LMFDB - Embedded newform 667.4.a.b.1.32

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			1.32
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)

$f(q)$	$=$	$q+3.82755 q^{2} -7.06313 q^{3} +6.65016 q^{4} +2.77976 q^{5} -27.0345 q^{6} +18.8683 q^{7} -5.16659 q^{8} +22.8877 q^{9} +O(q^{10})$	\(q+3.82755 q^{2} -7.06313 q^{3} +6.65016 q^{4} +2.77976 q^{5} -27.0345 q^{6} +18.8683 q^{7} -5.16659 q^{8} +22.8877 q^{9} +10.6397 q^{10} -51.8281 q^{11} -46.9709 q^{12} +65.3488 q^{13} +72.2193 q^{14} -19.6338 q^{15} -72.9767 q^{16} -46.4280 q^{17} +87.6041 q^{18} +100.528 q^{19} +18.4858 q^{20} -133.269 q^{21} -198.375 q^{22} -23.0000 q^{23} +36.4923 q^{24} -117.273 q^{25} +250.126 q^{26} +29.0454 q^{27} +125.477 q^{28} +29.0000 q^{29} -75.1493 q^{30} -218.761 q^{31} -237.989 q^{32} +366.069 q^{33} -177.705 q^{34} +52.4492 q^{35} +152.207 q^{36} +116.499 q^{37} +384.776 q^{38} -461.567 q^{39} -14.3619 q^{40} -336.205 q^{41} -510.094 q^{42} -350.812 q^{43} -344.665 q^{44} +63.6224 q^{45} -88.0337 q^{46} +67.2061 q^{47} +515.443 q^{48} +13.0114 q^{49} -448.868 q^{50} +327.927 q^{51} +434.580 q^{52} -635.998 q^{53} +111.173 q^{54} -144.070 q^{55} -97.4847 q^{56} -710.042 q^{57} +110.999 q^{58} +855.896 q^{59} -130.568 q^{60} -818.379 q^{61} -837.318 q^{62} +431.852 q^{63} -327.103 q^{64} +181.654 q^{65} +1401.15 q^{66} -532.409 q^{67} -308.753 q^{68} +162.452 q^{69} +200.752 q^{70} -1077.23 q^{71} -118.252 q^{72} +595.569 q^{73} +445.907 q^{74} +828.314 q^{75} +668.527 q^{76} -977.907 q^{77} -1766.67 q^{78} -170.497 q^{79} -202.857 q^{80} -823.120 q^{81} -1286.84 q^{82} -109.087 q^{83} -886.259 q^{84} -129.058 q^{85} -1342.75 q^{86} -204.831 q^{87} +267.775 q^{88} -732.497 q^{89} +243.518 q^{90} +1233.02 q^{91} -152.954 q^{92} +1545.13 q^{93} +257.235 q^{94} +279.443 q^{95} +1680.95 q^{96} +159.147 q^{97} +49.8018 q^{98} -1186.23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.82755	1.35324	0.676622	−	0.736330i	$-0.263443\pi$
$2$	3.82755	1.35324	0.676622	+	0.736330i	$0.263443\pi$
$3$	−7.06313	−1.35930	−0.679650	−	0.733537i	$-0.737868\pi$
$3$	−7.06313	−1.35930	−0.679650	+	0.733537i	$0.737868\pi$
$4$	6.65016	0.831270
$5$	2.77976	0.248629	0.124315	−	0.992243i	$-0.460327\pi$
$5$	2.77976	0.248629	0.124315	+	0.992243i	$0.460327\pi$
$6$	−27.0345	−1.83946
$7$	18.8683	1.01879	0.509395	−	0.860533i	$-0.329869\pi$
$7$	18.8683	1.01879	0.509395	+	0.860533i	$0.329869\pi$
$8$	−5.16659	−0.228333
$9$	22.8877	0.847694
$10$	10.6397	0.336456
$11$	−51.8281	−1.42062	−0.710308	−	0.703891i	$-0.751444\pi$
$11$	−51.8281	−1.42062	−0.710308	+	0.703891i	$0.751444\pi$
$12$	−46.9709	−1.12994
$13$	65.3488	1.39419	0.697096	−	0.716978i	$-0.254475\pi$
$13$	65.3488	1.39419	0.697096	+	0.716978i	$0.254475\pi$
$14$	72.2193	1.37867
$15$	−19.6338	−0.337961
$16$	−72.9767	−1.14026
$17$	−46.4280	−0.662379	−0.331189	−	0.943564i	$-0.607450\pi$
$17$	−46.4280	−0.662379	−0.331189	+	0.943564i	$0.607450\pi$
$18$	87.6041	1.14714
$19$	100.528	1.21383	0.606913	−	0.794768i	$-0.292408\pi$
$19$	100.528	1.21383	0.606913	+	0.794768i	$0.292408\pi$
$20$	18.4858	0.206678
$21$	−133.269	−1.38484
$22$	−198.375	−1.92244
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	36.4923	0.310373
$25$	−117.273	−0.938184
$26$	250.126	1.88668
$27$	29.0454	0.207029
$28$	125.477	0.846890
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−75.1493	−0.457344
$31$	−218.761	−1.26744	−0.633719	−	0.773563i	$-0.718472\pi$
$31$	−218.761	−1.26744	−0.633719	+	0.773563i	$0.718472\pi$
$32$	−237.989	−1.31472
$33$	366.069	1.93104
$34$	−177.705	−0.896360
$35$	52.4492	0.253301
$36$	152.207	0.704663
$37$	116.499	0.517632	0.258816	−	0.965927i	$-0.416668\pi$
$37$	116.499	0.517632	0.258816	+	0.965927i	$0.416668\pi$
$38$	384.776	1.64260
$39$	−461.567	−1.89512
$40$	−14.3619	−0.0567703
$41$	−336.205	−1.28065	−0.640323	−	0.768106i	$-0.721199\pi$
$41$	−336.205	−1.28065	−0.640323	+	0.768106i	$0.721199\pi$
$42$	−510.094	−1.87403
$43$	−350.812	−1.24415	−0.622073	−	0.782959i	$-0.713709\pi$
$43$	−350.812	−1.24415	−0.622073	+	0.782959i	$0.713709\pi$
$44$	−344.665	−1.18091
$45$	63.6224	0.210761
$46$	−88.0337	−0.282171
$47$	67.2061	0.208575	0.104287	−	0.994547i	$-0.466744\pi$
$47$	67.2061	0.208575	0.104287	+	0.994547i	$0.466744\pi$
$48$	515.443	1.54996
$49$	13.0114	0.0379341
$50$	−448.868	−1.26959
$51$	327.927	0.900371
$52$	434.580	1.15895
$53$	−635.998	−1.64832	−0.824161	−	0.566356i	$-0.808353\pi$
$53$	−635.998	−1.64832	−0.824161	+	0.566356i	$0.808353\pi$
$54$	111.173	0.280161
$55$	−144.070	−0.353206
$56$	−97.4847	−0.232624
$57$	−710.042	−1.64995
$58$	110.999	0.251291
$59$	855.896	1.88861	0.944307	−	0.329067i	$-0.106734\pi$
$59$	855.896	1.88861	0.944307	+	0.329067i	$0.106734\pi$
$60$	−130.568	−0.280937
$61$	−818.379	−1.71775	−0.858874	−	0.512186i	$-0.828836\pi$
$61$	−818.379	−1.71775	−0.858874	+	0.512186i	$0.828836\pi$
$62$	−837.318	−1.71515
$63$	431.852	0.863623
$64$	−327.103	−0.638873
$65$	181.654	0.346637
$66$	1401.15	2.61317
$67$	−532.409	−0.970808	−0.485404	−	0.874290i	$-0.661328\pi$
$67$	−532.409	−0.970808	−0.485404	+	0.874290i	$0.661328\pi$
$68$	−308.753	−0.550615
$69$	162.452	0.283433
$70$	200.752	0.342778
$71$	−1077.23	−1.80061	−0.900307	−	0.435254i	$-0.856658\pi$
$71$	−1077.23	−1.80061	−0.900307	+	0.435254i	$0.856658\pi$
$72$	−118.252	−0.193557
$73$	595.569	0.954877	0.477439	−	0.878665i	$-0.341565\pi$
$73$	595.569	0.954877	0.477439	+	0.878665i	$0.341565\pi$
$74$	445.907	0.700482
$75$	828.314	1.27527
$76$	668.527	1.00902
