LMFDB - Embedded newform 6033.2.a.d.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.10715 q^{2} -1.00000 q^{3} +2.44009 q^{4} +0.912218 q^{5} +2.10715 q^{6} +4.59060 q^{7} -0.927338 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.10715 q^{2} -1.00000 q^{3} +2.44009 q^{4} +0.912218 q^{5} +2.10715 q^{6} +4.59060 q^{7} -0.927338 q^{8} +1.00000 q^{9} -1.92218 q^{10} -4.52419 q^{11} -2.44009 q^{12} -3.85096 q^{13} -9.67309 q^{14} -0.912218 q^{15} -2.92614 q^{16} -4.99212 q^{17} -2.10715 q^{18} +1.31072 q^{19} +2.22589 q^{20} -4.59060 q^{21} +9.53317 q^{22} +4.10448 q^{23} +0.927338 q^{24} -4.16786 q^{25} +8.11457 q^{26} -1.00000 q^{27} +11.2015 q^{28} +0.357035 q^{29} +1.92218 q^{30} +3.71015 q^{31} +8.02050 q^{32} +4.52419 q^{33} +10.5192 q^{34} +4.18763 q^{35} +2.44009 q^{36} +10.2116 q^{37} -2.76189 q^{38} +3.85096 q^{39} -0.845935 q^{40} -7.19552 q^{41} +9.67309 q^{42} +4.37926 q^{43} -11.0394 q^{44} +0.912218 q^{45} -8.64876 q^{46} +0.670846 q^{47} +2.92614 q^{48} +14.0736 q^{49} +8.78231 q^{50} +4.99212 q^{51} -9.39670 q^{52} -6.39348 q^{53} +2.10715 q^{54} -4.12705 q^{55} -4.25704 q^{56} -1.31072 q^{57} -0.752328 q^{58} +8.26710 q^{59} -2.22589 q^{60} -11.3317 q^{61} -7.81785 q^{62} +4.59060 q^{63} -11.0481 q^{64} -3.51292 q^{65} -9.53317 q^{66} -1.40888 q^{67} -12.1812 q^{68} -4.10448 q^{69} -8.82397 q^{70} +1.98524 q^{71} -0.927338 q^{72} +9.99877 q^{73} -21.5174 q^{74} +4.16786 q^{75} +3.19828 q^{76} -20.7688 q^{77} -8.11457 q^{78} -6.10840 q^{79} -2.66928 q^{80} +1.00000 q^{81} +15.1621 q^{82} -2.56472 q^{83} -11.2015 q^{84} -4.55390 q^{85} -9.22777 q^{86} -0.357035 q^{87} +4.19546 q^{88} -5.50749 q^{89} -1.92218 q^{90} -17.6782 q^{91} +10.0153 q^{92} -3.71015 q^{93} -1.41357 q^{94} +1.19567 q^{95} -8.02050 q^{96} +1.04378 q^{97} -29.6552 q^{98} -4.52419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.10715	−1.48998	−0.744991	−	0.667075i	$-0.767546\pi$
$2$	−2.10715	−1.48998	−0.744991	+	0.667075i	$0.767546\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.44009	1.22005
$5$	0.912218	0.407956	0.203978	−	0.978975i	$-0.434613\pi$
$5$	0.912218	0.407956	0.203978	+	0.978975i	$0.434613\pi$
$6$	2.10715	0.860241
$7$	4.59060	1.73508	0.867542	−	0.497364i	$-0.165699\pi$
$7$	4.59060	1.73508	0.867542	+	0.497364i	$0.165699\pi$
$8$	−0.927338	−0.327864
$9$	1.00000	0.333333
$10$	−1.92218	−0.607847
$11$	−4.52419	−1.36410	−0.682048	−	0.731308i	$-0.738910\pi$
$11$	−4.52419	−1.36410	−0.682048	+	0.731308i	$0.738910\pi$
$12$	−2.44009	−0.704394
$13$	−3.85096	−1.06807	−0.534033	−	0.845464i	$-0.679324\pi$
$13$	−3.85096	−1.06807	−0.534033	+	0.845464i	$0.679324\pi$
$14$	−9.67309	−2.58524
$15$	−0.912218	−0.235534
$16$	−2.92614	−0.731535
$17$	−4.99212	−1.21077	−0.605384	−	0.795934i	$-0.706980\pi$
$17$	−4.99212	−1.21077	−0.605384	+	0.795934i	$0.706980\pi$
$18$	−2.10715	−0.496661
$19$	1.31072	0.300701	0.150350	−	0.988633i	$-0.451960\pi$
$19$	1.31072	0.300701	0.150350	+	0.988633i	$0.451960\pi$
$20$	2.22589	0.497725
$21$	−4.59060	−1.00175
$22$	9.53317	2.03248
$23$	4.10448	0.855843	0.427921	−	0.903816i	$-0.359246\pi$
$23$	4.10448	0.855843	0.427921	+	0.903816i	$0.359246\pi$
$24$	0.927338	0.189292
$25$	−4.16786	−0.833572
$26$	8.11457	1.59140
$27$	−1.00000	−0.192450
$28$	11.2015	2.11688
$29$	0.357035	0.0662998	0.0331499	−	0.999450i	$-0.489446\pi$
$29$	0.357035	0.0662998	0.0331499	+	0.999450i	$0.489446\pi$
$30$	1.92218	0.350941
$31$	3.71015	0.666362	0.333181	−	0.942863i	$-0.391878\pi$
$31$	3.71015	0.666362	0.333181	+	0.942863i	$0.391878\pi$
$32$	8.02050	1.41784
$33$	4.52419	0.787561
$34$	10.5192	1.80402
$35$	4.18763	0.707838
$36$	2.44009	0.406682
$37$	10.2116	1.67878	0.839388	−	0.543533i	$-0.182914\pi$
$37$	10.2116	1.67878	0.839388	+	0.543533i	$0.182914\pi$
$38$	−2.76189	−0.448038
$39$	3.85096	0.616648
$40$	−0.845935	−0.133754
$41$	−7.19552	−1.12375	−0.561876	−	0.827222i	$-0.689920\pi$
$41$	−7.19552	−1.12375	−0.561876	+	0.827222i	$0.689920\pi$
$42$	9.67309	1.49259
$43$	4.37926	0.667831	0.333915	−	0.942603i	$-0.391630\pi$
$43$	4.37926	0.667831	0.333915	+	0.942603i	$0.391630\pi$
$44$	−11.0394	−1.66426
$45$	0.912218	0.135985
$46$	−8.64876	−1.27519
$47$	0.670846	0.0978529	0.0489265	−	0.998802i	$-0.484420\pi$
$47$	0.670846	0.0978529	0.0489265	+	0.998802i	$0.484420\pi$
$48$	2.92614	0.422352
$49$	14.0736	2.01051
$50$	8.78231	1.24201
$51$	4.99212	0.699037
$52$	−9.39670	−1.30309
$53$	−6.39348	−0.878213	−0.439106	−	0.898435i	$-0.644705\pi$
$53$	−6.39348	−0.878213	−0.439106	+	0.898435i	$0.644705\pi$
$54$	2.10715	0.286747
$55$	−4.12705	−0.556491
$56$	−4.25704	−0.568871
$57$	−1.31072	−0.173610
$58$	−0.752328	−0.0987855
$59$	8.26710	1.07628	0.538142	−	0.842854i	$-0.319126\pi$
$59$	8.26710	1.07628	0.538142	+	0.842854i	$0.319126\pi$
$60$	−2.22589	−0.287362
$61$	−11.3317	−1.45087	−0.725436	−	0.688289i	$-0.758362\pi$
$61$	−11.3317	−1.45087	−0.725436	+	0.688289i	$0.758362\pi$
$62$	−7.81785	−0.992867
$63$	4.59060	0.578361
$64$	−11.0481	−1.38102
$65$	−3.51292	−0.435724
$66$	−9.53317	−1.17345
$67$	−1.40888	−0.172122	−0.0860608	−	0.996290i	$-0.527428\pi$
$67$	−1.40888	−0.172122	−0.0860608	+	0.996290i	$0.527428\pi$
$68$	−12.1812	−1.47719
$69$	−4.10448	−0.494121
$70$	−8.82397	−1.05467
$71$	1.98524	0.235604	0.117802	−	0.993037i	$-0.462415\pi$
$71$	1.98524	0.235604	0.117802	+	0.993037i	$0.462415\pi$
$72$	−0.927338	−0.109288
$73$	9.99877	1.17027	0.585134	−	0.810937i	$-0.301042\pi$
$73$	9.99877	1.17027	0.585134	+	0.810937i	$0.301042\pi$
$74$	−21.5174	−2.50135
$75$	4.16786	0.481263
$76$	3.19828	0.366868
