LMFDB - Embedded newform 4007.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9960560899$
Analytic rank:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81570 q^{2} -0.263068 q^{3} +5.92814 q^{4} +2.38290 q^{5} +0.740719 q^{6} -2.49985 q^{7} -11.0604 q^{8} -2.93080 q^{9} +O(q^{10})$	\(q-2.81570 q^{2} -0.263068 q^{3} +5.92814 q^{4} +2.38290 q^{5} +0.740719 q^{6} -2.49985 q^{7} -11.0604 q^{8} -2.93080 q^{9} -6.70951 q^{10} +4.65838 q^{11} -1.55950 q^{12} -0.720040 q^{13} +7.03882 q^{14} -0.626864 q^{15} +19.2866 q^{16} -7.77412 q^{17} +8.25223 q^{18} -3.14479 q^{19} +14.1261 q^{20} +0.657631 q^{21} -13.1166 q^{22} +2.20304 q^{23} +2.90965 q^{24} +0.678197 q^{25} +2.02741 q^{26} +1.56020 q^{27} -14.8195 q^{28} -1.23778 q^{29} +1.76506 q^{30} +2.01192 q^{31} -32.1842 q^{32} -1.22547 q^{33} +21.8896 q^{34} -5.95689 q^{35} -17.3742 q^{36} +11.1147 q^{37} +8.85476 q^{38} +0.189419 q^{39} -26.3559 q^{40} +10.4867 q^{41} -1.85169 q^{42} +1.55214 q^{43} +27.6155 q^{44} -6.98378 q^{45} -6.20310 q^{46} -1.44190 q^{47} -5.07368 q^{48} -0.750739 q^{49} -1.90960 q^{50} +2.04512 q^{51} -4.26850 q^{52} +11.5106 q^{53} -4.39305 q^{54} +11.1004 q^{55} +27.6495 q^{56} +0.827293 q^{57} +3.48520 q^{58} +4.45978 q^{59} -3.71614 q^{60} +12.0900 q^{61} -5.66496 q^{62} +7.32656 q^{63} +52.0478 q^{64} -1.71578 q^{65} +3.45055 q^{66} -7.18276 q^{67} -46.0861 q^{68} -0.579550 q^{69} +16.7728 q^{70} -4.47992 q^{71} +32.4159 q^{72} -7.32730 q^{73} -31.2957 q^{74} -0.178412 q^{75} -18.6427 q^{76} -11.6453 q^{77} -0.533348 q^{78} -15.1717 q^{79} +45.9579 q^{80} +8.38195 q^{81} -29.5273 q^{82} -9.39095 q^{83} +3.89853 q^{84} -18.5249 q^{85} -4.37036 q^{86} +0.325619 q^{87} -51.5237 q^{88} -0.186280 q^{89} +19.6642 q^{90} +1.79999 q^{91} +13.0600 q^{92} -0.529272 q^{93} +4.05995 q^{94} -7.49370 q^{95} +8.46663 q^{96} -11.3599 q^{97} +2.11385 q^{98} -13.6527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.81570	−1.99100	−0.995499	−	0.0947756i	$-0.969787\pi$
$2$	−2.81570	−1.99100	−0.995499	+	0.0947756i	$0.969787\pi$
$3$	−0.263068	−0.151882	−0.0759411	−	0.997112i	$-0.524196\pi$
$3$	−0.263068	−0.151882	−0.0759411	+	0.997112i	$0.524196\pi$
$4$	5.92814	2.96407
$5$	2.38290	1.06566	0.532832	−	0.846221i	$-0.321128\pi$
$5$	2.38290	1.06566	0.532832	+	0.846221i	$0.321128\pi$
$6$	0.740719	0.302397
$7$	−2.49985	−0.944855	−0.472428	−	0.881369i	$-0.656622\pi$
$7$	−2.49985	−0.944855	−0.472428	+	0.881369i	$0.656622\pi$
$8$	−11.0604	−3.91046
$9$	−2.93080	−0.976932
$10$	−6.70951	−2.12173
$11$	4.65838	1.40455	0.702277	−	0.711904i	$-0.252167\pi$
$11$	4.65838	1.40455	0.702277	+	0.711904i	$0.252167\pi$
$12$	−1.55950	−0.450190
$13$	−0.720040	−0.199703	−0.0998516	−	0.995002i	$-0.531837\pi$
$13$	−0.720040	−0.199703	−0.0998516	+	0.995002i	$0.531837\pi$
$14$	7.03882	1.88120
$15$	−0.626864	−0.161855
$16$	19.2866	4.82164
$17$	−7.77412	−1.88550	−0.942750	−	0.333499i	$-0.891771\pi$
$17$	−7.77412	−1.88550	−0.942750	+	0.333499i	$0.891771\pi$
$18$	8.25223	1.94507
$19$	−3.14479	−0.721464	−0.360732	−	0.932670i	$-0.617473\pi$
$19$	−3.14479	−0.721464	−0.360732	+	0.932670i	$0.617473\pi$
$20$	14.1261	3.15870
$21$	0.657631	0.143507
$22$	−13.1166	−2.79646
$23$	2.20304	0.459367	0.229683	−	0.973265i	$-0.426231\pi$
$23$	2.20304	0.459367	0.229683	+	0.973265i	$0.426231\pi$
$24$	2.90965	0.593929
$25$	0.678197	0.135639
$26$	2.02741	0.397609
$27$	1.56020	0.300261
$28$	−14.8195	−2.80062
$29$	−1.23778	−0.229849	−0.114925	−	0.993374i	$-0.536663\pi$
$29$	−1.23778	−0.229849	−0.114925	+	0.993374i	$0.536663\pi$
$30$	1.76506	0.322254
$31$	2.01192	0.361352	0.180676	−	0.983543i	$-0.442171\pi$
$31$	2.01192	0.361352	0.180676	+	0.983543i	$0.442171\pi$
$32$	−32.1842	−5.68942
$33$	−1.22547	−0.213327
$34$	21.8896	3.75403
$35$	−5.95689	−1.00690
$36$	−17.3742	−2.89569
$37$	11.1147	1.82725	0.913625	−	0.406558i	$-0.133271\pi$
$37$	11.1147	1.82725	0.913625	+	0.406558i	$0.133271\pi$
$38$	8.85476	1.43643
$39$	0.189419	0.0303314
$40$	−26.3559	−4.16723
$41$	10.4867	1.63775	0.818873	−	0.573974i	$-0.194599\pi$
$41$	10.4867	1.63775	0.818873	+	0.573974i	$0.194599\pi$
$42$	−1.85169	−0.285722
$43$	1.55214	0.236699	0.118350	−	0.992972i	$-0.462240\pi$
$43$	1.55214	0.236699	0.118350	+	0.992972i	$0.462240\pi$
$44$	27.6155	4.16319
$45$	−6.98378	−1.04108
$46$	−6.20310	−0.914598
$47$	−1.44190	−0.210323	−0.105161	−	0.994455i	$-0.533536\pi$
$47$	−1.44190	−0.210323	−0.105161	+	0.994455i	$0.533536\pi$
$48$	−5.07368	−0.732322
$49$	−0.750739	−0.107248
$50$	−1.90960	−0.270058
$51$	2.04512	0.286374
$52$	−4.26850	−0.591935
$53$	11.5106	1.58110	0.790551	−	0.612396i	$-0.209794\pi$
$53$	11.5106	1.58110	0.790551	+	0.612396i	$0.209794\pi$
$54$	−4.39305	−0.597819
$55$	11.1004	1.49678
$56$	27.6495	3.69482
$57$	0.827293	0.109578
$58$	3.48520	0.457629
$59$	4.45978	0.580614	0.290307	−	0.956934i	$-0.406243\pi$
$59$	4.45978	0.580614	0.290307	+	0.956934i	$0.406243\pi$
$60$	−3.71614	−0.479751
$61$	12.0900	1.54796	0.773981	−	0.633208i	$-0.218262\pi$
$61$	12.0900	1.54796	0.773981	+	0.633208i	$0.218262\pi$
$62$	−5.66496	−0.719451
$63$	7.32656	0.923059
$64$	52.0478	6.50598
$65$	−1.71578	−0.212817
$66$	3.45055	0.424733
$67$	−7.18276	−0.877513	−0.438757	−	0.898606i	$-0.644581\pi$
$67$	−7.18276	−0.877513	−0.438757	+	0.898606i	$0.644581\pi$
$68$	−46.0861	−5.58876
$69$	−0.579550	−0.0697697
$70$	16.7728	2.00473
$71$	−4.47992	−0.531668	−0.265834	−	0.964019i	$-0.585647\pi$
$71$	−4.47992	−0.531668	−0.265834	+	0.964019i	$0.585647\pi$
$72$	32.4159	3.82025
$73$	−7.32730	−0.857595	−0.428798	−	0.903401i	$-0.641063\pi$