$77$	−977.907	−1.44731
$78$	−1766.67	−2.56457
$79$	−170.497	−0.242815	−0.121407	−	0.992603i	$-0.538741\pi$
$79$	−170.497	−0.242815	−0.121407	+	0.992603i	$0.538741\pi$
$80$	−202.857	−0.283502
$81$	−823.120	−1.12911
$82$	−1286.84	−1.73303
$83$	−109.087	−0.144263	−0.0721313	−	0.997395i	$-0.522980\pi$
$83$	−109.087	−0.144263	−0.0721313	+	0.997395i	$0.522980\pi$
$84$	−886.259	−1.15118
$85$	−129.058	−0.164687
$86$	−1342.75	−1.68363
$87$	−204.831	−0.252416
$88$	267.775	0.324374
$89$	−732.497	−0.872410	−0.436205	−	0.899847i	$-0.643678\pi$
$89$	−732.497	−0.872410	−0.436205	+	0.899847i	$0.643678\pi$
$90$	243.518	0.285212
$91$	1233.02	1.42039
$92$	−152.954	−0.173332
$93$	1545.13	1.72283
$94$	257.235	0.282253
$95$	279.443	0.301792
$96$	1680.95	1.78709
$97$	159.147	0.166587	0.0832934	−	0.996525i	$-0.473456\pi$
$97$	159.147	0.166587	0.0832934	+	0.996525i	$0.473456\pi$
$98$	49.8018	0.0513341
$99$	−1186.23	−1.20425
$100$	−779.884	−0.779884
$101$	−1429.64	−1.40846	−0.704230	−	0.709972i	$-0.748708\pi$
$101$	−1429.64	−1.40846	−0.704230	+	0.709972i	$0.748708\pi$
$102$	1255.16	1.21842
$103$	1790.55	1.71290	0.856448	−	0.516234i	$-0.172666\pi$
$103$	1790.55	1.71290	0.856448	+	0.516234i	$0.172666\pi$
$104$	−337.631	−0.318340
$105$	−370.455	−0.344312
$106$	−2434.32	−2.23058
$107$	651.250	0.588399	0.294200	−	0.955744i	$-0.404947\pi$
$107$	651.250	0.588399	0.294200	+	0.955744i	$0.404947\pi$
$108$	193.156	0.172097
$109$	760.114	0.667943	0.333971	−	0.942583i	$-0.391611\pi$
$109$	760.114	0.667943	0.333971	+	0.942583i	$0.391611\pi$
$110$	−551.434	−0.477974
$111$	−822.849	−0.703616
$112$	−1376.94	−1.16169
$113$	−205.139	−0.170778	−0.0853888	−	0.996348i	$-0.527213\pi$
$113$	−205.139	−0.170778	−0.0853888	+	0.996348i	$0.527213\pi$
$114$	−2717.72	−2.23279
$115$	−63.9344	−0.0518427
$116$	192.855	0.154363
$117$	1495.69	1.18185
$118$	3275.99	2.55575
$119$	−876.015	−0.674825
$120$	101.440	0.0771678
$121$	1355.16	1.01815
$122$	−3132.39	−2.32453
$123$	2374.66	1.74078
$124$	−1454.79	−1.05358
$125$	−673.460	−0.481889
$126$	1652.94	1.16869
$127$	−1711.56	−1.19588	−0.597939	−	0.801542i	$-0.704014\pi$
$127$	−1711.56	−1.19588	−0.597939	+	0.801542i	$0.704014\pi$
$128$	651.910	0.450166
$129$	2477.83	1.69117
$130$	695.289	0.469084
$131$	−41.3344	−0.0275680	−0.0137840	−	0.999905i	$-0.504388\pi$
$131$	−41.3344	−0.0275680	−0.0137840	+	0.999905i	$0.504388\pi$
$132$	2434.41	1.60522
$133$	1896.79	1.23663
$134$	−2037.82	−1.31374
$135$	80.7390	0.0514734
$136$	239.874	0.151243
$137$	1968.59	1.22765	0.613825	−	0.789442i	$-0.289630\pi$
$137$	1968.59	1.22765	0.613825	+	0.789442i	$0.289630\pi$
$138$	621.793	0.383555
$139$	263.969	0.161076	0.0805380	−	0.996752i	$-0.474336\pi$
$139$	263.969	0.161076	0.0805380	+	0.996752i	$0.474336\pi$
$140$	348.795	0.210561
$141$	−474.685	−0.283516
$142$	−4123.15	−2.43667
$143$	−3386.91	−1.98061
$144$	−1670.27	−0.966592
$145$	80.6130	0.0461693
$146$	2279.57	1.29218
$147$	−91.9012	−0.0515638
$148$	774.739	0.430291
$149$	−1384.20	−0.761060	−0.380530	−	0.924769i	$-0.624258\pi$
$149$	−1384.20	−0.761060	−0.380530	+	0.924769i	$0.624258\pi$
$150$	3170.41	1.72575
$151$	−1211.32	−0.652819	−0.326409	−	0.945229i	$-0.605839\pi$
$151$	−1211.32	−0.652819	−0.326409	+	0.945229i	$0.605839\pi$
$152$	−519.387	−0.277157
$153$	−1062.63	−0.561495
$154$	−3742.99	−1.95856
$155$	−608.101	−0.315122
$156$	−3069.49	−1.57536
$157$	−116.103	−0.0590191	−0.0295095	−	0.999564i	$-0.509395\pi$
$157$	−116.103	−0.0590191	−0.0295095	+	0.999564i	$0.509395\pi$
$158$	−652.585	−0.328588
$159$	4492.14	2.24056
$160$	−661.552	−0.326877
$161$	−433.970	−0.212433
$162$	−3150.54	−1.52796
$163$	3074.46	1.47736	0.738682	−	0.674054i	$-0.235448\pi$
$163$	3074.46	1.47736	0.738682	+	0.674054i	$0.235448\pi$
$164$	−2235.82	−1.06456
$165$	1017.58	0.480113
$166$	−417.534	−0.195223
$167$	2628.72	1.21806	0.609030	−	0.793147i	$-0.291559\pi$
$167$	2628.72	1.21806	0.609030	+	0.793147i	$0.291559\pi$
$168$	688.546	0.316205
$169$	2073.46	0.943771
$170$	−493.978	−0.222861
$171$	2300.86	1.02895
$172$	−2332.95	−1.03422
$173$	−3422.09	−1.50391	−0.751956	−	0.659213i	$-0.770890\pi$
$173$	−3422.09	−1.50391	−0.751956	+	0.659213i	$0.770890\pi$
$174$	−784.000	−0.341580
$175$	−2212.74	−0.955813
$176$	3782.24	1.61987
$177$	−6045.30	−2.56719
$178$	−2803.67	−1.18058
$179$	−1357.01	−0.566635	−0.283317	−	0.959026i	$-0.591435\pi$
$179$	−1357.01	−0.566635	−0.283317	+	0.959026i	$0.591435\pi$
$180$	423.099	0.175200
$181$	2510.48	1.03095	0.515476	−	0.856904i	$-0.327615\pi$
$181$	2510.48	1.03095	0.515476	+	0.856904i	$0.327615\pi$
$182$	4719.44	1.92213
$183$	5780.31	2.33493
$184$	118.832	0.0476108
$185$	323.840	0.128698
$186$	5914.08	2.33141
$187$	2406.28	0.940985
$188$	446.931	0.173382
$189$	548.035	0.210919
$190$	1069.58	0.408399
$191$	3399.97	1.28803	0.644014	−	0.765014i	$-0.277268\pi$
$191$	3399.97	1.28803	0.644014	+	0.765014i	$0.277268\pi$
$192$	2310.37	0.868420
$193$	2381.78	0.888314	0.444157	−	0.895949i	$-0.353503\pi$
$193$	2381.78	0.888314	0.444157	+	0.895949i	$0.353503\pi$
$194$	609.143	0.225433
$195$	−1283.04	−0.471183
$196$	86.5279	0.0315335
$197$	−110.748	−0.0400530	−0.0200265	−	0.999799i	$-0.506375\pi$
$197$	−110.748	−0.0400530	−0.0200265	+	0.999799i	$0.506375\pi$
$198$	−4540.35	−1.62964
$199$	−650.560	−0.231744	−0.115872	−	0.993264i	$-0.536966\pi$
$199$	−650.560	−0.231744	−0.115872	+	0.993264i	$0.536966\pi$
$200$	605.902	0.214219
$201$	3760.47	1.31962
$202$	−5472.02	−1.90599
$203$	547.180	0.189185
$204$	2180.76	0.748451
$205$	−934.569	−0.318406
