LMFDB - Embedded newform 8027.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48946 q^{2} -0.455224 q^{3} +4.19741 q^{4} -1.13104 q^{5} +1.13326 q^{6} -1.16006 q^{7} -5.47036 q^{8} -2.79277 q^{9} +O(q^{10})$	\(q-2.48946 q^{2} -0.455224 q^{3} +4.19741 q^{4} -1.13104 q^{5} +1.13326 q^{6} -1.16006 q^{7} -5.47036 q^{8} -2.79277 q^{9} +2.81568 q^{10} +5.84848 q^{11} -1.91076 q^{12} +5.28477 q^{13} +2.88793 q^{14} +0.514876 q^{15} +5.22343 q^{16} +0.0550057 q^{17} +6.95249 q^{18} -5.92841 q^{19} -4.74743 q^{20} +0.528088 q^{21} -14.5595 q^{22} +1.00000 q^{23} +2.49024 q^{24} -3.72075 q^{25} -13.1562 q^{26} +2.63701 q^{27} -4.86926 q^{28} +0.117065 q^{29} -1.28176 q^{30} +9.05024 q^{31} -2.06279 q^{32} -2.66237 q^{33} -0.136934 q^{34} +1.31208 q^{35} -11.7224 q^{36} +3.51724 q^{37} +14.7585 q^{38} -2.40575 q^{39} +6.18719 q^{40} -5.29212 q^{41} -1.31465 q^{42} +1.58321 q^{43} +24.5484 q^{44} +3.15873 q^{45} -2.48946 q^{46} -8.67396 q^{47} -2.37783 q^{48} -5.65425 q^{49} +9.26266 q^{50} -0.0250399 q^{51} +22.1823 q^{52} +2.49150 q^{53} -6.56473 q^{54} -6.61485 q^{55} +6.34596 q^{56} +2.69875 q^{57} -0.291429 q^{58} +0.0402576 q^{59} +2.16115 q^{60} -11.3126 q^{61} -22.5302 q^{62} +3.23979 q^{63} -5.31162 q^{64} -5.97728 q^{65} +6.62785 q^{66} -9.65831 q^{67} +0.230881 q^{68} -0.455224 q^{69} -3.26636 q^{70} +0.908665 q^{71} +15.2775 q^{72} +9.84057 q^{73} -8.75603 q^{74} +1.69378 q^{75} -24.8840 q^{76} -6.78460 q^{77} +5.98902 q^{78} +3.52135 q^{79} -5.90790 q^{80} +7.17788 q^{81} +13.1745 q^{82} -13.5231 q^{83} +2.21660 q^{84} -0.0622136 q^{85} -3.94134 q^{86} -0.0532909 q^{87} -31.9933 q^{88} +3.13760 q^{89} -7.86354 q^{90} -6.13066 q^{91} +4.19741 q^{92} -4.11989 q^{93} +21.5935 q^{94} +6.70526 q^{95} +0.939032 q^{96} -4.80163 q^{97} +14.0760 q^{98} -16.3335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.48946	−1.76031	−0.880157	−	0.474683i	$-0.842563\pi$
$2$	−2.48946	−1.76031	−0.880157	+	0.474683i	$0.842563\pi$
$3$	−0.455224	−0.262824	−0.131412	−	0.991328i	$-0.541951\pi$
$3$	−0.455224	−0.262824	−0.131412	+	0.991328i	$0.541951\pi$
$4$	4.19741	2.09870
$5$	−1.13104	−0.505816	−0.252908	−	0.967490i	$-0.581387\pi$
$5$	−1.13104	−0.505816	−0.252908	+	0.967490i	$0.581387\pi$
$6$	1.13326	0.462652
$7$	−1.16006	−0.438462	−0.219231	−	0.975673i	$-0.570355\pi$
$7$	−1.16006	−0.438462	−0.219231	+	0.975673i	$0.570355\pi$
$8$	−5.47036	−1.93407
$9$	−2.79277	−0.930924
$10$	2.81568	0.890395
$11$	5.84848	1.76338	0.881691	−	0.471828i	$-0.156406\pi$
$11$	5.84848	1.76338	0.881691	+	0.471828i	$0.156406\pi$
$12$	−1.91076	−0.551589
$13$	5.28477	1.46573	0.732865	−	0.680374i	$-0.238183\pi$
$13$	5.28477	1.46573	0.732865	+	0.680374i	$0.238183\pi$
$14$	2.88793	0.771832
$15$	0.514876	0.132940
$16$	5.22343	1.30586
$17$	0.0550057	0.0133408	0.00667042	−	0.999978i	$-0.497877\pi$
$17$	0.0550057	0.0133408	0.00667042	+	0.999978i	$0.497877\pi$
$18$	6.95249	1.63872
$19$	−5.92841	−1.36007	−0.680035	−	0.733180i	$-0.738035\pi$
$19$	−5.92841	−1.36007	−0.680035	+	0.733180i	$0.738035\pi$
$20$	−4.74743	−1.06156
$21$	0.528088	0.115238
$22$	−14.5595	−3.10411
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.49024	0.508318
$25$	−3.72075	−0.744150
$26$	−13.1562	−2.58015
$27$	2.63701	0.507493
$28$	−4.86926	−0.920203
$29$	0.117065	0.0217385	0.0108692	−	0.999941i	$-0.496540\pi$
$29$	0.117065	0.0217385	0.0108692	+	0.999941i	$0.496540\pi$
$30$	−1.28176	−0.234017
$31$	9.05024	1.62547	0.812735	−	0.582633i	$-0.197977\pi$
$31$	9.05024	1.62547	0.812735	+	0.582633i	$0.197977\pi$
$32$	−2.06279	−0.364653
$33$	−2.66237	−0.463459
$34$	−0.136934	−0.0234841
$35$	1.31208	0.221781
$36$	−11.7224	−1.95373
$37$	3.51724	0.578231	0.289115	−	0.957294i	$-0.406639\pi$
$37$	3.51724	0.578231	0.289115	+	0.957294i	$0.406639\pi$
$38$	14.7585	2.39415
$39$	−2.40575	−0.385229
$40$	6.18719	0.978281
$41$	−5.29212	−0.826490	−0.413245	−	0.910620i	$-0.635605\pi$
$41$	−5.29212	−0.826490	−0.413245	+	0.910620i	$0.635605\pi$
$42$	−1.31465	−0.202856
$43$	1.58321	0.241438	0.120719	−	0.992687i	$-0.461480\pi$
$43$	1.58321	0.241438	0.120719	+	0.992687i	$0.461480\pi$
$44$	24.5484	3.70082
$45$	3.15873	0.470876
$46$	−2.48946	−0.367051
$47$	−8.67396	−1.26523	−0.632613	−	0.774468i	$-0.718018\pi$
$47$	−8.67396	−1.26523	−0.632613	+	0.774468i	$0.718018\pi$
$48$	−2.37783	−0.343210
$49$	−5.65425	−0.807751
$50$	9.26266	1.30994
$51$	−0.0250399	−0.00350629
$52$	22.1823	3.07614
$53$	2.49150	0.342234	0.171117	−	0.985251i	$-0.445262\pi$
$53$	2.49150	0.342234	0.171117	+	0.985251i	$0.445262\pi$
$54$	−6.56473	−0.893346
$55$	−6.61485	−0.891947
$56$	6.34596	0.848015
$57$	2.69875	0.357459
$58$	−0.291429	−0.0382665
$59$	0.0402576	0.00524110	0.00262055	−	0.999997i	$-0.499166\pi$
$59$	0.0402576	0.00524110	0.00262055	+	0.999997i	$0.499166\pi$
$60$	2.16115	0.279003
$61$	−11.3126	−1.44843	−0.724214	−	0.689575i	$-0.757797\pi$
$61$	−11.3126	−1.44843	−0.724214	+	0.689575i	$0.757797\pi$
$62$	−22.5302	−2.86134
$63$	3.23979	0.408175
$64$	−5.31162	−0.663953
$65$	−5.97728	−0.741390
$66$	6.62785	0.815832
$67$	−9.65831	−1.17995	−0.589975	−	0.807421i	$-0.700863\pi$
$67$	−9.65831	−1.17995	−0.589975	+	0.807421i	$0.700863\pi$
$68$	0.230881	0.0279985
$69$	−0.455224	−0.0548025
$70$	−3.26636	−0.390405
$71$	0.908665	0.107839	0.0539194	−	0.998545i	$-0.482829\pi$
$71$	0.908665	0.107839	0.0539194	+	0.998545i	$0.482829\pi$
$72$	15.2775	1.80047
$73$	9.84057	1.15175	0.575876	−	0.817537i	$-0.304661\pi$
$73$	9.84057	1.15175	0.575876	+	0.817537i	$0.304661\pi$
$74$	−8.75603	−1.01787
$75$	1.69378	0.195580
