LMFDB - Embedded newform 6029.2.a.a.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.40890 q^{2} -0.528400 q^{3} +3.80280 q^{4} +3.29514 q^{5} +1.27286 q^{6} -3.46004 q^{7} -4.34278 q^{8} -2.72079 q^{9} +O(q^{10})$	\(q-2.40890 q^{2} -0.528400 q^{3} +3.80280 q^{4} +3.29514 q^{5} +1.27286 q^{6} -3.46004 q^{7} -4.34278 q^{8} -2.72079 q^{9} -7.93767 q^{10} +4.17232 q^{11} -2.00940 q^{12} +6.20706 q^{13} +8.33490 q^{14} -1.74115 q^{15} +2.85571 q^{16} +3.67489 q^{17} +6.55412 q^{18} +6.04371 q^{19} +12.5308 q^{20} +1.82829 q^{21} -10.0507 q^{22} -3.73772 q^{23} +2.29472 q^{24} +5.85796 q^{25} -14.9522 q^{26} +3.02287 q^{27} -13.1579 q^{28} -3.64438 q^{29} +4.19427 q^{30} -9.51930 q^{31} +1.80643 q^{32} -2.20466 q^{33} -8.85244 q^{34} -11.4013 q^{35} -10.3466 q^{36} -2.44289 q^{37} -14.5587 q^{38} -3.27981 q^{39} -14.3101 q^{40} -7.47554 q^{41} -4.40416 q^{42} -9.18213 q^{43} +15.8665 q^{44} -8.96540 q^{45} +9.00380 q^{46} -3.23834 q^{47} -1.50896 q^{48} +4.97189 q^{49} -14.1112 q^{50} -1.94181 q^{51} +23.6042 q^{52} -10.0357 q^{53} -7.28179 q^{54} +13.7484 q^{55} +15.0262 q^{56} -3.19350 q^{57} +8.77895 q^{58} -6.91941 q^{59} -6.62127 q^{60} -3.89073 q^{61} +22.9310 q^{62} +9.41406 q^{63} -10.0629 q^{64} +20.4532 q^{65} +5.31080 q^{66} -15.3330 q^{67} +13.9749 q^{68} +1.97501 q^{69} +27.4647 q^{70} -2.47096 q^{71} +11.8158 q^{72} +7.18083 q^{73} +5.88469 q^{74} -3.09535 q^{75} +22.9831 q^{76} -14.4364 q^{77} +7.90075 q^{78} +1.14588 q^{79} +9.40997 q^{80} +6.56509 q^{81} +18.0078 q^{82} -0.998559 q^{83} +6.95262 q^{84} +12.1093 q^{85} +22.1188 q^{86} +1.92569 q^{87} -18.1195 q^{88} -13.7270 q^{89} +21.5968 q^{90} -21.4767 q^{91} -14.2138 q^{92} +5.03000 q^{93} +7.80085 q^{94} +19.9149 q^{95} -0.954519 q^{96} +13.6104 q^{97} -11.9768 q^{98} -11.3520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40890	−1.70335	−0.851675	−	0.524070i	$-0.824413\pi$
$2$	−2.40890	−1.70335	−0.851675	+	0.524070i	$0.824413\pi$
$3$	−0.528400	−0.305072	−0.152536	−	0.988298i	$-0.548744\pi$
$3$	−0.528400	−0.305072	−0.152536	+	0.988298i	$0.548744\pi$
$4$	3.80280	1.90140
$5$	3.29514	1.47363	0.736816	−	0.676093i	$-0.236328\pi$
$5$	3.29514	1.47363	0.736816	+	0.676093i	$0.236328\pi$
$6$	1.27286	0.519645
$7$	−3.46004	−1.30777	−0.653887	−	0.756593i	$-0.726863\pi$
$7$	−3.46004	−1.30777	−0.653887	+	0.756593i	$0.726863\pi$
$8$	−4.34278	−1.53540
$9$	−2.72079	−0.906931
$10$	−7.93767	−2.51011
$11$	4.17232	1.25800	0.629001	−	0.777405i	$-0.283464\pi$
$11$	4.17232	1.25800	0.629001	+	0.777405i	$0.283464\pi$
$12$	−2.00940	−0.580065
$13$	6.20706	1.72153	0.860765	−	0.509003i	$-0.169986\pi$
$13$	6.20706	1.72153	0.860765	+	0.509003i	$0.169986\pi$
$14$	8.33490	2.22760
$15$	−1.74115	−0.449564
$16$	2.85571	0.713927
$17$	3.67489	0.891291	0.445646	−	0.895209i	$-0.352974\pi$
$17$	3.67489	0.891291	0.445646	+	0.895209i	$0.352974\pi$
$18$	6.55412	1.54482
$19$	6.04371	1.38652	0.693261	−	0.720686i	$-0.256173\pi$
$19$	6.04371	1.38652	0.693261	+	0.720686i	$0.256173\pi$
$20$	12.5308	2.80197
$21$	1.82829	0.398965
$22$	−10.0507	−2.14282
$23$	−3.73772	−0.779369	−0.389685	−	0.920948i	$-0.627416\pi$
$23$	−3.73772	−0.779369	−0.389685	+	0.920948i	$0.627416\pi$
$24$	2.29472	0.468409
$25$	5.85796	1.17159
$26$	−14.9522	−2.93237
$27$	3.02287	0.581751
$28$	−13.1579	−2.48660
$29$	−3.64438	−0.676744	−0.338372	−	0.941012i	$-0.609876\pi$
$29$	−3.64438	−0.676744	−0.338372	+	0.941012i	$0.609876\pi$
$30$	4.19427	0.765765
$31$	−9.51930	−1.70972	−0.854858	−	0.518862i	$-0.826356\pi$
$31$	−9.51930	−1.70972	−0.854858	+	0.518862i	$0.826356\pi$
$32$	1.80643	0.319335
$33$	−2.20466	−0.383781
$34$	−8.85244	−1.51818
$35$	−11.4013	−1.92718
$36$	−10.3466	−1.72444
$37$	−2.44289	−0.401609	−0.200804	−	0.979631i	$-0.564356\pi$
$37$	−2.44289	−0.401609	−0.200804	+	0.979631i	$0.564356\pi$
$38$	−14.5587	−2.36173
$39$	−3.27981	−0.525191
$40$	−14.3101	−2.26262
$41$	−7.47554	−1.16748	−0.583742	−	0.811939i	$-0.698412\pi$
$41$	−7.47554	−1.16748	−0.583742	+	0.811939i	$0.698412\pi$
$42$	−4.40416	−0.679577
$43$	−9.18213	−1.40026	−0.700131	−	0.714014i	$-0.746875\pi$
$43$	−9.18213	−1.40026	−0.700131	+	0.714014i	$0.746875\pi$
$44$	15.8665	2.39197
$45$	−8.96540	−1.33648
$46$	9.00380	1.32754
$47$	−3.23834	−0.472361	−0.236180	−	0.971709i	$-0.575896\pi$
$47$	−3.23834	−0.472361	−0.236180	+	0.971709i	$0.575896\pi$
$48$	−1.50896	−0.217799
$49$	4.97189	0.710270
$50$	−14.1112	−1.99563
$51$	−1.94181	−0.271908
$52$	23.6042	3.27332
$53$	−10.0357	−1.37852	−0.689258	−	0.724516i	$-0.742063\pi$
$53$	−10.0357	−1.37852	−0.689258	+	0.724516i	$0.742063\pi$
$54$	−7.28179	−0.990926
$55$	13.7484	1.85383
$56$	15.0262	2.00796
$57$	−3.19350	−0.422989
$58$	8.77895	1.15273
$59$	−6.91941	−0.900830	−0.450415	−	0.892819i	$-0.648724\pi$
$59$	−6.91941	−0.900830	−0.450415	+	0.892819i	$0.648724\pi$
$60$	−6.62127	−0.854802
$61$	−3.89073	−0.498157	−0.249079	−	0.968483i	$-0.580128\pi$
$61$	−3.89073	−0.498157	−0.249079	+	0.968483i	$0.580128\pi$
$62$	22.9310	2.91225
$63$	9.41406	1.18606
$64$	−10.0629	−1.25787
$65$	20.4532	2.53690
$66$	5.31080	0.653714
$67$	−15.3330	−1.87323	−0.936613	−	0.350366i	$-0.886057\pi$
$67$	−15.3330	−1.87323	−0.936613	+	0.350366i	$0.886057\pi$
$68$	13.9749	1.69470
$69$	1.97501	0.237764
$70$	27.4647	3.28266
$71$	−2.47096	−0.293249	−0.146625	−	0.989192i	$-0.546841\pi$
$71$	−2.47096	−0.293249	−0.146625	+	0.989192i	$0.546841\pi$
$72$	11.8158	1.39250
$73$	7.18083	0.840453	0.420226	−	0.907419i	$-0.361951\pi$
$73$	7.18083	0.840453	0.420226	+	0.907419i	$0.361951\pi$
