q^{73} -109.043 q^{74} -348.989 q^{75} -301.510 q^{76} -233.121 q^{77} +431.558 q^{78} +1346.54 q^{79} +47.1123 q^{80} +81.0000 q^{81} -445.526 q^{82} -100.162 q^{83} -84.0000 q^{84} +157.397 q^{85} -578.013 q^{86} +228.236 q^{87} +266.424 q^{88} +82.5612 q^{89} +53.0014 q^{90} -503.484 q^{91} -92.0000 q^{92} +451.110 q^{93} -72.2423 q^{94} -221.951 q^{95} +96.0000 q^{96} -295.624 q^{97} +98.0000 q^{98} +299.727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 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 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * 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
$5$	2.94452	0.263366	0.131683	−	0.991292i	$-0.457962\pi$
$5$	2.94452	0.263366	0.131683	+	0.991292i	$0.457962\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	5.88904	0.186228
$11$	33.3030	0.912839	0.456420	−	0.889765i	$-0.349132\pi$
$11$	33.3030	0.912839	0.456420	+	0.889765i	$0.349132\pi$
$12$	12.0000	0.288675
$13$	71.9263	1.53452	0.767261	−	0.641335i	$-0.221619\pi$
$13$	71.9263	1.53452	0.767261	+	0.641335i	$0.221619\pi$
$14$	−14.0000	−0.267261
$15$	8.83356	0.152054
$16$	16.0000	0.250000
$17$	53.4542	0.762620	0.381310	−	0.924447i	$-0.375473\pi$
$17$	53.4542	0.762620	0.381310	+	0.924447i	$0.375473\pi$
$18$	18.0000	0.235702
$19$	−75.3776	−0.910148	−0.455074	−	0.890454i	$-0.650387\pi$
$19$	−75.3776	−0.910148	−0.455074	+	0.890454i	$0.650387\pi$
$20$	11.7781	0.131683
$21$	−21.0000	−0.218218
$22$	66.6060	0.645475
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−116.330	−0.930638
$26$	143.853	1.08507
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	76.0785	0.487153	0.243576	−	0.969882i	$-0.421679\pi$
$29$	76.0785	0.487153	0.243576	+	0.969882i	$0.421679\pi$
$30$	17.6671	0.107519
$31$	150.370	0.871201	0.435601	−	0.900140i	$-0.356536\pi$
$31$	150.370	0.871201	0.435601	+	0.900140i	$0.356536\pi$
$32$	32.0000	0.176777
$33$	99.9090	0.527028
$34$	106.908	0.539254
$35$	−20.6116	−0.0995430
$36$	36.0000	0.166667
$37$	−54.5216	−0.242251	−0.121126	−	0.992637i	$-0.538650\pi$
$37$	−54.5216	−0.242251	−0.121126	+	0.992637i	$0.538650\pi$
$38$	−150.755	−0.643572
$39$	215.779	0.885956
$40$	23.5562	0.0931139
$41$	−222.763	−0.848530	−0.424265	−	0.905538i	$-0.639468\pi$
$41$	−222.763	−0.848530	−0.424265	+	0.905538i	$0.639468\pi$
$42$	−42.0000	−0.154303
$43$	−289.007	−1.02496	−0.512478	−	0.858700i	$-0.671272\pi$
$43$	−289.007	−1.02496	−0.512478	+	0.858700i	$0.671272\pi$
$44$	133.212	0.456420
$45$	26.5007	0.0877887
$46$	−46.0000	−0.147442
$47$	−36.1212	−0.112102	−0.0560512	−	0.998428i	$-0.517851\pi$
$47$	−36.1212	−0.112102	−0.0560512	+	0.998428i	$0.517851\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−232.660	−0.658061
$51$	160.363	0.440299
$52$	287.705	0.767261
$53$	200.898	0.520669	0.260334	−	0.965519i	$-0.416167\pi$
$53$	200.898	0.520669	0.260334	+	0.965519i	$0.416167\pi$
$54$	54.0000	0.136083
$55$	98.0614	0.240411
$56$	−56.0000	−0.133631
$57$	−226.133	−0.525474
$58$	152.157	0.344469
$59$	904.079	1.99493	0.997467	−	0.0711347i	$-0.0226620\pi$
$59$	904.079	1.99493	0.997467	+	0.0711347i	$0.0226620\pi$
$60$	35.3343	0.0760272
$61$	630.351	1.32308	0.661542	−	0.749908i	$-0.269902\pi$
$61$	630.351	1.32308	0.661542	+	0.749908i	$0.269902\pi$
$62$	300.740	0.616032
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	211.789	0.404141
$66$	199.818	0.372665
$67$	898.686	1.63869	0.819343	−	0.573304i	$-0.194339\pi$
$67$	898.686	1.63869	0.819343	+	0.573304i	$0.194339\pi$
$68$	213.817	0.381310
$69$	−69.0000	−0.120386
$70$	−41.2233	−0.0703875
$71$	516.037	0.862567	0.431284	−	0.902216i	$-0.358061\pi$
$71$	516.037	0.862567	0.431284	+	0.902216i	$0.358061\pi$
$72$	72.0000	0.117851
$73$	−662.453	−1.06211	−0.531057	−	0.847336i	$-0.678205\pi$
$73$	−662.453	−1.06211	−0.531057	+	0.847336i	$0.678205\pi$
$74$	−109.043	−0.171298
$75$	−348.989	−0.537304
$76$	−301.510	−0.455074
$77$	−233.121	−0.345021
$78$	431.558	0.626466
$79$	1346.54	1.91769	0.958843	−	0.283938i	$-0.0916409\pi$
$79$	1346.54	1.91769	0.958843	+	0.283938i	$0.0916409\pi$
$80$	47.1123	0.0658415
$81$	81.0000	0.111111
$82$	−445.526	−0.600001
$83$	−100.162	−0.132461	−0.0662304	−	0.997804i	$-0.521097\pi$
$83$	−100.162	−0.132461	−0.0662304	+	0.997804i	$0.521097\pi$
$84$	−84.0000	−0.109109
$85$	157.397	0.200848
$86$	−578.013	−0.724753
$87$	228.236	0.281258
$88$	266.424	0.322737
$89$	82.5612	0.0983311	0.0491656	−	0.998791i	$-0.484344\pi$
$89$	82.5612	0.0983311	0.0491656	+	0.998791i	$0.484344\pi$
$90$	53.0014	0.0620760
$91$	−503.484	−0.579995
$92$	−92.0000	−0.104257
$93$	451.110	0.502988
$94$	−72.2423	−0.0792684
$95$	−221.951	−0.239702
$96$	96.0000	0.102062
$97$	−295.624	−0.309444	−0.154722	−	0.987958i	$-0.549448\pi$
$97$	−295.624	−0.309444	−0.154722	+	0.987958i	$0.549448\pi$
$98$	98.0000	0.101015
$99$	299.727	0.304280
$100$	−465.319	−0.465319
$101$	1762.47	1.73636	0.868181	−	0.496247i	$-0.165289\pi$
$101$	1762.47	1.73636	0.868181	+	0.496247i	$0.165289\pi$
$102$	320.725	0.311339
$103$	−1391.82	−1.33146	−0.665731	−	0.746192i	$-0.731880\pi$
$103$	−1391.82	−1.33146	−0.665731	+	0.746192i	$0.731880\pi$
$104$	575.411	0.542535
$105$	−61.8349	−0.0574712
$106$	401.796	0.368168
$107$	31.8292	0.0287574	0.0143787	−	0.999897i	$-0.495423\pi$
$107$	31.8292	0.0287574	0.0143787	+	0.999897i	$0.495423\pi$
$108$	108.000	0.0962250
$109$	−1391.24	−1.22254	−0.611268	−	0.791424i	$-0.709340\pi$
$109$	−1391.24	−1.22254	−0.611268	+	0.791424i	$0.709340\pi$
$110$	196.123	0.169996
$111$	−163.565	−0.139864
$112$	−112.000	−0.0944911
$113$	−524.351	−0.436520	−0.218260	−	0.975891i	$-0.570038\pi$
$113$	−524.351	−0.436520	−0.218260	+	0.975891i	$0.570038\pi$
