LMFDB - Embedded newform 667.4.a.b.1.27

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			1.27
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)

$f(q)$	$=$	$q+2.67771 q^{2} -1.01618 q^{3} -0.829880 q^{4} +17.5005 q^{5} -2.72103 q^{6} +31.3833 q^{7} -23.6438 q^{8} -25.9674 q^{9} +O(q^{10})$	\(q+2.67771 q^{2} -1.01618 q^{3} -0.829880 q^{4} +17.5005 q^{5} -2.72103 q^{6} +31.3833 q^{7} -23.6438 q^{8} -25.9674 q^{9} +46.8612 q^{10} -68.4067 q^{11} +0.843305 q^{12} -41.0352 q^{13} +84.0353 q^{14} -17.7836 q^{15} -56.6723 q^{16} -130.838 q^{17} -69.5331 q^{18} -67.0841 q^{19} -14.5233 q^{20} -31.8910 q^{21} -183.173 q^{22} -23.0000 q^{23} +24.0263 q^{24} +181.267 q^{25} -109.880 q^{26} +53.8243 q^{27} -26.0444 q^{28} +29.0000 q^{29} -47.6193 q^{30} +121.784 q^{31} +37.3990 q^{32} +69.5134 q^{33} -350.345 q^{34} +549.223 q^{35} +21.5498 q^{36} -282.944 q^{37} -179.632 q^{38} +41.6991 q^{39} -413.779 q^{40} +311.521 q^{41} -85.3948 q^{42} +20.3335 q^{43} +56.7694 q^{44} -454.442 q^{45} -61.5873 q^{46} -448.369 q^{47} +57.5891 q^{48} +641.910 q^{49} +485.380 q^{50} +132.954 q^{51} +34.0543 q^{52} -206.271 q^{53} +144.126 q^{54} -1197.15 q^{55} -742.021 q^{56} +68.1693 q^{57} +77.6535 q^{58} -602.896 q^{59} +14.7583 q^{60} +847.273 q^{61} +326.102 q^{62} -814.942 q^{63} +553.522 q^{64} -718.136 q^{65} +186.137 q^{66} +779.283 q^{67} +108.579 q^{68} +23.3721 q^{69} +1470.66 q^{70} +470.175 q^{71} +613.969 q^{72} +243.586 q^{73} -757.642 q^{74} -184.199 q^{75} +55.6717 q^{76} -2146.83 q^{77} +111.658 q^{78} -155.165 q^{79} -991.792 q^{80} +646.424 q^{81} +834.163 q^{82} -1326.50 q^{83} +26.4657 q^{84} -2289.72 q^{85} +54.4471 q^{86} -29.4692 q^{87} +1617.40 q^{88} +429.604 q^{89} -1216.86 q^{90} -1287.82 q^{91} +19.0872 q^{92} -123.754 q^{93} -1200.60 q^{94} -1174.00 q^{95} -38.0040 q^{96} -907.047 q^{97} +1718.85 q^{98} +1776.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.67771	0.946713	0.473356	−	0.880871i	$-0.343042\pi$
$2$	2.67771	0.946713	0.473356	+	0.880871i	$0.343042\pi$
$3$	−1.01618	−0.195563	−0.0977817	−	0.995208i	$-0.531175\pi$
$3$	−1.01618	−0.195563	−0.0977817	+	0.995208i	$0.531175\pi$
$4$	−0.829880	−0.103735
$5$	17.5005	1.56529	0.782645	−	0.622468i	$-0.213870\pi$
$5$	17.5005	1.56529	0.782645	+	0.622468i	$0.213870\pi$
$6$	−2.72103	−0.185142
$7$	31.3833	1.69454	0.847269	−	0.531164i	$-0.178245\pi$
$7$	31.3833	1.69454	0.847269	+	0.531164i	$0.178245\pi$
$8$	−23.6438	−1.04492
$9$	−25.9674	−0.961755
$10$	46.8612	1.48188
$11$	−68.4067	−1.87504	−0.937518	−	0.347936i	$-0.886883\pi$
$11$	−68.4067	−1.87504	−0.937518	+	0.347936i	$0.886883\pi$
$12$	0.843305	0.0202868
$13$	−41.0352	−0.875471	−0.437735	−	0.899104i	$-0.644219\pi$
$13$	−41.0352	−0.875471	−0.437735	+	0.899104i	$0.644219\pi$
$14$	84.0353	1.60424
$15$	−17.7836	−0.306114
$16$	−56.6723	−0.885504
$17$	−130.838	−1.86663	−0.933317	−	0.359054i	$-0.883099\pi$
$17$	−130.838	−1.86663	−0.933317	+	0.359054i	$0.883099\pi$
$18$	−69.5331	−0.910506
$19$	−67.0841	−0.810007	−0.405004	−	0.914315i	$-0.632730\pi$
$19$	−67.0841	−0.810007	−0.405004	+	0.914315i	$0.632730\pi$
$20$	−14.5233	−0.162375
$21$	−31.8910	−0.331390
$22$	−183.173	−1.77512
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0263	0.204348
$25$	181.267	1.45014
$26$	−109.880	−0.828820
$27$	53.8243	0.383648
$28$	−26.0444	−0.175783
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−47.6193	−0.289802
$31$	121.784	0.705582	0.352791	−	0.935702i	$-0.385233\pi$
$31$	121.784	0.705582	0.352791	+	0.935702i	$0.385233\pi$
$32$	37.3990	0.206602
$33$	69.5134	0.366689
$34$	−350.345	−1.76717
$35$	549.223	2.65244
$36$	21.5498	0.0997676
$37$	−282.944	−1.25718	−0.628591	−	0.777736i	$-0.716368\pi$
$37$	−282.944	−1.25718	−0.628591	+	0.777736i	$0.716368\pi$
$38$	−179.632	−0.766844
$39$	41.6991	0.171210
$40$	−413.779	−1.63560
$41$	311.521	1.18662	0.593310	−	0.804974i	$-0.297821\pi$
$41$	311.521	1.18662	0.593310	+	0.804974i	$0.297821\pi$
$42$	−85.3948	−0.313731
$43$	20.3335	0.0721122	0.0360561	−	0.999350i	$-0.488521\pi$
$43$	20.3335	0.0721122	0.0360561	+	0.999350i	$0.488521\pi$
$44$	56.7694	0.194507
$45$	−454.442	−1.50543
$46$	−61.5873	−0.197403
$47$	−448.369	−1.39152	−0.695759	−	0.718275i	$-0.744932\pi$
$47$	−448.369	−1.39152	−0.695759	+	0.718275i	$0.744932\pi$
$48$	57.5891	0.173172
$49$	641.910	1.87146
$50$	485.380	1.37286
$51$	132.954	0.365045
$52$	34.0543	0.0908170
$53$	−206.271	−0.534595	−0.267297	−	0.963614i	$-0.586131\pi$
$53$	−206.271	−0.534595	−0.267297	+	0.963614i	$0.586131\pi$
$54$	144.126	0.363204
$55$	−1197.15	−2.93498
$56$	−742.021	−1.77066
$57$	68.1693	0.158408
$58$	77.6535	0.175800
$59$	−602.896	−1.33035	−0.665173	−	0.746689i	$-0.731642\pi$
$59$	−602.896	−1.33035	−0.665173	+	0.746689i	$0.731642\pi$
$60$	14.7583	0.0317547
$61$	847.273	1.77840	0.889199	−	0.457522i	$-0.151263\pi$
$61$	847.273	1.77840	0.889199	+	0.457522i	$0.151263\pi$
$62$	326.102	0.667984
$63$	−814.942	−1.62973
$64$	553.522	1.08110
$65$	−718.136	−1.37037
$66$	186.137	0.347149
$67$	779.283	1.42096	0.710481	−	0.703716i	$-0.248477\pi$
$67$	779.283	1.42096	0.710481	+	0.703716i	$0.248477\pi$
$68$	108.579	0.193635
$69$	23.3721	0.0407778
$70$	1470.66	2.51110
$71$	470.175	0.785909	0.392955	−	0.919558i	$-0.371453\pi$
$71$	470.175	0.785909	0.392955	+	0.919558i	$0.371453\pi$
$72$	613.969	1.00496
$73$	243.586	0.390542	0.195271	−	0.980749i	$-0.437441\pi$
$73$	243.586	0.390542	0.195271	+	0.980749i	$0.437441\pi$
$74$	−757.642	−1.19019
$75$	−184.199	−0.283594
$76$	55.6717	0.0840261
$77$	−2146.83	−3.17732
