LMFDB - Embedded newform 667.4.a.b.1.25

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:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+1.50063 q^{2} +6.46705 q^{3} -5.74811 q^{4} -0.662294 q^{5} +9.70465 q^{6} +11.3293 q^{7} -20.6308 q^{8} +14.8227 q^{9} +O(q^{10})$	\(q+1.50063 q^{2} +6.46705 q^{3} -5.74811 q^{4} -0.662294 q^{5} +9.70465 q^{6} +11.3293 q^{7} -20.6308 q^{8} +14.8227 q^{9} -0.993858 q^{10} +15.0133 q^{11} -37.1733 q^{12} -73.5339 q^{13} +17.0011 q^{14} -4.28308 q^{15} +15.0256 q^{16} -89.5681 q^{17} +22.2434 q^{18} -47.9839 q^{19} +3.80694 q^{20} +73.2671 q^{21} +22.5294 q^{22} -23.0000 q^{23} -133.421 q^{24} -124.561 q^{25} -110.347 q^{26} -78.7513 q^{27} -65.1220 q^{28} +29.0000 q^{29} -6.42732 q^{30} +136.860 q^{31} +187.595 q^{32} +97.0917 q^{33} -134.409 q^{34} -7.50332 q^{35} -85.2024 q^{36} +65.6890 q^{37} -72.0062 q^{38} -475.547 q^{39} +13.6637 q^{40} -287.295 q^{41} +109.947 q^{42} +9.56530 q^{43} -86.2981 q^{44} -9.81697 q^{45} -34.5145 q^{46} +404.479 q^{47} +97.1714 q^{48} -214.647 q^{49} -186.921 q^{50} -579.241 q^{51} +422.681 q^{52} +601.538 q^{53} -118.177 q^{54} -9.94321 q^{55} -233.733 q^{56} -310.314 q^{57} +43.5183 q^{58} -496.582 q^{59} +24.6196 q^{60} -751.927 q^{61} +205.377 q^{62} +167.931 q^{63} +161.305 q^{64} +48.7010 q^{65} +145.699 q^{66} +91.2679 q^{67} +514.847 q^{68} -148.742 q^{69} -11.2597 q^{70} -1011.44 q^{71} -305.804 q^{72} -513.165 q^{73} +98.5749 q^{74} -805.544 q^{75} +275.817 q^{76} +170.090 q^{77} -713.621 q^{78} +369.565 q^{79} -9.95137 q^{80} -909.501 q^{81} -431.124 q^{82} -1245.49 q^{83} -421.147 q^{84} +59.3204 q^{85} +14.3540 q^{86} +187.544 q^{87} -309.737 q^{88} +1144.42 q^{89} -14.7316 q^{90} -833.087 q^{91} +132.206 q^{92} +885.082 q^{93} +606.974 q^{94} +31.7795 q^{95} +1213.18 q^{96} -390.140 q^{97} -322.106 q^{98} +222.537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) $ 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * 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 $

$2$	1.50063	0.530553	0.265276	−	0.964172i	$-0.414537\pi$
$2$	1.50063	0.530553	0.265276	+	0.964172i	$0.414537\pi$
$3$	6.46705	1.24458	0.622292	−	0.782785i	$-0.286202\pi$
$3$	6.46705	1.24458	0.622292	+	0.782785i	$0.286202\pi$
$4$	−5.74811	−0.718514
$5$	−0.662294	−0.0592373	−0.0296187	−	0.999561i	$-0.509429\pi$
$5$	−0.662294	−0.0592373	−0.0296187	+	0.999561i	$0.509429\pi$
$6$	9.70465	0.660317
$7$	11.3293	0.611724	0.305862	−	0.952076i	$-0.401055\pi$
$7$	11.3293	0.611724	0.305862	+	0.952076i	$0.401055\pi$
$8$	−20.6308	−0.911762
$9$	14.8227	0.548988
$10$	−0.993858	−0.0314285
$11$	15.0133	0.411516	0.205758	−	0.978603i	$-0.434034\pi$
$11$	15.0133	0.411516	0.205758	+	0.978603i	$0.434034\pi$
$12$	−37.1733	−0.894250
$13$	−73.5339	−1.56882	−0.784409	−	0.620244i	$-0.787034\pi$
$13$	−73.5339	−1.56882	−0.784409	+	0.620244i	$0.787034\pi$
$14$	17.0011	0.324552
$15$	−4.28308	−0.0737258
$16$	15.0256	0.234775
$17$	−89.5681	−1.27785	−0.638925	−	0.769269i	$-0.720621\pi$
$17$	−89.5681	−1.27785	−0.638925	+	0.769269i	$0.720621\pi$
$18$	22.2434	0.291267
$19$	−47.9839	−0.579383	−0.289691	−	0.957120i	$-0.593553\pi$
$19$	−47.9839	−0.579383	−0.289691	+	0.957120i	$0.593553\pi$
$20$	3.80694	0.0425628
$21$	73.2671	0.761342
$22$	22.5294	0.218331
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−133.421	−1.13476
$25$	−124.561	−0.996491
$26$	−110.347	−0.832341
$27$	−78.7513	−0.561322
$28$	−65.1220	−0.439532
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−6.42732	−0.0391155
$31$	136.860	0.792930	0.396465	−	0.918050i	$-0.370237\pi$
$31$	136.860	0.792930	0.396465	+	0.918050i	$0.370237\pi$
$32$	187.595	1.03632
$33$	97.0917	0.512167
$34$	−134.409	−0.677968
$35$	−7.50332	−0.0362369
$36$	−85.2024	−0.394456
$37$	65.6890	0.291870	0.145935	−	0.989294i	$-0.453381\pi$
$37$	65.6890	0.291870	0.145935	+	0.989294i	$0.453381\pi$
$38$	−72.0062	−0.307393
$39$	−475.547	−1.95253
$40$	13.6637	0.0540104
$41$	−287.295	−1.09434	−0.547170	−	0.837021i	$-0.684295\pi$
$41$	−287.295	−1.09434	−0.547170	+	0.837021i	$0.684295\pi$
$42$	109.947	0.403932
$43$	9.56530	0.0339231	0.0169616	−	0.999856i	$-0.494601\pi$
$43$	9.56530	0.0339231	0.0169616	+	0.999856i	$0.494601\pi$
$44$	−86.2981	−0.295680
$45$	−9.81697	−0.0325206
$46$	−34.5145	−0.110628
$47$	404.479	1.25531	0.627653	−	0.778493i	$-0.284016\pi$
$47$	404.479	1.25531	0.627653	+	0.778493i	$0.284016\pi$
$48$	97.1714	0.292198
$49$	−214.647	−0.625793
$50$	−186.921	−0.528691
$51$	−579.241	−1.59039
$52$	422.681	1.12722
$53$	601.538	1.55901	0.779506	−	0.626395i	$-0.215470\pi$
$53$	601.538	1.55901	0.779506	+	0.626395i	$0.215470\pi$
$54$	−118.177	−0.297811
$55$	−9.94321	−0.0243771
$56$	−233.733	−0.557747
$57$	−310.314	−0.721090
$58$	43.5183	0.0985212
$59$	−496.582	−1.09575	−0.547876	−	0.836559i	$-0.684564\pi$
$59$	−496.582	−1.09575	−0.547876	+	0.836559i	$0.684564\pi$
$60$	24.6196	0.0529730
$61$	−751.927	−1.57827	−0.789135	−	0.614220i	$-0.789471\pi$
$61$	−751.927	−1.57827	−0.789135	+	0.614220i	$0.789471\pi$
$62$	205.377	0.420691
$63$	167.931	0.335830
$64$	161.305	0.315049
$65$	48.7010	0.0929326
$66$	145.699	0.271731
$67$	91.2679	0.166420	0.0832101	−	0.996532i	$-0.473483\pi$
$67$	91.2679	0.166420	0.0832101	+	0.996532i	$0.473483\pi$
$68$	514.847	0.918153
$69$	−148.742	−0.259514
$70$	−11.2597	−0.0192256
$71$	−1011.44	−1.69064	−0.845319	−	0.534261i	$-0.820590\pi$
$71$	−1011.44	−1.69064	−0.845319	+	0.534261i	$0.820590\pi$
$72$	−305.804	−0.500547
$73$	−513.165	−0.822759	−0.411380	−	0.911464i	$-0.634953\pi$
