LMFDB - Embedded newform 6029.2.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, 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("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66544 q^{2} -2.15906 q^{3} +5.10457 q^{4} +0.849689 q^{5} +5.75486 q^{6} +1.23234 q^{7} -8.27506 q^{8} +1.66156 q^{9} +O(q^{10})$	\(q-2.66544 q^{2} -2.15906 q^{3} +5.10457 q^{4} +0.849689 q^{5} +5.75486 q^{6} +1.23234 q^{7} -8.27506 q^{8} +1.66156 q^{9} -2.26480 q^{10} +2.62582 q^{11} -11.0211 q^{12} +2.44615 q^{13} -3.28474 q^{14} -1.83453 q^{15} +11.8475 q^{16} +3.70374 q^{17} -4.42879 q^{18} +0.677600 q^{19} +4.33730 q^{20} -2.66071 q^{21} -6.99898 q^{22} +0.671719 q^{23} +17.8664 q^{24} -4.27803 q^{25} -6.52006 q^{26} +2.88978 q^{27} +6.29058 q^{28} +5.63592 q^{29} +4.88984 q^{30} -8.70933 q^{31} -15.0288 q^{32} -5.66933 q^{33} -9.87211 q^{34} +1.04711 q^{35} +8.48155 q^{36} -2.29105 q^{37} -1.80610 q^{38} -5.28139 q^{39} -7.03123 q^{40} -4.08963 q^{41} +7.09196 q^{42} +4.62801 q^{43} +13.4037 q^{44} +1.41181 q^{45} -1.79043 q^{46} -3.15034 q^{47} -25.5796 q^{48} -5.48133 q^{49} +11.4028 q^{50} -7.99662 q^{51} +12.4865 q^{52} +9.64340 q^{53} -7.70253 q^{54} +2.23113 q^{55} -10.1977 q^{56} -1.46298 q^{57} -15.0222 q^{58} -14.9693 q^{59} -9.36451 q^{60} +4.50086 q^{61} +23.2142 q^{62} +2.04761 q^{63} +16.3632 q^{64} +2.07846 q^{65} +15.1113 q^{66} +2.70328 q^{67} +18.9060 q^{68} -1.45029 q^{69} -2.79100 q^{70} +0.264031 q^{71} -13.7495 q^{72} +2.39974 q^{73} +6.10666 q^{74} +9.23654 q^{75} +3.45886 q^{76} +3.23592 q^{77} +14.0772 q^{78} -4.06573 q^{79} +10.0667 q^{80} -11.2239 q^{81} +10.9007 q^{82} -4.64859 q^{83} -13.5818 q^{84} +3.14703 q^{85} -12.3357 q^{86} -12.1683 q^{87} -21.7289 q^{88} +0.511832 q^{89} -3.76309 q^{90} +3.01449 q^{91} +3.42884 q^{92} +18.8040 q^{93} +8.39705 q^{94} +0.575750 q^{95} +32.4481 q^{96} -18.4893 q^{97} +14.6102 q^{98} +4.36297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.66544	−1.88475	−0.942376	−	0.334557i	$-0.891413\pi$
$2$	−2.66544	−1.88475	−0.942376	+	0.334557i	$0.891413\pi$
$3$	−2.15906	−1.24654	−0.623268	−	0.782008i	$-0.714196\pi$
$3$	−2.15906	−1.24654	−0.623268	+	0.782008i	$0.714196\pi$
$4$	5.10457	2.55229
$5$	0.849689	0.379993	0.189996	−	0.981785i	$-0.439152\pi$
$5$	0.849689	0.379993	0.189996	+	0.981785i	$0.439152\pi$
$6$	5.75486	2.34941
$7$	1.23234	0.465782	0.232891	−	0.972503i	$-0.425182\pi$
$7$	1.23234	0.465782	0.232891	+	0.972503i	$0.425182\pi$
$8$	−8.27506	−2.92567
$9$	1.66156	0.553853
$10$	−2.26480	−0.716191
$11$	2.62582	0.791716	0.395858	−	0.918312i	$-0.370447\pi$
$11$	2.62582	0.791716	0.395858	+	0.918312i	$0.370447\pi$
$12$	−11.0211	−3.18152
$13$	2.44615	0.678439	0.339220	−	0.940707i	$-0.389837\pi$
$13$	2.44615	0.678439	0.339220	+	0.940707i	$0.389837\pi$
$14$	−3.28474	−0.877882
$15$	−1.83453	−0.473675
$16$	11.8475	2.96188
$17$	3.70374	0.898290	0.449145	−	0.893459i	$-0.351729\pi$
$17$	3.70374	0.898290	0.449145	+	0.893459i	$0.351729\pi$
$18$	−4.42879	−1.04388
$19$	0.677600	0.155452	0.0777261	−	0.996975i	$-0.475234\pi$
$19$	0.677600	0.155452	0.0777261	+	0.996975i	$0.475234\pi$
$20$	4.33730	0.969850
$21$	−2.66071	−0.580614
$22$	−6.99898	−1.49219
$23$	0.671719	0.140063	0.0700316	−	0.997545i	$-0.477690\pi$
$23$	0.671719	0.140063	0.0700316	+	0.997545i	$0.477690\pi$
$24$	17.8664	3.64696
$25$	−4.27803	−0.855606
$26$	−6.52006	−1.27869
$27$	2.88978	0.556138
$28$	6.29058	1.18881
$29$	5.63592	1.04656	0.523282	−	0.852159i	$-0.324707\pi$
$29$	5.63592	1.04656	0.523282	+	0.852159i	$0.324707\pi$
$30$	4.88984	0.892759
$31$	−8.70933	−1.56424	−0.782121	−	0.623127i	$-0.785862\pi$
$31$	−8.70933	−1.56424	−0.782121	+	0.623127i	$0.785862\pi$
$32$	−15.0288	−2.65673
$33$	−5.66933	−0.986903
$34$	−9.87211	−1.69305
$35$	1.04711	0.176994
$36$	8.48155	1.41359
$37$	−2.29105	−0.376646	−0.188323	−	0.982107i	$-0.560305\pi$
$37$	−2.29105	−0.376646	−0.188323	+	0.982107i	$0.560305\pi$
$38$	−1.80610	−0.292989
$39$	−5.28139	−0.845699
$40$	−7.03123	−1.11173
$41$	−4.08963	−0.638693	−0.319347	−	0.947638i	$-0.603463\pi$
$41$	−4.08963	−0.638693	−0.319347	+	0.947638i	$0.603463\pi$
$42$	7.09196	1.09431
$43$	4.62801	0.705765	0.352882	−	0.935668i	$-0.385202\pi$
$43$	4.62801	0.705765	0.352882	+	0.935668i	$0.385202\pi$
$44$	13.4037	2.02069
$45$	1.41181	0.210460
$46$	−1.79043	−0.263984
$47$	−3.15034	−0.459524	−0.229762	−	0.973247i	$-0.573795\pi$
$47$	−3.15034	−0.459524	−0.229762	+	0.973247i	$0.573795\pi$
$48$	−25.5796	−3.69209
$49$	−5.48133	−0.783047
$50$	11.4028	1.61260
$51$	−7.99662	−1.11975
$52$	12.4865	1.73157
$53$	9.64340	1.32462	0.662311	−	0.749229i	$-0.269576\pi$
$53$	9.64340	1.32462	0.662311	+	0.749229i	$0.269576\pi$
$54$	−7.70253	−1.04818
$55$	2.23113	0.300846
$56$	−10.1977	−1.36273
$57$	−1.46298	−0.193777
$58$	−15.0222	−1.97251
$59$	−14.9693	−1.94884	−0.974420	−	0.224734i	$-0.927849\pi$
$59$	−14.9693	−1.94884	−0.974420	+	0.224734i	$0.927849\pi$
$60$	−9.36451	−1.20895
$61$	4.50086	0.576276	0.288138	−	0.957589i	$-0.406964\pi$
$61$	4.50086	0.576276	0.288138	+	0.957589i	$0.406964\pi$
$62$	23.2142	2.94821
$63$	2.04761	0.257975
$64$	16.3632	2.04540
$65$	2.07846	0.257802
$66$	15.1113	1.86007
$67$	2.70328	0.330258	0.165129	−	0.986272i	$-0.447196\pi$
$67$	2.70328	0.330258	0.165129	+	0.986272i	$0.447196\pi$
$68$	18.9060	2.29269
$69$	−1.45029	−0.174594
$70$	−2.79100	−0.333589
$71$	0.264031	0.0313347	0.0156674	−	0.999877i	$-0.495013\pi$
$71$	0.264031	0.0313347	0.0156674	+	0.999877i	$0.495013\pi$
$72$	−13.7495	−1.62039
$73$	2.39974	0.280868	0.140434	−	0.990090i	$-0.455150\pi$
