LMFDB - Embedded newform 4027.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73932 q^{2} -1.57093 q^{3} +5.50386 q^{4} +0.430202 q^{5} +4.30328 q^{6} +4.35305 q^{7} -9.59817 q^{8} -0.532177 q^{9} +O(q^{10})$	\(q-2.73932 q^{2} -1.57093 q^{3} +5.50386 q^{4} +0.430202 q^{5} +4.30328 q^{6} +4.35305 q^{7} -9.59817 q^{8} -0.532177 q^{9} -1.17846 q^{10} +1.10131 q^{11} -8.64618 q^{12} -0.711797 q^{13} -11.9244 q^{14} -0.675817 q^{15} +15.2847 q^{16} -2.28135 q^{17} +1.45780 q^{18} +6.76417 q^{19} +2.36777 q^{20} -6.83834 q^{21} -3.01684 q^{22} -5.24693 q^{23} +15.0781 q^{24} -4.81493 q^{25} +1.94984 q^{26} +5.54880 q^{27} +23.9585 q^{28} +1.04319 q^{29} +1.85128 q^{30} -3.38421 q^{31} -22.6734 q^{32} -1.73008 q^{33} +6.24935 q^{34} +1.87269 q^{35} -2.92902 q^{36} +8.44952 q^{37} -18.5292 q^{38} +1.11818 q^{39} -4.12915 q^{40} -2.20537 q^{41} +18.7324 q^{42} -9.09917 q^{43} +6.06146 q^{44} -0.228943 q^{45} +14.3730 q^{46} -1.54488 q^{47} -24.0112 q^{48} +11.9490 q^{49} +13.1896 q^{50} +3.58385 q^{51} -3.91763 q^{52} +4.98410 q^{53} -15.1999 q^{54} +0.473786 q^{55} -41.7813 q^{56} -10.6260 q^{57} -2.85764 q^{58} -0.799511 q^{59} -3.71960 q^{60} -4.02412 q^{61} +9.27042 q^{62} -2.31659 q^{63} +31.5400 q^{64} -0.306217 q^{65} +4.73925 q^{66} -2.34621 q^{67} -12.5562 q^{68} +8.24256 q^{69} -5.12989 q^{70} -9.31516 q^{71} +5.10792 q^{72} -16.5615 q^{73} -23.1459 q^{74} +7.56392 q^{75} +37.2290 q^{76} +4.79406 q^{77} -3.06306 q^{78} -5.02560 q^{79} +6.57552 q^{80} -7.12026 q^{81} +6.04121 q^{82} -12.4468 q^{83} -37.6372 q^{84} -0.981443 q^{85} +24.9255 q^{86} -1.63879 q^{87} -10.5706 q^{88} -16.3078 q^{89} +0.627149 q^{90} -3.09849 q^{91} -28.8783 q^{92} +5.31636 q^{93} +4.23190 q^{94} +2.90996 q^{95} +35.6183 q^{96} +8.41742 q^{97} -32.7321 q^{98} -0.586092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * 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 $

$2$	−2.73932	−1.93699	−0.968495	−	0.249034i	$-0.919887\pi$
$2$	−2.73932	−1.93699	−0.968495	+	0.249034i	$0.919887\pi$
$3$	−1.57093	−0.906977	−0.453489	−	0.891262i	$-0.649821\pi$
$3$	−1.57093	−0.906977	−0.453489	+	0.891262i	$0.649821\pi$
$4$	5.50386	2.75193
$5$	0.430202	0.192392	0.0961961	−	0.995362i	$-0.469332\pi$
$5$	0.430202	0.192392	0.0961961	+	0.995362i	$0.469332\pi$
$6$	4.30328	1.75681
$7$	4.35305	1.64530	0.822649	−	0.568550i	$-0.192495\pi$
$7$	4.35305	1.64530	0.822649	+	0.568550i	$0.192495\pi$
$8$	−9.59817	−3.39347
$9$	−0.532177	−0.177392
$10$	−1.17846	−0.372662
$11$	1.10131	0.332058	0.166029	−	0.986121i	$-0.446905\pi$
$11$	1.10131	0.332058	0.166029	+	0.986121i	$0.446905\pi$
$12$	−8.64618	−2.49594
$13$	−0.711797	−0.197417	−0.0987085	−	0.995116i	$-0.531471\pi$
$13$	−0.711797	−0.197417	−0.0987085	+	0.995116i	$0.531471\pi$
$14$	−11.9244	−3.18692
$15$	−0.675817	−0.174495
$16$	15.2847	3.82118
$17$	−2.28135	−0.553310	−0.276655	−	0.960969i	$-0.589226\pi$
$17$	−2.28135	−0.553310	−0.276655	+	0.960969i	$0.589226\pi$
$18$	1.45780	0.343607
$19$	6.76417	1.55181	0.775903	−	0.630852i	$-0.217295\pi$
$19$	6.76417	1.55181	0.775903	+	0.630852i	$0.217295\pi$
$20$	2.36777	0.529449
$21$	−6.83834	−1.49225
$22$	−3.01684	−0.643193
$23$	−5.24693	−1.09406	−0.547030	−	0.837113i	$-0.684242\pi$
$23$	−5.24693	−1.09406	−0.547030	+	0.837113i	$0.684242\pi$
$24$	15.0781	3.07780
$25$	−4.81493	−0.962985
$26$	1.94984	0.382395
$27$	5.54880	1.06787
$28$	23.9585	4.52774
$29$	1.04319	0.193716	0.0968581	−	0.995298i	$-0.469121\pi$
$29$	1.04319	0.193716	0.0968581	+	0.995298i	$0.469121\pi$
$30$	1.85128	0.337996
$31$	−3.38421	−0.607822	−0.303911	−	0.952700i	$-0.598293\pi$
$31$	−3.38421	−0.607822	−0.303911	+	0.952700i	$0.598293\pi$
$32$	−22.6734	−4.00812
$33$	−1.73008	−0.301169
$34$	6.24935	1.07176
$35$	1.87269	0.316542
$36$	−2.92902	−0.488171
$37$	8.44952	1.38909	0.694546	−	0.719448i	$-0.255605\pi$
$37$	8.44952	1.38909	0.694546	+	0.719448i	$0.255605\pi$
$38$	−18.5292	−3.00583
$39$	1.11818	0.179053
$40$	−4.12915	−0.652876
$41$	−2.20537	−0.344421	−0.172210	−	0.985060i	$-0.555091\pi$
$41$	−2.20537	−0.344421	−0.172210	+	0.985060i	$0.555091\pi$
$42$	18.7324	2.89047
$43$	−9.09917	−1.38761	−0.693805	−	0.720163i	$-0.744067\pi$
$43$	−9.09917	−1.38761	−0.693805	+	0.720163i	$0.744067\pi$
$44$	6.06146	0.913799
$45$	−0.228943	−0.0341289
$46$	14.3730	2.11918
$47$	−1.54488	−0.225343	−0.112672	−	0.993632i	$-0.535941\pi$
$47$	−1.54488	−0.225343	−0.112672	+	0.993632i	$0.535941\pi$
$48$	−24.0112	−3.46572
$49$	11.9490	1.70700
$50$	13.1896	1.86529
$51$	3.58385	0.501839
$52$	−3.91763	−0.543277
$53$	4.98410	0.684619	0.342309	−	0.939587i	$-0.388791\pi$
$53$	4.98410	0.684619	0.342309	+	0.939587i	$0.388791\pi$
$54$	−15.1999	−2.06845
$55$	0.473786	0.0638853
$56$	−41.7813	−5.58326
$57$	−10.6260	−1.40745
$58$	−2.85764	−0.375226
$59$	−0.799511	−0.104087	−0.0520437	−	0.998645i	$-0.516574\pi$
$59$	−0.799511	−0.104087	−0.0520437	+	0.998645i	$0.516574\pi$
$60$	−3.71960	−0.480199
$61$	−4.02412	−0.515236	−0.257618	−	0.966247i	$-0.582938\pi$
$61$	−4.02412	−0.515236	−0.257618	+	0.966247i	$0.582938\pi$
$62$	9.27042	1.17734
$63$	−2.31659	−0.291863
$64$	31.5400	3.94251
$65$	−0.306217	−0.0379815
$66$	4.73925	0.583361
$67$	−2.34621	−0.286635	−0.143317	−	0.989677i	$-0.545777\pi$
$67$	−2.34621	−0.286635	−0.143317	+	0.989677i	$0.545777\pi$
$68$	−12.5562	−1.52267
$69$	8.24256	0.992287
$70$	−5.12989	−0.613139
$71$	−9.31516	−1.10551	−0.552753	−	0.833345i	$-0.686423\pi$
$71$	−9.31516	−1.10551	−0.552753	+	0.833345i	$0.686423\pi$
$72$	5.10792	0.601974
