LMFDB - Embedded newform 6034.2.a.m.1.10

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:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.950934 q^{3} +1.00000 q^{4} -2.70877 q^{5} -0.950934 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.09572 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.950934 q^{3} +1.00000 q^{4} -2.70877 q^{5} -0.950934 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.09572 q^{9} -2.70877 q^{10} +1.16762 q^{11} -0.950934 q^{12} -6.37589 q^{13} +1.00000 q^{14} +2.57587 q^{15} +1.00000 q^{16} +5.68442 q^{17} -2.09572 q^{18} +3.93959 q^{19} -2.70877 q^{20} -0.950934 q^{21} +1.16762 q^{22} +2.75926 q^{23} -0.950934 q^{24} +2.33746 q^{25} -6.37589 q^{26} +4.84570 q^{27} +1.00000 q^{28} -8.04156 q^{29} +2.57587 q^{30} +7.39105 q^{31} +1.00000 q^{32} -1.11033 q^{33} +5.68442 q^{34} -2.70877 q^{35} -2.09572 q^{36} +9.23133 q^{37} +3.93959 q^{38} +6.06305 q^{39} -2.70877 q^{40} +3.34983 q^{41} -0.950934 q^{42} -9.44398 q^{43} +1.16762 q^{44} +5.67684 q^{45} +2.75926 q^{46} +0.544796 q^{47} -0.950934 q^{48} +1.00000 q^{49} +2.33746 q^{50} -5.40551 q^{51} -6.37589 q^{52} -2.70282 q^{53} +4.84570 q^{54} -3.16282 q^{55} +1.00000 q^{56} -3.74629 q^{57} -8.04156 q^{58} -10.7440 q^{59} +2.57587 q^{60} +4.95460 q^{61} +7.39105 q^{62} -2.09572 q^{63} +1.00000 q^{64} +17.2708 q^{65} -1.11033 q^{66} -10.0860 q^{67} +5.68442 q^{68} -2.62387 q^{69} -2.70877 q^{70} -9.18971 q^{71} -2.09572 q^{72} -2.53447 q^{73} +9.23133 q^{74} -2.22277 q^{75} +3.93959 q^{76} +1.16762 q^{77} +6.06305 q^{78} -12.0276 q^{79} -2.70877 q^{80} +1.67923 q^{81} +3.34983 q^{82} +10.6357 q^{83} -0.950934 q^{84} -15.3978 q^{85} -9.44398 q^{86} +7.64699 q^{87} +1.16762 q^{88} +5.37454 q^{89} +5.67684 q^{90} -6.37589 q^{91} +2.75926 q^{92} -7.02840 q^{93} +0.544796 q^{94} -10.6714 q^{95} -0.950934 q^{96} +0.731566 q^{97} +1.00000 q^{98} -2.44701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	−0.950934	−0.549022	−0.274511	−	0.961584i	$-0.588516\pi$
$3$	−0.950934	−0.549022	−0.274511	+	0.961584i	$0.588516\pi$
$4$	1.00000	0.500000
$5$	−2.70877	−1.21140	−0.605700	−	0.795693i	$-0.707107\pi$
$5$	−2.70877	−1.21140	−0.605700	+	0.795693i	$0.707107\pi$
$6$	−0.950934	−0.388217
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.09572	−0.698575
$10$	−2.70877	−0.856589
$11$	1.16762	0.352050	0.176025	−	0.984386i	$-0.443676\pi$
$11$	1.16762	0.352050	0.176025	+	0.984386i	$0.443676\pi$
$12$	−0.950934	−0.274511
$13$	−6.37589	−1.76835	−0.884177	−	0.467152i	$-0.845280\pi$
$13$	−6.37589	−1.76835	−0.884177	+	0.467152i	$0.845280\pi$
$14$	1.00000	0.267261
$15$	2.57587	0.665086
$16$	1.00000	0.250000
$17$	5.68442	1.37867	0.689337	−	0.724441i	$-0.257902\pi$
$17$	5.68442	1.37867	0.689337	+	0.724441i	$0.257902\pi$
$18$	−2.09572	−0.493967
$19$	3.93959	0.903803	0.451902	−	0.892068i	$-0.350746\pi$
$19$	3.93959	0.903803	0.451902	+	0.892068i	$0.350746\pi$
$20$	−2.70877	−0.605700
$21$	−0.950934	−0.207511
$22$	1.16762	0.248937
$23$	2.75926	0.575345	0.287672	−	0.957729i	$-0.407119\pi$
$23$	2.75926	0.575345	0.287672	+	0.957729i	$0.407119\pi$
$24$	−0.950934	−0.194109
$25$	2.33746	0.467491
$26$	−6.37589	−1.25042
$27$	4.84570	0.932555
$28$	1.00000	0.188982
$29$	−8.04156	−1.49328	−0.746640	−	0.665229i	$-0.768334\pi$
$29$	−8.04156	−1.49328	−0.746640	+	0.665229i	$0.768334\pi$
$30$	2.57587	0.470287
$31$	7.39105	1.32747	0.663736	−	0.747967i	$-0.268970\pi$
$31$	7.39105	1.32747	0.663736	+	0.747967i	$0.268970\pi$
$32$	1.00000	0.176777
$33$	−1.11033	−0.193283
$34$	5.68442	0.974870
$35$	−2.70877	−0.457866
$36$	−2.09572	−0.349287
$37$	9.23133	1.51762	0.758811	−	0.651311i	$-0.225781\pi$
$37$	9.23133	1.51762	0.758811	+	0.651311i	$0.225781\pi$
$38$	3.93959	0.639085
$39$	6.06305	0.970865
$40$	−2.70877	−0.428295
$41$	3.34983	0.523156	0.261578	−	0.965182i	$-0.415757\pi$
$41$	3.34983	0.523156	0.261578	+	0.965182i	$0.415757\pi$
$42$	−0.950934	−0.146732
$43$	−9.44398	−1.44019	−0.720097	−	0.693873i	$-0.755903\pi$
$43$	−9.44398	−1.44019	−0.720097	+	0.693873i	$0.755903\pi$
$44$	1.16762	0.176025
$45$	5.67684	0.846254
$46$	2.75926	0.406830
$47$	0.544796	0.0794667	0.0397333	−	0.999210i	$-0.487349\pi$
$47$	0.544796	0.0794667	0.0397333	+	0.999210i	$0.487349\pi$
$48$	−0.950934	−0.137256
$49$	1.00000	0.142857
$50$	2.33746	0.330566
$51$	−5.40551	−0.756922
$52$	−6.37589	−0.884177
$53$	−2.70282	−0.371260	−0.185630	−	0.982620i	$-0.559433\pi$
$53$	−2.70282	−0.371260	−0.185630	+	0.982620i	$0.559433\pi$
$54$	4.84570	0.659416
$55$	−3.16282	−0.426474
$56$	1.00000	0.133631
$57$	−3.74629	−0.496208
$58$	−8.04156	−1.05591
$59$	−10.7440	−1.39875	−0.699376	−	0.714754i	$-0.746539\pi$
$59$	−10.7440	−1.39875	−0.699376	+	0.714754i	$0.746539\pi$
$60$	2.57587	0.332543
$61$	4.95460	0.634372	0.317186	−	0.948363i	$-0.397262\pi$
$61$	4.95460	0.634372	0.317186	+	0.948363i	$0.397262\pi$
$62$	7.39105	0.938665
$63$	−2.09572	−0.264036
$64$	1.00000	0.125000
$65$	17.2708	2.14218
$66$	−1.11033	−0.136672
$67$	−10.0860	−1.23220	−0.616098	−	0.787669i	$-0.711288\pi$
$67$	−10.0860	−1.23220	−0.616098	+	0.787669i	$0.711288\pi$
$68$	5.68442	0.689337
$69$	−2.62387	−0.315877
$70$	−2.70877	−0.323760
$71$	−9.18971	−1.09062	−0.545309	−	0.838235i	$-0.683588\pi$
$71$	−9.18971	−1.09062	−0.545309	+	0.838235i	$0.683588\pi$
$72$	−2.09572	−0.246983
$73$	−2.53447	−0.296638	−0.148319	−	0.988940i	$-0.547386\pi$
$73$	−2.53447	−0.296638	−0.148319	+	0.988940i	$0.547386\pi$
$74$	9.23133	1.07312
$75$	−2.22277	−0.256663
$76$	3.93959	0.451902
$77$	1.16762	0.133063