$76$	−24.8840	−2.85439
$77$	−6.78460	−0.773177
$78$	5.98902	0.678123
$79$	3.52135	0.396183	0.198091	−	0.980184i	$-0.436526\pi$
$79$	3.52135	0.396183	0.198091	+	0.980184i	$0.436526\pi$
$80$	−5.90790	−0.660524
$81$	7.17788	0.797543
$82$	13.1745	1.45488
$83$	−13.5231	−1.48435	−0.742174	−	0.670207i	$-0.766205\pi$
$83$	−13.5231	−1.48435	−0.742174	+	0.670207i	$0.766205\pi$
$84$	2.21660	0.241851
$85$	−0.0622136	−0.00674801
$86$	−3.94134	−0.425006
$87$	−0.0532909	−0.00571338
$88$	−31.9933	−3.41050
$89$	3.13760	0.332585	0.166293	−	0.986076i	$-0.446820\pi$
$89$	3.13760	0.332585	0.166293	+	0.986076i	$0.446820\pi$
$90$	−7.86354	−0.828890
$91$	−6.13066	−0.642668
$92$	4.19741	0.437610
$93$	−4.11989	−0.427212
$94$	21.5935	2.22720
$95$	6.70526	0.687945
$96$	0.939032	0.0958396
$97$	−4.80163	−0.487532	−0.243766	−	0.969834i	$-0.578383\pi$
$97$	−4.80163	−0.487532	−0.243766	+	0.969834i	$0.578383\pi$
$98$	14.0760	1.42189
$99$	−16.3335	−1.64157
$100$	−15.6175	−1.56175
$101$	13.3183	1.32522	0.662612	−	0.748963i	$-0.269448\pi$
$101$	13.3183	1.32522	0.662612	+	0.748963i	$0.269448\pi$
$102$	0.0623359	0.00617217
$103$	10.2400	1.00897	0.504487	−	0.863419i	$-0.331682\pi$
$103$	10.2400	1.00897	0.504487	+	0.863419i	$0.331682\pi$
$104$	−28.9096	−2.83482
$105$	−0.597288	−0.0582894
$106$	−6.20249	−0.602439
$107$	9.14689	0.884263	0.442132	−	0.896950i	$-0.354222\pi$
$107$	9.14689	0.884263	0.442132	+	0.896950i	$0.354222\pi$
$108$	11.0686	1.06508
$109$	−8.89716	−0.852193	−0.426096	−	0.904678i	$-0.640112\pi$
$109$	−8.89716	−0.852193	−0.426096	+	0.904678i	$0.640112\pi$
$110$	16.4674	1.57011
$111$	−1.60113	−0.151973
$112$	−6.05951	−0.572569
$113$	−9.69446	−0.911978	−0.455989	−	0.889985i	$-0.650714\pi$
$113$	−9.69446	−0.911978	−0.455989	+	0.889985i	$0.650714\pi$
$114$	−6.71844	−0.629239
$115$	−1.13104	−0.105470
$116$	0.491371	0.0456226
$117$	−14.7591	−1.36448
$118$	−0.100220	−0.00922598
$119$	−0.0638100	−0.00584946
$120$	−2.81656	−0.257116
$121$	23.2047	2.10951
$122$	28.1622	2.54969
$123$	2.40910	0.217221
$124$	37.9876	3.41138
$125$	9.86351	0.882219
$126$	−8.06532	−0.718516
$127$	−15.6718	−1.39065	−0.695325	−	0.718695i	$-0.744740\pi$
$127$	−15.6718	−1.39065	−0.695325	+	0.718695i	$0.744740\pi$
$128$	17.3487	1.53342
$129$	−0.720716	−0.0634555
$130$	14.8802	1.30508
$131$	−7.70061	−0.672806	−0.336403	−	0.941718i	$-0.609210\pi$
$131$	−7.70061	−0.672806	−0.336403	+	0.941718i	$0.609210\pi$
$132$	−11.1750	−0.972663
$133$	6.87732	0.596340
$134$	24.0440	2.07708
$135$	−2.98256	−0.256698
$136$	−0.300901	−0.0258021
$137$	−18.0729	−1.54407	−0.772036	−	0.635578i	$-0.780762\pi$
$137$	−18.0729	−1.54407	−0.772036	+	0.635578i	$0.780762\pi$
$138$	1.13326	0.0964697
$139$	−16.9878	−1.44089	−0.720443	−	0.693514i	$-0.756062\pi$
$139$	−16.9878	−1.44089	−0.720443	+	0.693514i	$0.756062\pi$
$140$	5.50732	0.465454
$141$	3.94859	0.332532
$142$	−2.26209	−0.189830
$143$	30.9078	2.58464
$144$	−14.5878	−1.21565
$145$	−0.132405	−0.0109957
$146$	−24.4977	−2.02744
$147$	2.57395	0.212296
$148$	14.7633	1.21354
$149$	17.4973	1.43343	0.716717	−	0.697364i	$-0.245644\pi$
$149$	17.4973	1.43343	0.716717	+	0.697364i	$0.245644\pi$
$150$	−4.21659	−0.344283
$151$	21.7969	1.77381	0.886904	−	0.461954i	$-0.152852\pi$
$151$	21.7969	1.77381	0.886904	+	0.461954i	$0.152852\pi$
$152$	32.4305	2.63046
$153$	−0.153618	−0.0124193
$154$	16.8900	1.36103
$155$	−10.2362	−0.822189
$156$	−10.0979	−0.808481
$157$	4.30536	0.343605	0.171803	−	0.985131i	$-0.445041\pi$
$157$	4.30536	0.343605	0.171803	+	0.985131i	$0.445041\pi$
$158$	−8.76626	−0.697406
$159$	−1.13419	−0.0899472
$160$	2.33310	0.184448
$161$	−1.16006	−0.0914257
$162$	−17.8691	−1.40393
$163$	−17.6344	−1.38123	−0.690616	−	0.723222i	$-0.742660\pi$
$163$	−17.6344	−1.38123	−0.690616	+	0.723222i	$0.742660\pi$
$164$	−22.2132	−1.73456
$165$	3.01124	0.234425
$166$	33.6651	2.61292
$167$	11.0680	0.856465	0.428232	−	0.903669i	$-0.359137\pi$
$167$	11.0680	0.856465	0.428232	+	0.903669i	$0.359137\pi$
$168$	−2.88884	−0.222878
$169$	14.9288	1.14837
$170$	0.154878	0.0118786
$171$	16.5567	1.26612
$172$	6.64539	0.506706
$173$	13.6752	1.03970	0.519852	−	0.854256i	$-0.325987\pi$
$173$	13.6752	1.03970	0.519852	+	0.854256i	$0.325987\pi$
$174$	0.132666	0.0100573
$175$	4.31630	0.326282
$176$	30.5491	2.30272
$177$	−0.0183262	−0.00137749
$178$	−7.81094	−0.585454
$179$	−0.661684	−0.0494566	−0.0247283	−	0.999694i	$-0.507872\pi$
$179$	−0.661684	−0.0494566	−0.0247283	+	0.999694i	$0.507872\pi$
$180$	13.2585	0.988230
$181$	4.73503	0.351952	0.175976	−	0.984394i	$-0.443692\pi$
$181$	4.73503	0.351952	0.175976	+	0.984394i	$0.443692\pi$
$182$	15.2620	1.13130
$183$	5.14976	0.380681
$184$	−5.47036	−0.403281
$185$	−3.97814	−0.292478
$186$	10.2563	0.752028
$187$	0.321699	0.0235250
$188$	−36.4082	−2.65534
$189$	−3.05910	−0.222516
$190$	−16.6925	−1.21100
$191$	8.42149	0.609358	0.304679	−	0.952455i	$-0.401451\pi$
$191$	8.42149	0.609358	0.304679	+	0.952455i	$0.401451\pi$
$192$	2.41798	0.174503
$193$	−19.1907	−1.38138	−0.690690	−	0.723151i	$-0.742693\pi$
$193$	−19.1907	−1.38138	−0.690690	+	0.723151i	$0.742693\pi$
$194$	11.9535	0.858209
$195$	2.72100	0.194855
$196$	−23.7332	−1.69523
$197$	−6.98150	−0.497411	−0.248706	−	0.968579i	$-0.580005\pi$
$197$	−6.98150	−0.497411	−0.248706	+	0.968579i	$0.580005\pi$
$198$	40.6615	2.88968
$199$	0.705582	0.0500174	0.0250087	−	0.999687i	$-0.492039\pi$
$199$	0.705582	0.0500174	0.0250087	+	0.999687i	$0.492039\pi$
$200$	20.3539	1.43924
$201$	4.39670	0.310119
$202$	−33.1555	−2.33281
$203$	−0.135803	−0.00953150
$204$	−0.105103	−0.00735867