$73$	2.39974	0.280868	0.140434	+	0.990090i	$0.455150\pi$
$74$	6.10666	0.709885
$75$	9.23654	1.06654
$76$	3.45886	0.396758
$77$	3.23592	0.368767
$78$	14.0772	1.59393
$79$	−4.06573	−0.457430	−0.228715	−	0.973493i	$-0.573452\pi$
$79$	−4.06573	−0.457430	−0.228715	+	0.973493i	$0.573452\pi$
$80$	10.0667	1.12549
$81$	−11.2239	−1.24710
$82$	10.9007	1.20378
$83$	−4.64859	−0.510249	−0.255125	−	0.966908i	$-0.582116\pi$
$83$	−4.64859	−0.510249	−0.255125	+	0.966908i	$0.582116\pi$
$84$	−13.5818	−1.48189
$85$	3.14703	0.341343
$86$	−12.3357	−1.33019
$87$	−12.1683	−1.30458
$88$	−21.7289	−2.31630
$89$	0.511832	0.0542540	0.0271270	−	0.999632i	$-0.491364\pi$
$89$	0.511832	0.0542540	0.0271270	+	0.999632i	$0.491364\pi$
$90$	−3.76309	−0.396665
$91$	3.01449	0.316005
$92$	3.42884	0.357481
$93$	18.8040	1.94988
$94$	8.39705	0.866089
$95$	0.575750	0.0590707
$96$	32.4481	3.31172
$97$	−18.4893	−1.87731	−0.938654	−	0.344860i	$-0.887926\pi$
$97$	−18.4893	−1.87731	−0.938654	+	0.344860i	$0.887926\pi$
$98$	14.6102	1.47585
$99$	4.36297	0.438494
$100$	−21.8375	−2.18375
$101$	−16.5104	−1.64285	−0.821423	−	0.570319i	$-0.806819\pi$
$101$	−16.5104	−1.64285	−0.821423	+	0.570319i	$0.806819\pi$
$102$	21.3145	2.11045
$103$	−7.42096	−0.731209	−0.365605	−	0.930770i	$-0.619138\pi$
$103$	−7.42096	−0.731209	−0.365605	+	0.930770i	$0.619138\pi$
$104$	−20.2420	−1.98489
$105$	−2.26077	−0.220629
$106$	−25.7039	−2.49658
$107$	−12.4079	−1.19951	−0.599757	−	0.800182i	$-0.704736\pi$
$107$	−12.4079	−1.19951	−0.599757	+	0.800182i	$0.704736\pi$
$108$	14.7511	1.41942
$109$	−18.9335	−1.81350	−0.906751	−	0.421666i	$-0.861446\pi$
$109$	−18.9335	−1.81350	−0.906751	+	0.421666i	$0.861446\pi$
$110$	−5.94696	−0.567020
$111$	4.94653	0.469503
$112$	14.6002	1.37959
$113$	−21.1147	−1.98630	−0.993152	−	0.116825i	$-0.962728\pi$
$113$	−21.1147	−1.98630	−0.993152	+	0.116825i	$0.962728\pi$
$114$	3.89949	0.365221
$115$	0.570753	0.0532229
$116$	28.7690	2.67113
$117$	4.06442	0.375756
$118$	39.8999	3.67308
$119$	4.56428	0.418407
$120$	15.1809	1.38582
$121$	−4.10504	−0.373186
$122$	−11.9968	−1.08614
$123$	8.82978	0.796154
$124$	−44.4574	−3.99239
$125$	−7.88344	−0.705116
$126$	−5.45778	−0.486218
$127$	−5.09037	−0.451697	−0.225849	−	0.974162i	$-0.572515\pi$
$127$	−5.09037	−0.451697	−0.225849	+	0.974162i	$0.572515\pi$
$128$	−13.5577	−1.19834
$129$	−9.99217	−0.879761
$130$	−5.54002	−0.485892
$131$	2.30007	0.200958	0.100479	−	0.994939i	$-0.467963\pi$
$131$	2.30007	0.200958	0.100479	+	0.994939i	$0.467963\pi$
$132$	−28.9395	−2.51886
$133$	0.835035	0.0724068
$134$	−7.20542	−0.622453
$135$	2.45541	0.211328
$136$	−30.6487	−2.62810
$137$	16.0953	1.37512	0.687558	−	0.726130i	$-0.258683\pi$
$137$	16.0953	1.37512	0.687558	+	0.726130i	$0.258683\pi$
$138$	3.86565	0.329066
$139$	1.36741	0.115982	0.0579911	−	0.998317i	$-0.481530\pi$
$139$	1.36741	0.115982	0.0579911	+	0.998317i	$0.481530\pi$
$140$	5.34504	0.451738
$141$	6.80179	0.572814
$142$	−0.703759	−0.0590581
$143$	6.42315	0.537131
$144$	19.6854	1.64045
$145$	4.78878	0.397687
$146$	−6.39636	−0.529367
$147$	11.8346	0.976097
$148$	−11.6948	−0.961310
$149$	23.0390	1.88743	0.943715	−	0.330761i	$-0.107305\pi$
$149$	23.0390	1.88743	0.943715	+	0.330761i	$0.107305\pi$
$150$	−24.6194	−2.01017
$151$	−2.67815	−0.217945	−0.108972	−	0.994045i	$-0.534756\pi$
$151$	−2.67815	−0.217945	−0.108972	+	0.994045i	$0.534756\pi$
$152$	−5.60718	−0.454802
$153$	6.15399	0.497521
$154$	−8.62514	−0.695034
$155$	−7.40022	−0.594400
$156$	−26.9592	−2.15847
$157$	−6.80535	−0.543126	−0.271563	−	0.962421i	$-0.587541\pi$
$157$	−6.80535	−0.543126	−0.271563	+	0.962421i	$0.587541\pi$
$158$	10.8370	0.862143
$159$	−20.8207	−1.65119
$160$	−12.7698	−1.00954
$161$	0.827788	0.0652388
$162$	29.9166	2.35047
$163$	−14.9509	−1.17105	−0.585524	−	0.810655i	$-0.699111\pi$
$163$	−14.9509	−1.17105	−0.585524	+	0.810655i	$0.699111\pi$
$164$	−20.8758	−1.63013
$165$	−4.81716	−0.375016
$166$	12.3905	0.961692
$167$	20.9943	1.62459	0.812296	−	0.583246i	$-0.198218\pi$
$167$	20.9943	1.62459	0.812296	+	0.583246i	$0.198218\pi$
$168$	22.0175	1.69869
$169$	−7.01636	−0.539720
$170$	−8.38823	−0.643348
$171$	1.12587	0.0860977
$172$	23.6240	1.80131
$173$	0.411771	0.0313064	0.0156532	−	0.999877i	$-0.495017\pi$
$173$	0.411771	0.0313064	0.0156532	+	0.999877i	$0.495017\pi$
$174$	32.4339	2.45881
$175$	−5.27200	−0.398525
$176$	31.1095	2.34497
$177$	32.3197	2.42930
$178$	−1.36426	−0.102255
$179$	−6.94604	−0.519172	−0.259586	−	0.965720i	$-0.583586\pi$
$179$	−6.94604	−0.519172	−0.259586	+	0.965720i	$0.583586\pi$
$180$	7.20668	0.537155
$181$	−1.37144	−0.101938	−0.0509691	−	0.998700i	$-0.516231\pi$
$181$	−1.37144	−0.101938	−0.0509691	+	0.998700i	$0.516231\pi$
$182$	−8.03495	−0.595590
$183$	−9.71765	−0.718349
$184$	−5.55852	−0.409779
$185$	−1.94668	−0.143123
$186$	−50.1209	−3.67505
$187$	9.72538	0.711191
$188$	−16.0811	−1.17284
$189$	3.56120	0.259039
$190$	−1.53463	−0.111333
$191$	−8.46974	−0.612849	−0.306424	−	0.951895i	$-0.599133\pi$
$191$	−8.46974	−0.612849	−0.306424	+	0.951895i	$0.599133\pi$
$192$	−35.3292	−2.54967
$193$	14.8018	1.06546	0.532729	−	0.846286i	$-0.321166\pi$
$193$	14.8018	1.06546	0.532729	+	0.846286i	$0.321166\pi$
$194$	49.2822	3.53826
$195$	−4.48754	−0.321359
$196$	−27.9799	−1.99856
$197$	22.4175	1.59718	0.798590	−	0.601875i	$-0.205580\pi$
$197$	22.4175	1.59718	0.798590	+	0.601875i	$0.205580\pi$
$198$	−11.6292	−0.826453
$199$	−12.7967	−0.907137	−0.453569	−	0.891221i	$-0.649849\pi$
$199$	−12.7967	−0.907137	−0.453569	+	0.891221i	$0.649849\pi$