$78$	6.06305	0.686506
$79$	−12.0276	−1.35321	−0.676603	−	0.736348i	$-0.736548\pi$
$79$	−12.0276	−1.35321	−0.676603	+	0.736348i	$0.736548\pi$
$80$	−2.70877	−0.302850
$81$	1.67923	0.186581
$82$	3.34983	0.369927
$83$	10.6357	1.16742	0.583711	−	0.811962i	$-0.301600\pi$
$83$	10.6357	1.16742	0.583711	+	0.811962i	$0.301600\pi$
$84$	−0.950934	−0.103755
$85$	−15.3978	−1.67013
$86$	−9.44398	−1.01837
$87$	7.64699	0.819843
$88$	1.16762	0.124469
$89$	5.37454	0.569700	0.284850	−	0.958572i	$-0.408056\pi$
$89$	5.37454	0.569700	0.284850	+	0.958572i	$0.408056\pi$
$90$	5.67684	0.598392
$91$	−6.37589	−0.668375
$92$	2.75926	0.287672
$93$	−7.02840	−0.728812
$94$	0.544796	0.0561914
$95$	−10.6714	−1.09487
$96$	−0.950934	−0.0970543
$97$	0.731566	0.0742793	0.0371397	−	0.999310i	$-0.488175\pi$
$97$	0.731566	0.0742793	0.0371397	+	0.999310i	$0.488175\pi$
$98$	1.00000	0.101015
$99$	−2.44701	−0.245934
$100$	2.33746	0.233746
$101$	−1.40385	−0.139688	−0.0698441	−	0.997558i	$-0.522250\pi$
$101$	−1.40385	−0.139688	−0.0698441	+	0.997558i	$0.522250\pi$
$102$	−5.40551	−0.535225
$103$	−2.16667	−0.213488	−0.106744	−	0.994287i	$-0.534043\pi$
$103$	−2.16667	−0.213488	−0.106744	+	0.994287i	$0.534043\pi$
$104$	−6.37589	−0.625208
$105$	2.57587	0.251379
$106$	−2.70282	−0.262521
$107$	−10.4033	−1.00573	−0.502865	−	0.864365i	$-0.667721\pi$
$107$	−10.4033	−1.00573	−0.502865	+	0.864365i	$0.667721\pi$
$108$	4.84570	0.466278
$109$	−5.66932	−0.543023	−0.271511	−	0.962435i	$-0.587523\pi$
$109$	−5.66932	−0.543023	−0.271511	+	0.962435i	$0.587523\pi$
$110$	−3.16282	−0.301563
$111$	−8.77839	−0.833208
$112$	1.00000	0.0944911
$113$	−17.3226	−1.62957	−0.814787	−	0.579760i	$-0.803146\pi$
$113$	−17.3226	−1.62957	−0.814787	+	0.579760i	$0.803146\pi$
$114$	−3.74629	−0.350872
$115$	−7.47420	−0.696973
$116$	−8.04156	−0.746640
$117$	13.3621	1.23533
$118$	−10.7440	−0.989067
$119$	5.68442	0.521090
$120$	2.57587	0.235143
$121$	−9.63667	−0.876060
$122$	4.95460	0.448569
$123$	−3.18547	−0.287224
$124$	7.39105	0.663736
$125$	7.21223	0.645081
$126$	−2.09572	−0.186702
$127$	−2.88158	−0.255699	−0.127850	−	0.991794i	$-0.540807\pi$
$127$	−2.88158	−0.255699	−0.127850	+	0.991794i	$0.540807\pi$
$128$	1.00000	0.0883883
$129$	8.98061	0.790698
$130$	17.2708	1.51475
$131$	−17.0177	−1.48684	−0.743420	−	0.668825i	$-0.766798\pi$
$131$	−17.0177	−1.48684	−0.743420	+	0.668825i	$0.766798\pi$
$132$	−1.11033	−0.0966417
$133$	3.93959	0.341605
$134$	−10.0860	−0.871294
$135$	−13.1259	−1.12970
$136$	5.68442	0.487435
$137$	−2.33549	−0.199535	−0.0997673	−	0.995011i	$-0.531810\pi$
$137$	−2.33549	−0.199535	−0.0997673	+	0.995011i	$0.531810\pi$
$138$	−2.62387	−0.223359
$139$	4.34425	0.368475	0.184237	−	0.982882i	$-0.441018\pi$
$139$	4.34425	0.368475	0.184237	+	0.982882i	$0.441018\pi$
$140$	−2.70877	−0.228933
$141$	−0.518065	−0.0436289
$142$	−9.18971	−0.771183
$143$	−7.44461	−0.622550
$144$	−2.09572	−0.174644
$145$	21.7828	1.80896
$146$	−2.53447	−0.209754
$147$	−0.950934	−0.0784317
$148$	9.23133	0.758811
$149$	−7.58349	−0.621263	−0.310632	−	0.950530i	$-0.600541\pi$
$149$	−7.58349	−0.621263	−0.310632	+	0.950530i	$0.600541\pi$
$150$	−2.22277	−0.181488
$151$	6.79212	0.552735	0.276367	−	0.961052i	$-0.410869\pi$
$151$	6.79212	0.552735	0.276367	+	0.961052i	$0.410869\pi$
$152$	3.93959	0.319543
$153$	−11.9130	−0.963107
$154$	1.16762	0.0940894
$155$	−20.0207	−1.60810
$156$	6.06305	0.485433
$157$	−2.63726	−0.210477	−0.105238	−	0.994447i	$-0.533561\pi$
$157$	−2.63726	−0.210477	−0.105238	+	0.994447i	$0.533561\pi$
$158$	−12.0276	−0.956861
$159$	2.57020	0.203830
$160$	−2.70877	−0.214147
$161$	2.75926	0.217460
$162$	1.67923	0.131933
$163$	−1.40875	−0.110342	−0.0551708	−	0.998477i	$-0.517570\pi$
$163$	−1.40875	−0.110342	−0.0551708	+	0.998477i	$0.517570\pi$
$164$	3.34983	0.261578
$165$	3.00763	0.234144
$166$	10.6357	0.825492
$167$	−25.6584	−1.98551	−0.992754	−	0.120162i	$-0.961659\pi$
$167$	−25.6584	−1.98551	−0.992754	+	0.120162i	$0.961659\pi$
$168$	−0.950934	−0.0733662
$169$	27.6520	2.12708
$170$	−15.3978	−1.18096
$171$	−8.25629	−0.631374
$172$	−9.44398	−0.720097
$173$	3.23058	0.245617	0.122808	−	0.992430i	$-0.460810\pi$
$173$	3.23058	0.245617	0.122808	+	0.992430i	$0.460810\pi$
$174$	7.64699	0.579717
$175$	2.33746	0.176695
$176$	1.16762	0.0880126
$177$	10.2168	0.767945
$178$	5.37454	0.402839
$179$	15.2769	1.14185	0.570926	−	0.821002i	$-0.306584\pi$
$179$	15.2769	1.14185	0.570926	+	0.821002i	$0.306584\pi$
$180$	5.67684	0.423127
$181$	−6.03689	−0.448718	−0.224359	−	0.974507i	$-0.572029\pi$
$181$	−6.03689	−0.448718	−0.224359	+	0.974507i	$0.572029\pi$
$182$	−6.37589	−0.472612
$183$	−4.71150	−0.348284
$184$	2.75926	0.203415
$185$	−25.0056	−1.83845
$186$	−7.02840	−0.515348
$187$	6.63724	0.485363
$188$	0.544796	0.0397333
$189$	4.84570	0.352473
$190$	−10.6714	−0.774188
$191$	1.72938	0.125133	0.0625667	−	0.998041i	$-0.480071\pi$
$191$	1.72938	0.125133	0.0625667	+	0.998041i	$0.480071\pi$
$192$	−0.950934	−0.0686278
$193$	−8.72233	−0.627847	−0.313923	−	0.949448i	$-0.601644\pi$
$193$	−8.72233	−0.627847	−0.313923	+	0.949448i	$0.601644\pi$
$194$	0.731566	0.0525234
$195$	−16.4234	−1.17611
$196$	1.00000	0.0714286
$197$	21.9263	1.56218	0.781092	−	0.624416i	$-0.214663\pi$
$197$	21.9263	1.56218	0.781092	+	0.624416i	$0.214663\pi$
$198$	−2.44701	−0.173901
$199$	8.23073	0.583461	0.291731	−	0.956501i	$-0.405769\pi$
$199$	8.23073	0.583461	0.291731	+	0.956501i	$0.405769\pi$
$200$	2.33746	0.165283
$201$	9.59109	0.676503
$202$	−1.40385	−0.0987745
$203$	−8.04156	−0.564407
$204$	−5.40551	−0.378461