$114$	−452.266	−0.371566
$115$	−67.7240	−0.0549156
$116$	304.314	0.243576
$117$	647.337	0.511507
$118$	1808.16	1.41063
$119$	−374.179	−0.288243
$120$	70.6685	0.0537594
$121$	−221.910	−0.166724
$122$	1260.70	0.935562
$123$	−668.289	−0.489899
$124$	601.480	0.435601
$125$	−710.601	−0.508464
$126$	−126.000	−0.0890871
$127$	46.9541	0.0328071	0.0164036	−	0.999865i	$-0.494778\pi$
$127$	46.9541	0.0328071	0.0164036	+	0.999865i	$0.494778\pi$
$128$	128.000	0.0883883
$129$	−867.020	−0.591758
$130$	423.577	0.285771
$131$	−1398.47	−0.932712	−0.466356	−	0.884597i	$-0.654433\pi$
$131$	−1398.47	−0.932712	−0.466356	+	0.884597i	$0.654433\pi$
$132$	399.636	0.263514
$133$	527.643	0.344004
$134$	1797.37	1.15873
$135$	79.5021	0.0506848
$136$	427.634	0.269627
$137$	−1970.59	−1.22890	−0.614449	−	0.788957i	$-0.710622\pi$
$137$	−1970.59	−1.22890	−0.614449	+	0.788957i	$0.710622\pi$
$138$	−138.000	−0.0851257
$139$	574.110	0.350326	0.175163	−	0.984539i	$-0.443955\pi$
$139$	574.110	0.350326	0.175163	+	0.984539i	$0.443955\pi$
$140$	−82.4466	−0.0497715
$141$	−108.363	−0.0647223
$142$	1032.07	0.609927
$143$	2395.36	1.40077
$144$	144.000	0.0833333
$145$	224.015	0.128299
$146$	−1324.91	−0.751028
$147$	147.000	0.0824786
$148$	−218.087	−0.121126
$149$	−1934.41	−1.06358	−0.531788	−	0.846877i	$-0.678480\pi$
$149$	−1934.41	−1.06358	−0.531788	+	0.846877i	$0.678480\pi$
$150$	−697.979	−0.379932
$151$	1244.37	0.670631	0.335316	−	0.942106i	$-0.391157\pi$
$151$	1244.37	0.670631	0.335316	+	0.942106i	$0.391157\pi$
$152$	−603.021	−0.321786
$153$	481.088	0.254207
$154$	−466.242	−0.243967
$155$	442.767	0.229445
$156$	863.116	0.442978
$157$	−2599.68	−1.32151	−0.660754	−	0.750603i	$-0.729763\pi$
$157$	−2599.68	−1.32151	−0.660754	+	0.750603i	$0.729763\pi$
$158$	2693.07	1.35601
$159$	602.694	0.300608
$160$	94.2247	0.0465570
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	1146.93	0.551130	0.275565	−	0.961282i	$-0.411135\pi$
$163$	1146.93	0.551130	0.275565	+	0.961282i	$0.411135\pi$
$164$	−891.052	−0.424265
$165$	294.184	0.138801
$166$	−200.325	−0.0936639
$167$	−2287.66	−1.06003	−0.530013	−	0.847989i	$-0.677813\pi$
$167$	−2287.66	−1.06003	−0.530013	+	0.847989i	$0.677813\pi$
$168$	−168.000	−0.0771517
$169$	2976.40	1.35476
$170$	314.794	0.142021
$171$	−678.398	−0.303383
$172$	−1156.03	−0.512478
$173$	1127.23	0.495388	0.247694	−	0.968838i	$-0.420327\pi$
$173$	1127.23	0.495388	0.247694	+	0.968838i	$0.420327\pi$
$174$	456.471	0.198879
$175$	814.309	0.351748
$176$	532.848	0.228210
$177$	2712.24	1.15178
$178$	165.122	0.0695306
$179$	−137.792	−0.0575366	−0.0287683	−	0.999586i	$-0.509158\pi$
$179$	−137.792	−0.0575366	−0.0287683	+	0.999586i	$0.509158\pi$
$180$	106.003	0.0438943
$181$	−1012.20	−0.415671	−0.207835	−	0.978164i	$-0.566642\pi$
$181$	−1012.20	−0.415671	−0.207835	+	0.978164i	$0.566642\pi$
$182$	−1006.97	−0.410118
$183$	1891.05	0.763883
$184$	−184.000	−0.0737210
$185$	−160.540	−0.0638008
$186$	902.220	0.355666
$187$	1780.19	0.696150
$188$	−144.485	−0.0560512
$189$	−189.000	−0.0727393
$190$	−443.902	−0.169495
$191$	−2051.91	−0.777335	−0.388667	−	0.921378i	$-0.627064\pi$
$191$	−2051.91	−0.777335	−0.388667	+	0.921378i	$0.627064\pi$
$192$	192.000	0.0721688
$193$	1127.02	0.420333	0.210167	−	0.977666i	$-0.432599\pi$
$193$	1127.02	0.420333	0.210167	+	0.977666i	$0.432599\pi$
$194$	−591.248	−0.218810
$195$	635.366	0.233331
$196$	196.000	0.0714286
$197$	103.638	0.0374817	0.0187409	−	0.999824i	$-0.494034\pi$
$197$	103.638	0.0374817	0.0187409	+	0.999824i	$0.494034\pi$
$198$	599.454	0.215158
$199$	−569.184	−0.202756	−0.101378	−	0.994848i	$-0.532325\pi$
$199$	−569.184	−0.202756	−0.101378	+	0.994848i	$0.532325\pi$
$200$	−930.638	−0.329030
$201$	2696.06	0.946095
$202$	3524.95	1.22779
$203$	−532.550	−0.184126
$204$	641.450	0.220150
$205$	−655.930	−0.223474
$206$	−2783.65	−0.941486
$207$	−207.000	−0.0695048
$208$	1150.82	0.383630
$209$	−2510.30	−0.830819
$210$	−123.670	−0.0406383
$211$	−4048.85	−1.32102	−0.660509	−	0.750819i	$-0.729659\pi$
$211$	−4048.85	−1.32102	−0.660509	+	0.750819i	$0.729659\pi$
$212$	803.592	0.260334
$213$	1548.11	0.498003
$214$	63.6584	0.0203346
$215$	−850.986	−0.269938
$216$	216.000	0.0680414
$217$	−1052.59	−0.329283
$218$	−2782.47	−0.864463
$219$	−1987.36	−0.613212
$220$	392.246	0.120205
$221$	3844.76	1.17026
$222$	−327.130	−0.0988987
$223$	965.710	0.289994	0.144997	−	0.989432i	$-0.453683\pi$
$223$	965.710	0.289994	0.144997	+	0.989432i	$0.453683\pi$
$224$	−224.000	−0.0668153
$225$	−1046.97	−0.310213
$226$	−1048.70	−0.308666
$227$	−2823.71	−0.825623	−0.412811	−	0.910817i	$-0.635453\pi$
$227$	−2823.71	−0.825623	−0.412811	+	0.910817i	$0.635453\pi$
$228$	−904.531	−0.262737
$229$	2103.54	0.607012	0.303506	−	0.952829i	$-0.401843\pi$
$229$	2103.54	0.607012	0.303506	+	0.952829i	$0.401843\pi$
$230$	−135.448	−0.0388312
$231$	−699.363	−0.199198
$232$	608.628	0.172234
$233$	2434.86	0.684604	0.342302	−	0.939590i	$-0.388793\pi$
$233$	2434.86	0.684604	0.342302	+	0.939590i	$0.388793\pi$
$234$	1294.67	0.361690
$235$	−106.359	−0.0295240
$236$	3616.32	0.997467
$237$	4039.61	1.10718
$238$	−748.359	−0.203819
$239$	2452.42	0.663739	0.331870	−	0.943325i	$-0.392321\pi$
$239$	2452.42	0.663739	0.331870	+	0.943325i	$0.392321\pi$
$240$	141.337	0.0380136
$241$	−2085.36	−0.557384	−0.278692	−	0.960381i	$-0.589901\pi$
$241$	−2085.36	−0.557384	−0.278692	+	0.960381i	$0.589901\pi$
$242$	−443.820	−0.117892
$243$	243.000	0.0641500
$244$	2521.40	0.661542
$245$	144.282	0.0376237
$246$	−1336.58	−0.346411
$247$	−5421.64	−1.39664
$248$	1202.96	0.308016
$249$	−300.487	−0.0764763
$250$	−1421.20	−0.359539
