LMFDB - Embedded newform 4001.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68105 q^{2} -2.59933 q^{3} +5.18802 q^{4} -3.48579 q^{5} +6.96892 q^{6} -5.16960 q^{7} -8.54725 q^{8} +3.75650 q^{9} +O(q^{10})$	\(q-2.68105 q^{2} -2.59933 q^{3} +5.18802 q^{4} -3.48579 q^{5} +6.96892 q^{6} -5.16960 q^{7} -8.54725 q^{8} +3.75650 q^{9} +9.34557 q^{10} +0.876427 q^{11} -13.4854 q^{12} +0.747353 q^{13} +13.8600 q^{14} +9.06070 q^{15} +12.5395 q^{16} +4.37103 q^{17} -10.0714 q^{18} +3.62648 q^{19} -18.0843 q^{20} +13.4375 q^{21} -2.34974 q^{22} +4.16300 q^{23} +22.2171 q^{24} +7.15071 q^{25} -2.00369 q^{26} -1.96639 q^{27} -26.8200 q^{28} +6.77142 q^{29} -24.2922 q^{30} +8.64457 q^{31} -16.5246 q^{32} -2.27812 q^{33} -11.7189 q^{34} +18.0201 q^{35} +19.4888 q^{36} +0.671547 q^{37} -9.72276 q^{38} -1.94261 q^{39} +29.7939 q^{40} -12.1738 q^{41} -36.0266 q^{42} -2.88411 q^{43} +4.54692 q^{44} -13.0944 q^{45} -11.1612 q^{46} +4.06999 q^{47} -32.5944 q^{48} +19.7248 q^{49} -19.1714 q^{50} -11.3617 q^{51} +3.87728 q^{52} -10.3253 q^{53} +5.27199 q^{54} -3.05504 q^{55} +44.1859 q^{56} -9.42640 q^{57} -18.1545 q^{58} -7.85472 q^{59} +47.0071 q^{60} +1.75285 q^{61} -23.1765 q^{62} -19.4196 q^{63} +19.2242 q^{64} -2.60511 q^{65} +6.10775 q^{66} +10.2935 q^{67} +22.6770 q^{68} -10.8210 q^{69} -48.3129 q^{70} -13.3355 q^{71} -32.1077 q^{72} +4.52167 q^{73} -1.80045 q^{74} -18.5870 q^{75} +18.8142 q^{76} -4.53078 q^{77} +5.20824 q^{78} +14.6471 q^{79} -43.7102 q^{80} -6.15821 q^{81} +32.6385 q^{82} +7.13638 q^{83} +69.7140 q^{84} -15.2365 q^{85} +7.73244 q^{86} -17.6011 q^{87} -7.49103 q^{88} +11.2472 q^{89} +35.1066 q^{90} -3.86352 q^{91} +21.5978 q^{92} -22.4701 q^{93} -10.9119 q^{94} -12.6411 q^{95} +42.9529 q^{96} +0.565715 q^{97} -52.8831 q^{98} +3.29230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	−2.68105	−1.89579	−0.947894	−	0.318586i	$-0.896792\pi$
$2$	−2.68105	−1.89579	−0.947894	+	0.318586i	$0.896792\pi$
$3$	−2.59933	−1.50072	−0.750361	−	0.661028i	$-0.770120\pi$
$3$	−2.59933	−1.50072	−0.750361	+	0.661028i	$0.770120\pi$
$4$	5.18802	2.59401
$5$	−3.48579	−1.55889	−0.779446	−	0.626470i	$-0.784499\pi$
$5$	−3.48579	−1.55889	−0.779446	+	0.626470i	$0.784499\pi$
$6$	6.96892	2.84505
$7$	−5.16960	−1.95393	−0.976963	−	0.213408i	$-0.931544\pi$
$7$	−5.16960	−1.95393	−0.976963	+	0.213408i	$0.931544\pi$
$8$	−8.54725	−3.02191
$9$	3.75650	1.25217
$10$	9.34557	2.95533
$11$	0.876427	0.264253	0.132126	−	0.991233i	$-0.457820\pi$
$11$	0.876427	0.264253	0.132126	+	0.991233i	$0.457820\pi$
$12$	−13.4854	−3.89289
$13$	0.747353	0.207278	0.103639	−	0.994615i	$-0.466951\pi$
$13$	0.747353	0.207278	0.103639	+	0.994615i	$0.466951\pi$
$14$	13.8600	3.70423
$15$	9.06070	2.33946
$16$	12.5395	3.13488
$17$	4.37103	1.06013	0.530065	−	0.847957i	$-0.322167\pi$
$17$	4.37103	1.06013	0.530065	+	0.847957i	$0.322167\pi$
$18$	−10.0714	−2.37384
$19$	3.62648	0.831971	0.415985	−	0.909371i	$-0.363437\pi$
$19$	3.62648	0.831971	0.415985	+	0.909371i	$0.363437\pi$
$20$	−18.0843	−4.04378
$21$	13.4375	2.93230
$22$	−2.34974	−0.500967
$23$	4.16300	0.868046	0.434023	−	0.900902i	$-0.357094\pi$
$23$	4.16300	0.868046	0.434023	+	0.900902i	$0.357094\pi$
$24$	22.2171	4.53504
$25$	7.15071	1.43014
$26$	−2.00369	−0.392956
$27$	−1.96639	−0.378432
$28$	−26.8200	−5.06851
$29$	6.77142	1.25742	0.628711	−	0.777639i	$-0.283583\pi$
$29$	6.77142	1.25742	0.628711	+	0.777639i	$0.283583\pi$
$30$	−24.2922	−4.43512
$31$	8.64457	1.55261	0.776305	−	0.630357i	$-0.217092\pi$
$31$	8.64457	1.55261	0.776305	+	0.630357i	$0.217092\pi$
$32$	−16.5246	−2.92117
$33$	−2.27812	−0.396570
$34$	−11.7189	−2.00978
$35$	18.0201	3.04596
$36$	19.4888	3.24813
$37$	0.671547	0.110402	0.0552008	−	0.998475i	$-0.482420\pi$
$37$	0.671547	0.110402	0.0552008	+	0.998475i	$0.482420\pi$
$38$	−9.72276	−1.57724
$39$	−1.94261	−0.311067
$40$	29.7939	4.71083
$41$	−12.1738	−1.90122	−0.950611	−	0.310385i	$-0.899542\pi$
$41$	−12.1738	−1.90122	−0.950611	+	0.310385i	$0.899542\pi$
$42$	−36.0266	−5.55902
$43$	−2.88411	−0.439822	−0.219911	−	0.975520i	$-0.570577\pi$
$43$	−2.88411	−0.439822	−0.219911	+	0.975520i	$0.570577\pi$
$44$	4.54692	0.685474
$45$	−13.0944	−1.95199
$46$	−11.1612	−1.64563
$47$	4.06999	0.593670	0.296835	−	0.954929i	$-0.404069\pi$
$47$	4.06999	0.593670	0.296835	+	0.954929i	$0.404069\pi$
$48$	−32.5944	−4.70459
$49$	19.7248	2.81783
$50$	−19.1714	−2.71125
$51$	−11.3617	−1.59096
$52$	3.87728	0.537683
$53$	−10.3253	−1.41829	−0.709146	−	0.705062i	$-0.750919\pi$
$53$	−10.3253	−1.41829	−0.709146	+	0.705062i	$0.750919\pi$
$54$	5.27199	0.717427
$55$	−3.05504	−0.411941
$56$	44.1859	5.90459
$57$	−9.42640	−1.24856
$58$	−18.1545	−2.38380
$59$	−7.85472	−1.02260	−0.511299	−	0.859403i	$-0.670835\pi$
$59$	−7.85472	−1.02260	−0.511299	+	0.859403i	$0.670835\pi$
$60$	47.0071	6.06859
$61$	1.75285	0.224429	0.112214	−	0.993684i	$-0.464206\pi$
$61$	1.75285	0.224429	0.112214	+	0.993684i	$0.464206\pi$
$62$	−23.1765	−2.94342
$63$	−19.4196	−2.44664
$64$	19.2242	2.40303
$65$	−2.60511	−0.323125
$66$	6.10775	0.751812
$67$	10.2935	1.25755	0.628776	−	0.777586i	$-0.283556\pi$
$67$	10.2935	1.25755	0.628776	+	0.777586i	$0.283556\pi$
$68$	22.6770	2.74999
$69$	−10.8210	−1.30270
$70$	−48.3129	−5.77449
$71$	−13.3355	−1.58263	−0.791315	−	0.611409i	$-0.790603\pi$
$71$	−13.3355	−1.58263	−0.791315	+	0.611409i	$0.790603\pi$
$72$	−32.1077	−3.78393
$73$	4.52167	0.529221	0.264611	−	0.964355i	$-0.414757\pi$
$73$	4.52167	0.529221	0.264611	+	0.964355i	$0.414757\pi$