$73$	−16.5615	−1.93838	−0.969190	−	0.246316i	$-0.920780\pi$
$73$	−16.5615	−1.93838	−0.969190	+	0.246316i	$0.920780\pi$
$74$	−23.1459	−2.69066
$75$	7.56392	0.873406
$76$	37.2290	4.27046
$77$	4.79406	0.546334
$78$	−3.06306	−0.346823
$79$	−5.02560	−0.565424	−0.282712	−	0.959205i	$-0.591234\pi$
$79$	−5.02560	−0.565424	−0.282712	+	0.959205i	$0.591234\pi$
$80$	6.57552	0.735165
$81$	−7.12026	−0.791140
$82$	6.04121	0.667140
$83$	−12.4468	−1.36621	−0.683107	−	0.730319i	$-0.739372\pi$
$83$	−12.4468	−1.36621	−0.683107	+	0.730319i	$0.739372\pi$
$84$	−37.6372	−4.10656
$85$	−0.981443	−0.106452
$86$	24.9255	2.68779
$87$	−1.63879	−0.175696
$88$	−10.5706	−1.12683
$89$	−16.3078	−1.72863	−0.864314	−	0.502953i	$-0.832247\pi$
$89$	−16.3078	−1.72863	−0.864314	+	0.502953i	$0.832247\pi$
$90$	0.627149	0.0661073
$91$	−3.09849	−0.324810
$92$	−28.8783	−3.01077
$93$	5.31636	0.551281
$94$	4.23190	0.436488
$95$	2.90996	0.298555
$96$	35.6183	3.63527
$97$	8.41742	0.854660	0.427330	−	0.904096i	$-0.359454\pi$
$97$	8.41742	0.854660	0.427330	+	0.904096i	$0.359454\pi$
$98$	−32.7321	−3.30645
$99$	−0.586092	−0.0589045
$100$	−26.5007	−2.65007
$101$	10.1067	1.00565	0.502827	−	0.864387i	$-0.332293\pi$
$101$	10.1067	1.00565	0.502827	+	0.864387i	$0.332293\pi$
$102$	−9.81730	−0.972058
$103$	−19.7910	−1.95006	−0.975030	−	0.222072i	$-0.928718\pi$
$103$	−19.7910	−1.95006	−0.975030	+	0.222072i	$0.928718\pi$
$104$	6.83195	0.669928
$105$	−2.94187	−0.287097
$106$	−13.6530	−1.32610
$107$	−12.9540	−1.25231	−0.626154	−	0.779699i	$-0.715372\pi$
$107$	−12.9540	−1.25231	−0.626154	+	0.779699i	$0.715372\pi$
$108$	30.5398	2.93870
$109$	8.18618	0.784093	0.392047	−	0.919945i	$-0.371767\pi$
$109$	8.18618	0.784093	0.392047	+	0.919945i	$0.371767\pi$
$110$	−1.29785	−0.123745
$111$	−13.2736	−1.25988
$112$	66.5351	6.28698
$113$	−2.93722	−0.276311	−0.138155	−	0.990411i	$-0.544117\pi$
$113$	−2.93722	−0.276311	−0.138155	+	0.990411i	$0.544117\pi$
$114$	29.1081	2.72622
$115$	−2.25724	−0.210488
$116$	5.74159	0.533093
$117$	0.378802	0.0350202
$118$	2.19011	0.201616
$119$	−9.93085	−0.910359
$120$	6.48661	0.592144
$121$	−9.78711	−0.889738
$122$	11.0233	0.998007
$123$	3.46448	0.312382
$124$	−18.6262	−1.67268
$125$	−4.22240	−0.377663
$126$	6.34587	0.565335
$127$	4.46387	0.396105	0.198052	−	0.980191i	$-0.436538\pi$
$127$	4.46387	0.396105	0.198052	+	0.980191i	$0.436538\pi$
$128$	−41.0515	−3.62847
$129$	14.2942	1.25853
$130$	0.838824	0.0735697
$131$	11.4012	0.996130	0.498065	−	0.867140i	$-0.334044\pi$
$131$	11.4012	0.996130	0.498065	+	0.867140i	$0.334044\pi$
$132$	−9.52213	−0.828795
$133$	29.4447	2.55318
$134$	6.42700	0.555209
$135$	2.38711	0.205449
$136$	21.8968	1.87764
$137$	18.5527	1.58506	0.792532	−	0.609831i	$-0.208763\pi$
$137$	18.5527	1.58506	0.792532	+	0.609831i	$0.208763\pi$
$138$	−22.5790	−1.92205
$139$	11.9184	1.01090	0.505451	−	0.862855i	$-0.331326\pi$
$139$	11.9184	1.01090	0.505451	+	0.862855i	$0.331326\pi$
$140$	10.3070	0.871102
$141$	2.42689	0.204381
$142$	25.5172	2.14135
$143$	−0.783910	−0.0655539
$144$	−8.13417	−0.677848
$145$	0.448784	0.0372695
$146$	45.3672	3.75462
$147$	−18.7711	−1.54821
$148$	46.5049	3.82268
$149$	13.6681	1.11973	0.559867	−	0.828582i	$-0.310852\pi$
$149$	13.6681	1.11973	0.559867	+	0.828582i	$0.310852\pi$
$150$	−20.7200	−1.69178
$151$	14.2697	1.16125	0.580626	−	0.814171i	$-0.302808\pi$
$151$	14.2697	1.16125	0.580626	+	0.814171i	$0.302808\pi$
$152$	−64.9236	−5.26600
$153$	1.21408	0.0981528
$154$	−13.1324	−1.05824
$155$	−1.45589	−0.116940
$156$	6.15433	0.492740
$157$	−12.4181	−0.991069	−0.495534	−	0.868588i	$-0.665028\pi$
$157$	−12.4181	−0.991069	−0.495534	+	0.868588i	$0.665028\pi$
$158$	13.7667	1.09522
$159$	−7.82968	−0.620934
$160$	−9.75412	−0.771131
$161$	−22.8401	−1.80005
$162$	19.5046	1.53243
$163$	−20.3342	−1.59269	−0.796347	−	0.604840i	$-0.793237\pi$
$163$	−20.3342	−1.59269	−0.796347	+	0.604840i	$0.793237\pi$
$164$	−12.1380	−0.947822
$165$	−0.744285	−0.0579425
$166$	34.0957	2.64634
$167$	18.0819	1.39922	0.699611	−	0.714524i	$-0.253357\pi$
$167$	18.0819	1.39922	0.699611	+	0.714524i	$0.253357\pi$
$168$	65.6355	5.06389
$169$	−12.4933	−0.961027
$170$	2.68848	0.206197
$171$	−3.59973	−0.275278
$172$	−50.0805	−3.81860
$173$	2.87626	0.218678	0.109339	−	0.994005i	$-0.465127\pi$
$173$	2.87626	0.218678	0.109339	+	0.994005i	$0.465127\pi$
$174$	4.48915	0.340322
$175$	−20.9596	−1.58440
$176$	16.8332	1.26885
$177$	1.25598	0.0944050
$178$	44.6724	3.34833
$179$	2.46145	0.183978	0.0919889	−	0.995760i	$-0.470678\pi$
$179$	2.46145	0.183978	0.0919889	+	0.995760i	$0.470678\pi$
$180$	−1.26007	−0.0939202
$181$	16.0714	1.19458	0.597289	−	0.802026i	$-0.296245\pi$
$181$	16.0714	1.19458	0.597289	+	0.802026i	$0.296245\pi$
$182$	8.48774	0.629153
$183$	6.32162	0.467307
$184$	50.3609	3.71265
$185$	3.63500	0.267250
$186$	−14.5632	−1.06782
$187$	−2.51248	−0.183731
$188$	−8.50277	−0.620129
$189$	24.1542	1.75696
$190$	−7.97130	−0.578299
$191$	−15.0024	−1.08553	−0.542767	−	0.839884i	$-0.682623\pi$
$191$	−15.0024	−1.08553	−0.542767	+	0.839884i	$0.682623\pi$
$192$	−49.5472	−3.57576
$193$	4.59085	0.330457	0.165228	−	0.986255i	$-0.447164\pi$
$193$	4.59085	0.330457	0.165228	+	0.986255i	$0.447164\pi$
$194$	−23.0580	−1.65547
$195$	0.481045	0.0344483
$196$	65.7657	4.69755
$197$	−23.8359	−1.69824	−0.849119	−	0.528201i	$-0.822867\pi$
$197$	−23.8359	−1.69824	−0.849119	+	0.528201i	$0.822867\pi$
$198$	1.60549	0.114097
$199$	20.6228	1.46191	0.730957	−	0.682423i	$-0.239074\pi$
$199$	20.6228	1.46191	0.730957	+	0.682423i	$0.239074\pi$
$200$	46.2145	3.26786
