LMFDB - Embedded newform 667.4.a.b.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.57414 q^{2} +1.72681 q^{3} -1.37379 q^{4} +7.29105 q^{5} -4.44507 q^{6} +28.8124 q^{7} +24.1295 q^{8} -24.0181 q^{9} +O(q^{10})$	\(q-2.57414 q^{2} +1.72681 q^{3} -1.37379 q^{4} +7.29105 q^{5} -4.44507 q^{6} +28.8124 q^{7} +24.1295 q^{8} -24.0181 q^{9} -18.7682 q^{10} +14.0017 q^{11} -2.37228 q^{12} -51.2995 q^{13} -74.1672 q^{14} +12.5903 q^{15} -51.1224 q^{16} -33.1998 q^{17} +61.8261 q^{18} -73.1248 q^{19} -10.0164 q^{20} +49.7536 q^{21} -36.0424 q^{22} -23.0000 q^{23} +41.6671 q^{24} -71.8405 q^{25} +132.052 q^{26} -88.0988 q^{27} -39.5821 q^{28} +29.0000 q^{29} -32.4092 q^{30} -208.039 q^{31} -61.4394 q^{32} +24.1784 q^{33} +85.4610 q^{34} +210.073 q^{35} +32.9958 q^{36} +43.5339 q^{37} +188.234 q^{38} -88.5847 q^{39} +175.929 q^{40} +340.704 q^{41} -128.073 q^{42} +328.221 q^{43} -19.2354 q^{44} -175.117 q^{45} +59.2053 q^{46} -17.5386 q^{47} -88.2789 q^{48} +487.153 q^{49} +184.928 q^{50} -57.3298 q^{51} +70.4746 q^{52} -680.293 q^{53} +226.779 q^{54} +102.087 q^{55} +695.227 q^{56} -126.273 q^{57} -74.6501 q^{58} -9.64131 q^{59} -17.2964 q^{60} -918.450 q^{61} +535.523 q^{62} -692.019 q^{63} +567.133 q^{64} -374.027 q^{65} -62.2385 q^{66} -561.411 q^{67} +45.6095 q^{68} -39.7167 q^{69} -540.757 q^{70} -483.378 q^{71} -579.544 q^{72} +94.6060 q^{73} -112.062 q^{74} -124.055 q^{75} +100.458 q^{76} +403.423 q^{77} +228.030 q^{78} -583.577 q^{79} -372.736 q^{80} +496.359 q^{81} -877.022 q^{82} +1280.87 q^{83} -68.3510 q^{84} -242.061 q^{85} -844.887 q^{86} +50.0776 q^{87} +337.854 q^{88} +1140.98 q^{89} +450.777 q^{90} -1478.06 q^{91} +31.5971 q^{92} -359.245 q^{93} +45.1469 q^{94} -533.156 q^{95} -106.094 q^{96} +1061.10 q^{97} -1254.00 q^{98} -336.295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57414	−0.910097	−0.455048	−	0.890467i	$-0.650378\pi$
$2$	−2.57414	−0.910097	−0.455048	+	0.890467i	$0.650378\pi$
$3$	1.72681	0.332326	0.166163	−	0.986098i	$-0.446862\pi$
$3$	1.72681	0.332326	0.166163	+	0.986098i	$0.446862\pi$
$4$	−1.37379	−0.171724
$5$	7.29105	0.652132	0.326066	−	0.945347i	$-0.394277\pi$
$5$	7.29105	0.652132	0.326066	+	0.945347i	$0.394277\pi$
$6$	−4.44507	−0.302448
$7$	28.8124	1.55572	0.777861	−	0.628436i	$-0.216305\pi$
$7$	28.8124	1.55572	0.777861	+	0.628436i	$0.216305\pi$
$8$	24.1295	1.06638
$9$	−24.0181	−0.889560
$10$	−18.7682	−0.593503
$11$	14.0017	0.383789	0.191894	−	0.981416i	$-0.438537\pi$
$11$	14.0017	0.383789	0.191894	+	0.981416i	$0.438537\pi$
$12$	−2.37228	−0.0570681
$13$	−51.2995	−1.09445	−0.547227	−	0.836984i	$-0.684317\pi$
$13$	−51.2995	−1.09445	−0.547227	+	0.836984i	$0.684317\pi$
$14$	−74.1672	−1.41586
$15$	12.5903	0.216720
$16$	−51.1224	−0.798787
$17$	−33.1998	−0.473655	−0.236827	−	0.971552i	$-0.576108\pi$
$17$	−33.1998	−0.473655	−0.236827	+	0.971552i	$0.576108\pi$
$18$	61.8261	0.809586
$19$	−73.1248	−0.882946	−0.441473	−	0.897275i	$-0.645544\pi$
$19$	−73.1248	−0.882946	−0.441473	+	0.897275i	$0.645544\pi$
$20$	−10.0164	−0.111986
$21$	49.7536	0.517006
$22$	−36.0424	−0.349285
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	41.6671	0.354386
$25$	−71.8405	−0.574724
$26$	132.052	0.996060
$27$	−88.0988	−0.627949
$28$	−39.5821	−0.267154
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−32.4092	−0.197236
$31$	−208.039	−1.20532	−0.602660	−	0.797998i	$-0.705893\pi$
$31$	−208.039	−1.20532	−0.602660	+	0.797998i	$0.705893\pi$
$32$	−61.4394	−0.339408
$33$	24.1784	0.127543
$34$	85.4610	0.431072
$35$	210.073	1.01454
$36$	32.9958	0.152758
$37$	43.5339	0.193430	0.0967152	−	0.995312i	$-0.469166\pi$
$37$	43.5339	0.193430	0.0967152	+	0.995312i	$0.469166\pi$
$38$	188.234	0.803566
$39$	−88.5847	−0.363715
$40$	175.929	0.695421
$41$	340.704	1.29778	0.648891	−	0.760881i	$-0.275233\pi$
$41$	340.704	1.29778	0.648891	+	0.760881i	$0.275233\pi$
$42$	−128.073	−0.470526
$43$	328.221	1.16403	0.582014	−	0.813179i	$-0.302265\pi$
$43$	328.221	1.16403	0.582014	+	0.813179i	$0.302265\pi$
$44$	−19.2354	−0.0659056
$45$	−175.117	−0.580110
$46$	59.2053	0.189768
$47$	−17.5386	−0.0544313	−0.0272156	−	0.999630i	$-0.508664\pi$
$47$	−17.5386	−0.0544313	−0.0272156	+	0.999630i	$0.508664\pi$
$48$	−88.2789	−0.265458
$49$	487.153	1.42027
$50$	184.928	0.523055
$51$	−57.3298	−0.157408
$52$	70.4746	0.187944
$53$	−680.293	−1.76312	−0.881561	−	0.472070i	$-0.843507\pi$
$53$	−680.293	−1.76312	−0.881561	+	0.472070i	$0.843507\pi$
$54$	226.779	0.571494
$55$	102.087	0.250281
$56$	695.227	1.65899
$57$	−126.273	−0.293425
$58$	−74.6501	−0.169001
$59$	−9.64131	−0.0212744	−0.0106372	−	0.999943i	$-0.503386\pi$
$59$	−9.64131	−0.0212744	−0.0106372	+	0.999943i	$0.503386\pi$
$60$	−17.2964	−0.0372159
$61$	−918.450	−1.92779	−0.963897	−	0.266274i	$-0.914207\pi$
$61$	−918.450	−1.92779	−0.963897	+	0.266274i	$0.914207\pi$
$62$	535.523	1.09696
$63$	−692.019	−1.38391
$64$	567.133	1.10768
$65$	−374.027	−0.713729
$66$	−62.2385	−0.116076
$67$	−561.411	−1.02369	−0.511846	−	0.859077i	$-0.671038\pi$
$67$	−561.411	−1.02369	−0.511846	+	0.859077i	$0.671038\pi$
$68$	45.6095	0.0813377
$69$	−39.7167	−0.0692947
$70$	−540.757	−0.923326
$71$	−483.378	−0.807977	−0.403989	−	0.914764i	$-0.632376\pi$
$71$	−483.378	−0.807977	−0.403989	+	0.914764i	$0.632376\pi$
$72$	−579.544	−0.948610
$73$	94.6060	0.151682	0.0758411	−	0.997120i	$-0.475836\pi$
$73$	94.6060	0.151682	0.0758411	+	0.997120i	$0.475836\pi$
$74$	−112.062	−0.176040
$75$	−124.055	−0.190996
$76$	100.458	0.151623
$77$	403.423	0.597068
$78$	228.030	0.331016