$74$	−1.80045	−0.209298
$75$	−18.5870	−2.14625
$76$	18.8142	2.15814
$77$	−4.53078	−0.516330
$78$	5.20824	0.589718
$79$	14.6471	1.64793	0.823966	−	0.566640i	$-0.191757\pi$
$79$	14.6471	1.64793	0.823966	+	0.566640i	$0.191757\pi$
$80$	−43.7102	−4.88694
$81$	−6.15821	−0.684245
$82$	32.6385	3.60431
$83$	7.13638	0.783320	0.391660	−	0.920110i	$-0.371901\pi$
$83$	7.13638	0.783320	0.391660	+	0.920110i	$0.371901\pi$
$84$	69.7140	7.60642
$85$	−15.2365	−1.65263
$86$	7.73244	0.833810
$87$	−17.6011	−1.88704
$88$	−7.49103	−0.798547
$89$	11.2472	1.19220	0.596100	−	0.802910i	$-0.296716\pi$
$89$	11.2472	1.19220	0.596100	+	0.802910i	$0.296716\pi$
$90$	35.1066	3.70056
$91$	−3.86352	−0.405007
$92$	21.5978	2.25172
$93$	−22.4701	−2.33004
$94$	−10.9119	−1.12547
$95$	−12.6411	−1.29695
$96$	42.9529	4.38386
$97$	0.565715	0.0574396	0.0287198	−	0.999588i	$-0.490857\pi$
$97$	0.565715	0.0574396	0.0287198	+	0.999588i	$0.490857\pi$
$98$	−52.8831	−5.34200
$99$	3.29230	0.330888
$100$	37.0981	3.70981
$101$	−0.915682	−0.0911138	−0.0455569	−	0.998962i	$-0.514506\pi$
$101$	−0.915682	−0.0911138	−0.0455569	+	0.998962i	$0.514506\pi$
$102$	30.4614	3.01612
$103$	−5.97154	−0.588393	−0.294197	−	0.955745i	$-0.595052\pi$
$103$	−5.97154	−0.588393	−0.294197	+	0.955745i	$0.595052\pi$
$104$	−6.38781	−0.626376
$105$	−46.8402	−4.57114
$106$	27.6827	2.68878
$107$	2.56650	0.248113	0.124057	−	0.992275i	$-0.460410\pi$
$107$	2.56650	0.248113	0.124057	+	0.992275i	$0.460410\pi$
$108$	−10.2017	−0.981657
$109$	5.89465	0.564605	0.282303	−	0.959325i	$-0.408902\pi$
$109$	5.89465	0.564605	0.282303	+	0.959325i	$0.408902\pi$
$110$	8.19070	0.780953
$111$	−1.74557	−0.165682
$112$	−64.8244	−6.12533
$113$	13.6703	1.28600	0.642998	−	0.765868i	$-0.277690\pi$
$113$	13.6703	1.28600	0.642998	+	0.765868i	$0.277690\pi$
$114$	25.2726	2.36700
$115$	−14.5113	−1.35319
$116$	35.1303	3.26176
$117$	2.80743	0.259547
$118$	21.0589	1.93863
$119$	−22.5965	−2.07142
$120$	−77.4440	−7.06964
$121$	−10.2319	−0.930171
$122$	−4.69947	−0.425470
$123$	31.6436	2.85321
$124$	44.8482	4.02749
$125$	−7.49692	−0.670545
$126$	52.0649	4.63831
$127$	13.7879	1.22348	0.611738	−	0.791060i	$-0.290471\pi$
$127$	13.7879	1.22348	0.611738	+	0.791060i	$0.290471\pi$
$128$	−18.4919	−1.63447
$129$	7.49674	0.660051
$130$	6.98444	0.612576
$131$	2.16019	0.188736	0.0943682	−	0.995537i	$-0.469917\pi$
$131$	2.16019	0.188736	0.0943682	+	0.995537i	$0.469917\pi$
$132$	−11.8189	−1.02871
$133$	−18.7474	−1.62561
$134$	−27.5974	−2.38405
$135$	6.85442	0.589934
$136$	−37.3603	−3.20362
$137$	−3.67996	−0.314400	−0.157200	−	0.987567i	$-0.550247\pi$
$137$	−3.67996	−0.314400	−0.157200	+	0.987567i	$0.550247\pi$
$138$	29.0116	2.46964
$139$	21.3708	1.81264	0.906322	−	0.422588i	$-0.138878\pi$
$139$	21.3708	1.81264	0.906322	+	0.422588i	$0.138878\pi$
$140$	93.4889	7.90125
$141$	−10.5792	−0.890933
$142$	35.7531	3.00033
$143$	0.655000	0.0547738
$144$	47.1048	3.92540
$145$	−23.6037	−1.96018
$146$	−12.1228	−1.00329
$147$	−51.2712	−4.22878
$148$	3.48400	0.286383
$149$	2.39933	0.196561	0.0982804	−	0.995159i	$-0.468666\pi$
$149$	2.39933	0.196561	0.0982804	+	0.995159i	$0.468666\pi$
$150$	49.8328	4.06883
$151$	12.0064	0.977065	0.488533	−	0.872546i	$-0.337532\pi$
$151$	12.0064	0.977065	0.488533	+	0.872546i	$0.337532\pi$
$152$	−30.9964	−2.51414
$153$	16.4198	1.32746
$154$	12.1472	0.978852
$155$	−30.1331	−2.42035
$156$	−10.0783	−0.806912
$157$	−12.9825	−1.03612	−0.518060	−	0.855344i	$-0.673346\pi$
$157$	−12.9825	−1.03612	−0.518060	+	0.855344i	$0.673346\pi$
$158$	−39.2697	−3.12413
$159$	26.8389	2.12846
$160$	57.6013	4.55378
$161$	−21.5211	−1.69610
$162$	16.5105	1.29718
$163$	−14.6077	−1.14416	−0.572082	−	0.820196i	$-0.693864\pi$
$163$	−14.6077	−1.14416	−0.572082	+	0.820196i	$0.693864\pi$
$164$	−63.1578	−4.93179
$165$	7.94104	0.618209
$166$	−19.1330	−1.48501
$167$	12.4688	0.964867	0.482434	−	0.875933i	$-0.339753\pi$
$167$	12.4688	0.964867	0.482434	+	0.875933i	$0.339753\pi$
$168$	−114.854	−8.86114
$169$	−12.4415	−0.957036
$170$	40.8497	3.13303
$171$	13.6229	1.04177
$172$	−14.9628	−1.14090
$173$	14.8043	1.12555	0.562774	−	0.826611i	$-0.309734\pi$
$173$	14.8043	1.12555	0.562774	+	0.826611i	$0.309734\pi$
$174$	47.1895	3.57743
$175$	−36.9663	−2.79439
$176$	10.9900	0.828401
$177$	20.4170	1.53463
$178$	−30.1543	−2.26016
$179$	−16.2288	−1.21299	−0.606497	−	0.795086i	$-0.707426\pi$
$179$	−16.2288	−1.21299	−0.606497	+	0.795086i	$0.707426\pi$
$180$	−67.9338	−5.06349
$181$	−5.72393	−0.425456	−0.212728	−	0.977111i	$-0.568235\pi$
$181$	−5.72393	−0.425456	−0.212728	+	0.977111i	$0.568235\pi$
$182$	10.3583	0.767807
$183$	−4.55622	−0.336805
$184$	−35.5822	−2.62316
$185$	−2.34087	−0.172104
$186$	60.2433	4.41725
$187$	3.83089	0.280142
$188$	21.1152	1.53999
$189$	10.1655	0.739428
$190$	33.8915	2.45875
$191$	14.4684	1.04689	0.523447	−	0.852058i	$-0.324646\pi$
$191$	14.4684	1.04689	0.523447	+	0.852058i	$0.324646\pi$
$192$	−49.9701	−3.60628
$193$	−2.82574	−0.203401	−0.101701	−	0.994815i	$-0.532428\pi$
$193$	−2.82574	−0.203401	−0.101701	+	0.994815i	$0.532428\pi$
$194$	−1.51671	−0.108893
$195$	6.77154	0.484920
$196$	102.333	7.30948
$197$	−11.3114	−0.805904	−0.402952	−	0.915221i	$-0.632016\pi$
$197$	−11.3114	−0.805904	−0.402952	+	0.915221i	$0.632016\pi$
$198$	−8.82681	−0.627294
$199$	25.2559	1.79034	0.895170	−	0.445724i	$-0.147054\pi$
$199$	25.2559	1.79034	0.895170	+	0.445724i	$0.147054\pi$
$200$	−61.1189	−4.32176
$201$	−26.7562	−1.88724
$202$	2.45499	0.172732