$74$	5.88469	0.684081
$75$	−3.09535	−0.357420
$76$	22.9831	2.63634
$77$	−14.4364	−1.64518
$78$	7.90075	0.894584
$79$	1.14588	0.128922	0.0644610	−	0.997920i	$-0.479467\pi$
$79$	1.14588	0.128922	0.0644610	+	0.997920i	$0.479467\pi$
$80$	9.40997	1.05207
$81$	6.56509	0.729455
$82$	18.0078	1.98863
$83$	−0.998559	−0.109606	−0.0548030	−	0.998497i	$-0.517453\pi$
$83$	−0.998559	−0.109606	−0.0548030	+	0.998497i	$0.517453\pi$
$84$	6.95262	0.758593
$85$	12.1093	1.31344
$86$	22.1188	2.38514
$87$	1.92569	0.206456
$88$	−18.1195	−1.93154
$89$	−13.7270	−1.45506	−0.727529	−	0.686077i	$-0.759331\pi$
$89$	−13.7270	−1.45506	−0.727529	+	0.686077i	$0.759331\pi$
$90$	21.5968	2.27650
$91$	−21.4767	−2.25137
$92$	−14.2138	−1.48189
$93$	5.03000	0.521587
$94$	7.80085	0.804596
$95$	19.9149	2.04322
$96$	−0.954519	−0.0974202
$97$	13.6104	1.38192	0.690962	−	0.722891i	$-0.257187\pi$
$97$	13.6104	1.38192	0.690962	+	0.722891i	$0.257187\pi$
$98$	−11.9768	−1.20984
$99$	−11.3520	−1.14092
$100$	22.2767	2.22767
$101$	−5.64308	−0.561508	−0.280754	−	0.959780i	$-0.590584\pi$
$101$	−5.64308	−0.561508	−0.280754	+	0.959780i	$0.590584\pi$
$102$	4.67763	0.463155
$103$	−4.51717	−0.445090	−0.222545	−	0.974922i	$-0.571436\pi$
$103$	−4.51717	−0.445090	−0.222545	+	0.974922i	$0.571436\pi$
$104$	−26.9559	−2.64324
$105$	6.02447	0.587928
$106$	24.1751	2.34809
$107$	8.79898	0.850630	0.425315	−	0.905045i	$-0.360163\pi$
$107$	8.79898	0.850630	0.425315	+	0.905045i	$0.360163\pi$
$108$	11.4954	1.10614
$109$	0.721034	0.0690625	0.0345313	−	0.999404i	$-0.489006\pi$
$109$	0.721034	0.0690625	0.0345313	+	0.999404i	$0.489006\pi$
$110$	−33.1185	−3.15773
$111$	1.29083	0.122520
$112$	−9.88087	−0.933655
$113$	9.51673	0.895259	0.447629	−	0.894219i	$-0.352268\pi$
$113$	9.51673	0.895259	0.447629	+	0.894219i	$0.352268\pi$
$114$	7.69283	0.720499
$115$	−12.3163	−1.14850
$116$	−13.8589	−1.28676
$117$	−16.8881	−1.56131
$118$	16.6682	1.53443
$119$	−12.7153	−1.16561
$120$	7.56144	0.690262
$121$	6.40826	0.582569
$122$	9.37239	0.848536
$123$	3.95008	0.356167
$124$	−36.2000	−3.25086
$125$	2.82710	0.252863
$126$	−22.6775	−2.02028
$127$	−5.05358	−0.448432	−0.224216	−	0.974539i	$-0.571982\pi$
$127$	−5.05358	−0.448432	−0.224216	+	0.974539i	$0.571982\pi$
$128$	20.6277	1.82325
$129$	4.85184	0.427181
$130$	−49.2696	−4.32123
$131$	−10.0953	−0.882032	−0.441016	−	0.897499i	$-0.645382\pi$
$131$	−10.0953	−0.882032	−0.441016	+	0.897499i	$0.645382\pi$
$132$	−8.38387	−0.729722
$133$	−20.9115	−1.81326
$134$	36.9357	3.19076
$135$	9.96078	0.857288
$136$	−15.9592	−1.36849
$137$	−9.77234	−0.834908	−0.417454	−	0.908698i	$-0.637077\pi$
$137$	−9.77234	−0.834908	−0.417454	+	0.908698i	$0.637077\pi$
$138$	−4.75761	−0.404995
$139$	5.27418	0.447350	0.223675	−	0.974664i	$-0.428195\pi$
$139$	5.27418	0.447350	0.223675	+	0.974664i	$0.428195\pi$
$140$	−43.3570	−3.66434
$141$	1.71114	0.144104
$142$	5.95230	0.499506
$143$	25.8979	2.16569
$144$	−7.76979	−0.647483
$145$	−12.0087	−0.997272
$146$	−17.2979	−1.43159
$147$	−2.62715	−0.216684
$148$	−9.28984	−0.763620
$149$	−2.53909	−0.208010	−0.104005	−	0.994577i	$-0.533166\pi$
$149$	−2.53909	−0.208010	−0.104005	+	0.994577i	$0.533166\pi$
$150$	7.45639	0.608811
$151$	−6.65867	−0.541875	−0.270937	−	0.962597i	$-0.587334\pi$
$151$	−6.65867	−0.541875	−0.270937	+	0.962597i	$0.587334\pi$
$152$	−26.2465	−2.12887
$153$	−9.99861	−0.808340
$154$	34.7759	2.80232
$155$	−31.3674	−2.51949
$156$	−12.4725	−0.998598
$157$	4.82155	0.384802	0.192401	−	0.981316i	$-0.438373\pi$
$157$	4.82155	0.384802	0.192401	+	0.981316i	$0.438373\pi$
$158$	−2.76032	−0.219599
$159$	5.30289	0.420547
$160$	5.95245	0.470582
$161$	12.9327	1.01924
$162$	−15.8147	−1.24252
$163$	−2.70831	−0.212131	−0.106065	−	0.994359i	$-0.533825\pi$
$163$	−2.70831	−0.212131	−0.106065	+	0.994359i	$0.533825\pi$
$164$	−28.4280	−2.21986
$165$	−7.26465	−0.565552
$166$	2.40543	0.186698
$167$	−2.07995	−0.160951	−0.0804755	−	0.996757i	$-0.525644\pi$
$167$	−2.07995	−0.160951	−0.0804755	+	0.996757i	$0.525644\pi$
$168$	−7.93984	−0.612572
$169$	25.5276	1.96366
$170$	−29.1701	−2.23724
$171$	−16.4437	−1.25748
$172$	−34.9179	−2.66246
$173$	−4.65284	−0.353749	−0.176874	−	0.984233i	$-0.556599\pi$
$173$	−4.65284	−0.353749	−0.176874	+	0.984233i	$0.556599\pi$
$174$	−4.63880	−0.351667
$175$	−20.2688	−1.53218
$176$	11.9149	0.898122
$177$	3.65622	0.274818
$178$	33.0670	2.47847
$179$	−8.95593	−0.669398	−0.334699	−	0.942325i	$-0.608635\pi$
$179$	−8.95593	−0.669398	−0.334699	+	0.942325i	$0.608635\pi$
$180$	−34.0937	−2.54119
$181$	−14.9600	−1.11197	−0.555985	−	0.831192i	$-0.687659\pi$
$181$	−14.9600	−1.11197	−0.555985	+	0.831192i	$0.687659\pi$
$182$	51.7352	3.83487
$183$	2.05586	0.151974
$184$	16.2321	1.19665
$185$	−8.04968	−0.591824
$186$	−12.1168	−0.888445
$187$	15.3328	1.12125
$188$	−12.3148	−0.898148
$189$	−10.4593	−0.760799
$190$	−47.9730	−3.48033
$191$	16.5344	1.19639	0.598194	−	0.801352i	$-0.295885\pi$
$191$	16.5344	1.19639	0.598194	+	0.801352i	$0.295885\pi$
$192$	5.31726	0.383740
$193$	7.23817	0.521015	0.260507	−	0.965472i	$-0.416110\pi$
$193$	7.23817	0.521015	0.260507	+	0.965472i	$0.416110\pi$
$194$	−32.7861	−2.35390
$195$	−10.8075	−0.773938
$196$	18.9071	1.35051
$197$	13.3074	0.948112	0.474056	−	0.880495i	$-0.342789\pi$
$197$	13.3074	0.948112	0.474056	+	0.880495i	$0.342789\pi$
$198$	27.3459	1.94339
$199$	6.45330	0.457463	0.228731	−	0.973490i	$-0.426542\pi$
$199$	6.45330	0.457463	0.228731	+	0.973490i	$0.426542\pi$
$200$	−25.4398	−1.79887
$201$	8.10197	0.571469