$79$	−583.577	−0.831108	−0.415554	−	0.909569i	$-0.636412\pi$
$79$	−583.577	−0.831108	−0.415554	+	0.909569i	$0.636412\pi$
$80$	−372.736	−0.520915
$81$	496.359	0.680876
$82$	−877.022	−1.18111
$83$	1280.87	1.69390	0.846948	−	0.531675i	$-0.178437\pi$
$83$	1280.87	1.69390	0.846948	+	0.531675i	$0.178437\pi$
$84$	−68.3510	−0.0887822
$85$	−242.061	−0.308885
$86$	−844.887	−1.05938
$87$	50.0776	0.0617113
$88$	337.854	0.409265
$89$	1140.98	1.35892	0.679460	−	0.733712i	$-0.262214\pi$
$89$	1140.98	1.35892	0.679460	+	0.733712i	$0.262214\pi$
$90$	450.777	0.527956
$91$	−1478.06	−1.70267
$92$	31.5971	0.0358068
$93$	−359.245	−0.400559
$94$	45.1469	0.0495377
$95$	−533.156	−0.575797
$96$	−106.094	−0.112794
$97$	1061.10	1.11071	0.555353	−	0.831615i	$-0.312583\pi$
$97$	1061.10	1.11071	0.555353	+	0.831615i	$0.312583\pi$
$98$	−1254.00	−1.29258
$99$	−336.295	−0.341403
$100$	98.6937	0.0986937
$101$	−1842.15	−1.81486	−0.907429	−	0.420206i	$-0.861958\pi$
$101$	−1842.15	−1.81486	−0.907429	+	0.420206i	$0.861958\pi$
$102$	147.575	0.143256
$103$	1211.24	1.15871	0.579354	−	0.815076i	$-0.303305\pi$
$103$	1211.24	1.15871	0.579354	+	0.815076i	$0.303305\pi$
$104$	−1237.83	−1.16711
$105$	362.756	0.337156
$106$	1751.17	1.60461
$107$	−1192.57	−1.07748	−0.538739	−	0.842473i	$-0.681099\pi$
$107$	−1192.57	−1.07748	−0.538739	+	0.842473i	$0.681099\pi$
$108$	121.029	0.107834
$109$	−291.118	−0.255817	−0.127909	−	0.991786i	$-0.540826\pi$
$109$	−291.118	−0.255817	−0.127909	+	0.991786i	$0.540826\pi$
$110$	−262.787	−0.227780
$111$	75.1749	0.0642819
$112$	−1472.96	−1.24269
$113$	−1288.67	−1.07281	−0.536405	−	0.843961i	$-0.680218\pi$
$113$	−1288.67	−1.07281	−0.536405	+	0.843961i	$0.680218\pi$
$114$	325.044	0.267046
$115$	−167.694	−0.135979
$116$	−39.8399	−0.0318883
$117$	1232.12	0.973583
$118$	24.8181	0.0193618
$119$	−956.564	−0.736875
$120$	303.797	0.231106
$121$	−1134.95	−0.852706
$122$	2364.22	1.75448
$123$	588.333	0.431286
$124$	285.802	0.206982
$125$	−1435.17	−1.02693
$126$	1781.36	1.25949
$127$	619.756	0.433027	0.216514	−	0.976280i	$-0.430531\pi$
$127$	619.756	0.433027	0.216514	+	0.976280i	$0.430531\pi$
$128$	−968.366	−0.668690
$129$	566.776	0.386836
$130$	962.799	0.649562
$131$	−2795.06	−1.86417	−0.932084	−	0.362243i	$-0.882011\pi$
$131$	−2795.06	−1.86417	−0.932084	+	0.362243i	$0.882011\pi$
$132$	−33.2160	−0.0219021
$133$	−2106.90	−1.37362
$134$	1445.15	0.931658
$135$	−642.333	−0.409505
$136$	−801.093	−0.505097
$137$	753.127	0.469664	0.234832	−	0.972036i	$-0.424546\pi$
$137$	753.127	0.469664	0.234832	+	0.972036i	$0.424546\pi$
$138$	102.237	0.0630649
$139$	−1302.44	−0.794759	−0.397379	−	0.917654i	$-0.630080\pi$
$139$	−1302.44	−0.794759	−0.397379	+	0.917654i	$0.630080\pi$
$140$	−288.595	−0.174220
$141$	−30.2859	−0.0180889
$142$	1244.28	0.735338
$143$	−718.280	−0.420039
$144$	1227.86	0.710569
$145$	211.441	0.121098
$146$	−243.529	−0.138045
$147$	841.223	0.471992
$148$	−59.8063	−0.0332166
$149$	1625.15	0.893541	0.446771	−	0.894649i	$-0.352574\pi$
$149$	1625.15	0.893541	0.446771	+	0.894649i	$0.352574\pi$
$150$	319.336	0.173825
$151$	−3623.82	−1.95299	−0.976496	−	0.215534i	$-0.930851\pi$
$151$	−3623.82	−1.95299	−0.976496	+	0.215534i	$0.930851\pi$
$152$	−1764.46	−0.941557
$153$	797.396	0.421344
$154$	−1038.47	−0.543390
$155$	−1516.82	−0.786028
$156$	121.697	0.0624585
$157$	483.336	0.245697	0.122849	−	0.992425i	$-0.460797\pi$
$157$	483.336	0.245697	0.122849	+	0.992425i	$0.460797\pi$
$158$	1502.21	0.756389
$159$	−1174.74	−0.585931
$160$	−447.958	−0.221339
$161$	−662.685	−0.324390
$162$	−1277.70	−0.619663
$163$	1571.79	0.755290	0.377645	−	0.925950i	$-0.376734\pi$
$163$	1571.79	0.755290	0.377645	+	0.925950i	$0.376734\pi$
$164$	−468.056	−0.222860
$165$	176.286	0.0831747
$166$	−3297.13	−1.54161
$167$	−2297.06	−1.06438	−0.532190	−	0.846625i	$-0.678631\pi$
$167$	−2297.06	−1.06438	−0.532190	+	0.846625i	$0.678631\pi$
$168$	1200.53	0.551326
$169$	434.635	0.197831
$170$	623.100	0.281115
$171$	1756.32	0.785433
$172$	−450.906	−0.199891
$173$	4325.73	1.90103	0.950517	−	0.310672i	$-0.100554\pi$
$173$	4325.73	1.90103	0.950517	+	0.310672i	$0.100554\pi$
$174$	−128.907	−0.0561633
$175$	−2069.90	−0.894111
$176$	−715.801	−0.306566
$177$	−16.6487	−0.00707004
$178$	−2937.05	−1.23675
$179$	974.899	0.407080	0.203540	−	0.979067i	$-0.434755\pi$
$179$	974.899	0.407080	0.203540	+	0.979067i	$0.434755\pi$
$180$	240.574	0.0996186
$181$	642.110	0.263689	0.131844	−	0.991270i	$-0.457910\pi$
$181$	642.110	0.263689	0.131844	+	0.991270i	$0.457910\pi$
$182$	3804.74	1.54959
$183$	−1585.99	−0.640656
$184$	−554.978	−0.222356
$185$	317.408	0.126142
$186$	924.748	0.364547
$187$	−464.854	−0.181783
$188$	24.0944	0.00934713
$189$	−2538.34	−0.976914
$190$	1372.42	0.524031
$191$	−3286.73	−1.24513	−0.622564	−	0.782569i	$-0.713909\pi$
$191$	−3286.73	−1.24513	−0.622564	+	0.782569i	$0.713909\pi$
$192$	979.333	0.368111
$193$	2526.25	0.942193	0.471097	−	0.882082i	$-0.343858\pi$
$193$	2526.25	0.942193	0.471097	+	0.882082i	$0.343858\pi$
$194$	−2731.43	−1.01085
$195$	−645.875	−0.237190
$196$	−669.245	−0.243894
$197$	923.857	0.334122	0.167061	−	0.985947i	$-0.446572\pi$
$197$	923.857	0.334122	0.167061	+	0.985947i	$0.446572\pi$
$198$	865.671	0.310710
$199$	−3547.26	−1.26361	−0.631806	−	0.775126i	$-0.717686\pi$
$199$	−3547.26	−1.26361	−0.631806	+	0.775126i	$0.717686\pi$
$200$	−1733.47	−0.612876
$201$	−969.453	−0.340199
$202$	4741.95	1.65170
$203$	835.559	0.288890
$204$	78.7591	0.0270306
$205$	2484.09	0.846325
$206$	−3117.90	−1.05454
$207$	552.417	0.185486
