LMFDB - Embedded newform 6033.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16814 q^{2} -1.00000 q^{3} +2.70083 q^{4} +3.39119 q^{5} +2.16814 q^{6} +2.22873 q^{7} -1.51950 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16814 q^{2} -1.00000 q^{3} +2.70083 q^{4} +3.39119 q^{5} +2.16814 q^{6} +2.22873 q^{7} -1.51950 q^{8} +1.00000 q^{9} -7.35257 q^{10} -3.02614 q^{11} -2.70083 q^{12} +2.42724 q^{13} -4.83220 q^{14} -3.39119 q^{15} -2.10717 q^{16} -2.10534 q^{17} -2.16814 q^{18} -7.46446 q^{19} +9.15903 q^{20} -2.22873 q^{21} +6.56110 q^{22} -3.07203 q^{23} +1.51950 q^{24} +6.50016 q^{25} -5.26259 q^{26} -1.00000 q^{27} +6.01943 q^{28} +2.67632 q^{29} +7.35257 q^{30} -1.05696 q^{31} +7.60765 q^{32} +3.02614 q^{33} +4.56468 q^{34} +7.55805 q^{35} +2.70083 q^{36} +1.95456 q^{37} +16.1840 q^{38} -2.42724 q^{39} -5.15292 q^{40} -1.14573 q^{41} +4.83220 q^{42} +6.36716 q^{43} -8.17310 q^{44} +3.39119 q^{45} +6.66058 q^{46} -5.61753 q^{47} +2.10717 q^{48} -2.03276 q^{49} -14.0933 q^{50} +2.10534 q^{51} +6.55556 q^{52} +5.30487 q^{53} +2.16814 q^{54} -10.2622 q^{55} -3.38656 q^{56} +7.46446 q^{57} -5.80264 q^{58} -12.5824 q^{59} -9.15903 q^{60} +6.78056 q^{61} +2.29163 q^{62} +2.22873 q^{63} -12.2801 q^{64} +8.23122 q^{65} -6.56110 q^{66} -1.70416 q^{67} -5.68618 q^{68} +3.07203 q^{69} -16.3869 q^{70} -12.0975 q^{71} -1.51950 q^{72} +5.50240 q^{73} -4.23776 q^{74} -6.50016 q^{75} -20.1602 q^{76} -6.74445 q^{77} +5.26259 q^{78} -0.368892 q^{79} -7.14581 q^{80} +1.00000 q^{81} +2.48410 q^{82} -12.7031 q^{83} -6.01943 q^{84} -7.13962 q^{85} -13.8049 q^{86} -2.67632 q^{87} +4.59823 q^{88} +8.94416 q^{89} -7.35257 q^{90} +5.40966 q^{91} -8.29703 q^{92} +1.05696 q^{93} +12.1796 q^{94} -25.3134 q^{95} -7.60765 q^{96} -6.47851 q^{97} +4.40731 q^{98} -3.02614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.16814	−1.53311	−0.766553	−	0.642181i	$-0.778030\pi$
$2$	−2.16814	−1.53311	−0.766553	+	0.642181i	$0.778030\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.70083	1.35042
$5$	3.39119	1.51659	0.758293	−	0.651914i	$-0.226034\pi$
$5$	3.39119	1.51659	0.758293	+	0.651914i	$0.226034\pi$
$6$	2.16814	0.885140
$7$	2.22873	0.842381	0.421191	−	0.906972i	$-0.361612\pi$
$7$	2.22873	0.842381	0.421191	+	0.906972i	$0.361612\pi$
$8$	−1.51950	−0.537225
$9$	1.00000	0.333333
$10$	−7.35257	−2.32509
$11$	−3.02614	−0.912416	−0.456208	−	0.889873i	$-0.650793\pi$
$11$	−3.02614	−0.912416	−0.456208	+	0.889873i	$0.650793\pi$
$12$	−2.70083	−0.779663
$13$	2.42724	0.673194	0.336597	−	0.941649i	$-0.390724\pi$
$13$	2.42724	0.673194	0.336597	+	0.941649i	$0.390724\pi$
$14$	−4.83220	−1.29146
$15$	−3.39119	−0.875601
$16$	−2.10717	−0.526793
$17$	−2.10534	−0.510621	−0.255311	−	0.966859i	$-0.582178\pi$
$17$	−2.10534	−0.510621	−0.255311	+	0.966859i	$0.582178\pi$
$18$	−2.16814	−0.511036
$19$	−7.46446	−1.71246	−0.856232	−	0.516592i	$-0.827200\pi$
$19$	−7.46446	−1.71246	−0.856232	+	0.516592i	$0.827200\pi$
$20$	9.15903	2.04802
$21$	−2.22873	−0.486349
$22$	6.56110	1.39883
$23$	−3.07203	−0.640562	−0.320281	−	0.947323i	$-0.603777\pi$
$23$	−3.07203	−0.640562	−0.320281	+	0.947323i	$0.603777\pi$
$24$	1.51950	0.310167
$25$	6.50016	1.30003
$26$	−5.26259	−1.03208
$27$	−1.00000	−0.192450
$28$	6.01943	1.13756
$29$	2.67632	0.496980	0.248490	−	0.968634i	$-0.420066\pi$
$29$	2.67632	0.496980	0.248490	+	0.968634i	$0.420066\pi$
$30$	7.35257	1.34239
$31$	−1.05696	−0.189835	−0.0949174	−	0.995485i	$-0.530259\pi$
$31$	−1.05696	−0.189835	−0.0949174	+	0.995485i	$0.530259\pi$
$32$	7.60765	1.34485
$33$	3.02614	0.526783
$34$	4.56468	0.782837
$35$	7.55805	1.27754
$36$	2.70083	0.450139
$37$	1.95456	0.321328	0.160664	−	0.987009i	$-0.448636\pi$
$37$	1.95456	0.321328	0.160664	+	0.987009i	$0.448636\pi$
$38$	16.1840	2.62539
$39$	−2.42724	−0.388669
$40$	−5.15292	−0.814748
$41$	−1.14573	−0.178933	−0.0894664	−	0.995990i	$-0.528516\pi$
$41$	−1.14573	−0.178933	−0.0894664	+	0.995990i	$0.528516\pi$
$42$	4.83220	0.745625
$43$	6.36716	0.970983	0.485491	−	0.874241i	$-0.338641\pi$
$43$	6.36716	0.970983	0.485491	+	0.874241i	$0.338641\pi$
$44$	−8.17310	−1.23214
$45$	3.39119	0.505529
$46$	6.66058	0.982050
$47$	−5.61753	−0.819401	−0.409700	−	0.912220i	$-0.634367\pi$
$47$	−5.61753	−0.819401	−0.409700	+	0.912220i	$0.634367\pi$
$48$	2.10717	0.304144
$49$	−2.03276	−0.290394
$50$	−14.0933	−1.99309
$51$	2.10534	0.294807
$52$	6.55556	0.909092
$53$	5.30487	0.728680	0.364340	−	0.931266i	$-0.381295\pi$
$53$	5.30487	0.728680	0.364340	+	0.931266i	$0.381295\pi$
$54$	2.16814	0.295047
$55$	−10.2622	−1.38376
$56$	−3.38656	−0.452548
$57$	7.46446	0.988691
$58$	−5.80264	−0.761924
$59$	−12.5824	−1.63808	−0.819042	−	0.573734i	$-0.805494\pi$
$59$	−12.5824	−1.63808	−0.819042	+	0.573734i	$0.805494\pi$
$60$	−9.15903	−1.18243
$61$	6.78056	0.868161	0.434081	−	0.900874i	$-0.357073\pi$
$61$	6.78056	0.868161	0.434081	+	0.900874i	$0.357073\pi$
$62$	2.29163	0.291037
$63$	2.22873	0.280794
$64$	−12.2801	−1.53501
$65$	8.23122	1.02096
$66$	−6.56110	−0.807615
$67$	−1.70416	−0.208196	−0.104098	−	0.994567i	$-0.533196\pi$
$67$	−1.70416	−0.208196	−0.104098	+	0.994567i	$0.533196\pi$
$68$	−5.68618	−0.689551
$69$	3.07203	0.369829
$70$	−16.3869	−1.95861
$71$	−12.0975	−1.43571	−0.717857	−	0.696191i	$-0.754877\pi$
$71$	−12.0975	−1.43571	−0.717857	+	0.696191i	$0.754877\pi$
$72$	−1.51950	−0.179075
$73$	5.50240	0.644007	0.322003	−	0.946738i	$-0.395644\pi$
$73$	5.50240	0.644007	0.322003	+	0.946738i	$0.395644\pi$
$74$	−4.23776	−0.492630
$75$	−6.50016	−0.750574
