LMFDB - Embedded newform 4031.2.a.d.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.58392 q^{2} +3.19893 q^{3} +4.67665 q^{4} +1.67511 q^{5} -8.26577 q^{6} +1.22424 q^{7} -6.91625 q^{8} +7.23312 q^{9} +O(q^{10})$	\(q-2.58392 q^{2} +3.19893 q^{3} +4.67665 q^{4} +1.67511 q^{5} -8.26577 q^{6} +1.22424 q^{7} -6.91625 q^{8} +7.23312 q^{9} -4.32836 q^{10} -1.92574 q^{11} +14.9603 q^{12} +4.52264 q^{13} -3.16333 q^{14} +5.35857 q^{15} +8.51775 q^{16} +4.43128 q^{17} -18.6898 q^{18} -6.85021 q^{19} +7.83393 q^{20} +3.91624 q^{21} +4.97596 q^{22} -5.70550 q^{23} -22.1246 q^{24} -2.19399 q^{25} -11.6861 q^{26} +13.5415 q^{27} +5.72532 q^{28} +1.00000 q^{29} -13.8461 q^{30} +6.25954 q^{31} -8.17670 q^{32} -6.16029 q^{33} -11.4501 q^{34} +2.05074 q^{35} +33.8268 q^{36} +5.20598 q^{37} +17.7004 q^{38} +14.4676 q^{39} -11.5855 q^{40} -0.0792331 q^{41} -10.1193 q^{42} +12.0281 q^{43} -9.00600 q^{44} +12.1163 q^{45} +14.7426 q^{46} -7.55184 q^{47} +27.2477 q^{48} -5.50125 q^{49} +5.66910 q^{50} +14.1753 q^{51} +21.1508 q^{52} +9.89110 q^{53} -34.9900 q^{54} -3.22583 q^{55} -8.46713 q^{56} -21.9133 q^{57} -2.58392 q^{58} -10.2574 q^{59} +25.0601 q^{60} -1.20165 q^{61} -16.1742 q^{62} +8.85505 q^{63} +4.09245 q^{64} +7.57594 q^{65} +15.9177 q^{66} -2.37696 q^{67} +20.7235 q^{68} -18.2515 q^{69} -5.29894 q^{70} -0.597784 q^{71} -50.0261 q^{72} +2.24157 q^{73} -13.4518 q^{74} -7.01841 q^{75} -32.0360 q^{76} -2.35756 q^{77} -37.3831 q^{78} +11.9381 q^{79} +14.2682 q^{80} +21.6187 q^{81} +0.204732 q^{82} +8.22554 q^{83} +18.3149 q^{84} +7.42289 q^{85} -31.0797 q^{86} +3.19893 q^{87} +13.3189 q^{88} -2.06207 q^{89} -31.3076 q^{90} +5.53678 q^{91} -26.6826 q^{92} +20.0238 q^{93} +19.5134 q^{94} -11.4749 q^{95} -26.1567 q^{96} +15.3363 q^{97} +14.2148 q^{98} -13.9291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58392	−1.82711	−0.913554	−	0.406717i	$-0.866673\pi$
$2$	−2.58392	−1.82711	−0.913554	+	0.406717i	$0.866673\pi$
$3$	3.19893	1.84690	0.923450	−	0.383718i	$-0.125357\pi$
$3$	3.19893	1.84690	0.923450	+	0.383718i	$0.125357\pi$
$4$	4.67665	2.33832
$5$	1.67511	0.749134	0.374567	−	0.927200i	$-0.377791\pi$
$5$	1.67511	0.749134	0.374567	+	0.927200i	$0.377791\pi$
$6$	−8.26577	−3.37449
$7$	1.22424	0.462718	0.231359	−	0.972868i	$-0.425683\pi$
$7$	1.22424	0.462718	0.231359	+	0.972868i	$0.425683\pi$
$8$	−6.91625	−2.44526
$9$	7.23312	2.41104
$10$	−4.32836	−1.36875
$11$	−1.92574	−0.580632	−0.290316	−	0.956931i	$-0.593760\pi$
$11$	−1.92574	−0.580632	−0.290316	+	0.956931i	$0.593760\pi$
$12$	14.9603	4.31865
$13$	4.52264	1.25435	0.627177	−	0.778877i	$-0.284210\pi$
$13$	4.52264	1.25435	0.627177	+	0.778877i	$0.284210\pi$
$14$	−3.16333	−0.845435
$15$	5.35857	1.38358
$16$	8.51775	2.12944
$17$	4.43128	1.07474	0.537371	−	0.843346i	$-0.319417\pi$
$17$	4.43128	1.07474	0.537371	+	0.843346i	$0.319417\pi$
$18$	−18.6898	−4.40523
$19$	−6.85021	−1.57155	−0.785773	−	0.618515i	$-0.787735\pi$
$19$	−6.85021	−1.57155	−0.785773	+	0.618515i	$0.787735\pi$
$20$	7.83393	1.75172
$21$	3.91624	0.854594
$22$	4.97596	1.06088
$23$	−5.70550	−1.18968	−0.594839	−	0.803845i	$-0.702784\pi$
$23$	−5.70550	−1.18968	−0.594839	+	0.803845i	$0.702784\pi$
$24$	−22.1246	−4.51616
$25$	−2.19399	−0.438798
$26$	−11.6861	−2.29184
$27$	13.5415	2.60605
$28$	5.72532	1.08198
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−13.8461	−2.52794
$31$	6.25954	1.12425	0.562123	−	0.827054i	$-0.309985\pi$
$31$	6.25954	1.12425	0.562123	+	0.827054i	$0.309985\pi$
$32$	−8.17670	−1.44545
$33$	−6.16029	−1.07237
$34$	−11.4501	−1.96367
$35$	2.05074	0.346638
$36$	33.8268	5.63780
$37$	5.20598	0.855858	0.427929	−	0.903812i	$-0.359243\pi$
$37$	5.20598	0.855858	0.427929	+	0.903812i	$0.359243\pi$
$38$	17.7004	2.87139
$39$	14.4676	2.31667
$40$	−11.5855	−1.83183
$41$	−0.0792331	−0.0123741	−0.00618706	−	0.999981i	$-0.501969\pi$
$41$	−0.0792331	−0.0123741	−0.00618706	+	0.999981i	$0.501969\pi$
$42$	−10.1193	−1.56144
$43$	12.0281	1.83427	0.917136	−	0.398576i	$-0.130495\pi$
$43$	12.0281	1.83427	0.917136	+	0.398576i	$0.130495\pi$
$44$	−9.00600	−1.35771
$45$	12.1163	1.80619
$46$	14.7426	2.17367
$47$	−7.55184	−1.10155	−0.550774	−	0.834654i	$-0.685668\pi$
$47$	−7.55184	−1.10155	−0.550774	+	0.834654i	$0.685668\pi$
$48$	27.2477	3.93286
$49$	−5.50125	−0.785892
$50$	5.66910	0.801732
$51$	14.1753	1.98494
$52$	21.1508	2.93309
$53$	9.89110	1.35865	0.679323	−	0.733839i	$-0.262273\pi$
$53$	9.89110	1.35865	0.679323	+	0.733839i	$0.262273\pi$
$54$	−34.9900	−4.76154
$55$	−3.22583	−0.434971
$56$	−8.46713	−1.13147
$57$	−21.9133	−2.90249
$58$	−2.58392	−0.339286
$59$	−10.2574	−1.33541	−0.667703	−	0.744428i	$-0.732722\pi$
$59$	−10.2574	−1.33541	−0.667703	+	0.744428i	$0.732722\pi$
$60$	25.0601	3.23525
$61$	−1.20165	−0.153856	−0.0769279	−	0.997037i	$-0.524511\pi$
$61$	−1.20165	−0.153856	−0.0769279	+	0.997037i	$0.524511\pi$
$62$	−16.1742	−2.05412
$63$	8.85505	1.11563
$64$	4.09245	0.511556
$65$	7.57594	0.939680
$66$	15.9177	1.95934
$67$	−2.37696	−0.290391	−0.145196	−	0.989403i	$-0.546381\pi$
$67$	−2.37696	−0.290391	−0.145196	+	0.989403i	$0.546381\pi$
$68$	20.7235	2.51310
$69$	−18.2515	−2.19722
$70$	−5.29894	−0.633345
$71$	−0.597784	−0.0709439	−0.0354720	−	0.999371i	$-0.511293\pi$
$71$	−0.597784	−0.0709439	−0.0354720	+	0.999371i	$0.511293\pi$
$72$	−50.0261	−5.89564
$73$	2.24157	0.262356	0.131178	−	0.991359i	$-0.458124\pi$
$73$	2.24157	0.262356	0.131178	+	0.991359i	$0.458124\pi$
$74$	−13.4518	−1.56374
$75$	−7.01841	−0.810416
