LMFDB - Embedded newform 4021.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, 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("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49227 q^{2} -2.01078 q^{3} +4.21142 q^{4} +3.04731 q^{5} +5.01140 q^{6} -1.48654 q^{7} -5.51145 q^{8} +1.04322 q^{9} +O(q^{10})$	\(q-2.49227 q^{2} -2.01078 q^{3} +4.21142 q^{4} +3.04731 q^{5} +5.01140 q^{6} -1.48654 q^{7} -5.51145 q^{8} +1.04322 q^{9} -7.59472 q^{10} +1.81295 q^{11} -8.46822 q^{12} -0.734695 q^{13} +3.70486 q^{14} -6.12746 q^{15} +5.31320 q^{16} +7.10259 q^{17} -2.59999 q^{18} -7.26677 q^{19} +12.8335 q^{20} +2.98910 q^{21} -4.51837 q^{22} -7.33280 q^{23} +11.0823 q^{24} +4.28610 q^{25} +1.83106 q^{26} +3.93465 q^{27} -6.26044 q^{28} +0.894451 q^{29} +15.2713 q^{30} +3.59164 q^{31} -2.21904 q^{32} -3.64544 q^{33} -17.7016 q^{34} -4.52995 q^{35} +4.39343 q^{36} +5.71887 q^{37} +18.1108 q^{38} +1.47731 q^{39} -16.7951 q^{40} +0.487859 q^{41} -7.44965 q^{42} -5.93769 q^{43} +7.63510 q^{44} +3.17901 q^{45} +18.2753 q^{46} +8.29421 q^{47} -10.6837 q^{48} -4.79020 q^{49} -10.6821 q^{50} -14.2817 q^{51} -3.09411 q^{52} +6.24641 q^{53} -9.80621 q^{54} +5.52463 q^{55} +8.19300 q^{56} +14.6119 q^{57} -2.22922 q^{58} -6.10515 q^{59} -25.8053 q^{60} -10.4333 q^{61} -8.95134 q^{62} -1.55079 q^{63} -5.09596 q^{64} -2.23884 q^{65} +9.08543 q^{66} +1.55032 q^{67} +29.9120 q^{68} +14.7446 q^{69} +11.2899 q^{70} -15.8532 q^{71} -5.74966 q^{72} +2.48293 q^{73} -14.2530 q^{74} -8.61839 q^{75} -30.6034 q^{76} -2.69503 q^{77} -3.68185 q^{78} -2.62028 q^{79} +16.1910 q^{80} -11.0414 q^{81} -1.21588 q^{82} -3.52124 q^{83} +12.5884 q^{84} +21.6438 q^{85} +14.7983 q^{86} -1.79854 q^{87} -9.99201 q^{88} -13.4056 q^{89} -7.92297 q^{90} +1.09215 q^{91} -30.8815 q^{92} -7.22198 q^{93} -20.6714 q^{94} -22.1441 q^{95} +4.46199 q^{96} +4.09184 q^{97} +11.9385 q^{98} +1.89131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.49227	−1.76230	−0.881151	−	0.472835i	$-0.843231\pi$
$2$	−2.49227	−1.76230	−0.881151	+	0.472835i	$0.843231\pi$
$3$	−2.01078	−1.16092	−0.580461	−	0.814288i	$-0.697128\pi$
$3$	−2.01078	−1.16092	−0.580461	+	0.814288i	$0.697128\pi$
$4$	4.21142	2.10571
$5$	3.04731	1.36280	0.681399	−	0.731912i	$-0.261372\pi$
$5$	3.04731	1.36280	0.681399	+	0.731912i	$0.261372\pi$
$6$	5.01140	2.04590
$7$	−1.48654	−0.561860	−0.280930	−	0.959728i	$-0.590643\pi$
$7$	−1.48654	−0.561860	−0.280930	+	0.959728i	$0.590643\pi$
$8$	−5.51145	−1.94859
$9$	1.04322	0.347740
$10$	−7.59472	−2.40166
$11$	1.81295	0.546626	0.273313	−	0.961925i	$-0.411881\pi$
$11$	1.81295	0.546626	0.273313	+	0.961925i	$0.411881\pi$
$12$	−8.46822	−2.44456
$13$	−0.734695	−0.203768	−0.101884	−	0.994796i	$-0.532487\pi$
$13$	−0.734695	−0.203768	−0.101884	+	0.994796i	$0.532487\pi$
$14$	3.70486	0.990167
$15$	−6.12746	−1.58210
$16$	5.31320	1.32830
$17$	7.10259	1.72263	0.861316	−	0.508070i	$-0.169641\pi$
$17$	7.10259	1.72263	0.861316	+	0.508070i	$0.169641\pi$
$18$	−2.59999	−0.612823
$19$	−7.26677	−1.66711	−0.833556	−	0.552435i	$-0.813699\pi$
$19$	−7.26677	−1.66711	−0.833556	+	0.552435i	$0.813699\pi$
$20$	12.8335	2.86966
$21$	2.98910	0.652275
$22$	−4.51837	−0.963320
$23$	−7.33280	−1.52899	−0.764497	−	0.644627i	$-0.777013\pi$
$23$	−7.33280	−1.52899	−0.764497	+	0.644627i	$0.777013\pi$
$24$	11.0823	2.26216
$25$	4.28610	0.857220
$26$	1.83106	0.359100
$27$	3.93465	0.757223
$28$	−6.26044	−1.18311
$29$	0.894451	0.166095	0.0830477	−	0.996546i	$-0.473535\pi$
$29$	0.894451	0.166095	0.0830477	+	0.996546i	$0.473535\pi$
$30$	15.2713	2.78814
$31$	3.59164	0.645077	0.322539	−	0.946556i	$-0.395464\pi$
$31$	3.59164	0.645077	0.322539	+	0.946556i	$0.395464\pi$
$32$	−2.21904	−0.392274
$33$	−3.64544	−0.634590
$34$	−17.7016	−3.03580
$35$	−4.52995	−0.765702
$36$	4.39343	0.732239
$37$	5.71887	0.940176	0.470088	−	0.882620i	$-0.344222\pi$
$37$	5.71887	0.940176	0.470088	+	0.882620i	$0.344222\pi$
$38$	18.1108	2.93796
$39$	1.47731	0.236558
$40$	−16.7951	−2.65554
$41$	0.487859	0.0761907	0.0380954	−	0.999274i	$-0.487871\pi$
$41$	0.487859	0.0761907	0.0380954	+	0.999274i	$0.487871\pi$
$42$	−7.44965	−1.14951
$43$	−5.93769	−0.905489	−0.452744	−	0.891640i	$-0.649555\pi$
$43$	−5.93769	−0.905489	−0.452744	+	0.891640i	$0.649555\pi$
$44$	7.63510	1.15104
$45$	3.17901	0.473900
$46$	18.2753	2.69455
$47$	8.29421	1.20984	0.604918	−	0.796288i	$-0.293206\pi$
$47$	8.29421	1.20984	0.604918	+	0.796288i	$0.293206\pi$
$48$	−10.6837	−1.54205
$49$	−4.79020	−0.684314
$50$	−10.6821	−1.51068
$51$	−14.2817	−1.99984
$52$	−3.09411	−0.429075
$53$	6.24641	0.858011	0.429005	−	0.903302i	$-0.358864\pi$
$53$	6.24641	0.858011	0.429005	+	0.903302i	$0.358864\pi$
$54$	−9.80621	−1.33446
$55$	5.52463	0.744941
$56$	8.19300	1.09484
$57$	14.6119	1.93539
$58$	−2.22922	−0.292710
$59$	−6.10515	−0.794823	−0.397411	−	0.917641i	$-0.630091\pi$
$59$	−6.10515	−0.794823	−0.397411	+	0.917641i	$0.630091\pi$
$60$	−25.8053	−3.33145
$61$	−10.4333	−1.33584	−0.667921	−	0.744232i	$-0.732816\pi$
$61$	−10.4333	−1.33584	−0.667921	+	0.744232i	$0.732816\pi$
$62$	−8.95134	−1.13682
$63$	−1.55079	−0.195381
$64$	−5.09596	−0.636995
$65$	−2.23884	−0.277694
$66$	9.08543	1.11834
$67$	1.55032	0.189402	0.0947010	−	0.995506i	$-0.469810\pi$
$67$	1.55032	0.189402	0.0947010	+	0.995506i	$0.469810\pi$
$68$	29.9120	3.62736
$69$	14.7446	1.77504
$70$	11.2899	1.34940
$71$	−15.8532	−1.88143	−0.940716	−	0.339197i	$-0.889845\pi$
$71$	−15.8532	−1.88143	−0.940716	+	0.339197i	$0.889845\pi$
$72$	−5.74966	−0.677604
