LMFDB - Embedded newform 6034.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.10273.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + x + 2 $ x^4 - 2x^3 - 5x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.641043$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.64104 q^{3} +1.00000 q^{4} +2.78585 q^{5} +1.64104 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.306978 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.64104 q^{3} +1.00000 q^{4} +2.78585 q^{5} +1.64104 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.306978 q^{9} -2.78585 q^{10} -1.52113 q^{11} -1.64104 q^{12} +6.42689 q^{13} -1.00000 q^{14} -4.57170 q^{15} +1.00000 q^{16} -3.35896 q^{17} +0.306978 q^{18} -4.59879 q^{19} +2.78585 q^{20} -1.64104 q^{21} +1.52113 q^{22} -1.97511 q^{23} +1.64104 q^{24} +2.76096 q^{25} -6.42689 q^{26} +5.42689 q^{27} +1.00000 q^{28} +6.47887 q^{29} +4.57170 q^{30} -6.93066 q^{31} -1.00000 q^{32} +2.49624 q^{33} +3.35896 q^{34} +2.78585 q^{35} -0.306978 q^{36} +1.16217 q^{37} +4.59879 q^{38} -10.5468 q^{39} -2.78585 q^{40} +7.13368 q^{41} +1.64104 q^{42} -11.4872 q^{43} -1.52113 q^{44} -0.855193 q^{45} +1.97511 q^{46} -3.99859 q^{47} -1.64104 q^{48} +1.00000 q^{49} -2.76096 q^{50} +5.51219 q^{51} +6.42689 q^{52} -4.80321 q^{53} -5.42689 q^{54} -4.23763 q^{55} -1.00000 q^{56} +7.54681 q^{57} -6.47887 q^{58} -5.33407 q^{59} -4.57170 q^{60} +2.33407 q^{61} +6.93066 q^{62} -0.306978 q^{63} +1.00000 q^{64} +17.9044 q^{65} -2.49624 q^{66} +0.212742 q^{67} -3.35896 q^{68} +3.24124 q^{69} -2.78585 q^{70} -8.69381 q^{71} +0.306978 q^{72} -8.66672 q^{73} -1.16217 q^{74} -4.53085 q^{75} -4.59879 q^{76} -1.52113 q^{77} +10.5468 q^{78} +6.66813 q^{79} +2.78585 q^{80} -7.98483 q^{81} -7.13368 q^{82} -1.26613 q^{83} -1.64104 q^{84} -9.35755 q^{85} +11.4872 q^{86} -10.6321 q^{87} +1.52113 q^{88} +2.92533 q^{89} +0.855193 q^{90} +6.42689 q^{91} -1.97511 q^{92} +11.3735 q^{93} +3.99859 q^{94} -12.8115 q^{95} +1.64104 q^{96} -3.20302 q^{97} -1.00000 q^{98} +0.466952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - q^{10} - 13 q^{11} - 2 q^{12} + 11 q^{13} - 4 q^{14} + 2 q^{15} + 4 q^{16} - 18 q^{17} - 2 q^{18} + q^{20} - 2 q^{21} + 13 q^{22} - 2 q^{23} + 2 q^{24} - 5 q^{25} - 11 q^{26} + 7 q^{27} + 4 q^{28} + 19 q^{29} - 2 q^{30} - 12 q^{31} - 4 q^{32} + 11 q^{33} + 18 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 16 q^{39} - q^{40} - 6 q^{41} + 2 q^{42} + 2 q^{43} - 13 q^{44} - 9 q^{45} + 2 q^{46} + 19 q^{47} - 2 q^{48} + 4 q^{49} + 5 q^{50} - 4 q^{51} + 11 q^{52} - 17 q^{53} - 7 q^{54} + 2 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 20 q^{59} + 2 q^{60} + 8 q^{61} + 12 q^{62} + 2 q^{63} + 4 q^{64} + 15 q^{65} - 11 q^{66} - 24 q^{67} - 18 q^{68} + 25 q^{69} - q^{70} + q^{71} - 2 q^{72} + 3 q^{73} - 7 q^{74} - 19 q^{75} - 13 q^{77} + 16 q^{78} + 24 q^{79} + q^{80} - 20 q^{81} + 6 q^{82} - 23 q^{83} - 2 q^{84} - 7 q^{85} - 2 q^{86} - 5 q^{87} + 13 q^{88} - 6 q^{89} + 9 q^{90} + 11 q^{91} - 2 q^{92} - 12 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} + 6 q^{97} - 4 q^{98} + 5 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - q^10 - 13 * q^11 - 2 * q^12 + 11 * q^13 - 4 * q^14 + 2 * q^15 + 4 * q^16 - 18 * q^17 - 2 * q^18 + q^20 - 2 * q^21 + 13 * q^22 - 2 * q^23 + 2 * q^24 - 5 * q^25 - 11 * q^26 + 7 * q^27 + 4 * q^28 + 19 * q^29 - 2 * q^30 - 12 * q^31 - 4 * q^32 + 11 * q^33 + 18 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 16 * q^39 - q^40 - 6 * q^41 + 2 * q^42 + 2 * q^43 - 13 * q^44 - 9 * q^45 + 2 * q^46 + 19 * q^47 - 2 * q^48 + 4 * q^49 + 5 * q^50 - 4 * q^51 + 11 * q^52 - 17 * q^53 - 7 * q^54 + 2 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 20 * q^59 + 2 * q^60 + 8 * q^61 + 12 * q^62 + 2 * q^63 + 4 * q^64 + 15 * q^65 - 11 * q^66 - 24 * q^67 - 18 * q^68 + 25 * q^69 - q^70 + q^71 - 2 * q^72 + 3 * q^73 - 7 * q^74 - 19 * q^75 - 13 * q^77 + 16 * q^78 + 24 * q^79 + q^80 - 20 * q^81 + 6 * q^82 - 23 * q^83 - 2 * q^84 - 7 * q^85 - 2 * q^86 - 5 * q^87 + 13 * q^88 - 6 * q^89 + 9 * q^90 + 11 * q^91 - 2 * q^92 - 12 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 + 6 * q^97 - 4 * q^98 + 5 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.64104	−0.947457	−0.473728	−	0.880671i	$-0.657092\pi$
$3$	−1.64104	−0.947457	−0.473728	+	0.880671i	$0.657092\pi$
$4$	1.00000	0.500000
$5$	2.78585	1.24587	0.622935	−	0.782274i	$-0.285940\pi$
$5$	2.78585	1.24587	0.622935	+	0.782274i	$0.285940\pi$
$6$	1.64104	0.669953
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.306978	−0.102326
$10$	−2.78585	−0.880963
$11$	−1.52113	−0.458637	−0.229319	−	0.973351i	$-0.573650\pi$
$11$	−1.52113	−0.458637	−0.229319	+	0.973351i	$0.573650\pi$
$12$	−1.64104	−0.473728
$13$	6.42689	1.78250	0.891250	−	0.453513i	$-0.149829\pi$
$13$	6.42689	1.78250	0.891250	+	0.453513i	$0.149829\pi$
$14$	−1.00000	−0.267261
$15$	−4.57170	−1.18041
$16$	1.00000	0.250000
$17$	−3.35896	−0.814667	−0.407333	−	0.913280i	$-0.633541\pi$
$17$	−3.35896	−0.814667	−0.407333	+	0.913280i	$0.633541\pi$
$18$	0.306978	0.0723553
$19$	−4.59879	−1.05503	−0.527517	−	0.849544i	$-0.676877\pi$
$19$	−4.59879	−1.05503	−0.527517	+	0.849544i	$0.676877\pi$
$20$	2.78585	0.622935
$21$	−1.64104	−0.358105
$22$	1.52113	0.324306
$23$	−1.97511	−0.411839	−0.205919	−	0.978569i	$-0.566018\pi$
$23$	−1.97511	−0.411839	−0.205919	+	0.978569i	$0.566018\pi$
$24$	1.64104	0.334977
$25$	2.76096	0.552192
$26$	−6.42689	−1.26042
$27$	5.42689	1.04441
$28$	1.00000	0.188982
$29$	6.47887	1.20310	0.601548	−	0.798837i	$-0.294551\pi$
$29$	6.47887	1.20310	0.601548	+	0.798837i	$0.294551\pi$
$30$	4.57170	0.834674
$31$	−6.93066	−1.24478	−0.622391	−	0.782706i	$-0.713839\pi$
$31$	−6.93066	−1.24478	−0.622391	+	0.782706i	$0.713839\pi$
$32$	−1.00000	−0.176777
$33$	2.49624	0.434539
$34$	3.35896	0.576056
$35$	2.78585	0.470895
$36$	−0.306978	−0.0511629
$37$	1.16217	0.191060	0.0955299	−	0.995427i	$-0.469545\pi$
$37$	1.16217	0.191060	0.0955299	+	0.995427i	$0.469545\pi$
$38$	4.59879	0.746022
$39$	−10.5468	−1.68884
$40$	−2.78585	−0.440482
$41$	7.13368	1.11409	0.557046	−	0.830481i	$-0.311935\pi$