$76$	−32.0360	−3.67479
$77$	−2.35756	−0.268669
$78$	−37.3831	−4.23280
$79$	11.9381	1.34314	0.671570	−	0.740941i	$-0.265620\pi$
$79$	11.9381	1.34314	0.671570	+	0.740941i	$0.265620\pi$
$80$	14.2682	1.59524
$81$	21.6187	2.40208
$82$	0.204732	0.0226089
$83$	8.22554	0.902871	0.451435	−	0.892304i	$-0.350912\pi$
$83$	8.22554	0.902871	0.451435	+	0.892304i	$0.350912\pi$
$84$	18.3149	1.99832
$85$	7.42289	0.805126
$86$	−31.0797	−3.35141
$87$	3.19893	0.342961
$88$	13.3189	1.41980
$89$	−2.06207	−0.218579	−0.109289	−	0.994010i	$-0.534857\pi$
$89$	−2.06207	−0.218579	−0.109289	+	0.994010i	$0.534857\pi$
$90$	−31.3076	−3.30011
$91$	5.53678	0.580412
$92$	−26.6826	−2.78186
$93$	20.0238	2.07637
$94$	19.5134	2.01265
$95$	−11.4749	−1.17730
$96$	−26.1567	−2.66960
$97$	15.3363	1.55717	0.778583	−	0.627542i	$-0.215939\pi$
$97$	15.3363	1.55717	0.778583	+	0.627542i	$0.215939\pi$
$98$	14.2148	1.43591
$99$	−13.9291	−1.39993
$100$	−10.2605	−1.02605
$101$	11.3009	1.12448	0.562242	−	0.826973i	$-0.309939\pi$
$101$	11.3009	1.12448	0.562242	+	0.826973i	$0.309939\pi$
$102$	−36.6279	−3.62670
$103$	−6.24169	−0.615012	−0.307506	−	0.951546i	$-0.599494\pi$
$103$	−6.24169	−0.615012	−0.307506	+	0.951546i	$0.599494\pi$
$104$	−31.2797	−3.06723
$105$	6.56015	0.640205
$106$	−25.5578	−2.48239
$107$	16.6516	1.60977	0.804884	−	0.593433i	$-0.202228\pi$
$107$	16.6516	1.60977	0.804884	+	0.593433i	$0.202228\pi$
$108$	63.3286	6.09380
$109$	−0.147117	−0.0140912	−0.00704561	−	0.999975i	$-0.502243\pi$
$109$	−0.147117	−0.0140912	−0.00704561	+	0.999975i	$0.502243\pi$
$110$	8.33530	0.794740
$111$	16.6535	1.58068
$112$	10.4277	0.985329
$113$	−14.6953	−1.38242	−0.691208	−	0.722656i	$-0.742921\pi$
$113$	−14.6953	−1.38242	−0.691208	+	0.722656i	$0.742921\pi$
$114$	56.6223	5.30316
$115$	−9.55737	−0.891229
$116$	4.67665	0.434216
$117$	32.7128	3.02430
$118$	26.5044	2.43993
$119$	5.42493	0.497302
$120$	−37.0612	−3.38321
$121$	−7.29153	−0.662866
$122$	3.10498	0.281111
$123$	−0.253461	−0.0228538
$124$	29.2737	2.62885
$125$	−12.0508	−1.07785
$126$	−22.8808	−2.03838
$127$	16.5982	1.47285	0.736427	−	0.676516i	$-0.236511\pi$
$127$	16.5982	1.47285	0.736427	+	0.676516i	$0.236511\pi$
$128$	5.77884	0.510782
$129$	38.4771	3.38772
$130$	−19.5756	−1.71690
$131$	−1.17086	−0.102299	−0.0511493	−	0.998691i	$-0.516288\pi$
$131$	−1.17086	−0.102299	−0.0511493	+	0.998691i	$0.516288\pi$
$132$	−28.8095	−2.50755
$133$	−8.38628	−0.727182
$134$	6.14187	0.530577
$135$	22.6835	1.95228
$136$	−30.6478	−2.62803
$137$	−23.2728	−1.98833	−0.994166	−	0.107861i	$-0.965600\pi$
$137$	−23.2728	−1.98833	−0.994166	+	0.107861i	$0.965600\pi$
$138$	47.1604	4.01456
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	9.59057	0.810551
$141$	−24.1578	−2.03445
$142$	1.54463	0.129622
$143$	−8.70942	−0.728318
$144$	61.6100	5.13417
$145$	1.67511	0.139111
$146$	−5.79204	−0.479353
$147$	−17.5981	−1.45146
$148$	24.3465	2.00127
$149$	6.59371	0.540177	0.270089	−	0.962835i	$-0.412947\pi$
$149$	6.59371	0.540177	0.270089	+	0.962835i	$0.412947\pi$
$150$	18.1350	1.48072
$151$	−2.70779	−0.220357	−0.110178	−	0.993912i	$-0.535142\pi$
$151$	−2.70779	−0.220357	−0.110178	+	0.993912i	$0.535142\pi$
$152$	47.3778	3.84285
$153$	32.0520	2.59125
$154$	6.09175	0.490887
$155$	10.4854	0.842211
$156$	67.6598	5.41712
$157$	19.0637	1.52145	0.760724	−	0.649076i	$-0.224844\pi$
$157$	19.0637	1.52145	0.760724	+	0.649076i	$0.224844\pi$
$158$	−30.8471	−2.45406
$159$	31.6409	2.50929
$160$	−13.6969	−1.08284
$161$	−6.98488	−0.550486
$162$	−55.8611	−4.38886
$163$	8.03182	0.629101	0.314550	−	0.949241i	$-0.398146\pi$
$163$	8.03182	0.629101	0.314550	+	0.949241i	$0.398146\pi$
$164$	−0.370545	−0.0289347
$165$	−10.3192	−0.803349
$166$	−21.2542	−1.64964
$167$	7.39827	0.572496	0.286248	−	0.958156i	$-0.407592\pi$
$167$	7.39827	0.572496	0.286248	+	0.958156i	$0.407592\pi$
$168$	−27.0857	−2.08971
$169$	7.45426	0.573405
$170$	−19.1802	−1.47105
$171$	−49.5484	−3.78906
$172$	56.2513	4.28912
$173$	3.90986	0.297261	0.148631	−	0.988893i	$-0.452513\pi$
$173$	3.90986	0.297261	0.148631	+	0.988893i	$0.452513\pi$
$174$	−8.26577	−0.626627
$175$	−2.68596	−0.203040
$176$	−16.4030	−1.23642
$177$	−32.8128	−2.46636
$178$	5.32822	0.399367
$179$	14.2026	1.06155	0.530775	−	0.847513i	$-0.321901\pi$
$179$	14.2026	1.06155	0.530775	+	0.847513i	$0.321901\pi$
$180$	56.6638	4.22347
$181$	−6.65818	−0.494899	−0.247449	−	0.968901i	$-0.579592\pi$
$181$	−6.65818	−0.494899	−0.247449	+	0.968901i	$0.579592\pi$
$182$	−14.3066	−1.06048
$183$	−3.84400	−0.284156
$184$	39.4607	2.90908
$185$	8.72061	0.641152
$186$	−51.7399	−3.79375
$187$	−8.53348	−0.624030
$188$	−35.3173	−2.57578
$189$	16.5779	1.20587
$190$	29.6502	2.15105
$191$	−18.6559	−1.34989	−0.674946	−	0.737867i	$-0.735833\pi$
$191$	−18.6559	−1.34989	−0.674946	+	0.737867i	$0.735833\pi$
$192$	13.0914	0.944793
$193$	−2.67677	−0.192678	−0.0963391	−	0.995349i	$-0.530713\pi$
$193$	−2.67677	−0.192678	−0.0963391	+	0.995349i	$0.530713\pi$
$194$	−39.6278	−2.84511
$195$	24.2349	1.73549
$196$	−25.7274	−1.83767
$197$	−6.89057	−0.490933	−0.245466	−	0.969405i	$-0.578941\pi$
$197$	−6.89057	−0.490933	−0.245466	+	0.969405i	$0.578941\pi$
$198$	35.9917	2.55782
$199$	−8.19991	−0.581276	−0.290638	−	0.956833i	$-0.593868\pi$
$199$	−8.19991	−0.581276	−0.290638	+	0.956833i	$0.593868\pi$
$200$	15.1742	1.07298
$201$	−7.60371	−0.536324
$202$	−29.2007	−2.05455
$203$	1.22424	0.0859245
$204$	66.2930	4.64144
$205$	−0.132724	−0.00926988
$206$	16.1280	1.12369