$77$	−20.7688	−2.36682
$78$	−8.11457	−0.918794
$79$	−6.10840	−0.687249	−0.343625	−	0.939107i	$-0.611655\pi$
$79$	−6.10840	−0.687249	−0.343625	+	0.939107i	$0.611655\pi$
$80$	−2.66928	−0.298434
$81$	1.00000	0.111111
$82$	15.1621	1.67437
$83$	−2.56472	−0.281514	−0.140757	−	0.990044i	$-0.544954\pi$
$83$	−2.56472	−0.281514	−0.140757	+	0.990044i	$0.544954\pi$
$84$	−11.2015	−1.22218
$85$	−4.55390	−0.493940
$86$	−9.22777	−0.995056
$87$	−0.357035	−0.0382782
$88$	4.19546	0.447237
$89$	−5.50749	−0.583792	−0.291896	−	0.956450i	$-0.594286\pi$
$89$	−5.50749	−0.583792	−0.291896	+	0.956450i	$0.594286\pi$
$90$	−1.92218	−0.202616
$91$	−17.6782	−1.85318
$92$	10.0153	1.04417
$93$	−3.71015	−0.384724
$94$	−1.41357	−0.145799
$95$	1.19567	0.122673
$96$	−8.02050	−0.818588
$97$	1.04378	0.105979	0.0529897	−	0.998595i	$-0.483125\pi$
$97$	1.04378	0.105979	0.0529897	+	0.998595i	$0.483125\pi$
$98$	−29.6552	−2.99563
$99$	−4.52419	−0.454699
$100$	−10.1700	−1.01700
$101$	−4.50642	−0.448405	−0.224203	−	0.974543i	$-0.571978\pi$
$101$	−4.50642	−0.448405	−0.224203	+	0.974543i	$0.571978\pi$
$102$	−10.5192	−1.04155
$103$	8.94949	0.881819	0.440910	−	0.897552i	$-0.354656\pi$
$103$	8.94949	0.881819	0.440910	+	0.897552i	$0.354656\pi$
$104$	3.57115	0.350180
$105$	−4.18763	−0.408671
$106$	13.4720	1.30852
$107$	−3.71507	−0.359149	−0.179575	−	0.983744i	$-0.557472\pi$
$107$	−3.71507	−0.359149	−0.179575	+	0.983744i	$0.557472\pi$
$108$	−2.44009	−0.234798
$109$	11.0240	1.05590	0.527952	−	0.849274i	$-0.322960\pi$
$109$	11.0240	1.05590	0.527952	+	0.849274i	$0.322960\pi$
$110$	8.69633	0.829162
$111$	−10.2116	−0.969242
$112$	−13.4327	−1.26927
$113$	−1.27009	−0.119480	−0.0597400	−	0.998214i	$-0.519027\pi$
$113$	−1.27009	−0.119480	−0.0597400	+	0.998214i	$0.519027\pi$
$114$	2.76189	0.258675
$115$	3.74418	0.349146
$116$	0.871199	0.0808888
$117$	−3.85096	−0.356022
$118$	−17.4200	−1.60364
$119$	−22.9168	−2.10078
$120$	0.845935	0.0772229
$121$	9.46833	0.860757
$122$	23.8776	2.16177
$123$	7.19552	0.648798
$124$	9.05310	0.812992
$125$	−8.36309	−0.748017
$126$	−9.67309	−0.861748
$127$	−19.5763	−1.73711	−0.868556	−	0.495590i	$-0.834952\pi$
$127$	−19.5763	−1.73711	−0.868556	+	0.495590i	$0.834952\pi$
$128$	7.23910	0.639852
$129$	−4.37926	−0.385572
$130$	7.40226	0.649221
$131$	5.32189	0.464975	0.232488	−	0.972599i	$-0.425313\pi$
$131$	5.32189	0.464975	0.232488	+	0.972599i	$0.425313\pi$
$132$	11.0394	0.960860
$133$	6.01701	0.521741
$134$	2.96872	0.256458
$135$	−0.912218	−0.0785112
$136$	4.62939	0.396967
$137$	−0.833976	−0.0712514	−0.0356257	−	0.999365i	$-0.511342\pi$
$137$	−0.833976	−0.0712514	−0.0356257	+	0.999365i	$0.511342\pi$
$138$	8.64876	0.736231
$139$	11.8494	1.00505	0.502527	−	0.864562i	$-0.332404\pi$
$139$	11.8494	1.00505	0.502527	+	0.864562i	$0.332404\pi$
$140$	10.2182	0.863595
$141$	−0.670846	−0.0564954
$142$	−4.18320	−0.351046
$143$	17.4225	1.45694
$144$	−2.92614	−0.243845
$145$	0.325694	0.0270474
$146$	−21.0689	−1.74368
$147$	−14.0736	−1.16077
$148$	24.9172	2.04818
$149$	−20.9360	−1.71514	−0.857572	−	0.514363i	$-0.828028\pi$
$149$	−20.9360	−1.71514	−0.857572	+	0.514363i	$0.828028\pi$
$150$	−8.78231	−0.717073
$151$	−15.3483	−1.24902	−0.624512	−	0.781015i	$-0.714702\pi$
$151$	−15.3483	−1.24902	−0.624512	+	0.781015i	$0.714702\pi$
$152$	−1.21548	−0.0985888
$153$	−4.99212	−0.403589
$154$	43.7629	3.52652
$155$	3.38446	0.271847
$156$	9.39670	0.752338
$157$	4.67960	0.373473	0.186737	−	0.982410i	$-0.440209\pi$
$157$	4.67960	0.373473	0.186737	+	0.982410i	$0.440209\pi$
$158$	12.8713	1.02399
$159$	6.39348	0.507036
$160$	7.31644	0.578415
$161$	18.8420	1.48496
$162$	−2.10715	−0.165554
$163$	16.5323	1.29491	0.647453	−	0.762105i	$-0.275834\pi$
$163$	16.5323	1.29491	0.647453	+	0.762105i	$0.275834\pi$
$164$	−17.5577	−1.37103
$165$	4.12705	0.321290
$166$	5.40425	0.419451
$167$	−12.0802	−0.934797	−0.467398	−	0.884047i	$-0.654809\pi$
$167$	−12.0802	−0.934797	−0.467398	+	0.884047i	$0.654809\pi$
$168$	4.25704	0.328438
$169$	1.82993	0.140764
$170$	9.59577	0.735962
$171$	1.31072	0.100234
$172$	10.6858	0.814784
$173$	−16.0216	−1.21810	−0.609051	−	0.793131i	$-0.708450\pi$
$173$	−16.0216	−1.21810	−0.609051	+	0.793131i	$0.708450\pi$
$174$	0.752328	0.0570338
$175$	−19.1330	−1.44632
$176$	13.2384	0.997883
$177$	−8.26710	−0.621393
$178$	11.6051	0.869840
$179$	15.9421	1.19157	0.595783	−	0.803145i	$-0.296842\pi$
$179$	15.9421	1.19157	0.595783	+	0.803145i	$0.296842\pi$
$180$	2.22589	0.165908
$181$	−11.3089	−0.840583	−0.420292	−	0.907389i	$-0.638072\pi$
$181$	−11.3089	−0.840583	−0.420292	+	0.907389i	$0.638072\pi$
$182$	37.2507	2.76121
$183$	11.3317	0.837662
$184$	−3.80624	−0.280600
$185$	9.31520	0.684867
$186$	7.81785	0.573232
$187$	22.5853	1.65160
$188$	1.63693	0.119385
$189$	−4.59060	−0.333917
$190$	−2.51945	−0.182780
$191$	11.9618	0.865524	0.432762	−	0.901508i	$-0.357539\pi$
$191$	11.9618	0.865524	0.432762	+	0.901508i	$0.357539\pi$
$192$	11.0481	0.797330
$193$	4.78761	0.344620	0.172310	−	0.985043i	$-0.444877\pi$
$193$	4.78761	0.344620	0.172310	+	0.985043i	$0.444877\pi$
$194$	−2.19940	−0.157907
$195$	3.51292	0.251565
$196$	34.3409	2.45292
$197$	−8.14988	−0.580655	−0.290328	−	0.956927i	$-0.593764\pi$
$197$	−8.14988	−0.580655	−0.290328	+	0.956927i	$0.593764\pi$
$198$	9.53317	0.677493
$199$	−8.47899	−0.601060	−0.300530	−	0.953772i	$-0.597163\pi$
$199$	−8.47899	−0.601060	−0.300530	+	0.953772i	$0.597163\pi$
$200$	3.86501	0.273298
$201$	1.40888	0.0993745
$202$	9.49571	0.668116
$203$	1.63901	0.115036
$204$	12.1812	0.852857
$205$	−6.56388	−0.458441
