LMFDB - Embedded newform 8027.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55473 q^{2} -3.25140 q^{3} +4.52663 q^{4} +2.74770 q^{5} +8.30644 q^{6} +1.12543 q^{7} -6.45485 q^{8} +7.57160 q^{9} +O(q^{10})$	\(q-2.55473 q^{2} -3.25140 q^{3} +4.52663 q^{4} +2.74770 q^{5} +8.30644 q^{6} +1.12543 q^{7} -6.45485 q^{8} +7.57160 q^{9} -7.01962 q^{10} +3.97187 q^{11} -14.7179 q^{12} -1.86791 q^{13} -2.87516 q^{14} -8.93387 q^{15} +7.43711 q^{16} -3.39105 q^{17} -19.3434 q^{18} -1.11313 q^{19} +12.4378 q^{20} -3.65922 q^{21} -10.1470 q^{22} -1.00000 q^{23} +20.9873 q^{24} +2.54986 q^{25} +4.77201 q^{26} -14.8641 q^{27} +5.09440 q^{28} -0.263499 q^{29} +22.8236 q^{30} +5.63650 q^{31} -6.09010 q^{32} -12.9141 q^{33} +8.66320 q^{34} +3.09234 q^{35} +34.2738 q^{36} +1.83275 q^{37} +2.84373 q^{38} +6.07333 q^{39} -17.7360 q^{40} -6.42979 q^{41} +9.34830 q^{42} -2.45999 q^{43} +17.9792 q^{44} +20.8045 q^{45} +2.55473 q^{46} +4.16721 q^{47} -24.1810 q^{48} -5.73341 q^{49} -6.51419 q^{50} +11.0257 q^{51} -8.45535 q^{52} +7.71451 q^{53} +37.9737 q^{54} +10.9135 q^{55} -7.26447 q^{56} +3.61921 q^{57} +0.673169 q^{58} +3.54111 q^{59} -40.4403 q^{60} +5.55589 q^{61} -14.3997 q^{62} +8.52129 q^{63} +0.684308 q^{64} -5.13246 q^{65} +32.9921 q^{66} +3.33325 q^{67} -15.3500 q^{68} +3.25140 q^{69} -7.90009 q^{70} -15.5853 q^{71} -48.8735 q^{72} +1.08407 q^{73} -4.68217 q^{74} -8.29060 q^{75} -5.03870 q^{76} +4.47006 q^{77} -15.5157 q^{78} +5.07339 q^{79} +20.4350 q^{80} +25.6143 q^{81} +16.4264 q^{82} -12.0060 q^{83} -16.5639 q^{84} -9.31758 q^{85} +6.28459 q^{86} +0.856742 q^{87} -25.6378 q^{88} -4.16089 q^{89} -53.1498 q^{90} -2.10220 q^{91} -4.52663 q^{92} -18.3265 q^{93} -10.6461 q^{94} -3.05853 q^{95} +19.8013 q^{96} -12.7724 q^{97} +14.6473 q^{98} +30.0734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.55473	−1.80646	−0.903232	−	0.429152i	$-0.858812\pi$
$2$	−2.55473	−1.80646	−0.903232	+	0.429152i	$0.858812\pi$
$3$	−3.25140	−1.87720	−0.938598	−	0.345012i	$-0.887875\pi$
$3$	−3.25140	−1.87720	−0.938598	+	0.345012i	$0.887875\pi$
$4$	4.52663	2.26331
$5$	2.74770	1.22881	0.614404	−	0.788991i	$-0.289396\pi$
$5$	2.74770	1.22881	0.614404	+	0.788991i	$0.289396\pi$
$6$	8.30644	3.39109
$7$	1.12543	0.425372	0.212686	−	0.977121i	$-0.431779\pi$
$7$	1.12543	0.425372	0.212686	+	0.977121i	$0.431779\pi$
$8$	−6.45485	−2.28213
$9$	7.57160	2.52387
$10$	−7.01962	−2.21980
$11$	3.97187	1.19756	0.598782	−	0.800912i	$-0.295652\pi$
$11$	3.97187	1.19756	0.598782	+	0.800912i	$0.295652\pi$
$12$	−14.7179	−4.24869
$13$	−1.86791	−0.518066	−0.259033	−	0.965868i	$-0.583404\pi$
$13$	−1.86791	−0.518066	−0.259033	+	0.965868i	$0.583404\pi$
$14$	−2.87516	−0.768420
$15$	−8.93387	−2.30672
$16$	7.43711	1.85928
$17$	−3.39105	−0.822450	−0.411225	−	0.911534i	$-0.634899\pi$
$17$	−3.39105	−0.822450	−0.411225	+	0.911534i	$0.634899\pi$
$18$	−19.3434	−4.55927
$19$	−1.11313	−0.255368	−0.127684	−	0.991815i	$-0.540754\pi$
$19$	−1.11313	−0.255368	−0.127684	+	0.991815i	$0.540754\pi$
$20$	12.4378	2.78118
$21$	−3.65922	−0.798507
$22$	−10.1470	−2.16336
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	20.9873	4.28401
$25$	2.54986	0.509971
$26$	4.77201	0.935868
$27$	−14.8641	−2.86060
$28$	5.09440	0.962751
$29$	−0.263499	−0.0489306	−0.0244653	−	0.999701i	$-0.507788\pi$
$29$	−0.263499	−0.0489306	−0.0244653	+	0.999701i	$0.507788\pi$
$30$	22.8236	4.16700
$31$	5.63650	1.01234	0.506172	−	0.862432i	$-0.331060\pi$
$31$	5.63650	1.01234	0.506172	+	0.862432i	$0.331060\pi$
$32$	−6.09010	−1.07659
$33$	−12.9141	−2.24806
$34$	8.66320	1.48573
$35$	3.09234	0.522701
$36$	34.2738	5.71230
$37$	1.83275	0.301302	0.150651	−	0.988587i	$-0.451863\pi$
$37$	1.83275	0.301302	0.150651	+	0.988587i	$0.451863\pi$
$38$	2.84373	0.461314
$39$	6.07333	0.972511
$40$	−17.7360	−2.80431
$41$	−6.42979	−1.00417	−0.502083	−	0.864820i	$-0.667433\pi$
$41$	−6.42979	−1.00417	−0.502083	+	0.864820i	$0.667433\pi$
$42$	9.34830	1.44247
$43$	−2.45999	−0.375144	−0.187572	−	0.982251i	$-0.560062\pi$
$43$	−2.45999	−0.375144	−0.187572	+	0.982251i	$0.560062\pi$
$44$	17.9792	2.71046
$45$	20.8045	3.10135
$46$	2.55473	0.376674
$47$	4.16721	0.607850	0.303925	−	0.952696i	$-0.401703\pi$
$47$	4.16721	0.607850	0.303925	+	0.952696i	$0.401703\pi$
$48$	−24.1810	−3.49023
$49$	−5.73341	−0.819059
$50$	−6.51419	−0.921245
$51$	11.0257	1.54390
$52$	−8.45535	−1.17255
$53$	7.71451	1.05967	0.529835	−	0.848101i	$-0.322254\pi$
$53$	7.71451	1.05967	0.529835	+	0.848101i	$0.322254\pi$
$54$	37.9737	5.16756
$55$	10.9135	1.47158
$56$	−7.26447	−0.970756
$57$	3.61921	0.479377
$58$	0.673169	0.0883914
$59$	3.54111	0.461014	0.230507	−	0.973071i	$-0.425962\pi$
$59$	3.54111	0.461014	0.230507	+	0.973071i	$0.425962\pi$
$60$	−40.4403	−5.22082
$61$	5.55589	0.711359	0.355680	−	0.934608i	$-0.384249\pi$
$61$	5.55589	0.711359	0.355680	+	0.934608i	$0.384249\pi$
$62$	−14.3997	−1.82876
$63$	8.52129	1.07358
$64$	0.684308	0.0855385
$65$	−5.13246	−0.636604
$66$	32.9921	4.06105
$67$	3.33325	0.407221	0.203611	−	0.979052i	$-0.434732\pi$
$67$	3.33325	0.407221	0.203611	+	0.979052i	$0.434732\pi$
$68$	−15.3500	−1.86146
$69$	3.25140	0.391422
$70$	−7.90009	−0.944241
$71$	−15.5853	−1.84964	−0.924820	−	0.380405i	$-0.875784\pi$
$71$	−15.5853	−1.84964	−0.924820	+	0.380405i	$0.875784\pi$
$72$	−48.8735	−5.75980
$73$	1.08407	0.126881	0.0634403	−	0.997986i	$-0.479793\pi$
$73$	1.08407	0.126881	0.0634403	+	0.997986i	$0.479793\pi$
$74$	−4.68217	−0.544291
$75$	−8.29060	−0.957316