$73$	−7.32730	−0.857595	−0.428798	+	0.903401i	$0.641063\pi$
$74$	−31.2957	−3.63805
$75$	−0.178412	−0.0206012
$76$	−18.6427	−2.13847
$77$	−11.6453	−1.32710
$78$	−0.533348	−0.0603897
$79$	−15.1717	−1.70694	−0.853472	−	0.521138i	$-0.825508\pi$
$79$	−15.1717	−1.70694	−0.853472	+	0.521138i	$0.825508\pi$
$80$	45.9579	5.13825
$81$	8.38195	0.931327
$82$	−29.5273	−3.26075
$83$	−9.39095	−1.03079	−0.515395	−	0.856952i	$-0.672355\pi$
$83$	−9.39095	−1.03079	−0.515395	+	0.856952i	$0.672355\pi$
$84$	3.89853	0.425364
$85$	−18.5249	−2.00931
$86$	−4.37036	−0.471268
$87$	0.325619	0.0349100
$88$	−51.5237	−5.49245
$89$	−0.186280	−0.0197457	−0.00987284	−	0.999951i	$-0.503143\pi$
$89$	−0.186280	−0.0197457	−0.00987284	+	0.999951i	$0.503143\pi$
$90$	19.6642	2.07279
$91$	1.79999	0.188691
$92$	13.0600	1.36159
$93$	−0.529272	−0.0548830
$94$	4.05995	0.418752
$95$	−7.49370	−0.768838
$96$	8.46663	0.864122
$97$	−11.3599	−1.15342	−0.576709	−	0.816949i	$-0.695663\pi$
$97$	−11.3599	−1.15342	−0.576709	+	0.816949i	$0.695663\pi$
$98$	2.11385	0.213531
$99$	−13.6527	−1.37215
$100$	4.02045	0.402045
$101$	5.36626	0.533963	0.266982	−	0.963702i	$-0.413974\pi$
$101$	5.36626	0.533963	0.266982	+	0.963702i	$0.413974\pi$
$102$	−5.75844	−0.570170
$103$	14.4060	1.41947	0.709733	−	0.704471i	$-0.248816\pi$
$103$	14.4060	1.41947	0.709733	+	0.704471i	$0.248816\pi$
$104$	7.96397	0.780931
$105$	1.56707	0.152930
$106$	−32.4103	−3.14797
$107$	5.92877	0.573156	0.286578	−	0.958057i	$-0.407482\pi$
$107$	5.92877	0.573156	0.286578	+	0.958057i	$0.407482\pi$
$108$	9.24909	0.889995
$109$	−20.4621	−1.95991	−0.979956	−	0.199213i	$-0.936162\pi$
$109$	−20.4621	−1.95991	−0.979956	+	0.199213i	$0.936162\pi$
$110$	−31.2554	−2.98009
$111$	−2.92393	−0.277527
$112$	−48.2136	−4.55575
$113$	−3.54641	−0.333619	−0.166809	−	0.985989i	$-0.553346\pi$
$113$	−3.54641	−0.333619	−0.166809	+	0.985989i	$0.553346\pi$
$114$	−2.32940	−0.218169
$115$	5.24963	0.489530
$116$	−7.33771	−0.681289
$117$	2.11029	0.195096
$118$	−12.5574	−1.15600
$119$	19.4341	1.78153
$120$	6.93339	0.632929
$121$	10.7005	0.972769
$122$	−34.0417	−3.08199
$123$	−2.75871	−0.248745
$124$	11.9270	1.07107
$125$	−10.2984	−0.921118
$126$	−20.6293	−1.83781
$127$	−18.9153	−1.67846	−0.839231	−	0.543774i	$-0.816995\pi$
$127$	−18.9153	−1.67846	−0.839231	+	0.543774i	$0.816995\pi$
$128$	−82.1823	−7.26396
$129$	−0.408318	−0.0359504
$130$	4.83112	0.423717
$131$	−0.616156	−0.0538338	−0.0269169	−	0.999638i	$-0.508569\pi$
$131$	−0.616156	−0.0538338	−0.0269169	+	0.999638i	$0.508569\pi$
$132$	−7.26475	−0.632315
$133$	7.86150	0.681679
$134$	20.2245	1.74713
$135$	3.71780	0.319977
$136$	85.9852	7.37317
$137$	−14.3861	−1.22909	−0.614545	−	0.788882i	$-0.710660\pi$
$137$	−14.3861	−1.22909	−0.614545	+	0.788882i	$0.710660\pi$
$138$	1.63184	0.138911
$139$	−5.27517	−0.447434	−0.223717	−	0.974654i	$-0.571819\pi$
$139$	−5.27517	−0.447434	−0.223717	+	0.974654i	$0.571819\pi$
$140$	−35.3133	−2.98452
$141$	0.379318	0.0319443
$142$	12.6141	1.05855
$143$	−3.35422	−0.280494
$144$	−56.5250	−4.71042
$145$	−2.94949	−0.244942
$146$	20.6314	1.70747
$147$	0.197495	0.0162891
$148$	65.8897	5.41610
$149$	2.00621	0.164355	0.0821776	−	0.996618i	$-0.473813\pi$
$149$	2.00621	0.164355	0.0821776	+	0.996618i	$0.473813\pi$
$150$	0.502354	0.0410170
$151$	−5.89657	−0.479856	−0.239928	−	0.970791i	$-0.577124\pi$
$151$	−5.89657	−0.479856	−0.239928	+	0.970791i	$0.577124\pi$
$152$	34.7828	2.82125
$153$	22.7844	1.84201
$154$	32.7895	2.64225
$155$	4.79421	0.385080
$156$	1.12291	0.0899044
$157$	−18.7076	−1.49303	−0.746515	−	0.665369i	$-0.768274\pi$
$157$	−18.7076	−1.49303	−0.746515	+	0.665369i	$0.768274\pi$
$158$	42.7188	3.39852
$159$	−3.02807	−0.240141
$160$	−76.6917	−6.06301
$161$	−5.50729	−0.434035
$162$	−23.6010	−1.85427
$163$	21.5323	1.68654	0.843268	−	0.537493i	$-0.180629\pi$
$163$	21.5323	1.68654	0.843268	+	0.537493i	$0.180629\pi$
$164$	62.1666	4.85440
$165$	−2.92017	−0.227335
$166$	26.4421	2.05230
$167$	−4.21426	−0.326110	−0.163055	−	0.986617i	$-0.552135\pi$
$167$	−4.21426	−0.326110	−0.163055	+	0.986617i	$0.552135\pi$
$168$	−7.27369	−0.561177
$169$	−12.4815	−0.960119
$170$	52.1605	4.00053
$171$	9.21673	0.704821
$172$	9.20131	0.701593
$173$	−13.5764	−1.03220	−0.516099	−	0.856529i	$-0.672616\pi$
$173$	−13.5764	−1.03220	−0.516099	+	0.856529i	$0.672616\pi$
$174$	−0.916844	−0.0695058
$175$	−1.69539	−0.128160
$176$	89.8441	6.77225
$177$	−1.17323	−0.0881850
$178$	0.524509	0.0393136
$179$	1.91001	0.142761	0.0713804	−	0.997449i	$-0.477260\pi$
$179$	1.91001	0.142761	0.0713804	+	0.997449i	$0.477260\pi$
$180$	−41.4008	−3.08584
$181$	−20.4986	−1.52365	−0.761824	−	0.647784i	$-0.775696\pi$
$181$	−20.4986	−1.52365	−0.761824	+	0.647784i	$0.775696\pi$
$182$	−5.06824	−0.375683
$183$	−3.18048	−0.235108
$184$	−24.3667	−1.79633
$185$	26.4852	1.94723
$186$	1.49027	0.109272
$187$	−36.2148	−2.64829
$188$	−8.54779	−0.623411
$189$	−3.90027	−0.283703
$190$	21.1000	1.53075
$191$	−15.1336	−1.09503	−0.547515	−	0.836796i	$-0.684426\pi$
$191$	−15.1336	−1.09503	−0.547515	+	0.836796i	$0.684426\pi$
$192$	−13.6921	−0.988142
$193$	−8.49347	−0.611373	−0.305687	−	0.952132i	$-0.598886\pi$
$193$	−8.49347	−0.611373	−0.305687	+	0.952132i	$0.598886\pi$
$194$	31.9859	2.29645
$195$	0.451367	0.0323231
$196$	−4.45048	−0.317892
$197$	20.7786	1.48041	0.740207	−	0.672379i	$-0.234727\pi$
$197$	20.7786	1.48041	0.740207	+	0.672379i	$0.234727\pi$
$198$	38.4420	2.73195
$199$	−9.66285	−0.684981	−0.342491	−	0.939521i	$-0.611271\pi$
$199$	−9.66285	−0.684981	−0.342491	+	0.939521i	$0.611271\pi$
