LMFDB - Embedded newform 6031.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69025 q^{2} +1.94949 q^{3} +5.23745 q^{4} +2.83503 q^{5} -5.24461 q^{6} -1.45115 q^{7} -8.70956 q^{8} +0.800495 q^{9} +O(q^{10})$	\(q-2.69025 q^{2} +1.94949 q^{3} +5.23745 q^{4} +2.83503 q^{5} -5.24461 q^{6} -1.45115 q^{7} -8.70956 q^{8} +0.800495 q^{9} -7.62693 q^{10} +2.40832 q^{11} +10.2103 q^{12} -4.32438 q^{13} +3.90397 q^{14} +5.52684 q^{15} +12.9560 q^{16} +4.25359 q^{17} -2.15353 q^{18} -3.40235 q^{19} +14.8483 q^{20} -2.82900 q^{21} -6.47898 q^{22} -0.0271252 q^{23} -16.9792 q^{24} +3.03737 q^{25} +11.6337 q^{26} -4.28790 q^{27} -7.60035 q^{28} -0.00155070 q^{29} -14.8686 q^{30} +1.95616 q^{31} -17.4358 q^{32} +4.69498 q^{33} -11.4432 q^{34} -4.11406 q^{35} +4.19256 q^{36} +1.00000 q^{37} +9.15317 q^{38} -8.43032 q^{39} -24.6918 q^{40} -11.0359 q^{41} +7.61073 q^{42} -9.30297 q^{43} +12.6135 q^{44} +2.26942 q^{45} +0.0729736 q^{46} -10.0640 q^{47} +25.2575 q^{48} -4.89415 q^{49} -8.17129 q^{50} +8.29232 q^{51} -22.6487 q^{52} +4.55386 q^{53} +11.5355 q^{54} +6.82765 q^{55} +12.6389 q^{56} -6.63283 q^{57} +0.00417178 q^{58} -1.32043 q^{59} +28.9466 q^{60} -10.7248 q^{61} -5.26255 q^{62} -1.16164 q^{63} +20.9946 q^{64} -12.2597 q^{65} -12.6307 q^{66} -10.2483 q^{67} +22.2780 q^{68} -0.0528802 q^{69} +11.0678 q^{70} -6.72843 q^{71} -6.97196 q^{72} -0.463420 q^{73} -2.69025 q^{74} +5.92131 q^{75} -17.8196 q^{76} -3.49484 q^{77} +22.6797 q^{78} -5.99324 q^{79} +36.7306 q^{80} -10.7607 q^{81} +29.6893 q^{82} +14.3653 q^{83} -14.8168 q^{84} +12.0590 q^{85} +25.0273 q^{86} -0.00302307 q^{87} -20.9754 q^{88} +7.56366 q^{89} -6.10532 q^{90} +6.27534 q^{91} -0.142067 q^{92} +3.81350 q^{93} +27.0748 q^{94} -9.64574 q^{95} -33.9908 q^{96} +16.3384 q^{97} +13.1665 q^{98} +1.92785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.69025	−1.90229	−0.951147	−	0.308737i	$-0.900094\pi$
$2$	−2.69025	−1.90229	−0.951147	+	0.308737i	$0.900094\pi$
$3$	1.94949	1.12554	0.562768	−	0.826615i	$-0.309736\pi$
$3$	1.94949	1.12554	0.562768	+	0.826615i	$0.309736\pi$
$4$	5.23745	2.61873
$5$	2.83503	1.26786	0.633931	−	0.773390i	$-0.281440\pi$
$5$	2.83503	1.26786	0.633931	+	0.773390i	$0.281440\pi$
$6$	−5.24461	−2.14110
$7$	−1.45115	−0.548485	−0.274242	−	0.961661i	$-0.588427\pi$
$7$	−1.45115	−0.548485	−0.274242	+	0.961661i	$0.588427\pi$
$8$	−8.70956	−3.07929
$9$	0.800495	0.266832
$10$	−7.62693	−2.41185
$11$	2.40832	0.726136	0.363068	−	0.931763i	$-0.381729\pi$
$11$	2.40832	0.726136	0.363068	+	0.931763i	$0.381729\pi$
$12$	10.2103	2.94747
$13$	−4.32438	−1.19937	−0.599684	−	0.800237i	$-0.704707\pi$
$13$	−4.32438	−1.19937	−0.599684	+	0.800237i	$0.704707\pi$
$14$	3.90397	1.04338
$15$	5.52684	1.42702
$16$	12.9560	3.23900
$17$	4.25359	1.03165	0.515824	−	0.856695i	$-0.327486\pi$
$17$	4.25359	1.03165	0.515824	+	0.856695i	$0.327486\pi$
$18$	−2.15353	−0.507593
$19$	−3.40235	−0.780552	−0.390276	−	0.920698i	$-0.627620\pi$
$19$	−3.40235	−0.780552	−0.390276	+	0.920698i	$0.627620\pi$
$20$	14.8483	3.32018
$21$	−2.82900	−0.617339
$22$	−6.47898	−1.38132
$23$	−0.0271252	−0.00565600	−0.00282800	−	0.999996i	$-0.500900\pi$
$23$	−0.0271252	−0.00565600	−0.00282800	+	0.999996i	$0.500900\pi$
$24$	−16.9792	−3.46586
$25$	3.03737	0.607474
$26$	11.6337	2.28155
$27$	−4.28790	−0.825207
$28$	−7.60035	−1.43633
$29$	−0.00155070	−0.000287958 0	−0.000143979	−	1.00000i	$-0.500046\pi$
$29$	−0.00155070	−0.000287958 0	−0.000143979		1.00000i	$0.500046\pi$
$30$	−14.8686	−2.71462
$31$	1.95616	0.351336	0.175668	−	0.984449i	$-0.443791\pi$
$31$	1.95616	0.351336	0.175668	+	0.984449i	$0.443791\pi$
$32$	−17.4358	−3.08224
$33$	4.69498	0.817292
$34$	−11.4432	−1.96250
$35$	−4.11406	−0.695403
$36$	4.19256	0.698759
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.15317	1.48484
$39$	−8.43032	−1.34993
$40$	−24.6918	−3.90412
$41$	−11.0359	−1.72351	−0.861757	−	0.507321i	$-0.830636\pi$
$41$	−11.0359	−1.72351	−0.861757	+	0.507321i	$0.830636\pi$
$42$	7.61073	1.17436
$43$	−9.30297	−1.41869	−0.709345	−	0.704862i	$-0.751009\pi$
$43$	−9.30297	−1.41869	−0.709345	+	0.704862i	$0.751009\pi$
$44$	12.6135	1.90155
$45$	2.26942	0.338306
$46$	0.0729736	0.0107594
$47$	−10.0640	−1.46799	−0.733996	−	0.679154i	$-0.762347\pi$
$47$	−10.0640	−1.46799	−0.733996	+	0.679154i	$0.762347\pi$
$48$	25.2575	3.64561
$49$	−4.89415	−0.699165
$50$	−8.17129	−1.15559
$51$	8.29232	1.16116
$52$	−22.6487	−3.14081
$53$	4.55386	0.625521	0.312760	−	0.949832i	$-0.398746\pi$
$53$	4.55386	0.625521	0.312760	+	0.949832i	$0.398746\pi$
$54$	11.5355	1.56979
$55$	6.82765	0.920640
$56$	12.6389	1.68895
$57$	−6.63283	−0.878539
$58$	0.00417178	0.000547781 0
$59$	−1.32043	−0.171905	−0.0859526	−	0.996299i	$-0.527393\pi$
$59$	−1.32043	−0.171905	−0.0859526	+	0.996299i	$0.527393\pi$
$60$	28.9466	3.73699
$61$	−10.7248	−1.37317	−0.686583	−	0.727051i	$-0.740890\pi$
$61$	−10.7248	−1.37317	−0.686583	+	0.727051i	$0.740890\pi$
$62$	−5.26255	−0.668345
$63$	−1.16164	−0.146353
$64$	20.9946	2.62433
$65$	−12.2597	−1.52063
$66$	−12.6307	−1.55473
$67$	−10.2483	−1.25203	−0.626014	−	0.779811i	$-0.715315\pi$
$67$	−10.2483	−1.25203	−0.626014	+	0.779811i	$0.715315\pi$
$68$	22.2780	2.70160
$69$	−0.0528802	−0.00636603
$70$	11.0678	1.32286
$71$	−6.72843	−0.798517	−0.399259	−	0.916838i	$-0.630732\pi$
$71$	−6.72843	−0.798517	−0.399259	+	0.916838i	$0.630732\pi$
$72$	−6.97196	−0.821653
$73$	−0.463420	−0.0542393	−0.0271196	−	0.999632i	$-0.508634\pi$
$73$	−0.463420	−0.0542393	−0.0271196	+	0.999632i	$0.508634\pi$
$74$	−2.69025	−0.312735