$206$	−18.8579	−1.31389
$207$	4.10448	0.285281
$208$	11.2685	0.781327
$209$	−5.92997	−0.410184
$210$	8.82397	0.608912
$211$	−2.37837	−0.163734	−0.0818670	−	0.996643i	$-0.526088\pi$
$211$	−2.37837	−0.163734	−0.0818670	+	0.996643i	$0.526088\pi$
$212$	−15.6007	−1.07146
$213$	−1.98524	−0.136026
$214$	7.82821	0.535126
$215$	3.99484	0.272446
$216$	0.927338	0.0630974
$217$	17.0318	1.15619
$218$	−23.2292	−1.57328
$219$	−9.99877	−0.675655
$220$	−10.0704	−0.678945
$221$	19.2245	1.29318
$222$	21.5174	1.44415
$223$	−0.560654	−0.0375442	−0.0187721	−	0.999824i	$-0.505976\pi$
$223$	−0.560654	−0.0375442	−0.0187721	+	0.999824i	$0.505976\pi$
$224$	36.8189	2.46007
$225$	−4.16786	−0.277857
$226$	2.67627	0.178023
$227$	29.2217	1.93951	0.969755	−	0.244080i	$-0.0784860\pi$
$227$	29.2217	1.93951	0.969755	+	0.244080i	$0.0784860\pi$
$228$	−3.19828	−0.211812
$229$	0.0916488	0.00605633	0.00302816	−	0.999995i	$-0.499036\pi$
$229$	0.0916488	0.00605633	0.00302816	+	0.999995i	$0.499036\pi$
$230$	−7.88955	−0.520222
$231$	20.7688	1.36648
$232$	−0.331093	−0.0217373
$233$	−27.2870	−1.78763	−0.893814	−	0.448437i	$-0.851981\pi$
$233$	−27.2870	−1.78763	−0.893814	+	0.448437i	$0.851981\pi$
$234$	8.11457	0.530466
$235$	0.611958	0.0399197
$236$	20.1725	1.31312
$237$	6.10840	0.396783
$238$	48.2893	3.13013
$239$	−14.5074	−0.938407	−0.469203	−	0.883090i	$-0.655459\pi$
$239$	−14.5074	−0.938407	−0.469203	+	0.883090i	$0.655459\pi$
$240$	2.66928	0.172301
$241$	−27.9619	−1.80118	−0.900591	−	0.434667i	$-0.856866\pi$
$241$	−27.9619	−1.80118	−0.900591	+	0.434667i	$0.856866\pi$
$242$	−19.9512	−1.28251
$243$	−1.00000	−0.0641500
$244$	−27.6503	−1.77013
$245$	12.8382	0.820202
$246$	−15.1621	−0.966697
$247$	−5.04755	−0.321168
$248$	−3.44056	−0.218476
$249$	2.56472	0.162532
$250$	17.6223	1.11453
$251$	17.1578	1.08299	0.541497	−	0.840703i	$-0.317858\pi$
$251$	17.1578	1.08299	0.541497	+	0.840703i	$0.317858\pi$
$252$	11.2015	0.705627
$253$	−18.5694	−1.16745
$254$	41.2502	2.58827
$255$	4.55390	0.285177
$256$	6.84237	0.427648
$257$	−29.3453	−1.83051	−0.915255	−	0.402874i	$-0.868011\pi$
$257$	−29.3453	−1.83051	−0.915255	+	0.402874i	$0.868011\pi$
$258$	9.22777	0.574496
$259$	46.8773	2.91282
$260$	−8.57184	−0.531603
$261$	0.357035	0.0220999
$262$	−11.2140	−0.692805
$263$	−13.1551	−0.811178	−0.405589	−	0.914055i	$-0.632934\pi$
$263$	−13.1551	−0.811178	−0.405589	+	0.914055i	$0.632934\pi$
$264$	−4.19546	−0.258213
$265$	−5.83225	−0.358272
$266$	−12.6787	−0.777384
$267$	5.50749	0.337053
$268$	−3.43779	−0.209996
$269$	8.72950	0.532247	0.266123	−	0.963939i	$-0.414257\pi$
$269$	8.72950	0.532247	0.266123	+	0.963939i	$0.414257\pi$
$270$	1.92218	0.116980
$271$	−31.6728	−1.92399	−0.961993	−	0.273073i	$-0.911960\pi$
$271$	−31.6728	−1.92399	−0.961993	+	0.273073i	$0.911960\pi$
$272$	14.6076	0.885718
$273$	17.6782	1.06994
$274$	1.75731	0.106163
$275$	18.8562	1.13707
$276$	−10.0153	−0.602850
$277$	30.2102	1.81516	0.907578	−	0.419883i	$-0.137929\pi$
$277$	30.2102	1.81516	0.907578	+	0.419883i	$0.137929\pi$
$278$	−24.9685	−1.49751
$279$	3.71015	0.222121
$280$	−3.88335	−0.232074
$281$	−17.4884	−1.04327	−0.521634	−	0.853169i	$-0.674678\pi$
$281$	−17.4884	−1.04327	−0.521634	+	0.853169i	$0.674678\pi$
$282$	1.41357	0.0841771
$283$	9.34195	0.555321	0.277661	−	0.960679i	$-0.410441\pi$
$283$	9.34195	0.555321	0.277661	+	0.960679i	$0.410441\pi$
$284$	4.84416	0.287448
$285$	−1.19567	−0.0708251
$286$	−36.7119	−2.17082
$287$	−33.0317	−1.94980
$288$	8.02050	0.472612
$289$	7.92129	0.465958
$290$	−0.686287	−0.0403002
$291$	−1.04378	−0.0611873
$292$	24.3979	1.42778
$293$	6.89033	0.402538	0.201269	−	0.979536i	$-0.435494\pi$
$293$	6.89033	0.402538	0.201269	+	0.979536i	$0.435494\pi$
$294$	29.6552	1.72953
$295$	7.54140	0.439077
$296$	−9.46960	−0.550409
$297$	4.52419	0.262520
$298$	44.1154	2.55553
$299$	−15.8062	−0.914096
$300$	10.1700	0.587162
$301$	20.1034	1.15874
$302$	32.3411	1.86102
$303$	4.50642	0.258887
$304$	−3.83536	−0.219973
$305$	−10.3370	−0.591893
$306$	10.5192	0.601341
$307$	−25.7823	−1.47148	−0.735738	−	0.677267i	$-0.763164\pi$
$307$	−25.7823	−1.47148	−0.735738	+	0.677267i	$0.763164\pi$
$308$	−50.6777	−2.88763
$309$	−8.94949	−0.509119
$310$	−7.13158	−0.405047
$311$	−16.0173	−0.908259	−0.454129	−	0.890936i	$-0.650050\pi$
$311$	−16.0173	−0.908259	−0.454129	+	0.890936i	$0.650050\pi$
$312$	−3.57115	−0.202176
$313$	−16.1231	−0.911330	−0.455665	−	0.890151i	$-0.650598\pi$
$313$	−16.1231	−0.911330	−0.455665	+	0.890151i	$0.650598\pi$
$314$	−9.86064	−0.556468
$315$	4.18763	0.235946
$316$	−14.9051	−0.838475
$317$	−21.6839	−1.21789	−0.608946	−	0.793212i	$-0.708407\pi$
$317$	−21.6839	−1.21789	−0.608946	+	0.793212i	$0.708407\pi$
$318$	−13.4720	−0.755475
$319$	−1.61530	−0.0904393
$320$	−10.0783	−0.563394
$321$	3.71507	0.207355
$322$	−39.7030	−2.21256
$323$	−6.54329	−0.364078
$324$	2.44009	0.135561
$325$	16.0503	0.890309
$326$	−34.8360	−1.92939
$327$	−11.0240	−0.609626
$328$	6.67268	0.368437
$329$	3.07958	0.169783
$330$	−8.69633	−0.478717
$331$	−13.1339	−0.721907	−0.360953	−	0.932584i	$-0.617549\pi$
$331$	−13.1339	−0.721907	−0.360953	+	0.932584i	$0.617549\pi$
$332$	−6.25815	−0.343460
$333$	10.2116	0.559592
$334$	25.4549	1.39283
$335$	−1.28520	−0.0702181
$336$	13.4327	0.732815
$337$	0.982226	0.0535053	0.0267526	−	0.999642i	$-0.491483\pi$
$337$	0.982226	0.0535053	0.0267526	+	0.999642i	$0.491483\pi$
$338$	−3.85594	−0.209735
$339$	1.27009	0.0689818
$340$	−11.1119	−0.602630
$341$	−16.7854	−0.908982
$342$	−2.76189	−0.149346
$343$	32.4721	1.75333
$344$	−4.06106	−0.218957
