LMFDB - Embedded newform 667.4.a.c.1.33

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			1.33
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)

$f(q)$	$=$	$q+4.58159 q^{2} -1.47959 q^{3} +12.9910 q^{4} +19.0749 q^{5} -6.77885 q^{6} +28.2117 q^{7} +22.8666 q^{8} -24.8108 q^{9} +O(q^{10})$	\(q+4.58159 q^{2} -1.47959 q^{3} +12.9910 q^{4} +19.0749 q^{5} -6.77885 q^{6} +28.2117 q^{7} +22.8666 q^{8} -24.8108 q^{9} +87.3936 q^{10} +55.7888 q^{11} -19.2212 q^{12} -15.4774 q^{13} +129.254 q^{14} -28.2230 q^{15} +0.837468 q^{16} +74.5941 q^{17} -113.673 q^{18} -137.602 q^{19} +247.802 q^{20} -41.7415 q^{21} +255.602 q^{22} -23.0000 q^{23} -33.8330 q^{24} +238.854 q^{25} -70.9109 q^{26} +76.6585 q^{27} +366.497 q^{28} -29.0000 q^{29} -129.306 q^{30} -210.797 q^{31} -179.096 q^{32} -82.5443 q^{33} +341.759 q^{34} +538.136 q^{35} -322.317 q^{36} -146.357 q^{37} -630.436 q^{38} +22.9001 q^{39} +436.178 q^{40} -292.026 q^{41} -191.243 q^{42} -119.071 q^{43} +724.751 q^{44} -473.265 q^{45} -105.377 q^{46} +340.521 q^{47} -1.23910 q^{48} +452.898 q^{49} +1094.33 q^{50} -110.368 q^{51} -201.066 q^{52} -238.278 q^{53} +351.218 q^{54} +1064.17 q^{55} +645.104 q^{56} +203.594 q^{57} -132.866 q^{58} +598.784 q^{59} -366.644 q^{60} -137.412 q^{61} -965.783 q^{62} -699.955 q^{63} -827.242 q^{64} -295.230 q^{65} -378.184 q^{66} +260.584 q^{67} +969.049 q^{68} +34.0305 q^{69} +2465.52 q^{70} -645.144 q^{71} -567.338 q^{72} +637.182 q^{73} -670.546 q^{74} -353.404 q^{75} -1787.58 q^{76} +1573.90 q^{77} +104.919 q^{78} +1133.75 q^{79} +15.9747 q^{80} +556.470 q^{81} -1337.94 q^{82} +107.327 q^{83} -542.263 q^{84} +1422.88 q^{85} -545.534 q^{86} +42.9080 q^{87} +1275.70 q^{88} -1423.63 q^{89} -2168.31 q^{90} -436.642 q^{91} -298.792 q^{92} +311.891 q^{93} +1560.13 q^{94} -2624.75 q^{95} +264.987 q^{96} +812.843 q^{97} +2074.99 q^{98} -1384.17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.58159	1.61984	0.809918	−	0.586543i	$-0.199511\pi$
$2$	4.58159	1.61984	0.809918	+	0.586543i	$0.199511\pi$
$3$	−1.47959	−0.284746	−0.142373	−	0.989813i	$-0.545473\pi$
$3$	−1.47959	−0.284746	−0.142373	+	0.989813i	$0.545473\pi$
$4$	12.9910	1.62387
$5$	19.0749	1.70611	0.853057	−	0.521817i	$-0.174746\pi$
$5$	19.0749	1.70611	0.853057	+	0.521817i	$0.174746\pi$
$6$	−6.77885	−0.461242
$7$	28.2117	1.52329	0.761643	−	0.647997i	$-0.224393\pi$
$7$	28.2117	1.52329	0.761643	+	0.647997i	$0.224393\pi$
$8$	22.8666	1.01057
$9$	−24.8108	−0.918920
$10$	87.3936	2.76363
$11$	55.7888	1.52918	0.764590	−	0.644517i	$-0.222942\pi$
$11$	55.7888	1.52918	0.764590	+	0.644517i	$0.222942\pi$
$12$	−19.2212	−0.462391
$13$	−15.4774	−0.330204	−0.165102	−	0.986277i	$-0.552795\pi$
$13$	−15.4774	−0.330204	−0.165102	+	0.986277i	$0.552795\pi$
$14$	129.254	2.46748
$15$	−28.2230	−0.485810
$16$	0.837468	0.0130854
$17$	74.5941	1.06422	0.532109	−	0.846676i	$-0.321399\pi$
$17$	74.5941	1.06422	0.532109	+	0.846676i	$0.321399\pi$
$18$	−113.673	−1.48850
$19$	−137.602	−1.66148	−0.830739	−	0.556663i	$-0.812082\pi$
$19$	−137.602	−1.66148	−0.830739	+	0.556663i	$0.812082\pi$
$20$	247.802	2.77051
$21$	−41.7415	−0.433750
$22$	255.602	2.47702
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−33.8330	−0.287756
$25$	238.854	1.91083
$26$	−70.9109	−0.534876
$27$	76.6585	0.546405
$28$	366.497	2.47362
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−129.306	−0.786933
$31$	−210.797	−1.22130	−0.610648	−	0.791902i	$-0.709091\pi$
$31$	−210.797	−1.22130	−0.610648	+	0.791902i	$0.709091\pi$
$32$	−179.096	−0.989372
$33$	−82.5443	−0.435428
$34$	341.759	1.72386
$35$	538.136	2.59890
$36$	−322.317	−1.49221
$37$	−146.357	−0.650294	−0.325147	−	0.945664i	$-0.605414\pi$
$37$	−146.357	−0.650294	−0.325147	+	0.945664i	$0.605414\pi$
$38$	−630.436	−2.69132
$39$	22.9001	0.0940242
$40$	436.178	1.72415
$41$	−292.026	−1.11236	−0.556181	−	0.831061i	$-0.687734\pi$
$41$	−292.026	−1.11236	−0.556181	+	0.831061i	$0.687734\pi$
$42$	−191.243	−0.702604
$43$	−119.071	−0.422283	−0.211141	−	0.977456i	$-0.567718\pi$
$43$	−119.071	−0.422283	−0.211141	+	0.977456i	$0.567718\pi$
$44$	724.751	2.48319
$45$	−473.265	−1.56778
$46$	−105.377	−0.337759
$47$	340.521	1.05681	0.528405	−	0.848992i	$-0.322790\pi$
$47$	340.521	1.05681	0.528405	+	0.848992i	$0.322790\pi$
$48$	−1.23910	−0.00372603
$49$	452.898	1.32040
$50$	1094.33	3.09523
$51$	−110.368	−0.303032
$52$	−201.066	−0.536208
$53$	−238.278	−0.617547	−0.308773	−	0.951136i	$-0.599918\pi$
$53$	−238.278	−0.617547	−0.308773	+	0.951136i	$0.599918\pi$
$54$	351.218	0.885087
$55$	1064.17	2.60896
$56$	645.104	1.53939
$57$	203.594	0.473099
$58$	−132.866	−0.300796
$59$	598.784	1.32127	0.660636	−	0.750707i	$-0.270287\pi$
$59$	598.784	1.32127	0.660636	+	0.750707i	$0.270287\pi$
$60$	−366.644	−0.788892
$61$	−137.412	−0.288424	−0.144212	−	0.989547i	$-0.546065\pi$
$61$	−137.412	−0.288424	−0.144212	+	0.989547i	$0.546065\pi$
$62$	−965.783	−1.97830
$63$	−699.955	−1.39978
$64$	−827.242	−1.61571
$65$	−295.230	−0.563365
$66$	−378.184	−0.705322
$67$	260.584	0.475156	0.237578	−	0.971369i	$-0.423647\pi$
$67$	260.584	0.475156	0.237578	+	0.971369i	$0.423647\pi$
$68$	969.049	1.72815
$69$	34.0305	0.0593737
$70$	2465.52	4.20980
$71$	−645.144	−1.07837	−0.539187	−	0.842186i	$-0.681268\pi$
$71$	−645.144	−1.07837	−0.539187	+	0.842186i	$0.681268\pi$
$72$	−567.338	−0.928631
$73$	637.182	1.02160	0.510798	−	0.859701i	$-0.329350\pi$
$73$	637.182	1.02160	0.510798	+	0.859701i	$0.329350\pi$
$74$	−670.546	−1.05337
$75$	−353.404	−0.544101
$76$	−1787.58	−2.69802