$251$	783.617	0.197058	0.0985289	−	0.995134i	$-0.468586\pi$
$251$	783.617	0.197058	0.0985289	+	0.995134i	$0.468586\pi$
$252$	−252.000	−0.0629941
$253$	−765.969	−0.190340
$254$	93.9083	0.0231981
$255$	472.191	0.115960
$256$	256.000	0.0625000
$257$	−2932.94	−0.711875	−0.355937	−	0.934510i	$-0.615838\pi$
$257$	−2932.94	−0.711875	−0.355937	+	0.934510i	$0.615838\pi$
$258$	−1734.04	−0.418436
$259$	381.651	0.0915624
$260$	847.154	0.202070
$261$	684.707	0.162384
$262$	−2796.95	−0.659527
$263$	2494.46	0.584848	0.292424	−	0.956289i	$-0.405538\pi$
$263$	2494.46	0.584848	0.292424	+	0.956289i	$0.405538\pi$
$264$	799.272	0.186333
$265$	591.548	0.137126
$266$	1055.29	0.243247
$267$	247.684	0.0567715
$268$	3594.74	0.819343
$269$	−3438.38	−0.779337	−0.389669	−	0.920955i	$-0.627410\pi$
$269$	−3438.38	−0.779337	−0.389669	+	0.920955i	$0.627410\pi$
$270$	159.004	0.0358396
$271$	−6653.18	−1.49134	−0.745668	−	0.666318i	$-0.767869\pi$
$271$	−6653.18	−1.49134	−0.745668	+	0.666318i	$0.767869\pi$
$272$	855.267	0.190655
$273$	−1510.45	−0.334860
$274$	−3941.18	−0.868962
$275$	−3874.13	−0.849523
$276$	−276.000	−0.0601929
$277$	556.075	0.120618	0.0603092	−	0.998180i	$-0.480791\pi$
$277$	556.075	0.120618	0.0603092	+	0.998180i	$0.480791\pi$
$278$	1148.22	0.247718
$279$	1353.33	0.290400
$280$	−164.893	−0.0351938
$281$	−6620.16	−1.40543	−0.702714	−	0.711472i	$-0.748029\pi$
$281$	−6620.16	−1.40543	−0.702714	+	0.711472i	$0.748029\pi$
$282$	−216.727	−0.0457656
$283$	8294.89	1.74233	0.871167	−	0.490988i	$-0.163364\pi$
$283$	8294.89	1.74233	0.871167	+	0.490988i	$0.163364\pi$
$284$	2064.15	0.431284
$285$	−665.853	−0.138392
$286$	4790.73	0.990495
$287$	1559.34	0.320714
$288$	288.000	0.0589256
$289$	−2055.65	−0.418410
$290$	448.029	0.0907214
$291$	−886.873	−0.178658
$292$	−2649.81	−0.531057
$293$	5145.52	1.02595	0.512977	−	0.858402i	$-0.328543\pi$
$293$	5145.52	1.02595	0.512977	+	0.858402i	$0.328543\pi$
$294$	294.000	0.0583212
$295$	2662.08	0.525398
$296$	−436.173	−0.0856488
$297$	899.181	0.175676
$298$	−3868.82	−0.752062
$299$	−1654.31	−0.319970
$300$	−1395.96	−0.268652
$301$	2023.05	0.387397
$302$	2488.74	0.474208
$303$	5287.42	1.00249
$304$	−1206.04	−0.227537
$305$	1856.08	0.348456
$306$	962.176	0.179751
$307$	−1701.99	−0.316409	−0.158205	−	0.987406i	$-0.550571\pi$
$307$	−1701.99	−0.316409	−0.158205	+	0.987406i	$0.550571\pi$
$308$	−932.484	−0.172510
$309$	−4175.47	−0.768720
$310$	885.535	0.162242
$311$	−9623.56	−1.75467	−0.877334	−	0.479880i	$-0.840680\pi$
$311$	−9623.56	−1.75467	−0.877334	+	0.479880i	$0.840680\pi$
$312$	1726.23	0.313233
$313$	−4845.60	−0.875047	−0.437524	−	0.899207i	$-0.644144\pi$
$313$	−4845.60	−0.875047	−0.437524	+	0.899207i	$0.644144\pi$
$314$	−5199.35	−0.934447
$315$	−185.505	−0.0331810
$316$	5386.14	0.958843
$317$	−290.347	−0.0514433	−0.0257216	−	0.999669i	$-0.508188\pi$
$317$	−290.347	−0.0514433	−0.0257216	+	0.999669i	$0.508188\pi$
$318$	1205.39	0.212562
$319$	2533.64	0.444692
$320$	188.449	0.0329207
$321$	95.4876	0.0166031
$322$	322.000	0.0557278
$323$	−4029.25	−0.694097
$324$	324.000	0.0555556
$325$	−8367.18	−1.42808
$326$	2293.85	0.389708
$327$	−4173.71	−0.705831
$328$	−1782.10	−0.300001
$329$	252.848	0.0423707
$330$	588.368	0.0981473
$331$	8780.35	1.45804	0.729021	−	0.684491i	$-0.239976\pi$
$331$	8780.35	1.45804	0.729021	+	0.684491i	$0.239976\pi$
$332$	−400.649	−0.0662304
$333$	−490.695	−0.0807505
$334$	−4575.32	−0.749552
$335$	2646.20	0.431574
$336$	−336.000	−0.0545545
$337$	4249.59	0.686913	0.343457	−	0.939169i	$-0.388402\pi$
$337$	4249.59	0.686913	0.343457	+	0.939169i	$0.388402\pi$
$338$	5952.80	0.957957
$339$	−1573.05	−0.252025
$340$	629.588	0.100424
$341$	5007.77	0.795267
$342$	−1356.80	−0.214524
$343$	−343.000	−0.0539949
$344$	−2312.05	−0.362377
$345$	−203.172	−0.0317055
$346$	2254.47	0.350292
$347$	−1210.90	−0.187333	−0.0936666	−	0.995604i	$-0.529859\pi$
$347$	−1210.90	−0.187333	−0.0936666	+	0.995604i	$0.529859\pi$
$348$	912.942	0.140629
$349$	−12420.0	−1.90495	−0.952476	−	0.304613i	$-0.901473\pi$
$349$	−12420.0	−1.90495	−0.952476	+	0.304613i	$0.901473\pi$
$350$	1628.62	0.248724
$351$	1942.01	0.295319
$352$	1065.70	0.161369
$353$	2920.86	0.440401	0.220201	−	0.975455i	$-0.429329\pi$
$353$	2920.86	0.440401	0.220201	+	0.975455i	$0.429329\pi$
$354$	5424.47	0.814428
$355$	1519.48	0.227171
$356$	330.245	0.0491656
$357$	−1122.54	−0.166417
$358$	−275.584	−0.0406845
$359$	−8083.24	−1.18835	−0.594174	−	0.804336i	$-0.702521\pi$
$359$	−8083.24	−1.18835	−0.594174	+	0.804336i	$0.702521\pi$
$360$	212.006	0.0310380
$361$	−1177.22	−0.171631
$362$	−2024.40	−0.293923
$363$	−665.729	−0.0962582
$364$	−2013.94	−0.289997
$365$	−1950.61	−0.279725
$366$	3782.11	0.540147
$367$	−2067.09	−0.294009	−0.147005	−	0.989136i	$-0.546963\pi$
$367$	−2067.09	−0.294009	−0.147005	+	0.989136i	$0.546963\pi$
$368$	−368.000	−0.0521286
$369$	−2004.87	−0.282843
$370$	−321.080	−0.0451140
$371$	−1406.29	−0.196794
$372$	1804.44	0.251494
$373$	1597.92	0.221815	0.110908	−	0.993831i	$-0.464624\pi$
$373$	1597.92	0.221815	0.110908	+	0.993831i	$0.464624\pi$
$374$	3560.37	0.492252
$375$	−2131.80	−0.293562
$376$	−288.969	−0.0396342
$377$	5472.05	0.747546
$378$	−378.000	−0.0514344
$379$	10840.4	1.46922	0.734610	−	0.678490i	$-0.237365\pi$
$379$	10840.4	1.46922	0.734610	+	0.678490i	$0.237365\pi$
$380$	−887.804	−0.119851
$381$	140.862	0.0189412
$382$	−4103.82	−0.549659
$383$	−12198.6	−1.62747	−0.813733	−	0.581239i	$-0.802568\pi$
$383$	−12198.6	−1.62747	−0.813733	+	0.581239i	$0.802568\pi$
$384$	384.000	0.0510310
$385$	−686.430	−0.0908668
$386$	2254.03	0.297221
$387$	−2601.06	−0.341652
$388$	−1182.50	−0.154722