$203$	−35.0055	−2.45691
$204$	−58.9449	−4.12697
$205$	42.4351	2.96380
$206$	16.0100	1.11547
$207$	15.6383	1.08694
$208$	9.37146	0.649794
$209$	3.17834	0.219850
$210$	125.581	8.66591
$211$	9.06987	0.624396	0.312198	−	0.950017i	$-0.398935\pi$
$211$	9.06987	0.624396	0.312198	+	0.950017i	$0.398935\pi$
$212$	−53.5680	−3.67906
$213$	34.6632	2.37509
$214$	−6.88092	−0.470370
$215$	10.0534	0.685635
$216$	16.8072	1.14359
$217$	−44.6890	−3.03369
$218$	−15.8039	−1.07037
$219$	−11.7533	−0.794214
$220$	−15.8496	−1.06858
$221$	3.26670	0.219742
$222$	4.67996	0.314098
$223$	16.2622	1.08900	0.544499	−	0.838761i	$-0.316720\pi$
$223$	16.2622	1.08900	0.544499	+	0.838761i	$0.316720\pi$
$224$	85.4257	5.70775
$225$	26.8616	1.79078
$226$	−36.6508	−2.43798
$227$	−20.0618	−1.33155	−0.665775	−	0.746153i	$-0.731899\pi$
$227$	−20.0618	−1.33155	−0.665775	+	0.746153i	$0.731899\pi$
$228$	−48.9044	−3.23877
$229$	21.7895	1.43989	0.719946	−	0.694031i	$-0.244167\pi$
$229$	21.7895	1.43989	0.719946	+	0.694031i	$0.244167\pi$
$230$	38.9056	2.56536
$231$	11.7770	0.774868
$232$	−57.8770	−3.79981
$233$	−21.4003	−1.40198	−0.700992	−	0.713169i	$-0.747259\pi$
$233$	−21.4003	−1.40198	−0.700992	+	0.713169i	$0.747259\pi$
$234$	−7.52686	−0.492046
$235$	−14.1871	−0.925467
$236$	−40.7505	−2.65263
$237$	−38.0727	−2.47309
$238$	60.5823	3.92697
$239$	−25.7485	−1.66553	−0.832765	−	0.553627i	$-0.813243\pi$
$239$	−25.7485	−1.66553	−0.832765	+	0.553627i	$0.813243\pi$
$240$	113.617	7.33395
$241$	−8.58061	−0.552726	−0.276363	−	0.961053i	$-0.589129\pi$
$241$	−8.58061	−0.552726	−0.276363	+	0.961053i	$0.589129\pi$
$242$	27.4322	1.76341
$243$	21.9064	1.40529
$244$	9.09381	0.582171
$245$	−68.7564	−4.39269
$246$	−84.8380	−5.40907
$247$	2.71026	0.172450
$248$	−73.8873	−4.69185
$249$	−18.5498	−1.17554
$250$	20.0996	1.27121
$251$	1.61960	0.102228	0.0511142	−	0.998693i	$-0.483723\pi$
$251$	1.61960	0.102228	0.0511142	+	0.998693i	$0.483723\pi$
$252$	−100.749	−6.34662
$253$	3.64857	0.229383
$254$	−36.9660	−2.31945
$255$	39.6046	2.48014
$256$	11.1292	0.695575
$257$	−26.2702	−1.63869	−0.819345	−	0.573301i	$-0.805662\pi$
$257$	−26.2702	−1.63869	−0.819345	+	0.573301i	$0.805662\pi$
$258$	−20.0991	−1.25132
$259$	−3.47163	−0.215717
$260$	−13.5154	−0.838189
$261$	25.4368	1.57450
$262$	−5.79157	−0.357804
$263$	7.18538	0.443070	0.221535	−	0.975152i	$-0.428893\pi$
$263$	7.18538	0.443070	0.221535	+	0.975152i	$0.428893\pi$
$264$	19.4716	1.19840
$265$	35.9919	2.21096
$266$	50.2628	3.08181
$267$	−29.2351	−1.78916
$268$	53.4030	3.26211
$269$	17.6646	1.07703	0.538516	−	0.842615i	$-0.318985\pi$
$269$	17.6646	1.07703	0.538516	+	0.842615i	$0.318985\pi$
$270$	−18.3770	−1.11839
$271$	−16.6755	−1.01297	−0.506483	−	0.862250i	$-0.669055\pi$
$271$	−16.6755	−1.01297	−0.506483	+	0.862250i	$0.669055\pi$
$272$	54.8107	3.32339
$273$	10.0425	0.607803
$274$	9.86616	0.596036
$275$	6.26707	0.377919
$276$	−56.1396	−3.37921
$277$	−2.85615	−0.171609	−0.0858047	−	0.996312i	$-0.527346\pi$
$277$	−2.85615	−0.171609	−0.0858047	+	0.996312i	$0.527346\pi$
$278$	−57.2961	−3.43639
$279$	32.4733	1.94413
$280$	−154.023	−9.20461
$281$	8.28079	0.493991	0.246995	−	0.969017i	$-0.420557\pi$
$281$	8.28079	0.493991	0.246995	+	0.969017i	$0.420557\pi$
$282$	28.3635	1.68902
$283$	−20.5986	−1.22446	−0.612229	−	0.790680i	$-0.709727\pi$
$283$	−20.5986	−1.22446	−0.612229	+	0.790680i	$0.709727\pi$
$284$	−69.1847	−4.10536
$285$	32.8584	1.94636
$286$	−1.75609	−0.103840
$287$	62.9335	3.71485
$288$	−62.0748	−3.65779
$289$	2.10590	0.123876
$290$	63.2827	3.71609
$291$	−1.47048	−0.0862009
$292$	23.4585	1.37281
$293$	−15.4501	−0.902603	−0.451301	−	0.892372i	$-0.649040\pi$
$293$	−15.4501	−0.902603	−0.451301	+	0.892372i	$0.649040\pi$
$294$	137.461	8.01686
$295$	27.3799	1.59412
$296$	−5.73988	−0.333624
$297$	−1.72340	−0.100002
$298$	−6.43272	−0.372637
$299$	3.11123	0.179927
$300$	−96.4300	−5.56739
$301$	14.9097	0.859381
$302$	−32.1897	−1.85231
$303$	2.38016	0.136736
$304$	45.4743	2.60813
$305$	−6.11005	−0.349860
$306$	−44.0222	−2.51658
$307$	17.3595	0.990759	0.495380	−	0.868677i	$-0.335029\pi$
$307$	17.3595	0.990759	0.495380	+	0.868677i	$0.335029\pi$
$308$	−23.5058	−1.33937
$309$	15.5220	0.883015
$310$	80.7884	4.58847
$311$	−6.00112	−0.340292	−0.170146	−	0.985419i	$-0.554424\pi$
$311$	−6.00112	−0.340292	−0.170146	+	0.985419i	$0.554424\pi$
$312$	16.6040	0.940017
$313$	32.5860	1.84187	0.920936	−	0.389715i	$-0.127426\pi$
$313$	32.5860	1.84187	0.920936	+	0.389715i	$0.127426\pi$
$314$	34.8068	1.96426
$315$	67.6926	3.81405
$316$	75.9897	4.27475
$317$	15.3550	0.862421	0.431210	−	0.902251i	$-0.358087\pi$
$317$	15.3550	0.862421	0.431210	+	0.902251i	$0.358087\pi$
$318$	−71.9563	−4.03511
$319$	5.93465	0.332277
$320$	−67.0116	−3.74606
$321$	−6.67118	−0.372349
$322$	57.6991	3.21544
$323$	15.8514	0.881997
$324$	−31.9489	−1.77494
$325$	5.34411	0.296438
$326$	39.1640	2.16909
$327$	−15.3221	−0.847316
$328$	104.052	5.74532
$329$	−21.0403	−1.15999
$330$	−21.2903	−1.17199
$331$	−1.18210	−0.0649743	−0.0324872	−	0.999472i	$-0.510343\pi$
$331$	−1.18210	−0.0649743	−0.0324872	+	0.999472i	$0.510343\pi$
$332$	37.0237	2.03194
$333$	2.52267	0.138241
$334$	−33.4296	−1.82918
$335$	−35.8810	−1.96039
$336$	168.500	9.19242
$337$	5.30255	0.288848	0.144424	−	0.989516i	$-0.453867\pi$
$337$	5.30255	0.288848	0.144424	+	0.989516i	$0.453867\pi$
$338$	33.3562	1.81434
$339$	−35.5336	−1.92992
$340$	−79.0472	−4.28694
$341$	7.57633	0.410281
$342$	−36.5235	−1.97497