$206$	6853.43	2.31797
$207$	−526.418	−0.176756
$208$	−4768.94	−1.58974
$209$	−5210.18	−1.72438
$210$	−1417.94	−0.465938
$211$	3680.54	1.20085	0.600424	−	0.799682i	$-0.294998\pi$
$211$	3680.54	1.20085	0.600424	+	0.799682i	$0.294998\pi$
$212$	−4229.49	−1.37020
$213$	7608.61	2.44757
$214$	2492.69	0.796248
$215$	−975.171	−0.309331
$216$	−150.066	−0.0472716
$217$	−4127.63	−1.29125
$218$	2909.38	0.903889
$219$	−4206.58	−1.29796
$220$	−958.086	−0.293610
$221$	−3034.01	−0.923483
$222$	−3149.50	−0.952165
$223$	−240.329	−0.0721687	−0.0360843	−	0.999349i	$-0.511488\pi$
$223$	−240.329	−0.0721687	−0.0360843	+	0.999349i	$0.511488\pi$
$224$	−4490.44	−1.33942
$225$	−2684.11	−0.795293
$226$	−785.181	−0.231104
$227$	5756.96	1.68327	0.841636	−	0.540045i	$-0.181593\pi$
$227$	5756.96	1.68327	0.841636	+	0.540045i	$0.181593\pi$
$228$	−4721.89	−1.37156
$229$	799.826	0.230804	0.115402	−	0.993319i	$-0.463184\pi$
$229$	799.826	0.230804	0.115402	+	0.993319i	$0.463184\pi$
$230$	−244.712	−0.0701559
$231$	6907.08	1.96733
$232$	−149.831	−0.0424004
$233$	5002.15	1.40645	0.703223	−	0.710970i	$-0.251744\pi$
$233$	5002.15	1.40645	0.703223	+	0.710970i	$0.251744\pi$
$234$	5724.82	1.59933
$235$	186.817	0.0518578
$236$	5691.84	1.56995
$237$	1204.24	0.330058
$238$	−3352.99	−0.913203
$239$	4465.84	1.20867	0.604333	−	0.796732i	$-0.293440\pi$
$239$	4465.84	1.20867	0.604333	+	0.796732i	$0.293440\pi$
$240$	1432.81	0.385364
$241$	6868.02	1.83572	0.917859	−	0.396906i	$-0.129916\pi$
$241$	6868.02	1.83572	0.917859	+	0.396906i	$0.129916\pi$
$242$	5186.93	1.37780
$243$	5029.58	1.32777
$244$	−5442.35	−1.42791
$245$	36.1685	0.00943152
$246$	9089.14	2.35570
$247$	6569.38	1.69231
$248$	1130.25	0.289398
$249$	770.492	0.196096
$250$	−2577.70	−0.652113
$251$	−4478.12	−1.12612	−0.563060	−	0.826416i	$-0.690376\pi$
$251$	−4478.12	−1.12612	−0.563060	+	0.826416i	$0.690376\pi$
$252$	2871.88	0.717904
$253$	1192.05	0.296219
$254$	−6551.09	−1.61832
$255$	911.556	0.223858
$256$	5112.04	1.24806
$257$	−2373.27	−0.576033	−0.288017	−	0.957625i	$-0.592996\pi$
$257$	−2373.27	−0.576033	−0.288017	+	0.957625i	$0.592996\pi$
$258$	9484.01	2.28856
$259$	2198.14	0.527358
$260$	1208.03	0.288148
$261$	663.745	0.157413
$262$	−158.210	−0.0373062
$263$	−3904.83	−0.915522	−0.457761	−	0.889075i	$-0.651349\pi$
$263$	−3904.83	−0.915522	−0.457761	+	0.889075i	$0.651349\pi$
$264$	−1891.33	−0.440921
$265$	−1767.92	−0.409821
$266$	7260.06	1.67347
$267$	5173.72	1.18587
$268$	−3540.61	−0.807003
$269$	−4957.42	−1.12364	−0.561820	−	0.827260i	$-0.689899\pi$
$269$	−4957.42	−1.12364	−0.561820	+	0.827260i	$0.689899\pi$
$270$	309.033	0.0696561
$271$	−3338.06	−0.748239	−0.374119	−	0.927381i	$-0.622055\pi$
$271$	−3338.06	−0.748239	−0.374119	+	0.927381i	$0.622055\pi$
$272$	3388.16	0.755284
$273$	−8708.96	−1.93073
$274$	7534.89	1.66131
$275$	6078.04	1.33280
$276$	1080.33	0.235610
$277$	−5779.03	−1.25353	−0.626766	−	0.779208i	$-0.715622\pi$
$277$	−5779.03	−1.25353	−0.626766	+	0.779208i	$0.715622\pi$
$278$	1010.36	0.217975
$279$	−5006.94	−1.07440
$280$	−270.984	−0.0578370
$281$	−7478.33	−1.58762	−0.793808	−	0.608169i	$-0.791904\pi$
$281$	−7478.33	−1.58762	−0.793808	+	0.608169i	$0.791904\pi$
$282$	−1816.88	−0.383666
$283$	−2152.09	−0.452043	−0.226022	−	0.974122i	$-0.572572\pi$
$283$	−2152.09	−0.452043	−0.226022	+	0.974122i	$0.572572\pi$
$284$	−7163.75	−1.49680
$285$	−1973.74	−0.410226
$286$	−12963.6	−2.68025
$287$	−6343.61	−1.30471
$288$	−5447.04	−1.11448
$289$	−2757.44	−0.561255
$290$	308.550	0.0624783
$291$	−1124.08	−0.226441
$292$	3960.63	0.793760
$293$	−3854.53	−0.768547	−0.384274	−	0.923219i	$-0.625548\pi$
$293$	−3854.53	−0.768547	−0.384274	+	0.923219i	$0.625548\pi$
$294$	−351.757	−0.0697784
$295$	2379.18	0.469564
$296$	−601.905	−0.118193
$297$	−1505.37	−0.294108
$298$	−5298.09	−1.02990
$299$	−1503.02	−0.290709
$300$	5508.42	1.06010
$301$	−6619.21	−1.26752
$302$	−4636.38	−0.883423
$303$	10097.7	1.91452
$304$	−7336.20	−1.38408
$305$	−2274.89	−0.427082
$306$	−4067.28	−0.759839
$307$	4093.41	0.760988	0.380494	−	0.924783i	$-0.375754\pi$
$307$	4093.41	0.760988	0.380494	+	0.924783i	$0.375754\pi$
$308$	−6503.24	−1.20310
$309$	−12646.9	−2.32834
$310$	−2327.54	−0.426437
$311$	−10369.7	−1.89071	−0.945353	−	0.326050i	$-0.894282\pi$
$311$	−10369.7	−1.89071	−0.945353	+	0.326050i	$0.894282\pi$
$312$	2384.73	0.432720
$313$	−3592.40	−0.648735	−0.324368	−	0.945931i	$-0.605152\pi$
$313$	−3592.40	−0.648735	−0.324368	+	0.945931i	$0.605152\pi$
$314$	−444.389	−0.0798672
$315$	1200.44	0.214722
$316$	−1133.83	−0.201845
$317$	−9350.16	−1.65665	−0.828324	−	0.560249i	$-0.810705\pi$
$317$	−9350.16	−1.65665	−0.828324	+	0.560249i	$0.810705\pi$
$318$	17193.9	3.03203
$319$	−1503.02	−0.263802
$320$	−909.267	−0.158842
$321$	−4599.86	−0.799810
$322$	−1661.04	−0.287473
$323$	−4667.31	−0.804013
$324$	−5473.88	−0.938594
$325$	−7663.64	−1.30801
$326$	11767.7	1.99923
$327$	−5368.78	−0.907934
$328$	1737.04	0.292414
$329$	1268.06	0.212494
$330$	3894.85	0.649710
$331$	−10047.4	−1.66844	−0.834222	−	0.551429i	$-0.814083\pi$
$331$	−10047.4	−1.66844	−0.834222	+	0.551429i	$0.814083\pi$
$332$	−725.443	−0.119921
$333$	2666.41	0.438793
$334$	10061.5	1.64833
$335$	−1479.97	−0.241371
$336$	9725.52	1.57908
$337$	11284.6	1.82406	0.912032	−	0.410119i	$-0.134513\pi$
$337$	11284.6	1.82406	0.912032	+	0.410119i	$0.134513\pi$
$338$	7936.29	1.27715
$339$	1448.92	0.232138
$340$	−858.259	−0.136899
$341$	11338.0	1.80054
$342$	8806.66	1.39243
$343$	−6226.31	−0.980144
$344$	1812.50	0.284080
