LMFDB - Embedded newform 966.4.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 $ x^5 - x^4 - 351x^3 - 663x^2 + 18451*x - 19243
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.91860$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +20.6804 q^{10} -0.432547 q^{11} -12.0000 q^{12} +58.4854 q^{13} +14.0000 q^{14} +31.0206 q^{15} +16.0000 q^{16} +119.180 q^{17} -18.0000 q^{18} -124.465 q^{19} -41.3608 q^{20} +21.0000 q^{21} +0.865093 q^{22} -23.0000 q^{23} +24.0000 q^{24} -18.0804 q^{25} -116.971 q^{26} -27.0000 q^{27} -28.0000 q^{28} -263.013 q^{29} -62.0412 q^{30} -298.993 q^{31} -32.0000 q^{32} +1.29764 q^{33} -238.361 q^{34} +72.3814 q^{35} +36.0000 q^{36} +258.142 q^{37} +248.930 q^{38} -175.456 q^{39} +82.7216 q^{40} +468.112 q^{41} -42.0000 q^{42} -495.967 q^{43} -1.73019 q^{44} -93.0618 q^{45} +46.0000 q^{46} -429.041 q^{47} -48.0000 q^{48} +49.0000 q^{49} +36.1607 q^{50} -357.541 q^{51} +233.941 q^{52} +606.504 q^{53} +54.0000 q^{54} +4.47262 q^{55} +56.0000 q^{56} +373.395 q^{57} +526.026 q^{58} +389.469 q^{59} +124.082 q^{60} -532.099 q^{61} +597.986 q^{62} -63.0000 q^{63} +64.0000 q^{64} -604.750 q^{65} -2.59528 q^{66} +322.037 q^{67} +476.721 q^{68} +69.0000 q^{69} -144.763 q^{70} -547.122 q^{71} -72.0000 q^{72} -568.864 q^{73} -516.284 q^{74} +54.2411 q^{75} -497.860 q^{76} +3.02783 q^{77} +350.912 q^{78} +439.699 q^{79} -165.443 q^{80} +81.0000 q^{81} -936.224 q^{82} +305.368 q^{83} +84.0000 q^{84} -1232.35 q^{85} +991.935 q^{86} +789.039 q^{87} +3.46037 q^{88} -263.162 q^{89} +186.124 q^{90} -409.397 q^{91} -92.0000 q^{92} +896.979 q^{93} +858.082 q^{94} +1286.99 q^{95} +96.0000 q^{96} -902.223 q^{97} -98.0000 q^{98} -3.89292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−10.3402	−0.924855	−0.462428	−	0.886657i	$-0.653021\pi$
$5$	−10.3402	−0.924855	−0.462428	+	0.886657i	$0.653021\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	20.6804	0.653971
$11$	−0.432547	−0.0118562	−0.00592808	−	0.999982i	$-0.501887\pi$
$11$	−0.432547	−0.0118562	−0.00592808	+	0.999982i	$0.501887\pi$
$12$	−12.0000	−0.288675
$13$	58.4854	1.24776	0.623881	−	0.781519i	$-0.285555\pi$
$13$	58.4854	1.24776	0.623881	+	0.781519i	$0.285555\pi$
$14$	14.0000	0.267261
$15$	31.0206	0.533965
$16$	16.0000	0.250000
$17$	119.180	1.70032	0.850161	−	0.526523i	$-0.176505\pi$
$17$	119.180	1.70032	0.850161	+	0.526523i	$0.176505\pi$
$18$	−18.0000	−0.235702
$19$	−124.465	−1.50285	−0.751427	−	0.659816i	$-0.770634\pi$
$19$	−124.465	−1.50285	−0.751427	+	0.659816i	$0.770634\pi$
$20$	−41.3608	−0.462428
$21$	21.0000	0.218218
$22$	0.865093	0.00838357
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−18.0804	−0.144643
$26$	−116.971	−0.882302
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−263.013	−1.68415	−0.842074	−	0.539363i	$-0.818665\pi$
$29$	−263.013	−1.68415	−0.842074	+	0.539363i	$0.818665\pi$
$30$	−62.0412	−0.377571
$31$	−298.993	−1.73228	−0.866140	−	0.499801i	$-0.833407\pi$
$31$	−298.993	−1.73228	−0.866140	+	0.499801i	$0.833407\pi$
$32$	−32.0000	−0.176777
$33$	1.29764	0.00684515
$34$	−238.361	−1.20231
$35$	72.3814	0.349562
$36$	36.0000	0.166667
$37$	258.142	1.14698	0.573490	−	0.819213i	$-0.305589\pi$
$37$	258.142	1.14698	0.573490	+	0.819213i	$0.305589\pi$
$38$	248.930	1.06268
$39$	−175.456	−0.720396
$40$	82.7216	0.326986
$41$	468.112	1.78309	0.891547	−	0.452929i	$-0.149621\pi$
$41$	468.112	1.78309	0.891547	+	0.452929i	$0.149621\pi$
$42$	−42.0000	−0.154303
$43$	−495.967	−1.75894	−0.879469	−	0.475957i	$-0.842102\pi$
$43$	−495.967	−1.75894	−0.879469	+	0.475957i	$0.842102\pi$
$44$	−1.73019	−0.00592808
$45$	−93.0618	−0.308285
$46$	46.0000	0.147442
$47$	−429.041	−1.33153	−0.665767	−	0.746160i	$-0.731895\pi$
$47$	−429.041	−1.33153	−0.665767	+	0.746160i	$0.731895\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	36.1607	0.102278
$51$	−357.541	−0.981681
$52$	233.941	0.623881
$53$	606.504	1.57188	0.785941	−	0.618301i	$-0.212179\pi$
$53$	606.504	1.57188	0.785941	+	0.618301i	$0.212179\pi$
$54$	54.0000	0.136083
$55$	4.47262	0.0109652
$56$	56.0000	0.133631
$57$	373.395	0.867674
$58$	526.026	1.19087
$59$	389.469	0.859399	0.429700	−	0.902972i	$-0.358619\pi$
$59$	389.469	0.859399	0.429700	+	0.902972i	$0.358619\pi$
$60$	124.082	0.266983
$61$	−532.099	−1.11686	−0.558429	−	0.829553i	$-0.688596\pi$
$61$	−532.099	−1.11686	−0.558429	+	0.829553i	$0.688596\pi$
$62$	597.986	1.22491
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−604.750	−1.15400
$66$	−2.59528	−0.00484025
$67$	322.037	0.587210	0.293605	−	0.955927i	$-0.405145\pi$
$67$	322.037	0.587210	0.293605	+	0.955927i	$0.405145\pi$
$68$	476.721	0.850161
$69$	69.0000	0.120386
$70$	−144.763	−0.247178
$71$	−547.122	−0.914527	−0.457264	−	0.889331i	$-0.651170\pi$
$71$	−547.122	−0.914527	−0.457264	+	0.889331i	$0.651170\pi$
$72$	−72.0000	−0.117851
$73$	−568.864	−0.912061	−0.456030	−	0.889964i	$-0.650729\pi$
$73$	−568.864	−0.912061	−0.456030	+	0.889964i	$0.650729\pi$
$74$	−516.284	−0.811037
$75$	54.2411	0.0835096
$76$	−497.860	−0.751427
$77$	3.02783	0.00448121
$78$	350.912	0.509397
$79$	439.699	0.626203	0.313101	−	0.949720i	$-0.398632\pi$
$79$	439.699	0.626203	0.313101	+	0.949720i	$0.398632\pi$
$80$	−165.443	−0.231214
$81$	81.0000	0.111111
$82$	−936.224	−1.26084
$83$	305.368	0.403837	0.201919	−	0.979402i	$-0.435282\pi$
$83$	305.368	0.403837	0.201919	+	0.979402i	$0.435282\pi$
$84$	84.0000	0.109109
$85$	−1232.35	−1.57255
$86$	991.935	1.24376
