LMFDB - Embedded newform 4033.2.a.d.1.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.63
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.61628 q^{2} +0.630253 q^{3} +0.612362 q^{4} +2.23852 q^{5} +1.01867 q^{6} -1.90328 q^{7} -2.24281 q^{8} -2.60278 q^{9} +O(q^{10})$	\(q+1.61628 q^{2} +0.630253 q^{3} +0.612362 q^{4} +2.23852 q^{5} +1.01867 q^{6} -1.90328 q^{7} -2.24281 q^{8} -2.60278 q^{9} +3.61808 q^{10} +4.63848 q^{11} +0.385943 q^{12} -0.428377 q^{13} -3.07624 q^{14} +1.41084 q^{15} -4.84974 q^{16} -6.49539 q^{17} -4.20682 q^{18} -2.32414 q^{19} +1.37079 q^{20} -1.19955 q^{21} +7.49708 q^{22} -5.14690 q^{23} -1.41354 q^{24} +0.0109857 q^{25} -0.692377 q^{26} -3.53117 q^{27} -1.16550 q^{28} +3.15192 q^{29} +2.28031 q^{30} -7.90954 q^{31} -3.35291 q^{32} +2.92342 q^{33} -10.4984 q^{34} -4.26054 q^{35} -1.59384 q^{36} -1.00000 q^{37} -3.75647 q^{38} -0.269986 q^{39} -5.02059 q^{40} +5.97897 q^{41} -1.93881 q^{42} -5.92047 q^{43} +2.84043 q^{44} -5.82638 q^{45} -8.31884 q^{46} -5.62526 q^{47} -3.05656 q^{48} -3.37752 q^{49} +0.0177560 q^{50} -4.09374 q^{51} -0.262322 q^{52} +0.0284989 q^{53} -5.70736 q^{54} +10.3833 q^{55} +4.26870 q^{56} -1.46480 q^{57} +5.09439 q^{58} +11.5973 q^{59} +0.863943 q^{60} +2.96671 q^{61} -12.7840 q^{62} +4.95382 q^{63} +4.28023 q^{64} -0.958931 q^{65} +4.72506 q^{66} +14.0556 q^{67} -3.97753 q^{68} -3.24385 q^{69} -6.88623 q^{70} -4.24202 q^{71} +5.83755 q^{72} -0.745985 q^{73} -1.61628 q^{74} +0.00692380 q^{75} -1.42322 q^{76} -8.82832 q^{77} -0.436373 q^{78} -4.44069 q^{79} -10.8562 q^{80} +5.58281 q^{81} +9.66370 q^{82} +11.2861 q^{83} -0.734559 q^{84} -14.5401 q^{85} -9.56914 q^{86} +1.98651 q^{87} -10.4032 q^{88} -3.60188 q^{89} -9.41707 q^{90} +0.815321 q^{91} -3.15177 q^{92} -4.98502 q^{93} -9.09200 q^{94} -5.20265 q^{95} -2.11318 q^{96} -7.65467 q^{97} -5.45902 q^{98} -12.0729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.61628	1.14288	0.571441	−	0.820643i	$-0.306384\pi$
$2$	1.61628	1.14288	0.571441	+	0.820643i	$0.306384\pi$
$3$	0.630253	0.363877	0.181939	−	0.983310i	$-0.441763\pi$
$3$	0.630253	0.363877	0.181939	+	0.983310i	$0.441763\pi$
$4$	0.612362	0.306181
$5$	2.23852	1.00110	0.500549	−	0.865708i	$-0.333132\pi$
$5$	2.23852	1.00110	0.500549	+	0.865708i	$0.333132\pi$
$6$	1.01867	0.415869
$7$	−1.90328	−0.719373	−0.359686	−	0.933073i	$-0.617116\pi$
$7$	−1.90328	−0.719373	−0.359686	+	0.933073i	$0.617116\pi$
$8$	−2.24281	−0.792954
$9$	−2.60278	−0.867594
$10$	3.61808	1.14414
$11$	4.63848	1.39855	0.699277	−	0.714851i	$-0.253506\pi$
$11$	4.63848	1.39855	0.699277	+	0.714851i	$0.253506\pi$
$12$	0.385943	0.111412
$13$	−0.428377	−0.118810	−0.0594052	−	0.998234i	$-0.518920\pi$
$13$	−0.428377	−0.118810	−0.0594052	+	0.998234i	$0.518920\pi$
$14$	−3.07624	−0.822159
$15$	1.41084	0.364277
$16$	−4.84974	−1.21243
$17$	−6.49539	−1.57536	−0.787681	−	0.616083i	$-0.788719\pi$
$17$	−6.49539	−1.57536	−0.787681	+	0.616083i	$0.788719\pi$
$18$	−4.20682	−0.991558
$19$	−2.32414	−0.533195	−0.266598	−	0.963808i	$-0.585899\pi$
$19$	−2.32414	−0.533195	−0.266598	+	0.963808i	$0.585899\pi$
$20$	1.37079	0.306517
$21$	−1.19955	−0.261763
$22$	7.49708	1.59838
$23$	−5.14690	−1.07320	−0.536602	−	0.843836i	$-0.680292\pi$
$23$	−5.14690	−1.07320	−0.536602	+	0.843836i	$0.680292\pi$
$24$	−1.41354	−0.288538
$25$	0.0109857	0.00219715
$26$	−0.692377	−0.135786
$27$	−3.53117	−0.679574
$28$	−1.16550	−0.220258
$29$	3.15192	0.585297	0.292648	−	0.956220i	$-0.405463\pi$
$29$	3.15192	0.585297	0.292648	+	0.956220i	$0.405463\pi$
$30$	2.28031	0.416325
$31$	−7.90954	−1.42060	−0.710298	−	0.703901i	$-0.751440\pi$
$31$	−7.90954	−1.42060	−0.710298	+	0.703901i	$0.751440\pi$
$32$	−3.35291	−0.592716
$33$	2.92342	0.508901
$34$	−10.4984	−1.80045
$35$	−4.26054	−0.720163
$36$	−1.59384	−0.265641
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.75647	−0.609380
$39$	−0.269986	−0.0432323
$40$	−5.02059	−0.793824
$41$	5.97897	0.933759	0.466879	−	0.884321i	$-0.345378\pi$
$41$	5.97897	0.933759	0.466879	+	0.884321i	$0.345378\pi$
$42$	−1.93881	−0.299165
$43$	−5.92047	−0.902863	−0.451432	−	0.892306i	$-0.649087\pi$
$43$	−5.92047	−0.902863	−0.451432	+	0.892306i	$0.649087\pi$
$44$	2.84043	0.428210
$45$	−5.82638	−0.868546
$46$	−8.31884	−1.22655
$47$	−5.62526	−0.820529	−0.410264	−	0.911967i	$-0.634564\pi$
$47$	−5.62526	−0.820529	−0.410264	+	0.911967i	$0.634564\pi$
$48$	−3.05656	−0.441177
$49$	−3.37752	−0.482503
$50$	0.0177560	0.00251108
$51$	−4.09374	−0.573238
$52$	−0.262322	−0.0363775
$53$	0.0284989	0.00391463	0.00195731	−	0.999998i	$-0.499377\pi$
$53$	0.0284989	0.00391463	0.00195731	+	0.999998i	$0.499377\pi$
$54$	−5.70736	−0.776674
$55$	10.3833	1.40009
$56$	4.26870	0.570429
$57$	−1.46480	−0.194017
$58$	5.09439	0.668926
$59$	11.5973	1.50984	0.754918	−	0.655819i	$-0.227677\pi$
$59$	11.5973	1.50984	0.754918	+	0.655819i	$0.227677\pi$
$60$	0.863943	0.111535
$61$	2.96671	0.379848	0.189924	−	0.981799i	$-0.439176\pi$
$61$	2.96671	0.379848	0.189924	+	0.981799i	$0.439176\pi$
$62$	−12.7840	−1.62357
$63$	4.95382	0.624123
$64$	4.28023	0.535029
$65$	−0.958931	−0.118941
$66$	4.72506	0.581615
$67$	14.0556	1.71716	0.858580	−	0.512679i	$-0.171347\pi$
$67$	14.0556	1.71716	0.858580	+	0.512679i	$0.171347\pi$
$68$	−3.97753	−0.482346
$69$	−3.24385	−0.390514
$70$	−6.88623	−0.823061
$71$	−4.24202	−0.503435	−0.251718	−	0.967801i	$-0.580995\pi$
$71$	−4.24202	−0.503435	−0.251718	+	0.967801i	$0.580995\pi$
$72$	5.83755	0.687962
$73$	−0.745985	−0.0873109	−0.0436555	−	0.999047i	$-0.513900\pi$
$73$	−0.745985	−0.0873109	−0.0436555	+	0.999047i	$0.513900\pi$