$201$	3.68573	0.259971
$202$	−27.6854	−1.94794
$203$	4.54107	0.318721
$204$	19.7250	1.38103
$205$	−0.948755	−0.0662639
$206$	54.2137	3.77725
$207$	2.79229	0.194078
$208$	−10.8796	−0.754366
$209$	7.44945	0.515289
$210$	8.05870	0.556103
$211$	0.585315	0.0402948	0.0201474	−	0.999797i	$-0.493586\pi$
$211$	0.585315	0.0402948	0.0201474	+	0.999797i	$0.493586\pi$
$212$	27.4318	1.88402
$213$	14.6335	1.00267
$214$	35.4851	2.42571
$215$	−3.91448	−0.266965
$216$	−53.2584	−3.62377
$217$	−14.7316	−1.00005
$218$	−22.4245	−1.51878
$219$	26.0170	1.75807
$220$	2.60765	0.175808
$221$	1.62386	0.109233
$222$	36.3606	2.44036
$223$	−6.48849	−0.434502	−0.217251	−	0.976116i	$-0.569709\pi$
$223$	−6.48849	−0.434502	−0.217251	+	0.976116i	$0.569709\pi$
$224$	−98.6982	−6.59455
$225$	2.56239	0.170826
$226$	8.04598	0.535211
$227$	0.510980	0.0339149	0.0169575	−	0.999856i	$-0.494602\pi$
$227$	0.510980	0.0339149	0.0169575	+	0.999856i	$0.494602\pi$
$228$	−58.4842	−3.87321
$229$	12.0994	0.799551	0.399776	−	0.916613i	$-0.369088\pi$
$229$	12.0994	0.799551	0.399776	+	0.916613i	$0.369088\pi$
$230$	6.18329	0.407714
$231$	−7.53114	−0.495512
$232$	−10.0128	−0.657370
$233$	1.95030	0.127768	0.0638842	−	0.997957i	$-0.479651\pi$
$233$	1.95030	0.127768	0.0638842	+	0.997957i	$0.479651\pi$
$234$	−1.03766	−0.0678338
$235$	−0.664609	−0.0433543
$236$	−4.40039	−0.286441
$237$	7.89487	0.512827
$238$	27.2037	1.76336
$239$	2.42607	0.156930	0.0784649	−	0.996917i	$-0.474998\pi$
$239$	2.42607	0.156930	0.0784649	+	0.996917i	$0.474998\pi$
$240$	−10.3297	−0.666778
$241$	−20.4109	−1.31478	−0.657392	−	0.753549i	$-0.728340\pi$
$241$	−20.4109	−1.31478	−0.657392	+	0.753549i	$0.728340\pi$
$242$	26.8100	1.72341
$243$	−5.46098	−0.350322
$244$	−22.1482	−1.41789
$245$	5.14049	0.328414
$246$	−9.49032	−0.605081
$247$	−4.81472	−0.306353
$248$	32.4822	2.06262
$249$	19.5531	1.23912
$250$	11.5665	0.731529
$251$	−5.25827	−0.331899	−0.165950	−	0.986134i	$-0.553069\pi$
$251$	−5.25827	−0.331899	−0.165950	+	0.986134i	$0.553069\pi$
$252$	−12.7502	−0.803186
$253$	−5.77850	−0.363291
$254$	−12.2280	−0.767251
$255$	1.54178	0.0965500
$256$	49.3729	3.08581
$257$	25.7458	1.60598	0.802988	−	0.595995i	$-0.203242\pi$
$257$	25.7458	1.60598	0.802988	+	0.595995i	$0.203242\pi$
$258$	−39.1563	−2.43776
$259$	36.7811	2.28547
$260$	−1.68537	−0.104522
$261$	−0.555163	−0.0343638
$262$	−31.2316	−1.92949
$263$	1.28290	0.0791073	0.0395536	−	0.999217i	$-0.487406\pi$
$263$	1.28290	0.0791073	0.0395536	+	0.999217i	$0.487406\pi$
$264$	16.6056	1.02201
$265$	2.14417	0.131715
$266$	−80.6585	−4.94549
$267$	25.6185	1.56783
$268$	−12.9132	−0.788798
$269$	−10.2217	−0.623230	−0.311615	−	0.950209i	$-0.600870\pi$
$269$	−10.2217	−0.623230	−0.311615	+	0.950209i	$0.600870\pi$
$270$	−6.53904	−0.397953
$271$	−7.25588	−0.440763	−0.220382	−	0.975414i	$-0.570730\pi$
$271$	−7.25588	−0.440763	−0.220382	+	0.975414i	$0.570730\pi$
$272$	−34.8699	−2.11430
$273$	4.86751	0.294595
$274$	−50.8217	−3.07025
$275$	−5.30273	−0.319767
$276$	45.3658	2.73070
$277$	−30.4520	−1.82969	−0.914843	−	0.403809i	$-0.867686\pi$
$277$	−30.4520	−1.82969	−0.914843	+	0.403809i	$0.867686\pi$
$278$	−32.6482	−1.95811
$279$	1.80100	0.107823
$280$	−17.9744	−1.07418
$281$	−2.75494	−0.164346	−0.0821728	−	0.996618i	$-0.526186\pi$
$281$	−2.75494	−0.164346	−0.0821728	+	0.996618i	$0.526186\pi$
$282$	−6.64803	−0.395884
$283$	1.32039	0.0784889	0.0392444	−	0.999230i	$-0.487505\pi$
$283$	1.32039	0.0784889	0.0392444	+	0.999230i	$0.487505\pi$
$284$	−51.2693	−3.04227
$285$	−4.57134	−0.270783
$286$	2.14738	0.126977
$287$	−9.60008	−0.566675
$288$	12.0662	0.711009
$289$	−11.7954	−0.693848
$290$	−1.22936	−0.0721906
$291$	−13.2232	−0.775157
$292$	−91.1522	−5.33428
$293$	−3.60676	−0.210709	−0.105355	−	0.994435i	$-0.533598\pi$
$293$	−3.60676	−0.210709	−0.105355	+	0.994435i	$0.533598\pi$
$294$	51.4199	2.99887
$295$	−0.343951	−0.0200256
$296$	−81.0999	−4.71384
$297$	6.11096	0.354594
$298$	−37.4413	−2.16891
$299$	3.73475	0.215986
$300$	41.6307	2.40355
$301$	−39.6091	−2.28303
$302$	−39.0892	−2.24933
$303$	−15.8769	−0.912105
$304$	103.388	5.92973
$305$	−1.73119	−0.0991274
$306$	−3.32576	−0.190121
$307$	16.2312	0.926361	0.463180	−	0.886264i	$-0.346708\pi$
$307$	16.2312	0.926361	0.463180	+	0.886264i	$0.346708\pi$
$308$	26.3858	1.50347
$309$	31.0902	1.76866
$310$	3.98815	0.226512
$311$	−2.66711	−0.151238	−0.0756190	−	0.997137i	$-0.524093\pi$
$311$	−2.66711	−0.151238	−0.0756190	+	0.997137i	$0.524093\pi$
$312$	−10.7325	−0.607610
$313$	2.85219	0.161215	0.0806076	−	0.996746i	$-0.474314\pi$
$313$	2.85219	0.161215	0.0806076	+	0.996746i	$0.474314\pi$
$314$	34.0170	1.91969
$315$	−0.996601	−0.0561521
$316$	−27.6602	−1.55601
$317$	14.2887	0.802533	0.401267	−	0.915961i	$-0.368570\pi$
$317$	14.2887	0.802533	0.401267	+	0.915961i	$0.368570\pi$
$318$	21.4480	1.20274
$319$	1.14888	0.0643250
$320$	13.5686	0.758507
$321$	20.3498	1.13582
$322$	62.5663	3.48668
$323$	−15.4315	−0.858630
$324$	−39.1889	−2.17716
$325$	3.42725	0.190110
$326$	55.7017	3.08503
$327$	−12.8599	−0.711155
$328$	21.1675	1.16878
$329$	−6.72492	−0.370757
$330$	2.03883	0.112234
$331$	−1.20663	−0.0663224	−0.0331612	−	0.999450i	$-0.510557\pi$
$331$	−1.20663	−0.0663224	−0.0331612	+	0.999450i	$0.510557\pi$
$332$	−68.5054	−3.75972
$333$	−4.49664	−0.246414
$334$	−49.5321	−2.71028
$335$	−1.00934	−0.0551463
$336$	−104.522	−5.70215
$337$	8.43996	0.459754	0.229877	−	0.973220i	$-0.426168\pi$
$337$	8.43996	0.459754	0.229877	+	0.973220i	$0.426168\pi$
$338$	34.2232	1.86150
$339$	4.61417	0.250607