$87$	789.039	0.972343
$88$	3.46037	0.00419178
$89$	−263.162	−0.313428	−0.156714	−	0.987644i	$-0.550090\pi$
$89$	−263.162	−0.313428	−0.156714	+	0.987644i	$0.550090\pi$
$90$	186.124	0.217990
$91$	−409.397	−0.471610
$92$	−92.0000	−0.104257
$93$	896.979	1.00013
$94$	858.082	0.941537
$95$	1286.99	1.38992
$96$	96.0000	0.102062
$97$	−902.223	−0.944401	−0.472200	−	0.881491i	$-0.656540\pi$
$97$	−902.223	−0.944401	−0.472200	+	0.881491i	$0.656540\pi$
$98$	−98.0000	−0.101015
$99$	−3.89292	−0.00395205
$100$	−72.3215	−0.0723215
$101$	1386.53	1.36599	0.682996	−	0.730422i	$-0.260677\pi$
$101$	1386.53	1.36599	0.682996	+	0.730422i	$0.260677\pi$
$102$	715.082	0.694154
$103$	1344.50	1.28619	0.643097	−	0.765785i	$-0.277649\pi$
$103$	1344.50	1.28619	0.643097	+	0.765785i	$0.277649\pi$
$104$	−467.883	−0.441151
$105$	−217.144	−0.201820
$106$	−1213.01	−1.11149
$107$	−437.931	−0.395667	−0.197834	−	0.980236i	$-0.563391\pi$
$107$	−437.931	−0.395667	−0.197834	+	0.980236i	$0.563391\pi$
$108$	−108.000	−0.0962250
$109$	1053.37	0.925638	0.462819	−	0.886453i	$-0.346838\pi$
$109$	1053.37	0.925638	0.462819	+	0.886453i	$0.346838\pi$
$110$	−8.94523	−0.00775359
$111$	−774.425	−0.662209
$112$	−112.000	−0.0944911
$113$	1327.22	1.10491	0.552454	−	0.833543i	$-0.313692\pi$
$113$	1327.22	1.10491	0.552454	+	0.833543i	$0.313692\pi$
$114$	−746.790	−0.613538
$115$	237.824	0.192846
$116$	−1052.05	−0.842074
$117$	526.368	0.415921
$118$	−778.938	−0.607687
$119$	−834.262	−0.642661
$120$	−248.165	−0.188785
$121$	−1330.81	−0.999859
$122$	1064.20	0.789737
$123$	−1404.34	−1.02947
$124$	−1195.97	−0.866140
$125$	1479.48	1.05863
$126$	126.000	0.0890871
$127$	63.6591	0.0444790	0.0222395	−	0.999753i	$-0.492920\pi$
$127$	63.6591	0.0444790	0.0222395	+	0.999753i	$0.492920\pi$
$128$	−128.000	−0.0883883
$129$	1487.90	1.01552
$130$	1209.50	0.816001
$131$	−1056.98	−0.704954	−0.352477	−	0.935820i	$-0.614661\pi$
$131$	−1056.98	−0.704954	−0.352477	+	0.935820i	$0.614661\pi$
$132$	5.19056	0.00342258
$133$	871.255	0.568026
$134$	−644.074	−0.415220
$135$	279.185	0.177988
$136$	−953.443	−0.601155
$137$	−1093.78	−0.682101	−0.341050	−	0.940045i	$-0.610783\pi$
$137$	−1093.78	−0.682101	−0.341050	+	0.940045i	$0.610783\pi$
$138$	−138.000	−0.0851257
$139$	962.261	0.587179	0.293589	−	0.955932i	$-0.405150\pi$
$139$	962.261	0.587179	0.293589	+	0.955932i	$0.405150\pi$
$140$	289.525	0.174781
$141$	1287.12	0.768761
$142$	1094.24	0.646668
$143$	−25.2976	−0.0147937
$144$	144.000	0.0833333
$145$	2719.60	1.55759
$146$	1137.73	0.644924
$147$	−147.000	−0.0824786
$148$	1032.57	0.573490
$149$	2538.33	1.39562	0.697812	−	0.716281i	$-0.254157\pi$
$149$	2538.33	1.39562	0.697812	+	0.716281i	$0.254157\pi$
$150$	−108.482	−0.0590502
$151$	1727.52	0.931016	0.465508	−	0.885044i	$-0.345872\pi$
$151$	1727.52	0.931016	0.465508	+	0.885044i	$0.345872\pi$
$152$	995.720	0.531339
$153$	1072.62	0.566774
$154$	−6.05565	−0.00316869
$155$	3091.64	1.60211
$156$	−701.824	−0.360198
$157$	39.6442	0.0201526	0.0100763	−	0.999949i	$-0.496793\pi$
$157$	39.6442	0.0201526	0.0100763	+	0.999949i	$0.496793\pi$
$158$	−879.398	−0.442792
$159$	−1819.51	−0.907527
$160$	330.886	0.163493
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	2499.83	1.20124	0.600618	−	0.799536i	$-0.294921\pi$
$163$	2499.83	1.20124	0.600618	+	0.799536i	$0.294921\pi$
$164$	1872.45	0.891547
$165$	−13.4178	−0.00633078
$166$	−610.736	−0.285556
$167$	−939.805	−0.435475	−0.217737	−	0.976007i	$-0.569868\pi$
$167$	−939.805	−0.435475	−0.217737	+	0.976007i	$0.569868\pi$
$168$	−168.000	−0.0771517
$169$	1223.54	0.556912
$170$	2464.70	1.11196
$171$	−1120.19	−0.500952
$172$	−1983.87	−0.879469
$173$	1206.62	0.530277	0.265139	−	0.964210i	$-0.414582\pi$
$173$	1206.62	0.530277	0.265139	+	0.964210i	$0.414582\pi$
$174$	−1578.08	−0.687550
$175$	126.563	0.0546699
$176$	−6.92075	−0.00296404
$177$	−1168.41	−0.496174
$178$	526.323	0.221627
$179$	−2544.71	−1.06257	−0.531287	−	0.847192i	$-0.678291\pi$
$179$	−2544.71	−1.06257	−0.531287	+	0.847192i	$0.678291\pi$
$180$	−372.247	−0.154143
$181$	−2097.40	−0.861320	−0.430660	−	0.902514i	$-0.641719\pi$
$181$	−2097.40	−0.861320	−0.430660	+	0.902514i	$0.641719\pi$
$182$	818.795	0.333479
$183$	1596.30	0.644818
$184$	184.000	0.0737210
$185$	−2669.24	−1.06079
$186$	−1793.96	−0.707201
$187$	−51.5510	−0.0201593
$188$	−1716.16	−0.665767
$189$	189.000	0.0727393
$190$	−2573.99	−0.982824
$191$	2140.41	0.810862	0.405431	−	0.914126i	$-0.367122\pi$
$191$	2140.41	0.810862	0.405431	+	0.914126i	$0.367122\pi$
$192$	−192.000	−0.0721688
$193$	−561.409	−0.209384	−0.104692	−	0.994505i	$-0.533386\pi$
$193$	−561.409	−0.209384	−0.104692	+	0.994505i	$0.533386\pi$
$194$	1804.45	0.667792
$195$	1814.25	0.666262
$196$	196.000	0.0714286
$197$	3481.52	1.25913	0.629563	−	0.776949i	$-0.283234\pi$
$197$	3481.52	1.25913	0.629563	+	0.776949i	$0.283234\pi$
$198$	7.78584	0.00279452
$199$	3869.17	1.37828	0.689141	−	0.724628i	$-0.257988\pi$
$199$	3869.17	1.37828	0.689141	+	0.724628i	$0.257988\pi$
$200$	144.643	0.0511390
$201$	−966.111	−0.339026
$202$	−2773.07	−0.965902
$203$	1841.09	0.636548
$204$	−1430.16	−0.490841
$205$	−4840.37	−1.64910
$206$	−2689.01	−0.909476
$207$	−207.000	−0.0695048
$208$	935.766	0.311941
$209$	53.8369	0.0178181
$210$	434.288	0.142708
$211$	3412.74	1.11347	0.556737	−	0.830689i	$-0.312053\pi$
$211$	3412.74	1.11347	0.556737	+	0.830689i	$0.312053\pi$
$212$	2426.02	0.785941
$213$	1641.37	0.528003
$214$	875.862	0.279779
$215$	5128.40	1.62676
