LMFDB - Embedded newform 4009.2.a.c.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0938800 q^{2} -0.360675 q^{3} -1.99119 q^{4} +0.0340990 q^{5} +0.0338601 q^{6} -4.36413 q^{7} +0.374693 q^{8} -2.86991 q^{9} +O(q^{10})$	\(q-0.0938800 q^{2} -0.360675 q^{3} -1.99119 q^{4} +0.0340990 q^{5} +0.0338601 q^{6} -4.36413 q^{7} +0.374693 q^{8} -2.86991 q^{9} -0.00320122 q^{10} +1.03399 q^{11} +0.718170 q^{12} +3.19878 q^{13} +0.409705 q^{14} -0.0122987 q^{15} +3.94720 q^{16} +2.01602 q^{17} +0.269428 q^{18} +1.00000 q^{19} -0.0678975 q^{20} +1.57403 q^{21} -0.0970711 q^{22} +5.72059 q^{23} -0.135142 q^{24} -4.99884 q^{25} -0.300301 q^{26} +2.11713 q^{27} +8.68979 q^{28} +1.81982 q^{29} +0.00115460 q^{30} -7.33079 q^{31} -1.11995 q^{32} -0.372934 q^{33} -0.189264 q^{34} -0.148813 q^{35} +5.71453 q^{36} +1.18932 q^{37} -0.0938800 q^{38} -1.15372 q^{39} +0.0127767 q^{40} +7.70829 q^{41} -0.147770 q^{42} +0.974621 q^{43} -2.05887 q^{44} -0.0978613 q^{45} -0.537049 q^{46} -5.94995 q^{47} -1.42365 q^{48} +12.0456 q^{49} +0.469291 q^{50} -0.727126 q^{51} -6.36937 q^{52} +11.9863 q^{53} -0.198756 q^{54} +0.0352581 q^{55} -1.63521 q^{56} -0.360675 q^{57} -0.170845 q^{58} -1.81000 q^{59} +0.0244889 q^{60} +5.10805 q^{61} +0.688215 q^{62} +12.5247 q^{63} -7.78925 q^{64} +0.109075 q^{65} +0.0350111 q^{66} -3.06067 q^{67} -4.01426 q^{68} -2.06327 q^{69} +0.0139705 q^{70} +6.77101 q^{71} -1.07534 q^{72} -1.47538 q^{73} -0.111653 q^{74} +1.80295 q^{75} -1.99119 q^{76} -4.51247 q^{77} +0.108311 q^{78} -7.97334 q^{79} +0.134596 q^{80} +7.84615 q^{81} -0.723654 q^{82} +0.129829 q^{83} -3.13419 q^{84} +0.0687442 q^{85} -0.0914975 q^{86} -0.656363 q^{87} +0.387429 q^{88} -15.0652 q^{89} +0.00918722 q^{90} -13.9599 q^{91} -11.3908 q^{92} +2.64403 q^{93} +0.558582 q^{94} +0.0340990 q^{95} +0.403937 q^{96} +0.668794 q^{97} -1.13084 q^{98} -2.96746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−0.0938800	−0.0663832	−0.0331916	−	0.999449i	$-0.510567\pi$
$2$	−0.0938800	−0.0663832	−0.0331916	+	0.999449i	$0.510567\pi$
$3$	−0.360675	−0.208236	−0.104118	−	0.994565i	$-0.533202\pi$
$3$	−0.360675	−0.208236	−0.104118	+	0.994565i	$0.533202\pi$
$4$	−1.99119	−0.995593
$5$	0.0340990	0.0152496	0.00762478	−	0.999971i	$-0.497573\pi$
$5$	0.0340990	0.0152496	0.00762478	+	0.999971i	$0.497573\pi$
$6$	0.0338601	0.0138233
$7$	−4.36413	−1.64949	−0.824743	−	0.565508i	$-0.808680\pi$
$7$	−4.36413	−1.64949	−0.824743	+	0.565508i	$0.808680\pi$
$8$	0.374693	0.132474
$9$	−2.86991	−0.956638
$10$	−0.00320122	−0.00101231
$11$	1.03399	0.311760	0.155880	−	0.987776i	$-0.450179\pi$
$11$	1.03399	0.311760	0.155880	+	0.987776i	$0.450179\pi$
$12$	0.718170	0.207318
$13$	3.19878	0.887182	0.443591	−	0.896229i	$-0.353704\pi$
$13$	3.19878	0.887182	0.443591	+	0.896229i	$0.353704\pi$
$14$	0.409705	0.109498
$15$	−0.0122987	−0.00317550
$16$	3.94720	0.986799
$17$	2.01602	0.488956	0.244478	−	0.969655i	$-0.421383\pi$
$17$	2.01602	0.488956	0.244478	+	0.969655i	$0.421383\pi$
$18$	0.269428	0.0635047
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.0678975	−0.0151824
$21$	1.57403	0.343482
$22$	−0.0970711	−0.0206956
$23$	5.72059	1.19283	0.596413	−	0.802678i	$-0.296592\pi$
$23$	5.72059	1.19283	0.596413	+	0.802678i	$0.296592\pi$
$24$	−0.135142	−0.0275858
$25$	−4.99884	−0.999767
$26$	−0.300301	−0.0588940
$27$	2.11713	0.407442
$28$	8.68979	1.64222
$29$	1.81982	0.337932	0.168966	−	0.985622i	$-0.445957\pi$
$29$	1.81982	0.337932	0.168966	+	0.985622i	$0.445957\pi$
$30$	0.00115460	0.000210800 0
$31$	−7.33079	−1.31665	−0.658324	−	0.752735i	$-0.728734\pi$
$31$	−7.33079	−1.31665	−0.658324	+	0.752735i	$0.728734\pi$
$32$	−1.11995	−0.197981
$33$	−0.372934	−0.0649195
$34$	−0.189264	−0.0324585
$35$	−0.148813	−0.0251539
$36$	5.71453	0.952422
$37$	1.18932	0.195523	0.0977614	−	0.995210i	$-0.468832\pi$
$37$	1.18932	0.195523	0.0977614	+	0.995210i	$0.468832\pi$
$38$	−0.0938800	−0.0152294
$39$	−1.15372	−0.184743
$40$	0.0127767	0.00202017
$41$	7.70829	1.20383	0.601916	−	0.798559i	$-0.294404\pi$
$41$	7.70829	1.20383	0.601916	+	0.798559i	$0.294404\pi$
$42$	−0.147770	−0.0228014
$43$	0.974621	0.148628	0.0743142	−	0.997235i	$-0.476323\pi$
$43$	0.974621	0.148628	0.0743142	+	0.997235i	$0.476323\pi$
$44$	−2.05887	−0.310386
$45$	−0.0978613	−0.0145883
$46$	−0.537049	−0.0791836
$47$	−5.94995	−0.867890	−0.433945	−	0.900939i	$-0.642879\pi$
$47$	−5.94995	−0.867890	−0.433945	+	0.900939i	$0.642879\pi$
$48$	−1.42365	−0.205487
$49$	12.0456	1.72080
$50$	0.469291	0.0663678
$51$	−0.727126	−0.101818
$52$	−6.36937	−0.883272
$53$	11.9863	1.64644	0.823221	−	0.567721i	$-0.192175\pi$
$53$	11.9863	1.64644	0.823221	+	0.567721i	$0.192175\pi$
$54$	−0.198756	−0.0270473
$55$	0.0352581	0.00475420
$56$	−1.63521	−0.218514
$57$	−0.360675	−0.0477725
$58$	−0.170845	−0.0224330
$59$	−1.81000	−0.235642	−0.117821	−	0.993035i	$-0.537591\pi$
$59$	−1.81000	−0.235642	−0.117821	+	0.993035i	$0.537591\pi$
$60$	0.0244889	0.00316151
$61$	5.10805	0.654019	0.327009	−	0.945021i	$-0.393959\pi$
$61$	5.10805	0.654019	0.327009	+	0.945021i	$0.393959\pi$
$62$	0.688215	0.0874033
$63$	12.5247	1.57796
$64$	−7.78925	−0.973657
$65$	0.109075	0.0135291
$66$	0.0350111	0.00430957
$67$	−3.06067	−0.373921	−0.186960	−	0.982367i	$-0.559864\pi$
$67$	−3.06067	−0.373921	−0.186960	+	0.982367i	$0.559864\pi$
$68$	−4.01426	−0.486801
$69$	−2.06327	−0.248389
$70$	0.0139705	0.00166980
$71$	6.77101	0.803572	0.401786	−	0.915734i	$-0.368390\pi$
$71$	6.77101	0.803572	0.401786	+	0.915734i	$0.368390\pi$
$72$	−1.07534	−0.126730
$73$	−1.47538	−0.172680	−0.0863400	−	0.996266i	$-0.527517\pi$
$73$	−1.47538	−0.172680	−0.0863400	+	0.996266i	$0.527517\pi$
$74$	−0.111653	−0.0129794
$75$	1.80295	0.208187