$345$	−3.74418	−0.201580
$346$	33.7600	1.81495
$347$	−18.9672	−1.01822	−0.509108	−	0.860703i	$-0.670024\pi$
$347$	−18.9672	−1.01822	−0.509108	+	0.860703i	$0.670024\pi$
$348$	−0.871199	−0.0467012
$349$	−21.6428	−1.15851	−0.579256	−	0.815146i	$-0.696657\pi$
$349$	−21.6428	−1.15851	−0.579256	+	0.815146i	$0.696657\pi$
$350$	40.3161	2.15498
$351$	3.85096	0.205549
$352$	−36.2863	−1.93407
$353$	3.13764	0.167000	0.0835000	−	0.996508i	$-0.473390\pi$
$353$	3.13764	0.167000	0.0835000	+	0.996508i	$0.473390\pi$
$354$	17.4200	0.925865
$355$	1.81097	0.0961162
$356$	−13.4388	−0.712253
$357$	22.9168	1.21289
$358$	−33.5924	−1.77541
$359$	−7.65275	−0.403897	−0.201948	−	0.979396i	$-0.564727\pi$
$359$	−7.65275	−0.403897	−0.201948	+	0.979396i	$0.564727\pi$
$360$	−0.845935	−0.0445847
$361$	−17.2820	−0.909579
$362$	23.8296	1.25245
$363$	−9.46833	−0.496958
$364$	−43.1365	−2.26097
$365$	9.12106	0.477418
$366$	−23.8776	−1.24810
$367$	−2.13953	−0.111683	−0.0558414	−	0.998440i	$-0.517784\pi$
$367$	−2.13953	−0.111683	−0.0558414	+	0.998440i	$0.517784\pi$
$368$	−12.0103	−0.626079
$369$	−7.19552	−0.374584
$370$	−19.6285	−1.02044
$371$	−29.3499	−1.52377
$372$	−9.05310	−0.469381
$373$	−0.339947	−0.0176018	−0.00880088	−	0.999961i	$-0.502801\pi$
$373$	−0.339947	−0.0176018	−0.00880088	+	0.999961i	$0.502801\pi$
$374$	−47.5907	−2.46086
$375$	8.36309	0.431868
$376$	−0.622101	−0.0320824
$377$	−1.37493	−0.0708125
$378$	9.67309	0.497530
$379$	6.72230	0.345301	0.172651	−	0.984983i	$-0.444767\pi$
$379$	6.72230	0.345301	0.172651	+	0.984983i	$0.444767\pi$
$380$	2.91753	0.149666
$381$	19.5763	1.00292
$382$	−25.2053	−1.28961
$383$	−5.45061	−0.278513	−0.139257	−	0.990256i	$-0.544471\pi$
$383$	−5.45061	−0.278513	−0.139257	+	0.990256i	$0.544471\pi$
$384$	−7.23910	−0.369419
$385$	−18.9456	−0.965559
$386$	−10.0882	−0.513477
$387$	4.37926	0.222610
$388$	2.54691	0.129300
$389$	26.2701	1.33195	0.665975	−	0.745974i	$-0.268016\pi$
$389$	26.2701	1.33195	0.665975	+	0.745974i	$0.268016\pi$
$390$	−7.40226	−0.374828
$391$	−20.4901	−1.03623
$392$	−13.0510	−0.659175
$393$	−5.32189	−0.268454
$394$	17.1730	0.865166
$395$	−5.57220	−0.280368
$396$	−11.0394	−0.554753
$397$	15.3562	0.770707	0.385353	−	0.922769i	$-0.374080\pi$
$397$	15.3562	0.770707	0.385353	+	0.922769i	$0.374080\pi$
$398$	17.8665	0.895568
$399$	−6.01701	−0.301227
$400$	12.1957	0.609787
$401$	9.19486	0.459169	0.229585	−	0.973289i	$-0.426263\pi$
$401$	9.19486	0.459169	0.229585	+	0.973289i	$0.426263\pi$
$402$	−2.96872	−0.148066
$403$	−14.2876	−0.711718
$404$	−10.9961	−0.547075
$405$	0.912218	0.0453285
$406$	−3.45364	−0.171401
$407$	−46.1992	−2.29001
$408$	−4.62939	−0.229189
$409$	6.50495	0.321649	0.160824	−	0.986983i	$-0.448585\pi$
$409$	6.50495	0.321649	0.160824	+	0.986983i	$0.448585\pi$
$410$	13.8311	0.683069
$411$	0.833976	0.0411370
$412$	21.8376	1.07586
$413$	37.9510	1.86744
$414$	−8.64876	−0.425063
$415$	−2.33958	−0.114846
$416$	−30.8866	−1.51434
$417$	−11.8494	−0.580268
$418$	12.4953	0.611167
$419$	−18.1500	−0.886684	−0.443342	−	0.896353i	$-0.646207\pi$
$419$	−18.1500	−0.886684	−0.443342	+	0.896353i	$0.646207\pi$
$420$	−10.2182	−0.498597
$421$	30.5442	1.48863	0.744317	−	0.667826i	$-0.232775\pi$
$421$	30.5442	1.48863	0.744317	+	0.667826i	$0.232775\pi$
$422$	5.01159	0.243961
$423$	0.670846	0.0326176
$424$	5.92892	0.287934
$425$	20.8065	1.00926
$426$	4.18320	0.202676
$427$	−52.0192	−2.51739
$428$	−9.06510	−0.438178
$429$	−17.4225	−0.841167
$430$	−8.41774	−0.405939
$431$	13.4126	0.646063	0.323031	−	0.946388i	$-0.395298\pi$
$431$	13.4126	0.646063	0.323031	+	0.946388i	$0.395298\pi$
$432$	2.92614	0.140784
$433$	−13.0462	−0.626962	−0.313481	−	0.949594i	$-0.601495\pi$
$433$	−13.0462	−0.626962	−0.313481	+	0.949594i	$0.601495\pi$
$434$	−35.8886	−1.72271
$435$	−0.325694	−0.0156158
$436$	26.8995	1.28825
$437$	5.37983	0.257352
$438$	21.0689	1.00671
$439$	26.6544	1.27215	0.636073	−	0.771629i	$-0.280558\pi$
$439$	26.6544	1.27215	0.636073	+	0.771629i	$0.280558\pi$
$440$	3.82717	0.182453
$441$	14.0736	0.670171
$442$	−40.5089	−1.92681
$443$	37.6345	1.78807	0.894035	−	0.447996i	$-0.147862\pi$
$443$	37.6345	1.78807	0.894035	+	0.447996i	$0.147862\pi$
$444$	−24.9172	−1.18252
$445$	−5.02403	−0.238162
$446$	1.18138	0.0559401
$447$	20.9360	0.990239
$448$	−50.7175	−2.39618
$449$	−7.18627	−0.339141	−0.169570	−	0.985518i	$-0.554238\pi$
$449$	−7.18627	−0.339141	−0.169570	+	0.985518i	$0.554238\pi$
$450$	8.78231	0.414002
$451$	32.5539	1.53290
$452$	−3.09913	−0.145771
$453$	15.3483	0.721124
$454$	−61.5745	−2.88983
$455$	−16.1264	−0.756018
$456$	1.21548	0.0569203
$457$	−26.3183	−1.23112	−0.615558	−	0.788091i	$-0.711069\pi$
$457$	−26.3183	−1.23112	−0.615558	+	0.788091i	$0.711069\pi$
$458$	−0.193118	−0.00902382
$459$	4.99212	0.233012
$460$	9.13613	0.425974
$461$	−8.46710	−0.394352	−0.197176	−	0.980368i	$-0.563177\pi$
$461$	−8.46710	−0.394352	−0.197176	+	0.980368i	$0.563177\pi$
$462$	−43.7629	−2.03604
$463$	−20.2783	−0.942414	−0.471207	−	0.882023i	$-0.656181\pi$
$463$	−20.2783	−0.942414	−0.471207	+	0.882023i	$0.656181\pi$
$464$	−1.04473	−0.0485006
$465$	−3.38446	−0.156951
$466$	57.4978	2.66353
$467$	−11.1175	−0.514456	−0.257228	−	0.966351i	$-0.582809\pi$
$467$	−11.1175	−0.514456	−0.257228	+	0.966351i	$0.582809\pi$
$468$	−9.39670	−0.434363
$469$	−6.46759	−0.298645
$470$	−1.28949	−0.0594797
$471$	−4.67960	−0.215625
$472$	−7.66640	−0.352875
$473$	−19.8126	−0.910985
$474$	−12.8713	−0.591200
$475$	−5.46291	−0.250655
$476$	−55.9192	−2.56305
$477$	−6.39348	−0.292738
$478$	30.5693	1.39821