$202$	13.5936	0.956445
$203$	12.6097	0.885028
$204$	−7.38433	−0.517007
$205$	−24.6330	−1.72044
$206$	10.8814	0.758145
$207$	10.1696	0.706834
$208$	17.7256	1.22905
$209$	25.2163	1.74425
$210$	−14.5123	−1.00145
$211$	−14.2387	−0.980230	−0.490115	−	0.871658i	$-0.663045\pi$
$211$	−14.2387	−0.980230	−0.490115	+	0.871658i	$0.663045\pi$
$212$	−38.1640	−2.62111
$213$	1.30566	0.0894622
$214$	−21.1959	−1.44892
$215$	−30.2564	−2.06347
$216$	−13.1276	−0.893223
$217$	32.9372	2.23592
$218$	−1.73690	−0.117638
$219$	−3.79435	−0.256399
$220$	52.2824	3.52488
$221$	22.8103	1.53438
$222$	−3.10947	−0.208694
$223$	1.63718	0.109634	0.0548168	−	0.998496i	$-0.482543\pi$
$223$	1.63718	0.109634	0.0548168	+	0.998496i	$0.482543\pi$
$224$	−6.25033	−0.417618
$225$	−15.9383	−1.06255
$226$	−22.9249	−1.52494
$227$	28.0185	1.85965	0.929826	−	0.368000i	$-0.119957\pi$
$227$	28.0185	1.85965	0.929826	+	0.368000i	$0.119957\pi$
$228$	−12.1443	−0.804273
$229$	12.2277	0.808031	0.404016	−	0.914752i	$-0.367614\pi$
$229$	12.2277	0.808031	0.404016	+	0.914752i	$0.367614\pi$
$230$	29.6688	1.95630
$231$	7.62820	0.501899
$232$	15.8267	1.03908
$233$	−24.4807	−1.60378	−0.801892	−	0.597468i	$-0.796173\pi$
$233$	−24.4807	−1.60378	−0.801892	+	0.597468i	$0.796173\pi$
$234$	40.6818	2.65945
$235$	−10.6708	−0.696086
$236$	−26.3132	−1.71284
$237$	−0.605486	−0.0393305
$238$	30.6298	1.98544
$239$	−18.4156	−1.19121	−0.595603	−	0.803279i	$-0.703087\pi$
$239$	−18.4156	−1.19121	−0.595603	+	0.803279i	$0.703087\pi$
$240$	−4.97223	−0.320956
$241$	−0.868798	−0.0559642	−0.0279821	−	0.999608i	$-0.508908\pi$
$241$	−0.868798	−0.0559642	−0.0279821	+	0.999608i	$0.508908\pi$
$242$	−15.4369	−0.992319
$243$	−12.5376	−0.804288
$244$	−14.7957	−0.947197
$245$	16.3831	1.04668
$246$	−9.51535	−0.606677
$247$	37.5137	2.38694
$248$	41.3402	2.62510
$249$	0.527639	0.0334378
$250$	−6.81020	−0.430715
$251$	−28.2155	−1.78095	−0.890473	−	0.455035i	$-0.849627\pi$
$251$	−28.2155	−1.78095	−0.890473	+	0.455035i	$0.849627\pi$
$252$	35.7998	2.25518
$253$	−15.5950	−0.980448
$254$	12.1736	0.763838
$255$	−6.39855	−0.400693
$256$	−29.5643	−1.84777
$257$	24.4174	1.52312	0.761558	−	0.648097i	$-0.224435\pi$
$257$	24.4174	1.52312	0.761558	+	0.648097i	$0.224435\pi$
$258$	−11.6876	−0.727639
$259$	8.45251	0.525213
$260$	77.7793	4.82367
$261$	9.91560	0.613760
$262$	24.3186	1.50241
$263$	−12.6358	−0.779158	−0.389579	−	0.920993i	$-0.627380\pi$
$263$	−12.6358	−0.779158	−0.389579	+	0.920993i	$0.627380\pi$
$264$	9.57433	0.589259
$265$	−33.0692	−2.03142
$266$	50.3737	3.08861
$267$	7.25335	0.443898
$268$	−58.3084	−3.56175
$269$	−24.7818	−1.51097	−0.755485	−	0.655165i	$-0.772599\pi$
$269$	−24.7818	−1.51097	−0.755485	+	0.655165i	$0.772599\pi$
$270$	−23.9945	−1.46026
$271$	8.74460	0.531197	0.265598	−	0.964084i	$-0.414430\pi$
$271$	8.74460	0.531197	0.265598	+	0.964084i	$0.414430\pi$
$272$	10.4944	0.636317
$273$	11.3483	0.686830
$274$	23.5406	1.42214
$275$	24.4413	1.47386
$276$	7.51059	0.452084
$277$	27.0450	1.62497	0.812487	−	0.582980i	$-0.198113\pi$
$277$	27.0450	1.62497	0.812487	+	0.582980i	$0.198113\pi$
$278$	−12.7050	−0.761994
$279$	25.9000	1.55059
$280$	49.5134	2.95899
$281$	22.8916	1.36560	0.682798	−	0.730607i	$-0.260763\pi$
$281$	22.8916	1.36560	0.682798	+	0.730607i	$0.260763\pi$
$282$	−4.12197	−0.245460
$283$	−7.57198	−0.450107	−0.225054	−	0.974346i	$-0.572256\pi$
$283$	−7.57198	−0.450107	−0.225054	+	0.974346i	$0.572256\pi$
$284$	−9.39658	−0.557585
$285$	−10.5230	−0.623331
$286$	−62.3854	−3.68892
$287$	25.8657	1.52680
$288$	−4.91492	−0.289615
$289$	−3.49520	−0.205600
$290$	28.9279	1.69870
$291$	−7.19173	−0.421587
$292$	27.3073	1.59804
$293$	−15.2211	−0.889224	−0.444612	−	0.895723i	$-0.646658\pi$
$293$	−15.2211	−0.889224	−0.444612	+	0.895723i	$0.646658\pi$
$294$	6.32854	0.369088
$295$	−22.8004	−1.32749
$296$	10.6089	0.616632
$297$	12.6124	0.731844
$298$	6.11642	0.354315
$299$	−23.2003	−1.34171
$300$	−11.7710	−0.679599
$301$	31.7706	1.83123
$302$	16.0401	0.923003
$303$	2.98181	0.171300
$304$	17.2591	0.989876
$305$	−12.8205	−0.734100
$306$	24.0857	1.37689
$307$	−23.0482	−1.31543	−0.657715	−	0.753267i	$-0.728477\pi$
$307$	−23.0482	−1.31543	−0.657715	+	0.753267i	$0.728477\pi$
$308$	−54.8988	−3.12815
$309$	2.38688	0.135785
$310$	75.5610	4.29158
$311$	22.4214	1.27140	0.635700	−	0.771936i	$-0.280712\pi$
$311$	22.4214	1.27140	0.635700	+	0.771936i	$0.280712\pi$
$312$	14.2435	0.806379
$313$	11.3456	0.641290	0.320645	−	0.947199i	$-0.396100\pi$
$313$	11.3456	0.641290	0.320645	+	0.947199i	$0.396100\pi$
$314$	−11.6146	−0.655452
$315$	31.0207	1.74782
$316$	4.35757	0.245133
$317$	29.5106	1.65748	0.828740	−	0.559633i	$-0.189058\pi$
$317$	29.5106	1.65748	0.828740	+	0.559633i	$0.189058\pi$
$318$	−12.7741	−0.716338
$319$	−15.2055	−0.851346
$320$	−33.1588	−1.85363
$321$	−4.64938	−0.259503
$322$	−31.1535	−1.73612
$323$	22.2100	1.23580
$324$	24.9658	1.38699
$325$	36.3607	2.01693
$326$	6.52404	0.361333
$327$	−0.380995	−0.0210691
$328$	32.4646	1.79256
$329$	11.2048	0.617741
$330$	17.4998	0.963334
$331$	−22.3360	−1.22770	−0.613848	−	0.789424i	$-0.710379\pi$
$331$	−22.3360	−1.22770	−0.613848	+	0.789424i	$0.710379\pi$
$332$	−3.79732	−0.208405
$333$	6.64660	0.364232
$334$	5.01038	0.274156
$335$	−50.5244	−2.76045
$336$	5.22106	0.284832
$337$	−31.2287	−1.70113	−0.850567	−	0.525867i	$-0.823741\pi$
$337$	−31.2287	−1.70113	−0.850567	+	0.525867i	$0.823741\pi$
$338$	−61.4935	−3.34481
$339$	−5.02865	−0.273119
$340$	46.0492	2.49737
$341$	−39.7176	−2.15083