$208$	2622.55	0.874237
$209$	−1023.87	−0.338865
$210$	−933.787	−0.306845
$211$	−2159.93	−0.704718	−0.352359	−	0.935865i	$-0.614620\pi$
$211$	−2159.93	−0.704718	−0.352359	+	0.935865i	$0.614620\pi$
$212$	934.579	0.302770
$213$	−834.704	−0.268512
$214$	3069.85	0.980610
$215$	2393.08	0.759100
$216$	−2125.78	−0.669634
$217$	−5994.10	−1.87514
$218$	749.380	0.232818
$219$	163.367	0.0504079
$220$	−140.246	−0.0429791
$221$	1703.13	0.518393
$222$	−193.511	−0.0585027
$223$	−5375.63	−1.61425	−0.807127	−	0.590378i	$-0.798979\pi$
$223$	−5375.63	−1.61425	−0.807127	+	0.590378i	$0.798979\pi$
$224$	−1770.22	−0.528025
$225$	1725.47	0.511252
$226$	3317.21	0.976361
$227$	−3507.43	−1.02553	−0.512767	−	0.858528i	$-0.671380\pi$
$227$	−3507.43	−1.02553	−0.512767	+	0.858528i	$0.671380\pi$
$228$	173.472	0.0503881
$229$	4861.68	1.40292	0.701461	−	0.712708i	$-0.252532\pi$
$229$	4861.68	1.40292	0.701461	+	0.712708i	$0.252532\pi$
$230$	431.669	0.123754
$231$	696.636	0.198421
$232$	699.755	0.198022
$233$	−6089.14	−1.71207	−0.856036	−	0.516917i	$-0.827080\pi$
$233$	−6089.14	−1.71207	−0.856036	+	0.516917i	$0.827080\pi$
$234$	−3171.64	−0.886055
$235$	−127.875	−0.0354964
$236$	13.2451	0.00365332
$237$	−1007.73	−0.276198
$238$	2462.33	0.670628
$239$	2675.65	0.724156	0.362078	−	0.932148i	$-0.382067\pi$
$239$	2675.65	0.724156	0.362078	+	0.932148i	$0.382067\pi$
$240$	−643.646	−0.173113
$241$	6847.78	1.83031	0.915153	−	0.403106i	$-0.132069\pi$
$241$	6847.78	1.83031	0.915153	+	0.403106i	$0.132069\pi$
$242$	2921.53	0.776045
$243$	3235.79	0.854222
$244$	1261.76	0.331048
$245$	3551.86	0.926204
$246$	−1514.45	−0.392512
$247$	3751.26	0.966344
$248$	−5019.88	−1.28533
$249$	2211.82	0.562925
$250$	3694.35	0.934604
$251$	−1777.99	−0.447113	−0.223557	−	0.974691i	$-0.571767\pi$
$251$	−1777.99	−0.447113	−0.223557	+	0.974691i	$0.571767\pi$
$252$	950.688	0.237650
$253$	−322.039	−0.0800255
$254$	−1595.34	−0.394097
$255$	−417.995	−0.102650
$256$	−2044.35	−0.499109
$257$	4447.93	1.07959	0.539794	−	0.841797i	$-0.318502\pi$
$257$	4447.93	1.07959	0.539794	+	0.841797i	$0.318502\pi$
$258$	−1458.96	−0.352059
$259$	1254.31	0.300924
$260$	513.834	0.122564
$261$	−696.525	−0.165187
$262$	7194.90	1.69657
$263$	2650.96	0.621540	0.310770	−	0.950485i	$-0.399413\pi$
$263$	2650.96	0.621540	0.310770	+	0.950485i	$0.399413\pi$
$264$	583.411	0.136009
$265$	−4960.05	−1.14979
$266$	5423.46	1.25013
$267$	1970.27	0.451604
$268$	771.261	0.175792
$269$	−2298.63	−0.521004	−0.260502	−	0.965473i	$-0.583888\pi$
$269$	−2298.63	−0.521004	−0.260502	+	0.965473i	$0.583888\pi$
$270$	1653.46	0.372690
$271$	4426.60	0.992239	0.496120	−	0.868254i	$-0.334758\pi$
$271$	4426.60	0.992239	0.496120	+	0.868254i	$0.334758\pi$
$272$	1697.25	0.378349
$273$	−2552.33	−0.565840
$274$	−1938.66	−0.427440
$275$	−1005.89	−0.220573
$276$	54.5624	0.0118995
$277$	1700.96	0.368956	0.184478	−	0.982837i	$-0.440941\pi$
$277$	1700.96	0.368956	0.184478	+	0.982837i	$0.440941\pi$
$278$	3352.67	0.723308
$279$	4996.71	1.07220
$280$	5068.94	1.08188
$281$	2767.31	0.587486	0.293743	−	0.955884i	$-0.405099\pi$
$281$	2767.31	0.587486	0.293743	+	0.955884i	$0.405099\pi$
$282$	77.9603	0.0164627
$283$	6308.84	1.32516	0.662582	−	0.748989i	$-0.269460\pi$
$283$	6308.84	1.32516	0.662582	+	0.748989i	$0.269460\pi$
$284$	664.059	0.138749
$285$	−920.662	−0.191352
$286$	1848.96	0.382276
$287$	9816.50	2.01899
$288$	1475.66	0.301924
$289$	−3810.78	−0.775651
$290$	−544.278	−0.110211
$291$	1832.32	0.369116
$292$	−129.969	−0.0260474
$293$	−8564.09	−1.70758	−0.853788	−	0.520621i	$-0.825700\pi$
$293$	−8564.09	−1.70758	−0.853788	+	0.520621i	$0.825700\pi$
$294$	−2165.43	−0.429559
$295$	−70.2953	−0.0138737
$296$	1050.45	0.206271
$297$	−1233.53	−0.241000
$298$	−4183.37	−0.813209
$299$	1179.89	0.228210
$300$	170.426	0.0327985
$301$	9456.82	1.81090
$302$	9328.22	1.77741
$303$	−3181.05	−0.603123
$304$	3738.31	0.705286
$305$	−6696.47	−1.25718
$306$	−2052.61	−0.383464
$307$	−5193.73	−0.965543	−0.482771	−	0.875746i	$-0.660370\pi$
$307$	−5193.73	−0.965543	−0.482771	+	0.875746i	$0.660370\pi$
$308$	−554.217	−0.102531
$309$	2091.58	0.385068
$310$	3904.52	0.715361
$311$	−2810.66	−0.512469	−0.256235	−	0.966615i	$-0.582482\pi$
$311$	−2810.66	−0.512469	−0.256235	+	0.966615i	$0.582482\pi$
$312$	−2137.50	−0.387859
$313$	4020.83	0.726105	0.363052	−	0.931769i	$-0.381735\pi$
$313$	4020.83	0.726105	0.363052	+	0.931769i	$0.381735\pi$
$314$	−1244.18	−0.223608
$315$	−5045.55	−0.902490
$316$	801.711	0.142721
$317$	1577.38	0.279478	0.139739	−	0.990188i	$-0.455374\pi$
$317$	1577.38	0.279478	0.139739	+	0.990188i	$0.455374\pi$
$318$	3023.95	0.533254
$319$	406.050	0.0712678
$320$	4135.00	0.722354
$321$	−2059.35	−0.358074
$322$	1705.84	0.295227
$323$	2427.73	0.418211
$324$	−681.892	−0.116922
$325$	3685.38	0.629010
$326$	−4046.02	−0.687387
$327$	−502.707	−0.0850145
$328$	8221.01	1.38393
$329$	−505.329	−0.0846799
$330$	−453.785	−0.0756970
$331$	−5612.83	−0.932052	−0.466026	−	0.884771i	$-0.654315\pi$
$331$	−5612.83	−0.932052	−0.466026	+	0.884771i	$0.654315\pi$
$332$	−1759.64	−0.290882
$333$	−1045.60	−0.172068
$334$	5912.95	0.968690
$335$	−4093.28	−0.667582
$336$	−2543.52	−0.412978
$337$	4463.28	0.721455	0.360728	−	0.932671i	$-0.382528\pi$
$337$	4463.28	0.721455	0.360728	+	0.932671i	$0.382528\pi$
$338$	−1118.81	−0.180046
$339$	−2225.29	−0.356522
$340$	332.541	0.0530429
$341$	−2912.90	−0.462588
$342$	−4521.01	−0.714820
$343$	4153.39	0.653825
$344$	7919.80	1.24130
$345$	−289.577	−0.0451892
$346$	−11135.0	−1.73013
