LMFDB - Embedded newform 4031.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48847 q^{2} -3.00036 q^{3} +4.19251 q^{4} +0.297405 q^{5} +7.46633 q^{6} -2.60645 q^{7} -5.45599 q^{8} +6.00219 q^{9} +O(q^{10})$	\(q-2.48847 q^{2} -3.00036 q^{3} +4.19251 q^{4} +0.297405 q^{5} +7.46633 q^{6} -2.60645 q^{7} -5.45599 q^{8} +6.00219 q^{9} -0.740084 q^{10} +5.15470 q^{11} -12.5790 q^{12} -5.66007 q^{13} +6.48609 q^{14} -0.892322 q^{15} +5.19209 q^{16} -5.43937 q^{17} -14.9363 q^{18} -6.82150 q^{19} +1.24687 q^{20} +7.82030 q^{21} -12.8273 q^{22} -1.28089 q^{23} +16.3700 q^{24} -4.91155 q^{25} +14.0849 q^{26} -9.00765 q^{27} -10.9276 q^{28} +1.00000 q^{29} +2.22052 q^{30} -1.89186 q^{31} -2.00840 q^{32} -15.4660 q^{33} +13.5357 q^{34} -0.775170 q^{35} +25.1642 q^{36} -2.40701 q^{37} +16.9751 q^{38} +16.9823 q^{39} -1.62264 q^{40} -10.9922 q^{41} -19.4606 q^{42} +6.80983 q^{43} +21.6111 q^{44} +1.78508 q^{45} +3.18745 q^{46} -0.426011 q^{47} -15.5782 q^{48} -0.206415 q^{49} +12.2223 q^{50} +16.3201 q^{51} -23.7299 q^{52} +6.74224 q^{53} +22.4153 q^{54} +1.53303 q^{55} +14.2208 q^{56} +20.4670 q^{57} -2.48847 q^{58} -12.7719 q^{59} -3.74107 q^{60} +7.18371 q^{61} +4.70785 q^{62} -15.6444 q^{63} -5.38633 q^{64} -1.68333 q^{65} +38.4867 q^{66} -10.9304 q^{67} -22.8046 q^{68} +3.84313 q^{69} +1.92899 q^{70} -8.19888 q^{71} -32.7479 q^{72} +2.57362 q^{73} +5.98978 q^{74} +14.7364 q^{75} -28.5992 q^{76} -13.4355 q^{77} -42.2600 q^{78} +5.22582 q^{79} +1.54415 q^{80} +9.01967 q^{81} +27.3538 q^{82} -3.09234 q^{83} +32.7867 q^{84} -1.61769 q^{85} -16.9461 q^{86} -3.00036 q^{87} -28.1240 q^{88} -12.6475 q^{89} -4.44212 q^{90} +14.7527 q^{91} -5.37012 q^{92} +5.67628 q^{93} +1.06012 q^{94} -2.02875 q^{95} +6.02592 q^{96} +11.6912 q^{97} +0.513659 q^{98} +30.9395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * 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 $

$2$	−2.48847	−1.75962	−0.879809	−	0.475328i	$-0.842329\pi$
$2$	−2.48847	−1.75962	−0.879809	+	0.475328i	$0.842329\pi$
$3$	−3.00036	−1.73226	−0.866131	−	0.499818i	$-0.833400\pi$
$3$	−3.00036	−1.73226	−0.866131	+	0.499818i	$0.833400\pi$
$4$	4.19251	2.09625
$5$	0.297405	0.133003	0.0665017	−	0.997786i	$-0.478816\pi$
$5$	0.297405	0.133003	0.0665017	+	0.997786i	$0.478816\pi$
$6$	7.46633	3.04812
$7$	−2.60645	−0.985146	−0.492573	−	0.870271i	$-0.663943\pi$
$7$	−2.60645	−0.985146	−0.492573	+	0.870271i	$0.663943\pi$
$8$	−5.45599	−1.92899
$9$	6.00219	2.00073
$10$	−0.740084	−0.234035
$11$	5.15470	1.55420	0.777101	−	0.629376i	$-0.216690\pi$
$11$	5.15470	1.55420	0.777101	+	0.629376i	$0.216690\pi$
$12$	−12.5790	−3.63126
$13$	−5.66007	−1.56982	−0.784911	−	0.619609i	$-0.787291\pi$
$13$	−5.66007	−1.56982	−0.784911	+	0.619609i	$0.787291\pi$
$14$	6.48609	1.73348
$15$	−0.892322	−0.230397
$16$	5.19209	1.29802
$17$	−5.43937	−1.31924	−0.659621	−	0.751598i	$-0.729283\pi$
$17$	−5.43937	−1.31924	−0.659621	+	0.751598i	$0.729283\pi$
$18$	−14.9363	−3.52052
$19$	−6.82150	−1.56496	−0.782480	−	0.622675i	$-0.786046\pi$
$19$	−6.82150	−1.56496	−0.782480	+	0.622675i	$0.786046\pi$
$20$	1.24687	0.278809
$21$	7.82030	1.70653
$22$	−12.8273	−2.73480
$23$	−1.28089	−0.267083	−0.133542	−	0.991043i	$-0.542635\pi$
$23$	−1.28089	−0.267083	−0.133542	+	0.991043i	$0.542635\pi$
$24$	16.3700	3.34151
$25$	−4.91155	−0.982310
$26$	14.0849	2.76228
$27$	−9.00765	−1.73352
$28$	−10.9276	−2.06511
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.22052	0.405410
$31$	−1.89186	−0.339789	−0.169894	−	0.985462i	$-0.554343\pi$
$31$	−1.89186	−0.339789	−0.169894	+	0.985462i	$0.554343\pi$
$32$	−2.00840	−0.355038
$33$	−15.4660	−2.69228
$34$	13.5357	2.32136
$35$	−0.775170	−0.131028
$36$	25.1642	4.19403
$37$	−2.40701	−0.395710	−0.197855	−	0.980231i	$-0.563397\pi$
$37$	−2.40701	−0.395710	−0.197855	+	0.980231i	$0.563397\pi$
$38$	16.9751	2.75373
$39$	16.9823	2.71934
$40$	−1.62264	−0.256562
$41$	−10.9922	−1.71669	−0.858345	−	0.513073i	$-0.828507\pi$
$41$	−10.9922	−1.71669	−0.858345	+	0.513073i	$0.828507\pi$
$42$	−19.4606	−3.00284
$43$	6.80983	1.03849	0.519245	−	0.854626i	$-0.326213\pi$
$43$	6.80983	1.03849	0.519245	+	0.854626i	$0.326213\pi$
$44$	21.6111	3.25800
$45$	1.78508	0.266104
$46$	3.18745	0.469964
$47$	−0.426011	−0.0621401	−0.0310701	−	0.999517i	$-0.509891\pi$
$47$	−0.426011	−0.0621401	−0.0310701	+	0.999517i	$0.509891\pi$
$48$	−15.5782	−2.24851
$49$	−0.206415	−0.0294879
$50$	12.2223	1.72849
$51$	16.3201	2.28527
$52$	−23.7299	−3.29074
$53$	6.74224	0.926117	0.463059	−	0.886328i	$-0.346752\pi$
$53$	6.74224	0.926117	0.463059	+	0.886328i	$0.346752\pi$
$54$	22.4153	3.05034
$55$	1.53303	0.206714
$56$	14.2208	1.90033
$57$	20.4670	2.71092
$58$	−2.48847	−0.326753
$59$	−12.7719	−1.66276	−0.831378	−	0.555707i	$-0.812448\pi$
$59$	−12.7719	−1.66276	−0.831378	+	0.555707i	$0.812448\pi$
$60$	−3.74107	−0.482969
$61$	7.18371	0.919780	0.459890	−	0.887976i	$-0.347889\pi$
$61$	7.18371	0.919780	0.459890	+	0.887976i	$0.347889\pi$
$62$	4.70785	0.597898
$63$	−15.6444	−1.97101
$64$	−5.38633	−0.673292
$65$	−1.68333	−0.208792
$66$	38.4867	4.73739
$67$	−10.9304	−1.33536	−0.667681	−	0.744448i	$-0.732713\pi$
$67$	−10.9304	−1.33536	−0.667681	+	0.744448i	$0.732713\pi$
$68$	−22.8046	−2.76546
$69$	3.84313	0.462658
$70$	1.92899	0.230559
$71$	−8.19888	−0.973028	−0.486514	−	0.873673i	$-0.661732\pi$
$71$	−8.19888	−0.973028	−0.486514	+	0.873673i	$0.661732\pi$
$72$	−32.7479	−3.85938
$73$	2.57362	0.301220	0.150610	−	0.988593i	$-0.451876\pi$
$73$	2.57362	0.301220	0.150610	+	0.988593i	$0.451876\pi$