$200$	−7.50117	−0.530412
$201$	1.88955	0.133279
$202$	−15.1098	−1.06312
$203$	3.09426	0.217174
$204$	12.1238	0.848833
$205$	24.9887	1.74529
$206$	−40.5629	−2.82615
$207$	−6.45667	−0.448770
$208$	−13.8871	−0.962898
$209$	−14.6496	−1.01333
$210$	−4.41238	−0.304483
$211$	15.8860	1.09364	0.546820	−	0.837250i	$-0.315838\pi$
$211$	15.8860	1.09364	0.546820	+	0.837250i	$0.315838\pi$
$212$	68.2364	4.68650
$213$	1.17852	0.0807510
$214$	−16.6936	−1.14115
$215$	3.69859	0.252242
$216$	−17.2565	−1.17416
$217$	−5.02951	−0.341426
$218$	57.6150	3.90218
$219$	1.92758	0.130254
$220$	65.8049	4.43657
$221$	5.59768	0.376541
$222$	8.23289	0.552555
$223$	−23.6439	−1.58331	−0.791657	−	0.610965i	$-0.790781\pi$
$223$	−23.6439	−1.58331	−0.791657	+	0.610965i	$0.790781\pi$
$224$	80.4558	5.37568
$225$	−1.98766	−0.132510
$226$	9.98562	0.664234
$227$	−0.272956	−0.0181168	−0.00905838	−	0.999959i	$-0.502883\pi$
$227$	−0.272956	−0.0181168	−0.00905838	+	0.999959i	$0.502883\pi$
$228$	4.90431	0.324796
$229$	−11.8208	−0.781142	−0.390571	−	0.920573i	$-0.627722\pi$
$229$	−11.8208	−0.781142	−0.390571	+	0.920573i	$0.627722\pi$
$230$	−14.7814	−0.974654
$231$	3.06349	0.201563
$232$	13.6904	0.898816
$233$	9.09083	0.595560	0.297780	−	0.954635i	$-0.403754\pi$
$233$	9.09083	0.595560	0.297780	+	0.954635i	$0.403754\pi$
$234$	−5.94194	−0.388437
$235$	−3.43590	−0.224133
$236$	26.4382	1.72098
$237$	3.99117	0.259255
$238$	−54.7206	−3.54701
$239$	13.2932	0.859868	0.429934	−	0.902860i	$-0.358537\pi$
$239$	13.2932	0.859868	0.429934	+	0.902860i	$0.358537\pi$
$240$	−12.0900	−0.780409
$241$	−7.02159	−0.452300	−0.226150	−	0.974092i	$-0.572614\pi$
$241$	−7.02159	−0.452300	−0.226150	+	0.974092i	$0.572614\pi$
$242$	−30.1292	−1.93678
$243$	−6.88563	−0.441713
$244$	71.6711	4.58827
$245$	−1.78893	−0.114291
$246$	7.76769	0.495250
$247$	2.26437	0.144079
$248$	−22.2528	−1.41305
$249$	2.47046	0.156559
$250$	28.9972	1.83394
$251$	10.8617	0.685586	0.342793	−	0.939411i	$-0.388627\pi$
$251$	10.8617	0.685586	0.342793	+	0.939411i	$0.388627\pi$
$252$	43.4329	2.73601
$253$	10.2626	0.645205
$254$	53.2598	3.34182
$255$	4.87331	0.305179
$256$	127.305	7.95655
$257$	7.10859	0.443422	0.221711	−	0.975112i	$-0.428836\pi$
$257$	7.10859	0.443422	0.221711	+	0.975112i	$0.428836\pi$
$258$	1.14970	0.0715772
$259$	−27.7852	−1.72649
$260$	−10.1714	−0.630803
$261$	3.62767	0.224547
$262$	1.73491	0.107183
$263$	−27.7115	−1.70877	−0.854383	−	0.519643i	$-0.826065\pi$
$263$	−27.7115	−1.70877	−0.854383	+	0.519643i	$0.826065\pi$
$264$	13.5542	0.834205
$265$	27.4286	1.68492
$266$	−22.1356	−1.35722
$267$	0.0490044	0.00299902
$268$	−42.5804	−2.60101
$269$	4.00900	0.244433	0.122217	−	0.992503i	$-0.461000\pi$
$269$	4.00900	0.244433	0.122217	+	0.992503i	$0.461000\pi$
$270$	−10.4682	−0.637074
$271$	0.0509201	0.00309317	0.00154659	−	0.999999i	$-0.499508\pi$
$271$	0.0509201	0.00309317	0.00154659	+	0.999999i	$0.499508\pi$
$272$	−149.936	−9.09121
$273$	−0.473521	−0.0286588
$274$	40.5070	2.44711
$275$	3.15930	0.190513
$276$	−3.43566	−0.206802
$277$	−15.5028	−0.931474	−0.465737	−	0.884923i	$-0.654211\pi$
$277$	−15.5028	−0.931474	−0.465737	+	0.884923i	$0.654211\pi$
$278$	14.8533	0.890841
$279$	−5.89654	−0.353016
$280$	65.8859	3.93743
$281$	−3.49298	−0.208374	−0.104187	−	0.994558i	$-0.533224\pi$
$281$	−3.49298	−0.208374	−0.104187	+	0.994558i	$0.533224\pi$
$282$	−1.06804	−0.0636010
$283$	−4.44297	−0.264107	−0.132054	−	0.991243i	$-0.542157\pi$
$283$	−4.44297	−0.264107	−0.132054	+	0.991243i	$0.542157\pi$
$284$	−26.5576	−1.57590
$285$	1.97135	0.116773
$286$	9.44446	0.558463
$287$	−26.2152	−1.54743
$288$	94.3253	5.55817
$289$	43.4369	2.55511
$290$	8.30487	0.487679
$291$	2.98841	0.175184
$292$	−43.4373	−2.54197
$293$	10.6625	0.622912	0.311456	−	0.950261i	$-0.399183\pi$
$293$	10.6625	0.622912	0.311456	+	0.950261i	$0.399183\pi$
$294$	−0.556086	−0.0324316
$295$	10.6272	0.618740
$296$	−122.934	−7.14538
$297$	7.26801	0.421732
$298$	−5.64888	−0.327231
$299$	−1.58628	−0.0917370
$300$	−1.05765	−0.0610635
$301$	−3.88012	−0.223647
$302$	16.6029	0.955392
$303$	−1.41169	−0.0810995
$304$	−60.6522	−3.47864
$305$	28.8092	1.64961
$306$	−64.1538	−3.66743
$307$	22.4158	1.27933	0.639667	−	0.768652i	$-0.279072\pi$
$307$	22.4158	1.27933	0.639667	+	0.768652i	$0.279072\pi$
$308$	−69.0347	−3.93362
$309$	−3.78976	−0.215592
$310$	−13.4990	−0.766693
$311$	10.7675	0.610571	0.305286	−	0.952261i	$-0.401248\pi$
$311$	10.7675	0.610571	0.305286	+	0.952261i	$0.401248\pi$
$312$	−2.09506	−0.118610
$313$	−18.4773	−1.04440	−0.522200	−	0.852823i	$-0.674889\pi$
$313$	−18.4773	−1.04440	−0.522200	+	0.852823i	$0.674889\pi$
$314$	52.6749	2.97262
$315$	17.4584	0.983671
$316$	−89.9397	−5.05950
$317$	−6.60381	−0.370907	−0.185453	−	0.982653i	$-0.559375\pi$
$317$	−6.60381	−0.370907	−0.185453	+	0.982653i	$0.559375\pi$
$318$	8.52612	0.478121
$319$	−5.76602	−0.322835
$320$	124.025	6.93318
$321$	−1.55967	−0.0870522
$322$	15.5068	0.864162
$323$	24.4480	1.36032
$324$	49.6894	2.76052
$325$	−0.488329	−0.0270876
$326$	−60.6283	−3.35789
$327$	5.38292	0.297676
$328$	−115.988	−6.40434
$329$	3.60454	0.198725
$330$	8.22230	0.452623
$331$	−33.3846	−1.83498	−0.917492	−	0.397754i	$-0.869790\pi$
$331$	−33.3846	−1.83498	−0.917492	+	0.397754i	$0.869790\pi$
$332$	−55.6709	−3.05534
$333$	−32.5750	−1.78510
$334$	11.8661	0.649283
$335$	−17.1158	−0.935134
$336$	12.6834	0.691939
$337$	−13.4575	−0.733076	−0.366538	−	0.930403i	$-0.619457\pi$
$337$	−13.4575	−0.733076	−0.366538	+	0.930403i	$0.619457\pi$
$338$	35.1442	1.91159
$339$	0.932947	0.0506707