$41$	7.13368	1.11409	0.557046	+	0.830481i	$0.311935\pi$
$42$	1.64104	0.253218
$43$	−11.4872	−1.75178	−0.875890	−	0.482511i	$-0.839725\pi$
$43$	−11.4872	−1.75178	−0.875890	+	0.482511i	$0.839725\pi$
$44$	−1.52113	−0.229319
$45$	−0.855193	−0.127485
$46$	1.97511	0.291214
$47$	−3.99859	−0.583255	−0.291627	−	0.956532i	$-0.594197\pi$
$47$	−3.99859	−0.583255	−0.291627	+	0.956532i	$0.594197\pi$
$48$	−1.64104	−0.236864
$49$	1.00000	0.142857
$50$	−2.76096	−0.390458
$51$	5.51219	0.771861
$52$	6.42689	0.891250
$53$	−4.80321	−0.659772	−0.329886	−	0.944021i	$-0.607010\pi$
$53$	−4.80321	−0.659772	−0.329886	+	0.944021i	$0.607010\pi$
$54$	−5.42689	−0.738507
$55$	−4.23763	−0.571402
$56$	−1.00000	−0.133631
$57$	7.54681	0.999599
$58$	−6.47887	−0.850718
$59$	−5.33407	−0.694436	−0.347218	−	0.937784i	$-0.612874\pi$
$59$	−5.33407	−0.694436	−0.347218	+	0.937784i	$0.612874\pi$
$60$	−4.57170	−0.590204
$61$	2.33407	0.298846	0.149423	−	0.988773i	$-0.452258\pi$
$61$	2.33407	0.298846	0.149423	+	0.988773i	$0.452258\pi$
$62$	6.93066	0.880194
$63$	−0.306978	−0.0386755
$64$	1.00000	0.125000
$65$	17.9044	2.22076
$66$	−2.49624	−0.307265
$67$	0.212742	0.0259906	0.0129953	−	0.999916i	$-0.495863\pi$
$67$	0.212742	0.0259906	0.0129953	+	0.999916i	$0.495863\pi$
$68$	−3.35896	−0.407333
$69$	3.24124	0.390199
$70$	−2.78585	−0.332973
$71$	−8.69381	−1.03177	−0.515883	−	0.856659i	$-0.672536\pi$
$71$	−8.69381	−1.03177	−0.515883	+	0.856659i	$0.672536\pi$
$72$	0.306978	0.0361777
$73$	−8.66672	−1.01436	−0.507182	−	0.861839i	$-0.669313\pi$
$73$	−8.66672	−1.01436	−0.507182	+	0.861839i	$0.669313\pi$
$74$	−1.16217	−0.135100
$75$	−4.53085	−0.523178
$76$	−4.59879	−0.527517
$77$	−1.52113	−0.173349
$78$	10.5468	1.19419
$79$	6.66813	0.750223	0.375112	−	0.926980i	$-0.377604\pi$
$79$	6.66813	0.750223	0.375112	+	0.926980i	$0.377604\pi$
$80$	2.78585	0.311467
$81$	−7.98483	−0.887204
$82$	−7.13368	−0.787783
$83$	−1.26613	−0.138976	−0.0694879	−	0.997583i	$-0.522137\pi$
$83$	−1.26613	−0.138976	−0.0694879	+	0.997583i	$0.522137\pi$
$84$	−1.64104	−0.179052
$85$	−9.35755	−1.01497
$86$	11.4872	1.23870
$87$	−10.6321	−1.13988
$88$	1.52113	0.162153
$89$	2.92533	0.310084	0.155042	−	0.987908i	$-0.450449\pi$
$89$	2.92533	0.310084	0.155042	+	0.987908i	$0.450449\pi$
$90$	0.855193	0.0901453
$91$	6.42689	0.673721
$92$	−1.97511	−0.205919
$93$	11.3735	1.17938
$94$	3.99859	0.412423
$95$	−12.8115	−1.31444
$96$	1.64104	0.167488
$97$	−3.20302	−0.325217	−0.162609	−	0.986691i	$-0.551991\pi$
$97$	−3.20302	−0.325217	−0.162609	+	0.986691i	$0.551991\pi$
$98$	−1.00000	−0.101015
$99$	0.466952	0.0469305
$100$	2.76096	0.276096
$101$	−10.6894	−1.06364	−0.531818	−	0.846858i	$-0.678491\pi$
$101$	−10.6894	−1.06364	−0.531818	+	0.846858i	$0.678491\pi$
$102$	−5.51219	−0.545788
$103$	−4.09424	−0.403417	−0.201708	−	0.979446i	$-0.564649\pi$
$103$	−4.09424	−0.403417	−0.201708	+	0.979446i	$0.564649\pi$
$104$	−6.42689	−0.630209
$105$	−4.57170	−0.446152
$106$	4.80321	0.466529
$107$	−4.78365	−0.462453	−0.231227	−	0.972900i	$-0.574274\pi$
$107$	−4.78365	−0.462453	−0.231227	+	0.972900i	$0.574274\pi$
$108$	5.42689	0.522203
$109$	0.0270879	0.00259455	0.00129727	−	0.999999i	$-0.499587\pi$
$109$	0.0270879	0.00259455	0.00129727	+	0.999999i	$0.499587\pi$
$110$	4.23763	0.404043
$111$	−1.90717	−0.181021
$112$	1.00000	0.0944911
$113$	4.19005	0.394166	0.197083	−	0.980387i	$-0.436853\pi$
$113$	4.19005	0.394166	0.197083	+	0.980387i	$0.436853\pi$
$114$	−7.54681	−0.706823
$115$	−5.50236	−0.513097
$116$	6.47887	0.601548
$117$	−1.97291	−0.182396
$118$	5.33407	0.491041
$119$	−3.35896	−0.307915
$120$	4.57170	0.417337
$121$	−8.68617	−0.789652
$122$	−2.33407	−0.211316
$123$	−11.7067	−1.05555
$124$	−6.93066	−0.622391
$125$	−6.23763	−0.557911
$126$	0.306978	0.0273477
$127$	3.35896	0.298059	0.149030	−	0.988833i	$-0.452385\pi$
$127$	3.35896	0.298059	0.149030	+	0.988833i	$0.452385\pi$
$128$	−1.00000	−0.0883883
$129$	18.8510	1.65974
$130$	−17.9044	−1.57032
$131$	−12.1842	−1.06454	−0.532271	−	0.846574i	$-0.678661\pi$
$131$	−12.1842	−1.06454	−0.532271	+	0.846574i	$0.678661\pi$
$132$	2.49624	0.217270
$133$	−4.59879	−0.398765
$134$	−0.212742	−0.0183781
$135$	15.1185	1.30119
$136$	3.35896	0.288028
$137$	1.30917	0.111850	0.0559251	−	0.998435i	$-0.482189\pi$
$137$	1.30917	0.111850	0.0559251	+	0.998435i	$0.482189\pi$
$138$	−3.24124	−0.275913
$139$	−3.40745	−0.289016	−0.144508	−	0.989504i	$-0.546160\pi$
$139$	−3.40745	−0.289016	−0.144508	+	0.989504i	$0.546160\pi$
$140$	2.78585	0.235447
$141$	6.56186	0.552608
$142$	8.69381	0.729568
$143$	−9.77613	−0.817521
$144$	−0.306978	−0.0255815
$145$	18.0492	1.49890
$146$	8.66672	0.717263
$147$	−1.64104	−0.135351
$148$	1.16217	0.0955299
$149$	−12.1802	−0.997842	−0.498921	−	0.866648i	$-0.666270\pi$
$149$	−12.1802	−0.997842	−0.498921	+	0.866648i	$0.666270\pi$
$150$	4.53085	0.369942
$151$	17.4449	1.41965	0.709824	−	0.704379i	$-0.248774\pi$
$151$	17.4449	1.41965	0.709824	+	0.704379i	$0.248774\pi$
$152$	4.59879	0.373011
$153$	1.03112	0.0833615
$154$	1.52113	0.122576
$155$	−19.3078	−1.55084
$156$	−10.5468	−0.844420
$157$	−6.26331	−0.499867	−0.249933	−	0.968263i	$-0.580409\pi$
$157$	−6.26331	−0.499867	−0.249933	+	0.968263i	$0.580409\pi$
$158$	−6.66813	−0.530488
$159$	7.88228	0.625106
$160$	−2.78585	−0.220241
$161$	−1.97511	−0.155660
$162$	7.98483	0.627348
$163$	15.5725	1.21973	0.609866	−	0.792505i	$-0.291223\pi$
$163$	15.5725	1.21973	0.609866	+	0.792505i	$0.291223\pi$
$164$	7.13368	0.557046
$165$	6.95414	0.541379
$166$	1.26613	0.0982707
$167$	−8.29585	−0.641952	−0.320976	−	0.947087i	$-0.604011\pi$
$167$	−8.29585	−0.641952	−0.320976	+	0.947087i	$0.604011\pi$
$168$	1.64104	0.126609
$169$	28.3050	2.17730
$170$	9.35755	0.717691
$171$	1.41172	0.107957
$172$	−11.4872	−0.875890
$173$	−14.3367	−1.09000	−0.544999	−	0.838436i	$-0.683470\pi$
$173$	−14.3367	−1.09000	−0.544999	+	0.838436i	$0.683470\pi$
$174$	10.6321	0.806018
$175$	2.76096	0.208709
$176$	−1.52113	−0.114659
$177$	8.75343	0.657948
$178$	−2.92533	−0.219262
$179$	1.46151	0.109238	0.0546191	−	0.998507i	$-0.482606\pi$