$76$	−20.1602	−2.31254
$77$	−6.74445	−0.768602
$78$	5.26259	0.595871
$79$	−0.368892	−0.0415036	−0.0207518	−	0.999785i	$-0.506606\pi$
$79$	−0.368892	−0.0415036	−0.0207518	+	0.999785i	$0.506606\pi$
$80$	−7.14581	−0.798926
$81$	1.00000	0.111111
$82$	2.48410	0.274323
$83$	−12.7031	−1.39434	−0.697172	−	0.716904i	$-0.745558\pi$
$83$	−12.7031	−1.39434	−0.697172	+	0.716904i	$0.745558\pi$
$84$	−6.01943	−0.656773
$85$	−7.13962	−0.774401
$86$	−13.8049	−1.48862
$87$	−2.67632	−0.286932
$88$	4.59823	0.490173
$89$	8.94416	0.948079	0.474039	−	0.880504i	$-0.342795\pi$
$89$	8.94416	0.948079	0.474039	+	0.880504i	$0.342795\pi$
$90$	−7.35257	−0.775029
$91$	5.40966	0.567086
$92$	−8.29703	−0.865025
$93$	1.05696	0.109601
$94$	12.1796	1.25623
$95$	−25.3134	−2.59710
$96$	−7.60765	−0.776452
$97$	−6.47851	−0.657793	−0.328896	−	0.944366i	$-0.606677\pi$
$97$	−6.47851	−0.657793	−0.328896	+	0.944366i	$0.606677\pi$
$98$	4.40731	0.445205
$99$	−3.02614	−0.304139
$100$	17.5558	1.75558
$101$	4.18202	0.416127	0.208063	−	0.978115i	$-0.433284\pi$
$101$	4.18202	0.416127	0.208063	+	0.978115i	$0.433284\pi$
$102$	−4.56468	−0.451971
$103$	−14.8446	−1.46268	−0.731340	−	0.682013i	$-0.761105\pi$
$103$	−14.8446	−1.46268	−0.731340	+	0.682013i	$0.761105\pi$
$104$	−3.68819	−0.361657
$105$	−7.55805	−0.737590
$106$	−11.5017	−1.11714
$107$	15.8778	1.53496	0.767481	−	0.641072i	$-0.221510\pi$
$107$	15.8778	1.53496	0.767481	+	0.641072i	$0.221510\pi$
$108$	−2.70083	−0.259888
$109$	−8.75235	−0.838323	−0.419162	−	0.907912i	$-0.637676\pi$
$109$	−8.75235	−0.838323	−0.419162	+	0.907912i	$0.637676\pi$
$110$	22.2499	2.12145
$111$	−1.95456	−0.185519
$112$	−4.69632	−0.443760
$113$	−10.2479	−0.964039	−0.482020	−	0.876160i	$-0.660097\pi$
$113$	−10.2479	−0.964039	−0.482020	+	0.876160i	$0.660097\pi$
$114$	−16.1840	−1.51577
$115$	−10.4178	−0.971467
$116$	7.22829	0.671130
$117$	2.42724	0.224398
$118$	27.2803	2.51136
$119$	−4.69225	−0.430138
$120$	5.15292	0.470395
$121$	−1.84247	−0.167497
$122$	−14.7012	−1.33098
$123$	1.14573	0.103307
$124$	−2.85466	−0.256356
$125$	5.08732	0.455024
$126$	−4.83220	−0.430487
$127$	1.59643	0.141660	0.0708300	−	0.997488i	$-0.477435\pi$
$127$	1.59643	0.141660	0.0708300	+	0.997488i	$0.477435\pi$
$128$	11.4097	1.00848
$129$	−6.36716	−0.560597
$130$	−17.8464	−1.56524
$131$	−19.3711	−1.69246	−0.846232	−	0.532815i	$-0.821134\pi$
$131$	−19.3711	−1.69246	−0.846232	+	0.532815i	$0.821134\pi$
$132$	8.17310	0.711377
$133$	−16.6363	−1.44255
$134$	3.69486	0.319187
$135$	−3.39119	−0.291867
$136$	3.19908	0.274318
$137$	17.4078	1.48725	0.743623	−	0.668599i	$-0.233106\pi$
$137$	17.4078	1.48725	0.743623	+	0.668599i	$0.233106\pi$
$138$	−6.66058	−0.566987
$139$	15.3657	1.30330	0.651651	−	0.758519i	$-0.274077\pi$
$139$	15.3657	1.30330	0.651651	+	0.758519i	$0.274077\pi$
$140$	20.4130	1.72521
$141$	5.61753	0.473081
$142$	26.2292	2.20110
$143$	−7.34516	−0.614233
$144$	−2.10717	−0.175598
$145$	9.07591	0.753713
$146$	−11.9300	−0.987331
$147$	2.03276	0.167659
$148$	5.27894	0.433926
$149$	−9.40720	−0.770668	−0.385334	−	0.922777i	$-0.625914\pi$
$149$	−9.40720	−0.770668	−0.385334	+	0.922777i	$0.625914\pi$
$150$	14.0933	1.15071
$151$	8.30352	0.675731	0.337865	−	0.941194i	$-0.390295\pi$
$151$	8.30352	0.675731	0.337865	+	0.941194i	$0.390295\pi$
$152$	11.3423	0.919978
$153$	−2.10534	−0.170207
$154$	14.6229	1.17835
$155$	−3.58433	−0.287901
$156$	−6.55556	−0.524865
$157$	14.7725	1.17897	0.589485	−	0.807779i	$-0.299331\pi$
$157$	14.7725	1.17897	0.589485	+	0.807779i	$0.299331\pi$
$158$	0.799810	0.0636295
$159$	−5.30487	−0.420704
$160$	25.7990	2.03959
$161$	−6.84672	−0.539597
$162$	−2.16814	−0.170345
$163$	−8.18839	−0.641364	−0.320682	−	0.947187i	$-0.603912\pi$
$163$	−8.18839	−0.641364	−0.320682	+	0.947187i	$0.603912\pi$
$164$	−3.09442	−0.241634
$165$	10.2622	0.798912
$166$	27.5420	2.13768
$167$	−8.82717	−0.683067	−0.341534	−	0.939870i	$-0.610946\pi$
$167$	−8.82717	−0.683067	−0.341534	+	0.939870i	$0.610946\pi$
$168$	3.38656	0.261279
$169$	−7.10852	−0.546809
$170$	15.4797	1.18724
$171$	−7.46446	−0.570821
$172$	17.1966	1.31123
$173$	−13.9509	−1.06067	−0.530335	−	0.847788i	$-0.677934\pi$
$173$	−13.9509	−1.06067	−0.530335	+	0.847788i	$0.677934\pi$
$174$	5.80264	0.439897
$175$	14.4871	1.09512
$176$	6.37660	0.480654
$177$	12.5824	0.945748
$178$	−19.3922	−1.45351
$179$	−7.67368	−0.573558	−0.286779	−	0.957997i	$-0.592584\pi$
$179$	−7.67368	−0.573558	−0.286779	+	0.957997i	$0.592584\pi$
$180$	9.15903	0.682674
$181$	−26.4888	−1.96890	−0.984448	−	0.175675i	$-0.943789\pi$
$181$	−26.4888	−1.96890	−0.984448	+	0.175675i	$0.943789\pi$
$182$	−11.7289	−0.869404
$183$	−6.78056	−0.501233
$184$	4.66795	0.344126
$185$	6.62828	0.487321
$186$	−2.29163	−0.168030
$187$	6.37107	0.465899
$188$	−15.1720	−1.10653
$189$	−2.22873	−0.162116
$190$	54.8829	3.98163
$191$	−10.5521	−0.763520	−0.381760	−	0.924261i	$-0.624682\pi$
$191$	−10.5521	−0.763520	−0.381760	+	0.924261i	$0.624682\pi$
$192$	12.2801	0.886240
$193$	26.5672	1.91235	0.956175	−	0.292797i	$-0.0945859\pi$
$193$	26.5672	1.91235	0.956175	+	0.292797i	$0.0945859\pi$
$194$	14.0463	1.00847
$195$	−8.23122	−0.589450
$196$	−5.49014	−0.392153
$197$	−16.8831	−1.20287	−0.601435	−	0.798922i	$-0.705404\pi$
$197$	−16.8831	−1.20287	−0.601435	+	0.798922i	$0.705404\pi$
$198$	6.56110	0.466277
$199$	−5.00448	−0.354758	−0.177379	−	0.984143i	$-0.556762\pi$
$199$	−5.00448	−0.354758	−0.177379	+	0.984143i	$0.556762\pi$
$200$	−9.87700	−0.698410
$201$	1.70416	0.120202
$202$	−9.06721	−0.637967
$203$	5.96480	0.418647