$73$	2.48293	0.290605	0.145302	−	0.989387i	$-0.453585\pi$
$73$	2.48293	0.290605	0.145302	+	0.989387i	$0.453585\pi$
$74$	−14.2530	−1.65687
$75$	−8.61839	−0.995166
$76$	−30.6034	−3.51045
$77$	−2.69503	−0.307127
$78$	−3.68185	−0.416887
$79$	−2.62028	−0.294805	−0.147403	−	0.989077i	$-0.547091\pi$
$79$	−2.62028	−0.294805	−0.147403	+	0.989077i	$0.547091\pi$
$80$	16.1910	1.81021
$81$	−11.0414	−1.22682
$82$	−1.21588	−0.134271
$83$	−3.52124	−0.386507	−0.193253	−	0.981149i	$-0.561904\pi$
$83$	−3.52124	−0.386507	−0.193253	+	0.981149i	$0.561904\pi$
$84$	12.5884	1.37350
$85$	21.6438	2.34760
$86$	14.7983	1.59575
$87$	−1.79854	−0.192824
$88$	−9.99201	−1.06515
$89$	−13.4056	−1.42099	−0.710495	−	0.703702i	$-0.751529\pi$
$89$	−13.4056	−1.42099	−0.710495	+	0.703702i	$0.751529\pi$
$90$	−7.92297	−0.835154
$91$	1.09215	0.114489
$92$	−30.8815	−3.21962
$93$	−7.22198	−0.748885
$94$	−20.6714	−2.13210
$95$	−22.1441	−2.27194
$96$	4.46199	0.455400
$97$	4.09184	0.415464	0.207732	−	0.978186i	$-0.433392\pi$
$97$	4.09184	0.415464	0.207732	+	0.978186i	$0.433392\pi$
$98$	11.9385	1.20597
$99$	1.89131	0.190084
$100$	18.0506	1.80506
$101$	8.05217	0.801221	0.400610	−	0.916248i	$-0.368798\pi$
$101$	8.05217	0.801221	0.400610	+	0.916248i	$0.368798\pi$
$102$	35.5939	3.52432
$103$	−13.9340	−1.37295	−0.686477	−	0.727152i	$-0.740844\pi$
$103$	−13.9340	−1.37295	−0.686477	+	0.727152i	$0.740844\pi$
$104$	4.04923	0.397060
$105$	9.10872	0.888920
$106$	−15.5678	−1.51207
$107$	9.16976	0.886474	0.443237	−	0.896404i	$-0.353830\pi$
$107$	9.16976	0.886474	0.443237	+	0.896404i	$0.353830\pi$
$108$	16.5704	1.59449
$109$	9.83060	0.941600	0.470800	−	0.882240i	$-0.343965\pi$
$109$	9.83060	0.941600	0.470800	+	0.882240i	$0.343965\pi$
$110$	−13.7689	−1.31281
$111$	−11.4994	−1.09147
$112$	−7.89829	−0.746319
$113$	−0.698955	−0.0657521	−0.0328761	−	0.999459i	$-0.510467\pi$
$113$	−0.698955	−0.0657521	−0.0328761	+	0.999459i	$0.510467\pi$
$114$	−36.4167	−3.41074
$115$	−22.3453	−2.08371
$116$	3.76691	0.349749
$117$	−0.766448	−0.0708581
$118$	15.2157	1.40072
$119$	−10.5583	−0.967877
$120$	33.7712	3.08287
$121$	−7.71320	−0.701200
$122$	26.0025	2.35416
$123$	−0.980975	−0.0884515
$124$	15.1259	1.35835
$125$	−2.17547	−0.194580
$126$	3.86499	0.344321
$127$	12.5016	1.10934	0.554670	−	0.832071i	$-0.312845\pi$
$127$	12.5016	1.10934	0.554670	+	0.832071i	$0.312845\pi$
$128$	17.1386	1.51485
$129$	11.9394	1.05120
$130$	5.57980	0.489381
$131$	−2.29618	−0.200618	−0.100309	−	0.994956i	$-0.531983\pi$
$131$	−2.29618	−0.200618	−0.100309	+	0.994956i	$0.531983\pi$
$132$	−15.3525	−1.33626
$133$	10.8024	0.936683
$134$	−3.86382	−0.333784
$135$	11.9901	1.03194
$136$	−39.1456	−3.35671
$137$	19.3488	1.65308	0.826540	−	0.562878i	$-0.190306\pi$
$137$	19.3488	1.65308	0.826540	+	0.562878i	$0.190306\pi$
$138$	−36.7476	−3.12816
$139$	15.8109	1.34106	0.670532	−	0.741881i	$-0.266066\pi$
$139$	15.8109	1.34106	0.670532	+	0.741881i	$0.266066\pi$
$140$	−19.0775	−1.61234
$141$	−16.6778	−1.40452
$142$	39.5105	3.31565
$143$	−1.33197	−0.111385
$144$	5.54284	0.461903
$145$	2.72567	0.226355
$146$	−6.18813	−0.512133
$147$	9.63201	0.794435
$148$	24.0845	1.97974
$149$	−20.3051	−1.66346	−0.831728	−	0.555183i	$-0.812648\pi$
$149$	−20.3051	−1.66346	−0.831728	+	0.555183i	$0.812648\pi$
$150$	21.4794	1.75378
$151$	7.43802	0.605298	0.302649	−	0.953102i	$-0.402129\pi$
$151$	7.43802	0.605298	0.302649	+	0.953102i	$0.402129\pi$
$152$	40.0505	3.24852
$153$	7.40957	0.599028
$154$	6.71675	0.541251
$155$	10.9448	0.879111
$156$	6.22155	0.498123
$157$	0.278065	0.0221920	0.0110960	−	0.999938i	$-0.496468\pi$
$157$	0.278065	0.0221920	0.0110960	+	0.999938i	$0.496468\pi$
$158$	6.53046	0.519536
$159$	−12.5601	−0.996084
$160$	−6.76210	−0.534591
$161$	10.9005	0.859081
$162$	27.5180	2.16202
$163$	−12.6709	−0.992463	−0.496231	−	0.868190i	$-0.665283\pi$
$163$	−12.6709	−0.992463	−0.496231	+	0.868190i	$0.665283\pi$
$164$	2.05458	0.160436
$165$	−11.1088	−0.864819
$166$	8.77590	0.681142
$167$	−0.515837	−0.0399167	−0.0199583	−	0.999801i	$-0.506353\pi$
$167$	−0.515837	−0.0399167	−0.0199583	+	0.999801i	$0.506353\pi$
$168$	−16.4743	−1.27102
$169$	−12.4602	−0.958479
$170$	−53.9422	−4.13718
$171$	−7.58084	−0.579722
$172$	−25.0061	−1.90670
$173$	−14.5396	−1.10543	−0.552713	−	0.833372i	$-0.686407\pi$
$173$	−14.5396	−1.10543	−0.552713	+	0.833372i	$0.686407\pi$
$174$	4.48245	0.339814
$175$	−6.37146	−0.481637
$176$	9.63259	0.726084
$177$	12.2761	0.922727
$178$	33.4104	2.50421
$179$	−14.0619	−1.05103	−0.525517	−	0.850783i	$-0.676128\pi$
$179$	−14.0619	−1.05103	−0.525517	+	0.850783i	$0.676128\pi$
$180$	13.3882	0.997894
$181$	15.7429	1.17016	0.585079	−	0.810976i	$-0.301063\pi$
$181$	15.7429	1.17016	0.585079	+	0.810976i	$0.301063\pi$
$182$	−2.72194	−0.201764
$183$	20.9789	1.55081
$184$	40.4144	2.97939
$185$	17.4272	1.28127
$186$	17.9991	1.31976
$187$	12.8767	0.941635
$188$	34.9304	2.54756
$189$	−5.84901	−0.425453
$190$	55.1891	4.00384
$191$	9.92586	0.718210	0.359105	−	0.933297i	$-0.383082\pi$
$191$	9.92586	0.718210	0.359105	+	0.933297i	$0.383082\pi$
$192$	10.2468	0.739502
$193$	−3.93472	−0.283227	−0.141614	−	0.989922i	$-0.545229\pi$
$193$	−3.93472	−0.283227	−0.141614	+	0.989922i	$0.545229\pi$
$194$	−10.1980	−0.732173
$195$	4.50181	0.322381
$196$	−20.1735	−1.44097
$197$	1.85955	0.132487	0.0662437	−	0.997803i	$-0.478899\pi$
$197$	1.85955	0.132487	0.0662437	+	0.997803i	$0.478899\pi$
$198$	−4.71366	−0.334985
$199$	18.9615	1.34415	0.672073	−	0.740485i	$-0.265404\pi$
$199$	18.9615	1.34415	0.672073	+	0.740485i	$0.265404\pi$