$207$	−41.2686	−2.86837
$208$	38.5227	2.67107
$209$	13.1917	0.912490
$210$	−16.9509	−1.16972
$211$	13.1562	0.905708	0.452854	−	0.891585i	$-0.350406\pi$
$211$	13.1562	0.905708	0.452854	+	0.891585i	$0.350406\pi$
$212$	46.2572	3.17696
$213$	−1.91227	−0.131026
$214$	−43.0263	−2.94122
$215$	20.1485	1.37411
$216$	−93.6561	−6.37249
$217$	7.66315	0.520209
$218$	0.380138	0.0257462
$219$	7.17062	0.484545
$220$	−15.0861	−1.01710
$221$	20.0411	1.34811
$222$	−43.0314	−2.88808
$223$	4.95570	0.331858	0.165929	−	0.986138i	$-0.446938\pi$
$223$	4.95570	0.331858	0.165929	+	0.986138i	$0.446938\pi$
$224$	−10.0102	−0.668836
$225$	−15.8694	−1.05796
$226$	37.9715	2.52582
$227$	−21.2779	−1.41227	−0.706133	−	0.708079i	$-0.749562\pi$
$227$	−21.2779	−1.41227	−0.706133	+	0.708079i	$0.749562\pi$
$228$	−102.481	−6.78697
$229$	6.76399	0.446977	0.223488	−	0.974707i	$-0.428256\pi$
$229$	6.76399	0.446977	0.223488	+	0.974707i	$0.428256\pi$
$230$	24.6955	1.62837
$231$	−7.54165	−0.496204
$232$	−6.91625	−0.454074
$233$	−27.0977	−1.77523	−0.887613	−	0.460590i	$-0.847638\pi$
$233$	−27.0977	−1.77523	−0.887613	+	0.460590i	$0.847638\pi$
$234$	−84.5273	−5.52573
$235$	−12.6502	−0.825208
$236$	−47.9705	−3.12261
$237$	38.1891	2.48065
$238$	−14.0176	−0.908625
$239$	−25.9845	−1.68080	−0.840398	−	0.541969i	$-0.817679\pi$
$239$	−25.9845	−1.68080	−0.840398	+	0.541969i	$0.817679\pi$
$240$	45.6430	2.94624
$241$	−6.73931	−0.434117	−0.217058	−	0.976159i	$-0.569646\pi$
$241$	−6.73931	−0.434117	−0.217058	+	0.976159i	$0.569646\pi$
$242$	18.8407	1.21113
$243$	28.5323	1.83035
$244$	−5.61971	−0.359765
$245$	−9.21522	−0.588739
$246$	0.654923	0.0417563
$247$	−30.9810	−1.97128
$248$	−43.2925	−2.74908
$249$	26.3129	1.66751
$250$	31.1382	1.96935
$251$	−17.6695	−1.11529	−0.557644	−	0.830080i	$-0.688295\pi$
$251$	−17.6695	−1.11529	−0.557644	+	0.830080i	$0.688295\pi$
$252$	41.4120	2.60871
$253$	10.9873	0.690766
$254$	−42.8885	−2.69107
$255$	23.7453	1.48699
$256$	−23.1170	−1.44481
$257$	6.40721	0.399671	0.199836	−	0.979829i	$-0.435959\pi$
$257$	6.40721	0.399671	0.199836	+	0.979829i	$0.435959\pi$
$258$	−99.4217	−6.18972
$259$	6.37335	0.396021
$260$	35.4300	2.19728
$261$	7.23312	0.447719
$262$	3.02541	0.186910
$263$	−26.5994	−1.64019	−0.820096	−	0.572227i	$-0.806080\pi$
$263$	−26.5994	−1.64019	−0.820096	+	0.572227i	$0.806080\pi$
$264$	42.6062	2.62223
$265$	16.5687	1.01781
$266$	21.6695	1.32864
$267$	−6.59640	−0.403693
$268$	−11.1162	−0.679030
$269$	−3.07699	−0.187607	−0.0938037	−	0.995591i	$-0.529903\pi$
$269$	−3.07699	−0.187607	−0.0938037	+	0.995591i	$0.529903\pi$
$270$	−58.6123	−3.56703
$271$	−0.998848	−0.0606757	−0.0303378	−	0.999540i	$-0.509658\pi$
$271$	−0.998848	−0.0606757	−0.0303378	+	0.999540i	$0.509658\pi$
$272$	37.7445	2.28860
$273$	17.7117	1.07196
$274$	60.1352	3.63290
$275$	4.22505	0.254780
$276$	−85.3557	−5.13781
$277$	14.4822	0.870153	0.435076	−	0.900394i	$-0.356721\pi$
$277$	14.4822	0.870153	0.435076	+	0.900394i	$0.356721\pi$
$278$	2.58392	0.154973
$279$	45.2760	2.71060
$280$	−14.1834	−0.847621
$281$	3.32763	0.198510	0.0992549	−	0.995062i	$-0.468354\pi$
$281$	3.32763	0.198510	0.0992549	+	0.995062i	$0.468354\pi$
$282$	62.4218	3.71716
$283$	−15.0886	−0.896927	−0.448464	−	0.893801i	$-0.648029\pi$
$283$	−15.0886	−0.896927	−0.448464	+	0.893801i	$0.648029\pi$
$284$	−2.79563	−0.165890
$285$	−36.7073	−2.17435
$286$	22.5045	1.33072
$287$	−0.0970000	−0.00572573
$288$	−59.1431	−3.48504
$289$	2.63620	0.155071
$290$	−4.32836	−0.254170
$291$	49.0597	2.87593
$292$	10.4830	0.613474
$293$	31.1345	1.81890	0.909450	−	0.415814i	$-0.136503\pi$
$293$	31.1345	1.81890	0.909450	+	0.415814i	$0.136503\pi$
$294$	45.4720	2.65198
$295$	−17.1824	−1.00040
$296$	−36.0059	−2.09280
$297$	−26.0773	−1.51316
$298$	−17.0376	−0.986963
$299$	−25.8039	−1.49228
$300$	−32.8227	−1.89502
$301$	14.7253	0.848750
$302$	6.99671	0.402615
$303$	36.1508	2.07681
$304$	−58.3484	−3.34651
$305$	−2.01291	−0.115259
$306$	−82.8198	−4.73449
$307$	−28.1595	−1.60715	−0.803574	−	0.595205i	$-0.797071\pi$
$307$	−28.1595	−1.60715	−0.803574	+	0.595205i	$0.797071\pi$
$308$	−11.0255	−0.628235
$309$	−19.9667	−1.13587
$310$	−27.0936	−1.53881
$311$	−26.2669	−1.48946	−0.744729	−	0.667367i	$-0.767421\pi$
$311$	−26.2669	−1.48946	−0.744729	+	0.667367i	$0.767421\pi$
$312$	−100.061	−5.66487
$313$	−1.53123	−0.0865502	−0.0432751	−	0.999063i	$-0.513779\pi$
$313$	−1.53123	−0.0865502	−0.0432751	+	0.999063i	$0.513779\pi$
$314$	−49.2590	−2.77985
$315$	14.8332	0.835758
$316$	55.8303	3.14070
$317$	17.6521	0.991442	0.495721	−	0.868482i	$-0.334904\pi$
$317$	17.6521	0.991442	0.495721	+	0.868482i	$0.334904\pi$
$318$	−81.7576	−4.58474
$319$	−1.92574	−0.107821
$320$	6.85532	0.383224
$321$	53.2671	2.97308
$322$	18.0484	1.00580
$323$	−30.3552	−1.68901
$324$	101.103	5.61684
$325$	−9.92263	−0.550408
$326$	−20.7536	−1.14943
$327$	−0.470615	−0.0260251
$328$	0.547996	0.0302580
$329$	−9.24523	−0.509706
$330$	26.6640	1.46780
$331$	−0.404250	−0.0222196	−0.0111098	−	0.999938i	$-0.503536\pi$
$331$	−0.404250	−0.0222196	−0.0111098	+	0.999938i	$0.503536\pi$
$332$	38.4680	2.11121
$333$	37.6555	2.06351
$334$	−19.1166	−1.04601
$335$	−3.98168	−0.217542
$336$	33.3576	1.81980
$337$	9.69168	0.527939	0.263970	−	0.964531i	$-0.414968\pi$
$337$	9.69168	0.527939	0.263970	+	0.964531i	$0.414968\pi$
$338$	−19.2612	−1.04767
$339$	−47.0091	−2.55318
$340$	34.7143	1.88265
$341$	−12.0542	−0.652773
$342$	128.029	6.92303
$343$	−15.3045	−0.826364
$344$	−83.1895	−4.48528