$340$	−109.818	−5.95574
$341$	9.37230	0.507538
$342$	−25.9515	−1.40330
$343$	19.3757	1.04619
$344$	−17.1674	−0.925603
$345$	−1.38101	−0.0743510
$346$	38.2271	2.05510
$347$	31.7220	1.70293	0.851463	−	0.524415i	$-0.175716\pi$
$347$	31.7220	1.70293	0.851463	+	0.524415i	$0.175716\pi$
$348$	1.93032	0.103476
$349$	21.3140	1.14091	0.570457	−	0.821328i	$-0.306766\pi$
$349$	21.3140	1.14091	0.570457	+	0.821328i	$0.306766\pi$
$350$	4.77371	0.255166
$351$	−1.12341	−0.0599631
$352$	−149.926	−7.99109
$353$	−13.2100	−0.703096	−0.351548	−	0.936170i	$-0.614345\pi$
$353$	−13.2100	−0.703096	−0.351548	+	0.936170i	$0.614345\pi$
$354$	3.30345	0.175576
$355$	−10.6752	−0.566580
$356$	−1.10430	−0.0585276
$357$	−5.11250	−0.270582
$358$	−5.37801	−0.284236
$359$	−20.1937	−1.06578	−0.532892	−	0.846183i	$-0.678895\pi$
$359$	−20.1937	−1.06578	−0.532892	+	0.846183i	$0.678895\pi$
$360$	77.2438	4.07110
$361$	−9.11031	−0.479490
$362$	57.7178	3.03358
$363$	−2.81495	−0.147746
$364$	10.6706	0.559293
$365$	−17.4602	−0.913909
$366$	8.95527	0.468100
$367$	10.9039	0.569177	0.284588	−	0.958650i	$-0.408143\pi$
$367$	10.9039	0.569177	0.284588	+	0.958650i	$0.408143\pi$
$368$	42.4892	2.21490
$369$	−30.7344	−1.59997
$370$	−74.5744	−3.87694
$371$	−28.7748	−1.49391
$372$	−3.13760	−0.162677
$373$	−21.2687	−1.10125	−0.550625	−	0.834752i	$-0.685611\pi$
$373$	−21.2687	−1.10125	−0.550625	+	0.834752i	$0.685611\pi$
$374$	101.970	5.27273
$375$	2.70918	0.139901
$376$	15.9481	0.822459
$377$	0.891249	0.0459016
$378$	10.9820	0.564852
$379$	−11.5032	−0.590878	−0.295439	−	0.955362i	$-0.595466\pi$
$379$	−11.5032	−0.590878	−0.295439	+	0.955362i	$0.595466\pi$
$380$	−44.4237	−2.27889
$381$	4.97601	0.254929
$382$	42.6116	2.18020
$383$	−2.88277	−0.147303	−0.0736514	−	0.997284i	$-0.523465\pi$
$383$	−2.88277	−0.147303	−0.0736514	+	0.997284i	$0.523465\pi$
$384$	21.6195	1.10327
$385$	−27.7494	−1.41424
$386$	23.9150	1.21724
$387$	−4.54901	−0.231239
$388$	−67.3428	−3.41881
$389$	−16.8166	−0.852635	−0.426317	−	0.904574i	$-0.640189\pi$
$389$	−16.8166	−0.852635	−0.426317	+	0.904574i	$0.640189\pi$
$390$	−1.27091	−0.0643551
$391$	−17.1267	−0.866136
$392$	8.30351	0.419390
$393$	0.162091	0.00817640
$394$	−58.5062	−2.94750
$395$	−36.1525	−1.81903
$396$	−80.9354	−4.06716
$397$	−36.3848	−1.82610	−0.913050	−	0.407847i	$-0.866280\pi$
$397$	−36.3848	−1.82610	−0.913050	+	0.407847i	$0.866280\pi$
$398$	27.2076	1.36380
$399$	−2.06811	−0.103535
$400$	13.0801	0.654005
$401$	−11.1826	−0.558434	−0.279217	−	0.960228i	$-0.590075\pi$
$401$	−11.1826	−0.558434	−0.279217	+	0.960228i	$0.590075\pi$
$402$	−5.32040	−0.265358
$403$	−1.44867	−0.0721632
$404$	31.8120	1.58270
$405$	19.9733	0.992482
$406$	−8.71248	−0.432393
$407$	51.7766	2.56647
$408$	−22.6200	−1.11985
$409$	19.6238	0.970332	0.485166	−	0.874422i	$-0.338759\pi$
$409$	19.6238	0.970332	0.485166	+	0.874422i	$0.338759\pi$
$410$	−70.3606	−3.47486
$411$	3.78453	0.186677
$412$	85.4008	4.20740
$413$	−11.1488	−0.548597
$414$	18.1800	0.893499
$415$	−22.3777	−1.09848
$416$	23.1739	1.13620
$417$	1.38773	0.0679574
$418$	41.2488	2.01755
$419$	−5.72972	−0.279915	−0.139958	−	0.990157i	$-0.544697\pi$
$419$	−5.72972	−0.279915	−0.139958	+	0.990157i	$0.544697\pi$
$420$	9.28979	0.453295
$421$	−26.6379	−1.29825	−0.649125	−	0.760681i	$-0.724865\pi$
$421$	−26.6379	−1.29825	−0.649125	+	0.760681i	$0.724865\pi$
$422$	−44.7303	−2.17744
$423$	4.22591	0.205471
$424$	−127.312	−6.18283
$425$	−5.27239	−0.255748
$426$	−3.31836	−0.160775
$427$	−30.2231	−1.46260
$428$	35.1466	1.69887
$429$	0.882387	0.0426021
$430$	−10.4141	−0.502213
$431$	19.6224	0.945177	0.472589	−	0.881283i	$-0.343320\pi$
$431$	19.6224	0.945177	0.472589	+	0.881283i	$0.343320\pi$
$432$	30.0909	1.44775
$433$	−8.84956	−0.425283	−0.212641	−	0.977130i	$-0.568207\pi$
$433$	−8.84956	−0.425283	−0.212641	+	0.977130i	$0.568207\pi$
$434$	14.1616	0.679777
$435$	0.775916	0.0372023
$436$	−121.302	−5.80932
$437$	−6.92811	−0.331416
$438$	−5.42747	−0.259335
$439$	−30.1100	−1.43707	−0.718536	−	0.695490i	$-0.755187\pi$
$439$	−30.1100	−1.43707	−0.718536	+	0.695490i	$0.755187\pi$
$440$	−122.776	−5.85310
$441$	2.20026	0.104774
$442$	−15.7614	−0.749692
$443$	−2.09024	−0.0993101	−0.0496551	−	0.998766i	$-0.515812\pi$
$443$	−2.09024	−0.0993101	−0.0496551	+	0.998766i	$0.515812\pi$
$444$	−17.3335	−0.822609
$445$	−0.443887	−0.0210423
$446$	66.5741	3.15238
$447$	−0.527770	−0.0249627
$448$	−130.112	−6.14721
$449$	14.3500	0.677220	0.338610	−	0.940927i	$-0.390043\pi$
$449$	14.3500	0.677220	0.338610	+	0.940927i	$0.390043\pi$
$450$	5.59664	0.263828
$451$	48.8510	2.30030
$452$	−21.0236	−0.988869
$453$	1.55120	0.0728816
$454$	0.768562	0.0360704
$455$	4.28920	0.201081
$456$	−9.15023	−0.428499
$457$	41.6389	1.94779	0.973893	−	0.227009i	$-0.0728947\pi$
$457$	41.6389	1.94779	0.973893	+	0.227009i	$0.0728947\pi$
$458$	33.2839	1.55525
$459$	−12.1292	−0.566142
$460$	31.1205	1.45100
$461$	−21.2947	−0.991795	−0.495897	−	0.868381i	$-0.665161\pi$
$461$	−21.2947	−0.991795	−0.495897	+	0.868381i	$0.665161\pi$
$462$	−8.62586	−0.401311
$463$	7.48750	0.347974	0.173987	−	0.984748i	$-0.444335\pi$
$463$	7.48750	0.347974	0.173987	+	0.984748i	$0.444335\pi$
$464$	−23.8724	−1.10825
$465$	−1.26120	−0.0584868
$466$	−25.5970	−1.18576
$467$	6.76981	0.313269	0.156635	−	0.987657i	$-0.449935\pi$
$467$	6.76981	0.313269	0.156635	+	0.987657i	$0.449935\pi$
$468$	12.5101	0.578280
$469$	17.9558	0.829123
$470$	9.67445	0.446249
$471$	4.92137	0.226765
$472$	−49.3272	−2.27047
$473$	7.23046	0.332457
$474$	−11.2379	−0.516175
$475$	−2.13279	−0.0978589