$179$	1.46151	0.109238	0.0546191	+	0.998507i	$0.482606\pi$
$180$	−0.855193	−0.0637424
$181$	8.41858	0.625748	0.312874	−	0.949795i	$-0.398708\pi$
$181$	8.41858	0.625748	0.312874	+	0.949795i	$0.398708\pi$
$182$	−6.42689	−0.476393
$183$	−3.83030	−0.283144
$184$	1.97511	0.145607
$185$	3.23763	0.238036
$186$	−11.3735	−0.833946
$187$	5.10940	0.373637
$188$	−3.99859	−0.291627
$189$	5.42689	0.394748
$190$	12.8115	0.929446
$191$	−10.8107	−0.782238	−0.391119	−	0.920340i	$-0.627912\pi$
$191$	−10.8107	−0.782238	−0.391119	+	0.920340i	$0.627912\pi$
$192$	−1.64104	−0.118432
$193$	−14.4908	−1.04307	−0.521535	−	0.853230i	$-0.674640\pi$
$193$	−14.4908	−1.04307	−0.521535	+	0.853230i	$0.674640\pi$
$194$	3.20302	0.229963
$195$	−29.3818	−2.10408
$196$	1.00000	0.0714286
$197$	11.5899	0.825743	0.412871	−	0.910789i	$-0.364526\pi$
$197$	11.5899	0.825743	0.412871	+	0.910789i	$0.364526\pi$
$198$	−0.466952	−0.0331848
$199$	20.0145	1.41879	0.709397	−	0.704809i	$-0.248967\pi$
$199$	20.0145	1.41879	0.709397	+	0.704809i	$0.248967\pi$
$200$	−2.76096	−0.195229
$201$	−0.349119	−0.0246250
$202$	10.6894	0.752105
$203$	6.47887	0.454728
$204$	5.51219	0.385931
$205$	19.8733	1.38801
$206$	4.09424	0.285259
$207$	0.606314	0.0421417
$208$	6.42689	0.445625
$209$	6.99534	0.483878
$210$	4.57170	0.315477
$211$	15.2059	1.04682	0.523408	−	0.852082i	$-0.324660\pi$
$211$	15.2059	1.04682	0.523408	+	0.852082i	$0.324660\pi$
$212$	−4.80321	−0.329886
$213$	14.2669	0.977553
$214$	4.78365	0.327004
$215$	−32.0016	−2.18249
$216$	−5.42689	−0.369253
$217$	−6.93066	−0.470484
$218$	−0.0270879	−0.00183462
$219$	14.2225	0.961065
$220$	−4.23763	−0.285701
$221$	−21.5877	−1.45214
$222$	1.90717	0.128001
$223$	25.6653	1.71868	0.859338	−	0.511408i	$-0.170876\pi$
$223$	25.6653	1.71868	0.859338	+	0.511408i	$0.170876\pi$
$224$	−1.00000	−0.0668153
$225$	−0.847552	−0.0565035
$226$	−4.19005	−0.278718
$227$	14.1110	0.936579	0.468289	−	0.883575i	$-0.344870\pi$
$227$	14.1110	0.936579	0.468289	+	0.883575i	$0.344870\pi$
$228$	7.54681	0.499800
$229$	−5.91560	−0.390914	−0.195457	−	0.980712i	$-0.562619\pi$
$229$	−5.91560	−0.390914	−0.195457	+	0.980712i	$0.562619\pi$
$230$	5.50236	0.362815
$231$	2.49624	0.164240
$232$	−6.47887	−0.425359
$233$	4.30557	0.282067	0.141034	−	0.990005i	$-0.454957\pi$
$233$	4.30557	0.282067	0.141034	+	0.990005i	$0.454957\pi$
$234$	1.97291	0.128973
$235$	−11.1395	−0.726659
$236$	−5.33407	−0.347218
$237$	−10.9427	−0.710804
$238$	3.35896	0.217729
$239$	−11.0216	−0.712931	−0.356465	−	0.934309i	$-0.616018\pi$
$239$	−11.0216	−0.712931	−0.356465	+	0.934309i	$0.616018\pi$
$240$	−4.57170	−0.295102
$241$	0.198868	0.0128102	0.00640511	−	0.999979i	$-0.497961\pi$
$241$	0.198868	0.0128102	0.00640511	+	0.999979i	$0.497961\pi$
$242$	8.68617	0.558368
$243$	−3.17722	−0.203819
$244$	2.33407	0.149423
$245$	2.78585	0.177981
$246$	11.7067	0.746390
$247$	−29.5559	−1.88060
$248$	6.93066	0.440097
$249$	2.07777	0.131674
$250$	6.23763	0.394503
$251$	18.7271	1.18205	0.591023	−	0.806655i	$-0.298724\pi$
$251$	18.7271	1.18205	0.591023	+	0.806655i	$0.298724\pi$
$252$	−0.306978	−0.0193378
$253$	3.00439	0.188885
$254$	−3.35896	−0.210760
$255$	15.3561	0.961639
$256$	1.00000	0.0625000
$257$	4.09283	0.255304	0.127652	−	0.991819i	$-0.459256\pi$
$257$	4.09283	0.255304	0.127652	+	0.991819i	$0.459256\pi$
$258$	−18.8510	−1.17361
$259$	1.16217	0.0722138
$260$	17.9044	1.11038
$261$	−1.98887	−0.123108
$262$	12.1842	0.752745
$263$	19.9177	1.22818	0.614089	−	0.789237i	$-0.289524\pi$
$263$	19.9177	1.22818	0.614089	+	0.789237i	$0.289524\pi$
$264$	−2.49624	−0.153633
$265$	−13.3810	−0.821990
$266$	4.59879	0.281970
$267$	−4.80059	−0.293791
$268$	0.212742	0.0129953
$269$	−4.40330	−0.268474	−0.134237	−	0.990949i	$-0.542858\pi$
$269$	−4.40330	−0.268474	−0.134237	+	0.990949i	$0.542858\pi$
$270$	−15.1185	−0.920083
$271$	−2.95241	−0.179346	−0.0896732	−	0.995971i	$-0.528582\pi$
$271$	−2.95241	−0.179346	−0.0896732	+	0.995971i	$0.528582\pi$
$272$	−3.35896	−0.203667
$273$	−10.5468	−0.638322
$274$	−1.30917	−0.0790901
$275$	−4.19977	−0.253256
$276$	3.24124	0.195100
$277$	−11.2912	−0.678422	−0.339211	−	0.940710i	$-0.610160\pi$
$277$	−11.2912	−0.678422	−0.339211	+	0.940710i	$0.610160\pi$
$278$	3.40745	0.204365
$279$	2.12756	0.127373
$280$	−2.78585	−0.166486
$281$	−17.1402	−1.02250	−0.511248	−	0.859433i	$-0.670817\pi$
$281$	−17.1402	−1.02250	−0.511248	+	0.859433i	$0.670817\pi$
$282$	−6.56186	−0.390753
$283$	−12.6238	−0.750407	−0.375203	−	0.926943i	$-0.622427\pi$
$283$	−12.6238	−0.750407	−0.375203	+	0.926943i	$0.622427\pi$
$284$	−8.69381	−0.515883
$285$	21.0243	1.24537
$286$	9.77613	0.578074
$287$	7.13368	0.421088
$288$	0.306978	0.0180888
$289$	−5.71741	−0.336318
$290$	−18.0492	−1.05988
$291$	5.25629	0.308129
$292$	−8.66672	−0.507182
$293$	9.28366	0.542357	0.271179	−	0.962529i	$-0.412587\pi$
$293$	9.28366	0.542357	0.271179	+	0.962529i	$0.412587\pi$
$294$	1.64104	0.0957076
$295$	−14.8599	−0.865177
$296$	−1.16217	−0.0675498
$297$	−8.25500	−0.479004
$298$	12.1802	0.705581
$299$	−12.6938	−0.734102
$300$	−4.53085	−0.261589
$301$	−11.4872	−0.662110
$302$	−17.4449	−1.00384
$303$	17.5418	1.00775
$304$	−4.59879	−0.263759
$305$	6.50236	0.372324
$306$	−1.03112	−0.0589455
$307$	−23.4344	−1.33747	−0.668736	−	0.743500i	$-0.733165\pi$
$307$	−23.4344	−1.33747	−0.668736	+	0.743500i	$0.733165\pi$
$308$	−1.52113	−0.0866743
$309$	6.71882	0.382220
$310$	19.3078	1.09661
$311$	−4.57739	−0.259560	−0.129780	−	0.991543i	$-0.541427\pi$
$311$	−4.57739	−0.259560	−0.129780	+	0.991543i	$0.541427\pi$
$312$	10.5468	0.597095
$313$	−26.3419	−1.48893	−0.744465	−	0.667661i	$-0.767296\pi$
$313$	−26.3419	−1.48893	−0.744465	+	0.667661i	$0.767296\pi$
$314$	6.26331	0.353459
$315$	−0.855193	−0.0481847
$316$	6.66813	0.375112
$317$	−25.9481	−1.45739	−0.728695	−	0.684839i	$-0.759873\pi$
$317$	−25.9481	−1.45739	−0.728695	+	0.684839i	$0.759873\pi$
$318$	−7.88228	−0.442016
$319$	−9.85519	−0.551785
$320$	2.78585	0.155734
$321$	7.85018	0.438154
$322$	1.97511	0.110068
$323$	15.4471	0.859501
$324$	−7.98483	−0.443602
$325$	17.7444	0.984281
$326$	−15.5725	−0.862480
$327$	−0.0444524	−0.00245822