$74$	−1.61628	−0.187889
$75$	0.00692380	0.000799491 0
$76$	−1.42322	−0.163254
$77$	−8.82832	−1.00608
$78$	−0.436373	−0.0494095
$79$	−4.44069	−0.499617	−0.249809	−	0.968295i	$-0.580368\pi$
$79$	−4.44069	−0.499617	−0.249809	+	0.968295i	$0.580368\pi$
$80$	−10.8562	−1.21377
$81$	5.58281	0.620312
$82$	9.66370	1.06718
$83$	11.2861	1.23881	0.619406	−	0.785071i	$-0.287374\pi$
$83$	11.2861	1.23881	0.619406	+	0.785071i	$0.287374\pi$
$84$	−0.734559	−0.0801469
$85$	−14.5401	−1.57709
$86$	−9.56914	−1.03187
$87$	1.98651	0.212976
$88$	−10.4032	−1.10899
$89$	−3.60188	−0.381799	−0.190899	−	0.981610i	$-0.561140\pi$
$89$	−3.60188	−0.381799	−0.190899	+	0.981610i	$0.561140\pi$
$90$	−9.41707	−0.992646
$91$	0.815321	0.0854689
$92$	−3.15177	−0.328595
$93$	−4.98502	−0.516922
$94$	−9.09200	−0.937768
$95$	−5.20265	−0.533781
$96$	−2.11318	−0.215676
$97$	−7.65467	−0.777214	−0.388607	−	0.921404i	$-0.627044\pi$
$97$	−7.65467	−0.777214	−0.388607	+	0.921404i	$0.627044\pi$
$98$	−5.45902	−0.551444
$99$	−12.0729	−1.21338
$100$	0.00672725	0.000672725 0
$101$	−17.7019	−1.76140	−0.880702	−	0.473672i	$-0.842928\pi$
$101$	−17.7019	−1.76140	−0.880702	+	0.473672i	$0.842928\pi$
$102$	−6.61663	−0.655144
$103$	0.130132	0.0128223	0.00641114	−	0.999979i	$-0.497959\pi$
$103$	0.130132	0.0128223	0.00641114	+	0.999979i	$0.497959\pi$
$104$	0.960768	0.0942111
$105$	−2.68522	−0.262051
$106$	0.0460622	0.00447396
$107$	5.14891	0.497764	0.248882	−	0.968534i	$-0.419937\pi$
$107$	5.14891	0.497764	0.248882	+	0.968534i	$0.419937\pi$
$108$	−2.16236	−0.208073
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	16.7824	1.60014
$111$	−0.630253	−0.0598210
$112$	9.23041	0.872192
$113$	10.5572	0.993135	0.496568	−	0.867998i	$-0.334593\pi$
$113$	10.5572	0.993135	0.496568	+	0.867998i	$0.334593\pi$
$114$	−2.36753	−0.221739
$115$	−11.5215	−1.07438
$116$	1.93012	0.179207
$117$	1.11497	0.103079
$118$	18.7444	1.72557
$119$	12.3625	1.13327
$120$	−3.16424	−0.288854
$121$	10.5155	0.955951
$122$	4.79503	0.434122
$123$	3.76827	0.339773
$124$	−4.84351	−0.434960
$125$	−11.1680	−0.998898
$126$	8.00677	0.713300
$127$	−19.1467	−1.69899	−0.849496	−	0.527595i	$-0.823094\pi$
$127$	−19.1467	−1.69899	−0.849496	+	0.527595i	$0.823094\pi$
$128$	13.6239	1.20419
$129$	−3.73140	−0.328531
$130$	−1.54990	−0.135935
$131$	−6.11260	−0.534060	−0.267030	−	0.963688i	$-0.586042\pi$
$131$	−6.11260	−0.534060	−0.267030	+	0.963688i	$0.586042\pi$
$132$	1.79019	0.155816
$133$	4.42350	0.383566
$134$	22.7177	1.96251
$135$	−7.90461	−0.680320
$136$	14.5679	1.24919
$137$	11.0073	0.940421	0.470211	−	0.882554i	$-0.344178\pi$
$137$	11.0073	0.940421	0.470211	+	0.882554i	$0.344178\pi$
$138$	−5.24298	−0.446312
$139$	−3.89241	−0.330150	−0.165075	−	0.986281i	$-0.552787\pi$
$139$	−3.89241	−0.330150	−0.165075	+	0.986281i	$0.552787\pi$
$140$	−2.60899	−0.220500
$141$	−3.54534	−0.298571
$142$	−6.85629	−0.575367
$143$	−1.98701	−0.166163
$144$	12.6228	1.05190
$145$	7.05565	0.585940
$146$	−1.20572	−0.0997862
$147$	−2.12869	−0.175572
$148$	−0.612362	−0.0503359
$149$	17.5825	1.44042	0.720209	−	0.693757i	$-0.244046\pi$
$149$	17.5825	1.44042	0.720209	+	0.693757i	$0.244046\pi$
$150$	0.0111908	0.000913725 0
$151$	−17.3666	−1.41328	−0.706639	−	0.707574i	$-0.749789\pi$
$151$	−17.3666	−1.41328	−0.706639	+	0.707574i	$0.749789\pi$
$152$	5.21262	0.422799
$153$	16.9061	1.36677
$154$	−14.2690	−1.14983
$155$	−17.7057	−1.42216
$156$	−0.165329	−0.0132369
$157$	−18.5938	−1.48395	−0.741973	−	0.670430i	$-0.766110\pi$
$157$	−18.5938	−1.48395	−0.741973	+	0.670430i	$0.766110\pi$
$158$	−7.17741	−0.571004
$159$	0.0179615	0.00142444
$160$	−7.50557	−0.593367
$161$	9.79601	0.772033
$162$	9.02338	0.708944
$163$	13.7480	1.07683	0.538415	−	0.842680i	$-0.319023\pi$
$163$	13.7480	1.07683	0.538415	+	0.842680i	$0.319023\pi$
$164$	3.66130	0.285899
$165$	6.54413	0.509460
$166$	18.2415	1.41582
$167$	−20.9020	−1.61745	−0.808723	−	0.588189i	$-0.799841\pi$
$167$	−20.9020	−1.61745	−0.808723	+	0.588189i	$0.799841\pi$
$168$	2.69036	0.207566
$169$	−12.8165	−0.985884
$170$	−23.5008	−1.80243
$171$	6.04924	0.462597
$172$	−3.62547	−0.276440
$173$	0.860056	0.0653889	0.0326944	−	0.999465i	$-0.489591\pi$
$173$	0.860056	0.0653889	0.0326944	+	0.999465i	$0.489591\pi$
$174$	3.21076	0.243407
$175$	−0.0209089	−0.00158057
$176$	−22.4954	−1.69565
$177$	7.30922	0.549395
$178$	−5.82165	−0.436351
$179$	−0.102267	−0.00764380	−0.00382190	−	0.999993i	$-0.501217\pi$
$179$	−0.102267	−0.00764380	−0.00382190	+	0.999993i	$0.501217\pi$
$180$	−3.56786	−0.265932
$181$	5.33948	0.396881	0.198440	−	0.980113i	$-0.436412\pi$
$181$	5.33948	0.396881	0.198440	+	0.980113i	$0.436412\pi$
$182$	1.31779	0.0976809
$183$	1.86978	0.138218
$184$	11.5435	0.851001
$185$	−2.23852	−0.164579
$186$	−8.05719	−0.590782
$187$	−30.1287	−2.20323
$188$	−3.44470	−0.251230
$189$	6.72081	0.488867
$190$	−8.40894	−0.610049
$191$	−3.48827	−0.252402	−0.126201	−	0.992005i	$-0.540278\pi$
$191$	−3.48827	−0.252402	−0.126201	+	0.992005i	$0.540278\pi$
$192$	2.69763	0.194685
$193$	3.75623	0.270379	0.135190	−	0.990820i	$-0.456836\pi$
$193$	3.75623	0.270379	0.135190	+	0.990820i	$0.456836\pi$
$194$	−12.3721	−0.888265
$195$	−0.604370	−0.0432798
$196$	−2.06827	−0.147733
$197$	9.43497	0.672214	0.336107	−	0.941824i	$-0.390890\pi$
$197$	9.43497	0.672214	0.336107	+	0.941824i	$0.390890\pi$
$198$	−19.5132	−1.38675
$199$	0.977732	0.0693096	0.0346548	−	0.999399i	$-0.488967\pi$
$199$	0.977732	0.0693096	0.0346548	+	0.999399i	$0.488967\pi$
$200$	−0.0246389	−0.00174224
$201$	8.85857	0.624835
$202$	−28.6112	−2.01308
$203$	−5.99899	−0.421047
$204$	−2.50685	−0.175515
