LMFDB - Embedded newform 667.4.a.c.1.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.34
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.62904 q^{2} +8.41827 q^{3} +13.4280 q^{4} -0.0242112 q^{5} +38.9685 q^{6} -12.4584 q^{7} +25.1264 q^{8} +43.8673 q^{9} +O(q^{10})$	\(q+4.62904 q^{2} +8.41827 q^{3} +13.4280 q^{4} -0.0242112 q^{5} +38.9685 q^{6} -12.4584 q^{7} +25.1264 q^{8} +43.8673 q^{9} -0.112075 q^{10} +48.1740 q^{11} +113.041 q^{12} +21.7570 q^{13} -57.6706 q^{14} -0.203817 q^{15} +8.88727 q^{16} -19.3877 q^{17} +203.063 q^{18} +126.153 q^{19} -0.325108 q^{20} -104.879 q^{21} +222.999 q^{22} -23.0000 q^{23} +211.521 q^{24} -124.999 q^{25} +100.714 q^{26} +141.994 q^{27} -167.292 q^{28} -29.0000 q^{29} -0.943475 q^{30} -58.4385 q^{31} -159.872 q^{32} +405.542 q^{33} -89.7462 q^{34} +0.301634 q^{35} +589.050 q^{36} +188.224 q^{37} +583.966 q^{38} +183.156 q^{39} -0.608342 q^{40} -435.405 q^{41} -485.487 q^{42} -168.205 q^{43} +646.880 q^{44} -1.06208 q^{45} -106.468 q^{46} +305.925 q^{47} +74.8155 q^{48} -187.787 q^{49} -578.627 q^{50} -163.211 q^{51} +292.153 q^{52} -42.8819 q^{53} +657.294 q^{54} -1.16635 q^{55} -313.036 q^{56} +1061.99 q^{57} -134.242 q^{58} +578.330 q^{59} -2.73685 q^{60} +52.5828 q^{61} -270.514 q^{62} -546.518 q^{63} -811.152 q^{64} -0.526762 q^{65} +1877.27 q^{66} +781.523 q^{67} -260.338 q^{68} -193.620 q^{69} +1.39628 q^{70} +651.237 q^{71} +1102.23 q^{72} -770.367 q^{73} +871.298 q^{74} -1052.28 q^{75} +1693.98 q^{76} -600.173 q^{77} +847.836 q^{78} -962.115 q^{79} -0.215172 q^{80} +10.9234 q^{81} -2015.51 q^{82} -133.469 q^{83} -1408.31 q^{84} +0.469399 q^{85} -778.628 q^{86} -244.130 q^{87} +1210.44 q^{88} -437.000 q^{89} -4.91642 q^{90} -271.058 q^{91} -308.844 q^{92} -491.951 q^{93} +1416.14 q^{94} -3.05431 q^{95} -1345.85 q^{96} -1047.11 q^{97} -869.275 q^{98} +2113.26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) $ 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * 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 $

$2$	4.62904	1.63661	0.818306	−	0.574782i	$-0.194913\pi$
$2$	4.62904	1.63661	0.818306	+	0.574782i	$0.194913\pi$
$3$	8.41827	1.62010	0.810049	−	0.586363i	$-0.199441\pi$
$3$	8.41827	1.62010	0.810049	+	0.586363i	$0.199441\pi$
$4$	13.4280	1.67850
$5$	−0.0242112	−0.00216552	−0.00108276	−	0.999999i	$-0.500345\pi$
$5$	−0.0242112	−0.00216552	−0.00108276	+	0.999999i	$0.500345\pi$
$6$	38.9685	2.65147
$7$	−12.4584	−0.672692	−0.336346	−	0.941738i	$-0.609191\pi$
$7$	−12.4584	−0.672692	−0.336346	+	0.941738i	$0.609191\pi$
$8$	25.1264	1.11044
$9$	43.8673	1.62472
$10$	−0.112075	−0.00354411
$11$	48.1740	1.32045	0.660227	−	0.751066i	$-0.270460\pi$
$11$	48.1740	1.32045	0.660227	+	0.751066i	$0.270460\pi$
$12$	113.041	2.71933
$13$	21.7570	0.464176	0.232088	−	0.972695i	$-0.425444\pi$
$13$	21.7570	0.464176	0.232088	+	0.972695i	$0.425444\pi$
$14$	−57.6706	−1.10094
$15$	−0.203817	−0.00350835
$16$	8.88727	0.138864
$17$	−19.3877	−0.276600	−0.138300	−	0.990390i	$-0.544164\pi$
$17$	−19.3877	−0.276600	−0.138300	+	0.990390i	$0.544164\pi$
$18$	203.063	2.65903
$19$	126.153	1.52323	0.761617	−	0.648027i	$-0.224406\pi$
$19$	126.153	1.52323	0.761617	+	0.648027i	$0.224406\pi$
$20$	−0.325108	−0.00363482
$21$	−104.879	−1.08983
$22$	222.999	2.16107
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	211.521	1.79902
$25$	−124.999	−0.999995
$26$	100.714	0.759677
$27$	141.994	1.01210
$28$	−167.292	−1.12911
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−0.943475	−0.00574181
$31$	−58.4385	−0.338576	−0.169288	−	0.985567i	$-0.554147\pi$
$31$	−58.4385	−0.338576	−0.169288	+	0.985567i	$0.554147\pi$
$32$	−159.872	−0.883177
$33$	405.542	2.13926
$34$	−89.7462	−0.452687
$35$	0.301634	0.00145673
$36$	589.050	2.72709
$37$	188.224	0.836321	0.418161	−	0.908373i	$-0.362675\pi$
$37$	188.224	0.836321	0.418161	+	0.908373i	$0.362675\pi$
$38$	583.966	2.49294
$39$	183.156	0.752011
$40$	−0.608342	−0.00240468
$41$	−435.405	−1.65851	−0.829254	−	0.558872i	$-0.811234\pi$
$41$	−435.405	−1.65851	−0.829254	+	0.558872i	$0.811234\pi$
$42$	−485.487	−1.78362
$43$	−168.205	−0.596536	−0.298268	−	0.954482i	$-0.596409\pi$
$43$	−168.205	−0.596536	−0.298268	+	0.954482i	$0.596409\pi$
$44$	646.880	2.21638
$45$	−1.06208	−0.00351835
$46$	−106.468	−0.341257
$47$	305.925	0.949440	0.474720	−	0.880137i	$-0.342549\pi$
$47$	305.925	0.949440	0.474720	+	0.880137i	$0.342549\pi$
$48$	74.8155	0.224973
$49$	−187.787	−0.547485
$50$	−578.627	−1.63660
$51$	−163.211	−0.448119
$52$	292.153	0.779120
$53$	−42.8819	−0.111137	−0.0555687	−	0.998455i	$-0.517697\pi$
$53$	−42.8819	−0.111137	−0.0555687	+	0.998455i	$0.517697\pi$
$54$	657.294	1.65641
$55$	−1.16635	−0.00285947
$56$	−313.036	−0.746986
$57$	1061.99	2.46779
$58$	−134.242	−0.303911
$59$	578.330	1.27614	0.638069	−	0.769979i	$-0.279734\pi$
$59$	578.330	1.27614	0.638069	+	0.769979i	$0.279734\pi$
$60$	−2.73685	−0.00588877
$61$	52.5828	0.110369	0.0551847	−	0.998476i	$-0.482425\pi$
$61$	52.5828	0.110369	0.0551847	+	0.998476i	$0.482425\pi$
$62$	−270.514	−0.554118
$63$	−546.518	−1.09293
$64$	−811.152	−1.58428
$65$	−0.526762	−0.00100518
$66$	1877.27	3.50115
$67$	781.523	1.42505	0.712524	−	0.701648i	$-0.247552\pi$
$67$	781.523	1.42505	0.712524	+	0.701648i	$0.247552\pi$
$68$	−260.338	−0.464273
$69$	−193.620	−0.337814
$70$	1.39628	0.00238410
$71$	651.237	1.08856	0.544279	−	0.838904i	$-0.316803\pi$
$71$	651.237	1.08856	0.544279	+	0.838904i	$0.316803\pi$
$72$	1102.23	1.80415
$73$	−770.367	−1.23513	−0.617566	−	0.786519i	$-0.711881\pi$
$73$	−770.367	−1.23513	−0.617566	+	0.786519i	$0.711881\pi$