$200$	35.4009	2.50322
$201$	−5.83655	−0.411678
$202$	44.0075	3.09636
$203$	6.94538	0.487470
$204$	−40.8194	−2.85793
$205$	−3.47492	−0.242699
$206$	19.7801	1.37815
$207$	1.11610	0.0775744
$208$	28.9808	2.00946
$209$	1.77926	0.123074
$210$	6.02596	0.415831
$211$	20.0005	1.37689	0.688447	−	0.725287i	$-0.258293\pi$
$211$	20.0005	1.37689	0.688447	+	0.725287i	$0.258293\pi$
$212$	49.2254	3.38082
$213$	−0.570060	−0.0390599
$214$	33.0724	2.26078
$215$	3.93237	0.268185
$216$	−23.9131	−1.62708
$217$	−10.7329	−0.728595
$218$	50.4662	3.41800
$219$	−5.18119	−0.350112
$220$	11.3890	0.767846
$221$	9.05990	0.609435
$222$	−13.1847	−0.884897
$223$	−25.4704	−1.70562	−0.852811	−	0.522220i	$-0.825104\pi$
$223$	−25.4704	−1.70562	−0.852811	+	0.522220i	$0.825104\pi$
$224$	−18.5206	−1.23746
$225$	−7.10820	−0.473880
$226$	56.2800	3.74369
$227$	−9.67614	−0.642228	−0.321114	−	0.947041i	$-0.604057\pi$
$227$	−9.67614	−0.642228	−0.321114	+	0.947041i	$0.604057\pi$
$228$	−7.46790	−0.494574
$229$	−6.73856	−0.445297	−0.222648	−	0.974899i	$-0.571470\pi$
$229$	−6.73856	−0.445297	−0.222648	+	0.974899i	$0.571470\pi$
$230$	−1.52131	−0.100312
$231$	−6.98655	−0.459681
$232$	−46.6376	−3.06191
$233$	27.2951	1.78816	0.894081	−	0.447904i	$-0.147830\pi$
$233$	27.2951	1.78816	0.894081	+	0.447904i	$0.147830\pi$
$234$	−10.8335	−0.708206
$235$	−2.67681	−0.174616
$236$	−76.4120	−4.97400
$237$	8.77817	0.570204
$238$	−12.1658	−0.788593
$239$	0.953976	0.0617076	0.0308538	−	0.999524i	$-0.490177\pi$
$239$	0.953976	0.0617076	0.0308538	+	0.999524i	$0.490177\pi$
$240$	−21.7347	−1.40297
$241$	−13.7233	−0.883995	−0.441998	−	0.897016i	$-0.645730\pi$
$241$	−13.7233	−0.883995	−0.441998	+	0.897016i	$0.645730\pi$
$242$	10.9417	0.703362
$243$	15.5638	0.998417
$244$	22.9750	1.47082
$245$	−4.65743	−0.297552
$246$	−23.5353	−1.50055
$247$	1.65751	0.105465
$248$	72.0702	4.57646
$249$	10.0366	0.636044
$250$	21.0128	1.32897
$251$	13.5520	0.855394	0.427697	−	0.903922i	$-0.359325\pi$
$251$	13.5520	0.855394	0.427697	+	0.903922i	$0.359325\pi$
$252$	10.4522	0.658425
$253$	1.76382	0.110890
$254$	13.5681	0.851337
$255$	−6.79464	−0.425497
$256$	3.41072	0.213170
$257$	27.8413	1.73669	0.868346	−	0.495959i	$-0.165183\pi$
$257$	27.8413	1.73669	0.868346	+	0.495959i	$0.165183\pi$
$258$	26.6335	1.65813
$259$	−2.82336	−0.175435
$260$	10.6097	0.657984
$261$	9.36442	0.579643
$262$	−6.13069	−0.378755
$263$	−30.9034	−1.90559	−0.952793	−	0.303619i	$-0.901805\pi$
$263$	−30.9034	−1.90559	−0.952793	+	0.303619i	$0.901805\pi$
$264$	46.9140	2.88736
$265$	8.19389	0.503347
$266$	−2.22574	−0.136469
$267$	−1.10508	−0.0676296
$268$	13.7991	0.842912
$269$	−8.58065	−0.523171	−0.261586	−	0.965180i	$-0.584245\pi$
$269$	−8.58065	−0.523171	−0.261586	+	0.965180i	$0.584245\pi$
$270$	−6.54476	−0.398301
$271$	−25.0629	−1.52246	−0.761230	−	0.648482i	$-0.775404\pi$
$271$	−25.0629	−1.52246	−0.761230	+	0.648482i	$0.775404\pi$
$272$	43.8802	2.66063
$273$	−6.50848	−0.393911
$274$	−42.9011	−2.59175
$275$	−11.2334	−0.677397
$276$	−7.40309	−0.445614
$277$	12.3281	0.740724	0.370362	−	0.928888i	$-0.379234\pi$
$277$	12.3281	0.740724	0.370362	+	0.928888i	$0.379234\pi$
$278$	−3.64475	−0.218598
$279$	−14.4711	−0.866360
$280$	−8.66488	−0.517825
$281$	13.1984	0.787349	0.393674	−	0.919250i	$-0.371204\pi$
$281$	13.1984	0.787349	0.393674	+	0.919250i	$0.371204\pi$
$282$	−18.1298	−1.07961
$283$	4.78413	0.284387	0.142194	−	0.989839i	$-0.454584\pi$
$283$	4.78413	0.284387	0.142194	+	0.989839i	$0.454584\pi$
$284$	1.34777	0.0799751
$285$	−1.24308	−0.0736337
$286$	−17.1205	−1.01236
$287$	−5.03983	−0.297492
$288$	−24.9712	−1.47144
$289$	−3.28228	−0.193075
$290$	−12.7642	−0.749540
$291$	39.9197	2.34013
$292$	12.2496	0.716856
$293$	13.7903	0.805638	0.402819	−	0.915280i	$-0.368030\pi$
$293$	13.7903	0.805638	0.402819	+	0.915280i	$0.368030\pi$
$294$	−31.5443	−1.83970
$295$	−12.7193	−0.740545
$296$	18.9586	1.10194
$297$	7.58805	0.440304
$298$	−61.4091	−3.55733
$299$	1.64312	0.0950243
$300$	47.1486	2.72213
$301$	5.70329	0.328732
$302$	7.13845	0.410772
$303$	35.6470	2.04787
$304$	8.02789	0.460431
$305$	3.82433	0.218981
$306$	−16.4031	−0.937703
$307$	10.6603	0.608417	0.304209	−	0.952605i	$-0.401608\pi$
$307$	10.6603	0.608417	0.304209	+	0.952605i	$0.401608\pi$
$308$	16.5180	0.941199
$309$	16.0223	0.911479
$310$	19.7249	1.12030
$311$	−27.7227	−1.57201	−0.786005	−	0.618220i	$-0.787854\pi$
$311$	−27.7227	−1.57201	−0.786005	+	0.618220i	$0.787854\pi$
$312$	43.7038	2.47424
$313$	22.0944	1.24885	0.624426	−	0.781084i	$-0.285333\pi$
$313$	22.0944	1.24885	0.624426	+	0.781084i	$0.285333\pi$
$314$	18.1393	1.02366
$315$	1.73983	0.0980285
$316$	−20.7538	−1.16749
$317$	18.6885	1.04965	0.524824	−	0.851211i	$-0.324131\pi$
$317$	18.6885	1.04965	0.524824	+	0.851211i	$0.324131\pi$
$318$	55.4964	3.11208
$319$	14.7989	0.828582
$320$	13.9036	0.777238
$321$	26.7894	1.49524
$322$	−2.20642	−0.122959
$323$	2.50966	0.139641
$324$	−57.2932	−3.18296
$325$	−10.4647	−0.580476
$326$	39.8508	2.20713
$327$	40.8787	2.26060
$328$	33.8419	1.86861
$329$	−3.88230	−0.214038
$330$	12.8399	0.706811
$331$	30.8893	1.69783	0.848916	−	0.528528i	$-0.177256\pi$
$331$	30.8893	1.69783	0.848916	+	0.528528i	$0.177256\pi$
$332$	−23.7291	−1.30230
$333$	−3.80672	−0.208607
$334$	−55.9592	−3.06195
$335$	2.29694	0.125495
$336$	−31.5228	−1.71971
$337$	−31.0910	−1.69363	−0.846816	−	0.531886i	$-0.821484\pi$
$337$	−31.0910	−1.69363	−0.846816	+	0.531886i	$0.821484\pi$
$338$	18.7017	1.01724
$339$	45.5880	2.47600
$340$	16.0643	0.871206
$341$	−22.8692	−1.23844