$75$	5.92131	0.683734
$76$	−17.8196	−2.04405
$77$	−3.49484	−0.398274
$78$	22.6797	2.56797
$79$	−5.99324	−0.674293	−0.337146	−	0.941452i	$-0.609462\pi$
$79$	−5.99324	−0.674293	−0.337146	+	0.941452i	$0.609462\pi$
$80$	36.7306	4.10660
$81$	−10.7607	−1.19563
$82$	29.6893	3.27863
$83$	14.3653	1.57679	0.788397	−	0.615166i	$-0.210911\pi$
$83$	14.3653	1.57679	0.788397	+	0.615166i	$0.210911\pi$
$84$	−14.8168	−1.61664
$85$	12.0590	1.30799
$86$	25.0273	2.69877
$87$	−0.00302307	−0.000324107 0
$88$	−20.9754	−2.23598
$89$	7.56366	0.801747	0.400873	−	0.916133i	$-0.368707\pi$
$89$	7.56366	0.801747	0.400873	+	0.916133i	$0.368707\pi$
$90$	−6.10532	−0.643557
$91$	6.27534	0.657835
$92$	−0.142067	−0.0148115
$93$	3.81350	0.395442
$94$	27.0748	2.79255
$95$	−9.64574	−0.989632
$96$	−33.9908	−3.46917
$97$	16.3384	1.65892	0.829458	−	0.558569i	$-0.188650\pi$
$97$	16.3384	1.65892	0.829458	+	0.558569i	$0.188650\pi$
$98$	13.1665	1.33002
$99$	1.92785	0.193756
$100$	15.9081	1.59081
$101$	−10.6654	−1.06124	−0.530622	−	0.847608i	$-0.678042\pi$
$101$	−10.6654	−1.06124	−0.530622	+	0.847608i	$0.678042\pi$
$102$	−22.3084	−2.20886
$103$	12.7286	1.25419	0.627095	−	0.778943i	$-0.284244\pi$
$103$	12.7286	1.25419	0.627095	+	0.778943i	$0.284244\pi$
$104$	37.6634	3.69320
$105$	−8.02030	−0.782701
$106$	−12.2510	−1.18992
$107$	9.05657	0.875531	0.437766	−	0.899089i	$-0.355770\pi$
$107$	9.05657	0.875531	0.437766	+	0.899089i	$0.355770\pi$
$108$	−22.4577	−2.16099
$109$	5.07607	0.486199	0.243100	−	0.970001i	$-0.421836\pi$
$109$	5.07607	0.486199	0.243100	+	0.970001i	$0.421836\pi$
$110$	−18.3681	−1.75133
$111$	1.94949	0.185037
$112$	−18.8011	−1.77654
$113$	−14.3699	−1.35181	−0.675903	−	0.736990i	$-0.736246\pi$
$113$	−14.3699	−1.35181	−0.675903	+	0.736990i	$0.736246\pi$
$114$	17.8440	1.67124
$115$	−0.0769007	−0.00717103
$116$	−0.00812173	−0.000754083 0
$117$	−3.46165	−0.320029
$118$	3.55228	0.327014
$119$	−6.17262	−0.565843
$120$	−48.1364	−4.39423
$121$	−5.20000	−0.472727
$122$	28.8523	2.61217
$123$	−21.5143	−1.93988
$124$	10.2453	0.920053
$125$	−5.56411	−0.497669
$126$	3.12511	0.278407
$127$	12.7499	1.13137	0.565684	−	0.824622i	$-0.308612\pi$
$127$	12.7499	1.13137	0.565684	+	0.824622i	$0.308612\pi$
$128$	−21.6092	−1.91000
$129$	−18.1360	−1.59679
$130$	32.9818	2.89269
$131$	−6.68279	−0.583878	−0.291939	−	0.956437i	$-0.594300\pi$
$131$	−6.68279	−0.583878	−0.291939	+	0.956437i	$0.594300\pi$
$132$	24.5898	2.14026
$133$	4.93733	0.428121
$134$	27.5705	2.38173
$135$	−12.1563	−1.04625
$136$	−37.0469	−3.17675
$137$	1.27800	0.109187	0.0545934	−	0.998509i	$-0.482614\pi$
$137$	1.27800	0.109187	0.0545934	+	0.998509i	$0.482614\pi$
$138$	0.142261	0.0121101
$139$	−21.0206	−1.78295	−0.891474	−	0.453073i	$-0.850328\pi$
$139$	−21.0206	−1.78295	−0.891474	+	0.453073i	$0.850328\pi$
$140$	−21.5472	−1.82107
$141$	−19.6197	−1.65228
$142$	18.1012	1.51902
$143$	−10.4145	−0.870903
$144$	10.3712	0.864268
$145$	−0.00439628	−0.000365091 0
$146$	1.24672	0.103179
$147$	−9.54108	−0.786935
$148$	5.23745	0.430516
$149$	−13.5619	−1.11104	−0.555518	−	0.831505i	$-0.687480\pi$
$149$	−13.5619	−1.11104	−0.555518	+	0.831505i	$0.687480\pi$
$150$	−15.9298	−1.30066
$151$	3.73277	0.303769	0.151884	−	0.988398i	$-0.451466\pi$
$151$	3.73277	0.303769	0.151884	+	0.988398i	$0.451466\pi$
$152$	29.6329	2.40355
$153$	3.40498	0.275276
$154$	9.40200	0.757635
$155$	5.54576	0.445446
$156$	−44.1534	−3.53510
$157$	16.9731	1.35460	0.677301	−	0.735706i	$-0.263150\pi$
$157$	16.9731	1.35460	0.677301	+	0.735706i	$0.263150\pi$
$158$	16.1233	1.28270
$159$	8.87769	0.704046
$160$	−49.4308	−3.90785
$161$	0.0393629	0.00310223
$162$	28.9490	2.27445
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	−57.7999	−4.51341
$165$	13.3104	1.03621
$166$	−38.6462	−2.99953
$167$	0.250939	0.0194182	0.00970911	−	0.999953i	$-0.496909\pi$
$167$	0.250939	0.0194182	0.00970911	+	0.999953i	$0.496909\pi$
$168$	24.6394	1.90097
$169$	5.70027	0.438482
$170$	−32.4419	−2.48818
$171$	−2.72356	−0.208276
$172$	−48.7239	−3.71516
$173$	−20.5173	−1.55990	−0.779952	−	0.625839i	$-0.784757\pi$
$173$	−20.5173	−1.55990	−0.779952	+	0.625839i	$0.784757\pi$
$174$	0.00813282	0.000616548 0
$175$	−4.40769	−0.333190
$176$	31.2022	2.35195
$177$	−2.57416	−0.193485
$178$	−20.3482	−1.52516
$179$	15.9298	1.19065	0.595324	−	0.803486i	$-0.297024\pi$
$179$	15.9298	1.19065	0.595324	+	0.803486i	$0.297024\pi$
$180$	11.8860	0.885930
$181$	2.55997	0.190281	0.0951407	−	0.995464i	$-0.469670\pi$
$181$	2.55997	0.190281	0.0951407	+	0.995464i	$0.469670\pi$
$182$	−16.8822	−1.25140
$183$	−20.9078	−1.54555
$184$	0.236249	0.0174165
$185$	2.83503	0.208435
$186$	−10.2593	−0.752247
$187$	10.2440	0.749116
$188$	−52.7099	−3.84427
$189$	6.22241	0.452614
$190$	25.9495	1.88257
$191$	17.8726	1.29322	0.646609	−	0.762822i	$-0.276187\pi$
$191$	17.8726	1.29322	0.646609	+	0.762822i	$0.276187\pi$
$192$	40.9287	2.95377
$193$	−0.886214	−0.0637910	−0.0318955	−	0.999491i	$-0.510154\pi$
$193$	−0.886214	−0.0637910	−0.0318955	+	0.999491i	$0.510154\pi$
$194$	−43.9545	−3.15575
$195$	−23.9002	−1.71153
$196$	−25.6329	−1.83092
$197$	−12.9306	−0.921269	−0.460634	−	0.887590i	$-0.652378\pi$
$197$	−12.9306	−0.921269	−0.460634	+	0.887590i	$0.652378\pi$
$198$	−5.18640	−0.368581
$199$	−19.3808	−1.37387	−0.686935	−	0.726718i	$-0.741044\pi$
$199$	−19.3808	−1.37387	−0.686935	+	0.726718i	$0.741044\pi$
$200$	−26.4541	−1.87059
$201$	−19.9789	−1.40920
$202$	28.6926	2.01880
$203$	0.00225031	0.000157941 0
$204$	43.4306	3.04075
$205$	−31.2870	−2.18518
$206$	−34.2432	−2.38584