$200$	−23.6226	−1.67037
$201$	−3.11735	−0.219881
$202$	−20.0682	−1.41199
$203$	−1.32964	−0.0933223
$204$	−60.1463	−4.21108
$205$	1.48666	0.103833
$206$	34.7272	2.41956
$207$	−7.64972	−0.531693
$208$	−3.90358	−0.270665
$209$	−13.1743	−0.911287
$210$	−22.7014	−1.56655
$211$	12.8299	0.883243	0.441622	−	0.897201i	$-0.354403\pi$
$211$	12.8299	0.883243	0.441622	+	0.897201i	$0.354403\pi$
$212$	26.3063	1.80672
$213$	31.8773	2.18419
$214$	−22.8535	−1.56223
$215$	−18.0940	−1.23400
$216$	−21.6856	−1.47552
$217$	−5.33912	−0.362443
$218$	−24.5005	−1.65938
$219$	−4.99261	−0.337369
$220$	23.2665	1.56863
$221$	−5.21824	−0.351016
$222$	28.6595	1.92350
$223$	−12.1613	−0.814384	−0.407192	−	0.913343i	$-0.633492\pi$
$223$	−12.1613	−0.814384	−0.407192	+	0.913343i	$0.633492\pi$
$224$	3.29869	0.220403
$225$	4.47135	0.298090
$226$	1.74198	0.115875
$227$	3.60780	0.239458	0.119729	−	0.992807i	$-0.461797\pi$
$227$	3.60780	0.239458	0.119729	+	0.992807i	$0.461797\pi$
$228$	61.5366	4.07536
$229$	−0.397109	−0.0262417	−0.0131209	−	0.999914i	$-0.504177\pi$
$229$	−0.397109	−0.0262417	−0.0131209	+	0.999914i	$0.504177\pi$
$230$	55.6906	3.67213
$231$	5.41910	0.356551
$232$	−4.92973	−0.323652
$233$	2.37248	0.155426	0.0777132	−	0.996976i	$-0.475238\pi$
$233$	2.37248	0.155426	0.0777132	+	0.996976i	$0.475238\pi$
$234$	1.91020	0.124873
$235$	25.2750	1.64876
$236$	−25.7113	−1.67367
$237$	5.26881	0.342246
$238$	26.3141	1.70569
$239$	−6.20313	−0.401247	−0.200624	−	0.979668i	$-0.564297\pi$
$239$	−6.20313	−0.401247	−0.200624	+	0.979668i	$0.564297\pi$
$240$	−32.5564	−2.10151
$241$	27.9970	1.80345	0.901724	−	0.432313i	$-0.142302\pi$
$241$	27.9970	1.80345	0.901724	+	0.432313i	$0.142302\pi$
$242$	19.2234	1.23573
$243$	10.3977	0.667016
$244$	−43.9388	−2.81289
$245$	−14.5972	−0.932582
$246$	2.44486	0.155878
$247$	5.33886	0.339703
$248$	−19.7952	−1.25699
$249$	7.08043	0.448704
$250$	5.42187	0.342909
$251$	−12.7734	−0.806252	−0.403126	−	0.915145i	$-0.632076\pi$
$251$	−12.7734	−0.806252	−0.403126	+	0.915145i	$0.632076\pi$
$252$	−6.53102	−0.411416
$253$	−13.2940	−0.835788
$254$	−31.1574	−1.95499
$255$	−43.5208	−2.72538
$256$	−32.5221	−2.03263
$257$	14.7897	0.922553	0.461277	−	0.887256i	$-0.347392\pi$
$257$	14.7897	0.922553	0.461277	+	0.887256i	$0.347392\pi$
$258$	−29.7561	−1.85254
$259$	−8.50133	−0.528247
$260$	−9.42870	−0.584743
$261$	0.933110	0.0577580
$262$	5.72269	0.353549
$263$	9.62545	0.593530	0.296765	−	0.954950i	$-0.404092\pi$
$263$	9.62545	0.593530	0.296765	+	0.954950i	$0.404092\pi$
$264$	20.0917	1.23656
$265$	19.0348	1.16930
$266$	−26.9224	−1.65072
$267$	26.9556	1.64966
$268$	6.52906	0.398826
$269$	−2.87302	−0.175171	−0.0875855	−	0.996157i	$-0.527915\pi$
$269$	−2.87302	−0.175171	−0.0875855	+	0.996157i	$0.527915\pi$
$270$	−29.8826	−1.81859
$271$	−13.2464	−0.804664	−0.402332	−	0.915494i	$-0.631800\pi$
$271$	−13.2464	−0.804664	−0.402332	+	0.915494i	$0.631800\pi$
$272$	37.7375	2.28817
$273$	−2.19608	−0.132913
$274$	−48.2225	−2.91323
$275$	7.77050	0.468579
$276$	62.0958	3.73773
$277$	−18.5693	−1.11572	−0.557862	−	0.829934i	$-0.688378\pi$
$277$	−18.5693	−1.11572	−0.557862	+	0.829934i	$0.688378\pi$
$278$	−39.4051	−2.36336
$279$	3.74687	0.224319
$280$	24.9666	1.49204
$281$	−7.62473	−0.454853	−0.227427	−	0.973795i	$-0.573031\pi$
$281$	−7.62473	−0.454853	−0.227427	+	0.973795i	$0.573031\pi$
$282$	41.5656	2.47520
$283$	−20.7301	−1.23227	−0.616137	−	0.787639i	$-0.711303\pi$
$283$	−20.7301	−1.23227	−0.616137	+	0.787639i	$0.711303\pi$
$284$	−66.7645	−3.96175
$285$	44.5268	2.63754
$286$	3.31962	0.196293
$287$	−0.725222	−0.0428085
$288$	−2.31494	−0.136409
$289$	33.4468	1.96746
$290$	−6.79311	−0.398905
$291$	−8.22778	−0.482321
$292$	10.4566	0.611929
$293$	−7.54055	−0.440524	−0.220262	−	0.975441i	$-0.570691\pi$
$293$	−7.54055	−0.440524	−0.220262	+	0.975441i	$0.570691\pi$
$294$	−24.0056	−1.40003
$295$	−18.6043	−1.08318
$296$	−31.5193	−1.83202
$297$	7.13333	0.413918
$298$	50.6057	2.93151
$299$	5.38737	0.311560
$300$	−36.2956	−2.09553
$301$	8.82662	0.508758
$302$	−18.5376	−1.06672
$303$	−16.1911	−0.930155
$304$	−38.6098	−2.21443
$305$	−31.7934	−1.82048
$306$	−18.4666	−1.05567
$307$	−11.6224	−0.663324	−0.331662	−	0.943398i	$-0.607609\pi$
$307$	−11.6224	−0.663324	−0.331662	+	0.943398i	$0.607609\pi$
$308$	−11.3499	−0.646720
$309$	28.0181	1.59389
$310$	−27.2775	−1.54926
$311$	−17.5002	−0.992347	−0.496174	−	0.868223i	$-0.665262\pi$
$311$	−17.5002	−0.992347	−0.496174	+	0.868223i	$0.665262\pi$
$312$	−8.14210	−0.460956
$313$	−19.3837	−1.09563	−0.547816	−	0.836599i	$-0.684541\pi$
$313$	−19.3837	−1.09563	−0.547816	+	0.836599i	$0.684541\pi$
$314$	−0.693013	−0.0391090
$315$	−4.72574	−0.266265
$316$	−11.0351	−0.620774
$317$	−31.1785	−1.75116	−0.875579	−	0.483075i	$-0.839520\pi$
$317$	−31.1785	−1.75116	−0.875579	+	0.483075i	$0.839520\pi$
$318$	31.3033	1.75540
$319$	1.62160	0.0907921
$320$	−15.5290	−0.868096
$321$	−18.4383	−1.02913
$322$	−27.1670	−1.51396
$323$	−51.6129	−2.87182
$324$	−46.4997	−2.58332
$325$	−3.14897	−0.174674
$326$	31.5794	1.74902
$327$	−19.7671	−1.09312
$328$	−2.68881	−0.148465
$329$	−12.3297	−0.679758
$330$	27.6861	1.52407
$331$	−7.32259	−0.402486	−0.201243	−	0.979541i	$-0.564498\pi$
$331$	−7.32259	−0.402486	−0.201243	+	0.979541i	$0.564498\pi$
$332$	−14.8294	−0.813871
$333$	5.96604	0.326937
$334$	1.28561	0.0703452
$335$	4.72431	0.258117
$336$	15.8817	0.866418
$337$	2.10284	0.114549	0.0572744	−	0.998358i	$-0.481759\pi$
$337$	2.10284	0.114549	0.0572744	+	0.998358i	$0.481759\pi$
$338$	31.0543	1.68913