$205$	−9.07394	−0.633752
$206$	−2.16667	−0.150959
$207$	−5.78264	−0.401921
$208$	−6.37589	−0.442089
$209$	4.59994	0.318184
$210$	2.57587	0.177752
$211$	−19.7467	−1.35942	−0.679708	−	0.733483i	$-0.737893\pi$
$211$	−19.7467	−1.35942	−0.679708	+	0.733483i	$0.737893\pi$
$212$	−2.70282	−0.185630
$213$	8.73880	0.598773
$214$	−10.4033	−0.711158
$215$	25.5816	1.74465
$216$	4.84570	0.329708
$217$	7.39105	0.501737
$218$	−5.66932	−0.383975
$219$	2.41012	0.162861
$220$	−3.16282	−0.213237
$221$	−36.2432	−2.43798
$222$	−8.77839	−0.589167
$223$	11.4398	0.766066	0.383033	−	0.923735i	$-0.374880\pi$
$223$	11.4398	0.766066	0.383033	+	0.923735i	$0.374880\pi$
$224$	1.00000	0.0668153
$225$	−4.89866	−0.326577
$226$	−17.3226	−1.15228
$227$	−18.3255	−1.21630	−0.608152	−	0.793820i	$-0.708089\pi$
$227$	−18.3255	−1.21630	−0.608152	+	0.793820i	$0.708089\pi$
$228$	−3.74629	−0.248104
$229$	−4.35068	−0.287501	−0.143750	−	0.989614i	$-0.545916\pi$
$229$	−4.35068	−0.287501	−0.143750	+	0.989614i	$0.545916\pi$
$230$	−7.47420	−0.492834
$231$	−1.11033	−0.0730543
$232$	−8.04156	−0.527954
$233$	−8.68005	−0.568649	−0.284325	−	0.958728i	$-0.591769\pi$
$233$	−8.68005	−0.568649	−0.284325	+	0.958728i	$0.591769\pi$
$234$	13.3621	0.873508
$235$	−1.47573	−0.0962659
$236$	−10.7440	−0.699376
$237$	11.4374	0.742940
$238$	5.68442	0.368466
$239$	0.836732	0.0541237	0.0270618	−	0.999634i	$-0.491385\pi$
$239$	0.836732	0.0541237	0.0270618	+	0.999634i	$0.491385\pi$
$240$	2.57587	0.166271
$241$	−17.0874	−1.10069	−0.550347	−	0.834936i	$-0.685505\pi$
$241$	−17.0874	−1.10069	−0.550347	+	0.834936i	$0.685505\pi$
$242$	−9.63667	−0.619468
$243$	−16.1339	−1.03499
$244$	4.95460	0.317186
$245$	−2.70877	−0.173057
$246$	−3.18547	−0.203098
$247$	−25.1184	−1.59824
$248$	7.39105	0.469332
$249$	−10.1139	−0.640940
$250$	7.21223	0.456141
$251$	−6.22386	−0.392846	−0.196423	−	0.980519i	$-0.562933\pi$
$251$	−6.22386	−0.392846	−0.196423	+	0.980519i	$0.562933\pi$
$252$	−2.09572	−0.132018
$253$	3.22176	0.202550
$254$	−2.88158	−0.180807
$255$	14.6423	0.916936
$256$	1.00000	0.0625000
$257$	−3.61636	−0.225582	−0.112791	−	0.993619i	$-0.535979\pi$
$257$	−3.61636	−0.225582	−0.112791	+	0.993619i	$0.535979\pi$
$258$	8.98061	0.559108
$259$	9.23133	0.573607
$260$	17.2708	1.07109
$261$	16.8529	1.04317
$262$	−17.0177	−1.05135
$263$	7.42519	0.457857	0.228928	−	0.973443i	$-0.426478\pi$
$263$	7.42519	0.457857	0.228928	+	0.973443i	$0.426478\pi$
$264$	−1.11033	−0.0683360
$265$	7.32132	0.449745
$266$	3.93959	0.241552
$267$	−5.11083	−0.312778
$268$	−10.0860	−0.616098
$269$	−0.478600	−0.0291807	−0.0145904	−	0.999894i	$-0.504644\pi$
$269$	−0.478600	−0.0291807	−0.0145904	+	0.999894i	$0.504644\pi$
$270$	−13.1259	−0.798817
$271$	14.5586	0.884372	0.442186	−	0.896923i	$-0.354203\pi$
$271$	14.5586	0.884372	0.442186	+	0.896923i	$0.354203\pi$
$272$	5.68442	0.344668
$273$	6.06305	0.366953
$274$	−2.33549	−0.141092
$275$	2.72926	0.164580
$276$	−2.62387	−0.157939
$277$	9.64751	0.579663	0.289831	−	0.957078i	$-0.406401\pi$
$277$	9.64751	0.579663	0.289831	+	0.957078i	$0.406401\pi$
$278$	4.34425	0.260551
$279$	−15.4896	−0.927338
$280$	−2.70877	−0.161880
$281$	18.8996	1.12746	0.563729	−	0.825960i	$-0.309366\pi$
$281$	18.8996	1.12746	0.563729	+	0.825960i	$0.309366\pi$
$282$	−0.518065	−0.0308503
$283$	−30.3165	−1.80213	−0.901064	−	0.433686i	$-0.857213\pi$
$283$	−30.3165	−1.80213	−0.901064	+	0.433686i	$0.857213\pi$
$284$	−9.18971	−0.545309
$285$	10.1478	0.601106
$286$	−7.44461	−0.440209
$287$	3.34983	0.197734
$288$	−2.09572	−0.123492
$289$	15.3126	0.900741
$290$	21.7828	1.27913
$291$	−0.695671	−0.0407810
$292$	−2.53447	−0.148319
$293$	3.40339	0.198828	0.0994142	−	0.995046i	$-0.468303\pi$
$293$	3.40339	0.198828	0.0994142	+	0.995046i	$0.468303\pi$
$294$	−0.950934	−0.0554596
$295$	29.1031	1.69445
$296$	9.23133	0.536560
$297$	5.65793	0.328306
$298$	−7.58349	−0.439300
$299$	−17.5927	−1.01741
$300$	−2.22277	−0.128331
$301$	−9.44398	−0.544342
$302$	6.79212	0.390842
$303$	1.33497	0.0766919
$304$	3.93959	0.225951
$305$	−13.4209	−0.768478
$306$	−11.9130	−0.681019
$307$	−13.4622	−0.768327	−0.384164	−	0.923265i	$-0.625510\pi$
$307$	−13.4622	−0.768327	−0.384164	+	0.923265i	$0.625510\pi$
$308$	1.16762	0.0665313
$309$	2.06036	0.117210
$310$	−20.0207	−1.13710
$311$	17.9361	1.01706	0.508531	−	0.861044i	$-0.330189\pi$
$311$	17.9361	1.01706	0.508531	+	0.861044i	$0.330189\pi$
$312$	6.06305	0.343253
$313$	17.7445	1.00298	0.501490	−	0.865163i	$-0.332785\pi$
$313$	17.7445	1.00298	0.501490	+	0.865163i	$0.332785\pi$
$314$	−2.63726	−0.148829
$315$	5.67684	0.319854
$316$	−12.0276	−0.676603
$317$	−9.51798	−0.534583	−0.267292	−	0.963616i	$-0.586129\pi$
$317$	−9.51798	−0.534583	−0.267292	+	0.963616i	$0.586129\pi$
$318$	2.57020	0.144130
$319$	−9.38948	−0.525710
$320$	−2.70877	−0.151425
$321$	9.89290	0.552168
$322$	2.75926	0.153767
$323$	22.3943	1.24605
$324$	1.67923	0.0932907
$325$	−14.9034	−0.826690
$326$	−1.40875	−0.0780233
$327$	5.39115	0.298132
$328$	3.34983	0.184964
$329$	0.544796	0.0300356
$330$	3.00763	0.165565
$331$	−24.5123	−1.34732	−0.673660	−	0.739042i	$-0.735279\pi$
$331$	−24.5123	−1.34732	−0.673660	+	0.739042i	$0.735279\pi$
$332$	10.6357	0.583711
$333$	−19.3463	−1.06017
$334$	−25.6584	−1.40397
$335$	27.3206	1.49268
$336$	−0.950934	−0.0518777
$337$	21.0010	1.14399	0.571997	−	0.820255i	$-0.306169\pi$
$337$	21.0010	1.14399	0.571997	+	0.820255i	$0.306169\pi$
$338$	27.6520	1.50407
$339$	16.4727	0.894672
$340$	−15.3978	−0.835063
$341$	8.62993	0.467337
$342$	−8.25629	−0.446449
