LMFDB - Embedded newform 6034.2.a.k.1.18

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$2.16480$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.16480 q^{3} +1.00000 q^{4} +2.31808 q^{5} -2.16480 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.68636 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.16480 q^{3} +1.00000 q^{4} +2.31808 q^{5} -2.16480 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.68636 q^{9} -2.31808 q^{10} -2.02748 q^{11} +2.16480 q^{12} -6.49960 q^{13} -1.00000 q^{14} +5.01819 q^{15} +1.00000 q^{16} -0.702324 q^{17} -1.68636 q^{18} +5.38439 q^{19} +2.31808 q^{20} +2.16480 q^{21} +2.02748 q^{22} -5.42533 q^{23} -2.16480 q^{24} +0.373505 q^{25} +6.49960 q^{26} -2.84377 q^{27} +1.00000 q^{28} -6.36220 q^{29} -5.01819 q^{30} -1.22501 q^{31} -1.00000 q^{32} -4.38910 q^{33} +0.702324 q^{34} +2.31808 q^{35} +1.68636 q^{36} -10.0433 q^{37} -5.38439 q^{38} -14.0703 q^{39} -2.31808 q^{40} -11.7428 q^{41} -2.16480 q^{42} +4.20358 q^{43} -2.02748 q^{44} +3.90912 q^{45} +5.42533 q^{46} -2.99155 q^{47} +2.16480 q^{48} +1.00000 q^{49} -0.373505 q^{50} -1.52039 q^{51} -6.49960 q^{52} -14.0555 q^{53} +2.84377 q^{54} -4.69988 q^{55} -1.00000 q^{56} +11.6561 q^{57} +6.36220 q^{58} +6.33839 q^{59} +5.01819 q^{60} -5.37609 q^{61} +1.22501 q^{62} +1.68636 q^{63} +1.00000 q^{64} -15.0666 q^{65} +4.38910 q^{66} +12.6623 q^{67} -0.702324 q^{68} -11.7448 q^{69} -2.31808 q^{70} +16.2922 q^{71} -1.68636 q^{72} +7.68520 q^{73} +10.0433 q^{74} +0.808563 q^{75} +5.38439 q^{76} -2.02748 q^{77} +14.0703 q^{78} -4.54547 q^{79} +2.31808 q^{80} -11.2153 q^{81} +11.7428 q^{82} +4.58808 q^{83} +2.16480 q^{84} -1.62805 q^{85} -4.20358 q^{86} -13.7729 q^{87} +2.02748 q^{88} -5.32923 q^{89} -3.90912 q^{90} -6.49960 q^{91} -5.42533 q^{92} -2.65190 q^{93} +2.99155 q^{94} +12.4815 q^{95} -2.16480 q^{96} +0.483759 q^{97} -1.00000 q^{98} -3.41907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	2.16480	1.24985	0.624924	−	0.780686i	$-0.285130\pi$
$3$	2.16480	1.24985	0.624924	+	0.780686i	$0.285130\pi$
$4$	1.00000	0.500000
$5$	2.31808	1.03668	0.518339	−	0.855175i	$-0.326551\pi$
$5$	2.31808	1.03668	0.518339	+	0.855175i	$0.326551\pi$
$6$	−2.16480	−0.883776
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.68636	0.562120
$10$	−2.31808	−0.733042
$11$	−2.02748	−0.611310	−0.305655	−	0.952142i	$-0.598875\pi$
$11$	−2.02748	−0.611310	−0.305655	+	0.952142i	$0.598875\pi$
$12$	2.16480	0.624924
$13$	−6.49960	−1.80266	−0.901332	−	0.433128i	$-0.857410\pi$
$13$	−6.49960	−1.80266	−0.901332	+	0.433128i	$0.857410\pi$
$14$	−1.00000	−0.267261
$15$	5.01819	1.29569
$16$	1.00000	0.250000
$17$	−0.702324	−0.170339	−0.0851693	−	0.996366i	$-0.527143\pi$
$17$	−0.702324	−0.170339	−0.0851693	+	0.996366i	$0.527143\pi$
$18$	−1.68636	−0.397479
$19$	5.38439	1.23526	0.617632	−	0.786467i	$-0.288092\pi$
$19$	5.38439	1.23526	0.617632	+	0.786467i	$0.288092\pi$
$20$	2.31808	0.518339
$21$	2.16480	0.472398
$22$	2.02748	0.432261
$23$	−5.42533	−1.13126	−0.565630	−	0.824659i	$-0.691367\pi$
$23$	−5.42533	−1.13126	−0.565630	+	0.824659i	$0.691367\pi$
$24$	−2.16480	−0.441888
$25$	0.373505	0.0747009
$26$	6.49960	1.27468
$27$	−2.84377	−0.547283
$28$	1.00000	0.188982
$29$	−6.36220	−1.18143	−0.590715	−	0.806880i	$-0.701154\pi$
$29$	−6.36220	−1.18143	−0.590715	+	0.806880i	$0.701154\pi$
$30$	−5.01819	−0.916191
$31$	−1.22501	−0.220018	−0.110009	−	0.993931i	$-0.535088\pi$
$31$	−1.22501	−0.220018	−0.110009	+	0.993931i	$0.535088\pi$
$32$	−1.00000	−0.176777
$33$	−4.38910	−0.764044
$34$	0.702324	0.120448
$35$	2.31808	0.391827
$36$	1.68636	0.281060
$37$	−10.0433	−1.65111	−0.825557	−	0.564319i	$-0.809139\pi$
$37$	−10.0433	−1.65111	−0.825557	+	0.564319i	$0.809139\pi$
$38$	−5.38439	−0.873464
$39$	−14.0703	−2.25306
$40$	−2.31808	−0.366521
$41$	−11.7428	−1.83391	−0.916957	−	0.398985i	$-0.869362\pi$
$41$	−11.7428	−1.83391	−0.916957	+	0.398985i	$0.869362\pi$
$42$	−2.16480	−0.334036
$43$	4.20358	0.641039	0.320520	−	0.947242i	$-0.396142\pi$
$43$	4.20358	0.641039	0.320520	+	0.947242i	$0.396142\pi$
$44$	−2.02748	−0.305655
$45$	3.90912	0.582738
$46$	5.42533	0.799921
$47$	−2.99155	−0.436362	−0.218181	−	0.975908i	$-0.570012\pi$
$47$	−2.99155	−0.436362	−0.218181	+	0.975908i	$0.570012\pi$
$48$	2.16480	0.312462
$49$	1.00000	0.142857
$50$	−0.373505	−0.0528215
$51$	−1.52039	−0.212897
$52$	−6.49960	−0.901332
$53$	−14.0555	−1.93067	−0.965337	−	0.261008i	$-0.915945\pi$
$53$	−14.0555	−1.93067	−0.965337	+	0.261008i	$0.915945\pi$
$54$	2.84377	0.386988
$55$	−4.69988	−0.633731
$56$	−1.00000	−0.133631
$57$	11.6561	1.54389
$58$	6.36220	0.835398
$59$	6.33839	0.825187	0.412594	−	0.910915i	$-0.364623\pi$
$59$	6.33839	0.825187	0.412594	+	0.910915i	$0.364623\pi$
$60$	5.01819	0.647845
$61$	−5.37609	−0.688338	−0.344169	−	0.938908i	$-0.611839\pi$
$61$	−5.37609	−0.688338	−0.344169	+	0.938908i	$0.611839\pi$
$62$	1.22501	0.155576
$63$	1.68636	0.212462
$64$	1.00000	0.125000
$65$	−15.0666	−1.86878
$66$	4.38910	0.540261
$67$	12.6623	1.54694	0.773471	−	0.633831i	$-0.218519\pi$
$67$	12.6623	1.54694	0.773471	+	0.633831i	$0.218519\pi$
$68$	−0.702324	−0.0851693
$69$	−11.7448	−1.41390
$70$	−2.31808	−0.277064
$71$	16.2922	1.93353	0.966765	−	0.255668i	$-0.0822955\pi$
$71$	16.2922	1.93353	0.966765	+	0.255668i	$0.0822955\pi$
$72$	−1.68636	−0.198740
$73$	7.68520	0.899485	0.449743	−	0.893158i	$-0.351516\pi$
$73$	7.68520	0.899485	0.449743	+	0.893158i	$0.351516\pi$
$74$	10.0433	1.16751
$75$	0.808563	0.0933648
$76$	5.38439	0.617632
$77$	−2.02748	−0.231053