$339$	1.40544	0.0763331
$340$	91.1511	4.94336
$341$	6.51147	0.352616
$342$	18.8935	1.02164
$343$	17.5266	0.946348
$344$	32.7253	1.76443
$345$	44.9314	2.41903
$346$	36.2366	1.94809
$347$	8.14453	0.437221	0.218611	−	0.975812i	$-0.429848\pi$
$347$	8.14453	0.437221	0.218611	+	0.975812i	$0.429848\pi$
$348$	−7.57441	−0.406031
$349$	26.2246	1.40377	0.701886	−	0.712289i	$-0.252341\pi$
$349$	26.2246	1.40377	0.701886	+	0.712289i	$0.252341\pi$
$350$	15.8794	0.848791
$351$	−2.89076	−0.154298
$352$	−4.02301	−0.214427
$353$	1.76259	0.0938135	0.0469067	−	0.998899i	$-0.485064\pi$
$353$	1.76259	0.0938135	0.0469067	+	0.998899i	$0.485064\pi$
$354$	−30.5953	−1.62612
$355$	−48.3097	−2.56401
$356$	−56.4565	−2.99219
$357$	21.2304	1.12363
$358$	35.0460	1.85224
$359$	−14.8849	−0.785595	−0.392797	−	0.919625i	$-0.628493\pi$
$359$	−14.8849	−0.785595	−0.392797	+	0.919625i	$0.628493\pi$
$360$	−17.5210	−0.923437
$361$	33.8060	1.77926
$362$	−39.2355	−2.06217
$363$	15.5095	0.814039
$364$	4.59951	0.241080
$365$	7.56625	0.396036
$366$	−52.2852	−2.73299
$367$	−13.5553	−0.707579	−0.353789	−	0.935325i	$-0.615107\pi$
$367$	−13.5553	−0.707579	−0.353789	+	0.935325i	$0.615107\pi$
$368$	−38.9607	−2.03096
$369$	0.508944	0.0264946
$370$	−43.4332	−2.25799
$371$	−9.28555	−0.482082
$372$	−30.4148	−1.57693
$373$	−1.10446	−0.0571869	−0.0285934	−	0.999591i	$-0.509103\pi$
$373$	−1.10446	−0.0571869	−0.0285934	+	0.999591i	$0.509103\pi$
$374$	−32.0921	−1.65945
$375$	4.37439	0.225893
$376$	−45.7132	−2.35748
$377$	−0.657149	−0.0338449
$378$	14.5773	0.749777
$379$	12.7896	0.656959	0.328479	−	0.944511i	$-0.393464\pi$
$379$	12.7896	0.656959	0.328479	+	0.944511i	$0.393464\pi$
$380$	−93.2581	−4.78404
$381$	−25.1380	−1.28786
$382$	−24.7379	−1.26570
$383$	15.8206	0.808397	0.404198	−	0.914671i	$-0.367551\pi$
$383$	15.8206	0.808397	0.404198	+	0.914671i	$0.367551\pi$
$384$	−34.4619	−1.75862
$385$	−8.21259	−0.418552
$386$	9.80640	0.499132
$387$	−6.19431	−0.314875
$388$	17.2325	0.874846
$389$	−19.8797	−1.00794	−0.503971	−	0.863721i	$-0.668128\pi$
$389$	−19.8797	−1.00794	−0.503971	+	0.863721i	$0.668128\pi$
$390$	−11.2197	−0.568133
$391$	−52.0819	−2.63389
$392$	26.4009	1.33345
$393$	4.61710	0.232902
$394$	−4.63450	−0.233483
$395$	−7.98482	−0.401760
$396$	7.96509	0.400261
$397$	−35.5478	−1.78409	−0.892046	−	0.451945i	$-0.850730\pi$
$397$	−35.5478	−1.78409	−0.892046	+	0.451945i	$0.850730\pi$
$398$	−47.2572	−2.36879
$399$	−21.7211	−1.08742
$400$	22.7729	1.13865
$401$	−9.54487	−0.476648	−0.238324	−	0.971186i	$-0.576598\pi$
$401$	−9.54487	−0.476648	−0.238324	+	0.971186i	$0.576598\pi$
$402$	7.76929	0.387497
$403$	−2.63876	−0.131446
$404$	33.9111	1.68714
$405$	−33.6464	−1.67190
$406$	3.31382	0.164462
$407$	10.3680	0.513925
$408$	78.7130	3.89688
$409$	3.91223	0.193447	0.0967236	−	0.995311i	$-0.469164\pi$
$409$	3.91223	0.193447	0.0967236	+	0.995311i	$0.469164\pi$
$410$	−3.70515	−0.182984
$411$	−38.9061	−1.91910
$412$	−58.6817	−2.89104
$413$	9.07556	0.446579
$414$	19.0652	0.937003
$415$	−10.7303	−0.526731
$416$	1.63032	0.0799328
$417$	−31.7922	−1.55687
$418$	32.8340	1.60596
$419$	19.7545	0.965071	0.482536	−	0.875876i	$-0.339716\pi$
$419$	19.7545	0.965071	0.482536	+	0.875876i	$0.339716\pi$
$420$	38.3606	1.87181
$421$	26.6962	1.30109	0.650547	−	0.759466i	$-0.274540\pi$
$421$	26.6962	1.30109	0.650547	+	0.759466i	$0.274540\pi$
$422$	−31.9755	−1.55654
$423$	8.65269	0.420708
$424$	−34.4268	−1.67191
$425$	30.4424	1.47667
$426$	−79.4468	−3.84921
$427$	15.5095	0.750556
$428$	38.6177	1.86666
$429$	2.67829	0.129309
$430$	45.0951	2.17468
$431$	−5.57555	−0.268565	−0.134282	−	0.990943i	$-0.542873\pi$
$431$	−5.57555	−0.268565	−0.134282	+	0.990943i	$0.542873\pi$
$432$	20.9056	1.00582
$433$	−36.9350	−1.77498	−0.887490	−	0.460826i	$-0.847553\pi$
$433$	−36.9350	−1.77498	−0.887490	+	0.460826i	$0.847553\pi$
$434$	13.3065	0.638734
$435$	−5.48071	−0.262780
$436$	41.4007	1.98274
$437$	53.2858	2.54901
$438$	12.4429	0.594547
$439$	−16.8592	−0.804645	−0.402322	−	0.915498i	$-0.631797\pi$
$439$	−16.8592	−0.804645	−0.402322	+	0.915498i	$0.631797\pi$
$440$	−30.4487	−1.45159
$441$	−4.99723	−0.237963
$442$	13.0053	0.618597
$443$	−32.8414	−1.56034	−0.780171	−	0.625566i	$-0.784868\pi$
$443$	−32.8414	−1.56034	−0.780171	+	0.625566i	$0.784868\pi$
$444$	−48.4286	−2.29832
$445$	−40.8510	−1.93652
$446$	30.3094	1.43519
$447$	40.8289	1.93114
$448$	7.57535	0.357902
$449$	−33.4724	−1.57966	−0.789830	−	0.613326i	$-0.789831\pi$
$449$	−33.4724	−1.57966	−0.789830	+	0.613326i	$0.789831\pi$
$450$	−11.1438	−0.525324
$451$	0.884465	0.0416478
$452$	−2.94359	−0.138455
$453$	−14.9562	−0.702703
$454$	−8.99162	−0.421997
$455$	3.32813	0.156025
$456$	−80.5325	−3.77128
$457$	−1.45656	−0.0681349	−0.0340674	−	0.999420i	$-0.510846\pi$
$457$	−1.45656	−0.0681349	−0.0340674	+	0.999420i	$0.510846\pi$
$458$	0.989704	0.0462458
$459$	27.9462	1.30442
$460$	−94.1055	−4.38769
$461$	−28.8383	−1.34313	−0.671566	−	0.740945i	$-0.734378\pi$
$461$	−28.8383	−1.34313	−0.671566	+	0.740945i	$0.734378\pi$
$462$	−13.5059	−0.628350
$463$	1.65131	0.0767427	0.0383713	−	0.999264i	$-0.487783\pi$
$463$	1.65131	0.0767427	0.0383713	+	0.999264i	$0.487783\pi$
$464$	4.75240	0.220625
$465$	−22.0076	−1.02058
$466$	−5.91287	−0.273908
$467$	−11.1947	−0.518028	−0.259014	−	0.965874i	$-0.583398\pi$
$467$	−11.1947	−0.518028	−0.259014	+	0.965874i	$0.583398\pi$
$468$	−3.22783	−0.149207
$469$	−2.30462	−0.106417
$470$	−62.9923	−2.90562
$471$	−0.559126	−0.0257632
$472$	33.6482	1.54879
$473$	−10.7648	−0.494964