$76$	−1.99119	−0.228405
$77$	−4.51247	−0.514243
$78$	0.108311	0.0122638
$79$	−7.97334	−0.897071	−0.448535	−	0.893765i	$-0.648054\pi$
$79$	−7.97334	−0.897071	−0.448535	+	0.893765i	$0.648054\pi$
$80$	0.134596	0.0150482
$81$	7.84615	0.871794
$82$	−0.723654	−0.0799143
$83$	0.129829	0.0142506	0.00712530	−	0.999975i	$-0.497732\pi$
$83$	0.129829	0.0142506	0.00712530	+	0.999975i	$0.497732\pi$
$84$	−3.13419	−0.341968
$85$	0.0687442	0.00745636
$86$	−0.0914975	−0.00986643
$87$	−0.656363	−0.0703695
$88$	0.387429	0.0413001
$89$	−15.0652	−1.59691	−0.798453	−	0.602057i	$-0.794348\pi$
$89$	−15.0652	−1.59691	−0.798453	+	0.602057i	$0.794348\pi$
$90$	0.00918722	0.000968418 0
$91$	−13.9599	−1.46339
$92$	−11.3908	−1.18757
$93$	2.64403	0.274173
$94$	0.558582	0.0576133
$95$	0.0340990	0.00349849
$96$	0.403937	0.0412266
$97$	0.668794	0.0679057	0.0339529	−	0.999423i	$-0.489190\pi$
$97$	0.668794	0.0679057	0.0339529	+	0.999423i	$0.489190\pi$
$98$	−1.13084	−0.114232
$99$	−2.96746	−0.298241
$100$	9.95362	0.995362
$101$	12.9482	1.28839	0.644195	−	0.764861i	$-0.277192\pi$
$101$	12.9482	1.28839	0.644195	+	0.764861i	$0.277192\pi$
$102$	0.0682626	0.00675900
$103$	−4.92688	−0.485460	−0.242730	−	0.970094i	$-0.578043\pi$
$103$	−4.92688	−0.485460	−0.242730	+	0.970094i	$0.578043\pi$
$104$	1.19856	0.117528
$105$	0.0536729	0.00523794
$106$	−1.12527	−0.109296
$107$	−11.5245	−1.11411	−0.557056	−	0.830475i	$-0.688069\pi$
$107$	−11.5245	−1.11411	−0.557056	+	0.830475i	$0.688069\pi$
$108$	−4.21560	−0.405646
$109$	−3.00419	−0.287749	−0.143875	−	0.989596i	$-0.545956\pi$
$109$	−3.00419	−0.287749	−0.143875	+	0.989596i	$0.545956\pi$
$110$	−0.00331003	−0.000315599 0
$111$	−0.428957	−0.0407148
$112$	−17.2261	−1.62771
$113$	−8.97653	−0.844441	−0.422220	−	0.906493i	$-0.638749\pi$
$113$	−8.97653	−0.844441	−0.422220	+	0.906493i	$0.638749\pi$
$114$	0.0338601	0.00317129
$115$	0.195067	0.0181901
$116$	−3.62360	−0.336443
$117$	−9.18022	−0.848712
$118$	0.169923	0.0156427
$119$	−8.79815	−0.806525
$120$	−0.00460822	−0.000420671 0
$121$	−9.93086	−0.902806
$122$	−0.479544	−0.0434159
$123$	−2.78018	−0.250681
$124$	14.5970	1.31085
$125$	−0.340951	−0.0304956
$126$	−1.17582	−0.104750
$127$	−15.6712	−1.39059	−0.695295	−	0.718724i	$-0.744726\pi$
$127$	−15.6712	−1.39059	−0.695295	+	0.718724i	$0.744726\pi$
$128$	2.97115	0.262615
$129$	−0.351521	−0.0309497
$130$	−0.0102400	−0.000898107 0
$131$	3.68714	0.322147	0.161073	−	0.986942i	$-0.448504\pi$
$131$	3.68714	0.322147	0.161073	+	0.986942i	$0.448504\pi$
$132$	0.742582	0.0646334
$133$	−4.36413	−0.378418
$134$	0.287336	0.0248220
$135$	0.0721920	0.00621330
$136$	0.755387	0.0647739
$137$	0.184734	0.0157829	0.00789145	−	0.999969i	$-0.497488\pi$
$137$	0.184734	0.0157829	0.00789145	+	0.999969i	$0.497488\pi$
$138$	0.193700	0.0164888
$139$	−20.6715	−1.75334	−0.876668	−	0.481097i	$-0.840239\pi$
$139$	−20.6715	−1.75334	−0.876668	+	0.481097i	$0.840239\pi$
$140$	0.296314	0.0250431
$141$	2.14600	0.180726
$142$	−0.635663	−0.0533437
$143$	3.30751	0.276588
$144$	−11.3281	−0.944010
$145$	0.0620542	0.00515332
$146$	0.138509	0.0114631
$147$	−4.34455	−0.358332
$148$	−2.36816	−0.194661
$149$	5.59058	0.457998	0.228999	−	0.973427i	$-0.426455\pi$
$149$	5.59058	0.457998	0.228999	+	0.973427i	$0.426455\pi$
$150$	−0.169261	−0.0138201
$151$	22.6790	1.84559	0.922796	−	0.385289i	$-0.125898\pi$
$151$	22.6790	1.84559	0.922796	+	0.385289i	$0.125898\pi$
$152$	0.374693	0.0303916
$153$	−5.78579	−0.467754
$154$	0.423631	0.0341371
$155$	−0.249973	−0.0200783
$156$	2.29727	0.183929
$157$	−15.9170	−1.27032	−0.635159	−	0.772382i	$-0.719065\pi$
$157$	−15.9170	−1.27032	−0.635159	+	0.772382i	$0.719065\pi$
$158$	0.748537	0.0595504
$159$	−4.32315	−0.342848
$160$	−0.0381892	−0.00301912
$161$	−24.9654	−1.96755
$162$	−0.736597	−0.0578725
$163$	−24.8137	−1.94356	−0.971780	−	0.235887i	$-0.924200\pi$
$163$	−24.8137	−1.94356	−0.971780	+	0.235887i	$0.924200\pi$
$164$	−15.3486	−1.19853
$165$	−0.0127167	−0.000989993 0
$166$	−0.0121884	−0.000946001 0
$167$	17.4073	1.34702	0.673508	−	0.739180i	$-0.264787\pi$
$167$	17.4073	1.34702	0.673508	+	0.739180i	$0.264787\pi$
$168$	0.589778	0.0455023
$169$	−2.76781	−0.212909
$170$	−0.00645371	−0.000494977 0
$171$	−2.86991	−0.219468
$172$	−1.94065	−0.147973
$173$	16.2399	1.23470	0.617349	−	0.786689i	$-0.288206\pi$
$173$	16.2399	1.23470	0.617349	+	0.786689i	$0.288206\pi$
$174$	0.0616194	0.00467136
$175$	21.8156	1.64910
$176$	4.08137	0.307644
$177$	0.652822	0.0490691
$178$	1.41432	0.106008
$179$	11.0935	0.829166	0.414583	−	0.910012i	$-0.363927\pi$
$179$	11.0935	0.829166	0.414583	+	0.910012i	$0.363927\pi$
$180$	0.194860	0.0145240
$181$	−15.7437	−1.17022	−0.585109	−	0.810954i	$-0.698948\pi$
$181$	−15.7437	−1.17022	−0.585109	+	0.810954i	$0.698948\pi$
$182$	1.31055	0.0971447
$183$	−1.84234	−0.136190
$184$	2.14346	0.158018
$185$	0.0405546	0.00298163
$186$	−0.248221	−0.0182005
$187$	2.08454	0.152437
$188$	11.8475	0.864065
$189$	−9.23942	−0.672069
$190$	−0.00320122	−0.000232241 0
$191$	−18.7298	−1.35524	−0.677620	−	0.735412i	$-0.736989\pi$
$191$	−18.7298	−1.35524	−0.677620	+	0.735412i	$0.736989\pi$
$192$	2.80939	0.202750
$193$	−7.01286	−0.504797	−0.252398	−	0.967623i	$-0.581219\pi$
$193$	−7.01286	−0.504797	−0.252398	+	0.967623i	$0.581219\pi$
$194$	−0.0627864	−0.00450780
$195$	−0.0393407	−0.00281724
$196$	−23.9851	−1.71322
$197$	−4.17527	−0.297476	−0.148738	−	0.988877i	$-0.547521\pi$
$197$	−4.17527	−0.297476	−0.148738	+	0.988877i	$0.547521\pi$
$198$	0.278586	0.0197982
$199$	10.4630	0.741701	0.370851	−	0.928693i	$-0.379066\pi$
$199$	10.4630	0.741701	0.370851	+	0.928693i	$0.379066\pi$
$200$	−1.87303	−0.132443
$201$	1.10391	0.0778636
$202$	−1.21557	−0.0855275
$203$	−7.94194	−0.557415