$78$	111.658	0.162087
$79$	−155.165	−0.220980	−0.110490	−	0.993877i	$-0.535242\pi$
$79$	−155.165	−0.220980	−0.110490	+	0.993877i	$0.535242\pi$
$80$	−991.792	−1.38607
$81$	646.424	0.886727
$82$	834.163	1.12339
$83$	−1326.50	−1.75425	−0.877123	−	0.480265i	$-0.840540\pi$
$83$	−1326.50	−1.75425	−0.877123	+	0.480265i	$0.840540\pi$
$84$	26.4657	0.0343767
$85$	−2289.72	−2.92182
$86$	54.4471	0.0682695
$87$	−29.4692	−0.0363152
$88$	1617.40	1.95926
$89$	429.604	0.511662	0.255831	−	0.966721i	$-0.417651\pi$
$89$	429.604	0.511662	0.255831	+	0.966721i	$0.417651\pi$
$90$	−1216.86	−1.42521
$91$	−1287.82	−1.48352
$92$	19.0872	0.0216302
$93$	−123.754	−0.137986
$94$	−1200.60	−1.31737
$95$	−1174.00	−1.26790
$96$	−38.0040	−0.0404038
$97$	−907.047	−0.949451	−0.474725	−	0.880134i	$-0.657453\pi$
$97$	−907.047	−0.949451	−0.474725	+	0.880134i	$0.657453\pi$
$98$	1718.85	1.77173
$99$	1776.34	1.80333
$100$	−150.430	−0.150430
$101$	−422.196	−0.415942	−0.207971	−	0.978135i	$-0.566686\pi$
$101$	−422.196	−0.415942	−0.207971	+	0.978135i	$0.566686\pi$
$102$	356.013	0.345593
$103$	146.913	0.140542	0.0702708	−	0.997528i	$-0.477614\pi$
$103$	146.913	0.140542	0.0702708	+	0.997528i	$0.477614\pi$
$104$	970.230	0.914797
$105$	−558.108	−0.518721
$106$	−552.334	−0.506108
$107$	−1408.87	−1.27290	−0.636451	−	0.771317i	$-0.719598\pi$
$107$	−1408.87	−1.27290	−0.636451	+	0.771317i	$0.719598\pi$
$108$	−44.6677	−0.0397977
$109$	308.778	0.271335	0.135668	−	0.990754i	$-0.456682\pi$
$109$	308.778	0.271335	0.135668	+	0.990754i	$0.456682\pi$
$110$	−3205.62	−2.77858
$111$	287.522	0.245859
$112$	−1778.56	−1.50052
$113$	−4.69111	−0.00390533	−0.00195267	−	0.999998i	$-0.500622\pi$
$113$	−4.69111	−0.00390533	−0.00195267	+	0.999998i	$0.500622\pi$
$114$	182.538	0.149967
$115$	−402.511	−0.326386
$116$	−24.0665	−0.0192631
$117$	1065.58	0.841989
$118$	−1614.38	−1.25946
$119$	−4106.11	−3.16308
$120$	420.473	0.319864
$121$	3348.48	2.51576
$122$	2268.75	1.68363
$123$	−316.561	−0.232060
$124$	−101.066	−0.0731936
$125$	984.700	0.704594
$126$	−2182.18	−1.54289
$127$	−344.710	−0.240851	−0.120425	−	0.992722i	$-0.538426\pi$
$127$	−344.710	−0.240851	−0.120425	+	0.992722i	$0.538426\pi$
$128$	1182.98	0.816886
$129$	−20.6624	−0.0141025
$130$	−1922.96	−1.29734
$131$	1922.70	1.28234	0.641171	−	0.767398i	$-0.278449\pi$
$131$	1922.70	1.28234	0.641171	+	0.767398i	$0.278449\pi$
$132$	−57.6878	−0.0380384
$133$	−2105.32	−1.37259
$134$	2086.69	1.34524
$135$	941.951	0.600520
$136$	3093.50	1.95048
$137$	−373.441	−0.232885	−0.116442	−	0.993197i	$-0.537149\pi$
$137$	−373.441	−0.232885	−0.116442	+	0.993197i	$0.537149\pi$
$138$	62.5836	0.0386049
$139$	1396.65	0.852244	0.426122	−	0.904666i	$-0.359879\pi$
$139$	1396.65	0.852244	0.426122	+	0.904666i	$0.359879\pi$
$140$	−455.789	−0.275151
$141$	455.623	0.272130
$142$	1258.99	0.744030
$143$	2807.08	1.64154
$144$	1471.63	0.851638
$145$	507.514	0.290667
$146$	652.252	0.369731
$147$	−652.295	−0.365989
$148$	234.810	0.130414
$149$	−1726.30	−0.949152	−0.474576	−	0.880215i	$-0.657399\pi$
$149$	−1726.30	−0.949152	−0.474576	+	0.880215i	$0.657399\pi$
$150$	−493.232	−0.268482
$151$	−1038.53	−0.559696	−0.279848	−	0.960044i	$-0.590284\pi$
$151$	−1038.53	−0.559696	−0.279848	+	0.960044i	$0.590284\pi$
$152$	1586.12	0.846393
$153$	3397.51	1.79524
$154$	−5748.58	−3.00801
$155$	2131.28	1.10444
$156$	−34.6052	−0.0177605
$157$	−2409.98	−1.22508	−0.612540	−	0.790439i	$-0.709852\pi$
$157$	−2409.98	−1.22508	−0.612540	+	0.790439i	$0.709852\pi$
$158$	−415.486	−0.209204
$159$	209.608	0.104547
$160$	654.500	0.323392
$161$	−721.815	−0.353336
$162$	1730.94	0.839476
$163$	−1038.79	−0.499167	−0.249583	−	0.968353i	$-0.580294\pi$
$163$	−1038.79	−0.499167	−0.249583	+	0.968353i	$0.580294\pi$
$164$	−258.525	−0.123094
$165$	1216.52	0.573974
$166$	−3551.98	−1.66077
$167$	1946.70	0.902039	0.451020	−	0.892514i	$-0.351060\pi$
$167$	1946.70	0.902039	0.451020	+	0.892514i	$0.351060\pi$
$168$	754.025	0.346276
$169$	−513.111	−0.233551
$170$	−6131.20	−2.76613
$171$	1742.00	0.779028
$172$	−16.8743	−0.00748056
$173$	−1076.15	−0.472938	−0.236469	−	0.971639i	$-0.575990\pi$
$173$	−1076.15	−0.472938	−0.236469	+	0.971639i	$0.575990\pi$
$174$	−78.9098	−0.0343801
$175$	5688.75	2.45731
$176$	3876.76	1.66035
$177$	612.650	0.260167
$178$	1150.35	0.484397
$179$	117.274	0.0489691	0.0244845	−	0.999700i	$-0.492206\pi$
$179$	117.274	0.0489691	0.0244845	+	0.999700i	$0.492206\pi$
$180$	377.132	0.156165
$181$	3620.94	1.48697	0.743487	−	0.668750i	$-0.233170\pi$
$181$	3620.94	1.48697	0.743487	+	0.668750i	$0.233170\pi$
$182$	−3448.41	−1.40447
$183$	−860.980	−0.347790
$184$	543.808	0.217881
$185$	−4951.66	−1.96786
$186$	−331.378	−0.130633
$187$	8950.17	3.50001
$188$	372.093	0.144349
$189$	1689.18	0.650105
$190$	−3143.64	−1.20033
$191$	675.805	0.256018	0.128009	−	0.991773i	$-0.459141\pi$
$191$	675.805	0.256018	0.128009	+	0.991773i	$0.459141\pi$
$192$	−562.476	−0.211423
$193$	−1326.15	−0.494604	−0.247302	−	0.968938i	$-0.579544\pi$
$193$	−1326.15	−0.494604	−0.247302	+	0.968938i	$0.579544\pi$
$194$	−2428.81	−0.898857
$195$	729.754	0.267994
$196$	−532.708	−0.194136
$197$	−4592.15	−1.66080	−0.830399	−	0.557168i	$-0.811888\pi$
$197$	−4592.15	−1.66080	−0.830399	+	0.557168i	$0.811888\pi$
$198$	4756.53	1.70723
$199$	−2684.69	−0.956344	−0.478172	−	0.878266i	$-0.658700\pi$
$199$	−2684.69	−0.956344	−0.478172	+	0.878266i	$0.658700\pi$
$200$	−4285.85	−1.51528
$201$	−791.890	−0.277888
$202$	−1130.52	−0.393777
$203$	910.115	0.314668
$204$	−110.336	−0.0378680
$205$	5451.77	1.85741