$347$	3074.72	0.475677	0.237838	−	0.971305i	$-0.423561\pi$
$347$	3074.72	0.475677	0.237838	+	0.971305i	$0.423561\pi$
$348$	−68.7961	−0.0105973
$349$	921.911	0.141400	0.0707002	−	0.997498i	$-0.477477\pi$
$349$	921.911	0.141400	0.0707002	+	0.997498i	$0.477477\pi$
$350$	5328.21	0.813728
$351$	4519.42	0.687262
$352$	−860.257	−0.130261
$353$	−7540.39	−1.13693	−0.568463	−	0.822709i	$-0.692462\pi$
$353$	−7540.39	−1.13693	−0.568463	+	0.822709i	$0.692462\pi$
$354$	42.8563	0.00643442
$355$	−3524.33	−0.526908
$356$	−1567.47	−0.233359
$357$	−1651.81	−0.244882
$358$	−2509.53	−0.370483
$359$	91.1285	0.0133971	0.00669857	−	0.999978i	$-0.497868\pi$
$359$	91.1285	0.0133971	0.00669857	+	0.999978i	$0.497868\pi$
$360$	−4225.49	−0.618619
$361$	−1511.77	−0.220407
$362$	−1652.88	−0.239982
$363$	−1959.85	−0.283376
$364$	2030.54	0.292388
$365$	689.778	0.0989168
$366$	4082.57	0.583059
$367$	11718.5	1.66675	0.833377	−	0.552705i	$-0.186404\pi$
$367$	11718.5	1.66675	0.833377	+	0.552705i	$0.186404\pi$
$368$	1175.82	0.166559
$369$	−8183.07	−1.15445
$370$	−817.053	−0.114802
$371$	−19600.9	−2.74293
$372$	493.527	0.0687854
$373$	7645.72	1.06134	0.530670	−	0.847578i	$-0.321940\pi$
$373$	7645.72	1.06134	0.530670	+	0.847578i	$0.321940\pi$
$374$	1196.60	0.165440
$375$	−2478.28	−0.341274
$376$	−423.198	−0.0580445
$377$	−1487.68	−0.203235
$378$	6534.04	0.889087
$379$	1804.27	0.244536	0.122268	−	0.992497i	$-0.460983\pi$
$379$	1804.27	0.244536	0.122268	+	0.992497i	$0.460983\pi$
$380$	732.444	0.0988779
$381$	1070.20	0.143906
$382$	8460.52	1.13319
$383$	11661.5	1.55581	0.777907	−	0.628379i	$-0.216281\pi$
$383$	11661.5	1.55581	0.777907	+	0.628379i	$0.216281\pi$
$384$	−1672.19	−0.222223
$385$	2941.38	0.389367
$386$	−6502.92	−0.857487
$387$	−7883.24	−1.03547
$388$	−1457.73	−0.190734
$389$	−9492.18	−1.23720	−0.618602	−	0.785704i	$-0.712301\pi$
$389$	−9492.18	−1.23720	−0.618602	+	0.785704i	$0.712301\pi$
$390$	1662.58	0.215866
$391$	763.595	0.0987638
$392$	11754.7	1.51455
$393$	−4826.56	−0.619511
$394$	−2378.14	−0.304084
$395$	−4254.89	−0.541992
$396$	461.998	0.0586269
$397$	−14917.2	−1.88582	−0.942912	−	0.333042i	$-0.891925\pi$
$397$	−14917.2	−1.88582	−0.942912	+	0.333042i	$0.891925\pi$
$398$	9131.16	1.15001
$399$	−3638.22	−0.456488
$400$	3672.66	0.459083
$401$	7596.96	0.946070	0.473035	−	0.881044i	$-0.343158\pi$
$401$	7596.96	0.946070	0.473035	+	0.881044i	$0.343158\pi$
$402$	2495.51	0.309614
$403$	10672.3	1.31917
$404$	2530.72	0.311654
$405$	3618.98	0.444021
$406$	−2150.85	−0.262918
$407$	609.549	0.0742364
$408$	−1383.34	−0.167857
$409$	−8840.84	−1.06883	−0.534415	−	0.845222i	$-0.679468\pi$
$409$	−8840.84	−1.06883	−0.534415	+	0.845222i	$0.679468\pi$
$410$	−6394.41	−0.770238
$411$	1300.51	0.156081
$412$	−1663.99	−0.198977
$413$	−277.789	−0.0330971
$414$	−1422.00	−0.168810
$415$	9338.87	1.10464
$416$	3151.81	0.371467
$417$	−2249.07	−0.264119
$418$	2635.59	0.308400
$419$	12194.7	1.42184	0.710918	−	0.703275i	$-0.248280\pi$
$419$	12194.7	1.42184	0.710918	+	0.703275i	$0.248280\pi$
$420$	−498.351	−0.0578977
$421$	13341.7	1.54450	0.772250	−	0.635319i	$-0.219131\pi$
$421$	13341.7	1.54450	0.772250	+	0.635319i	$0.219131\pi$
$422$	5559.96	0.641362
$423$	421.244	0.0484199
$424$	−16415.1	−1.88016
$425$	2385.09	0.272221
$426$	2148.65	0.244372
$427$	−26462.7	−2.99911
$428$	1638.34	0.185028
$429$	−1240.34	−0.139590
$430$	−6160.12	−0.690854
$431$	−6058.42	−0.677086	−0.338543	−	0.940951i	$-0.609934\pi$
$431$	−6058.42	−0.677086	−0.338543	+	0.940951i	$0.609934\pi$
$432$	4503.82	0.501598
$433$	4759.64	0.528253	0.264126	−	0.964488i	$-0.414916\pi$
$433$	4759.64	0.528253	0.264126	+	0.964488i	$0.414916\pi$
$434$	15429.7	1.70656
$435$	365.119	0.0402439
$436$	399.935	0.0439298
$437$	1681.87	0.184107
$438$	−420.530	−0.0458760
$439$	16651.9	1.81037	0.905185	−	0.425017i	$-0.139732\pi$
$439$	16651.9	1.81037	0.905185	+	0.425017i	$0.139732\pi$
$440$	2463.31	0.266895
$441$	−11700.5	−1.26342
$442$	−4384.10	−0.471788
$443$	15849.0	1.69980	0.849898	−	0.526948i	$-0.176664\pi$
$443$	15849.0	1.69980	0.849898	+	0.526948i	$0.176664\pi$
$444$	−103.274	−0.0110387
$445$	8318.97	0.886195
$446$	13837.6	1.46913
$447$	2806.34	0.296947
$448$	16340.4	1.72324
$449$	−8139.92	−0.855560	−0.427780	−	0.903883i	$-0.640704\pi$
$449$	−8139.92	−0.855560	−0.427780	+	0.903883i	$0.640704\pi$
$450$	−4441.62	−0.465289
$451$	4770.44	0.498074
$452$	1770.36	0.184227
$453$	−6257.66	−0.649029
$454$	9028.62	0.933336
$455$	−10776.6	−1.11036
$456$	−3046.90	−0.312904
$457$	−10548.7	−1.07976	−0.539879	−	0.841743i	$-0.681530\pi$
$457$	−10548.7	−1.07976	−0.539879	+	0.841743i	$0.681530\pi$
$458$	−12514.7	−1.27679
$459$	2924.86	0.297431
$460$	230.376	0.0233508
$461$	−11352.4	−1.14693	−0.573464	−	0.819230i	$-0.694401\pi$
$461$	−11352.4	−1.14693	−0.573464	+	0.819230i	$0.694401\pi$
$462$	−1793.24	−0.180582
$463$	404.261	0.0405780	0.0202890	−	0.999794i	$-0.493541\pi$
$463$	404.261	0.0405780	0.0202890	+	0.999794i	$0.493541\pi$
$464$	−1482.55	−0.148331
$465$	−2619.27	−0.261217
$466$	15674.3	1.55815
$467$	−13309.5	−1.31883	−0.659413	−	0.751781i	$-0.729195\pi$
$467$	−13309.5	−1.31883	−0.659413	+	0.751781i	$0.729195\pi$
$468$	−1692.67	−0.167187
$469$	−16175.6	−1.59258
$470$	329.168	0.0323051
$471$	834.632	0.0816514
$472$	−232.640	−0.0226867
$473$	4595.65	0.446741
$474$	2594.04	0.251367
$475$	5253.32	0.507450
$476$	1314.12	0.126539
$477$	16339.4	1.56840
$478$	−6887.50	−0.659052
$479$	−14726.8	−1.40477	−0.702387	−	0.711796i	$-0.747882\pi$
$479$	−14726.8	−1.40477	−0.702387	+	0.711796i	$0.747882\pi$