$204$	1.44784	0.101369
$205$	0.262845	0.0183579
$206$	0.462536	0.0322264
$207$	−16.4176	−1.14110
$208$	12.6262	0.875470
$209$	1.03399	0.0715226
$210$	−0.00503881	−0.000347711 0
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−23.8669	−1.63919
$213$	−2.44213	−0.167332
$214$	1.08192	0.0739583
$215$	0.0332336	0.00226652
$216$	0.793273	0.0539754
$217$	31.9925	2.17179
$218$	0.282034	0.0191017
$219$	0.532132	0.0359581
$220$	−0.0702054	−0.00473325
$221$	6.44879	0.433793
$222$	0.0402705	0.00270278
$223$	10.8193	0.724514	0.362257	−	0.932078i	$-0.382006\pi$
$223$	10.8193	0.724514	0.362257	+	0.932078i	$0.382006\pi$
$224$	4.88760	0.326566
$225$	14.3462	0.956415
$226$	0.842717	0.0560567
$227$	4.38639	0.291135	0.145567	−	0.989348i	$-0.453499\pi$
$227$	4.38639	0.291135	0.145567	+	0.989348i	$0.453499\pi$
$228$	0.718170	0.0475620
$229$	−18.6154	−1.23014	−0.615069	−	0.788473i	$-0.710872\pi$
$229$	−18.6154	−1.23014	−0.615069	+	0.788473i	$0.710872\pi$
$230$	−0.0183129	−0.00120751
$231$	1.62753	0.107084
$232$	0.681874	0.0447672
$233$	−23.9716	−1.57043	−0.785216	−	0.619222i	$-0.787448\pi$
$233$	−23.9716	−1.57043	−0.785216	+	0.619222i	$0.787448\pi$
$234$	0.861839	0.0563402
$235$	−0.202888	−0.0132349
$236$	3.60406	0.234604
$237$	2.87578	0.186802
$238$	0.825971	0.0535397
$239$	11.8174	0.764402	0.382201	−	0.924079i	$-0.375166\pi$
$239$	11.8174	0.764402	0.382201	+	0.924079i	$0.375166\pi$
$240$	−0.0485452	−0.00313358
$241$	−0.287258	−0.0185039	−0.00925194	−	0.999957i	$-0.502945\pi$
$241$	−0.287258	−0.0185039	−0.00925194	+	0.999957i	$0.502945\pi$
$242$	0.932310	0.0599311
$243$	−9.18129	−0.588980
$244$	−10.1711	−0.651137
$245$	0.410744	0.0262415
$246$	0.261004	0.0166410
$247$	3.19878	0.203533
$248$	−2.74679	−0.174421
$249$	−0.0468261	−0.00296748
$250$	0.0320085	0.00202439
$251$	11.7169	0.739563	0.369782	−	0.929119i	$-0.379432\pi$
$251$	11.7169	0.739563	0.369782	+	0.929119i	$0.379432\pi$
$252$	−24.9390	−1.57101
$253$	5.91504	0.371875
$254$	1.47121	0.0923118
$255$	−0.0247943	−0.00155268
$256$	15.2996	0.956223
$257$	18.2066	1.13569	0.567847	−	0.823134i	$-0.307777\pi$
$257$	18.2066	1.13569	0.567847	+	0.823134i	$0.307777\pi$
$258$	0.0330008	0.00205454
$259$	−5.19034	−0.322512
$260$	−0.217189	−0.0134695
$261$	−5.22273	−0.323279
$262$	−0.346149	−0.0213851
$263$	−16.0451	−0.989384	−0.494692	−	0.869068i	$-0.664719\pi$
$263$	−16.0451	−0.989384	−0.494692	+	0.869068i	$0.664719\pi$
$264$	−0.139736	−0.00860014
$265$	0.408721	0.0251075
$266$	0.409705	0.0251206
$267$	5.43363	0.332533
$268$	6.09437	0.372273
$269$	8.62303	0.525755	0.262878	−	0.964829i	$-0.415328\pi$
$269$	8.62303	0.525755	0.262878	+	0.964829i	$0.415328\pi$
$270$	−0.00677739	−0.000412459 0
$271$	12.6034	0.765602	0.382801	−	0.923831i	$-0.374960\pi$
$271$	12.6034	0.765602	0.382801	+	0.923831i	$0.374960\pi$
$272$	7.95761	0.482501
$273$	5.03497	0.304730
$274$	−0.0173428	−0.00104772
$275$	−5.16875	−0.311687
$276$	4.10836	0.247294
$277$	−21.4089	−1.28634	−0.643168	−	0.765725i	$-0.722380\pi$
$277$	−21.4089	−1.28634	−0.643168	+	0.765725i	$0.722380\pi$
$278$	1.94064	0.116392
$279$	21.0387	1.25956
$280$	−0.0557590	−0.00333224
$281$	25.5679	1.52525	0.762625	−	0.646840i	$-0.223910\pi$
$281$	25.5679	1.52525	0.762625	+	0.646840i	$0.223910\pi$
$282$	−0.201466	−0.0119971
$283$	10.6402	0.632497	0.316248	−	0.948676i	$-0.397577\pi$
$283$	10.6402	0.632497	0.316248	+	0.948676i	$0.397577\pi$
$284$	−13.4824	−0.800030
$285$	−0.0122987	−0.000728509 0
$286$	−0.310509	−0.0183608
$287$	−33.6400	−1.98570
$288$	3.21416	0.189396
$289$	−12.9357	−0.760922
$290$	−0.00582565	−0.000342094 0
$291$	−0.241217	−0.0141404
$292$	2.93776	0.171919
$293$	4.60577	0.269072	0.134536	−	0.990909i	$-0.457046\pi$
$293$	4.60577	0.269072	0.134536	+	0.990909i	$0.457046\pi$
$294$	0.407866	0.0237872
$295$	−0.0617194	−0.00359344
$296$	0.445629	0.0259017
$297$	2.18909	0.127024
$298$	−0.524844	−0.0304034
$299$	18.2989	1.05825
$300$	−3.59002	−0.207270
$301$	−4.25337	−0.245160
$302$	−2.12911	−0.122516
$303$	−4.67007	−0.268289
$304$	3.94720	0.226387
$305$	0.174180	0.00997349
$306$	0.543170	0.0310510
$307$	−30.7036	−1.75235	−0.876175	−	0.481994i	$-0.839913\pi$
$307$	−30.7036	−1.75235	−0.876175	+	0.481994i	$0.839913\pi$
$308$	8.98517	0.511977
$309$	1.77700	0.101090
$310$	0.0234675	0.00133286
$311$	−28.7706	−1.63143	−0.815715	−	0.578454i	$-0.803656\pi$
$311$	−28.7706	−1.63143	−0.815715	+	0.578454i	$0.803656\pi$
$312$	−0.432290	−0.0244736
$313$	−19.7310	−1.11526	−0.557631	−	0.830089i	$-0.688290\pi$
$313$	−19.7310	−1.11526	−0.557631	+	0.830089i	$0.688290\pi$
$314$	1.49429	0.0843278
$315$	0.427079	0.0240632
$316$	15.8764	0.893117
$317$	−7.97900	−0.448145	−0.224073	−	0.974572i	$-0.571935\pi$
$317$	−7.97900	−0.448145	−0.224073	+	0.974572i	$0.571935\pi$
$318$	0.405857	0.0227593
$319$	1.88168	0.105354
$320$	−0.265606	−0.0148478
$321$	4.15658	0.231998
$322$	2.34375	0.130612
$323$	2.01602	0.112174
$324$	−15.6231	−0.867952
$325$	−15.9902	−0.886975
$326$	2.32951	0.129020
$327$	1.08354	0.0599196
$328$	2.88824	0.159476
$329$	25.9664	1.43157
$330$	0.00119384	6.57189e−5 0
$331$	−2.87207	−0.157863	−0.0789316	−	0.996880i	$-0.525151\pi$
$331$	−2.87207	−0.157863	−0.0789316	+	0.996880i	$0.525151\pi$
$332$	−0.258514	−0.0141878
$333$	−3.41324	−0.187045
$334$	−1.63420	−0.0894192
$335$	−0.104366	−0.00570212
$336$	6.21301	0.338947
$337$	15.1389	0.824671	0.412336	−	0.911032i	$-0.364713\pi$
$337$	15.1389	0.824671	0.412336	+	0.911032i	$0.364713\pi$
$338$	0.259842	0.0141336
$339$	3.23761	0.175843
$340$	−0.136883	−0.00742350
$341$	−7.57996	−0.410478
$342$	0.269428	0.0145690
$343$	−22.0197	−1.18895
$344$	0.365183	0.0196894
$345$	−0.0703556	−0.00378782
$346$	−1.52461	−0.0819633
