LMFDB - Embedded newform 6033.2.a.d.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.59128 q^{2} -1.00000 q^{3} +4.71472 q^{4} -3.30142 q^{5} +2.59128 q^{6} +3.98473 q^{7} -7.03459 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59128 q^{2} -1.00000 q^{3} +4.71472 q^{4} -3.30142 q^{5} +2.59128 q^{6} +3.98473 q^{7} -7.03459 q^{8} +1.00000 q^{9} +8.55491 q^{10} -3.24496 q^{11} -4.71472 q^{12} -3.67196 q^{13} -10.3255 q^{14} +3.30142 q^{15} +8.79914 q^{16} -2.06333 q^{17} -2.59128 q^{18} +4.30629 q^{19} -15.5653 q^{20} -3.98473 q^{21} +8.40858 q^{22} -3.80665 q^{23} +7.03459 q^{24} +5.89940 q^{25} +9.51507 q^{26} -1.00000 q^{27} +18.7869 q^{28} +6.89116 q^{29} -8.55491 q^{30} -6.07651 q^{31} -8.73183 q^{32} +3.24496 q^{33} +5.34666 q^{34} -13.1553 q^{35} +4.71472 q^{36} +2.76995 q^{37} -11.1588 q^{38} +3.67196 q^{39} +23.2242 q^{40} +6.50958 q^{41} +10.3255 q^{42} -11.7879 q^{43} -15.2991 q^{44} -3.30142 q^{45} +9.86410 q^{46} +3.65511 q^{47} -8.79914 q^{48} +8.87805 q^{49} -15.2870 q^{50} +2.06333 q^{51} -17.3123 q^{52} +12.1723 q^{53} +2.59128 q^{54} +10.7130 q^{55} -28.0309 q^{56} -4.30629 q^{57} -17.8569 q^{58} -1.81677 q^{59} +15.5653 q^{60} +6.78079 q^{61} +15.7459 q^{62} +3.98473 q^{63} +5.02831 q^{64} +12.1227 q^{65} -8.40858 q^{66} +8.12468 q^{67} -9.72802 q^{68} +3.80665 q^{69} +34.0890 q^{70} -13.6632 q^{71} -7.03459 q^{72} -5.09926 q^{73} -7.17771 q^{74} -5.89940 q^{75} +20.3030 q^{76} -12.9303 q^{77} -9.51507 q^{78} +5.25630 q^{79} -29.0497 q^{80} +1.00000 q^{81} -16.8681 q^{82} +9.05075 q^{83} -18.7869 q^{84} +6.81193 q^{85} +30.5457 q^{86} -6.89116 q^{87} +22.8269 q^{88} -7.51584 q^{89} +8.55491 q^{90} -14.6318 q^{91} -17.9473 q^{92} +6.07651 q^{93} -9.47140 q^{94} -14.2169 q^{95} +8.73183 q^{96} -12.4569 q^{97} -23.0055 q^{98} -3.24496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59128	−1.83231	−0.916155	−	0.400824i	$-0.868724\pi$
$2$	−2.59128	−1.83231	−0.916155	+	0.400824i	$0.868724\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.71472	2.35736
$5$	−3.30142	−1.47644	−0.738221	−	0.674559i	$-0.764334\pi$
$5$	−3.30142	−1.47644	−0.738221	+	0.674559i	$0.764334\pi$
$6$	2.59128	1.05788
$7$	3.98473	1.50609	0.753043	−	0.657972i	$-0.228585\pi$
$7$	3.98473	1.50609	0.753043	+	0.657972i	$0.228585\pi$
$8$	−7.03459	−2.48710
$9$	1.00000	0.333333
$10$	8.55491	2.70530
$11$	−3.24496	−0.978391	−0.489195	−	0.872174i	$-0.662710\pi$
$11$	−3.24496	−0.978391	−0.489195	+	0.872174i	$0.662710\pi$
$12$	−4.71472	−1.36102
$13$	−3.67196	−1.01842	−0.509209	−	0.860643i	$-0.670062\pi$
$13$	−3.67196	−1.01842	−0.509209	+	0.860643i	$0.670062\pi$
$14$	−10.3255	−2.75961
$15$	3.30142	0.852424
$16$	8.79914	2.19978
$17$	−2.06333	−0.500431	−0.250216	−	0.968190i	$-0.580501\pi$
$17$	−2.06333	−0.500431	−0.250216	+	0.968190i	$0.580501\pi$
$18$	−2.59128	−0.610770
$19$	4.30629	0.987931	0.493966	−	0.869481i	$-0.335547\pi$
$19$	4.30629	0.987931	0.493966	+	0.869481i	$0.335547\pi$
$20$	−15.5653	−3.48050
$21$	−3.98473	−0.869539
$22$	8.40858	1.79272
$23$	−3.80665	−0.793742	−0.396871	−	0.917874i	$-0.629904\pi$
$23$	−3.80665	−0.793742	−0.396871	+	0.917874i	$0.629904\pi$
$24$	7.03459	1.43593
$25$	5.89940	1.17988
$26$	9.51507	1.86606
$27$	−1.00000	−0.192450
$28$	18.7869	3.55038
$29$	6.89116	1.27966	0.639828	−	0.768518i	$-0.279006\pi$
$29$	6.89116	1.27966	0.639828	+	0.768518i	$0.279006\pi$
$30$	−8.55491	−1.56191
$31$	−6.07651	−1.09137	−0.545687	−	0.837989i	$-0.683731\pi$
$31$	−6.07651	−1.09137	−0.545687	+	0.837989i	$0.683731\pi$
$32$	−8.73183	−1.54358
$33$	3.24496	0.564874
$34$	5.34666	0.916945
$35$	−13.1553	−2.22365
$36$	4.71472	0.785787
$37$	2.76995	0.455377	0.227689	−	0.973734i	$-0.426883\pi$
$37$	2.76995	0.455377	0.227689	+	0.973734i	$0.426883\pi$
$38$	−11.1588	−1.81020
$39$	3.67196	0.587984
$40$	23.2242	3.67206
$41$	6.50958	1.01663	0.508313	−	0.861173i	$-0.330269\pi$
$41$	6.50958	1.01663	0.508313	+	0.861173i	$0.330269\pi$
$42$	10.3255	1.59326
$43$	−11.7879	−1.79764	−0.898819	−	0.438320i	$-0.855574\pi$
$43$	−11.7879	−1.79764	−0.898819	+	0.438320i	$0.855574\pi$
$44$	−15.2991	−2.30642
$45$	−3.30142	−0.492147
$46$	9.86410	1.45438
$47$	3.65511	0.533152	0.266576	−	0.963814i	$-0.414108\pi$
$47$	3.65511	0.533152	0.266576	+	0.963814i	$0.414108\pi$
$48$	−8.79914	−1.27005
$49$	8.87805	1.26829
$50$	−15.2870	−2.16191
$51$	2.06333	0.288924
$52$	−17.3123	−2.40078
$53$	12.1723	1.67199	0.835996	−	0.548736i	$-0.184891\pi$
$53$	12.1723	1.67199	0.835996	+	0.548736i	$0.184891\pi$
$54$	2.59128	0.352628
$55$	10.7130	1.44454
$56$	−28.0309	−3.74579
$57$	−4.30629	−0.570382
$58$	−17.8569	−2.34473
$59$	−1.81677	−0.236524	−0.118262	−	0.992982i	$-0.537732\pi$
$59$	−1.81677	−0.236524	−0.118262	+	0.992982i	$0.537732\pi$
$60$	15.5653	2.00947
$61$	6.78079	0.868191	0.434096	−	0.900867i	$-0.357068\pi$
$61$	6.78079	0.868191	0.434096	+	0.900867i	$0.357068\pi$
$62$	15.7459	1.99974
$63$	3.98473	0.502028
$64$	5.02831	0.628539
$65$	12.1227	1.50364
$66$	−8.40858	−1.03502
$67$	8.12468	0.992588	0.496294	−	0.868155i	$-0.334694\pi$
$67$	8.12468	0.992588	0.496294	+	0.868155i	$0.334694\pi$
$68$	−9.72802	−1.17970
$69$	3.80665	0.458267
$70$	34.0890	4.07441
$71$	−13.6632	−1.62152	−0.810762	−	0.585375i	$-0.800947\pi$
$71$	−13.6632	−1.62152	−0.810762	+	0.585375i	$0.800947\pi$
$72$	−7.03459	−0.829034
$73$	−5.09926	−0.596823	−0.298412	−	0.954437i	$-0.596457\pi$
$73$	−5.09926	−0.596823	−0.298412	+	0.954437i	$0.596457\pi$
$74$	−7.17771	−0.834392
$75$	−5.89940	−0.681205
$76$	20.3030	2.32891