$480$	−773.540	−0.0735565
$481$	−2233.26	−0.211701
$482$	−17627.2	−1.66576
$483$	−1144.33	−0.107803
$484$	1559.18	0.146430
$485$	7736.54	0.724326
$486$	−8329.38	−0.777424
$487$	3086.23	0.287167	0.143584	−	0.989638i	$-0.454137\pi$
$487$	3086.23	0.287167	0.143584	+	0.989638i	$0.454137\pi$
$488$	−22161.7	−2.05577
$489$	2714.20	0.251002
$490$	−9142.99	−0.842935
$491$	−15635.1	−1.43707	−0.718535	−	0.695491i	$-0.755187\pi$
$491$	−15635.1	−1.43707	−0.718535	+	0.695491i	$0.755187\pi$
$492$	−808.245	−0.0740620
$493$	−962.793	−0.0879554
$494$	−9656.28	−0.879467
$495$	−2451.94	−0.222640
$496$	10635.5	0.962795
$497$	−13927.3	−1.25699
$498$	−5693.54	−0.512316
$499$	−2580.82	−0.231530	−0.115765	−	0.993277i	$-0.536932\pi$
$499$	−2580.82	−0.231530	−0.115765	+	0.993277i	$0.536932\pi$
$500$	1971.63	0.176348
$501$	−3966.59	−0.353721
$502$	4576.79	0.406916
$503$	−13578.6	−1.20365	−0.601827	−	0.798626i	$-0.705560\pi$
$503$	−13578.6	−1.20365	−0.601827	+	0.798626i	$0.705560\pi$
$504$	−16698.0	−1.47577
$505$	−13431.2	−1.18353
$506$	828.975	0.0728309
$507$	750.535	0.0657444
$508$	−851.414	−0.0743610
$509$	−11040.0	−0.961371	−0.480686	−	0.876893i	$-0.659612\pi$
$509$	−11040.0	−0.961371	−0.480686	+	0.876893i	$0.659612\pi$
$510$	1075.98	0.0934218
$511$	2725.82	0.235975
$512$	13009.4	1.12293
$513$	6442.20	0.554445
$514$	−11449.6	−0.982530
$515$	8831.21	0.755630
$516$	−778.631	−0.0664289
$517$	−245.571	−0.0208901
$518$	−3228.78	−0.273870
$519$	7469.73	0.631762
$520$	−9025.08	−0.761107
$521$	−17800.3	−1.49682	−0.748410	−	0.663236i	$-0.769182\pi$
$521$	−17800.3	−1.49682	−0.748410	+	0.663236i	$0.769182\pi$
$522$	1792.96	0.150336
$523$	21711.8	1.81528	0.907638	−	0.419755i	$-0.137884\pi$
$523$	21711.8	1.81528	0.907638	+	0.419755i	$0.137884\pi$
$524$	3839.83	0.320122
$525$	−3574.33	−0.297136
$526$	−6823.94	−0.565662
$527$	6906.85	0.570906
$528$	−1236.06	−0.101880
$529$	529.000	0.0434783
$530$	12767.9	1.04642
$531$	231.566	0.0189249
$532$	2894.43	0.235883
$533$	−17477.9	−1.42036
$534$	−5071.75	−0.411004
$535$	−8695.10	−0.702658
$536$	−13546.6	−1.09165
$537$	1683.47	0.135283
$538$	5917.00	0.474164
$539$	6820.98	0.545084
$540$	882.430	0.0703217
$541$	−14301.5	−1.13654	−0.568270	−	0.822842i	$-0.692387\pi$
$541$	−14301.5	−1.13654	−0.568270	+	0.822842i	$0.692387\pi$
$542$	−11394.7	−0.903034
$543$	1108.81	0.0876306
$544$	2039.77	0.160762
$545$	−2122.56	−0.166826
$546$	6570.07	0.514969
$547$	8858.17	0.692410	0.346205	−	0.938159i	$-0.387470\pi$
$547$	8858.17	0.692410	0.346205	+	0.938159i	$0.387470\pi$
$548$	−1034.64	−0.0806524
$549$	22059.4	1.71489
$550$	2589.31	0.200743
$551$	−2120.62	−0.163959
$552$	−958.344	−0.0738946
$553$	−16814.2	−1.29297
$554$	−4378.51	−0.335785
$555$	548.104	0.0419202
$556$	1789.28	0.136479
$557$	−11356.8	−0.863917	−0.431959	−	0.901893i	$-0.642177\pi$
$557$	−11356.8	−0.863917	−0.431959	+	0.901893i	$0.642177\pi$
$558$	−12862.2	−0.975810
$559$	−16837.6	−1.27398
$560$	−10739.4	−0.810398
$561$	−802.716	−0.0604112
$562$	−7123.44	−0.534669
$563$	−17418.1	−1.30388	−0.651942	−	0.758269i	$-0.726045\pi$
$563$	−17418.1	−1.30388	−0.651942	+	0.758269i	$0.726045\pi$
$564$	41.6065	0.00310629
$565$	−9395.74	−0.699613
$566$	−16239.9	−1.20603
$567$	14301.3	1.05925
$568$	−11663.7	−0.861613
$569$	101.880	0.00750619	0.00375310	−	0.999993i	$-0.498805\pi$
$569$	101.880	0.00750619	0.00375310	+	0.999993i	$0.498805\pi$
$570$	2369.92	0.174149
$571$	9645.45	0.706917	0.353458	−	0.935450i	$-0.385006\pi$
$571$	9645.45	0.706917	0.353458	+	0.935450i	$0.385006\pi$
$572$	986.765	0.0721307
$573$	−5675.58	−0.413788
$574$	−25269.1	−1.83748
$575$	1652.33	0.119838
$576$	−13621.5	−0.985349
$577$	−1402.18	−0.101167	−0.0505836	−	0.998720i	$-0.516108\pi$
$577$	−1402.18	−0.101167	−0.0505836	+	0.998720i	$0.516108\pi$
$578$	9809.48	0.705918
$579$	4362.36	0.313115
$580$	−290.475	−0.0207953
$581$	36904.8	2.63523
$582$	−4716.66	−0.335931
$583$	−9525.27	−0.676666
$584$	2282.79	0.161751
$585$	8983.43	0.634904
$586$	22045.2	1.55406
$587$	−17766.8	−1.24926	−0.624629	−	0.780922i	$-0.714750\pi$
$587$	−17766.8	−1.24926	−0.624629	+	0.780922i	$0.714750\pi$
$588$	−1155.66	−0.0810522
$589$	15212.8	1.06423
$590$	180.950	0.0126264
$591$	1595.33	0.111037
$592$	−2225.56	−0.154510
$593$	−2190.76	−0.151710	−0.0758548	−	0.997119i	$-0.524169\pi$
$593$	−2190.76	−0.151710	−0.0758548	+	0.997119i	$0.524169\pi$
$594$	3175.29	0.219333
$595$	−6974.36	−0.480539
$596$	−2232.62	−0.153442
$597$	−6125.47	−0.419931
$598$	−3037.20	−0.207693
$599$	20624.9	1.40687	0.703433	−	0.710762i	$-0.251650\pi$
$599$	20624.9	1.40687	0.703433	+	0.710762i	$0.251650\pi$
$600$	−2993.39	−0.203674
$601$	25503.0	1.73093	0.865466	−	0.500968i	$-0.167023\pi$
$601$	25503.0	1.73093	0.865466	+	0.500968i	$0.167023\pi$
$602$	−24343.2	−1.64810
$603$	13484.0	0.910635
$604$	4978.36	0.335375
$605$	−8275.00	−0.556077
$606$	8188.47	0.548901
$607$	−22863.6	−1.52884	−0.764418	−	0.644720i	$-0.776974\pi$
$607$	−22863.6	−1.52884	−0.764418	+	0.644720i	$0.776974\pi$
$608$	4492.74	0.299679
$609$	1442.86	0.0960057
$610$	17237.7	1.14415
$611$	899.722	0.0595726
$612$	−1095.45	−0.0723547
$613$	3593.58	0.236775	0.118388	−	0.992967i	$-0.462227\pi$
$613$	3593.58	0.236775	0.118388	+	0.992967i	$0.462227\pi$
$614$	13369.4	0.878738
$615$	4289.57	0.281255
$616$	9734.37	0.636703
$617$	24525.4	1.60025	0.800127	−	0.599830i	$-0.204765\pi$
$617$	24525.4	1.60025	0.800127	+	0.599830i	$0.204765\pi$
$618$	−5384.04	−0.350449
$619$	−10797.6	−0.701120	−0.350560	−	0.936540i	$-0.614009\pi$