$342$	−3.00095	−0.162273
$343$	−15.3813	−0.830511
$344$	−38.2970	−2.06484
$345$	−1.23229	−0.0663443
$346$	−1.09755	−0.0590047
$347$	−4.75129	−0.255062	−0.127531	−	0.991835i	$-0.540705\pi$
$347$	−4.75129	−0.255062	−0.127531	+	0.991835i	$0.540705\pi$
$348$	−62.1141	−3.32966
$349$	5.49987	0.294401	0.147201	−	0.989107i	$-0.452974\pi$
$349$	5.49987	0.294401	0.147201	+	0.989107i	$0.452974\pi$
$350$	14.0522	0.751121
$351$	7.06882	0.377306
$352$	−39.4629	−2.10338
$353$	12.0032	0.638865	0.319432	−	0.947609i	$-0.396508\pi$
$353$	12.0032	0.638865	0.319432	+	0.947609i	$0.396508\pi$
$354$	−86.1464	−4.57863
$355$	0.224344	0.0119070
$356$	2.61268	0.138472
$357$	−9.85458	−0.521560
$358$	18.5143	0.978509
$359$	33.0359	1.74357	0.871783	−	0.489892i	$-0.162964\pi$
$359$	33.0359	1.74357	0.871783	+	0.489892i	$0.162964\pi$
$360$	−11.6828	−0.615738
$361$	−18.5409	−0.975835
$362$	3.65548	0.192128
$363$	8.86305	0.465190
$364$	15.3877	0.806534
$365$	2.03903	0.106728
$366$	25.9018	1.35391
$367$	8.94660	0.467009	0.233504	−	0.972356i	$-0.424981\pi$
$367$	8.94660	0.467009	0.233504	+	0.972356i	$0.424981\pi$
$368$	7.95821	0.414850
$369$	−6.79517	−0.353742
$370$	5.18876	0.269751
$371$	11.8840	0.616985
$372$	95.9864	4.97666
$373$	−9.49142	−0.491447	−0.245724	−	0.969340i	$-0.579026\pi$
$373$	−9.49142	−0.491447	−0.245724	+	0.969340i	$0.579026\pi$
$374$	−25.9224	−1.34042
$375$	17.0209	0.878953
$376$	26.0692	1.34442
$377$	13.7863	0.710030
$378$	−9.49216	−0.488224
$379$	−8.08279	−0.415185	−0.207592	−	0.978215i	$-0.566563\pi$
$379$	−8.08279	−0.415185	−0.207592	+	0.978215i	$0.566563\pi$
$380$	2.93896	0.150765
$381$	10.9904	0.563057
$382$	22.5756	1.15507
$383$	−19.0134	−0.971539	−0.485769	−	0.874087i	$-0.661461\pi$
$383$	−19.0134	−0.971539	−0.485769	+	0.874087i	$0.661461\pi$
$384$	29.2719	1.49377
$385$	2.74952	0.140129
$386$	−39.4534	−2.00812
$387$	7.68971	0.390890
$388$	−94.3802	−4.79143
$389$	−1.11976	−0.0567743	−0.0283872	−	0.999597i	$-0.509037\pi$
$389$	−1.11976	−0.0567743	−0.0283872	+	0.999597i	$0.509037\pi$
$390$	11.9613	0.605682
$391$	2.48788	0.125817
$392$	45.3583	2.29094
$393$	−4.96599	−0.250501
$394$	−59.7525	−3.01029
$395$	−3.45461	−0.173820
$396$	22.2711	1.11916
$397$	−7.71507	−0.387208	−0.193604	−	0.981080i	$-0.562018\pi$
$397$	−7.71507	−0.387208	−0.193604	+	0.981080i	$0.562018\pi$
$398$	34.1090	1.70973
$399$	−1.80290	−0.0902577
$400$	−50.6840	−2.53420
$401$	−15.0034	−0.749234	−0.374617	−	0.927180i	$-0.622226\pi$
$401$	−15.0034	−0.749234	−0.374617	+	0.927180i	$0.622226\pi$
$402$	15.5570	0.775911
$403$	−21.3043	−1.06124
$404$	−84.2786	−4.19301
$405$	−9.53682	−0.473889
$406$	−18.5125	−0.918761
$407$	−6.01590	−0.298197
$408$	66.1725	3.27603
$409$	−7.35713	−0.363787	−0.181893	−	0.983318i	$-0.558223\pi$
$409$	−7.35713	−0.363787	−0.181893	+	0.983318i	$0.558223\pi$
$410$	9.26218	0.457427
$411$	−34.7508	−1.71413
$412$	−37.8809	−1.86626
$413$	−18.4473	−0.907734
$414$	−2.97490	−0.146208
$415$	−3.94986	−0.193891
$416$	−36.7626	−1.80243
$417$	−2.95233	−0.144576
$418$	−4.74251	−0.231964
$419$	37.7643	1.84491	0.922453	−	0.386110i	$-0.126181\pi$
$419$	37.7643	1.84491	0.922453	+	0.386110i	$0.126181\pi$
$420$	−11.5403	−0.563108
$421$	4.23154	0.206233	0.103116	−	0.994669i	$-0.467119\pi$
$421$	4.23154	0.206233	0.103116	+	0.994669i	$0.467119\pi$
$422$	−53.3102	−2.59510
$423$	−5.23448	−0.254509
$424$	−79.7997	−3.87541
$425$	−15.8447	−0.768582
$426$	1.51946	0.0736181
$427$	5.54660	0.268419
$428$	−63.3369	−3.06150
$429$	−13.8680	−0.669554
$430$	−10.4815	−0.505463
$431$	28.4591	1.37083	0.685413	−	0.728155i	$-0.259622\pi$
$431$	28.4591	1.37083	0.685413	+	0.728155i	$0.259622\pi$
$432$	34.2367	1.64722
$433$	10.1734	0.488900	0.244450	−	0.969662i	$-0.421393\pi$
$433$	10.1734	0.488900	0.244450	+	0.969662i	$0.421393\pi$
$434$	28.6078	1.37322
$435$	−10.3393	−0.495731
$436$	−96.6476	−4.62858
$437$	0.455157	0.0217731
$438$	13.8102	0.659875
$439$	9.22476	0.440274	0.220137	−	0.975469i	$-0.429350\pi$
$439$	9.22476	0.440274	0.220137	+	0.975469i	$0.429350\pi$
$440$	−18.4628	−0.880178
$441$	−9.10756	−0.433693
$442$	−24.1486	−1.14863
$443$	−11.0263	−0.523875	−0.261937	−	0.965085i	$-0.584361\pi$
$443$	−11.0263	−0.523875	−0.261937	+	0.965085i	$0.584361\pi$
$444$	25.2499	1.19831
$445$	0.434898	0.0206161
$446$	67.8897	3.21467
$447$	−49.7427	−2.35275
$448$	20.1651	0.952711
$449$	−32.9620	−1.55557	−0.777787	−	0.628528i	$-0.783658\pi$
$449$	−32.9620	−1.55557	−0.777787	+	0.628528i	$0.783658\pi$
$450$	18.9465	0.893146
$451$	−10.7387	−0.505664
$452$	−107.782	−5.06962
$453$	5.78230	0.271676
$454$	25.7912	1.21044
$455$	2.56138	0.120079
$456$	12.1063	0.566928
$457$	−7.36804	−0.344663	−0.172331	−	0.985039i	$-0.555130\pi$
$457$	−7.36804	−0.344663	−0.172331	+	0.985039i	$0.555130\pi$
$458$	17.9612	0.839273
$459$	10.7030	0.499573
$460$	2.91345	0.135840
$461$	−23.4982	−1.09442	−0.547211	−	0.836995i	$-0.684311\pi$
$461$	−23.4982	−1.09442	−0.547211	+	0.836995i	$0.684311\pi$
$462$	18.6222	0.866385
$463$	23.8016	1.10615	0.553076	−	0.833131i	$-0.313454\pi$
$463$	23.8016	1.10615	0.553076	+	0.833131i	$0.313454\pi$
$464$	66.7717	3.09980
$465$	15.9776	0.740941
$466$	−72.7535	−3.37024
$467$	−3.99596	−0.184911	−0.0924554	−	0.995717i	$-0.529472\pi$
$467$	−3.99596	−0.184911	−0.0924554	+	0.995717i	$0.529472\pi$
$468$	20.7471	0.959036
$469$	3.33136	0.153828
$470$	7.13488	0.329107
$471$	14.6932	0.677027
$472$	123.872	5.70167
$473$	12.1523	0.558765
$474$	−23.3977	−1.07469
$475$	−2.89879	−0.133006
$476$	23.2987	1.06789
$477$	16.0231	0.733647