$77$	1573.90	2.32938
$78$	104.919	0.152304
$79$	1133.75	1.61464	0.807322	−	0.590111i	$-0.200916\pi$
$79$	1133.75	1.61464	0.807322	+	0.590111i	$0.200916\pi$
$80$	15.9747	0.0223253
$81$	556.470	0.763333
$82$	−1337.94	−1.80184
$83$	107.327	0.141936	0.0709679	−	0.997479i	$-0.477391\pi$
$83$	107.327	0.141936	0.0709679	+	0.997479i	$0.477391\pi$
$84$	−542.263	−0.704354
$85$	1422.88	1.81568
$86$	−545.534	−0.684029
$87$	42.9080	0.0528761
$88$	1275.70	1.54534
$89$	−1423.63	−1.69556	−0.847781	−	0.530347i	$-0.822062\pi$
$89$	−1423.63	−1.69556	−0.847781	+	0.530347i	$0.822062\pi$
$90$	−2168.31	−2.53955
$91$	−436.642	−0.502995
$92$	−298.792	−0.338600
$93$	311.891	0.347759
$94$	1560.13	1.71186
$95$	−2624.75	−2.83467
$96$	264.987	0.281720
$97$	812.843	0.850843	0.425421	−	0.904995i	$-0.360126\pi$
$97$	812.843	0.850843	0.425421	+	0.904995i	$0.360126\pi$
$98$	2074.99	2.13884
$99$	−1384.17	−1.40519
$100$	3102.94	3.10294
$101$	−55.5220	−0.0546994	−0.0273497	−	0.999626i	$-0.508707\pi$
$101$	−55.5220	−0.0546994	−0.0273497	+	0.999626i	$0.508707\pi$
$102$	−505.662	−0.490863
$103$	19.3714	0.0185313	0.00926565	−	0.999957i	$-0.497051\pi$
$103$	19.3714	0.0185313	0.00926565	+	0.999957i	$0.497051\pi$
$104$	−353.914	−0.333693
$105$	−796.218	−0.740028
$106$	−1091.69	−1.00033
$107$	−700.223	−0.632646	−0.316323	−	0.948652i	$-0.602448\pi$
$107$	−700.223	−0.632646	−0.316323	+	0.948652i	$0.602448\pi$
$108$	995.868	0.887291
$109$	1961.98	1.72407	0.862033	−	0.506852i	$-0.169191\pi$
$109$	1961.98	1.72407	0.862033	+	0.506852i	$0.169191\pi$
$110$	4875.59	4.22608
$111$	216.547	0.185169
$112$	23.6264	0.0199329
$113$	−2260.77	−1.88209	−0.941043	−	0.338287i	$-0.890153\pi$
$113$	−2260.77	−1.88209	−0.941043	+	0.338287i	$0.890153\pi$
$114$	932.784	0.766344
$115$	−438.724	−0.355750
$116$	−376.738	−0.301545
$117$	384.006	0.303431
$118$	2743.38	2.14024
$119$	2104.42	1.62111
$120$	−645.363	−0.490944
$121$	1781.40	1.33839
$122$	−629.568	−0.467200
$123$	432.077	0.316741
$124$	−2738.45	−1.98323
$125$	2171.75	1.55398
$126$	−3206.91	−2.26741
$127$	−831.206	−0.580769	−0.290384	−	0.956910i	$-0.593783\pi$
$127$	−831.206	−0.580769	−0.290384	+	0.956910i	$0.593783\pi$
$128$	−2357.32	−1.62781
$129$	176.176	0.120243
$130$	−1352.62	−0.912560
$131$	1848.20	1.23265	0.616327	−	0.787491i	$-0.288620\pi$
$131$	1848.20	1.23265	0.616327	+	0.787491i	$0.288620\pi$
$132$	−1072.33	−0.707079
$133$	−3881.98	−2.53091
$134$	1193.89	0.769675
$135$	1462.26	0.932230
$136$	1705.71	1.07547
$137$	842.167	0.525191	0.262596	−	0.964906i	$-0.415421\pi$
$137$	842.167	0.525191	0.262596	+	0.964906i	$0.415421\pi$
$138$	155.914	0.0961757
$139$	−2568.58	−1.56737	−0.783683	−	0.621161i	$-0.786661\pi$
$139$	−2568.58	−1.56737	−0.783683	+	0.621161i	$0.786661\pi$
$140$	6990.90	4.22028
$141$	−503.829	−0.300923
$142$	−2955.79	−1.74679
$143$	−863.464	−0.504940
$144$	−20.7783	−0.0120245
$145$	−553.173	−0.316818
$146$	2919.31	1.65482
$147$	−670.101	−0.375979
$148$	−1901.31	−1.05599
$149$	1506.91	0.828531	0.414266	−	0.910156i	$-0.364038\pi$
$149$	1506.91	0.828531	0.414266	+	0.910156i	$0.364038\pi$
$150$	−1619.15	−0.881355
$151$	2214.55	1.19349	0.596746	−	0.802430i	$-0.296460\pi$
$151$	2214.55	1.19349	0.596746	+	0.802430i	$0.296460\pi$
$152$	−3146.48	−1.67904
$153$	−1850.74	−0.977931
$154$	7210.95	3.77321
$155$	−4020.93	−2.08367
$156$	297.494	0.152683
$157$	−2319.36	−1.17901	−0.589507	−	0.807763i	$-0.700678\pi$
$157$	−2319.36	−1.17901	−0.589507	+	0.807763i	$0.700678\pi$
$158$	5194.38	2.61546
$159$	352.552	0.175844
$160$	−3416.24	−1.68798
$161$	−648.868	−0.317627
$162$	2549.52	1.23647
$163$	62.9131	0.0302315	0.0151157	−	0.999886i	$-0.495188\pi$
$163$	62.9131	0.0302315	0.0151157	+	0.999886i	$0.495188\pi$
$164$	−3793.70	−1.80633
$165$	−1574.53	−0.742890
$166$	491.729	0.229913
$167$	−2748.76	−1.27369	−0.636843	−	0.770994i	$-0.719760\pi$
$167$	−2748.76	−1.27369	−0.636843	+	0.770994i	$0.719760\pi$
$168$	−954.486	−0.438334
$169$	−1957.45	−0.890966
$170$	6519.04	2.94110
$171$	3414.02	1.52676
$172$	−1546.85	−0.685733
$173$	1006.05	0.442131	0.221066	−	0.975259i	$-0.429047\pi$
$173$	1006.05	0.442131	0.221066	+	0.975259i	$0.429047\pi$
$174$	196.587	0.0856506
$175$	6738.45	2.91074
$176$	46.7214	0.0200100
$177$	−885.951	−0.376227
$178$	−6522.51	−2.74653
$179$	−1077.68	−0.450000	−0.225000	−	0.974359i	$-0.572238\pi$
$179$	−1077.68	−0.450000	−0.225000	+	0.974359i	$0.572238\pi$
$180$	−6148.17	−2.54588
$181$	−993.060	−0.407810	−0.203905	−	0.978991i	$-0.565363\pi$
$181$	−993.060	−0.407810	−0.203905	+	0.978991i	$0.565363\pi$
$182$	−2000.51	−0.814769
$183$	203.313	0.0821277
$184$	−525.931	−0.210718
$185$	−2791.74	−1.10948
$186$	1428.96	0.563314
$187$	4161.52	1.62738
$188$	4423.69	1.71612
$189$	2162.66	0.832332
$190$	−12025.5	−4.59170
$191$	1496.43	0.566899	0.283449	−	0.958987i	$-0.408521\pi$
$191$	1496.43	0.566899	0.283449	+	0.958987i	$0.408521\pi$
$192$	1223.97	0.460067
$193$	218.554	0.0815121	0.0407561	−	0.999169i	$-0.487023\pi$
$193$	218.554	0.0815121	0.0407561	+	0.999169i	$0.487023\pi$
$194$	3724.11	1.37823
$195$	436.818	0.160416
$196$	5883.58	2.14416
$197$	−1188.55	−0.429853	−0.214926	−	0.976630i	$-0.568951\pi$
$197$	−1188.55	−0.429853	−0.214926	+	0.976630i	$0.568951\pi$
$198$	−6341.69	−2.27618
$199$	−605.242	−0.215600	−0.107800	−	0.994173i	$-0.534381\pi$
$199$	−605.242	−0.215600	−0.107800	+	0.994173i	$0.534381\pi$
$200$	5461.76	1.93102
$201$	−385.557	−0.135299
$202$	−254.379	−0.0886041
$203$	−818.138	−0.282867
$204$	−1433.79	−0.492085
$205$	−5570.38	−1.89782
