LMFDB - Embedded newform 966.4.a.f.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:	$3$
Coefficient field:	3.3.12197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 15x - 4 $ x^3 - x^2 - 15*x - 4
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			1.2
Root			$-0.272991$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +9.63795 q^{10} +43.0349 q^{11} -12.0000 q^{12} +48.6845 q^{13} +14.0000 q^{14} -14.4569 q^{15} +16.0000 q^{16} -24.7735 q^{17} +18.0000 q^{18} +63.2479 q^{19} +19.2759 q^{20} -21.0000 q^{21} +86.0698 q^{22} -23.0000 q^{23} -24.0000 q^{24} -101.777 q^{25} +97.3689 q^{26} -27.0000 q^{27} +28.0000 q^{28} -4.70005 q^{29} -28.9138 q^{30} -88.4310 q^{31} +32.0000 q^{32} -129.105 q^{33} -49.5470 q^{34} +33.7328 q^{35} +36.0000 q^{36} -168.863 q^{37} +126.496 q^{38} -146.053 q^{39} +38.5518 q^{40} +465.750 q^{41} -42.0000 q^{42} +254.877 q^{43} +172.140 q^{44} +43.3708 q^{45} -46.0000 q^{46} -513.188 q^{47} -48.0000 q^{48} +49.0000 q^{49} -203.555 q^{50} +74.3206 q^{51} +194.738 q^{52} +428.489 q^{53} -54.0000 q^{54} +207.384 q^{55} +56.0000 q^{56} -189.744 q^{57} -9.40009 q^{58} +158.984 q^{59} -57.8277 q^{60} -28.2878 q^{61} -176.862 q^{62} +63.0000 q^{63} +64.0000 q^{64} +234.609 q^{65} -258.209 q^{66} +797.236 q^{67} -99.0941 q^{68} +69.0000 q^{69} +67.4656 q^{70} -778.422 q^{71} +72.0000 q^{72} +526.081 q^{73} -337.726 q^{74} +305.332 q^{75} +252.992 q^{76} +301.244 q^{77} -292.107 q^{78} -108.025 q^{79} +77.1036 q^{80} +81.0000 q^{81} +931.500 q^{82} +409.259 q^{83} -84.0000 q^{84} -119.383 q^{85} +509.754 q^{86} +14.1001 q^{87} +344.279 q^{88} +888.952 q^{89} +86.7415 q^{90} +340.791 q^{91} -92.0000 q^{92} +265.293 q^{93} -1026.38 q^{94} +304.790 q^{95} -96.0000 q^{96} -255.899 q^{97} +98.0000 q^{98} +387.314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9 + 18 * q^10 + 53 * q^11 - 36 * q^12 + 61 * q^13 + 42 * q^14 - 27 * q^15 + 48 * q^16 - 2 * q^17 + 54 * q^18 + 63 * q^19 + 36 * q^20 - 63 * q^21 + 106 * q^22 - 69 * q^23 - 72 * q^24 - 72 * q^25 + 122 * q^26 - 81 * q^27 + 84 * q^28 + 312 * q^29 - 54 * q^30 + 220 * q^31 + 96 * q^32 - 159 * q^33 - 4 * q^34 + 63 * q^35 + 108 * q^36 - 44 * q^37 + 126 * q^38 - 183 * q^39 + 72 * q^40 + 171 * q^41 - 126 * q^42 - 627 * q^43 + 212 * q^44 + 81 * q^45 - 138 * q^46 + 353 * q^47 - 144 * q^48 + 147 * q^49 - 144 * q^50 + 6 * q^51 + 244 * q^52 - 504 * q^53 - 162 * q^54 + 1181 * q^55 + 168 * q^56 - 189 * q^57 + 624 * q^58 + 538 * q^59 - 108 * q^60 + 256 * q^61 + 440 * q^62 + 189 * q^63 + 192 * q^64 + 244 * q^65 - 318 * q^66 + 1113 * q^67 - 8 * q^68 + 207 * q^69 + 126 * q^70 + 53 * q^71 + 216 * q^72 + 360 * q^73 - 88 * q^74 + 216 * q^75 + 252 * q^76 + 371 * q^77 - 366 * q^78 + 134 * q^79 + 144 * q^80 + 243 * q^81 + 342 * q^82 + 1506 * q^83 - 252 * q^84 + 577 * q^85 - 1254 * q^86 - 936 * q^87 + 424 * q^88 + 2381 * q^89 + 162 * q^90 + 427 * q^91 - 276 * q^92 - 660 * q^93 + 706 * q^94 + 945 * q^95 - 288 * q^96 - 88 * q^97 + 294 * q^98 + 477 * 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
$5$	4.81897	0.431022	0.215511	−	0.976501i	$-0.430858\pi$
$5$	4.81897	0.431022	0.215511	+	0.976501i	$0.430858\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	9.63795	0.304779
$11$	43.0349	1.17959	0.589796	−	0.807553i	$-0.299208\pi$
$11$	43.0349	1.17959	0.589796	+	0.807553i	$0.299208\pi$
$12$	−12.0000	−0.288675
$13$	48.6845	1.03866	0.519332	−	0.854572i	$-0.326181\pi$
$13$	48.6845	1.03866	0.519332	+	0.854572i	$0.326181\pi$
$14$	14.0000	0.267261
$15$	−14.4569	−0.248851
$16$	16.0000	0.250000
$17$	−24.7735	−0.353439	−0.176719	−	0.984261i	$-0.556549\pi$
$17$	−24.7735	−0.353439	−0.176719	+	0.984261i	$0.556549\pi$
$18$	18.0000	0.235702
$19$	63.2479	0.763687	0.381844	−	0.924227i	$-0.375289\pi$
$19$	63.2479	0.763687	0.381844	+	0.924227i	$0.375289\pi$
$20$	19.2759	0.215511
$21$	−21.0000	−0.218218
$22$	86.0698	0.834097
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	−101.777	−0.814220
$26$	97.3689	0.734447
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−4.70005	−0.0300957	−0.0150479	−	0.999887i	$-0.504790\pi$
$29$	−4.70005	−0.0300957	−0.0150479	+	0.999887i	$0.504790\pi$
$30$	−28.9138	−0.175964
$31$	−88.4310	−0.512345	−0.256172	−	0.966631i	$-0.582461\pi$
$31$	−88.4310	−0.512345	−0.256172	+	0.966631i	$0.582461\pi$
$32$	32.0000	0.176777
$33$	−129.105	−0.681037
$34$	−49.5470	−0.249919
$35$	33.7328	0.162911
$36$	36.0000	0.166667
$37$	−168.863	−0.750294	−0.375147	−	0.926965i	$-0.622408\pi$
$37$	−168.863	−0.750294	−0.375147	+	0.926965i	$0.622408\pi$
$38$	126.496	0.540009
$39$	−146.053	−0.599673
$40$	38.5518	0.152389
$41$	465.750	1.77410	0.887048	−	0.461677i	$-0.152752\pi$
$41$	465.750	1.77410	0.887048	+	0.461677i	$0.152752\pi$
$42$	−42.0000	−0.154303
$43$	254.877	0.903915	0.451958	−	0.892039i	$-0.350726\pi$
$43$	254.877	0.903915	0.451958	+	0.892039i	$0.350726\pi$
$44$	172.140	0.589796
$45$	43.3708	0.143674
$46$	−46.0000	−0.147442
$47$	−513.188	−1.59268	−0.796342	−	0.604847i	$-0.793234\pi$
$47$	−513.188	−1.59268	−0.796342	+	0.604847i	$0.793234\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−203.555	−0.575740
$51$	74.3206	0.204058
$52$	194.738	0.519332
$53$	428.489	1.11052	0.555259	−	0.831677i	$-0.312619\pi$
$53$	428.489	1.11052	0.555259	+	0.831677i	$0.312619\pi$
$54$	−54.0000	−0.136083
$55$	207.384	0.508430
$56$	56.0000	0.133631
$57$	−189.744	−0.440915
$58$	−9.40009	−0.0212809
$59$	158.984	0.350812	0.175406	−	0.984496i	$-0.443876\pi$
$59$	158.984	0.350812	0.175406	+	0.984496i	$0.443876\pi$
$60$	−57.8277	−0.124425
$61$	−28.2878	−0.0593752	−0.0296876	−	0.999559i	$-0.509451\pi$
$61$	−28.2878	−0.0593752	−0.0296876	+	0.999559i	$0.509451\pi$
$62$	−176.862	−0.362282
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	234.609	0.447687
$66$	−258.209	−0.481566
$67$	797.236	1.45370	0.726850	−	0.686796i	$-0.240984\pi$
$67$	797.236	1.45370	0.726850	+	0.686796i	$0.240984\pi$
$68$	−99.0941	−0.176719
