LMFDB - Embedded newform 8027.2.a.c.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.70535 q^{2} -0.945977 q^{3} +5.31892 q^{4} +2.14258 q^{5} +2.55920 q^{6} -0.218411 q^{7} -8.97883 q^{8} -2.10513 q^{9} +O(q^{10})$	\(q-2.70535 q^{2} -0.945977 q^{3} +5.31892 q^{4} +2.14258 q^{5} +2.55920 q^{6} -0.218411 q^{7} -8.97883 q^{8} -2.10513 q^{9} -5.79642 q^{10} -1.79643 q^{11} -5.03157 q^{12} +2.07299 q^{13} +0.590878 q^{14} -2.02683 q^{15} +13.6530 q^{16} -3.67110 q^{17} +5.69511 q^{18} -1.21881 q^{19} +11.3962 q^{20} +0.206612 q^{21} +4.85997 q^{22} +1.00000 q^{23} +8.49376 q^{24} -0.409366 q^{25} -5.60816 q^{26} +4.82933 q^{27} -1.16171 q^{28} -3.42261 q^{29} +5.48328 q^{30} -0.353943 q^{31} -18.9786 q^{32} +1.69938 q^{33} +9.93160 q^{34} -0.467962 q^{35} -11.1970 q^{36} -3.97438 q^{37} +3.29731 q^{38} -1.96100 q^{39} -19.2378 q^{40} +10.0789 q^{41} -0.558957 q^{42} -4.06260 q^{43} -9.55505 q^{44} -4.51040 q^{45} -2.70535 q^{46} +4.70185 q^{47} -12.9155 q^{48} -6.95230 q^{49} +1.10748 q^{50} +3.47277 q^{51} +11.0261 q^{52} +10.0858 q^{53} -13.0650 q^{54} -3.84899 q^{55} +1.96107 q^{56} +1.15297 q^{57} +9.25936 q^{58} +7.35475 q^{59} -10.7805 q^{60} -0.244877 q^{61} +0.957539 q^{62} +0.459783 q^{63} +24.0376 q^{64} +4.44154 q^{65} -4.59742 q^{66} -4.13299 q^{67} -19.5263 q^{68} -0.945977 q^{69} +1.26600 q^{70} +6.53542 q^{71} +18.9016 q^{72} +14.7732 q^{73} +10.7521 q^{74} +0.387251 q^{75} -6.48275 q^{76} +0.392360 q^{77} +5.30519 q^{78} -4.66528 q^{79} +29.2527 q^{80} +1.74695 q^{81} -27.2670 q^{82} -9.99076 q^{83} +1.09895 q^{84} -7.86561 q^{85} +10.9907 q^{86} +3.23771 q^{87} +16.1298 q^{88} +16.3756 q^{89} +12.2022 q^{90} -0.452764 q^{91} +5.31892 q^{92} +0.334822 q^{93} -12.7202 q^{94} -2.61139 q^{95} +17.9533 q^{96} -17.9396 q^{97} +18.8084 q^{98} +3.78171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.70535	−1.91297	−0.956486	−	0.291780i	$-0.905753\pi$
$2$	−2.70535	−1.91297	−0.956486	+	0.291780i	$0.905753\pi$
$3$	−0.945977	−0.546160	−0.273080	−	0.961991i	$-0.588042\pi$
$3$	−0.945977	−0.546160	−0.273080	+	0.961991i	$0.588042\pi$
$4$	5.31892	2.65946
$5$	2.14258	0.958189	0.479095	−	0.877763i	$-0.340965\pi$
$5$	2.14258	0.958189	0.479095	+	0.877763i	$0.340965\pi$
$6$	2.55920	1.04479
$7$	−0.218411	−0.0825516	−0.0412758	−	0.999148i	$-0.513142\pi$
$7$	−0.218411	−0.0825516	−0.0412758	+	0.999148i	$0.513142\pi$
$8$	−8.97883	−3.17450
$9$	−2.10513	−0.701709
$10$	−5.79642	−1.83299
$11$	−1.79643	−0.541644	−0.270822	−	0.962629i	$-0.587295\pi$
$11$	−1.79643	−0.541644	−0.270822	+	0.962629i	$0.587295\pi$
$12$	−5.03157	−1.45249
$13$	2.07299	0.574944	0.287472	−	0.957789i	$-0.407185\pi$
$13$	2.07299	0.574944	0.287472	+	0.957789i	$0.407185\pi$
$14$	0.590878	0.157919
$15$	−2.02683	−0.523325
$16$	13.6530	3.41326
$17$	−3.67110	−0.890372	−0.445186	−	0.895438i	$-0.646862\pi$
$17$	−3.67110	−0.890372	−0.445186	+	0.895438i	$0.646862\pi$
$18$	5.69511	1.34235
$19$	−1.21881	−0.279614	−0.139807	−	0.990179i	$-0.544648\pi$
$19$	−1.21881	−0.279614	−0.139807	+	0.990179i	$0.544648\pi$
$20$	11.3962	2.54826
$21$	0.206612	0.0450864
$22$	4.85997	1.03615
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	8.49376	1.73378
$25$	−0.409366	−0.0818732
$26$	−5.60816	−1.09985
$27$	4.82933	0.929405
$28$	−1.16171	−0.219542
$29$	−3.42261	−0.635563	−0.317782	−	0.948164i	$-0.602938\pi$
$29$	−3.42261	−0.635563	−0.317782	+	0.948164i	$0.602938\pi$
$30$	5.48328	1.00110
$31$	−0.353943	−0.0635700	−0.0317850	−	0.999495i	$-0.510119\pi$
$31$	−0.353943	−0.0635700	−0.0317850	+	0.999495i	$0.510119\pi$
$32$	−18.9786	−3.35497
$33$	1.69938	0.295824
$34$	9.93160	1.70326
$35$	−0.467962	−0.0791001
$36$	−11.1970	−1.86617
$37$	−3.97438	−0.653383	−0.326692	−	0.945131i	$-0.605934\pi$
$37$	−3.97438	−0.653383	−0.326692	+	0.945131i	$0.605934\pi$
$38$	3.29731	0.534894
$39$	−1.96100	−0.314011
$40$	−19.2378	−3.04177
$41$	10.0789	1.57406	0.787030	−	0.616915i	$-0.211618\pi$
$41$	10.0789	1.57406	0.787030	+	0.616915i	$0.211618\pi$
$42$	−0.558957	−0.0862489
$43$	−4.06260	−0.619540	−0.309770	−	0.950811i	$-0.600252\pi$
$43$	−4.06260	−0.619540	−0.309770	+	0.950811i	$0.600252\pi$
$44$	−9.55505	−1.44048
$45$	−4.51040	−0.672370
$46$	−2.70535	−0.398882
$47$	4.70185	0.685836	0.342918	−	0.939365i	$-0.388585\pi$
$47$	4.70185	0.685836	0.342918	+	0.939365i	$0.388585\pi$
$48$	−12.9155	−1.86419
$49$	−6.95230	−0.993185
$50$	1.10748	0.156621
$51$	3.47277	0.486285
$52$	11.0261	1.52904
$53$	10.0858	1.38539	0.692696	−	0.721229i	$-0.256423\pi$
$53$	10.0858	1.38539	0.692696	+	0.721229i	$0.256423\pi$
$54$	−13.0650	−1.77793
$55$	−3.84899	−0.518997
$56$	1.96107	0.262060
$57$	1.15297	0.152714
$58$	9.25936	1.21581
$59$	7.35475	0.957506	0.478753	−	0.877950i	$-0.341089\pi$
$59$	7.35475	0.957506	0.478753	+	0.877950i	$0.341089\pi$
$60$	−10.7805	−1.39176
$61$	−0.244877	−0.0313533	−0.0156766	−	0.999877i	$-0.504990\pi$
$61$	−0.244877	−0.0313533	−0.0156766	+	0.999877i	$0.504990\pi$
$62$	0.957539	0.121608
$63$	0.459783	0.0579272
$64$	24.0376	3.00470
$65$	4.44154	0.550905
$66$	−4.59742	−0.565903
$67$	−4.13299	−0.504925	−0.252463	−	0.967607i	$-0.581240\pi$
$67$	−4.13299	−0.504925	−0.252463	+	0.967607i	$0.581240\pi$
$68$	−19.5263	−2.36791
$69$	−0.945977	−0.113882
$70$	1.26600	0.151316
$71$	6.53542	0.775612	0.387806	−	0.921741i	$-0.373233\pi$
$71$	6.53542	0.775612	0.387806	+	0.921741i	$0.373233\pi$
$72$	18.9016	2.22757
$73$	14.7732	1.72907	0.864535	−	0.502573i	$-0.167613\pi$
$73$	14.7732	1.72907	0.864535	+	0.502573i	$0.167613\pi$
$74$	10.7521	1.24990
