LMFDB - Embedded newform 8027.2.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.31347 q^{2} +1.92997 q^{3} +3.35213 q^{4} +3.01701 q^{5} -4.46493 q^{6} -2.82894 q^{7} -3.12810 q^{8} +0.724803 q^{9} +O(q^{10})$	\(q-2.31347 q^{2} +1.92997 q^{3} +3.35213 q^{4} +3.01701 q^{5} -4.46493 q^{6} -2.82894 q^{7} -3.12810 q^{8} +0.724803 q^{9} -6.97976 q^{10} -0.304614 q^{11} +6.46952 q^{12} +1.16828 q^{13} +6.54467 q^{14} +5.82276 q^{15} +0.532504 q^{16} +0.136266 q^{17} -1.67681 q^{18} -1.71041 q^{19} +10.1134 q^{20} -5.45979 q^{21} +0.704714 q^{22} +1.00000 q^{23} -6.03716 q^{24} +4.10236 q^{25} -2.70278 q^{26} -4.39107 q^{27} -9.48298 q^{28} -1.83099 q^{29} -13.4708 q^{30} +9.74701 q^{31} +5.02427 q^{32} -0.587897 q^{33} -0.315246 q^{34} -8.53496 q^{35} +2.42963 q^{36} -7.34938 q^{37} +3.95697 q^{38} +2.25476 q^{39} -9.43752 q^{40} +6.10173 q^{41} +12.6310 q^{42} -6.04017 q^{43} -1.02111 q^{44} +2.18674 q^{45} -2.31347 q^{46} -9.72612 q^{47} +1.02772 q^{48} +1.00292 q^{49} -9.49067 q^{50} +0.262990 q^{51} +3.91623 q^{52} -12.9269 q^{53} +10.1586 q^{54} -0.919024 q^{55} +8.84922 q^{56} -3.30105 q^{57} +4.23594 q^{58} +0.0175008 q^{59} +19.5186 q^{60} -0.273104 q^{61} -22.5494 q^{62} -2.05043 q^{63} -12.6885 q^{64} +3.52472 q^{65} +1.36008 q^{66} +13.0164 q^{67} +0.456780 q^{68} +1.92997 q^{69} +19.7453 q^{70} -15.1190 q^{71} -2.26726 q^{72} -4.05723 q^{73} +17.0026 q^{74} +7.91745 q^{75} -5.73351 q^{76} +0.861736 q^{77} -5.21631 q^{78} -7.29338 q^{79} +1.60657 q^{80} -10.6491 q^{81} -14.1161 q^{82} -1.82374 q^{83} -18.3019 q^{84} +0.411116 q^{85} +13.9737 q^{86} -3.53377 q^{87} +0.952864 q^{88} -11.4172 q^{89} -5.05895 q^{90} -3.30501 q^{91} +3.35213 q^{92} +18.8115 q^{93} +22.5011 q^{94} -5.16032 q^{95} +9.69672 q^{96} -3.70703 q^{97} -2.32022 q^{98} -0.220785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.31347	−1.63587	−0.817934	−	0.575312i	$-0.804881\pi$
$2$	−2.31347	−1.63587	−0.817934	+	0.575312i	$0.804881\pi$
$3$	1.92997	1.11427	0.557136	−	0.830421i	$-0.311900\pi$
$3$	1.92997	1.11427	0.557136	+	0.830421i	$0.311900\pi$
$4$	3.35213	1.67606
$5$	3.01701	1.34925	0.674624	−	0.738161i	$-0.264306\pi$
$5$	3.01701	1.34925	0.674624	+	0.738161i	$0.264306\pi$
$6$	−4.46493	−1.82280
$7$	−2.82894	−1.06924	−0.534620	−	0.845093i	$-0.679545\pi$
$7$	−2.82894	−1.06924	−0.534620	+	0.845093i	$0.679545\pi$
$8$	−3.12810	−1.10595
$9$	0.724803	0.241601
$10$	−6.97976	−2.20719
$11$	−0.304614	−0.0918446	−0.0459223	−	0.998945i	$-0.514623\pi$
$11$	−0.304614	−0.0918446	−0.0459223	+	0.998945i	$0.514623\pi$
$12$	6.46952	1.86759
$13$	1.16828	0.324023	0.162012	−	0.986789i	$-0.448202\pi$
$13$	1.16828	0.324023	0.162012	+	0.986789i	$0.448202\pi$
$14$	6.54467	1.74914
$15$	5.82276	1.50343
$16$	0.532504	0.133126
$17$	0.136266	0.0330493	0.0165247	−	0.999863i	$-0.494740\pi$
$17$	0.136266	0.0330493	0.0165247	+	0.999863i	$0.494740\pi$
$18$	−1.67681	−0.395227
$19$	−1.71041	−0.392395	−0.196197	−	0.980564i	$-0.562859\pi$
$19$	−1.71041	−0.392395	−0.196197	+	0.980564i	$0.562859\pi$
$20$	10.1134	2.26143
$21$	−5.45979	−1.19142
$22$	0.704714	0.150246
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−6.03716	−1.23233
$25$	4.10236	0.820472
$26$	−2.70278	−0.530060
$27$	−4.39107	−0.845062
$28$	−9.48298	−1.79211
$29$	−1.83099	−0.340006	−0.170003	−	0.985444i	$-0.554378\pi$
$29$	−1.83099	−0.340006	−0.170003	+	0.985444i	$0.554378\pi$
$30$	−13.4708	−2.45941
$31$	9.74701	1.75061	0.875307	−	0.483568i	$-0.160659\pi$
$31$	9.74701	1.75061	0.875307	+	0.483568i	$0.160659\pi$
$32$	5.02427	0.888174
$33$	−0.587897	−0.102340
$34$	−0.315246	−0.0540643
$35$	−8.53496	−1.44267
$36$	2.42963	0.404939
$37$	−7.34938	−1.20823	−0.604116	−	0.796897i	$-0.706474\pi$
$37$	−7.34938	−1.20823	−0.604116	+	0.796897i	$0.706474\pi$
$38$	3.95697	0.641906
$39$	2.25476	0.361050
$40$	−9.43752	−1.49220
$41$	6.10173	0.952930	0.476465	−	0.879193i	$-0.341918\pi$
$41$	6.10173	0.952930	0.476465	+	0.879193i	$0.341918\pi$
$42$	12.6310	1.94901
$43$	−6.04017	−0.921117	−0.460559	−	0.887629i	$-0.652351\pi$
$43$	−6.04017	−0.921117	−0.460559	+	0.887629i	$0.652351\pi$
$44$	−1.02111	−0.153937
$45$	2.18674	0.325980
$46$	−2.31347	−0.341102
$47$	−9.72612	−1.41870	−0.709350	−	0.704856i	$-0.751012\pi$
$47$	−9.72612	−1.41870	−0.709350	+	0.704856i	$0.751012\pi$
$48$	1.02772	0.148338
$49$	1.00292	0.143274
$50$	−9.49067	−1.34218
$51$	0.262990	0.0368259
$52$	3.91623	0.543084
$53$	−12.9269	−1.77564	−0.887822	−	0.460188i	$-0.847782\pi$
$53$	−12.9269	−1.77564	−0.887822	+	0.460188i	$0.847782\pi$
$54$	10.1586	1.38241
$55$	−0.919024	−0.123921
$56$	8.84922	1.18253
$57$	−3.30105	−0.437234
$58$	4.23594	0.556206
$59$	0.0175008	0.00227841	0.00113920	−	0.999999i	$-0.499637\pi$
$59$	0.0175008	0.00227841	0.00113920	+	0.999999i	$0.499637\pi$
$60$	19.5186	2.51984
$61$	−0.273104	−0.0349674	−0.0174837	−	0.999847i	$-0.505566\pi$
$61$	−0.273104	−0.0349674	−0.0174837	+	0.999847i	$0.505566\pi$
$62$	−22.5494	−2.86377
$63$	−2.05043	−0.258329
$64$	−12.6885	−1.58606
$65$	3.52472	0.437188
$66$	1.36008	0.167414
$67$	13.0164	1.59020	0.795101	−	0.606477i	$-0.207418\pi$
$67$	13.0164	1.59020	0.795101	+	0.606477i	$0.207418\pi$
$68$	0.456780	0.0553928
$69$	1.92997	0.232342
$70$	19.7453	2.36002
$71$	−15.1190	−1.79429	−0.897147	−	0.441733i	$-0.854364\pi$
$71$	−15.1190	−1.79429	−0.897147	+	0.441733i	$0.854364\pi$
$72$	−2.26726	−0.267199
$73$	−4.05723	−0.474862	−0.237431	−	0.971404i	$-0.576305\pi$
$73$	−4.05723	−0.474862	−0.237431	+	0.971404i	$0.576305\pi$
$74$	17.0026	1.97651
$75$	7.91745	0.914229