$78$	14.0703	1.59315
$79$	−4.54547	−0.511405	−0.255702	−	0.966756i	$-0.582307\pi$
$79$	−4.54547	−0.511405	−0.255702	+	0.966756i	$0.582307\pi$
$80$	2.31808	0.259169
$81$	−11.2153	−1.24614
$82$	11.7428	1.29677
$83$	4.58808	0.503608	0.251804	−	0.967778i	$-0.418976\pi$
$83$	4.58808	0.503608	0.251804	+	0.967778i	$0.418976\pi$
$84$	2.16480	0.236199
$85$	−1.62805	−0.176586
$86$	−4.20358	−0.453283
$87$	−13.7729	−1.47661
$88$	2.02748	0.216131
$89$	−5.32923	−0.564897	−0.282449	−	0.959282i	$-0.591147\pi$
$89$	−5.32923	−0.564897	−0.282449	+	0.959282i	$0.591147\pi$
$90$	−3.90912	−0.412058
$91$	−6.49960	−0.681343
$92$	−5.42533	−0.565630
$93$	−2.65190	−0.274989
$94$	2.99155	0.308554
$95$	12.4815	1.28057
$96$	−2.16480	−0.220944
$97$	0.483759	0.0491183	0.0245592	−	0.999698i	$-0.492182\pi$
$97$	0.483759	0.0491183	0.0245592	+	0.999698i	$0.492182\pi$
$98$	−1.00000	−0.101015
$99$	−3.41907	−0.343630
$100$	0.373505	0.0373505
$101$	5.01242	0.498755	0.249377	−	0.968406i	$-0.419774\pi$
$101$	5.01242	0.498755	0.249377	+	0.968406i	$0.419774\pi$
$102$	1.52039	0.150541
$103$	−4.87426	−0.480275	−0.240138	−	0.970739i	$-0.577193\pi$
$103$	−4.87426	−0.480275	−0.240138	+	0.970739i	$0.577193\pi$
$104$	6.49960	0.637338
$105$	5.01819	0.489725
$106$	14.0555	1.36519
$107$	3.18736	0.308134	0.154067	−	0.988060i	$-0.450763\pi$
$107$	3.18736	0.308134	0.154067	+	0.988060i	$0.450763\pi$
$108$	−2.84377	−0.273642
$109$	3.46908	0.332278	0.166139	−	0.986102i	$-0.446870\pi$
$109$	3.46908	0.332278	0.166139	+	0.986102i	$0.446870\pi$
$110$	4.69988	0.448116
$111$	−21.7418	−2.06364
$112$	1.00000	0.0944911
$113$	−5.63928	−0.530499	−0.265249	−	0.964180i	$-0.585454\pi$
$113$	−5.63928	−0.530499	−0.265249	+	0.964180i	$0.585454\pi$
$114$	−11.6561	−1.09170
$115$	−12.5764	−1.17275
$116$	−6.36220	−0.590715
$117$	−10.9607	−1.01331
$118$	−6.33839	−0.583496
$119$	−0.702324	−0.0643820
$120$	−5.01819	−0.458096
$121$	−6.88931	−0.626301
$122$	5.37609	0.486728
$123$	−25.4208	−2.29211
$124$	−1.22501	−0.110009
$125$	−10.7246	−0.959237
$126$	−1.68636	−0.150233
$127$	−8.28688	−0.735341	−0.367671	−	0.929956i	$-0.619845\pi$
$127$	−8.28688	−0.735341	−0.367671	+	0.929956i	$0.619845\pi$
$128$	−1.00000	−0.0883883
$129$	9.09990	0.801202
$130$	15.0666	1.32143
$131$	−12.2588	−1.07106	−0.535530	−	0.844516i	$-0.679888\pi$
$131$	−12.2588	−1.07106	−0.535530	+	0.844516i	$0.679888\pi$
$132$	−4.38910	−0.382022
$133$	5.38439	0.466886
$134$	−12.6623	−1.09385
$135$	−6.59208	−0.567356
$136$	0.702324	0.0602238
$137$	13.5579	1.15833	0.579165	−	0.815211i	$-0.303379\pi$
$137$	13.5579	1.15833	0.579165	+	0.815211i	$0.303379\pi$
$138$	11.7448	0.999780
$139$	11.4226	0.968851	0.484425	−	0.874833i	$-0.339029\pi$
$139$	11.4226	0.968851	0.484425	+	0.874833i	$0.339029\pi$
$140$	2.31808	0.195914
$141$	−6.47610	−0.545386
$142$	−16.2922	−1.36721
$143$	13.1778	1.10199
$144$	1.68636	0.140530
$145$	−14.7481	−1.22476
$146$	−7.68520	−0.636032
$147$	2.16480	0.178550
$148$	−10.0433	−0.825557
$149$	8.76538	0.718088	0.359044	−	0.933321i	$-0.383103\pi$
$149$	8.76538	0.718088	0.359044	+	0.933321i	$0.383103\pi$
$150$	−0.808563	−0.0660189
$151$	−16.8115	−1.36810	−0.684050	−	0.729435i	$-0.739783\pi$
$151$	−16.8115	−1.36810	−0.684050	+	0.729435i	$0.739783\pi$
$152$	−5.38439	−0.436732
$153$	−1.18437	−0.0957508
$154$	2.02748	0.163379
$155$	−2.83967	−0.228088
$156$	−14.0703	−1.12653
$157$	−17.8909	−1.42785	−0.713923	−	0.700224i	$-0.753084\pi$
$157$	−17.8909	−1.42785	−0.713923	+	0.700224i	$0.753084\pi$
$158$	4.54547	0.361618
$159$	−30.4274	−2.41305
$160$	−2.31808	−0.183260
$161$	−5.42533	−0.427576
$162$	11.2153	0.881155
$163$	16.7641	1.31307	0.656533	−	0.754298i	$-0.272022\pi$
$163$	16.7641	1.31307	0.656533	+	0.754298i	$0.272022\pi$
$164$	−11.7428	−0.916957
$165$	−10.1743	−0.792068
$166$	−4.58808	−0.356104
$167$	23.8146	1.84283	0.921414	−	0.388581i	$-0.127035\pi$
$167$	23.8146	1.84283	0.921414	+	0.388581i	$0.127035\pi$
$168$	−2.16480	−0.167018
$169$	29.2448	2.24960
$170$	1.62805	0.124865
$171$	9.08003	0.694367
$172$	4.20358	0.320520
$173$	−7.54430	−0.573582	−0.286791	−	0.957993i	$-0.592589\pi$
$173$	−7.54430	−0.573582	−0.286791	+	0.957993i	$0.592589\pi$
$174$	13.7729	1.04412
$175$	0.373505	0.0282343
$176$	−2.02748	−0.152827
$177$	13.7213	1.03136
$178$	5.32923	0.399443
$179$	−5.99628	−0.448183	−0.224091	−	0.974568i	$-0.571941\pi$
$179$	−5.99628	−0.448183	−0.224091	+	0.974568i	$0.571941\pi$
$180$	3.90912	0.291369
$181$	0.451470	0.0335575	0.0167788	−	0.999859i	$-0.494659\pi$
$181$	0.451470	0.0335575	0.0167788	+	0.999859i	$0.494659\pi$
$182$	6.49960	0.481782
$183$	−11.6382	−0.860318
$184$	5.42533	0.399961
$185$	−23.2813	−1.71167
$186$	2.65190	0.194447
$187$	1.42395	0.104130
$188$	−2.99155	−0.218181
$189$	−2.84377	−0.206854
$190$	−12.4815	−0.905501
$191$	−26.5612	−1.92190	−0.960952	−	0.276716i	$-0.910754\pi$
$191$	−26.5612	−1.92190	−0.960952	+	0.276716i	$0.910754\pi$
$192$	2.16480	0.156231
$193$	16.4767	1.18602	0.593011	−	0.805195i	$-0.297939\pi$
$193$	16.4767	1.18602	0.593011	+	0.805195i	$0.297939\pi$
$194$	−0.483759	−0.0347319
$195$	−32.6162	−2.33569
$196$	1.00000	0.0714286
$197$	−18.6023	−1.32536	−0.662678	−	0.748905i	$-0.730580\pi$
$197$	−18.6023	−1.32536	−0.662678	+	0.748905i	$0.730580\pi$
$198$	3.41907	0.242983
$199$	9.75627	0.691604	0.345802	−	0.938308i	$-0.387607\pi$
$199$	9.75627	0.691604	0.345802	+	0.938308i	$0.387607\pi$
$200$	−0.373505	−0.0264108
$201$	27.4113	1.93344
$202$	−5.01242	−0.352673
$203$	−6.36220	−0.446539
$204$	−1.52039	−0.106449
$205$	−27.2207	−1.90118