$389$	−3120.09	−0.406671	−0.203335	−	0.979109i	$-0.565178\pi$
$389$	−3120.09	−0.406671	−0.203335	+	0.979109i	$0.565178\pi$
$390$	1270.73	0.164990
$391$	−1229.45	−0.159017
$392$	392.000	0.0505076
$393$	−4195.42	−0.538502
$394$	207.276	0.0265036
$395$	3964.90	0.505053
$396$	1198.91	0.152140
$397$	−307.495	−0.0388734	−0.0194367	−	0.999811i	$-0.506187\pi$
$397$	−307.495	−0.0388734	−0.0194367	+	0.999811i	$0.506187\pi$
$398$	−1138.37	−0.143370
$399$	1582.93	0.198611
$400$	−1861.28	−0.232660
$401$	−8087.81	−1.00720	−0.503598	−	0.863938i	$-0.667991\pi$
$401$	−8087.81	−1.00720	−0.503598	+	0.863938i	$0.667991\pi$
$402$	5392.11	0.668990
$403$	10815.6	1.33688
$404$	7049.89	0.868181
$405$	238.506	0.0292629
$406$	−1065.10	−0.130197
$407$	−1815.73	−0.221137
$408$	1282.90	0.155669
$409$	−2563.65	−0.309937	−0.154968	−	0.987919i	$-0.549528\pi$
$409$	−2563.65	−0.309937	−0.154968	+	0.987919i	$0.549528\pi$
$410$	−1311.86	−0.158020
$411$	−5911.77	−0.709504
$412$	−5567.30	−0.665731
$413$	−6328.55	−0.754014
$414$	−414.000	−0.0491473
$415$	−294.930	−0.0348857
$416$	2301.64	0.271268
$417$	1722.33	0.202261
$418$	−5020.60	−0.587478
$419$	−4312.73	−0.502842	−0.251421	−	0.967878i	$-0.580898\pi$
$419$	−4312.73	−0.502842	−0.251421	+	0.967878i	$0.580898\pi$
$420$	−247.340	−0.0287356
$421$	−9798.57	−1.13433	−0.567165	−	0.823604i	$-0.691960\pi$
$421$	−9798.57	−1.13433	−0.567165	+	0.823604i	$0.691960\pi$
$422$	−8097.71	−0.934100
$423$	−325.090	−0.0373675
$424$	1607.18	0.184084
$425$	−6218.32	−0.709724
$426$	3096.22	0.352142
$427$	−4412.46	−0.500079
$428$	127.317	0.0143787
$429$	7186.09	0.808736
$430$	−1701.97	−0.190875
$431$	295.391	0.0330127	0.0165064	−	0.999864i	$-0.494746\pi$
$431$	295.391	0.0330127	0.0165064	+	0.999864i	$0.494746\pi$
$432$	432.000	0.0481125
$433$	12791.4	1.41966	0.709831	−	0.704372i	$-0.248771\pi$
$433$	12791.4	1.41966	0.709831	+	0.704372i	$0.248771\pi$
$434$	−2105.18	−0.232838
$435$	672.044	0.0740737
$436$	−5564.95	−0.611268
$437$	1733.68	0.189779
$438$	−3974.72	−0.433606
$439$	17695.4	1.92382	0.961910	−	0.273365i	$-0.0881367\pi$
$439$	17695.4	1.92382	0.961910	+	0.273365i	$0.0881367\pi$
$440$	784.491	0.0849981
$441$	441.000	0.0476190
$442$	7689.53	0.827497
$443$	3077.45	0.330054	0.165027	−	0.986289i	$-0.447229\pi$
$443$	3077.45	0.330054	0.165027	+	0.986289i	$0.447229\pi$
$444$	−654.260	−0.0699320
$445$	243.103	0.0258971
$446$	1931.42	0.205057
$447$	−5803.23	−0.614056
$448$	−448.000	−0.0472456
$449$	−15712.1	−1.65145	−0.825726	−	0.564072i	$-0.809234\pi$
$449$	−15712.1	−1.65145	−0.825726	+	0.564072i	$0.809234\pi$
$450$	−2093.94	−0.219354
$451$	−7418.68	−0.774572
$452$	−2097.40	−0.218260
$453$	3733.11	0.387189
$454$	−5647.42	−0.583803
$455$	−1482.52	−0.152751
$456$	−1809.06	−0.185783
$457$	3434.37	0.351539	0.175769	−	0.984431i	$-0.443759\pi$
$457$	3434.37	0.351539	0.175769	+	0.984431i	$0.443759\pi$
$458$	4207.08	0.429222
$459$	1443.26	0.146766
$460$	−270.896	−0.0274578
$461$	14522.0	1.46715	0.733577	−	0.679606i	$-0.237849\pi$
$461$	14522.0	1.46715	0.733577	+	0.679606i	$0.237849\pi$
$462$	−1398.73	−0.140854
$463$	−12851.4	−1.28997	−0.644985	−	0.764196i	$-0.723136\pi$
$463$	−12851.4	−1.28997	−0.644985	+	0.764196i	$0.723136\pi$
$464$	1217.26	0.121788
$465$	1328.30	0.132470
$466$	4869.71	0.484088
$467$	−13061.3	−1.29423	−0.647116	−	0.762392i	$-0.724025\pi$
$467$	−13061.3	−1.29423	−0.647116	+	0.762392i	$0.724025\pi$
$468$	2589.35	0.255754
$469$	−6290.80	−0.619365
$470$	−212.719	−0.0208766
$471$	−7799.03	−0.762973
$472$	7232.63	0.705315
$473$	−9624.79	−0.935620
$474$	8079.22	0.782892
$475$	8768.66	0.847018
$476$	−1496.72	−0.144122
$477$	1808.08	0.173556
$478$	4904.83	0.469334
$479$	−17584.0	−1.67732	−0.838659	−	0.544657i	$-0.816660\pi$
$479$	−17584.0	−1.67732	−0.838659	+	0.544657i	$0.816660\pi$
$480$	282.674	0.0268797
$481$	−3921.54	−0.371740
$482$	−4170.71	−0.394130
$483$	483.000	0.0455016
$484$	−887.639	−0.0833620
$485$	−870.472	−0.0814971
$486$	486.000	0.0453609
$487$	10252.0	0.953923	0.476962	−	0.878924i	$-0.341738\pi$
$487$	10252.0	0.953923	0.476962	+	0.878924i	$0.341738\pi$
$488$	5042.81	0.467781
$489$	3440.78	0.318195
$490$	288.563	0.0266040
$491$	15948.2	1.46585	0.732926	−	0.680309i	$-0.238154\pi$
$491$	15948.2	1.46585	0.732926	+	0.680309i	$0.238154\pi$
$492$	−2673.16	−0.244950
$493$	4066.72	0.371512
$494$	−10843.3	−0.987574
$495$	882.553	0.0801370
$496$	2405.92	0.217800
$497$	−3612.26	−0.326020
$498$	−600.974	−0.0540769
$499$	19414.2	1.74169	0.870843	−	0.491562i	$-0.163574\pi$
$499$	19414.2	1.74169	0.870843	+	0.491562i	$0.163574\pi$
$500$	−2842.40	−0.254232
$501$	−6862.98	−0.612007
$502$	1567.23	0.139341
$503$	−14362.5	−1.27315	−0.636575	−	0.771215i	$-0.719649\pi$
$503$	−14362.5	−1.27315	−0.636575	+	0.771215i	$0.719649\pi$
$504$	−504.000	−0.0445435
$505$	5189.64	0.457299
$506$	−1531.94	−0.134591
$507$	8929.20	0.782169
$508$	187.817	0.0164036
$509$	−7843.00	−0.682976	−0.341488	−	0.939886i	$-0.610931\pi$
$509$	−7843.00	−0.682976	−0.341488	+	0.939886i	$0.610931\pi$
$510$	944.382	0.0819960
$511$	4637.17	0.401441
$512$	512.000	0.0441942
$513$	−2035.20	−0.175158
$514$	−5865.88	−0.503371
$515$	−4098.26	−0.350662
$516$	−3468.08	−0.295879
$517$	−1202.94	−0.102331
$518$	763.303	0.0647444
$519$	3381.70	0.286012
$520$	1694.31	0.142885
$521$	−14344.2	−1.20620	−0.603099	−	0.797666i	$-0.706068\pi$
$521$	−14344.2	−1.20620	−0.603099	+	0.797666i	$0.706068\pi$
$522$	1369.41	0.114823
$523$	7691.98	0.643110	0.321555	−	0.946891i	$-0.395794\pi$
$523$	7691.98	0.643110	0.321555	+	0.946891i	$0.395794\pi$
$524$	−5593.90	−0.466356
$525$	2442.93	0.203082
$526$	4988.92	0.413550
$527$	8037.90	0.664396