$345$	−30.5733	−1.64601
$346$	−10.1028	−0.543129
$347$	24.7146	1.32675	0.663375	−	0.748287i	$-0.269123\pi$
$347$	24.7146	1.32675	0.663375	+	0.748287i	$0.269123\pi$
$348$	14.9603	0.801954
$349$	−21.1175	−1.13040	−0.565198	−	0.824955i	$-0.691200\pi$
$349$	−21.1175	−1.13040	−0.565198	+	0.824955i	$0.691200\pi$
$350$	6.94032	0.370975
$351$	61.2431	3.26891
$352$	15.7462	0.839275
$353$	13.6589	0.726989	0.363495	−	0.931596i	$-0.381583\pi$
$353$	13.6589	0.726989	0.363495	+	0.931596i	$0.381583\pi$
$354$	84.7857	4.50631
$355$	−1.00136	−0.0531465
$356$	−9.64356	−0.511108
$357$	17.3539	0.918468
$358$	−36.6983	−1.93957
$359$	−31.1677	−1.64497	−0.822485	−	0.568787i	$-0.807413\pi$
$359$	−31.1677	−1.64497	−0.822485	+	0.568787i	$0.807413\pi$
$360$	−83.7995	−4.41662
$361$	27.9254	1.46976
$362$	17.2042	0.904234
$363$	−23.3251	−1.22425
$364$	25.8936	1.35719
$365$	3.75489	0.196540
$366$	9.93258	0.519185
$367$	−19.4791	−1.01680	−0.508401	−	0.861121i	$-0.669763\pi$
$367$	−19.4791	−1.01680	−0.508401	+	0.861121i	$0.669763\pi$
$368$	−48.5980	−2.53335
$369$	−0.573103	−0.0298345
$370$	−22.5334	−1.17145
$371$	12.1090	0.628670
$372$	93.6443	4.85523
$373$	−18.9619	−0.981808	−0.490904	−	0.871214i	$-0.663333\pi$
$373$	−18.9619	−0.981808	−0.490904	+	0.871214i	$0.663333\pi$
$374$	22.0498	1.14017
$375$	−38.5495	−1.99069
$376$	52.2304	2.69358
$377$	4.52264	0.232928
$378$	−42.8361	−2.20325
$379$	6.66234	0.342221	0.171111	−	0.985252i	$-0.445264\pi$
$379$	6.66234	0.342221	0.171111	+	0.985252i	$0.445264\pi$
$380$	−53.6641	−2.75291
$381$	53.0965	2.72022
$382$	48.2053	2.46640
$383$	−33.2311	−1.69803	−0.849014	−	0.528370i	$-0.822804\pi$
$383$	−33.2311	−1.69803	−0.849014	+	0.528370i	$0.822804\pi$
$384$	18.4861	0.943364
$385$	−3.94918	−0.201269
$386$	6.91656	0.352044
$387$	87.0009	4.42250
$388$	71.7225	3.64116
$389$	29.2147	1.48125	0.740623	−	0.671921i	$-0.234530\pi$
$389$	29.2147	1.48125	0.740623	+	0.671921i	$0.234530\pi$
$390$	−62.6210	−3.17094
$391$	−25.2826	−1.27860
$392$	38.0480	1.92171
$393$	−3.74549	−0.188935
$394$	17.8047	0.896987
$395$	19.9977	1.00619
$396$	−65.1416	−3.27349
$397$	−10.7440	−0.539227	−0.269614	−	0.962969i	$-0.586896\pi$
$397$	−10.7440	−0.539227	−0.269614	+	0.962969i	$0.586896\pi$
$398$	21.1879	1.06206
$399$	−26.8271	−1.34303
$400$	−18.6879	−0.934394
$401$	−23.5581	−1.17643	−0.588217	−	0.808703i	$-0.700170\pi$
$401$	−23.5581	−1.17643	−0.588217	+	0.808703i	$0.700170\pi$
$402$	19.6474	0.979922
$403$	28.3096	1.41020
$404$	52.8505	2.62941
$405$	36.2138	1.79948
$406$	−3.16333	−0.156993
$407$	−10.0254	−0.496938
$408$	−98.0401	−4.85371
$409$	−17.0281	−0.841986	−0.420993	−	0.907064i	$-0.638318\pi$
$409$	−17.0281	−0.841986	−0.420993	+	0.907064i	$0.638318\pi$
$410$	0.342950	0.0169371
$411$	−74.4481	−3.67225
$412$	−29.1902	−1.43810
$413$	−12.5575	−0.617916
$414$	106.635	5.24081
$415$	13.7787	0.676371
$416$	−36.9803	−1.81311
$417$	−3.19893	−0.156652
$418$	−34.0864	−1.66722
$419$	−26.0015	−1.27026	−0.635128	−	0.772407i	$-0.719053\pi$
$419$	−26.0015	−1.27026	−0.635128	+	0.772407i	$0.719053\pi$
$420$	30.6795	1.49701
$421$	−7.98511	−0.389171	−0.194585	−	0.980886i	$-0.562336\pi$
$421$	−7.98511	−0.389171	−0.194585	+	0.980886i	$0.562336\pi$
$422$	−33.9945	−1.65483
$423$	−54.6234	−2.65588
$424$	−68.4093	−3.32225
$425$	−9.72218	−0.471595
$426$	4.94115	0.239399
$427$	−1.47111	−0.0711918
$428$	77.8735	3.76416
$429$	−27.8608	−1.34513
$430$	−52.0621	−2.51066
$431$	−16.8541	−0.811835	−0.405917	−	0.913910i	$-0.633048\pi$
$431$	−16.8541	−0.811835	−0.405917	+	0.913910i	$0.633048\pi$
$432$	115.343	5.54943
$433$	14.7962	0.711058	0.355529	−	0.934665i	$-0.384301\pi$
$433$	14.7962	0.711058	0.355529	+	0.934665i	$0.384301\pi$
$434$	−19.8010	−0.950477
$435$	5.35857	0.256924
$436$	−0.688013	−0.0329498
$437$	39.0839	1.86964
$438$	−18.5283	−0.885317
$439$	−32.6499	−1.55829	−0.779147	−	0.626841i	$-0.784347\pi$
$439$	−32.6499	−1.55829	−0.779147	+	0.626841i	$0.784347\pi$
$440$	22.3107	1.06362
$441$	−39.7912	−1.89482
$442$	−51.7845	−2.46314
$443$	22.4326	1.06581	0.532903	−	0.846176i	$-0.321101\pi$
$443$	22.4326	1.06581	0.532903	+	0.846176i	$0.321101\pi$
$444$	77.8828	3.69615
$445$	−3.45420	−0.163745
$446$	−12.8051	−0.606341
$447$	21.0928	0.997654
$448$	5.01012	0.236706
$449$	24.7699	1.16896	0.584481	−	0.811407i	$-0.301298\pi$
$449$	24.7699	1.16896	0.584481	+	0.811407i	$0.301298\pi$
$450$	41.0053	1.93301
$451$	0.152582	0.00718481
$452$	−68.7247	−3.23254
$453$	−8.66201	−0.406977
$454$	54.9805	2.58036
$455$	9.27474	0.434806
$456$	151.558	7.09736
$457$	−26.4211	−1.23593	−0.617963	−	0.786207i	$-0.712042\pi$
$457$	−26.4211	−1.23593	−0.617963	+	0.786207i	$0.712042\pi$
$458$	−17.4776	−0.816675
$459$	60.0059	2.80084
$460$	−44.6965	−2.08398
$461$	5.39383	0.251216	0.125608	−	0.992080i	$-0.459912\pi$
$461$	5.39383	0.251216	0.125608	+	0.992080i	$0.459912\pi$
$462$	19.4870	0.906619
$463$	10.9662	0.509642	0.254821	−	0.966988i	$-0.417983\pi$
$463$	10.9662	0.509642	0.254821	+	0.966988i	$0.417983\pi$
$464$	8.51775	0.395427
$465$	33.5421	1.55548
$466$	70.0182	3.24353
$467$	−16.5653	−0.766550	−0.383275	−	0.923634i	$-0.625204\pi$
$467$	−16.5653	−0.766550	−0.383275	+	0.923634i	$0.625204\pi$
$468$	152.986	7.07180
$469$	−2.90996	−0.134369
$470$	32.6871	1.50774
$471$	60.9833	2.80996
$472$	70.9431	3.26542
$473$	−23.1630	−1.06504
$474$	−98.6775	−4.53241
$475$	15.0293	0.689592
$476$	25.3705	1.16285
$477$	71.5435	3.27575
$478$	67.1419	3.07100
$479$	13.6963	0.625801	0.312900	−	0.949786i	$-0.398699\pi$