$69$	69.0000	0.120386
$70$	67.4656	0.115196
$71$	−778.422	−1.30115	−0.650576	−	0.759442i	$-0.725472\pi$
$71$	−778.422	−1.30115	−0.650576	+	0.759442i	$0.725472\pi$
$72$	72.0000	0.117851
$73$	526.081	0.843468	0.421734	−	0.906720i	$-0.361422\pi$
$73$	526.081	0.843468	0.421734	+	0.906720i	$0.361422\pi$
$74$	−337.726	−0.530538
$75$	305.332	0.470090
$76$	252.992	0.381844
$77$	301.244	0.445844
$78$	−292.107	−0.424033
$79$	−108.025	−0.153845	−0.0769223	−	0.997037i	$-0.524509\pi$
$79$	−108.025	−0.153845	−0.0769223	+	0.997037i	$0.524509\pi$
$80$	77.1036	0.107756
$81$	81.0000	0.111111
$82$	931.500	1.25448
$83$	409.259	0.541229	0.270615	−	0.962688i	$-0.412773\pi$
$83$	409.259	0.541229	0.270615	+	0.962688i	$0.412773\pi$
$84$	−84.0000	−0.109109
$85$	−119.383	−0.152340
$86$	509.754	0.639165
$87$	14.1001	0.0173758
$88$	344.279	0.417049
$89$	888.952	1.05875	0.529375	−	0.848388i	$-0.322427\pi$
$89$	888.952	1.05875	0.529375	+	0.848388i	$0.322427\pi$
$90$	86.7415	0.101593
$91$	340.791	0.392578
$92$	−92.0000	−0.104257
$93$	265.293	0.295802
$94$	−1026.38	−1.12620
$95$	304.790	0.329166
$96$	−96.0000	−0.102062
$97$	−255.899	−0.267862	−0.133931	−	0.990991i	$-0.542760\pi$
$97$	−255.899	−0.267862	−0.133931	+	0.990991i	$0.542760\pi$
$98$	98.0000	0.101015
$99$	387.314	0.393197
$100$	−407.110	−0.407110
$101$	726.548	0.715784	0.357892	−	0.933763i	$-0.383496\pi$
$101$	726.548	0.715784	0.357892	+	0.933763i	$0.383496\pi$
$102$	148.641	0.144291
$103$	623.121	0.596097	0.298048	−	0.954551i	$-0.403664\pi$
$103$	623.121	0.596097	0.298048	+	0.954551i	$0.403664\pi$
$104$	389.476	0.367223
$105$	−101.198	−0.0940567
$106$	856.978	0.785255
$107$	−34.0096	−0.0307274	−0.0153637	−	0.999882i	$-0.504891\pi$
$107$	−34.0096	−0.0307274	−0.0153637	+	0.999882i	$0.504891\pi$
$108$	−108.000	−0.0962250
$109$	−177.207	−0.155719	−0.0778596	−	0.996964i	$-0.524809\pi$
$109$	−177.207	−0.155719	−0.0778596	+	0.996964i	$0.524809\pi$
$110$	414.768	0.359514
$111$	506.589	0.433183
$112$	112.000	0.0944911
$113$	−1011.65	−0.842196	−0.421098	−	0.907015i	$-0.638355\pi$
$113$	−1011.65	−0.842196	−0.421098	+	0.907015i	$0.638355\pi$
$114$	−379.487	−0.311774
$115$	−110.836	−0.0898743
$116$	−18.8002	−0.0150479
$117$	438.160	0.346222
$118$	317.967	0.248062
$119$	−173.415	−0.133587
$120$	−115.655	−0.0879820
$121$	521.001	0.391436
$122$	−56.5757	−0.0419846
$123$	−1397.25	−1.02427
$124$	−353.724	−0.256172
$125$	−1092.83	−0.781969
$126$	126.000	0.0890871
$127$	−1522.05	−1.06346	−0.531731	−	0.846913i	$-0.678458\pi$
$127$	−1522.05	−1.06346	−0.531731	+	0.846913i	$0.678458\pi$
$128$	128.000	0.0883883
$129$	−764.631	−0.521876
$130$	469.218	0.316563
$131$	2533.05	1.68941	0.844707	−	0.535228i	$-0.179774\pi$
$131$	2533.05	1.68941	0.844707	+	0.535228i	$0.179774\pi$
$132$	−516.419	−0.340519
$133$	442.735	0.288647
$134$	1594.47	1.02792
$135$	−130.112	−0.0829502
$136$	−198.188	−0.124960
$137$	18.5942	0.0115957	0.00579783	−	0.999983i	$-0.498154\pi$
$137$	18.5942	0.0115957	0.00579783	+	0.999983i	$0.498154\pi$
$138$	138.000	0.0851257
$139$	2684.26	1.63796	0.818979	−	0.573824i	$-0.194541\pi$
$139$	2684.26	1.63796	0.818979	+	0.573824i	$0.194541\pi$
$140$	134.931	0.0814555
$141$	1539.56	0.919537
$142$	−1556.84	−0.920053
$143$	2095.13	1.22520
$144$	144.000	0.0833333
$145$	−22.6494	−0.0129719
$146$	1052.16	0.596422
$147$	−147.000	−0.0824786
$148$	−675.452	−0.375147
$149$	71.6799	0.0394111	0.0197055	−	0.999806i	$-0.493727\pi$
$149$	71.6799	0.0394111	0.0197055	+	0.999806i	$0.493727\pi$
$150$	610.665	0.332404
$151$	−1287.00	−0.693604	−0.346802	−	0.937938i	$-0.612732\pi$
$151$	−1287.00	−0.693604	−0.346802	+	0.937938i	$0.612732\pi$
$152$	505.983	0.270004
$153$	−222.962	−0.117813
$154$	602.488	0.315259
$155$	−426.147	−0.220832
$156$	−584.214	−0.299837
$157$	−1520.90	−0.773128	−0.386564	−	0.922262i	$-0.626338\pi$
$157$	−1520.90	−0.773128	−0.386564	+	0.922262i	$0.626338\pi$
$158$	−216.049	−0.108785
$159$	−1285.47	−0.641158
$160$	154.207	0.0761947
$161$	−161.000	−0.0788110
$162$	162.000	0.0785674
$163$	2629.34	1.26347	0.631736	−	0.775184i	$-0.282343\pi$
$163$	2629.34	1.26347	0.631736	+	0.775184i	$0.282343\pi$
$164$	1863.00	0.887048
$165$	−622.152	−0.293542
$166$	818.518	0.382707
$167$	254.418	0.117889	0.0589445	−	0.998261i	$-0.481227\pi$
$167$	254.418	0.117889	0.0589445	+	0.998261i	$0.481227\pi$
$168$	−168.000	−0.0771517
$169$	173.177	0.0788242
$170$	−238.766	−0.107721
$171$	569.231	0.254562
$172$	1019.51	0.451958
$173$	−1451.24	−0.637780	−0.318890	−	0.947792i	$-0.603310\pi$
$173$	−1451.24	−0.637780	−0.318890	+	0.947792i	$0.603310\pi$
$174$	28.2003	0.0122865
$175$	−712.442	−0.307746
$176$	688.558	0.294898
$177$	−476.951	−0.202541
$178$	1777.90	0.748649
$179$	1382.02	0.577078	0.288539	−	0.957468i	$-0.406830\pi$
$179$	1382.02	0.577078	0.288539	+	0.957468i	$0.406830\pi$
$180$	173.483	0.0718370
$181$	825.918	0.339171	0.169586	−	0.985515i	$-0.445757\pi$
$181$	825.918	0.339171	0.169586	+	0.985515i	$0.445757\pi$
$182$	681.582	0.277595
$183$	84.8635	0.0342803
$184$	−184.000	−0.0737210
$185$	−813.746	−0.323393
$186$	530.586	0.209164
$187$	−1066.13	−0.416914
$188$	−2052.75	−0.796342
$189$	−189.000	−0.0727393
$190$	609.580	0.232756
$191$	1746.50	0.661636	0.330818	−	0.943695i	$-0.392675\pi$
$191$	1746.50	0.661636	0.330818	+	0.943695i	$0.392675\pi$
$192$	−192.000	−0.0721688
$193$	2592.01	0.966720	0.483360	−	0.875422i	$-0.339416\pi$
$193$	2592.01	0.966720	0.483360	+	0.875422i	$0.339416\pi$
$194$	−511.798	−0.189407
$195$	−703.827	−0.258472
$196$	196.000	0.0714286
$197$	−2101.75	−0.760120	−0.380060	−	0.924962i	$-0.624097\pi$
$197$	−2101.75	−0.760120	−0.380060	+	0.924962i	$0.624097\pi$
$198$	774.628	0.278032
$199$	3228.44	1.15004	0.575020	−	0.818139i	$-0.304994\pi$
$199$	3228.44	1.15004	0.575020	+	0.818139i	$0.304994\pi$
$200$	−814.220	−0.287870
$201$	−2391.71	−0.839294
$202$	1453.10	0.506136
$203$	−32.9003	−0.0113751
$204$	297.282	0.102029
$205$	2244.44	0.764675