$342$	39.6112	2.14193
$343$	7.01734	0.378901
$344$	39.8759	2.14997
$345$	6.50795	0.350376
$346$	11.2082	0.602558
$347$	1.05575	0.0566755	0.0283377	−	0.999598i	$-0.490979\pi$
$347$	1.05575	0.0566755	0.0283377	+	0.999598i	$0.490979\pi$
$348$	7.32303	0.392555
$349$	1.30147	0.0696661	0.0348330	−	0.999393i	$-0.488910\pi$
$349$	1.30147	0.0696661	0.0348330	+	0.999393i	$0.488910\pi$
$350$	48.8255	2.60983
$351$	18.7631	1.00150
$352$	7.53701	0.401724
$353$	−12.6285	−0.672148	−0.336074	−	0.941836i	$-0.609099\pi$
$353$	−12.6285	−0.672148	−0.336074	+	0.941836i	$0.609099\pi$
$354$	−8.80747	−0.468112
$355$	−8.14217	−0.432142
$356$	−52.2011	−2.76665
$357$	6.71875	0.355594
$358$	21.5739	1.14022
$359$	5.51942	0.291304	0.145652	−	0.989336i	$-0.453472\pi$
$359$	5.51942	0.291304	0.145652	+	0.989336i	$0.453472\pi$
$360$	38.9347	2.05204
$361$	17.5265	0.922445
$362$	36.0372	1.89407
$363$	−3.38613	−0.177725
$364$	−81.6717	−4.28076
$365$	23.6619	1.23852
$366$	−4.95237	−0.258865
$367$	−23.0663	−1.20405	−0.602025	−	0.798477i	$-0.705639\pi$
$367$	−23.0663	−1.20405	−0.602025	+	0.798477i	$0.705639\pi$
$368$	−10.6738	−0.556413
$369$	20.3394	1.05883
$370$	19.3909	1.00808
$371$	34.7241	1.80278
$372$	19.1281	0.991746
$373$	−14.6926	−0.760754	−0.380377	−	0.924831i	$-0.624206\pi$
$373$	−14.6926	−0.760754	−0.380377	+	0.924831i	$0.624206\pi$
$374$	−36.9352	−1.90987
$375$	−1.49384	−0.0771415
$376$	14.0634	0.725264
$377$	−22.6209	−1.16504
$378$	25.1953	1.29591
$379$	−15.6895	−0.805913	−0.402957	−	0.915219i	$-0.632017\pi$
$379$	−15.6895	−0.805913	−0.402957	+	0.915219i	$0.632017\pi$
$380$	75.7324	3.88499
$381$	2.67031	0.136804
$382$	−39.8297	−2.03787
$383$	39.1221	1.99904	0.999522	−	0.0309018i	$-0.00983792\pi$
$383$	39.1221	1.99904	0.999522	+	0.0309018i	$0.00983792\pi$
$384$	−10.8997	−0.556223
$385$	−47.5700	−2.42439
$386$	−17.4360	−0.887470
$387$	24.9827	1.26994
$388$	51.7576	2.62759
$389$	15.1597	0.768630	0.384315	−	0.923202i	$-0.374438\pi$
$389$	15.1597	0.768630	0.384315	+	0.923202i	$0.374438\pi$
$390$	26.0341	1.31829
$391$	−13.7357	−0.694645
$392$	−21.5918	−1.09055
$393$	5.33437	0.269083
$394$	−32.0562	−1.61497
$395$	3.77585	0.189984
$396$	−43.1695	−2.16935
$397$	−28.6798	−1.43940	−0.719700	−	0.694285i	$-0.755721\pi$
$397$	−28.6798	−1.43940	−0.719700	+	0.694285i	$0.755721\pi$
$398$	−15.5454	−0.779219
$399$	11.0496	0.553174
$400$	16.7286	0.836431
$401$	6.21492	0.310358	0.155179	−	0.987886i	$-0.450405\pi$
$401$	6.21492	0.310358	0.155179	+	0.987886i	$0.450405\pi$
$402$	−19.5168	−0.973412
$403$	−59.0869	−2.94333
$404$	−21.4595	−1.06765
$405$	21.6329	1.07495
$406$	−30.3755	−1.50751
$407$	−10.1925	−0.505225
$408$	8.43286	0.417489
$409$	−23.9543	−1.18446	−0.592231	−	0.805768i	$-0.701753\pi$
$409$	−23.9543	−1.18446	−0.592231	+	0.805768i	$0.701753\pi$
$410$	59.3384	2.93051
$411$	5.16371	0.254707
$412$	−17.1779	−0.846295
$413$	23.9414	1.17808
$414$	−24.4975	−1.20399
$415$	−3.29039	−0.161519
$416$	11.2126	0.549744
$417$	−2.78688	−0.136474
$418$	−60.7436	−2.97107
$419$	20.3515	0.994237	0.497118	−	0.867683i	$-0.334391\pi$
$419$	20.3515	0.994237	0.497118	+	0.867683i	$0.334391\pi$
$420$	22.9099	1.11789
$421$	5.16318	0.251638	0.125819	−	0.992053i	$-0.459844\pi$
$421$	5.16318	0.251638	0.125819	+	0.992053i	$0.459844\pi$
$422$	34.2995	1.66967
$423$	8.81086	0.428399
$424$	43.5830	2.11658
$425$	21.5273	1.04423
$426$	−3.14520	−0.152385
$427$	13.4621	0.651476
$428$	33.4608	1.61739
$429$	−13.6844	−0.660691
$430$	72.8847	3.51481
$431$	−0.498614	−0.0240174	−0.0120087	−	0.999928i	$-0.503823\pi$
$431$	−0.498614	−0.0240174	−0.0120087	+	0.999928i	$0.503823\pi$
$432$	8.63244	0.415328
$433$	23.7507	1.14138	0.570692	−	0.821164i	$-0.306675\pi$
$433$	23.7507	1.14138	0.570692	+	0.821164i	$0.306675\pi$
$434$	−79.3424	−3.80856
$435$	6.34543	0.304240
$436$	2.74195	0.131316
$437$	−22.5897	−1.08061
$438$	9.14022	0.436737
$439$	−18.1343	−0.865501	−0.432750	−	0.901514i	$-0.642457\pi$
$439$	−18.1343	−0.865501	−0.432750	+	0.901514i	$0.642457\pi$
$440$	−59.7062	−2.84638
$441$	−13.5275	−0.644166
$442$	−54.9477	−2.61359
$443$	28.8373	1.37010	0.685050	−	0.728496i	$-0.259780\pi$
$443$	28.8373	1.37010	0.685050	+	0.728496i	$0.259780\pi$
$444$	4.90875	0.232959
$445$	−45.2324	−2.14422
$446$	−3.94380	−0.186744
$447$	1.34166	0.0634582
$448$	34.8182	1.64500
$449$	−22.6819	−1.07042	−0.535212	−	0.844718i	$-0.679768\pi$
$449$	−22.6819	−1.07042	−0.535212	+	0.844718i	$0.679768\pi$
$450$	38.3938	1.80990
$451$	−31.1904	−1.46870
$452$	36.1903	1.70225
$453$	3.51844	0.165311
$454$	−67.4937	−3.16764
$455$	−70.7688	−3.31769
$456$	13.8687	0.649459
$457$	0.374529	0.0175197	0.00875985	−	0.999962i	$-0.497212\pi$
$457$	0.374529	0.0175197	0.00875985	+	0.999962i	$0.497212\pi$
$458$	−29.4554	−1.37636
$459$	11.1087	0.518510
$460$	−46.8366	−2.18377
$461$	20.5562	0.957397	0.478698	−	0.877979i	$-0.341109\pi$
$461$	20.5562	0.957397	0.478698	+	0.877979i	$0.341109\pi$
$462$	−18.3756	−0.854909
$463$	17.5969	0.817798	0.408899	−	0.912580i	$-0.365913\pi$
$463$	17.5969	0.817798	0.408899	+	0.912580i	$0.365913\pi$
$464$	−10.4073	−0.483146
$465$	16.5746	0.768627
$466$	58.9716	2.73181
$467$	24.0631	1.11351	0.556755	−	0.830677i	$-0.312046\pi$
$467$	24.0631	1.11351	0.556755	+	0.830677i	$0.312046\pi$
$468$	−64.2223	−2.96867
$469$	53.0529	2.44975
$470$	25.7049	1.18568
$471$	−2.54771	−0.117392
$472$	30.0494	1.38314
$473$	−38.3108	−1.76153
$474$	1.45856	0.0669937
$475$	35.4038	1.62444
$476$	−48.3537	−2.21629
$477$	27.3052	1.25022
$478$	44.3614	2.02904