$528$	1598.54	0.131757
$529$	529.000	0.0434783
$530$	1183.10	0.0969630
$531$	8136.71	0.664978
$532$	2110.57	0.172002
$533$	−16022.5	−1.30209
$534$	495.367	0.0401435
$535$	93.7217	0.00757373
$536$	7189.48	0.579363
$537$	−413.376	−0.0332188
$538$	−6876.76	−0.551074
$539$	1631.85	0.130406
$540$	318.008	0.0253424
$541$	21129.9	1.67920	0.839599	−	0.543207i	$-0.182790\pi$
$541$	21129.9	1.67920	0.839599	+	0.543207i	$0.182790\pi$
$542$	−13306.4	−1.05453
$543$	−3036.61	−0.239987
$544$	1710.53	0.134814
$545$	−4096.53	−0.321974
$546$	−3020.91	−0.236782
$547$	−24249.4	−1.89549	−0.947744	−	0.319033i	$-0.896642\pi$
$547$	−24249.4	−1.89549	−0.947744	+	0.319033i	$0.896642\pi$
$548$	−7882.36	−0.614449
$549$	5673.16	0.441028
$550$	−7748.26	−0.600704
$551$	−5734.62	−0.443381
$552$	−552.000	−0.0425628
$553$	−9425.75	−0.724817
$554$	1112.15	0.0852901
$555$	−481.620	−0.0368354
$556$	2296.44	0.175163
$557$	6400.10	0.486860	0.243430	−	0.969918i	$-0.421727\pi$
$557$	6400.10	0.486860	0.243430	+	0.969918i	$0.421727\pi$
$558$	2706.66	0.205344
$559$	−20787.2	−1.57282
$560$	−329.786	−0.0248857
$561$	5340.56	0.401922
$562$	−13240.3	−0.993788
$563$	−19067.7	−1.42737	−0.713685	−	0.700467i	$-0.752975\pi$
$563$	−19067.7	−1.42737	−0.713685	+	0.700467i	$0.752975\pi$
$564$	−433.454	−0.0323612
$565$	−1543.96	−0.114964
$566$	16589.8	1.23202
$567$	−567.000	−0.0419961
$568$	4128.29	0.304964
$569$	−378.905	−0.0279165	−0.0139583	−	0.999903i	$-0.504443\pi$
$569$	−378.905	−0.0279165	−0.0139583	+	0.999903i	$0.504443\pi$
$570$	−1331.71	−0.0978579
$571$	20250.2	1.48414	0.742071	−	0.670321i	$-0.233844\pi$
$571$	20250.2	1.48414	0.742071	+	0.670321i	$0.233844\pi$
$572$	9581.45	0.700386
$573$	−6155.73	−0.448794
$574$	3118.68	0.226779
$575$	2675.59	0.194052
$576$	576.000	0.0416667
$577$	−11763.4	−0.848730	−0.424365	−	0.905491i	$-0.639503\pi$
$577$	−11763.4	−0.848730	−0.424365	+	0.905491i	$0.639503\pi$
$578$	−4111.30	−0.295861
$579$	3381.05	0.242680
$580$	896.059	0.0641497
$581$	701.136	0.0500655
$582$	−1773.75	−0.126330
$583$	6690.50	0.475287
$584$	−5299.63	−0.375514
$585$	1906.10	0.134714
$586$	10291.0	0.725459
$587$	4307.93	0.302909	0.151454	−	0.988464i	$-0.451604\pi$
$587$	4307.93	0.302909	0.151454	+	0.988464i	$0.451604\pi$
$588$	588.000	0.0412393
$589$	−11334.5	−0.792922
$590$	5324.16	0.371512
$591$	310.914	0.0216401
$592$	−872.346	−0.0605628
$593$	−3726.45	−0.258055	−0.129028	−	0.991641i	$-0.541186\pi$
$593$	−3726.45	−0.258055	−0.129028	+	0.991641i	$0.541186\pi$
$594$	1798.36	0.124222
$595$	−1101.78	−0.0759135
$596$	−7737.63	−0.531788
$597$	−1707.55	−0.117061
$598$	−3308.61	−0.226253
$599$	−1077.77	−0.0735163	−0.0367582	−	0.999324i	$-0.511703\pi$
$599$	−1077.77	−0.0735163	−0.0367582	+	0.999324i	$0.511703\pi$
$600$	−2791.92	−0.189966
$601$	9085.00	0.616614	0.308307	−	0.951287i	$-0.400238\pi$
$601$	9085.00	0.616614	0.308307	+	0.951287i	$0.400238\pi$
$602$	4046.09	0.273931
$603$	8088.17	0.546228
$604$	4977.47	0.335316
$605$	−653.418	−0.0439094
$606$	10574.8	0.708867
$607$	−21094.5	−1.41055	−0.705273	−	0.708936i	$-0.749176\pi$
$607$	−21094.5	−1.41055	−0.705273	+	0.708936i	$0.749176\pi$
$608$	−2412.08	−0.160893
$609$	−1597.65	−0.106305
$610$	3712.16	0.246395
$611$	−2598.06	−0.172023
$612$	1924.35	0.127103
$613$	11427.4	0.752931	0.376465	−	0.926431i	$-0.377139\pi$
$613$	11427.4	0.752931	0.376465	+	0.926431i	$0.377139\pi$
$614$	−3403.98	−0.223735
$615$	−1967.79	−0.129023
$616$	−1864.97	−0.121983
$617$	10113.8	0.659911	0.329955	−	0.943997i	$-0.392966\pi$
$617$	10113.8	0.659911	0.329955	+	0.943997i	$0.392966\pi$
$618$	−8350.95	−0.543567
$619$	−13563.4	−0.880706	−0.440353	−	0.897825i	$-0.645147\pi$
$619$	−13563.4	−0.880706	−0.440353	+	0.897825i	$0.645147\pi$
$620$	1771.07	0.114722
$621$	−621.000	−0.0401286
$622$	−19247.1	−1.24074
$623$	−577.928	−0.0371657
$624$	3452.46	0.221489
$625$	12448.8	0.796726
$626$	−9691.21	−0.618752
$627$	−7530.90	−0.479673
$628$	−10398.7	−0.660754
$629$	−2914.41	−0.184746
$630$	−371.010	−0.0234625
$631$	−2862.30	−0.180580	−0.0902902	−	0.995915i	$-0.528779\pi$
$631$	−2862.30	−0.180580	−0.0902902	+	0.995915i	$0.528779\pi$
$632$	10772.3	0.678004
$633$	−12146.6	−0.762690
$634$	−580.694	−0.0363759
$635$	138.257	0.00864028
$636$	2410.77	0.150304
$637$	3524.39	0.219217
$638$	5067.29	0.314445
$639$	4644.33	0.287522
$640$	376.899	0.0232785
$641$	1986.61	0.122413	0.0612064	−	0.998125i	$-0.480505\pi$
$641$	1986.61	0.122413	0.0612064	+	0.998125i	$0.480505\pi$
$642$	190.975	0.0117402
$643$	−6395.67	−0.392256	−0.196128	−	0.980578i	$-0.562837\pi$
$643$	−6395.67	−0.392256	−0.196128	+	0.980578i	$0.562837\pi$
$644$	644.000	0.0394055
$645$	−2552.96	−0.155849
$646$	−8058.50	−0.490801
$647$	−9918.22	−0.602667	−0.301333	−	0.953519i	$-0.597432\pi$
$647$	−9918.22	−0.602667	−0.301333	+	0.953519i	$0.597432\pi$
$648$	648.000	0.0392837
$649$	30108.6	1.82105
$650$	−16734.4	−1.00981
$651$	−3157.77	−0.190112
$652$	4587.71	0.275565
$653$	2677.52	0.160459	0.0802294	−	0.996776i	$-0.474435\pi$
$653$	2677.52	0.160459	0.0802294	+	0.996776i	$0.474435\pi$
$654$	−8347.42	−0.499098
$655$	−4117.84	−0.245645
$656$	−3564.21	−0.212133
$657$	−5962.08	−0.354038
$658$	505.696	0.0299606
$659$	17641.4	1.04281	0.521405	−	0.853309i	$-0.325408\pi$
$659$	17641.4	1.04281	0.521405	+	0.853309i	$0.325408\pi$
$660$	1176.74	0.0694006
$661$	18089.5	1.06445	0.532224	−	0.846604i	$-0.321356\pi$
$661$	18089.5	1.06445	0.532224	+	0.846604i	$0.321356\pi$
$662$	17560.7	1.03099
$663$	11534.3	0.675648
$664$	−801.299	−0.0468320
$665$	1553.66	0.0905988
$666$	−981.389	−0.0570992
$667$	−1749.81	−0.101578
$668$	−9150.64	−0.530013
$669$	2897.13	0.167428