$216$	216.000	0.0680414
$217$	2092.95	0.654741
$218$	−2106.74	−0.654525
$219$	1706.59	0.526579
$220$	17.8905	0.00548261
$221$	6970.30	2.12160
$222$	1548.85	0.468253
$223$	−3712.10	−1.11471	−0.557356	−	0.830274i	$-0.688184\pi$
$223$	−3712.10	−1.11471	−0.557356	+	0.830274i	$0.688184\pi$
$224$	224.000	0.0668153
$225$	−162.723	−0.0482143
$226$	−2654.44	−0.781288
$227$	1753.63	0.512741	0.256371	−	0.966579i	$-0.417473\pi$
$227$	1753.63	0.512741	0.256371	+	0.966579i	$0.417473\pi$
$228$	1493.58	0.433837
$229$	−1415.43	−0.408446	−0.204223	−	0.978924i	$-0.565467\pi$
$229$	−1415.43	−0.408446	−0.204223	+	0.978924i	$0.565467\pi$
$230$	−475.649	−0.136362
$231$	−9.08348	−0.00258722
$232$	2104.10	0.595436
$233$	3163.07	0.889354	0.444677	−	0.895691i	$-0.353318\pi$
$233$	3163.07	0.889354	0.444677	+	0.895691i	$0.353318\pi$
$234$	−1052.74	−0.294101
$235$	4436.37	1.23148
$236$	1557.88	0.429700
$237$	−1319.10	−0.361538
$238$	1668.52	0.454430
$239$	4143.03	1.12130	0.560649	−	0.828053i	$-0.310552\pi$
$239$	4143.03	1.12130	0.560649	+	0.828053i	$0.310552\pi$
$240$	496.329	0.133491
$241$	−2878.68	−0.769427	−0.384714	−	0.923036i	$-0.625700\pi$
$241$	−2878.68	−0.769427	−0.384714	+	0.923036i	$0.625700\pi$
$242$	2661.63	0.707007
$243$	−243.000	−0.0641500
$244$	−2128.40	−0.558429
$245$	−506.670	−0.132122
$246$	2808.67	0.727945
$247$	−7279.38	−1.87521
$248$	2391.94	0.612454
$249$	−916.104	−0.233156
$250$	−2958.96	−0.748564
$251$	5977.97	1.50329	0.751645	−	0.659568i	$-0.229261\pi$
$251$	5977.97	1.50329	0.751645	+	0.659568i	$0.229261\pi$
$252$	−252.000	−0.0629941
$253$	9.94857	0.00247218
$254$	−127.318	−0.0314514
$255$	3697.04	0.907913
$256$	256.000	0.0625000
$257$	−3868.37	−0.938920	−0.469460	−	0.882954i	$-0.655551\pi$
$257$	−3868.37	−0.938920	−0.469460	+	0.882954i	$0.655551\pi$
$258$	−2975.80	−0.718083
$259$	−1806.99	−0.433518
$260$	−2419.00	−0.577000
$261$	−2367.12	−0.561382
$262$	2113.97	0.498478
$263$	3073.54	0.720618	0.360309	−	0.932833i	$-0.382671\pi$
$263$	3073.54	0.720618	0.360309	+	0.932833i	$0.382671\pi$
$264$	−10.3811	−0.00242013
$265$	−6271.37	−1.45376
$266$	−1742.51	−0.401655
$267$	789.485	0.180958
$268$	1288.15	0.293605
$269$	−2508.94	−0.568672	−0.284336	−	0.958725i	$-0.591773\pi$
$269$	−2508.94	−0.568672	−0.284336	+	0.958725i	$0.591773\pi$
$270$	−558.371	−0.125857
$271$	−1653.33	−0.370601	−0.185300	−	0.982682i	$-0.559326\pi$
$271$	−1653.33	−0.370601	−0.185300	+	0.982682i	$0.559326\pi$
$272$	1906.89	0.425080
$273$	1228.19	0.272284
$274$	2187.56	0.482318
$275$	7.82060	0.00171491
$276$	276.000	0.0601929
$277$	6688.13	1.45073	0.725363	−	0.688367i	$-0.241672\pi$
$277$	6688.13	1.45073	0.725363	+	0.688367i	$0.241672\pi$
$278$	−1924.52	−0.415198
$279$	−2690.94	−0.577427
$280$	−579.051	−0.123589
$281$	2244.31	0.476457	0.238228	−	0.971209i	$-0.423433\pi$
$281$	2244.31	0.476457	0.238228	+	0.971209i	$0.423433\pi$
$282$	−2574.25	−0.543596
$283$	3553.67	0.746444	0.373222	−	0.927742i	$-0.378253\pi$
$283$	3553.67	0.746444	0.373222	+	0.927742i	$0.378253\pi$
$284$	−2188.49	−0.457264
$285$	−3860.98	−0.802472
$286$	50.5953	0.0104607
$287$	−3276.78	−0.673946
$288$	−288.000	−0.0589256
$289$	9290.95	1.89109
$290$	−5439.21	−1.10138
$291$	2706.67	0.545250
$292$	−2275.45	−0.456030
$293$	−8467.65	−1.68835	−0.844173	−	0.536070i	$-0.819908\pi$
$293$	−8467.65	−1.68835	−0.844173	+	0.536070i	$0.819908\pi$
$294$	294.000	0.0583212
$295$	−4027.19	−0.794820
$296$	−2065.13	−0.405519
$297$	11.6788	0.00228172
$298$	−5076.66	−0.986856
$299$	−1345.16	−0.260177
$300$	216.964	0.0417548
$301$	3471.77	0.664816
$302$	−3455.03	−0.658328
$303$	−4159.60	−0.788656
$304$	−1991.44	−0.375714
$305$	5502.01	1.03293
$306$	−2145.25	−0.400770
$307$	5968.27	1.10954	0.554768	−	0.832005i	$-0.312807\pi$
$307$	5968.27	1.10954	0.554768	+	0.832005i	$0.312807\pi$
$308$	12.1113	0.00224060
$309$	−4033.51	−0.742584
$310$	−6183.29	−1.13286
$311$	4875.47	0.888947	0.444473	−	0.895792i	$-0.353391\pi$
$311$	4875.47	0.888947	0.444473	+	0.895792i	$0.353391\pi$
$312$	1403.65	0.254699
$313$	1656.71	0.299177	0.149589	−	0.988748i	$-0.452205\pi$
$313$	1656.71	0.299177	0.149589	+	0.988748i	$0.452205\pi$
$314$	−79.2885	−0.0142500
$315$	651.432	0.116521
$316$	1758.80	0.313101
$317$	6464.34	1.14534	0.572671	−	0.819785i	$-0.305907\pi$
$317$	6464.34	1.14534	0.572671	+	0.819785i	$0.305907\pi$
$318$	3639.03	0.641718
$319$	113.765	0.0199675
$320$	−661.772	−0.115607
$321$	1313.79	0.228439
$322$	−322.000	−0.0557278
$323$	−14833.8	−2.55534
$324$	324.000	0.0555556
$325$	−1057.44	−0.180480
$326$	−4999.65	−0.849402
$327$	−3160.11	−0.534418
$328$	−3744.90	−0.630419
$329$	3003.29	0.503272
$330$	26.8357	0.00447653
$331$	4283.23	0.711262	0.355631	−	0.934627i	$-0.384266\pi$
$331$	4283.23	0.711262	0.355631	+	0.934627i	$0.384266\pi$
$332$	1221.47	0.201919
$333$	2323.28	0.382327
$334$	1879.61	0.307927
$335$	−3329.93	−0.543085
$336$	336.000	0.0545545
$337$	−11333.3	−1.83194	−0.915969	−	0.401249i	$-0.868576\pi$
$337$	−11333.3	−1.83194	−0.915969	+	0.401249i	$0.868576\pi$
$338$	−2447.07	−0.393796
$339$	−3981.67	−0.637919
$340$	−4929.39	−0.786276
$341$	129.328	0.0205382
$342$	2240.37	0.354226
$343$	−343.000	−0.0539949
$344$	3967.74	0.621878
$345$	−713.473	−0.111339
$346$	−2413.25	−0.374963
$347$	3090.87	0.478175	0.239087	−	0.970998i	$-0.423152\pi$
$347$	3090.87	0.478175	0.239087	+	0.970998i	$0.423152\pi$
$348$	3156.16	0.486171
$349$	−7158.14	−1.09790	−0.548949	−	0.835856i	$-0.684972\pi$