$205$	5.98559	0.418052
$206$	−25.4920	−1.77611
$207$	−2.79277	−0.194111
$208$	27.6046	1.91404
$209$	−34.6721	−2.39832
$210$	1.48693	0.102608
$211$	−0.155358	−0.0106953	−0.00534766	−	0.999986i	$-0.501702\pi$
$211$	−0.155358	−0.0106953	−0.00534766	+	0.999986i	$0.501702\pi$
$212$	10.4579	0.718248
$213$	−0.413646	−0.0283426
$214$	−22.7708	−1.55658
$215$	−1.79067	−0.122123
$216$	−14.4254	−0.981524
$217$	−10.4988	−0.712708
$218$	22.1491	1.50013
$219$	−4.47966	−0.302707
$220$	−27.7652	−1.87193
$221$	0.290692	0.0195541
$222$	3.98596	0.267520
$223$	−1.34185	−0.0898568	−0.0449284	−	0.998990i	$-0.514306\pi$
$223$	−1.34185	−0.0898568	−0.0449284	+	0.998990i	$0.514306\pi$
$224$	2.39297	0.159887
$225$	10.3912	0.692747
$226$	24.1340	1.60537
$227$	7.76901	0.515647	0.257824	−	0.966192i	$-0.416995\pi$
$227$	7.76901	0.515647	0.257824	+	0.966192i	$0.416995\pi$
$228$	11.3278	0.750200
$229$	4.73228	0.312718	0.156359	−	0.987700i	$-0.450024\pi$
$229$	4.73228	0.312718	0.156359	+	0.987700i	$0.450024\pi$
$230$	2.81568	0.185660
$231$	3.08851	0.203209
$232$	−0.640389	−0.0420436
$233$	21.7060	1.42201	0.711003	−	0.703189i	$-0.248241\pi$
$233$	21.7060	1.42201	0.711003	+	0.703189i	$0.248241\pi$
$234$	36.7423	2.40192
$235$	9.81058	0.639972
$236$	0.168978	0.0109995
$237$	−1.60300	−0.104126
$238$	0.158853	0.0102969
$239$	−13.8624	−0.896682	−0.448341	−	0.893863i	$-0.647985\pi$
$239$	−13.8624	−0.896682	−0.448341	+	0.893863i	$0.647985\pi$
$240$	2.68942	0.173601
$241$	−9.82776	−0.633061	−0.316531	−	0.948582i	$-0.602518\pi$
$241$	−9.82776	−0.633061	−0.316531	+	0.948582i	$0.602518\pi$
$242$	−57.7671	−3.71341
$243$	−11.1786	−0.717106
$244$	−47.4835	−3.03982
$245$	6.39518	0.408573
$246$	−5.99736	−0.382377
$247$	−31.3302	−1.99350
$248$	−49.5081	−3.14377
$249$	6.15602	0.390122
$250$	−24.5548	−1.55298
$251$	20.6313	1.30223	0.651117	−	0.758978i	$-0.274301\pi$
$251$	20.6313	1.30223	0.651117	+	0.758978i	$0.274301\pi$
$252$	13.5987	0.856639
$253$	5.84848	0.367690
$254$	39.0144	2.44798
$255$	0.0283211	0.00177354
$256$	−32.5655	−2.03535
$257$	−8.63131	−0.538406	−0.269203	−	0.963083i	$-0.586760\pi$
$257$	−8.63131	−0.538406	−0.269203	+	0.963083i	$0.586760\pi$
$258$	1.79419	0.111702
$259$	−4.08022	−0.253533
$260$	−25.0891	−1.55596
$261$	−0.326936	−0.0202368
$262$	19.1704	1.18435
$263$	1.75750	0.108372	0.0541862	−	0.998531i	$-0.482744\pi$
$263$	1.75750	0.108372	0.0541862	+	0.998531i	$0.482744\pi$
$264$	14.5641	0.896359
$265$	−2.81798	−0.173107
$266$	−17.1208	−1.04974
$267$	−1.42831	−0.0874113
$268$	−40.5399	−2.47637
$269$	19.8146	1.20812	0.604059	−	0.796940i	$-0.293549\pi$
$269$	19.8146	1.20812	0.604059	+	0.796940i	$0.293549\pi$
$270$	7.42496	0.451869
$271$	−14.9302	−0.906944	−0.453472	−	0.891271i	$-0.649815\pi$
$271$	−14.9302	−0.906944	−0.453472	+	0.891271i	$0.649815\pi$
$272$	0.287318	0.0174212
$273$	2.79082	0.168908
$274$	44.9918	2.71805
$275$	−21.7607	−1.31222
$276$	−1.91076	−0.115014
$277$	−28.5504	−1.71543	−0.857713	−	0.514129i	$-0.828115\pi$
$277$	−28.5504	−1.71543	−0.857713	+	0.514129i	$0.828115\pi$
$278$	42.2904	2.53641
$279$	−25.2752	−1.51319
$280$	−7.17753	−0.428940
$281$	6.66663	0.397698	0.198849	−	0.980030i	$-0.436280\pi$
$281$	6.66663	0.397698	0.198849	+	0.980030i	$0.436280\pi$
$282$	−9.82987	−0.585360
$283$	−23.6052	−1.40318	−0.701592	−	0.712579i	$-0.747527\pi$
$283$	−23.6052	−1.40318	−0.701592	+	0.712579i	$0.747527\pi$
$284$	3.81404	0.226322
$285$	−3.05240	−0.180808
$286$	−76.9438	−4.54978
$287$	6.13919	0.362385
$288$	5.76090	0.339464
$289$	−16.9970	−0.999822
$290$	0.329618	0.0193558
$291$	2.18582	0.128135
$292$	41.3049	2.41719
$293$	15.5547	0.908717	0.454359	−	0.890819i	$-0.349869\pi$
$293$	15.5547	0.908717	0.454359	+	0.890819i	$0.349869\pi$
$294$	−6.40775	−0.373708
$295$	−0.0455330	−0.00265103
$296$	−19.2406	−1.11834
$297$	15.4225	0.894903
$298$	−43.5588	−2.52329
$299$	5.28477	0.305626
$300$	7.10947	0.410465
$301$	−1.83663	−0.105861
$302$	−54.2625	−3.12246
$303$	−6.06283	−0.348300
$304$	−30.9666	−1.77606
$305$	12.7950	0.732638
$306$	0.382427	0.0218619
$307$	0.195787	0.0111742	0.00558708	−	0.999984i	$-0.498222\pi$
$307$	0.195787	0.0111742	0.00558708	+	0.999984i	$0.498222\pi$
$308$	−28.4777	−1.62267
$309$	−4.66148	−0.265182
$310$	25.4825	1.44731
$311$	−5.20667	−0.295243	−0.147622	−	0.989044i	$-0.547162\pi$
$311$	−5.20667	−0.295243	−0.147622	+	0.989044i	$0.547162\pi$
$312$	13.1603	0.745058
$313$	−9.82584	−0.555389	−0.277695	−	0.960669i	$-0.589570\pi$
$313$	−9.82584	−0.555389	−0.277695	+	0.960669i	$0.589570\pi$
$314$	−10.7180	−0.604853
$315$	−3.66433	−0.206461
$316$	14.7805	0.831471
$317$	17.8071	1.00015	0.500074	−	0.865983i	$-0.333306\pi$
$317$	17.8071	1.00015	0.500074	+	0.865983i	$0.333306\pi$
$318$	2.82352	0.158335
$319$	0.684653	0.0383332
$320$	6.00765	0.335838
$321$	−4.16388	−0.232405
$322$	2.88793	0.160938
$323$	−0.326096	−0.0181445
$324$	30.1285	1.67381
$325$	−19.6633	−1.09072
$326$	43.9001	2.43140
$327$	4.05020	0.223977
$328$	28.9498	1.59849
$329$	10.0623	0.554754
$330$	−7.49636	−0.412661
$331$	23.4611	1.28954	0.644771	−	0.764376i	$-0.276953\pi$
$331$	23.4611	1.28954	0.644771	+	0.764376i	$0.276953\pi$
$332$	−56.7618	−3.11521
$333$	−9.82285	−0.538289
$334$	−27.5532	−1.50765
$335$	10.9239	0.596838
$336$	2.75843	0.150485
$337$	−19.8210	−1.07972	−0.539859	−	0.841755i	$-0.681523\pi$
$337$	−19.8210	−1.07972	−0.539859	+	0.841755i	$0.681523\pi$
$338$	−37.1645	−2.02148
$339$	4.41315	0.239690
$340$	−0.261136	−0.0141621
$341$	52.9301	2.86633
$342$	−41.2172	−2.22877
$343$	14.6797	0.792631
$344$	−8.66075	−0.466956