$74$	871.298	1.36873
$75$	−1052.28	−1.62009
$76$	1693.98	2.55675
$77$	−600.173	−0.888260
$78$	847.836	1.23075
$79$	−962.115	−1.37021	−0.685103	−	0.728446i	$-0.740243\pi$
$79$	−962.115	−1.37021	−0.685103	+	0.728446i	$0.740243\pi$
$80$	−0.215172	−0.000300712 0
$81$	10.9234	0.0149841
$82$	−2015.51	−2.71433
$83$	−133.469	−0.176507	−0.0882535	−	0.996098i	$-0.528129\pi$
$83$	−133.469	−0.176507	−0.0882535	+	0.996098i	$0.528129\pi$
$84$	−1408.31	−1.82928
$85$	0.469399	0.000598982 0
$86$	−778.628	−0.976298
$87$	−244.130	−0.300845
$88$	1210.44	1.46629
$89$	−437.000	−0.520471	−0.260235	−	0.965545i	$-0.583800\pi$
$89$	−437.000	−0.520471	−0.260235	+	0.965545i	$0.583800\pi$
$90$	−4.91642	−0.00575817
$91$	−271.058	−0.312248
$92$	−308.844	−0.349992
$93$	−491.951	−0.548526
$94$	1416.14	1.55387
$95$	−3.05431	−0.00329859
$96$	−1345.85	−1.43083
$97$	−1047.11	−1.09606	−0.548030	−	0.836459i	$-0.684622\pi$
$97$	−1047.11	−1.09606	−0.548030	+	0.836459i	$0.684622\pi$
$98$	−869.275	−0.896021
$99$	2113.26	2.14536
$100$	−1678.49	−1.67849
$101$	−1164.75	−1.14749	−0.573746	−	0.819033i	$-0.694511\pi$
$101$	−1164.75	−1.14749	−0.573746	+	0.819033i	$0.694511\pi$
$102$	−755.508	−0.733397
$103$	571.059	0.546293	0.273146	−	0.961972i	$-0.411936\pi$
$103$	571.059	0.546293	0.273146	+	0.961972i	$0.411936\pi$
$104$	546.675	0.515441
$105$	2.53924	0.00236004
$106$	−198.502	−0.181889
$107$	−117.636	−0.106283	−0.0531417	−	0.998587i	$-0.516923\pi$
$107$	−117.636	−0.106283	−0.0531417	+	0.998587i	$0.516923\pi$
$108$	1906.69	1.69881
$109$	−112.887	−0.0991979	−0.0495989	−	0.998769i	$-0.515794\pi$
$109$	−112.887	−0.0991979	−0.0495989	+	0.998769i	$0.515794\pi$
$110$	−5.39908	−0.00467984
$111$	1584.52	1.35492
$112$	−110.722	−0.0934125
$113$	−771.486	−0.642259	−0.321130	−	0.947035i	$-0.604063\pi$
$113$	−771.486	−0.642259	−0.321130	+	0.947035i	$0.604063\pi$
$114$	4915.99	4.03881
$115$	0.556858	0.000451542 0
$116$	−389.412	−0.311690
$117$	954.419	0.754155
$118$	2677.11	2.08854
$119$	241.540	0.186067
$120$	−5.12119	−0.00389582
$121$	989.732	0.743601
$122$	243.408	0.180632
$123$	−3665.36	−2.68694
$124$	−784.712	−0.568300
$125$	6.05279	0.00433102
$126$	−2529.85	−1.78871
$127$	−10.4728	−0.00731744	−0.00365872	−	0.999993i	$-0.501165\pi$
$127$	−10.4728	−0.00731744	−0.00365872	+	0.999993i	$0.501165\pi$
$128$	−2475.88	−1.70968
$129$	−1416.00	−0.966446
$130$	−2.43840	−0.00164509
$131$	−2504.88	−1.67063	−0.835313	−	0.549775i	$-0.814714\pi$
$131$	−2504.88	−1.67063	−0.835313	+	0.549775i	$0.814714\pi$
$132$	5445.62	3.59076
$133$	−1571.67	−1.02467
$134$	3617.70	2.33225
$135$	−3.43784	−0.00219172
$136$	−487.143	−0.307148
$137$	−1081.54	−0.674468	−0.337234	−	0.941421i	$-0.609491\pi$
$137$	−1081.54	−0.674468	−0.337234	+	0.941421i	$0.609491\pi$
$138$	−896.276	−0.552870
$139$	−1616.73	−0.986540	−0.493270	−	0.869876i	$-0.664199\pi$
$139$	−1616.73	−0.986540	−0.493270	+	0.869876i	$0.664199\pi$
$140$	4.05034	0.00244512
$141$	2575.36	1.53819
$142$	3014.60	1.78155
$143$	1048.12	0.612924
$144$	389.861	0.225614
$145$	0.702125	0.000402127 0
$146$	−3566.06	−2.02143
$147$	−1580.84	−0.886979
$148$	2527.48	1.40377
$149$	3307.37	1.81846	0.909230	−	0.416294i	$-0.136671\pi$
$149$	3307.37	1.81846	0.909230	+	0.416294i	$0.136671\pi$
$150$	−4871.04	−2.65146
$151$	3588.98	1.93422	0.967108	−	0.254364i	$-0.0818662\pi$
$151$	3588.98	1.93422	0.967108	+	0.254364i	$0.0818662\pi$
$152$	3169.77	1.69146
$153$	−850.484	−0.449396
$154$	−2778.22	−1.45374
$155$	1.41487	0.000733192 0
$156$	2459.42	1.26225
$157$	1871.92	0.951566	0.475783	−	0.879563i	$-0.342165\pi$
$157$	1871.92	0.951566	0.475783	+	0.879563i	$0.342165\pi$
$158$	−4453.67	−2.24250
$159$	−360.992	−0.180054
$160$	3.87070	0.00191253
$161$	286.544	0.140266
$162$	50.5648	0.0245231
$163$	701.947	0.337305	0.168652	−	0.985676i	$-0.446058\pi$
$163$	701.947	0.337305	0.168652	+	0.985676i	$0.446058\pi$
$164$	−5846.62	−2.78381
$165$	−9.81866	−0.00463262
$166$	−617.831	−0.288873
$167$	−2058.65	−0.953913	−0.476956	−	0.878927i	$-0.658260\pi$
$167$	−2058.65	−0.953913	−0.476956	+	0.878927i	$0.658260\pi$
$168$	−2635.22	−1.21019
$169$	−1723.63	−0.784540
$170$	2.17287	0.000980301 0
$171$	5533.99	2.47482
$172$	−2258.66	−1.00129
$173$	1346.23	0.591631	0.295815	−	0.955245i	$-0.404409\pi$
$173$	1346.23	0.591631	0.295815	+	0.955245i	$0.404409\pi$
$174$	−1130.09	−0.492366
$175$	1557.30	0.672689
$176$	428.135	0.183363
$177$	4868.54	2.06747
$178$	−2022.89	−0.851809
$179$	−2028.85	−0.847169	−0.423585	−	0.905857i	$-0.639228\pi$
$179$	−2028.85	−0.847169	−0.423585	+	0.905857i	$0.639228\pi$
$180$	−14.2616	−0.00590555
$181$	3403.80	1.39780	0.698901	−	0.715218i	$-0.253673\pi$
$181$	3403.80	1.39780	0.698901	+	0.715218i	$0.253673\pi$
$182$	−1254.74	−0.511029
$183$	442.656	0.178809
$184$	−577.908	−0.231543
$185$	−4.55714	−0.00181107
$186$	−2277.26	−0.897725
$187$	−933.981	−0.365238
$188$	4107.96	1.59364
$189$	−1769.02	−0.680831
$190$	−14.1385	−0.00539851
$191$	−1494.79	−0.566278	−0.283139	−	0.959079i	$-0.591376\pi$
$191$	−1494.79	−0.566278	−0.283139	+	0.959079i	$0.591376\pi$
$192$	−6828.50	−2.56669
$193$	−4820.72	−1.79794	−0.898972	−	0.438005i	$-0.855685\pi$
$193$	−4820.72	−1.79794	−0.898972	+	0.438005i	$0.855685\pi$
$194$	−4847.11	−1.79382
$195$	−4.43443	−0.00162849
$196$	−2521.61	−0.918954
$197$	−1317.27	−0.476404	−0.238202	−	0.971216i	$-0.576558\pi$
$197$	−1317.27	−0.476404	−0.238202	+	0.971216i	$0.576558\pi$
$198$	9782.38	3.51113
$199$	1035.69	0.368937	0.184468	−	0.982838i	$-0.440944\pi$
$199$	1035.69	0.368937	0.184468	+	0.982838i	$0.440944\pi$
$200$	−3140.79	−1.11044