$76$	−5.03870	−0.577979
$77$	4.47006	0.509410
$78$	−15.5157	−1.75681
$79$	5.07339	0.570801	0.285400	−	0.958408i	$-0.407873\pi$
$79$	5.07339	0.570801	0.285400	+	0.958408i	$0.407873\pi$
$80$	20.4350	2.28470
$81$	25.6143	2.84603
$82$	16.4264	1.81399
$83$	−12.0060	−1.31783	−0.658915	−	0.752217i	$-0.728984\pi$
$83$	−12.0060	−1.31783	−0.658915	+	0.752217i	$0.728984\pi$
$84$	−16.5639	−1.80727
$85$	−9.31758	−1.01063
$86$	6.28459	0.677685
$87$	0.856742	0.0918523
$88$	−25.6378	−2.73300
$89$	−4.16089	−0.441054	−0.220527	−	0.975381i	$-0.570778\pi$
$89$	−4.16089	−0.441054	−0.220527	+	0.975381i	$0.570778\pi$
$90$	−53.1498	−5.60248
$91$	−2.10220	−0.220371
$92$	−4.52663	−0.471934
$93$	−18.3265	−1.90037
$94$	−10.6461	−1.09806
$95$	−3.05853	−0.313799
$96$	19.8013	2.02097
$97$	−12.7724	−1.29684	−0.648420	−	0.761282i	$-0.724570\pi$
$97$	−12.7724	−1.29684	−0.648420	+	0.761282i	$0.724570\pi$
$98$	14.6473	1.47960
$99$	30.0734	3.02249
$100$	11.5423	1.15423
$101$	19.3169	1.92211	0.961053	−	0.276365i	$-0.0891300\pi$
$101$	19.3169	1.92211	0.961053	+	0.276365i	$0.0891300\pi$
$102$	−28.1675	−2.78900
$103$	−9.52724	−0.938746	−0.469373	−	0.883000i	$-0.655520\pi$
$103$	−9.52724	−0.938746	−0.469373	+	0.883000i	$0.655520\pi$
$104$	12.0571	1.18230
$105$	−10.0544	−0.981212
$106$	−19.7085	−1.91426
$107$	−3.11887	−0.301512	−0.150756	−	0.988571i	$-0.548171\pi$
$107$	−3.11887	−0.301512	−0.150756	+	0.988571i	$0.548171\pi$
$108$	−67.2842	−6.47443
$109$	−1.77618	−0.170127	−0.0850636	−	0.996376i	$-0.527109\pi$
$109$	−1.77618	−0.170127	−0.0850636	+	0.996376i	$0.527109\pi$
$110$	−27.8810	−2.65835
$111$	−5.95899	−0.565603
$112$	8.36994	0.790885
$113$	−9.55434	−0.898797	−0.449399	−	0.893331i	$-0.648362\pi$
$113$	−9.55434	−0.898797	−0.449399	+	0.893331i	$0.648362\pi$
$114$	−9.24610	−0.865977
$115$	−2.74770	−0.256224
$116$	−1.19276	−0.110745
$117$	−14.1431	−1.30753
$118$	−9.04658	−0.832805
$119$	−3.81638	−0.349847
$120$	57.6668	5.26423
$121$	4.77575	0.434159
$122$	−14.1938	−1.28505
$123$	20.9058	1.88502
$124$	25.5143	2.29125
$125$	−6.73226	−0.602152
$126$	−21.7696	−1.93939
$127$	−7.24667	−0.643038	−0.321519	−	0.946903i	$-0.604193\pi$
$127$	−7.24667	−0.643038	−0.321519	+	0.946903i	$0.604193\pi$
$128$	10.4320	0.922065
$129$	7.99840	0.704219
$130$	13.1120	1.15000
$131$	−3.44415	−0.300917	−0.150458	−	0.988616i	$-0.548075\pi$
$131$	−3.44415	−0.300917	−0.150458	+	0.988616i	$0.548075\pi$
$132$	−58.4575	−5.08807
$133$	−1.25274	−0.108627
$134$	−8.51554	−0.735630
$135$	−40.8421	−3.51512
$136$	21.8887	1.87694
$137$	−9.23063	−0.788626	−0.394313	−	0.918976i	$-0.629017\pi$
$137$	−9.23063	−0.788626	−0.394313	+	0.918976i	$0.629017\pi$
$138$	−8.30644	−0.707091
$139$	12.3474	1.04729	0.523646	−	0.851936i	$-0.324571\pi$
$139$	12.3474	1.04729	0.523646	+	0.851936i	$0.324571\pi$
$140$	13.9979	1.18304
$141$	−13.5493	−1.14105
$142$	39.8163	3.34131
$143$	−7.41911	−0.620417
$144$	56.3108	4.69257
$145$	−0.724017	−0.0601263
$146$	−2.76950	−0.229205
$147$	18.6416	1.53753
$148$	8.29617	0.681941
$149$	1.32663	0.108682	0.0543409	−	0.998522i	$-0.482694\pi$
$149$	1.32663	0.108682	0.0543409	+	0.998522i	$0.482694\pi$
$150$	21.1802	1.72936
$151$	−18.8101	−1.53075	−0.765373	−	0.643588i	$-0.777445\pi$
$151$	−18.8101	−1.53075	−0.765373	+	0.643588i	$0.777445\pi$
$152$	7.18505	0.582785
$153$	−25.6757	−2.07575
$154$	−11.4198	−0.920232
$155$	15.4874	1.24398
$156$	27.4917	2.20110
$157$	−0.235957	−0.0188314	−0.00941570	−	0.999956i	$-0.502997\pi$
$157$	−0.235957	−0.0188314	−0.00941570	+	0.999956i	$0.502997\pi$
$158$	−12.9611	−1.03113
$159$	−25.0830	−1.98921
$160$	−16.7338	−1.32292
$161$	−1.12543	−0.0886962
$162$	−65.4375	−5.14126
$163$	4.91475	0.384953	0.192476	−	0.981302i	$-0.438348\pi$
$163$	4.91475	0.384953	0.192476	+	0.981302i	$0.438348\pi$
$164$	−29.1053	−2.27274
$165$	−35.4842	−2.76244
$166$	30.6721	2.38061
$167$	10.2113	0.790172	0.395086	−	0.918644i	$-0.370715\pi$
$167$	10.2113	0.790172	0.395086	+	0.918644i	$0.370715\pi$
$168$	23.6197	1.82230
$169$	−9.51090	−0.731608
$170$	23.8039	1.82567
$171$	−8.42813	−0.644516
$172$	−11.1354	−0.849069
$173$	−6.86597	−0.522010	−0.261005	−	0.965337i	$-0.584054\pi$
$173$	−6.86597	−0.522010	−0.261005	+	0.965337i	$0.584054\pi$
$174$	−2.18874	−0.165928
$175$	2.86968	0.216928
$176$	29.5392	2.22660
$177$	−11.5136	−0.865413
$178$	10.6299	0.796748
$179$	3.57587	0.267273	0.133636	−	0.991030i	$-0.457335\pi$
$179$	3.57587	0.267273	0.133636	+	0.991030i	$0.457335\pi$
$180$	94.1742	7.01933
$181$	−23.6155	−1.75533	−0.877665	−	0.479275i	$-0.840900\pi$
$181$	−23.6155	−1.75533	−0.877665	+	0.479275i	$0.840900\pi$
$182$	5.37055	0.398092
$183$	−18.0644	−1.33536
$184$	6.45485	0.475858
$185$	5.03584	0.370242
$186$	46.8192	3.43295
$187$	−13.4688	−0.984937
$188$	18.8634	1.37576
$189$	−16.7285	−1.21682
$190$	7.81372	0.566867
$191$	3.75172	0.271465	0.135733	−	0.990746i	$-0.456661\pi$
$191$	3.75172	0.271465	0.135733	+	0.990746i	$0.456661\pi$
$192$	−2.22496	−0.160573
$193$	−19.2153	−1.38315	−0.691575	−	0.722305i	$-0.743083\pi$
$193$	−19.2153	−1.38315	−0.691575	+	0.722305i	$0.743083\pi$
$194$	32.6300	2.34270
$195$	16.6877	1.19503
$196$	−25.9530	−1.85379
$197$	−14.8823	−1.06032	−0.530162	−	0.847897i	$-0.677869\pi$
$197$	−14.8823	−1.06032	−0.530162	+	0.847897i	$0.677869\pi$
$198$	−76.8293	−5.46002
$199$	2.24053	0.158827	0.0794133	−	0.996842i	$-0.474695\pi$
$199$	2.24053	0.158827	0.0794133	+	0.996842i	$0.474695\pi$
$200$	−16.4589	−1.16382
$201$	−10.8377	−0.764434
$202$	−49.3495	−3.47222