$204$	5.68618	0.398112
$205$	−3.88538	−0.271367
$206$	32.1851	2.24245
$207$	−3.07203	−0.213521
$208$	−5.11460	−0.354634
$209$	22.5885	1.56248
$210$	16.3869	1.13080
$211$	0.922639	0.0635171	0.0317586	−	0.999496i	$-0.489889\pi$
$211$	0.922639	0.0635171	0.0317586	+	0.999496i	$0.489889\pi$
$212$	14.3276	0.984021
$213$	12.0975	0.828909
$214$	−34.4252	−2.35326
$215$	21.5922	1.47258
$216$	1.51950	0.103389
$217$	−2.35567	−0.159913
$218$	18.9763	1.28524
$219$	−5.50240	−0.371818
$220$	−27.7165	−1.86865
$221$	−5.11017	−0.343747
$222$	4.23776	0.284420
$223$	26.2675	1.75900	0.879501	−	0.475897i	$-0.157877\pi$
$223$	26.2675	1.75900	0.879501	+	0.475897i	$0.157877\pi$
$224$	16.9554	1.13288
$225$	6.50016	0.433344
$226$	22.2188	1.47798
$227$	−28.5596	−1.89557	−0.947783	−	0.318917i	$-0.896681\pi$
$227$	−28.5596	−1.89557	−0.947783	+	0.318917i	$0.896681\pi$
$228$	20.1602	1.33514
$229$	−7.99551	−0.528358	−0.264179	−	0.964474i	$-0.585101\pi$
$229$	−7.99551	−0.528358	−0.264179	+	0.964474i	$0.585101\pi$
$230$	22.5873	1.48936
$231$	6.74445	0.443752
$232$	−4.06667	−0.266990
$233$	−9.86546	−0.646307	−0.323154	−	0.946346i	$-0.604743\pi$
$233$	−9.86546	−0.646307	−0.323154	+	0.946346i	$0.604743\pi$
$234$	−5.26259	−0.344026
$235$	−19.0501	−1.24269
$236$	−33.9828	−2.21209
$237$	0.368892	0.0239621
$238$	10.1734	0.659447
$239$	3.07686	0.199025	0.0995127	−	0.995036i	$-0.468272\pi$
$239$	3.07686	0.199025	0.0995127	+	0.995036i	$0.468272\pi$
$240$	7.14581	0.461260
$241$	0.644781	0.0415340	0.0207670	−	0.999784i	$-0.493389\pi$
$241$	0.644781	0.0415340	0.0207670	+	0.999784i	$0.493389\pi$
$242$	3.99474	0.256791
$243$	−1.00000	−0.0641500
$244$	18.3131	1.17238
$245$	−6.89347	−0.440407
$246$	−2.48410	−0.158381
$247$	−18.1180	−1.15282
$248$	1.60605	0.101984
$249$	12.7031	0.805024
$250$	−11.0300	−0.697600
$251$	19.6173	1.23823	0.619115	−	0.785300i	$-0.287491\pi$
$251$	19.6173	1.23823	0.619115	+	0.785300i	$0.287491\pi$
$252$	6.01943	0.379188
$253$	9.29638	0.584459
$254$	−3.46128	−0.217180
$255$	7.13962	0.447100
$256$	−0.177602	−0.0111002
$257$	−9.73568	−0.607295	−0.303647	−	0.952784i	$-0.598204\pi$
$257$	−9.73568	−0.607295	−0.303647	+	0.952784i	$0.598204\pi$
$258$	13.8049	0.859455
$259$	4.35619	0.270680
$260$	22.2311	1.37872
$261$	2.67632	0.165660
$262$	41.9993	2.59473
$263$	−0.686565	−0.0423354	−0.0211677	−	0.999776i	$-0.506738\pi$
$263$	−0.686565	−0.0423354	−0.0211677	+	0.999776i	$0.506738\pi$
$264$	−4.59823	−0.283001
$265$	17.9898	1.10511
$266$	36.0698	2.21158
$267$	−8.94416	−0.547373
$268$	−4.60265	−0.281151
$269$	7.15422	0.436201	0.218100	−	0.975926i	$-0.430014\pi$
$269$	7.15422	0.436201	0.218100	+	0.975926i	$0.430014\pi$
$270$	7.35257	0.447463
$271$	23.6524	1.43678	0.718391	−	0.695639i	$-0.244879\pi$
$271$	23.6524	1.43678	0.718391	+	0.695639i	$0.244879\pi$
$272$	4.43632	0.268991
$273$	−5.40966	−0.327407
$274$	−37.7425	−2.28011
$275$	−19.6704	−1.18617
$276$	8.29703	0.499422
$277$	−24.9623	−1.49984	−0.749919	−	0.661530i	$-0.769907\pi$
$277$	−24.9623	−1.49984	−0.749919	+	0.661530i	$0.769907\pi$
$278$	−33.3150	−1.99810
$279$	−1.05696	−0.0632782
$280$	−11.4845	−0.686328
$281$	−10.3275	−0.616086	−0.308043	−	0.951372i	$-0.599674\pi$
$281$	−10.3275	−0.616086	−0.308043	+	0.951372i	$0.599674\pi$
$282$	−12.1796	−0.725284
$283$	19.8435	1.17957	0.589787	−	0.807559i	$-0.299212\pi$
$283$	19.8435	1.17957	0.589787	+	0.807559i	$0.299212\pi$
$284$	−32.6734	−1.93881
$285$	25.3134	1.49943
$286$	15.9253	0.941685
$287$	−2.55352	−0.150730
$288$	7.60765	0.448285
$289$	−12.5675	−0.739266
$290$	−19.6778	−1.15552
$291$	6.47851	0.379777
$292$	14.8611	0.869677
$293$	−13.1407	−0.767688	−0.383844	−	0.923398i	$-0.625400\pi$
$293$	−13.1407	−0.767688	−0.383844	+	0.923398i	$0.625400\pi$
$294$	−4.40731	−0.257039
$295$	−42.6692	−2.48429
$296$	−2.96996	−0.172625
$297$	3.02614	0.175594
$298$	20.3961	1.18152
$299$	−7.45654	−0.431223
$300$	−17.5558	−1.01359
$301$	14.1907	0.817938
$302$	−18.0032	−1.03597
$303$	−4.18202	−0.240251
$304$	15.7289	0.902113
$305$	22.9941	1.31664
$306$	4.56468	0.260946
$307$	21.9331	1.25179	0.625893	−	0.779909i	$-0.284735\pi$
$307$	21.9331	1.25179	0.625893	+	0.779909i	$0.284735\pi$
$308$	−18.2156	−1.03793
$309$	14.8446	0.844479
$310$	7.77134	0.441382
$311$	19.4373	1.10219	0.551094	−	0.834443i	$-0.314211\pi$
$311$	19.4373	1.10219	0.551094	+	0.834443i	$0.314211\pi$
$312$	3.68819	0.208803
$313$	−20.5895	−1.16379	−0.581893	−	0.813265i	$-0.697688\pi$
$313$	−20.5895	−1.16379	−0.581893	+	0.813265i	$0.697688\pi$
$314$	−32.0288	−1.80749
$315$	7.55805	0.425848
$316$	−0.996316	−0.0560472
$317$	−5.90948	−0.331909	−0.165955	−	0.986133i	$-0.553071\pi$
$317$	−5.90948	−0.331909	−0.165955	+	0.986133i	$0.553071\pi$
$318$	11.5017	0.644983
$319$	−8.09892	−0.453453
$320$	−41.6441	−2.32798
$321$	−15.8778	−0.886211
$322$	14.8447	0.827260
$323$	15.7153	0.874420
$324$	2.70083	0.150046
$325$	15.7774	0.875174
$326$	17.7536	0.983279
$327$	8.75235	0.484006
$328$	1.74094	0.0961272
$329$	−12.5200	−0.690248
$330$	−22.2499	−1.22482
$331$	9.90453	0.544402	0.272201	−	0.962240i	$-0.412248\pi$
$331$	9.90453	0.544402	0.272201	+	0.962240i	$0.412248\pi$
$332$	−34.3089	−1.88294
$333$	1.95456	0.107109
$334$	19.1385	1.04721
$335$	−5.77912	−0.315747
$336$	4.69632	0.256205
$337$	0.0764699	0.00416558	0.00208279	−	0.999998i	$-0.499337\pi$
$337$	0.0764699	0.00416558	0.00208279	+	0.999998i	$0.499337\pi$
$338$	15.4123	0.838317
$339$	10.2479	0.556588
$340$	−19.2829	−1.04576
$341$	3.19850	0.173208
$342$	16.1840	0.875130
$343$	−20.1316	−1.08700