$73$	−513.165	−0.822759	−0.411380	+	0.911464i	$0.634953\pi$
$74$	98.5749	0.154853
$75$	−805.544	−1.24022
$76$	275.817	0.416294
$77$	170.090	0.251735
$78$	−713.621	−1.03592
$79$	369.565	0.526320	0.263160	−	0.964752i	$-0.415235\pi$
$79$	369.565	0.526320	0.263160	+	0.964752i	$0.415235\pi$
$80$	−9.95137	−0.0139075
$81$	−909.501	−1.24760
$82$	−431.124	−0.580606
$83$	−1245.49	−1.64712	−0.823559	−	0.567230i	$-0.808015\pi$
$83$	−1245.49	−1.64712	−0.823559	+	0.567230i	$0.808015\pi$
$84$	−421.147	−0.547035
$85$	59.3204	0.0756965
$86$	14.3540	0.0179980
$87$	187.544	0.231113
$88$	−309.737	−0.375205
$89$	1144.42	1.36301	0.681507	−	0.731811i	$-0.261325\pi$
$89$	1144.42	1.36301	0.681507	+	0.731811i	$0.261325\pi$
$90$	−14.7316	−0.0172539
$91$	−833.087	−0.959685
$92$	132.206	0.149820
$93$	885.082	0.986868
$94$	606.974	0.666006
$95$	31.7795	0.0343211
$96$	1213.18	1.28979
$97$	−390.140	−0.408379	−0.204189	−	0.978931i	$-0.565456\pi$
$97$	−390.140	−0.408379	−0.204189	+	0.978931i	$0.565456\pi$
$98$	−322.106	−0.332016
$99$	222.537	0.225918
$100$	715.992	0.715992
$101$	−115.386	−0.113676	−0.0568382	−	0.998383i	$-0.518102\pi$
$101$	−115.386	−0.113676	−0.0568382	+	0.998383i	$0.518102\pi$
$102$	−869.227	−0.843787
$103$	−670.416	−0.641341	−0.320670	−	0.947191i	$-0.603908\pi$
$103$	−670.416	−0.641341	−0.320670	+	0.947191i	$0.603908\pi$
$104$	1517.07	1.43039
$105$	−48.5243	−0.0450999
$106$	902.686	0.827138
$107$	1020.43	0.921952	0.460976	−	0.887413i	$-0.347499\pi$
$107$	1020.43	0.921952	0.460976	+	0.887413i	$0.347499\pi$
$108$	452.671	0.403317
$109$	1866.39	1.64007	0.820034	−	0.572315i	$-0.193955\pi$
$109$	1866.39	1.64007	0.820034	+	0.572315i	$0.193955\pi$
$110$	−14.9211	−0.0129334
$111$	424.814	0.363257
$112$	170.230	0.143618
$113$	−1048.91	−0.873218	−0.436609	−	0.899651i	$-0.643821\pi$
$113$	−1048.91	−0.873218	−0.436609	+	0.899651i	$0.643821\pi$
$114$	−465.667	−0.382577
$115$	15.2328	0.0123518
$116$	−166.695	−0.133425
$117$	−1089.97	−0.861263
$118$	−745.185	−0.581355
$119$	−1014.74	−0.781693
$120$	88.3636	0.0672204
$121$	−1105.60	−0.830654
$122$	−1128.37	−0.837355
$123$	−1857.95	−1.36200
$124$	−786.688	−0.569731
$125$	165.283	0.118267
$126$	252.002	0.178175
$127$	1666.81	1.16461	0.582307	−	0.812969i	$-0.302150\pi$
$127$	1666.81	1.16461	0.582307	+	0.812969i	$0.302150\pi$
$128$	−1258.70	−0.869173
$129$	61.8593	0.0422202
$130$	73.0823	0.0493057
$131$	491.101	0.327540	0.163770	−	0.986499i	$-0.447635\pi$
$131$	491.101	0.327540	0.163770	+	0.986499i	$0.447635\pi$
$132$	−558.094	−0.367999
$133$	−543.624	−0.354423
$134$	136.959	0.0882947
$135$	52.1565	0.0332512
$136$	1847.87	1.16510
$137$	2522.93	1.57335	0.786674	−	0.617369i	$-0.211801\pi$
$137$	2522.93	1.57335	0.786674	+	0.617369i	$0.211801\pi$
$138$	−223.207	−0.137686
$139$	487.110	0.297239	0.148619	−	0.988894i	$-0.452517\pi$
$139$	487.110	0.297239	0.148619	+	0.988894i	$0.452517\pi$
$140$	43.1299	0.0260367
$141$	2615.79	1.56233
$142$	−1517.79	−0.896973
$143$	−1103.99	−0.645594
$144$	222.720	0.128889
$145$	−19.2065	−0.0110001
$146$	−770.071	−0.436517
$147$	−1388.13	−0.778852
$148$	−377.587	−0.209713
$149$	2373.57	1.30503	0.652517	−	0.757774i	$-0.273713\pi$
$149$	2373.57	1.30503	0.652517	+	0.757774i	$0.273713\pi$
$150$	−1208.82	−0.658000
$151$	270.063	0.145546	0.0727728	−	0.997349i	$-0.476815\pi$
$151$	270.063	0.145546	0.0727728	+	0.997349i	$0.476815\pi$
$152$	989.949	0.528259
$153$	−1327.64	−0.701525
$154$	255.242	0.133559
$155$	−90.6417	−0.0469711
$156$	2733.50	1.40292
$157$	−417.847	−0.212407	−0.106203	−	0.994344i	$-0.533869\pi$
$157$	−417.847	−0.212407	−0.106203	+	0.994344i	$0.533869\pi$
$158$	554.580	0.279241
$159$	3890.17	1.94032
$160$	−124.243	−0.0613890
$161$	−260.574	−0.127553
$162$	−1364.82	−0.661918
$163$	865.874	0.416077	0.208038	−	0.978121i	$-0.433292\pi$
$163$	865.874	0.416077	0.208038	+	0.978121i	$0.433292\pi$
$164$	1651.40	0.786299
$165$	−64.3032	−0.0303394
$166$	−1869.03	−0.873884
$167$	−2151.10	−0.996750	−0.498375	−	0.866962i	$-0.666070\pi$
$167$	−2151.10	−0.996750	−0.498375	+	0.866962i	$0.666070\pi$
$168$	−1511.56	−0.694163
$169$	3210.24	1.46119
$170$	89.0180	0.0401610
$171$	−711.251	−0.318074
$172$	−54.9824	−0.0243742
$173$	2000.83	0.879307	0.439653	−	0.898168i	$-0.355101\pi$
$173$	2000.83	0.879307	0.439653	+	0.898168i	$0.355101\pi$
$174$	281.435	0.122618
$175$	−1411.19	−0.609578
$176$	225.584	0.0966139
$177$	−3211.42	−1.36376
$178$	1717.35	0.723152
$179$	−1998.53	−0.834508	−0.417254	−	0.908790i	$-0.637008\pi$
$179$	−1998.53	−0.834508	−0.417254	+	0.908790i	$0.637008\pi$
$180$	56.4290	0.0233665
$181$	−150.798	−0.0619267	−0.0309634	−	0.999521i	$-0.509858\pi$
$181$	−150.798	−0.0619267	−0.0309634	+	0.999521i	$0.509858\pi$
$182$	−1250.16	−0.509163
$183$	−4862.75	−1.96429
$184$	474.509	0.190116
$185$	−43.5054	−0.0172896
$186$	1328.18	0.523586
$187$	−1344.71	−0.525857
$188$	−2324.99	−0.901954
$189$	−892.196	−0.343374
$190$	47.6892	0.0182092
$191$	790.285	0.299387	0.149694	−	0.988732i	$-0.452171\pi$
$191$	790.285	0.299387	0.149694	+	0.988732i	$0.452171\pi$
$192$	1043.17	0.392105
$193$	2859.17	1.06636	0.533180	−	0.846002i	$-0.320997\pi$
$193$	2859.17	1.06636	0.533180	+	0.846002i	$0.320997\pi$
$194$	−585.456	−0.216666
$195$	314.952	0.115662
$196$	1233.81	0.449641
$197$	−3264.39	−1.18060	−0.590300	−	0.807184i	$-0.700991\pi$
$197$	−3264.39	−1.18060	−0.590300	+	0.807184i	$0.700991\pi$
$198$	333.946	0.119861
$199$	−2659.33	−0.947311	−0.473656	−	0.880710i	$-0.657066\pi$
$199$	−2659.33	−0.947311	−0.473656	+	0.880710i	$0.657066\pi$
$200$	2569.80	0.908563
$201$	590.234	0.207124