$201$	6579.07	2.30872
$202$	−5391.67	−1.87800
$203$	361.295	0.124916
$204$	−2191.59	−0.752168
$205$	10.5417	0.00359153
$206$	2643.46	0.894070
$207$	−1008.95	−0.338777
$208$	193.360	0.0644572
$209$	6077.28	2.01136
$210$	11.7542	0.00386247
$211$	4697.99	1.53281	0.766405	−	0.642357i	$-0.222043\pi$
$211$	4697.99	1.53281	0.766405	+	0.642357i	$0.222043\pi$
$212$	−575.819	−0.186544
$213$	5482.29	1.76357
$214$	−544.542	−0.173945
$215$	4.07245	0.00129181
$216$	3567.79	1.12388
$217$	728.052	0.227758
$218$	−522.556	−0.162349
$219$	−6485.16	−2.00103
$220$	−15.6618	−0.00479962
$221$	−421.816	−0.128391
$222$	7334.82	2.21748
$223$	4606.69	1.38335	0.691675	−	0.722209i	$-0.256873\pi$
$223$	4606.69	1.38335	0.691675	+	0.722209i	$0.256873\pi$
$224$	1991.76	0.594106
$225$	−5483.39	−1.62471
$226$	−3571.24	−1.05113
$227$	1081.58	0.316241	0.158120	−	0.987420i	$-0.449457\pi$
$227$	1081.58	0.316241	0.158120	+	0.987420i	$0.449457\pi$
$228$	14260.4	4.14218
$229$	−856.028	−0.247022	−0.123511	−	0.992343i	$-0.539415\pi$
$229$	−856.028	−0.247022	−0.123511	+	0.992343i	$0.539415\pi$
$230$	2.57772	0.000738999 0
$231$	−5052.42	−1.43907
$232$	−728.667	−0.206204
$233$	5626.70	1.58205	0.791025	−	0.611784i	$-0.209548\pi$
$233$	5626.70	1.58205	0.791025	+	0.611784i	$0.209548\pi$
$234$	4418.04	1.23426
$235$	−7.40681	−0.00205603
$236$	7765.81	2.14200
$237$	−8099.34	−2.21987
$238$	1118.10	0.304519
$239$	4187.46	1.13332	0.566661	−	0.823951i	$-0.308235\pi$
$239$	4187.46	1.13332	0.566661	+	0.823951i	$0.308235\pi$
$240$	−1.81137	−0.000487182 0
$241$	1794.17	0.479555	0.239777	−	0.970828i	$-0.422926\pi$
$241$	1794.17	0.479555	0.239777	+	0.970828i	$0.422926\pi$
$242$	4581.51	1.21699
$243$	−3741.87	−0.987824
$244$	706.082	0.185255
$245$	4.54656	0.00118559
$246$	−16967.1	−4.39748
$247$	2744.70	0.707049
$248$	−1468.35	−0.375969
$249$	−1123.57	−0.285958
$250$	28.0186	0.00708821
$251$	6518.25	1.63916	0.819579	−	0.572966i	$-0.194207\pi$
$251$	6518.25	1.63916	0.819579	+	0.572966i	$0.194207\pi$
$252$	−7338.65	−1.83449
$253$	−1108.00	−0.275334
$254$	−48.4792	−0.0119758
$255$	3.95153	0.000970409 0
$256$	−4971.72	−1.21380
$257$	−4904.16	−1.19032	−0.595162	−	0.803606i	$-0.702912\pi$
$257$	−4904.16	−1.19032	−0.595162	+	0.803606i	$0.702912\pi$
$258$	−6554.71	−1.58170
$259$	−2344.98	−0.562587
$260$	−7.07337	−0.00168720
$261$	−1272.15	−0.301702
$262$	−11595.2	−2.73417
$263$	−1044.43	−0.244876	−0.122438	−	0.992476i	$-0.539071\pi$
$263$	−1044.43	−0.244876	−0.122438	+	0.992476i	$0.539071\pi$
$264$	10189.8	2.37553
$265$	1.03822	0.000240670 0
$266$	−7275.31	−1.67698
$267$	−3678.78	−0.843213
$268$	10494.3	2.39194
$269$	1693.78	0.383909	0.191954	−	0.981404i	$-0.438517\pi$
$269$	1693.78	0.383909	0.191954	+	0.981404i	$0.438517\pi$
$270$	−15.9139	−0.00358699
$271$	−451.781	−0.101268	−0.0506342	−	0.998717i	$-0.516124\pi$
$271$	−451.781	−0.101268	−0.0506342	+	0.998717i	$0.516124\pi$
$272$	−172.303	−0.0384097
$273$	−2281.84	−0.505872
$274$	−5006.49	−1.10384
$275$	−6021.72	−1.32045
$276$	−2599.93	−0.567020
$277$	92.0360	0.0199636	0.00998178	−	0.999950i	$-0.496823\pi$
$277$	92.0360	0.0199636	0.00998178	+	0.999950i	$0.496823\pi$
$278$	−7483.90	−1.61458
$279$	−2563.54	−0.550090
$280$	7.57899	0.00161761
$281$	8580.72	1.82165	0.910823	−	0.412796i	$-0.135448\pi$
$281$	8580.72	1.82165	0.910823	+	0.412796i	$0.135448\pi$
$282$	11921.4	2.51741
$283$	−1118.04	−0.234843	−0.117421	−	0.993082i	$-0.537463\pi$
$283$	−1118.04	−0.234843	−0.117421	+	0.993082i	$0.537463\pi$
$284$	8744.82	1.82715
$285$	−25.7120	−0.00534404
$286$	4851.78	1.00312
$287$	5424.46	1.11567
$288$	−7013.16	−1.43491
$289$	−4537.12	−0.923493
$290$	3.25017	0.000658125 0
$291$	−8814.85	−1.77572
$292$	−10344.5	−2.07317
$293$	1094.87	0.218303	0.109152	−	0.994025i	$-0.465187\pi$
$293$	1094.87	0.218303	0.109152	+	0.994025i	$0.465187\pi$
$294$	−7317.79	−1.45164
$295$	−14.0021	−0.00276350
$296$	4729.41	0.928687
$297$	6840.40	1.33643
$298$	15310.0	2.97611
$299$	−500.410	−0.0967875
$300$	−14130.0	−2.71932
$301$	2095.57	0.401285
$302$	16613.5	3.16556
$303$	−9805.17	−1.85905
$304$	1121.15	0.211522
$305$	−1.27309	−0.000239007 0
$306$	−3936.93	−0.735487
$307$	9984.95	1.85626	0.928129	−	0.372258i	$-0.121416\pi$
$307$	9984.95	1.85626	0.928129	+	0.372258i	$0.121416\pi$
$308$	−8059.12	−1.49094
$309$	4807.33	0.885048
$310$	6.54947	0.00119995
$311$	−4094.52	−0.746556	−0.373278	−	0.927720i	$-0.621766\pi$
$311$	−4094.52	−0.746556	−0.373278	+	0.927720i	$0.621766\pi$
$312$	4602.06	0.835065
$313$	1620.32	0.292606	0.146303	−	0.989240i	$-0.453263\pi$
$313$	1620.32	0.292606	0.146303	+	0.989240i	$0.453263\pi$
$314$	8665.21	1.55734
$315$	13.2319	0.00236677
$316$	−12919.3	−2.29989
$317$	−1375.05	−0.243630	−0.121815	−	0.992553i	$-0.538871\pi$
$317$	−1375.05	−0.243630	−0.121815	+	0.992553i	$0.538871\pi$
$318$	−1671.04	−0.294678
$319$	−1397.05	−0.245202
$320$	19.6390	0.00343079
$321$	−990.293	−0.172189
$322$	1326.42	0.229561
$323$	−2445.81	−0.421326
$324$	146.679	0.0251508
$325$	−2719.61	−0.464174
$326$	3249.34	0.552038
$327$	−950.310	−0.160710
$328$	−10940.2	−1.84168
$329$	−3811.34	−0.638681
$330$	−45.4510	−0.00758180
$331$	5444.47	0.904093	0.452047	−	0.891994i	$-0.350694\pi$
$331$	5444.47	0.904093	0.452047	+	0.891994i	$0.350694\pi$
$332$	−1792.22	−0.296267
$333$	8256.89	1.35878
$334$	−9529.59	−1.56119
$335$	−18.9216	−0.00308596
$336$	−932.084	−0.151337
$337$	−2627.12	−0.424654	−0.212327	−	0.977199i	$-0.568104\pi$
$337$	−2627.12	−0.424654	−0.212327	+	0.977199i	$0.568104\pi$
$338$	−7978.77	−1.28399
$339$	−6494.58	−1.04052
$340$	6.30309	0.00100539
$341$	−2815.21	−0.447074
