LMFDB - Embedded newform 4007.2.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.72706 q^{2} -2.54460 q^{3} +5.43687 q^{4} -1.96557 q^{5} +6.93928 q^{6} -3.80223 q^{7} -9.37255 q^{8} +3.47499 q^{9} +O(q^{10})$	\(q-2.72706 q^{2} -2.54460 q^{3} +5.43687 q^{4} -1.96557 q^{5} +6.93928 q^{6} -3.80223 q^{7} -9.37255 q^{8} +3.47499 q^{9} +5.36024 q^{10} +0.142734 q^{11} -13.8346 q^{12} -4.10786 q^{13} +10.3689 q^{14} +5.00160 q^{15} +14.6858 q^{16} -0.664228 q^{17} -9.47651 q^{18} -4.51271 q^{19} -10.6866 q^{20} +9.67515 q^{21} -0.389244 q^{22} -4.46669 q^{23} +23.8494 q^{24} -1.13652 q^{25} +11.2024 q^{26} -1.20865 q^{27} -20.6722 q^{28} +6.00885 q^{29} -13.6397 q^{30} +0.367354 q^{31} -21.3039 q^{32} -0.363201 q^{33} +1.81139 q^{34} +7.47357 q^{35} +18.8930 q^{36} -2.21354 q^{37} +12.3064 q^{38} +10.4529 q^{39} +18.4224 q^{40} -7.33405 q^{41} -26.3847 q^{42} -1.98760 q^{43} +0.776025 q^{44} -6.83035 q^{45} +12.1809 q^{46} +11.1902 q^{47} -37.3694 q^{48} +7.45695 q^{49} +3.09935 q^{50} +1.69020 q^{51} -22.3339 q^{52} -5.68854 q^{53} +3.29608 q^{54} -0.280554 q^{55} +35.6366 q^{56} +11.4830 q^{57} -16.3865 q^{58} +8.85357 q^{59} +27.1930 q^{60} -8.67842 q^{61} -1.00180 q^{62} -13.2127 q^{63} +28.7256 q^{64} +8.07430 q^{65} +0.990471 q^{66} +10.4317 q^{67} -3.61132 q^{68} +11.3659 q^{69} -20.3809 q^{70} +6.17474 q^{71} -32.5695 q^{72} +0.392149 q^{73} +6.03646 q^{74} +2.89198 q^{75} -24.5350 q^{76} -0.542707 q^{77} -28.5056 q^{78} -14.9512 q^{79} -28.8660 q^{80} -7.34942 q^{81} +20.0004 q^{82} -4.38023 q^{83} +52.6025 q^{84} +1.30559 q^{85} +5.42031 q^{86} -15.2901 q^{87} -1.33778 q^{88} +11.9949 q^{89} +18.6268 q^{90} +15.6190 q^{91} -24.2848 q^{92} -0.934769 q^{93} -30.5163 q^{94} +8.87006 q^{95} +54.2100 q^{96} +14.8107 q^{97} -20.3356 q^{98} +0.495999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.72706	−1.92832	−0.964162	−	0.265314i	$-0.914524\pi$
$2$	−2.72706	−1.92832	−0.964162	+	0.265314i	$0.914524\pi$
$3$	−2.54460	−1.46913	−0.734563	−	0.678541i	$-0.762613\pi$
$3$	−2.54460	−1.46913	−0.734563	+	0.678541i	$0.762613\pi$
$4$	5.43687	2.71843
$5$	−1.96557	−0.879032	−0.439516	−	0.898235i	$-0.644850\pi$
$5$	−1.96557	−0.879032	−0.439516	+	0.898235i	$0.644850\pi$
$6$	6.93928	2.83295
$7$	−3.80223	−1.43711	−0.718554	−	0.695471i	$-0.755196\pi$
$7$	−3.80223	−1.43711	−0.718554	+	0.695471i	$0.755196\pi$
$8$	−9.37255	−3.31370
$9$	3.47499	1.15833
$10$	5.36024	1.69506
$11$	0.142734	0.0430359	0.0215179	−	0.999768i	$-0.493150\pi$
$11$	0.142734	0.0430359	0.0215179	+	0.999768i	$0.493150\pi$
$12$	−13.8346	−3.99372
$13$	−4.10786	−1.13931	−0.569657	−	0.821882i	$-0.692924\pi$
$13$	−4.10786	−1.13931	−0.569657	+	0.821882i	$0.692924\pi$
$14$	10.3689	2.77121
$15$	5.00160	1.29141
$16$	14.6858	3.67145
$17$	−0.664228	−0.161099	−0.0805495	−	0.996751i	$-0.525668\pi$
$17$	−0.664228	−0.161099	−0.0805495	+	0.996751i	$0.525668\pi$
$18$	−9.47651	−2.23363
$19$	−4.51271	−1.03529	−0.517643	−	0.855597i	$-0.673190\pi$
$19$	−4.51271	−1.03529	−0.517643	+	0.855597i	$0.673190\pi$
$20$	−10.6866	−2.38959
$21$	9.67515	2.11129
$22$	−0.389244	−0.0829871
$23$	−4.46669	−0.931368	−0.465684	−	0.884951i	$-0.654192\pi$
$23$	−4.46669	−0.931368	−0.465684	+	0.884951i	$0.654192\pi$
$24$	23.8494	4.86823
$25$	−1.13652	−0.227303
$26$	11.2024	2.19697
$27$	−1.20865	−0.232606
$28$	−20.6722	−3.90668
$29$	6.00885	1.11582	0.557908	−	0.829903i	$-0.311604\pi$
$29$	6.00885	1.11582	0.557908	+	0.829903i	$0.311604\pi$
$30$	−13.6397	−2.49025
$31$	0.367354	0.0659787	0.0329894	−	0.999456i	$-0.489497\pi$
$31$	0.367354	0.0659787	0.0329894	+	0.999456i	$0.489497\pi$
$32$	−21.3039	−3.76604
$33$	−0.363201	−0.0632251
$34$	1.81139	0.310651
$35$	7.47357	1.26326
$36$	18.8930	3.14884
$37$	−2.21354	−0.363903	−0.181952	−	0.983307i	$-0.558241\pi$
$37$	−2.21354	−0.363903	−0.181952	+	0.983307i	$0.558241\pi$
$38$	12.3064	1.99637
$39$	10.4529	1.67380
$40$	18.4224	2.91284
$41$	−7.33405	−1.14539	−0.572693	−	0.819770i	$-0.694101\pi$
$41$	−7.33405	−1.14539	−0.572693	+	0.819770i	$0.694101\pi$
$42$	−26.3847	−4.07125
$43$	−1.98760	−0.303106	−0.151553	−	0.988449i	$-0.548427\pi$
$43$	−1.98760	−0.303106	−0.151553	+	0.988449i	$0.548427\pi$
$44$	0.776025	0.116990
$45$	−6.83035	−1.01821
$46$	12.1809	1.79598
$47$	11.1902	1.63226	0.816128	−	0.577871i	$-0.196116\pi$
$47$	11.1902	1.63226	0.816128	+	0.577871i	$0.196116\pi$
$48$	−37.3694	−5.39381
$49$	7.45695	1.06528
$50$	3.09935	0.438314
$51$	1.69020	0.236675
$52$	−22.3339	−3.09715
$53$	−5.68854	−0.781380	−0.390690	−	0.920522i	$-0.627764\pi$
$53$	−5.68854	−0.781380	−0.390690	+	0.920522i	$0.627764\pi$
$54$	3.29608	0.448539
$55$	−0.280554	−0.0378299
$56$	35.6366	4.76214
$57$	11.4830	1.52096
$58$	−16.3865	−2.15166
$59$	8.85357	1.15264	0.576319	−	0.817225i	$-0.304489\pi$
$59$	8.85357	1.15264	0.576319	+	0.817225i	$0.304489\pi$
$60$	27.1930	3.51061
$61$	−8.67842	−1.11116	−0.555579	−	0.831464i	$-0.687503\pi$
$61$	−8.67842	−1.11116	−0.555579	+	0.831464i	$0.687503\pi$
$62$	−1.00180	−0.127228
$63$	−13.2127	−1.66464
$64$	28.7256	3.59070
$65$	8.07430	1.00149
$66$	0.990471	0.121919
$67$	10.4317	1.27443	0.637216	−	0.770685i	$-0.280086\pi$
$67$	10.4317	1.27443	0.637216	+	0.770685i	$0.280086\pi$
$68$	−3.61132	−0.437937
$69$	11.3659	1.36830
$70$	−20.3809	−2.43598
$71$	6.17474	0.732806	0.366403	−	0.930456i	$-0.380589\pi$
$71$	6.17474	0.732806	0.366403	+	0.930456i	$0.380589\pi$
$72$	−32.5695	−3.83835
$73$	0.392149	0.0458976	0.0229488	−	0.999737i	$-0.492695\pi$