$206$	4.87426	0.339606
$207$	−9.14907	−0.635904
$208$	−6.49960	−0.450666
$209$	−10.9168	−0.755129
$210$	−5.01819	−0.346288
$211$	19.3837	1.33443	0.667214	−	0.744866i	$-0.267487\pi$
$211$	19.3837	1.33443	0.667214	+	0.744866i	$0.267487\pi$
$212$	−14.0555	−0.965337
$213$	35.2694	2.41662
$214$	−3.18736	−0.217883
$215$	9.74423	0.664551
$216$	2.84377	0.193494
$217$	−1.22501	−0.0831591
$218$	−3.46908	−0.234956
$219$	16.6369	1.12422
$220$	−4.69988	−0.316866
$221$	4.56483	0.307063
$222$	21.7418	1.45921
$223$	19.2154	1.28676	0.643378	−	0.765549i	$-0.277532\pi$
$223$	19.2154	1.28676	0.643378	+	0.765549i	$0.277532\pi$
$224$	−1.00000	−0.0668153
$225$	0.629863	0.0419909
$226$	5.63928	0.375119
$227$	21.8926	1.45306	0.726530	−	0.687135i	$-0.241132\pi$
$227$	21.8926	1.45306	0.726530	+	0.687135i	$0.241132\pi$
$228$	11.6561	0.771947
$229$	−4.82395	−0.318775	−0.159388	−	0.987216i	$-0.550952\pi$
$229$	−4.82395	−0.318775	−0.159388	+	0.987216i	$0.550952\pi$
$230$	12.5764	0.829261
$231$	−4.38910	−0.288782
$232$	6.36220	0.417699
$233$	15.3063	1.00275	0.501373	−	0.865231i	$-0.332828\pi$
$233$	15.3063	1.00275	0.501373	+	0.865231i	$0.332828\pi$
$234$	10.9607	0.716522
$235$	−6.93465	−0.452367
$236$	6.33839	0.412594
$237$	−9.84003	−0.639178
$238$	0.702324	0.0455249
$239$	23.9954	1.55213	0.776065	−	0.630652i	$-0.217213\pi$
$239$	23.9954	1.55213	0.776065	+	0.630652i	$0.217213\pi$
$240$	5.01819	0.323922
$241$	5.40550	0.348199	0.174099	−	0.984728i	$-0.444299\pi$
$241$	5.40550	0.348199	0.174099	+	0.984728i	$0.444299\pi$
$242$	6.88931	0.442861
$243$	−15.7475	−1.01020
$244$	−5.37609	−0.344169
$245$	2.31808	0.148097
$246$	25.4208	1.62077
$247$	−34.9964	−2.22677
$248$	1.22501	0.0777882
$249$	9.93228	0.629433
$250$	10.7246	0.678283
$251$	−14.8552	−0.937653	−0.468826	−	0.883290i	$-0.655323\pi$
$251$	−14.8552	−0.937653	−0.468826	+	0.883290i	$0.655323\pi$
$252$	1.68636	0.106231
$253$	10.9998	0.691550
$254$	8.28688	0.519965
$255$	−3.52439	−0.220706
$256$	1.00000	0.0625000
$257$	30.3163	1.89108	0.945540	−	0.325506i	$-0.105535\pi$
$257$	30.3163	1.89108	0.945540	+	0.325506i	$0.105535\pi$
$258$	−9.09990	−0.566535
$259$	−10.0433	−0.624062
$260$	−15.0666	−0.934391
$261$	−10.7290	−0.664106
$262$	12.2588	0.757354
$263$	20.7403	1.27890	0.639452	−	0.768831i	$-0.279161\pi$
$263$	20.7403	1.27890	0.639452	+	0.768831i	$0.279161\pi$
$264$	4.38910	0.270130
$265$	−32.5818	−2.00149
$266$	−5.38439	−0.330138
$267$	−11.5367	−0.706036
$268$	12.6623	0.773471
$269$	0.0392147	0.00239096	0.00119548	−	0.999999i	$-0.499619\pi$
$269$	0.0392147	0.00239096	0.00119548	+	0.999999i	$0.499619\pi$
$270$	6.59208	0.401181
$271$	−13.9430	−0.846978	−0.423489	−	0.905901i	$-0.639195\pi$
$271$	−13.9430	−0.846978	−0.423489	+	0.905901i	$0.639195\pi$
$272$	−0.702324	−0.0425847
$273$	−14.0703	−0.851575
$274$	−13.5579	−0.819063
$275$	−0.757275	−0.0456654
$276$	−11.7448	−0.706951
$277$	−1.57868	−0.0948538	−0.0474269	−	0.998875i	$-0.515102\pi$
$277$	−1.57868	−0.0948538	−0.0474269	+	0.998875i	$0.515102\pi$
$278$	−11.4226	−0.685081
$279$	−2.06581	−0.123677
$280$	−2.31808	−0.138532
$281$	−18.1946	−1.08540	−0.542700	−	0.839926i	$-0.682598\pi$
$281$	−18.1946	−1.08540	−0.542700	+	0.839926i	$0.682598\pi$
$282$	6.47610	0.385646
$283$	−9.16440	−0.544767	−0.272384	−	0.962189i	$-0.587812\pi$
$283$	−9.16440	−0.544767	−0.272384	+	0.962189i	$0.587812\pi$
$284$	16.2922	0.966765
$285$	27.0199	1.60052
$286$	−13.1778	−0.779222
$287$	−11.7428	−0.693155
$288$	−1.68636	−0.0993698
$289$	−16.5067	−0.970985
$290$	14.7481	0.866038
$291$	1.04724	0.0613904
$292$	7.68520	0.449743
$293$	30.7639	1.79725	0.898623	−	0.438721i	$-0.144568\pi$
$293$	30.7639	1.79725	0.898623	+	0.438721i	$0.144568\pi$
$294$	−2.16480	−0.126254
$295$	14.6929	0.855454
$296$	10.0433	0.583757
$297$	5.76569	0.334559
$298$	−8.76538	−0.507765
$299$	35.2625	2.03928
$300$	0.808563	0.0466824
$301$	4.20358	0.242290
$302$	16.8115	0.967393
$303$	10.8509	0.623368
$304$	5.38439	0.308816
$305$	−12.4622	−0.713584
$306$	1.18437	0.0677061
$307$	−8.77039	−0.500552	−0.250276	−	0.968174i	$-0.580521\pi$
$307$	−8.77039	−0.500552	−0.250276	+	0.968174i	$0.580521\pi$
$308$	−2.02748	−0.115527
$309$	−10.5518	−0.600271
$310$	2.83967	0.161283
$311$	−7.55604	−0.428464	−0.214232	−	0.976783i	$-0.568725\pi$
$311$	−7.55604	−0.428464	−0.214232	+	0.976783i	$0.568725\pi$
$312$	14.0703	0.796576
$313$	11.9917	0.677809	0.338905	−	0.940821i	$-0.389944\pi$
$313$	11.9917	0.677809	0.338905	+	0.940821i	$0.389944\pi$
$314$	17.8909	1.00964
$315$	3.90912	0.220254
$316$	−4.54547	−0.255702
$317$	6.07267	0.341075	0.170537	−	0.985351i	$-0.445450\pi$
$317$	6.07267	0.341075	0.170537	+	0.985351i	$0.445450\pi$
$318$	30.4274	1.70628
$319$	12.8993	0.722220
$320$	2.31808	0.129585
$321$	6.89999	0.385120
$322$	5.42533	0.302342
$323$	−3.78159	−0.210413
$324$	−11.2153	−0.623071
$325$	−2.42763	−0.134661
$326$	−16.7641	−0.928477
$327$	7.50986	0.415296
$328$	11.7428	0.648387
$329$	−2.99155	−0.164929
$330$	10.1743	0.560076
$331$	7.35697	0.404375	0.202188	−	0.979347i	$-0.435195\pi$
$331$	7.35697	0.404375	0.202188	+	0.979347i	$0.435195\pi$
$332$	4.58808	0.251804
$333$	−16.9367	−0.928124
$334$	−23.8146	−1.30308
$335$	29.3522	1.60368
$336$	2.16480	0.118100
$337$	−8.57353	−0.467030	−0.233515	−	0.972353i	$-0.575023\pi$
$337$	−8.57353	−0.467030	−0.233515	+	0.972353i	$0.575023\pi$
$338$	−29.2448	−1.59071
$339$	−12.2079	−0.663043
$340$	−1.62805	−0.0882932
$341$	2.48369	0.134499
$342$	−9.08003	−0.490992
$343$	1.00000	0.0539949
$344$	−4.20358	−0.226642
$345$	−27.2253	−1.46576