$342$	25617.0	4.05032
$343$	6612.78	1.04098
$344$	−4226.40	−0.662419
$345$	4.68778	0.000731541 0
$346$	6231.76	0.968271
$347$	−2411.51	−0.373074	−0.186537	−	0.982448i	$-0.559726\pi$
$347$	−2411.51	−0.373074	−0.186537	+	0.982448i	$0.559726\pi$
$348$	−3278.18	−0.504968
$349$	202.068	0.0309928	0.0154964	−	0.999880i	$-0.495067\pi$
$349$	202.068	0.0309928	0.0154964	+	0.999880i	$0.495067\pi$
$350$	7208.79	1.10093
$351$	3089.35	0.469793
$352$	−7701.67	−1.16619
$353$	5582.88	0.841775	0.420888	−	0.907113i	$-0.361719\pi$
$353$	5582.88	0.841775	0.420888	+	0.907113i	$0.361719\pi$
$354$	22536.6	3.38364
$355$	−15.7673	−0.00235729
$356$	−5868.04	−0.873610
$357$	2033.35	0.301446
$358$	−9391.62	−1.38649
$359$	2139.68	0.314562	0.157281	−	0.987554i	$-0.449727\pi$
$359$	2139.68	0.314562	0.157281	+	0.987554i	$0.449727\pi$
$360$	−26.6863	−0.00390692
$361$	9055.54	1.32024
$362$	15756.3	2.28766
$363$	8331.84	1.20471
$364$	−3639.76	−0.524108
$365$	18.6515	0.00267470
$366$	2049.07	0.292641
$367$	2610.29	0.371270	0.185635	−	0.982619i	$-0.440566\pi$
$367$	2610.29	0.371270	0.185635	+	0.982619i	$0.440566\pi$
$368$	−204.407	−0.0289551
$369$	−19100.0	−2.69460
$370$	−21.0952	−0.00296402
$371$	534.242	0.0747613
$372$	−6605.92	−0.920701
$373$	−7223.65	−1.00275	−0.501376	−	0.865229i	$-0.667173\pi$
$373$	−7223.65	−1.00275	−0.501376	+	0.865229i	$0.667173\pi$
$374$	−4323.43	−0.597752
$375$	50.9540	0.00701668
$376$	7686.80	1.05430
$377$	−630.952	−0.0861954
$378$	−8188.86	−1.11426
$379$	2965.67	0.401943	0.200971	−	0.979597i	$-0.435590\pi$
$379$	2965.67	0.401943	0.200971	+	0.979597i	$0.435590\pi$
$380$	−41.0133	−0.00553668
$381$	−88.1633	−0.0118550
$382$	−6919.43	−0.926777
$383$	13449.5	1.79435	0.897175	−	0.441675i	$-0.145616\pi$
$383$	13449.5	1.79435	0.897175	+	0.441675i	$0.145616\pi$
$384$	−20842.6	−2.76985
$385$	14.5309	0.00192354
$386$	−22315.3	−2.94254
$387$	−7378.71	−0.969201
$388$	−14060.6	−1.83974
$389$	−11723.7	−1.52806	−0.764028	−	0.645183i	$-0.776781\pi$
$389$	−11723.7	−1.52806	−0.764028	+	0.645183i	$0.776781\pi$
$390$	−20.5272	−0.00266521
$391$	445.916	0.0576751
$392$	−4718.43	−0.607951
$393$	−21086.7	−2.70658
$394$	−6097.69	−0.779688
$395$	23.2940	0.00296721
$396$	28376.9	3.60099
$397$	5724.07	0.723634	0.361817	−	0.932249i	$-0.382156\pi$
$397$	5724.07	0.723634	0.361817	+	0.932249i	$0.382156\pi$
$398$	4794.27	0.603806
$399$	−13230.7	−1.66006
$400$	−1110.90	−0.138863
$401$	−8845.00	−1.10149	−0.550746	−	0.834673i	$-0.685657\pi$
$401$	−8845.00	−1.10149	−0.550746	+	0.834673i	$0.685657\pi$
$402$	30454.8	3.77847
$403$	−1271.44	−0.157159
$404$	−15640.2	−1.92607
$405$	−0.264469	−3.24483e−5 0
$406$	1672.45	0.204439
$407$	9067.51	1.10432
$408$	−4100.90	−0.497610
$409$	−2811.78	−0.339935	−0.169967	−	0.985450i	$-0.554366\pi$
$409$	−2811.78	−0.339935	−0.169967	+	0.985450i	$0.554366\pi$
$410$	48.7979	0.00587794
$411$	−9104.70	−1.09270
$412$	7668.19	0.916953
$413$	−7205.08	−0.858448
$414$	−4670.46	−0.554446
$415$	3.23144	0.000382229 0
$416$	−3478.33	−0.409950
$417$	−13610.1	−1.59829
$418$	28132.0	3.29182
$419$	−3033.37	−0.353674	−0.176837	−	0.984240i	$-0.556587\pi$
$419$	−3033.37	−0.353674	−0.176837	+	0.984240i	$0.556587\pi$
$420$	34.0969	0.00396133
$421$	−6793.52	−0.786451	−0.393225	−	0.919442i	$-0.628641\pi$
$421$	−6793.52	−0.786451	−0.393225	+	0.919442i	$0.628641\pi$
$422$	21747.2	2.50862
$423$	13420.1	1.54257
$424$	−1077.47	−0.123412
$425$	2423.45	0.276599
$426$	25377.8	2.88628
$427$	−655.099	−0.0742447
$428$	−1579.62	−0.178397
$429$	8823.35	0.992996
$430$	18.8515	0.00211419
$431$	7698.92	0.860426	0.430213	−	0.902727i	$-0.358438\pi$
$431$	7698.92	0.860426	0.430213	+	0.902727i	$0.358438\pi$
$432$	1261.94	0.140544
$433$	−4603.20	−0.510891	−0.255445	−	0.966824i	$-0.582222\pi$
$433$	−4603.20	−0.510891	−0.255445	+	0.966824i	$0.582222\pi$
$434$	3370.18	0.372751
$435$	5.91068	0.000651484 0
$436$	−1515.84	−0.166504
$437$	−2901.52	−0.317616
$438$	−30020.0	−3.27492
$439$	−1027.31	−0.111687	−0.0558435	−	0.998440i	$-0.517785\pi$
$439$	−1027.31	−0.111687	−0.0558435	+	0.998440i	$0.517785\pi$
$440$	−29.3063	−0.00317527
$441$	−8237.72	−0.889507
$442$	−1952.60	−0.210127
$443$	4309.79	0.462221	0.231111	−	0.972927i	$-0.425764\pi$
$443$	4309.79	0.462221	0.231111	+	0.972927i	$0.425764\pi$
$444$	21277.0	2.27424
$445$	10.5803	0.00112709
$446$	21324.6	2.26401
$447$	27842.4	2.94608
$448$	10105.7	1.06573
$449$	9313.48	0.978909	0.489455	−	0.872029i	$-0.337196\pi$
$449$	9313.48	0.978909	0.489455	+	0.872029i	$0.337196\pi$
$450$	−25382.8	−2.65902
$451$	−20975.2	−2.18998
$452$	−10359.5	−1.07803
$453$	30213.0	3.13362
$454$	5006.65	0.517564
$455$	6.56264	0.000676178 0
$456$	26684.0	2.74034
$457$	−6255.04	−0.640259	−0.320130	−	0.947374i	$-0.603726\pi$
$457$	−6255.04	−0.640259	−0.320130	+	0.947374i	$0.603726\pi$
$458$	−3962.59	−0.404279
$459$	−2752.92	−0.279947
$460$	7.47749	0.000757913 0
$461$	−8342.23	−0.842812	−0.421406	−	0.906872i	$-0.638463\pi$
$461$	−8342.23	−0.842812	−0.421406	+	0.906872i	$0.638463\pi$
$462$	−23387.8	−2.35520
$463$	8359.53	0.839093	0.419547	−	0.907734i	$-0.362189\pi$
$463$	8359.53	0.839093	0.419547	+	0.907734i	$0.362189\pi$
$464$	−257.731	−0.0257863
$465$	11.9107	0.00118784
$466$	26046.2	2.58920
$467$	−13556.2	−1.34327	−0.671633	−	0.740884i	$-0.734407\pi$
$467$	−13556.2	−1.34327	−0.671633	+	0.740884i	$0.734407\pi$
$468$	12815.9	1.26585
$469$	−9736.55	−0.958619
$470$	−34.2864	−0.00336492
$471$	15758.4	1.54163
$472$	14531.4	1.41708
$473$	−8103.11	−0.787699
$474$	−37492.2	−3.63306
$475$	−15769.0	−1.52323
$476$	3243.40	0.312313
$477$	−1881.11	−0.180567