$73$	0.392149	0.0458976	0.0229488	+	0.999737i	$0.492695\pi$
$74$	6.03646	0.701724
$75$	2.89198	0.333937
$76$	−24.5350	−2.81436
$77$	−0.542707	−0.0618472
$78$	−28.5056	−3.22762
$79$	−14.9512	−1.68214	−0.841069	−	0.540927i	$-0.818073\pi$
$79$	−14.9512	−1.68214	−0.841069	+	0.540927i	$0.818073\pi$
$80$	−28.8660	−3.22732
$81$	−7.34942	−0.816602
$82$	20.0004	2.20868
$83$	−4.38023	−0.480792	−0.240396	−	0.970675i	$-0.577277\pi$
$83$	−4.38023	−0.480792	−0.240396	+	0.970675i	$0.577277\pi$
$84$	52.6025	5.73940
$85$	1.30559	0.141611
$86$	5.42031	0.584487
$87$	−15.2901	−1.63927
$88$	−1.33778	−0.142608
$89$	11.9949	1.27145	0.635727	−	0.771914i	$-0.280700\pi$
$89$	11.9949	1.27145	0.635727	+	0.771914i	$0.280700\pi$
$90$	18.6268	1.96344
$91$	15.6190	1.63732
$92$	−24.2848	−2.53186
$93$	−0.934769	−0.0969310
$94$	−30.5163	−3.14752
$95$	8.87006	0.910049
$96$	54.2100	5.53279
$97$	14.8107	1.50380	0.751902	−	0.659275i	$-0.229137\pi$
$97$	14.8107	1.50380	0.751902	+	0.659275i	$0.229137\pi$
$98$	−20.3356	−2.05420
$99$	0.495999	0.0498497
$100$	−6.17908	−0.617908
$101$	7.84833	0.780938	0.390469	−	0.920616i	$-0.372313\pi$
$101$	7.84833	0.780938	0.390469	+	0.920616i	$0.372313\pi$
$102$	−4.60927	−0.456385
$103$	3.92955	0.387190	0.193595	−	0.981082i	$-0.437985\pi$
$103$	3.92955	0.387190	0.193595	+	0.981082i	$0.437985\pi$
$104$	38.5011	3.77534
$105$	−19.0172	−1.85589
$106$	15.5130	1.50675
$107$	−2.33347	−0.225585	−0.112793	−	0.993619i	$-0.535980\pi$
$107$	−2.33347	−0.225585	−0.112793	+	0.993619i	$0.535980\pi$
$108$	−6.57130	−0.632323
$109$	−11.5318	−1.10455	−0.552275	−	0.833662i	$-0.686240\pi$
$109$	−11.5318	−1.10455	−0.552275	+	0.833662i	$0.686240\pi$
$110$	0.765089	0.0729483
$111$	5.63257	0.534620
$112$	−55.8387	−5.27626
$113$	−2.46481	−0.231870	−0.115935	−	0.993257i	$-0.536986\pi$
$113$	−2.46481	−0.231870	−0.115935	+	0.993257i	$0.536986\pi$
$114$	−31.3149	−2.93291
$115$	8.77961	0.818702
$116$	32.6693	3.03327
$117$	−14.2748	−1.31970
$118$	−24.1442	−2.22266
$119$	2.52555	0.231517
$120$	−46.8778	−4.27933
$121$	−10.9796	−0.998148
$122$	23.6666	2.14267
$123$	18.6622	1.68272
$124$	1.99725	0.179359
$125$	12.0618	1.07884
$126$	36.0319	3.20997
$127$	−0.592185	−0.0525479	−0.0262739	−	0.999655i	$-0.508364\pi$
$127$	−0.592185	−0.0525479	−0.0262739	+	0.999655i	$0.508364\pi$
$128$	−35.7286	−3.15799
$129$	5.05765	0.445301
$130$	−22.0191	−1.93120
$131$	−2.54411	−0.222280	−0.111140	−	0.993805i	$-0.535450\pi$
$131$	−2.54411	−0.222280	−0.111140	+	0.993805i	$0.535450\pi$
$132$	−1.97467	−0.171873
$133$	17.1583	1.48782
$134$	−28.4478	−2.45752
$135$	2.37570	0.204468
$136$	6.22551	0.533833
$137$	5.40320	0.461626	0.230813	−	0.972998i	$-0.425861\pi$
$137$	5.40320	0.461626	0.230813	+	0.972998i	$0.425861\pi$
$138$	−30.9956	−2.63852
$139$	−7.23810	−0.613928	−0.306964	−	0.951721i	$-0.599313\pi$
$139$	−7.23810	−0.613928	−0.306964	+	0.951721i	$0.599313\pi$
$140$	40.6328	3.43410
$141$	−28.4745	−2.39799
$142$	−16.8389	−1.41309
$143$	−0.586330	−0.0490314
$144$	51.0329	4.25274
$145$	−11.8109	−0.980838
$146$	−1.06942	−0.0885055
$147$	−18.9750	−1.56503
$148$	−12.0347	−0.989247
$149$	19.1230	1.56661	0.783307	−	0.621635i	$-0.213531\pi$
$149$	19.1230	1.56661	0.783307	+	0.621635i	$0.213531\pi$
$150$	−7.88660	−0.643938
$151$	−2.34239	−0.190621	−0.0953106	−	0.995448i	$-0.530384\pi$
$151$	−2.34239	−0.190621	−0.0953106	+	0.995448i	$0.530384\pi$
$152$	42.2956	3.43062
$153$	−2.30819	−0.186606
$154$	1.48000	0.119261
$155$	−0.722062	−0.0579974
$156$	56.8308	4.55010
$157$	17.7546	1.41697	0.708487	−	0.705724i	$-0.249378\pi$
$157$	17.7546	1.41697	0.708487	+	0.705724i	$0.249378\pi$
$158$	40.7728	3.24371
$159$	14.4750	1.14795
$160$	41.8745	3.31047
$161$	16.9834	1.33848
$162$	20.0423	1.57467
$163$	20.1552	1.57867	0.789337	−	0.613960i	$-0.210424\pi$
$163$	20.1552	1.57867	0.789337	+	0.613960i	$0.210424\pi$
$164$	−39.8742	−3.11366
$165$	0.713898	0.0555769
$166$	11.9451	0.927123
$167$	20.8675	1.61478	0.807388	−	0.590021i	$-0.200880\pi$
$167$	20.8675	1.61478	0.807388	+	0.590021i	$0.200880\pi$
$168$	−90.6808	−6.99618
$169$	3.87449	0.298038
$170$	−3.56043	−0.273072
$171$	−15.6816	−1.19920
$172$	−10.8063	−0.823974
$173$	−11.1178	−0.845273	−0.422637	−	0.906299i	$-0.638895\pi$
$173$	−11.1178	−0.845273	−0.422637	+	0.906299i	$0.638895\pi$
$174$	41.6971	3.16105
$175$	4.32129	0.326659
$176$	2.09616	0.158004
$177$	−22.5288	−1.69337
$178$	−32.7108	−2.45178
$179$	17.0286	1.27278	0.636389	−	0.771368i	$-0.280427\pi$
$179$	17.0286	1.27278	0.636389	+	0.771368i	$0.280427\pi$
$180$	−37.1357	−2.76793
$181$	10.6833	0.794082	0.397041	−	0.917801i	$-0.370037\pi$
$181$	10.6833	0.794082	0.397041	+	0.917801i	$0.370037\pi$
$182$	−42.5940	−3.15728
$183$	22.0831	1.63243
$184$	41.8642	3.08627
$185$	4.35087	0.319883
$186$	2.54917	0.186914
$187$	−0.0948079	−0.00693304
$188$	60.8396	4.43718
$189$	4.59558	0.334280
$190$	−24.1892	−1.75487
$191$	−0.260586	−0.0188553	−0.00942766	−	0.999956i	$-0.503001\pi$
$191$	−0.260586	−0.0188553	−0.00942766	+	0.999956i	$0.503001\pi$
$192$	−73.0952	−5.27519
$193$	−12.4547	−0.896511	−0.448255	−	0.893906i	$-0.647954\pi$
$193$	−12.4547	−0.896511	−0.448255	+	0.893906i	$0.647954\pi$
$194$	−40.3898	−2.89982
$195$	−20.5459	−1.47132
$196$	40.5424	2.89589
$197$	−2.36201	−0.168286	−0.0841432	−	0.996454i	$-0.526815\pi$
$197$	−2.36201	−0.168286	−0.0841432	+	0.996454i	$0.526815\pi$
$198$	−1.35262	−0.0961264
$199$	16.6942	1.18342	0.591711	−	0.806150i	$-0.298453\pi$
$199$	16.6942	1.18342	0.591711	+	0.806150i	$0.298453\pi$
$200$	10.6520	0.753213