$478$	−2.54277	−0.116303
$479$	3.63234	0.165966	0.0829829	−	0.996551i	$-0.473555\pi$
$479$	3.63234	0.165966	0.0829829	+	0.996551i	$0.473555\pi$
$480$	27.5708	1.25843
$481$	−5.60425	−0.255532
$482$	36.5786	1.66611
$483$	−1.78725	−0.0813226
$484$	−20.9545	−0.952477
$485$	−15.7102	−0.713363
$486$	−41.4843	−1.88177
$487$	4.39881	0.199329	0.0996645	−	0.995021i	$-0.468223\pi$
$487$	4.39881	0.199329	0.0996645	+	0.995021i	$0.468223\pi$
$488$	−37.2449	−1.68600
$489$	32.2800	1.45975
$490$	12.4141	0.560812
$491$	−27.7056	−1.25034	−0.625168	−	0.780490i	$-0.714970\pi$
$491$	−27.7056	−1.25034	−0.625168	+	0.780490i	$0.714970\pi$
$492$	45.0723	2.03201
$493$	20.8740	0.940118
$494$	−4.41799	−0.198775
$495$	3.70716	0.166625
$496$	−103.184	−4.63310
$497$	0.325376	0.0145951
$498$	−26.7520	−1.19878
$499$	−10.0631	−0.450485	−0.225242	−	0.974303i	$-0.572317\pi$
$499$	−10.0631	−0.450485	−0.225242	+	0.974303i	$0.572317\pi$
$500$	−40.2416	−1.79966
$501$	−45.3281	−2.02511
$502$	−36.1220	−1.61220
$503$	−41.4893	−1.84992	−0.924959	−	0.380067i	$-0.875901\pi$
$503$	−41.4893	−1.84992	−0.924959	+	0.380067i	$0.875901\pi$
$504$	−16.9441	−0.754750
$505$	−14.0287	−0.624269
$506$	−4.70135	−0.209001
$507$	15.1488	0.672781
$508$	−25.9842	−1.15286
$509$	−11.8878	−0.526917	−0.263459	−	0.964671i	$-0.584863\pi$
$509$	−11.8878	−0.526917	−0.263459	+	0.964671i	$0.584863\pi$
$510$	18.1107	0.801956
$511$	2.95730	0.130823
$512$	18.0243	0.796567
$513$	1.95811	0.0864529
$514$	−74.2093	−3.27323
$515$	−6.30551	−0.277854
$516$	−51.0058	−2.24540
$517$	−8.27224	−0.363813
$518$	7.52549	0.330651
$519$	−0.889040	−0.0390245
$520$	−17.1994	−0.754244
$521$	7.67268	0.336146	0.168073	−	0.985775i	$-0.446245\pi$
$521$	7.67268	0.336146	0.168073	+	0.985775i	$0.446245\pi$
$522$	−24.9603	−1.09248
$523$	7.49489	0.327729	0.163864	−	0.986483i	$-0.447604\pi$
$523$	7.49489	0.327729	0.163864	+	0.986483i	$0.447604\pi$
$524$	11.7409	0.512902
$525$	11.3826	0.496776
$526$	82.3712	3.59156
$527$	−32.2571	−1.40514
$528$	−67.1675	−2.92309
$529$	−22.5488	−0.980382
$530$	−21.8403	−0.948683
$531$	−24.8724	−1.07937
$532$	4.26250	0.184803
$533$	−10.0038	−0.433314
$534$	2.94552	0.127465
$535$	−10.5428	−0.455806
$536$	−22.3698	−0.966226
$537$	14.9970	0.647166
$538$	22.8712	0.986048
$539$	−14.3930	−0.619951
$540$	12.5338	0.539371
$541$	42.8360	1.84166	0.920832	−	0.389960i	$-0.127511\pi$
$541$	42.8360	1.84166	0.920832	+	0.389960i	$0.127511\pi$
$542$	66.8036	2.86946
$543$	2.96102	0.127070
$544$	−55.6627	−2.38652
$545$	−16.0876	−0.689117
$546$	17.3480	0.742425
$547$	−40.3633	−1.72581	−0.862905	−	0.505367i	$-0.831357\pi$
$547$	−40.3633	−1.72581	−0.862905	+	0.505367i	$0.831357\pi$
$548$	82.1597	3.50969
$549$	7.47845	0.319172
$550$	29.9418	1.27672
$551$	3.81890	0.162691
$552$	12.0012	0.510805
$553$	−5.01037	−0.213063
$554$	−32.8598	−1.39608
$555$	4.20301	0.178408
$556$	6.98005	0.296020
$557$	6.74054	0.285606	0.142803	−	0.989751i	$-0.454388\pi$
$557$	6.74054	0.285606	0.142803	+	0.989751i	$0.454388\pi$
$558$	38.5718	1.63287
$559$	11.3208	0.478818
$560$	12.4056	0.524234
$561$	−20.9977	−0.886525
$562$	−35.1795	−1.48396
$563$	28.2492	1.19056	0.595280	−	0.803518i	$-0.297041\pi$
$563$	28.2492	1.19056	0.595280	+	0.803518i	$0.297041\pi$
$564$	34.7202	1.46199
$565$	−17.9409	−0.754781
$566$	−12.7518	−0.535999
$567$	−13.8317	−0.580876
$568$	−2.18487	−0.0916751
$569$	17.1263	0.717970	0.358985	−	0.933343i	$-0.383123\pi$
$569$	17.1263	0.717970	0.358985	+	0.933343i	$0.383123\pi$
$570$	3.31336	0.138781
$571$	21.2524	0.889386	0.444693	−	0.895683i	$-0.353313\pi$
$571$	21.2524	0.889386	0.444693	+	0.895683i	$0.353313\pi$
$572$	32.7875	1.37091
$573$	18.2867	0.763938
$574$	13.4334	0.560698
$575$	−2.87363	−0.119839
$576$	27.1885	1.13285
$577$	23.4291	0.975364	0.487682	−	0.873021i	$-0.337843\pi$
$577$	23.4291	0.975364	0.487682	+	0.873021i	$0.337843\pi$
$578$	8.74871	0.363899
$579$	−31.9581	−1.32813
$580$	24.4447	1.01501
$581$	−5.72865	−0.237665
$582$	−106.404	−4.41057
$583$	25.3219	1.04872
$584$	−19.8580	−0.821729
$585$	3.45349	0.142784
$586$	−36.7572	−1.51843
$587$	−32.3850	−1.33667	−0.668336	−	0.743859i	$-0.732993\pi$
$587$	−32.3850	−1.33667	−0.668336	+	0.743859i	$0.732993\pi$
$588$	60.4103	2.49128
$589$	−5.90144	−0.243165
$590$	33.9025	1.39574
$591$	−48.4008	−1.99094
$592$	−27.1433	−1.11558
$593$	36.5540	1.50109	0.750546	−	0.660818i	$-0.229791\pi$
$593$	36.5540	1.50109	0.750546	+	0.660818i	$0.229791\pi$
$594$	−20.2255	−0.829863
$595$	3.87822	0.158992
$596$	117.604	4.81726
$597$	27.6290	1.13078
$598$	−4.37965	−0.179097
$599$	−8.22046	−0.335879	−0.167939	−	0.985797i	$-0.553711\pi$
$599$	−8.22046	−0.335879	−0.167939	+	0.985797i	$0.553711\pi$
$600$	−76.4329	−3.12036
$601$	−24.7618	−1.01005	−0.505027	−	0.863103i	$-0.668518\pi$
$601$	−24.7618	−1.01005	−0.505027	+	0.863103i	$0.668518\pi$
$602$	−15.2018	−0.619578
$603$	4.49165	0.182914
$604$	−13.6708	−0.556258
$605$	−3.48801	−0.141808
$606$	−95.0150	−3.85972
$607$	−21.0573	−0.854691	−0.427345	−	0.904088i	$-0.640551\pi$
$607$	−21.0573	−0.854691	−0.427345	+	0.904088i	$0.640551\pi$
$608$	−10.1835	−0.412995
$609$	−14.9955	−0.607650
$610$	−10.1935	−0.412724
$611$	−7.70620	−0.311759
$612$	31.4135	1.26982
$613$	41.0378	1.65750	0.828750	−	0.559619i	$-0.189053\pi$
$613$	41.0378	1.65750	0.828750	+	0.559619i	$0.189053\pi$
$614$	−28.4145	−1.14672
$615$	7.50257	0.302533
$616$	−26.7774	−1.07889
$617$	−16.8212	−0.677195	−0.338597	−	0.940931i	$-0.609952\pi$
$617$	−16.8212	−0.677195	−0.338597	+	0.940931i	$0.609952\pi$
$618$	−42.7066	−1.71791