$74$	5.98978	0.696298
$75$	14.7364	1.70162
$76$	−28.5992	−3.28055
$77$	−13.4355	−1.53112
$78$	−42.2600	−4.78500
$79$	5.22582	0.587951	0.293975	−	0.955813i	$-0.405022\pi$
$79$	5.22582	0.587951	0.293975	+	0.955813i	$0.405022\pi$
$80$	1.54415	0.172641
$81$	9.01967	1.00219
$82$	27.3538	3.02072
$83$	−3.09234	−0.339428	−0.169714	−	0.985493i	$-0.554284\pi$
$83$	−3.09234	−0.339428	−0.169714	+	0.985493i	$0.554284\pi$
$84$	32.7867	3.57732
$85$	−1.61769	−0.175464
$86$	−16.9461	−1.82734
$87$	−3.00036	−0.321673
$88$	−28.1240	−2.99803
$89$	−12.6475	−1.34064	−0.670318	−	0.742074i	$-0.733842\pi$
$89$	−12.6475	−1.34064	−0.670318	+	0.742074i	$0.733842\pi$
$90$	−4.44212	−0.468241
$91$	14.7527	1.54650
$92$	−5.37012	−0.559874
$93$	5.67628	0.588603
$94$	1.06012	0.109343
$95$	−2.02875	−0.208145
$96$	6.02592	0.615018
$97$	11.6912	1.18706	0.593532	−	0.804810i	$-0.297733\pi$
$97$	11.6912	1.18706	0.593532	+	0.804810i	$0.297733\pi$
$98$	0.513659	0.0518874
$99$	30.9395	3.10954
$100$	−20.5917	−2.05917
$101$	16.6447	1.65621	0.828105	−	0.560572i	$-0.189419\pi$
$101$	16.6447	1.65621	0.828105	+	0.560572i	$0.189419\pi$
$102$	−40.6122	−4.02120
$103$	−11.6058	−1.14356	−0.571778	−	0.820409i	$-0.693746\pi$
$103$	−11.6058	−1.14356	−0.571778	+	0.820409i	$0.693746\pi$
$104$	30.8813	3.02816
$105$	2.32579	0.226974
$106$	−16.7779	−1.62961
$107$	7.24273	0.700181	0.350091	−	0.936716i	$-0.386151\pi$
$107$	7.24273	0.700181	0.350091	+	0.936716i	$0.386151\pi$
$108$	−37.7646	−3.63390
$109$	−3.88194	−0.371823	−0.185911	−	0.982567i	$-0.559524\pi$
$109$	−3.88194	−0.371823	−0.185911	+	0.982567i	$0.559524\pi$
$110$	−3.81491	−0.363738
$111$	7.22190	0.685473
$112$	−13.5329	−1.27874
$113$	−9.98518	−0.939327	−0.469663	−	0.882846i	$-0.655625\pi$
$113$	−9.98518	−0.939327	−0.469663	+	0.882846i	$0.655625\pi$
$114$	−50.9316	−4.77018
$115$	−0.380942	−0.0355230
$116$	4.19251	0.389264
$117$	−33.9728	−3.14079
$118$	31.7825	2.92581
$119$	14.1775	1.29965
$120$	4.86850	0.444432
$121$	15.5710	1.41554
$122$	−17.8765	−1.61846
$123$	32.9805	2.97376
$124$	−7.93165	−0.712283
$125$	−2.94774	−0.263654
$126$	38.9307	3.46822
$127$	−5.52375	−0.490153	−0.245077	−	0.969504i	$-0.578813\pi$
$127$	−5.52375	−0.490153	−0.245077	+	0.969504i	$0.578813\pi$
$128$	17.4206	1.53977
$129$	−20.4320	−1.79893
$130$	4.18893	0.367393
$131$	−16.1952	−1.41498	−0.707489	−	0.706725i	$-0.750172\pi$
$131$	−16.1952	−1.41498	−0.707489	+	0.706725i	$0.750172\pi$
$132$	−64.8412	−5.64371
$133$	17.7799	1.54171
$134$	27.2000	2.34973
$135$	−2.67892	−0.230564
$136$	29.6772	2.54480
$137$	−4.15480	−0.354968	−0.177484	−	0.984124i	$-0.556796\pi$
$137$	−4.15480	−0.354968	−0.177484	+	0.984124i	$0.556796\pi$
$138$	−9.56352	−0.814101
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−3.24991	−0.274667
$141$	1.27819	0.107643
$142$	20.4027	1.71216
$143$	−29.1760	−2.43982
$144$	31.1639	2.59699
$145$	0.297405	0.0246981
$146$	−6.40439	−0.530031
$147$	0.619321	0.0510807
$148$	−10.0914	−0.829508
$149$	−9.08660	−0.744403	−0.372202	−	0.928152i	$-0.621397\pi$
$149$	−9.08660	−0.744403	−0.372202	+	0.928152i	$0.621397\pi$
$150$	−36.6713	−2.99420
$151$	−23.3746	−1.90220	−0.951099	−	0.308886i	$-0.900044\pi$
$151$	−23.3746	−1.90220	−0.951099	+	0.308886i	$0.900044\pi$
$152$	37.2181	3.01879
$153$	−32.6481	−2.63944
$154$	33.4338	2.69418
$155$	−0.562649	−0.0451931
$156$	71.1983	5.70042
$157$	−14.7356	−1.17603	−0.588015	−	0.808850i	$-0.700090\pi$
$157$	−14.7356	−1.17603	−0.588015	+	0.808850i	$0.700090\pi$
$158$	−13.0043	−1.03457
$159$	−20.2292	−1.60428
$160$	−0.597307	−0.0472212
$161$	3.33857	0.263116
$162$	−22.4452	−1.76346
$163$	−23.3154	−1.82620	−0.913101	−	0.407734i	$-0.866319\pi$
$163$	−23.3154	−1.82620	−0.913101	+	0.407734i	$0.866319\pi$
$164$	−46.0848	−3.59862
$165$	−4.59966	−0.358083
$166$	7.69521	0.597264
$167$	−12.4082	−0.960177	−0.480089	−	0.877220i	$-0.659396\pi$
$167$	−12.4082	−0.960177	−0.480089	+	0.877220i	$0.659396\pi$
$168$	−42.6675	−3.29187
$169$	19.0364	1.46434
$170$	4.02559	0.308749
$171$	−40.9439	−3.13106
$172$	28.5503	2.17694
$173$	−3.74606	−0.284808	−0.142404	−	0.989809i	$-0.545483\pi$
$173$	−3.74606	−0.284808	−0.142404	+	0.989809i	$0.545483\pi$
$174$	7.46633	0.566021
$175$	12.8017	0.967719
$176$	26.7637	2.01739
$177$	38.3203	2.88033
$178$	31.4731	2.35901
$179$	−12.5208	−0.935851	−0.467926	−	0.883768i	$-0.654998\pi$
$179$	−12.5208	−0.935851	−0.467926	+	0.883768i	$0.654998\pi$
$180$	7.48395	0.557821
$181$	7.85080	0.583545	0.291773	−	0.956488i	$-0.405755\pi$
$181$	7.85080	0.583545	0.291773	+	0.956488i	$0.405755\pi$
$182$	−36.7117	−2.72125
$183$	−21.5537	−1.59330
$184$	6.98851	0.515200
$185$	−0.715856	−0.0526308
$186$	−14.1253	−1.03572
$187$	−28.0384	−2.05037
$188$	−1.78605	−0.130261
$189$	23.4780	1.70777
$190$	5.04849	0.366256
$191$	1.60955	0.116463	0.0582315	−	0.998303i	$-0.481454\pi$
$191$	1.60955	0.116463	0.0582315	+	0.998303i	$0.481454\pi$
$192$	16.1610	1.16632
$193$	25.2004	1.81396	0.906981	−	0.421172i	$-0.138381\pi$
$193$	25.2004	1.81396	0.906981	+	0.421172i	$0.138381\pi$
$194$	−29.0933	−2.08878
$195$	5.05061	0.361681
$196$	−0.865397	−0.0618141
$197$	−6.52488	−0.464878	−0.232439	−	0.972611i	$-0.574671\pi$
$197$	−6.52488	−0.464878	−0.232439	+	0.972611i	$0.574671\pi$
$198$	−76.9921	−5.47159
$199$	15.6948	1.11258	0.556289	−	0.830989i	$-0.312225\pi$
$199$	15.6948	1.11258	0.556289	+	0.830989i	$0.312225\pi$
$200$	26.7974	1.89486
$201$	32.7952	2.31319
$202$	−41.4199	−2.91430
$203$	−2.60645	−0.182937
$204$	68.4221	4.79051