$206$	88.7520	0.0300177
$207$	570.649	0.191608
$208$	−12.9618	−0.00432086
$209$	−7676.66	−2.54070
$210$	−3647.94	−1.19872
$211$	−3637.33	−1.18675	−0.593374	−	0.804927i	$-0.702204\pi$
$211$	−3637.33	−1.18675	−0.593374	+	0.804927i	$0.702204\pi$
$212$	−3095.46	−1.00282
$213$	954.545	0.307063
$214$	−3208.13	−1.02478
$215$	−2271.27	−0.720463
$216$	1752.92	0.552180
$217$	−5946.92	−1.86038
$218$	8988.97	2.79271
$219$	−942.765	−0.290896
$220$	13824.6	4.23661
$221$	−1154.52	−0.351409
$222$	992.129	0.299943
$223$	−558.095	−0.167591	−0.0837955	−	0.996483i	$-0.526704\pi$
$223$	−558.095	−0.167591	−0.0837955	+	0.996483i	$0.526704\pi$
$224$	−5052.58	−1.50710
$225$	−5926.15	−1.75590
$226$	−10357.9	−3.04867
$227$	−2639.68	−0.771813	−0.385907	−	0.922538i	$-0.626111\pi$
$227$	−2639.68	−0.771813	−0.385907	+	0.922538i	$0.626111\pi$
$228$	2644.88	0.768252
$229$	−299.921	−0.0865474	−0.0432737	−	0.999063i	$-0.513779\pi$
$229$	−299.921	−0.0865474	−0.0432737	+	0.999063i	$0.513779\pi$
$230$	−2010.05	−0.576256
$231$	−2328.71	−0.663282
$232$	−663.130	−0.187658
$233$	3248.17	0.913283	0.456641	−	0.889651i	$-0.349052\pi$
$233$	3248.17	0.913283	0.456641	+	0.889651i	$0.349052\pi$
$234$	1759.36	0.491508
$235$	6495.42	1.80304
$236$	7778.78	2.14557
$237$	−1677.48	−0.459764
$238$	9641.60	2.62593
$239$	1150.63	0.311415	0.155707	−	0.987803i	$-0.450234\pi$
$239$	1150.63	0.311415	0.155707	+	0.987803i	$0.450234\pi$
$240$	−23.6359	−0.00635703
$241$	−5958.35	−1.59258	−0.796289	−	0.604916i	$-0.793207\pi$
$241$	−5958.35	−1.59258	−0.796289	+	0.604916i	$0.793207\pi$
$242$	8161.62	2.16797
$243$	−2893.12	−0.763761
$244$	−1785.12	−0.468363
$245$	8639.00	2.25276
$246$	1979.60	0.513068
$247$	2129.72	0.548626
$248$	−4820.19	−1.23420
$249$	−158.800	−0.0404157
$250$	9950.07	2.51719
$251$	−2797.07	−0.703386	−0.351693	−	0.936115i	$-0.614394\pi$
$251$	−2797.07	−0.703386	−0.351693	+	0.936115i	$0.614394\pi$
$252$	−9093.09	−2.27306
$253$	−1283.14	−0.318856
$254$	−3808.25	−0.940751
$255$	−2105.27	−0.517008
$256$	−4182.33	−1.02108
$257$	−6467.98	−1.56989	−0.784945	−	0.619566i	$-0.787309\pi$
$257$	−6467.98	−1.56989	−0.784945	+	0.619566i	$0.787309\pi$
$258$	807.165	0.194775
$259$	−4128.96	−0.990584
$260$	−3835.32	−0.914832
$261$	719.514	0.170639
$262$	8467.67	1.99670
$263$	−7985.03	−1.87216	−0.936080	−	0.351787i	$-0.885574\pi$
$263$	−7985.03	−1.87216	−0.936080	+	0.351787i	$0.885574\pi$
$264$	−1887.51	−0.440030
$265$	−4545.14	−1.05361
$266$	−17785.6	−4.09965
$267$	2106.39	0.482805
$268$	3385.24	0.771591
$269$	8064.19	1.82782	0.913908	−	0.405922i	$-0.133050\pi$
$269$	8064.19	1.82782	0.913908	+	0.405922i	$0.133050\pi$
$270$	6699.46	1.51006
$271$	−2377.32	−0.532886	−0.266443	−	0.963851i	$-0.585848\pi$
$271$	−2377.32	−0.532886	−0.266443	+	0.963851i	$0.585848\pi$
$272$	62.4701	0.0139258
$273$	646.049	0.143226
$274$	3858.46	0.850724
$275$	13325.4	2.92200
$276$	442.088	0.0964152
$277$	7496.87	1.62615	0.813074	−	0.582160i	$-0.197792\pi$
$277$	7496.87	1.62615	0.813074	+	0.582160i	$0.197792\pi$
$278$	−11768.2	−2.53888
$279$	5230.04	1.12227
$280$	12305.3	2.62637
$281$	8339.35	1.77041	0.885203	−	0.465205i	$-0.154019\pi$
$281$	8339.35	1.77041	0.885203	+	0.465205i	$0.154019\pi$
$282$	−2308.34	−0.487446
$283$	9461.89	1.98746	0.993730	−	0.111806i	$-0.0356636\pi$
$283$	9461.89	1.98746	0.993730	+	0.111806i	$0.0356636\pi$
$284$	−8381.04	−1.75114
$285$	3883.54	0.807162
$286$	−3956.04	−0.817921
$287$	−8238.54	−1.69445
$288$	4443.51	0.909154
$289$	651.276	0.132562
$290$	−2534.41	−0.513193
$291$	−1202.67	−0.242274
$292$	8277.61	1.65894
$293$	1400.11	0.279165	0.139583	−	0.990210i	$-0.455424\pi$
$293$	1400.11	0.279165	0.139583	+	0.990210i	$0.455424\pi$
$294$	−3070.13	−0.609025
$295$	11421.8	2.25424
$296$	−3346.67	−0.657167
$297$	4276.69	0.835551
$298$	6904.06	1.34209
$299$	355.979	0.0688522
$300$	−4591.06	−0.883550
$301$	−3359.19	−0.643258
$302$	10146.1	1.93326
$303$	82.1495	0.0155755
$304$	−115.237	−0.0217412
$305$	−2621.14	−0.492084
$306$	−8479.33	−1.58409
$307$	339.463	0.0631080	0.0315540	−	0.999502i	$-0.489954\pi$
$307$	339.463	0.0631080	0.0315540	+	0.999502i	$0.489954\pi$
$308$	20446.4	3.78261
$309$	−28.6617	−0.00527672
$310$	−18422.3	−3.37521
$311$	1892.72	0.345100	0.172550	−	0.985001i	$-0.444799\pi$
$311$	1892.72	0.345100	0.172550	+	0.985001i	$0.444799\pi$
$312$	523.646	0.0950180
$313$	4992.51	0.901577	0.450789	−	0.892631i	$-0.351143\pi$
$313$	4992.51	0.901577	0.450789	+	0.892631i	$0.351143\pi$
$314$	−10626.4	−1.90981
$315$	−13351.6	−2.38818
$316$	14728.5	2.62197
$317$	−8431.61	−1.49390	−0.746950	−	0.664880i	$-0.768483\pi$
$317$	−8431.61	−1.49390	−0.746950	+	0.664880i	$0.768483\pi$
$318$	1615.25	0.284839
$319$	−1617.88	−0.283961
$320$	−15779.6	−2.75658
$321$	1036.04	0.180144
$322$	−2972.85	−0.514504
$323$	−10264.3	−1.76818
$324$	7229.08	1.23955
$325$	−3696.82	−0.630962
$326$	288.242	0.0489701
$327$	−2902.91	−0.490921
$328$	−6677.63	−1.12412
$329$	9606.66	1.60982
$330$	−7213.85	−1.20336
$331$	200.804	0.0333450	0.0166725	−	0.999861i	$-0.494693\pi$
$331$	200.804	0.0333450	0.0166725	+	0.999861i	$0.494693\pi$
$332$	1394.28	0.230485
$333$	3631.23	0.597568
$334$	−12593.7	−2.06316
$335$	4970.63	0.810670
$336$	−34.9572	−0.00567581
$337$	1399.12	0.226157	0.113079	−	0.993586i	$-0.463929\pi$
$337$	1399.12	0.226157	0.113079	+	0.993586i	$0.463929\pi$
$338$	−8968.24	−1.44322
$339$	3345.01	0.535917
$340$	18484.6	2.94843
$341$	−11760.1	−1.86758
$342$	15641.6	2.47311
$343$	3100.40	0.488064
$344$	−2722.74	−0.426746