$77$	−12.9303	−1.47354
$78$	−9.51507	−1.07737
$79$	5.25630	0.591380	0.295690	−	0.955284i	$-0.404450\pi$
$79$	5.25630	0.591380	0.295690	+	0.955284i	$0.404450\pi$
$80$	−29.0497	−3.24785
$81$	1.00000	0.111111
$82$	−16.8681	−1.86277
$83$	9.05075	0.993448	0.496724	−	0.867908i	$-0.334536\pi$
$83$	9.05075	0.993448	0.496724	+	0.867908i	$0.334536\pi$
$84$	−18.7869	−2.04982
$85$	6.81193	0.738857
$86$	30.5457	3.29383
$87$	−6.89116	−0.738810
$88$	22.8269	2.43336
$89$	−7.51584	−0.796678	−0.398339	−	0.917238i	$-0.630413\pi$
$89$	−7.51584	−0.796678	−0.398339	+	0.917238i	$0.630413\pi$
$90$	8.55491	0.901766
$91$	−14.6318	−1.53383
$92$	−17.9473	−1.87114
$93$	6.07651	0.630105
$94$	−9.47140	−0.976900
$95$	−14.2169	−1.45862
$96$	8.73183	0.891188
$97$	−12.4569	−1.26480	−0.632401	−	0.774641i	$-0.717930\pi$
$97$	−12.4569	−1.26480	−0.632401	+	0.774641i	$0.717930\pi$
$98$	−23.0055	−2.32391
$99$	−3.24496	−0.326130
$100$	27.8140	2.78140
$101$	5.62077	0.559287	0.279644	−	0.960104i	$-0.409784\pi$
$101$	5.62077	0.559287	0.279644	+	0.960104i	$0.409784\pi$
$102$	−5.34666	−0.529398
$103$	−7.24838	−0.714205	−0.357102	−	0.934065i	$-0.616235\pi$
$103$	−7.24838	−0.714205	−0.357102	+	0.934065i	$0.616235\pi$
$104$	25.8307	2.53291
$105$	13.1553	1.28382
$106$	−31.5418	−3.06361
$107$	−9.52640	−0.920952	−0.460476	−	0.887672i	$-0.652321\pi$
$107$	−9.52640	−0.920952	−0.460476	+	0.887672i	$0.652321\pi$
$108$	−4.71472	−0.453674
$109$	−1.62685	−0.155824	−0.0779122	−	0.996960i	$-0.524825\pi$
$109$	−1.62685	−0.155824	−0.0779122	+	0.996960i	$0.524825\pi$
$110$	−27.7603	−2.64684
$111$	−2.76995	−0.262912
$112$	35.0622	3.31306
$113$	9.91025	0.932278	0.466139	−	0.884712i	$-0.345645\pi$
$113$	9.91025	0.932278	0.466139	+	0.884712i	$0.345645\pi$
$114$	11.1588	1.04512
$115$	12.5674	1.17191
$116$	32.4899	3.01661
$117$	−3.67196	−0.339473
$118$	4.70776	0.433385
$119$	−8.22181	−0.753692
$120$	−23.2242	−2.12007
$121$	−0.470264	−0.0427513
$122$	−17.5709	−1.59080
$123$	−6.50958	−0.586949
$124$	−28.6491	−2.57276
$125$	−2.96932	−0.265584
$126$	−10.3255	−0.919872
$127$	−20.8200	−1.84748	−0.923739	−	0.383022i	$-0.874883\pi$
$127$	−20.8200	−1.84748	−0.923739	+	0.383022i	$0.874883\pi$
$128$	4.43390	0.391905
$129$	11.7879	1.03787
$130$	−31.4133	−2.75513
$131$	16.5095	1.44244	0.721222	−	0.692704i	$-0.243581\pi$
$131$	16.5095	1.44244	0.721222	+	0.692704i	$0.243581\pi$
$132$	15.2991	1.33161
$133$	17.1594	1.48791
$134$	−21.0533	−1.81873
$135$	3.30142	0.284141
$136$	14.5147	1.24462
$137$	0.919542	0.0785618	0.0392809	−	0.999228i	$-0.487493\pi$
$137$	0.919542	0.0785618	0.0392809	+	0.999228i	$0.487493\pi$
$138$	−9.86410	−0.839688
$139$	4.29808	0.364559	0.182279	−	0.983247i	$-0.441652\pi$
$139$	4.29808	0.364559	0.182279	+	0.983247i	$0.441652\pi$
$140$	−62.0234	−5.24194
$141$	−3.65511	−0.307816
$142$	35.4052	2.97114
$143$	11.9153	0.996412
$144$	8.79914	0.733262
$145$	−22.7506	−1.88934
$146$	13.2136	1.09357
$147$	−8.87805	−0.732249
$148$	13.0595	1.07349
$149$	19.6594	1.61056	0.805279	−	0.592897i	$-0.202016\pi$
$149$	19.6594	1.61056	0.805279	+	0.592897i	$0.202016\pi$
$150$	15.2870	1.24818
$151$	12.0738	0.982553	0.491276	−	0.871004i	$-0.336530\pi$
$151$	12.0738	0.982553	0.491276	+	0.871004i	$0.336530\pi$
$152$	−30.2930	−2.45709
$153$	−2.06333	−0.166810
$154$	33.5059	2.69998
$155$	20.0611	1.61135
$156$	17.3123	1.38609
$157$	19.3225	1.54210	0.771050	−	0.636774i	$-0.219732\pi$
$157$	19.3225	1.54210	0.771050	+	0.636774i	$0.219732\pi$
$158$	−13.6205	−1.08359
$159$	−12.1723	−0.965325
$160$	28.8275	2.27901
$161$	−15.1685	−1.19544
$162$	−2.59128	−0.203590
$163$	−18.5861	−1.45577	−0.727886	−	0.685698i	$-0.759497\pi$
$163$	−18.5861	−1.45577	−0.727886	+	0.685698i	$0.759497\pi$
$164$	30.6908	2.39655
$165$	−10.7130	−0.834004
$166$	−23.4530	−1.82031
$167$	−3.83611	−0.296847	−0.148424	−	0.988924i	$-0.547420\pi$
$167$	−3.83611	−0.296847	−0.148424	+	0.988924i	$0.547420\pi$
$168$	28.0309	2.16263
$169$	0.483296	0.0371766
$170$	−17.6516	−1.35382
$171$	4.30629	0.329310
$172$	−55.5766	−4.23768
$173$	−24.0596	−1.82921	−0.914607	−	0.404343i	$-0.867500\pi$
$173$	−24.0596	−1.82921	−0.914607	+	0.404343i	$0.867500\pi$
$174$	17.8569	1.35373
$175$	23.5075	1.77700
$176$	−28.5528	−2.15225
$177$	1.81677	0.136557
$178$	19.4756	1.45976
$179$	−11.1238	−0.831430	−0.415715	−	0.909495i	$-0.636469\pi$
$179$	−11.1238	−0.831430	−0.415715	+	0.909495i	$0.636469\pi$
$180$	−15.5653	−1.16017
$181$	8.25265	0.613415	0.306707	−	0.951804i	$-0.400773\pi$
$181$	8.25265	0.613415	0.306707	+	0.951804i	$0.400773\pi$
$182$	37.9150	2.81044
$183$	−6.78079	−0.501250
$184$	26.7782	1.97412
$185$	−9.14479	−0.672338
$186$	−15.7459	−1.15455
$187$	6.69541	0.489617
$188$	17.2328	1.25683
$189$	−3.98473	−0.289846
$190$	36.8399	2.67265
$191$	22.1980	1.60619	0.803096	−	0.595849i	$-0.203185\pi$
$191$	22.1980	1.60619	0.803096	+	0.595849i	$0.203185\pi$
$192$	−5.02831	−0.362887
$193$	16.6529	1.19870	0.599350	−	0.800487i	$-0.295426\pi$
$193$	16.6529	1.19870	0.599350	+	0.800487i	$0.295426\pi$
$194$	32.2792	2.31751
$195$	−12.1227	−0.868125
$196$	41.8575	2.98982
$197$	15.1216	1.07737	0.538683	−	0.842508i	$-0.318922\pi$
$197$	15.1216	1.07737	0.538683	+	0.842508i	$0.318922\pi$
$198$	8.40858	0.597572
$199$	−0.540852	−0.0383400	−0.0191700	−	0.999816i	$-0.506102\pi$
$199$	−0.540852	−0.0383400	−0.0191700	+	0.999816i	$0.506102\pi$
$200$	−41.4999	−2.93449
$201$	−8.12468	−0.573071
$202$	−14.5650	−1.02479
$203$	27.4594	1.92727
$204$	9.72802	0.681098
$205$	−21.4909	−1.50099