$347$	21.7884	1.16966	0.584832	−	0.811154i	$-0.301160\pi$
$347$	21.7884	1.16966	0.584832	+	0.811154i	$0.301160\pi$
$348$	1.30694	0.0700594
$349$	−10.0264	−0.536703	−0.268351	−	0.963321i	$-0.586479\pi$
$349$	−10.0264	−0.536703	−0.268351	+	0.963321i	$0.586479\pi$
$350$	−2.04805	−0.109473
$351$	6.77223	0.361475
$352$	−1.15802	−0.0617225
$353$	25.9701	1.38225	0.691125	−	0.722735i	$-0.257115\pi$
$353$	25.9701	1.38225	0.691125	+	0.722735i	$0.257115\pi$
$354$	−0.0612870	−0.00325737
$355$	0.230885	0.0122541
$356$	29.9976	1.58987
$357$	3.17327	0.167947
$358$	−1.04146	−0.0550427
$359$	11.2602	0.594292	0.297146	−	0.954832i	$-0.403965\pi$
$359$	11.2602	0.594292	0.297146	+	0.954832i	$0.403965\pi$
$360$	−0.0366679	−0.00193257
$361$	1.00000	0.0526316
$362$	1.47802	0.0776829
$363$	3.58181	0.187996
$364$	27.7967	1.45694
$365$	−0.0503090	−0.00263329
$366$	0.172959	0.00904073
$367$	18.3024	0.955380	0.477690	−	0.878529i	$-0.341474\pi$
$367$	18.3024	0.955380	0.477690	+	0.878529i	$0.341474\pi$
$368$	22.5803	1.17708
$369$	−22.1221	−1.15163
$370$	−0.00380727	−0.000197931 0
$371$	−52.3097	−2.71578
$372$	−5.26475	−0.272965
$373$	−7.39422	−0.382858	−0.191429	−	0.981506i	$-0.561312\pi$
$373$	−7.39422	−0.382858	−0.191429	+	0.981506i	$0.561312\pi$
$374$	−0.195697	−0.0101192
$375$	0.122972	0.00635026
$376$	−2.22940	−0.114973
$377$	5.82121	0.299807
$378$	0.867397	0.0446141
$379$	8.88785	0.456538	0.228269	−	0.973598i	$-0.426693\pi$
$379$	8.88785	0.456538	0.228269	+	0.973598i	$0.426693\pi$
$380$	−0.0678975	−0.00348307
$381$	5.65219	0.289570
$382$	1.75835	0.0899652
$383$	−31.0706	−1.58763	−0.793816	−	0.608158i	$-0.791909\pi$
$383$	−31.0706	−1.58763	−0.793816	+	0.608158i	$0.791909\pi$
$384$	−1.07162	−0.0546858
$385$	−0.153871	−0.00784198
$386$	0.658367	0.0335100
$387$	−2.79708	−0.142184
$388$	−1.33169	−0.0676065
$389$	−9.84823	−0.499325	−0.249662	−	0.968333i	$-0.580320\pi$
$389$	−9.84823	−0.499325	−0.249662	+	0.968333i	$0.580320\pi$
$390$	0.00369330	0.000187018 0
$391$	11.5328	0.583239
$392$	4.51340	0.227961
$393$	−1.32986	−0.0670824
$394$	0.391975	0.0197474
$395$	−0.271883	−0.0136799
$396$	5.90878	0.296927
$397$	−26.2222	−1.31605	−0.658026	−	0.752995i	$-0.728608\pi$
$397$	−26.2222	−1.31605	−0.658026	+	0.752995i	$0.728608\pi$
$398$	−0.982265	−0.0492365
$399$	1.57403	0.0788001
$400$	−19.7314	−0.986570
$401$	−7.90213	−0.394613	−0.197307	−	0.980342i	$-0.563219\pi$
$401$	−7.90213	−0.394613	−0.197307	+	0.980342i	$0.563219\pi$
$402$	−0.103635	−0.00516883
$403$	−23.4496	−1.16811
$404$	−25.7822	−1.28271
$405$	0.267546	0.0132945
$406$	0.745589	0.0370030
$407$	1.22974	0.0609562
$408$	−0.272449	−0.0134882
$409$	−5.76932	−0.285275	−0.142637	−	0.989775i	$-0.545558\pi$
$409$	−5.76932	−0.285275	−0.142637	+	0.989775i	$0.545558\pi$
$410$	−0.0246759	−0.00121866
$411$	−0.0666289	−0.00328656
$412$	9.81034	0.483321
$413$	7.89909	0.388689
$414$	1.54129	0.0757500
$415$	0.00442705	0.000217315 0
$416$	−3.58247	−0.175645
$417$	7.45569	0.365107
$418$	−0.0970711	−0.00474790
$419$	−1.53845	−0.0751581	−0.0375790	−	0.999294i	$-0.511965\pi$
$419$	−1.53845	−0.0751581	−0.0375790	+	0.999294i	$0.511965\pi$
$420$	−0.106873	−0.00521486
$421$	−0.302580	−0.0147468	−0.00737342	−	0.999973i	$-0.502347\pi$
$421$	−0.302580	−0.0147468	−0.00737342	+	0.999973i	$0.502347\pi$
$422$	−0.0938800	−0.00457001
$423$	17.0759	0.830256
$424$	4.49117	0.218111
$425$	−10.0777	−0.488842
$426$	0.229268	0.0111080
$427$	−22.2922	−1.07879
$428$	22.9474	1.10920
$429$	−1.19293	−0.0575954
$430$	−0.00311998	−0.000150459 0
$431$	−37.3880	−1.80092	−0.900459	−	0.434940i	$-0.856769\pi$
$431$	−37.3880	−1.80092	−0.900459	+	0.434940i	$0.856769\pi$
$432$	8.35672	0.402063
$433$	8.16115	0.392200	0.196100	−	0.980584i	$-0.437172\pi$
$433$	8.16115	0.392200	0.196100	+	0.980584i	$0.437172\pi$
$434$	−3.00346	−0.144171
$435$	−0.0223814	−0.00107310
$436$	5.98190	0.286481
$437$	5.72059	0.273653
$438$	−0.0499566	−0.00238702
$439$	−36.5133	−1.74269	−0.871343	−	0.490675i	$-0.836750\pi$
$439$	−36.5133	−1.74269	−0.871343	+	0.490675i	$0.836750\pi$
$440$	0.0132110	0.000629807 0
$441$	−34.5699	−1.64618
$442$	−0.605413	−0.0287965
$443$	35.4264	1.68316	0.841580	−	0.540132i	$-0.181626\pi$
$443$	35.4264	1.68316	0.841580	+	0.540132i	$0.181626\pi$
$444$	0.854133	0.0405354
$445$	−0.513708	−0.0243521
$446$	−1.01572	−0.0480956
$447$	−2.01638	−0.0953714
$448$	33.9933	1.60603
$449$	28.1781	1.32981	0.664903	−	0.746930i	$-0.268473\pi$
$449$	28.1781	1.32981	0.664903	+	0.746930i	$0.268473\pi$
$450$	−1.34682	−0.0634899
$451$	7.97030	0.375307
$452$	17.8739	0.840720
$453$	−8.17974	−0.384318
$454$	−0.411794	−0.0193265
$455$	−0.476018	−0.0223161
$456$	−0.135142	−0.00632861
$457$	19.2200	0.899073	0.449536	−	0.893262i	$-0.351589\pi$
$457$	19.2200	0.899073	0.449536	+	0.893262i	$0.351589\pi$
$458$	1.74761	0.0816605
$459$	4.26817	0.199221
$460$	−0.388414	−0.0181099
$461$	−0.0980547	−0.00456686	−0.00228343	−	0.999997i	$-0.500727\pi$
$461$	−0.0980547	−0.00456686	−0.00228343	+	0.999997i	$0.500727\pi$
$462$	−0.152793	−0.00710857
$463$	0.705512	0.0327879	0.0163940	−	0.999866i	$-0.494781\pi$
$463$	0.705512	0.0327879	0.0163940	+	0.999866i	$0.494781\pi$
$464$	7.18319	0.333471
$465$	0.0901588	0.00418101
$466$	2.25045	0.104250
$467$	−36.1441	−1.67255	−0.836275	−	0.548310i	$-0.815271\pi$
$467$	−36.1441	−1.67255	−0.836275	+	0.548310i	$0.815271\pi$
$468$	18.2795	0.844972
$469$	13.3572	0.616776
$470$	0.0190471	0.000878577 0
$471$	5.74087	0.264525
$472$	−0.678195	−0.0312165
$473$	1.00775	0.0463364
$474$	−0.269978	−0.0124005
$475$	−4.99884	−0.229362
$476$	17.5188	0.802971
$477$	−34.3996	−1.57505
$478$	−1.10942	−0.0507435
$479$	−9.32009	−0.425846	−0.212923	−	0.977069i	$-0.568298\pi$