$344$	−9.67491	−0.521636
$345$	10.4178	0.560877
$346$	30.2476	1.62612
$347$	21.3806	1.14777	0.573885	−	0.818936i	$-0.305436\pi$
$347$	21.3806	1.14777	0.573885	+	0.818936i	$0.305436\pi$
$348$	−7.22829	−0.387477
$349$	17.3184	0.927033	0.463517	−	0.886088i	$-0.346587\pi$
$349$	17.3184	0.927033	0.463517	+	0.886088i	$0.346587\pi$
$350$	−31.4101	−1.67894
$351$	−2.42724	−0.129556
$352$	−23.0218	−1.22707
$353$	−30.6251	−1.63001	−0.815006	−	0.579453i	$-0.803266\pi$
$353$	−30.6251	−1.63001	−0.815006	+	0.579453i	$0.803266\pi$
$354$	−27.2803	−1.44993
$355$	−41.0250	−2.17738
$356$	24.1567	1.28030
$357$	4.69225	0.248340
$358$	16.6376	0.879325
$359$	−7.12235	−0.375903	−0.187952	−	0.982178i	$-0.560185\pi$
$359$	−7.12235	−0.375903	−0.187952	+	0.982178i	$0.560185\pi$
$360$	−5.15292	−0.271583
$361$	36.7181	1.93253
$362$	57.4314	3.01853
$363$	1.84247	0.0967047
$364$	14.6106	0.765802
$365$	18.6597	0.976692
$366$	14.7012	0.768444
$367$	−9.34872	−0.487999	−0.244000	−	0.969775i	$-0.578460\pi$
$367$	−9.34872	−0.487999	−0.244000	+	0.969775i	$0.578460\pi$
$368$	6.47328	0.337443
$369$	−1.14573	−0.0596443
$370$	−14.3710	−0.747115
$371$	11.8231	0.613826
$372$	2.85466	0.148007
$373$	9.06904	0.469577	0.234789	−	0.972046i	$-0.424560\pi$
$373$	9.06904	0.469577	0.234789	+	0.972046i	$0.424560\pi$
$374$	−13.8134	−0.714272
$375$	−5.08732	−0.262708
$376$	8.53584	0.440202
$377$	6.49606	0.334564
$378$	4.83220	0.248542
$379$	19.3921	0.996106	0.498053	−	0.867147i	$-0.334049\pi$
$379$	19.3921	0.996106	0.498053	+	0.867147i	$0.334049\pi$
$380$	−68.3672	−3.50716
$381$	−1.59643	−0.0817874
$382$	22.8783	1.17056
$383$	10.7476	0.549178	0.274589	−	0.961562i	$-0.411458\pi$
$383$	10.7476	0.549178	0.274589	+	0.961562i	$0.411458\pi$
$384$	−11.4097	−0.582248
$385$	−22.8717	−1.16565
$386$	−57.6014	−2.93184
$387$	6.36716	0.323661
$388$	−17.4974	−0.888294
$389$	−24.9923	−1.26716	−0.633579	−	0.773678i	$-0.718415\pi$
$389$	−24.9923	−1.26716	−0.633579	+	0.773678i	$0.718415\pi$
$390$	17.8464	0.903689
$391$	6.46767	0.327084
$392$	3.08878	0.156007
$393$	19.3711	0.977144
$394$	36.6049	1.84413
$395$	−1.25098	−0.0629438
$396$	−8.17310	−0.410714
$397$	8.64447	0.433853	0.216927	−	0.976188i	$-0.430397\pi$
$397$	8.64447	0.433853	0.216927	+	0.976188i	$0.430397\pi$
$398$	10.8504	0.543882
$399$	16.6363	0.832855
$400$	−13.6969	−0.684847
$401$	16.7405	0.835979	0.417989	−	0.908452i	$-0.362735\pi$
$401$	16.7405	0.835979	0.417989	+	0.908452i	$0.362735\pi$
$402$	−3.69486	−0.184283
$403$	−2.56548	−0.127796
$404$	11.2949	0.561944
$405$	3.39119	0.168510
$406$	−12.9325	−0.641830
$407$	−5.91478	−0.293185
$408$	−3.19908	−0.158378
$409$	−3.02811	−0.149730	−0.0748651	−	0.997194i	$-0.523853\pi$
$409$	−3.02811	−0.149730	−0.0748651	+	0.997194i	$0.523853\pi$
$410$	8.42405	0.416034
$411$	−17.4078	−0.858662
$412$	−40.0927	−1.97523
$413$	−28.0427	−1.37989
$414$	6.66058	0.327350
$415$	−43.0785	−2.11464
$416$	18.4656	0.905348
$417$	−15.3657	−0.752461
$418$	−48.9750	−2.39545
$419$	14.7522	0.720690	0.360345	−	0.932819i	$-0.382659\pi$
$419$	14.7522	0.720690	0.360345	+	0.932819i	$0.382659\pi$
$420$	−20.4130	−0.996053
$421$	−19.9893	−0.974217	−0.487108	−	0.873342i	$-0.661948\pi$
$421$	−19.9893	−0.974217	−0.487108	+	0.873342i	$0.661948\pi$
$422$	−2.00041	−0.0973785
$423$	−5.61753	−0.273134
$424$	−8.06076	−0.391465
$425$	−13.6851	−0.663824
$426$	−26.2292	−1.27081
$427$	15.1120	0.731323
$428$	42.8832	2.07284
$429$	7.34516	0.354628
$430$	−46.8150	−2.25762
$431$	−31.5957	−1.52191	−0.760957	−	0.648803i	$-0.775270\pi$
$431$	−31.5957	−1.52191	−0.760957	+	0.648803i	$0.775270\pi$
$432$	2.10717	0.101381
$433$	11.9380	0.573704	0.286852	−	0.957975i	$-0.407391\pi$
$433$	11.9380	0.573704	0.286852	+	0.957975i	$0.407391\pi$
$434$	5.10742	0.245164
$435$	−9.07591	−0.435156
$436$	−23.6386	−1.13208
$437$	22.9310	1.09694
$438$	11.9300	0.570036
$439$	11.2762	0.538182	0.269091	−	0.963115i	$-0.413277\pi$
$439$	11.2762	0.538182	0.269091	+	0.963115i	$0.413277\pi$
$440$	15.5935	0.743389
$441$	−2.03276	−0.0967980
$442$	11.0796	0.527001
$443$	−23.1831	−1.10146	−0.550731	−	0.834683i	$-0.685651\pi$
$443$	−23.1831	−1.10146	−0.550731	+	0.834683i	$0.685651\pi$
$444$	−5.27894	−0.250527
$445$	30.3313	1.43784
$446$	−56.9516	−2.69674
$447$	9.40720	0.444945
$448$	−27.3690	−1.29307
$449$	22.9417	1.08268	0.541342	−	0.840803i	$-0.317916\pi$
$449$	22.9417	1.08268	0.541342	+	0.840803i	$0.317916\pi$
$450$	−14.0933	−0.664362
$451$	3.46714	0.163261
$452$	−27.6778	−1.30185
$453$	−8.30352	−0.390133
$454$	61.9212	2.90610
$455$	18.3452	0.860035
$456$	−11.3423	−0.531150
$457$	−10.0606	−0.470617	−0.235308	−	0.971921i	$-0.575610\pi$
$457$	−10.0606	−0.470617	−0.235308	+	0.971921i	$0.575610\pi$
$458$	17.3354	0.810029
$459$	2.10534	0.0982691
$460$	−28.1368	−1.31188
$461$	−26.8568	−1.25085	−0.625424	−	0.780285i	$-0.715074\pi$
$461$	−26.8568	−1.25085	−0.625424	+	0.780285i	$0.715074\pi$
$462$	−14.6229	−0.680320
$463$	24.5782	1.14225	0.571123	−	0.820864i	$-0.306508\pi$
$463$	24.5782	1.14225	0.571123	+	0.820864i	$0.306508\pi$
$464$	−5.63946	−0.261806
$465$	3.58433	0.166220
$466$	21.3897	0.990858
$467$	−27.1984	−1.25859	−0.629296	−	0.777166i	$-0.716657\pi$
$467$	−27.1984	−1.25859	−0.629296	+	0.777166i	$0.716657\pi$
$468$	6.55556	0.303031
$469$	−3.79811	−0.175381
$470$	41.3033	1.90518
$471$	−14.7725	−0.680679
$472$	19.1189	0.880020
$473$	−19.2679	−0.885940
$474$	−0.799810	−0.0367365
$475$	−48.5201	−2.22626
$476$	−12.6730	−0.580865
$477$	5.30487	0.242893
$478$	−6.67106	−0.305127
