LMFDB - Embedded newform 667.4.a.b.1.9

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			1.9
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.06003 q^{2} +6.74784 q^{3} +8.48386 q^{4} +12.9697 q^{5} -27.3964 q^{6} -17.1781 q^{7} -1.96449 q^{8} +18.5333 q^{9} +O(q^{10})$	\(q-4.06003 q^{2} +6.74784 q^{3} +8.48386 q^{4} +12.9697 q^{5} -27.3964 q^{6} -17.1781 q^{7} -1.96449 q^{8} +18.5333 q^{9} -52.6574 q^{10} -21.3520 q^{11} +57.2477 q^{12} -19.9634 q^{13} +69.7437 q^{14} +87.5175 q^{15} -59.8950 q^{16} +62.3401 q^{17} -75.2459 q^{18} -55.2829 q^{19} +110.033 q^{20} -115.915 q^{21} +86.6898 q^{22} -23.0000 q^{23} -13.2561 q^{24} +43.2134 q^{25} +81.0520 q^{26} -57.1318 q^{27} -145.737 q^{28} +29.0000 q^{29} -355.324 q^{30} -162.016 q^{31} +258.892 q^{32} -144.080 q^{33} -253.103 q^{34} -222.795 q^{35} +157.234 q^{36} -389.965 q^{37} +224.450 q^{38} -134.710 q^{39} -25.4789 q^{40} -176.862 q^{41} +470.619 q^{42} -193.080 q^{43} -181.147 q^{44} +240.372 q^{45} +93.3807 q^{46} +278.135 q^{47} -404.162 q^{48} -47.9123 q^{49} -175.448 q^{50} +420.661 q^{51} -169.367 q^{52} -167.256 q^{53} +231.957 q^{54} -276.929 q^{55} +33.7463 q^{56} -373.040 q^{57} -117.741 q^{58} -255.400 q^{59} +742.487 q^{60} +119.086 q^{61} +657.789 q^{62} -318.368 q^{63} -571.948 q^{64} -258.919 q^{65} +584.969 q^{66} +296.581 q^{67} +528.884 q^{68} -155.200 q^{69} +904.556 q^{70} +467.761 q^{71} -36.4086 q^{72} +296.963 q^{73} +1583.27 q^{74} +291.597 q^{75} -469.012 q^{76} +366.787 q^{77} +546.926 q^{78} -176.177 q^{79} -776.821 q^{80} -885.916 q^{81} +718.066 q^{82} +432.432 q^{83} -983.408 q^{84} +808.533 q^{85} +783.912 q^{86} +195.687 q^{87} +41.9458 q^{88} +364.145 q^{89} -975.918 q^{90} +342.934 q^{91} -195.129 q^{92} -1093.26 q^{93} -1129.24 q^{94} -717.003 q^{95} +1746.96 q^{96} +895.049 q^{97} +194.525 q^{98} -395.724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.06003	−1.43544	−0.717719	−	0.696333i	$-0.754814\pi$
$2$	−4.06003	−1.43544	−0.717719	+	0.696333i	$0.754814\pi$
$3$	6.74784	1.29862	0.649311	−	0.760523i	$-0.275057\pi$
$3$	6.74784	1.29862	0.649311	+	0.760523i	$0.275057\pi$
$4$	8.48386	1.06048
$5$	12.9697	1.16005	0.580023	−	0.814600i	$-0.303043\pi$
$5$	12.9697	1.16005	0.580023	+	0.814600i	$0.303043\pi$
$6$	−27.3964	−1.86409
$7$	−17.1781	−0.927531	−0.463766	−	0.885958i	$-0.653502\pi$
$7$	−17.1781	−0.927531	−0.463766	+	0.885958i	$0.653502\pi$
$8$	−1.96449	−0.0868191
$9$	18.5333	0.686419
$10$	−52.6574	−1.66517
$11$	−21.3520	−0.585261	−0.292631	−	0.956226i	$-0.594531\pi$
$11$	−21.3520	−0.585261	−0.292631	+	0.956226i	$0.594531\pi$
$12$	57.2477	1.37717
$13$	−19.9634	−0.425911	−0.212956	−	0.977062i	$-0.568309\pi$
$13$	−19.9634	−0.425911	−0.212956	+	0.977062i	$0.568309\pi$
$14$	69.7437	1.33141
$15$	87.5175	1.50646
$16$	−59.8950	−0.935859
$17$	62.3401	0.889393	0.444697	−	0.895681i	$-0.353312\pi$
$17$	62.3401	0.889393	0.444697	+	0.895681i	$0.353312\pi$
$18$	−75.2459	−0.985313
$19$	−55.2829	−0.667514	−0.333757	−	0.942659i	$-0.608316\pi$
$19$	−55.2829	−0.667514	−0.333757	+	0.942659i	$0.608316\pi$
$20$	110.033	1.23021
$21$	−115.915	−1.20451
$22$	86.6898	0.840106
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−13.2561	−0.112745
$25$	43.2134	0.345707
$26$	81.0520	0.611370
$27$	−57.1318	−0.407223
$28$	−145.737	−0.983631
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−355.324	−2.16243
$31$	−162.016	−0.938674	−0.469337	−	0.883019i	$-0.655507\pi$
$31$	−162.016	−0.938674	−0.469337	+	0.883019i	$0.655507\pi$
$32$	258.892	1.43019
$33$	−144.080	−0.760033
$34$	−253.103	−1.27667
$35$	−222.795	−1.07598
$36$	157.234	0.727936
$37$	−389.965	−1.73270	−0.866349	−	0.499439i	$-0.833539\pi$
$37$	−389.965	−1.73270	−0.866349	+	0.499439i	$0.833539\pi$
$38$	224.450	0.958175
$39$	−134.710	−0.553098
$40$	−25.4789	−0.100714
$41$	−176.862	−0.673688	−0.336844	−	0.941560i	$-0.609360\pi$
$41$	−176.862	−0.673688	−0.336844	+	0.941560i	$0.609360\pi$
$42$	470.619	1.72900
$43$	−193.080	−0.684755	−0.342377	−	0.939563i	$-0.611232\pi$
$43$	−193.080	−0.684755	−0.342377	+	0.939563i	$0.611232\pi$
$44$	−181.147	−0.620659
$45$	240.372	0.796278
$46$	93.3807	0.299310
$47$	278.135	0.863195	0.431598	−	0.902066i	$-0.357950\pi$
$47$	278.135	0.863195	0.431598	+	0.902066i	$0.357950\pi$
$48$	−404.162	−1.21533
$49$	−47.9123	−0.139686
$50$	−175.448	−0.496242
$51$	420.661	1.15499
$52$	−169.367	−0.451672
$53$	−167.256	−0.433479	−0.216740	−	0.976229i	$-0.569542\pi$
$53$	−167.256	−0.433479	−0.216740	+	0.976229i	$0.569542\pi$
$54$	231.957	0.584543
$55$	−276.929	−0.678930
$56$	33.7463	0.0805274
$57$	−373.040	−0.866848
$58$	−117.741	−0.266554
$59$	−255.400	−0.563563	−0.281781	−	0.959479i	$-0.590925\pi$
$59$	−255.400	−0.563563	−0.281781	+	0.959479i	$0.590925\pi$
$60$	742.487	1.59758
$61$	119.086	0.249957	0.124978	−	0.992159i	$-0.460114\pi$
$61$	119.086	0.249957	0.124978	+	0.992159i	$0.460114\pi$
$62$	657.789	1.34741
$63$	−318.368	−0.636675
$64$	−571.948	−1.11709
$65$	−258.919	−0.494077
$66$	584.969	1.09098
$67$	296.581	0.540793	0.270397	−	0.962749i	$-0.412845\pi$
$67$	296.581	0.540793	0.270397	+	0.962749i	$0.412845\pi$
$68$	528.884	0.943186
$69$	−155.200	−0.270781
$70$	904.556	1.54450
$71$	467.761	0.781874	0.390937	−	0.920417i	$-0.372151\pi$
$71$	467.761	0.781874	0.390937	+	0.920417i	$0.372151\pi$
$72$	−36.4086	−0.0595943
$73$	296.963	0.476122	0.238061	−	0.971250i	$-0.423488\pi$
$73$	296.963	0.476122	0.238061	+	0.971250i	$0.423488\pi$
$74$	1583.27	2.48718
$75$	291.597	0.448943