$619$	20.1367	0.809362	0.404681	−	0.914458i	$-0.367383\pi$
$619$	20.1367	0.809362	0.404681	+	0.914458i	$0.367383\pi$
$620$	−37.7750	−1.51708
$621$	1.94112	0.0778945
$622$	73.8932	2.96285
$623$	0.630752	0.0252705
$624$	−62.5714	−2.50486
$625$	14.6917	0.587667
$626$	−58.8914	−2.35377
$627$	−3.84154	−0.153416
$628$	−34.7384	−1.38621
$629$	−8.48547	−0.338338
$630$	−4.63742	−0.184759
$631$	−30.3475	−1.20812	−0.604058	−	0.796940i	$-0.706451\pi$
$631$	−30.3475	−1.20812	−0.604058	+	0.796940i	$0.706451\pi$
$632$	33.6442	1.33829
$633$	−43.1824	−1.71635
$634$	−49.8130	−1.97833
$635$	−4.32523	−0.171642
$636$	−106.281	−4.21431
$637$	−13.4081	−0.531250
$638$	−39.4457	−1.56167
$639$	0.438703	0.0173548
$640$	−11.5198	−0.455360
$641$	0.784801	0.0309978	0.0154989	−	0.999880i	$-0.495066\pi$
$641$	0.784801	0.0309978	0.0154989	+	0.999880i	$0.495066\pi$
$642$	−71.4055	−2.81815
$643$	11.0953	0.437554	0.218777	−	0.975775i	$-0.429793\pi$
$643$	11.0953	0.437554	0.218777	+	0.975775i	$0.429793\pi$
$644$	4.22551	0.166508
$645$	−8.49024	−0.334303
$646$	−6.68934	−0.263189
$647$	−43.1658	−1.69702	−0.848511	−	0.529178i	$-0.822500\pi$
$647$	−43.1658	−1.69702	−0.848511	+	0.529178i	$0.822500\pi$
$648$	92.8784	3.64861
$649$	−39.3068	−1.54293
$650$	27.8930	1.09405
$651$	23.1730	0.908220
$652$	−76.3182	−2.98885
$653$	10.8138	0.423178	0.211589	−	0.977359i	$-0.432136\pi$
$653$	10.8138	0.423178	0.211589	+	0.977359i	$0.432136\pi$
$654$	−108.960	−4.26066
$655$	1.95434	0.0763625
$656$	−48.4520	−1.89173
$657$	3.98731	0.155560
$658$	10.3480	0.403408
$659$	−5.94281	−0.231499	−0.115749	−	0.993278i	$-0.536927\pi$
$659$	−5.94281	−0.231499	−0.115749	+	0.993278i	$0.536927\pi$
$660$	−24.5896	−0.957148
$661$	−9.80190	−0.381250	−0.190625	−	0.981663i	$-0.561051\pi$
$661$	−9.80190	−0.381250	−0.190625	+	0.981663i	$0.561051\pi$
$662$	−82.3337	−3.19999
$663$	−19.5609	−0.759683
$664$	38.4673	1.49282
$665$	0.709521	0.0275140
$666$	10.1466	0.393172
$667$	3.78576	0.146585
$668$	107.167	4.14642
$669$	54.9922	2.12612
$670$	−6.12237	−0.236528
$671$	11.8185	0.456247
$672$	39.9871	1.54254
$673$	−26.0716	−1.00499	−0.502493	−	0.864581i	$-0.667584\pi$
$673$	−26.0716	−1.00499	−0.502493	+	0.864581i	$0.667584\pi$
$674$	82.8711	3.19207
$675$	−12.3626	−0.475835
$676$	−35.8155	−1.37752
$677$	−45.7795	−1.75945	−0.879724	−	0.475485i	$-0.842273\pi$
$677$	−45.7795	−1.75945	−0.879724	+	0.475485i	$0.842273\pi$
$678$	−121.512	−4.66665
$679$	−22.7852	−0.874416
$680$	−26.0419	−0.998660
$681$	20.8914	0.800561
$682$	60.9564	2.33414
$683$	−45.7664	−1.75120	−0.875600	−	0.483036i	$-0.839534\pi$
$683$	−45.7664	−1.75120	−0.875600	+	0.483036i	$0.839534\pi$
$684$	5.74710	0.219746
$685$	13.6760	0.522534
$686$	40.9979	1.56531
$687$	14.5490	0.555078
$688$	54.8304	2.09039
$689$	23.5892	0.898676
$690$	3.28460	0.125043
$691$	−8.17198	−0.310877	−0.155438	−	0.987846i	$-0.549679\pi$
$691$	−8.17198	−0.310877	−0.155438	+	0.987846i	$0.549679\pi$
$692$	2.10192	0.0799029
$693$	5.37667	0.204243
$694$	12.6643	0.480729
$695$	1.16187	0.0440724
$696$	100.694	3.81678
$697$	−15.1470	−0.573732
$698$	−14.6596	−0.554873
$699$	−58.9319	−2.22901
$700$	−26.9113	−1.01715
$701$	−42.1515	−1.59204	−0.796019	−	0.605271i	$-0.793065\pi$
$701$	−42.1515	−1.59204	−0.796019	+	0.605271i	$0.793065\pi$
$702$	−18.8415	−0.711128
$703$	−1.55242	−0.0585505
$704$	42.9670	1.61938
$705$	5.77941	0.217665
$706$	−31.9938	−1.20410
$707$	−20.3465	−0.765208
$708$	164.979	6.20027
$709$	31.7692	1.19312	0.596559	−	0.802569i	$-0.296534\pi$
$709$	31.7692	1.19312	0.596559	+	0.802569i	$0.296534\pi$
$710$	−0.597976	−0.0224416
$711$	−6.75545	−0.253349
$712$	−4.23543	−0.158730
$713$	−5.85022	−0.219093
$714$	26.2668	0.983010
$715$	5.45768	0.204106
$716$	−35.4566	−1.32507
$717$	−2.05970	−0.0769207
$718$	−88.0551	−3.28619
$719$	6.81824	0.254278	0.127139	−	0.991885i	$-0.459421\pi$
$719$	6.81824	0.254278	0.127139	+	0.991885i	$0.459421\pi$
$720$	16.7264	0.623358
$721$	−9.14517	−0.340584
$722$	49.4196	1.83921
$723$	29.6295	1.10193
$724$	−7.00060	−0.260175
$725$	−24.1106	−0.895446
$726$	−23.6239	−0.876767
$727$	16.7781	0.622264	0.311132	−	0.950367i	$-0.399292\pi$
$727$	16.7781	0.622264	0.311132	+	0.950367i	$0.399292\pi$
$728$	−24.9451	−0.924526
$729$	0.0684792	0.00253627
$730$	−5.43492	−0.201155
$731$	17.1410	0.633981
$732$	−49.6045	−1.83343
$733$	27.7883	1.02639	0.513193	−	0.858273i	$-0.328463\pi$
$733$	27.7883	1.02639	0.513193	+	0.858273i	$0.328463\pi$
$734$	−23.8466	−0.880195
$735$	10.0557	0.370910
$736$	−10.0951	−0.372111
$737$	7.09833	0.261470
$738$	18.1121	0.666716
$739$	16.2322	0.597112	0.298556	−	0.954392i	$-0.403495\pi$
$739$	16.2322	0.597112	0.298556	+	0.954392i	$0.403495\pi$
$740$	−9.93697	−0.365290
$741$	−3.57867	−0.131466
$742$	−31.6760	−1.16286
$743$	−7.52095	−0.275917	−0.137959	−	0.990438i	$-0.544054\pi$
$743$	−7.52095	−0.275917	−0.137959	+	0.990438i	$0.544054\pi$
$744$	−155.604	−5.70473
$745$	19.5760	0.717209
$746$	25.2988	0.926255
$747$	−7.72391	−0.282603
$748$	49.6439	1.81516
$749$	−15.2907	−0.558711
$750$	−45.3681	−1.65661
$751$	−42.7932	−1.56154	−0.780772	−	0.624816i	$-0.785174\pi$
$751$	−42.7932	−1.56154	−0.780772	+	0.624816i	$0.785174\pi$
$752$	−37.3237	−1.36106
$753$	−29.2596	−1.06628
$754$	−36.7465	−1.33823
$755$	−2.27560	−0.0828174
$756$	18.1784	0.661142
$757$	−24.6702	−0.896655	−0.448328	−	0.893869i	$-0.647980\pi$
$757$	−24.6702	−0.896655	−0.448328	+	0.893869i	$0.647980\pi$
$758$	21.5442	0.782520
$759$	−3.80820	−0.138229
$760$	−4.76436	−0.172822