$345$	0.514876	0.0277200
$346$	−34.0438	−1.83021
$347$	1.69715	0.0911075	0.0455538	−	0.998962i	$-0.485495\pi$
$347$	1.69715	0.0911075	0.0455538	+	0.998962i	$0.485495\pi$
$348$	−0.223684	−0.0119907
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−10.7453	−0.574359
$351$	13.9360	0.743847
$352$	−12.0642	−0.643023
$353$	−29.7712	−1.58456	−0.792280	−	0.610158i	$-0.791106\pi$
$353$	−29.7712	−1.58456	−0.792280	+	0.610158i	$0.791106\pi$
$354$	0.0456225	0.00242481
$355$	−1.02774	−0.0545466
$356$	13.1698	0.697998
$357$	0.0290479	0.00153738
$358$	1.64724	0.0870592
$359$	−8.59618	−0.453689	−0.226844	−	0.973931i	$-0.572841\pi$
$359$	−8.59618	−0.453689	−0.226844	+	0.973931i	$0.572841\pi$
$360$	−17.2794	−0.910705
$361$	16.1460	0.849790
$362$	−11.7877	−0.619546
$363$	−10.5633	−0.554430
$364$	−25.7329	−1.34877
$365$	−11.1301	−0.582574
$366$	−12.8201	−0.670118
$367$	−10.2461	−0.534840	−0.267420	−	0.963580i	$-0.586171\pi$
$367$	−10.2461	−0.534840	−0.267420	+	0.963580i	$0.586171\pi$
$368$	5.22343	0.272290
$369$	14.7797	0.769399
$370$	9.90341	0.514854
$371$	−2.89030	−0.150057
$372$	−17.2929	−0.896593
$373$	−1.78368	−0.0923554	−0.0461777	−	0.998933i	$-0.514704\pi$
$373$	−1.78368	−0.0923554	−0.0461777	+	0.998933i	$0.514704\pi$
$374$	−0.800858	−0.0414114
$375$	−4.49011	−0.231868
$376$	47.4497	2.44703
$377$	0.618662	0.0318627
$378$	7.61549	0.391699
$379$	23.8900	1.22715	0.613573	−	0.789638i	$-0.289732\pi$
$379$	23.8900	1.22715	0.613573	+	0.789638i	$0.289732\pi$
$380$	28.1447	1.44379
$381$	7.13420	0.365496
$382$	−20.9650	−1.07266
$383$	25.5267	1.30435	0.652177	−	0.758067i	$-0.273856\pi$
$383$	25.5267	1.30435	0.652177	+	0.758067i	$0.273856\pi$
$384$	−7.89753	−0.403019
$385$	7.67364	0.391085
$386$	47.7746	2.43166
$387$	−4.42155	−0.224760
$388$	−20.1544	−1.02319
$389$	36.6086	1.85613	0.928064	−	0.372420i	$-0.121472\pi$
$389$	36.6086	1.85613	0.928064	+	0.372420i	$0.121472\pi$
$390$	−6.77382	−0.343006
$391$	0.0550057	0.00278176
$392$	30.9308	1.56224
$393$	3.50550	0.176829
$394$	17.3802	0.875600
$395$	−3.98278	−0.200396
$396$	−68.5582	−3.44518
$397$	−16.0630	−0.806179	−0.403089	−	0.915161i	$-0.632064\pi$
$397$	−16.0630	−0.806179	−0.403089	+	0.915161i	$0.632064\pi$
$398$	−1.75652	−0.0880463
$399$	−3.13072	−0.156732
$400$	−19.4351	−0.971754
$401$	15.4678	0.772426	0.386213	−	0.922410i	$-0.373783\pi$
$401$	15.4678	0.772426	0.386213	+	0.922410i	$0.373783\pi$
$402$	−10.9454	−0.545907
$403$	47.8284	2.38250
$404$	55.9025	2.78126
$405$	−8.11847	−0.403410
$406$	0.338076	0.0167784
$407$	20.5705	1.01964
$408$	0.136977	0.00678139
$409$	12.8176	0.633787	0.316894	−	0.948461i	$-0.397360\pi$
$409$	12.8176	0.633787	0.316894	+	0.948461i	$0.397360\pi$
$410$	−14.9009	−0.735903
$411$	8.22722	0.405819
$412$	42.9813	2.11754
$413$	−0.0467014	−0.00229803
$414$	6.95249	0.341696
$415$	15.2951	0.750807
$416$	−10.9014	−0.534484
$417$	7.73325	0.378699
$418$	86.3149	4.22180
$419$	−37.9956	−1.85621	−0.928104	−	0.372320i	$-0.878562\pi$
$419$	−37.9956	−1.85621	−0.928104	+	0.372320i	$0.878562\pi$
$420$	−2.50706	−0.122332
$421$	28.8983	1.40842	0.704208	−	0.709994i	$-0.251302\pi$
$421$	28.8983	1.40842	0.704208	+	0.709994i	$0.251302\pi$
$422$	0.386759	0.0188271
$423$	24.2244	1.17783
$424$	−13.6294	−0.661903
$425$	−0.204662	−0.00992759
$426$	1.02976	0.0498918
$427$	13.1233	0.635081
$428$	38.3933	1.85581
$429$	−14.0700	−0.679305
$430$	4.45781	0.214975
$431$	−20.9079	−1.00710	−0.503549	−	0.863967i	$-0.667973\pi$
$431$	−20.9079	−1.00710	−0.503549	+	0.863967i	$0.667973\pi$
$432$	13.7742	0.662713
$433$	−6.23267	−0.299523	−0.149761	−	0.988722i	$-0.547851\pi$
$433$	−6.23267	−0.299523	−0.149761	+	0.988722i	$0.547851\pi$
$434$	26.1364	1.25459
$435$	0.0602741	0.00288992
$436$	−37.3450	−1.78850
$437$	−5.92841	−0.283594
$438$	11.1519	0.532860
$439$	−27.9524	−1.33410	−0.667048	−	0.745015i	$-0.732442\pi$
$439$	−27.9524	−1.33410	−0.667048	+	0.745015i	$0.732442\pi$
$440$	36.1856	1.72508
$441$	15.7910	0.751954
$442$	−0.723667	−0.0344213
$443$	−26.0024	−1.23541	−0.617705	−	0.786410i	$-0.711937\pi$
$443$	−26.0024	−1.23541	−0.617705	+	0.786410i	$0.711937\pi$
$444$	−6.72061	−0.318946
$445$	−3.54875	−0.168227
$446$	3.34048	0.158176
$447$	−7.96519	−0.376740
$448$	6.16182	0.291118
$449$	7.67939	0.362413	0.181206	−	0.983445i	$-0.442000\pi$
$449$	7.67939	0.362413	0.181206	+	0.983445i	$0.442000\pi$
$450$	−25.8685	−1.21945
$451$	−30.9508	−1.45742
$452$	−40.6916	−1.91397
$453$	−9.92248	−0.466199
$454$	−19.3406	−0.907701
$455$	6.93401	0.325072
$456$	−14.7632	−0.691348
$457$	−8.24734	−0.385794	−0.192897	−	0.981219i	$-0.561788\pi$
$457$	−8.24734	−0.385794	−0.192897	+	0.981219i	$0.561788\pi$
$458$	−11.7808	−0.550481
$459$	0.145050	0.00677038
$460$	−4.74743	−0.221350
$461$	31.0360	1.44549	0.722745	−	0.691114i	$-0.242880\pi$
$461$	31.0360	1.44549	0.722745	+	0.691114i	$0.242880\pi$
$462$	−7.68873	−0.357712
$463$	23.8721	1.10943	0.554715	−	0.832040i	$-0.312827\pi$
$463$	23.8721	1.10943	0.554715	+	0.832040i	$0.312827\pi$
$464$	0.611482	0.0283873
$465$	4.65975	0.216091
$466$	−54.0361	−2.50318
$467$	−22.5557	−1.04375	−0.521876	−	0.853021i	$-0.674768\pi$
$467$	−22.5557	−1.04375	−0.521876	+	0.853021i	$0.674768\pi$
$468$	−61.9502	−2.86365
$469$	11.2042	0.517364
$470$	−24.4231	−1.12655
$471$	−1.95990	−0.0903076
$472$	−0.220224	−0.0101366
$473$	9.25938	0.425747
$474$	3.99061	0.183295
$475$	22.0581	1.01210
$476$	−0.267837	−0.0122763
$477$	−6.95819	−0.318594
$478$	34.5098	1.57844
$479$	30.4996	1.39356	0.696781	−	0.717284i	$-0.254615\pi$
$479$	30.4996	1.39356	0.696781	+	0.717284i	$0.254615\pi$