$206$	1246.24	0.421504
$207$	−207.000	−0.0695048
$208$	778.951	0.259666
$209$	2721.87	0.900839
$210$	−202.397	−0.0665082
$211$	−2689.98	−0.877658	−0.438829	−	0.898570i	$-0.644607\pi$
$211$	−2689.98	−0.877658	−0.438829	+	0.898570i	$0.644607\pi$
$212$	1713.96	0.555259
$213$	2335.27	0.751220
$214$	−68.0193	−0.0217276
$215$	1228.24	0.389607
$216$	−216.000	−0.0680414
$217$	−619.017	−0.193648
$218$	−354.415	−0.110110
$219$	−1578.24	−0.486976
$220$	829.536	0.254215
$221$	−1206.09	−0.367105
$222$	1013.18	0.306306
$223$	−2592.25	−0.778429	−0.389214	−	0.921147i	$-0.627253\pi$
$223$	−2592.25	−0.778429	−0.389214	+	0.921147i	$0.627253\pi$
$224$	224.000	0.0668153
$225$	−915.997	−0.271407
$226$	−2023.30	−0.595522
$227$	5463.45	1.59745	0.798726	−	0.601695i	$-0.205508\pi$
$227$	5463.45	1.59745	0.798726	+	0.601695i	$0.205508\pi$
$228$	−758.975	−0.220458
$229$	663.825	0.191558	0.0957790	−	0.995403i	$-0.469466\pi$
$229$	663.825	0.191558	0.0957790	+	0.995403i	$0.469466\pi$
$230$	−221.673	−0.0635507
$231$	−903.733	−0.257408
$232$	−37.6004	−0.0106405
$233$	−3961.76	−1.11392	−0.556961	−	0.830539i	$-0.688033\pi$
$233$	−3961.76	−1.11392	−0.556961	+	0.830539i	$0.688033\pi$
$234$	876.320	0.244816
$235$	−2473.04	−0.686482
$236$	635.935	0.175406
$237$	324.074	0.0888222
$238$	−346.829	−0.0944605
$239$	−2991.95	−0.809763	−0.404881	−	0.914369i	$-0.632687\pi$
$239$	−2991.95	−0.809763	−0.404881	+	0.914369i	$0.632687\pi$
$240$	−231.311	−0.0622127
$241$	−5740.49	−1.53435	−0.767173	−	0.641441i	$-0.778337\pi$
$241$	−5740.49	−1.53435	−0.767173	+	0.641441i	$0.778337\pi$
$242$	1042.00	0.276787
$243$	−243.000	−0.0641500
$244$	−113.151	−0.0296876
$245$	236.130	0.0615746
$246$	−2794.50	−0.724272
$247$	3079.19	0.793215
$248$	−707.448	−0.181141
$249$	−1227.78	−0.312479
$250$	−2185.67	−0.552936
$251$	1505.93	0.378698	0.189349	−	0.981910i	$-0.439362\pi$
$251$	1505.93	0.378698	0.189349	+	0.981910i	$0.439362\pi$
$252$	252.000	0.0629941
$253$	−989.802	−0.245962
$254$	−3044.09	−0.751982
$255$	358.149	0.0879535
$256$	256.000	0.0625000
$257$	−5987.31	−1.45322	−0.726611	−	0.687050i	$-0.758906\pi$
$257$	−5987.31	−1.45322	−0.726611	+	0.687050i	$0.758906\pi$
$258$	−1529.26	−0.369022
$259$	−1182.04	−0.283585
$260$	938.437	0.223844
$261$	−42.3004	−0.0100319
$262$	5066.09	1.19460
$263$	−1898.18	−0.445046	−0.222523	−	0.974927i	$-0.571429\pi$
$263$	−1898.18	−0.445046	−0.222523	+	0.974927i	$0.571429\pi$
$264$	−1032.84	−0.240783
$265$	2064.88	0.478658
$266$	885.470	0.204104
$267$	−2666.86	−0.611269
$268$	3188.94	0.726850
$269$	4317.05	0.978496	0.489248	−	0.872145i	$-0.337271\pi$
$269$	4317.05	0.978496	0.489248	+	0.872145i	$0.337271\pi$
$270$	−260.225	−0.0586547
$271$	−5978.25	−1.34005	−0.670024	−	0.742340i	$-0.733716\pi$
$271$	−5978.25	−1.34005	−0.670024	+	0.742340i	$0.733716\pi$
$272$	−396.376	−0.0883597
$273$	−1022.37	−0.226655
$274$	37.1883	0.00819938
$275$	−4379.98	−0.960447
$276$	276.000	0.0601929
$277$	4212.43	0.913719	0.456859	−	0.889539i	$-0.348974\pi$
$277$	4212.43	0.913719	0.456859	+	0.889539i	$0.348974\pi$
$278$	5368.52	1.15821
$279$	−795.879	−0.170782
$280$	269.863	0.0575978
$281$	4850.74	1.02979	0.514895	−	0.857253i	$-0.327831\pi$
$281$	4850.74	1.02979	0.514895	+	0.857253i	$0.327831\pi$
$282$	3079.13	0.650211
$283$	689.593	0.144848	0.0724241	−	0.997374i	$-0.476926\pi$
$283$	689.593	0.144848	0.0724241	+	0.997374i	$0.476926\pi$
$284$	−3113.69	−0.650576
$285$	−914.370	−0.190044
$286$	4190.26	0.866347
$287$	3260.25	0.670545
$288$	288.000	0.0589256
$289$	−4299.27	−0.875081
$290$	−45.2988	−0.00917254
$291$	767.696	0.154650
$292$	2104.32	0.421734
$293$	−1099.32	−0.219191	−0.109596	−	0.993976i	$-0.534956\pi$
$293$	−1099.32	−0.219191	−0.109596	+	0.993976i	$0.534956\pi$
$294$	−294.000	−0.0583212
$295$	766.138	0.151208
$296$	−1350.90	−0.265269
$297$	−1161.94	−0.227012
$298$	143.360	0.0278678
$299$	−1119.74	−0.216577
$300$	1221.33	0.235045
$301$	1784.14	0.341648
$302$	−2573.99	−0.490452
$303$	−2179.64	−0.413258
$304$	1011.97	0.190922
$305$	−136.318	−0.0255920
$306$	−445.923	−0.0833064
$307$	−3586.44	−0.666739	−0.333369	−	0.942796i	$-0.608186\pi$
$307$	−3586.44	−0.666739	−0.333369	+	0.942796i	$0.608186\pi$
$308$	1204.98	0.222922
$309$	−1869.36	−0.344157
$310$	−852.294	−0.156152
$311$	1271.25	0.231787	0.115894	−	0.993262i	$-0.463027\pi$
$311$	1271.25	0.231787	0.115894	+	0.993262i	$0.463027\pi$
$312$	−1168.43	−0.212017
$313$	−7502.44	−1.35483	−0.677417	−	0.735599i	$-0.736901\pi$
$313$	−7502.44	−1.35483	−0.677417	+	0.735599i	$0.736901\pi$
$314$	−3041.80	−0.546684
$315$	303.595	0.0543037
$316$	−432.099	−0.0769223
$317$	−7578.44	−1.34274	−0.671369	−	0.741123i	$-0.734293\pi$
$317$	−7578.44	−1.34274	−0.671369	+	0.741123i	$0.734293\pi$
$318$	−2570.93	−0.453367
$319$	−202.266	−0.0355007
$320$	308.414	0.0538778
$321$	102.029	0.0177405
$322$	−322.000	−0.0557278
$323$	−1566.87	−0.269917
$324$	324.000	0.0555556
$325$	−4954.98	−0.845701
$326$	5258.68	0.893410
$327$	531.622	0.0899045
$328$	3726.00	0.627238
$329$	−3592.32	−0.601978
$330$	−1244.30	−0.207566
$331$	−5168.33	−0.858240	−0.429120	−	0.903248i	$-0.641176\pi$
$331$	−5168.33	−0.858240	−0.429120	+	0.903248i	$0.641176\pi$
$332$	1637.04	0.270615
$333$	−1519.77	−0.250098
$334$	508.836	0.0833601
$335$	3841.86	0.626577
$336$	−336.000	−0.0545545
$337$	−3372.75	−0.545180	−0.272590	−	0.962130i	$-0.587880\pi$
$337$	−3372.75	−0.545180	−0.272590	+	0.962130i	$0.587880\pi$
$338$	346.354	0.0557372
$339$	3034.95	0.486242
$340$	−477.532	−0.0761700
$341$	−3805.62	−0.604357
$342$	1138.46	0.180003
$343$	343.000	0.0539949
$344$	2039.01	0.319582
$345$	332.509	0.0518890
$346$	−2902.48	−0.450978
$347$	4931.32	0.762903	0.381451	−	0.924389i	$-0.375424\pi$
$347$	4931.32	0.762903	0.381451	+	0.924389i	$0.375424\pi$
$348$	56.4005	0.00868789
$349$	−8112.70	−1.24431	−0.622153	−	0.782895i	$-0.713742\pi$
$349$	−8112.70	−1.24431	−0.622153	+	0.782895i	$0.713742\pi$
$350$	−1424.88	−0.217609
$351$	−1314.48	−0.199891