$340$	−5.40172	−0.292950
$341$	−3.72707	−0.201832
$342$	9.86080	0.533211
$343$	21.5433	1.16323
$344$	87.3354	4.70881
$345$	3.54596	0.190908
$346$	−7.87899	−0.423577
$347$	−31.5412	−1.69322	−0.846611	−	0.532212i	$-0.821361\pi$
$347$	−31.5412	−1.69322	−0.846611	+	0.532212i	$0.821361\pi$
$348$	−9.01964	−0.483503
$349$	−17.2006	−0.920728	−0.460364	−	0.887730i	$-0.652281\pi$
$349$	−17.2006	−0.920728	−0.460364	+	0.887730i	$0.652281\pi$
$350$	57.4150	3.06896
$351$	−3.94962	−0.210815
$352$	−24.9704	−1.33093
$353$	−28.2117	−1.50156	−0.750778	−	0.660555i	$-0.770321\pi$
$353$	−28.2117	−1.50156	−0.750778	+	0.660555i	$0.770321\pi$
$354$	−3.44052	−0.182861
$355$	−4.00740	−0.212691
$356$	−89.7560	−4.75706
$357$	15.6007	0.825675
$358$	−6.74270	−0.356363
$359$	28.2751	1.49230	0.746151	−	0.665777i	$-0.231900\pi$
$359$	28.2751	1.49230	0.746151	+	0.665777i	$0.231900\pi$
$360$	2.19744	0.115815
$361$	26.7540	1.40810
$362$	−44.0246	−2.31388
$363$	15.3749	0.806972
$364$	−17.0536	−0.893853
$365$	−7.12480	−0.372929
$366$	−17.3169	−0.905170
$367$	−4.18012	−0.218201	−0.109100	−	0.994031i	$-0.534797\pi$
$367$	−4.18012	−0.218201	−0.109100	+	0.994031i	$0.534797\pi$
$368$	−80.1978	−4.18060
$369$	1.17365	0.0610976
$370$	−9.95741	−0.517661
$371$	21.6960	1.12640
$372$	29.2605	1.51708
$373$	−9.98754	−0.517135	−0.258568	−	0.965993i	$-0.583250\pi$
$373$	−9.98754	−0.517135	−0.258568	+	0.965993i	$0.583250\pi$
$374$	6.88248	0.355885
$375$	6.63310	0.342532
$376$	14.8280	0.764695
$377$	−0.742543	−0.0382429
$378$	−66.1660	−3.40321
$379$	−21.0027	−1.07884	−0.539419	−	0.842037i	$-0.681356\pi$
$379$	−21.0027	−1.07884	−0.539419	+	0.842037i	$0.681356\pi$
$380$	16.0160	0.821603
$381$	−7.01244	−0.359258
$382$	41.0962	2.10267
$383$	2.59558	0.132628	0.0663141	−	0.997799i	$-0.478876\pi$
$383$	2.59558	0.132628	0.0663141	+	0.997799i	$0.478876\pi$
$384$	64.4890	3.29094
$385$	2.06241	0.105110
$386$	−12.5758	−0.640091
$387$	4.84237	0.246151
$388$	46.3283	2.35196
$389$	33.3513	1.69098	0.845488	−	0.533994i	$-0.179310\pi$
$389$	33.3513	1.69098	0.845488	+	0.533994i	$0.179310\pi$
$390$	−1.31773	−0.0667261
$391$	11.9701	0.605354
$392$	−114.689	−5.79266
$393$	−17.9105	−0.903468
$394$	65.2941	3.28947
$395$	−2.16202	−0.108783
$396$	−3.22577	−0.162101
$397$	7.55922	0.379387	0.189693	−	0.981843i	$-0.439251\pi$
$397$	7.55922	0.379387	0.189693	+	0.981843i	$0.439251\pi$
$398$	−56.4925	−2.83171
$399$	−46.2556	−2.31568
$400$	−73.5948	−3.67974
$401$	5.13373	0.256366	0.128183	−	0.991751i	$-0.459085\pi$
$401$	5.13373	0.256366	0.128183	+	0.991751i	$0.459085\pi$
$402$	−10.0964	−0.503562
$403$	2.40887	0.119994
$404$	55.6258	2.76749
$405$	−3.06315	−0.152209
$406$	−12.4394	−0.617359
$407$	9.30555	0.461259
$408$	−34.3984	−1.70298
$409$	−35.7090	−1.76570	−0.882848	−	0.469660i	$-0.844377\pi$
$409$	−35.7090	−1.76570	−0.882848	+	0.469660i	$0.844377\pi$
$410$	2.59894	0.128352
$411$	−29.1450	−1.43762
$412$	−108.927	−5.36643
$413$	−3.48031	−0.171255
$414$	−7.64897	−0.375926
$415$	−5.35464	−0.262849
$416$	16.1388	0.791271
$417$	−18.7229	−0.916865
$418$	−20.4064	−0.998110
$419$	1.51590	0.0740563	0.0370282	−	0.999314i	$-0.488211\pi$
$419$	1.51590	0.0740563	0.0370282	+	0.999314i	$0.488211\pi$
$420$	−16.1916	−0.790069
$421$	18.9741	0.924743	0.462371	−	0.886686i	$-0.346999\pi$
$421$	18.9741	0.924743	0.462371	+	0.886686i	$0.346999\pi$
$422$	−1.60336	−0.0780505
$423$	0.822147	0.0399741
$424$	−47.8383	−2.32323
$425$	10.9846	0.532829
$426$	−40.0857	−1.94216
$427$	−17.5172	−0.847716
$428$	−71.2968	−3.44626
$429$	1.23147	0.0594559
$430$	10.7230	0.517109
$431$	−2.71318	−0.130689	−0.0653445	−	0.997863i	$-0.520815\pi$
$431$	−2.71318	−0.130689	−0.0653445	+	0.997863i	$0.520815\pi$
$432$	84.8119	4.08052
$433$	11.9090	0.572308	0.286154	−	0.958184i	$-0.407623\pi$
$433$	11.9090	0.572308	0.286154	+	0.958184i	$0.407623\pi$
$434$	40.3546	1.93708
$435$	−0.705009	−0.0338026
$436$	45.0555	2.15777
$437$	−35.4911	−1.69777
$438$	−71.2688	−3.40536
$439$	−1.35003	−0.0644336	−0.0322168	−	0.999481i	$-0.510257\pi$
$439$	−1.35003	−0.0644336	−0.0322168	+	0.999481i	$0.510257\pi$
$440$	−4.54748	−0.216793
$441$	−6.35899	−0.302809
$442$	−4.44827	−0.211583
$443$	−31.7093	−1.50656	−0.753278	−	0.657702i	$-0.771529\pi$
$443$	−31.7093	−1.50656	−0.753278	+	0.657702i	$0.771529\pi$
$444$	−73.0560	−3.46709
$445$	−7.01567	−0.332574
$446$	17.7740	0.841625
$447$	−21.4716	−1.01557
$448$	137.295	6.48659
$449$	−35.7223	−1.68584	−0.842920	−	0.538038i	$-0.819166\pi$
$449$	−35.7223	−1.68584	−0.842920	+	0.538038i	$0.819166\pi$
$450$	−7.01920	−0.330888
$451$	−2.42880	−0.114368
$452$	−16.1660	−0.760387
$453$	−22.4167	−1.05323
$454$	−1.39974	−0.0656929
$455$	−1.33298	−0.0624908
$456$	101.991	4.77614
$457$	27.6878	1.29518	0.647591	−	0.761988i	$-0.275776\pi$
$457$	27.6878	1.29518	0.647591	+	0.761988i	$0.275776\pi$
$458$	−33.1441	−1.54872
$459$	−12.6588	−0.590862
$460$	−12.4235	−0.579249
$461$	−13.2647	−0.617800	−0.308900	−	0.951095i	$-0.599961\pi$
$461$	−13.2647	−0.617800	−0.308900	+	0.951095i	$0.599961\pi$
$462$	20.6302	0.959802
$463$	−36.8778	−1.71386	−0.856929	−	0.515434i	$-0.827631\pi$
$463$	−36.8778	−1.71386	−0.856929	+	0.515434i	$0.827631\pi$
$464$	15.9449	0.740225
$465$	2.28711	0.106062
$466$	−5.34249	−0.247486
$467$	15.5228	0.718311	0.359156	−	0.933278i	$-0.383065\pi$
$467$	15.5228	0.718311	0.359156	+	0.933278i	$0.383065\pi$
$468$	2.08487	0.0963732
$469$	−10.2131	−0.471599
$470$	1.82057	0.0839768
$471$	19.5079	0.898877
$472$	7.67384	0.353217
$473$	−10.0210	−0.460767
$474$	−21.6265	−0.993340