$343$	−65.7821	−3.55190
$344$	24.6512	1.32910
$345$	37.7197	2.03076
$346$	−39.6910	−2.13380
$347$	9.90287	0.531614	0.265807	−	0.964026i	$-0.414362\pi$
$347$	9.90287	0.531614	0.265807	+	0.964026i	$0.414362\pi$
$348$	−91.3151	−4.89500
$349$	5.73195	0.306824	0.153412	−	0.988162i	$-0.450974\pi$
$349$	5.73195	0.306824	0.153412	+	0.988162i	$0.450974\pi$
$350$	99.1086	5.29758
$351$	−1.46959	−0.0784408
$352$	−14.4826	−0.771926
$353$	7.84835	0.417725	0.208863	−	0.977945i	$-0.433024\pi$
$353$	7.84835	0.417725	0.208863	+	0.977945i	$0.433024\pi$
$354$	−54.7389	−2.90934
$355$	46.4846	2.46715
$356$	58.3507	3.09258
$357$	58.7356	3.10862
$358$	43.5101	2.29958
$359$	2.98498	0.157541	0.0787707	−	0.996893i	$-0.474901\pi$
$359$	2.98498	0.157541	0.0787707	+	0.996893i	$0.474901\pi$
$360$	111.921	5.89874
$361$	−5.84867	−0.307825
$362$	15.3461	0.806575
$363$	26.5960	1.39593
$364$	−20.0440	−1.05059
$365$	−15.7616	−0.824998
$366$	12.2154	0.638512
$367$	21.2046	1.10687	0.553434	−	0.832893i	$-0.313317\pi$
$367$	21.2046	1.10687	0.553434	+	0.832893i	$0.313317\pi$
$368$	52.2021	2.72122
$369$	−45.7307	−2.38065
$370$	6.27599	0.326273
$371$	53.3778	2.77124
$372$	−116.575	−6.04414
$373$	−17.1844	−0.889775	−0.444887	−	0.895587i	$-0.646756\pi$
$373$	−17.1844	−0.889775	−0.444887	+	0.895587i	$0.646756\pi$
$374$	−10.2708	−0.531090
$375$	19.4870	1.00630
$376$	−34.7872	−1.79402
$377$	5.06064	0.260636
$378$	−27.2541	−1.40180
$379$	8.96136	0.460314	0.230157	−	0.973154i	$-0.426076\pi$
$379$	8.96136	0.460314	0.230157	+	0.973154i	$0.426076\pi$
$380$	−65.5824	−3.36431
$381$	−35.8392	−1.83610
$382$	−38.7904	−1.98469
$383$	13.7675	0.703486	0.351743	−	0.936097i	$-0.385589\pi$
$383$	13.7675	0.703486	0.351743	+	0.936097i	$0.385589\pi$
$384$	48.0665	2.45288
$385$	15.7933	0.804902
$386$	7.57594	0.385605
$387$	−10.8342	−0.550731
$388$	2.93494	0.148999
$389$	−18.3355	−0.929647	−0.464823	−	0.885403i	$-0.653882\pi$
$389$	−18.3355	−0.929647	−0.464823	+	0.885403i	$0.653882\pi$
$390$	−18.1548	−0.919306
$391$	18.1966	0.920242
$392$	−168.593	−8.51522
$393$	−5.61503	−0.283241
$394$	30.3264	1.52782
$395$	−51.0568	−2.56895
$396$	17.0805	0.858328
$397$	20.4665	1.02719	0.513593	−	0.858034i	$-0.328314\pi$
$397$	20.4665	1.02719	0.513593	+	0.858034i	$0.328314\pi$
$398$	−67.7122	−3.39411
$399$	48.7307	2.43959
$400$	89.6666	4.48333
$401$	20.4937	1.02341	0.511703	−	0.859163i	$-0.329015\pi$
$401$	20.4937	1.02341	0.511703	+	0.859163i	$0.329015\pi$
$402$	71.7347	3.57780
$403$	6.46054	0.321823
$404$	−4.75058	−0.236350
$405$	21.4662	1.06666
$406$	93.8516	4.65778
$407$	0.588562	0.0291739
$408$	97.1115	4.80774
$409$	−24.7995	−1.22626	−0.613129	−	0.789983i	$-0.710089\pi$
$409$	−24.7995	−1.22626	−0.613129	+	0.789983i	$0.710089\pi$
$410$	−113.771	−5.61873
$411$	9.56542	0.471828
$412$	−30.9805	−1.52630
$413$	40.6058	1.99808
$414$	−41.9271	−2.06060
$415$	−24.8759	−1.22111
$416$	−12.3497	−0.605495
$417$	−55.5496	−2.72028
$418$	−8.52128	−0.416790
$419$	2.55337	0.124740	0.0623702	−	0.998053i	$-0.480134\pi$
$419$	2.55337	0.124740	0.0623702	+	0.998053i	$0.480134\pi$
$420$	−243.008	−11.8576
$421$	3.17201	0.154594	0.0772972	−	0.997008i	$-0.475371\pi$
$421$	3.17201	0.154594	0.0772972	+	0.997008i	$0.475371\pi$
$422$	−24.3168	−1.18372
$423$	15.2889	0.743373
$424$	88.2530	4.28595
$425$	31.2560	1.51614
$426$	−92.9339	−4.50266
$427$	−9.06152	−0.438518
$428$	13.3151	0.643609
$429$	−1.70256	−0.0822003
$430$	−26.9536	−1.29982
$431$	−5.48399	−0.264154	−0.132077	−	0.991239i	$-0.542165\pi$
$431$	−5.48399	−0.264154	−0.132077	+	0.991239i	$0.542165\pi$
$432$	−24.6576	−1.18634
$433$	1.03307	0.0496462	0.0248231	−	0.999692i	$-0.492098\pi$
$433$	1.03307	0.0496462	0.0248231	+	0.999692i	$0.492098\pi$
$434$	119.813	5.75122
$435$	61.3538	2.94169
$436$	30.5816	1.46459
$437$	15.0970	0.722189
$438$	31.5111	1.50566
$439$	−27.3336	−1.30456	−0.652280	−	0.757978i	$-0.726187\pi$
$439$	−27.3336	−1.30456	−0.652280	+	0.757978i	$0.726187\pi$
$440$	26.1121	1.24485
$441$	74.0962	3.52839
$442$	−8.75819	−0.416584
$443$	23.2589	1.10507	0.552533	−	0.833491i	$-0.313662\pi$
$443$	23.2589	1.10507	0.552533	+	0.833491i	$0.313662\pi$
$444$	−9.05606	−0.429782
$445$	−39.2053	−1.85851
$446$	−43.5998	−2.06451
$447$	−6.23664	−0.294983
$448$	−99.3817	−4.69535
$449$	−21.4726	−1.01336	−0.506678	−	0.862135i	$-0.669127\pi$
$449$	−21.4726	−1.01336	−0.506678	+	0.862135i	$0.669127\pi$
$450$	−72.0174	−3.39493
$451$	−10.6694	−0.502403
$452$	70.9220	3.33589
$453$	−31.2085	−1.46630
$454$	53.7867	2.52434
$455$	13.4674	0.631361
$456$	80.5697	3.77302
$457$	−30.9583	−1.44817	−0.724084	−	0.689711i	$-0.757737\pi$
$457$	−30.9583	−1.44817	−0.724084	+	0.689711i	$0.757737\pi$
$458$	−58.4187	−2.72973
$459$	−8.59515	−0.401187
$460$	−75.2852	−3.51019
$461$	8.38181	0.390380	0.195190	−	0.980765i	$-0.437468\pi$
$461$	8.38181	0.390380	0.195190	+	0.980765i	$0.437468\pi$
$462$	−31.5746	−1.46898
$463$	37.7697	1.75531	0.877653	−	0.479297i	$-0.159108\pi$
$463$	37.7697	1.75531	0.877653	+	0.479297i	$0.159108\pi$
$464$	84.9105	3.94187
$465$	78.3258	3.63227
$466$	57.3754	2.65786
$467$	15.1792	0.702411	0.351205	−	0.936298i	$-0.385772\pi$
$467$	15.1792	0.702411	0.351205	+	0.936298i	$0.385772\pi$
$468$	14.5650	0.673268
$469$	−53.2134	−2.45717
$470$	38.0364	1.75449
$471$	33.7459	1.55493
$472$	67.1362	3.09020
$473$	−2.52771	−0.116224
$474$	102.075	4.68845
$475$	25.9319	1.18984
$476$	−117.231	−5.37328
$477$	−38.7871	−1.77594
$478$	69.0329	3.15749
$479$	24.6932	1.12826	0.564131	−	0.825685i	$-0.309211\pi$