$76$	−469.012	−0.707887
$77$	366.787	0.542848
$78$	546.926	0.793938
$79$	−176.177	−0.250904	−0.125452	−	0.992100i	$-0.540038\pi$
$79$	−176.177	−0.250904	−0.125452	+	0.992100i	$0.540038\pi$
$80$	−776.821	−1.08564
$81$	−885.916	−1.21525
$82$	718.066	0.967038
$83$	432.432	0.571874	0.285937	−	0.958248i	$-0.407695\pi$
$83$	432.432	0.571874	0.285937	+	0.958248i	$0.407695\pi$
$84$	−983.408	−1.27736
$85$	808.533	1.03174
$86$	783.912	0.982923
$87$	195.687	0.241148
$88$	41.9458	0.0508118
$89$	364.145	0.433700	0.216850	−	0.976205i	$-0.430422\pi$
$89$	364.145	0.433700	0.216850	+	0.976205i	$0.430422\pi$
$90$	−975.918	−1.14301
$91$	342.934	0.395046
$92$	−195.129	−0.221126
$93$	−1093.26	−1.21898
$94$	−1129.24	−1.23906
$95$	−717.003	−0.774347
$96$	1746.96	1.85727
$97$	895.049	0.936891	0.468446	−	0.883492i	$-0.344814\pi$
$97$	895.049	0.936891	0.468446	+	0.883492i	$0.344814\pi$
$98$	194.525	0.200511
$99$	−395.724	−0.401735
$100$	366.617	0.366617
$101$	−638.146	−0.628692	−0.314346	−	0.949308i	$-0.601785\pi$
$101$	−638.146	−0.628692	−0.314346	+	0.949308i	$0.601785\pi$
$102$	−1707.90	−1.65791
$103$	−279.701	−0.267570	−0.133785	−	0.991010i	$-0.542713\pi$
$103$	−279.701	−0.267570	−0.133785	+	0.991010i	$0.542713\pi$
$104$	39.2179	0.0369773
$105$	−1503.39	−1.39729
$106$	679.065	0.622232
$107$	481.204	0.434764	0.217382	−	0.976087i	$-0.430248\pi$
$107$	481.204	0.434764	0.217382	+	0.976087i	$0.430248\pi$
$108$	−484.698	−0.431853
$109$	−1627.72	−1.43034	−0.715170	−	0.698950i	$-0.753651\pi$
$109$	−1627.72	−1.43034	−0.715170	+	0.698950i	$0.753651\pi$
$110$	1124.34	0.974562
$111$	−2631.42	−2.25012
$112$	1028.88	0.868039
$113$	−934.470	−0.777943	−0.388972	−	0.921250i	$-0.627170\pi$
$113$	−934.470	−0.777943	−0.388972	+	0.921250i	$0.627170\pi$
$114$	1514.55	1.24431
$115$	−298.303	−0.241886
$116$	246.032	0.196927
$117$	−369.988	−0.292354
$118$	1036.93	0.808959
$119$	−1070.88	−0.824940
$120$	−171.928	−0.130790
$121$	−875.092	−0.657470
$122$	−483.492	−0.358798
$123$	−1193.44	−0.874866
$124$	−1374.52	−0.995448
$125$	−1060.75	−0.759010
$126$	1292.58	0.913908
$127$	1004.03	0.701520	0.350760	−	0.936465i	$-0.385923\pi$
$127$	1004.03	0.701520	0.350760	+	0.936465i	$0.385923\pi$
$128$	250.995	0.173321
$129$	−1302.87	−0.889237
$130$	1051.22	0.709217
$131$	1812.33	1.20873	0.604367	−	0.796706i	$-0.293426\pi$
$131$	1812.33	1.20873	0.604367	+	0.796706i	$0.293426\pi$
$132$	−1222.35	−0.806002
$133$	949.656	0.619140
$134$	−1204.13	−0.776276
$135$	−740.983	−0.472397
$136$	−122.467	−0.0772163
$137$	377.182	0.235218	0.117609	−	0.993060i	$-0.462477\pi$
$137$	377.182	0.235218	0.117609	+	0.993060i	$0.462477\pi$
$138$	630.118	0.388690
$139$	−1102.73	−0.672897	−0.336448	−	0.941702i	$-0.609226\pi$
$139$	−1102.73	−0.672897	−0.336448	+	0.941702i	$0.609226\pi$
$140$	−1890.16	−1.14106
$141$	1876.81	1.12096
$142$	−1899.13	−1.12233
$143$	426.258	0.249269
$144$	−1110.05	−0.642392
$145$	376.122	0.215415
$146$	−1205.68	−0.683443
$147$	−323.304	−0.181399
$148$	−3308.41	−1.83750
$149$	−1906.36	−1.04815	−0.524077	−	0.851671i	$-0.675590\pi$
$149$	−1906.36	−1.04815	−0.524077	+	0.851671i	$0.675590\pi$
$150$	−1183.89	−0.644430
$151$	1597.59	0.860993	0.430497	−	0.902592i	$-0.358338\pi$
$151$	1597.59	0.860993	0.430497	+	0.902592i	$0.358338\pi$
$152$	108.603	0.0579530
$153$	1155.37	0.610497
$154$	−1489.17	−0.779224
$155$	−2101.30	−1.08891
$156$	−1142.86	−0.586551
$157$	−2942.40	−1.49572	−0.747862	−	0.663854i	$-0.768920\pi$
$157$	−2942.40	−1.49572	−0.747862	+	0.663854i	$0.768920\pi$
$158$	715.283	0.360157
$159$	−1128.62	−0.562926
$160$	3357.75	1.65908
$161$	395.097	0.193404
$162$	3596.85	1.74441
$163$	−1303.98	−0.626598	−0.313299	−	0.949655i	$-0.601434\pi$
$163$	−1303.98	−0.626598	−0.313299	+	0.949655i	$0.601434\pi$
$164$	−1500.47	−0.714435
$165$	−1868.67	−0.881673
$166$	−1755.69	−0.820890
$167$	449.810	0.208427	0.104214	−	0.994555i	$-0.466767\pi$
$167$	449.810	0.208427	0.104214	+	0.994555i	$0.466767\pi$
$168$	227.714	0.104575
$169$	−1798.46	−0.818599
$170$	−3282.67	−1.48099
$171$	−1024.58	−0.458194
$172$	−1638.07	−0.726170
$173$	148.530	0.0652746	0.0326373	−	0.999467i	$-0.489609\pi$
$173$	148.530	0.0652746	0.0326373	+	0.999467i	$0.489609\pi$
$174$	−794.497	−0.346153
$175$	−742.325	−0.320654
$176$	1278.88	0.547722
$177$	−1723.39	−0.731855
$178$	−1478.44	−0.622550
$179$	−4300.20	−1.79560	−0.897798	−	0.440407i	$-0.854834\pi$
$179$	−4300.20	−1.79560	−0.897798	+	0.440407i	$0.854834\pi$
$180$	2039.28	0.844439
$181$	−988.586	−0.405973	−0.202986	−	0.979182i	$-0.565065\pi$
$181$	−988.586	−0.405973	−0.202986	+	0.979182i	$0.565065\pi$
$182$	−1392.32	−0.567064
$183$	803.572	0.324600
$184$	45.1833	0.0181030
$185$	−5057.73	−2.01001
$186$	4438.66	1.74977
$187$	−1331.08	−0.520527
$188$	2359.66	0.915404
$189$	981.416	0.377712
$190$	2911.06	1.11153
$191$	3541.02	1.34146	0.670731	−	0.741701i	$-0.265981\pi$
$191$	3541.02	1.34146	0.670731	+	0.741701i	$0.265981\pi$
$192$	−3859.41	−1.45067
$193$	756.605	0.282185	0.141092	−	0.989996i	$-0.454939\pi$
$193$	756.605	0.282185	0.141092	+	0.989996i	$0.454939\pi$
$194$	−3633.93	−1.34485
$195$	−1747.15	−0.641619
$196$	−406.481	−0.148135
$197$	−3596.47	−1.30070	−0.650349	−	0.759635i	$-0.725377\pi$
$197$	−3596.47	−1.30070	−0.650349	+	0.759635i	$0.725377\pi$
$198$	1606.65	0.576665
$199$	4485.15	1.59771	0.798854	−	0.601525i	$-0.205440\pi$
$199$	4485.15	1.59771	0.798854	+	0.601525i	$0.205440\pi$
$200$	−84.8925	−0.0300140
$201$	2001.28	0.702286
$202$	2590.89	0.902449
$203$	−498.165	−0.172238