$670$	5292.40	0.305169
$671$	20992.6	1.20776
$672$	−672.000	−0.0385758
$673$	7886.75	0.451727	0.225863	−	0.974159i	$-0.427480\pi$
$673$	7886.75	0.451727	0.225863	+	0.974159i	$0.427480\pi$
$674$	8499.18	0.485721
$675$	−3140.90	−0.179101
$676$	11905.6	0.677378
$677$	3790.70	0.215197	0.107599	−	0.994194i	$-0.465684\pi$
$677$	3790.70	0.215197	0.107599	+	0.994194i	$0.465684\pi$
$678$	−3146.10	−0.178209
$679$	2069.37	0.116959
$680$	1259.18	0.0710106
$681$	−8471.14	−0.476674
$682$	10015.5	0.562339
$683$	25479.3	1.42743	0.713717	−	0.700435i	$-0.247010\pi$
$683$	25479.3	1.42743	0.713717	+	0.700435i	$0.247010\pi$
$684$	−2713.59	−0.151691
$685$	−5802.45	−0.323650
$686$	−686.000	−0.0381802
$687$	6310.62	0.350459
$688$	−4624.11	−0.256239
$689$	14449.8	0.798977
$690$	−406.344	−0.0224192
$691$	25749.2	1.41758	0.708790	−	0.705420i	$-0.249242\pi$
$691$	25749.2	1.41758	0.708790	+	0.705420i	$0.249242\pi$
$692$	4508.94	0.247694
$693$	−2098.09	−0.115007
$694$	−2421.80	−0.132465
$695$	1690.48	0.0922640
$696$	1825.88	0.0994396
$697$	−11907.6	−0.647106
$698$	−24840.0	−1.34700
$699$	7304.57	0.395256
$700$	3257.23	0.175874
$701$	−30576.6	−1.64745	−0.823726	−	0.566988i	$-0.808108\pi$
$701$	−30576.6	−1.64745	−0.823726	+	0.566988i	$0.808108\pi$
$702$	3884.02	0.208822
$703$	4109.71	0.220485
$704$	2131.39	0.114105
$705$	−319.078	−0.0170457
$706$	5841.72	0.311411
$707$	−12337.3	−0.656283
$708$	10848.9	0.575888
$709$	3594.18	0.190384	0.0951921	−	0.995459i	$-0.469653\pi$
$709$	3594.18	0.190384	0.0951921	+	0.995459i	$0.469653\pi$
$710$	3038.96	0.160634
$711$	12118.8	0.639228
$712$	660.490	0.0347653
$713$	−3458.51	−0.181658
$714$	−2245.08	−0.117675
$715$	7053.20	0.368916
$716$	−551.167	−0.0287683
$717$	7357.25	0.383210
$718$	−16166.5	−0.840290
$719$	−18314.9	−0.949974	−0.474987	−	0.879993i	$-0.657547\pi$
$719$	−18314.9	−0.949974	−0.474987	+	0.879993i	$0.657547\pi$
$720$	424.011	0.0219472
$721$	9742.77	0.503245
$722$	−2354.43	−0.121361
$723$	−6256.07	−0.321806
$724$	−4048.81	−0.207835
$725$	−8850.20	−0.453363
$726$	−1331.46	−0.0680648
$727$	12672.9	0.646511	0.323255	−	0.946312i	$-0.395223\pi$
$727$	12672.9	0.646511	0.323255	+	0.946312i	$0.395223\pi$
$728$	−4027.88	−0.205059
$729$	729.000	0.0370370
$730$	−3901.21	−0.197795
$731$	−15448.6	−0.781652
$732$	7564.21	0.381942
$733$	18048.3	0.909454	0.454727	−	0.890631i	$-0.349737\pi$
$733$	18048.3	0.909454	0.454727	+	0.890631i	$0.349737\pi$
$734$	−4134.18	−0.207896
$735$	432.845	0.0217221
$736$	−736.000	−0.0368605
$737$	29928.9	1.49586
$738$	−4009.73	−0.200000
$739$	31405.8	1.56330	0.781652	−	0.623715i	$-0.214377\pi$
$739$	31405.8	1.56330	0.781652	+	0.623715i	$0.214377\pi$
$740$	−642.160	−0.0319004
$741$	−16264.9	−0.806351
$742$	−2812.57	−0.139155
$743$	−23718.8	−1.17114	−0.585571	−	0.810621i	$-0.699129\pi$
$743$	−23718.8	−1.17114	−0.585571	+	0.810621i	$0.699129\pi$
$744$	3608.88	0.177833
$745$	−5695.91	−0.280110
$746$	3195.84	0.156847
$747$	−901.461	−0.0441536
$748$	7120.74	0.348075
$749$	−222.804	−0.0108693
$750$	−4263.60	−0.207580
$751$	4139.21	0.201121	0.100561	−	0.994931i	$-0.467936\pi$
$751$	4139.21	0.201121	0.100561	+	0.994931i	$0.467936\pi$
$752$	−577.938	−0.0280256
$753$	2350.85	0.113771
$754$	10944.1	0.528595
$755$	3664.07	0.176621
$756$	−756.000	−0.0363696
$757$	−7001.52	−0.336162	−0.168081	−	0.985773i	$-0.553757\pi$
$757$	−7001.52	−0.336162	−0.168081	+	0.985773i	$0.553757\pi$
$758$	21680.8	1.03890
$759$	−2297.91	−0.109893
$760$	−1775.61	−0.0847474
$761$	−36988.0	−1.76191	−0.880955	−	0.473200i	$-0.843099\pi$
$761$	−36988.0	−1.76191	−0.880955	+	0.473200i	$0.843099\pi$
$762$	281.725	0.0133935
$763$	9738.66	0.462075
$764$	−8207.63	−0.388667
$765$	1416.57	0.0669494
$766$	−24397.2	−1.15079
$767$	65027.1	3.06127
$768$	768.000	0.0360844
$769$	2125.31	0.0996626	0.0498313	−	0.998758i	$-0.484132\pi$
$769$	2125.31	0.0996626	0.0498313	+	0.998758i	$0.484132\pi$
$770$	−1372.86	−0.0642525
$771$	−8798.82	−0.411001
$772$	4508.06	0.210167
$773$	−19747.6	−0.918851	−0.459425	−	0.888216i	$-0.651945\pi$
$773$	−19747.6	−0.918851	−0.459425	+	0.888216i	$0.651945\pi$
$774$	−5202.12	−0.241584
$775$	−17492.5	−0.810773
$776$	−2364.99	−0.109405
$777$	1144.95	0.0528636
$778$	−6240.18	−0.287560
$779$	16791.3	0.772288
$780$	2541.46	0.116665
$781$	17185.6	0.787385
$782$	−2458.89	−0.112442
$783$	2054.12	0.0937525
$784$	784.000	0.0357143
$785$	−7654.80	−0.348040
$786$	−8390.85	−0.380778
$787$	−25946.4	−1.17521	−0.587604	−	0.809149i	$-0.699929\pi$
$787$	−25946.4	−1.17521	−0.587604	+	0.809149i	$0.699929\pi$
$788$	414.552	0.0187409
$789$	7483.38	0.337662
$790$	7929.81	0.357126
$791$	3670.45	0.164989
$792$	2397.82	0.107579
$793$	45338.8	2.03030
$794$	−614.990	−0.0274876
$795$	1774.64	0.0791700
$796$	−2276.74	−0.101378
$797$	−25491.1	−1.13293	−0.566463	−	0.824087i	$-0.691689\pi$
$797$	−25491.1	−1.13293	−0.566463	+	0.824087i	$0.691689\pi$
$798$	3165.86	0.140439
$799$	−1930.83	−0.0854916
$800$	−3722.55	−0.164515
$801$	743.051	0.0327770
$802$	−16175.6	−0.712196
$803$	−22061.7	−0.969539
$804$	10784.2	0.473048
$805$	474.068	0.0207561
$806$	21631.1	0.945315
$807$	−10315.1	−0.449950
$808$	14099.8	0.613897
$809$	2372.35	0.103100	0.0515498	−	0.998670i	$-0.483584\pi$
$809$	2372.35	0.103100	0.0515498	+	0.998670i	$0.483584\pi$
$810$	477.012	0.0206920
$811$	−16891.1	−0.731350	−0.365675	−	0.930743i	$-0.619162\pi$
$811$	−16891.1	−0.731350	−0.365675	+	0.930743i	$0.619162\pi$
$812$	−2130.20	−0.0920632
$813$	−19959.5	−0.861023
$814$	−3631.47	−0.156367
$815$	3377.15	0.145149
$816$	2565.80	0.110075
$817$	21784.6	0.932861
$818$	−5127.29	−0.219158
$819$	−4531.36	−0.193332