$205$	13.3841	0.934784
$206$	0.210330	0.0146544
$207$	13.3963	0.931105
$208$	2.07751	0.144050
$209$	−10.7805	−0.745702
$210$	−4.34007	−0.299493
$211$	23.8557	1.64229	0.821146	−	0.570718i	$-0.193335\pi$
$211$	23.8557	1.64229	0.821146	+	0.570718i	$0.193335\pi$
$212$	0.0174517	0.00119858
$213$	−2.67355	−0.183189
$214$	8.32208	0.568886
$215$	−13.2531	−0.903855
$216$	7.91975	0.538871
$217$	15.0541	1.02194
$218$	−1.61628	−0.109468
$219$	−0.470160	−0.0317704
$220$	6.35836	0.428681
$221$	2.78247	0.187169
$222$	−1.01867	−0.0683684
$223$	−10.9045	−0.730220	−0.365110	−	0.930964i	$-0.618969\pi$
$223$	−10.9045	−0.730220	−0.365110	+	0.930964i	$0.618969\pi$
$224$	6.38153	0.426384
$225$	−0.0285935	−0.00190623
$226$	17.0634	1.13504
$227$	7.17426	0.476172	0.238086	−	0.971244i	$-0.423480\pi$
$227$	7.17426	0.476172	0.238086	+	0.971244i	$0.423480\pi$
$228$	−0.896988	−0.0594045
$229$	−2.11264	−0.139607	−0.0698036	−	0.997561i	$-0.522237\pi$
$229$	−2.11264	−0.139607	−0.0698036	+	0.997561i	$0.522237\pi$
$230$	−18.6219	−1.22789
$231$	−5.56408	−0.366090
$232$	−7.06916	−0.464113
$233$	−19.4763	−1.27593	−0.637967	−	0.770063i	$-0.720225\pi$
$233$	−19.4763	−1.27593	−0.637967	+	0.770063i	$0.720225\pi$
$234$	1.80210	0.117807
$235$	−12.5923	−0.821429
$236$	7.10173	0.462283
$237$	−2.79876	−0.181799
$238$	19.9813	1.29520
$239$	−13.1482	−0.850488	−0.425244	−	0.905079i	$-0.639812\pi$
$239$	−13.1482	−0.850488	−0.425244	+	0.905079i	$0.639812\pi$
$240$	−6.84219	−0.441661
$241$	1.97290	0.127085	0.0635427	−	0.997979i	$-0.479760\pi$
$241$	1.97290	0.127085	0.0635427	+	0.997979i	$0.479760\pi$
$242$	16.9959	1.09254
$243$	14.1121	0.905292
$244$	1.81670	0.116302
$245$	−7.56066	−0.483033
$246$	6.09058	0.388321
$247$	0.995609	0.0633491
$248$	17.7396	1.12647
$249$	7.11311	0.450775
$250$	−18.0507	−1.14162
$251$	16.1334	1.01833	0.509165	−	0.860669i	$-0.329954\pi$
$251$	16.1334	1.01833	0.509165	+	0.860669i	$0.329954\pi$
$252$	3.03353	0.191095
$253$	−23.8738	−1.50093
$254$	−30.9464	−1.94175
$255$	−9.16393	−0.573868
$256$	13.4595	0.841221
$257$	−27.8893	−1.73969	−0.869843	−	0.493329i	$-0.835780\pi$
$257$	−27.8893	−1.73969	−0.869843	+	0.493329i	$0.835780\pi$
$258$	−6.03098	−0.375473
$259$	1.90328	0.118264
$260$	−0.587213	−0.0364174
$261$	−8.20376	−0.507800
$262$	−9.87967	−0.610368
$263$	−6.74387	−0.415845	−0.207923	−	0.978145i	$-0.566670\pi$
$263$	−6.74387	−0.415845	−0.207923	+	0.978145i	$0.566670\pi$
$264$	−6.55667	−0.403535
$265$	0.0637955	0.00391893
$266$	7.14962	0.438371
$267$	−2.27010	−0.138928
$268$	8.60710	0.525762
$269$	19.2821	1.17565	0.587824	−	0.808989i	$-0.299985\pi$
$269$	19.2821	1.17565	0.587824	+	0.808989i	$0.299985\pi$
$270$	−12.7761	−0.777527
$271$	12.2552	0.744448	0.372224	−	0.928143i	$-0.378595\pi$
$271$	12.2552	0.744448	0.372224	+	0.928143i	$0.378595\pi$
$272$	31.5009	1.91002
$273$	0.513859	0.0311002
$274$	17.7910	1.07479
$275$	0.0509571	0.00307283
$276$	−1.98641	−0.119568
$277$	−0.238694	−0.0143417	−0.00717086	−	0.999974i	$-0.502283\pi$
$277$	−0.238694	−0.0143417	−0.00717086	+	0.999974i	$0.502283\pi$
$278$	−6.29123	−0.377323
$279$	20.5868	1.23250
$280$	9.55559	0.571056
$281$	−16.5477	−0.987152	−0.493576	−	0.869703i	$-0.664311\pi$
$281$	−16.5477	−0.987152	−0.493576	+	0.869703i	$0.664311\pi$
$282$	−5.73026	−0.341232
$283$	−0.750759	−0.0446280	−0.0223140	−	0.999751i	$-0.507103\pi$
$283$	−0.750759	−0.0446280	−0.0223140	+	0.999751i	$0.507103\pi$
$284$	−2.59765	−0.154142
$285$	−3.27899	−0.194231
$286$	−3.21157	−0.189904
$287$	−11.3797	−0.671721
$288$	8.72689	0.514237
$289$	25.1900	1.48177
$290$	11.4039	0.669660
$291$	−4.82438	−0.282810
$292$	−0.456813	−0.0267330
$293$	31.1403	1.81924	0.909618	−	0.415445i	$-0.136374\pi$
$293$	31.1403	1.81924	0.909618	+	0.415445i	$0.136374\pi$
$294$	−3.44057	−0.200658
$295$	25.9608	1.51149
$296$	2.24281	0.130361
$297$	−16.3793	−0.950421
$298$	28.4183	1.64623
$299$	2.20481	0.127508
$300$	0.00423987	0.000244789 0
$301$	11.2683	0.649495
$302$	−28.0694	−1.61521
$303$	−11.1567	−0.640934
$304$	11.2715	0.646464
$305$	6.64105	0.380265
$306$	27.3249	1.56206
$307$	−13.7200	−0.783039	−0.391520	−	0.920170i	$-0.628050\pi$
$307$	−13.7200	−0.783039	−0.391520	+	0.920170i	$0.628050\pi$
$308$	−5.40613	−0.308043
$309$	0.0820161	0.00466574
$310$	−28.6174	−1.62536
$311$	2.84297	0.161210	0.0806050	−	0.996746i	$-0.474315\pi$
$311$	2.84297	0.161210	0.0806050	+	0.996746i	$0.474315\pi$
$312$	0.605527	0.0342812
$313$	−6.64949	−0.375852	−0.187926	−	0.982183i	$-0.560176\pi$
$313$	−6.64949	−0.375852	−0.187926	+	0.982183i	$0.560176\pi$
$314$	−30.0528	−1.69598
$315$	11.0892	0.624808
$316$	−2.71931	−0.152973
$317$	23.0967	1.29724	0.648619	−	0.761113i	$-0.275347\pi$
$317$	23.0967	1.29724	0.648619	+	0.761113i	$0.275347\pi$
$318$	0.0290309	0.00162797
$319$	14.6201	0.818569
$320$	9.58139	0.535616
$321$	3.24512	0.181125
$322$	15.8331	0.882344
$323$	15.0962	0.839976
$324$	3.41870	0.189928
$325$	−0.00470603	−0.000261044 0
$326$	22.2207	1.23069
$327$	−0.630253	−0.0348531
$328$	−13.4097	−0.740428
$329$	10.7065	0.590266
$330$	10.5772	0.582253
$331$	−19.4435	−1.06871	−0.534357	−	0.845259i	$-0.679446\pi$
$331$	−19.4435	−1.06871	−0.534357	+	0.845259i	$0.679446\pi$
$332$	6.91119	0.379301
$333$	2.60278	0.142631
$334$	−33.7835	−1.84855
$335$	31.4637	1.71905
$336$	5.81750	0.317371
$337$	−7.77975	−0.423790	−0.211895	−	0.977292i	$-0.567963\pi$
$337$	−7.77975	−0.423790	−0.211895	+	0.977292i	$0.567963\pi$
$338$	−20.7150	−1.12675
$339$	6.65370	0.361379
$340$	−8.90379	−0.482876
$341$	−36.6882	−1.98678
$342$	9.77726	0.528694
$343$	19.7513	1.06647