$478$	19383.9	1.85481
$479$	−15485.4	−1.47713	−0.738567	−	0.674180i	$-0.764497\pi$
$479$	−15485.4	−1.47713	−0.738567	+	0.674180i	$0.764497\pi$
$480$	32.5846	0.00309849
$481$	4095.19	0.388201
$482$	8305.29	0.784845
$483$	2412.21	0.227245
$484$	13290.1	1.24813
$485$	25.3518	0.00237354
$486$	−17321.3	−1.61668
$487$	18601.2	1.73080	0.865401	−	0.501080i	$-0.167064\pi$
$487$	18601.2	1.73080	0.865401	+	0.501080i	$0.167064\pi$
$488$	1321.22	0.122559
$489$	5909.18	0.546467
$490$	21.0462	0.00194035
$491$	−3602.91	−0.331155	−0.165578	−	0.986197i	$-0.552949\pi$
$491$	−3602.91	−0.331155	−0.165578	+	0.986197i	$0.552949\pi$
$492$	−49218.4	−4.51004
$493$	562.242	0.0513633
$494$	12705.3	1.15717
$495$	−51.1647	−0.00464582
$496$	−519.359	−0.0470159
$497$	−8113.40	−0.732265
$498$	−5201.07	−0.468003
$499$	19322.7	1.73347	0.866737	−	0.498765i	$-0.166213\pi$
$499$	19322.7	1.73347	0.866737	+	0.498765i	$0.166213\pi$
$500$	81.2769	0.00726963
$501$	−17330.3	−1.54543
$502$	30173.3	2.68267
$503$	12974.3	1.15009	0.575045	−	0.818122i	$-0.304984\pi$
$503$	12974.3	1.15009	0.575045	+	0.818122i	$0.304984\pi$
$504$	−13732.1	−1.21364
$505$	28.2000	0.00248492
$506$	−5128.98	−0.450615
$507$	−14510.0	−1.27103
$508$	−140.629	−0.0122823
$509$	−4104.75	−0.357446	−0.178723	−	0.983899i	$-0.557197\pi$
$509$	−4104.75	−0.357446	−0.178723	+	0.983899i	$0.557197\pi$
$510$	18.2918	0.00158818
$511$	9597.56	0.830863
$512$	−3207.27	−0.276841
$513$	17912.9	1.54166
$514$	−22701.5	−1.94810
$515$	−13.8260	−0.00118301
$516$	−19014.0	−1.62218
$517$	14737.6	1.25369
$518$	−10855.0	−0.920737
$519$	11332.9	0.958500
$520$	−13.2357	−0.00111620
$521$	−1121.76	−0.0943285	−0.0471643	−	0.998887i	$-0.515018\pi$
$521$	−1121.76	−0.0943285	−0.0471643	+	0.998887i	$0.515018\pi$
$522$	−5888.84	−0.493769
$523$	12142.3	1.01519	0.507597	−	0.861594i	$-0.330534\pi$
$523$	12142.3	1.01519	0.507597	+	0.861594i	$0.330534\pi$
$524$	−33635.5	−2.80415
$525$	13109.8	1.08982
$526$	−4834.70	−0.400766
$527$	1132.98	0.0936501
$528$	3604.16	0.297066
$529$	529.000	0.0434783
$530$	4.80598	0.000393884 0
$531$	25369.8	2.07336
$532$	−21104.4	−1.71991
$533$	−9473.08	−0.769840
$534$	−17029.2	−1.38001
$535$	2.84812	0.000230158 0
$536$	19636.9	1.58243
$537$	−17079.4	−1.37250
$538$	7840.56	0.628310
$539$	−9046.46	−0.722929
$540$	−46.1633	−0.00367880
$541$	−8928.58	−0.709556	−0.354778	−	0.934951i	$-0.615443\pi$
$541$	−8928.58	−0.709556	−0.354778	+	0.934951i	$0.615443\pi$
$542$	−2091.31	−0.165737
$543$	28654.1	2.26458
$544$	3099.54	0.244287
$545$	2.73312	0.000214815 0
$546$	−10562.7	−0.827917
$547$	4741.62	0.370634	0.185317	−	0.982679i	$-0.440669\pi$
$547$	4741.62	0.370634	0.185317	+	0.982679i	$0.440669\pi$
$548$	−14522.9	−1.13210
$549$	2306.67	0.179319
$550$	−27874.8	−2.16106
$551$	−3658.43	−0.282857
$552$	−4864.99	−0.375123
$553$	11986.4	0.921728
$554$	426.038	0.0326726
$555$	−38.3632	−0.00293411
$556$	−21709.4	−1.65591
$557$	23586.4	1.79424	0.897118	−	0.441791i	$-0.145657\pi$
$557$	23586.4	1.79424	0.897118	+	0.441791i	$0.145657\pi$
$558$	−11866.7	−0.900283
$559$	−3659.63	−0.276898
$560$	2.68070	0.000202286 0
$561$	−7862.50	−0.591720
$562$	39720.5	2.98133
$563$	4867.14	0.364343	0.182172	−	0.983267i	$-0.441687\pi$
$563$	4867.14	0.364343	0.182172	+	0.983267i	$0.441687\pi$
$564$	34581.9	2.58184
$565$	18.6786	0.00139082
$566$	−5175.45	−0.384347
$567$	−136.088	−0.0100797
$568$	16363.3	1.20878
$569$	−25324.1	−1.86580	−0.932899	−	0.360137i	$-0.882730\pi$
$569$	−25324.1	−1.86580	−0.932899	+	0.360137i	$0.882730\pi$
$570$	−119.022	−0.00874612
$571$	−24887.0	−1.82397	−0.911987	−	0.410220i	$-0.865452\pi$
$571$	−24887.0	−1.82397	−0.911987	+	0.410220i	$0.865452\pi$
$572$	14074.1	1.02879
$573$	−12583.5	−0.917425
$574$	25110.1	1.82591
$575$	2874.99	0.208513
$576$	−35583.1	−2.57401
$577$	−12129.5	−0.875142	−0.437571	−	0.899184i	$-0.644161\pi$
$577$	−12129.5	−0.875142	−0.437571	+	0.899184i	$0.644161\pi$
$578$	−21002.5	−1.51140
$579$	−40582.2	−2.91285
$580$	9.42814	0.000674970 0
$581$	1662.81	0.118735
$582$	−40804.3	−2.90617
$583$	−2065.79	−0.146752
$584$	−19356.6	−1.37154
$585$	−23.1077	−0.00163313
$586$	5068.19	0.357278
$587$	8353.31	0.587356	0.293678	−	0.955904i	$-0.405121\pi$
$587$	8353.31	0.587356	0.293678	+	0.955904i	$0.405121\pi$
$588$	−21227.6	−1.48879
$589$	−7372.18	−0.515730
$590$	−64.8161	−0.00452278
$591$	−11089.1	−0.771820
$592$	1672.80	0.116135
$593$	14986.8	1.03783	0.518916	−	0.854825i	$-0.326336\pi$
$593$	14986.8	1.03783	0.518916	+	0.854825i	$0.326336\pi$
$594$	31664.5	2.18722
$595$	−5.84798	−0.000402931 0
$596$	44411.4	3.05229
$597$	8718.75	0.597713
$598$	−2316.42	−0.158404
$599$	8986.23	0.612967	0.306483	−	0.951876i	$-0.400848\pi$
$599$	8986.23	0.612967	0.306483	+	0.951876i	$0.400848\pi$
$600$	−26440.0	−1.79902
$601$	−3487.05	−0.236672	−0.118336	−	0.992974i	$-0.537756\pi$
$601$	−3487.05	−0.236672	−0.118336	+	0.992974i	$0.537756\pi$
$602$	9700.49	0.656749
$603$	34283.3	2.31530
$604$	48192.8	3.24658
$605$	−23.9626	−0.00161028
$606$	−45388.5	−3.04254
$607$	19857.3	1.32782	0.663908	−	0.747815i	$-0.268897\pi$
$607$	19857.3	1.32782	0.663908	+	0.747815i	$0.268897\pi$
$608$	−20168.3	−1.34528
$609$	3041.48	0.202376
$610$	−5.89320	−0.000391162 0
$611$	6655.99	0.440708
$612$	−11420.3	−0.754311
$613$	−2902.39	−0.191234	−0.0956171	−	0.995418i	$-0.530482\pi$
$613$	−2902.39	−0.191234	−0.0956171	+	0.995418i	$0.530482\pi$
$614$	46220.7	3.03798
$615$	88.7427	0.00581862
$616$	−15080.2	−0.986362
$617$	4416.85	0.288194	0.144097	−	0.989564i	$-0.453972\pi$
$617$	4416.85	0.288194	0.144097	+	0.989564i	$0.453972\pi$