$475$	−32.5690	−1.49437
$476$	−54.6579	−2.50524
$477$	−2.65242	−0.121446
$478$	−6.64579	−0.303971
$479$	−13.1582	−0.601216	−0.300608	−	0.953748i	$-0.597190\pi$
$479$	−13.1582	−0.601216	−0.300608	+	0.953748i	$0.597190\pi$
$480$	15.3230	0.699398
$481$	−6.01434	−0.274230
$482$	55.9120	2.54672
$483$	35.8802	1.63261
$484$	−53.8669	−2.44849
$485$	3.62119	0.164430
$486$	14.9594	0.678570
$487$	41.1922	1.86660	0.933298	−	0.359104i	$-0.116918\pi$
$487$	41.1922	1.86660	0.933298	+	0.359104i	$0.116918\pi$
$488$	38.6242	1.74844
$489$	31.9435	1.44454
$490$	−14.0814	−0.636134
$491$	28.4144	1.28232	0.641162	−	0.767406i	$-0.278453\pi$
$491$	28.4144	1.28232	0.641162	+	0.767406i	$0.278453\pi$
$492$	19.0680	0.859653
$493$	−2.37990	−0.107185
$494$	13.1890	0.593403
$495$	−0.252138	−0.0113328
$496$	−51.7267	−2.32260
$497$	−40.5493	−1.81889
$498$	−53.5620	−2.40017
$499$	21.2498	0.951271	0.475635	−	0.879643i	$-0.342218\pi$
$499$	21.2498	0.951271	0.475635	+	0.879643i	$0.342218\pi$
$500$	−23.2395	−1.03930
$501$	−28.4055	−1.26906
$502$	14.4041	0.642885
$503$	19.0667	0.850141	0.425070	−	0.905160i	$-0.360249\pi$
$503$	19.0667	0.850141	0.425070	+	0.905160i	$0.360249\pi$
$504$	22.2350	0.990427
$505$	4.34792	0.193480
$506$	15.8291	0.703691
$507$	19.6262	0.871629
$508$	24.5685	1.09005
$509$	−25.3309	−1.12277	−0.561386	−	0.827554i	$-0.689732\pi$
$509$	−25.3309	−1.12277	−0.561386	+	0.827554i	$0.689732\pi$
$510$	−4.22342	−0.187016
$511$	−72.0931	−3.18921
$512$	−53.1451	−2.34870
$513$	37.5330	1.65712
$514$	−70.5258	−3.11076
$515$	−8.51411	−0.375176
$516$	78.6730	3.46339
$517$	−1.70139	−0.0748270
$518$	−100.755	−4.42693
$519$	−4.51841	−0.198336
$520$	2.93912	0.128889
$521$	−9.81039	−0.429801	−0.214900	−	0.976636i	$-0.568943\pi$
$521$	−9.81039	−0.429801	−0.214900	+	0.976636i	$0.568943\pi$
$522$	1.52077	0.0665622
$523$	−2.00874	−0.0878359	−0.0439180	−	0.999035i	$-0.513984\pi$
$523$	−2.00874	−0.0878359	−0.0439180	+	0.999035i	$0.513984\pi$
$524$	62.7507	2.74128
$525$	32.9261	1.43701
$526$	−3.51428	−0.153230
$527$	7.72058	0.336314
$528$	−26.4438	−1.15082
$529$	4.53022	0.196966
$530$	−5.87356	−0.255131
$531$	0.425481	0.0184643
$532$	162.060	7.02618
$533$	1.56978	0.0679946
$534$	−70.1772	−3.03686
$535$	−5.57283	−0.240934
$536$	22.5193	0.972685
$537$	−3.86677	−0.166864
$538$	28.0005	1.20719
$539$	13.1596	0.566824
$540$	13.1383	0.565382
$541$	2.94807	0.126747	0.0633737	−	0.997990i	$-0.479814\pi$
$541$	2.94807	0.126747	0.0633737	+	0.997990i	$0.479814\pi$
$542$	19.8761	0.853754
$543$	−25.2470	−1.08345
$544$	51.7260	2.21773
$545$	3.52171	0.150853
$546$	−13.3336	−0.570627
$547$	9.87470	0.422212	0.211106	−	0.977463i	$-0.432294\pi$
$547$	9.87470	0.422212	0.211106	+	0.977463i	$0.432294\pi$
$548$	102.111	4.36198
$549$	2.14154	0.0913989
$550$	14.5259	0.619385
$551$	7.05634	0.300610
$552$	−79.1135	−3.36729
$553$	−21.8767	−0.930291
$554$	83.4178	3.54408
$555$	−5.71033	−0.242390
$556$	65.5969	2.78193
$557$	−3.66922	−0.155470	−0.0777350	−	0.996974i	$-0.524769\pi$
$557$	−3.66922	−0.155470	−0.0777350	+	0.996974i	$0.524769\pi$
$558$	−4.93350	−0.208852
$559$	6.47676	0.273938
$560$	28.6235	1.20957
$561$	3.94694	0.166640
$562$	7.54664	0.318336
$563$	21.0158	0.885710	0.442855	−	0.896593i	$-0.353966\pi$
$563$	21.0158	0.885710	0.442855	+	0.896593i	$0.353966\pi$
$564$	13.3573	0.562443
$565$	−1.26360	−0.0531600
$566$	−3.61696	−0.152032
$567$	−30.9948	−1.30166
$568$	89.4085	3.75150
$569$	19.4728	0.816342	0.408171	−	0.912905i	$-0.366167\pi$
$569$	19.4728	0.816342	0.408171	+	0.912905i	$0.366167\pi$
$570$	12.5224	0.524504
$571$	−21.6355	−0.905417	−0.452709	−	0.891658i	$-0.649542\pi$
$571$	−21.6355	−0.905417	−0.452709	+	0.891658i	$0.649542\pi$
$572$	−4.31453	−0.180400
$573$	23.5677	0.984554
$574$	26.2977	1.09764
$575$	25.2636	1.05356
$576$	−16.7849	−0.699370
$577$	−21.7021	−0.903471	−0.451736	−	0.892152i	$-0.649195\pi$
$577$	−21.7021	−0.903471	−0.451736	+	0.892152i	$0.649195\pi$
$578$	32.3114	1.34398
$579$	−7.21191	−0.299717
$580$	2.47004	0.102563
$581$	−54.1815	−2.24783
$582$	36.2225	1.50147
$583$	5.48905	0.227333
$584$	158.960	6.57782
$585$	0.162961	0.00673762
$586$	9.88007	0.408142
$587$	−16.3050	−0.672978	−0.336489	−	0.941687i	$-0.609240\pi$
$587$	−16.3050	−0.672978	−0.336489	+	0.941687i	$0.609240\pi$
$588$	−103.313	−4.26057
$589$	−22.8914	−0.943222
$590$	0.942191	0.0387894
$591$	37.4446	1.54026
$592$	129.149	5.30797
$593$	−40.9852	−1.68306	−0.841531	−	0.540209i	$-0.818345\pi$
$593$	−40.9852	−1.68306	−0.841531	+	0.540209i	$0.818345\pi$
$594$	−16.7399	−0.686845
$595$	−4.27227	−0.175146
$596$	75.2273	3.08143
$597$	−32.3970	−1.32592
$598$	−10.2307	−0.418363
$599$	2.48186	0.101406	0.0507031	−	0.998714i	$-0.483854\pi$
$599$	2.48186	0.101406	0.0507031	+	0.998714i	$0.483854\pi$
$600$	−72.5998	−2.96387
$601$	15.5682	0.635038	0.317519	−	0.948252i	$-0.397150\pi$
$601$	15.5682	0.635038	0.317519	+	0.948252i	$0.397150\pi$
$602$	108.502	4.42221
$603$	1.24860	0.0508468
$604$	78.5384	3.19568
$605$	−4.21044	−0.171179
$606$	43.4919	1.76674
$607$	23.9444	0.971872	0.485936	−	0.873994i	$-0.338479\pi$
$607$	23.9444	0.971872	0.485936	+	0.873994i	$0.338479\pi$
$608$	−153.366	−6.21983
$609$	−7.13371	−0.289073
$610$	4.74227	0.192009
$611$	1.09964	0.0444866
$612$	6.68214	0.270110
$613$	−39.7024	−1.60356	−0.801782	−	0.597617i	$-0.796114\pi$
$613$	−39.7024	−1.60356	−0.801782	+	0.597617i	$0.796114\pi$
$614$	−44.4623	−1.79435
$615$	1.49043	0.0600998
$616$	−46.0142	−1.85397
$617$	30.3608	1.22228	0.611140	−	0.791522i	$-0.290711\pi$