$345$	649.129	0.101298
$346$	4609.32	0.716180
$347$	3497.27	0.541046	0.270523	−	0.962713i	$-0.412803\pi$
$347$	3497.27	0.541046	0.270523	+	0.962713i	$0.412803\pi$
$348$	557.416	0.0858639
$349$	9976.40	1.53016	0.765078	−	0.643938i	$-0.222701\pi$
$349$	9976.40	1.53016	0.765078	+	0.643938i	$0.222701\pi$
$350$	30872.8	4.71492
$351$	−1186.47	−0.180425
$352$	−9991.53	−1.51293
$353$	−1118.84	−0.168697	−0.0843483	−	0.996436i	$-0.526881\pi$
$353$	−1118.84	−0.168697	−0.0843483	+	0.996436i	$0.526881\pi$
$354$	−4059.07	−0.609426
$355$	−12306.1	−1.83983
$356$	−18494.4	−2.75337
$357$	−3113.67	−0.461605
$358$	−4937.51	−0.728926
$359$	10757.4	1.58149	0.790746	−	0.612145i	$-0.209693\pi$
$359$	10757.4	1.58149	0.790746	+	0.612145i	$0.209693\pi$
$360$	−10821.9	−1.58435
$361$	12075.3	1.76051
$362$	−4549.80	−0.660585
$363$	−2635.73	−0.381101
$364$	−5672.40	−0.816798
$365$	12154.2	1.74296
$366$	931.499	0.133033
$367$	10795.9	1.53554	0.767771	−	0.640725i	$-0.221366\pi$
$367$	10795.9	1.53554	0.767771	+	0.640725i	$0.221366\pi$
$368$	−19.2618	−0.00272850
$369$	7245.41	1.02217
$370$	−12790.6	−1.79717
$371$	−6722.21	−0.940701
$372$	4051.77	0.564716
$373$	−9044.79	−1.25555	−0.627777	−	0.778393i	$-0.716035\pi$
$373$	−9044.79	−1.25555	−0.627777	+	0.778393i	$0.716035\pi$
$374$	19066.4	2.63609
$375$	−3213.29	−0.442489
$376$	7786.54	1.06798
$377$	448.843	0.0613173
$378$	9908.44	1.34824
$379$	4382.76	0.594003	0.297002	−	0.954877i	$-0.404013\pi$
$379$	4382.76	0.594003	0.297002	+	0.954877i	$0.404013\pi$
$380$	−34098.0	−4.60314
$381$	1229.84	0.165372
$382$	6856.02	0.918284
$383$	−3599.90	−0.480278	−0.240139	−	0.970739i	$-0.577193\pi$
$383$	−3599.90	−0.480278	−0.240139	+	0.970739i	$0.577193\pi$
$384$	3487.85	0.463513
$385$	30022.0	3.97419
$386$	1001.32	0.132036
$387$	2954.25	0.388044
$388$	10559.6	1.38166
$389$	−1340.33	−0.174697	−0.0873487	−	0.996178i	$-0.527839\pi$
$389$	−1340.33	−0.174697	−0.0873487	+	0.996178i	$0.527839\pi$
$390$	2001.32	0.259848
$391$	−1715.66	−0.221905
$392$	10356.2	1.33436
$393$	−2734.56	−0.350993
$394$	−5445.47	−0.696291
$395$	21626.2	2.75477
$396$	−17981.7	−2.28185
$397$	8694.35	1.09914	0.549568	−	0.835449i	$-0.314792\pi$
$397$	8694.35	1.09914	0.549568	+	0.835449i	$0.314792\pi$
$398$	−2772.97	−0.349238
$399$	5743.72	0.720666
$400$	200.032	0.0250040
$401$	3623.68	0.451267	0.225634	−	0.974212i	$-0.427555\pi$
$401$	3623.68	0.451267	0.225634	+	0.974212i	$0.427555\pi$
$402$	−1766.46	−0.219162
$403$	3262.57	0.403276
$404$	−721.284	−0.0888248
$405$	10614.6	1.30233
$406$	−3748.37	−0.458199
$407$	−8165.06	−0.994416
$408$	−2523.74	−0.306235
$409$	15330.6	1.85342	0.926710	−	0.375776i	$-0.122624\pi$
$409$	15330.6	1.85342	0.926710	+	0.375776i	$0.122624\pi$
$410$	−25521.2	−3.07415
$411$	−1246.06	−0.149546
$412$	251.654	0.0300924
$413$	16892.7	2.01267
$414$	2614.48	0.310374
$415$	2047.26	0.242159
$416$	2771.93	0.326694
$417$	3800.43	0.446302
$418$	−35171.3	−4.11551
$419$	−9394.55	−1.09536	−0.547678	−	0.836690i	$-0.684488\pi$
$419$	−9394.55	−1.09536	−0.547678	+	0.836690i	$0.684488\pi$
$420$	−10343.6	−1.20171
$421$	−16887.6	−1.95499	−0.977495	−	0.210957i	$-0.932342\pi$
$421$	−16887.6	−1.95499	−0.977495	+	0.210957i	$0.932342\pi$
$422$	−16664.7	−1.92234
$423$	−8448.60	−0.971123
$424$	−5448.60	−0.624074
$425$	17817.1	2.03354
$426$	4373.34	0.497392
$427$	−3876.63	−0.439352
$428$	−9096.57	−1.02734
$429$	1277.57	0.143780
$430$	−10406.0	−1.16703
$431$	−9698.10	−1.08385	−0.541927	−	0.840426i	$-0.682305\pi$
$431$	−9698.10	−1.08385	−0.541927	+	0.840426i	$0.682305\pi$
$432$	64.1991	0.00714995
$433$	−4179.07	−0.463819	−0.231909	−	0.972737i	$-0.574497\pi$
$433$	−4179.07	−0.463819	−0.231909	+	0.972737i	$0.574497\pi$
$434$	−27246.3	−3.01352
$435$	818.467	0.0902126
$436$	25488.0	2.79966
$437$	3164.85	0.346442
$438$	−4319.36	−0.471203
$439$	−14137.6	−1.53702	−0.768510	−	0.639838i	$-0.779001\pi$
$439$	−14137.6	−1.53702	−0.768510	+	0.639838i	$0.779001\pi$
$440$	24333.9	2.63653
$441$	−11236.8	−1.21334
$442$	−5289.53	−0.569225
$443$	−9969.40	−1.06921	−0.534606	−	0.845102i	$-0.679540\pi$
$443$	−9969.40	−1.06921	−0.534606	+	0.845102i	$0.679540\pi$
$444$	2813.15	0.300690
$445$	−27155.7	−2.89282
$446$	−2556.96	−0.271470
$447$	−2229.61	−0.235921
$448$	−23337.9	−2.46118
$449$	1773.21	0.186376	0.0931881	−	0.995649i	$-0.470294\pi$
$449$	1773.21	0.186376	0.0931881	+	0.995649i	$0.470294\pi$
$450$	−27151.2	−2.84427
$451$	−16291.8	−1.70100
$452$	−29369.6	−3.05626
$453$	−3276.61	−0.339842
$454$	−12093.9	−1.25021
$455$	−8328.92	−0.858167
$456$	4655.49	0.478099
$457$	6034.44	0.617679	0.308839	−	0.951114i	$-0.400059\pi$
$457$	6034.44	0.617679	0.308839	+	0.951114i	$0.400059\pi$
$458$	−1374.12	−0.140193
$459$	5718.27	0.581495
$460$	−5699.45	−0.577691
$461$	6666.33	0.673497	0.336748	−	0.941595i	$-0.390673\pi$
$461$	6666.33	0.673497	0.336748	+	0.941595i	$0.390673\pi$
$462$	−10669.2	−1.07441
$463$	−489.696	−0.0491536	−0.0245768	−	0.999698i	$-0.507824\pi$
$463$	−489.696	−0.0491536	−0.0245768	+	0.999698i	$0.507824\pi$
$464$	−24.2866	−0.00242990
$465$	5949.31	0.593318
$466$	14881.8	1.47937
$467$	7409.10	0.734159	0.367079	−	0.930190i	$-0.380358\pi$
$467$	7409.10	0.734159	0.367079	+	0.930190i	$0.380358\pi$
$468$	4988.61	0.492732
$469$	7351.51	0.723798
$470$	29759.3	2.92063
$471$	3431.69	0.335720
$472$	13692.1	1.33524
$473$	−6642.83	−0.645746
$474$	−7685.53	−0.744742
$475$	−32866.7	−3.17480
$476$	27338.5	2.63247
$477$	5911.87	0.567476
$478$	5271.71	0.504441
$479$	2890.25	0.275697	0.137848	−	0.990453i	$-0.455981\pi$