$203$	−0.296550	−0.0208137
$204$	49.9090	3.49433
$205$	−17.6671	−1.23393
$206$	24.3395	1.69581
$207$	−7.57160	−0.526262
$208$	−13.8919	−0.963228
$209$	−4.42119	−0.305820
$210$	25.6863	1.77253
$211$	23.0395	1.58610	0.793052	−	0.609154i	$-0.208491\pi$
$211$	23.0395	1.58610	0.793052	+	0.609154i	$0.208491\pi$
$212$	34.9207	2.39837
$213$	50.6742	3.47214
$214$	7.96785	0.544671
$215$	−6.75930	−0.460981
$216$	95.9454	6.52826
$217$	6.34348	0.430623
$218$	4.53766	0.307329
$219$	−3.52474	−0.238180
$220$	49.4014	3.33064
$221$	6.33418	0.426083
$222$	15.2236	1.02174
$223$	−12.5824	−0.842579	−0.421289	−	0.906926i	$-0.638422\pi$
$223$	−12.5824	−0.842579	−0.421289	+	0.906926i	$0.638422\pi$
$224$	−6.85397	−0.457950
$225$	19.3065	1.28710
$226$	24.4087	1.62365
$227$	8.74103	0.580163	0.290081	−	0.957002i	$-0.406318\pi$
$227$	8.74103	0.580163	0.290081	+	0.957002i	$0.406318\pi$
$228$	16.3828	1.08498
$229$	−24.3196	−1.60709	−0.803543	−	0.595247i	$-0.797054\pi$
$229$	−24.3196	−1.60709	−0.803543	+	0.595247i	$0.797054\pi$
$230$	7.01962	0.462860
$231$	−14.5339	−0.956263
$232$	1.70085	0.111666
$233$	6.03661	0.395471	0.197736	−	0.980255i	$-0.436641\pi$
$233$	6.03661	0.395471	0.197736	+	0.980255i	$0.436641\pi$
$234$	36.1317	2.36200
$235$	11.4502	0.746931
$236$	16.0293	1.04342
$237$	−16.4956	−1.07150
$238$	9.74982	0.631987
$239$	6.94244	0.449069	0.224535	−	0.974466i	$-0.427914\pi$
$239$	6.94244	0.449069	0.224535	+	0.974466i	$0.427914\pi$
$240$	−66.4422	−4.28883
$241$	4.11458	0.265043	0.132522	−	0.991180i	$-0.457693\pi$
$241$	4.11458	0.265043	0.132522	+	0.991180i	$0.457693\pi$
$242$	−12.2007	−0.784294
$243$	−38.6900	−2.48197
$244$	25.1495	1.61003
$245$	−15.7537	−1.00647
$246$	−53.4087	−3.40521
$247$	2.07922	0.132298
$248$	−36.3827	−2.31031
$249$	39.0363	2.47383
$250$	17.1991	1.08777
$251$	−10.2050	−0.644134	−0.322067	−	0.946717i	$-0.604378\pi$
$251$	−10.2050	−0.644134	−0.322067	+	0.946717i	$0.604378\pi$
$252$	38.5727	2.42985
$253$	−3.97187	−0.249709
$254$	18.5133	1.16163
$255$	30.2952	1.89716
$256$	−28.0195	−1.75122
$257$	13.2221	0.824771	0.412386	−	0.911009i	$-0.364696\pi$
$257$	13.2221	0.824771	0.412386	+	0.911009i	$0.364696\pi$
$258$	−20.4337	−1.27215
$259$	2.06263	0.128165
$260$	−23.2328	−1.44083
$261$	−1.99511	−0.123494
$262$	8.79887	0.543596
$263$	9.03473	0.557106	0.278553	−	0.960421i	$-0.410145\pi$
$263$	9.03473	0.557106	0.278553	+	0.960421i	$0.410145\pi$
$264$	83.3588	5.13038
$265$	21.1972	1.30213
$266$	3.20042	0.196230
$267$	13.5287	0.827944
$268$	15.0884	0.921669
$269$	13.3404	0.813381	0.406690	−	0.913566i	$-0.366683\pi$
$269$	13.3404	0.813381	0.406690	+	0.913566i	$0.366683\pi$
$270$	104.340	6.34995
$271$	17.5765	1.06770	0.533849	−	0.845580i	$-0.320745\pi$
$271$	17.5765	1.06770	0.533849	+	0.845580i	$0.320745\pi$
$272$	−25.2196	−1.52916
$273$	6.83510	0.413679
$274$	23.5817	1.42462
$275$	10.1277	0.610723
$276$	14.7179	0.885912
$277$	−21.3226	−1.28115	−0.640574	−	0.767896i	$-0.721304\pi$
$277$	−21.3226	−1.28115	−0.640574	+	0.767896i	$0.721304\pi$
$278$	−31.5442	−1.89190
$279$	42.6773	2.55502
$280$	−19.9606	−1.19287
$281$	−24.0470	−1.43453	−0.717263	−	0.696802i	$-0.754605\pi$
$281$	−24.0470	−1.43453	−0.717263	+	0.696802i	$0.754605\pi$
$282$	34.6147	2.06127
$283$	7.20451	0.428264	0.214132	−	0.976805i	$-0.431308\pi$
$283$	7.20451	0.428264	0.214132	+	0.976805i	$0.431308\pi$
$284$	−70.5491	−4.18632
$285$	9.94451	0.589062
$286$	18.9538	1.12076
$287$	−7.23628	−0.427144
$288$	−46.1118	−2.71716
$289$	−5.50079	−0.323576
$290$	1.84967	0.108616
$291$	41.5282	2.43443
$292$	4.90718	0.287171
$293$	−3.14292	−0.183611	−0.0918055	−	0.995777i	$-0.529264\pi$
$293$	−3.14292	−0.183611	−0.0918055	+	0.995777i	$0.529264\pi$
$294$	−47.6242	−2.77750
$295$	9.72992	0.566498
$296$	−11.8301	−0.687611
$297$	−59.0382	−3.42575
$298$	−3.38918	−0.196330
$299$	1.86791	0.108024
$300$	−37.5285	−2.16671
$301$	−2.76854	−0.159576
$302$	48.0547	2.76524
$303$	−62.8070	−3.60817
$304$	−8.27844	−0.474801
$305$	15.2659	0.874124
$306$	65.5943	3.74978
$307$	−27.6435	−1.57770	−0.788848	−	0.614588i	$-0.789322\pi$
$307$	−27.6435	−1.57770	−0.788848	+	0.614588i	$0.789322\pi$
$308$	20.2343	1.15296
$309$	30.9768	1.76221
$310$	−39.5661	−2.24720
$311$	31.1243	1.76490	0.882448	−	0.470409i	$-0.155894\pi$
$311$	31.1243	1.76490	0.882448	+	0.470409i	$0.155894\pi$
$312$	−39.2024	−2.21940
$313$	14.8966	0.842006	0.421003	−	0.907059i	$-0.361678\pi$
$313$	14.8966	0.842006	0.421003	+	0.907059i	$0.361678\pi$
$314$	0.602805	0.0340183
$315$	23.4140	1.31923
$316$	22.9653	1.29190
$317$	−5.45442	−0.306351	−0.153175	−	0.988199i	$-0.548950\pi$
$317$	−5.45442	−0.306351	−0.153175	+	0.988199i	$0.548950\pi$
$318$	64.0801	3.59344
$319$	−1.04659	−0.0585975
$320$	1.88027	0.105110
$321$	10.1407	0.565998
$322$	2.87516	0.160227
$323$	3.77466	0.210028
$324$	115.946	6.44147
$325$	−4.76291	−0.264199
$326$	−12.5558	−0.695404
$327$	5.77507	0.319362
$328$	41.5033	2.29164
$329$	4.68990	0.258562
$330$	90.6524	4.99025
$331$	−8.72795	−0.479731	−0.239866	−	0.970806i	$-0.577103\pi$
$331$	−8.72795	−0.479731	−0.239866	+	0.970806i	$0.577103\pi$
$332$	−54.3467	−2.98267
$333$	13.8768	0.760445
$334$	−26.0870	−1.42742
$335$	9.15877	0.500397
$336$	−27.2140	−1.48465
$337$	29.6372	1.61444	0.807220	−	0.590250i	$-0.200971\pi$
$337$	29.6372	1.61444	0.807220	+	0.590250i	$0.200971\pi$
$338$	24.2978	1.32162
$339$	31.0650	1.68722
$340$	−42.1772	−2.28738
$341$	22.3874	1.21235
$342$	21.5316	1.16429
$343$	−14.3305	−0.773777
$344$	15.8788	0.856129