$349$	−7158.14	−1.09790	−0.548949	+	0.835856i	$0.684972\pi$
$350$	−253.125	−0.0386574
$351$	−1579.10	−0.240132
$352$	13.8415	0.00209589
$353$	−1301.42	−0.196225	−0.0981126	−	0.995175i	$-0.531281\pi$
$353$	−1301.42	−0.196225	−0.0981126	+	0.995175i	$0.531281\pi$
$354$	2336.81	0.350848
$355$	5657.35	0.845805
$356$	−1052.65	−0.156714
$357$	2502.79	0.371041
$358$	5089.42	0.751353
$359$	−5035.04	−0.740221	−0.370111	−	0.928988i	$-0.620680\pi$
$359$	−5035.04	−0.740221	−0.370111	+	0.928988i	$0.620680\pi$
$360$	744.494	0.108995
$361$	8632.55	1.25857
$362$	4194.81	0.609045
$363$	3992.44	0.577269
$364$	−1637.59	−0.235805
$365$	5882.16	0.843524
$366$	−3192.59	−0.455955
$367$	−7217.30	−1.02654	−0.513269	−	0.858228i	$-0.671566\pi$
$367$	−7217.30	−1.02654	−0.513269	+	0.858228i	$0.671566\pi$
$368$	−368.000	−0.0521286
$369$	4213.01	0.594364
$370$	5338.47	0.750092
$371$	−4245.53	−0.594116
$372$	3587.91	0.500066
$373$	870.591	0.120851	0.0604256	−	0.998173i	$-0.480754\pi$
$373$	870.591	0.120851	0.0604256	+	0.998173i	$0.480754\pi$
$374$	103.102	0.0142548
$375$	−4438.44	−0.611200
$376$	3432.33	0.470768
$377$	−15382.4	−2.10142
$378$	−378.000	−0.0514344
$379$	−12466.8	−1.68965	−0.844823	−	0.535045i	$-0.820295\pi$
$379$	−12466.8	−1.68965	−0.844823	+	0.535045i	$0.820295\pi$
$380$	5147.97	0.694962
$381$	−190.977	−0.0256799
$382$	−4280.82	−0.573366
$383$	−3629.39	−0.484212	−0.242106	−	0.970250i	$-0.577838\pi$
$383$	−3629.39	−0.484212	−0.242106	+	0.970250i	$0.577838\pi$
$384$	384.000	0.0510310
$385$	−31.3083	−0.00414447
$386$	1122.82	0.148057
$387$	−4463.71	−0.586312
$388$	−3608.89	−0.472200
$389$	11031.1	1.43779	0.718896	−	0.695118i	$-0.244648\pi$
$389$	11031.1	1.43779	0.718896	+	0.695118i	$0.244648\pi$
$390$	−3628.50	−0.471119
$391$	−2741.15	−0.354542
$392$	−392.000	−0.0505076
$393$	3170.95	0.407006
$394$	−6963.04	−0.890337
$395$	−4546.57	−0.579147
$396$	−15.5717	−0.00197603
$397$	12002.9	1.51740	0.758698	−	0.651442i	$-0.225836\pi$
$397$	12002.9	1.51740	0.758698	+	0.651442i	$0.225836\pi$
$398$	−7738.33	−0.974592
$399$	−2613.77	−0.327950
$400$	−289.286	−0.0361607
$401$	−3705.09	−0.461404	−0.230702	−	0.973024i	$-0.574102\pi$
$401$	−3705.09	−0.461404	−0.230702	+	0.973024i	$0.574102\pi$
$402$	1932.22	0.239728
$403$	−17486.7	−2.16148
$404$	5546.13	0.682996
$405$	−837.556	−0.102762
$406$	−3682.18	−0.450107
$407$	−111.658	−0.0135988
$408$	2860.33	0.347077
$409$	8490.89	1.02652	0.513261	−	0.858233i	$-0.328437\pi$
$409$	8490.89	1.02652	0.513261	+	0.858233i	$0.328437\pi$
$410$	9680.74	1.16609
$411$	3281.34	0.393811
$412$	5378.02	0.643097
$413$	−2726.28	−0.324822
$414$	414.000	0.0491473
$415$	−3157.57	−0.373491
$416$	−1871.53	−0.220575
$417$	−2886.78	−0.339008
$418$	−107.674	−0.0125993
$419$	1659.99	0.193546	0.0967730	−	0.995306i	$-0.469148\pi$
$419$	1659.99	0.193546	0.0967730	+	0.995306i	$0.469148\pi$
$420$	−868.576	−0.100910
$421$	2439.98	0.282464	0.141232	−	0.989977i	$-0.454894\pi$
$421$	2439.98	0.282464	0.141232	+	0.989977i	$0.454894\pi$
$422$	−6825.48	−0.787345
$423$	−3861.37	−0.443845
$424$	−4852.04	−0.555745
$425$	−2154.82	−0.245940
$426$	−3282.73	−0.373354
$427$	3724.69	0.422132
$428$	−1751.72	−0.197834
$429$	75.8929	0.00854113
$430$	−10256.8	−1.15029
$431$	8536.40	0.954023	0.477012	−	0.878897i	$-0.341720\pi$
$431$	8536.40	0.954023	0.477012	+	0.878897i	$0.341720\pi$
$432$	−432.000	−0.0481125
$433$	−6078.77	−0.674658	−0.337329	−	0.941387i	$-0.609523\pi$
$433$	−6078.77	−0.674658	−0.337329	+	0.941387i	$0.609523\pi$
$434$	−4185.90	−0.462971
$435$	−8158.81	−0.899276
$436$	4213.48	0.462819
$437$	2862.70	0.313367
$438$	−3413.18	−0.372347
$439$	−8767.75	−0.953216	−0.476608	−	0.879116i	$-0.658134\pi$
$439$	−8767.75	−0.953216	−0.476608	+	0.879116i	$0.658134\pi$
$440$	−35.7809	−0.00387679
$441$	441.000	0.0476190
$442$	−13940.6	−1.50020
$443$	2691.45	0.288656	0.144328	−	0.989530i	$-0.453898\pi$
$443$	2691.45	0.288656	0.144328	+	0.989530i	$0.453898\pi$
$444$	−3097.70	−0.331105
$445$	2721.14	0.289875
$446$	7424.20	0.788220
$447$	−7614.99	−0.805764
$448$	−448.000	−0.0472456
$449$	11532.1	1.21210	0.606050	−	0.795427i	$-0.292753\pi$
$449$	11532.1	1.21210	0.606050	+	0.795427i	$0.292753\pi$
$450$	325.447	0.0340927
$451$	−202.480	−0.0211406
$452$	5308.89	0.552454
$453$	−5182.55	−0.537522
$454$	−3507.25	−0.362563
$455$	4233.25	0.436171
$456$	−2987.16	−0.306769
$457$	−2710.86	−0.277480	−0.138740	−	0.990329i	$-0.544305\pi$
$457$	−2710.86	−0.277480	−0.138740	+	0.990329i	$0.544305\pi$
$458$	2830.85	0.288815
$459$	−3217.87	−0.327227
$460$	951.298	0.0964228
$461$	−17646.7	−1.78284	−0.891418	−	0.453182i	$-0.850289\pi$
$461$	−17646.7	−1.78284	−0.891418	+	0.453182i	$0.850289\pi$
$462$	18.1670	0.00182944
$463$	9616.38	0.965251	0.482625	−	0.875827i	$-0.339683\pi$
$463$	9616.38	0.965251	0.482625	+	0.875827i	$0.339683\pi$
$464$	−4208.21	−0.421037
$465$	−9274.93	−0.924978
$466$	−6326.14	−0.628869
$467$	−18488.3	−1.83198	−0.915992	−	0.401197i	$-0.868594\pi$
$467$	−18488.3	−1.83198	−0.915992	+	0.401197i	$0.868594\pi$
$468$	2105.47	0.207960
$469$	−2254.26	−0.221945
$470$	−8872.74	−0.870785
$471$	−118.933	−0.0116351
$472$	−3115.75	−0.303844
$473$	214.529	0.0208542
$474$	2638.19	0.255646
$475$	2250.37	0.217377
$476$	−3337.05	−0.321331
$477$	5458.54	0.523961
$478$	−8286.06	−0.792878
$479$	15943.0	1.52078	0.760388	−	0.649469i	$-0.225009\pi$
$479$	15943.0	1.52078	0.760388	+	0.649469i	$0.225009\pi$
$480$	−992.659	−0.0943926
$481$	15097.5	1.43116