$206$	18.7826	1.30864
$207$	−3.80665	−0.264581
$208$	−32.3101	−2.24030
$209$	−13.9737	−0.966583
$210$	−34.0890	−2.35236
$211$	11.0075	0.757787	0.378893	−	0.925440i	$-0.376305\pi$
$211$	11.0075	0.757787	0.378893	+	0.925440i	$0.376305\pi$
$212$	57.3889	3.94148
$213$	13.6632	0.936188
$214$	24.6856	1.68747
$215$	38.9169	2.65411
$216$	7.03459	0.478643
$217$	−24.2132	−1.64370
$218$	4.21563	0.285519
$219$	5.09926	0.344576
$220$	50.5087	3.40529
$221$	7.57647	0.509648
$222$	7.17771	0.481737
$223$	9.74717	0.652719	0.326359	−	0.945246i	$-0.394178\pi$
$223$	9.74717	0.652719	0.326359	+	0.945246i	$0.394178\pi$
$224$	−34.7939	−2.32477
$225$	5.89940	0.393294
$226$	−25.6802	−1.70822
$227$	2.99370	0.198699	0.0993496	−	0.995053i	$-0.468324\pi$
$227$	2.99370	0.198699	0.0993496	+	0.995053i	$0.468324\pi$
$228$	−20.3030	−1.34460
$229$	−8.83798	−0.584030	−0.292015	−	0.956414i	$-0.594326\pi$
$229$	−8.83798	−0.584030	−0.292015	+	0.956414i	$0.594326\pi$
$230$	−32.5656	−2.14731
$231$	12.9303	0.850749
$232$	−48.4765	−3.18264
$233$	2.84191	0.186180	0.0930899	−	0.995658i	$-0.470326\pi$
$233$	2.84191	0.186180	0.0930899	+	0.995658i	$0.470326\pi$
$234$	9.51507	0.622020
$235$	−12.0671	−0.787169
$236$	−8.56558	−0.557571
$237$	−5.25630	−0.341434
$238$	21.3050	1.38100
$239$	−5.83679	−0.377551	−0.188775	−	0.982020i	$-0.560452\pi$
$239$	−5.83679	−0.377551	−0.188775	+	0.982020i	$0.560452\pi$
$240$	29.0497	1.87515
$241$	−2.82967	−0.182275	−0.0911376	−	0.995838i	$-0.529050\pi$
$241$	−2.82967	−0.182275	−0.0911376	+	0.995838i	$0.529050\pi$
$242$	1.21858	0.0783336
$243$	−1.00000	−0.0641500
$244$	31.9695	2.04664
$245$	−29.3102	−1.87256
$246$	16.8681	1.07547
$247$	−15.8125	−1.00613
$248$	42.7458	2.71436
$249$	−9.05075	−0.573568
$250$	7.69432	0.486632
$251$	−14.3893	−0.908244	−0.454122	−	0.890940i	$-0.650047\pi$
$251$	−14.3893	−0.908244	−0.454122	+	0.890940i	$0.650047\pi$
$252$	18.7869	1.18346
$253$	12.3524	0.776590
$254$	53.9505	3.38515
$255$	−6.81193	−0.426580
$256$	−21.5461	−1.34663
$257$	0.506110	0.0315703	0.0157851	−	0.999875i	$-0.494975\pi$
$257$	0.506110	0.0315703	0.0157851	+	0.999875i	$0.494975\pi$
$258$	−30.5457	−1.90169
$259$	11.0375	0.685837
$260$	57.1551	3.54461
$261$	6.89116	0.426552
$262$	−42.7808	−2.64300
$263$	−25.7932	−1.59048	−0.795239	−	0.606296i	$-0.792655\pi$
$263$	−25.7932	−1.59048	−0.795239	+	0.606296i	$0.792655\pi$
$264$	−22.8269	−1.40490
$265$	−40.1859	−2.46860
$266$	−44.4648	−2.72631
$267$	7.51584	0.459962
$268$	38.3056	2.33989
$269$	1.01990	0.0621843	0.0310922	−	0.999517i	$-0.490101\pi$
$269$	1.01990	0.0621843	0.0310922	+	0.999517i	$0.490101\pi$
$270$	−8.55491	−0.520635
$271$	22.5099	1.36738	0.683691	−	0.729772i	$-0.260374\pi$
$271$	22.5099	1.36738	0.683691	+	0.729772i	$0.260374\pi$
$272$	−18.1555	−1.10084
$273$	14.6318	0.885554
$274$	−2.38279	−0.143950
$275$	−19.1433	−1.15438
$276$	17.9473	1.08030
$277$	−15.6018	−0.937420	−0.468710	−	0.883352i	$-0.655281\pi$
$277$	−15.6018	−0.937420	−0.468710	+	0.883352i	$0.655281\pi$
$278$	−11.1375	−0.667984
$279$	−6.07651	−0.363791
$280$	92.5420	5.53044
$281$	−14.0149	−0.836058	−0.418029	−	0.908434i	$-0.637279\pi$
$281$	−14.0149	−0.836058	−0.418029	+	0.908434i	$0.637279\pi$
$282$	9.47140	0.564014
$283$	0.368217	0.0218883	0.0109441	−	0.999940i	$-0.496516\pi$
$283$	0.368217	0.0218883	0.0109441	+	0.999940i	$0.496516\pi$
$284$	−64.4182	−3.82252
$285$	14.2169	0.842137
$286$	−30.8760	−1.82573
$287$	25.9389	1.53112
$288$	−8.73183	−0.514528
$289$	−12.7427	−0.749569
$290$	58.9532	3.46185
$291$	12.4569	0.730234
$292$	−24.0416	−1.40693
$293$	27.0457	1.58003	0.790013	−	0.613090i	$-0.210074\pi$
$293$	27.0457	1.58003	0.790013	+	0.613090i	$0.210074\pi$
$294$	23.0055	1.34171
$295$	5.99794	0.349214
$296$	−19.4855	−1.13257
$297$	3.24496	0.188291
$298$	−50.9428	−2.95104
$299$	13.9779	0.808362
$300$	−27.8140	−1.60584
$301$	−46.9716	−2.70740
$302$	−31.2866	−1.80034
$303$	−5.62077	−0.322905
$304$	37.8917	2.17324
$305$	−22.3863	−1.28183
$306$	5.34666	0.305648
$307$	28.7770	1.64239	0.821194	−	0.570649i	$-0.193308\pi$
$307$	28.7770	1.64239	0.821194	+	0.570649i	$0.193308\pi$
$308$	−60.9626	−3.47366
$309$	7.24838	0.412346
$310$	−51.9840	−2.95249
$311$	−28.3186	−1.60580	−0.802899	−	0.596115i	$-0.796710\pi$
$311$	−28.3186	−1.60580	−0.802899	+	0.596115i	$0.796710\pi$
$312$	−25.8307	−1.46238
$313$	10.4793	0.592322	0.296161	−	0.955138i	$-0.404293\pi$
$313$	10.4793	0.592322	0.296161	+	0.955138i	$0.404293\pi$
$314$	−50.0699	−2.82561
$315$	−13.1553	−0.741216
$316$	24.7820	1.39410
$317$	−8.38996	−0.471227	−0.235614	−	0.971847i	$-0.575710\pi$
$317$	−8.38996	−0.471227	−0.235614	+	0.971847i	$0.575710\pi$
$318$	31.5418	1.76877
$319$	−22.3615	−1.25200
$320$	−16.6006	−0.928001
$321$	9.52640	0.531712
$322$	39.3057	2.19042
$323$	−8.88530	−0.494392
$324$	4.71472	0.261929
$325$	−21.6624	−1.20161
$326$	48.1616	2.66743
$327$	1.62685	0.0899652
$328$	−45.7922	−2.52845
$329$	14.5646	0.802973
$330$	27.7603	1.52815
$331$	20.6908	1.13727	0.568635	−	0.822590i	$-0.307472\pi$
$331$	20.6908	1.13727	0.568635	+	0.822590i	$0.307472\pi$
$332$	42.6717	2.34191
$333$	2.76995	0.151792
$334$	9.94043	0.543916
$335$	−26.8230	−1.46550
$336$	−35.0622	−1.91280
$337$	−8.90914	−0.485312	−0.242656	−	0.970112i	$-0.578019\pi$
$337$	−8.90914	−0.485312	−0.242656	+	0.970112i	$0.578019\pi$
$338$	−1.25235	−0.0681190
$339$	−9.91025	−0.538251
$340$	32.1163	1.74175
$341$	19.7180	1.06779
$342$	−11.1588	−0.603399
$343$	7.48352	0.404072
$344$	82.9231	4.47091
$345$	−12.5674	−0.676605