$202$	−173.151	−0.0603113
$203$	328.550	0.113594
$204$	3329.54	1.14272
$205$	190.274	0.0648258
$206$	−1006.05	−0.340265
$207$	−340.922	−0.114472
$208$	−1104.89	−0.368320
$209$	−720.397	−0.238426
$210$	−72.8171	−0.0239279
$211$	1420.17	0.463358	0.231679	−	0.972792i	$-0.425578\pi$
$211$	1420.17	0.463358	0.231679	+	0.972792i	$0.425578\pi$
$212$	−3457.71	−1.12017
$213$	−6541.00	−2.10414
$214$	1531.29	0.489144
$215$	−6.33504	−0.00200952
$216$	1624.70	0.511792
$217$	1550.53	0.485055
$218$	2800.76	0.870143
$219$	−3318.66	−1.02399
$220$	57.1547	0.0175153
$221$	6586.30	2.00472
$222$	637.488	0.192727
$223$	2741.22	0.823165	0.411582	−	0.911373i	$-0.364976\pi$
$223$	2741.22	0.823165	0.411582	+	0.911373i	$0.364976\pi$
$224$	2125.31	0.633944
$225$	−1846.33	−0.547062
$226$	−1574.03	−0.463288
$227$	764.901	0.223649	0.111824	−	0.993728i	$-0.464331\pi$
$227$	764.901	0.223649	0.111824	+	0.993728i	$0.464331\pi$
$228$	1783.72	0.518113
$229$	−5115.32	−1.47611	−0.738056	−	0.674740i	$-0.764256\pi$
$229$	−5115.32	−1.47611	−0.738056	+	0.674740i	$0.764256\pi$
$230$	22.8587	0.00655331
$231$	1099.98	0.313305
$232$	−598.294	−0.169310
$233$	5901.10	1.65920	0.829601	−	0.558356i	$-0.188568\pi$
$233$	5901.10	1.65920	0.829601	+	0.558356i	$0.188568\pi$
$234$	−1635.64	−0.456946
$235$	−267.884	−0.0743610
$236$	2854.41	0.787313
$237$	2389.99	0.655049
$238$	−1522.76	−0.414729
$239$	−3083.01	−0.834406	−0.417203	−	0.908813i	$-0.636990\pi$
$239$	−3083.01	−0.834406	−0.417203	+	0.908813i	$0.636990\pi$
$240$	−64.3560	−0.0173090
$241$	−3422.62	−0.914815	−0.457407	−	0.889257i	$-0.651222\pi$
$241$	−3422.62	−0.914815	−0.457407	+	0.889257i	$0.651222\pi$
$242$	−1659.10	−0.440706
$243$	−3755.50	−0.991421
$244$	4322.16	1.13401
$245$	142.159	0.0370703
$246$	−2788.10	−0.722612
$247$	3528.45	0.908946
$248$	−2823.54	−0.722964
$249$	−8054.67	−2.04998
$250$	248.029	0.0627468
$251$	−2425.13	−0.609851	−0.304926	−	0.952376i	$-0.598632\pi$
$251$	−2425.13	−0.609851	−0.304926	+	0.952376i	$0.598632\pi$
$252$	−965.283	−0.241298
$253$	−345.306	−0.0858071
$254$	2501.27	0.617889
$255$	383.628	0.0942106
$256$	−3179.28	−0.776191
$257$	−6423.80	−1.55916	−0.779582	−	0.626300i	$-0.784569\pi$
$257$	−6423.80	−1.55916	−0.779582	+	0.626300i	$0.784569\pi$
$258$	92.8279	0.0224000
$259$	744.210	0.178544
$260$	−279.939	−0.0667734
$261$	429.858	0.101945
$262$	736.961	0.173777
$263$	949.395	0.222594	0.111297	−	0.993787i	$-0.464500\pi$
$263$	949.395	0.222594	0.111297	+	0.993787i	$0.464500\pi$
$264$	−2003.08	−0.466974
$265$	−398.395	−0.0923517
$266$	−815.779	−0.188040
$267$	7401.02	1.69639
$268$	−524.618	−0.119575
$269$	3834.71	0.869170	0.434585	−	0.900631i	$-0.356895\pi$
$269$	3834.71	0.869170	0.434585	+	0.900631i	$0.356895\pi$
$270$	78.2676	0.0176415
$271$	−8176.93	−1.83289	−0.916445	−	0.400160i	$-0.868955\pi$
$271$	−8176.93	−1.83289	−0.916445	+	0.400160i	$0.868955\pi$
$272$	−1345.82	−0.300008
$273$	−5387.61	−1.19441
$274$	3785.99	0.834744
$275$	−1870.08	−0.410072
$276$	854.986	0.186464
$277$	4615.83	1.00122	0.500610	−	0.865673i	$-0.333109\pi$
$277$	4615.83	1.00122	0.500610	+	0.865673i	$0.333109\pi$
$278$	730.972	0.157701
$279$	2028.64	0.435309
$280$	154.800	0.0330395
$281$	8813.07	1.87097	0.935487	−	0.353362i	$-0.114962\pi$
$281$	8813.07	1.87097	0.935487	+	0.353362i	$0.114962\pi$
$282$	3925.33	0.828900
$283$	5629.23	1.18241	0.591206	−	0.806520i	$-0.298652\pi$
$283$	5629.23	1.18241	0.591206	+	0.806520i	$0.298652\pi$
$284$	5813.84	1.21475
$285$	205.519	0.0427155
$286$	−1656.68	−0.342522
$287$	−3254.85	−0.669435
$288$	2780.65	0.568929
$289$	3109.45	0.632903
$290$	−28.8219	−0.00583613
$291$	−2523.05	−0.508261
$292$	2949.73	0.591164
$293$	−6863.25	−1.36845	−0.684224	−	0.729272i	$-0.739859\pi$
$293$	−6863.25	−1.36845	−0.684224	+	0.729272i	$0.739859\pi$
$294$	−2083.07	−0.413222
$295$	328.883	0.0649095
$296$	−1355.22	−0.266116
$297$	−1182.32	−0.230993
$298$	3561.85	0.692390
$299$	1691.28	0.327121
$300$	4630.36	0.891112
$301$	108.368	0.0207516
$302$	405.264	0.0772196
$303$	−746.205	−0.141480
$304$	−720.989	−0.136025
$305$	497.997	0.0934925
$306$	−1992.30	−0.372196
$307$	4625.90	0.859980	0.429990	−	0.902834i	$-0.358517\pi$
$307$	4625.90	0.859980	0.429990	+	0.902834i	$0.358517\pi$
$308$	−977.696	−0.180875
$309$	−4335.61	−0.798202
$310$	−136.020	−0.0249206
$311$	505.399	0.0921496	0.0460748	−	0.998938i	$-0.485329\pi$
$311$	505.399	0.0921496	0.0460748	+	0.998938i	$0.485329\pi$
$312$	9810.93	1.78024
$313$	1476.55	0.266643	0.133322	−	0.991073i	$-0.457436\pi$
$313$	1476.55	0.266643	0.133322	+	0.991073i	$0.457436\pi$
$314$	−627.035	−0.112693
$315$	−111.219	−0.0198937
$316$	−2124.30	−0.378168
$317$	6073.85	1.07615	0.538077	−	0.842895i	$-0.319151\pi$
$317$	6073.85	1.07615	0.538077	+	0.842895i	$0.319151\pi$
$318$	5837.71	1.02944
$319$	435.386	0.0764167
$320$	−106.831	−0.0186627
$321$	6599.18	1.14745
$322$	−391.025	−0.0676738
$323$	4297.83	0.740365
$324$	5227.91	0.896418
$325$	9159.48	1.56331
$326$	1299.36	0.220751
$327$	12070.0	2.04120
$328$	5927.14	0.997779
$329$	4582.46	0.767901
$330$	−96.4954	−0.0160966
$331$	4463.42	0.741183	0.370592	−	0.928796i	$-0.379155\pi$
$331$	4463.42	0.741183	0.370592	+	0.928796i	$0.379155\pi$
$332$	7159.24	1.18348
$333$	973.687	0.160233
$334$	−3228.01	−0.528829
$335$	−60.4462	−0.00985829
$336$	1100.88	0.178744
$337$	−6424.00	−1.03839	−0.519196	−	0.854655i	$-0.673768\pi$
$337$	−6424.00	−1.03839	−0.519196	+	0.854655i	$0.673768\pi$
$338$	4817.38	0.775239
$339$	−6783.38	−1.08679
$340$	−340.980	−0.0543890
$341$	2054.72	0.326304
$342$	−1067.32	−0.168755