$207$	−0.0217136	−0.00150920
$208$	−56.0267	−3.88475
$209$	−8.19394	−0.566786
$210$	21.5766	1.48893
$211$	−14.7187	−1.01328	−0.506640	−	0.862158i	$-0.669113\pi$
$211$	−14.7187	−1.01328	−0.506640	+	0.862158i	$0.669113\pi$
$212$	23.8506	1.63807
$213$	−13.1170	−0.898760
$214$	−24.3644	−1.66552
$215$	−26.3742	−1.79870
$216$	37.3457	2.54106
$217$	−2.83869	−0.192702
$218$	−13.6559	−0.924894
$219$	−0.903432	−0.0610483
$220$	35.7595	2.41090
$221$	−18.3942	−1.23732
$222$	−5.24461	−0.351995
$223$	17.9835	1.20426	0.602131	−	0.798397i	$-0.294318\pi$
$223$	17.9835	1.20426	0.602131	+	0.798397i	$0.294318\pi$
$224$	25.3020	1.69056
$225$	2.43140	0.162093
$226$	38.6586	2.57153
$227$	3.11426	0.206701	0.103351	−	0.994645i	$-0.467044\pi$
$227$	3.11426	0.206701	0.103351	+	0.994645i	$0.467044\pi$
$228$	−34.7391	−2.30065
$229$	10.9448	0.723256	0.361628	−	0.932323i	$-0.382221\pi$
$229$	10.9448	0.723256	0.361628	+	0.932323i	$0.382221\pi$
$230$	0.206882	0.0136414
$231$	−6.81314	−0.448272
$232$	0.0135059	0.000886708 0
$233$	7.09317	0.464689	0.232345	−	0.972634i	$-0.425360\pi$
$233$	7.09317	0.464689	0.232345	+	0.972634i	$0.425360\pi$
$234$	9.31270	0.608790
$235$	−28.5318	−1.86121
$236$	−6.91568	−0.450172
$237$	−11.6837	−0.758941
$238$	16.6059	1.07640
$239$	5.01137	0.324159	0.162079	−	0.986778i	$-0.448180\pi$
$239$	5.01137	0.324159	0.162079	+	0.986778i	$0.448180\pi$
$240$	71.6057	4.62213
$241$	6.86166	0.441998	0.220999	−	0.975274i	$-0.429068\pi$
$241$	6.86166	0.441998	0.220999	+	0.975274i	$0.429068\pi$
$242$	13.9893	0.899266
$243$	−8.11411	−0.520520
$244$	−56.1705	−3.59595
$245$	−13.8750	−0.886444
$246$	57.8788	3.69022
$247$	14.7130	0.936169
$248$	−17.0373	−1.08187
$249$	28.0049	1.77474
$250$	14.9688	0.946713
$251$	8.65944	0.546579	0.273290	−	0.961932i	$-0.411888\pi$
$251$	8.65944	0.546579	0.273290	+	0.961932i	$0.411888\pi$
$252$	−6.08404	−0.383259
$253$	−0.0653262	−0.00410702
$254$	−34.3004	−2.15220
$255$	23.5089	1.47219
$256$	16.1450	1.00906
$257$	−0.425678	−0.0265531	−0.0132765	−	0.999912i	$-0.504226\pi$
$257$	−0.425678	−0.0265531	−0.0132765	+	0.999912i	$0.504226\pi$
$258$	48.7904	3.03756
$259$	−1.45115	−0.0901703
$260$	−64.2097	−3.98212
$261$	−0.00124133	−7.68364e−5 0
$262$	17.9784	1.11071
$263$	−12.6383	−0.779310	−0.389655	−	0.920961i	$-0.627406\pi$
$263$	−12.6383	−0.779310	−0.389655	+	0.920961i	$0.627406\pi$
$264$	−40.8912	−2.51668
$265$	12.9103	0.793074
$266$	−13.2827	−0.814412
$267$	14.7453	0.902395
$268$	−53.6750	−3.27872
$269$	−17.6068	−1.07350	−0.536752	−	0.843740i	$-0.680349\pi$
$269$	−17.6068	−1.07350	−0.536752	+	0.843740i	$0.680349\pi$
$270$	32.7035	1.99027
$271$	9.96820	0.605525	0.302763	−	0.953066i	$-0.402091\pi$
$271$	9.96820	0.605525	0.302763	+	0.953066i	$0.402091\pi$
$272$	55.1095	3.34151
$273$	12.2337	0.740417
$274$	−3.43814	−0.207705
$275$	7.31496	0.441108
$276$	−0.276958	−0.0166709
$277$	13.4301	0.806934	0.403467	−	0.914994i	$-0.367805\pi$
$277$	13.4301	0.806934	0.403467	+	0.914994i	$0.367805\pi$
$278$	56.5508	3.39169
$279$	1.56589	0.0937477
$280$	35.8316	2.14135
$281$	−2.18094	−0.130104	−0.0650519	−	0.997882i	$-0.520721\pi$
$281$	−2.18094	−0.130104	−0.0650519	+	0.997882i	$0.520721\pi$
$282$	52.7820	3.14312
$283$	16.6805	0.991554	0.495777	−	0.868450i	$-0.334883\pi$
$283$	16.6805	0.991554	0.495777	+	0.868450i	$0.334883\pi$
$284$	−35.2398	−2.09110
$285$	−18.8042	−1.11387
$286$	28.0176	1.65672
$287$	16.0148	0.945321
$288$	−13.9573	−0.822439
$289$	1.09306	0.0642974
$290$	0.0118271	0.000694511 0
$291$	31.8515	1.86717
$292$	−2.42714	−0.142038
$293$	21.0688	1.23085	0.615425	−	0.788195i	$-0.288984\pi$
$293$	21.0688	1.23085	0.615425	+	0.788195i	$0.288984\pi$
$294$	25.6679	1.49698
$295$	−3.74345	−0.217952
$296$	−8.70956	−0.506233
$297$	−10.3266	−0.599212
$298$	36.4850	2.11352
$299$	0.117300	0.00678362
$300$	31.0126	1.79051
$301$	13.5000	0.778130
$302$	−10.0421	−0.577858
$303$	−20.7920	−1.19447
$304$	−44.0808	−2.52821
$305$	−30.4050	−1.74099
$306$	−9.16026	−0.523657
$307$	17.9240	1.02298	0.511488	−	0.859291i	$-0.329095\pi$
$307$	17.9240	1.02298	0.511488	+	0.859291i	$0.329095\pi$
$308$	−18.3041	−1.04297
$309$	24.8143	1.41164
$310$	−14.9195	−0.847369
$311$	6.72128	0.381129	0.190564	−	0.981675i	$-0.438968\pi$
$311$	6.72128	0.381129	0.190564	+	0.981675i	$0.438968\pi$
$312$	73.4244	4.15684
$313$	17.9813	1.01636	0.508181	−	0.861250i	$-0.330318\pi$
$313$	17.9813	1.01636	0.508181	+	0.861250i	$0.330318\pi$
$314$	−45.6619	−2.57685
$315$	−3.29328	−0.185556
$316$	−31.3893	−1.76579
$317$	−26.6030	−1.49417	−0.747085	−	0.664728i	$-0.768547\pi$
$317$	−26.6030	−1.49417	−0.747085	+	0.664728i	$0.768547\pi$
$318$	−23.8832	−1.33930
$319$	−0.00373459	−0.000209097 0
$320$	59.5202	3.32728
$321$	17.6556	0.985442
$322$	−0.105896	−0.00590135
$323$	−14.4722	−0.805255
$324$	−56.3586	−3.13103
$325$	−13.1347	−0.728584
$326$	−2.69025	−0.148999
$327$	9.89572	0.547235
$328$	96.1176	5.30721
$329$	14.6045	0.805171
$330$	−35.8083	−1.97118
$331$	3.46097	0.190232	0.0951161	−	0.995466i	$-0.469678\pi$
$331$	3.46097	0.190232	0.0951161	+	0.995466i	$0.469678\pi$
$332$	75.2375	4.12919
$333$	0.800495	0.0438669
$334$	−0.675088	−0.0369392
$335$	−29.0542	−1.58740
$336$	−36.6526	−1.99956
$337$	−13.5719	−0.739306	−0.369653	−	0.929170i	$-0.620523\pi$
$337$	−13.5719	−0.739306	−0.369653	+	0.929170i	$0.620523\pi$
$338$	−15.3352	−0.834123
$339$	−28.0139	−1.52151
$340$	63.1587	3.42526
$341$	4.71105	0.255118
$342$	7.32707	0.396202
$343$	17.2602	0.931966
$344$	81.0248	4.36856
$345$	−0.149917	−0.00807125
$346$	55.1968	2.96740