$352$	1377.12	0.208524
$353$	1934.09	0.291618	0.145809	−	0.989313i	$-0.453421\pi$
$353$	1934.09	0.291618	0.145809	+	0.989313i	$0.453421\pi$
$354$	−953.902	−0.143218
$355$	−3751.20	−0.560825
$356$	3555.81	0.529375
$357$	520.244	0.0771267
$358$	2764.04	0.408056
$359$	−308.167	−0.0453049	−0.0226524	−	0.999743i	$-0.507211\pi$
$359$	−308.167	−0.0453049	−0.0226524	+	0.999743i	$0.507211\pi$
$360$	346.966	0.0507964
$361$	−2858.70	−0.416782
$362$	1651.84	0.239830
$363$	−1563.00	−0.225996
$364$	1363.16	0.196289
$365$	2535.17	0.363553
$366$	169.727	0.0242398
$367$	−6831.82	−0.971711	−0.485856	−	0.874039i	$-0.661492\pi$
$367$	−6831.82	−0.971711	−0.485856	+	0.874039i	$0.661492\pi$
$368$	−368.000	−0.0521286
$369$	4191.75	0.591365
$370$	−1627.49	−0.228674
$371$	2999.42	0.419737
$372$	1061.17	0.147901
$373$	−10390.3	−1.44232	−0.721162	−	0.692766i	$-0.756392\pi$
$373$	−10390.3	−1.44232	−0.721162	+	0.692766i	$0.756392\pi$
$374$	−2132.25	−0.294802
$375$	3278.50	0.451470
$376$	−4105.50	−0.563099
$377$	−228.819	−0.0312594
$378$	−378.000	−0.0514344
$379$	4526.85	0.613532	0.306766	−	0.951785i	$-0.400753\pi$
$379$	4526.85	0.613532	0.306766	+	0.951785i	$0.400753\pi$
$380$	1219.16	0.164583
$381$	4566.14	0.613990
$382$	3493.00	0.467847
$383$	−1271.78	−0.169674	−0.0848369	−	0.996395i	$-0.527037\pi$
$383$	−1271.78	−0.169674	−0.0848369	+	0.996395i	$0.527037\pi$
$384$	−384.000	−0.0510310
$385$	1451.69	0.192168
$386$	5184.02	0.683575
$387$	2293.89	0.301305
$388$	−1023.60	−0.133931
$389$	−9955.76	−1.29763	−0.648813	−	0.760948i	$-0.724734\pi$
$389$	−9955.76	−1.29763	−0.648813	+	0.760948i	$0.724734\pi$
$390$	−1407.65	−0.182768
$391$	569.791	0.0736971
$392$	392.000	0.0505076
$393$	−7599.14	−0.975384
$394$	−4203.51	−0.537486
$395$	−520.568	−0.0663104
$396$	1549.26	0.196599
$397$	6168.22	0.779784	0.389892	−	0.920861i	$-0.372512\pi$
$397$	6168.22	0.779784	0.389892	+	0.920861i	$0.372512\pi$
$398$	6456.88	0.813201
$399$	−1328.21	−0.166650
$400$	−1628.44	−0.203555
$401$	−5134.86	−0.639458	−0.319729	−	0.947509i	$-0.603592\pi$
$401$	−5134.86	−0.639458	−0.319729	+	0.947509i	$0.603592\pi$
$402$	−4783.42	−0.593470
$403$	−4305.22	−0.532154
$404$	2906.19	0.357892
$405$	390.337	0.0478913
$406$	−65.8006	−0.00804343
$407$	−7266.99	−0.885041
$408$	594.565	0.0721454
$409$	−6805.93	−0.822816	−0.411408	−	0.911451i	$-0.634963\pi$
$409$	−6805.93	−0.822816	−0.411408	+	0.911451i	$0.634963\pi$
$410$	4488.87	0.540707
$411$	−55.7825	−0.00669476
$412$	2492.49	0.298048
$413$	1112.89	0.132594
$414$	−414.000	−0.0491473
$415$	1972.21	0.233282
$416$	1557.90	0.183612
$417$	−8052.79	−0.945675
$418$	5443.73	0.636989
$419$	9403.51	1.09640	0.548200	−	0.836347i	$-0.315313\pi$
$419$	9403.51	1.09640	0.548200	+	0.836347i	$0.315313\pi$
$420$	−404.794	−0.0470284
$421$	2153.32	0.249279	0.124639	−	0.992202i	$-0.460223\pi$
$421$	2153.32	0.249279	0.124639	+	0.992202i	$0.460223\pi$
$422$	−5379.96	−0.620598
$423$	−4618.69	−0.530895
$424$	3427.91	0.392628
$425$	2521.39	0.287777
$426$	4670.53	0.531193
$427$	−198.015	−0.0224417
$428$	−136.039	−0.0153637
$429$	−6285.39	−0.707369
$430$	2456.49	0.275494
$431$	6346.56	0.709287	0.354644	−	0.935002i	$-0.384602\pi$
$431$	6346.56	0.709287	0.354644	+	0.935002i	$0.384602\pi$
$432$	−432.000	−0.0481125
$433$	−718.947	−0.0797931	−0.0398965	−	0.999204i	$-0.512703\pi$
$433$	−718.947	−0.0797931	−0.0398965	+	0.999204i	$0.512703\pi$
$434$	−1238.03	−0.136930
$435$	67.9482	0.00748935
$436$	−708.830	−0.0778596
$437$	−1454.70	−0.159240
$438$	−3156.49	−0.344344
$439$	7477.10	0.812898	0.406449	−	0.913673i	$-0.366767\pi$
$439$	7477.10	0.812898	0.406449	+	0.913673i	$0.366767\pi$
$440$	1659.07	0.179757
$441$	441.000	0.0476190
$442$	−2412.17	−0.259582
$443$	12703.0	1.36239	0.681196	−	0.732101i	$-0.261460\pi$
$443$	12703.0	1.36239	0.681196	+	0.732101i	$0.261460\pi$
$444$	2026.35	0.216591
$445$	4283.84	0.456345
$446$	−5184.49	−0.550432
$447$	−215.040	−0.0227540
$448$	448.000	0.0472456
$449$	634.326	0.0666719	0.0333359	−	0.999444i	$-0.489387\pi$
$449$	634.326	0.0666719	0.0333359	+	0.999444i	$0.489387\pi$
$450$	−1831.99	−0.191913
$451$	20043.5	2.09271
$452$	−4046.60	−0.421098
$453$	3860.99	0.400453
$454$	10926.9	1.12957
$455$	1642.26	0.169210
$456$	−1517.95	−0.155887
$457$	1586.41	0.162384	0.0811918	−	0.996698i	$-0.474127\pi$
$457$	1586.41	0.162384	0.0811918	+	0.996698i	$0.474127\pi$
$458$	1327.65	0.135452
$459$	668.885	0.0680194
$460$	−443.346	−0.0449372
$461$	12274.6	1.24010	0.620051	−	0.784562i	$-0.287112\pi$
$461$	12274.6	1.24010	0.620051	+	0.784562i	$0.287112\pi$
$462$	−1807.47	−0.182015
$463$	−11981.2	−1.20262	−0.601312	−	0.799014i	$-0.705355\pi$
$463$	−11981.2	−1.20262	−0.601312	+	0.799014i	$0.705355\pi$
$464$	−75.2007	−0.00752394
$465$	1278.44	0.127497
$466$	−7923.52	−0.787661
$467$	4935.51	0.489054	0.244527	−	0.969643i	$-0.421367\pi$
$467$	4935.51	0.489054	0.244527	+	0.969643i	$0.421367\pi$
$468$	1752.64	0.173111
$469$	5580.65	0.549447
$470$	−4946.08	−0.485416
$471$	4562.71	0.446366
$472$	1271.87	0.124031
$473$	10968.6	1.06625
$474$	648.148	0.0628068
$475$	−6437.21	−0.621809
$476$	−693.659	−0.0667937
$477$	3856.40	0.370173
$478$	−5983.91	−0.572589
$479$	−7814.60	−0.745424	−0.372712	−	0.927947i	$-0.621572\pi$
$479$	−7814.60	−0.745424	−0.372712	+	0.927947i	$0.621572\pi$
$480$	−462.621	−0.0439910
$481$	−8221.00	−0.779304
$482$	−11481.0	−1.08495
$483$	483.000	0.0455016
$484$	2084.00	0.195718
$485$	−1233.17	−0.115454
$486$	−486.000	−0.0453609
$487$	−1993.13	−0.185457	−0.0927284	−	0.995691i	$-0.529559\pi$
$487$	−1993.13	−0.185457	−0.0927284	+	0.995691i	$0.529559\pi$
$488$	−226.303	−0.0209923
$489$	−7888.02	−0.729466
$490$	472.259	0.0435398
$491$	−2069.52	−0.190216	−0.0951081	−	0.995467i	$-0.530320\pi$
$491$	−2069.52	−0.190216	−0.0951081	+	0.995467i	$0.530320\pi$
$492$	−5589.00	−0.512137
$493$	116.437	0.0106370
$494$	6158.38	0.560888
$495$	1866.46	0.169477
$496$	−1414.90	−0.128086
$497$	−5448.96	−0.491789