$201$	−26.5445	−1.87230
$202$	−21.4029	−1.50590
$203$	−22.8470	−1.60355
$204$	9.18937	0.643384
$205$	14.4156	1.00683
$206$	−10.7161	−0.746628
$207$	−15.5217	−1.07883
$208$	−60.3271	−4.18293
$209$	−0.644116	−0.0445544
$210$	51.8612	3.57876
$211$	10.5569	0.726765	0.363382	−	0.931640i	$-0.381622\pi$
$211$	10.5569	0.726765	0.363382	+	0.931640i	$0.381622\pi$
$212$	−30.9278	−2.12413
$213$	−15.7122	−1.07658
$214$	6.36352	0.435001
$215$	3.90678	0.266440
$216$	11.3282	0.770785
$217$	−1.39676	−0.0948185
$218$	31.4480	2.12993
$219$	−0.997864	−0.0674294
$220$	−1.52534	−0.102838
$221$	2.72856	0.183542
$222$	−15.3604	−1.03092
$223$	27.5600	1.84555	0.922776	−	0.385336i	$-0.125915\pi$
$223$	27.5600	1.84555	0.922776	+	0.385336i	$0.125915\pi$
$224$	81.0025	5.41221
$225$	−3.94938	−0.263292
$226$	6.72170	0.447121
$227$	17.4875	1.16068	0.580342	−	0.814373i	$-0.302919\pi$
$227$	17.4875	1.16068	0.580342	+	0.814373i	$0.302919\pi$
$228$	62.4317	4.13464
$229$	13.0268	0.860835	0.430417	−	0.902630i	$-0.358366\pi$
$229$	13.0268	0.860835	0.430417	+	0.902630i	$0.358366\pi$
$230$	−23.9425	−1.57872
$231$	1.38097	0.0908613
$232$	−56.3183	−3.69748
$233$	4.20894	0.275737	0.137869	−	0.990451i	$-0.455975\pi$
$233$	4.20894	0.275737	0.137869	+	0.990451i	$0.455975\pi$
$234$	38.9281	2.54481
$235$	−21.9952	−1.43481
$236$	48.1357	3.13337
$237$	38.0448	2.47127
$238$	−6.88733	−0.446439
$239$	−4.31907	−0.279378	−0.139689	−	0.990195i	$-0.544610\pi$
$239$	−4.31907	−0.279378	−0.139689	+	0.990195i	$0.544610\pi$
$240$	73.4524	4.74133
$241$	−26.7865	−1.72547	−0.862734	−	0.505658i	$-0.831250\pi$
$241$	−26.7865	−1.72547	−0.862734	+	0.505658i	$0.831250\pi$
$242$	29.9421	1.92475
$243$	22.3273	1.43230
$244$	−47.1834	−3.02061
$245$	−14.6572	−0.936414
$246$	−50.8930	−3.24482
$247$	18.5376	1.17952
$248$	−3.44304	−0.218633
$249$	11.1459	0.706344
$250$	−32.8932	−2.08035
$251$	−17.1638	−1.08337	−0.541685	−	0.840582i	$-0.682213\pi$
$251$	−17.1638	−1.08337	−0.541685	+	0.840582i	$0.682213\pi$
$252$	−71.8357	−4.52522
$253$	−0.637547	−0.0400823
$254$	1.61492	0.101329
$255$	−3.32221	−0.208045
$256$	39.9830	2.49894
$257$	−10.2932	−0.642072	−0.321036	−	0.947067i	$-0.604031\pi$
$257$	−10.2932	−0.642072	−0.321036	+	0.947067i	$0.604031\pi$
$258$	−13.7925	−0.858685
$259$	8.41638	0.522968
$260$	43.8989	2.72249
$261$	20.8807	1.29248
$262$	6.93795	0.428628
$263$	15.3325	0.945441	0.472720	−	0.881213i	$-0.343272\pi$
$263$	15.3325	0.945441	0.472720	+	0.881213i	$0.343272\pi$
$264$	3.40412	0.209509
$265$	11.1812	0.686858
$266$	−46.7919	−2.86899
$267$	−30.5222	−1.86793
$268$	56.7157	3.46446
$269$	14.8245	0.903863	0.451932	−	0.892053i	$-0.350735\pi$
$269$	14.8245	0.903863	0.451932	+	0.892053i	$0.350735\pi$
$270$	−6.47869	−0.394280
$271$	−4.49970	−0.273337	−0.136669	−	0.990617i	$-0.543640\pi$
$271$	−4.49970	−0.273337	−0.136669	+	0.990617i	$0.543640\pi$
$272$	−9.75471	−0.591466
$273$	−39.7441	−2.40543
$274$	−14.7349	−0.890165
$275$	−0.162219	−0.00978219
$276$	61.7950	3.71962
$277$	−0.822625	−0.0494268	−0.0247134	−	0.999695i	$-0.507867\pi$
$277$	−0.822625	−0.0494268	−0.0247134	+	0.999695i	$0.507867\pi$
$278$	19.7387	1.18385
$279$	1.27655	0.0764251
$280$	−70.0464	−4.18607
$281$	16.9558	1.01150	0.505750	−	0.862680i	$-0.331216\pi$
$281$	16.9558	1.01150	0.505750	+	0.862680i	$0.331216\pi$
$282$	77.6519	4.62410
$283$	12.5333	0.745025	0.372512	−	0.928027i	$-0.378496\pi$
$283$	12.5333	0.745025	0.372512	+	0.928027i	$0.378496\pi$
$284$	33.5712	1.99209
$285$	−22.5708	−1.33698
$286$	1.59896	0.0945485
$287$	27.8857	1.64604
$288$	−74.0310	−4.36232
$289$	−16.5588	−0.974047
$290$	32.2089	1.89137
$291$	−37.6874	−2.20928
$292$	2.13206	0.124770
$293$	−20.7109	−1.20994	−0.604971	−	0.796247i	$-0.706815\pi$
$293$	−20.7109	−1.20994	−0.604971	+	0.796247i	$0.706815\pi$
$294$	51.7459	3.01788
$295$	−17.4024	−1.01320
$296$	20.7465	1.20587
$297$	−0.172516	−0.0100104
$298$	−52.1495	−3.02094
$299$	18.3485	1.06112
$300$	15.7233	0.907784
$301$	7.55732	0.435597
$302$	6.38785	0.367579
$303$	−19.9708	−1.14730
$304$	−66.2726	−3.80100
$305$	17.0581	0.976743
$306$	6.29457	0.359836
$307$	−23.8232	−1.35966	−0.679831	−	0.733369i	$-0.737947\pi$
$307$	−23.8232	−1.35966	−0.679831	+	0.733369i	$0.737947\pi$
$308$	−2.95063	−0.168128
$309$	−9.99913	−0.568831
$310$	1.96911	0.111838
$311$	−15.7605	−0.893698	−0.446849	−	0.894610i	$-0.647454\pi$
$311$	−15.7605	−0.893698	−0.446849	+	0.894610i	$0.647454\pi$
$312$	−97.9699	−5.54645
$313$	−13.7594	−0.777729	−0.388864	−	0.921295i	$-0.627133\pi$
$313$	−13.7594	−0.777729	−0.388864	+	0.921295i	$0.627133\pi$
$314$	−48.4180	−2.73239
$315$	25.9706	1.46328
$316$	−81.2876	−4.57278
$317$	−17.3459	−0.974243	−0.487121	−	0.873334i	$-0.661953\pi$
$317$	−17.3459	−0.974243	−0.487121	+	0.873334i	$0.661953\pi$
$318$	−39.4743	−2.21361
$319$	0.857667	0.0480201
$320$	−56.4623	−3.15634
$321$	5.93775	0.331413
$322$	−46.3147	−2.58102
$323$	2.99747	0.166784
$324$	−39.9578	−2.21988
$325$	4.66864	0.258970
$326$	−54.9644	−3.04420
$327$	29.3439	1.62272
$328$	68.7387	3.79546
$329$	−42.5477	−2.34573
$330$	−1.94684	−0.107170
$331$	−23.6412	−1.29944	−0.649718	−	0.760176i	$-0.725113\pi$
$331$	−23.6412	−1.29944	−0.649718	+	0.760176i	$0.725113\pi$
$332$	−23.8147	−1.30700
$333$	−7.69202	−0.421520
$334$	−56.9070	−3.11381
$335$	−20.5043	−1.12027
$336$	142.087	7.75149
$337$	−14.3085	−0.779431	−0.389716	−	0.920935i	$-0.627427\pi$
$337$	−14.3085	−0.779431	−0.389716	+	0.920935i	$0.627427\pi$
$338$	−10.5660	−0.574713
$339$	6.27196	0.340646
$340$	7.09832	0.384961