$344$	13.2785	0.715929
$345$	−7.26144	−0.390943
$346$	1.39009	0.0747318
$347$	3.91971	0.210421	0.105211	−	0.994450i	$-0.466448\pi$
$347$	3.91971	0.210421	0.105211	+	0.994450i	$0.466448\pi$
$348$	1.21646	0.0652092
$349$	−3.14916	−0.168571	−0.0842853	−	0.996442i	$-0.526861\pi$
$349$	−3.14916	−0.168571	−0.0842853	+	0.996442i	$0.526861\pi$
$350$	−0.0337947	−0.00180640
$351$	1.51267	0.0807404
$352$	−15.5524	−0.828945
$353$	22.8958	1.21862	0.609310	−	0.792932i	$-0.291446\pi$
$353$	22.8958	1.21862	0.609310	+	0.792932i	$0.291446\pi$
$354$	11.8137	0.627894
$355$	−9.49586	−0.503988
$356$	−2.20566	−0.116900
$357$	7.79154	0.412372
$358$	−0.165292	−0.00873597
$359$	16.1382	0.851742	0.425871	−	0.904784i	$-0.359968\pi$
$359$	16.1382	0.851742	0.425871	+	0.904784i	$0.359968\pi$
$360$	13.0675	0.688717
$361$	−13.5984	−0.715703
$362$	8.63010	0.453588
$363$	6.62740	0.347849
$364$	0.499272	0.0261690
$365$	−1.66990	−0.0874068
$366$	3.02209	0.157967
$367$	23.1462	1.20822	0.604112	−	0.796899i	$-0.293528\pi$
$367$	23.1462	1.20822	0.604112	+	0.796899i	$0.293528\pi$
$368$	24.9611	1.30119
$369$	−15.5620	−0.810123
$370$	−3.61808	−0.188095
$371$	−0.0542415	−0.00281608
$372$	−3.05264	−0.158272
$373$	−10.7474	−0.556480	−0.278240	−	0.960512i	$-0.589751\pi$
$373$	−10.7474	−0.556480	−0.278240	+	0.960512i	$0.589751\pi$
$374$	−48.6964	−2.51803
$375$	−7.03869	−0.363476
$376$	12.6164	0.650641
$377$	−1.35021	−0.0695393
$378$	10.8627	0.558718
$379$	1.73682	0.0892143	0.0446072	−	0.999005i	$-0.485796\pi$
$379$	1.73682	0.0892143	0.0446072	+	0.999005i	$0.485796\pi$
$380$	−3.18591	−0.163434
$381$	−12.0673	−0.618224
$382$	−5.63802	−0.288466
$383$	26.0913	1.33320	0.666602	−	0.745413i	$-0.267748\pi$
$383$	26.0913	1.33320	0.666602	+	0.745413i	$0.267748\pi$
$384$	8.58649	0.438178
$385$	−19.7624	−1.00719
$386$	6.07112	0.309012
$387$	15.4097	0.783318
$388$	−4.68743	−0.237968
$389$	14.9724	0.759133	0.379567	−	0.925164i	$-0.376073\pi$
$389$	14.9724	0.759133	0.379567	+	0.925164i	$0.376073\pi$
$390$	−0.976831	−0.0494637
$391$	33.4311	1.69068
$392$	7.57514	0.382602
$393$	−3.85249	−0.194332
$394$	15.2496	0.768261
$395$	−9.94060	−0.500166
$396$	−7.39301	−0.371513
$397$	−27.7666	−1.39357	−0.696784	−	0.717281i	$-0.745386\pi$
$397$	−27.7666	−1.39357	−0.696784	+	0.717281i	$0.745386\pi$
$398$	1.58029	0.0792127
$399$	2.78793	0.139571
$400$	−0.0532779	−0.00266390
$401$	22.6271	1.12994	0.564971	−	0.825111i	$-0.308887\pi$
$401$	22.6271	1.12994	0.564971	+	0.825111i	$0.308887\pi$
$402$	14.3179	0.714114
$403$	3.38826	0.168781
$404$	−10.8400	−0.539308
$405$	12.4972	0.620993
$406$	−9.69605	−0.481207
$407$	−4.63848	−0.229921
$408$	9.18149	0.454551
$409$	−20.1803	−0.997851	−0.498925	−	0.866645i	$-0.666272\pi$
$409$	−20.1803	−0.997851	−0.498925	+	0.866645i	$0.666272\pi$
$410$	21.6324	1.06835
$411$	6.93742	0.342198
$412$	0.0796879	0.00392594
$413$	−22.0729	−1.08613
$414$	21.6521	1.06414
$415$	25.2642	1.24017
$416$	1.43631	0.0704208
$417$	−2.45321	−0.120134
$418$	−17.4243	−0.852250
$419$	−26.3577	−1.28766	−0.643829	−	0.765170i	$-0.722655\pi$
$419$	−26.3577	−1.28766	−0.643829	+	0.765170i	$0.722655\pi$
$420$	−1.64433	−0.0802349
$421$	−14.7271	−0.717755	−0.358877	−	0.933385i	$-0.616840\pi$
$421$	−14.7271	−0.717755	−0.358877	+	0.933385i	$0.616840\pi$
$422$	38.5575	1.87695
$423$	14.6413	0.711885
$424$	−0.0639177	−0.00310412
$425$	−0.0713566	−0.00346130
$426$	−4.32120	−0.209363
$427$	−5.64648	−0.273252
$428$	3.15300	0.152406
$429$	−1.25232	−0.0604627
$430$	−21.4207	−1.03300
$431$	21.2049	1.02140	0.510701	−	0.859758i	$-0.329386\pi$
$431$	21.2049	1.02140	0.510701	+	0.859758i	$0.329386\pi$
$432$	17.1253	0.823939
$433$	0.101518	0.00487865	0.00243932	−	0.999997i	$-0.499224\pi$
$433$	0.101518	0.00487865	0.00243932	+	0.999997i	$0.499224\pi$
$434$	24.3316	1.16796
$435$	4.44685	0.213210
$436$	−0.612362	−0.0293268
$437$	11.9621	0.572227
$438$	−0.759910	−0.0363099
$439$	−18.5468	−0.885188	−0.442594	−	0.896722i	$-0.645942\pi$
$439$	−18.5468	−0.885188	−0.442594	+	0.896722i	$0.645942\pi$
$440$	−23.2879	−1.11021
$441$	8.79094	0.418616
$442$	4.49725	0.213913
$443$	14.8278	0.704490	0.352245	−	0.935908i	$-0.385418\pi$
$443$	14.8278	0.704490	0.352245	+	0.935908i	$0.385418\pi$
$444$	−0.385943	−0.0183161
$445$	−8.06290	−0.382218
$446$	−17.6248	−0.834556
$447$	11.0815	0.524135
$448$	−8.14648	−0.384885
$449$	0.470774	0.0222172	0.0111086	−	0.999938i	$-0.496464\pi$
$449$	0.470774	0.0222172	0.0111086	+	0.999938i	$0.496464\pi$
$450$	−0.0462150	−0.00217860
$451$	27.7333	1.30591
$452$	6.46481	0.304079
$453$	−10.9454	−0.514259
$454$	11.5956	0.544209
$455$	1.82512	0.0855627
$456$	3.28527	0.153847
$457$	0.274458	0.0128386	0.00641930	−	0.999979i	$-0.497957\pi$
$457$	0.274458	0.0128386	0.00641930	+	0.999979i	$0.497957\pi$
$458$	−3.41462	−0.159555
$459$	22.9363	1.07058
$460$	−7.05531	−0.328955
$461$	24.3648	1.13478	0.567390	−	0.823449i	$-0.307953\pi$
$461$	24.3648	1.13478	0.567390	+	0.823449i	$0.307953\pi$
$462$	−8.99312	−0.418398
$463$	−5.93949	−0.276032	−0.138016	−	0.990430i	$-0.544072\pi$
$463$	−5.93949	−0.276032	−0.138016	+	0.990430i	$0.544072\pi$
$464$	−15.2860	−0.709634
$465$	−11.1591	−0.517490
$466$	−31.4792	−1.45824
$467$	−27.2045	−1.25888	−0.629438	−	0.777051i	$-0.716715\pi$
$467$	−27.2045	−1.25888	−0.629438	+	0.777051i	$0.716715\pi$
$468$	0.682766	0.0315609
$469$	−26.7517	−1.23528
$470$	−20.3526	−0.938798
$471$	−11.7188	−0.539974
$472$	−26.0105	−1.19723
$473$	−27.4620	−1.26270
$474$	−4.52359	−0.207775
$475$	−0.0255324	−0.00117151
$476$	7.57035	0.346987
$477$	−0.0741764	−0.00339631
$478$	−21.2512	−0.972009