$474$	−13.1313	−0.603140
$475$	−31.1461	−1.42908
$476$	−44.4654	−2.03807
$477$	6.51638	0.298365
$478$	15.4599	0.707119
$479$	−19.9607	−0.912027	−0.456013	−	0.889973i	$-0.650723\pi$
$479$	−19.9607	−0.912027	−0.456013	+	0.889973i	$0.650723\pi$
$480$	13.5971	0.620618
$481$	−4.20162	−0.191577
$482$	−69.7762	−3.17822
$483$	−21.9185	−0.997326
$484$	−32.4835	−1.47652
$485$	12.4691	0.566193
$486$	−25.9140	−1.17548
$487$	−23.2666	−1.05431	−0.527155	−	0.849769i	$-0.676741\pi$
$487$	−23.2666	−1.05431	−0.527155	+	0.849769i	$0.676741\pi$
$488$	57.5024	2.60301
$489$	25.4784	1.15217
$490$	36.3802	1.64349
$491$	11.4382	0.516197	0.258099	−	0.966119i	$-0.416904\pi$
$491$	11.4382	0.516197	0.258099	+	0.966119i	$0.416904\pi$
$492$	−4.13129	−0.186253
$493$	6.35292	0.286121
$494$	−13.3059	−0.598660
$495$	5.76341	0.259046
$496$	19.0831	0.856857
$497$	23.5665	1.05710
$498$	−17.6464	−0.790752
$499$	36.0134	1.61218	0.806090	−	0.591793i	$-0.201580\pi$
$499$	36.0134	1.61218	0.806090	+	0.591793i	$0.201580\pi$
$500$	−9.16183	−0.409730
$501$	1.03723	0.0463401
$502$	31.8349	1.42086
$503$	−22.1046	−0.985597	−0.492798	−	0.870144i	$-0.664026\pi$
$503$	−22.1046	−0.985597	−0.492798	+	0.870144i	$0.664026\pi$
$504$	8.54710	0.380718
$505$	24.5375	1.09190
$506$	33.1323	1.47291
$507$	25.0547	1.11272
$508$	52.6496	2.33595
$509$	−10.1137	−0.448282	−0.224141	−	0.974557i	$-0.571958\pi$
$509$	−10.1137	−0.448282	−0.224141	+	0.974557i	$0.571958\pi$
$510$	108.466	4.80294
$511$	−3.69097	−0.163279
$512$	46.7767	2.06726
$513$	−28.5922	−1.26238
$514$	−36.8598	−1.62582
$515$	−42.4611	−1.87106
$516$	50.2816	2.21353
$517$	15.0370	0.661328
$518$	21.1876	0.930931
$519$	29.2359	1.28331
$520$	12.3393	0.541113
$521$	−8.77705	−0.384530	−0.192265	−	0.981343i	$-0.561583\pi$
$521$	−8.77705	−0.384530	−0.192265	+	0.981343i	$0.561583\pi$
$522$	−2.32556	−0.101787
$523$	0.378503	0.0165508	0.00827540	−	0.999966i	$-0.497366\pi$
$523$	0.378503	0.0165508	0.00827540	+	0.999966i	$0.497366\pi$
$524$	−9.67016	−0.422443
$525$	12.8116	0.559143
$526$	−23.9892	−1.04598
$527$	25.5099	1.11123
$528$	−19.3690	−0.842927
$529$	30.7700	1.33783
$530$	−47.4398	−2.06065
$531$	−6.36901	−0.276392
$532$	45.4932	1.97238
$533$	−0.358427	−0.0155252
$534$	−67.1808	−2.90720
$535$	27.9431	1.20809
$536$	−8.54453	−0.369067
$537$	28.2753	1.22017
$538$	7.16034	0.308704
$539$	−8.68440	−0.374064
$540$	50.4953	2.17297
$541$	24.0453	1.03379	0.516894	−	0.856049i	$-0.327088\pi$
$541$	24.0453	1.03379	0.516894	+	0.856049i	$0.327088\pi$
$542$	33.0137	1.41806
$543$	−31.6554	−1.35846
$544$	−15.7609	−0.675744
$545$	29.9569	1.28321
$546$	5.47322	0.234232
$547$	15.3017	0.654254	0.327127	−	0.944980i	$-0.393920\pi$
$547$	15.3017	0.654254	0.327127	+	0.944980i	$0.393920\pi$
$548$	81.4859	3.48091
$549$	−10.8842	−0.464526
$550$	−19.3662	−0.825777
$551$	−6.49978	−0.276900
$552$	−81.2643	−3.45884
$553$	3.89516	0.165639
$554$	46.2798	1.96624
$555$	−35.0421	−1.48746
$556$	66.5863	2.82389
$557$	−44.3719	−1.88010	−0.940048	−	0.341043i	$-0.889220\pi$
$557$	−44.3719	−1.88010	−0.940048	+	0.341043i	$0.889220\pi$
$558$	−9.33822	−0.395318
$559$	4.36239	0.184509
$560$	−24.0686	−1.01708
$561$	−25.8921	−1.09316
$562$	19.0029	0.801589
$563$	45.9532	1.93669	0.968347	−	0.249606i	$-0.0803013\pi$
$563$	45.9532	1.93669	0.968347	+	0.249606i	$0.0803013\pi$
$564$	−70.2372	−2.95752
$565$	−2.12993	−0.0896069
$566$	51.6649	2.17164
$567$	16.4134	0.689299
$568$	87.3743	3.66614
$569$	15.6044	0.654171	0.327086	−	0.944995i	$-0.393933\pi$
$569$	15.6044	0.654171	0.327086	+	0.944995i	$0.393933\pi$
$570$	−110.973	−4.64815
$571$	−23.1792	−0.970020	−0.485010	−	0.874509i	$-0.661184\pi$
$571$	−23.1792	−0.970020	−0.485010	+	0.874509i	$0.661184\pi$
$572$	−5.60947	−0.234544
$573$	−19.9587	−0.833786
$574$	1.80745	0.0754415
$575$	−31.4291	−1.31068
$576$	−5.31621	−0.221509
$577$	5.25001	0.218561	0.109280	−	0.994011i	$-0.465145\pi$
$577$	5.25001	0.218561	0.109280	+	0.994011i	$0.465145\pi$
$578$	−83.3585	−3.46726
$579$	7.91184	0.328805
$580$	11.4789	0.476637
$581$	5.23447	0.217163
$582$	20.5059	0.849995
$583$	11.3245	0.469011
$584$	−13.6845	−0.566270
$585$	−2.33561	−0.0965654
$586$	18.7931	0.776336
$587$	−19.2267	−0.793572	−0.396786	−	0.917911i	$-0.629874\pi$
$587$	−19.2267	−0.793572	−0.396786	+	0.917911i	$0.629874\pi$
$588$	40.5644	1.67285
$589$	−26.0996	−1.07542
$590$	46.3669	1.90890
$591$	−3.73914	−0.153807
$592$	30.3855	1.24884
$593$	20.7962	0.853997	0.426999	−	0.904252i	$-0.359571\pi$
$593$	20.7962	0.853997	0.426999	+	0.904252i	$0.359571\pi$
$594$	−17.7782	−0.729448
$595$	−32.1744	−1.31902
$596$	−85.5131	−3.50275
$597$	−38.1273	−1.56045
$598$	−13.4268	−0.549062
$599$	6.37206	0.260355	0.130178	−	0.991491i	$-0.458445\pi$
$599$	6.37206	0.260355	0.130178	+	0.991491i	$0.458445\pi$
$600$	47.4998	1.93917
$601$	−21.3356	−0.870298	−0.435149	−	0.900358i	$-0.643304\pi$
$601$	−21.3356	−0.870298	−0.435149	+	0.900358i	$0.643304\pi$
$602$	−21.9983	−0.896585
$603$	1.61733	0.0658627
$604$	31.3246	1.27458
$605$	−23.5045	−0.955594
$606$	40.3526	1.63921
$607$	−8.37527	−0.339942	−0.169971	−	0.985449i	$-0.554367\pi$
$607$	−8.37527	−0.339942	−0.169971	+	0.985449i	$0.554367\pi$
$608$	16.1252	0.653965
$609$	2.67361	0.108340
$610$	79.2377	3.20824
$611$	−6.09371	−0.246525
$612$	31.2048	1.26138
$613$	−25.7291	−1.03919	−0.519594	−	0.854414i	$-0.673917\pi$
$613$	−25.7291	−1.03919	−0.519594	+	0.854414i	$0.673917\pi$
$614$	28.9661	1.16898
$615$	−2.98933	−0.120542
$616$	14.8535	0.598466
$617$	−24.0046	−0.966387	−0.483194	−	0.875513i	$-0.660523\pi$