$205$	−3.26912	−0.228326
$206$	28.8808	2.01222
$207$	−7.68812	−0.534361
$208$	−29.3876	−2.03766
$209$	−35.1628	−2.43226
$210$	−5.78768	−0.399388
$211$	5.28427	0.363784	0.181892	−	0.983318i	$-0.441778\pi$
$211$	5.28427	0.363784	0.181892	+	0.983318i	$0.441778\pi$
$212$	28.2669	1.94138
$213$	24.5996	1.68554
$214$	−18.0234	−1.23205
$215$	2.02528	0.138123
$216$	49.1457	3.34394
$217$	4.93105	0.334741
$218$	9.66011	0.654265
$219$	−7.72180	−0.521791
$220$	6.42725	0.433325
$221$	30.7872	2.07097
$222$	−17.9715	−1.20617
$223$	−29.7220	−1.99033	−0.995165	−	0.0982160i	$-0.968686\pi$
$223$	−29.7220	−1.99033	−0.995165	+	0.0982160i	$0.968686\pi$
$224$	5.23479	0.349764
$225$	−29.4800	−1.96534
$226$	24.8479	1.65286
$227$	9.39033	0.623258	0.311629	−	0.950204i	$-0.399125\pi$
$227$	9.39033	0.623258	0.311629	+	0.950204i	$0.399125\pi$
$228$	85.8080	5.68277
$229$	−3.87584	−0.256123	−0.128061	−	0.991766i	$-0.540875\pi$
$229$	−3.87584	−0.256123	−0.128061	+	0.991766i	$0.540875\pi$
$230$	0.947963	0.0625068
$231$	40.3113	2.65229
$232$	−5.45599	−0.358204
$233$	3.21783	0.210807	0.105403	−	0.994430i	$-0.466387\pi$
$233$	3.21783	0.210807	0.105403	+	0.994430i	$0.466387\pi$
$234$	84.5404	5.52658
$235$	−0.126698	−0.00826485
$236$	−53.5462	−3.48556
$237$	−15.6794	−1.01848
$238$	−35.2802	−2.28688
$239$	−10.7192	−0.693366	−0.346683	−	0.937982i	$-0.612692\pi$
$239$	−10.7192	−0.693366	−0.346683	+	0.937982i	$0.612692\pi$
$240$	−4.63302	−0.299060
$241$	25.7864	1.66105	0.830523	−	0.556985i	$-0.188042\pi$
$241$	25.7864	1.66105	0.830523	+	0.556985i	$0.188042\pi$
$242$	−38.7480	−2.49081
$243$	−0.0393564	−0.00252471
$244$	30.1177	1.92809
$245$	−0.0613888	−0.00392199
$246$	−82.0712	−5.23267
$247$	38.6102	2.45671
$248$	10.3220	0.655447
$249$	9.27814	0.587978
$250$	7.33538	0.463930
$251$	−18.2531	−1.15213	−0.576063	−	0.817405i	$-0.695412\pi$
$251$	−18.2531	−1.15213	−0.576063	+	0.817405i	$0.695412\pi$
$252$	−65.5892	−4.13173
$253$	−6.60259	−0.415101
$254$	13.7457	0.862482
$255$	4.85367	0.303949
$256$	−32.5779	−2.03612
$257$	−27.4754	−1.71387	−0.856935	−	0.515425i	$-0.827634\pi$
$257$	−27.4754	−1.71387	−0.856935	+	0.515425i	$0.827634\pi$
$258$	50.8444	3.16544
$259$	6.27375	0.389832
$260$	−7.05737	−0.437680
$261$	6.00219	0.371526
$262$	40.3012	2.48982
$263$	0.338138	0.0208505	0.0104252	−	0.999946i	$-0.496681\pi$
$263$	0.338138	0.0208505	0.0104252	+	0.999946i	$0.496681\pi$
$264$	84.3823	5.19337
$265$	2.00517	0.123177
$266$	−44.2449	−2.71283
$267$	37.9472	2.32233
$268$	−45.8258	−2.79926
$269$	1.87872	0.114547	0.0572737	−	0.998359i	$-0.481759\pi$
$269$	1.87872	0.114547	0.0572737	+	0.998359i	$0.481759\pi$
$270$	6.66642	0.405705
$271$	−2.61823	−0.159046	−0.0795231	−	0.996833i	$-0.525340\pi$
$271$	−2.61823	−0.159046	−0.0795231	+	0.996833i	$0.525340\pi$
$272$	−28.2417	−1.71241
$273$	−44.2635	−2.67895
$274$	10.3391	0.624608
$275$	−25.3176	−1.52671
$276$	16.1123	0.969848
$277$	−24.0131	−1.44281	−0.721403	−	0.692516i	$-0.756502\pi$
$277$	−24.0131	−1.44281	−0.721403	+	0.692516i	$0.756502\pi$
$278$	2.48847	0.149249
$279$	−11.3553	−0.679825
$280$	4.22933	0.252751
$281$	−16.7106	−0.996874	−0.498437	−	0.866926i	$-0.666092\pi$
$281$	−16.7106	−0.996874	−0.498437	+	0.866926i	$0.666092\pi$
$282$	−3.18074	−0.189410
$283$	14.5699	0.866089	0.433045	−	0.901372i	$-0.357439\pi$
$283$	14.5699	0.866089	0.433045	+	0.901372i	$0.357439\pi$
$284$	−34.3738	−2.03971
$285$	6.08698	0.360562
$286$	72.6037	4.29315
$287$	28.6506	1.69119
$288$	−12.0548	−0.710334
$289$	12.5868	0.740399
$290$	−0.740084	−0.0434592
$291$	−35.0779	−2.05631
$292$	10.7899	0.631432
$293$	20.9662	1.22486	0.612430	−	0.790525i	$-0.290192\pi$
$293$	20.9662	1.22486	0.612430	+	0.790525i	$0.290192\pi$
$294$	−1.54116	−0.0898825
$295$	−3.79841	−0.221152
$296$	13.1326	0.763318
$297$	−46.4318	−2.69424
$298$	22.6118	1.30986
$299$	7.24991	0.419273
$300$	61.7826	3.56702
$301$	−17.7495	−1.02306
$302$	58.1671	3.34714
$303$	−49.9402	−2.86899
$304$	−35.4179	−2.03135
$305$	2.13647	0.122334
$306$	81.2440	4.64441
$307$	−18.5129	−1.05659	−0.528293	−	0.849062i	$-0.677168\pi$
$307$	−18.5129	−1.05659	−0.528293	+	0.849062i	$0.677168\pi$
$308$	−56.3283	−3.20960
$309$	34.8217	1.98094
$310$	1.40014	0.0795225
$311$	0.476586	0.0270247	0.0135124	−	0.999909i	$-0.495699\pi$
$311$	0.476586	0.0270247	0.0135124	+	0.999909i	$0.495699\pi$
$312$	−92.6552	−5.24557
$313$	20.8981	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$313$	20.8981	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$314$	36.6692	2.06936
$315$	−4.65272	−0.262151
$316$	21.9093	1.23249
$317$	5.20011	0.292067	0.146034	−	0.989280i	$-0.453349\pi$
$317$	5.20011	0.292067	0.146034	+	0.989280i	$0.453349\pi$
$318$	50.3398	2.82291
$319$	5.15470	0.288608
$320$	−1.60192	−0.0895501
$321$	−21.7308	−1.21290
$322$	−8.30794	−0.462983
$323$	37.1047	2.06456
$324$	37.8150	2.10083
$325$	27.7997	1.54205
$326$	58.0197	3.21342
$327$	11.6472	0.644094
$328$	59.9733	3.31147
$329$	1.11038	0.0612171
$330$	11.4461	0.630089
$331$	5.32477	0.292676	0.146338	−	0.989235i	$-0.453251\pi$
$331$	5.32477	0.292676	0.146338	+	0.989235i	$0.453251\pi$
$332$	−12.9646	−0.711527
$333$	−14.4473	−0.791708
$334$	30.8776	1.68954
$335$	−3.25075	−0.177608
$336$	40.6037	2.21511
$337$	23.4188	1.27570	0.637851	−	0.770160i	$-0.279823\pi$
$337$	23.4188	1.27570	0.637851	+	0.770160i	$0.279823\pi$
$338$	−47.3716	−2.57667
$339$	29.9592	1.62716
$340$	−6.78219	−0.367816
$341$	−9.75200	−0.528100
$342$	101.888	5.50947
$343$	18.7832	1.01420
$344$	−37.1544	−2.00323