$480$	−1.06208	−0.0484772
$481$	18.5878	0.847531
$482$	24.4658	1.11439
$483$	0.528088	0.0240289
$484$	97.3995	4.42725
$485$	5.43083	0.246601
$486$	27.8286	1.26233
$487$	−31.6421	−1.43384	−0.716920	−	0.697156i	$-0.754449\pi$
$487$	−31.6421	−1.43384	−0.716920	+	0.697156i	$0.754449\pi$
$488$	61.8839	2.80135
$489$	8.02759	0.363020
$490$	−15.9205	−0.719217
$491$	−24.5450	−1.10770	−0.553851	−	0.832616i	$-0.686842\pi$
$491$	−24.5450	−1.10770	−0.553851	+	0.832616i	$0.686842\pi$
$492$	10.1120	0.455883
$493$	0.00643925	0.000290009 0
$494$	77.9954	3.50918
$495$	18.4738	0.830334
$496$	47.2733	2.12263
$497$	−1.05411	−0.0472832
$498$	−15.3252	−0.686737
$499$	33.1735	1.48505	0.742526	−	0.669818i	$-0.233628\pi$
$499$	33.1735	1.48505	0.742526	+	0.669818i	$0.233628\pi$
$500$	41.4012	1.85152
$501$	−5.03840	−0.225099
$502$	−51.3607	−2.29234
$503$	5.76781	0.257174	0.128587	−	0.991698i	$-0.458956\pi$
$503$	5.76781	0.257174	0.128587	+	0.991698i	$0.458956\pi$
$504$	−17.7228	−0.789437
$505$	−15.0636	−0.670320
$506$	−14.5595	−0.647251
$507$	−6.79593	−0.301818
$508$	−65.7811	−2.91857
$509$	−12.4163	−0.550343	−0.275171	−	0.961395i	$-0.588735\pi$
$509$	−12.4163	−0.550343	−0.275171	+	0.961395i	$0.588735\pi$
$510$	−0.0705043	−0.00312198
$511$	−11.4157	−0.505000
$512$	46.3733	2.04943
$513$	−15.6333	−0.690225
$514$	21.4873	0.947764
$515$	−11.5818	−0.510355
$516$	−3.02514	−0.133174
$517$	−50.7294	−2.23108
$518$	10.1575	0.446297
$519$	−6.22527	−0.273259
$520$	32.6979	1.43390
$521$	0.500481	0.0219265	0.0109632	−	0.999940i	$-0.496510\pi$
$521$	0.500481	0.0219265	0.0109632	+	0.999940i	$0.496510\pi$
$522$	0.813895	0.0356232
$523$	−7.40179	−0.323658	−0.161829	−	0.986819i	$-0.551739\pi$
$523$	−7.40179	−0.323658	−0.161829	+	0.986819i	$0.551739\pi$
$524$	−32.3226	−1.41202
$525$	−1.96489	−0.0857546
$526$	−4.37524	−0.190769
$527$	0.497815	0.0216851
$528$	−13.9067	−0.605211
$529$	1.00000	0.0434783
$530$	7.01526	0.304723
$531$	−0.112430	−0.00487906
$532$	28.8669	1.25154
$533$	−27.9676	−1.21141
$534$	3.55573	0.153871
$535$	−10.3455	−0.447275
$536$	52.8345	2.28210
$537$	0.301215	0.0129984
$538$	−49.3277	−2.12667
$539$	−33.0688	−1.42437
$540$	−12.5190	−0.538733
$541$	−36.1240	−1.55309	−0.776547	−	0.630059i	$-0.783031\pi$
$541$	−36.1240	−1.55309	−0.776547	+	0.630059i	$0.783031\pi$
$542$	37.1681	1.59651
$543$	−2.15550	−0.0925014
$544$	−0.113465	−0.00486478
$545$	10.0630	0.431053
$546$	−6.94764	−0.297332
$547$	13.0710	0.558874	0.279437	−	0.960164i	$-0.409852\pi$
$547$	13.0710	0.558874	0.279437	+	0.960164i	$0.409852\pi$
$548$	−75.8594	−3.24055
$549$	31.5935	1.34838
$550$	54.1724	2.30992
$551$	−0.694010	−0.0295658
$552$	2.49024	0.105992
$553$	−4.08499	−0.173711
$554$	71.0750	3.01969
$555$	1.81094	0.0768703
$556$	−71.3048	−3.02400
$557$	11.4455	0.484960	0.242480	−	0.970156i	$-0.422039\pi$
$557$	11.4455	0.484960	0.242480	+	0.970156i	$0.422039\pi$
$558$	62.9217	2.66369
$559$	8.36691	0.353882
$560$	6.85354	0.289615
$561$	−0.146445	−0.00618293
$562$	−16.5963	−0.700073
$563$	−9.34586	−0.393881	−0.196941	−	0.980415i	$-0.563101\pi$
$563$	−9.34586	−0.393881	−0.196941	+	0.980415i	$0.563101\pi$
$564$	16.5739	0.697886
$565$	10.9648	0.461293
$566$	58.7642	2.47005
$567$	−8.32679	−0.349692
$568$	−4.97073	−0.208567
$569$	5.93683	0.248885	0.124443	−	0.992227i	$-0.460286\pi$
$569$	5.93683	0.248885	0.124443	+	0.992227i	$0.460286\pi$
$570$	7.59882	0.318279
$571$	13.5540	0.567216	0.283608	−	0.958940i	$-0.408469\pi$
$571$	13.5540	0.567216	0.283608	+	0.958940i	$0.408469\pi$
$572$	129.733	5.42440
$573$	−3.83367	−0.160154
$574$	−15.2833	−0.637911
$575$	−3.72075	−0.155166
$576$	14.8341	0.618090
$577$	2.03539	0.0847343	0.0423672	−	0.999102i	$-0.486510\pi$
$577$	2.03539	0.0847343	0.0423672	+	0.999102i	$0.486510\pi$
$578$	42.3133	1.76000
$579$	8.73609	0.363060
$580$	−0.555759	−0.0230766
$581$	15.6876	0.650831
$582$	−5.44151	−0.225558
$583$	14.5715	0.603489
$584$	−53.8315	−2.22756
$585$	16.6932	0.690177
$586$	−38.7229	−1.59963
$587$	16.3622	0.675339	0.337670	−	0.941265i	$-0.390361\pi$
$587$	16.3622	0.675339	0.337670	+	0.941265i	$0.390361\pi$
$588$	10.8039	0.445547
$589$	−53.6535	−2.21075
$590$	0.113352	0.00466665
$591$	3.17815	0.130731
$592$	18.3721	0.755087
$593$	−22.0827	−0.906826	−0.453413	−	0.891300i	$-0.649794\pi$
$593$	−22.0827	−0.906826	−0.453413	+	0.891300i	$0.649794\pi$
$594$	−38.3936	−1.57531
$595$	0.0721716	0.00295875
$596$	73.4433	3.00835
$597$	−0.321198	−0.0131458
$598$	−13.1562	−0.537998
$599$	4.35379	0.177891	0.0889454	−	0.996037i	$-0.471650\pi$
$599$	4.35379	0.177891	0.0889454	+	0.996037i	$0.471650\pi$
$600$	−9.26557	−0.378265
$601$	−9.13278	−0.372534	−0.186267	−	0.982499i	$-0.559639\pi$
$601$	−9.13278	−0.372534	−0.186267	+	0.982499i	$0.559639\pi$
$602$	4.57220	0.186349
$603$	26.9735	1.09844
$604$	91.4906	3.72270
$605$	−26.2454	−1.06703
$606$	15.0932	0.613118
$607$	30.3938	1.23365	0.616823	−	0.787102i	$-0.288419\pi$
$607$	30.3938	1.23365	0.616823	+	0.787102i	$0.288419\pi$
$608$	12.2291	0.495954
$609$	0.0618208	0.00250510
$610$	−31.8526	−1.28967
$611$	−45.8398	−1.85448
$612$	−0.644799	−0.0260645
$613$	−26.9086	−1.08683	−0.543415	−	0.839464i	$-0.682869\pi$
$613$	−26.9086	−1.08683	−0.543415	+	0.839464i	$0.682869\pi$
$614$	−0.487404	−0.0196700
$615$	−2.72479	−0.109874
$616$	37.1142	1.49537
$617$	−34.2716	−1.37972	−0.689861	−	0.723941i	$-0.742329\pi$
$617$	−34.2716	−1.37972	−0.689861	+	0.723941i	$0.742329\pi$
$618$	11.6046	0.466804
$619$	−26.2129	−1.05359	−0.526793	−	0.849994i	$-0.676606\pi$