$341$	0.0524339	0.00283945
$342$	42.7647	2.31245
$343$	−1.73743	−0.0938125
$344$	18.6289	1.00440
$345$	−22.3406	−1.20278
$346$	30.3190	1.62996
$347$	28.6883	1.54007	0.770034	−	0.638002i	$-0.220239\pi$
$347$	28.6883	1.54007	0.770034	+	0.638002i	$0.220239\pi$
$348$	−83.1304	−4.45626
$349$	0.432125	0.0231311	0.0115655	−	0.999933i	$-0.496318\pi$
$349$	0.432125	0.0231311	0.0115655	+	0.999933i	$0.496318\pi$
$350$	−11.7844	−0.629904
$351$	4.96498	0.265011
$352$	−3.04080	−0.162075
$353$	−20.1175	−1.07074	−0.535372	−	0.844616i	$-0.679829\pi$
$353$	−20.1175	−1.07074	−0.535372	+	0.844616i	$0.679829\pi$
$354$	61.4374	3.26536
$355$	−12.1369	−0.644160
$356$	65.2145	3.45636
$357$	−6.42651	−0.340127
$358$	−46.4381	−2.45433
$359$	3.08133	0.162626	0.0813132	−	0.996689i	$-0.474089\pi$
$359$	3.08133	0.162626	0.0813132	+	0.996689i	$0.474089\pi$
$360$	64.0178	3.37403
$361$	1.36452	0.0718170
$362$	−29.1340	−1.53125
$363$	27.9388	1.46640
$364$	84.9185	4.45094
$365$	−0.770799	−0.0403455
$366$	−60.2220	−3.14785
$367$	10.4095	0.543370	0.271685	−	0.962386i	$-0.412419\pi$
$367$	10.4095	0.543370	0.271685	+	0.962386i	$0.412419\pi$
$368$	−65.5968	−3.41947
$369$	−25.4857	−1.32673
$370$	−11.8651	−0.616837
$371$	21.6291	1.12293
$372$	−5.08221	−0.263500
$373$	−27.2573	−1.41133	−0.705665	−	0.708545i	$-0.749352\pi$
$373$	−27.2573	−1.41133	−0.705665	+	0.708545i	$0.749352\pi$
$374$	0.258547	0.0133691
$375$	−30.6924	−1.58495
$376$	−104.881	−5.40880
$377$	−24.6835	−1.27127
$378$	−12.5324	−0.644599
$379$	−13.8948	−0.713729	−0.356864	−	0.934156i	$-0.616154\pi$
$379$	−13.8948	−0.713729	−0.356864	+	0.934156i	$0.616154\pi$
$380$	48.2254	2.47391
$381$	1.50687	0.0771994
$382$	0.710633	0.0363592
$383$	7.34319	0.375219	0.187610	−	0.982244i	$-0.439926\pi$
$383$	7.34319	0.375219	0.187610	+	0.982244i	$0.439926\pi$
$384$	90.9151	4.63949
$385$	1.06673	0.0543657
$386$	33.9648	1.72876
$387$	−6.90689	−0.351097
$388$	80.5241	4.08799
$389$	11.7851	0.597526	0.298763	−	0.954327i	$-0.403426\pi$
$389$	11.7851	0.597526	0.298763	+	0.954327i	$0.403426\pi$
$390$	56.0298	2.83718
$391$	2.96690	0.150043
$392$	−69.8906	−3.53001
$393$	6.47375	0.326557
$394$	6.44136	0.324511
$395$	29.3877	1.47865
$396$	2.69668	0.135513
$397$	−29.9392	−1.50261	−0.751304	−	0.659956i	$-0.770575\pi$
$397$	−29.9392	−1.50261	−0.751304	+	0.659956i	$0.770575\pi$
$398$	−45.5262	−2.28202
$399$	−43.6611	−2.18579
$400$	−16.6906	−0.834531
$401$	−1.36070	−0.0679502	−0.0339751	−	0.999423i	$-0.510817\pi$
$401$	−1.36070	−0.0679502	−0.0339751	+	0.999423i	$0.510817\pi$
$402$	72.3884	3.61040
$403$	−1.50904	−0.0751705
$404$	42.6703	2.12293
$405$	14.4458	0.717820
$406$	62.3053	3.09216
$407$	−0.315947	−0.0156609
$408$	−15.8414	−0.784268
$409$	24.8727	1.22988	0.614939	−	0.788575i	$-0.289181\pi$
$409$	24.8727	1.22988	0.614939	+	0.788575i	$0.289181\pi$
$410$	−39.3123	−1.94150
$411$	−13.7490	−0.678187
$412$	21.3644	1.05255
$413$	−33.6633	−1.65646
$414$	42.3286	2.08034
$415$	8.60966	0.422632
$416$	87.5136	4.29071
$417$	18.4181	0.901937
$418$	1.75654	0.0859154
$419$	−31.1747	−1.52298	−0.761492	−	0.648174i	$-0.775533\pi$
$419$	−31.1747	−1.52298	−0.761492	+	0.648174i	$0.775533\pi$
$420$	−103.394	−5.04512
$421$	−24.9842	−1.21766	−0.608828	−	0.793302i	$-0.708360\pi$
$421$	−24.9842	−1.21766	−0.608828	+	0.793302i	$0.708360\pi$
$422$	−28.7892	−1.40144
$423$	38.8858	1.89069
$424$	53.3161	2.58926
$425$	0.754906	0.0366183
$426$	42.8482	2.07600
$427$	32.9973	1.59685
$428$	−12.6868	−0.613238
$429$	1.49198	0.0720333
$430$	−10.6540	−0.513783
$431$	−27.0608	−1.30347	−0.651736	−	0.758446i	$-0.725959\pi$
$431$	−27.0608	−1.30347	−0.651736	+	0.758446i	$0.725959\pi$
$432$	−17.7500	−0.853999
$433$	−4.17239	−0.200512	−0.100256	−	0.994962i	$-0.531966\pi$
$433$	−4.17239	−0.200512	−0.100256	+	0.994962i	$0.531966\pi$
$434$	3.80906	0.182841
$435$	30.0539	1.44097
$436$	−62.6971	−3.00264
$437$	20.1568	0.964233
$438$	2.72124	0.130026
$439$	37.6702	1.79790	0.898950	−	0.438051i	$-0.144331\pi$
$439$	37.6702	1.79790	0.898950	+	0.438051i	$0.144331\pi$
$440$	2.62951	0.125357
$441$	25.9128	1.23394
$442$	−7.44094	−0.353929
$443$	−30.8743	−1.46688	−0.733440	−	0.679754i	$-0.762087\pi$
$443$	−30.8743	−1.46688	−0.733440	+	0.679754i	$0.762087\pi$
$444$	30.6235	1.45333
$445$	−23.5768	−1.11765
$446$	−75.1578	−3.55882
$447$	−48.6603	−2.30155
$448$	−109.221	−5.16023
$449$	−33.0044	−1.55757	−0.778786	−	0.627290i	$-0.784164\pi$
$449$	−33.0044	−1.55757	−0.778786	+	0.627290i	$0.784164\pi$
$450$	10.7702	0.507712
$451$	−1.04682	−0.0492927
$452$	−13.4009	−0.630323
$453$	5.96045	0.280046
$454$	−47.6894	−2.23818
$455$	−30.7003	−1.43925
$456$	−107.625	−5.04002
$457$	−10.5091	−0.491597	−0.245799	−	0.969321i	$-0.579050\pi$
$457$	−10.5091	−0.491597	−0.245799	+	0.969321i	$0.579050\pi$
$458$	−35.5249	−1.65997
$459$	0.802823	0.0374726
$460$	47.7335	2.22559
$461$	26.7393	1.24537	0.622686	−	0.782472i	$-0.286041\pi$
$461$	26.7393	1.24537	0.622686	+	0.782472i	$0.286041\pi$
$462$	−3.76600	−0.175210
$463$	7.22302	0.335682	0.167841	−	0.985814i	$-0.446320\pi$
$463$	7.22302	0.335682	0.167841	+	0.985814i	$0.446320\pi$
$464$	88.2447	4.09666
$465$	1.83736	0.0852054
$466$	−11.4780	−0.531710
$467$	5.10611	0.236282	0.118141	−	0.992997i	$-0.462306\pi$
$467$	5.10611	0.236282	0.118141	+	0.992997i	$0.462306\pi$
$468$	−77.6099	−3.58752
$469$	−39.6637	−1.83150
$470$	59.9821	2.76677
$471$	−45.1785	−2.08171
$472$	−82.9805	−3.81949
$473$	−0.283698	−0.0130445
$474$	−103.750	−4.76541
$475$	5.12876	0.235324