$345$	1.14296	0.0615351
$346$	9.32197	0.501152
$347$	−10.0539	−0.539721	−0.269861	−	0.962899i	$-0.586978\pi$
$347$	−10.0539	−0.539721	−0.269861	+	0.962899i	$0.586978\pi$
$348$	−12.5790	−0.674307
$349$	21.9627	1.17564	0.587819	−	0.808992i	$-0.299987\pi$
$349$	21.9627	1.17564	0.587819	+	0.808992i	$0.299987\pi$
$350$	−31.8567	−1.70281
$351$	50.9839	2.72132
$352$	−10.3527	−0.551800
$353$	0.965376	0.0513818	0.0256909	−	0.999670i	$-0.491821\pi$
$353$	0.965376	0.0513818	0.0256909	+	0.999670i	$0.491821\pi$
$354$	−95.3590	−5.06828
$355$	−2.43838	−0.129416
$356$	−53.0249	−2.81031
$357$	−42.5375	−2.25133
$358$	31.1578	1.64674
$359$	−34.2328	−1.80674	−0.903369	−	0.428864i	$-0.858914\pi$
$359$	−34.2328	−1.80674	−0.903369	+	0.428864i	$0.858914\pi$
$360$	−9.73937	−0.513310
$361$	27.5329	1.44910
$362$	−19.5365	−1.02682
$363$	−46.7186	−2.45209
$364$	61.8508	3.24186
$365$	0.765407	0.0400632
$366$	53.6359	2.80360
$367$	−5.57862	−0.291201	−0.145601	−	0.989343i	$-0.546511\pi$
$367$	−5.57862	−0.291201	−0.145601	+	0.989343i	$0.546511\pi$
$368$	−6.65048	−0.346680
$369$	−65.9771	−3.43463
$370$	1.78139	0.0926100
$371$	−17.5733	−0.912361
$372$	23.7978	1.23386
$373$	7.78465	0.403074	0.201537	−	0.979481i	$-0.435406\pi$
$373$	7.78465	0.403074	0.201537	+	0.979481i	$0.435406\pi$
$374$	69.7727	3.60786
$375$	8.84430	0.456718
$376$	2.32431	0.119867
$377$	−5.66007	−0.291508
$378$	−58.4244	−3.00503
$379$	−4.23687	−0.217633	−0.108817	−	0.994062i	$-0.534706\pi$
$379$	−4.23687	−0.217633	−0.108817	+	0.994062i	$0.534706\pi$
$380$	−8.50553	−0.436325
$381$	16.5733	0.849074
$382$	−4.00533	−0.204930
$383$	26.4144	1.34971	0.674855	−	0.737950i	$-0.264206\pi$
$383$	26.4144	1.34971	0.674855	+	0.737950i	$0.264206\pi$
$384$	−52.2680	−2.66729
$385$	−3.99577	−0.203643
$386$	−62.7104	−3.19188
$387$	40.8739	2.07774
$388$	49.0155	2.48839
$389$	35.3183	1.79071	0.895354	−	0.445356i	$-0.146923\pi$
$389$	35.3183	1.79071	0.895354	+	0.445356i	$0.146923\pi$
$390$	−12.5683	−0.636421
$391$	6.96722	0.352347
$392$	1.12620	0.0568817
$393$	48.5914	2.45111
$394$	16.2370	0.818008
$395$	1.55418	0.0781994
$396$	129.714	6.51837
$397$	−16.9579	−0.851093	−0.425546	−	0.904937i	$-0.639918\pi$
$397$	−16.9579	−0.851093	−0.425546	+	0.904937i	$0.639918\pi$
$398$	−39.0562	−1.95771
$399$	−53.3462	−2.67065
$400$	−25.5012	−1.27506
$401$	12.8410	0.641247	0.320623	−	0.947207i	$-0.396108\pi$
$401$	12.8410	0.641247	0.320623	+	0.947207i	$0.396108\pi$
$402$	−81.6100	−4.07034
$403$	10.7081	0.533408
$404$	69.7830	3.47184
$405$	2.68249	0.133294
$406$	6.48609	0.321899
$407$	−12.4074	−0.615013
$408$	−89.0424	−4.40825
$409$	−20.3750	−1.00748	−0.503739	−	0.863856i	$-0.668043\pi$
$409$	−20.3750	−1.00748	−0.503739	+	0.863856i	$0.668043\pi$
$410$	8.13513	0.401766
$411$	12.4659	0.614897
$412$	−48.6575	−2.39718
$413$	33.2893	1.63806
$414$	19.1317	0.940271
$415$	−0.919676	−0.0451451
$416$	11.3677	0.557346
$417$	3.00036	0.146928
$418$	87.5018	4.27985
$419$	−9.61962	−0.469949	−0.234975	−	0.972002i	$-0.575501\pi$
$419$	−9.61962	−0.469949	−0.234975	+	0.972002i	$0.575501\pi$
$420$	9.75090	0.475795
$421$	−0.863824	−0.0421002	−0.0210501	−	0.999778i	$-0.506701\pi$
$421$	−0.863824	−0.0421002	−0.0210501	+	0.999778i	$0.506701\pi$
$422$	−13.1498	−0.640121
$423$	−2.55700	−0.124326
$424$	−36.7856	−1.78647
$425$	26.7158	1.29590
$426$	−61.2155	−2.96590
$427$	−18.7240	−0.906117
$428$	30.3652	1.46776
$429$	87.5386	4.22640
$430$	−5.03985	−0.243043
$431$	−17.3020	−0.833410	−0.416705	−	0.909042i	$-0.636815\pi$
$431$	−17.3020	−0.833410	−0.416705	+	0.909042i	$0.636815\pi$
$432$	−46.7685	−2.25015
$433$	12.1875	0.585695	0.292848	−	0.956159i	$-0.405397\pi$
$433$	12.1875	0.585695	0.292848	+	0.956159i	$0.405397\pi$
$434$	−12.2708	−0.589017
$435$	−0.892322	−0.0427836
$436$	−16.2751	−0.779434
$437$	8.73757	0.417975
$438$	19.2155	0.918153
$439$	23.8677	1.13914	0.569572	−	0.821941i	$-0.307109\pi$
$439$	23.8677	1.13914	0.569572	+	0.821941i	$0.307109\pi$
$440$	−8.36422	−0.398748
$441$	−1.23894	−0.0589973
$442$	−76.6133	−3.64412
$443$	12.5463	0.596092	0.298046	−	0.954551i	$-0.403665\pi$
$443$	12.5463	0.596092	0.298046	+	0.954551i	$0.403665\pi$
$444$	30.2779	1.43692
$445$	−3.76144	−0.178309
$446$	73.9624	3.50222
$447$	27.2631	1.28950
$448$	14.0392	0.663291
$449$	−16.2861	−0.768586	−0.384293	−	0.923211i	$-0.625555\pi$
$449$	−16.2861	−0.768586	−0.384293	+	0.923211i	$0.625555\pi$
$450$	73.3603	3.45824
$451$	−56.6614	−2.66808
$452$	−41.8629	−1.96907
$453$	70.1323	3.29510
$454$	−23.3676	−1.09670
$455$	4.38752	0.205690
$456$	−111.668	−5.22932
$457$	−8.34554	−0.390388	−0.195194	−	0.980765i	$-0.562534\pi$
$457$	−8.34554	−0.390388	−0.195194	+	0.980765i	$0.562534\pi$
$458$	9.64493	0.450678
$459$	48.9960	2.28694
$460$	−1.59710	−0.0744651
$461$	−4.14378	−0.192995	−0.0964975	−	0.995333i	$-0.530764\pi$
$461$	−4.14378	−0.192995	−0.0964975	+	0.995333i	$0.530764\pi$
$462$	−100.314	−4.66702
$463$	−8.72839	−0.405642	−0.202821	−	0.979216i	$-0.565011\pi$
$463$	−8.72839	−0.405642	−0.202821	+	0.979216i	$0.565011\pi$
$464$	5.19209	0.241037
$465$	1.68815	0.0782862
$466$	−8.00748	−0.370939
$467$	34.4701	1.59508	0.797542	−	0.603264i	$-0.206133\pi$
$467$	34.4701	1.59508	0.797542	+	0.603264i	$0.206133\pi$
$468$	−142.431	−6.58388
$469$	28.4896	1.31553
$470$	0.315284	0.0145430
$471$	44.2122	2.03719
$472$	69.6833	3.20743
$473$	35.1027	1.61402
$474$	39.0177	1.79214
$475$	33.5042	1.53728
$476$	59.4391	2.72439
$477$	40.4682	1.85291
$478$	26.6744	1.22006
$479$	7.69798	0.351730	0.175865	−	0.984414i	$-0.443728\pi$