$76$	−5.73351	−0.657678
$77$	0.861736	0.0982039
$78$	−5.21631	−0.590630
$79$	−7.29338	−0.820569	−0.410285	−	0.911958i	$-0.634571\pi$
$79$	−7.29338	−0.820569	−0.410285	+	0.911958i	$0.634571\pi$
$80$	1.60657	0.179620
$81$	−10.6491	−1.18323
$82$	−14.1161	−1.55887
$83$	−1.82374	−0.200181	−0.100091	−	0.994978i	$-0.531913\pi$
$83$	−1.82374	−0.200181	−0.100091	+	0.994978i	$0.531913\pi$
$84$	−18.3019	−1.99690
$85$	0.411116	0.0445918
$86$	13.9737	1.50683
$87$	−3.53377	−0.378860
$88$	0.952864	0.101576
$89$	−11.4172	−1.21022	−0.605111	−	0.796141i	$-0.706871\pi$
$89$	−11.4172	−1.21022	−0.605111	+	0.796141i	$0.706871\pi$
$90$	−5.05895	−0.533260
$91$	−3.30501	−0.346459
$92$	3.35213	0.349483
$93$	18.8115	1.95066
$94$	22.5011	2.32081
$95$	−5.16032	−0.529438
$96$	9.69672	0.989668
$97$	−3.70703	−0.376392	−0.188196	−	0.982131i	$-0.560264\pi$
$97$	−3.70703	−0.376392	−0.188196	+	0.982131i	$0.560264\pi$
$98$	−2.32022	−0.234378
$99$	−0.220785	−0.0221897
$100$	13.7516	1.37516
$101$	14.6967	1.46237	0.731186	−	0.682178i	$-0.238967\pi$
$101$	14.6967	1.46237	0.731186	+	0.682178i	$0.238967\pi$
$102$	−0.608418	−0.0602423
$103$	−0.692680	−0.0682518	−0.0341259	−	0.999418i	$-0.510865\pi$
$103$	−0.692680	−0.0682518	−0.0341259	+	0.999418i	$0.510865\pi$
$104$	−3.65451	−0.358354
$105$	−16.4722	−1.60753
$106$	29.9059	2.90472
$107$	4.63406	0.447991	0.223996	−	0.974590i	$-0.428090\pi$
$107$	4.63406	0.447991	0.223996	+	0.974590i	$0.428090\pi$
$108$	−14.7194	−1.41638
$109$	11.2982	1.08217	0.541084	−	0.840968i	$-0.318014\pi$
$109$	11.2982	1.08217	0.541084	+	0.840968i	$0.318014\pi$
$110$	2.12613	0.202719
$111$	−14.1841	−1.34630
$112$	−1.50642	−0.142344
$113$	−1.99916	−0.188065	−0.0940325	−	0.995569i	$-0.529976\pi$
$113$	−1.99916	−0.188065	−0.0940325	+	0.995569i	$0.529976\pi$
$114$	7.63686	0.715257
$115$	3.01701	0.281338
$116$	−6.13772	−0.569873
$117$	0.846775	0.0782844
$118$	−0.0404874	−0.00372717
$119$	−0.385488	−0.0353377
$120$	−18.2142	−1.66272
$121$	−10.9072	−0.991565
$122$	0.631817	0.0572020
$123$	11.7762	1.06182
$124$	32.6732	2.93414
$125$	−2.70819	−0.242228
$126$	4.74359	0.422593
$127$	12.5046	1.10961	0.554804	−	0.831981i	$-0.312793\pi$
$127$	12.5046	1.10961	0.554804	+	0.831981i	$0.312793\pi$
$128$	19.3059	1.70641
$129$	−11.6574	−1.02637
$130$	−8.15433	−0.715182
$131$	9.64368	0.842573	0.421286	−	0.906928i	$-0.361579\pi$
$131$	9.64368	0.842573	0.421286	+	0.906928i	$0.361579\pi$
$132$	−1.97071	−0.171528
$133$	4.83865	0.419564
$134$	−30.1129	−2.60136
$135$	−13.2479	−1.14020
$136$	−0.426253	−0.0365509
$137$	2.38980	0.204175	0.102087	−	0.994775i	$-0.467448\pi$
$137$	2.38980	0.204175	0.102087	+	0.994775i	$0.467448\pi$
$138$	−4.46493	−0.380080
$139$	−4.44872	−0.377335	−0.188668	−	0.982041i	$-0.560417\pi$
$139$	−4.44872	−0.377335	−0.188668	+	0.982041i	$0.560417\pi$
$140$	−28.6103	−2.41801
$141$	−18.7712	−1.58082
$142$	34.9773	2.93523
$143$	−0.355875	−0.0297598
$144$	0.385960	0.0321634
$145$	−5.52412	−0.458753
$146$	9.38625	0.776812
$147$	1.93561	0.159646
$148$	−24.6361	−2.02507
$149$	2.57617	0.211048	0.105524	−	0.994417i	$-0.466348\pi$
$149$	2.57617	0.211048	0.105524	+	0.994417i	$0.466348\pi$
$150$	−18.3168	−1.49556
$151$	13.5402	1.10188	0.550941	−	0.834544i	$-0.314269\pi$
$151$	13.5402	1.10188	0.550941	+	0.834544i	$0.314269\pi$
$152$	5.35033	0.433969
$153$	0.0987659	0.00798475
$154$	−1.99360	−0.160649
$155$	29.4068	2.36201
$156$	7.55823	0.605143
$157$	0.0439969	0.00351134	0.00175567	−	0.999998i	$-0.499441\pi$
$157$	0.0439969	0.00351134	0.00175567	+	0.999998i	$0.499441\pi$
$158$	16.8730	1.34234
$159$	−24.9485	−1.97855
$160$	15.1583	1.19837
$161$	−2.82894	−0.222952
$162$	24.6363	1.93561
$163$	−9.13698	−0.715663	−0.357832	−	0.933786i	$-0.616484\pi$
$163$	−9.13698	−0.715663	−0.357832	+	0.933786i	$0.616484\pi$
$164$	20.4538	1.59717
$165$	−1.77369	−0.138082
$166$	4.21916	0.327470
$167$	−21.0606	−1.62972	−0.814858	−	0.579661i	$-0.803185\pi$
$167$	−21.0606	−1.62972	−0.814858	+	0.579661i	$0.803185\pi$
$168$	17.0788	1.31766
$169$	−11.6351	−0.895009
$170$	−0.951102	−0.0729462
$171$	−1.23971	−0.0948029
$172$	−20.2474	−1.54385
$173$	−1.89432	−0.144023	−0.0720114	−	0.997404i	$-0.522942\pi$
$173$	−1.89432	−0.144023	−0.0720114	+	0.997404i	$0.522942\pi$
$174$	8.17525	0.619764
$175$	−11.6053	−0.877282
$176$	−0.162208	−0.0122269
$177$	0.0337760	0.00253876
$178$	26.4133	1.97976
$179$	12.1238	0.906178	0.453089	−	0.891465i	$-0.350322\pi$
$179$	12.1238	0.906178	0.453089	+	0.891465i	$0.350322\pi$
$180$	7.33023	0.546363
$181$	−2.40796	−0.178982	−0.0894910	−	0.995988i	$-0.528524\pi$
$181$	−2.40796	−0.178982	−0.0894910	+	0.995988i	$0.528524\pi$
$182$	7.64602	0.566761
$183$	−0.527084	−0.0389632
$184$	−3.12810	−0.230607
$185$	−22.1732	−1.63020
$186$	−43.5197	−3.19102
$187$	−0.0415085	−0.00303540
$188$	−32.6032	−2.37783
$189$	12.4221	0.903575
$190$	11.9382	0.866091
$191$	1.79303	0.129739	0.0648697	−	0.997894i	$-0.479337\pi$
$191$	1.79303	0.129739	0.0648697	+	0.997894i	$0.479337\pi$
$192$	−24.4885	−1.76730
$193$	−3.54436	−0.255129	−0.127564	−	0.991830i	$-0.540716\pi$
$193$	−3.54436	−0.255129	−0.127564	+	0.991830i	$0.540716\pi$
$194$	8.57610	0.615728
$195$	6.80263	0.487146
$196$	3.36191	0.240137
$197$	−3.40199	−0.242382	−0.121191	−	0.992629i	$-0.538671\pi$
$197$	−3.40199	−0.242382	−0.121191	+	0.992629i	$0.538671\pi$
$198$	0.510779	0.0362995
$199$	9.82264	0.696308	0.348154	−	0.937437i	$-0.386809\pi$
$199$	9.82264	0.696308	0.348154	+	0.937437i	$0.386809\pi$
$200$	−12.8326	−0.907402
$201$	25.1213	1.77192
$202$	−34.0002	−2.39225
$203$	5.17977	0.363549