$345$	8.93387	0.480983
$346$	17.5407	0.942992
$347$	−12.7536	−0.684651	−0.342326	−	0.939581i	$-0.611215\pi$
$347$	−12.7536	−0.684651	−0.342326	+	0.939581i	$0.611215\pi$
$348$	3.87815	0.207891
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−7.33125	−0.391872
$351$	27.7648	1.48198
$352$	−24.1891	−1.28928
$353$	1.14559	0.0609735	0.0304868	−	0.999535i	$-0.490294\pi$
$353$	1.14559	0.0609735	0.0304868	+	0.999535i	$0.490294\pi$
$354$	29.4140	1.56334
$355$	−42.8238	−2.27285
$356$	−18.8348	−0.998243
$357$	12.4086	0.656732
$358$	−9.13536	−0.482819
$359$	19.6744	1.03837	0.519186	−	0.854661i	$-0.326235\pi$
$359$	19.6744	1.03837	0.519186	+	0.854661i	$0.326235\pi$
$360$	−134.290	−7.07769
$361$	−17.7610	−0.934787
$362$	60.3313	3.17094
$363$	−15.5279	−0.815003
$364$	−9.51589	−0.498768
$365$	2.97870	0.155912
$366$	46.1497	2.41228
$367$	6.61254	0.345172	0.172586	−	0.984994i	$-0.444788\pi$
$367$	6.61254	0.345172	0.172586	+	0.984994i	$0.444788\pi$
$368$	−7.43711	−0.387686
$369$	−48.6838	−2.53438
$370$	−12.8652	−0.668830
$371$	8.68214	0.450754
$372$	−82.9573	−4.30113
$373$	−4.02805	−0.208565	−0.104282	−	0.994548i	$-0.533255\pi$
$373$	−4.02805	−0.208565	−0.104282	+	0.994548i	$0.533255\pi$
$374$	34.4091	1.77925
$375$	21.8893	1.13036
$376$	−26.8987	−1.38719
$377$	0.492194	0.0253493
$378$	42.7367	2.19814
$379$	−28.1198	−1.44442	−0.722209	−	0.691675i	$-0.756873\pi$
$379$	−28.1198	−1.44442	−0.722209	+	0.691675i	$0.756873\pi$
$380$	−13.8448	−0.710226
$381$	23.5618	1.20711
$382$	−9.58463	−0.490392
$383$	5.91714	0.302351	0.151176	−	0.988507i	$-0.451694\pi$
$383$	5.91714	0.302351	0.151176	+	0.988507i	$0.451694\pi$
$384$	−33.9185	−1.73090
$385$	12.2824	0.625968
$386$	49.0899	2.49861
$387$	−18.6260	−0.946814
$388$	−57.8159	−2.93516
$389$	−27.7457	−1.40676	−0.703382	−	0.710812i	$-0.748328\pi$
$389$	−27.7457	−1.40676	−0.703382	+	0.710812i	$0.748328\pi$
$390$	−42.6325	−2.15878
$391$	3.39105	0.171493
$392$	37.0083	1.86920
$393$	11.1983	0.564880
$394$	38.0203	1.91544
$395$	13.9401	0.701405
$396$	136.131	6.84085
$397$	17.5443	0.880524	0.440262	−	0.897869i	$-0.354886\pi$
$397$	17.5443	0.880524	0.440262	+	0.897869i	$0.354886\pi$
$398$	−5.72393	−0.286915
$399$	4.07317	0.203913
$400$	18.9636	0.948178
$401$	4.70581	0.234997	0.117498	−	0.993073i	$-0.462513\pi$
$401$	4.70581	0.234997	0.117498	+	0.993073i	$0.462513\pi$
$402$	27.6874	1.38092
$403$	−10.5285	−0.524461
$404$	87.4405	4.35033
$405$	70.3804	3.49723
$406$	0.757604	0.0375992
$407$	7.27944	0.360828
$408$	−71.1689	−3.52339
$409$	4.33594	0.214398	0.107199	−	0.994238i	$-0.465812\pi$
$409$	4.33594	0.214398	0.107199	+	0.994238i	$0.465812\pi$
$410$	45.1347	2.22905
$411$	30.0125	1.48041
$412$	−43.1263	−2.12468
$413$	3.98527	0.196102
$414$	19.3434	0.950674
$415$	−32.9889	−1.61936
$416$	11.3758	0.557743
$417$	−40.1463	−1.96597
$418$	11.2949	0.552453
$419$	14.9666	0.731166	0.365583	−	0.930779i	$-0.380870\pi$
$419$	14.9666	0.731166	0.365583	+	0.930779i	$0.380870\pi$
$420$	−45.5127	−2.22079
$421$	−26.8671	−1.30942	−0.654711	−	0.755879i	$-0.727210\pi$
$421$	−26.8671	−1.30942	−0.654711	+	0.755879i	$0.727210\pi$
$422$	−58.8596	−2.86524
$423$	31.5524	1.53413
$424$	−49.7960	−2.41831
$425$	−8.64668	−0.419426
$426$	−129.459	−6.27229
$427$	6.25276	0.302592
$428$	−14.1180	−0.682417
$429$	24.1225	1.16464
$430$	17.2682	0.832745
$431$	2.06569	0.0995007	0.0497503	−	0.998762i	$-0.484157\pi$
$431$	2.06569	0.0995007	0.0497503	+	0.998762i	$0.484157\pi$
$432$	−110.546	−5.31864
$433$	28.1563	1.35311	0.676553	−	0.736394i	$-0.263473\pi$
$433$	28.1563	1.35311	0.676553	+	0.736394i	$0.263473\pi$
$434$	−16.2058	−0.777906
$435$	2.35407	0.112869
$436$	−8.04011	−0.385051
$437$	1.11313	0.0532480
$438$	9.00475	0.430264
$439$	4.91691	0.234671	0.117336	−	0.993092i	$-0.462565\pi$
$439$	4.91691	0.234671	0.117336	+	0.993092i	$0.462565\pi$
$440$	−70.4450	−3.35833
$441$	−43.4111	−2.06719
$442$	−16.1821	−0.769704
$443$	−24.9945	−1.18753	−0.593763	−	0.804640i	$-0.702358\pi$
$443$	−24.9945	−1.18753	−0.593763	+	0.804640i	$0.702358\pi$
$444$	−26.9742	−1.28014
$445$	−11.4329	−0.541970
$446$	32.1446	1.52209
$447$	−4.31341	−0.204017
$448$	0.770140	0.0363857
$449$	−32.6254	−1.53969	−0.769844	−	0.638233i	$-0.779666\pi$
$449$	−32.6254	−1.53969	−0.769844	+	0.638233i	$0.779666\pi$
$450$	−49.3228	−2.32510
$451$	−25.5383	−1.20255
$452$	−43.2490	−2.03426
$453$	61.1592	2.87351
$454$	−22.3310	−1.04804
$455$	−5.77622	−0.270794
$456$	−23.3615	−1.09400
$457$	−17.0026	−0.795350	−0.397675	−	0.917526i	$-0.630183\pi$
$457$	−17.0026	−0.795350	−0.397675	+	0.917526i	$0.630183\pi$
$458$	62.1300	2.90314
$459$	50.4048	2.35270
$460$	−12.4378	−0.579916
$461$	34.7785	1.61980	0.809898	−	0.586571i	$-0.199522\pi$
$461$	34.7785	1.61980	0.809898	+	0.586571i	$0.199522\pi$
$462$	37.1303	1.72746
$463$	−10.5327	−0.489495	−0.244748	−	0.969587i	$-0.578705\pi$
$463$	−10.5327	−0.489495	−0.244748	+	0.969587i	$0.578705\pi$
$464$	−1.95967	−0.0909756
$465$	−50.3557	−2.33519
$466$	−15.4219	−0.714405
$467$	5.98144	0.276788	0.138394	−	0.990377i	$-0.455806\pi$
$467$	5.98144	0.276788	0.138394	+	0.990377i	$0.455806\pi$
$468$	−64.0205	−2.95935
$469$	3.75133	0.173220
$470$	−29.2522	−1.34931
$471$	0.767190	0.0353502
$472$	−22.8573	−1.05209
$473$	−9.77074	−0.449259
$474$	42.1418	1.93564
$475$	−2.83831	−0.130231
$476$	−17.2754	−0.791815
$477$	58.4112	2.67447
$478$	−17.7360	−0.811227
$479$	38.1603	1.74359	0.871795	−	0.489870i	$-0.162956\pi$
$479$	38.1603	1.74359	0.871795	+	0.489870i	$0.162956\pi$