$343$	−6317.75	−0.994537
$344$	−197.340	−0.0309298
$345$	98.5109	0.0153729
$346$	3002.50	0.466519
$347$	2141.22	0.331258	0.165629	−	0.986188i	$-0.447035\pi$
$347$	2141.22	0.331258	0.165629	+	0.986188i	$0.447035\pi$
$348$	−1078.03	−0.166058
$349$	4080.49	0.625856	0.312928	−	0.949777i	$-0.398690\pi$
$349$	4080.49	0.625856	0.312928	+	0.949777i	$0.398690\pi$
$350$	−2117.68	−0.323413
$351$	5790.89	0.880612
$352$	2816.41	0.426464
$353$	5385.83	0.812065	0.406032	−	0.913859i	$-0.366912\pi$
$353$	5385.83	0.812065	0.406032	+	0.913859i	$0.366912\pi$
$354$	−4819.15	−0.723545
$355$	669.867	0.100149
$356$	−6578.25	−0.979345
$357$	−6562.40	−0.972882
$358$	−2999.05	−0.442751
$359$	9132.26	1.34257	0.671284	−	0.741200i	$-0.265743\pi$
$359$	9132.26	1.34257	0.671284	+	0.741200i	$0.265743\pi$
$360$	202.532	0.0296511
$361$	−4556.54	−0.664316
$362$	−226.292	−0.0328554
$363$	−7149.97	−1.03382
$364$	4788.68	0.689546
$365$	339.866	0.0487381
$366$	−7297.19	−1.04216
$367$	−8491.82	−1.20782	−0.603909	−	0.797053i	$-0.706391\pi$
$367$	−8491.82	−1.20782	−0.603909	+	0.797053i	$0.706391\pi$
$368$	−345.589	−0.0489540
$369$	−4258.49	−0.600780
$370$	−65.2855	−0.00917306
$371$	6815.00	0.953686
$372$	−5087.55	−0.709078
$373$	5624.32	0.780741	0.390371	−	0.920658i	$-0.372347\pi$
$373$	5624.32	0.780741	0.390371	+	0.920658i	$0.372347\pi$
$374$	−2017.92	−0.278995
$375$	1068.89	0.147193
$376$	−8344.74	−1.14454
$377$	−2132.48	−0.291322
$378$	−1338.86	−0.182178
$379$	356.309	0.0482912	0.0241456	−	0.999708i	$-0.492313\pi$
$379$	356.309	0.0482912	0.0241456	+	0.999708i	$0.492313\pi$
$380$	−182.672	−0.0246602
$381$	10779.4	1.44946
$382$	1185.92	0.158841
$383$	−13192.5	−1.76006	−0.880032	−	0.474915i	$-0.842479\pi$
$383$	−13192.5	−1.76006	−0.880032	+	0.474915i	$0.842479\pi$
$384$	−8140.05	−1.08176
$385$	−112.650	−0.0149121
$386$	4290.55	0.565760
$387$	141.783	0.0186234
$388$	2242.57	0.293426
$389$	2720.40	0.354576	0.177288	−	0.984159i	$-0.443268\pi$
$389$	2720.40	0.354576	0.177288	+	0.984159i	$0.443268\pi$
$390$	472.626	0.0613650
$391$	2060.07	0.266450
$392$	4428.35	0.570575
$393$	3175.97	0.407650
$394$	−4898.65	−0.626371
$395$	−244.760	−0.0311778
$396$	−1279.17	−0.162325
$397$	−12503.2	−1.58065	−0.790323	−	0.612690i	$-0.790087\pi$
$397$	−12503.2	−1.58065	−0.790323	+	0.612690i	$0.790087\pi$
$398$	−3990.67	−0.502599
$399$	−3515.64	−0.441109
$400$	−1871.61	−0.233952
$401$	7607.74	0.947412	0.473706	−	0.880683i	$-0.342916\pi$
$401$	7607.74	0.947412	0.473706	+	0.880683i	$0.342916\pi$
$402$	885.723	0.109890
$403$	−10063.9	−1.24396
$404$	663.250	0.0816780
$405$	602.356	0.0739045
$406$	493.031	0.0602678
$407$	986.208	0.120109
$408$	11950.2	1.45006
$409$	5046.41	0.610095	0.305047	−	0.952337i	$-0.401328\pi$
$409$	5046.41	0.610095	0.305047	+	0.952337i	$0.401328\pi$
$410$	285.531	0.0343935
$411$	16315.9	1.95816
$412$	3853.63	0.460812
$413$	−5625.92	−0.670299
$414$	−511.598	−0.0607334
$415$	824.883	0.0975709
$416$	−13794.6	−1.62580
$417$	3150.16	0.369938
$418$	−1081.05	−0.126497
$419$	−6276.60	−0.731818	−0.365909	−	0.930651i	$-0.619242\pi$
$419$	−6276.60	−0.731818	−0.365909	+	0.930651i	$0.619242\pi$
$420$	278.923	0.0324049
$421$	−14745.6	−1.70703	−0.853513	−	0.521071i	$-0.825533\pi$
$421$	−14745.6	−1.70703	−0.853513	+	0.521071i	$0.825533\pi$
$422$	2131.15	0.245836
$423$	5995.47	0.689148
$424$	−12410.2	−1.42145
$425$	11156.7	1.27337
$426$	−9815.62	−1.11636
$427$	−8518.81	−0.965466
$428$	−5865.55	−0.662435
$429$	−7139.53	−0.803496
$430$	−9.50655	−0.00106616
$431$	3044.99	0.340307	0.170153	−	0.985418i	$-0.445574\pi$
$431$	3044.99	0.340307	0.170153	+	0.985418i	$0.445574\pi$
$432$	−1183.29	−0.131785
$433$	−6889.21	−0.764606	−0.382303	−	0.924037i	$-0.624869\pi$
$433$	−6889.21	−0.764606	−0.382303	+	0.924037i	$0.624869\pi$
$434$	2326.77	0.257347
$435$	−124.209	−0.0136905
$436$	−10728.2	−1.17841
$437$	1103.63	0.120810
$438$	−4980.09	−0.543282
$439$	6917.31	0.752039	0.376019	−	0.926612i	$-0.377293\pi$
$439$	6917.31	0.752039	0.376019	+	0.926612i	$0.377293\pi$
$440$	205.137	0.0222262
$441$	−3181.65	−0.343553
$442$	9883.60	1.06361
$443$	3160.98	0.339013	0.169506	−	0.985529i	$-0.445783\pi$
$443$	3160.98	0.339013	0.169506	+	0.985529i	$0.445783\pi$
$444$	−2441.87	−0.261005
$445$	−757.942	−0.0807414
$446$	4113.56	0.436733
$447$	15350.0	1.62423
$448$	1827.47	0.192723
$449$	746.359	0.0784473	0.0392237	−	0.999230i	$-0.487512\pi$
$449$	746.359	0.0784473	0.0392237	+	0.999230i	$0.487512\pi$
$450$	−2770.66	−0.290245
$451$	−4313.25	−0.450339
$452$	6029.27	0.627419
$453$	1746.51	0.181144
$454$	1147.83	0.118658
$455$	551.749	0.0568492
$456$	6402.04	0.657463
$457$	5760.40	0.589628	0.294814	−	0.955555i	$-0.404742\pi$
$457$	5760.40	0.589628	0.294814	+	0.955555i	$0.404742\pi$
$458$	−7676.20	−0.783155
$459$	7053.60	0.717286
$460$	−87.5595	−0.00887496
$461$	−18540.2	−1.87311	−0.936553	−	0.350526i	$-0.886003\pi$
$461$	−18540.2	−1.87311	−0.936553	+	0.350526i	$0.886003\pi$
$462$	1650.66	0.166225
$463$	−16880.6	−1.69440	−0.847201	−	0.531272i	$-0.821714\pi$
$463$	−16880.6	−1.69440	−0.847201	+	0.531272i	$0.821714\pi$
$464$	435.743	0.0435967
$465$	−586.184	−0.0584594
$466$	8855.37	0.880295
$467$	−4368.61	−0.432880	−0.216440	−	0.976296i	$-0.569445\pi$
$467$	−4368.61	−0.432880	−0.216440	+	0.976296i	$0.569445\pi$
$468$	6265.27	0.618829
$469$	1034.00	0.101803
$470$	−401.995	−0.0394524
$471$	−2702.24	−0.264358
$472$	10244.9	0.999066
$473$	143.607	0.0139599
$474$	3586.49	0.347538
$475$	5976.95	0.577350
$476$	5832.86	0.561657
$477$	8916.41	0.855879
$478$	−4626.45	−0.442697