$346$	7.54430	0.405584
$347$	−6.87172	−0.368893	−0.184447	−	0.982843i	$-0.559049\pi$
$347$	−6.87172	−0.368893	−0.184447	+	0.982843i	$0.559049\pi$
$348$	−13.7729	−0.738305
$349$	−18.5455	−0.992720	−0.496360	−	0.868117i	$-0.665330\pi$
$349$	−18.5455	−0.992720	−0.496360	+	0.868117i	$0.665330\pi$
$350$	−0.373505	−0.0199647
$351$	18.4833	0.986568
$352$	2.02748	0.108065
$353$	−18.7309	−0.996947	−0.498473	−	0.866905i	$-0.666106\pi$
$353$	−18.7309	−0.996947	−0.498473	+	0.866905i	$0.666106\pi$
$354$	−13.7213	−0.729281
$355$	37.7667	2.00445
$356$	−5.32923	−0.282449
$357$	−1.52039	−0.0804677
$358$	5.99628	0.316913
$359$	−18.5018	−0.976487	−0.488244	−	0.872707i	$-0.662362\pi$
$359$	−18.5018	−0.976487	−0.488244	+	0.872707i	$0.662362\pi$
$360$	−3.90912	−0.206029
$361$	9.99169	0.525878
$362$	−0.451470	−0.0237287
$363$	−14.9140	−0.782781
$364$	−6.49960	−0.340672
$365$	17.8149	0.932476
$366$	11.6382	0.608336
$367$	−28.6834	−1.49726	−0.748629	−	0.662989i	$-0.769288\pi$
$367$	−28.6834	−1.49726	−0.748629	+	0.662989i	$0.769288\pi$
$368$	−5.42533	−0.282815
$369$	−19.8026	−1.03088
$370$	23.2813	1.21034
$371$	−14.0555	−0.729726
$372$	−2.65190	−0.137495
$373$	31.8010	1.64659	0.823296	−	0.567612i	$-0.192133\pi$
$373$	31.8010	1.64659	0.823296	+	0.567612i	$0.192133\pi$
$374$	−1.42395	−0.0736308
$375$	−23.2166	−1.19890
$376$	2.99155	0.154277
$377$	41.3518	2.12972
$378$	2.84377	0.146268
$379$	−1.53343	−0.0787672	−0.0393836	−	0.999224i	$-0.512539\pi$
$379$	−1.53343	−0.0787672	−0.0393836	+	0.999224i	$0.512539\pi$
$380$	12.4815	0.640286
$381$	−17.9394	−0.919065
$382$	26.5612	1.35899
$383$	−1.13254	−0.0578701	−0.0289351	−	0.999581i	$-0.509212\pi$
$383$	−1.13254	−0.0578701	−0.0289351	+	0.999581i	$0.509212\pi$
$384$	−2.16480	−0.110472
$385$	−4.69988	−0.239528
$386$	−16.4767	−0.838644
$387$	7.08875	0.360341
$388$	0.483759	0.0245592
$389$	−10.8319	−0.549199	−0.274600	−	0.961559i	$-0.588545\pi$
$389$	−10.8319	−0.549199	−0.274600	+	0.961559i	$0.588545\pi$
$390$	32.6162	1.65159
$391$	3.81034	0.192697
$392$	−1.00000	−0.0505076
$393$	−26.5380	−1.33866
$394$	18.6023	0.937168
$395$	−10.5368	−0.530162
$396$	−3.41907	−0.171815
$397$	−14.6882	−0.737178	−0.368589	−	0.929593i	$-0.620159\pi$
$397$	−14.6882	−0.737178	−0.368589	+	0.929593i	$0.620159\pi$
$398$	−9.75627	−0.489038
$399$	11.6561	0.583537
$400$	0.373505	0.0186752
$401$	−37.2346	−1.85941	−0.929704	−	0.368307i	$-0.879938\pi$
$401$	−37.2346	−1.85941	−0.929704	+	0.368307i	$0.879938\pi$
$402$	−27.4113	−1.36715
$403$	7.96208	0.396619
$404$	5.01242	0.249377
$405$	−25.9979	−1.29185
$406$	6.36220	0.315751
$407$	20.3627	1.00934
$408$	1.52039	0.0752706
$409$	17.8814	0.884178	0.442089	−	0.896971i	$-0.354238\pi$
$409$	17.8814	0.884178	0.442089	+	0.896971i	$0.354238\pi$
$410$	27.2207	1.34434
$411$	29.3501	1.44774
$412$	−4.87426	−0.240138
$413$	6.33839	0.311892
$414$	9.14907	0.449652
$415$	10.6356	0.522079
$416$	6.49960	0.318669
$417$	24.7276	1.21092
$418$	10.9168	0.533957
$419$	−11.6499	−0.569134	−0.284567	−	0.958656i	$-0.591850\pi$
$419$	−11.6499	−0.569134	−0.284567	+	0.958656i	$0.591850\pi$
$420$	5.01819	0.244862
$421$	−20.7317	−1.01040	−0.505201	−	0.863002i	$-0.668582\pi$
$421$	−20.7317	−1.01040	−0.505201	+	0.863002i	$0.668582\pi$
$422$	−19.3837	−0.943583
$423$	−5.04483	−0.245288
$424$	14.0555	0.682596
$425$	−0.262321	−0.0127245
$426$	−35.2694	−1.70881
$427$	−5.37609	−0.260167
$428$	3.18736	0.154067
$429$	28.5274	1.37732
$430$	−9.74423	−0.469909
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−2.84377	−0.136821
$433$	17.2282	0.827934	0.413967	−	0.910292i	$-0.364143\pi$
$433$	17.2282	0.827934	0.413967	+	0.910292i	$0.364143\pi$
$434$	1.22501	0.0588024
$435$	−31.9267	−1.53077
$436$	3.46908	0.166139
$437$	−29.2121	−1.39740
$438$	−16.6369	−0.794944
$439$	4.81685	0.229896	0.114948	−	0.993372i	$-0.463330\pi$
$439$	4.81685	0.229896	0.114948	+	0.993372i	$0.463330\pi$
$440$	4.69988	0.224058
$441$	1.68636	0.0803029
$442$	−4.56483	−0.217127
$443$	39.3775	1.87088	0.935441	−	0.353482i	$-0.115002\pi$
$443$	39.3775	1.87088	0.935441	+	0.353482i	$0.115002\pi$
$444$	−21.7418	−1.03182
$445$	−12.3536	−0.585617
$446$	−19.2154	−0.909874
$447$	18.9753	0.897501
$448$	1.00000	0.0472456
$449$	−30.3244	−1.43110	−0.715549	−	0.698562i	$-0.753823\pi$
$449$	−30.3244	−1.43110	−0.715549	+	0.698562i	$0.753823\pi$
$450$	−0.629863	−0.0296921
$451$	23.8083	1.12109
$452$	−5.63928	−0.265249
$453$	−36.3935	−1.70992
$454$	−21.8926	−1.02747
$455$	−15.0666	−0.706333
$456$	−11.6561	−0.545849
$457$	26.9422	1.26030	0.630152	−	0.776471i	$-0.282992\pi$
$457$	26.9422	1.26030	0.630152	+	0.776471i	$0.282992\pi$
$458$	4.82395	0.225408
$459$	1.99725	0.0932235
$460$	−12.5764	−0.586376
$461$	−25.7048	−1.19719	−0.598596	−	0.801051i	$-0.704274\pi$
$461$	−25.7048	−1.19719	−0.598596	+	0.801051i	$0.704274\pi$
$462$	4.38910	0.204199
$463$	−4.23308	−0.196728	−0.0983639	−	0.995151i	$-0.531361\pi$
$463$	−4.23308	−0.196728	−0.0983639	+	0.995151i	$0.531361\pi$
$464$	−6.36220	−0.295358
$465$	−6.14733	−0.285076
$466$	−15.3063	−0.709049
$467$	−16.6278	−0.769443	−0.384722	−	0.923033i	$-0.625703\pi$
$467$	−16.6278	−0.769443	−0.384722	+	0.923033i	$0.625703\pi$
$468$	−10.9607	−0.506657
$469$	12.6623	0.584689
$470$	6.93465	0.319871
$471$	−38.7302	−1.78459
$472$	−6.33839	−0.291748
$473$	−8.52269	−0.391874
$474$	9.84003	0.451967
$475$	2.01110	0.0922754
$476$	−0.702324	−0.0321910
$477$	−23.7027	−1.08527
$478$	−23.9954	−1.09752
$479$	24.1760	1.10463	0.552315	−	0.833635i	$-0.313744\pi$
$479$	24.1760	1.10463	0.552315	+	0.833635i	$0.313744\pi$