$479$	13.6963	0.625801	0.312900	+	0.949786i	$0.398699\pi$
$480$	−43.8154	−1.99989
$481$	23.5448	1.07355
$482$	17.4138	0.793178
$483$	−22.3441	−1.01669
$484$	−34.0999	−1.55000
$485$	25.6901	1.16653
$486$	−73.7253	−3.34425
$487$	5.51487	0.249903	0.124951	−	0.992163i	$-0.460123\pi$
$487$	5.51487	0.249903	0.124951	+	0.992163i	$0.460123\pi$
$488$	8.31093	0.376218
$489$	25.6932	1.16189
$490$	23.8114	1.07569
$491$	−7.35301	−0.331837	−0.165918	−	0.986139i	$-0.553059\pi$
$491$	−7.35301	−0.331837	−0.165918	+	0.986139i	$0.553059\pi$
$492$	−1.18535	−0.0534396
$493$	4.43128	0.199575
$494$	80.0526	3.60174
$495$	−23.3329	−1.04873
$496$	53.3172	2.39401
$497$	−0.731829	−0.0328270
$498$	−67.9905	−3.04673
$499$	40.9480	1.83308	0.916542	−	0.399938i	$-0.130968\pi$
$499$	40.9480	1.83308	0.916542	+	0.399938i	$0.130968\pi$
$500$	−56.3572	−2.52037
$501$	23.6665	1.05734
$502$	45.6566	2.03775
$503$	−26.8800	−1.19852	−0.599260	−	0.800554i	$-0.704538\pi$
$503$	−26.8800	−1.19852	−0.599260	+	0.800554i	$0.704538\pi$
$504$	−61.2438	−2.72802
$505$	18.9304	0.842390
$506$	−28.3903	−1.26210
$507$	23.8456	1.05902
$508$	77.6241	3.44401
$509$	13.0699	0.579311	0.289656	−	0.957131i	$-0.406459\pi$
$509$	13.0699	0.579311	0.289656	+	0.957131i	$0.406459\pi$
$510$	−61.3560	−2.71689
$511$	2.74421	0.121397
$512$	48.1747	2.12904
$513$	−92.7618	−4.09553
$514$	−16.5557	−0.730242
$515$	−10.4555	−0.460726
$516$	179.944	7.92158
$517$	14.5429	0.639594
$518$	−16.4682	−0.723572
$519$	12.5074	0.549012
$520$	−52.3971	−2.29777
$521$	−10.6058	−0.464647	−0.232323	−	0.972639i	$-0.574633\pi$
$521$	−10.6058	−0.464647	−0.232323	+	0.972639i	$0.574633\pi$
$522$	−18.6898	−0.818031
$523$	6.62592	0.289731	0.144866	−	0.989451i	$-0.453725\pi$
$523$	6.62592	0.289731	0.144866	+	0.989451i	$0.453725\pi$
$524$	−5.47570	−0.239207
$525$	−8.59219	−0.374994
$526$	68.7308	2.99681
$527$	27.7377	1.20827
$528$	−52.4719	−2.28355
$529$	9.55273	0.415336
$530$	−42.8123	−1.85965
$531$	−74.1934	−3.21972
$532$	−39.2197	−1.70039
$533$	−0.358343	−0.0155215
$534$	17.0446	0.737591
$535$	27.8933	1.20593
$536$	16.4396	0.710084
$537$	45.4330	1.96058
$538$	7.95070	0.342779
$539$	10.5940	0.456314
$540$	106.083	4.56507
$541$	−12.9876	−0.558380	−0.279190	−	0.960236i	$-0.590066\pi$
$541$	−12.9876	−0.558380	−0.279190	+	0.960236i	$0.590066\pi$
$542$	2.58094	0.110861
$543$	−21.2990	−0.914029
$544$	−36.2332	−1.55349
$545$	−0.246437	−0.0105562
$546$	−45.7657	−1.95859
$547$	3.00382	0.128434	0.0642171	−	0.997936i	$-0.479545\pi$
$547$	3.00382	0.128434	0.0642171	+	0.997936i	$0.479545\pi$
$548$	−108.839	−4.64937
$549$	−8.69170	−0.370953
$550$	−10.9172	−0.465511
$551$	−6.85021	−0.291829
$552$	126.232	5.37278
$553$	14.6150	0.621495
$554$	−37.4209	−1.58986
$555$	27.8966	1.18414
$556$	−4.67665	−0.198334
$557$	13.6251	0.577314	0.288657	−	0.957433i	$-0.406791\pi$
$557$	13.6251	0.577314	0.288657	+	0.957433i	$0.406791\pi$
$558$	−116.990	−4.95257
$559$	54.3988	2.30083
$560$	17.4677	0.738144
$561$	−27.2980	−1.15252
$562$	−8.59834	−0.362699
$563$	11.1042	0.467988	0.233994	−	0.972238i	$-0.424820\pi$
$563$	11.1042	0.467988	0.233994	+	0.972238i	$0.424820\pi$
$564$	−112.977	−4.75721
$565$	−24.6163	−1.03561
$566$	38.9879	1.63878
$567$	26.4664	1.11149
$568$	4.13443	0.173477
$569$	38.8749	1.62972	0.814861	−	0.579656i	$-0.196813\pi$
$569$	38.8749	1.62972	0.814861	+	0.579656i	$0.196813\pi$
$570$	94.8488	3.97278
$571$	21.9466	0.918436	0.459218	−	0.888324i	$-0.348130\pi$
$571$	21.9466	0.918436	0.459218	+	0.888324i	$0.348130\pi$
$572$	−40.7309	−1.70304
$573$	−59.6788	−2.49312
$574$	0.250640	0.0104615
$575$	12.5178	0.522029
$576$	29.6012	1.23338
$577$	8.03722	0.334594	0.167297	−	0.985907i	$-0.446496\pi$
$577$	8.03722	0.334594	0.167297	+	0.985907i	$0.446496\pi$
$578$	−6.81174	−0.283331
$579$	−8.56279	−0.355857
$580$	7.83393	0.325286
$581$	10.0700	0.417774
$582$	−126.766	−5.25464
$583$	−19.0477	−0.788874
$584$	−15.5033	−0.641530
$585$	54.7977	2.26561
$586$	−80.4492	−3.32333
$587$	16.4598	0.679368	0.339684	−	0.940540i	$-0.389680\pi$
$587$	16.4598	0.679368	0.339684	+	0.940540i	$0.389680\pi$
$588$	−82.3000	−3.39400
$589$	−42.8792	−1.76680
$590$	44.3980	1.82784
$591$	−22.0424	−0.906704
$592$	44.3433	1.82250
$593$	−38.9360	−1.59891	−0.799456	−	0.600725i	$-0.794879\pi$
$593$	−38.9360	−1.59891	−0.799456	+	0.600725i	$0.794879\pi$
$594$	67.3817	2.76470
$595$	9.08738	0.372546
$596$	30.8365	1.26311
$597$	−26.2309	−1.07356
$598$	66.6753	2.72656
$599$	13.4747	0.550563	0.275281	−	0.961364i	$-0.411229\pi$
$599$	13.4747	0.550563	0.275281	+	0.961364i	$0.411229\pi$
$600$	48.5411	1.98168
$601$	1.22950	0.0501523	0.0250762	−	0.999686i	$-0.492017\pi$
$601$	1.22950	0.0501523	0.0250762	+	0.999686i	$0.492017\pi$
$602$	−38.0489	−1.55076
$603$	−17.1928	−0.700146
$604$	−12.6634	−0.515265
$605$	−12.2142	−0.496576
$606$	−93.4109	−3.79456
$607$	33.5162	1.36038	0.680191	−	0.733035i	$-0.261897\pi$
$607$	33.5162	1.36038	0.680191	+	0.733035i	$0.261897\pi$
$608$	56.0122	2.27159
$609$	3.91624	0.158694
$610$	5.20119	0.210590
$611$	−34.1542	−1.38173
$612$	149.896	6.05918
$613$	28.3948	1.14686	0.573428	−	0.819256i	$-0.305613\pi$
$613$	28.3948	1.14686	0.573428	+	0.819256i	$0.305613\pi$
$614$	72.7619	2.93643
$615$	−0.424576	−0.0171205
$616$	16.3055	0.656966
$617$	17.7690	0.715351	0.357676	−	0.933846i	$-0.383569\pi$
$617$	17.7690	0.715351	0.357676	+	0.933846i	$0.383569\pi$
$618$	51.5924	2.07535
$619$	−16.4912	−0.662838	−0.331419	−	0.943484i	$-0.607527\pi$