$346$	62.3450	3.35169
$347$	8.82641	0.473827	0.236913	−	0.971531i	$-0.423864\pi$
$347$	8.82641	0.473827	0.236913	+	0.971531i	$0.423864\pi$
$348$	−32.4899	−1.74164
$349$	1.92822	0.103215	0.0516077	−	0.998667i	$-0.483565\pi$
$349$	1.92822	0.103215	0.0516077	+	0.998667i	$0.483565\pi$
$350$	−60.9145	−3.25602
$351$	3.67196	0.195995
$352$	28.3344	1.51023
$353$	12.7236	0.677206	0.338603	−	0.940929i	$-0.390046\pi$
$353$	12.7236	0.677206	0.338603	+	0.940929i	$0.390046\pi$
$354$	−4.70776	−0.250215
$355$	45.1081	2.39409
$356$	−35.4351	−1.87806
$357$	8.22181	0.435144
$358$	28.8248	1.52344
$359$	−12.8405	−0.677697	−0.338849	−	0.940841i	$-0.610037\pi$
$359$	−12.8405	−0.677697	−0.338849	+	0.940841i	$0.610037\pi$
$360$	23.2242	1.22402
$361$	−0.455840	−0.0239916
$362$	−21.3849	−1.12397
$363$	0.470264	0.0246825
$364$	−68.9846	−3.61578
$365$	16.8348	0.881175
$366$	17.5709	0.918446
$367$	−0.313735	−0.0163768	−0.00818842	−	0.999966i	$-0.502606\pi$
$367$	−0.313735	−0.0163768	−0.00818842	+	0.999966i	$0.502606\pi$
$368$	−33.4953	−1.74606
$369$	6.50958	0.338875
$370$	23.6967	1.23193
$371$	48.5032	2.51816
$372$	28.6491	1.48538
$373$	21.9441	1.13622	0.568111	−	0.822952i	$-0.307674\pi$
$373$	21.9441	1.13622	0.568111	+	0.822952i	$0.307674\pi$
$374$	−17.3497	−0.897130
$375$	2.96932	0.153335
$376$	−25.7122	−1.32601
$377$	−25.3041	−1.30323
$378$	10.3255	0.531088
$379$	19.0351	0.977766	0.488883	−	0.872349i	$-0.337404\pi$
$379$	19.0351	0.977766	0.488883	+	0.872349i	$0.337404\pi$
$380$	−67.0287	−3.43850
$381$	20.8200	1.06664
$382$	−57.5212	−2.94304
$383$	23.6276	1.20731	0.603657	−	0.797244i	$-0.293710\pi$
$383$	23.6276	1.20731	0.603657	+	0.797244i	$0.293710\pi$
$384$	−4.43390	−0.226267
$385$	42.6883	2.17560
$386$	−43.1522	−2.19639
$387$	−11.7879	−0.599213
$388$	−58.7306	−2.98159
$389$	24.7990	1.25736	0.628679	−	0.777665i	$-0.283596\pi$
$389$	24.7990	1.25736	0.628679	+	0.777665i	$0.283596\pi$
$390$	31.4133	1.59067
$391$	7.85438	0.397213
$392$	−62.4534	−3.15438
$393$	−16.5095	−0.832795
$394$	−39.1841	−1.97407
$395$	−17.3533	−0.873139
$396$	−15.2991	−0.768806
$397$	−27.6383	−1.38713	−0.693563	−	0.720396i	$-0.743960\pi$
$397$	−27.6383	−1.38713	−0.693563	+	0.720396i	$0.743960\pi$
$398$	1.40150	0.0702507
$399$	−17.1594	−0.859045
$400$	51.9097	2.59548
$401$	3.82333	0.190928	0.0954640	−	0.995433i	$-0.469567\pi$
$401$	3.82333	0.190928	0.0954640	+	0.995433i	$0.469567\pi$
$402$	21.0533	1.05004
$403$	22.3127	1.11148
$404$	26.5003	1.31844
$405$	−3.30142	−0.164049
$406$	−71.1549	−3.53136
$407$	−8.98837	−0.445537
$408$	−14.5147	−0.718584
$409$	−20.0729	−0.992539	−0.496269	−	0.868169i	$-0.665297\pi$
$409$	−20.0729	−0.992539	−0.496269	+	0.868169i	$0.665297\pi$
$410$	55.6888	2.75028
$411$	−0.919542	−0.0453577
$412$	−34.1741	−1.68364
$413$	−7.23935	−0.356225
$414$	9.86410	0.484794
$415$	−29.8804	−1.46677
$416$	32.0629	1.57201
$417$	−4.29808	−0.210478
$418$	36.2098	1.77108
$419$	2.88887	0.141131	0.0705653	−	0.997507i	$-0.477520\pi$
$419$	2.88887	0.141131	0.0705653	+	0.997507i	$0.477520\pi$
$420$	62.0234	3.02643
$421$	−16.3316	−0.795953	−0.397977	−	0.917396i	$-0.630288\pi$
$421$	−16.3316	−0.795953	−0.397977	+	0.917396i	$0.630288\pi$
$422$	−28.5235	−1.38850
$423$	3.65511	0.177717
$424$	−85.6270	−4.15842
$425$	−12.1724	−0.590449
$426$	−35.4052	−1.71539
$427$	27.0196	1.30757
$428$	−44.9143	−2.17102
$429$	−11.9153	−0.575278
$430$	−100.844	−4.86315
$431$	−26.8909	−1.29529	−0.647644	−	0.761943i	$-0.724245\pi$
$431$	−26.8909	−1.29529	−0.647644	+	0.761943i	$0.724245\pi$
$432$	−8.79914	−0.423349
$433$	6.37001	0.306123	0.153062	−	0.988217i	$-0.451087\pi$
$433$	6.37001	0.306123	0.153062	+	0.988217i	$0.451087\pi$
$434$	62.7432	3.01177
$435$	22.7506	1.09081
$436$	−7.67016	−0.367334
$437$	−16.3926	−0.784163
$438$	−13.2136	−0.631370
$439$	31.2650	1.49220	0.746098	−	0.665836i	$-0.231925\pi$
$439$	31.2650	1.49220	0.746098	+	0.665836i	$0.231925\pi$
$440$	−75.3614	−3.59271
$441$	8.87805	0.422764
$442$	−19.6327	−0.933834
$443$	−30.3348	−1.44125	−0.720624	−	0.693326i	$-0.756145\pi$
$443$	−30.3348	−1.44125	−0.720624	+	0.693326i	$0.756145\pi$
$444$	−13.0595	−0.619779
$445$	24.8130	1.17625
$446$	−25.2576	−1.19598
$447$	−19.6594	−0.929856
$448$	20.0365	0.946633
$449$	−15.1724	−0.716031	−0.358015	−	0.933716i	$-0.616546\pi$
$449$	−15.1724	−0.716031	−0.358015	+	0.933716i	$0.616546\pi$
$450$	−15.2870	−0.720636
$451$	−21.1233	−0.994657
$452$	46.7240	2.19771
$453$	−12.0738	−0.567277
$454$	−7.75752	−0.364078
$455$	48.3057	2.26460
$456$	30.2930	1.41860
$457$	−17.6811	−0.827087	−0.413543	−	0.910484i	$-0.635709\pi$
$457$	−17.6811	−0.827087	−0.413543	+	0.910484i	$0.635709\pi$
$458$	22.9017	1.07012
$459$	2.06333	0.0963080
$460$	59.2517	2.76262
$461$	26.6389	1.24070	0.620349	−	0.784326i	$-0.286991\pi$
$461$	26.6389	1.24070	0.620349	+	0.784326i	$0.286991\pi$
$462$	−33.5059	−1.55884
$463$	−27.9340	−1.29820	−0.649102	−	0.760702i	$-0.724855\pi$
$463$	−27.9340	−1.29820	−0.649102	+	0.760702i	$0.724855\pi$
$464$	60.6362	2.81497
$465$	−20.0611	−0.930314
$466$	−7.36418	−0.341139
$467$	−27.1079	−1.25440	−0.627202	−	0.778856i	$-0.715800\pi$
$467$	−27.1079	−1.25440	−0.627202	+	0.778856i	$0.715800\pi$
$468$	−17.3123	−0.800260
$469$	32.3746	1.49492
$470$	31.2691	1.44234
$471$	−19.3225	−0.890332
$472$	12.7803	0.588259
$473$	38.2512	1.75879
$474$	13.6205	0.625612
$475$	25.4046	1.16564
$476$	−38.7635	−1.77672
$477$	12.1723	0.557330
$478$	15.1247	0.691790
$479$	−16.6125	−0.759047	−0.379523	−	0.925182i	$-0.623912\pi$