$479$	7.69798	0.351730	0.175865	+	0.984414i	$0.443728\pi$
$480$	1.79214	0.0817995
$481$	13.6238	0.621194
$482$	−64.1687	−2.92280
$483$	−10.0169	−0.455786
$484$	65.2814	2.96733
$485$	3.47703	0.157884
$486$	0.0979374	0.00444253
$487$	−5.07532	−0.229985	−0.114992	−	0.993366i	$-0.536684\pi$
$487$	−5.07532	−0.229985	−0.114992	+	0.993366i	$0.536684\pi$
$488$	−39.1943	−1.77424
$489$	69.9546	3.16346
$490$	0.152765	0.00690120
$491$	4.34887	0.196262	0.0981309	−	0.995174i	$-0.468714\pi$
$491$	4.34887	0.196262	0.0981309	+	0.995174i	$0.468714\pi$
$492$	138.271	6.23374
$493$	−5.43937	−0.244977
$494$	−96.0805	−4.32287
$495$	9.20155	0.413579
$496$	−9.82273	−0.441053
$497$	21.3700	0.958574
$498$	−23.0884	−1.03462
$499$	−11.9803	−0.536314	−0.268157	−	0.963375i	$-0.586415\pi$
$499$	−11.9803	−0.536314	−0.268157	+	0.963375i	$0.586415\pi$
$500$	−12.3584	−0.552685
$501$	37.2292	1.66328
$502$	45.4224	2.02730
$503$	20.4281	0.910843	0.455422	−	0.890276i	$-0.349488\pi$
$503$	20.4281	0.910843	0.455422	+	0.890276i	$0.349488\pi$
$504$	85.3557	3.80205
$505$	4.95021	0.220282
$506$	16.4304	0.730419
$507$	−57.1161	−2.53662
$508$	−23.1583	−1.02749
$509$	−24.7740	−1.09809	−0.549044	−	0.835794i	$-0.685008\pi$
$509$	−24.7740	−1.09809	−0.549044	+	0.835794i	$0.685008\pi$
$510$	−12.0782	−0.534834
$511$	−6.70802	−0.296745
$512$	46.2282	2.04302
$513$	61.4457	2.71289
$514$	68.3719	3.01575
$515$	−3.45162	−0.152097
$516$	−85.6612	−3.77102
$517$	−2.19596	−0.0965783
$518$	−15.6121	−0.685955
$519$	11.2395	0.493361
$520$	9.18424	0.402756
$521$	−21.0130	−0.920596	−0.460298	−	0.887764i	$-0.652257\pi$
$521$	−21.0130	−0.920596	−0.460298	+	0.887764i	$0.652257\pi$
$522$	−14.9363	−0.653743
$523$	−34.8990	−1.52603	−0.763014	−	0.646382i	$-0.776281\pi$
$523$	−34.8990	−1.52603	−0.763014	+	0.646382i	$0.776281\pi$
$524$	−67.8983	−2.96615
$525$	−38.4098	−1.67634
$526$	−0.841447	−0.0366888
$527$	10.2906	0.448264
$528$	−80.3008	−3.49464
$529$	−21.3593	−0.928667
$530$	−4.98982	−0.216744
$531$	−76.6592	−3.32672
$532$	74.5424	3.23182
$533$	62.2165	2.69490
$534$	−94.4307	−4.08641
$535$	2.15402	0.0931265
$536$	59.6362	2.57589
$537$	37.5671	1.62114
$538$	−4.67514	−0.201560
$539$	−1.06401	−0.0458301
$540$	−11.2314	−0.483321
$541$	44.4258	1.91001	0.955006	−	0.296585i	$-0.0958478\pi$
$541$	44.4258	1.91001	0.955006	+	0.296585i	$0.0958478\pi$
$542$	6.51540	0.279860
$543$	−23.5553	−1.01085
$544$	10.9244	0.468381
$545$	−1.15451	−0.0494537
$546$	110.148	4.71392
$547$	−1.81882	−0.0777670	−0.0388835	−	0.999244i	$-0.512380\pi$
$547$	−1.81882	−0.0777670	−0.0388835	+	0.999244i	$0.512380\pi$
$548$	−17.4190	−0.744103
$549$	43.1180	1.84023
$550$	63.0022	2.68642
$551$	−6.82150	−0.290606
$552$	−20.9681	−0.892460
$553$	−13.6208	−0.579217
$554$	59.7559	2.53879
$555$	2.14783	0.0911702
$556$	−4.19251	−0.177802
$557$	23.1927	0.982704	0.491352	−	0.870961i	$-0.336503\pi$
$557$	23.1927	0.982704	0.491352	+	0.870961i	$0.336503\pi$
$558$	28.2574	1.19623
$559$	−38.5441	−1.63024
$560$	−4.02476	−0.170077
$561$	84.1253	3.55177
$562$	41.5840	1.75412
$563$	−2.77274	−0.116857	−0.0584285	−	0.998292i	$-0.518609\pi$
$563$	−2.77274	−0.116857	−0.0584285	+	0.998292i	$0.518609\pi$
$564$	5.35881	0.225647
$565$	−2.96964	−0.124934
$566$	−36.2568	−1.52399
$567$	−23.5093	−0.987299
$568$	44.7330	1.87696
$569$	20.7517	0.869955	0.434978	−	0.900441i	$-0.356756\pi$
$569$	20.7517	0.869955	0.434978	+	0.900441i	$0.356756\pi$
$570$	−15.1473	−0.634450
$571$	−1.67103	−0.0699304	−0.0349652	−	0.999389i	$-0.511132\pi$
$571$	−1.67103	−0.0699304	−0.0349652	+	0.999389i	$0.511132\pi$
$572$	−122.320	−5.11448
$573$	−4.82924	−0.201744
$574$	−71.2962	−2.97585
$575$	6.29114	0.262359
$576$	−32.3298	−1.34707
$577$	12.0070	0.499860	0.249930	−	0.968264i	$-0.419592\pi$
$577$	12.0070	0.499860	0.249930	+	0.968264i	$0.419592\pi$
$578$	−31.3219	−1.30282
$579$	−75.6103	−3.14225
$580$	1.24687	0.0517735
$581$	8.06003	0.334386
$582$	87.2906	3.61831
$583$	34.7542	1.43937
$584$	−14.0417	−0.581048
$585$	−10.1037	−0.417735
$586$	−52.1739	−2.15528
$587$	−44.2437	−1.82613	−0.913066	−	0.407813i	$-0.866292\pi$
$587$	−44.2437	−1.82613	−0.913066	+	0.407813i	$0.866292\pi$
$588$	2.59651	0.107078
$589$	12.9054	0.531756
$590$	9.45226	0.389143
$591$	19.5770	0.805291
$592$	−12.4974	−0.513640
$593$	−21.4347	−0.880219	−0.440109	−	0.897944i	$-0.645060\pi$
$593$	−21.4347	−0.880219	−0.440109	+	0.897944i	$0.645060\pi$
$594$	115.544	4.74084
$595$	4.21644	0.172857
$596$	−38.0956	−1.56046
$597$	−47.0902	−1.92727
$598$	−18.0412	−0.737760
$599$	17.1528	0.700846	0.350423	−	0.936592i	$-0.386038\pi$
$599$	17.1528	0.700846	0.350423	+	0.936592i	$0.386038\pi$
$600$	−80.4019	−3.28239
$601$	−32.6640	−1.33239	−0.666197	−	0.745776i	$-0.732079\pi$
$601$	−32.6640	−1.33239	−0.666197	+	0.745776i	$0.732079\pi$
$602$	44.1691	1.80020
$603$	−65.6063	−2.67170
$604$	−97.9982	−3.98749
$605$	4.63088	0.188272
$606$	124.275	5.04832
$607$	39.6536	1.60949	0.804745	−	0.593620i	$-0.202302\pi$
$607$	39.6536	1.60949	0.804745	+	0.593620i	$0.202302\pi$
$608$	13.7003	0.555620
$609$	7.82030	0.316895
$610$	−5.31655	−0.215261
$611$	2.41125	0.0975489
$612$	−136.877	−5.53294
$613$	−46.0437	−1.85969	−0.929843	−	0.367957i	$-0.880058\pi$
$613$	−46.0437	−1.85969	−0.929843	+	0.367957i	$0.880058\pi$
$614$	46.0688	1.85919
$615$	9.80856	0.395520
$616$	73.3039	2.95350
$617$	42.3542	1.70511	0.852557	−	0.522634i	$-0.175050\pi$
$617$	42.3542	1.70511	0.852557	+	0.522634i	$0.175050\pi$
$618$	−86.6529	−3.48569