$75$	0.387251	0.0447158
$76$	−6.48275	−0.743622
$77$	0.392360	0.0447135
$78$	5.30519	0.600694
$79$	−4.66528	−0.524885	−0.262442	−	0.964948i	$-0.584528\pi$
$79$	−4.66528	−0.524885	−0.262442	+	0.964948i	$0.584528\pi$
$80$	29.2527	3.27055
$81$	1.74695	0.194105
$82$	−27.2670	−3.01113
$83$	−9.99076	−1.09663	−0.548314	−	0.836272i	$-0.684730\pi$
$83$	−9.99076	−1.09663	−0.548314	+	0.836272i	$0.684730\pi$
$84$	1.09895	0.119905
$85$	−7.86561	−0.853145
$86$	10.9907	1.18516
$87$	3.23771	0.347119
$88$	16.1298	1.71945
$89$	16.3756	1.73581	0.867907	−	0.496727i	$-0.165465\pi$
$89$	16.3756	1.73581	0.867907	+	0.496727i	$0.165465\pi$
$90$	12.2022	1.28623
$91$	−0.452764	−0.0474625
$92$	5.31892	0.554535
$93$	0.334822	0.0347194
$94$	−12.7202	−1.31198
$95$	−2.61139	−0.267923
$96$	17.9533	1.83235
$97$	−17.9396	−1.82149	−0.910743	−	0.412974i	$-0.864490\pi$
$97$	−17.9396	−1.82149	−0.910743	+	0.412974i	$0.864490\pi$
$98$	18.8084	1.89993
$99$	3.78171	0.380076
$100$	−2.17738	−0.217738
$101$	14.1406	1.40704	0.703519	−	0.710676i	$-0.251611\pi$
$101$	14.1406	1.40704	0.703519	+	0.710676i	$0.251611\pi$
$102$	−9.39506	−0.930250
$103$	8.90460	0.877396	0.438698	−	0.898635i	$-0.355440\pi$
$103$	8.90460	0.877396	0.438698	+	0.898635i	$0.355440\pi$
$104$	−18.6130	−1.82516
$105$	0.442681	0.0432013
$106$	−27.2856	−2.65022
$107$	9.83091	0.950390	0.475195	−	0.879880i	$-0.342377\pi$
$107$	9.83091	0.950390	0.475195	+	0.879880i	$0.342377\pi$
$108$	25.6868	2.47171
$109$	0.293993	0.0281594	0.0140797	−	0.999901i	$-0.495518\pi$
$109$	0.293993	0.0281594	0.0140797	+	0.999901i	$0.495518\pi$
$110$	10.4129	0.992827
$111$	3.75967	0.356852
$112$	−2.98197	−0.281770
$113$	12.3871	1.16528	0.582640	−	0.812731i	$-0.302020\pi$
$113$	12.3871	1.16528	0.582640	+	0.812731i	$0.302020\pi$
$114$	−3.11918	−0.292138
$115$	2.14258	0.199796
$116$	−18.2046	−1.69025
$117$	−4.36391	−0.403443
$118$	−19.8972	−1.83168
$119$	0.801808	0.0735016
$120$	18.1985	1.66129
$121$	−7.77284	−0.706622
$122$	0.662478	0.0599779
$123$	−9.53441	−0.859689
$124$	−1.88259	−0.169062
$125$	−11.5900	−1.03664
$126$	−1.24387	−0.110813
$127$	5.56569	0.493875	0.246937	−	0.969031i	$-0.420576\pi$
$127$	5.56569	0.493875	0.246937	+	0.969031i	$0.420576\pi$
$128$	−27.0730	−2.39294
$129$	3.84312	0.338368
$130$	−12.0159	−1.05387
$131$	16.9752	1.48313	0.741565	−	0.670881i	$-0.234084\pi$
$131$	16.9752	1.48313	0.741565	+	0.670881i	$0.234084\pi$
$132$	9.03886	0.786732
$133$	0.266201	0.0230826
$134$	11.1812	0.965907
$135$	10.3472	0.890546
$136$	32.9621	2.82648
$137$	0.482439	0.0412176	0.0206088	−	0.999788i	$-0.493440\pi$
$137$	0.482439	0.0412176	0.0206088	+	0.999788i	$0.493440\pi$
$138$	2.55920	0.217853
$139$	19.1492	1.62421	0.812106	−	0.583510i	$-0.198321\pi$
$139$	19.1492	1.62421	0.812106	+	0.583510i	$0.198321\pi$
$140$	−2.48905	−0.210363
$141$	−4.44784	−0.374576
$142$	−17.6806	−1.48372
$143$	−3.72398	−0.311415
$144$	−28.7414	−2.39512
$145$	−7.33321	−0.608990
$146$	−39.9666	−3.30766
$147$	6.57671	0.542438
$148$	−21.1394	−1.73765
$149$	−19.8693	−1.62776	−0.813878	−	0.581036i	$-0.802648\pi$
$149$	−19.8693	−1.62776	−0.813878	+	0.581036i	$0.802648\pi$
$150$	−1.04765	−0.0855401
$151$	−11.3866	−0.926629	−0.463315	−	0.886194i	$-0.653340\pi$
$151$	−11.3866	−0.926629	−0.463315	+	0.886194i	$0.653340\pi$
$152$	10.9435	0.887634
$153$	7.72813	0.624782
$154$	−1.06147	−0.0855357
$155$	−0.758350	−0.0609121
$156$	−10.4304	−0.835100
$157$	−21.1877	−1.69096	−0.845480	−	0.534007i	$-0.820686\pi$
$157$	−21.1877	−1.69096	−0.845480	+	0.534007i	$0.820686\pi$
$158$	12.6212	1.00409
$159$	−9.54094	−0.756646
$160$	−40.6631	−3.21470
$161$	−0.218411	−0.0172132
$162$	−4.72611	−0.371318
$163$	−13.4950	−1.05701	−0.528505	−	0.848930i	$-0.677247\pi$
$163$	−13.4950	−1.05701	−0.528505	+	0.848930i	$0.677247\pi$
$164$	53.6088	4.18615
$165$	3.64105	0.283455
$166$	27.0285	2.09782
$167$	−13.5563	−1.04902	−0.524508	−	0.851405i	$-0.675751\pi$
$167$	−13.5563	−1.04902	−0.524508	+	0.851405i	$0.675751\pi$
$168$	−1.85513	−0.143126
$169$	−8.70272	−0.669440
$170$	21.2792	1.63204
$171$	2.56575	0.196208
$172$	−21.6086	−1.64764
$173$	0.0757298	0.00575763	0.00287881	−	0.999996i	$-0.499084\pi$
$173$	0.0757298	0.00575763	0.00287881	+	0.999996i	$0.499084\pi$
$174$	−8.75914	−0.664029
$175$	0.0894100	0.00675876
$176$	−24.5267	−1.84877
$177$	−6.95742	−0.522952
$178$	−44.3018	−3.32056
$179$	−25.4226	−1.90017	−0.950087	−	0.311985i	$-0.899006\pi$
$179$	−25.4226	−1.90017	−0.950087	+	0.311985i	$0.899006\pi$
$180$	−23.9904	−1.78814
$181$	−20.0945	−1.49361	−0.746807	−	0.665040i	$-0.768414\pi$
$181$	−20.0945	−1.49361	−0.746807	+	0.665040i	$0.768414\pi$
$182$	1.22488	0.0907944
$183$	0.231648	0.0171239
$184$	−8.97883	−0.661928
$185$	−8.51541	−0.626065
$186$	−0.905810	−0.0664172
$187$	6.59486	0.482264
$188$	25.0088	1.82395
$189$	−1.05478	−0.0767239
$190$	7.06473	0.512530
$191$	9.62757	0.696626	0.348313	−	0.937378i	$-0.386755\pi$
$191$	9.62757	0.696626	0.348313	+	0.937378i	$0.386755\pi$
$192$	−22.7390	−1.64105
$193$	−7.79073	−0.560789	−0.280395	−	0.959885i	$-0.590465\pi$
$193$	−7.79073	−0.560789	−0.280395	+	0.959885i	$0.590465\pi$
$194$	48.5328	3.48445
$195$	−4.20159	−0.300882
$196$	−36.9787	−2.64133
$197$	−19.1896	−1.36720	−0.683601	−	0.729856i	$-0.739587\pi$
$197$	−19.1896	−1.36720	−0.683601	+	0.729856i	$0.739587\pi$
$198$	−10.2309	−0.727075
$199$	−13.6890	−0.970388	−0.485194	−	0.874406i	$-0.661251\pi$
$199$	−13.6890	−0.970388	−0.485194	+	0.874406i	$0.661251\pi$
$200$	3.67563	0.259906
$201$	3.90971	0.275770
$202$	−38.2552	−2.69162