$479$	24.6932	1.12826	0.564131	+	0.825685i	$0.309211\pi$
$480$	−149.725	−6.83396
$481$	0.501883	0.0228839
$482$	23.0050	1.04785
$483$	55.9403	2.54537
$484$	−53.0832	−2.41287
$485$	−1.97196	−0.0895422
$486$	−58.7320	−2.66414
$487$	23.2653	1.05425	0.527125	−	0.849787i	$-0.323270\pi$
$487$	23.2653	1.05425	0.527125	+	0.849787i	$0.323270\pi$
$488$	−14.9820	−0.678204
$489$	37.9702	1.71707
$490$	184.339	8.32760
$491$	−24.0510	−1.08541	−0.542704	−	0.839924i	$-0.682600\pi$
$491$	−24.0510	−1.08541	−0.542704	+	0.839924i	$0.682600\pi$
$492$	164.168	7.40125
$493$	29.5981	1.33303
$494$	−7.26633	−0.326928
$495$	−11.4762	−0.515819
$496$	108.399	4.86725
$497$	68.9391	3.09234
$498$	49.7329	2.22858
$499$	−32.8536	−1.47073	−0.735365	−	0.677671i	$-0.762989\pi$
$499$	−32.8536	−1.47073	−0.735365	+	0.677671i	$0.762989\pi$
$500$	−38.8942	−1.73940
$501$	−32.4106	−1.44800
$502$	−4.34224	−0.193804
$503$	37.9490	1.69206	0.846030	−	0.533135i	$-0.178986\pi$
$503$	37.9490	1.69206	0.846030	+	0.533135i	$0.178986\pi$
$504$	165.984	7.39352
$505$	3.19187	0.142036
$506$	−9.78199	−0.434862
$507$	32.3394	1.43624
$508$	71.5318	3.17371
$509$	−17.0253	−0.754635	−0.377317	−	0.926084i	$-0.623153\pi$
$509$	−17.0253	−0.754635	−0.377317	+	0.926084i	$0.623153\pi$
$510$	−106.182	−4.70181
$511$	−23.3752	−1.03406
$512$	7.14588	0.315806
$513$	−7.13107	−0.314844
$514$	70.4317	3.10661
$515$	20.8155	0.917241
$516$	38.8933	1.71218
$517$	3.56705	0.156879
$518$	9.30761	0.408953
$519$	−38.4811	−1.68913
$520$	22.2665	0.976453
$521$	−16.4070	−0.718804	−0.359402	−	0.933183i	$-0.617019\pi$
$521$	−16.4070	−0.718804	−0.359402	+	0.933183i	$0.617019\pi$
$522$	−68.1974	−2.98492
$523$	−38.4907	−1.68308	−0.841540	−	0.540194i	$-0.818351\pi$
$523$	−38.4907	−1.68308	−0.841540	+	0.540194i	$0.818351\pi$
$524$	11.2071	0.489584
$525$	96.0876	4.19361
$526$	−19.2644	−0.839966
$527$	37.7857	1.64597
$528$	−28.5666	−1.24320
$529$	−5.66940	−0.246496
$530$	−96.4959	−4.19152
$531$	−29.5063	−1.28046
$532$	−97.2622	−4.21685
$533$	−9.09810	−0.394082
$534$	78.3808	3.39187
$535$	−8.94629	−0.386782
$536$	−87.9812	−3.80021
$537$	42.1839	1.82037
$538$	−47.3598	−2.04183
$539$	17.2873	0.744618
$540$	35.5609	1.53030
$541$	−29.8843	−1.28483	−0.642414	−	0.766358i	$-0.722067\pi$
$541$	−29.8843	−1.28483	−0.642414	+	0.766358i	$0.722067\pi$
$542$	44.7079	1.92037
$543$	14.8784	0.638492
$544$	−72.2296	−3.09682
$545$	−20.5475	−0.880159
$546$	−26.9246	−1.15226
$547$	20.3017	0.868038	0.434019	−	0.900904i	$-0.357095\pi$
$547$	20.3017	0.868038	0.434019	+	0.900904i	$0.357095\pi$
$548$	−19.0917	−0.815558
$549$	6.58457	0.281022
$550$	−16.8023	−0.716454
$551$	24.5564	1.04614
$552$	92.4898	3.93663
$553$	−75.7199	−3.21994
$554$	7.65748	0.325335
$555$	6.08469	0.258281
$556$	110.872	4.70202
$557$	5.33868	0.226207	0.113104	−	0.993583i	$-0.463921\pi$
$557$	5.33868	0.226207	0.113104	+	0.993583i	$0.463921\pi$
$558$	−87.0626	−3.68565
$559$	−2.15545	−0.0911657
$560$	225.964	9.54873
$561$	−9.95772	−0.420415
$562$	−22.2012	−0.936502
$563$	−1.04621	−0.0440925	−0.0220463	−	0.999757i	$-0.507018\pi$
$563$	−1.04621	−0.0440925	−0.0220463	+	0.999757i	$0.507018\pi$
$564$	−54.8854	−2.31109
$565$	−47.6519	−2.00473
$566$	55.2258	2.32131
$567$	31.8355	1.33696
$568$	113.982	4.78256
$569$	−27.6822	−1.16050	−0.580249	−	0.814439i	$-0.697045\pi$
$569$	−27.6822	−1.16050	−0.580249	+	0.814439i	$0.697045\pi$
$570$	−88.0950	−3.68989
$571$	−14.0987	−0.590012	−0.295006	−	0.955495i	$-0.595322\pi$
$571$	−14.0987	−0.590012	−0.295006	+	0.955495i	$0.595322\pi$
$572$	3.39815	0.142084
$573$	−37.6080	−1.57110
$574$	−168.728	−7.04256
$575$	29.7684	1.24143
$576$	72.2159	3.00900
$577$	7.17715	0.298789	0.149394	−	0.988778i	$-0.452268\pi$
$577$	7.17715	0.298789	0.149394	+	0.988778i	$0.452268\pi$
$578$	−5.64601	−0.234843
$579$	7.34502	0.305249
$580$	−122.457	−5.08474
$581$	−36.8923	−1.53055
$582$	3.94242	0.163419
$583$	−9.04938	−0.374787
$584$	−38.6478	−1.59926
$585$	−9.78611	−0.404606
$586$	41.4224	1.71114
$587$	−19.8595	−0.819690	−0.409845	−	0.912155i	$-0.634417\pi$
$587$	−19.8595	−0.819690	−0.409845	+	0.912155i	$0.634417\pi$
$588$	−265.996	−10.9695
$589$	31.3493	1.29173
$590$	−73.4068	−3.02211
$591$	29.4020	1.20944
$592$	8.42089	0.346096
$593$	10.8390	0.445105	0.222553	−	0.974921i	$-0.428561\pi$
$593$	10.8390	0.445105	0.222553	+	0.974921i	$0.428561\pi$
$594$	4.62051	0.189582
$595$	78.7665	3.22911
$596$	12.4478	0.509881
$597$	−65.6482	−2.68680
$598$	−8.34137	−0.341104
$599$	3.82319	0.156211	0.0781056	−	0.996945i	$-0.475113\pi$
$599$	3.82319	0.156211	0.0781056	+	0.996945i	$0.475113\pi$
$600$	158.868	6.48576
$601$	46.1006	1.88048	0.940241	−	0.340511i	$-0.110600\pi$
$601$	46.1006	1.88048	0.940241	+	0.340511i	$0.110600\pi$
$602$	−39.9736	−1.62920
$603$	38.6676	1.57467
$604$	62.2894	2.53452
$605$	35.6661	1.45003
$606$	−6.38132	−0.259223
$607$	8.72839	0.354274	0.177137	−	0.984186i	$-0.443316\pi$
$607$	8.72839	0.354274	0.177137	+	0.984186i	$0.443316\pi$
$608$	−59.9262	−2.43033
$609$	90.9909	3.68714
$610$	16.3813	0.663261
$611$	3.04172	0.123055
$612$	85.1862	3.44345
$613$	−23.1545	−0.935200	−0.467600	−	0.883940i	$-0.654881\pi$
$613$	−23.1545	−0.935200	−0.467600	+	0.883940i	$0.654881\pi$
$614$	−46.5417	−1.87827
$615$	−110.303	−4.44784
$616$	38.7257	1.56030
$617$	−22.5030	−0.905938	−0.452969	−	0.891526i	$-0.649635\pi$
$617$	−22.5030	−0.905938	−0.452969	+	0.891526i	$0.649635\pi$
$618$	−41.6152	−1.67401