$619$	−16.4912	−0.662838	−0.331419	+	0.943484i	$0.607527\pi$
$620$	49.0367	1.96936
$621$	−77.2607	−3.10037
$622$	67.8715	2.72140
$623$	−2.52446	−0.101140
$624$	123.231	4.93320
$625$	−9.21645	−0.368658
$626$	3.95658	0.158137
$627$	42.1993	1.68528
$628$	89.1542	3.55764
$629$	23.0691	0.919826
$630$	−38.3279	−1.52702
$631$	10.1130	0.402591	0.201295	−	0.979531i	$-0.435485\pi$
$631$	10.1130	0.402591	0.201295	+	0.979531i	$0.435485\pi$
$632$	−82.5668	−3.28433
$633$	42.0856	1.67275
$634$	−45.6117	−1.81147
$635$	27.8039	1.10337
$636$	147.973	5.86752
$637$	−24.8801	−0.985787
$638$	4.97596	0.197000
$639$	−4.32385	−0.171049
$640$	9.68022	0.382644
$641$	5.26520	0.207963	0.103981	−	0.994579i	$-0.466842\pi$
$641$	5.26520	0.207963	0.103981	+	0.994579i	$0.466842\pi$
$642$	−137.638	−5.43214
$643$	8.31969	0.328097	0.164048	−	0.986452i	$-0.447545\pi$
$643$	8.31969	0.328097	0.164048	+	0.986452i	$0.447545\pi$
$644$	−32.6658	−1.28721
$645$	64.4535	2.53785
$646$	78.4354	3.08600
$647$	6.75696	0.265644	0.132822	−	0.991140i	$-0.457596\pi$
$647$	6.75696	0.265644	0.132822	+	0.991140i	$0.457596\pi$
$648$	−149.521	−5.87372
$649$	19.7532	0.775379
$650$	25.6393	1.00566
$651$	24.5138	0.960773
$652$	37.5620	1.47104
$653$	−35.1357	−1.37497	−0.687483	−	0.726201i	$-0.741284\pi$
$653$	−35.1357	−1.37497	−0.687483	+	0.726201i	$0.741284\pi$
$654$	1.21603	0.0475506
$655$	−1.96132	−0.0766353
$656$	−0.674888	−0.0263499
$657$	16.2136	0.632551
$658$	23.8890	0.931288
$659$	40.1824	1.56529	0.782643	−	0.622471i	$-0.213871\pi$
$659$	40.1824	1.56529	0.782643	+	0.622471i	$0.213871\pi$
$660$	−48.2593	−1.87849
$661$	−34.8637	−1.35604	−0.678021	−	0.735043i	$-0.737162\pi$
$661$	−34.8637	−1.35604	−0.678021	+	0.735043i	$0.737162\pi$
$662$	1.04455	0.0405976
$663$	64.1099	2.48982
$664$	−56.8899	−2.20776
$665$	−14.0480	−0.544757
$666$	−97.2988	−3.77025
$667$	−5.70550	−0.220918
$668$	34.5991	1.33868
$669$	15.8529	0.612909
$670$	10.2883	0.397473
$671$	2.31407	0.0893336
$672$	−32.0219	−1.23527
$673$	−45.9845	−1.77257	−0.886286	−	0.463139i	$-0.846723\pi$
$673$	−45.9845	−1.77257	−0.886286	+	0.463139i	$0.846723\pi$
$674$	−25.0425	−0.964602
$675$	−29.7098	−1.14353
$676$	34.8610	1.34081
$677$	−49.9708	−1.92053	−0.960266	−	0.279085i	$-0.909969\pi$
$677$	−49.9708	−1.92053	−0.960266	+	0.279085i	$0.909969\pi$
$678$	121.468	4.66495
$679$	18.7753	0.720528
$680$	−51.3386	−1.96875
$681$	−68.0665	−2.60831
$682$	31.1472	1.19269
$683$	−28.2617	−1.08140	−0.540701	−	0.841215i	$-0.681841\pi$
$683$	−28.2617	−1.08140	−0.540701	+	0.841215i	$0.681841\pi$
$684$	−231.721	−8.86006
$685$	−38.9847	−1.48953
$686$	39.5456	1.50986
$687$	21.6375	0.825522
$688$	102.453	3.90597
$689$	44.7339	1.70422
$690$	78.9990	3.00744
$691$	−14.5107	−0.552012	−0.276006	−	0.961156i	$-0.589011\pi$
$691$	−14.5107	−0.552012	−0.276006	+	0.961156i	$0.589011\pi$
$692$	18.2851	0.695094
$693$	−17.0525	−0.647772
$694$	−63.8607	−2.42412
$695$	−1.67511	−0.0635407
$696$	−22.1246	−0.838630
$697$	−0.351104	−0.0132990
$698$	54.5661	2.06536
$699$	−86.6834	−3.27867
$700$	−12.5613	−0.474773
$701$	48.5073	1.83210	0.916049	−	0.401067i	$-0.131361\pi$
$701$	48.5073	1.83210	0.916049	+	0.401067i	$0.131361\pi$
$702$	−158.247	−5.97266
$703$	−35.6621	−1.34502
$704$	−7.88098	−0.297026
$705$	−40.4670	−1.52408
$706$	−35.2935	−1.32829
$707$	13.8350	0.520319
$708$	−153.454	−5.76715
$709$	33.6867	1.26513	0.632564	−	0.774508i	$-0.282002\pi$
$709$	33.6867	1.26513	0.632564	+	0.774508i	$0.282002\pi$
$710$	2.58743	0.0971045
$711$	86.3497	3.23837
$712$	14.2618	0.534482
$713$	−35.7138	−1.33749
$714$	−44.8412	−1.67814
$715$	−14.5893	−0.545608
$716$	66.4204	2.48225
$717$	−83.1224	−3.10426
$718$	80.5350	3.00554
$719$	−16.7948	−0.626340	−0.313170	−	0.949697i	$-0.601391\pi$
$719$	−16.7948	−0.626340	−0.313170	+	0.949697i	$0.601391\pi$
$720$	103.204	3.84618
$721$	−7.64130	−0.284577
$722$	−72.1571	−2.68541
$723$	−21.5585	−0.801771
$724$	−31.1380	−1.15723
$725$	−2.19399	−0.0814828
$726$	60.2701	2.23683
$727$	−8.69219	−0.322375	−0.161188	−	0.986924i	$-0.551532\pi$
$727$	−8.69219	−0.322375	−0.161188	+	0.986924i	$0.551532\pi$
$728$	−38.2938	−1.41926
$729$	26.4166	0.978393
$730$	−9.70234	−0.359100
$731$	53.2999	1.97137
$732$	−17.9770	−0.664450
$733$	47.4931	1.75420	0.877099	−	0.480310i	$-0.159476\pi$
$733$	47.4931	1.75420	0.877099	+	0.480310i	$0.159476\pi$
$734$	50.3325	1.85781
$735$	−29.4788	−1.08734
$736$	46.6522	1.71962
$737$	4.57740	0.168611
$738$	1.48085	0.0545109
$739$	9.26881	0.340959	0.170479	−	0.985361i	$-0.445468\pi$
$739$	9.26881	0.340959	0.170479	+	0.985361i	$0.445468\pi$
$740$	40.7833	1.49922
$741$	−99.1060	−3.64075
$742$	−31.2888	−1.14865
$743$	−49.7310	−1.82445	−0.912227	−	0.409686i	$-0.865638\pi$
$743$	−49.7310	−1.82445	−0.912227	+	0.409686i	$0.865638\pi$
$744$	−138.490	−5.07728
$745$	11.0452	0.404665
$746$	48.9960	1.79387
$747$	59.4964	2.17686
$748$	−39.9081	−1.45918
$749$	20.3854	0.744868
$750$	99.6088	3.63720
$751$	−10.3849	−0.378951	−0.189476	−	0.981885i	$-0.560679\pi$
$751$	−10.3849	−0.378951	−0.189476	+	0.981885i	$0.560679\pi$
$752$	−64.3247	−2.34568
$753$	−56.5234	−2.05983
$754$	−11.6861	−0.425584
$755$	−4.53585	−0.165077
$756$	77.5292	2.81971
$757$	12.3402	0.448514	0.224257	−	0.974530i	$-0.428005\pi$
$757$	12.3402	0.448514	0.224257	+	0.974530i	$0.428005\pi$
$758$	−17.2150	−0.625275
$759$	35.1476	1.27578
$760$	79.3633	2.87881
$761$	−1.12174	−0.0406629	−0.0203315	−	0.999793i	$-0.506472\pi$