$203$	0.747536	0.0524667
$204$	18.4714	1.29326
$205$	21.5948	1.50825
$206$	−24.0900	−1.67843
$207$	−2.10513	−0.146317
$208$	28.3026	1.96243
$209$	2.18950	0.151451
$210$	−1.19761	−0.0826428
$211$	11.0418	0.760151	0.380075	−	0.924956i	$-0.375898\pi$
$211$	11.0418	0.760151	0.380075	+	0.924956i	$0.375898\pi$
$212$	53.6456	3.68439
$213$	−6.18235	−0.423608
$214$	−26.5961	−1.81807
$215$	−8.70442	−0.593637
$216$	−43.3617	−2.95039
$217$	0.0773050	0.00524781
$218$	−0.795354	−0.0538681
$219$	−13.9751	−0.944348
$220$	−20.4724	−1.38025
$221$	−7.61014	−0.511914
$222$	−10.1712	−0.682647
$223$	−10.6470	−0.712977	−0.356488	−	0.934300i	$-0.616026\pi$
$223$	−10.6470	−0.712977	−0.356488	+	0.934300i	$0.616026\pi$
$224$	4.14513	0.276958
$225$	0.861768	0.0574512
$226$	−33.5114	−2.22915
$227$	−22.2274	−1.47529	−0.737643	−	0.675191i	$-0.764061\pi$
$227$	−22.2274	−1.47529	−0.737643	+	0.675191i	$0.764061\pi$
$228$	6.13253	0.406137
$229$	6.71558	0.443778	0.221889	−	0.975072i	$-0.428778\pi$
$229$	6.71558	0.443778	0.221889	+	0.975072i	$0.428778\pi$
$230$	−5.79642	−0.382205
$231$	−0.371163	−0.0244207
$232$	30.7310	2.01759
$233$	−19.3776	−1.26947	−0.634733	−	0.772732i	$-0.718890\pi$
$233$	−19.3776	−1.26947	−0.634733	+	0.772732i	$0.718890\pi$
$234$	11.8059	0.771776
$235$	10.0741	0.657161
$236$	39.1193	2.54645
$237$	4.41324	0.286671
$238$	−2.16917	−0.140606
$239$	26.2186	1.69594	0.847971	−	0.530043i	$-0.177824\pi$
$239$	26.2186	1.69594	0.847971	+	0.530043i	$0.177824\pi$
$240$	−27.6723	−1.78624
$241$	22.2552	1.43358	0.716792	−	0.697287i	$-0.245610\pi$
$241$	22.2552	1.43358	0.716792	+	0.697287i	$0.245610\pi$
$242$	21.0283	1.35175
$243$	−16.1406	−1.03542
$244$	−1.30248	−0.0833828
$245$	−14.8958	−0.951660
$246$	25.7939	1.64456
$247$	−2.52658	−0.160762
$248$	3.17799	0.201803
$249$	9.45103	0.598935
$250$	31.3549	1.98306
$251$	9.75805	0.615923	0.307961	−	0.951399i	$-0.400353\pi$
$251$	9.75805	0.615923	0.307961	+	0.951399i	$0.400353\pi$
$252$	2.44555	0.154055
$253$	−1.79643	−0.112941
$254$	−15.0571	−0.944768
$255$	7.44068	0.465953
$256$	25.1667	1.57292
$257$	−22.4855	−1.40261	−0.701305	−	0.712862i	$-0.747399\pi$
$257$	−22.4855	−1.40261	−0.701305	+	0.712862i	$0.747399\pi$
$258$	−10.3970	−0.647288
$259$	0.868047	0.0539378
$260$	23.6242	1.46511
$261$	7.20504	0.445981
$262$	−45.9238	−2.83718
$263$	−15.5510	−0.958913	−0.479457	−	0.877566i	$-0.659166\pi$
$263$	−15.5510	−0.958913	−0.479457	+	0.877566i	$0.659166\pi$
$264$	−15.2584	−0.939092
$265$	21.6096	1.32747
$266$	−0.720168	−0.0441563
$267$	−15.4910	−0.948032
$268$	−21.9830	−1.34283
$269$	−13.1145	−0.799603	−0.399801	−	0.916602i	$-0.630921\pi$
$269$	−13.1145	−0.799603	−0.399801	+	0.916602i	$0.630921\pi$
$270$	−27.9928	−1.70359
$271$	22.1532	1.34571	0.672856	−	0.739773i	$-0.265067\pi$
$271$	22.1532	1.34571	0.672856	+	0.739773i	$0.265067\pi$
$272$	−50.1216	−3.03907
$273$	0.428304	0.0259221
$274$	−1.30517	−0.0788480
$275$	0.735397	0.0443461
$276$	−5.03157	−0.302865
$277$	19.4440	1.16828	0.584138	−	0.811654i	$-0.301433\pi$
$277$	19.4440	1.16828	0.584138	+	0.811654i	$0.301433\pi$
$278$	−51.8052	−3.10707
$279$	0.745095	0.0446077
$280$	4.20175	0.251103
$281$	19.7702	1.17939	0.589694	−	0.807627i	$-0.299248\pi$
$281$	19.7702	1.17939	0.589694	+	0.807627i	$0.299248\pi$
$282$	12.0330	0.716553
$283$	21.1452	1.25695	0.628475	−	0.777829i	$-0.283679\pi$
$283$	21.1452	1.25695	0.628475	+	0.777829i	$0.283679\pi$
$284$	34.7614	2.06271
$285$	2.47032	0.146329
$286$	10.0747	0.595727
$287$	−2.20134	−0.129941
$288$	39.9523	2.35421
$289$	−3.52305	−0.207238
$290$	19.8389	1.16498
$291$	16.9704	0.994822
$292$	78.5773	4.59839
$293$	−12.4788	−0.729021	−0.364510	−	0.931199i	$-0.618764\pi$
$293$	−12.4788	−0.729021	−0.364510	+	0.931199i	$0.618764\pi$
$294$	−17.7923	−1.03767
$295$	15.7581	0.917472
$296$	35.6852	2.07416
$297$	−8.67555	−0.503407
$298$	53.7534	3.11385
$299$	2.07299	0.119884
$300$	2.05975	0.118920
$301$	0.887316	0.0511440
$302$	30.8048	1.77262
$303$	−13.3766	−0.768468
$304$	−16.6405	−0.954396
$305$	−0.524668	−0.0300424
$306$	−20.9073	−1.19519
$307$	−21.3132	−1.21641	−0.608205	−	0.793780i	$-0.708110\pi$
$307$	−21.3132	−1.21641	−0.608205	+	0.793780i	$0.708110\pi$
$308$	2.08693	0.118914
$309$	−8.42354	−0.479198
$310$	2.05160	0.116523
$311$	−34.9901	−1.98410	−0.992052	−	0.125829i	$-0.959841\pi$
$311$	−34.9901	−1.98410	−0.992052	+	0.125829i	$0.959841\pi$
$312$	17.6075	0.996827
$313$	6.78823	0.383694	0.191847	−	0.981425i	$-0.438552\pi$
$313$	6.78823	0.383694	0.191847	+	0.981425i	$0.438552\pi$
$314$	57.3200	3.23476
$315$	0.985120	0.0555053
$316$	−24.8142	−1.39591
$317$	−16.7574	−0.941188	−0.470594	−	0.882350i	$-0.655960\pi$
$317$	−16.7574	−0.941188	−0.470594	+	0.882350i	$0.655960\pi$
$318$	25.8116	1.44744
$319$	6.14848	0.344249
$320$	51.5024	2.87907
$321$	−9.29981	−0.519065
$322$	0.590878	0.0329283
$323$	4.47437	0.248961
$324$	9.29188	0.516215
$325$	−0.848611	−0.0470725
$326$	36.5087	2.02203
$327$	−0.278110	−0.0153795
$328$	−90.4967	−4.99685
$329$	−1.02694	−0.0566168
$330$	−9.85032	−0.542242
$331$	5.29376	0.290971	0.145486	−	0.989360i	$-0.453526\pi$
$331$	5.29376	0.290971	0.145486	+	0.989360i	$0.453526\pi$
$332$	−53.1400	−2.91644
$333$	8.36657	0.458485
$334$	36.6745	2.00674
$335$	−8.85525	−0.483814
$336$	2.82088	0.153891
$337$	13.8486	0.754380	0.377190	−	0.926136i	$-0.376890\pi$
$337$	13.8486	0.754380	0.377190	+	0.926136i	$0.376890\pi$
$338$	23.5439	1.28062
$339$	−11.7179	−0.636429
$340$	−41.8365	−2.26890
$341$	0.635833	0.0344323
$342$	−6.94125	−0.375340
$343$	3.04733	0.164541