$479$	2890.25	0.275697	0.137848	+	0.990453i	$0.455981\pi$
$480$	5054.61	0.480647
$481$	2265.21	0.214729
$482$	−27298.7	−2.57972
$483$	960.056	0.0904432
$484$	23142.0	2.17337
$485$	15504.9	1.45164
$486$	−13255.1	−1.23717
$487$	10501.3	0.977126	0.488563	−	0.872528i	$-0.337521\pi$
$487$	10501.3	0.977126	0.488563	+	0.872528i	$0.337521\pi$
$488$	−3142.15	−0.291472
$489$	−93.0852	−0.00860830
$490$	39580.4	3.64910
$491$	−6174.13	−0.567484	−0.283742	−	0.958901i	$-0.591576\pi$
$491$	−6174.13	−0.567484	−0.283742	+	0.958901i	$0.591576\pi$
$492$	5613.10	0.514346
$493$	−2163.23	−0.197620
$494$	9757.48	0.888684
$495$	−26402.9	−2.39742
$496$	−176.535	−0.0159812
$497$	−18200.6	−1.64267
$498$	−727.554	−0.0654668
$499$	15929.1	1.42902	0.714512	−	0.699623i	$-0.246649\pi$
$499$	15929.1	1.42902	0.714512	+	0.699623i	$0.246649\pi$
$500$	28213.1	2.52346
$501$	4067.02	0.362677
$502$	−12815.0	−1.13937
$503$	−16723.4	−1.48242	−0.741211	−	0.671272i	$-0.765748\pi$
$503$	−16723.4	−1.48242	−0.741211	+	0.671272i	$0.765748\pi$
$504$	−16005.6	−1.41457
$505$	−1059.08	−0.0933235
$506$	−5878.84	−0.516494
$507$	2896.22	0.253699
$508$	−10798.2	−0.943093
$509$	17049.6	1.48470	0.742349	−	0.670013i	$-0.233712\pi$
$509$	17049.6	1.48470	0.742349	+	0.670013i	$0.233712\pi$
$510$	−9645.48	−0.837469
$511$	17976.0	1.55618
$512$	−303.187	−0.0261701
$513$	−10548.4	−0.907840
$514$	−29633.6	−2.54296
$515$	369.509	0.0316165
$516$	2288.69	0.195260
$517$	18997.3	1.61605
$518$	−18917.2	−1.60458
$519$	−1488.54	−0.125895
$520$	−6750.89	−0.569319
$521$	21028.5	1.76828	0.884141	−	0.467219i	$-0.154744\pi$
$521$	21028.5	1.76828	0.884141	+	0.467219i	$0.154744\pi$
$522$	3296.52	0.276407
$523$	3713.26	0.310458	0.155229	−	0.987879i	$-0.450388\pi$
$523$	3713.26	0.310458	0.155229	+	0.987879i	$0.450388\pi$
$524$	24009.8	2.00167
$525$	−9970.12	−0.828822
$526$	−36584.1	−3.03259
$527$	−15724.2	−1.29973
$528$	−69.1282	−0.00569777
$529$	529.000	0.0434783
$530$	−20824.0	−1.70667
$531$	−14856.3	−1.21414
$532$	−50430.7	−4.10986
$533$	4519.79	0.367306
$534$	9650.61	0.782065
$535$	−13356.7	−1.07937
$536$	5958.67	0.480177
$537$	1594.53	0.128136
$538$	36946.8	2.96076
$539$	25266.6	2.01913
$540$	18996.1	1.51382
$541$	−1462.87	−0.116255	−0.0581273	−	0.998309i	$-0.518513\pi$
$541$	−1462.87	−0.116255	−0.0581273	+	0.998309i	$0.518513\pi$
$542$	−10891.9	−0.863188
$543$	1469.32	0.116122
$544$	−13359.5	−1.05291
$545$	37424.6	2.94145
$546$	2959.93	0.232002
$547$	8880.01	0.694117	0.347058	−	0.937844i	$-0.387181\pi$
$547$	8880.01	0.694117	0.347058	+	0.937844i	$0.387181\pi$
$548$	10940.6	0.852843
$549$	3409.32	0.265038
$550$	61051.3	4.73316
$551$	3990.46	0.308529
$552$	778.159	0.0600012
$553$	31985.0	2.45957
$554$	34347.6	2.63410
$555$	4130.62	0.315919
$556$	−33368.3	−2.54520
$557$	−11608.6	−0.883077	−0.441538	−	0.897242i	$-0.645567\pi$
$557$	−11608.6	−0.883077	−0.441538	+	0.897242i	$0.645567\pi$
$558$	23961.9	1.81790
$559$	1842.90	0.139439
$560$	450.672	0.0340078
$561$	−6157.32	−0.463391
$562$	38207.5	2.86777
$563$	8771.39	0.656608	0.328304	−	0.944572i	$-0.393523\pi$
$563$	8771.39	0.656608	0.328304	+	0.944572i	$0.393523\pi$
$564$	−6545.23	−0.488660
$565$	−43124.1	−3.21106
$566$	43350.5	3.21936
$567$	15698.9	1.16277
$568$	−14752.2	−1.08977
$569$	−6931.66	−0.510704	−0.255352	−	0.966848i	$-0.582191\pi$
$569$	−6931.66	−0.510704	−0.255352	+	0.966848i	$0.582191\pi$
$570$	17792.8	1.30747
$571$	−15024.2	−1.10112	−0.550562	−	0.834794i	$-0.685586\pi$
$571$	−15024.2	−1.10112	−0.550562	+	0.834794i	$0.685586\pi$
$572$	−11217.2	−0.819958
$573$	−2214.09	−0.161422
$574$	−37745.6	−2.74472
$575$	−5493.63	−0.398435
$576$	20524.6	1.48470
$577$	2069.83	0.149338	0.0746692	−	0.997208i	$-0.476210\pi$
$577$	2069.83	0.149338	0.0746692	+	0.997208i	$0.476210\pi$
$578$	2983.88	0.214728
$579$	−323.369	−0.0232103
$580$	−7186.26	−0.514471
$581$	3027.87	0.216209
$582$	−5510.14	−0.392445
$583$	−13293.2	−0.944340
$584$	14570.2	1.03239
$585$	7324.89	0.517687
$586$	6414.74	0.452202
$587$	−6007.43	−0.422407	−0.211204	−	0.977442i	$-0.567738\pi$
$587$	−6007.43	−0.422407	−0.211204	+	0.977442i	$0.567738\pi$
$588$	−8705.26	−0.610542
$589$	29006.0	2.02916
$590$	52329.9	3.65150
$591$	1758.57	0.122399
$592$	−122.569	−0.00850938
$593$	−4325.47	−0.299537	−0.149769	−	0.988721i	$-0.547853\pi$
$593$	−4325.47	−0.299537	−0.149769	+	0.988721i	$0.547853\pi$
$594$	19594.0	1.35346
$595$	40141.7	2.76580
$596$	19576.3	1.34543
$597$	895.507	0.0613914
$598$	1630.95	0.111529
$599$	4211.95	0.287305	0.143652	−	0.989628i	$-0.454115\pi$
$599$	4211.95	0.287305	0.143652	+	0.989628i	$0.454115\pi$
$600$	−8081.14	−0.549852
$601$	−6704.60	−0.455052	−0.227526	−	0.973772i	$-0.573064\pi$
$601$	−6704.60	−0.455052	−0.227526	+	0.973772i	$0.573064\pi$
$602$	−15390.4	−1.04197
$603$	−6465.31	−0.436630
$604$	28769.1	1.93808
$605$	33980.0	2.28345
$606$	376.375	0.0252297
$607$	353.624	0.0236461	0.0118230	−	0.999930i	$-0.496237\pi$
$607$	353.624	0.0236461	0.0118230	+	0.999930i	$0.496237\pi$
$608$	24643.9	1.64382
$609$	1210.50	0.0805454
$610$	−12009.0	−0.797096
$611$	−5270.36	−0.348962
$612$	−24042.9	−1.58803
$613$	12820.6	0.844728	0.422364	−	0.906426i	$-0.361200\pi$
$613$	12820.6	0.844728	0.422364	+	0.906426i	$0.361200\pi$
$614$	1555.28	0.102225
$615$	8241.85	0.540396
$616$	35989.6	2.35400
$617$	6955.40	0.453831	0.226915	−	0.973914i	$-0.427136\pi$
$617$	6955.40	0.453831	0.226915	+	0.973914i	$0.427136\pi$
$618$	−131.316	−0.00854742
$619$	−12006.3	−0.779599	−0.389800	−	0.920900i	$-0.627456\pi$