$619$	−26.2129	−1.05359	−0.526793	+	0.849994i	$0.676606\pi$
$620$	−42.9654	−1.72553
$621$	2.63701	0.105820
$622$	12.9618	0.519721
$623$	−3.63982	−0.145826
$624$	−12.5663	−0.503054
$625$	7.44774	0.297910
$626$	24.4610	0.977659
$627$	15.7836	0.630336
$628$	18.0714	0.721126
$629$	0.193468	0.00771408
$630$	9.12220	0.363437
$631$	−31.5324	−1.25528	−0.627642	−	0.778502i	$-0.715980\pi$
$631$	−31.5324	−1.25528	−0.627642	+	0.778502i	$0.715980\pi$
$632$	−19.2631	−0.766243
$633$	0.0707229	0.00281098
$634$	−44.3301	−1.76057
$635$	17.7255	0.703413
$636$	−4.76066	−0.188773
$637$	−29.8814	−1.18394
$638$	−1.70442	−0.0674785
$639$	−2.53769	−0.100390
$640$	−19.6220	−0.775628
$641$	−5.07221	−0.200340	−0.100170	−	0.994970i	$-0.531939\pi$
$641$	−5.07221	−0.200340	−0.100170	+	0.994970i	$0.531939\pi$
$642$	10.3658	0.409106
$643$	3.32706	0.131207	0.0656033	−	0.997846i	$-0.479103\pi$
$643$	3.32706	0.131207	0.0656033	+	0.997846i	$0.479103\pi$
$644$	−4.86926	−0.191876
$645$	0.815158	0.0320968
$646$	0.811803	0.0319400
$647$	−20.4253	−0.803003	−0.401501	−	0.915858i	$-0.631512\pi$
$647$	−20.4253	−0.803003	−0.401501	+	0.915858i	$0.631512\pi$
$648$	−39.2656	−1.54250
$649$	0.235446	0.00924206
$650$	48.9510	1.92002
$651$	4.77933	0.187317
$652$	−74.0187	−2.89880
$653$	−16.0270	−0.627185	−0.313592	−	0.949558i	$-0.601533\pi$
$653$	−16.0270	−0.627185	−0.313592	+	0.949558i	$0.601533\pi$
$654$	−10.0828	−0.394269
$655$	8.70969	0.340316
$656$	−27.6430	−1.07928
$657$	−27.4824	−1.07219
$658$	−25.0498	−0.976542
$659$	−15.5991	−0.607655	−0.303827	−	0.952727i	$-0.598265\pi$
$659$	−15.5991	−0.607655	−0.303827	+	0.952727i	$0.598265\pi$
$660$	12.6394	0.491988
$661$	−34.5752	−1.34482	−0.672410	−	0.740179i	$-0.734741\pi$
$661$	−34.5752	−1.34482	−0.672410	+	0.740179i	$0.734741\pi$
$662$	−58.4056	−2.27000
$663$	−0.132330	−0.00513927
$664$	73.9760	2.87083
$665$	−7.77852	−0.301638
$666$	24.4536	0.947557
$667$	0.117065	0.00453278
$668$	46.4568	1.79747
$669$	0.610841	0.0236165
$670$	−27.1947	−1.05062
$671$	−66.1614	−2.55413
$672$	−1.08934	−0.0420220
$673$	15.2813	0.589052	0.294526	−	0.955643i	$-0.404838\pi$
$673$	15.2813	0.589052	0.294526	+	0.955643i	$0.404838\pi$
$674$	49.3436	1.90064
$675$	−9.81165	−0.377651
$676$	62.6621	2.41008
$677$	15.6071	0.599829	0.299914	−	0.953966i	$-0.403042\pi$
$677$	15.6071	0.599829	0.299914	+	0.953966i	$0.403042\pi$
$678$	−10.9864	−0.421929
$679$	5.57020	0.213764
$680$	0.340331	0.0130511
$681$	−3.53664	−0.135524
$682$	−131.767	−5.04563
$683$	7.38158	0.282448	0.141224	−	0.989978i	$-0.454896\pi$
$683$	7.38158	0.282448	0.141224	+	0.989978i	$0.454896\pi$
$684$	69.4952	2.65722
$685$	20.4412	0.781017
$686$	−36.5446	−1.39528
$687$	−2.15425	−0.0821896
$688$	8.26980	0.315283
$689$	13.1670	0.501623
$690$	−1.28176	−0.0487959
$691$	−45.0779	−1.71484	−0.857422	−	0.514614i	$-0.827935\pi$
$691$	−45.0779	−1.71484	−0.857422	+	0.514614i	$0.827935\pi$
$692$	57.4003	2.18203
$693$	18.9478	0.719768
$694$	−4.22498	−0.160378
$695$	19.2139	0.728823
$696$	0.291520	0.0110501
$697$	−0.291097	−0.0110261
$698$	−2.48946	−0.0942274
$699$	−9.88108	−0.373737
$700$	18.1173	0.684769
$701$	13.6721	0.516390	0.258195	−	0.966093i	$-0.416872\pi$
$701$	13.6721	0.516390	0.258195	+	0.966093i	$0.416872\pi$
$702$	−34.6930	−1.30940
$703$	−20.8516	−0.786434
$704$	−31.0649	−1.17080
$705$	−4.46601	−0.168200
$706$	74.1142	2.78932
$707$	−15.4501	−0.581061
$708$	−0.0769228	−0.00289093
$709$	−11.8448	−0.444839	−0.222420	−	0.974951i	$-0.571396\pi$
$709$	−11.8448	−0.444839	−0.222420	+	0.974951i	$0.571396\pi$
$710$	2.55851	0.0960191
$711$	−9.83432	−0.368816
$712$	−17.1638	−0.643242
$713$	9.05024	0.338934
$714$	−0.0723135	−0.00270626
$715$	−34.9580	−1.30735
$716$	−2.77736	−0.103795
$717$	6.31049	0.235669
$718$	21.3998	0.798635
$719$	27.2594	1.01660	0.508302	−	0.861179i	$-0.330273\pi$
$719$	27.2594	1.01660	0.508302	+	0.861179i	$0.330273\pi$
$720$	16.4994	0.614897
$721$	−11.8790	−0.442397
$722$	−40.1949	−1.49590
$723$	4.47383	0.166384
$724$	19.8749	0.738644
$725$	−0.435570	−0.0161767
$726$	26.2970	0.975972
$727$	−18.0683	−0.670118	−0.335059	−	0.942197i	$-0.608756\pi$
$727$	−18.0683	−0.670118	−0.335059	+	0.942197i	$0.608756\pi$
$728$	33.5369	1.24296
$729$	−16.4449	−0.609070
$730$	27.7078	1.02551
$731$	0.0870857	0.00322098
$732$	21.6157	0.798937
$733$	−32.3433	−1.19463	−0.597313	−	0.802008i	$-0.703765\pi$
$733$	−32.3433	−1.19463	−0.597313	+	0.802008i	$0.703765\pi$
$734$	25.5072	0.941487
$735$	−2.91124	−0.107383
$736$	−2.06279	−0.0760355
$737$	−56.4864	−2.08070
$738$	−36.7934	−1.35438
$739$	10.8654	0.399690	0.199845	−	0.979827i	$-0.435956\pi$
$739$	10.8654	0.399690	0.199845	+	0.979827i	$0.435956\pi$
$740$	−16.6979	−0.613826
$741$	14.2623	0.523938
$742$	7.19528	0.264147
$743$	−39.4929	−1.44886	−0.724428	−	0.689351i	$-0.757896\pi$
$743$	−39.4929	−1.44886	−0.724428	+	0.689351i	$0.757896\pi$
$744$	22.5373	0.826257
$745$	−19.7901	−0.725054
$746$	4.44040	0.162574
$747$	37.7668	1.38182
$748$	1.35030	0.0493720
$749$	−10.6110	−0.387716
$750$	11.1779	0.408161
$751$	−5.74497	−0.209637	−0.104818	−	0.994491i	$-0.533426\pi$
$751$	−5.74497	−0.209637	−0.104818	+	0.994491i	$0.533426\pi$
$752$	−45.3078	−1.65221
$753$	−9.39184	−0.342258
$754$	−1.54013	−0.0560884
$755$	−24.6532	−0.897220
$756$	−12.8403	−0.466996
$757$	−40.5526	−1.47391	−0.736954	−	0.675943i	$-0.763737\pi$
$757$	−40.5526	−1.47391	−0.736954	+	0.675943i	$0.763737\pi$
$758$	−59.4731	−2.16016
$759$	−2.66237	−0.0966378
$760$	−36.6802	−1.33053
$761$	14.5333	0.526832	0.263416	−	0.964682i	$-0.415151\pi$