$479$	22.0244	1.00632	0.503161	−	0.864193i	$-0.332170\pi$
$479$	22.0244	1.00632	0.503161	+	0.864193i	$0.332170\pi$
$480$	−25.7990	−1.17756
$481$	4.74418	0.216316
$482$	−1.39797	−0.0636760
$483$	6.84672	0.311537
$484$	−4.97621	−0.226191
$485$	−21.9698	−0.997599
$486$	2.16814	0.0983488
$487$	8.10535	0.367289	0.183644	−	0.982993i	$-0.441211\pi$
$487$	8.10535	0.367289	0.183644	+	0.982993i	$0.441211\pi$
$488$	−10.3031	−0.466398
$489$	8.18839	0.370292
$490$	14.9460	0.675192
$491$	−26.6428	−1.20237	−0.601186	−	0.799109i	$-0.705305\pi$
$491$	−26.6428	−1.20237	−0.601186	+	0.799109i	$0.705305\pi$
$492$	3.09442	0.139507
$493$	−5.63458	−0.253769
$494$	39.2824	1.76740
$495$	−10.2622	−0.461252
$496$	2.22719	0.100004
$497$	−26.9621	−1.20942
$498$	−27.5420	−1.23419
$499$	1.22584	0.0548761	0.0274380	−	0.999624i	$-0.491265\pi$
$499$	1.22584	0.0548761	0.0274380	+	0.999624i	$0.491265\pi$
$500$	13.7400	0.614471
$501$	8.82717	0.394369
$502$	−42.5330	−1.89834
$503$	−29.7443	−1.32623	−0.663117	−	0.748516i	$-0.730767\pi$
$503$	−29.7443	−1.32623	−0.663117	+	0.748516i	$0.730767\pi$
$504$	−3.38656	−0.150849
$505$	14.1820	0.631092
$506$	−20.1559	−0.896038
$507$	7.10852	0.315700
$508$	4.31168	0.191300
$509$	−32.1605	−1.42549	−0.712744	−	0.701424i	$-0.752548\pi$
$509$	−32.1605	−1.42549	−0.712744	+	0.701424i	$0.752548\pi$
$510$	−15.4797	−0.685453
$511$	12.2634	0.542499
$512$	−22.4343	−0.991466
$513$	7.46446	0.329564
$514$	21.1083	0.931048
$515$	−50.3408	−2.21828
$516$	−17.1966	−0.757039
$517$	16.9994	0.747634
$518$	−9.44483	−0.414982
$519$	13.9509	0.612378
$520$	−12.5074	−0.548484
$521$	2.82725	0.123864	0.0619321	−	0.998080i	$-0.480274\pi$
$521$	2.82725	0.123864	0.0619321	+	0.998080i	$0.480274\pi$
$522$	−5.80264	−0.253975
$523$	−30.9261	−1.35230	−0.676151	−	0.736763i	$-0.736353\pi$
$523$	−30.9261	−1.35230	−0.676151	+	0.736763i	$0.736353\pi$
$524$	−52.3182	−2.28553
$525$	−14.4871	−0.632269
$526$	1.48857	0.0649047
$527$	2.22525	0.0969336
$528$	−6.37660	−0.277506
$529$	−13.5627	−0.589681
$530$	−39.0044	−1.69424
$531$	−12.5824	−0.546028
$532$	−44.9318	−1.94804
$533$	−2.78096	−0.120457
$534$	19.3922	0.839182
$535$	53.8445	2.32790
$536$	2.58947	0.111848
$537$	7.67368	0.331144
$538$	−15.5114	−0.668742
$539$	6.15141	0.264960
$540$	−9.15903	−0.394142
$541$	−11.2918	−0.485473	−0.242737	−	0.970092i	$-0.578045\pi$
$541$	−11.2918	−0.485473	−0.242737	+	0.970092i	$0.578045\pi$
$542$	−51.2818	−2.20274
$543$	26.4888	1.13674
$544$	−16.0167	−0.686711
$545$	−29.6809	−1.27139
$546$	11.7289	0.501950
$547$	−44.2071	−1.89016	−0.945080	−	0.326838i	$-0.894017\pi$
$547$	−44.2071	−1.89016	−0.945080	+	0.326838i	$0.894017\pi$
$548$	47.0154	2.00840
$549$	6.78056	0.289387
$550$	42.6482	1.81852
$551$	−19.9773	−0.851060
$552$	−4.66795	−0.198681
$553$	−0.822162	−0.0349619
$554$	54.1217	2.29941
$555$	−6.62828	−0.281355
$556$	41.5002	1.76000
$557$	10.5087	0.445269	0.222634	−	0.974902i	$-0.428534\pi$
$557$	10.5087	0.445269	0.222634	+	0.974902i	$0.428534\pi$
$558$	2.29163	0.0970123
$559$	15.4546	0.653660
$560$	−15.9261	−0.673000
$561$	−6.37107	−0.268987
$562$	22.3914	0.944525
$563$	−30.2833	−1.27629	−0.638145	−	0.769916i	$-0.720298\pi$
$563$	−30.2833	−1.27629	−0.638145	+	0.769916i	$0.720298\pi$
$564$	15.1720	0.638856
$565$	−34.7525	−1.46205
$566$	−43.0235	−1.80841
$567$	2.22873	0.0935979
$568$	18.3822	0.771301
$569$	−3.07027	−0.128713	−0.0643563	−	0.997927i	$-0.520499\pi$
$569$	−3.07027	−0.128713	−0.0643563	+	0.997927i	$0.520499\pi$
$570$	−54.8829	−2.29879
$571$	−35.2089	−1.47345	−0.736723	−	0.676194i	$-0.763628\pi$
$571$	−35.2089	−1.47345	−0.736723	+	0.676194i	$0.763628\pi$
$572$	−19.8380	−0.829470
$573$	10.5521	0.440819
$574$	5.53639	0.231085
$575$	−19.9687	−0.832751
$576$	−12.2801	−0.511671
$577$	24.9903	1.04036	0.520179	−	0.854057i	$-0.325865\pi$
$577$	24.9903	1.04036	0.520179	+	0.854057i	$0.325865\pi$
$578$	27.2482	1.13337
$579$	−26.5672	−1.10410
$580$	24.5125	1.01783
$581$	−28.3117	−1.17457
$582$	−14.0463	−0.582239
$583$	−16.0533	−0.664859
$584$	−8.36090	−0.345977
$585$	8.23122	0.340319
$586$	28.4909	1.17695
$587$	32.7437	1.35148	0.675738	−	0.737142i	$-0.263825\pi$
$587$	32.7437	1.35148	0.675738	+	0.737142i	$0.263825\pi$
$588$	5.49014	0.226409
$589$	7.88959	0.325085
$590$	92.5127	3.80869
$591$	16.8831	0.694478
$592$	−4.11859	−0.169273
$593$	4.82704	0.198223	0.0991113	−	0.995076i	$-0.468400\pi$
$593$	4.82704	0.198223	0.0991113	+	0.995076i	$0.468400\pi$
$594$	−6.56110	−0.269205
$595$	−15.9123	−0.652340
$596$	−25.4073	−1.04072
$597$	5.00448	0.204820
$598$	16.1668	0.661110
$599$	4.41456	0.180374	0.0901871	−	0.995925i	$-0.471254\pi$
$599$	4.41456	0.180374	0.0901871	+	0.995925i	$0.471254\pi$
$600$	9.87700	0.403227
$601$	8.46892	0.345454	0.172727	−	0.984970i	$-0.444742\pi$
$601$	8.46892	0.345454	0.172727	+	0.984970i	$0.444742\pi$
$602$	−30.7674	−1.25399
$603$	−1.70416	−0.0693987
$604$	22.4264	0.912518
$605$	−6.24817	−0.254024
$606$	9.06721	0.368330
$607$	−26.0856	−1.05878	−0.529391	−	0.848378i	$-0.677579\pi$
$607$	−26.0856	−1.05878	−0.529391	+	0.848378i	$0.677579\pi$
$608$	−56.7869	−2.30301
$609$	−5.96480	−0.241706
$610$	−49.8545	−2.01855
$611$	−13.6351	−0.551616
$612$	−5.68618	−0.229850
$613$	7.94895	0.321055	0.160528	−	0.987031i	$-0.448680\pi$
$613$	7.94895	0.321055	0.160528	+	0.987031i	$0.448680\pi$
$614$	−47.5540	−1.91912
$615$	3.88538	0.156674
$616$	10.2482	0.412912
$617$	0.376801	0.0151695	0.00758473	−	0.999971i	$-0.497586\pi$
$617$	0.376801	0.0151695	0.00758473	+	0.999971i	$0.497586\pi$
$618$	−32.1851	−1.29468