$479$	−8219.01	−0.784000	−0.392000	−	0.919965i	$-0.628217\pi$
$479$	−8219.01	−0.784000	−0.392000	+	0.919965i	$0.628217\pi$
$480$	−803.483	−0.0764038
$481$	−4830.37	−0.457891
$482$	−5136.09	−0.485358
$483$	−1685.14	−0.158751
$484$	6355.11	0.596836
$485$	258.387	0.0241913
$486$	−5635.61	−0.526001
$487$	−13439.2	−1.25049	−0.625245	−	0.780429i	$-0.715001\pi$
$487$	−13439.2	−1.25049	−0.625245	+	0.780429i	$0.715001\pi$
$488$	15512.9	1.43901
$489$	5599.65	0.517842
$490$	213.329	0.0196678
$491$	−20755.8	−1.90773	−0.953866	−	0.300234i	$-0.902935\pi$
$491$	−20755.8	−1.90773	−0.953866	+	0.300234i	$0.902935\pi$
$492$	10679.7	0.978614
$493$	−2597.48	−0.237291
$494$	5294.90	0.482244
$495$	−147.385	−0.0133828
$496$	2056.41	0.186160
$497$	−11458.9	−1.03420
$498$	−12087.1	−1.08762
$499$	5577.26	0.500346	0.250173	−	0.968201i	$-0.419513\pi$
$499$	5577.26	0.500346	0.250173	+	0.968201i	$0.419513\pi$
$500$	−950.064	−0.0849763
$501$	−13911.3	−1.24054
$502$	−3639.22	−0.323558
$503$	7021.60	0.622421	0.311210	−	0.950341i	$-0.399266\pi$
$503$	7021.60	0.622421	0.311210	+	0.950341i	$0.399266\pi$
$504$	−3464.55	−0.306197
$505$	76.4193	0.00673389
$506$	−518.176	−0.0455252
$507$	20760.7	1.81857
$508$	−9581.03	−0.836790
$509$	−13582.1	−1.18275	−0.591373	−	0.806398i	$-0.701414\pi$
$509$	−13582.1	−1.18275	−0.591373	+	0.806398i	$0.701414\pi$
$510$	575.684	0.0499837
$511$	−5813.80	−0.503302
$512$	5298.65	0.457362
$513$	3778.80	0.325220
$514$	−9639.74	−0.827220
$515$	444.012	0.0379913
$516$	−355.574	−0.0303358
$517$	6072.57	0.516579
$518$	1116.78	0.0947271
$519$	12939.4	1.09437
$520$	−1004.74	−0.0847325
$521$	1584.58	0.133247	0.0666235	−	0.997778i	$-0.478777\pi$
$521$	1584.58	0.133247	0.0666235	+	0.997778i	$0.478777\pi$
$522$	645.058	0.0540870
$523$	−22290.5	−1.86367	−0.931833	−	0.362888i	$-0.881791\pi$
$523$	−22290.5	−1.86367	−0.931833	+	0.362888i	$0.881791\pi$
$524$	−2822.90	−0.235342
$525$	−9126.25	−0.758671
$526$	1424.69	0.118098
$527$	−12258.3	−1.01325
$528$	1458.86	0.120244
$529$	529.000	0.0434783
$530$	−597.843	−0.0489975
$531$	−7360.67	−0.601556
$532$	3124.81	0.254657
$533$	21125.9	1.71682
$534$	11106.2	0.900023
$535$	−675.825	−0.0546140
$536$	−1882.93	−0.151736
$537$	−12924.6	−1.03862
$538$	5754.49	0.461140
$539$	−3222.56	−0.257524
$540$	−299.801	−0.0238914
$541$	23857.6	1.89597	0.947985	−	0.318314i	$-0.103117\pi$
$541$	23857.6	1.89597	0.947985	+	0.318314i	$0.103117\pi$
$542$	−12270.6	−0.972446
$543$	−975.218	−0.0770730
$544$	−16802.5	−1.32427
$545$	−1236.10	−0.0971533
$546$	−8084.82	−0.633696
$547$	4200.90	0.328369	0.164184	−	0.986430i	$-0.447501\pi$
$547$	4200.90	0.328369	0.164184	+	0.986430i	$0.447501\pi$
$548$	−14502.1	−1.13047
$549$	−11145.6	−0.866452
$550$	−2806.29	−0.217565
$551$	−1391.53	−0.107589
$552$	3068.67	0.236615
$553$	4186.91	0.321963
$554$	6926.65	0.531201
$555$	−281.351	−0.0215184
$556$	−2799.96	−0.213570
$557$	−14380.7	−1.09395	−0.546973	−	0.837150i	$-0.684220\pi$
$557$	−14380.7	−1.09395	−0.546973	+	0.837150i	$0.684220\pi$
$558$	3044.23	0.230955
$559$	−703.374	−0.0532193
$560$	−112.742	−0.00850754
$561$	−8696.32	−0.654472
$562$	13225.2	0.992650
$563$	715.346	0.0535492	0.0267746	−	0.999641i	$-0.491476\pi$
$563$	715.346	0.0535492	0.0267746	+	0.999641i	$0.491476\pi$
$564$	−15035.8	−1.12256
$565$	694.689	0.0517271
$566$	8447.39	0.627332
$567$	−10304.0	−0.763188
$568$	20866.8	1.54146
$569$	4294.98	0.316441	0.158220	−	0.987404i	$-0.449424\pi$
$569$	4294.98	0.316441	0.158220	+	0.987404i	$0.449424\pi$
$570$	308.408	0.0226628
$571$	−10340.1	−0.757825	−0.378913	−	0.925432i	$-0.623702\pi$
$571$	−10340.1	−0.757825	−0.378913	+	0.925432i	$0.623702\pi$
$572$	6345.84	0.463868
$573$	5110.81	0.372613
$574$	−4884.33	−0.355171
$575$	2864.91	0.207783
$576$	2390.97	0.172958
$577$	14576.0	1.05166	0.525830	−	0.850589i	$-0.323755\pi$
$577$	14576.0	1.05166	0.525830	+	0.850589i	$0.323755\pi$
$578$	4666.14	0.335789
$579$	18490.4	1.32717
$580$	110.401	0.00790372
$581$	−14110.6	−1.00758
$582$	−3786.17	−0.269660
$583$	9031.07	0.641559
$584$	10587.0	0.750161
$585$	721.880	0.0510189
$586$	−10299.2	−0.726035
$587$	−13702.9	−0.963506	−0.481753	−	0.876307i	$-0.660000\pi$
$587$	−13702.9	−0.963506	−0.481753	+	0.876307i	$0.660000\pi$
$588$	7979.14	0.559616
$589$	−6567.10	−0.459410
$590$	493.532	0.0344379
$591$	−21111.0	−1.46936
$592$	987.018	0.0685240
$593$	23701.6	1.64133	0.820666	−	0.571409i	$-0.193603\pi$
$593$	23701.6	1.64133	0.820666	+	0.571409i	$0.193603\pi$
$594$	−1774.22	−0.122554
$595$	672.059	0.0463054
$596$	−13643.5	−0.937685
$597$	−17198.0	−1.17901
$598$	2537.99	0.173555
$599$	−28692.5	−1.95717	−0.978586	−	0.205839i	$-0.934008\pi$
$599$	−28692.5	−1.95717	−0.978586	+	0.205839i	$0.934008\pi$
$600$	16619.0	1.13078
$601$	25868.6	1.75574	0.877871	−	0.478898i	$-0.158964\pi$
$601$	25868.6	1.75574	0.877871	+	0.478898i	$0.158964\pi$
$602$	162.621	0.0110098
$603$	1352.84	0.0913627
$604$	−1552.35	−0.104576
$605$	732.232	0.0492058
$606$	−1119.78	−0.0750625
$607$	19153.4	1.28075	0.640374	−	0.768064i	$-0.278780\pi$
$607$	19153.4	1.28075	0.640374	+	0.768064i	$0.278780\pi$
$608$	−9001.53	−0.600428
$609$	2124.75	0.141378
$610$	747.309	0.0496027
$611$	−29742.9	−1.96935
$612$	7631.42	0.504055
$613$	−1449.93	−0.0955337	−0.0477669	−	0.998859i	$-0.515210\pi$
$613$	−1449.93	−0.0955337	−0.0477669	+	0.998859i	$0.515210\pi$
$614$	6941.76	0.456265
$615$	1230.51	0.0806812
$616$	−3509.10	−0.229522
$617$	−29503.5	−1.92507	−0.962533	−	0.271165i	$-0.912591\pi$
$617$	−29503.5	−1.92507	−0.962533	+	0.271165i	$0.912591\pi$
$618$	−6506.15	−0.423488