$476$	115.208	5.28057
$477$	−33.7352	−1.54463
$478$	−37.4297	−1.71199
$479$	7.24158	0.330876	0.165438	−	0.986220i	$-0.447096\pi$
$479$	7.24158	0.330876	0.165438	+	0.986220i	$0.447096\pi$
$480$	20.1751	0.920864
$481$	−8.00305	−0.364908
$482$	19.7706	0.900528
$483$	1.44879	0.0659222
$484$	63.4338	2.88336
$485$	−27.0694	−1.22916
$486$	19.3878	0.879450
$487$	−5.70639	−0.258581	−0.129291	−	0.991607i	$-0.541270\pi$
$487$	−5.70639	−0.258581	−0.129291	+	0.991607i	$0.541270\pi$
$488$	−133.721	−6.05324
$489$	−5.66444	−0.256155
$490$	5.03709	0.227553
$491$	4.47764	0.202073	0.101037	−	0.994883i	$-0.467784\pi$
$491$	4.47764	0.202073	0.101037	+	0.994883i	$0.467784\pi$
$492$	−16.3540	−0.737297
$493$	9.62262	0.433381
$494$	−6.37579	−0.286860
$495$	−32.5331	−1.46225
$496$	38.8031	1.74231
$497$	11.1991	0.502350
$498$	−6.95606	−0.311708
$499$	−15.8139	−0.707928	−0.353964	−	0.935259i	$-0.615166\pi$
$499$	−15.8139	−0.707928	−0.353964	+	0.935259i	$0.615166\pi$
$500$	−61.0504	−2.73026
$501$	1.10864	0.0495303
$502$	−30.5833	−1.36500
$503$	22.3134	0.994904	0.497452	−	0.867491i	$-0.334269\pi$
$503$	22.3134	0.994904	0.497452	+	0.867491i	$0.334269\pi$
$504$	−81.0350	−3.60959
$505$	12.7872	0.569025
$506$	−28.8964	−1.28460
$507$	3.28349	0.145825
$508$	−112.133	−4.97508
$509$	−18.0673	−0.800821	−0.400410	−	0.916336i	$-0.631132\pi$
$509$	−18.0673	−0.800821	−0.400410	+	0.916336i	$0.631132\pi$
$510$	−13.7218	−0.607610
$511$	18.3172	0.810304
$512$	−194.087	−8.57751
$513$	−4.90650	−0.216627
$514$	−20.0156	−0.882852
$515$	34.3280	1.51267
$516$	−2.42057	−0.106560
$517$	−6.71691	−0.295409
$518$	78.2346	3.43743
$519$	3.57153	0.156773
$520$	18.9773	0.832210
$521$	39.2826	1.72100	0.860500	−	0.509450i	$-0.170151\pi$
$521$	39.2826	1.72100	0.860500	+	0.509450i	$0.170151\pi$
$522$	−10.2144	−0.447072
$523$	25.9029	1.13266	0.566328	−	0.824180i	$-0.308364\pi$
$523$	25.9029	1.13266	0.566328	+	0.824180i	$0.308364\pi$
$524$	−3.65266	−0.159567
$525$	0.446003	0.0194652
$526$	78.0273	3.40215
$527$	−15.6409	−0.681330
$528$	−23.6351	−1.02859
$529$	−18.1466	−0.788982
$530$	−77.2305	−3.35468
$531$	−13.0707	−0.567221
$532$	46.6041	2.02054
$533$	−7.55084	−0.327063
$534$	−0.137981	−0.00597104
$535$	14.1276	0.610791
$536$	79.4445	3.43148
$537$	−0.502462	−0.0216828
$538$	−11.2881	−0.486666
$539$	−3.49722	−0.150636
$540$	22.0396	0.948435
$541$	26.8916	1.15616	0.578080	−	0.815980i	$-0.303802\pi$
$541$	26.8916	1.15616	0.578080	+	0.815980i	$0.303802\pi$
$542$	−0.143375	−0.00615850
$543$	5.39252	0.231415
$544$	250.204	10.7274
$545$	−48.7590	−2.08861
$546$	1.33329	0.0570596
$547$	−21.8052	−0.932321	−0.466161	−	0.884700i	$-0.654363\pi$
$547$	−21.8052	−0.932321	−0.466161	+	0.884700i	$0.654363\pi$
$548$	−85.2830	−3.64311
$549$	−35.4332	−1.51225
$550$	−8.89562	−0.379310
$551$	3.89254	0.165828
$552$	6.41009	0.272831
$553$	37.9269	1.61282
$554$	43.6512	1.85456
$555$	−6.96742	−0.295750
$556$	−31.2720	−1.32623
$557$	30.2837	1.28316	0.641581	−	0.767055i	$-0.278279\pi$
$557$	30.2837	1.28316	0.641581	+	0.767055i	$0.278279\pi$
$558$	16.6029	0.702855
$559$	−1.11760	−0.0472696
$560$	−114.888	−4.85490
$561$	9.52694	0.402228
$562$	9.83516	0.414871
$563$	2.09477	0.0882839	0.0441419	−	0.999025i	$-0.485945\pi$
$563$	2.09477	0.0882839	0.0441419	+	0.999025i	$0.485945\pi$
$564$	2.24865	0.0946852
$565$	−8.45074	−0.355525
$566$	12.5100	0.525837
$567$	−20.9536	−0.879970
$568$	49.5499	2.07907
$569$	17.2606	0.723603	0.361802	−	0.932255i	$-0.382162\pi$
$569$	17.2606	0.723603	0.361802	+	0.932255i	$0.382162\pi$
$570$	−5.55073	−0.232494
$571$	−2.58825	−0.108315	−0.0541575	−	0.998532i	$-0.517247\pi$
$571$	−2.58825	−0.108315	−0.0541575	+	0.998532i	$0.517247\pi$
$572$	−19.8843	−0.831404
$573$	3.98116	0.166316
$574$	73.8140	3.08094
$575$	1.49410	0.0623082
$576$	−152.541	−6.35589
$577$	12.6322	0.525885	0.262942	−	0.964812i	$-0.415307\pi$
$577$	12.6322	0.525885	0.262942	+	0.964812i	$0.415307\pi$
$578$	−122.305	−5.08722
$579$	2.23436	0.0928568
$580$	−17.4850	−0.726025
$581$	23.4760	0.973948
$582$	−8.41446	−0.348791
$583$	53.6207	2.22074
$584$	81.0432	3.35359
$585$	5.02861	0.207907
$586$	−30.0225	−1.24022
$587$	−40.8478	−1.68597	−0.842984	−	0.537939i	$-0.819203\pi$
$587$	−40.8478	−1.68597	−0.842984	+	0.537939i	$0.819203\pi$
$588$	1.17078	0.0482821
$589$	−6.32707	−0.260703
$590$	−29.9230	−1.23191
$591$	−5.46618	−0.224849
$592$	214.365	8.81035
$593$	12.3677	0.507882	0.253941	−	0.967220i	$-0.418273\pi$
$593$	12.3677	0.507882	0.253941	+	0.967220i	$0.418273\pi$
$594$	−20.4645	−0.839668
$595$	46.3096	1.89851
$596$	11.8931	0.487161
$597$	2.54199	0.104037
$598$	4.46648	0.182648
$599$	42.4486	1.73440	0.867202	−	0.497956i	$-0.165916\pi$
$599$	42.4486	1.73440	0.867202	+	0.497956i	$0.165916\pi$
$600$	1.97332	0.0805603
$601$	−24.3854	−0.994703	−0.497351	−	0.867549i	$-0.665694\pi$
$601$	−24.3854	−0.994703	−0.497351	+	0.867549i	$0.665694\pi$
$602$	10.9252	0.445280
$603$	21.0512	0.857271
$604$	−34.9557	−1.42233
$605$	25.4981	1.03665
$606$	3.97489	0.161469
$607$	−20.7521	−0.842303	−0.421152	−	0.906990i	$-0.638374\pi$
$607$	−20.7521	−0.842303	−0.421152	+	0.906990i	$0.638374\pi$
$608$	101.213	4.10471
$609$	−0.813999	−0.0329849
$610$	−81.1178	−3.28436
$611$	1.03823	0.0420021
$612$	135.069	5.45983
$613$	−28.8269	−1.16431	−0.582153	−	0.813079i	$-0.697789\pi$
$613$	−28.8269	−1.16431	−0.582153	+	0.813079i	$0.697789\pi$
$614$	−63.1159	−2.54715
$615$	−6.57373	−0.265078
$616$	128.802	5.18957
$617$	−12.5650	−0.505850	−0.252925	−	0.967486i	$-0.581393\pi$
$617$	−12.5650	−0.505850	−0.252925	+	0.967486i	$0.581393\pi$