$479$	0.287509	0.0131366	0.00656830	−	0.999978i	$-0.497909\pi$
$479$	0.287509	0.0131366	0.00656830	+	0.999978i	$0.497909\pi$
$480$	−7.31644	−0.333948
$481$	−39.3245	−1.79304
$482$	58.9199	2.68373
$483$	−18.8420	−0.857341
$484$	23.1036	1.05016
$485$	0.952152	0.0432350
$486$	2.10715	0.0955824
$487$	−25.1381	−1.13912	−0.569559	−	0.821951i	$-0.692886\pi$
$487$	−25.1381	−1.13912	−0.569559	+	0.821951i	$0.692886\pi$
$488$	10.5083	0.475688
$489$	−16.5323	−0.747615
$490$	−27.0520	−1.22209
$491$	22.9212	1.03442	0.517210	−	0.855858i	$-0.326971\pi$
$491$	22.9212	1.03442	0.517210	+	0.855858i	$0.326971\pi$
$492$	17.5577	0.791563
$493$	−1.78236	−0.0802737
$494$	10.6360	0.478534
$495$	−4.12705	−0.185497
$496$	−10.8564	−0.487467
$497$	9.11342	0.408793
$498$	−5.40425	−0.242170
$499$	−30.9265	−1.38446	−0.692229	−	0.721678i	$-0.743371\pi$
$499$	−30.9265	−1.38446	−0.692229	+	0.721678i	$0.743371\pi$
$500$	−20.4067	−0.912615
$501$	12.0802	0.539705
$502$	−36.1542	−1.61364
$503$	15.9458	0.710988	0.355494	−	0.934679i	$-0.384313\pi$
$503$	15.9458	0.710988	0.355494	+	0.934679i	$0.384313\pi$
$504$	−4.25704	−0.189624
$505$	−4.11084	−0.182930
$506$	39.1287	1.73948
$507$	−1.82993	−0.0812700
$508$	−47.7679	−2.11936
$509$	17.7283	0.785792	0.392896	−	0.919583i	$-0.371473\pi$
$509$	17.7283	0.785792	0.392896	+	0.919583i	$0.371473\pi$
$510$	−9.59577	−0.424908
$511$	45.9004	2.03051
$512$	−28.8961	−1.27704
$513$	−1.31072	−0.0578699
$514$	61.8351	2.72743
$515$	8.16388	0.359744
$516$	−10.6858	−0.470416
$517$	−3.03504	−0.133481
$518$	−98.7777	−4.34004
$519$	16.0216	0.703272
$520$	3.25766	0.142858
$521$	10.9615	0.480231	0.240116	−	0.970744i	$-0.422815\pi$
$521$	10.9615	0.480231	0.240116	+	0.970744i	$0.422815\pi$
$522$	−0.752328	−0.0329285
$523$	0.961945	0.0420629	0.0210315	−	0.999779i	$-0.493305\pi$
$523$	0.961945	0.0420629	0.0210315	+	0.999779i	$0.493305\pi$
$524$	12.9859	0.567291
$525$	19.1330	0.835031
$526$	27.7198	1.20864
$527$	−18.5215	−0.806810
$528$	−13.2384	−0.576128
$529$	−6.15327	−0.267533
$530$	12.2894	0.533819
$531$	8.26710	0.358762
$532$	14.6820	0.636547
$533$	27.7097	1.20024
$534$	−11.6051	−0.502202
$535$	−3.38895	−0.146517
$536$	1.30651	0.0564324
$537$	−15.9421	−0.687951
$538$	−18.3944	−0.793038
$539$	−63.6717	−2.74253
$540$	−2.22589	−0.0957873
$541$	5.50601	0.236722	0.118361	−	0.992971i	$-0.462236\pi$
$541$	5.50601	0.236722	0.118361	+	0.992971i	$0.462236\pi$
$542$	66.7394	2.86670
$543$	11.3089	0.485311
$544$	−40.0393	−1.71667
$545$	10.0563	0.430762
$546$	−37.2507	−1.59418
$547$	−25.0585	−1.07142	−0.535711	−	0.844401i	$-0.679956\pi$
$547$	−25.0585	−1.07142	−0.535711	+	0.844401i	$0.679956\pi$
$548$	−2.03498	−0.0869299
$549$	−11.3317	−0.483624
$550$	−39.7329	−1.69422
$551$	0.467975	0.0199364
$552$	3.80624	0.162004
$553$	−28.0412	−1.19243
$554$	−63.6576	−2.70455
$555$	−9.31520	−0.395408
$556$	28.9136	1.22621
$557$	1.68878	0.0715560	0.0357780	−	0.999360i	$-0.488609\pi$
$557$	1.68878	0.0715560	0.0357780	+	0.999360i	$0.488609\pi$
$558$	−7.81785	−0.330956
$559$	−16.8644	−0.713287
$560$	−12.2536	−0.517808
$561$	−22.5853	−0.953553
$562$	36.8507	1.55445
$563$	−7.65043	−0.322427	−0.161213	−	0.986920i	$-0.551541\pi$
$563$	−7.65043	−0.322427	−0.161213	+	0.986920i	$0.551541\pi$
$564$	−1.63693	−0.0689270
$565$	−1.15860	−0.0487426
$566$	−19.6849	−0.827419
$567$	4.59060	0.192787
$568$	−1.84099	−0.0772460
$569$	−6.55991	−0.275006	−0.137503	−	0.990501i	$-0.543908\pi$
$569$	−6.55991	−0.275006	−0.137503	+	0.990501i	$0.543908\pi$
$570$	2.51945	0.105528
$571$	−45.9655	−1.92360	−0.961798	−	0.273759i	$-0.911733\pi$
$571$	−45.9655	−1.92360	−0.961798	+	0.273759i	$0.911733\pi$
$572$	42.5125	1.77754
$573$	−11.9618	−0.499710
$574$	69.6029	2.90517
$575$	−17.1069	−0.713406
$576$	−11.0481	−0.460339
$577$	30.6151	1.27452	0.637261	−	0.770648i	$-0.280067\pi$
$577$	30.6151	1.27452	0.637261	+	0.770648i	$0.280067\pi$
$578$	−16.6914	−0.694269
$579$	−4.78761	−0.198966
$580$	0.794723	0.0329991
$581$	−11.7736	−0.488451
$582$	2.19940	0.0911679
$583$	28.9254	1.19797
$584$	−9.27225	−0.383688
$585$	−3.51292	−0.145241
$586$	−14.5190	−0.599774
$587$	−7.99392	−0.329944	−0.164972	−	0.986298i	$-0.552753\pi$
$587$	−7.99392	−0.329944	−0.164972	+	0.986298i	$0.552753\pi$
$588$	−34.3409	−1.41619
$589$	4.86298	0.200375
$590$	−15.8909	−0.654217
$591$	8.14988	0.335241
$592$	−29.8805	−1.22808
$593$	−10.6312	−0.436570	−0.218285	−	0.975885i	$-0.570046\pi$
$593$	−10.6312	−0.436570	−0.218285	+	0.975885i	$0.570046\pi$
$594$	−9.53317	−0.391151
$595$	−20.9051	−0.857028
$596$	−51.0858	−2.09255
$597$	8.47899	0.347022
$598$	33.3061	1.36199
$599$	6.18188	0.252585	0.126292	−	0.991993i	$-0.459692\pi$
$599$	6.18188	0.252585	0.126292	+	0.991993i	$0.459692\pi$
$600$	−3.86501	−0.157789
$601$	20.0655	0.818487	0.409244	−	0.912425i	$-0.365793\pi$
$601$	20.0655	0.818487	0.409244	+	0.912425i	$0.365793\pi$
$602$	−42.3610	−1.72650
$603$	−1.40888	−0.0573739
$604$	−37.4512	−1.52387
$605$	8.63718	0.351151
$606$	−9.49571	−0.385737
$607$	45.9125	1.86353	0.931765	−	0.363062i	$-0.118269\pi$
$607$	45.9125	1.86353	0.931765	+	0.363062i	$0.118269\pi$
$608$	10.5127	0.426344
$609$	−1.63901	−0.0664159
$610$	21.7816	0.881909
$611$	−2.58340	−0.104513
$612$	−12.1812	−0.492397
$613$	34.5243	1.39442	0.697212	−	0.716865i	$-0.254424\pi$
$613$	34.5243	1.39442	0.697212	+	0.716865i	$0.254424\pi$
$614$	54.3273	2.19247
$615$	6.56388	0.264681
$616$	19.2597	0.775994
$617$	−8.51484	−0.342795	−0.171397	−	0.985202i	$-0.554828\pi$
$617$	−8.51484	−0.342795	−0.171397	+	0.985202i	$0.554828\pi$