$479$	−16.6125	−0.759047	−0.379523	+	0.925182i	$0.623912\pi$
$480$	−28.8275	−1.31579
$481$	−10.1712	−0.463765
$482$	7.33247	0.333985
$483$	15.1685	0.690190
$484$	−2.21716	−0.100780
$485$	41.1254	1.86741
$486$	2.59128	0.117543
$487$	−16.0477	−0.727192	−0.363596	−	0.931557i	$-0.618451\pi$
$487$	−16.0477	−0.727192	−0.363596	+	0.931557i	$0.618451\pi$
$488$	−47.7001	−2.15928
$489$	18.5861	0.840491
$490$	75.9509	3.43111
$491$	8.16038	0.368273	0.184136	−	0.982901i	$-0.441051\pi$
$491$	8.16038	0.368273	0.184136	+	0.982901i	$0.441051\pi$
$492$	−30.6908	−1.38365
$493$	−14.2187	−0.640379
$494$	40.9747	1.84354
$495$	10.7130	0.481512
$496$	−53.4681	−2.40079
$497$	−54.4442	−2.44215
$498$	23.4530	1.05095
$499$	26.6104	1.19124	0.595622	−	0.803265i	$-0.296906\pi$
$499$	26.6104	1.19124	0.595622	+	0.803265i	$0.296906\pi$
$500$	−13.9995	−0.626076
$501$	3.83611	0.171385
$502$	37.2866	1.66418
$503$	14.3020	0.637696	0.318848	−	0.947806i	$-0.396704\pi$
$503$	14.3020	0.637696	0.318848	+	0.947806i	$0.396704\pi$
$504$	−28.0309	−1.24860
$505$	−18.5565	−0.825755
$506$	−32.0086	−1.42295
$507$	−0.483296	−0.0214639
$508$	−98.1606	−4.35517
$509$	−38.4695	−1.70513	−0.852565	−	0.522622i	$-0.824954\pi$
$509$	−38.4695	−1.70513	−0.852565	+	0.522622i	$0.824954\pi$
$510$	17.6516	0.781626
$511$	−20.3192	−0.898867
$512$	46.9641	2.07554
$513$	−4.30629	−0.190127
$514$	−1.31147	−0.0578465
$515$	23.9300	1.05448
$516$	55.5766	2.44663
$517$	−11.8607	−0.521631
$518$	−28.6012	−1.25667
$519$	24.0596	1.05610
$520$	−85.2782	−3.73970
$521$	22.3159	0.977679	0.488839	−	0.872374i	$-0.337420\pi$
$521$	22.3159	0.977679	0.488839	+	0.872374i	$0.337420\pi$
$522$	−17.8569	−0.781575
$523$	−8.61329	−0.376633	−0.188316	−	0.982108i	$-0.560303\pi$
$523$	−8.61329	−0.376633	−0.188316	+	0.982108i	$0.560303\pi$
$524$	77.8378	3.40036
$525$	−23.5075	−1.02595
$526$	66.8374	2.91425
$527$	12.5379	0.546157
$528$	28.5528	1.24260
$529$	−8.50939	−0.369973
$530$	104.133	4.52324
$531$	−1.81677	−0.0788412
$532$	80.9018	3.50754
$533$	−23.9029	−1.03535
$534$	−19.4756	−0.842793
$535$	31.4507	1.35973
$536$	−57.1538	−2.46867
$537$	11.1238	0.480026
$538$	−2.64284	−0.113941
$539$	−28.8089	−1.24089
$540$	15.5653	0.669823
$541$	15.4637	0.664836	0.332418	−	0.943132i	$-0.392136\pi$
$541$	15.4637	0.664836	0.332418	+	0.943132i	$0.392136\pi$
$542$	−58.3295	−2.50547
$543$	−8.25265	−0.354155
$544$	18.0166	0.772457
$545$	5.37094	0.230066
$546$	−37.9150	−1.62261
$547$	−21.5171	−0.920005	−0.460003	−	0.887918i	$-0.652152\pi$
$547$	−21.5171	−0.920005	−0.460003	+	0.887918i	$0.652152\pi$
$548$	4.33538	0.185198
$549$	6.78079	0.289397
$550$	49.6056	2.11519
$551$	29.6753	1.26421
$552$	−26.7782	−1.13976
$553$	20.9449	0.890669
$554$	40.4285	1.71764
$555$	9.14479	0.388175
$556$	20.2643	0.859396
$557$	−29.1035	−1.23315	−0.616577	−	0.787295i	$-0.711481\pi$
$557$	−29.1035	−1.23315	−0.616577	+	0.787295i	$0.711481\pi$
$558$	15.7459	0.666578
$559$	43.2847	1.83075
$560$	−115.755	−4.89155
$561$	−6.69541	−0.282681
$562$	36.3164	1.53192
$563$	−36.1769	−1.52468	−0.762338	−	0.647179i	$-0.775948\pi$
$563$	−36.1769	−1.52468	−0.762338	+	0.647179i	$0.775948\pi$
$564$	−17.2328	−0.725632
$565$	−32.7179	−1.37645
$566$	−0.954154	−0.0401061
$567$	3.98473	0.167343
$568$	96.1151	4.03290
$569$	−29.9280	−1.25465	−0.627323	−	0.778759i	$-0.715849\pi$
$569$	−29.9280	−1.25465	−0.627323	+	0.778759i	$0.715849\pi$
$570$	−36.8399	−1.54306
$571$	−10.1342	−0.424102	−0.212051	−	0.977259i	$-0.568014\pi$
$571$	−10.1342	−0.424102	−0.212051	+	0.977259i	$0.568014\pi$
$572$	56.1775	2.34890
$573$	−22.1980	−0.927336
$574$	−67.2149	−2.80549
$575$	−22.4570	−0.936521
$576$	5.02831	0.209513
$577$	−33.8031	−1.40724	−0.703621	−	0.710575i	$-0.748435\pi$
$577$	−33.8031	−1.40724	−0.703621	+	0.710575i	$0.748435\pi$
$578$	33.0198	1.37344
$579$	−16.6529	−0.692070
$580$	−107.263	−4.45385
$581$	36.0647	1.49622
$582$	−32.2792	−1.33801
$583$	−39.4985	−1.63586
$584$	35.8712	1.48436
$585$	12.1227	0.501212
$586$	−70.0829	−2.89510
$587$	−25.2424	−1.04186	−0.520932	−	0.853598i	$-0.674416\pi$
$587$	−25.2424	−1.04186	−0.520932	+	0.853598i	$0.674416\pi$
$588$	−41.8575	−1.72617
$589$	−26.1672	−1.07820
$590$	−15.5423	−0.639867
$591$	−15.1216	−0.622018
$592$	24.3732	1.00173
$593$	−38.6821	−1.58848	−0.794242	−	0.607601i	$-0.792132\pi$
$593$	−38.6821	−1.58848	−0.794242	+	0.607601i	$0.792132\pi$
$594$	−8.40858	−0.345008
$595$	27.1437	1.11278
$596$	92.6883	3.79666
$597$	0.540852	0.0221356
$598$	−36.2206	−1.48117
$599$	−21.5580	−0.880836	−0.440418	−	0.897793i	$-0.645170\pi$
$599$	−21.5580	−0.880836	−0.440418	+	0.897793i	$0.645170\pi$
$600$	41.4999	1.69423
$601$	21.6980	0.885081	0.442541	−	0.896749i	$-0.354077\pi$
$601$	21.6980	0.885081	0.442541	+	0.896749i	$0.354077\pi$
$602$	121.716	4.96079
$603$	8.12468	0.330863
$604$	56.9246	2.31623
$605$	1.55254	0.0631198
$606$	14.5650	0.591661
$607$	−8.04710	−0.326622	−0.163311	−	0.986575i	$-0.552217\pi$
$607$	−8.04710	−0.326622	−0.163311	+	0.986575i	$0.552217\pi$
$608$	−37.6018	−1.52495
$609$	−27.4594	−1.11271
$610$	58.0090	2.34872
$611$	−13.4214	−0.542972
$612$	−9.72802	−0.393232
$613$	−27.1518	−1.09665	−0.548325	−	0.836266i	$-0.684734\pi$
$613$	−27.1518	−1.09665	−0.548325	+	0.836266i	$0.684734\pi$
$614$	−74.5691	−3.00936
$615$	21.4909	0.866596
$616$	90.9591	3.66485
$617$	−5.06124	−0.203758	−0.101879	−	0.994797i	$-0.532485\pi$
$617$	−5.06124	−0.203758	−0.101879	+	0.994797i	$0.532485\pi$
$618$	−18.7826	−0.755546