$206$	393.391	0.133053
$207$	597.250	0.200540
$208$	2325.56	0.775233
$209$	4589.00	1.51879
$210$	−1494.45	−0.491080
$211$	1210.18	0.394844	0.197422	−	0.980319i	$-0.436743\pi$
$211$	1210.18	0.394844	0.197422	+	0.980319i	$0.436743\pi$
$212$	171.180	0.0554562
$213$	−477.782	−0.153695
$214$	−3772.54	−1.20507
$215$	355.845	0.112877
$216$	−1272.61	−0.400881
$217$	3821.98	1.19564
$218$	826.817	0.256877
$219$	−247.526	−0.0763757
$220$	993.491	0.304460
$221$	5368.95	1.63418
$222$	769.899	0.232758
$223$	−1676.43	−0.503416	−0.251708	−	0.967803i	$-0.580992\pi$
$223$	−1676.43	−0.503416	−0.251708	+	0.967803i	$0.580992\pi$
$224$	1173.70	0.350095
$225$	−4707.03	−1.39468
$226$	−12.5614	−0.00369723
$227$	3528.58	1.03172	0.515859	−	0.856673i	$-0.327473\pi$
$227$	3528.58	1.03172	0.515859	+	0.856673i	$0.327473\pi$
$228$	−56.5723	−0.0164324
$229$	−3047.87	−0.879516	−0.439758	−	0.898116i	$-0.644936\pi$
$229$	−3047.87	−0.879516	−0.439758	+	0.898116i	$0.644936\pi$
$230$	−1077.81	−0.308994
$231$	2181.56	0.621368
$232$	−685.671	−0.194037
$233$	90.7611	0.0255191	0.0127596	−	0.999919i	$-0.495938\pi$
$233$	90.7611	0.0255191	0.0127596	+	0.999919i	$0.495938\pi$
$234$	2853.30	0.797121
$235$	−7846.68	−2.17813
$236$	500.331	0.138003
$237$	157.675	0.0432156
$238$	−10995.0	−2.99453
$239$	−3521.78	−0.953159	−0.476579	−	0.879132i	$-0.658123\pi$
$239$	−3521.78	−0.953159	−0.476579	+	0.879132i	$0.658123\pi$
$240$	1007.84	0.271065
$241$	1620.53	0.433142	0.216571	−	0.976267i	$-0.430513\pi$
$241$	1620.53	0.433142	0.216571	+	0.976267i	$0.430513\pi$
$242$	8966.25	2.38170
$243$	−2110.14	−0.557059
$244$	−703.135	−0.184482
$245$	11233.7	2.92938
$246$	−847.658	−0.219694
$247$	2752.81	0.709138
$248$	−2879.44	−0.737277
$249$	1347.96	0.343067
$250$	2636.74	0.667048
$251$	3628.41	0.912442	0.456221	−	0.889866i	$-0.349203\pi$
$251$	3628.41	0.912442	0.456221	+	0.889866i	$0.349203\pi$
$252$	676.304	0.169060
$253$	1573.35	0.390972
$254$	−923.032	−0.228016
$255$	2326.76	0.571402
$256$	−1260.50	−0.307740
$257$	677.105	0.164345	0.0821725	−	0.996618i	$-0.473814\pi$
$257$	677.105	0.164345	0.0821725	+	0.996618i	$0.473814\pi$
$258$	−55.3279	−0.0133510
$259$	−8879.72	−2.13034
$260$	595.967	0.142155
$261$	−753.054	−0.178593
$262$	5148.42	1.21401
$263$	−5917.68	−1.38745	−0.693726	−	0.720239i	$-0.744032\pi$
$263$	−5917.68	−1.38745	−0.693726	+	0.720239i	$0.744032\pi$
$264$	−1643.56	−0.383160
$265$	−3609.84	−0.836796
$266$	−5637.43	−1.29945
$267$	−436.554	−0.100062
$268$	−646.711	−0.147404
$269$	−2088.11	−0.473288	−0.236644	−	0.971596i	$-0.576047\pi$
$269$	−2088.11	−0.473288	−0.236644	+	0.971596i	$0.576047\pi$
$270$	2522.27	0.568520
$271$	1029.32	0.230725	0.115362	−	0.993323i	$-0.463197\pi$
$271$	1029.32	0.230725	0.115362	+	0.993323i	$0.463197\pi$
$272$	7414.86	1.65291
$273$	1308.65	0.290122
$274$	−999.966	−0.220475
$275$	−12399.9	−2.71906
$276$	−19.3960	−0.00423008
$277$	−4983.70	−1.08102	−0.540508	−	0.841339i	$-0.681768\pi$
$277$	−4983.70	−1.08102	−0.540508	+	0.841339i	$0.681768\pi$
$278$	3739.81	0.806830
$279$	−3162.41	−0.678597
$280$	−12985.7	−2.77159
$281$	−3008.32	−0.638652	−0.319326	−	0.947645i	$-0.603457\pi$
$281$	−3008.32	−0.638652	−0.319326	+	0.947645i	$0.603457\pi$
$282$	1220.02	0.257629
$283$	4416.68	0.927718	0.463859	−	0.885909i	$-0.346464\pi$
$283$	4416.68	0.927718	0.463859	+	0.885909i	$0.346464\pi$
$284$	−390.189	−0.0815263
$285$	1193.00	0.247954
$286$	7516.55	1.55407
$287$	9776.56	2.01077
$288$	−971.153	−0.198700
$289$	12205.5	2.48432
$290$	1358.97	0.275178
$291$	921.721	0.185678
$292$	−202.147	−0.0405129
$293$	−6832.42	−1.36230	−0.681151	−	0.732143i	$-0.738520\pi$
$293$	−6832.42	−1.36230	−0.681151	+	0.732143i	$0.738520\pi$
$294$	−1746.66	−0.346486
$295$	−10551.0	−2.08238
$296$	6689.89	1.31365
$297$	−3681.94	−0.719353
$298$	−4622.51	−0.898574
$299$	943.810	0.182548
$300$	152.863	0.0294186
$301$	638.131	0.122197
$302$	−2780.87	−0.529872
$303$	429.026	0.0813430
$304$	3801.81	0.717265
$305$	14827.7	2.78371
$306$	9097.54	1.69958
$307$	−7680.64	−1.42787	−0.713937	−	0.700210i	$-0.753090\pi$
$307$	−7680.64	−1.42787	−0.713937	+	0.700210i	$0.753090\pi$
$308$	1781.61	0.329599
$309$	−149.290	−0.0274848
$310$	5706.94	1.04559
$311$	5559.20	1.01361	0.506806	−	0.862060i	$-0.330826\pi$
$311$	5559.20	1.01361	0.506806	+	0.862060i	$0.330826\pi$
$312$	−985.926	−0.178901
$313$	−6088.09	−1.09942	−0.549711	−	0.835355i	$-0.685262\pi$
$313$	−6088.09	−1.09942	−0.549711	+	0.835355i	$0.685262\pi$
$314$	−6453.23	−1.15980
$315$	−14261.9	−2.55100
$316$	128.768	0.0229233
$317$	−4908.68	−0.869712	−0.434856	−	0.900500i	$-0.643201\pi$
$317$	−4908.68	−0.869712	−0.434856	+	0.900500i	$0.643201\pi$
$318$	561.269	0.0989761
$319$	−1983.79	−0.348186
$320$	9686.90	1.69223
$321$	1431.66	0.248933
$322$	−1932.81	−0.334507
$323$	8777.11	1.51199
$324$	−536.455	−0.0919847
$325$	−7438.33	−1.26955
$326$	−2781.57	−0.472568
$327$	−313.773	−0.0530633
$328$	−7365.56	−1.23992
$329$	−14071.3	−2.35798
$330$	3257.48	0.543389
$331$	−7141.71	−1.18593	−0.592966	−	0.805227i	$-0.702043\pi$
$331$	−7141.71	−1.18593	−0.592966	+	0.805227i	$0.702043\pi$
$332$	1100.84	0.181977
$333$	7347.32	1.20910
$334$	5212.71	0.853972
$335$	13637.8	2.22422
$336$	1807.33	0.293447
$337$	−4552.60	−0.735892	−0.367946	−	0.929847i	$-0.619939\pi$
$337$	−4552.60	−0.735892	−0.367946	+	0.929847i	$0.619939\pi$
$338$	−1373.96	−0.221105
$339$	4.76700	0.000763740 0
$340$	1900.19	0.303095
$341$	−8330.84	−1.32299
$342$	4664.56	0.737516
$343$	9380.79	1.47672
$344$	−480.761	−0.0753515
$345$	409.023	0.0638291