$761$	−20.0582	−0.727110	−0.363555	−	0.931573i	$-0.618437\pi$
$761$	−20.0582	−0.727110	−0.363555	+	0.931573i	$0.618437\pi$
$762$	−29.2943	−1.06122
$763$	−23.3326	−0.844696
$764$	−43.2344	−1.56417
$765$	5.22898	0.189054
$766$	50.6791	1.83111
$767$	−36.6172	−1.32217
$768$	−7.36397	−0.265724
$769$	−29.9216	−1.07900	−0.539500	−	0.841986i	$-0.681387\pi$
$769$	−29.9216	−1.07900	−0.539500	+	0.841986i	$0.681387\pi$
$770$	−7.32869	−0.264108
$771$	−60.1111	−2.16485
$772$	75.5570	2.71936
$773$	39.7402	1.42935	0.714677	−	0.699454i	$-0.246574\pi$
$773$	39.7402	1.42935	0.714677	+	0.699454i	$0.246574\pi$
$774$	−20.4965	−0.736731
$775$	37.2588	1.33837
$776$	153.000	5.49239
$777$	6.09581	0.218686
$778$	2.98467	0.107005
$779$	−2.77114	−0.0992862
$780$	−22.9070	−0.820201
$781$	0.693299	0.0248082
$782$	−6.63129	−0.237134
$783$	16.2866	0.582034
$784$	−64.9402	−2.31929
$785$	−5.78243	−0.206384
$786$	13.2366	0.472132
$787$	−26.5531	−0.946515	−0.473258	−	0.880924i	$-0.656922\pi$
$787$	−26.5531	−0.946515	−0.473258	+	0.880924i	$0.656922\pi$
$788$	114.432	4.07646
$789$	66.7225	2.37538
$790$	9.20805	0.327608
$791$	−26.0206	−0.925184
$792$	−36.1038	−1.28289
$793$	11.0098	0.390968
$794$	20.5641	0.729792
$795$	−17.6911	−0.627440
$796$	−65.3219	−2.31527
$797$	−23.6770	−0.838682	−0.419341	−	0.907829i	$-0.637739\pi$
$797$	−23.6770	−0.838682	−0.419341	+	0.907829i	$0.637739\pi$
$798$	4.80551	0.170113
$799$	−11.6681	−0.412786
$800$	64.2935	2.27312
$801$	0.850439	0.0300488
$802$	39.9907	1.41212
$803$	6.30130	0.222368
$804$	−29.7931	−1.05072
$805$	0.703363	0.0247903
$806$	56.7853	2.00018
$807$	18.5262	0.652152
$808$	136.625	4.80643
$809$	27.2509	0.958091	0.479046	−	0.877790i	$-0.340983\pi$
$809$	27.2509	0.958091	0.479046	+	0.877790i	$0.340983\pi$
$810$	25.4198	0.893162
$811$	−18.8196	−0.660847	−0.330423	−	0.943833i	$-0.607192\pi$
$811$	−18.8196	−0.660847	−0.330423	+	0.943833i	$0.607192\pi$
$812$	35.4532	1.24416
$813$	54.1123	1.89780
$814$	16.0350	0.562027
$815$	−12.7037	−0.444990
$816$	−94.7402	−3.31657
$817$	3.13594	0.109713
$818$	19.6100	0.685648
$819$	5.00876	0.175020
$820$	−17.7380	−0.619437
$821$	−16.5780	−0.578577	−0.289289	−	0.957242i	$-0.593419\pi$
$821$	−16.5780	−0.578577	−0.289289	+	0.957242i	$0.593419\pi$
$822$	92.6262	3.23071
$823$	8.43365	0.293978	0.146989	−	0.989138i	$-0.453042\pi$
$823$	8.43365	0.293978	0.146989	+	0.989138i	$0.453042\pi$
$824$	61.4089	2.13928
$825$	24.2535	0.844400
$826$	49.1703	1.71085
$827$	36.6640	1.27493	0.637466	−	0.770478i	$-0.279983\pi$
$827$	36.6640	1.27493	0.637466	+	0.770478i	$0.279983\pi$
$828$	5.69722	0.197992
$829$	−14.4841	−0.503054	−0.251527	−	0.967850i	$-0.580933\pi$
$829$	−14.4841	−0.503054	−0.251527	+	0.967850i	$0.580933\pi$
$830$	10.5281	0.365436
$831$	−26.6172	−0.923339
$832$	40.0268	1.38768
$833$	−20.3015	−0.703404
$834$	7.86925	0.272490
$835$	17.8387	0.617332
$836$	9.08236	0.314120
$837$	−25.1680	−0.869934
$838$	−100.658	−3.47719
$839$	18.8114	0.649443	0.324721	−	0.945810i	$-0.394729\pi$
$839$	18.8114	0.649443	0.324721	+	0.945810i	$0.394729\pi$
$840$	18.7080	0.645488
$841$	2.76361	0.0952969
$842$	−11.2789	−0.388697
$843$	−28.4961	−0.981459
$844$	102.094	3.51423
$845$	−5.96173	−0.205090
$846$	13.9522	0.479686
$847$	−5.05882	−0.173823
$848$	114.250	3.92337
$849$	−10.3292	−0.354499
$850$	42.2332	1.44859
$851$	−1.53894	−0.0527543
$852$	−2.90991	−0.0996919
$853$	−5.54466	−0.189846	−0.0949228	−	0.995485i	$-0.530260\pi$
$853$	−5.54466	−0.189846	−0.0949228	+	0.995485i	$0.530260\pi$
$854$	−14.7841	−0.505903
$855$	0.956642	0.0327165
$856$	102.676	3.50939
$857$	−5.83082	−0.199177	−0.0995885	−	0.995029i	$-0.531753\pi$
$857$	−5.83082	−0.199177	−0.0995885	+	0.995029i	$0.531753\pi$
$858$	36.9643	1.26194
$859$	−18.3633	−0.626548	−0.313274	−	0.949663i	$-0.601426\pi$
$859$	−18.3633	−0.626548	−0.313274	+	0.949663i	$0.601426\pi$
$860$	20.0731	0.684486
$861$	10.8813	0.370834
$862$	−75.8560	−2.58366
$863$	29.4479	1.00242	0.501210	−	0.865326i	$-0.332889\pi$
$863$	29.4479	1.00242	0.501210	+	0.865326i	$0.332889\pi$
$864$	−43.4298	−1.47751
$865$	0.349877	0.0118962
$866$	−27.1165	−0.921455
$867$	7.08665	0.240675
$868$	−54.7867	−1.85958
$869$	−10.6759	−0.362155
$870$	27.5588	0.934329
$871$	6.61261	0.224060
$872$	156.676	5.30572
$873$	−30.7211	−1.03975
$874$	−1.21319	−0.0410369
$875$	−9.71510	−0.328430
$876$	−26.4478	−0.893588
$877$	2.41305	0.0814830	0.0407415	−	0.999170i	$-0.487028\pi$
$877$	2.41305	0.0814830	0.0407415	+	0.999170i	$0.487028\pi$
$878$	−24.5881	−0.829807
$879$	−29.7741	−1.00426
$880$	26.4334	0.891071
$881$	−52.4649	−1.76759	−0.883794	−	0.467877i	$-0.845019\pi$
$881$	−52.4649	−1.76759	−0.883794	+	0.467877i	$0.845019\pi$
$882$	24.2757	0.817404
$883$	20.0919	0.676146	0.338073	−	0.941120i	$-0.390225\pi$
$883$	20.0919	0.676146	0.338073	+	0.941120i	$0.390225\pi$
$884$	46.2469	1.55545
$885$	27.4617	0.923116
$886$	29.3899	0.987374
$887$	−29.0291	−0.974702	−0.487351	−	0.873206i	$-0.662037\pi$
$887$	−29.0291	−0.974702	−0.487351	+	0.873206i	$0.662037\pi$
$888$	−40.9328	−1.37361
$889$	−6.27308	−0.210392
$890$	−1.15919	−0.0388563
$891$	−29.4720	−0.987349
$892$	−130.015	−4.35324
$893$	−2.13467	−0.0714341
$894$	132.586	4.43435
$895$	−5.90198	−0.197281
$896$	−16.7077	−0.558165
$897$	−3.54761	−0.118451
$898$	87.8583	2.93187
$899$	−49.0851	−1.63708
$900$	−36.2843	−1.20948
$901$	35.7167	1.18990
$902$	28.6233	0.953050
$903$	−12.3138	−0.409777
$904$	174.725	5.81128
$905$	−1.16530	−0.0387357
$906$	−15.4124	−0.512042
$907$	−34.6771	−1.15143	−0.575716	−	0.817649i	$-0.695277\pi$