$480$	−5.01819	−0.229048
$481$	65.2776	2.97640
$482$	−5.40550	−0.246214
$483$	−11.7448	−0.534405
$484$	−6.88931	−0.313150
$485$	1.12139	0.0509199
$486$	15.7475	0.714322
$487$	14.3081	0.648363	0.324182	−	0.945995i	$-0.394911\pi$
$487$	14.3081	0.648363	0.324182	+	0.945995i	$0.394911\pi$
$488$	5.37609	0.243364
$489$	36.2909	1.64113
$490$	−2.31808	−0.104720
$491$	−9.88313	−0.446019	−0.223010	−	0.974816i	$-0.571588\pi$
$491$	−9.88313	−0.446019	−0.223010	+	0.974816i	$0.571588\pi$
$492$	−25.4208	−1.14606
$493$	4.46833	0.201243
$494$	34.9964	1.57456
$495$	−7.92569	−0.356233
$496$	−1.22501	−0.0550046
$497$	16.2922	0.730805
$498$	−9.93228	−0.445076
$499$	−10.3264	−0.462274	−0.231137	−	0.972921i	$-0.574244\pi$
$499$	−10.3264	−0.462274	−0.231137	+	0.972921i	$0.574244\pi$
$500$	−10.7246	−0.479619
$501$	51.5538	2.30326
$502$	14.8552	0.663020
$503$	−36.2568	−1.61661	−0.808306	−	0.588762i	$-0.799615\pi$
$503$	−36.2568	−1.61661	−0.808306	+	0.588762i	$0.799615\pi$
$504$	−1.68636	−0.0751165
$505$	11.6192	0.517048
$506$	−10.9998	−0.489000
$507$	63.3091	2.81166
$508$	−8.28688	−0.367671
$509$	3.17604	0.140776	0.0703878	−	0.997520i	$-0.477576\pi$
$509$	3.17604	0.140776	0.0703878	+	0.997520i	$0.477576\pi$
$510$	3.52439	0.156063
$511$	7.68520	0.339973
$512$	−1.00000	−0.0441942
$513$	−15.3120	−0.676039
$514$	−30.3163	−1.33720
$515$	−11.2989	−0.497891
$516$	9.09990	0.400601
$517$	6.06531	0.266752
$518$	10.0433	0.441279
$519$	−16.3319	−0.716891
$520$	15.0666	0.660714
$521$	−15.9030	−0.696721	−0.348361	−	0.937361i	$-0.613262\pi$
$521$	−15.9030	−0.696721	−0.348361	+	0.937361i	$0.613262\pi$
$522$	10.7290	0.469594
$523$	−21.5458	−0.942132	−0.471066	−	0.882098i	$-0.656131\pi$
$523$	−21.5458	−0.942132	−0.471066	+	0.882098i	$0.656131\pi$
$524$	−12.2588	−0.535530
$525$	0.808563	0.0352886
$526$	−20.7403	−0.904321
$527$	0.860354	0.0374776
$528$	−4.38910	−0.191011
$529$	6.43421	0.279748
$530$	32.5818	1.41526
$531$	10.6888	0.463855
$532$	5.38439	0.233443
$533$	76.3234	3.30593
$534$	11.5367	0.499243
$535$	7.38856	0.319435
$536$	−12.6623	−0.546927
$537$	−12.9807	−0.560160
$538$	−0.0392147	−0.00169067
$539$	−2.02748	−0.0873299
$540$	−6.59208	−0.283678
$541$	22.4657	0.965877	0.482938	−	0.875654i	$-0.339570\pi$
$541$	22.4657	0.965877	0.482938	+	0.875654i	$0.339570\pi$
$542$	13.9430	0.598904
$543$	0.977343	0.0419418
$544$	0.702324	0.0301119
$545$	8.04161	0.344465
$546$	14.0703	0.602155
$547$	28.9745	1.23886	0.619429	−	0.785052i	$-0.287364\pi$
$547$	28.9745	1.23886	0.619429	+	0.785052i	$0.287364\pi$
$548$	13.5579	0.579165
$549$	−9.06603	−0.386929
$550$	0.757275	0.0322903
$551$	−34.2566	−1.45938
$552$	11.7448	0.499890
$553$	−4.54547	−0.193293
$554$	1.57868	0.0670718
$555$	−50.3993	−2.13933
$556$	11.4226	0.484425
$557$	4.30895	0.182576	0.0912881	−	0.995825i	$-0.470902\pi$
$557$	4.30895	0.182576	0.0912881	+	0.995825i	$0.470902\pi$
$558$	2.06581	0.0874527
$559$	−27.3216	−1.15558
$560$	2.31808	0.0979568
$561$	3.08257	0.130146
$562$	18.1946	0.767494
$563$	−27.4471	−1.15676	−0.578379	−	0.815768i	$-0.696315\pi$
$563$	−27.4471	−1.15676	−0.578379	+	0.815768i	$0.696315\pi$
$564$	−6.47610	−0.272693
$565$	−13.0723	−0.549956
$566$	9.16440	0.385208
$567$	−11.2153	−0.470997
$568$	−16.2922	−0.683606
$569$	2.41700	0.101326	0.0506629	−	0.998716i	$-0.483867\pi$
$569$	2.41700	0.101326	0.0506629	+	0.998716i	$0.483867\pi$
$570$	−27.0199	−1.13174
$571$	13.7059	0.573574	0.286787	−	0.957994i	$-0.407413\pi$
$571$	13.7059	0.573574	0.286787	+	0.957994i	$0.407413\pi$
$572$	13.1778	0.550993
$573$	−57.4998	−2.40209
$574$	11.7428	0.490134
$575$	−2.02639	−0.0845061
$576$	1.68636	0.0702650
$577$	28.2130	1.17452	0.587262	−	0.809397i	$-0.300206\pi$
$577$	28.2130	1.17452	0.587262	+	0.809397i	$0.300206\pi$
$578$	16.5067	0.686590
$579$	35.6689	1.48235
$580$	−14.7481	−0.612382
$581$	4.58808	0.190346
$582$	−1.04724	−0.0434096
$583$	28.4973	1.18024
$584$	−7.68520	−0.318016
$585$	−25.4077	−1.05048
$586$	−30.7639	−1.27085
$587$	28.1175	1.16053	0.580267	−	0.814427i	$-0.302948\pi$
$587$	28.1175	1.16053	0.580267	+	0.814427i	$0.302948\pi$
$588$	2.16480	0.0892749
$589$	−6.59594	−0.271781
$590$	−14.6929	−0.604897
$591$	−40.2702	−1.65649
$592$	−10.0433	−0.412778
$593$	−12.9531	−0.531921	−0.265961	−	0.963984i	$-0.585689\pi$
$593$	−12.9531	−0.531921	−0.265961	+	0.963984i	$0.585689\pi$
$594$	−5.76569	−0.236569
$595$	−1.62805	−0.0667434
$596$	8.76538	0.359044
$597$	21.1204	0.864400
$598$	−35.2625	−1.44199
$599$	−38.6911	−1.58087	−0.790437	−	0.612544i	$-0.790146\pi$
$599$	−38.6911	−1.58087	−0.790437	+	0.612544i	$0.790146\pi$
$600$	−0.808563	−0.0330094
$601$	−45.4628	−1.85446	−0.927232	−	0.374487i	$-0.877819\pi$
$601$	−45.4628	−1.85446	−0.927232	+	0.374487i	$0.877819\pi$
$602$	−4.20358	−0.171325
$603$	21.3532	0.869568
$604$	−16.8115	−0.684050
$605$	−15.9700	−0.649272
$606$	−10.8509	−0.440788
$607$	22.8692	0.928232	0.464116	−	0.885774i	$-0.346372\pi$
$607$	22.8692	0.928232	0.464116	+	0.885774i	$0.346372\pi$
$608$	−5.38439	−0.218366
$609$	−13.7729	−0.558106
$610$	12.4622	0.504580
$611$	19.4438	0.786614
$612$	−1.18437	−0.0478754
$613$	9.68719	0.391262	0.195631	−	0.980678i	$-0.437325\pi$
$613$	9.68719	0.391262	0.195631	+	0.980678i	$0.437325\pi$
$614$	8.77039	0.353944
$615$	−58.9275	−2.37618
$616$	2.02748	0.0816897
$617$	−34.4442	−1.38667	−0.693336	−	0.720614i	$-0.743860\pi$
$617$	−34.4442	−1.38667	−0.693336	+	0.720614i	$0.743860\pi$
$618$	10.5518	0.424456
$619$	−46.1594	−1.85530	−0.927651	−	0.373449i	$-0.878175\pi$