$328$	−7.13368	−0.393891
$329$	−3.99859	−0.220450
$330$	−6.95414	−0.382813
$331$	−2.85818	−0.157100	−0.0785498	−	0.996910i	$-0.525029\pi$
$331$	−2.85818	−0.157100	−0.0785498	+	0.996910i	$0.525029\pi$
$332$	−1.26613	−0.0694879
$333$	−0.356760	−0.0195504
$334$	8.29585	0.453929
$335$	0.592668	0.0323809
$336$	−1.64104	−0.0895262
$337$	25.3311	1.37987	0.689937	−	0.723869i	$-0.257638\pi$
$337$	25.3311	1.37987	0.689937	+	0.723869i	$0.257638\pi$
$338$	−28.3050	−1.53959
$339$	−6.87605	−0.373456
$340$	−9.35755	−0.507484
$341$	10.5424	0.570904
$342$	−1.41172	−0.0763373
$343$	1.00000	0.0539949
$344$	11.4872	0.619348
$345$	9.02960	0.486137
$346$	14.3367	0.770745
$347$	9.81827	0.527072	0.263536	−	0.964650i	$-0.415111\pi$
$347$	9.81827	0.527072	0.263536	+	0.964650i	$0.415111\pi$
$348$	−10.6321	−0.569941
$349$	−21.7960	−1.16671	−0.583357	−	0.812216i	$-0.698261\pi$
$349$	−21.7960	−1.16671	−0.583357	+	0.812216i	$0.698261\pi$
$350$	−2.76096	−0.147579
$351$	34.8781	1.86165
$352$	1.52113	0.0810764
$353$	11.8649	0.631506	0.315753	−	0.948841i	$-0.397743\pi$
$353$	11.8649	0.631506	0.315753	+	0.948841i	$0.397743\pi$
$354$	−8.75343	−0.465240
$355$	−24.2196	−1.28545
$356$	2.92533	0.155042
$357$	5.51219	0.291736
$358$	−1.46151	−0.0772431
$359$	−29.1670	−1.53938	−0.769688	−	0.638421i	$-0.779588\pi$
$359$	−29.1670	−1.53938	−0.769688	+	0.638421i	$0.779588\pi$
$360$	0.855193	0.0450727
$361$	2.14884	0.113097
$362$	−8.41858	−0.442471
$363$	14.2544	0.748161
$364$	6.42689	0.336861
$365$	−24.1442	−1.26376
$366$	3.83030	0.200213
$367$	−8.84125	−0.461509	−0.230755	−	0.973012i	$-0.574119\pi$
$367$	−8.84125	−0.461509	−0.230755	+	0.973012i	$0.574119\pi$
$368$	−1.97511	−0.102960
$369$	−2.18988	−0.114001
$370$	−3.23763	−0.168317
$371$	−4.80321	−0.249370
$372$	11.3735	0.589689
$373$	9.48511	0.491120	0.245560	−	0.969381i	$-0.421028\pi$
$373$	9.48511	0.491120	0.245560	+	0.969381i	$0.421028\pi$
$374$	−5.10940	−0.264201
$375$	10.2362	0.528596
$376$	3.99859	0.206212
$377$	41.6390	2.14452
$378$	−5.42689	−0.279129
$379$	−21.3765	−1.09804	−0.549018	−	0.835810i	$-0.684998\pi$
$379$	−21.3765	−1.09804	−0.549018	+	0.835810i	$0.684998\pi$
$380$	−12.8115	−0.657218
$381$	−5.51219	−0.282398
$382$	10.8107	0.553126
$383$	−9.71521	−0.496424	−0.248212	−	0.968706i	$-0.579843\pi$
$383$	−9.71521	−0.496424	−0.248212	+	0.968706i	$0.579843\pi$
$384$	1.64104	0.0837441
$385$	−4.23763	−0.215970
$386$	14.4908	0.737562
$387$	3.52631	0.179252
$388$	−3.20302	−0.162609
$389$	−7.43363	−0.376900	−0.188450	−	0.982083i	$-0.560346\pi$
$389$	−7.43363	−0.376900	−0.188450	+	0.982083i	$0.560346\pi$
$390$	29.3818	1.48781
$391$	6.63430	0.335511
$392$	−1.00000	−0.0505076
$393$	19.9949	1.00861
$394$	−11.5899	−0.583888
$395$	18.5764	0.934681
$396$	0.466952	0.0234652
$397$	16.8754	0.846953	0.423477	−	0.905907i	$-0.360810\pi$
$397$	16.8754	0.846953	0.423477	+	0.905907i	$0.360810\pi$
$398$	−20.0145	−1.00324
$399$	7.54681	0.377813
$400$	2.76096	0.138048
$401$	35.4505	1.77032	0.885158	−	0.465291i	$-0.154050\pi$
$401$	35.4505	1.77032	0.885158	+	0.465291i	$0.154050\pi$
$402$	0.349119	0.0174125
$403$	−44.5426	−2.21882
$404$	−10.6894	−0.531818
$405$	−22.2445	−1.10534
$406$	−6.47887	−0.321541
$407$	−1.76781	−0.0876271
$408$	−5.51219	−0.272894
$409$	15.6689	0.774778	0.387389	−	0.921916i	$-0.373377\pi$
$409$	15.6689	0.774778	0.387389	+	0.921916i	$0.373377\pi$
$410$	−19.8733	−0.981475
$411$	−2.14841	−0.105973
$412$	−4.09424	−0.201708
$413$	−5.33407	−0.262472
$414$	−0.606314	−0.0297987
$415$	−3.52725	−0.173146
$416$	−6.42689	−0.315104
$417$	5.59177	0.273830
$418$	−6.99534	−0.342153
$419$	−37.6168	−1.83770	−0.918851	−	0.394604i	$-0.870882\pi$
$419$	−37.6168	−1.83770	−0.918851	+	0.394604i	$0.870882\pi$
$420$	−4.57170	−0.223076
$421$	4.87025	0.237361	0.118681	−	0.992932i	$-0.462134\pi$
$421$	4.87025	0.237361	0.118681	+	0.992932i	$0.462134\pi$
$422$	−15.2059	−0.740211
$423$	1.22748	0.0596820
$424$	4.80321	0.233265
$425$	−9.27394	−0.449852
$426$	−14.2669	−0.691234
$427$	2.33407	0.112953
$428$	−4.78365	−0.231227
$429$	16.0430	0.774565
$430$	32.0016	1.54325
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.42689	0.261101
$433$	−8.71106	−0.418627	−0.209313	−	0.977849i	$-0.567123\pi$
$433$	−8.71106	−0.418627	−0.209313	+	0.977849i	$0.567123\pi$
$434$	6.93066	0.332682
$435$	−29.6195	−1.42014
$436$	0.0270879	0.00129727
$437$	9.08310	0.434504
$438$	−14.2225	−0.679576
$439$	32.8552	1.56810	0.784048	−	0.620701i	$-0.213152\pi$
$439$	32.8552	1.56810	0.784048	+	0.620701i	$0.213152\pi$
$440$	4.23763	0.202021
$441$	−0.306978	−0.0146180
$442$	21.5877	1.02682
$443$	−18.3666	−0.872623	−0.436312	−	0.899796i	$-0.643715\pi$
$443$	−18.3666	−0.872623	−0.436312	+	0.899796i	$0.643715\pi$
$444$	−1.90717	−0.0905104
$445$	8.14952	0.386324
$446$	−25.6653	−1.21529
$447$	19.9882	0.945412
$448$	1.00000	0.0472456
$449$	−4.50596	−0.212649	−0.106325	−	0.994331i	$-0.533908\pi$
$449$	−4.50596	−0.212649	−0.106325	+	0.994331i	$0.533908\pi$
$450$	0.847552	0.0399540
$451$	−10.8512	−0.510965
$452$	4.19005	0.197083
$453$	−28.6279	−1.34506
$454$	−14.1110	−0.662261
$455$	17.9044	0.839369
$456$	−7.54681	−0.353412
$457$	−4.18706	−0.195863	−0.0979313	−	0.995193i	$-0.531223\pi$
$457$	−4.18706	−0.195863	−0.0979313	+	0.995193i	$0.531223\pi$
$458$	5.91560	0.276418
$459$	−18.2287	−0.850843
$460$	−5.50236	−0.256549
$461$	−31.4396	−1.46429	−0.732144	−	0.681150i	$-0.761480\pi$
$461$	−31.4396	−1.46429	−0.732144	+	0.681150i	$0.761480\pi$
$462$	−2.49624	−0.116135
$463$	37.4173	1.73893	0.869466	−	0.493994i	$-0.164463\pi$
$463$	37.4173	1.73893	0.869466	+	0.493994i	$0.164463\pi$
$464$	6.47887	0.300774
$465$	31.6849	1.46935
$466$	−4.30557	−0.199452
$467$	−16.5202	−0.764461	−0.382231	−	0.924067i	$-0.624844\pi$
$467$	−16.5202	−0.764461	−0.382231	+	0.924067i	$0.624844\pi$
$468$	−1.97291	−0.0911979
$469$	0.212742	0.00982353
$470$	11.1395	0.513826
$471$	10.2784	0.473602
$472$	5.33407	0.245520
$473$	17.4735	0.803432
$474$	10.9427	0.502614
$475$	−12.6971	−0.582581
$476$	−3.35896	−0.153958
$477$	1.47448	0.0675118
$478$	11.0216	0.504118
$479$	−31.8207	−1.45393	−0.726964	−	0.686676i	$-0.759069\pi$