$204$	0.881575	0.0617226
$205$	18.4090	1.28574
$206$	1.60249	0.111651
$207$	0.724803	0.0503773
$208$	0.622115	0.0431359
$209$	0.521014	0.0360393
$210$	38.1080	2.62970
$211$	−18.3594	−1.26391	−0.631955	−	0.775005i	$-0.717747\pi$
$211$	−18.3594	−1.26391	−0.631955	+	0.775005i	$0.717747\pi$
$212$	−43.3325	−2.97609
$213$	−29.1793	−1.99933
$214$	−10.7207	−0.732854
$215$	−18.2233	−1.24282
$216$	13.7357	0.934598
$217$	−27.5737	−1.87183
$218$	−26.1380	−1.77029
$219$	−7.83034	−0.529125
$220$	−3.08069	−0.207700
$221$	0.159197	0.0107088
$222$	32.8145	2.20237
$223$	−19.9411	−1.33536	−0.667678	−	0.744450i	$-0.732712\pi$
$223$	−19.9411	−1.33536	−0.667678	+	0.744450i	$0.732712\pi$
$224$	−14.2134	−0.949672
$225$	2.97340	0.198227
$226$	4.62499	0.307650
$227$	13.5931	0.902204	0.451102	−	0.892472i	$-0.351031\pi$
$227$	13.5931	0.902204	0.451102	+	0.892472i	$0.351031\pi$
$228$	−11.0655	−0.732832
$229$	6.16499	0.407394	0.203697	−	0.979034i	$-0.434704\pi$
$229$	6.16499	0.407394	0.203697	+	0.979034i	$0.434704\pi$
$230$	−6.97976	−0.460231
$231$	1.66313	0.109426
$232$	5.72753	0.376031
$233$	−27.4324	−1.79716	−0.898579	−	0.438813i	$-0.855399\pi$
$233$	−27.4324	−1.79716	−0.898579	+	0.438813i	$0.855399\pi$
$234$	−1.95899	−0.128063
$235$	−29.3438	−1.91418
$236$	0.0586648	0.00381875
$237$	−14.0760	−0.914337
$238$	0.891814	0.0578077
$239$	−27.0848	−1.75197	−0.875985	−	0.482339i	$-0.839787\pi$
$239$	−27.0848	−1.75197	−0.875985	+	0.482339i	$0.839787\pi$
$240$	3.10064	0.200146
$241$	14.9434	0.962589	0.481295	−	0.876559i	$-0.340167\pi$
$241$	14.9434	0.962589	0.481295	+	0.876559i	$0.340167\pi$
$242$	25.2335	1.62207
$243$	−7.37922	−0.473377
$244$	−0.915479	−0.0586076
$245$	3.02582	0.193313
$246$	−27.2438	−1.73700
$247$	−1.99824	−0.127145
$248$	−30.4896	−1.93609
$249$	−3.51977	−0.223057
$250$	6.26530	0.396252
$251$	3.68266	0.232447	0.116224	−	0.993223i	$-0.462921\pi$
$251$	3.68266	0.232447	0.116224	+	0.993223i	$0.462921\pi$
$252$	−6.87329	−0.432977
$253$	−0.304614	−0.0191509
$254$	−28.9291	−1.81517
$255$	0.793443	0.0496873
$256$	−19.2865	−1.20541
$257$	9.08180	0.566507	0.283254	−	0.959045i	$-0.408586\pi$
$257$	9.08180	0.566507	0.283254	+	0.959045i	$0.408586\pi$
$258$	26.9690	1.67901
$259$	20.7910	1.29189
$260$	11.8153	0.732755
$261$	−1.32711	−0.0821459
$262$	−22.3103	−1.37834
$263$	−8.96946	−0.553081	−0.276540	−	0.961002i	$-0.589188\pi$
$263$	−8.96946	−0.553081	−0.276540	+	0.961002i	$0.589188\pi$
$264$	1.83900	0.113183
$265$	−39.0005	−2.39578
$266$	−11.1941	−0.686351
$267$	−22.0349	−1.34851
$268$	43.6325	2.66528
$269$	3.54489	0.216136	0.108068	−	0.994144i	$-0.465534\pi$
$269$	3.54489	0.216136	0.108068	+	0.994144i	$0.465534\pi$
$270$	30.6486	1.86522
$271$	8.66832	0.526563	0.263281	−	0.964719i	$-0.415195\pi$
$271$	8.66832	0.526563	0.263281	+	0.964719i	$0.415195\pi$
$272$	0.0725621	0.00439972
$273$	−6.37858	−0.386049
$274$	−5.52873	−0.334003
$275$	−1.24964	−0.0753559
$276$	6.46952	0.389419
$277$	9.16215	0.550500	0.275250	−	0.961373i	$-0.411239\pi$
$277$	9.16215	0.550500	0.275250	+	0.961373i	$0.411239\pi$
$278$	10.2920	0.617271
$279$	7.06466	0.422950
$280$	26.6982	1.59552
$281$	3.36160	0.200536	0.100268	−	0.994960i	$-0.468030\pi$
$281$	3.36160	0.200536	0.100268	+	0.994960i	$0.468030\pi$
$282$	43.4265	2.58601
$283$	−11.7858	−0.700594	−0.350297	−	0.936639i	$-0.613919\pi$
$283$	−11.7858	−0.700594	−0.350297	+	0.936639i	$0.613919\pi$
$284$	−50.6808	−3.00735
$285$	−9.95929	−0.589938
$286$	0.823306	0.0486831
$287$	−17.2614	−1.01891
$288$	3.64161	0.214584
$289$	−16.9814	−0.998908
$290$	12.7799	0.750460
$291$	−7.15448	−0.419403
$292$	−13.6003	−0.795899
$293$	10.2717	0.600080	0.300040	−	0.953927i	$-0.403000\pi$
$293$	10.2717	0.600080	0.300040	+	0.953927i	$0.403000\pi$
$294$	−4.47797	−0.261160
$295$	0.0528000	0.00307414
$296$	22.9896	1.33624
$297$	1.33758	0.0776144
$298$	−5.95987	−0.345246
$299$	1.16828	0.0675636
$300$	26.5403	1.53231
$301$	17.0873	0.984895
$302$	−31.3247	−1.80253
$303$	28.3642	1.62948
$304$	−0.910799	−0.0522379
$305$	−0.823958	−0.0471797
$306$	−0.228492	−0.0130620
$307$	23.5296	1.34291	0.671453	−	0.741047i	$-0.265671\pi$
$307$	23.5296	1.34291	0.671453	+	0.741047i	$0.265671\pi$
$308$	2.88865	0.164596
$309$	−1.33686	−0.0760510
$310$	−68.0317	−3.86394
$311$	−25.2223	−1.43023	−0.715113	−	0.699009i	$-0.753625\pi$
$311$	−25.2223	−1.43023	−0.715113	+	0.699009i	$0.753625\pi$
$312$	−7.05311	−0.399304
$313$	−29.7669	−1.68253	−0.841263	−	0.540626i	$-0.818187\pi$
$313$	−29.7669	−1.68253	−0.841263	+	0.540626i	$0.818187\pi$
$314$	−0.101785	−0.00574408
$315$	−6.18616	−0.348551
$316$	−24.4483	−1.37533
$317$	−26.9832	−1.51553	−0.757763	−	0.652530i	$-0.773708\pi$
$317$	−26.9832	−1.51553	−0.757763	+	0.652530i	$0.773708\pi$
$318$	57.7176	3.23664
$319$	0.557746	0.0312278
$320$	−38.2813	−2.13999
$321$	8.94361	0.499184
$322$	6.54467	0.364720
$323$	−0.233070	−0.0129684
$324$	−35.6970	−1.98317
$325$	4.79272	0.265852
$326$	21.1381	1.17073
$327$	21.8052	1.20583
$328$	−19.0868	−1.05389
$329$	27.5146	1.51693
$330$	4.10338	0.225884
$331$	2.59369	0.142562	0.0712812	−	0.997456i	$-0.477291\pi$
$331$	2.59369	0.142562	0.0712812	+	0.997456i	$0.477291\pi$
$332$	−6.11341	−0.335517
$333$	−5.32686	−0.291910
$334$	48.7229	2.66600
$335$	39.2705	2.14558
$336$	−2.90736	−0.158609
$337$	−11.4640	−0.624483	−0.312241	−	0.950003i	$-0.601080\pi$
$337$	−11.4640	−0.624483	−0.312241	+	0.950003i	$0.601080\pi$
$338$	26.9174	1.46412
$339$	−3.85833	−0.209556
$340$	1.37811	0.0747386
$341$	−2.96907	−0.160784
$342$	2.86803	0.155085
$343$	16.9654	0.916046