$480$	54.4081	2.48338
$481$	−3.42341	−0.156094
$482$	−10.5116	−0.478791
$483$	3.65922	0.166500
$484$	21.6181	0.982639
$485$	−35.0947	−1.59357
$486$	98.8425	4.48359
$487$	−17.6180	−0.798347	−0.399173	−	0.916875i	$-0.630703\pi$
$487$	−17.6180	−0.798347	−0.399173	+	0.916875i	$0.630703\pi$
$488$	−35.8624	−1.62342
$489$	−15.9798	−0.722632
$490$	40.2464	1.81815
$491$	24.5509	1.10797	0.553983	−	0.832528i	$-0.313107\pi$
$491$	24.5509	1.10797	0.553983	+	0.832528i	$0.313107\pi$
$492$	94.6329	4.26638
$493$	0.893539	0.0402430
$494$	−5.31184	−0.238991
$495$	82.6327	3.71406
$496$	41.9193	1.88223
$497$	−17.5402	−0.786785
$498$	−99.7272	−4.46888
$499$	−8.29866	−0.371499	−0.185750	−	0.982597i	$-0.559471\pi$
$499$	−8.29866	−0.371499	−0.185750	+	0.982597i	$0.559471\pi$
$500$	−30.4744	−1.36286
$501$	−33.2009	−1.48331
$502$	26.0710	1.16361
$503$	−4.26330	−0.190091	−0.0950457	−	0.995473i	$-0.530300\pi$
$503$	−4.26330	−0.190091	−0.0950457	+	0.995473i	$0.530300\pi$
$504$	−55.0037	−2.45006
$505$	53.0771	2.36190
$506$	10.1470	0.451091
$507$	30.9237	1.37337
$508$	−32.8030	−1.45540
$509$	17.3393	0.768550	0.384275	−	0.923219i	$-0.374452\pi$
$509$	17.3393	0.768550	0.384275	+	0.923219i	$0.374452\pi$
$510$	−77.3959	−3.42715
$511$	1.22004	0.0539715
$512$	50.7181	2.24145
$513$	16.5456	0.730506
$514$	−33.7788	−1.48992
$515$	−26.1780	−1.15354
$516$	36.2058	1.59387
$517$	16.5516	0.727939
$518$	−5.26945	−0.231526
$519$	22.3240	0.979915
$520$	33.1293	1.45281
$521$	−41.4685	−1.81677	−0.908383	−	0.418139i	$-0.862682\pi$
$521$	−41.4685	−1.81677	−0.908383	+	0.418139i	$0.862682\pi$
$522$	5.09696	0.223088
$523$	−26.9951	−1.18041	−0.590207	−	0.807252i	$-0.700954\pi$
$523$	−26.9951	−1.18041	−0.590207	+	0.807252i	$0.700954\pi$
$524$	−15.5904	−0.681070
$525$	−9.33048	−0.407216
$526$	−23.0813	−1.00639
$527$	−19.1136	−0.832603
$528$	−96.0439	−4.17977
$529$	1.00000	0.0434783
$530$	−54.1530	−2.35226
$531$	26.8119	1.16354
$532$	−5.67070	−0.245856
$533$	12.0103	0.520224
$534$	−34.5622	−1.49565
$535$	−8.56971	−0.370501
$536$	−21.5156	−0.929333
$537$	−11.6266	−0.501723
$538$	−34.0812	−1.46934
$539$	−22.7724	−0.980875
$540$	−184.877	−7.95583
$541$	−26.4716	−1.13810	−0.569052	−	0.822302i	$-0.692690\pi$
$541$	−26.4716	−1.13810	−0.569052	+	0.822302i	$0.692690\pi$
$542$	−44.9032	−1.92876
$543$	76.7836	3.29510
$544$	20.6518	0.885439
$545$	−4.88041	−0.209054
$546$	−17.4618	−0.747297
$547$	−10.6426	−0.455043	−0.227522	−	0.973773i	$-0.573062\pi$
$547$	−10.6426	−0.455043	−0.227522	+	0.973773i	$0.573062\pi$
$548$	−41.7836	−1.78491
$549$	42.0670	1.79537
$550$	−25.8735	−1.10325
$551$	0.293308	0.0124953
$552$	−20.9873	−0.893278
$553$	5.70974	0.242803
$554$	54.4733	2.31435
$555$	−16.3735	−0.695018
$556$	55.8921	2.37035
$557$	5.49025	0.232630	0.116315	−	0.993212i	$-0.462892\pi$
$557$	5.49025	0.232630	0.116315	+	0.993212i	$0.462892\pi$
$558$	−109.029	−4.61556
$559$	4.59504	0.194349
$560$	22.9981	0.971847
$561$	43.7925	1.84892
$562$	61.4336	2.59142
$563$	−5.11674	−0.215645	−0.107822	−	0.994170i	$-0.534388\pi$
$563$	−5.11674	−0.215645	−0.107822	+	0.994170i	$0.534388\pi$
$564$	−61.3325	−2.58256
$565$	−26.2525	−1.10445
$566$	−18.4056	−0.773643
$567$	28.8271	1.21062
$568$	100.601	4.22112
$569$	5.28458	0.221541	0.110771	−	0.993846i	$-0.464668\pi$
$569$	5.28458	0.221541	0.110771	+	0.993846i	$0.464668\pi$
$570$	−25.4055	−1.06412
$571$	9.57799	0.400826	0.200413	−	0.979711i	$-0.435772\pi$
$571$	9.57799	0.400826	0.200413	+	0.979711i	$0.435772\pi$
$572$	−33.5835	−1.40420
$573$	−12.1983	−0.509593
$574$	18.4867	0.771620
$575$	−2.54986	−0.106336
$576$	5.18130	0.215888
$577$	6.10723	0.254247	0.127124	−	0.991887i	$-0.459426\pi$
$577$	6.10723	0.254247	0.127124	+	0.991887i	$0.459426\pi$
$578$	14.0530	0.584529
$579$	62.4767	2.59644
$580$	−3.27736	−0.136085
$581$	−13.5119	−0.560568
$582$	−106.093	−4.39770
$583$	30.6411	1.26902
$584$	−6.99750	−0.289559
$585$	−38.8610	−1.60670
$586$	8.02929	0.331687
$587$	30.8842	1.27473	0.637363	−	0.770563i	$-0.280025\pi$
$587$	30.8842	1.27473	0.637363	+	0.770563i	$0.280025\pi$
$588$	84.3836	3.47992
$589$	−6.27413	−0.258521
$590$	−24.8573	−1.02336
$591$	48.3885	1.99044
$592$	13.6304	0.560204
$593$	−26.3244	−1.08101	−0.540507	−	0.841340i	$-0.681767\pi$
$593$	−26.3244	−1.08101	−0.540507	+	0.841340i	$0.681767\pi$
$594$	150.827	6.18849
$595$	−10.4863	−0.429896
$596$	6.00517	0.245981
$597$	−7.28484	−0.298149
$598$	−4.77201	−0.195142
$599$	27.1238	1.10825	0.554125	−	0.832434i	$-0.313053\pi$
$599$	27.1238	1.10825	0.554125	+	0.832434i	$0.313053\pi$
$600$	53.5146	2.18472
$601$	−32.0002	−1.30532	−0.652658	−	0.757653i	$-0.726346\pi$
$601$	−32.0002	−1.30532	−0.652658	+	0.757653i	$0.726346\pi$
$602$	7.07286	0.288268
$603$	25.2380	1.02777
$604$	−85.1464	−3.46456
$605$	13.1223	0.533499
$606$	160.455	6.51803
$607$	20.3709	0.826830	0.413415	−	0.910543i	$-0.364336\pi$
$607$	20.3709	0.826830	0.413415	+	0.910543i	$0.364336\pi$
$608$	6.77904	0.274926
$609$	0.964202	0.0390714
$610$	−39.0003	−1.57907
$611$	−7.78398	−0.314906
$612$	−116.224	−4.69808
$613$	−18.4519	−0.745263	−0.372632	−	0.927979i	$-0.621545\pi$
$613$	−18.4519	−0.745263	−0.372632	+	0.927979i	$0.621545\pi$
$614$	70.6215	2.85005
$615$	57.4429	2.31632
$616$	−28.8535	−1.16254
$617$	−27.7152	−1.11577	−0.557886	−	0.829918i	$-0.688387\pi$
$617$	−27.7152	−1.11577	−0.557886	+	0.829918i	$0.688387\pi$
$618$	−79.1374	−3.18337
$619$	−18.8391	−0.757206	−0.378603	−	0.925559i	$-0.623595\pi$