$344$	36.4774	1.96673
$345$	−2.02683	−0.109121
$346$	−0.204875	−0.0110142
$347$	18.9339	1.01643	0.508213	−	0.861231i	$-0.330306\pi$
$347$	18.9339	1.01643	0.508213	+	0.861231i	$0.330306\pi$
$348$	17.2211	0.923149
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−0.241885	−0.0129293
$351$	10.0112	0.534356
$352$	34.0937	1.81720
$353$	−20.3907	−1.08529	−0.542643	−	0.839963i	$-0.682577\pi$
$353$	−20.3907	−1.08529	−0.542643	+	0.839963i	$0.682577\pi$
$354$	18.8222	1.00039
$355$	14.0026	0.743183
$356$	87.1006	4.61633
$357$	−0.758491	−0.0401436
$358$	68.7770	3.63498
$359$	−5.40186	−0.285099	−0.142550	−	0.989788i	$-0.545530\pi$
$359$	−5.40186	−0.285099	−0.142550	+	0.989788i	$0.545530\pi$
$360$	40.4981	2.13444
$361$	−17.5145	−0.921816
$362$	54.3627	2.85724
$363$	7.35293	0.385929
$364$	−2.40821	−0.126225
$365$	31.6527	1.65678
$366$	−0.626689	−0.0327575
$367$	−15.6026	−0.814450	−0.407225	−	0.913328i	$-0.633503\pi$
$367$	−15.6026	−0.814450	−0.407225	+	0.913328i	$0.633503\pi$
$368$	13.6530	0.711714
$369$	−21.2174	−1.10453
$370$	23.0372	1.19764
$371$	−2.20285	−0.114366
$372$	1.78089	0.0923348
$373$	−1.39193	−0.0720714	−0.0360357	−	0.999351i	$-0.511473\pi$
$373$	−1.39193	−0.0720714	−0.0360357	+	0.999351i	$0.511473\pi$
$374$	−17.8414	−0.922557
$375$	10.9639	0.566171
$376$	−42.2171	−2.17718
$377$	−7.09504	−0.365413
$378$	2.85355	0.146771
$379$	−6.36366	−0.326879	−0.163440	−	0.986553i	$-0.552259\pi$
$379$	−6.36366	−0.326879	−0.163440	+	0.986553i	$0.552259\pi$
$380$	−13.8898	−0.712531
$381$	−5.26501	−0.269735
$382$	−26.0459	−1.33263
$383$	19.5062	0.996719	0.498359	−	0.866971i	$-0.333936\pi$
$383$	19.5062	0.996719	0.498359	+	0.866971i	$0.333936\pi$
$384$	25.6104	1.30693
$385$	0.840661	0.0428440
$386$	21.0766	1.07277
$387$	8.55229	0.434737
$388$	−95.4190	−4.84416
$389$	−5.15667	−0.261453	−0.130727	−	0.991418i	$-0.541731\pi$
$389$	−5.15667	−0.261453	−0.130727	+	0.991418i	$0.541731\pi$
$390$	11.3668	0.575579
$391$	−3.67110	−0.185655
$392$	62.4235	3.15286
$393$	−16.0581	−0.810026
$394$	51.9146	2.61542
$395$	−9.99572	−0.502939
$396$	20.1146	1.01080
$397$	−15.3787	−0.771835	−0.385918	−	0.922533i	$-0.626115\pi$
$397$	−15.3787	−0.771835	−0.385918	+	0.922533i	$0.626115\pi$
$398$	37.0336	1.85632
$399$	−0.251820	−0.0126068
$400$	−5.58909	−0.279454
$401$	−13.2709	−0.662719	−0.331359	−	0.943505i	$-0.607507\pi$
$401$	−13.2709	−0.662719	−0.331359	+	0.943505i	$0.607507\pi$
$402$	−10.5771	−0.527540
$403$	−0.733720	−0.0365492
$404$	75.2125	3.74196
$405$	3.74297	0.185990
$406$	−2.02235	−0.100367
$407$	7.13968	0.353901
$408$	−31.1814	−1.54371
$409$	12.4102	0.613644	0.306822	−	0.951767i	$-0.400734\pi$
$409$	12.4102	0.613644	0.306822	+	0.951767i	$0.400734\pi$
$410$	−58.4215	−2.88523
$411$	−0.456376	−0.0225114
$412$	47.3628	2.33340
$413$	−1.60636	−0.0790437
$414$	5.69511	0.279899
$415$	−21.4060	−1.05078
$416$	−39.3424	−1.92892
$417$	−18.1147	−0.887079
$418$	−5.92338	−0.289722
$419$	6.55331	0.320150	0.160075	−	0.987105i	$-0.448826\pi$
$419$	6.55331	0.320150	0.160075	+	0.987105i	$0.448826\pi$
$420$	2.35459	0.114892
$421$	−3.97478	−0.193719	−0.0968594	−	0.995298i	$-0.530880\pi$
$421$	−3.97478	−0.193719	−0.0968594	+	0.995298i	$0.530880\pi$
$422$	−29.8720	−1.45415
$423$	−9.89800	−0.481257
$424$	−90.5588	−4.39792
$425$	1.50282	0.0728976
$426$	16.7254	0.810350
$427$	0.0534838	0.00258826
$428$	52.2898	2.52752
$429$	3.52280	0.170082
$430$	23.5485	1.13561
$431$	31.5135	1.51795	0.758977	−	0.651118i	$-0.225700\pi$
$431$	31.5135	1.51795	0.758977	+	0.651118i	$0.225700\pi$
$432$	65.9351	3.17230
$433$	−17.3598	−0.834258	−0.417129	−	0.908847i	$-0.636964\pi$
$433$	−17.3598	−0.834258	−0.417129	+	0.908847i	$0.636964\pi$
$434$	−0.209137	−0.0100389
$435$	6.93704	0.332606
$436$	1.56372	0.0748888
$437$	−1.21881	−0.0583036
$438$	37.8075	1.80651
$439$	−37.4950	−1.78954	−0.894769	−	0.446530i	$-0.852660\pi$
$439$	−37.4950	−1.78954	−0.894769	+	0.446530i	$0.852660\pi$
$440$	34.5594	1.64755
$441$	14.6355	0.696927
$442$	20.5881	0.979276
$443$	5.70292	0.270954	0.135477	−	0.990780i	$-0.456743\pi$
$443$	5.70292	0.270954	0.135477	+	0.990780i	$0.456743\pi$
$444$	19.9974	0.949033
$445$	35.0861	1.66324
$446$	28.8039	1.36390
$447$	18.7959	0.889015
$448$	−5.25008	−0.248043
$449$	37.9478	1.79087	0.895433	−	0.445197i	$-0.146866\pi$
$449$	37.9478	1.79087	0.895433	+	0.445197i	$0.146866\pi$
$450$	−2.33138	−0.109902
$451$	−18.1060	−0.852580
$452$	65.8859	3.09901
$453$	10.7715	0.506088
$454$	60.1329	2.82218
$455$	−0.970081	−0.0454781
$456$	−10.3523	−0.484790
$457$	23.4659	1.09769	0.548845	−	0.835924i	$-0.315068\pi$
$457$	23.4659	1.09769	0.548845	+	0.835924i	$0.315068\pi$
$458$	−18.1680	−0.848935
$459$	−17.7289	−0.827516
$460$	11.3962	0.531350
$461$	−5.50279	−0.256290	−0.128145	−	0.991755i	$-0.540902\pi$
$461$	−5.50279	−0.256290	−0.128145	+	0.991755i	$0.540902\pi$
$462$	1.00413	0.0467162
$463$	6.37030	0.296053	0.148026	−	0.988983i	$-0.452708\pi$
$463$	6.37030	0.296053	0.148026	+	0.988983i	$0.452708\pi$
$464$	−46.7290	−2.16934
$465$	0.717381	0.0332678
$466$	52.4230	2.42845
$467$	−28.7774	−1.33166	−0.665831	−	0.746103i	$-0.731923\pi$
$467$	−28.7774	−1.33166	−0.665831	+	0.746103i	$0.731923\pi$
$468$	−23.2113	−1.07294
$469$	0.902691	0.0416824
$470$	−27.2539	−1.25713
$471$	20.0430	0.923534
$472$	−66.0370	−3.03960
$473$	7.29817	0.335570
$474$	−11.9394	−0.548393
$475$	0.498939	0.0228929
$476$	4.26475	0.195474
$477$	−21.2319	−0.972143
$478$	−70.9305	−3.24429
$479$	30.6428	1.40011	0.700054	−	0.714090i	$-0.253159\pi$