$820$	−2623.72	−0.111737
$821$	−1307.96	−0.0556006	−0.0278003	−	0.999613i	$-0.508850\pi$
$821$	−1307.96	−0.0556006	−0.0278003	+	0.999613i	$0.508850\pi$
$822$	−11823.5	−0.501695
$823$	20512.2	0.868784	0.434392	−	0.900724i	$-0.356963\pi$
$823$	20512.2	0.868784	0.434392	+	0.900724i	$0.356963\pi$
$824$	−11134.6	−0.470743
$825$	−11622.4	−0.490473
$826$	−12657.1	−0.533168
$827$	−39485.2	−1.66026	−0.830129	−	0.557571i	$-0.811733\pi$
$827$	−39485.2	−1.66026	−0.830129	+	0.557571i	$0.811733\pi$
$828$	−828.000	−0.0347524
$829$	9471.20	0.396801	0.198401	−	0.980121i	$-0.436425\pi$
$829$	9471.20	0.396801	0.198401	+	0.980121i	$0.436425\pi$
$830$	−589.860	−0.0246679
$831$	1668.22	0.0696391
$832$	4603.29	0.191815
$833$	2619.26	0.108946
$834$	3444.66	0.143020
$835$	−6736.07	−0.279175
$836$	−10041.2	−0.415409
$837$	4059.99	0.167663
$838$	−8625.46	−0.355563
$839$	2416.73	0.0994455	0.0497228	−	0.998763i	$-0.484166\pi$
$839$	2416.73	0.0994455	0.0497228	+	0.998763i	$0.484166\pi$
$840$	−494.680	−0.0203191
$841$	−18601.1	−0.762682
$842$	−19597.1	−0.802093
$843$	−19860.5	−0.811425
$844$	−16195.4	−0.660509
$845$	8764.07	0.356797
$846$	−650.181	−0.0264228
$847$	1553.37	0.0630158
$848$	3214.37	0.130167
$849$	24884.7	1.00594
$850$	−12436.6	−0.501851
$851$	1254.00	0.0505129
$852$	6192.44	0.249002
$853$	−12555.6	−0.503980	−0.251990	−	0.967730i	$-0.581085\pi$
$853$	−12555.6	−0.503980	−0.251990	+	0.967730i	$0.581085\pi$
$854$	−8824.91	−0.353609
$855$	−1997.56	−0.0799007
$856$	254.634	0.0101673
$857$	−38397.6	−1.53050	−0.765250	−	0.643734i	$-0.777385\pi$
$857$	−38397.6	−1.53050	−0.765250	+	0.643734i	$0.777385\pi$
$858$	14372.2	0.571863
$859$	48766.2	1.93700	0.968498	−	0.249021i	$-0.0801088\pi$
$859$	48766.2	1.93700	0.968498	+	0.249021i	$0.0801088\pi$
$860$	−3403.94	−0.134969
$861$	4678.02	0.185164
$862$	590.782	0.0233435
$863$	40228.1	1.58677	0.793383	−	0.608722i	$-0.208318\pi$
$863$	40228.1	1.58677	0.793383	+	0.608722i	$0.208318\pi$
$864$	864.000	0.0340207
$865$	3319.17	0.130468
$866$	25582.7	1.00385
$867$	−6166.95	−0.241569
$868$	−4210.36	−0.164642
$869$	44843.7	1.75054
$870$	1344.09	0.0523780
$871$	64639.2	2.51460
$872$	−11129.9	−0.432231
$873$	−2660.62	−0.103148
$874$	3467.37	0.134194
$875$	4974.20	0.192181
$876$	−7949.44	−0.306606
$877$	15873.3	0.611179	0.305589	−	0.952163i	$-0.401147\pi$
$877$	15873.3	0.611179	0.305589	+	0.952163i	$0.401147\pi$
$878$	35390.9	1.36035
$879$	15436.6	0.592335
$880$	1568.98	0.0601027
$881$	367.109	0.0140388	0.00701942	−	0.999975i	$-0.497766\pi$
$881$	367.109	0.0140388	0.00701942	+	0.999975i	$0.497766\pi$
$882$	882.000	0.0336718
$883$	40251.3	1.53405	0.767024	−	0.641618i	$-0.221737\pi$
$883$	40251.3	1.53405	0.767024	+	0.641618i	$0.221737\pi$
$884$	15379.1	0.585129
$885$	7986.24	0.303338
$886$	6154.90	0.233384
$887$	16530.2	0.625739	0.312870	−	0.949796i	$-0.398710\pi$
$887$	16530.2	0.625739	0.312870	+	0.949796i	$0.398710\pi$
$888$	−1308.52	−0.0494494
$889$	−328.679	−0.0123999
$890$	486.206	0.0183120
$891$	2697.54	0.101427
$892$	3862.84	0.144997
$893$	2722.73	0.102030
$894$	−11606.5	−0.434203
$895$	−405.731	−0.0151532
$896$	−896.000	−0.0334077
$897$	−4962.92	−0.184735
$898$	−31424.3	−1.16775
$899$	11439.9	0.424408
$900$	−4187.87	−0.155106
$901$	10738.8	0.397073
$902$	−14837.4	−0.547705
$903$	6069.14	0.223664
$904$	−4194.80	−0.154333
$905$	−2980.45	−0.109473
$906$	7466.21	0.273784
$907$	12082.3	0.442322	0.221161	−	0.975237i	$-0.429015\pi$
$907$	12082.3	0.442322	0.221161	+	0.975237i	$0.429015\pi$
$908$	−11294.8	−0.412811
$909$	15862.3	0.578788
$910$	−2965.04	−0.108011
$911$	30313.0	1.10243	0.551216	−	0.834362i	$-0.314164\pi$
$911$	30313.0	1.10243	0.551216	+	0.834362i	$0.314164\pi$
$912$	−3618.12	−0.131369
$913$	−3335.71	−0.120915
$914$	6868.75	0.248575
$915$	5568.25	0.201181
$916$	8414.16	0.303506
$917$	9789.32	0.352532
$918$	2886.53	0.103780
$919$	17257.0	0.619430	0.309715	−	0.950829i	$-0.399766\pi$
$919$	17257.0	0.619430	0.309715	+	0.950829i	$0.399766\pi$
$920$	−541.792	−0.0194156
$921$	−5105.97	−0.182679
$922$	29044.1	1.03743
$923$	37116.6	1.32363
$924$	−2797.45	−0.0995990
$925$	6342.49	0.225448
$926$	−25702.8	−0.912146
$927$	−12526.4	−0.443821
$928$	2434.51	0.0861172
$929$	11354.5	0.401002	0.200501	−	0.979694i	$-0.435743\pi$
$929$	11354.5	0.401002	0.200501	+	0.979694i	$0.435743\pi$
$930$	2656.60	0.0936704
$931$	−3693.50	−0.130021
$932$	9739.42	0.342302
$933$	−28870.7	−1.01306
$934$	−26122.7	−0.915160
$935$	5241.79	0.183342
$936$	5178.70	0.180845
$937$	12607.4	0.439558	0.219779	−	0.975550i	$-0.429466\pi$
$937$	12607.4	0.439558	0.219779	+	0.975550i	$0.429466\pi$
$938$	−12581.6	−0.437957
$939$	−14536.8	−0.505209
$940$	−425.438	−0.0147620
$941$	−39798.4	−1.37873	−0.689367	−	0.724412i	$-0.742111\pi$
$941$	−39798.4	−1.37873	−0.689367	+	0.724412i	$0.742111\pi$
$942$	−15598.1	−0.539503
$943$	5123.55	0.176931
$944$	14465.3	0.498733
$945$	−556.514	−0.0191571
$946$	−19249.6	−0.661583
$947$	36620.0	1.25659	0.628296	−	0.777975i	$-0.283753\pi$
$947$	36620.0	1.25659	0.628296	+	0.777975i	$0.283753\pi$
$948$	16158.4	0.553588
$949$	−47647.8	−1.62984
$950$	17537.3	0.598932
$951$	−871.041	−0.0297008
$952$	−2993.44	−0.101909
$953$	−39926.4	−1.35713	−0.678565	−	0.734541i	$-0.737398\pi$
$953$	−39926.4	−1.35713	−0.678565	+	0.734541i	$0.737398\pi$
$954$	3616.16	0.122723
$955$	−6041.89	−0.204723
$956$	9809.67	0.331870
$957$	7600.93	0.256743
$958$	−35168.1	−1.18604
$959$	13794.1	0.464480
$960$	565.348	0.0190068
$961$	−7179.88	−0.241008
$962$	−7843.08	−0.262860
$963$	286.463	0.00958581
$964$	−8341.42	−0.278692
$965$	3318.52	0.110702
$966$	966.000	0.0321745