$204$	3568.83	1.22484
$205$	−2293.85	−0.781509
$206$	1135.59	0.384080
$207$	−426.266	−0.143128
$208$	1195.71	0.398593
$209$	1180.40	0.390670
$210$	6103.80	2.00572
$211$	−2211.79	−0.721640	−0.360820	−	0.932636i	$-0.617503\pi$
$211$	−2211.79	−0.721640	−0.360820	+	0.932636i	$0.617503\pi$
$212$	−1418.98	−0.459697
$213$	3156.38	1.01536
$214$	−1953.70	−0.624076
$215$	−2504.19	−0.794347
$216$	112.235	0.0353547
$217$	2783.13	0.870649
$218$	6608.59	2.05317
$219$	2003.86	0.618302
$220$	−2349.43	−0.719993
$221$	−1244.52	−0.378803
$222$	10683.6	3.22991
$223$	1519.05	0.456158	0.228079	−	0.973643i	$-0.426756\pi$
$223$	1519.05	0.456158	0.228079	+	0.973643i	$0.426756\pi$
$224$	−4447.27	−1.32654
$225$	800.888	0.237300
$226$	3793.98	1.11669
$227$	−600.000	−0.175434	−0.0877168	−	0.996145i	$-0.527957\pi$
$227$	−600.000	−0.175434	−0.0877168	+	0.996145i	$0.527957\pi$
$228$	−3164.82	−0.919277
$229$	25.5855	0.00738312	0.00369156	−	0.999993i	$-0.498825\pi$
$229$	25.5855	0.00738312	0.00369156	+	0.999993i	$0.498825\pi$
$230$	1211.12	0.347213
$231$	2475.02	0.704954
$232$	−56.9703	−0.0161219
$233$	−1285.06	−0.361318	−0.180659	−	0.983546i	$-0.557823\pi$
$233$	−1285.06	−0.361318	−0.180659	+	0.983546i	$0.557823\pi$
$234$	1502.16	0.419656
$235$	3607.33	1.00135
$236$	−2166.77	−0.597648
$237$	−1188.81	−0.325830
$238$	4347.83	1.18415
$239$	1425.83	0.385897	0.192949	−	0.981209i	$-0.438195\pi$
$239$	1425.83	0.385897	0.192949	+	0.981209i	$0.438195\pi$
$240$	−5241.86	−1.40984
$241$	6267.07	1.67509	0.837546	−	0.546366i	$-0.183989\pi$
$241$	6267.07	1.67509	0.837546	+	0.546366i	$0.183989\pi$
$242$	3552.90	0.943757
$243$	−4435.46	−1.17092
$244$	1010.31	0.265075
$245$	−621.408	−0.162042
$246$	4845.39	1.25582
$247$	1103.63	0.284302
$248$	318.279	0.0814949
$249$	2917.98	0.742649
$250$	4306.67	1.08951
$251$	2163.38	0.544028	0.272014	−	0.962293i	$-0.412310\pi$
$251$	2163.38	0.544028	0.272014	+	0.962293i	$0.412310\pi$
$252$	−2700.99	−0.675183
$253$	491.096	0.122035
$254$	−4076.38	−1.00699
$255$	5455.85	1.33984
$256$	3556.54	0.868295
$257$	143.739	0.0348879	0.0174439	−	0.999848i	$-0.494447\pi$
$257$	143.739	0.0348879	0.0174439	+	0.999848i	$0.494447\pi$
$258$	5289.71	1.27645
$259$	6698.86	1.60713
$260$	−2196.64	−0.523960
$261$	537.466	0.127465
$262$	−7358.12	−1.73506
$263$	2451.17	0.574697	0.287349	−	0.957826i	$-0.407226\pi$
$263$	2451.17	0.574697	0.287349	+	0.957826i	$0.407226\pi$
$264$	283.044	0.0659854
$265$	−2169.26	−0.502856
$266$	−3855.63	−0.888737
$267$	2457.19	0.563213
$268$	2516.15	0.573502
$269$	−3116.98	−0.706490	−0.353245	−	0.935531i	$-0.614922\pi$
$269$	−3116.98	−0.706490	−0.353245	+	0.935531i	$0.614922\pi$
$270$	3008.41	0.678097
$271$	5851.02	1.31153	0.655764	−	0.754966i	$-0.272347\pi$
$271$	5851.02	1.31153	0.655764	+	0.754966i	$0.272347\pi$
$272$	−3733.86	−0.832347
$273$	2314.06	0.513016
$274$	−1531.37	−0.337641
$275$	−922.693	−0.202329
$276$	−1316.70	−0.287159
$277$	4594.66	0.996630	0.498315	−	0.866996i	$-0.333952\pi$
$277$	4594.66	0.996630	0.498315	+	0.866996i	$0.333952\pi$
$278$	4477.13	0.965902
$279$	−3002.69	−0.644324
$280$	437.680	0.0934156
$281$	−1788.31	−0.379650	−0.189825	−	0.981818i	$-0.560792\pi$
$281$	−1788.31	−0.379650	−0.189825	+	0.981818i	$0.560792\pi$
$282$	−7619.91	−1.60908
$283$	−4488.73	−0.942852	−0.471426	−	0.881906i	$-0.656261\pi$
$283$	−4488.73	−0.942852	−0.471426	+	0.881906i	$0.656261\pi$
$284$	3968.42	0.829164
$285$	−4838.22	−1.00558
$286$	−1730.62	−0.357811
$287$	3038.16	0.624867
$288$	4798.12	0.981708
$289$	−1026.72	−0.208980
$290$	−1527.07	−0.309215
$291$	6039.64	1.21667
$292$	2519.39	0.504919
$293$	−6853.73	−1.36655	−0.683275	−	0.730161i	$-0.739445\pi$
$293$	−6853.73	−1.36655	−0.683275	+	0.730161i	$0.739445\pi$
$294$	1312.63	0.260387
$295$	−3312.46	−0.653759
$296$	766.083	0.150431
$297$	1219.88	0.238332
$298$	7739.87	1.50456
$299$	459.158	0.0888087
$300$	2473.87	0.476097
$301$	3316.75	0.635131
$302$	−6486.26	−1.23590
$303$	−4306.11	−0.816434
$304$	3311.17	0.624699
$305$	1544.51	0.289962
$306$	−4690.83	−0.876330
$307$	6739.70	1.25295	0.626474	−	0.779442i	$-0.284497\pi$
$307$	6739.70	1.25295	0.626474	+	0.779442i	$0.284497\pi$
$308$	3111.77	0.575681
$309$	−1887.37	−0.347472
$310$	8531.34	1.56306
$311$	−1226.77	−0.223678	−0.111839	−	0.993726i	$-0.535674\pi$
$311$	−1226.77	−0.223678	−0.111839	+	0.993726i	$0.535674\pi$
$312$	264.636	0.0480195
$313$	−8247.41	−1.48936	−0.744682	−	0.667419i	$-0.767399\pi$
$313$	−8247.41	−1.48936	−0.744682	+	0.667419i	$0.767399\pi$
$314$	11946.2	2.14702
$315$	−4129.14	−0.738573
$316$	−1494.66	−0.266080
$317$	−6774.26	−1.20025	−0.600127	−	0.799905i	$-0.704883\pi$
$317$	−6774.26	−1.20025	−0.600127	+	0.799905i	$0.704883\pi$
$318$	4582.22	0.808045
$319$	−619.208	−0.108680
$320$	−7418.00	−1.29587
$321$	3247.08	0.564594
$322$	−1604.11	−0.277619
$323$	−3446.34	−0.593682
$324$	−7515.99	−1.28875
$325$	−862.687	−0.147241
$326$	5294.20	0.899443
$327$	−10983.6	−1.85747
$328$	347.444	0.0584890
$329$	−4777.84	−0.800641
$330$	7586.88	1.26559
$331$	−7726.20	−1.28299	−0.641496	−	0.767127i	$-0.721686\pi$
$331$	−7726.20	−1.28299	−0.641496	+	0.767127i	$0.721686\pi$
$332$	3668.69	0.606463
$333$	−7227.34	−1.18936
$334$	−1826.24	−0.299184
$335$	3846.57	0.627345
$336$	6942.74	1.12725
$337$	−578.089	−0.0934436	−0.0467218	−	0.998908i	$-0.514877\pi$
$337$	−578.089	−0.0934436	−0.0467218	+	0.998908i	$0.514877\pi$
$338$	7301.82	1.17505
$339$	−6305.66	−1.01025
$340$	6859.48	1.09414
$341$	3459.36	0.549369
$342$	4159.81	0.657710
$343$	6715.14	1.05709