$619$	−46.1594	−1.85530	−0.927651	+	0.373449i	$0.878175\pi$
$620$	−2.83967	−0.114044
$621$	15.4284	0.619119
$622$	7.55604	0.302970
$623$	−5.32923	−0.213511
$624$	−14.0703	−0.563264
$625$	−26.7280	−1.06912
$626$	−11.9917	−0.479284
$627$	−23.6326	−0.943797
$628$	−17.8909	−0.713923
$629$	7.05367	0.281248
$630$	−3.90912	−0.155743
$631$	10.5852	0.421389	0.210694	−	0.977552i	$-0.432428\pi$
$631$	10.5852	0.421389	0.210694	+	0.977552i	$0.432428\pi$
$632$	4.54547	0.180809
$633$	41.9618	1.66783
$634$	−6.07267	−0.241176
$635$	−19.2097	−0.762312
$636$	−30.4274	−1.20652
$637$	−6.49960	−0.257524
$638$	−12.8993	−0.510687
$639$	27.4745	1.08688
$640$	−2.31808	−0.0916302
$641$	12.1383	0.479435	0.239717	−	0.970843i	$-0.422945\pi$
$641$	12.1383	0.479435	0.239717	+	0.970843i	$0.422945\pi$
$642$	−6.89999	−0.272321
$643$	−30.7622	−1.21314	−0.606572	−	0.795029i	$-0.707456\pi$
$643$	−30.7622	−1.21314	−0.606572	+	0.795029i	$0.707456\pi$
$644$	−5.42533	−0.213788
$645$	21.0943	0.830588
$646$	3.78159	0.148785
$647$	−22.9837	−0.903583	−0.451792	−	0.892124i	$-0.649215\pi$
$647$	−22.9837	−0.903583	−0.451792	+	0.892124i	$0.649215\pi$
$648$	11.2153	0.440577
$649$	−12.8510	−0.504445
$650$	2.42763	0.0952195
$651$	−2.65190	−0.103936
$652$	16.7641	0.656533
$653$	−6.20485	−0.242815	−0.121407	−	0.992603i	$-0.538741\pi$
$653$	−6.20485	−0.242815	−0.121407	+	0.992603i	$0.538741\pi$
$654$	−7.50986	−0.293659
$655$	−28.4170	−1.11034
$656$	−11.7428	−0.458479
$657$	12.9600	0.505619
$658$	2.99155	0.116623
$659$	−30.3117	−1.18077	−0.590387	−	0.807120i	$-0.701025\pi$
$659$	−30.3117	−1.18077	−0.590387	+	0.807120i	$0.701025\pi$
$660$	−10.1743	−0.396034
$661$	−12.0263	−0.467769	−0.233885	−	0.972264i	$-0.575144\pi$
$661$	−12.0263	−0.467769	−0.233885	+	0.972264i	$0.575144\pi$
$662$	−7.35697	−0.285937
$663$	9.88194	0.383783
$664$	−4.58808	−0.178052
$665$	12.4815	0.484010
$666$	16.9367	0.656283
$667$	34.5170	1.33651
$668$	23.8146	0.921414
$669$	41.5974	1.60825
$670$	−29.3522	−1.13397
$671$	10.8999	0.420787
$672$	−2.16480	−0.0835090
$673$	−11.3154	−0.436176	−0.218088	−	0.975929i	$-0.569982\pi$
$673$	−11.3154	−0.436176	−0.218088	+	0.975929i	$0.569982\pi$
$674$	8.57353	0.330240
$675$	−1.06216	−0.0408825
$676$	29.2448	1.12480
$677$	−2.56745	−0.0986751	−0.0493376	−	0.998782i	$-0.515711\pi$
$677$	−2.56745	−0.0986751	−0.0493376	+	0.998782i	$0.515711\pi$
$678$	12.2079	0.468842
$679$	0.483759	0.0185650
$680$	1.62805	0.0624327
$681$	47.3930	1.81610
$682$	−2.48369	−0.0951054
$683$	−8.15899	−0.312195	−0.156098	−	0.987742i	$-0.549891\pi$
$683$	−8.15899	−0.312195	−0.156098	+	0.987742i	$0.549891\pi$
$684$	9.08003	0.347184
$685$	31.4283	1.20081
$686$	−1.00000	−0.0381802
$687$	−10.4429	−0.398421
$688$	4.20358	0.160260
$689$	91.3552	3.48036
$690$	27.2253	1.03645
$691$	29.2654	1.11331	0.556653	−	0.830745i	$-0.312085\pi$
$691$	29.2654	1.11331	0.556653	+	0.830745i	$0.312085\pi$
$692$	−7.54430	−0.286791
$693$	−3.41907	−0.129880
$694$	6.87172	0.260847
$695$	26.4785	1.00439
$696$	13.7729	0.522060
$697$	8.24724	0.312387
$698$	18.5455	0.701959
$699$	33.1350	1.25328
$700$	0.373505	0.0141171
$701$	38.8064	1.46570	0.732849	−	0.680392i	$-0.238190\pi$
$701$	38.8064	1.46570	0.732849	+	0.680392i	$0.238190\pi$
$702$	−18.4833	−0.697609
$703$	−54.0772	−2.03956
$704$	−2.02748	−0.0764137
$705$	−15.0121	−0.565390
$706$	18.7309	0.704948
$707$	5.01242	0.188512
$708$	13.7213	0.515680
$709$	45.3992	1.70500	0.852502	−	0.522724i	$-0.175084\pi$
$709$	45.3992	1.70500	0.852502	+	0.522724i	$0.175084\pi$
$710$	−37.7667	−1.41736
$711$	−7.66530	−0.287471
$712$	5.32923	0.199721
$713$	6.64609	0.248898
$714$	1.52039	0.0568992
$715$	30.5473	1.14240
$716$	−5.99628	−0.224091
$717$	51.9452	1.93993
$718$	18.5018	0.690481
$719$	−3.59408	−0.134037	−0.0670183	−	0.997752i	$-0.521349\pi$
$719$	−3.59408	−0.134037	−0.0670183	+	0.997752i	$0.521349\pi$
$720$	3.90912	0.145684
$721$	−4.87426	−0.181527
$722$	−9.99169	−0.371852
$723$	11.7018	0.435196
$724$	0.451470	0.0167788
$725$	−2.37631	−0.0882540
$726$	14.9140	0.553509
$727$	−11.3776	−0.421973	−0.210987	−	0.977489i	$-0.567668\pi$
$727$	−11.3776	−0.421973	−0.210987	+	0.977489i	$0.567668\pi$
$728$	6.49960	0.240891
$729$	−0.444435	−0.0164606
$730$	−17.8149	−0.659360
$731$	−2.95227	−0.109194
$732$	−11.6382	−0.430159
$733$	−19.4830	−0.719621	−0.359810	−	0.933025i	$-0.617159\pi$
$733$	−19.4830	−0.719621	−0.359810	+	0.933025i	$0.617159\pi$
$734$	28.6834	1.05872
$735$	5.01819	0.185099
$736$	5.42533	0.199980
$737$	−25.6726	−0.945661
$738$	19.8026	0.728943
$739$	14.1362	0.520010	0.260005	−	0.965607i	$-0.416276\pi$
$739$	14.1362	0.520010	0.260005	+	0.965607i	$0.416276\pi$
$740$	−23.2813	−0.855836
$741$	−75.7602	−2.78312
$742$	14.0555	0.515994
$743$	−45.9001	−1.68391	−0.841956	−	0.539546i	$-0.818596\pi$
$743$	−45.9001	−1.68391	−0.841956	+	0.539546i	$0.818596\pi$
$744$	2.65190	0.0972235
$745$	20.3189	0.744426
$746$	−31.8010	−1.16432
$747$	7.73716	0.283088
$748$	1.42395	0.0520648
$749$	3.18736	0.116464
$750$	23.2166	0.847751
$751$	17.2948	0.631095	0.315547	−	0.948910i	$-0.397812\pi$
$751$	17.2948	0.631095	0.315547	+	0.948910i	$0.397812\pi$
$752$	−2.99155	−0.109090
$753$	−32.1586	−1.17192
$754$	−41.3518	−1.50594
$755$	−38.9704	−1.41828
$756$	−2.84377	−0.103427
$757$	13.0294	0.473562	0.236781	−	0.971563i	$-0.423908\pi$
$757$	13.0294	0.473562	0.236781	+	0.971563i	$0.423908\pi$
$758$	1.53343	0.0556968
$759$	23.8123	0.864332
$760$	−12.4815	−0.452750
$761$	−2.94293	−0.106681	−0.0533405	−	0.998576i	$-0.516987\pi$
$761$	−2.94293	−0.106681	−0.0533405	+	0.998576i	$0.516987\pi$