$482$	5757.35	0.544067
$483$	−483.000	−0.0455016
$484$	−5323.25	−0.499930
$485$	9329.16	0.873434
$486$	486.000	0.0453609
$487$	5277.63	0.491072	0.245536	−	0.969387i	$-0.421036\pi$
$487$	5277.63	0.491072	0.245536	+	0.969387i	$0.421036\pi$
$488$	4256.79	0.394869
$489$	−7499.48	−0.693534
$490$	1013.34	0.0934245
$491$	13895.3	1.27716	0.638579	−	0.769556i	$-0.279522\pi$
$491$	13895.3	1.27716	0.638579	+	0.769556i	$0.279522\pi$
$492$	−5617.35	−0.514735
$493$	−31346.0	−2.86359
$494$	14558.8	1.32597
$495$	40.2535	0.00365508
$496$	−4783.89	−0.433070
$497$	3829.85	0.345659
$498$	1832.21	0.164866
$499$	12826.2	1.15066	0.575329	−	0.817922i	$-0.304874\pi$
$499$	12826.2	1.15066	0.575329	+	0.817922i	$0.304874\pi$
$500$	5917.92	0.529314
$501$	2819.41	0.251421
$502$	−11955.9	−1.06299
$503$	−509.018	−0.0451213	−0.0225606	−	0.999745i	$-0.507182\pi$
$503$	−509.018	−0.0451213	−0.0225606	+	0.999745i	$0.507182\pi$
$504$	504.000	0.0445435
$505$	−14337.0	−1.26334
$506$	−19.8971	−0.00174809
$507$	−3670.61	−0.321533
$508$	254.636	0.0222395
$509$	10162.0	0.884919	0.442460	−	0.896788i	$-0.354106\pi$
$509$	10162.0	0.884919	0.442460	+	0.896788i	$0.354106\pi$
$510$	−7394.09	−0.641991
$511$	3982.04	0.344727
$512$	−512.000	−0.0441942
$513$	3360.56	0.289225
$514$	7736.74	0.663917
$515$	−13902.4	−1.18954
$516$	5951.61	0.507761
$517$	185.580	0.0157869
$518$	3613.99	0.306543
$519$	−3619.87	−0.306156
$520$	4838.00	0.408001
$521$	17924.5	1.50727	0.753635	−	0.657293i	$-0.228299\pi$
$521$	17924.5	1.50727	0.753635	+	0.657293i	$0.228299\pi$
$522$	4734.23	0.396957
$523$	1260.42	0.105381	0.0526905	−	0.998611i	$-0.483220\pi$
$523$	1260.42	0.105381	0.0526905	+	0.998611i	$0.483220\pi$
$524$	−4227.93	−0.352477
$525$	−379.688	−0.0315637
$526$	−6147.08	−0.509554
$527$	−35634.1	−2.94543
$528$	20.7622	0.00171129
$529$	529.000	0.0434783
$530$	12542.7	1.02797
$531$	3505.22	0.286466
$532$	3485.02	0.284013
$533$	27377.7	2.22488
$534$	−1578.97	−0.127956
$535$	4528.29	0.365935
$536$	−2576.30	−0.207610
$537$	7634.13	0.613477
$538$	5017.88	0.402112
$539$	−21.1948	−0.00169374
$540$	1116.74	0.0889942
$541$	−1465.06	−0.116429	−0.0582143	−	0.998304i	$-0.518541\pi$
$541$	−1465.06	−0.116429	−0.0582143	+	0.998304i	$0.518541\pi$
$542$	3306.66	0.262054
$543$	6292.21	0.497283
$544$	−3813.77	−0.300577
$545$	−10892.1	−0.856081
$546$	−2456.38	−0.192534
$547$	120.094	0.00938732	0.00469366	−	0.999989i	$-0.498506\pi$
$547$	120.094	0.00938732	0.00469366	+	0.999989i	$0.498506\pi$
$548$	−4375.11	−0.341050
$549$	−4788.89	−0.372286
$550$	−15.6412	−0.00121262
$551$	32735.9	2.53103
$552$	−552.000	−0.0425628
$553$	−3077.89	−0.236682
$554$	−13376.3	−1.02582
$555$	8007.71	0.612447
$556$	3849.04	0.293589
$557$	−16526.2	−1.25716	−0.628581	−	0.777744i	$-0.716364\pi$
$557$	−16526.2	−1.25716	−0.628581	+	0.777744i	$0.716364\pi$
$558$	5381.87	0.408302
$559$	−29006.8	−2.19474
$560$	1158.10	0.0873906
$561$	154.653	0.0116390
$562$	−4488.62	−0.336906
$563$	−15277.5	−1.14364	−0.571820	−	0.820379i	$-0.693762\pi$
$563$	−15277.5	−1.14364	−0.571820	+	0.820379i	$0.693762\pi$
$564$	5148.49	0.384381
$565$	−13723.7	−1.02188
$566$	−7107.34	−0.527816
$567$	−567.000	−0.0419961
$568$	4376.98	0.323334
$569$	3979.82	0.293221	0.146611	−	0.989194i	$-0.453164\pi$
$569$	3979.82	0.293221	0.146611	+	0.989194i	$0.453164\pi$
$570$	7721.96	0.567434
$571$	10846.2	0.794919	0.397459	−	0.917620i	$-0.369892\pi$
$571$	10846.2	0.794919	0.397459	+	0.917620i	$0.369892\pi$
$572$	−101.191	−0.00739683
$573$	−6421.23	−0.468151
$574$	6553.57	0.476552
$575$	415.848	0.0301601
$576$	576.000	0.0416667
$577$	−14286.1	−1.03074	−0.515372	−	0.856967i	$-0.672346\pi$
$577$	−14286.1	−1.03074	−0.515372	+	0.856967i	$0.672346\pi$
$578$	−18581.9	−1.33721
$579$	1684.23	0.120888
$580$	10878.4	0.778796
$581$	−2137.58	−0.152636
$582$	−5413.34	−0.385550
$583$	−262.341	−0.0186365
$584$	4550.91	0.322462
$585$	−5442.75	−0.384667
$586$	16935.3	1.19384
$587$	3676.60	0.258517	0.129259	−	0.991611i	$-0.458740\pi$
$587$	3676.60	0.258517	0.129259	+	0.991611i	$0.458740\pi$
$588$	−588.000	−0.0412393
$589$	37214.2	2.60337
$590$	8054.37	0.562023
$591$	−10444.6	−0.726957
$592$	4130.27	0.286745
$593$	25212.1	1.74593	0.872965	−	0.487783i	$-0.162194\pi$
$593$	25212.1	1.74593	0.872965	+	0.487783i	$0.162194\pi$
$594$	−23.3575	−0.00161342
$595$	8626.43	0.594369
$596$	10153.3	0.697812
$597$	−11607.5	−0.795751
$598$	2690.33	0.183973
$599$	−7943.80	−0.541862	−0.270931	−	0.962599i	$-0.587331\pi$
$599$	−7943.80	−0.541862	−0.270931	+	0.962599i	$0.587331\pi$
$600$	−433.929	−0.0295251
$601$	15178.4	1.03018	0.515090	−	0.857136i	$-0.327758\pi$
$601$	15178.4	1.03018	0.515090	+	0.857136i	$0.327758\pi$
$602$	−6943.54	−0.470096
$603$	2898.33	0.195737
$604$	6910.07	0.465508
$605$	13760.9	0.924725
$606$	8319.20	0.557664
$607$	−10292.6	−0.688243	−0.344121	−	0.938925i	$-0.611823\pi$
$607$	−10292.6	−0.688243	−0.344121	+	0.938925i	$0.611823\pi$
$608$	3982.88	0.265670
$609$	−5523.27	−0.367511
$610$	−11004.0	−0.730393
$611$	−25092.6	−1.66144
$612$	4290.49	0.283387
$613$	−7009.66	−0.461855	−0.230928	−	0.972971i	$-0.574176\pi$
$613$	−7009.66	−0.461855	−0.230928	+	0.972971i	$0.574176\pi$
$614$	−11936.5	−0.784560
$615$	14521.1	0.952110
$616$	−24.2226	−0.00158435
$617$	−19338.4	−1.26181	−0.630903	−	0.775861i	$-0.717316\pi$
$617$	−19338.4	−1.26181	−0.630903	+	0.775861i	$0.717316\pi$
$618$	8067.03	0.525086
$619$	15759.9	1.02334	0.511668	−	0.859183i	$-0.329028\pi$