$619$	−12.1324	−0.487643	−0.243821	−	0.969820i	$-0.578401\pi$
$619$	−12.1324	−0.487643	−0.243821	+	0.969820i	$0.578401\pi$
$620$	−2.35891	−0.0947361
$621$	11.5378	0.462995
$622$	−1.18597	−0.0475532
$623$	32.9652	1.32072
$624$	88.1735	3.52976
$625$	23.6811	0.947243
$626$	−52.0045	−2.07852
$627$	105.501	4.21332
$628$	−61.7791	−2.46526
$629$	13.0926	0.522037
$630$	11.5782	0.461285
$631$	35.0456	1.39514	0.697571	−	0.716516i	$-0.254264\pi$
$631$	35.0456	1.39514	0.697571	+	0.716516i	$0.254264\pi$
$632$	−28.5120	−1.13415
$633$	−15.8547	−0.630169
$634$	−12.9403	−0.513926
$635$	−1.64279	−0.0651921
$636$	−84.8109	−3.36297
$637$	1.16832	0.0462907
$638$	−12.8273	−0.507840
$639$	−49.2112	−1.94676
$640$	5.18095	0.204795
$641$	−41.4723	−1.63806	−0.819028	−	0.573753i	$-0.805487\pi$
$641$	−41.4723	−1.63806	−0.819028	+	0.573753i	$0.805487\pi$
$642$	54.0766	2.13423
$643$	−26.1143	−1.02985	−0.514924	−	0.857236i	$-0.672180\pi$
$643$	−26.1143	−1.02985	−0.514924	+	0.857236i	$0.672180\pi$
$644$	13.9970	0.551558
$645$	−6.07656	−0.239264
$646$	−92.3341	−3.63284
$647$	−22.1548	−0.870994	−0.435497	−	0.900190i	$-0.643427\pi$
$647$	−22.1548	−0.870994	−0.435497	+	0.900190i	$0.643427\pi$
$648$	−49.2113	−1.93320
$649$	−65.8352	−2.58426
$650$	−69.1789	−2.71342
$651$	−14.7949	−0.579860
$652$	−97.7498	−3.82818
$653$	−21.0584	−0.824080	−0.412040	−	0.911166i	$-0.635184\pi$
$653$	−21.0584	−0.824080	−0.412040	+	0.911166i	$0.635184\pi$
$654$	−28.9839	−1.13336
$655$	−4.81651	−0.188197
$656$	−57.0724	−2.22830
$657$	15.4474	0.602659
$658$	−2.76315	−0.107719
$659$	−28.4265	−1.10734	−0.553669	−	0.832737i	$-0.686773\pi$
$659$	−28.4265	−1.10734	−0.553669	+	0.832737i	$0.686773\pi$
$660$	−19.2841	−0.750632
$661$	−30.3202	−1.17932	−0.589659	−	0.807652i	$-0.700738\pi$
$661$	−30.3202	−1.17932	−0.589659	+	0.807652i	$0.700738\pi$
$662$	−13.2506	−0.514998
$663$	−92.3729	−3.58747
$664$	16.8718	0.654752
$665$	5.28783	0.205053
$666$	35.9518	1.39310
$667$	−1.28089	−0.0495961
$668$	−52.0216	−2.01277
$669$	89.1767	3.44777
$670$	8.08942	0.312521
$671$	37.0299	1.42952
$672$	−15.7063	−0.605883
$673$	47.8904	1.84604	0.923020	−	0.384751i	$-0.125713\pi$
$673$	47.8904	1.84604	0.923020	+	0.384751i	$0.125713\pi$
$674$	−58.2771	−2.24475
$675$	44.2415	1.70286
$676$	79.8102	3.06962
$677$	9.87335	0.379464	0.189732	−	0.981836i	$-0.439238\pi$
$677$	9.87335	0.379464	0.189732	+	0.981836i	$0.439238\pi$
$678$	−74.5526	−2.86318
$679$	−30.4726	−1.16943
$680$	8.82613	0.338467
$681$	−28.1744	−1.07965
$682$	24.2676	0.929254
$683$	3.59809	0.137677	0.0688385	−	0.997628i	$-0.478071\pi$
$683$	3.59809	0.137677	0.0688385	+	0.997628i	$0.478071\pi$
$684$	−171.658	−6.56349
$685$	−1.23566	−0.0472120
$686$	−46.7414	−1.78460
$687$	11.6289	0.443671
$688$	35.3573	1.34798
$689$	−38.1615	−1.45384
$690$	−2.84424	−0.108278
$691$	44.2523	1.68344	0.841718	−	0.539917i	$-0.181544\pi$
$691$	44.2523	1.68344	0.841718	+	0.539917i	$0.181544\pi$
$692$	−15.7054	−0.597029
$693$	−80.6422	−3.06335
$694$	25.0189	0.949703
$695$	−0.297405	−0.0112812
$696$	16.3700	0.620502
$697$	59.7906	2.26473
$698$	−54.6537	−2.06867
$699$	−9.65465	−0.365173
$700$	53.6713	2.02858
$701$	8.30881	0.313820	0.156910	−	0.987613i	$-0.449847\pi$
$701$	8.30881	0.313820	0.156910	+	0.987613i	$0.449847\pi$
$702$	−126.872	−4.78848
$703$	16.4194	0.619270
$704$	−27.7650	−1.04643
$705$	0.380139	0.0143169
$706$	−2.40231	−0.0904122
$707$	−43.3836	−1.63161
$708$	160.658	6.03790
$709$	8.69937	0.326712	0.163356	−	0.986567i	$-0.447768\pi$
$709$	8.69937	0.326712	0.163356	+	0.986567i	$0.447768\pi$
$710$	6.06786	0.227723
$711$	31.3663	1.17633
$712$	69.0049	2.58607
$713$	2.42326	0.0907519
$714$	105.854	3.96147
$715$	−8.67707	−0.324504
$716$	−52.4937	−1.96178
$717$	32.1614	1.20109
$718$	85.1875	3.17917
$719$	37.3836	1.39417	0.697086	−	0.716988i	$-0.254480\pi$
$719$	37.3836	1.39417	0.697086	+	0.716988i	$0.254480\pi$
$720$	9.26829	0.345409
$721$	30.2500	1.12657
$722$	−68.5150	−2.54986
$723$	−77.3685	−2.87736
$724$	32.9145	1.22326
$725$	−4.91155	−0.182410
$726$	116.258	4.31474
$727$	41.3939	1.53522	0.767608	−	0.640919i	$-0.221447\pi$
$727$	41.3939	1.53522	0.767608	+	0.640919i	$0.221447\pi$
$728$	−80.4906	−2.98318
$729$	−26.9409	−0.997812
$730$	−1.90470	−0.0704960
$731$	−37.0412	−1.37002
$732$	−90.3642	−3.33996
$733$	−20.0164	−0.739322	−0.369661	−	0.929167i	$-0.620526\pi$
$733$	−20.0164	−0.739322	−0.369661	+	0.929167i	$0.620526\pi$
$734$	13.8822	0.512403
$735$	0.184189	0.00679391
$736$	2.57253	0.0948247
$737$	−56.3430	−2.07542
$738$	164.182	6.04363
$739$	0.699312	0.0257246	0.0128623	−	0.999917i	$-0.495906\pi$
$739$	0.699312	0.0257246	0.0128623	+	0.999917i	$0.495906\pi$
$740$	−3.00123	−0.110327
$741$	−115.845	−4.25566
$742$	43.7307	1.60541
$743$	−16.0045	−0.587147	−0.293573	−	0.955937i	$-0.594845\pi$
$743$	−16.0045	−0.587147	−0.293573	+	0.955937i	$0.594845\pi$
$744$	−30.9697	−1.13541
$745$	−2.70240	−0.0990081
$746$	−19.3719	−0.709256
$747$	−18.5608	−0.679104
$748$	−117.551	−4.29809
$749$	−18.8778	−0.689781
$750$	−22.0088	−0.803648
$751$	−16.3978	−0.598365	−0.299183	−	0.954196i	$-0.596714\pi$
$751$	−16.3978	−0.598365	−0.299183	+	0.954196i	$0.596714\pi$
$752$	−2.21189	−0.0806593
$753$	54.7660	1.99578
$754$	14.0849	0.512943
$755$	−6.95172	−0.252999
$756$	98.4316	3.57992
$757$	−28.9157	−1.05096	−0.525480	−	0.850806i	$-0.676114\pi$
$757$	−28.9157	−1.05096	−0.525480	+	0.850806i	$0.676114\pi$
$758$	10.5433	0.382951
$759$	19.8102	0.719064
$760$	11.0688	0.401509
$761$	9.35854	0.339247	0.169623	−	0.985509i	$-0.445745\pi$