$345$	451.577	0.0704698
$346$	−13098.2	−2.03516
$347$	11281.4	1.74529	0.872644	−	0.488357i	$-0.162404\pi$
$347$	11281.4	1.74529	0.872644	+	0.488357i	$0.162404\pi$
$348$	−1362.16	−0.209825
$349$	−8595.63	−1.31838	−0.659188	−	0.751978i	$-0.729100\pi$
$349$	−8595.63	−1.31838	−0.659188	+	0.751978i	$0.729100\pi$
$350$	−8469.37	−1.29345
$351$	1898.08	0.288638
$352$	12334.5	1.86771
$353$	−1738.31	−0.262098	−0.131049	−	0.991376i	$-0.541835\pi$
$353$	−1738.31	−0.262098	−0.131049	+	0.991376i	$0.541835\pi$
$354$	−23138.7	−3.47404
$355$	−2994.44	−0.447685
$356$	−4871.22	−0.725208
$357$	6187.41	0.917289
$358$	−5194.02	−0.766795
$359$	6460.77	0.949823	0.474912	−	0.880033i	$-0.342480\pi$
$359$	6460.77	0.949823	0.474912	+	0.880033i	$0.342480\pi$
$360$	−328.711	−0.0481239
$361$	3246.88	0.473375
$362$	9608.98	1.39513
$363$	−9571.64	−1.38397
$364$	8199.76	1.18073
$365$	1655.54	0.237410
$366$	22124.5	3.15974
$367$	−7584.38	−1.07875	−0.539375	−	0.842066i	$-0.681339\pi$
$367$	−7584.38	−1.07875	−0.539375	+	0.842066i	$0.681339\pi$
$368$	1678.46	0.237761
$369$	−7694.98	−1.08560
$370$	1239.51	0.174160
$371$	−12000.2	−1.67929
$372$	10275.4	1.43213
$373$	7787.42	1.08101	0.540506	−	0.841340i	$-0.318233\pi$
$373$	7787.42	1.08101	0.540506	+	0.841340i	$0.318233\pi$
$374$	9210.14	1.27338
$375$	4756.73	0.655031
$376$	−347.227	−0.0476246
$377$	1895.11	0.258895
$378$	2097.63	0.285425
$379$	−6088.76	−0.825220	−0.412610	−	0.910908i	$-0.635383\pi$
$379$	−6088.76	−0.825220	−0.412610	+	0.910908i	$0.635383\pi$
$380$	1858.34	0.250871
$381$	12089.0	1.62556
$382$	13013.6	1.74302
$383$	10002.3	1.33445	0.667224	−	0.744857i	$-0.267482\pi$
$383$	10002.3	1.33445	0.667224	+	0.744857i	$0.267482\pi$
$384$	−4604.52	−0.611910
$385$	−2718.34	−0.359843
$386$	9116.40	1.20211
$387$	−8029.29	−1.05466
$388$	1058.35	0.138479
$389$	8098.22	1.05552	0.527758	−	0.849395i	$-0.323033\pi$
$389$	8098.22	1.05552	0.527758	+	0.849395i	$0.323033\pi$
$390$	−4910.92	−0.637625
$391$	1067.84	0.138115
$392$	−67.2246	−0.00866163
$393$	291.950	0.0374731
$394$	−423.893	−0.0542015
$395$	−473.939	−0.0603708
$396$	−7888.61	−1.00105
$397$	10227.9	1.29300	0.646500	−	0.762914i	$-0.276232\pi$
$397$	10227.9	1.29300	0.646500	+	0.762914i	$0.276232\pi$
$398$	−2490.05	−0.313606
$399$	−13397.3	−1.68096
$400$	8558.19	1.06977
$401$	−12859.4	−1.60141	−0.800707	−	0.599056i	$-0.795543\pi$
$401$	−12859.4	−1.60141	−0.800707	+	0.599056i	$0.795543\pi$
$402$	14393.4	1.78577
$403$	−14295.7	−1.76705
$404$	−9507.33	−1.17081
$405$	−2288.07	−0.280729
$406$	2094.36	0.256013
$407$	−6037.94	−0.735356
$408$	−1694.26	−0.205585
$409$	5637.25	0.681526	0.340763	−	0.940149i	$-0.389315\pi$
$409$	5637.25	0.681526	0.340763	+	0.940149i	$0.389315\pi$
$410$	−3577.11	−0.430880
$411$	−13904.4	−1.66874
$412$	11907.4	1.42388
$413$	16149.3	1.92410
$414$	−2014.89	−0.239195
$415$	−303.234	−0.0358679
$416$	−15552.3	−1.83297
$417$	−1864.45	−0.218950
$418$	−19942.2	−2.33351
$419$	9297.63	1.08405	0.542027	−	0.840361i	$-0.317657\pi$
$419$	9297.63	1.08405	0.542027	+	0.840361i	$0.317657\pi$
$420$	−2463.59	−0.286216
$421$	−1210.20	−0.140099	−0.0700493	−	0.997544i	$-0.522316\pi$
$421$	−1210.20	−0.140099	−0.0700493	+	0.997544i	$0.522316\pi$
$422$	14087.5	1.62504
$423$	1538.20	0.176808
$424$	3285.94	0.376367
$425$	5444.74	0.621433
$426$	29122.4	3.31217
$427$	−15441.4	−1.75003
$428$	4330.91	0.489118
$429$	23922.1	2.69224
$430$	−3732.52	−0.418600
$431$	−14665.0	−1.63895	−0.819473	−	0.573117i	$-0.805734\pi$
$431$	−14665.0	−1.63895	−0.819473	+	0.573117i	$0.805734\pi$
$432$	−2119.63	−0.236067
$433$	−7521.10	−0.834736	−0.417368	−	0.908737i	$-0.637047\pi$
$433$	−7521.10	−0.834736	−0.417368	+	0.908737i	$0.637047\pi$
$434$	−15798.7	−1.74738
$435$	−569.379	−0.0627578
$436$	5054.88	0.555240
$437$	−2312.14	−0.253100
$438$	−16100.9	−1.75646
$439$	6893.64	0.749466	0.374733	−	0.927133i	$-0.377734\pi$
$439$	6893.64	0.749466	0.374733	+	0.927133i	$0.377734\pi$
$440$	744.349	0.0806488
$441$	297.802	0.0321565
$442$	−11612.8	−1.24970
$443$	−6723.67	−0.721108	−0.360554	−	0.932738i	$-0.617412\pi$
$443$	−6723.67	−0.721108	−0.360554	+	0.932738i	$0.617412\pi$
$444$	−5472.08	−0.584895
$445$	−2036.16	−0.216907
$446$	−919.871	−0.0976618
$447$	9776.76	1.03451
$448$	−6171.87	−0.650878
$449$	−8592.89	−0.903170	−0.451585	−	0.892228i	$-0.649141\pi$
$449$	−8592.89	−0.903170	−0.451585	+	0.892228i	$0.649141\pi$
$450$	−10273.6	−1.07623
$451$	17424.9	1.81930
$452$	−1364.21	−0.141962
$453$	8555.69	0.887376
$454$	22035.1	2.27788
$455$	3427.49	0.353150
$456$	3668.50	0.376739
$457$	19106.1	1.95568	0.977839	−	0.209359i	$-0.0671376\pi$
$457$	19106.1	1.95568	0.977839	+	0.209359i	$0.0671376\pi$
$458$	3061.38	0.312334
$459$	−1348.52	−0.137132
$460$	−425.174	−0.0430953
$461$	−7709.54	−0.778892	−0.389446	−	0.921049i	$-0.627334\pi$
$461$	−7709.54	−0.778892	−0.389446	+	0.921049i	$0.627334\pi$
$462$	26437.2	2.66227
$463$	1099.41	0.110354	0.0551771	−	0.998477i	$-0.482428\pi$
$463$	1099.41	0.110354	0.0551771	+	0.998477i	$0.482428\pi$
$464$	−2116.32	−0.211741
$465$	4295.10	0.428345
$466$	19146.0	1.90326
$467$	−5247.21	−0.519940	−0.259970	−	0.965617i	$-0.583713\pi$
$467$	−5247.21	−0.519940	−0.259970	+	0.965617i	$0.583713\pi$
$468$	9946.55	0.982435
$469$	−10045.6	−0.989050
$470$	715.050	0.0701762
$471$	820.047	0.0802246
$472$	−4422.07	−0.431233
$473$	18181.9	1.76745
$474$	4609.29	0.446649
$475$	−11789.2	−1.13879
$476$	−5825.64	−0.560962
$477$	−14556.6	−1.39727
$478$	17093.2	1.63562
$479$	12840.4	1.22483	0.612415	−	0.790536i	$-0.290198\pi$