$619$	3385.90	0.219856	0.109928	−	0.993940i	$-0.464938\pi$
$619$	3385.90	0.219856	0.109928	+	0.993940i	$0.464938\pi$
$620$	521.018	0.0337494
$621$	1811.28	0.117044
$622$	758.417	0.0488903
$623$	12965.5	0.833790
$624$	−7145.39	−0.458405
$625$	15460.7	0.989485
$626$	2215.75	0.141468
$627$	−4658.84	−0.296740
$628$	2401.83	0.152617
$629$	−5883.64	−0.372967
$630$	−166.899	−0.0105546
$631$	−14225.4	−0.897471	−0.448736	−	0.893665i	$-0.648125\pi$
$631$	−14225.4	−0.897471	−0.448736	+	0.893665i	$0.648125\pi$
$632$	−7624.42	−0.479879
$633$	9184.30	0.576688
$634$	9114.60	0.570957
$635$	−1103.92	−0.0689886
$636$	−22361.1	−1.39415
$637$	15783.8	0.981756
$638$	653.353	0.0405431
$639$	−14992.2	−0.928141
$640$	833.627	0.0514875
$641$	−7658.40	−0.471901	−0.235951	−	0.971765i	$-0.575820\pi$
$641$	−7658.40	−0.471901	−0.235951	+	0.971765i	$0.575820\pi$
$642$	9902.93	0.608781
$643$	−22324.3	−1.36918	−0.684591	−	0.728927i	$-0.740019\pi$
$643$	−22324.3	−1.36918	−0.684591	+	0.728927i	$0.740019\pi$
$644$	1497.81	0.0916488
$645$	−40.9690	−0.00250101
$646$	6449.46	0.392803
$647$	14432.4	0.876963	0.438482	−	0.898740i	$-0.355516\pi$
$647$	14432.4	0.876963	0.438482	+	0.898740i	$0.355516\pi$
$648$	18763.7	1.13751
$649$	−7455.33	−0.450920
$650$	13745.0	0.829420
$651$	10027.4	0.603691
$652$	−4977.14	−0.298957
$653$	−3950.87	−0.236768	−0.118384	−	0.992968i	$-0.537771\pi$
$653$	−3950.87	−0.236768	−0.118384	+	0.992968i	$0.537771\pi$
$654$	18112.6	1.08297
$655$	−325.253	−0.0194026
$656$	−4316.79	−0.256924
$657$	−7606.49	−0.451685
$658$	6876.59	0.407412
$659$	−6542.07	−0.386711	−0.193356	−	0.981129i	$-0.561937\pi$
$659$	−6542.07	−0.386711	−0.193356	+	0.981129i	$0.561937\pi$
$660$	369.622	0.0217993
$661$	−5703.98	−0.335642	−0.167821	−	0.985818i	$-0.553673\pi$
$661$	−5703.98	−0.335642	−0.167821	+	0.985818i	$0.553673\pi$
$662$	6697.94	0.393237
$663$	42593.9	2.49504
$664$	25695.6	1.50178
$665$	360.039	0.0209951
$666$	1461.14	0.0850123
$667$	−667.000	−0.0387202
$668$	12364.8	0.716178
$669$	17727.6	1.02450
$670$	−90.7074	−0.00523034
$671$	−11288.9	−0.649484
$672$	13744.5	0.788997
$673$	−13486.8	−0.772478	−0.386239	−	0.922399i	$-0.626226\pi$
$673$	−13486.8	−0.772478	−0.386239	+	0.922399i	$0.626226\pi$
$674$	−9640.06	−0.550922
$675$	9809.36	0.559352
$676$	−18452.8	−1.04989
$677$	−19902.7	−1.12987	−0.564934	−	0.825136i	$-0.691099\pi$
$677$	−19902.7	−1.12987	−0.564934	+	0.825136i	$0.691099\pi$
$678$	−10179.3	−0.576601
$679$	−4420.01	−0.249815
$680$	−1223.83	−0.0690172
$681$	4946.65	0.278350
$682$	3083.38	0.173121
$683$	−31214.8	−1.74876	−0.874379	−	0.485244i	$-0.838731\pi$
$683$	−31214.8	−1.74876	−0.874379	+	0.485244i	$0.838731\pi$
$684$	4088.35	0.228541
$685$	−1670.92	−0.0932010
$686$	−9480.60	−0.527655
$687$	−33081.0	−1.83714
$688$	143.725	0.00796432
$689$	−44233.5	−2.44581
$690$	147.828	0.00815614
$691$	3899.84	0.214699	0.107350	−	0.994221i	$-0.465764\pi$
$691$	3899.84	0.214699	0.107350	+	0.994221i	$0.465764\pi$
$692$	−11501.0	−0.631794
$693$	2521.19	0.138199
$694$	3213.17	0.175750
$695$	−322.610	−0.0176076
$696$	−3869.20	−0.210720
$697$	25732.5	1.39840
$698$	6123.31	0.332049
$699$	38162.7	2.06502
$700$	8111.69	0.437990
$701$	−15472.5	−0.833650	−0.416825	−	0.908987i	$-0.636857\pi$
$701$	−15472.5	−0.833650	−0.416825	+	0.908987i	$0.636857\pi$
$702$	8689.98	0.467211
$703$	−3152.02	−0.169105
$704$	2421.72	0.129648
$705$	−1732.42	−0.0925484
$706$	8082.14	0.430843
$707$	−1307.24	−0.0695386
$708$	18459.6	0.979877
$709$	10293.1	0.545227	0.272613	−	0.962124i	$-0.412112\pi$
$709$	10293.1	0.545227	0.272613	+	0.962124i	$0.412112\pi$
$710$	1005.22	0.0531343
$711$	5477.94	0.288943
$712$	−23610.3	−1.24275
$713$	−3147.79	−0.165337
$714$	−9847.73	−0.516165
$715$	731.163	0.0382433
$716$	11487.8	0.599606
$717$	−19937.9	−1.03849
$718$	13704.1	0.712304
$719$	−10233.0	−0.530772	−0.265386	−	0.964142i	$-0.585499\pi$
$719$	−10233.0	−0.530772	−0.265386	+	0.964142i	$0.585499\pi$
$720$	−147.506	−0.00763504
$721$	−7595.34	−0.392324
$722$	−6837.68	−0.352455
$723$	−22134.2	−1.13856
$724$	866.804	0.0444952
$725$	−3612.28	−0.185044
$726$	−10729.5	−0.548496
$727$	31447.7	1.60431	0.802153	−	0.597119i	$-0.203688\pi$
$727$	31447.7	1.60431	0.802153	+	0.597119i	$0.203688\pi$
$728$	17187.3	0.875004
$729$	269.537	0.0136939
$730$	510.013	0.0258581
$731$	−856.747	−0.0433487
$732$	27951.6	1.41137
$733$	13612.4	0.685931	0.342965	−	0.939348i	$-0.388569\pi$
$733$	13612.4	0.685931	0.342965	+	0.939348i	$0.388569\pi$
$734$	−12743.1	−0.640811
$735$	919.351	0.0461371
$736$	−4314.67	−0.216088
$737$	1370.23	0.0684846
$738$	−6390.41	−0.318746
$739$	16449.5	0.818815	0.409408	−	0.912352i	$-0.365735\pi$
$739$	16449.5	0.818815	0.409408	+	0.912352i	$0.365735\pi$
$740$	250.074	0.0124228
$741$	22818.6	1.13126
$742$	10226.8	0.505981
$743$	−37333.5	−1.84338	−0.921692	−	0.387921i	$-0.873193\pi$
$743$	−37333.5	−1.84338	−0.921692	+	0.387921i	$0.873193\pi$
$744$	−18260.0	−0.899789
$745$	−1572.00	−0.0773068
$746$	8440.03	0.414225
$747$	−18461.6	−0.904249
$748$	7729.56	0.377835
$749$	11560.8	0.563980
$750$	1604.01	0.0780936
$751$	−23673.5	−1.15028	−0.575139	−	0.818056i	$-0.695052\pi$
$751$	−23673.5	−1.15028	−0.575139	+	0.818056i	$0.695052\pi$
$752$	6077.55	0.294715
$753$	−15683.4	−0.759011
$754$	−3200.07	−0.154562
$755$	−178.861	−0.00862173
$756$	5128.44	0.246719
$757$	−38050.3	−1.82690	−0.913449	−	0.406953i	$-0.866591\pi$
$757$	−38050.3	−1.82690	−0.913449	+	0.406953i	$0.866591\pi$
$758$	534.688	0.0256210
$759$	−2233.11	−0.106794
$760$	−655.637	−0.0312927
$761$	−17066.4	−0.812954	−0.406477	−	0.913661i	$-0.633243\pi$