$619$	4.71542	0.189529	0.0947644	−	0.995500i	$-0.469790\pi$
$619$	4.71542	0.189529	0.0947644	+	0.995500i	$0.469790\pi$
$620$	94.5827	3.79853
$621$	3.80665	0.152756
$622$	73.3812	2.94232
$623$	−29.9486	−1.19986
$624$	32.3101	1.29344
$625$	−19.6940	−0.787762
$626$	−27.1546	−1.08532
$627$	13.9737	0.558057
$628$	91.1000	3.63529
$629$	−5.71532	−0.227885
$630$	34.0890	1.35814
$631$	32.2693	1.28462	0.642310	−	0.766445i	$-0.277976\pi$
$631$	32.2693	1.28462	0.642310	+	0.766445i	$0.277976\pi$
$632$	−36.9759	−1.47082
$633$	−11.0075	−0.437508
$634$	21.7407	0.863434
$635$	68.7358	2.72770
$636$	−57.3889	−2.27562
$637$	−32.5999	−1.29165
$638$	57.9448	2.29406
$639$	−13.6632	−0.540508
$640$	−14.6382	−0.578626
$641$	3.81671	0.150751	0.0753755	−	0.997155i	$-0.475984\pi$
$641$	3.81671	0.150751	0.0753755	+	0.997155i	$0.475984\pi$
$642$	−24.6856	−0.974261
$643$	16.0836	0.634274	0.317137	−	0.948380i	$-0.397278\pi$
$643$	16.0836	0.634274	0.317137	+	0.948380i	$0.397278\pi$
$644$	−71.5151	−2.81809
$645$	−38.9169	−1.53235
$646$	23.0243	0.905878
$647$	8.96830	0.352580	0.176290	−	0.984338i	$-0.443590\pi$
$647$	8.96830	0.352580	0.176290	+	0.984338i	$0.443590\pi$
$648$	−7.03459	−0.276345
$649$	5.89535	0.231413
$650$	56.1332	2.20173
$651$	24.2132	0.948992
$652$	−87.6280	−3.43178
$653$	−2.89987	−0.113481	−0.0567403	−	0.998389i	$-0.518071\pi$
$653$	−2.89987	−0.113481	−0.0567403	+	0.998389i	$0.518071\pi$
$654$	−4.21563	−0.164844
$655$	−54.5049	−2.12968
$656$	57.2787	2.23636
$657$	−5.09926	−0.198941
$658$	−37.7409	−1.47130
$659$	−47.5855	−1.85367	−0.926835	−	0.375469i	$-0.877482\pi$
$659$	−47.5855	−1.85367	−0.926835	+	0.375469i	$0.877482\pi$
$660$	−50.5087	−1.96605
$661$	−8.62313	−0.335401	−0.167700	−	0.985838i	$-0.553634\pi$
$661$	−8.62313	−0.335401	−0.167700	+	0.985838i	$0.553634\pi$
$662$	−53.6156	−2.08383
$663$	−7.57647	−0.294246
$664$	−63.6683	−2.47081
$665$	−56.6505	−2.19681
$666$	−7.17771	−0.278131
$667$	−26.2322	−1.01572
$668$	−18.0862	−0.699776
$669$	−9.74717	−0.376847
$670$	69.5059	2.68525
$671$	−22.0034	−0.849430
$672$	34.7939	1.34221
$673$	16.5416	0.637631	0.318815	−	0.947817i	$-0.396715\pi$
$673$	16.5416	0.637631	0.318815	+	0.947817i	$0.396715\pi$
$674$	23.0861	0.889242
$675$	−5.89940	−0.227068
$676$	2.27860	0.0876386
$677$	−40.3330	−1.55012	−0.775062	−	0.631885i	$-0.782281\pi$
$677$	−40.3330	−1.55012	−0.775062	+	0.631885i	$0.782281\pi$
$678$	25.6802	0.986242
$679$	−49.6372	−1.90490
$680$	−47.9191	−1.83761
$681$	−2.99370	−0.114719
$682$	−51.0948	−1.95652
$683$	−36.7009	−1.40432	−0.702160	−	0.712019i	$-0.747781\pi$
$683$	−36.7009	−1.40432	−0.702160	+	0.712019i	$0.747781\pi$
$684$	20.3030	0.776303
$685$	−3.03580	−0.115992
$686$	−19.3919	−0.740385
$687$	8.83798	0.337190
$688$	−103.723	−3.95442
$689$	−44.6961	−1.70279
$690$	32.5656	1.23975
$691$	33.4257	1.27157	0.635787	−	0.771865i	$-0.280676\pi$
$691$	33.4257	1.27157	0.635787	+	0.771865i	$0.280676\pi$
$692$	−113.434	−4.31212
$693$	−12.9303	−0.491180
$694$	−22.8717	−0.868197
$695$	−14.1898	−0.538250
$696$	48.4765	1.83750
$697$	−13.4314	−0.508751
$698$	−4.99656	−0.189123
$699$	−2.84191	−0.107491
$700$	110.831	4.18903
$701$	16.2717	0.614574	0.307287	−	0.951617i	$-0.400579\pi$
$701$	16.2717	0.614574	0.307287	+	0.951617i	$0.400579\pi$
$702$	−9.51507	−0.359123
$703$	11.9282	0.449881
$704$	−16.3166	−0.614957
$705$	12.0671	0.454472
$706$	−32.9703	−1.24085
$707$	22.3972	0.842334
$708$	8.56558	0.321914
$709$	−23.0670	−0.866298	−0.433149	−	0.901322i	$-0.642598\pi$
$709$	−23.0670	−0.866298	−0.433149	+	0.901322i	$0.642598\pi$
$710$	−116.888	−4.38671
$711$	5.25630	0.197127
$712$	52.8709	1.98142
$713$	23.1312	0.866270
$714$	−21.3050	−0.797319
$715$	−39.3376	−1.47114
$716$	−52.4455	−1.95998
$717$	5.83679	0.217979
$718$	33.2734	1.24175
$719$	−36.5103	−1.36160	−0.680801	−	0.732468i	$-0.738368\pi$
$719$	−36.5103	−1.36160	−0.680801	+	0.732468i	$0.738368\pi$
$720$	−29.0497	−1.08262
$721$	−28.8828	−1.07565
$722$	1.18121	0.0439600
$723$	2.82967	0.105237
$724$	38.9089	1.44604
$725$	40.6537	1.50984
$726$	−1.21858	−0.0452259
$727$	−47.3335	−1.75550	−0.877752	−	0.479115i	$-0.840958\pi$
$727$	−47.3335	−1.75550	−0.877752	+	0.479115i	$0.840958\pi$
$728$	102.928	3.81478
$729$	1.00000	0.0370370
$730$	−43.6237	−1.61459
$731$	24.3223	0.899594
$732$	−31.9695	−1.18163
$733$	−19.9106	−0.735416	−0.367708	−	0.929941i	$-0.619857\pi$
$733$	−19.9106	−0.735416	−0.367708	+	0.929941i	$0.619857\pi$
$734$	0.812974	0.0300074
$735$	29.3102	1.08112
$736$	33.2390	1.22521
$737$	−26.3642	−0.971139
$738$	−16.8681	−0.620924
$739$	14.9312	0.549255	0.274627	−	0.961551i	$-0.411446\pi$
$739$	14.9312	0.549255	0.274627	+	0.961551i	$0.411446\pi$
$740$	−43.1151	−1.58494
$741$	15.8125	0.580888
$742$	−125.685	−4.61405
$743$	49.6973	1.82322	0.911609	−	0.411059i	$-0.134841\pi$
$743$	49.6973	1.82322	0.911609	+	0.411059i	$0.134841\pi$
$744$	−42.7458	−1.56714
$745$	−64.9039	−2.37789
$746$	−56.8633	−2.08191
$747$	9.05075	0.331149
$748$	31.5670	1.15420
$749$	−37.9601	−1.38703
$750$	−7.69432	−0.280957
$751$	−16.3687	−0.597302	−0.298651	−	0.954362i	$-0.596537\pi$
$751$	−16.3687	−0.597302	−0.298651	+	0.954362i	$0.596537\pi$
$752$	32.1618	1.17282
$753$	14.3893	0.524375
$754$	65.5698	2.38791
$755$	−39.8608	−1.45068
$756$	−18.7869	−0.683272
$757$	−9.65129	−0.350782	−0.175391	−	0.984499i	$-0.556119\pi$
$757$	−9.65129	−0.350782	−0.175391	+	0.984499i	$0.556119\pi$
$758$	−49.3252	−1.79157
$759$	−12.3524	−0.448364
$760$	100.010	3.62775
$761$	12.8928	0.467362	0.233681	−	0.972313i	$-0.424923\pi$