$344$	379.304	0.0594498
$345$	−2012.90	−0.314119
$346$	−603.035	−0.0936976
$347$	9774.68	1.51220	0.756099	−	0.654458i	$-0.227103\pi$
$347$	9774.68	1.51220	0.756099	+	0.654458i	$0.227103\pi$
$348$	1660.18	0.255733
$349$	999.371	0.153281	0.0766406	−	0.997059i	$-0.475581\pi$
$349$	999.371	0.153281	0.0766406	+	0.997059i	$0.475581\pi$
$350$	3013.87	0.460280
$351$	1140.54	0.173441
$352$	−5527.85	−0.837033
$353$	8775.82	1.32320	0.661600	−	0.749857i	$-0.269878\pi$
$353$	8775.82	1.32320	0.661600	+	0.749857i	$0.269878\pi$
$354$	6997.04	1.05053
$355$	6066.73	0.907010
$356$	3089.36	0.459931
$357$	−7226.16	−1.07129
$358$	17458.9	2.57747
$359$	−5709.24	−0.839337	−0.419669	−	0.907677i	$-0.637854\pi$
$359$	−5709.24	−0.839337	−0.419669	+	0.907677i	$0.637854\pi$
$360$	−472.209	−0.0691322
$361$	−3802.80	−0.554425
$362$	4013.69	0.582749
$363$	−5904.98	−0.853804
$364$	2909.40	0.418940
$365$	3851.52	0.552323
$366$	−3262.53	−0.465943
$367$	−2996.74	−0.426236	−0.213118	−	0.977026i	$-0.568362\pi$
$367$	−2996.74	−0.426236	−0.213118	+	0.977026i	$0.568362\pi$
$368$	1377.58	0.195140
$369$	−3277.84	−0.462433
$370$	20534.5	2.88524
$371$	2873.14	0.402065
$372$	−9275.04	−1.29271
$373$	−1913.48	−0.265620	−0.132810	−	0.991142i	$-0.542400\pi$
$373$	−1913.48	−0.265620	−0.132810	+	0.991142i	$0.542400\pi$
$374$	5404.25	0.747184
$375$	−7157.76	−0.985667
$376$	−546.394	−0.0749419
$377$	−578.938	−0.0790898
$378$	−3984.58	−0.542182
$379$	6912.90	0.936917	0.468459	−	0.883485i	$-0.344810\pi$
$379$	6912.90	0.936917	0.468459	+	0.883485i	$0.344810\pi$
$380$	−6082.95	−0.821181
$381$	6775.01	0.911009
$382$	−14376.6	−1.92558
$383$	−133.659	−0.0178319	−0.00891597	−	0.999960i	$-0.502838\pi$
$383$	−133.659	−0.0178319	−0.00891597	+	0.999960i	$0.502838\pi$
$384$	1693.67	0.225078
$385$	4757.12	0.629729
$386$	−3071.84	−0.405058
$387$	−3578.42	−0.470029
$388$	7593.47	0.993557
$389$	−9327.95	−1.21580	−0.607900	−	0.794014i	$-0.707988\pi$
$389$	−9327.95	−1.21580	−0.607900	+	0.794014i	$0.707988\pi$
$390$	7093.47	0.921005
$391$	−1433.82	−0.185451
$392$	94.1233	0.0121274
$393$	12229.3	1.56969
$394$	14601.8	1.86707
$395$	−2284.96	−0.291060
$396$	−3357.26	−0.426032
$397$	2152.25	0.272087	0.136043	−	0.990703i	$-0.456561\pi$
$397$	2152.25	0.272087	0.136043	+	0.990703i	$0.456561\pi$
$398$	−18209.9	−2.29341
$399$	6408.12	0.804029
$400$	−2588.27	−0.323533
$401$	8080.80	1.00632	0.503162	−	0.864192i	$-0.332170\pi$
$401$	8080.80	1.00632	0.503162	+	0.864192i	$0.332170\pi$
$402$	−8125.27	−1.00809
$403$	3234.38	0.399792
$404$	−5413.94	−0.666717
$405$	−11490.1	−1.40974
$406$	2022.57	0.247237
$407$	8326.53	1.01408
$408$	−826.385	−0.100275
$409$	12500.0	1.51121	0.755607	−	0.655025i	$-0.227342\pi$
$409$	12500.0	1.51121	0.755607	+	0.655025i	$0.227342\pi$
$410$	9313.11	1.12181
$411$	2545.16	0.305459
$412$	−2372.94	−0.283753
$413$	4387.28	0.522722
$414$	1730.66	0.205452
$415$	5608.52	0.663401
$416$	−5168.35	−0.609133
$417$	−7441.07	−0.873839
$418$	−4792.46	−0.560782
$419$	−7116.61	−0.829759	−0.414880	−	0.909876i	$-0.636176\pi$
$419$	−7116.61	−0.829759	−0.414880	+	0.909876i	$0.636176\pi$
$420$	−12754.5	−1.48180
$421$	−15883.4	−1.83874	−0.919370	−	0.393394i	$-0.871301\pi$
$421$	−15883.4	−1.83874	−0.919370	+	0.393394i	$0.871301\pi$
$422$	8979.94	1.03587
$423$	5154.77	0.592514
$424$	328.573	0.0376343
$425$	2693.93	0.307470
$426$	−12815.0	−1.45749
$427$	−2045.67	−0.231843
$428$	4082.46	0.461059
$429$	2876.32	0.323707
$430$	10167.1	1.14024
$431$	9294.59	1.03876	0.519379	−	0.854544i	$-0.326163\pi$
$431$	9294.59	1.03876	0.519379	+	0.854544i	$0.326163\pi$
$432$	3421.91	0.381103
$433$	1258.30	0.139654	0.0698270	−	0.997559i	$-0.477755\pi$
$433$	1258.30	0.139654	0.0698270	+	0.997559i	$0.477755\pi$
$434$	−11299.6	−1.24976
$435$	2538.01	0.279743
$436$	−13809.3	−1.51685
$437$	1271.51	0.139186
$438$	−8135.73	−0.887535
$439$	65.8380	0.00715780	0.00357890	−	0.999994i	$-0.498861\pi$
$439$	65.8380	0.00715780	0.00357890	+	0.999994i	$0.498861\pi$
$440$	544.026	0.0589441
$441$	−887.974	−0.0958831
$442$	5052.79	0.543748
$443$	4395.87	0.471454	0.235727	−	0.971819i	$-0.424253\pi$
$443$	4395.87	0.471454	0.235727	+	0.971819i	$0.424253\pi$
$444$	−22324.6	−2.38621
$445$	4722.86	0.503112
$446$	−6167.40	−0.654786
$447$	−12863.8	−1.36116
$448$	9824.99	1.03613
$449$	−1077.72	−0.113276	−0.0566378	−	0.998395i	$-0.518038\pi$
$449$	−1077.72	−0.113276	−0.0566378	+	0.998395i	$0.518038\pi$
$450$	−3251.63	−0.340630
$451$	3776.36	0.394283
$452$	−7927.92	−0.824995
$453$	10780.3	1.11810
$454$	2436.02	0.251824
$455$	4447.75	0.458272
$456$	732.834	0.0752590
$457$	11494.4	1.17655	0.588277	−	0.808659i	$-0.299806\pi$
$457$	11494.4	1.17655	0.588277	+	0.808659i	$0.299806\pi$
$458$	−103.878	−0.0105980
$459$	−3561.60	−0.362181
$460$	−2530.76	−0.256516
$461$	−7854.76	−0.793563	−0.396782	−	0.917913i	$-0.629873\pi$
$461$	−7854.76	−0.793563	−0.396782	+	0.917913i	$0.629873\pi$
$462$	−10048.7	−1.01192
$463$	12328.7	1.23750	0.618752	−	0.785586i	$-0.287639\pi$
$463$	12328.7	1.23750	0.618752	+	0.785586i	$0.287639\pi$
$464$	−1736.95	−0.173785
$465$	−14179.2	−1.41408
$466$	5217.38	0.518649
$467$	−5141.47	−0.509463	−0.254731	−	0.967012i	$-0.581987\pi$
$467$	−5141.47	−0.509463	−0.254731	+	0.967012i	$0.581987\pi$
$468$	−3138.93	−0.310036
$469$	−5094.71	−0.501603
$470$	−14645.9	−1.43737
$471$	−19854.8	−1.94238
$472$	501.731	0.0489280
$473$	4122.65	0.400760
$474$	4826.62	0.467708
$475$	−2388.96	−0.230764
$476$	−9085.24	−0.874834
$477$	−3099.81	−0.297548
$478$	−5788.93	−0.553932