$343$	1.00000	0.0539949
$344$	−9.44398	−0.509185
$345$	7.10748	0.382654
$346$	3.23058	0.173677
$347$	7.37139	0.395717	0.197859	−	0.980231i	$-0.436601\pi$
$347$	7.37139	0.395717	0.197859	+	0.980231i	$0.436601\pi$
$348$	7.64699	0.409922
$349$	−0.627525	−0.0335906	−0.0167953	−	0.999859i	$-0.505346\pi$
$349$	−0.627525	−0.0335906	−0.0167953	+	0.999859i	$0.505346\pi$
$350$	2.33746	0.124942
$351$	−30.8956	−1.64909
$352$	1.16762	0.0622343
$353$	−33.5692	−1.78671	−0.893353	−	0.449355i	$-0.851654\pi$
$353$	−33.5692	−1.78671	−0.893353	+	0.449355i	$0.851654\pi$
$354$	10.2168	0.543019
$355$	24.8928	1.32117
$356$	5.37454	0.284850
$357$	−5.40551	−0.286090
$358$	15.2769	0.807411
$359$	1.58871	0.0838491	0.0419246	−	0.999121i	$-0.486651\pi$
$359$	1.58871	0.0838491	0.0419246	+	0.999121i	$0.486651\pi$
$360$	5.67684	0.299196
$361$	−3.47966	−0.183140
$362$	−6.03689	−0.317292
$363$	9.16383	0.480977
$364$	−6.37589	−0.334187
$365$	6.86531	0.359347
$366$	−4.71150	−0.246274
$367$	15.6865	0.818827	0.409413	−	0.912349i	$-0.365733\pi$
$367$	15.6865	0.818827	0.409413	+	0.912349i	$0.365733\pi$
$368$	2.75926	0.143836
$369$	−7.02033	−0.365464
$370$	−25.0056	−1.29998
$371$	−2.70282	−0.140323
$372$	−7.02840	−0.364406
$373$	−33.9739	−1.75910	−0.879551	−	0.475805i	$-0.842157\pi$
$373$	−33.9739	−1.75910	−0.879551	+	0.475805i	$0.842157\pi$
$374$	6.63724	0.343203
$375$	−6.85836	−0.354164
$376$	0.544796	0.0280957
$377$	51.2721	2.64065
$378$	4.84570	0.249236
$379$	−17.9830	−0.923725	−0.461863	−	0.886951i	$-0.652819\pi$
$379$	−17.9830	−0.923725	−0.461863	+	0.886951i	$0.652819\pi$
$380$	−10.6714	−0.547434
$381$	2.74020	0.140385
$382$	1.72938	0.0884827
$383$	30.4025	1.55350	0.776748	−	0.629811i	$-0.216868\pi$
$383$	30.4025	1.55350	0.776748	+	0.629811i	$0.216868\pi$
$384$	−0.950934	−0.0485272
$385$	−3.16282	−0.161192
$386$	−8.72233	−0.443955
$387$	19.7920	1.00608
$388$	0.731566	0.0371397
$389$	−20.3762	−1.03311	−0.516557	−	0.856253i	$-0.672787\pi$
$389$	−20.3762	−1.03311	−0.516557	+	0.856253i	$0.672787\pi$
$390$	−16.4234	−0.831633
$391$	15.6848	0.793213
$392$	1.00000	0.0505076
$393$	16.1827	0.816308
$394$	21.9263	1.10463
$395$	32.5799	1.63927
$396$	−2.44701	−0.122967
$397$	−16.7228	−0.839295	−0.419648	−	0.907687i	$-0.637846\pi$
$397$	−16.7228	−0.839295	−0.419648	+	0.907687i	$0.637846\pi$
$398$	8.23073	0.412569
$399$	−3.74629	−0.187549
$400$	2.33746	0.116873
$401$	−25.7891	−1.28785	−0.643923	−	0.765090i	$-0.722694\pi$
$401$	−25.7891	−1.28785	−0.643923	+	0.765090i	$0.722694\pi$
$402$	9.59109	0.478360
$403$	−47.1245	−2.34744
$404$	−1.40385	−0.0698441
$405$	−4.54866	−0.226025
$406$	−8.04156	−0.399096
$407$	10.7787	0.534279
$408$	−5.40551	−0.267612
$409$	20.6167	1.01943	0.509715	−	0.860344i	$-0.329751\pi$
$409$	20.6167	1.01943	0.509715	+	0.860344i	$0.329751\pi$
$410$	−9.07394	−0.448130
$411$	2.22090	0.109549
$412$	−2.16667	−0.106744
$413$	−10.7440	−0.528678
$414$	−5.78264	−0.284201
$415$	−28.8098	−1.41422
$416$	−6.37589	−0.312604
$417$	−4.13110	−0.202301
$418$	4.59994	0.224990
$419$	30.2385	1.47725	0.738623	−	0.674119i	$-0.235477\pi$
$419$	30.2385	1.47725	0.738623	+	0.674119i	$0.235477\pi$
$420$	2.57587	0.125689
$421$	9.70016	0.472757	0.236378	−	0.971661i	$-0.424040\pi$
$421$	9.70016	0.472757	0.236378	+	0.971661i	$0.424040\pi$
$422$	−19.7467	−0.961252
$423$	−1.14174	−0.0555134
$424$	−2.70282	−0.131260
$425$	13.2871	0.644518
$426$	8.73880	0.423396
$427$	4.95460	0.239770
$428$	−10.4033	−0.502865
$429$	7.07934	0.341794
$430$	25.5816	1.23365
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	4.84570	0.233139
$433$	−30.1505	−1.44894	−0.724471	−	0.689306i	$-0.757916\pi$
$433$	−30.1505	−1.44894	−0.724471	+	0.689306i	$0.757916\pi$
$434$	7.39105	0.354782
$435$	−20.7140	−0.993159
$436$	−5.66932	−0.271511
$437$	10.8703	0.519998
$438$	2.41012	0.115160
$439$	−1.38860	−0.0662744	−0.0331372	−	0.999451i	$-0.510550\pi$
$439$	−1.38860	−0.0662744	−0.0331372	+	0.999451i	$0.510550\pi$
$440$	−3.16282	−0.150781
$441$	−2.09572	−0.0997964
$442$	−36.2432	−1.72391
$443$	−13.5234	−0.642516	−0.321258	−	0.946992i	$-0.604106\pi$
$443$	−13.5234	−0.642516	−0.321258	+	0.946992i	$0.604106\pi$
$444$	−8.77839	−0.416604
$445$	−14.5584	−0.690135
$446$	11.4398	0.541690
$447$	7.21140	0.341087
$448$	1.00000	0.0472456
$449$	3.11630	0.147067	0.0735336	−	0.997293i	$-0.476572\pi$
$449$	3.11630	0.147067	0.0735336	+	0.997293i	$0.476572\pi$
$450$	−4.89866	−0.230925
$451$	3.91133	0.184177
$452$	−17.3226	−0.814787
$453$	−6.45886	−0.303464
$454$	−18.3255	−0.860057
$455$	17.2708	0.809670
$456$	−3.74629	−0.175436
$457$	26.7811	1.25277	0.626383	−	0.779516i	$-0.284535\pi$
$457$	26.7811	1.25277	0.626383	+	0.779516i	$0.284535\pi$
$458$	−4.35068	−0.203294
$459$	27.5450	1.28569
$460$	−7.47420	−0.348487
$461$	−29.6759	−1.38214	−0.691072	−	0.722786i	$-0.742861\pi$
$461$	−29.6759	−1.38214	−0.691072	+	0.722786i	$0.742861\pi$
$462$	−1.11033	−0.0516572
$463$	9.37096	0.435506	0.217753	−	0.976004i	$-0.430127\pi$
$463$	9.37096	0.435506	0.217753	+	0.976004i	$0.430127\pi$
$464$	−8.04156	−0.373320
$465$	19.0384	0.882883
$466$	−8.68005	−0.402096
$467$	31.2231	1.44483	0.722417	−	0.691458i	$-0.243031\pi$
$467$	31.2231	1.44483	0.722417	+	0.691458i	$0.243031\pi$
$468$	13.3621	0.617664
$469$	−10.0860	−0.465726
$470$	−1.47573	−0.0680703
$471$	2.50786	0.115556
$472$	−10.7440	−0.494533
$473$	−11.0270	−0.507021
$474$	11.4374	0.525338
$475$	9.20861	0.422520
$476$	5.68442	0.260545
$477$	5.66436	0.259353
$478$	0.836732	0.0382712
$479$	−12.3321	−0.563468	−0.281734	−	0.959493i	$-0.590910\pi$