$619$	−10797.6	−0.701120	−0.350560	+	0.936540i	$0.614009\pi$
$620$	2083.80	0.134980
$621$	2026.27	0.130936
$622$	7235.04	0.466397
$623$	32874.4	2.11410
$624$	4528.66	0.290531
$625$	−1483.87	−0.0949676
$626$	−10350.2	−0.660826
$627$	−1768.04	−0.112613
$628$	−664.002	−0.0421920
$629$	−1445.31	−0.0916192
$630$	12988.0	0.821353
$631$	27974.8	1.76491	0.882456	−	0.470395i	$-0.155888\pi$
$631$	27974.8	1.76491	0.882456	+	0.470395i	$0.155888\pi$
$632$	−14081.4	−0.886278
$633$	−3729.79	−0.234196
$634$	−4060.40	−0.254352
$635$	4518.68	0.282391
$636$	1613.84	0.100618
$637$	−24990.7	−1.55442
$638$	−1045.23	−0.0648606
$639$	11609.8	0.718744
$640$	−7060.41	−0.436074
$641$	11373.5	0.700819	0.350409	−	0.936597i	$-0.386042\pi$
$641$	11373.5	0.700819	0.350409	+	0.936597i	$0.386042\pi$
$642$	5301.06	0.325882
$643$	20748.4	1.27253	0.636264	−	0.771471i	$-0.280479\pi$
$643$	20748.4	1.27253	0.636264	+	0.771471i	$0.280479\pi$
$644$	910.389	0.0557055
$645$	4132.40	0.252268
$646$	−6249.31	−0.380613
$647$	15032.0	0.913402	0.456701	−	0.889620i	$-0.349031\pi$
$647$	15032.0	0.913402	0.456701	+	0.889620i	$0.349031\pi$
$648$	11976.9	0.726074
$649$	−134.995	−0.00816488
$650$	−9486.70	−0.572460
$651$	−10350.7	−0.623158
$652$	−2159.31	−0.129701
$653$	−13121.8	−0.786365	−0.393182	−	0.919461i	$-0.628626\pi$
$653$	−13121.8	−0.786365	−0.393182	+	0.919461i	$0.628626\pi$
$654$	1294.04	0.0773715
$655$	−20379.0	−1.21568
$656$	−17417.6	−1.03665
$657$	−2272.26	−0.134930
$658$	1300.79	0.0770670
$659$	−6084.89	−0.359687	−0.179844	−	0.983695i	$-0.557559\pi$
$659$	−6084.89	−0.359687	−0.179844	+	0.983695i	$0.557559\pi$
$660$	−242.179	−0.0142831
$661$	12709.1	0.747848	0.373924	−	0.927459i	$-0.378012\pi$
$661$	12709.1	0.747848	0.373924	+	0.927459i	$0.378012\pi$
$662$	14448.2	0.848257
$663$	2940.99	0.172275
$664$	30906.6	1.80634
$665$	−15361.5	−0.895780
$666$	2691.53	0.156598
$667$	−667.000	−0.0387202
$668$	3155.67	0.182779
$669$	−9282.71	−0.536458
$670$	10536.7	0.607564
$671$	−12859.9	−0.739866
$672$	−3056.83	−0.175476
$673$	−21100.2	−1.20855	−0.604274	−	0.796776i	$-0.706537\pi$
$673$	−21100.2	−1.20855	−0.604274	+	0.796776i	$0.706537\pi$
$674$	−11489.1	−0.656594
$675$	6329.07	0.360898
$676$	−597.097	−0.0339723
$677$	10443.7	0.592887	0.296443	−	0.955050i	$-0.404199\pi$
$677$	10443.7	0.592887	0.296443	+	0.955050i	$0.404199\pi$
$678$	5728.21	0.324470
$679$	30572.8	1.72795
$680$	−5840.81	−0.329390
$681$	−6056.68	−0.340811
$682$	7498.23	0.421000
$683$	14739.5	0.825755	0.412878	−	0.910787i	$-0.364524\pi$
$683$	14739.5	0.825755	0.412878	+	0.910787i	$0.364524\pi$
$684$	−2412.81	−0.134877
$685$	5491.09	0.306283
$686$	−10691.4	−0.595044
$687$	8395.22	0.466227
$688$	−16779.4	−0.929811
$689$	34898.7	1.92966
$690$	745.412	0.0411266
$691$	15355.2	0.845354	0.422677	−	0.906280i	$-0.361091\pi$
$691$	15355.2	0.845354	0.422677	+	0.906280i	$0.361091\pi$
$692$	−5942.63	−0.326452
$693$	−9689.45	−0.531128
$694$	−7914.78	−0.432912
$695$	−9496.16	−0.518287
$696$	1208.35	0.0658078
$697$	−11311.3	−0.614700
$698$	−2373.13	−0.128688
$699$	−10514.8	−0.568965
$700$	2843.60	0.153540
$701$	−8889.45	−0.478959	−0.239479	−	0.970901i	$-0.576977\pi$
$701$	−8889.45	−0.478959	−0.239479	+	0.970901i	$0.576977\pi$
$702$	−11633.6	−0.625475
$703$	−3183.40	−0.170789
$704$	7940.83	0.425116
$705$	−220.816	−0.0117963
$706$	19410.0	1.03471
$707$	−53076.7	−2.82341
$708$	22.8719	0.00121409
$709$	11569.5	0.612836	0.306418	−	0.951897i	$-0.400870\pi$
$709$	11569.5	0.612836	0.306418	+	0.951897i	$0.400870\pi$
$710$	9072.14	0.479537
$711$	14016.4	0.739320
$712$	27531.3	1.44913
$713$	4784.90	0.251327
$714$	4251.99	0.222867
$715$	−5237.02	−0.273921
$716$	−1339.31	−0.0699053
$717$	4620.34	0.240655
$718$	−234.578	−0.0121927
$719$	−1280.23	−0.0664042	−0.0332021	−	0.999449i	$-0.510571\pi$
$719$	−1280.23	−0.0664042	−0.0332021	+	0.999449i	$0.510571\pi$
$720$	8952.42	0.463385
$721$	34898.7	1.80263
$722$	3891.51	0.200592
$723$	11824.8	0.608258
$724$	−882.124	−0.0452816
$725$	−2083.38	−0.106724
$726$	5044.94	0.257900
$727$	7423.16	0.378693	0.189346	−	0.981910i	$-0.439363\pi$
$727$	7423.16	0.378693	0.189346	+	0.981910i	$0.439363\pi$
$728$	−35664.8	−1.81569
$729$	−7814.08	−0.396996
$730$	−1775.59	−0.0900238
$731$	−10896.9	−0.551347
$732$	2178.82	0.110016
$733$	21452.1	1.08097	0.540486	−	0.841353i	$-0.318240\pi$
$733$	21452.1	1.08097	0.540486	+	0.841353i	$0.318240\pi$
$734$	−30165.0	−1.51691
$735$	6133.40	0.307801
$736$	1413.11	0.0707715
$737$	−7860.72	−0.392881
$738$	21064.4	1.05067
$739$	−2776.56	−0.138210	−0.0691052	−	0.997609i	$-0.522014\pi$
$739$	−2776.56	−0.138210	−0.0691052	+	0.997609i	$0.522014\pi$
$740$	−436.051	−0.0216616
$741$	6477.73	0.321141
$742$	50455.4	2.49633
$743$	7793.15	0.384795	0.192398	−	0.981317i	$-0.438374\pi$
$743$	7793.15	0.384795	0.192398	+	0.981317i	$0.438374\pi$
$744$	−8668.39	−0.427149
$745$	11849.1	0.582707
$746$	−19681.2	−0.965923
$747$	−30764.0	−1.50682
$748$	638.611	0.0312165
$749$	−34360.8	−1.67626
$750$	6379.45	0.310593
$751$	−3484.49	−0.169309	−0.0846543	−	0.996410i	$-0.526979\pi$
$751$	−3484.49	−0.169309	−0.0846543	+	0.996410i	$0.526979\pi$
$752$	896.616	0.0434790
$753$	−3070.25	−0.148587
$754$	3829.51	0.184964
$755$	−26421.4	−1.27361
$756$	3487.14	0.167759
$757$	−17996.4	−0.864057	−0.432029	−	0.901860i	$-0.642202\pi$
$757$	−17996.4	−0.864057	−0.432029	+	0.901860i	$0.642202\pi$
$758$	−4644.45	−0.222551
$759$	−556.102	−0.0265945
$760$	−12864.8	−0.614019
$761$	−21679.0	−1.03267	−0.516335	−	0.856386i	$-0.672704\pi$