$479$	−9.32009	−0.425846	−0.212923	+	0.977069i	$0.568298\pi$
$480$	0.0137739	0.000628688 0
$481$	3.80437	0.173464
$482$	0.0269678	0.00122835
$483$	9.00438	0.409714
$484$	19.7742	0.898827
$485$	0.0228052	0.00103553
$486$	0.861940	0.0390984
$487$	−18.4018	−0.833866	−0.416933	−	0.908937i	$-0.636895\pi$
$487$	−18.4018	−0.833866	−0.416933	+	0.908937i	$0.636895\pi$
$488$	1.91395	0.0866404
$489$	8.94968	0.404718
$490$	−0.0385606	−0.00174199
$491$	−33.8313	−1.52679	−0.763393	−	0.645934i	$-0.776468\pi$
$491$	−33.8313	−1.52679	−0.763393	+	0.645934i	$0.776468\pi$
$492$	5.53586	0.249576
$493$	3.66879	0.165234
$494$	−0.300301	−0.0135112
$495$	−0.101188	−0.00454805
$496$	−28.9361	−1.29927
$497$	−29.5496	−1.32548
$498$	0.00439603	0.000196991 0
$499$	12.8111	0.573502	0.286751	−	0.958005i	$-0.407425\pi$
$499$	12.8111	0.573502	0.286751	+	0.958005i	$0.407425\pi$
$500$	0.678896	0.0303612
$501$	−6.27836	−0.280497
$502$	−1.09998	−0.0490946
$503$	−11.6682	−0.520261	−0.260131	−	0.965573i	$-0.583766\pi$
$503$	−11.6682	−0.520261	−0.260131	+	0.965573i	$0.583766\pi$
$504$	4.69290	0.209039
$505$	0.441520	0.0196474
$506$	−0.555304	−0.0246863
$507$	0.998280	0.0443352
$508$	31.2042	1.38446
$509$	−10.5497	−0.467609	−0.233805	−	0.972284i	$-0.575118\pi$
$509$	−10.5497	−0.467609	−0.233805	+	0.972284i	$0.575118\pi$
$510$	0.00232769	0.000103072 0
$511$	6.43874	0.284833
$512$	−7.37863	−0.326092
$513$	2.11713	0.0934735
$514$	−1.70923	−0.0753910
$515$	−0.168002	−0.00740305
$516$	0.699944	0.0308133
$517$	−6.15220	−0.270573
$518$	0.487269	0.0214094
$519$	−5.85733	−0.257108
$520$	0.0408697	0.00179226
$521$	16.4316	0.719881	0.359940	−	0.932975i	$-0.382797\pi$
$521$	16.4316	0.719881	0.359940	+	0.932975i	$0.382797\pi$
$522$	0.490310	0.0214603
$523$	−28.9217	−1.26466	−0.632328	−	0.774701i	$-0.717901\pi$
$523$	−28.9217	−1.26466	−0.632328	+	0.774701i	$0.717901\pi$
$524$	−7.34178	−0.320727
$525$	−7.86832	−0.343402
$526$	1.50632	0.0656785
$527$	−14.7790	−0.643783
$528$	−1.47204	−0.0640625
$529$	9.72516	0.422833
$530$	−0.0383707	−0.00166672
$531$	5.19456	0.225425
$532$	8.68979	0.376750
$533$	24.6571	1.06802
$534$	−0.510109	−0.0220746
$535$	−0.392973	−0.0169897
$536$	−1.14681	−0.0495347
$537$	−4.00114	−0.172662
$538$	−0.809530	−0.0349013
$539$	12.4551	0.536477
$540$	−0.143748	−0.00618592
$541$	−39.3268	−1.69079	−0.845396	−	0.534141i	$-0.820635\pi$
$541$	−39.3268	−1.69079	−0.845396	+	0.534141i	$0.820635\pi$
$542$	−1.18321	−0.0508231
$543$	5.67835	0.243681
$544$	−2.25783	−0.0968038
$545$	−0.102440	−0.00438805
$546$	−0.472684	−0.0202290
$547$	27.9286	1.19414	0.597070	−	0.802189i	$-0.296331\pi$
$547$	27.9286	1.19414	0.597070	+	0.802189i	$0.296331\pi$
$548$	−0.367840	−0.0157133
$549$	−14.6597	−0.625659
$550$	0.485243	0.0206908
$551$	1.81982	0.0775270
$552$	−0.773093	−0.0329050
$553$	34.7967	1.47970
$554$	2.00987	0.0853911
$555$	−0.0146270	−0.000620882 0
$556$	41.1608	1.74561
$557$	17.6752	0.748921	0.374461	−	0.927243i	$-0.377828\pi$
$557$	17.6752	0.748921	0.374461	+	0.927243i	$0.377828\pi$
$558$	−1.97512	−0.0836133
$559$	3.11760	0.131860
$560$	−0.587392	−0.0248219
$561$	−0.751841	−0.0317428
$562$	−2.40031	−0.101251
$563$	31.6893	1.33554	0.667772	−	0.744366i	$-0.267248\pi$
$563$	31.6893	1.33554	0.667772	+	0.744366i	$0.267248\pi$
$564$	−4.27308	−0.179929
$565$	−0.306091	−0.0128773
$566$	−0.998906	−0.0419872
$567$	−34.2416	−1.43801
$568$	2.53705	0.106452
$569$	−10.5350	−0.441650	−0.220825	−	0.975313i	$-0.570875\pi$
$569$	−10.5350	−0.441650	−0.220825	+	0.975313i	$0.570875\pi$
$570$	0.00115460	4.83608e−5 0
$571$	8.09327	0.338693	0.169346	−	0.985557i	$-0.445834\pi$
$571$	8.09327	0.338693	0.169346	+	0.985557i	$0.445834\pi$
$572$	−6.58586	−0.275369
$573$	6.75536	0.282209
$574$	3.15812	0.131817
$575$	−28.5963	−1.19255
$576$	22.3545	0.931437
$577$	−39.2819	−1.63532	−0.817662	−	0.575698i	$-0.804730\pi$
$577$	−39.2819	−1.63532	−0.817662	+	0.575698i	$0.804730\pi$
$578$	1.21440	0.0505125
$579$	2.52936	0.105117
$580$	−0.123561	−0.00513061
$581$	−0.566591	−0.0235062
$582$	0.0226455	0.000938684 0
$583$	12.3937	0.513295
$584$	−0.552814	−0.0228756
$585$	−0.313037	−0.0129425
$586$	−0.432390	−0.0178618
$587$	16.5166	0.681712	0.340856	−	0.940115i	$-0.389283\pi$
$587$	16.5166	0.681712	0.340856	+	0.940115i	$0.389283\pi$
$588$	8.65080	0.356753
$589$	−7.33079	−0.302060
$590$	0.00579422	0.000238544 0
$591$	1.50591	0.0619451
$592$	4.69447	0.192942
$593$	30.4318	1.24968	0.624842	−	0.780751i	$-0.285163\pi$
$593$	30.4318	1.24968	0.624842	+	0.780751i	$0.285163\pi$
$594$	−0.205512	−0.00843226
$595$	−0.300009	−0.0122992
$596$	−11.1319	−0.455980
$597$	−3.77373	−0.154449
$598$	−1.71790	−0.0702502
$599$	22.1774	0.906144	0.453072	−	0.891474i	$-0.350328\pi$
$599$	22.1774	0.906144	0.453072	+	0.891474i	$0.350328\pi$
$600$	0.675554	0.0275794
$601$	1.72282	0.0702752	0.0351376	−	0.999382i	$-0.488813\pi$
$601$	1.72282	0.0702752	0.0351376	+	0.999382i	$0.488813\pi$
$602$	0.399307	0.0162745
$603$	8.78386	0.357707
$604$	−45.1581	−1.83746
$605$	−0.338633	−0.0137674
$606$	0.438427	0.0178099
$607$	43.1214	1.75025	0.875123	−	0.483901i	$-0.160781\pi$
$607$	43.1214	1.75025	0.875123	+	0.483901i	$0.160781\pi$
$608$	−1.11995	−0.0454199
$609$	2.86445	0.116074
$610$	−0.0163520	−0.000662073 0
$611$	−19.0326	−0.769976
$612$	11.5206	0.465692
$613$	−16.3875	−0.661885	−0.330943	−	0.943651i	$-0.607367\pi$
$613$	−16.3875	−0.661885	−0.330943	+	0.943651i	$0.607367\pi$
$614$	2.88246	0.116327
$615$	−0.0948016	−0.00382277
$616$	−1.69079	−0.0681238
$617$	0.703511	0.0283223	0.0141611	−	0.999900i	$-0.495492\pi$
$617$	0.703511	0.0283223	0.0141611	+	0.999900i	$0.495492\pi$
$618$	−0.166825	−0.00671068
$619$	−15.4126	−0.619483	−0.309742	−	0.950821i	$-0.600243\pi$