$347$	9.56208	0.513319	0.256660	−	0.966502i	$-0.417378\pi$
$347$	9.56208	0.513319	0.256660	+	0.966502i	$0.417378\pi$
$348$	−0.0158332	−0.000848748 0
$349$	28.3459	1.51732	0.758661	−	0.651485i	$-0.225854\pi$
$349$	28.3459	1.51732	0.758661	+	0.651485i	$0.225854\pi$
$350$	11.8578	0.633826
$351$	18.5425	0.989727
$352$	−41.9909	−2.23812
$353$	−20.2121	−1.07578	−0.537891	−	0.843014i	$-0.680779\pi$
$353$	−20.2121	−1.07578	−0.537891	+	0.843014i	$0.680779\pi$
$354$	6.92513	0.368066
$355$	−19.0753	−1.01241
$356$	39.6143	2.09956
$357$	−12.0334	−0.636877
$358$	−42.8551	−2.26496
$359$	−22.0624	−1.16441	−0.582203	−	0.813043i	$-0.697809\pi$
$359$	−22.0624	−1.16441	−0.582203	+	0.813043i	$0.697809\pi$
$360$	−19.7657	−1.04174
$361$	−7.42404	−0.390739
$362$	−6.88697	−0.361971
$363$	−10.1373	−0.532072
$364$	32.8668	1.72269
$365$	−1.31381	−0.0687679
$366$	56.2472	2.94009
$367$	−10.9743	−0.572854	−0.286427	−	0.958102i	$-0.592468\pi$
$367$	−10.9743	−0.572854	−0.286427	+	0.958102i	$0.592468\pi$
$368$	−0.351434	−0.0183198
$369$	−8.83417	−0.459889
$370$	−7.62693	−0.396505
$371$	−6.60835	−0.343089
$372$	19.9730	1.03555
$373$	−5.58134	−0.288991	−0.144495	−	0.989505i	$-0.546156\pi$
$373$	−5.58134	−0.288991	−0.144495	+	0.989505i	$0.546156\pi$
$374$	−27.5590	−1.42504
$375$	−10.8471	−0.560144
$376$	87.6534	4.52038
$377$	0.00670583	0.000345368 0
$378$	−16.7398	−0.861004
$379$	−4.15096	−0.213221	−0.106610	−	0.994301i	$-0.534000\pi$
$379$	−4.15096	−0.213221	−0.106610	+	0.994301i	$0.534000\pi$
$380$	−50.5191	−2.59157
$381$	24.8557	1.27340
$382$	−48.0819	−2.46008
$383$	33.8582	1.73008	0.865038	−	0.501707i	$-0.167294\pi$
$383$	33.8582	1.73008	0.865038	+	0.501707i	$0.167294\pi$
$384$	−42.1269	−2.14978
$385$	−9.90797	−0.504957
$386$	2.38414	0.121349
$387$	−7.44699	−0.378552
$388$	85.5717	4.34425
$389$	−10.5900	−0.536936	−0.268468	−	0.963289i	$-0.586517\pi$
$389$	−10.5900	−0.536936	−0.268468	+	0.963289i	$0.586517\pi$
$390$	64.2975	3.25583
$391$	−0.115380	−0.00583500
$392$	42.6259	2.15293
$393$	−13.0280	−0.657176
$394$	34.7866	1.75253
$395$	−16.9910	−0.854910
$396$	10.0970	0.507394
$397$	−27.3279	−1.37155	−0.685774	−	0.727814i	$-0.740536\pi$
$397$	−27.3279	−1.37155	−0.685774	+	0.727814i	$0.740536\pi$
$398$	52.1393	2.61351
$399$	9.62525	0.481865
$400$	39.3521	1.96761
$401$	−35.0078	−1.74821	−0.874104	−	0.485739i	$-0.838551\pi$
$401$	−35.0078	−1.74821	−0.874104	+	0.485739i	$0.838551\pi$
$402$	53.7483	2.68072
$403$	−8.45917	−0.421381
$404$	−55.8594	−2.77911
$405$	−30.5068	−1.51590
$406$	−0.00605389	−0.000300450 0
$407$	2.40832	0.119376
$408$	−72.2224	−3.57554
$409$	26.5020	1.31044	0.655219	−	0.755439i	$-0.272576\pi$
$409$	26.5020	1.31044	0.655219	+	0.755439i	$0.272576\pi$
$410$	84.1699	4.15685
$411$	2.49144	0.122894
$412$	66.6656	3.28438
$413$	1.91614	0.0942873
$414$	0.0584151	0.00287094
$415$	40.7259	1.99916
$416$	75.3989	3.69674
$417$	−40.9794	−2.00677
$418$	22.0437	1.07820
$419$	−10.3020	−0.503287	−0.251644	−	0.967820i	$-0.580971\pi$
$419$	−10.3020	−0.503287	−0.251644	+	0.967820i	$0.580971\pi$
$420$	−42.0059	−2.04968
$421$	−18.2364	−0.888787	−0.444393	−	0.895832i	$-0.646581\pi$
$421$	−18.2364	−0.888787	−0.444393	+	0.895832i	$0.646581\pi$
$422$	39.5971	1.92756
$423$	−8.05622	−0.391707
$424$	−39.6621	−1.92616
$425$	12.9197	0.626699
$426$	35.2880	1.70971
$427$	15.5633	0.753160
$428$	47.4333	2.29278
$429$	−20.3029	−0.980233
$430$	70.9531	3.42166
$431$	−34.6925	−1.67108	−0.835539	−	0.549431i	$-0.814845\pi$
$431$	−34.6925	−1.67108	−0.835539	+	0.549431i	$0.814845\pi$
$432$	−55.5541	−2.67285
$433$	38.6449	1.85716	0.928578	−	0.371138i	$-0.121032\pi$
$433$	38.6449	1.85716	0.928578	+	0.371138i	$0.121032\pi$
$434$	7.63678	0.366577
$435$	−0.00857049	−0.000410923 0
$436$	26.5857	1.27322
$437$	0.0922894	0.00441480
$438$	2.43046	0.116132
$439$	−7.62116	−0.363738	−0.181869	−	0.983323i	$-0.558215\pi$
$439$	−7.62116	−0.363738	−0.181869	+	0.983323i	$0.558215\pi$
$440$	−59.4658	−2.83492
$441$	−3.91775	−0.186559
$442$	49.4849	2.35376
$443$	36.3405	1.72659	0.863294	−	0.504701i	$-0.168397\pi$
$443$	36.3405	1.72659	0.863294	+	0.504701i	$0.168397\pi$
$444$	10.2103	0.484561
$445$	21.4432	1.01650
$446$	−48.3801	−2.29086
$447$	−26.4388	−1.25051
$448$	−30.4664	−1.43940
$449$	31.8658	1.50384	0.751919	−	0.659256i	$-0.229128\pi$
$449$	31.8658	1.50384	0.751919	+	0.659256i	$0.229128\pi$
$450$	−6.54108	−0.308349
$451$	−26.5779	−1.25151
$452$	−75.2616	−3.54001
$453$	7.27699	0.341903
$454$	−8.37815	−0.393206
$455$	17.7908	0.834043
$456$	57.7690	2.70528
$457$	11.2055	0.524173	0.262087	−	0.965044i	$-0.415589\pi$
$457$	11.2055	0.524173	0.262087	+	0.965044i	$0.415589\pi$
$458$	−29.4444	−1.37585
$459$	−18.2390	−0.851323
$460$	−0.402764	−0.0187789
$461$	4.16774	0.194111	0.0970554	−	0.995279i	$-0.469058\pi$
$461$	4.16774	0.194111	0.0970554	+	0.995279i	$0.469058\pi$
$462$	18.3291	0.852746
$463$	−34.8322	−1.61879	−0.809395	−	0.587264i	$-0.800205\pi$
$463$	−34.8322	−1.61879	−0.809395	+	0.587264i	$0.800205\pi$
$464$	−0.0200909	−0.000932696 0
$465$	10.8114	0.501365
$466$	−19.0824	−0.883976
$467$	−21.6511	−1.00189	−0.500946	−	0.865479i	$-0.667014\pi$
$467$	−21.6511	−1.00189	−0.500946	+	0.865479i	$0.667014\pi$
$468$	−18.1302	−0.838069
$469$	14.8719	0.686719
$470$	76.7578	3.54057
$471$	33.0888	1.52465
$472$	11.5003	0.529346
$473$	−22.4045	−1.03016
$474$	31.4322	1.44373
$475$	−10.3342	−0.474165
$476$	−32.3288	−1.48179
$477$	3.64534	0.166909
$478$	−13.4818	−0.616645
$479$	−1.25054	−0.0571385	−0.0285693	−	0.999592i	$-0.509095\pi$