$479$	15.0309	0.686779	0.343389	−	0.939193i	$-0.388425\pi$
$479$	15.0309	0.686779	0.343389	+	0.939193i	$0.388425\pi$
$480$	−3.14528	−0.143562
$481$	−15.1632	−0.691382
$482$	2.09285	0.0953267
$483$	−6.83363	−0.310941
$484$	24.3693	1.10770
$485$	44.8481	2.03645
$486$	30.2019	1.36998
$487$	−23.5419	−1.06679	−0.533393	−	0.845868i	$-0.679083\pi$
$487$	−23.5419	−1.06679	−0.533393	+	0.845868i	$0.679083\pi$
$488$	16.8966	0.764872
$489$	1.43107	0.0647152
$490$	−39.4652	−1.78286
$491$	0.893030	0.0403019	0.0201509	−	0.999797i	$-0.493585\pi$
$491$	0.893030	0.0403019	0.0201509	+	0.999797i	$0.493585\pi$
$492$	15.0214	0.677216
$493$	−13.3927	−0.603176
$494$	−90.3668	−4.06579
$495$	−37.4065	−1.68130
$496$	−27.1843	−1.22061
$497$	8.54963	0.383503
$498$	−1.27103	−0.0569562
$499$	−33.6019	−1.50423	−0.752114	−	0.659033i	$-0.770966\pi$
$499$	−33.6019	−1.50423	−0.752114	+	0.659033i	$0.770966\pi$
$500$	10.7509	0.480795
$501$	1.09904	0.0491017
$502$	67.9684	3.03358
$503$	3.01515	0.134439	0.0672196	−	0.997738i	$-0.478587\pi$
$503$	3.01515	0.134439	0.0672196	+	0.997738i	$0.478587\pi$
$504$	−40.8831	−1.82108
$505$	−18.5948	−0.827456
$506$	37.5668	1.67005
$507$	−13.4888	−0.599059
$508$	−19.2178	−0.852650
$509$	26.5922	1.17868	0.589339	−	0.807886i	$-0.299388\pi$
$509$	26.5922	1.17868	0.589339	+	0.807886i	$0.299388\pi$
$510$	15.4135	0.682520
$511$	−24.8460	−1.09912
$512$	29.9621	1.32415
$513$	18.2694	0.806612
$514$	−58.8191	−2.59440
$515$	−14.8847	−0.655899
$516$	18.4506	0.812243
$517$	−13.5114	−0.594231
$518$	−20.3613	−0.894622
$519$	2.45856	0.107919
$520$	−88.8234	−3.89517
$521$	−4.51572	−0.197837	−0.0989186	−	0.995096i	$-0.531538\pi$
$521$	−4.51572	−0.197837	−0.0989186	+	0.995096i	$0.531538\pi$
$522$	−23.8857	−1.04545
$523$	−14.6566	−0.640888	−0.320444	−	0.947267i	$-0.603832\pi$
$523$	−14.6566	−0.640888	−0.320444	+	0.947267i	$0.603832\pi$
$524$	−38.3905	−1.67710
$525$	10.7100	0.467424
$526$	30.4384	1.32718
$527$	−34.9824	−1.52386
$528$	−6.29586	−0.273992
$529$	−9.02943	−0.392584
$530$	79.6604	3.46023
$531$	18.8263	0.816991
$532$	−79.5223	−3.44773
$533$	−46.4012	−2.00986
$534$	−17.4726	−0.756113
$535$	28.9939	1.25352
$536$	66.5878	2.87616
$537$	4.73232	0.204215
$538$	59.6968	2.57371
$539$	20.7443	0.893521
$540$	37.8789	1.63005
$541$	−5.71545	−0.245726	−0.122863	−	0.992424i	$-0.539208\pi$
$541$	−5.71545	−0.245726	−0.122863	+	0.992424i	$0.539208\pi$
$542$	−21.0649	−0.904814
$543$	7.90488	0.339231
$544$	6.63843	0.284620
$545$	2.37591	0.101773
$546$	−27.3369	−1.16991
$547$	−8.50469	−0.363634	−0.181817	−	0.983332i	$-0.558198\pi$
$547$	−8.50469	−0.363634	−0.181817	+	0.983332i	$0.558198\pi$
$548$	−37.1623	−1.58749
$549$	10.5859	0.451794
$550$	−58.8766	−2.51051
$551$	−22.0256	−0.938321
$552$	−8.57704	−0.365063
$553$	−3.96481	−0.168601
$554$	−65.1486	−2.76790
$555$	4.25345	0.180549
$556$	20.0567	0.850592
$557$	−24.9205	−1.05592	−0.527958	−	0.849271i	$-0.677042\pi$
$557$	−24.9205	−1.05592	−0.527958	+	0.849271i	$0.677042\pi$
$558$	−62.3906	−2.64121
$559$	−56.9941	−2.41059
$560$	−32.5589	−1.37586
$561$	−8.10186	−0.342061
$562$	−55.1435	−2.32609
$563$	−26.0800	−1.09914	−0.549571	−	0.835447i	$-0.685209\pi$
$563$	−26.0800	−1.09914	−0.549571	+	0.835447i	$0.685209\pi$
$564$	6.50713	0.274000
$565$	31.3590	1.31928
$566$	18.2401	0.766691
$567$	−22.7155	−0.953961
$568$	10.7308	0.450256
$569$	−20.1695	−0.845549	−0.422774	−	0.906235i	$-0.638944\pi$
$569$	−20.1695	−0.845549	−0.422774	+	0.906235i	$0.638944\pi$
$570$	25.3490	1.06175
$571$	−44.6870	−1.87009	−0.935046	−	0.354526i	$-0.884642\pi$
$571$	−44.6870	−1.87009	−0.935046	+	0.354526i	$0.884642\pi$
$572$	98.4845	4.11784
$573$	−8.73678	−0.364984
$574$	−62.3079	−2.60068
$575$	−21.8954	−0.913102
$576$	27.3792	1.14080
$577$	14.7705	0.614904	0.307452	−	0.951564i	$-0.400524\pi$
$577$	14.7705	0.614904	0.307452	+	0.951564i	$0.400524\pi$
$578$	8.41958	0.350208
$579$	−3.82465	−0.158947
$580$	−45.6669	−1.89622
$581$	3.45506	0.143340
$582$	17.3242	0.718110
$583$	−41.8723	−1.73417
$584$	−31.1847	−1.29043
$585$	−55.6488	−2.30079
$586$	36.6660	1.51466
$587$	−26.2846	−1.08488	−0.542441	−	0.840094i	$-0.682500\pi$
$587$	−26.2846	−1.08488	−0.542441	+	0.840094i	$0.682500\pi$
$588$	−9.99053	−0.412003
$589$	−57.5319	−2.37056
$590$	54.9240	2.26118
$591$	−7.03163	−0.289243
$592$	−6.97619	−0.286720
$593$	−25.1797	−1.03401	−0.517003	−	0.855984i	$-0.672952\pi$
$593$	−25.1797	−1.03401	−0.517003	+	0.855984i	$0.672952\pi$
$594$	−30.3820	−1.24659
$595$	−41.8986	−1.71768
$596$	−9.65566	−0.395511
$597$	−3.40993	−0.139559
$598$	55.8872	2.28540
$599$	−1.53236	−0.0626107	−0.0313053	−	0.999510i	$-0.509966\pi$
$599$	−1.53236	−0.0626107	−0.0313053	+	0.999510i	$0.509966\pi$
$600$	13.4424	0.548784
$601$	32.4289	1.32280	0.661401	−	0.750033i	$-0.269962\pi$
$601$	32.4289	1.32280	0.661401	+	0.750033i	$0.269962\pi$
$602$	−76.5322	−3.11922
$603$	41.7179	1.69889
$604$	−25.3216	−1.03032
$605$	21.1161	0.858492
$606$	−7.18288	−0.291785
$607$	24.3298	0.987515	0.493758	−	0.869600i	$-0.335623\pi$
$607$	24.3298	0.987515	0.493758	+	0.869600i	$0.335623\pi$
$608$	10.9175	0.442765
$609$	−6.66297	−0.269997
$610$	30.8833	1.25043
$611$	−20.1006	−0.813183
$612$	−38.0228	−1.53698
$613$	−7.28119	−0.294085	−0.147042	−	0.989130i	$-0.546975\pi$
$613$	−7.28119	−0.294085	−0.147042	+	0.989130i	$0.546975\pi$
$614$	55.5209	2.24064
$615$	13.0161	0.524859
$616$	62.6941	2.52602
$617$	−0.106026	−0.00426843	−0.00213421	−	0.999998i	$-0.500679\pi$
$617$	−0.106026	−0.00426843	−0.00213421	+	0.999998i	$0.500679\pi$