$479$	−2661.51	−0.253878	−0.126939	−	0.991911i	$-0.540515\pi$
$479$	−2661.51	−0.253878	−0.126939	+	0.991911i	$0.540515\pi$
$480$	22657.5	2.15452
$481$	7785.02	0.737976
$482$	−25444.5	−2.40449
$483$	2666.05	0.251158
$484$	−7424.16	−0.697235
$485$	11608.5	1.08684
$486$	18008.1	1.68079
$487$	−2167.13	−0.201646	−0.100823	−	0.994904i	$-0.532148\pi$
$487$	−2167.13	−0.201646	−0.100823	+	0.994904i	$0.532148\pi$
$488$	−233.943	−0.0217010
$489$	−8799.04	−0.813714
$490$	2522.94	0.232601
$491$	−21278.5	−1.95577	−0.977885	−	0.209142i	$-0.932933\pi$
$491$	−21278.5	−1.95577	−0.977885	+	0.209142i	$0.932933\pi$
$492$	−10125.0	−0.927781
$493$	1807.86	0.165156
$494$	−4480.79	−0.408098
$495$	−5132.42	−0.466031
$496$	9703.93	0.878467
$497$	−8035.26	−0.725213
$498$	−11847.1	−1.06603
$499$	−7419.24	−0.665593	−0.332797	−	0.942999i	$-0.607992\pi$
$499$	−7419.24	−0.665593	−0.332797	+	0.942999i	$0.607992\pi$
$500$	−8999.24	−0.804917
$501$	3035.25	0.270668
$502$	−8783.38	−0.780919
$503$	−9037.58	−0.801125	−0.400563	−	0.916269i	$-0.631185\pi$
$503$	−9037.58	−0.801125	−0.400563	+	0.916269i	$0.631185\pi$
$504$	625.431	0.0552756
$505$	−8276.57	−0.729312
$506$	−1993.87	−0.175174
$507$	−12135.7	−1.06305
$508$	8518.03	0.743949
$509$	15228.2	1.32609	0.663043	−	0.748582i	$-0.269265\pi$
$509$	15228.2	1.32609	0.663043	+	0.748582i	$0.269265\pi$
$510$	−22150.9	−1.92325
$511$	−5101.27	−0.441618
$512$	−16447.6	−1.41970
$513$	3158.41	0.271827
$514$	−583.585	−0.0500794
$515$	−3627.64	−0.310394
$516$	−11053.4	−0.943021
$517$	−5938.74	−0.505195
$518$	−27197.6	−2.30694
$519$	1002.25	0.0847670
$520$	508.645	0.0428953
$521$	20740.2	1.74404	0.872020	−	0.489470i	$-0.162810\pi$
$521$	20740.2	1.74404	0.872020	+	0.489470i	$0.162810\pi$
$522$	−2182.13	−0.182968
$523$	2148.79	0.179656	0.0898280	−	0.995957i	$-0.471368\pi$
$523$	2148.79	0.179656	0.0898280	+	0.995957i	$0.471368\pi$
$524$	15375.6	1.28184
$525$	−5009.09	−0.416409
$526$	−9951.81	−0.824942
$527$	−10100.1	−0.834850
$528$	8629.66	0.711284
$529$	529.000	0.0434783
$530$	8807.28	0.721818
$531$	−4733.40	−0.386840
$532$	8056.75	0.656587
$533$	3530.77	0.286932
$534$	−9976.28	−0.808457
$535$	6241.07	0.504346
$536$	−582.632	−0.0469512
$537$	−29017.0	−2.33180
$538$	12655.1	1.01412
$539$	1023.02	0.0817527
$540$	−6286.39	−0.500969
$541$	8289.29	0.658751	0.329376	−	0.944199i	$-0.393162\pi$
$541$	8289.29	0.658751	0.329376	+	0.944199i	$0.393162\pi$
$542$	−23755.3	−1.88262
$543$	−6670.82	−0.527205
$544$	16139.3	1.27200
$545$	−21111.0	−1.65926
$546$	−9395.16	−0.736402
$547$	17441.9	1.36337	0.681685	−	0.731646i	$-0.261248\pi$
$547$	17441.9	1.36337	0.681685	+	0.731646i	$0.261248\pi$
$548$	3199.96	0.249444
$549$	2207.06	0.171575
$550$	3746.16	0.290431
$551$	−1603.20	−0.123954
$552$	304.890	0.0235090
$553$	3026.38	0.232721
$554$	−18654.5	−1.43060
$555$	−34128.7	−2.61024
$556$	−9355.44	−0.713595
$557$	−17467.7	−1.32878	−0.664391	−	0.747386i	$-0.731309\pi$
$557$	−17467.7	−1.32878	−0.664391	+	0.747386i	$0.731309\pi$
$558$	12191.0	0.924887
$559$	3854.53	0.291645
$560$	13344.3	1.00696
$561$	−8981.95	−0.675968
$562$	7260.59	0.544964
$563$	6860.04	0.513528	0.256764	−	0.966474i	$-0.417344\pi$
$563$	6860.04	0.513528	0.256764	+	0.966474i	$0.417344\pi$
$564$	15922.6	1.18876
$565$	−12119.8	−0.902450
$566$	18224.4	1.35341
$567$	15218.4	1.12718
$568$	−918.914	−0.0678816
$569$	26276.1	1.93594	0.967971	−	0.251064i	$-0.0807804\pi$
$569$	26276.1	1.93594	0.967971	+	0.251064i	$0.0807804\pi$
$570$	19643.3	1.44345
$571$	4985.18	0.365364	0.182682	−	0.983172i	$-0.441522\pi$
$571$	4985.18	0.365364	0.182682	+	0.983172i	$0.441522\pi$
$572$	3616.32	0.264346
$573$	23894.2	1.74205
$574$	−12335.0	−0.896958
$575$	−993.909	−0.0720850
$576$	−10600.1	−0.766789
$577$	12928.8	0.932816	0.466408	−	0.884570i	$-0.345548\pi$
$577$	12928.8	0.932816	0.466408	+	0.884570i	$0.345548\pi$
$578$	4168.51	0.299978
$579$	5105.45	0.366451
$580$	3190.96	0.228444
$581$	−7428.37	−0.530431
$582$	−24521.2	−1.74645
$583$	3571.25	0.253698
$584$	−583.382	−0.0413365
$585$	−4798.64	−0.339144
$586$	27826.4	1.96160
$587$	−9713.56	−0.683001	−0.341500	−	0.939882i	$-0.610935\pi$
$587$	−9713.56	−0.683001	−0.341500	+	0.939882i	$0.610935\pi$
$588$	−2742.87	−0.192371
$589$	8956.70	0.626578
$590$	13448.7	0.938430
$591$	−24268.4	−1.68912
$592$	23356.9	1.62156
$593$	22980.2	1.59138	0.795688	−	0.605707i	$-0.207110\pi$
$593$	22980.2	1.59138	0.795688	+	0.605707i	$0.207110\pi$
$594$	−4952.74	−0.342110
$595$	−13889.1	−0.956968
$596$	−16173.3	−1.11155
$597$	30265.1	2.07482
$598$	−1864.20	−0.127479
$599$	13394.0	0.913633	0.456816	−	0.889561i	$-0.348990\pi$
$599$	13394.0	0.913633	0.456816	+	0.889561i	$0.348990\pi$
$600$	−572.841	−0.0389769
$601$	11829.3	0.802877	0.401438	−	0.915886i	$-0.368510\pi$
$601$	11829.3	0.802877	0.401438	+	0.915886i	$0.368510\pi$
$602$	−13466.1	−0.911692
$603$	5496.64	0.371211
$604$	13553.7	0.913068
$605$	−11349.7	−0.762695
$606$	17482.9	1.17194
$607$	−1309.74	−0.0875794	−0.0437897	−	0.999041i	$-0.513943\pi$
$607$	−1309.74	−0.0875794	−0.0437897	+	0.999041i	$0.513943\pi$
$608$	−14312.3	−0.954670
$609$	−3361.54	−0.223672
$610$	−6270.75	−0.416222
$611$	−5552.52	−0.367645
$612$	9801.98	0.647421
$613$	999.269	0.0658403	0.0329201	−	0.999458i	$-0.489519\pi$
$613$	999.269	0.0658403	0.0329201	+	0.999458i	$0.489519\pi$
$614$	−27363.4	−1.79853
$615$	−15478.5	−1.01489
$616$	−720.551	−0.0471296
$617$	4081.18	0.266292	0.133146	−	0.991096i	$-0.457492\pi$
$617$	4081.18	0.266292	0.133146	+	0.991096i	$0.457492\pi$