$761$	14.5333	0.526832	0.263416	+	0.964682i	$0.415151\pi$
$762$	−17.7603	−0.643388
$763$	10.3213	0.373655
$764$	35.3485	1.27886
$765$	0.173748	0.00628188
$766$	−63.5477	−2.29607
$767$	0.212752	0.00768204
$768$	14.8246	0.534937
$769$	−10.6391	−0.383657	−0.191829	−	0.981428i	$-0.561442\pi$
$769$	−10.6391	−0.383657	−0.191829	+	0.981428i	$0.561442\pi$
$770$	−19.1032	−0.688432
$771$	3.92918	0.141506
$772$	−80.5514	−2.89911
$773$	20.5701	0.739855	0.369928	−	0.929061i	$-0.379382\pi$
$773$	20.5701	0.739855	0.369928	+	0.929061i	$0.379382\pi$
$774$	11.0073	0.395648
$775$	−33.6737	−1.20959
$776$	26.2667	0.942919
$777$	1.85741	0.0666344
$778$	−91.1356	−3.26737
$779$	31.3738	1.12408
$780$	11.4212	0.408943
$781$	5.31431	0.190161
$782$	−0.136934	−0.00489677
$783$	0.308702	0.0110321
$784$	−29.5346	−1.05481
$785$	−4.86953	−0.173801
$786$	−8.72681	−0.311275
$787$	20.9805	0.747873	0.373936	−	0.927454i	$-0.378008\pi$
$787$	20.9805	0.747873	0.373936	+	0.927454i	$0.378008\pi$
$788$	−29.3042	−1.04392
$789$	−0.800058	−0.0284828
$790$	9.91498	0.352759
$791$	11.2462	0.399868
$792$	89.3499	3.17491
$793$	−59.7844	−2.12300
$794$	39.9882	1.41913
$795$	1.28281	0.0454967
$796$	2.96162	0.104972
$797$	23.4733	0.831465	0.415733	−	0.909487i	$-0.363525\pi$
$797$	23.4733	0.831465	0.415733	+	0.909487i	$0.363525\pi$
$798$	7.79381	0.275898
$799$	−0.477117	−0.0168792
$800$	7.67513	0.271357
$801$	−8.76261	−0.309611
$802$	−38.5065	−1.35971
$803$	57.5523	2.03098
$804$	18.4547	0.650848
$805$	1.31208	0.0462446
$806$	−119.067	−4.19395
$807$	−9.02009	−0.317522
$808$	−72.8562	−2.56307
$809$	−21.6630	−0.761630	−0.380815	−	0.924651i	$-0.624356\pi$
$809$	−21.6630	−0.761630	−0.380815	+	0.924651i	$0.624356\pi$
$810$	20.2106	0.710128
$811$	8.03902	0.282288	0.141144	−	0.989989i	$-0.454922\pi$
$811$	8.03902	0.282288	0.141144	+	0.989989i	$0.454922\pi$
$812$	−0.570021	−0.0200038
$813$	6.79658	0.238366
$814$	−51.2094	−1.79489
$815$	19.9452	0.698649
$816$	−0.130794	−0.00457871
$817$	−9.38593	−0.328372
$818$	−31.9088	−1.11566
$819$	17.1215	0.598275
$820$	25.1240	0.877368
$821$	−2.18283	−0.0761813	−0.0380907	−	0.999274i	$-0.512128\pi$
$821$	−2.18283	−0.0761813	−0.0380907	+	0.999274i	$0.512128\pi$
$822$	−20.4813	−0.714369
$823$	−12.7333	−0.443855	−0.221927	−	0.975063i	$-0.571235\pi$
$823$	−12.7333	−0.443855	−0.221927	+	0.975063i	$0.571235\pi$
$824$	−56.0163	−1.95142
$825$	9.90600	0.344883
$826$	0.116261	0.00404525
$827$	16.4486	0.571974	0.285987	−	0.958234i	$-0.407679\pi$
$827$	16.4486	0.571974	0.285987	+	0.958234i	$0.407679\pi$
$828$	−11.7224	−0.407382
$829$	−41.5107	−1.44173	−0.720864	−	0.693077i	$-0.756255\pi$
$829$	−41.5107	−1.44173	−0.720864	+	0.693077i	$0.756255\pi$
$830$	−38.0765	−1.32166
$831$	12.9968	0.450855
$832$	−28.0707	−0.973176
$833$	−0.311016	−0.0107761
$834$	−19.2516	−0.666629
$835$	−12.5183	−0.433213
$836$	−145.533	−5.03337
$837$	23.8656	0.824914
$838$	94.5886	3.26751
$839$	40.4106	1.39513	0.697565	−	0.716521i	$-0.254267\pi$
$839$	40.4106	1.39513	0.697565	+	0.716521i	$0.254267\pi$
$840$	3.26738	0.112735
$841$	−28.9863	−0.999527
$842$	−71.9411	−2.47925
$843$	−3.03481	−0.104524
$844$	−0.652103	−0.0224463
$845$	−16.8850	−0.580862
$846$	−60.3056	−2.07335
$847$	−26.9189	−0.924943
$848$	13.0142	0.446909
$849$	10.7457	0.368790
$850$	0.509499	0.0174757
$851$	3.51724	0.120569
$852$	−1.73624	−0.0594827
$853$	25.4302	0.870713	0.435356	−	0.900258i	$-0.356622\pi$
$853$	25.4302	0.870713	0.435356	+	0.900258i	$0.356622\pi$
$854$	−32.6699	−1.11794
$855$	−18.7263	−0.640424
$856$	−50.0368	−1.71022
$857$	−47.4242	−1.61998	−0.809989	−	0.586445i	$-0.800527\pi$
$857$	−47.4242	−1.61998	−0.809989	+	0.586445i	$0.800527\pi$
$858$	35.0267	1.19579
$859$	16.8899	0.576276	0.288138	−	0.957589i	$-0.406964\pi$
$859$	16.8899	0.576276	0.288138	+	0.957589i	$0.406964\pi$
$860$	−7.51620	−0.256300
$861$	−2.79471	−0.0952433
$862$	52.0494	1.77281
$863$	−51.7905	−1.76297	−0.881484	−	0.472214i	$-0.843455\pi$
$863$	−51.7905	−1.76297	−0.881484	+	0.472214i	$0.843455\pi$
$864$	−5.43960	−0.185059
$865$	−15.4672	−0.525899
$866$	15.5160	0.527254
$867$	7.73743	0.262777
$868$	−44.0680	−1.49576
$869$	20.5945	0.698621
$870$	−0.150050	−0.00508717
$871$	−51.0419	−1.72949
$872$	48.6707	1.64820
$873$	13.4099	0.453855
$874$	14.7585	0.499215
$875$	−11.4423	−0.386820
$876$	−18.8030	−0.635294
$877$	−6.56653	−0.221736	−0.110868	−	0.993835i	$-0.535363\pi$
$877$	−6.56653	−0.221736	−0.110868	+	0.993835i	$0.535363\pi$
$878$	69.5864	2.34843
$879$	−7.08089	−0.238832
$880$	−34.5522	−1.16476
$881$	−12.8924	−0.434358	−0.217179	−	0.976132i	$-0.569685\pi$
$881$	−12.8924	−0.434358	−0.217179	+	0.976132i	$0.569685\pi$
$882$	−39.3112	−1.32368
$883$	−24.5766	−0.827068	−0.413534	−	0.910489i	$-0.635706\pi$
$883$	−24.5766	−0.827068	−0.413534	+	0.910489i	$0.635706\pi$
$884$	1.22015	0.0410382
$885$	0.0207277	0.000696754 0
$886$	64.7318	2.17471
$887$	−49.8058	−1.67231	−0.836157	−	0.548490i	$-0.815203\pi$
$887$	−49.8058	−1.67231	−0.836157	+	0.548490i	$0.815203\pi$
$888$	8.75878	0.293925
$889$	18.1803	0.609748
$890$	8.83447	0.296132
$891$	41.9797	1.40637
$892$	−5.63229	−0.188583
$893$	51.4228	1.72080
$894$	19.8290	0.663181
$895$	0.748391	0.0250159
$896$	−20.1255	−0.672347
$897$	−2.40575	−0.0803257
$898$	−19.1175	−0.637960
$899$	1.05947	0.0353352
$900$	43.6161	1.45387
$901$	0.137047	0.00456569
$902$	77.0508	2.56551
$903$	0.836076	0.0278229
$904$	53.0322	1.76383
$905$	−5.35551	−0.178023
$906$	24.7016	0.820656
$907$	9.56694	0.317665	0.158832	−	0.987306i	$-0.449227\pi$
$907$	9.56694	0.317665	0.158832	+	0.987306i	$0.449227\pi$