$761$	−17066.4	−0.812954	−0.406477	+	0.913661i	$0.633243\pi$
$762$	16175.8	0.769014
$763$	21144.8	1.00327
$764$	−4542.64	−0.215114
$765$	879.288	0.0415565
$766$	−19797.0	−0.933807
$767$	36515.6	1.71904
$768$	−20560.5	−0.966035
$769$	6605.89	0.309772	0.154886	−	0.987932i	$-0.450499\pi$
$769$	6605.89	0.309772	0.154886	+	0.987932i	$0.450499\pi$
$770$	−169.045	−0.00791165
$771$	−41543.0	−1.94051
$772$	−16434.8	−0.766194
$773$	−19376.9	−0.901602	−0.450801	−	0.892624i	$-0.648862\pi$
$773$	−19376.9	−0.901602	−0.450801	+	0.892624i	$0.648862\pi$
$774$	212.765	0.00988071
$775$	−17047.5	−0.790148
$776$	8048.91	0.372344
$777$	4812.84	0.222213
$778$	4082.32	0.188121
$779$	13785.6	0.634042
$780$	−1810.38	−0.0831050
$781$	−15185.0	−0.695725
$782$	3091.40	0.141366
$783$	−2283.79	−0.104235
$784$	−3225.21	−0.146921
$785$	276.738	0.0125824
$786$	4765.96	0.216280
$787$	39059.5	1.76915	0.884575	−	0.466398i	$-0.154449\pi$
$787$	39059.5	1.76915	0.884575	+	0.466398i	$0.154449\pi$
$788$	18764.1	0.848278
$789$	6139.78	0.277037
$790$	−367.295	−0.0165415
$791$	−11883.5	−0.534169
$792$	−4591.13	−0.205983
$793$	55292.2	2.47602
$794$	−18762.7	−0.838617
$795$	−2576.44	−0.114939
$796$	15286.1	0.680656
$797$	34943.3	1.55302	0.776508	−	0.630107i	$-0.216989\pi$
$797$	34943.3	1.55302	0.776508	+	0.630107i	$0.216989\pi$
$798$	−5275.68	−0.234031
$799$	−36228.5	−1.60409
$800$	−23367.0	−1.03269
$801$	16963.4	0.748279
$802$	11416.4	0.502652
$803$	−7704.30	−0.338579
$804$	−3392.73	−0.148821
$805$	172.576	0.00755592
$806$	−15102.2	−0.659988
$807$	24799.3	1.08175
$808$	2380.50	0.103646
$809$	26825.9	1.16582	0.582910	−	0.812537i	$-0.301914\pi$
$809$	26825.9	1.16582	0.582910	+	0.812537i	$0.301914\pi$
$810$	903.914	0.0392103
$811$	−23568.9	−1.02049	−0.510245	−	0.860029i	$-0.670445\pi$
$811$	−23568.9	−1.02049	−0.510245	+	0.860029i	$0.670445\pi$
$812$	−1888.54	−0.0816191
$813$	−52880.6	−2.28119
$814$	1479.93	0.0637244
$815$	−573.463	−0.0246473
$816$	−8703.46	−0.373385
$817$	−458.981	−0.0196545
$818$	7572.79	0.323688
$819$	−12348.6	−0.526856
$820$	−1093.71	−0.0465782
$821$	−21314.1	−0.906050	−0.453025	−	0.891498i	$-0.649655\pi$
$821$	−21314.1	−0.906050	−0.453025	+	0.891498i	$0.649655\pi$
$822$	24484.2	1.03891
$823$	44691.0	1.89287	0.946434	−	0.322898i	$-0.104657\pi$
$823$	44691.0	1.89287	0.946434	+	0.322898i	$0.104657\pi$
$824$	13831.2	0.584750
$825$	−12093.9	−0.510369
$826$	−8442.43	−0.355629
$827$	−24000.9	−1.00918	−0.504591	−	0.863358i	$-0.668357\pi$
$827$	−24000.9	−1.00918	−0.504591	+	0.863358i	$0.668357\pi$
$828$	1959.66	0.0822497
$829$	44533.9	1.86577	0.932886	−	0.360171i	$-0.117282\pi$
$829$	44533.9	1.86577	0.932886	+	0.360171i	$0.117282\pi$
$830$	1237.84	0.0517665
$831$	29850.8	1.24610
$832$	−11861.4	−0.494255
$833$	19225.5	0.799670
$834$	4727.23	0.196272
$835$	1424.66	0.0590448
$836$	4140.92	0.171312
$837$	−10777.9	−0.445089
$838$	−9418.85	−0.388268
$839$	−10820.1	−0.445235	−0.222617	−	0.974906i	$-0.571460\pi$
$839$	−10820.1	−0.445235	−0.222617	+	0.974906i	$0.571460\pi$
$840$	1001.10	0.0411204
$841$	841.000	0.0344828
$842$	−22127.7	−0.905668
$843$	56994.5	2.32858
$844$	−8163.29	−0.332929
$845$	−2126.12	−0.0865571
$846$	8996.98	0.365630
$847$	−12525.7	−0.508132
$848$	9038.48	0.366018
$849$	36404.5	1.47161
$850$	16742.1	0.675589
$851$	−1510.85	−0.0608592
$852$	37598.4	1.51185
$853$	−8705.90	−0.349454	−0.174727	−	0.984617i	$-0.555904\pi$
$853$	−8705.90	−0.349454	−0.174727	+	0.984617i	$0.555904\pi$
$854$	−12783.6	−0.512231
$855$	471.057	0.0188419
$856$	−21052.3	−0.840601
$857$	8201.83	0.326919	0.163459	−	0.986550i	$-0.447735\pi$
$857$	8201.83	0.326919	0.163459	+	0.986550i	$0.447735\pi$
$858$	−10713.8	−0.426297
$859$	15970.3	0.634340	0.317170	−	0.948369i	$-0.397267\pi$
$859$	15970.3	0.634340	0.317170	+	0.948369i	$0.397267\pi$
$860$	36.4145	0.00144387
$861$	−21049.3	−0.833168
$862$	4569.41	0.180551
$863$	−38121.0	−1.50366	−0.751828	−	0.659360i	$-0.770827\pi$
$863$	−38121.0	−1.50366	−0.751828	+	0.659360i	$0.770827\pi$
$864$	−14773.3	−0.581711
$865$	−1325.13	−0.0520878
$866$	−10338.2	−0.405664
$867$	20109.0	0.787701
$868$	−8912.62	−0.348518
$869$	5548.38	0.216589
$870$	−186.392	−0.00726356
$871$	−6711.29	−0.261083
$872$	−38505.1	−1.49535
$873$	−5782.92	−0.224195
$874$	1656.14	0.0640959
$875$	1872.54	0.0723467
$876$	19076.0	0.735753
$877$	10853.1	0.417881	0.208941	−	0.977928i	$-0.432998\pi$
$877$	10853.1	0.417881	0.208941	+	0.977928i	$0.432998\pi$
$878$	10380.3	0.398996
$879$	−44385.0	−1.70315
$880$	−149.403	−0.00572315
$881$	−20905.6	−0.799464	−0.399732	−	0.916632i	$-0.630897\pi$
$881$	−20905.6	−0.799464	−0.399732	+	0.916632i	$0.630897\pi$
$882$	−4774.47	−0.182273
$883$	9207.57	0.350917	0.175458	−	0.984487i	$-0.443859\pi$
$883$	9207.57	0.350917	0.175458	+	0.984487i	$0.443859\pi$
$884$	−37858.7	−1.44042
$885$	2126.90	0.0807853
$886$	4743.46	0.179864
$887$	−35797.5	−1.35509	−0.677543	−	0.735483i	$-0.736955\pi$
$887$	−35797.5	−1.35509	−0.677543	+	0.735483i	$0.736955\pi$
$888$	−8764.26	−0.331204
$889$	18883.8	0.712422
$890$	−1137.39	−0.0428376
$891$	−13654.6	−0.513408
$892$	−15756.8	−0.591455
$893$	−19408.5	−0.727302
$894$	23034.6	0.861737
$895$	1323.61	0.0494341
$896$	−14260.2	−0.531694
$897$	10937.6	0.407130
$898$	1120.01	0.0416205
$899$	3968.95	0.147243
$900$	10612.9	0.393071
$901$	−53878.7	−1.99218
$902$	−6472.59	−0.238929
$903$	700.822	0.0258271
$904$	21640.0	0.796167
$905$	99.8726	0.00366837
$906$	2620.86	0.0961063
$907$	−12264.5	−0.448991	−0.224496	−	0.974475i	$-0.572073\pi$