$618$	7662.80	0.498775
$619$	−8912.08	−0.578686	−0.289343	−	0.957225i	$-0.593437\pi$
$619$	−8912.08	−0.578686	−0.289343	+	0.957225i	$0.593437\pi$
$620$	−17827.1	−1.15477
$621$	1314.03	0.0849118
$622$	4980.73	0.321076
$623$	−6255.33	−0.402270
$624$	8068.44	0.517622
$625$	−19159.3	−1.22619
$626$	33484.7	2.13789
$627$	7965.15	0.507332
$628$	−24962.9	−1.58619
$629$	−24310.4	−1.54105
$630$	16764.4	1.06018
$631$	−6779.90	−0.427739	−0.213870	−	0.976862i	$-0.568607\pi$
$631$	−6779.90	−0.427739	−0.213870	+	0.976862i	$0.568607\pi$
$632$	346.098	0.0217833
$633$	−14924.8	−0.937137
$634$	27503.7	1.72289
$635$	13021.9	0.813795
$636$	−9575.03	−0.596973
$637$	956.492	0.0594938
$638$	2514.00	0.156004
$639$	8669.17	0.536694
$640$	3255.33	0.201060
$641$	10251.0	0.631652	0.315826	−	0.948817i	$-0.397718\pi$
$641$	10251.0	0.631652	0.315826	+	0.948817i	$0.397718\pi$
$642$	−13183.3	−0.810439
$643$	−22850.8	−1.40147	−0.700737	−	0.713420i	$-0.747145\pi$
$643$	−22850.8	−1.40147	−0.700737	+	0.713420i	$0.747145\pi$
$644$	3351.95	0.205101
$645$	−16897.9	−1.03156
$646$	13992.2	0.852194
$647$	−9517.94	−0.578345	−0.289172	−	0.957277i	$-0.593380\pi$
$647$	−9517.94	−0.578345	−0.289172	+	0.957277i	$0.593380\pi$
$648$	1740.37	0.105507
$649$	5453.29	0.329831
$650$	3502.54	0.211355
$651$	18780.1	1.13064
$652$	−11062.8	−0.664496
$653$	−10225.0	−0.612767	−0.306384	−	0.951908i	$-0.599119\pi$
$653$	−10225.0	−0.612767	−0.306384	+	0.951908i	$0.599119\pi$
$654$	44593.7	2.66629
$655$	23505.4	1.40219
$656$	10593.2	0.630477
$657$	5503.71	0.326819
$658$	19398.2	1.14927
$659$	13342.4	0.788686	0.394343	−	0.918963i	$-0.370972\pi$
$659$	13342.4	0.788686	0.394343	+	0.918963i	$0.370972\pi$
$660$	−15853.6	−0.934999
$661$	14852.0	0.873943	0.436971	−	0.899475i	$-0.356051\pi$
$661$	14852.0	0.873943	0.436971	+	0.899475i	$0.356051\pi$
$662$	31368.6	1.84165
$663$	−8397.81	−0.491922
$664$	−849.509	−0.0496496
$665$	12316.8	0.718231
$666$	29343.2	1.70725
$667$	−667.000	−0.0387202
$668$	3816.13	0.221034
$669$	10250.3	0.592377
$670$	−15617.2	−0.900516
$671$	−2542.72	−0.146290
$672$	−30009.5	−1.72268
$673$	−6421.33	−0.367792	−0.183896	−	0.982946i	$-0.558871\pi$
$673$	−6421.33	−0.367792	−0.183896	+	0.982946i	$0.558871\pi$
$674$	2347.06	0.134133
$675$	−2468.86	−0.140780
$676$	−15257.9	−0.868110
$677$	14668.5	0.832728	0.416364	−	0.909198i	$-0.363304\pi$
$677$	14668.5	0.832728	0.416364	+	0.909198i	$0.363304\pi$
$678$	25601.2	1.45016
$679$	−15375.3	−0.868996
$680$	−1588.36	−0.0895745
$681$	−4048.71	−0.227822
$682$	−14045.1	−0.788586
$683$	−8324.80	−0.466383	−0.233192	−	0.972431i	$-0.574917\pi$
$683$	−8324.80	−0.466383	−0.233192	+	0.972431i	$0.574917\pi$
$684$	−8692.36	−0.485907
$685$	4891.94	0.272863
$686$	−27263.7	−1.51739
$687$	172.647	0.00958788
$688$	11564.5	0.640834
$689$	3339.00	0.184624
$690$	8172.45	0.450898
$691$	−1163.14	−0.0640346	−0.0320173	−	0.999487i	$-0.510193\pi$
$691$	−1163.14	−0.0640346	−0.0320173	+	0.999487i	$0.510193\pi$
$692$	1260.11	0.0692226
$693$	6797.79	0.372621
$694$	−39685.5	−2.17067
$695$	−14302.1	−0.780591
$696$	−384.426	−0.0209363
$697$	−11025.6	−0.599174
$698$	−4057.48	−0.220026
$699$	−8671.37	−0.469215
$700$	−6297.79	−0.340048
$701$	27289.8	1.47036	0.735179	−	0.677873i	$-0.237098\pi$
$701$	27289.8	1.47036	0.735179	+	0.677873i	$0.237098\pi$
$702$	−4630.65	−0.248964
$703$	21558.4	1.15660
$704$	12212.2	0.653787
$705$	24341.7	1.30037
$706$	−35630.1	−1.89937
$707$	10962.1	0.583132
$708$	−14621.0	−0.776119
$709$	17489.0	0.926392	0.463196	−	0.886256i	$-0.346703\pi$
$709$	17489.0	0.926392	0.463196	+	0.886256i	$0.346703\pi$
$710$	−24631.1	−1.30196
$711$	−3265.14	−0.172225
$712$	−715.360	−0.0376535
$713$	3726.36	0.195727
$714$	29338.4	1.53776
$715$	5528.45	0.289164
$716$	−36482.3	−1.90420
$717$	9621.29	0.501135
$718$	23179.7	1.20482
$719$	26550.7	1.37715	0.688576	−	0.725164i	$-0.258236\pi$
$719$	26550.7	1.37715	0.688576	+	0.725164i	$0.258236\pi$
$720$	−14397.1	−0.745204
$721$	4804.73	0.248180
$722$	15439.5	0.795843
$723$	42289.2	2.17531
$724$	−8387.03	−0.430527
$725$	1253.19	0.0641963
$726$	23974.4	1.22558
$727$	−8079.58	−0.412180	−0.206090	−	0.978533i	$-0.566074\pi$
$727$	−8079.58	−0.412180	−0.206090	+	0.978533i	$0.566074\pi$
$728$	−673.690	−0.0342976
$729$	−6010.03	−0.305341
$730$	−15637.3	−0.792826
$731$	−12036.6	−0.609016
$732$	6817.39	0.344232
$733$	7782.70	0.392170	0.196085	−	0.980587i	$-0.437177\pi$
$733$	7782.70	0.392170	0.196085	+	0.980587i	$0.437177\pi$
$734$	12166.9	0.611836
$735$	−4193.16	−0.210432
$736$	−5954.50	−0.298215
$737$	−6332.60	−0.316505
$738$	13308.1	0.663793
$739$	20733.3	1.03205	0.516027	−	0.856572i	$-0.327410\pi$
$739$	20733.3	1.03205	0.516027	+	0.856572i	$0.327410\pi$
$740$	−42909.1	−2.13158
$741$	7447.14	0.369201
$742$	−11665.1	−0.577140
$743$	−16161.7	−0.798001	−0.399001	−	0.916951i	$-0.630643\pi$
$743$	−16161.7	−0.798001	−0.399001	+	0.916951i	$0.630643\pi$
$744$	2147.69	0.105831
$745$	−24724.9	−1.21591
$746$	7768.79	0.381281
$747$	8014.40	0.392546
$748$	−11292.7	−0.552010
$749$	−8266.17	−0.403257
$750$	29060.7	1.41486
$751$	−15293.1	−0.743079	−0.371540	−	0.928417i	$-0.621170\pi$
$751$	−15293.1	−0.743079	−0.371540	+	0.928417i	$0.621170\pi$
$752$	−16658.9	−0.807829
$753$	14598.1	0.706487
$754$	2350.51	0.113528
$755$	20720.3	0.998792
$756$	8326.20	0.400557
$757$	−28775.1	−1.38157	−0.690786	−	0.723060i	$-0.742735\pi$
$757$	−28775.1	−1.38157	−0.690786	+	0.723060i	$0.742735\pi$
$758$	−28066.6	−1.34489
$759$	3313.84	0.158478
$760$	1408.55	0.0672281