$618$	22253.3	1.44848
$619$	5695.95	0.369854	0.184927	−	0.982752i	$-0.440795\pi$
$619$	5695.95	0.369854	0.184927	+	0.982752i	$0.440795\pi$
$620$	18.9988	0.00123066
$621$	−3265.85	−0.211037
$622$	−18953.7	−1.22182
$623$	5444.33	0.350117
$624$	1627.76	0.104427
$625$	15624.8	0.999986
$626$	7500.50	0.478882
$627$	51160.2	3.25860
$628$	25136.2	1.59720
$629$	−3649.23	−0.231326
$630$	61.2509	0.00387348
$631$	−10529.7	−0.664314	−0.332157	−	0.943224i	$-0.607776\pi$
$631$	−10529.7	−0.664314	−0.332157	+	0.943224i	$0.607776\pi$
$632$	−24174.5	−1.52154
$633$	39549.0	2.48330
$634$	−6365.18	−0.398728
$635$	0.253560	1.58460e−5 0
$636$	−4847.40	−0.302220
$637$	−4085.68	−0.254130
$638$	−6466.98	−0.401301
$639$	28568.0	1.76860
$640$	59.9441	0.00370234
$641$	17869.3	1.10109	0.550543	−	0.834807i	$-0.314421\pi$
$641$	17869.3	1.10109	0.550543	+	0.834807i	$0.314421\pi$
$642$	−4584.11	−0.281807
$643$	11038.4	0.677000	0.338500	−	0.940966i	$-0.390080\pi$
$643$	11038.4	0.677000	0.338500	+	0.940966i	$0.390080\pi$
$644$	3847.72	0.235437
$645$	34.2830	0.00209286
$646$	−11321.7	−0.689548
$647$	−4291.27	−0.260753	−0.130376	−	0.991465i	$-0.541619\pi$
$647$	−4291.27	−0.260753	−0.130376	+	0.991465i	$0.541619\pi$
$648$	274.466	0.0166390
$649$	27860.4	1.68508
$650$	−12589.2	−0.759673
$651$	6128.94	0.368989
$652$	9425.74	0.566167
$653$	−19274.8	−1.15510	−0.577549	−	0.816356i	$-0.695991\pi$
$653$	−19274.8	−1.15510	−0.577549	+	0.816356i	$0.695991\pi$
$654$	−4399.02	−0.263020
$655$	60.6461	0.00361777
$656$	−3869.56	−0.230306
$657$	−33793.9	−2.00674
$658$	−17642.8	−1.04527
$659$	18737.3	1.10759	0.553795	−	0.832653i	$-0.313179\pi$
$659$	18737.3	1.10759	0.553795	+	0.832653i	$0.313179\pi$
$660$	−131.845	−0.00777585
$661$	32954.0	1.93912	0.969562	−	0.244844i	$-0.0787369\pi$
$661$	32954.0	1.93912	0.969562	+	0.244844i	$0.0787369\pi$
$662$	25202.6	1.47965
$663$	−3550.97	−0.208006
$664$	−3353.59	−0.196001
$665$	38.0520	0.00221894
$666$	38221.5	2.22380
$667$	667.000	0.0387202
$668$	−27643.6	−1.60114
$669$	38780.4	2.24116
$670$	−87.5889	−0.00505053
$671$	2533.12	0.145738
$672$	16767.1	0.962510
$673$	−11536.9	−0.660794	−0.330397	−	0.943842i	$-0.607183\pi$
$673$	−11536.9	−0.660794	−0.330397	+	0.943842i	$0.607183\pi$
$674$	−12161.0	−0.694994
$675$	−17749.1	−1.01209
$676$	−23145.0	−1.31685
$677$	23292.6	1.32232	0.661158	−	0.750247i	$-0.270065\pi$
$677$	23292.6	1.32232	0.661158	+	0.750247i	$0.270065\pi$
$678$	−30063.7	−1.70293
$679$	13045.3	0.737311
$680$	11.7943	0.000665135 0
$681$	9105.00	0.512341
$682$	−13031.7	−0.731687
$683$	−11743.8	−0.657925	−0.328962	−	0.944343i	$-0.606699\pi$
$683$	−11743.8	−0.657925	−0.328962	+	0.944343i	$0.606699\pi$
$684$	74310.4	4.15399
$685$	26.1854	0.00146057
$686$	30610.8	1.70368
$687$	−7206.28	−0.400199
$688$	−1494.89	−0.0828372
$689$	−932.980	−0.0515874
$690$	21.6999	0.00119725
$691$	−17419.5	−0.958998	−0.479499	−	0.877543i	$-0.659182\pi$
$691$	−17419.5	−0.958998	−0.479499	+	0.877543i	$0.659182\pi$
$692$	18077.2	0.993053
$693$	−26328.0	−1.44317
$694$	−11163.0	−0.610578
$695$	39.1429	0.00213637
$696$	−6134.12	−0.334071
$697$	8441.48	0.458743
$698$	935.383	0.0507232
$699$	47367.1	2.56307
$700$	20911.4	1.12911
$701$	12420.0	0.669183	0.334591	−	0.942363i	$-0.391402\pi$
$701$	12420.0	0.669183	0.334591	+	0.942363i	$0.391402\pi$
$702$	14300.7	0.768869
$703$	23745.0	1.27391
$704$	−39076.4	−2.09197
$705$	−62.3525	−0.00333097
$706$	25843.4	1.37766
$707$	14510.9	0.771910
$708$	65374.7	3.47024
$709$	27990.0	1.48263	0.741316	−	0.671157i	$-0.234202\pi$
$709$	27990.0	1.48263	0.741316	+	0.671157i	$0.234202\pi$
$710$	−72.9872	−0.00385797
$711$	−42205.4	−2.22620
$712$	−10980.3	−0.577953
$713$	1344.08	0.0705980
$714$	9412.45	0.493350
$715$	−25.3762	−0.00132730
$716$	−27243.4	−1.42197
$717$	35251.2	1.83609
$718$	9904.64	0.514816
$719$	15446.2	0.801174	0.400587	−	0.916259i	$-0.368806\pi$
$719$	15446.2	0.801174	0.400587	+	0.916259i	$0.368806\pi$
$720$	−9.43901	−0.000488571 0
$721$	−7114.51	−0.367487
$722$	41918.4	2.16072
$723$	15103.8	0.776925
$724$	45706.2	2.34621
$725$	3624.98	0.185694
$726$	38568.4	1.97164
$727$	−21449.9	−1.09427	−0.547135	−	0.837045i	$-0.684281\pi$
$727$	−21449.9	−1.09427	−0.547135	+	0.837045i	$0.684281\pi$
$728$	−6810.72	−0.346733
$729$	−31795.0	−1.61535
$730$	86.3386	0.00437745
$731$	3261.10	0.165002
$732$	5943.99	0.300131
$733$	−3158.35	−0.159149	−0.0795745	−	0.996829i	$-0.525356\pi$
$733$	−3158.35	−0.159149	−0.0795745	+	0.996829i	$0.525356\pi$
$734$	12083.1	0.607625
$735$	38.2742	0.00192077
$736$	3677.06	0.184155
$737$	37649.1	1.88171
$738$	−88414.8	−4.41002
$739$	2440.95	0.121504	0.0607521	−	0.998153i	$-0.480650\pi$
$739$	2440.95	0.121504	0.0607521	+	0.998153i	$0.480650\pi$
$740$	−61.1933	−0.00303988
$741$	23105.6	1.14549
$742$	2473.03	0.122355
$743$	1443.40	0.0712695	0.0356348	−	0.999365i	$-0.488655\pi$
$743$	1443.40	0.0712695	0.0356348	+	0.999365i	$0.488655\pi$
$744$	−12361.0	−0.609107
$745$	−80.0755	−0.00393791
$746$	−33438.6	−1.64112
$747$	−5854.90	−0.286773
$748$	−12541.5	−0.613052
$749$	1465.56	0.0714960
$750$	235.868	0.0114836
$751$	−29570.6	−1.43681	−0.718406	−	0.695624i	$-0.755128\pi$
$751$	−29570.6	−1.43681	−0.718406	+	0.695624i	$0.755128\pi$
$752$	2718.84	0.131843
$753$	54872.4	2.65559
$754$	−2920.70	−0.141068
$755$	−86.8935	−0.00418858
$756$	−23754.4	−1.14278
$757$	164.880	0.00791636	0.00395818	−	0.999992i	$-0.498740\pi$
$757$	164.880	0.00791636	0.00395818	+	0.999992i	$0.498740\pi$
$758$	13728.2	0.657825
$759$	−9327.46	−0.446068
$760$	−76.7441	−0.00366289
$761$	−3144.76	−0.149800	−0.0748998	−	0.997191i	$-0.523864\pi$