$479$	12840.4	1.22483	0.612415	+	0.790536i	$0.290198\pi$
$480$	4672.63	0.444324
$481$	7613.09	0.721678
$482$	26287.7	2.48418
$483$	3065.19	0.288759
$484$	9012.00	0.846356
$485$	442.390	0.0414183
$486$	19251.0	1.79679
$487$	−6309.93	−0.587126	−0.293563	−	0.955940i	$-0.594841\pi$
$487$	−6309.93	−0.587126	−0.293563	+	0.955940i	$0.594841\pi$
$488$	4228.23	0.392219
$489$	−21715.3	−2.00818
$490$	138.437	0.0127632
$491$	−12340.2	−1.13422	−0.567112	−	0.823641i	$-0.691939\pi$
$491$	−12340.2	−1.13422	−0.567112	+	0.823641i	$0.691939\pi$
$492$	15791.9	1.44706
$493$	−1346.41	−0.123001
$494$	25144.7	2.29010
$495$	−3297.43	−0.299411
$496$	15964.4	1.44521
$497$	−20325.5	−1.83445
$498$	2949.10	0.265366
$499$	11361.5	1.01926	0.509632	−	0.860393i	$-0.329782\pi$
$499$	11361.5	1.01926	0.509632	+	0.860393i	$0.329782\pi$
$500$	−4478.61	−0.400579
$501$	−18567.0	−1.65571
$502$	−17140.2	−1.52392
$503$	5461.95	0.484168	0.242084	−	0.970255i	$-0.422169\pi$
$503$	5461.95	0.484168	0.242084	+	0.970255i	$0.422169\pi$
$504$	−2231.20	−0.197194
$505$	−3974.05	−0.350184
$506$	4562.62	0.400856
$507$	−14645.1	−1.28287
$508$	−11382.2	−0.994097
$509$	2127.91	0.185301	0.0926504	−	0.995699i	$-0.470466\pi$
$509$	2127.91	0.185301	0.0926504	+	0.995699i	$0.470466\pi$
$510$	3489.03	0.302935
$511$	11237.3	0.972820
$512$	14351.3	1.23876
$513$	2919.87	0.251297
$514$	−9083.82	−0.779514
$515$	4977.30	0.425876
$516$	16477.9	1.40582
$517$	−3483.17	−0.296305
$518$	8413.50	0.713644
$519$	24170.7	2.04427
$520$	−938.531	−0.0791487
$521$	7750.57	0.651744	0.325872	−	0.945414i	$-0.394342\pi$
$521$	7750.57	0.651744	0.325872	+	0.945414i	$0.394342\pi$
$522$	2540.52	0.213018
$523$	−20124.4	−1.68256	−0.841279	−	0.540601i	$-0.818197\pi$
$523$	−20124.4	−1.68256	−0.841279	+	0.540601i	$0.818197\pi$
$524$	−274.881	−0.0229164
$525$	15628.8	1.29924
$526$	−14946.0	−1.23893
$527$	10156.6	0.839524
$528$	−26714.5	−2.20189
$529$	529.000	0.0434783
$530$	−6766.81	−0.554587
$531$	19589.5	1.60097
$532$	12613.9	1.02798
$533$	−21970.6	−1.78546
$534$	19802.7	1.60477
$535$	1810.32	0.146293
$536$	2750.74	0.221668
$537$	9584.72	0.770226
$538$	−18974.8	−1.52056
$539$	−674.357	−0.0538898
$540$	536.927	0.0427883
$541$	7474.41	0.593993	0.296996	−	0.954879i	$-0.404015\pi$
$541$	7474.41	0.593993	0.296996	+	0.954879i	$0.404015\pi$
$542$	−12776.6	−1.01255
$543$	−17731.8	−1.40137
$544$	11049.4	0.870841
$545$	2112.93	0.166070
$546$	−33334.0	−2.61275
$547$	14648.5	1.14502	0.572508	−	0.819899i	$-0.305971\pi$
$547$	14648.5	1.14502	0.572508	+	0.819899i	$0.305971\pi$
$548$	13091.4	1.02051
$549$	−18730.8	−1.45613
$550$	23264.0	1.80360
$551$	2915.31	0.225402
$552$	−839.323	−0.0647173
$553$	−3216.98	−0.247378
$554$	−22119.5	−1.69633
$555$	−2287.32	−0.174939
$556$	1755.44	0.133898
$557$	1035.83	0.0787966	0.0393983	−	0.999224i	$-0.487456\pi$
$557$	1035.83	0.0787966	0.0393983	+	0.999224i	$0.487456\pi$
$558$	−19164.3	−1.45393
$559$	−22925.1	−1.73458
$560$	−3827.57	−0.288829
$561$	−16995.8	−1.27908
$562$	−28623.7	−2.14843
$563$	−8158.09	−0.610697	−0.305348	−	0.952241i	$-0.598773\pi$
$563$	−8158.09	−0.610697	−0.305348	+	0.952241i	$0.598773\pi$
$564$	−3156.73	−0.235678
$565$	−570.237	−0.0424603
$566$	−8237.23	−0.611725
$567$	−15530.8	−1.15033
$568$	5565.61	0.411140
$569$	−6701.38	−0.493737	−0.246868	−	0.969049i	$-0.579402\pi$
$569$	−6701.38	−0.493737	−0.246868	+	0.969049i	$0.579402\pi$
$570$	−7554.61	−0.555136
$571$	2685.37	0.196811	0.0984057	−	0.995146i	$-0.468626\pi$
$571$	2685.37	0.196811	0.0984057	+	0.995146i	$0.468626\pi$
$572$	−22523.5	−1.64642
$573$	−24014.4	−1.75082
$574$	−24280.5	−1.76559
$575$	2697.28	0.195625
$576$	−7486.65	−0.541569
$577$	11585.1	0.835868	0.417934	−	0.908477i	$-0.362754\pi$
$577$	11585.1	0.835868	0.417934	+	0.908477i	$0.362754\pi$
$578$	−10554.3	−0.759514
$579$	−16822.8	−1.20748
$580$	536.089	0.0383791
$581$	−2058.27	−0.146973
$582$	−4302.46	−0.306431
$583$	32962.6	2.34163
$584$	−3077.06	−0.218030
$585$	4157.65	0.293842
$586$	−14753.4	−1.04003
$587$	20195.7	1.42005	0.710023	−	0.704178i	$-0.248684\pi$
$587$	20195.7	1.42005	0.710023	+	0.704178i	$0.248684\pi$
$588$	−611.157	−0.0428634
$589$	−21991.6	−1.53845
$590$	9106.45	0.635435
$591$	782.225	0.0544440
$592$	−8501.73	−0.590235
$593$	11302.9	0.782723	0.391361	−	0.920237i	$-0.372004\pi$
$593$	11302.9	0.782723	0.391361	+	0.920237i	$0.372004\pi$
$594$	−5761.87	−0.398001
$595$	−2435.11	−0.167781
$596$	−9205.13	−0.632646
$597$	4594.99	0.315009
$598$	−5752.90	−0.393400
$599$	5581.81	0.380745	0.190373	−	0.981712i	$-0.439030\pi$
$599$	5581.81	0.380745	0.190373	+	0.981712i	$0.439030\pi$
$600$	−4279.56	−0.291187
$601$	−20623.0	−1.39972	−0.699858	−	0.714282i	$-0.746753\pi$
$601$	−20623.0	−1.39972	−0.699858	+	0.714282i	$0.746753\pi$
$602$	−25335.4	−1.71527
$603$	−12185.7	−0.822949
$604$	−8055.45	−0.542668
$605$	3767.00	0.253141
$606$	38649.6	2.59081
$607$	23358.1	1.56190	0.780951	−	0.624592i	$-0.214735\pi$
$607$	23358.1	1.56190	0.780951	+	0.624592i	$0.214735\pi$
$608$	−23924.6	−1.59584
$609$	−3864.80	−0.257159
$610$	−8707.28	−0.577947
$611$	4391.84	0.290793
$612$	−7066.67	−0.466753
$613$	−14260.6	−0.939611	−0.469805	−	0.882770i	$-0.655676\pi$
$613$	−14260.6	−0.939611	−0.469805	+	0.882770i	$0.655676\pi$
$614$	15667.8	1.02980
$615$	6600.98	0.432808
$616$	5052.45	0.330469
$617$	−13678.5	−0.892507	−0.446253	−	0.894907i	$-0.647242\pi$
$617$	−13678.5	−0.892507	−0.446253	+	0.894907i	$0.647242\pi$
$618$	−48406.6	−3.15081
$619$	17493.3	1.13589	0.567945	−	0.823067i	$-0.307739\pi$