$762$	17.9394	0.649877
$763$	3.46908	0.125589
$764$	−26.5612	−0.960952
$765$	−2.74547	−0.0992628
$766$	1.13254	0.0409204
$767$	−41.1970	−1.48754
$768$	2.16480	0.0781155
$769$	4.83847	0.174480	0.0872399	−	0.996187i	$-0.472195\pi$
$769$	4.83847	0.174480	0.0872399	+	0.996187i	$0.472195\pi$
$770$	4.69988	0.169372
$771$	65.6288	2.36356
$772$	16.4767	0.593011
$773$	−5.96998	−0.214725	−0.107363	−	0.994220i	$-0.534241\pi$
$773$	−5.96998	−0.214725	−0.107363	+	0.994220i	$0.534241\pi$
$774$	−7.08875	−0.254800
$775$	−0.457547	−0.0164356
$776$	−0.483759	−0.0173659
$777$	−21.7418	−0.779983
$778$	10.8319	0.388342
$779$	−63.2278	−2.26537
$780$	−32.6162	−1.16785
$781$	−33.0322	−1.18198
$782$	−3.81034	−0.136258
$783$	18.0926	0.646577
$784$	1.00000	0.0357143
$785$	−41.4725	−1.48022
$786$	26.5380	0.946577
$787$	−17.7074	−0.631200	−0.315600	−	0.948892i	$-0.602206\pi$
$787$	−17.7074	−0.631200	−0.315600	+	0.948892i	$0.602206\pi$
$788$	−18.6023	−0.662678
$789$	44.8987	1.59844
$790$	10.5368	0.374881
$791$	−5.63928	−0.200510
$792$	3.41907	0.121491
$793$	34.9424	1.24084
$794$	14.6882	0.521263
$795$	−70.5332	−2.50155
$796$	9.75627	0.345802
$797$	−11.1750	−0.395841	−0.197920	−	0.980218i	$-0.563419\pi$
$797$	−11.1750	−0.395841	−0.197920	+	0.980218i	$0.563419\pi$
$798$	−11.6561	−0.412623
$799$	2.10104	0.0743293
$800$	−0.373505	−0.0132054
$801$	−8.98701	−0.317540
$802$	37.2346	1.31480
$803$	−15.5816	−0.549864
$804$	27.4113	0.966722
$805$	−12.5764	−0.443258
$806$	−7.96208	−0.280452
$807$	0.0848920	0.00298834
$808$	−5.01242	−0.176336
$809$	−49.2048	−1.72995	−0.864973	−	0.501818i	$-0.832665\pi$
$809$	−49.2048	−1.72995	−0.864973	+	0.501818i	$0.832665\pi$
$810$	25.9979	0.913474
$811$	11.5912	0.407023	0.203512	−	0.979073i	$-0.434765\pi$
$811$	11.5912	0.407023	0.203512	+	0.979073i	$0.434765\pi$
$812$	−6.36220	−0.223269
$813$	−30.1839	−1.05859
$814$	−20.3627	−0.713712
$815$	38.8606	1.36123
$816$	−1.52039	−0.0532244
$817$	22.6337	0.791853
$818$	−17.8814	−0.625208
$819$	−10.9607	−0.382997
$820$	−27.2207	−0.950589
$821$	9.70845	0.338827	0.169414	−	0.985545i	$-0.445813\pi$
$821$	9.70845	0.338827	0.169414	+	0.985545i	$0.445813\pi$
$822$	−29.3501	−1.02370
$823$	43.9325	1.53139	0.765696	−	0.643203i	$-0.222395\pi$
$823$	43.9325	1.53139	0.765696	+	0.643203i	$0.222395\pi$
$824$	4.87426	0.169803
$825$	−1.63935	−0.0570748
$826$	−6.33839	−0.220541
$827$	1.37634	0.0478599	0.0239300	−	0.999714i	$-0.492382\pi$
$827$	1.37634	0.0478599	0.0239300	+	0.999714i	$0.492382\pi$
$828$	−9.14907	−0.317952
$829$	−45.5864	−1.58328	−0.791640	−	0.610987i	$-0.790773\pi$
$829$	−45.5864	−1.58328	−0.791640	+	0.610987i	$0.790773\pi$
$830$	−10.6356	−0.369165
$831$	−3.41753	−0.118553
$832$	−6.49960	−0.225333
$833$	−0.702324	−0.0243341
$834$	−24.7276	−0.856247
$835$	55.2042	1.91042
$836$	−10.9168	−0.377565
$837$	3.48364	0.120412
$838$	11.6499	0.402439
$839$	−34.8081	−1.20171	−0.600855	−	0.799358i	$-0.705173\pi$
$839$	−34.8081	−1.20171	−0.600855	+	0.799358i	$0.705173\pi$
$840$	−5.01819	−0.173144
$841$	11.4776	0.395779
$842$	20.7317	0.714462
$843$	−39.3877	−1.35659
$844$	19.3837	0.667214
$845$	67.7918	2.33211
$846$	5.04483	0.173445
$847$	−6.88931	−0.236719
$848$	−14.0555	−0.482668
$849$	−19.8391	−0.680876
$850$	0.262321	0.00899755
$851$	54.4884	1.86784
$852$	35.2694	1.20831
$853$	−40.7641	−1.39574	−0.697869	−	0.716226i	$-0.745868\pi$
$853$	−40.7641	−1.39574	−0.697869	+	0.716226i	$0.745868\pi$
$854$	5.37609	0.183966
$855$	21.0483	0.719835
$856$	−3.18736	−0.108942
$857$	25.1657	0.859644	0.429822	−	0.902914i	$-0.358576\pi$
$857$	25.1657	0.859644	0.429822	+	0.902914i	$0.358576\pi$
$858$	−28.5274	−0.973909
$859$	−8.39169	−0.286321	−0.143160	−	0.989699i	$-0.545726\pi$
$859$	−8.39169	−0.286321	−0.143160	+	0.989699i	$0.545726\pi$
$860$	9.74423	0.332276
$861$	−25.4208	−0.866338
$862$	−1.00000	−0.0340601
$863$	33.0710	1.12575	0.562875	−	0.826542i	$-0.309695\pi$
$863$	33.0710	1.12575	0.562875	+	0.826542i	$0.309695\pi$
$864$	2.84377	0.0967469
$865$	−17.4883	−0.594620
$866$	−17.2282	−0.585438
$867$	−35.7338	−1.21358
$868$	−1.22501	−0.0415796
$869$	9.21586	0.312627
$870$	31.9267	1.08242
$871$	−82.2997	−2.78862
$872$	−3.46908	−0.117478
$873$	0.815793	0.0276104
$874$	29.2121	0.988114
$875$	−10.7246	−0.362558
$876$	16.6369	0.562110
$877$	7.29708	0.246405	0.123203	−	0.992382i	$-0.460684\pi$
$877$	7.29708	0.246405	0.123203	+	0.992382i	$0.460684\pi$
$878$	−4.81685	−0.162561
$879$	66.5977	2.24629
$880$	−4.69988	−0.158433
$881$	−35.8959	−1.20937	−0.604683	−	0.796467i	$-0.706700\pi$
$881$	−35.8959	−1.20937	−0.604683	+	0.796467i	$0.706700\pi$
$882$	−1.68636	−0.0567827
$883$	1.36628	0.0459791	0.0229896	−	0.999736i	$-0.492682\pi$
$883$	1.36628	0.0459791	0.0229896	+	0.999736i	$0.492682\pi$
$884$	4.56483	0.153532
$885$	31.8072	1.06919
$886$	−39.3775	−1.32291
$887$	51.1645	1.71793	0.858967	−	0.512031i	$-0.171107\pi$
$887$	51.1645	1.71793	0.858967	+	0.512031i	$0.171107\pi$
$888$	21.7418	0.729607
$889$	−8.28688	−0.277933
$890$	12.3536	0.414094
$891$	22.7388	0.761778
$892$	19.2154	0.643378
$893$	−16.1077	−0.539022
$894$	−18.9753	−0.634629
$895$	−13.8999	−0.464621
$896$	−1.00000	−0.0334077
$897$	76.3362	2.54879
$898$	30.3244	1.01194
$899$	7.79376	0.259936
$900$	0.629863	0.0209954
$901$	9.87153	0.328868
$902$	−23.8083	−0.792730
$903$	9.09990	0.302826
$904$	5.63928	0.187560
$905$	1.04654	0.0347883
$906$	36.3935	1.20909
$907$	−21.0555	−0.699136	−0.349568	−	0.936911i	$-0.613672\pi$
$907$	−21.0555	−0.699136	−0.349568	+	0.936911i	$0.613672\pi$