$479$	−12.3321	−0.563468	−0.281734	+	0.959493i	$0.590910\pi$
$480$	2.57587	0.117572
$481$	−58.8580	−2.68369
$482$	−17.0874	−0.778309
$483$	−2.62387	−0.119390
$484$	−9.63667	−0.438030
$485$	−1.98165	−0.0899820
$486$	−16.1339	−0.731850
$487$	12.8601	0.582746	0.291373	−	0.956609i	$-0.405888\pi$
$487$	12.8601	0.582746	0.291373	+	0.956609i	$0.405888\pi$
$488$	4.95460	0.224284
$489$	1.33963	0.0605800
$490$	−2.70877	−0.122370
$491$	−33.6978	−1.52076	−0.760381	−	0.649478i	$-0.774988\pi$
$491$	−33.6978	−1.52076	−0.760381	+	0.649478i	$0.774988\pi$
$492$	−3.18547	−0.143612
$493$	−45.7116	−2.05875
$494$	−25.1184	−1.13013
$495$	6.62839	0.297924
$496$	7.39105	0.331868
$497$	−9.18971	−0.412215
$498$	−10.1139	−0.453213
$499$	31.5403	1.41194	0.705968	−	0.708243i	$-0.250512\pi$
$499$	31.5403	1.41194	0.705968	+	0.708243i	$0.250512\pi$
$500$	7.21223	0.322541
$501$	24.3995	1.09009
$502$	−6.22386	−0.277784
$503$	−21.5753	−0.961994	−0.480997	−	0.876722i	$-0.659725\pi$
$503$	−21.5753	−0.961994	−0.480997	+	0.876722i	$0.659725\pi$
$504$	−2.09572	−0.0933510
$505$	3.80271	0.169218
$506$	3.22176	0.143225
$507$	−26.2952	−1.16781
$508$	−2.88158	−0.127850
$509$	−41.7048	−1.84853	−0.924266	−	0.381750i	$-0.875322\pi$
$509$	−41.7048	−1.84853	−0.924266	+	0.381750i	$0.875322\pi$
$510$	14.6423	0.648372
$511$	−2.53447	−0.112118
$512$	1.00000	0.0441942
$513$	19.0900	0.842846
$514$	−3.61636	−0.159511
$515$	5.86902	0.258620
$516$	8.98061	0.395349
$517$	0.636114	0.0279763
$518$	9.23133	0.405601
$519$	−3.07207	−0.134849
$520$	17.2708	0.757377
$521$	−39.6817	−1.73849	−0.869244	−	0.494383i	$-0.835394\pi$
$521$	−39.6817	−1.73849	−0.869244	+	0.494383i	$0.835394\pi$
$522$	16.8529	0.737631
$523$	18.2632	0.798594	0.399297	−	0.916822i	$-0.369254\pi$
$523$	18.2632	0.798594	0.399297	+	0.916822i	$0.369254\pi$
$524$	−17.0177	−0.743420
$525$	−2.22277	−0.0970095
$526$	7.42519	0.323754
$527$	42.0138	1.83015
$528$	−1.11033	−0.0483209
$529$	−15.3865	−0.668978
$530$	7.32132	0.318018
$531$	22.5165	0.977132
$532$	3.93959	0.170803
$533$	−21.3582	−0.925125
$534$	−5.11083	−0.221167
$535$	28.1803	1.21834
$536$	−10.0860	−0.435647
$537$	−14.5274	−0.626902
$538$	−0.478600	−0.0206339
$539$	1.16762	0.0502929
$540$	−13.1259	−0.564849
$541$	−22.8894	−0.984091	−0.492045	−	0.870570i	$-0.663751\pi$
$541$	−22.8894	−0.984091	−0.492045	+	0.870570i	$0.663751\pi$
$542$	14.5586	0.625345
$543$	5.74068	0.246356
$544$	5.68442	0.243717
$545$	15.3569	0.657818
$546$	6.06305	0.259475
$547$	−31.5255	−1.34793	−0.673966	−	0.738762i	$-0.735411\pi$
$547$	−31.5255	−1.34793	−0.673966	+	0.738762i	$0.735411\pi$
$548$	−2.33549	−0.0997673
$549$	−10.3835	−0.443156
$550$	2.72926	0.116376
$551$	−31.6804	−1.34963
$552$	−2.62387	−0.111679
$553$	−12.0276	−0.511464
$554$	9.64751	0.409883
$555$	23.7787	1.00935
$556$	4.34425	0.184237
$557$	11.0858	0.469718	0.234859	−	0.972029i	$-0.424537\pi$
$557$	11.0858	0.469718	0.234859	+	0.972029i	$0.424537\pi$
$558$	−15.4896	−0.655727
$559$	60.2138	2.54677
$560$	−2.70877	−0.114467
$561$	−6.31157	−0.266475
$562$	18.8996	0.797233
$563$	−34.0747	−1.43608	−0.718039	−	0.696003i	$-0.754960\pi$
$563$	−34.0747	−1.43608	−0.718039	+	0.696003i	$0.754960\pi$
$564$	−0.518065	−0.0218145
$565$	46.9230	1.97407
$566$	−30.3165	−1.27430
$567$	1.67923	0.0705211
$568$	−9.18971	−0.385591
$569$	30.5691	1.28152	0.640762	−	0.767739i	$-0.278618\pi$
$569$	30.5691	1.28152	0.640762	+	0.767739i	$0.278618\pi$
$570$	10.1478	0.425046
$571$	35.7995	1.49816	0.749080	−	0.662479i	$-0.230496\pi$
$571$	35.7995	1.49816	0.749080	+	0.662479i	$0.230496\pi$
$572$	−7.44461	−0.311275
$573$	−1.64453	−0.0687010
$574$	3.34983	0.139819
$575$	6.44964	0.268969
$576$	−2.09572	−0.0873218
$577$	29.2167	1.21631	0.608154	−	0.793819i	$-0.291910\pi$
$577$	29.2167	1.21631	0.608154	+	0.793819i	$0.291910\pi$
$578$	15.3126	0.636920
$579$	8.29436	0.344702
$580$	21.7828	0.904480
$581$	10.6357	0.441244
$582$	−0.695671	−0.0288365
$583$	−3.15586	−0.130702
$584$	−2.53447	−0.104877
$585$	−36.1949	−1.49648
$586$	3.40339	0.140593
$587$	21.1506	0.872979	0.436489	−	0.899709i	$-0.356222\pi$
$587$	21.1506	0.872979	0.436489	+	0.899709i	$0.356222\pi$
$588$	−0.950934	−0.0392159
$589$	29.1177	1.19977
$590$	29.1031	1.19816
$591$	−20.8505	−0.857673
$592$	9.23133	0.379405
$593$	−14.8923	−0.611553	−0.305777	−	0.952103i	$-0.598916\pi$
$593$	−14.8923	−0.611553	−0.305777	+	0.952103i	$0.598916\pi$
$594$	5.65793	0.232148
$595$	−15.3978	−0.631248
$596$	−7.58349	−0.310632
$597$	−7.82689	−0.320333
$598$	−17.5927	−0.719420
$599$	−29.1329	−1.19034	−0.595170	−	0.803600i	$-0.702915\pi$
$599$	−29.1329	−1.19034	−0.595170	+	0.803600i	$0.702915\pi$
$600$	−2.22277	−0.0907441
$601$	−34.9608	−1.42608	−0.713040	−	0.701124i	$-0.752682\pi$
$601$	−34.9608	−1.42608	−0.713040	+	0.701124i	$0.752682\pi$
$602$	−9.44398	−0.384908
$603$	21.1374	0.860781
$604$	6.79212	0.276367
$605$	26.1035	1.06126
$606$	1.33497	0.0542294
$607$	−27.9139	−1.13299	−0.566496	−	0.824065i	$-0.691701\pi$
$607$	−27.9139	−1.13299	−0.566496	+	0.824065i	$0.691701\pi$
$608$	3.93959	0.159771
$609$	7.64699	0.309872
$610$	−13.4209	−0.543396
$611$	−3.47356	−0.140525
$612$	−11.9130	−0.481553
$613$	45.1543	1.82377	0.911883	−	0.410450i	$-0.134628\pi$
$613$	45.1543	1.82377	0.911883	+	0.410450i	$0.134628\pi$
$614$	−13.4622	−0.543289
$615$	8.62872	0.347944
$616$	1.16762	0.0470447
$617$	−23.1786	−0.933136	−0.466568	−	0.884485i	$-0.654510\pi$
$617$	−23.1786	−0.933136	−0.466568	+	0.884485i	$0.654510\pi$
$618$	2.06036	0.0828798