$967$	−37120.0	−1.23444	−0.617218	−	0.786792i	$-0.711740\pi$
$967$	−37120.0	−1.23444	−0.617218	+	0.786792i	$0.711740\pi$
$968$	−1775.28	−0.0589459
$969$	−12087.7	−0.400737
$970$	−1740.94	−0.0576271
$971$	58985.1	1.94946	0.974729	−	0.223392i	$-0.0717128\pi$
$971$	58985.1	1.94946	0.974729	+	0.223392i	$0.0717128\pi$
$972$	972.000	0.0320750
$973$	−4018.77	−0.132411
$974$	20503.9	0.674526
$975$	−25101.5	−0.824505
$976$	10085.6	0.330771
$977$	53661.1	1.75719	0.878593	−	0.477572i	$-0.158483\pi$
$977$	53661.1	1.75719	0.878593	+	0.477572i	$0.158483\pi$
$978$	6881.56	0.224998
$979$	2749.54	0.0897605
$980$	577.126	0.0188119
$981$	−12521.1	−0.407512
$982$	31896.4	1.03651
$983$	28944.6	0.939155	0.469578	−	0.882891i	$-0.344406\pi$
$983$	28944.6	0.939155	0.469578	+	0.882891i	$0.344406\pi$
$984$	−5346.31	−0.173205
$985$	305.164	0.00987141
$986$	8133.43	0.262699
$987$	758.544	0.0244627
$988$	−21686.5	−0.698321
$989$	6647.15	0.213718
$990$	1765.11	0.0566654
$991$	−44674.1	−1.43201	−0.716003	−	0.698097i	$-0.754030\pi$
$991$	−44674.1	−1.43201	−0.716003	+	0.698097i	$0.754030\pi$
$992$	4811.84	0.154008
$993$	26341.1	0.841801
$994$	−7224.51	−0.230531
$995$	−1675.97	−0.0533990
$996$	−1201.95	−0.0382381
$997$	−33719.5	−1.07112	−0.535561	−	0.844497i	$-0.679900\pi$
$997$	−33719.5	−1.07112	−0.535561	+	0.844497i	$0.679900\pi$
$998$	38828.5	1.23156
$999$	−1472.08	−0.0466213

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.q.1.3	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +2.94452 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +2.94452 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +5.88904 q^{10} +33.3030 q^{11} +12.0000 q^{12} +71.9263 q^{13} -14.0000 q^{14} +8.83356 q^{15} +16.0000 q^{16} +53.4542 q^{17} +18.0000 q^{18} -75.3776 q^{19} +11.7781 q^{20} -21.0000 q^{21} +66.6060 q^{22} -23.0000 q^{23} +24.0000 q^{24} -116.330 q^{25} +143.853 q^{26} +27.0000 q^{27} -28.0000 q^{28} +76.0785 q^{29} +17.6671 q^{30} +150.370 q^{31} +32.0000 q^{32} +99.9090 q^{33} +106.908 q^{34} -20.6116 q^{35} +36.0000 q^{36} -54.5216 q^{37} -150.755 q^{38} +215.779 q^{39} +23.5562 q^{40} -222.763 q^{41} -42.0000 q^{42} -289.007 q^{43} +133.212 q^{44} +26.5007 q^{45} -46.0000 q^{46} -36.1212 q^{47} +48.0000 q^{48} +49.0000 q^{49} -232.660 q^{50} +160.363 q^{51} +287.705 q^{52} +200.898 q^{53} +54.0000 q^{54} +98.0614 q^{55} -56.0000 q^{56} -226.133 q^{57} +152.157 q^{58} +904.079 q^{59} +35.3343 q^{60} +630.351 q^{61} +300.740 q^{62} -63.0000 q^{63} +64.0000 q^{64} +211.789 q^{65} +199.818 q^{66} +898.686 q^{67} +213.817 q^{68} -69.0000 q^{69} -41.2233 q^{70} +516.037 q^{71} +72.0000 q^{72} -662.453 q^{73} -109.043 q^{74} -348.989 q^{75} -301.510 q^{76} -233.121 q^{77} +431.558 q^{78} +1346.54 q^{79} +47.1123 q^{80} +81.0000 q^{81} -445.526 q^{82} -100.162 q^{83} -84.0000 q^{84} +157.397 q^{85} -578.013 q^{86} +228.236 q^{87} +266.424 q^{88} +82.5612 q^{89} +53.0014 q^{90} -503.484 q^{91} -92.0000 q^{92} +451.110 q^{93} -72.2423 q^{94} -221.951 q^{95} +96.0000 q^{96} -295.624 q^{97} +98.0000 q^{98} +299.727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} - 10 q^{5} + 30 q^{6} - 35 q^{7} + 40 q^{8} + 45 q^{9} - 20 q^{10} + 47 q^{11} + 60 q^{12} + 74 q^{13} - 70 q^{14} - 30 q^{15} + 80 q^{16} - 4 q^{17} + 90 q^{18} + 215 q^{19} - 40 q^{20} - 105 q^{21} + 94 q^{22} - 115 q^{23} + 120 q^{24} + 535 q^{25} + 148 q^{26} + 135 q^{27} - 140 q^{28} + 273 q^{29} - 60 q^{30} + 660 q^{31} + 160 q^{32} + 141 q^{33} - 8 q^{34} + 70 q^{35} + 180 q^{36} - 71 q^{37} + 430 q^{38} + 222 q^{39} - 80 q^{40} + 428 q^{41} - 210 q^{42} + 606 q^{43} + 188 q^{44} - 90 q^{45} - 230 q^{46} + 514 q^{47} + 240 q^{48} + 245 q^{49} + 1070 q^{50} - 12 q^{51} + 296 q^{52} + 376 q^{53} + 270 q^{54} - 395 q^{55} - 280 q^{56} + 645 q^{57} + 546 q^{58} + 1062 q^{59} - 120 q^{60} + 60 q^{61} + 1320 q^{62} - 315 q^{63} + 320 q^{64} + 1755 q^{65} + 282 q^{66} + 671 q^{67} - 16 q^{68} - 345 q^{69} + 140 q^{70} + 1885 q^{71} + 360 q^{72} + 790 q^{73} - 142 q^{74} + 1605 q^{75} + 860 q^{76} - 329 q^{77} + 444 q^{78} + 738 q^{79} - 160 q^{80} + 405 q^{81} + 856 q^{82} + 774 q^{83} - 420 q^{84} + 781 q^{85} + 1212 q^{86} + 819 q^{87} + 376 q^{88} + 131 q^{89} - 180 q^{90} - 518 q^{91} - 460 q^{92} + 1980 q^{93} + 1028 q^{94} + 625 q^{95} + 480 q^{96} - 51 q^{97} + 490 q^{98} + 423 q^{99}+O(q^{100}) \) 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 + 47 * q^11 + 60 * q^12 + 74 * q^13 - 70 * q^14 - 30 * q^15 + 80 * q^16 - 4 * q^17 + 90 * q^18 + 215 * q^19 - 40 * q^20 - 105 * q^21 + 94 * q^22 - 115 * q^23 + 120 * q^24 + 535 * q^25 + 148 * q^26 + 135 * q^27 - 140 * q^28 + 273 * q^29 - 60 * q^30 + 660 * q^31 + 160 * q^32 + 141 * q^33 - 8 * q^34 + 70 * q^35 + 180 * q^36 - 71 * q^37 + 430 * q^38 + 222 * q^39 - 80 * q^40 + 428 * q^41 - 210 * q^42 + 606 * q^43 + 188 * q^44 - 90 * q^45 - 230 * q^46 + 514 * q^47 + 240 * q^48 + 245 * q^49 + 1070 * q^50 - 12 * q^51 + 296 * q^52 + 376 * q^53 + 270 * q^54 - 395 * q^55 - 280 * q^56 + 645 * q^57 + 546 * q^58 + 1062 * q^59 - 120 * q^60 + 60 * q^61 + 1320 * q^62 - 315 * q^63 + 320 * q^64 + 1755 * q^65 + 282 * q^66 + 671 * q^67 - 16 * q^68 - 345 * q^69 + 140 * q^70 + 1885 * q^71 + 360 * q^72 + 790 * q^73 - 142 * q^74 + 1605 * q^75 + 860 * q^76 - 329 * q^77 + 444 * q^78 + 738 * q^79 - 160 * q^80 + 405 * q^81 + 856 * q^82 + 774 * q^83 - 420 * q^84 + 781 * q^85 + 1212 * q^86 + 819 * q^87 + 376 * q^88 + 131 * q^89 - 180 * q^90 - 518 * q^91 - 460 * q^92 + 1980 * q^93 + 1028 * q^94 + 625 * q^95 + 480 * q^96 - 51 * q^97 + 490 * q^98 + 423 * q^99

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