$479$	30.6428	1.40011	0.700054	+	0.714090i	$0.253159\pi$
$480$	38.4663	1.75574
$481$	−8.23884	−0.375659
$482$	−60.2082	−2.74241
$483$	0.206612	0.00940116
$484$	−41.3431	−1.87923
$485$	−38.4369	−1.74533
$486$	43.6659	1.98072
$487$	−19.7957	−0.897030	−0.448515	−	0.893775i	$-0.648047\pi$
$487$	−19.7957	−0.897030	−0.448515	+	0.893775i	$0.648047\pi$
$488$	2.19871	0.0995309
$489$	12.7659	0.577296
$490$	40.2984	1.82050
$491$	−36.1581	−1.63179	−0.815895	−	0.578200i	$-0.803755\pi$
$491$	−36.1581	−1.63179	−0.815895	+	0.578200i	$0.803755\pi$
$492$	−50.7127	−2.28631
$493$	12.5647	0.565887
$494$	6.83528	0.307534
$495$	8.10261	0.364185
$496$	−4.83240	−0.216981
$497$	−1.42741	−0.0640280
$498$	−25.5683	−1.14574
$499$	−12.3432	−0.552557	−0.276278	−	0.961078i	$-0.589101\pi$
$499$	−12.3432	−0.552557	−0.276278	+	0.961078i	$0.589101\pi$
$500$	−61.6461	−2.75690
$501$	12.8239	0.572930
$502$	−26.3989	−1.17824
$503$	−20.7626	−0.925757	−0.462878	−	0.886422i	$-0.653183\pi$
$503$	−20.7626	−0.925757	−0.462878	+	0.886422i	$0.653183\pi$
$504$	−4.12831	−0.183890
$505$	30.2972	1.34821
$506$	4.85997	0.216052
$507$	8.23257	0.365621
$508$	29.6034	1.31344
$509$	−0.902663	−0.0400099	−0.0200049	−	0.999800i	$-0.506368\pi$
$509$	−0.902663	−0.0400099	−0.0200049	+	0.999800i	$0.506368\pi$
$510$	−20.1296	−0.891355
$511$	−3.22662	−0.142737
$512$	−13.9387	−0.616010
$513$	−5.88604	−0.259875
$514$	60.8312	2.68315
$515$	19.0788	0.840711
$516$	20.4412	0.899876
$517$	−8.44654	−0.371479
$518$	−2.34837	−0.103182
$519$	−0.0716386	−0.00314458
$520$	−39.8798	−1.74885
$521$	41.6377	1.82418	0.912089	−	0.409991i	$-0.134468\pi$
$521$	41.6377	1.82418	0.912089	+	0.409991i	$0.134468\pi$
$522$	−19.4921	−0.853148
$523$	−17.7623	−0.776691	−0.388345	−	0.921514i	$-0.626953\pi$
$523$	−17.7623	−0.776691	−0.388345	+	0.921514i	$0.626953\pi$
$524$	90.2897	3.94432
$525$	−0.0845798	−0.00369136
$526$	42.0708	1.83437
$527$	1.29936	0.0566009
$528$	23.2017	1.00972
$529$	1.00000	0.0434783
$530$	−58.4616	−2.53941
$531$	−15.4827	−0.671891
$532$	1.41590	0.0613872
$533$	20.8935	0.904996
$534$	41.9085	1.81356
$535$	21.0635	0.910654
$536$	37.1094	1.60288
$537$	24.0492	1.03780
$538$	35.4792	1.52962
$539$	12.4893	0.537952
$540$	55.0360	2.36837
$541$	39.5802	1.70169	0.850843	−	0.525420i	$-0.176092\pi$
$541$	39.5802	1.70169	0.850843	+	0.525420i	$0.176092\pi$
$542$	−59.9322	−2.57431
$543$	19.0090	0.815753
$544$	69.6722	2.98717
$545$	0.629902	0.0269820
$546$	−1.15871	−0.0495883
$547$	17.5559	0.750637	0.375319	−	0.926896i	$-0.377533\pi$
$547$	17.5559	0.750637	0.375319	+	0.926896i	$0.377533\pi$
$548$	2.56605	0.109616
$549$	0.515498	0.0220009
$550$	−1.98950	−0.0848328
$551$	4.17151	0.177712
$552$	8.49376	0.361519
$553$	1.01895	0.0433301
$554$	−52.6028	−2.23488
$555$	8.05538	0.341932
$556$	101.853	4.31952
$557$	−34.6434	−1.46789	−0.733944	−	0.679210i	$-0.762323\pi$
$557$	−34.6434	−1.46789	−0.733944	+	0.679210i	$0.762323\pi$
$558$	−2.01574	−0.0853332
$559$	−8.42172	−0.356201
$560$	−6.38911	−0.269989
$561$	−6.23859	−0.263393
$562$	−53.4852	−2.25614
$563$	7.95995	0.335472	0.167736	−	0.985832i	$-0.446354\pi$
$563$	7.95995	0.335472	0.167736	+	0.985832i	$0.446354\pi$
$564$	−23.6577	−0.996169
$565$	26.5403	1.11656
$566$	−57.2051	−2.40451
$567$	−0.381553	−0.0160237
$568$	−58.6804	−2.46218
$569$	0.714062	0.0299350	0.0149675	−	0.999888i	$-0.495236\pi$
$569$	0.714062	0.0299350	0.0149675	+	0.999888i	$0.495236\pi$
$570$	−6.68307	−0.279923
$571$	−28.9016	−1.20949	−0.604747	−	0.796418i	$-0.706726\pi$
$571$	−28.9016	−1.20949	−0.604747	+	0.796418i	$0.706726\pi$
$572$	−19.8075	−0.828194
$573$	−9.10746	−0.380469
$574$	5.95540	0.248574
$575$	−0.409366	−0.0170717
$576$	−50.6023	−2.10843
$577$	1.32994	0.0553662	0.0276831	−	0.999617i	$-0.491187\pi$
$577$	1.32994	0.0553662	0.0276831	+	0.999617i	$0.491187\pi$
$578$	9.53108	0.396441
$579$	7.36985	0.306280
$580$	−39.0047	−1.61958
$581$	2.18209	0.0905284
$582$	−45.9109	−1.90307
$583$	−18.1184	−0.750389
$584$	−132.646	−5.48892
$585$	−9.35001	−0.386575
$586$	33.7596	1.39460
$587$	30.6146	1.26360	0.631800	−	0.775132i	$-0.282316\pi$
$587$	30.6146	1.26360	0.631800	+	0.775132i	$0.282316\pi$
$588$	34.9810	1.44259
$589$	0.431389	0.0177751
$590$	−42.6312	−1.75510
$591$	18.1529	0.746711
$592$	−54.2623	−2.23017
$593$	−2.19549	−0.0901580	−0.0450790	−	0.998983i	$-0.514354\pi$
$593$	−2.19549	−0.0901580	−0.0450790	+	0.998983i	$0.514354\pi$
$594$	23.4704	0.963002
$595$	1.71793	0.0704285
$596$	−105.683	−4.32895
$597$	12.9495	0.529987
$598$	−5.60816	−0.229335
$599$	2.41767	0.0987832	0.0493916	−	0.998779i	$-0.484272\pi$
$599$	2.41767	0.0987832	0.0493916	+	0.998779i	$0.484272\pi$
$600$	−3.47706	−0.141950
$601$	−44.1031	−1.79900	−0.899502	−	0.436916i	$-0.856071\pi$
$601$	−44.1031	−1.79900	−0.899502	+	0.436916i	$0.856071\pi$
$602$	−2.40050	−0.0978370
$603$	8.70048	0.354311
$604$	−60.5644	−2.46433
$605$	−16.6539	−0.677078
$606$	36.1885	1.47006
$607$	−47.9115	−1.94467	−0.972334	−	0.233594i	$-0.924951\pi$
$607$	−47.9115	−1.94467	−0.972334	+	0.233594i	$0.924951\pi$
$608$	23.1313	0.938097
$609$	−0.707152	−0.0286552
$610$	1.41941	0.0574702
$611$	9.74689	0.394317
$612$	41.1053	1.66158
$613$	12.5307	0.506111	0.253056	−	0.967452i	$-0.418564\pi$
$613$	12.5307	0.506111	0.253056	+	0.967452i	$0.418564\pi$
$614$	57.6597	2.32696
$615$	−20.4282	−0.823744
$616$	−3.52293	−0.141943
$617$	−9.66134	−0.388951	−0.194476	−	0.980907i	$-0.562300\pi$
$617$	−9.66134	−0.388951	−0.194476	+	0.980907i	$0.562300\pi$
$618$	22.7886	0.916693
$619$	−26.0583	−1.04737	−0.523686	−	0.851911i	$-0.675444\pi$