$907$	−34.6771	−1.15143	−0.575716	+	0.817649i	$0.695277\pi$
$908$	−49.3926	−1.63915
$909$	−27.4330	−0.909896
$910$	−6.82721	−0.226320
$911$	−9.69363	−0.321164	−0.160582	−	0.987022i	$-0.551337\pi$
$911$	−9.69363	−0.321164	−0.160582	+	0.987022i	$0.551337\pi$
$912$	−17.3327	−0.573944
$913$	−12.2064	−0.403972
$914$	19.6391	0.649603
$915$	−8.25698	−0.272967
$916$	−34.3975	−1.13652
$917$	2.83447	0.0936024
$918$	−28.5282	−0.941571
$919$	−14.0210	−0.462509	−0.231255	−	0.972893i	$-0.574283\pi$
$919$	−14.0210	−0.462509	−0.231255	+	0.972893i	$0.574283\pi$
$920$	−4.72301	−0.155713
$921$	−23.0163	−0.758414
$922$	62.6332	2.06271
$923$	0.645858	0.0212587
$924$	−35.6634	−1.17324
$925$	9.80118	0.322261
$926$	−63.4417	−2.08482
$927$	−12.3304	−0.404983
$928$	−84.7009	−2.78044
$929$	9.18380	0.301311	0.150655	−	0.988586i	$-0.451862\pi$
$929$	9.18380	0.301311	0.150655	+	0.988586i	$0.451862\pi$
$930$	−42.5872	−1.39649
$931$	−3.71415	−0.121726
$932$	139.330	4.56390
$933$	59.8551	1.95957
$934$	10.6510	0.348511
$935$	8.26355	0.270247
$936$	−33.6333	−1.09934
$937$	−10.6753	−0.348746	−0.174373	−	0.984680i	$-0.555790\pi$
$937$	−10.6753	−0.348746	−0.174373	+	0.984680i	$0.555790\pi$
$938$	−8.87954	−0.289927
$939$	−47.7033	−1.55674
$940$	−13.6640	−0.445670
$941$	60.4378	1.97021	0.985107	−	0.171941i	$-0.0550039\pi$
$941$	60.4378	1.97021	0.985107	+	0.171941i	$0.0550039\pi$
$942$	−39.1638	−1.27603
$943$	−2.74708	−0.0894574
$944$	−177.349	−5.77223
$945$	3.02591	0.0984329
$946$	−32.3913	−1.05313
$947$	−11.9385	−0.387949	−0.193975	−	0.981007i	$-0.562138\pi$
$947$	−11.9385	−0.387949	−0.193975	+	0.981007i	$0.562138\pi$
$948$	44.8088	1.45532
$949$	5.87012	0.190552
$950$	7.72656	0.250683
$951$	−40.3496	−1.30842
$952$	−37.7697	−1.22412
$953$	13.8409	0.448350	0.224175	−	0.974549i	$-0.428031\pi$
$953$	13.8409	0.448350	0.224175	+	0.974549i	$0.428031\pi$
$954$	−42.7086	−1.38274
$955$	−7.19664	−0.232878
$956$	4.86964	0.157495
$957$	−31.9519	−1.03286
$958$	−9.68179	−0.312804
$959$	19.8349	0.640503
$960$	−30.0189	−0.968855
$961$	44.8524	1.44685
$962$	14.9378	0.481614
$963$	−20.6164	−0.664354
$964$	−70.0516	−2.25621
$965$	12.5769	0.404866
$966$	4.76380	0.153273
$967$	21.0274	0.676195	0.338097	−	0.941111i	$-0.390217\pi$
$967$	21.0274	0.676195	0.338097	+	0.941111i	$0.390217\pi$
$968$	33.9695	1.09182
$969$	−5.41851	−0.174068
$970$	41.8746	1.34451
$971$	−8.24592	−0.264624	−0.132312	−	0.991208i	$-0.542240\pi$
$971$	−8.24592	−0.264624	−0.132312	+	0.991208i	$0.542240\pi$
$972$	79.4465	2.54825
$973$	1.68512	0.0540224
$974$	−11.7248	−0.375686
$975$	22.5939	0.723585
$976$	53.3241	1.70686
$977$	13.3552	0.427269	0.213635	−	0.976914i	$-0.431470\pi$
$977$	13.3552	0.427269	0.213635	+	0.976914i	$0.431470\pi$
$978$	−86.0406	−2.75127
$979$	1.34398	0.0429538
$980$	−23.7742	−0.759439
$981$	−31.4592	−1.00441
$982$	73.8476	2.35657
$983$	−46.3065	−1.47695	−0.738474	−	0.674282i	$-0.764453\pi$
$983$	−46.3065	−1.47695	−0.738474	+	0.674282i	$0.764453\pi$
$984$	−73.0669	−2.32929
$985$	19.0479	0.606916
$986$	−55.6384	−1.77189
$987$	8.38213	0.266806
$988$	8.46088	0.269177
$989$	3.10872	0.0988516
$990$	−9.88123	−0.314046
$991$	23.2054	0.737144	0.368572	−	0.929599i	$-0.379847\pi$
$991$	23.2054	0.737144	0.368572	+	0.929599i	$0.379847\pi$
$992$	130.890	4.15577
$993$	−66.6921	−2.11641
$994$	−0.867272	−0.0275082
$995$	−10.8733	−0.344705
$996$	51.2326	1.62337
$997$	9.40146	0.297747	0.148874	−	0.988856i	$-0.452435\pi$
$997$	9.40146	0.297747	0.148874	+	0.988856i	$0.452435\pi$
$998$	26.8225	0.849052
$999$	−6.62063	−0.209467

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.6	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.6	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66544 q^{2} -2.15906 q^{3} +5.10457 q^{4} +0.849689 q^{5} +5.75486 q^{6} +1.23234 q^{7} -8.27506 q^{8} +1.66156 q^{9} +O(q^{10})\)	\(q-2.66544 q^{2} -2.15906 q^{3} +5.10457 q^{4} +0.849689 q^{5} +5.75486 q^{6} +1.23234 q^{7} -8.27506 q^{8} +1.66156 q^{9} -2.26480 q^{10} +2.62582 q^{11} -11.0211 q^{12} +2.44615 q^{13} -3.28474 q^{14} -1.83453 q^{15} +11.8475 q^{16} +3.70374 q^{17} -4.42879 q^{18} +0.677600 q^{19} +4.33730 q^{20} -2.66071 q^{21} -6.99898 q^{22} +0.671719 q^{23} +17.8664 q^{24} -4.27803 q^{25} -6.52006 q^{26} +2.88978 q^{27} +6.29058 q^{28} +5.63592 q^{29} +4.88984 q^{30} -8.70933 q^{31} -15.0288 q^{32} -5.66933 q^{33} -9.87211 q^{34} +1.04711 q^{35} +8.48155 q^{36} -2.29105 q^{37} -1.80610 q^{38} -5.28139 q^{39} -7.03123 q^{40} -4.08963 q^{41} +7.09196 q^{42} +4.62801 q^{43} +13.4037 q^{44} +1.41181 q^{45} -1.79043 q^{46} -3.15034 q^{47} -25.5796 q^{48} -5.48133 q^{49} +11.4028 q^{50} -7.99662 q^{51} +12.4865 q^{52} +9.64340 q^{53} -7.70253 q^{54} +2.23113 q^{55} -10.1977 q^{56} -1.46298 q^{57} -15.0222 q^{58} -14.9693 q^{59} -9.36451 q^{60} +4.50086 q^{61} +23.2142 q^{62} +2.04761 q^{63} +16.3632 q^{64} +2.07846 q^{65} +15.1113 q^{66} +2.70328 q^{67} +18.9060 q^{68} -1.45029 q^{69} -2.79100 q^{70} +0.264031 q^{71} -13.7495 q^{72} +2.39974 q^{73} +6.10666 q^{74} +9.23654 q^{75} +3.45886 q^{76} +3.23592 q^{77} +14.0772 q^{78} -4.06573 q^{79} +10.0667 q^{80} -11.2239 q^{81} +10.9007 q^{82} -4.64859 q^{83} -13.5818 q^{84} +3.14703 q^{85} -12.3357 q^{86} -12.1683 q^{87} -21.7289 q^{88} +0.511832 q^{89} -3.76309 q^{90} +3.01449 q^{91} +3.42884 q^{92} +18.8040 q^{93} +8.39705 q^{94} +0.575750 q^{95} +32.4481 q^{96} -18.4893 q^{97} +14.6102 q^{98} +4.36297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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