$618$	−5.74975	−0.231289
$619$	−26.7103	−1.07358	−0.536789	−	0.843716i	$-0.680363\pi$
$619$	−26.7103	−1.07358	−0.536789	+	0.843716i	$0.680363\pi$
$620$	−119.284	−4.79057
$621$	−11.2986	−0.453399
$622$	−54.0109	−2.16564
$623$	47.4960	1.90289
$624$	−9.36620	−0.374948
$625$	−19.9741	−0.798964
$626$	−27.3304	−1.09234
$627$	−13.3243	−0.532121
$628$	18.3354	0.731662
$629$	−8.97736	−0.357951
$630$	−74.7257	−2.97714
$631$	−36.3936	−1.44881	−0.724404	−	0.689376i	$-0.757885\pi$
$631$	−36.3936	−1.44881	−0.724404	+	0.689376i	$0.757885\pi$
$632$	−4.97632	−0.197947
$633$	7.52371	0.299041
$634$	−71.0881	−2.82327
$635$	−16.6523	−0.660825
$636$	20.1659	0.799628
$637$	30.8608	1.22275
$638$	36.6286	1.45014
$639$	6.72298	0.265957
$640$	67.9713	2.68680
$641$	27.1942	1.07411	0.537053	−	0.843549i	$-0.319538\pi$
$641$	27.1942	1.07411	0.537053	+	0.843549i	$0.319538\pi$
$642$	11.1999	0.442025
$643$	−27.1348	−1.07009	−0.535046	−	0.844823i	$-0.679706\pi$
$643$	−27.1348	−1.07009	−0.535046	+	0.844823i	$0.679706\pi$
$644$	49.1804	1.93798
$645$	15.9875	0.629508
$646$	−53.5016	−2.10499
$647$	−13.9863	−0.549857	−0.274929	−	0.961465i	$-0.588654\pi$
$647$	−13.9863	−0.549857	−0.274929	+	0.961465i	$0.588654\pi$
$648$	−28.5107	−1.12001
$649$	−28.8700	−1.13325
$650$	−87.5894	−3.43554
$651$	−17.4040	−0.682117
$652$	−10.2992	−0.403346
$653$	30.0159	1.17461	0.587307	−	0.809364i	$-0.300188\pi$
$653$	30.0159	1.17461	0.587307	+	0.809364i	$0.300188\pi$
$654$	0.917779	0.0358880
$655$	−33.2655	−1.29979
$656$	−21.3480	−0.833498
$657$	−19.5376	−0.762233
$658$	−26.9913	−1.05223
$659$	−11.4381	−0.445565	−0.222782	−	0.974868i	$-0.571514\pi$
$659$	−11.4381	−0.445565	−0.222782	+	0.974868i	$0.571514\pi$
$660$	−27.6261	−1.07534
$661$	−15.3742	−0.597988	−0.298994	−	0.954255i	$-0.596651\pi$
$661$	−15.3742	−0.597988	−0.298994	+	0.954255i	$0.596651\pi$
$662$	53.8051	2.09120
$663$	−12.0530	−0.468098
$664$	4.33652	0.168290
$665$	−68.9064	−2.67207
$666$	−16.0110	−0.620414
$667$	13.6217	0.527434
$668$	−7.90962	−0.306033
$669$	−0.865086	−0.0334461
$670$	121.708	4.70200
$671$	−16.2334	−0.626683
$672$	3.30268	0.127403
$673$	38.1757	1.47157	0.735783	−	0.677217i	$-0.236814\pi$
$673$	38.1757	1.47157	0.735783	+	0.677217i	$0.236814\pi$
$674$	75.2268	2.89763
$675$	17.7078	0.681575
$676$	97.0766	3.73371
$677$	36.8931	1.41792	0.708959	−	0.705250i	$-0.249165\pi$
$677$	36.8931	1.41792	0.708959	+	0.705250i	$0.249165\pi$
$678$	12.1135	0.465217
$679$	−47.0925	−1.80724
$680$	−52.5879	−2.01665
$681$	−14.8050	−0.567328
$682$	95.6757	3.66361
$683$	20.0328	0.766532	0.383266	−	0.923638i	$-0.374799\pi$
$683$	20.0328	0.766532	0.383266	+	0.923638i	$0.374799\pi$
$684$	−62.5321	−2.39098
$685$	−32.2013	−1.23035
$686$	−16.9041	−0.645401
$687$	−6.46114	−0.246508
$688$	−26.2215	−0.999685
$689$	−62.2925	−2.37315
$690$	−15.6770	−0.596814
$691$	21.9498	0.835009	0.417505	−	0.908675i	$-0.362905\pi$
$691$	21.9498	0.835009	0.417505	+	0.908675i	$0.362905\pi$
$692$	−17.6938	−0.672618
$693$	39.2785	1.49207
$694$	−2.54319	−0.0965382
$695$	17.3792	0.659229
$696$	−8.36285	−0.316993
$697$	−27.4718	−1.04057
$698$	−3.13511	−0.118666
$699$	12.9356	0.489270
$700$	−77.0782	−2.91328
$701$	−7.57655	−0.286163	−0.143081	−	0.989711i	$-0.545701\pi$
$701$	−7.57655	−0.286163	−0.143081	+	0.989711i	$0.545701\pi$
$702$	−45.1985	−1.70591
$703$	−14.7641	−0.556840
$704$	−41.9858	−1.58240
$705$	5.63845	0.212356
$706$	30.4209	1.14490
$707$	19.5253	0.734325
$708$	13.9039	0.522540
$709$	15.3707	0.577259	0.288629	−	0.957441i	$-0.406800\pi$
$709$	15.3707	0.577259	0.288629	+	0.957441i	$0.406800\pi$
$710$	19.6137	0.736088
$711$	−3.11771	−0.116923
$712$	59.6132	2.23410
$713$	35.5805	1.33250
$714$	−16.1848	−0.605701
$715$	85.3371	3.19143
$716$	−34.0576	−1.27279
$717$	9.73081	0.363404
$718$	−13.2957	−0.496192
$719$	48.0537	1.79210	0.896049	−	0.443954i	$-0.146425\pi$
$719$	48.0537	1.79210	0.896049	+	0.443954i	$0.146425\pi$
$720$	−25.6026	−0.954151
$721$	15.6296	0.582077
$722$	−42.2195	−1.57125
$723$	0.459073	0.0170731
$724$	−56.8900	−2.11430
$725$	−21.3486	−0.792868
$726$	8.15684	0.302729
$727$	35.3136	1.30971	0.654854	−	0.755755i	$-0.272730\pi$
$727$	35.3136	1.30971	0.654854	+	0.755755i	$0.272730\pi$
$728$	93.2685	3.45676
$729$	−13.0704	−0.484089
$730$	−56.9991	−2.10963
$731$	−33.7433	−1.24804
$732$	7.81805	0.288963
$733$	−12.6239	−0.466275	−0.233137	−	0.972444i	$-0.574899\pi$
$733$	−12.6239	−0.466275	−0.233137	+	0.972444i	$0.574899\pi$
$734$	55.5644	2.05092
$735$	−8.65683	−0.319312
$736$	−6.75194	−0.248880
$737$	−63.9742	−2.35652
$738$	−48.9956	−1.80355
$739$	30.8322	1.13418	0.567090	−	0.823656i	$-0.308069\pi$
$739$	30.8322	1.13418	0.567090	+	0.823656i	$0.308069\pi$
$740$	−30.6113	−1.12530
$741$	−19.8223	−0.728189
$742$	−83.6469	−3.07077
$743$	34.4932	1.26543	0.632717	−	0.774383i	$-0.281940\pi$
$743$	34.4932	1.26543	0.632717	+	0.774383i	$0.281940\pi$
$744$	−21.8442	−0.800846
$745$	−8.36666	−0.306531
$746$	35.3930	1.29583
$747$	2.71687	0.0994051
$748$	58.3077	2.13194
$749$	−30.4448	−1.11243
$750$	3.59851	0.131399
$751$	27.6279	1.00815	0.504077	−	0.863659i	$-0.331833\pi$
$751$	27.6279	1.00815	0.504077	+	0.863659i	$0.331833\pi$
$752$	−9.24776	−0.337231
$753$	14.9091	0.543317
$754$	54.4915	1.98446
$755$	−21.9413	−0.798524
$756$	−39.7745	−1.44658
$757$	40.8576	1.48499	0.742497	−	0.669849i	$-0.233641\pi$
$757$	40.8576	1.48499	0.742497	+	0.669849i	$0.233641\pi$
$758$	37.7943	1.37275
$759$	8.24039	0.299107
$760$	−86.4859	−3.13717