$479$	−31.8207	−1.45393	−0.726964	+	0.686676i	$0.759069\pi$
$480$	4.57170	0.208669
$481$	7.46915	0.340564
$482$	−0.198868	−0.00905820
$483$	3.24124	0.147481
$484$	−8.68617	−0.394826
$485$	−8.92313	−0.405178
$486$	3.17722	0.144122
$487$	−4.82627	−0.218699	−0.109349	−	0.994003i	$-0.534877\pi$
$487$	−4.82627	−0.218699	−0.109349	+	0.994003i	$0.534877\pi$
$488$	−2.33407	−0.105658
$489$	−25.5551	−1.15564
$490$	−2.78585	−0.125852
$491$	5.54136	0.250078	0.125039	−	0.992152i	$-0.460094\pi$
$491$	5.54136	0.250078	0.125039	+	0.992152i	$0.460094\pi$
$492$	−11.7067	−0.527777
$493$	−21.7623	−0.980123
$494$	29.5559	1.32978
$495$	1.30086	0.0584692
$496$	−6.93066	−0.311196
$497$	−8.69381	−0.389971
$498$	−2.07777	−0.0931073
$499$	−10.9436	−0.489904	−0.244952	−	0.969535i	$-0.578772\pi$
$499$	−10.9436	−0.489904	−0.244952	+	0.969535i	$0.578772\pi$
$500$	−6.23763	−0.278955
$501$	13.6138	0.608222
$502$	−18.7271	−0.835833
$503$	−31.5574	−1.40708	−0.703538	−	0.710657i	$-0.748398\pi$
$503$	−31.5574	−1.40708	−0.703538	+	0.710657i	$0.748398\pi$
$504$	0.306978	0.0136739
$505$	−29.7791	−1.32515
$506$	−3.00439	−0.133562
$507$	−46.4496	−2.06290
$508$	3.35896	0.149030
$509$	12.5908	0.558077	0.279038	−	0.960280i	$-0.409984\pi$
$509$	12.5908	0.558077	0.279038	+	0.960280i	$0.409984\pi$
$510$	−15.3561	−0.679981
$511$	−8.66672	−0.383393
$512$	−1.00000	−0.0441942
$513$	−24.9571	−1.10188
$514$	−4.09283	−0.180527
$515$	−11.4059	−0.502605
$516$	18.8510	0.829868
$517$	6.08237	0.267502
$518$	−1.16217	−0.0510629
$519$	23.5271	1.03273
$520$	−17.9044	−0.785158
$521$	−29.6202	−1.29769	−0.648843	−	0.760922i	$-0.724747\pi$
$521$	−29.6202	−1.29769	−0.648843	+	0.760922i	$0.724747\pi$
$522$	1.98887	0.0870504
$523$	14.2405	0.622694	0.311347	−	0.950296i	$-0.399220\pi$
$523$	14.2405	0.622694	0.311347	+	0.950296i	$0.399220\pi$
$524$	−12.1842	−0.532271
$525$	−4.53085	−0.197743
$526$	−19.9177	−0.868452
$527$	23.2798	1.01408
$528$	2.49624	0.108635
$529$	−19.0989	−0.830389
$530$	13.3810	0.581235
$531$	1.63744	0.0710588
$532$	−4.59879	−0.199383
$533$	45.8474	1.98587
$534$	4.80059	0.207742
$535$	−13.3265	−0.576157
$536$	−0.212742	−0.00918907
$537$	−2.39840	−0.103498
$538$	4.40330	0.189840
$539$	−1.52113	−0.0655196
$540$	15.1185	0.650597
$541$	9.66092	0.415355	0.207678	−	0.978197i	$-0.433409\pi$
$541$	9.66092	0.415355	0.207678	+	0.978197i	$0.433409\pi$
$542$	2.95241	0.126817
$543$	−13.8152	−0.592869
$544$	3.35896	0.144014
$545$	0.0754627	0.00323247
$546$	10.5468	0.451362
$547$	−11.3780	−0.486490	−0.243245	−	0.969965i	$-0.578212\pi$
$547$	−11.3780	−0.486490	−0.243245	+	0.969965i	$0.578212\pi$
$548$	1.30917	0.0559251
$549$	−0.716506	−0.0305797
$550$	4.19977	0.179079
$551$	−29.7950	−1.26931
$552$	−3.24124	−0.137956
$553$	6.66813	0.283558
$554$	11.2912	0.479717
$555$	−5.31310	−0.225528
$556$	−3.40745	−0.144508
$557$	−31.5651	−1.33746	−0.668729	−	0.743506i	$-0.733161\pi$
$557$	−31.5651	−1.33746	−0.668729	+	0.743506i	$0.733161\pi$
$558$	−2.12756	−0.0900666
$559$	−73.8269	−3.12255
$560$	2.78585	0.117724
$561$	−8.38475	−0.354004
$562$	17.1402	0.723014
$563$	−3.26080	−0.137426	−0.0687132	−	0.997636i	$-0.521889\pi$
$563$	−3.26080	−0.137426	−0.0687132	+	0.997636i	$0.521889\pi$
$564$	6.56186	0.276304
$565$	11.6728	0.491080
$566$	12.6238	0.530618
$567$	−7.98483	−0.335331
$568$	8.69381	0.364784
$569$	−31.5401	−1.32223	−0.661114	−	0.750285i	$-0.729916\pi$
$569$	−31.5401	−1.32223	−0.661114	+	0.750285i	$0.729916\pi$
$570$	−21.0243	−0.880610
$571$	−11.7027	−0.489745	−0.244872	−	0.969555i	$-0.578746\pi$
$571$	−11.7027	−0.489745	−0.244872	+	0.969555i	$0.578746\pi$
$572$	−9.77613	−0.408760
$573$	17.7409	0.741136
$574$	−7.13368	−0.297754
$575$	−5.45319	−0.227414
$576$	−0.306978	−0.0127907
$577$	23.5432	0.980116	0.490058	−	0.871690i	$-0.336976\pi$
$577$	23.5432	0.980116	0.490058	+	0.871690i	$0.336976\pi$
$578$	5.71741	0.237813
$579$	23.7800	0.988264
$580$	18.0492	0.749451
$581$	−1.26613	−0.0525279
$582$	−5.25629	−0.217880
$583$	7.30630	0.302596
$584$	8.66672	0.358632
$585$	−5.49624	−0.227241
$586$	−9.28366	−0.383505
$587$	17.3441	0.715866	0.357933	−	0.933747i	$-0.383482\pi$
$587$	17.3441	0.715866	0.357933	+	0.933747i	$0.383482\pi$
$588$	−1.64104	−0.0676755
$589$	31.8726	1.31329
$590$	14.8599	0.611773
$591$	−19.0194	−0.782355
$592$	1.16217	0.0477649
$593$	24.9773	1.02569	0.512847	−	0.858480i	$-0.328591\pi$
$593$	24.9773	1.02569	0.512847	+	0.858480i	$0.328591\pi$
$594$	8.25500	0.338707
$595$	−9.35755	−0.383622
$596$	−12.1802	−0.498921
$597$	−32.8447	−1.34425
$598$	12.6938	0.519089
$599$	6.61835	0.270418	0.135209	−	0.990817i	$-0.456829\pi$
$599$	6.61835	0.270418	0.135209	+	0.990817i	$0.456829\pi$
$600$	4.53085	0.184971
$601$	−0.234763	−0.00957619	−0.00478809	−	0.999989i	$-0.501524\pi$
$601$	−0.234763	−0.00957619	−0.00478809	+	0.999989i	$0.501524\pi$
$602$	11.4872	0.468183
$603$	−0.0653071	−0.00265951
$604$	17.4449	0.709824
$605$	−24.1984	−0.983803
$606$	−17.5418	−0.712587
$607$	−19.2779	−0.782464	−0.391232	−	0.920292i	$-0.627951\pi$
$607$	−19.2779	−0.782464	−0.391232	+	0.920292i	$0.627951\pi$
$608$	4.59879	0.186505
$609$	−10.6321	−0.430835
$610$	−6.50236	−0.263273
$611$	−25.6985	−1.03965
$612$	1.03112	0.0416807
$613$	−31.0221	−1.25297	−0.626485	−	0.779434i	$-0.715507\pi$
$613$	−31.0221	−1.25297	−0.626485	+	0.779434i	$0.715507\pi$
$614$	23.4344	0.945736
$615$	−32.6130	−1.31508
$616$	1.52113	0.0612880
$617$	−27.5664	−1.10978	−0.554890	−	0.831924i	$-0.687240\pi$
$617$	−27.5664	−1.10978	−0.554890	+	0.831924i	$0.687240\pi$
$618$	−6.71882	−0.270270
$619$	−27.3462	−1.09913	−0.549567	−	0.835449i	$-0.685207\pi$
$619$	−27.3462	−1.09913	−0.549567	+	0.835449i	$0.685207\pi$
$620$	−19.3078	−0.775419
$621$	−10.7187	−0.430127
$622$	4.57739	0.183536
$623$	2.92533	0.117201
$624$	−10.5468	−0.422210
$625$	−31.1819	−1.24728
$626$	26.3419	1.05283
$627$	−11.4797	−0.458453
$628$	−6.26331	−0.249933
$629$	−3.90368	−0.155650
$630$	0.855193	0.0340717
$631$	−23.5590	−0.937871	−0.468935	−	0.883232i	$-0.655362\pi$
$631$	−23.5590	−0.937871	−0.468935	+	0.883232i	$0.655362\pi$
$632$	−6.66813	−0.265244