$344$	18.8943	1.01871
$345$	5.82276	0.313487
$346$	4.38245	0.235602
$347$	−2.19624	−0.117900	−0.0589501	−	0.998261i	$-0.518775\pi$
$347$	−2.19624	−0.117900	−0.0589501	+	0.998261i	$0.518775\pi$
$348$	−11.8456	−0.634993
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	26.8486	1.43512
$351$	−5.13002	−0.273820
$352$	−1.53046	−0.0815740
$353$	−31.1545	−1.65819	−0.829093	−	0.559111i	$-0.811143\pi$
$353$	−31.1545	−1.65819	−0.829093	+	0.559111i	$0.811143\pi$
$354$	−0.0781397	−0.00415308
$355$	−45.6142	−2.42095
$356$	−38.2719	−2.02841
$357$	−0.743983	−0.0393757
$358$	−28.0481	−1.48239
$359$	−13.0030	−0.686273	−0.343137	−	0.939285i	$-0.611489\pi$
$359$	−13.0030	−0.686273	−0.343137	+	0.939285i	$0.611489\pi$
$360$	−6.84034	−0.360518
$361$	−16.0745	−0.846026
$362$	5.57073	0.292791
$363$	−21.0506	−1.10487
$364$	−11.0788	−0.580687
$365$	−12.2407	−0.640707
$366$	1.21939	0.0637386
$367$	−13.0045	−0.678827	−0.339413	−	0.940637i	$-0.610229\pi$
$367$	−13.0045	−0.678827	−0.339413	+	0.940637i	$0.610229\pi$
$368$	0.532504	0.0277587
$369$	4.42255	0.230229
$370$	51.2969	2.66680
$371$	36.5694	1.89859
$372$	63.0585	3.26943
$373$	−12.0089	−0.621797	−0.310898	−	0.950443i	$-0.600630\pi$
$373$	−12.0089	−0.621797	−0.310898	+	0.950443i	$0.600630\pi$
$374$	0.0960285	0.00496551
$375$	−5.22673	−0.269907
$376$	30.4243	1.56901
$377$	−2.13912	−0.110170
$378$	−28.7381	−1.47813
$379$	−21.3592	−1.09715	−0.548574	−	0.836102i	$-0.684829\pi$
$379$	−21.3592	−1.09715	−0.548574	+	0.836102i	$0.684829\pi$
$380$	−17.2981	−0.887372
$381$	24.1336	1.23640
$382$	−4.14813	−0.212237
$383$	31.4376	1.60639	0.803193	−	0.595719i	$-0.203133\pi$
$383$	31.4376	1.60639	0.803193	+	0.595719i	$0.203133\pi$
$384$	37.2598	1.90141
$385$	2.59987	0.132501
$386$	8.19977	0.417357
$387$	−4.37793	−0.222543
$388$	−12.4264	−0.630857
$389$	3.25772	0.165173	0.0825865	−	0.996584i	$-0.473682\pi$
$389$	3.25772	0.165173	0.0825865	+	0.996584i	$0.473682\pi$
$390$	−15.7377	−0.796907
$391$	0.136266	0.00689126
$392$	−3.13723	−0.158454
$393$	18.6121	0.938855
$394$	7.87038	0.396504
$395$	−22.0042	−1.10715
$396$	−0.740100	−0.0371914
$397$	31.1146	1.56160	0.780800	−	0.624782i	$-0.214812\pi$
$397$	31.1146	1.56160	0.780800	+	0.624782i	$0.214812\pi$
$398$	−22.7243	−1.13907
$399$	9.33847	0.467508
$400$	2.18452	0.109226
$401$	13.6144	0.679870	0.339935	−	0.940449i	$-0.389595\pi$
$401$	13.6144	0.679870	0.339935	+	0.940449i	$0.389595\pi$
$402$	−58.1172	−2.89862
$403$	11.3873	0.567240
$404$	49.2651	2.45103
$405$	−32.1284	−1.59647
$406$	−11.9832	−0.594717
$407$	2.23873	0.110970
$408$	−0.822658	−0.0407277
$409$	19.2562	0.952160	0.476080	−	0.879402i	$-0.342057\pi$
$409$	19.2562	0.952160	0.476080	+	0.879402i	$0.342057\pi$
$410$	−42.5886	−2.10330
$411$	4.61226	0.227506
$412$	−2.32195	−0.114394
$413$	−0.0495087	−0.00243616
$414$	−1.67681	−0.0824106
$415$	−5.50225	−0.270095
$416$	5.86977	0.287789
$417$	−8.58591	−0.420454
$418$	−1.20535	−0.0589556
$419$	35.6546	1.74184	0.870921	−	0.491424i	$-0.163523\pi$
$419$	35.6546	1.74184	0.870921	+	0.491424i	$0.163523\pi$
$420$	−55.2171	−2.69432
$421$	−31.7733	−1.54853	−0.774267	−	0.632859i	$-0.781881\pi$
$421$	−31.7733	−1.54853	−0.774267	+	0.632859i	$0.781881\pi$
$422$	42.4738	2.06759
$423$	−7.04952	−0.342759
$424$	40.4366	1.96377
$425$	0.559012	0.0271160
$426$	67.5052	3.27064
$427$	0.772596	0.0373885
$428$	15.5339	0.750862
$429$	−0.686831	−0.0331605
$430$	42.1589	2.03308
$431$	7.06211	0.340170	0.170085	−	0.985429i	$-0.445596\pi$
$431$	7.06211	0.340170	0.170085	+	0.985429i	$0.445596\pi$
$432$	−2.33826	−0.112500
$433$	18.8379	0.905294	0.452647	−	0.891690i	$-0.350480\pi$
$433$	18.8379	0.905294	0.452647	+	0.891690i	$0.350480\pi$
$434$	63.7909	3.06206
$435$	−10.6614	−0.511176
$436$	37.8729	1.81378
$437$	−1.71041	−0.0818199
$438$	18.1152	0.865579
$439$	−28.2167	−1.34671	−0.673355	−	0.739319i	$-0.735148\pi$
$439$	−28.2167	−1.34671	−0.673355	+	0.739319i	$0.735148\pi$
$440$	2.87480	0.137051
$441$	0.726919	0.0346152
$442$	−0.368297	−0.0175181
$443$	16.2347	0.771333	0.385666	−	0.922638i	$-0.373972\pi$
$443$	16.2347	0.771333	0.385666	+	0.922638i	$0.373972\pi$
$444$	−47.5470	−2.25648
$445$	−34.4458	−1.63289
$446$	46.1331	2.18447
$447$	4.97193	0.235164
$448$	35.8950	1.69588
$449$	5.67389	0.267767	0.133884	−	0.990997i	$-0.457255\pi$
$449$	5.67389	0.267767	0.133884	+	0.990997i	$0.457255\pi$
$450$	−6.87887	−0.324273
$451$	−1.85867	−0.0875215
$452$	−6.70144	−0.315209
$453$	26.1322	1.22780
$454$	−31.4471	−1.47589
$455$	−9.97124	−0.467459
$456$	10.3260	0.483560
$457$	33.4570	1.56505	0.782527	−	0.622617i	$-0.213930\pi$
$457$	33.4570	1.56505	0.782527	+	0.622617i	$0.213930\pi$
$458$	−14.2625	−0.666442
$459$	−0.598353	−0.0279287
$460$	10.1134	0.471540
$461$	28.2621	1.31630	0.658148	−	0.752888i	$-0.271340\pi$
$461$	28.2621	1.31630	0.658148	+	0.752888i	$0.271340\pi$
$462$	−3.84759	−0.179006
$463$	−22.7210	−1.05594	−0.527968	−	0.849264i	$-0.677046\pi$
$463$	−22.7210	−1.05594	−0.527968	+	0.849264i	$0.677046\pi$
$464$	−0.975010	−0.0452637
$465$	56.7544	2.63192
$466$	63.4640	2.93991
$467$	26.3775	1.22060	0.610302	−	0.792169i	$-0.291048\pi$
$467$	26.3775	1.22060	0.610302	+	0.792169i	$0.291048\pi$
$468$	2.83850	0.131210
$469$	−36.8226	−1.70031
$470$	67.8859	3.13135
$471$	0.0849129	0.00391258
$472$	−0.0547442	−0.00251981
$473$	1.83992	0.0845996
$474$	32.5644	1.49573
$475$	−7.01671	−0.321949
$476$	−1.29221	−0.0592282
$477$	−9.36944	−0.428997
$478$	62.6597	2.86599
$479$	−17.0941	−0.781050	−0.390525	−	0.920592i	$-0.627707\pi$