$619$	−12006.3	−0.779599	−0.389800	+	0.920900i	$0.627456\pi$
$620$	−52235.8	−3.38361
$621$	−1763.15	−0.113933
$622$	8671.64	0.559005
$623$	−40163.1	−2.58283
$624$	19.1781	0.00123035
$625$	11569.3	0.740436
$626$	22873.7	1.46041
$627$	11358.3	0.723454
$628$	−30130.8	−1.91457
$629$	−10917.3	−0.692055
$630$	−61171.5	−3.86846
$631$	7913.76	0.499274	0.249637	−	0.968340i	$-0.419689\pi$
$631$	7913.76	0.499274	0.249637	+	0.968340i	$0.419689\pi$
$632$	25925.0	1.63171
$633$	5381.73	0.337922
$634$	−38630.2	−2.41988
$635$	−15855.2	−0.990858
$636$	4580.00	0.285548
$637$	−7009.66	−0.436001
$638$	−7412.45	−0.459971
$639$	16006.6	0.990938
$640$	−44965.7	−2.77723
$641$	16771.5	1.03344	0.516720	−	0.856154i	$-0.327153\pi$
$641$	16771.5	1.03344	0.516720	+	0.856154i	$0.327153\pi$
$642$	4746.71	0.291803
$643$	1777.80	0.109035	0.0545176	−	0.998513i	$-0.482638\pi$
$643$	1777.80	0.109035	0.0545176	+	0.998513i	$0.482638\pi$
$644$	−8429.42	−0.515785
$645$	3360.54	0.205149
$646$	−47026.8	−2.86415
$647$	−9313.42	−0.565917	−0.282959	−	0.959132i	$-0.591316\pi$
$647$	−9313.42	−0.565917	−0.282959	+	0.959132i	$0.591316\pi$
$648$	12724.5	0.771400
$649$	33405.5	2.02046
$650$	−16937.3	−1.02206
$651$	8798.97	0.529737
$652$	817.301	0.0490920
$653$	16056.1	0.962214	0.481107	−	0.876662i	$-0.340235\pi$
$653$	16056.1	0.962214	0.481107	+	0.876662i	$0.340235\pi$
$654$	−13299.9	−0.795212
$655$	35254.2	2.10305
$656$	−244.563	−0.0145557
$657$	−15809.0	−0.938765
$658$	44013.8	2.60765
$659$	−21010.8	−1.24198	−0.620989	−	0.783820i	$-0.713269\pi$
$659$	−21010.8	−1.24198	−0.620989	+	0.783820i	$0.713269\pi$
$660$	−20454.7	−1.20636
$661$	8908.16	0.524187	0.262093	−	0.965043i	$-0.415587\pi$
$661$	8908.16	0.524187	0.262093	+	0.965043i	$0.415587\pi$
$662$	920.002	0.0540134
$663$	1708.21	0.100062
$664$	2454.20	0.143436
$665$	−74048.6	−4.31802
$666$	16636.8	0.967962
$667$	667.000	0.0387202
$668$	−35709.1	−2.06830
$669$	825.749	0.0477209
$670$	22773.4	1.31315
$671$	−7666.08	−0.441052
$672$	7475.73	0.429140
$673$	12123.1	0.694369	0.347185	−	0.937797i	$-0.387138\pi$
$673$	12123.1	0.694369	0.347185	+	0.937797i	$0.387138\pi$
$674$	6410.20	0.366338
$675$	18310.2	1.04409
$676$	−25429.2	−1.44681
$677$	16951.4	0.962326	0.481163	−	0.876631i	$-0.340215\pi$
$677$	16951.4	0.962326	0.481163	+	0.876631i	$0.340215\pi$
$678$	15325.5	0.868098
$679$	22931.7	1.29608
$680$	32536.3	1.83487
$681$	3905.63	0.219771
$682$	−53879.9	−3.02517
$683$	−13741.1	−0.769823	−0.384911	−	0.922954i	$-0.625768\pi$
$683$	−13741.1	−0.769823	−0.384911	+	0.922954i	$0.625768\pi$
$684$	44351.4	2.47927
$685$	16064.3	0.896037
$686$	14204.8	0.790583
$687$	443.759	0.0246441
$688$	−99.7181	−0.00552575
$689$	3687.91	0.203916
$690$	2974.04	0.164087
$691$	29443.9	1.62098	0.810491	−	0.585752i	$-0.199201\pi$
$691$	29443.9	1.62098	0.810491	+	0.585752i	$0.199201\pi$
$692$	13069.6	0.717964
$693$	−39049.7	−2.14051
$694$	16023.0	0.876407
$695$	−48995.5	−2.67411
$696$	981.158	0.0534349
$697$	−21783.4	−1.18380
$698$	45707.8	2.47860
$699$	−4805.95	−0.260054
$700$	87539.0	4.72666
$701$	−14392.0	−0.775432	−0.387716	−	0.921779i	$-0.626736\pi$
$701$	−14392.0	−0.775432	−0.387716	+	0.921779i	$0.626736\pi$
$702$	−5435.93	−0.292259
$703$	20139.0	1.08045
$704$	−46150.9	−2.47071
$705$	−9610.52	−0.513409
$706$	−5126.07	−0.273261
$707$	−1566.37	−0.0833229
$708$	−11509.4	−0.610944
$709$	1369.74	0.0725551	0.0362776	−	0.999342i	$-0.488450\pi$
$709$	1369.74	0.0725551	0.0362776	+	0.999342i	$0.488450\pi$
$710$	−56381.4	−2.98022
$711$	−28129.3	−1.48373
$712$	−32553.6	−1.71348
$713$	4848.32	0.254658
$714$	−14265.6	−0.747725
$715$	−16470.5	−0.861486
$716$	−14000.2	−0.730741
$717$	−1702.45	−0.0886741
$718$	49286.1	2.56176
$719$	22025.9	1.14246	0.571229	−	0.820790i	$-0.306467\pi$
$719$	22025.9	1.14246	0.571229	+	0.820790i	$0.306467\pi$
$720$	−396.344	−0.0205151
$721$	546.500	0.0282285
$722$	55324.1	2.85173
$723$	8815.89	0.453481
$724$	−12900.8	−0.662231
$725$	−6926.75	−0.354832
$726$	−12075.8	−0.617322
$727$	−22196.4	−1.13235	−0.566176	−	0.824284i	$-0.691578\pi$
$727$	−22196.4	−1.13235	−0.566176	+	0.824284i	$0.691578\pi$
$728$	−9984.50	−0.508311
$729$	−10744.1	−0.545855
$730$	55685.6	2.82331
$731$	−8881.99	−0.449401
$732$	2641.24	0.133365
$733$	−11459.5	−0.577445	−0.288722	−	0.957413i	$-0.593230\pi$
$733$	−11459.5	−0.577445	−0.288722	+	0.957413i	$0.593230\pi$
$734$	49462.6	2.48733
$735$	−12782.1	−0.641464
$736$	4119.20	0.206298
$737$	14537.7	0.726598
$738$	33195.5	1.65575
$739$	1182.74	0.0588740	0.0294370	−	0.999567i	$-0.490629\pi$
$739$	1182.74	0.0588740	0.0294370	+	0.999567i	$0.490629\pi$
$740$	−36267.4	−1.80165
$741$	−3151.10	−0.156219
$742$	−30798.4	−1.52378
$743$	6685.09	0.330083	0.165042	−	0.986287i	$-0.447224\pi$
$743$	6685.09	0.330083	0.165042	+	0.986287i	$0.447224\pi$
$744$	7131.88	0.351435
$745$	28744.3	1.41357
$746$	−41439.5	−2.03379
$747$	−2662.87	−0.130428
$748$	54062.1	2.64266
$749$	−19754.5	−0.963701
$750$	−14722.0	−0.716760
$751$	3099.40	0.150597	0.0752986	−	0.997161i	$-0.476009\pi$
$751$	3099.40	0.150597	0.0752986	+	0.997161i	$0.476009\pi$
$752$	285.175	0.0138288
$753$	4138.51	0.200286
$754$	2056.42	0.0993240
$755$	42242.3	2.03623
$756$	28095.1	1.35160
$757$	−26581.2	−1.27624	−0.638118	−	0.769939i	$-0.720287\pi$
$757$	−26581.2	−1.27624	−0.638118	+	0.769939i	$0.720287\pi$
$758$	20080.0	0.962189
$759$	1898.52	0.0907930
$760$	−60019.0	−2.86463
$761$	−9425.96	−0.449003	−0.224501	−	0.974474i	$-0.572075\pi$
$761$	−9425.96	−0.449003	−0.224501	+	0.974474i	$0.572075\pi$
$762$	5634.62	0.267875