$619$	−11.0141	−0.442694	−0.221347	−	0.975195i	$-0.571045\pi$
$619$	−11.0141	−0.442694	−0.221347	+	0.975195i	$0.571045\pi$
$620$	−20.0207	−0.804050
$621$	13.3705	0.536541
$622$	17.9361	0.719171
$623$	5.37454	0.215326
$624$	6.06305	0.242716
$625$	−31.2236	−1.24894
$626$	17.7445	0.709214
$627$	−4.37424	−0.174690
$628$	−2.63726	−0.105238
$629$	52.4747	2.09230
$630$	5.67684	0.226171
$631$	19.0942	0.760128	0.380064	−	0.924960i	$-0.375902\pi$
$631$	19.0942	0.760128	0.380064	+	0.924960i	$0.375902\pi$
$632$	−12.0276	−0.478430
$633$	18.7778	0.746349
$634$	−9.51798	−0.378007
$635$	7.80556	0.309754
$636$	2.57020	0.101915
$637$	−6.37589	−0.252622
$638$	−9.38948	−0.371733
$639$	19.2591	0.761878
$640$	−2.70877	−0.107074
$641$	36.8681	1.45620	0.728102	−	0.685469i	$-0.240403\pi$
$641$	36.8681	1.45620	0.728102	+	0.685469i	$0.240403\pi$
$642$	9.89290	0.390441
$643$	2.85723	0.112678	0.0563390	−	0.998412i	$-0.482057\pi$
$643$	2.85723	0.112678	0.0563390	+	0.998412i	$0.482057\pi$
$644$	2.75926	0.108730
$645$	−24.3264	−0.957852
$646$	22.3943	0.881090
$647$	−16.8980	−0.664328	−0.332164	−	0.943222i	$-0.607779\pi$
$647$	−16.8980	−0.664328	−0.332164	+	0.943222i	$0.607779\pi$
$648$	1.67923	0.0659665
$649$	−12.5449	−0.492431
$650$	−14.9034	−0.584558
$651$	−7.02840	−0.275465
$652$	−1.40875	−0.0551708
$653$	−0.220970	−0.00864721	−0.00432360	−	0.999991i	$-0.501376\pi$
$653$	−0.220970	−0.00864721	−0.00432360	+	0.999991i	$0.501376\pi$
$654$	5.39115	0.210811
$655$	46.0970	1.80116
$656$	3.34983	0.130789
$657$	5.31156	0.207224
$658$	0.544796	0.0212384
$659$	−41.1106	−1.60144	−0.800721	−	0.599037i	$-0.795550\pi$
$659$	−41.1106	−1.60144	−0.800721	+	0.599037i	$0.795550\pi$
$660$	3.00763	0.117072
$661$	−20.9468	−0.814735	−0.407367	−	0.913264i	$-0.633553\pi$
$661$	−20.9468	−0.814735	−0.407367	+	0.913264i	$0.633553\pi$
$662$	−24.5123	−0.952699
$663$	34.4649	1.33851
$664$	10.6357	0.412746
$665$	−10.6714	−0.413821
$666$	−19.3463	−0.749655
$667$	−22.1887	−0.859151
$668$	−25.6584	−0.992754
$669$	−10.8785	−0.420587
$670$	27.3206	1.05549
$671$	5.78509	0.223331
$672$	−0.950934	−0.0366831
$673$	−19.7395	−0.760903	−0.380451	−	0.924801i	$-0.624231\pi$
$673$	−19.7395	−0.760903	−0.380451	+	0.924801i	$0.624231\pi$
$674$	21.0010	0.808927
$675$	11.3266	0.435961
$676$	27.6520	1.06354
$677$	−0.375575	−0.0144345	−0.00721727	−	0.999974i	$-0.502297\pi$
$677$	−0.375575	−0.0144345	−0.00721727	+	0.999974i	$0.502297\pi$
$678$	16.4727	0.632629
$679$	0.731566	0.0280749
$680$	−15.3978	−0.590479
$681$	17.4263	0.667778
$682$	8.62993	0.330457
$683$	−37.9908	−1.45368	−0.726839	−	0.686808i	$-0.759011\pi$
$683$	−37.9908	−1.45368	−0.726839	+	0.686808i	$0.759011\pi$
$684$	−8.25629	−0.315687
$685$	6.32632	0.241716
$686$	1.00000	0.0381802
$687$	4.13721	0.157844
$688$	−9.44398	−0.360048
$689$	17.2329	0.656520
$690$	7.10748	0.270577
$691$	−9.08714	−0.345691	−0.172846	−	0.984949i	$-0.555296\pi$
$691$	−9.08714	−0.345691	−0.172846	+	0.984949i	$0.555296\pi$
$692$	3.23058	0.122808
$693$	−2.44701	−0.0929541
$694$	7.37139	0.279814
$695$	−11.7676	−0.446371
$696$	7.64699	0.289858
$697$	19.0419	0.721262
$698$	−0.627525	−0.0237522
$699$	8.25416	0.312201
$700$	2.33746	0.0883475
$701$	25.8563	0.976578	0.488289	−	0.872682i	$-0.337621\pi$
$701$	25.8563	0.976578	0.488289	+	0.872682i	$0.337621\pi$
$702$	−30.8956	−1.16608
$703$	36.3676	1.37163
$704$	1.16762	0.0440063
$705$	1.40332	0.0528521
$706$	−33.5692	−1.26339
$707$	−1.40385	−0.0527972
$708$	10.2168	0.383973
$709$	33.7372	1.26703	0.633513	−	0.773732i	$-0.281612\pi$
$709$	33.7372	1.26703	0.633513	+	0.773732i	$0.281612\pi$
$710$	24.8928	0.934211
$711$	25.2064	0.945315
$712$	5.37454	0.201419
$713$	20.3938	0.763754
$714$	−5.40551	−0.202296
$715$	20.1658	0.754157
$716$	15.2769	0.570926
$717$	−0.795677	−0.0297151
$718$	1.58871	0.0592903
$719$	−24.9600	−0.930850	−0.465425	−	0.885087i	$-0.654098\pi$
$719$	−24.9600	−0.930850	−0.465425	+	0.885087i	$0.654098\pi$
$720$	5.67684	0.211563
$721$	−2.16667	−0.0806910
$722$	−3.47966	−0.129500
$723$	16.2490	0.604306
$724$	−6.03689	−0.224359
$725$	−18.7968	−0.698095
$726$	9.16383	0.340102
$727$	8.01767	0.297359	0.148679	−	0.988885i	$-0.452498\pi$
$727$	8.01767	0.297359	0.148679	+	0.988885i	$0.452498\pi$
$728$	−6.37589	−0.236306
$729$	10.3046	0.381652
$730$	6.86531	0.254097
$731$	−53.6835	−1.98556
$732$	−4.71150	−0.174142
$733$	33.0855	1.22204	0.611020	−	0.791615i	$-0.290759\pi$
$733$	33.0855	1.22204	0.611020	+	0.791615i	$0.290759\pi$
$734$	15.6865	0.578998
$735$	2.57587	0.0950122
$736$	2.75926	0.101708
$737$	−11.7766	−0.433795
$738$	−7.02033	−0.258422
$739$	−14.8267	−0.545411	−0.272705	−	0.962098i	$-0.587918\pi$
$739$	−14.8267	−0.545411	−0.272705	+	0.962098i	$0.587918\pi$
$740$	−25.0056	−0.919224
$741$	23.8859	0.877471
$742$	−2.70282	−0.0992235
$743$	34.0993	1.25098	0.625490	−	0.780232i	$-0.284899\pi$
$743$	34.0993	1.25098	0.625490	+	0.780232i	$0.284899\pi$
$744$	−7.02840	−0.257674
$745$	20.5420	0.752599
$746$	−33.9739	−1.24387
$747$	−22.2895	−0.815531
$748$	6.63724	0.242681
$749$	−10.4033	−0.380130
$750$	−6.85836	−0.250432
$751$	3.98227	0.145315	0.0726575	−	0.997357i	$-0.476852\pi$
$751$	3.98227	0.145315	0.0726575	+	0.997357i	$0.476852\pi$
$752$	0.544796	0.0198667
$753$	5.91848	0.215681
$754$	51.2721	1.86722
$755$	−18.3983	−0.669583
$756$	4.84570	0.176236
$757$	22.4006	0.814165	0.407082	−	0.913391i	$-0.366546\pi$
$757$	22.4006	0.814165	0.407082	+	0.913391i	$0.366546\pi$
$758$	−17.9830	−0.653172
$759$	−3.06368	−0.111205
$760$	−10.6714	−0.387094
$761$	44.2175	1.60288	0.801442	−	0.598073i	$-0.204067\pi$