$476$	13.7311	0.629363
$477$	−19.7676	−0.905096
$478$	11.7784	0.538730
$479$	−15.2018	−0.694589	−0.347294	−	0.937756i	$-0.612900\pi$
$479$	−15.2018	−0.694589	−0.347294	+	0.937756i	$0.612900\pi$
$480$	−106.554	−4.86350
$481$	9.09290	0.414600
$482$	73.0484	3.32726
$483$	−43.2159	−1.96639
$484$	−59.6948	−2.71340
$485$	−29.1116	−1.32189
$486$	−60.8879	−2.76193
$487$	−33.3596	−1.51167	−0.755833	−	0.654764i	$-0.772768\pi$
$487$	−33.3596	−1.51167	−0.755833	+	0.654764i	$0.772768\pi$
$488$	81.3389	3.68204
$489$	−51.2868	−2.31927
$490$	39.9711	1.80571
$491$	−7.43255	−0.335426	−0.167713	−	0.985836i	$-0.553638\pi$
$491$	−7.43255	−0.335426	−0.167713	+	0.985836i	$0.553638\pi$
$492$	101.464	4.57435
$493$	−3.99125	−0.179757
$494$	−50.5531	−2.27449
$495$	−0.974922	−0.0438195
$496$	5.39488	0.242237
$497$	−23.4778	−1.05312
$498$	−30.3956	−1.36206
$499$	33.0394	1.47905	0.739524	−	0.673130i	$-0.235050\pi$
$499$	33.0394	1.47905	0.739524	+	0.673130i	$0.235050\pi$
$500$	65.5783	2.93275
$501$	−53.0995	−2.37231
$502$	46.8068	2.08909
$503$	22.1765	0.988802	0.494401	−	0.869234i	$-0.335387\pi$
$503$	22.1765	0.988802	0.494401	+	0.869234i	$0.335387\pi$
$504$	123.837	5.51612
$505$	−15.4265	−0.686469
$506$	1.73863	0.0772916
$507$	−9.85903	−0.437855
$508$	−3.21963	−0.142848
$509$	−26.0570	−1.15496	−0.577479	−	0.816406i	$-0.695963\pi$
$509$	−26.0570	−1.15496	−0.577479	+	0.816406i	$0.695963\pi$
$510$	9.05986	0.401177
$511$	−1.49104	−0.0659598
$512$	−37.5788	−1.66076
$513$	5.45431	0.240813
$514$	28.0702	1.23812
$515$	−7.72382	−0.340352
$516$	27.4978	1.21052
$517$	1.59722	0.0702456
$518$	−22.9520	−1.00845
$519$	28.2904	1.24181
$520$	−75.6768	−3.31865
$521$	6.23595	0.273202	0.136601	−	0.990626i	$-0.456382\pi$
$521$	6.23595	0.273202	0.136601	+	0.990626i	$0.456382\pi$
$522$	−56.9430	−2.49233
$523$	−20.8876	−0.913353	−0.456676	−	0.889633i	$-0.650960\pi$
$523$	−20.8876	−0.913353	−0.456676	+	0.889633i	$0.650960\pi$
$524$	−13.8320	−0.604254
$525$	−10.9960	−0.479903
$526$	−41.8126	−1.82312
$527$	−0.244007	−0.0106291
$528$	−5.33389	−0.232128
$529$	−3.04872	−0.132553
$530$	−30.4919	−1.32449
$531$	30.7661	1.33513
$532$	93.2876	4.04453
$533$	30.1272	1.30496
$534$	83.2358	3.60197
$535$	4.58661	0.198296
$536$	−97.7714	−4.22308
$537$	−43.3310	−1.86987
$538$	−40.4272	−1.74294
$539$	1.06436	0.0458452
$540$	12.9164	0.555832
$541$	26.5379	1.14095	0.570477	−	0.821313i	$-0.306758\pi$
$541$	26.5379	1.14095	0.570477	+	0.821313i	$0.306758\pi$
$542$	12.2709	0.527082
$543$	−27.1847	−1.16661
$544$	14.1507	0.606706
$545$	22.6667	0.970934
$546$	108.385	4.63844
$547$	30.8661	1.31974	0.659870	−	0.751379i	$-0.270611\pi$
$547$	30.8661	1.31974	0.659870	+	0.751379i	$0.270611\pi$
$548$	29.3765	1.25490
$549$	−30.1574	−1.28709
$550$	0.442382	0.0188632
$551$	−27.1162	−1.15519
$552$	−106.528	−4.53412
$553$	56.8478	2.41741
$554$	2.24335	0.0953108
$555$	−11.0712	−0.469948
$556$	−39.3526	−1.66892
$557$	20.3039	0.860304	0.430152	−	0.902757i	$-0.358460\pi$
$557$	20.3039	0.860304	0.430152	+	0.902757i	$0.358460\pi$
$558$	−3.48123	−0.147372
$559$	8.16478	0.345334
$560$	109.755	4.63800
$561$	0.241248	0.0101855
$562$	−46.2396	−1.95050
$563$	35.0957	1.47911	0.739553	−	0.673098i	$-0.235037\pi$
$563$	35.0957	1.47911	0.739553	+	0.673098i	$0.235037\pi$
$564$	−154.812	−6.51877
$565$	4.84478	0.203821
$566$	−34.1790	−1.43665
$567$	27.9442	1.17355
$568$	−57.8730	−2.42830
$569$	−14.2911	−0.599112	−0.299556	−	0.954079i	$-0.596839\pi$
$569$	−14.2911	−0.599112	−0.299556	+	0.954079i	$0.596839\pi$
$570$	61.5519	2.57812
$571$	−23.7354	−0.993296	−0.496648	−	0.867952i	$-0.665436\pi$
$571$	−23.7354	−0.993296	−0.496648	+	0.867952i	$0.665436\pi$
$572$	−3.18780	−0.133289
$573$	0.663086	0.0277008
$574$	−76.0461	−3.17410
$575$	5.07646	0.211703
$576$	99.8212	4.15922
$577$	27.1785	1.13146	0.565729	−	0.824592i	$-0.308595\pi$
$577$	27.1785	1.13146	0.565729	+	0.824592i	$0.308595\pi$
$578$	45.1569	1.87828
$579$	31.6923	1.31709
$580$	−64.2140	−2.66634
$581$	16.6546	0.690950
$582$	102.776	4.26020
$583$	−0.811947	−0.0336274
$584$	−3.67544	−0.152091
$585$	28.0581	1.16006
$586$	56.4798	2.33316
$587$	−6.84395	−0.282480	−0.141240	−	0.989975i	$-0.545109\pi$
$587$	−6.84395	−0.282480	−0.141240	+	0.989975i	$0.545109\pi$
$588$	−103.164	−4.25442
$589$	−1.65776	−0.0683068
$590$	47.4573	1.95379
$591$	6.01038	0.247234
$592$	−32.5075	−1.33605
$593$	1.42340	0.0584521	0.0292261	−	0.999573i	$-0.490696\pi$
$593$	1.42340	0.0584521	0.0292261	+	0.999573i	$0.490696\pi$
$594$	0.470462	0.0193033
$595$	−4.96416	−0.203511
$596$	103.969	4.25874
$597$	−42.4801	−1.73859
$598$	−50.0375	−2.04619
$599$	−11.4690	−0.468612	−0.234306	−	0.972163i	$-0.575282\pi$
$599$	−11.4690	−0.468612	−0.234306	+	0.972163i	$0.575282\pi$
$600$	−27.1052	−1.10656
$601$	15.1448	0.617768	0.308884	−	0.951100i	$-0.400045\pi$
$601$	15.1448	0.617768	0.308884	+	0.951100i	$0.400045\pi$
$602$	−20.6093	−0.839971
$603$	36.2500	1.47621
$604$	−12.7353	−0.518191
$605$	21.5813	0.877404
$606$	54.4617	2.21236
$607$	−25.8145	−1.04778	−0.523890	−	0.851786i	$-0.675520\pi$
$607$	−25.8145	−1.04778	−0.523890	+	0.851786i	$0.675520\pi$
$608$	96.1385	3.89893
$609$	58.1366	2.35581
$610$	−46.5184	−1.88348
$611$	−45.9677	−1.85965
$612$	−12.5493	−0.507275
$613$	19.6741	0.794630	0.397315	−	0.917682i	$-0.369942\pi$
$613$	19.6741	0.794630	0.397315	+	0.917682i	$0.369942\pi$
$614$	64.9673	2.62187
$615$	−36.6820	−1.47916
$616$	5.08655	0.204943
$617$	−15.6383	−0.629576	−0.314788	−	0.949162i	$-0.601933\pi$