$479$	−17.0941	−0.781050	−0.390525	+	0.920592i	$0.627707\pi$
$480$	29.2551	1.33531
$481$	−8.58616	−0.391495
$482$	−34.5711	−1.57467
$483$	−5.45979	−0.248429
$484$	−36.5624	−1.66193
$485$	−11.1842	−0.507847
$486$	17.0716	0.774382
$487$	19.5903	0.887721	0.443861	−	0.896096i	$-0.353609\pi$
$487$	19.5903	0.887721	0.443861	+	0.896096i	$0.353609\pi$
$488$	0.854297	0.0386722
$489$	−17.6341	−0.797443
$490$	−7.00013	−0.316234
$491$	39.4950	1.78238	0.891191	−	0.453628i	$-0.149870\pi$
$491$	39.4950	1.78238	0.891191	+	0.453628i	$0.149870\pi$
$492$	39.4753	1.77968
$493$	−0.249502	−0.0112370
$494$	4.62287	0.207993
$495$	−0.666111	−0.0299395
$496$	5.19032	0.233052
$497$	42.7708	1.91853
$498$	8.14288	0.364891
$499$	1.19429	0.0534636	0.0267318	−	0.999643i	$-0.491490\pi$
$499$	1.19429	0.0534636	0.0267318	+	0.999643i	$0.491490\pi$
$500$	−9.07819	−0.405989
$501$	−40.6464	−1.81595
$502$	−8.51970	−0.380253
$503$	37.2369	1.66031	0.830155	−	0.557533i	$-0.188252\pi$
$503$	37.2369	1.66031	0.830155	+	0.557533i	$0.188252\pi$
$504$	6.41394	0.285700
$505$	44.3400	1.97310
$506$	0.704714	0.0313284
$507$	−22.4555	−0.997283
$508$	41.9171	1.85977
$509$	−44.7440	−1.98324	−0.991622	−	0.129170i	$-0.958769\pi$
$509$	−44.7440	−1.98324	−0.991622	+	0.129170i	$0.958769\pi$
$510$	−1.83560	−0.0812819
$511$	11.4777	0.507742
$512$	6.00690	0.265470
$513$	7.51053	0.331598
$514$	−21.0104	−0.926731
$515$	−2.08982	−0.0920887
$516$	−39.0770	−1.72027
$517$	2.96271	0.130300
$518$	−48.0993	−2.11336
$519$	−3.65600	−0.160480
$520$	−11.0257	−0.483509
$521$	−7.75966	−0.339957	−0.169978	−	0.985448i	$-0.554370\pi$
$521$	−7.75966	−0.339957	−0.169978	+	0.985448i	$0.554370\pi$
$522$	3.07022	0.134380
$523$	−33.7804	−1.47711	−0.738556	−	0.674192i	$-0.764492\pi$
$523$	−33.7804	−1.47711	−0.738556	+	0.674192i	$0.764492\pi$
$524$	32.3269	1.41221
$525$	−22.3980	−0.977530
$526$	20.7506	0.904767
$527$	1.32818	0.0578566
$528$	−0.313058	−0.0136241
$529$	1.00000	0.0434783
$530$	90.2265	3.91919
$531$	0.0126846	0.000550465 0
$532$	16.2198	0.703216
$533$	7.12855	0.308772
$534$	50.9770	2.20599
$535$	13.9810	0.604451
$536$	−40.7165	−1.75869
$537$	23.3987	1.00973
$538$	−8.20099	−0.353570
$539$	−0.305503	−0.0131590
$540$	−44.4087	−1.91105
$541$	−19.1706	−0.824209	−0.412105	−	0.911137i	$-0.635206\pi$
$541$	−19.1706	−0.824209	−0.412105	+	0.911137i	$0.635206\pi$
$542$	−20.0539	−0.861387
$543$	−4.64730	−0.199435
$544$	0.684637	0.0293536
$545$	34.0867	1.46012
$546$	14.7566	0.631526
$547$	−0.981529	−0.0419671	−0.0209836	−	0.999780i	$-0.506680\pi$
$547$	−0.981529	−0.0419671	−0.0209836	+	0.999780i	$0.506680\pi$
$548$	8.01092	0.342210
$549$	−0.197947	−0.00844815
$550$	2.89099	0.123272
$551$	3.13174	0.133417
$552$	−6.03716	−0.256959
$553$	20.6326	0.877386
$554$	−21.1963	−0.900545
$555$	−42.7937	−1.81649
$556$	−14.9127	−0.632438
$557$	38.6251	1.63660	0.818299	−	0.574793i	$-0.194917\pi$
$557$	38.6251	1.63660	0.818299	+	0.574793i	$0.194917\pi$
$558$	−16.3439	−0.691890
$559$	−7.05663	−0.298464
$560$	−4.54490	−0.192057
$561$	−0.0801103	−0.00338226
$562$	−7.77695	−0.328051
$563$	−5.57553	−0.234981	−0.117490	−	0.993074i	$-0.537485\pi$
$563$	−5.57553	−0.234981	−0.117490	+	0.993074i	$0.537485\pi$
$564$	−62.9233	−2.64955
$565$	−6.03149	−0.253747
$566$	27.2661	1.14608
$567$	30.1256	1.26516
$568$	47.2937	1.98440
$569$	14.7844	0.619795	0.309898	−	0.950770i	$-0.399705\pi$
$569$	14.7844	0.619795	0.309898	+	0.950770i	$0.399705\pi$
$570$	23.0405	0.965060
$571$	−3.46207	−0.144883	−0.0724416	−	0.997373i	$-0.523079\pi$
$571$	−3.46207	−0.144883	−0.0724416	+	0.997373i	$0.523079\pi$
$572$	−1.19294	−0.0498793
$573$	3.46051	0.144565
$574$	39.9338	1.66680
$575$	4.10236	0.171080
$576$	−9.19666	−0.383194
$577$	−26.7954	−1.11551	−0.557754	−	0.830006i	$-0.688337\pi$
$577$	−26.7954	−1.11551	−0.557754	+	0.830006i	$0.688337\pi$
$578$	39.2860	1.63408
$579$	−6.84053	−0.284283
$580$	−18.5176	−0.768900
$581$	5.15926	0.214042
$582$	16.5517	0.686088
$583$	3.93771	0.163083
$584$	12.6914	0.525174
$585$	2.55473	0.105625
$586$	−23.7633	−0.981652
$587$	3.20722	0.132376	0.0661881	−	0.997807i	$-0.478916\pi$
$587$	3.20722	0.132376	0.0661881	+	0.997807i	$0.478916\pi$
$588$	6.48841	0.267577
$589$	−16.6714	−0.686932
$590$	−0.122151	−0.00502888
$591$	−6.56575	−0.270079
$592$	−3.91358	−0.160847
$593$	−36.2237	−1.48753	−0.743765	−	0.668442i	$-0.766962\pi$
$593$	−36.2237	−1.48753	−0.743765	+	0.668442i	$0.766962\pi$
$594$	−3.09445	−0.126967
$595$	−1.16302	−0.0476793
$596$	8.63563	0.353729
$597$	18.9574	0.775877
$598$	−2.70278	−0.110525
$599$	−13.9281	−0.569088	−0.284544	−	0.958663i	$-0.591842\pi$
$599$	−13.9281	−0.569088	−0.284544	+	0.958663i	$0.591842\pi$
$600$	−24.7666	−1.01109
$601$	22.1469	0.903390	0.451695	−	0.892173i	$-0.350820\pi$
$601$	22.1469	0.903390	0.451695	+	0.892173i	$0.350820\pi$
$602$	−39.5309	−1.61116
$603$	9.43430	0.384195
$604$	45.3883	1.84683
$605$	−32.9072	−1.33787
$606$	−65.6196	−2.66561
$607$	−36.8473	−1.49559	−0.747794	−	0.663931i	$-0.768887\pi$
$607$	−36.8473	−1.49559	−0.747794	+	0.663931i	$0.768887\pi$
$608$	−8.59356	−0.348515
$609$	9.99682	0.405092
$610$	1.90620	0.0771798
$611$	−11.3629	−0.459692
$612$	0.331076	0.0133829
$613$	3.46259	0.139853	0.0699263	−	0.997552i	$-0.477724\pi$
$613$	3.46259	0.139853	0.0699263	+	0.997552i	$0.477724\pi$
$614$	−54.4350	−2.19682
$615$	35.5289	1.43266
$616$	−2.69560	−0.108609
$617$	−20.6342	−0.830702	−0.415351	−	0.909661i	$-0.636341\pi$
$617$	−20.6342	−0.830702	−0.415351	+	0.909661i	$0.636341\pi$
$618$	3.09277	0.124409
$619$	−28.2649	−1.13606	−0.568031	−	0.823007i	$-0.692295\pi$