$498$	−2455.56	−0.220956
$499$	−16681.6	−1.49654	−0.748268	−	0.663397i	$-0.769114\pi$
$499$	−16681.6	−1.49654	−0.748268	+	0.663397i	$0.769114\pi$
$500$	−4371.34	−0.390984
$501$	−763.254	−0.0680632
$502$	3011.85	0.267780
$503$	547.940	0.0485714	0.0242857	−	0.999705i	$-0.492269\pi$
$503$	547.940	0.0485714	0.0242857	+	0.999705i	$0.492269\pi$
$504$	504.000	0.0445435
$505$	3501.21	0.308519
$506$	−1979.60	−0.173921
$507$	−519.531	−0.0455092
$508$	−6088.18	−0.531731
$509$	12549.1	1.09279	0.546395	−	0.837528i	$-0.316000\pi$
$509$	12549.1	1.09279	0.546395	+	0.837528i	$0.316000\pi$
$510$	716.298	0.0621925
$511$	3682.57	0.318801
$512$	512.000	0.0441942
$513$	−1707.69	−0.146972
$514$	−11974.6	−1.02758
$515$	3002.81	0.256931
$516$	−3058.52	−0.260938
$517$	−22085.0	−1.87872
$518$	−2364.08	−0.200525
$519$	4353.73	0.368222
$520$	1876.87	0.158281
$521$	15526.1	1.30559	0.652794	−	0.757536i	$-0.273597\pi$
$521$	15526.1	1.30559	0.652794	+	0.757536i	$0.273597\pi$
$522$	−84.6008	−0.00709363
$523$	15227.7	1.27316	0.636579	−	0.771212i	$-0.280349\pi$
$523$	15227.7	1.27316	0.636579	+	0.771212i	$0.280349\pi$
$524$	10132.2	0.844707
$525$	2137.33	0.177677
$526$	−3796.37	−0.314695
$527$	2190.75	0.181083
$528$	−2065.67	−0.170259
$529$	529.000	0.0434783
$530$	4129.75	0.338462
$531$	1430.85	0.116937
$532$	1770.94	0.144323
$533$	22674.8	1.84269
$534$	−5333.71	−0.432233
$535$	−163.892	−0.0132442
$536$	6377.89	0.513960
$537$	−4146.06	−0.333176
$538$	8634.11	0.691901
$539$	2108.71	0.168513
$540$	−520.449	−0.0414751
$541$	−18557.1	−1.47473	−0.737367	−	0.675493i	$-0.763931\pi$
$541$	−18557.1	−1.47473	−0.737367	+	0.675493i	$0.763931\pi$
$542$	−11956.5	−0.947557
$543$	−2477.75	−0.195821
$544$	−792.753	−0.0624798
$545$	−853.958	−0.0671184
$546$	−2044.75	−0.160269
$547$	−2032.79	−0.158895	−0.0794476	−	0.996839i	$-0.525316\pi$
$547$	−2032.79	−0.158895	−0.0794476	+	0.996839i	$0.525316\pi$
$548$	74.3766	0.00579783
$549$	−254.591	−0.0197917
$550$	−8759.96	−0.679138
$551$	−297.268	−0.0229837
$552$	552.000	0.0425628
$553$	−756.172	−0.0581478
$554$	8424.85	0.646097
$555$	2441.24	0.186711
$556$	10737.0	0.818979
$557$	−11605.7	−0.882855	−0.441428	−	0.897297i	$-0.645528\pi$
$557$	−11605.7	−0.882855	−0.441428	+	0.897297i	$0.645528\pi$
$558$	−1591.76	−0.120761
$559$	12408.5	0.938865
$560$	539.725	0.0407278
$561$	3198.38	0.240705
$562$	9701.48	0.728171
$563$	154.171	0.0115409	0.00577047	−	0.999983i	$-0.498163\pi$
$563$	154.171	0.0115409	0.00577047	+	0.999983i	$0.498163\pi$
$564$	6158.26	0.459768
$565$	−4875.12	−0.363005
$566$	1379.19	0.102423
$567$	567.000	0.0419961
$568$	−6227.38	−0.460026
$569$	−20639.0	−1.52062	−0.760309	−	0.649562i	$-0.774952\pi$
$569$	−20639.0	−1.52062	−0.760309	+	0.649562i	$0.774952\pi$
$570$	−1828.74	−0.134382
$571$	−22691.0	−1.66303	−0.831515	−	0.555502i	$-0.812526\pi$
$571$	−22691.0	−1.66303	−0.831515	+	0.555502i	$0.812526\pi$
$572$	8380.52	0.612600
$573$	−5239.51	−0.381996
$574$	6520.50	0.474147
$575$	2340.88	0.169777
$576$	576.000	0.0416667
$577$	−53.9391	−0.00389171	−0.00194585	−	0.999998i	$-0.500619\pi$
$577$	−53.9391	−0.00389171	−0.00194585	+	0.999998i	$0.500619\pi$
$578$	−8598.55	−0.618776
$579$	−7776.03	−0.558136
$580$	−90.5976	−0.00648597
$581$	2864.81	0.204565
$582$	1535.39	0.109354
$583$	18440.0	1.30996
$584$	4208.65	0.298211
$585$	2111.48	0.149229
$586$	−2198.64	−0.154991
$587$	17794.4	1.25120	0.625600	−	0.780144i	$-0.284854\pi$
$587$	17794.4	1.25120	0.625600	+	0.780144i	$0.284854\pi$
$588$	−588.000	−0.0412393
$589$	−5593.08	−0.391271
$590$	1532.28	0.106920
$591$	6305.26	0.438856
$592$	−2701.81	−0.187574
$593$	−27738.6	−1.92089	−0.960444	−	0.278474i	$-0.910171\pi$
$593$	−27738.6	−1.92089	−0.960444	+	0.278474i	$0.910171\pi$
$594$	−2323.88	−0.160522
$595$	−835.681	−0.0575791
$596$	286.720	0.0197055
$597$	−9685.32	−0.663976
$598$	−2239.49	−0.153143
$599$	2927.43	0.199686	0.0998428	−	0.995003i	$-0.468166\pi$
$599$	2927.43	0.199686	0.0998428	+	0.995003i	$0.468166\pi$
$600$	2442.66	0.166202
$601$	−9902.60	−0.672106	−0.336053	−	0.941843i	$-0.609092\pi$
$601$	−9902.60	−0.672106	−0.336053	+	0.941843i	$0.609092\pi$
$602$	3568.28	0.241582
$603$	7175.12	0.484567
$604$	−5147.98	−0.346802
$605$	2510.69	0.168717
$606$	−4359.29	−0.292218
$607$	4754.02	0.317891	0.158946	−	0.987287i	$-0.449191\pi$
$607$	4754.02	0.317891	0.158946	+	0.987287i	$0.449191\pi$
$608$	2023.93	0.135002
$609$	98.7010	0.00656743
$610$	−272.637	−0.0180963
$611$	−24984.3	−1.65426
$612$	−891.847	−0.0589065
$613$	−24542.3	−1.61706	−0.808529	−	0.588457i	$-0.799736\pi$
$613$	−24542.3	−1.61706	−0.808529	+	0.588457i	$0.799736\pi$
$614$	−7172.88	−0.471456
$615$	−6733.31	−0.441485
$616$	2409.95	0.157630
$617$	24061.2	1.56996	0.784981	−	0.619520i	$-0.212673\pi$
$617$	24061.2	1.56996	0.784981	+	0.619520i	$0.212673\pi$
$618$	−3738.73	−0.243355
$619$	668.751	0.0434239	0.0217119	−	0.999764i	$-0.493088\pi$
$619$	668.751	0.0434239	0.0217119	+	0.999764i	$0.493088\pi$
$620$	−1704.59	−0.110416
$621$	621.000	0.0401286
$622$	2542.49	0.163898
$623$	6222.66	0.400170
$624$	−2336.85	−0.149918
$625$	7455.84	0.477174
$626$	−15004.9	−0.958013
$627$	−8165.60	−0.520100
$628$	−6083.61	−0.386564
$629$	4183.33	0.265183
$630$	607.191	0.0383985
$631$	−22237.5	−1.40295	−0.701476	−	0.712693i	$-0.747475\pi$
$631$	−22237.5	−1.40295	−0.701476	+	0.712693i	$0.747475\pi$
$632$	−864.197	−0.0543923
$633$	8069.94	0.506716
$634$	−15156.9	−0.949459
$635$	−7334.70	−0.458376
$636$	−5141.87	−0.320579
$637$	2385.54	0.148381
$638$	−404.532	−0.0251028
$639$	−7005.80	−0.433717
$640$	616.829	0.0380973
$641$	−6268.56	−0.386261	−0.193131	−	0.981173i	$-0.561864\pi$
$641$	−6268.56	−0.386261	−0.193131	+	0.981173i	$0.561864\pi$
$642$	204.058	0.0125444
$643$	−3657.99	−0.224350	−0.112175	−	0.993688i	$-0.535782\pi$
$643$	−3657.99	−0.224350	−0.112175	+	0.993688i	$0.535782\pi$
$644$	−644.000	−0.0394055
$645$	−3684.73	−0.224940
$646$	−3133.75	−0.190860