$479$	14.4712	0.661206	0.330603	−	0.943770i	$-0.392748\pi$
$479$	14.4712	0.661206	0.330603	+	0.943770i	$0.392748\pi$
$480$	−4.73041	−0.215913
$481$	0.428377	0.0195323
$482$	3.18875	0.145244
$483$	6.17397	0.280925
$484$	6.43927	0.292694
$485$	−17.1352	−0.778068
$486$	22.8091	1.03464
$487$	−31.0831	−1.40851	−0.704255	−	0.709947i	$-0.748719\pi$
$487$	−31.0831	−1.40851	−0.704255	+	0.709947i	$0.748719\pi$
$488$	−6.65377	−0.301202
$489$	8.66475	0.391834
$490$	−12.2201	−0.552050
$491$	−8.10105	−0.365595	−0.182798	−	0.983151i	$-0.558515\pi$
$491$	−8.10105	−0.365595	−0.182798	+	0.983151i	$0.558515\pi$
$492$	2.30754	0.104032
$493$	−20.4729	−0.922055
$494$	1.60918	0.0724006
$495$	−27.0255	−1.21471
$496$	38.3592	1.72238
$497$	8.07376	0.362158
$498$	11.4968	0.515183
$499$	−25.5991	−1.14597	−0.572986	−	0.819565i	$-0.694215\pi$
$499$	−25.5991	−1.14597	−0.572986	+	0.819565i	$0.694215\pi$
$500$	−6.83887	−0.305844
$501$	−13.1736	−0.588552
$502$	26.0761	1.16383
$503$	15.8313	0.705882	0.352941	−	0.935646i	$-0.385182\pi$
$503$	15.8313	0.705882	0.352941	+	0.935646i	$0.385182\pi$
$504$	−11.1105	−0.494901
$505$	−39.6261	−1.76334
$506$	−38.5867	−1.71539
$507$	−8.07764	−0.358741
$508$	−11.7247	−0.520199
$509$	−7.13936	−0.316447	−0.158223	−	0.987403i	$-0.550577\pi$
$509$	−7.13936	−0.316447	−0.158223	+	0.987403i	$0.550577\pi$
$510$	−14.8115	−0.655863
$511$	1.41982	0.0628091
$512$	−5.49336	−0.242775
$513$	8.20695	0.362346
$514$	−45.0769	−1.98826
$515$	0.291303	0.0128364
$516$	−2.28497	−0.100590
$517$	−26.0926	−1.14755
$518$	3.07624	0.135162
$519$	0.542053	0.0237935
$520$	2.15070	0.0943145
$521$	28.2415	1.23728	0.618641	−	0.785674i	$-0.287684\pi$
$521$	28.2415	1.23728	0.618641	+	0.785674i	$0.287684\pi$
$522$	−13.2596	−0.580356
$523$	−28.6777	−1.25399	−0.626993	−	0.779025i	$-0.715715\pi$
$523$	−28.6777	−1.25399	−0.626993	+	0.779025i	$0.715715\pi$
$524$	−3.74312	−0.163519
$525$	−0.0131779	−0.000575132 0
$526$	−10.9000	−0.475262
$527$	51.3755	2.23795
$528$	−14.1778	−0.617009
$529$	3.49062	0.151766
$530$	0.103111	0.00447887
$531$	−30.1851	−1.30992
$532$	2.70878	0.117441
$533$	−2.56125	−0.110940
$534$	−3.66912	−0.158778
$535$	11.5260	0.498310
$536$	−31.5240	−1.36163
$537$	−0.0644542	−0.00278140
$538$	31.1652	1.34363
$539$	−15.6665	−0.674806
$540$	−4.84048	−0.208301
$541$	−16.7531	−0.720272	−0.360136	−	0.932900i	$-0.617270\pi$
$541$	−16.7531	−0.720272	−0.360136	+	0.932900i	$0.617270\pi$
$542$	19.8078	0.850816
$543$	3.36523	0.144416
$544$	21.7784	0.933743
$545$	−2.23852	−0.0958878
$546$	0.830540	0.0355438
$547$	−31.0786	−1.32883	−0.664413	−	0.747365i	$-0.731318\pi$
$547$	−31.0786	−1.32883	−0.664413	+	0.747365i	$0.731318\pi$
$548$	6.74048	0.287939
$549$	−7.72169	−0.329554
$550$	0.0823609	0.00351188
$551$	−7.32552	−0.312078
$552$	7.27535	0.309660
$553$	8.45189	0.359411
$554$	−0.385796	−0.0163909
$555$	−1.41084	−0.0598867
$556$	−2.38357	−0.101086
$557$	3.62181	0.153461	0.0767304	−	0.997052i	$-0.475552\pi$
$557$	3.62181	0.153461	0.0767304	+	0.997052i	$0.475552\pi$
$558$	33.2741	1.40860
$559$	2.53619	0.107269
$560$	20.6625	0.873150
$561$	−18.9887	−0.801704
$562$	−26.7457	−1.12820
$563$	0.567404	0.0239132	0.0119566	−	0.999929i	$-0.496194\pi$
$563$	0.567404	0.0239132	0.0119566	+	0.999929i	$0.496194\pi$
$564$	−2.17103	−0.0914169
$565$	23.6325	0.994226
$566$	−1.21344	−0.0510046
$567$	−10.6257	−0.446236
$568$	9.51405	0.399201
$569$	−0.125568	−0.00526408	−0.00263204	−	0.999997i	$-0.500838\pi$
$569$	−0.125568	−0.00526408	−0.00263204	+	0.999997i	$0.500838\pi$
$570$	−5.29976	−0.221983
$571$	29.6105	1.23916	0.619580	−	0.784933i	$-0.287303\pi$
$571$	29.6105	1.23916	0.619580	+	0.784933i	$0.287303\pi$
$572$	−1.21677	−0.0508758
$573$	−2.19849	−0.0918434
$574$	−18.3927	−0.767698
$575$	−0.0565425	−0.00235799
$576$	−11.1405	−0.464188
$577$	22.4527	0.934720	0.467360	−	0.884067i	$-0.345205\pi$
$577$	22.4527	0.934720	0.467360	+	0.884067i	$0.345205\pi$
$578$	40.7141	1.69349
$579$	2.36738	0.0983849
$580$	4.32061	0.179404
$581$	−21.4806	−0.891167
$582$	−7.79756	−0.323219
$583$	0.132192	0.00547481
$584$	1.67310	0.0692335
$585$	2.49589	0.103192
$586$	50.3315	2.07917
$587$	−28.6307	−1.18172	−0.590858	−	0.806776i	$-0.701211\pi$
$587$	−28.6307	−1.18172	−0.590858	+	0.806776i	$0.701211\pi$
$588$	−1.30353	−0.0537567
$589$	18.3829	0.757455
$590$	41.9599	1.72746
$591$	5.94642	0.244603
$592$	4.84974	0.199323
$593$	27.0898	1.11245	0.556223	−	0.831033i	$-0.312250\pi$
$593$	27.0898	1.11245	0.556223	+	0.831033i	$0.312250\pi$
$594$	−26.4735	−1.08622
$595$	27.6738	1.13452
$596$	10.7669	0.441029
$597$	0.616219	0.0252202
$598$	3.56360	0.145726
$599$	20.5501	0.839653	0.419827	−	0.907604i	$-0.362091\pi$
$599$	20.5501	0.839653	0.419827	+	0.907604i	$0.362091\pi$
$600$	−0.0155288	−0.000633960 0
$601$	21.6586	0.883473	0.441737	−	0.897145i	$-0.354363\pi$
$601$	21.6586	0.883473	0.441737	+	0.897145i	$0.354363\pi$
$602$	18.2128	0.742297
$603$	−36.5836	−1.48980
$604$	−10.6347	−0.432719
$605$	23.5391	0.957000
$606$	−18.0323	−0.732513
$607$	−20.2839	−0.823297	−0.411649	−	0.911343i	$-0.635047\pi$
$607$	−20.2839	−0.823297	−0.411649	+	0.911343i	$0.635047\pi$
$608$	7.79265	0.316034
$609$	−3.78089	−0.153209
$610$	10.7338	0.434598
$611$	2.40973	0.0974872
$612$	10.3526	0.418480
$613$	20.3861	0.823388	0.411694	−	0.911322i	$-0.364937\pi$
$613$	20.3861	0.823388	0.411694	+	0.911322i	$0.364937\pi$
$614$	−22.1753	−0.894922
$615$	8.43536	0.340146
$616$	19.8003	0.797776
$617$	−43.9680	−1.77009	−0.885043	−	0.465508i	$-0.845872\pi$
$617$	−43.9680	−1.77009	−0.885043	+	0.465508i	$0.845872\pi$
$618$	0.132561	0.00533239