$619$	−26.0583	−1.04737	−0.523686	+	0.851911i	$0.675444\pi$
$620$	−4.03360	−0.161993
$621$	4.82933	0.193794
$622$	94.6603	3.79553
$623$	−3.57662	−0.143294
$624$	−26.7736	−1.07180
$625$	−22.7856	−0.911424
$626$	−18.3645	−0.733995
$627$	−2.07122	−0.0827166
$628$	−112.695	−4.49704
$629$	14.5903	0.581754
$630$	−2.66510	−0.106180
$631$	−21.4025	−0.852020	−0.426010	−	0.904718i	$-0.640081\pi$
$631$	−21.4025	−0.852020	−0.426010	+	0.904718i	$0.640081\pi$
$632$	41.8887	1.66624
$633$	−10.4453	−0.415164
$634$	45.3346	1.80047
$635$	11.9249	0.473226
$636$	−50.7475	−2.01227
$637$	−14.4120	−0.571026
$638$	−16.6338	−0.658538
$639$	−13.7579	−0.544254
$640$	−58.0060	−2.29289
$641$	0.279836	0.0110529	0.00552643	−	0.999985i	$-0.498241\pi$
$641$	0.279836	0.0110529	0.00552643	+	0.999985i	$0.498241\pi$
$642$	25.1592	0.992956
$643$	−13.8161	−0.544855	−0.272428	−	0.962176i	$-0.587827\pi$
$643$	−13.8161	−0.544855	−0.272428	+	0.962176i	$0.587827\pi$
$644$	−1.16171	−0.0457778
$645$	8.23418	0.324221
$646$	−12.1047	−0.476254
$647$	−36.8528	−1.44883	−0.724417	−	0.689362i	$-0.757891\pi$
$647$	−36.8528	−1.44883	−0.724417	+	0.689362i	$0.757891\pi$
$648$	−15.6856	−0.616187
$649$	−13.2123	−0.518627
$650$	2.29579	0.0900483
$651$	−0.0731287	−0.00286614
$652$	−71.7787	−2.81107
$653$	−9.36851	−0.366618	−0.183309	−	0.983055i	$-0.558681\pi$
$653$	−9.36851	−0.366618	−0.183309	+	0.983055i	$0.558681\pi$
$654$	0.752386	0.0294206
$655$	36.3707	1.42112
$656$	137.608	5.37268
$657$	−31.0994	−1.21330
$658$	2.77822	0.108306
$659$	30.8947	1.20349	0.601744	−	0.798689i	$-0.294473\pi$
$659$	30.8947	1.20349	0.601744	+	0.798689i	$0.294473\pi$
$660$	19.3664	0.753838
$661$	−20.9300	−0.814084	−0.407042	−	0.913409i	$-0.633440\pi$
$661$	−20.9300	−0.814084	−0.407042	+	0.913409i	$0.633440\pi$
$662$	−14.3215	−0.556620
$663$	7.19902	0.279587
$664$	89.7053	3.48124
$665$	0.570357	0.0221175
$666$	−22.6345	−0.877069
$667$	−3.42261	−0.132524
$668$	−72.1047	−2.78981
$669$	10.0718	0.389399
$670$	23.9566	0.925522
$671$	0.439904	0.0169823
$672$	−3.92120	−0.151263
$673$	−10.7984	−0.416249	−0.208125	−	0.978102i	$-0.566736\pi$
$673$	−10.7984	−0.416249	−0.208125	+	0.978102i	$0.566736\pi$
$674$	−37.4653	−1.44311
$675$	−1.97696	−0.0760934
$676$	−46.2890	−1.78035
$677$	−15.8517	−0.609232	−0.304616	−	0.952475i	$-0.598528\pi$
$677$	−15.8517	−0.609232	−0.304616	+	0.952475i	$0.598528\pi$
$678$	31.7010	1.21747
$679$	3.91819	0.150367
$680$	70.6239	2.70830
$681$	21.0266	0.805742
$682$	−1.72015	−0.0658680
$683$	−32.0851	−1.22770	−0.613851	−	0.789422i	$-0.710380\pi$
$683$	−32.0851	−1.22770	−0.613851	+	0.789422i	$0.710380\pi$
$684$	13.6470	0.521807
$685$	1.03366	0.0394942
$686$	−8.24411	−0.314761
$687$	−6.35278	−0.242374
$688$	−55.4668	−2.11465
$689$	20.9078	0.796523
$690$	5.48328	0.208745
$691$	47.0210	1.78876	0.894381	−	0.447305i	$-0.147616\pi$
$691$	47.0210	1.78876	0.894381	+	0.447305i	$0.147616\pi$
$692$	0.402800	0.0153122
$693$	−0.825968	−0.0313759
$694$	−51.2229	−1.94439
$695$	41.0286	1.55630
$696$	−29.0709	−1.10193
$697$	−37.0006	−1.40150
$698$	−2.70535	−0.102399
$699$	18.3307	0.693331
$700$	0.475564	0.0179746
$701$	−10.3664	−0.391535	−0.195767	−	0.980650i	$-0.562720\pi$
$701$	−10.3664	−0.391535	−0.195767	+	0.980650i	$0.562720\pi$
$702$	−27.0837	−1.02221
$703$	4.84401	0.182695
$704$	−43.1819	−1.62748
$705$	−9.52984	−0.358915
$706$	55.1639	2.07612
$707$	−3.08845	−0.116153
$708$	−37.0059	−1.39077
$709$	−31.7130	−1.19101	−0.595504	−	0.803353i	$-0.703047\pi$
$709$	−31.7130	−1.19101	−0.595504	+	0.803353i	$0.703047\pi$
$710$	−37.8820	−1.42169
$711$	9.82101	0.368317
$712$	−147.034	−5.51033
$713$	−0.353943	−0.0132553
$714$	2.05198	0.0767936
$715$	−7.97891	−0.298394
$716$	−135.221	−5.05343
$717$	−24.8022	−0.926255
$718$	14.6139	0.545386
$719$	38.6881	1.44282	0.721411	−	0.692507i	$-0.243494\pi$
$719$	38.6881	1.44282	0.721411	+	0.692507i	$0.243494\pi$
$720$	−61.5806	−2.29497
$721$	−1.94486	−0.0724304
$722$	47.3829	1.76341
$723$	−21.0529	−0.782967
$724$	−106.881	−3.97221
$725$	1.40110	0.0520356
$726$	−19.8922	−0.738270
$727$	27.4536	1.01820	0.509099	−	0.860708i	$-0.329979\pi$
$727$	27.4536	1.01820	0.509099	+	0.860708i	$0.329979\pi$
$728$	4.06529	0.150670
$729$	10.0278	0.371398
$730$	−85.6315	−3.16936
$731$	14.9142	0.551621
$732$	1.23212	0.0455403
$733$	−7.27766	−0.268806	−0.134403	−	0.990927i	$-0.542912\pi$
$733$	−7.27766	−0.268806	−0.134403	+	0.990927i	$0.542912\pi$
$734$	42.2105	1.55802
$735$	14.0911	0.519758
$736$	−18.9786	−0.699560
$737$	7.42463	0.273490
$738$	57.4004	2.11294
$739$	−29.3254	−1.07875	−0.539376	−	0.842065i	$-0.681340\pi$
$739$	−29.3254	−1.07875	−0.539376	+	0.842065i	$0.681340\pi$
$740$	−45.2927	−1.66499
$741$	2.39009	0.0878020
$742$	5.95948	0.218780
$743$	9.10410	0.333997	0.166998	−	0.985957i	$-0.446593\pi$
$743$	9.10410	0.333997	0.166998	+	0.985957i	$0.446593\pi$
$744$	−3.00631	−0.110217
$745$	−42.5715	−1.55970
$746$	3.76566	0.137870
$747$	21.0318	0.769515
$748$	35.0775	1.28256
$749$	−2.14718	−0.0784562
$750$	−29.6610	−1.08307
$751$	−22.8030	−0.832092	−0.416046	−	0.909344i	$-0.636584\pi$
$751$	−22.8030	−0.832092	−0.416046	+	0.909344i	$0.636584\pi$
$752$	64.1946	2.34094
$753$	−9.23089	−0.336392
$754$	19.1946	0.699024
$755$	−24.3967	−0.887887
$756$	−5.61028	−0.204044
$757$	40.3962	1.46822	0.734112	−	0.679029i	$-0.237599\pi$
$757$	40.3962	1.46822	0.734112	+	0.679029i	$0.237599\pi$
$758$	17.2159	0.625311
$759$	1.69938	0.0616836
$760$	23.4473	0.850521
$761$	−35.9050	−1.30155	−0.650777	−	0.759269i	$-0.725557\pi$