$346$	−2881.62	−0.447736
$347$	6334.23	0.979941	0.489970	−	0.871739i	$-0.337008\pi$
$347$	6334.23	0.979941	0.489970	+	0.871739i	$0.337008\pi$
$348$	24.4559	0.00376716
$349$	2188.77	0.335708	0.167854	−	0.985812i	$-0.446316\pi$
$349$	2188.77	0.335708	0.167854	+	0.985812i	$0.446316\pi$
$350$	15232.8	2.32637
$351$	−2208.69	−0.335872
$352$	−2558.34	−0.387386
$353$	7438.79	1.12161	0.560803	−	0.827949i	$-0.310492\pi$
$353$	7438.79	1.12161	0.560803	+	0.827949i	$0.310492\pi$
$354$	1640.50	0.246303
$355$	8228.30	1.23018
$356$	−356.520	−0.0530773
$357$	4172.54	0.618583
$358$	314.025	0.0463597
$359$	3779.19	0.555594	0.277797	−	0.960640i	$-0.410396\pi$
$359$	3779.19	0.555594	0.277797	+	0.960640i	$0.410396\pi$
$360$	10744.7	1.57305
$361$	−2358.73	−0.343888
$362$	9695.82	1.40774
$363$	−3402.65	−0.491991
$364$	1068.74	0.153893
$365$	4262.87	0.611312
$366$	−2305.45	−0.329257
$367$	12182.5	1.73275	0.866376	−	0.499392i	$-0.166443\pi$
$367$	12182.5	1.73275	0.866376	+	0.499392i	$0.166443\pi$
$368$	1303.46	0.184640
$369$	−8089.39	−1.14124
$370$	−13259.1	−1.86299
$371$	−6473.46	−0.905891
$372$	102.701	0.0143140
$373$	−1348.24	−0.187156	−0.0935778	−	0.995612i	$-0.529830\pi$
$373$	−1348.24	−0.187156	−0.0935778	+	0.995612i	$0.529830\pi$
$374$	23965.9	3.31350
$375$	−1000.63	−0.137793
$376$	10601.2	1.45403
$377$	−1190.02	−0.162571
$378$	4523.14	0.615463
$379$	−5507.30	−0.746414	−0.373207	−	0.927748i	$-0.621742\pi$
$379$	−5507.30	−0.746414	−0.373207	+	0.927748i	$0.621742\pi$
$380$	974.282	0.131525
$381$	350.286	0.0471016
$382$	1809.61	0.242376
$383$	−4100.77	−0.547101	−0.273551	−	0.961858i	$-0.588198\pi$
$383$	−4100.77	−0.547101	−0.273551	+	0.961858i	$0.588198\pi$
$384$	−1202.12	−0.159753
$385$	−37570.5	−4.97343
$386$	−3551.05	−0.468248
$387$	−528.007	−0.0693543
$388$	752.740	0.0984912
$389$	−9850.74	−1.28394	−0.641970	−	0.766730i	$-0.721882\pi$
$389$	−9850.74	−1.28394	−0.641970	+	0.766730i	$0.721882\pi$
$390$	1954.07	0.253713
$391$	3009.26	0.389220
$392$	−15177.2	−1.95552
$393$	−1953.80	−0.250779
$394$	−12296.4	−1.57230
$395$	−2715.46	−0.345897
$396$	−1474.15	−0.187068
$397$	11201.6	1.41610	0.708048	−	0.706164i	$-0.249576\pi$
$397$	11201.6	1.41610	0.708048	+	0.706164i	$0.249576\pi$
$398$	−7188.81	−0.905383
$399$	2139.38	0.268428
$400$	−10272.8	−1.28410
$401$	1155.37	0.143882	0.0719410	−	0.997409i	$-0.477081\pi$
$401$	1155.37	0.143882	0.0719410	+	0.997409i	$0.477081\pi$
$402$	−2120.45	−0.263081
$403$	−4997.43	−0.617717
$404$	350.372	0.0431477
$405$	11312.7	1.38799
$406$	2437.02	0.297900
$407$	19355.3	2.35726
$408$	−3143.55	−0.381443
$409$	−12060.8	−1.45811	−0.729057	−	0.684453i	$-0.760041\pi$
$409$	−12060.8	−1.45811	−0.729057	+	0.684453i	$0.760041\pi$
$410$	14598.3	1.75843
$411$	379.482	0.0455438
$412$	−121.920	−0.0145791
$413$	−18920.9	−2.25432
$414$	1599.26	0.189854
$415$	−23214.4	−2.74591
$416$	−1534.67	−0.180874
$417$	−1419.24	−0.166668
$418$	12288.0	1.43786
$419$	−11637.8	−1.35690	−0.678451	−	0.734645i	$-0.737349\pi$
$419$	−11637.8	−1.35690	−0.678451	+	0.734645i	$0.737349\pi$
$420$	463.162	0.0538095
$421$	−5041.16	−0.583589	−0.291795	−	0.956481i	$-0.594252\pi$
$421$	−5041.16	−0.583589	−0.291795	+	0.956481i	$0.594252\pi$
$422$	3240.50	0.373804
$423$	11643.0	1.33830
$424$	4877.04	0.558609
$425$	−23716.5	−2.70687
$426$	−1279.36	−0.145505
$427$	26590.2	3.01356
$428$	1169.19	0.132044
$429$	−2852.50	−0.321025
$430$	952.850	0.106862
$431$	12688.1	1.41801	0.709005	−	0.705203i	$-0.249144\pi$
$431$	12688.1	1.41801	0.709005	+	0.705203i	$0.249144\pi$
$432$	−3050.34	−0.339722
$433$	11098.0	1.23172	0.615860	−	0.787855i	$-0.288808\pi$
$433$	11098.0	1.23172	0.615860	+	0.787855i	$0.288808\pi$
$434$	10234.2	1.13192
$435$	−515.724	−0.0568439
$436$	−256.249	−0.0281470
$437$	1542.93	0.168898
$438$	−662.804	−0.0723059
$439$	17139.9	1.86343	0.931713	−	0.363195i	$-0.118314\pi$
$439$	17139.9	1.86343	0.931713	+	0.363195i	$0.118314\pi$
$440$	28305.2	3.06682
$441$	−16668.7	−1.79988
$442$	14376.5	1.54710
$443$	1969.11	0.211186	0.105593	−	0.994409i	$-0.466326\pi$
$443$	1969.11	0.211186	0.105593	+	0.994409i	$0.466326\pi$
$444$	−238.608	−0.0255042
$445$	7518.28	0.800901
$446$	−4488.98	−0.476591
$447$	1754.22	0.185619
$448$	17371.3	1.83196
$449$	−1224.35	−0.128687	−0.0643435	−	0.997928i	$-0.520495\pi$
$449$	−1224.35	−0.128687	−0.0643435	+	0.997928i	$0.520495\pi$
$450$	−12604.0	−1.32036
$451$	−21310.1	−2.22496
$452$	3.89306	0.000405119 0
$453$	1055.33	0.109456
$454$	9448.51	0.976741
$455$	−22537.5	−2.32214
$456$	−1611.78	−0.165524
$457$	−6225.61	−0.637247	−0.318623	−	0.947881i	$-0.603221\pi$
$457$	−6225.61	−0.637247	−0.318623	+	0.947881i	$0.603221\pi$
$458$	−8161.32	−0.832649
$459$	−7042.24	−0.716130
$460$	334.036	0.0338576
$461$	3281.49	0.331527	0.165764	−	0.986165i	$-0.446991\pi$
$461$	3281.49	0.331527	0.165764	+	0.986165i	$0.446991\pi$
$462$	5841.58	0.588257
$463$	7580.45	0.760893	0.380446	−	0.924803i	$-0.375770\pi$
$463$	7580.45	0.760893	0.380446	+	0.924803i	$0.375770\pi$
$464$	−1643.50	−0.164434
$465$	−2165.76	−0.215988
$466$	243.032	0.0241593
$467$	2339.97	0.231865	0.115932	−	0.993257i	$-0.463014\pi$
$467$	2339.97	0.231865	0.115932	+	0.993257i	$0.463014\pi$
$468$	−884.301	−0.0873437
$469$	24456.4	2.40788
$470$	−21011.1	−2.06206
$471$	2448.97	0.239581
$472$	14254.8	1.39010
$473$	−1390.95	−0.135213
$474$	422.207	0.0409127
$475$	−12160.1	−1.17462
$476$	3407.58	0.328122
$477$	5356.32	0.514149
$478$	−9430.29	−0.902367
$479$	15706.8	1.49825	0.749127	−	0.662426i	$-0.230473\pi$
$479$	15706.8	1.49825	0.749127	+	0.662426i	$0.230473\pi$