$619$	−15.4126	−0.619483	−0.309742	+	0.950821i	$0.600243\pi$
$620$	0.497742	0.0199898
$621$	12.1112	0.486007
$622$	2.70098	0.108300
$623$	65.7464	2.63407
$624$	−4.55395	−0.182304
$625$	24.9826	0.999302
$626$	1.85235	0.0740347
$627$	−0.372934	−0.0148936
$628$	31.6938	1.26472
$629$	2.39769	0.0956020
$630$	−0.0400942	−0.00159739
$631$	−10.4908	−0.417632	−0.208816	−	0.977955i	$-0.566961\pi$
$631$	−10.4908	−0.417632	−0.208816	+	0.977955i	$0.566961\pi$
$632$	−2.98755	−0.118838
$633$	−0.360675	−0.0143355
$634$	0.749069	0.0297493
$635$	−0.534371	−0.0212059
$636$	8.60819	0.341337
$637$	38.5313	1.52666
$638$	−0.176652	−0.00699372
$639$	−19.4322	−0.768727
$640$	0.101313	0.00400477
$641$	19.1164	0.755054	0.377527	−	0.925999i	$-0.376775\pi$
$641$	19.1164	0.755054	0.377527	+	0.925999i	$0.376775\pi$
$642$	−0.390220	−0.0154008
$643$	−24.8698	−0.980770	−0.490385	−	0.871506i	$-0.663144\pi$
$643$	−24.8698	−0.980770	−0.490385	+	0.871506i	$0.663144\pi$
$644$	49.7107	1.95888
$645$	−0.0119865	−0.000471969 0
$646$	−0.189264	−0.00744648
$647$	−30.4827	−1.19840	−0.599199	−	0.800600i	$-0.704514\pi$
$647$	−30.4827	−1.19840	−0.599199	+	0.800600i	$0.704514\pi$
$648$	2.93989	0.115490
$649$	−1.87153	−0.0734639
$650$	1.50116	0.0588803
$651$	−11.5389	−0.452244
$652$	49.4088	1.93500
$653$	15.6369	0.611919	0.305960	−	0.952044i	$-0.401023\pi$
$653$	15.6369	0.611919	0.305960	+	0.952044i	$0.401023\pi$
$654$	−0.101722	−0.00397766
$655$	0.125728	0.00491259
$656$	30.4261	1.18794
$657$	4.23421	0.165192
$658$	−2.43772	−0.0950323
$659$	1.57640	0.0614080	0.0307040	−	0.999529i	$-0.490225\pi$
$659$	1.57640	0.0614080	0.0307040	+	0.999529i	$0.490225\pi$
$660$	0.0253213	0.000985631 0
$661$	3.28744	0.127867	0.0639333	−	0.997954i	$-0.479636\pi$
$661$	3.28744	0.127867	0.0639333	+	0.997954i	$0.479636\pi$
$662$	0.269630	0.0104795
$663$	−2.32591	−0.0903310
$664$	0.0486460	0.00188783
$665$	−0.148813	−0.00577070
$666$	0.320435	0.0124166
$667$	10.4105	0.403094
$668$	−34.6611	−1.34108
$669$	−3.90225	−0.150870
$670$	0.00979788	0.000378525 0
$671$	5.28168	0.203897
$672$	−1.76283	−0.0680027
$673$	24.9218	0.960664	0.480332	−	0.877087i	$-0.340516\pi$
$673$	24.9218	0.960664	0.480332	+	0.877087i	$0.340516\pi$
$674$	−1.42125	−0.0547443
$675$	−10.5832	−0.407347
$676$	5.51123	0.211971
$677$	23.8077	0.915003	0.457501	−	0.889209i	$-0.348745\pi$
$677$	23.8077	0.915003	0.457501	+	0.889209i	$0.348745\pi$
$678$	−0.303947	−0.0116730
$679$	−2.91870	−0.112009
$680$	0.0257580	0.000987773 0
$681$	−1.58206	−0.0606246
$682$	0.711607	0.0272489
$683$	−8.24928	−0.315650	−0.157825	−	0.987467i	$-0.550448\pi$
$683$	−8.24928	−0.315650	−0.157825	+	0.987467i	$0.550448\pi$
$684$	5.71453	0.218501
$685$	0.00629925	0.000240682 0
$686$	2.06721	0.0789265
$687$	6.71409	0.256159
$688$	3.84702	0.146666
$689$	38.3415	1.46069
$690$	0.00660498	0.000251447 0
$691$	−35.8599	−1.36418	−0.682088	−	0.731270i	$-0.738928\pi$
$691$	−35.8599	−1.36418	−0.682088	+	0.731270i	$0.738928\pi$
$692$	−32.3367	−1.22926
$693$	12.9504	0.491945
$694$	−2.04550	−0.0776461
$695$	−0.704879	−0.0267376
$696$	−0.245935	−0.00932213
$697$	15.5400	0.588621
$698$	0.941282	0.0356280
$699$	8.64595	0.327020
$700$	−43.4389	−1.64183
$701$	46.0238	1.73830	0.869148	−	0.494553i	$-0.164668\pi$
$701$	46.0238	1.73830	0.869148	+	0.494553i	$0.164668\pi$
$702$	−0.635777	−0.0239959
$703$	1.18932	0.0448560
$704$	−8.05402	−0.303547
$705$	0.0731764	0.00275598
$706$	−2.43808	−0.0917582
$707$	−56.5075	−2.12518
$708$	−1.29989	−0.0488529
$709$	33.6447	1.26355	0.631776	−	0.775151i	$-0.282326\pi$
$709$	33.6447	1.26355	0.631776	+	0.775151i	$0.282326\pi$
$710$	−0.0216755	−0.000813467 0
$711$	22.8828	0.858172
$712$	−5.64481	−0.211548
$713$	−41.9364	−1.57053
$714$	−0.297907	−0.0111489
$715$	0.112783	0.00421784
$716$	−22.0892	−0.825512
$717$	−4.26223	−0.159176
$718$	−1.05711	−0.0394510
$719$	0.491591	0.0183333	0.00916663	−	0.999958i	$-0.497082\pi$
$719$	0.491591	0.0183333	0.00916663	+	0.999958i	$0.497082\pi$
$720$	−0.386278	−0.0143957
$721$	21.5015	0.800760
$722$	−0.0938800	−0.00349385
$723$	0.103606	0.00385317
$724$	31.3486	1.16506
$725$	−9.09699	−0.337854
$726$	−0.336260	−0.0124798
$727$	−33.5897	−1.24577	−0.622887	−	0.782312i	$-0.714040\pi$
$727$	−33.5897	−1.24577	−0.622887	+	0.782312i	$0.714040\pi$
$728$	−5.23067	−0.193861
$729$	−20.2270	−0.749148
$730$	0.00472301	0.000174807 0
$731$	1.96485	0.0726727
$732$	3.66845	0.135590
$733$	7.92363	0.292666	0.146333	−	0.989235i	$-0.453253\pi$
$733$	7.92363	0.292666	0.146333	+	0.989235i	$0.453253\pi$
$734$	−1.71823	−0.0634212
$735$	−0.148145	−0.00546441
$736$	−6.40677	−0.236157
$737$	−3.16471	−0.116573
$738$	2.07683	0.0764490
$739$	−48.4189	−1.78112	−0.890559	−	0.454868i	$-0.849686\pi$
$739$	−48.4189	−1.78112	−0.890559	+	0.454868i	$0.849686\pi$
$740$	−0.0807518	−0.00296850
$741$	−1.15372	−0.0423829
$742$	4.91083	0.180282
$743$	13.1737	0.483296	0.241648	−	0.970364i	$-0.422312\pi$
$743$	13.1737	0.483296	0.241648	+	0.970364i	$0.422312\pi$
$744$	0.990698	0.0363208
$745$	0.190633	0.00698426
$746$	0.694169	0.0254153
$747$	−0.372598	−0.0136327
$748$	−4.15071	−0.151765
$749$	50.2942	1.83771
$750$	−0.0115446	−0.000421551 0
$751$	−18.4827	−0.674442	−0.337221	−	0.941425i	$-0.609487\pi$
$751$	−18.4827	−0.674442	−0.337221	+	0.941425i	$0.609487\pi$
$752$	−23.4856	−0.856433
$753$	−4.22598	−0.154003
$754$	−0.546495	−0.0199022
$755$	0.773333	0.0281445
$756$	18.3974	0.669107
$757$	−34.2248	−1.24392	−0.621960	−	0.783049i	$-0.713663\pi$
$757$	−34.2248	−1.24392	−0.621960	+	0.783049i	$0.713663\pi$
$758$	−0.834392	−0.0303065
$759$	−2.13340	−0.0774376
$760$	0.0127767	0.000463458 0
$761$	−20.7337	−0.751595	−0.375797	−	0.926702i	$-0.622631\pi$