$619$	−18.8391	−0.757206	−0.378603	+	0.925559i	$0.623595\pi$
$620$	70.1057	2.81551
$621$	14.8641	0.596475
$622$	−79.5141	−3.18822
$623$	−4.68279	−0.187612
$624$	45.1680	1.80817
$625$	−31.2475	−1.24990
$626$	−38.0568	−1.52105
$627$	14.3750	0.574084
$628$	−1.06809	−0.0426214
$629$	−6.21494	−0.247806
$630$	−59.8163	−2.38314
$631$	−8.03753	−0.319969	−0.159985	−	0.987120i	$-0.551144\pi$
$631$	−8.03753	−0.319969	−0.159985	+	0.987120i	$0.551144\pi$
$632$	−32.7479	−1.30264
$633$	−74.9105	−2.97743
$634$	13.9346	0.553412
$635$	−19.9117	−0.790171
$636$	−113.541	−4.50221
$637$	10.7095	0.424326
$638$	2.67374	0.105854
$639$	−118.006	−4.66824
$640$	28.6639	1.13304
$641$	−35.2717	−1.39315	−0.696574	−	0.717485i	$-0.745293\pi$
$641$	−35.2717	−1.39315	−0.696574	+	0.717485i	$0.745293\pi$
$642$	−25.9067	−1.02245
$643$	−33.6186	−1.32579	−0.662895	−	0.748713i	$-0.730672\pi$
$643$	−33.6186	−1.32579	−0.662895	+	0.748713i	$0.730672\pi$
$644$	−5.09440	−0.200747
$645$	21.9772	0.865351
$646$	−9.64323	−0.379408
$647$	−8.19642	−0.322234	−0.161117	−	0.986935i	$-0.551510\pi$
$647$	−8.19642	−0.322234	−0.161117	+	0.986935i	$0.551510\pi$
$648$	−165.336	−6.49503
$649$	14.0648	0.552093
$650$	12.1679	0.477265
$651$	−20.6252	−0.808364
$652$	22.2472	0.871269
$653$	46.7312	1.82873	0.914366	−	0.404888i	$-0.132690\pi$
$653$	46.7312	1.82873	0.914366	+	0.404888i	$0.132690\pi$
$654$	−14.7537	−0.576917
$655$	−9.46349	−0.369769
$656$	−47.8191	−1.86702
$657$	8.20813	0.320230
$658$	−11.9814	−0.467084
$659$	−26.7621	−1.04250	−0.521251	−	0.853403i	$-0.674534\pi$
$659$	−26.7621	−1.04250	−0.521251	+	0.853403i	$0.674534\pi$
$660$	−160.624	−6.25227
$661$	−24.2491	−0.943180	−0.471590	−	0.881818i	$-0.656320\pi$
$661$	−24.2491	−0.943180	−0.471590	+	0.881818i	$0.656320\pi$
$662$	22.2975	0.866618
$663$	−20.5950	−0.799842
$664$	77.4969	3.00746
$665$	−3.44216	−0.133481
$666$	−35.4515	−1.37372
$667$	0.263499	0.0102027
$668$	46.2226	1.78841
$669$	40.9104	1.58169
$670$	−23.3981	−0.903949
$671$	22.0673	0.851898
$672$	22.2850	0.859662
$673$	43.1226	1.66225	0.831126	−	0.556084i	$-0.187697\pi$
$673$	43.1226	1.66225	0.831126	+	0.556084i	$0.187697\pi$
$674$	−75.7149	−2.91643
$675$	−37.9013	−1.45882
$676$	−43.0523	−1.65586
$677$	28.2556	1.08595	0.542976	−	0.839748i	$-0.317298\pi$
$677$	28.2556	1.08595	0.542976	+	0.839748i	$0.317298\pi$
$678$	−79.3626	−3.04790
$679$	−14.3744	−0.551640
$680$	60.1436	2.30640
$681$	−28.4206	−1.08908
$682$	−57.1938	−2.19006
$683$	47.1358	1.80360	0.901801	−	0.432152i	$-0.142246\pi$
$683$	47.1358	1.80360	0.901801	+	0.432152i	$0.142246\pi$
$684$	−38.1510	−1.45874
$685$	−25.3630	−0.969071
$686$	36.6106	1.39780
$687$	79.0728	3.01681
$688$	−18.2952	−0.697498
$689$	−14.4100	−0.548979
$690$	−22.8236	−0.868880
$691$	16.9390	0.644390	0.322195	−	0.946673i	$-0.395579\pi$
$691$	16.9390	0.644390	0.322195	+	0.946673i	$0.395579\pi$
$692$	−31.0797	−1.18147
$693$	33.8455	1.28568
$694$	32.5821	1.23680
$695$	33.9269	1.28692
$696$	−5.53014	−0.209619
$697$	21.8037	0.825876
$698$	2.55473	0.0966978
$699$	−19.6274	−0.742377
$700$	12.9900	0.490975
$701$	15.1203	0.571084	0.285542	−	0.958366i	$-0.407826\pi$
$701$	15.1203	0.571084	0.285542	+	0.958366i	$0.407826\pi$
$702$	−70.9315	−2.67714
$703$	−2.04008	−0.0769430
$704$	2.71798	0.102438
$705$	−37.2293	−1.40214
$706$	−2.92667	−0.110147
$707$	21.7398	0.817610
$708$	−52.1177	−1.95870
$709$	−10.9457	−0.411075	−0.205537	−	0.978649i	$-0.565894\pi$
$709$	−10.9457	−0.411075	−0.205537	+	0.978649i	$0.565894\pi$
$710$	109.403	4.10583
$711$	38.4136	1.44062
$712$	26.8579	1.00654
$713$	−5.63650	−0.211088
$714$	−31.7006	−1.18636
$715$	−20.3855	−0.762374
$716$	16.1866	0.604922
$717$	−22.5726	−0.842991
$718$	−50.2626	−1.87578
$719$	1.94659	0.0725956	0.0362978	−	0.999341i	$-0.488444\pi$
$719$	1.94659	0.0725956	0.0362978	+	0.999341i	$0.488444\pi$
$720$	154.725	5.76627
$721$	−10.7222	−0.399317
$722$	45.3744	1.68866
$723$	−13.3781	−0.497538
$724$	−106.899	−3.97286
$725$	−0.671885	−0.0249532
$726$	39.6695	1.47227
$727$	−16.2894	−0.604142	−0.302071	−	0.953285i	$-0.597678\pi$
$727$	−16.2894	−0.604142	−0.302071	+	0.953285i	$0.597678\pi$
$728$	13.5694	0.502915
$729$	48.9539	1.81311
$730$	−7.60976	−0.281650
$731$	8.34193	0.308537
$732$	−81.7709	−3.02234
$733$	21.9613	0.811158	0.405579	−	0.914060i	$-0.367070\pi$
$733$	21.9613	0.811158	0.405579	+	0.914060i	$0.367070\pi$
$734$	−16.8932	−0.623541
$735$	51.2215	1.88933
$736$	6.09010	0.224484
$737$	13.2392	0.487673
$738$	124.374	4.57826
$739$	18.8091	0.691904	0.345952	−	0.938252i	$-0.387556\pi$
$739$	18.8091	0.691904	0.345952	+	0.938252i	$0.387556\pi$
$740$	22.7954	0.837975
$741$	−6.76038	−0.248349
$742$	−22.1805	−0.814271
$743$	38.2942	1.40488	0.702438	−	0.711745i	$-0.252095\pi$
$743$	38.2942	1.40488	0.702438	+	0.711745i	$0.252095\pi$
$744$	118.295	4.33690
$745$	3.64518	0.133549
$746$	10.2906	0.376765
$747$	−90.9047	−3.32603
$748$	−60.9683	−2.22922
$749$	−3.51006	−0.128255
$750$	−55.9211	−2.04195
$751$	−1.47761	−0.0539188	−0.0269594	−	0.999637i	$-0.508582\pi$
$751$	−1.47761	−0.0539188	−0.0269594	+	0.999637i	$0.508582\pi$
$752$	30.9920	1.13016
$753$	33.1806	1.20917
$754$	−1.25742	−0.0457926
$755$	−51.6845	−1.88099
$756$	−75.7236	−2.75404
$757$	3.36308	0.122233	0.0611167	−	0.998131i	$-0.480534\pi$
$757$	3.36308	0.122233	0.0611167	+	0.998131i	$0.480534\pi$
$758$	71.8385	2.60929
$759$	12.9141	0.468753
$760$	19.7424	0.716131
$761$	−7.00746	−0.254020	−0.127010	−	0.991901i	$-0.540538\pi$
$761$	−7.00746	−0.254020	−0.127010	+	0.991901i	$0.540538\pi$