$619$	27.1122	1.08973	0.544865	−	0.838524i	$-0.316581\pi$
$619$	27.1122	1.08973	0.544865	+	0.838524i	$0.316581\pi$
$620$	−9.68068	−0.388786
$621$	3.07203	0.123276
$622$	−42.1428	−1.68977
$623$	19.9341	0.798644
$624$	5.11460	0.204748
$625$	−15.2487	−0.609949
$626$	44.6409	1.78421
$627$	−22.5885	−0.902098
$628$	39.8979	1.59210
$629$	−4.11502	−0.164077
$630$	−16.3869	−0.652870
$631$	−28.2238	−1.12357	−0.561787	−	0.827282i	$-0.689886\pi$
$631$	−28.2238	−1.12357	−0.561787	+	0.827282i	$0.689886\pi$
$632$	0.560533	0.0222968
$633$	−0.922639	−0.0366716
$634$	12.8126	0.508853
$635$	5.41378	0.214839
$636$	−14.3276	−0.568125
$637$	−4.93399	−0.195492
$638$	17.5596	0.695191
$639$	−12.0975	−0.478571
$640$	38.6924	1.52945
$641$	48.8961	1.93128	0.965640	−	0.259885i	$-0.0836846\pi$
$641$	48.8961	1.93128	0.965640	+	0.259885i	$0.0836846\pi$
$642$	34.4252	1.35866
$643$	12.8466	0.506621	0.253310	−	0.967385i	$-0.418481\pi$
$643$	12.8466	0.506621	0.253310	+	0.967385i	$0.418481\pi$
$644$	−18.4918	−0.728681
$645$	−21.5922	−0.850194
$646$	−34.0729	−1.34058
$647$	32.0707	1.26083	0.630414	−	0.776259i	$-0.282885\pi$
$647$	32.0707	1.26083	0.630414	+	0.776259i	$0.282885\pi$
$648$	−1.51950	−0.0596917
$649$	38.0760	1.49461
$650$	−34.2077	−1.34174
$651$	2.35567	0.0923259
$652$	−22.1155	−0.866108
$653$	−14.2959	−0.559443	−0.279721	−	0.960081i	$-0.590242\pi$
$653$	−14.2959	−0.559443	−0.279721	+	0.960081i	$0.590242\pi$
$654$	−18.9763	−0.742033
$655$	−65.6911	−2.56677
$656$	2.41425	0.0942605
$657$	5.50240	0.214669
$658$	27.1450	1.05822
$659$	−31.2733	−1.21824	−0.609118	−	0.793080i	$-0.708476\pi$
$659$	−31.2733	−1.21824	−0.609118	+	0.793080i	$0.708476\pi$
$660$	27.7165	1.07886
$661$	26.8449	1.04415	0.522074	−	0.852900i	$-0.325159\pi$
$661$	26.8449	1.04415	0.522074	+	0.852900i	$0.325159\pi$
$662$	−21.4744	−0.834627
$663$	5.11017	0.198463
$664$	19.3023	0.749076
$665$	−56.4167	−2.18775
$666$	−4.23776	−0.164210
$667$	−8.22173	−0.318347
$668$	−23.8407	−0.922425
$669$	−26.2675	−1.01556
$670$	12.5300	0.484074
$671$	−20.5189	−0.792124
$672$	−16.9554	−0.654069
$673$	24.0486	0.927004	0.463502	−	0.886096i	$-0.346593\pi$
$673$	24.0486	0.927004	0.463502	+	0.886096i	$0.346593\pi$
$674$	−0.165797	−0.00638628
$675$	−6.50016	−0.250191
$676$	−19.1989	−0.738420
$677$	31.6718	1.21725	0.608623	−	0.793459i	$-0.291722\pi$
$677$	31.6718	1.21725	0.608623	+	0.793459i	$0.291722\pi$
$678$	−22.2188	−0.853309
$679$	−14.4389	−0.554112
$680$	10.8487	0.416027
$681$	28.5596	1.09441
$682$	−6.93479	−0.265547
$683$	5.82039	0.222711	0.111355	−	0.993781i	$-0.464481\pi$
$683$	5.82039	0.222711	0.111355	+	0.993781i	$0.464481\pi$
$684$	−20.1602	−0.770846
$685$	59.0330	2.25554
$686$	43.6481	1.66649
$687$	7.99551	0.305048
$688$	−13.4167	−0.511507
$689$	12.8762	0.490543
$690$	−22.5873	−0.859884
$691$	31.6852	1.20536	0.602681	−	0.797982i	$-0.294099\pi$
$691$	31.6852	1.20536	0.602681	+	0.797982i	$0.294099\pi$
$692$	−37.6791	−1.43234
$693$	−6.74445	−0.256201
$694$	−46.3561	−1.75965
$695$	52.1080	1.97657
$696$	4.06667	0.154147
$697$	2.41215	0.0913669
$698$	−37.5487	−1.42124
$699$	9.86546	0.373146
$700$	39.1272	1.47887
$701$	21.9085	0.827474	0.413737	−	0.910396i	$-0.364223\pi$
$701$	21.9085	0.827474	0.413737	+	0.910396i	$0.364223\pi$
$702$	5.26259	0.198624
$703$	−14.5897	−0.550262
$704$	37.1613	1.40057
$705$	19.0501	0.717468
$706$	66.3996	2.49898
$707$	9.32061	0.350537
$708$	33.9828	1.27715
$709$	−27.3320	−1.02648	−0.513238	−	0.858246i	$-0.671554\pi$
$709$	−27.3320	−1.02648	−0.513238	+	0.858246i	$0.671554\pi$
$710$	88.9480	3.33816
$711$	−0.368892	−0.0138345
$712$	−13.5907	−0.509332
$713$	3.24699	0.121601
$714$	−10.1734	−0.380732
$715$	−24.9088	−0.931537
$716$	−20.7253	−0.774541
$717$	−3.07686	−0.114907
$718$	15.4422	0.576300
$719$	16.3535	0.609882	0.304941	−	0.952371i	$-0.401363\pi$
$719$	16.3535	0.609882	0.304941	+	0.952371i	$0.401363\pi$
$720$	−7.14581	−0.266309
$721$	−33.0846	−1.23213
$722$	−79.6100	−2.96278
$723$	−0.644781	−0.0239796
$724$	−71.5418	−2.65883
$725$	17.3965	0.646090
$726$	−3.99474	−0.148259
$727$	−42.5703	−1.57884	−0.789422	−	0.613851i	$-0.789619\pi$
$727$	−42.5703	−1.57884	−0.789422	+	0.613851i	$0.789619\pi$
$728$	−8.21999	−0.304653
$729$	1.00000	0.0370370
$730$	−40.4568	−1.49737
$731$	−13.4051	−0.495804
$732$	−18.3131	−0.676873
$733$	−33.8802	−1.25139	−0.625697	−	0.780066i	$-0.715185\pi$
$733$	−33.8802	−1.25139	−0.625697	+	0.780066i	$0.715185\pi$
$734$	20.2693	0.748155
$735$	6.89347	0.254269
$736$	−23.3709	−0.861462
$737$	5.15703	0.189961
$738$	2.48410	0.0914410
$739$	9.44684	0.347508	0.173754	−	0.984789i	$-0.444410\pi$
$739$	9.44684	0.347508	0.173754	+	0.984789i	$0.444410\pi$
$740$	17.9019	0.658086
$741$	18.1180	0.665581
$742$	−25.6342	−0.941061
$743$	−28.2922	−1.03794	−0.518970	−	0.854792i	$-0.673684\pi$
$743$	−28.2922	−1.03794	−0.518970	+	0.854792i	$0.673684\pi$
$744$	−1.60605	−0.0588805
$745$	−31.9016	−1.16878
$746$	−19.6629	−0.719912
$747$	−12.7031	−0.464781
$748$	17.2072	0.629157
$749$	35.3873	1.29302
$750$	11.0300	0.402760
$751$	18.3910	0.671098	0.335549	−	0.942023i	$-0.391078\pi$
$751$	18.3910	0.671098	0.335549	+	0.942023i	$0.391078\pi$
$752$	11.8371	0.431654
$753$	−19.6173	−0.714893
$754$	−14.0844	−0.512923
$755$	28.1588	1.02480
$756$	−6.01943	−0.218924
$757$	2.31790	0.0842456	0.0421228	−	0.999112i	$-0.486588\pi$
$757$	2.31790	0.0842456	0.0421228	+	0.999112i	$0.486588\pi$
$758$	−42.0448	−1.52714
$759$	−9.29638	−0.337437
$760$	38.4637	1.39523
$761$	−3.89373	−0.141148	−0.0705739	−	0.997507i	$-0.522483\pi$