$761$	−35.9050	−1.30155	−0.650777	+	0.759269i	$0.725557\pi$
$762$	14.2437	0.515995
$763$	−0.0642113	−0.00232460
$764$	51.2082	1.85265
$765$	16.5581	0.598660
$766$	−52.7710	−1.90669
$767$	15.2463	0.550512
$768$	−23.8071	−0.859065
$769$	−48.8707	−1.76232	−0.881162	−	0.472815i	$-0.843238\pi$
$769$	−48.8707	−1.76232	−0.881162	+	0.472815i	$0.843238\pi$
$770$	−2.27428	−0.0819594
$771$	21.2708	0.766049
$772$	−41.4382	−1.49139
$773$	−8.41007	−0.302489	−0.151245	−	0.988496i	$-0.548328\pi$
$773$	−8.41007	−0.302489	−0.151245	+	0.988496i	$0.548328\pi$
$774$	−23.1369	−0.831640
$775$	0.144892	0.00520468
$776$	161.076	5.78230
$777$	−0.821153	−0.0294587
$778$	13.9506	0.500153
$779$	−12.2843	−0.440130
$780$	−22.3479	−0.800184
$781$	−11.7404	−0.420105
$782$	9.93160	0.355153
$783$	−16.5289	−0.590696
$784$	−94.9200	−3.39000
$785$	−45.3962	−1.62026
$786$	43.4429	1.54956
$787$	33.1068	1.18013	0.590065	−	0.807355i	$-0.299102\pi$
$787$	33.1068	1.18013	0.590065	+	0.807355i	$0.299102\pi$
$788$	−102.068	−3.63602
$789$	14.7108	0.523720
$790$	27.0419	0.962108
$791$	−2.70548	−0.0961957
$792$	−33.9553	−1.20655
$793$	−0.507627	−0.0180264
$794$	41.6048	1.47650
$795$	−20.4422	−0.725010
$796$	−72.8107	−2.58071
$797$	−45.9180	−1.62650	−0.813250	−	0.581915i	$-0.802304\pi$
$797$	−45.9180	−1.62650	−0.813250	+	0.581915i	$0.802304\pi$
$798$	0.681262	0.0241164
$799$	−17.2610	−0.610649
$800$	7.76918	0.274682
$801$	−34.4728	−1.21804
$802$	35.9025	1.26776
$803$	−26.5390	−0.936539
$804$	20.7954	0.733399
$805$	−0.467962	−0.0164935
$806$	1.98497	0.0699175
$807$	12.4060	0.436711
$808$	−126.966	−4.46664
$809$	−21.3456	−0.750472	−0.375236	−	0.926929i	$-0.622438\pi$
$809$	−21.3456	−0.750472	−0.375236	+	0.926929i	$0.622438\pi$
$810$	−10.1260	−0.355793
$811$	32.2588	1.13276	0.566380	−	0.824144i	$-0.308343\pi$
$811$	32.2588	1.13276	0.566380	+	0.824144i	$0.308343\pi$
$812$	3.97608	0.139533
$813$	−20.9564	−0.734974
$814$	−19.3153	−0.677002
$815$	−28.9141	−1.01282
$816$	47.4139	1.65982
$817$	4.95153	0.173232
$818$	−33.5739	−1.17388
$819$	0.953125	0.0333049
$820$	114.861	4.01112
$821$	−28.3502	−0.989428	−0.494714	−	0.869056i	$-0.664727\pi$
$821$	−28.3502	−0.989428	−0.494714	+	0.869056i	$0.664727\pi$
$822$	1.23466	0.0430636
$823$	13.2469	0.461758	0.230879	−	0.972982i	$-0.425840\pi$
$823$	13.2469	0.461758	0.230879	+	0.972982i	$0.425840\pi$
$824$	−79.9528	−2.78529
$825$	−0.695668	−0.0242200
$826$	4.34576	0.151208
$827$	35.9260	1.24927	0.624635	−	0.780917i	$-0.285248\pi$
$827$	35.9260	1.24927	0.624635	+	0.780917i	$0.285248\pi$
$828$	−11.1970	−0.389123
$829$	−12.5916	−0.437326	−0.218663	−	0.975800i	$-0.570169\pi$
$829$	−12.5916	−0.437326	−0.218663	+	0.975800i	$0.570169\pi$
$830$	57.9106	2.01011
$831$	−18.3936	−0.638065
$832$	49.8297	1.72753
$833$	25.5226	0.884304
$834$	49.0065	1.69696
$835$	−29.0454	−1.00516
$836$	11.6458	0.402778
$837$	−1.70931	−0.0590823
$838$	−17.7290	−0.612438
$839$	18.8932	0.652266	0.326133	−	0.945324i	$-0.394254\pi$
$839$	18.8932	0.652266	0.326133	+	0.945324i	$0.394254\pi$
$840$	−3.97476	−0.137142
$841$	−17.2857	−0.596060
$842$	10.7532	0.370578
$843$	−18.7021	−0.644135
$844$	58.7305	2.02159
$845$	−18.6462	−0.641450
$846$	26.7776	0.920631
$847$	1.69767	0.0583328
$848$	137.702	4.72870
$849$	−20.0029	−0.686496
$850$	−4.06566	−0.139451
$851$	−3.97438	−0.136240
$852$	−32.8834	−1.12657
$853$	29.5804	1.01281	0.506407	−	0.862294i	$-0.330973\pi$
$853$	29.5804	1.01281	0.506407	+	0.862294i	$0.330973\pi$
$854$	−0.144692	−0.00495127
$855$	5.49732	0.188004
$856$	−88.2701	−3.01701
$857$	−47.6466	−1.62758	−0.813789	−	0.581160i	$-0.802599\pi$
$857$	−47.6466	−1.62758	−0.813789	+	0.581160i	$0.802599\pi$
$858$	−9.53039	−0.325362
$859$	31.0402	1.05908	0.529539	−	0.848286i	$-0.322365\pi$
$859$	31.0402	1.05908	0.529539	+	0.848286i	$0.322365\pi$
$860$	−46.2981	−1.57875
$861$	2.08242	0.0709687
$862$	−85.2551	−2.90380
$863$	14.2704	0.485770	0.242885	−	0.970055i	$-0.421906\pi$
$863$	14.2704	0.485770	0.242885	+	0.970055i	$0.421906\pi$
$864$	−91.6539	−3.11813
$865$	0.162257	0.00551690
$866$	46.9643	1.59591
$867$	3.33272	0.113185
$868$	0.411179	0.0139563
$869$	8.38084	0.284301
$870$	−18.7671	−0.636265
$871$	−8.56765	−0.290304
$872$	−2.63971	−0.0893919
$873$	37.7651	1.27815
$874$	3.29731	0.111533
$875$	2.53138	0.0855762
$876$	−74.3323	−2.51145
$877$	2.78172	0.0939321	0.0469661	−	0.998896i	$-0.485045\pi$
$877$	2.78172	0.0939321	0.0469661	+	0.998896i	$0.485045\pi$
$878$	101.437	3.42333
$879$	11.8047	0.398162
$880$	−52.5503	−1.77147
$881$	6.31671	0.212815	0.106408	−	0.994323i	$-0.466065\pi$
$881$	6.31671	0.212815	0.106408	+	0.994323i	$0.466065\pi$
$882$	−39.5941	−1.33320
$883$	−42.9125	−1.44412	−0.722060	−	0.691830i	$-0.756805\pi$
$883$	−42.9125	−1.44412	−0.722060	+	0.691830i	$0.756805\pi$
$884$	−40.4777	−1.36141
$885$	−14.9068	−0.501087
$886$	−15.4284	−0.518327
$887$	−15.4037	−0.517205	−0.258602	−	0.965984i	$-0.583262\pi$
$887$	−15.4037	−0.517205	−0.258602	+	0.965984i	$0.583262\pi$
$888$	−33.7574	−1.13282
$889$	−1.21561	−0.0407702
$890$	−94.9201	−3.18173
$891$	−3.13827	−0.105136
$892$	−56.6306	−1.89613
$893$	−5.73066	−0.191769
$894$	−50.8495	−1.70066
$895$	−54.4699	−1.82073
$896$	5.91304	0.197541
$897$	−1.96100	−0.0654759
$898$	−102.662	−3.42587
$899$	1.21141	0.0404028
$900$	4.58367	0.152789
$901$	−37.0260	−1.23351
$902$	48.9831	1.63096
$903$	−0.839380	−0.0279328
$904$	−111.222	−3.69917
$905$	−43.0541	−1.43117
$906$	−29.1406	−0.968131
$907$	32.4776	1.07840	0.539201	−	0.842177i	$-0.318726\pi$