$479$	−1.25054	−0.0571385	−0.0285693	+	0.999592i	$0.509095\pi$
$480$	−96.3647	−4.39843
$481$	−4.32438	−0.197175
$482$	−18.4596	−0.840811
$483$	0.0767373	0.00349167
$484$	−27.2347	−1.23794
$485$	46.3199	2.10328
$486$	21.8290	0.990183
$487$	−41.7862	−1.89351	−0.946757	−	0.321949i	$-0.895662\pi$
$487$	−41.7862	−1.89351	−0.946757	+	0.321949i	$0.895662\pi$
$488$	93.4080	4.22838
$489$	1.94949	0.0881588
$490$	37.3274	1.68628
$491$	−17.7757	−0.802206	−0.401103	−	0.916033i	$-0.631373\pi$
$491$	−17.7757	−0.802206	−0.401103	+	0.916033i	$0.631373\pi$
$492$	−112.680	−5.08001
$493$	−0.00659606	−0.000297071 0
$494$	−39.5818	−1.78087
$495$	5.46550	0.245656
$496$	25.3440	1.13798
$497$	9.76398	0.437975
$498$	−75.3403	−3.37608
$499$	20.0735	0.898613	0.449307	−	0.893378i	$-0.351671\pi$
$499$	20.0735	0.898613	0.449307	+	0.893378i	$0.351671\pi$
$500$	−29.1417	−1.30326
$501$	0.489201	0.0218559
$502$	−23.2961	−1.03976
$503$	−13.1878	−0.588016	−0.294008	−	0.955803i	$-0.594989\pi$
$503$	−13.1878	−0.588016	−0.294008	+	0.955803i	$0.594989\pi$
$504$	10.1174	0.450664
$505$	−30.2366	−1.34551
$506$	0.175744	0.00781277
$507$	11.1126	0.493528
$508$	66.7769	2.96275
$509$	0.703400	0.0311777	0.0155888	−	0.999878i	$-0.495038\pi$
$509$	0.703400	0.0311777	0.0155888	+	0.999878i	$0.495038\pi$
$510$	−63.2450	−2.80053
$511$	0.672494	0.0297494
$512$	−0.215740	−0.00953447
$513$	14.5889	0.644117
$514$	1.14518	0.0505118
$515$	36.0860	1.59014
$516$	−94.9865	−4.18155
$517$	−24.2374	−1.06596
$518$	3.90397	0.171531
$519$	−39.9983	−1.75573
$520$	106.777	4.68247
$521$	25.6117	1.12207	0.561035	−	0.827792i	$-0.310403\pi$
$521$	25.6117	1.12207	0.561035	+	0.827792i	$0.310403\pi$
$522$	0.00333949	0.000146165 0
$523$	9.94491	0.434861	0.217430	−	0.976076i	$-0.430233\pi$
$523$	9.94491	0.434861	0.217430	+	0.976076i	$0.430233\pi$
$524$	−35.0008	−1.52902
$525$	−8.59273	−0.375018
$526$	34.0002	1.48248
$527$	8.32070	0.362455
$528$	60.8282	2.64721
$529$	−22.9993	−0.999968
$530$	−34.7320	−1.50866
$531$	−1.05700	−0.0458697
$532$	25.8590	1.12113
$533$	47.7233	2.06713
$534$	−39.6684	−1.71662
$535$	25.6756	1.11005
$536$	89.2581	3.85536
$537$	31.0549	1.34012
$538$	47.3667	2.04212
$539$	−11.7867	−0.507688
$540$	−63.6681	−2.73984
$541$	9.77847	0.420409	0.210205	−	0.977657i	$-0.432587\pi$
$541$	9.77847	0.420409	0.210205	+	0.977657i	$0.432587\pi$
$542$	−26.8170	−1.15189
$543$	4.99063	0.214169
$544$	−74.1647	−3.17978
$545$	14.3908	0.616433
$546$	−32.9117	−1.40849
$547$	−16.1603	−0.690964	−0.345482	−	0.938425i	$-0.612285\pi$
$547$	−16.1603	−0.690964	−0.345482	+	0.938425i	$0.612285\pi$
$548$	6.69346	0.285930
$549$	−8.58513	−0.366404
$550$	−19.6791	−0.839118
$551$	0.00527603	0.000224766 0
$552$	0.460563	0.0196029
$553$	8.69712	0.369839
$554$	−36.1302	−1.53503
$555$	5.52684	0.234601
$556$	−110.095	−4.66905
$557$	2.95036	0.125011	0.0625054	−	0.998045i	$-0.480091\pi$
$557$	2.95036	0.125011	0.0625054	+	0.998045i	$0.480091\pi$
$558$	−4.21265	−0.178336
$559$	40.2296	1.70153
$560$	−53.3017	−2.25241
$561$	19.9706	0.843157
$562$	5.86727	0.247496
$563$	−34.1717	−1.44017	−0.720083	−	0.693888i	$-0.755896\pi$
$563$	−34.1717	−1.44017	−0.720083	+	0.693888i	$0.755896\pi$
$564$	−102.757	−4.32686
$565$	−40.7390	−1.71390
$566$	−44.8748	−1.88623
$567$	15.6154	0.655786
$568$	58.6016	2.45887
$569$	−3.53856	−0.148344	−0.0741721	−	0.997245i	$-0.523631\pi$
$569$	−3.53856	−0.148344	−0.0741721	+	0.997245i	$0.523631\pi$
$570$	50.5881	2.11890
$571$	−20.2867	−0.848970	−0.424485	−	0.905435i	$-0.639545\pi$
$571$	−20.2867	−0.848970	−0.424485	+	0.905435i	$0.639545\pi$
$572$	−54.5454	−2.28066
$573$	34.8424	1.45556
$574$	−43.0837	−1.79828
$575$	−0.0823893	−0.00343587
$576$	16.8061	0.700253
$577$	−14.9036	−0.620444	−0.310222	−	0.950664i	$-0.600403\pi$
$577$	−14.9036	−0.620444	−0.310222	+	0.950664i	$0.600403\pi$
$578$	−2.94060	−0.122313
$579$	−1.72766	−0.0717991
$580$	−0.0230253	−0.000956074 0
$581$	−20.8462	−0.864848
$582$	−85.6886	−3.55191
$583$	10.9671	0.454213
$584$	4.03619	0.167019
$585$	−9.81386	−0.405753
$586$	−56.6803	−2.34144
$587$	46.7343	1.92893	0.964465	−	0.264210i	$-0.0851113\pi$
$587$	46.7343	1.92893	0.964465	+	0.264210i	$0.0851113\pi$
$588$	−49.9710	−2.06077
$589$	−6.65553	−0.274236
$590$	10.0708	0.414609
$591$	−25.2081	−1.03692
$592$	12.9560	0.532488
$593$	−26.5239	−1.08921	−0.544603	−	0.838694i	$-0.683320\pi$
$593$	−26.5239	−1.08921	−0.544603	+	0.838694i	$0.683320\pi$
$594$	27.7813	1.13988
$595$	−17.4995	−0.717411
$596$	−71.0299	−2.90950
$597$	−37.7827	−1.54634
$598$	−0.315566	−0.0129044
$599$	−26.1359	−1.06788	−0.533941	−	0.845522i	$-0.679290\pi$
$599$	−26.1359	−1.06788	−0.533941	+	0.845522i	$0.679290\pi$
$600$	−51.5720	−2.10542
$601$	3.98758	0.162657	0.0813283	−	0.996687i	$-0.474084\pi$
$601$	3.98758	0.162657	0.0813283	+	0.996687i	$0.474084\pi$
$602$	−36.3185	−1.48023
$603$	−8.20372	−0.334081
$604$	19.5502	0.795487
$605$	−14.7421	−0.599353
$606$	55.9357	2.27223
$607$	24.1516	0.980285	0.490142	−	0.871642i	$-0.336945\pi$
$607$	24.1516	0.980285	0.490142	+	0.871642i	$0.336945\pi$
$608$	59.3225	2.40585
$609$	0.00438694	0.000177768 0
$610$	81.7971	3.31187
$611$	43.5208	1.76066
$612$	17.8334	0.720874
$613$	41.4301	1.67334	0.836672	−	0.547704i	$-0.184498\pi$
$613$	41.4301	1.67334	0.836672	+	0.547704i	$0.184498\pi$
$614$	−48.2200	−1.94600
$615$	−60.9936	−2.45950
$616$	30.4385	1.22640
$617$	−22.6171	−0.910531	−0.455266	−	0.890356i	$-0.650456\pi$
$617$	−22.6171	−0.910531	−0.455266	+	0.890356i	$0.650456\pi$
$618$	−66.7567	−2.68535