$761$	−3.89373	−0.141148	−0.0705739	+	0.997507i	$0.522483\pi$
$762$	3.46128	0.125389
$763$	−19.5066	−0.706187
$764$	−28.4993	−1.03107
$765$	−7.13962	−0.258134
$766$	−23.3024	−0.841948
$767$	−30.5404	−1.10275
$768$	0.177602	0.00640868
$769$	6.41674	0.231394	0.115697	−	0.993285i	$-0.463090\pi$
$769$	6.41674	0.231394	0.115697	+	0.993285i	$0.463090\pi$
$770$	49.5891	1.78707
$771$	9.73568	0.350622
$772$	71.7536	2.58247
$773$	3.88921	0.139885	0.0699426	−	0.997551i	$-0.477718\pi$
$773$	3.88921	0.139885	0.0699426	+	0.997551i	$0.477718\pi$
$774$	−13.8049	−0.496207
$775$	−6.87038	−0.246791
$776$	9.84411	0.353383
$777$	−4.35619	−0.156277
$778$	54.1867	1.94269
$779$	8.55224	0.306416
$780$	−22.2311	−0.796002
$781$	36.6088	1.30997
$782$	−14.0228	−0.501455
$783$	−2.67632	−0.0956439
$784$	4.28337	0.152977
$785$	50.0962	1.78801
$786$	−41.9993	−1.49807
$787$	18.0979	0.645121	0.322561	−	0.946549i	$-0.395456\pi$
$787$	18.0979	0.645121	0.322561	+	0.946549i	$0.395456\pi$
$788$	−45.5984	−1.62438
$789$	0.686565	0.0244424
$790$	2.71231	0.0964996
$791$	−22.8398	−0.812089
$792$	4.59823	0.163391
$793$	16.4580	0.584441
$794$	−18.7424	−0.665143
$795$	−17.9898	−0.638033
$796$	−13.5163	−0.479071
$797$	−30.3842	−1.07626	−0.538132	−	0.842860i	$-0.680870\pi$
$797$	−30.3842	−1.07626	−0.538132	+	0.842860i	$0.680870\pi$
$798$	−36.0698	−1.27686
$799$	11.8268	0.418403
$800$	49.4509	1.74835
$801$	8.94416	0.316026
$802$	−36.2957	−1.28164
$803$	−16.6510	−0.587602
$804$	4.60265	0.162323
$805$	−23.2185	−0.818345
$806$	5.56232	0.195924
$807$	−7.15422	−0.251841
$808$	−6.35459	−0.223554
$809$	38.0806	1.33884	0.669422	−	0.742883i	$-0.266542\pi$
$809$	38.0806	1.33884	0.669422	+	0.742883i	$0.266542\pi$
$810$	−7.35257	−0.258343
$811$	3.50122	0.122944	0.0614722	−	0.998109i	$-0.480420\pi$
$811$	3.50122	0.122944	0.0614722	+	0.998109i	$0.480420\pi$
$812$	16.1099	0.565347
$813$	−23.6524	−0.829527
$814$	12.8241	0.449483
$815$	−27.7684	−0.972683
$816$	−4.43632	−0.155302
$817$	−47.5274	−1.66277
$818$	6.56536	0.229552
$819$	5.40966	0.189029
$820$	−10.4938	−0.366458
$821$	46.1447	1.61046	0.805230	−	0.592962i	$-0.202042\pi$
$821$	46.1447	1.61046	0.805230	+	0.592962i	$0.202042\pi$
$822$	37.7425	1.31642
$823$	−19.5462	−0.681336	−0.340668	−	0.940184i	$-0.610653\pi$
$823$	−19.5462	−0.681336	−0.340668	+	0.940184i	$0.610653\pi$
$824$	22.5564	0.785789
$825$	19.6704	0.684835
$826$	60.8005	2.11552
$827$	−23.4433	−0.815204	−0.407602	−	0.913160i	$-0.633635\pi$
$827$	−23.4433	−0.815204	−0.407602	+	0.913160i	$0.633635\pi$
$828$	−8.29703	−0.288342
$829$	13.0848	0.454452	0.227226	−	0.973842i	$-0.427034\pi$
$829$	13.0848	0.454452	0.227226	+	0.973842i	$0.427034\pi$
$830$	93.4002	3.24197
$831$	24.9623	0.865932
$832$	−29.8067	−1.03336
$833$	4.27966	0.148281
$834$	33.3150	1.15360
$835$	−29.9346	−1.03593
$836$	61.0077	2.11000
$837$	1.05696	0.0365337
$838$	−31.9848	−1.10490
$839$	1.06096	0.0366285	0.0183143	−	0.999832i	$-0.494170\pi$
$839$	1.06096	0.0366285	0.0183143	+	0.999832i	$0.494170\pi$
$840$	11.4845	0.396252
$841$	−21.8373	−0.753011
$842$	43.3395	1.49358
$843$	10.3275	0.355697
$844$	2.49189	0.0857745
$845$	−24.1063	−0.829283
$846$	12.1796	0.418743
$847$	−4.10637	−0.141097
$848$	−11.1783	−0.383863
$849$	−19.8435	−0.681028
$850$	29.6712	1.01771
$851$	−6.00446	−0.205830
$852$	32.6734	1.11937
$853$	16.6159	0.568916	0.284458	−	0.958688i	$-0.408186\pi$
$853$	16.6159	0.568916	0.284458	+	0.958688i	$0.408186\pi$
$854$	−32.7650	−1.12120
$855$	−25.3134	−0.865699
$856$	−24.1263	−0.824620
$857$	−26.4306	−0.902853	−0.451427	−	0.892308i	$-0.649085\pi$
$857$	−26.4306	−0.902853	−0.451427	+	0.892308i	$0.649085\pi$
$858$	−15.9253	−0.543682
$859$	36.8574	1.25756	0.628779	−	0.777584i	$-0.283555\pi$
$859$	36.8574	1.25756	0.628779	+	0.777584i	$0.283555\pi$
$860$	58.3170	1.98859
$861$	2.55352	0.0870238
$862$	68.5040	2.33326
$863$	−17.9838	−0.612177	−0.306088	−	0.952003i	$-0.599020\pi$
$863$	−17.9838	−0.612177	−0.306088	+	0.952003i	$0.599020\pi$
$864$	−7.60765	−0.258817
$865$	−47.3102	−1.60860
$866$	−25.8833	−0.879550
$867$	12.5675	0.426815
$868$	−6.36226	−0.215949
$869$	1.11632	0.0378686
$870$	19.6778	0.667141
$871$	−4.13640	−0.140157
$872$	13.2992	0.450368
$873$	−6.47851	−0.219264
$874$	−49.7176	−1.68172
$875$	11.3383	0.383303
$876$	−14.8611	−0.502108
$877$	−5.56385	−0.187878	−0.0939390	−	0.995578i	$-0.529946\pi$
$877$	−5.56385	−0.187878	−0.0939390	+	0.995578i	$0.529946\pi$
$878$	−24.4483	−0.825091
$879$	13.1407	0.443225
$880$	21.6242	0.728953
$881$	−10.7733	−0.362962	−0.181481	−	0.983394i	$-0.558089\pi$
$881$	−10.7733	−0.362962	−0.181481	+	0.983394i	$0.558089\pi$
$882$	4.40731	0.148402
$883$	−26.8941	−0.905060	−0.452530	−	0.891749i	$-0.649478\pi$
$883$	−26.8941	−0.905060	−0.452530	+	0.891749i	$0.649478\pi$
$884$	−13.8017	−0.464202
$885$	42.6692	1.43431
$886$	50.2642	1.68866
$887$	17.3417	0.582277	0.291139	−	0.956681i	$-0.405966\pi$
$887$	17.3417	0.582277	0.291139	+	0.956681i	$0.405966\pi$
$888$	2.96996	0.0996653
$889$	3.55801	0.119332
$890$	−65.7626	−2.20437
$891$	−3.02614	−0.101380
$892$	70.9441	2.37538
$893$	41.9318	1.40319
$894$	−20.3961	−0.682149
$895$	−26.0229	−0.869849
$896$	25.4291	0.849527
$897$	7.45654	0.248967
$898$	−49.7407	−1.65987
$899$	−2.82875	−0.0943441
$900$	17.5558	0.585195
$901$	−11.1686	−0.372079
$902$	−7.51724	−0.250297
$903$	−14.1907	−0.472236
$904$	15.5717	0.517906
$905$	−89.8285	−2.98600
$906$	18.0032	0.598116
$907$	21.1162	0.701152	0.350576	−	0.936534i	$-0.385986\pi$