$761$	−1.12174	−0.0406629	−0.0203315	+	0.999793i	$0.506472\pi$
$762$	−137.197	−4.97013
$763$	−0.180105	−0.00652025
$764$	−87.2470	−3.15649
$765$	53.6907	1.94119
$766$	85.8665	3.10248
$767$	−46.3907	−1.67507
$768$	−73.9495	−2.66842
$769$	−23.6982	−0.854577	−0.427289	−	0.904115i	$-0.640531\pi$
$769$	−23.6982	−0.854577	−0.427289	+	0.904115i	$0.640531\pi$
$770$	10.2044	0.367740
$771$	20.4962	0.738153
$772$	−12.5183	−0.450544
$773$	−38.5858	−1.38783	−0.693917	−	0.720055i	$-0.744117\pi$
$773$	−38.5858	−1.38783	−0.693917	+	0.720055i	$0.744117\pi$
$774$	−224.803	−8.08039
$775$	−13.7334	−0.493317
$776$	−106.070	−3.80768
$777$	20.3879	0.731411
$778$	−75.4886	−2.70640
$779$	0.542763	0.0194465
$780$	113.338	4.05815
$781$	1.15118	0.0411923
$782$	65.3284	2.33614
$783$	13.5415	0.483932
$784$	−46.8583	−1.67351
$785$	31.9338	1.13977
$786$	9.67806	0.345205
$787$	−3.57646	−0.127487	−0.0637436	−	0.997966i	$-0.520304\pi$
$787$	−3.57646	−0.127487	−0.0637436	+	0.997966i	$0.520304\pi$
$788$	−32.2248	−1.14796
$789$	−85.0896	−3.02927
$790$	−51.6724	−1.83842
$791$	−17.9905	−0.639668
$792$	96.3372	3.42319
$793$	−5.43464	−0.192990
$794$	27.7617	0.985227
$795$	53.0021	1.87979
$796$	−38.3481	−1.35921
$797$	12.9043	0.457094	0.228547	−	0.973533i	$-0.426603\pi$
$797$	12.9043	0.457094	0.228547	+	0.973533i	$0.426603\pi$
$798$	69.3191	2.45387
$799$	−33.4643	−1.18388
$800$	17.9396	0.634261
$801$	−14.9152	−0.527002
$802$	60.8722	2.14947
$803$	−4.31668	−0.152332
$804$	−35.5599	−1.25410
$805$	−11.7005	−0.412388
$806$	−73.1498	−2.57659
$807$	−9.84307	−0.346492
$808$	−78.1601	−2.74966
$809$	20.0081	0.703448	0.351724	−	0.936104i	$-0.385596\pi$
$809$	20.0081	0.703448	0.351724	+	0.936104i	$0.385596\pi$
$810$	−93.5737	−3.28785
$811$	−2.64409	−0.0928467	−0.0464234	−	0.998922i	$-0.514782\pi$
$811$	−2.64409	−0.0928467	−0.0464234	+	0.998922i	$0.514782\pi$
$812$	5.72532	0.200919
$813$	−3.19524	−0.112062
$814$	25.9047	0.907960
$815$	13.4542	0.471281
$816$	120.742	4.22681
$817$	−82.3952	−2.88264
$818$	43.9993	1.53840
$819$	40.0482	1.39940
$820$	−0.620706	−0.0216760
$821$	−13.4255	−0.468554	−0.234277	−	0.972170i	$-0.575272\pi$
$821$	−13.4255	−0.468554	−0.234277	+	0.972170i	$0.575272\pi$
$822$	192.368	6.70960
$823$	37.7879	1.31720	0.658601	−	0.752492i	$-0.271148\pi$
$823$	37.7879	1.31720	0.658601	+	0.752492i	$0.271148\pi$
$824$	43.1691	1.50387
$825$	13.5156	0.470554
$826$	32.4477	1.12900
$827$	−43.8395	−1.52445	−0.762224	−	0.647313i	$-0.775893\pi$
$827$	−43.8395	−1.52445	−0.762224	+	0.647313i	$0.775893\pi$
$828$	−192.999	−6.70717
$829$	16.6210	0.577272	0.288636	−	0.957439i	$-0.406798\pi$
$829$	16.6210	0.577272	0.288636	+	0.957439i	$0.406798\pi$
$830$	−35.6032	−1.23580
$831$	46.3276	1.60709
$832$	18.5087	0.641673
$833$	−24.3775	−0.844632
$834$	8.26577	0.286220
$835$	12.3930	0.428876
$836$	61.6930	2.13370
$837$	84.7632	2.92985
$838$	67.1858	2.32090
$839$	1.05504	0.0364240	0.0182120	−	0.999834i	$-0.494203\pi$
$839$	1.05504	0.0364240	0.0182120	+	0.999834i	$0.494203\pi$
$840$	−45.3717	−1.56547
$841$	1.00000	0.0344828
$842$	20.6329	0.711057
$843$	10.6448	0.366628
$844$	61.5268	2.11784
$845$	12.4867	0.429557
$846$	141.143	4.85258
$847$	−8.92656	−0.306720
$848$	84.2499	2.89315
$849$	−48.2675	−1.65654
$850$	25.1213	0.861655
$851$	−29.7027	−1.01820
$852$	−8.94301	−0.306382
$853$	−37.5168	−1.28455	−0.642276	−	0.766474i	$-0.722010\pi$
$853$	−37.5168	−1.28455	−0.642276	+	0.766474i	$0.722010\pi$
$854$	3.80122	0.130075
$855$	−82.9993	−2.83852
$856$	−115.166	−3.93631
$857$	16.5438	0.565126	0.282563	−	0.959249i	$-0.408815\pi$
$857$	16.5438	0.565126	0.282563	+	0.959249i	$0.408815\pi$
$858$	71.9901	2.45770
$859$	0.985468	0.0336237	0.0168119	−	0.999859i	$-0.494648\pi$
$859$	0.985468	0.0336237	0.0168119	+	0.999859i	$0.494648\pi$
$860$	94.2274	3.21313
$861$	−0.310296	−0.0105749
$862$	43.5497	1.48331
$863$	−33.9693	−1.15633	−0.578165	−	0.815920i	$-0.696231\pi$
$863$	−33.9693	−1.15633	−0.578165	+	0.815920i	$0.696231\pi$
$864$	−110.724	−3.76692
$865$	6.54947	0.222689
$866$	−38.2321	−1.29918
$867$	8.43301	0.286400
$868$	35.8379	1.21642
$869$	−22.9896	−0.779870
$870$	−13.8461	−0.469427
$871$	−10.7501	−0.364254
$872$	1.01750	0.0344567
$873$	110.929	3.75439
$874$	−100.990	−3.41603
$875$	−14.7530	−0.498742
$876$	33.5345	1.13302
$877$	20.4903	0.691910	0.345955	−	0.938251i	$-0.387555\pi$
$877$	20.4903	0.691910	0.345955	+	0.938251i	$0.387555\pi$
$878$	84.3647	2.84717
$879$	99.5971	3.35933
$880$	−27.4769	−0.926245
$881$	41.5965	1.40142	0.700710	−	0.713446i	$-0.252867\pi$
$881$	41.5965	1.40142	0.700710	+	0.713446i	$0.252867\pi$
$882$	102.817	3.46204
$883$	−31.0921	−1.04633	−0.523166	−	0.852231i	$-0.675249\pi$
$883$	−31.0921	−1.04633	−0.523166	+	0.852231i	$0.675249\pi$
$884$	93.7250	3.15231
$885$	−54.9652	−1.84764
$886$	−57.9641	−1.94734
$887$	5.52241	0.185424	0.0927122	−	0.995693i	$-0.470446\pi$
$887$	5.52241	0.185424	0.0927122	+	0.995693i	$0.470446\pi$
$888$	−115.180	−3.86519
$889$	20.3202	0.681516
$890$	8.92537	0.299179
$891$	−41.6320	−1.39472
$892$	23.1761	0.775992
$893$	51.7317	1.73114
$894$	−54.5021	−1.82282
$895$	23.7909	0.795243
$896$	7.07467	0.236348
$897$	−82.5448	−2.75609
$898$	−64.0034	−2.13582
$899$	6.25954	0.208767
$900$	−74.2157	−2.47386
$901$	43.8302	1.46019
$902$	−0.394260	−0.0131274
$903$	47.1050	1.56756
$904$	101.636	3.38037
$905$	−11.1532	−0.370746
$906$	22.3819	0.743590
$907$	−35.6794	−1.18472	−0.592358	−	0.805675i	$-0.701803\pi$
$907$	−35.6794	−1.18472	−0.592358	+	0.805675i	$0.701803\pi$