$617$	−15.6383	−0.629576	−0.314788	+	0.949162i	$0.601933\pi$
$618$	27.2682	1.09689
$619$	−9.39145	−0.377474	−0.188737	−	0.982028i	$-0.560439\pi$
$619$	−9.39145	−0.377474	−0.188737	+	0.982028i	$0.560439\pi$
$620$	−3.92575	−0.157662
$621$	5.39868	0.216642
$622$	42.9799	1.72334
$623$	−45.6073	−1.82722
$624$	153.508	6.14525
$625$	−18.0258	−0.721030
$626$	37.5228	1.49971
$627$	1.63902	0.0654561
$628$	96.5296	3.85195
$629$	1.47029	0.0586245
$630$	−70.8233	−2.82167
$631$	11.8689	0.472495	0.236247	−	0.971693i	$-0.424082\pi$
$631$	11.8689	0.472495	0.236247	+	0.971693i	$0.424082\pi$
$632$	140.131	5.57410
$633$	−26.8630	−1.06771
$634$	47.3033	1.87866
$635$	1.16398	0.0461913
$636$	78.6989	3.12061
$637$	−30.6321	−1.21369
$638$	−2.33891	−0.0925984
$639$	21.4571	0.848831
$640$	70.2273	2.77598
$641$	13.8697	0.547819	0.273909	−	0.961755i	$-0.411683\pi$
$641$	13.8697	0.547819	0.273909	+	0.961755i	$0.411683\pi$
$642$	−16.1926	−0.639071
$643$	16.8827	0.665790	0.332895	−	0.942964i	$-0.391975\pi$
$643$	16.8827	0.665790	0.332895	+	0.942964i	$0.391975\pi$
$644$	92.3363	3.63856
$645$	−9.94119	−0.391434
$646$	−8.17428	−0.321613
$647$	−6.26822	−0.246429	−0.123215	−	0.992380i	$-0.539320\pi$
$647$	−6.26822	−0.246429	−0.123215	+	0.992380i	$0.539320\pi$
$648$	68.8828	2.70597
$649$	1.26370	0.0496048
$650$	−12.7317	−0.499377
$651$	3.55421	0.139300
$652$	109.581	4.29152
$653$	24.5018	0.958828	0.479414	−	0.877589i	$-0.340849\pi$
$653$	24.5018	0.958828	0.479414	+	0.877589i	$0.340849\pi$
$654$	−80.0227	−3.12913
$655$	5.00064	0.195391
$656$	−107.706	−4.20522
$657$	1.36271	0.0531646
$658$	116.030	4.52332
$659$	49.9409	1.94542	0.972711	−	0.232021i	$-0.0745338\pi$
$659$	49.9409	1.94542	0.972711	+	0.232021i	$0.0745338\pi$
$660$	3.88137	0.151082
$661$	17.1065	0.665364	0.332682	−	0.943039i	$-0.392046\pi$
$661$	17.1065	0.665364	0.332682	+	0.943039i	$0.392046\pi$
$662$	64.4709	2.50573
$663$	−6.94308	−0.269647
$664$	41.0539	1.59320
$665$	−33.7260	−1.30784
$666$	20.9766	0.812827
$667$	−26.8397	−1.03924
$668$	113.454	4.38966
$669$	−70.1291	−2.71135
$670$	55.9164	2.16024
$671$	−1.23870	−0.0478196
$672$	−206.119	−7.95121
$673$	−36.9614	−1.42476	−0.712379	−	0.701795i	$-0.752382\pi$
$673$	−36.9614	−1.42476	−0.712379	+	0.701795i	$0.752382\pi$
$674$	39.0200	1.50300
$675$	1.37365	0.0528720
$676$	21.0651	0.810196
$677$	−17.0125	−0.653844	−0.326922	−	0.945051i	$-0.606012\pi$
$677$	−17.0125	−0.653844	−0.326922	+	0.945051i	$0.606012\pi$
$678$	−17.1040	−0.656876
$679$	−56.3139	−2.16113
$680$	−12.2367	−0.469256
$681$	−44.4986	−1.70519
$682$	−0.142990	−0.00547538
$683$	−25.5166	−0.976364	−0.488182	−	0.872742i	$-0.662340\pi$
$683$	−25.5166	−0.976364	−0.488182	+	0.872742i	$0.662340\pi$
$684$	−85.2588	−3.25995
$685$	−10.6204	−0.405784
$686$	4.73808	0.180901
$687$	−33.1480	−1.26467
$688$	−29.1895	−1.11284
$689$	23.3677	0.890238
$690$	60.9242	2.31934
$691$	33.0966	1.25905	0.629527	−	0.776979i	$-0.283249\pi$
$691$	33.0966	1.25905	0.629527	+	0.776979i	$0.283249\pi$
$692$	−60.4462	−2.29782
$693$	−1.88590	−0.0716394
$694$	−78.2348	−2.96975
$695$	14.2270	0.539662
$696$	143.307	5.43206
$697$	4.87148	0.184521
$698$	−1.17843	−0.0446042
$699$	−10.7101	−0.405092
$700$	23.4943	0.888000
$701$	29.5091	1.11454	0.557272	−	0.830330i	$-0.311848\pi$
$701$	29.5091	1.11454	0.557272	+	0.830330i	$0.311848\pi$
$702$	−13.5398	−0.511027
$703$	9.98905	0.376744
$704$	4.10012	0.154529
$705$	55.9689	2.10791
$706$	54.8616	2.06474
$707$	−29.8411	−1.12229
$708$	−122.486	−4.60331
$709$	−11.0921	−0.416572	−0.208286	−	0.978068i	$-0.566788\pi$
$709$	−11.0921	−0.416572	−0.208286	+	0.978068i	$0.566788\pi$
$710$	33.0981	1.24215
$711$	−51.9552	−1.94847
$712$	−112.423	−4.21321
$713$	−1.64085	−0.0614505
$714$	17.5255	0.655875
$715$	1.15248	0.0431002
$716$	92.5823	3.45996
$717$	10.9903	0.410441
$718$	−8.40298	−0.313596
$719$	−40.0943	−1.49527	−0.747633	−	0.664112i	$-0.768810\pi$
$719$	−40.0943	−1.49527	−0.747633	+	0.664112i	$0.768810\pi$
$720$	−100.309	−3.73830
$721$	−14.9410	−0.556434
$722$	−3.72114	−0.138486
$723$	68.1608	2.53493
$724$	58.0836	2.15866
$725$	−6.82915	−0.253628
$726$	−76.1907	−2.82770
$727$	−42.3050	−1.56901	−0.784503	−	0.620125i	$-0.787082\pi$
$727$	−42.3050	−1.56901	−0.784503	+	0.620125i	$0.787082\pi$
$728$	−146.390	−5.42557
$729$	−34.7658	−1.28762
$730$	2.10202	0.0777991
$731$	1.32022	0.0488301
$732$	120.063	4.43765
$733$	38.3412	1.41616	0.708082	−	0.706131i	$-0.249561\pi$
$733$	38.3412	1.41616	0.708082	+	0.706131i	$0.249561\pi$
$734$	−28.3873	−1.04779
$735$	37.2967	1.37571
$736$	95.1580	3.50757
$737$	1.48895	0.0548463
$738$	69.5012	2.55837
$739$	4.84061	0.178065	0.0890323	−	0.996029i	$-0.471623\pi$
$739$	4.84061	0.178065	0.0890323	+	0.996029i	$0.471623\pi$
$740$	23.6551	0.869580
$741$	−47.1707	−1.73286
$742$	−58.9839	−2.16537
$743$	16.8026	0.616426	0.308213	−	0.951317i	$-0.400269\pi$
$743$	16.8026	0.616426	0.308213	+	0.951317i	$0.400269\pi$
$744$	8.76116	0.321200
$745$	−37.5876	−1.37710
$746$	74.3324	2.72150
$747$	−15.2212	−0.556916
$748$	−0.515458	−0.0188470
$749$	8.87239	0.324190
$750$	83.7001	3.05629
$751$	29.9334	1.09229	0.546143	−	0.837692i	$-0.316096\pi$
$751$	29.9334	1.09229	0.546143	+	0.837692i	$0.316096\pi$
$752$	164.337	5.99274
$753$	43.6750	1.59161
$754$	67.3135	2.45141
$755$	4.60415	0.167562
$756$	24.9856	0.908717
$757$	−12.2590	−0.445562	−0.222781	−	0.974868i	$-0.571514\pi$
$757$	−12.2590	−0.445562	−0.222781	+	0.974868i	$0.571514\pi$
$758$	37.8920	1.37630
$759$	1.62230	0.0588859
$760$	−83.1351	−3.01563