$480$	−665.088	−0.0632437
$481$	11610.7	1.10063
$482$	4339.30	0.410062
$483$	733.493	0.0690995
$484$	−2778.84	−0.260973
$485$	−15873.8	−1.48617
$486$	−5650.33	−0.527375
$487$	10640.9	0.990112	0.495056	−	0.868861i	$-0.335148\pi$
$487$	10640.9	0.990112	0.495056	+	0.868861i	$0.335148\pi$
$488$	−20032.8	−1.85828
$489$	1055.59	0.0976188
$490$	30080.7	2.77328
$491$	−12631.8	−1.16103	−0.580516	−	0.814249i	$-0.697149\pi$
$491$	−12631.8	−1.16103	−0.580516	+	0.814249i	$0.697149\pi$
$492$	262.707	0.0240727
$493$	−3794.29	−0.346625
$494$	7371.22	0.671350
$495$	31086.9	2.82273
$496$	−6901.77	−0.624796
$497$	14755.6	1.33175
$498$	3609.45	0.324786
$499$	16369.0	1.46849	0.734246	−	0.678884i	$-0.237536\pi$
$499$	16369.0	1.46849	0.734246	+	0.678884i	$0.237536\pi$
$500$	−817.182	−0.0730910
$501$	−1978.20	−0.176406
$502$	9715.81	0.863821
$503$	−5219.06	−0.462637	−0.231318	−	0.972878i	$-0.574304\pi$
$503$	−5219.06	−0.462637	−0.231318	+	0.972878i	$0.574304\pi$
$504$	19268.4	1.70294
$505$	−7388.64	−0.651070
$506$	4212.98	0.370138
$507$	521.411	0.0456740
$508$	286.067	0.0249846
$509$	−3177.41	−0.276692	−0.138346	−	0.990384i	$-0.544179\pi$
$509$	−3177.41	−0.276692	−0.138346	+	0.990384i	$0.544179\pi$
$510$	6230.39	0.540954
$511$	7644.52	0.661788
$512$	−12839.1	−1.10823
$513$	−3610.75	−0.310757
$514$	1813.09	0.155588
$515$	2571.05	0.219989
$516$	17.1473	0.00146292
$517$	30671.5	2.60915
$518$	−23777.3	−2.01682
$519$	1093.56	0.0924893
$520$	16979.5	1.43192
$521$	6092.22	0.512293	0.256147	−	0.966638i	$-0.417547\pi$
$521$	6092.22	0.512293	0.256147	+	0.966638i	$0.417547\pi$
$522$	−2016.46	−0.169077
$523$	−15483.2	−1.29451	−0.647257	−	0.762271i	$-0.724084\pi$
$523$	−15483.2	−1.29451	−0.647257	+	0.762271i	$0.724084\pi$
$524$	−1595.61	−0.133024
$525$	−5780.78	−0.480560
$526$	−15845.8	−1.31352
$527$	−15933.9	−1.31706
$528$	−3939.48	−0.324704
$529$	529.000	0.0434783
$530$	−9666.11	−0.792206
$531$	15655.6	1.27947
$532$	1747.16	0.142385
$533$	−12783.3	−1.03885
$534$	−1168.96	−0.0947304
$535$	−24655.9	−1.99246
$536$	−18425.2	−1.48479
$537$	−119.171	−0.00957656
$538$	−5591.36	−0.448068
$539$	−43911.0	−3.50905
$540$	−781.706	−0.0622949
$541$	−8913.02	−0.708319	−0.354160	−	0.935185i	$-0.615233\pi$
$541$	−8913.02	−0.708319	−0.354160	+	0.935185i	$0.615233\pi$
$542$	2756.21	0.218430
$543$	−3679.52	−0.290798
$544$	−4893.19	−0.385650
$545$	5403.76	0.424719
$546$	3504.19	0.274662
$547$	−6817.20	−0.532875	−0.266437	−	0.963852i	$-0.585847\pi$
$547$	−6817.20	−0.532875	−0.266437	+	0.963852i	$0.585847\pi$
$548$	309.911	0.0241583
$549$	−22001.5	−1.71038
$550$	−33203.3	−2.57417
$551$	−1945.44	−0.150415
$552$	−552.606	−0.0426095
$553$	−4869.58	−0.374458
$554$	−13344.9	−1.02341
$555$	5031.77	0.384841
$556$	−1159.05	−0.0884075
$557$	24721.6	1.88059	0.940293	−	0.340366i	$-0.110551\pi$
$557$	24721.6	1.88059	0.940293	+	0.340366i	$0.110551\pi$
$558$	−8468.02	−0.642437
$559$	−834.388	−0.0631321
$560$	−31125.7	−2.34875
$561$	−9094.96	−0.684473
$562$	−8055.40	−0.604620
$563$	10340.9	0.774101	0.387051	−	0.922059i	$-0.373494\pi$
$563$	10340.9	0.774101	0.387051	+	0.922059i	$0.373494\pi$
$564$	−378.112	−0.0282294
$565$	−82.0967	−0.00611298
$566$	11826.6	0.878282
$567$	20286.9	1.50259
$568$	−11116.8	−0.821212
$569$	−14374.5	−1.05907	−0.529534	−	0.848289i	$-0.677633\pi$
$569$	−14374.5	−1.05907	−0.529534	+	0.848289i	$0.677633\pi$
$570$	3194.50	0.234742
$571$	18763.8	1.37520	0.687600	−	0.726089i	$-0.258664\pi$
$571$	18763.8	1.37520	0.687600	+	0.726089i	$0.258664\pi$
$572$	−2329.54	−0.170285
$573$	−686.738	−0.0500679
$574$	26178.8	1.90362
$575$	−4169.14	−0.302374
$576$	−14373.5	−1.03975
$577$	−16522.6	−1.19210	−0.596052	−	0.802946i	$-0.703265\pi$
$577$	−16522.6	−1.19210	−0.596052	+	0.802946i	$0.703265\pi$
$578$	32682.7	2.35194
$579$	1347.61	0.0967264
$580$	−421.176	−0.0301524
$581$	−41630.0	−2.97264
$582$	2468.10	0.175784
$583$	14110.3	1.00238
$584$	−5759.30	−0.408085
$585$	18648.1	1.31796
$586$	−18295.2	−1.28971
$587$	−1100.83	−0.0774038	−0.0387019	−	0.999251i	$-0.512322\pi$
$587$	−1100.83	−0.0774038	−0.0387019	+	0.999251i	$0.512322\pi$
$588$	541.326	0.0379659
$589$	−8169.77	−0.571527
$590$	−28252.4	−1.97141
$591$	4666.44	0.324792
$592$	16035.1	1.11324
$593$	−8176.23	−0.566201	−0.283101	−	0.959090i	$-0.591363\pi$
$593$	−8176.23	−0.566201	−0.283101	+	0.959090i	$0.591363\pi$
$594$	−9859.17	−0.681021
$595$	−71859.0	−4.95114
$596$	1432.62	0.0984602
$597$	2728.12	0.187026
$598$	2527.25	0.172821
$599$	4180.19	0.285138	0.142569	−	0.989785i	$-0.454464\pi$
$599$	4180.19	0.285138	0.142569	+	0.989785i	$0.454464\pi$
$600$	4355.18	0.296333
$601$	−22416.9	−1.52147	−0.760737	−	0.649060i	$-0.775162\pi$
$601$	−22416.9	−1.52147	−0.760737	+	0.649060i	$0.775162\pi$
$602$	1708.73	0.115685
$603$	−20235.9	−1.36662
$604$	861.853	0.0580601
$605$	58600.0	3.93790
$606$	1148.81	0.0770084
$607$	−4613.43	−0.308490	−0.154245	−	0.988033i	$-0.549294\pi$
$607$	−4613.43	−0.308490	−0.154245	+	0.988033i	$0.549294\pi$
$608$	−2508.87	−0.167349
$609$	−924.839	−0.0615375
$610$	39704.2	2.63537
$611$	18398.9	1.21823
$612$	−2819.52	−0.186230
$613$	13761.7	0.906736	0.453368	−	0.891323i	$-0.350222\pi$
$613$	13761.7	0.906736	0.453368	+	0.891323i	$0.350222\pi$
$614$	−20566.5	−1.35179
$615$	−5539.97	−0.363241
$616$	50759.2	3.32005
$617$	−3541.96	−0.231108	−0.115554	−	0.993301i	$-0.536864\pi$
$617$	−3541.96	−0.231108	−0.115554	+	0.993301i	$0.536864\pi$
$618$	−399.755	−0.0260202
$619$	−15284.4	−0.992461	−0.496231	−	0.868191i	$-0.665283\pi$