$619$	15759.9	1.02334	0.511668	+	0.859183i	$0.329028\pi$
$620$	12366.6	0.801054
$621$	621.000	0.0401286
$622$	−9750.94	−0.628580
$623$	1842.13	0.118465
$624$	−2807.30	−0.180099
$625$	−13038.1	−0.834435
$626$	−3313.41	−0.211550
$627$	−161.511	−0.0102873
$628$	158.577	0.0100763
$629$	30765.4	1.95023
$630$	−1302.86	−0.0823926
$631$	−25011.3	−1.57795	−0.788974	−	0.614427i	$-0.789387\pi$
$631$	−25011.3	−1.57795	−0.788974	+	0.614427i	$0.789387\pi$
$632$	−3517.59	−0.221396
$633$	−10238.2	−0.642864
$634$	−12928.7	−0.809879
$635$	−658.247	−0.0411366
$636$	−7278.05	−0.453763
$637$	2865.78	0.178252
$638$	−227.531	−0.0141192
$639$	−4924.10	−0.304842
$640$	1323.54	0.0817464
$641$	28607.7	1.76277	0.881385	−	0.472398i	$-0.156612\pi$
$641$	28607.7	1.76277	0.881385	+	0.472398i	$0.156612\pi$
$642$	−2627.59	−0.161530
$643$	15357.1	0.941873	0.470936	−	0.882167i	$-0.343916\pi$
$643$	15357.1	0.941873	0.470936	+	0.882167i	$0.343916\pi$
$644$	644.000	0.0394055
$645$	−15385.2	−0.939212
$646$	29667.6	1.80690
$647$	12909.6	0.784435	0.392218	−	0.919872i	$-0.371708\pi$
$647$	12909.6	0.784435	0.392218	+	0.919872i	$0.371708\pi$
$648$	−648.000	−0.0392837
$649$	−168.464	−0.0101892
$650$	2114.87	0.127619
$651$	−6278.85	−0.378015
$652$	9999.30	0.600618
$653$	−3348.78	−0.200686	−0.100343	−	0.994953i	$-0.531994\pi$
$653$	−3348.78	−0.200686	−0.100343	+	0.994953i	$0.531994\pi$
$654$	6320.22	0.377890
$655$	10929.4	0.651981
$656$	7489.79	0.445773
$657$	−5119.77	−0.304020
$658$	−6006.58	−0.355867
$659$	−17045.6	−1.00759	−0.503795	−	0.863823i	$-0.668063\pi$
$659$	−17045.6	−1.00759	−0.503795	+	0.863823i	$0.668063\pi$
$660$	−53.6714	−0.00316539
$661$	−10026.5	−0.589993	−0.294997	−	0.955498i	$-0.595318\pi$
$661$	−10026.5	−0.589993	−0.294997	+	0.955498i	$0.595318\pi$
$662$	−8566.46	−0.502938
$663$	−20910.9	−1.22491
$664$	−2442.94	−0.142778
$665$	−9008.95	−0.525342
$666$	−4646.55	−0.270346
$667$	6049.30	0.351169
$668$	−3759.22	−0.217737
$669$	11136.3	0.643579
$670$	6659.85	0.384019
$671$	230.158	0.0132416
$672$	−672.000	−0.0385758
$673$	−14133.9	−0.809539	−0.404770	−	0.914419i	$-0.632648\pi$
$673$	−14133.9	−0.809539	−0.404770	+	0.914419i	$0.632648\pi$
$674$	22666.6	1.29538
$675$	488.170	0.0278365
$676$	4894.15	0.278456
$677$	18169.1	1.03145	0.515726	−	0.856753i	$-0.327522\pi$
$677$	18169.1	1.03145	0.515726	+	0.856753i	$0.327522\pi$
$678$	7963.33	0.451077
$679$	6315.56	0.356950
$680$	9858.78	0.555981
$681$	−5260.88	−0.296031
$682$	−258.657	−0.0145227
$683$	3878.44	0.217283	0.108642	−	0.994081i	$-0.465350\pi$
$683$	3878.44	0.217283	0.108642	+	0.994081i	$0.465350\pi$
$684$	−4480.74	−0.250476
$685$	11309.9	0.630844
$686$	686.000	0.0381802
$687$	4246.28	0.235816
$688$	−7935.48	−0.439734
$689$	35471.6	1.96134
$690$	1426.95	0.0787289
$691$	21964.7	1.20923	0.604614	−	0.796518i	$-0.293327\pi$
$691$	21964.7	1.20923	0.604614	+	0.796518i	$0.293327\pi$
$692$	4826.50	0.265139
$693$	27.2504	0.00149374
$694$	−6181.74	−0.338121
$695$	−9949.96	−0.543056
$696$	−6312.31	−0.343775
$697$	55789.8	3.03183
$698$	14316.3	0.776332
$699$	−9489.21	−0.513469
$700$	506.250	0.0273349
$701$	−12937.2	−0.697049	−0.348524	−	0.937300i	$-0.613317\pi$
$701$	−12937.2	−0.697049	−0.348524	+	0.937300i	$0.613317\pi$
$702$	3158.21	0.169799
$703$	−32129.6	−1.72374
$704$	−27.6830	−0.00148202
$705$	−13309.1	−0.710993
$706$	2602.84	0.138752
$707$	−9705.73	−0.516296
$708$	−4673.63	−0.248087
$709$	25846.6	1.36910	0.684550	−	0.728966i	$-0.259999\pi$
$709$	25846.6	1.36910	0.684550	+	0.728966i	$0.259999\pi$
$710$	−11314.7	−0.598075
$711$	3957.29	0.208734
$712$	2105.29	0.110813
$713$	6876.84	0.361205
$714$	−5005.57	−0.262365
$715$	261.583	0.0136820
$716$	−10178.8	−0.531287
$717$	−12429.1	−0.647382
$718$	10070.1	0.523415
$719$	22479.5	1.16599	0.582993	−	0.812477i	$-0.301881\pi$
$719$	22479.5	1.16599	0.582993	+	0.812477i	$0.301881\pi$
$720$	−1488.99	−0.0770713
$721$	−9411.53	−0.486136
$722$	−17265.1	−0.889945
$723$	8636.03	0.444229
$724$	−8389.62	−0.430660
$725$	4755.37	0.243600
$726$	−7984.88	−0.408191
$727$	−18571.9	−0.947445	−0.473723	−	0.880674i	$-0.657090\pi$
$727$	−18571.9	−0.947445	−0.473723	+	0.880674i	$0.657090\pi$
$728$	3275.18	0.166739
$729$	729.000	0.0370370
$730$	−11764.3	−0.596462
$731$	−59109.5	−2.99076
$732$	6385.19	0.322409
$733$	−31782.6	−1.60153	−0.800763	−	0.598981i	$-0.795572\pi$
$733$	−31782.6	−1.60153	−0.800763	+	0.598981i	$0.795572\pi$
$734$	14434.6	0.725873
$735$	1520.01	0.0762808
$736$	736.000	0.0368605
$737$	−139.296	−0.00696206
$738$	−8426.02	−0.420279
$739$	−11096.6	−0.552363	−0.276181	−	0.961106i	$-0.589069\pi$
$739$	−11096.6	−0.552363	−0.276181	+	0.961106i	$0.589069\pi$
$740$	−10676.9	−0.530395
$741$	21838.1	1.08265
$742$	8491.06	0.420103
$743$	27453.5	1.35555	0.677774	−	0.735271i	$-0.262945\pi$
$743$	27453.5	1.35555	0.677774	+	0.735271i	$0.262945\pi$
$744$	−7175.83	−0.353600
$745$	−26246.8	−1.29075
$746$	−1741.18	−0.0854546
$747$	2748.31	0.134612
$748$	−206.204	−0.0100796
$749$	3065.52	0.149548
$750$	8876.87	0.432183
$751$	10079.9	0.489775	0.244888	−	0.969551i	$-0.421249\pi$
$751$	10079.9	0.489775	0.244888	+	0.969551i	$0.421249\pi$
$752$	−6864.66	−0.332883
$753$	−17933.9	−0.867925
$754$	30764.8	1.48593
$755$	−17862.9	−0.861055
$756$	756.000	0.0363696
$757$	30494.3	1.46411	0.732057	−	0.681244i	$-0.238561\pi$
$757$	30494.3	1.46411	0.732057	+	0.681244i	$0.238561\pi$
$758$	24933.6	1.19476
$759$	−29.8457	−0.00142731
$760$	−10295.9	−0.491412