$762$	−60.1940	−2.18060
$763$	−1.99897	−0.0723674
$764$	16.9827	0.614411
$765$	−70.5490	−2.55070
$766$	−15.1167	−0.546187
$767$	−6.61449	−0.238835
$768$	91.1024	3.28738
$769$	17.8701	0.644413	0.322207	−	0.946669i	$-0.395575\pi$
$769$	17.8701	0.644413	0.322207	+	0.946669i	$0.395575\pi$
$770$	−31.3781	−1.13079
$771$	−42.9903	−1.54826
$772$	−86.9807	−3.13050
$773$	−47.5197	−1.70916	−0.854582	−	0.519317i	$-0.826186\pi$
$773$	−47.5197	−1.70916	−0.854582	+	0.519317i	$0.826186\pi$
$774$	47.5844	1.71039
$775$	14.3723	0.516267
$776$	82.4439	2.95956
$777$	−6.70642	−0.240592
$778$	70.8827	2.54127
$779$	7.15716	0.256432
$780$	75.5390	2.70473
$781$	−61.9030	−2.21506
$782$	−8.66320	−0.309795
$783$	3.91668	0.139971
$784$	−42.6400	−1.52286
$785$	−0.648338	−0.0231402
$786$	−28.6086	−1.02044
$787$	−30.2552	−1.07848	−0.539241	−	0.842152i	$-0.681289\pi$
$787$	−30.2552	−1.07848	−0.539241	+	0.842152i	$0.681289\pi$
$788$	−67.3669	−2.39985
$789$	−29.3755	−1.04580
$790$	−35.6133	−1.26706
$791$	−10.7527	−0.382323
$792$	−194.119	−6.89773
$793$	−10.3779	−0.368531
$794$	−44.8209	−1.59064
$795$	−68.9205	−2.44436
$796$	10.1420	0.359475
$797$	42.6684	1.51139	0.755696	−	0.654922i	$-0.227299\pi$
$797$	42.6684	1.51139	0.755696	+	0.654922i	$0.227299\pi$
$798$	−10.4058	−0.368362
$799$	−14.1312	−0.499926
$800$	−15.5289	−0.549028
$801$	−31.5046	−1.11316
$802$	−12.0220	−0.424513
$803$	4.30578	0.151948
$804$	−49.0583	−1.73015
$805$	−3.09234	−0.108991
$806$	26.8974	0.947421
$807$	−43.3751	−1.52688
$808$	−124.688	−4.38650
$809$	4.47666	0.157391	0.0786956	−	0.996899i	$-0.474924\pi$
$809$	4.47666	0.157391	0.0786956	+	0.996899i	$0.474924\pi$
$810$	−179.803	−6.31762
$811$	12.7345	0.447169	0.223585	−	0.974685i	$-0.428224\pi$
$811$	12.7345	0.447169	0.223585	+	0.974685i	$0.428224\pi$
$812$	−1.34237	−0.0471080
$813$	−57.1483	−2.00428
$814$	−18.5970	−0.651823
$815$	13.5043	0.473033
$816$	81.9990	2.87054
$817$	2.73827	0.0958000
$818$	−11.0771	−0.387303
$819$	−15.9170	−0.556186
$820$	−79.9726	−2.79277
$821$	−13.2778	−0.463398	−0.231699	−	0.972788i	$-0.574428\pi$
$821$	−13.2778	−0.463398	−0.231699	+	0.972788i	$0.574428\pi$
$822$	−76.6736	−2.67430
$823$	12.3267	0.429682	0.214841	−	0.976649i	$-0.431077\pi$
$823$	12.3267	0.429682	0.214841	+	0.976649i	$0.431077\pi$
$824$	61.4968	2.14234
$825$	−32.9292	−1.14645
$826$	−10.1813	−0.354252
$827$	16.6945	0.580524	0.290262	−	0.956947i	$-0.406258\pi$
$827$	16.6945	0.580524	0.290262	+	0.956947i	$0.406258\pi$
$828$	−34.2738	−1.19110
$829$	−29.9811	−1.04129	−0.520643	−	0.853775i	$-0.674308\pi$
$829$	−29.9811	−1.04129	−0.520643	+	0.853775i	$0.674308\pi$
$830$	84.2777	2.92532
$831$	69.3282	2.40497
$832$	−1.27823	−0.0443146
$833$	19.4423	0.673635
$834$	102.563	3.55146
$835$	28.0575	0.970970
$836$	−20.0131	−0.692167
$837$	−83.7814	−2.89591
$838$	−38.2355	−1.32082
$839$	−25.6447	−0.885352	−0.442676	−	0.896682i	$-0.645971\pi$
$839$	−25.6447	−0.885352	−0.442676	+	0.896682i	$0.645971\pi$
$840$	64.8998	2.23926
$841$	−28.9306	−0.997606
$842$	68.6381	2.36542
$843$	78.1865	2.69289
$844$	104.291	3.58985
$845$	−26.1331	−0.899006
$846$	−80.6078	−2.77135
$847$	5.37477	0.184679
$848$	57.3737	1.97022
$849$	−23.4247	−0.803935
$850$	22.0899	0.757678
$851$	−1.83275	−0.0628258
$852$	229.383	7.85854
$853$	37.9498	1.29938	0.649689	−	0.760200i	$-0.274899\pi$
$853$	37.9498	1.29938	0.649689	+	0.760200i	$0.274899\pi$
$854$	−15.9741	−0.546622
$855$	−23.1580	−0.791986
$856$	20.1318	0.688091
$857$	−4.62155	−0.157869	−0.0789345	−	0.996880i	$-0.525152\pi$
$857$	−4.62155	−0.157869	−0.0789345	+	0.996880i	$0.525152\pi$
$858$	−61.6263	−2.10389
$859$	5.78867	0.197507	0.0987534	−	0.995112i	$-0.468515\pi$
$859$	5.78867	0.197507	0.0987534	+	0.995112i	$0.468515\pi$
$860$	−30.5969	−1.04334
$861$	23.5280	0.801833
$862$	−5.27727	−0.179744
$863$	−6.91353	−0.235339	−0.117670	−	0.993053i	$-0.537542\pi$
$863$	−6.91353	−0.235339	−0.117670	+	0.993053i	$0.537542\pi$
$864$	90.5237	3.07968
$865$	−18.8656	−0.641450
$866$	−71.9316	−2.44434
$867$	17.8853	0.607416
$868$	28.7146	0.974636
$869$	20.1508	0.683570
$870$	−6.01400	−0.203894
$871$	−6.22622	−0.210967
$872$	11.4650	0.388253
$873$	−96.7075	−3.27305
$874$	−2.84373	−0.0961906
$875$	−7.57668	−0.256139
$876$	−15.9552	−0.539076
$877$	−40.2168	−1.35802	−0.679012	−	0.734128i	$-0.737591\pi$
$877$	−40.2168	−1.35802	−0.679012	+	0.734128i	$0.737591\pi$
$878$	−12.5613	−0.423925
$879$	10.2189	0.344674
$880$	81.1650	2.73607
$881$	−34.3023	−1.15568	−0.577838	−	0.816152i	$-0.696103\pi$
$881$	−34.3023	−1.15568	−0.577838	+	0.816152i	$0.696103\pi$
$882$	110.903	3.73431
$883$	−1.61844	−0.0544648	−0.0272324	−	0.999629i	$-0.508669\pi$
$883$	−1.61844	−0.0544648	−0.0272324	+	0.999629i	$0.508669\pi$
$884$	28.6725	0.964360
$885$	−31.6359	−1.06343
$886$	63.8542	2.14522
$887$	23.7648	0.797944	0.398972	−	0.916963i	$-0.369367\pi$
$887$	23.7648	0.797944	0.398972	+	0.916963i	$0.369367\pi$
$888$	38.4644	1.29078
$889$	−8.15561	−0.273530
$890$	29.2079	0.979050
$891$	101.737	3.40831
$892$	−56.9558	−1.90702
$893$	−4.63863	−0.155226
$894$	11.0196	0.368550
$895$	9.82541	0.328427
$896$	11.7404	0.392221
$897$	−6.07333	−0.202783
$898$	83.3490	2.78139
$899$	−1.48521	−0.0495346
$900$	87.3933	2.91311
$901$	−26.1603	−0.871526
$902$	65.2434	2.17237
$903$	9.00163	0.299555
$904$	61.6718	2.05117
$905$	−64.8884	−2.15696
$906$	−156.245	−5.19089
$907$	−23.5734	−0.782743	−0.391371	−	0.920233i	$-0.627999\pi$
$907$	−23.5734	−0.782743	−0.391371	+	0.920233i	$0.627999\pi$