$761$	9.35854	0.339247	0.169623	+	0.985509i	$0.445745\pi$
$762$	−41.2421	−1.49404
$763$	10.1181	0.366299
$764$	6.74805	0.244136
$765$	−9.70970	−0.351055
$766$	−65.7314	−2.37497
$767$	72.2897	2.61023
$768$	97.7457	3.52709
$769$	48.0574	1.73299	0.866497	−	0.499183i	$-0.166366\pi$
$769$	48.0574	1.73299	0.866497	+	0.499183i	$0.166366\pi$
$770$	9.94338	0.358335
$771$	82.4362	2.96887
$772$	105.653	3.80252
$773$	19.3450	0.695791	0.347896	−	0.937533i	$-0.386896\pi$
$773$	19.3450	0.695791	0.347896	+	0.937533i	$0.386896\pi$
$774$	−101.714	−3.65602
$775$	9.29198	0.333778
$776$	−63.7873	−2.28983
$777$	−18.8235	−0.675291
$778$	−87.8886	−3.15096
$779$	74.9832	2.68655
$780$	21.1747	0.758176
$781$	−42.2628	−1.51228
$782$	−17.3377	−0.619997
$783$	−9.00765	−0.321907
$784$	−1.07173	−0.0382759
$785$	−4.38244	−0.156416
$786$	−120.918	−4.31302
$787$	−30.4664	−1.08601	−0.543005	−	0.839729i	$-0.682714\pi$
$787$	−30.4664	−1.08601	−0.543005	+	0.839729i	$0.682714\pi$
$788$	−27.3556	−0.974503
$789$	−1.01454	−0.0361184
$790$	−3.86755	−0.137601
$791$	26.0259	0.925374
$792$	−168.806	−5.99825
$793$	−40.6603	−1.44389
$794$	42.1993	1.49760
$795$	−6.01625	−0.213374
$796$	65.8007	2.33224
$797$	−19.0093	−0.673345	−0.336672	−	0.941622i	$-0.609301\pi$
$797$	−19.0093	−0.673345	−0.336672	+	0.941622i	$0.609301\pi$
$798$	132.751	4.69932
$799$	2.31723	0.0819779
$800$	9.86435	0.348757
$801$	−75.9128	−2.68225
$802$	−31.9544	−1.12835
$803$	13.2663	0.468156
$804$	137.494	4.84904
$805$	0.992905	0.0349953
$806$	−26.6468	−0.938593
$807$	−5.63683	−0.198426
$808$	−90.8134	−3.19481
$809$	−17.9350	−0.630561	−0.315280	−	0.948999i	$-0.602099\pi$
$809$	−17.9350	−0.630561	−0.315280	+	0.948999i	$0.602099\pi$
$810$	−6.67531	−0.234547
$811$	−20.2196	−0.710006	−0.355003	−	0.934865i	$-0.615520\pi$
$811$	−20.2196	−0.710006	−0.355003	+	0.934865i	$0.615520\pi$
$812$	−10.9276	−0.383482
$813$	7.85565	0.275510
$814$	30.8755	1.08219
$815$	−6.93410	−0.242891
$816$	84.7355	2.96633
$817$	−46.4533	−1.62519
$818$	50.7026	1.77277
$819$	88.5484	3.09413
$820$	−13.7058	−0.478628
$821$	−0.521169	−0.0181889	−0.00909446	−	0.999959i	$-0.502895\pi$
$821$	−0.521169	−0.0181889	−0.00909446	+	0.999959i	$0.502895\pi$
$822$	−31.0211	−1.08198
$823$	−12.4734	−0.434795	−0.217397	−	0.976083i	$-0.569757\pi$
$823$	−12.4734	−0.434795	−0.217397	+	0.976083i	$0.569757\pi$
$824$	63.3213	2.20590
$825$	75.9620	2.64466
$826$	−82.8395	−2.88235
$827$	−24.8180	−0.863006	−0.431503	−	0.902111i	$-0.642017\pi$
$827$	−24.8180	−0.863006	−0.431503	+	0.902111i	$0.642017\pi$
$828$	−32.2325	−1.12016
$829$	−12.0474	−0.418424	−0.209212	−	0.977870i	$-0.567090\pi$
$829$	−12.0474	−0.418424	−0.209212	+	0.977870i	$0.567090\pi$
$830$	2.28859	0.0794381
$831$	72.0479	2.49932
$832$	30.4870	1.05695
$833$	1.12277	0.0389017
$834$	−7.46633	−0.258538
$835$	−3.69026	−0.127707
$836$	−147.420	−5.09864
$837$	17.0412	0.589032
$838$	23.9382	0.826931
$839$	−20.0104	−0.690836	−0.345418	−	0.938449i	$-0.612263\pi$
$839$	−20.0104	−0.690836	−0.345418	+	0.938449i	$0.612263\pi$
$840$	−12.6895	−0.437830
$841$	1.00000	0.0344828
$842$	2.14960	0.0740802
$843$	50.1380	1.72685
$844$	22.1543	0.762584
$845$	5.66151	0.194762
$846$	6.36303	0.218765
$847$	−40.5850	−1.39452
$848$	35.0063	1.20212
$849$	−43.7149	−1.50029
$850$	−66.4815	−2.28030
$851$	3.08311	0.105687
$852$	103.134	3.53331
$853$	−17.9588	−0.614898	−0.307449	−	0.951565i	$-0.599475\pi$
$853$	−17.9588	−0.614898	−0.307449	+	0.951565i	$0.599475\pi$
$854$	46.5942	1.59442
$855$	−12.1769	−0.416442
$856$	−39.5163	−1.35064
$857$	37.8927	1.29439	0.647195	−	0.762324i	$-0.275942\pi$
$857$	37.8927	1.29439	0.647195	+	0.762324i	$0.275942\pi$
$858$	−217.838	−7.43685
$859$	30.4622	1.03936	0.519679	−	0.854361i	$-0.326051\pi$
$859$	30.4622	1.03936	0.519679	+	0.854361i	$0.326051\pi$
$860$	8.49098	0.289540
$861$	−85.9621	−2.92958
$862$	43.0557	1.46648
$863$	51.5557	1.75498	0.877489	−	0.479597i	$-0.159217\pi$
$863$	51.5557	1.75498	0.877489	+	0.479597i	$0.159217\pi$
$864$	18.0909	0.615466
$865$	−1.11410	−0.0378804
$866$	−30.3284	−1.03060
$867$	−37.7649	−1.28256
$868$	20.6735	0.701703
$869$	26.9376	0.913794
$870$	2.22052	0.0752827
$871$	61.8669	2.09628
$872$	21.1798	0.717240
$873$	70.1729	2.37499
$874$	−21.7432	−0.735476
$875$	7.68314	0.259738
$876$	−32.3737	−1.09381
$877$	20.7542	0.700820	0.350410	−	0.936596i	$-0.386042\pi$
$877$	20.7542	0.700820	0.350410	+	0.936596i	$0.386042\pi$
$878$	−59.3942	−2.00446
$879$	−62.9063	−2.12178
$880$	7.95964	0.268320
$881$	12.4468	0.419344	0.209672	−	0.977772i	$-0.432760\pi$
$881$	12.4468	0.419344	0.209672	+	0.977772i	$0.432760\pi$
$882$	3.08308	0.103813
$883$	51.3897	1.72940	0.864700	−	0.502289i	$-0.167509\pi$
$883$	51.3897	1.72940	0.864700	+	0.502289i	$0.167509\pi$
$884$	129.076	4.34128
$885$	11.3966	0.383093
$886$	−31.2211	−1.04889
$887$	10.3154	0.346358	0.173179	−	0.984890i	$-0.444596\pi$
$887$	10.3154	0.346358	0.173179	+	0.984890i	$0.444596\pi$
$888$	−39.4027	−1.32227
$889$	14.3974	0.482873
$890$	9.36024	0.313756
$891$	46.4937	1.55760
$892$	−124.610	−4.17224
$893$	2.90604	0.0972468
$894$	−67.8435	−2.26903
$895$	−3.72375	−0.124471
$896$	−45.4058	−1.51690
$897$	−21.7524	−0.726290
$898$	40.5274	1.35242
$899$	−1.89186	−0.0630972
$900$	−123.595	−4.11984
$901$	−36.6735	−1.22177
$902$	141.001	4.69480
$903$	53.2549	1.77221
$904$	54.4791	1.81195
$905$	2.33486	0.0776135
$906$	−174.523	−5.79812
$907$	4.55423	0.151221	0.0756103	−	0.997137i	$-0.475910\pi$
$907$	4.55423	0.151221	0.0756103	+	0.997137i	$0.475910\pi$