$619$	16.3434	0.656897	0.328448	−	0.944522i	$-0.393474\pi$
$619$	16.3434	0.656897	0.328448	+	0.944522i	$0.393474\pi$
$620$	−156.331	−6.27842
$621$	−8.18609	−0.328497
$622$	16.0893	0.645122
$623$	−58.1435	−2.32947
$624$	−24.3595	−0.975160
$625$	−9.62088	−0.384835
$626$	−87.3647	−3.49180
$627$	−8.26154	−0.329934
$628$	−67.3537	−2.68771
$629$	2.93535	0.117040
$630$	−181.487	−7.23063
$631$	19.9320	0.793482	0.396741	−	0.917931i	$-0.370141\pi$
$631$	19.9320	0.793482	0.396741	+	0.917931i	$0.370141\pi$
$632$	−125.193	−4.97990
$633$	−23.5756	−0.937044
$634$	−41.1674	−1.63497
$635$	−48.0616	−1.90727
$636$	139.241	5.52125
$637$	14.7414	0.584075
$638$	−15.9111	−0.629926
$639$	−50.0947	−1.98172
$640$	64.4588	2.54796
$641$	2.36150	0.0932737	0.0466368	−	0.998912i	$-0.485150\pi$
$641$	2.36150	0.0932737	0.0466368	+	0.998912i	$0.485150\pi$
$642$	17.8858	0.705895
$643$	15.3925	0.607019	0.303510	−	0.952828i	$-0.401842\pi$
$643$	15.3925	0.607019	0.303510	+	0.952828i	$0.401842\pi$
$644$	−111.652	−4.39970
$645$	−26.1320	−1.02895
$646$	−42.4985	−1.67208
$647$	18.7879	0.738627	0.369313	−	0.929305i	$-0.379593\pi$
$647$	18.7879	0.738627	0.369313	+	0.929305i	$0.379593\pi$
$648$	52.6357	2.06773
$649$	−6.88409	−0.270224
$650$	−14.3278	−0.561983
$651$	116.161	4.55272
$652$	−75.7852	−2.96798
$653$	14.6954	0.575075	0.287538	−	0.957769i	$-0.407163\pi$
$653$	14.6954	0.575075	0.287538	+	0.957769i	$0.407163\pi$
$654$	41.0794	1.60633
$655$	−7.52995	−0.294220
$656$	−152.653	−5.96011
$657$	16.9856	0.662673
$658$	56.4100	2.19909
$659$	−8.89957	−0.346678	−0.173339	−	0.984862i	$-0.555456\pi$
$659$	−8.89957	−0.346678	−0.173339	+	0.984862i	$0.555456\pi$
$660$	41.1983	1.60364
$661$	−49.6246	−1.93017	−0.965086	−	0.261933i	$-0.915640\pi$
$661$	−49.6246	−1.93017	−0.965086	+	0.261933i	$0.915640\pi$
$662$	3.16928	0.123178
$663$	−8.49122	−0.329772
$664$	−60.9964	−2.36712
$665$	65.3496	2.53415
$666$	−6.76339	−0.262076
$667$	28.1894	1.09150
$668$	64.6886	2.50288
$669$	−42.2708	−1.63428
$670$	96.1987	3.71648
$671$	1.53624	0.0593059
$672$	−222.049	−8.56574
$673$	8.50990	0.328033	0.164016	−	0.986458i	$-0.447555\pi$
$673$	8.50990	0.328033	0.164016	+	0.986458i	$0.447555\pi$
$674$	−14.2164	−0.547595
$675$	−14.0611	−0.541212
$676$	−64.5466	−2.48256
$677$	12.5579	0.482639	0.241319	−	0.970446i	$-0.422420\pi$
$677$	12.5579	0.482639	0.241319	+	0.970446i	$0.422420\pi$
$678$	95.2675	3.65872
$679$	−2.92452	−0.112233
$680$	130.230	4.99409
$681$	52.1472	1.99829
$682$	−20.3125	−0.777806
$683$	−28.8857	−1.10528	−0.552639	−	0.833420i	$-0.686379\pi$
$683$	−28.8857	−1.10528	−0.552639	+	0.833420i	$0.686379\pi$
$684$	70.6757	2.70235
$685$	12.8276	0.490116
$686$	176.365	6.73365
$687$	−56.6380	−2.16088
$688$	−36.1654	−1.37879
$689$	−7.71666	−0.293981
$690$	−101.128	−3.84989
$691$	−21.6329	−0.822953	−0.411476	−	0.911420i	$-0.634987\pi$
$691$	−21.6329	−0.822953	−0.411476	+	0.911420i	$0.634987\pi$
$692$	76.8049	2.91968
$693$	−17.0199	−0.646531
$694$	−26.5501	−1.00783
$695$	−74.4939	−2.82572
$696$	150.441	5.70246
$697$	−53.2119	−2.01554
$698$	−15.3676	−0.581674
$699$	55.6265	2.10399
$700$	−191.782	−7.24869
$701$	16.4987	0.623148	0.311574	−	0.950222i	$-0.399144\pi$
$701$	16.4987	0.623148	0.311574	+	0.950222i	$0.399144\pi$
$702$	3.94004	0.148707
$703$	2.43535	0.0918509
$704$	16.8486	0.635007
$705$	36.8770	1.38887
$706$	−21.0418	−0.791919
$707$	4.73371	0.178030
$708$	105.924	3.98086
$709$	17.8019	0.668565	0.334282	−	0.942473i	$-0.391506\pi$
$709$	17.8019	0.668565	0.334282	+	0.942473i	$0.391506\pi$
$710$	−124.628	−4.67719
$711$	55.0219	2.06348
$712$	−96.1326	−3.60272
$713$	35.9874	1.34774
$714$	−157.473	−5.89328
$715$	−2.28319	−0.0853865
$716$	−84.1952	−3.14652
$717$	66.9287	2.49950
$718$	−8.00288	−0.298665
$719$	5.51006	0.205491	0.102745	−	0.994708i	$-0.467237\pi$
$719$	5.51006	0.205491	0.102745	+	0.994708i	$0.467237\pi$
$720$	−164.197	−6.11927
$721$	30.8705	1.14968
$722$	15.6806	0.583570
$723$	22.3038	0.829488
$724$	−29.6959	−1.10364
$725$	48.4205	1.79829
$726$	−71.3052	−2.64638
$727$	−50.0027	−1.85450	−0.927248	−	0.374447i	$-0.877833\pi$
$727$	−50.0027	−1.85450	−0.927248	+	0.374447i	$0.877833\pi$
$728$	33.0224	1.22389
$729$	−38.4672	−1.42471
$730$	42.2575	1.56402
$731$	−12.6065	−0.466269
$732$	−23.6378	−0.873677
$733$	−17.1710	−0.634224	−0.317112	−	0.948388i	$-0.602713\pi$
$733$	−17.1710	−0.634224	−0.317112	+	0.948388i	$0.602713\pi$
$734$	−56.8504	−2.09839
$735$	178.720	6.59220
$736$	−68.7921	−2.53571
$737$	9.02151	0.332311
$738$	122.606	4.51320
$739$	−24.8717	−0.914920	−0.457460	−	0.889230i	$-0.651241\pi$
$739$	−24.8717	−0.914920	−0.457460	+	0.889230i	$0.651241\pi$
$740$	−12.1445	−0.446440
$741$	−7.04485	−0.258799
$742$	−143.108	−5.25368
$743$	6.44568	0.236469	0.118234	−	0.992986i	$-0.462277\pi$
$743$	6.44568	0.236469	0.118234	+	0.992986i	$0.462277\pi$
$744$	192.057	7.04116
$745$	−8.36355	−0.306417
$746$	46.0722	1.68682
$747$	26.8078	0.980847
$748$	19.8747	0.726692
$749$	−13.2678	−0.484795
$750$	−52.2455	−1.90773
$751$	43.9422	1.60348	0.801738	−	0.597676i	$-0.203909\pi$
$751$	43.9422	1.60348	0.801738	+	0.597676i	$0.203909\pi$
$752$	51.0359	1.86109
$753$	−4.20988	−0.153417
$754$	−13.5678	−0.494111
$755$	−41.8517	−1.52314
$756$	52.7386	1.91809
$757$	−11.0556	−0.401823	−0.200912	−	0.979609i	$-0.564390\pi$
$757$	−11.0556	−0.401823	−0.200912	+	0.979609i	$0.564390\pi$
$758$	−24.0258	−0.872658
$759$	−9.48382	−0.344241
$760$	108.047	3.91927
$761$	17.5540	0.636332	0.318166	−	0.948035i	$-0.396933\pi$