$761$	−3144.76	−0.149800	−0.0748998	+	0.997191i	$0.523864\pi$
$762$	−408.111	−0.0194020
$763$	1406.39	0.0667297
$764$	−20072.0	−0.950497
$765$	20.5913	0.000973175 0
$766$	62258.2	2.93666
$767$	12582.7	0.592353
$768$	−41853.3	−1.96647
$769$	9030.76	0.423482	0.211741	−	0.977326i	$-0.432087\pi$
$769$	9030.76	0.423482	0.211741	+	0.977326i	$0.432087\pi$
$770$	67.2642	0.00314809
$771$	−41284.6	−1.92844
$772$	−64732.7	−3.01785
$773$	−17151.2	−0.798043	−0.399022	−	0.916942i	$-0.630650\pi$
$773$	−17151.2	−0.798043	−0.399022	+	0.916942i	$0.630650\pi$
$774$	−34156.3	−1.58621
$775$	7304.77	0.338574
$776$	−26310.1	−1.21711
$777$	−19740.7	−0.911446
$778$	−54269.4	−2.50084
$779$	−54927.5	−2.52629
$780$	−59.5455	−0.00273343
$781$	31372.7	1.43739
$782$	2064.16	0.0943917
$783$	−4117.81	−0.187942
$784$	−1668.92	−0.0760258
$785$	−45.3216	−0.00206063
$786$	−97611.3	−4.42962
$787$	−24971.6	−1.13106	−0.565529	−	0.824728i	$-0.691328\pi$
$787$	−24971.6	−1.13106	−0.565529	+	0.824728i	$0.691328\pi$
$788$	−17688.3	−0.799644
$789$	−8792.29	−0.396722
$790$	107.829	0.00485617
$791$	9611.51	0.432043
$792$	53098.8	2.38230
$793$	1144.04	0.0512309
$794$	26496.9	1.18431
$795$	8.74005	0.000389909 0
$796$	13907.3	0.619260
$797$	14106.6	0.626951	0.313475	−	0.949596i	$-0.398507\pi$
$797$	14106.6	0.626951	0.313475	+	0.949596i	$0.398507\pi$
$798$	−61245.5	−2.71688
$799$	−5931.16	−0.262615
$800$	19983.9	0.883172
$801$	−19170.0	−0.845616
$802$	−40943.8	−1.80271
$803$	−37111.6	−1.63093
$804$	88343.8	3.87518
$805$	−6.93758	−0.000303749 0
$806$	−5885.56	−0.257208
$807$	14258.7	0.621969
$808$	−29266.0	−1.27423
$809$	−17549.2	−0.762665	−0.381332	−	0.924438i	$-0.624535\pi$
$809$	−17549.2	−0.762665	−0.381332	+	0.924438i	$0.624535\pi$
$810$	−1.22424	−5.31053e−5 0
$811$	29379.6	1.27208	0.636041	−	0.771655i	$-0.280571\pi$
$811$	29379.6	1.27208	0.636041	+	0.771655i	$0.280571\pi$
$812$	4851.47	0.209671
$813$	−3803.22	−0.164065
$814$	41973.9	1.80735
$815$	−16.9950	−0.000730440 0
$816$	−1450.50	−0.0622274
$817$	−21219.6	−0.908664
$818$	−13015.8	−0.556342
$819$	−11890.6	−0.507314
$820$	141.554	0.00602838
$821$	−1060.59	−0.0450849	−0.0225424	−	0.999746i	$-0.507176\pi$
$821$	−1060.59	−0.0450849	−0.0225424	+	0.999746i	$0.507176\pi$
$822$	−42146.0	−1.78833
$823$	−25702.3	−1.08861	−0.544306	−	0.838887i	$-0.683207\pi$
$823$	−25702.3	−1.08861	−0.544306	+	0.838887i	$0.683207\pi$
$824$	14348.7	0.606627
$825$	−50692.5	−2.13925
$826$	−33352.6	−1.40495
$827$	−27609.9	−1.16093	−0.580466	−	0.814285i	$-0.697130\pi$
$827$	−27609.9	−1.16093	−0.580466	+	0.814285i	$0.697130\pi$
$828$	−13548.2	−0.568637
$829$	−28850.6	−1.20871	−0.604357	−	0.796714i	$-0.706570\pi$
$829$	−28850.6	−1.20871	−0.604357	+	0.796714i	$0.706570\pi$
$830$	14.9584	0.000625560 0
$831$	774.784	0.0323429
$832$	−17648.2	−0.735386
$833$	3640.76	0.151434
$834$	−63001.5	−2.61578
$835$	49.8425	0.00206571
$836$	81605.8	3.37607
$837$	−8297.89	−0.342673
$838$	−14041.6	−0.578828
$839$	−42071.3	−1.73118	−0.865591	−	0.500752i	$-0.833057\pi$
$839$	−42071.3	−1.73118	−0.865591	+	0.500752i	$0.833057\pi$
$840$	63.8020	0.00262069
$841$	841.000	0.0344828
$842$	−31447.5	−1.28711
$843$	72234.8	2.95124
$844$	63084.6	2.57282
$845$	41.7313	0.00169894
$846$	62122.1	2.52459
$847$	−12330.5	−0.500214
$848$	−381.103	−0.0154330
$849$	−9411.96	−0.380468
$850$	11218.2	0.452685
$851$	−4329.16	−0.174385
$852$	73616.3	2.96015
$853$	−27876.5	−1.11896	−0.559480	−	0.828844i	$-0.688999\pi$
$853$	−27876.5	−1.11896	−0.559480	+	0.828844i	$0.688999\pi$
$854$	−3032.48	−0.121510
$855$	−133.985	−0.00535927
$856$	−2955.78	−0.118022
$857$	1524.51	0.0607659	0.0303829	−	0.999538i	$-0.490327\pi$
$857$	1524.51	0.0607659	0.0303829	+	0.999538i	$0.490327\pi$
$858$	40843.6	1.62515
$859$	22939.1	0.911141	0.455571	−	0.890200i	$-0.349435\pi$
$859$	22939.1	0.911141	0.455571	+	0.890200i	$0.349435\pi$
$860$	54.6849	0.00216830
$861$	45664.6	1.80749
$862$	35638.6	1.40818
$863$	8644.90	0.340992	0.170496	−	0.985358i	$-0.445463\pi$
$863$	8644.90	0.340992	0.170496	+	0.985358i	$0.445463\pi$
$864$	−22700.8	−0.893862
$865$	−32.5939	−0.00128119
$866$	−21308.4	−0.836130
$867$	−38194.7	−1.49615
$868$	9776.28	0.382291
$869$	−46348.9	−1.80930
$870$	27.3608	0.00106623
$871$	17003.6	0.661473
$872$	−2836.44	−0.110154
$873$	−45933.8	−1.78078
$874$	−13431.2	−0.519815
$875$	−75.4083	−0.00291345
$876$	−87082.7	−3.35873
$877$	−25032.0	−0.963819	−0.481910	−	0.876221i	$-0.660057\pi$
$877$	−25032.0	−0.963819	−0.481910	+	0.876221i	$0.660057\pi$
$878$	−4755.44	−0.182788
$879$	9216.90	0.353673
$880$	−10.3657	−0.000397076 0
$881$	−22140.7	−0.846696	−0.423348	−	0.905967i	$-0.639145\pi$
$881$	−22140.7	−0.846696	−0.423348	+	0.905967i	$0.639145\pi$
$882$	−38132.8	−1.45578
$883$	30254.5	1.15305	0.576526	−	0.817079i	$-0.304408\pi$
$883$	30254.5	1.15305	0.576526	+	0.817079i	$0.304408\pi$
$884$	−5664.15	−0.215505
$885$	−117.873	−0.00447714
$886$	19950.2	0.756477
$887$	−15512.8	−0.587227	−0.293613	−	0.955924i	$-0.594858\pi$
$887$	−15512.8	−0.587227	−0.293613	+	0.955924i	$0.594858\pi$
$888$	39813.4	1.50456
$889$	130.475	0.00492239
$890$	48.9766	0.00184461
$891$	526.223	0.0197858
$892$	61858.7	2.32195
$893$	38593.2	1.44622
$894$	128883.	4.82159
$895$	49.1209	0.00183456
$896$	30845.6	1.15009
$897$	−4212.59	−0.156805
$898$	43112.5	1.60210
$899$	1694.72	0.0628720
$900$	−73631.0	−2.72707
$901$	831.380	0.0307406
$902$	−97094.9	−3.58415
$903$	17641.1	0.650121
$904$	−19384.7	−0.713192
$905$	−82.4101	−0.00302697
$906$	139857.	5.12852
$907$	5641.16	0.206518	0.103259	−	0.994655i	$-0.467073\pi$