$618$	10.6708	0.429243
$619$	35.3354	1.42025	0.710125	−	0.704076i	$-0.248639\pi$
$619$	35.3354	1.42025	0.710125	+	0.704076i	$0.248639\pi$
$620$	28.4207	1.14140
$621$	3.43719	0.137930
$622$	−30.3181	−1.21565
$623$	0.465673	0.0186568
$624$	3.65325	0.146247
$625$	−27.9310	−1.11724
$626$	52.0265	2.07940
$627$	3.85384	0.153908
$628$	−110.901	−4.42544
$629$	−86.4072	−3.44528
$630$	−49.1576	−1.95849
$631$	0.774764	0.0308429	0.0154214	−	0.999881i	$-0.495091\pi$
$631$	0.774764	0.0308429	0.0154214	+	0.999881i	$0.495091\pi$
$632$	167.805	6.67494
$633$	−4.17911	−0.166105
$634$	18.5943	0.738474
$635$	−45.0732	−1.78868
$636$	−17.9508	−0.711796
$637$	0.540562	0.0214179
$638$	16.2354	0.642764
$639$	13.1297	0.519404
$640$	−195.832	−7.74094
$641$	10.6711	0.421485	0.210742	−	0.977542i	$-0.432412\pi$
$641$	10.6711	0.421485	0.210742	+	0.977542i	$0.432412\pi$
$642$	4.39155	0.173321
$643$	23.9935	0.946209	0.473105	−	0.881006i	$-0.343133\pi$
$643$	23.9935	0.946209	0.473105	+	0.881006i	$0.343133\pi$
$644$	−32.6480	−1.28651
$645$	−0.972981	−0.0383111
$646$	−68.8380	−2.70839
$647$	14.0822	0.553628	0.276814	−	0.960924i	$-0.410721\pi$
$647$	14.0822	0.553628	0.276814	+	0.960924i	$0.410721\pi$
$648$	−92.7081	−3.64192
$649$	20.7753	0.815504
$650$	1.37499	0.0539314
$651$	1.32310	0.0518565
$652$	127.646	4.99901
$653$	−14.9198	−0.583855	−0.291928	−	0.956440i	$-0.594297\pi$
$653$	−14.9198	−0.583855	−0.291928	+	0.956440i	$0.594297\pi$
$654$	−15.1567	−0.592672
$655$	−1.46824	−0.0573687
$656$	202.252	7.89663
$657$	21.4748	0.837812
$658$	−10.1493	−0.395660
$659$	−48.1954	−1.87743	−0.938713	−	0.344699i	$-0.887981\pi$
$659$	−48.1954	−1.87743	−0.938713	+	0.344699i	$0.887981\pi$
$660$	−17.3112	−0.673836
$661$	−18.8164	−0.731874	−0.365937	−	0.930640i	$-0.619251\pi$
$661$	−18.8164	−0.731874	−0.365937	+	0.930640i	$0.619251\pi$
$662$	94.0009	3.65345
$663$	−1.47257	−0.0571899
$664$	103.868	4.03087
$665$	18.7332	0.726441
$666$	91.7212	3.55413
$667$	−2.72688	−0.105585
$668$	−24.9828	−0.966612
$669$	6.21996	0.240477
$670$	48.1928	1.86185
$671$	56.3196	2.17420
$672$	−21.1653	−0.816470
$673$	−14.5870	−0.562286	−0.281143	−	0.959666i	$-0.590714\pi$
$673$	−14.5870	−0.562286	−0.281143	+	0.959666i	$0.590714\pi$
$674$	37.8922	1.45955
$675$	1.05812	0.0407272
$676$	−73.9923	−2.84586
$677$	−8.54560	−0.328434	−0.164217	−	0.986424i	$-0.552510\pi$
$677$	−8.54560	−0.328434	−0.164217	+	0.986424i	$0.552510\pi$
$678$	−2.62690	−0.100885
$679$	28.3980	1.08981
$680$	204.894	7.85732
$681$	0.0718061	0.00275161
$682$	−26.3895	−1.01051
$683$	−12.3001	−0.470649	−0.235325	−	0.971917i	$-0.575615\pi$
$683$	−12.3001	−0.470649	−0.235325	+	0.971917i	$0.575615\pi$
$684$	54.6381	2.08914
$685$	−34.2807	−1.30980
$686$	−54.5561	−2.08296
$687$	3.10968	0.118642
$688$	29.9355	1.14128
$689$	−8.28809	−0.315751
$690$	3.88850	0.148033
$691$	−23.0688	−0.877579	−0.438790	−	0.898590i	$-0.644593\pi$
$691$	−23.0688	−0.877579	−0.438790	+	0.898590i	$0.644593\pi$
$692$	−80.4831	−3.05951
$693$	34.1298	1.29649
$694$	−89.3195	−3.39052
$695$	−12.5702	−0.476815
$696$	−3.60149	−0.136514
$697$	−81.5248	−3.08797
$698$	−60.0138	−2.27155
$699$	−2.39150	−0.0904550
$700$	−10.0505	−0.379874
$701$	−16.5778	−0.626137	−0.313068	−	0.949731i	$-0.601357\pi$
$701$	−16.5778	−0.626137	−0.313068	+	0.949731i	$0.601357\pi$
$702$	3.16318	0.119386
$703$	−34.9535	−1.31829
$704$	242.458	9.13799
$705$	0.903875	0.0340419
$706$	37.1953	1.39986
$707$	−13.4149	−0.504518
$708$	−6.95505	−0.261387
$709$	−21.3471	−0.801705	−0.400853	−	0.916143i	$-0.631286\pi$
$709$	−21.3471	−0.801705	−0.400853	+	0.916143i	$0.631286\pi$
$710$	30.0581	1.12806
$711$	44.4650	1.66757
$712$	2.06034	0.0772147
$713$	4.43236	0.165993
$714$	14.3952	0.538728
$715$	−7.99276	−0.298912
$716$	11.3228	0.423153
$717$	−3.49702	−0.130599
$718$	56.8593	2.12197
$719$	−17.2238	−0.642341	−0.321170	−	0.947021i	$-0.604076\pi$
$719$	−17.2238	−0.642341	−0.321170	+	0.947021i	$0.604076\pi$
$720$	−134.693	−5.01972
$721$	−36.0129	−1.34119
$722$	25.6519	0.954663
$723$	1.84715	0.0686964
$724$	−121.518	−4.51620
$725$	−0.839456	−0.0311766
$726$	7.92604	0.294163
$727$	27.7248	1.02826	0.514128	−	0.857713i	$-0.328115\pi$
$727$	27.7248	1.02826	0.514128	+	0.857713i	$0.328115\pi$
$728$	−19.9087	−0.737867
$729$	−23.3345	−0.864239
$730$	49.1626	1.81959
$731$	−12.0665	−0.446297
$732$	−18.8544	−0.696877
$733$	−7.16151	−0.264516	−0.132258	−	0.991215i	$-0.542223\pi$
$733$	−7.16151	−0.264516	−0.132258	+	0.991215i	$0.542223\pi$
$734$	−30.7019	−1.13323
$735$	0.470611	0.0173587
$736$	−70.9033	−2.61353
$737$	−33.4600	−1.23251
$738$	86.5386	3.18553
$739$	−24.1144	−0.887062	−0.443531	−	0.896259i	$-0.646274\pi$
$739$	−24.1144	−0.887062	−0.443531	+	0.896259i	$0.646274\pi$
$740$	157.008	5.77174
$741$	−0.595684	−0.0218830
$742$	81.0210	2.97438
$743$	−25.9356	−0.951485	−0.475742	−	0.879585i	$-0.657821\pi$
$743$	−25.9356	−0.951485	−0.475742	+	0.879585i	$0.657821\pi$
$744$	5.85399	0.214618
$745$	4.78060	0.175147
$746$	59.8861	2.19259
$747$	27.5230	1.00701
$748$	−214.686	−7.84971
$749$	−14.8210	−0.541549
$750$	−7.62823	−0.278543
$751$	14.1372	0.515873	0.257936	−	0.966162i	$-0.416957\pi$
$751$	14.1372	0.515873	0.257936	+	0.966162i	$0.416957\pi$
$752$	−27.8093	−1.01410
$753$	−2.85737	−0.104128
$754$	−2.50948	−0.0913900
$755$	−14.0509	−0.511365
$756$	−23.1214	−0.840916
$757$	1.91400	0.0695655	0.0347827	−	0.999395i	$-0.488926\pi$
$757$	1.91400	0.0695655	0.0347827	+	0.999395i	$0.488926\pi$
$758$	32.3894	1.17644
$759$	−2.69976	−0.0979952
$760$	82.8837	3.00651