$619$	−15284.4	−0.992461	−0.496231	+	0.868191i	$0.665283\pi$
$620$	−1768.71	−0.114569
$621$	−1237.96	−0.0799961
$622$	14885.9	0.959600
$623$	13482.4	0.867031
$624$	−2363.18	−0.151607
$625$	−5425.65	−0.347242
$626$	−16302.1	−1.04084
$627$	−4663.24	−0.297020
$628$	2000.00	0.127084
$629$	37019.7	2.34670
$630$	−38189.1	−2.41507
$631$	3189.69	0.201235	0.100618	−	0.994925i	$-0.467918\pi$
$631$	3189.69	0.201235	0.100618	+	0.994925i	$0.467918\pi$
$632$	3668.69	0.230906
$633$	−1229.76	−0.0772171
$634$	−13144.0	−0.823368
$635$	−6032.58	−0.377001
$636$	−173.950	−0.0108452
$637$	−26340.9	−1.63841
$638$	−5312.02	−0.329632
$639$	−12209.2	−0.755852
$640$	20702.7	1.27866
$641$	9138.14	0.563081	0.281540	−	0.959549i	$-0.409155\pi$
$641$	9138.14	0.563081	0.281540	+	0.959549i	$0.409155\pi$
$642$	3833.57	0.235668
$643$	2074.16	0.127211	0.0636057	−	0.997975i	$-0.479740\pi$
$643$	2074.16	0.127211	0.0636057	+	0.997975i	$0.479740\pi$
$644$	599.020	0.0366533
$645$	−361.602	−0.0220745
$646$	23502.5	1.43142
$647$	5537.59	0.336484	0.168242	−	0.985746i	$-0.446191\pi$
$647$	5537.59	0.336484	0.168242	+	0.985746i	$0.446191\pi$
$648$	−15284.0	−0.926559
$649$	41242.2	2.49445
$650$	−19917.7	−1.20190
$651$	−3883.81	−0.233823
$652$	862.069	0.0517811
$653$	15558.2	0.932373	0.466186	−	0.884686i	$-0.345628\pi$
$653$	15558.2	0.932373	0.466186	+	0.884686i	$0.345628\pi$
$654$	−840.193	−0.0502357
$655$	33648.2	2.00724
$656$	−17654.6	−1.05076
$657$	−6325.29	−0.375606
$658$	−37678.8	−2.23233
$659$	−10246.1	−0.605664	−0.302832	−	0.953044i	$-0.597932\pi$
$659$	−10246.1	−0.605664	−0.302832	+	0.953044i	$0.597932\pi$
$660$	−1009.56	−0.0595412
$661$	−581.658	−0.0342267	−0.0171134	−	0.999854i	$-0.505448\pi$
$661$	−581.658	−0.0342267	−0.0171134	+	0.999854i	$0.505448\pi$
$662$	−19123.4	−1.12274
$663$	−5455.81	−0.319587
$664$	31363.6	1.83305
$665$	−36844.1	−2.14850
$666$	19674.0	1.14467
$667$	−667.000	−0.0387202
$668$	−1615.53	−0.0935730
$669$	1703.55	0.0984499
$670$	36518.1	2.10570
$671$	−57959.2	−3.33456
$672$	−1192.69	−0.0684658
$673$	−12806.8	−0.733531	−0.366765	−	0.930313i	$-0.619535\pi$
$673$	−12806.8	−0.733531	−0.366765	+	0.930313i	$0.619535\pi$
$674$	−12190.5	−0.696679
$675$	9756.56	0.556341
$676$	425.820	0.0242274
$677$	−30164.1	−1.71241	−0.856204	−	0.516638i	$-0.827183\pi$
$677$	−30164.1	−1.71241	−0.856204	+	0.516638i	$0.827183\pi$
$678$	12.7646	0.000723043 0
$679$	−28466.1	−1.60888
$680$	54137.8	3.05307
$681$	−3585.67	−0.201767
$682$	−22307.6	−1.25249
$683$	18088.2	1.01336	0.506680	−	0.862134i	$-0.330873\pi$
$683$	18088.2	1.01336	0.506680	+	0.862134i	$0.330873\pi$
$684$	−1445.65	−0.0808125
$685$	−6535.40	−0.364533
$686$	25119.0	1.39803
$687$	3097.18	0.172001
$688$	−1152.34	−0.0638556
$689$	8464.38	0.468022
$690$	1095.24	0.0604279
$691$	14658.4	0.806993	0.403497	−	0.914981i	$-0.367795\pi$
$691$	14658.4	0.806993	0.403497	+	0.914981i	$0.367795\pi$
$692$	893.075	0.0490602
$693$	55747.5	3.05580
$694$	16961.2	0.927723
$695$	24442.0	1.33401
$696$	696.764	0.0379465
$697$	−40758.7	−2.21499
$698$	5860.89	0.317819
$699$	−92.2294	−0.00499061
$700$	−4720.98	−0.254909
$701$	−2.17947	−0.000117429 0	−5.87143e−5	−	1.00000i	$-0.500019\pi$
$701$	−2.17947	−0.000117429 0	−5.87143e−5		1.00000i	$0.500019\pi$
$702$	−5914.23	−0.317975
$703$	18981.0	1.01833
$704$	−37864.6	−2.02710
$705$	7973.62	0.425963
$706$	19918.9	1.06184
$707$	−13249.9	−0.704829
$708$	−508.426	−0.0269884
$709$	−8208.18	−0.434788	−0.217394	−	0.976084i	$-0.569756\pi$
$709$	−8208.18	−0.434788	−0.217394	+	0.976084i	$0.569756\pi$
$710$	22033.0	1.16462
$711$	4029.22	0.212528
$712$	−10157.5	−0.534646
$713$	−2801.03	−0.147124
$714$	11172.8	0.585621
$715$	49125.3	2.56949
$716$	−97.3233	−0.00507981
$717$	3578.75	0.186403
$718$	10119.6	0.525988
$719$	−546.629	−0.0283530	−0.0141765	−	0.999900i	$-0.504513\pi$
$719$	−546.629	−0.0283530	−0.0141765	+	0.999900i	$0.504513\pi$
$720$	25754.2	1.33306
$721$	4610.62	0.238153
$722$	−6315.99	−0.325563
$723$	−1646.74	−0.0847069
$724$	−3004.95	−0.154251
$725$	5256.74	0.269283
$726$	−9111.30	−0.465774
$727$	−7243.23	−0.369514	−0.184757	−	0.982784i	$-0.559150\pi$
$727$	−7243.23	−0.369514	−0.184757	+	0.982784i	$0.559150\pi$
$728$	30449.0	1.55016
$729$	−15309.2	−0.777787
$730$	11414.7	0.578737
$731$	−2660.38	−0.134607
$732$	714.510	0.0360779
$733$	−3532.13	−0.177984	−0.0889918	−	0.996032i	$-0.528365\pi$
$733$	−3532.13	−0.177984	−0.0889918	+	0.996032i	$0.528365\pi$
$734$	32621.1	1.64042
$735$	−11415.5	−0.572879
$736$	−860.176	−0.0430795
$737$	−53308.2	−2.66436
$738$	−21661.0	−1.08042
$739$	10442.5	0.519802	0.259901	−	0.965635i	$-0.416310\pi$
$739$	10442.5	0.519802	0.259901	+	0.965635i	$0.416310\pi$
$740$	4109.28	0.204135
$741$	−2797.34	−0.138681
$742$	−17334.0	−0.857618
$743$	17311.0	0.854751	0.427375	−	0.904074i	$-0.359438\pi$
$743$	17311.0	0.854751	0.427375	+	0.904074i	$0.359438\pi$
$744$	2926.02	0.144184
$745$	−30211.0	−1.48570
$746$	−3610.18	−0.177183
$747$	34445.8	1.68716
$748$	−7427.56	−0.363073
$749$	−44214.9	−2.15698
$750$	−2679.39	−0.130450
$751$	−35459.2	−1.72294	−0.861468	−	0.507812i	$-0.830454\pi$
$751$	−35459.2	−1.72294	−0.861468	+	0.507812i	$0.830454\pi$
$752$	25410.1	1.23220
$753$	−3687.11	−0.178440
$754$	−3186.53	−0.153908
$755$	−18174.7	−0.876088
$756$	−1401.82	−0.0674387
$757$	−32682.5	−1.56918	−0.784588	−	0.620017i	$-0.787126\pi$
$757$	−32682.5	−1.56918	−0.784588	+	0.620017i	$0.787126\pi$
$758$	−14746.9	−0.706639
$759$	−1598.81	−0.0764599
$760$	27758.0	1.32485
$761$	34063.7	1.62261	0.811306	−	0.584622i	$-0.198757\pi$