$761$	12.8928	0.467362	0.233681	+	0.972313i	$0.424923\pi$
$762$	−53.9505	−1.95442
$763$	−6.48257	−0.234685
$764$	104.657	3.78637
$765$	6.81193	0.246286
$766$	−61.2257	−2.21217
$767$	6.67112	0.240880
$768$	21.5461	0.777478
$769$	14.3951	0.519102	0.259551	−	0.965729i	$-0.416425\pi$
$769$	14.3951	0.519102	0.259551	+	0.965729i	$0.416425\pi$
$770$	−110.617	−3.98637
$771$	−0.506110	−0.0182271
$772$	78.5137	2.82577
$773$	20.8960	0.751578	0.375789	−	0.926705i	$-0.377372\pi$
$773$	20.8960	0.751578	0.375789	+	0.926705i	$0.377372\pi$
$774$	30.5457	1.09794
$775$	−35.8478	−1.28769
$776$	87.6288	3.14569
$777$	−11.0375	−0.395968
$778$	−64.2611	−2.30387
$779$	28.0321	1.00436
$780$	−57.1551	−2.04648
$781$	44.3365	1.58649
$782$	−20.3529	−0.727818
$783$	−6.89116	−0.246270
$784$	78.1192	2.78997
$785$	−63.7917	−2.27682
$786$	42.7808	1.52594
$787$	−33.2551	−1.18542	−0.592708	−	0.805418i	$-0.701941\pi$
$787$	−33.2551	−1.18542	−0.592708	+	0.805418i	$0.701941\pi$
$788$	71.2939	2.53974
$789$	25.7932	0.918263
$790$	44.9672	1.59986
$791$	39.4896	1.40409
$792$	22.8269	0.811120
$793$	−24.8988	−0.884182
$794$	71.6185	2.54165
$795$	40.1859	1.42525
$796$	−2.54997	−0.0903811
$797$	−47.1945	−1.67172	−0.835858	−	0.548946i	$-0.815029\pi$
$797$	−47.1945	−1.67172	−0.835858	+	0.548946i	$0.815029\pi$
$798$	44.4648	1.57404
$799$	−7.54170	−0.266806
$800$	−51.5126	−1.82124
$801$	−7.51584	−0.265559
$802$	−9.90731	−0.349839
$803$	16.5469	0.583927
$804$	−38.3056	−1.35093
$805$	50.0776	1.76500
$806$	−57.8184	−2.03657
$807$	−1.01990	−0.0359021
$808$	−39.5398	−1.39101
$809$	−27.5069	−0.967090	−0.483545	−	0.875320i	$-0.660651\pi$
$809$	−27.5069	−0.967090	−0.483545	+	0.875320i	$0.660651\pi$
$810$	8.55491	0.300589
$811$	18.1208	0.636307	0.318154	−	0.948039i	$-0.396937\pi$
$811$	18.1208	0.636307	0.318154	+	0.948039i	$0.396937\pi$
$812$	129.463	4.54327
$813$	−22.5099	−0.789458
$814$	23.2914	0.816362
$815$	61.3605	2.14936
$816$	18.1555	0.635571
$817$	−50.7622	−1.77594
$818$	52.0143	1.81864
$819$	−14.6318	−0.511275
$820$	−101.323	−3.53837
$821$	−10.9913	−0.383599	−0.191800	−	0.981434i	$-0.561432\pi$
$821$	−10.9913	−0.383599	−0.191800	+	0.981434i	$0.561432\pi$
$822$	2.38279	0.0831093
$823$	42.1912	1.47069	0.735347	−	0.677691i	$-0.237019\pi$
$823$	42.1912	1.47069	0.735347	+	0.677691i	$0.237019\pi$
$824$	50.9894	1.77630
$825$	19.1433	0.666484
$826$	18.7592	0.652714
$827$	40.6982	1.41522	0.707608	−	0.706606i	$-0.249774\pi$
$827$	40.6982	1.41522	0.707608	+	0.706606i	$0.249774\pi$
$828$	−17.9473	−0.623712
$829$	21.1688	0.735223	0.367611	−	0.929979i	$-0.380176\pi$
$829$	21.1688	0.735223	0.367611	+	0.929979i	$0.380176\pi$
$830$	77.4283	2.68758
$831$	15.6018	0.541220
$832$	−18.4638	−0.640116
$833$	−18.3183	−0.634693
$834$	11.1375	0.385661
$835$	12.6646	0.438278
$836$	−65.8822	−2.27858
$837$	6.07651	0.210035
$838$	−7.48586	−0.258595
$839$	−39.2857	−1.35629	−0.678146	−	0.734927i	$-0.737216\pi$
$839$	−39.2857	−1.35629	−0.678146	+	0.734927i	$0.737216\pi$
$840$	−92.5420	−3.19300
$841$	18.4880	0.637519
$842$	42.3197	1.45843
$843$	14.0149	0.482698
$844$	51.8972	1.78638
$845$	−1.59556	−0.0548891
$846$	−9.47140	−0.325633
$847$	−1.87387	−0.0643871
$848$	107.106	3.67802
$849$	−0.368217	−0.0126372
$850$	31.5421	1.08189
$851$	−10.5442	−0.361452
$852$	64.4182	2.20693
$853$	42.7511	1.46377	0.731884	−	0.681429i	$-0.238641\pi$
$853$	42.7511	1.46377	0.731884	+	0.681429i	$0.238641\pi$
$854$	−70.0153	−2.39587
$855$	−14.2169	−0.486208
$856$	67.0143	2.29050
$857$	−0.470259	−0.0160637	−0.00803186	−	0.999968i	$-0.502557\pi$
$857$	−0.470259	−0.0160637	−0.00803186	+	0.999968i	$0.502557\pi$
$858$	30.8760	1.05409
$859$	−40.8943	−1.39529	−0.697647	−	0.716442i	$-0.745770\pi$
$859$	−40.8943	−1.39529	−0.697647	+	0.716442i	$0.745770\pi$
$860$	183.482	6.25669
$861$	−25.9389	−0.883995
$862$	69.6817	2.37337
$863$	−41.7198	−1.42016	−0.710080	−	0.704121i	$-0.751341\pi$
$863$	−41.7198	−1.42016	−0.710080	+	0.704121i	$0.751341\pi$
$864$	8.73183	0.297063
$865$	79.4308	2.70073
$866$	−16.5065	−0.560913
$867$	12.7427	0.432764
$868$	−114.159	−3.87480
$869$	−17.0565	−0.578601
$870$	−58.9532	−1.99870
$871$	−29.8335	−1.01087
$872$	11.4443	0.387551
$873$	−12.4569	−0.421601
$874$	42.4777	1.43683
$875$	−11.8319	−0.399992
$876$	24.0416	0.812290
$877$	−30.2236	−1.02058	−0.510290	−	0.860002i	$-0.670462\pi$
$877$	−30.2236	−1.02058	−0.510290	+	0.860002i	$0.670462\pi$
$878$	−81.0162	−2.73417
$879$	−27.0457	−0.912228
$880$	94.2650	3.17767
$881$	−1.45713	−0.0490921	−0.0245461	−	0.999699i	$-0.507814\pi$
$881$	−1.45713	−0.0490921	−0.0245461	+	0.999699i	$0.507814\pi$
$882$	−23.0055	−0.774635
$883$	8.72182	0.293513	0.146756	−	0.989173i	$-0.453117\pi$
$883$	8.72182	0.293513	0.146756	+	0.989173i	$0.453117\pi$
$884$	35.7209	1.20142
$885$	−5.99794	−0.201619
$886$	78.6058	2.64081
$887$	−13.0788	−0.439144	−0.219572	−	0.975596i	$-0.570466\pi$
$887$	−13.0788	−0.439144	−0.219572	+	0.975596i	$0.570466\pi$
$888$	19.4855	0.653890
$889$	−82.9621	−2.78246
$890$	−64.2973	−2.15525
$891$	−3.24496	−0.108710
$892$	45.9552	1.53869
$893$	15.7400	0.526718
$894$	50.9428	1.70378
$895$	36.7243	1.22756
$896$	17.6679	0.590243
$897$	−13.9779	−0.466708
$898$	39.3160	1.31199
$899$	−41.8742	−1.39658
$900$	27.8140	0.927135
$901$	−25.1154	−0.836716
$902$	54.7363	1.82252
$903$	46.9716	1.56312
$904$	−69.7145	−2.31867
$905$	−27.2455	−0.905672
$906$	31.2866	1.03943
$907$	−13.1158	−0.435504	−0.217752	−	0.976004i	$-0.569872\pi$
$907$	−13.1158	−0.435504	−0.217752	+	0.976004i	$0.569872\pi$