$761$	−19866.0	−0.946310	−0.473155	−	0.880979i	$-0.656885\pi$
$761$	−19866.0	−0.946310	−0.473155	+	0.880979i	$0.656885\pi$
$762$	381.954	0.0181585
$763$	−7373.59	−0.349858
$764$	8561.64	0.405431
$765$	−11091.1	−0.524184
$766$	7258.79	0.342390
$767$	22778.2	1.07233
$768$	−768.000	−0.0360844
$769$	−29343.9	−1.37603	−0.688016	−	0.725696i	$-0.741518\pi$
$769$	−29343.9	−1.37603	−0.688016	+	0.725696i	$0.741518\pi$
$770$	62.6166	0.00293058
$771$	11605.1	0.542086
$772$	−2245.64	−0.104692
$773$	−13207.1	−0.614523	−0.307261	−	0.951625i	$-0.599413\pi$
$773$	−13207.1	−0.614523	−0.307261	+	0.951625i	$0.599413\pi$
$774$	8927.41	0.414585
$775$	5405.90	0.250562
$776$	7217.78	0.333896
$777$	5420.98	0.250291
$778$	−22062.3	−1.01667
$779$	−58263.6	−2.67973
$780$	7257.00	0.333131
$781$	236.656	0.0108428
$782$	5482.29	0.250699
$783$	7101.35	0.324114
$784$	784.000	0.0357143
$785$	−409.929	−0.0186382
$786$	−6341.90	−0.287796
$787$	21714.2	0.983518	0.491759	−	0.870731i	$-0.336354\pi$
$787$	21714.2	0.983518	0.491759	+	0.870731i	$0.336354\pi$
$788$	13926.1	0.629563
$789$	−9220.62	−0.416049
$790$	9093.15	0.409519
$791$	−9290.56	−0.417616
$792$	31.1434	0.00139726
$793$	−31120.0	−1.39357
$794$	−24005.7	−1.07296
$795$	18814.1	0.839331
$796$	15476.7	0.689141
$797$	8315.34	0.369567	0.184783	−	0.982779i	$-0.440842\pi$
$797$	8315.34	0.369567	0.184783	+	0.982779i	$0.440842\pi$
$798$	5227.53	0.231896
$799$	−51133.3	−2.26404
$800$	578.572	0.0255695
$801$	−2368.46	−0.104476
$802$	7410.17	0.326262
$803$	246.060	0.0108135
$804$	−3864.45	−0.169513
$805$	−1664.77	−0.0728888
$806$	34973.4	1.52839
$807$	7526.82	0.328323
$808$	−11092.3	−0.482951
$809$	9669.91	0.420242	0.210121	−	0.977675i	$-0.432614\pi$
$809$	9669.91	0.420242	0.210121	+	0.977675i	$0.432614\pi$
$810$	1675.11	0.0726635
$811$	−9543.33	−0.413208	−0.206604	−	0.978425i	$-0.566241\pi$
$811$	−9543.33	−0.413208	−0.206604	+	0.978425i	$0.566241\pi$
$812$	7364.36	0.318274
$813$	4960.00	0.213966
$814$	223.317	0.00961578
$815$	−25848.7	−1.11097
$816$	−5720.66	−0.245420
$817$	61730.6	2.64343
$818$	−16981.8	−0.725860
$819$	−3684.58	−0.157203
$820$	−19361.5	−0.824552
$821$	1330.39	0.0565543	0.0282772	−	0.999600i	$-0.490998\pi$
$821$	1330.39	0.0565543	0.0282772	+	0.999600i	$0.490998\pi$
$822$	−6562.67	−0.278467
$823$	28171.2	1.19318	0.596589	−	0.802547i	$-0.296522\pi$
$823$	28171.2	1.19318	0.596589	+	0.802547i	$0.296522\pi$
$824$	−10756.0	−0.454738
$825$	−23.4618	−0.000990103 0
$826$	5452.57	0.229684
$827$	−26955.6	−1.13342	−0.566709	−	0.823918i	$-0.691784\pi$
$827$	−26955.6	−1.13342	−0.566709	+	0.823918i	$0.691784\pi$
$828$	−828.000	−0.0347524
$829$	42904.8	1.79752	0.898762	−	0.438437i	$-0.144468\pi$
$829$	42904.8	1.79752	0.898762	+	0.438437i	$0.144468\pi$
$830$	6315.13	0.264098
$831$	−20064.4	−0.837577
$832$	3743.06	0.155970
$833$	5839.84	0.242903
$834$	5773.56	0.239715
$835$	9717.76	0.402751
$836$	215.348	0.00890904
$837$	8072.81	0.333378
$838$	−3319.98	−0.136858
$839$	−20517.2	−0.844257	−0.422128	−	0.906536i	$-0.638717\pi$
$839$	−20517.2	−0.844257	−0.422128	+	0.906536i	$0.638717\pi$
$840$	1737.15	0.0713541
$841$	44786.8	1.83635
$842$	−4879.96	−0.199732
$843$	−6732.93	−0.275082
$844$	13651.0	0.556737
$845$	−12651.6	−0.515063
$846$	7722.74	0.313846
$847$	9315.69	0.377911
$848$	9704.07	0.392971
$849$	−10661.0	−0.430960
$850$	4309.65	0.173906
$851$	−5937.26	−0.239162
$852$	6565.46	0.264001
$853$	40699.4	1.63367	0.816836	−	0.576870i	$-0.195726\pi$
$853$	40699.4	1.63367	0.816836	+	0.576870i	$0.195726\pi$
$854$	−7449.39	−0.298493
$855$	11582.9	0.463308
$856$	3503.45	0.139890
$857$	4553.33	0.181492	0.0907461	−	0.995874i	$-0.471075\pi$
$857$	4553.33	0.181492	0.0907461	+	0.995874i	$0.471075\pi$
$858$	−151.786	−0.00603949
$859$	−33835.4	−1.34394	−0.671972	−	0.740576i	$-0.734553\pi$
$859$	−33835.4	−1.34394	−0.671972	+	0.740576i	$0.734553\pi$
$860$	20513.6	0.813381
$861$	9830.35	0.389103
$862$	−17072.8	−0.674596
$863$	23062.8	0.909696	0.454848	−	0.890569i	$-0.349694\pi$
$863$	23062.8	0.909696	0.454848	+	0.890569i	$0.349694\pi$
$864$	864.000	0.0340207
$865$	−12476.7	−0.490430
$866$	12157.5	0.477055
$867$	−27872.8	−1.09182
$868$	8371.80	0.327370
$869$	−190.190	−0.00742435
$870$	16317.6	0.635884
$871$	18834.5	0.732699
$872$	−8426.96	−0.327263
$873$	−8120.01	−0.314800
$874$	−5725.39	−0.221584
$875$	−10356.4	−0.400124
$876$	6826.36	0.263289
$877$	455.054	0.0175212	0.00876060	−	0.999962i	$-0.497211\pi$
$877$	455.054	0.0175212	0.00876060	+	0.999962i	$0.497211\pi$
$878$	17535.5	0.674025
$879$	25403.0	0.974767
$880$	71.5619	0.00274131
$881$	−11371.1	−0.434849	−0.217425	−	0.976077i	$-0.569766\pi$
$881$	−11371.1	−0.434849	−0.217425	+	0.976077i	$0.569766\pi$
$882$	−882.000	−0.0336718
$883$	32228.8	1.22830	0.614149	−	0.789190i	$-0.289500\pi$
$883$	32228.8	1.22830	0.614149	+	0.789190i	$0.289500\pi$
$884$	27881.2	1.06080
$885$	12081.6	0.458889
$886$	−5382.90	−0.204111
$887$	29855.0	1.13014	0.565069	−	0.825044i	$-0.308850\pi$
$887$	29855.0	1.13014	0.565069	+	0.825044i	$0.308850\pi$
$888$	6195.40	0.234126
$889$	−445.613	−0.0168115
$890$	−5442.29	−0.204973
$891$	−35.0363	−0.00131735
$892$	−14848.4	−0.557356
$893$	53400.6	2.00110
$894$	15230.0	0.569761
$895$	26312.8	0.982726
$896$	896.000	0.0334077
$897$	4035.49	0.150213
$898$	−23064.2	−0.857084
$899$	78639.0	2.91742
$900$	−650.893	−0.0241072
$901$	72283.4	2.67271
$902$	404.961	0.0149487
$903$	−10415.3	−0.383832
$904$	−10617.8	−0.390644
$905$	21687.6	0.796596