$647$	29876.0	1.81537	0.907687	−	0.419647i	$-0.137846\pi$
$647$	29876.0	1.81537	0.907687	+	0.419647i	$0.137846\pi$
$648$	648.000	0.0392837
$649$	6841.84	0.413815
$650$	−9909.96	−0.598001
$651$	1857.05	0.111803
$652$	10517.4	0.631736
$653$	−15406.4	−0.923274	−0.461637	−	0.887069i	$-0.652738\pi$
$653$	−15406.4	−0.923274	−0.461637	+	0.887069i	$0.652738\pi$
$654$	1063.24	0.0635721
$655$	12206.7	0.728175
$656$	7452.00	0.443524
$657$	4734.73	0.281156
$658$	−7184.63	−0.425663
$659$	11969.6	0.707543	0.353772	−	0.935332i	$-0.384899\pi$
$659$	11969.6	0.707543	0.353772	+	0.935332i	$0.384899\pi$
$660$	−2488.61	−0.146771
$661$	19192.9	1.12938	0.564688	−	0.825304i	$-0.308996\pi$
$661$	19192.9	1.12938	0.564688	+	0.825304i	$0.308996\pi$
$662$	−10336.7	−0.606867
$663$	3618.26	0.211948
$664$	3274.07	0.191353
$665$	2133.53	0.124413
$666$	−3039.53	−0.176846
$667$	108.101	0.00627540
$668$	1017.67	0.0589445
$669$	7776.74	0.449426
$670$	7683.72	0.443057
$671$	−1217.36	−0.0700385
$672$	−672.000	−0.0385758
$673$	−17503.4	−1.00253	−0.501267	−	0.865293i	$-0.667133\pi$
$673$	−17503.4	−1.00253	−0.501267	+	0.865293i	$0.667133\pi$
$674$	−6745.51	−0.385500
$675$	2747.99	0.156697
$676$	692.708	0.0394121
$677$	−27542.0	−1.56355	−0.781776	−	0.623560i	$-0.785686\pi$
$677$	−27542.0	−1.56355	−0.781776	+	0.623560i	$0.785686\pi$
$678$	6069.91	0.343825
$679$	−1791.29	−0.101242
$680$	−955.064	−0.0538603
$681$	−16390.3	−0.922290
$682$	−7611.24	−0.427345
$683$	4505.08	0.252389	0.126195	−	0.992005i	$-0.459724\pi$
$683$	4505.08	0.252389	0.126195	+	0.992005i	$0.459724\pi$
$684$	2276.92	0.127281
$685$	89.6048	0.00499799
$686$	686.000	0.0381802
$687$	−1991.47	−0.110596
$688$	4078.03	0.225979
$689$	20860.8	1.15346
$690$	665.018	0.0366910
$691$	−19738.4	−1.08666	−0.543332	−	0.839518i	$-0.682838\pi$
$691$	−19738.4	−1.08666	−0.543332	+	0.839518i	$0.682838\pi$
$692$	−5804.97	−0.318890
$693$	2711.20	0.148615
$694$	9862.65	0.539454
$695$	12935.4	0.705996
$696$	112.801	0.00614327
$697$	−11538.3	−0.627035
$698$	−16225.4	−0.879858
$699$	11885.3	0.643123
$700$	−2849.77	−0.153873
$701$	16160.7	0.870727	0.435364	−	0.900255i	$-0.356620\pi$
$701$	16160.7	0.870727	0.435364	+	0.900255i	$0.356620\pi$
$702$	−2628.96	−0.141344
$703$	−10680.2	−0.572990
$704$	2754.23	0.147449
$705$	7419.12	0.396341
$706$	3868.18	0.206205
$707$	5085.83	0.270541
$708$	−1907.80	−0.101271
$709$	−19644.9	−1.04059	−0.520295	−	0.853987i	$-0.674178\pi$
$709$	−19644.9	−1.04059	−0.520295	+	0.853987i	$0.674178\pi$
$710$	−7502.39	−0.396563
$711$	−972.222	−0.0512815
$712$	7111.62	0.374325
$713$	2033.91	0.106831
$714$	1040.49	0.0545368
$715$	10096.4	0.528088
$716$	5528.08	0.288539
$717$	8975.86	0.467517
$718$	−616.334	−0.0320354
$719$	8964.56	0.464982	0.232491	−	0.972599i	$-0.425312\pi$
$719$	8964.56	0.464982	0.232491	+	0.972599i	$0.425312\pi$
$720$	693.932	0.0359185
$721$	4361.85	0.225303
$722$	−5717.41	−0.294709
$723$	17221.5	0.885855
$724$	3303.67	0.169586
$725$	478.359	0.0245046
$726$	−3126.01	−0.159803
$727$	−10420.1	−0.531581	−0.265791	−	0.964031i	$-0.585633\pi$
$727$	−10420.1	−0.531581	−0.265791	+	0.964031i	$0.585633\pi$
$728$	2726.33	0.138797
$729$	729.000	0.0370370
$730$	5070.34	0.257071
$731$	−6314.20	−0.319479
$732$	339.454	0.0171401
$733$	−30932.4	−1.55868	−0.779341	−	0.626600i	$-0.784446\pi$
$733$	−30932.4	−1.55868	−0.779341	+	0.626600i	$0.784446\pi$
$734$	−13663.6	−0.687103
$735$	−708.389	−0.0355501
$736$	−736.000	−0.0368605
$737$	34309.0	1.71477
$738$	8383.50	0.418158
$739$	−35846.9	−1.78437	−0.892185	−	0.451671i	$-0.850828\pi$
$739$	−35846.9	−1.78437	−0.892185	+	0.451671i	$0.850828\pi$
$740$	−3254.98	−0.161697
$741$	−9237.57	−0.457963
$742$	5998.85	0.296799
$743$	−8603.86	−0.424825	−0.212412	−	0.977180i	$-0.568132\pi$
$743$	−8603.86	−0.424825	−0.212412	+	0.977180i	$0.568132\pi$
$744$	2122.34	0.104582
$745$	345.424	0.0169870
$746$	−20780.5	−1.01988
$747$	3683.33	0.180410
$748$	−4264.50	−0.208457
$749$	−238.067	−0.0116139
$750$	6557.01	0.319237
$751$	−16424.7	−0.798065	−0.399033	−	0.916937i	$-0.630654\pi$
$751$	−16424.7	−0.798065	−0.399033	+	0.916937i	$0.630654\pi$
$752$	−8211.01	−0.398171
$753$	−4517.78	−0.218641
$754$	−457.638	−0.0221037
$755$	−6202.00	−0.298959
$756$	−756.000	−0.0363696
$757$	29277.3	1.40568	0.702842	−	0.711346i	$-0.251914\pi$
$757$	29277.3	1.40568	0.702842	+	0.711346i	$0.251914\pi$
$758$	9053.70	0.433833
$759$	2969.41	0.142006
$760$	2438.32	0.116378
$761$	−4987.56	−0.237580	−0.118790	−	0.992919i	$-0.537902\pi$
$761$	−4987.56	−0.237580	−0.118790	+	0.992919i	$0.537902\pi$
$762$	9132.28	0.434157
$763$	−1240.45	−0.0588563
$764$	6986.01	0.330818
$765$	−1074.45	−0.0507800
$766$	−2543.56	−0.119977
$767$	7740.03	0.364376
$768$	−768.000	−0.0360844
$769$	23529.1	1.10336	0.551679	−	0.834057i	$-0.313987\pi$
$769$	23529.1	1.10336	0.551679	+	0.834057i	$0.313987\pi$
$770$	2903.38	0.135884
$771$	17961.9	0.839018
$772$	10368.0	0.483360
$773$	13327.5	0.620125	0.310063	−	0.950716i	$-0.399650\pi$
$773$	13327.5	0.620125	0.310063	+	0.950716i	$0.399650\pi$
$774$	4587.78	0.213055
$775$	9000.29	0.417161
$776$	−2047.19	−0.0947034
$777$	3546.12	0.163728
$778$	−19911.5	−0.917561
$779$	29457.7	1.35485
$780$	−2815.31	−0.129236
$781$	−33499.3	−1.53483
$782$	1139.58	0.0521117
$783$	126.901	0.00579193
$784$	784.000	0.0357143
$785$	−7329.19	−0.333235
$786$	−15198.3	−0.689701
$787$	13967.1	0.632624	0.316312	−	0.948655i	$-0.397555\pi$
$787$	13967.1	0.632624	0.316312	+	0.948655i	$0.397555\pi$
$788$	−8407.01	−0.380060
$789$	5694.55	0.256947
$790$	−1041.14	−0.0468885
$791$	−7081.56	−0.318320
$792$	3098.51	0.139016
$793$	−1377.18	−0.0616709
$794$	12336.4	0.551391
$795$	−6194.63	−0.276353
$796$	12913.8	0.575020
$797$	24891.3	1.10627	0.553133	−	0.833093i	$-0.313432\pi$
$797$	24891.3	1.10627	0.553133	+	0.833093i	$0.313432\pi$
$798$	−2656.41	−0.117840
$799$	12713.5	0.562917
$800$	−3256.88	−0.143935
$801$	8000.57	0.352917
$802$	−10269.7	−0.452165
$803$	22639.8	0.994947