$907$	32.4776	1.07840	0.539201	+	0.842177i	$0.318726\pi$
$908$	−118.226	−3.92346
$909$	−29.7677	−0.987332
$910$	2.62441	0.0869982
$911$	−5.34142	−0.176969	−0.0884845	−	0.996078i	$-0.528202\pi$
$911$	−5.34142	−0.176969	−0.0884845	+	0.996078i	$0.528202\pi$
$912$	15.7415	0.521253
$913$	17.9477	0.593982
$914$	−63.4835	−2.09985
$915$	0.496324	0.0164079
$916$	35.7196	1.18021
$917$	−3.70757	−0.122435
$918$	47.9630	1.58301
$919$	43.7748	1.44400	0.721998	−	0.691895i	$-0.243224\pi$
$919$	43.7748	1.44400	0.721998	+	0.691895i	$0.243224\pi$
$920$	−19.2378	−0.634252
$921$	20.1618	0.664354
$922$	14.8870	0.490276
$923$	13.5479	0.445933
$924$	−1.97419	−0.0649459
$925$	1.62697	0.0534946
$926$	−17.2339	−0.566341
$927$	−18.7453	−0.615677
$928$	64.9563	2.13230
$929$	25.4519	0.835050	0.417525	−	0.908665i	$-0.362898\pi$
$929$	25.4519	0.835050	0.417525	+	0.908665i	$0.362898\pi$
$930$	−1.94077	−0.0636402
$931$	8.47353	0.277709
$932$	−103.068	−3.37609
$933$	33.0998	1.08364
$934$	77.8531	2.54743
$935$	14.1300	0.462100
$936$	39.1828	1.28073
$937$	43.4186	1.41842	0.709212	−	0.704995i	$-0.249051\pi$
$937$	43.4186	1.41842	0.709212	+	0.704995i	$0.249051\pi$
$938$	−2.44209	−0.0797372
$939$	−6.42151	−0.209558
$940$	53.5832	1.74769
$941$	43.3252	1.41236	0.706181	−	0.708032i	$-0.250417\pi$
$941$	43.3252	1.41236	0.706181	+	0.708032i	$0.250417\pi$
$942$	−54.2234	−1.76669
$943$	10.0789	0.328214
$944$	100.415	3.26822
$945$	−2.25995	−0.0735160
$946$	−19.7441	−0.641936
$947$	33.5705	1.09090	0.545448	−	0.838145i	$-0.316360\pi$
$947$	33.5705	1.09090	0.545448	+	0.838145i	$0.316360\pi$
$948$	23.4737	0.762390
$949$	30.6246	0.994117
$950$	−1.34980	−0.0437934
$951$	15.8521	0.514039
$952$	−7.19929	−0.233330
$953$	−6.88723	−0.223099	−0.111550	−	0.993759i	$-0.535581\pi$
$953$	−6.88723	−0.223099	−0.111550	+	0.993759i	$0.535581\pi$
$954$	57.4398	1.85968
$955$	20.6278	0.667500
$956$	139.455	4.51028
$957$	−5.81632	−0.188015
$958$	−82.8996	−2.67836
$959$	−0.105370	−0.00340258
$960$	−48.7201	−1.57243
$961$	−30.8747	−0.995959
$962$	22.2889	0.718624
$963$	−20.6953	−0.666898
$964$	118.374	3.81256
$965$	−16.6922	−0.537342
$966$	−0.558957	−0.0179841
$967$	−16.2785	−0.523481	−0.261741	−	0.965138i	$-0.584296\pi$
$967$	−16.2785	−0.523481	−0.261741	+	0.965138i	$0.584296\pi$
$968$	69.7910	2.24317
$969$	−4.23265	−0.135972
$970$	103.985	3.33876
$971$	−18.6134	−0.597332	−0.298666	−	0.954358i	$-0.596542\pi$
$971$	−18.6134	−0.597332	−0.298666	+	0.954358i	$0.596542\pi$
$972$	−85.8503	−2.75365
$973$	−4.18239	−0.134081
$974$	53.5544	1.71599
$975$	0.802766	0.0257091
$976$	−3.34332	−0.107017
$977$	30.5742	0.978154	0.489077	−	0.872241i	$-0.337334\pi$
$977$	30.5742	0.978154	0.489077	+	0.872241i	$0.337334\pi$
$978$	−34.5363	−1.10435
$979$	−29.4177	−0.940193
$980$	−79.2297	−2.53090
$981$	−0.618893	−0.0197597
$982$	97.8202	3.12157
$983$	44.1539	1.40829	0.704146	−	0.710055i	$-0.251330\pi$
$983$	44.1539	1.40829	0.704146	+	0.710055i	$0.251330\pi$
$984$	85.6078	2.72908
$985$	−41.1152	−1.31004
$986$	−33.9920	−1.08253
$987$	0.971458	0.0309218
$988$	−13.4387	−0.427541
$989$	−4.06260	−0.129183
$990$	−21.9204	−0.696676
$991$	17.1601	0.545109	0.272554	−	0.962140i	$-0.412132\pi$
$991$	17.1601	0.545109	0.272554	+	0.962140i	$0.412132\pi$
$992$	6.71733	0.213276
$993$	−5.00777	−0.158917
$994$	3.86164	0.122484
$995$	−29.3298	−0.929816
$996$	50.2692	1.59284
$997$	−41.7049	−1.32081	−0.660404	−	0.750910i	$-0.729615\pi$
$997$	−41.7049	−1.32081	−0.660404	+	0.750910i	$0.729615\pi$
$998$	33.3926	1.05703
$999$	−19.1936	−0.607258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.4	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.70535 q^{2} -0.945977 q^{3} +5.31892 q^{4} +2.14258 q^{5} +2.55920 q^{6} -0.218411 q^{7} -8.97883 q^{8} -2.10513 q^{9} +O(q^{10})\)	\(q-2.70535 q^{2} -0.945977 q^{3} +5.31892 q^{4} +2.14258 q^{5} +2.55920 q^{6} -0.218411 q^{7} -8.97883 q^{8} -2.10513 q^{9} -5.79642 q^{10} -1.79643 q^{11} -5.03157 q^{12} +2.07299 q^{13} +0.590878 q^{14} -2.02683 q^{15} +13.6530 q^{16} -3.67110 q^{17} +5.69511 q^{18} -1.21881 q^{19} +11.3962 q^{20} +0.206612 q^{21} +4.85997 q^{22} +1.00000 q^{23} +8.49376 q^{24} -0.409366 q^{25} -5.60816 q^{26} +4.82933 q^{27} -1.16171 q^{28} -3.42261 q^{29} +5.48328 q^{30} -0.353943 q^{31} -18.9786 q^{32} +1.69938 q^{33} +9.93160 q^{34} -0.467962 q^{35} -11.1970 q^{36} -3.97438 q^{37} +3.29731 q^{38} -1.96100 q^{39} -19.2378 q^{40} +10.0789 q^{41} -0.558957 q^{42} -4.06260 q^{43} -9.55505 q^{44} -4.51040 q^{45} -2.70535 q^{46} +4.70185 q^{47} -12.9155 q^{48} -6.95230 q^{49} +1.10748 q^{50} +3.47277 q^{51} +11.0261 q^{52} +10.0858 q^{53} -13.0650 q^{54} -3.84899 q^{55} +1.96107 q^{56} +1.15297 q^{57} +9.25936 q^{58} +7.35475 q^{59} -10.7805 q^{60} -0.244877 q^{61} +0.957539 q^{62} +0.459783 q^{63} +24.0376 q^{64} +4.44154 q^{65} -4.59742 q^{66} -4.13299 q^{67} -19.5263 q^{68} -0.945977 q^{69} +1.26600 q^{70} +6.53542 q^{71} +18.9016 q^{72} +14.7732 q^{73} +10.7521 q^{74} +0.387251 q^{75} -6.48275 q^{76} +0.392360 q^{77} +5.30519 q^{78} -4.66528 q^{79} +29.2527 q^{80} +1.74695 q^{81} -27.2670 q^{82} -9.99076 q^{83} +1.09895 q^{84} -7.86561 q^{85} +10.9907 q^{86} +3.23771 q^{87} +16.1298 q^{88} +16.3756 q^{89} +12.2022 q^{90} -0.452764 q^{91} +5.31892 q^{92} +0.334822 q^{93} -12.7202 q^{94} -2.61139 q^{95} +17.9533 q^{96} -17.9396 q^{97} +18.8084 q^{98} +3.78171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 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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