$761$	9.50561	0.344578	0.172289	−	0.985046i	$-0.444884\pi$
$761$	9.50561	0.344578	0.172289	+	0.985046i	$0.444884\pi$
$762$	−6.43252	−0.233026
$763$	−2.49481	−0.0903181
$764$	62.8771	2.27481
$765$	−32.9468	−1.19120
$766$	−94.2412	−3.40507
$767$	−42.9492	−1.55081
$768$	15.6218	0.563703
$769$	−9.33883	−0.336767	−0.168383	−	0.985722i	$-0.553855\pi$
$769$	−9.33883	−0.336767	−0.168383	+	0.985722i	$0.553855\pi$
$770$	114.591	4.12959
$771$	−12.9022	−0.464660
$772$	27.5253	0.990658
$773$	33.9375	1.22065	0.610324	−	0.792152i	$-0.291039\pi$
$773$	33.9375	1.22065	0.610324	+	0.792152i	$0.291039\pi$
$774$	−60.1808	−2.16315
$775$	−55.7636	−2.00309
$776$	−59.1068	−2.12181
$777$	−4.46631	−0.160228
$778$	−36.5183	−1.30925
$779$	−45.1800	−1.61874
$780$	−41.0986	−1.47157
$781$	−10.3096	−0.368908
$782$	33.0880	1.18322
$783$	−11.0165	−0.393697
$784$	14.1983	0.507081
$785$	15.8877	0.567056
$786$	−12.8500	−0.458343
$787$	43.6541	1.55610	0.778051	−	0.628202i	$-0.216209\pi$
$787$	43.6541	1.55610	0.778051	+	0.628202i	$0.216209\pi$
$788$	50.6054	1.80274
$789$	6.67677	0.237699
$790$	−9.09565	−0.323609
$791$	−32.9283	−1.17080
$792$	49.2993	1.75177
$793$	−24.1500	−0.857592
$794$	69.0869	2.45180
$795$	17.4738	0.619731
$796$	24.5407	0.869820
$797$	46.9724	1.66385	0.831924	−	0.554889i	$-0.187239\pi$
$797$	46.9724	1.66385	0.831924	+	0.554889i	$0.187239\pi$
$798$	−26.6175	−0.942249
$799$	−11.9005	−0.421011
$800$	10.5820	0.374130
$801$	37.3483	1.31964
$802$	−14.9711	−0.528649
$803$	29.9607	1.05729
$804$	30.8102	1.08659
$805$	42.6150	1.50198
$806$	142.334	5.01352
$807$	13.0947	0.460955
$808$	24.5067	0.862141
$809$	48.6107	1.70906	0.854531	−	0.519401i	$-0.173845\pi$
$809$	48.6107	1.70906	0.854531	+	0.519401i	$0.173845\pi$
$810$	−52.1115	−1.83101
$811$	−52.3044	−1.83666	−0.918328	−	0.395820i	$-0.870460\pi$
$811$	−52.3044	−1.83666	−0.918328	+	0.395820i	$0.870460\pi$
$812$	47.9522	1.68279
$813$	−4.62065	−0.162053
$814$	24.5528	0.860575
$815$	−8.92425	−0.312603
$816$	−5.54525	−0.194123
$817$	−55.4942	−1.94150
$818$	57.7035	2.01755
$819$	58.4337	2.04184
$820$	−93.6744	−3.27125
$821$	27.1663	0.948110	0.474055	−	0.880495i	$-0.342790\pi$
$821$	27.1663	0.948110	0.474055	+	0.880495i	$0.342790\pi$
$822$	−12.4389	−0.433855
$823$	19.0680	0.664668	0.332334	−	0.943162i	$-0.392164\pi$
$823$	19.0680	0.664668	0.332334	+	0.943162i	$0.392164\pi$
$824$	19.6171	0.683393
$825$	−12.9148	−0.449635
$826$	−57.6726	−2.00669
$827$	−27.6440	−0.961277	−0.480638	−	0.876919i	$-0.659595\pi$
$827$	−27.6440	−0.961277	−0.480638	+	0.876919i	$0.659595\pi$
$828$	38.6729	1.34398
$829$	6.29686	0.218699	0.109350	−	0.994003i	$-0.465123\pi$
$829$	6.29686	0.218699	0.109350	+	0.994003i	$0.465123\pi$
$830$	7.92623	0.275123
$831$	−14.2906	−0.495734
$832$	−62.4612	−2.16545
$833$	18.2711	0.633058
$834$	6.71331	0.232463
$835$	−6.85371	−0.237183
$836$	95.8927	3.31652
$837$	−28.7756	−0.994630
$838$	−49.0248	−1.69353
$839$	−23.2866	−0.803944	−0.401972	−	0.915652i	$-0.631675\pi$
$839$	−23.2866	−0.803944	−0.401972	+	0.915652i	$0.631675\pi$
$840$	−26.1629	−0.902706
$841$	−15.7185	−0.542017
$842$	−12.4376	−0.428628
$843$	−12.0959	−0.416605
$844$	−54.1468	−1.86381
$845$	84.1171	2.89372
$846$	−21.2245	−0.729713
$847$	−22.1728	−0.761868
$848$	−28.6592	−0.984160
$849$	4.00104	0.137315
$850$	−51.8572	−1.77869
$851$	9.13085	0.313002
$852$	4.96516	0.170104
$853$	34.8236	1.19234	0.596168	−	0.802860i	$-0.296689\pi$
$853$	34.8236	1.19234	0.596168	+	0.802860i	$0.296689\pi$
$854$	−32.4289	−1.10969
$855$	−54.1843	−1.85306
$856$	−38.2120	−1.30606
$857$	−18.4851	−0.631439	−0.315720	−	0.948853i	$-0.602246\pi$
$857$	−18.4851	−0.631439	−0.315720	+	0.948853i	$0.602246\pi$
$858$	32.9645	1.12539
$859$	−44.6209	−1.52244	−0.761222	−	0.648492i	$-0.775400\pi$
$859$	−44.6209	−1.52244	−0.761222	+	0.648492i	$0.775400\pi$
$860$	−115.059	−3.92349
$861$	−13.6674	−0.465785
$862$	1.20111	0.0409100
$863$	−14.5200	−0.494267	−0.247134	−	0.968981i	$-0.579489\pi$
$863$	−14.5200	−0.494267	−0.247134	+	0.968981i	$0.579489\pi$
$864$	5.46060	0.185774
$865$	−15.3318	−0.521295
$866$	−57.2130	−1.94418
$867$	1.84686	0.0627228
$868$	125.254	4.25138
$869$	4.78100	0.162184
$870$	−15.2855	−0.518227
$871$	−95.1730	−3.22481
$872$	−3.13129	−0.106039
$873$	−37.0310	−1.25331
$874$	54.4164	1.84066
$875$	−9.78187	−0.330688
$876$	−14.4292	−0.487517
$877$	−13.5159	−0.456401	−0.228200	−	0.973614i	$-0.573284\pi$
$877$	−13.5159	−0.456401	−0.228200	+	0.973614i	$0.573284\pi$
$878$	43.6836	1.47425
$879$	8.04281	0.271277
$880$	39.2614	1.32350
$881$	58.7563	1.97955	0.989776	−	0.142632i	$-0.0455565\pi$
$881$	58.7563	1.97955	0.989776	+	0.142632i	$0.0455565\pi$
$882$	32.5864	1.09724
$883$	−35.8829	−1.20756	−0.603779	−	0.797152i	$-0.706339\pi$
$883$	−35.8829	−1.20756	−0.603779	+	0.797152i	$0.706339\pi$
$884$	86.7429	2.91748
$885$	12.0478	0.404981
$886$	−69.4662	−2.33376
$887$	31.2057	1.04779	0.523893	−	0.851784i	$-0.324479\pi$
$887$	31.2057	1.04779	0.523893	+	0.851784i	$0.324479\pi$
$888$	−5.60576	−0.188117
$889$	17.4856	0.586448
$890$	108.960	3.65236
$891$	27.3917	0.917656
$892$	6.22587	0.208457
$893$	−19.5716	−0.654939
$894$	−3.23192	−0.108092
$895$	−29.5111	−0.986446
$896$	−71.3729	−2.38440
$897$	12.2590	0.409317
$898$	54.6384	1.82331
$899$	34.6919	1.15704
$900$	−60.6102	−2.02034
$901$	−36.8802	−1.22866
$902$	75.1345	2.50170
$903$	−16.7876	−0.558656
$904$	−41.3290	−1.37458
$905$	−49.2954	−1.63863
$906$	−8.47558	−0.281582
$907$	10.0859	0.334896	0.167448	−	0.985881i	$-0.446447\pi$