$619$	−32.8200	−1.31915	−0.659573	−	0.751640i	$-0.729263\pi$
$619$	−32.8200	−1.31915	−0.659573	+	0.751640i	$0.729263\pi$
$620$	−10.8423	−0.435437
$621$	18.1746	0.729322
$622$	4.59504	0.184244
$623$	6.85540	0.274656
$624$	1.30936	0.0524164
$625$	−25.0548	−1.00219
$626$	−10.7474	−0.429554
$627$	−6.79444	−0.271344
$628$	−11.3861	−0.454356
$629$	6.49539	0.258988
$630$	17.9233	0.714083
$631$	−11.2838	−0.449202	−0.224601	−	0.974451i	$-0.572108\pi$
$631$	−11.2838	−0.449202	−0.224601	+	0.974451i	$0.572108\pi$
$632$	9.95964	0.396173
$633$	15.0351	0.597592
$634$	37.3307	1.48259
$635$	−42.8603	−1.70086
$636$	0.0109990	0.000436137 0
$637$	1.44685	0.0573263
$638$	23.6302	0.935528
$639$	11.0410	0.436777
$640$	30.4974	1.20551
$641$	4.82189	0.190453	0.0952265	−	0.995456i	$-0.469642\pi$
$641$	4.82189	0.190453	0.0952265	+	0.995456i	$0.469642\pi$
$642$	5.24502	0.207004
$643$	−47.2742	−1.86431	−0.932157	−	0.362054i	$-0.882076\pi$
$643$	−47.2742	−1.86431	−0.932157	+	0.362054i	$0.882076\pi$
$644$	5.99870	0.236382
$645$	−8.35282	−0.328892
$646$	24.3997	0.959994
$647$	−9.72507	−0.382332	−0.191166	−	0.981558i	$-0.561227\pi$
$647$	−9.72507	−0.382332	−0.191166	+	0.981558i	$0.561227\pi$
$648$	−12.5212	−0.491879
$649$	53.7937	2.11159
$650$	−0.00760627	−0.000298342 0
$651$	9.48789	0.371860
$652$	8.41878	0.329705
$653$	−8.78627	−0.343833	−0.171917	−	0.985111i	$-0.554996\pi$
$653$	−8.78627	−0.343833	−0.171917	+	0.985111i	$0.554996\pi$
$654$	−1.01867	−0.0398330
$655$	−13.6832	−0.534647
$656$	−28.9964	−1.13212
$657$	1.94164	0.0757504
$658$	17.3046	0.674605
$659$	0.677824	0.0264043	0.0132021	−	0.999913i	$-0.495798\pi$
$659$	0.677824	0.0264043	0.0132021	+	0.999913i	$0.495798\pi$
$660$	4.00738	0.155987
$661$	−10.5696	−0.411111	−0.205556	−	0.978645i	$-0.565900\pi$
$661$	−10.5696	−0.411111	−0.205556	+	0.978645i	$0.565900\pi$
$662$	−31.4262	−1.22141
$663$	1.75366	0.0681066
$664$	−25.3126	−0.982320
$665$	9.90211	0.383987
$666$	4.20682	0.163011
$667$	−16.2226	−0.628143
$668$	−12.7996	−0.495232
$669$	−6.87261	−0.265710
$670$	50.8542	1.96467
$671$	13.7610	0.531238
$672$	4.02198	0.155151
$673$	45.4408	1.75161	0.875807	−	0.482662i	$-0.160330\pi$
$673$	45.4408	1.75161	0.875807	+	0.482662i	$0.160330\pi$
$674$	−12.5743	−0.484342
$675$	−0.0387925	−0.00149312
$676$	−7.84833	−0.301859
$677$	−9.18545	−0.353026	−0.176513	−	0.984298i	$-0.556482\pi$
$677$	−9.18545	−0.353026	−0.176513	+	0.984298i	$0.556482\pi$
$678$	10.7542	0.413014
$679$	14.5690	0.559107
$680$	32.6106	1.25056
$681$	4.52160	0.173268
$682$	−59.2985	−2.27066
$683$	24.2326	0.927235	0.463617	−	0.886036i	$-0.346551\pi$
$683$	24.2326	0.927235	0.463617	+	0.886036i	$0.346551\pi$
$684$	3.70432	0.141638
$685$	24.6402	0.941454
$686$	31.9237	1.21885
$687$	−1.33150	−0.0507998
$688$	28.7127	1.09466
$689$	−0.0122083	−0.000465098 0
$690$	−11.7365	−0.446802
$691$	15.2177	0.578910	0.289455	−	0.957192i	$-0.406526\pi$
$691$	15.2177	0.578910	0.289455	+	0.957192i	$0.406526\pi$
$692$	0.526666	0.0200208
$693$	22.9782	0.872869
$694$	6.33535	0.240487
$695$	−8.71326	−0.330513
$696$	−4.45537	−0.168880
$697$	−38.8357	−1.47101
$698$	−5.08993	−0.192657
$699$	−12.2750	−0.464283
$700$	−0.0128038	−0.000483940 0
$701$	22.3845	0.845452	0.422726	−	0.906257i	$-0.361073\pi$
$701$	22.3845	0.845452	0.422726	+	0.906257i	$0.361073\pi$
$702$	2.44490	0.0922768
$703$	2.32414	0.0876568
$704$	19.8537	0.748266
$705$	−7.93632	−0.298899
$706$	37.0060	1.39274
$707$	33.6917	1.26711
$708$	4.47589	0.168214
$709$	11.1918	0.420317	0.210159	−	0.977667i	$-0.432602\pi$
$709$	11.1918	0.420317	0.210159	+	0.977667i	$0.432602\pi$
$710$	−15.3480	−0.575999
$711$	11.5582	0.433465
$712$	8.07834	0.302749
$713$	40.7097	1.52459
$714$	12.5933	0.471293
$715$	−4.44798	−0.166345
$716$	−0.0626245	−0.00234039
$717$	−8.28672	−0.309473
$718$	26.0839	0.973442
$719$	−36.2427	−1.35163	−0.675813	−	0.737073i	$-0.736207\pi$
$719$	−36.2427	−1.35163	−0.675813	+	0.737073i	$0.736207\pi$
$720$	28.2564	1.05306
$721$	−0.247678	−0.00922400
$722$	−21.9788	−0.817964
$723$	1.24342	0.0462435
$724$	3.26970	0.121517
$725$	0.0346262	0.00128598
$726$	10.7117	0.397550
$727$	−47.8111	−1.77322	−0.886609	−	0.462520i	$-0.846945\pi$
$727$	−47.8111	−1.77322	−0.886609	+	0.462520i	$0.846945\pi$
$728$	−1.82861	−0.0677729
$729$	−7.85423	−0.290897
$730$	−2.69903	−0.0998957
$731$	38.4557	1.42234
$732$	1.14498	0.0423197
$733$	−29.9034	−1.10451	−0.552254	−	0.833676i	$-0.686232\pi$
$733$	−29.9034	−1.10451	−0.552254	+	0.833676i	$0.686232\pi$
$734$	37.4108	1.38086
$735$	−4.76513	−0.175764
$736$	17.2571	0.636105
$737$	65.1964	2.40154
$738$	−25.1525	−0.925876
$739$	22.6842	0.834453	0.417226	−	0.908803i	$-0.363002\pi$
$739$	22.6842	0.834453	0.417226	+	0.908803i	$0.363002\pi$
$740$	−1.37079	−0.0503911
$741$	0.627486	0.0230513
$742$	−0.0876694	−0.00321845
$743$	−6.95505	−0.255156	−0.127578	−	0.991829i	$-0.540720\pi$
$743$	−6.95505	−0.255156	−0.127578	+	0.991829i	$0.540720\pi$
$744$	11.1805	0.409895
$745$	39.3589	1.44200
$746$	−17.3708	−0.635992
$747$	−29.3753	−1.07478
$748$	−18.4497	−0.674587
$749$	−9.79982	−0.358078
$750$	−11.3765	−0.415411
$751$	32.0106	1.16808	0.584042	−	0.811723i	$-0.301470\pi$
$751$	32.0106	1.16808	0.584042	+	0.811723i	$0.301470\pi$
$752$	27.2810	0.994837
$753$	10.1681	0.370547
$754$	−2.18232	−0.0794753
$755$	−38.8756	−1.41483
$756$	4.11557	0.149682
$757$	−6.72372	−0.244378	−0.122189	−	0.992507i	$-0.538991\pi$
$757$	−6.72372	−0.244378	−0.122189	+	0.992507i	$0.538991\pi$
$758$	2.80718	0.101962
$759$	−15.0465	−0.546155
$760$	11.6686	0.423263
$761$	35.3837	1.28266	0.641329	−	0.767266i	$-0.278383\pi$