$908$	14.1145	0.468405
$909$	5.62077	0.186429
$910$	−125.173	−4.14946
$911$	−38.4112	−1.27262	−0.636311	−	0.771433i	$-0.719540\pi$
$911$	−38.4112	−1.27262	−0.636311	+	0.771433i	$0.719540\pi$
$912$	−37.8917	−1.25472
$913$	−29.3693	−0.971981
$914$	45.8166	1.51548
$915$	22.3863	0.740067
$916$	−41.6686	−1.37677
$917$	65.7859	2.17244
$918$	−5.34666	−0.176466
$919$	1.81472	0.0598622	0.0299311	−	0.999552i	$-0.490471\pi$
$919$	1.81472	0.0598622	0.0299311	+	0.999552i	$0.490471\pi$
$920$	−88.4064	−2.91467
$921$	−28.7770	−0.948233
$922$	−69.0288	−2.27334
$923$	50.1708	1.65139
$924$	60.9626	2.00552
$925$	16.3411	0.537291
$926$	72.3848	2.37871
$927$	−7.24838	−0.238068
$928$	−60.1724	−1.97526
$929$	6.80296	0.223198	0.111599	−	0.993753i	$-0.464403\pi$
$929$	6.80296	0.223198	0.111599	+	0.993753i	$0.464403\pi$
$930$	51.9840	1.70462
$931$	38.2315	1.25299
$932$	13.3988	0.438893
$933$	28.3186	0.927108
$934$	70.2441	2.29846
$935$	−22.1044	−0.722891
$936$	25.8307	0.844304
$937$	−11.4425	−0.373809	−0.186905	−	0.982378i	$-0.559846\pi$
$937$	−11.4425	−0.373809	−0.186905	+	0.982378i	$0.559846\pi$
$938$	−83.8917	−2.73916
$939$	−10.4793	−0.341977
$940$	−56.8928	−1.85564
$941$	49.0181	1.59795	0.798973	−	0.601367i	$-0.205377\pi$
$941$	49.0181	1.59795	0.798973	+	0.601367i	$0.205377\pi$
$942$	50.0699	1.63136
$943$	−24.7797	−0.806938
$944$	−15.9860	−0.520301
$945$	13.1553	0.427941
$946$	−99.1195	−3.22265
$947$	45.6849	1.48456	0.742280	−	0.670089i	$-0.233744\pi$
$947$	45.6849	1.48456	0.742280	+	0.670089i	$0.233744\pi$
$948$	−24.7820	−0.804882
$949$	18.7243	0.607816
$950$	−65.8303	−2.13582
$951$	8.38996	0.272063
$952$	57.8370	1.87451
$953$	29.3462	0.950616	0.475308	−	0.879819i	$-0.342337\pi$
$953$	29.3462	0.950616	0.475308	+	0.879819i	$0.342337\pi$
$954$	−31.5418	−1.02120
$955$	−73.2851	−2.37145
$956$	−27.5188	−0.890023
$957$	22.3615	0.722845
$958$	43.0477	1.39081
$959$	3.66413	0.118321
$960$	16.6006	0.535782
$961$	5.92401	0.191097
$962$	26.3563	0.849761
$963$	−9.52640	−0.306984
$964$	−13.3411	−0.429688
$965$	−54.9782	−1.76981
$966$	−39.3057	−1.26464
$967$	−37.9908	−1.22170	−0.610852	−	0.791745i	$-0.709173\pi$
$967$	−37.9908	−1.22170	−0.610852	+	0.791745i	$0.709173\pi$
$968$	3.30811	0.106327
$969$	8.88530	0.285437
$970$	−106.567	−3.42167
$971$	−1.17217	−0.0376168	−0.0188084	−	0.999823i	$-0.505987\pi$
$971$	−1.17217	−0.0376168	−0.0188084	+	0.999823i	$0.505987\pi$
$972$	−4.71472	−0.151225
$973$	17.1267	0.549056
$974$	41.5841	1.33244
$975$	21.6624	0.693751
$976$	59.6651	1.90983
$977$	−24.1381	−0.772247	−0.386123	−	0.922447i	$-0.626186\pi$
$977$	−24.1381	−0.772247	−0.386123	+	0.922447i	$0.626186\pi$
$978$	−48.1616	−1.54004
$979$	24.3886	0.779462
$980$	−138.189	−4.41430
$981$	−1.62685	−0.0519415
$982$	−21.1458	−0.674789
$983$	13.3539	0.425925	0.212962	−	0.977060i	$-0.431689\pi$
$983$	13.3539	0.425925	0.212962	+	0.977060i	$0.431689\pi$
$984$	45.7922	1.45980
$985$	−49.9227	−1.59067
$986$	36.8447	1.17337
$987$	−14.5646	−0.463597
$988$	−74.5517	−2.37180
$989$	44.8725	1.42686
$990$	−27.7603	−0.882280
$991$	−25.6290	−0.814132	−0.407066	−	0.913399i	$-0.633448\pi$
$991$	−25.6290	−0.814132	−0.407066	+	0.913399i	$0.633448\pi$
$992$	53.0591	1.68463
$993$	−20.6908	−0.656603
$994$	141.080	4.47478
$995$	1.78558	0.0566068
$996$	−42.6717	−1.35211
$997$	8.69924	0.275508	0.137754	−	0.990466i	$-0.456012\pi$
$997$	8.69924	0.275508	0.137754	+	0.990466i	$0.456012\pi$
$998$	−68.9549	−2.18273
$999$	−2.76995	−0.0876374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.7	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.59128 q^{2} -1.00000 q^{3} +4.71472 q^{4} -3.30142 q^{5} +2.59128 q^{6} +3.98473 q^{7} -7.03459 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59128 q^{2} -1.00000 q^{3} +4.71472 q^{4} -3.30142 q^{5} +2.59128 q^{6} +3.98473 q^{7} -7.03459 q^{8} +1.00000 q^{9} +8.55491 q^{10} -3.24496 q^{11} -4.71472 q^{12} -3.67196 q^{13} -10.3255 q^{14} +3.30142 q^{15} +8.79914 q^{16} -2.06333 q^{17} -2.59128 q^{18} +4.30629 q^{19} -15.5653 q^{20} -3.98473 q^{21} +8.40858 q^{22} -3.80665 q^{23} +7.03459 q^{24} +5.89940 q^{25} +9.51507 q^{26} -1.00000 q^{27} +18.7869 q^{28} +6.89116 q^{29} -8.55491 q^{30} -6.07651 q^{31} -8.73183 q^{32} +3.24496 q^{33} +5.34666 q^{34} -13.1553 q^{35} +4.71472 q^{36} +2.76995 q^{37} -11.1588 q^{38} +3.67196 q^{39} +23.2242 q^{40} +6.50958 q^{41} +10.3255 q^{42} -11.7879 q^{43} -15.2991 q^{44} -3.30142 q^{45} +9.86410 q^{46} +3.65511 q^{47} -8.79914 q^{48} +8.87805 q^{49} -15.2870 q^{50} +2.06333 q^{51} -17.3123 q^{52} +12.1723 q^{53} +2.59128 q^{54} +10.7130 q^{55} -28.0309 q^{56} -4.30629 q^{57} -17.8569 q^{58} -1.81677 q^{59} +15.5653 q^{60} +6.78079 q^{61} +15.7459 q^{62} +3.98473 q^{63} +5.02831 q^{64} +12.1227 q^{65} -8.40858 q^{66} +8.12468 q^{67} -9.72802 q^{68} +3.80665 q^{69} +34.0890 q^{70} -13.6632 q^{71} -7.03459 q^{72} -5.09926 q^{73} -7.17771 q^{74} -5.89940 q^{75} +20.3030 q^{76} -12.9303 q^{77} -9.51507 q^{78} +5.25630 q^{79} -29.0497 q^{80} +1.00000 q^{81} -16.8681 q^{82} +9.05075 q^{83} -18.7869 q^{84} +6.81193 q^{85} +30.5457 q^{86} -6.89116 q^{87} +22.8269 q^{88} -7.51584 q^{89} +8.55491 q^{90} -14.6318 q^{91} -17.9473 q^{92} +6.07651 q^{93} -9.47140 q^{94} -14.2169 q^{95} +8.73183 q^{96} -12.4569 q^{97} -23.0055 q^{98} -3.24496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 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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