$761$	17.5540	0.636332	0.318166	+	0.948035i	$0.396933\pi$
$762$	96.0866	3.48085
$763$	−30.4730	−1.10320
$764$	75.0622	2.71565
$765$	−57.2358	−2.06937
$766$	−36.9113	−1.33366
$767$	−5.87025	−0.211962
$768$	−28.9284	−1.04386
$769$	−25.6853	−0.926236	−0.463118	−	0.886297i	$-0.653269\pi$
$769$	−25.6853	−0.926236	−0.463118	+	0.886297i	$0.653269\pi$
$770$	−42.3427	−1.52592
$771$	68.2848	2.45922
$772$	−14.6600	−0.527625
$773$	−8.40534	−0.302319	−0.151160	−	0.988509i	$-0.548301\pi$
$773$	−8.40534	−0.302319	−0.151160	+	0.988509i	$0.548301\pi$
$774$	29.0469	1.04407
$775$	61.8148	2.22045
$776$	−4.83530	−0.173577
$777$	9.02390	0.323731
$778$	49.1584	1.76241
$779$	−44.1479	−1.58176
$780$	35.1309	1.25789
$781$	−11.6876	−0.418214
$782$	−48.7860	−1.74458
$783$	−13.3153	−0.475848
$784$	247.340	8.83357
$785$	45.2544	1.61520
$786$	15.0542	0.536965
$787$	−42.4076	−1.51167	−0.755834	−	0.654764i	$-0.772768\pi$
$787$	−42.4076	−1.51167	−0.755834	+	0.654764i	$0.772768\pi$
$788$	−58.6838	−2.09052
$789$	−18.6772	−0.664924
$790$	136.886	4.87018
$791$	−70.6702	−2.51274
$792$	−28.1401	−0.999914
$793$	1.30999	0.0465193
$794$	−54.8718	−1.94733
$795$	−93.5546	−3.31804
$796$	131.028	4.64416
$797$	36.6030	1.29655	0.648273	−	0.761408i	$-0.275492\pi$
$797$	36.6030	1.29655	0.648273	+	0.761408i	$0.275492\pi$
$798$	−130.649	−4.62494
$799$	17.7901	0.629367
$800$	−118.163	−4.17769
$801$	42.2501	1.49283
$802$	−54.9445	−1.94016
$803$	3.96291	0.139848
$804$	−138.812	−4.89551
$805$	75.0179	2.64403
$806$	−17.3210	−0.610107
$807$	−45.9162	−1.61633
$808$	7.82656	0.275337
$809$	40.1918	1.41307	0.706535	−	0.707678i	$-0.250257\pi$
$809$	40.1918	1.41307	0.706535	+	0.707678i	$0.250257\pi$
$810$	−57.5519	−2.02217
$811$	−35.0857	−1.23203	−0.616013	−	0.787736i	$-0.711253\pi$
$811$	−35.0857	−1.23203	−0.616013	+	0.787736i	$0.711253\pi$
$812$	−181.610	−6.37325
$813$	43.3452	1.52018
$814$	−1.57796	−0.0553076
$815$	50.9194	1.78363
$816$	−142.471	−4.98748
$817$	−10.4592	−0.365919
$818$	66.4888	2.32472
$819$	−14.5133	−0.507136
$820$	220.155	7.68813
$821$	32.3118	1.12769	0.563844	−	0.825881i	$-0.309322\pi$
$821$	32.3118	1.12769	0.563844	+	0.825881i	$0.309322\pi$
$822$	−25.6454	−0.894485
$823$	−17.0148	−0.593100	−0.296550	−	0.955017i	$-0.595836\pi$
$823$	−17.0148	−0.593100	−0.296550	+	0.955017i	$0.595836\pi$
$824$	51.0402	1.77807
$825$	−16.2902	−0.567151
$826$	−108.866	−3.78794
$827$	1.15823	0.0402756	0.0201378	−	0.999797i	$-0.493590\pi$
$827$	1.15823	0.0402756	0.0201378	+	0.999797i	$0.493590\pi$
$828$	81.1320	2.81953
$829$	7.70413	0.267576	0.133788	−	0.991010i	$-0.457286\pi$
$829$	7.70413	0.267576	0.133788	+	0.991010i	$0.457286\pi$
$830$	66.6935	2.31497
$831$	7.42407	0.257538
$832$	14.3673	0.498096
$833$	86.2176	2.98726
$834$	148.931	5.15706
$835$	−43.4637	−1.50412
$836$	16.4893	0.570294
$837$	−16.9986	−0.587557
$838$	−6.84572	−0.236482
$839$	−45.8973	−1.58455	−0.792276	−	0.610163i	$-0.791104\pi$
$839$	−45.8973	−1.58455	−0.792276	+	0.610163i	$0.791104\pi$
$840$	400.355	13.8136
$841$	16.8521	0.581108
$842$	−8.50432	−0.293078
$843$	−21.5245	−0.741343
$844$	47.0547	1.61969
$845$	43.3683	1.49191
$846$	−40.9904	−1.40928
$847$	52.8947	1.81748
$848$	−129.475	−4.44618
$849$	53.5424	1.83757
$850$	−83.7988	−2.87427
$851$	2.79565	0.0958337
$852$	179.834	6.16100
$853$	15.9270	0.545328	0.272664	−	0.962109i	$-0.412095\pi$
$853$	15.9270	0.545328	0.272664	+	0.962109i	$0.412095\pi$
$854$	24.2944	0.831336
$855$	−47.4864	−1.62400
$856$	−21.9365	−0.749776
$857$	−16.3697	−0.559179	−0.279590	−	0.960120i	$-0.590198\pi$
$857$	−16.3697	−0.559179	−0.279590	+	0.960120i	$0.590198\pi$
$858$	4.56464	0.155834
$859$	35.9599	1.22694	0.613468	−	0.789720i	$-0.289774\pi$
$859$	35.9599	1.22694	0.613468	+	0.789720i	$0.289774\pi$
$860$	52.1572	1.77855
$861$	−163.585	−5.57495
$862$	14.7028	0.500781
$863$	−23.3613	−0.795228	−0.397614	−	0.917553i	$-0.630162\pi$
$863$	−23.3613	−0.795228	−0.397614	+	0.917553i	$0.630162\pi$
$864$	32.4939	1.10546
$865$	−51.6045	−1.75461
$866$	−2.76971	−0.0941186
$867$	−5.47391	−0.185904
$868$	−231.847	−7.86942
$869$	12.8371	0.435470
$870$	−164.493	−5.57682
$871$	7.69289	0.260664
$872$	−50.3831	−1.70619
$873$	2.12511	0.0719240
$874$	−40.4759	−1.36912
$875$	38.7561	1.31020
$876$	−60.9763	−2.06020
$877$	−11.0060	−0.371646	−0.185823	−	0.982583i	$-0.559495\pi$
$877$	−11.0060	−0.371646	−0.185823	+	0.982583i	$0.559495\pi$
$878$	73.2826	2.47317
$879$	40.1598	1.35456
$880$	−38.3087	−1.29139
$881$	30.4744	1.02671	0.513354	−	0.858177i	$-0.328403\pi$
$881$	30.4744	1.02671	0.513354	+	0.858177i	$0.328403\pi$
$882$	−198.656	−6.68908
$883$	2.53253	0.0852266	0.0426133	−	0.999092i	$-0.486432\pi$
$883$	2.53253	0.0852266	0.0426133	+	0.999092i	$0.486432\pi$
$884$	16.9477	0.570014
$885$	−71.1693	−2.39233
$886$	−62.3583	−2.09497
$887$	38.8851	1.30563	0.652817	−	0.757516i	$-0.273587\pi$
$887$	38.8851	1.30563	0.652817	+	0.757516i	$0.273587\pi$
$888$	14.9198	0.500676
$889$	−71.2778	−2.39058
$890$	105.111	3.52334
$891$	−5.39722	−0.180814
$892$	84.3688	2.82488
$893$	14.7597	0.493916
$894$	16.7207	0.559225
$895$	56.5700	1.89093
$896$	95.5958	3.19363
$897$	−8.08711	−0.270021
$898$	57.5692	1.92111
$899$	58.5360	1.95228
$900$	139.359	4.64530
$901$	−45.1323	−1.50357
$902$	28.6052	0.952449
$903$	−38.7552	−1.28969
$904$	−116.844	−3.88616
$905$	19.9524	0.663240
$906$	83.6715	2.77980
$907$	−20.5975	−0.683930	−0.341965	−	0.939713i	$-0.611092\pi$
$907$	−20.5975	−0.683930	−0.341965	+	0.939713i	$0.611092\pi$