$761$	−20.7337	−0.751595	−0.375797	+	0.926702i	$0.622631\pi$
$762$	−0.530628	−0.0192226
$763$	13.1107	0.474638
$764$	37.2945	1.34927
$765$	−0.197290	−0.00713303
$766$	2.91691	0.105392
$767$	−5.78980	−0.209058
$768$	−5.51817	−0.199120
$769$	28.8120	1.03899	0.519494	−	0.854474i	$-0.326121\pi$
$769$	28.8120	1.03899	0.519494	+	0.854474i	$0.326121\pi$
$770$	0.0144454	0.000520576 0
$771$	−6.56664	−0.236492
$772$	13.9639	0.502572
$773$	−22.2472	−0.800177	−0.400088	−	0.916477i	$-0.631021\pi$
$773$	−22.2472	−0.800177	−0.400088	+	0.916477i	$0.631021\pi$
$774$	0.262590	0.00943860
$775$	36.6454	1.31634
$776$	0.250592	0.00899574
$777$	1.87202	0.0671585
$778$	0.924552	0.0331468
$779$	7.70829	0.276178
$780$	0.0783346	0.00280483
$781$	7.00117	0.250521
$782$	−1.08270	−0.0387173
$783$	3.85280	0.137688
$784$	47.5464	1.69809
$785$	−0.542755	−0.0193718
$786$	0.124847	0.00445315
$787$	29.2427	1.04239	0.521194	−	0.853438i	$-0.325487\pi$
$787$	29.2427	1.04239	0.521194	+	0.853438i	$0.325487\pi$
$788$	8.31375	0.296165
$789$	5.78706	0.206025
$790$	0.0255244	0.000908117 0
$791$	39.1747	1.39289
$792$	−1.11189	−0.0395092
$793$	16.3395	0.580233
$794$	2.46174	0.0873638
$795$	−0.147415	−0.00522828
$796$	−20.8338	−0.738433
$797$	24.1175	0.854287	0.427144	−	0.904184i	$-0.359520\pi$
$797$	24.1175	0.854287	0.427144	+	0.904184i	$0.359520\pi$
$798$	−0.147770	−0.00523100
$799$	−11.9952	−0.424360
$800$	5.59844	0.197935
$801$	43.2358	1.52766
$802$	0.741852	0.0261957
$803$	−1.52553	−0.0538347
$804$	−2.19808	−0.0775204
$805$	−0.851296	−0.0300042
$806$	2.20145	0.0775426
$807$	−3.11011	−0.109481
$808$	4.85158	0.170678
$809$	16.7972	0.590558	0.295279	−	0.955411i	$-0.404587\pi$
$809$	16.7972	0.590558	0.295279	+	0.955411i	$0.404587\pi$
$810$	−0.0251172	−0.000882530 0
$811$	−28.4757	−0.999918	−0.499959	−	0.866049i	$-0.666652\pi$
$811$	−28.4757	−0.999918	−0.499959	+	0.866049i	$0.666652\pi$
$812$	15.8139	0.554958
$813$	−4.54572	−0.159425
$814$	−0.115448	−0.00404647
$815$	−0.846124	−0.0296384
$816$	−2.87011	−0.100474
$817$	0.974621	0.0340977
$818$	0.541624	0.0189375
$819$	40.0637	1.39994
$820$	−0.523374	−0.0182770
$821$	−43.5756	−1.52080	−0.760399	−	0.649456i	$-0.774997\pi$
$821$	−43.5756	−1.52080	−0.760399	+	0.649456i	$0.774997\pi$
$822$	0.00625512	0.000218172 0
$823$	17.1995	0.599538	0.299769	−	0.954012i	$-0.403090\pi$
$823$	17.1995	0.599538	0.299769	+	0.954012i	$0.403090\pi$
$824$	−1.84607	−0.0643108
$825$	1.86424	0.0649044
$826$	−0.741567	−0.0258024
$827$	−34.2305	−1.19031	−0.595156	−	0.803610i	$-0.702910\pi$
$827$	−34.2305	−1.19031	−0.595156	+	0.803610i	$0.702910\pi$
$828$	32.6905	1.13607
$829$	24.3036	0.844097	0.422049	−	0.906573i	$-0.361311\pi$
$829$	24.3036	0.844097	0.422049	+	0.906573i	$0.361311\pi$
$830$	−0.000415611 0	−1.44261e−5 0
$831$	7.72165	0.267861
$832$	−24.9161	−0.863810
$833$	24.2842	0.841396
$834$	−0.699940	−0.0242370
$835$	0.593572	0.0205414
$836$	−2.05887	−0.0712075
$837$	−15.5202	−0.536457
$838$	0.144430	0.00498924
$839$	−41.3689	−1.42821	−0.714107	−	0.700036i	$-0.753167\pi$
$839$	−41.3689	−1.42821	−0.714107	+	0.700036i	$0.753167\pi$
$840$	0.0201108	0.000693890 0
$841$	−25.6882	−0.885802
$842$	0.0284062	0.000978943 0
$843$	−9.22168	−0.317611
$844$	−1.99119	−0.0685395
$845$	−0.0943798	−0.00324676
$846$	−1.60308	−0.0551151
$847$	43.3396	1.48916
$848$	47.3122	1.62471
$849$	−3.83766	−0.131708
$850$	0.946098	0.0324509
$851$	6.80360	0.233225
$852$	4.86274	0.166595
$853$	−27.4047	−0.938319	−0.469160	−	0.883113i	$-0.655443\pi$
$853$	−27.4047	−0.938319	−0.469160	+	0.883113i	$0.655443\pi$
$854$	2.09279	0.0716138
$855$	−0.0978613	−0.00334679
$856$	−4.31813	−0.147591
$857$	−17.3872	−0.593935	−0.296967	−	0.954888i	$-0.595975\pi$
$857$	−17.3872	−0.593935	−0.296967	+	0.954888i	$0.595975\pi$
$858$	0.111993	0.00382337
$859$	−20.1617	−0.687909	−0.343954	−	0.938986i	$-0.611767\pi$
$859$	−20.1617	−0.687909	−0.343954	+	0.938986i	$0.611767\pi$
$860$	−0.0661744	−0.00225653
$861$	12.1331	0.413494
$862$	3.50999	0.119551
$863$	−24.4607	−0.832652	−0.416326	−	0.909215i	$-0.636682\pi$
$863$	−24.4607	−0.832652	−0.416326	+	0.909215i	$0.636682\pi$
$864$	−2.37108	−0.0806656
$865$	0.553766	0.0188286
$866$	−0.766170	−0.0260355
$867$	4.66557	0.158451
$868$	−63.7030	−2.16222
$869$	−8.24436	−0.279671
$870$	0.00210116	7.12361e−5 0
$871$	−9.79041	−0.331735
$872$	−1.12565	−0.0381193
$873$	−1.91938	−0.0649612
$874$	−0.537049	−0.0181660
$875$	1.48795	0.0503020
$876$	−1.05957	−0.0357997
$877$	35.6214	1.20285	0.601425	−	0.798929i	$-0.294600\pi$
$877$	35.6214	1.20285	0.601425	+	0.798929i	$0.294600\pi$
$878$	3.42787	0.115685
$879$	−1.66118	−0.0560303
$880$	0.139171	0.00469144
$881$	45.3789	1.52885	0.764427	−	0.644710i	$-0.223022\pi$
$881$	45.3789	1.52885	0.764427	+	0.644710i	$0.223022\pi$
$882$	3.24542	0.109279
$883$	−5.82907	−0.196164	−0.0980819	−	0.995178i	$-0.531271\pi$
$883$	−5.82907	−0.196164	−0.0980819	+	0.995178i	$0.531271\pi$
$884$	−12.8407	−0.431881
$885$	0.0222606	0.000748282 0
$886$	−3.32583	−0.111734
$887$	−51.3263	−1.72337	−0.861684	−	0.507445i	$-0.830590\pi$
$887$	−51.3263	−1.72337	−0.861684	+	0.507445i	$0.830590\pi$
$888$	−0.160727	−0.00539365
$889$	68.3909	2.29376
$890$	0.0482269	0.00161657
$891$	8.11284	0.271790
$892$	−21.5433	−0.721322
$893$	−5.94995	−0.199108
$894$	0.189298	0.00633106
$895$	0.378277	0.0126444
$896$	−12.9665	−0.433180
$897$	−6.59995	−0.220366
$898$	−2.64536	−0.0882768
$899$	−13.3407	−0.444938
$900$	−28.5660	−0.952201
$901$	24.1645	0.805037
$902$	−0.748252	−0.0249141
$903$	1.53408	0.0510511
$904$	−3.36344	−0.111866
$905$	−0.536844	−0.0178453
$906$	0.767915	0.0255123
$907$	33.0141	1.09622	0.548108	−	0.836408i	$-0.315348\pi$
$907$	33.0141	1.09622	0.548108	+	0.836408i	$0.315348\pi$