$761$	35.3837	1.28266	0.641329	+	0.767266i	$0.278383\pi$
$762$	−19.5041	−0.706558
$763$	1.90328	0.0689034
$764$	−2.13608	−0.0772808
$765$	37.8446	1.36827
$766$	42.1709	1.52370
$767$	−4.96800	−0.179384
$768$	8.48292	0.306101
$769$	−12.9164	−0.465778	−0.232889	−	0.972503i	$-0.574818\pi$
$769$	−12.9164	−0.465778	−0.232889	+	0.972503i	$0.574818\pi$
$770$	−31.9416	−1.15110
$771$	−17.5773	−0.633032
$772$	2.30017	0.0827851
$773$	−25.3821	−0.912932	−0.456466	−	0.889741i	$-0.650885\pi$
$773$	−25.3821	−0.912932	−0.456466	+	0.889741i	$0.650885\pi$
$774$	24.9064	0.895241
$775$	−0.0868922	−0.00312126
$776$	17.1680	0.616295
$777$	1.19955	0.0430336
$778$	24.1997	0.867600
$779$	−13.8960	−0.497876
$780$	−0.370093	−0.0132515
$781$	−19.6765	−0.704081
$782$	54.0341	1.93225
$783$	−11.1300	−0.397753
$784$	16.3801	0.585003
$785$	−41.6226	−1.48558
$786$	−6.22670	−0.222099
$787$	−21.7739	−0.776154	−0.388077	−	0.921627i	$-0.626861\pi$
$787$	−21.7739	−0.776154	−0.388077	+	0.921627i	$0.626861\pi$
$788$	5.77762	0.205819
$789$	−4.25035	−0.151316
$790$	−16.0668	−0.571631
$791$	−20.0933	−0.714435
$792$	27.0773	0.962151
$793$	−1.27087	−0.0451299
$794$	−44.8787	−1.59268
$795$	0.0402073	0.00142601
$796$	0.598726	0.0212213
$797$	18.0075	0.637859	0.318930	−	0.947778i	$-0.396677\pi$
$797$	18.0075	0.637859	0.318930	+	0.947778i	$0.396677\pi$
$798$	4.50607	0.159513
$799$	36.5382	1.29263
$800$	−0.0368342	−0.00130229
$801$	9.37491	0.331246
$802$	36.5717	1.29139
$803$	−3.46023	−0.122109
$804$	5.42465	0.191313
$805$	21.9286	0.772881
$806$	5.47638	0.192897
$807$	12.1526	0.427791
$808$	39.7020	1.39671
$809$	−8.84340	−0.310917	−0.155459	−	0.987842i	$-0.549686\pi$
$809$	−8.84340	−0.310917	−0.155459	+	0.987842i	$0.549686\pi$
$810$	20.1991	0.709722
$811$	14.4618	0.507823	0.253911	−	0.967227i	$-0.418283\pi$
$811$	14.4618	0.507823	0.253911	+	0.967227i	$0.418283\pi$
$812$	−3.67355	−0.128917
$813$	7.72385	0.270887
$814$	−7.49708	−0.262772
$815$	30.7753	1.07801
$816$	19.8536	0.695014
$817$	13.7600	0.481402
$818$	−32.6170	−1.14043
$819$	−2.12210	−0.0741523
$820$	8.19590	0.286213
$821$	3.54970	0.123885	0.0619427	−	0.998080i	$-0.480270\pi$
$821$	3.54970	0.123885	0.0619427	+	0.998080i	$0.480270\pi$
$822$	11.2128	0.391092
$823$	9.16800	0.319576	0.159788	−	0.987151i	$-0.448919\pi$
$823$	9.16800	0.319576	0.159788	+	0.987151i	$0.448919\pi$
$824$	−0.291862	−0.0101675
$825$	0.0321159	0.00111813
$826$	−35.6759	−1.24132
$827$	18.0470	0.627555	0.313777	−	0.949497i	$-0.398405\pi$
$827$	18.0470	0.627555	0.313777	+	0.949497i	$0.398405\pi$
$828$	8.20336	0.285087
$829$	43.4808	1.51015	0.755075	−	0.655639i	$-0.227600\pi$
$829$	43.4808	1.51015	0.755075	+	0.655639i	$0.227600\pi$
$830$	40.8341	1.41737
$831$	−0.150438	−0.00521862
$832$	−1.83355	−0.0635669
$833$	21.9383	0.760117
$834$	−3.96507	−0.137299
$835$	−46.7897	−1.61922
$836$	−6.60156	−0.228320
$837$	27.9300	0.965401
$838$	−42.6014	−1.47164
$839$	−28.4207	−0.981191	−0.490596	−	0.871387i	$-0.663221\pi$
$839$	−28.4207	−0.981191	−0.490596	+	0.871387i	$0.663221\pi$
$840$	6.02244	0.207794
$841$	−19.0654	−0.657428
$842$	−23.8031	−0.820310
$843$	−10.4292	−0.359202
$844$	14.6083	0.502839
$845$	−28.6900	−0.986967
$846$	23.6645	0.813601
$847$	−20.0139	−0.687685
$848$	−0.138212	−0.00474623
$849$	−0.473168	−0.0162391
$850$	−0.115332	−0.00395586
$851$	5.14690	0.176434
$852$	−1.63718	−0.0560889
$853$	32.5463	1.11437	0.557183	−	0.830390i	$-0.311882\pi$
$853$	32.5463	1.11437	0.557183	+	0.830390i	$0.311882\pi$
$854$	−9.12630	−0.312295
$855$	13.5414	0.463105
$856$	−11.5480	−0.394704
$857$	−24.8347	−0.848338	−0.424169	−	0.905583i	$-0.639434\pi$
$857$	−24.8347	−0.848338	−0.424169	+	0.905583i	$0.639434\pi$
$858$	−2.02410	−0.0691018
$859$	10.5964	0.361545	0.180773	−	0.983525i	$-0.442140\pi$
$859$	10.5964	0.361545	0.180773	+	0.983525i	$0.442140\pi$
$860$	−8.11570	−0.276743
$861$	−7.17208	−0.244424
$862$	34.2730	1.16734
$863$	−25.6665	−0.873697	−0.436848	−	0.899535i	$-0.643905\pi$
$863$	−25.6665	−0.873697	−0.436848	+	0.899535i	$0.643905\pi$
$864$	11.8397	0.402795
$865$	1.92526	0.0654607
$866$	0.164082	0.00557572
$867$	15.8761	0.539181
$868$	9.21855	0.312898
$869$	−20.5981	−0.698741
$870$	7.18735	0.243674
$871$	−6.02108	−0.204016
$872$	2.24281	0.0759512
$873$	19.9234	0.674306
$874$	19.3342	0.653988
$875$	21.2559	0.718580
$876$	−0.287908	−0.00972751
$877$	−39.7948	−1.34378	−0.671888	−	0.740653i	$-0.734516\pi$
$877$	−39.7948	−1.34378	−0.671888	+	0.740653i	$0.734516\pi$
$878$	−29.9768	−1.01167
$879$	19.6263	0.661978
$880$	−50.3564	−1.69752
$881$	−19.6983	−0.663652	−0.331826	−	0.943341i	$-0.607665\pi$
$881$	−19.6983	−0.663652	−0.331826	+	0.943341i	$0.607665\pi$
$882$	14.2086	0.478429
$883$	−22.3004	−0.750469	−0.375234	−	0.926930i	$-0.622438\pi$
$883$	−22.3004	−0.750469	−0.375234	+	0.926930i	$0.622438\pi$
$884$	1.70388	0.0573077
$885$	16.3619	0.549998
$886$	23.9659	0.805149
$887$	41.9210	1.40757	0.703785	−	0.710413i	$-0.251492\pi$
$887$	41.9210	1.40757	0.703785	+	0.710413i	$0.251492\pi$
$888$	1.41354	0.0474353
$889$	36.4415	1.22221
$890$	−13.0319	−0.436830
$891$	25.8957	0.867539
$892$	−6.67751	−0.223580
$893$	13.0739	0.437502
$894$	17.9107	0.599025
$895$	−0.228927	−0.00765220
$896$	−25.9301	−0.866263
$897$	1.38959	0.0463971
$898$	0.760904	0.0253917
$899$	−24.9303	−0.831471
$900$	−0.0175095	−0.000583652 0
$901$	−0.185111	−0.00616696
$902$	44.8248	1.49250
$903$	7.10190	0.236336
$904$	−23.6778	−0.787510
$905$	11.9526	0.397317
$906$	−17.6908	−0.587738
$907$	−8.51233	−0.282647	−0.141324	−	0.989963i	$-0.545136\pi$