$618$	18.8579	0.758577
$619$	10.9245	0.439093	0.219547	−	0.975602i	$-0.429542\pi$
$619$	10.9245	0.439093	0.219547	+	0.975602i	$0.429542\pi$
$620$	8.25840	0.331665
$621$	−4.10448	−0.164707
$622$	33.7509	1.35329
$623$	−25.2827	−1.01293
$624$	−11.2685	−0.451099
$625$	13.2103	0.528413
$626$	33.9738	1.35786
$627$	5.92997	0.236820
$628$	11.4187	0.455654
$629$	−50.9775	−2.03261
$630$	−8.82397	−0.351555
$631$	41.1953	1.63996	0.819980	−	0.572392i	$-0.193985\pi$
$631$	41.1953	1.63996	0.819980	+	0.572392i	$0.193985\pi$
$632$	5.66456	0.225324
$633$	2.37837	0.0945318
$634$	45.6914	1.81464
$635$	−17.8578	−0.708666
$636$	15.6007	0.618607
$637$	−54.1969	−2.14736
$638$	3.40368	0.134753
$639$	1.98524	0.0785347
$640$	6.60364	0.261032
$641$	−22.8009	−0.900580	−0.450290	−	0.892882i	$-0.648679\pi$
$641$	−22.8009	−0.900580	−0.450290	+	0.892882i	$0.648679\pi$
$642$	−7.82821	−0.308955
$643$	29.4958	1.16320	0.581601	−	0.813474i	$-0.302427\pi$
$643$	29.4958	1.16320	0.581601	+	0.813474i	$0.302427\pi$
$644$	45.9762	1.81172
$645$	−3.99484	−0.157297
$646$	13.7877	0.542470
$647$	−31.1627	−1.22513	−0.612567	−	0.790419i	$-0.709863\pi$
$647$	−31.1627	−1.22513	−0.612567	+	0.790419i	$0.709863\pi$
$648$	−0.927338	−0.0364293
$649$	−37.4020	−1.46816
$650$	−33.8204	−1.32654
$651$	−17.0318	−0.667529
$652$	40.3402	1.57984
$653$	−10.0302	−0.392510	−0.196255	−	0.980553i	$-0.562878\pi$
$653$	−10.0302	−0.392510	−0.196255	+	0.980553i	$0.562878\pi$
$654$	23.2292	0.908332
$655$	4.85472	0.189690
$656$	21.0551	0.822063
$657$	9.99877	0.390089
$658$	−6.48915	−0.252974
$659$	32.6430	1.27159	0.635795	−	0.771858i	$-0.280673\pi$
$659$	32.6430	1.27159	0.635795	+	0.771858i	$0.280673\pi$
$660$	10.0704	0.391989
$661$	32.7468	1.27370	0.636852	−	0.770986i	$-0.280236\pi$
$661$	32.7468	1.27370	0.636852	+	0.770986i	$0.280236\pi$
$662$	27.6752	1.07563
$663$	−19.2245	−0.746617
$664$	2.37836	0.0922983
$665$	5.48882	0.212847
$666$	−21.5174	−0.833782
$667$	1.46544	0.0567422
$668$	−29.4769	−1.14049
$669$	0.560654	0.0216761
$670$	2.70812	0.104624
$671$	51.2667	1.97913
$672$	−36.8189	−1.42032
$673$	19.7880	0.762770	0.381385	−	0.924416i	$-0.375447\pi$
$673$	19.7880	0.762770	0.381385	+	0.924416i	$0.375447\pi$
$674$	−2.06970	−0.0797219
$675$	4.16786	0.160421
$676$	4.46519	0.171738
$677$	−17.2655	−0.663567	−0.331783	−	0.943356i	$-0.607650\pi$
$677$	−17.2655	−0.663567	−0.331783	+	0.943356i	$0.607650\pi$
$678$	−2.67627	−0.102782
$679$	4.79156	0.183883
$680$	4.22301	0.161945
$681$	−29.2217	−1.11978
$682$	35.3694	1.35437
$683$	−9.36509	−0.358345	−0.179173	−	0.983818i	$-0.557342\pi$
$683$	−9.36509	−0.358345	−0.179173	+	0.983818i	$0.557342\pi$
$684$	3.19828	0.122289
$685$	−0.760768	−0.0290675
$686$	−68.4236	−2.61243
$687$	−0.0916488	−0.00349662
$688$	−12.8143	−0.488541
$689$	24.6211	0.937989
$690$	7.88955	0.300350
$691$	−30.9237	−1.17639	−0.588197	−	0.808718i	$-0.700162\pi$
$691$	−30.9237	−1.17639	−0.588197	+	0.808718i	$0.700162\pi$
$692$	−39.0943	−1.48614
$693$	−20.7688	−0.788940
$694$	39.9669	1.51712
$695$	10.8092	0.410018
$696$	0.331093	0.0125500
$697$	35.9209	1.36060
$698$	45.6047	1.72616
$699$	27.2870	1.03209
$700$	−46.6862	−1.76457
$701$	5.56247	0.210092	0.105046	−	0.994467i	$-0.466501\pi$
$701$	5.56247	0.210092	0.105046	+	0.994467i	$0.466501\pi$
$702$	−8.11457	−0.306265
$703$	13.3846	0.504809
$704$	49.9839	1.88384
$705$	−0.611958	−0.0230477
$706$	−6.61149	−0.248827
$707$	−20.6872	−0.778021
$708$	−20.1725	−0.758128
$709$	−41.9185	−1.57428	−0.787142	−	0.616772i	$-0.788440\pi$
$709$	−41.9185	−1.57428	−0.787142	+	0.616772i	$0.788440\pi$
$710$	−3.81599	−0.143211
$711$	−6.10840	−0.229083
$712$	5.10730	0.191404
$713$	15.2282	0.570301
$714$	−48.2893	−1.80718
$715$	15.8931	0.594369
$716$	38.9001	1.45376
$717$	14.5074	0.541789
$718$	16.1255	0.601799
$719$	3.79119	0.141387	0.0706937	−	0.997498i	$-0.477479\pi$
$719$	3.79119	0.141387	0.0706937	+	0.997498i	$0.477479\pi$
$720$	−2.66928	−0.0994781
$721$	41.0835	1.53003
$722$	36.4158	1.35526
$723$	27.9619	1.03991
$724$	−27.5947	−1.02555
$725$	−1.48807	−0.0552656
$726$	19.9512	0.740459
$727$	−13.2697	−0.492146	−0.246073	−	0.969251i	$-0.579140\pi$
$727$	−13.2697	−0.492146	−0.246073	+	0.969251i	$0.579140\pi$
$728$	16.3937	0.607591
$729$	1.00000	0.0370370
$730$	−19.2195	−0.711344
$731$	−21.8618	−0.808588
$732$	27.6503	1.02199
$733$	−20.3036	−0.749932	−0.374966	−	0.927039i	$-0.622346\pi$
$733$	−20.3036	−0.749932	−0.374966	+	0.927039i	$0.622346\pi$
$734$	4.50832	0.166405
$735$	−12.8382	−0.473544
$736$	32.9199	1.21345
$737$	6.37403	0.234790
$738$	15.1621	0.558123
$739$	0.471998	0.0173627	0.00868137	−	0.999962i	$-0.497237\pi$
$739$	0.471998	0.0173627	0.00868137	+	0.999962i	$0.497237\pi$
$740$	22.7299	0.835569
$741$	5.04755	0.185426
$742$	61.8448	2.27039
$743$	−36.2085	−1.32836	−0.664181	−	0.747572i	$-0.731219\pi$
$743$	−36.2085	−1.32836	−0.664181	+	0.747572i	$0.731219\pi$
$744$	3.44056	0.126137
$745$	−19.0982	−0.699704
$746$	0.716319	0.0262263
$747$	−2.56472	−0.0938381
$748$	55.1103	2.01503
$749$	−17.0544	−0.623154
$750$	−17.6223	−0.643475
$751$	9.49068	0.346320	0.173160	−	0.984894i	$-0.444602\pi$
$751$	9.49068	0.346320	0.173160	+	0.984894i	$0.444602\pi$
$752$	−1.96299	−0.0715828
$753$	−17.1578	−0.625267
$754$	2.89719	0.105509
$755$	−14.0010	−0.509547
$756$	−11.2015	−0.407394
$757$	−35.4258	−1.28757	−0.643787	−	0.765205i	$-0.722638\pi$
$757$	−35.4258	−1.28757	−0.643787	+	0.765205i	$0.722638\pi$
$758$	−14.1649	−0.514493
$759$	18.5694	0.674028
$760$	−1.10879	−0.0402199
$761$	21.6029	0.783104	0.391552	−	0.920156i	$-0.371938\pi$