$908$	39.5674	1.31309
$909$	146.260	4.85114
$910$	14.7567	0.489179
$911$	42.2375	1.39939	0.699695	−	0.714441i	$-0.253319\pi$
$911$	42.2375	1.39939	0.699695	+	0.714441i	$0.253319\pi$
$912$	26.9165	0.891294
$913$	−47.6863	−1.57819
$914$	43.4371	1.43677
$915$	−49.6356	−1.64090
$916$	−110.086	−3.63734
$917$	−3.87615	−0.128002
$918$	−128.771	−4.25006
$919$	27.3077	0.900798	0.450399	−	0.892827i	$-0.351282\pi$
$919$	27.3077	0.900798	0.450399	+	0.892827i	$0.351282\pi$
$920$	17.7360	0.584738
$921$	89.8800	2.96165
$922$	−88.8495	−2.92610
$923$	29.1121	0.958235
$924$	−65.7898	−2.16432
$925$	4.67324	0.153655
$926$	26.9081	0.884256
$927$	−72.1364	−2.36927
$928$	1.60474	0.0526780
$929$	−5.14270	−0.168727	−0.0843633	−	0.996435i	$-0.526886\pi$
$929$	−5.14270	−0.168727	−0.0843633	+	0.996435i	$0.526886\pi$
$930$	128.645	4.21844
$931$	6.38200	0.209162
$932$	27.3255	0.895076
$933$	−101.197	−3.31306
$934$	−15.2809	−0.500008
$935$	−37.0082	−1.21030
$936$	91.2914	2.98395
$937$	55.8826	1.82560	0.912802	−	0.408402i	$-0.133914\pi$
$937$	55.8826	1.82560	0.912802	+	0.408402i	$0.133914\pi$
$938$	−9.58363	−0.312917
$939$	−48.4348	−1.58061
$940$	51.8310	1.69054
$941$	−36.7385	−1.19764	−0.598821	−	0.800883i	$-0.704364\pi$
$941$	−36.7385	−1.19764	−0.598821	+	0.800883i	$0.704364\pi$
$942$	−1.95996	−0.0638589
$943$	6.42979	0.209383
$944$	26.3357	0.857153
$945$	−45.9648	−1.49524
$946$	24.9616	0.811571
$947$	11.8158	0.383962	0.191981	−	0.981399i	$-0.438509\pi$
$947$	11.8158	0.383962	0.191981	+	0.981399i	$0.438509\pi$
$948$	−74.6695	−2.42515
$949$	−2.02495	−0.0657325
$950$	7.25110	0.235257
$951$	17.7345	0.575081
$952$	24.6342	0.798398
$953$	30.2943	0.981330	0.490665	−	0.871348i	$-0.336754\pi$
$953$	30.2943	0.981330	0.490665	+	0.871348i	$0.336754\pi$
$954$	−149.225	−4.83133
$955$	10.3086	0.333579
$956$	31.4258	1.01638
$957$	3.40287	0.109999
$958$	−97.4892	−3.14973
$959$	−10.3884	−0.335460
$960$	−6.11352	−0.197313
$961$	0.770094	0.0248418
$962$	8.74588	0.281979
$963$	−23.6148	−0.760977
$964$	18.6252	0.599876
$965$	−52.7980	−1.69963
$966$	−9.34830	−0.300777
$967$	42.0215	1.35132	0.675659	−	0.737214i	$-0.263859\pi$
$967$	42.0215	1.35132	0.675659	+	0.737214i	$0.263859\pi$
$968$	−30.8268	−0.990810
$969$	−12.2729	−0.394263
$970$	89.6575	2.87873
$971$	−21.7668	−0.698530	−0.349265	−	0.937024i	$-0.613569\pi$
$971$	−21.7668	−0.698530	−0.349265	+	0.937024i	$0.613569\pi$
$972$	−175.135	−5.61747
$973$	13.8961	0.445489
$974$	45.0091	1.44219
$975$	15.4861	0.495953
$976$	41.3198	1.32261
$977$	3.28279	0.105026	0.0525129	−	0.998620i	$-0.483277\pi$
$977$	3.28279	0.105026	0.0525129	+	0.998620i	$0.483277\pi$
$978$	40.8240	1.30541
$979$	−16.5265	−0.528190
$980$	−71.3111	−2.27795
$981$	−13.4485	−0.429378
$982$	−62.7208	−2.00150
$983$	5.27776	0.168334	0.0841672	−	0.996452i	$-0.473177\pi$
$983$	5.27776	0.168334	0.0841672	+	0.996452i	$0.473177\pi$
$984$	−134.944	−4.30186
$985$	−40.8922	−1.30293
$986$	−2.28275	−0.0726975
$987$	−15.2487	−0.485372
$988$	9.41186	0.299431
$989$	2.45999	0.0782230
$990$	−211.104	−6.70932
$991$	11.3525	0.360625	0.180312	−	0.983609i	$-0.442289\pi$
$991$	11.3525	0.360625	0.180312	+	0.983609i	$0.442289\pi$
$992$	−34.3268	−1.08988
$993$	28.3780	0.900550
$994$	44.8104	1.42130
$995$	6.15629	0.195168
$996$	176.703	5.59905
$997$	−24.6547	−0.780823	−0.390412	−	0.920640i	$-0.627667\pi$
$997$	−24.6547	−0.780823	−0.390412	+	0.920640i	$0.627667\pi$
$998$	21.2008	0.671100
$999$	−27.2421	−0.861903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.10	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.10	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55473 q^{2} -3.25140 q^{3} +4.52663 q^{4} +2.74770 q^{5} +8.30644 q^{6} +1.12543 q^{7} -6.45485 q^{8} +7.57160 q^{9} +O(q^{10})\)	\(q-2.55473 q^{2} -3.25140 q^{3} +4.52663 q^{4} +2.74770 q^{5} +8.30644 q^{6} +1.12543 q^{7} -6.45485 q^{8} +7.57160 q^{9} -7.01962 q^{10} +3.97187 q^{11} -14.7179 q^{12} -1.86791 q^{13} -2.87516 q^{14} -8.93387 q^{15} +7.43711 q^{16} -3.39105 q^{17} -19.3434 q^{18} -1.11313 q^{19} +12.4378 q^{20} -3.65922 q^{21} -10.1470 q^{22} -1.00000 q^{23} +20.9873 q^{24} +2.54986 q^{25} +4.77201 q^{26} -14.8641 q^{27} +5.09440 q^{28} -0.263499 q^{29} +22.8236 q^{30} +5.63650 q^{31} -6.09010 q^{32} -12.9141 q^{33} +8.66320 q^{34} +3.09234 q^{35} +34.2738 q^{36} +1.83275 q^{37} +2.84373 q^{38} +6.07333 q^{39} -17.7360 q^{40} -6.42979 q^{41} +9.34830 q^{42} -2.45999 q^{43} +17.9792 q^{44} +20.8045 q^{45} +2.55473 q^{46} +4.16721 q^{47} -24.1810 q^{48} -5.73341 q^{49} -6.51419 q^{50} +11.0257 q^{51} -8.45535 q^{52} +7.71451 q^{53} +37.9737 q^{54} +10.9135 q^{55} -7.26447 q^{56} +3.61921 q^{57} +0.673169 q^{58} +3.54111 q^{59} -40.4403 q^{60} +5.55589 q^{61} -14.3997 q^{62} +8.52129 q^{63} +0.684308 q^{64} -5.13246 q^{65} +32.9921 q^{66} +3.33325 q^{67} -15.3500 q^{68} +3.25140 q^{69} -7.90009 q^{70} -15.5853 q^{71} -48.8735 q^{72} +1.08407 q^{73} -4.68217 q^{74} -8.29060 q^{75} -5.03870 q^{76} +4.47006 q^{77} -15.5157 q^{78} +5.07339 q^{79} +20.4350 q^{80} +25.6143 q^{81} +16.4264 q^{82} -12.0060 q^{83} -16.5639 q^{84} -9.31758 q^{85} +6.28459 q^{86} +0.856742 q^{87} -25.6378 q^{88} -4.16089 q^{89} -53.1498 q^{90} -2.10220 q^{91} -4.52663 q^{92} -18.3265 q^{93} -10.6461 q^{94} -3.05853 q^{95} +19.8013 q^{96} -12.7724 q^{97} +14.6473 q^{98} +30.0734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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