$908$	−99.5094	−3.30234
$909$	81.7410	2.71118
$910$	−23.9652	−0.794439
$911$	52.4530	1.73785	0.868923	−	0.494948i	$-0.164813\pi$
$911$	52.4530	1.73785	0.868923	+	0.494948i	$0.164813\pi$
$912$	−186.652	−6.18067
$913$	−15.8402	−0.524236
$914$	68.2700	2.25817
$915$	−6.43914	−0.212871
$916$	31.6328	1.04518
$917$	−1.43341	−0.0473353
$918$	−155.051	−5.11743
$919$	51.2339	1.69005	0.845025	−	0.534727i	$-0.179585\pi$
$919$	51.2339	1.69005	0.845025	+	0.534727i	$0.179585\pi$
$920$	66.1012	2.17929
$921$	−90.0801	−2.96824
$922$	−13.9372	−0.458999
$923$	−2.70356	−0.0889889
$924$	−35.2697	−1.16029
$925$	−11.4219	−0.375549
$926$	−28.3358	−0.931171
$927$	−45.1469	−1.48282
$928$	−8.17670	−0.268413
$929$	28.2357	0.926384	0.463192	−	0.886258i	$-0.346704\pi$
$929$	28.2357	0.926384	0.463192	+	0.886258i	$0.346704\pi$
$930$	−86.6703	−2.84203
$931$	37.6847	1.23507
$932$	−126.726	−4.15106
$933$	−84.0258	−2.75088
$934$	42.8034	1.40057
$935$	−14.2946	−0.467482
$936$	−226.250	−7.39522
$937$	−37.5693	−1.22734	−0.613668	−	0.789564i	$-0.710307\pi$
$937$	−37.5693	−1.22734	−0.613668	+	0.789564i	$0.710307\pi$
$938$	7.51910	0.245507
$939$	−4.89829	−0.159850
$940$	−59.1605	−1.92960
$941$	49.9611	1.62869	0.814343	−	0.580383i	$-0.197097\pi$
$941$	49.9611	1.62869	0.814343	+	0.580383i	$0.197097\pi$
$942$	−157.576	−5.13410
$943$	0.452064	0.0147212
$944$	−87.3704	−2.84366
$945$	27.7699	0.903356
$946$	59.8514	1.94594
$947$	−9.97315	−0.324084	−0.162042	−	0.986784i	$-0.551808\pi$
$947$	−9.97315	−0.324084	−0.162042	+	0.986784i	$0.551808\pi$
$948$	178.597	5.80056
$949$	10.1378	0.329087
$950$	−38.8345	−1.25996
$951$	56.4678	1.83109
$952$	−37.5202	−1.21604
$953$	44.8372	1.45242	0.726210	−	0.687473i	$-0.241280\pi$
$953$	44.8372	1.45242	0.726210	+	0.687473i	$0.241280\pi$
$954$	−184.863	−5.98516
$955$	−31.2507	−1.01125
$956$	−121.520	−3.93025
$957$	−6.16029	−0.199134
$958$	−35.3902	−1.14341
$959$	−28.4914	−0.920037
$960$	21.9297	0.707777
$961$	8.18180	0.263929
$962$	−60.8378	−1.96149
$963$	120.443	3.88122
$964$	−31.5174	−1.01511
$965$	−4.48390	−0.144342
$966$	57.7354	1.85761
$967$	36.9149	1.18710	0.593552	−	0.804796i	$-0.297725\pi$
$967$	36.9149	1.18710	0.593552	+	0.804796i	$0.297725\pi$
$968$	50.4301	1.62088
$969$	−97.1040	−3.11943
$970$	−66.3811	−2.13137
$971$	−23.9204	−0.767641	−0.383820	−	0.923408i	$-0.625392\pi$
$971$	−23.9204	−0.767641	−0.383820	+	0.923408i	$0.625392\pi$
$972$	133.436	4.27995
$973$	−1.22424	−0.0392472
$974$	−14.2500	−0.456599
$975$	−31.7417	−1.01655
$976$	−10.2354	−0.327627
$977$	44.0651	1.40977	0.704884	−	0.709323i	$-0.250999\pi$
$977$	44.0651	1.40977	0.704884	+	0.709323i	$0.250999\pi$
$978$	−66.3892	−2.12289
$979$	3.97100	0.126914
$980$	−43.0963	−1.37666
$981$	−1.06411	−0.0339745
$982$	18.9996	0.606302
$983$	−38.7765	−1.23678	−0.618388	−	0.785873i	$-0.712214\pi$
$983$	−38.7765	−1.23678	−0.618388	+	0.785873i	$0.712214\pi$
$984$	1.75300	0.0558836
$985$	−11.5425	−0.367774
$986$	−11.4501	−0.364644
$987$	−29.5748	−0.941377
$988$	−144.887	−4.60948
$989$	−68.6264	−2.18219
$990$	60.2903	1.91615
$991$	−7.09428	−0.225357	−0.112679	−	0.993631i	$-0.535943\pi$
$991$	−7.09428	−0.225357	−0.112679	+	0.993631i	$0.535943\pi$
$992$	−51.1824	−1.62504
$993$	−1.29317	−0.0410374
$994$	1.89099	0.0599785
$995$	−13.7358	−0.435454
$996$	123.056	3.89919
$997$	14.1818	0.449142	0.224571	−	0.974458i	$-0.427902\pi$
$997$	14.1818	0.449142	0.224571	+	0.974458i	$0.427902\pi$
$998$	−105.806	−3.34924
$999$	70.4965	2.23041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.7	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.58392 q^{2} +3.19893 q^{3} +4.67665 q^{4} +1.67511 q^{5} -8.26577 q^{6} +1.22424 q^{7} -6.91625 q^{8} +7.23312 q^{9} +O(q^{10})\)	\(q-2.58392 q^{2} +3.19893 q^{3} +4.67665 q^{4} +1.67511 q^{5} -8.26577 q^{6} +1.22424 q^{7} -6.91625 q^{8} +7.23312 q^{9} -4.32836 q^{10} -1.92574 q^{11} +14.9603 q^{12} +4.52264 q^{13} -3.16333 q^{14} +5.35857 q^{15} +8.51775 q^{16} +4.43128 q^{17} -18.6898 q^{18} -6.85021 q^{19} +7.83393 q^{20} +3.91624 q^{21} +4.97596 q^{22} -5.70550 q^{23} -22.1246 q^{24} -2.19399 q^{25} -11.6861 q^{26} +13.5415 q^{27} +5.72532 q^{28} +1.00000 q^{29} -13.8461 q^{30} +6.25954 q^{31} -8.17670 q^{32} -6.16029 q^{33} -11.4501 q^{34} +2.05074 q^{35} +33.8268 q^{36} +5.20598 q^{37} +17.7004 q^{38} +14.4676 q^{39} -11.5855 q^{40} -0.0792331 q^{41} -10.1193 q^{42} +12.0281 q^{43} -9.00600 q^{44} +12.1163 q^{45} +14.7426 q^{46} -7.55184 q^{47} +27.2477 q^{48} -5.50125 q^{49} +5.66910 q^{50} +14.1753 q^{51} +21.1508 q^{52} +9.89110 q^{53} -34.9900 q^{54} -3.22583 q^{55} -8.46713 q^{56} -21.9133 q^{57} -2.58392 q^{58} -10.2574 q^{59} +25.0601 q^{60} -1.20165 q^{61} -16.1742 q^{62} +8.85505 q^{63} +4.09245 q^{64} +7.57594 q^{65} +15.9177 q^{66} -2.37696 q^{67} +20.7235 q^{68} -18.2515 q^{69} -5.29894 q^{70} -0.597784 q^{71} -50.0261 q^{72} +2.24157 q^{73} -13.4518 q^{74} -7.01841 q^{75} -32.0360 q^{76} -2.35756 q^{77} -37.3831 q^{78} +11.9381 q^{79} +14.2682 q^{80} +21.6187 q^{81} +0.204732 q^{82} +8.22554 q^{83} +18.3149 q^{84} +7.42289 q^{85} -31.0797 q^{86} +3.19893 q^{87} +13.3189 q^{88} -2.06207 q^{89} -31.3076 q^{90} +5.53678 q^{91} -26.6826 q^{92} +20.0238 q^{93} +19.5134 q^{94} -11.4749 q^{95} -26.1567 q^{96} +15.3363 q^{97} +14.2148 q^{98} -13.9291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 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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