$619$	17493.3	1.13589	0.567945	+	0.823067i	$0.307739\pi$
$620$	−4043.97	−0.261951
$621$	−668.043	−0.0431685
$622$	−39690.4	−2.55859
$623$	−13820.9	−0.888804
$624$	33683.6	2.16093
$625$	12787.1	0.818372
$626$	−13750.1	−0.877897
$627$	36800.1	2.34395
$628$	−772.101	−0.0490608
$629$	−5408.83	−0.342868
$630$	4594.76	0.290571
$631$	8054.40	0.508147	0.254073	−	0.967185i	$-0.418230\pi$
$631$	8054.40	0.508147	0.254073	+	0.967185i	$0.418230\pi$
$632$	880.887	0.0554427
$633$	−25996.1	−1.63231
$634$	−35788.2	−2.24185
$635$	−4757.73	−0.297330
$636$	29873.4	1.86251
$637$	850.280	0.0528874
$638$	−5752.87	−0.356988
$639$	−24655.4	−1.52637
$640$	1812.15	0.111924
$641$	7902.06	0.486915	0.243458	−	0.969912i	$-0.421718\pi$
$641$	7902.06	0.486915	0.243458	+	0.969912i	$0.421718\pi$
$642$	−17606.2	−1.08234
$643$	4695.94	0.288009	0.144004	−	0.989577i	$-0.454002\pi$
$643$	4695.94	0.288009	0.144004	+	0.989577i	$0.454002\pi$
$644$	−2885.97	−0.176589
$645$	6887.76	0.420473
$646$	−17864.4	−1.08803
$647$	16615.3	1.00961	0.504804	−	0.863234i	$-0.331565\pi$
$647$	16615.3	1.00961	0.504804	+	0.863234i	$0.331565\pi$
$648$	4252.73	0.257813
$649$	−44359.5	−2.68299
$650$	−29333.0	−1.77005
$651$	29154.0	1.75520
$652$	20445.7	1.22809
$653$	11189.6	0.670570	0.335285	−	0.942117i	$-0.391167\pi$
$653$	11189.6	0.670570	0.335285	+	0.942117i	$0.391167\pi$
$654$	−20549.3	−1.22866
$655$	−114.900	−0.00685420
$656$	24535.1	1.46027
$657$	13631.2	0.809444
$658$	4853.58	0.287556
$659$	−9639.58	−0.569810	−0.284905	−	0.958556i	$-0.591962\pi$
$659$	−9639.58	−0.569810	−0.284905	+	0.958556i	$0.591962\pi$
$660$	6767.08	0.399103
$661$	−16037.4	−0.943697	−0.471849	−	0.881680i	$-0.656413\pi$
$661$	−16037.4	−0.943697	−0.471849	+	0.881680i	$0.656413\pi$
$662$	−38456.9	−2.25781
$663$	21429.6	1.25529
$664$	563.606	0.0329400
$665$	5272.61	0.307463
$666$	10205.8	0.593795
$667$	−667.000	−0.0387202
$668$	17481.4	1.01254
$669$	1697.47	0.0980988
$670$	−5664.66	−0.326634
$671$	42415.1	2.44026
$672$	31716.6	1.82067
$673$	−7710.03	−0.441604	−0.220802	−	0.975319i	$-0.570868\pi$
$673$	−7710.03	−0.441604	−0.220802	+	0.975319i	$0.570868\pi$
$674$	43192.3	2.46840
$675$	−3406.23	−0.194231
$676$	13788.9	0.784528
$677$	−15905.1	−0.902929	−0.451465	−	0.892289i	$-0.649098\pi$
$677$	−15905.1	−0.902929	−0.451465	+	0.892289i	$0.649098\pi$
$678$	5545.83	0.314139
$679$	3002.83	0.169717
$680$	666.793	0.0376034
$681$	−40662.1	−2.28807
$682$	43396.6	2.43657
$683$	190.097	0.0106499	0.00532493	−	0.999986i	$-0.498305\pi$
$683$	190.097	0.0106499	0.00532493	+	0.999986i	$0.498305\pi$
$684$	15301.1	0.855338
$685$	5472.21	0.305230
$686$	−23831.5	−1.32637
$687$	−5649.27	−0.313731
$688$	25601.1	1.41865
$689$	−41561.7	−2.29808
$690$	1728.43	0.0953628
$691$	−9736.33	−0.536017	−0.268008	−	0.963417i	$-0.586365\pi$
$691$	−9736.33	−0.536017	−0.268008	+	0.963417i	$0.586365\pi$
$692$	−22757.5	−1.25016
$693$	−22382.1	−1.22688
$694$	43180.0	2.36180
$695$	733.770	0.0400482
$696$	1058.28	0.0576349
$697$	15609.3	0.848272
$698$	−32900.2	−1.78408
$699$	−35330.8	−1.91178
$700$	−14715.0	−0.794538
$701$	32948.3	1.77523	0.887617	−	0.460583i	$-0.152360\pi$
$701$	32948.3	1.77523	0.887617	+	0.460583i	$0.152360\pi$
$702$	7264.99	0.390598
$703$	11711.4	0.628315
$704$	16953.1	0.907593
$705$	−1319.51	−0.0704902
$706$	−6653.46	−0.354683
$707$	−26974.8	−1.43493
$708$	−40202.2	−2.13403
$709$	−14455.8	−0.765727	−0.382864	−	0.923805i	$-0.625062\pi$
$709$	−14455.8	−0.765727	−0.382864	+	0.923805i	$0.625062\pi$
$710$	−11461.4	−0.605827
$711$	−3902.29	−0.205833
$712$	3784.51	0.199200
$713$	5031.49	0.264279
$714$	23682.6	1.24132
$715$	−9414.78	−0.492437
$716$	−9024.32	−0.471026
$717$	−31542.8	−1.64294
$718$	24729.0	1.28534
$719$	2369.08	0.122882	0.0614408	−	0.998111i	$-0.480430\pi$
$719$	2369.08	0.122882	0.0614408	+	0.998111i	$0.480430\pi$
$720$	−4642.95	−0.240323
$721$	33784.6	1.74508
$722$	12427.6	0.640591
$723$	−48509.7	−2.49529
$724$	16695.1	0.856999
$725$	−3400.92	−0.174216
$726$	−36635.9	−1.87285
$727$	15117.7	0.771229	0.385614	−	0.922660i	$-0.373990\pi$
$727$	15117.7	0.771229	0.385614	+	0.922660i	$0.373990\pi$
$728$	−6370.50	−0.324322
$729$	−13300.3	−0.675725
$730$	6336.65	0.321274
$731$	16287.5	0.824096
$732$	38440.0	1.94096
$733$	−37122.0	−1.87058	−0.935288	−	0.353886i	$-0.884860\pi$
$733$	−37122.0	−1.87058	−0.935288	+	0.353886i	$0.884860\pi$
$734$	−29029.6	−1.45981
$735$	−255.463	−0.0128203
$736$	5473.75	0.274138
$737$	27593.8	1.37915
$738$	−29452.9	−1.46908
$739$	39017.6	1.94220	0.971099	−	0.238676i	$-0.0767134\pi$
$739$	39017.6	1.94220	0.971099	+	0.238676i	$0.0767134\pi$
$740$	2153.59	0.106983
$741$	−46400.4	−2.30035
$742$	−45931.3	−2.27250
$743$	−17391.7	−0.858732	−0.429366	−	0.903131i	$-0.641263\pi$
$743$	−17391.7	−0.858732	−0.429366	+	0.903131i	$0.641263\pi$
$744$	−7983.08	−0.393379
$745$	−3847.73	−0.189221
$746$	29806.8	1.46287
$747$	−2496.74	−0.122291
$748$	16002.1	0.782213
$749$	12288.0	0.599455
$750$	18206.6	0.886417
$751$	−7359.01	−0.357569	−0.178784	−	0.983888i	$-0.557216\pi$
$751$	−7359.01	−0.357569	−0.178784	+	0.983888i	$0.557216\pi$
$752$	−4904.48	−0.237830
$753$	31629.5	1.53073
$754$	7253.65	0.350348
$755$	−3367.17	−0.162310
$756$	3644.52	0.175331
$757$	−5010.85	−0.240584	−0.120292	−	0.992739i	$-0.538383\pi$
$757$	−5010.85	−0.240584	−0.120292	+	0.992739i	$0.538383\pi$
$758$	−23305.0	−1.11672
$759$	−8419.58	−0.402650
$760$	−1443.77	−0.0689093
$761$	−114.661	−0.00546183	−0.00273092	−	0.999996i	$-0.500869\pi$
$761$	−114.661	−0.00546183	−0.00273092	+	0.999996i	$0.500869\pi$