$761$	8.52480	0.309024	0.154512	−	0.987991i	$-0.450620\pi$
$761$	8.52480	0.309024	0.154512	+	0.987991i	$0.450620\pi$
$762$	−14.0109	−0.507563
$763$	51.1522	1.85183
$764$	−89.7141	−3.24574
$765$	54.2928	1.96296
$766$	8.11701	0.293280
$767$	−3.21122	−0.115951
$768$	−33.4898	−1.20846
$769$	41.0048	1.47867	0.739335	−	0.673337i	$-0.235140\pi$
$769$	41.0048	1.47867	0.739335	+	0.673337i	$0.235140\pi$
$770$	78.1339	2.81575
$771$	−1.87004	−0.0673479
$772$	−50.3505	−1.81215
$773$	−27.0258	−0.972050	−0.486025	−	0.873945i	$-0.661554\pi$
$773$	−27.0258	−0.972050	−0.486025	+	0.873945i	$0.661554\pi$
$774$	12.8086	0.460396
$775$	1.36448	0.0490136
$776$	125.645	4.51040
$777$	7.30939	0.262223
$778$	47.3504	1.69759
$779$	−32.9784	−1.18157
$780$	2.67577	0.0958078
$781$	−20.8691	−0.746757
$782$	48.2237	1.72447
$783$	−1.93118	−0.0690147
$784$	−14.4792	−0.517113
$785$	−44.5783	−1.59107
$786$	−0.456398	−0.0162792
$787$	48.7019	1.73604	0.868018	−	0.496534i	$-0.165394\pi$
$787$	48.7019	1.73604	0.868018	+	0.496534i	$0.165394\pi$
$788$	123.178	4.38805
$789$	7.29002	0.259531
$790$	101.794	3.62168
$791$	8.86551	0.315221
$792$	151.005	5.36575
$793$	−8.70527	−0.309133
$794$	102.448	3.63576
$795$	−7.21557	−0.255910
$796$	−57.2827	−2.03033
$797$	−0.0566429	−0.00200639	−0.00100320	−	0.999999i	$-0.500319\pi$
$797$	−0.0566429	−0.00200639	−0.00100320	+	0.999999i	$0.500319\pi$
$798$	5.82317	0.206138
$799$	11.2095	0.396564
$800$	−21.8272	−0.771710
$801$	0.545950	0.0192902
$802$	31.4869	1.11184
$803$	−34.1333	−1.20454
$804$	11.2015	0.395048
$805$	−13.1233	−0.462535
$806$	4.07900	0.143677
$807$	−1.05464	−0.0371251
$808$	−59.3533	−2.08804
$809$	46.8705	1.64788	0.823940	−	0.566677i	$-0.191771\pi$
$809$	46.8705	1.64788	0.823940	+	0.566677i	$0.191771\pi$
$810$	−56.2388	−1.97603
$811$	31.4052	1.10278	0.551392	−	0.834246i	$-0.314097\pi$
$811$	31.4052	1.10278	0.551392	+	0.834246i	$0.314097\pi$
$812$	18.3432	0.643720
$813$	−0.0133954	−0.000469798 0
$814$	−145.787	−5.10983
$815$	51.3091	1.79728
$816$	39.4434	1.38079
$817$	−4.88115	−0.170770
$818$	−55.2545	−1.93193
$819$	−5.27542	−0.184338
$820$	148.137	5.17315
$821$	9.46392	0.330293	0.165147	−	0.986269i	$-0.447190\pi$
$821$	9.46392	0.330293	0.165147	+	0.986269i	$0.447190\pi$
$822$	−10.6561	−0.371673
$823$	2.12023	0.0739067	0.0369533	−	0.999317i	$-0.488235\pi$
$823$	2.12023	0.0739067	0.0369533	+	0.999317i	$0.488235\pi$
$824$	−159.337	−5.55076
$825$	−0.831110	−0.0289355
$826$	31.3916	1.09225
$827$	−27.4981	−0.956201	−0.478101	−	0.878305i	$-0.658675\pi$
$827$	−27.4981	−0.956201	−0.478101	+	0.878305i	$0.658675\pi$
$828$	−38.2761	−1.33019
$829$	−12.5878	−0.437193	−0.218597	−	0.975815i	$-0.570148\pi$
$829$	−12.5878	−0.437193	−0.218597	+	0.975815i	$0.570148\pi$
$830$	63.0087	2.18706
$831$	4.07829	0.141474
$832$	−37.4765	−1.29926
$833$	5.83633	0.202217
$834$	−3.90742	−0.135303
$835$	−10.0422	−0.347523
$836$	−86.8449	−3.00359
$837$	3.13901	0.108500
$838$	16.1332	0.557311
$839$	−11.2077	−0.386932	−0.193466	−	0.981107i	$-0.561973\pi$
$839$	−11.2077	−0.386932	−0.193466	+	0.981107i	$0.561973\pi$
$840$	−17.3325	−0.598027
$841$	−27.4679	−0.947169
$842$	75.0042	2.58481
$843$	0.918890	0.0316483
$844$	94.1747	3.24163
$845$	−29.7422	−1.02316
$846$	−11.8989	−0.409092
$847$	−26.7496	−0.919126
$848$	222.000	7.62351
$849$	1.16880	0.0401132
$850$	14.8454	0.509194
$851$	24.4862	0.839377
$852$	6.98645	0.239352
$853$	27.7329	0.949557	0.474778	−	0.880105i	$-0.342528\pi$
$853$	27.7329	0.949557	0.474778	+	0.880105i	$0.342528\pi$
$854$	85.0992	2.91203
$855$	21.9625	0.751102
$856$	−65.5748	−2.24130
$857$	9.82959	0.335772	0.167886	−	0.985806i	$-0.446306\pi$
$857$	9.82959	0.335772	0.167886	+	0.985806i	$0.446306\pi$
$858$	−2.48453	−0.0848206
$859$	−41.2895	−1.40878	−0.704390	−	0.709813i	$-0.748779\pi$
$859$	−41.2895	−1.40878	−0.704390	+	0.709813i	$0.748779\pi$
$860$	21.9258	0.747663
$861$	6.89637	0.235028
$862$	−55.2507	−1.88185
$863$	−25.7950	−0.878072	−0.439036	−	0.898469i	$-0.644680\pi$
$863$	−25.7950	−0.878072	−0.439036	+	0.898469i	$0.644680\pi$
$864$	−50.2139	−1.70831
$865$	−32.3513	−1.09998
$866$	24.9177	0.846736
$867$	−11.4269	−0.388076
$868$	−29.8157	−1.01201
$869$	−70.6753	−2.39749
$870$	−2.18474	−0.0740698
$871$	5.17187	0.175242
$872$	226.320	7.66416
$873$	33.2934	1.12681
$874$	19.5074	0.659849
$875$	25.7445	0.870323
$876$	11.4269	0.386081
$877$	−41.9038	−1.41499	−0.707496	−	0.706718i	$-0.750175\pi$
$877$	−41.9038	−1.41499	−0.707496	+	0.706718i	$0.750175\pi$
$878$	84.7806	2.86121
$879$	−2.80497	−0.0946093
$880$	214.089	7.21695
$881$	−15.2358	−0.513306	−0.256653	−	0.966504i	$-0.582620\pi$
$881$	−15.2358	−0.513306	−0.256653	+	0.966504i	$0.582620\pi$
$882$	−6.19527	−0.208605
$883$	14.9357	0.502626	0.251313	−	0.967906i	$-0.419138\pi$
$883$	14.9357	0.502626	0.251313	+	0.967906i	$0.419138\pi$
$884$	33.1838	1.11609
$885$	−2.79568	−0.0939756
$886$	5.88547	0.197726
$887$	50.0590	1.68082	0.840408	−	0.541954i	$-0.182315\pi$
$887$	50.0590	1.68082	0.840408	+	0.541954i	$0.182315\pi$
$888$	32.3399	1.08526
$889$	47.2855	1.58590
$890$	1.24985	0.0418951
$891$	39.0463	1.30810
$892$	−140.165	−4.69306
$893$	4.53447	0.151740
$894$	1.48604	0.0497006
$895$	4.55136	0.152135
$896$	205.444	6.86339
$897$	0.417300	0.0139332
$898$	−40.4053	−1.34834
$899$	−2.49031	−0.0830565
$900$	−11.7831	−0.392770
$901$	−89.4847	−2.98117
$902$	−137.549	−4.57989
$903$	1.02074	0.0339680
$904$	39.2249	1.30460
$905$	−48.8460	−1.62370
$906$	−4.36770	−0.145107
$907$	19.1903	0.637203	0.318602	−	0.947889i	$-0.396787\pi$