$619$	−28.2649	−1.13606	−0.568031	+	0.823007i	$0.692295\pi$
$620$	98.5755	3.95889
$621$	−4.39107	−0.176208
$622$	58.3510	2.33966
$623$	32.2986	1.29402
$624$	1.20067	0.0480652
$625$	−28.6824	−1.14730
$626$	68.8648	2.75239
$627$	1.00554	0.0401576
$628$	0.147483	0.00588522
$629$	−1.00147	−0.0399312
$630$	14.3115	0.570183
$631$	0.254060	0.0101140	0.00505698	−	0.999987i	$-0.498390\pi$
$631$	0.254060	0.0101140	0.00505698	+	0.999987i	$0.498390\pi$
$632$	22.8144	0.907509
$633$	−35.4331	−1.40834
$634$	62.4247	2.47920
$635$	37.7266	1.49714
$636$	−83.6307	−3.31617
$637$	1.17169	0.0464242
$638$	−1.29033	−0.0510845
$639$	−10.9583	−0.433503
$640$	58.2460	2.30238
$641$	10.0321	0.396246	0.198123	−	0.980177i	$-0.436515\pi$
$641$	10.0321	0.396246	0.198123	+	0.980177i	$0.436515\pi$
$642$	−20.6907	−0.816599
$643$	−27.5283	−1.08561	−0.542806	−	0.839858i	$-0.682638\pi$
$643$	−27.5283	−1.08561	−0.542806	+	0.839858i	$0.682638\pi$
$644$	−9.48298	−0.373682
$645$	−35.1704	−1.38483
$646$	0.539200	0.0212146
$647$	6.85173	0.269369	0.134685	−	0.990889i	$-0.456998\pi$
$647$	6.85173	0.269369	0.134685	+	0.990889i	$0.456998\pi$
$648$	33.3114	1.30859
$649$	−0.00533098	−0.000209259 0
$650$	−11.0878	−0.434899
$651$	−53.2166	−2.08572
$652$	−30.6283	−1.19950
$653$	−21.6775	−0.848304	−0.424152	−	0.905591i	$-0.639428\pi$
$653$	−21.6775	−0.848304	−0.424152	+	0.905591i	$0.639428\pi$
$654$	−50.4456	−1.97258
$655$	29.0951	1.13684
$656$	3.24920	0.126860
$657$	−2.94069	−0.114727
$658$	−63.6542	−2.48150
$659$	−5.74974	−0.223978	−0.111989	−	0.993709i	$-0.535722\pi$
$659$	−5.74974	−0.223978	−0.111989	+	0.993709i	$0.535722\pi$
$660$	−5.94565	−0.231434
$661$	31.2095	1.21391	0.606954	−	0.794737i	$-0.292391\pi$
$661$	31.2095	1.21391	0.606954	+	0.794737i	$0.292391\pi$
$662$	−6.00042	−0.233213
$663$	0.307246	0.0119325
$664$	5.70484	0.221391
$665$	14.5983	0.566096
$666$	12.3235	0.477526
$667$	−1.83099	−0.0708963
$668$	−70.5977	−2.73151
$669$	−38.4859	−1.48795
$670$	−90.8511	−3.50988
$671$	0.0831913	0.00321156
$672$	−27.4315	−1.05819
$673$	17.9287	0.691100	0.345550	−	0.938400i	$-0.387692\pi$
$673$	17.9287	0.691100	0.345550	+	0.938400i	$0.387692\pi$
$674$	26.5215	1.02157
$675$	−18.0138	−0.693350
$676$	−39.0024	−1.50009
$677$	−32.0592	−1.23214	−0.616069	−	0.787693i	$-0.711276\pi$
$677$	−32.0592	−1.23214	−0.616069	+	0.787693i	$0.711276\pi$
$678$	8.92611	0.342805
$679$	10.4870	0.402454
$680$	−1.28601	−0.0493163
$681$	26.2343	1.00530
$682$	6.86885	0.263022
$683$	46.4556	1.77758	0.888788	−	0.458319i	$-0.151548\pi$
$683$	46.4556	1.77758	0.888788	+	0.458319i	$0.151548\pi$
$684$	−4.15566	−0.158896
$685$	7.21006	0.275482
$686$	−39.2489	−1.49853
$687$	11.8983	0.453947
$688$	−3.21641	−0.122625
$689$	−15.1023	−0.575350
$690$	−13.4708	−0.512823
$691$	−0.519798	−0.0197741	−0.00988703	−	0.999951i	$-0.503147\pi$
$691$	−0.519798	−0.0197741	−0.00988703	+	0.999951i	$0.503147\pi$
$692$	−6.35001	−0.241391
$693$	0.624589	0.0237262
$694$	5.08092	0.192869
$695$	−13.4218	−0.509119
$696$	11.0540	0.419000
$697$	0.831457	0.0314937
$698$	−2.31347	−0.0875660
$699$	−52.9439	−2.00252
$700$	−38.9026	−1.47038
$701$	36.0958	1.36332	0.681659	−	0.731670i	$-0.261259\pi$
$701$	36.0958	1.36332	0.681659	+	0.731670i	$0.261259\pi$
$702$	11.8681	0.447933
$703$	12.5705	0.474104
$704$	3.86509	0.145671
$705$	−56.6328	−2.13292
$706$	72.0749	2.71257
$707$	−41.5760	−1.56363
$708$	0.113222	0.00425513
$709$	18.5555	0.696865	0.348433	−	0.937334i	$-0.386714\pi$
$709$	18.5555	0.696865	0.348433	+	0.937334i	$0.386714\pi$
$710$	105.527	3.96035
$711$	−5.28626	−0.198250
$712$	35.7142	1.33845
$713$	9.74701	0.365028
$714$	1.72118	0.0644135
$715$	−1.07368	−0.0401534
$716$	40.6406	1.51881
$717$	−52.2730	−1.95217
$718$	30.0821	1.12265
$719$	23.6771	0.883008	0.441504	−	0.897259i	$-0.354445\pi$
$719$	23.6771	0.883008	0.441504	+	0.897259i	$0.354445\pi$
$720$	1.16445	0.0433964
$721$	1.95955	0.0729776
$722$	37.1878	1.38399
$723$	28.8404	1.07259
$724$	−8.07178	−0.299985
$725$	−7.51139	−0.278966
$726$	48.7000	1.80742
$727$	−14.6675	−0.543987	−0.271993	−	0.962299i	$-0.587683\pi$
$727$	−14.6675	−0.543987	−0.271993	+	0.962299i	$0.587683\pi$
$728$	10.3384	0.383167
$729$	17.7055	0.655759
$730$	28.3184	1.04811
$731$	−0.823069	−0.0304423
$732$	−1.76685	−0.0653047
$733$	−38.7928	−1.43285	−0.716423	−	0.697666i	$-0.754222\pi$
$733$	−38.7928	−1.43285	−0.716423	+	0.697666i	$0.754222\pi$
$734$	30.0854	1.11047
$735$	5.83976	0.215403
$736$	5.02427	0.185197
$737$	−3.96497	−0.146052
$738$	−10.2314	−0.376624
$739$	−16.0245	−0.589469	−0.294735	−	0.955579i	$-0.595231\pi$
$739$	−16.0245	−0.589469	−0.294735	+	0.955579i	$0.595231\pi$
$740$	−74.3273	−2.73233
$741$	−3.85656	−0.141674
$742$	−84.6021	−3.10584
$743$	−25.6940	−0.942620	−0.471310	−	0.881968i	$-0.656219\pi$
$743$	−25.6940	−0.942620	−0.471310	+	0.881968i	$0.656219\pi$
$744$	−58.8442	−2.15733
$745$	7.77232	0.284756
$746$	27.7822	1.01718
$747$	−1.32185	−0.0483640
$748$	−0.139142	−0.00508753
$749$	−13.1095	−0.479010
$750$	12.0919	0.441533
$751$	−31.3516	−1.14404	−0.572019	−	0.820240i	$-0.693840\pi$
$751$	−31.3516	−1.14404	−0.572019	+	0.820240i	$0.693840\pi$
$752$	−5.17920	−0.188866
$753$	7.10743	0.259009
$754$	4.94877	0.180224
$755$	40.8508	1.48671
$756$	41.6405	1.51445
$757$	−29.6374	−1.07719	−0.538595	−	0.842565i	$-0.681045\pi$
$757$	−29.6374	−1.07719	−0.538595	+	0.842565i	$0.681045\pi$
$758$	49.4138	1.79479
$759$	−0.587897	−0.0213393
$760$	16.1420	0.585532
$761$	−0.204675	−0.00741945	−0.00370972	−	0.999993i	$-0.501181\pi$