$761$	27477.0	1.30886	0.654429	−	0.756123i	$-0.272909\pi$
$761$	27477.0	1.30886	0.654429	+	0.756123i	$0.272909\pi$
$762$	−27506.8	−1.30770
$763$	27961.1	1.32669
$764$	30041.5	1.42260
$765$	14984.8	0.708204
$766$	542.658	0.0255967
$767$	5098.64	0.240028
$768$	23998.9	1.12759
$769$	−25292.1	−1.18603	−0.593014	−	0.805192i	$-0.702062\pi$
$769$	−25292.1	−1.18603	−0.593014	+	0.805192i	$0.702062\pi$
$770$	−19314.1	−0.903936
$771$	969.927	0.0453062
$772$	6418.93	0.299252
$773$	27958.6	1.30091	0.650453	−	0.759546i	$-0.274579\pi$
$773$	27958.6	1.30091	0.650453	+	0.759546i	$0.274579\pi$
$774$	14528.5	0.674697
$775$	−7001.26	−0.324507
$776$	−1758.32	−0.0813401
$777$	45202.8	2.08706
$778$	37871.8	1.74521
$779$	9777.44	0.449696
$780$	−14822.6	−0.680426
$781$	−9987.64	−0.457600
$782$	5821.36	0.266204
$783$	−1656.82	−0.0756194
$784$	2869.70	0.130726
$785$	−38162.0	−1.73511
$786$	−49651.4	−2.25319
$787$	−15521.8	−0.703039	−0.351519	−	0.936181i	$-0.614335\pi$
$787$	−15521.8	−0.703039	−0.351519	+	0.936181i	$0.614335\pi$
$788$	−30511.9	−1.37937
$789$	16540.1	0.746314
$790$	9277.02	0.417799
$791$	16052.4	0.721567
$792$	777.396	0.0348782
$793$	−2377.36	−0.106460
$794$	−8738.22	−0.390564
$795$	−14637.8	−0.653020
$796$	38051.4	1.69434
$797$	9069.02	0.403063	0.201532	−	0.979482i	$-0.435408\pi$
$797$	9069.02	0.403063	0.201532	+	0.979482i	$0.435408\pi$
$798$	−26017.2	−1.15413
$799$	17339.0	0.767720
$800$	11187.6	0.494426
$801$	6748.82	0.297700
$802$	−32808.3	−1.44452
$803$	−6340.76	−0.278656
$804$	16978.6	0.744763
$805$	5124.29	0.224357
$806$	−13131.7	−0.573877
$807$	−21032.9	−0.917464
$808$	1253.63	0.0545825
$809$	39943.3	1.73588	0.867942	−	0.496666i	$-0.165442\pi$
$809$	39943.3	1.73588	0.867942	+	0.496666i	$0.165442\pi$
$810$	46650.1	2.02360
$811$	20916.6	0.905648	0.452824	−	0.891600i	$-0.350417\pi$
$811$	20916.6	0.905648	0.452824	+	0.891600i	$0.350417\pi$
$812$	−4226.37	−0.182656
$813$	39481.7	1.70318
$814$	−33806.0	−1.45565
$815$	−16912.2	−0.726883
$816$	−25195.5	−1.08090
$817$	10674.0	0.457083
$818$	−50750.5	−2.16925
$819$	6355.70	0.271167
$820$	−19460.7	−0.828777
$821$	12053.6	0.512392	0.256196	−	0.966625i	$-0.417531\pi$
$821$	12053.6	0.512392	0.256196	+	0.966625i	$0.417531\pi$
$822$	−10333.4	−0.438467
$823$	5475.97	0.231932	0.115966	−	0.993253i	$-0.463004\pi$
$823$	5475.97	0.231932	0.115966	+	0.993253i	$0.463004\pi$
$824$	549.470	0.0232302
$825$	−6226.19	−0.262749
$826$	−17812.5	−0.750335
$827$	16224.0	0.682183	0.341092	−	0.940030i	$-0.389203\pi$
$827$	16224.0	0.682183	0.341092	+	0.940030i	$0.389203\pi$
$828$	−3616.39	−0.151785
$829$	−24409.4	−1.02264	−0.511322	−	0.859389i	$-0.670844\pi$
$829$	−24409.4	−1.02264	−0.511322	+	0.859389i	$0.670844\pi$
$830$	−22770.8	−0.952271
$831$	31004.0	1.29425
$832$	11418.0	0.475780
$833$	−2986.85	−0.124236
$834$	30211.0	1.25434
$835$	5833.91	0.241785
$836$	10014.4	0.414299
$837$	9256.25	0.382249
$838$	28893.7	1.19107
$839$	−13529.5	−0.556723	−0.278362	−	0.960476i	$-0.589791\pi$
$839$	−13529.5	−0.556723	−0.278362	+	0.960476i	$0.589791\pi$
$840$	2953.39	0.121312
$841$	841.000	0.0344828
$842$	64487.1	2.63940
$843$	−12067.2	−0.493021
$844$	−18764.5	−0.765286
$845$	−23325.5	−0.949613
$846$	−20928.5	−0.850517
$847$	15032.4	0.609823
$848$	10017.8	0.405675
$849$	−30289.2	−1.22441
$850$	−10937.4	−0.441354
$851$	8969.19	0.361292
$852$	26778.3	1.07677
$853$	11194.7	0.449353	0.224676	−	0.974433i	$-0.427867\pi$
$853$	11194.7	0.449353	0.224676	+	0.974433i	$0.427867\pi$
$854$	8305.48	0.332796
$855$	−13288.4	−0.531527
$856$	−945.321	−0.0377458
$857$	−45497.4	−1.81349	−0.906746	−	0.421677i	$-0.861442\pi$
$857$	−45497.4	−1.81349	−0.906746	+	0.421677i	$0.861442\pi$
$858$	−11678.0	−0.464661
$859$	−42450.3	−1.68613	−0.843066	−	0.537811i	$-0.819252\pi$
$859$	−42450.3	−1.68613	−0.843066	+	0.537811i	$0.819252\pi$
$860$	−21245.2	−0.842391
$861$	20501.0	0.811466
$862$	−37736.3	−1.49107
$863$	27127.4	1.07002	0.535011	−	0.844845i	$-0.320308\pi$
$863$	27127.4	1.07002	0.535011	+	0.844845i	$0.320308\pi$
$864$	−14790.9	−0.582405
$865$	1926.39	0.0757215
$866$	−5108.75	−0.200465
$867$	−6928.13	−0.271386
$868$	23611.7	0.923309
$869$	3761.73	0.146844
$870$	−10304.4	−0.401554
$871$	−5920.77	−0.230330
$872$	3197.64	0.124181
$873$	16588.2	0.643100
$874$	−5162.36	−0.199793
$875$	18221.7	0.704005
$876$	17000.5	0.655699
$877$	−8375.57	−0.322489	−0.161245	−	0.986914i	$-0.551551\pi$
$877$	−8375.57	−0.322489	−0.161245	+	0.986914i	$0.551551\pi$
$878$	−267.304	−0.0102746
$879$	−46247.9	−1.77463
$880$	16586.7	0.635383
$881$	−39317.8	−1.50358	−0.751788	−	0.659405i	$-0.770808\pi$
$881$	−39317.8	−1.50358	−0.751788	+	0.659405i	$0.770808\pi$
$882$	3605.20	0.137634
$883$	−4644.75	−0.177020	−0.0885098	−	0.996075i	$-0.528210\pi$
$883$	−4644.75	−0.177020	−0.0885098	+	0.996075i	$0.528210\pi$
$884$	−10558.3	−0.401714
$885$	−22351.9	−0.848985
$886$	−17847.4	−0.676742
$887$	−40730.1	−1.54181	−0.770903	−	0.636952i	$-0.780195\pi$
$887$	−40730.1	−1.54181	−0.770903	+	0.636952i	$0.780195\pi$
$888$	5169.40	0.195353
$889$	−17247.3	−0.650681
$890$	−19175.0	−0.722186
$891$	18916.1	0.711237
$892$	12887.4	0.483748
$893$	−15376.1	−0.576195
$894$	52227.4	1.95385
$895$	−55772.3	−2.08298
$896$	−4311.62	−0.160760
$897$	3098.32	0.115329
$898$	4375.58	0.162600
$899$	−4698.46	−0.174307
$900$	6794.63	0.251653
$901$	−10426.8	−0.385533
$902$	−15332.1	−0.565969
$903$	22380.9	0.824795
$904$	1835.76	0.0675403
$905$	−12821.7	−0.470947
$906$	−43768.3	−1.60497
$907$	−24539.5	−0.898369	−0.449184	−	0.893439i	$-0.648285\pi$