$633$	−24.9535	−0.991813
$634$	25.9481	1.03053
$635$	9.35755	0.371343
$636$	7.88228	0.312553
$637$	6.42689	0.254643
$638$	9.85519	0.390171
$639$	2.66881	0.105576
$640$	−2.78585	−0.110120
$641$	−7.41156	−0.292739	−0.146369	−	0.989230i	$-0.546759\pi$
$641$	−7.41156	−0.292739	−0.146369	+	0.989230i	$0.546759\pi$
$642$	−7.85018	−0.309822
$643$	−1.85256	−0.0730580	−0.0365290	−	0.999333i	$-0.511630\pi$
$643$	−1.85256	−0.0730580	−0.0365290	+	0.999333i	$0.511630\pi$
$644$	−1.97511	−0.0778302
$645$	52.5160	2.06781
$646$	−15.4471	−0.607759
$647$	16.2784	0.639969	0.319984	−	0.947423i	$-0.396322\pi$
$647$	16.2784	0.639969	0.319984	+	0.947423i	$0.396322\pi$
$648$	7.98483	0.313674
$649$	8.11380	0.318494
$650$	−17.7444	−0.695992
$651$	11.3735	0.445763
$652$	15.5725	0.609866
$653$	−12.0775	−0.472631	−0.236315	−	0.971676i	$-0.575940\pi$
$653$	−12.0775	−0.472631	−0.236315	+	0.971676i	$0.575940\pi$
$654$	0.0444524	0.00173823
$655$	−33.9435	−1.32628
$656$	7.13368	0.278523
$657$	2.66049	0.103796
$658$	3.99859	0.155881
$659$	−26.8532	−1.04605	−0.523025	−	0.852317i	$-0.675197\pi$
$659$	−26.8532	−1.04605	−0.523025	+	0.852317i	$0.675197\pi$
$660$	6.95414	0.270690
$661$	24.6569	0.959042	0.479521	−	0.877530i	$-0.340810\pi$
$661$	24.6569	0.959042	0.479521	+	0.877530i	$0.340810\pi$
$662$	2.85818	0.111086
$663$	35.4263	1.37584
$664$	1.26613	0.0491354
$665$	−12.8115	−0.496810
$666$	0.356760	0.0138242
$667$	−12.7965	−0.495482
$668$	−8.29585	−0.320976
$669$	−42.1179	−1.62837
$670$	−0.592668	−0.0228968
$671$	−3.55041	−0.137062
$672$	1.64104	0.0633046
$673$	−0.214825	−0.00828088	−0.00414044	−	0.999991i	$-0.501318\pi$
$673$	−0.214825	−0.00828088	−0.00414044	+	0.999991i	$0.501318\pi$
$674$	−25.3311	−0.975719
$675$	14.9834	0.576712
$676$	28.3050	1.08865
$677$	8.67515	0.333413	0.166707	−	0.986007i	$-0.446687\pi$
$677$	8.67515	0.333413	0.166707	+	0.986007i	$0.446687\pi$
$678$	6.87605	0.264073
$679$	−3.20302	−0.122921
$680$	9.35755	0.358846
$681$	−23.1567	−0.887368
$682$	−10.5424	−0.403690
$683$	−13.7488	−0.526082	−0.263041	−	0.964785i	$-0.584725\pi$
$683$	−13.7488	−0.526082	−0.263041	+	0.964785i	$0.584725\pi$
$684$	1.41172	0.0539786
$685$	3.64716	0.139351
$686$	−1.00000	−0.0381802
$687$	9.70776	0.370374
$688$	−11.4872	−0.437945
$689$	−30.8697	−1.17604
$690$	−9.02960	−0.343751
$691$	−43.3811	−1.65030	−0.825148	−	0.564916i	$-0.808908\pi$
$691$	−43.3811	−1.65030	−0.825148	+	0.564916i	$0.808908\pi$
$692$	−14.3367	−0.544999
$693$	0.466952	0.0177380
$694$	−9.81827	−0.372696
$695$	−9.49263	−0.360076
$696$	10.6321	0.403009
$697$	−23.9617	−0.907614
$698$	21.7960	0.824991
$699$	−7.06563	−0.267246
$700$	2.76096	0.104354
$701$	30.8568	1.16544	0.582722	−	0.812672i	$-0.301988\pi$
$701$	30.8568	1.16544	0.582722	+	0.812672i	$0.301988\pi$
$702$	−34.8781	−1.31639
$703$	−5.34458	−0.201575
$704$	−1.52113	−0.0573297
$705$	18.2804	0.688478
$706$	−11.8649	−0.446542
$707$	−10.6894	−0.402017
$708$	8.75343	0.328974
$709$	7.40671	0.278165	0.139082	−	0.990281i	$-0.455585\pi$
$709$	7.40671	0.278165	0.139082	+	0.990281i	$0.455585\pi$
$710$	24.2196	0.908947
$711$	−2.04697	−0.0767673
$712$	−2.92533	−0.109631
$713$	13.6888	0.512650
$714$	−5.51219	−0.206289
$715$	−27.2348	−1.01852
$716$	1.46151	0.0546191
$717$	18.0870	0.675471
$718$	29.1670	1.08850
$719$	25.1184	0.936758	0.468379	−	0.883528i	$-0.344838\pi$
$719$	25.1184	0.936758	0.468379	+	0.883528i	$0.344838\pi$
$720$	−0.855193	−0.0318712
$721$	−4.09424	−0.152477
$722$	−2.14884	−0.0799717
$723$	−0.326351	−0.0121371
$724$	8.41858	0.312874
$725$	17.8879	0.664340
$726$	−14.2544	−0.529030
$727$	−34.2961	−1.27197	−0.635986	−	0.771701i	$-0.719406\pi$
$727$	−34.2961	−1.27197	−0.635986	+	0.771701i	$0.719406\pi$
$728$	−6.42689	−0.238196
$729$	29.1685	1.08031
$730$	24.1442	0.893616
$731$	38.5850	1.42712
$732$	−3.83030	−0.141572
$733$	−4.61592	−0.170493	−0.0852465	−	0.996360i	$-0.527168\pi$
$733$	−4.61592	−0.170493	−0.0852465	+	0.996360i	$0.527168\pi$
$734$	8.84125	0.326336
$735$	−4.57170	−0.168630
$736$	1.97511	0.0728035
$737$	−0.323608	−0.0119203
$738$	2.18988	0.0806105
$739$	9.81545	0.361067	0.180534	−	0.983569i	$-0.442218\pi$
$739$	9.81545	0.361067	0.180534	+	0.983569i	$0.442218\pi$
$740$	3.23763	0.119018
$741$	48.5025	1.78178
$742$	4.80321	0.176332
$743$	−53.7770	−1.97289	−0.986443	−	0.164105i	$-0.947526\pi$
$743$	−53.7770	−1.97289	−0.986443	+	0.164105i	$0.947526\pi$
$744$	−11.3735	−0.416973
$745$	−33.9322	−1.24318
$746$	−9.48511	−0.347274
$747$	0.388673	0.0142208
$748$	5.10940	0.186818
$749$	−4.78365	−0.174791
$750$	−10.2362	−0.373774
$751$	14.1172	0.515144	0.257572	−	0.966259i	$-0.417077\pi$
$751$	14.1172	0.515144	0.257572	+	0.966259i	$0.417077\pi$
$752$	−3.99859	−0.145814
$753$	−30.7320	−1.11994
$754$	−41.6390	−1.51640
$755$	48.5990	1.76870
$756$	5.42689	0.197374
$757$	36.0879	1.31164	0.655819	−	0.754918i	$-0.272323\pi$
$757$	36.0879	1.31164	0.655819	+	0.754918i	$0.272323\pi$
$758$	21.3765	0.776429
$759$	−4.93034	−0.178960
$760$	12.8115	0.464723
$761$	−33.7547	−1.22361	−0.611804	−	0.791010i	$-0.709556\pi$
$761$	−33.7547	−1.22361	−0.611804	+	0.791010i	$0.709556\pi$
$762$	5.51219	0.199686
$763$	0.0270879	0.000980647 0
$764$	−10.8107	−0.391119
$765$	2.87256	0.103858
$766$	9.71521	0.351025
$767$	−34.2815	−1.23783
$768$	−1.64104	−0.0592160
$769$	−31.4843	−1.13535	−0.567676	−	0.823252i	$-0.692157\pi$
$769$	−31.4843	−1.13535	−0.567676	+	0.823252i	$0.692157\pi$
$770$	4.23763	0.152714
$771$	−6.71651	−0.241889
$772$	−14.4908	−0.521535
$773$	33.8933	1.21906	0.609529	−	0.792764i	$-0.291358\pi$
$773$	33.8933	1.21906	0.609529	+	0.792764i	$0.291358\pi$
$774$	−3.52631	−0.126751
$775$	−19.1353	−0.687359
$776$	3.20302	0.114982
$777$	−1.90717	−0.0684194
$778$	7.43363	0.266509
$779$	−32.8063	−1.17541
$780$	−29.3818	−1.05204
$781$	13.2244	0.473206
$782$	−6.63430	−0.237242
$783$	35.1601	1.25652
$784$	1.00000	0.0357143
$785$	−17.4487	−0.622769
$786$	−19.9949	−0.713194
$787$	22.1439	0.789346	0.394673	−	0.918822i	$-0.370858\pi$
$787$	22.1439	0.789346	0.394673	+	0.918822i	$0.370858\pi$
$788$	11.5899	0.412871
$789$	−32.6858	−1.16364
$790$	−18.5764	−0.660919