$907$	19.1903	0.637203	0.318602	+	0.947889i	$0.396787\pi$
$908$	−1.61812	−0.0536993
$909$	−15.7274	−0.521645
$910$	−12.0771	−0.400351
$911$	−11.2479	−0.372660	−0.186330	−	0.982487i	$-0.559659\pi$
$911$	−11.2479	−0.372660	−0.186330	+	0.982487i	$0.559659\pi$
$912$	15.9556	0.528344
$913$	−43.7466	−1.44780
$914$	−117.242	−3.87804
$915$	−7.57876	−0.250546
$916$	−70.0755	−2.31536
$917$	1.54030	0.0508651
$918$	34.1521	1.12719
$919$	−4.90075	−0.161661	−0.0808304	−	0.996728i	$-0.525757\pi$
$919$	−4.90075	−0.161661	−0.0808304	+	0.996728i	$0.525757\pi$
$920$	−58.0632	−1.91429
$921$	−5.89686	−0.194308
$922$	59.9595	1.97466
$923$	3.22572	0.106176
$924$	18.1608	0.597447
$925$	7.53798	0.247847
$926$	−21.0825	−0.692814
$927$	−42.2211	−1.38672
$928$	39.8368	1.30771
$929$	−24.4878	−0.803420	−0.401710	−	0.915767i	$-0.631584\pi$
$929$	−24.4878	−0.803420	−0.401710	+	0.915767i	$0.631584\pi$
$930$	3.55116	0.116447
$931$	2.36091	0.0773758
$932$	53.8917	1.76528
$933$	−2.83260	−0.0927350
$934$	−19.0617	−0.623718
$935$	−86.2961	−2.82218
$936$	−23.3408	−0.762917
$937$	19.0649	0.622822	0.311411	−	0.950275i	$-0.399198\pi$
$937$	19.0649	0.622822	0.311411	+	0.950275i	$0.399198\pi$
$938$	−50.5582	−1.65078
$939$	4.86079	0.158626
$940$	−20.3685	−0.664347
$941$	28.1193	0.916661	0.458331	−	0.888782i	$-0.348448\pi$
$941$	28.1193	0.916661	0.458331	+	0.888782i	$0.348448\pi$
$942$	−13.8571	−0.451488
$943$	23.1027	0.752326
$944$	86.0139	2.79951
$945$	−9.29395	−0.302332
$946$	−20.3588	−0.661921
$947$	4.31879	0.140342	0.0701709	−	0.997535i	$-0.477646\pi$
$947$	4.31879	0.140342	0.0701709	+	0.997535i	$0.477646\pi$
$948$	23.6602	0.768449
$949$	5.27595	0.171265
$950$	6.00528	0.194837
$951$	1.73725	0.0563342
$952$	−214.950	−6.96658
$953$	−12.1682	−0.394167	−0.197083	−	0.980387i	$-0.563147\pi$
$953$	−12.1682	−0.394167	−0.197083	+	0.980387i	$0.563147\pi$
$954$	94.9880	3.07535
$955$	−36.0618	−1.16693
$956$	78.8041	2.54871
$957$	1.51686	0.0490330
$958$	−20.3901	−0.658774
$959$	35.9632	1.16131
$960$	−32.6269	−1.05303
$961$	−26.9522	−0.869425
$962$	22.5342	0.726530
$963$	−17.3760	−0.559934
$964$	−41.6250	−1.34065
$965$	−20.2391	−0.651518
$966$	−4.07935	−0.131251
$967$	21.3762	0.687412	0.343706	−	0.939077i	$-0.388318\pi$
$967$	21.3762	0.687412	0.343706	+	0.939077i	$0.388318\pi$
$968$	−118.352	−3.80397
$969$	−6.43147	−0.206609
$970$	76.2191	2.44725
$971$	17.6263	0.565655	0.282827	−	0.959171i	$-0.408728\pi$
$971$	17.6263	0.565655	0.282827	+	0.959171i	$0.408728\pi$
$972$	−40.8190	−1.30927
$973$	13.1872	0.422761
$974$	16.0675	0.514835
$975$	0.128464	0.00411413
$976$	233.174	7.46372
$977$	−9.48143	−0.303338	−0.151669	−	0.988431i	$-0.548465\pi$
$977$	−9.48143	−0.303338	−0.151669	+	0.988431i	$0.548465\pi$
$978$	15.9493	0.510004
$979$	−0.867764	−0.0277339
$980$	−10.6050	−0.338766
$981$	59.9702	1.91470
$982$	−12.6077	−0.402327
$983$	16.2858	0.519438	0.259719	−	0.965684i	$-0.416370\pi$
$983$	16.2858	0.519438	0.259719	+	0.965684i	$0.416370\pi$
$984$	30.5126	0.972706
$985$	49.5133	1.57762
$986$	−27.0944	−0.862860
$987$	−0.948238	−0.0301827
$988$	13.4235	0.427059
$989$	3.41944	0.108732
$990$	91.6033	2.91134
$991$	29.7736	0.945789	0.472894	−	0.881119i	$-0.343209\pi$
$991$	29.7736	0.945789	0.472894	+	0.881119i	$0.343209\pi$
$992$	−64.7522	−2.05588
$993$	8.78242	0.278702
$994$	−31.5333	−1.00018
$995$	−23.0256	−0.729960
$996$	14.6452	0.464052
$997$	45.1203	1.42897	0.714487	−	0.699649i	$-0.246660\pi$
$997$	45.1203	1.42897	0.714487	+	0.699649i	$0.246660\pi$
$998$	44.5272	1.40948
$999$	17.3412	0.548652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.1	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.1	✓	139	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81570 q^{2} -0.263068 q^{3} +5.92814 q^{4} +2.38290 q^{5} +0.740719 q^{6} -2.49985 q^{7} -11.0604 q^{8} -2.93080 q^{9} +O(q^{10})\)	\(q-2.81570 q^{2} -0.263068 q^{3} +5.92814 q^{4} +2.38290 q^{5} +0.740719 q^{6} -2.49985 q^{7} -11.0604 q^{8} -2.93080 q^{9} -6.70951 q^{10} +4.65838 q^{11} -1.55950 q^{12} -0.720040 q^{13} +7.03882 q^{14} -0.626864 q^{15} +19.2866 q^{16} -7.77412 q^{17} +8.25223 q^{18} -3.14479 q^{19} +14.1261 q^{20} +0.657631 q^{21} -13.1166 q^{22} +2.20304 q^{23} +2.90965 q^{24} +0.678197 q^{25} +2.02741 q^{26} +1.56020 q^{27} -14.8195 q^{28} -1.23778 q^{29} +1.76506 q^{30} +2.01192 q^{31} -32.1842 q^{32} -1.22547 q^{33} +21.8896 q^{34} -5.95689 q^{35} -17.3742 q^{36} +11.1147 q^{37} +8.85476 q^{38} +0.189419 q^{39} -26.3559 q^{40} +10.4867 q^{41} -1.85169 q^{42} +1.55214 q^{43} +27.6155 q^{44} -6.98378 q^{45} -6.20310 q^{46} -1.44190 q^{47} -5.07368 q^{48} -0.750739 q^{49} -1.90960 q^{50} +2.04512 q^{51} -4.26850 q^{52} +11.5106 q^{53} -4.39305 q^{54} +11.1004 q^{55} +27.6495 q^{56} +0.827293 q^{57} +3.48520 q^{58} +4.45978 q^{59} -3.71614 q^{60} +12.0900 q^{61} -5.66496 q^{62} +7.32656 q^{63} +52.0478 q^{64} -1.71578 q^{65} +3.45055 q^{66} -7.18276 q^{67} -46.0861 q^{68} -0.579550 q^{69} +16.7728 q^{70} -4.47992 q^{71} +32.4159 q^{72} -7.32730 q^{73} -31.2957 q^{74} -0.178412 q^{75} -18.6427 q^{76} -11.6453 q^{77} -0.533348 q^{78} -15.1717 q^{79} +45.9579 q^{80} +8.38195 q^{81} -29.5273 q^{82} -9.39095 q^{83} +3.89853 q^{84} -18.5249 q^{85} -4.37036 q^{86} +0.325619 q^{87} -51.5237 q^{88} -0.186280 q^{89} +19.6642 q^{90} +1.79999 q^{91} +13.0600 q^{92} -0.529272 q^{93} +4.05995 q^{94} -7.49370 q^{95} +8.46663 q^{96} -11.3599 q^{97} +2.11385 q^{98} -13.6527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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