$761$	−0.204675	−0.00741945	−0.00370972	+	0.999993i	$0.501181\pi$
$762$	−55.8324	−2.02259
$763$	−31.9619	−1.15710
$764$	6.01048	0.217452
$765$	0.297978	0.0107734
$766$	−72.7298	−2.62784
$767$	0.0204459	0.000738257 0
$768$	−37.2224	−1.34315
$769$	−42.9381	−1.54839	−0.774193	−	0.632949i	$-0.781844\pi$
$769$	−42.9381	−1.54839	−0.774193	+	0.632949i	$0.781844\pi$
$770$	−6.01471	−0.216755
$771$	17.5277	0.631243
$772$	−11.8812	−0.427612
$773$	−6.85074	−0.246404	−0.123202	−	0.992382i	$-0.539316\pi$
$773$	−6.85074	−0.246404	−0.123202	+	0.992382i	$0.539316\pi$
$774$	10.1282	0.364051
$775$	39.9857	1.43633
$776$	11.5960	0.416271
$777$	40.1261	1.43952
$778$	−7.53663	−0.270201
$779$	−10.4365	−0.373925
$780$	22.8033	0.816488
$781$	4.60545	0.164796
$782$	−0.315246	−0.0112732
$783$	8.04002	0.287327
$784$	0.534058	0.0190735
$785$	0.132739	0.00473767
$786$	−43.0584	−1.53584
$787$	42.5267	1.51591	0.757957	−	0.652305i	$-0.226198\pi$
$787$	42.5267	1.51591	0.757957	+	0.652305i	$0.226198\pi$
$788$	−11.4039	−0.406247
$789$	−17.3108	−0.616282
$790$	50.9060	1.81115
$791$	5.65551	0.201087
$792$	0.690638	0.0245408
$793$	−0.319063	−0.0113303
$794$	−71.9827	−2.55457
$795$	−75.2701	−2.66955
$796$	32.9267	1.16706
$797$	36.6527	1.29830	0.649152	−	0.760659i	$-0.275124\pi$
$797$	36.6527	1.29830	0.649152	+	0.760659i	$0.275124\pi$
$798$	−21.6042	−0.764782
$799$	−1.32534	−0.0468871
$800$	20.6114	0.728722
$801$	−8.27522	−0.292391
$802$	−31.4964	−1.11218
$803$	1.23589	0.0436135
$804$	84.2097	2.96985
$805$	−8.53496	−0.300818
$806$	−26.3441	−0.927930
$807$	6.84155	0.240834
$808$	−45.9726	−1.61731
$809$	−39.6839	−1.39521	−0.697605	−	0.716482i	$-0.745751\pi$
$809$	−39.6839	−1.39521	−0.697605	+	0.716482i	$0.745751\pi$
$810$	74.3279	2.61162
$811$	−10.6109	−0.372600	−0.186300	−	0.982493i	$-0.559650\pi$
$811$	−10.6109	−0.372600	−0.186300	+	0.982493i	$0.559650\pi$
$812$	17.3632	0.609331
$813$	16.7296	0.586734
$814$	−5.17922	−0.181531
$815$	−27.5664	−0.965608
$816$	0.140043	0.00490249
$817$	10.3312	0.361442
$818$	−44.5487	−1.55761
$819$	−2.39548	−0.0837048
$820$	61.7093	2.15498
$821$	2.34892	0.0819780	0.0409890	−	0.999160i	$-0.486949\pi$
$821$	2.34892	0.0819780	0.0409890	+	0.999160i	$0.486949\pi$
$822$	−10.6703	−0.372169
$823$	−24.5777	−0.856726	−0.428363	−	0.903607i	$-0.640909\pi$
$823$	−24.5777	−0.856726	−0.428363	+	0.903607i	$0.640909\pi$
$824$	2.16677	0.0754831
$825$	−2.41177	−0.0839670
$826$	0.114537	0.00398524
$827$	−0.0976187	−0.00339453	−0.00169727	−	0.999999i	$-0.500540\pi$
$827$	−0.0976187	−0.00339453	−0.00169727	+	0.999999i	$0.500540\pi$
$828$	2.42963	0.0844355
$829$	−51.4428	−1.78668	−0.893342	−	0.449377i	$-0.851646\pi$
$829$	−51.4428	−1.78668	−0.893342	+	0.449377i	$0.851646\pi$
$830$	12.7293	0.441839
$831$	17.6827	0.613406
$832$	−14.8238	−0.513921
$833$	0.136664	0.00473511
$834$	19.8632	0.687807
$835$	−63.5400	−2.19889
$836$	1.74651	0.0604042
$837$	−42.7998	−1.47938
$838$	−82.4857	−2.84942
$839$	27.2411	0.940467	0.470234	−	0.882542i	$-0.344170\pi$
$839$	27.2411	0.940467	0.470234	+	0.882542i	$0.344170\pi$
$840$	51.5269	1.77785
$841$	−25.6475	−0.884396
$842$	73.5064	2.53320
$843$	6.48781	0.223452
$844$	−61.5429	−2.11839
$845$	−35.1033	−1.20759
$846$	16.3088	0.560709
$847$	30.8559	1.06022
$848$	−6.88361	−0.236384
$849$	−22.7463	−0.780652
$850$	−1.29325	−0.0443583
$851$	−7.34938	−0.251934
$852$	−97.8126	−3.35100
$853$	−13.7334	−0.470221	−0.235111	−	0.971969i	$-0.575545\pi$
$853$	−13.7334	−0.470221	−0.235111	+	0.971969i	$0.575545\pi$
$854$	−1.78737	−0.0611627
$855$	−3.74022	−0.127913
$856$	−14.4958	−0.495456
$857$	−7.84428	−0.267955	−0.133978	−	0.990984i	$-0.542775\pi$
$857$	−7.84428	−0.267955	−0.133978	+	0.990984i	$0.542775\pi$
$858$	1.58896	0.0542462
$859$	15.3698	0.524411	0.262206	−	0.965012i	$-0.415550\pi$
$859$	15.3698	0.524411	0.262206	+	0.965012i	$0.415550\pi$
$860$	−61.0867	−2.08304
$861$	−33.3142	−1.13534
$862$	−16.3379	−0.556473
$863$	37.0779	1.26215	0.631073	−	0.775723i	$-0.282615\pi$
$863$	37.0779	1.26215	0.631073	+	0.775723i	$0.282615\pi$
$864$	−22.0620	−0.750563
$865$	−5.71520	−0.194323
$866$	−43.5809	−1.48094
$867$	−32.7737	−1.11305
$868$	−92.4306	−3.13730
$869$	2.22167	0.0753648
$870$	24.6648	0.836216
$871$	15.2068	0.515263
$872$	−35.3418	−1.19683
$873$	−2.68687	−0.0909367
$874$	3.95697	0.133847
$875$	7.66131	0.259000
$876$	−26.2483	−0.886848
$877$	−6.91922	−0.233645	−0.116823	−	0.993153i	$-0.537271\pi$
$877$	−6.91922	−0.233645	−0.116823	+	0.993153i	$0.537271\pi$
$878$	65.2784	2.20304
$879$	19.8242	0.668653
$880$	−0.489384	−0.0164971
$881$	−26.8174	−0.903501	−0.451751	−	0.892144i	$-0.649200\pi$
$881$	−26.8174	−0.903501	−0.451751	+	0.892144i	$0.649200\pi$
$882$	−1.68170	−0.0566259
$883$	−15.3993	−0.518226	−0.259113	−	0.965847i	$-0.583430\pi$
$883$	−15.3993	−0.518226	−0.259113	+	0.965847i	$0.583430\pi$
$884$	0.533649	0.0179486
$885$	0.101903	0.00342542
$886$	−37.5584	−1.26180
$887$	9.97202	0.334828	0.167414	−	0.985887i	$-0.446458\pi$
$887$	9.97202	0.334828	0.167414	+	0.985887i	$0.446458\pi$
$888$	44.3694	1.48894
$889$	−35.3749	−1.18644
$890$	79.6893	2.67119
$891$	3.24386	0.108673
$892$	−66.8452	−2.23814
$893$	16.6356	0.556690
$894$	−11.5024	−0.384698
$895$	36.5778	1.22266
$896$	−54.6152	−1.82457
$897$	2.25476	0.0752842
$898$	−13.1264	−0.438032
$899$	−17.8467	−0.595220
$900$	9.96723	0.332241
$901$	−1.76149	−0.0586838
$902$	4.29998	0.143174
$903$	32.9781	1.09744
$904$	6.25357	0.207991
$905$	−7.26483	−0.241491
$906$	−60.4559	−2.00851
$907$	15.4443	0.512818	0.256409	−	0.966568i	$-0.417461\pi$