$907$	−8.51233	−0.282647	−0.141324	+	0.989963i	$0.545136\pi$
$908$	4.39324	0.145795
$909$	46.0741	1.52818
$910$	2.94990	0.0977882
$911$	−33.7443	−1.11800	−0.558999	−	0.829168i	$-0.688814\pi$
$911$	−33.7443	−1.11800	−0.558999	+	0.829168i	$0.688814\pi$
$912$	7.10389	0.235233
$913$	52.3503	1.73254
$914$	0.443601	0.0146730
$915$	4.18554	0.138370
$916$	−1.29370	−0.0427451
$917$	11.6340	0.384188
$918$	37.0715	1.22354
$919$	33.5546	1.10686	0.553431	−	0.832895i	$-0.313318\pi$
$919$	33.5546	1.10686	0.553431	+	0.832895i	$0.313318\pi$
$920$	25.8405	0.851935
$921$	−8.64705	−0.284930
$922$	39.3803	1.29692
$923$	1.81718	0.0598133
$924$	−3.40723	−0.112090
$925$	−0.0109857	−0.000361209 0
$926$	−9.59989	−0.315472
$927$	−0.338705	−0.0111245
$928$	−10.5681	−0.346915
$929$	−2.92797	−0.0960634	−0.0480317	−	0.998846i	$-0.515295\pi$
$929$	−2.92797	−0.0960634	−0.0480317	+	0.998846i	$0.515295\pi$
$930$	−18.0362	−0.591430
$931$	7.84984	0.257268
$932$	−11.9265	−0.390667
$933$	1.79179	0.0586606
$934$	−43.9701	−1.43875
$935$	−67.4438	−2.20565
$936$	−2.50067	−0.0817369
$937$	20.9056	0.682955	0.341477	−	0.939890i	$-0.389073\pi$
$937$	20.9056	0.682955	0.341477	+	0.939890i	$0.389073\pi$
$938$	−43.2382	−1.41178
$939$	−4.19087	−0.136764
$940$	−7.71103	−0.251506
$941$	−7.24843	−0.236292	−0.118146	−	0.992996i	$-0.537695\pi$
$941$	−7.24843	−0.236292	−0.118146	+	0.992996i	$0.537695\pi$
$942$	−18.9409	−0.617127
$943$	−30.7732	−1.00211
$944$	−56.2437	−1.83058
$945$	15.0447	0.489404
$946$	−44.3862	−1.44312
$947$	−33.8594	−1.10028	−0.550142	−	0.835071i	$-0.685426\pi$
$947$	−33.8594	−1.10028	−0.550142	+	0.835071i	$0.685426\pi$
$948$	−1.71386	−0.0556635
$949$	0.319563	0.0103734
$950$	−0.0412676	−0.00133890
$951$	14.5568	0.472035
$952$	−27.7269	−0.898633
$953$	−34.1380	−1.10584	−0.552918	−	0.833235i	$-0.686486\pi$
$953$	−34.1380	−1.10584	−0.552918	+	0.833235i	$0.686486\pi$
$954$	−0.119890	−0.00388158
$955$	−7.80857	−0.252679
$956$	−8.05148	−0.260403
$957$	9.21437	0.297858
$958$	23.3895	0.755681
$959$	−20.9501	−0.676513
$960$	6.03871	0.194898
$961$	31.5609	1.01809
$962$	0.692377	0.0223231
$963$	−13.4015	−0.431857
$964$	1.20813	0.0389111
$965$	8.40841	0.270676
$966$	9.97886	0.321065
$967$	−39.4049	−1.26718	−0.633588	−	0.773671i	$-0.718418\pi$
$967$	−39.4049	−1.26718	−0.633588	+	0.773671i	$0.718418\pi$
$968$	−23.5842	−0.758025
$969$	9.51444	0.305648
$970$	−27.6952	−0.889240
$971$	36.2288	1.16264	0.581319	−	0.813676i	$-0.302537\pi$
$971$	36.2288	1.16264	0.581319	+	0.813676i	$0.302537\pi$
$972$	8.64172	0.277183
$973$	7.40836	0.237501
$974$	−50.2390	−1.60976
$975$	−0.00296599	−9.49878e−5 0
$976$	−14.3878	−0.460541
$977$	−6.69618	−0.214230	−0.107115	−	0.994247i	$-0.534161\pi$
$977$	−6.69618	−0.214230	−0.107115	+	0.994247i	$0.534161\pi$
$978$	14.0047	0.447820
$979$	−16.7072	−0.533966
$980$	−4.62986	−0.147895
$981$	2.60278	0.0831004
$982$	−13.0936	−0.417832
$983$	8.79124	0.280397	0.140198	−	0.990123i	$-0.455226\pi$
$983$	8.79124	0.280397	0.140198	+	0.990123i	$0.455226\pi$
$984$	−8.45152	−0.269425
$985$	21.1204	0.672952
$986$	−33.0900	−1.05380
$987$	6.74778	0.214784
$988$	0.609673	0.0193963
$989$	30.4721	0.968956
$990$	−43.6809	−1.38827
$991$	31.7211	1.00765	0.503827	−	0.863805i	$-0.331925\pi$
$991$	31.7211	1.00765	0.503827	+	0.863805i	$0.331925\pi$
$992$	26.5200	0.842011
$993$	−12.2544	−0.388880
$994$	13.0495	0.413904
$995$	2.18868	0.0693857
$996$	4.35580	0.138019
$997$	−43.3903	−1.37418	−0.687092	−	0.726570i	$-0.741113\pi$
$997$	−43.3903	−1.37418	−0.687092	+	0.726570i	$0.741113\pi$
$998$	−41.3753	−1.30971
$999$	3.53117	0.111721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.63	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.63	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q+1.61628 q^{2} +0.630253 q^{3} +0.612362 q^{4} +2.23852 q^{5} +1.01867 q^{6} -1.90328 q^{7} -2.24281 q^{8} -2.60278 q^{9} +O(q^{10})\)	\(q+1.61628 q^{2} +0.630253 q^{3} +0.612362 q^{4} +2.23852 q^{5} +1.01867 q^{6} -1.90328 q^{7} -2.24281 q^{8} -2.60278 q^{9} +3.61808 q^{10} +4.63848 q^{11} +0.385943 q^{12} -0.428377 q^{13} -3.07624 q^{14} +1.41084 q^{15} -4.84974 q^{16} -6.49539 q^{17} -4.20682 q^{18} -2.32414 q^{19} +1.37079 q^{20} -1.19955 q^{21} +7.49708 q^{22} -5.14690 q^{23} -1.41354 q^{24} +0.0109857 q^{25} -0.692377 q^{26} -3.53117 q^{27} -1.16550 q^{28} +3.15192 q^{29} +2.28031 q^{30} -7.90954 q^{31} -3.35291 q^{32} +2.92342 q^{33} -10.4984 q^{34} -4.26054 q^{35} -1.59384 q^{36} -1.00000 q^{37} -3.75647 q^{38} -0.269986 q^{39} -5.02059 q^{40} +5.97897 q^{41} -1.93881 q^{42} -5.92047 q^{43} +2.84043 q^{44} -5.82638 q^{45} -8.31884 q^{46} -5.62526 q^{47} -3.05656 q^{48} -3.37752 q^{49} +0.0177560 q^{50} -4.09374 q^{51} -0.262322 q^{52} +0.0284989 q^{53} -5.70736 q^{54} +10.3833 q^{55} +4.26870 q^{56} -1.46480 q^{57} +5.09439 q^{58} +11.5973 q^{59} +0.863943 q^{60} +2.96671 q^{61} -12.7840 q^{62} +4.95382 q^{63} +4.28023 q^{64} -0.958931 q^{65} +4.72506 q^{66} +14.0556 q^{67} -3.97753 q^{68} -3.24385 q^{69} -6.88623 q^{70} -4.24202 q^{71} +5.83755 q^{72} -0.745985 q^{73} -1.61628 q^{74} +0.00692380 q^{75} -1.42322 q^{76} -8.82832 q^{77} -0.436373 q^{78} -4.44069 q^{79} -10.8562 q^{80} +5.58281 q^{81} +9.66370 q^{82} +11.2861 q^{83} -0.734559 q^{84} -14.5401 q^{85} -9.56914 q^{86} +1.98651 q^{87} -10.4032 q^{88} -3.60188 q^{89} -9.41707 q^{90} +0.815321 q^{91} -3.15177 q^{92} -4.98502 q^{93} -9.09200 q^{94} -5.20265 q^{95} -2.11318 q^{96} -7.65467 q^{97} -5.45902 q^{98} -12.0729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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