$617$	30.3608	1.22228	0.611140	+	0.791522i	$0.290711\pi$
$618$	−85.1659	−3.42588
$619$	14.7069	0.591122	0.295561	−	0.955324i	$-0.404493\pi$
$619$	14.7069	0.591122	0.295561	+	0.955324i	$0.404493\pi$
$620$	−8.01303	−0.321811
$621$	−29.1142	−1.16831
$622$	7.30607	0.292947
$623$	−70.9888	−2.84411
$624$	17.0911	0.684193
$625$	22.2581	0.890326
$626$	−7.81304	−0.312272
$627$	−11.7026	−0.467356
$628$	−68.3472	−2.72735
$629$	−19.2763	−0.768598
$630$	2.73001	0.108766
$631$	−29.7467	−1.18420	−0.592099	−	0.805865i	$-0.701701\pi$
$631$	−29.7467	−1.18420	−0.592099	+	0.805865i	$0.701701\pi$
$632$	48.2366	1.91875
$633$	−0.919490	−0.0365464
$634$	−39.1413	−1.55450
$635$	1.92037	0.0762074
$636$	−43.0934	−1.70876
$637$	−8.50528	−0.336991
$638$	−3.14715	−0.124597
$639$	4.95731	0.196108
$640$	−17.6604	−0.698090
$641$	−8.06443	−0.318526	−0.159263	−	0.987236i	$-0.550912\pi$
$641$	−8.06443	−0.318526	−0.159263	+	0.987236i	$0.550912\pi$
$642$	−55.7446	−2.20006
$643$	−50.3749	−1.98659	−0.993296	−	0.115602i	$-0.963120\pi$
$643$	−50.3749	−1.98659	−0.993296	+	0.115602i	$0.963120\pi$
$644$	−125.709	−4.95362
$645$	6.14938	0.242132
$646$	42.2717	1.66316
$647$	−34.2659	−1.34713	−0.673566	−	0.739127i	$-0.735238\pi$
$647$	−34.2659	−1.34713	−0.673566	+	0.739127i	$0.735238\pi$
$648$	68.3415	2.68471
$649$	−0.880510	−0.0345631
$650$	−9.38833	−0.368240
$651$	23.1424	0.907021
$652$	−111.916	−4.38298
$653$	−25.1970	−0.986034	−0.493017	−	0.870020i	$-0.664106\pi$
$653$	−25.1970	−0.986034	−0.493017	+	0.870020i	$0.664106\pi$
$654$	35.2274	1.37750
$655$	4.90483	0.191648
$656$	−33.7085	−1.31609
$657$	8.81365	0.343853
$658$	18.4217	0.718152
$659$	28.9505	1.12775	0.563875	−	0.825860i	$-0.309310\pi$
$659$	28.9505	1.12775	0.563875	+	0.825860i	$0.309310\pi$
$660$	−4.09644	−0.159454
$661$	0.913834	0.0355440	0.0177720	−	0.999842i	$-0.494343\pi$
$661$	0.913834	0.0355440	0.0177720	+	0.999842i	$0.494343\pi$
$662$	3.30534	0.128466
$663$	−2.55097	−0.0990717
$664$	119.467	4.63620
$665$	12.6672	0.491212
$666$	12.3177	0.477302
$667$	−5.47356	−0.211937
$668$	99.5203	3.85056
$669$	10.1930	0.394083
$670$	2.76491	0.106818
$671$	−4.43181	−0.171088
$672$	155.048	5.98111
$673$	12.9334	0.498548	0.249274	−	0.968433i	$-0.419808\pi$
$673$	12.9334	0.498548	0.249274	+	0.968433i	$0.419808\pi$
$674$	−23.1197	−0.890538
$675$	−26.7171	−1.02834
$676$	−68.7616	−2.64468
$677$	−43.8551	−1.68549	−0.842745	−	0.538313i	$-0.819062\pi$
$677$	−43.8551	−1.68549	−0.842745	+	0.538313i	$0.819062\pi$
$678$	−12.6397	−0.485424
$679$	36.6414	1.40617
$680$	9.42006	0.361243
$681$	−0.802714	−0.0307601
$682$	10.2096	0.390947
$683$	−40.7262	−1.55834	−0.779172	−	0.626811i	$-0.784360\pi$
$683$	−40.7262	−1.55834	−0.779172	+	0.626811i	$0.784360\pi$
$684$	−19.8124	−0.757546
$685$	7.98140	0.304954
$686$	−59.0140	−2.25316
$687$	−19.0073	−0.725175
$688$	−139.078	−5.30231
$689$	−3.54767	−0.135155
$690$	−9.71352	−0.369787
$691$	17.8614	0.679479	0.339739	−	0.940520i	$-0.389661\pi$
$691$	17.8614	0.679479	0.339739	+	0.940520i	$0.389661\pi$
$692$	15.8305	0.601786
$693$	−2.55129	−0.0969154
$694$	86.4014	3.27975
$695$	5.12730	0.194490
$696$	15.7293	0.596219
$697$	5.03123	0.190572
$698$	47.1179	1.78344
$699$	−3.06379	−0.115883
$700$	−115.359	−4.36015
$701$	−6.57618	−0.248379	−0.124189	−	0.992259i	$-0.539633\pi$
$701$	−6.57618	−0.248379	−0.124189	+	0.992259i	$0.539633\pi$
$702$	10.8193	0.408347
$703$	57.1540	2.15560
$704$	34.7354	1.30914
$705$	1.04405	0.0393213
$706$	77.2807	2.90850
$707$	43.9949	1.65460
$708$	6.91271	0.259796
$709$	−45.7366	−1.71767	−0.858836	−	0.512250i	$-0.828812\pi$
$709$	−45.7366	−1.71767	−0.858836	+	0.512250i	$0.828812\pi$
$710$	10.9775	0.411980
$711$	2.67451	0.100302
$712$	156.526	5.86604
$713$	17.7567	0.664993
$714$	−42.7352	−1.59932
$715$	−0.337240	−0.0126121
$716$	13.5475	0.506294
$717$	−3.81120	−0.142332
$718$	−77.4544	−2.89057
$719$	44.5029	1.65968	0.829839	−	0.558002i	$-0.188432\pi$
$719$	44.5029	1.65968	0.829839	+	0.558002i	$0.188432\pi$
$720$	−3.49934	−0.130413
$721$	−86.1509	−3.20843
$722$	−73.2876	−2.72748
$723$	32.0642	1.19248
$724$	88.4546	3.28739
$725$	−5.02290	−0.186546
$726$	−42.1167	−1.56310
$727$	−21.1327	−0.783767	−0.391884	−	0.920015i	$-0.628176\pi$
$727$	−21.1327	−0.783767	−0.391884	+	0.920015i	$0.628176\pi$
$728$	29.7398	1.10223
$729$	29.9396	1.10887
$730$	19.5171	0.722359
$731$	20.7584	0.767779
$732$	34.7933	1.28600
$733$	31.1435	1.15031	0.575156	−	0.818044i	$-0.304941\pi$
$733$	31.1435	1.15031	0.575156	+	0.818044i	$0.304941\pi$
$734$	11.4507	0.422652
$735$	−8.07536	−0.297864
$736$	118.965	4.38512
$737$	−2.58390	−0.0951793
$738$	−3.21499	−0.118345
$739$	−28.1585	−1.03583	−0.517914	−	0.855433i	$-0.673291\pi$
$739$	−28.1585	−1.03583	−0.517914	+	0.855433i	$0.673291\pi$
$740$	20.0065	0.735454
$741$	7.56358	0.277855
$742$	−59.4323	−2.18183
$743$	−32.2826	−1.18433	−0.592167	−	0.805815i	$-0.701727\pi$
$743$	−32.2826	−1.18433	−0.592167	+	0.805815i	$0.701727\pi$
$744$	−51.0273	−1.87075
$745$	5.88004	0.215428
$746$	27.3590	1.00169
$747$	6.62389	0.242356
$748$	−13.8283	−0.505614
$749$	−56.3893	−2.06042
$750$	−18.1702	−0.663480
$751$	49.4263	1.80359	0.901795	−	0.432164i	$-0.142250\pi$
$751$	49.4263	1.80359	0.901795	+	0.432164i	$0.142250\pi$
$752$	−23.6130	−0.861077
$753$	8.26038	0.301025
$754$	2.03406	0.0740761
$755$	6.13885	0.223416
$756$	132.941	4.83503
$757$	−17.2618	−0.627390	−0.313695	−	0.949524i	$-0.601567\pi$
$757$	−17.2618	−0.627390	−0.313695	+	0.949524i	$0.601567\pi$
$758$	57.5331	2.08970
$759$	9.07762	0.329497
$760$	−27.9303	−1.01314