$907$	21.1162	0.701152	0.350576	+	0.936534i	$0.385986\pi$
$908$	−77.1346	−2.55980
$909$	4.18202	0.138709
$910$	−39.7749	−1.31853
$911$	−16.6077	−0.550239	−0.275120	−	0.961410i	$-0.588717\pi$
$911$	−16.6077	−0.550239	−0.275120	+	0.961410i	$0.588717\pi$
$912$	−15.7289	−0.520835
$913$	38.4413	1.27222
$914$	21.8129	0.721505
$915$	−22.9941	−0.760163
$916$	−21.5945	−0.713503
$917$	−43.1730	−1.42570
$918$	−4.56468	−0.150657
$919$	7.68495	0.253503	0.126752	−	0.991934i	$-0.459545\pi$
$919$	7.68495	0.253503	0.126752	+	0.991934i	$0.459545\pi$
$920$	15.8299	0.521896
$921$	−21.9331	−0.722719
$922$	58.2294	1.91768
$923$	−29.3636	−0.966514
$924$	18.2156	0.599250
$925$	12.7050	0.417736
$926$	−53.2890	−1.75119
$927$	−14.8446	−0.487560
$928$	20.3605	0.668366
$929$	16.5937	0.544420	0.272210	−	0.962238i	$-0.412245\pi$
$929$	16.5937	0.544420	0.272210	+	0.962238i	$0.412245\pi$
$930$	−7.77134	−0.254832
$931$	15.1734	0.497289
$932$	−26.6449	−0.872784
$933$	−19.4373	−0.636348
$934$	58.9699	1.92955
$935$	21.6055	0.706575
$936$	−3.68819	−0.120552
$937$	3.56607	0.116498	0.0582491	−	0.998302i	$-0.481448\pi$
$937$	3.56607	0.116498	0.0582491	+	0.998302i	$0.481448\pi$
$938$	8.23484	0.268877
$939$	20.5895	0.671913
$940$	−51.4511	−1.67815
$941$	50.2156	1.63698	0.818491	−	0.574520i	$-0.194811\pi$
$941$	50.2156	1.63698	0.818491	+	0.574520i	$0.194811\pi$
$942$	32.0288	1.04355
$943$	3.51971	0.114618
$944$	26.5132	0.862931
$945$	−7.55805	−0.245863
$946$	41.7756	1.35824
$947$	2.26209	0.0735082	0.0367541	−	0.999324i	$-0.488298\pi$
$947$	2.26209	0.0735082	0.0367541	+	0.999324i	$0.488298\pi$
$948$	0.996316	0.0323589
$949$	13.3556	0.433542
$950$	105.198	3.41309
$951$	5.90948	0.191628
$952$	7.12988	0.231081
$953$	50.7243	1.64312	0.821561	−	0.570121i	$-0.193104\pi$
$953$	50.7243	1.64312	0.821561	+	0.570121i	$0.193104\pi$
$954$	−11.5017	−0.372381
$955$	−35.7840	−1.15794
$956$	8.31007	0.268767
$957$	8.09892	0.261801
$958$	−47.7520	−1.54280
$959$	38.7972	1.25283
$960$	41.6441	1.34406
$961$	−29.8828	−0.963963
$962$	−10.2861	−0.331636
$963$	15.8778	0.511654
$964$	1.74144	0.0560881
$965$	90.0944	2.90024
$966$	−14.8447	−0.477619
$967$	−19.4473	−0.625383	−0.312691	−	0.949855i	$-0.601231\pi$
$967$	−19.4473	−0.625383	−0.312691	+	0.949855i	$0.601231\pi$
$968$	2.79964	0.0899838
$969$	−15.7153	−0.504847
$970$	47.6337	1.52943
$971$	28.7059	0.921216	0.460608	−	0.887604i	$-0.347631\pi$
$971$	28.7059	0.921216	0.460608	+	0.887604i	$0.347631\pi$
$972$	−2.70083	−0.0866292
$973$	34.2460	1.09788
$974$	−17.5735	−0.563093
$975$	−15.7774	−0.505282
$976$	−14.2878	−0.457341
$977$	−55.2668	−1.76814	−0.884071	−	0.467353i	$-0.845208\pi$
$977$	−55.2668	−1.76814	−0.884071	+	0.467353i	$0.845208\pi$
$978$	−17.7536	−0.567697
$979$	−27.0663	−0.865042
$980$	−18.6181	−0.594733
$981$	−8.75235	−0.279441
$982$	57.7653	1.84337
$983$	44.1225	1.40729	0.703645	−	0.710552i	$-0.251555\pi$
$983$	44.1225	1.40729	0.703645	+	0.710552i	$0.251555\pi$
$984$	−1.74094	−0.0554991
$985$	−57.2537	−1.82426
$986$	12.2166	0.389054
$987$	12.5200	0.398515
$988$	−48.9337	−1.55679
$989$	−19.5601	−0.621974
$990$	22.2499	0.707149
$991$	26.1188	0.829691	0.414846	−	0.909892i	$-0.363836\pi$
$991$	26.1188	0.829691	0.414846	+	0.909892i	$0.363836\pi$
$992$	−8.04094	−0.255300
$993$	−9.90453	−0.314311
$994$	58.4577	1.85417
$995$	−16.9711	−0.538021
$996$	34.3089	1.08712
$997$	32.3371	1.02413	0.512063	−	0.858948i	$-0.328882\pi$
$997$	32.3371	1.02413	0.512063	+	0.858948i	$0.328882\pi$
$998$	−2.65779	−0.0841309
$999$	−1.95456	−0.0618396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.14	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.14	✓	84	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16814 q^{2} -1.00000 q^{3} +2.70083 q^{4} +3.39119 q^{5} +2.16814 q^{6} +2.22873 q^{7} -1.51950 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16814 q^{2} -1.00000 q^{3} +2.70083 q^{4} +3.39119 q^{5} +2.16814 q^{6} +2.22873 q^{7} -1.51950 q^{8} +1.00000 q^{9} -7.35257 q^{10} -3.02614 q^{11} -2.70083 q^{12} +2.42724 q^{13} -4.83220 q^{14} -3.39119 q^{15} -2.10717 q^{16} -2.10534 q^{17} -2.16814 q^{18} -7.46446 q^{19} +9.15903 q^{20} -2.22873 q^{21} +6.56110 q^{22} -3.07203 q^{23} +1.51950 q^{24} +6.50016 q^{25} -5.26259 q^{26} -1.00000 q^{27} +6.01943 q^{28} +2.67632 q^{29} +7.35257 q^{30} -1.05696 q^{31} +7.60765 q^{32} +3.02614 q^{33} +4.56468 q^{34} +7.55805 q^{35} +2.70083 q^{36} +1.95456 q^{37} +16.1840 q^{38} -2.42724 q^{39} -5.15292 q^{40} -1.14573 q^{41} +4.83220 q^{42} +6.36716 q^{43} -8.17310 q^{44} +3.39119 q^{45} +6.66058 q^{46} -5.61753 q^{47} +2.10717 q^{48} -2.03276 q^{49} -14.0933 q^{50} +2.10534 q^{51} +6.55556 q^{52} +5.30487 q^{53} +2.16814 q^{54} -10.2622 q^{55} -3.38656 q^{56} +7.46446 q^{57} -5.80264 q^{58} -12.5824 q^{59} -9.15903 q^{60} +6.78056 q^{61} +2.29163 q^{62} +2.22873 q^{63} -12.2801 q^{64} +8.23122 q^{65} -6.56110 q^{66} -1.70416 q^{67} -5.68618 q^{68} +3.07203 q^{69} -16.3869 q^{70} -12.0975 q^{71} -1.51950 q^{72} +5.50240 q^{73} -4.23776 q^{74} -6.50016 q^{75} -20.1602 q^{76} -6.74445 q^{77} +5.26259 q^{78} -0.368892 q^{79} -7.14581 q^{80} +1.00000 q^{81} +2.48410 q^{82} -12.7031 q^{83} -6.01943 q^{84} -7.13962 q^{85} -13.8049 q^{86} -2.67632 q^{87} +4.59823 q^{88} +8.94416 q^{89} -7.35257 q^{90} +5.40966 q^{91} -8.29703 q^{92} +1.05696 q^{93} +12.1796 q^{94} -25.3134 q^{95} -7.60765 q^{96} -6.47851 q^{97} +4.40731 q^{98} -3.02614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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