$619$	4.13778	0.166311	0.0831557	−	0.996537i	$-0.473500\pi$
$619$	4.13778	0.166311	0.0831557	+	0.996537i	$0.473500\pi$
$620$	29.0456	1.16650
$621$	0.116310	0.00466737
$622$	−18.0819	−0.725019
$623$	−10.9760	−0.439746
$624$	−109.223	−4.37243
$625$	−30.9612	−1.23845
$626$	−48.3741	−1.93342
$627$	−15.9740	−0.637939
$628$	88.8958	3.54733
$629$	4.25359	0.169602
$630$	8.85976	0.352981
$631$	39.1540	1.55870	0.779348	−	0.626592i	$-0.215551\pi$
$631$	39.1540	1.55870	0.779348	+	0.626592i	$0.215551\pi$
$632$	52.1985	2.07635
$633$	−28.6940	−1.14048
$634$	71.5686	2.84235
$635$	36.1462	1.43442
$636$	46.4964	1.84370
$637$	21.1642	0.838555
$638$	0.0100470	0.000397763 0
$639$	−5.38607	−0.213070
$640$	−61.2627	−2.42162
$641$	30.1753	1.19185	0.595925	−	0.803040i	$-0.296785\pi$
$641$	30.1753	1.19185	0.595925	+	0.803040i	$0.296785\pi$
$642$	−47.4981	−1.87460
$643$	−8.83603	−0.348459	−0.174229	−	0.984705i	$-0.555743\pi$
$643$	−8.83603	−0.348459	−0.174229	+	0.984705i	$0.555743\pi$
$644$	0.206161	0.00812388
$645$	−51.4161	−2.02451
$646$	38.9339	1.53183
$647$	−19.8056	−0.778638	−0.389319	−	0.921103i	$-0.627290\pi$
$647$	−19.8056	−0.778638	−0.389319	+	0.921103i	$0.627290\pi$
$648$	93.7209	3.68170
$649$	−3.18001	−0.124826
$650$	35.3358	1.38598
$651$	−5.53398	−0.216894
$652$	5.23745	0.205114
$653$	−28.6629	−1.12166	−0.560832	−	0.827929i	$-0.689519\pi$
$653$	−28.6629	−1.12166	−0.560832	+	0.827929i	$0.689519\pi$
$654$	−26.6220	−1.04100
$655$	−18.9459	−0.740277
$656$	−142.981	−5.58246
$657$	−0.370966	−0.0144728
$658$	−39.2897	−1.53167
$659$	8.15232	0.317569	0.158785	−	0.987313i	$-0.449242\pi$
$659$	8.15232	0.317569	0.158785	+	0.987313i	$0.449242\pi$
$660$	69.7126	2.71356
$661$	35.5143	1.38134	0.690672	−	0.723168i	$-0.257315\pi$
$661$	35.5143	1.38134	0.690672	+	0.723168i	$0.257315\pi$
$662$	−9.31089	−0.361878
$663$	−35.8592	−1.39265
$664$	−125.115	−4.85541
$665$	13.9975	0.542798
$666$	−2.15353	−0.0834477
$667$	4.20631e−5 0	1.62869e−6 0
$668$	1.31428	0.0508510
$669$	35.0585	1.35544
$670$	78.1631	3.01970
$671$	−25.8287	−0.997105
$672$	49.3259	1.90279
$673$	17.2372	0.664446	0.332223	−	0.943201i	$-0.392201\pi$
$673$	17.2372	0.664446	0.332223	+	0.943201i	$0.392201\pi$
$674$	36.5117	1.40638
$675$	−13.0239	−0.501292
$676$	29.8549	1.14827
$677$	−20.9128	−0.803745	−0.401872	−	0.915696i	$-0.631640\pi$
$677$	−20.9128	−0.803745	−0.401872	+	0.915696i	$0.631640\pi$
$678$	75.3645	2.89435
$679$	−23.7096	−0.909890
$680$	−105.029	−4.02768
$681$	6.07122	0.232649
$682$	−12.6739	−0.485309
$683$	−49.3988	−1.89019	−0.945097	−	0.326790i	$-0.894033\pi$
$683$	−49.3988	−1.89019	−0.945097	+	0.326790i	$0.894033\pi$
$684$	−14.2645	−0.545418
$685$	3.62316	0.138434
$686$	−46.4344	−1.77287
$687$	21.3368	0.814051
$688$	−120.529	−4.59514
$689$	−19.6926	−0.750229
$690$	0.403314	0.0153539
$691$	20.4336	0.777331	0.388666	−	0.921379i	$-0.372936\pi$
$691$	20.4336	0.777331	0.388666	+	0.921379i	$0.372936\pi$
$692$	−107.459	−4.08496
$693$	−2.79760	−0.106272
$694$	−25.7244	−0.976485
$695$	−59.5940	−2.26053
$696$	0.0263296	0.000998022 0
$697$	−46.9421	−1.77806
$698$	−76.2577	−2.88640
$699$	13.8280	0.523025
$700$	−23.0851	−0.872533
$701$	19.0889	0.720976	0.360488	−	0.932764i	$-0.382610\pi$
$701$	19.0889	0.720976	0.360488	+	0.932764i	$0.382610\pi$
$702$	−49.8841	−1.88275
$703$	−3.40235	−0.128322
$704$	50.5617	1.90562
$705$	−55.6224	−2.09486
$706$	54.3757	2.04646
$707$	15.4771	0.582077
$708$	−13.4820	−0.506685
$709$	2.58861	0.0972174	0.0486087	−	0.998818i	$-0.484521\pi$
$709$	2.58861	0.0972174	0.0486087	+	0.998818i	$0.484521\pi$
$710$	51.3173	1.92590
$711$	−4.79756	−0.179923
$712$	−65.8762	−2.46881
$713$	−0.0530612	−0.00198716
$714$	32.3730	1.21153
$715$	−29.5253	−1.10419
$716$	83.4314	3.11798
$717$	9.76960	0.364852
$718$	59.3533	2.21505
$719$	−31.5034	−1.17488	−0.587440	−	0.809268i	$-0.699864\pi$
$719$	−31.5034	−1.17488	−0.587440	+	0.809268i	$0.699864\pi$
$720$	29.4027	1.09577
$721$	−18.4712	−0.687904
$722$	19.9725	0.743300
$723$	13.3767	0.497485
$724$	13.4077	0.498295
$725$	−0.00471006	−0.000174927 0
$726$	27.2719	1.01216
$727$	13.8144	0.512349	0.256174	−	0.966631i	$-0.417538\pi$
$727$	13.8144	0.512349	0.256174	+	0.966631i	$0.417538\pi$
$728$	−54.6555	−2.02567
$729$	16.4637	0.609768
$730$	3.53448	0.130817
$731$	−39.5711	−1.46359
$732$	−109.504	−4.04737
$733$	−6.12737	−0.226320	−0.113160	−	0.993577i	$-0.536097\pi$
$733$	−6.12737	−0.226320	−0.113160	+	0.993577i	$0.536097\pi$
$734$	29.5236	1.08974
$735$	−27.0492	−0.997725
$736$	0.472949	0.0174331
$737$	−24.6812	−0.909143
$738$	23.7661	0.874844
$739$	−21.4298	−0.788307	−0.394153	−	0.919045i	$-0.628962\pi$
$739$	−21.4298	−0.788307	−0.394153	+	0.919045i	$0.628962\pi$
$740$	14.8483	0.545835
$741$	28.6829	1.05369
$742$	17.7781	0.652656
$743$	−1.45072	−0.0532217	−0.0266109	−	0.999646i	$-0.508471\pi$
$743$	−1.45072	−0.0532217	−0.0266109	+	0.999646i	$0.508471\pi$
$744$	−33.2139	−1.21768
$745$	−38.4484	−1.40864
$746$	15.0152	0.549746
$747$	11.4993	0.420739
$748$	53.6525	1.96173
$749$	−13.1425	−0.480215
$750$	29.1816	1.06556
$751$	−16.4780	−0.601289	−0.300645	−	0.953736i	$-0.597202\pi$
$751$	−16.4780	−0.601289	−0.300645	+	0.953736i	$0.597202\pi$
$752$	−130.390	−4.75482
$753$	16.8815	0.615195
$754$	−0.0180404	−0.000656991 0
$755$	10.5825	0.385137
$756$	32.5896	1.18527
$757$	−3.35649	−0.121994	−0.0609969	−	0.998138i	$-0.519428\pi$
$757$	−3.35649	−0.121994	−0.0609969	+	0.998138i	$0.519428\pi$
$758$	11.1671	0.405608
$759$	−0.127352	−0.00462260
$760$	84.0101	3.04737
$761$	−22.0061	−0.797719	−0.398859	−	0.917012i	$-0.630594\pi$