$908$	−104.081	−3.45405
$909$	−3.43976	−0.114090
$910$	−36.1068	−1.19693
$911$	−47.3267	−1.56800	−0.784001	−	0.620759i	$-0.786824\pi$
$911$	−47.3267	−1.56800	−0.784001	+	0.620759i	$0.786824\pi$
$912$	−118.203	−3.91408
$913$	6.25451	0.206994
$914$	83.0007	2.74542
$915$	15.8820	0.525043
$916$	113.044	3.73509
$917$	−11.1673	−0.368777
$918$	23.0440	0.760566
$919$	−44.2802	−1.46067	−0.730335	−	0.683089i	$-0.760636\pi$
$919$	−44.2802	−1.46067	−0.730335	+	0.683089i	$0.760636\pi$
$920$	124.032	4.08921
$921$	−45.1230	−1.48685
$922$	−22.4720	−0.740077
$923$	−9.96630	−0.328045
$924$	61.0992	2.01002
$925$	4.80204	0.157890
$926$	−101.262	−3.32769
$927$	−22.4321	−0.736766
$928$	−111.895	−3.67314
$929$	−42.2540	−1.38631	−0.693155	−	0.720788i	$-0.743780\pi$
$929$	−42.2540	−1.38631	−0.693155	+	0.720788i	$0.743780\pi$
$930$	−209.995	−6.88602
$931$	71.5315	2.34435
$932$	−111.026	−3.63676
$933$	15.5989	0.510684
$934$	−40.6962	−1.33162
$935$	−13.3537	−0.436711
$936$	−23.9958	−0.784327
$937$	−19.0600	−0.622665	−0.311332	−	0.950301i	$-0.600775\pi$
$937$	−19.0600	−0.622665	−0.311332	+	0.950301i	$0.600775\pi$
$938$	142.668	4.65826
$939$	−84.7017	−2.76414
$940$	−73.6032	−2.40067
$941$	−28.9026	−0.942197	−0.471098	−	0.882081i	$-0.656142\pi$
$941$	−28.9026	−0.942197	−0.471098	+	0.882081i	$0.656142\pi$
$942$	−90.4743	−2.94781
$943$	−50.6794	−1.65035
$944$	−98.4946	−3.20573
$945$	−35.4346	−1.15269
$946$	6.77691	0.220336
$947$	48.2970	1.56944	0.784721	−	0.619849i	$-0.212806\pi$
$947$	48.2970	1.56944	0.784721	+	0.619849i	$0.212806\pi$
$948$	−197.522	−6.41522
$949$	3.37928	0.109696
$950$	−69.5247	−2.25568
$951$	−39.9126	−1.29425
$952$	193.138	6.25963
$953$	38.9193	1.26072	0.630360	−	0.776303i	$-0.282907\pi$
$953$	38.9193	1.26072	0.630360	+	0.776303i	$0.282907\pi$
$954$	103.990	3.36680
$955$	−50.4336	−1.63199
$956$	−133.584	−4.32040
$957$	−15.4261	−0.498655
$958$	−66.2038	−2.13895
$959$	19.0239	0.614315
$960$	174.185	5.62180
$961$	43.7286	1.41060
$962$	−1.34557	−0.0433830
$963$	9.64108	0.310679
$964$	−44.5164	−1.43378
$965$	9.84992	0.317080
$966$	−149.979	−4.82549
$967$	17.9995	0.578823	0.289412	−	0.957205i	$-0.406540\pi$
$967$	17.9995	0.578823	0.289412	+	0.957205i	$0.406540\pi$
$968$	87.4544	2.81089
$969$	−41.2031	−1.32363
$970$	5.28693	0.169753
$971$	51.1998	1.64308	0.821540	−	0.570150i	$-0.193115\pi$
$971$	51.1998	1.64308	0.821540	+	0.570150i	$0.193115\pi$
$972$	113.651	3.64535
$973$	−110.478	−3.54177
$974$	−62.3754	−1.99864
$975$	−13.8911	−0.444870
$976$	21.9799	0.703559
$977$	−29.4243	−0.941366	−0.470683	−	0.882302i	$-0.655992\pi$
$977$	−29.4243	−0.941366	−0.470683	+	0.882302i	$0.655992\pi$
$978$	−101.800	−3.25521
$979$	9.85734	0.315042
$980$	−356.710	−11.3947
$981$	22.1433	0.706980
$982$	64.4820	2.05770
$983$	7.77916	0.248117	0.124058	−	0.992275i	$-0.460409\pi$
$983$	7.77916	0.248117	0.124058	+	0.992275i	$0.460409\pi$
$984$	−270.466	−8.62213
$985$	39.4291	1.25632
$986$	−79.3539	−2.52714
$987$	54.6905	1.74082
$988$	14.0609	0.447336
$989$	−12.0066	−0.381786
$990$	30.7684	0.977883
$991$	49.1705	1.56195	0.780976	−	0.624561i	$-0.214722\pi$
$991$	49.1705	1.56195	0.780976	+	0.624561i	$0.214722\pi$
$992$	−142.848	−4.53544
$993$	3.07268	0.0975084
$994$	−184.829	−5.86242
$995$	−88.0366	−2.79095
$996$	−96.2367	−3.04938
$997$	−22.6434	−0.717124	−0.358562	−	0.933506i	$-0.616733\pi$
$997$	−22.6434	−0.717124	−0.358562	+	0.933506i	$0.616733\pi$
$998$	88.0821	2.78819
$999$	−1.32052	−0.0417795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.8	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.8	✓	184	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68105 q^{2} -2.59933 q^{3} +5.18802 q^{4} -3.48579 q^{5} +6.96892 q^{6} -5.16960 q^{7} -8.54725 q^{8} +3.75650 q^{9} +O(q^{10})\)	\(q-2.68105 q^{2} -2.59933 q^{3} +5.18802 q^{4} -3.48579 q^{5} +6.96892 q^{6} -5.16960 q^{7} -8.54725 q^{8} +3.75650 q^{9} +9.34557 q^{10} +0.876427 q^{11} -13.4854 q^{12} +0.747353 q^{13} +13.8600 q^{14} +9.06070 q^{15} +12.5395 q^{16} +4.37103 q^{17} -10.0714 q^{18} +3.62648 q^{19} -18.0843 q^{20} +13.4375 q^{21} -2.34974 q^{22} +4.16300 q^{23} +22.2171 q^{24} +7.15071 q^{25} -2.00369 q^{26} -1.96639 q^{27} -26.8200 q^{28} +6.77142 q^{29} -24.2922 q^{30} +8.64457 q^{31} -16.5246 q^{32} -2.27812 q^{33} -11.7189 q^{34} +18.0201 q^{35} +19.4888 q^{36} +0.671547 q^{37} -9.72276 q^{38} -1.94261 q^{39} +29.7939 q^{40} -12.1738 q^{41} -36.0266 q^{42} -2.88411 q^{43} +4.54692 q^{44} -13.0944 q^{45} -11.1612 q^{46} +4.06999 q^{47} -32.5944 q^{48} +19.7248 q^{49} -19.1714 q^{50} -11.3617 q^{51} +3.87728 q^{52} -10.3253 q^{53} +5.27199 q^{54} -3.05504 q^{55} +44.1859 q^{56} -9.42640 q^{57} -18.1545 q^{58} -7.85472 q^{59} +47.0071 q^{60} +1.75285 q^{61} -23.1765 q^{62} -19.4196 q^{63} +19.2242 q^{64} -2.60511 q^{65} +6.10775 q^{66} +10.2935 q^{67} +22.6770 q^{68} -10.8210 q^{69} -48.3129 q^{70} -13.3355 q^{71} -32.1077 q^{72} +4.52167 q^{73} -1.80045 q^{74} -18.5870 q^{75} +18.8142 q^{76} -4.53078 q^{77} +5.20824 q^{78} +14.6471 q^{79} -43.7102 q^{80} -6.15821 q^{81} +32.6385 q^{82} +7.13638 q^{83} +69.7140 q^{84} -15.2365 q^{85} +7.73244 q^{86} -17.6011 q^{87} -7.49103 q^{88} +11.2472 q^{89} +35.1066 q^{90} -3.86352 q^{91} +21.5978 q^{92} -22.4701 q^{93} -10.9119 q^{94} -12.6411 q^{95} +42.9529 q^{96} +0.565715 q^{97} -52.8831 q^{98} +3.29230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

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