$907$	15.4443	0.512818	0.256409	+	0.966568i	$0.417461\pi$
$908$	45.5657	1.51215
$909$	10.6522	0.353310
$910$	23.0681	0.764701
$911$	30.7366	1.01835	0.509175	−	0.860663i	$-0.329951\pi$
$911$	30.7366	1.01835	0.509175	+	0.860663i	$0.329951\pi$
$912$	−1.75782	−0.0582072
$913$	0.555537	0.0183856
$914$	−77.4017	−2.56022
$915$	−1.59022	−0.0525710
$916$	20.6658	0.682818
$917$	−27.2814	−0.900912
$918$	1.38427	0.0456877
$919$	19.7989	0.653105	0.326553	−	0.945179i	$-0.394113\pi$
$919$	19.7989	0.653105	0.326553	+	0.945179i	$0.394113\pi$
$920$	−9.43752	−0.311146
$921$	45.4116	1.49636
$922$	−65.3834	−2.15329
$923$	−17.6633	−0.581393
$924$	5.57502	0.183405
$925$	−30.1498	−0.991320
$926$	52.5644	1.72737
$927$	−0.502057	−0.0164897
$928$	−9.19940	−0.301985
$929$	−37.7084	−1.23717	−0.618586	−	0.785717i	$-0.712294\pi$
$929$	−37.7084	−1.23717	−0.618586	+	0.785717i	$0.712294\pi$
$930$	−131.300	−4.30548
$931$	−1.71540	−0.0562200
$932$	−91.9569	−3.01215
$933$	−48.6784	−1.59366
$934$	−61.0234	−1.99675
$935$	−0.125232	−0.00409551
$936$	−2.64880	−0.0865787
$937$	3.46905	0.113329	0.0566645	−	0.998393i	$-0.481953\pi$
$937$	3.46905	0.113329	0.0566645	+	0.998393i	$0.481953\pi$
$938$	85.1878	2.78148
$939$	−57.4494	−1.87479
$940$	−98.3642	−3.20829
$941$	58.6141	1.91077	0.955383	−	0.295370i	$-0.0954428\pi$
$941$	58.6141	1.91077	0.955383	+	0.295370i	$0.0954428\pi$
$942$	−0.196443	−0.00640047
$943$	6.10173	0.198700
$944$	0.00931923	0.000303315 0
$945$	37.4776	1.21915
$946$	−4.25659	−0.138394
$947$	21.6595	0.703838	0.351919	−	0.936030i	$-0.385529\pi$
$947$	21.6595	0.703838	0.351919	+	0.936030i	$0.385529\pi$
$948$	−47.1847	−1.53249
$949$	−4.73999	−0.153867
$950$	16.2329	0.526666
$951$	−52.0768	−1.68871
$952$	1.20585	0.0390817
$953$	−30.7311	−0.995477	−0.497739	−	0.867327i	$-0.665836\pi$
$953$	−30.7311	−0.995477	−0.497739	+	0.867327i	$0.665836\pi$
$954$	21.6759	0.701783
$955$	5.40961	0.175051
$956$	−90.7917	−2.93641
$957$	1.07643	0.0347962
$958$	39.5467	1.27769
$959$	−6.76061	−0.218312
$960$	−73.8820	−2.38453
$961$	64.0041	2.06465
$962$	19.8638	0.640435
$963$	3.35878	0.108235
$964$	50.0922	1.61336
$965$	−10.6934	−0.344232
$966$	12.6310	0.406397
$967$	−2.39858	−0.0771331	−0.0385666	−	0.999256i	$-0.512279\pi$
$967$	−2.39858	−0.0771331	−0.0385666	+	0.999256i	$0.512279\pi$
$968$	34.1189	1.09662
$969$	−0.449820	−0.0144503
$970$	25.8742	0.830770
$971$	27.5427	0.883886	0.441943	−	0.897043i	$-0.354289\pi$
$971$	27.5427	0.883886	0.441943	+	0.897043i	$0.354289\pi$
$972$	−24.7361	−0.793410
$973$	12.5852	0.403462
$974$	−45.3215	−1.45219
$975$	9.24983	0.296232
$976$	−0.145429	−0.00465507
$977$	54.0667	1.72975	0.864874	−	0.501989i	$-0.167398\pi$
$977$	54.0667	1.72975	0.864874	+	0.501989i	$0.167398\pi$
$978$	40.7960	1.30451
$979$	3.47784	0.111152
$980$	10.1429	0.324004
$981$	8.18895	0.261453
$982$	−91.3703	−2.91574
$983$	15.6888	0.500394	0.250197	−	0.968195i	$-0.419505\pi$
$983$	15.6888	0.500394	0.250197	+	0.968195i	$0.419505\pi$
$984$	−36.8371	−1.17432
$985$	−10.2638	−0.327033
$986$	0.577213	0.0183822
$987$	53.1026	1.69027
$988$	−6.69836	−0.213103
$989$	−6.04017	−0.192066
$990$	1.54103	0.0489770
$991$	−46.8283	−1.48755	−0.743775	−	0.668430i	$-0.766966\pi$
$991$	−46.8283	−1.48755	−0.743775	+	0.668430i	$0.766966\pi$
$992$	48.9716	1.55485
$993$	5.00576	0.158853
$994$	−98.9487	−3.13846
$995$	29.6350	0.939493
$996$	−11.7987	−0.373857
$997$	−12.8075	−0.405617	−0.202808	−	0.979218i	$-0.565007\pi$
$997$	−12.8075	−0.405617	−0.202808	+	0.979218i	$0.565007\pi$
$998$	−2.76294	−0.0874593
$999$	32.2717	1.02103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.19	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.31347 q^{2} +1.92997 q^{3} +3.35213 q^{4} +3.01701 q^{5} -4.46493 q^{6} -2.82894 q^{7} -3.12810 q^{8} +0.724803 q^{9} +O(q^{10})\)	\(q-2.31347 q^{2} +1.92997 q^{3} +3.35213 q^{4} +3.01701 q^{5} -4.46493 q^{6} -2.82894 q^{7} -3.12810 q^{8} +0.724803 q^{9} -6.97976 q^{10} -0.304614 q^{11} +6.46952 q^{12} +1.16828 q^{13} +6.54467 q^{14} +5.82276 q^{15} +0.532504 q^{16} +0.136266 q^{17} -1.67681 q^{18} -1.71041 q^{19} +10.1134 q^{20} -5.45979 q^{21} +0.704714 q^{22} +1.00000 q^{23} -6.03716 q^{24} +4.10236 q^{25} -2.70278 q^{26} -4.39107 q^{27} -9.48298 q^{28} -1.83099 q^{29} -13.4708 q^{30} +9.74701 q^{31} +5.02427 q^{32} -0.587897 q^{33} -0.315246 q^{34} -8.53496 q^{35} +2.42963 q^{36} -7.34938 q^{37} +3.95697 q^{38} +2.25476 q^{39} -9.43752 q^{40} +6.10173 q^{41} +12.6310 q^{42} -6.04017 q^{43} -1.02111 q^{44} +2.18674 q^{45} -2.31347 q^{46} -9.72612 q^{47} +1.02772 q^{48} +1.00292 q^{49} -9.49067 q^{50} +0.262990 q^{51} +3.91623 q^{52} -12.9269 q^{53} +10.1586 q^{54} -0.919024 q^{55} +8.84922 q^{56} -3.30105 q^{57} +4.23594 q^{58} +0.0175008 q^{59} +19.5186 q^{60} -0.273104 q^{61} -22.5494 q^{62} -2.05043 q^{63} -12.6885 q^{64} +3.52472 q^{65} +1.36008 q^{66} +13.0164 q^{67} +0.456780 q^{68} +1.92997 q^{69} +19.7453 q^{70} -15.1190 q^{71} -2.26726 q^{72} -4.05723 q^{73} +17.0026 q^{74} +7.91745 q^{75} -5.73351 q^{76} +0.861736 q^{77} -5.21631 q^{78} -7.29338 q^{79} +1.60657 q^{80} -10.6491 q^{81} -14.1161 q^{82} -1.82374 q^{83} -18.3019 q^{84} +0.411116 q^{85} +13.9737 q^{86} -3.53377 q^{87} +0.952864 q^{88} -11.4172 q^{89} -5.05895 q^{90} -3.30501 q^{91} +3.35213 q^{92} +18.8115 q^{93} +22.5011 q^{94} -5.16032 q^{95} +9.69672 q^{96} -3.70703 q^{97} -2.32022 q^{98} -0.220785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 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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