$907$	−24539.5	−0.898369	−0.449184	+	0.893439i	$0.648285\pi$
$908$	−5090.32	−0.186044
$909$	−11827.0	−0.431547
$910$	−18058.0	−0.657821
$911$	41045.7	1.49276	0.746381	−	0.665519i	$-0.231790\pi$
$911$	41045.7	1.49276	0.746381	+	0.665519i	$0.231790\pi$
$912$	22343.2	0.811248
$913$	−9233.29	−0.334696
$914$	−46667.6	−1.68887
$915$	10422.1	0.376550
$916$	217.063	0.00782967
$917$	−31132.4	−1.12114
$918$	14460.2	0.519889
$919$	−2626.27	−0.0942685	−0.0471343	−	0.998889i	$-0.515009\pi$
$919$	−2626.27	−0.0942685	−0.0471343	+	0.998889i	$0.515009\pi$
$920$	586.015	0.0210004
$921$	45478.4	1.62711
$922$	31890.6	1.13911
$923$	−9338.11	−0.333009
$924$	20997.7	0.747592
$925$	−16851.7	−0.599006
$926$	−50055.0	−1.77636
$927$	−5183.78	−0.183665
$928$	7507.85	0.265579
$929$	14364.5	0.507302	0.253651	−	0.967296i	$-0.418368\pi$
$929$	14364.5	0.507302	0.253651	+	0.967296i	$0.418368\pi$
$930$	57568.1	2.02982
$931$	2648.73	0.0932423
$932$	−10902.3	−0.383171
$933$	−8278.05	−0.290473
$934$	20874.5	0.731302
$935$	−17263.8	−0.603836
$936$	726.839	0.0253819
$937$	−2672.29	−0.0931695	−0.0465847	−	0.998914i	$-0.514834\pi$
$937$	−2672.29	−0.0931695	−0.0465847	+	0.998914i	$0.514834\pi$
$938$	20684.7	0.720020
$939$	−55652.2	−1.93412
$940$	30604.1	1.06191
$941$	5819.40	0.201601	0.100801	−	0.994907i	$-0.467860\pi$
$941$	5819.40	0.201601	0.100801	+	0.994907i	$0.467860\pi$
$942$	80611.2	2.78817
$943$	4067.83	0.140474
$944$	15297.2	0.527415
$945$	12728.7	0.438163
$946$	−16738.1	−0.575266
$947$	40253.6	1.38127	0.690636	−	0.723203i	$-0.257331\pi$
$947$	40253.6	1.38127	0.690636	+	0.723203i	$0.257331\pi$
$948$	−10085.7	−0.345537
$949$	−5928.39	−0.202786
$950$	9699.27	0.331248
$951$	−45711.6	−1.55868
$952$	2103.74	0.0716206
$953$	40020.5	1.36033	0.680163	−	0.733061i	$-0.261909\pi$
$953$	40020.5	1.36033	0.680163	+	0.733061i	$0.261909\pi$
$954$	12585.3	0.427112
$955$	45926.0	1.55616
$956$	12096.6	0.409238
$957$	−4178.32	−0.141135
$958$	10805.8	0.364426
$959$	−6479.28	−0.218172
$960$	−50055.5	−1.68285
$961$	−3541.89	−0.118891
$962$	−31607.4	−1.05932
$963$	8918.30	0.298430
$964$	53168.9	1.77641
$965$	9812.95	0.327347
$966$	−10824.2	−0.360522
$967$	21733.2	0.722743	0.361372	−	0.932422i	$-0.382309\pi$
$967$	21733.2	0.722743	0.361372	+	0.932422i	$0.382309\pi$
$968$	1719.11	0.0570809
$969$	−23255.3	−0.770969
$970$	−47131.0	−1.56009
$971$	−1089.98	−0.0360237	−0.0180119	−	0.999838i	$-0.505734\pi$
$971$	−1089.98	−0.0360237	−0.0180119	+	0.999838i	$0.505734\pi$
$972$	−37629.8	−1.24175
$973$	18942.9	0.624133
$974$	8798.60	0.289451
$975$	−5821.27	−0.191210
$976$	−7132.64	−0.233924
$977$	−38981.9	−1.27650	−0.638251	−	0.769829i	$-0.720342\pi$
$977$	−38981.9	−1.27650	−0.638251	+	0.769829i	$0.720342\pi$
$978$	35724.4	1.16804
$979$	−7775.23	−0.253828
$980$	−5271.94	−0.171843
$981$	−30167.0	−0.981814
$982$	86391.2	2.80739
$983$	−14313.2	−0.464414	−0.232207	−	0.972666i	$-0.574595\pi$
$983$	−14313.2	−0.464414	−0.232207	+	0.972666i	$0.574595\pi$
$984$	2344.50	0.0759551
$985$	−46645.1	−1.50887
$986$	−7339.98	−0.237071
$987$	−32240.1	−1.03973
$988$	9363.08	0.301497
$989$	4440.84	0.142781
$990$	20837.8	0.668958
$991$	31052.1	0.995360	0.497680	−	0.867361i	$-0.334185\pi$
$991$	31052.1	0.995360	0.497680	+	0.867361i	$0.334185\pi$
$992$	−41944.5	−1.34248
$993$	−52135.1	−1.66612
$994$	32623.4	1.04100
$995$	58171.1	1.85342
$996$	24755.7	0.787566
$997$	−39169.8	−1.24425	−0.622126	−	0.782917i	$-0.713731\pi$
$997$	−39169.8	−1.24425	−0.622126	+	0.782917i	$0.713731\pi$
$998$	30122.4	0.955418
$999$	22279.4	0.705594

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-4.06003 q^{2} +6.74784 q^{3} +8.48386 q^{4} +12.9697 q^{5} -27.3964 q^{6} -17.1781 q^{7} -1.96449 q^{8} +18.5333 q^{9} +O(q^{10})\)	\(q-4.06003 q^{2} +6.74784 q^{3} +8.48386 q^{4} +12.9697 q^{5} -27.3964 q^{6} -17.1781 q^{7} -1.96449 q^{8} +18.5333 q^{9} -52.6574 q^{10} -21.3520 q^{11} +57.2477 q^{12} -19.9634 q^{13} +69.7437 q^{14} +87.5175 q^{15} -59.8950 q^{16} +62.3401 q^{17} -75.2459 q^{18} -55.2829 q^{19} +110.033 q^{20} -115.915 q^{21} +86.6898 q^{22} -23.0000 q^{23} -13.2561 q^{24} +43.2134 q^{25} +81.0520 q^{26} -57.1318 q^{27} -145.737 q^{28} +29.0000 q^{29} -355.324 q^{30} -162.016 q^{31} +258.892 q^{32} -144.080 q^{33} -253.103 q^{34} -222.795 q^{35} +157.234 q^{36} -389.965 q^{37} +224.450 q^{38} -134.710 q^{39} -25.4789 q^{40} -176.862 q^{41} +470.619 q^{42} -193.080 q^{43} -181.147 q^{44} +240.372 q^{45} +93.3807 q^{46} +278.135 q^{47} -404.162 q^{48} -47.9123 q^{49} -175.448 q^{50} +420.661 q^{51} -169.367 q^{52} -167.256 q^{53} +231.957 q^{54} -276.929 q^{55} +33.7463 q^{56} -373.040 q^{57} -117.741 q^{58} -255.400 q^{59} +742.487 q^{60} +119.086 q^{61} +657.789 q^{62} -318.368 q^{63} -571.948 q^{64} -258.919 q^{65} +584.969 q^{66} +296.581 q^{67} +528.884 q^{68} -155.200 q^{69} +904.556 q^{70} +467.761 q^{71} -36.4086 q^{72} +296.963 q^{73} +1583.27 q^{74} +291.597 q^{75} -469.012 q^{76} +366.787 q^{77} +546.926 q^{78} -176.177 q^{79} -776.821 q^{80} -885.916 q^{81} +718.066 q^{82} +432.432 q^{83} -983.408 q^{84} +808.533 q^{85} +783.912 q^{86} +195.687 q^{87} +41.9458 q^{88} +364.145 q^{89} -975.918 q^{90} +342.934 q^{91} -195.129 q^{92} -1093.26 q^{93} -1129.24 q^{94} -717.003 q^{95} +1746.96 q^{96} +895.049 q^{97} +194.525 q^{98} -395.724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 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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