$908$	39.3690	1.30651
$909$	99.9047	3.31363
$910$	−10.9182	−0.361936
$911$	−9.09685	−0.301392	−0.150696	−	0.988580i	$-0.548151\pi$
$911$	−9.09685	−0.301392	−0.150696	+	0.988580i	$0.548151\pi$
$912$	106.267	3.51884
$913$	−15.9401	−0.527540
$914$	20.7677	0.686933
$915$	−6.41018	−0.211914
$916$	−16.2495	−0.536898
$917$	42.2119	1.39396
$918$	−121.925	−4.02413
$919$	−38.9281	−1.28412	−0.642060	−	0.766655i	$-0.721920\pi$
$919$	−38.9281	−1.28412	−0.642060	+	0.766655i	$0.721920\pi$
$920$	2.07841	0.0685233
$921$	55.5454	1.83028
$922$	10.3117	0.339597
$923$	46.4062	1.52748
$924$	169.005	5.55987
$925$	11.8221	0.388710
$926$	21.7204	0.713775
$927$	−69.6603	−2.28794
$928$	−2.00840	−0.0659289
$929$	−43.4053	−1.42408	−0.712041	−	0.702138i	$-0.752229\pi$
$929$	−43.4053	−1.42408	−0.712041	+	0.702138i	$0.752229\pi$
$930$	−4.20092	−0.137754
$931$	1.40806	0.0461474
$932$	13.4908	0.441904
$933$	−1.42993	−0.0468139
$934$	−85.7778	−2.80674
$935$	−8.33874	−0.272706
$936$	185.355	6.05853
$937$	−6.86575	−0.224294	−0.112147	−	0.993692i	$-0.535773\pi$
$937$	−6.86575	−0.224294	−0.112147	+	0.993692i	$0.535773\pi$
$938$	−70.8955	−2.31482
$939$	−62.7020	−2.04620
$940$	−0.531181	−0.0173252
$941$	36.9051	1.20307	0.601536	−	0.798846i	$-0.294556\pi$
$941$	36.9051	1.20307	0.601536	+	0.798846i	$0.294556\pi$
$942$	−110.021	−3.58468
$943$	14.0797	0.458499
$944$	−66.3127	−2.15830
$945$	6.98246	0.227140
$946$	−87.3521	−2.84006
$947$	−39.7543	−1.29184	−0.645921	−	0.763404i	$-0.723526\pi$
$947$	−39.7543	−1.29184	−0.645921	+	0.763404i	$0.723526\pi$
$948$	−65.7358	−2.13500
$949$	−14.5669	−0.472861
$950$	−83.3743	−2.70502
$951$	−15.6022	−0.505936
$952$	−77.3521	−2.50700
$953$	−35.8779	−1.16220	−0.581100	−	0.813832i	$-0.697378\pi$
$953$	−35.8779	−1.16220	−0.581100	+	0.813832i	$0.697378\pi$
$954$	−100.704	−3.26041
$955$	0.478688	0.0154900
$956$	−44.9402	−1.45347
$957$	−15.4660	−0.499944
$958$	−19.1562	−0.618910
$959$	10.8293	0.349695
$960$	4.80635	0.155124
$961$	−27.4209	−0.884544
$962$	−33.9026	−1.09306
$963$	43.4722	1.40087
$964$	108.109	3.48197
$965$	7.49470	0.241263
$966$	24.9268	0.802008
$967$	39.8533	1.28160	0.640798	−	0.767710i	$-0.278604\pi$
$967$	39.8533	1.28160	0.640798	+	0.767710i	$0.278604\pi$
$968$	−84.9551	−2.73056
$969$	−111.328	−3.57636
$970$	−8.65249	−0.277815
$971$	25.6014	0.821589	0.410795	−	0.911728i	$-0.365251\pi$
$971$	25.6014	0.821589	0.410795	+	0.911728i	$0.365251\pi$
$972$	−0.165002	−0.00529244
$973$	2.60645	0.0835590
$974$	12.6298	0.404685
$975$	−83.4093	−2.67124
$976$	37.2985	1.19389
$977$	3.51973	0.112606	0.0563031	−	0.998414i	$-0.482069\pi$
$977$	3.51973	0.112606	0.0563031	+	0.998414i	$0.482069\pi$
$978$	−174.080	−5.56647
$979$	−65.1943	−2.08362
$980$	−0.257373	−0.00822148
$981$	−23.3001	−0.743916
$982$	−10.8221	−0.345346
$983$	−56.7958	−1.81151	−0.905753	−	0.423806i	$-0.860694\pi$
$983$	−56.7958	−1.81151	−0.905753	+	0.423806i	$0.860694\pi$
$984$	−179.942	−5.73633
$985$	−1.94053	−0.0618304
$986$	13.5357	0.431066
$987$	−3.33154	−0.106044
$988$	161.873	5.14988
$989$	−8.72262	−0.277363
$990$	−22.8978	−0.727740
$991$	−53.9060	−1.71238	−0.856190	−	0.516660i	$-0.827175\pi$
$991$	−53.9060	−1.71238	−0.856190	+	0.516660i	$0.827175\pi$
$992$	3.79961	0.120638
$993$	−15.9763	−0.506991
$994$	−53.1786	−1.68672
$995$	4.66772	0.147977
$996$	38.8987	1.23255
$997$	−21.7939	−0.690220	−0.345110	−	0.938562i	$-0.612158\pi$
$997$	−21.7939	−0.690220	−0.345110	+	0.938562i	$0.612158\pi$
$998$	29.8128	0.943707
$999$	21.6815	0.685972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.9	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.9	✓	98	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48847 q^{2} -3.00036 q^{3} +4.19251 q^{4} +0.297405 q^{5} +7.46633 q^{6} -2.60645 q^{7} -5.45599 q^{8} +6.00219 q^{9} +O(q^{10})\)	\(q-2.48847 q^{2} -3.00036 q^{3} +4.19251 q^{4} +0.297405 q^{5} +7.46633 q^{6} -2.60645 q^{7} -5.45599 q^{8} +6.00219 q^{9} -0.740084 q^{10} +5.15470 q^{11} -12.5790 q^{12} -5.66007 q^{13} +6.48609 q^{14} -0.892322 q^{15} +5.19209 q^{16} -5.43937 q^{17} -14.9363 q^{18} -6.82150 q^{19} +1.24687 q^{20} +7.82030 q^{21} -12.8273 q^{22} -1.28089 q^{23} +16.3700 q^{24} -4.91155 q^{25} +14.0849 q^{26} -9.00765 q^{27} -10.9276 q^{28} +1.00000 q^{29} +2.22052 q^{30} -1.89186 q^{31} -2.00840 q^{32} -15.4660 q^{33} +13.5357 q^{34} -0.775170 q^{35} +25.1642 q^{36} -2.40701 q^{37} +16.9751 q^{38} +16.9823 q^{39} -1.62264 q^{40} -10.9922 q^{41} -19.4606 q^{42} +6.80983 q^{43} +21.6111 q^{44} +1.78508 q^{45} +3.18745 q^{46} -0.426011 q^{47} -15.5782 q^{48} -0.206415 q^{49} +12.2223 q^{50} +16.3201 q^{51} -23.7299 q^{52} +6.74224 q^{53} +22.4153 q^{54} +1.53303 q^{55} +14.2208 q^{56} +20.4670 q^{57} -2.48847 q^{58} -12.7719 q^{59} -3.74107 q^{60} +7.18371 q^{61} +4.70785 q^{62} -15.6444 q^{63} -5.38633 q^{64} -1.68333 q^{65} +38.4867 q^{66} -10.9304 q^{67} -22.8046 q^{68} +3.84313 q^{69} +1.92899 q^{70} -8.19888 q^{71} -32.7479 q^{72} +2.57362 q^{73} +5.98978 q^{74} +14.7364 q^{75} -28.5992 q^{76} -13.4355 q^{77} -42.2600 q^{78} +5.22582 q^{79} +1.54415 q^{80} +9.01967 q^{81} +27.3538 q^{82} -3.09234 q^{83} +32.7867 q^{84} -1.61769 q^{85} -16.9461 q^{86} -3.00036 q^{87} -28.1240 q^{88} -12.6475 q^{89} -4.44212 q^{90} +14.7527 q^{91} -5.37012 q^{92} +5.67628 q^{93} +1.06012 q^{94} -2.02875 q^{95} +6.02592 q^{96} +11.6912 q^{97} +0.513659 q^{98} +30.9395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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