$761$	34063.7	1.62261	0.811306	+	0.584622i	$0.198757\pi$
$762$	937.964	0.0445917
$763$	9690.46	0.459788
$764$	−560.837	−0.0265581
$765$	59458.1	2.81008
$766$	−10980.7	−0.517948
$767$	24740.0	1.16468
$768$	1280.90	0.0601828
$769$	25422.5	1.19214	0.596072	−	0.802931i	$-0.296727\pi$
$769$	25422.5	1.19214	0.596072	+	0.802931i	$0.296727\pi$
$770$	−100603.	−4.70841
$771$	−688.059	−0.0321399
$772$	1100.55	0.0513077
$773$	5380.67	0.250361	0.125181	−	0.992134i	$-0.460049\pi$
$773$	5380.67	0.250361	0.125181	+	0.992134i	$0.460049\pi$
$774$	−1413.85	−0.0656586
$775$	22075.4	1.02319
$776$	21446.1	0.992100
$777$	9023.37	0.416617
$778$	−26377.4	−1.21552
$779$	−20898.1	−0.961171
$780$	−605.608	−0.0278003
$781$	−32163.2	−1.47361
$782$	8057.93	0.368480
$783$	1560.90	0.0712416
$784$	−36378.5	−1.65718
$785$	−42175.9	−1.91761
$786$	−5231.71	−0.237416
$787$	−11537.3	−0.522566	−0.261283	−	0.965262i	$-0.584146\pi$
$787$	−11537.3	−0.522566	−0.261283	+	0.965262i	$0.584146\pi$
$788$	3810.94	0.172283
$789$	6013.41	0.271335
$790$	−7271.20	−0.327466
$791$	−147.222	−0.00661773
$792$	−41999.6	−1.88433
$793$	−34768.0	−1.55693
$794$	29994.5	1.34064
$795$	3668.24	0.163647
$796$	2227.97	0.0992063
$797$	−38327.1	−1.70341	−0.851704	−	0.524023i	$-0.824431\pi$
$797$	−38327.1	−1.70341	−0.851704	+	0.524023i	$0.824431\pi$
$798$	5728.63	0.254124
$799$	58663.5	2.59746
$800$	6779.20	0.299601
$801$	−11155.7	−0.492094
$802$	3093.76	0.136215
$803$	−16662.9	−0.732280
$804$	657.173	0.0288268
$805$	−12632.1	−0.553073
$806$	−13381.7	−0.584800
$807$	2121.89	0.0925578
$808$	9982.34	0.434626
$809$	4265.56	0.185376	0.0926880	−	0.995695i	$-0.470454\pi$
$809$	4265.56	0.185376	0.0926880	+	0.995695i	$0.470454\pi$
$810$	30292.2	1.31402
$811$	22885.6	0.990902	0.495451	−	0.868636i	$-0.335003\pi$
$811$	22885.6	0.990902	0.495451	+	0.868636i	$0.335003\pi$
$812$	−755.286	−0.0326421
$813$	−1045.97	−0.0451214
$814$	51827.8	2.23165
$815$	−18179.3	−0.781341
$816$	−7534.82	−0.323249
$817$	−1364.05	−0.0584114
$818$	−32295.3	−1.38041
$819$	33441.3	1.42678
$820$	−4524.32	−0.192678
$821$	690.180	0.0293392	0.0146696	−	0.999892i	$-0.495330\pi$
$821$	690.180	0.0293392	0.0146696	+	0.999892i	$0.495330\pi$
$822$	1016.14	0.0431169
$823$	−28642.0	−1.21312	−0.606561	−	0.795037i	$-0.707451\pi$
$823$	−28642.0	−1.21312	−0.606561	+	0.795037i	$0.707451\pi$
$824$	−3473.59	−0.146855
$825$	12600.5	0.531748
$826$	−50664.5	−2.13419
$827$	−10726.9	−0.451042	−0.225521	−	0.974238i	$-0.572408\pi$
$827$	−10726.9	−0.451042	−0.225521	+	0.974238i	$0.572408\pi$
$828$	−495.646	−0.0208030
$829$	12813.3	0.536819	0.268410	−	0.963305i	$-0.413502\pi$
$829$	12813.3	0.536819	0.268410	+	0.963305i	$0.413502\pi$
$830$	−62161.5	−2.59958
$831$	5064.32	0.211407
$832$	−22713.9	−0.946469
$833$	−83986.0	−3.49333
$834$	−3800.31	−0.157787
$835$	34068.3	1.41195
$836$	−3808.32	−0.157552
$837$	6554.94	0.270695
$838$	−31162.5	−1.28460
$839$	−38250.9	−1.57398	−0.786989	−	0.616966i	$-0.788361\pi$
$839$	−38250.9	−1.57398	−0.786989	+	0.616966i	$0.788361\pi$
$840$	13195.8	0.542022
$841$	841.000	0.0344828
$842$	−13498.8	−0.552492
$843$	3056.99	0.124897
$844$	−1004.30	−0.0409592
$845$	−8979.68	−0.365575
$846$	31176.5	1.26699
$847$	105086.	4.26305
$848$	11689.8	0.473386
$849$	−4488.13	−0.181428
$850$	−63505.9	−2.56263
$851$	6507.72	0.262141
$852$	396.501	0.0159436
$853$	−35832.0	−1.43829	−0.719147	−	0.694858i	$-0.755467\pi$
$853$	−35832.0	−1.43829	−0.719147	+	0.694858i	$0.755467\pi$
$854$	71200.8	2.85298
$855$	30485.8	1.21941
$856$	33311.1	1.33008
$857$	−19200.8	−0.765330	−0.382665	−	0.923887i	$-0.624994\pi$
$857$	−19200.8	−0.765330	−0.382665	+	0.923887i	$0.624994\pi$
$858$	−7638.15	−0.303919
$859$	34530.8	1.37157	0.685783	−	0.727807i	$-0.259460\pi$
$859$	34530.8	1.37157	0.685783	+	0.727807i	$0.259460\pi$
$860$	−295.309	−0.0117092
$861$	−9934.72	−0.393234
$862$	33974.9	1.34245
$863$	−36092.9	−1.42366	−0.711829	−	0.702353i	$-0.752133\pi$
$863$	−36092.9	−1.42366	−0.711829	+	0.702353i	$0.752133\pi$
$864$	2012.97	0.0792624
$865$	−18833.2	−0.740285
$866$	29717.2	1.16609
$867$	−12402.9	−0.485842
$868$	−3171.79	−0.124029
$869$	10614.3	0.414345
$870$	−1380.96	−0.0538148
$871$	−31978.0	−1.24401
$872$	−7300.70	−0.283524
$873$	23553.6	0.913139
$874$	4131.52	0.159898
$875$	30903.1	1.19396
$876$	205.417	0.00792284
$877$	2482.11	0.0955701	0.0477850	−	0.998858i	$-0.484784\pi$
$877$	2482.11	0.0955701	0.0477850	+	0.998858i	$0.484784\pi$
$878$	45895.7	1.76413
$879$	6942.95	0.266416
$880$	67845.2	2.59893
$881$	40481.3	1.54807	0.774034	−	0.633144i	$-0.218236\pi$
$881$	40481.3	1.54807	0.774034	+	0.633144i	$0.218236\pi$
$882$	−44634.0	−1.70397
$883$	−19105.3	−0.728137	−0.364068	−	0.931372i	$-0.618613\pi$
$883$	−19105.3	−0.728137	−0.364068	+	0.931372i	$0.618613\pi$
$884$	−4455.58	−0.169522
$885$	10721.7	0.407237
$886$	5272.71	0.199933
$887$	−32157.4	−1.21730	−0.608648	−	0.793440i	$-0.708288\pi$
$887$	−32157.4	−1.21730	−0.608648	+	0.793440i	$0.708288\pi$
$888$	−6798.11	−0.256903
$889$	−10818.1	−0.408130
$890$	20131.8	0.758223
$891$	−44219.8	−1.66265
$892$	1391.23	0.0522219
$893$	30078.4	1.12714
$894$	4697.30	0.175728
$895$	2052.35	0.0766509
$896$	37125.7	1.38424
$897$	−959.079	−0.0356998
$898$	−3278.44	−0.121830
$899$	3531.74	0.131023
$900$	3906.27	0.144677
$901$	26988.0	0.997892
$902$	−57062.3	−2.10639
$903$	−648.454	−0.0238972
$904$	110.916	0.00408076
$905$	63368.2	2.32755
$906$	2825.86	0.103624
$907$	−20381.4	−0.746146	−0.373073	−	0.927802i	$-0.621696\pi$
$907$	−20381.4	−0.746146	−0.373073	+	0.927802i	$0.621696\pi$