$761$	21.6029	0.783104	0.391552	+	0.920156i	$0.371938\pi$
$762$	−41.2502	−1.49434
$763$	50.6066	1.83208
$764$	29.1878	1.05598
$765$	−4.55390	−0.164647
$766$	11.4853	0.414980
$767$	−31.8363	−1.14954
$768$	−6.84237	−0.246903
$769$	18.5096	0.667472	0.333736	−	0.942667i	$-0.391691\pi$
$769$	18.5096	0.667472	0.333736	+	0.942667i	$0.391691\pi$
$770$	39.9213	1.43867
$771$	29.3453	1.05685
$772$	11.6822	0.420452
$773$	−18.6644	−0.671311	−0.335655	−	0.941985i	$-0.608958\pi$
$773$	−18.6644	−0.671311	−0.335655	+	0.941985i	$0.608958\pi$
$774$	−9.22777	−0.331685
$775$	−15.4634	−0.555461
$776$	−0.967934	−0.0347468
$777$	−46.8773	−1.68172
$778$	−55.3552	−1.98458
$779$	−9.43133	−0.337913
$780$	8.57184	0.306921
$781$	−8.98159	−0.321387
$782$	43.1757	1.54396
$783$	−0.357035	−0.0127594
$784$	−41.1813	−1.47076
$785$	4.26882	0.152361
$786$	11.2140	0.399991
$787$	−43.8102	−1.56166	−0.780832	−	0.624741i	$-0.785205\pi$
$787$	−43.8102	−1.56166	−0.780832	+	0.624741i	$0.785205\pi$
$788$	−19.8865	−0.708426
$789$	13.1551	0.468334
$790$	11.7415	0.417743
$791$	−5.83047	−0.207308
$792$	4.19546	0.149079
$793$	43.6379	1.54963
$794$	−32.3579	−1.14834
$795$	5.83225	0.206849
$796$	−20.6895	−0.733320
$797$	−10.9732	−0.388691	−0.194346	−	0.980933i	$-0.562258\pi$
$797$	−10.9732	−0.388691	−0.194346	+	0.980933i	$0.562258\pi$
$798$	12.6787	0.448823
$799$	−3.34895	−0.118477
$800$	−33.4283	−1.18187
$801$	−5.50749	−0.194597
$802$	−19.3750	−0.684154
$803$	−45.2364	−1.59636
$804$	3.43779	0.121241
$805$	17.1880	0.605798
$806$	30.1062	1.06045
$807$	−8.72950	−0.307293
$808$	4.17897	0.147016
$809$	−1.47716	−0.0519343	−0.0259672	−	0.999663i	$-0.508267\pi$
$809$	−1.47716	−0.0519343	−0.0259672	+	0.999663i	$0.508267\pi$
$810$	−1.92218	−0.0675386
$811$	−21.7455	−0.763587	−0.381793	−	0.924248i	$-0.624693\pi$
$811$	−21.7455	−0.763587	−0.381793	+	0.924248i	$0.624693\pi$
$812$	3.99932	0.140349
$813$	31.6728	1.11081
$814$	97.3488	3.41207
$815$	15.0810	0.528265
$816$	−14.6076	−0.511370
$817$	5.74000	0.200817
$818$	−13.7069	−0.479251
$819$	−17.6782	−0.617728
$820$	−16.0165	−0.559319
$821$	18.1702	0.634143	0.317072	−	0.948402i	$-0.397300\pi$
$821$	18.1702	0.634143	0.317072	+	0.948402i	$0.397300\pi$
$822$	−1.75731	−0.0612934
$823$	−45.2016	−1.57563	−0.787814	−	0.615913i	$-0.788787\pi$
$823$	−45.2016	−1.57563	−0.787814	+	0.615913i	$0.788787\pi$
$824$	−8.29920	−0.289116
$825$	−18.8562	−0.656489
$826$	−79.9684	−2.78246
$827$	−48.9279	−1.70139	−0.850696	−	0.525659i	$-0.823819\pi$
$827$	−48.9279	−1.70139	−0.850696	+	0.525659i	$0.823819\pi$
$828$	10.0153	0.348056
$829$	35.8559	1.24533	0.622663	−	0.782490i	$-0.286051\pi$
$829$	35.8559	1.24533	0.622663	+	0.782490i	$0.286051\pi$
$830$	4.92986	0.171118
$831$	−30.2102	−1.04798
$832$	42.5460	1.47502
$833$	−70.2571	−2.43427
$834$	24.9685	0.864588
$835$	−11.0198	−0.381356
$836$	−14.4697	−0.500444
$837$	−3.71015	−0.128241
$838$	38.2447	1.32114
$839$	6.23408	0.215224	0.107612	−	0.994193i	$-0.465680\pi$
$839$	6.23408	0.215224	0.107612	+	0.994193i	$0.465680\pi$
$840$	3.88335	0.133988
$841$	−28.8725	−0.995604
$842$	−64.3613	−2.21804
$843$	17.4884	0.602332
$844$	−5.80345	−0.199763
$845$	1.66929	0.0574255
$846$	−1.41357	−0.0485997
$847$	43.4653	1.49349
$848$	18.7082	0.642443
$849$	−9.34195	−0.320615
$850$	−43.8424	−1.50378
$851$	41.9133	1.43677
$852$	−4.84416	−0.165958
$853$	15.9961	0.547697	0.273849	−	0.961773i	$-0.411703\pi$
$853$	15.9961	0.547697	0.273849	+	0.961773i	$0.411703\pi$
$854$	109.612	3.75086
$855$	1.19567	0.0408909
$856$	3.44513	0.117752
$857$	57.3498	1.95903	0.979516	−	0.201365i	$-0.0645376\pi$
$857$	57.3498	1.95903	0.979516	+	0.201365i	$0.0645376\pi$
$858$	36.7119	1.25332
$859$	52.8576	1.80348	0.901739	−	0.432281i	$-0.142291\pi$
$859$	52.8576	1.80348	0.901739	+	0.432281i	$0.142291\pi$
$860$	9.74777	0.332396
$861$	33.0317	1.12572
$862$	−28.2624	−0.962622
$863$	−28.1092	−0.956848	−0.478424	−	0.878129i	$-0.658792\pi$
$863$	−28.1092	−0.956848	−0.478424	+	0.878129i	$0.658792\pi$
$864$	−8.02050	−0.272863
$865$	−14.6152	−0.496933
$866$	27.4904	0.934162
$867$	−7.92129	−0.269021
$868$	41.5591	1.41061
$869$	27.6356	0.937474
$870$	0.686287	0.0232673
$871$	5.42553	0.183837
$872$	−10.2229	−0.346192
$873$	1.04378	0.0353265
$874$	−11.3361	−0.383450
$875$	−38.3916	−1.29787
$876$	−24.3979	−0.824329
$877$	−10.3656	−0.350021	−0.175010	−	0.984567i	$-0.555996\pi$
$877$	−10.3656	−0.350021	−0.175010	+	0.984567i	$0.555996\pi$
$878$	−56.1650	−1.89548
$879$	−6.89033	−0.232405
$880$	12.0763	0.407093
$881$	−34.3012	−1.15564	−0.577818	−	0.816165i	$-0.696096\pi$
$881$	−34.3012	−1.15564	−0.577818	+	0.816165i	$0.696096\pi$
$882$	−29.6552	−0.998543
$883$	−2.73446	−0.0920220	−0.0460110	−	0.998941i	$-0.514651\pi$
$883$	−2.73446	−0.0920220	−0.0460110	+	0.998941i	$0.514651\pi$
$884$	46.9095	1.57774
$885$	−7.54140	−0.253501
$886$	−79.3017	−2.66419
$887$	−26.4514	−0.888150	−0.444075	−	0.895990i	$-0.646468\pi$
$887$	−26.4514	−0.888150	−0.444075	+	0.895990i	$0.646468\pi$
$888$	9.46960	0.317779
$889$	−89.8668	−3.01404
$890$	10.5864	0.354857
$891$	−4.52419	−0.151566
$892$	−1.36805	−0.0458056
$893$	0.879293	0.0294244
$894$	−44.1154	−1.47544
$895$	14.5426	0.486107
$896$	33.2318	1.11020
$897$	15.8062	0.527754
$898$	15.1426	0.505314
$899$	1.32465	0.0441797
$900$	−10.1700	−0.338998
$901$	31.9171	1.06331
$902$	−68.5961	−2.28400
$903$	−20.1034	−0.669000
$904$	1.17780	0.0391731
$905$	−10.3162	−0.342921
$906$	−32.3411	−1.07446
$907$	−13.5901	−0.451251	−0.225626	−	0.974214i	$-0.572443\pi$