$907$	5641.16	0.206518	0.103259	+	0.994655i	$0.467073\pi$
$908$	14523.4	0.530810
$909$	−51094.4	−1.86435
$910$	30.3787	0.00110664
$911$	45408.0	1.65141	0.825705	−	0.564102i	$-0.190777\pi$
$911$	45408.0	1.65141	0.825705	+	0.564102i	$0.190777\pi$
$912$	9438.19	0.342686
$913$	−6429.71	−0.233069
$914$	−28954.8	−1.04786
$915$	−10.7172	−0.000387214 0
$916$	−11494.8	−0.414626
$917$	31206.8	1.12382
$918$	−12743.4	−0.458164
$919$	−17497.2	−0.628051	−0.314025	−	0.949415i	$-0.601678\pi$
$919$	−17497.2	−0.628051	−0.314025	+	0.949415i	$0.601678\pi$
$920$	13.9919	0.000501411 0
$921$	84056.1	3.00732
$922$	−38616.5	−1.37936
$923$	14168.9	0.505283
$924$	−67843.9	−2.41548
$925$	−23527.9	−0.836317
$926$	38696.6	1.37327
$927$	25050.8	0.887570
$928$	4636.29	0.164002
$929$	22034.7	0.778186	0.389093	−	0.921198i	$-0.372788\pi$
$929$	22034.7	0.778186	0.389093	+	0.921198i	$0.372788\pi$
$930$	55.1352	0.00194404
$931$	−23689.9	−0.833948
$932$	75555.4	2.65547
$933$	−34468.8	−1.20949
$934$	−62752.1	−2.19841
$935$	22.6128	0.000790928 0
$936$	23981.2	0.837445
$937$	11677.4	0.407133	0.203567	−	0.979061i	$-0.434747\pi$
$937$	11677.4	0.407133	0.203567	+	0.979061i	$0.434747\pi$
$938$	−45070.9	−1.56889
$939$	13640.3	0.474050
$940$	−99.4586	−0.00345105
$941$	−23844.5	−0.826046	−0.413023	−	0.910721i	$-0.635527\pi$
$941$	−23844.5	−0.826046	−0.413023	+	0.910721i	$0.635527\pi$
$942$	72946.1	2.52305
$943$	10014.3	0.345823
$944$	5139.78	0.177209
$945$	42.8301	0.00147435
$946$	−37509.6	−1.28916
$947$	−31494.7	−1.08072	−0.540359	−	0.841435i	$-0.681712\pi$
$947$	−31494.7	−1.08072	−0.540359	+	0.841435i	$0.681712\pi$
$948$	−108758.	−3.72605
$949$	−16760.8	−0.573319
$950$	−72995.5	−2.49293
$951$	−11575.6	−0.394705
$952$	6069.04	0.206616
$953$	−57027.8	−1.93842	−0.969208	−	0.246243i	$-0.920804\pi$
$953$	−57027.8	−1.93842	−0.969208	+	0.246243i	$0.920804\pi$
$954$	−8707.75	−0.295518
$955$	36.1906	0.00122628
$956$	56229.2	1.90228
$957$	−11760.7	−0.397252
$958$	−71682.6	−2.41750
$959$	13474.3	0.453710
$960$	165.326	0.00555821
$961$	−26375.9	−0.885366
$962$	18956.8	0.635334
$963$	−5160.38	−0.172680
$964$	24092.1	0.804933
$965$	116.716	0.00389348
$966$	11166.2	0.371911
$967$	31968.5	1.06312	0.531561	−	0.847020i	$-0.321606\pi$
$967$	31968.5	1.06312	0.531561	+	0.847020i	$0.321606\pi$
$968$	24868.5	0.825726
$969$	−20589.5	−0.682590
$970$	117.354	0.00388456
$971$	−9281.08	−0.306739	−0.153370	−	0.988169i	$-0.549013\pi$
$971$	−9281.08	−0.306739	−0.153370	+	0.988169i	$0.549013\pi$
$972$	−50245.9	−1.65806
$973$	20141.9	0.663638
$974$	86105.6	2.83265
$975$	−22894.4	−0.752007
$976$	467.318	0.0153263
$977$	−9926.81	−0.325063	−0.162532	−	0.986703i	$-0.551966\pi$
$977$	−9926.81	−0.325063	−0.162532	+	0.986703i	$0.551966\pi$
$978$	27353.8	0.894355
$979$	−21052.0	−0.687258
$980$	61.0512	0.00199001
$981$	−4952.03	−0.161168
$982$	−16678.0	−0.541973
$983$	51652.3	1.67594	0.837971	−	0.545714i	$-0.183742\pi$
$983$	51652.3	1.67594	0.837971	+	0.545714i	$0.183742\pi$
$984$	−92097.4	−2.98370
$985$	31.8927	0.00103166
$986$	2602.64	0.0840618
$987$	−32084.9	−1.03473
$988$	36855.9	1.18678
$989$	3868.72	0.124386
$990$	−236.843	−0.00760341
$991$	−30757.3	−0.985912	−0.492956	−	0.870054i	$-0.664084\pi$
$991$	−30757.3	−0.985912	−0.492956	+	0.870054i	$0.664084\pi$
$992$	9342.67	0.299022
$993$	45833.0	1.46472
$994$	−37557.2	−1.19843
$995$	−25.0754	−0.000798939 0
$996$	−15087.4	−0.479981
$997$	−5756.94	−0.182873	−0.0914363	−	0.995811i	$-0.529146\pi$
$997$	−5756.94	−0.182873	−0.0914363	+	0.995811i	$0.529146\pi$
$998$	89445.6	2.83703
$999$	26726.6	0.846440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.c.1.34	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.c.1.34	✓	39	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+4.62904 q^{2} +8.41827 q^{3} +13.4280 q^{4} -0.0242112 q^{5} +38.9685 q^{6} -12.4584 q^{7} +25.1264 q^{8} +43.8673 q^{9} +O(q^{10})\)	\(q+4.62904 q^{2} +8.41827 q^{3} +13.4280 q^{4} -0.0242112 q^{5} +38.9685 q^{6} -12.4584 q^{7} +25.1264 q^{8} +43.8673 q^{9} -0.112075 q^{10} +48.1740 q^{11} +113.041 q^{12} +21.7570 q^{13} -57.6706 q^{14} -0.203817 q^{15} +8.88727 q^{16} -19.3877 q^{17} +203.063 q^{18} +126.153 q^{19} -0.325108 q^{20} -104.879 q^{21} +222.999 q^{22} -23.0000 q^{23} +211.521 q^{24} -124.999 q^{25} +100.714 q^{26} +141.994 q^{27} -167.292 q^{28} -29.0000 q^{29} -0.943475 q^{30} -58.4385 q^{31} -159.872 q^{32} +405.542 q^{33} -89.7462 q^{34} +0.301634 q^{35} +589.050 q^{36} +188.224 q^{37} +583.966 q^{38} +183.156 q^{39} -0.608342 q^{40} -435.405 q^{41} -485.487 q^{42} -168.205 q^{43} +646.880 q^{44} -1.06208 q^{45} -106.468 q^{46} +305.925 q^{47} +74.8155 q^{48} -187.787 q^{49} -578.627 q^{50} -163.211 q^{51} +292.153 q^{52} -42.8819 q^{53} +657.294 q^{54} -1.16635 q^{55} -313.036 q^{56} +1061.99 q^{57} -134.242 q^{58} +578.330 q^{59} -2.73685 q^{60} +52.5828 q^{61} -270.514 q^{62} -546.518 q^{63} -811.152 q^{64} -0.526762 q^{65} +1877.27 q^{66} +781.523 q^{67} -260.338 q^{68} -193.620 q^{69} +1.39628 q^{70} +651.237 q^{71} +1102.23 q^{72} -770.367 q^{73} +871.298 q^{74} -1052.28 q^{75} +1693.98 q^{76} -600.173 q^{77} +847.836 q^{78} -962.115 q^{79} -0.215172 q^{80} +10.9234 q^{81} -2015.51 q^{82} -133.469 q^{83} -1408.31 q^{84} +0.469399 q^{85} -778.628 q^{86} -244.130 q^{87} +1210.44 q^{88} -437.000 q^{89} -4.91642 q^{90} -271.058 q^{91} -308.844 q^{92} -491.951 q^{93} +1416.14 q^{94} -3.05431 q^{95} -1345.85 q^{96} -1047.11 q^{97} -869.275 q^{98} +2113.26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * q^99

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