$761$	−21679.0	−1.03267	−0.516335	+	0.856386i	$0.672704\pi$
$762$	−2754.86	−0.130969
$763$	−8387.80	−0.397980
$764$	4515.28	0.213818
$765$	5813.86	0.274772
$766$	−30018.5	−1.41594
$767$	494.594	0.0232839
$768$	−3530.22	−0.165867
$769$	−7977.33	−0.374083	−0.187042	−	0.982352i	$-0.559890\pi$
$769$	−7977.33	−0.374083	−0.187042	+	0.982352i	$0.559890\pi$
$770$	−7571.52	−0.354362
$771$	7680.75	0.358775
$772$	−3470.53	−0.161797
$773$	3833.05	0.178351	0.0891755	−	0.996016i	$-0.471577\pi$
$773$	3833.05	0.178351	0.0891755	+	0.996016i	$0.471577\pi$
$774$	20292.6	0.942380
$775$	14945.6	0.692727
$776$	25603.8	1.18444
$777$	2165.97	0.100005
$778$	24434.2	1.12598
$779$	−24913.9	−1.14587
$780$	887.296	0.0407312
$781$	−6768.12	−0.310093
$782$	−1965.60	−0.0898846
$783$	−2554.87	−0.116607
$784$	−24904.4	−1.13449
$785$	3524.03	0.160227
$786$	12424.2	0.563815
$787$	41461.3	1.87793	0.938967	−	0.344006i	$-0.111784\pi$
$787$	41461.3	1.87793	0.938967	+	0.344006i	$0.111784\pi$
$788$	−1269.18	−0.0573767
$789$	4577.71	0.206554
$790$	10952.7	0.493265
$791$	−37129.5	−1.66899
$792$	−8114.61	−0.364066
$793$	47116.0	2.10988
$794$	38399.0	1.71628
$795$	−8565.09	−0.382104
$796$	4873.19	0.216992
$797$	7712.52	0.342775	0.171387	−	0.985204i	$-0.445175\pi$
$797$	7712.52	0.342775	0.171387	+	0.985204i	$0.445175\pi$
$798$	9365.30	0.415449
$799$	582.278	0.0257816
$800$	4413.84	0.195066
$801$	−27404.3	−1.20884
$802$	−19555.7	−0.861015
$803$	1324.65	0.0582139
$804$	1331.82	0.0584202
$805$	−4831.67	−0.211545
$806$	−27472.0	−1.20057
$807$	−3969.31	−0.173143
$808$	−44450.1	−1.93533
$809$	42730.1	1.85700	0.928498	−	0.371337i	$-0.121101\pi$
$809$	42730.1	1.85700	0.928498	+	0.371337i	$0.121101\pi$
$810$	−9315.77	−0.404102
$811$	−55.4478	−0.00240078	−0.00120039	−	0.999999i	$-0.500382\pi$
$811$	−55.4478	−0.00240078	−0.00120039	+	0.999999i	$0.500382\pi$
$812$	−1147.88	−0.0496093
$813$	7643.92	0.329746
$814$	−1569.07	−0.0675623
$815$	11460.0	0.492549
$816$	2930.84	0.125735
$817$	−24001.1	−1.02777
$818$	22757.6	0.972739
$819$	35500.2	1.51462
$820$	−3412.62	−0.145334
$821$	−20925.7	−0.889541	−0.444771	−	0.895645i	$-0.646715\pi$
$821$	−20925.7	−0.889541	−0.444771	+	0.895645i	$0.646715\pi$
$822$	−3347.70	−0.142049
$823$	−6095.34	−0.258165	−0.129083	−	0.991634i	$-0.541203\pi$
$823$	−6095.34	−0.258165	−0.129083	+	0.991634i	$0.541203\pi$
$824$	29226.6	1.23563
$825$	−1736.99	−0.0733019
$826$	715.068	0.0301216
$827$	16853.6	0.708653	0.354326	−	0.935122i	$-0.384710\pi$
$827$	16853.6	0.708653	0.354326	+	0.935122i	$0.384710\pi$
$828$	−758.904	−0.0318523
$829$	8748.94	0.366542	0.183271	−	0.983062i	$-0.441331\pi$
$829$	8748.94	0.366542	0.183271	+	0.983062i	$0.441331\pi$
$830$	−24039.6	−1.00533
$831$	2937.24	0.122613
$832$	−29093.6	−1.21231
$833$	−16173.4	−0.672718
$834$	5789.43	0.240374
$835$	−16748.0	−0.694116
$836$	1406.58	0.0581910
$837$	18328.0	0.756880
$838$	−31390.8	−1.29401
$839$	−1648.75	−0.0678442	−0.0339221	−	0.999424i	$-0.510800\pi$
$839$	−1648.75	−0.0678442	−0.0339221	+	0.999424i	$0.510800\pi$
$840$	8753.12	0.359537
$841$	841.000	0.0344828
$842$	−34343.4	−1.40564
$843$	4778.62	0.195237
$844$	2967.28	0.121017
$845$	3168.95	0.129012
$846$	−1084.34	−0.0440668
$847$	−32700.7	−1.32657
$848$	34778.2	1.40836
$849$	10894.2	0.440386
$850$	−6139.56	−0.247747
$851$	−1001.28	−0.0403330
$852$	1146.71	0.0461098
$853$	−27205.1	−1.09201	−0.546006	−	0.837781i	$-0.683852\pi$
$853$	−27205.1	−1.09201	−0.546006	+	0.837781i	$0.683852\pi$
$854$	68118.8	2.72948
$855$	12805.4	0.512206
$856$	−28776.1	−1.14900
$857$	−26300.1	−1.04830	−0.524151	−	0.851626i	$-0.675617\pi$
$857$	−26300.1	−1.04830	−0.524151	+	0.851626i	$0.675617\pi$
$858$	3192.80	0.127040
$859$	47420.5	1.88355	0.941773	−	0.336248i	$-0.109158\pi$
$859$	47420.5	1.88355	0.941773	+	0.336248i	$0.109158\pi$
$860$	−3287.58	−0.130355
$861$	16951.3	0.670962
$862$	15595.2	0.616213
$863$	43605.5	1.71999	0.859994	−	0.510305i	$-0.170467\pi$
$863$	43605.5	1.71999	0.859994	+	0.510305i	$0.170467\pi$
$864$	5412.74	0.213131
$865$	31539.1	1.23972
$866$	−12252.0	−0.480761
$867$	−6580.50	−0.257769
$868$	8234.63	0.322006
$869$	−8171.07	−0.318970
$870$	−939.867	−0.0366258
$871$	28800.1	1.12038
$872$	−7024.53	−0.272799
$873$	−25485.6	−0.988039
$874$	−4329.37	−0.167555
$875$	−41350.8	−1.59761
$876$	−224.432	−0.00865622
$877$	−36045.9	−1.38789	−0.693947	−	0.720026i	$-0.744130\pi$
$877$	−36045.9	−1.38789	−0.693947	+	0.720026i	$0.744130\pi$
$878$	−42864.4	−1.64761
$879$	−14788.6	−0.567471
$880$	−5218.94	−0.199921
$881$	4476.73	0.171197	0.0855986	−	0.996330i	$-0.472720\pi$
$881$	4476.73	0.171197	0.0855986	+	0.996330i	$0.472720\pi$
$882$	30118.7	1.14983
$883$	19809.4	0.754969	0.377485	−	0.926016i	$-0.376789\pi$
$883$	19809.4	0.754969	0.377485	+	0.926016i	$0.376789\pi$
$884$	−2339.74	−0.0890204
$885$	−121.387	−0.00461059
$886$	−40797.6	−1.54698
$887$	4931.51	0.186679	0.0933394	−	0.995634i	$-0.470246\pi$
$887$	4931.51	0.186679	0.0933394	+	0.995634i	$0.470246\pi$
$888$	1813.93	0.0685490
$889$	17856.7	0.673670
$890$	−21414.2	−0.806524
$891$	6949.87	0.261313
$892$	7384.98	0.277206
$893$	1282.51	0.0480599
$894$	−7223.91	−0.270250
$895$	7108.04	0.265470
$896$	−27900.9	−1.04030
$897$	2037.45	0.0758399
$898$	20953.3	0.778643
$899$	−6033.14	−0.223822
$900$	−2370.44	−0.0877940
$901$	22585.6	0.835111
$902$	−12279.8	−0.453296
$903$	16330.2	0.601810
$904$	−31094.8	−1.14403
$905$	4681.66	0.171960
$906$	16108.1	0.590680
$907$	53742.3	1.96746	0.983728	−	0.179664i	$-0.0575012\pi$
$907$	53742.3	1.96746	0.983728	+	0.179664i	$0.0575012\pi$