$761$	−0.784523	−0.0284389	−0.0142195	−	0.999899i	$-0.504526\pi$
$761$	−0.784523	−0.0284389	−0.0142195	+	0.999899i	$0.504526\pi$
$762$	19.2093	0.695879
$763$	35.6348	1.29007
$764$	−82.5709	−2.98731
$765$	0.522301	0.0188838
$766$	−7.11013	−0.256899
$767$	0.569090	0.0205486
$768$	−77.5614	−2.79876
$769$	−25.1028	−0.905231	−0.452616	−	0.891706i	$-0.649509\pi$
$769$	−25.1028	−0.905231	−0.452616	+	0.891706i	$0.649509\pi$
$770$	−5.64961	−0.203598
$771$	−40.4448	−1.45658
$772$	25.2674	0.909393
$773$	11.6787	0.420055	0.210028	−	0.977695i	$-0.432645\pi$
$773$	11.6787	0.420055	0.210028	+	0.977695i	$0.432645\pi$
$774$	−13.2648	−0.476792
$775$	16.2947	0.585324
$776$	−80.7919	−2.90026
$777$	−57.7806	−2.07287
$778$	−91.3597	−3.27540
$779$	−14.9175	−0.534475
$780$	2.64760	0.0947994
$781$	−10.2589	−0.367092
$782$	−32.7899	−1.17256
$783$	5.78848	0.206863
$784$	182.637	6.52277
$785$	−5.34227	−0.190674
$786$	49.0627	1.75001
$787$	3.90646	0.139250	0.0696251	−	0.997573i	$-0.477820\pi$
$787$	3.90646	0.139250	0.0696251	+	0.997573i	$0.477820\pi$
$788$	−131.189	−4.67343
$789$	−2.01535	−0.0717485
$790$	5.92246	0.210712
$791$	−12.7859	−0.454613
$792$	5.62541	0.199890
$793$	2.86436	0.101716
$794$	−20.7071	−0.734868
$795$	−3.36834	−0.119463
$796$	113.505	4.02308
$797$	9.40642	0.333193	0.166596	−	0.986025i	$-0.446722\pi$
$797$	9.40642	0.333193	0.166596	+	0.986025i	$0.446722\pi$
$798$	126.709	4.48545
$799$	3.52441	0.124685
$800$	109.171	3.85976
$801$	8.67865	0.306645
$802$	−14.0629	−0.496578
$803$	−18.2394	−0.643654
$804$	20.2857	0.715422
$805$	−9.82586	−0.346316
$806$	−6.59866	−0.232428
$807$	16.0576	0.565255
$808$	−97.0058	−3.41265
$809$	−39.5379	−1.39008	−0.695039	−	0.718972i	$-0.744613\pi$
$809$	−39.5379	−1.39008	−0.695039	+	0.718972i	$0.744613\pi$
$810$	8.39094	0.294827
$811$	−33.9718	−1.19291	−0.596455	−	0.802647i	$-0.703425\pi$
$811$	−33.9718	−1.19291	−0.596455	+	0.802647i	$0.703425\pi$
$812$	24.9934	0.877097
$813$	11.3985	0.399762
$814$	−25.4908	−0.893454
$815$	−8.74779	−0.306422
$816$	54.7782	1.91762
$817$	−61.5483	−2.15330
$818$	97.8182	3.42013
$819$	1.64894	0.0576187
$820$	−5.22181	−0.182353
$821$	4.80849	0.167818	0.0839088	−	0.996473i	$-0.473260\pi$
$821$	4.80849	0.167818	0.0839088	+	0.996473i	$0.473260\pi$
$822$	79.8374	2.78465
$823$	−10.5173	−0.366609	−0.183305	−	0.983056i	$-0.558679\pi$
$823$	−10.5173	−0.366609	−0.183305	+	0.983056i	$0.558679\pi$
$824$	189.957	6.61746
$825$	8.33023	0.290021
$826$	9.53367	0.331719
$827$	46.3473	1.61165	0.805827	−	0.592151i	$-0.201721\pi$
$827$	46.3473	1.61165	0.805827	+	0.592151i	$0.201721\pi$
$828$	15.3684	0.534088
$829$	4.41143	0.153215	0.0766076	−	0.997061i	$-0.475591\pi$
$829$	4.41143	0.153215	0.0766076	+	0.997061i	$0.475591\pi$
$830$	14.6680	0.509135
$831$	47.8381	1.65948
$832$	−22.4501	−0.778318
$833$	−27.2600	−0.944501
$834$	51.2880	1.77596
$835$	7.77888	0.269199
$836$	41.0007	1.41804
$837$	−18.7783	−0.649074
$838$	−4.15252	−0.143446
$839$	13.7760	0.475600	0.237800	−	0.971314i	$-0.423574\pi$
$839$	13.7760	0.475600	0.237800	+	0.971314i	$0.423574\pi$
$840$	28.2365	0.974253
$841$	−27.9117	−0.962474
$842$	−51.9762	−1.79122
$843$	4.32781	0.149058
$844$	3.22149	0.110888
$845$	−5.37466	−0.184894
$846$	−2.25212	−0.0774295
$847$	−42.6038	−1.46388
$848$	76.1806	2.61605
$849$	−2.07424	−0.0711876
$850$	−30.0902	−1.03208
$851$	−44.3340	−1.51975
$852$	80.5405	2.75927
$853$	26.3565	0.902430	0.451215	−	0.892415i	$-0.350991\pi$
$853$	26.3565	0.902430	0.451215	+	0.892415i	$0.350991\pi$
$854$	47.9851	1.64202
$855$	−1.54861	−0.0529614
$856$	124.335	4.24967
$857$	−34.8146	−1.18924	−0.594622	−	0.804005i	$-0.702698\pi$
$857$	−34.8146	−1.18924	−0.594622	+	0.804005i	$0.702698\pi$
$858$	−3.37338	−0.115165
$859$	37.7334	1.28745	0.643724	−	0.765258i	$-0.277389\pi$
$859$	37.7334	1.28745	0.643724	+	0.765258i	$0.277389\pi$
$860$	−21.5447	−0.734670
$861$	15.0811	0.513961
$862$	7.43225	0.253143
$863$	−52.3045	−1.78047	−0.890233	−	0.455505i	$-0.849459\pi$
$863$	−52.3045	−1.78047	−0.890233	+	0.455505i	$0.849459\pi$
$864$	−125.810	−4.28014
$865$	1.23737	0.0420719
$866$	−32.6224	−1.10856
$867$	18.5298	0.629305
$868$	−81.0807	−2.75206
$869$	−5.53475	−0.187753
$870$	1.93124	0.0654752
$871$	1.67002	0.0565866
$872$	−78.5723	−2.66079
$873$	−4.47956	−0.151610
$874$	97.2213	3.28856
$875$	−18.3803	−0.621368
$876$	143.194	4.83807
$877$	−43.4308	−1.46655	−0.733277	−	0.679930i	$-0.762010\pi$
$877$	−43.4308	−1.46655	−0.733277	+	0.679930i	$0.762010\pi$
$878$	3.69817	0.124807
$879$	5.66598	0.191109
$880$	7.24169	0.244117
$881$	−3.53318	−0.119036	−0.0595179	−	0.998227i	$-0.518956\pi$
$881$	−3.53318	−0.119036	−0.0595179	+	0.998227i	$0.518956\pi$
$882$	17.4193	0.586538
$883$	−8.76642	−0.295013	−0.147507	−	0.989061i	$-0.547125\pi$
$883$	−8.76642	−0.295013	−0.147507	+	0.989061i	$0.547125\pi$
$884$	8.93750	0.300601
$885$	0.540324	0.0181628
$886$	86.8619	2.91818
$887$	10.7201	0.359945	0.179972	−	0.983672i	$-0.442399\pi$
$887$	10.7201	0.359945	0.179972	+	0.983672i	$0.442399\pi$
$888$	127.402	4.27534
$889$	19.4314	0.651710
$890$	19.2181	0.644193
$891$	−7.84162	−0.262704
$892$	−35.7117	−1.19572
$893$	−10.4498	−0.349689
$894$	58.8176	1.96716
$895$	1.05892	0.0353959
$896$	−178.699	−5.96991
$897$	−5.86703	−0.195894
$898$	97.8548	3.26546
$899$	−3.53039	−0.117745
$900$	14.1030	0.470101
$901$	−11.3705	−0.378806
$902$	6.65325	0.221529
$903$	62.2232	2.07066
$904$	28.1920	0.937651
$905$	6.91395	0.229827
$906$	61.4065	2.04009
$907$	−4.66312	−0.154836	−0.0774182	−	0.996999i	$-0.524668\pi$