$907$	−13.5901	−0.451251	−0.225626	+	0.974214i	$0.572443\pi$
$908$	71.3035	2.36629
$909$	−4.50642	−0.149468
$910$	33.9808	1.12645
$911$	−52.9408	−1.75401	−0.877003	−	0.480484i	$-0.840461\pi$
$911$	−52.9408	−1.75401	−0.877003	+	0.480484i	$0.840461\pi$
$912$	3.83536	0.127001
$913$	11.6033	0.384013
$914$	55.4566	1.83434
$915$	10.3370	0.341729
$916$	0.223632	0.00738899
$917$	24.4307	0.806771
$918$	−10.5192	−0.347184
$919$	−20.9528	−0.691170	−0.345585	−	0.938387i	$-0.612319\pi$
$919$	−20.9528	−0.691170	−0.345585	+	0.938387i	$0.612319\pi$
$920$	−3.47212	−0.114472
$921$	25.7823	0.849557
$922$	17.8415	0.587578
$923$	−7.64508	−0.251641
$924$	50.6777	1.66717
$925$	−42.5605	−1.39938
$926$	42.7295	1.40418
$927$	8.94949	0.293940
$928$	2.86360	0.0940023
$929$	−19.0510	−0.625042	−0.312521	−	0.949911i	$-0.601173\pi$
$929$	−19.0510	−0.625042	−0.312521	+	0.949911i	$0.601173\pi$
$930$	7.13158	0.233854
$931$	18.4466	0.604563
$932$	−66.5827	−2.18099
$933$	16.0173	0.524383
$934$	23.4262	0.766530
$935$	20.6027	0.673782
$936$	3.57115	0.116727
$937$	−28.7625	−0.939628	−0.469814	−	0.882765i	$-0.655679\pi$
$937$	−28.7625	−0.939628	−0.469814	+	0.882765i	$0.655679\pi$
$938$	13.6282	0.444976
$939$	16.1231	0.526156
$940$	1.49323	0.0487039
$941$	−32.2310	−1.05070	−0.525351	−	0.850886i	$-0.676066\pi$
$941$	−32.2310	−1.05070	−0.525351	+	0.850886i	$0.676066\pi$
$942$	9.86064	0.321277
$943$	−29.5338	−0.961754
$944$	−24.1907	−0.787340
$945$	−4.18763	−0.136224
$946$	41.7482	1.35735
$947$	1.66559	0.0541245	0.0270622	−	0.999634i	$-0.491385\pi$
$947$	1.66559	0.0541245	0.0270622	+	0.999634i	$0.491385\pi$
$948$	14.9051	0.484094
$949$	−38.5049	−1.24992
$950$	11.5112	0.373472
$951$	21.6839	0.703150
$952$	21.2517	0.688770
$953$	15.7121	0.508965	0.254483	−	0.967077i	$-0.418095\pi$
$953$	15.7121	0.508965	0.254483	+	0.967077i	$0.418095\pi$
$954$	13.4720	0.436174
$955$	10.9118	0.353096
$956$	−35.3994	−1.14490
$957$	1.61530	0.0522151
$958$	−0.605824	−0.0195733
$959$	−3.82845	−0.123627
$960$	10.0783	0.325276
$961$	−17.2348	−0.555962
$962$	82.8627	2.67160
$963$	−3.71507	−0.119716
$964$	−68.2295	−2.19752
$965$	4.36734	0.140590
$966$	39.7030	1.27742
$967$	−37.2621	−1.19827	−0.599135	−	0.800648i	$-0.704489\pi$
$967$	−37.2621	−1.19827	−0.599135	+	0.800648i	$0.704489\pi$
$968$	−8.78034	−0.282211
$969$	6.54329	0.210201
$970$	−2.00633	−0.0644193
$971$	−19.3381	−0.620588	−0.310294	−	0.950641i	$-0.600427\pi$
$971$	−19.3381	−0.620588	−0.310294	+	0.950641i	$0.600427\pi$
$972$	−2.44009	−0.0782659
$973$	54.3959	1.74385
$974$	52.9699	1.69726
$975$	−16.0503	−0.514020
$976$	33.1581	1.06136
$977$	−12.0720	−0.386218	−0.193109	−	0.981177i	$-0.561857\pi$
$977$	−12.0720	−0.386218	−0.193109	+	0.981177i	$0.561857\pi$
$978$	34.8360	1.11393
$979$	24.9169	0.796349
$980$	31.3264	1.00068
$981$	11.0240	0.351968
$982$	−48.2985	−1.54127
$983$	−9.02559	−0.287871	−0.143936	−	0.989587i	$-0.545976\pi$
$983$	−9.02559	−0.287871	−0.143936	+	0.989587i	$0.545976\pi$
$984$	−6.67268	−0.212717
$985$	−7.43447	−0.236882
$986$	3.75571	0.119606
$987$	−3.07958	−0.0980243
$988$	−12.3165	−0.391839
$989$	17.9746	0.571558
$990$	8.69633	0.276387
$991$	50.0186	1.58889	0.794446	−	0.607335i	$-0.207761\pi$
$991$	50.0186	1.58889	0.794446	+	0.607335i	$0.207761\pi$
$992$	29.7572	0.944793
$993$	13.1339	0.416793
$994$	−19.2034	−0.609094
$995$	−7.73469	−0.245206
$996$	6.25815	0.198297
$997$	24.1523	0.764912	0.382456	−	0.923974i	$-0.375078\pi$
$997$	24.1523	0.764912	0.382456	+	0.923974i	$0.375078\pi$
$998$	65.1668	2.06282
$999$	−10.2116	−0.323081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.15	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.10715 q^{2} -1.00000 q^{3} +2.44009 q^{4} +0.912218 q^{5} +2.10715 q^{6} +4.59060 q^{7} -0.927338 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.10715 q^{2} -1.00000 q^{3} +2.44009 q^{4} +0.912218 q^{5} +2.10715 q^{6} +4.59060 q^{7} -0.927338 q^{8} +1.00000 q^{9} -1.92218 q^{10} -4.52419 q^{11} -2.44009 q^{12} -3.85096 q^{13} -9.67309 q^{14} -0.912218 q^{15} -2.92614 q^{16} -4.99212 q^{17} -2.10715 q^{18} +1.31072 q^{19} +2.22589 q^{20} -4.59060 q^{21} +9.53317 q^{22} +4.10448 q^{23} +0.927338 q^{24} -4.16786 q^{25} +8.11457 q^{26} -1.00000 q^{27} +11.2015 q^{28} +0.357035 q^{29} +1.92218 q^{30} +3.71015 q^{31} +8.02050 q^{32} +4.52419 q^{33} +10.5192 q^{34} +4.18763 q^{35} +2.44009 q^{36} +10.2116 q^{37} -2.76189 q^{38} +3.85096 q^{39} -0.845935 q^{40} -7.19552 q^{41} +9.67309 q^{42} +4.37926 q^{43} -11.0394 q^{44} +0.912218 q^{45} -8.64876 q^{46} +0.670846 q^{47} +2.92614 q^{48} +14.0736 q^{49} +8.78231 q^{50} +4.99212 q^{51} -9.39670 q^{52} -6.39348 q^{53} +2.10715 q^{54} -4.12705 q^{55} -4.25704 q^{56} -1.31072 q^{57} -0.752328 q^{58} +8.26710 q^{59} -2.22589 q^{60} -11.3317 q^{61} -7.81785 q^{62} +4.59060 q^{63} -11.0481 q^{64} -3.51292 q^{65} -9.53317 q^{66} -1.40888 q^{67} -12.1812 q^{68} -4.10448 q^{69} -8.82397 q^{70} +1.98524 q^{71} -0.927338 q^{72} +9.99877 q^{73} -21.5174 q^{74} +4.16786 q^{75} +3.19828 q^{76} -20.7688 q^{77} -8.11457 q^{78} -6.10840 q^{79} -2.66928 q^{80} +1.00000 q^{81} +15.1621 q^{82} -2.56472 q^{83} -11.2015 q^{84} -4.55390 q^{85} -9.22777 q^{86} -0.357035 q^{87} +4.19546 q^{88} -5.50749 q^{89} -1.92218 q^{90} -17.6782 q^{91} +10.0153 q^{92} -3.71015 q^{93} -1.41357 q^{94} +1.19567 q^{95} -8.02050 q^{96} +1.04378 q^{97} -29.6552 q^{98} -4.52419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 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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