$617$	−24.0046	−0.966387	−0.483194	+	0.875513i	$0.660523\pi$
$618$	−69.8286	−2.80892
$619$	−20.7203	−0.832821	−0.416411	−	0.909177i	$-0.636712\pi$
$619$	−20.7203	−0.832821	−0.416411	+	0.909177i	$0.636712\pi$
$620$	46.0933	1.85115
$621$	−28.8520	−1.15779
$622$	43.6153	1.74882
$623$	19.9280	0.798397
$624$	7.84923	0.314221
$625$	−28.0598	−1.12239
$626$	48.3095	1.93084
$627$	26.4906	1.05793
$628$	1.17105	0.0467299
$629$	40.6188	1.61958
$630$	11.7778	0.469239
$631$	30.7767	1.22520	0.612601	−	0.790392i	$-0.290123\pi$
$631$	30.7767	1.22520	0.612601	+	0.790392i	$0.290123\pi$
$632$	14.4416	0.574455
$633$	−25.7980	−1.02538
$634$	77.7053	3.08607
$635$	38.0963	1.51181
$636$	−52.8960	−2.09746
$637$	3.51933	0.139441
$638$	−4.04146	−0.160003
$639$	−16.5384	−0.654249
$640$	52.2266	2.06444
$641$	−34.9482	−1.38037	−0.690186	−	0.723632i	$-0.742471\pi$
$641$	−34.9482	−1.38037	−0.690186	+	0.723632i	$0.742471\pi$
$642$	45.9533	1.81363
$643$	−24.1299	−0.951589	−0.475795	−	0.879556i	$-0.657839\pi$
$643$	−24.1299	−0.951589	−0.475795	+	0.879556i	$0.657839\pi$
$644$	45.9066	1.80897
$645$	36.3829	1.43258
$646$	128.633	5.06101
$647$	−38.9842	−1.53263	−0.766314	−	0.642467i	$-0.777911\pi$
$647$	−38.9842	−1.53263	−0.766314	+	0.642467i	$0.777911\pi$
$648$	60.8539	2.39057
$649$	−11.0684	−0.434471
$650$	7.84810	0.307828
$651$	10.7358	0.420768
$652$	−53.3625	−2.08984
$653$	27.0495	1.05853	0.529264	−	0.848457i	$-0.322468\pi$
$653$	27.0495	1.05853	0.529264	+	0.848457i	$0.322468\pi$
$654$	49.2651	1.92642
$655$	−6.99716	−0.273402
$656$	2.59209	0.101204
$657$	2.59024	0.101055
$658$	30.7289	1.19794
$659$	46.4477	1.80935	0.904674	−	0.426105i	$-0.140115\pi$
$659$	46.4477	1.80935	0.904674	+	0.426105i	$0.140115\pi$
$660$	−46.7838	−1.82106
$661$	15.3565	0.597298	0.298649	−	0.954363i	$-0.403464\pi$
$661$	15.3565	0.597298	0.298649	+	0.954363i	$0.403464\pi$
$662$	18.2499	0.709302
$663$	10.4927	0.407503
$664$	19.4072	0.753144
$665$	32.9181	1.27651
$666$	−14.8690	−0.576161
$667$	−6.55883	−0.253959
$668$	−2.17241	−0.0840529
$669$	24.4537	0.945436
$670$	−11.7743	−0.454880
$671$	−18.9150	−0.730206
$672$	−6.63293	−0.255871
$673$	22.1275	0.852952	0.426476	−	0.904499i	$-0.359755\pi$
$673$	22.1275	0.852952	0.426476	+	0.904499i	$0.359755\pi$
$674$	−5.24084	−0.201870
$675$	16.8643	0.649107
$676$	−52.4752	−2.01828
$677$	45.0914	1.73300	0.866501	−	0.499175i	$-0.166363\pi$
$677$	45.0914	1.73300	0.866501	+	0.499175i	$0.166363\pi$
$678$	−3.50274	−0.134522
$679$	−6.08269	−0.233432
$680$	−119.289	−4.57452
$681$	−7.25448	−0.277992
$682$	−16.2284	−0.621416
$683$	6.70640	0.256613	0.128307	−	0.991735i	$-0.459046\pi$
$683$	6.70640	0.256613	0.128307	+	0.991735i	$0.459046\pi$
$684$	−31.9261	−1.22072
$685$	58.9618	2.25282
$686$	−43.6811	−1.66775
$687$	0.798497	0.0304646
$688$	−31.5481	−1.20276
$689$	−4.58921	−0.174835
$690$	−111.981	−4.26306
$691$	−14.2057	−0.540409	−0.270205	−	0.962803i	$-0.587091\pi$
$691$	−14.2057	−0.540409	−0.270205	+	0.962803i	$0.587091\pi$
$692$	−61.2323	−2.32770
$693$	−2.81151	−0.106800
$694$	−20.2984	−0.770516
$695$	48.1807	1.82760
$696$	9.91258	0.375735
$697$	3.46506	0.131249
$698$	−65.3589	−2.47387
$699$	−4.77053	−0.180438
$700$	−26.8329	−1.01419
$701$	−15.2076	−0.574382	−0.287191	−	0.957873i	$-0.592722\pi$
$701$	−15.2076	−0.574382	−0.287191	+	0.957873i	$0.592722\pi$
$702$	7.20457	0.271919
$703$	−41.5577	−1.56738
$704$	−9.23874	−0.348198
$705$	−50.8225	−1.91408
$706$	−4.39286	−0.165328
$707$	−11.9699	−0.450174
$708$	51.6997	1.94300
$709$	−40.2206	−1.51052	−0.755258	−	0.655428i	$-0.772488\pi$
$709$	−40.2206	−1.51052	−0.755258	+	0.655428i	$0.772488\pi$
$710$	120.401	4.51856
$711$	−2.73353	−0.102516
$712$	73.8843	2.76893
$713$	−26.3368	−0.986320
$714$	−52.9118	−1.98018
$715$	−4.05892	−0.151795
$716$	−59.2204	−2.21317
$717$	12.4731	0.465817
$718$	37.0972	1.38446
$719$	−13.0822	−0.487885	−0.243943	−	0.969790i	$-0.578441\pi$
$719$	−13.0822	−0.487885	−0.243943	+	0.969790i	$0.578441\pi$
$720$	16.8908	0.629481
$721$	20.7134	0.771407
$722$	−84.2537	−3.13560
$723$	−56.2958	−2.09366
$724$	66.2998	2.46401
$725$	3.83371	0.142380
$726$	−38.6539	−1.43458
$727$	52.3050	1.93988	0.969942	−	0.243337i	$-0.0782422\pi$
$727$	52.3050	1.93988	0.969942	+	0.243337i	$0.0782422\pi$
$728$	−6.01935	−0.223092
$729$	12.2165	0.452464
$730$	−18.8571	−0.697934
$731$	−42.1730	−1.55982
$732$	88.3511	3.26555
$733$	36.8407	1.36074	0.680371	−	0.732867i	$-0.261818\pi$
$733$	36.8407	1.36074	0.680371	+	0.732867i	$0.261818\pi$
$734$	33.7834	1.24697
$735$	29.3517	1.08265
$736$	16.2718	0.599785
$737$	2.81066	0.103532
$738$	−1.26843	−0.0466914
$739$	−19.2840	−0.709374	−0.354687	−	0.934985i	$-0.615413\pi$
$739$	−19.2840	−0.709374	−0.354687	+	0.934985i	$0.615413\pi$
$740$	73.3931	2.69798
$741$	−10.7352	−0.394369
$742$	23.1421	0.849574
$743$	44.5137	1.63305	0.816525	−	0.577311i	$-0.195898\pi$
$743$	44.5137	1.63305	0.816525	+	0.577311i	$0.195898\pi$
$744$	39.8036	1.45927
$745$	−61.8758	−2.26696
$746$	2.75262	0.100781
$747$	−3.67343	−0.134404
$748$	54.2290	1.98281
$749$	−13.6312	−0.498074
$750$	−10.9022	−0.398091
$751$	52.6786	1.92227	0.961134	−	0.276082i	$-0.0890363\pi$
$751$	52.6786	1.92227	0.961134	+	0.276082i	$0.0890363\pi$
$752$	44.0688	1.60703
$753$	25.6845	0.935995
$754$	1.63779	0.0596449
$755$	22.6660	0.824899
$756$	−24.6326	−0.895880
$757$	−5.41857	−0.196941	−0.0984706	−	0.995140i	$-0.531395\pi$
$757$	−5.41857	−0.196941	−0.0984706	+	0.995140i	$0.531395\pi$
$758$	−31.8752	−1.15776
$759$	26.7313	0.970285
$760$	122.046	4.42708