$762$	46271.2	2.19977
$763$	14342.0	0.680494
$764$	22610.4	1.07070
$765$	−2953.86	−0.139604
$766$	38284.3	1.80583
$767$	55931.8	2.63309
$768$	−36107.0	−1.69648
$769$	−5413.75	−0.253868	−0.126934	−	0.991911i	$-0.540514\pi$
$769$	−5413.75	−0.253868	−0.126934	+	0.991911i	$0.540514\pi$
$770$	−10404.6	−0.486956
$771$	16762.7	0.783002
$772$	15839.2	0.738428
$773$	−25458.6	−1.18458	−0.592291	−	0.805724i	$-0.701776\pi$
$773$	−25458.6	−1.18458	−0.592291	+	0.805724i	$0.701776\pi$
$774$	−30732.5	−1.42721
$775$	25654.7	1.18909
$776$	−822.248	−0.0380373
$777$	−15525.7	−0.716838
$778$	30996.3	1.42837
$779$	−33798.0	−1.55448
$780$	−8532.44	−0.391680
$781$	55830.8	2.55798
$782$	4087.23	0.186904
$783$	842.315	0.0384443
$784$	−949.529	−0.0432548
$785$	−322.737	−0.0146739
$786$	1117.46	0.0507103
$787$	1420.96	0.0643605	0.0321803	−	0.999482i	$-0.489755\pi$
$787$	1420.96	0.0643605	0.0321803	+	0.999482i	$0.489755\pi$
$788$	−736.489	−0.0332949
$789$	27580.3	1.24447
$790$	−1814.03	−0.0816965
$791$	−3870.62	−0.173987
$792$	6128.77	0.274970
$793$	−53480.1	−2.39487
$794$	39147.7	1.74975
$795$	12487.0	0.557069
$796$	−4326.33	−0.192641
$797$	13273.7	0.589935	0.294967	−	0.955507i	$-0.404691\pi$
$797$	13273.7	0.589935	0.294967	+	0.955507i	$0.404691\pi$
$798$	−51278.7	−2.27474
$799$	−3120.24	−0.138156
$800$	27909.7	1.23345
$801$	−16765.2	−0.739537
$802$	−49220.0	−2.16710
$803$	−30867.2	−1.35651
$804$	25007.7	1.09696
$805$	−1206.33	−0.0528169
$806$	−54717.7	−2.39125
$807$	35014.9	1.52736
$808$	7386.37	0.321598
$809$	38732.0	1.68324	0.841622	−	0.540067i	$-0.181601\pi$
$809$	38732.0	1.68324	0.841622	+	0.540067i	$0.181601\pi$
$810$	−8757.72	−0.379895
$811$	−19574.5	−0.847536	−0.423768	−	0.905771i	$-0.639293\pi$
$811$	−19574.5	−0.847536	−0.423768	+	0.905771i	$0.639293\pi$
$812$	3638.83	0.157263
$813$	23577.1	1.01708
$814$	−23110.5	−0.995116
$815$	8546.26	0.367316
$816$	−23931.0	−1.02666
$817$	−35266.4	−1.51018
$818$	21576.9	0.922272
$819$	28221.0	1.20406
$820$	−6215.03	−0.264681
$821$	−31832.6	−1.35319	−0.676593	−	0.736357i	$-0.736545\pi$
$821$	−31832.6	−1.35319	−0.676593	+	0.736357i	$0.736545\pi$
$822$	−53219.9	−2.25822
$823$	−29645.3	−1.25561	−0.627807	−	0.778369i	$-0.716047\pi$
$823$	−29645.3	−1.25561	−0.627807	+	0.778369i	$0.716047\pi$
$824$	−9251.05	−0.391111
$825$	−42930.0	−1.81167
$826$	61812.2	2.60378
$827$	−8088.66	−0.340109	−0.170055	−	0.985435i	$-0.554394\pi$
$827$	−8088.66	−0.340109	−0.170055	+	0.985435i	$0.554394\pi$
$828$	−3500.76	−0.146932
$829$	−8259.42	−0.346033	−0.173017	−	0.984919i	$-0.555351\pi$
$829$	−8259.42	−0.346033	−0.173017	+	0.984919i	$0.555351\pi$
$830$	−1160.64	−0.0485380
$831$	40818.0	1.70392
$832$	−21375.8	−0.890712
$833$	−604.093	−0.0251268
$834$	−7136.27	−0.296293
$835$	7307.19	0.302845
$836$	−34648.5	−1.43343
$837$	−6353.98	−0.262396
$838$	35587.2	1.46699
$839$	8312.62	0.342054	0.171027	−	0.985266i	$-0.445291\pi$
$839$	8312.62	0.342054	0.171027	+	0.985266i	$0.445291\pi$
$840$	1913.99	0.0786178
$841$	841.000	0.0344828
$842$	−4632.10	−0.189588
$843$	52820.4	2.15804
$844$	24476.2	0.998229
$845$	5763.73	0.234649
$846$	5887.53	0.239264
$847$	25569.4	1.03728
$848$	46413.0	1.87952
$849$	15200.5	0.614462
$850$	20840.0	0.840950
$851$	−2679.48	−0.107934
$852$	50598.5	2.03459
$853$	−22001.2	−0.883127	−0.441563	−	0.897230i	$-0.645576\pi$
$853$	−22001.2	−0.883127	−0.441563	+	0.897230i	$0.645576\pi$
$854$	−59102.7	−2.36821
$855$	6395.83	0.255828
$856$	−3364.74	−0.134351
$857$	30071.1	1.19861	0.599305	−	0.800521i	$-0.295444\pi$
$857$	30071.1	1.19861	0.599305	+	0.800521i	$0.295444\pi$
$858$	91563.3	3.64326
$859$	−26238.8	−1.04221	−0.521105	−	0.853493i	$-0.674480\pi$
$859$	−26238.8	−1.04221	−0.521105	+	0.853493i	$0.674480\pi$
$860$	−6485.04	−0.257137
$861$	44805.7	1.77349
$862$	−56130.9	−2.21790
$863$	35783.7	1.41146	0.705730	−	0.708481i	$-0.250619\pi$
$863$	35783.7	1.41146	0.705730	+	0.708481i	$0.250619\pi$
$864$	−6912.48	−0.272184
$865$	−9512.59	−0.373916
$866$	−28787.4	−1.12960
$867$	19476.2	0.762913
$868$	−27449.4	−1.07338
$869$	8836.53	0.344947
$870$	−2179.33	−0.0849267
$871$	−34792.3	−1.35349
$872$	−3927.20	−0.152514
$873$	3642.52	0.141215
$874$	−8849.85	−0.342506
$875$	−12707.0	−0.490944
$876$	−27974.4	−1.07896
$877$	−21927.2	−0.844274	−0.422137	−	0.906532i	$-0.638720\pi$
$877$	−21927.2	−0.844274	−0.422137	+	0.906532i	$0.638720\pi$
$878$	26385.8	1.01421
$879$	27225.1	1.04469
$880$	10513.7	0.402747
$881$	7028.72	0.268790	0.134395	−	0.990928i	$-0.457091\pi$
$881$	7028.72	0.268790	0.134395	+	0.990928i	$0.457091\pi$
$882$	1139.85	0.0435157
$883$	−13934.4	−0.531063	−0.265531	−	0.964102i	$-0.585547\pi$
$883$	−13934.4	−0.531063	−0.265531	+	0.964102i	$0.585547\pi$
$884$	−20176.7	−0.767663
$885$	−16804.5	−0.638278
$886$	−25735.2	−0.975836
$887$	−173.443	−0.00656557	−0.00328278	−	0.999995i	$-0.501045\pi$
$887$	−173.443	−0.00656557	−0.00328278	+	0.999995i	$0.501045\pi$
$888$	4251.33	0.160659
$889$	−32294.2	−1.21835
$890$	−7793.52	−0.293528
$891$	42660.8	1.60403
$892$	−1598.22	−0.0599916
$893$	6756.09	0.253174
$894$	37421.1	1.39994
$895$	−3772.15	−0.140882
$896$	12300.4	0.458625
$897$	10616.0	0.395161
$898$	−32889.7	−1.22221
$899$	−6344.06	−0.235357
$900$	−17849.8	−0.661103
$901$	29528.1	1.09181
$902$	66694.7	2.46196
$903$	46752.3	1.72294
$904$	1059.87	0.0389942
$905$	6978.51	0.256324
$906$	32747.3	1.20084
$907$	7444.39	0.272532	0.136266	−	0.990672i	$-0.456490\pi$
$907$	7444.39	0.272532	0.136266	+	0.990672i	$0.456490\pi$
$908$	38284.7	1.39925