$761$	33.6122	1.21844	0.609220	−	0.793001i	$-0.291483\pi$
$761$	33.6122	1.21844	0.609220	+	0.793001i	$0.291483\pi$
$762$	−4.10934	−0.148866
$763$	43.8467	1.58736
$764$	−1.41677	−0.0512569
$765$	4.53691	0.164032
$766$	−20.0253	−0.723544
$767$	−36.3692	−1.31322
$768$	−101.741	−3.67125
$769$	−32.6590	−1.17771	−0.588857	−	0.808237i	$-0.700422\pi$
$769$	−32.6590	−1.17771	−0.588857	+	0.808237i	$0.700422\pi$
$770$	−2.90904	−0.104835
$771$	26.1921	0.943284
$772$	−67.7147	−2.43710
$773$	19.6815	0.707893	0.353946	−	0.935266i	$-0.384840\pi$
$773$	19.6815	0.707893	0.353946	+	0.935266i	$0.384840\pi$
$774$	18.8355	0.677029
$775$	−0.417503	−0.0149972
$776$	−138.814	−4.98315
$777$	−21.4163	−0.768306
$778$	−32.1386	−1.15222
$779$	33.0964	1.18580
$780$	−111.705	−3.99969
$781$	0.881344	0.0315370
$782$	−8.09092	−0.289331
$783$	−7.26263	−0.259545
$784$	109.511	3.91111
$785$	−34.8981	−1.24557
$786$	−17.6543	−0.629708
$787$	39.8047	1.41888	0.709442	−	0.704764i	$-0.248947\pi$
$787$	39.8047	1.41888	0.709442	+	0.704764i	$0.248947\pi$
$788$	−12.8419	−0.457475
$789$	−39.0150	−1.38897
$790$	−80.1420	−2.85132
$791$	9.37179	0.333222
$792$	−4.64877	−0.165187
$793$	35.6497	1.26596
$794$	81.6462	2.89751
$795$	−28.4518	−1.00908
$796$	90.7642	3.21705
$797$	−19.2965	−0.683518	−0.341759	−	0.939788i	$-0.611023\pi$
$797$	−19.2965	−0.683518	−0.341759	+	0.939788i	$0.611023\pi$
$798$	119.067	4.21491
$799$	−7.43284	−0.262955
$800$	24.2123	0.856033
$801$	41.6821	1.47276
$802$	3.71072	0.131030
$803$	0.0559730	0.00197525
$804$	−144.319	−5.08973
$805$	−33.3821	−1.17656
$806$	4.11524	0.144953
$807$	−37.7223	−1.32789
$808$	−73.5588	−2.58779
$809$	−44.4120	−1.56144	−0.780721	−	0.624880i	$-0.785148\pi$
$809$	−44.4120	−1.56144	−0.780721	+	0.624880i	$0.785148\pi$
$810$	−39.3947	−1.38419
$811$	−37.8971	−1.33075	−0.665374	−	0.746510i	$-0.731728\pi$
$811$	−37.8971	−1.33075	−0.665374	+	0.746510i	$0.731728\pi$
$812$	−124.216	−4.35914
$813$	11.4499	0.401566
$814$	0.861607	0.0301993
$815$	−39.6165	−1.38771
$816$	24.8218	0.868938
$817$	8.96946	0.313802
$818$	−67.8295	−2.37160
$819$	54.2759	1.89655
$820$	78.3758	2.73700
$821$	22.9046	0.799374	0.399687	−	0.916652i	$-0.369119\pi$
$821$	22.9046	0.799374	0.399687	+	0.916652i	$0.369119\pi$
$822$	37.4943	1.30776
$823$	−43.1994	−1.50584	−0.752919	−	0.658113i	$-0.771355\pi$
$823$	−43.1994	−1.50584	−0.752919	+	0.658113i	$0.771355\pi$
$824$	−36.8299	−1.28303
$825$	0.412783	0.0143713
$826$	91.8020	3.19420
$827$	−19.1898	−0.667296	−0.333648	−	0.942698i	$-0.608280\pi$
$827$	−19.1898	−0.667296	−0.333648	+	0.942698i	$0.608280\pi$
$828$	−84.3893	−2.93273
$829$	27.8684	0.967910	0.483955	−	0.875093i	$-0.339200\pi$
$829$	27.8684	0.967910	0.483955	+	0.875093i	$0.339200\pi$
$830$	−23.4791	−0.814971
$831$	2.09325	0.0726141
$832$	−118.001	−4.09094
$833$	−4.95312	−0.171615
$834$	−50.2272	−1.73923
$835$	−41.0167	−1.41944
$836$	−3.50197	−0.121118
$837$	−0.444004	−0.0153470
$838$	85.0154	2.93681
$839$	−48.4215	−1.67170	−0.835849	−	0.548960i	$-0.815024\pi$
$839$	−48.4215	−1.67170	−0.835849	+	0.548960i	$0.815024\pi$
$840$	178.240	6.14986
$841$	7.10633	0.245046
$842$	68.1335	2.34804
$843$	−43.1458	−1.48602
$844$	57.3963	1.97566
$845$	−7.61560	−0.261985
$846$	−106.044	−3.64586
$847$	41.7471	1.43445
$848$	−83.5406	−2.86880
$849$	−31.8921	−1.09453
$850$	−2.05867	−0.0706119
$851$	9.88718	0.338928
$852$	−85.4253	−2.92662
$853$	31.9882	1.09525	0.547627	−	0.836722i	$-0.315531\pi$
$853$	31.9882	1.09525	0.547627	+	0.836722i	$0.315531\pi$
$854$	−89.9858	−3.07925
$855$	30.8234	1.05414
$856$	21.8706	0.747520
$857$	−3.96156	−0.135324	−0.0676622	−	0.997708i	$-0.521554\pi$
$857$	−3.96156	−0.135324	−0.0676622	+	0.997708i	$0.521554\pi$
$858$	−4.06871	−0.138904
$859$	30.9636	1.05646	0.528232	−	0.849100i	$-0.322855\pi$
$859$	30.9636	1.05646	0.528232	+	0.849100i	$0.322855\pi$
$860$	21.2406	0.724300
$861$	−70.9580	−2.41824
$862$	73.7964	2.51351
$863$	−24.5230	−0.834774	−0.417387	−	0.908729i	$-0.637054\pi$
$863$	−24.5230	−0.834774	−0.417387	+	0.908729i	$0.637054\pi$
$864$	25.7491	0.876003
$865$	21.8529	0.743022
$866$	11.3784	0.386652
$867$	42.1355	1.43100
$868$	−7.59402	−0.257758
$869$	−2.13404	−0.0723923
$870$	−81.9588	−2.77866
$871$	−42.8519	−1.45198
$872$	108.083	3.66014
$873$	51.4672	1.74190
$874$	−54.9690	−1.85935
$875$	−45.8617	−1.55041
$876$	−5.42525	−0.183302
$877$	42.4802	1.43445	0.717227	−	0.696840i	$-0.245411\pi$
$877$	42.4802	1.43445	0.717227	+	0.696840i	$0.245411\pi$
$878$	−102.729	−3.46693
$879$	52.7009	1.77756
$880$	−4.12016	−0.138890
$881$	22.8969	0.771415	0.385707	−	0.922621i	$-0.373957\pi$
$881$	22.8969	0.771415	0.385707	+	0.922621i	$0.373957\pi$
$882$	−70.6659	−2.37944
$883$	−51.9610	−1.74863	−0.874313	−	0.485363i	$-0.838688\pi$
$883$	−51.9610	−1.74863	−0.874313	+	0.485363i	$0.838688\pi$
$884$	14.8348	0.498948
$885$	44.2820	1.48852
$886$	84.1960	2.82862
$887$	−38.6714	−1.29846	−0.649229	−	0.760593i	$-0.724909\pi$
$887$	−38.6714	−1.29846	−0.649229	+	0.760593i	$0.724909\pi$
$888$	−52.7915	−1.77157
$889$	2.25162	0.0755170
$890$	64.2955	2.15519
$891$	−1.04901	−0.0351432
$892$	149.840	5.01701
$893$	−50.4980	−1.68985
$894$	132.700	4.43814
$895$	−33.4710	−1.11881
$896$	135.848	4.53838
$897$	−46.6896	−1.55892
$898$	90.0049	3.00350
$899$	2.20738	0.0736201
$900$	−21.4722	−0.715741
$901$	3.77849	0.125880
$902$	2.85474	0.0950523
$903$	−19.2303	−0.639946
$904$	23.1016	0.768347
$905$	−20.9988	−0.698024
$906$	−16.2545	−0.540020
$907$	−42.8420	−1.42254	−0.711272	−	0.702916i	$-0.751881\pi$