$804$	−9566.83	−0.419647
$805$	−775.855	−0.0339693
$806$	−8610.43	−0.376290
$807$	−12951.2	−0.564935
$808$	5812.38	0.253068
$809$	44812.2	1.94748	0.973742	−	0.227656i	$-0.0731061\pi$
$809$	44812.2	1.94748	0.973742	+	0.227656i	$0.0731061\pi$
$810$	780.674	0.0338643
$811$	−11709.4	−0.506994	−0.253497	−	0.967336i	$-0.581581\pi$
$811$	−11709.4	−0.506994	−0.253497	+	0.967336i	$0.581581\pi$
$812$	−131.601	−0.00568756
$813$	17934.8	0.773677
$814$	−14534.0	−0.625818
$815$	12670.7	0.544584
$816$	1189.13	0.0510145
$817$	16120.4	0.690309
$818$	−13611.9	−0.581819
$819$	3067.12	0.130859
$820$	8977.75	0.382337
$821$	8677.96	0.368895	0.184448	−	0.982842i	$-0.440950\pi$
$821$	8677.96	0.368895	0.184448	+	0.982842i	$0.440950\pi$
$822$	−111.565	−0.00473391
$823$	22764.2	0.964169	0.482084	−	0.876125i	$-0.339880\pi$
$823$	22764.2	0.964169	0.482084	+	0.876125i	$0.339880\pi$
$824$	4984.97	0.210752
$825$	13139.9	0.554514
$826$	2225.77	0.0937585
$827$	−2370.25	−0.0996634	−0.0498317	−	0.998758i	$-0.515868\pi$
$827$	−2370.25	−0.0996634	−0.0498317	+	0.998758i	$0.515868\pi$
$828$	−828.000	−0.0347524
$829$	32978.6	1.38166	0.690830	−	0.723017i	$-0.257245\pi$
$829$	32978.6	1.38166	0.690830	+	0.723017i	$0.257245\pi$
$830$	3944.42	0.164955
$831$	−12637.3	−0.527536
$832$	3115.81	0.129833
$833$	−1213.90	−0.0504913
$834$	−16105.6	−0.668693
$835$	1226.03	0.0508127
$836$	10887.5	0.450420
$837$	2387.64	0.0986008
$838$	18807.0	0.775272
$839$	21927.5	0.902289	0.451145	−	0.892451i	$-0.351016\pi$
$839$	21927.5	0.902289	0.451145	+	0.892451i	$0.351016\pi$
$840$	−809.588	−0.0332541
$841$	−24366.9	−0.999094
$842$	4306.64	0.176267
$843$	−14552.2	−0.594549
$844$	−10759.9	−0.438829
$845$	834.535	0.0339750
$846$	−9237.38	−0.375399
$847$	3647.01	0.147949
$848$	6855.82	0.277630
$849$	−2068.78	−0.0836282
$850$	5042.77	0.203489
$851$	3883.85	0.156447
$852$	9341.07	0.375610
$853$	−21082.6	−0.846253	−0.423126	−	0.906071i	$-0.639067\pi$
$853$	−21082.6	−0.846253	−0.423126	+	0.906071i	$0.639067\pi$
$854$	−396.030	−0.0158687
$855$	2743.11	0.109722
$856$	−272.077	−0.0108638
$857$	34147.1	1.36108	0.680538	−	0.732713i	$-0.261746\pi$
$857$	34147.1	1.36108	0.680538	+	0.732713i	$0.261746\pi$
$858$	−12570.8	−0.500186
$859$	15856.5	0.629822	0.314911	−	0.949121i	$-0.398025\pi$
$859$	15856.5	0.629822	0.314911	+	0.949121i	$0.398025\pi$
$860$	4912.98	0.194804
$861$	−9780.75	−0.387139
$862$	12693.1	0.501542
$863$	−34127.0	−1.34611	−0.673057	−	0.739590i	$-0.735019\pi$
$863$	−34127.0	−1.34611	−0.673057	+	0.739590i	$0.735019\pi$
$864$	−864.000	−0.0340207
$865$	−6993.50	−0.274897
$866$	−1437.89	−0.0564222
$867$	12897.8	0.505228
$868$	−2476.07	−0.0968240
$869$	−4648.83	−0.181474
$870$	135.896	0.00529577
$871$	38813.0	1.50991
$872$	−1417.66	−0.0550551
$873$	−2303.09	−0.0892872
$874$	−2909.40	−0.112600
$875$	−7649.84	−0.295556
$876$	−6312.97	−0.243488
$877$	22085.6	0.850373	0.425187	−	0.905106i	$-0.360208\pi$
$877$	22085.6	0.850373	0.425187	+	0.905106i	$0.360208\pi$
$878$	14954.2	0.574806
$879$	3297.96	0.126550
$880$	3318.14	0.127107
$881$	17543.1	0.670876	0.335438	−	0.942062i	$-0.391116\pi$
$881$	17543.1	0.670876	0.335438	+	0.942062i	$0.391116\pi$
$882$	882.000	0.0336718
$883$	2720.55	0.103685	0.0518424	−	0.998655i	$-0.483491\pi$
$883$	2720.55	0.103685	0.0518424	+	0.998655i	$0.483491\pi$
$884$	−4824.34	−0.183552
$885$	−2298.41	−0.0872998
$886$	25406.1	0.963356
$887$	−9800.00	−0.370972	−0.185486	−	0.982647i	$-0.559386\pi$
$887$	−9800.00	−0.370972	−0.185486	+	0.982647i	$0.559386\pi$
$888$	4052.71	0.153153
$889$	−10654.3	−0.401951
$890$	8567.67	0.322684
$891$	3485.83	0.131066
$892$	−10369.0	−0.389214
$893$	−32458.1	−1.21631
$894$	−430.080	−0.0160895
$895$	6659.92	0.248733
$896$	896.000	0.0334077
$897$	3359.23	0.125041
$898$	1268.65	0.0471441
$899$	415.630	0.0154194
$900$	−3663.99	−0.135703
$901$	−10615.2	−0.392500
$902$	40087.0	1.47977
$903$	−5352.41	−0.197250
$904$	−8093.21	−0.297761
$905$	3980.08	0.146190
$906$	7721.97	0.283163
$907$	−22361.9	−0.818650	−0.409325	−	0.912389i	$-0.634236\pi$
$907$	−22361.9	−0.818650	−0.409325	+	0.912389i	$0.634236\pi$
$908$	21853.8	0.798726
$909$	6538.93	0.238595
$910$	3284.53	0.119649
$911$	20460.4	0.744109	0.372055	−	0.928211i	$-0.378653\pi$
$911$	20460.4	0.744109	0.372055	+	0.928211i	$0.378653\pi$
$912$	−3035.90	−0.110229
$913$	17612.4	0.638429
$914$	3172.83	0.114823
$915$	408.955	0.0147756
$916$	2655.30	0.0957790
$917$	17731.3	0.638539
$918$	1337.77	0.0480969
$919$	24141.2	0.866534	0.433267	−	0.901266i	$-0.357361\pi$
$919$	24141.2	0.866534	0.433267	+	0.901266i	$0.357361\pi$
$920$	−886.691	−0.0317754
$921$	10759.3	0.384942
$922$	24549.3	0.876884
$923$	−37897.1	−1.35146
$924$	−3614.93	−0.128704
$925$	17186.4	0.610905
$926$	−23962.5	−0.850384
$927$	5608.09	0.198699
$928$	−150.401	−0.00532023
$929$	−27309.5	−0.964475	−0.482237	−	0.876041i	$-0.660176\pi$
$929$	−27309.5	−0.964475	−0.482237	+	0.876041i	$0.660176\pi$
$930$	2556.88	0.0901542
$931$	3099.15	0.109098
$932$	−15847.0	−0.556961
$933$	−3813.74	−0.133822
$934$	9871.02	0.345813
$935$	−5137.63	−0.179699
$936$	3505.28	0.122408
$937$	−47133.7	−1.64332	−0.821659	−	0.569979i	$-0.806951\pi$
$937$	−47133.7	−1.64332	−0.821659	+	0.569979i	$0.806951\pi$
$938$	11161.3	0.388518
$939$	22507.3	0.782214
$940$	−9892.16	−0.343241
$941$	−20018.7	−0.693508	−0.346754	−	0.937956i	$-0.612716\pi$
$941$	−20018.7	−0.693508	−0.346754	+	0.937956i	$0.612716\pi$
$942$	9125.41	0.315628
$943$	−10712.3	−0.369925
$944$	2543.74	0.0877030
$945$	−910.786	−0.0313522
$946$	21937.2	0.753953
$947$	−5601.37	−0.192207	−0.0961035	−	0.995371i	$-0.530638\pi$
$947$	−5601.37	−0.192207	−0.0961035	+	0.995371i	$0.530638\pi$
$948$	1296.30	0.0444111
$949$	25612.0	0.876080
$950$	−12874.4	−0.439686
$951$	22735.3	0.775230
$952$	−1387.32	−0.0472303
$953$	23276.4	0.791182	0.395591	−	0.918427i	$-0.370540\pi$
$953$	23276.4	0.791182	0.395591	+	0.918427i	$0.370540\pi$
$954$	7712.80	0.261752
$955$	8416.35	0.285180