$907$	−12264.5	−0.448991	−0.224496	+	0.974475i	$0.572073\pi$
$908$	−4396.73	−0.160695
$909$	−1710.33	−0.0624070
$910$	827.971	0.0301615
$911$	34771.6	1.26458	0.632292	−	0.774730i	$-0.282114\pi$
$911$	34771.6	1.26458	0.632292	+	0.774730i	$0.282114\pi$
$912$	−4662.67	−0.169294
$913$	−18699.0	−0.677816
$914$	8644.22	0.312829
$915$	3220.57	0.116359
$916$	29403.4	1.06061
$917$	5563.83	0.200364
$918$	10584.9	0.380558
$919$	−3491.90	−0.125340	−0.0626699	−	0.998034i	$-0.519962\pi$
$919$	−3491.90	−0.125340	−0.0626699	+	0.998034i	$0.519962\pi$
$920$	−314.264	−0.0112619
$921$	29915.9	1.07032
$922$	−27821.9	−0.993782
$923$	74374.8	2.65230
$924$	−6322.81	−0.225114
$925$	−8182.31	−0.290846
$926$	−25331.6	−0.898970
$927$	−9937.37	−0.352088
$928$	5440.24	0.192440
$929$	−9639.22	−0.340423	−0.170211	−	0.985408i	$-0.554445\pi$
$929$	−9639.22	−0.340423	−0.170211	+	0.985408i	$0.554445\pi$
$930$	−879.646	−0.0310158
$931$	10299.6	0.362574
$932$	−33920.2	−1.19216
$933$	3268.44	0.114688
$934$	−6555.67	−0.229666
$935$	890.595	0.0311503
$936$	22487.0	0.785267
$937$	−26520.1	−0.924624	−0.462312	−	0.886717i	$-0.652980\pi$
$937$	−26520.1	−0.924624	−0.462312	+	0.886717i	$0.652980\pi$
$938$	1551.65	0.0540120
$939$	9548.89	0.331860
$940$	1539.83	0.0534294
$941$	−6668.39	−0.231013	−0.115506	−	0.993307i	$-0.536849\pi$
$941$	−6668.39	−0.231013	−0.115506	+	0.993307i	$0.536849\pi$
$942$	−4055.06	−0.140256
$943$	6607.79	0.228186
$944$	−7461.45	−0.257256
$945$	590.896	0.0203406
$946$	215.501	0.00740648
$947$	31019.4	1.06441	0.532204	−	0.846616i	$-0.321364\pi$
$947$	31019.4	1.06441	0.532204	+	0.846616i	$0.321364\pi$
$948$	−13737.9	−0.470662
$949$	37735.0	1.29076
$950$	8969.19	0.306315
$951$	39279.8	1.33936
$952$	20935.0	0.712718
$953$	−8758.22	−0.297698	−0.148849	−	0.988860i	$-0.547557\pi$
$953$	−8758.22	−0.297698	−0.148849	+	0.988860i	$0.547557\pi$
$954$	13380.2	0.454089
$955$	−523.400	−0.0177349
$956$	17721.5	0.599532
$957$	2815.66	0.0951069
$958$	−12333.7	−0.415954
$959$	28583.1	0.962456
$960$	−690.883	−0.0232272
$961$	−11060.3	−0.371262
$962$	−7248.60	−0.242936
$963$	15125.5	0.506141
$964$	19673.6	0.657307
$965$	−1893.61	−0.0631683
$966$	−2528.78	−0.0842257
$967$	54121.5	1.79982	0.899912	−	0.436071i	$-0.143630\pi$
$967$	54121.5	1.79982	0.899912	+	0.436071i	$0.143630\pi$
$968$	22809.5	0.757359
$969$	27794.3	0.921446
$970$	387.744	0.0128347
$971$	31887.2	1.05387	0.526936	−	0.849905i	$-0.323341\pi$
$971$	31887.2	1.05387	0.526936	+	0.849905i	$0.323341\pi$
$972$	21587.0	0.712349
$973$	5518.62	0.181828
$974$	−20167.3	−0.663451
$975$	59234.8	1.94567
$976$	−11298.2	−0.370539
$977$	−59373.7	−1.94425	−0.972125	−	0.234462i	$-0.924667\pi$
$977$	−59373.7	−1.94425	−0.972125	+	0.234462i	$0.924667\pi$
$978$	8403.00	0.274743
$979$	17181.5	0.560903
$980$	−817.148	−0.0266355
$981$	27664.9	0.900378
$982$	−31146.8	−1.01215
$983$	−48773.8	−1.58255	−0.791274	−	0.611462i	$-0.790582\pi$
$983$	−48773.8	−1.58255	−0.791274	+	0.611462i	$0.790582\pi$
$984$	38331.1	1.24182
$985$	2161.99	0.0699356
$986$	−3897.85	−0.125895
$987$	29635.0	0.955717
$988$	−20281.9	−0.653090
$989$	−220.002	−0.00707346
$990$	−221.171	−0.00710026
$991$	−53972.2	−1.73006	−0.865028	−	0.501724i	$-0.832699\pi$
$991$	−53972.2	−1.73006	−0.865028	+	0.501724i	$0.832699\pi$
$992$	25674.2	0.821732
$993$	28865.1	0.922464
$994$	−17195.5	−0.548700
$995$	1761.26	0.0561162
$996$	46299.1	1.47294
$997$	28404.8	0.902295	0.451148	−	0.892449i	$-0.351015\pi$
$997$	28404.8	0.902295	0.451148	+	0.892449i	$0.351015\pi$
$998$	8369.41	0.265460
$999$	−5173.09	−0.163833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.25	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.25	✓	38	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)

\(f(q)\)	\(=\)	\(q+1.50063 q^{2} +6.46705 q^{3} -5.74811 q^{4} -0.662294 q^{5} +9.70465 q^{6} +11.3293 q^{7} -20.6308 q^{8} +14.8227 q^{9} +O(q^{10})\)	\(q+1.50063 q^{2} +6.46705 q^{3} -5.74811 q^{4} -0.662294 q^{5} +9.70465 q^{6} +11.3293 q^{7} -20.6308 q^{8} +14.8227 q^{9} -0.993858 q^{10} +15.0133 q^{11} -37.1733 q^{12} -73.5339 q^{13} +17.0011 q^{14} -4.28308 q^{15} +15.0256 q^{16} -89.5681 q^{17} +22.2434 q^{18} -47.9839 q^{19} +3.80694 q^{20} +73.2671 q^{21} +22.5294 q^{22} -23.0000 q^{23} -133.421 q^{24} -124.561 q^{25} -110.347 q^{26} -78.7513 q^{27} -65.1220 q^{28} +29.0000 q^{29} -6.42732 q^{30} +136.860 q^{31} +187.595 q^{32} +97.0917 q^{33} -134.409 q^{34} -7.50332 q^{35} -85.2024 q^{36} +65.6890 q^{37} -72.0062 q^{38} -475.547 q^{39} +13.6637 q^{40} -287.295 q^{41} +109.947 q^{42} +9.56530 q^{43} -86.2981 q^{44} -9.81697 q^{45} -34.5145 q^{46} +404.479 q^{47} +97.1714 q^{48} -214.647 q^{49} -186.921 q^{50} -579.241 q^{51} +422.681 q^{52} +601.538 q^{53} -118.177 q^{54} -9.94321 q^{55} -233.733 q^{56} -310.314 q^{57} +43.5183 q^{58} -496.582 q^{59} +24.6196 q^{60} -751.927 q^{61} +205.377 q^{62} +167.931 q^{63} +161.305 q^{64} +48.7010 q^{65} +145.699 q^{66} +91.2679 q^{67} +514.847 q^{68} -148.742 q^{69} -11.2597 q^{70} -1011.44 q^{71} -305.804 q^{72} -513.165 q^{73} +98.5749 q^{74} -805.544 q^{75} +275.817 q^{76} +170.090 q^{77} -713.621 q^{78} +369.565 q^{79} -9.95137 q^{80} -909.501 q^{81} -431.124 q^{82} -1245.49 q^{83} -421.147 q^{84} +59.3204 q^{85} +14.3540 q^{86} +187.544 q^{87} -309.737 q^{88} +1144.42 q^{89} -14.7316 q^{90} -833.087 q^{91} +132.206 q^{92} +885.082 q^{93} +606.974 q^{94} +31.7795 q^{95} +1213.18 q^{96} -390.140 q^{97} -322.106 q^{98} +222.537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

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