$908$	32.6097	1.08219
$909$	−37.1951	−1.23368
$910$	−17.2620	−0.572228
$911$	−25.4856	−0.844376	−0.422188	−	0.906508i	$-0.638738\pi$
$911$	−25.4856	−0.844376	−0.422188	+	0.906508i	$0.638738\pi$
$912$	14.0967	0.466790
$913$	−79.0893	−2.61747
$914$	20.5314	0.679119
$915$	−5.82458	−0.192555
$916$	19.8633	0.656302
$917$	8.93320	0.295000
$918$	−0.361097	−0.0119180
$919$	−34.2023	−1.12823	−0.564115	−	0.825697i	$-0.690782\pi$
$919$	−34.2023	−1.12823	−0.564115	+	0.825697i	$0.690782\pi$
$920$	6.18719	0.203986
$921$	−0.0891270	−0.00293684
$922$	−77.2629	−2.54452
$923$	4.80208	0.158063
$924$	12.9637	0.426476
$925$	−13.0868	−0.430291
$926$	−59.4286	−1.95294
$927$	−28.5979	−0.939277
$928$	−0.241481	−0.00792700
$929$	−28.9568	−0.950041	−0.475020	−	0.879975i	$-0.657559\pi$
$929$	−28.9568	−0.950041	−0.475020	+	0.879975i	$0.657559\pi$
$930$	−11.6003	−0.380388
$931$	33.5207	1.09860
$932$	91.1088	2.98437
$933$	2.37020	0.0775970
$934$	56.1514	1.83733
$935$	−0.363855	−0.0118993
$936$	80.7379	2.63900
$937$	−32.0501	−1.04703	−0.523516	−	0.852016i	$-0.675380\pi$
$937$	−32.0501	−1.04703	−0.523516	+	0.852016i	$0.675380\pi$
$938$	−27.8925	−0.910723
$939$	4.47296	0.145969
$940$	41.1790	1.34311
$941$	−12.4203	−0.404891	−0.202446	−	0.979294i	$-0.564889\pi$
$941$	−12.4203	−0.404891	−0.202446	+	0.979294i	$0.564889\pi$
$942$	4.87910	0.158970
$943$	−5.29212	−0.172335
$944$	0.210283	0.00684413
$945$	3.45996	0.112552
$946$	−23.0508	−0.749448
$947$	2.21427	0.0719542	0.0359771	−	0.999353i	$-0.488546\pi$
$947$	2.21427	0.0719542	0.0359771	+	0.999353i	$0.488546\pi$
$948$	−6.72846	−0.218530
$949$	52.0051	1.68816
$950$	−54.9128	−1.78161
$951$	−8.10623	−0.262863
$952$	0.349064	0.0113132
$953$	−59.9133	−1.94078	−0.970391	−	0.241540i	$-0.922347\pi$
$953$	−59.9133	−1.94078	−0.970391	+	0.241540i	$0.922347\pi$
$954$	17.3221	0.560825
$955$	−9.52504	−0.308223
$956$	−58.1861	−1.88187
$957$	−0.311670	−0.0100749
$958$	−75.9275	−2.45311
$959$	20.9657	0.677018
$960$	−2.73483	−0.0882662
$961$	50.9068	1.64216
$962$	−46.2736	−1.49192
$963$	−25.5452	−0.823182
$964$	−41.2511	−1.32861
$965$	21.7055	0.698724
$966$	−1.31465	−0.0422983
$967$	−59.2406	−1.90505	−0.952524	−	0.304463i	$-0.901523\pi$
$967$	−59.2406	−1.90505	−0.952524	+	0.304463i	$0.901523\pi$
$968$	−126.938	−4.07994
$969$	0.148447	0.00476880
$970$	−13.5198	−0.434096
$971$	45.1247	1.44812	0.724061	−	0.689736i	$-0.242274\pi$
$971$	45.1247	1.44812	0.724061	+	0.689736i	$0.242274\pi$
$972$	−46.9210	−1.50499
$973$	19.7069	0.631775
$974$	78.7717	2.52401
$975$	8.95121	0.286668
$976$	−59.0905	−1.89144
$977$	−44.1985	−1.41403	−0.707017	−	0.707197i	$-0.749960\pi$
$977$	−44.1985	−1.41403	−0.707017	+	0.707197i	$0.749960\pi$
$978$	−19.9844	−0.639030
$979$	18.3502	0.586475
$980$	26.8432	0.857475
$981$	24.8477	0.793327
$982$	61.1039	1.94990
$983$	−13.6678	−0.435937	−0.217968	−	0.975956i	$-0.569943\pi$
$983$	−13.6678	−0.435937	−0.217968	+	0.975956i	$0.569943\pi$
$984$	−13.1787	−0.420120
$985$	7.89634	0.251598
$986$	−0.0160303	−0.000510507 0
$987$	−4.58062	−0.145803
$988$	−131.506	−4.18376
$989$	1.58321	0.0503432
$990$	−45.9897	−1.46165
$991$	−2.32542	−0.0738693	−0.0369346	−	0.999318i	$-0.511759\pi$
$991$	−2.32542	−0.0738693	−0.0369346	+	0.999318i	$0.511759\pi$
$992$	−18.6688	−0.592733
$993$	−10.6801	−0.338922
$994$	2.62416	0.0832333
$995$	−0.798041	−0.0252996
$996$	25.8393	0.818751
$997$	32.0714	1.01571	0.507856	−	0.861442i	$-0.330438\pi$
$997$	32.0714	1.01571	0.507856	+	0.861442i	$0.330438\pi$
$998$	−82.5842	−2.61416
$999$	9.27499	0.293448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.13	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.13	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48946 q^{2} -0.455224 q^{3} +4.19741 q^{4} -1.13104 q^{5} +1.13326 q^{6} -1.16006 q^{7} -5.47036 q^{8} -2.79277 q^{9} +O(q^{10})\)	\(q-2.48946 q^{2} -0.455224 q^{3} +4.19741 q^{4} -1.13104 q^{5} +1.13326 q^{6} -1.16006 q^{7} -5.47036 q^{8} -2.79277 q^{9} +2.81568 q^{10} +5.84848 q^{11} -1.91076 q^{12} +5.28477 q^{13} +2.88793 q^{14} +0.514876 q^{15} +5.22343 q^{16} +0.0550057 q^{17} +6.95249 q^{18} -5.92841 q^{19} -4.74743 q^{20} +0.528088 q^{21} -14.5595 q^{22} +1.00000 q^{23} +2.49024 q^{24} -3.72075 q^{25} -13.1562 q^{26} +2.63701 q^{27} -4.86926 q^{28} +0.117065 q^{29} -1.28176 q^{30} +9.05024 q^{31} -2.06279 q^{32} -2.66237 q^{33} -0.136934 q^{34} +1.31208 q^{35} -11.7224 q^{36} +3.51724 q^{37} +14.7585 q^{38} -2.40575 q^{39} +6.18719 q^{40} -5.29212 q^{41} -1.31465 q^{42} +1.58321 q^{43} +24.5484 q^{44} +3.15873 q^{45} -2.48946 q^{46} -8.67396 q^{47} -2.37783 q^{48} -5.65425 q^{49} +9.26266 q^{50} -0.0250399 q^{51} +22.1823 q^{52} +2.49150 q^{53} -6.56473 q^{54} -6.61485 q^{55} +6.34596 q^{56} +2.69875 q^{57} -0.291429 q^{58} +0.0402576 q^{59} +2.16115 q^{60} -11.3126 q^{61} -22.5302 q^{62} +3.23979 q^{63} -5.31162 q^{64} -5.97728 q^{65} +6.62785 q^{66} -9.65831 q^{67} +0.230881 q^{68} -0.455224 q^{69} -3.26636 q^{70} +0.908665 q^{71} +15.2775 q^{72} +9.84057 q^{73} -8.75603 q^{74} +1.69378 q^{75} -24.8840 q^{76} -6.78460 q^{77} +5.98902 q^{78} +3.52135 q^{79} -5.90790 q^{80} +7.17788 q^{81} +13.1745 q^{82} -13.5231 q^{83} +2.21660 q^{84} -0.0622136 q^{85} -3.94134 q^{86} -0.0532909 q^{87} -31.9933 q^{88} +3.13760 q^{89} -7.86354 q^{90} -6.13066 q^{91} +4.19741 q^{92} -4.11989 q^{93} +21.5935 q^{94} +6.70526 q^{95} +0.939032 q^{96} -4.80163 q^{97} +14.0760 q^{98} -16.3335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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