$908$	4818.47	0.176108
$909$	44244.9	1.61442
$910$	27740.5	1.01054
$911$	−23556.4	−0.856705	−0.428353	−	0.903612i	$-0.640906\pi$
$911$	−23556.4	−0.856705	−0.428353	+	0.903612i	$0.640906\pi$
$912$	6455.37	0.234385
$913$	17934.3	0.650098
$914$	27154.0	0.982684
$915$	−11563.6	−0.417792
$916$	−6678.93	−0.240915
$917$	−80532.5	−2.90013
$918$	−7529.01	−0.270691
$919$	7409.48	0.265959	0.132979	−	0.991119i	$-0.457546\pi$
$919$	7409.48	0.265959	0.132979	+	0.991119i	$0.457546\pi$
$920$	−4046.37	−0.145005
$921$	−8968.60	−0.320875
$922$	29222.7	1.04382
$923$	24797.0	0.884295
$924$	−957.031	−0.0340736
$925$	−3127.50	−0.111169
$926$	−1040.63	−0.0369299
$927$	−29091.7	−1.03074
$928$	−1781.74	−0.0630265
$929$	−7916.03	−0.279566	−0.139783	−	0.990182i	$-0.544640\pi$
$929$	−7916.03	−0.279566	−0.139783	+	0.990182i	$0.544640\pi$
$930$	6742.39	0.237733
$931$	−35622.9	−1.25402
$932$	8365.19	0.294003
$933$	−4853.49	−0.170307
$934$	34260.6	1.20026
$935$	−3389.27	−0.118547
$936$	29730.3	1.03821
$937$	6857.40	0.239084	0.119542	−	0.992829i	$-0.461857\pi$
$937$	6857.40	0.239084	0.119542	+	0.992829i	$0.461857\pi$
$938$	41638.3	1.44940
$939$	6943.23	0.241303
$940$	175.673	0.00609556
$941$	−18108.8	−0.627343	−0.313672	−	0.949532i	$-0.601559\pi$
$941$	−18108.8	−0.627343	−0.313672	+	0.949532i	$0.601559\pi$
$942$	−2148.46	−0.0743107
$943$	−7836.20	−0.270606
$944$	492.887	0.0169937
$945$	−18507.1	−0.637077
$946$	−11829.9	−0.406577
$947$	−40344.7	−1.38440	−0.692200	−	0.721706i	$-0.743358\pi$
$947$	−40344.7	−1.38440	−0.692200	+	0.721706i	$0.743358\pi$
$948$	1384.41	0.0474298
$949$	−4853.24	−0.166009
$950$	−13522.8	−0.461829
$951$	2723.84	0.0928776
$952$	−23081.4	−0.785790
$953$	29926.2	1.01721	0.508607	−	0.860999i	$-0.330161\pi$
$953$	29926.2	1.01721	0.508607	+	0.860999i	$0.330161\pi$
$954$	−42059.8	−1.42740
$955$	−23963.7	−0.811988
$956$	−3675.77	−0.124355
$957$	701.172	0.0236841
$958$	37909.0	1.27848
$959$	21699.4	0.730666
$960$	7140.37	0.240057
$961$	13489.3	0.452798
$962$	5748.74	0.192668
$963$	28643.3	0.958481
$964$	−9407.40	−0.314307
$965$	18419.0	0.614434
$966$	2945.68	0.0981114
$967$	−33303.9	−1.10753	−0.553765	−	0.832673i	$-0.686809\pi$
$967$	−33303.9	−1.10753	−0.553765	+	0.832673i	$0.686809\pi$
$968$	−27385.8	−0.909311
$969$	4192.23	0.138982
$970$	−19915.0	−0.659207
$971$	26919.3	0.889681	0.444841	−	0.895610i	$-0.353260\pi$
$971$	26919.3	0.889681	0.444841	+	0.895610i	$0.353260\pi$
$972$	−4445.29	−0.146690
$973$	−37526.4	−1.23642
$974$	−7944.40	−0.261350
$975$	6363.97	0.209036
$976$	46953.4	1.53990
$977$	2614.48	0.0856137	0.0428068	−	0.999083i	$-0.486370\pi$
$977$	2614.48	0.0856137	0.0428068	+	0.999083i	$0.486370\pi$
$978$	−6986.73	−0.228436
$979$	15975.7	0.521538
$980$	−4879.50	−0.159051
$981$	6992.11	0.227565
$982$	40246.9	1.30787
$983$	−3823.95	−0.124074	−0.0620372	−	0.998074i	$-0.519760\pi$
$983$	−3823.95	−0.124074	−0.0620372	+	0.998074i	$0.519760\pi$
$984$	14196.2	0.459916
$985$	6735.89	0.217892
$986$	2478.37	0.0800480
$987$	−872.610	−0.0281413
$988$	−5153.44	−0.165944
$989$	−7549.08	−0.242717
$990$	6311.65	0.202624
$991$	−43484.0	−1.39386	−0.696929	−	0.717140i	$-0.745451\pi$
$991$	−43484.0	−1.39386	−0.696929	+	0.717140i	$0.745451\pi$
$992$	12781.8	0.409096
$993$	−9692.32	−0.309745
$994$	35850.8	1.14398
$995$	−25863.3	−0.824042
$996$	−3038.57	−0.0966675
$997$	−5292.08	−0.168106	−0.0840531	−	0.996461i	$-0.526787\pi$
$997$	−5292.08	−0.168106	−0.0840531	+	0.996461i	$0.526787\pi$
$998$	6643.40	0.210714
$999$	−3835.28	−0.121464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.14	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.57414 q^{2} +1.72681 q^{3} -1.37379 q^{4} +7.29105 q^{5} -4.44507 q^{6} +28.8124 q^{7} +24.1295 q^{8} -24.0181 q^{9} +O(q^{10})\)	\(q-2.57414 q^{2} +1.72681 q^{3} -1.37379 q^{4} +7.29105 q^{5} -4.44507 q^{6} +28.8124 q^{7} +24.1295 q^{8} -24.0181 q^{9} -18.7682 q^{10} +14.0017 q^{11} -2.37228 q^{12} -51.2995 q^{13} -74.1672 q^{14} +12.5903 q^{15} -51.1224 q^{16} -33.1998 q^{17} +61.8261 q^{18} -73.1248 q^{19} -10.0164 q^{20} +49.7536 q^{21} -36.0424 q^{22} -23.0000 q^{23} +41.6671 q^{24} -71.8405 q^{25} +132.052 q^{26} -88.0988 q^{27} -39.5821 q^{28} +29.0000 q^{29} -32.4092 q^{30} -208.039 q^{31} -61.4394 q^{32} +24.1784 q^{33} +85.4610 q^{34} +210.073 q^{35} +32.9958 q^{36} +43.5339 q^{37} +188.234 q^{38} -88.5847 q^{39} +175.929 q^{40} +340.704 q^{41} -128.073 q^{42} +328.221 q^{43} -19.2354 q^{44} -175.117 q^{45} +59.2053 q^{46} -17.5386 q^{47} -88.2789 q^{48} +487.153 q^{49} +184.928 q^{50} -57.3298 q^{51} +70.4746 q^{52} -680.293 q^{53} +226.779 q^{54} +102.087 q^{55} +695.227 q^{56} -126.273 q^{57} -74.6501 q^{58} -9.64131 q^{59} -17.2964 q^{60} -918.450 q^{61} +535.523 q^{62} -692.019 q^{63} +567.133 q^{64} -374.027 q^{65} -62.2385 q^{66} -561.411 q^{67} +45.6095 q^{68} -39.7167 q^{69} -540.757 q^{70} -483.378 q^{71} -579.544 q^{72} +94.6060 q^{73} -112.062 q^{74} -124.055 q^{75} +100.458 q^{76} +403.423 q^{77} +228.030 q^{78} -583.577 q^{79} -372.736 q^{80} +496.359 q^{81} -877.022 q^{82} +1280.87 q^{83} -68.3510 q^{84} -242.061 q^{85} -844.887 q^{86} +50.0776 q^{87} +337.854 q^{88} +1140.98 q^{89} +450.777 q^{90} -1478.06 q^{91} +31.5971 q^{92} -359.245 q^{93} +45.1469 q^{94} -533.156 q^{95} -106.094 q^{96} +1061.10 q^{97} -1254.00 q^{98} -336.295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 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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