$909$	−32721.2	−1.19394
$910$	13118.9	0.477898
$911$	−7318.54	−0.266162	−0.133081	−	0.991105i	$-0.542487\pi$
$911$	−7318.54	−0.266162	−0.133081	+	0.991105i	$0.542487\pi$
$912$	51816.5	1.88138
$913$	5653.75	0.204942
$914$	73129.5	2.64651
$915$	16067.9	0.580533
$916$	5318.97	0.191860
$917$	−779.909	−0.0280860
$918$	−5161.52	−0.185572
$919$	22320.4	0.801179	0.400590	−	0.916258i	$-0.368805\pi$
$919$	22320.4	0.801179	0.400590	+	0.916258i	$0.368805\pi$
$920$	330.323	0.0118374
$921$	−28912.3	−1.03441
$922$	−29508.7	−1.05403
$923$	−70395.7	−2.51040
$924$	45933.2	1.63538
$925$	−13662.2	−0.485634
$926$	4208.06	0.149336
$927$	40981.7	1.45201
$928$	−6901.69	−0.244137
$929$	11941.1	0.421715	0.210858	−	0.977517i	$-0.432374\pi$
$929$	11941.1	0.421715	0.210858	+	0.977517i	$0.432374\pi$
$930$	16439.7	0.579655
$931$	1308.01	0.0460454
$932$	33265.1	1.16914
$933$	73242.2	2.57003
$934$	−20084.0	−0.703606
$935$	6688.86	0.233956
$936$	−7727.61	−0.269855
$937$	−31194.2	−1.08759	−0.543793	−	0.839219i	$-0.683012\pi$
$937$	−31194.2	−1.08759	−0.543793	+	0.839219i	$0.683012\pi$
$938$	−38450.2	−1.33843
$939$	25373.5	0.881826
$940$	1242.36	0.0431078
$941$	−44879.5	−1.55476	−0.777381	−	0.629030i	$-0.783452\pi$
$941$	−44879.5	−1.55476	−0.777381	+	0.629030i	$0.783452\pi$
$942$	3138.77	0.108563
$943$	7732.72	0.267033
$944$	−62460.4	−2.15351
$945$	1523.41	0.0524406
$946$	69592.2	2.39179
$947$	13898.7	0.476925	0.238462	−	0.971152i	$-0.423357\pi$
$947$	13898.7	0.476925	0.238462	+	0.971152i	$0.423357\pi$
$948$	8008.38	0.274367
$949$	38919.7	1.33128
$950$	−45123.8	−1.54106
$951$	66041.4	2.25188
$952$	4526.01	0.154085
$953$	−17653.8	−0.600066	−0.300033	−	0.953929i	$-0.596998\pi$
$953$	−17653.8	−0.600066	−0.300033	+	0.953929i	$0.596998\pi$
$954$	−55716.0	−1.89085
$955$	9451.10	0.320241
$956$	29698.5	1.00473
$957$	10616.0	0.358585
$958$	49147.4	1.65750
$959$	37143.9	1.25072
$960$	6422.27	0.215914
$961$	18065.2	0.606399
$962$	29139.5	0.976606
$963$	14905.6	0.498783
$964$	45673.4	1.52598
$965$	6620.78	0.220861
$966$	11732.2	0.390762
$967$	7109.81	0.236438	0.118219	−	0.992988i	$-0.462281\pi$
$967$	7109.81	0.236438	0.118219	+	0.992988i	$0.462281\pi$
$968$	−7001.54	−0.232477
$969$	32965.8	1.09289
$970$	1693.27	0.0560491
$971$	−1573.60	−0.0520073	−0.0260037	−	0.999662i	$-0.508278\pi$
$971$	−1573.60	−0.0520073	−0.0260037	+	0.999662i	$0.508278\pi$
$972$	33447.5	1.10373
$973$	4980.64	0.164103
$974$	−24151.6	−0.794525
$975$	54129.3	1.77797
$976$	59722.6	1.95868
$977$	−54554.5	−1.78644	−0.893221	−	0.449619i	$-0.851560\pi$
$977$	−54554.5	−1.78644	−0.893221	+	0.449619i	$0.851560\pi$
$978$	−83116.5	−2.71756
$979$	37964.0	1.23936
$980$	240.527	0.00784014
$981$	17397.3	0.566211
$982$	−47232.6	−1.53488
$983$	1707.43	0.0554002	0.0277001	−	0.999616i	$-0.491182\pi$
$983$	1707.43	0.0554002	0.0277001	+	0.999616i	$0.491182\pi$
$984$	−12268.9	−0.397478
$985$	−307.852	−0.00995834
$986$	−5153.46	−0.166450
$987$	−8956.49	−0.288843
$988$	43687.4	1.40676
$989$	8068.67	0.259422
$990$	−12621.1	−0.405176
$991$	13339.5	0.427591	0.213796	−	0.976878i	$-0.431417\pi$
$991$	13339.5	0.427591	0.213796	+	0.976878i	$0.431417\pi$
$992$	52062.7	1.66632
$993$	70966.0	2.26791
$994$	−77796.8	−2.48246
$995$	−1808.40	−0.0576182
$996$	5123.89	0.163009
$997$	−969.143	−0.0307854	−0.0153927	−	0.999882i	$-0.504900\pi$
$997$	−969.143	−0.0307854	−0.0153927	+	0.999882i	$0.504900\pi$
$998$	43486.9	1.37931
$999$	3383.76	0.107165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.32	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.32	✓	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)

\(f(q)\)	\(=\)	\(q+3.82755 q^{2} -7.06313 q^{3} +6.65016 q^{4} +2.77976 q^{5} -27.0345 q^{6} +18.8683 q^{7} -5.16659 q^{8} +22.8877 q^{9} +O(q^{10})\)	\(q+3.82755 q^{2} -7.06313 q^{3} +6.65016 q^{4} +2.77976 q^{5} -27.0345 q^{6} +18.8683 q^{7} -5.16659 q^{8} +22.8877 q^{9} +10.6397 q^{10} -51.8281 q^{11} -46.9709 q^{12} +65.3488 q^{13} +72.2193 q^{14} -19.6338 q^{15} -72.9767 q^{16} -46.4280 q^{17} +87.6041 q^{18} +100.528 q^{19} +18.4858 q^{20} -133.269 q^{21} -198.375 q^{22} -23.0000 q^{23} +36.4923 q^{24} -117.273 q^{25} +250.126 q^{26} +29.0454 q^{27} +125.477 q^{28} +29.0000 q^{29} -75.1493 q^{30} -218.761 q^{31} -237.989 q^{32} +366.069 q^{33} -177.705 q^{34} +52.4492 q^{35} +152.207 q^{36} +116.499 q^{37} +384.776 q^{38} -461.567 q^{39} -14.3619 q^{40} -336.205 q^{41} -510.094 q^{42} -350.812 q^{43} -344.665 q^{44} +63.6224 q^{45} -88.0337 q^{46} +67.2061 q^{47} +515.443 q^{48} +13.0114 q^{49} -448.868 q^{50} +327.927 q^{51} +434.580 q^{52} -635.998 q^{53} +111.173 q^{54} -144.070 q^{55} -97.4847 q^{56} -710.042 q^{57} +110.999 q^{58} +855.896 q^{59} -130.568 q^{60} -818.379 q^{61} -837.318 q^{62} +431.852 q^{63} -327.103 q^{64} +181.654 q^{65} +1401.15 q^{66} -532.409 q^{67} -308.753 q^{68} +162.452 q^{69} +200.752 q^{70} -1077.23 q^{71} -118.252 q^{72} +595.569 q^{73} +445.907 q^{74} +828.314 q^{75} +668.527 q^{76} -977.907 q^{77} -1766.67 q^{78} -170.497 q^{79} -202.857 q^{80} -823.120 q^{81} -1286.84 q^{82} -109.087 q^{83} -886.259 q^{84} -129.058 q^{85} -1342.75 q^{86} -204.831 q^{87} +267.775 q^{88} -732.497 q^{89} +243.518 q^{90} +1233.02 q^{91} -152.954 q^{92} +1545.13 q^{93} +257.235 q^{94} +279.443 q^{95} +1680.95 q^{96} +159.147 q^{97} +49.8018 q^{98} -1186.23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 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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