$908$	−2928.30	−0.107025
$909$	10963.3	0.400034
$910$	−60348.8	−2.19840
$911$	−47022.2	−1.71012	−0.855058	−	0.518532i	$-0.826479\pi$
$911$	−47022.2	−1.71012	−0.855058	+	0.518532i	$0.826479\pi$
$912$	−3863.31	−0.140271
$913$	90741.6	3.28928
$914$	−16670.4	−0.603290
$915$	−15067.6	−0.544392
$916$	2529.37	0.0912366
$917$	60340.6	2.17298
$918$	−18857.1	−0.677969
$919$	32173.2	1.15484	0.577419	−	0.816448i	$-0.304060\pi$
$919$	32173.2	1.15484	0.577419	+	0.816448i	$0.304060\pi$
$920$	9516.91	0.341047
$921$	7804.90	0.279240
$922$	8786.87	0.313861
$923$	−19293.7	−0.688041
$924$	−1810.43	−0.0644576
$925$	−51288.4	−1.82308
$926$	20298.2	0.720347
$927$	−3814.95	−0.135167
$928$	1084.57	0.0383650
$929$	16858.8	0.595391	0.297695	−	0.954661i	$-0.403782\pi$
$929$	16858.8	0.595391	0.297695	+	0.954661i	$0.403782\pi$
$930$	−5799.27	−0.204479
$931$	−43061.9	−1.51590
$932$	−75.3208	−0.00264723
$933$	−5649.14	−0.198226
$934$	6265.76	0.219509
$935$	156632.	5.47853
$936$	−25194.3	−0.879811
$937$	16061.6	0.559989	0.279994	−	0.960002i	$-0.409667\pi$
$937$	16061.6	0.559989	0.279994	+	0.960002i	$0.409667\pi$
$938$	65487.2	2.27957
$939$	6186.58	0.215007
$940$	6511.80	0.225948
$941$	53880.0	1.86656	0.933282	−	0.359144i	$-0.116931\pi$
$941$	53880.0	1.86656	0.933282	+	0.359144i	$0.116931\pi$
$942$	6557.63	0.226814
$943$	−7164.99	−0.247427
$944$	34167.5	1.17803
$945$	29561.5	1.01760
$946$	−3724.55	−0.128008
$947$	40039.4	1.37392	0.686962	−	0.726694i	$-0.258944\pi$
$947$	40039.4	1.37392	0.686962	+	0.726694i	$0.258944\pi$
$948$	−130.851	−0.00448296
$949$	−9995.60	−0.341908
$950$	−32561.3	−1.11203
$951$	4988.09	0.170084
$952$	97084.3	3.30517
$953$	37326.8	1.26876	0.634382	−	0.773019i	$-0.281254\pi$
$953$	37326.8	1.26876	0.634382	+	0.773019i	$0.281254\pi$
$954$	14342.7	0.486751
$955$	11826.9	0.400743
$956$	2922.65	0.0988759
$957$	2015.89	0.0680924
$958$	42058.3	1.41842
$959$	−11719.8	−0.394632
$960$	−9843.61	−0.330939
$961$	−14959.7	−0.502154
$962$	31090.0	1.04198
$963$	36584.6	1.22422
$964$	−1344.84	−0.0449320
$965$	−23208.3	−0.774199
$966$	1964.08	0.0654174
$967$	−16306.5	−0.542275	−0.271138	−	0.962541i	$-0.587400\pi$
$967$	−16306.5	−0.542275	−0.271138	+	0.962541i	$0.587400\pi$
$968$	−79170.9	−2.62877
$969$	−8919.11	−0.295689
$970$	−42505.3	−1.40697
$971$	50837.9	1.68019	0.840096	−	0.542438i	$-0.182499\pi$
$971$	50837.9	1.68019	0.840096	+	0.542438i	$0.182499\pi$
$972$	1751.16	0.0577865
$973$	43831.3	1.44416
$974$	28493.2	0.937352
$975$	7558.67	0.248278
$976$	−48016.9	−1.57478
$977$	−10375.7	−0.339761	−0.169881	−	0.985465i	$-0.554338\pi$
$977$	−10375.7	−0.339761	−0.169881	+	0.985465i	$0.554338\pi$
$978$	2826.57	0.0924169
$979$	−29387.8	−0.959386
$980$	−9322.66	−0.303879
$981$	−8018.15	−0.260958
$982$	−33824.4	−1.09916
$983$	−13159.6	−0.426985	−0.213493	−	0.976945i	$-0.568484\pi$
$983$	−13159.6	−0.426985	−0.213493	+	0.976945i	$0.568484\pi$
$984$	7484.71	0.242484
$985$	−80364.9	−2.59963
$986$	−10160.0	−0.328154
$987$	14298.9	0.461135
$988$	−2284.50	−0.0735624
$989$	−467.670	−0.0150364
$990$	83241.6	2.67231
$991$	62122.4	1.99130	0.995652	−	0.0931464i	$-0.0296925\pi$
$991$	62122.4	1.99130	0.995652	+	0.0931464i	$0.0296925\pi$
$992$	4554.59	0.145775
$993$	7257.24	0.231925
$994$	39511.3	1.26079
$995$	−46983.3	−1.49696
$996$	−1118.65	−0.0355880
$997$	14843.9	0.471526	0.235763	−	0.971811i	$-0.424241\pi$
$997$	14843.9	0.471526	0.235763	+	0.971811i	$0.424241\pi$
$998$	43831.4	1.39024
$999$	−15229.3	−0.482315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.27	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.27	✓	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)

\(f(q)\)	\(=\)	\(q+2.67771 q^{2} -1.01618 q^{3} -0.829880 q^{4} +17.5005 q^{5} -2.72103 q^{6} +31.3833 q^{7} -23.6438 q^{8} -25.9674 q^{9} +O(q^{10})\)	\(q+2.67771 q^{2} -1.01618 q^{3} -0.829880 q^{4} +17.5005 q^{5} -2.72103 q^{6} +31.3833 q^{7} -23.6438 q^{8} -25.9674 q^{9} +46.8612 q^{10} -68.4067 q^{11} +0.843305 q^{12} -41.0352 q^{13} +84.0353 q^{14} -17.7836 q^{15} -56.6723 q^{16} -130.838 q^{17} -69.5331 q^{18} -67.0841 q^{19} -14.5233 q^{20} -31.8910 q^{21} -183.173 q^{22} -23.0000 q^{23} +24.0263 q^{24} +181.267 q^{25} -109.880 q^{26} +53.8243 q^{27} -26.0444 q^{28} +29.0000 q^{29} -47.6193 q^{30} +121.784 q^{31} +37.3990 q^{32} +69.5134 q^{33} -350.345 q^{34} +549.223 q^{35} +21.5498 q^{36} -282.944 q^{37} -179.632 q^{38} +41.6991 q^{39} -413.779 q^{40} +311.521 q^{41} -85.3948 q^{42} +20.3335 q^{43} +56.7694 q^{44} -454.442 q^{45} -61.5873 q^{46} -448.369 q^{47} +57.5891 q^{48} +641.910 q^{49} +485.380 q^{50} +132.954 q^{51} +34.0543 q^{52} -206.271 q^{53} +144.126 q^{54} -1197.15 q^{55} -742.021 q^{56} +68.1693 q^{57} +77.6535 q^{58} -602.896 q^{59} +14.7583 q^{60} +847.273 q^{61} +326.102 q^{62} -814.942 q^{63} +553.522 q^{64} -718.136 q^{65} +186.137 q^{66} +779.283 q^{67} +108.579 q^{68} +23.3721 q^{69} +1470.66 q^{70} +470.175 q^{71} +613.969 q^{72} +243.586 q^{73} -757.642 q^{74} -184.199 q^{75} +55.6717 q^{76} -2146.83 q^{77} +111.658 q^{78} -155.165 q^{79} -991.792 q^{80} +646.424 q^{81} +834.163 q^{82} -1326.50 q^{83} +26.4657 q^{84} -2289.72 q^{85} +54.4471 q^{86} -29.4692 q^{87} +1617.40 q^{88} +429.604 q^{89} -1216.86 q^{90} -1287.82 q^{91} +19.0872 q^{92} -123.754 q^{93} -1200.60 q^{94} -1174.00 q^{95} -38.0040 q^{96} -907.047 q^{97} +1718.85 q^{98} +1776.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 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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