$907$	−4.66312	−0.154836	−0.0774182	+	0.996999i	$0.524668\pi$
$908$	2.81236	0.0933315
$909$	−5.37854	−0.178395
$910$	3.65144	0.121044
$911$	9.20159	0.304862	0.152431	−	0.988314i	$-0.451290\pi$
$911$	9.20159	0.304862	0.152431	+	0.988314i	$0.451290\pi$
$912$	−162.416	−5.37813
$913$	−13.7078	−0.453662
$914$	−75.8458	−2.50876
$915$	2.71957	0.0899063
$916$	66.5934	2.20031
$917$	49.6301	1.63893
$918$	34.6764	1.14449
$919$	23.8796	0.787715	0.393857	−	0.919172i	$-0.371140\pi$
$919$	23.8796	0.787715	0.393857	+	0.919172i	$0.371140\pi$
$920$	21.6654	0.714286
$921$	−25.4980	−0.840188
$922$	36.3363	1.19667
$923$	6.63051	0.218246
$924$	−41.4503	−1.36361
$925$	−40.6838	−1.33768
$926$	101.020	3.31973
$927$	10.5323	0.345925
$928$	−23.6527	−0.776438
$929$	22.7646	0.746881	0.373441	−	0.927654i	$-0.378178\pi$
$929$	22.7646	0.746881	0.373441	+	0.927654i	$0.378178\pi$
$930$	−6.26511	−0.205441
$931$	80.8252	2.64894
$932$	10.7342	0.351609
$933$	4.18985	0.137170
$934$	−42.5220	−1.39136
$935$	−1.08087	−0.0353484
$936$	−3.63581	−0.118840
$937$	−5.94358	−0.194168	−0.0970842	−	0.995276i	$-0.530952\pi$
$937$	−5.94358	−0.194168	−0.0970842	+	0.995276i	$0.530952\pi$
$938$	27.9770	0.913483
$939$	−4.48059	−0.146218
$940$	−3.65791	−0.119308
$941$	51.8602	1.69060	0.845298	−	0.534296i	$-0.179423\pi$
$941$	51.8602	1.69060	0.845298	+	0.534296i	$0.179423\pi$
$942$	−53.4383	−1.74111
$943$	11.5714	0.376817
$944$	−12.2203	−0.397737
$945$	10.3912	0.338025
$946$	27.4507	0.892501
$947$	12.6954	0.412545	0.206272	−	0.978495i	$-0.433867\pi$
$947$	12.6954	0.412545	0.206272	+	0.978495i	$0.433867\pi$
$948$	43.4522	1.41126
$949$	11.7884	0.382669
$950$	89.2167	2.89457
$951$	−22.4466	−0.727879
$952$	95.3180	3.08927
$953$	5.42171	0.175626	0.0878132	−	0.996137i	$-0.472012\pi$
$953$	5.42171	0.175626	0.0878132	+	0.996137i	$0.472012\pi$
$954$	7.26582	0.235240
$955$	−6.45405	−0.208848
$956$	13.3528	0.431859
$957$	−1.80481	−0.0583413
$958$	36.0446	1.16455
$959$	80.7607	2.60790
$960$	−21.3153	−0.687949
$961$	−19.5471	−0.630552
$962$	16.4752	0.531182
$963$	6.89380	0.222150
$964$	−112.339	−3.61819
$965$	1.97499	0.0635773
$966$	−98.2873	−3.16234
$967$	24.0998	0.774997	0.387499	−	0.921870i	$-0.373339\pi$
$967$	24.0998	0.774997	0.387499	+	0.921870i	$0.373339\pi$
$968$	93.9384	3.01929
$969$	24.2418	0.778758
$970$	−9.91959	−0.318499
$971$	9.18241	0.294677	0.147339	−	0.989086i	$-0.452929\pi$
$971$	9.18241	0.294677	0.147339	+	0.989086i	$0.452929\pi$
$972$	−30.0565	−0.964061
$973$	51.8812	1.66323
$974$	−112.838	−3.61558
$975$	−5.38397	−0.172425
$976$	−61.5076	−1.96881
$977$	−25.4682	−0.814799	−0.407399	−	0.913250i	$-0.633564\pi$
$977$	−25.4682	−0.814799	−0.407399	+	0.913250i	$0.633564\pi$
$978$	−87.5035	−2.79805
$979$	−17.9600	−0.574005
$980$	28.2925	0.903772
$981$	−4.35649	−0.139092
$982$	−77.8360	−2.48385
$983$	−40.2857	−1.28492	−0.642458	−	0.766321i	$-0.722085\pi$
$983$	−40.2857	−1.28492	−0.642458	+	0.766321i	$0.722085\pi$
$984$	−33.2527	−1.06006
$985$	−10.2543	−0.326728
$986$	6.51929	0.207616
$987$	10.5644	0.336268
$988$	−26.4995	−0.843061
$989$	47.7427	1.51813
$990$	0.690686	0.0219514
$991$	10.8526	0.344745	0.172372	−	0.985032i	$-0.444857\pi$
$991$	10.8526	0.344745	0.172372	+	0.985032i	$0.444857\pi$
$992$	76.7314	2.43622
$993$	1.89553	0.0601529
$994$	111.077	3.52316
$995$	8.87198	0.281261
$996$	107.617	3.40998
$997$	−22.4709	−0.711660	−0.355830	−	0.934551i	$-0.615802\pi$
$997$	−22.4709	−0.711660	−0.355830	+	0.934551i	$0.615802\pi$
$998$	−58.2099	−1.84260
$999$	46.8847	1.48337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.3	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.3	✓	159	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73932 q^{2} -1.57093 q^{3} +5.50386 q^{4} +0.430202 q^{5} +4.30328 q^{6} +4.35305 q^{7} -9.59817 q^{8} -0.532177 q^{9} +O(q^{10})\)	\(q-2.73932 q^{2} -1.57093 q^{3} +5.50386 q^{4} +0.430202 q^{5} +4.30328 q^{6} +4.35305 q^{7} -9.59817 q^{8} -0.532177 q^{9} -1.17846 q^{10} +1.10131 q^{11} -8.64618 q^{12} -0.711797 q^{13} -11.9244 q^{14} -0.675817 q^{15} +15.2847 q^{16} -2.28135 q^{17} +1.45780 q^{18} +6.76417 q^{19} +2.36777 q^{20} -6.83834 q^{21} -3.01684 q^{22} -5.24693 q^{23} +15.0781 q^{24} -4.81493 q^{25} +1.94984 q^{26} +5.54880 q^{27} +23.9585 q^{28} +1.04319 q^{29} +1.85128 q^{30} -3.38421 q^{31} -22.6734 q^{32} -1.73008 q^{33} +6.24935 q^{34} +1.87269 q^{35} -2.92902 q^{36} +8.44952 q^{37} -18.5292 q^{38} +1.11818 q^{39} -4.12915 q^{40} -2.20537 q^{41} +18.7324 q^{42} -9.09917 q^{43} +6.06146 q^{44} -0.228943 q^{45} +14.3730 q^{46} -1.54488 q^{47} -24.0112 q^{48} +11.9490 q^{49} +13.1896 q^{50} +3.58385 q^{51} -3.91763 q^{52} +4.98410 q^{53} -15.1999 q^{54} +0.473786 q^{55} -41.7813 q^{56} -10.6260 q^{57} -2.85764 q^{58} -0.799511 q^{59} -3.71960 q^{60} -4.02412 q^{61} +9.27042 q^{62} -2.31659 q^{63} +31.5400 q^{64} -0.306217 q^{65} +4.73925 q^{66} -2.34621 q^{67} -12.5562 q^{68} +8.24256 q^{69} -5.12989 q^{70} -9.31516 q^{71} +5.10792 q^{72} -16.5615 q^{73} -23.1459 q^{74} +7.56392 q^{75} +37.2290 q^{76} +4.79406 q^{77} -3.06306 q^{78} -5.02560 q^{79} +6.57552 q^{80} -7.12026 q^{81} +6.04121 q^{82} -12.4468 q^{83} -37.6372 q^{84} -0.981443 q^{85} +24.9255 q^{86} -1.63879 q^{87} -10.5706 q^{88} -16.3078 q^{89} +0.627149 q^{90} -3.09849 q^{91} -28.8783 q^{92} +5.31636 q^{93} +4.23190 q^{94} +2.90996 q^{95} +35.6183 q^{96} +8.41742 q^{97} -32.7321 q^{98} -0.586092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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