$791$	4.19005	0.148981
$792$	−0.466952	−0.0165924
$793$	15.0008	0.532694
$794$	−16.8754	−0.598887
$795$	21.9589	0.778800
$796$	20.0145	0.709397
$797$	−31.9959	−1.13335	−0.566677	−	0.823940i	$-0.691771\pi$
$797$	−31.9959	−1.13335	−0.566677	+	0.823940i	$0.691771\pi$
$798$	−7.54681	−0.267154
$799$	13.4311	0.475158
$800$	−2.76096	−0.0976146
$801$	−0.898009	−0.0317296
$802$	−35.4505	−1.25180
$803$	13.1832	0.465225
$804$	−0.349119	−0.0123125
$805$	−5.50236	−0.193933
$806$	44.5426	1.56895
$807$	7.22600	0.254367
$808$	10.6894	0.376052
$809$	−47.7594	−1.67913	−0.839565	−	0.543259i	$-0.817190\pi$
$809$	−47.7594	−1.67913	−0.839565	+	0.543259i	$0.817190\pi$
$810$	22.2445	0.781594
$811$	−4.07165	−0.142975	−0.0714876	−	0.997441i	$-0.522775\pi$
$811$	−4.07165	−0.142975	−0.0714876	+	0.997441i	$0.522775\pi$
$812$	6.47887	0.227364
$813$	4.84504	0.169923
$814$	1.76781	0.0619617
$815$	43.3826	1.51963
$816$	5.51219	0.192965
$817$	52.8271	1.84819
$818$	−15.6689	−0.547851
$819$	−1.97291	−0.0689391
$820$	19.8733	0.694007
$821$	−2.12665	−0.0742207	−0.0371104	−	0.999311i	$-0.511815\pi$
$821$	−2.12665	−0.0742207	−0.0371104	+	0.999311i	$0.511815\pi$
$822$	2.14841	0.0749344
$823$	23.9926	0.836331	0.418165	−	0.908371i	$-0.362673\pi$
$823$	23.9926	0.836331	0.418165	+	0.908371i	$0.362673\pi$
$824$	4.09424	0.142629
$825$	6.89200	0.239949
$826$	5.33407	0.185596
$827$	−16.8652	−0.586462	−0.293231	−	0.956042i	$-0.594730\pi$
$827$	−16.8652	−0.586462	−0.293231	+	0.956042i	$0.594730\pi$
$828$	0.606314	0.0210709
$829$	4.21040	0.146233	0.0731166	−	0.997323i	$-0.476705\pi$
$829$	4.21040	0.146233	0.0731166	+	0.997323i	$0.476705\pi$
$830$	3.52725	0.122433
$831$	18.5293	0.642775
$832$	6.42689	0.222812
$833$	−3.35896	−0.116381
$834$	−5.59177	−0.193627
$835$	−23.1110	−0.799788
$836$	6.99534	0.241939
$837$	−37.6119	−1.30006
$838$	37.6168	1.29945
$839$	51.4691	1.77691	0.888455	−	0.458963i	$-0.151779\pi$
$839$	51.4691	1.77691	0.888455	+	0.458963i	$0.151779\pi$
$840$	4.57170	0.157739
$841$	12.9758	0.447441
$842$	−4.87025	−0.167840
$843$	28.1277	0.968770
$844$	15.2059	0.523408
$845$	78.8533	2.71264
$846$	−1.22748	−0.0422016
$847$	−8.68617	−0.298460
$848$	−4.80321	−0.164943
$849$	20.7162	0.710978
$850$	9.27394	0.318094
$851$	−2.29541	−0.0786858
$852$	14.2669	0.488777
$853$	36.4803	1.24906	0.624531	−	0.781000i	$-0.285290\pi$
$853$	36.4803	1.24906	0.624531	+	0.781000i	$0.285290\pi$
$854$	−2.33407	−0.0798701
$855$	3.93285	0.134501
$856$	4.78365	0.163502
$857$	9.29570	0.317535	0.158767	−	0.987316i	$-0.449248\pi$
$857$	9.29570	0.317535	0.158767	+	0.987316i	$0.449248\pi$
$858$	−16.0430	−0.547701
$859$	−17.6335	−0.601648	−0.300824	−	0.953680i	$-0.597262\pi$
$859$	−17.6335	−0.601648	−0.300824	+	0.953680i	$0.597262\pi$
$860$	−32.0016	−1.09124
$861$	−11.7067	−0.398962
$862$	−1.00000	−0.0340601
$863$	25.0420	0.852439	0.426220	−	0.904620i	$-0.359845\pi$
$863$	25.0420	0.852439	0.426220	+	0.904620i	$0.359845\pi$
$864$	−5.42689	−0.184627
$865$	−39.9399	−1.35800
$866$	8.71106	0.296014
$867$	9.38251	0.318647
$868$	−6.93066	−0.235242
$869$	−10.1431	−0.344080
$870$	29.6195	1.00419
$871$	1.36727	0.0463283
$872$	−0.0270879	−0.000917311 0
$873$	0.983255	0.0332781
$874$	−9.08310	−0.307241
$875$	−6.23763	−0.210871
$876$	14.2225	0.480533
$877$	25.9415	0.875983	0.437992	−	0.898979i	$-0.355690\pi$
$877$	25.9415	0.875983	0.437992	+	0.898979i	$0.355690\pi$
$878$	−32.8552	−1.10881
$879$	−15.2349	−0.513860
$880$	−4.23763	−0.142851
$881$	25.9868	0.875519	0.437759	−	0.899092i	$-0.355772\pi$
$881$	25.9868	0.875519	0.437759	+	0.899092i	$0.355772\pi$
$882$	0.306978	0.0103365
$883$	45.8432	1.54275	0.771373	−	0.636383i	$-0.219570\pi$
$883$	45.8432	1.54275	0.771373	+	0.636383i	$0.219570\pi$
$884$	−21.5877	−0.726071
$885$	24.3857	0.819718
$886$	18.3666	0.617038
$887$	18.4249	0.618648	0.309324	−	0.950957i	$-0.399897\pi$
$887$	18.4249	0.618648	0.309324	+	0.950957i	$0.399897\pi$
$888$	1.90717	0.0640005
$889$	3.35896	0.112656
$890$	−8.14952	−0.273172
$891$	12.1460	0.406905
$892$	25.6653	0.859338
$893$	18.3887	0.615353
$894$	−19.9882	−0.668507
$895$	4.07154	0.136097
$896$	−1.00000	−0.0334077
$897$	20.8311	0.695530
$898$	4.50596	0.150366
$899$	−44.9028	−1.49759
$900$	−0.847552	−0.0282517
$901$	16.1338	0.537494
$902$	10.8512	0.361307
$903$	18.8510	0.627321
$904$	−4.19005	−0.139359
$905$	23.4529	0.779600
$906$	28.6279	0.951098
$907$	−50.7916	−1.68651	−0.843253	−	0.537516i	$-0.819363\pi$
$907$	−50.7916	−1.68651	−0.843253	+	0.537516i	$0.819363\pi$
$908$	14.1110	0.468289
$909$	3.28141	0.108838
$910$	−17.9044	−0.593524
$911$	−27.1495	−0.899504	−0.449752	−	0.893154i	$-0.648488\pi$
$911$	−27.1495	−0.899504	−0.449752	+	0.893154i	$0.648488\pi$
$912$	7.54681	0.249900
$913$	1.92595	0.0637395
$914$	4.18706	0.138496
$915$	−10.6706	−0.352761
$916$	−5.91560	−0.195457
$917$	−12.1842	−0.402359
$918$	18.2287	0.601637
$919$	34.5642	1.14017	0.570084	−	0.821586i	$-0.306911\pi$
$919$	34.5642	1.14017	0.570084	+	0.821586i	$0.306911\pi$
$920$	5.50236	0.181407
$921$	38.4569	1.26720
$922$	31.4396	1.03541
$923$	−55.8742	−1.83912
$924$	2.49624	0.0821202
$925$	3.20871	0.105502
$926$	−37.4173	−1.22961
$927$	1.25684	0.0412800
$928$	−6.47887	−0.212679
$929$	11.9168	0.390978	0.195489	−	0.980706i	$-0.437371\pi$
$929$	11.9168	0.390978	0.195489	+	0.980706i	$0.437371\pi$
$930$	−31.6849	−1.03899
$931$	−4.59879	−0.150719
$932$	4.30557	0.141034
$933$	7.51169	0.245922
$934$	16.5202	0.540556
$935$	14.2340	0.465503
$936$	1.97291	0.0644867
$937$	17.0016	0.555417	0.277709	−	0.960665i	$-0.410425\pi$
$937$	17.0016	0.555417	0.277709	+	0.960665i	$0.410425\pi$
$938$	−0.212742	−0.00694628
$939$	43.2282	1.41070
$940$	−11.1395	−0.363330
$941$	−40.6819	−1.32619	−0.663097	−	0.748534i	$-0.730758\pi$
$941$	−40.6819	−1.32619	−0.663097	+	0.748534i	$0.730758\pi$
$942$	−10.2784	−0.334887
$943$	−14.0898	−0.458826
$944$	−5.33407	−0.173609
$945$	15.1185	0.491805
$946$	−17.4735	−0.568112
$947$	−14.2619	−0.463448	−0.231724	−	0.972782i	$-0.574437\pi$
$947$	−14.2619	−0.463448	−0.231724	+	0.972782i	$0.574437\pi$
$948$	−10.9427	−0.355402
$949$	−55.7001	−1.80810