$908$	−8.73411	−0.289852
$909$	−37.1601	−1.23252
$910$	0.0446886	0.00148141
$911$	−27.5969	−0.914327	−0.457164	−	0.889383i	$-0.651135\pi$
$911$	−27.5969	−0.914327	−0.457164	+	0.889383i	$0.651135\pi$
$912$	−1.42365	−0.0471419
$913$	0.134242	0.00444277
$914$	−1.80437	−0.0596833
$915$	−0.0628221	−0.00207684
$916$	37.0667	1.22472
$917$	−16.0911	−0.531376
$918$	−0.400696	−0.0132249
$919$	−18.0357	−0.594942	−0.297471	−	0.954731i	$-0.596143\pi$
$919$	−18.0357	−0.594942	−0.297471	+	0.954731i	$0.596143\pi$
$920$	0.0730901	0.00240971
$921$	11.0740	0.364901
$922$	0.00920538	0.000303163 0
$923$	21.6590	0.712914
$924$	−3.24072	−0.106612
$925$	−5.94521	−0.195477
$926$	−0.0662335	−0.00217657
$927$	14.1397	0.464410
$928$	−2.03811	−0.0669041
$929$	−11.4561	−0.375863	−0.187932	−	0.982182i	$-0.560178\pi$
$929$	−11.4561	−0.375863	−0.187932	+	0.982182i	$0.560178\pi$
$930$	−0.00846411	−0.000277549 0
$931$	12.0456	0.394779
$932$	47.7319	1.56351
$933$	10.3768	0.339722
$934$	3.39321	0.111029
$935$	0.0710809	0.00232459
$936$	−3.43976	−0.112432
$937$	8.84586	0.288982	0.144491	−	0.989506i	$-0.453846\pi$
$937$	8.84586	0.288982	0.144491	+	0.989506i	$0.453846\pi$
$938$	−1.25397	−0.0409436
$939$	7.11647	0.232237
$940$	0.403987	0.0131766
$941$	14.0761	0.458869	0.229434	−	0.973324i	$-0.426312\pi$
$941$	14.0761	0.458869	0.229434	+	0.973324i	$0.426312\pi$
$942$	−0.538953	−0.0175600
$943$	44.0960	1.43596
$944$	−7.14444	−0.232532
$945$	−0.315055	−0.0102488
$946$	−0.0946075	−0.00307596
$947$	1.75443	0.0570114	0.0285057	−	0.999594i	$-0.490925\pi$
$947$	1.75443	0.0570114	0.0285057	+	0.999594i	$0.490925\pi$
$948$	−5.72622	−0.185979
$949$	−4.71941	−0.153199
$950$	0.469291	0.0152258
$951$	2.87782	0.0933198
$952$	−3.29660	−0.106844
$953$	54.8187	1.77575	0.887876	−	0.460083i	$-0.152180\pi$
$953$	54.8187	1.77575	0.887876	+	0.460083i	$0.152180\pi$
$954$	3.22944	0.104557
$955$	−0.638668	−0.0206668
$956$	−23.5306	−0.761034
$957$	−0.678674	−0.0219384
$958$	0.874970	0.0282690
$959$	−0.806203	−0.0260336
$960$	0.0957973	0.00309185
$961$	22.7404	0.733562
$962$	−0.357154	−0.0115151
$963$	33.0742	1.06580
$964$	0.571983	0.0184223
$965$	−0.239132	−0.00769792
$966$	−0.845332	−0.0271981
$967$	−18.3629	−0.590511	−0.295256	−	0.955418i	$-0.595405\pi$
$967$	−18.3629	−0.590511	−0.295256	+	0.955418i	$0.595405\pi$
$968$	−3.72102	−0.119598
$969$	−0.727126	−0.0233586
$970$	−0.00214096	−6.87419e−5 0
$971$	−45.3654	−1.45585	−0.727923	−	0.685659i	$-0.759514\pi$
$971$	−45.3654	−1.45585	−0.727923	+	0.685659i	$0.759514\pi$
$972$	18.2817	0.586385
$973$	90.2131	2.89210
$974$	1.72756	0.0553547
$975$	5.76725	0.184700
$976$	20.1625	0.645385
$977$	16.0462	0.513364	0.256682	−	0.966496i	$-0.417371\pi$
$977$	16.0462	0.513364	0.256682	+	0.966496i	$0.417371\pi$
$978$	−0.840196	−0.0268665
$979$	−15.5773	−0.497851
$980$	−0.817868	−0.0261258
$981$	8.62177	0.275272
$982$	3.17608	0.101353
$983$	−4.91014	−0.156609	−0.0783045	−	0.996929i	$-0.524951\pi$
$983$	−4.91014	−0.156609	−0.0783045	+	0.996929i	$0.524951\pi$
$984$	−1.04171	−0.0332086
$985$	−0.142373	−0.00453637
$986$	−0.344426	−0.0109688
$987$	−9.36541	−0.298104
$988$	−6.36937	−0.202637
$989$	5.57541	0.177288
$990$	0.00949950	0.000301914 0
$991$	−10.0918	−0.320576	−0.160288	−	0.987070i	$-0.551242\pi$
$991$	−10.0918	−0.320576	−0.160288	+	0.987070i	$0.551242\pi$
$992$	8.21010	0.260671
$993$	1.03588	0.0328727
$994$	2.77412	0.0879896
$995$	0.356778	0.0113106
$996$	0.0932394	0.00295440
$997$	22.9185	0.725835	0.362918	−	0.931821i	$-0.381781\pi$
$997$	22.9185	0.725835	0.362918	+	0.931821i	$0.381781\pi$
$998$	−1.20270	−0.0380709
$999$	2.51794	0.0796641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.40	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.40	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0938800 q^{2} -0.360675 q^{3} -1.99119 q^{4} +0.0340990 q^{5} +0.0338601 q^{6} -4.36413 q^{7} +0.374693 q^{8} -2.86991 q^{9} +O(q^{10})\)	\(q-0.0938800 q^{2} -0.360675 q^{3} -1.99119 q^{4} +0.0340990 q^{5} +0.0338601 q^{6} -4.36413 q^{7} +0.374693 q^{8} -2.86991 q^{9} -0.00320122 q^{10} +1.03399 q^{11} +0.718170 q^{12} +3.19878 q^{13} +0.409705 q^{14} -0.0122987 q^{15} +3.94720 q^{16} +2.01602 q^{17} +0.269428 q^{18} +1.00000 q^{19} -0.0678975 q^{20} +1.57403 q^{21} -0.0970711 q^{22} +5.72059 q^{23} -0.135142 q^{24} -4.99884 q^{25} -0.300301 q^{26} +2.11713 q^{27} +8.68979 q^{28} +1.81982 q^{29} +0.00115460 q^{30} -7.33079 q^{31} -1.11995 q^{32} -0.372934 q^{33} -0.189264 q^{34} -0.148813 q^{35} +5.71453 q^{36} +1.18932 q^{37} -0.0938800 q^{38} -1.15372 q^{39} +0.0127767 q^{40} +7.70829 q^{41} -0.147770 q^{42} +0.974621 q^{43} -2.05887 q^{44} -0.0978613 q^{45} -0.537049 q^{46} -5.94995 q^{47} -1.42365 q^{48} +12.0456 q^{49} +0.469291 q^{50} -0.727126 q^{51} -6.36937 q^{52} +11.9863 q^{53} -0.198756 q^{54} +0.0352581 q^{55} -1.63521 q^{56} -0.360675 q^{57} -0.170845 q^{58} -1.81000 q^{59} +0.0244889 q^{60} +5.10805 q^{61} +0.688215 q^{62} +12.5247 q^{63} -7.78925 q^{64} +0.109075 q^{65} +0.0350111 q^{66} -3.06067 q^{67} -4.01426 q^{68} -2.06327 q^{69} +0.0139705 q^{70} +6.77101 q^{71} -1.07534 q^{72} -1.47538 q^{73} -0.111653 q^{74} +1.80295 q^{75} -1.99119 q^{76} -4.51247 q^{77} +0.108311 q^{78} -7.97334 q^{79} +0.134596 q^{80} +7.84615 q^{81} -0.723654 q^{82} +0.129829 q^{83} -3.13419 q^{84} +0.0687442 q^{85} -0.0914975 q^{86} -0.656363 q^{87} +0.387429 q^{88} -15.0652 q^{89} +0.00918722 q^{90} -13.9599 q^{91} -11.3908 q^{92} +2.64403 q^{93} +0.558582 q^{94} +0.0340990 q^{95} +0.403937 q^{96} +0.668794 q^{97} -1.13084 q^{98} -2.96746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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