$761$	44.2175	1.60288	0.801442	+	0.598073i	$0.204067\pi$
$762$	2.74020	0.0992668
$763$	−5.66932	−0.205243
$764$	1.72938	0.0625667
$765$	32.2695	1.16671
$766$	30.4025	1.09849
$767$	68.5027	2.47349
$768$	−0.950934	−0.0343139
$769$	23.2528	0.838517	0.419258	−	0.907867i	$-0.362290\pi$
$769$	23.2528	0.838517	0.419258	+	0.907867i	$0.362290\pi$
$770$	−3.16282	−0.113980
$771$	3.43892	0.123850
$772$	−8.72233	−0.313923
$773$	−4.01058	−0.144251	−0.0721253	−	0.997396i	$-0.522978\pi$
$773$	−4.01058	−0.144251	−0.0721253	+	0.997396i	$0.522978\pi$
$774$	19.7920	0.711408
$775$	17.2763	0.620581
$776$	0.731566	0.0262617
$777$	−8.77839	−0.314923
$778$	−20.3762	−0.730522
$779$	13.1970	0.472830
$780$	−16.4234	−0.588053
$781$	−10.7301	−0.383952
$782$	15.6848	0.560886
$783$	−38.9670	−1.39257
$784$	1.00000	0.0357143
$785$	7.14375	0.254971
$786$	16.1827	0.577217
$787$	−12.9111	−0.460230	−0.230115	−	0.973163i	$-0.573910\pi$
$787$	−12.9111	−0.460230	−0.230115	+	0.973163i	$0.573910\pi$
$788$	21.9263	0.781092
$789$	−7.06087	−0.251374
$790$	32.5799	1.15914
$791$	−17.3226	−0.615921
$792$	−2.44701	−0.0869506
$793$	−31.5900	−1.12179
$794$	−16.7228	−0.593471
$795$	−6.96209	−0.246920
$796$	8.23073	0.291731
$797$	31.3398	1.11011	0.555057	−	0.831813i	$-0.312697\pi$
$797$	31.3398	1.11011	0.555057	+	0.831813i	$0.312697\pi$
$798$	−3.74629	−0.132617
$799$	3.09685	0.109559
$800$	2.33746	0.0826415
$801$	−11.2635	−0.397978
$802$	−25.7891	−0.910645
$803$	−2.95930	−0.104431
$804$	9.59109	0.338252
$805$	−7.47420	−0.263431
$806$	−47.1245	−1.65989
$807$	0.455117	0.0160209
$808$	−1.40385	−0.0493872
$809$	−20.4015	−0.717279	−0.358640	−	0.933476i	$-0.616759\pi$
$809$	−20.4015	−0.717279	−0.358640	+	0.933476i	$0.616759\pi$
$810$	−4.54866	−0.159824
$811$	30.4751	1.07013	0.535063	−	0.844812i	$-0.320288\pi$
$811$	30.4751	1.07013	0.535063	+	0.844812i	$0.320288\pi$
$812$	−8.04156	−0.282203
$813$	−13.8443	−0.485540
$814$	10.7787	0.377793
$815$	3.81598	0.133668
$816$	−5.40551	−0.189231
$817$	−37.2054	−1.30165
$818$	20.6167	0.720845
$819$	13.3621	0.466910
$820$	−9.07394	−0.316876
$821$	17.4908	0.610433	0.305216	−	0.952283i	$-0.401271\pi$
$821$	17.4908	0.610433	0.305216	+	0.952283i	$0.401271\pi$
$822$	2.22090	0.0774628
$823$	19.1967	0.669154	0.334577	−	0.942368i	$-0.391406\pi$
$823$	19.1967	0.669154	0.334577	+	0.942368i	$0.391406\pi$
$824$	−2.16667	−0.0754795
$825$	−2.59534	−0.0903583
$826$	−10.7440	−0.373832
$827$	26.6024	0.925058	0.462529	−	0.886604i	$-0.346942\pi$
$827$	26.6024	0.925058	0.462529	+	0.886604i	$0.346942\pi$
$828$	−5.78264	−0.200961
$829$	37.2769	1.29468	0.647341	−	0.762201i	$-0.275881\pi$
$829$	37.2769	1.29468	0.647341	+	0.762201i	$0.275881\pi$
$830$	−28.8098	−1.00000
$831$	−9.17415	−0.318248
$832$	−6.37589	−0.221044
$833$	5.68442	0.196953
$834$	−4.13110	−0.143048
$835$	69.5029	2.40525
$836$	4.59994	0.159092
$837$	35.8148	1.23794
$838$	30.2385	1.04457
$839$	37.6548	1.29999	0.649993	−	0.759940i	$-0.274772\pi$
$839$	37.6548	1.29999	0.649993	+	0.759940i	$0.274772\pi$
$840$	2.57587	0.0888758
$841$	35.6666	1.22988
$842$	9.70016	0.334290
$843$	−17.9723	−0.618999
$844$	−19.7467	−0.679708
$845$	−74.9030	−2.57674
$846$	−1.14174	−0.0392539
$847$	−9.63667	−0.331120
$848$	−2.70282	−0.0928151
$849$	28.8290	0.989408
$850$	13.2871	0.455743
$851$	25.4716	0.873156
$852$	8.73880	0.299387
$853$	9.67004	0.331096	0.165548	−	0.986202i	$-0.447061\pi$
$853$	9.67004	0.331096	0.165548	+	0.986202i	$0.447061\pi$
$854$	4.95460	0.169543
$855$	22.3644	0.764847
$856$	−10.4033	−0.355579
$857$	−22.6422	−0.773444	−0.386722	−	0.922196i	$-0.626393\pi$
$857$	−22.6422	−0.773444	−0.386722	+	0.922196i	$0.626393\pi$
$858$	7.07934	0.241685
$859$	29.3558	1.00161	0.500804	−	0.865561i	$-0.333038\pi$
$859$	29.3558	1.00161	0.500804	+	0.865561i	$0.333038\pi$
$860$	25.5816	0.872326
$861$	−3.18547	−0.108561
$862$	−1.00000	−0.0340601
$863$	24.0034	0.817085	0.408542	−	0.912739i	$-0.366037\pi$
$863$	24.0034	0.817085	0.408542	+	0.912739i	$0.366037\pi$
$864$	4.84570	0.164854
$865$	−8.75092	−0.297540
$866$	−30.1505	−1.02456
$867$	−14.5613	−0.494527
$868$	7.39105	0.250869
$869$	−14.0436	−0.476397
$870$	−20.7140	−0.702269
$871$	64.3070	2.17896
$872$	−5.66932	−0.191988
$873$	−1.53316	−0.0518896
$874$	10.8703	0.367694
$875$	7.21223	0.243818
$876$	2.41012	0.0814303
$877$	3.84138	0.129714	0.0648571	−	0.997895i	$-0.479341\pi$
$877$	3.84138	0.129714	0.0648571	+	0.997895i	$0.479341\pi$
$878$	−1.38860	−0.0468631
$879$	−3.23640	−0.109161
$880$	−3.16282	−0.106619
$881$	−24.1036	−0.812072	−0.406036	−	0.913857i	$-0.633089\pi$
$881$	−24.1036	−0.812072	−0.406036	+	0.913857i	$0.633089\pi$
$882$	−2.09572	−0.0705667
$883$	9.58499	0.322561	0.161280	−	0.986909i	$-0.448438\pi$
$883$	9.58499	0.322561	0.161280	+	0.986909i	$0.448438\pi$
$884$	−36.2432	−1.21899
$885$	−27.6751	−0.930289
$886$	−13.5234	−0.454327
$887$	22.1777	0.744653	0.372326	−	0.928102i	$-0.378560\pi$
$887$	22.1777	0.744653	0.372326	+	0.928102i	$0.378560\pi$
$888$	−8.77839	−0.294583
$889$	−2.88158	−0.0966452
$890$	−14.5584	−0.487999
$891$	1.96070	0.0656861
$892$	11.4398	0.383033
$893$	2.14627	0.0718222
$894$	7.21140	0.241185
$895$	−41.3817	−1.38324
$896$	1.00000	0.0334077
$897$	16.7295	0.558582
$898$	3.11630	0.103992
$899$	−59.4356	−1.98229
$900$	−4.89866	−0.163289
$901$	−15.3639	−0.511847
$902$	3.91133	0.130233
$903$	8.98061	0.298856
$904$	−17.3226	−0.576142
$905$	16.3526	0.543577
$906$	−6.45886	−0.214581
$907$	−51.8988	−1.72327	−0.861636	−	0.507526i	$-0.830560\pi$