$956$	−11967.8	−0.404881
$957$	606.798	0.0204963
$958$	−15629.2	−0.527094
$959$	130.159	0.00438275
$960$	−925.243	−0.0311063
$961$	−21971.0	−0.737503
$962$	−16442.0	−0.551051
$963$	−306.087	−0.0102425
$964$	−22961.9	−0.767173
$965$	12490.8	0.416678
$966$	966.000	0.0321745
$967$	43459.8	1.44527	0.722634	−	0.691231i	$-0.242931\pi$
$967$	43459.8	1.44527	0.722634	+	0.691231i	$0.242931\pi$
$968$	4168.01	0.138393
$969$	4700.62	0.155837
$970$	−2466.34	−0.0816385
$971$	−53549.4	−1.76981	−0.884904	−	0.465774i	$-0.845776\pi$
$971$	−53549.4	−1.76981	−0.884904	+	0.465774i	$0.845776\pi$
$972$	−972.000	−0.0320750
$973$	18789.8	0.619090
$974$	−3986.27	−0.131138
$975$	14864.9	0.488266
$976$	−452.605	−0.0148438
$977$	30132.4	0.986717	0.493358	−	0.869826i	$-0.335769\pi$
$977$	30132.4	0.986717	0.493358	+	0.869826i	$0.335769\pi$
$978$	−15776.0	−0.515810
$979$	38255.9	1.24889
$980$	944.519	0.0307873
$981$	−1594.87	−0.0519064
$982$	−4139.04	−0.134503
$983$	10266.6	0.333117	0.166558	−	0.986032i	$-0.446735\pi$
$983$	10266.6	0.333117	0.166558	+	0.986032i	$0.446735\pi$
$984$	−11178.0	−0.362136
$985$	−10128.3	−0.327629
$986$	232.873	0.00752150
$987$	10776.9	0.347552
$988$	12316.8	0.396608
$989$	−5862.17	−0.188479
$990$	3732.91	0.119838
$991$	−8356.87	−0.267876	−0.133938	−	0.990990i	$-0.542762\pi$
$991$	−8356.87	−0.267876	−0.133938	+	0.990990i	$0.542762\pi$
$992$	−2829.79	−0.0905706
$993$	15505.0	0.495505
$994$	−10897.9	−0.347747
$995$	15557.8	0.495693
$996$	−4911.11	−0.156239
$997$	−25381.3	−0.806254	−0.403127	−	0.915144i	$-0.632077\pi$
$997$	−25381.3	−0.806254	−0.403127	+	0.915144i	$0.632077\pi$
$998$	−33363.2	−1.05821
$999$	4559.30	0.144394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.f.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.f.1.2	✓	3	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +4.81897 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +9.63795 q^{10} +43.0349 q^{11} -12.0000 q^{12} +48.6845 q^{13} +14.0000 q^{14} -14.4569 q^{15} +16.0000 q^{16} -24.7735 q^{17} +18.0000 q^{18} +63.2479 q^{19} +19.2759 q^{20} -21.0000 q^{21} +86.0698 q^{22} -23.0000 q^{23} -24.0000 q^{24} -101.777 q^{25} +97.3689 q^{26} -27.0000 q^{27} +28.0000 q^{28} -4.70005 q^{29} -28.9138 q^{30} -88.4310 q^{31} +32.0000 q^{32} -129.105 q^{33} -49.5470 q^{34} +33.7328 q^{35} +36.0000 q^{36} -168.863 q^{37} +126.496 q^{38} -146.053 q^{39} +38.5518 q^{40} +465.750 q^{41} -42.0000 q^{42} +254.877 q^{43} +172.140 q^{44} +43.3708 q^{45} -46.0000 q^{46} -513.188 q^{47} -48.0000 q^{48} +49.0000 q^{49} -203.555 q^{50} +74.3206 q^{51} +194.738 q^{52} +428.489 q^{53} -54.0000 q^{54} +207.384 q^{55} +56.0000 q^{56} -189.744 q^{57} -9.40009 q^{58} +158.984 q^{59} -57.8277 q^{60} -28.2878 q^{61} -176.862 q^{62} +63.0000 q^{63} +64.0000 q^{64} +234.609 q^{65} -258.209 q^{66} +797.236 q^{67} -99.0941 q^{68} +69.0000 q^{69} +67.4656 q^{70} -778.422 q^{71} +72.0000 q^{72} +526.081 q^{73} -337.726 q^{74} +305.332 q^{75} +252.992 q^{76} +301.244 q^{77} -292.107 q^{78} -108.025 q^{79} +77.1036 q^{80} +81.0000 q^{81} +931.500 q^{82} +409.259 q^{83} -84.0000 q^{84} -119.383 q^{85} +509.754 q^{86} +14.1001 q^{87} +344.279 q^{88} +888.952 q^{89} +86.7415 q^{90} +340.791 q^{91} -92.0000 q^{92} +265.293 q^{93} -1026.38 q^{94} +304.790 q^{95} -96.0000 q^{96} -255.899 q^{97} +98.0000 q^{98} +387.314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 9 q^{5} - 18 q^{6} + 21 q^{7} + 24 q^{8} + 27 q^{9} + 18 q^{10} + 53 q^{11} - 36 q^{12} + 61 q^{13} + 42 q^{14} - 27 q^{15} + 48 q^{16} - 2 q^{17} + 54 q^{18} + 63 q^{19} + 36 q^{20} - 63 q^{21} + 106 q^{22} - 69 q^{23} - 72 q^{24} - 72 q^{25} + 122 q^{26} - 81 q^{27} + 84 q^{28} + 312 q^{29} - 54 q^{30} + 220 q^{31} + 96 q^{32} - 159 q^{33} - 4 q^{34} + 63 q^{35} + 108 q^{36} - 44 q^{37} + 126 q^{38} - 183 q^{39} + 72 q^{40} + 171 q^{41} - 126 q^{42} - 627 q^{43} + 212 q^{44} + 81 q^{45} - 138 q^{46} + 353 q^{47} - 144 q^{48} + 147 q^{49} - 144 q^{50} + 6 q^{51} + 244 q^{52} - 504 q^{53} - 162 q^{54} + 1181 q^{55} + 168 q^{56} - 189 q^{57} + 624 q^{58} + 538 q^{59} - 108 q^{60} + 256 q^{61} + 440 q^{62} + 189 q^{63} + 192 q^{64} + 244 q^{65} - 318 q^{66} + 1113 q^{67} - 8 q^{68} + 207 q^{69} + 126 q^{70} + 53 q^{71} + 216 q^{72} + 360 q^{73} - 88 q^{74} + 216 q^{75} + 252 q^{76} + 371 q^{77} - 366 q^{78} + 134 q^{79} + 144 q^{80} + 243 q^{81} + 342 q^{82} + 1506 q^{83} - 252 q^{84} + 577 q^{85} - 1254 q^{86} - 936 q^{87} + 424 q^{88} + 2381 q^{89} + 162 q^{90} + 427 q^{91} - 276 q^{92} - 660 q^{93} + 706 q^{94} + 945 q^{95} - 288 q^{96} - 88 q^{97} + 294 q^{98} + 477 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 9 * q^5 - 18 * q^6 + 21 * q^7 + 24 * q^8 + 27 * q^9 + 18 * q^10 + 53 * q^11 - 36 * q^12 + 61 * q^13 + 42 * q^14 - 27 * q^15 + 48 * q^16 - 2 * q^17 + 54 * q^18 + 63 * q^19 + 36 * q^20 - 63 * q^21 + 106 * q^22 - 69 * q^23 - 72 * q^24 - 72 * q^25 + 122 * q^26 - 81 * q^27 + 84 * q^28 + 312 * q^29 - 54 * q^30 + 220 * q^31 + 96 * q^32 - 159 * q^33 - 4 * q^34 + 63 * q^35 + 108 * q^36 - 44 * q^37 + 126 * q^38 - 183 * q^39 + 72 * q^40 + 171 * q^41 - 126 * q^42 - 627 * q^43 + 212 * q^44 + 81 * q^45 - 138 * q^46 + 353 * q^47 - 144 * q^48 + 147 * q^49 - 144 * q^50 + 6 * q^51 + 244 * q^52 - 504 * q^53 - 162 * q^54 + 1181 * q^55 + 168 * q^56 - 189 * q^57 + 624 * q^58 + 538 * q^59 - 108 * q^60 + 256 * q^61 + 440 * q^62 + 189 * q^63 + 192 * q^64 + 244 * q^65 - 318 * q^66 + 1113 * q^67 - 8 * q^68 + 207 * q^69 + 126 * q^70 + 53 * q^71 + 216 * q^72 + 360 * q^73 - 88 * q^74 + 216 * q^75 + 252 * q^76 + 371 * q^77 - 366 * q^78 + 134 * q^79 + 144 * q^80 + 243 * q^81 + 342 * q^82 + 1506 * q^83 - 252 * q^84 + 577 * q^85 - 1254 * q^86 - 936 * q^87 + 424 * q^88 + 2381 * q^89 + 162 * q^90 + 427 * q^91 - 276 * q^92 - 660 * q^93 + 706 * q^94 + 945 * q^95 - 288 * q^96 - 88 * q^97 + 294 * q^98 + 477 * q^99

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