$761$	−28.3297	−1.02695	−0.513476	−	0.858104i	$-0.671643\pi$
$761$	−28.3297	−1.02695	−0.513476	+	0.858104i	$0.671643\pi$
$762$	62.6506	2.26959
$763$	−14.6136	−0.529047
$764$	41.8019	1.51234
$765$	22.5792	0.816354
$766$	−39.4293	−1.42464
$767$	4.48542	0.161959
$768$	65.3947	2.35973
$769$	−26.6659	−0.961598	−0.480799	−	0.876831i	$-0.659653\pi$
$769$	−26.6659	−0.961598	−0.480799	+	0.876831i	$0.659653\pi$
$770$	20.4680	0.737616
$771$	−29.7387	−1.07101
$772$	−16.5708	−0.596395
$773$	−11.3726	−0.409045	−0.204523	−	0.978862i	$-0.565564\pi$
$773$	−11.3726	−0.409045	−0.204523	+	0.978862i	$0.565564\pi$
$774$	15.4379	0.554904
$775$	15.3941	0.552973
$776$	−22.5520	−0.809570
$777$	17.0943	0.613254
$778$	49.5456	1.77630
$779$	−3.54516	−0.127018
$780$	18.9590	0.678841
$781$	−28.7411	−1.02844
$782$	129.802	4.64172
$783$	3.51935	0.125771
$784$	−25.4513	−0.908974
$785$	0.847350	0.0302432
$786$	−11.5071	−0.410443
$787$	−42.0610	−1.49931	−0.749656	−	0.661828i	$-0.769781\pi$
$787$	−42.0610	−1.49931	−0.749656	+	0.661828i	$0.769781\pi$
$788$	7.83133	0.278980
$789$	−19.3546	−0.689043
$790$	19.9003	0.708022
$791$	1.03902	0.0369435
$792$	−10.4239	−0.370396
$793$	7.66526	0.272201
$794$	88.5947	3.14411
$795$	−38.2746	−1.35746
$796$	79.8548	2.83038
$797$	−36.8507	−1.30532	−0.652659	−	0.757652i	$-0.726347\pi$
$797$	−36.8507	−1.30532	−0.652659	+	0.757652i	$0.726347\pi$
$798$	54.1349	1.91636
$799$	58.9104	2.08410
$800$	−9.51102	−0.336265
$801$	−13.9850	−0.494135
$802$	23.7884	0.839997
$803$	4.50143	0.158852
$804$	−13.1285	−0.463005
$805$	33.2172	1.17075
$806$	6.57650	0.231647
$807$	5.77700	0.203360
$808$	−44.3792	−1.56125
$809$	−31.1210	−1.09416	−0.547078	−	0.837081i	$-0.684260\pi$
$809$	−31.1210	−1.09416	−0.547078	+	0.837081i	$0.684260\pi$
$810$	83.8560	2.94640
$811$	−12.3799	−0.434717	−0.217359	−	0.976092i	$-0.569744\pi$
$811$	−12.3799	−0.434717	−0.217359	+	0.976092i	$0.569744\pi$
$812$	−5.59966	−0.196510
$813$	26.6356	0.934153
$814$	−25.8400	−0.905690
$815$	−38.6122	−1.35253
$816$	−75.8817	−2.65639
$817$	43.1478	1.50955
$818$	−9.75033	−0.340912
$819$	1.13936	0.0398123
$820$	6.26093	0.218641
$821$	−38.7074	−1.35090	−0.675449	−	0.737407i	$-0.736050\pi$
$821$	−38.7074	−1.35090	−0.675449	+	0.737407i	$0.736050\pi$
$822$	96.9646	3.38203
$823$	3.21963	0.112229	0.0561146	−	0.998424i	$-0.482129\pi$
$823$	3.21963	0.112229	0.0561146	+	0.998424i	$0.482129\pi$
$824$	76.7964	2.67533
$825$	−15.6247	−0.543983
$826$	−22.6187	−0.787007
$827$	−40.6278	−1.41277	−0.706383	−	0.707829i	$-0.749675\pi$
$827$	−40.6278	−1.41277	−0.706383	+	0.707829i	$0.749675\pi$
$828$	−32.2162	−1.11959
$829$	−49.0885	−1.70491	−0.852457	−	0.522797i	$-0.824889\pi$
$829$	−49.0885	−1.70491	−0.852457	+	0.522797i	$0.824889\pi$
$830$	26.7429	0.928259
$831$	37.3388	1.29527
$832$	3.74397	0.129799
$833$	−34.0228	−1.17882
$834$	79.2348	2.74368
$835$	−1.57192	−0.0543984
$836$	−55.4826	−1.91890
$837$	14.1318	0.488468
$838$	−49.2336	−1.70075
$839$	−33.8274	−1.16785	−0.583925	−	0.811807i	$-0.698484\pi$
$839$	−33.8274	−1.16785	−0.583925	+	0.811807i	$0.698484\pi$
$840$	−50.2023	−1.73214
$841$	−28.2000	−0.972412
$842$	−66.5342	−2.29292
$843$	15.3316	0.528049
$844$	54.0319	1.85985
$845$	−37.9702	−1.30621
$846$	−21.5649	−0.741415
$847$	11.4660	0.393976
$848$	33.1885	1.13970
$849$	41.6835	1.43057
$850$	−75.8708	−2.60235
$851$	−41.9353	−1.43752
$852$	134.249	4.59928
$853$	18.6848	0.639754	0.319877	−	0.947459i	$-0.396358\pi$
$853$	18.6848	0.639754	0.319877	+	0.947459i	$0.396358\pi$
$854$	−38.6538	−1.32271
$855$	−23.1012	−0.790044
$856$	−50.5387	−1.72738
$857$	41.1963	1.40724	0.703620	−	0.710577i	$-0.251566\pi$
$857$	41.1963	1.40724	0.703620	+	0.710577i	$0.251566\pi$
$858$	−6.67502	−0.227881
$859$	25.7853	0.879783	0.439892	−	0.898051i	$-0.355017\pi$
$859$	25.7853	0.879783	0.439892	+	0.898051i	$0.355017\pi$
$860$	−76.2013	−2.59844
$861$	1.45826	0.0496973
$862$	13.8958	0.473292
$863$	26.3058	0.895461	0.447731	−	0.894169i	$-0.352232\pi$
$863$	26.3058	0.895461	0.447731	+	0.894169i	$0.352232\pi$
$864$	−8.73113	−0.297039
$865$	−44.3067	−1.50647
$866$	92.0519	3.12805
$867$	−67.2540	−2.28407
$868$	−22.4853	−0.763199
$869$	−4.75045	−0.161148
$870$	13.6594	0.463098
$871$	−1.13901	−0.0385940
$872$	−54.1809	−1.83480
$873$	4.26869	0.144473
$874$	−132.803	−4.49212
$875$	3.23393	0.109327
$876$	−21.0260	−0.710401
$877$	34.1517	1.15322	0.576610	−	0.817020i	$-0.304375\pi$
$877$	34.1517	1.15322	0.576610	+	0.817020i	$0.304375\pi$
$878$	42.0177	1.41803
$879$	15.1624	0.511414
$880$	29.3535	0.989506
$881$	−29.6422	−0.998670	−0.499335	−	0.866409i	$-0.666422\pi$
$881$	−29.6422	−0.998670	−0.499335	+	0.866409i	$0.666422\pi$
$882$	12.4544	0.419363
$883$	5.95819	0.200509	0.100255	−	0.994962i	$-0.468034\pi$
$883$	5.95819	0.200509	0.100255	+	0.994962i	$0.468034\pi$
$884$	−21.9762	−0.739139
$885$	37.4091	1.25749
$886$	81.8497	2.74979
$887$	−39.9739	−1.34219	−0.671096	−	0.741371i	$-0.734176\pi$
$887$	−39.9739	−1.34219	−0.671096	+	0.741371i	$0.734176\pi$
$888$	63.3782	2.12683
$889$	−18.5842	−0.623293
$890$	101.812	3.41274
$891$	−20.0175	−0.670610
$892$	−51.2165	−1.71486
$893$	−60.2722	−2.01693
$894$	−101.757	−3.40326
$895$	−42.8509	−1.43235
$896$	−25.4772	−0.851134
$897$	−10.8328	−0.361696
$898$	83.4223	2.78384
$899$	3.21255	0.107144
$900$	18.8307	0.627690
$901$	44.3657	1.47804
$902$	−2.20433	−0.0733961
$903$	−17.7483	−0.590628
$904$	3.85226	0.128124
$905$	47.9734	1.59469
$906$	37.2749	1.23838
$907$	−17.9986	−0.597635	−0.298818	−	0.954310i	$-0.596592\pi$