$906$	10365.1	0.380086
$907$	−16902.8	−0.618795	−0.309397	−	0.950933i	$-0.600127\pi$
$907$	−16902.8	−0.618795	−0.309397	+	0.950933i	$0.600127\pi$
$908$	7014.51	0.256371
$909$	12478.8	0.455331
$910$	−8466.50	−0.308419
$911$	−43667.1	−1.58810	−0.794048	−	0.607855i	$-0.792030\pi$
$911$	−43667.1	−1.58810	−0.794048	+	0.607855i	$0.792030\pi$
$912$	5974.32	0.216918
$913$	−132.086	−0.00478796
$914$	5421.71	0.196208
$915$	−16506.0	−0.596363
$916$	−5661.71	−0.204223
$917$	7398.88	0.266448
$918$	6435.74	0.231385
$919$	29867.2	1.07207	0.536033	−	0.844197i	$-0.319922\pi$
$919$	29867.2	1.07207	0.536033	+	0.844197i	$0.319922\pi$
$920$	−1902.60	−0.0681812
$921$	−17904.8	−0.640591
$922$	35293.3	1.26066
$923$	−31998.6	−1.14111
$924$	−36.3339	−0.00129361
$925$	−4667.30	−0.165903
$926$	−19232.8	−0.682535
$927$	12100.5	0.428731
$928$	8416.41	0.297718
$929$	15720.8	0.555201	0.277600	−	0.960697i	$-0.410461\pi$
$929$	15720.8	0.555201	0.277600	+	0.960697i	$0.410461\pi$
$930$	18549.9	0.654058
$931$	−6098.79	−0.214694
$932$	12652.3	0.444677
$933$	−14626.4	−0.513234
$934$	36976.6	1.29541
$935$	533.048	0.0186444
$936$	−4210.95	−0.147050
$937$	19570.3	0.682321	0.341160	−	0.940005i	$-0.389180\pi$
$937$	19570.3	0.682321	0.341160	+	0.940005i	$0.389180\pi$
$938$	4508.52	0.156939
$939$	−4970.12	−0.172730
$940$	17745.5	0.615738
$941$	4350.58	0.150717	0.0753586	−	0.997157i	$-0.475990\pi$
$941$	4350.58	0.150717	0.0753586	+	0.997157i	$0.475990\pi$
$942$	237.865	0.00822725
$943$	−10766.6	−0.371801
$944$	6231.51	0.214850
$945$	−1954.30	−0.0672733
$946$	−429.058	−0.0147462
$947$	9017.19	0.309419	0.154709	−	0.987960i	$-0.450556\pi$
$947$	9017.19	0.309419	0.154709	+	0.987960i	$0.450556\pi$
$948$	−5276.39	−0.180769
$949$	−33270.2	−1.13804
$950$	−4500.75	−0.153709
$951$	−19393.0	−0.661264
$952$	6674.10	0.227215
$953$	−49070.5	−1.66794	−0.833971	−	0.551808i	$-0.813938\pi$
$953$	−49070.5	−1.66794	−0.833971	+	0.551808i	$0.813938\pi$
$954$	−10917.1	−0.370496
$955$	−22132.3	−0.749930
$956$	16572.1	0.560649
$957$	−341.296	−0.0115282
$958$	−31885.9	−1.07535
$959$	7656.45	0.257810
$960$	1985.32	0.0667457
$961$	59605.7	2.00080
$962$	−30195.0	−1.01198
$963$	−3941.38	−0.131889
$964$	−11514.7	−0.384714
$965$	5805.08	0.193650
$966$	966.000	0.0321745
$967$	8814.46	0.293127	0.146563	−	0.989201i	$-0.453179\pi$
$967$	8814.46	0.293127	0.146563	+	0.989201i	$0.453179\pi$
$968$	10646.5	0.353504
$969$	44501.4	1.47532
$970$	−18658.3	−0.617611
$971$	−12757.8	−0.421644	−0.210822	−	0.977524i	$-0.567614\pi$
$971$	−12757.8	−0.421644	−0.210822	+	0.977524i	$0.567614\pi$
$972$	−972.000	−0.0320750
$973$	−6735.82	−0.221933
$974$	−10555.3	−0.347241
$975$	3172.31	0.104200
$976$	−8513.58	−0.279214
$977$	−34111.6	−1.11702	−0.558509	−	0.829498i	$-0.688627\pi$
$977$	−34111.6	−1.11702	−0.558509	+	0.829498i	$0.688627\pi$
$978$	14999.0	0.490403
$979$	113.830	0.00371605
$980$	−2026.68	−0.0660611
$981$	9480.33	0.308546
$982$	−27790.6	−0.903088
$983$	5868.96	0.190428	0.0952139	−	0.995457i	$-0.469646\pi$
$983$	5868.96	0.190428	0.0952139	+	0.995457i	$0.469646\pi$
$984$	11234.7	0.363972
$985$	−35999.6	−1.16451
$986$	62691.9	2.02487
$987$	−9009.87	−0.290565
$988$	−29117.5	−0.937603
$989$	11407.2	0.366764
$990$	−80.5071	−0.00258453
$991$	50157.4	1.60777	0.803886	−	0.594784i	$-0.202762\pi$
$991$	50157.4	1.60777	0.803886	+	0.594784i	$0.202762\pi$
$992$	9567.77	0.306227
$993$	−12849.7	−0.410647
$994$	−7659.71	−0.244418
$995$	−40007.9	−1.27471
$996$	−3664.42	−0.116578
$997$	−22486.2	−0.714289	−0.357145	−	0.934049i	$-0.616250\pi$
$997$	−22486.2	−0.714289	−0.357145	+	0.934049i	$0.616250\pi$
$998$	−25652.3	−0.813638
$999$	−6969.83	−0.220736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.m.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.m.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.3402 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +20.6804 q^{10} -0.432547 q^{11} -12.0000 q^{12} +58.4854 q^{13} +14.0000 q^{14} +31.0206 q^{15} +16.0000 q^{16} +119.180 q^{17} -18.0000 q^{18} -124.465 q^{19} -41.3608 q^{20} +21.0000 q^{21} +0.865093 q^{22} -23.0000 q^{23} +24.0000 q^{24} -18.0804 q^{25} -116.971 q^{26} -27.0000 q^{27} -28.0000 q^{28} -263.013 q^{29} -62.0412 q^{30} -298.993 q^{31} -32.0000 q^{32} +1.29764 q^{33} -238.361 q^{34} +72.3814 q^{35} +36.0000 q^{36} +258.142 q^{37} +248.930 q^{38} -175.456 q^{39} +82.7216 q^{40} +468.112 q^{41} -42.0000 q^{42} -495.967 q^{43} -1.73019 q^{44} -93.0618 q^{45} +46.0000 q^{46} -429.041 q^{47} -48.0000 q^{48} +49.0000 q^{49} +36.1607 q^{50} -357.541 q^{51} +233.941 q^{52} +606.504 q^{53} +54.0000 q^{54} +4.47262 q^{55} +56.0000 q^{56} +373.395 q^{57} +526.026 q^{58} +389.469 q^{59} +124.082 q^{60} -532.099 q^{61} +597.986 q^{62} -63.0000 q^{63} +64.0000 q^{64} -604.750 q^{65} -2.59528 q^{66} +322.037 q^{67} +476.721 q^{68} +69.0000 q^{69} -144.763 q^{70} -547.122 q^{71} -72.0000 q^{72} -568.864 q^{73} -516.284 q^{74} +54.2411 q^{75} -497.860 q^{76} +3.02783 q^{77} +350.912 q^{78} +439.699 q^{79} -165.443 q^{80} +81.0000 q^{81} -936.224 q^{82} +305.368 q^{83} +84.0000 q^{84} -1232.35 q^{85} +991.935 q^{86} +789.039 q^{87} +3.46037 q^{88} -263.162 q^{89} +186.124 q^{90} -409.397 q^{91} -92.0000 q^{92} +896.979 q^{93} +858.082 q^{94} +1286.99 q^{95} +96.0000 q^{96} -902.223 q^{97} -98.0000 q^{98} -3.89292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

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