$761$	−22.0061	−0.797719	−0.398859	+	0.917012i	$0.630594\pi$
$762$	−66.8681	−2.42238
$763$	−7.36615	−0.266673
$764$	93.6070	3.38658
$765$	9.65321	0.349013
$766$	−91.0872	−3.29111
$767$	5.71003	0.206177
$768$	31.4745	1.13574
$769$	6.57322	0.237036	0.118518	−	0.992952i	$-0.462186\pi$
$769$	6.57322	0.237036	0.118518	+	0.992952i	$0.462186\pi$
$770$	26.6549	0.960576
$771$	−0.829854	−0.0298865
$772$	−4.64150	−0.167051
$773$	−22.6669	−0.815272	−0.407636	−	0.913145i	$-0.633647\pi$
$773$	−22.6669	−0.815272	−0.407636	+	0.913145i	$0.633647\pi$
$774$	20.0343	0.720117
$775$	5.94157	0.213428
$776$	−142.300	−5.10829
$777$	−2.82900	−0.101490
$778$	28.4898	1.02141
$779$	37.5479	1.34529
$780$	−125.176	−4.48202
$781$	−16.2042	−0.579832
$782$	0.310400	0.0110999
$783$	0.00664926	0.000237625 0
$784$	−63.4086	−2.26459
$785$	48.1192	1.71745
$786$	35.0486	1.25014
$787$	−26.9958	−0.962297	−0.481148	−	0.876639i	$-0.659780\pi$
$787$	−26.9958	−0.962297	−0.481148	+	0.876639i	$0.659780\pi$
$788$	−67.7235	−2.41255
$789$	−24.6382	−0.877142
$790$	45.7101	1.62629
$791$	20.8529	0.741445
$792$	−16.7907	−0.596632
$793$	46.3780	1.64693
$794$	73.5190	2.60909
$795$	25.1685	0.892633
$796$	−101.506	−3.59779
$797$	37.4204	1.32550	0.662750	−	0.748841i	$-0.269389\pi$
$797$	37.4204	1.32550	0.662750	+	0.748841i	$0.269389\pi$
$798$	−25.8943	−0.916650
$799$	−42.8084	−1.51445
$800$	−52.9589	−1.87238
$801$	6.05468	0.213932
$802$	94.1799	3.32561
$803$	−1.11606	−0.0393851
$804$	−104.639	−3.69032
$805$	0.111595	0.00393320
$806$	22.7573	0.801591
$807$	−34.3242	−1.20827
$808$	92.8907	3.26789
$809$	−22.6429	−0.796081	−0.398040	−	0.917368i	$-0.630310\pi$
$809$	−22.6429	−0.796081	−0.398040	+	0.917368i	$0.630310\pi$
$810$	82.0711	2.88368
$811$	18.9588	0.665733	0.332866	−	0.942974i	$-0.391984\pi$
$811$	18.9588	0.665733	0.332866	+	0.942974i	$0.391984\pi$
$812$	0.0117859	0.000413603 0
$813$	19.4329	0.681541
$814$	−6.47898	−0.227088
$815$	2.83503	0.0993066
$816$	107.435	3.76099
$817$	31.6519	1.10736
$818$	−71.2969	−2.49284
$819$	5.02338	0.175531
$820$	−163.864	−5.72238
$821$	50.6320	1.76707	0.883535	−	0.468364i	$-0.155157\pi$
$821$	50.6320	1.76707	0.883535	+	0.468364i	$0.155157\pi$
$822$	−6.70260	−0.233780
$823$	23.0793	0.804495	0.402247	−	0.915531i	$-0.368229\pi$
$823$	23.0793	0.804495	0.402247	+	0.915531i	$0.368229\pi$
$824$	−110.861	−3.86202
$825$	14.2604	0.496483
$826$	−5.15491	−0.179362
$827$	4.29432	0.149328	0.0746641	−	0.997209i	$-0.476212\pi$
$827$	4.29432	0.149328	0.0746641	+	0.997209i	$0.476212\pi$
$828$	−0.113724	−0.00395218
$829$	−10.6216	−0.368903	−0.184451	−	0.982842i	$-0.559051\pi$
$829$	−10.6216	−0.368903	−0.184451	+	0.982842i	$0.559051\pi$
$830$	−109.563	−3.80299
$831$	26.1817	0.908234
$832$	−90.7887	−3.14753
$833$	−20.8177	−0.721292
$834$	110.245	3.81747
$835$	0.711417	0.0246196
$836$	−42.9153	−1.48426
$837$	−8.38781	−0.289925
$838$	27.7151	0.957401
$839$	45.3335	1.56509	0.782543	−	0.622596i	$-0.213922\pi$
$839$	45.3335	1.56509	0.782543	+	0.622596i	$0.213922\pi$
$840$	69.8533	2.41017
$841$	−29.0000	−1.00000
$842$	49.0604	1.69073
$843$	−4.25171	−0.146437
$844$	−77.0887	−2.65350
$845$	16.1604	0.555935
$846$	21.6733	0.745142
$847$	7.54600	0.259284
$848$	58.9998	2.02606
$849$	32.5184	1.11603
$850$	−34.7573	−1.19217
$851$	−0.0271252	−0.000929840 0
$852$	−68.6995	−2.35361
$853$	47.7293	1.63422	0.817111	−	0.576481i	$-0.195575\pi$
$853$	47.7293	1.63422	0.817111	+	0.576481i	$0.195575\pi$
$854$	−41.8692	−1.43273
$855$	−7.72137	−0.264065
$856$	−78.8787	−2.69602
$857$	35.3599	1.20787	0.603935	−	0.797033i	$-0.293599\pi$
$857$	35.3599	1.20787	0.603935	+	0.797033i	$0.293599\pi$
$858$	54.6199	1.86469
$859$	3.10743	0.106024	0.0530121	−	0.998594i	$-0.483118\pi$
$859$	3.10743	0.106024	0.0530121	+	0.998594i	$0.483118\pi$
$860$	−138.133	−4.71031
$861$	31.2205	1.06399
$862$	93.3315	3.17888
$863$	14.0803	0.479299	0.239649	−	0.970860i	$-0.422968\pi$
$863$	14.0803	0.479299	0.239649	+	0.970860i	$0.422968\pi$
$864$	74.7629	2.54349
$865$	−58.1672	−1.97774
$866$	−103.964	−3.53286
$867$	2.13090	0.0723691
$868$	−14.8675	−0.504635
$869$	−14.4336	−0.489628
$870$	0.0230568	0.000781697 0
$871$	44.3175	1.50164
$872$	−44.2103	−1.49715
$873$	13.0788	0.442651
$874$	−0.248282	−0.00839825
$875$	8.07438	0.272964
$876$	−4.73168	−0.159869
$877$	16.8874	0.570248	0.285124	−	0.958491i	$-0.407965\pi$
$877$	16.8874	0.570248	0.285124	+	0.958491i	$0.407965\pi$
$878$	20.5028	0.691938
$879$	41.0733	1.38537
$880$	88.4590	2.98195
$881$	−40.1702	−1.35337	−0.676685	−	0.736273i	$-0.736584\pi$
$881$	−40.1702	−1.35337	−0.676685	+	0.736273i	$0.736584\pi$
$882$	10.5397	0.354891
$883$	−5.38629	−0.181263	−0.0906316	−	0.995884i	$-0.528889\pi$
$883$	−5.38629	−0.181263	−0.0906316	+	0.995884i	$0.528889\pi$
$884$	−96.3385	−3.24021
$885$	−7.29780	−0.245313
$886$	−97.7650	−3.28448
$887$	−2.35142	−0.0789531	−0.0394766	−	0.999220i	$-0.512569\pi$
$887$	−2.35142	−0.0789531	−0.0394766	+	0.999220i	$0.512569\pi$
$888$	−16.9792	−0.569783
$889$	−18.5020	−0.620538
$890$	−57.6875	−1.93369
$891$	−25.9152	−0.868191
$892$	94.1876	3.15363
$893$	34.2414	1.14584
$894$	71.1269	2.37884
$895$	45.1613	1.50958
$896$	31.3583	1.04761
$897$	0.228674	0.00763521
$898$	−85.7269	−2.86074
$899$	−0.00303342	−0.000101170 0
$900$	12.7343	0.424478
$901$	19.3703	0.645317
$902$	71.5013	2.38073
$903$	26.3181	0.875813
$904$	125.155	4.16261
$905$	7.25759	0.241250
$906$	−19.5769	−0.650400
$907$	−28.4863	−0.945872	−0.472936	−	0.881097i	$-0.656806\pi$
$907$	−28.4863	−0.945872	−0.472936	+	0.881097i	$0.656806\pi$