$907$	−17.9986	−0.597635	−0.298818	+	0.954310i	$0.596592\pi$
$908$	15.1939	0.504229
$909$	8.40019	0.278617
$910$	−8.29461	−0.274964
$911$	−42.8797	−1.42067	−0.710335	−	0.703864i	$-0.751456\pi$
$911$	−42.8797	−1.42067	−0.710335	+	0.703864i	$0.751456\pi$
$912$	77.6357	2.57078
$913$	−6.38385	−0.211275
$914$	3.63014	0.120074
$915$	63.9294	2.11344
$916$	−1.67239	−0.0552574
$917$	3.41336	0.112719
$918$	−69.6495	−2.29878
$919$	−30.7738	−1.01513	−0.507566	−	0.861613i	$-0.669455\pi$
$919$	−30.7738	−1.01513	−0.507566	+	0.861613i	$0.669455\pi$
$920$	123.155	4.06031
$921$	23.3700	0.770068
$922$	71.8728	2.36700
$923$	11.6473	0.383375
$924$	22.8221	0.750792
$925$	24.5116	0.805938
$926$	−4.11550	−0.135244
$927$	−14.5362	−0.477431
$928$	−1.98482	−0.0651550
$929$	42.3287	1.38876	0.694380	−	0.719609i	$-0.255679\pi$
$929$	42.3287	1.38876	0.694380	+	0.719609i	$0.255679\pi$
$930$	54.8490	1.79857
$931$	34.8093	1.14083
$932$	9.99151	0.327283
$933$	35.1891	1.15204
$934$	27.9002	0.912922
$935$	39.2392	1.28326
$936$	4.22424	0.138074
$937$	−35.4622	−1.15850	−0.579250	−	0.815150i	$-0.696655\pi$
$937$	−35.4622	−1.15850	−0.579250	+	0.815150i	$0.696655\pi$
$938$	5.74373	0.187540
$939$	38.9763	1.27194
$940$	106.444	3.47181
$941$	29.9952	0.977816	0.488908	−	0.872335i	$-0.337395\pi$
$941$	29.9952	0.977816	0.488908	+	0.872335i	$0.337395\pi$
$942$	1.39349	0.0454025
$943$	−3.57737	−0.116495
$944$	−32.4379	−1.05576
$945$	−17.8238	−0.579807
$946$	26.8287	0.872276
$947$	−47.5511	−1.54520	−0.772601	−	0.634892i	$-0.781045\pi$
$947$	−47.5511	−1.54520	−0.772601	+	0.634892i	$0.781045\pi$
$948$	22.1891	0.720670
$949$	−1.82419	−0.0592158
$950$	77.6246	2.51847
$951$	62.6930	2.03296
$952$	58.1915	1.88600
$953$	−10.7101	−0.346935	−0.173468	−	0.984840i	$-0.555497\pi$
$953$	−10.7101	−0.346935	−0.173468	+	0.984840i	$0.555497\pi$
$954$	−16.2406	−0.525809
$955$	30.2472	0.978776
$956$	−26.1240	−0.844910
$957$	−3.26067	−0.105403
$958$	49.7474	1.60727
$959$	−28.7628	−0.928799
$960$	31.2253	1.00779
$961$	−18.1001	−0.583875
$962$	10.4716	0.337617
$963$	9.56607	0.308262
$964$	117.907	3.79753
$965$	−11.9903	−0.385982
$966$	54.6268	1.75759
$967$	−6.24475	−0.200818	−0.100409	−	0.994946i	$-0.532015\pi$
$967$	−6.24475	−0.200818	−0.100409	+	0.994946i	$0.532015\pi$
$968$	42.5109	1.36635
$969$	103.782	3.33396
$970$	−31.0764	−0.997804
$971$	−49.1036	−1.57581	−0.787905	−	0.615797i	$-0.788834\pi$
$971$	−49.1036	−1.57581	−0.787905	+	0.615797i	$0.788834\pi$
$972$	43.7893	1.40454
$973$	−23.5036	−0.753489
$974$	57.9867	1.85801
$975$	6.33188	0.202783
$976$	−55.4340	−1.77440
$977$	56.4243	1.80517	0.902587	−	0.430508i	$-0.141665\pi$
$977$	56.4243	1.80517	0.902587	+	0.430508i	$0.141665\pi$
$978$	−63.4990	−2.03047
$979$	−24.3037	−0.776750
$980$	−61.4750	−1.96375
$981$	10.2555	0.327432
$982$	−28.5070	−0.909696
$983$	−25.4853	−0.812856	−0.406428	−	0.913683i	$-0.633226\pi$
$983$	−25.4853	−0.812856	−0.406428	+	0.913683i	$0.633226\pi$
$984$	5.40660	0.172356
$985$	5.66662	0.180554
$986$	−15.8332	−0.504232
$987$	24.7922	0.789146
$988$	22.4842	0.715316
$989$	43.5399	1.38449
$990$	−14.3640	−0.456517
$991$	−23.9611	−0.761149	−0.380574	−	0.924750i	$-0.624274\pi$
$991$	−23.9611	−0.761149	−0.380574	+	0.924750i	$0.624274\pi$
$992$	−7.96998	−0.253047
$993$	14.7241	0.467255
$994$	−58.7340	−1.86293
$995$	57.7816	1.83180
$996$	29.8187	0.944840
$997$	−58.4761	−1.85196	−0.925978	−	0.377578i	$-0.876757\pi$
$997$	−58.4761	−1.85196	−0.925978	+	0.377578i	$0.876757\pi$
$998$	−89.7551	−2.84115
$999$	22.5017	0.711923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.12	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.12	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49227 q^{2} -2.01078 q^{3} +4.21142 q^{4} +3.04731 q^{5} +5.01140 q^{6} -1.48654 q^{7} -5.51145 q^{8} +1.04322 q^{9} +O(q^{10})\)	\(q-2.49227 q^{2} -2.01078 q^{3} +4.21142 q^{4} +3.04731 q^{5} +5.01140 q^{6} -1.48654 q^{7} -5.51145 q^{8} +1.04322 q^{9} -7.59472 q^{10} +1.81295 q^{11} -8.46822 q^{12} -0.734695 q^{13} +3.70486 q^{14} -6.12746 q^{15} +5.31320 q^{16} +7.10259 q^{17} -2.59999 q^{18} -7.26677 q^{19} +12.8335 q^{20} +2.98910 q^{21} -4.51837 q^{22} -7.33280 q^{23} +11.0823 q^{24} +4.28610 q^{25} +1.83106 q^{26} +3.93465 q^{27} -6.26044 q^{28} +0.894451 q^{29} +15.2713 q^{30} +3.59164 q^{31} -2.21904 q^{32} -3.64544 q^{33} -17.7016 q^{34} -4.52995 q^{35} +4.39343 q^{36} +5.71887 q^{37} +18.1108 q^{38} +1.47731 q^{39} -16.7951 q^{40} +0.487859 q^{41} -7.44965 q^{42} -5.93769 q^{43} +7.63510 q^{44} +3.17901 q^{45} +18.2753 q^{46} +8.29421 q^{47} -10.6837 q^{48} -4.79020 q^{49} -10.6821 q^{50} -14.2817 q^{51} -3.09411 q^{52} +6.24641 q^{53} -9.80621 q^{54} +5.52463 q^{55} +8.19300 q^{56} +14.6119 q^{57} -2.22922 q^{58} -6.10515 q^{59} -25.8053 q^{60} -10.4333 q^{61} -8.95134 q^{62} -1.55079 q^{63} -5.09596 q^{64} -2.23884 q^{65} +9.08543 q^{66} +1.55032 q^{67} +29.9120 q^{68} +14.7446 q^{69} +11.2899 q^{70} -15.8532 q^{71} -5.74966 q^{72} +2.48293 q^{73} -14.2530 q^{74} -8.61839 q^{75} -30.6034 q^{76} -2.69503 q^{77} -3.68185 q^{78} -2.62028 q^{79} +16.1910 q^{80} -11.0414 q^{81} -1.21588 q^{82} -3.52124 q^{83} +12.5884 q^{84} +21.6438 q^{85} +14.7983 q^{86} -1.79854 q^{87} -9.99201 q^{88} -13.4056 q^{89} -7.92297 q^{90} +1.09215 q^{91} -30.8815 q^{92} -7.22198 q^{93} -20.6714 q^{94} -22.1441 q^{95} +4.46199 q^{96} +4.09184 q^{97} +11.9385 q^{98} +1.89131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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