$763$	55350.6	2.62625
$764$	19440.0	0.920570
$765$	−35302.8	−1.66846
$766$	−16493.3	−0.777972
$767$	−9267.59	−0.436289
$768$	6188.12	0.290748
$769$	17129.1	0.803241	0.401620	−	0.915806i	$-0.368447\pi$
$769$	17129.1	0.803241	0.401620	+	0.915806i	$0.368447\pi$
$770$	137548.	6.43753
$771$	9569.93	0.447020
$772$	2839.22	0.132365
$773$	9514.32	0.442699	0.221350	−	0.975195i	$-0.428954\pi$
$773$	9514.32	0.442699	0.221350	+	0.975195i	$0.428954\pi$
$774$	13535.2	0.628568
$775$	−50349.5	−2.33369
$776$	18586.9	0.859835
$777$	6109.15	0.282065
$778$	−6140.83	−0.282981
$779$	40183.4	1.84816
$780$	5674.68	0.260495
$781$	−35991.8	−1.64903
$782$	−7860.47	−0.359450
$783$	−2223.10	−0.101465
$784$	379.287	0.0172780
$785$	−44241.7	−2.01153
$786$	−12528.6	−0.568552
$787$	−1540.64	−0.0697814	−0.0348907	−	0.999391i	$-0.511108\pi$
$787$	−1540.64	−0.0697814	−0.0348907	+	0.999391i	$0.511108\pi$
$788$	−15440.5	−0.698025
$789$	11814.5	0.533091
$790$	99082.5	4.46227
$791$	−63780.2	−2.86696
$792$	−31651.1	−1.42004
$793$	2126.78	0.0952386
$794$	39833.9	1.78042
$795$	6724.92	0.300010
$796$	−7862.68	−0.350107
$797$	33887.2	1.50608	0.753040	−	0.657975i	$-0.228587\pi$
$797$	33887.2	1.50608	0.753040	+	0.657975i	$0.228587\pi$
$798$	26315.4	1.16736
$799$	25400.8	1.12468
$800$	−42777.6	−1.89052
$801$	35321.5	1.55808
$802$	16602.2	0.730979
$803$	35547.7	1.56220
$804$	−5008.75	−0.219708
$805$	−12377.1	−0.541908
$806$	14947.8	0.653242
$807$	−11931.7	−0.520464
$808$	−1269.60	−0.0552775
$809$	−11630.6	−0.505450	−0.252725	−	0.967538i	$-0.581327\pi$
$809$	−11630.6	−0.505450	−0.252725	+	0.967538i	$0.581327\pi$
$810$	48631.9	2.10957
$811$	−32435.3	−1.40439	−0.702194	−	0.711986i	$-0.747796\pi$
$811$	−32435.3	−1.40439	−0.702194	+	0.711986i	$0.747796\pi$
$812$	−10628.4	−0.459340
$813$	3517.45	0.151737
$814$	−37409.0	−1.61079
$815$	1200.06	0.0515784
$816$	−92.4299	−0.00396531
$817$	16384.4	0.701613
$818$	70238.5	3.00224
$819$	10833.4	0.462212
$820$	−72364.6	−3.08181
$821$	−5605.25	−0.238276	−0.119138	−	0.992878i	$-0.538013\pi$
$821$	−5605.25	−0.238276	−0.119138	+	0.992878i	$0.538013\pi$
$822$	−5708.93	−0.242240
$823$	3056.55	0.129459	0.0647294	−	0.997903i	$-0.479382\pi$
$823$	3056.55	0.129459	0.0647294	+	0.997903i	$0.479382\pi$
$824$	442.958	0.0187272
$825$	−19716.0	−0.832028
$826$	77395.4	3.26020
$827$	−37265.1	−1.56691	−0.783455	−	0.621449i	$-0.786544\pi$
$827$	−37265.1	−1.56691	−0.783455	+	0.621449i	$0.786544\pi$
$828$	7413.28	0.311147
$829$	38147.9	1.59823	0.799114	−	0.601180i	$-0.205303\pi$
$829$	38147.9	1.59823	0.799114	+	0.601180i	$0.205303\pi$
$830$	9379.70	0.392258
$831$	−11092.3	−0.463040
$832$	12803.5	0.533512
$833$	33783.5	1.40520
$834$	17412.0	0.722936
$835$	−52432.5	−2.17305
$836$	−99727.2	−4.12576
$837$	−16159.4	−0.667322
$838$	−43042.0	−1.77430
$839$	10368.3	0.426643	0.213321	−	0.976982i	$-0.431572\pi$
$839$	10368.3	0.426643	0.213321	+	0.976982i	$0.431572\pi$
$840$	−18206.8	−0.747849
$841$	841.000	0.0344828
$842$	−77372.0	−3.16677
$843$	−12338.8	−0.504117
$844$	−47252.4	−1.92713
$845$	−37338.3	−1.52009
$846$	−38708.0	−1.57306
$847$	50256.1	2.03875
$848$	−199.550	−0.00808087
$849$	−13999.7	−0.565922
$850$	81630.5	3.29400
$851$	3366.20	0.135596
$852$	12400.5	0.498630
$853$	70.6298	0.00283507	0.00141754	−	0.999999i	$-0.499549\pi$
$853$	70.6298	0.00283507	0.00141754	+	0.999999i	$0.499549\pi$
$854$	−17761.1	−0.711679
$855$	65122.2	2.60483
$856$	−16011.7	−0.639332
$857$	39274.9	1.56547	0.782733	−	0.622357i	$-0.213825\pi$
$857$	39274.9	1.56547	0.782733	+	0.622357i	$0.213825\pi$
$858$	5853.29	0.232900
$859$	−20321.3	−0.807165	−0.403582	−	0.914943i	$-0.632235\pi$
$859$	−20321.3	−0.807165	−0.403582	+	0.914943i	$0.632235\pi$
$860$	−29506.0	−1.16994
$861$	12189.6	0.482487
$862$	−44432.7	−1.75567
$863$	−29491.7	−1.16328	−0.581640	−	0.813447i	$-0.697589\pi$
$863$	−29491.7	−1.16328	−0.581640	+	0.813447i	$0.697589\pi$
$864$	−13729.2	−0.540598
$865$	19190.4	0.754327
$866$	−19146.8	−0.751311
$867$	−963.618	−0.0377465
$868$	−77256.2	−3.02102
$869$	63250.6	2.46908
$870$	3749.88	0.146130
$871$	−4033.16	−0.156898
$872$	44863.6	1.74229
$873$	−20167.3	−0.781856
$874$	14500.0	0.561179
$875$	61268.7	2.36715
$876$	−12247.4	−0.472377
$877$	−13052.9	−0.502584	−0.251292	−	0.967911i	$-0.580855\pi$
$877$	−13052.9	−0.502584	−0.251292	+	0.967911i	$0.580855\pi$
$878$	−64772.8	−2.48972
$879$	−2071.58	−0.0794912
$880$	891.208	0.0341393
$881$	40830.5	1.56142	0.780712	−	0.624891i	$-0.214857\pi$
$881$	40830.5	1.56142	0.780712	+	0.624891i	$0.214857\pi$
$882$	−51482.3	−1.96542
$883$	−42068.2	−1.60329	−0.801646	−	0.597799i	$-0.796042\pi$
$883$	−42068.2	−1.60329	−0.801646	+	0.597799i	$0.796042\pi$
$884$	−14998.3	−0.570643
$885$	−16899.5	−0.641887
$886$	−45675.7	−1.73195
$887$	3491.43	0.132165	0.0660827	−	0.997814i	$-0.478950\pi$
$887$	3491.43	0.132165	0.0660827	+	0.997814i	$0.478950\pi$
$888$	4951.68	0.187126
$889$	−23449.7	−0.884677
$890$	−124416.	−4.68590
$891$	31044.8	1.16727
$892$	−7250.19	−0.272146
$893$	−46856.3	−1.75587
$894$	−10215.1	−0.382154
$895$	−20556.8	−0.767751
$896$	−66503.9	−2.47962
$897$	−526.702	−0.0196054
$898$	8124.11	0.301899
$899$	6113.10	0.226789
$900$	−76986.5	−2.85135
$901$	−17774.1	−0.657205
$902$	−74642.4	−2.75534
$903$	4970.21	0.183165
$904$	−51696.1	−1.90198
$905$	−18942.6	−0.695771
$906$	−15012.1	−0.550489
$907$	−17193.0	−0.629421	−0.314711	−	0.949188i	$-0.601908\pi$
$907$	−17193.0	−0.629421	−0.314711	+	0.949188i	$0.601908\pi$
$908$	−34292.0	−1.25333
$909$	1377.55	0.0502644