$908$	21.8926	0.726530
$909$	8.45276	0.280360
$910$	15.0666	0.499453
$911$	−21.0007	−0.695784	−0.347892	−	0.937535i	$-0.613102\pi$
$911$	−21.0007	−0.695784	−0.347892	+	0.937535i	$0.613102\pi$
$912$	11.6561	0.385973
$913$	−9.30227	−0.307860
$914$	−26.9422	−0.891170
$915$	−26.9782	−0.891872
$916$	−4.82395	−0.159388
$917$	−12.2588	−0.404823
$918$	−1.99725	−0.0659189
$919$	13.5100	0.445654	0.222827	−	0.974858i	$-0.428472\pi$
$919$	13.5100	0.445654	0.222827	+	0.974858i	$0.428472\pi$
$920$	12.5764	0.414630
$921$	−18.9861	−0.625614
$922$	25.7048	0.846542
$923$	−105.893	−3.48550
$924$	−4.38910	−0.144391
$925$	−3.75123	−0.123340
$926$	4.23308	0.139108
$927$	−8.21977	−0.269973
$928$	6.36220	0.208849
$929$	−60.1494	−1.97344	−0.986719	−	0.162434i	$-0.948066\pi$
$929$	−60.1494	−1.97344	−0.986719	+	0.162434i	$0.948066\pi$
$930$	6.14733	0.201579
$931$	5.38439	0.176466
$932$	15.3063	0.501373
$933$	−16.3573	−0.535515
$934$	16.6278	0.544079
$935$	3.30084	0.107949
$936$	10.9607	0.358261
$937$	−50.2817	−1.64263	−0.821316	−	0.570474i	$-0.806760\pi$
$937$	−50.2817	−1.64263	−0.821316	+	0.570474i	$0.806760\pi$
$938$	−12.6623	−0.413438
$939$	25.9596	0.847159
$940$	−6.93465	−0.226183
$941$	12.7632	0.416069	0.208034	−	0.978122i	$-0.433293\pi$
$941$	12.7632	0.416069	0.208034	+	0.978122i	$0.433293\pi$
$942$	38.7302	1.26190
$943$	63.7085	2.07463
$944$	6.33839	0.206297
$945$	−6.59208	−0.214440
$946$	8.52269	0.277096
$947$	−29.5336	−0.959712	−0.479856	−	0.877347i	$-0.659311\pi$
$947$	−29.5336	−0.959712	−0.479856	+	0.877347i	$0.659311\pi$
$948$	−9.84003	−0.319589
$949$	−49.9508	−1.62147
$950$	−2.01110	−0.0652485
$951$	13.1461	0.426292
$952$	0.702324	0.0227625
$953$	−3.78596	−0.122639	−0.0613197	−	0.998118i	$-0.519531\pi$
$953$	−3.78596	−0.122639	−0.0613197	+	0.998118i	$0.519531\pi$
$954$	23.7027	0.767402
$955$	−61.5711	−1.99239
$956$	23.9954	0.776065
$957$	27.9243	0.902665
$958$	−24.1760	−0.781092
$959$	13.5579	0.437807
$960$	5.01819	0.161961
$961$	−29.4994	−0.951592
$962$	−65.2776	−2.10463
$963$	5.37504	0.173208
$964$	5.40550	0.174099
$965$	38.1944	1.22952
$966$	11.7448	0.377881
$967$	7.35326	0.236465	0.118232	−	0.992986i	$-0.462277\pi$
$967$	7.35326	0.236465	0.118232	+	0.992986i	$0.462277\pi$
$968$	6.88931	0.221431
$969$	−8.18639	−0.262985
$970$	−1.12139	−0.0360058
$971$	−54.7014	−1.75545	−0.877726	−	0.479162i	$-0.840941\pi$
$971$	−54.7014	−1.75545	−0.877726	+	0.479162i	$0.840941\pi$
$972$	−15.7475	−0.505102
$973$	11.4226	0.366191
$974$	−14.3081	−0.458462
$975$	−5.25533	−0.168305
$976$	−5.37609	−0.172084
$977$	−12.4456	−0.398169	−0.199084	−	0.979982i	$-0.563797\pi$
$977$	−12.4456	−0.398169	−0.199084	+	0.979982i	$0.563797\pi$
$978$	−36.2909	−1.16046
$979$	10.8049	0.345327
$980$	2.31808	0.0740484
$981$	5.85012	0.186780
$982$	9.88313	0.315383
$983$	−43.2429	−1.37923	−0.689617	−	0.724174i	$-0.742221\pi$
$983$	−43.2429	−1.37923	−0.689617	+	0.724174i	$0.742221\pi$
$984$	25.4208	0.810385
$985$	−43.1215	−1.37397
$986$	−4.46833	−0.142301
$987$	−6.47610	−0.206137
$988$	−34.9964	−1.11338
$989$	−22.8058	−0.725182
$990$	7.92569	0.251895
$991$	62.0253	1.97030	0.985149	−	0.171700i	$-0.0549258\pi$
$991$	62.0253	1.97030	0.985149	+	0.171700i	$0.0549258\pi$
$992$	1.22501	0.0388941
$993$	15.9264	0.505408
$994$	−16.2922	−0.516757
$995$	22.6158	0.716970
$996$	9.93228	0.314716
$997$	18.9284	0.599468	0.299734	−	0.954023i	$-0.403102\pi$
$997$	18.9284	0.599468	0.299734	+	0.954023i	$0.403102\pi$
$998$	10.3264	0.326877
$999$	28.5609	0.903626

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.18	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.18	✓	20	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.16480 q^{3} +1.00000 q^{4} +2.31808 q^{5} -2.16480 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.68636 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.16480 q^{3} +1.00000 q^{4} +2.31808 q^{5} -2.16480 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.68636 q^{9} -2.31808 q^{10} -2.02748 q^{11} +2.16480 q^{12} -6.49960 q^{13} -1.00000 q^{14} +5.01819 q^{15} +1.00000 q^{16} -0.702324 q^{17} -1.68636 q^{18} +5.38439 q^{19} +2.31808 q^{20} +2.16480 q^{21} +2.02748 q^{22} -5.42533 q^{23} -2.16480 q^{24} +0.373505 q^{25} +6.49960 q^{26} -2.84377 q^{27} +1.00000 q^{28} -6.36220 q^{29} -5.01819 q^{30} -1.22501 q^{31} -1.00000 q^{32} -4.38910 q^{33} +0.702324 q^{34} +2.31808 q^{35} +1.68636 q^{36} -10.0433 q^{37} -5.38439 q^{38} -14.0703 q^{39} -2.31808 q^{40} -11.7428 q^{41} -2.16480 q^{42} +4.20358 q^{43} -2.02748 q^{44} +3.90912 q^{45} +5.42533 q^{46} -2.99155 q^{47} +2.16480 q^{48} +1.00000 q^{49} -0.373505 q^{50} -1.52039 q^{51} -6.49960 q^{52} -14.0555 q^{53} +2.84377 q^{54} -4.69988 q^{55} -1.00000 q^{56} +11.6561 q^{57} +6.36220 q^{58} +6.33839 q^{59} +5.01819 q^{60} -5.37609 q^{61} +1.22501 q^{62} +1.68636 q^{63} +1.00000 q^{64} -15.0666 q^{65} +4.38910 q^{66} +12.6623 q^{67} -0.702324 q^{68} -11.7448 q^{69} -2.31808 q^{70} +16.2922 q^{71} -1.68636 q^{72} +7.68520 q^{73} +10.0433 q^{74} +0.808563 q^{75} +5.38439 q^{76} -2.02748 q^{77} +14.0703 q^{78} -4.54547 q^{79} +2.31808 q^{80} -11.2153 q^{81} +11.7428 q^{82} +4.58808 q^{83} +2.16480 q^{84} -1.62805 q^{85} -4.20358 q^{86} -13.7729 q^{87} +2.02748 q^{88} -5.32923 q^{89} -3.90912 q^{90} -6.49960 q^{91} -5.42533 q^{92} -2.65190 q^{93} +2.99155 q^{94} +12.4815 q^{95} -2.16480 q^{96} +0.483759 q^{97} -1.00000 q^{98} -3.41907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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