$908$	16.3108	0.541293
$909$	−8.53759	−0.283174
$910$	−47.8616	−1.58660
$911$	54.8161	1.81614	0.908069	−	0.418821i	$-0.137557\pi$
$911$	54.8161	1.81614	0.908069	+	0.418821i	$0.137557\pi$
$912$	−85.9349	−2.84559
$913$	34.5962	1.14497
$914$	−30.1457	−0.997132
$915$	−59.2741	−1.95954
$916$	57.3231	1.89401
$917$	9.69776	0.320248
$918$	49.0675	1.61947
$919$	8.50277	0.280481	0.140240	−	0.990118i	$-0.455213\pi$
$919$	8.50277	0.280481	0.140240	+	0.990118i	$0.455213\pi$
$920$	0.669771	0.0220817
$921$	34.9425	1.15140
$922$	−11.2123	−0.369256
$923$	29.0963	0.957716
$924$	−35.6835	−1.17390
$925$	3.03737	0.0998681
$926$	93.7074	3.07942
$927$	10.1892	0.334658
$928$	0.0270377	0.000887555 0
$929$	−32.9202	−1.08008	−0.540038	−	0.841641i	$-0.681590\pi$
$929$	−32.9202	−1.08008	−0.540038	+	0.841641i	$0.681590\pi$
$930$	−29.0853	−0.953745
$931$	16.6516	0.545734
$932$	37.1502	1.21689
$933$	13.1030	0.428974
$934$	58.2468	1.90589
$935$	29.0420	0.949776
$936$	30.1494	0.985464
$937$	−42.1978	−1.37854	−0.689271	−	0.724503i	$-0.742069\pi$
$937$	−42.1978	−1.37854	−0.689271	+	0.724503i	$0.742069\pi$
$938$	−40.0090	−1.30634
$939$	35.0542	1.14395
$940$	−149.434	−4.87400
$941$	−2.90385	−0.0946628	−0.0473314	−	0.998879i	$-0.515072\pi$
$941$	−2.90385	−0.0946628	−0.0473314	+	0.998879i	$0.515072\pi$
$942$	−89.0173	−2.90034
$943$	0.299351	0.00974820
$944$	−17.1075	−0.556800
$945$	17.6407	0.573851
$946$	60.2738	1.95967
$947$	−11.2749	−0.366384	−0.183192	−	0.983077i	$-0.558643\pi$
$947$	−11.2749	−0.366384	−0.183192	+	0.983077i	$0.558643\pi$
$948$	−61.1931	−1.98746
$949$	2.00401	0.0650528
$950$	27.8016	0.902001
$951$	−51.8621	−1.68174
$952$	53.7608	1.74240
$953$	−40.4946	−1.31175	−0.655874	−	0.754870i	$-0.727700\pi$
$953$	−40.4946	−1.31175	−0.655874	+	0.754870i	$0.727700\pi$
$954$	−9.80689	−0.317510
$955$	50.6694	1.63962
$956$	26.2468	0.848882
$957$	−0.00728052	−0.000235346 0
$958$	3.36426	0.108694
$959$	−1.85457	−0.0598873
$960$	116.034	3.74498
$961$	−27.1734	−0.876563
$962$	11.6337	0.375085
$963$	7.24974	0.233620
$964$	35.9376	1.15747
$965$	−2.51244	−0.0808782
$966$	−0.206443	−0.00664219
$967$	44.5890	1.43388	0.716942	−	0.697133i	$-0.245541\pi$
$967$	44.5890	1.43388	0.716942	+	0.697133i	$0.245541\pi$
$968$	45.2897	1.45567
$969$	−28.2133	−0.906343
$970$	−124.612	−4.00105
$971$	−44.4030	−1.42496	−0.712481	−	0.701692i	$-0.752428\pi$
$971$	−44.4030	−1.42496	−0.712481	+	0.701692i	$0.752428\pi$
$972$	−42.4973	−1.36310
$973$	30.5042	0.977919
$974$	112.415	3.60202
$975$	−25.6060	−0.820048
$976$	−138.950	−4.44768
$977$	−49.8619	−1.59522	−0.797612	−	0.603171i	$-0.793904\pi$
$977$	−49.8619	−1.59522	−0.797612	+	0.603171i	$0.793904\pi$
$978$	−5.24461	−0.167704
$979$	18.2157	0.582177
$980$	−72.6699	−2.32135
$981$	4.06337	0.129733
$982$	47.8211	1.52603
$983$	38.4881	1.22758	0.613789	−	0.789470i	$-0.289645\pi$
$983$	38.4881	1.22758	0.613789	+	0.789470i	$0.289645\pi$
$984$	187.380	5.97346
$985$	−36.6587	−1.16804
$986$	0.0177450	0.000565117 0
$987$	28.4712	0.906249
$988$	77.0589	2.45157
$989$	0.252345	0.00802411
$990$	−14.7036	−0.467310
$991$	0.253297	0.00804625	0.00402313	−	0.999992i	$-0.498719\pi$
$991$	0.253297	0.00804625	0.00402313	+	0.999992i	$0.498719\pi$
$992$	−34.1071	−1.08290
$993$	6.74712	0.214113
$994$	−26.2676	−0.833157
$995$	−54.9452	−1.74188
$996$	146.674	4.64756
$997$	−19.9496	−0.631809	−0.315905	−	0.948791i	$-0.602308\pi$
$997$	−19.9496	−0.631809	−0.315905	+	0.948791i	$0.602308\pi$
$998$	−54.0028	−1.70943
$999$	−4.28790	−0.135663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.4	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.4	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69025 q^{2} +1.94949 q^{3} +5.23745 q^{4} +2.83503 q^{5} -5.24461 q^{6} -1.45115 q^{7} -8.70956 q^{8} +0.800495 q^{9} +O(q^{10})\)	\(q-2.69025 q^{2} +1.94949 q^{3} +5.23745 q^{4} +2.83503 q^{5} -5.24461 q^{6} -1.45115 q^{7} -8.70956 q^{8} +0.800495 q^{9} -7.62693 q^{10} +2.40832 q^{11} +10.2103 q^{12} -4.32438 q^{13} +3.90397 q^{14} +5.52684 q^{15} +12.9560 q^{16} +4.25359 q^{17} -2.15353 q^{18} -3.40235 q^{19} +14.8483 q^{20} -2.82900 q^{21} -6.47898 q^{22} -0.0271252 q^{23} -16.9792 q^{24} +3.03737 q^{25} +11.6337 q^{26} -4.28790 q^{27} -7.60035 q^{28} -0.00155070 q^{29} -14.8686 q^{30} +1.95616 q^{31} -17.4358 q^{32} +4.69498 q^{33} -11.4432 q^{34} -4.11406 q^{35} +4.19256 q^{36} +1.00000 q^{37} +9.15317 q^{38} -8.43032 q^{39} -24.6918 q^{40} -11.0359 q^{41} +7.61073 q^{42} -9.30297 q^{43} +12.6135 q^{44} +2.26942 q^{45} +0.0729736 q^{46} -10.0640 q^{47} +25.2575 q^{48} -4.89415 q^{49} -8.17129 q^{50} +8.29232 q^{51} -22.6487 q^{52} +4.55386 q^{53} +11.5355 q^{54} +6.82765 q^{55} +12.6389 q^{56} -6.63283 q^{57} +0.00417178 q^{58} -1.32043 q^{59} +28.9466 q^{60} -10.7248 q^{61} -5.26255 q^{62} -1.16164 q^{63} +20.9946 q^{64} -12.2597 q^{65} -12.6307 q^{66} -10.2483 q^{67} +22.2780 q^{68} -0.0528802 q^{69} +11.0678 q^{70} -6.72843 q^{71} -6.97196 q^{72} -0.463420 q^{73} -2.69025 q^{74} +5.92131 q^{75} -17.8196 q^{76} -3.49484 q^{77} +22.6797 q^{78} -5.99324 q^{79} +36.7306 q^{80} -10.7607 q^{81} +29.6893 q^{82} +14.3653 q^{83} -14.8168 q^{84} +12.0590 q^{85} +25.0273 q^{86} -0.00302307 q^{87} -20.9754 q^{88} +7.56366 q^{89} -6.10532 q^{90} +6.27534 q^{91} -0.142067 q^{92} +3.81350 q^{93} +27.0748 q^{94} -9.64574 q^{95} -33.9908 q^{96} +16.3384 q^{97} +13.1665 q^{98} +1.92785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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