$910$	−38159.7	−1.39009
$911$	−47739.7	−1.73621	−0.868105	−	0.496380i	$-0.834662\pi$
$911$	−47739.7	−1.73621	−0.868105	+	0.496380i	$0.834662\pi$
$912$	170.503	0.00619071
$913$	5987.65	0.217045
$914$	27647.3	1.00054
$915$	3878.19	0.140119
$916$	−3896.27	−0.140542
$917$	52140.7	1.87768
$918$	26198.8	0.941926
$919$	34684.7	1.24499	0.622493	−	0.782626i	$-0.286120\pi$
$919$	34684.7	1.24499	0.622493	+	0.782626i	$0.286120\pi$
$920$	−10032.1	−0.359509
$921$	−502.264	−0.0179698
$922$	30542.4	1.09095
$923$	9985.12	0.356083
$924$	−30252.2	−1.07708
$925$	−34957.8	−1.24260
$926$	−2243.59	−0.0796208
$927$	−480.621	−0.0170288
$928$	5193.77	0.183722
$929$	−8349.69	−0.294881	−0.147440	−	0.989071i	$-0.547103\pi$
$929$	−8349.69	−0.294881	−0.147440	+	0.989071i	$0.547103\pi$
$930$	27257.3	0.961078
$931$	−62319.6	−2.19382
$932$	42196.9	1.48305
$933$	−2800.43	−0.0982659
$934$	33945.4	1.18922
$935$	79380.7	2.77650
$936$	8780.90	0.306637
$937$	2631.15	0.0917352	0.0458676	−	0.998948i	$-0.485395\pi$
$937$	2631.15	0.0917352	0.0458676	+	0.998948i	$0.485395\pi$
$938$	33681.6	1.17243
$939$	−7386.85	−0.256721
$940$	84381.7	2.92790
$941$	−2652.59	−0.0918938	−0.0459469	−	0.998944i	$-0.514630\pi$
$941$	−2652.59	−0.0918938	−0.0459469	+	0.998944i	$0.514630\pi$
$942$	15722.6	0.543812
$943$	6716.60	0.231943
$944$	501.462	0.0172894
$945$	41252.7	1.42005
$946$	−30434.7	−1.04600
$947$	−5660.84	−0.194248	−0.0971239	−	0.995272i	$-0.530964\pi$
$947$	−5660.84	−0.194248	−0.0971239	+	0.995272i	$0.530964\pi$
$948$	−21792.1	−0.746597
$949$	−9861.89	−0.337335
$950$	−150582.	−5.14265
$951$	12475.3	0.425383
$952$	48120.9	1.63824
$953$	36346.1	1.23543	0.617716	−	0.786401i	$-0.288058\pi$
$953$	36346.1	1.23543	0.617716	+	0.786401i	$0.288058\pi$
$954$	27085.8	0.919218
$955$	28544.3	0.967195
$956$	14947.8	0.505697
$957$	2393.79	0.0808570
$958$	13241.9	0.446584
$959$	23758.9	0.800017
$960$	23347.3	0.784926
$961$	14644.2	0.491564
$962$	10378.3	0.347826
$963$	17373.1	0.581351
$964$	−77404.8	−2.58614
$965$	4168.90	0.139069
$966$	4398.58	0.146503
$967$	−46545.8	−1.54789	−0.773946	−	0.633252i	$-0.781720\pi$
$967$	−46545.8	−1.54789	−0.773946	+	0.633252i	$0.781720\pi$
$968$	40734.4	1.35253
$969$	15186.9	0.503481
$970$	71037.3	2.35141
$971$	14748.4	0.487436	0.243718	−	0.969846i	$-0.421633\pi$
$971$	14748.4	0.487436	0.243718	+	0.969846i	$0.421633\pi$
$972$	−37584.5	−1.24025
$973$	−72463.8	−2.38755
$974$	48112.8	1.58279
$975$	5469.76	0.179664
$976$	−115.079	−0.00377415
$977$	59358.4	1.94375	0.971876	−	0.235495i	$-0.0756710\pi$
$977$	59358.4	1.94375	0.971876	+	0.235495i	$0.0756710\pi$
$978$	−426.478	−0.0139440
$979$	−79422.9	−2.59282
$980$	112229.	3.65819
$981$	−48678.2	−1.58428
$982$	−28287.3	−0.919231
$983$	51385.7	1.66729	0.833647	−	0.552297i	$-0.186249\pi$
$983$	51385.7	1.66729	0.833647	+	0.552297i	$0.186249\pi$
$984$	9880.12	0.320088
$985$	−22671.6	−0.733378
$986$	−9911.02	−0.320113
$987$	−14213.9	−0.458391
$988$	27667.1	0.890897
$989$	2738.63	0.0880520
$990$	−120967.	−3.88343
$991$	−48050.1	−1.54022	−0.770111	−	0.637910i	$-0.779799\pi$
$991$	−48050.1	−1.54022	−0.770111	+	0.637910i	$0.779799\pi$
$992$	37752.7	1.20832
$993$	−297.107	−0.00949486
$994$	−83387.6	−2.66086
$995$	−11545.0	−0.367839
$996$	−2062.96	−0.0656299
$997$	−49697.6	−1.57867	−0.789337	−	0.613961i	$-0.789575\pi$
$997$	−49697.6	−1.57867	−0.789337	+	0.613961i	$0.789575\pi$
$998$	72980.4	2.31478
$999$	−11219.5	−0.355324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.c.1.33	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.c.1.33	✓	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)

\(f(q)\)	\(=\)	\(q+4.58159 q^{2} -1.47959 q^{3} +12.9910 q^{4} +19.0749 q^{5} -6.77885 q^{6} +28.2117 q^{7} +22.8666 q^{8} -24.8108 q^{9} +O(q^{10})\)	\(q+4.58159 q^{2} -1.47959 q^{3} +12.9910 q^{4} +19.0749 q^{5} -6.77885 q^{6} +28.2117 q^{7} +22.8666 q^{8} -24.8108 q^{9} +87.3936 q^{10} +55.7888 q^{11} -19.2212 q^{12} -15.4774 q^{13} +129.254 q^{14} -28.2230 q^{15} +0.837468 q^{16} +74.5941 q^{17} -113.673 q^{18} -137.602 q^{19} +247.802 q^{20} -41.7415 q^{21} +255.602 q^{22} -23.0000 q^{23} -33.8330 q^{24} +238.854 q^{25} -70.9109 q^{26} +76.6585 q^{27} +366.497 q^{28} -29.0000 q^{29} -129.306 q^{30} -210.797 q^{31} -179.096 q^{32} -82.5443 q^{33} +341.759 q^{34} +538.136 q^{35} -322.317 q^{36} -146.357 q^{37} -630.436 q^{38} +22.9001 q^{39} +436.178 q^{40} -292.026 q^{41} -191.243 q^{42} -119.071 q^{43} +724.751 q^{44} -473.265 q^{45} -105.377 q^{46} +340.521 q^{47} -1.23910 q^{48} +452.898 q^{49} +1094.33 q^{50} -110.368 q^{51} -201.066 q^{52} -238.278 q^{53} +351.218 q^{54} +1064.17 q^{55} +645.104 q^{56} +203.594 q^{57} -132.866 q^{58} +598.784 q^{59} -366.644 q^{60} -137.412 q^{61} -965.783 q^{62} -699.955 q^{63} -827.242 q^{64} -295.230 q^{65} -378.184 q^{66} +260.584 q^{67} +969.049 q^{68} +34.0305 q^{69} +2465.52 q^{70} -645.144 q^{71} -567.338 q^{72} +637.182 q^{73} -670.546 q^{74} -353.404 q^{75} -1787.58 q^{76} +1573.90 q^{77} +104.919 q^{78} +1133.75 q^{79} +15.9747 q^{80} +556.470 q^{81} -1337.94 q^{82} +107.327 q^{83} -542.263 q^{84} +1422.88 q^{85} -545.534 q^{86} +42.9080 q^{87} +1275.70 q^{88} -1423.63 q^{89} -2168.31 q^{90} -436.642 q^{91} -298.792 q^{92} +311.891 q^{93} +1560.13 q^{94} -2624.75 q^{95} +264.987 q^{96} +812.843 q^{97} +2074.99 q^{98} -1384.17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) \) 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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