$950$	12.6971	0.411947
$951$	42.5819	1.38081
$952$	3.35896	0.108864
$953$	−49.3293	−1.59793	−0.798967	−	0.601375i	$-0.794620\pi$
$953$	−49.3293	−1.59793	−0.798967	+	0.601375i	$0.794620\pi$
$954$	−1.47448	−0.0477380
$955$	−30.1171	−0.974566
$956$	−11.0216	−0.356465
$957$	16.1728	0.522792
$958$	31.8207	1.02808
$959$	1.30917	0.0422754
$960$	−4.57170	−0.147551
$961$	17.0340	0.549484
$962$	−7.46915	−0.240815
$963$	1.46847	0.0473209
$964$	0.198868	0.00640511
$965$	−40.3692	−1.29953
$966$	−3.24124	−0.104285
$967$	−57.6267	−1.85315	−0.926575	−	0.376110i	$-0.877262\pi$
$967$	−57.6267	−1.85315	−0.926575	+	0.376110i	$0.877262\pi$
$968$	8.68617	0.279184
$969$	−25.3494	−0.814340
$970$	8.92313	0.286504
$971$	47.0514	1.50995	0.754976	−	0.655753i	$-0.227649\pi$
$971$	47.0514	1.50995	0.754976	+	0.655753i	$0.227649\pi$
$972$	−3.17722	−0.101910
$973$	−3.40745	−0.109238
$974$	4.82627	0.154644
$975$	−29.1193	−0.932564
$976$	2.33407	0.0747116
$977$	−27.7239	−0.886966	−0.443483	−	0.896283i	$-0.646257\pi$
$977$	−27.7239	−0.886966	−0.443483	+	0.896283i	$0.646257\pi$
$978$	25.5551	0.817163
$979$	−4.44979	−0.142216
$980$	2.78585	0.0889907
$981$	−0.00831537	−0.000265489 0
$982$	−5.54136	−0.176832
$983$	29.5720	0.943200	0.471600	−	0.881813i	$-0.343677\pi$
$983$	29.5720	0.943200	0.471600	+	0.881813i	$0.343677\pi$
$984$	11.7067	0.373195
$985$	32.2876	1.02877
$986$	21.7623	0.693051
$987$	6.56186	0.208866
$988$	−29.5559	−0.940299
$989$	22.6884	0.721450
$990$	−1.30086	−0.0413440
$991$	−17.8842	−0.568110	−0.284055	−	0.958808i	$-0.591680\pi$
$991$	−17.8842	−0.568110	−0.284055	+	0.958808i	$0.591680\pi$
$992$	6.93066	0.220049
$993$	4.69039	0.148845
$994$	8.69381	0.275751
$995$	55.7575	1.76763
$996$	2.07777	0.0658368
$997$	36.1027	1.14338	0.571691	−	0.820469i	$-0.306287\pi$
$997$	36.1027	1.14338	0.571691	+	0.820469i	$0.306287\pi$
$998$	10.9436	0.346414
$999$	6.30698	0.199544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.j.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.j.1.2	✓	4	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.64104 q^{3} +1.00000 q^{4} +2.78585 q^{5} +1.64104 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.306978 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.64104 q^{3} +1.00000 q^{4} +2.78585 q^{5} +1.64104 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.306978 q^{9} -2.78585 q^{10} -1.52113 q^{11} -1.64104 q^{12} +6.42689 q^{13} -1.00000 q^{14} -4.57170 q^{15} +1.00000 q^{16} -3.35896 q^{17} +0.306978 q^{18} -4.59879 q^{19} +2.78585 q^{20} -1.64104 q^{21} +1.52113 q^{22} -1.97511 q^{23} +1.64104 q^{24} +2.76096 q^{25} -6.42689 q^{26} +5.42689 q^{27} +1.00000 q^{28} +6.47887 q^{29} +4.57170 q^{30} -6.93066 q^{31} -1.00000 q^{32} +2.49624 q^{33} +3.35896 q^{34} +2.78585 q^{35} -0.306978 q^{36} +1.16217 q^{37} +4.59879 q^{38} -10.5468 q^{39} -2.78585 q^{40} +7.13368 q^{41} +1.64104 q^{42} -11.4872 q^{43} -1.52113 q^{44} -0.855193 q^{45} +1.97511 q^{46} -3.99859 q^{47} -1.64104 q^{48} +1.00000 q^{49} -2.76096 q^{50} +5.51219 q^{51} +6.42689 q^{52} -4.80321 q^{53} -5.42689 q^{54} -4.23763 q^{55} -1.00000 q^{56} +7.54681 q^{57} -6.47887 q^{58} -5.33407 q^{59} -4.57170 q^{60} +2.33407 q^{61} +6.93066 q^{62} -0.306978 q^{63} +1.00000 q^{64} +17.9044 q^{65} -2.49624 q^{66} +0.212742 q^{67} -3.35896 q^{68} +3.24124 q^{69} -2.78585 q^{70} -8.69381 q^{71} +0.306978 q^{72} -8.66672 q^{73} -1.16217 q^{74} -4.53085 q^{75} -4.59879 q^{76} -1.52113 q^{77} +10.5468 q^{78} +6.66813 q^{79} +2.78585 q^{80} -7.98483 q^{81} -7.13368 q^{82} -1.26613 q^{83} -1.64104 q^{84} -9.35755 q^{85} +11.4872 q^{86} -10.6321 q^{87} +1.52113 q^{88} +2.92533 q^{89} +0.855193 q^{90} +6.42689 q^{91} -1.97511 q^{92} +11.3735 q^{93} +3.99859 q^{94} -12.8115 q^{95} +1.64104 q^{96} -3.20302 q^{97} -1.00000 q^{98} +0.466952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q - 4 q^{2} - 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - q^{10} - 13 q^{11} - 2 q^{12} + 11 q^{13} - 4 q^{14} + 2 q^{15} + 4 q^{16} - 18 q^{17} - 2 q^{18} + q^{20} - 2 q^{21} + 13 q^{22} - 2 q^{23} + 2 q^{24} - 5 q^{25} - 11 q^{26} + 7 q^{27} + 4 q^{28} + 19 q^{29} - 2 q^{30} - 12 q^{31} - 4 q^{32} + 11 q^{33} + 18 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 16 q^{39} - q^{40} - 6 q^{41} + 2 q^{42} + 2 q^{43} - 13 q^{44} - 9 q^{45} + 2 q^{46} + 19 q^{47} - 2 q^{48} + 4 q^{49} + 5 q^{50} - 4 q^{51} + 11 q^{52} - 17 q^{53} - 7 q^{54} + 2 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 20 q^{59} + 2 q^{60} + 8 q^{61} + 12 q^{62} + 2 q^{63} + 4 q^{64} + 15 q^{65} - 11 q^{66} - 24 q^{67} - 18 q^{68} + 25 q^{69} - q^{70} + q^{71} - 2 q^{72} + 3 q^{73} - 7 q^{74} - 19 q^{75} - 13 q^{77} + 16 q^{78} + 24 q^{79} + q^{80} - 20 q^{81} + 6 q^{82} - 23 q^{83} - 2 q^{84} - 7 q^{85} - 2 q^{86} - 5 q^{87} + 13 q^{88} - 6 q^{89} + 9 q^{90} + 11 q^{91} - 2 q^{92} - 12 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} + 6 q^{97} - 4 q^{98} + 5 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - q^10 - 13 * q^11 - 2 * q^12 + 11 * q^13 - 4 * q^14 + 2 * q^15 + 4 * q^16 - 18 * q^17 - 2 * q^18 + q^20 - 2 * q^21 + 13 * q^22 - 2 * q^23 + 2 * q^24 - 5 * q^25 - 11 * q^26 + 7 * q^27 + 4 * q^28 + 19 * q^29 - 2 * q^30 - 12 * q^31 - 4 * q^32 + 11 * q^33 + 18 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 16 * q^39 - q^40 - 6 * q^41 + 2 * q^42 + 2 * q^43 - 13 * q^44 - 9 * q^45 + 2 * q^46 + 19 * q^47 - 2 * q^48 + 4 * q^49 + 5 * q^50 - 4 * q^51 + 11 * q^52 - 17 * q^53 - 7 * q^54 + 2 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 20 * q^59 + 2 * q^60 + 8 * q^61 + 12 * q^62 + 2 * q^63 + 4 * q^64 + 15 * q^65 - 11 * q^66 - 24 * q^67 - 18 * q^68 + 25 * q^69 - q^70 + q^71 - 2 * q^72 + 3 * q^73 - 7 * q^74 - 19 * q^75 - 13 * q^77 + 16 * q^78 + 24 * q^79 + q^80 - 20 * q^81 + 6 * q^82 - 23 * q^83 - 2 * q^84 - 7 * q^85 - 2 * q^86 - 5 * q^87 + 13 * q^88 - 6 * q^89 + 9 * q^90 + 11 * q^91 - 2 * q^92 - 12 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 + 6 * q^97 - 4 * q^98 + 5 * q^99

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