$907$	−42.8420	−1.42254	−0.711272	+	0.702916i	$0.751881\pi$
$908$	95.0771	3.15524
$909$	27.2728	0.904583
$910$	83.7218	2.77535
$911$	37.3632	1.23790	0.618950	−	0.785431i	$-0.287558\pi$
$911$	37.3632	1.23790	0.618950	+	0.785431i	$0.287558\pi$
$912$	168.637	5.58414
$913$	−0.625207	−0.0206913
$914$	28.6591	0.947958
$915$	−43.4060	−1.43496
$916$	70.8249	2.34012
$917$	9.67330	0.319440
$918$	−2.18935	−0.0722592
$919$	47.0601	1.55237	0.776185	−	0.630505i	$-0.217152\pi$
$919$	47.0601	1.55237	0.776185	+	0.630505i	$0.217152\pi$
$920$	−82.2873	−2.71293
$921$	60.6205	1.99751
$922$	−72.9197	−2.40148
$923$	−25.3649	−0.834897
$924$	7.50816	0.247000
$925$	2.51572	0.0827163
$926$	−19.6976	−0.647304
$927$	13.6551	0.448493
$928$	−128.012	−4.20221
$929$	57.4339	1.88434	0.942172	−	0.335129i	$-0.108780\pi$
$929$	57.4339	1.88434	0.942172	+	0.335129i	$0.108780\pi$
$930$	−5.01059	−0.164304
$931$	−33.6510	−1.10287
$932$	22.8835	0.749573
$933$	40.1042	1.31295
$934$	−13.9247	−0.455629
$935$	0.186352	0.00609436
$936$	133.791	4.37309
$937$	−30.7612	−1.00492	−0.502462	−	0.864599i	$-0.667572\pi$
$937$	−30.7612	−1.00492	−0.502462	+	0.864599i	$0.667572\pi$
$938$	108.165	3.53172
$939$	35.0122	1.14258
$940$	−119.585	−3.90042
$941$	39.1231	1.27538	0.637688	−	0.770295i	$-0.279891\pi$
$941$	39.1231	1.27538	0.637688	+	0.770295i	$0.279891\pi$
$942$	123.204	4.01422
$943$	32.7589	1.06678
$944$	130.022	4.23184
$945$	−9.03296	−0.293842
$946$	0.773662	0.0251539
$947$	21.6827	0.704594	0.352297	−	0.935888i	$-0.385401\pi$
$947$	21.6827	0.704594	0.352297	+	0.935888i	$0.385401\pi$
$948$	206.844	6.71799
$949$	−1.61089	−0.0522918
$950$	−13.9864	−0.453780
$951$	44.1384	1.43128
$952$	−23.6708	−0.767176
$953$	0.319616	0.0103534	0.00517669	−	0.999987i	$-0.498352\pi$
$953$	0.319616	0.0103534	0.00517669	+	0.999987i	$0.498352\pi$
$954$	53.9074	1.74532
$955$	0.512201	0.0165744
$956$	−23.4822	−0.759469
$957$	−2.18242	−0.0705476
$958$	41.4563	1.33939
$959$	−20.5442	−0.663407
$960$	143.674	4.63706
$961$	−30.8651	−0.995647
$962$	−24.7969	−0.799484
$963$	−8.10878	−0.261302
$964$	−145.634	−4.69057
$965$	24.4807	0.788062
$966$	117.852	3.79184
$967$	18.2008	0.585298	0.292649	−	0.956220i	$-0.405463\pi$
$967$	18.2008	0.585298	0.292649	+	0.956220i	$0.405463\pi$
$968$	102.907	3.30756
$969$	−7.62736	−0.245026
$970$	79.3892	2.54903
$971$	−22.9203	−0.735547	−0.367773	−	0.929915i	$-0.619880\pi$
$971$	−22.9203	−0.735547	−0.367773	+	0.929915i	$0.619880\pi$
$972$	121.391	3.89360
$973$	27.5209	0.882280
$974$	90.9736	2.91498
$975$	−11.8798	−0.380459
$976$	−127.449	−4.07955
$977$	6.79182	0.217290	0.108645	−	0.994081i	$-0.465349\pi$
$977$	6.79182	0.217290	0.108645	+	0.994081i	$0.465349\pi$
$978$	139.862	4.47231
$979$	1.71208	0.0547182
$980$	−79.6892	−2.54558
$981$	−40.0730	−1.27943
$982$	20.2690	0.646811
$983$	8.98601	0.286609	0.143305	−	0.989679i	$-0.454227\pi$
$983$	8.98601	0.286609	0.143305	+	0.989679i	$0.454227\pi$
$984$	−174.913	−5.57601
$985$	4.64271	0.147929
$986$	10.8844	0.346630
$987$	108.267	3.44617
$988$	100.786	3.20644
$989$	8.87799	0.282304
$990$	2.65867	0.0844982
$991$	17.8021	0.565502	0.282751	−	0.959193i	$-0.408753\pi$
$991$	17.8021	0.565502	0.282751	+	0.959193i	$0.408753\pi$
$992$	−7.82609	−0.248479
$993$	60.1573	1.90903
$994$	64.0253	2.03076
$995$	−32.8137	−1.04027
$996$	60.5989	1.92015
$997$	26.4380	0.837300	0.418650	−	0.908148i	$-0.362503\pi$
$997$	26.4380	0.837300	0.418650	+	0.908148i	$0.362503\pi$
$998$	−90.1006	−2.85209
$999$	2.67540	0.0846460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.3	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.72706 q^{2} -2.54460 q^{3} +5.43687 q^{4} -1.96557 q^{5} +6.93928 q^{6} -3.80223 q^{7} -9.37255 q^{8} +3.47499 q^{9} +O(q^{10})\)	\(q-2.72706 q^{2} -2.54460 q^{3} +5.43687 q^{4} -1.96557 q^{5} +6.93928 q^{6} -3.80223 q^{7} -9.37255 q^{8} +3.47499 q^{9} +5.36024 q^{10} +0.142734 q^{11} -13.8346 q^{12} -4.10786 q^{13} +10.3689 q^{14} +5.00160 q^{15} +14.6858 q^{16} -0.664228 q^{17} -9.47651 q^{18} -4.51271 q^{19} -10.6866 q^{20} +9.67515 q^{21} -0.389244 q^{22} -4.46669 q^{23} +23.8494 q^{24} -1.13652 q^{25} +11.2024 q^{26} -1.20865 q^{27} -20.6722 q^{28} +6.00885 q^{29} -13.6397 q^{30} +0.367354 q^{31} -21.3039 q^{32} -0.363201 q^{33} +1.81139 q^{34} +7.47357 q^{35} +18.8930 q^{36} -2.21354 q^{37} +12.3064 q^{38} +10.4529 q^{39} +18.4224 q^{40} -7.33405 q^{41} -26.3847 q^{42} -1.98760 q^{43} +0.776025 q^{44} -6.83035 q^{45} +12.1809 q^{46} +11.1902 q^{47} -37.3694 q^{48} +7.45695 q^{49} +3.09935 q^{50} +1.69020 q^{51} -22.3339 q^{52} -5.68854 q^{53} +3.29608 q^{54} -0.280554 q^{55} +35.6366 q^{56} +11.4830 q^{57} -16.3865 q^{58} +8.85357 q^{59} +27.1930 q^{60} -8.67842 q^{61} -1.00180 q^{62} -13.2127 q^{63} +28.7256 q^{64} +8.07430 q^{65} +0.990471 q^{66} +10.4317 q^{67} -3.61132 q^{68} +11.3659 q^{69} -20.3809 q^{70} +6.17474 q^{71} -32.5695 q^{72} +0.392149 q^{73} +6.03646 q^{74} +2.89198 q^{75} -24.5350 q^{76} -0.542707 q^{77} -28.5056 q^{78} -14.9512 q^{79} -28.8660 q^{80} -7.34942 q^{81} +20.0004 q^{82} -4.38023 q^{83} +52.6025 q^{84} +1.30559 q^{85} +5.42031 q^{86} -15.2901 q^{87} -1.33778 q^{88} +11.9949 q^{89} +18.6268 q^{90} +15.6190 q^{91} -24.2848 q^{92} -0.934769 q^{93} -30.5163 q^{94} +8.87006 q^{95} +54.2100 q^{96} +14.8107 q^{97} -20.3356 q^{98} +0.495999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 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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