$907$	10.0859	0.334896	0.167448	+	0.985881i	$0.446447\pi$
$908$	106.549	3.53595
$909$	15.3537	0.509249
$910$	170.475	5.65119
$911$	−3.25195	−0.107742	−0.0538709	−	0.998548i	$-0.517156\pi$
$911$	−3.25195	−0.107742	−0.0538709	+	0.998548i	$0.517156\pi$
$912$	−9.11971	−0.301984
$913$	−4.16631	−0.137885
$914$	−0.902202	−0.0298422
$915$	6.77436	0.223954
$916$	46.4997	1.53639
$917$	34.9302	1.15350
$918$	−26.7598	−0.883204
$919$	19.6251	0.647374	0.323687	−	0.946164i	$-0.395078\pi$
$919$	19.6251	0.647374	0.323687	+	0.946164i	$0.395078\pi$
$920$	53.4870	1.76342
$921$	12.1787	0.401301
$922$	−49.5178	−1.63078
$923$	−15.3374	−0.504837
$924$	29.0086	0.954311
$925$	−14.3104	−0.470522
$926$	−42.3892	−1.39300
$927$	12.2903	0.403666
$928$	−6.58332	−0.216108
$929$	−0.563049	−0.0184730	−0.00923651	−	0.999957i	$-0.502940\pi$
$929$	−0.563049	−0.0184730	−0.00923651	+	0.999957i	$0.502940\pi$
$930$	−39.9265	−1.30924
$931$	30.0487	0.984806
$932$	−93.0953	−3.04944
$933$	−11.8475	−0.387869
$934$	−57.9657	−1.89670
$935$	50.5238	1.65230
$936$	73.3414	2.39724
$937$	5.71142	0.186584	0.0932919	−	0.995639i	$-0.470261\pi$
$937$	5.71142	0.186584	0.0932919	+	0.995639i	$0.470261\pi$
$938$	−127.799	−4.17279
$939$	−5.99501	−0.195640
$940$	−40.5789	−1.32354
$941$	−23.7471	−0.774133	−0.387067	−	0.922052i	$-0.626512\pi$
$941$	−23.7471	−0.774133	−0.387067	+	0.922052i	$0.626512\pi$
$942$	6.13718	0.199960
$943$	27.9415	0.909901
$944$	−19.7598	−0.643127
$945$	−34.4647	−1.12114
$946$	92.2869	3.00051
$947$	17.5413	0.570016	0.285008	−	0.958525i	$-0.408004\pi$
$947$	17.5413	0.570016	0.285008	+	0.958525i	$0.408004\pi$
$948$	−2.30254	−0.0747831
$949$	44.5719	1.44686
$950$	−85.2843	−2.76699
$951$	−15.5934	−0.505651
$952$	55.2196	1.78968
$953$	−58.1147	−1.88252	−0.941260	−	0.337682i	$-0.890357\pi$
$953$	−58.1147	−1.88252	−0.941260	+	0.337682i	$0.890357\pi$
$954$	−65.7755	−2.12956
$955$	54.4832	1.76303
$956$	−70.0309	−2.26496
$957$	8.03460	0.259722
$958$	−36.2079	−1.16982
$959$	33.8127	1.09187
$960$	17.5211	0.565492
$961$	59.6170	1.92313
$962$	36.5266	1.17767
$963$	−23.9402	−0.771462
$964$	−3.30387	−0.106410
$965$	23.8508	0.767784
$966$	16.4615	0.529641
$967$	35.6869	1.14761	0.573807	−	0.818991i	$-0.305466\pi$
$967$	35.6869	1.14761	0.573807	+	0.818991i	$0.305466\pi$
$968$	−27.8296	−0.894478
$969$	−11.7358	−0.377007
$970$	−108.035	−3.46879
$971$	59.6628	1.91467	0.957335	−	0.288981i	$-0.0933166\pi$
$971$	59.6628	1.91467	0.957335	+	0.288981i	$0.0933166\pi$
$972$	−47.6781	−1.52927
$973$	−18.2489	−0.585032
$974$	56.7101	1.81711
$975$	−19.2130	−0.615309
$976$	−11.1108	−0.355648
$977$	−43.4713	−1.39077	−0.695385	−	0.718637i	$-0.744766\pi$
$977$	−43.4713	−1.39077	−0.695385	+	0.718637i	$0.744766\pi$
$978$	−3.44730	−0.110233
$979$	−57.2734	−1.83047
$980$	62.3017	1.99015
$981$	−1.96178	−0.0626350
$982$	−2.15122	−0.0686482
$983$	54.2955	1.73176	0.865879	−	0.500253i	$-0.166760\pi$
$983$	54.2955	1.73176	0.865879	+	0.500253i	$0.166760\pi$
$984$	−17.1543	−0.546859
$985$	43.8497	1.39717
$986$	32.2617	1.02742
$987$	−5.92062	−0.188455
$988$	142.657	4.53853
$989$	34.3203	1.09132
$990$	90.1086	2.86384
$991$	10.7924	0.342831	0.171416	−	0.985199i	$-0.445166\pi$
$991$	10.7924	0.342831	0.171416	+	0.985199i	$0.445166\pi$
$992$	−17.1960	−0.545972
$993$	11.8023	0.374536
$994$	−20.5952	−0.653241
$995$	21.2646	0.674132
$996$	2.00651	0.0635786
$997$	12.4139	0.393151	0.196576	−	0.980489i	$-0.437018\pi$
$997$	12.4139	0.393151	0.196576	+	0.980489i	$0.437018\pi$
$998$	80.9437	2.56223
$999$	−7.38454	−0.233637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.19	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.40890 q^{2} -0.528400 q^{3} +3.80280 q^{4} +3.29514 q^{5} +1.27286 q^{6} -3.46004 q^{7} -4.34278 q^{8} -2.72079 q^{9} +O(q^{10})\)	\(q-2.40890 q^{2} -0.528400 q^{3} +3.80280 q^{4} +3.29514 q^{5} +1.27286 q^{6} -3.46004 q^{7} -4.34278 q^{8} -2.72079 q^{9} -7.93767 q^{10} +4.17232 q^{11} -2.00940 q^{12} +6.20706 q^{13} +8.33490 q^{14} -1.74115 q^{15} +2.85571 q^{16} +3.67489 q^{17} +6.55412 q^{18} +6.04371 q^{19} +12.5308 q^{20} +1.82829 q^{21} -10.0507 q^{22} -3.73772 q^{23} +2.29472 q^{24} +5.85796 q^{25} -14.9522 q^{26} +3.02287 q^{27} -13.1579 q^{28} -3.64438 q^{29} +4.19427 q^{30} -9.51930 q^{31} +1.80643 q^{32} -2.20466 q^{33} -8.85244 q^{34} -11.4013 q^{35} -10.3466 q^{36} -2.44289 q^{37} -14.5587 q^{38} -3.27981 q^{39} -14.3101 q^{40} -7.47554 q^{41} -4.40416 q^{42} -9.18213 q^{43} +15.8665 q^{44} -8.96540 q^{45} +9.00380 q^{46} -3.23834 q^{47} -1.50896 q^{48} +4.97189 q^{49} -14.1112 q^{50} -1.94181 q^{51} +23.6042 q^{52} -10.0357 q^{53} -7.28179 q^{54} +13.7484 q^{55} +15.0262 q^{56} -3.19350 q^{57} +8.77895 q^{58} -6.91941 q^{59} -6.62127 q^{60} -3.89073 q^{61} +22.9310 q^{62} +9.41406 q^{63} -10.0629 q^{64} +20.4532 q^{65} +5.31080 q^{66} -15.3330 q^{67} +13.9749 q^{68} +1.97501 q^{69} +27.4647 q^{70} -2.47096 q^{71} +11.8158 q^{72} +7.18083 q^{73} +5.88469 q^{74} -3.09535 q^{75} +22.9831 q^{76} -14.4364 q^{77} +7.90075 q^{78} +1.14588 q^{79} +9.40997 q^{80} +6.56509 q^{81} +18.0078 q^{82} -0.998559 q^{83} +6.95262 q^{84} +12.1093 q^{85} +22.1188 q^{86} +1.92569 q^{87} -18.1195 q^{88} -13.7270 q^{89} +21.5968 q^{90} -21.4767 q^{91} -14.2138 q^{92} +5.03000 q^{93} +7.80085 q^{94} +19.9149 q^{95} -0.954519 q^{96} +13.6104 q^{97} -11.9768 q^{98} -11.3520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 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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