$907$	−51.8988	−1.72327	−0.861636	+	0.507526i	$0.830560\pi$
$908$	−18.3255	−0.608152
$909$	2.94208	0.0975826
$910$	17.2708	0.572523
$911$	−27.8650	−0.923210	−0.461605	−	0.887086i	$-0.652726\pi$
$911$	−27.8650	−0.923210	−0.461605	+	0.887086i	$0.652726\pi$
$912$	−3.74629	−0.124052
$913$	12.4185	0.410991
$914$	26.7811	0.885839
$915$	12.7624	0.421912
$916$	−4.35068	−0.143750
$917$	−17.0177	−0.561973
$918$	27.5450	0.909120
$919$	−17.8665	−0.589360	−0.294680	−	0.955596i	$-0.595213\pi$
$919$	−17.8665	−0.589360	−0.294680	+	0.955596i	$0.595213\pi$
$920$	−7.47420	−0.246417
$921$	12.8016	0.421829
$922$	−29.6759	−0.977323
$923$	58.5926	1.92860
$924$	−1.11033	−0.0365271
$925$	21.5778	0.709475
$926$	9.37096	0.307949
$927$	4.54074	0.149138
$928$	−8.04156	−0.263977
$929$	−12.9564	−0.425084	−0.212542	−	0.977152i	$-0.568174\pi$
$929$	−12.9564	−0.425084	−0.212542	+	0.977152i	$0.568174\pi$
$930$	19.0384	0.624292
$931$	3.93959	0.129115
$932$	−8.68005	−0.284325
$933$	−17.0560	−0.558389
$934$	31.2231	1.02165
$935$	−17.9788	−0.587969
$936$	13.3621	0.436754
$937$	21.7930	0.711946	0.355973	−	0.934496i	$-0.384149\pi$
$937$	21.7930	0.711946	0.355973	+	0.934496i	$0.384149\pi$
$938$	−10.0860	−0.329318
$939$	−16.8739	−0.550659
$940$	−1.47573	−0.0481330
$941$	56.0917	1.82854	0.914268	−	0.405110i	$-0.132767\pi$
$941$	56.0917	1.82854	0.914268	+	0.405110i	$0.132767\pi$
$942$	2.50786	0.0817106
$943$	9.24305	0.300995
$944$	−10.7440	−0.349688
$945$	−13.1259	−0.426986
$946$	−11.0270	−0.358518
$947$	−16.7552	−0.544471	−0.272236	−	0.962231i	$-0.587763\pi$
$947$	−16.7552	−0.544471	−0.272236	+	0.962231i	$0.587763\pi$
$948$	11.4374	0.371470
$949$	16.1595	0.524560
$950$	9.20861	0.298767
$951$	9.05098	0.293498
$952$	5.68442	0.184233
$953$	−32.3444	−1.04774	−0.523868	−	0.851799i	$-0.675512\pi$
$953$	−32.3444	−1.04774	−0.523868	+	0.851799i	$0.675512\pi$
$954$	5.66436	0.183390
$955$	−4.68450	−0.151587
$956$	0.836732	0.0270618
$957$	8.92877	0.288626
$958$	−12.3321	−0.398432
$959$	−2.33549	−0.0754170
$960$	2.57587	0.0831357
$961$	23.6276	0.762182
$962$	−58.8580	−1.89766
$963$	21.8025	0.702577
$964$	−17.0874	−0.550347
$965$	23.6268	0.760574
$966$	−2.62387	−0.0844217
$967$	59.5811	1.91600	0.958000	−	0.286768i	$-0.0925808\pi$
$967$	59.5811	1.91600	0.958000	+	0.286768i	$0.0925808\pi$
$968$	−9.63667	−0.309734
$969$	−21.2955	−0.684109
$970$	−1.98165	−0.0636269
$971$	12.8554	0.412549	0.206275	−	0.978494i	$-0.433866\pi$
$971$	12.8554	0.412549	0.206275	+	0.978494i	$0.433866\pi$
$972$	−16.1339	−0.517496
$973$	4.34425	0.139270
$974$	12.8601	0.412064
$975$	14.1721	0.453871
$976$	4.95460	0.158593
$977$	−35.1469	−1.12445	−0.562225	−	0.826984i	$-0.690054\pi$
$977$	−35.1469	−1.12445	−0.562225	+	0.826984i	$0.690054\pi$
$978$	1.33963	0.0428365
$979$	6.27541	0.200563
$980$	−2.70877	−0.0865286
$981$	11.8813	0.379342
$982$	−33.6978	−1.07534
$983$	−34.4243	−1.09797	−0.548983	−	0.835833i	$-0.684985\pi$
$983$	−34.4243	−1.09797	−0.548983	+	0.835833i	$0.684985\pi$
$984$	−3.18547	−0.101549
$985$	−59.3934	−1.89243
$986$	−45.7116	−1.45575
$987$	−0.518065	−0.0164902
$988$	−25.1184	−0.799122
$989$	−26.0584	−0.828608
$990$	6.62839	0.210664
$991$	41.8140	1.32826	0.664132	−	0.747615i	$-0.268801\pi$
$991$	41.8140	1.32826	0.664132	+	0.747615i	$0.268801\pi$
$992$	7.39105	0.234666
$993$	23.3096	0.739708
$994$	−9.18971	−0.291480
$995$	−22.2952	−0.706805
$996$	−10.1139	−0.320470
$997$	50.6094	1.60282	0.801408	−	0.598119i	$-0.204085\pi$
$997$	50.6094	1.60282	0.801408	+	0.598119i	$0.204085\pi$
$998$	31.5403	0.998390
$999$	44.7322	1.41527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.10	✓	21	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.950934 q^{3} +1.00000 q^{4} -2.70877 q^{5} -0.950934 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.09572 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.950934 q^{3} +1.00000 q^{4} -2.70877 q^{5} -0.950934 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.09572 q^{9} -2.70877 q^{10} +1.16762 q^{11} -0.950934 q^{12} -6.37589 q^{13} +1.00000 q^{14} +2.57587 q^{15} +1.00000 q^{16} +5.68442 q^{17} -2.09572 q^{18} +3.93959 q^{19} -2.70877 q^{20} -0.950934 q^{21} +1.16762 q^{22} +2.75926 q^{23} -0.950934 q^{24} +2.33746 q^{25} -6.37589 q^{26} +4.84570 q^{27} +1.00000 q^{28} -8.04156 q^{29} +2.57587 q^{30} +7.39105 q^{31} +1.00000 q^{32} -1.11033 q^{33} +5.68442 q^{34} -2.70877 q^{35} -2.09572 q^{36} +9.23133 q^{37} +3.93959 q^{38} +6.06305 q^{39} -2.70877 q^{40} +3.34983 q^{41} -0.950934 q^{42} -9.44398 q^{43} +1.16762 q^{44} +5.67684 q^{45} +2.75926 q^{46} +0.544796 q^{47} -0.950934 q^{48} +1.00000 q^{49} +2.33746 q^{50} -5.40551 q^{51} -6.37589 q^{52} -2.70282 q^{53} +4.84570 q^{54} -3.16282 q^{55} +1.00000 q^{56} -3.74629 q^{57} -8.04156 q^{58} -10.7440 q^{59} +2.57587 q^{60} +4.95460 q^{61} +7.39105 q^{62} -2.09572 q^{63} +1.00000 q^{64} +17.2708 q^{65} -1.11033 q^{66} -10.0860 q^{67} +5.68442 q^{68} -2.62387 q^{69} -2.70877 q^{70} -9.18971 q^{71} -2.09572 q^{72} -2.53447 q^{73} +9.23133 q^{74} -2.22277 q^{75} +3.93959 q^{76} +1.16762 q^{77} +6.06305 q^{78} -12.0276 q^{79} -2.70877 q^{80} +1.67923 q^{81} +3.34983 q^{82} +10.6357 q^{83} -0.950934 q^{84} -15.3978 q^{85} -9.44398 q^{86} +7.64699 q^{87} +1.16762 q^{88} +5.37454 q^{89} +5.67684 q^{90} -6.37589 q^{91} +2.75926 q^{92} -7.02840 q^{93} +0.544796 q^{94} -10.6714 q^{95} -0.950934 q^{96} +0.731566 q^{97} +1.00000 q^{98} -2.44701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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